[ { "path": ".clang-format", "content": "---\n# We'll use defaults from the Google style.\n# See http://clang.llvm.org/docs/ClangFormat.html for help.\n#\n# We include the full configuration to avoid changes with our code\n# formatting when there are changes added in clang-format or changes\n# in Google's style\nLanguage: Cpp\n\n# BasedOnStyle: Google\nAccessModifierOffset: -1\nAlignAfterOpenBracket: Align\nAlignConsecutiveAssignments: false\nAlignConsecutiveDeclarations: false\nAlignEscapedNewlines: Left\nAlignOperands: true\nAlignTrailingComments: true\nAllowAllParametersOfDeclarationOnNextLine: true\nAllowShortBlocksOnASingleLine: false\nAllowShortCaseLabelsOnASingleLine: false\nAllowShortFunctionsOnASingleLine: All\nAlwaysBreakAfterDefinitionReturnType: None\nAlwaysBreakAfterReturnType: None\nAlwaysBreakBeforeMultilineStrings: true\nAlwaysBreakTemplateDeclarations: true\nBinPackArguments: true\nBinPackParameters: true\nBraceWrapping:\n AfterClass: false\n AfterControlStatement: false\n AfterEnum: false\n AfterFunction: false\n AfterNamespace: false\n AfterObjCDeclaration: false\n AfterStruct: false\n AfterUnion: false\n BeforeCatch: false\n BeforeElse: false\n IndentBraces: false\n SplitEmptyFunction: true\n SplitEmptyRecord: true\n SplitEmptyNamespace: true\nBreakBeforeBinaryOperators: None\nBreakBeforeBraces: Attach\nBreakBeforeInheritanceComma: false\nBreakBeforeTernaryOperators: true\nBreakConstructorInitializersBeforeComma: false\nBreakConstructorInitializers: BeforeColon\nBreakAfterJavaFieldAnnotations: false\nBreakStringLiterals: true\nColumnLimit: 80\nCompactNamespaces: false\nConstructorInitializerAllOnOneLineOrOnePerLine: true\nConstructorInitializerIndentWidth: 4\nContinuationIndentWidth: 4\nCpp11BracedListStyle: true\nDisableFormat: false\nExperimentalAutoDetectBinPacking: false\nFixNamespaceComments: true\nForEachMacros:\n - foreach\n - Q_FOREACH\n - BOOST_FOREACH\nIncludeCategories:\n - Regex: '^<.*'\n Priority: 1\n - Regex: '.*'\n Priority: 2\nIncludeIsMainRegex: '([-_](test|unittest))?$'\nIndentCaseLabels: true\nIndentWidth: 2\nIndentWrappedFunctionNames: false\nJavaScriptQuotes: Leave\nJavaScriptWrapImports: true\nKeepEmptyLinesAtTheStartOfBlocks: false\nMacroBlockBegin: ''\nMacroBlockEnd: ''\nMaxEmptyLinesToKeep: 1\nNamespaceIndentation: None\nObjCBlockIndentWidth: 2\nObjCSpaceAfterProperty: false\nObjCSpaceBeforeProtocolList: false\nPenaltyBreakAssignment: 2\nPenaltyBreakBeforeFirstCallParameter: 1\nPenaltyBreakComment: 300\nPenaltyBreakFirstLessLess: 120\nPenaltyBreakString: 1000\nPenaltyExcessCharacter: 1000000\nPenaltyReturnTypeOnItsOwnLine: 200\nReflowComments: true\nSortIncludes: true\nSortUsingDeclarations: true\nSpaceAfterCStyleCast: false\nSpaceAfterTemplateKeyword: true\nSpaceBeforeAssignmentOperators: true\nSpaceBeforeParens: ControlStatements\nSpaceInEmptyParentheses: false\nSpacesBeforeTrailingComments: 2\nSpacesInAngles: false\nSpacesInContainerLiterals: true\nSpacesInCStyleCastParentheses: false\nSpacesInParentheses: false\nSpacesInSquareBrackets: false\nStandard: Auto\nTabWidth: 8\nUseTab: Never\n\nAllowShortIfStatementsOnASingleLine: false\nAllowShortLoopsOnASingleLine: false\nPointerAlignment: Left\nDerivePointerAlignment: false\n...\n" }, { "path": ".clang-tidy", "content": "# Define the checks we want to use and remove with comments as to why.\n#\n# Here is a list of the quirks with clang-tidy file format:\n# - no apostrophes in the comments\n# - every comment line in the checks must end with a comma\n# - every line in the checks must start at the beginning of the line\nChecks: '*,\n-abseil-*,\n-altera-*,\n-android-*,\n-bugprone-easily-swappable-parameters,\n-bugprone-exception-escape,\n# complains about Catch macros having infinite loops,\n-bugprone-infinite-loop,\n# false positive: Catch2 CHECK(a == b) expands to Decomposer() <= a == b,\n# which triggers the chained comparison check on macro-generated code.,\n-bugprone-chained-comparison,\n-bugprone-macro-parentheses,\n# useless as it triggers on calls to value() which already do a check,\n# and is too aggressive as it requires the check to be immediately before the\n# access.\n-bugprone-unchecked-optional-access,\n# Official justification is not public, unofficial justification has nothing,\n# specific to iterators and is basically \"never create mutable temporaries\",,\n# which is against standard practice everywhere else.,\n-cert-dcl21-cpp,\n# many static variables we use do not throw and if they do we,\n# want to terminate anyway,\n-cert-err58-cpp,\n-cert-msc51-cpp,\n-cert-msc32-c,\n# checks for incorrectly implemented self-assignment,\n# checks. However, it is broken.,\n-cert-oop54-cpp,\n-cppcoreguidelines-avoid-c-arrays,\n-cppcoreguidelines-avoid-do-while,\n# too many inconvenient positives for us to deal with,\n-cppcoreguidelines-avoid-magic-numbers,\n# false positives,\n-cppcoreguidelines-c-copy-assignment-signature,\n# sometimes macros are the right answer.,\n-cppcoreguidelines-macro-usage,\n# public and protected member variables are fine,\n-cppcoreguidelines-non-private-member-variables-in-classes,\n# We do not use gsl::owner,\n-cppcoreguidelines-owning-memory,\n-fuchsia-*,\n# defaulting virtual functions in CoordinateMap,\n-google-default-arguments,\n# Documented as redundant with -Wold-style-cast. Has more false positives.,\n-google-readability-casting,\n# specifying int32_t and int64_t instead of just int,\n-google-runtime-int,\n# redundant with other checks,\n-hicpp-*,\n# We use pragma once instead of include guards,\n-llvm-header-guard,\n# Makes code less portable because some implementation-defined STL,\n# types can be pointers or not. Same as,\n# readability-qualified-auto below,\n-llvm-qualified-auto,\n# We are not developing LLVM libc,\n-llvmlibc-*,\n# anonymous namespaces are the idiomatic C++ way to restrict visibility;,\n# conflicts with misc-use-anonymous-namespace which prefers anonymous namespaces.,\n-llvm-prefer-static-over-anonymous-namespace,\n# Triggers when \"l\" is used because it is \"too similar\" to \"I\",\n-misc-confusable-identifiers,\n# thinks constexpr variables in header files cause ODR violations,\n-misc-definitions-in-headers,\n# Insufficiently configurable, does not handle system headers well,\n-misc-include-cleaner,\n# false positives,\n-misc-noexcept-move-constructor,\n-misc-non-private-member-variables-in-classes,\n# false positives,\n-misc-unconventional-assign-operator,\n-modernize-raw-string-literal,\n# should be used, but requires possibly a lot of code changes that,\n# we do not have the resources for,\n-modernize-use-nodiscard,\n# this wants everything to use trailing return type syntax, which,\n# is silly.,\n-modernize-use-trailing-return-type,\n-performance-noexcept-move-constructor,\n# complains about decltype(auto),\n-readability-const-return-type,\n# style choice, discussed in issue #145,\n-readability-else-after-return,\n-llvm-else-after-return,\n# flagged code that is not very complex,\n-readability-function-cognitive-complexity,\n# We have lots of \"x\", \"p\", & \"os\" variable names,\n-readability-identifier-length,\n-readability-magic-numbers,\n-misc-confusable-identifiers\n# Same as llvm-qualified-auto above.,\n-readability-qualified-auto,\n# Access specifiers can be useful to structure code,\n-readability-redundant-access-specifiers,\n# We can have two of: methods are static when possible, static,\n# methods are not called through instances, and methods of,\n# calling, e.g., x.size(), are consistent across classes. We,\n# choose to lose this one.,\n-readability-static-accessed-through-instance,\n# we are okay with lower case,\n-readability-uppercase-literal-suffix,'\nCheckOptions:\n - key: cppcoreguidelines-avoid-do-while.IgnoreMacros\n value: true\n - key: cppcoreguidelines-special-member-functions.AllowMissingMoveFunctions\n value: true\n - key: cppcoreguidelines-special-member-functions.AllowSoleDefaultDtor\n value: true\n - key: performance-move-const-arg.CheckTriviallyCopyableMove\n value: false\n # The fix for this is not supported by GCC 9.\n - key: modernize-loop-convert.UseCxx20ReverseRanges\n value: false\nWarningsAsErrors: '*'\n# It is unclear if the header filter actually works or how to use it so\n# just include all headers\nHeaderFilterRegex: ''\nFormatStyle: none\n" }, { "path": ".claude/hooks/PostFormat.sh", "content": "#!/usr/bin/env bash\n\n# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Claude Code PostToolUse hook: auto-format files after Edit/Write.\n#\n# - C++ (.cpp, .hpp, .tpp):\n# Edit -> git-clang-format -f (diff-only formatting)\n# Write -> clang-format -i (whole-file formatting)\n# - Python (.py):\n# black -q && isort -q (single-file formatting)\n\n# Returns the path to the best available git-clang-format binary.\n# Prefers the unversioned `git-clang-format`, then falls back to the\n# highest-versioned `git-clang-format-N` found in PATH.\nfind_git_clang_format() {\n if command -v git-clang-format &>/dev/null; then\n echo \"git-clang-format\"\n return\n fi\n local best_ver=0 best_bin=\"\"\n IFS=: read -ra dirs <<< \"$PATH\"\n for dir in \"${dirs[@]}\"; do\n for bin in \"$dir\"/git-clang-format-*; do\n [[ -x \"$bin\" ]] || continue\n local ver=\"${bin##*-}\"\n [[ \"$ver\" =~ ^[0-9]+$ ]] || continue\n (( ver > best_ver )) && { best_ver=$ver; best_bin=$bin; }\n done\n done\n echo \"$best_bin\"\n}\n\nINPUT=$(cat)\nFILE=$(echo \"$INPUT\" | jq -r '.tool_input.file_path // empty')\nTOOL=$(echo \"$INPUT\" | jq -r '.tool_name // empty')\n\nif [[ -z \"$FILE\" || ! -f \"$FILE\" ]]; then\n exit 0\nfi\n\ncase \"$FILE\" in\n *.cpp|*.hpp|*.tpp)\n if [[ \"$TOOL\" == \"Write\" ]]; then\n clang-format -i \"$FILE\" 2>/dev/null\n else\n gcf=$(find_git_clang_format)\n if [[ -n \"$gcf\" ]]; then\n \"$gcf\" -f -- \"$FILE\" 2>/dev/null\n else\n clang-format -i \"$FILE\" 2>/dev/null\n fi\n fi\n ;;\n *.py)\n black -q \"$FILE\" 2>/dev/null\n isort -q \"$FILE\" 2>/dev/null\n ;;\nesac\n\nexit 0\n" }, { "path": ".claude/rules/CMake.md", "content": "---\ntriggers:\n - glob: \"**/CMakeLists.txt\"\n---\n\n- Files listed in spectre_target_sources() and spectre_target_headers() must be\n in alphabetical order (case-insensitive). When adding or removing entries,\n maintain the sorted order.\n- Use ${LIBRARY} variable in CMake target calls, not hardcoded library names.\n" }, { "path": ".claude/rules/Cxx.md", "content": "---\ntriggers:\n - glob: \"**/*.{hpp,cpp,tpp}\"\n---\n\n# SpECTRE Code Rules Reference\n\n## Banned Patterns\n- `#include ` -> `Parallel/Printf/Printf.hpp` with `Parallel::printf`\n- `#include ` -> `#include `\n- `std::enable_if` -> C++20 `requires` clause\n- `||` `&&` `!` (logical operators) -> `or` `and` `not` (C++ alternative\n tokens). Note: `!=` is fine.\n- `.ckLocal()` -> `Parallel::local(proxy)`\n- `.ckLocalBranch()` -> `Parallel::local_branch(proxy)`\n- `return Py_None;` -> `Py_RETURN_NONE`\n- `TEST_CASE(` -> `SPECTRE_TEST_CASE(`\n- `Approx(` in tests -> `approx` from `Framework/TestingFramework.hpp`\n- `namespace _details` / `namespace details` -> `_detail` / `detail`\n- `boost::optional` / `boost/optional.hpp` -> `std::optional`\n- `mutable` member variables -> avoid (race conditions in parallel); discuss\n with core devs\n- `struct TD;` / `class TD;` -> remove (debug artifacts)\n- `Ls` as abbreviation -> use `List`\n- `int` for container sizes/indices -> `size_t`\n- `noexcept` -> don't add unless overriding a signature that requires it\n\n## Prefer-Library Patterns\nWhen you see manual loops over Tensor indices, suggest the existing utility:\n- Dot product -> `DataStructures/Tensor/EagerMath/DotProduct.hpp`\n- Cross product -> `EagerMath/CrossProduct.hpp`\n- Trace -> `EagerMath/Trace.hpp`\n- Determinant -> `EagerMath/Determinant.hpp` or `DeterminantAndInverse.hpp`\n- Magnitude/norm -> `EagerMath/Magnitude.hpp` or `Norms.hpp`\n- Outer product -> `EagerMath/OuterProduct.hpp`\n- Raise/lower index -> `EagerMath/RaiseOrLowerIndex.hpp`\n- Gram-Schmidt -> `EagerMath/GramSchmidtOrthonormalize.hpp`\n- Frame transform -> `EagerMath/FrameTransform.hpp`\n- Cartesian<->Spherical -> `EagerMath/CartesianToSpherical.hpp`\n\nIf you spot a tensor loop not covered above, grep\n`src/DataStructures/Tensor/EagerMath/` and `src/NumericalAlgorithms/` for an\nexisting utility before suggesting the author write their own. Encourage use\nof tensor expressions `src/DataStructures/Tensor/Expressions/`.\n\nFor general relativity, generalized harmonic, CCZ4, apparent horizons, and\nGRMHD, many manipulations like shift from spacetime metric, lapse from spacetime\nmetric, derivative of shift, etc. are implemented as functions in\n`src/PointwiseFunctions/GeneralRelativity` or `src/PointwiseFunctions/Hydro`.\n\n## Style Rules\n- **Naming**: CamelCase for classes, template params, files, dirs. snake_case\n for functions, variables. SCREAMING_SNAKE_CASE for macros. Trailing `_` on\n private members. Unused params: `/*name*/`.\n- **Names**: Use full, descriptive names (e.g., `block_id` not `blk_id`).\n- **Almost always `auto`** except expression templates (e.g. `DataVector`)\n- **Braces on all loops and if/else** (no braceless one-liners)\n- **Return by value** preferred. Mutable out-params: `gsl::not_null` (listed\n first in arg list).\n- **`std::move`** into members from by-value constructor parameters\n- **`get(tensor)`** when indices are compile-time known\n- **Explicit double literals**: `2.0` or `2.`, never bare `2` in floating-point\n context\n- **`#pragma once`** for header guards (not `#ifndef`)\n- **`override`** keyword on all virtual overrides\n- **`const`** on all immutable objects\n- **No top-level `const` on value parameters in declarations**: In `.hpp`\n forward declarations, don't mark value parameters (including pointer-by-value)\n as `const`. `const` is fine in the corresponding definition. Example:\n `void foo(int x, double* ptr);` (declaration) vs\n `void foo(const int x, double* const ptr) { ... }` (definition).\n- **Templates**: prefer definitions in `.cpp` with explicit instantiations\n (`GENERATE_EXPLICIT_INSTANTIATIONS`)\n- **Internal namespaces**: `LibraryOrFile_detail` (e.g. `Tensor_detail`)\n- **Macros**: avoid if possible; use `constexpr` or templates. Macro vars: add\n suffix to avoid collisions.\n- **Error messages**: descriptive, include runtime values. Bad: \"Size\n mismatch\". Good: \"The number of grid points in matrix 'F' (N) != determinant\n grid points (M).\"\n- **Header order**: (1) TestingFramework.hpp + blank (tests), (2) corresponding\n .hpp + blank (.cpp files), (3) STL/external `<>` alphabetical, (4) blank, (5)\n SpECTRE `\"\"` alphabetical\n- **Doxygen**: required for all public API in `.hpp`. Use `///` or `/*!`. NO\n doxygen in `.cpp`. Use `\\f$...\\f$` for inline math, `align` env (not\n `eqnarray`) for multi-line. Blank doxygen line before/after out-of-line\n equations.\n- **CMake lists**: alphabetical. Use `${LIBRARY}` variable, not hardcoded names.\n\n## Test Requirements\n- Files: `tests/Unit//Test_.cpp`\n- Include order: `\"Framework/TestingFramework.hpp\"`, blank line,\n system/external includes, blank line, spectre includes.\n- All helper classes/functions in anonymous `namespace {}`\n- Test macro: `SPECTRE_TEST_CASE(\"Unit.Category.Name\", \"[Unit][Category]\")`\n- Floating-point: `CHECK_ITERABLE_APPROX` (not `Approx`)\n- Completion: < 5 seconds (prefer < 0.5s)\n- Random values: `MAKE_GENERATOR(gen)`, test 10^4 times for tolerance\n- Error tests: `CHECK_THROWS_WITH` inside `#ifdef SPECTRE_DEBUG`\n- Pointwise functions: test with analytic solution AND random-value comparison\n via `pypp::check_with_random_values()`\n- Use metamorphic tests: like `sin^2(x)+cos^2(x)=1` or that a spacetime vector\n in general relativity that should be null is actually null. I.e, test\n identities.\n- Name tests after the component and behavior (e.g.,\n `Test_ApparentHorizonFinder`).\n- Prefer a single `SPECTRE_TEST_CASE` that calls several anonymous-namespace\n helper functions over many small `SPECTRE_TEST_CASE`s.\n- Increase test timeouts sparingly. If necessary, use `// [[TimeOut, SECONDS]]`\n on the line before `SPECTRE_TEST_CASE`. Default timeout is 2 seconds.\n" }, { "path": ".claude/settings.json", "content": "{\n \"permissions\": {\n \"allow\": [\n \"Skill(spectre-fix-ci)\",\n \"Skill(spectre-fix-issue)\",\n \"Skill(spectre-fix-pr)\",\n \"Skill(spectre-review)\"\n ]\n },\n \"hooks\": {\n \"PostToolUse\": [\n {\n \"matcher\": \"Edit|Update|Write\",\n \"hooks\": [\n {\n \"type\": \"command\",\n \"command\": \"$CLAUDE_PROJECT_DIR/.claude/hooks/PostFormat.sh\"\n }\n ]\n }\n ]\n }\n}\n" }, { "path": ".claude/skills/spectre-fix-ci/SKILL.md", "content": "---\nname: spectre-fix-ci\ndescription: >\n Fetch and analyze a failed GitHub Actions job log. When viewing a job\n in GitHub Actions, the job ID is the last number in the URL, e.g. in\n \"runs/24319442407/job/71002790711\" the job ID is \"71002790711\".\nallowed-tools: [\"Bash\"]\nargument-hint: \"JOB_ID [--owner OWNER]\"\nuser-invocable: true\nmodel-invocable: false\n---\n\nRead and follow instructions in file\n`$(git rev-parse --show-toplevel)/.skills/spectre-fix-ci/SKILL.md`\n" }, { "path": ".claude/skills/spectre-fix-issue/SKILL.md", "content": "---\nname: spectre-fix-issue\ndescription: >\n Fetch a GitHub issue by number. Trigger when the user references a GitHub\n issue (e.g. \"fix issue #1727\", \"work on #1727\").\nallowed-tools: [\"Bash\", \"Read\"]\nargument-hint: \"ISSUE_NUMBER [--repo OWNER/REPO] [--full]\"\n---\n\nRead and follow instructions in file\n`$(git rev-parse --show-toplevel)/.skills/spectre-fix-issue/SKILL.md`\n" }, { "path": ".claude/skills/spectre-fix-pr/SKILL.md", "content": "---\nname: spectre-fix-pr\ndescription: >\n Fetch PR review comments. Trigger when users reference a PR\n (e.g. \"address comments on PR #1234\", \"work on PR #1234 reviews\").\nallowed-tools: [\"Bash\", \"Read\"]\nargument-hint: \"PR_NUMBER [--repo OWNER/REPO]\"\n---\n\nRead and follow instructions in file\n`$(git rev-parse --show-toplevel)/.skills/spectre-fix-pr/SKILL.md`\n" }, { "path": ".claude/skills/spectre-review/SKILL.md", "content": "---\nname: spectre-review\ndescription: SpECTRE code review (PR or local commits)\nargument-hint: \"[PR#] [clang-tidy] [coverage]\"\nallowed-tools: [\"Bash\", \"Read\", \"Grep\", \"Glob\", \"Agent\", \"AskUserQuestion\", \"TaskCreate\", \"TaskUpdate\", \"TaskList\"]\ndisable-model-invocation: true\n---\n\nRead and follow instructions in file\n`$(git rev-parse --show-toplevel)/.skills/spectre-review/SKILL.md`\n" }, { "path": ".codecov.yaml", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Disable PR comments\ncomment: false\n\ncoverage:\n status:\n # Check that PRs increase overall coverage\n project:\n default:\n target: auto\n # Account for random-value tests sometimes taking different code paths\n threshold: 0.3%\n # Check that PRs are fully tested\n patch:\n default:\n target: 100%\n" }, { "path": ".devcontainer/cmake-kits.json", "content": "[\n {\n \"name\": \"Default\",\n \"compilers\": {\n \"C\": \"clang\",\n \"CXX\": \"clang++\",\n \"Fortran\": \"gfortran\"\n },\n \"cmakeSettings\": {\n \"BUILD_SHARED_LIBS\": \"ON\",\n \"MEMORY_ALLOCATOR\": \"SYSTEM\"\n },\n \"preferredGenerator\": {\n \"name\": \"Unix Makefiles\"\n }\n }\n]\n" }, { "path": ".devcontainer/devcontainer.json", "content": "{\n \"name\": \"SpECTRE development environment\",\n \"image\": \"sxscollaboration/spectre:dev\",\n \"workspaceMount\": \"source=${localWorkspaceFolder},target=${localWorkspaceFolder},type=bind,consistency=delegated\",\n \"workspaceFolder\": \"${localWorkspaceFolder}\",\n \"customizations\": {\n \"vscode\": {\n \"extensions\": [\n \"eamodio.gitlens\",\n \"foxundermoon.shell-format\",\n \"github.vscode-pull-request-github\",\n \"gruntfuggly.format-modified\",\n \"ms-python.black-formatter\",\n \"ms-python.python\",\n \"ms-vscode.cmake-tools\",\n \"ms-vscode.cpptools\",\n \"ms-vsliveshare.vsliveshare\",\n \"redhat.vscode-yaml\",\n \"stkb.rewrap\",\n \"streetsidesoftware.code-spell-checker\",\n \"twxs.cmake\"\n ],\n \"settings\": {\n \"cmake.buildDirectory\": \"${localWorkspaceFolder}/build-${buildKit}-${buildType}\",\n \"editor.rulers\": [80],\n \"editor.wordWrap\": \"off\",\n \"editor.formatOnSave\": false,\n \"editor.formatOnPaste\": true,\n \"editor.formatOnType\": true,\n \"python.pythonPath\": \"/usr/bin/python3\",\n \"[python]\": {\n \"editor.defaultFormatter\": \"ms-python.black-formatter\"\n }\n }\n }\n },\n \"remoteEnv\": {\n \"SPECTRE_HOME\": \"${localWorkspaceFolder}\"\n },\n \"postCreateCommand\": \"git config --global --add safe.directory ${localWorkspaceFolder} && mkdir -p /root/.local/share/CMakeTools && cp ${localWorkspaceFolder}/.devcontainer/cmake-kits.json /root/.local/share/CMakeTools/cmake-tools-kits.json\"\n}\n" }, { "path": ".dockerignore", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Build directories\n# Ignore build dirs named similarly to the example in the installation notes;\n# in general arbitrary names are possible and cannot all be ignored. This will\n# keep the size of the context down and prevent errors in the demo image where\n# we create our own `build` directory in the container\nbuild*\ncontainers/Dockerfile.buildenv\n" }, { "path": ".github/ISSUE_TEMPLATE.md", "content": "# Bug reports:\n\n### Expected behavior:\n\n\n\n### Current behavior:\n\n\n\n### Environment:\n\nAdd as an attachment `$SPECTRE_BUILD_DIR/BuildInfo.txt` or\nadd its contents here.\n\n# Feature request:\n\n### Component:\n\n- [ ] Code\n- [ ] Documentation\n- [ ] Build system\n- [ ] Continuous integration\n\n### Desired feature:\n\n- [ ] Detail 1\n- [ ] Detail 2\n- [ ] Detail 3\n\n### Detailed discussion:\n" }, { "path": ".github/PULL_REQUEST_TEMPLATE.md", "content": "## Proposed changes\n\n\n\n### Upgrade instructions\n\n\n\n\n\n\n### Code review checklist\n\n- [ ] The code is documented and the documentation renders correctly. Run\n `make doc` to generate the documentation locally into `BUILD_DIR/docs/html`.\n Then open `index.html`.\n- [ ] The code follows the stylistic and code quality guidelines listed in the\n [code review guide](https://spectre-code.org/code_review_guide.html).\n- [ ] The PR lists upgrade instructions and is labeled `bugfix` or\n `new feature` if appropriate.\n- [ ] If a coding agent is used, have one of\n \"Co-Authored-By: Claude Sonnet 4.6 \",\n \"Co-Authored-by: Codex \", or\n \"Co-Authored-By: GitHub Copilot CLI \"\n as the last line of the commit, depending on the agent.\n\n### Further comments\n\n\n" }, { "path": ".github/actions/parse-compiler/action.yaml", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nname: Parse compiler\n\ndescription: |\n Parse the compiler name and version from the input and set the environment\n variables CC, CXX, FC, COMPILER_ID, and COMPILER_VERSION.\n For nvcc, it sets CC, CXX, and FC to the host compilers (gcc, g++, gfortran).\n\ninputs:\n compiler:\n description: Compiler to parse, e.g. 'gcc-10'\n required: true\n\nruns:\n using: \"composite\"\n steps:\n - run: |\n if [[ ${{ inputs.compiler }} =~ (gcc|clang|nvcc)-([0-9\\.\\-]+) ]]; then\n COMPILER_ID=${BASH_REMATCH[1]}\n COMPILER_VERSION=${BASH_REMATCH[2]}\n if [[ $COMPILER_ID = gcc ]]; then\n CC=gcc-${COMPILER_VERSION};\n CXX=g++-${COMPILER_VERSION};\n FC=gfortran-${COMPILER_VERSION};\n elif [[ $COMPILER_ID = clang ]]; then\n CC=clang-${COMPILER_VERSION};\n CXX=clang++-${COMPILER_VERSION};\n FC=gfortran-11;\n elif [[ $COMPILER_ID = nvcc ]]; then\n # Set host compilers\n CC=gcc;\n CXX=g++;\n FC=gfortran-11;\n fi\n fi\n echo \"CC=$CC\" >> $GITHUB_ENV\n echo \"CXX=$CXX\" >> $GITHUB_ENV\n echo \"FC=$FC\" >> $GITHUB_ENV\n echo \"COMPILER_ID=$COMPILER_ID\" >> $GITHUB_ENV\n echo \"COMPILER_VERSION=$COMPILER_VERSION\" >> $GITHUB_ENV\n shell: bash\n" }, { "path": ".github/problem_matchers/ClangTidy.json", "content": "{\n \"problemMatcher\": [\n {\n \"owner\": \"clang-tidy\",\n \"pattern\": [\n {\n \"regexp\": \"^(?:\\\\x1b\\\\[[\\\\d;]+m)*(.+):(\\\\d+):(\\\\d+):\\\\s(?:\\\\x1b\\\\[[\\\\d;]+m)*(error):\\\\s(?:\\\\x1b\\\\[[\\\\d;]+m)*(.+)\\\\s\\\\[(.+)\\\\](?:\\\\x1b\\\\[[\\\\d;]+m)*$\",\n \"file\": 1,\n \"line\": 2,\n \"column\": 3,\n \"severity\": 4,\n \"message\": 5,\n \"code\": 6\n }\n ]\n }\n ]\n}\n" }, { "path": ".github/scripts/Release.py", "content": "#!/usr/bin/env python\n\n# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nimport datetime\nimport difflib\nimport logging\nimport operator\nimport os\nimport pathlib\nimport re\nimport tempfile\nimport textwrap\nimport urllib\nfrom typing import List\n\nimport git\nimport pybtex.database\nimport requests\nimport uplink\nimport yaml\nfrom cffconvert.citation import Citation\nfrom pybtex.backends.plaintext import Backend as PlaintextBackend\nfrom pybtex.style.formatting.plain import Style as PlainStyle\n\nlogger = logging.getLogger(__name__)\n\nVERSION_PATTERN = r\"(\\d{4})\\.(\\d{2})\\.(\\d{2})(\\.\\d+)?\"\nPUBLICATION_DATE_PATTERN = r\"\\d{4}-\\d{2}-\\d{2}\"\nDOI_PATTERN = r\"10\\.\\d{4,9}/zenodo\\.\\d+\"\nZENODO_ID_PATTERN = r\"\\d+\"\n\n\ndef report_check_only(msg: str):\n logger.info(f\"CHECK ONLY: {msg}\")\n\n\ndef new_version_id_from_response(response):\n \"\"\"Retrieves the ID of the new version draft from the API response\n\n The \"New version\" action of the Zenodo API returns the ID of the created\n version draft in the 'links' section, as documented\n [here](https://developers.zenodo.org/#new-version). This function parses the\n ID out of the link.\n \"\"\"\n new_version_url = response.json()[\"links\"][\"latest_draft\"]\n return int(\n pathlib.PurePosixPath(\n urllib.parse.urlparse(new_version_url).path\n ).parts[-1]\n )\n\n\ndef raise_for_status(response):\n try:\n response.raise_for_status()\n except requests.exceptions.HTTPError as err:\n if response.status_code >= 400 and response.status_code < 500:\n raise requests.exceptions.HTTPError(\n yaml.safe_dump(response.json(), allow_unicode=True)\n ) from err\n else:\n raise\n return response\n\n\n@uplink.response_handler(raise_for_status)\nclass Zenodo(uplink.Consumer):\n \"\"\"Abstraction of the [Zenodo API](https://developers.zenodo.org)\"\"\"\n\n @uplink.returns.json\n @uplink.get(\"deposit/depositions/{id}\")\n def get_deposition(self, id: uplink.Path):\n \"\"\"Retrieves a deposition by ID.\"\"\"\n pass\n\n @uplink.returns.json\n @uplink.get(\"records/{id}\")\n def get_record(self, id: uplink.Path):\n \"\"\"Retrieves a published record by ID.\"\"\"\n pass\n\n @uplink.returns.json(\n key=(\"metadata\", \"relations\", \"version\", 0, \"is_last\"),\n type=bool,\n )\n @uplink.get(\"records/{id}\")\n def is_latest_version(self, record_id: uplink.Path(name=\"id\")):\n \"\"\"Checks whether the record is the latest version.\"\"\"\n pass\n\n @uplink.response_handler(new_version_id_from_response)\n @uplink.post(\"deposit/depositions/{id}/actions/newversion\")\n def new_version(self, latest_version_id: uplink.Path(name=\"id\")):\n \"\"\"Invoke the \"New version\" action on a deposition.\n\n Returns:\n The ID of the new version.\n \"\"\"\n pass\n\n @uplink.returns.json\n @uplink.post(\"deposit/depositions/{id}/actions/publish\")\n def publish(self, id: uplink.Path):\n \"\"\"Invoke the \"Publish\" action on a deposition.\"\"\"\n pass\n\n @uplink.json\n @uplink.returns.json\n @uplink.put(\"deposit/depositions/{id}\")\n def update_deposition(self, id: uplink.Path, **body: uplink.Body):\n \"\"\"Update the deposition with the metadata\"\"\"\n pass\n\n @uplink.returns.json\n @uplink.put(\"files/{bucket_id}/{filename}\")\n def upload_file(\n self, bucket_id: uplink.Path, filename: uplink.Path, file: uplink.Body\n ):\n \"\"\"Uploads a file to the bucket.\"\"\"\n pass\n\n\n@uplink.response_handler(raise_for_status)\nclass Github(uplink.Consumer):\n \"\"\"Abstraction of the [GitHub REST API](https://docs.github.com/en/rest)\"\"\"\n\n # This endpoint is not currently implemented in PyGithub, so we wrap it\n # here manually\n @uplink.headers({\"Content-Type\": \"text/x-markdown\"})\n @uplink.response_handler(operator.attrgetter(\"text\"))\n @uplink.post(\"markdown/raw\")\n def render_markdown_raw(self, text: uplink.Body):\n \"\"\"Render Markdown in plain format like a README.md file on GitHub\"\"\"\n pass\n\n @uplink.returns.json\n @uplink.get(\"repos/{user}/{repo}/releases/tags/{tag}\")\n def get_release_by_tag(\n self, user: uplink.Path, repo: uplink.Path, tag: uplink.Path\n ):\n pass\n\n @uplink.returns.json\n @uplink.get(\"repos/{user}/{repo}/releases/{release_id}/assets\")\n def get_assets(\n self, user: uplink.Path, repo: uplink.Path, release_id: uplink.Path\n ):\n pass\n\n\ndef to_plaintext_reference(\n bib_entry: pybtex.database.Entry,\n style=PlainStyle(),\n backend=PlaintextBackend(),\n) -> str:\n # pybtex doesn't support 'software' bibtex types for some reason:\n # https://bitbucket.org/pybtex-devs/pybtex/issues/157/support-for-software-and-patent-entries-in\n if bib_entry.type == \"software\":\n bib_entry.type = \"misc\"\n return style.format_entry(label=bib_entry.key, entry=bib_entry).text.render(\n backend\n )\n\n\ndef collect_zenodo_metadata(\n metadata: dict, references: List[pybtex.database.Entry], github: Github\n) -> dict:\n \"\"\"Produces the metadata that we send to Zenodo\n\n Args:\n metadata: The project metadata read from the YAML file. This is the main\n source of information for this function.\n references: List of references resolved from 'metadata[\"References\"]'.\n They will be formatted and sent to Zenodo.\n github: The GitHub API client. We use it to render the description to\n HTML in a way that's consistent with GitHub's rendering.\n\n Returns:\n Metadata in the format that the Zenodo API expects.\n \"\"\"\n # Generate the DOI author list from the authors in the project metadata\n zenodo_creators = []\n for author_tier in [\"Core\", \"Developers\", \"Contributors\"]:\n for author in metadata[\"Authors\"][author_tier][\"List\"]:\n zenodo_creator = dict(name=author[\"Name\"])\n if \"Orcid\" in author:\n zenodo_creator[\"orcid\"] = author[\"Orcid\"]\n if \"Affiliations\" in author and len(author[\"Affiliations\"]) > 0:\n zenodo_creator[\"affiliation\"] = \" and \".join(\n author[\"Affiliations\"]\n )\n zenodo_creators.append(zenodo_creator)\n # Render the description to HTML\n rendered_description = github.render_markdown_raw(metadata[\"Description\"])\n # Format references as plain text for Zenodo\n formatted_references = [\n to_plaintext_reference(entry) for entry in references\n ]\n # Construct Zenodo metadata\n return dict(\n title=metadata[\"Name\"],\n version=metadata[\"Version\"],\n publication_date=metadata[\"PublicationDate\"].isoformat(),\n doi=metadata[\"Doi\"],\n description=rendered_description,\n creators=zenodo_creators,\n related_identifiers=[\n dict(\n identifier=metadata[\"Homepage\"],\n relation=\"isDocumentedBy\",\n scheme=\"url\",\n resource_type=\"publication-softwaredocumentation\",\n ),\n dict(\n identifier=(\"https://github.com/\" + metadata[\"GitHub\"]),\n relation=\"isSupplementTo\",\n scheme=\"url\",\n resource_type=\"software\",\n ),\n ],\n language=\"eng\",\n communities=[dict(identifier=\"sxs\")],\n keywords=metadata[\"Keywords\"],\n license=metadata[\"License\"],\n upload_type=\"software\",\n access_right=\"open\",\n references=formatted_references,\n )\n\n\ndef to_cff_person(person: pybtex.database.Person) -> dict:\n \"\"\"BibTeX to CFF conversion for person objects.\n\n The format is defined here:\n https://github.com/citation-file-format/citation-file-format/blob/main/schema-guide.md#definitionsperson\n \"\"\"\n # Map BibTeX to CFF fields\n name_fields = {\n \"last\": \"family-names\",\n \"bibtex_first\": \"given-names\",\n \"prelast\": \"name-particle\",\n \"lineage\": \"name-suffix\",\n }\n result = {\n cff_field: \" \".join(person.get_part(bibtex_field))\n for bibtex_field, cff_field in name_fields.items()\n if person.get_part(bibtex_field)\n }\n # Use CFF \"entity\" format if BibTex has no first & last names\n if list(result.keys()) == [\"family-names\"]:\n return {\"name\": result[\"family-names\"]}\n return result\n\n\ndef to_cff_reference(bib_entry: pybtex.database.Entry) -> dict:\n \"\"\"BibTeX to CFF conversion for references.\n\n The format is defined here:\n https://github.com/citation-file-format/citation-file-format/blob/main/schema-guide.md#definitionsreference\n \"\"\"\n\n def _cff_transform(cff_field, bib_value):\n if cff_field == \"type\":\n if bib_value == \"inproceedings\":\n return \"article\"\n elif bib_value == \"incollection\":\n return \"article\"\n elif cff_field == \"publisher\":\n return {\"name\": bib_value}\n elif cff_field == \"month\":\n try:\n return int(bib_value)\n except ValueError:\n return {\n \"jan\": 1,\n \"feb\": 2,\n \"mar\": 3,\n \"apr\": 4,\n \"may\": 5,\n \"jun\": 6,\n \"jul\": 7,\n \"aug\": 8,\n \"sep\": 9,\n \"oct\": 10,\n \"nov\": 11,\n \"dec\": 12,\n }[bib_value[:3].lower()]\n return bib_value\n\n cff_reference = {\n \"type\": _cff_transform(cff_field=\"type\", bib_value=bib_entry.type),\n \"authors\": [\n to_cff_person(person) for person in bib_entry.persons[\"author\"]\n ],\n }\n # Map BibTeX to CFF fields. This is just a subset of the most relevant\n # fields.\n fields = {\n \"doi\": \"doi\",\n \"edition\": \"edition\",\n \"isbn\": \"isbn\",\n \"license\": \"license\",\n \"month\": \"month\",\n \"number\": \"number\",\n \"pages\": \"pages\",\n \"publisher\": \"publisher\",\n \"title\": \"title\",\n \"url\": \"url\",\n \"version\": \"version\",\n \"volume\": \"volume\",\n \"year\": \"year\",\n \"booktitle\": \"collection-title\",\n }\n for bibtex_field, value in bib_entry.fields.items():\n bibtex_field = bibtex_field.lower()\n if bibtex_field in fields:\n cff_field = fields[bibtex_field]\n cff_reference[cff_field] = _cff_transform(\n cff_field=cff_field, bib_value=value\n )\n return cff_reference\n\n\ndef collect_citation_metadata(\n metadata: dict, references: List[pybtex.database.Entry]\n) -> dict:\n \"\"\"Produces the data stored in the CITATION.cff file\n\n Args:\n metadata: The project metadata read from the YAML file. This is the main\n source of information for this function.\n references: List of references resolved from 'metadata[\"References\"]'.\n They will be converted to CFF.\n\n Returns:\n Citation data in the [Citation File Format](https://github.com/citation-file-format/citation-file-format)\n \"\"\"\n # Author list\n citation_authors = []\n for author_tier in [\"Core\", \"Developers\", \"Contributors\"]:\n for author in metadata[\"Authors\"][author_tier][\"List\"]:\n family_names, given_names = author[\"Name\"].split(\", \")\n citation_author = {\n \"family-names\": family_names,\n \"given-names\": given_names,\n }\n if \"Orcid\" in author:\n citation_author[\"orcid\"] = (\n \"https://orcid.org/\" + author[\"Orcid\"]\n )\n if \"Affiliations\" in author and len(author[\"Affiliations\"]) > 0:\n citation_author[\"affiliation\"] = \" and \".join(\n author[\"Affiliations\"]\n )\n citation_authors.append(citation_author)\n # References in CITATION.cff format\n citation_references = [to_cff_reference(entry) for entry in references]\n return {\n \"cff-version\": \"1.2.0\",\n \"message\": (\n \"Please cite SpECTRE in any publications that make use of its code\"\n \" or data. Cite the latest version that you use in your\"\n \" publication. The citation for this version is listed below.\"\n ),\n \"title\": metadata[\"Name\"],\n \"url\": metadata[\"Homepage\"],\n \"repository-code\": \"https://github.com/\" + metadata[\"GitHub\"],\n \"version\": metadata[\"Version\"],\n \"date-released\": metadata[\"PublicationDate\"],\n \"doi\": metadata[\"Doi\"],\n \"authors\": citation_authors,\n \"keywords\": metadata[\"Keywords\"],\n \"license\": metadata[\"License\"],\n \"references\": citation_references,\n }\n\n\ndef build_bibtex_entry(metadata: dict):\n \"\"\"Builds a BibTeX entry that we suggest people cite in publications\n\n Args:\n metadata: The project metadata read from the YAML file\n\n Returns:\n A pybtex.database.Entry. Use the `to_string` member function to convert to\n a string in BibTeX, YAML or other formats.\n \"\"\"\n # We truncate the author list in the BibTeX entry after 'Developers',\n # because not all journals are happy with printing an excessively long\n # author list, e.g. Phys. Rev. wants at most 15 authors. By truncating the\n # author list here, the user who copies the BibTeX entry doesn't have to\n # make the decision where to truncate.\n authors = [\n pybtex.database.Person(author[\"Name\"])\n for author in (\n metadata[\"Authors\"][\"Core\"][\"List\"]\n + metadata[\"Authors\"][\"Developers\"][\"List\"]\n )\n ] + [pybtex.database.Person(\"others\")]\n entry = pybtex.database.Entry(\n \"software\",\n persons=dict(author=authors),\n fields=dict(\n title=(\n r\"\\texttt{\"\n + metadata[\"Name\"]\n + \" v\"\n + metadata[\"Version\"]\n + \"}\"\n ),\n # The 'version' field is not used by revtex4-2, so we also put the\n # version in the title\n version=metadata[\"Version\"],\n publisher=\"Zenodo\",\n doi=metadata[\"Doi\"],\n url=metadata[\"Homepage\"],\n howpublished=(\n r\"\\href{https://doi.org/\"\n + metadata[\"Doi\"]\n + \"}{\"\n + metadata[\"Doi\"]\n + \"}\"\n ),\n license=metadata[\"License\"],\n year=str(metadata[\"PublicationDate\"].year),\n month=str(metadata[\"PublicationDate\"].month),\n ),\n )\n entry.key = \"spectrecode\"\n return entry\n\n\ndef prepare(\n metadata: dict,\n version_name: str,\n metadata_file: str,\n citation_file: str,\n bib_file: str,\n references_file: str,\n readme_file: str,\n zenodo: Zenodo,\n github: Github,\n update_only: bool,\n check_only: bool,\n):\n # Validate new version name\n match_version_name = re.match(VERSION_PATTERN + \"$\", version_name)\n if not match_version_name:\n raise ValueError(\n f\"Version name '{version_name}' doesn't match \"\n f\"pattern '{VERSION_PATTERN}'.\"\n )\n publication_date = datetime.date(\n year=int(match_version_name.group(1)),\n month=int(match_version_name.group(2)),\n day=int(match_version_name.group(3)),\n )\n\n if update_only:\n # Don't try to create a new version draft on Zenodo but update the\n # existing one. We assume that the metadata in the repository already\n # point to the existing version draft on Zenodo that we want to update.\n # This is the case when the user has run this script without the\n # `--update-only` option before and has thus created the new version\n # draft on Zenodo, and is now running it again with the `--update-only`\n # option to push updated metadata to the draft.\n new_version_id = metadata[\"ZenodoId\"]\n else:\n # Zenodo doesn't have a draft for the new version yet, or the metadata\n # in the repository is not yet updated. Either way, we use the ID from\n # the metadata to obtain the latest version on Zenodo and create a new\n # draft. Zenodo doesn't create another draft if one already exists, but\n # just returns it.\n latest_version_id = metadata[\"ZenodoId\"]\n try:\n assert zenodo.is_latest_version(record_id=latest_version_id), (\n \"The latest Zenodo version ID in the repository is\"\n f\" {latest_version_id}, but Zenodo reports it is not the latest\"\n \" version.\"\n )\n except requests.exceptions.HTTPError as err:\n raise requests.exceptions.HTTPError(\n f\"No published record with ID {latest_version_id} found on \"\n \"Zenodo. Use the '--update-only' flag if you're re-running \"\n \"the script over a repository that already has an unpublished \"\n \"new version ID inserted into Metadata.yaml.\"\n ) from err\n logger.info(f\"The latest Zenodo version ID is {latest_version_id}.\")\n # Reserve a DOI by creating a new version on Zenodo. It will remain a\n # draft until we publish it in the `publish` subprogram.\n if check_only:\n report_check_only(\n \"Would create new version on Zenodo with \"\n f\"ID {latest_version_id}.\"\n )\n new_version_id = latest_version_id\n else:\n new_version_id = zenodo.new_version(\n latest_version_id=latest_version_id\n )\n new_version_draft = zenodo.get_deposition(id=new_version_id)\n new_version_doi = new_version_draft[\"metadata\"][\"prereserve_doi\"][\"doi\"]\n assert new_version_doi, (\n \"Zenodo did not return a reserved DOI for the new version draft. \"\n \"You may want to visit {} to reserve one, save the draft and re-run \"\n \"this script with the '--update-only' flag.\"\n ).format(new_version_draft[\"links\"][\"html\"])\n logger.info(\n \"The new version draft on Zenodo has \"\n f\"ID {new_version_id} and DOI {new_version_doi}.\"\n )\n\n # Insert the new version information into the metadata file. We have to\n # resort to regex-replacements because pyyaml doesn't support\n # format-preserving round-trips.\n def replace_in_yaml(content, key, value, validate_value_pattern):\n content, num_subs = re.subn(\n r\"^{}: {}$\".format(key, validate_value_pattern),\n r\"{}: {}\".format(key, value),\n content,\n flags=re.MULTILINE,\n )\n if num_subs == 0:\n match = re.search(\n r\"^{}: (.*)$\".format(key), content, flags=re.MULTILINE\n )\n if match:\n raise ValueError(\n f\"The value of '{key}' in the file '{metadata_file}' \"\n f\"does not match the pattern '{validate_value_pattern}': \"\n f\"{match.group(1)}\"\n )\n else:\n raise ValueError(\n f\"Could not find '{key}' in root of file '{metadata_file}'.\"\n )\n elif num_subs > 1:\n raise ValueError(\n f\"Found more than one '{key}' in file '{metadata_file}'.\"\n )\n return content\n\n with open(metadata_file, \"r\" if check_only else \"r+\") as open_metadata_file:\n content_original = open_metadata_file.read()\n content_new = replace_in_yaml(\n content_original, \"Version\", version_name, VERSION_PATTERN\n )\n content_new = replace_in_yaml(\n content_new,\n \"PublicationDate\",\n publication_date.isoformat(),\n PUBLICATION_DATE_PATTERN,\n )\n content_new = replace_in_yaml(\n content_new, \"Doi\", new_version_doi, DOI_PATTERN\n )\n content_new = replace_in_yaml(\n content_new, \"ZenodoId\", new_version_id, ZENODO_ID_PATTERN\n )\n content_diff = \"\\n\".join(\n difflib.context_diff(\n content_original.split(\"\\n\"),\n content_new.split(\"\\n\"),\n lineterm=\"\",\n fromfile=metadata_file,\n tofile=metadata_file,\n )\n )\n if check_only:\n report_check_only(f\"Would apply diff:\\n{content_diff}\")\n else:\n logger.debug(f\"Applying diff:\\n{content_diff}\")\n open_metadata_file.seek(0)\n open_metadata_file.write(content_new)\n open_metadata_file.truncate()\n logger.info(f\"Inserted new version info into '{metadata_file}'.\")\n # Also update the the metadata dict to make sure we don't accidentally use\n # the old values somewhere\n metadata[\"Version\"] = version_name\n metadata[\"PublicationDate\"] = publication_date\n metadata[\"Doi\"] = new_version_doi\n metadata[\"ZenodoId\"] = new_version_id\n\n def write_file_or_check(filename, content_new):\n with open(filename, \"r\" if check_only else \"r+\") as open_file:\n content_original = open_file.read()\n content_diff = \"\\n\".join(\n difflib.context_diff(\n content_original.split(\"\\n\"),\n content_new.split(\"\\n\"),\n lineterm=\"\",\n fromfile=filename,\n tofile=filename,\n )\n )\n if check_only:\n report_check_only(f\"Would apply diff:\\n{content_diff}\")\n else:\n logger.debug(f\"Applying diff:\\n{content_diff}\")\n open_file.seek(0)\n open_file.write(content_new)\n open_file.truncate()\n\n # Write the CITATION.cff file\n reference_keys = metadata[\"References\"][\"List\"]\n all_references = pybtex.database.parse_file(references_file)\n references = [all_references.entries[key] for key in reference_keys]\n citation_data = collect_citation_metadata(metadata, references)\n citation_file_content = \"\"\"# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# This file is automatically generated. It will be overwritten at every\n# release. See .github/scripts/Release.py for details.\n\n\"\"\"\n citation_file_content += yaml.safe_dump(citation_data, allow_unicode=True)\n write_file_or_check(citation_file, citation_file_content)\n # Validate the CFF file\n Citation(citation_file_content, src=citation_file).validate()\n\n # Get the BibTeX entry and write to file\n bibtex_entry = build_bibtex_entry(metadata)\n bib_file_content = bibtex_entry.to_string(\n \"bibtex\",\n # LaTeX-encode special characters, instead of writing unicode symbols\n encoding=\"ASCII\",\n )\n # Fix an issue with encoded accents (a space in the author list is\n # recognized as delimiter between names)\n bib_file_content = bib_file_content.replace(r\"\\c c\", r\"\\c{c}\")\n # Wrap long lines in BibTeX output\n bib_file_content = \"\\n\".join(\n [textwrap.fill(line, width=80) for line in bib_file_content.split(\"\\n\")]\n )\n write_file_or_check(bib_file, bib_file_content)\n\n # Insert the new version information into the README\n def replace_badge_in_readme(content, key, image_url, link_url):\n content, num_subs = re.subn(\n r\"\\[!\\[{}\\]\\(.*\\)\\]\\(.*\\)\".format(key),\n r\"[![{}]({})]({})\".format(key, image_url, link_url),\n content,\n flags=re.MULTILINE,\n )\n assert (\n num_subs > 0\n ), f\"Could not find badge '{key}' in file '{readme_file}'.\"\n return content\n\n def replace_doi_in_readme(content, doi, doi_url):\n content, num_subs = re.subn(\n r\"DOI: \\[{}\\]\\(.*\\)\".format(DOI_PATTERN),\n r\"DOI: [{}]({})\".format(doi, doi_url),\n content,\n flags=re.MULTILINE,\n )\n assert (\n num_subs > 0\n ), \"Could not find DOI (matching '{}') with link in file '{}'.\".format(\n DOI_PATTERN, readme_file\n )\n return content\n\n def replace_link_in_readme(content, link_text, link_url):\n content, num_subs = re.subn(\n r\"\\[{}\\]\\(.*\\)\".format(link_text),\n r\"[{}]({})\".format(link_text, link_url),\n content,\n flags=re.MULTILINE,\n )\n assert num_subs > 0, (\n f\"Could not find link with text '{link_text}' in \"\n f\"file '{readme_file}'.\"\n )\n return content\n\n def replace_bibtex_entry_in_readme(content, bibtex_entry):\n bibtex_entry_string = bib_file_content\n # Work around an issue with escaping LaTeX commands\n bibtex_entry_string = bibtex_entry_string.replace(\"\\\\\", \"\\\\\\\\\")\n FENCE_PATTERN = \"\"\n content, num_subs = re.subn(\n (FENCE_PATTERN + \"(.*)\" + FENCE_PATTERN),\n (\n FENCE_PATTERN\n + \"\\n```bib\\n\"\n + bibtex_entry_string.strip()\n + \"\\n```\\n\"\n + FENCE_PATTERN\n ),\n content,\n flags=re.DOTALL,\n )\n assert (\n num_subs > 0\n ), f\"Could not find a BibTeX entry in file '{readme_file}'.\"\n return content\n\n with open(readme_file, \"r\" if check_only else \"r+\") as open_readme_file:\n content_original = open_readme_file.read()\n content = replace_badge_in_readme(\n content_original,\n \"release\",\n f\"https://img.shields.io/badge/release-v{version_name}-informational\",\n \"https://github.com/{}/releases/tag/v{}\".format(\n metadata[\"GitHub\"], version_name\n ),\n )\n content = replace_badge_in_readme(\n content,\n \"DOI\",\n f\"https://zenodo.org/badge/doi/{new_version_doi}.svg\",\n f\"https://doi.org/{new_version_doi}\",\n )\n content = replace_doi_in_readme(\n content, new_version_doi, f\"https://doi.org/{new_version_doi}\"\n )\n # We don't currently link to the Zenodo BibTeX entry because it isn't\n # very good. Instead, we generate our own.\n content = replace_bibtex_entry_in_readme(content, bibtex_entry)\n content_diff = \"\\n\".join(\n difflib.context_diff(\n content_original.split(\"\\n\"),\n content.split(\"\\n\"),\n lineterm=\"\",\n fromfile=readme_file,\n tofile=readme_file,\n )\n )\n if check_only:\n report_check_only(f\"Would apply diff:\\n{content_diff}\")\n else:\n logger.debug(f\"Applying diff:\\n{content_diff}\")\n open_readme_file.seek(0)\n open_readme_file.write(content)\n open_readme_file.truncate()\n\n # Upload the updated metadata to Zenodo\n zenodo_metadata = collect_zenodo_metadata(metadata, references, github)\n logger.debug(\n \"The metadata we'll send to Zenodo are:\\n{}\".format(\n yaml.safe_dump(zenodo_metadata, allow_unicode=True)\n )\n )\n if check_only:\n report_check_only(\"Would upload metadata to Zenodo.\")\n else:\n zenodo.update_deposition(id=new_version_id, metadata=zenodo_metadata)\n logger.debug(\n (\n \"New Zenodo version draft is now prepared. You can edit \"\n \"it here:\\n{}\"\n ).format(new_version_draft[\"links\"][\"html\"])\n )\n\n\ndef publish(\n metadata: dict,\n zenodo: Zenodo,\n github: Github,\n auto_publish: bool,\n check_only: bool,\n):\n version_name = metadata[\"Version\"]\n new_version_id = metadata[\"ZenodoId\"]\n\n # Retrieve the Zenodo deposition for the version draft that we have\n # prepared before\n new_version_draft = zenodo.get_deposition(id=new_version_id)\n\n # Retrieve the file \"bucket\" ID for uploading data\n bucket_id = pathlib.PurePosixPath(\n urllib.parse.urlparse(new_version_draft[\"links\"][\"bucket\"]).path\n ).parts[-1]\n\n # Retrieve the URL of the GitHub release archive that we want to upload\n # to Zenodo\n gh_user, gh_repo = metadata[\"GitHub\"].split(\"/\")\n # Alternatively we could use the release ID that GitHub's\n # 'actions/create-release' returns to retrieve the release\n gh_release = github.get_release_by_tag(\n user=gh_user, repo=gh_repo, tag=\"v\" + version_name\n )\n logger.debug(\n \"The release on GitHub is:\\n{}\".format(\n yaml.safe_dump(gh_release, allow_unicode=True)\n )\n )\n zipball_url = gh_release[\"zipball_url\"]\n\n # Stream the release archive to Zenodo.\n # We keep the file name for the archive on Zenodo the same for each\n # release so we can just overwrite it. Note that the _unpacked_ directory\n # name contains the version as expected, since the unpacked directory name\n # is determined by the GitHub release.\n archive_filename = gh_repo + \".zip\"\n if check_only:\n report_check_only(\n f\"Would stream release zipball '{zipball_url}' as \"\n f\"filename '{archive_filename}' to bucket '{bucket_id}'.\"\n )\n else:\n # Download the zipball from GitHub, then upload to Zenodo.\n # Note: Something like this should also work to stream the file\n # directly from GitHub to Zenodo without temporarily saving it, but\n # Zenodo doesn't currently document their new \"bucket\" file API so it\n # is difficult to debug:\n # with requests.get(zipball_url, stream=True) as zipball_stream:\n # zipball_stream.raise_for_status()\n # uploaded_file = zenodo.upload_file(bucket_id=bucket_id,\n # file=zipball_stream,\n # filename=archive_filename)\n zipball_download = requests.get(zipball_url, stream=True)\n with tempfile.TemporaryFile() as open_tmp_file:\n for chunk in zipball_download.iter_content():\n open_tmp_file.write(chunk)\n open_tmp_file.seek(0)\n uploaded_file = zenodo.upload_file(\n bucket_id=bucket_id,\n file=open_tmp_file,\n filename=archive_filename,\n )\n logger.debug(\n \"Release archive upload complete:\\n{}\".format(\n yaml.safe_dump(uploaded_file, allow_unicode=True)\n )\n )\n\n # Publish!\n if auto_publish:\n if check_only:\n report_check_only(\n f\"Would publish Zenodo record {new_version_id} now!\"\n )\n else:\n published_record = zenodo.publish(id=new_version_id)\n logger.debug(\n \"Zenodo record published:\\n{}\".format(\n yaml.safe_dump(published_record, allow_unicode=True)\n )\n )\n logger.info(\n (\n \"Zenodo record is now public! Here's the link to the \"\n \"record:\\n{}\"\n ).format(published_record[\"links\"][\"record_html\"])\n )\n else:\n logger.info(\n (\n \"Release is ready to be published on Zenodo. Go to this \"\n \"website, make sure everything looks fine and then hit the \"\n \"'Publish' button:\\n{}\"\n ).format(new_version_draft[\"links\"][\"html\"])\n )\n\n\nif __name__ == \"__main__\":\n # Always work with the repository that contains this file\n repo = git.Repo(__file__, search_parent_directories=True)\n\n import argparse\n\n parser = argparse.ArgumentParser(\n description=(\n \"Prepare the repository and publish releases on Zenodo as part of\"\n \" the automatic versioning procedure. This script is not intended\"\n \" to be run outside of GitHub actions. The 'prepare' subprogram\"\n \" reserves a DOI on Zenodo and inserts it into the repository\"\n \" along with the new version name. Once the release archive has\"\n \" been created, the 'publish'subprogram uploads it to Zenodo.\"\n f\" Repository: {repo.working_dir}.\"\n )\n )\n parent_parser = argparse.ArgumentParser(add_help=False)\n parent_parser.add_argument(\n \"--zenodo-token\",\n required=True,\n help=(\n \"Zenodo access token. Refer to the Zenodo documentation \"\n \"for instructions on creating a personal access token.\"\n ),\n )\n parent_parser.add_argument(\n \"--zenodo-sandbox\",\n action=\"store_true\",\n help=\"Use the Zenodo sandbox instead of the public version of Zenodo\",\n )\n parent_parser.add_argument(\n \"--github-token\",\n required=False,\n help=(\n \"Access token for GitHub queries. Refer to the GitHub documentation\"\n \" for instructions on creating a personal access token.\"\n ),\n )\n parent_parser.add_argument(\n \"-v\",\n \"--verbose\",\n action=\"count\",\n default=0,\n help=\"Verbosity (-v, -vv, ...)\",\n )\n parent_parser.add_argument(\n \"--check-only\",\n action=\"store_true\",\n help=(\n \"Dry mode, only check that all files are consistent. Nothing is\"\n \" edited or uploaded to Zenodo. Used in CI tests to make sure\"\n \" changes to the repository remain compatible with this script.\"\n ),\n )\n subparsers = parser.add_subparsers()\n parser_prepare = subparsers.add_parser(\"prepare\", parents=[parent_parser])\n parser_prepare.set_defaults(subprogram=prepare)\n parser_prepare.add_argument(\n \"--update-only\",\n action=\"store_true\",\n help=(\n \"Only update an existing version draft on Zenodo, not creating a \"\n \"new one. Use this flag if the metadata in the repository already \"\n \"reference the new version draft on Zenodo.\"\n ),\n )\n parser_prepare.add_argument(\n \"--version-name\",\n required=False,\n help=(\n \"The name of the new version. Will be inserted into the \"\n \"'--metadata-file'. Required unless '--check-only'.\"\n ),\n )\n parser_publish = subparsers.add_parser(\"publish\", parents=[parent_parser])\n parser_publish.set_defaults(subprogram=publish)\n parser_publish.add_argument(\n \"--auto-publish\",\n action=\"store_true\",\n help=(\n \"Publish the Zenodo record once it's ready. \"\n \"WARNING: Published records cannot be deleted and editing is \"\n \"limited. Omit this argument to print out the link to the \"\n \"prepared draft on Zenodo so you can do a manual sanity-check \"\n \"before publishing it.\"\n ),\n )\n args = parser.parse_args()\n\n # Set the log level\n logging.basicConfig(level=logging.WARNING - args.verbose * 10)\n logging.getLogger(\"pykwalify\").setLevel(logging.CRITICAL)\n del args.verbose\n\n # Load the project metadata\n metadata_file = os.path.join(repo.working_dir, \"Metadata.yaml\")\n args.metadata = yaml.safe_load(open(metadata_file, \"r\"))\n if args.subprogram == prepare:\n args.metadata_file = metadata_file\n\n # Make passing a version name optional in check-only mode\n if args.subprogram == prepare:\n assert args.check_only or args.version_name, (\n \"The '--version-name' argument is required unless you run in \"\n \"'--check-only' mode.\"\n )\n if args.check_only and not args.version_name:\n args.version_name = args.metadata[\"Version\"]\n\n # Locate project files\n if args.subprogram == prepare:\n args.readme_file = os.path.join(repo.working_dir, \"README.md\")\n args.citation_file = os.path.join(repo.working_dir, \"CITATION.cff\")\n args.bib_file = os.path.join(repo.working_dir, \"citation.bib\")\n args.references_file = os.path.join(\n repo.working_dir, args.metadata[\"References\"][\"BibliographyFile\"]\n )\n\n # Configure the Zenodo API client\n args.zenodo = Zenodo(\n base_url=(\n \"https://sandbox.zenodo.org/api/\"\n if args.zenodo_sandbox\n else \"https://zenodo.org/api/\"\n ),\n auth=uplink.auth.BearerToken(args.zenodo_token),\n )\n del args.zenodo_sandbox\n del args.zenodo_token\n\n # Configure the GitHub API client\n args.github = Github(\n base_url=\"https://api.github.com/\",\n auth=(\n uplink.auth.BearerToken(args.github_token)\n if args.github_token\n else None\n ),\n )\n del args.github_token\n\n # Dispatch to the selected subprogram\n subprogram = args.subprogram\n del args.subprogram\n subprogram(**vars(args))\n" }, { "path": ".github/scripts/requirements-release.txt", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Required Python packages for the release workflow\n\nGitPython~=3.1.11\npybtex~=0.24.0\nPyGithub~=1.53\nPyYAML~=5.3.1\ntqdm~=4.55.1\nuplink==0.9.7\ncffconvert==2.0.0\n" }, { "path": ".github/workflows/BuildDockerContainer.yaml", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# This workflow can be run manually on any branch to build and push our Docker\n# containers.\n#\n# We build containers that run both an AMD64/x86-64 and on ARM64. We used to use\n# a cross-compilation approach with Docker's buildx support, but this can be\n# quite fragile since cross-compilation is notoriously difficult. While buildx\n# used an emulator, QEMU, this is still found to be quite fragile with difficult\n# to diagnose segmentation faults and other errors. To get around this we use\n# the GitHub Actions ARM64 runners to build the ARM image and the x86-64 runners\n# to build that image. Then, once both images are pushed to Dockerhub, we create\n# what Docker calls a \"manifest\", which is essentially a file that tells Docker\n# which image to download depending on what it wants. This means for ARM64 it\n# will automatically download the ARM64 container and similar for\n# x86-64. The net result is extremely similar to the cross-compilation approach\n# but since the builds are always native, it is simpler.\nname: Build Docker container\n\non:\n workflow_dispatch:\n inputs:\n image_name:\n description: >\n Image name to push to DockerHub\n required: true\n default: 'sxscollaboration/spectre'\n build_arm:\n type: boolean\n description: >\n Build ARM container in addition to x86_64\n default: true\n\njobs:\n build:\n name: Build (${{ matrix.arch }})\n runs-on: ${{ matrix.runner }}\n # This environment can be protected to require manual approval before\n # deployment. On forks where you set your own secrets for authentication\n # with DockerHub you can choose not to protect this environment.\n environment: deploy-containers\n strategy:\n fail-fast: true\n # Dynamically set the matrix based on the build_arm input. GitHub Actions\n # expressions lack a ternary operator, so we use short-circuit evaluation:\n # condition && value_if_true || value_if_false\n # fromJSON() then parses the resulting JSON string into an array for\n # `include`. The multi-line ${{ }} works because YAML folds unquoted\n # scalars into a single line before the expression is evaluated.\n # Docs:\n # https://docs.github.com/en/actions/reference/workflows-and-actions/expressions\n # https://docs.github.com/en/actions/using-jobs/using-a-matrix-for-your-jobs#expanding-or-adding-matrix-configurations\n matrix:\n include: ${{ fromJSON(inputs.build_arm\n && '[{\"arch\":\"amd64\",\"runner\":\"ubuntu-latest\"},\n {\"arch\":\"arm64\",\"runner\":\"ubuntu-24.04-arm\"}]'\n || '[{\"arch\":\"amd64\",\"runner\":\"ubuntu-latest\"}]') }}\n steps:\n - name: Checkout repository\n uses: actions/checkout@v5\n - name: Set up Docker Buildx\n uses: docker/setup-buildx-action@v4\n - name: Login to DockerHub\n uses: docker/login-action@v4\n with:\n username: ${{ secrets.DOCKERHUB_USERNAME }}\n password: ${{ secrets.DOCKERHUB_TOKEN }}\n # We could also push containers to GitHub instead of DockerHub\n # - name: Login to GitHub container registry\n # uses: docker/login-action@v3\n # with:\n # registry: ghcr.io\n # username: ${{ github.actor }}\n # password: ${{ secrets.GITHUB_TOKEN }}\n - name: Build dev container\n uses: docker/build-push-action@v7\n with:\n push: true\n context: .\n file: \"./containers/Dockerfile.buildenv\"\n target: dev\n tags: ${{ inputs.image_name }}:dev-${{ matrix.arch }}\n platforms: linux/${{ matrix.arch }}\n build-args: |\n PARALLEL_MAKE_ARG=-j4\n UBUNTU_VERSION=22.04\n # The 18.04 container only supports amd64\n - name: Build dev1804 container\n if: ${{ matrix.arch == 'amd64' }}\n uses: docker/build-push-action@v7\n with:\n push: true\n context: .\n file: \"./containers/Dockerfile.buildenv\"\n target: dev\n tags: ${{ inputs.image_name }}:dev1804\n platforms: linux/amd64\n build-args: |\n PARALLEL_MAKE_ARG=-j4\n UBUNTU_VERSION=18.04\n\n create_manifest:\n name: Create multi-arch manifest\n needs: build\n runs-on: ubuntu-latest\n environment: deploy-containers\n steps:\n - name: Login to DockerHub\n uses: docker/login-action@v4\n with:\n username: ${{ secrets.DOCKERHUB_USERNAME }}\n password: ${{ secrets.DOCKERHUB_TOKEN }}\n - name: Set up Docker Buildx\n uses: docker/setup-buildx-action@v4\n - name: Create dev manifest\n run: |\n SOURCES=\"${{ inputs.image_name }}:dev-amd64\"\n if [ \"${{ inputs.build_arm }}\" = \"true\" ]; then\n SOURCES=\"$SOURCES ${{ inputs.image_name }}:dev-arm64\"\n fi\n docker buildx imagetools create \\\n --tag ${{ inputs.image_name }}:dev $SOURCES\n - name: Inspect manifest\n run: >\n docker buildx imagetools inspect ${{ inputs.image_name }}:dev\n\n run_tests:\n name: Test\n uses: ./.github/workflows/Tests.yaml\n needs: create_manifest\n secrets: inherit\n with:\n container: ${{ inputs.image_name }}:dev\n" }, { "path": ".github/workflows/ClobberCache.yaml", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Dump a large file into the cache to force GitHub to clobber it.\nname: Clobber Cache\n\non:\n workflow_dispatch:\n\njobs:\n clobber_cache:\n name: Clobber Cache\n runs-on: ubuntu-latest\n strategy:\n fail-fast: false\n steps:\n # Configure the clobber cache\n - name: Restore cache\n uses: actions/cache@v4\n with:\n path: cache\n key: \"clobber-cache\"\n restore-keys: |\n clobber-cache\n # Generate the random file to clobber the cache.\n # Note that the file size must be updated as GitHub expands the cache\n # size limits.\n - name: Clobber cache\n run: >\n mkdir -p cache\n\n cd ./cache\n\n rm -rf ./*\n\n head -c 9900MB /dev/urandom > clobber.txt\n" }, { "path": ".github/workflows/DemoContainer.yaml", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nname: Deploy containers\n\non:\n workflow_dispatch:\n inputs:\n image_name:\n description: Image name to push to DockerHub\n default: 'sxscollaboration/spectre'\n build_arm:\n type: boolean\n description: Build ARM container in addition to x86_64\n default: true\n\n workflow_call:\n inputs:\n image_name:\n type: string\n description: Image name to push to DockerHub\n default: 'sxscollaboration/spectre'\n build_arm:\n type: boolean\n description: Build ARM container in addition to x86_64\n default: true\n secrets:\n DOCKERHUB_USERNAME:\n required: true\n DOCKERHUB_TOKEN:\n required: true\n\njobs:\n build:\n name: Build (${{ matrix.arch }})\n runs-on: ${{ matrix.runner }}\n environment: deploy-containers\n strategy:\n fail-fast: true\n matrix:\n include: ${{ fromJSON(inputs.build_arm\n && '[{\"arch\":\"amd64\",\"runner\":\"ubuntu-latest\"},\n {\"arch\":\"arm64\",\"runner\":\"ubuntu-24.04-arm\"}]'\n || '[{\"arch\":\"amd64\",\"runner\":\"ubuntu-latest\"}]') }}\n steps:\n - name: Checkout repository\n uses: actions/checkout@v5\n - name: Set up Docker Buildx\n uses: docker/setup-buildx-action@v4\n - name: Login to DockerHub\n uses: docker/login-action@v4\n with:\n username: ${{ secrets.DOCKERHUB_USERNAME }}\n password: ${{ secrets.DOCKERHUB_TOKEN }}\n - name: Build and push deploy container\n uses: docker/build-push-action@v7\n with:\n push: true\n context: .\n file: \"./containers/Dockerfile.buildenv\"\n target: deploy\n tags: ${{ inputs.image_name }}:deploy-${{ matrix.arch }}\n platforms: linux/${{ matrix.arch }}\n build-args: PARALLEL_MAKE_ARG=-j4\n - name: Build and push demo container\n uses: docker/build-push-action@v5\n with:\n push: true\n context: .\n file: \"./containers/Dockerfile.buildenv\"\n target: demo\n tags: ${{ inputs.image_name }}:demo-${{ matrix.arch }}\n platforms: linux/${{ matrix.arch }}\n build-args: PARALLEL_MAKE_ARG=-j4\n\n create_manifests:\n name: Create multi-arch manifests\n needs: build\n runs-on: ubuntu-latest\n environment: deploy-containers\n steps:\n - name: Login to DockerHub\n uses: docker/login-action@v4\n with:\n username: ${{ secrets.DOCKERHUB_USERNAME }}\n password: ${{ secrets.DOCKERHUB_TOKEN }}\n - name: Set up Docker Buildx\n uses: docker/setup-buildx-action@v4\n - name: Create deploy manifest\n run: |\n SOURCES=\"${{ inputs.image_name }}:deploy-amd64\"\n if [ \"${{ inputs.build_arm }}\" = \"true\" ]; then\n SOURCES=\"$SOURCES ${{ inputs.image_name }}:deploy-arm64\"\n fi\n docker buildx imagetools create \\\n --tag ${{ inputs.image_name }}:deploy \\\n --tag ${{ inputs.image_name }}:latest \\\n $SOURCES\n - name: Create demo manifest\n run: |\n SOURCES=\"${{ inputs.image_name }}:demo-amd64\"\n if [ \"${{ inputs.build_arm }}\" = \"true\" ]; then\n SOURCES=\"$SOURCES ${{ inputs.image_name }}:demo-arm64\"\n fi\n docker buildx imagetools create \\\n --tag ${{ inputs.image_name }}:demo $SOURCES\n - name: Inspect manifests\n run: |\n docker buildx imagetools inspect ${{ inputs.image_name }}:deploy\n docker buildx imagetools inspect ${{ inputs.image_name }}:demo\n" }, { "path": ".github/workflows/DeployStaticExecutables.yaml", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nname: Deploy static executables\n\non:\n release:\n types: [published]\n workflow_dispatch:\n inputs:\n tag_name:\n type: string\n required: true\n description: The name of the release tag\n\njobs:\n deploy_static_execs:\n name: Deploy static executables and libraries\n runs-on: ubuntu-latest\n env:\n RELEASE_TAG_NAME: ${{ inputs.tag_name || github.event.release.tag_name }}\n steps:\n - name: Checkout repository\n uses: actions/checkout@v5\n # Build static executables in a Docker container with an older version\n # of Ubuntu so that the glibc is compatible with most Linux distros.\n - name: Set up Docker Buildx\n uses: docker/setup-buildx-action@v4\n - name: Build static executables\n uses: docker/build-push-action@v7\n with:\n push: false\n context: .\n file: \"./containers/Dockerfile.buildenv\"\n target: deploy_static_execs_and_libs\n tags: sxs-collaboration/spectre:deploy_static_execs_and_libs\n platforms: linux/amd64\n load: true\n build-args: |\n UBUNTU_VERSION=18.04\n PARALLEL_MAKE_ARG=-j4\n - name: Run Docker container\n run: >\n docker run --name static-execs\n sxs-collaboration/spectre:deploy_static_execs_and_libs\n - name: Install python dependencies\n run: >\n pip3 install numpy h5py gdown\n - name: Download extra data to include for CCE\n run: |\n gdown \\\n \"https://drive.google.com/uc?id=1CmgLLfuLod8stc13EtmjHUvBoIgSVD-Y\"\n gdown \\\n \"https://drive.google.com/uc?id=1mN1oFQ7UcB1wsiXw9dphwAprQqufLia0\"\n gdown \\\n \"https://drive.google.com/uc?id=1yYMM4PVUec9pIjKTxI4aCpo0Umqconr8\"\n - name: Copy CCE executables from the container\n run: >\n mkdir CceExecutables;\n mkdir ./CceExecutables/PreprocessCceWorldtube;\n mkdir ./CceExecutables/Tests;\n\n cp ./tests/InputFiles/Cce/CharacteristicExtract.yaml\n ./CceExecutables/CharacteristicExtract.yaml\n\n cp\n ./tests/InputFiles/PreprocessCceWorldtube/PreprocessCceWorldtube.yaml\n ./CceExecutables/PreprocessCceWorldtube/PreprocessCceWorldtube.yaml\n\n cp\n ./tests/InputFiles/PreprocessCceWorldtube/AdmFirstOrderDriverPreprocessCceWorldtube.yaml\n ./CceExecutables/PreprocessCceWorldtube/AdmFirstOrderDriverPreprocessCceWorldtube.yaml\n\n cp\n ./tests/InputFiles/PreprocessCceWorldtube/AdmSecondOrderDriverPreprocessCceWorldtube.yaml\n ./CceExecutables/PreprocessCceWorldtube/AdmSecondOrderDriverPreprocessCceWorldtube.yaml\n\n docker cp\n static-execs:/work/spectre/build/bin/CharacteristicExtract\n ./CceExecutables/\n\n docker cp static-execs:/work/spectre/build/bin/PreprocessCceWorldtube\n ./CceExecutables/PreprocessCceWorldtube/\n\n docker cp\n static-execs:/work/spectre/build/bin/WriteCceWorldtubeCoordsToFile\n ./CceExecutables/PreprocessCceWorldtube/\n - name: Test CCE executable outside of container\n run: |\n mv BondiSachsCceR0200.h5 ./CceExecutables/Tests/\n mv CheckCceOutput.py ./CceExecutables/Tests/\n mv CharacteristicExtractReduction_Expected.h5 \\\n ./CceExecutables/Tests/\n\n sed -i 's/CceR0257/Tests\\/BondiSachsCceR0200/g' \\\n ./CceExecutables/CharacteristicExtract.yaml\n\n cd ./CceExecutables/\n\n ./CharacteristicExtract \\\n --input-file ./CharacteristicExtract.yaml\n python ./Tests/CheckCceOutput.py\n rm CharacteristicExtractReduction.h5\n\n cd ../\n - name: Create CCE executables release asset\n # Note: We use xz compression since it's much better than gzip, even\n # though it's a decent bit slower. Specifically, xz is two thirds the\n # size of gzip.\n run: |\n tar cJf CceExecutables.tar.xz CceExecutables\n - name: Upload to release\n uses: softprops/action-gh-release@v3\n with:\n tag_name: ${{ env.RELEASE_TAG_NAME }}\n fail_on_unmatched_files: true\n files: |\n CceExecutables.tar.xz\n" }, { "path": ".github/workflows/NewContributors.yaml", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Add new contributors when their first PR was merged\nname: New contributors\n\non:\n pull_request_target:\n branches: [develop]\n types: [closed]\n\njobs:\n new_contributors:\n if: github.event.pull_request.merged == true\n name: Notify\n runs-on: ubuntu-latest\n steps:\n - uses: actions/checkout@v5\n - name: Check PR author is new\n id: check_pr_author\n shell: python\n run: |\n import yaml\n\n def all_authors():\n authors = yaml.safe_load(open('Metadata.yaml', 'r'))['Authors']\n for tier in ['Core', 'Developers', 'Contributors']:\n for author in authors[tier]['List']:\n yield author['GitHub']\n\n pr_author = '${{ github.event.pull_request.user.login }}'\n if pr_author not in all_authors():\n print('::set-output name=is_new::true')\n - name: Comment on PR\n if: steps.check_pr_author.outputs.is_new\n uses: peter-evans/create-or-update-comment@v5\n with:\n issue-number: ${{ github.event.pull_request.number }}\n body: > # Newlines are line breaks, body renders as GitHub markdown\n @${{ github.event.pull_request.user.login }} looks like this is your\n first contribution to SpECTRE. Welcome! 🎉 Your contribution\n is much appreciated, and we invite you to add your name to the\n author list:\n\n\n 1. Edit the [`Metadata.yaml`](https://github.com/${{ github.event.pull_request.user.login }}/spectre/blob/develop/Metadata.yaml)\n file in the repository.\n\n 2. Add an entry to the list in `Authors.Contributors` with your\n name, affiliation, etc. Note that the list is ordered\n alphabetically by last name.\n\n 3. Commit the change on a new branch and open a pull request with\n the change.\n\n\n Once the pull request is merged, your name will appear on the\n [SpECTRE DOI on Zenodo](https://doi.org/10.5281/zenodo.4290404)\n with the next public release.\n" }, { "path": ".github/workflows/PostRelease.yaml", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Automations that run on published releases\nname: Post release\n\non:\n release:\n types: [published]\n workflow_dispatch:\n inputs:\n tag_name:\n description: 'Tag name of the release'\n required: true\n\njobs:\n add_spack_version:\n name: Add version to Spack\n # Checksum the new release and send a PR to Spack that adds the new version.\n # The 'sxs-bot' GitHub account is the author of the commit and the PR.\n # - This job requires a repository secret named `GH_TOKEN_SXSBOT_SPACK` that\n # has write access to the `sxs-bot/spack` repository.\n runs-on: ubuntu-latest\n env:\n RELEASE_TAG_NAME: ${{ inputs.tag_name || github.event.release.tag_name }}\n steps:\n - name: Download Spack\n uses: actions/checkout@v5\n with:\n repository: spack/spack\n fetch-depth: 0\n token: ${{ secrets.GH_TOKEN_SXSBOT_SPACK }}\n - name: Add spack-python to path\n run: |\n echo \"$GITHUB_WORKSPACE/bin\" >> $GITHUB_PATH\n - name: Checksum new version\n # Download and checksum the release tarball, and add a line to Spack's\n # `spectre/package.py`` file with the new version.\n #\n # The package file defines versions in lines like this:\n #\n # version('develop', branch='develop')\n # version('2022.01.03', sha256='872a0d1...')\n # ...\n #\n # The `spack.util.format.get_version_lines` function returns a string\n # with lines like this for the new version(s), including the correct\n # indentation. Therefore, we insert the new lines into the file right\n # below the 'develop' version.\n shell: spack-python {0}\n run: |\n import spack.spec\n import spack.stage\n import spack.repo\n import spack.util.format\n import os\n\n # The tag name includes the 'v' prefix\n release_name = '${{ env.RELEASE_TAG_NAME }}'[1:]\n\n # Get the URL for the release tarball. The\n # 'github.event.release.tarball_url' points to a slightly different\n # 'https://api.github.com/...' URL, which has a different checksum\n # than the tarball listed on the GitHub release page and used by\n # Spack.\n pkg_cls = spack.repo.PATH.get_pkg_class('spectre')\n pkg = pkg_cls(spack.spec.Spec('spectre'))\n release_url = pkg.url_for_version(release_name)\n\n url_dict = {\n release_name: release_url,\n }\n version_hashes = spack.stage.get_checksums_for_versions(\n url_dict,\n pkg.name,\n fetch_options=pkg.fetch_options,\n )\n version_lines = spack.util.format.get_version_lines(\n version_hashes, url_dict\n )\n\n package_file = os.path.join(pkg.package_dir, 'package.py')\n with open(package_file, 'r') as open_package_file:\n package_file_lines = open_package_file.readlines()\n with open(package_file, 'w') as open_package_file:\n for line in package_file_lines:\n open_package_file.write(line)\n if line.strip().startswith('version(\"develop\"'):\n open_package_file.write(version_lines + \"\\n\")\n - name: Fix code formatting\n run: |\n spack style --fix `git diff --name-only`\n # Formatting can also be fixed later by Spack maintainers in the PR, so\n # it's fine if it fails here for some reason\n continue-on-error: true\n - name: Print diff\n run: |\n git diff\n - name: Send pull request to Spack\n uses: peter-evans/create-pull-request@v8\n with:\n token: ${{ secrets.GH_TOKEN_SXSBOT_SPACK }}\n commit-message: \"spectre: add ${{ env.RELEASE_TAG_NAME }}\"\n committer: \"sxs-bot \"\n branch: \"spectre-${{ env.RELEASE_TAG_NAME }}\"\n delete-branch: true\n push-to-fork: sxs-bot/spack\n title: \"spectre: add ${{ env.RELEASE_TAG_NAME }}\"\n body: \"\"\n # Build and push the `demo` container to DockerHub on releases. This is\n # because the `demo` container has pre-built executables that we want to keep\n # up to date.\n docker:\n uses: ./.github/workflows/DemoContainer.yaml\n secrets: inherit\n" }, { "path": ".github/workflows/Spack.yaml", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Installation test with the Spack package manager\nname: Spack\n\non:\n # Could run this on a schedule once Spack is stable enough to not break every\n # week.\n # schedule:\n # - cron: '0 0 * * 1' # every Monday morning\n workflow_dispatch:\n\nconcurrency:\n group: spack\n cancel-in-progress: true\n\njobs:\n spack_install:\n name: Install\n strategy:\n matrix:\n host: [ubuntu-latest, macos-latest]\n compiler: [gcc, llvm, apple-clang]\n exclude:\n - host: ubuntu-latest\n compiler: apple-clang\n version:\n # A non-exhaustive set of versions to test, e.g., versions listed in\n # published papers.\n - 'develop'\n - '2021.12.15'\n fail-fast: false\n runs-on: ${{ matrix.host }}\n env:\n # This is the configuration (\"spec\") that we'll install with Spack\n # - Build a subset of executables, and Python bindings\n # - Disable debug symbols to fit in the memory of the GitHub Actions VM\n # - Select the 'multicore' backend for Charm++, since we're running on a\n # single node.\n # - Select HDF5 without MPI to avoid compiling MPI.\n SPECTRE_SPEC: >- # Line breaks are spaces, no trailing newline\n spectre@${{ matrix.version }}\n executables=SolvePoisson1D\n +python\n ~debug_symbols\n ^${{ matrix.compiler }}\n ^charmpp backend=multicore\n ^hdf5~mpi\n SPACK_COLOR: always\n steps:\n - name: Install compiler\n if: matrix.host == 'macos-latest' && matrix.compiler == 'llvm'\n run: |\n brew install llvm\n echo \"$(brew --prefix llvm)/bin\" >> $GITHUB_PATH\n - name: Install Spack\n run: |\n git clone -c feature.manyFiles=true --depth=1 \\\n https://github.com/spack/spack.git\n echo $PWD/spack/bin >> $GITHUB_PATH\n - name: Configure Spack\n run: |\n spack debug report\n spack compiler find\n spack compiler info ${{ matrix.compiler }}\n spack external find\n - name: Print packages to install\n run: |\n spack spec -I ${SPECTRE_SPEC}\n - name: Install SpECTRE\n run: |\n spack install --show-log-on-error ${SPECTRE_SPEC}\n" }, { "path": ".github/workflows/Tests.yaml", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Continuous integration tests that pull requests are required to pass. This\n# workflow can also be dispatched manually to tag and release versions.\nname: Tests\n\n# Set any defaults for the runs below.\n# - use bash as the default shell since this is almost certainly what\n# is always expected. We use regular expressions in a few places\n# that rely on bash.\ndefaults:\n run:\n shell: bash\n\n# Note that by default the jobs only run on the base repository, testing pull\n# requests and merge commits. Enable GitHub Actions in your fork's repository\n# settings to also run the tests on every push to one of your branches.\non:\n # We run all jobs when pull requests are opened, commits are pushed, or pull\n # requests are re-opened after being closed.\n # The jobs triggered by this event run on the base repository of the pull\n # request, so they have access to its caches.\n pull_request:\n # We run those jobs that require no information about a pull request (e.g.\n # unit tests) also on `push` events. This setup tests merge commits into\n # `develop` and also builds up caches on `develop` that can be re-used by PRs.\n # It also runs the jobs on forks if they have GitHub Actions enabled.\n push:\n branches-ignore:\n - gh-pages\n # Allow running the workflow manually to run tests and optionally release a\n # version on success (see the dev guide on \"Automatic versioning\")\n workflow_dispatch:\n inputs:\n release_version:\n description: >\n Enter a version name YYYY.MM.DD[.TWEAK] to create a release on success\n required: false\n default: ''\n timezone:\n description: >\n Timezone used for validating the version name. The release must be\n approved by the end of the day in the specified timezone. See\n /usr/share/zoneinfo for a list of possible values.\n required: false\n default: 'America/Los_Angeles'\n clear_ccache:\n description: >\n Enter 'yes' without quotes to clear ccache before running\n required: false\n default: ''\n container:\n description: >\n Container to use for builds\n required: false\n default: 'sxscollaboration/spectre:dev'\n # Allow running this workflow as a job in another workflow. This is used to\n # test a new Docker container before publishing it.\n workflow_call:\n inputs:\n container:\n description: >\n Container to use for builds\n required: false\n type: string\n default: 'sxscollaboration/spectre:dev'\n\n# Cancel all other queued or in-progress runs of this workflow when it is\n# scheduled, so repeated pushes to a branch or a PR don't block CI. Repeated\n# pushes to 'develop' and 'release' are not canceled, so every merge commit is\n# tested.\nconcurrency:\n group: ${{ github.ref }}\n cancel-in-progress: ${{ github.ref != 'refs/heads/develop'\n && github.ref != 'refs/heads/release' }}\n\njobs:\n # Make sure no commits are prefixed with `fixup` or similar keywords. See\n # `tools/CheckCommits.sh` for details.\n check_commits:\n name: Commits\n # Only run on pull requests since we don't check _all_ commits, but only\n # those that came after the PR's base ref.\n if: github.event_name == 'pull_request'\n runs-on: ubuntu-latest\n steps:\n - name: Checkout repository\n uses: actions/checkout@v5\n with:\n fetch-depth: 0\n - name: Check commits\n # `CheckCommits.sh` tests against the local `develop` branch, so that's\n # where we fetch the pull-request's base-branch to. Typically, it is\n # the upstream `sxs-collaboration/spectre/develop` branch.\n run: >\n cd $GITHUB_WORKSPACE\n\n git remote add upstream\n https://github.com/${{ github.repository }}.git\n\n git remote -v\n\n git fetch upstream ${{ github.base_ref }}:develop\n\n ./tools/CheckCommits.sh\n\n # - Run simple textual checks over files in the repository, e.g. checking for\n # a license, line length limits etc. See `tools/CheckFiles.sh` for details.\n # - Run format checker for python to make sure the code is formatted correctly\n # - Check the metadata are consistent\n check_files_and_formatting:\n name: Files and formatting\n runs-on: ubuntu-latest\n container:\n image: ${{ inputs.container || 'sxscollaboration/spectre:dev' }}\n steps:\n - name: Checkout repository\n uses: actions/checkout@v5\n with:\n fetch-depth: 0\n # Work around https://github.com/actions/checkout/issues/760\n - name: Trust checkout\n run: |\n git config --global --add safe.directory $GITHUB_WORKSPACE\n # The action above checks out the `github.ref` by default, which points to\n # the merge commit with the target branch for pull-request events. For\n # this job we check out the pull-request HEAD instead. It makes\n # git-related issues easier to debug because the state matches the local\n # repository. It also prevents releases that happened since the\n # pull-request branch was last rebased from disrupting tests that involve\n # the latest release tag.\n - name: Checkout pull-request HEAD\n if: github.event_name == 'pull_request'\n run: |\n git checkout ${{ github.event.pull_request.head.sha }}\n # Some tests involve release tags, which may not have been pushed to\n # forks. Fetching them here.\n - name: Fetch upstream tags on forks\n if: github.repository != 'sxs-collaboration/spectre'\n run: |\n git fetch --tags https://github.com/sxs-collaboration/spectre\n - name: Install Python dependencies\n run: |\n pip3 install -r .github/scripts/requirements-release.txt\n pip3 install -r support/Python/dev_requirements.txt\n - name: Test tools\n run: |\n python3 -m unittest discover -p 'Test_CompileReleaseNotes.py' \\\n tests.tools -v\n - name: Check Python formatting\n run: |\n cd $GITHUB_WORKSPACE\n echo \"Using 'black' to check Python formatting...\"\n black --check --extend-exclude '/external/' .\n echo \"Using 'isort' to check Python formatting...\"\n isort --check-only --extend-skip external .\n - name: Test script\n run: |\n cd $GITHUB_WORKSPACE\n ./tools/CheckFiles.sh --test\n - name: Check files\n run: |\n cd $GITHUB_WORKSPACE\n ./tools/CheckFiles.sh\n - name: Check metadata\n run: |\n python3 tools/CheckMetadata.py\n - name: Check the metadata is consistent with the releases\n # No need to check this on forks. They would need to set a Zenodo token\n # for this test. Also disable on PRs because they don't have access to\n # the repo's secrets.\n if: >\n github.repository == 'sxs-collaboration/spectre'\n && github.event_name != 'pull_request'\n run: |\n python3 .github/scripts/Release.py prepare -vv --check-only \\\n --zenodo-token ${{ secrets.ZENODO_READONLY_TOKEN }} \\\n --github-token ${{ secrets.GITHUB_TOKEN }}\n python3 .github/scripts/Release.py publish -vv --check-only \\\n --zenodo-token ${{ secrets.ZENODO_READONLY_TOKEN }} \\\n --github-token ${{ secrets.GITHUB_TOKEN }} \\\n --auto-publish\n - name: Check release notes\n run: |\n python3 tools/CompileReleaseNotes.py -vv -o release_notes.md \\\n --github-token ${{ secrets.GITHUB_TOKEN }}\n - name: Upload release notes\n uses: actions/upload-artifact@v7\n with:\n name: release-notes\n path: release_notes.md\n # GitHub doesn't display artifacts until the workflow has completed, so we\n # print the release notes here to be able to review them before approving\n # a release\n - name: Print release notes\n run: |\n cat release_notes.md\n\n # Lint with clang-tidy. We check only code that changed relative to the\n # nearest common ancestor commit with `sxs-collaboration/spectre/develop`.\n clang_tidy:\n name: Clang-tidy\n if: >\n (github.event_name == 'pull_request'\n && github.repository == 'sxs-collaboration/spectre'\n && github.base_ref == 'develop')\n || github.ref != 'refs/heads/develop'\n runs-on: ubuntu-latest\n container:\n image: ${{ inputs.container || 'sxscollaboration/spectre:dev' }}\n strategy:\n matrix:\n build_type: [Debug, Release]\n steps:\n - name: Checkout repository\n uses: actions/checkout@v5\n with:\n fetch-depth: 0\n # Work around https://github.com/actions/checkout/issues/760\n - name: Trust checkout\n run: |\n git config --global --add safe.directory $GITHUB_WORKSPACE\n # Some cpp20 features aren't supported until clang-tidy-16. See:\n # https://stackoverflow.com/questions/46114214/lambda-implicit-capture-fails-with-variable-declared-from-structured-binding#comment135007519_46115028\n # The clang-tidy-diff tool doesn't report exit codes until version\n # 18.1.0, so we grab the version that does:\n # https://github.com/llvm/llvm-project/commit/4294bca5e4f6e6e8cfdbd9fbe8751c5e5415fd47\n - name: Install clang-tidy-16\n run: |\n apt-get update -y\n apt-get remove -y clang-tidy clang-tidy-14\n apt-get install -y clang-tidy-16\n ln -s /usr/bin/clang-tidy-16 /usr/bin/clang-tidy\n wget https://raw.githubusercontent.com/llvm/llvm-project/4294bca5e4f6e6e8cfdbd9fbe8751c5e5415fd47/clang-tools-extra/clang-tidy/tool/clang-tidy-diff.py\n chmod +x clang-tidy-diff.py\n mv clang-tidy-diff.py /usr/bin/clang-tidy-diff.py\n ln -s /usr/bin/clang-tidy-diff.py /usr/bin/clang-tidy-diff\n - name: Configure annotations\n # Has to be accessible outside the container, see issue:\n # https://github.com/actions/toolkit/issues/305\n run: |\n cp .github/problem_matchers/ClangTidy.json \"$HOME/\"\n echo \"::add-matcher::$HOME/ClangTidy.json\"\n - name: Fetch sxs-collaboration/spectre/develop\n run: >\n cd $GITHUB_WORKSPACE\n\n git remote add upstream\n https://github.com/sxs-collaboration/spectre.git\n\n git remote -v\n\n git fetch upstream develop\n - name: Configure with cmake\n run: >\n mkdir build && cd build\n\n cmake\n -D CMAKE_C_COMPILER=clang-14\n -D CMAKE_CXX_COMPILER=clang++-14\n -D CMAKE_Fortran_COMPILER=gfortran\n -D CHARM_ROOT=${CHARM_ROOT}\n -D CMAKE_BUILD_TYPE=${{ matrix.build_type }}\n -D OVERRIDE_ARCH=x86-64\n -D USE_CCACHE=OFF\n -D USE_PCH=OFF\n -D DEBUG_SYMBOLS=OFF\n -D BUILD_PYTHON_BINDINGS=ON\n -D SPECTRE_AUTODIFF=ON\n -D SPECTRE_FETCH_MISSING_DEPS=ON\n $GITHUB_WORKSPACE\n\n make -j4 module_All Libsharp-external\n - name: Check clang-tidy\n run: >\n UPSTREAM_HASH=$(git merge-base HEAD upstream/develop)\n\n echo \"Running clang-tidy relative to: $UPSTREAM_HASH\\n\"\n\n git diff -U0 $UPSTREAM_HASH |\n clang-tidy-diff -path build -p1 -use-color -j4 \\\n -extra-arg=-I/usr/include/hdf5/serial \\\n -extra-arg=-I$GITHUB_WORKSPACE/build/_deps/autodiff-src\n\n\n # Build the documentation and check for problems, then upload as a workflow\n # artifact and deploy to gh-pages.\n doc_check:\n name: Documentation\n needs: check_files_and_formatting\n runs-on: ubuntu-latest\n container:\n image: ${{ inputs.container || 'sxscollaboration/spectre:dev' }}\n env:\n CCACHE_DIR: /work/ccache\n CCACHE_READONLY: 1\n CCACHE_COMPILERCHECK: content\n CCACHE_BASEDIR: $GITHUB_WORKSPACE\n steps:\n - name: Checkout repository\n uses: actions/checkout@v5\n # Work around https://github.com/actions/checkout/issues/760\n - name: Trust checkout\n run: |\n git config --global --add safe.directory $GITHUB_WORKSPACE\n # These can be installed directly in the Docker container instead\n - name: Install Python dependencies\n run: |\n python3 -m pip install -r support/Python/dev_requirements.txt\n - name: Download release notes\n uses: actions/download-artifact@v8\n id: release-notes\n with:\n name: release-notes\n path: /work\n - name: Append release notes to changelog\n # The sed command escapes @ symbols at beginning of words (GitHub\n # usernames) so they aren't interpreted as Doxygen commands\n run: |\n echo \"\" >> docs/Changelog.md\n cat /work/release_notes.md | sed 's/\\(\\B\\@\\)/\\\\\\1/g' \\\n >> docs/Changelog.md\n - name: Restore ccache\n uses: actions/cache/restore@v5\n id: restore-ccache\n env:\n CACHE_KEY_PREFIX: ccache-gcc-11-Debug-pch-ON\n with:\n path: /work/ccache\n key: \"${{ env.CACHE_KEY_PREFIX }}-${{ github.run_id }}\"\n restore-keys: |\n ${{ env.CACHE_KEY_PREFIX }}-\n # - Make sure to use the same build configuration as the unit tests from\n # which we restore the ccache.\n # - Set `BUILD_TESTING=OFF` to test a CMake configuration with tests\n # turned off.\n - name: Configure with cmake\n run: >\n mkdir build && cd build\n\n cmake\n -D CMAKE_C_COMPILER=gcc-11\n -D CMAKE_CXX_COMPILER=g++-11\n -D CMAKE_Fortran_COMPILER=gfortran-11\n -D CMAKE_CXX_FLAGS=\"-Werror\"\n -D OVERRIDE_ARCH=x86-64\n -D CHARM_ROOT=${CHARM_ROOT}\n -D CMAKE_BUILD_TYPE=Debug\n -D SPECTRE_DEBUG_Og=ON\n -D DEBUG_SYMBOLS=OFF\n -D USE_PCH=ON\n -D USE_XSIMD=ON\n -D USE_CCACHE=ON\n -D ENABLE_OPENMP=ON\n -D BUILD_PYTHON_BINDINGS=ON\n -D BUILD_SHARED_LIBS=ON\n -D MEMORY_ALLOCATOR=SYSTEM\n -D BUILD_DOCS=ON\n -D BUILD_TESTING=OFF\n -D SPECTRE_AUTODIFF=ON\n -D SPECTRE_FETCH_MISSING_DEPS=ON\n $GITHUB_WORKSPACE\n - name: Check documentation\n working-directory: build\n run: |\n make doc-check\n # Re-build with coverage information on pushes to develop for deployment\n # to gh-pages.\n - name: Build documentation with coverage\n if: github.event_name == 'push' && github.ref == 'refs/heads/develop'\n working-directory: build\n run: |\n make doc-coverage\n - name: Build Python docs\n working-directory: build\n run: |\n make py-docs -j4\n # Upload as an artifact to make available to deployment and to PRs\n - name: Prepare for upload\n working-directory: build\n run: |\n tar -cf docs-html.tar --directory docs/html .\n - name: Upload documentation\n uses: actions/upload-artifact@v7\n with:\n name: docs-html\n path: build/docs-html.tar\n\n # Deploy to gh-pages on pushes to develop\n # See docs: https://github.com/actions/deploy-pages\n docs-deploy:\n name: Deploy documentation\n if: github.event_name == 'push' && github.ref == 'refs/heads/develop'\n needs: doc_check\n runs-on: ubuntu-latest\n permissions:\n pages: write\n id-token: write\n environment:\n name: github-pages\n url: ${{ steps.deploy.outputs.page_url }}\n steps:\n - uses: actions/deploy-pages@v5\n id: deploy\n with:\n artifact_name: docs-html\n\n # Build all test executables and run unit tests on a variety of compiler\n # configurations.\n unit_tests:\n name: Unit tests\n runs-on: ubuntu-latest\n timeout-minutes: 345\n strategy:\n fail-fast: false\n matrix:\n # We have a sparse clang test configuration to reduce the amount of\n # GitHub cache space we use. GCC being the production compiler on\n # supercomputers means we need to thoroughly test it.\n compiler:\n - gcc-10\n - gcc-11\n - gcc-13\n build_type: [Debug, Release]\n include:\n # Generate code coverage report for a single build\n # Note: currently disabled because it exceeds the available disk space\n # - compiler: gcc-9\n # build_type: Debug\n # COVERAGE: ON\n # TEST_TIMEOUT_FACTOR: 3\n # This configuration seems to run consistently slower than newer gcc\n # or clang builds, so we increase the test timeout a bit\n - compiler: gcc-10\n build_type: Debug\n TEST_TIMEOUT_FACTOR: 2\n # Test 3D rendering with ParaView\n # Note: currently disabled because of some unknown upstream issue\n # test_3d_rendering: ON\n # Need Python version consistent with ParaView\n PYTHON_VERSION: \"3.9\"\n # Test with Kokkos enabled but without CUDA\n - compiler: gcc-10\n build_type: Release\n KOKKOS: ON\n # Disable FMA optimizations to avoid this issue:\n # https://github.com/sxs-collaboration/spectre/issues/5145\n EXTRA_CXX_FLAGS: \"-mno-fma\"\n # Don't modify the gcc-11 Debug build so its cache can be reused for\n # the documentation build\n # - compiler: gcc-11\n # build_type: Debug\n # Test with Python 3.8 so that we retain backwards compatibility. We\n # keep track of Python versions on supercomputers in this issue:\n # https://github.com/sxs-collaboration/spectre/issues/442\n - compiler: gcc-11\n build_type: Release\n PYTHON_VERSION: \"3.8\"\n # Disable building executable for this build for now because it\n # exceeds the available memory. See issue:\n # https://github.com/sxs-collaboration/spectre/issues/5472\n test_executables: OFF\n # Test building with static libraries. Do so with clang in release\n # mode because these builds use up little disk space compared to GCC\n # builds or clang Debug builds\n - compiler: clang-13\n build_type: Release\n BUILD_SHARED_LIBS: OFF\n use_xsimd: ON\n MEMORY_ALLOCATOR: JEMALLOC\n # Add a test without PCH to the build matrix, which only builds core\n # libraries. Building all the tests without the PCH takes very long\n # and the most we would catch is a missing include of something that's\n # in the PCH.\n # Use this test also to build and test all input files with \"normal\"\n # or higher priority. The other configurations only test input files\n # with \"high\" priority to reduce the total build time.\n - compiler: clang-13\n build_type: Debug\n use_pch: OFF\n unit_tests: OFF\n input_file_tests_min_priority: \"normal\"\n # Test with ASAN\n - compiler: clang-14\n build_type: Debug\n # When building with ASAN we also need python bindings to be\n # disabled because otherwise we get link errors. See issue:\n # https://github.com/sxs-collaboration/spectre/issues/1890\n # So we are also using this build to test building without Python\n # bindings enabled.\n ASAN: ON\n BUILD_PYTHON_BINDINGS: OFF\n MEMORY_ALLOCATOR: JEMALLOC\n TEST_TIMEOUT_FACTOR: 2\n - compiler: clang-14\n build_type: Release\n # Test compatibility with oldest supported CMake version\n CMAKE_VERSION: \"3.18.2\"\n # Use an MPI version of Charm\n CHARM_ROOT: /work/charm_7_0_0/mpi-linux-x86_64-smp-clang\n # MPI running tests is a bit slower than multicore\n TEST_TIMEOUT_FACTOR: 3\n # If MPI should be tested\n USE_MPI: ON\n # Test `install` target with clang in Release mode because it uses\n # little disk space\n install: ON\n # Test compiling with nvcc and CUDA\n - compiler: nvcc-12-6\n SPECTRE_AUTODIFF: OFF\n CUDA: ON\n KOKKOS: ON\n # Compile for NVIDIA Ampere architecture. Can't run this on\n # GitHub-hosted runners because they don't have the GPU hardware,\n # but we can test the compilation.\n KOKKOS_ARCH: \"AMPERE80\"\n # Compile in Release mode to speed up the build\n build_type: Release\n # Build with static libs because Kokkos CUDA doesn't support shared\n # libs\n BUILD_SHARED_LIBS: OFF\n # Build only a subset of the code because compiling the full code is\n # too slow and exceeds the available memory. We should extend this\n # to the full code once we have a better solution for the memory\n # issue. See 'Test nvcc support' step below.\n unit_tests: OFF\n test_executables: OFF\n # Enable PlaneWave3D.yaml input file test\n input_file_tests_min_priority: \"normal\"\n # Disable pybindings until they support nvcc\n BUILD_PYTHON_BINDINGS: OFF\n # Disable warnings as nvcc emits a lot of them from system headers\n ENABLE_WARNINGS: OFF\n\n container:\n image: ${{ inputs.container || 'sxscollaboration/spectre:dev' }}\n env:\n # We make sure to use a fixed absolute path for the ccache directory\n CCACHE_DIR: /work/ccache\n # Use a separate temp directory to conserve cache space on GitHub\n CCACHE_TEMPDIR: /work/ccache-tmp\n # Control the max cache size. We evict unused entries in a step below to\n # make sure that each build only uses what it need of this max size.\n CCACHE_MAXSIZE: \"2G\"\n # Control the compression level. The ccache docs recommend at most level\n # 5 to avoid slowing down compilation.\n CCACHE_COMPRESS: 1\n CCACHE_COMPRESSLEVEL: 5\n # We hash the content of the compiler rather than the location and mtime\n # to make sure the cache works across the different machines\n CCACHE_COMPILERCHECK: content\n # Rewrite absolute paths starting with this base dir to relative paths\n # before hashing. This is needed to reuse the cache for the formaline\n # test below, which builds in a different directory.\n CCACHE_BASEDIR: $GITHUB_WORKSPACE\n # These vars are to allow running charm with MPI as root inside the\n # container which arises from using the \"--privileged\" flag just below.\n OMPI_ALLOW_RUN_AS_ROOT: 1\n OMPI_ALLOW_RUN_AS_ROOT_CONFIRM: 1\n # The number of cores to run on. This is given at:\n # https://docs.github.com/en/actions/using-github-hosted-runners/about-github-hosted-runners/about-github-hosted-runners#standard-github-hosted-runners-for-public-repositories\n NUMBER_OF_CORES: 4\n # See https://lists.cs.illinois.edu/lists/arc/charm/2018-10/msg00011.html\n # for why we need this\n options: --privileged\n steps:\n - name: Record start time\n id: start\n run: |\n echo \"time=$(date +%s)\" >> \"$GITHUB_OUTPUT\"\n - name: Checkout repository\n uses: actions/checkout@v5\n # Work around https://github.com/actions/checkout/issues/760\n - name: Trust checkout\n run: |\n git config --global --add safe.directory $GITHUB_WORKSPACE\n - uses: ./.github/actions/parse-compiler\n with:\n compiler: ${{ matrix.compiler }}\n # Install the selected compiler. We don't bundle all of them in the\n # container because they take up a lot of space.\n - name: Install compiler\n run: |\n add-apt-repository ppa:ubuntu-toolchain-r/test\n apt-get update -y\n if [[ $COMPILER_ID = gcc ]]; then\n apt-get install -y $CC $CXX $FC\n elif [[ $COMPILER_ID = clang ]]; then\n apt-get install -y $CC $FC\n elif [[ $COMPILER_ID = nvcc ]]; then\n # Install CUDA\n wget https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2204/x86_64/cuda-keyring_1.1-1_all.deb\n dpkg -i cuda-keyring_1.1-1_all.deb\n apt-get update -y\n apt-get install -y cuda-nvcc-${COMPILER_VERSION} \\\n build-essential libc6-dev pkg-config\n echo \"/usr/local/cuda-${COMPILER_VERSION/-/.}/bin\" >> $GITHUB_PATH\n fi\n - name: Install Kokkos\n if: matrix.KOKKOS == 'ON'\n working-directory: /work\n run: |\n KOKKOS_VERSION=4.4.00\n wget -O kokkos.tar.gz \"https://github.com/kokkos/kokkos/releases/download/${KOKKOS_VERSION}/kokkos-${KOKKOS_VERSION}.tar.gz\"\n tar -xzf kokkos.tar.gz && mv kokkos-* kokkos && cd kokkos\n mkdir build && cd build\n cmake .. \\\n -D CMAKE_BUILD_TYPE=${{ matrix.build_type }} \\\n -D CMAKE_INSTALL_PREFIX=/usr/local \\\n -D Kokkos_ENABLE_SERIAL=ON \\\n -D Kokkos_ENABLE_OPENMP=ON \\\n -D Kokkos_ENABLE_CUDA=${{ matrix.CUDA || 'OFF' }} \\\n -D Kokkos_ARCH_${{ matrix.KOKKOS_ARCH || 'X86_64' }}=ON \\\n -D Kokkos_ENABLE_CUDA_CONSTEXPR=ON \\\n -D Kokkos_ENABLE_CUDA_RELOCATABLE_DEVICE_CODE=ON \\\n -D CMAKE_POSITION_INDEPENDENT_CODE=ON\n make -j ${NUMBER_OF_CORES} install\n cd ../../ && rm -rf kokkos.tar.gz kokkos\n # Use Kokkos compiler wrapper for nvcc\n if [[ $COMPILER_ID = nvcc ]]; then\n echo \"CXX=/usr/local/bin/nvcc_wrapper\" >> $GITHUB_ENV\n fi\n # Install specific CMake version if requested\n - name: Install CMake version\n if: matrix.CMAKE_VERSION\n working-directory: /work\n run: |\n CMAKE_VERSION=${{ matrix.CMAKE_VERSION }}\n wget -O cmake-install.sh \"https://github.com/Kitware/CMake/releases/download/v${CMAKE_VERSION}/cmake-${CMAKE_VERSION}-linux-x86_64.sh\"\n sh cmake-install.sh --prefix=/usr --skip-license\n rm cmake-install.sh\n - name: Install Python version\n if: matrix.PYTHON_VERSION\n run: |\n add-apt-repository ppa:deadsnakes/ppa\n apt install -y python${{ matrix.PYTHON_VERSION }}-dev \\\n python${{ matrix.PYTHON_VERSION }}-venv \\\n python${{ matrix.PYTHON_VERSION }}-distutils\n update-alternatives --install /usr/bin/python3 python3 \\\n /usr/bin/python${{ matrix.PYTHON_VERSION }} 1\n - name: Install Python dependencies\n if: matrix.PYTHON_VERSION\n run: |\n python${{ matrix.PYTHON_VERSION }} -m pip install \\\n -r support/Python/requirements.txt \\\n -r support/Python/dev_requirements.txt\n python${{ matrix.PYTHON_VERSION }} -m pip list -v\n - name: Install ParaView\n if: matrix.test_3d_rendering == 'ON'\n working-directory: /work\n # Can't just `apt-get install python3-paraview` because we need the\n # headless build of ParaView. So we download a binary from paraview.org\n # (which is built for a specific Python version unfortunately).\n run: |\n apt-get install -y libglvnd-dev # Needed to find 'libglapi.so'\n wget -O paraview.tar.gz --no-check-certificate \"https://www.paraview.org/paraview-downloads/download.php?submit=Download&version=v5.10&type=binary&os=Linux&downloadFile=ParaView-5.10.1-osmesa-MPI-Linux-Python3.9-x86_64.tar.gz\"\n tar -xzf paraview.tar.gz\n rm paraview.tar.gz\n mv ParaView-* /opt/paraview\n echo \"/opt/paraview/bin\" >> $GITHUB_PATH\n # Make 'paraview' Python package available\n PYTHONPATH=/opt/paraview/lib/python3.9/site-packages:$PYTHONPATH\n # Give system-installed Python packages priority over ParaView's\n PYTHONPATH=$pythonLocation/lib/python3.9/site-packages:$PYTHONPATH\n echo \"PYTHONPATH=$PYTHONPATH\" >> $GITHUB_ENV\n - name: Install MPI and Charm++\n if: matrix.USE_MPI == 'ON'\n working-directory: /work\n run: |\n apt-get install -y libopenmpi-dev\n cd /work/charm_7_0_0 && ./build charm++ mpi-linux-x86_64-smp clang \\\n -j ${NUMBER_OF_CORES} -g0 -O1 --build-shared --with-production\n\n # Assign a unique cache key for every run.\n # - We will save the cache using this unique key, but only on the develop\n # branch. This way we regularly update the cache without filling up the\n # storage space with caches from other branches.\n # - To restore the most recent cache we provide a partially-matched\n # \"restore key\".\n - name: Restore ccache\n uses: actions/cache/restore@v5\n id: restore-ccache\n env:\n CACHE_KEY_PREFIX: \"ccache-${{ matrix.compiler }}-\\\n${{ matrix.build_type }}-pch-${{ matrix.use_pch || 'ON' }}\"\n with:\n path: /work/ccache\n key: \"${{ env.CACHE_KEY_PREFIX }}-${{ github.run_id }}\"\n restore-keys: |\n ${{ env.CACHE_KEY_PREFIX }}-\n - name: Configure ccache\n # Print the ccache configuration and reset statistics\n run: |\n ccache -pz\n - name: Clear ccache\n # Clear ccache if requested\n if: >\n github.event_name == 'workflow_dispatch'\n && github.event.inputs.clear_ccache == 'yes'\n run: |\n ccache -C\n - name: Configure build with cmake\n # Notes on the build configuration:\n # - We don't need debug symbols during CI, so we turn them off to reduce\n # memory usage.\n # - We run unit tests with the following compiler flags:\n # -Werror: Treat warnings as error.\n # -march=x86-64: Make sure we are building on a consistent\n # architecture so caching works. This is necessary because GitHub may\n # run the job on different hardware.\n run: >\n mkdir build && cd build\n\n ENABLE_WARNINGS=${{ matrix.ENABLE_WARNINGS }}\n WERROR=\"${{ matrix.WERROR != 'OFF' && '-Werror' || '' }}\"\n CXX_FLAGS=\"${WERROR} ${{ matrix.EXTRA_CXX_FLAGS }}\"\n PYTHON_VERSION=${{ matrix.PYTHON_VERSION }}\n BUILD_PYTHON_BINDINGS=${{ matrix.BUILD_PYTHON_BINDINGS }}\n BUILD_SHARED_LIBS=${{ matrix.BUILD_SHARED_LIBS }}\n KOKKOS=${{ matrix.KOKKOS }}\n MATRIX_CHARM_ROOT=${{ matrix.CHARM_ROOT }}\n ASAN=${{ matrix.ASAN }}\n MEMORY_ALLOCATOR=${{ matrix.MEMORY_ALLOCATOR }}\n UBSAN_UNDEFINED=${{ matrix.UBSAN_UNDEFINED }}\n UBSAN_INTEGER=${{ matrix.UBSAN_INTEGER }}\n USE_PCH=${{ matrix.use_pch }}\n USE_XSIMD=${{ matrix.use_xsimd }}\n COVERAGE=${{ matrix.COVERAGE }}\n TEST_TIMEOUT_FACTOR=${{ matrix.TEST_TIMEOUT_FACTOR }}\n INPUT_FILE_MIN_PRIO=${{ matrix.input_file_tests_min_priority }}\n SPECTRE_AUTODIFF=${{ matrix.SPECTRE_AUTODIFF }}\n\n cmake --version\n\n cmake\n -D CMAKE_C_COMPILER=${CC}\n -D CMAKE_CXX_COMPILER=${CXX}\n -D CMAKE_Fortran_COMPILER=${FC}\n -D Python_EXECUTABLE=/usr/bin/python${PYTHON_VERSION:-'3'}\n -D CMAKE_CXX_FLAGS=\"${CXX_FLAGS}\"\n -D OVERRIDE_ARCH=x86-64\n -D ENABLE_WARNINGS=${ENABLE_WARNINGS:-'ON'}\n -D CHARM_ROOT=${MATRIX_CHARM_ROOT:-$CHARM_ROOT}\n -D CMAKE_BUILD_TYPE=${{ matrix.build_type }}\n -D SPECTRE_DEBUG_Og=ON\n -D DEBUG_SYMBOLS=OFF\n -D BACKTRACE_LIB=/usr/local/lib/libbacktrace.a\n -D BACKTRACE_HEADER_DIR=/usr/local/include\n -D UNIT_TESTS_IN_TEST_EXECUTABLES=OFF\n -D SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY=${INPUT_FILE_MIN_PRIO:-'high'}\n -D STRIP_SYMBOLS=ON\n -D STUB_EXECUTABLE_OBJECT_FILES=ON\n -D STUB_LIBRARY_OBJECT_FILES=ON\n -D USE_PCH=${USE_PCH:-'ON'}\n -D USE_XSIMD=${USE_XSIMD:-'ON'}\n -D USE_CCACHE=ON\n -D ENABLE_OPENMP=ON\n -D SPECTRE_KOKKOS=${KOKKOS:-'OFF'}\n -D COVERAGE=${COVERAGE:-'OFF'}\n -D BUILD_PYTHON_BINDINGS=${BUILD_PYTHON_BINDINGS:-'ON'}\n -D BUILD_SHARED_LIBS=${BUILD_SHARED_LIBS:-'ON'}\n -D ASAN=${ASAN:-'OFF'}\n -D UBSAN_UNDEFINED=${UBSAN_UNDEFINED:-'OFF'}\n -D UBSAN_INTEGER=${UBSAN_INTEGER:-'OFF'}\n -D MEMORY_ALLOCATOR=${MEMORY_ALLOCATOR:-'SYSTEM'}\n -D SPECTRE_UNIT_TEST_TIMEOUT_FACTOR=${TEST_TIMEOUT_FACTOR:-'1'}\n -D SPECTRE_INPUT_FILE_TEST_TIMEOUT_FACTOR=${TEST_TIMEOUT_FACTOR:-'1'}\n -D SPECTRE_PYTHON_TEST_TIMEOUT_FACTOR=${TEST_TIMEOUT_FACTOR:-'1'}\n -D CMAKE_INSTALL_PREFIX=/work/spectre_install\n -D BUILD_DOCS=OFF\n -D SPECTRE_AUTODIFF=${SPECTRE_AUTODIFF:-'ON'}\n -D SPECTRE_FETCH_MISSING_DEPS=ON\n --warn-uninitialized\n $GITHUB_WORKSPACE 2>&1 | tee CMakeOutput.txt 2>&1\n - name: Check for CMake warnings\n working-directory: build\n run: |\n ! grep -A 6 \"CMake Warning\" ./CMakeOutput.txt\n - name: Build unit tests\n if: matrix.unit_tests != 'OFF'\n working-directory: build\n run: |\n make -j${NUMBER_OF_CORES} unit-tests\n - name: Run unit tests\n if: matrix.unit_tests != 'OFF' && matrix.COVERAGE != 'ON'\n working-directory: build\n run: |\n # We get occasional random timeouts, repeat tests to see if\n # it is a random timeout or systematic.\n #\n # We run ctest -L unit before build test-executables to make\n # sure that all the unit tests are actually built by the\n # unit-tests target.\n ctest -j${NUMBER_OF_CORES} -L unit \\\n --output-on-failure --repeat after-timeout:3\n - name: Run unit tests with coverage reporting\n if: matrix.COVERAGE == 'ON'\n working-directory: build\n run: |\n make unit-test-coverage\n rm -r docs/html/unit-test-coverage\n - name: Upload coverage report to codecov.io\n if: matrix.COVERAGE == 'ON'\n uses: codecov/codecov-action@v4\n with:\n files: build/tmp/coverage.info\n token: ${{ secrets.CODECOV_TOKEN }}\n # Display the job as failed if upload fails (defaults to false for\n # some reason)\n fail_ci_if_error: true\n # We currently don't require codecov in our guidelines, so don't fail\n # the CI build if codecov fails to upload\n continue-on-error: true\n # Test only a few unit tests with nvcc for now because compiling the full\n # suite is too slow and exceed the available memory. We should extend this\n # to the full suite once we have a better solution for the memory issue.\n - name: Test nvcc support\n if: matrix.CUDA == 'ON'\n working-directory: build\n run: |\n make -j${NUMBER_OF_CORES} \\\n Test_DataStructures \\\n Test_Tensor \\\n Test_Kokkos \\\n Test_Spectral \\\n Test_Utilities \\\n EvolveScalarWave3D\n # Can't run these tests on GitHub-hosted runners because they don't\n # have GPU hardware.\n # ./bin/Test_DataStructures\n # ./bin/Test_Tensor\n # ./bin/Test_Kokkos\n # ./bin/Test_Spectral\n # ./bin/Test_Utilities\n # ctest -R PlaneWave3D.yaml --output-on-failure\n # Avoid running out of disk space by cleaning up the build directory\n - name: Clean up unit tests\n working-directory: build\n run: |\n pwd\n ls | xargs du -sh\n du -sh .\n rm -f bin/Test_*\n # Build the executables in a single thread to reduce memory usage\n # sufficiently so they compile on the GitHub-hosted runners\n - name: Build executables\n if: matrix.COVERAGE != 'ON' && matrix.test_executables != 'OFF'\n working-directory: build\n run: |\n make test-executables\n - name: Build Benchmark executable\n if: matrix.build_type == 'Release'\n working-directory: build\n run: |\n make -j${NUMBER_OF_CORES} Benchmark\n # Delete unused cache entries before uploading the cache\n - name: Clean up ccache\n if: github.ref == 'refs/heads/develop'\n run: |\n now=$(date +%s)\n job_duration=$((now - ${{ steps.start.outputs.time }}))\n ccache --evict-older-than \"${job_duration}s\"\n # Save the cache after everything has been built. Also save on failure or\n # on cancellation (`always()`) because a partial cache is better than no\n # cache.\n - name: Save ccache\n if: always() && github.ref == 'refs/heads/develop'\n uses: actions/cache/save@v5\n with:\n path: /work/ccache\n key: ${{ steps.restore-ccache.outputs.cache-primary-key }}\n - name: Print size of build directory\n working-directory: build\n run: |\n pwd\n ls | xargs du -sh\n du -sh .\n - name: Diagnose ccache\n run: |\n ccache -s\n - name: Run non-unit tests\n if: matrix.COVERAGE != 'ON' && matrix.test_executables != 'OFF'\n working-directory: build\n run: |\n # We get occasional random timeouts, repeat tests to see if\n # it is a random timeout or systematic\n #\n # Only use 2 cores because these tests run more slowly.\n ctest -j2 -LE unit --output-on-failure \\\n --repeat after-timeout:3\n - name: Install\n if: matrix.install == 'ON'\n working-directory: build\n # Make sure the `install` target runs without error. We could add some\n # basic smoke tests here to make sure the installation worked.\n run: |\n make install\n - name: Print size of install directory\n if: matrix.install == 'ON'\n working-directory: /work/spectre_install\n # Remove files post-install to reduce disk space for later on.\n run: |\n pwd\n ls | xargs du -sh\n du -sh .\n rm -r ./*\n - name: Test formaline tar can be built\n # - We only run the formaline tests in debug mode to reduce total build\n # time in CI. We don't run them with ASAN because then we run out of\n # disk space.\n # - We do run for all compilers, though, because formaline injects data\n # at the linking stage, which means we are somewhat tied to the\n # compiler version.\n # - We make sure to use the same compiler flags as the full build above\n # so ccache is able to speed up the build.\n if: >\n matrix.build_type == 'Debug'\n && matrix.ASAN != 'ON'\n && matrix.test_executables != 'OFF'\n working-directory: build\n run: >\n make EvolveBurgers -j${NUMBER_OF_CORES}\n\n if [ ! -f ./bin/EvolveBurgers ]; then\n echo \"Could not find the executable EvolveBurgers\";\n echo \"which we use for testing formaline\";\n exit 1\n fi\n\n # We disable ASAN's leak sanitizer because Charm++ has false\n # positives that would cause the build to fail. We disable\n # leak sanitizer for the ctest runs inside CMake anyway.\n\n ASAN_OPTIONS=detect_leaks=0 ./bin/EvolveBurgers\n --dump-source-tree-as spectre_src --dump-only\n\n mkdir spectre_src;\n mv spectre_src.tar.gz spectre_src;\n cd spectre_src;\n tar xf spectre_src.tar.gz;\n mkdir build-formaline;\n cd build-formaline\n\n ENABLE_WARNINGS=${{ matrix.ENABLE_WARNINGS }}\n WERROR=\"${{ matrix.WERROR != 'OFF' && '-Werror' || '' }}\"\n CXX_FLAGS=\"${WERROR} ${{ matrix.EXTRA_CXX_FLAGS }}\"\n PYTHON_VERSION=${{ matrix.PYTHON_VERSION }}\n BUILD_PYTHON_BINDINGS=${{ matrix.BUILD_PYTHON_BINDINGS }}\n MATRIX_CHARM_ROOT=${{ matrix.CHARM_ROOT }}\n MEMORY_ALLOCATOR=${{ matrix.MEMORY_ALLOCATOR }};\n USE_PCH=${{ matrix.use_pch }};\n USE_XSIMD=${{ matrix.use_xsimd }}\n\n cmake\n -D CMAKE_C_COMPILER=${CC}\n -D CMAKE_CXX_COMPILER=${CXX}\n -D CMAKE_Fortran_COMPILER=${FC}\n -D Python_EXECUTABLE=/usr/bin/python${PYTHON_VERSION:-'3'}\n -D CMAKE_CXX_FLAGS=\"${CXX_FLAGS}\"\n -D OVERRIDE_ARCH=x86-64\n -D ENABLE_WARNINGS=${ENABLE_WARNINGS:-'ON'}\n -D BUILD_SHARED_LIBS=ON\n -D CHARM_ROOT=${MATRIX_CHARM_ROOT:-$CHARM_ROOT}\n -D CMAKE_BUILD_TYPE=${{ matrix.build_type }}\n -D SPECTRE_DEBUG_Og=ON\n -D DEBUG_SYMBOLS=OFF\n -D UNIT_TESTS_IN_TEST_EXECUTABLES=OFF\n -D STRIP_SYMBOLS=ON\n -D STUB_EXECUTABLE_OBJECT_FILES=ON\n -D STUB_LIBRARY_OBJECT_FILES=ON\n -D USE_PCH=${USE_PCH:-'ON'}\n -D USE_XSIMD=${USE_XSIMD:-'ON'}\n -D USE_CCACHE=ON\n -D BUILD_PYTHON_BINDINGS=${BUILD_PYTHON_BINDINGS:-'ON'}\n -D MEMORY_ALLOCATOR=${MEMORY_ALLOCATOR:-'SYSTEM'}\n -D BUILD_DOCS=OFF\n -D SPECTRE_AUTODIFF=ON\n -D SPECTRE_FETCH_MISSING_DEPS=ON\n ..\n\n make EvolveBurgers -j${NUMBER_OF_CORES}\n\n # Run on multiple cores to run both the \"parse\" and \"execute\" tests\n # simultaneously.\n\n ctest -j${NUMBER_OF_CORES} -R InputFiles.Burgers.Step.yaml\n --output-on-failure\n\n cd .. && rm -r build-formaline\n - name: Test bundled exporter\n if: matrix.ASAN != 'ON' && matrix.CUDA != 'ON'\n working-directory: build\n run: |\n make -j${NUMBER_OF_CORES} BundledExporter\n mkdir build-test-exporter && cd build-test-exporter\n cmake -D SPECTRE_ROOT=$GITHUB_WORKSPACE/build \\\n $GITHUB_WORKSPACE/tests/Unit/IO/Exporter/BundledExporter\n make -j${NUMBER_OF_CORES}\n ./TestSpectreExporter \\\n $GITHUB_WORKSPACE/tests/Unit/Visualization/Python/VolTestData0.h5 \\\n element_data 0 Psi 0 0 0 -0.07059806932542323\n cd .. && rm -r build-test-exporter\n - name: Diagnose ccache\n run: |\n ccache -s\n\n # Build all test executables and run unit tests on macOS\n unit_tests_macos:\n name: Unit tests on macOS\n timeout-minutes: 345\n strategy:\n fail-fast: false\n matrix:\n os:\n - macos-15-intel\n - macos-15\n runs-on: ${{ matrix.os }}\n env:\n # We install some low-level dependencies with Homebrew. They get picked up\n # by `spack external find`.\n SPECTRE_BREW_DEPS: >- # Line breaks are spaces, no trailing newline\n autoconf automake boost catch2 ccache cmake gsl hdf5 openblas yaml-cpp xsimd\n # We install these packages with Spack and cache them. The full specs are\n # listed below. This list is only needed to create the cache.\n SPECTRE_SPACK_DEPS: blaze charmpp libxsmm\n CCACHE_DIR: $HOME/ccache\n CCACHE_TEMPDIR: $HOME/ccache-tmp\n CCACHE_MAXSIZE: \"2G\"\n CCACHE_COMPRESS: 1\n CCACHE_COMPRESSLEVEL: 5\n CCACHE_COMPILERCHECK: content\n SPACK_SKIP_MODULES: true\n SPACK_COLOR: always\n NUM_CORES: ${{ matrix.NUM_CORES }}\n steps:\n - name: Record start time\n id: start\n run: |\n echo \"time=$(date +%s)\" >> \"$GITHUB_OUTPUT\"\n - name: Get CPU cores\n id: get_cores\n run: |\n CORES=$(sysctl -n hw.ncpu)\n echo \"NUM_CORES=$CORES\" >> $GITHUB_ENV\n echo \"Detect $CORES cores\"\n - name: Checkout repository\n uses: actions/checkout@v5\n - uses: actions/setup-python@v6\n with:\n python-version: '3.12'\n - name: Install Homebrew dependencies\n # uninstall cmake to avoid conflict between brew taps\n run: |\n brew uninstall cmake\n brew install $SPECTRE_BREW_DEPS\n # We install the remaining dependencies with Spack and cache them.\n # See the `unit_tests` job above for details on the cache configuration.\n - name: Restore dependency cache\n uses: actions/cache/restore@v5\n id: restore-dependencies\n env:\n CACHE_KEY_PREFIX: \"dependencies-${{ matrix.os }}\"\n with:\n path: ~/dependencies\n key: \"${{ env.CACHE_KEY_PREFIX }}-${{ github.run_id }}\"\n restore-keys: |\n ${{ env.CACHE_KEY_PREFIX }}-\n - name: Install Spack\n # Pin a specific version of Spack to avoid breaking CI builds when\n # Spack changes.\n run: |\n cd $HOME\n git clone -c feature.manyFiles=true \\\n https://github.com/spack/spack.git\n cd spack\n git checkout 7d1de58378fa210b7db887964fcc17187a504ad8\n - name: Configure Spack\n # - To avoid re-building packages that are already installed by Homebrew\n # we let Spack find them.\n # - Add the dependency cache as binary mirror.\n run: |\n source $HOME/spack/share/spack/setup-env.sh\n spack debug report\n spack compiler find && spack compiler list\n spack external find\n spack config get packages\n spack mirror add dependencies file://$HOME/dependencies/spack\n # Install the remaining dependencies from source with Spack. We install\n # them in an environment that we can activate later. After building the\n # dependencies from source we cache them as compressed tarballs.\n - name: Install Spack dependencies\n run: |\n source $HOME/spack/share/spack/setup-env.sh\n spack env create spectre\n spack env activate spectre\n spack add blaze@3.8.2 ~blas ~lapack smp=none\n # Support installing charm 7.0.0 with CMake 4.0\n export CMAKE_POLICY_VERSION_MINIMUM=3.5\n spack add charmpp@7.0.0 +shared backend=multicore build-target=charm++\n # Use main branch until spack has 2.0 release\n spack add libxsmm@main\n spack concretize --reuse\n spack install --no-check-signature\n spack find -v\n - name: Update dependency cache\n if: github.ref == 'refs/heads/develop'\n run: |\n source $HOME/spack/share/spack/setup-env.sh\n # Clear existing buildcache so we don't accumulate old versions of\n # packages in the cache\n rm -rf $HOME/dependencies\n spack buildcache create -uf dependencies $SPECTRE_SPACK_DEPS\n # Allow the buildcache creation to fail without failing the job, since\n # it sometimes runs out of memory\n continue-on-error: true\n - name: Save dependency cache\n if: github.ref == 'refs/heads/develop'\n uses: actions/cache/save@v5\n with:\n path: ~/dependencies\n key: ${{ steps.restore-dependencies.outputs.cache-primary-key }}\n # Install remaining pure Python dependencies with pip because the Spack\n # package index can be incomplete (it can't mirror all of pip)\n - name: Install Python dependencies\n run: |\n source $HOME/spack/share/spack/setup-env.sh\n spack env activate spectre\n pip install -r support/Python/requirements.txt\n # Replace the ccache directory that building the dependencies may have\n # generated with the cached ccache directory.\n - name: Clear ccache from dependencies\n run: |\n ccache --clear\n rm -rf $CCACHE_DIR\n mkdir -p $CCACHE_DIR\n - name: Restore ccache\n uses: actions/cache/restore@v5\n id: restore-ccache\n env:\n CACHE_KEY_PREFIX: \"ccache-${{ matrix.os }}\"\n with:\n path: ~/ccache\n key: \"${{ env.CACHE_KEY_PREFIX }}-${{ github.run_id }}\"\n restore-keys: |\n ${{ env.CACHE_KEY_PREFIX }}-\n - name: Configure ccache\n run: |\n ccache -pz\n - name: Clear ccache\n # Clear ccache if requested\n if: >\n github.event_name == 'workflow_dispatch'\n && github.event.inputs.clear_ccache == 'yes'\n run: |\n ccache -C\n # Configure, build and run tests. See the `unit_tests` job above for\n # details.\n # - We increase the timeout for tests because the GitHub-hosted macOS VMs\n # appear to be quite slow.\n - name: Configure build with cmake\n run: |\n source $HOME/spack/share/spack/setup-env.sh\n spack env activate spectre\n mkdir build && cd build\n cmake \\\n -D CMAKE_C_COMPILER=clang \\\n -D CMAKE_CXX_COMPILER=clang++ \\\n -D CMAKE_Fortran_COMPILER=gfortran-14 \\\n -D CMAKE_CXX_FLAGS=\"-Werror\" \\\n -D BUILD_SHARED_LIBS=ON \\\n -D BUILD_PYTHON_BINDINGS=ON \\\n -D MEMORY_ALLOCATOR=SYSTEM \\\n -D CHARM_ROOT=$(spack location --install-dir charmpp) \\\n -D BLAS_ROOT=$(brew --prefix openblas) \\\n -D LAPACK_ROOT=$(brew --prefix openblas) \\\n -D CMAKE_BUILD_TYPE=Debug \\\n -D SPECTRE_DEBUG_Og=ON \\\n -D DEBUG_SYMBOLS=OFF \\\n -D UNIT_TESTS_IN_TEST_EXECUTABLES=OFF \\\n -D STUB_EXECUTABLE_OBJECT_FILES=ON \\\n -D STUB_LIBRARY_OBJECT_FILES=ON \\\n -D USE_PCH=ON \\\n -D USE_CCACHE=ON \\\n -D SPECTRE_TEST_TIMEOUT_FACTOR=10 \\\n -D CMAKE_INSTALL_PREFIX=../install \\\n -D BUILD_DOCS=OFF \\\n -D CMAKE_OSX_SYSROOT=macosx \\\n $GITHUB_WORKSPACE\n - name: Build unit tests\n working-directory: build\n run: |\n make -j${NUM_CORES} unit-tests\n - name: Build executables\n working-directory: build\n run: |\n make test-executables\n - name: Clean up ccache\n if: github.ref == 'refs/heads/develop'\n run: |\n now=$(date +%s)\n job_duration=$((now - ${{ steps.start.outputs.time }}))\n ccache --evict-older-than \"${job_duration}s\"\n - name: Save ccache\n if: always() && github.ref == 'refs/heads/develop'\n uses: actions/cache/save@v5\n with:\n path: ~/ccache\n key: ${{ steps.restore-ccache.outputs.cache-primary-key }}\n - name: Print size of build directory\n working-directory: build\n run: |\n ls | xargs du -sh\n du -sh .\n - name: Diagnose ccache\n run: |\n ccache -s\n - name: Run unit tests\n working-directory: build\n run: |\n ctest -E TestingFramework.Abort -j${NUM_CORES} \\\n --repeat after-timeout:3 --output-on-failure\n - name: Install\n working-directory: build\n run: |\n make install\n - name: Print size of install directory\n working-directory: install\n run: |\n ls | xargs du -sh\n du -sh .\n rm -r ./*\n\n # Release a new version on manual events when requested and the tests pass.\n # Only enable this on the `sxs-collaboration/spectre` repository (not on\n # forks).\n release_version:\n name: Release version\n # Running in a protected environment that provides the necessary secrets\n environment: release\n runs-on: ubuntu-latest\n if: >\n github.repository == 'sxs-collaboration/spectre'\n && github.ref == 'refs/heads/develop'\n && github.event_name == 'workflow_dispatch'\n && github.event.inputs.release_version != ''\n needs:\n - check_files_and_formatting\n - doc_check\n - unit_tests\n env:\n TZ: ${{ github.event.inputs.timezone }}\n steps:\n - uses: actions/checkout@v5\n with:\n fetch-depth: 0\n # Using a personal access token with admin privileges here so this\n # action can push to protected branches. Note that this also means\n # that the pushes can trigger additional workflows (GitHub only\n # prevents pushes with the default GITHUB_TOKEN from triggering\n # additional workflows).\n #\n # Note: sxs-bot has the personal access token configured.\n #\n # GitHub has 2 forms of personal access tokens.\n # For Fine-Grained Access:\n # \"Only selected repositories\"\n # - Contents: Access: Read and write\n # - Deployments: Access: Read and write\n #\n # For Tokens (classic):\n # repo: (off)\n # public_repo: on\n # Everything else is off.\n token: ${{ secrets.GH_TOKEN_RELEASE }}\n - uses: actions/setup-python@v6\n with:\n python-version: '3.8'\n - name: Install Python dependencies\n run: |\n pip3 install -r .github/scripts/requirements-release.txt\n # We use the current date as tag name, unless a tag name was specified\n # as input to the `workflow_dispatch` event\n - name: Determine release version\n id: get_version\n run: |\n INPUT_RELEASE_VERSION=${{ github.event.inputs.release_version }}\n RELEASE_VERSION=${INPUT_RELEASE_VERSION:-$(date +'%Y.%m.%d')}\n echo \"Release version is: ${RELEASE_VERSION}\"\n echo \"RELEASE_VERSION=$RELEASE_VERSION\" >> $GITHUB_ENV\n - name: Validate release version\n run: |\n VERSION_PATTERN=\"^([0-9]{4})\\.([0-9]{2})\\.([0-9]{2})(\\.[0-9]+)?$\"\n if [[ $RELEASE_VERSION =~ $VERSION_PATTERN ]]; then\n if [ $(date +'%Y') != ${BASH_REMATCH[1]} ] ||\n [ $(date +'%m') != ${BASH_REMATCH[2]} ] ||\n [ $(date +'%d') != ${BASH_REMATCH[3]} ]; then\n TODAY=$(date +'%Y.%m.%d')\n echo \"'$RELEASE_VERSION' doesn't match current date '$TODAY'\"\n exit 1\n fi\n else\n echo \"'$RELEASE_VERSION' doesn't match '$VERSION_PATTERN'\"\n exit 1\n fi\n if [ $(git tag -l \"v$RELEASE_VERSION\") ]; then\n echo \"Tag 'v$RELEASE_VERSION' already exists\"\n exit 1\n fi\n if [ $(git rev-parse HEAD) == $(git rev-parse origin/release) ]; then\n echo \"Nothing changed since last release $(git describe release).\"\n exit 1\n fi\n - name: Reserve Zenodo DOI and prepare repository\n run: |\n python3 .github/scripts/Release.py prepare -vv \\\n --version $RELEASE_VERSION \\\n --zenodo-token ${{ secrets.ZENODO_READWRITE_TOKEN }} \\\n --github-token ${{ secrets.GITHUB_TOKEN }}\n git diff\n - name: Download release notes\n uses: actions/download-artifact@v8\n id: release-notes\n with:\n name: release-notes\n path: ~/release-notes\n # Push a commit tagged with the new version to `develop` and `release`.\n # The push will trigger the workflow again because we're using a personal\n # access token. The triggered workflow will build and deploy the\n # documentation so we don't need to do that here.\n - name: Commit and push\n run: |\n git config user.name sxs-bot\n git config user.email sxs-bot@black-holes.org\n git commit -a -m \"Prepare release $RELEASE_VERSION\"\n git show HEAD\n git status\n git tag -a v$RELEASE_VERSION -m \"Release $RELEASE_VERSION\" HEAD\n git push origin HEAD:develop\n git push origin HEAD:release\n git push origin v$RELEASE_VERSION\n - name: Create release on GitHub\n uses: softprops/action-gh-release@v2\n with:\n token: ${{ secrets.GH_TOKEN_RELEASE }}\n tag_name: v${{ env.RELEASE_VERSION }}\n name: Release ${{ env.RELEASE_VERSION }}\n body_path: >-\n ${{ steps.release-notes.outputs.download-path }}/release_notes.md\n # Publish the Zenodo record. Once published, the record can't be deleted\n # anymore and editing is limited.\n - name: Publish to Zenodo\n run: |\n python3 .github/scripts/Release.py publish -vv \\\n --zenodo-token ${{ secrets.ZENODO_PUBLISH_TOKEN }} \\\n --github-token ${{ secrets.GITHUB_TOKEN }} \\\n --auto-publish\n\n arch_datastructures_tests:\n name: Archs\n runs-on: ubuntu-latest\n strategy:\n fail-fast: false\n matrix:\n compiler:\n - gcc-10\n - gcc-11\n - clang-13\n - clang-14\n include:\n - sde_arch: (\"-nhm;nehalem\" \"-snb;sandybridge\" \"-hsw;haswell\"\n \"-skl;skylake\" \"-icx;icelake-server\")\n compiler: gcc-10\n - sde_arch: (\"-nhm;nehalem\" \"-snb;sandybridge\" \"-hsw;haswell\"\n \"-skl;skylake\" \"-icx;icelake-server\")\n compiler: gcc-11\n - sde_arch: (\"-nhm;nehalem\" \"-snb;sandybridge\" \"-hsw;haswell\"\n \"-skl;skylake\" \"-icx;icelake-server\")\n compiler: clang-13\n - sde_arch: (\"-nhm;nehalem\" \"-snb;sandybridge\" \"-hsw;haswell\"\n \"-skl;skylake\" \"-icx;icelake-server\" \"-tgl;tigerlake\")\n compiler: clang-14\n container:\n image: ${{ inputs.container || 'sxscollaboration/spectre:dev' }}\n env:\n # See the unit test job for the reasons for these configuration choices\n CXXFLAGS: \"-Werror\"\n steps:\n - name: Checkout repository\n uses: actions/checkout@v5\n # Work around https://github.com/actions/checkout/issues/760\n - name: Trust checkout\n run: |\n git config --global --add safe.directory $GITHUB_WORKSPACE\n - uses: ./.github/actions/parse-compiler\n with:\n compiler: ${{ matrix.compiler }}\n - name: Install compiler\n run: |\n apt-get update -y\n apt-get install --reinstall ca-certificates\n if [[ $COMPILER_ID = gcc ]]; then\n apt-get install -y $CC $CXX $FC\n else\n apt-get install -y $CC $FC\n fi\n - name: Install Intel SDE\n working-directory: /work\n run: |\n wget -O sde-external.tar.xz https://downloadmirror.intel.com/913594/sde-external-10.7.0-2026-02-18-lin.tar.xz\n tar -xJf sde-external.tar.xz\n mv sde-external-* sde\n rm sde-*\n - name: Configure, build, and run tests\n working-directory: /work\n # Notes on the build configuration:\n # - We don't need debug symbols during CI, so we turn them off to reduce\n # memory usage.\n run: >\n ARCH_PARAM_LIST=${{ matrix.sde_arch }}\n\n for ARCH_PARAM in ${ARCH_PARAM_LIST[@]}; do\n OVERRIDE_ARCH=`echo ${ARCH_PARAM} | cut -d\";\" -f2`\n SDE_FLAG=`echo ${ARCH_PARAM} | cut -d\";\" -f1`\n echo \"CMake arch flag: $OVERRIDE_ARCH\"\n echo \"Intel SDE arch flag: $SDE_FLAG\"\n cd /work\n BUILD_DIR=build$OVERRIDE_ARCH\n mkdir $BUILD_DIR && cd $BUILD_DIR\n\n cmake\\\n -D CMAKE_C_COMPILER=${CC}\\\n -D CMAKE_CXX_COMPILER=${CXX}\\\n -D CMAKE_Fortran_COMPILER=${FC}\\\n -D CMAKE_CXX_FLAGS=\"${CXXFLAGS}\"\\\n -D OVERRIDE_ARCH=${OVERRIDE_ARCH}\\\n -D CHARM_ROOT=${CHARM_ROOT}\\\n -D CMAKE_BUILD_TYPE=Debug\\\n -D SPECTRE_DEBUG_Og=ON\\\n -D DEBUG_SYMBOLS=OFF\\\n -D STRIP_SYMBOLS=ON\\\n -D STUB_EXECUTABLE_OBJECT_FILES=ON\\\n -D STUB_LIBRARY_OBJECT_FILES=ON\\\n -D USE_PCH=ON\\\n -D USE_CCACHE=ON\\\n -D BUILD_DOCS=OFF\\\n -D SPECTRE_AUTODIFF=ON\\\n -D SPECTRE_FETCH_MISSING_DEPS=ON\\\n $GITHUB_WORKSPACE\n\n make -j4 TestArchitectureVectorization\n\n /work/sde/sde ${SDE_FLAG}\\\n -- ./bin/TestArchitectureVectorization [Unit]\n done\n\n shell: bash\n" }, { "path": ".gitignore", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Build directories\n# Ignore build dirs named similarly to the example in the installation notes;\n# in general arbitrary names are possible and cannot all be ignored.\n/build*\n\n# Editor configurations\n.vscode\ncompile_commands.json\n.idea\nCMakeUserPresets.json\n\n# Spack\n/support/spack/\n.spack-env\n/support/DevEnvironments/spack.lock\n\n# Python environments\n# These are conventional locations where people may install Python packages\n# related to the project. They are mentioned in the Python docs:\n# https://docs.python.org/3/library/venv.html\n/.venv\n/env\n\n# Temporary files\n*~\n*.swp\n\\#*\\#\n.\\#*\n.DS_Store\n.dir-locals.el\n.cquery_cached_index\n.ycm_extra_conf.py\n.clangd\n.cache\n.projectile-cache.eld\n\n# TeX products\n*.aux\n*.log\n*.toc\n*.bbl\n*.bbg\n*.blg\n*.out\n*.bak\ndocs/auto\n\n# Python related files\n*.pyc\n.ipynb_checkpoints\n\n# charm++ runtime files\ncharmrun.*\n\n# Observer output\n*.xmf\n*.h5\n\n# Ignore deploy SSH keys and other TravisCI related files\n.travis/deploy_key\ncoverage.info\n\n# ClangFormat git hook file\n.clang_format_diff.patch\n\n# CTags, ETags and GNU Global Tags files\nGPATH\nGRTAGS\nGTAGS\nTAGS\ntags\n# Keep Tags/ directories on case-insensitive file systems\n!Tags/\n\n# AI/LLM Agent/CLI tools\nAGENTS.md\n\n.aider*\n\nCLAUDE.md\n.claude/settings.local.json\nCLAUDE.local.md\n" }, { "path": ".skills/scripts/FetchCiLog.py", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n\"\"\"Fetch a failed GitHub Actions job log and extract failure context.\n\nRetrieves the job summary and full log via the gh CLI, locates failure\nlines, and prints a context window around each failure for the LLM.\n\"\"\"\n\nimport argparse\nimport re\nimport subprocess\nimport sys\n\nFAILURE_PATTERNS = [\n re.compile(r\"FAILED:\"),\n re.compile(r\"\\berror:\"),\n re.compile(r\"The following tests FAILED\"),\n re.compile(r\"##\\[error\\]\"),\n re.compile(r\"Process completed with exit code\"),\n re.compile(r\"\\*\\*\\*Failed\"),\n]\n\n# Patterns where only context *after* the failure line is useful\n# (e.g. CTest's \"***Failed\" line is followed by the test output)\nAFTER_ONLY_PATTERNS = {r\"\\*\\*\\*Failed\"}\n\n# Timestamp prefix on every GH Actions log line\nTIMESTAMP_RE = re.compile(r\"^\\d{4}-\\d{2}-\\d{2}T\\d{2}:\\d{2}:\\d{2}\\.\\d+Z\\s?\")\n\n\ndef fetch_job_summary(job_id, owner, repo):\n \"\"\"Fetch the job summary via 'gh run view --job'.\"\"\"\n cmd = [\n \"gh\",\n \"run\",\n \"view\",\n \"--job\",\n str(job_id),\n \"-R\",\n f\"{owner}/{repo}\",\n ]\n result = subprocess.run(cmd, capture_output=True, text=True)\n if result.returncode != 0:\n print(\n f\"Warning: could not fetch job summary: {result.stderr.strip()}\",\n file=sys.stderr,\n )\n return None\n return result.stdout\n\n\ndef fetch_job_log(job_id, owner, repo):\n \"\"\"Fetch the full job log via the GitHub API.\"\"\"\n cmd = [\n \"gh\",\n \"api\",\n f\"repos/{owner}/{repo}/actions/jobs/{job_id}/logs\",\n ]\n result = subprocess.run(cmd, capture_output=True, text=True)\n if result.returncode != 0:\n print(f\"Error fetching log: {result.stderr.strip()}\", file=sys.stderr)\n sys.exit(1)\n return result.stdout\n\n\ndef strip_timestamps(lines):\n \"\"\"Remove GH Actions timestamp prefixes from each line.\"\"\"\n return [TIMESTAMP_RE.sub(\"\", line) for line in lines]\n\n\ndef find_failure_lines(lines):\n \"\"\"Return sorted list of (line_index, after_only) tuples.\n\n ``after_only`` is True when the matched pattern only needs context\n after the failure line (e.g. CTest's ``***Failed`` output).\n \"\"\"\n hits = {}\n for i, line in enumerate(lines):\n for pattern in FAILURE_PATTERNS:\n if pattern.search(line):\n after_only = pattern.pattern in AFTER_ONLY_PATTERNS\n hits[i] = after_only\n break\n return hits\n\n\ndef merge_windows(hits, context, total_lines):\n \"\"\"Merge overlapping [start, end] windows around each hit.\n\n ``hits`` is a dict {line_index: after_only}. For after-only hits\n the window starts at the hit line itself (no before-context).\n \"\"\"\n if not hits:\n return []\n windows = []\n for hit in sorted(hits):\n after_only = hits[hit]\n start = hit if after_only else max(0, hit - context)\n end = min(total_lines - 1, hit + context)\n if windows and start <= windows[-1][1] + 1:\n windows[-1] = (windows[-1][0], end, windows[-1][2] | {hit})\n else:\n windows.append((start, end, {hit}))\n return windows\n\n\ndef print_window(lines, start, end, failure_indices):\n \"\"\"Print a window of lines with line numbers, marking failures.\"\"\"\n for i in range(start, end + 1):\n marker = \">>>\" if i in failure_indices else \" \"\n print(f\"{marker} {i + 1:>6d} | {lines[i]}\")\n\n\ndef main():\n parser = argparse.ArgumentParser(\n description=(\n \"Fetch a failed GitHub Actions job log and extract failure context.\"\n )\n )\n parser.add_argument(\"job_id\", help=\"GitHub Actions job ID\")\n parser.add_argument(\n \"--owner\",\n default=\"sxs-collaboration\",\n help=\"Repository owner (default: sxs-collaboration)\",\n )\n parser.add_argument(\n \"--repo\",\n default=\"spectre\",\n help=\"Repository name (default: spectre)\",\n )\n parser.add_argument(\n \"--context\",\n type=int,\n default=50,\n help=\"Number of lines before and after each failure (default: 50)\",\n )\n args = parser.parse_args()\n\n # -- Job summary --\n summary = fetch_job_summary(args.job_id, args.owner, args.repo)\n if summary:\n print(\"=\" * 60)\n print(\"JOB SUMMARY\")\n print(\"=\" * 60)\n print(summary.rstrip())\n print()\n\n # -- Fetch and process log --\n raw_log = fetch_job_log(args.job_id, args.owner, args.repo)\n raw_lines = raw_log.splitlines()\n lines = strip_timestamps(raw_lines)\n\n hits = find_failure_lines(lines)\n if not hits:\n print(\"No failure patterns found in the log.\")\n print(f\"Total log lines: {len(lines)}\")\n sys.exit(1)\n\n windows = merge_windows(hits, args.context, len(lines))\n num_hits = len(hits)\n\n print(\"=\" * 60)\n print(f\"FAILURE LOG (job {args.job_id}, {args.owner}/{args.repo})\")\n print(\n f\" {num_hits} failure line(s) found, {len(windows)} context window(s)\"\n )\n print(f\" Total log lines: {len(lines)}\")\n print(\"=\" * 60)\n\n for idx, (start, end, failure_indices) in enumerate(windows):\n print()\n print(\n f\"--- Window {idx + 1}/{len(windows)} \"\n f\"(lines {start + 1}-{end + 1}) ---\"\n )\n print_window(lines, start, end, failure_indices)\n\n print()\n print(\"=\" * 60)\n print(\"END OF FAILURE CONTEXT\")\n print(\"=\" * 60)\n\n\nif __name__ == \"__main__\":\n main()\n" }, { "path": ".skills/scripts/FetchIssue.py", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n\"\"\"Fetch a GitHub issue and print it in a structured format for Claude.\n\nIf the issue is a random test failure (title contains 'random failure in'\nand the body/comments contain MAKE_GENERATOR seed lines), a compact\n[RANDOM_FAILURE] format is emitted instead of the full issue text.\n\"\"\"\n\nimport argparse\nimport json\nimport re\nimport subprocess\nimport sys\n\n\ndef is_random_failure(title, all_text):\n \"\"\"Return True if this looks like a MAKE_GENERATOR random failure issue.\"\"\"\n if \"random failure in\" not in title.lower():\n return False\n return bool(re.search(r\"Seed is:\\s*\\d+\\s+from\", all_text))\n\n\ndef extract_make_generator_seeds(all_text):\n \"\"\"Parse 'Seed is: N from path:line' entries, returning {path:line: [seeds]}.\n\n CI logs often wrap long paths at '/' boundaries, so we strip\n timestamps and collapse continuation lines before matching.\n \"\"\"\n # Strip CI log timestamps (e.g. \"2023-09-11T19:44:29.1292895Z \")\n text = re.sub(r\"\\d{4}-\\d{2}-\\d{2}T\\d{2}:\\d{2}:\\d{2}\\.\\d+Z\\s*\", \"\", all_text)\n # Collapse lines where a path wraps after a '/'\n text = re.sub(r\"/\\s*\\n\\s*\", \"/\", text)\n pattern = r\"Seed is:\\s*(\\d+)\\s+from\\s+(.*?\\.[hct]pp:\\d+)\"\n matches = re.findall(pattern, text)\n\n grouped = {}\n for seed, raw_path in matches:\n # Canonicalize: keep only the part after tests/Unit/\n m = re.search(r\"tests/Unit/(.*)\", raw_path)\n canonical = m.group(1) if m else raw_path\n grouped.setdefault(canonical, [])\n if seed not in grouped[canonical]:\n grouped[canonical].append(seed)\n return grouped\n\n\ndef extract_test_name(title):\n \"\"\"Extract the test name from a 'Random failure in TEST' title.\"\"\"\n m = re.search(r\"[Rr]andom\\s+[Ff]ailure\\s+in\\s+(\\S+)\", title)\n return m.group(1) if m else title\n\n\ndef main():\n parser = argparse.ArgumentParser(\n description=\"Fetch a GitHub issue via gh CLI\"\n )\n parser.add_argument(\"issue_number\", help=\"Issue number (e.g. 1727)\")\n parser.add_argument(\n \"--repo\",\n default=None,\n help=\"Repository in owner/repo form (default: current repo)\",\n )\n parser.add_argument(\n \"--full\",\n action=\"store_true\",\n help=\"Always print full issue text, bypassing random-failure detection\",\n )\n args = parser.parse_args()\n\n cmd = [\n \"gh\",\n \"issue\",\n \"view\",\n str(args.issue_number),\n \"--json\",\n (\n \"number,title,state,author,assignees,\"\n \"createdAt,labels,url,body,comments\"\n ),\n ]\n if args.repo:\n cmd.extend([\"--repo\", args.repo])\n\n result = subprocess.run(cmd, capture_output=True, text=True)\n if result.returncode != 0:\n print(f\"Error: {result.stderr.strip()}\", file=sys.stderr)\n sys.exit(1)\n\n data = json.loads(result.stdout)\n\n title = data.get(\"title\", \"\")\n body = data.get(\"body\", \"\") or \"\"\n comments = data.get(\"comments\", [])\n all_text = body + \"\\n\" + \"\\n\".join((c.get(\"body\") or \"\") for c in comments)\n\n # --- Random failure detection ---\n if not args.full and is_random_failure(title, all_text):\n seeds = extract_make_generator_seeds(all_text)\n test_name = extract_test_name(title)\n print(\"[RANDOM_FAILURE]\")\n print(f\"Issue #{data['number']}: {title}\")\n print(f\"URL: {data.get('url', '')}\")\n print(f\"Test: {test_name}\")\n print()\n print(\"Seeds by location (paths relative to tests/Unit/):\")\n for path_line, seed_list in seeds.items():\n print(f\" {path_line} -> {', '.join(seed_list)}\")\n sys.exit(0)\n\n # --- Normal issue output ---\n author = (data.get(\"author\") or {}).get(\"login\", \"ghost\")\n labels = \", \".join(lbl[\"name\"] for lbl in data.get(\"labels\", []))\n assignees = \", \".join(a[\"login\"] for a in data.get(\"assignees\", []))\n\n print(f\"Issue #{data['number']}: {data['title']}\")\n print(f\"URL: {data.get('url', '')}\")\n print(f\"State: {data['state']}\")\n print(f\"Author: {author}\")\n print(f\"Created: {data['createdAt']}\")\n if assignees:\n print(f\"Assigned: {assignees}\")\n if labels:\n print(f\"Labels: {labels}\")\n print()\n print((data.get(\"body\") or \"\").strip())\n\n for comment in comments:\n comment_author = (comment.get(\"author\") or {}).get(\"login\", \"ghost\")\n print()\n print(\"---\")\n print(f\"Comment by: {comment_author} at {comment['createdAt']}\")\n print((comment.get(\"body\") or \"\").strip())\n\n\nif __name__ == \"__main__\":\n main()\n" }, { "path": ".skills/scripts/FetchPrComments.py", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n\"\"\"Fetch PR review data and print it in a structured format for Claude.\"\"\"\n\nimport argparse\nimport json\nimport subprocess\nimport sys\n\n\ndef run_gh_command(cmd):\n \"\"\"Run a gh CLI command and return parsed JSON, or exit on error.\"\"\"\n result = subprocess.run(cmd, capture_output=True, text=True)\n if result.returncode != 0:\n print(f\"Error: {result.stderr.strip()}\", file=sys.stderr)\n sys.exit(1)\n return json.loads(result.stdout)\n\n\ndef fetch_pr_metadata(pr_number, repo=None):\n \"\"\"Fetch PR metadata, comments, reviews, and files via gh pr view.\"\"\"\n cmd = [\n \"gh\",\n \"pr\",\n \"view\",\n str(pr_number),\n \"--json\",\n (\n \"number,title,state,author,baseRefName,headRefName,\"\n \"body,comments,reviews,files,url,createdAt,reviewDecision\"\n ),\n ]\n if repo:\n cmd.extend([\"--repo\", repo])\n return run_gh_command(cmd)\n\n\ndef fetch_review_threads(pr_number, repo=None):\n \"\"\"Fetch review threads with resolution status via GraphQL API.\"\"\"\n if repo:\n owner, name = repo.split(\"/\", 1)\n else:\n detect_cmd = [\"gh\", \"repo\", \"view\", \"--json\", \"owner,name\"]\n repo_data = run_gh_command(detect_cmd)\n owner = repo_data[\"owner\"][\"login\"]\n name = repo_data[\"name\"]\n\n query = \"\"\"query {\n repository(owner:\"%s\", name:\"%s\") {\n pullRequest(number:%d) {\n reviewThreads(first:100) {\n totalCount\n pageInfo { hasNextPage }\n nodes {\n isResolved\n isOutdated\n path\n line\n originalLine\n startLine\n originalStartLine\n subjectType\n comments(first:50) {\n nodes {\n body\n author { login }\n path\n diffHunk\n line\n originalLine\n startLine\n originalStartLine\n createdAt\n }\n }\n }\n }\n }\n }\n }\"\"\" % (owner, name, int(pr_number))\n\n cmd = [\"gh\", \"api\", \"graphql\", \"-f\", f\"query={query}\"]\n data = run_gh_command(cmd)\n\n threads_data = (\n data.get(\"data\", {})\n .get(\"repository\", {})\n .get(\"pullRequest\", {})\n .get(\"reviewThreads\", {})\n )\n\n if threads_data.get(\"pageInfo\", {}).get(\"hasNextPage\"):\n print(\n (\n \"WARNING: PR has more than 100 review threads. \"\n \"Only the first 100 are shown.\"\n ),\n file=sys.stderr,\n )\n\n return threads_data.get(\"nodes\", [])\n\n\ndef print_pr_header(data):\n \"\"\"Print PR metadata header.\"\"\"\n author = (data.get(\"author\") or {}).get(\"login\", \"ghost\")\n print(f\"PR #{data['number']}: {data['title']}\")\n print(f\"URL: {data.get('url', '')}\")\n print(f\"State: {data['state']}\")\n print(f\"Author: {author}\")\n print(f\"Created: {data['createdAt']}\")\n print(f\"Base <- Head: {data['baseRefName']} <- {data['headRefName']}\")\n print(f\"Review decision: {data.get('reviewDecision', 'NONE')}\")\n\n\ndef print_changed_files(files):\n \"\"\"Print changed files list with addition/deletion counts.\"\"\"\n print()\n print(\"=\" * 60)\n print(\"CHANGED FILES\")\n print(\"=\" * 60)\n for f in files:\n print(f\" +{f['additions']:-4d} -{f['deletions']:-4d} {f['path']}\")\n total_add = sum(f[\"additions\"] for f in files)\n total_del = sum(f[\"deletions\"] for f in files)\n print(f\" {'':>10} ({len(files)} files, +{total_add} -{total_del} total)\")\n\n\ndef print_pr_body(body):\n \"\"\"Print PR description.\"\"\"\n body = (body or \"\").strip()\n if body:\n print()\n print(\"=\" * 60)\n print(\"PR DESCRIPTION\")\n print(\"=\" * 60)\n print(body)\n\n\ndef print_top_level_comments(comments):\n \"\"\"Print top-level PR conversation comments.\"\"\"\n if not comments:\n return\n print()\n print(\"=\" * 60)\n print(f\"TOP-LEVEL COMMENTS ({len(comments)})\")\n print(\"=\" * 60)\n for c in comments:\n author = (c.get(\"author\") or {}).get(\"login\", \"ghost\")\n print()\n print(f\"--- Comment by {author} at {c['createdAt']} ---\")\n print((c.get(\"body\") or \"\").strip())\n\n\ndef print_review_summaries(reviews):\n \"\"\"Print review summaries (APPROVED, CHANGES_REQUESTED, etc.).\"\"\"\n summaries = [r for r in reviews if (r.get(\"body\") or \"\").strip()]\n if not summaries:\n return\n print()\n print(\"=\" * 60)\n print(f\"REVIEW SUMMARIES ({len(summaries)})\")\n print(\"=\" * 60)\n for r in summaries:\n author = (r.get(\"author\") or {}).get(\"login\", \"ghost\")\n state = r.get(\"state\", \"COMMENTED\")\n print()\n print(f\"--- [{state}] Review by {author} at {r['submittedAt']} ---\")\n print((r.get(\"body\") or \"\").strip())\n\n\ndef print_review_threads(threads):\n \"\"\"Print inline review threads grouped by resolution status.\"\"\"\n if not threads:\n print()\n print(\"=\" * 60)\n print(\"INLINE REVIEW THREADS\")\n print(\"=\" * 60)\n print(\" (none)\")\n return\n\n unresolved = [t for t in threads if not t[\"isResolved\"]]\n resolved = [t for t in threads if t[\"isResolved\"]]\n\n print()\n print(\"=\" * 60)\n print(\n \"INLINE REVIEW THREADS \"\n f\"({len(unresolved)} unresolved, {len(resolved)} resolved)\"\n )\n print(\"=\" * 60)\n\n for label, group in [(\"UNRESOLVED\", unresolved), (\"RESOLVED\", resolved)]:\n if not group:\n continue\n print()\n print(f\"--- {label} THREADS ---\")\n for i, thread in enumerate(group, 1):\n status_tags = []\n if thread[\"isResolved\"]:\n status_tags.append(\"[RESOLVED]\")\n else:\n status_tags.append(\"[UNRESOLVED]\")\n if thread[\"isOutdated\"]:\n status_tags.append(\"[OUTDATED]\")\n\n path = thread.get(\"path\", \"unknown\")\n line = thread.get(\"line\") or thread.get(\"originalLine\")\n line_info = f\":{line}\" if line else \"\"\n\n print()\n print(f\" Thread {i}: {' '.join(status_tags)} {path}{line_info}\")\n\n comments = thread.get(\"comments\", {}).get(\"nodes\", [])\n for j, c in enumerate(comments):\n author = (c.get(\"author\") or {}).get(\"login\", \"ghost\")\n print(f\" [{author} at {c['createdAt']}]\")\n\n diff_hunk = c.get(\"diffHunk\", \"\")\n if diff_hunk and j == 0:\n for hunk_line in diff_hunk.split(\"\\n\"):\n print(f\" {hunk_line}\")\n\n body = (c.get(\"body\") or \"\").strip()\n if body:\n for body_line in body.split(\"\\n\"):\n print(f\" {body_line}\")\n\n\ndef main():\n parser = argparse.ArgumentParser(\n description=\"Fetch PR review data via gh CLI and GraphQL\"\n )\n parser.add_argument(\"pr_number\", help=\"Pull request number (e.g. 1234)\")\n parser.add_argument(\n \"--repo\",\n default=None,\n help=\"Repository in owner/repo form (default: current repo)\",\n )\n args = parser.parse_args()\n\n pr_data = fetch_pr_metadata(args.pr_number, args.repo)\n threads = fetch_review_threads(args.pr_number, args.repo)\n\n print_pr_header(pr_data)\n print_changed_files(pr_data.get(\"files\", []))\n print_pr_body(pr_data.get(\"body\"))\n print_top_level_comments(pr_data.get(\"comments\", []))\n print_review_summaries(pr_data.get(\"reviews\", []))\n print_review_threads(threads)\n\n\nif __name__ == \"__main__\":\n main()\n" }, { "path": ".skills/spectre-fix-ci/SKILL.md", "content": "Run the fetch script to retrieve and analyze the CI job log:\n\n```\npython3 \\\n \"$(git rev-parse --show-toplevel)/.skills/scripts/FetchCiLog.py\" \\\n [--owner OWNER] [--context LINES]\n```\n\n- Extract the job ID from the user's message (required).\n- Pass `--owner OWNER` if the user specifies an owner (default is\n `sxs-collaboration`).\n- `--context` defaults to 50 lines before and after each failure.\n\nAfter the script returns:\n\n1. **Summarize the failure**: which step failed, which test(s) failed,\n and what the error was.\n2. **Identify source locations**: find file paths and line numbers in the\n error output that point to the failing code.\n3. **Suggest next steps**: propose a fix or further investigation.\n\nIf the context window seems too narrow to understand the failure, re-run\nwith `--context 150` for more surrounding lines.\n" }, { "path": ".skills/spectre-fix-issue/RANDOM_FAILURE.md", "content": "# Fixing a Random Test Failure\n\nYou have a random test failure issue. The script output above contains\nthe test name and a list of `file:line` locations with their failing seeds.\n\nRandom failures are almost always caused by a **numerical bug in the source\ncode**, not by overly tight test tolerances. Your job is to find and fix\nthe source-level bug. Increasing a test tolerance is a last resort, gated\nbehind mandatory investigation.\n\n## 1. Background\n\n`MAKE_GENERATOR(gen)` (defined in `tests/Unit/Framework/TestHelpers.hpp`)\ncreates a `std::mt19937` with a random seed. `MAKE_GENERATOR(gen, SEED)`\nuses the provided constant instead, making the test deterministic. On\nfailure, prints `Seed is: N from file:line` so the failure can be replayed.\n\n### Seeding a test file\n\nWhen the `file:line` points to a test file (not `CheckWithRandomValues.hpp`):\nopen the file at the indicated line (line numbers may have shifted -- search\nnearby for `MAKE_GENERATOR`) and change `MAKE_GENERATOR(gen);` to\n`MAKE_GENERATOR(gen, SEED);` using the first seed listed for that location.\n\n### Seeding CheckWithRandomValues\n\nWhen the `file:line` points to `Framework/CheckWithRandomValues.hpp`:\n`check_with_random_values()` accepts `epsilon` and `seed` parameters. Find\nthe calling test's `check_with_random_values` invocation and pass the failing\nseed as the last argument. For example, if the original call is:\n```cpp\npypp::check_with_random_values<1>(\n &Foo::bar, klass, \"Module\", \"function\",\n {{{-10.0, 10.0}}}, member_vars, used_for_size);\n```\nadd `epsilon` (default is `1.0e-12`) and the seed:\n```cpp\npypp::check_with_random_values<1>(\n &Foo::bar, klass, \"Module\", \"function\",\n {{{-10.0, 10.0}}}, member_vars, used_for_size,\n 1.0e-12, FAILING_SEED);\n```\n\n## 2. Reproduce the Failure\n\nFor each `file:line` + seed entry from the script output:\n\n1. **Set the seed** per Section 1 above.\n2. **Find the build target**:\n ```\n cd build && ctest --show-only=json-v1 -R \"TEST_NAME\"\n ```\n Parse the JSON output for the binary path (first element of `\"command\"`).\n3. **Build**: `ninja -C build `\n4. **Run**: `build/bin/ \"TEST_NAME\"`\n5. **If the test does NOT fail**: STOP and report to the user that the failure\n cannot be reproduced (code may have changed since the issue was filed).\n\n## 3. Investigate the Root Cause (REQUIRED)\n\nThis is the most important section. You MUST complete this investigation\nbefore considering any tolerance change.\n\n### 3a. Trace the call chain\n\n1. Read the error output to identify the **exact failing comparison** -- which\n values were compared, what the expected vs. actual values were, and what the\n discrepancy is.\n2. Identify which **function under test** produces the incorrect value.\n3. **Read the source code** of that function. Trace through its arithmetic step\n by step. Identify the specific operation (e.g., \"the subtraction on line 438\n of Wedge.cpp\") that amplifies floating-point error.\n4. If the function calls other functions, trace into those as well. Follow the\n data flow until you reach the arithmetic that is numerically unstable.\n\nYou MUST identify a specific line and operation in the source code. \"The\ncomputation accumulates floating-point error\" is not sufficient -- you need to\nsay *where* and *why*.\n\n### 3b. Numerical patterns checklist\n\nSearch the source code in the call chain for these common floating-point\npitfalls. For each pattern found, attempt the listed fix:\n\n- **Catastrophic cancellation**: subtraction of nearly-equal values\n (`a - b` where `a ~ b`). Fix: rearrange the algebra to avoid the subtraction,\n use compensated forms, or factor out common terms.\n\n- **Division by near-zero**: a denominator that approaches zero for certain\n inputs (e.g., near coordinate boundaries, poles, or special points). Fix:\n reformulate to multiply instead of divide, combine fractions to cancel the\n small denominator, or restructure the expression analytically.\n\n- **`atan` instead of `atan2`**: `atan(y/x)` loses quadrant information and\n divides by near-zero when `x ~ 0`. Fix: replace with `atan2(y, x)`.\n\n- **Missing precision-preserving library functions**: `log(1+x)` loses\n precision when `x ~ 0`; `exp(x)-1` loses precision when `x ~ 0`;\n `sqrt(x*x + y*y)` can overflow for large values. Fix: use `log1p(x)`,\n `expm1(x)`, and `hypot(x, y)`.\n\n- **Naive summation of many terms**: summing a long list of floating-point\n numbers accumulates round-off. Fix: use Kahan (compensated) summation, or\n sort terms by magnitude before summing.\n\n- **Unstable polynomial evaluation**: monomial form\n (`a*x^3 + b*x^2 + c*x + d`) accumulates error for large `x`. Fix: use\n Horner's method (`((a*x + b)*x + c)*x + d`).\n\n- **Numerically unstable quadratic formula**: the standard formula\n `(-b +/- sqrt(b^2 - 4ac)) / 2a` loses precision when `b^2 >> 4ac` due to\n catastrophic cancellation in the numerator. Fix: use the numerically stable\n form (compute one root via the standard formula, the other via\n `c / (a * first_root)`).\n\n- **Accumulation of terms with widely varying magnitudes**: adding a tiny\n correction to a large value drops the correction entirely. Fix: reorder\n operations so values of similar magnitude are combined first, or use\n compensated summation.\n\n### 3c. Attempt a source-level fix\n\nBased on the pattern(s) you identified in 3a and 3b:\n\n1. **Implement a fix in the source code** (not the test). For example:\n rearrange an expression to avoid cancellation, replace a division with a\n multiplication, switch `atan` to `atan2`, etc.\n2. **Build and run with the failing seed** to verify the fix resolves the\n failure.\n3. If the fix works, skip Section 4 entirely and go to Section 5 (Verify).\n4. If the fix does not fully resolve the issue, document what you tried and\n why it was insufficient, then continue investigating. Only proceed to\n Section 4 after exhausting source-level options.\n\n## 4. LAST RESORT -- Tolerance Adjustment\n\n**MANDATORY GATE -- you may NOT adjust any tolerance until ALL of the\nfollowing are true:**\n\n1. You have identified the full call chain from the test to the failing\n arithmetic operation.\n2. You have named the specific source-code operation (file, line, expression)\n that produces the numerical error.\n3. You have attempted at least one source-level fix and can explain why it\n did not work.\n4. You have confirmed the error is inherent to the algorithm in double\n precision and cannot be eliminated by rearranging the arithmetic.\n\n**If you cannot satisfy all four conditions, go back to Section 3.**\n\n### Adjusting tolerance in a test file\n\n- `Approx custom_approx = Approx::custom().epsilon(TOL).scale(1.0);`\n- For scalars: `CHECK(expected == custom_approx(computed));`\n- For iterables:\n `CHECK_ITERABLE_CUSTOM_APPROX(expected, computed, custom_approx);`\n- Start with `1.0e-14` and multiply by 10 until the test passes. Keep the\n tolerance as small as possible.\n\n### Adjusting tolerance in CheckWithRandomValues\n\nAdjust the `epsilon` parameter in the `check_with_random_values` call.\nStart at `1.0e-12` and multiply by 10. Keep as small as possible.\n\n### Required documentation\n\nAdd a C++ comment next to the tolerance change explaining:\n- What source-level operation causes the error\n- Why a source-level fix is not feasible\n- What magnitude of error is expected\n\n## 5. Verify\n\n1. **Remove the explicit seed** so the generator returns to\n `MAKE_GENERATOR(gen);` (or remove the seed argument from\n `check_with_random_values`).\n2. **Run**: `ctest --repeat-until-fail 1000 -R \"TEST_NAME\"` in the build\n directory.\n3. If any iterations fail, return to Section 3 and investigate the new failure.\n Repeat until all 1000 iterations pass.\n\n## 6. Report Summary\n\nAfter all `file:line` entries are resolved, report:\n- Every file and line changed\n- For **source-level fixes**: what the numerical issue was and how it was fixed\n- For **tolerance adjustments**: the root cause, why a source fix wasn't\n feasible, and the new tolerance value\n\n## Important Notes\n\n- The build directory is `build/` under the repository root.\n- Do NOT modify global `approx` in `tests/Unit/Framework/TestingFramework.hpp`.\n- Always remove explicit seeds before committing -- the seed is only for\n reproducing the failure, not for the final code.\n- If multiple distinct test files have seeds, investigate each independently.\n" }, { "path": ".skills/spectre-fix-issue/SKILL.md", "content": "Run the fetch script to retrieve the issue title, body, and comments:\n\n```\npython3 \\\n \"$(git rev-parse --show-toplevel)/.skills/scripts/FetchIssue.py\" \\\n [--repo owner/repo] [--full]\n```\n\n- Extract the issue number from the user's message.\n- Pass `--repo owner/repo` if the user specifies a repo or says \"upstream\"\n (for SpECTRE, upstream is `sxs-collaboration/spectre`).\n- Pass `--full` if the user explicitly asks for the full/unshortened issue\n text (e.g. \"show me the full issue\", \"don't shorten it\", \"skip random\n failure handling\"). Do NOT pass `--full` by default.\n\n**If the output starts with `[RANDOM_FAILURE]`**: Read and follow the\ninstructions in\n`$(git rev-parse --show-toplevel)/.skills/spectre-fix-issue/RANDOM_FAILURE.md`\nusing the seed data from the script output. Mention to the user that they can\nask for the full issue text if they need it.\n\n**Otherwise**: Summarize the issue, then proceed with the user's request.\n" }, { "path": ".skills/spectre-fix-pr/SKILL.md", "content": "Run the fetch script to retrieve PR metadata, review comments, and changed\nfiles:\n\n```\npython3 \\\n \"$(git rev-parse --show-toplevel)/.skills/scripts/FetchPrComments.py\" \\\n [--repo owner/repo]\n```\n\n- Extract the PR number from the user's message.\n- Pass `--repo owner/repo` if the user specifies a repo or says \"upstream\"\n (for SpECTRE, upstream is `sxs-collaboration/spectre`).\n\nAfter fetching the PR data:\n\n1. **Summarize the review** before starting work: list the total number of\n threads, how many are unresolved, and the files affected.\n2. **Prioritize UNRESOLVED threads** -- these are the comments that still need\n to be addressed. Start with unresolved, non-outdated threads first.\n3. **Group by file** -- work through comments file-by-file rather than jumping\n around, since multiple threads often apply to the same file.\n4. **Use the diff hunk context** -- each inline comment includes the surrounding\n diff hunk so you can understand exactly what code the reviewer is referring\n to.\n5. **Check OUTDATED threads** -- these refer to code that has since changed.\n Verify whether the concern still applies before making changes.\n6. **Skip resolved threads** unless the user specifically asks about them.\n" }, { "path": ".skills/spectre-review/SKILL.md", "content": "# SpECTRE Code Review\n\n**Arguments**: $ARGUMENTS\n**Current branch**: !`git branch --show-current`\n\nPerform a thorough code review of SpECTRE changes. Follow every step below\nprecisely. The full SpECTRE code rules reference (provide to review agents):\n!`tail -n +5 .claude/rules/Cxx.md`\n\n## Step 1: Parse Arguments & Acquire Diff\n\nParse `$ARGUMENTS`:\n- **Number present** (e.g. `1234`): PR mode. Fetch with:\n `gh pr diff --repo sxs-collaboration/spectre` and\n `gh pr view --repo sxs-collaboration/spectre --json\n title,body,headRefName,baseRefName`\n- **No number**: Local mode. Use `git diff develop...HEAD` for committed\n changes, plus `git diff` and `git diff --cached` for uncommitted changes. If\n no diff, fall back to `git diff HEAD~1`.\n- **\"clang-tidy\" present**: Enable the clang-tidy step.\n- **\"coverage\" present**: Enable the targeted code coverage step.\n\nSave the diff. Extract the list of changed files categorized by type (C++\n`.cpp/.hpp/.tpp`, Python `.py`, CMake `CMakeLists.txt`, other).\n\nCreate a task list tracking all review steps.\n\n## Step 2: Formatting Checks (run in parallel)\n\n### C++ (clang-format)\nFor each changed C++ file:\n1. Parse diff hunk headers (`@@ +START,COUNT @@`) to get changed line ranges\n2. Expand each range by +/-4 lines (clamped to file bounds)\n3. Run: `clang-format -style=file --lines=START:END [--lines=...] FILEPATH`\n4. Diff against original. Collect any formatting differences.\n\n### Python (black + isort)\nFor each changed `.py` file (excluding `external/`):\n```\nblack --check --diff FILEPATH\nisort --check-only --diff FILEPATH\n```\n\n## Step 3: CI Pre-Checks on Changed Files (run in parallel)\n\nCheck each changed file for issues that SpECTRE CI (`tools/FileTestDefs.sh`,\n`tools/CheckFiles.sh`) will flag. Only check lines/patterns introduced in the\ndiff, not pre-existing issues.\n\n**All files**: lines >80 chars (excluding URLs, NOLINT, #include, \\snippet,\n\\image, \\link, import); missing MIT license header; no final newline; tabs;\ntrailing whitespace; carriage returns\n\n**C++ files (.cpp/.hpp/.tpp)**:\n- Missing `#pragma once` in headers\n- `#include ` -> use `Parallel/Printf/Printf.hpp`\n- `#include ` -> use ``\n- `std::enable_if` -> use `requires`\n- `namespace _details` -> use `_detail`\n- `struct TD;` / `class TD;` (debug artifacts)\n- `.ckLocal()` -> `Parallel::local()`\n- `.ckLocalBranch()` -> `Parallel::local_branch()`\n- `return Py_None;` -> `Py_RETURN_NONE`\n- Text after `/*!` on same line\n- `Ls` abbreviation -> use `List`\n- Doxygen (`///` or `/*!`) in `.cpp` files (only use `//` comments in cpp)\n- Top-level `const` on value parameters in function declarations (`.hpp`) ->\n remove `const` from the declaration (keep in definition)\n- TODO/FIXME comments (not allowed)\n\n**Test files**:\n- `TEST_CASE` instead of `SPECTRE_TEST_CASE`\n- `Approx(` instead of `approx`\n\n**CMake**: New C++ files in a directory must be listed in that directory's\nCMakeLists.txt; removed files must be removed; entries should be alphabetical.\n\n**LLM Comments**: Identify comments that seem like notes from a coding agent\nduring its thinking process.\n\n### Include Order (C++ files in diff)\nVerify:\n1. (Tests) `\"Framework/TestingFramework.hpp\"` first, then blank line\n2. (`.cpp` with `.hpp`) Corresponding `.hpp`, then blank line\n3. STL/external `` alphabetical\n4. Blank line\n5. SpECTRE `\"headers\"` alphabetical\n\n### Commit Messages (local mode only)\nCheck no commit starts with (case-insensitive): fixup, wip, fixme, deleteme,\nrebaseme, testing, rebase.\n\n## Step 4: Code Review (2 Parallel Agents)\n\nLaunch 2 parallel agents. Provide each with the full diff and the\nSpECTRE code rules reference shown above.\n\n### Agent A: Style, Patterns & Idioms\nInstructions for the agent:\n- Check the diff against every rule in **Banned Patterns** and **Style Rules**\n- Check for **Prefer-Library Patterns** (manual tensor loops that should use\n EagerMath)\n- When you spot a suspicious pattern NOT in the checklist (e.g., a manual matrix\n operation, a loop that looks like it reimplements an existing utility), use\n `grep -r` in `src/DataStructures/Tensor/EagerMath/`, `src/DataStructures/`,\n `src/NumericalAlgorithms/`, or `src/Utilities/` to find an existing utility\n- Only flag issues in lines that the diff introduces (not pre-existing code)\n- For each finding: `file:line`, severity (`critical`/`important`/`suggestion`),\n explanation\n\n### Agent B: Bugs, Logic, Tests & Documentation\nInstructions for the agent:\n- Read each changed file in full (not just the diff) to understand surrounding\n context\n- Look for: logic errors, off-by-one, uninitialized variables, NaN handling,\n race conditions, incorrect template instantiations, virtual inheritance issues\n (most-derived must init virtual bases)\n- Check that new/changed public API in `.hpp` files has Doxygen documentation\n- Check that new source files have corresponding tests (`src/Foo/Bar.hpp` ->\n `tests/Unit/Foo/Test_Bar.cpp`)\n- Check that new `.cpp`/`.hpp` files are listed in their `CMakeLists.txt`\n- Only flag issues introduced by the diff\n- For each finding: `file:line`, severity, explanation\n- Check for potentially problematic floating point math like:\n - Catastrophic cancellation: subtraction of nearly-equal values\n (`a - b` where `a ~ b`).\n - Division by near-zero: a denominator that approaches zero for certain\n inputs (e.g., near coordinate boundaries, poles, or special points).\n - Naive summation of many terms: summing a long list of floating-point\n numbers accumulates round-off.\n - Unstable polynomial evaluation: monomial form\n (`a*x^3 + b*x^2 + c*x + d`), instead use Horner's method,\n `evaluate_polynomial()` from `src/Utilities/Math.hpp`\n - Numerically unstable quadratic formula: the standard formula\n `(-b +/- sqrt(b^2 - 4ac)) / 2a` loses precision.\n - Accumulation of terms with widely varying magnitudes: adding a tiny\n correction to a large value drops the correction entirely.\n - Make sure the code always uses `atan2` instead of `atan`, `log1p(x)` instead\n of `log(1+x)`, `expm1(x)` instead of `exp(x)-1`, `hypot(x,y)` instead of\n `sqrt(x*x+y*y)`.\n\n## Step 5: clang-tidy (if requested, run in parallel)\n\nIf \"clang-tidy\" was in arguments:\n1. Check for `build/compile_commands.json`. If missing, report that clang-tidy\n requires a configured build directory and skip.\n2. For each changed `.cpp` file: `clang-tidy -p build/ FILEPATH 2>&1`\n3. Filter output to only warnings on lines in the diff.\n\n## Step 6: Code Coverage (if requested, run in parallel)\n\nIf \"coverage\" was in arguments:\nRead `references/coverage-steps.md` and follow those instructions exactly.\n\n## Step 7: Self-Review Prune\n\nCombine all findings from steps 2-6. Review each finding and REMOVE only clear\nnon-issues:\n- False positives (pattern match that isn't the actual flagged issue)\n- Pre-existing issues not introduced by this diff\n- Issues suppressed by `// NOLINT(...)` comments\n- Exact duplicates between agents or between agents and formatting/CI checks\n\nAssign each remaining finding a confidence score (0-100). Remove findings\nbelow 50. Keep all findings scoring 50 or above -- err on the side of including\nborderline issues rather than missing real ones.\n\n## Step 8: Lightweight Model Critique\n\nSpawn an agent using the cheapest available model (Claude Code: `haiku`;\nCodex: `gpt-5.4-mini`). Provide it with:\n- The SpECTRE code rules reference (from Step 1)\n- The list of pruned findings (with scores)\n- A summary of what the diff does\n\nAsk the critique agent to:\n1. Score each finding 0-100 for \"is this a real, actionable issue?\"\n2. Flag any remaining false positives with reasoning\n3. Note if important issues seem to be missing\n4. Return scores and feedback\n\nAfter receiving the critique agent's feedback:\n- Remove findings scored < 40\n- Downgrade severity (e.g., important -> suggestion) for findings scored\n 40-60\n- Consider adding issues the critique agent suggested (verify them first)\n\n## Step 9: Final Report\n\nRead `references/report-template.md` and present the report in that format.\n" }, { "path": ".skills/spectre-review/references/coverage-steps.md", "content": "# Code Coverage Steps\n\nThese instructions are followed by the orchestrator when \"coverage\" was in\nthe review arguments. Execute all sub-steps below exactly as written.\n\n### 6a. Check out PR branch (PR mode only)\n\nCoverage must be measured against the actual PR code, not the current working\ntree. Before building or running any tests:\n\n1. Record the current branch and stash any uncommitted changes so they can be\n restored afterwards:\n ```bash\n ORIGINAL_BRANCH=$(git branch --show-current)\n STASH_RESULT=$(git stash push --include-untracked -m \"coverage-stash\" 2>&1)\n STASHED=$([[ \"$STASH_RESULT\" == *\"Saved\"* ]] && echo yes || echo no)\n ```\n2. Attempt to check out the PR branch using the GitHub CLI:\n ```bash\n gh pr checkout --repo sxs-collaboration/spectre 2>&1\n ```\n If that fails (e.g. SSH key / remote mismatch), fall back to:\n ```bash\n git fetch upstream pull//head:pr- 2>&1\n git checkout pr- 2>&1\n ```\n3. **Handle checkout conflicts explicitly.** If checkout fails with any error\n (e.g. \"Your local changes to the following files would be overwritten\",\n \"untracked working tree files would be overwritten by checkout\", or \"Please\n commit your changes or stash them\"), do NOT attempt to force-checkout.\n Instead, abort coverage and report clearly:\n > \"Coverage analysis skipped: checking out PR branch '' failed\n > because the following local files conflict with the PR:\n > \n > Please resolve the conflict manually (commit, stash, or delete those files)\n > and re-run the review with 'coverage'.\"\n Then restore the original branch and pop the stash (step 5) and skip all\n remaining coverage steps.\n4. Verify the checkout succeeded by comparing HEAD to the expected PR commit:\n ```bash\n git log --oneline -1\n gh pr view --repo sxs-collaboration/spectre \\\n --json headRefOid -q .headRefOid\n ```\n The two commit hashes should match (or the local log should show the PR\n branch name). If they differ, report: \"Coverage skipped: checkout succeeded\n but HEAD does not match PR head — local branch may be stale.\"\n5. **Restore step (must run after all coverage steps, or on any failure after\n this point):** at the end of Step 6f, restore the original working state:\n ```bash\n git checkout \"$ORIGINAL_BRANCH\"\n [[ \"$STASHED\" == \"yes\" ]] && git stash pop\n ```\n\n### 6b. Prerequisites & Build Verification\n\n1. Check `build/compile_commands.json` exists. If missing, skip with: \"Coverage\n requires a configured build directory.\"\n2. Check `build/CMakeCache.txt` for `COVERAGE:BOOL=ON`. If not found, skip with:\n \"Build not compiled with -DCOVERAGE=ON. Rebuild with\n `cmake -DCOVERAGE=ON ..` to enable coverage.\"\n3. Check `lcov` is available.\n4. **Verify the gcov wrapper is functional.** For Clang builds,\n `build/llvm-gcov.sh` may contain `LLVM_COV_BIN-NOTFOUND` if `llvm-cov` was\n not found at CMake configure time. Check:\n ```bash\n grep \"NOTFOUND\" build/llvm-gcov.sh\n ```\n If found, locate the correct binary and fix the wrapper in-place:\n ```bash\n LLVM_VER=$(clang++ --version | grep -oP '\\d+' | head -1)\n LLVM_COV=$(which llvm-cov-${LLVM_VER} 2>/dev/null || which llvm-cov)\n printf '#!/bin/bash\\nexec %s gcov \"$@\"\\n' \"$LLVM_COV\" > build/llvm-gcov.sh\n chmod +x build/llvm-gcov.sh\n ```\n5. Determine the gcov tool and **always use its absolute path** to avoid lcov\n failing with \"No such file or directory\" when it resolves relative paths\n from a different working directory:\n - Clang: `GCOV=$(realpath build/llvm-gcov.sh)`\n - GNU: `GCOV=$(which gcov)`\n6. **Verify objects are instrumented.** Pick one `.o` file for a changed source\n and check it has coverage symbols:\n ```bash\n nm 2>/dev/null | grep -c \"__llvm_gcov_ctr\\|__gcov_\"\n ```\n If the count is 0, objects were compiled before coverage was enabled —\n rebuild the relevant test targets:\n ```bash\n cmake --build build --target -- -j$(nproc)\n ```\n Re-check instrumentation after the rebuild. If still 0, skip coverage with:\n \"Objects lack coverage instrumentation even after rebuild. Check that the\n build was configured with -DCOVERAGE=ON before compiling.\"\n\n### 6c. Map changed files to test targets\nFor each changed C++ file under `src/`:\n1. Find the corresponding test directory: `src/A/B/C.hpp` -> `tests/Unit/A/B/`\n2. Walk up directories reading `CMakeLists.txt` files for `set(LIBRARY\n \"Test_...\")` to find the test binary name. Test naming is NOT a simple\n transform (e.g., `Test_DomainCreators`, `Test_EllipticDG`, `Test_DgSubcell`),\n so CMakeLists.txt parsing is required.\n3. Verify each binary exists in `build/bin/`. If not, build it: `cmake --build\n build --target -- -j$(nproc)`\n4. If >5 unique test targets, ask the user before proceeding.\n\n### 6d. Run tests and capture coverage\nFor each test target (using `$GCOV` absolute path from Step 6b):\n```bash\nlcov --gcov-tool $GCOV --directory build/ --zerocounters\nbuild/bin/\nlcov --gcov-tool $GCOV --capture --rc lcov_branch_coverage=0 \\\n --directory build/ --output-file /tmp/coverage_.info\n```\nAfter the lcov capture, verify `.gcda` files were actually produced:\n```bash\nfind build/ -name \"*.gcda\" | grep -q .\n```\nIf no `.gcda` files are found, report:\n> \"No coverage data files (.gcda) generated. Possible causes: (1) objects were\n> not compiled with --coverage (rebuild required after confirming\n> -DCOVERAGE=ON), (2) test binary exited before writing data, (3) build\n> directory path mismatch between compile and run.\"\nThen skip remaining coverage steps (but still run Step 6f to restore the\nbranch).\n\n### 6e. Filter to changed lines only\n1. Merge .info files: `lcov --add-tracefile ... --output-file\n /tmp/coverage_merged.info`\n2. Extract only changed source files: `lcov --extract /tmp/coverage_merged.info\n '' ... -o /tmp/coverage_filtered.info`\n3. Parse `DA:,` entries from the filtered .info file\n4. Cross-reference with diff hunk headers: only report lines that are both NEW\n in the diff AND have execution_count == 0. **Use new-file line numbers from\n the diff** — after checking out the PR branch these match the files on disk\n exactly. Do not use base-branch line numbers, which are offset from the PR.\n5. Group uncovered lines into contiguous ranges\n\n### 6f. Cleanup\nRemove temporary .info files to avoid polluting subsequent builds:\n```bash\nrm -f /tmp/coverage_*.info /tmp/coverage_merged.info /tmp/coverage_filtered.info\n```\nThen restore the original branch and unstash local changes (PR mode only):\n```bash\ngit checkout \"$ORIGINAL_BRANCH\"\n[[ \"$STASHED\" == \"yes\" ]] && git stash pop\n```\n" }, { "path": ".skills/spectre-review/references/report-template.md", "content": "# Final Report Template\n\nPresent a clean report in the format below. Be brief and specific. No emojis.\nLink to files and lines.\n\n```\n### SpECTRE Code Review\n\n**Reviewing**: [PR #N: title | local changes on branch `name`]\n**Files changed**: N (X C++, Y Python, Z CMake)\n\n#### Formatting\n[clang-format / black / isort changes, or \"No formatting issues.\"]\n\n#### Critical Issues\nN. **Description** `file:line`\n Explanation and suggested fix.\n\n#### Important Issues\nN. **Description** `file:line`\n Explanation.\n\n#### Suggestions\nN. **Description** `file:line`\n Explanation.\n\n#### CI Pre-Check Warnings\n[Issues that CI will flag, or \"None.\"]\n\n[If clang-tidy ran:]\n#### clang-tidy\n[Findings or \"No issues.\"]\n\n[If coverage ran:]\n#### Code Coverage (changed lines)\n[Uncovered changed lines per file, or \"All changed lines are covered by tests.\"]\n[Files with no test target: \"Coverage not checked: file1.cpp, file2.hpp (no test\ntarget found)\"]\n```\n\nIf no issues at all: \"No issues found. Checked style, patterns, bugs,\nformatting, and CI compliance.\"\n" }, { "path": "CITATION.cff", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# This file is automatically generated. It will be overwritten at every\n# release. See .github/scripts/Release.py for details.\n\nauthors:\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Deppe\n given-names: Nils\n orcid: https://orcid.org/0000-0003-4557-4115\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Throwe\n given-names: William\n orcid: https://orcid.org/0000-0001-5059-4378\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Kidder\n given-names: Lawrence E.\n orcid: https://orcid.org/0000-0001-5392-7342\n- affiliation: Max Planck Institute for Gravitational Physics (Albert Einstein Institute),\n Am Mühlenberg 1, Potsdam 14476, Germany\n family-names: Vu\n given-names: Nils L.\n orcid: https://orcid.org/0000-0002-5767-3949\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Nelli\n given-names: Kyle C.\n orcid: https://orcid.org/0000-0003-2426-8768\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Armaza\n given-names: Cristóbal\n orcid: https://orcid.org/0000-0002-1791-0743\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Bonilla\n given-names: Marceline S.\n orcid: https://orcid.org/0000-0003-4502-528X\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Hébert\n given-names: François\n orcid: https://orcid.org/0000-0001-9009-6955\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Kim\n given-names: Yoonsoo\n orcid: https://orcid.org/0000-0002-4305-6026\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Kumar\n given-names: Prayush\n orcid: https://orcid.org/0000-0001-5523-4603\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Lovelace\n given-names: Geoffrey\n orcid: https://orcid.org/0000-0002-7084-1070\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Macedo\n given-names: Alexandra\n orcid: https://orcid.org/0009-0001-7671-6377\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Moxon\n given-names: Jordan\n orcid: https://orcid.org/0000-0001-9891-8677\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: O'Shea\n given-names: Eamonn\n- affiliation: Max Planck Institute for Gravitational Physics (Albert Einstein Institute),\n Am Mühlenberg 1, Potsdam 14476, Germany\n family-names: Pfeiffer\n given-names: Harald P.\n orcid: https://orcid.org/0000-0001-9288-519X\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Scheel\n given-names: Mark A.\n orcid: https://orcid.org/0000-0001-6656-9134\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA and Cornell Center\n for Astrophysics and Planetary Science, Cornell University, Ithaca, New York 14853,\n USA\n family-names: Teukolsky\n given-names: Saul A.\n orcid: https://orcid.org/0000-0001-9765-4526\n- affiliation: Max Planck Institute for Gravitational Physics (Albert Einstein Institute),\n Am Mühlenberg 1, Potsdam 14476, Germany\n family-names: Wittek\n given-names: Nikolas A.\n orcid: https://orcid.org/0000-0001-8575-5450\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Anantpurkar\n given-names: Isha\n orcid: https://orcid.org/0000-0002-5814-4109\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Anderson\n given-names: Carter\n orcid: https://orcid.org/0009-0009-0359-6763\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Boyle\n given-names: Michael\n orcid: https://orcid.org/0000-0002-5075-5116\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Carpenter\n given-names: Alexander\n orcid: https://orcid.org/0000-0002-9183-8006\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Ceja\n given-names: Andrea\n orcid: https://orcid.org/0000-0002-1681-7299\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Chaudhary\n given-names: Himanshu\n orcid: https://orcid.org/0000-0002-4101-0534\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Corso\n given-names: Nicholas\n orcid: https://orcid.org/0000-0002-0088-2563\n- affiliation: Max Planck Institute for Gravitational Physics (Albert Einstein Institute),\n Am Mühlenberg 1, Potsdam 14476, Germany\n family-names: Dittmer\n given-names: Clemens\n orcid: https://orcid.org/0009-0007-3833-9252\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Fayyazuddin Ljungberg\n given-names: Nora\n orcid: https://orcid.org/0000-0002-7074-4545\n- affiliation: Department of Physics & Astronomy, University of New Hampshire, 9 Library\n Way, Durham NH 03824, USA\n family-names: Foucart\n given-names: Francois\n orcid: https://orcid.org/0000-0003-4617-4738\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Ghadiri\n given-names: Noora\n orcid: https://orcid.org/0000-0001-9162-4449\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Giesler\n given-names: Matthew\n orcid: https://orcid.org/0000-0003-2300-893X\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Guo\n given-names: Jason S.\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Habib\n given-names: Sarah\n orcid: https://orcid.org/0000-0002-4725-4978\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Huang\n given-names: Chenhang\n orcid: https://orcid.org/0000-0003-2617-1011\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Iozzo\n given-names: Dante A. B.\n orcid: https://orcid.org/0000-0002-7244-1900\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Jones\n given-names: Ken Z.\n orcid: https://orcid.org/0009-0003-1034-0498\n- affiliation: Max Planck Institute for Gravitational Physics (Albert Einstein Institute),\n Am Mühlenberg 1, Potsdam 14476, Germany\n family-names: Lara\n given-names: Guillermo\n orcid: https://orcid.org/0000-0001-9461-6292\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Legred\n given-names: Isaac\n orcid: https://orcid.org/0000-0002-9523-9617\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Li\n given-names: Dongjun\n orcid: https://orcid.org/0000-0002-1962-680X\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Ma\n given-names: Sizheng\n orcid: https://orcid.org/0000-0002-4645-453X\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Melchor\n given-names: Denyz\n orcid: https://orcid.org/0000-0002-7854-1953\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA and Department of\n Physics and Astronomy, Oberlin College, Oberlin, Ohio 44074, USA\n family-names: Mendes\n given-names: Iago\n orcid: https://orcid.org/0009-0007-9845-8448\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Morales\n given-names: Marlo\n orcid: https://orcid.org/0000-0002-0593-4318\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Most\n given-names: Elias R.\n orcid: https://orcid.org/0000-0002-0491-1210\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Murphy\n given-names: Michael\n orcid: https://orcid.org/0000-0003-3865-3034\n- affiliation: Max Planck Institute for Gravitational Physics (Albert Einstein Institute),\n Am Mühlenberg 1, Potsdam 14476, Germany\n family-names: Nee\n given-names: Peter James\n orcid: https://orcid.org/0000-0002-2362-5420\n- affiliation: Max Planck Institute for Gravitational Physics (Albert Einstein Institute),\n Am Mühlenberg 1, Potsdam 14476, Germany\n family-names: Nishimura\n given-names: Nami\n orcid: https://orcid.org/0009-0002-4398-9130\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Osorio\n given-names: Alejandro\n orcid: https://orcid.org/0009-0000-5024-0086\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Pajkos\n given-names: Michael A.\n orcid: https://orcid.org/0000-0002-4983-4589\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Pannone\n given-names: Kyle\n orcid: https://orcid.org/0009-0005-8607-2113\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Pineda\n given-names: Jose Maria\n orcid: https://orcid.org/0009-0007-6694-8434\n- affiliation: International Centre for Theoretical Sciences - Tata Institute of Fundamental\n Research (ICTS-TIFR), Survey No. 151, Shivakote, Hesaraghatta Hobli, Bengaluru\n - 560 089, Karnataka, India.\n family-names: Prasad\n given-names: Vaishak\n orcid: https://orcid.org/0000-0001-6712-2457\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Ramirez\n given-names: Teresita\n orcid: https://orcid.org/0000-0003-0994-115X\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Ring\n given-names: Noah\n orcid: https://orcid.org/0000-0001-6510-4300\n- affiliation: CFisUC, Department of Physics, University of Coimbra, 3004-516 Coimbra,\n Portugal\n family-names: Rüter\n given-names: Hannes R.\n orcid: https://orcid.org/0000-0002-3442-5360\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Sanchez\n given-names: Jennifer\n orcid: https://orcid.org/0000-0002-5335-4924\n- affiliation: Department of Physics and Astronomy, University of Mississippi, University,\n Mississippi 38677, USA\n family-names: Stein\n given-names: Leo C.\n orcid: https://orcid.org/0000-0001-7559-9597\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Tellez\n given-names: Daniel\n orcid: https://orcid.org/0009-0008-7784-2528\n- affiliation: Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California 92831,\n USA\n family-names: Thomas\n given-names: Sierra\n orcid: https://orcid.org/0000-0003-3574-2090\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Tommasini\n given-names: Vittoria\n orcid: https://orcid.org/0009-0001-4440-9751\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA and I. Physikalisches Institut, Universität zu Köln,\n Zülpicher Straße 77, 50937, Köln, Germany\n family-names: Vieira\n given-names: Daniel\n orcid: https://orcid.org/0000-0001-8019-0390\n- affiliation: Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics,\n California Institute of Technology, Pasadena, CA 91125, USA\n family-names: Wang\n given-names: Xiyue\n orcid: https://orcid.org/0009-0006-3331-0832\n- affiliation: Max Planck Institute for Gravitational Physics (Albert Einstein Institute),\n Am Mühlenberg 1, Potsdam 14476, Germany\n family-names: Wlodarczyk\n given-names: Tom\n orcid: https://orcid.org/0000-0003-0005-348X\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Wu\n given-names: David\n orcid: https://orcid.org/0000-0002-5287-4389\n- affiliation: Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n family-names: Yoo\n given-names: Jooheon\n orcid: https://orcid.org/0000-0002-3251-0924\ncff-version: 1.2.0\ndate-released: 2026-04-01\ndoi: 10.5281/zenodo.19373346\nkeywords:\n- Software\n- Astrophysics\n- General Relativity\n- Numerical Relativity\n- Multiphysics\n- Gravitational Waves\n- Discontinuous Galerkin\n- Finite Difference\n- Finite Volume\nlicense: MIT\nmessage: Please cite SpECTRE in any publications that make use of its code or data.\n Cite the latest version that you use in your publication. The citation for this\n version is listed below.\nreferences:\n- authors:\n - family-names: Iglberger\n given-names: Klaus\n - family-names: Hager\n given-names: Georg\n - family-names: Treibig\n given-names: Jan\n - family-names: Rüde\n given-names: Ulrich\n collection-title: 2012 International Conference on High Performance Computing \\&\n Simulation (HPCS)\n doi: 10.1109/HPCSim.2012.6266939\n pages: 367-373\n title: High performance smart expression template math libraries\n type: article\n year: '2012'\n- authors:\n - family-names: Iglberger\n given-names: Klaus\n - family-names: Hager\n given-names: Georg\n - family-names: Treibig\n given-names: Jan\n - family-names: R\\\"{u}de\n given-names: Ulrich\n doi: 10.1137/110830125\n number: '2'\n pages: C42-C69\n title: 'Expression Templates Revisited: A Performance Analysis of Current Methodologies'\n type: article\n url: https://doi.org/10.1137/110830125\n volume: '34'\n year: '2012'\n- authors:\n - family-names: Kale\n given-names: Laxmikant\n - family-names: Acun\n given-names: Bilge\n - family-names: Bak\n given-names: Seonmyeong\n - family-names: Becker\n given-names: Aaron\n - family-names: Bhandarkar\n given-names: Milind\n - family-names: Bhat\n given-names: Nitin\n - family-names: Bhatele\n given-names: Abhinav\n - family-names: Bohm\n given-names: Eric\n - family-names: Bordage\n given-names: Cyril\n - family-names: Brunner\n given-names: Robert\n - family-names: Buch\n given-names: Ronak\n - family-names: Chakravorty\n given-names: Sayantan\n - family-names: Chandrasekar\n given-names: Kavitha\n - family-names: Choi\n given-names: Jaemin\n - family-names: Denardo\n given-names: Michael\n - family-names: DeSouza\n given-names: Jayant\n - family-names: Diener\n given-names: Matthias\n - family-names: Dokania\n given-names: Harshit\n - family-names: Dooley\n given-names: Isaac\n - family-names: Fenton\n given-names: Wayne\n - family-names: Galvez\n given-names: Juan\n - family-names: Gioachin\n given-names: Fillipo\n - family-names: Gupta\n given-names: Abhishek\n - family-names: Gupta\n given-names: Gagan\n - family-names: Gupta\n given-names: Manish\n - family-names: Gursoy\n given-names: Attila\n - family-names: Harsh\n given-names: Vipul\n - family-names: Hu\n given-names: Fang\n - family-names: Huang\n given-names: Chao\n - family-names: Jagathesan\n given-names: Narain\n - family-names: Jain\n given-names: Nikhil\n - family-names: Jetley\n given-names: Pritish\n - family-names: Jindal\n given-names: Prateek\n - family-names: Kanakagiri\n given-names: Raghavendra\n - family-names: Koenig\n given-names: Greg\n - family-names: Krishnan\n given-names: Sanjeev\n - family-names: Kumar\n given-names: Sameer\n - family-names: Kunzman\n given-names: David\n - family-names: Lang\n given-names: Michael\n - family-names: Langer\n given-names: Akhil\n - family-names: Lawlor\n given-names: Orion\n - family-names: Wai Lee\n given-names: Chee\n - family-names: Lifflander\n given-names: Jonathan\n - family-names: Mahesh\n given-names: Karthik\n - family-names: Mendes\n given-names: Celso\n - family-names: Menon\n given-names: Harshitha\n - family-names: Mei\n given-names: Chao\n - family-names: Meneses\n given-names: Esteban\n - family-names: Mikida\n given-names: Eric\n - family-names: Miller\n given-names: Phil\n - family-names: Mokos\n given-names: Ryan\n - family-names: Narayanan\n given-names: Venkatasubrahmanian\n - family-names: Ni\n given-names: Xiang\n - family-names: Nomura\n given-names: Kevin\n - family-names: Paranjpye\n given-names: Sameer\n - family-names: Ramachandran\n given-names: Parthasarathy\n - family-names: Ramkumar\n given-names: Balkrishna\n - family-names: Ramos\n given-names: Evan\n - family-names: Robson\n given-names: Michael\n - family-names: Saboo\n given-names: Neelam\n - family-names: Saletore\n given-names: Vikram\n - family-names: Sarood\n given-names: Osman\n - family-names: Senthil\n given-names: Karthik\n - family-names: Shah\n given-names: Nimish\n - family-names: Shu\n given-names: Wennie\n - family-names: B. Sinha\n given-names: Amitabh\n - family-names: Sun\n given-names: Yanhua\n - family-names: Sura\n given-names: Zehra\n - family-names: Totoni\n given-names: Ehsan\n - family-names: Varadarajan\n given-names: Krishnan\n - family-names: Venkataraman\n given-names: Ramprasad\n - family-names: Wang\n given-names: Jackie\n - family-names: Wesolowski\n given-names: Lukasz\n - family-names: White\n given-names: Sam\n - family-names: Wilmarth\n given-names: Terry\n - family-names: Wright\n given-names: Jeff\n - family-names: Yelon\n given-names: Joshua\n - family-names: Zheng\n given-names: Gengbin\n doi: 10.5281/zenodo.3370873\n month: 8\n title: '{The Charm++ Parallel Programming System}'\n type: software\n url: https://charm.cs.illinois.edu\n year: '2019'\n- authors:\n - family-names: Kale\n given-names: Laxmikant\n - family-names: Acun\n given-names: Bilge\n - family-names: Bak\n given-names: Seonmyeong\n - family-names: Becker\n given-names: Aaron\n - family-names: Bhandarkar\n given-names: Milind\n - family-names: Bhat\n given-names: Nitin\n - family-names: Bhatele\n given-names: Abhinav\n - family-names: Bohm\n given-names: Eric\n - family-names: Bordage\n given-names: Cyril\n - family-names: Brunner\n given-names: Robert\n - family-names: Buch\n given-names: Ronak\n - family-names: Chakravorty\n given-names: Sayantan\n - family-names: Chandrasekar\n given-names: Kavitha\n - family-names: Choi\n given-names: Jaemin\n - family-names: Denardo\n given-names: Michael\n - family-names: DeSouza\n given-names: Jayant\n - family-names: Diener\n given-names: Matthias\n - family-names: Dokania\n given-names: Harshit\n - family-names: Dooley\n given-names: Isaac\n - family-names: Fenton\n given-names: Wayne\n - family-names: Fink\n given-names: Zane\n - family-names: Galvez\n given-names: Juan\n - family-names: Ghosh\n given-names: Pathikrit\n - family-names: Gioachin\n given-names: Fillipo\n - family-names: Gupta\n given-names: Abhishek\n - family-names: Gupta\n given-names: Gagan\n - family-names: Gupta\n given-names: Manish\n - family-names: Gursoy\n given-names: Attila\n - family-names: Harsh\n given-names: Vipul\n - family-names: Hu\n given-names: Fang\n - family-names: Huang\n given-names: Chao\n - family-names: Jagathesan\n given-names: Narain\n - family-names: Jain\n given-names: Nikhil\n - family-names: Jetley\n given-names: Pritish\n - family-names: Jindal\n given-names: Prateek\n - family-names: Kanakagiri\n given-names: Raghavendra\n - family-names: Koenig\n given-names: Greg\n - family-names: Krishnan\n given-names: Sanjeev\n - family-names: Kumar\n given-names: Sameer\n - family-names: Kunzman\n given-names: David\n - family-names: Lang\n given-names: Michael\n - family-names: Langer\n given-names: Akhil\n - family-names: Lawlor\n given-names: Orion\n - family-names: Lee\n given-names: Chee Wai\n - family-names: Lifflander\n given-names: Jonathan\n - family-names: Mahesh\n given-names: Karthik\n - family-names: Mendes\n given-names: Celso\n - family-names: Menon\n given-names: Harshitha\n - family-names: Mei\n given-names: Chao\n - family-names: Meneses\n given-names: Esteban\n - family-names: Mikida\n given-names: Eric\n - family-names: Miller\n given-names: Phil\n - family-names: Mokos\n given-names: Ryan\n - family-names: Narayanan\n given-names: Venkatasubrahmanian\n - family-names: Ni\n given-names: Xiang\n - family-names: Nomura\n given-names: Kevin\n - family-names: Paranjpye\n given-names: Sameer\n - family-names: Ramachandran\n given-names: Parthasarathy\n - family-names: Ramkumar\n given-names: Balkrishna\n - family-names: Ramos\n given-names: Evan\n - family-names: Robson\n given-names: Michael\n - family-names: Saboo\n given-names: Neelam\n - family-names: Saletore\n given-names: Vikram\n - family-names: Sarood\n given-names: Osman\n - family-names: Senthil\n given-names: Karthik\n - family-names: Shah\n given-names: Nimish\n - family-names: Shu\n given-names: Wennie\n - family-names: Sinha\n given-names: Amitabh B.\n - family-names: Sun\n given-names: Yanhua\n - family-names: Sura\n given-names: Zehra\n - family-names: Szaday\n given-names: Justin\n - family-names: Totoni\n given-names: Ehsan\n - family-names: Varadarajan\n given-names: Krishnan\n - family-names: Venkataraman\n given-names: Ramprasad\n - family-names: Wang\n given-names: Jackie\n - family-names: Wesolowski\n given-names: Lukasz\n - family-names: White\n given-names: Sam\n - family-names: Wilmarth\n given-names: Terry\n - family-names: Wright\n given-names: Jeff\n - family-names: Yelon\n given-names: Joshua\n - family-names: Zheng\n given-names: Gengbin\n doi: 10.5281/zenodo.5597907\n month: 10\n publisher:\n name: Zenodo\n title: '{UIUC-PPL}/charm: {Charm++} version 7.0.0'\n type: software\n url: https://doi.org/10.5281/zenodo.5597907\n version: v7.0.0\n year: '2021'\n- authors:\n - family-names: Kale\n given-names: Laxmikant V\n - family-names: Krishnan\n given-names: Sanjeev\n collection-title: Parallel programming using C++\n pages: 175--213\n publisher:\n name: The MIT Press\n title: 'Charm++: Parallel programming with message-driven objects'\n type: article\n year: '1996'\n- authors:\n - family-names: Galassi\n given-names: M.\n - name: others\n edition: '3'\n isbn: '9780954612078'\n publisher:\n name: Network Theory Ltd.\n title: '{GNU} Scientific Library Reference Manual'\n type: book\n year: '2009'\n- authors:\n - name: '{The HDF Group}'\n title: '{Hierarchical Data Format, version 5}'\n type: software\n year: 1997-2023\n- authors:\n - family-names: '{Reinecke}'\n given-names: M.\n - family-names: '{Seljebotn}'\n given-names: D. S.\n doi: 10.1051/0004-6361/201321494\n month: 6\n pages: A112\n title: '{Libsharp - spherical harmonic transforms revisited}'\n type: article\n volume: '554'\n year: '2013'\n- authors:\n - family-names: Heinecke\n given-names: Alexander\n - family-names: Henry\n given-names: Greg\n - family-names: Hutchinson\n given-names: Maxwell\n - family-names: Pabst\n given-names: Hans\n collection-title: Proceedings of the International Conference for High Performance\n Computing, Networking, Storage and Analysis\n isbn: '9781467388153'\n pages: 1-11\n publisher:\n name: IEEE Press\n title: '{LIBXSMM}: {Accelerating} Small Matrix Multiplications by Runtime Code Generation'\n type: article\n year: '2016'\n- authors:\n - family-names: Hunter\n given-names: J. D.\n doi: 10.1109/MCSE.2007.55\n number: '3'\n pages: 90--95\n publisher:\n name: IEEE COMPUTER SOC\n title: 'Matplotlib: A 2D graphics environment'\n type: article\n volume: '9'\n year: '2007'\n- authors:\n - family-names: Caswell\n given-names: Thomas A\n - family-names: Droettboom\n given-names: Michael\n - family-names: Lee\n given-names: Antony\n - family-names: Hunter\n given-names: John\n - family-names: Firing\n given-names: Eric\n - family-names: Andrade\n given-names: Elliott Sales\n name-particle: de\n - family-names: Hoffmann\n given-names: Tim\n - family-names: Stansby\n given-names: David\n - family-names: Klymak\n given-names: Jody\n - family-names: Varoquaux\n given-names: Nelle\n - family-names: Nielsen\n given-names: Jens Hedegaard\n - family-names: Root\n given-names: Benjamin\n - family-names: May\n given-names: Ryan\n - family-names: Elson\n given-names: Phil\n - family-names: Dale\n given-names: Darren\n - family-names: Lee\n given-names: Jae-Joon\n - family-names: Seppänen\n given-names: Jouni K.\n - family-names: McDougall\n given-names: Damon\n - family-names: Straw\n given-names: Andrew\n - family-names: Hobson\n given-names: Paul\n - family-names: Gohlke\n given-names: Christoph\n - family-names: Yu\n given-names: Tony S\n - family-names: Ma\n given-names: Eric\n - family-names: Vincent\n given-names: Adrien F.\n - family-names: Silvester\n given-names: Steven\n - family-names: Moad\n given-names: Charlie\n - family-names: Kniazev\n given-names: Nikita\n - name: hannah\n - family-names: Ernest\n given-names: Elan\n - family-names: Ivanov\n given-names: Paul\n doi: 10.5281/zenodo.3948793\n month: 7\n publisher:\n name: Zenodo\n title: 'matplotlib/matplotlib: {REL:} v3.3.0'\n type: software\n url: https://doi.org/10.5281/zenodo.3948793\n version: v3.3.0\n year: '2020'\n- authors:\n - family-names: Harris\n given-names: Charles R.\n - family-names: Millman\n given-names: K. Jarrod\n - family-names: Walt\n given-names: St{\\'{e}}fan J.\n name-particle: van der\n - family-names: Gommers\n given-names: Ralf\n - family-names: Virtanen\n given-names: Pauli\n - family-names: Cournapeau\n given-names: David\n - family-names: Wieser\n given-names: Eric\n - family-names: Taylor\n given-names: Julian\n - family-names: Berg\n given-names: Sebastian\n - family-names: Smith\n given-names: Nathaniel J.\n - family-names: Kern\n given-names: Robert\n - family-names: Picus\n given-names: Matti\n - family-names: Hoyer\n given-names: Stephan\n - family-names: Kerkwijk\n given-names: Marten H.\n name-particle: van\n - family-names: Brett\n given-names: Matthew\n - family-names: Haldane\n given-names: Allan\n - family-names: R{\\'{i}}o\n given-names: Jaime Fern{\\'{a}}ndez\n name-particle: del\n - family-names: Wiebe\n given-names: Mark\n - family-names: Peterson\n given-names: Pearu\n - family-names: G{\\'{e}}rard-Marchant\n given-names: Pierre\n - family-names: Sheppard\n given-names: Kevin\n - family-names: Reddy\n given-names: Tyler\n - family-names: Weckesser\n given-names: Warren\n - family-names: Abbasi\n given-names: Hameer\n - family-names: Gohlke\n given-names: Christoph\n - family-names: Oliphant\n given-names: Travis E.\n doi: 10.1038/s41586-020-2649-2\n month: 9\n number: '7825'\n pages: 357--362\n publisher:\n name: Springer Science and Business Media {LLC}\n title: Array programming with {NumPy}\n type: article\n url: https://doi.org/10.1038/s41586-020-2649-2\n volume: '585'\n year: '2020'\n- authors:\n - family-names: Ayachit\n given-names: Utkarsh\n isbn: '1930934300'\n publisher:\n name: Kitware, Inc.\n title: 'The ParaView Guide: A Parallel Visualization Application'\n type: book\n year: '2015'\n- authors:\n - family-names: Ahrens\n given-names: J.\n - family-names: Geveci\n given-names: Berk\n - family-names: Law\n given-names: C.\n isbn: '9780123875822'\n publisher:\n name: Elsevier\n title: '{ParaView}: {An} end-user tool for large-data visualization'\n type: book\n year: '2005'\n- authors:\n - family-names: Jakob\n given-names: Wenzel\n - family-names: Rhinelander\n given-names: Jason\n - family-names: Moldovan\n given-names: Dean\n title: pybind11 -- Seamless operability between C++11 and Python\n type: software\n year: '2017'\n- authors:\n - family-names: Beder\n given-names: Jesse\n - family-names: Woehlke\n given-names: Matthew\n - family-names: Breitbart\n given-names: Jens\n - family-names: Wolchok\n given-names: Scott\n - family-names: Hackimov\n given-names: Azamat H.\n - family-names: Snape\n given-names: Jamie\n - family-names: Hamlet\n given-names: Oliver\n - family-names: Novotny\n given-names: Paul\n - family-names: Tambre\n given-names: Raul\n - family-names: Reinhold\n given-names: Stefan\n - family-names: Vaucher\n given-names: Alain\n - family-names: Zaitsev\n given-names: Alexander\n - family-names: Anokhin\n given-names: Alexander\n - family-names: Karatarakis\n given-names: Alexander\n - family-names: Maloney\n given-names: Andy\n - family-names: Polukhin\n given-names: Antony\n - family-names: Brandenburg\n given-names: Craig M.\n - family-names: Ibanez\n given-names: Dan\n - family-names: Gladkikh\n given-names: Denis\n - family-names: Eich\n given-names: Florian\n - family-names: Dumont\n given-names: Guillaume\n - family-names: Trigg\n given-names: Haydn\n - family-names: King\n given-names: Jim\n - family-names: Frederico\n given-names: Joel\n - family-names: Hamilton\n given-names: Jonathan\n - family-names: Langley\n given-names: Joseph\n - family-names: Hämäläinen\n given-names: Lassi\n - family-names: Blair\n given-names: Matt\n - family-names: Duggan\n given-names: Michael Welsh\n - family-names: Wang\n given-names: Olli\n - family-names: Stotko\n given-names: Patrick\n - family-names: Levine\n given-names: Peter\n - family-names: Bena\n given-names: Petr\n - family-names: Cordoba\n given-names: Rodrigo Hernandez\n - family-names: Schmidt\n given-names: Ryan\n - family-names: Gottlieb\n given-names: Simon Gene\n - family-names: Prilmeier\n given-names: Franz\n - family-names: Zhang\n given-names: Tanki\n - family-names: Ishi\n given-names: Tatsuyuki\n - family-names: Lyngmo\n given-names: Ted\n - family-names: Mataré\n given-names: Victor\n - family-names: Konečný\n given-names: Michael\n - name: USDOE\n doi: 10.11578/dc.20220817.13\n month: 9\n title: yaml-cpp\n type: software\n url: https://www.osti.gov/biblio/1881863\n year: '2009'\nrepository-code: https://github.com/sxs-collaboration/spectre\ntitle: SpECTRE\nurl: https://spectre-code.org\nversion: 2026.04.01\n" }, { "path": "CMakeLists.txt", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\ncmake_minimum_required(VERSION 3.18.0)\n\nlist(APPEND CMAKE_MODULE_PATH \"${CMAKE_SOURCE_DIR}/cmake\")\n\n# Create a new (or overwrite existing) info file at start of configuration\nfile(WRITE \"${CMAKE_BINARY_DIR}/BuildInfo.txt\" \"\")\n\n# Determine the project version and other metadata\ninclude(SpectreLoadMetadata)\n\n# Set up the project. Notes:\n# - Fortran is needed for SPHEREPACK\nproject(${SPECTRE_NAME} VERSION ${SPECTRE_VERSION} LANGUAGES CXX C Fortran)\n\n# Unset the CMake-defined version variable because it strips zeros from the\n# version components, e.g. 2020.12.07 becomes 2020.12.7\nunset(${SPECTRE_NAME}_VERSION)\n# Also unset the version-component variables because they have no meaning in\n# our versioning scheme\nunset(${SPECTRE_NAME}_VERSION_MAJOR)\nunset(${SPECTRE_NAME}_VERSION_MINOR)\nunset(${SPECTRE_NAME}_VERSION_PATCH)\n\n# Policies\n# The `cmake_minimum_required` above sets policies to `NEW` that are compatible\n# with the given minimum cmake version. Here we overwrite policies that we\n# have back-ported in our cmake code.\n# - We use test names with '.' characters in them\nif (CMAKE_VERSION VERSION_GREATER_EQUAL 3.19)\n cmake_policy(SET CMP0110 NEW)\nendif ()\n# - We allow both uppercase and case-preserved hints in `find_package` calls, so\n# `PACKAGENAME_ROOT` and `PackageName_ROOT` are both searched in\n# `FindPackageName.cmake` (NEW behavior). The OLD behavior was to search only\n# `PackageName_ROOT` (before CMake v3.27). We have backported the NEW behavior\n# by adding the uppercase name explicitly to the list of hints.\nif (CMAKE_VERSION VERSION_GREATER_EQUAL 3.27)\n cmake_policy(SET CMP0144 NEW)\nendif()\n# - The `NEW` behavior of `DOWNLOAD_EXTRACT_TIMESTAMP` is recommended.\nif (CMAKE_VERSION VERSION_GREATER_EQUAL 3.24)\n cmake_policy(SET CMP0135 NEW)\nendif()\n# - We allow CMake 3.30 and above to load Boost's CMake config file that is\n# installed alongside Boost. Before, CMake provided its own FindBoost module.\nif (CMAKE_VERSION VERSION_GREATER_EQUAL 3.30)\n cmake_policy(SET CMP0167 NEW)\nendif ()\n\n# FetchContent can be used to download and build some dependencies. We can\n# consider turning this on by default later.\noption(SPECTRE_FETCH_MISSING_DEPS \"Download missing dependencies\" OFF)\n# - Mark FetchContent as 'SYSTEM' to suppress warnings.\n# Supported since CMake version 3.25.\nif (CMAKE_VERSION VERSION_GREATER_EQUAL 3.25)\n set(SPECTRE_FETCHCONTENT_BASE_ARGS SYSTEM)\nelse()\n set(SPECTRE_FETCHCONTENT_BASE_ARGS \"\")\nendif()\n\n# Define standard installation directories\ninclude(GNUInstallDirs)\n# Disable `make install` depending on `make all` since we want to control what\n# we install more closely. With this setting, and targets marked as `OPTIONAL`,\n# only targets that were built will be installed.\nset(CMAKE_SKIP_INSTALL_ALL_DEPENDENCY ON)\n\nset(CMAKE_VERBOSE_MAKEFILE OFF)\n\ninclude(SpectreGetGitHash)\ninclude(SpectreSetSiteName)\n\n# We need Python in the build system and throughout the code. Setting it up\n# early so we can rely on a consistent Python version in the build system.\noption(ENABLE_PYTHON \"Enable Python\" ON)\nif (ENABLE_PYTHON)\n find_package(Python 3.8 REQUIRED)\n # Define the location of Python code in the build directory. Unit tests etc. can\n # add this location to their `PYTHONPATH`.\n set(SPECTRE_PYTHON_PREFIX_PARENT \"${CMAKE_BINARY_DIR}/bin/python\")\n get_filename_component(\n SPECTRE_PYTHON_PREFIX_PARENT \"${SPECTRE_PYTHON_PREFIX_PARENT}\" ABSOLUTE)\n set(SPECTRE_PYTHON_SITE_PACKAGES \"${CMAKE_BINARY_DIR}/lib/\\\npython${Python_VERSION_MAJOR}.${Python_VERSION_MINOR}/site-packages\")\n set(PYTHONPATH \"${SPECTRE_PYTHON_PREFIX_PARENT}:\\\n${SPECTRE_PYTHON_SITE_PACKAGES}\")\n if(DEFINED ENV{PYTHONPATH})\n set(PYTHONPATH \"${PYTHONPATH}:$ENV{PYTHONPATH}\")\n endif()\n message(STATUS \"PYTHONPATH: ${PYTHONPATH}\")\n include(BootstrapPyDeps)\nelse()\n # We still need minimal Python for linking purpose.\n find_package(Python REQUIRED)\nendif()\n\noption(BUILD_DOCS \"Enable building documentation\" ON)\noption(\n DOCS_ONLY\n \"Skip all initialization not required for rendering documentation\"\n OFF\n)\nif (BUILD_DOCS AND DOCS_ONLY)\n include(SetupDoxygen)\n return()\nendif()\n\noption(USE_PCH \"Use precompiled headers\" ON)\n\ninclude(SpectreInitializeVariables)\n\ninclude(CheckCompilerVersion)\ninclude(ProhibitInSourceBuild)\ninclude(SpectreSetupFlagsTarget)\ninclude(SetupFortran)\ninclude(SetupNinjaColors)\ninclude(SetOutputDirectory)\ninclude(SpectreAddInterfaceLibraryHeaders)\ninclude(SpectreTargetHeaders)\ninclude(SpectreTargetSources)\ninclude(SetupFormaline)\ninclude(SetupGitHooks)\ninclude(SetupLicenseInfo)\ninclude(SetBuildType)\ninclude(SetupPic)\ninclude(SetupLinkTimeOptimization)\ninclude(SetCxxStandard)\ninclude(StripSymbols)\n# We need Boost for InfoAtLink\ninclude(SetupBoost)\ninclude(SetupInformer)\ninclude(SetupCCache)\ninclude(SetupCharm)\ninclude(EnableWarnings)\ninclude(SetupGoldOrLldLinker)\n\n# In order to use certain code analysis tools like clang-tidy and cppcheck the\n# compile commands need to be accessible. CMake can write these to a\n# \"compile_commands.json\" file.\nset(CMAKE_EXPORT_COMPILE_COMMANDS ON)\n\ninclude(SetupLIBCXX)\ninclude(SetupSpectreInlining)\ninclude(SetupCxxFlags)\ninclude(SetupProfiling)\ninclude(SetupSanitizers)\ninclude(SetupListTargets)\ninclude(AddSpectreExecutable)\ninclude(CheckBrokenArray0)\n\n# Blaze depends on both Blas and Lapack, since LIBXSMM is a Blas\n# alternative we set it up early too. Finally, Blaze uses the GSL\n# blas headers, so we need to set that up before Blaze as well.\ninclude(SetupBlas)\ninclude(SetupLapack)\ninclude(SetupLIBXSMM)\ninclude(SetupGsl)\n\ninclude(SetupAutodiff)\ninclude(SetupBlaze)\ninclude(SetupFuka)\ninclude(SetupGoogleBenchmark)\ninclude(SetupHdf5)\ninclude(SetupAllocator)\ninclude(SetupPapi)\ninclude(SetupPybind11)\ninclude(SetupSpec)\ninclude(SetupStl)\ninclude(SetupXsimd)\ninclude(SetupYamlCpp)\ninclude(SetupOpenMP)\ninclude(SetupParaView)\n\nadd_subdirectory(external)\n\ninclude(SetupKokkos)\n\ninclude(SetupLIBCXXCharm)\n# The precompiled header must be setup after all libraries have been found\nif (USE_PCH)\n include(SetupPch)\nendif()\n\n# All special targets and configs that need to be applied to *all*\n# executables must be added at once in the 'UpdateAddExecutables' file.\n# This is because of what is likely a bug in CMake where if a function is\n# overridden multiple times (using the _function_name(...) method) then some\n# versions of CMake (at least 3.13.2) segfault.\ninclude(UpdateAddExecutables)\n\n# The ClangFormat, clang-tidy, Doxygen, and CodeCov are intentionally\n# after the PCH setup because that way they are able to change their\n# dependencies on the PCH if necessary.\ninclude(SetupClangFormat)\ninclude(SetupClangTidy)\nif(BUILD_DOCS)\n include(SetupDoxygen)\n include(SetupSphinx)\nendif()\ninclude(CodeCoverageDetection)\ninclude(SpectreAddLibraries)\n\ninclude(SpectreSetupTesting)\nif(BUILD_TESTING)\n include(SetupCatch)\n include(SetupPypp)\n include(SpectreAddTestLibs)\n include(SpectreAddCatchTests)\n include(AddInputFileTests)\n include(AddStandaloneTests)\nendif()\n\ninclude(SpectreSetupPythonPackage)\n\n# Set global include directory for all targets\ninclude_directories(${CMAKE_SOURCE_DIR}/src)\n# Charm++ generated headers are created in the build directory\n# (by `add_charm_module`)\ninclude_directories(SYSTEM ${CMAKE_BINARY_DIR}/src)\n\nadd_subdirectory(src)\nadd_subdirectory(support)\nif(BUILD_TESTING)\n add_subdirectory(tests)\nendif()\nadd_subdirectory(tools)\n\ninclude(PrintUsefulCMakeInfo)\n\ninclude(SpectreCheckDependencies)\n" }, { "path": "LICENSE.txt", "content": "==============================================================================\nSpECTRE Release License\n==============================================================================\n\nCopyright 2017 - 2026 Simulating eXtreme Spacetimes Collaboration\n\nPermission is hereby granted, free of charge, to any person obtaining a copy\nof this software and associated documentation files (the \"Software\"), to deal\nin the Software without restriction, including without limitation the rights\nto use, copy, modify, merge, publish, distribute, sublicense, and/or sell\ncopies of the Software, and to permit persons to whom the Software is\nfurnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in\nall copies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN\nTHE SOFTWARE.\n" }, { "path": "Metadata.yaml", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nName: SpECTRE\n\nLicense: MIT\n\nHomepage: https://spectre-code.org\n\nGitHub: sxs-collaboration/spectre\n\nVersion: 2026.04.01\n\nPublicationDate: 2026-04-01\n\nDoi: 10.5281/zenodo.19373346\n\nZenodoId: 19373346\n\nDescription: |\n SpECTRE is an open-source code for multi-scale, multi-physics problems\n in astrophysics and gravitational physics. In the future, we hope that\n it can be applied to problems across discipline boundaries in fluid\n dynamics, geoscience, plasma physics, nuclear physics, and\n engineering. It runs at petascale and is designed for future exascale\n computers.\n\n SpECTRE is being developed in support of our collaborative Simulating\n eXtreme Spacetimes (SXS) research program into the multi-messenger\n astrophysics of neutron star mergers, core-collapse supernovae, and\n gamma-ray bursts.\n\nKeywords:\n - Software\n - Astrophysics\n - General Relativity\n - Numerical Relativity\n - Multiphysics\n - Gravitational Waves\n - Discontinuous Galerkin\n - Finite Difference\n - Finite Volume\n\nAffiliations:\n - &aei\n Max Planck Institute for Gravitational Physics (Albert Einstein Institute),\n Am Mühlenberg 1, Potsdam 14476, Germany\n - &caltech\n Theoretical Astrophysics, Walter Burke Institute for Theoretical\n Physics, California Institute of Technology, Pasadena, CA 91125, USA\n - &cornell\n Cornell Center for Astrophysics and Planetary Science, Cornell University,\n Ithaca, New York 14853, USA\n - &coimbra\n CFisUC, Department of Physics, University of Coimbra,\n 3004-516 Coimbra, Portugal\n - &fullerton\n Nicholas and Lee Begovich Center for Gravitational-Wave Physics and\n Astronomy, California State University, Fullerton, Fullerton, California\n 92831, USA\n - &icts\n International Centre for Theoretical Sciences - Tata Institute of\n Fundamental Research (ICTS-TIFR), Survey No. 151, Shivakote,\n Hesaraghatta Hobli, Bengaluru - 560 089, Karnataka, India.\n - &new_hampshire\n Department of Physics & Astronomy, University of New Hampshire, 9 Library\n Way, Durham NH 03824, USA\n - &koln\n I. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77,\n 50937, Köln, Germany\n - &umiss\n Department of Physics and Astronomy, University of Mississippi,\n University, Mississippi 38677, USA\n - &oberlin\n Department of Physics and Astronomy, Oberlin College, Oberlin, Ohio 44074,\n USA\n\nAuthors:\n Description: |\n We maintain three tiers of authors for the code as a whole: Core, Developers\n and Contributors. The full author list for the SpECTRE DOI is built by\n concatenating all authors in the order they are listed here.\n\n The primary goal of this author list is to recognize infrastructure work\n that does not or cannot have any science papers and results associated with\n it. Through authorship on the SpECTRE DOI such work gains recognition that\n holds value in academia. Authorship on the SpECTRE DOI does not directly\n entitle a person for authorship rights on other publications. Authorship\n rights on publications related to SpECTRE are governed by our publication\n policy (see `docs/PublicationPolicy.md`).\n\n Note that the placement of authors in these tiers is inherently a subjective\n topic since we are forced to compare different projects people work on.\n Nevertheless, having guidelines and some way of promoting healthy and\n constructive discussions is vital for ensuring the collaborative aspect of\n the code is healthy.\n\n Core:\n Description: |\n For the time a Developer serves as Core developer they take on some\n project-management responsibilities, such as initiating and signing off on\n code reviews, maintaining compatibility with third-party libraries,\n maintaining the CI/CD infrastructure and overseeing the code as a whole.\n\n Guidelines on becoming a Core developer:\n\n - Have at least 4-5 major infrastructure contributions, each taking\n roughly 4-5 weeks of full-time work for an existing Core developer.\n - Seek out PRs to review and volunteer when calls for a reviewer are\n made.\n - Reach out to any of the existing Core developers and express your\n interest in taking on the responsibilities that come with this role. The\n Core developers will discuss the request and either appoint you to Core\n developer or provide you with feedback on what they think remains to be\n done.\n\n Note that most people will not end up in the Core developer list since a\n lot of work will lead to science results and authorship on science papers,\n which pay dividends for the work. Supervising students and postdocs does\n not count towards Core developer status.\n\n Guidelines on stepping down as Core developer:\n\n - After a Core developer leaves the project they will remain in this tier\n for at least two years. At that point the Core developers will discuss\n if the person should be moved to the Developer tier.\n - A Core developer can step down from the Core developer role at any time.\n\n The author list order is decided by the Core developers.\n List:\n - Name: Deppe, Nils\n Orcid: 0000-0003-4557-4115\n Affiliations: [*caltech]\n GitHub: nilsdeppe\n - Name: Throwe, William\n Orcid: 0000-0001-5059-4378\n Affiliations: [*cornell]\n GitHub: wthrowe\n - Name: Kidder, Lawrence E.\n Orcid: 0000-0001-5392-7342\n Affiliations: [*cornell]\n GitHub: kidder\n - Name: Vu, Nils L.\n Orcid: 0000-0002-5767-3949\n Affiliations: [*aei]\n GitHub: nilsvu\n - Name: Nelli, Kyle C.\n Orcid: 0000-0003-2426-8768\n Affiliations: [*caltech]\n GitHub: knelli2\n\n Developers:\n Description: |\n Developers have contributed major features to SpECTRE and remain in this\n list indefinitely unless they wish to be removed.\n\n Guidelines on becoming a Developer:\n\n - Do some code review, does not need to be self-initiated.\n - Somewhere around 40 commits and 10k-15k lines of code should trigger a\n discussion among the Core developers to move someone from Contributors\n to Developers. These are guidelines and being above or below these\n arbitrary cutoffs does not automatically include or exclude you. E.g.\n someone doing complicated low-level code will likely become a Developer\n with far fewer lines of code contributed.\n - Anyone supervising a Core developer or two Developers may be considered\n for Developer status. Whether to be placed as Developer or Contributor\n will depend on how active the supervision is. If most of the supervision\n is coming from the Core developers then Contributor status is\n appropriate. This will be discussed with the person supervising the Core\n developer and/or Developers.\n\n This author list is ordered by last name.\n List:\n - Name: Armaza, Cristóbal\n Orcid: 0000-0002-1791-0743\n Affiliations: [*cornell]\n GitHub: carmaza\n - Name: Bonilla, Marceline S.\n Orcid: 0000-0003-4502-528X\n Affiliations: [*fullerton]\n GitHub: mar-celine\n - Name: Hébert, François\n Orcid: 0000-0001-9009-6955\n Affiliations: [*caltech]\n GitHub: fmahebert\n - Name: Kim, Yoonsoo\n Orcid: 0000-0002-4305-6026\n Affiliations: [*caltech]\n GitHub: yoonso0-0\n - Name: Kumar, Prayush\n Orcid: 0000-0001-5523-4603\n Affiliations: [*cornell]\n GitHub: prayush\n - Name: Lovelace, Geoffrey\n Orcid: 0000-0002-7084-1070\n Affiliations: [*fullerton]\n GitHub: geoffrey4444\n - Name: Macedo, Alexandra\n Orcid: 0009-0001-7671-6377\n Affiliations: [*fullerton]\n GitHub: macedo22\n - Name: Moxon, Jordan\n Orcid: 0000-0001-9891-8677\n Affiliations: [*caltech]\n GitHub: moxcodes\n - Name: O'Shea, Eamonn\n Affiliations: [*cornell]\n GitHub: osheamonn\n - Name: Pfeiffer, Harald P.\n Orcid: 0000-0001-9288-519X\n Affiliations: [*aei]\n GitHub: haraldp271\n - Name: Scheel, Mark A.\n Orcid: 0000-0001-6656-9134\n Affiliations: [*caltech]\n GitHub: markscheel\n - Name: Teukolsky, Saul A.\n Orcid: 0000-0001-9765-4526\n Affiliations: [*caltech, *cornell]\n GitHub: teukolsky\n - Name: Wittek, Nikolas A.\n Orcid: 0000-0001-8575-5450\n Affiliations: [*aei]\n GitHub: nikwit\n\n Contributors:\n Description: |\n Anyone who has contributed to SpECTRE will be added to this list and\n remain a Contributor indefinitely unless they wish to be removed.\n\n Guidelines on becoming a Contributor:\n\n - See our guidelines in `docs/CONTRIBUTING.md` for information on how to\n get involved with SpECTRE development.\n - Having any PR merged qualifies for this list. If multiple people worked\n on the PR together, e.g. several undergraduate students contributing to\n a single PR, all persons involved will become a Contributor.\n - Supervising a project that results in a merged PR qualifies for this\n list. The supervision must be active, i.e. not primarily done by the\n Core developers.\n - Having an idea for a contribution does not count towards any contributor\n status. There must be active supervision of the person(s) implementing\n the idea, such as advice on debugging, how to best implement the idea,\n etc. The supervision is what will be counted for contributor status.\n Generally, a paper is written where the person who came up with the idea\n is a co-author, which is how credit is given for the idea. An example is\n suggesting \"We should try reconstruction scheme X\" without continued\n guidance throughout the implementation process would not be counted for\n contributor status.\n\n This author list is ordered by last name.\n List:\n - Name: Anantpurkar, Isha\n Orcid: 0000-0002-5814-4109\n Affiliations: [*cornell]\n GitHub: isha1810\n - Name: Anderson, Carter\n Orcid: 0009-0009-0359-6763\n Affiliations: [*caltech]\n GitHub: ctrandrsn\n - Name: Boyle, Michael\n Orcid: 0000-0002-5075-5116\n Affiliations: [*cornell]\n GitHub: moble\n - Name: Carpenter, Alexander\n Orcid: 0000-0002-9183-8006\n Affiliations: [*fullerton]\n GitHub: AlexCarpenter46\n - Name: Ceja, Andrea\n Orcid: 0000-0002-1681-7299\n Affiliations: [*fullerton]\n GitHub: acifajkya\n - Name: Chaudhary, Himanshu\n Orcid: 0000-0002-4101-0534\n Affiliations: [*caltech]\n GitHub: GitHimanshuc\n - Name: Corso, Nicholas\n Orcid: 0000-0002-0088-2563\n Affiliations: [*cornell]\n GitHub: ncorsobh\n - Name: Dittmer, Clemens\n Orcid: 0009-0007-3833-9252\n Affiliations: [*aei]\n GitHub: clemensdittmer\n - Name: Fayyazuddin Ljungberg, Nora\n Orcid: 0000-0002-7074-4545\n Affiliations: [*cornell]\n GitHub: norafl\n - Name: Foucart, Francois\n Orcid: 0000-0003-4617-4738\n Affiliations: [*new_hampshire]\n GitHub: ffoucart\n - Name: Ghadiri, Noora\n Orcid: 0000-0001-9162-4449\n Affiliations: [*fullerton]\n GitHub: noora-gn\n - Name: Giesler, Matthew\n Orcid: 0000-0003-2300-893X\n Affiliations: [*cornell]\n GitHub: mgiesler\n - Name: Guo, Jason S.\n Affiliations: [*cornell]\n GitHub: erfz\n - Name: Habib, Sarah\n Orcid: 0000-0002-4725-4978\n Affiliations: [*caltech]\n GitHub: shabibti\n - Name: Huang, Chenhang\n Orcid: 0000-0003-2617-1011\n Affiliations: [*cornell]\n GitHub: hen-w\n - Name: Iozzo, Dante A. B.\n Orcid: 0000-0002-7244-1900\n Affiliations: [*cornell]\n GitHub: \"10220\"\n - Name: Jones, Ken Z.\n Orcid: 0009-0003-1034-0498\n Affiliations: [*fullerton]\n GitHub: \"kenzenjones\"\n - Name: Lara, Guillermo\n Orcid: 0000-0001-9461-6292\n Affiliations: [*aei]\n GitHub: guilara\n - Name: Legred, Isaac\n Orcid: 0000-0002-9523-9617\n Affiliations: [*caltech]\n GitHub: isaaclegred\n - Name: Li, Dongjun\n Orcid: 0000-0002-1962-680X\n Affiliations: [*caltech]\n GitHub: dongjun826\n - Name: Ma, Sizheng\n Orcid: 0000-0002-4645-453X\n Affiliations: [*caltech]\n GitHub: Sizheng-Ma\n - Name: Melchor, Denyz\n Orcid: 0000-0002-7854-1953\n Affiliations: [*fullerton]\n GitHub: denyzamelchor\n - Name: Mendes, Iago\n Orcid: 0009-0007-9845-8448\n Affiliations: [*caltech, *oberlin]\n GitHub: iago-mendes\n - Name: Morales, Marlo\n Orcid: 0000-0002-0593-4318\n Affiliations: [*fullerton]\n GitHub: MarloMo\n - Name: Most, Elias R.\n Orcid: 0000-0002-0491-1210\n Affiliations: [*caltech]\n GitHub: ermost\n - Name: Murphy, Michael\n Orcid: 0000-0003-3865-3034\n Affiliations: [*cornell]\n GitHub: michaeldmurphy1\n - Name: Nee, Peter James\n Orcid: 0000-0002-2362-5420\n Affiliations: [*aei]\n GitHub: PunJustice\n - Name: Nishimura, Nami\n Orcid: 0009-0002-4398-9130\n Affiliations: [*aei]\n GitHub: NamiNishimura73\n - Name: Osorio, Alejandro\n Orcid: 0009-0000-5024-0086\n Affiliations: [*fullerton]\n GitHub: ajosorio3\n - Name: Pajkos, Michael A.\n Orcid: 0000-0002-4983-4589\n Affiliations: [*caltech]\n GitHub: pajkosmi\n - Name: Pannone, Kyle\n Orcid: 0009-0005-8607-2113\n Affiliations: [*fullerton]\n GitHub: Bronoulli\n - Name: Pineda, Jose Maria\n Orcid: 0009-0007-6694-8434\n Affiliations: [*fullerton]\n GitHub: JosePineda684\n - Name: Prasad, Vaishak\n Orcid: 0000-0001-6712-2457\n Affiliations: [*icts]\n GitHub: vaishakp\n - Name: Ramirez, Teresita\n Orcid: 0000-0003-0994-115X\n Affiliations: [*fullerton]\n GitHub: trami18\n - Name: Ring, Noah\n Orcid: 0000-0001-6510-4300\n Affiliations: [*cornell]\n GitHub: nring21\n - Name: Rüter, Hannes R.\n Orcid: 0000-0002-3442-5360\n Affiliations: [*coimbra]\n GitHub: hrueter\n - Name: Sanchez, Jennifer\n Orcid: 0000-0002-5335-4924\n Affiliations: [*fullerton]\n GitHub: jennifersanchez\n - Name: Stein, Leo C.\n Orcid: 0000-0001-7559-9597\n Affiliations: [*umiss]\n GitHub: duetosymmetry\n - Name: Tellez, Daniel\n Orcid: 0009-0008-7784-2528\n Affiliations: [*fullerton]\n GitHub: daniel20tellez\n - Name: Thomas, Sierra\n Orcid: 0000-0003-3574-2090\n Affiliations: [*fullerton]\n GitHub: sierracthomas\n - Name: Tommasini, Vittoria\n Orcid: 0009-0001-4440-9751\n Affiliations: [*caltech]\n GitHub: vtommasini\n - Name: Vieira, Daniel\n Orcid: 0000-0001-8019-0390\n Affiliations: [*cornell, *koln]\n GitHub: dkvieira\n - Name: Wang, Xiyue\n Orcid: 0009-0006-3331-0832\n Affiliations: [*caltech]\n GitHub: EmilyWang0130\n - Name: Wlodarczyk, Tom\n Orcid: 0000-0003-0005-348X\n Affiliations: [*aei]\n GitHub: tomwlodarczyk\n - Name: Wu, David\n Orcid: 0000-0002-5287-4389\n Affiliations: [*cornell]\n GitHub: DavidWu421\n - Name: Yoo, Jooheon\n Orcid: 0000-0002-3251-0924\n Affiliations: [*cornell]\n GitHub: jyoo1042\n\nReferences:\n Description: |\n SpECTRE depends on these references. The keys refer to entries in the\n 'BibliographyFile'. We use BibTeX for our references so we can also cite\n them in publications.\n BibliographyFile: docs/Dependencies.bib\n List:\n - Blaze1\n - Blaze2\n - Charmpp1\n - Charmpp2\n - Charmpp3\n - Gsl\n - Hdf5\n - Libsharp\n - Libxsmm\n - MatplotLib1\n - MatplotLib2\n - NumPy\n - Paraview1\n - Paraview2\n - Pybind11\n - Yamlcpp\n" }, { "path": "README.md", "content": "[//]: # (Distributed under the MIT License.)\n[//]: # (See LICENSE.txt for details.)\n\n[![license](https://img.shields.io/badge/license-MIT-blue.svg)](https://github.com/sxs-collaboration/spectre/blob/develop/LICENSE.txt)\n[![Standard](https://img.shields.io/badge/c%2B%2B-20-blue.svg)](https://en.wikipedia.org/wiki/C%2B%2B#Standardization)\n[![Build Status](https://github.com/sxs-collaboration/spectre/workflows/Tests/badge.svg?branch=develop)](https://github.com/sxs-collaboration/spectre/actions)\n[![codecov](https://codecov.io/gh/sxs-collaboration/spectre/graph/badge.svg?token=yyJ3uBPUE2)](https://codecov.io/gh/sxs-collaboration/spectre)\n[![release](https://img.shields.io/badge/release-v2026.04.01-informational)](https://github.com/sxs-collaboration/spectre/releases/tag/v2026.04.01)\n[![DOI](https://zenodo.org/badge/doi/10.5281/zenodo.19373346.svg)](https://doi.org/10.5281/zenodo.19373346)\n\n![banner](docs/Images/banner.png)\n\n## What is SpECTRE?\n\nSpECTRE is an open-source code for multi-scale, multi-physics problems in\nastrophysics and gravitational physics. It is based on high-order spectral\nfinite element methods and massive parallelism. In the future, we hope that\nit can be applied to problems across discipline boundaries in fluid\ndynamics, geoscience, plasma physics, nuclear physics, and\nengineering. It runs at petascale and is designed for future exascale\ncomputers.\n\nSpECTRE is being developed in support of our collaborative Simulating\neXtreme Spacetimes (SXS) research program into the multi-messenger\nastrophysics of black hole and neutron star mergers, core-collapse supernovae,\nand gamma-ray bursts.\n\n## Gallery\n\nFor an overview of some of SpECTRE's features and some simulations performed\nwith SpECTRE, visit the gallery:\n\n- Gallery: https://spectre-code.org/gallery\n\n## Documentation\n\nYou find instructions on installing and running the code, as well as many guides\nand tutorials, in the documentation:\n\n- Documentation: https://spectre-code.org/\n\n## Citing SpECTRE\n\nPlease cite SpECTRE in any publications that make use of its code or data. Cite\nthe latest version that you use in your publication. The DOI for this version\nis:\n\n- DOI: [10.5281/zenodo.19373346](https://doi.org/10.5281/zenodo.19373346)\n\nYou can cite this BibTeX entry in your publication:\n\n\n\n```bib\n@software{spectrecode,\n author = \"Deppe, Nils and Throwe, William and Kidder, Lawrence E. and Vu,\nNils L. and Nelli, Kyle C. and Armaza, Crist\\'obal and Bonilla, Marceline S. and\nH\\'ebert, Fran\\c{c}ois and Kim, Yoonsoo and Kumar, Prayush and Lovelace,\nGeoffrey and Macedo, Alexandra and Moxon, Jordan and O'Shea, Eamonn and\nPfeiffer, Harald P. and Scheel, Mark A. and Teukolsky, Saul A. and Wittek,\nNikolas A. and others\",\n title = \"\\texttt{SpECTRE v2026.04.01}\",\n version = \"2026.04.01\",\n publisher = \"Zenodo\",\n doi = \"10.5281/zenodo.19373346\",\n url = \"https://spectre-code.org\",\n howpublished =\n\"\\href{https://doi.org/10.5281/zenodo.19373346}{10.5281/zenodo.19373346}\",\n license = \"MIT\",\n year = \"2026\",\n month = \"4\"\n}\n```\n\n\nTo aid reproducibility of your scientific results with SpECTRE, we recommend you\nkeep track of the version(s) you used and report this information in your\npublication. We also recommend you supply the YAML input files and, if\nappropriate, any additional C++ code you wrote to compile SpECTRE executables as\nsupplemental material to the publication.\n\nSee our [publication policy](https://spectre-code.org/publication_policies.html)\nfor more information.\n\n## Logos and visuals\n\nYou can find logos and other visuals (e.g. to put on slides) in various formats,\ncolors, and sizes here:\n\n- [Logos and visuals](https://drive.google.com/drive/folders/1GEvVrXNqlGojr3NBf7RMFo6BzFmf9Ww7?usp=share_link)\n" }, { "path": "citation.bib", "content": "@software{spectrecode,\n author = \"Deppe, Nils and Throwe, William and Kidder, Lawrence E. and Vu,\nNils L. and Nelli, Kyle C. and Armaza, Crist\\'obal and Bonilla, Marceline S. and\nH\\'ebert, Fran\\c{c}ois and Kim, Yoonsoo and Kumar, Prayush and Lovelace,\nGeoffrey and Macedo, Alexandra and Moxon, Jordan and O'Shea, Eamonn and\nPfeiffer, Harald P. and Scheel, Mark A. and Teukolsky, Saul A. and Wittek,\nNikolas A. and others\",\n title = \"\\texttt{SpECTRE v2026.04.01}\",\n version = \"2026.04.01\",\n publisher = \"Zenodo\",\n doi = \"10.5281/zenodo.19373346\",\n url = \"https://spectre-code.org\",\n howpublished =\n\"\\href{https://doi.org/10.5281/zenodo.19373346}{10.5281/zenodo.19373346}\",\n license = \"MIT\",\n year = \"2026\",\n month = \"4\"\n}\n" }, { "path": "cmake/AddCxxFlag.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Have to compile a file (can be empty) to check for flags.\n# Kokkos' nvcc_wrapper doesn't support taking the file as stdin, so we\n# have to write it to a file.\nset(_CHECK_CXX_FLAGS_SOURCE \"${CMAKE_BINARY_DIR}/CMakeFiles/CheckCxxFlags.cpp\")\nwrite_file(${_CHECK_CXX_FLAGS_SOURCE} \"\")\n\n# Checks if a flag is supported by the compiler and creates the target\n# TARGET_NAME whose INTERFACE_COMPILE_OPTIONS are set to the FLAG_TO_CHECK\n# - LANGUAGE: language to check, setting the compiler and generated property\n# - XTYPE: language as passed to the -x compiler flag\n# - FLAG_TO_CHECK: the CXX flag to add if the compiler supports it\n# - TARGET_NAME: the name of the target whose INTERFACE_COMPILE_OPTIONS are\n# set\nfunction(create_compile_flag_target LANGUAGE XTYPE FLAG_TO_CHECK TARGET_NAME)\n # In order to check for a -Wno-* flag in gcc, you have to check the\n # -W* version instead. See http://gcc.gnu.org/wiki/FAQ#wnowarning\n string(REGEX REPLACE ^-Wno- -W POSITIVE_FLAG_TO_CHECK ${FLAG_TO_CHECK})\n # Escape quotes for compiler command\n string(REPLACE \"\\\"\" \"\\\\\\\"\" POSITIVE_FLAG_TO_CHECK ${POSITIVE_FLAG_TO_CHECK})\n execute_process(\n COMMAND\n bash -c\n \"LC_ALL=POSIX ${CMAKE_${LANGUAGE}_COMPILER} -Werror \\\n${POSITIVE_FLAG_TO_CHECK} -x ${XTYPE} \\\n-c ${_CHECK_CXX_FLAGS_SOURCE} -o /dev/null\"\n RESULT_VARIABLE RESULT\n ERROR_VARIABLE ERROR_FROM_COMPILATION\n OUTPUT_QUIET)\n if(NOT TARGET ${TARGET_NAME})\n add_library(${TARGET_NAME} INTERFACE)\n endif(NOT TARGET ${TARGET_NAME})\n if(${RESULT} EQUAL 0)\n string(REPLACE \" \" \";\" FLAG_TO_CHECK ${FLAG_TO_CHECK})\n set_property(TARGET ${TARGET_NAME}\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$:${FLAG_TO_CHECK}>)\n endif(${RESULT} EQUAL 0)\nendfunction()\n\n# Checks if a CXX flag is supported by the compiler and creates the target\n# TARGET_NAME whose INTERFACE_COMPILE_OPTIONS are set to the FLAG_TO_CHECK\n# - FLAG_TO_CHECK: the CXX flag to add if the compiler supports it\n# - TARGET_NAME: the name of the target whose INTERFACE_COMPILE_OPTIONS are\n# set\nfunction(create_cxx_flag_target FLAG_TO_CHECK TARGET_NAME)\n create_compile_flag_target(CXX c++ \"${FLAG_TO_CHECK}\" \"${TARGET_NAME}\")\nendfunction()\n\n# Same, but for C.\nfunction(create_c_flag_target FLAG_TO_CHECK TARGET_NAME)\n create_compile_flag_target(C c \"${FLAG_TO_CHECK}\" \"${TARGET_NAME}\")\nendfunction()\n\n# Checks which of the CXX FLAGS_TO_CHECK are supported by the compiler\n# and creates the target TARGET_NAME whose INTERFACE_COMPILE_OPTIONS\n# are set to the FLAGS_TO_CHECK that are supported. If adding many flags,\n# this will be much faster than calling create_cxx_flags_target multiple times.\n# - LANGUAGE: language to check, setting the compiler and generated property\n# - XTYPE: language as passed to the -x compiler flag\n# - FLAGS_TO_CHECK: a semicolon separated string of CXX flags to try to add\n# for compilation.\n# - TARGET_NAME: the name of the target whose INTERFACE_COMPILE_OPTIONS are\n# set\nfunction(create_compile_flags_target LANGUAGE XTYPE FLAGS_TO_CHECK TARGET_NAME)\n # In order to check for a -Wno-* flag in gcc, you have to check the\n # -W* version instead. See http://gcc.gnu.org/wiki/FAQ#wnowarning\n set(POSITIVE_FLAGS_TO_CHECK)\n foreach(FLAG_TO_CHECK ${FLAGS_TO_CHECK})\n string(REGEX REPLACE ^-Wno- -W POSITIVE_FLAG_TO_CHECK ${FLAG_TO_CHECK})\n list(APPEND POSITIVE_FLAGS_TO_CHECK ${POSITIVE_FLAG_TO_CHECK})\n endforeach()\n string(REPLACE \";\" \" \"\n POSITIVE_FLAGS_WITH_SPACES \"${POSITIVE_FLAGS_TO_CHECK}\")\n execute_process(\n COMMAND\n bash -c\n \"LC_ALL=POSIX ${CMAKE_${LANGUAGE}_COMPILER} -Werror \\\n${POSITIVE_FLAGS_WITH_SPACES} -x ${XTYPE} \\\n-c ${_CHECK_CXX_FLAGS_SOURCE} -o /dev/null\"\n RESULT_VARIABLE RESULT\n ERROR_VARIABLE ERROR_FROM_COMPILATION\n OUTPUT_QUIET)\n\n if(NOT TARGET ${TARGET_NAME})\n add_library(${TARGET_NAME} INTERFACE)\n endif(NOT TARGET ${TARGET_NAME})\n if(${RESULT} EQUAL 0)\n set_property(TARGET ${TARGET_NAME}\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$:${FLAGS_TO_CHECK}>)\n else(${RESULT} EQUAL 0)\n # Check each flag to see if it was marked as \"invalid\" in the output\n unset(FLAGS_TO_ADD)\n foreach(FLAG ${POSITIVE_FLAGS_TO_CHECK})\n string(FIND \"${ERROR_FROM_COMPILATION}\" \"'${FLAG}'\" FOUND_POS)\n if(${FOUND_POS} EQUAL -1)\n # For some reason:\n # list(FIND ${POSITIVE_FLAGS_TO_CHECK} ${FLAG} INDEX_OF_FLAG)\n # doesn't work with some compilers. This makes no sense but such is\n # life. As a work around we basically implement a find manually.\n\n # Find the index of the current flag in the POSITIVE_FLAGS_TO_CHECK\n # list. This is the index we use to get the original flag in the\n # FLAGS_TO_CHECK list.\n set(INDEX 0)\n foreach(POS_FLAG ${POSITIVE_FLAGS_TO_CHECK})\n if(\"${POS_FLAG}\" STREQUAL \"${FLAG}\")\n break()\n endif()\n MATH(EXPR INDEX \"${INDEX}+1\")\n endforeach()\n set(TARGET_INDEX ${INDEX})\n set(INDEX 0)\n # Get original flag\n set(NEW_FLAG \"\")\n foreach(ORIGINAL_FLAG ${FLAGS_TO_CHECK})\n if(${INDEX} EQUAL ${TARGET_INDEX})\n set(NEW_FLAG ${ORIGINAL_FLAG})\n break()\n endif()\n MATH(EXPR INDEX \"${INDEX}+1\")\n endforeach()\n # Add the flag to the list of flags to add.\n set(FLAGS_TO_ADD \"${FLAGS_TO_ADD};${NEW_FLAG}\")\n endif(${FOUND_POS} EQUAL -1)\n endforeach(FLAG ${FLAGS_TO_CHECK})\n set_property(TARGET ${TARGET_NAME}\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$:${FLAGS_TO_ADD}>)\n\n endif(${RESULT} EQUAL 0)\nendfunction()\n\n# Checks which of the CXX FLAGS_TO_CHECK are supported by the compiler\n# and creates the target TARGET_NAME whose INTERFACE_COMPILE_OPTIONS\n# are set to the FLAGS_TO_CHECK that are supported. If adding many flags,\n# this will be much faster than calling create_cxx_flags_target multiple times.\n# - FLAGS_TO_CHECK: a semicolon separated string of CXX flags to try to add\n# for compilation.\n# - TARGET_NAME: the name of the target whose INTERFACE_COMPILE_OPTIONS are\n# set\nfunction(create_cxx_flags_target FLAGS_TO_CHECK TARGET_NAME)\n create_compile_flags_target(CXX c++ \"${FLAGS_TO_CHECK}\" \"${TARGET_NAME}\")\nendfunction()\n\n# Same, but for C.\nfunction(create_c_flags_target FLAGS_TO_CHECK TARGET_NAME)\n create_compile_flags_target(C c \"${FLAGS_TO_CHECK}\" \"${TARGET_NAME}\")\nendfunction()\n\nset(CMAKE_SUPPORTS_LINK_OPTIONS OFF)\nif(CMAKE_VERSION VERSION_EQUAL 3.13 OR CMAKE_VERSION VERSION_GREATER 3.13)\n set(CMAKE_SUPPORTS_LINK_OPTIONS ON)\nendif(CMAKE_VERSION VERSION_EQUAL 3.13 OR CMAKE_VERSION VERSION_GREATER 3.13)\n\nif(CMAKE_SUPPORTS_LINK_OPTIONS)\n # Creates a target named TARGET_NAME that, if the linker flag FLAG_TO_CHECK\n # is supported, defines ${FLAG_TO_CHECK} as an INTERFACE_LINK_OPTION\n function(create_cxx_link_flag_target FLAG_TO_CHECK TARGET_NAME)\n include(CheckLinkerFlag)\n unset(CXX_LINKER_FLAG_WORKS CACHE)\n set(CMAKE_REQUIRED_QUIET 1)\n check_linker_flag(CXX ${FLAG_TO_CHECK} CXX_LINKER_FLAG_WORKS)\n unset(CMAKE_REQUIRED_QUIET)\n\n add_library(${TARGET_NAME} INTERFACE)\n if(CXX_LINKER_FLAG_WORKS)\n set_property(TARGET ${TARGET_NAME}\n APPEND PROPERTY\n INTERFACE_LINK_OPTIONS $<$:${FLAG_TO_CHECK}>)\n endif()\n endfunction()\nendif(CMAKE_SUPPORTS_LINK_OPTIONS)\n\n# Checks if a flag is supported by the linker and adds it if it is\nfunction(check_and_add_cxx_link_flag FLAG_TO_CHECK)\n include(CheckLinkerFlag)\n unset(CXX_LINKER_FLAG_WORKS CACHE)\n set(CMAKE_REQUIRED_QUIET 1)\n check_linker_flag(CXX ${FLAG_TO_CHECK} CXX_LINKER_FLAG_WORKS)\n unset(CMAKE_REQUIRED_QUIET)\n if(CXX_LINKER_FLAG_WORKS)\n set(CMAKE_CXX_LINK_FLAGS\n \"${CMAKE_CXX_LINK_FLAGS} ${FLAG_TO_CHECK}\" PARENT_SCOPE)\n endif()\nendfunction()\n" }, { "path": "cmake/AddInputFileTests.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nspectre_define_test_timeout_factor_option(INPUT_FILE \"input file\")\n\noption(SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY \"Minimum priority of input file \\\ntests to run. Possible values are: low (not usually run on CI), normal \\\n(run at least once on CI), high (run always on CI).\" \"normal\")\n\n# Convert priority string to a number.\nif (NOT SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY)\n set(SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY \"normal\")\nendif()\nstring(TOLOWER \"${SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY}\"\n SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY)\nif (${SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY} STREQUAL \"high\")\n set(SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY 1)\nelseif (${SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY} STREQUAL \"normal\")\n set(SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY 0)\nelseif (${SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY} STREQUAL \"low\")\n set(SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY -1)\nelse()\n message(FATAL_ERROR \"Unknown priority in option \"\n \"SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY: \"\n \"${SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY}. \"\n \"Possible values are: high, normal, low\")\nendif()\n\n# Environment variables for test\nset(_INPUT_FILE_TEST_ENV_VARS \"\")\n# - Disable ASAN's leak sanitizer because Charm++ has false positives\nlist(APPEND _INPUT_FILE_TEST_ENV_VARS \"ASAN_OPTIONS=detect_leaks=0\")\n# - Set PYTHONPATH to find Python modules\nlist(APPEND _INPUT_FILE_TEST_ENV_VARS \"PYTHONPATH=${PYTHONPATH}\")\n\nfunction(add_single_input_file_test)\n cmake_parse_arguments(\n ARG \"\"\n \"INPUT_FILE;EXECUTABLE;CHECK_TYPE;TIMEOUT\"\n \"COMMAND_LINE_ARGS;EXPECTED_EXIT_CODE;COPY_FILES\"\n ${ARGN})\n # Extract just the name of the input file\n get_filename_component(INPUT_FILE_NAME \"${INPUT_FILE}\" NAME)\n get_filename_component(INPUT_FILE_DIR \"${INPUT_FILE}\" DIRECTORY)\n\n # Extract the main subdirectory name\n string(FIND \"${ARG_INPUT_FILE}\" \"tests/InputFiles/\"\n POSITION_OF_INPUT_FILE_DIR)\n math(EXPR\n POSITION_OF_INPUT_FILE_DIR\n ${POSITION_OF_INPUT_FILE_DIR}+17\n # 17 is the length of \"tests/InputFiles/\"\n )\n string(SUBSTRING \"${ARG_INPUT_FILE}\" ${POSITION_OF_INPUT_FILE_DIR}\n -1 TEMP)\n string(FIND \"${TEMP}\" \"/\" POSITION_OF_SLASH)\n string(SUBSTRING \"${TEMP}\" 0 ${POSITION_OF_SLASH}\n EXECUTABLE_DIR_NAME)\n\n # Set tags for the test\n set(TAGS \"InputFiles;${EXECUTABLE_DIR_NAME};${ARG_CHECK_TYPE}\")\n string(TOLOWER \"${TAGS}\" TAGS)\n # Add the executable name as label, without converting to lower case. This\n # allows running all input file tests for a particular executable.\n list(APPEND TAGS ${ARG_EXECUTABLE})\n\n set(\n CTEST_NAME\n \"InputFiles.${EXECUTABLE_DIR_NAME}.${INPUT_FILE_NAME}.${ARG_CHECK_TYPE}\"\n )\n set(\n RUN_DIRECTORY\n \"${EXECUTABLE_DIR_NAME}.${INPUT_FILE_NAME}.${ARG_CHECK_TYPE}\"\n )\n if(\"${ARG_CHECK_TYPE}\" STREQUAL \"execute_check_output\")\n set(_CHECK_OUTPUT_FILES \"true\")\n else()\n set(_CHECK_OUTPUT_FILES \"false\")\n endif()\n\n if (\"${ARG_CHECK_TYPE}\" STREQUAL \"parse\")\n add_test(\n NAME ${CTEST_NAME}\n # This script is written below, and only once\n COMMAND sh\n ${PROJECT_BINARY_DIR}/tmp/RunInputFileTest.sh ${ARG_EXECUTABLE}\n ${ARG_INPUT_FILE} ${RUN_DIRECTORY} 0 false false\n \"${ARG_COMMAND_LINE_ARGS} --check-options\"\n \"${ARG_COPY_FILES}\"\n )\n elseif(\"${ARG_CHECK_TYPE}\" STREQUAL \"execute\" OR\n \"${ARG_CHECK_TYPE}\" STREQUAL \"execute_check_output\")\n add_test(\n NAME ${CTEST_NAME}\n # This script is written below, and only once\n COMMAND sh ${PROJECT_BINARY_DIR}/tmp/RunInputFileTest.sh\n ${ARG_EXECUTABLE} ${ARG_INPUT_FILE} ${RUN_DIRECTORY}\n ${ARG_EXPECTED_EXIT_CODE} ${_CHECK_OUTPUT_FILES} true\n \"${ARG_COMMAND_LINE_ARGS}\"\n \"${ARG_COPY_FILES}\"\n )\n else()\n message(FATAL_ERROR \"Unknown check for input file: ${ARG_CHECK_TYPE}.\"\n \"Known checks are: execute\")\n endif()\n\n # Increase timeout if address sanitizer is enabled.\n if (ASAN)\n math(EXPR TIMEOUT \"4 * ${ARG_TIMEOUT}\")\n else()\n set(TIMEOUT ${ARG_TIMEOUT})\n endif()\n\n spectre_test_timeout(TIMEOUT ARG_INPUT_FILE ${TIMEOUT})\n\n set_tests_properties(\n ${CTEST_NAME}\n PROPERTIES\n TIMEOUT ${TIMEOUT}\n LABELS \"${TAGS}\"\n ENVIRONMENT \"${_INPUT_FILE_TEST_ENV_VARS}\")\nendfunction()\n\n# Searches the directory INPUT_FILE_DIR for .yaml files and adds a test for each\n# one. See `WritingTests.md` for details on controlling input file tests. Add\n# input files to the whitelist at the bottom of this file to ignore those tests\nfunction(add_input_file_tests INPUT_FILE_DIR INPUT_FILE_WHITELIST)\n set(INPUT_FILE_LIST \"\")\n file(GLOB_RECURSE INPUT_FILE_LIST ${INPUT_FILE_DIR} \"${INPUT_FILE_DIR}*.yaml\")\n set(TIMEOUT 2)\n list(TRANSFORM INPUT_FILE_WHITELIST PREPEND ${INPUT_FILE_DIR})\n\n foreach(INPUT_FILE ${INPUT_FILE_LIST})\n # Only parse the input file if we are allowed to\n if (${INPUT_FILE} IN_LIST INPUT_FILE_WHITELIST)\n continue()\n endif()\n if (INPUT_FILE MATCHES \"\\\\.overlay_[0-9]*\\\\.yaml$\")\n continue()\n endif()\n\n file(READ ${INPUT_FILE} INPUT_FILE_CONTENTS)\n\n # Read the priority of the test specified in input file, empty is accepted.\n string(REGEX MATCH \"Priority:[^\\n]+\"\n INPUT_FILE_PRIORITY \"${INPUT_FILE_CONTENTS}\")\n if(\"${INPUT_FILE_PRIORITY}\" STREQUAL \"\")\n set(INPUT_FILE_PRIORITY \"normal\")\n else()\n string(REGEX REPLACE \"Priority:[ ]*\" \"\"\n INPUT_FILE_PRIORITY \"${INPUT_FILE_PRIORITY}\")\n string(STRIP \"${INPUT_FILE_PRIORITY}\" INPUT_FILE_PRIORITY)\n endif()\n # Translate strings to numbers\n string(TOLOWER \"${INPUT_FILE_PRIORITY}\" INPUT_FILE_PRIORITY)\n if (${INPUT_FILE_PRIORITY} STREQUAL \"high\")\n set(INPUT_FILE_PRIORITY 1)\n elseif (${INPUT_FILE_PRIORITY} STREQUAL \"normal\")\n set(INPUT_FILE_PRIORITY 0)\n elseif (${INPUT_FILE_PRIORITY} STREQUAL \"low\")\n set(INPUT_FILE_PRIORITY -1)\n else()\n message(FATAL_ERROR \"Unknown priority in input file ${INPUT_FILE}: \"\n \"${INPUT_FILE_PRIORITY}. Possible values are: high, normal, low\")\n endif()\n\n # Only add tests with at least the priority specified in\n # `SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY`\n if (${INPUT_FILE_PRIORITY} LESS\n ${SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY})\n continue()\n endif()\n\n # Check if the executable name is present\n string(REGEX MATCH \"Executable:[^\\n]+\"\n INPUT_FILE_EXECUTABLE \"${INPUT_FILE_CONTENTS}\")\n if(\"${INPUT_FILE_EXECUTABLE}\" STREQUAL \"\")\n message(FATAL_ERROR \"Could not find the executable in input \"\n \"file ${INPUT_FILE}. You must supply a line of the form:\"\n \"'Executable: EXECUTABLE_NAME'\")\n endif()\n # Extract executable name, and remove trailing white space\n string(REGEX REPLACE \"Executable:[ ]*\" \"\"\n INPUT_FILE_EXECUTABLE \"${INPUT_FILE_EXECUTABLE}\")\n string(STRIP \"${INPUT_FILE_EXECUTABLE}\" INPUT_FILE_EXECUTABLE)\n\n string(REGEX MATCH \"CommandLineArgs:[^\\n]+\"\n COMMAND_LINE_ARGS \"${INPUT_FILE_CONTENTS}\")\n string(REGEX REPLACE \"CommandLineArgs:[ ]*\" \"\"\n COMMAND_LINE_ARGS \"${COMMAND_LINE_ARGS}\")\n string(STRIP \"${COMMAND_LINE_ARGS}\" COMMAND_LINE_ARGS)\n\n string(REGEX MATCH \"ExpectedExitCode:[^\\n]+\"\n EXPECTED_EXIT_CODE \"${INPUT_FILE_CONTENTS}\")\n string(REGEX REPLACE \"ExpectedExitCode:[ ]*\" \"\"\n EXPECTED_EXIT_CODE \"${EXPECTED_EXIT_CODE}\")\n string(STRIP \"${EXPECTED_EXIT_CODE}\" EXPECTED_EXIT_CODE)\n if(\"${EXPECTED_EXIT_CODE}\" STREQUAL \"\")\n set(EXPECTED_EXIT_CODE \"0\")\n endif()\n\n # Read what tests to do. Currently \"execute\" and \"parse\" are available.\n string(REGEX MATCH \"Check:[^\\n]+\"\n INPUT_FILE_CHECKS \"${INPUT_FILE_CONTENTS}\")\n # Extract list of checks to perform\n string(REGEX REPLACE \"Check:[ ]*\" \"\"\n INPUT_FILE_CHECKS \"${INPUT_FILE_CHECKS}\")\n string(STRIP \"${INPUT_FILE_CHECKS}\" INPUT_FILE_CHECKS)\n set(INPUT_FILE_CHECKS \"${INPUT_FILE_CHECKS}\")\n list(REMOVE_DUPLICATES \"INPUT_FILE_CHECKS\")\n # Convert all the checks to lower case to make life easier.\n string(TOLOWER \"${INPUT_FILE_CHECKS}\" INPUT_FILE_CHECKS)\n\n # Make sure that the 'parse' check is listed. If not, print an\n # error message that explains that it's needed and why.\n list(FIND \"INPUT_FILE_CHECKS\" \"parse\" FOUND_PARSE)\n if (${FOUND_PARSE} EQUAL -1)\n message(FATAL_ERROR\n \"The input file: \"\n \"'${INPUT_FILE}' \"\n \"does not specify the 'parse' check. All input file tests must\"\n \" specify the 'parse' check which runs the executable passing\"\n \" the '--check-options' flag. With this flag the executable\"\n \" should check that the input file parses correctly and that\"\n \" the values specified in the input file do not violate any\"\n \" bounds or sanity checks.\")\n endif (${FOUND_PARSE} EQUAL -1)\n\n # Read the timeout duration specified in input file, empty is accepted.\n # The default duration is 2 seconds.\n string(REGEX MATCH \"Timeout:[^\\n]+\"\n INPUT_FILE_TIMEOUT \"${INPUT_FILE_CONTENTS}\")\n if(\"${INPUT_FILE_TIMEOUT}\" STREQUAL \"\")\n set(INPUT_FILE_TIMEOUT \"${TIMEOUT}\")\n else()\n string(REGEX REPLACE \"Timeout:[ ]*\" \"\"\n INPUT_FILE_TIMEOUT \"${INPUT_FILE_TIMEOUT}\")\n string(STRIP \"${INPUT_FILE_TIMEOUT}\" INPUT_FILE_TIMEOUT)\n endif()\n\n # Read out the semicolon list of files to copy to the run directory.\n # The files are currently restricted to being in the same location\n # as the input file. This can be relaxed if necessary.\n set(COPY_FILES \"\")\n string(REGEX MATCH \"CopyFiles:[^\\n]+\"\n COPY_FILES \"${INPUT_FILE_CONTENTS}\")\n if(NOT \"${COPY_FILES}\" STREQUAL \"\")\n string(REPLACE \"CopyFiles: \" \"\" COPY_FILES ${COPY_FILES})\n string(REPLACE \"CopyFiles:\" \"\" COPY_FILES ${COPY_FILES})\n endif()\n\n foreach(CHECK_TYPE ${INPUT_FILE_CHECKS})\n add_single_input_file_test(\n INPUT_FILE ${INPUT_FILE}\n EXECUTABLE ${INPUT_FILE_EXECUTABLE}\n COMMAND_LINE_ARGS \"${COMMAND_LINE_ARGS}\"\n CHECK_TYPE ${CHECK_TYPE}\n TIMEOUT ${INPUT_FILE_TIMEOUT}\n EXPECTED_EXIT_CODE ${EXPECTED_EXIT_CODE}\n COPY_FILES \"${COPY_FILES}\"\n )\n endforeach()\n add_dependencies(test-executables ${INPUT_FILE_EXECUTABLE})\n endforeach()\nendfunction()\n\n# Dependencies will be added as the tests are processed.\nadd_custom_target(test-executables)\n\n# Write command to execute an input file and clean its output into a shell\n# script, which makes it easier to chain multiple commands\nconfigure_file(\n ${CMAKE_SOURCE_DIR}/cmake/RunInputFileTest.sh\n ${PROJECT_BINARY_DIR}/tmp/RunInputFileTest.sh\n @ONLY)\n\n# These paths should be relative to the input file directory passed to\n# `add_input_file_tests`\nset(INPUT_FILE_WHITELIST\n \"PreprocessCceWorldtube/PreprocessCceWorldtube.yaml\"\n \"PreprocessCceWorldtube/AdmFirstOrderDriverPreprocessCceWorldtube.yaml\"\n \"PreprocessCceWorldtube/AdmSecondOrderDriverPreprocessCceWorldtube.yaml\")\n\nadd_input_file_tests(\"${CMAKE_SOURCE_DIR}/tests/InputFiles/\" \"${INPUT_FILE_WHITELIST}\")\n" }, { "path": "cmake/AddSpectreExecutable.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Adds an executable by wrapping CMake's 'add_executable' but allows\n# us to inject dependencies, flags, etc. into the targets.\nfunction(add_spectre_executable TARGET_NAME)\n add_executable(${TARGET_NAME} ${ARGN})\n # We need to link custom allocators before we link anything else so that\n # any third-party libraries, which generally should all be built as shared\n # libraries, use the allocator that we use. Unfortunately, how exactly\n # CMake decides on the linking order is not clear when using\n # INTERFACE_LINK_LIBRARIES and targets. To this end, we set a global\n # property SPECTRE_ALLOCATOR_LIBRARY that contains the link flag to link\n # to the memory allocator. By linking to the allocator library first\n # explicitly in target_link_libraries CMake correctly places the allocator\n # library as the first entry in the link libraries. We also link to the\n # SpectreAllocator target to pull in any additional allocator-related\n # flags, such as include directories.\n get_property(\n SPECTRE_ALLOCATOR_LIBRARY\n GLOBAL\n PROPERTY SPECTRE_ALLOCATOR_LIBRARY\n )\n target_link_libraries(\n ${TARGET_NAME}\n PUBLIC\n ${SPECTRE_ALLOCATOR_LIBRARY}\n SpectreAllocator\n )\n\n set(SPECTRE_KOKKOS_LAUNCHER \"\")\n if(SPECTRE_KOKKOS)\n # We need to make sure we don't drop the Kokkos link wrapper\n get_target_property(\n _RULE_LAUNCH_LINK\n ${TARGET_NAME}\n RULE_LAUNCH_LINK)\n if (_RULE_LAUNCH_LINK)\n set(SPECTRE_KOKKOS_LAUNCHER ${_RULE_LAUNCH_LINK})\n endif()\n endif()\n set_target_properties(\n ${TARGET_NAME}\n PROPERTIES\n RULE_LAUNCH_LINK\n \"${CMAKE_BINARY_DIR}/tmp/WrapExecutableLinker.sh ${SPECTRE_KOKKOS_LAUNCHER}\"\n LINK_DEPENDS \"${CMAKE_BINARY_DIR}/tmp/WrapExecutableLinker.sh\"\n # Expose readable symbol names in backtrace (adds flags like -rdynamic)\n ENABLE_EXPORTS ON\n )\n target_link_options(${TARGET_NAME} PRIVATE \"-DEXECUTABLE_NAME=${TARGET_NAME}\")\n # The `WrapExecutableLinker.sh` script needs the `InfoAtLink_flags.txt` file\n # generated by the `InfoAtLink` target\n add_dependencies(\n ${TARGET_NAME}\n InfoAtLink\n )\n target_link_libraries(\n ${TARGET_NAME}\n PRIVATE\n CharmModuleInit\n SpectreFlags\n )\n install(TARGETS ${TARGET_NAME} OPTIONAL\n RUNTIME DESTINATION ${CMAKE_INSTALL_BINDIR})\nendfunction()\n" }, { "path": "cmake/AddStandaloneTests.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nspectre_define_test_timeout_factor_option(STANDALONE \"standalone\")\n\n# Helper function to set up a CMake target for a test executable. It\n# can safely be called multiple times for the same executable.\nfunction(add_standalone_test_executable EXECUTABLE_NAME)\n add_dependencies(test-executables ${EXECUTABLE_NAME})\n\n if (TARGET ${EXECUTABLE_NAME})\n return()\n endif()\n\n add_spectre_executable(\n ${EXECUTABLE_NAME}\n ${EXECUTABLE_NAME}.cpp\n )\n\n target_link_libraries(\n ${EXECUTABLE_NAME}\n PRIVATE\n Catch2::Catch2\n )\n\n add_dependencies(\n ${EXECUTABLE_NAME}\n module_GlobalCache\n module_Main\n )\nendfunction()\n\n# Helper function to set standard test properties for standalone tests.\nfunction(set_standalone_test_properties TEST_NAME)\n spectre_test_timeout(TIMEOUT STANDALONE 10)\n\n set_tests_properties(\n \"${TEST_NAME}\"\n PROPERTIES\n TIMEOUT \"${TIMEOUT}\"\n LABELS \"standalone\"\n ENVIRONMENT \"ASAN_OPTIONS=detect_leaks=0\")\nendfunction()\n\n# For tests that result in a failure it is necessary to redirect\n# output from stderr to stdout. However, it was necessary at least on\n# some systems to do this redirect inside a shell command.\nfind_program(SHELL_EXECUTABLE \"sh\")\nif (NOT SHELL_EXECUTABLE)\n message(FATAL_ERROR\n \"Could not find 'sh' shell to execute standalone failure tests\")\nendif()\n\n# Add a standalone test named TEST_NAME that runs an executable with\n# no arguments. A test named Foo.Bar.Baz will run the executable\n# Test_Baz by default.\n#\n# A REGEX_TO_MATCH named argument may be passed, in which case the\n# test will pass if the output matches it, otherwise the test will\n# pass if the executable succeeds without any \"ERROR\" output.\n#\n# An EXECUTABLE named argument can be passed to override the\n# executable name.\n#\n# An INPUT_FILE named argument can be passed to pass an input file to\n# the executable.\nfunction(add_standalone_test TEST_NAME)\n cmake_parse_arguments(\n ARG\n \"\"\n \"REGEX_TO_MATCH;EXECUTABLE;INPUT_FILE\"\n \"\"\n ${ARGN})\n\n if(DEFINED ARG_EXECUTABLE)\n set(EXECUTABLE_NAME \"${ARG_EXECUTABLE}\")\n else()\n # Extract last component of test name as executable name\n string(REGEX MATCH \"[^.]*$\" EXECUTABLE_NAME \"${TEST_NAME}\")\n set(EXECUTABLE_NAME \"Test_${EXECUTABLE_NAME}\")\n endif()\n\n add_standalone_test_executable(\"${EXECUTABLE_NAME}\")\n if(DEFINED ARG_INPUT_FILE)\n set(INPUT_FILE_ARGS\n \"--input-file ${CMAKE_CURRENT_SOURCE_DIR}/${ARG_INPUT_FILE}\")\n else()\n set(INPUT_FILE_ARGS \"\")\n endif()\n add_test(\n NAME \"${TEST_NAME}\"\n COMMAND\n ${SHELL_EXECUTABLE}\n -c\n \"${SPECTRE_TEST_RUNNER} ${CMAKE_BINARY_DIR}/bin/${EXECUTABLE_NAME} ${INPUT_FILE_ARGS} 2>&1\"\n )\n\n set_standalone_test_properties(\"${TEST_NAME}\")\n if(NOT DEFINED ARG_REGEX_TO_MATCH)\n set_tests_properties(\n \"${TEST_NAME}\"\n PROPERTIES\n FAIL_REGULAR_EXPRESSION \"ERROR\")\n else()\n set_tests_properties(\n \"${TEST_NAME}\"\n PROPERTIES\n PASS_REGULAR_EXPRESSION\n \"${ARG_REGEX_TO_MATCH}\")\n endif()\nendfunction()\n" }, { "path": "cmake/BootstrapPyDeps.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(BOOTSTRAP_PY_DEPS\n \"Install missing Python dependencies in the build directory\"\n ${SPECTRE_FETCH_MISSING_DEPS})\noption(BOOTSTRAP_PY_DEV_DEPS\n \"Install missing Python dev dependencies in the build directory\"\n ${SPECTRE_FETCH_MISSING_DEPS})\n\nif (NOT (BOOTSTRAP_PY_DEPS OR BOOTSTRAP_PY_DEV_DEPS))\n return()\nendif()\n\nmessage(STATUS \"Bootstrapping missing Python dependencies to: \\\n${SPECTRE_PYTHON_SITE_PACKAGES}\")\n\n# Install the packages with pip\nset(_BOOTSTRAP_PY_DEPS_FLAG \"\")\nif (BOOTSTRAP_PY_DEPS)\n set(_BOOTSTRAP_PY_DEPS_FLAG\n -r ${CMAKE_SOURCE_DIR}/support/Python/requirements.txt)\nendif()\nset(_BOOTSTRAP_PY_DEV_DEPS_FLAG \"\")\nif (BOOTSTRAP_PY_DEV_DEPS)\n set(_BOOTSTRAP_PY_DEV_DEPS_FLAG\n -r ${CMAKE_SOURCE_DIR}/support/Python/dev_requirements.txt)\nendif()\nset(_BOOTSTRAP_PY_DEPS_LOG_FILE \"${CMAKE_BINARY_DIR}/BootstrapPyDeps.log\")\nexecute_process(COMMAND\n ${CMAKE_COMMAND} -E env\n PYTHONPATH=${PYTHONPATH}\n ${Python_EXECUTABLE} -m pip install --disable-pip-version-check\n --prefix ${CMAKE_BINARY_DIR} --no-warn-script-location\n ${_BOOTSTRAP_PY_DEPS_FLAG} ${_BOOTSTRAP_PY_DEV_DEPS_FLAG}\n RESULT_VARIABLE _BOOTSTRAP_PY_DEPS_RESULT\n OUTPUT_FILE ${_BOOTSTRAP_PY_DEPS_LOG_FILE}\n ERROR_FILE ${_BOOTSTRAP_PY_DEPS_LOG_FILE}\n )\nif (NOT _BOOTSTRAP_PY_DEPS_RESULT EQUAL 0)\n message(WARNING \"Bootstrapping of Python dependencies failed.\"\n \"See log file: ${_BOOTSTRAP_PY_DEPS_LOG_FILE}\")\nendif()\n" }, { "path": "cmake/CheckBrokenArray0.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Check whether the standard library is affected by\n# https://bugs.llvm.org/show_bug.cgi?id=35491\n# This LLVM bug is fixed by commit 59cdf90ac8bea16abbb9d637c5124e69d2c75c09,\n# which is included in the LLVM 7 release.\n\nmessage(STATUS \"Checking for broken std::array<..., 0>\")\ntry_compile(\n ARRAY0_WORKS\n ${CMAKE_BINARY_DIR}\n ${CMAKE_SOURCE_DIR}/cmake/CheckBrokenArray0.cpp\n CMAKE_FLAGS\n -DCMAKE_CXX_STANDARD=${CMAKE_CXX_STANDARD}\n -DCMAKE_CXX_STANDARD_REQUIRED=${CMAKE_CXX_STANDARD_REQUIRED}\n -DCMAKE_CXX_EXTENSIONS=${CMAKE_CXX_EXTENSIONS}\n OUTPUT_VARIABLE TRY_COMPILE_OUTPUT\n )\nif (ARRAY0_WORKS)\n message(STATUS \"Checking for broken std::array<..., 0> -- works\")\nelse (ARRAY0_WORKS)\n message(STATUS \"Checking for broken std::array<..., 0> -- broken\")\n add_definitions(-DHAVE_BROKEN_ARRAY0)\n message(STATUS \"Output when trying to compile broken array test:\\n${TRY_COMPILE_OUTPUT}\")\nendif (ARRAY0_WORKS)\n" }, { "path": "cmake/CheckBrokenArray0.cpp", "content": "// Distributed under the MIT License.\n// Copyright (c) 2009-2017 by the contributors to libc++, listed at\n// https://llvm.org/svn/llvm-project/libcxx/trunk/CREDITS.TXT\n\n// This is a portion of\n// https://llvm.org/svn/llvm-project/libcxx/trunk/test/std/containers/sequences/array/begin.pass.cpp\n\n#include \n#include \n\nint main() {\n struct NoDefault {\n NoDefault(int) {}\n };\n typedef NoDefault T;\n typedef std::array C;\n C c = {};\n assert(c.begin() == c.end());\n}\n" }, { "path": "cmake/CheckCompilerVersion.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nif (\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"GNU\")\n if (CMAKE_CXX_COMPILER_VERSION VERSION_LESS 9.1)\n message(FATAL_ERROR \"GCC version must be at least 9.1\")\n endif ()\nelseif (\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"Clang\")\n if (CMAKE_CXX_COMPILER_VERSION VERSION_LESS 13.0)\n message(FATAL_ERROR \"Clang version must be at least 13.0\")\n endif ()\nelseif (\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"Intel\")\n message(FATAL_ERROR \"Intel compiler is not supported.\")\nelseif (\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"AppleClang\")\n if (CMAKE_CXX_COMPILER_VERSION VERSION_LESS 13.0.0)\n message(FATAL_ERROR \"AppleClang version must be at least 13.0.0\")\n endif ()\nelse ()\n message(\n WARNING \"The compiler ${CMAKE_CXX_COMPILER_ID} is unsupported! \"\n \"Compilation has only been tested with Clang and GCC.\"\n )\nendif ()\n" }, { "path": "cmake/CodeCoverage.cmake", "content": "################################################################################\n#\n# \\file cmake/CodeCoverage.cmake\n# \\author J. Bakosi\n# \\copyright 2012-2015, Jozsef Bakosi, 2016, Los Alamos National Security, LLC.\n# \\brief Setup target for code coverage analysis\n# \\date Wed 22 Feb 2017 07:39:09 AM MST\n#\n# Modifications:\n# 1) Change \"Quinoa\" to \"SpECTRE\" and \"quinoa\" to \"spectre\"\n# 2) Split lines to make commands more legible\n# 3) Silence CMake warnings on uninitialized variables in\n# `cmake_parse_arguments`\n################################################################################\n\n# ##############################################################################\n# Function to add code coverage target\n#\n# setup_target_for_coverage( \n# [TESTRUNNER_ARGS ...]\n# [DEPENDS dep1 dep2 ... ] )\n#\n# Mandatory arguments:\n# --------------------\n#\n# TEST_SUITE - Test TEST_SUITE name to be displayed in HTML report title.\n#\n# OUTPUT_PATH - Path to prepend to where the report is generated:\n# ${TARGET_NAME}/index.html.\n#\n# TARGET_NAME - The name of the code coverage target. The HTML report on code\n# coverage is generated at the OUTPUT_PATH /${TARGET_NAME}/index.html.\n#\n# TEST_RUNNER - Command line of the test runner.\n#\n# Optional arguments:\n# -------------------\n#\n# TESTRUNNER_ARGS arg1 arg2 ... - Optional arguments to test runner. Pass them\n# in list form, e.g.: \"-v;-g;group\" for passing '-v -g group'. Default: \"\".\n#\n# DEPENDS dep1 dep2 ... - Optional dependencies added to test coverage target.\n# Default: \"\". Here all dependencies should be given that should be covered by\n# the test suite the coverage is being setup for, as well as those that are\n# required for successfully building the tests and the test runner.\n#\n# Author: J. Bakosi\n#\n# ##############################################################################\nfunction(SETUP_TARGET_FOR_COVERAGE\n TEST_SUITE OUTPUT_PATH TARGET_NAME TEST_RUNNER)\n if (NOT IS_ABSOLUTE ${OUTPUT_PATH})\n set(OUTPUT_PATH ${CMAKE_BINARY_DIR}/${OUTPUT_PATH})\n endif()\n if(NOT EXISTS ${CMAKE_SOURCE_DIR}/.git)\n message(FATAL_ERROR, \"Not running in a git repo so we can't do \"\n \"code coverage\")\n endif()\n\n set(multiValueArgs TESTRUNNER_ARGS DEPENDS IGNORE_COV)\n cmake_parse_arguments(\n ARG \"\" \"\" \"${multiValueArgs}\"\n ${ARGN})\n\n if(NOT LCOV)\n MESSAGE(FATAL_ERROR \"lcov not found! Aborting...\")\n endif()\n\n if(NOT GENHTML)\n MESSAGE(FATAL_ERROR \"genhtml not found! Aborting...\")\n endif()\n\n if(NOT SED)\n MESSAGE(FATAL_ERROR \"sed not found! Aborting...\")\n endif()\n\n if(NOT GIT_HASH)\n message(FATAL_ERROR \"Git hash not found! Aborting...\")\n endif()\n\n # Set shortcut for output: OUTPUT_PATH/target\n set(OUTPUT ${OUTPUT_PATH}/${TARGET_NAME})\n file(MAKE_DIRECTORY ${OUTPUT_PATH})\n\n # Setup code coverage target\n add_custom_target(\n ${TARGET_NAME}\n # Cleanup any old intermediate data\n COMMAND ${CMAKE_COMMAND} -E remove ${OUTPUT}.base.info\n ${OUTPUT}.test.info ${OUTPUT}.total.info\n ${OUTPUT}.filtered.info\n # Cleanup lcov\n COMMAND ${LCOV} --gcov-tool ${GCOV} --directory . --zerocounters\n # Capture initial state yielding zero coverage baseline\n COMMAND ${LCOV} --gcov-tool ${GCOV} --capture --initial\n --directory . --output-file ${OUTPUT}.base.info\n # Run test TEST_SUITE\n COMMAND ${TEST_RUNNER} ${ARG_TESTRUNNER_ARGS}\n # Capture lcov counters\n COMMAND ${LCOV} --gcov-tool ${GCOV} --capture\n --rc lcov_branch_coverage=0 --directory .\n --output-file ${OUTPUT}.test.info\n # Combine trace files\n COMMAND ${LCOV} --gcov-tool ${GCOV} --rc lcov_branch_coverage=0\n --add-tracefile ${OUTPUT}.base.info\n --add-tracefile ${OUTPUT}.test.info\n --output-file ${OUTPUT}.total.info\n # Filter out unwanted files\n COMMAND ${LCOV} --gcov-tool ${GCOV} --rc lcov_branch_coverage=0\n --remove ${OUTPUT}.total.info '*/c++/*' '*/include/*'\n '*/boost/*' '*/charm/*' '*.decl.h' '*.def.h'\n '*/STDIN' '*/tut/*' '*/moduleinit*' '*InfoFromBuild.cpp'\n '${CMAKE_SOURCE_DIR}/src/Executables/*'\n ${ARG_IGNORE_COV}\n --output-file ${OUTPUT}.filtered.info\n # Generate HTML report\n COMMAND ${GENHTML} --legend --demangle-cpp\n --title ${GIT_HASH}\n -o ${OUTPUT} ${OUTPUT}.filtered.info\n # Customize page headers in generated html to own\n COMMAND find ${OUTPUT} -type f -print | xargs file | grep text |\n cut -f1 -d: | xargs ${SED} -i'.bak' 's/LCOV - code coverage\n report/SpECTRE ${TEST_SUITE} Test Code Coverage Report/g'\n COMMAND find ${OUTPUT} -type f -name \\\"*.bak\\\" -print | xargs file |\n grep text | cut -f1 -d: | xargs rm\n COMMAND find ${OUTPUT} -type f -print | xargs file | grep text |\n cut -f1 -d: | xargs ${SED} -i'.bak'\n 's^Test:^Commit:^g'\n COMMAND find ${OUTPUT} -type f -name \\\"*.bak\\\" -print | xargs file |\n grep text | cut -f1 -d: | xargs rm\n COMMAND find ${OUTPUT} -type f -print | xargs file | grep text |\n cut -f1 -d:\n | xargs ${SED} -i'.bak' 's^\\\\\\([a-z0-9]\\\\{40\\\\}\\\\\\)^\n \\\\1^g'\n # Delete backup files created by sed\n COMMAND find ${OUTPUT} -type f -name \\\"*.bak\\\" -print | xargs file |\n grep text | cut -f1 -d: | xargs rm\n # Cleanup any intermediate data\n COMMAND ${CMAKE_COMMAND} -E remove ${OUTPUT}.base.info\n ${OUTPUT}.test.info ${OUTPUT}.total.info\n # Copy output into coverage.info to be used by codecov\n COMMAND mv ${OUTPUT}.filtered.info ${CMAKE_BINARY_DIR}/tmp/coverage.info\n # Set work directory for target\n WORKING_DIRECTORY ${CMAKE_BINARY_DIR}\n # Echo what is being done\n COMMENT \"SpECTRE ${TEST_SUITE} Test Code Coverage Report\"\n )\n\n # Make test coverage target dependent on optional dependencies passed in using\n # keyword DEPENDS\n add_dependencies(${TARGET_NAME} ${ARG_DEPENDS})\n\n # Output code coverage target enabled\n string(REPLACE \";\" \" \" ARGUMENTS \"${ARG_TESTRUNNER_ARGS}\")\n message(\n STATUS\n \"Enabling code coverage target '${TARGET_NAME}' tested by \"\n \"'${TEST_RUNNER} ${ARGUMENTS}', dependencies {${ARG_DEPENDS}}, \"\n \"report at ${OUTPUT}/index.html\"\n )\n\nendfunction()\n" }, { "path": "cmake/CodeCoverageDetection.cmake", "content": "################################################################################\n#\n# \\file cmake/CodeCoverageDetection.cmake\n# \\author J. Bakosi\n# \\copyright 2012-2015, Jozsef Bakosi, 2016, Los Alamos National Security, LLC.\n# \\brief Detect prerequesites for code coverage analysis\n# \\date Fri 03 Mar 2017 11:50:24 AM MST\n#\n# Modifications for SpECTRE:\n# 1) Auto find either llvm-cov or llvm-cov-${LLVM_VERSION} instead of using\n# a shell script that hard codes the LLVM version\n# 2) Formatting changes\n################################################################################\n\n# Attempt to find tools required for code coverage analysis\n\nif(NOT LLVM_COV_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(LLVM_COV_ROOT \"\")\n set(LLVM_COV_ROOT $ENV{LLVM_COV_ROOT})\nendif()\n\noption(COVERAGE \"Enable code coverage analysis.\" OFF)\n\n# Code coverage analysis only supported if all prerequisites found and the user\n# has requested it via the cmake variable COVERAGE=on..\nif(COVERAGE)\n if(CMAKE_CXX_COMPILER_ID MATCHES \"Clang\" )\n string(\n REGEX MATCH \"^[0-9]+.[0-9]+\" LLVM_VERSION\n \"${CMAKE_CXX_COMPILER_VERSION}\"\n )\n find_program(\n LLVM_COV_BIN\n NAMES \"llvm-cov-${LLVM_VERSION}\" \"llvm-cov\"\n HINTS ${LLVM_COV_ROOT}\n )\n configure_file(\n \"${CMAKE_SOURCE_DIR}/tools/llvm-gcov.sh\"\n \"${CMAKE_BINARY_DIR}/llvm-gcov.sh\"\n )\n set(GCOV \"${CMAKE_BINARY_DIR}/llvm-gcov.sh\")\n elseif( CMAKE_CXX_COMPILER_ID STREQUAL \"GNU\" )\n find_program(GCOV gcov REQUIRED)\n endif()\n\n find_program(LCOV lcov REQUIRED)\n find_program(GENHTML genhtml REQUIRED)\n find_program(SED sed REQUIRED)\n\n set(CMAKE_CXX_FLAGS \"${CMAKE_CXX_FLAGS} --coverage\")\n set(CMAKE_EXE_LINKER_FLAGS \"${CMAKE_EXE_LINKER_FLAGS} --coverage\")\n\n # Enable code coverage analysis.\n SET(CODE_COVERAGE ON)\n\n # Make flag enabling code coverage analysis available in parent cmake scope\n mark_as_advanced(CODE_COVERAGE)\n\n # Only include code coverage cmake functions if all prerequisites are met\n include(CodeCoverage)\nelseif(COVERAGE)\n message(FATAL_ERROR \"Failed to enable code coverage analysis. Not all \"\n \"prerequisites found: gcov:${GCOV}, lcov:${LCOV}, genhtml:${GENHTML},\"\n \" sed:${SED}\")\nendif()\n" }, { "path": "cmake/EnableWarnings.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\ninclude(AddCxxFlag)\n\n# On systems where we can't use -isystem (Cray), we don't want\n# all the warnings enabled because we get flooded with system warnings.\noption(ENABLE_WARNINGS \"Enable the default warning level\" ON)\nif(${ENABLE_WARNINGS})\n create_cxx_flags_target(\n \"-W;\\\n-Wall;\\\n-Wcast-align;\\\n-Wcast-qual;\\\n-Wdisabled-optimization;\\\n-Wdocumentation;\\\n-Wextra;\\\n-Wformat-nonliteral;\\\n-Wformat-security;\\\n-Wformat-y2k;\\\n-Wformat=2;\\\n-Winvalid-pch;\\\n-Wmissing-declarations;\\\n-Wmissing-field-initializers;\\\n-Wmissing-format-attribute;\\\n-Wmissing-include-dirs;\\\n-Wmissing-noreturn;\\\n-Wnewline-eof;\\\n-Wnon-virtual-dtor;\\\n-Wold-style-cast;\\\n-Woverloaded-virtual;\\\n-Wpacked;\\\n-Wpedantic;\\\n-Wpointer-arith;\\\n-Wredundant-decls;\\\n-Wshadow;\\\n-Wsign-conversion;\\\n-Wstack-protector;\\\n-Wswitch-default;\\\n-Wunreachable-code;\\\n-Wwrite-strings\" SpectreWarnings)\nelse()\n add_library(SpectreWarnings INTERFACE)\nendif()\n\n# Disable some warnings\ncreate_cxx_flags_target(\n \"-Wno-dangling-reference;\\\n-Wno-documentation-unknown-command;\\\n-Wno-mismatched-tags;\\\n-Wno-interference-size;\\\n-Wno-non-template-friend;\\\n-Wno-type-limits;\\\n-Wno-undefined-var-template;\\\n-Wno-gnu-zero-variadic-macro-arguments;\\\n-Wno-noexcept-type\"\n SpectreDisableSomeWarnings)\ntarget_link_libraries(\n SpectreWarnings\n INTERFACE\n SpectreDisableSomeWarnings\n )\n\n# - GCC versions below 13 don't respect 'GCC diagnostic' pragmas to disable\n# warnings by the preprocessor:\n# https://gcc.gnu.org/bugzilla/show_bug.cgi?id=53431\n# So we disable the warning about unknown pragmas because we can't silence it.\n# - GCC has many false positives for `stringop-overflow`, `array-bounds`, and\n# `restrict`, specifically in libstdc++ with C++20, leading to\n# warnings from `__builtin_memcpy`.\n# - GCC has false-positive `use-after-free` warnings from Blaze's DynamicMatrix\n# constructor that gets inlined in many places. Rather than silencing the\n# warning at every call site or forcing no-inline, we silence it here.\nif (CMAKE_CXX_COMPILER_ID STREQUAL \"GNU\")\n create_cxx_flags_target(\n \"-Wno-unknown-pragmas;\\\n-Wno-stringop-overflow;\\\n-Wno-stringop-overread;\\\n-Wno-maybe-uninitialized;\\\n-Wno-array-bounds;\\\n-Wno-restrict;\\\n-Wno-use-after-free\"\n SpectreDisableGccWarnings)\n target_link_libraries(\n SpectreWarnings\n INTERFACE\n SpectreDisableGccWarnings\n )\nendif()\n\n# Suppress CUDA warnings that we don't want\ncreate_cxx_flag_target(\n \"-Xcudafe \\\"--diag_suppress=177,186,191,554,1301,1305,2189,3060,20012\\\"\"\n SpectreCudaWarnings)\ntarget_link_libraries(\n SpectreWarnings\n INTERFACE\n SpectreCudaWarnings\n )\n\ntarget_link_libraries(\n SpectreFlags\n INTERFACE\n SpectreWarnings\n )\n" }, { "path": "cmake/FindBlaze.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nif(NOT BLAZE_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(BLAZE_ROOT \"\")\n set(BLAZE_ROOT $ENV{BLAZE_ROOT})\nendif()\n\nfind_path(\n BLAZE_INCLUDE_DIR\n PATH_SUFFIXES include\n NAMES blaze/Blaze.h\n HINTS ${BLAZE_ROOT}\n DOC \"Blaze include directory. Used BLAZE_ROOT to set a search dir.\"\n)\n\nset(BLAZE_INCLUDE_DIRS ${BLAZE_INCLUDE_DIR})\n\nset(BLAZE_VERSION \"\")\n\nif(EXISTS \"${BLAZE_INCLUDE_DIRS}/blaze/system/Version.h\")\n # Extract version info from header\n file(READ\n \"${BLAZE_INCLUDE_DIRS}/blaze/system/Version.h\"\n BLAZE_FIND_HEADER_CONTENTS)\n\n string(REGEX MATCH \"#define BLAZE_MAJOR_VERSION [0-9]+\"\n BLAZE_MAJOR_VERSION \"${BLAZE_FIND_HEADER_CONTENTS}\")\n string(REPLACE \"#define BLAZE_MAJOR_VERSION \" \"\"\n BLAZE_MAJOR_VERSION\n ${BLAZE_MAJOR_VERSION})\n\n string(REGEX MATCH \"#define BLAZE_MINOR_VERSION [0-9]+\"\n BLAZE_MINOR_VERSION \"${BLAZE_FIND_HEADER_CONTENTS}\")\n string(REPLACE \"#define BLAZE_MINOR_VERSION \" \"\"\n BLAZE_MINOR_VERSION\n ${BLAZE_MINOR_VERSION})\n\n set(BLAZE_VERSION\n \"${BLAZE_MAJOR_VERSION}.${BLAZE_MINOR_VERSION}\"\n )\nelseif(BLAZE_INCLUDE_DIRS)\n message(WARNING \"Failed to find file \"\n \"'${BLAZE_INCLUDE_DIRS}/blaze/system/Version.h' \"\n \"while detecting the Blaze version.\")\nendif()\n\nset(Blaze_VERSION ${BLAZE_VERSION})\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(\n Blaze\n FOUND_VAR BLAZE_FOUND\n REQUIRED_VARS BLAZE_INCLUDE_DIR BLAZE_INCLUDE_DIRS\n VERSION_VAR BLAZE_VERSION\n )\nmark_as_advanced(BLAZE_INCLUDE_DIR BLAZE_INCLUDE_DIRS\n BLAZE_VERSION BLAZE_MAJOR_VERSION BLAZE_MINOR_VERSION\n Blaze_VERSION\n )\n" }, { "path": "cmake/FindBreathe.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nif(NOT BREATHE_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(BREATHE_ROOT \"\")\n set(BREATHE_ROOT $ENV{BREATHE_ROOT})\nendif()\n\n# Look for an executable called breathe-apidoc\nfind_program(\n BREATHE_APIDOC_EXECUTABLE\n NAMES breathe-apidoc\n PATHS ${BREATHE_ROOT}\n DOC \"Path to breathe-apidoc executable\")\n\nexecute_process(COMMAND \"${BREATHE_APIDOC_EXECUTABLE}\" \"--version\"\n RESULT_VARIABLE VERSION_RESULT\n OUTPUT_VARIABLE VERSION_OUTPUT\n OUTPUT_STRIP_TRAILING_WHITESPACE)\n\ninclude(FindPackageHandleStandardArgs)\n\nif(VERSION_RESULT MATCHES 0)\n string(REGEX MATCH \"[0-9]+\\.[0-9]+[\\.]?[0-9]*\"\n BREATHE_APIDOC_VERSION ${VERSION_OUTPUT})\n set(BREATHE_VERSION ${BREATHE_APIDOC_VERSION})\nendif(VERSION_RESULT MATCHES 0)\n\n# Handle standard arguments to find_package like REQUIRED and QUIET\nfind_package_handle_standard_args(Breathe\n REQUIRED_VARS BREATHE_APIDOC_EXECUTABLE BREATHE_VERSION\n BREATHE_APIDOC_VERSION\n VERSION_VAR BREATHE_VERSION)\n" }, { "path": "cmake/FindCharm.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# FindCharm.cmake\n#\n# Finds a suitable Charm++ installation and exposes it via imported targets.\n#\n# This module requires you have set the `CHARM_ROOT` variable to a Charm++\n# installation directory, e.g.:\n#\n# cmake -D CHARM_ROOT=/path/to/charm++/build-dir\n#\n# This is to ensure that SpECTRE builds with the Charm++ installation that you\n# intended to use. The `CHARM_ROOT/bin` directory should contain the Charm++\n# compiler `charmc`. All information on include directories, library paths,\n# compiler flags etc. will be retrieved by invoking `charmc` with the\n# `-print-building-blocks` flag. Note that we do _not_ use `charmc` to wrap the\n# CMake compiler configuration. Instead, the information retrieved from `charmc`\n# is made available to CMake via imported targets.\n#\n# This module supports CMake \"components\" to load additional Charm++ modules.\n# You can load additional Charm++ modules like this:\n#\n# find_package(Charm 7.0.0 COMPONENTS EveryLB)\n#\n# This module exposes the following targets:\n#\n# - `Charmxx::charmxx`: All Charm++ libraries.\n# - `Charmxx::pup`: Only the Charm++ PUP serialization library.\n# - `Charmxx::main`: Defines the Charm++ main function. Link to compile\n# executables.\n# - `CharmModuleInit`: Provides the generated definitions of Charm++'s\n# module-init functions.\n\noption(CHARM_SHARED_LIBS \"Link Charm++ shared libraries. Defaults to the \\\nvalue of 'BUILD_SHARED_LIBS' but can be overriden to enforce shared or static \\\nlibraries for Charm++.\" ${BUILD_SHARED_LIBS})\n\noption(CHARM_USE_MPI \"Find and link MPI with Charm++. An attempt is made to \\\ndetermine automatically if MPI is needed, but this flag can be turned on to \\\nenable linking MPI if the automatic check fails.\" OFF)\n\noption(CHARM_TRACE_PROJECTIONS \"Charm++ was built with projections support on. \\\nEnables '-tracemode projections'\" OFF)\n\noption(CHARM_TRACE_SUMMARY \"Charm++ was built with projections support on. \\\nEnables '-tracemode summary'\" OFF)\n\nif (DEFINED ENV{CHARM_ROOT} AND \"${CHARM_ROOT}\" STREQUAL \"\")\n set(CHARM_ROOT \"$ENV{CHARM_ROOT}\")\nendif()\n\nif (NOT EXISTS \"${CHARM_ROOT}\")\n if (\"${CHARM_ROOT}\" STREQUAL \"\")\n message(\n FATAL_ERROR \"CHARM_ROOT was not set. Pass it as a command-line arg: \"\n \"cmake -D CHARM_ROOT=/path/to/charm++/build-dir\")\n endif()\n message(\n FATAL_ERROR \"CHARM_ROOT=${CHARM_ROOT} does not exist. \"\n \"Please pass it as a command-line definition to cmake, i.e. \"\n \"cmake -D CHARM_ROOT=/path/to/charm++/build-dir\"\n )\nendif ()\n\n# Find the Charm compiler `charmc` first so we can retrieve build info from it\nfind_program(CHARM_COMPILER\n NAMES charmc\n PATH_SUFFIXES bin\n HINTS ${CHARM_ROOT} ENV CHARM_ROOT\n NO_DEFAULT_PATH\n DOC \"The full path to the charm++ compiler 'charmc'\"\n )\nif(CHARM_COMPILER STREQUAL \"CHARM_COMPILER-NOTFOUND\")\n message(FATAL_ERROR \"The Charm++ compiler 'charmc' could not be found. Make \"\n \"sure you have set 'CHARM_ROOT' to the path that contains 'bin/charmc'.\")\nendif()\n\n# Assemble options for invoking `charmc`:\n# - Use static or shared libs\nif(CHARM_SHARED_LIBS)\n list(APPEND CHARMC_OPTIONS \"-charm-shared\")\nendif()\n# - Not linking the main function by default. We expose an extra target that\n# links it because we sometimes want to link Charm++ without a main function.\nlist(APPEND CHARMC_OPTIONS \"-nomain\")\nlist(APPEND CHARMC_OPTIONS \"-nomain-module\")\nif(CHARM_TRACE_PROJECTIONS)\n list(APPEND CHARMC_OPTIONS \"-tracemode projections\")\nendif()\nif(CHARM_TRACE_SUMMARY)\n list(APPEND CHARMC_OPTIONS \"-tracemode summary\")\nendif()\n# - Request optional Charm++ modules. They can be specified as `COMPONENTS` when\n# calling CMake's `find_package`.\nif(Charm_FIND_COMPONENTS)\n list(JOIN Charm_FIND_COMPONENTS \",\" CHARM_COMPONENTS_JOINED)\n list(APPEND CHARMC_OPTIONS \"-modules ${CHARM_COMPONENTS_JOINED}\")\nendif()\n\n# Invoke 'charmc' so that it outputs build info\nlist(JOIN CHARMC_OPTIONS \" \" CHARMC_OPTIONS_JOINED)\nset(CHARM_BUILDING_BLOCKS_CMD\n \"${CHARM_COMPILER} -print-building-blocks ${CHARMC_OPTIONS_JOINED}\")\nmessage(STATUS \"Charm++ 'charmc' is invoked as: ${CHARM_BUILDING_BLOCKS_CMD}\")\nexecute_process(\n COMMAND bash -c \"${CHARM_BUILDING_BLOCKS_CMD}\"\n OUTPUT_VARIABLE CHARM_BUILDING_BLOCKS\n ERROR_VARIABLE CHARM_BUILDING_BLOCKS_ERROR\n OUTPUT_STRIP_TRAILING_WHITESPACE\n )\nif(NOT CHARM_BUILDING_BLOCKS)\n if(CHARM_BUILDING_BLOCKS_ERROR MATCHES \"lib_so directory not found\"\n AND CHARM_SHARED_LIBS)\n message(STATUS \"Charm++ is not built with shared-library support so we \"\n \"fall back to static libraries. Build Charm++ with the '--build-shared' \"\n \"option to enable shared libraries.\")\n set(CHARM_SHARED_LIBS OFF)\n list(REMOVE_ITEM CHARMC_OPTIONS \"-charm-shared\")\n list(JOIN CHARMC_OPTIONS \" \" CHARMC_OPTIONS_JOINED)\n set(CHARM_BUILDING_BLOCKS_CMD\n \"${CHARM_COMPILER} -print-building-blocks ${CHARMC_OPTIONS_JOINED}\")\n execute_process(\n COMMAND bash -c \"${CHARM_BUILDING_BLOCKS_CMD}\"\n OUTPUT_VARIABLE CHARM_BUILDING_BLOCKS\n ERROR_VARIABLE CHARM_BUILDING_BLOCKS_ERROR\n OUTPUT_STRIP_TRAILING_WHITESPACE\n )\n else()\n message(FATAL_ERROR \"Failed retrieving Charm++ building blocks with \"\n \"command:\\n ${CHARM_BUILDING_BLOCKS_CMD}\\nPlease make sure the Charm++ \"\n \"version is at least 6.9.0. Error message:\\n\"\n \"${CHARM_BUILDING_BLOCKS_ERROR}\")\n endif()\nendif()\nstring(REGEX REPLACE \";\" \"\\\\\\\\;\"\n CHARM_BUILDING_BLOCKS_LIST \"${CHARM_BUILDING_BLOCKS}\")\nstring(REGEX REPLACE \"\\n\" \";\" CHARM_BUILDING_BLOCKS_LIST\n \"${CHARM_BUILDING_BLOCKS_LIST}\")\n\n# Load the charm building blocks into CMake variables\nforeach(CHARM_BUILDING_BLOCK IN LISTS CHARM_BUILDING_BLOCKS_LIST)\n if(CHARM_BUILDING_BLOCK MATCHES \"^([^=]+)='(.*)'$\")\n set(${CMAKE_MATCH_1} \"${CMAKE_MATCH_2}\")\n string(STRIP \"${${CMAKE_MATCH_1}}\" ${CMAKE_MATCH_1})\n else()\n message(SEND_ERROR \"Unexpected output from charmc: ${CHARM_BUILDING_BLOCK}\")\n endif()\nendforeach()\n# Validate the charm building blocks\nlist(APPEND CHARM_REQUIRED_BUILDING_BLOCKS\n CHARM_CXX\n CHARM_CXX_FLAGS\n CHARM_LDXX_FLAGS\n CHARMINC\n # Not needed but available, could be added if needed:\n # CHARM_CC\n # CHARM_LD\n # CHARM_LDXX\n # CHARM_CC_FLAGS\n # CHARM_LD_FLAGS\n # CHARMBIN\n )\nif(CHARM_SHARED_LIBS)\n list(APPEND CHARM_REQUIRED_BUILDING_BLOCKS CHARMLIBSO)\nelse()\n list(APPEND CHARM_REQUIRED_BUILDING_BLOCKS CHARMLIB)\nendif()\nforeach(CHARM_REQUIRED_BUILDING_BLOCK IN LISTS CHARM_REQUIRED_BUILDING_BLOCKS)\n if(NOT ${CHARM_REQUIRED_BUILDING_BLOCK})\n message(FATAL_ERROR \"Could not find ${CHARM_REQUIRED_BUILDING_BLOCK} \"\n \"variable in output of command: ${CHARM_BUILDING_BLOCKS_CMD}\")\n endif()\nendforeach()\n\n# Split flags into lists\nseparate_arguments(CHARM_CXX_FLAGS)\nseparate_arguments(CHARM_LDXX_FLAGS)\n# Define variables with standard names for compatibility, though these should\n# not be used outside this script.\nget_filename_component(CHARM_INCLUDE_DIR ${CHARMINC} ABSOLUTE)\nset(CHARM_INCLUDE_DIRS ${CHARM_INCLUDE_DIR})\nif(CHARM_SHARED_LIBS)\n set(CHARM_LIBRARIES ${CHARMLIBSO})\nelse()\n set(CHARM_LIBRARIES ${CHARMLIB})\nendif()\n\n# Find version file\nif(EXISTS \"${CHARM_INCLUDE_DIR}/charm-version.h\")\n set(CHARM_VERSION_FILE_VERSION \"6_11\")\n set(CHARM_VERSION_FILE_LOCATION \"${CHARM_INCLUDE_DIR}/charm-version.h\")\nelseif(EXISTS \"${CHARM_INCLUDE_DIR}/VERSION\")\n set(CHARM_VERSION_FILE_VERSION \"pre_6_11\")\n set(CHARM_VERSION_FILE_LOCATION \"${CHARM_INCLUDE_DIR}/VERSION\")\nelseif(EXISTS \"${CHARM_ROOT}/VERSION\")\n set(CHARM_VERSION_FILE_VERSION \"pre_6_11\")\n set(CHARM_VERSION_FILE_LOCATION \"${CHARM_ROOT}/VERSION\")\nelse()\n message(FATAL_ERROR \"Failed to find Charm++ version file\")\nendif()\n\n# Parse version from file\nfile(READ \"${CHARM_VERSION_FILE_LOCATION}\" CHARM_VERSION_FILE)\nif(CHARM_VERSION_FILE_VERSION STREQUAL \"6_11\")\n # Since version 6.11 the file is C++-compatible\n if(CHARM_VERSION_FILE MATCHES \"#define CHARM_VERSION_MAJOR ([0-9]+)\")\n set(CHARM_VERSION_MAJOR ${CMAKE_MATCH_1})\n else()\n message(FATAL_ERROR \"Could not parse CHARM_VERSION_MAJOR from file: \"\n \"${CHARM_VERSION_FILE_LOCATION}\")\n endif()\n if(CHARM_VERSION_FILE MATCHES \"#define CHARM_VERSION_MINOR ([0-9]+)\")\n set(CHARM_VERSION_MINOR ${CMAKE_MATCH_1})\n else()\n message(FATAL_ERROR \"Could not parse CHARM_VERSION_MINOR from file: \"\n \"${CHARM_VERSION_FILE_LOCATION}\")\n endif()\n if(CHARM_VERSION_FILE MATCHES \"#define CHARM_VERSION_PATCH ([0-9]+)\")\n set(CHARM_VERSION_PATCH ${CMAKE_MATCH_1})\n else()\n message(FATAL_ERROR \"Could not parse CHARM_VERSION_PATCH from file: \"\n \"${CHARM_VERSION_FILE_LOCATION}\")\n endif()\nelseif(CHARM_VERSION_FILE_VERSION STREQUAL \"pre_6_11\")\n # Before version 6.11 the file contains only a string\n string(REGEX REPLACE \"\\n\" \"\" CHARM_VERSION_FILE \"${CHARM_VERSION_FILE}\")\n string(\n REGEX REPLACE\n \"([0-9])1([0-9])0([0-9])\"\n \"\\\\1;1\\\\2;\\\\3\"\n CHARM_VERSIONS_PARSED\n ${CHARM_VERSION_FILE}\n )\n list(GET CHARM_VERSIONS_PARSED 0 CHARM_VERSION_MAJOR)\n list(GET CHARM_VERSIONS_PARSED 1 CHARM_VERSION_MINOR)\n list(GET CHARM_VERSIONS_PARSED 2 CHARM_VERSION_PATCH)\nendif()\nset(CHARM_VERSION\n \"${CHARM_VERSION_MAJOR}.${CHARM_VERSION_MINOR}.${CHARM_VERSION_PATCH}\")\n\n# Filter the compiler and linker flags:\n# - Remove the macOS deployment target so the CMake setting is used.\nlist(FILTER CHARM_CXX_FLAGS EXCLUDE REGEX \"^-mmacosx-version-min=\")\nlist(FILTER CHARM_LDXX_FLAGS EXCLUDE REGEX \"^-mmacosx-version-min=\")\n# - Remove the C++ standard flag so the CMake setting is used.\nlist(FILTER CHARM_CXX_FLAGS EXCLUDE REGEX \"^-std=\")\n# - Remove the standard library flag so the CMake setting is used.\nlist(FILTER CHARM_CXX_FLAGS EXCLUDE REGEX \"^-stdlib=\")\nlist(FILTER CHARM_LDXX_FLAGS EXCLUDE REGEX \"^-stdlib=\")\n# - Remove the -fPIC and -fPIE flags so the CMake setting is used.\nlist(FILTER CHARM_CXX_FLAGS EXCLUDE REGEX \"-fPI[CE]\")\nlist(FILTER CHARM_CXX_FLAGS EXCLUDE REGEX \"-fpi[ce]\")\nlist(FILTER CHARM_LDXX_FLAGS EXCLUDE REGEX \"-fPI[CE]\")\nlist(FILTER CHARM_LDXX_FLAGS EXCLUDE REGEX \"-fpi[ce]\")\n# - Remove the -rdynamic flag so the CMake setting is used. This flag is needed\n# for `backtrace` functions. We handle the flag in our own build system\n# (instead of taking it over from Charm++).\nlist(FILTER CHARM_CXX_FLAGS EXCLUDE REGEX \"-dynamic\")\nlist(FILTER CHARM_LDXX_FLAGS EXCLUDE REGEX \"-rdynamic\")\n# - Extract the include directories so we can set them properly with CMake.\n# That's better because they are declared as \"SYSTEM\", which silences warnings\n# from those headers.\nlist(FILTER CHARM_CXX_FLAGS EXCLUDE REGEX \"^-I${CHARMINC}$\")\nset(CHARM_INCLUDE_EXTRA ${CHARM_CXX_FLAGS})\nlist(FILTER CHARM_INCLUDE_EXTRA INCLUDE REGEX \"^-I.+\")\nlist(FILTER CHARM_CXX_FLAGS EXCLUDE REGEX \"^-I.+\")\nlist(TRANSFORM CHARM_INCLUDE_EXTRA REPLACE \"^-I\" \"\")\n# Filter out relative paths to `./proc_management` that are added for some\n# backends (ucx and ofi), since those paths don't seem to exist\nlist(FILTER CHARM_INCLUDE_EXTRA EXCLUDE REGEX \"^[.]/proc_management\")\nlist(APPEND CHARM_INCLUDE_DIRS ${CHARM_INCLUDE_EXTRA})\n# - Remove the rpath linker argument, since CMake adds it automatically.\nlist(FILTER CHARM_LDXX_FLAGS EXCLUDE REGEX \"^-Wl,-rpath,${CHARM_LIBRARIES}/?$\")\n# - Extract lib directories\nlist(FILTER CHARM_LDXX_FLAGS EXCLUDE REGEX \"^-L${CHARM_LIBRARIES}$\")\nset(CHARM_LIBRARIES_EXTRA ${CHARM_LDXX_FLAGS})\nlist(FILTER CHARM_LIBRARIES_EXTRA INCLUDE REGEX \"^-L.+\")\nlist(FILTER CHARM_LDXX_FLAGS EXCLUDE REGEX \"^-L.+\")\nlist(TRANSFORM CHARM_LIBRARIES_EXTRA REPLACE \"^-L\" \"\")\nlist(APPEND CHARM_LIBRARIES ${CHARM_LIBRARIES_EXTRA})\n# - Remove the link directory and find the libraries on the system so we can\n# configure them properly with CMake. That's more robust when switching\n# between static and shared libs builds. Instead of parsing the list of libs\n# below we could just hard-code lib names, but that may break with future\n# Charm versions and could be annoying to debug. However, it would give us\n# more control over which libs to link. Ideally, Charm++ would provide\n# exported targets with these libs.\nset(CHARM_LIB_NAMES ${CHARM_LDXX_FLAGS})\nlist(FILTER CHARM_LIB_NAMES INCLUDE REGEX \"^-l.+\")\nlist(FILTER CHARM_LDXX_FLAGS EXCLUDE REGEX \"^-l.+\")\nlist(TRANSFORM CHARM_LIB_NAMES REPLACE \"^-l\" \"\")\nlist(JOIN CHARM_LIB_NAMES \", \" CHARM_LIB_NAMES_OUTPUT)\nmessage(STATUS \"Charm++ lib names: ${CHARM_LIB_NAMES_OUTPUT}\")\nset(CHARM_LIBS_TO_FIND ${CHARM_LIB_NAMES})\n# Also find the 'ckmain' library, which isn't included in the list of lib names\n# because we invoked charmc with '-nomain'\nlist(APPEND CHARM_LIBS_TO_FIND ckmain)\nforeach(CHARM_LIB_NAME IN LISTS CHARM_LIBS_TO_FIND)\n # First, find the lib _only_ in CHARM_LIBRARIES. This ensures we prefer the\n # shared libs in the separate CHARM_ROOT/lib_so directory if requested.\n find_library(CHARM_LIB_${CHARM_LIB_NAME}\n NAMES ${CHARM_LIB_NAME}\n HINTS ${CHARM_LIBRARIES}\n NO_DEFAULT_PATH\n )\n # Second, fall back to a wider search on the system\n find_library(CHARM_LIB_${CHARM_LIB_NAME}\n NAMES ${CHARM_LIB_NAME}\n HINTS ENV LIBRARY_PATH\n )\n if (\"${CHARM_LIB_${CHARM_LIB_NAME}}\"\n STREQUAL \"CHARM_LIB_${CHARM_LIB_NAME}-NOTFOUND\")\n message(SEND_ERROR \"Could not find Charm++ library '${CHARM_LIB_NAME}'. \"\n \"Make sure you have built Charm++ with support for this library, and you \\\nhave loaded the appropriate modules.\")\n endif()\n list(APPEND CHARM_LIBS ${CHARM_LIB_${CHARM_LIB_NAME}})\n # Collect libs for the PUP serialization library so we can link it separately\n # if we want. The PUP functionality is in `conv-util` in Charm++ 6.10.2 and\n # in the combined `converse` lib in later versions.\n if(CHARM_LIB_NAME STREQUAL conv-util OR CHARM_LIB_NAME STREQUAL converse)\n list(APPEND PUP_LIBS ${CHARM_LIB_${CHARM_LIB_NAME}})\n endif()\nendforeach()\n# - Extract libraries that are linked as object files (`conv-static` in Charm++\n# 6.10.2).\nset(CHARM_LIB_conv-static ${CHARM_LDXX_FLAGS})\nlist(FILTER CHARM_LIB_conv-static INCLUDE REGEX \"conv-static.o$\")\nlist(FILTER CHARM_LDXX_FLAGS EXCLUDE REGEX \"conv-static.o$\")\n\n# Report remaining flags that will be ignored. They have been used to compile\n# Charm++ but may not be compatible with the compiler that the SpECTRE build is\n# configured with. They may also include flags that have been chosen differently\n# for the SpECTRE build, e.g. optimization settings. The ignored flags are\n# printed out to catch cases where adding one of the flags could be useful.\nlist(JOIN CHARM_CXX_FLAGS \" \" CHARM_CXX_FLAGS_OUTPUT)\nmessage(STATUS \"These Charm++ compiler flags will be ignored: \"\n \"${CHARM_CXX_FLAGS_OUTPUT}\")\nlist(JOIN CHARM_LDXX_FLAGS \" \" CHARM_LDXX_FLAGS_OUTPUT)\nmessage(STATUS \"These Charm++ linker flags will be ignored: \"\n \"${CHARM_LDXX_FLAGS_OUTPUT}\")\n\n# Invoke `charmc` to generate definitions for the module-init functions.\n#\n# `charmc` writes a tiny temporary `moduleinit$$.C` file with a few functions\n# that often do nothing, compiles it and links it into every Charm module. We\n# have `charmc` generate this file and compile it into an object library that\n# can be linked into executables. The interface for this could be improved on\n# the Charm++ side. See this upstream issue:\n# https://github.com/UIUC-PPL/charm/issues/3210\nset(CHARM_MODULEINIT_CMD\n \"${CHARM_COMPILER} ${CHARMC_OPTIONS_JOINED} -o unused -save\")\nexecute_process(\n COMMAND\n bash -c \"(${CHARM_MODULEINIT_CMD} || mv moduleinit*.C CharmModuleInit.C) \\\n && rm moduleinit*\"\n WORKING_DIRECTORY ${CMAKE_BINARY_DIR}/tmp/\n ERROR_VARIABLE CHARM_MODULEINIT_ERROR\n )\nconfigure_file(\n ${CMAKE_BINARY_DIR}/tmp/CharmModuleInit.C\n ${CMAKE_BINARY_DIR}\n )\nadd_library(CharmModuleInit OBJECT ${CMAKE_BINARY_DIR}/CharmModuleInit.C)\n# -w -- suppress all warnings because this is charm-generated source\nset_property(TARGET CharmModuleInit\n APPEND PROPERTY COMPILE_OPTIONS $<$:-fPIC -w>)\n\n# Use the charm building blocks to construct imported targets\n# - Imported target with all Charm libs\nadd_library(Charmxx::charmxx INTERFACE IMPORTED)\ntarget_include_directories(Charmxx::charmxx INTERFACE ${CHARM_INCLUDE_DIRS})\ntarget_link_libraries(Charmxx::charmxx INTERFACE ${CHARM_LIBS})\n# - Target just for the PUP serialization library.\nadd_library(Charmxx::pup INTERFACE IMPORTED)\ntarget_include_directories(Charmxx::pup INTERFACE ${CHARM_INCLUDE_DIRS})\ntarget_link_libraries(Charmxx::pup INTERFACE ${PUP_LIBS})\n# - Target that defines the Charm++ main function.\nadd_library(Charmxx::main INTERFACE IMPORTED)\ntarget_link_libraries(\n Charmxx::main\n INTERFACE\n Charmxx::charmxx\n ${CHARM_LIB_ckmain}\n ${CHARM_LIB_conv-static}\n )\n# Add a preprocessing definition to indicate that a Charm++ main module is\n# available. This is used to conditionally compile Charm++-specific code\n# that assumes it is running in a Charm++ environment, such as the\n# `Parallel/CharmRegistration.hpp` code.\ntarget_compile_definitions(\n Charmxx::main\n INTERFACE\n SPECTRE_CHARM_HAS_MAIN\n )\n\n# Find and link MPI if necessary\n#\n# We currently check if `CHARM_CXX` obviously calls into an MPI compiler wrapper\n# to turn MPI linking on automatically. In the future it may be necessary to\n# further extend support for Charm++ wrapping other compiler wrappers and turn\n# them into CMake targets, as is done with MPI here.\nif (CHARM_CXX MATCHES \".*mpicxx.*\")\n set(CHARM_USE_MPI ON)\nendif()\nif (CHARM_USE_MPI)\n find_package(MPI REQUIRED)\n target_link_libraries(Charmxx::charmxx INTERFACE MPI::MPI_CXX)\nendif()\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(\n Charm\n # Only these paths are input variables, i.e. they are searched on the system\n # and can be specified on the command line to select the Charm installation.\n REQUIRED_VARS CHARM_COMPILER\n VERSION_VAR CHARM_VERSION\n )\n\nmark_as_advanced(\n CHARM_COMPILER\n CHARM_INCLUDE_DIR\n CHARM_USE_MPI\n CHARM_VERSION_MAJOR\n CHARM_VERSION_MINOR\n CHARM_VERSION_PATCH\n CHARM_VERSION\n )\n" }, { "path": "cmake/FindClangFormat.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nif(NOT CLANG_FORMAT_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(CLANG_FORMAT_ROOT \"\")\n set(CLANG_FORMAT_ROOT $ENV{CLANG_FORMAT_ROOT})\nendif()\n\nif(CMAKE_CXX_COMPILER_ID MATCHES \"Clang\")\n string(\n REGEX MATCH \"^[0-9]+.[0-9]+\" LLVM_VERSION\n \"${CMAKE_CXX_COMPILER_VERSION}\"\n )\n find_program(\n CLANG_FORMAT_BIN\n NAMES \"clang-format-${LLVM_VERSION}\" \"clang-format\"\n HINTS ${CLANG_FORMAT_ROOT}\n )\nelse()\n find_program(\n CLANG_FORMAT_BIN\n NAMES\n \"clang-format-4.0\"\n \"clang-format-3.9\"\n \"clang-format-3.8\"\n \"clang-format\"\n )\nendif()\n\nif (CLANG_FORMAT_BIN)\n execute_process(COMMAND ${CLANG_FORMAT_BIN} --version\n RESULT_VARIABLE CLANG_FORMAT_VERSION_RESULT\n OUTPUT_VARIABLE CLANG_FORMAT_VERSION\n OUTPUT_STRIP_TRAILING_WHITESPACE)\n\n if(CLANG_FORMAT_VERSION_RESULT MATCHES 0)\n string(REGEX REPLACE \"clang-format version \" \"\"\n CLANG_FORMAT_VERSION ${CLANG_FORMAT_VERSION})\n endif()\n\n # Look for a git-clang-format program in the same place as\n # clang-format. Versions of git-clang-format are not always\n # compatible with other clang-format executables.\n get_filename_component(CLANG_FORMAT_DIR ${CLANG_FORMAT_BIN} DIRECTORY)\n get_filename_component(CLANG_FORMAT_NAME ${CLANG_FORMAT_BIN} NAME)\n find_program(\n GIT_CLANG_FORMAT_BIN\n NAMES git-${CLANG_FORMAT_NAME}\n HINTS ${CLANG_FORMAT_DIR}\n NO_DEFAULT_PATH\n )\nendif()\n\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(\n ClangFormat REQUIRED_VARS CLANG_FORMAT_BIN VERSION_VAR CLANG_FORMAT_VERSION\n )\n\nmark_as_advanced(CLANG_FORMAT_VERSION)\n" }, { "path": "cmake/FindFFTW.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Find FFTW3 (The Fastest Fourier Transform in the West)\n# http://www.fftw.org/\n#\n# Defines the `FFTW::FFTW` target to link against.\n\nif(NOT FFTW_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(FFTW_ROOT \"\")\n set(FFTW_ROOT $ENV{FFTW_ROOT})\nendif()\n\nfind_path(FFTW_INCLUDE_DIR\n NAMES fftw3.h\n PATH_SUFFIXES include\n HINTS ${FFTW_ROOT}\n )\n\nfind_library(FFTW_LIB\n NAMES fftw3\n PATH_SUFFIXES lib64 lib\n HINTS ${FFTW_ROOT}\n )\n\nif (FFTW_INCLUDE_DIR AND FFTW_LIB)\n add_library(FFTW::FFTW INTERFACE IMPORTED)\n target_include_directories(FFTW::FFTW INTERFACE ${FFTW_INCLUDE_DIR})\n target_link_libraries(FFTW::FFTW INTERFACE ${FFTW_LIB})\nendif()\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(FFTW\n REQUIRED_VARS FFTW_INCLUDE_DIR FFTW_LIB)\nmark_as_advanced(FFTW_INCLUDE_DIR FFTW_LIB)\n" }, { "path": "cmake/FindFUKA.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Find the FUKA initial data code (https://bitbucket.org/fukaws/fuka/src/fuka/)\n#\n# Pass `FUKA_ROOT` to the CMake build configuration to set up the following\n# targets:\n#\n# - FUKA::Exporter: Functionality to load FUKA volume data and interpolate to\n# arbitrary points.\n\nif(NOT FUKA_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(FUKA_ROOT \"\")\n set(FUKA_ROOT $ENV{FUKA_ROOT})\nendif()\n\nfind_library(\n FUKA_LIB\n NAMES libkadath.a\n PATHS ${FUKA_ROOT}\n NO_DEFAULT_PATHS\n )\n\n# Link MPI (should be the same MPI that FUKA was built with)\nfind_package(MPI COMPONENTS C)\n\nif (FUKA_LIB AND MPI_C_FOUND)\n find_package(FFTW)\n if (FFTW_FOUND)\n add_library(FUKA::Exporter INTERFACE IMPORTED)\n target_link_libraries(\n FUKA::Exporter\n INTERFACE\n MPI::MPI_C\n FFTW::FFTW\n ${FUKA_LIB}\n )\n endif()\nendif()\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(\n FUKA\n REQUIRED_VARS\n FUKA_LIB\n )\n" }, { "path": "cmake/FindGoogleBenchmark.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Find GOOGLE_BENCHMARK: https://github.com/google/benchmark\n# If not in one of the default paths specify\n# -DGOOGLE_BENCHMARK_ROOT=/path/to/GOOGLE_BENCHMARK to search there as well.\n\nif(NOT GOOGLE_BENCHMARK_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(GOOGLE_BENCHMARK_ROOT \"\")\n set(GOOGLE_BENCHMARK_ROOT $ENV{GOOGLE_BENCHMARK_ROOT})\nendif()\n\nif(NOT GoogleBenchmark_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(GoogleBenchmark_ROOT \"\")\n set(GoogleBenchmark_ROOT $ENV{GoogleBenchmark_ROOT})\nendif()\n\nfind_path(GoogleBenchmark_INCLUDE_DIRS benchmark.h\n PATH_SUFFIXES include/benchmark\n HINTS ${GOOGLE_BENCHMARK_ROOT})\n\nfind_library(GoogleBenchmark_LIBRARIES\n NAMES benchmark\n PATH_SUFFIXES lib64 lib\n HINTS ${GOOGLE_BENCHMARK_ROOT} ${GoogleBenchmark_ROOT})\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(GoogleBenchmark\n FOUND_VAR GoogleBenchmark_FOUND\n REQUIRED_VARS GoogleBenchmark_INCLUDE_DIRS GoogleBenchmark_LIBRARIES)\nmark_as_advanced(GoogleBenchmark_INCLUDE_DIRS GoogleBenchmark_LIBRARIES)\n" }, { "path": "cmake/FindJEMALLOC.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Find jemalloc: https://github.com/jemalloc/jemalloc\n# If not in one of the default paths specify -D JEMALLOC_ROOT=/path/to/jemalloc\n# to search there as well.\n\nif(NOT JEMALLOC_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(JEMALLOC_ROOT \"\")\n set(JEMALLOC_ROOT $ENV{JEMALLOC_ROOT})\nendif()\n\n# find the jemalloc include directory\nfind_path(JEMALLOC_INCLUDE_DIRS jemalloc/jemalloc.h\n PATH_SUFFIXES include\n HINTS ${JEMALLOC_ROOT})\n\nfind_library(JEMALLOC_LIBRARIES\n NAMES jemalloc\n PATH_SUFFIXES lib64 lib\n HINTS ${JEMALLOC_ROOT})\n\nset(JEMALLOC_VERSION \"\")\n\nif(EXISTS \"${JEMALLOC_INCLUDE_DIRS}/jemalloc/jemalloc.h\")\n # Extract version info from header\n file(READ\n \"${JEMALLOC_INCLUDE_DIRS}/jemalloc/jemalloc.h\"\n JEMALLOC_FIND_HEADER_CONTENTS)\n\n string(REGEX MATCH \"#define JEMALLOC_VERSION_MAJOR [0-9]+\"\n JEMALLOC_MAJOR_VERSION \"${JEMALLOC_FIND_HEADER_CONTENTS}\")\n string(REPLACE \"#define JEMALLOC_VERSION_MAJOR \" \"\"\n JEMALLOC_MAJOR_VERSION\n \"${JEMALLOC_MAJOR_VERSION}\")\n\n string(REGEX MATCH \"#define JEMALLOC_VERSION_MINOR [0-9]+\"\n JEMALLOC_MINOR_VERSION \"${JEMALLOC_FIND_HEADER_CONTENTS}\")\n string(REPLACE \"#define JEMALLOC_VERSION_MINOR \" \"\"\n JEMALLOC_MINOR_VERSION\n \"${JEMALLOC_MINOR_VERSION}\")\n\n string(REGEX MATCH \"#define JEMALLOC_VERSION_BUGFIX [0-9]+\"\n JEMALLOC_SUBMINOR_VERSION \"${JEMALLOC_FIND_HEADER_CONTENTS}\")\n string(REPLACE \"#define JEMALLOC_VERSION_BUGFIX \" \"\"\n JEMALLOC_SUBMINOR_VERSION\n \"${JEMALLOC_SUBMINOR_VERSION}\")\n\n set(JEMALLOC_VERSION\n \"${JEMALLOC_MAJOR_VERSION}.${JEMALLOC_MINOR_VERSION}\\\n.${JEMALLOC_SUBMINOR_VERSION}\"\n )\nelse()\n message(WARNING \"Failed to find file \"\n \"'${JEMALLOC_INCLUDE_DIRS}/jemalloc/jemalloc.h' \"\n \"while detecting the JEMALLOC version.\")\nendif(EXISTS \"${JEMALLOC_INCLUDE_DIRS}/jemalloc/jemalloc.h\")\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(\n JEMALLOC\n FOUND_VAR JEMALLOC_FOUND\n REQUIRED_VARS JEMALLOC_INCLUDE_DIRS JEMALLOC_LIBRARIES\n VERSION_VAR JEMALLOC_VERSION\n )\nmark_as_advanced(JEMALLOC_INCLUDE_DIRS JEMALLOC_LIBRARIES\n JEMALLOC_MAJOR_VERSION JEMALLOC_MINOR_VERSION JEMALLOC_SUBMINOR_VERSION\n JEMALLOC_VERSION)\n" }, { "path": "cmake/FindLIBCXX.cmake", "content": "################################################################################\n#\n# \\file cmake/FindLIBCXX.cmake\n# \\author J. Bakosi\n# \\copyright 2012-2015, Jozsef Bakosi, 2016, Los Alamos National Security, LLC.\n# \\brief Find libc++\n# \\date Fri 20 Jan 2017 12:42:21 PM MST\n#\n################################################################################\n\n# From Quinoa: https://github.com/quinoacomputing/quinoa\n#\n# SpECTRE modifications:\n# - allow finding shared objects of libc++ and libc++abi\n\n# Find libc++.\n# See libc++: http://libcxx.llvm.org, libc++abi: http://libcxxabi.llvm.org.\n#\n# LIBCXX_FOUND - System has libc++\n# LIBCXX_INCLUDE_DIRS - The libc++ include directory\n# LIBCXX_LIBRARIES - The libraries needed to use libc++\n# LIBCXXABI_LIBRARIES - The libraries needed to use libc++abi\n#\n# Set the LIBCXX_ROOT cmake variable or shell environment variable before\n# calling find_package to a path to add an additional search path, e.g.,\n#\n# Usage:\n#\n# set(LIBCXX_ROOT \"/path/to/custom/libc++\") # prefer over system\n# find_package(LibCXX)\n# if(LIBCXX_FOUND)\n# target_link_libraries (TARGET ${LIBCXX_LIBRARIES} ${LIBCXXABI_LIBRARIES})\n# endif()\n\nif(NOT LIBCXX_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(LIBCXX_ROOT \"\")\n set(LIBCXX_ROOT $ENV{LIBCXX_ROOT})\nendif()\n\n# Extract a reasonable place to look for the libraries from the compiler path\nstring(REGEX REPLACE \"/bin/clang\\\\+\\\\+\" \"\"\n LIBCXX_PATH_FROM_COMPILER ${CMAKE_CXX_COMPILER})\n\n# If already in cache, be silent\nif(LIBCXX_INCLUDE_DIRS AND LIBCXX_LIBRARIES AND LIBCXXABI_LIBRARIES)\n set (LIBCXX_FIND_QUIETLY TRUE)\nendif()\n\nfind_path(LIBCXX_INCLUDE_DIR NAMES cmath\n HINTS ${LIBCXX_ROOT}/include/c++/v1\n ${LIBCXX_PATH_FROM_COMPILER}/include/c++/v1\n /usr/include/c++/v1)\n\nif(BUILD_SHARED_LIBS)\n find_library(LIBCXX_LIBRARIES NAMES c++\n HINTS ${LIBCXX_ROOT}/lib\n ${LIBCXX_PATH_FROM_COMPILER}/lib)\n find_library(LIBCXXABI_LIBRARIES NAMES c++abi\n HINTS ${LIBCXX_ROOT}/lib\n ${LIBCXX_PATH_FROM_COMPILER}/lib)\nelse()\n find_library(LIBCXX_LIBRARIES NAMES libc++.a libc++.so\n HINTS ${LIBCXX_ROOT}/lib\n ${LIBCXX_PATH_FROM_COMPILER}/lib)\n if(ARCH MATCHES \"ppc64\")\n set(LIBCXXABI_LIBRARIES \" \")\n else()\n find_library(LIBCXXABI_LIBRARIES NAMES libc++abi.a libc++abi.so\n HINTS ${LIBCXX_ROOT}/lib\n ${LIBCXX_PATH_FROM_COMPILER}/lib)\n endif()\nendif()\n\nset(LIBCXX_INCLUDE_DIRS ${LIBCXX_INCLUDE_DIR})\n\n# Handle the QUIETLY and REQUIRED arguments and set LIBCXX_FOUND to TRUE if\n# all listed variables are TRUE.\nINCLUDE(FindPackageHandleStandardArgs)\nFIND_PACKAGE_HANDLE_STANDARD_ARGS(\n LIBCXX\n DEFAULT_MSG\n LIBCXX_LIBRARIES\n LIBCXXABI_LIBRARIES\n LIBCXX_INCLUDE_DIRS\n)\n\nMARK_AS_ADVANCED(LIBCXX_INCLUDE_DIRS LIBCXX_LIBRARIES LIBCXXABI_LIBRARIES)\n" }, { "path": "cmake/FindLIBXSMM.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Find LIBXSMM: https://github.com/libxsmm/libxsmm\n# If not in one of the default paths specify -D LIBXSMM_ROOT=/path/to/LIBXSMM\n# to search there as well.\n\nif(NOT LIBXSMM_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(LIBXSMM_ROOT \"\")\n set(LIBXSMM_ROOT $ENV{LIBXSMM_ROOT})\nendif()\n\n# find the LIBXSMM include directory\nfind_path(LIBXSMM_INCLUDE_DIRS libxsmm.h\n PATH_SUFFIXES include\n HINTS ${LIBXSMM_ROOT})\n\nfind_library(LIBXSMM_LIBRARIES\n NAMES xsmm\n PATH_SUFFIXES lib64 lib\n HINTS ${LIBXSMM_ROOT})\n\nset(LIBXSMM_VERSION \"\")\n\nfunction(get_libxsmm_version FILE MAJOR_PREFIX MINOR_PREFIX PATCH_PREFIX)\n if(NOT EXISTS ${FILE})\n return()\n endif()\n # Extract version info from header\n file(READ ${FILE} LIBXSMM_FIND_HEADER_CONTENTS)\n\n string(REGEX MATCH \"${MAJOR_PREFIX}[0-9]+\"\n LIBXSMM_MAJOR_VERSION \"${LIBXSMM_FIND_HEADER_CONTENTS}\")\n if(\"${LIBXSMM_MAJOR_VERSION}\" STREQUAL \"\")\n return()\n endif()\n\n string(REPLACE \"${MAJOR_PREFIX}\" \"\" LIBXSMM_MAJOR_VERSION\n \"${LIBXSMM_MAJOR_VERSION}\")\n\n string(REGEX MATCH \"${MINOR_PREFIX}[0-9]+\"\n LIBXSMM_MINOR_VERSION \"${LIBXSMM_FIND_HEADER_CONTENTS}\")\n string(REPLACE \"${MINOR_PREFIX}\" \"\" LIBXSMM_MINOR_VERSION\n \"${LIBXSMM_MINOR_VERSION}\")\n\n string(REGEX MATCH \"${PATCH_PREFIX}[0-9]+\"\n LIBXSMM_SUBMINOR_VERSION \"${LIBXSMM_FIND_HEADER_CONTENTS}\")\n string(REPLACE \"${PATCH_PREFIX}\" \"\" LIBXSMM_SUBMINOR_VERSION\n \"${LIBXSMM_SUBMINOR_VERSION}\")\n\n set(LIBXSMM_VERSION\n \"${LIBXSMM_MAJOR_VERSION}.${LIBXSMM_MINOR_VERSION}.${LIBXSMM_SUBMINOR_VERSION}\"\n )\n set(LIBXSMM_VERSION ${LIBXSMM_VERSION} PARENT_SCOPE)\nendfunction(get_libxsmm_version FILE MAJOR_REGEX MINOR_REGEX PATCH_REGEX)\n\nif (LIBXSMM_INCLUDE_DIRS)\n get_libxsmm_version(\n ${LIBXSMM_INCLUDE_DIRS}/libxsmm.h\n \"#define LIBXSMM_VERSION_MAJOR \"\n \"#define LIBXSMM_VERSION_MINOR \"\n \"#define LIBXSMM_VERSION_UPDATE \"\n )\n\n get_libxsmm_version(\n ${LIBXSMM_INCLUDE_DIRS}/libxsmm_config.h\n \"#define LIBXSMM_CONFIG_VERSION_MAJOR \"\n \"#define LIBXSMM_CONFIG_VERSION_MINOR \"\n \"#define LIBXSMM_CONFIG_VERSION_UPDATE \"\n )\n\n get_libxsmm_version(\n ${LIBXSMM_INCLUDE_DIRS}/libxsmm_version.h\n \"#define LIBXSMM_CONFIG_VERSION_MAJOR \"\n \"#define LIBXSMM_CONFIG_VERSION_MINOR \"\n \"#define LIBXSMM_CONFIG_VERSION_UPDATE \"\n )\n\n if(\"${LIBXSMM_VERSION}\" STREQUAL \"\")\n message(WARNING \"Failed to detect LIBXSMM version.\")\n endif()\nendif()\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(\n LIBXSMM\n FOUND_VAR LIBXSMM_FOUND\n REQUIRED_VARS LIBXSMM_INCLUDE_DIRS LIBXSMM_LIBRARIES\n VERSION_VAR LIBXSMM_VERSION)\nmark_as_advanced(LIBXSMM_INCLUDE_DIRS LIBXSMM_LIBRARIES\n LIBXSMM_VERSION)\n\nif (NOT LIBXSMM_FOUND)\n return()\nendif()\n\n# Define imported target\nadd_library(Libxsmm INTERFACE IMPORTED)\nset_property(TARGET Libxsmm\n APPEND PROPERTY INTERFACE_INCLUDE_DIRECTORIES ${LIBXSMM_INCLUDE_DIRS})\nset_property(TARGET Libxsmm\n APPEND PROPERTY INTERFACE_LINK_LIBRARIES ${LIBXSMM_LIBRARIES})\n# LIBXSMM falls back to BLAS\nfind_package(BLAS REQUIRED)\ntarget_link_libraries(Libxsmm INTERFACE BLAS::BLAS)\n\nadd_interface_lib_headers(\n TARGET Libxsmm\n HEADERS\n libxsmm.h\n )\n" }, { "path": "cmake/FindNumPy.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nexecute_process(COMMAND ${CMAKE_COMMAND} -E env\n PYTHONPATH=${PYTHONPATH} ${Python_EXECUTABLE} \"-c\"\n \"import numpy as n; print(n.__version__); print(n.get_include());\"\n RESULT_VARIABLE RESULT\n OUTPUT_VARIABLE OUTPUT\n OUTPUT_STRIP_TRAILING_WHITESPACE)\n\nif(RESULT MATCHES 0)\n string(REGEX REPLACE \";\" \"\\\\\\\\;\" VALUES ${OUTPUT})\n string(REGEX REPLACE \"\\r?\\n\" \";\" VALUES ${VALUES})\n list(GET VALUES 0 NUMPY_VERSION)\n list(GET VALUES 1 NUMPY_INCLUDE_DIRS)\n\n string(REGEX MATCH \"^([0-9])+\\\\.([0-9])+\\\\.([0-9])+\" __ver_check \"${NUMPY_VERSION}\")\n if(\"${__ver_check}\" STREQUAL \"\")\n unset(NUMPY_VERSION)\n unset(NUMPY_INCLUDE_DIRS)\n message(STATUS \"Failed to retrieve NumPy version and include path, but got instead:\\n${OUTPUT}\\n\")\n endif()\nendif()\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(NumPy REQUIRED_VARS NUMPY_INCLUDE_DIRS NUMPY_VERSION\n VERSION_VAR NUMPY_VERSION)\n\nif(NUMPY_FOUND)\n message(STATUS \"NumPy ver. ${NUMPY_VERSION} found (include: ${NUMPY_INCLUDE_DIRS})\")\nelse()\n message(STATUS \"NumPy not found!\")\nendif()\n" }, { "path": "cmake/FindPAPI.cmake", "content": "# Obtained from: https://github.com/LLNL/perf-dump\n\n# Try to find PAPI headers and libraries.\n#\n# Usage of this module as follows:\n#\n# find_package(PAPI)\n#\n# Variables used by this module, they can change the default behaviour and need\n# to be set before calling find_package:\n#\n# PAPI_PREFIX Set this variable to the root installation of\n# libpapi if the module has problems finding the\n# proper installation path.\n#\n# Variables defined by this module:\n#\n# PAPI_FOUND System has PAPI libraries and headers\n# PAPI_LIBRARIES The PAPI library\n# PAPI_INCLUDE_DIRS The location of PAPI headers\n\nif(NOT PAPI_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(PAPI_ROOT \"\")\n set(PAPI_ROOT $ENV{PAPI_ROOT})\nendif()\n\nfind_path(\n PAPI_PREFIX\n NAMES include/papi.h\n HINTS ${PAPI_ROOT}\n)\n\nfind_library(\n PAPI_LIBRARIES\n # Pick the static library first for easier run-time linking.\n NAMES libpapi.a papi\n HINTS ${PAPI_PREFIX}/lib ${HILTIDEPS}/lib\n)\n\nfind_path(\n PAPI_INCLUDE_DIRS\n NAMES papi.h\n HINTS ${PAPI_PREFIX}/include ${HILTIDEPS}/include\n)\n\ninclude(FindPackageHandleStandardArgs)\n\nfind_package_handle_standard_args(\n PAPI\n DEFAULT_MSG\n PAPI_LIBRARIES\n PAPI_INCLUDE_DIRS\n)\n\nmark_as_advanced(\n PAPI_PREFIX_DIRS\n PAPI_LIBRARIES\n PAPI_INCLUDE_DIRS\n)\n" }, { "path": "cmake/FindParaView.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_program(PVPYTHON_EXEC pvpython)\n\n# Get version and runtime environment variables\nif (PVPYTHON_EXEC)\n execute_process(\n COMMAND ${PVPYTHON_EXEC} --print --version\n OUTPUT_VARIABLE _OUTPUT\n ERROR_VARIABLE _OUTPUT\n OUTPUT_STRIP_TRAILING_WHITESPACE\n ERROR_STRIP_TRAILING_WHITESPACE)\n string(REPLACE \"\\n\" \";\" _OUTPUT \"${_OUTPUT}\")\n foreach(_ENTRY ${_OUTPUT})\n # Extract the ParaView version from the output\n string(FIND \"${_ENTRY}\" \"paraview version \" _FOUND)\n if(NOT ${_FOUND} EQUAL -1)\n set(PARAVIEW_VERSION ${_ENTRY})\n endif()\n\n # On some machines ParaView needs specific environment variables set, e.g.\n # on CaltechHPC we need to set LD_LIBRARY_PATH. If other env variables\n # need to be set, then we need to possibly update this.\n string(FIND \"${_ENTRY}\" \"LD_LIBRARY_PATH=\" _FOUND)\n if(NOT ${_FOUND} EQUAL -1)\n set(PARAVIEW_PYTHON_ENV_VARS ${_ENTRY})\n endif()\n endforeach()\n string(REPLACE \"paraview version \" \"\" PARAVIEW_VERSION \"${PARAVIEW_VERSION}\")\nendif()\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(ParaView\n REQUIRED_VARS PVPYTHON_EXEC\n VERSION_VAR PARAVIEW_VERSION)\n\n# Get Python environment variables\nexecute_process(\n COMMAND ${PVPYTHON_EXEC} -m paraview.inspect\n OUTPUT_VARIABLE _OUTPUT\n OUTPUT_STRIP_TRAILING_WHITESPACE\n RESULT_VARIABLE _RESULT\n ERROR_QUIET)\nif (_RESULT EQUAL 0)\n string(REPLACE \"\\n\" \";\" _OUTPUT \"${_OUTPUT}\")\n list(GET _OUTPUT 0 PARAVIEW_PYTHON_VERSION)\n list(GET _OUTPUT 1 PARAVIEW_PYTHONPATH)\n string(REPLACE \"version: \" \"\"\n PARAVIEW_PYTHON_VERSION \"${PARAVIEW_PYTHON_VERSION}\")\n string(REPLACE \"pythonpath entry: \" \"\"\n PARAVIEW_PYTHONPATH \"${PARAVIEW_PYTHONPATH}\")\nelse()\n # If for whatever reason pvpython call didn't work, try another search\n get_filename_component(PVPYTHON_BINDIR ${PVPYTHON_EXEC} DIRECTORY)\n get_filename_component(PVPYTHON_BASEDIR ${PVPYTHON_BINDIR} DIRECTORY)\n file(GLOB_RECURSE\n PARAVIEW_PYTHONPATH\n ${PVPYTHON_BASEDIR}\n \"${PVPYTHON_BASEDIR}/lib*/python*/site-packages/paraview/simple.py\"\n )\n find_file(PARAVIEW_PYTHONPATH\n NAMES \"simple.py\"\n PATHS \"${PVPYTHON_BASEDIR}\"\n PATH_SUFFIXES \"/.*\"\n REQUIRED)\n # go back up to the site-packages\n get_filename_component(PARAVIEW_PYTHONPATH ${PARAVIEW_PYTHONPATH} DIRECTORY)\n get_filename_component(PARAVIEW_PYTHONPATH ${PARAVIEW_PYTHONPATH} DIRECTORY)\nendif()\n" }, { "path": "cmake/FindPythonModule.cmake", "content": "# From: https://github.com/ivansafrin/Polycode/\n\n# Find if a Python module is installed\n# Found at http://www.cmake.org/pipermail/cmake/2011-January/041666.html\n# To use do: find_python_module(PyQt4 REQUIRED) # if required\n# or: find_python_module(PyQt4) # if optional, check PY_PyQt4_FOUND\n# if(PY_PyQt4_FOUND)\n# # do stuff...\n# endif()\nfunction(find_python_module module)\n # Terminate early if the package has already been found\n if(PY_${module}_FOUND)\n return()\n endif()\n cmake_parse_arguments(ARG \"REQUIRED\" \"\" \"\" ${ARGN})\n # Try to import the module and get its location, if it's not already cached\n if(NOT PY_${module}_LOCATION)\n # A module's location is usually a directory, but for binary modules\n # it's a .so file.\n execute_process(COMMAND ${CMAKE_COMMAND} -E env\n PYTHONPATH=${PYTHONPATH} ${Python_EXECUTABLE} \"-c\"\n \"import re, ${module}; print(re.compile('/__init__.py.*').sub('',${module}.__file__))\"\n RESULT_VARIABLE _${module}_status\n OUTPUT_VARIABLE _${module}_location\n ERROR_QUIET\n OUTPUT_STRIP_TRAILING_WHITESPACE)\n if(_${module}_status EQUAL 0)\n set(PY_${module}_LOCATION ${_${module}_location} CACHE STRING\n \"Location of Python module ${module}\")\n endif()\n endif()\n # Make `find_package_handle_standard_args` error if the package is not found\n if(ARG_REQUIRED)\n set(PY_${module}_FIND_REQUIRED TRUE)\n endif()\n find_package_handle_standard_args(PY_${module}\n REQUIRED_VARS PY_${module}_LOCATION)\n set(PY_${module}_FOUND ${PY_${module}_FOUND} PARENT_SCOPE)\nendfunction(find_python_module)\n" }, { "path": "cmake/FindScotch.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Find Scotch: https://www.labri.fr/perso/pelegrin/scotch/\n# If not in one of the default paths specify -D SCOTCH_ROOT=/path/to/Scotch\n# to search there as well.\n\nif(NOT SCOTCH_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(SCOTCH_ROOT \"\")\n set(SCOTCH_ROOT $ENV{SCOTCH_ROOT})\nendif()\n\n# Find the Scotch include directory\nfind_path(SCOTCH_INCLUDE_DIR scotch.h\n PATH_SUFFIXES include\n HINTS ${SCOTCH_ROOT})\n\nfind_library(SCOTCH_LIB\n NAMES scotch\n PATH_SUFFIXES lib64 lib\n HINTS ${SCOTCH_ROOT})\n\nfind_library(SCOTCH_ERR_LIB\n NAMES scotcherr\n PATH_SUFFIXES lib64 lib\n HINTS ${SCOTCH_ROOT})\n\nset(SCOTCH_LIBRARIES \"${SCOTCH_LIB};${SCOTCH_ERR_LIB}\")\n\nset(SCOTCH_VERSION \"\")\n\nfile(READ \"${SCOTCH_INCLUDE_DIR}/scotch.h\" SCOTCH_FIND_HEADER_CONTENTS)\n\nset(SCOTCH_MAJOR_PREFIX \"#define SCOTCH_VERSION \")\nset(SCOTCH_MINOR_PREFIX \"#define SCOTCH_RELEASE \")\nset(SCOTCH_PATCH_PREFIX \"#define SCOTCH_PATCHLEVEL \")\n\nstring(REGEX MATCH \"${SCOTCH_MAJOR_PREFIX}[0-9]+\"\n SCOTCH_MAJOR_VERSION \"${SCOTCH_FIND_HEADER_CONTENTS}\")\nstring(REPLACE \"${SCOTCH_MAJOR_PREFIX}\" \"\" SCOTCH_MAJOR_VERSION\n \"${SCOTCH_MAJOR_VERSION}\")\n\nstring(REGEX MATCH \"${SCOTCH_MINOR_PREFIX}[0-9]+\"\n SCOTCH_MINOR_VERSION \"${SCOTCH_FIND_HEADER_CONTENTS}\")\nstring(REPLACE \"${SCOTCH_MINOR_PREFIX}\" \"\" SCOTCH_MINOR_VERSION\n \"${SCOTCH_MINOR_VERSION}\")\n\nstring(REGEX MATCH \"${SCOTCH_PATCH_PREFIX}[0-9]+\"\n SCOTCH_SUBMINOR_VERSION \"${SCOTCH_FIND_HEADER_CONTENTS}\")\nstring(REPLACE \"${SCOTCH_PATCH_PREFIX}\" \"\" SCOTCH_SUBMINOR_VERSION\n \"${SCOTCH_SUBMINOR_VERSION}\")\n\nset(SCOTCH_VERSION\n \"${SCOTCH_MAJOR_VERSION}.${SCOTCH_MINOR_VERSION}.${SCOTCH_SUBMINOR_VERSION}\"\n )\n\nset(Scotch_VERSION ${SCOTCH_VERSION})\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(\n Scotch\n FOUND_VAR SCOTCH_FOUND\n REQUIRED_VARS SCOTCH_INCLUDE_DIR SCOTCH_LIBRARIES\n VERSION_VAR SCOTCH_VERSION)\nmark_as_advanced(SCOTCH_INCLUDE_DIR SCOTCH_LIBRARIES\n SCOTCH_MAJOR_VERSION SCOTCH_MINOR_VERSION SCOTCH_PATCH_VERSION\n SCOTCH_VERSION Scotch_VERSION)\n" }, { "path": "cmake/FindSleef.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Find Sleef: https://github.com/shibatch/sleef\n# If not in one of the default paths specify -D SLEEF_ROOT=/path/to/Sleef\n# to search there as well.\n\nif(NOT SLEEF_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(SLEEF_ROOT \"\")\n set(SLEEF_ROOT $ENV{SLEEF_ROOT})\nendif()\n\n# find the SLEEF include directory\nfind_path(SLEEF_INCLUDE_DIR sleef.h\n PATH_SUFFIXES include\n HINTS ${SLEEF_ROOT})\n\nfind_library(SLEEF_LIBRARIES\n NAMES sleef\n PATH_SUFFIXES lib64 lib\n HINTS ${SLEEF_ROOT})\n\nset(SLEEF_VERSION \"\")\n\nif (EXISTS \"${SLEEF_INCLUDE_DIR}/sleef.h\")\n\n file(READ \"${SLEEF_INCLUDE_DIR}/sleef.h\" SLEEF_FIND_HEADER_CONTENTS)\n\n set(SLEEF_MAJOR_PREFIX \"#define SLEEF_VERSION_MAJOR \")\n set(SLEEF_MINOR_PREFIX \"#define SLEEF_VERSION_MINOR \")\n set(SLEEF_PATCH_PREFIX \"#define SLEEF_VERSION_PATCHLEVEL \")\n\n string(REGEX MATCH \"${SLEEF_MAJOR_PREFIX}[0-9]+\"\n SLEEF_MAJOR_VERSION \"${SLEEF_FIND_HEADER_CONTENTS}\")\n string(REPLACE \"${SLEEF_MAJOR_PREFIX}\" \"\" SLEEF_MAJOR_VERSION\n \"${SLEEF_MAJOR_VERSION}\")\n\n string(REGEX MATCH \"${SLEEF_MINOR_PREFIX}[0-9]+\"\n SLEEF_MINOR_VERSION \"${SLEEF_FIND_HEADER_CONTENTS}\")\n string(REPLACE \"${SLEEF_MINOR_PREFIX}\" \"\" SLEEF_MINOR_VERSION\n \"${SLEEF_MINOR_VERSION}\")\n\n string(REGEX MATCH \"${SLEEF_PATCH_PREFIX}[0-9]+\"\n SLEEF_SUBMINOR_VERSION \"${SLEEF_FIND_HEADER_CONTENTS}\")\n string(REPLACE \"${SLEEF_PATCH_PREFIX}\" \"\" SLEEF_SUBMINOR_VERSION\n \"${SLEEF_SUBMINOR_VERSION}\")\n\n set(SLEEF_VERSION\n \"${SLEEF_MAJOR_VERSION}.${SLEEF_MINOR_VERSION}.${SLEEF_SUBMINOR_VERSION}\"\n )\nendif()\n\nset(Sleef_VERSION ${SLEEF_VERSION})\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(\n Sleef\n FOUND_VAR SLEEF_FOUND\n REQUIRED_VARS SLEEF_INCLUDE_DIR SLEEF_LIBRARIES\n VERSION_VAR SLEEF_VERSION)\nmark_as_advanced(SLEEF_INCLUDE_DIR SLEEF_LIBRARIES\n SLEEF_MAJOR_VERSION SLEEF_MINOR_VERSION SLEEF_PATCH_VERSION\n SLEEF_VERSION Sleef_VERSION)\n\nadd_library(Sleef INTERFACE IMPORTED)\nset_property(TARGET Sleef PROPERTY\n INTERFACE_INCLUDE_DIRECTORIES ${SLEEF_INCLUDE_DIR})\nset_property(TARGET Sleef\n APPEND PROPERTY INTERFACE_LINK_LIBRARIES ${SLEEF_LIBRARIES})\n\nadd_interface_lib_headers(\n TARGET Sleef\n HEADERS\n sleef.h\n )\n" }, { "path": "cmake/FindSpEC.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Optionally link SpEC libraries. Pass `SPEC_ROOT` to the CMake build\n# configuration to set up the following targets:\n#\n# - SpEC::Exporter: Functionality to load SpEC volume data and interpolate to\n# arbitrary points.\n\nif(NOT SPEC_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(SPEC_ROOT \"\")\n set(SPEC_ROOT $ENV{SPEC_ROOT})\nendif()\n\nif (SPEC_ROOT)\n set(SPEC_EXPORTER_ROOT ${SPEC_ROOT}/Support/ApplyObservers/Exporter)\nelse()\n set(SPEC_EXPORTER_ROOT \"\")\nendif()\n\nfind_library(\n SPEC_PACKAGED_EXPORTER_LIB\n NAMES libPackagedExporter.a\n PATHS ${SPEC_EXPORTER_ROOT}\n NO_DEFAULT_PATHS\n )\nfind_file(\n SPEC_EXPORTER_FACTORY_OBJECTS\n NAMES ExporterFactoryObjects.o\n PATHS ${SPEC_EXPORTER_ROOT}\n NO_DEFAULT_PATHS\n )\nfind_path(\n SPEC_EXPORTER_INCLUDE_DIR\n NAMES Exporter.hpp\n PATHS ${SPEC_EXPORTER_ROOT}\n NO_DEFAULT_PATHS\n )\n\n# SpEC needs MPI.\n# NOTE: You should use the same MPI as SpEC. At least the same distribution. So\n# mixing OpenMPI and MPICH would be bad.\nfind_package(MPI COMPONENTS C)\n\nif (SPEC_PACKAGED_EXPORTER_LIB AND SPEC_EXPORTER_FACTORY_OBJECTS AND\n SPEC_EXPORTER_INCLUDE_DIR AND MPI_C_FOUND)\n add_library(SpEC::Exporter INTERFACE IMPORTED)\n target_include_directories(\n SpEC::Exporter INTERFACE ${SPEC_EXPORTER_INCLUDE_DIR})\n add_interface_lib_headers(\n TARGET SpEC::Exporter\n HEADERS\n Exporter.hpp\n )\n target_link_libraries(\n SpEC::Exporter\n INTERFACE\n MPI::MPI_C\n # The order of these next two lines is important\n ${SPEC_EXPORTER_FACTORY_OBJECTS}\n ${SPEC_PACKAGED_EXPORTER_LIB}\n )\n\n # Deal with FFTW3\n #\n # If it was dynamically linked into SpEC then we need to dynamically link it\n # into SpECTRE.\n set(_MACHINE_DEF_FILE\n ${SPEC_ROOT}/MakefileRules/this_machine.def)\n if (EXISTS ${_MACHINE_DEF_FILE})\n file(STRINGS ${_MACHINE_DEF_FILE} _MACHINE_DEF)\n # Filter starting comments\n list(FILTER _MACHINE_DEF EXCLUDE REGEX \"^[ ]*#\")\n # Remove inline comments\n list(TRANSFORM _MACHINE_DEF REPLACE \"[ ]*#.*\" \"\")\n string(REGEX MATCH \"FFTW_LIB[^;]+\"\n _FFTW3_DEF \"${_MACHINE_DEF}\")\n string(FIND ${_FFTW3_DEF} \"-lfftw3\" _FOUND_FFTW3_SHARED)\n # If we found a shared FFTW lib in SpEC, find and link FFTW here\n if(NOT ${_FOUND_FFTW3_SHARED} STREQUAL \"-1\")\n find_package(FFTW REQUIRED)\n target_link_libraries(SpEC::Exporter INTERFACE FFTW::FFTW)\n endif()\n endif()\nendif()\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(\n SpEC\n REQUIRED_VARS\n SPEC_PACKAGED_EXPORTER_LIB\n SPEC_EXPORTER_FACTORY_OBJECTS\n SPEC_EXPORTER_INCLUDE_DIR\n )\n" }, { "path": "cmake/FindTCMALLOC.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Find tcmalloc: https://github.com/gperftools/gperftools\n# If not in one of the default paths specify -D TCMALLOC_ROOT=/path/to/tcmalloc\n# to search there as well.\n\nif(NOT TCMALLOC_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(TCMALLOC_ROOT \"\")\n set(TCMALLOC_ROOT $ENV{TCMALLOC_ROOT})\nendif()\n\n# find the tcmalloc include directory\nfind_path(TCMALLOC_INCLUDE_DIRS gperftools/tcmalloc.h\n PATH_SUFFIXES include\n HINTS ${TCMALLOC_ROOT})\n\nfind_library(TCMALLOC_LIBRARIES\n NAMES tcmalloc\n PATH_SUFFIXES lib64 lib\n HINTS ${TCMALLOC_ROOT})\n\nset(TCMALLOC_VERSION \"\")\n\nif(EXISTS \"${TCMALLOC_INCLUDE_DIRS}/gperftools/tcmalloc.h\")\n # Extract version info from header\n file(READ\n \"${TCMALLOC_INCLUDE_DIRS}/gperftools/tcmalloc.h\"\n TCMALLOC_FIND_HEADER_CONTENTS)\n\n string(REGEX MATCH \"#define TC_VERSION_MAJOR [0-9]+\"\n TCMALLOC_MAJOR_VERSION \"${TCMALLOC_FIND_HEADER_CONTENTS}\")\n string(REPLACE \"#define TC_VERSION_MAJOR \" \"\"\n TCMALLOC_MAJOR_VERSION\n \"${TCMALLOC_MAJOR_VERSION}\")\n\n string(REGEX MATCH \"#define TC_VERSION_MINOR [0-9]+\"\n TCMALLOC_MINOR_VERSION \"${TCMALLOC_FIND_HEADER_CONTENTS}\")\n string(REPLACE \"#define TC_VERSION_MINOR \" \"\"\n TCMALLOC_MINOR_VERSION\n \"${TCMALLOC_MINOR_VERSION}\")\n\n\n set(TCMALLOC_VERSION\n \"${TCMALLOC_MAJOR_VERSION}.${TCMALLOC_MINOR_VERSION}\"\n )\nelse()\n message(WARNING \"Failed to find file \"\n \"'${TCMALLOC_INCLUDE_DIRS}/gperftools/tcmalloc.h' \"\n \"while detecting the TCMALLOC version.\")\nendif(EXISTS \"${TCMALLOC_INCLUDE_DIRS}/gperftools/tcmalloc.h\")\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(\n TCMALLOC\n FOUND_VAR TCMALLOC_FOUND\n REQUIRED_VARS TCMALLOC_INCLUDE_DIRS TCMALLOC_LIBRARIES\n VERSION_VAR TCMALLOC_VERSION\n )\nmark_as_advanced(TCMALLOC_INCLUDE_DIRS TCMALLOC_LIBRARIES\n TCMALLOC_MAJOR_VERSION TCMALLOC_MINOR_VERSION\n TCMALLOC_VERSION)\n" }, { "path": "cmake/Findccache.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_program(CCACHE_EXEC ccache)\n\nif (CCACHE_EXEC)\n # Get version\n execute_process(COMMAND ${CCACHE_EXEC} --version\n OUTPUT_VARIABLE CCACHE_VERSION\n OUTPUT_STRIP_TRAILING_WHITESPACE\n )\n # Keep only first line of output\n string(REGEX REPLACE \"\\n.*\" \"\" CCACHE_VERSION ${CCACHE_VERSION})\n # Remove \"ccache version \" prefix\n string(REGEX REPLACE \"ccache version \" \"\" CCACHE_VERSION ${CCACHE_VERSION})\nendif()\n\ninclude(FindPackageHandleStandardArgs)\nfind_package_handle_standard_args(\n ccache REQUIRED_VARS CCACHE_EXEC VERSION_VAR CCACHE_VERSION\n )\nmark_as_advanced(CCACHE_VERSION)\n" }, { "path": "cmake/PrintUsefulCMakeInfo.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# First append useful info to BuildInfo.txt\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"CMake version: ${CMAKE_VERSION}\\n\"\n \"CMAKE_CXX_FLAGS: ${CMAKE_CXX_FLAGS}\\n\"\n \"CMAKE_CXX_LINK_FLAGS: ${CMAKE_CXX_LINK_FLAGS}\\n\"\n \"CMAKE_CXX_FLAGS_DEBUG: ${CMAKE_CXX_FLAGS_DEBUG}\\n\"\n \"CMAKE_CXX_FLAGS_RELEASE: ${CMAKE_CXX_FLAGS_RELEASE}\\n\"\n \"CMAKE_C_FLAGS: ${CMAKE_C_FLAGS}\\n\"\n \"CMAKE_C_FLAGS_DEBUG: ${CMAKE_C_FLAGS_DEBUG}\\n\"\n \"CMAKE_C_FLAGS_RELEASE: ${CMAKE_C_FLAGS_RELEASE}\\n\"\n \"CMAKE_Fortran_FLAGS: ${CMAKE_Fortran_FLAGS}\\n\"\n \"CMAKE_Fortran_FLAGS_DEBUG: ${CMAKE_Fortran_FLAGS_DEBUG}\\n\"\n \"CMAKE_Fortran_FLAGS_RELEASE: ${CMAKE_Fortran_FLAGS_RELEASE}\\n\"\n \"CMAKE_EXE_LINKER_FLAGS: ${CMAKE_EXE_LINKER_FLAGS}\\n\"\n \"CMAKE_BUILD_TYPE: ${CMAKE_BUILD_TYPE}\\n\"\n \"CMAKE_CXX_COMPILER: ${CMAKE_CXX_COMPILER}\\n\"\n \"CMAKE_CXX_COMPILER_VERSION: ${CMAKE_CXX_COMPILER_VERSION}\\n\"\n \"CMAKE_C_COMPILER: ${CMAKE_C_COMPILER}\\n\"\n \"CMAKE_C_COMPILER_VERSION: ${CMAKE_C_COMPILER_VERSION}\\n\"\n \"CMAKE_Fortran_COMPILER: ${CMAKE_Fortran_COMPILER}\\n\"\n \"CMAKE_Fortran_COMPILER_VERSION: ${CMAKE_Fortran_COMPILER_VERSION}\\n\"\n \"Python version: ${Python_VERSION}\\n\"\n )\n\n# Then write (slightly expanded) useful info to command line\nmessage(STATUS \"\\nUseful Information:\")\nmessage(STATUS \"Git description: ${GIT_DESCRIPTION}\")\nmessage(STATUS \"Git branch: ${GIT_BRANCH}\")\nmessage(STATUS \"Git hash: ${GIT_HASH}\")\nmessage(STATUS \"Build directory: ${CMAKE_BINARY_DIR}\")\nmessage(STATUS \"Source directory: ${CMAKE_SOURCE_DIR}\")\nmessage(STATUS \"Bin directory: ${CMAKE_RUNTIME_OUTPUT_DIRECTORY}\")\nmessage(STATUS \"CMake modules path: ${CMAKE_MODULE_PATH}\")\nmessage(STATUS \"CMAKE_CXX_FLAGS: ${CMAKE_CXX_FLAGS}\")\nmessage(STATUS \"CMAKE_CXX_LINK_FLAGS: ${CMAKE_CXX_LINK_FLAGS}\")\nmessage(STATUS \"CMAKE_CXX_FLAGS_DEBUG: ${CMAKE_CXX_FLAGS_DEBUG}\")\nmessage(STATUS \"CMAKE_CXX_FLAGS_RELEASE: ${CMAKE_CXX_FLAGS_RELEASE}\")\nmessage(STATUS \"CMAKE_EXE_LINKER_FLAGS: ${CMAKE_EXE_LINKER_FLAGS}\")\nmessage(STATUS \"CMAKE_BUILD_TYPE: ${CMAKE_BUILD_TYPE}\")\nmessage(STATUS \"CMAKE_CXX_COMPILER: ${CMAKE_CXX_COMPILER}\")\nmessage(STATUS \"BUILD_SHARED_LIBS: ${BUILD_SHARED_LIBS}\")\nmessage(STATUS \"USE_PCH: ${USE_PCH}\")\nmessage(STATUS \"ASAN: ${ASAN}\")\nmessage(STATUS \"UBSAN_UNDEFINED: ${UBSAN_UNDEFINED}\")\nmessage(STATUS \"UBSAN_INTEGER: ${UBSAN_INTEGER}\")\n\nif (Python_FOUND)\n message(STATUS \"Python: ${Python_EXECUTABLE}\")\n message(STATUS \"Python version: ${Python_VERSION}\")\nelse()\n message(STATUS \"Python: Not found\")\nendif()\nmessage(STATUS \"BUILD_PYTHON_BINDINGS: ${BUILD_PYTHON_BINDINGS}\")\n\nif(CLANG_TIDY_BIN)\n message(STATUS \"Found clang-tidy: ${CLANG_TIDY_BIN}\")\nelseif(CMAKE_CXX_COMPILER_ID MATCHES \"Clang\")\n message(\n STATUS\n \"Could not find clang-tidy even though LLVM clang is installed\"\n )\nendif()\n\nif (CODE_COVERAGE)\n message(STATUS \"Code coverage enabled. All prerequisites found:\")\n message(STATUS \" gcov: ${GCOV}\")\n message(STATUS \" lcov: ${LCOV}\")\n message(STATUS \" genhtml: ${GENHTML}\")\n message(STATUS \" sed: ${SED}\")\nendif()\n\nif(DOXYGEN_FOUND)\n message(STATUS \"Doxygen: ${DOXYGEN_EXECUTABLE}\")\nelse()\n message(STATUS \"Doxygen: Not found, documentation cannot be built.\")\nendif()\n" }, { "path": "cmake/ProhibitInSourceBuild.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nstring(\n REGEX REPLACE\n \"^${CMAKE_SOURCE_DIR}/([^/]*)/?.*$\" \"\\\\1\"\n SUBDIR_OF_SOURCE_DIR ${CMAKE_BINARY_DIR}\n)\nset(PROHIBITED_SUBDIRS \"cmake\" \"containers\" \"docs\" \"external\" \"src\"\n \"support\" \"tests\" \"tools\")\n\nif (\"${CMAKE_BINARY_DIR}\" STREQUAL \"${CMAKE_SOURCE_DIR}\" OR\n ${SUBDIR_OF_SOURCE_DIR} IN_LIST PROHIBITED_SUBDIRS)\n message(FATAL_ERROR \"\\n\"\n \"You attempted to build ${PROJECT_NAME} in the directory:\\n\"\n \" ${CMAKE_BINARY_DIR}\\n\"\n \"In-source builds, however, are not allowed. \"\n \"Please create a directory and run cmake from there, passing the path \"\n \"to the source directory as the last argument; for example:\\n\"\n \" cd ${CMAKE_SOURCE_DIR}\\n\"\n \" mkdir build\\n\"\n \" cd build\\n\"\n \" cmake [OPTIONS] ${CMAKE_SOURCE_DIR}\\n\"\n \"You also need to remove the CMakeCache.txt file and the \"\n \"CMakeFiles directory in the source directory, or you will trigger \"\n \"this error again, even when doing an out-of-source build. Run:\\n\"\n \" rm -r ${CMAKE_BINARY_DIR}/CMakeCache.txt \"\n \"${CMAKE_BINARY_DIR}/CMakeFiles\\n\"\n )\nendif()\n" }, { "path": "cmake/RunInputFileTest.sh", "content": "#!/bin/sh -e\n\n# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Positional arguments to this script:\n# - $1: executable name\n# - $2: path to input file\n# - $3: directory name\n# - $4: space-separated list of expected exit codes\n# - $5: \"true\" to check output files or \"false\" to skip the check\n# - $6: \"true\" to check output files are present or \"false\" to skip\n# - $7: additional command-line arguments forwarded to the executable\n# - $8: extra files to copy\n\n# Set up test directory\ntest_dir=@CMAKE_BINARY_DIR@/tests/InputFiles/$3\nrm -rf $test_dir\nmkdir -p $test_dir\ncd $test_dir\n\ninput_file=$2\ncheck_output_values=$5\ncheck_output_present=$6\n\ninput_dir=`dirname $input_file`\nfor file in $8;\ndo\n cp $input_dir/$file $test_dir\ndone\n\n# Run the executable\nrestart=\nfor expected_code in $4 ; do\n if [ -z \"$restart\" ] ; then\n @SPECTRE_TEST_RUNNER@ @CMAKE_BINARY_DIR@/bin/$1 --input-file \\\n $input_file $7\n exit_code=$?\n restart=0\n else\n if [ $exit_code -ne 2 ] ; then\n echo \"Must restart after exit code 2\" >&2\n exit 1\n fi\n @SPECTRE_TEST_RUNNER@ @CMAKE_BINARY_DIR@/bin/$1 \\\n +restart Checkpoints/Checkpoint_$(printf %04d $restart)\n exit_code=$?\n restart=$(expr $restart + 1)\n fi\n if [ $exit_code -ne $expected_code ]; then\n echo \"ERROR: Exited with ${exit_code} instead of ${expected_code}\" >&2\n exit 1\n fi\ndone\n\n# Check output and clean up\nif [ \"$check_output_values\" = \"true\" ]; then\n @Python_EXECUTABLE@ @CMAKE_SOURCE_DIR@/tools/CheckOutputFiles.py \\\n --input-file $input_file --run-directory $test_dir \\\n --cmake-source-directory @CMAKE_SOURCE_DIR@ \\\n --cmake-bin-directory @CMAKE_BINARY_DIR@ \\\n || exit 1\nfi\nif [ \"$check_output_present\" = \"true\" ]; then\n @Python_EXECUTABLE@ -m spectre.tools.CleanOutput \\\n --output-dir $test_dir $input_file \\\n || exit 1\nfi\nrm -rf $test_dir\n" }, { "path": "cmake/SetBuildType.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# CMake lets the user define CMAKE_BUILD_TYPE on the command line and recognizes\n# the values \"Debug\", \"Release\", \"RelWithDebInfo\", and \"MinSizeRel\", which add\n# specific compiler or linker flags. CMake's default behavior is to add no\n# additional compiler or linker flags if the user does not define\n# CMAKE_BUILD_TYPE on the command line, or passes an unrecognized value.\n# We add a sanity check that checks if CMAKE_BUILD_TYPE is one of the recognized\n# values, and we also set the CMAKE_BUILD_TYPE to \"Debug\" if the user does not\n# specify it on the command line. In addition, we add \"None\" as a valid value\n# for CMAKE_BUILD_TYPE whose behavior is to add no additional compiler or linker\n# flags. This is done by defining the following flags analagous to those used by\n# the other build types. Additional build types can be defined in a similar\n# manner by defining the appropriate flags, and adding the name of the build\n# type to CMAKE_BUILD_TYPES below.\nset(CMAKE_CXX_FLAGS_NONE \"\" CACHE STRING\n \"Additional flags used by the compiler for Build type None.\"\n FORCE)\n\nset(CMAKE_C_FLAGS_NONE \"\" CACHE STRING\n \"Additional flags used by the compiler for Build type None.\"\n FORCE)\n\nset(CMAKE_EXE_LINKER_FLAGS_NONE \"\" CACHE STRING\n \"Additional flags used by the linker for Build type None.\"\n FORCE)\n\nset(CMAKE_Fortran_FLAGS_NONE \"\" CACHE STRING\n \"Additional flags used by the compiler for Build type None.\"\n FORCE)\n\nset(CMAKE_MODULE_LINKER_FLAGS_NONE \"\" CACHE STRING\n \"Additional flags used by the linker for Build type None.\"\n FORCE)\n\nset(CMAKE_SHARED_LINKER_FLAGS_NONE \"\" CACHE STRING\n \"Additional flags used by the linker for Build type None.\"\n FORCE)\n\nset(CMAKE_STATIC_LINKER_FLAGS_NONE \"\" CACHE STRING\n \"Additional flags used by the linker for Build type None.\"\n FORCE)\n\nmark_as_advanced(\n CMAKE_CXX_FLAGS_NONE\n CMAKE_C_FLAGS_NONE\n CMAKE_EXE_LINKER_FLAGS_NONE\n CMAKE_Fortran_FLAGS_NONE\n CMAKE_MODULE_LINKER_FLAGS_NONE\n CMAKE_SHARED_LINKER_FLAGS_NONE\n CMAKE_STATIC_LINKER_FLAGS_NONE\n )\n\nset(CMAKE_BUILD_TYPES \"Debug\" \"Release\" \"None\" \"RelWithDebInfo\" \"MinSizeRel\")\n\nif (NOT CMAKE_BUILD_TYPE)\n message(STATUS \"CMAKE_BUILD_TYPE not specified, setting to 'Debug'\")\n set(\n CMAKE_BUILD_TYPE Debug\n CACHE STRING \"Choose the type of build: ${CMAKE_BUILD_TYPES}\"\n FORCE\n )\nelse()\n if(NOT ${CMAKE_BUILD_TYPE} IN_LIST CMAKE_BUILD_TYPES)\n message(\n FATAL_ERROR \"\\n\"\n \"Invalid value for CMAKE_BUILD_TYPE: ${CMAKE_BUILD_TYPE}\\n\"\n \"Valid values: ${CMAKE_BUILD_TYPES}\\n\"\n )\n endif()\n message(STATUS \"CMAKE_BUILD_TYPE: ${CMAKE_BUILD_TYPE}\")\nendif()\n" }, { "path": "cmake/SetCxxStandard.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nset(CMAKE_CXX_STANDARD 20)\nset(CMAKE_CXX_STANDARD_REQUIRED ON)\nset(CMAKE_CXX_EXTENSIONS OFF)\n" }, { "path": "cmake/SetOutputDirectory.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Set the directory where the libraries and executables are placed\n# The default can be overridden by specifying\n# `-D CMAKE_RUNTIME_OUTPUT_DIRECTORY=/path/`\nif (NOT CMAKE_RUNTIME_OUTPUT_DIRECTORY)\n set(\n CMAKE_RUNTIME_OUTPUT_DIRECTORY\n \"${CMAKE_BINARY_DIR}/bin/\"\n CACHE STRING \"Choose the directory where executables are placed\" FORCE\n )\nendif (NOT CMAKE_RUNTIME_OUTPUT_DIRECTORY)\n\nif (NOT CMAKE_LIBRARY_OUTPUT_DIRECTORY)\n set(\n CMAKE_LIBRARY_OUTPUT_DIRECTORY\n \"${CMAKE_BINARY_DIR}/lib/\"\n CACHE STRING \"Choose the directory where shared libraries are placed\" FORCE\n )\nendif (NOT CMAKE_LIBRARY_OUTPUT_DIRECTORY)\n\nif (NOT CMAKE_ARCHIVE_OUTPUT_DIRECTORY)\n set(\n CMAKE_ARCHIVE_OUTPUT_DIRECTORY\n \"${CMAKE_BINARY_DIR}/lib/\"\n CACHE STRING \"Choose the directory where static libraries are placed\" FORCE\n )\nendif (NOT CMAKE_ARCHIVE_OUTPUT_DIRECTORY)\n" }, { "path": "cmake/SetupAllocator.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Always create the target and global property so that we don't need to\n# special case elsewhere in the code.\nset_property(GLOBAL\n PROPERTY\n SPECTRE_ALLOCATOR_LIBRARY\n \"\")\n\nadd_library(SpectreAllocator INTERFACE)\n\n# At some point we had issues with jemalloc/tcmalloc when using the sanitizers.\n# If this becomes an issue again then we can re-add the if(NOT ASAN) block\n# around the allocator setup.\n\noption(MEMORY_ALLOCATOR\n \"Which allocator to use: SYSTEM, TCMALLOC, JEMALLOC (default)\"\n OFF)\n\nset(JEMALLOC_LIB_TYPE \"\")\n\n# We need to link custom allocators before we link anything else so that\n# any third-party libraries, which generally should all be built as shared\n# libraries, use the allocator that we use. Unfortunately, how exactly\n# CMake decides on the linking order is not clear when using\n# INTERFACE_LINK_LIBRARIES and targets. To this end, we set a global\n# property SPECTRE_ALLOCATOR_LIBRARY that contains the link flag to link\n# to the memory allocator. By linking to the allocator library first\n# explicitly in target_link_libraries CMake correctly places the allocator\n# library as the first entry in the link libraries. We also link to the\n# SpectreAllocator target to pull in any additional allocator-related\n# flags, such as include directories.\n#\n# Targets can grab the link flags using:\n#\n# get_property(\n# SPECTRE_ALLOCATOR_LIBRARY\n# GLOBAL\n# PROPERTY SPECTRE_ALLOCATOR_LIBRARY\n# )\n# target_link_libraries(${TARGET_NAME}\n# PUBLIC\n# ${SPECTRE_ALLOCATOR_LIBRARY}\n# SpectreAllocator\n# )\n#\n# These need to be the first call to target_link_libraries of the target.\nif(\"${MEMORY_ALLOCATOR}\" STREQUAL \"JEMALLOC\"\n OR \"${MEMORY_ALLOCATOR}\" STREQUAL \"OFF\")\n include(SetupJemalloc)\n target_link_libraries(\n SpectreAllocator\n INTERFACE\n Jemalloc\n )\n get_property(\n SPECTRE_ALLOCATOR_LIBRARY\n TARGET Jemalloc\n PROPERTY INTERFACE_LINK_LIBRARIES\n )\n set_property(GLOBAL\n PROPERTY\n SPECTRE_ALLOCATOR_LIBRARY\n ${SPECTRE_ALLOCATOR_LIBRARY})\nelseif(\"${MEMORY_ALLOCATOR}\" STREQUAL \"TCMALLOC\")\n include(SetupTcmalloc)\n target_link_libraries(\n SpectreAllocator\n INTERFACE\n Tcmalloc\n )\n get_property(\n SPECTRE_ALLOCATOR_LIBRARY\n TARGET Tcmalloc\n PROPERTY INTERFACE_LINK_LIBRARIES\n )\n set_property(GLOBAL\n PROPERTY\n SPECTRE_ALLOCATOR_LIBRARY\n ${SPECTRE_ALLOCATOR_LIBRARY})\nelseif(NOT \"${MEMORY_ALLOCATOR}\" STREQUAL \"SYSTEM\")\n message(FATAL_ERROR\n \"Unknown memory allocator specified '${MEMORY_ALLOCATOR}'. \"\n \"Known options are:\\n\"\n \" SYSTEM, TCMALLOC, JEMALLOC (default)\")\nelse()\n message(STATUS \"Using system default memory allocator.\")\nendif()\n" }, { "path": "cmake/SetupAutodiff.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Find autodiff (https://github.com/autodiff/autodiff)\n#\n# Note that Boost also has an autodiff module, but it uses templates to\n# distinguish multiple variables. This means a std::array or Tensor can't hold\n# the Boost autodiff variables. For example, to evaluate a 2D function f(x, y),\n# the type for x would be fvar and the type for y would be the nested\n# fvar>. On the other hand, the autodiff library works with a\n# simpler autodiff::dual or autodiff::var type, which can be stored in a\n# std::array or Tensor.\n\noption(SPECTRE_AUTODIFF \"Enable automatic differentiation\" OFF)\n\nif (NOT SPECTRE_AUTODIFF)\n return()\nendif()\n\n# we assume the found autodiff is newer than the GIT_TAG below,\n# which has not been in autodiff's official release.\nfind_package(autodiff QUIET)\n\nif (NOT autodiff_FOUND)\n if (NOT SPECTRE_FETCH_MISSING_DEPS)\n message(FATAL_ERROR \"Could not find autodiff. If you want to fetch \"\n \"missing dependencies automatically, set SPECTRE_FETCH_MISSING_DEPS=ON.\")\n endif()\n\n message(STATUS \"Fetching autodiff\")\n include(FetchContent)\n FetchContent_Declare(autodiff\n GIT_REPOSITORY https://github.com/autodiff/autodiff\n # Choose an unreleased version on top of v1.1.2 that makes dependence on\n # Eigen optional.\n GIT_TAG cc2aa5726fdbb258d097f87b97da3d1022f8394e\n ${SPECTRE_FETCHCONTENT_BASE_ARGS}\n )\n set(AUTODIFF_BUILD_TESTS OFF CACHE BOOL \"Build autodiff tests\")\n set(AUTODIFF_BUILD_EXAMPLES OFF CACHE BOOL \"Build autodiff examples\")\n set(AUTODIFF_BUILD_PYTHON OFF CACHE BOOL \"Build autodiff Python bindings\")\n set(AUTODIFF_BUILD_DOCS OFF CACHE BOOL \"Build autodiff documentation\")\n FetchContent_MakeAvailable(autodiff)\n\n if (CMAKE_VERSION VERSION_LESS 3.25)\n get_target_property(AUTODIFF_IID autodiff INTERFACE_INCLUDE_DIRECTORIES)\n set_target_properties(autodiff PROPERTIES INTERFACE_SYSTEM_INCLUDE_DIRECTORIES \"${AUTODIFF_IID}\")\n endif()\nendif()\n\nset_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n autodiff::autodiff\n )\n" }, { "path": "cmake/SetupBlas.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_package(BLAS REQUIRED)\nmessage(STATUS \"BLAS libs: \" ${BLAS_LIBRARIES})\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"BLAS_LIBRARIES: ${BLAS_LIBRARIES}\\n\"\n )\n\nset_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n BLAS::BLAS\n )\n\n# Check if we have found OpenBLAS and can disable its multithreading, since it\n# conflicts with Charm++ parallelism. Details:\n# https://github.com/xianyi/OpenBLAS/wiki/Faq#multi-threaded\n# We use `execute_process` instead of `try_compile` to avoid potentially slow\n# disk IO.\nset(\n CHECK_DISABLE_OPENBLAS_MULTITHREADING_SOURCE\n \"extern \\\"C\\\" { void openblas_set_num_threads(int); }\\n\\\nint main() { openblas_set_num_threads(1); }\"\n )\nstring(REPLACE \";\" \" \" BLAS_LIBRARIES_JOINED_WITH_SPACES \"${BLAS_LIBRARIES}\")\nexecute_process(\n COMMAND\n bash -c\n \"${CMAKE_CXX_COMPILER} ${BLAS_LIBRARIES_JOINED_WITH_SPACES} -x c++ - <<< $'\\\n${CHECK_DISABLE_OPENBLAS_MULTITHREADING_SOURCE}' -o /dev/null\"\n RESULT_VARIABLE CHECK_DISABLE_OPENBLAS_MULTITHREADING_RESULT\n ERROR_VARIABLE CHECK_DISABLE_OPENBLAS_MULTITHREADING_ERROR\n OUTPUT_QUIET\n )\nif(${CHECK_DISABLE_OPENBLAS_MULTITHREADING_RESULT} EQUAL 0)\n set(DISABLE_OPENBLAS_MULTITHREADING ON)\n add_definitions(-DDISABLE_OPENBLAS_MULTITHREADING)\n message(STATUS \"Disabled OpenBLAS multithreading\")\nelse()\n message(STATUS \"BLAS vendor is probably not OpenBLAS. Make sure it doesn't \"\n \"try to do multithreading that might conflict with Charm++ parallelism.\")\nendif()\n" }, { "path": "cmake/SetupBlaze.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(USE_SLEEF \"Use Sleef to add more vectorized instructions.\" OFF)\n\nif(USE_SLEEF)\n # Try to find Sleef to increase vectorization\n find_package(Sleef)\nendif()\n\nif(SLEEF_FOUND)\n message(STATUS \"Sleef libs: ${SLEEF_LIBRARIES}\")\n message(STATUS \"Sleef incl: ${SLEEF_INCLUDE_DIR}\")\n message(STATUS \"Sleef vers: ${SLEEF_VERSION}\")\n\n file(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"Sleef version: ${SLEEF_VERSION}\\n\"\n )\nendif()\n\n# Every time we've upgraded blaze compatibility in the past, we've had to change\n# vector code, so we should expect to need changes again on each subsequent\n# release, so we should specify an exact version requirement. However, Blaze\n# hasn't been consistent in naming releases (version 3.8.2 has 3.9.0 written\n# in Version.h).\nfind_package(Blaze 3.8)\n\nif (NOT Blaze_FOUND)\n if (NOT SPECTRE_FETCH_MISSING_DEPS)\n message(FATAL_ERROR \"Could not find Blaze. If you want to fetch \"\n \"missing dependencies automatically, set SPECTRE_FETCH_MISSING_DEPS=ON.\")\n endif()\n message(STATUS \"Fetching Blaze\")\n include(FetchContent)\n FetchContent_Declare(Blaze\n URL https://bitbucket.org/blaze-lib/blaze/downloads/blaze-3.8.2.tar.gz\n ${SPECTRE_FETCHCONTENT_BASE_ARGS}\n )\n # Configure Blaze CMake variables. Most configuration is done below.\n set(BLAZE_SHARED_MEMORY_PARALLELIZATION 0 CACHE INTERNAL \"Blaze SMP mode\")\n FetchContent_MakeAvailable(Blaze)\n set(BLAZE_INCLUDE_DIR ${blaze_SOURCE_DIR})\n set(BLAZE_VERSION \"3.8.2\")\nendif()\n\nmessage(STATUS \"Blaze incl: ${BLAZE_INCLUDE_DIR}\")\nmessage(STATUS \"Blaze vers: ${BLAZE_VERSION}\")\n\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"Blaze version: ${BLAZE_VERSION}\\n\"\n )\n\nfind_package(BLAS REQUIRED)\nfind_package(GSL REQUIRED)\nfind_package(LAPACK REQUIRED)\n\nadd_library(Blaze INTERFACE IMPORTED)\nset_property(TARGET Blaze PROPERTY\n INTERFACE_INCLUDE_DIRECTORIES ${BLAZE_INCLUDE_DIR})\ntarget_link_libraries(\n Blaze\n INTERFACE\n BLAS::BLAS\n GSL::gsl # for BLAS header\n LAPACK::LAPACK\n )\nset(_BLAZE_USE_SLEEF 0)\n\nif(SLEEF_FOUND)\n target_link_libraries(\n Blaze\n INTERFACE\n Sleef\n )\n set_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n Sleef\n )\n set(_BLAZE_USE_SLEEF 1)\nendif()\n\n# If BLAZE_USE_STRONG_INLINE=ON, Blaze will use this keyword to increase the\n# likelihood of inlining. If BLAZE_USE_STRONG_INLINE=OFF, uses inline keyword\n# as a fallback.\noption(BLAZE_USE_STRONG_INLINE \"Increase likelihood of Blaze inlining.\" ON)\n\nset(_BLAZE_USE_STRONG_INLINE 0)\n\nif(BLAZE_USE_STRONG_INLINE)\n set(_BLAZE_USE_STRONG_INLINE 1)\nendif()\n\n# If BLAZE_USE_ALWAYS_INLINE=ON, Blaze will use this keyword to force inlining.\n# If BLAZE_USE_ALWAYS_INLINE=OFF or if the platform being used cannot 100%\n# guarantee inlining, uses BLAZE_STRONG_INLINE as a fallback.\noption(BLAZE_USE_ALWAYS_INLINE \"Force Blaze inlining.\" ON)\n\nset(_BLAZE_USE_ALWAYS_INLINE 0)\n\nif(BLAZE_USE_ALWAYS_INLINE)\n set(_BLAZE_USE_ALWAYS_INLINE 1)\nendif()\n\n# Configure Blaze. Some of the Blaze configuration options could be optimized\n# for the machine we are running on. See documentation:\n# https://bitbucket.org/blaze-lib/blaze/wiki/Configuration%20and%20Installation#!step-2-configuration\ntarget_compile_definitions(Blaze\n INTERFACE\n # - Enable external BLAS kernels\n BLAZE_BLAS_MODE=1\n # - Use BLAS header from GSL. We could also find and include a (or\n # similarly named) header that may be distributed with the BLAS\n # implementation, but it's not guaranteed to be available and may conflict\n # with the GSL header. Since we use GSL anyway, it's easier to use their\n # BLAS header.\n BLAZE_BLAS_INCLUDE_FILE=\n # - Set default matrix storage order to column-major, since many of our\n # functions are implemented for column-major layout. This default reduces\n # conversions.\n BLAZE_DEFAULT_STORAGE_ORDER=blaze::columnMajor\n # - Disable SMP parallelization. This disables SMP parallelization for all\n # possible backends (OpenMP, C++11 threads, Boost, HPX):\n # https://bitbucket.org/blaze-lib/blaze/wiki/Serial%20Execution#!option-3-deactivation-of-parallel-execution\n BLAZE_USE_SHARED_MEMORY_PARALLELIZATION=0\n # - Disable MPI parallelization\n BLAZE_MPI_PARALLEL_MODE=0\n # - Using the default cache size, which may have been configured automatically\n # by the Blaze CMake configuration for the machine we are running on. We\n # could override it here explicitly to tune performance.\n # BLAZE_CACHE_SIZE\n # - Disable padding for dynamic matrices.\n # Blaze warns that this may decrease performance:\n # https://bitbucket.org/blaze-lib/blaze/src/c4d9e85414370e880e5e79c86e3c8d4d38dcde7a/blaze/config/Optimizations.h#lines-52\n # We haven't tested this much, so we may want to try enabling padding again.\n # To support padding, explicit calls to LAPACK functions need to pass\n # `.spacing()` instead of `.rows()/.columns()` to the `LDA`, `LDB`, etc.\n # parameters (see `[matrix_spacing]` in `Test_Spectral.cpp`).\n BLAZE_USE_PADDING=0\n # - Always enable non-temporal stores for cache optimization of large data\n # structures: https://bitbucket.org/blaze-lib/blaze/wiki/Configuration%20Files#!streaming-non-temporal-stores\n BLAZE_USE_STREAMING=1\n # - Skip initializing default-constructed structures for fundamental types\n BLAZE_USE_DEFAULT_INITIALIZATON=0\n # Use Sleef for vectorization of more math functions\n BLAZE_USE_SLEEF=${_BLAZE_USE_SLEEF}\n # Set inlining settings\n BLAZE_USE_STRONG_INLINE=${_BLAZE_USE_STRONG_INLINE}\n BLAZE_USE_ALWAYS_INLINE=${_BLAZE_USE_ALWAYS_INLINE}\n )\n\n# We need to make sure `BlazeExceptions.hpp` is included. It is included in the\n# PCH (see tools/SpectrePch.hpp). If there's no PCH, we need to include it here.\nif (NOT USE_PCH)\n target_compile_options(Blaze\n INTERFACE\n \"$<$:SHELL:-include Utilities/BlazeExceptions.hpp>\")\nendif()\n\nadd_interface_lib_headers(\n TARGET Blaze\n HEADERS\n blaze/math/CustomVector.h\n blaze/math/DynamicMatrix.h\n blaze/math/DynamicVector.h\n blaze/system/Optimizations.h\n blaze/system/Version.h\n blaze/util/typetraits/RemoveConst.h\n )\n\nset_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n Blaze\n )\n" }, { "path": "cmake/SetupBoost.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_package(Boost 1.60.0 REQUIRED COMPONENTS program_options)\n\n# CMake versions don't set this consistently\nset(Boost_VERSION \"${Boost_MAJOR_VERSION}.${Boost_MINOR_VERSION}.${Boost_SUBMINOR_VERSION}\")\n\nmessage(STATUS \"Boost libraries: ${Boost_LIBRARIES}\")\nmessage(STATUS \"Boost include: ${Boost_INCLUDE_DIRS}\")\nmessage(STATUS \"Boost version: ${Boost_VERSION}\")\n\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"Boost version: ${Boost_VERSION}\\n\"\n )\n\n# Boost organizes targets as:\n# - Boost::boost is the header-only parts of Boost\n# - Boost::COMPONENT are the components that need linking, e.g. program_options\n\nadd_interface_lib_headers(\n TARGET Boost::boost\n HEADERS\n boost/algorithm/string.hpp\n boost/config.hpp\n boost/core/demangle.hpp\n boost/functional/hash.hpp\n boost/integer/common_factor_rt.hpp\n boost/iterator/transform_iterator.hpp\n boost/iterator/zip_iterator.hpp\n boost/make_shared.hpp\n boost/math/interpolators/barycentric_rational.hpp\n boost/math/special_functions/binomial.hpp\n boost/math/tools/roots.hpp\n boost/multi_array.hpp\n boost/multi_array/base.hpp\n boost/multi_array/extent_gen.hpp\n boost/numeric/odeint.hpp\n boost/numeric/odeint/integrate/integrate_adaptive.hpp>\n boost/numeric/odeint/stepper/controlled_runge_kutta.hpp\n boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp\n boost/numeric/odeint/stepper/generation/make_dense_output.hpp\n boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp\n boost/parameter/name.hpp\n boost/preprocessor.hpp\n boost/preprocessor/arithmetic/dec.hpp\n boost/preprocessor/arithmetic/inc.hpp\n boost/preprocessor/arithmetic/sub.hpp\n boost/preprocessor/control/expr_iif.hpp\n boost/preprocessor/control/iif.hpp\n boost/preprocessor/control/while.hpp\n boost/preprocessor/list/adt.hpp\n boost/preprocessor/list/fold_left.hpp\n boost/preprocessor/list/fold_right.hpp\n boost/preprocessor/list/for_each.hpp\n boost/preprocessor/list/for_each_product.hpp\n boost/preprocessor/list/size.hpp\n boost/preprocessor/list/to_tuple.hpp\n boost/preprocessor/list/transform.hpp\n boost/preprocessor/logical/bitand.hpp\n boost/preprocessor/logical/bool.hpp\n boost/preprocessor/logical/compl.hpp\n boost/preprocessor/punctuation/comma_if.hpp\n boost/preprocessor/repetition/for.hpp\n boost/preprocessor/repetition/repeat.hpp\n boost/preprocessor/tuple/elem.hpp\n boost/preprocessor/tuple/enum.hpp\n boost/preprocessor/tuple/reverse.hpp\n boost/preprocessor/tuple/size.hpp\n boost/preprocessor/tuple/to_list.hpp\n boost/preprocessor/variadic/elem.hpp\n boost/preprocessor/variadic/to_list.hpp\n boost/range/combine.hpp\n boost/shared_ptr.hpp\n boost/tuple/tuple.hpp\n boost/tuple/tuple_comparison.hpp\n boost/variant.hpp\n boost/variant/get.hpp\n boost/variant/variant.hpp\n )\n\nset_property(\n TARGET Boost::program_options\n APPEND PROPERTY PUBLIC_HEADER\n boost/program_options.hpp\n )\n\nset_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n Boost::boost Boost::program_options\n )\n\n# We disable thread safety of Boost::shared_ptr since it makes them faster\n# to use and we do not share them between threads. If a thread-safe\n# shared_ptr is desired it must be implemented to work with Charm++'s threads\n# anyway.\nset_property(TARGET Boost::boost\n APPEND PROPERTY\n INTERFACE_COMPILE_DEFINITIONS\n $<$:BOOST_SP_DISABLE_THREADS>\n)\n\n# Some older versions of boost don't play nice with new versions of Clang and\n# GCC-12. We can just blanket enable the BOOST_NO_CXX98_FUNCTION_BASE macro,\n# which is what boost does anyway with newer versions.\nset_property(TARGET Boost::boost\n APPEND PROPERTY\n INTERFACE_COMPILE_DEFINITIONS\n $<$:BOOST_NO_CXX98_FUNCTION_BASE>\n)\n\n# With newer versions of boost, sometimes there are internal boost warnings\n# about deprecated headers. This disables those as we have no control over what\n# boost does internally.\nset_property(TARGET Boost::boost\n APPEND PROPERTY\n INTERFACE_COMPILE_DEFINITIONS\n $<$:BOOST_ALLOW_DEPRECATED_HEADERS>)\n\n# Old versions of boost only enabled variadic macros for known compilers.\n# This changed in boost 1.75.0, where variadic macros are always enabled.\n# We enable this here manually for older versions of boost so the code compiles\n# with nvcc.\nif(Boost_VERSION VERSION_LESS 1.75.0)\n set_property(TARGET Boost::boost\n APPEND PROPERTY\n INTERFACE_COMPILE_DEFINITIONS\n $<$:BOOST_PP_VARIADICS=1>)\nendif()\n\n# Override the boost index type to match the STL for Boost.MultiArray\n# (std::ptrdiff_t to std::size_t)\n# Note: This header guard changed in Boost 1.73.0\nif(Boost_VERSION VERSION_GREATER_EQUAL 1.73.0)\n set(BOOST_MULTI_ARRAY_TYPES_HEADER_GUARD BOOST_MULTI_ARRAY_TYPES_HPP)\nelse()\n set(BOOST_MULTI_ARRAY_TYPES_HEADER_GUARD BOOST_MULTI_ARRAY_TYPES_RG071801_HPP)\nendif()\nset_property(TARGET Boost::boost\n APPEND PROPERTY\n INTERFACE_COMPILE_DEFINITIONS\n $<$:${BOOST_MULTI_ARRAY_TYPES_HEADER_GUARD}>)\n\n# Work around boost not building with clang 15 (fixed in boost 1.83.0)\n# (https://github.com/boostorg/functional/pull/21)\nif (CMAKE_CXX_COMPILER_ID MATCHES \"Clang\" AND BOOST_VERSION VERSION_LESS 1.83.0)\n if(CMAKE_CXX_COMPILER_VERSION VERSION_GREATER \"15.0.0\" OR\n CMAKE_CXX_COMPILER_VERSION VERSION_EQUAL \"15.0.0\")\n target_compile_definitions(Boost::boost INTERFACE _HAS_AUTO_PTR_ETC=0)\n endif()\nendif()\n\n" }, { "path": "cmake/SetupCCache.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Use CCache if available to speed up builds\n#\n# CCache is particularly useful for speeding up builds on CI, where we can share\n# the cache between runs. It is also very useful for general development.\n#\n# To support precompiled headers (PCH) we follow the recommendations in the\n# ccache docs:\n# https://ccache.dev/manual/latest.html#_precompiled_headers\n# Our requirements for CCache with PCH are:\n# - Works with GCC and Clang.\n# - Deleting and recreating the build directory retains ~100% cache hit rate.\n# - `make clean` retains ~100% cache hit rate.\n# - Changing the PCH file in tools/SpectrePch.hpp invalidates the cache.\n# - Sharing caches between runs on CI works.\n\noption(USE_CCACHE \"Use CCache if available to speed up builds\" ON)\n\nset(CCACHE_LAUNCHER_EXTRA_ENV_VARS \"\" CACHE STRING \"Env vars for ccache\")\n\nif(NOT USE_CCACHE)\n return()\nendif()\n\nfind_package(ccache)\n\nif (NOT CCACHE_EXEC)\n return()\nendif()\n\nexecute_process(COMMAND realpath ${CCACHE_EXEC}\n OUTPUT_STRIP_TRAILING_WHITESPACE\n OUTPUT_VARIABLE REAL_CCACHE_EXEC)\n\n# Configure ccache with environment variables\nset(_CCACHE_LAUNCHER_ENV_VARS\n ${CCACHE_LAUNCHER_EXTRA_ENV_VARS}\n \"CCACHE_SLOPPINESS=pch_defines,time_macros,include_file_mtime,\\\ninclude_file_ctime\")\n# The `locale` sloppiness is only available in ccache 3.6 and later\nif (CCACHE_VERSION VERSION_GREATER_EQUAL 3.6)\n string(APPEND _CCACHE_LAUNCHER_ENV_VARS \",locale\")\nendif()\n\n# Invoke compiler through ccache\nset(CMAKE_CXX_COMPILER_LAUNCHER\n ${_CCACHE_LAUNCHER_ENV_VARS} ${REAL_CCACHE_EXEC})\nset(CMAKE_C_COMPILER_LAUNCHER ${CMAKE_CXX_COMPILER_LAUNCHER})\nmessage(STATUS \"Using ccache for compilation. It is invoked as: \"\n \"${CMAKE_CXX_COMPILER_LAUNCHER}\")\n\n# Add `-fno-pch-timestamp` flag to Clang to support precompiled headers\n# (see https://ccache.dev/manual/4.8.2.html#_precompiled_headers)\n# Note that `CMAKE_CXX_COMPILE_OPTIONS_CREATE_PCH` isn't part of the public API\n# so this may break in the future. For a discussion see:\n# https://discourse.cmake.org/t/ccache-clang-and-fno-pch-timestamp/7253/6\nif(CMAKE_CXX_COMPILER_ID MATCHES \"Clang\")\n list(APPEND CMAKE_CXX_COMPILE_OPTIONS_CREATE_PCH -Xclang -fno-pch-timestamp)\nendif()\n" }, { "path": "cmake/SetupCatch.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_package(Catch2 3.4.0)\n\nif (NOT Catch2_FOUND)\n if (NOT SPECTRE_FETCH_MISSING_DEPS)\n message(FATAL_ERROR \"Could not find Catch2. If you want to fetch \"\n \"missing dependencies automatically, set SPECTRE_FETCH_MISSING_DEPS=ON.\")\n endif()\n message(STATUS \"Fetching Catch2\")\n include(FetchContent)\n FetchContent_Declare(Catch2\n GIT_REPOSITORY https://github.com/catchorg/Catch2.git\n GIT_TAG v3.4.0\n GIT_SHALLOW TRUE\n ${SPECTRE_FETCHCONTENT_BASE_ARGS}\n )\n FetchContent_MakeAvailable(Catch2)\nendif()\n" }, { "path": "cmake/SetupCharm.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nset(SPECTRE_REQUIRED_CHARM_VERSION 7.0.0)\n\noption(USE_SCOTCH_LB \"Use the charm++ ScotchLB module\" OFF)\n\nset(SCOTCHLB_COMPONENT \"\")\nif (USE_SCOTCH_LB)\n find_package(Scotch REQUIRED)\n\n message(STATUS \"Scotch libs: \" ${SCOTCH_LIBRARIES})\n message(STATUS \"Scotch incl: \" ${SCOTCH_INCLUDE_DIR})\n message(STATUS \"Scotch vers: \" ${SCOTCH_VERSION})\n\n file(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"Scotch version: ${SCOTCH_VERSION}\\n\"\n )\n\n add_library(Scotch INTERFACE IMPORTED)\n set_property(TARGET Scotch\n APPEND PROPERTY INTERFACE_INCLUDE_DIRECTORIES ${SCOTCH_INCLUDE_DIR})\n set_property(TARGET Scotch\n APPEND PROPERTY INTERFACE_LINK_LIBRARIES ${SCOTCH_LIBRARIES})\n\n add_interface_lib_headers(\n TARGET Scotch\n HEADERS\n scotch.h\n )\n\n set(SCOTCHLB_COMPONENT ScotchLB)\nendif()\n\nfind_package(Charm ${SPECTRE_REQUIRED_CHARM_VERSION} REQUIRED\n COMPONENTS\n EveryLB\n ${SCOTCHLB_COMPONENT}\n )\nif(CHARM_VERSION VERSION_LESS 8.0.0)\n message(NOTICE \"Charm++ versions less than 8.0.0 have known bugs with \\\nelement creation. Dynamic h-refinement is disabled.\")\nendif()\n\nif (USE_SCOTCH_LB)\n target_link_libraries(Charmxx::charmxx INTERFACE Scotch)\nendif()\n\nif(CHARM_TRACE_PROJECTIONS OR CHARM_TRACE_PROJECTIONS)\n set_property(TARGET SpectreFlags\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n -DSPECTRE_CHARM_PROJECTIONS\n -DSPECTRE_CHARM_NON_ACTION_WALLTIME_EVENT_ID=1000\n )\nendif()\n\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"Charm++ version: ${CHARM_VERSION}\\n\"\n \"CHARM_COMPILER: ${CHARM_COMPILER}\\n\"\n \"CHARM_SHARED_LIBS: ${CHARM_SHARED_LIBS}\\n\"\n \"CHARM_BUILDING_BLOCKS:\\n${CHARM_BUILDING_BLOCKS}\\n\"\n )\n\nadd_interface_lib_headers(\n TARGET\n Charmxx::charmxx\n HEADERS\n charm++.h\n )\nadd_interface_lib_headers(\n TARGET\n Charmxx::pup\n HEADERS\n pup.h\n pup_stl.h\n )\nset_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n Charmxx::charmxx Charmxx::pup\n )\n\nget_filename_component(CHARM_BINDIR ${CHARM_COMPILER} DIRECTORY)\n# In order to avoid problems when compiling in parallel we manually copy the\n# charmrun script over, rather than having charmc do it for us.\nconfigure_file(\n \"${CHARM_BINDIR}/charmrun\"\n \"${CMAKE_RUNTIME_OUTPUT_DIRECTORY}/charmrun\" COPYONLY\n)\n\ninclude(SetupCharmModuleFunctions)\n\n# Make sure Charm++ was patched. If not you can get thread local storage errors\n# when loading the python bindings.\nif(NOT APPLE AND CHARM_VERSION VERSION_EQUAL 7.0.0 AND BUILD_PYTHON_BINDINGS)\n # Check that the patch was applied:\n set(CHARM_CHECK_FILE \"${CHARM_INCLUDE_DIR}/conv-mach-opt.sh\")\n if (EXISTS ${CHARM_CHECK_FILE})\n set(_CHARM_CMAKE_FILE_TO_CHECK ${CHARM_CHECK_FILE})\n file(READ ${_CHARM_CMAKE_FILE_TO_CHECK} FILE_CONTENTS)\n set(_EXPECTED_TLS_STRING \"-ftls-model=initial-exec\")\n string(FIND \"${FILE_CONTENTS}\"\n ${_EXPECTED_TLS_STRING} _LOCATION_OF_TLS)\n if (NOT ${_LOCATION_OF_TLS} EQUAL -1)\n message(FATAL_ERROR \"Found -ftls-model=initial-exec flag. \"\n \"It looks like you forgot to apply the Charm++ patch. \"\n \"This is necessary when using the python bindings.\")\n endif()\n else()\n message(STATUS \"Unable to check if Charm++ was patched. \"\n \"Missing file ${CHARM_CHECK_FILE}\")\n endif()\nendif()\n" }, { "path": "cmake/SetupCharmModuleFunctions.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Add a function to generate the charm interface files for the module.\nfunction(add_charm_module MODULE)\n # Arguments:\n # MODULE: Name of the Charm++ module.\n\n if (NOT TARGET module_All)\n # Target that will have all the Charm modules as dependencies\n add_custom_target(module_All)\n endif()\n\n set(_VERSION_SUFFIX \"_v${CHARM_VERSION}\")\n\n add_custom_command(\n OUTPUT ${MODULE}.decl.h ${MODULE}.def.h\n DEPENDS ${CMAKE_CURRENT_SOURCE_DIR}/${MODULE}.ci\n COMMAND cp ${CMAKE_CURRENT_SOURCE_DIR}/${MODULE}.ci ${MODULE}.ci\n COMMAND ${CHARM_COMPILER} -no-charmrun ${MODULE}.ci\n COMMAND ${CMAKE_SOURCE_DIR}/tools/patch_charm_modules.sh ${MODULE} ${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_SOURCE_DIR} `pwd` ${_VERSION_SUFFIX}\n )\n add_custom_target(\n module_${MODULE}\n DEPENDS ${MODULE}.decl.h ${MODULE}.def.h\n )\n add_dependencies(\n module_All\n module_${MODULE}\n )\nendfunction()\n" }, { "path": "cmake/SetupClangFormat.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_package(ClangFormat)\n\nif(CLANG_FORMAT_BIN AND EXISTS ${CMAKE_SOURCE_DIR}/.git AND Git_FOUND)\n get_filename_component(CLANG_FORMAT_NAME ${CLANG_FORMAT_BIN} NAME)\n add_custom_target(\n git-clang-format\n COMMAND\n export PATH=${CMAKE_SOURCE_DIR}/tools:$$PATH\n && cd ${CMAKE_SOURCE_DIR}\n && ${GIT_EXECUTABLE} ${CLANG_FORMAT_NAME} -f\n )\nendif()\n" }, { "path": "cmake/SetupClangTidy.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nif(NOT CLANG_TIDY_ROOT)\n # Need to set to empty to avoid warnings with --warn-uninitialized\n set(CLANG_TIDY_ROOT \"\")\n set(CLANG_TIDY_ROOT $ENV{CLANG_TIDY_ROOT})\nendif()\n\nif(NOT CMAKE_CXX_CLANG_TIDY AND CMAKE_CXX_COMPILER_ID MATCHES \"Clang\")\n string(\n REGEX MATCH \"^[0-9]+.[0-9]+\" LLVM_VERSION\n \"${CMAKE_CXX_COMPILER_VERSION}\"\n )\n find_program(\n CLANG_TIDY_BIN\n NAMES \"clang-tidy-${LLVM_VERSION}\" \"clang-tidy\"\n HINTS ${CLANG_TIDY_ROOT}\n )\nelseif(CMAKE_CXX_CLANG_TIDY)\n set(CLANG_TIDY_BIN \"${CMAKE_CXX_CLANG_TIDY}\")\nendif()\n\nif (CLANG_TIDY_BIN)\n message(STATUS \"clang-tidy: ${CLANG_TIDY_BIN}\")\n set(MODULES_TO_DEPEND_ON\n module_All\n Libsharp\n )\n if (TARGET SpectrePch)\n list(APPEND MODULES_TO_DEPEND_ON SpectrePch)\n endif()\n configure_file(\n ${CMAKE_SOURCE_DIR}/tools/ClangTidyAll.sh\n ${CMAKE_BINARY_DIR}/ClangTidyAll.sh\n @ONLY IMMEDIATE\n )\n add_custom_target(\n clang-tidy\n COMMAND\n ${CLANG_TIDY_BIN}\n --quiet\n -p ${CMAKE_BINARY_DIR}\n \\${FILE}\n )\n add_dependencies(\n clang-tidy\n ${MODULES_TO_DEPEND_ON}\n )\n add_custom_target(\n clang-tidy-all\n COMMAND ${CMAKE_BINARY_DIR}/ClangTidyAll.sh\n \\${NUM_THREADS}\n )\n add_dependencies(\n clang-tidy-all\n ${MODULES_TO_DEPEND_ON}\n )\n add_custom_target(\n clang-tidy-hash\n COMMAND ${CMAKE_SOURCE_DIR}/tools/ClangTidyHash.sh\n ${CMAKE_BINARY_DIR}\n ${CMAKE_SOURCE_DIR}\n \\${HASH}\n \\${NUM_THREADS}\n )\n add_dependencies(\n clang-tidy-hash\n ${MODULES_TO_DEPEND_ON}\n )\nelse()\n message(STATUS \"clang-tidy: Not using clang or couldn't find clang-tidy.\")\nendif()\n" }, { "path": "cmake/SetupCxxFlags.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(DEBUG_SYMBOLS \"Add -g to CMAKE_CXX_FLAGS if ON, -g0 if OFF.\" ON)\n\noption(OVERRIDE_ARCH \"The architecture to use. Default is native.\" OFF)\n\noption(SPECTRE_DEBUG \"Enable ASSERTs and other SPECTRE_DEBUG options\"\n OFF)\n\n# Because of a bug in macOS on Apple Silicon, executables larger than 2GB in\n# size cannot run. This option minimizes executable size to avoid this bug. It\n# is enabled by default on Apple Silicon.\nset(_SPECTRE_OPTIMIZE_SIZE_DEFAULT OFF)\nif(APPLE AND \"${CMAKE_HOST_SYSTEM_PROCESSOR}\" STREQUAL \"arm64\")\n set(_SPECTRE_OPTIMIZE_SIZE_DEFAULT ON)\nendif()\noption(SPECTRE_OPTIMIZE_SIZE \"Optimize for executable size instead of speed\"\n ${_SPECTRE_OPTIMIZE_SIZE_DEFAULT})\n\noption(SPECTRE_DEBUG_Og \"Compile Debug builds with -Og instead of -O0\" OFF)\n\nif (CMAKE_BUILD_TYPE STREQUAL \"Debug\")\n set(SPECTRE_DEBUG ON)\nendif()\n\nif(${SPECTRE_DEBUG})\n set_property(TARGET SpectreFlags\n APPEND PROPERTY INTERFACE_COMPILE_DEFINITIONS SPECTRE_DEBUG)\nendif()\n\noption(SPECTRE_NAN_INIT \"Initialize memory to NaN is various places\"\n ${SPECTRE_DEBUG})\n\nif(${SPECTRE_NAN_INIT})\n set_property(TARGET SpectreFlags\n APPEND PROPERTY INTERFACE_COMPILE_DEFINITIONS SPECTRE_NAN_INIT)\nendif()\n\nset(CMAKE_CXX_FLAGS_DEBUG \"${CMAKE_CXX_FLAGS_DEBUG} -DSPECTRE_DEBUG\")\n\nif(${SPECTRE_OPTIMIZE_SIZE})\n set(CMAKE_CXX_FLAGS_DEBUG \"${CMAKE_CXX_FLAGS_DEBUG} -Oz\")\nelseif(${SPECTRE_DEBUG_Og})\n set(CMAKE_CXX_FLAGS_DEBUG \"${CMAKE_CXX_FLAGS_DEBUG} -Og\")\n set(CMAKE_C_FLAGS_DEBUG \"${CMAKE_C_FLAGS_DEBUG} -Og\")\n set(CMAKE_Fortran_FLAGS_DEBUG \"${CMAKE_Fortran_FLAGS_DEBUG} -Og\")\nendif()\n\nif(NOT ${DEBUG_SYMBOLS})\n string(REPLACE \"-g \" \"-g0 \" CMAKE_CXX_FLAGS_DEBUG ${CMAKE_CXX_FLAGS_DEBUG})\nendif()\n\n# Always build with -g so we can view backtraces, etc. when production code\n# fails. This can be overridden by passing `-D DEBUG_SYMBOLS=OFF` to CMake\nif(${DEBUG_SYMBOLS})\n set_property(TARGET SpectreFlags\n APPEND PROPERTY INTERFACE_COMPILE_OPTIONS -g)\nendif(${DEBUG_SYMBOLS})\n\n# Always compile only for the current architecture. This can be overridden\n# by passing `-D OVERRIDE_ARCH=THE_ARCHITECTURE` to CMake\nif(NOT \"${OVERRIDE_ARCH}\" STREQUAL \"OFF\")\n set_property(TARGET SpectreFlags\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n # The -mno-avx512f flag is necessary to avoid a Blaze 3.8 bug. The flag\n # should be re-enabled when we can insist on Blaze 3.9 which will include\n # a fix that allows this vectorization flag again.\n $<$:-march=${OVERRIDE_ARCH} -mno-avx512f>\n $<$:-march=${OVERRIDE_ARCH} -mno-avx512f>\n $<$:-march=${OVERRIDE_ARCH} -mno-avx512f>)\nelse()\n # Apple Silicon Macs do not support the -march flag or the -mno-avx512f flag\n if((NOT APPLE OR NOT \"${CMAKE_HOST_SYSTEM_PROCESSOR}\" STREQUAL \"arm64\")\n # sometimes ARM architectures use the name \"aarch64\"\n AND NOT \"${CMAKE_HOST_SYSTEM_PROCESSOR}\" STREQUAL \"aarch64\"\n )\n set_property(TARGET SpectreFlags\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$:-march=native -mno-avx512f>\n $<$:-march=native -mno-avx512f>\n $<$:-march=native -mno-avx512f>)\n endif()\nendif()\n\n# We are getting multiple types of linker warnings on macOS:\n# - \"ranlib: archive library: tmp/libSpectrePchLib.a the table of contents is\n# empty (no object file members in the library define global symbols)\":\n# Yes, some of our libs have no symbols. Doesn't seem like a problem.\n# - \"-undefined dynamic_lookup may not work with chained fixups\":\n# This warning appears when compiling Python bindings. Chained fixups were\n# introduced in AppleClang 13 and enabled by default in macOS 12. See these\n# upstream issues:\n# - CPython: https://github.com/python/cpython/issues/97524\n# - Pybind11: https://github.com/pybind/pybind11/pull/4301\n# - CMake: https://gitlab.kitware.com/cmake/cmake/-/issues/24044\n# Disabling chained fixups with `-Wl-no_fixup_chains` leads to linker warnings\n# about inconsistent visibility settings in different translation units. We\n# probably have to wait for an upstream solution to this issue.\n# - \"could not create compact unwind for SYMBOL: registers X and\n# Y not saved contiguously in frame\":\n# We have seen these warnings on Apple Silicon chips.\n# Disabling compact unwind with the flags\n# -Wl,-keep_dwarf_unwind\n# -Wl,-no_compact_unwind\n# seems to work on some machines, but leads to segfaults on others. We haven't\n# investigated this in any more detail.\n# For now we just suppress these linker warnings altogether, since we haven't\n# encountered any problems with them and some are upstream issues.\nif(APPLE)\n target_link_options(\n SpectreFlags\n INTERFACE\n -Wl,-w\n )\nendif()\n\n# We always want a detailed backtrace of template errors to make debugging them\n# easier\nset_property(TARGET SpectreFlags\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$:-ftemplate-backtrace-limit=0>)\n\n# Increase bracket depth for fold expressions\n# (see also https://github.com/llvm/llvm-project/issues/48973)\nif (CMAKE_CXX_COMPILER_ID MATCHES \"Clang\"\n AND CMAKE_CXX_COMPILER_VERSION VERSION_GREATER_EQUAL 12.0)\n set_property(TARGET SpectreFlags\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$:-fbracket-depth=1024>)\nendif()\n\n# Disable cmath setting the error flag. This allows the compiler to more\n# aggressively vectorize code since it doesn't need to respect some global\n# state.\nset_property(TARGET SpectreFlags\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$:-fno-math-errno>\n $<$:-fno-math-errno>\n $<$:-fno-math-errno>)\n\n# Allow the compiler to transform divisions into multiplication by the\n# reciprocal.\nset_property(TARGET SpectreFlags\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$:-freciprocal-math>\n $<$:-freciprocal-math>\n $<$:-freciprocal-math>)\n\n# -ffp-exception-behavior=maytrap - By default, the LLVM optimizer assumes\n# floating point exceptions are ignored.\n# -fnon-call-exceptions - By default, GCC does not allow signal handlers to\n# throw exceptions.\n# Note: -ffp-exception-behavior is not supported on ARM64 architectures\nif((NOT APPLE OR NOT \"${CMAKE_HOST_SYSTEM_PROCESSOR}\" STREQUAL \"arm64\")\n AND NOT \"${CMAKE_HOST_SYSTEM_PROCESSOR}\" STREQUAL \"aarch64\"\n )\n create_c_flags_target(\n \"-ffp-exception-behavior=maytrap;-fnon-call-exceptions\"\n SpectreFpExceptions\n )\n create_cxx_flags_target(\n \"-ffp-exception-behavior=maytrap;-fnon-call-exceptions\"\n SpectreFpExceptions\n )\n target_link_libraries(\n SpectreFlags\n INTERFACE\n SpectreFpExceptions\n )\nelse()\n # On ARM64, we can't trap FP exceptions, so just enable non-call exceptions\n create_c_flags_target(\n \"-fnon-call-exceptions\"\n SpectreFpExceptions\n )\n create_cxx_flags_target(\n \"-fnon-call-exceptions\"\n SpectreFpExceptions\n )\n target_link_libraries(\n SpectreFlags\n INTERFACE\n SpectreFpExceptions\n )\nendif()\n\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"SPECTRE_DEBUG: ${SPECTRE_DEBUG}\\n\"\n \"SPECTRE_NAN_INIT: ${SPECTRE_NAN_INIT}\\n\"\n )\n" }, { "path": "cmake/SetupDoxygen.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Targets to preprocess the documentation\n# - Convert all `.ipynb` files in `docs/` to markdown, so they get picked up by\n# Doxygen.\nget_filename_component(_PY_BIN_DIR ${Python_EXECUTABLE} DIRECTORY)\nfind_program(NBCONVERT jupyter-nbconvert HINTS ${_PY_BIN_DIR})\nif (NBCONVERT STREQUAL \"NBCONVERT-NOTFOUND\")\n message(STATUS \"jupyter-nbconvert not found. Preprocessing .ipynb files for \\\ndocumentation disabled.\")\nelse()\n message(STATUS \"Found jupyter-nbconvert: ${NBCONVERT}\")\n add_custom_target(\n doc-notebooks-to-markdown\n COMMAND find ${CMAKE_SOURCE_DIR}/docs -name \"*.ipynb\"\n | xargs ${NBCONVERT} --to markdown --log-level=WARN\n --output-dir ${CMAKE_BINARY_DIR}/docs/tmp/notebooks_md\n )\nendif()\n\nfind_package(Doxygen)\nif (DOXYGEN_FOUND)\n set(SPECTRE_DOXYGEN_GROUPS \"${CMAKE_BINARY_DIR}/docs/tmp/GroupDefs.hpp\")\n # The layout file is doxygen version dependent. There was a significant\n # change in version 1.9.8 to support C++ modules. Doxygen modules were\n # renamed topics. Minor changes in doxygen version may cause warnings\n # about the layout file, but can appear to cause no problems\n if(DOXYGEN_VERSION VERSION_LESS 1.9.8)\n set(DOXYGEN_LAYOUT_FILE\n \"${PROJECT_SOURCE_DIR}/docs/config/DoxygenLayout_1_8_10.xml\")\n else()\n set(DOXYGEN_LAYOUT_FILE\n \"${PROJECT_SOURCE_DIR}/docs/config/DoxygenLayout_1_9_8.xml\"\n )\n endif()\n\n # For INPUT_FILTER in Doxyfile. Using Python instead of Perl here increases\n # docs generation time by ~25%. Runtimes are 102s (no filter), 108s (Perl) and\n # 135s (Python) at the time of writing (Mar 2022).\n find_package(Perl)\n\n set(SPECTRE_DOX_GENERATE_HTML \"YES\")\n set(SPECTRE_DOX_GENERATE_XML \"NO\")\n configure_file(\n docs/Doxyfile.in\n ${PROJECT_BINARY_DIR}/docs/DoxyfileHtml @ONLY IMMEDIATE\n )\n # Configure file that contains doxygen groups\n configure_file(docs/GroupDefs.hpp ${SPECTRE_DOXYGEN_GROUPS})\n\n # Construct the command that calls Doxygen\n set(\n GENERATE_DOCS_COMMAND\n \"${DOXYGEN_EXECUTABLE} ${PROJECT_BINARY_DIR}/docs/DoxyfileHtml\"\n )\n\n # Make sure the Doxygen version is compatible with the CSS, or print a\n # warning. Notes:\n # - We use https://github.com/jothepro/doxygen-awesome-css release v2.2.0,\n # which ensures compatibility with Doxygen v1.9.1 - v1.9.4 and v1.9.6.\n # When upgrading Doxygen, it's probably also a good idea to upgrade the CSS\n # files in `docs/config/`.\n # - The Doxygen release v1.9.1 has a bug so namespaces don't show up in\n # groups. It is fixed in v1.9.2.\n # - The Doxygen release v1.9.2 breaks the ordering of pages in the tree view\n # (sidebar). It is fixed in v1.9.3.\n if(DOXYGEN_VERSION VERSION_LESS 1.9.3)\n set(_DOX_WARNING \"Your Doxygen version ${DOXYGEN_VERSION} may not be \\\ncompatible with the stylesheet, so the documentation may look odd or not \\\nfunction correctly. Use Doxygen version 1.9.3 or higher.\")\n message(STATUS ${_DOX_WARNING})\n # The 'warning' in this message will fail the `doc-check` target (see below)\n set(\n GENERATE_DOCS_COMMAND\n \"${GENERATE_DOCS_COMMAND} && echo 'WARNING: ${_DOX_WARNING}'\"\n )\n endif()\n\n # Construct the command that calls doxygen, but only outputs warnings with a\n # few lines of context to stderr. Fails with exit code 1 if warnings are\n # found. Remains silent and succeeds with exit code 0 if everything is fine.\n # We write this into a shell script to make it easier to append the\n # postprocessing command.\n set(\n GENERATE_AND_CHECK_DOCS_SCRIPT \"\\\n#!/bin/sh\\n\\\n! (${GENERATE_DOCS_COMMAND}) 2>&1 | grep -A 6 -i 'warning' >&2\\n\"\n )\n\n include(FindPythonModule)\n find_python_module(bs4)\n find_python_module(pybtex)\n if (PY_bs4_FOUND AND PY_pybtex_FOUND)\n # Construct the command that runs the postprocessing over the Doxygen HTML\n # output\n set(\n DOCS_POST_PROCESS_COMMAND\n \"${Python_EXECUTABLE} \\\n${CMAKE_SOURCE_DIR}/docs/config/postprocess_docs.py \\\n--html-dir ${PROJECT_BINARY_DIR}/docs/html \\\n--references-files ${CMAKE_SOURCE_DIR}/docs/References.bib \\\n${CMAKE_SOURCE_DIR}/docs/Dependencies.bib\"\n )\n # Append postprocessing to doxygen commands\n # The commands are supposed to run the postprocessing even if the doc\n # generation failed with warnings, so that we output useful documentation\n # in any case. The commands exit successfully only if both generation and\n # postprocessing succeeded.\n set(\n GENERATE_DOCS_COMMAND\n \"${GENERATE_DOCS_COMMAND} && ${DOCS_POST_PROCESS_COMMAND} -v\"\n )\n set(\n GENERATE_AND_CHECK_DOCS_SCRIPT \"${GENERATE_AND_CHECK_DOCS_SCRIPT}\\\ngenerate_docs_exit=$?\\n\\\n${DOCS_POST_PROCESS_COMMAND} && exit \\${generate_docs_exit}\\n\"\n )\n else()\n message(WARNING \"Doxygen documentation postprocessing is disabled because\"\n \" Python dependencies were not found:\")\n if (NOT PY_bs4_FOUND)\n message(WARNING \"BeautifulSoup4 missing. \"\n \"Install with: pip install beautifulsoup4\")\n endif()\n if (NOT PY_pybtex_FOUND)\n message(WARNING \"Pybtex missing. Install with: pip install pybtex\")\n endif()\n endif()\n\n # Parse the command into a CMake list for the `add_custom_target`\n separate_arguments(GENERATE_DOCS_COMMAND)\n\n add_custom_target(\n doc\n COMMAND ${GENERATE_DOCS_COMMAND}\n DEPENDS\n ${PROJECT_BINARY_DIR}/docs/DoxyfileHtml\n ${SPECTRE_DOXYGEN_GROUPS}\n )\n\n # Write the shell script to a file to call it in the `add_custom_target`\n file(\n WRITE\n ${PROJECT_BINARY_DIR}/docs/tmp/GenerateAndCheckDocs.sh\n ${GENERATE_AND_CHECK_DOCS_SCRIPT}\n )\n\n add_custom_target(\n doc-check\n COMMAND sh ${PROJECT_BINARY_DIR}/docs/tmp/GenerateAndCheckDocs.sh\n DEPENDS\n ${PROJECT_BINARY_DIR}/docs/DoxyfileHtml\n ${SPECTRE_DOXYGEN_GROUPS}\n )\n\n set(SPECTRE_DOX_GENERATE_HTML \"NO\")\n set(SPECTRE_DOX_GENERATE_XML \"YES\")\n configure_file(\n docs/Doxyfile.in\n ${PROJECT_BINARY_DIR}/docs/DoxyfileXml @ONLY IMMEDIATE\n )\n\n add_custom_target(\n doc-xml\n COMMAND ${DOXYGEN_EXECUTABLE} ${PROJECT_BINARY_DIR}/docs/DoxyfileXml\n DEPENDS\n ${PROJECT_BINARY_DIR}/docs/DoxyfileXml\n ${SPECTRE_DOXYGEN_GROUPS}\n )\n\n if (TARGET doc-notebooks-to-markdown)\n add_dependencies(doc doc-notebooks-to-markdown)\n add_dependencies(doc-check doc-notebooks-to-markdown)\n add_dependencies(doc-xml doc-notebooks-to-markdown)\n endif()\n\n find_program(LCOV lcov)\n find_program(GENHTML genhtml)\n find_program(SED sed)\n\n # Use [coverxygen](https://github.com/psycofdj/coverxygen) to check the level\n # of documentation coverage.\n find_python_module(coverxygen)\n if (LCOV AND GENHTML AND SED AND PY_coverxygen_FOUND\n AND EXISTS ${CMAKE_SOURCE_DIR}/.git AND Git_FOUND)\n set(DOX_COVERAGE_OUTPUT \"${CMAKE_BINARY_DIR}/docs/html/doc_coverage/\")\n add_custom_target(\n doc-coverage\n\n COMMAND ${Python_EXECUTABLE}\n -m coverxygen\n --xml-dir ${CMAKE_BINARY_DIR}/docs/xml\n --src-dir ${CMAKE_SOURCE_DIR}\n --output ${CMAKE_BINARY_DIR}/docs/tmp/doc_coverage.info\n\n COMMAND ${LCOV}\n --remove ${CMAKE_BINARY_DIR}/docs/tmp/doc_coverage.info\n '${CMAKE_SOURCE_DIR}/src/Executables/*'\n '${CMAKE_SOURCE_DIR}/tests/*'\n '${CMAKE_SOURCE_DIR}/citelist'\n '${CMAKE_SOURCE_DIR}/[generated]'\n --output ${CMAKE_BINARY_DIR}/docs/tmp/doc_coverage.info\n\n COMMAND\n ${LCOV} --summary ${CMAKE_BINARY_DIR}/docs/tmp/doc_coverage.info\n\n COMMAND\n ${GENHTML} --legend\n --no-function-coverage\n --no-branch-coverage\n --title ${GIT_HASH}\n ${CMAKE_BINARY_DIR}/docs/tmp/doc_coverage.info\n -o ${DOX_COVERAGE_OUTPUT}\n\n COMMAND\n find ${DOX_COVERAGE_OUTPUT} -type f -print\n | xargs file\n | grep text\n | cut -f1 -d:\n | xargs ${SED} -i'.bak' 's/LCOV - code coverage report/\n SpECTRE Documentation Coverage Report/g'\n\n COMMAND find ${DOX_COVERAGE_OUTPUT} -type f -print | xargs file\n | grep text\n | cut -f1 -d:\n | xargs ${SED} -i'.bak' 's^Test:^\n Commit:^g'\n\n COMMAND find ${DOX_COVERAGE_OUTPUT} -type f -print | xargs file\n | grep text\n | cut -f1 -d:\n | xargs ${SED} -i'.bak' 's^\\\\\\([a-z0-9]\\\\{40\\\\}\\\\\\)^\n \\\\1^g'\n\n # Delete backup files created by sed\n COMMAND find ${DOX_COVERAGE_OUTPUT} -type f -name \\\"*.bak\\\" -print\n | xargs file | grep text | cut -f1 -d: | xargs rm\n\n DEPENDS\n ${PROJECT_BINARY_DIR}/docs/DoxyfileXml\n ${SPECTRE_DOXYGEN_GROUPS}\n doc-xml\n\n # Set work directory for target\n WORKING_DIRECTORY ${CMAKE_BINARY_DIR}\n\n COMMENT \"SpECTRE Documentation Coverage\"\n )\n endif()\nelse(DOXYGEN_FOUND)\n message(WARNING \"Doxygen is needed to build the documentation.\")\nendif (DOXYGEN_FOUND)\n" }, { "path": "cmake/SetupFormaline.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# When running formaline when SpECTRE was not built from a Git repository\n# we need a list of all the files and directories in the root of the source\n# directory that are tracked by Git. I.e.\n# git ls-tree --full-tree --name-only HEAD\nset(SPECTRE_FORMALINE_LOCATIONS\n .claude\n .clang-format\n .clang-tidy\n .claude\n .codecov.yaml\n .codex\n .devcontainer\n .dockerignore\n .github\n .gitignore\n citation.bib\n CITATION.cff\n cmake\n CMakeLists.txt\n containers\n docs\n external\n LICENSE.txt\n Metadata.yaml\n pyproject.toml\n README.md\n .skills\n setup.cfg\n src\n support\n tests\n tools\n )\n\nfind_package(Git)\n\nif(EXISTS ${CMAKE_SOURCE_DIR}/.git AND Git_FOUND)\n execute_process(\n COMMAND ${GIT_EXECUTABLE} ls-tree --full-tree --name-only HEAD\n WORKING_DIRECTORY ${CMAKE_SOURCE_DIR}\n OUTPUT_VARIABLE FORMALINE_GIT_FILES_TRACKED\n OUTPUT_STRIP_TRAILING_WHITESPACE\n )\n string(REPLACE \"\\n\" \";\" FORMALINE_GIT_FILES_TRACKED\n \"${FORMALINE_GIT_FILES_TRACKED}\")\n\n # Check all elements in SPECTRE_FORMALINE_LOCATIONS are in\n # FORMALINE_GIT_FILES_TRACKED. We don't just check that the sorted lists\n # are equal because we want to be able to print out exactly which file\n # or directory is missing.\n foreach(FILE ${SPECTRE_FORMALINE_LOCATIONS})\n list(FIND FORMALINE_GIT_FILES_TRACKED ${FILE} FOUND_FILE)\n if(${FOUND_FILE} EQUAL -1)\n message(FATAL_ERROR\n \"Couldn't find the file or directory \\\"${FILE}\\\" in the \"\n \"source directory. You need to remove the entry \\\"${FILE}\\\" \"\n \"from the CMake variable SPECTRE_FORMALINE_LOCATIONS in \"\n \"cmake/SetupFormaline.cmake\")\n endif()\n endforeach()\n\n # Check all elements in FORMALINE_GIT_FILES_TRACKED are in\n # SPECTRE_FORMALINE_LOCATIONS. We don't just check that the sorted lists\n # are equal because we want to be able to print out exactly which file\n # or directory is missing.\n foreach(FILE ${FORMALINE_GIT_FILES_TRACKED})\n list(FIND SPECTRE_FORMALINE_LOCATIONS ${FILE} FOUND_FILE)\n if(${FOUND_FILE} EQUAL -1)\n message(FATAL_ERROR\n \"Couldn't find the file or directory \\\"${FILE}\\\" in the \"\n \"CMake variable SPECTRE_FORMALINE_LOCATIONS in \"\n \"cmake/SetupFormaline.cmake. You need to add \\\"${FILE}\\\" \"\n \"to the CMake variable SPECTRE_FORMALINE_LOCATIONS in \"\n \"cmake/SetupFormaline.cmake\")\n endif()\n endforeach()\nendif()\n\noption(USE_FORMALINE\n \"Use Formaline to encode the source tree into executables and output files.\"\n ON)\n\n# APPLE instead of ${APPLE} is intentional\nif (APPLE)\n set(USE_FORMALINE OFF)\nendif (APPLE)\n\nif (USE_FORMALINE)\n # Create a variable that is space-delimited to insert into the Formaline\n # shell script\n string(REPLACE \";\" \" \" SPECTRE_FORMALINE_LOCATIONS_SHELL\n \"${SPECTRE_FORMALINE_LOCATIONS}\")\n\n configure_file(\n ${CMAKE_SOURCE_DIR}/tools/Formaline.sh\n ${CMAKE_BINARY_DIR}/tmp/Formaline.sh\n @ONLY\n )\nelse()\n file(REMOVE ${CMAKE_BINARY_DIR}/tmp/Formaline.sh)\nendif()\n" }, { "path": "cmake/SetupFortran.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(SPECTRE_Fortran_STATIC_LIBS\n \"Link static versions of libgfortran and libquadmath\" OFF)\n\nif(SPECTRE_Fortran_STATIC_LIBS)\n unset(CMAKE_Fortran_IMPLICIT_LINK_LIBRARIES)\n find_library(gfortran NAMES libgfortran.a)\n find_library(quadmath NAMES libquadmath.a)\nendif()\n" }, { "path": "cmake/SetupFuka.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_package(FUKA)\n\nif (FUKA_FOUND)\n file(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"FUKA: ${FUKA_ROOT}\\n\"\n )\nendif()\n" }, { "path": "cmake/SetupGitHooks.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Allow disabling the Git hooks because if you are running the code in a\n# container the host may not have all the right things installed.\noption(\n USE_GIT_HOOKS\n \"Set up the git hooks for sanity checks.\"\n ON)\n\nif(USE_GIT_HOOKS)\n # Check that the source dir is writable. If it is we set up git hooks, if not\n # then there probably won't be any commits anyway...\n EXECUTE_PROCESS(COMMAND test -w ${CMAKE_SOURCE_DIR}\n RESULT_VARIABLE CHECK_SOURCE_DIR_WRITABLE_RESULT)\n\n # The logic is inverted because shell\n if(NOT CHECK_SOURCE_DIR_WRITABLE_RESULT AND EXISTS ${CMAKE_SOURCE_DIR}/.git)\n find_package(ClangFormat)\n find_package(Git)\n\n # We use several client-side git hooks to ensure commits are correct as\n # early as possible.\n configure_file(\n ${CMAKE_SOURCE_DIR}/tools/Hooks/pre-commit.sh\n ${CMAKE_SOURCE_DIR}/.git/hooks/pre-commit\n @ONLY\n )\n\n configure_file(\n ${CMAKE_SOURCE_DIR}/tools/Hooks/CheckFileSize.py\n ${CMAKE_SOURCE_DIR}/.git/hooks/CheckFileSize.py\n @ONLY\n )\n endif()\nendif()\n" }, { "path": "cmake/SetupGoldOrLldLinker.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(USE_LD\n \"Override the default linker. Options are: ld, gold, lld\"\n OFF)\n\nif (USE_LD)\n if(\"${USE_LD}\" STREQUAL \"gold\")\n find_program(GNU_GOLD_LINKER \"ld.gold\")\n if (NOT GNU_GOLD_LINKER)\n message(FATAL_ERROR\n \"ld.gold requested but could not find executable\")\n endif()\n check_and_add_cxx_link_flag(\"-fuse-ld=gold\")\n elseif(\"${USE_LD}\" STREQUAL \"lld\")\n if (\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"GNU\")\n message(FATAL_ERROR \"GCC does not support linking with LLD. \"\n \"If this has changed please remove this error message \"\n \"and submit a pull request.\")\n endif()\n find_program(LLD_LINKER \"ld.lld\")\n if (NOT LLD_LINKER)\n message(FATAL_ERROR\n \"ld.lld requested but could not find executable\")\n endif()\n check_and_add_cxx_link_flag(\"-fuse-ld=lld\")\n elseif(NOT \"${USE_LD}\" STREQUAL \"ld\")\n message(FATAL_ERROR\n \"USE_LD must be one of 'ld', 'gold' or 'lld' but got '${USE_LD}'\")\n endif()\nelse()\n if (\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"GNU\")\n # GCC currently only supports linking with ld.gold, not ld.lld\n find_program(GNU_GOLD_LINKER \"ld.gold\")\n if (GNU_GOLD_LINKER)\n check_and_add_cxx_link_flag(\"-fuse-ld=gold\")\n endif()\n else()\n find_program(LLD_LINKER \"ld.lld\")\n if (LLD_LINKER)\n check_and_add_cxx_link_flag(\"-fuse-ld=lld\")\n else()\n find_program(GNU_GOLD_LINKER \"ld.gold\")\n if (GNU_GOLD_LINKER)\n check_and_add_cxx_link_flag(\"-fuse-ld=gold\")\n endif()\n endif()\n endif()\nendif()\n" }, { "path": "cmake/SetupGoogleBenchmark.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_package(GoogleBenchmark QUIET)\n\n\nif (${GoogleBenchmark_FOUND})\n message(STATUS \"Google Benchmark libs: \" ${GoogleBenchmark_LIBRARIES})\n message(STATUS \"Google Benchmark incl: \" ${GoogleBenchmark_INCLUDE_DIRS})\n\n file(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"Google Benchmark found\\n\"\n )\n\n add_library(GoogleBenchmark INTERFACE IMPORTED)\n set_property(TARGET GoogleBenchmark PROPERTY\n INTERFACE_INCLUDE_DIRECTORIES ${GoogleBenchmark_INCLUDE_DIRS})\n set_property(TARGET GoogleBenchmark PROPERTY\n INTERFACE_LINK_LIBRARIES ${GoogleBenchmark_LIBRARIES})\n set_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n GoogleBenchmark\n )\nendif()\n" }, { "path": "cmake/SetupGsl.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(GSL_STATIC\n \"Link static versions of GNU Scientific Library\" OFF)\n\nif(${GSL_STATIC})\n set(_BACKUP_CMAKE_FIND_LIBRARY_SUFFIXES ${CMAKE_FIND_LIBRARY_SUFFIXES})\n set(CMAKE_FIND_LIBRARY_SUFFIXES \".a\")\nendif(${GSL_STATIC})\nfind_package(GSL REQUIRED)\nif(${GSL_STATIC})\n set(CMAKE_FIND_LIBRARY_SUFFIXES ${_BACKUP_CMAKE_FIND_LIBRARY_SUFFIXES})\nendif(${GSL_STATIC})\n\nmessage(STATUS \"GSL libs: ${GSL_LIBRARIES}\")\nmessage(STATUS \"GSL incl: ${GSL_INCLUDE_DIR}\")\nmessage(STATUS \"GSL vers: ${GSL_VERSION}\")\n\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"GSL version: ${GSL_VERSION}\\n\"\n )\n\n# Link external BLAS library. We don't need the GSL::gslcblas target.\nfind_package(BLAS REQUIRED)\ntarget_link_libraries(\n GSL::gsl\n INTERFACE\n BLAS::BLAS\n )\n\nset_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n GSL::gsl GSL::gslcblas\n )\n" }, { "path": "cmake/SetupHdf5.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_package(HDF5 REQUIRED COMPONENTS C)\n\nmessage(STATUS \"HDF5 libs: \" ${HDF5_C_LIBRARIES})\nmessage(STATUS \"HDF5 incl: \" ${HDF5_C_INCLUDE_DIRS})\nmessage(STATUS \"HDF5 vers: \" ${HDF5_VERSION})\n\nif(NOT TARGET hdf5::hdf5)\n add_library(hdf5::hdf5 INTERFACE IMPORTED)\n set_target_properties(\n hdf5::hdf5\n PROPERTIES\n INTERFACE_INCLUDE_DIRECTORIES \"${HDF5_C_INCLUDE_DIRS}\"\n INTERFACE_LINK_LIBRARIES \"${HDF5_C_LIBRARIES}\"\n )\n if(DEFINED HDF5_C_DEFINITIONS)\n set_target_properties(\n hdf5::hdf5\n PROPERTIES\n INTERFACE_COMPILE_FLAGS \"${HDF5_C_DEFINITIONS}\"\n )\n endif()\nendif()\n\nif(NOT TARGET HDF5::HDF5)\n add_library(HDF5::HDF5 INTERFACE IMPORTED)\n set_target_properties(\n HDF5::HDF5\n PROPERTIES\n INTERFACE_INCLUDE_DIRECTORIES \"${HDF5_C_INCLUDE_DIRS}\"\n INTERFACE_LINK_LIBRARIES \"${HDF5_C_LIBRARIES}\"\n )\n if(DEFINED HDF5_C_DEFINITIONS)\n set_target_properties(\n HDF5::HDF5\n PROPERTIES\n INTERFACE_COMPILE_FLAGS \"${HDF5_C_DEFINITIONS}\"\n )\n endif()\nendif()\n\nif(HDF5_IS_PARALLEL)\n find_package(MPI COMPONENTS C)\n if(MPI_FOUND)\n target_link_libraries(hdf5::hdf5 INTERFACE MPI::MPI_C)\n target_link_libraries(HDF5::HDF5 INTERFACE MPI::MPI_C)\n else()\n message(WARNING \"HDF5 is built with MPI support, but MPI was not found. \"\n \"You may encounter build issues with HDF5, such as missing headers.\")\n endif()\nendif()\n\nif(HDF5_USE_STATIC_LIBRARIES)\n # If we are using static libraries for HDF5, try to use static libraries\n # for the libsz and transitive libaec dependency. These aren't very\n # common, while other dependencies like libz are, so we leave those\n # as shared library dependencies.\n get_target_property(\n _HDF5_INTERFACE_LINK_LIBS HDF5::HDF5 INTERFACE_LINK_LIBRARIES)\n string(FIND\n \"${_HDF5_INTERFACE_LINK_LIBS}\" \"libsz.so\" _LOCATION_OF_LIBSZ)\n if (NOT ${_LOCATION_OF_LIBSZ} EQUAL -1)\n find_library(_libsz NAMES libsz.a)\n if(_libsz)\n string(REPLACE\n \"libsz.so\" \"libsz.a\" _HDF5_INTERFACE_LINK_LIBS\n \"${_HDF5_INTERFACE_LINK_LIBS}\")\n find_library(_libaec NAMES libaec.a)\n if(_libaec)\n list(APPEND _HDF5_INTERFACE_LINK_LIBS ${_libaec})\n endif()\n endif()\n endif()\n string(FIND\n \"${_HDF5_INTERFACE_LINK_LIBS}\" \"libcrypto.so\" _LOCATION_OF_LIBCRYPTO)\n if (NOT ${_LOCATION_OF_LIBCRYPTO} EQUAL -1)\n find_library(_libcrypto NAMES libcrypto.a)\n if(_libcrypto)\n string(REPLACE\n \"libcrypto.so\" \"libcrypto.a\" _HDF5_INTERFACE_LINK_LIBS\n \"${_HDF5_INTERFACE_LINK_LIBS}\")\n endif()\n endif()\n string(FIND\n \"${_HDF5_INTERFACE_LINK_LIBS}\" \"libz.so\" _LOCATION_OF_LIBZ)\n if (NOT ${_LOCATION_OF_LIBZ} EQUAL -1)\n find_library(_libz NAMES libz.a)\n if(_libz)\n string(REPLACE\n \"libz.so\" \"libz.a\" _HDF5_INTERFACE_LINK_LIBS\n \"${_HDF5_INTERFACE_LINK_LIBS}\")\n endif()\n endif()\n set_target_properties(\n HDF5::HDF5\n PROPERTIES\n INTERFACE_LINK_LIBRARIES \"${_HDF5_INTERFACE_LINK_LIBS}\"\n )\nendif()\n\n# Check if file locking API is available. The versions supporting this feature\n# are listed here:\n# https://github.com/HDFGroup/hdf5/blob/develop/doc/file-locking.md\ninclude(CheckCXXSourceCompiles)\nset(CMAKE_REQUIRED_LIBRARIES HDF5::HDF5)\ncheck_cxx_source_compiles(\n \"#include \\n\\\nint main() {\\n\\\n const hid_t fapl_id = H5Pcopy(H5P_DEFAULT);\\n\\\n H5Pset_file_locking(fapl_id, false, true);\\n\\\n}\"\n HDF5_SUPPORTS_SET_FILE_LOCKING)\nif(${HDF5_SUPPORTS_SET_FILE_LOCKING})\n set_property(\n TARGET hdf5::hdf5\n APPEND PROPERTY INTERFACE_COMPILE_DEFINITIONS\n HDF5_SUPPORTS_SET_FILE_LOCKING)\nelse()\n message(WARNING \"The HDF5 library does not support 'H5Pset_file_locking'. \"\n \"This means that simulations may crash when you read H5 files while \"\n \"the simulation is trying to access them. To avoid this, set the \"\n \"environment variable\\n\"\n \" HDF5_USE_FILE_LOCKING=FALSE\\n\"\n \"when running simulations, or load an HDF5 module that supports \"\n \"'H5Pset_file_locking'. Supporting versions are listed here:\\n\"\n \"https://github.com/HDFGroup/hdf5/blob/develop/doc/file-locking.md\")\nendif()\n\ninclude(CheckCXXSourceRuns)\nset(CMAKE_REQUIRED_LIBRARIES HDF5::HDF5)\n# Logic from src/Utilities/ErrorHandling/FloatingPointExceptions.cpp\ncheck_cxx_source_runs(\n [=[\n#include \n\n#ifdef __APPLE__\n#ifndef __arm64__\n#define SPECTRE_FPE_CSR 1\n#include \n#endif\n#else\n#define SPECTRE_FPE_FENV 1\n#include \n#endif\n\nint main(int /*argc*/, char** /*argv*/) {\n#if SPECTRE_FPE_CSR\n _mm_setcsr(_MM_MASK_MASK &\n ~(_MM_MASK_OVERFLOW | _MM_MASK_INVALID | _MM_MASK_DIV_ZERO));\n#elif SPECTRE_FPE_FENV\n feenableexcept(FE_DIVBYZERO | FE_INVALID | FE_OVERFLOW);\n#endif\n H5Tcopy(H5T_NATIVE_DOUBLE);\n return 0;\n}\n]=]\n HDF5_INIT_WITHOUT_FPES\n )\nif(NOT HDF5_INIT_WITHOUT_FPES)\n message(FATAL_ERROR\n \"The HDF5 library triggers FPEs during initialization. See upstream bug \"\n \"https://github.com/HDFGroup/hdf5/issues/3831. Either switch to an \"\n \"unaffected version or apply the patch referenced from that issue.\")\nendif()\n\nset_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n HDF5::HDF5\n )\n\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"HDF5 version: ${HDF5_VERSION}\\n\"\n )\n\n# Find HDF5 tools\nget_filename_component(HDF5_TOOLS_DIR HDF5_DIFF_EXECUTABLE DIRECTORY)\nfind_program(HDF5_REPACK_EXECUTABLE h5repack HINTS ${HDF5_TOOLS_DIR})\n" }, { "path": "cmake/SetupInformer.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Configure info from build to give access to unit test path,\n# SpECTRE version, etc. (things known at CMake time)\nconfigure_file(\n ${CMAKE_SOURCE_DIR}/src/Informer/InfoAtCompile.cpp\n ${CMAKE_BINARY_DIR}/Informer/InfoAtCompile.cpp\n )\n\noption(\n STUB_EXECUTABLE_OBJECT_FILES\n \"Replace executable object files with stubs to reduce disk usage.\"\n OFF\n )\n\nset(WRAP_EXECUTABLE_LINKER_USE_STUB_OBJECT_FILES \"false\")\nif (STUB_EXECUTABLE_OBJECT_FILES)\n set(WRAP_EXECUTABLE_LINKER_USE_STUB_OBJECT_FILES \"true\")\nendif (STUB_EXECUTABLE_OBJECT_FILES)\n\nconfigure_file(\n ${CMAKE_SOURCE_DIR}/tools/WrapExecutableLinker.sh\n ${CMAKE_BINARY_DIR}/tmp/WrapExecutableLinker.sh\n @ONLY\n )\n\noption(\n STUB_LIBRARY_OBJECT_FILES\n \"Replace library object files with stubs to reduce disk usage.\"\n OFF\n )\n\nset(WRAP_LIBRARY_LINKER_USE_STUB_OBJECT_FILES \"false\")\nif (STUB_LIBRARY_OBJECT_FILES)\n set(WRAP_LIBRARY_LINKER_USE_STUB_OBJECT_FILES \"true\")\nendif (STUB_LIBRARY_OBJECT_FILES)\n\nconfigure_file(\n ${CMAKE_SOURCE_DIR}/tools/WrapLibraryLinker.sh\n ${CMAKE_BINARY_DIR}/tmp/WrapLibraryLinker.sh\n @ONLY\n )\n" }, { "path": "cmake/SetupJemalloc.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_package(JEMALLOC REQUIRED)\n\nmessage(STATUS \"jemalloc libs: \" ${JEMALLOC_LIBRARIES})\nmessage(STATUS \"jemalloc incl: \" ${JEMALLOC_INCLUDE_DIRS})\nmessage(STATUS \"jemalloc vers: \" ${JEMALLOC_VERSION})\n\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"jemalloc version: ${JEMALLOC_VERSION}\\n\"\n )\n\nadd_library(Jemalloc INTERFACE IMPORTED)\nset_property(TARGET Jemalloc\n APPEND PROPERTY INTERFACE_LINK_LIBRARIES ${JEMALLOC_LIBRARIES})\nset_property(TARGET Jemalloc PROPERTY\n INTERFACE_INCLUDE_DIRECTORIES ${JEMALLOC_INCLUDE_DIRS})\n\nset_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n Jemalloc\n )\n\n# Determine whether we are using JEMALLOC as a shared or static library.\n# Since libraries can be named, e.g. libjemalloc.so.2 we just search for\n# the extension after stripping the directories. It's unlikely jemalloc\n# will rename themselves to \"alloc.so\" and then we'd have libs like\n# \"alloc.so.a\"\nget_filename_component(\n JEMALLOC_LIB_NAME\n ${JEMALLOC_LIBRARIES}\n NAME\n )\nif(APPLE)\n string(FIND \"${JEMALLOC_LIB_NAME}\" \".dylib\" FOUND_SHARED)\nelse()\n string(FIND \"${JEMALLOC_LIB_NAME}\" \".so\" FOUND_SHARED)\nendif()\nif(${FOUND_SHARED} STREQUAL -1)\n string(FIND \"${JEMALLOC_LIB_NAME}\" \".a\" FOUND_STATIC)\n if(${FOUND_STATIC} EQUAL -1)\n message(FATAL_ERROR \"Failed to determine whether JEMALLOC is a shared or \"\n \"static library. Found: ${JEMALLOC_LIBRARIES}\")\n endif()\n set(JEMALLOC_LIB_TYPE STATIC)\nelse()\n set(JEMALLOC_LIB_TYPE SHARED)\nendif()\n\nmark_as_advanced(JEMALLOC_LIB_TYPE)\n\nif(\"${JEMALLOC_LIB_TYPE}\" STREQUAL STATIC)\n message(WARNING \"It's probably a better idea to use jemalloc as a shared \"\n \"library. Statically linking jemalloc might work but has not been tested.\")\nendif()\n" }, { "path": "cmake/SetupKokkos.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(SPECTRE_KOKKOS \"Use Kokkos\" OFF)\n\nif(SPECTRE_KOKKOS)\n find_package(Kokkos)\n\n if (Kokkos_FOUND)\n # Found external Kokkos installation, so just check that a few important\n # features are enabled\n if (Kokkos_ENABLE_CUDA)\n # Allow constexpr functions to be called from device code\n # without the need for a device annotation.\n # See https://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html#constexpr-functions-and-function-templates\n if (NOT Kokkos_ENABLE_CUDA_CONSTEXPR)\n message(FATAL_ERROR \"Kokkos_ENABLE_CUDA_CONSTEXPR must be ON. \"\n \"Please recompile Kokkos with this option enabled.\")\n endif()\n # Allow CUDA code in static libs, see\n # https://docs.nvidia.com/cuda/cuda-compiler-driver-nvcc/index.html#using-separate-compilation-in-cuda\n # We may have to look into LTO if this has a performance penalty.\n if (NOT Kokkos_ENABLE_CUDA_RELOCATABLE_DEVICE_CODE)\n message(FATAL_ERROR \"Kokkos_ENABLE_CUDA_RELOCATABLE_DEVICE_CODE \"\n \"must be ON. Please recompile Kokkos with this option enabled.\")\n endif()\n if (BUILD_SHARED_LIBS)\n message(FATAL_ERROR \"Building with shared libs is not supported when \"\n \"building with CUDA support. Set BUILD_SHARED_LIBS=OFF.\")\n endif()\n endif() # Kokkos_ENABLE_CUDA\n else() # Kokkos_FOUND\n # Kokkos not found, so we will try to fetch it.\n if (NOT SPECTRE_FETCH_MISSING_DEPS)\n message(FATAL_ERROR \"Could not find Kokkos. If you want to fetch \"\n \"missing dependencies automatically, set SPECTRE_FETCH_MISSING_DEPS=ON.\")\n endif()\n\n # Configure the Kokkos build\n set(Kokkos_ENABLE_AGGRESSIVE_VECTORIZATION ON CACHE BOOL\n \"Kokkos aggressive vectorization\")\n\n if (CMAKE_BUILD_TYPE STREQUAL \"Debug\" OR SPECTRE_DEBUG)\n message(STATUS \"Enabling Kokkos debug mode\")\n set(Kokkos_ENABLE_DEBUG ON CACHE BOOL \"Most general debug settings\")\n set(Kokkos_ENABLE_DEBUG_BOUNDS_CHECK ON CACHE BOOL\n \"Bounds checking on Kokkos views\")\n set(Kokkos_ENABLE_DEBUG_DUALVIEW_MODIFY_CHECK ON CACHE BOOL\n \"Sanity checks on Kokkos DualView\")\n endif()\n\n if(Kokkos_ENABLE_CUDA)\n set(CMAKE_CUDA_STANDARD 20)\n set(CMAKE_CUDA_STANDARD_REQUIRED ON)\n enable_language(CUDA)\n find_package(CUDAToolkit REQUIRED)\n set(Kokkos_ENABLE_CUDA_CONSTEXPR ON CACHE BOOL\n \"Enable constexpr in CUDA\")\n set(Kokkos_ENABLE_CUDA_RELOCATABLE_DEVICE_CODE ON CACHE BOOL\n \"Enable relocatable device code in CUDA\")\n if (BUILD_SHARED_LIBS)\n message(FATAL_ERROR \"Building with shared libs is not supported when \"\n \"building with CUDA support. Set BUILD_SHARED_LIBS=OFF.\")\n endif()\n endif()\n\n message(STATUS \"Fetching Kokkos\")\n include(FetchContent)\n FetchContent_Declare(Kokkos\n GIT_REPOSITORY https://github.com/kokkos/kokkos.git\n GIT_TAG 4.4.00\n GIT_SHALLOW TRUE\n ${SPECTRE_FETCHCONTENT_BASE_ARGS}\n )\n FetchContent_MakeAvailable(Kokkos)\n endif()\nendif()\n\n# Determine if the compiler is NVIDIA's nvcc (if not already determined by\n# Kokkos)\nif (NOT DEFINED KOKKOS_CXX_COMPILER_ID)\n execute_process(\n COMMAND ${CMAKE_CXX_COMPILER} --version\n OUTPUT_VARIABLE _COMPILER_VERSION\n OUTPUT_STRIP_TRAILING_WHITESPACE)\n string(REPLACE \"\\n\" \" \" _COMPILER_VERSION ${_COMPILER_VERSION})\n string(FIND ${_COMPILER_VERSION} \"nvcc\" _COMPILER_IS_NVCC)\n if(${_COMPILER_IS_NVCC} GREATER -1)\n set(KOKKOS_CXX_COMPILER_ID \"NVIDIA\")\n else()\n set(KOKKOS_CXX_COMPILER_ID ${CMAKE_CXX_COMPILER_ID})\n endif()\nendif()\n\n# Include CUDA as system headers to suppress warnings. NVCC seems to include\n# CUDA headers as `-I` instead of `-isystem` for some reason (as of\n# version 12.6).\nif (CUDAToolkit_INCLUDE_DIRS)\n create_cxx_flag_target(\n \"-Xcompiler \\\"-isystem${CUDAToolkit_INCLUDE_DIRS}\\\"\"\n SpectreCudaSystemInclude)\n target_link_libraries(\n SpectreWarnings\n INTERFACE\n SpectreCudaSystemInclude\n )\nendif()\n" }, { "path": "cmake/SetupLIBCXX.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nif (\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"Clang\")\n if (NOT USE_LIBCXX)\n option(USE_LIBCXX \"Use libc++ as standard library\" OFF)\n endif()\n if (USE_LIBCXX)\n include(CheckCXXCompilerFlag)\n unset(CXX_FLAG_WORKS CACHE)\n set(CMAKE_REQUIRED_QUIET 1)\n check_cxx_compiler_flag(\"-stdlib=libc++\" CXX_FLAG_WORKS)\n unset(CMAKE_REQUIRED_QUIET)\n # If we cannot use the -stdlib=libc++ flag directly we must find libc++\n # explicity by searching on the file system\n if (CXX_FLAG_WORKS AND NOT LIBCXX_ROOT)\n message(STATUS \"libc++: Compiler supports -stdlib=libc++, no need to find \"\n \"libc++ explicity. Specify `LIBCXX_ROOT` to use a specified version of \"\n \"libc++. If the specified version is not found we fall back to the \"\n \"system libc++, if available.\")\n else()\n find_package(LIBCXX REQUIRED)\n set(\n CMAKE_EXE_LINKER_FLAGS \"${CMAKE_EXE_LINKER_FLAGS}\\\n -L${LIBCXXABI_LIBRARIES} -L${LIBCXX_LIBRARIES}\"\n )\n include_directories(${LIBCXX_INCLUDE_DIRS})\n message(STATUS \"libc++ include: ${LIBCXX_INCLUDE_DIRS}\")\n message(STATUS \"libc++ libraries: ${LIBCXX_LIBRARIES}\")\n endif()\n\n set(CMAKE_CXX_FLAGS \"-stdlib=libc++ ${CMAKE_CXX_FLAGS}\")\n\n option(\n LIBCXX_DEBUG\n \"Enable debug mode for libc++ in Debug builds\"\n OFF\n )\n if(LIBCXX_DEBUG)\n set(CMAKE_CXX_FLAGS_DEBUG \"${CMAKE_CXX_FLAGS_DEBUG} -D_LIBCPP_DEBUG=0\")\n endif()\n endif()\nendif()\n" }, { "path": "cmake/SetupLIBCXXCharm.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# We need to add the link flag after finding packages because adding a\n# compilation flag to the linker flags causes packages/libraries to not be\n# always be found correctly.\nif (\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"Clang\" AND USE_LIBCXX)\n set(CMAKE_EXE_LINKER_FLAGS \"${CMAKE_EXE_LINKER_FLAGS} -stdlib=libc++\")\nendif()\n" }, { "path": "cmake/SetupLIBXSMM.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_package(LIBXSMM 1.16.1)\n\nif (NOT LIBXSMM_FOUND)\n if (NOT SPECTRE_FETCH_MISSING_DEPS)\n message(FATAL_ERROR \"Could not find LIBXSMM. If you want to fetch \"\n \"missing dependencies automatically, set SPECTRE_FETCH_MISSING_DEPS=ON.\")\n endif()\n message(STATUS \"Fetching LIBXSMM\")\n\n # This FetchContent code is adapted from the libxsmm docs:\n # https://libxsmm.readthedocs.io/en/latest/#rules-for-building-libxsmm\n include(FetchContent)\n\n FetchContent_GetProperties(xsmm)\n if(NOT xsmm_POPULATED)\n # Need an unreleased version to be compatible with newer glibc versions\n FetchContent_Populate(xsmm\n GIT_REPOSITORY https://github.com/libxsmm/libxsmm.git\n GIT_TAG 10b7dc82b3c46157e76eb40e4e959555f895b24d\n SUBBUILD_DIR ${CMAKE_BINARY_DIR}/_deps/xsmm-subbuild\n SOURCE_DIR ${CMAKE_BINARY_DIR}/_deps/xsmm-src\n BINARY_DIR ${CMAKE_BINARY_DIR}/_deps/xsmm-build\n )\n endif()\n\n set(LIBXSMMROOT ${xsmm_SOURCE_DIR})\n file(GLOB _GLOB_XSMM_SRCS LIST_DIRECTORIES false CONFIGURE_DEPENDS ${LIBXSMMROOT}/src/*.c)\n list(REMOVE_ITEM _GLOB_XSMM_SRCS ${LIBXSMMROOT}/src/libxsmm_generator_gemm_driver.c)\n list(REMOVE_ITEM _GLOB_XSMM_SRCS ${LIBXSMMROOT}/src/libxsmm_binaryexport_generator.c)\n set(XSMM_INCLUDE_DIRS ${LIBXSMMROOT}/include)\n\n add_library(xsmm STATIC ${_GLOB_XSMM_SRCS})\n target_include_directories(xsmm SYSTEM PUBLIC ${XSMM_INCLUDE_DIRS})\n target_compile_definitions(xsmm PUBLIC LIBXSMM_DEFAULT_CONFIG)\n\n # Link BLAS\n find_package(BLAS REQUIRED)\n target_link_libraries(xsmm PUBLIC BLAS::BLAS)\n\n # Provide `Libxsmm` target\n add_library(Libxsmm ALIAS xsmm)\nendif()\n\nset_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n Libxsmm\n )\n" }, { "path": "cmake/SetupLapack.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_package(LAPACK REQUIRED)\nmessage(STATUS \"LAPACK libs: \" ${LAPACK_LIBRARIES})\n\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"LAPACK_LIBRARIES: ${LAPACK_LIBRARIES}\\n\"\n )\n\nset_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n LAPACK::LAPACK\n )\n" }, { "path": "cmake/SetupLicenseInfo.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nset(_LIST_OF_3PLS\n Blaze\n Boost\n Brigand\n Catch2\n Charm\n Gsl\n Hdf5\n Jemalloc\n Libbacktrace\n Libsharp\n Libxsmm\n OpenBlas\n Pybind11\n Xsimd\n YamlCpp\n)\n\nfile(READ \"${CMAKE_SOURCE_DIR}/LICENSE.txt\" SPECTRE_MIT_LICENSE)\nfile(READ \"${CMAKE_SOURCE_DIR}/external/Licenses/SpectreGpl3License.txt\"\n SPECTRE_GPL3_LICENSE)\nset(SPECTRE_LICENSE_CXX_STRING \"\nSpECTRE source code is distributed under the MIT License, while SpECTRE\nexecutables and libraries, generally machine code, is distributed under the GNU\nPublic License v3, or GPL3. The SpECTRE source code is freely available at\nhttps://github.com/sxs-collaboration/spectre/\n\nSpECTRE copyright for source, executables, libraries, and machine code is:\nCopyright 2017 - 2026 Simulating eXtreme Spacetimes Collaboration\n\nSpECTRE source code MIT license:\n${SPECTRE_MIT_LICENSE}\n\nSpECTRE executable, library, and machine code license:\n${SPECTRE_GPL3_LICENSE}\n\n\n\n\nThird Party Libraries:\n\")\n\n# Note: C++ compilers only need to support 65,000 characters in raw string\n# literals, so we split this over 3 strings. 1 for the SpECTRE licenses,\n# and two of the 3PLs.\nset(SPECTRE_3PL_CXX_STRING0 \"\")\nset(SPECTRE_3PL_CXX_STRING1 \"\")\n\nset(SPECTRE_3PL_DOX_STRING \"${SPECTRE_LICENSE_CXX_STRING}\")\n\nforeach(_3PL ${_LIST_OF_3PLS})\n if(EXISTS \"${CMAKE_SOURCE_DIR}/external/Licenses/${_3PL}Copyright.txt\")\n file(READ \"${CMAKE_SOURCE_DIR}/external/Licenses/${_3PL}Copyright.txt\"\n _3PL_COPYRIGHT)\n else()\n set(_3PL_COPYRIGHT \"\")\n endif()\n file(READ \"${CMAKE_SOURCE_DIR}/external/Licenses/${_3PL}License.txt\"\n _3PL_LICENSE)\n string(COMPARE LESS ${_3PL} \"Libbacktrace\" _STRING_0_or_1)\n if(_STRING_0_or_1)\n set(SPECTRE_3PL_CXX_STRING0\n \"${SPECTRE_3PL_CXX_STRING0}${_3PL}\\n${_3PL_COPYRIGHT}\\nDistributed under \\\nthe license\\n${_3PL_LICENSE}\\n\\n\\n\")\n else()\n set(SPECTRE_3PL_CXX_STRING1\n \"${SPECTRE_3PL_CXX_STRING1}${_3PL}\\n${_3PL_COPYRIGHT}\\nDistributed under \\\nthe license\\n${_3PL_LICENSE}\\n\\n\\n\")\n endif()\n set(SPECTRE_3PL_DOX_STRING\n \"${SPECTRE_3PL_DOX_STRING}###${_3PL}\\n${_3PL_COPYRIGHT}\\nDistributed under \\\nthe license\\n```\\n${_3PL_LICENSE}\\n```\\n\\n\\n\")\nendforeach()\n" }, { "path": "cmake/SetupLinkTimeOptimization.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(SPECTRE_LTO \"Use link-time optimization if available\" OFF)\n\ninclude(CheckIPOSupported)\ncheck_ipo_supported(RESULT _RESULT OUTPUT _OUTPUT)\nif(_RESULT AND SPECTRE_LTO)\n option(SPECTRE_LTO_CORES \"Number of cores to use for LTO\" OFF)\n if (NOT SPECTRE_LTO_CORES)\n set(SPECTRE_LTO_CORES \"auto\")\n endif()\n target_link_options(SpectreFlags\n INTERFACE\n -flto=${SPECTRE_LTO_CORES})\n message(STATUS \"Link-time optimizations enabled with ${SPECTRE_LTO_CORES}\")\nelse()\n target_link_options(SpectreFlags\n INTERFACE\n -fno-lto)\n message(STATUS \"Link-time optimizations disabled (no LTO)\")\nendif()\n" }, { "path": "cmake/SetupListTargets.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nadd_custom_target(\n list-targets\n COMMAND\n ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target help\n | grep -v \" depend$\"\n | grep -v \" edit_cache$\"\n | grep -v \" module_\"\n VERBATIM\n)\n\nadd_custom_target(targets COMMAND DEPENDS list-targets)\n\nadd_custom_target(list COMMAND DEPENDS list-targets)\n" }, { "path": "cmake/SetupNinjaColors.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nif (\"${CMAKE_GENERATOR}\" STREQUAL \"Ninja\")\n if (\"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"GNU\")\n set_property(TARGET SpectreFlags\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$,$>:\n -fdiagnostics-color=always>)\n elseif (\n \"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"Clang\" OR\n \"${CMAKE_CXX_COMPILER_ID}\" STREQUAL \"AppleClang\")\n set_property(TARGET SpectreFlags\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$,$>:\n -fcolor-diagnostics>)\n else ()\n message(\n WARNING \"Not sure how to get color output with\"\n \" Ninja and compiler id ${CMAKE_CXX_COMPILER_ID}\")\n endif ()\nendif ()\n" }, { "path": "cmake/SetupOpenMP.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(ENABLE_OPENMP \"Enable OpenMP in some parts of the code\" OFF)\n\nif (ENABLE_OPENMP)\n find_package(OpenMP COMPONENTS CXX)\nendif()\n" }, { "path": "cmake/SetupPapi.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nif(NOT USE_PAPI)\n option(USE_PAPI \"Search for and include PAPI\" OFF)\nendif()\n\n# Do not set up PAPI again if it was already done once\nif(USE_PAPI AND NOT TARGET Papi)\n find_package(PAPI REQUIRED)\n add_library(Papi INTERFACE IMPORTED)\n set_property(TARGET Papi\n APPEND PROPERTY\n INTERFACE_INCLUDE_DIRECTORIES ${PAPI_INCLUDE_DIRS})\n set_property(TARGET Papi\n APPEND PROPERTY\n INTERFACE_COMPILE_DEFINITIONS \"SPECTRE_USE_PAPI\")\n set_property(TARGET Papi\n APPEND PROPERTY\n INTERFACE_LINK_LIBRARIES ${PAPI_LIBRARIES})\n\n set_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n Papi\n )\nendif(USE_PAPI AND NOT TARGET Papi)\n" }, { "path": "cmake/SetupParaView.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(ENABLE_PARAVIEW \"Try to find ParaView to enable 3D rendering tools\" OFF)\n\nif (NOT ENABLE_PARAVIEW)\n return()\nendif()\n\nfind_package(ParaView REQUIRED)\n\n# Help `find_python_module` find ParaView\nif (PARAVIEW_PYTHONPATH)\n set(PY_paraview_LOCATION ${PARAVIEW_PYTHONPATH}/paraview)\nendif()\n" }, { "path": "cmake/SetupPch.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Support for precompiled headers (PCH)\n# =====================================\n#\n# Precompiled headers are a way to speed up compilation by precompiling\n# frequently used headers.\n#\n# We have the following requirements on the PCH:\n# - it must be rebuilt whenever anything it includes is changed.\n# - it must be removed when running `make clean`\n# - it must be generated before any object files are built that\n# use it\n# - it must be able to use flags from other targets (since in modern CMake\n# flags, etc. are propagated via targets)\n# - the correct flags to include the PCH must be propagated to any targets\n# that use the PCH.\n#\n# We use CMake's PCH support to accomplish this. It is documented here:\n# https://cmake.org/cmake/help/latest/command/target_precompile_headers.html.\n#\n# The PCH is generated by compiling a source file that includes all the headers\n# we want to precompile. These precompiled headers are listed in\n# `tools/SpectrePch.hpp`.\n#\n# Instructions for using the PCH:\n# -------------------------------\n#\n# Targets can use the PCH generated for the `SpectrePch` library. They must also\n# link the `SpectrePchFlags` library so they compile with the same flags as the\n# PCH. Make sure to check the PCH exist before using them:\n#\n# if(TARGET SpectrePch)\n# target_precompile_headers(${TARGET_NAME} REUSE_FROM SpectrePch)\n# target_link_libraries(${TARGET_NAME} PRIVATE SpectrePchFlags)\n# endif()\n\n# This library tracks all compiler flags to build the PCH. Targets that use\n# the PCH must link this library so they compile with the same flags as the\n# PCH.\nadd_library(SpectrePchFlags INTERFACE)\ntarget_link_libraries(\n SpectrePchFlags\n INTERFACE\n Blaze\n Brigand\n Charmxx::charmxx\n Charmxx::pup\n HDF5::HDF5\n SpectreFlags\n SpectreKokkos\n )\n\n# Targets can reuse the PCH generated for this library. They must also link\n# the `SpectrePchFlags` library. Notes:\n# - We store the PCH header in ${CMAKE_SOURCE_DIR}/tools so that it is not\n# accidentally included anywhere.\n# - We also store a source file that just includes the PCH header so the\n# library has something to compile.\n# - This is an object library because we don't need to actually link it, we\n# only need to build it so it generates the PCH.\nconfigure_file(\n ${CMAKE_SOURCE_DIR}/tools/SpectrePch.hpp\n ${CMAKE_BINARY_DIR}\n )\nset(SPECTRE_PCH_HEADER ${CMAKE_BINARY_DIR}/SpectrePch.hpp)\nfile(GENERATE\n OUTPUT ${CMAKE_BINARY_DIR}/SpectrePch.cpp\n CONTENT \"#include \\\"${SPECTRE_PCH_HEADER}\\\"\\n\")\nadd_library(\n SpectrePch\n OBJECT\n ${CMAKE_BINARY_DIR}/SpectrePch.cpp)\ntarget_precompile_headers(\n SpectrePch\n PRIVATE\n ${SPECTRE_PCH_HEADER}\n )\ntarget_link_libraries(\n SpectrePch\n PRIVATE\n SpectrePchFlags\n )\n" }, { "path": "cmake/SetupPic.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Set up position independent code by default since this is required\n# for our python libraries.\n#\n# We cannot use CMake's set(CMAKE_POSITION_INDEPENDENT_CODE ON)\n# because that enables -fPIC in shared libraries and -fPIE on executables.\n# While what CMake does is technically the optimal thing to do, it means\n# we would need to generate two PCHs, one built with -fPIC and one with\n# -fPIE. More specifically, we'd need to generate one using a library target\n# and one using an executable target, which would double the amount of code\n# in SetupPch.cmake for a currently unknown benefit.\nset_property(TARGET SpectreFlags\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$:-fPIC>\n $<$:-fPIC>\n $<$:-fPIC>)\n" }, { "path": "cmake/SetupProfiling.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(ENABLE_PROFILING \"Enables various options to make profiling easier\" OFF)\n\noption(KEEP_FRAME_POINTER \"Add keep frame pointer for profiling\" OFF)\n\nadd_library(Profiling::KeepFramePointer IMPORTED INTERFACE)\nadd_library(Profiling::EnableProfiling IMPORTED INTERFACE)\n\nif (KEEP_FRAME_POINTER OR ENABLE_PROFILING)\n set_property(\n TARGET Profiling::KeepFramePointer\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$:-fno-omit-frame-pointer>\n $<$:-mno-omit-leaf-frame-pointer>\n )\nendif()\n\nif (ENABLE_PROFILING)\n set_property(\n TARGET Profiling::EnableProfiling\n APPEND PROPERTY\n INTERFACE_COMPILE_DEFINITIONS\n $<$:SPECTRE_PROFILING>\n )\nendif()\n\ntarget_link_libraries(\n SpectreFlags\n INTERFACE\n Profiling::EnableProfiling\n Profiling::KeepFramePointer\n )\n" }, { "path": "cmake/SetupPybind11.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(BUILD_PYTHON_BINDINGS \"Build the python bindings for SpECTRE\" ON)\n\nif(BUILD_PYTHON_BINDINGS)\n # Make sure to find Python first so it's consistent with pybind11\n find_package(Python REQUIRED COMPONENTS Interpreter Development)\n\n # Try to find the pybind11-config tool to find pybind11's CMake config files\n find_program(PYBIND11_CONFIG_TOOL pybind11-config)\n set(PYBIND11_CMAKEDIR \"\")\n if(PYBIND11_CONFIG_TOOL)\n execute_process(\n COMMAND \"${PYBIND11_CONFIG_TOOL}\" \"--cmakedir\"\n OUTPUT_VARIABLE PYBIND11_CMAKEDIR\n OUTPUT_STRIP_TRAILING_WHITESPACE)\n message(STATUS \"Found pybind11-config tool (${PYBIND11_CONFIG_TOOL}) and \"\n \"determined CMake dir: ${PYBIND11_CMAKEDIR}\")\n endif()\n\n find_package(pybind11 2.7.0 REQUIRED\n HINTS\n ${PYBIND11_CMAKEDIR}\n ${SPECTRE_PYTHON_SITE_PACKAGES}\n ${Python_SITEARCH}\n ${Python_SITELIB}\n ${Python_STDARCH}\n ${Python_STDLIB}\n )\n\n set_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n pybind11::headers\n )\n\n message(STATUS \"Pybind11 include: ${pybind11_INCLUDE_DIR}\")\nendif()\n" }, { "path": "cmake/SetupPypp.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# To run Python tests we need the development component (libs and include dirs).\n# It provides the `Python::Python` imported target. We find the interpreter\n# component as well to make sure the find is consistent with earlier finds that\n# only looked for the interpreter, possibly guided by the Python_EXECUTABLE\n# variable set by the user.\nfind_package(Python REQUIRED COMPONENTS Interpreter Development)\n\n# CMake's FindPython has trouble finding NumPy when it isn't installed in the\n# Python executable's directory, and can't be given hints either (as of CMake\n# version 3.25). So we find NumPy ourselves (which isn't much different to\n# what FindPython does internally anyway).\nfind_package(NumPy 1.10 REQUIRED)\n\nmessage(STATUS \"NumPy incl: \" ${NUMPY_INCLUDE_DIRS})\nmessage(STATUS \"NumPy vers: \" ${NUMPY_VERSION})\n\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"NumPy version: ${NUMPY_VERSION}\\n\"\n )\n\n# Also check that SciPy is installed\ninclude(FindPythonModule)\nfind_python_module(scipy REQUIRED)\n\nadd_library(Python::NumPy INTERFACE IMPORTED)\nset_property(TARGET Python::NumPy PROPERTY\n INTERFACE_INCLUDE_DIRECTORIES ${NUMPY_INCLUDE_DIRS})\n\nset_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n Python::NumPy Python::Python\n )\n" }, { "path": "cmake/SetupSanitizers.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(ASAN \"Add AddressSanitizer compile flags\" OFF)\n\n# We handle the sanitizers using targets for the compile options, but modify\n# CMAKE_EXE_LINKER_FLAGS for the linker flags because the sanitizers should\n# only be linked into the final executable and CMake doesn't support linker\n# interface flags before CMake 3.13.\nadd_library(Sanitizers IMPORTED INTERFACE)\nadd_library(Sanitizers::Address IMPORTED INTERFACE)\nadd_library(Sanitizers::UbInteger IMPORTED INTERFACE)\nadd_library(Sanitizers::UbUndefined IMPORTED INTERFACE)\n\nif (ASAN)\n set_property(\n TARGET Sanitizers::Address\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$:-fno-omit-frame-pointer -fsanitize=address>\n )\n set(\n CMAKE_EXE_LINKER_FLAGS\n \"${CMAKE_EXE_LINKER_FLAGS} -fsanitize=address\"\n )\nendif ()\n\noption(UBSAN_UNDEFINED \"Add UBSan undefined behavior compile flags\" OFF)\nif (UBSAN_UNDEFINED)\n set_property(\n TARGET Sanitizers::UbUndefined\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$:-fno-omit-frame-pointer -fsanitize=undefined>\n )\n set(\n CMAKE_EXE_LINKER_FLAGS\n \"${CMAKE_EXE_LINKER_FLAGS} -fsanitize=undefined\"\n )\nendif()\n\noption(UBSAN_INTEGER \"Add UBSan unsigned integer overflow compile flags\" OFF)\nif (UBSAN_INTEGER)\n set_property(\n TARGET Sanitizers::UbInteger\n APPEND PROPERTY\n INTERFACE_COMPILE_OPTIONS\n $<$:-fno-omit-frame-pointer -fsanitize=integer>\n )\n set(\n CMAKE_CXX_FLAGS\n \"${CMAKE_CXX_FLAGS} -fno-omit-frame-pointer -fsanitize=integer\"\n )\n set(\n CMAKE_EXE_LINKER_FLAGS\n \"${CMAKE_EXE_LINKER_FLAGS} -fsanitize=integer\"\n )\nendif()\n\ntarget_link_libraries(\n SpectreFlags\n INTERFACE\n Sanitizers::Address\n Sanitizers::UbInteger\n Sanitizers::UbUndefined\n )\n" }, { "path": "cmake/SetupSpec.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_package(SpEC)\n\n# Make SpEC scripts available in Python. These can be used until we have ported\n# them to SpECTRE.\nif (SPEC_ROOT)\n set(PYTHONPATH \"${SPEC_ROOT}/Support/Python:\\\n${SPEC_ROOT}/Support/DatDataManip:${PYTHONPATH}\")\nendif()\n\nif (NOT SpEC_FOUND)\n return()\nendif()\n\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"SpEC exporter: ${SPEC_EXPORTER_ROOT}\\n\"\n )\n" }, { "path": "cmake/SetupSpectreInlining.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(SPECTRE_USE_ALWAYS_INLINE \"Force SpECTRE inlining.\" ON)\n\nset(_SPECTRE_USE_ALWAYS_INLINE 0)\n\nif(SPECTRE_USE_ALWAYS_INLINE)\n set(_SPECTRE_USE_ALWAYS_INLINE 1)\nendif()\n\nset_property(\n TARGET SpectreFlags\n APPEND PROPERTY\n INTERFACE_COMPILE_DEFINITIONS\n $<$:SPECTRE_USE_ALWAYS_INLINE=${_SPECTRE_USE_ALWAYS_INLINE}>\n)\n" }, { "path": "cmake/SetupSphinx.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Setup Sphinx to generate documentation for our Python modules. The HTML output\n# is placed in docs/html/py/ so we can link to it from Doxygen.\n\n# We have also experimented with generating our C++ documentation with Sphinx.\n# See issue: https://github.com/sxs-collaboration/spectre/issues/2138\n\nset(SPHINX_SOURCE ${CMAKE_BINARY_DIR}/docs/sphinx)\nset(SPHINX_BUILD ${CMAKE_BINARY_DIR}/docs/html/py)\n\nconfigure_file(\n ${CMAKE_SOURCE_DIR}/docs/conf.py\n ${SPHINX_SOURCE}/conf.py\n @ONLY\n )\n\nconfigure_file(\n ${CMAKE_SOURCE_DIR}/docs/index.rst\n ${SPHINX_SOURCE}/index.rst\n )\nconfigure_file(\n ${CMAKE_SOURCE_DIR}/docs/cli.rst\n ${SPHINX_SOURCE}/cli.rst\n )\n\nfile(\n COPY ${CMAKE_SOURCE_DIR}/docs/_templates\n DESTINATION ${SPHINX_SOURCE}\n)\n\nadd_custom_target(py-docs\n COMMAND\n ${CMAKE_COMMAND} -E env\n ${CMAKE_BINARY_DIR}/bin/python-spectre -m sphinx -b html\n ${SPHINX_SOURCE} ${SPHINX_BUILD}\n WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}\n COMMENT \"Generating Python documentation\"\n )\nadd_dependencies(py-docs all-pybindings)\n" }, { "path": "cmake/SetupStl.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Create an C++ standard library target for tracking dependencies\n# through includes throughout SpECTRE.\nif(NOT TARGET Stl)\n add_library(Stl INTERFACE IMPORTED)\n\n add_interface_lib_headers(\n TARGET Stl\n HEADERS\n algorithm\n any\n array\n atomic\n barrier\n bit\n bitset\n cassert\n cctype\n cerrno\n cfenv\n cfloat\n charconv\n chrono\n cinttypes\n climits\n clocale\n cmath\n codecvt\n compare\n complex\n concepts\n condition_variable\n coroutine\n csetjmp\n csignal\n cstdarg\n cstddef\n cstdint\n cstdio\n cstdlib\n cstring\n ctime\n cuchar\n cwchar\n cwctype\n deque\n exception\n execution\n format\n forward_list\n fstream\n functional\n future\n initializer_list\n iomanip\n ios\n iosfwd\n iostream\n istream\n iterator\n latch\n limits\n list\n locale\n map\n memory\n memory_resource\n mutex\n new\n numbers\n numeric\n optional\n ostream\n queue\n random\n ranges\n ratio\n regex\n scoped_allocator\n semaphore\n set\n shared_mutex\n source_location\n span\n sstream\n stack\n stdexcept\n stop_token\n streambuf\n string\n string_view\n strstream\n syncstream\n system_error\n thread\n tuple\n type_traits\n typeindex\n typeinfo\n unordered_map\n unordered_set\n utility\n valarray\n variant\n vector\n version\n\n # UNIX/Linux specific headers\n dirent.h\n libgen.h\n sys/stat.h\n sys/types.h\n unistd.h\n xmmintrin.h\n )\n\n set_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n Stl\n )\nendif(NOT TARGET Stl)\n" }, { "path": "cmake/SetupTcmalloc.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_package(TCMALLOC REQUIRED)\n\nmessage(STATUS \"tcmalloc libs: \" ${TCMALLOC_LIBRARIES})\nmessage(STATUS \"tcmalloc incl: \" ${TCMALLOC_INCLUDE_DIRS})\n\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"tcmalloc version: ${TCMALLOC_VERSION}\\n\"\n )\n\nadd_library(Tcmalloc INTERFACE IMPORTED)\nset_property(TARGET Tcmalloc\n APPEND PROPERTY INTERFACE_LINK_LIBRARIES ${TCMALLOC_LIBRARIES})\nset_property(TARGET Tcmalloc PROPERTY\n INTERFACE_INCLUDE_DIRECTORIES ${TCMALLOC_INCLUDE_DIRS})\n\nset_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n Tcmalloc\n )\n" }, { "path": "cmake/SetupXsimd.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# To turn this off, one should provide an alternative\n# SIMD backend that supports elementary functions\n# or the auto-differentiation in SpECTRE ceases to\n# work\noption(USE_XSIMD \"Use xsimd if it is available\" ON)\n\nif(USE_XSIMD)\n find_package(xsimd QUIET)\n\n if (NOT xsimd_FOUND)\n if (NOT SPECTRE_FETCH_MISSING_DEPS)\n message(FATAL_ERROR \"Could not find xsimd. If you want to fetch \"\n \"missing dependencies automatically, set SPECTRE_FETCH_MISSING_DEPS=ON.\")\n endif()\n\n message(STATUS \"Fetching xsimd\")\n include(FetchContent)\n FetchContent_Declare(xsimd\n GIT_REPOSITORY https://github.com/xtensor-stack/xsimd\n GIT_TAG 13.2.0\n ${SPECTRE_FETCHCONTENT_BASE_ARGS}\n )\n FetchContent_MakeAvailable(xsimd)\n set(xsimd_INCLUDE_DIRS ${xsimd_SOURCE_DIR}/include)\n set(xsimd_VERSION \"13.2.0\")\n if (NOT CMAKE_VERSION VERSION_GREATER_EQUAL 3.25)\n get_target_property(XSIMD_IID xsimd INTERFACE_INCLUDE_DIRECTORIES)\n set_target_properties(xsimd PROPERTIES INTERFACE_SYSTEM_INCLUDE_DIRECTORIES \"${XSIMD_IID}\")\n endif()\n endif()\n\n if(xsimd_VERSION VERSION_LESS 11.0.1)\n message(FATAL_ERROR \"xsimd must be at least 11.0.1, got ${xsimd_VERSION}\")\n endif()\n\n message(STATUS \"xsimd incld: ${xsimd_INCLUDE_DIRS}\")\n message(STATUS \"xsimd vers: ${xsimd_VERSION}\")\n\n file(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"xsimd version: ${xsimd_VERSION}\\n\"\n )\n\n add_interface_lib_headers(\n TARGET xsimd\n HEADERS\n xsimd/xsimd.hpp\n )\n\n # As long as we want xsimd support to be optional we need to be\n # able to figure out if we have it available.\n #\n # To enable use with Blaze, add:\n # -DBLAZE_USE_XSIMD=1\n target_compile_definitions(\n xsimd\n INTERFACE\n $<$:SPECTRE_USE_XSIMD>\n )\n\n set_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n xsimd\n )\n\n # Currently we still have some compatibility bugs to sort out between Blaze\n # and xsimd. Once that's done we will enable combining the two.\n #\n # target_link_libraries(\n # Blaze\n # INTERFACE\n # xsimd\n # )\nendif()\n" }, { "path": "cmake/SetupYamlCpp.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfind_package(YAML_CPP NAMES yaml-cpp)\n\nif (NOT YAML_CPP_FOUND)\n if (NOT SPECTRE_FETCH_MISSING_DEPS)\n message(FATAL_ERROR \"Could not find yaml-cpp. If you want to fetch \"\n \"missing dependencies automatically, set SPECTRE_FETCH_MISSING_DEPS=ON.\")\n endif()\n message(STATUS \"Fetching yaml-cpp\")\n include(FetchContent)\n FetchContent_Declare(yaml-cpp\n GIT_REPOSITORY https://github.com/jbeder/yaml-cpp.git\n GIT_TAG 0.8.0\n GIT_SHALLOW TRUE\n ${SPECTRE_FETCHCONTENT_BASE_ARGS}\n )\n FetchContent_MakeAvailable(yaml-cpp)\nendif()\n\n# New versions of yaml-cpp define the target `yaml-cpp::yaml-cpp`. Old versions\n# define the deprecated target `yaml-cpp`.\nif (NOT TARGET yaml-cpp::yaml-cpp)\n add_library(yaml-cpp::yaml-cpp INTERFACE IMPORTED)\n target_link_libraries(yaml-cpp::yaml-cpp INTERFACE yaml-cpp)\nendif()\n\nset_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n yaml-cpp::yaml-cpp\n )\n" }, { "path": "cmake/SpectreAddCatchTests.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n#\n# This file contains functions used by CMake to add Catch tests to CTest.\n#\n# Catch is a testing framework available on Github:\n# https://github.com/philsquared/Catch\n# It supports a variety of different styles of tests including BDD and fixture\n# tests.\n#\n# Usage\n# =====\n# To run the tests, type 'ctest' in the build directory. You can specify\n# a regex to match the test name using 'ctest -R Unit.Blah', or run all\n# tests with a certain tag using 'ctest -L tag'\n#\n# Attributes\n# ==========\n# Attributes allow you to modify properties of the test. Attributes are\n# specified as follows:\n# // [[TimeOut, 10]]\n# // [[OutputRegex, A regular expression that is expected to match the output\n# // from the test]]\n# SPECTRE_TEST_CASE(\"Unit.Blah\", \"[Unit]\") {\n#\n# Note the space after the comma!\n#\n# Available attributes are:\n# TimeOut - override the default timeout and set the timeout to N seconds. This\n# should be set very sparingly since unit tests are designed to be\n# short. If your test is too long you should consider testing smaller\n# portions of the code if possible, or writing an integration test\n# instead.\n# OutputRegex - When testing failure modes the exact error message must be\n# tested, not just that the test failed. Since the string passed\n# is a regular expression you must escape any regex tokens. For\n# example, to match \"some (word) and\" you must specify the\n# string \"some \\(word\\) and\".\n\nadd_custom_target(unit-tests)\n\nspectre_define_test_timeout_factor_option(UNIT \"unit\")\n\n# Environment variables for test\nset(_CATCH_TEST_ENV_VARS \"\")\n# - Disable ASAN's leak sanitizer because Charm++ has false positives\nlist(APPEND _CATCH_TEST_ENV_VARS \"ASAN_OPTIONS=detect_leaks=0\")\n# - Set PYTHONPATH to find Python modules\nlist(APPEND _CATCH_TEST_ENV_VARS \"PYTHONPATH=${PYTHONPATH}\")\n\n# Main function - the only one designed to be called from outside this module.\nfunction(spectre_add_catch_tests TEST_TARGET)\n get_target_property(SOURCE_FILES ${TEST_TARGET} SOURCES)\n list(FILTER SOURCE_FILES EXCLUDE REGEX \"TestMain.*$\")\n # For each of the source files, we use spectre_parse_file to find all the\n # Catch tests inside the source file and add them to CTest.\n # We ignore the Charm++ generated header files.\n\n file(MAKE_DIRECTORY \"${CMAKE_BINARY_DIR}/tmp\")\n\n unset(ABSOLUTE_SOURCE_FILES)\n foreach (SOURCE_FILE ${SOURCE_FILES})\n string(REGEX MATCH \".*(decl.h|def.h)\" CHARM_INTERFACE_FILE\n \"${SOURCE_FILE}\")\n if (NOT CHARM_INTERFACE_FILE)\n if (NOT IS_ABSOLUTE ${SOURCE_FILE})\n set(SOURCE_FILE ${CMAKE_CURRENT_LIST_DIR}/${SOURCE_FILE})\n endif()\n set(ABSOLUTE_SOURCE_FILES \"${ABSOLUTE_SOURCE_FILES};${SOURCE_FILE}\")\n endif()\n endforeach()\n\n execute_process(\n COMMAND\n ${Python_EXECUTABLE}\n ${CMAKE_SOURCE_DIR}/cmake/SpectreParseTests.py\n ${ABSOLUTE_SOURCE_FILES}\n WORKING_DIRECTORY ${CMAKE_BINARY_DIR}/tmp\n RESULT_VARIABLE PARSED_TESTS_SUCCESSFULLY)\n if (${PARSED_TESTS_SUCCESSFULLY} GREATER 0)\n message(FATAL_ERROR \"Failed to parse test files\")\n endif()\n\n set_property(GLOBAL PROPERTY SPECTRE_FAILURE_TESTS_PROPERTY \"\")\n\n foreach (SOURCE_FILE ${ABSOLUTE_SOURCE_FILES})\n spectre_parse_file(${SOURCE_FILE} ${TEST_TARGET})\n endforeach ()\n\n get_property(\n SPECTRE_FAILURE_TESTS\n GLOBAL\n PROPERTY\n SPECTRE_FAILURE_TESTS_PROPERTY)\n set_property(GLOBAL PROPERTY SPECTRE_FAILURE_TESTS_PROPERTY \"\")\n\n # Generate shell script that runs all non-failure tests manually\n string(REPLACE \";\" \" \" SPECTRE_FAILURE_TESTS \"${SPECTRE_FAILURE_TESTS}\")\n file(WRITE\n \"${CMAKE_BINARY_DIR}/tmp/NonFailureTests${TEST_TARGET}.sh\"\n \"#!/bin/bash -e\\n\"\n \"${CMAKE_RUNTIME_OUTPUT_DIRECTORY}/${TEST_TARGET} ${SPECTRE_FAILURE_TESTS}\")\n file(COPY\n \"${CMAKE_BINARY_DIR}/tmp/NonFailureTests${TEST_TARGET}.sh\"\n DESTINATION \"${CMAKE_RUNTIME_OUTPUT_DIRECTORY}\"\n FILE_PERMISSIONS OWNER_READ OWNER_WRITE OWNER_EXECUTE\n )\n file(REMOVE \"${CMAKE_BINARY_DIR}/tmp/NonFailureTests${TEST_TARGET}.sh\")\nendfunction()\n\n# Parses the cpp file and extracts the tests specified in it. Each test is then\n# added to CTest, and the run command is adjusted according to timeout,\n# willfail, and serialization needs.\nfunction(spectre_parse_file SOURCE_FILE TEST_TARGET)\n if (NOT EXISTS ${SOURCE_FILE})\n message(WARNING \"Could not find source file:\\n\\\"${SOURCE_FILE}\\\"\\nfor \\\n tests\\n.\")\n return()\n endif ()\n\n file(STRINGS ${SOURCE_FILE} CONTENTS NEWLINE_CONSUME)\n\n # Remove commented out tests so they are not added to ctest\n string(REGEX REPLACE \"\\n[ \\t]*//+[^\\n]+\" \"\\n\" CONTENTS \"${CONTENTS}\")\n\n # The regex searches for SPECTRE_TEST_CASE_METHOD, SCENARIO and SPECTRE_TEST_CASE\n # to find tests that need to be added. TESTS will be a list of all tests\n # found in the SOURCE_FILE.\n string(REGEX MATCHALL\n \"(CATCH_)?(SPECTRE_TEST_CASE_METHOD|SCENARIO|SPECTRE_TEST_CASE)[ \\t]*\\\\([^\\)]+\\\\)[ \\t]*{\"\n TESTS\n \"${CONTENTS}\")\n\n set(FAILURE_TESTS \"\")\n foreach (TEST_NAME ${TESTS})\n # Get test type and fixture if applicable\n string(REGEX MATCH \"(CATCH_)?(SPECTRE_TEST_CASE_METHOD|SCENARIO|SPECTRE_TEST_CASE)\"\n TEST_TYPE \"${TEST_NAME}\")\n\n # Get string parts of test definition\n string(REGEX MATCHALL \"\\\"[^\\\"]+\\\"\" TEST_STRINGS \"${TEST_NAME}\")\n\n # Strip wrapping quotation marks of each element of the list\n # TEST_STRINGS\n string(REGEX REPLACE \"^\\\"(.*)\\\"$\" \"\\\\1\" TEST_STRINGS \"${TEST_STRINGS}\")\n # If a test name went on multiple lines, there will either be a sequence\n # .\";\" or \";\". from the line break (after replacing all the whitespace with\n # ;) Remove these from the test string\n string(REPLACE \".\\\";\\\"\" \".\" TEST_STRINGS \"${TEST_STRINGS}\")\n string(REPLACE \"\\\";\\\".\" \".\" TEST_STRINGS \"${TEST_STRINGS}\")\n # Remove the last set of quotation marks\n string(REPLACE \"\\\";\\\"\" \";\" TEST_STRINGS \"${TEST_STRINGS}\")\n\n # Validate that a test name and tags have been provided\n list(LENGTH TEST_STRINGS TEST_STRINGS_LENGTH)\n if (NOT TEST_STRINGS_LENGTH EQUAL 2)\n message(FATAL_ERROR\n \"You must provide a valid test name and tags \"\n \"for all tests in ${SOURCE_FILE}. Cannot use the test:\\n\"\n \"\\\"${TEST_STRINGS}\\\"\\n\")\n endif ()\n\n # Assign name and tags\n list(GET TEST_STRINGS 0 NAME)\n if (\"${TEST_TYPE}\" STREQUAL \"SCENARIO\")\n set(NAME \"Scenario: ${NAME}\")\n endif ()\n set(CTEST_NAME \"${NAME}\")\n\n # Gets the TAGS of the test which is element 1 of TEST_STRINGS,\n # strips the enclosing brackets, and makes a list\n list(GET TEST_STRINGS 1 TAGS)\n string(TOLOWER \"${TAGS}\" TAGS)\n string(REPLACE \"]\" \";\" TAGS \"${TAGS}\")\n string(REPLACE \"[\" \"\" TAGS \"${TAGS}\")\n\n # These files are generated by the SpectreParseTests.py\n if(NOT EXISTS \"${CMAKE_BINARY_DIR}/tmp/${CTEST_NAME}.output_regex\")\n message(FATAL_ERROR\n \"Failed to parse out the test ${TEST_NAME} in the file ${SOURCE_FILE}.\"\n \" This means the python script cmake/SpectreParseTests.py failed to \"\n \"correctly identify the tests.\")\n endif()\n file(READ \"${CMAKE_BINARY_DIR}/tmp/${CTEST_NAME}.output_regex\" OUTPUT_REGEX)\n file(REMOVE \"${CMAKE_BINARY_DIR}/tmp/${CTEST_NAME}.output_regex\")\n file(READ \"${CMAKE_BINARY_DIR}/tmp/${CTEST_NAME}.timeout\" TIMEOUT)\n file(REMOVE \"${CMAKE_BINARY_DIR}/tmp/${CTEST_NAME}.timeout\")\n\n # The default TIMEOUT is set to -1, but overwritten by each type\n # of test or a specified TIMEOUT attribute for a given test.\n # Thus we can use it to check if each test has been tagged by an\n # appropriate type.\n if (TIMEOUT EQUAL -1)\n message(FATAL_ERROR\n \"You must set at least one tag of value [unit] \"\n \"for \\\"${NAME}\\\" in ${SOURCE_FILE}\\n\")\n endif ()\n\n # Triple timeout if address sanitizer is enabled.\n if (ASAN)\n math(EXPR TIMEOUT \"3 * ${TIMEOUT}\")\n endif()\n\n spectre_test_timeout(TIMEOUT UNIT ${TIMEOUT})\n\n # Add the test and set its properties\n # - Skip benchmarks during unit testing\n add_test(NAME ${CTEST_NAME}\n COMMAND ${SPECTRE_TEST_RUNNER} $\n \\\"${NAME}\\\" --durations yes\n --warn NoAssertions\n --skip-benchmarks\n --name \"\\\"$.${CTEST_NAME}\\\"\")\n\n # Check if the test is supposed to fail. If so then let ctest know\n # that a failed test is actually a pass.\n if (NOT \"${OUTPUT_REGEX}\" STREQUAL \"\")\n if (NOT \"${CMAKE_BUILD_TYPE}\" STREQUAL \"Debug\")\n set(OUTPUT_REGEX\n \"${OUTPUT_REGEX}|### No ASSERT tests in release mode ###\")\n endif()\n set_tests_properties(\n ${CTEST_NAME} PROPERTIES\n FAIL_REGULAR_EXPRESSION \"No tests ran\"\n TIMEOUT ${TIMEOUT}\n PASS_REGULAR_EXPRESSION \"${OUTPUT_REGEX}\"\n LABELS \"${TAGS}\"\n ENVIRONMENT \"${_CATCH_TEST_ENV_VARS}\")\n set(FAILURE_TESTS \"\\\"~${CTEST_NAME}\\\";${FAILURE_TESTS}\")\n else ()\n set_tests_properties(\n ${CTEST_NAME} PROPERTIES\n FAIL_REGULAR_EXPRESSION \"No tests ran\"\n TIMEOUT ${TIMEOUT}\n LABELS \"${TAGS}\"\n ENVIRONMENT \"${_CATCH_TEST_ENV_VARS}\")\n endif ()\n endforeach ()\n set_property(GLOBAL PROPERTY SPECTRE_FAILURE_TESTS ${FAILURE_TESTS})\n get_property(\n SPECTRE_FAILURE_TESTS\n GLOBAL\n PROPERTY\n SPECTRE_FAILURE_TESTS_PROPERTY)\n set(SPECTRE_FAILURE_TESTS\n \"${SPECTRE_FAILURE_TESTS};${FAILURE_TESTS}\")\n set_property(GLOBAL\n PROPERTY\n SPECTRE_FAILURE_TESTS_PROPERTY\n ${SPECTRE_FAILURE_TESTS})\nendfunction()\n" }, { "path": "cmake/SpectreAddInterfaceLibraryHeaders.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Adds the header files to the target.\n#\n# Usage:\n#\n# add_interface_lib_headers(\n# TARGET TARGET_NAME\n# HEADERS\n# A.hpp\n# B.hpp\n# C.hpp\n# )\n#\n# This function is intended to be used with libraries added using add_library\n# or added by CMake's provided find_package (e.g. Boost). The\n# add_spectre_library handles adding header files for targets correctly and\n# so this function does not need to be used for libraries added with\n# add_spectre_library.\nfunction(add_interface_lib_headers)\n cmake_parse_arguments(\n ARG \"\" \"TARGET\" \"HEADERS\"\n ${ARGN})\n\n if(NOT TARGET ${ARG_TARGET})\n message(FATAL_ERROR\n \"Unknown target '${ARG_TARGET}'\"\n )\n endif(NOT TARGET ${ARG_TARGET})\n\n get_target_property(\n TARGET_TYPE\n ${ARG_TARGET}\n TYPE\n )\n if(NOT ${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\n message(FATAL_ERROR\n \"The target '${ARG_TARGET}' is not an INTERFACE library and so \"\n \"add_interface_lib_headers should not be used to add header files \"\n \"to it.\"\n )\n endif(NOT ${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\n\n get_property(\n SPECTRE_INTERFACE_LIBRARY_HEADERS\n GLOBAL\n PROPERTY SPECTRE_INTERFACE_LIBRARY_HEADERS\n )\n\n # Switch to delimiting the headers by ':' because CMake uses ';' to delimit\n # elements of a list.\n string(REPLACE \";\" \":\" TARGET_HEADERS\n \"${ARG_TARGET}=${ARG_HEADERS}\")\n\n # BEGIN ADD EXISTING HEADERS\n # This block checks if the current target already has a list of header files\n # associated with it. If so, then we parse the current headers from the\n # string SPECTRE_INTERFACE_LIBRARY_HEADERS. Once we've parsed out the\n # _PREVIOUS_HEADERS we append them to the list of current headers,\n # (TARGET_HEADERS). Finally, we remove the current target from the interface\n # libaries string (SPECTRE_INTERFACE_LIBRARY_HEADERS) because we add it with\n # the new headers later.\n set(_PREVIOUS_HEADERS \"\")\n string(FIND \"${SPECTRE_INTERFACE_LIBRARY_HEADERS}\" \"${ARG_TARGET}=\"\n _POSITION_OF_TARGET)\n if (NOT ${_POSITION_OF_TARGET} EQUAL -1)\n string(SUBSTRING \"${SPECTRE_INTERFACE_LIBRARY_HEADERS}\"\n ${_POSITION_OF_TARGET} -1 _PREVIOUS_HEADERS)\n string(FIND \"${_PREVIOUS_HEADERS}\" \"=\"\n POSITION_OF_THIS_EQUALS)\n math(EXPR POSITION_OF_THIS_EQUALS_PLUS_ONE\n \"${POSITION_OF_THIS_EQUALS} + 1\")\n string(SUBSTRING \"${_PREVIOUS_HEADERS}\" ${POSITION_OF_THIS_EQUALS_PLUS_ONE}\n -1 _PREVIOUS_HEADERS)\n string(FIND \"${_PREVIOUS_HEADERS}\" \"=\"\n POSITION_OF_NEXT_EQUALS)\n string(SUBSTRING \"${_PREVIOUS_HEADERS}\" 0 ${POSITION_OF_NEXT_EQUALS}\n _PREVIOUS_HEADERS)\n string(FIND \"${_PREVIOUS_HEADERS}\" \";\" POSITION_OF_LAST_SEMI REVERSE)\n string(SUBSTRING \"${_PREVIOUS_HEADERS}\" 0 ${POSITION_OF_LAST_SEMI}\n _PREVIOUS_HEADERS)\n set(TARGET_HEADERS \"${TARGET_HEADERS}:${_PREVIOUS_HEADERS}\")\n string(REPLACE \"${ARG_TARGET}=${_PREVIOUS_HEADERS}\" \"\"\n SPECTRE_INTERFACE_LIBRARY_HEADERS \"${SPECTRE_INTERFACE_LIBRARY_HEADERS}\")\n endif()\n\n string(REPLACE \";;\" \";\"\n SPECTRE_INTERFACE_LIBRARY_HEADERS \"${SPECTRE_INTERFACE_LIBRARY_HEADERS}\")\n list(APPEND SPECTRE_INTERFACE_LIBRARY_HEADERS ${TARGET_HEADERS})\n # END ADD EXISTING HEADERS\n\n set_property(\n GLOBAL PROPERTY SPECTRE_INTERFACE_LIBRARY_HEADERS\n ${SPECTRE_INTERFACE_LIBRARY_HEADERS}\n )\nendfunction(add_interface_lib_headers)\n\n# Returns a list of all the header files for the target `TARGET`\n# by setting the variable with the name `${RESULT_NAME}`\n#\n# Usage:\n# get_target_headers(MyTarget MY_TARGET_HEADERS)\nfunction(get_target_headers TARGET RESULT_NAME)\n get_target_property(\n TARGET_TYPE\n ${TARGET}\n TYPE\n )\n if(${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\n get_property(\n _SPECTRE_INTERFACE_LIBRARY_HEADERS\n GLOBAL\n PROPERTY SPECTRE_INTERFACE_LIBRARY_HEADERS\n )\n foreach(_LIB ${_SPECTRE_INTERFACE_LIBRARY_HEADERS})\n string(REPLACE \"${TARGET}=\" \"\" _LIB_HEADERS ${_LIB})\n if(NOT ${_LIB} STREQUAL ${_LIB_HEADERS})\n string(REPLACE \":\" \";\" _LIB_HEADERS ${_LIB_HEADERS})\n set(${RESULT_NAME} ${_LIB_HEADERS} PARENT_SCOPE)\n break()\n endif(NOT ${_LIB} STREQUAL ${_LIB_HEADERS})\n endforeach(_LIB ${_SPECTRE_INTERFACE_LIBRARY_HEADERS})\n\n else(${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\n get_property(\n _HEADER_FILES\n TARGET ${TARGET}\n PROPERTY PUBLIC_HEADER\n )\n set(${RESULT_NAME} ${_HEADER_FILES} PARENT_SCOPE)\n endif(${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\nendfunction(get_target_headers TARGET)\n" }, { "path": "cmake/SpectreAddLibraries.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nadd_custom_target(libs)\n\nfunction(ADD_SPECTRE_LIBRARY LIBRARY_NAME)\n add_library(${LIBRARY_NAME} ${ARGN})\n add_dependencies(libs ${LIBRARY_NAME})\n\n get_target_property(\n LIBRARY_IS_IMPORTED\n ${LIBRARY_NAME}\n IMPORTED\n )\n get_target_property(\n LIBRARY_TYPE\n ${LIBRARY_NAME}\n TYPE\n )\n\n # We do _not_ link a custom allocator here, such as jemalloc or tcmalloc, but\n # only dynamically link it into executables. This allows to use the libraries\n # in Python bindings, where the custom allocator would cause problems.\n if (NOT ${LIBRARY_TYPE} STREQUAL INTERFACE_LIBRARY)\n set(SPECTRE_KOKKOS_LAUNCHER \"\")\n if(SPECTRE_KOKKOS)\n # We need to make sure we don't drop the Kokkos link wrapper\n get_target_property(\n _RULE_LAUNCH_LINK\n ${LIBRARY_NAME}\n RULE_LAUNCH_LINK)\n if (_RULE_LAUNCH_LINK)\n set(SPECTRE_KOKKOS_LAUNCHER ${_RULE_LAUNCH_LINK})\n endif()\n endif()\n set_target_properties(\n ${LIBRARY_NAME}\n PROPERTIES\n RULE_LAUNCH_LINK\n \"${CMAKE_BINARY_DIR}/tmp/WrapLibraryLinker.sh ${SPECTRE_KOKKOS_LAUNCHER}\"\n LINK_DEPENDS \"${CMAKE_BINARY_DIR}/tmp/WrapLibraryLinker.sh\"\n )\n endif (NOT ${LIBRARY_TYPE} STREQUAL INTERFACE_LIBRARY)\n if (NOT \"${LIBRARY_NAME}\" MATCHES \"^SpectrePch\"\n AND NOT ${LIBRARY_IS_IMPORTED}\n AND NOT ${LIBRARY_TYPE} STREQUAL INTERFACE_LIBRARY\n AND TARGET SpectrePch)\n target_precompile_headers(${LIBRARY_NAME} REUSE_FROM SpectrePch)\n target_link_libraries(${LIBRARY_NAME} PRIVATE SpectrePchFlags)\n endif()\n if (${LIBRARY_TYPE} STREQUAL INTERFACE_LIBRARY)\n target_link_libraries(\n ${LIBRARY_NAME}\n INTERFACE\n SpectreFlags\n )\n else()\n target_link_libraries(\n ${LIBRARY_NAME}\n PUBLIC\n SpectreFlags\n )\n set_property(\n TARGET ${LIBRARY_NAME}\n PROPERTY FOLDER ${CMAKE_CURRENT_SOURCE_DIR}\n )\n endif()\n if (BUILD_SHARED_LIBS\n AND NOT ${LIBRARY_TYPE} STREQUAL INTERFACE_LIBRARY)\n install(TARGETS ${LIBRARY_NAME} OPTIONAL\n LIBRARY DESTINATION ${CMAKE_INSTALL_LIBDIR})\n endif()\nendfunction()\n" }, { "path": "cmake/SpectreAddTestLibs.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Add an executable with Catch2 unit tests and register them with CTest.\n#\n# This function is named `add_test_library` although it adds an executable for\n# historical reasons. We can refactor this in the future. We can also switch to\n# `catch_discover_tests` instead of our own test parsing code in the future.\n# At that point we can remove the `SOURCE_FILES` argument of this function and\n# instead use the standard `target_sources` to add the source files (currently\n# the `SOURCE_FILES` are needed to parse the tests).\n#\n# Parameters:\n# - TEST_EXEC_NAME The name of the test executable to add\n# - SOURCE_FILES The source files to compile into the executable\nfunction(add_test_library TEST_EXEC_NAME SOURCE_FILES)\n cmake_parse_arguments(ARG WITH_CHARM \"\" \"\" ${ARGN})\n\n add_spectre_executable(\n ${TEST_EXEC_NAME}\n ${SOURCE_FILES}\n )\n add_dependencies(unit-tests ${TEST_EXEC_NAME})\n target_link_libraries(\n ${TEST_EXEC_NAME}\n PRIVATE\n Catch2::Catch2\n Framework\n )\n\n # Use either the Charm++ or the non-Charm++ TestMain\n if (ARG_WITH_CHARM)\n target_sources(\n ${TEST_EXEC_NAME}\n PRIVATE\n ${CMAKE_SOURCE_DIR}/tests/Unit/TestMainCharm.cpp\n )\n add_dependencies(\n ${TEST_EXEC_NAME}\n module_TestMainCharm\n )\n else()\n target_sources(\n ${TEST_EXEC_NAME}\n PRIVATE\n ${CMAKE_SOURCE_DIR}/tests/Unit/TestMain.cpp\n )\n endif()\n\n # Register the tests with CTest.\n # We may want to switch to `catch_discover_tests` and remove our own test\n # parsing code in the future. Before we do, we should check if it supports all\n # the features we use.\n # catch_discover_tests(${TEST_EXEC_NAME})\n spectre_add_catch_tests(${TEST_EXEC_NAME})\nendfunction()\n\n# Shared test libs are currently unsupported on macOS because Catch2 static\n# variables are not properly initialized. This is only needed for test helper\n# libraries with Catch2 assertions in them.\nset(SPECTRE_TEST_LIBS_TYPE \"\")\nif(APPLE)\n set(SPECTRE_TEST_LIBS_TYPE STATIC)\nendif()\n" }, { "path": "cmake/SpectreCheckDependencies.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\ninclude(SpectreCheckTargetDependencies)\n\nfunction(check_spectre_libs_dependencies)\n get_property(\n SPECTRE_TPLS GLOBAL PROPERTY SPECTRE_THIRD_PARTY_LIBS\n )\n\n get_property(\n SPECTRE_LIBS\n TARGET libs\n PROPERTY MANUALLY_ADDED_DEPENDENCIES\n )\n\n foreach(TARGET_TO_CHECK ${ARGN})\n check_target_dependencies(\n TARGET ${TARGET_TO_CHECK}\n ALL_TARGETS\n ${SPECTRE_TPLS}\n ${SPECTRE_LIBS}\n ALLOWED_EXTRA_TARGETS\n SpectreAllocator\n SpectreFlags\n SpectrePchFlags\n ERROR_ON_FAILURE\n )\n endforeach(TARGET_TO_CHECK ${ARGN})\nendfunction(check_spectre_libs_dependencies)\n\noption(CHECK_LIBRARY_DEPENDENCIES\n \"Check link dependencies of SpECTRE libraries\" OFF)\n\noption(CHECK_ALL_DEPENDENCIES\n \"Check link dependencies of all SpECTRE targets\" OFF)\n\nif(CHECK_LIBRARY_DEPENDENCIES OR CHECK_ALL_DEPENDENCIES)\n get_property(\n SPECTRE_LIBS\n TARGET libs\n PROPERTY MANUALLY_ADDED_DEPENDENCIES\n )\n check_spectre_libs_dependencies(\n ${SPECTRE_LIBS}\n )\nendif(CHECK_LIBRARY_DEPENDENCIES OR CHECK_ALL_DEPENDENCIES)\n" }, { "path": "cmake/SpectreCheckTargetDependencies.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\ninclude(SpectreAddInterfaceLibraryHeaders)\n\n# Get the list of absolute paths of header files for target `TARGET_NAME`.\n#\n# Sets the variable `HEADER_FILES` in parent scope to return the result\nfunction(_absolute_header_paths TARGET_NAME)\n get_target_headers(${TARGET_NAME} _HEADER_FILES)\n get_property(\n _INCLUDE_DIR\n TARGET ${TARGET_NAME}\n PROPERTY INTERFACE_INCLUDE_DIRECTORIES\n )\n list(LENGTH _INCLUDE_DIR _NUMBER_OF_INCLUDE_DIRS)\n if(${_NUMBER_OF_INCLUDE_DIRS} GREATER 1)\n message(FATAL_ERROR\n \"Currently _absolute_header_paths only supports a single \"\n \"INTERFACE_INCLUDE_DIRECTORIES for finding header files. Support for \"\n \"multiple INTERFACE_INCLUDE_DIRECTORIES can be added if needed.\")\n endif(${_NUMBER_OF_INCLUDE_DIRS} GREATER 1)\n\n unset(_ABS_HEADER_FILES)\n foreach(HEADER ${_HEADER_FILES})\n if(IS_ABSOLUTE ${HEADER})\n list(APPEND _ABS_HEADER_FILES ${HEADER})\n else()\n list(APPEND _ABS_HEADER_FILES \"${_INCLUDE_DIR}/${HEADER}\")\n endif()\n endforeach(HEADER ${_HEADER_FILES})\n # \"Return\" HEADER_FILES by setting it in PARENT_SCOPE\n set(HEADER_FILES ${_ABS_HEADER_FILES} PARENT_SCOPE)\nendfunction(_absolute_header_paths TARGET_NAME)\n\n# Get the list of absolute paths of source files for target `TARGET_NAME`.\n#\n# Sets the variable `SOURCE_FILES` in parent scope to return the result\nfunction(_absolute_source_paths TARGET_NAME)\n get_property(\n _SOURCE_FILES\n TARGET ${TARGET_NAME}\n PROPERTY SOURCES\n )\n get_property(\n _LOCATION\n TARGET ${TARGET_NAME}\n PROPERTY FOLDER\n )\n\n unset(_ABS_SOURCE_FILES)\n foreach(SOURCE ${_SOURCE_FILES})\n if(IS_ABSOLUTE ${SOURCE})\n list(APPEND _ABS_SOURCE_FILES ${SOURCE})\n else()\n list(APPEND _ABS_SOURCE_FILES \"${_LOCATION}/${SOURCE}\")\n endif()\n endforeach(SOURCE ${_SOURCE_FILES})\n # \"Return\" SOURCE_FILES by setting it in PARENT_SCOPE\n set(SOURCE_FILES ${_ABS_SOURCE_FILES} PARENT_SCOPE)\nendfunction(_absolute_source_paths TARGET_NAME)\n\n# Get the list of SpECTRE includes (i.e. not for 3rd party libraries)\n# for the target `TARGET_NAME`.\n#\n# Sets the variable `SPECTRE_INCLUDES` in parent scope to return the result\nfunction(_extract_spectre_includes FILE_NAME)\n file(READ ${FILE_NAME} FILE_CONTENTS)\n string(REGEX MATCHALL \"\\n#include \\\"[^\\n]+\\\"\"\n _RAW_SPECTRE_INCLUDES ${FILE_CONTENTS})\n unset(SPECTRE_INCLUDES)\n foreach(INCLUDE ${_RAW_SPECTRE_INCLUDES})\n string(REPLACE \"\\n#include \\\"\" \"\" INCLUDE \"${INCLUDE}\")\n string(REPLACE \"\\\"\" \"\" INCLUDE \"${INCLUDE}\")\n list(APPEND SPECTRE_INCLUDES ${INCLUDE})\n endforeach(INCLUDE ${_RAW_SPECTRE_INCLUDES})\n # \"Return\" SPECTRE_INCLUDES by setting it in PARENT_SCOPE\n set(SPECTRE_INCLUDES ${SPECTRE_INCLUDES} PARENT_SCOPE)\nendfunction(_extract_spectre_includes FILE_NAME)\n\n# Get the list of 3rd party library includes for the target `TARGET_NAME`.\n#\n# Sets the variable `TPL_INCLUDES` in parent scope to return the result\nfunction(_extract_tpl_includes FILE_NAME)\n file(READ ${FILE_NAME} FILE_CONTENTS)\n string(REGEX MATCHALL \"\\n#include <[^\\n]+>\"\n _RAW_TPL_INCLUDES ${FILE_CONTENTS})\n unset(TPL_INCLUDES)\n foreach(INCLUDE ${_RAW_TPL_INCLUDES})\n string(REPLACE \"\\n#include <\" \"\" INCLUDE \"${INCLUDE}\")\n string(REPLACE \">\" \"\" INCLUDE \"${INCLUDE}\")\n list(APPEND TPL_INCLUDES ${INCLUDE})\n endforeach(INCLUDE ${_RAW_TPL_INCLUDES})\n # \"Return\" TPL_INCLUDES by setting it in PARENT_SCOPE\n set(TPL_INCLUDES ${TPL_INCLUDES} PARENT_SCOPE)\nendfunction(_extract_tpl_includes FILE_NAME)\n\n# Make the path of `HEADER_FILE` which belongs to the target `TARGET_NAME`\n# an absolute path.\n#\n# Sets the variable `ABS_HEADER_FILE` in parent scope to return the result\nfunction(_make_header_path_absolute TARGET_NAME HEADER_FILE)\n get_property(\n _INCLUDE_DIR\n TARGET ${TARGET_NAME}\n PROPERTY INTERFACE_INCLUDE_DIRECTORIES\n )\n if(IS_ABSOLUTE ${HEADER_FILE})\n set(_ABS_HEADER_FILE ${HEADER_FILE})\n else()\n set(_ABS_HEADER_FILE \"${_INCLUDE_DIR}/${HEADER_FILE}\")\n endif()\n # \"Return\" ABS_HEADER_FILE by setting it in PARENT_SCOPE\n set(ABS_HEADER_FILE ${_ABS_HEADER_FILE} PARENT_SCOPE)\nendfunction(_make_header_path_absolute TARGET_NAME HEADER_FILE)\n\n# Gets the dependencies for a list of includes of one of the source or\n# header files of the target `TARGET_NAME`\n#\n# The `_get_deps_for_includes` function builds a list of all dependencies\n# by finding the target that provides each header file in `INCLUDES_OF_FILE`.\n# `INCLUDES_OF_FILE` must be a list of includes from a file (either header\n# or source file) of the target `TARGET_NAME`. If `RECURSE_THROUGH_INCLUDES`\n# is `TRUE` then for each header file in `INCLUDES_OF_FILE` that is also an\n# include of the target `TARGET_NAME` then the header file will also have its\n# dependencies searched and added to the list of dependencies.\n#\n# Example usage:\n#\n# _get_deps_for_includes(\n# TARGET_C\n# \"TARGET_A;TARGET_B;TARGET_C;TARGET_D\"\n# \"cmath;utility;vector\"\n# FALSE\n# )\n#\n# Arguments:\n#\n# TARGET_NAME: the target for which to check the link libraries/dependencies\n# LIST_OF_ALL_TARGETS: a list of all the targets that might be dependencies\n# of the target ${TARGET_NAME}\n# INCLUDES_OF_FILE:\n# a list of header files for which to get the dependencies.\n# RECURSE_THROUGH_INCLUDES:\n# if TRUE then any include in any of ${INCLUDES_OF_FILE}\n# that is also an include of the target ${TARGET_NAME} has its\n# dependencies added.\n#\n# Since the recursion will cause an infinite loop if there are cyclic includes\n# we limit the recursion depth to 20, at which point an error message is\n# displayed that there may be cyclic dependencies\n#\n# Returns by setting `TARGET_DEPS` in parent scope\nfunction(_get_deps_for_includes TARGET_NAME LIST_OF_ALL_TARGETS\n INCLUDES_OF_FILE RECURSE_THROUGH_INCLUDES)\n # Implement guard against infinite recursion when there are cyclic\n # includes in a library.\n get_property(\n GET_DEPS_FOR_SPECTRE_INCLUDES_PATH\n GLOBAL PROPERTY GET_DEPS_FOR_SPECTRE_INCLUDES_PATH\n )\n list(LENGTH GET_DEPS_FOR_SPECTRE_INCLUDES_PATH RECURSE_DEPTH)\n if(${RECURSE_DEPTH} GREATER 20)\n message(FATAL_ERROR\n \" Found what appears to be a cyclic loop in the header files.\"\n \" The header path is: ${GET_DEPS_FOR_SPECTRE_INCLUDES_PATH}\"\n )\n endif(${RECURSE_DEPTH} GREATER 20)\n\n get_target_headers(${TARGET_NAME} TARGET_HEADER_FILES)\n\n unset(_TARGET_DEPS)\n # Now loop over all spectre targets to see if any of them\n # expose these includes\n foreach(CURRENT_INCLUDE ${INCLUDES_OF_FILE})\n # If we are checking header files and the header file is part of\n # this target, possibly recurse the header files, and skipping search\n # through targets for which one provides the header file (we know it's us).\n if(${CURRENT_INCLUDE} IN_LIST TARGET_HEADER_FILES)\n if(RECURSE_THROUGH_INCLUDES)\n # Sets ABS_HEADER_FILE\n _make_header_path_absolute(${TARGET_NAME} ${CURRENT_INCLUDE})\n # Sets SPECTRE_INCLUDES\n _extract_spectre_includes(${ABS_HEADER_FILE})\n set_property(\n GLOBAL APPEND PROPERTY GET_DEPS_FOR_CURRENT_INCLUDES_PATH\n ${CURRENT_INCLUDE}\n )\n # Sets TARGET_DEPS\n _get_deps_for_includes(${TARGET_NAME} \"${LIST_OF_ALL_TARGETS}\"\n \"${CURRENT_INCLUDES}\" ${RECURSE_THROUGH_INCLUDES})\n # \"Pop\" last element by setting the property to what it was at the\n # start of the function call.\n set_property(\n GLOBAL PROPERTY GET_DEPS_FOR_CURRENT_INCLUDES_PATH\n ${GET_DEPS_FOR_CURRENT_INCLUDES_PATH}\n )\n # Get the dependencies of the header file, since these are all\n # also PRIVATE dependencies of the target.\n foreach(_TARGET ${TARGET_DEPS})\n if(NOT ${_TARGET} IN_LIST _TARGET_DEPS)\n list(APPEND _TARGET_DEPS ${_TARGET})\n endif(NOT ${_TARGET} IN_LIST _TARGET_DEPS)\n endforeach(_TARGET ${TARGET_DEPS})\n continue()\n else(RECURSE_THROUGH_INCLUDES)\n continue()\n endif(RECURSE_THROUGH_INCLUDES)\n endif(${CURRENT_INCLUDE} IN_LIST TARGET_HEADER_FILES)\n\n unset(_TARGET_WITH_INCLUDE)\n foreach(DEP_TARGET ${LIST_OF_ALL_TARGETS})\n if(${DEP_TARGET} STREQUAL ${TARGET_NAME})\n continue()\n endif(${DEP_TARGET} STREQUAL ${TARGET_NAME})\n\n # Get the header files of DEP_TARGET and see if any of the\n # includes are part of DEP_TARGET.\n get_target_headers(${DEP_TARGET} _DEP_TARGET_HEADERS)\n if(${CURRENT_INCLUDE} IN_LIST _DEP_TARGET_HEADERS)\n set(_TARGET_WITH_INCLUDE ${DEP_TARGET})\n break()\n endif(${CURRENT_INCLUDE} IN_LIST _DEP_TARGET_HEADERS)\n endforeach(DEP_TARGET ${LIST_OF_ALL_TARGETS})\n if(NOT _TARGET_WITH_INCLUDE)\n message(FATAL_ERROR\n \"No known targets supply the file ${CURRENT_INCLUDE} included in \"\n \"file ${HEADER_OR_SOURCE} of target ${TARGET_NAME}.\"\n )\n endif(NOT _TARGET_WITH_INCLUDE)\n\n if(NOT ${_TARGET_WITH_INCLUDE} IN_LIST _TARGET_DEPS)\n list(APPEND _TARGET_DEPS ${_TARGET_WITH_INCLUDE})\n endif(NOT ${_TARGET_WITH_INCLUDE} IN_LIST _TARGET_DEPS)\n endforeach(CURRENT_INCLUDE ${INCLUDES_OF_FILE})\n\n # \"Return\" TARGET_DEPS by setting it in PARENT_SCOPE\n set(TARGET_DEPS ${_TARGET_DEPS} PARENT_SCOPE)\nendfunction(_get_deps_for_includes TARGET_NAME LIST_OF_ALL_TARGETS\n INCLUDES_OF_FILE RECURSE_THROUGH_INCLUDES)\n\n# Returns the dependencies for the target\n#\n# Arguments\n#\n# TARGET_NAME:\n# the target for which to check the link libraries/dependencies\n# LIST_OF_ALL_TARGETS:\n# a list of all the targets that might be dependencies\n# of the target ${TARGET_NAME}\n# LIST_OF_FILES:\n# a list of the files for which to get the dependencies. Can be\n# header/tpp or source files.\n# RECURSE_INCLUDES:\n# if TRUE then the dependencies of the target's included header files\n# will also be added. This is used when source files are passed because\n# the dependencies of the header files must be marked as PUBLIC\n#\n# Returns by setting `TARGET_DEPS` in parent scope\nfunction(_get_deps_for_target TARGET_NAME LIST_OF_ALL_TARGETS\n LIST_OF_FILES RECURSE_INCLUDES)\n unset(_TARGET_DEPS)\n foreach(HEADER_OR_SOURCE ${LIST_OF_FILES})\n if(IS_ABSOLUTE \"${HEADER_OR_SOURCE}\")\n # Sets SPECTRE_INCLUDES\n _extract_spectre_includes(\"${HEADER_OR_SOURCE}\")\n else()\n message(FATAL_ERROR\n \"All paths of files passed to _get_deps_for_target must be absolute \"\n \"but received ${HEADER_OR_SOURCE}.\")\n endif()\n\n # Sets TARGET_DEPS\n _get_deps_for_includes(${TARGET_NAME} \"${LIST_OF_ALL_TARGETS}\"\n \"${SPECTRE_INCLUDES}\" ${RECURSE_INCLUDES})\n foreach(_TARGET ${TARGET_DEPS})\n if(NOT ${_TARGET} IN_LIST _TARGET_DEPS)\n list(APPEND _TARGET_DEPS ${_TARGET})\n endif(NOT ${_TARGET} IN_LIST _TARGET_DEPS)\n endforeach(_TARGET ${TARGET_DEPS})\n\n # Third party library includes\n\n # Sets TPL_INCLUDES\n _extract_tpl_includes(\"${HEADER_OR_SOURCE}\")\n # Sets TARGET_DEPS\n _get_deps_for_includes(${TARGET_NAME} \"${LIST_OF_ALL_TARGETS}\"\n \"${TPL_INCLUDES}\" FALSE)\n foreach(_TARGET ${TARGET_DEPS})\n if(NOT ${_TARGET} IN_LIST _TARGET_DEPS)\n list(APPEND _TARGET_DEPS ${_TARGET})\n endif(NOT ${_TARGET} IN_LIST _TARGET_DEPS)\n endforeach(_TARGET ${TARGET_DEPS})\n\n endforeach(HEADER_OR_SOURCE ${LIST_OF_FILES})\n # Alphabetize the list of dependencies\n list(SORT _TARGET_DEPS)\n # \"Return\" the target dependencies\n set(TARGET_DEPS ${_TARGET_DEPS} PARENT_SCOPE)\nendfunction(_get_deps_for_target TARGET_NAME LIST_OF_FILES LIST_OF_ALL_TARGETS)\n\n# Add the libraries for the `target_link_libraries` command\n# for a target.\n#\n# Arguments\n#\n# TARGET_DEPS:\n# dependencies of the target\n# TARGET_DEPS_TYPE:\n# the type of dependencies, INTERFACE/PRIVATE/PUBLIC\n# TARGET_LINK_LIBRARIES_COMMAND:\n# the target_link_libraries command so far\n#\n# Returns by setting `TARGET_LINK_LIBS_COMMAND` in parent scope\nfunction(_add_targets_to_link_libs TARGET_DEPS TARGET_DEPS_TYPE\n TARGET_LINK_LIBS_COMMAND)\n list(LENGTH TARGET_DEPS _NUM_TARGET_DEPS)\n set(_TARGET_LINK_LIBS_COMMAND\n \"${TARGET_LINK_LIBS_COMMAND}\"\n )\n if(${_NUM_TARGET_DEPS} GREATER 0)\n set(\n _TARGET_LINK_LIBS_COMMAND\n \"${_TARGET_LINK_LIBS_COMMAND}\\n\"\n \" ${TARGET_DEPS_TYPE}\"\n )\n foreach(_DEP ${TARGET_DEPS})\n set(\n _TARGET_LINK_LIBS_COMMAND\n \"${_TARGET_LINK_LIBS_COMMAND}\\n\"\n \" ${_DEP}\"\n )\n endforeach(_DEP ${_TARGET_DEPS})\n set(_TARGET_LINK_LIBS_COMMAND\n \"${_TARGET_LINK_LIBS_COMMAND}\\n \"\n )\n string(REPLACE \";\" \"\" _TARGET_LINK_LIBS_COMMAND\n ${_TARGET_LINK_LIBS_COMMAND})\n endif(${_NUM_TARGET_DEPS} GREATER 0)\n # \"Return\" the target dependencies\n set(TARGET_LINK_LIBS_COMMAND ${_TARGET_LINK_LIBS_COMMAND} PARENT_SCOPE)\nendfunction(_add_targets_to_link_libs TARGET_DEPS TARGET_DEPS_TYPE\n TARGET_LINK_LIBS_COMMAND)\n\n# Queries the INTERFACE_LINK_LIBRARIES of TARGET. This is done recursively.\nfunction(_get_interface_link_libraries TARGET)\n get_target_property(_INTERFACE_LIBS ${TARGET} INTERFACE_LINK_LIBRARIES)\n set(LINK_LIBS_FOR_TARGET \"\")\n foreach(_INTERFACE_LIB ${_INTERFACE_LIBS})\n if (_INTERFACE_LIB)\n list(APPEND LINK_LIBS_FOR_TARGET ${_INTERFACE_LIB})\n if (TARGET ${_INTERFACE_LIB})\n set(OUTPUT_LIST \"\")\n _get_interface_link_libraries(${_INTERFACE_LIB})\n list(APPEND LINK_LIBS_FOR_TARGET ${OUTPUT_LIST})\n endif()\n endif()\n endforeach()\n # \"Return\" dependencies to calling function\n set(OUTPUT_LIST ${LINK_LIBS_FOR_TARGET} PARENT_SCOPE)\nendfunction(_get_interface_link_libraries OUTPUT_LIST TARGET)\n\n# Checks the dependencies for the target ${TARGET_NAME} and if they are\n# incorrect produces an error message with the correct dependencies.\n#\n# TARGET_NAME:\n# the target for which to check the link libraries/dependencies\n# TARGET_LINK_LIBS_COMMAND:\n# the target_link_libraries CMake command so far\n# TARGET_INTERFACE_DEPS:\n# the INTERFACE link libraries for the target\n# TARGET_PRIVATE_DEPS:\n# the PRIVATE link libraries for the target\n# TARGET_PUBLIC_DEPS:\n# the PUBLIC link libraries for the target\n# LIST_OF_ALLOWED_EXTRA_TARGETS:\n# a list of allowed extra dependencies. An example of an extra dependency\n# is the SpectreFlags target, which supplies no header files and there is\n# not strictly a dependency of ${TARGET_NAME} but can be specified as a\n# dependency in order to add compiler flags or definitions to the target.\n# ERROR_ON_FAILURE:\n# if specified, then CMake will produce an error if the dependencies are\n# incorrect. Otherwise the variable TARGET_DEPENDENCIES_ERROR_MESSAGE\n# is set in the parent scope\nfunction(_check_and_print_dependencies\n TARGET_NAME TARGET_LINK_LIBS_COMMAND\n TARGET_INTERFACE_DEPS TARGET_PRIVATE_DEPS TARGET_PUBLIC_DEPS\n LIST_OF_ALLOWED_EXTRA_TARGETS)\n cmake_parse_arguments(\n ARG \"ERROR_ON_FAILURE\" \"\" \"\" ${ARGN})\n\n # We add the dependencies of allowed targets as additional allowed targets.\n # This avoids the situation where target A is allowed, but A depends on B,\n # and therefore every target has a dependency on B. The helper function\n # ensures the dependencies are added recursively.\n set(WORKING_LIST ${LIST_OF_ALLOWED_EXTRA_TARGETS})\n foreach(_ALLOWED_EXTRA_TARGET ${LIST_OF_ALLOWED_EXTRA_TARGETS})\n set(OUTPUT_LIST \"\")\n _get_interface_link_libraries(${_ALLOWED_EXTRA_TARGET})\n list(APPEND WORKING_LIST ${OUTPUT_LIST})\n endforeach()\n list(REMOVE_DUPLICATES WORKING_LIST)\n set(LIST_OF_ALLOWED_EXTRA_TARGETS ${WORKING_LIST})\n\n get_property(\n _INTERFACE_LIBS\n TARGET ${TARGET_NAME}\n PROPERTY INTERFACE_LINK_LIBRARIES\n )\n # The property INTERFACE_LINK_LIBRARIES contains generator expressions for\n # private link-time dependencies. We will be handling these private\n # dependencies explicitly below, so here we want to remove them from the list\n # of interface dependencies. The generators have format \"$\"\n list(FILTER _INTERFACE_LIBS EXCLUDE REGEX \"\\\\$\")\n\n unset(_MISSING_INTERFACE_LIBS)\n foreach(_INTERFACE_DEP ${TARGET_INTERFACE_DEPS})\n if(NOT ${_INTERFACE_DEP} IN_LIST _INTERFACE_LIBS)\n list(APPEND _MISSING_INTERFACE_LIBS ${_INTERFACE_DEP})\n endif(NOT ${_INTERFACE_DEP} IN_LIST _INTERFACE_LIBS)\n endforeach(_INTERFACE_DEP ${TARGET_INTERFACE_DEPS})\n\n get_target_property(\n TARGET_TYPE\n ${TARGET_NAME}\n TYPE\n )\n set(_NUM_MISSING_PRIVATE_LIBS 0)\n set(_NUM_MISSING_PUBLIC_LIBS 0)\n unset(_EXTRA_INTERFACE_LIBS)\n unset(_EXTRA_PRIVATE_LIBS)\n unset(_EXTRA_PUBLIC_LIBS)\n if(NOT ${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\n get_property(\n _PRIVATE_LIBS\n TARGET ${TARGET_NAME}\n PROPERTY LINK_LIBRARIES\n )\n\n # Check to see if any interface-only dependencies are also\n # PRIVATE/PUBLIC\n foreach(_INTERFACE_DEP ${TARGET_INTERFACE_DEPS})\n if(${_INTERFACE_DEP} IN_LIST _PRIVATE_LIBS)\n list(APPEND _MISSING_INTERFACE_LIBS ${_INTERFACE_DEP})\n endif(${_INTERFACE_DEP} IN_LIST _PRIVATE_LIBS)\n endforeach(_INTERFACE_DEP ${TARGET_INTERFACE_DEPS})\n\n unset(_MISSING_PRIVATE_LIBS)\n foreach(_PRIVATE_DEP ${TARGET_PRIVATE_DEPS})\n if(NOT ${_PRIVATE_DEP} IN_LIST _PRIVATE_LIBS)\n list(APPEND _MISSING_PRIVATE_LIBS ${_PRIVATE_DEP})\n endif(NOT ${_PRIVATE_DEP} IN_LIST _PRIVATE_LIBS)\n endforeach(_PRIVATE_DEP ${TARGET_PRIVATE_DEPS})\n list(LENGTH _MISSING_PRIVATE_LIBS _NUM_MISSING_PRIVATE_LIBS)\n\n unset(_MISSING_PUBLIC_LIBS)\n foreach(_PUBLIC_DEP ${TARGET_PUBLIC_DEPS})\n if(NOT ${_PUBLIC_DEP} IN_LIST _PRIVATE_LIBS\n OR NOT ${_PUBLIC_DEP} IN_LIST _INTERFACE_LIBS)\n list(APPEND _MISSING_PUBLIC_LIBS ${_PUBLIC_DEP})\n endif(NOT ${_PUBLIC_DEP} IN_LIST _PRIVATE_LIBS\n OR NOT ${_PUBLIC_DEP} IN_LIST _INTERFACE_LIBS)\n endforeach(_PUBLIC_DEP ${TARGET_PUBLIC_DEPS})\n list(LENGTH _MISSING_PUBLIC_LIBS _NUM_MISSING_PUBLIC_LIBS)\n\n # Now check for extra target link libraries that aren't needed.\n unset(_PUBLIC_LIBS)\n foreach(_INTERFACE_LIB ${_INTERFACE_LIBS})\n if(${_INTERFACE_LIB} IN_LIST _PRIVATE_LIBS)\n list(APPEND _PUBLIC_LIBS ${_INTERFACE_LIB})\n endif(${_INTERFACE_LIB} IN_LIST _PRIVATE_LIBS)\n endforeach(_INTERFACE_LIB ${_INTERFACE_LIBS})\n\n foreach(_PUBLIC_LIB ${_PUBLIC_LIBS})\n list(REMOVE_ITEM _INTERFACE_LIBS ${_PUBLIC_LIB})\n list(REMOVE_ITEM _PRIVATE_LIBS ${_PUBLIC_LIB})\n if(NOT ${_PUBLIC_LIB} IN_LIST TARGET_PUBLIC_DEPS AND\n NOT ${_PUBLIC_LIB} IN_LIST LIST_OF_ALLOWED_EXTRA_TARGETS)\n list(APPEND _EXTRA_PUBLIC_LIBS ${_PUBLIC_LIB})\n endif(NOT ${_PUBLIC_LIB} IN_LIST TARGET_PUBLIC_DEPS AND\n NOT ${_PUBLIC_LIB} IN_LIST LIST_OF_ALLOWED_EXTRA_TARGETS)\n endforeach(_PUBLIC_LIB ${_PUBLIC_LIBS})\n\n foreach(_PRIVATE_LIB ${_PRIVATE_LIBS})\n if(NOT ${_PRIVATE_LIB} IN_LIST TARGET_PRIVATE_DEPS AND\n NOT ${_PRIVATE_LIB} IN_LIST LIST_OF_ALLOWED_EXTRA_TARGETS)\n list(APPEND _EXTRA_PRIVATE_LIBS ${_PRIVATE_LIB})\n endif(NOT ${_PRIVATE_LIB} IN_LIST TARGET_PRIVATE_DEPS AND\n NOT ${_PRIVATE_LIB} IN_LIST LIST_OF_ALLOWED_EXTRA_TARGETS)\n endforeach(_PRIVATE_LIB ${_PRIVATE_LIBS})\n\n foreach(_INTERFACE_LIB ${_INTERFACE_LIBS})\n if(NOT ${_INTERFACE_LIB} IN_LIST TARGET_INTERFACE_DEPS AND\n NOT ${_INTERFACE_LIB} IN_LIST LIST_OF_ALLOWED_EXTRA_TARGETS)\n list(APPEND _EXTRA_INTERFACE_LIBS ${_INTERFACE_LIB})\n endif(NOT ${_INTERFACE_LIB} IN_LIST TARGET_INTERFACE_DEPS AND\n NOT ${_INTERFACE_LIB} IN_LIST LIST_OF_ALLOWED_EXTRA_TARGETS)\n endforeach(_INTERFACE_LIB ${_INTERFACE_LIBS})\n else(NOT ${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\n foreach(_INTERFACE_DEP ${_INTERFACE_LIBS})\n if(NOT ${_INTERFACE_DEP} IN_LIST TARGET_INTERFACE_DEPS AND\n NOT ${_INTERFACE_DEP} IN_LIST LIST_OF_ALLOWED_EXTRA_TARGETS)\n list(APPEND _EXTRA_INTERFACE_LIBS ${_INTERFACE_DEP})\n endif()\n endforeach(_INTERFACE_DEP ${_INTERFACE_LIBS})\n endif(NOT ${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\n\n list(LENGTH _MISSING_INTERFACE_LIBS _NUM_MISSING_INTERFACE_LIBS)\n\n list(LENGTH _EXTRA_INTERFACE_LIBS _NUM_EXTRA_INTERFACE_LIBS)\n list(LENGTH _EXTRA_PRIVATE_LIBS _NUM_EXTRA_PRIVATE_LIBS)\n list(LENGTH _EXTRA_PUBLIC_LIBS _NUM_EXTRA_PUBLIC_LIBS)\n\n set(_MISSING_LIBS FALSE)\n set(_ERROR_MSG \" Missing dependencies for target ${TARGET_NAME}\")\n if(${_NUM_MISSING_INTERFACE_LIBS} GREATER 0)\n set(_ERROR_MSG\n \"${_ERROR_MSG}\\n Missing interface libs:\\n ${_MISSING_INTERFACE_LIBS}\")\n set(_MISSING_LIBS TRUE)\n endif(${_NUM_MISSING_INTERFACE_LIBS} GREATER 0)\n if(${_NUM_MISSING_PRIVATE_LIBS} GREATER 0)\n set(_ERROR_MSG\n \"${_ERROR_MSG}\\n Missing private libs:\\n ${_MISSING_PRIVATE_LIBS}\")\n set(_MISSING_LIBS TRUE)\n endif(${_NUM_MISSING_PRIVATE_LIBS} GREATER 0)\n if(${_NUM_MISSING_PUBLIC_LIBS} GREATER 0)\n set(_ERROR_MSG\n \"${_ERROR_MSG}\\n Missing public libs:\\n ${_MISSING_PUBLIC_LIBS}\")\n set(_MISSING_LIBS TRUE)\n endif(${_NUM_MISSING_PUBLIC_LIBS} GREATER 0)\n\n if(${_NUM_EXTRA_INTERFACE_LIBS} GREATER 0 OR\n ${_NUM_EXTRA_PRIVATE_LIBS} GREATER 0 OR\n ${_NUM_EXTRA_PUBLIC_LIBS} GREATER 0)\n set(_ERROR_MSG \" Extra dependencies for target ${TARGET_NAME}\")\n endif()\n if(${_NUM_EXTRA_INTERFACE_LIBS} GREATER 0)\n set(_ERROR_MSG\n \"${_ERROR_MSG}\\n Extra interface libs:\\n ${_EXTRA_INTERFACE_LIBS}\")\n set(_MISSING_LIBS TRUE)\n endif(${_NUM_EXTRA_INTERFACE_LIBS} GREATER 0)\n if(${_NUM_EXTRA_PRIVATE_LIBS} GREATER 0)\n set(_ERROR_MSG\n \"${_ERROR_MSG}\\n Extra private libs:\\n ${_EXTRA_PRIVATE_LIBS}\")\n set(_MISSING_LIBS TRUE)\n endif(${_NUM_EXTRA_PRIVATE_LIBS} GREATER 0)\n if(${_NUM_EXTRA_PUBLIC_LIBS} GREATER 0)\n set(_ERROR_MSG\n \"${_ERROR_MSG}\\n Extra public libs:\\n ${_EXTRA_PUBLIC_LIBS}\")\n set(_MISSING_LIBS TRUE)\n endif(${_NUM_EXTRA_PUBLIC_LIBS} GREATER 0)\n\n if(NOT ARG_ERROR_ON_FAILURE)\n set(\n TARGET_DEPS_ERROR_MESSAGE\n \"\"\n PARENT_SCOPE\n )\n endif(NOT ARG_ERROR_ON_FAILURE)\n\n if(_MISSING_LIBS)\n set(TARGET_LINK_LIBS_COMMAND\n \" target_link_libraries(\\n\"\n \" ${TARGET_NAME}\"\n )\n _add_targets_to_link_libs(\n \"${TARGET_INTERFACE_DEPS}\" \"INTERFACE\"\n \"${TARGET_LINK_LIBS_COMMAND}\")\n _add_targets_to_link_libs(\n \"${TARGET_PRIVATE_DEPS}\" \"PRIVATE\"\n \"${TARGET_LINK_LIBS_COMMAND}\")\n _add_targets_to_link_libs(\n \"${TARGET_PUBLIC_DEPS}\" \"PUBLIC\"\n \"${TARGET_LINK_LIBS_COMMAND}\")\n set(TARGET_LINK_LIBS_COMMAND\n \"${TARGET_LINK_LIBS_COMMAND} )\"\n )\n\n if(${ARG_ERROR_ON_FAILURE})\n message(FATAL_ERROR\n \"${_ERROR_MSG}\\n \\n\"\n \" Correct target_link_libraries command is:\\n\"\n \"${TARGET_LINK_LIBS_COMMAND}\"\n )\n else(${ARG_ERROR_ON_FAILURE})\n set(\n TARGET_DEPS_ERROR_MESSAGE\n \"${_ERROR_MSG}\\n \\n\\\n Correct target_link_libraries command is:\\n\\\n${TARGET_LINK_LIBS_COMMAND}\"\n PARENT_SCOPE\n )\n endif(${ARG_ERROR_ON_FAILURE})\n endif(_MISSING_LIBS)\nendfunction(_check_and_print_dependencies\n TARGET_NAME TARGET_LINK_LIBS_COMMAND\n TARGET_INTERFACE_DEPS TARGET_PRIVATE_DEPS TARGET_PUBLIC_DEPS\n LIST_OF_ALLOWED_EXTRA_TARGETS)\n\n# Check that the link libraries of the target are correct and if not,\n# provide an error with the correct target link libraries.\n#\n# Example usage:\n#\n# check_target_dependencies(\n# TARGET ${TARGET_TO_CHECK}\n# ALL_TARGETS\n# ${SPECTRE_TPLS}\n# ${SPECTRE_LIBS}\n# ALLOWED_EXTRA_TARGETS\n# SpectreFlags\n# ERROR_ON_FAILURE\n# )\n#\n# Arguments:\n#\n# TARGET:\n# the target for which to check the link libraries/dependencies\n# ALL_TARGETS:\n# a list of all the targets that might be dependencies of the target\n# ${TARGET}\n# ALLOWED_EXTRA_TARGETS:\n# a list of allowed extra dependencies. An example of an extra dependency\n# is the SpectreFlags target, which supplies no header files and therefore\n# is not strictly a dependency of ${TARGET} but can be specified as\n# dependency in order to add compiler flags or definitions to the target.\n# ERROR_ON_FAILURE:\n# if specified, then CMake will produce an error if the dependencies are\n# incorrect. Otherwise the variable TARGET_DEPENDENCIES_ERROR_MESSAGE\n# is set in the parent scope\nfunction(check_target_dependencies)\n cmake_parse_arguments(\n ARG\n \"ERROR_ON_FAILURE\"\n \"TARGET\"\n \"ALL_TARGETS;ALLOWED_EXTRA_TARGETS\" ${ARGN})\n\n # Sets HEADER_FILES\n _absolute_header_paths(${ARG_TARGET})\n\n # Sets TARGET_DEPS\n _get_deps_for_target(${ARG_TARGET}\n \"${ARG_ALL_TARGETS}\" \"${HEADER_FILES}\" FALSE)\n set(_TARGET_INTERFACE_DEPS ${TARGET_DEPS})\n list(REMOVE_ITEM _TARGET_INTERFACE_DEPS Stl)\n\n get_target_property(\n TARGET_TYPE\n ${ARG_TARGET}\n TYPE\n )\n\n unset(_TARGET_PRIVATE_DEPS)\n unset(_TARGET_PUBLIC_DEPS)\n if(NOT ${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\n # Sets SOURCE_FILES\n _absolute_source_paths(${ARG_TARGET})\n\n # Sets TARGET_DEPS\n _get_deps_for_target(${ARG_TARGET}\n \"${ARG_ALL_TARGETS}\" \"${SOURCE_FILES}\" TRUE)\n set(_TARGET_PRIVATE_DEPS ${TARGET_DEPS})\n # We only use the Stl target to be able to keep track of all header files\n # and to be able to claim with certainly that an extra header file is\n # present. Since there are no explicit includes or link dependencies that\n # need to be added, we don't want the extra noise of explicitly depending\n # on Stl everywhere in the code and so we remove it from the list.\n list(REMOVE_ITEM _TARGET_PRIVATE_DEPS Stl)\n\n # Now need to figure out what the PUBLIC libraries are\n unset(_TARGET_PUBLIC_DEPS)\n foreach(_PRIVATE_DEP ${_TARGET_PRIVATE_DEPS})\n if(${_PRIVATE_DEP} IN_LIST _TARGET_INTERFACE_DEPS)\n list(APPEND _TARGET_PUBLIC_DEPS ${_PRIVATE_DEP})\n endif(${_PRIVATE_DEP} IN_LIST _TARGET_INTERFACE_DEPS)\n endforeach(_PRIVATE_DEP ${_TARGET_PRIVATE_DEPS})\n # Remove PRIVATE deps from INTERFACE and PUBLIC lists\n foreach(_PUBLIC_DEP ${_TARGET_PUBLIC_DEPS})\n list(REMOVE_ITEM _TARGET_PRIVATE_DEPS ${_PUBLIC_DEP})\n list(REMOVE_ITEM _TARGET_INTERFACE_DEPS ${_PUBLIC_DEP})\n endforeach(_PUBLIC_DEP ${_TARGET_PUBLIC_DEPS})\n endif(NOT ${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\n\n set(ERROR_ON_FAILURE \"\")\n if(ARG_ERROR_ON_FAILURE)\n set(ERROR_ON_FAILURE ERROR_ON_FAILURE)\n endif(ARG_ERROR_ON_FAILURE)\n _check_and_print_dependencies(\n ${ARG_TARGET}\n \"${TARGET_LINK_LIBS_COMMAND}\"\n \"${_TARGET_INTERFACE_DEPS}\"\n \"${_TARGET_PRIVATE_DEPS}\"\n \"${_TARGET_PUBLIC_DEPS}\"\n \"${ARG_ALLOWED_EXTRA_TARGETS}\"\n ${ERROR_ON_FAILURE}\n )\n if(NOT ARG_ERROR_ON_FAILURE)\n set(\n TARGET_DEPS_ERROR_MESSAGE\n \"${TARGET_DEPS_ERROR_MESSAGE}\"\n PARENT_SCOPE\n )\n endif(NOT ARG_ERROR_ON_FAILURE)\nendfunction(check_target_dependencies)\n" }, { "path": "cmake/SpectreGetGitHash.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nset(GIT_HASH \"\")\nset(GIT_BRANCH_COMMAND \"\")\nset(GIT_BRANCH \"\")\nset(GIT_DESCRIPTION_COMMAND \"\")\nset(GIT_DESCRIPTION \"\")\n\nif(EXISTS ${CMAKE_SOURCE_DIR}/.git)\n find_package(Git)\n\n if(Git_FOUND)\n execute_process(\n COMMAND ${GIT_EXECUTABLE} rev-parse HEAD\n WORKING_DIRECTORY ${CMAKE_SOURCE_DIR}\n OUTPUT_VARIABLE GIT_HASH\n OUTPUT_STRIP_TRAILING_WHITESPACE\n )\n set(GIT_BRANCH_COMMAND \"${GIT_EXECUTABLE} rev-parse --abbrev-ref HEAD\")\n execute_process(\n COMMAND bash -c \"${GIT_BRANCH_COMMAND}\"\n WORKING_DIRECTORY ${CMAKE_SOURCE_DIR}\n OUTPUT_VARIABLE GIT_BRANCH\n OUTPUT_STRIP_TRAILING_WHITESPACE\n )\n set(GIT_DESCRIPTION_COMMAND \"${GIT_EXECUTABLE} describe \\\n--always --first-parent --match 'v[0-9]*' HEAD\")\n execute_process(\n COMMAND bash -c \"${GIT_DESCRIPTION_COMMAND}\"\n WORKING_DIRECTORY ${CMAKE_SOURCE_DIR}\n OUTPUT_VARIABLE GIT_DESCRIPTION\n OUTPUT_STRIP_TRAILING_WHITESPACE\n ERROR_VARIABLE GIT_DESCRIPTION_ERROR\n ERROR_STRIP_TRAILING_WHITESPACE\n )\n if(GIT_DESCRIPTION)\n message(STATUS \"Git description: ${GIT_DESCRIPTION}\")\n else()\n message(STATUS \"Could not determine git description (\"\n \"${GIT_DESCRIPTION_ERROR}). Using commit hash instead.\")\n set(GIT_DESCRIPTION ${GIT_HASH})\n endif()\n endif()\nelse()\n message(STATUS \"Not running in a git repository. Some features are disabled.\")\nendif()\n\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"Git description: ${GIT_DESCRIPTION}\\n\"\n \"Git branch: ${GIT_BRANCH}\\n\"\n \"Git hash: ${GIT_HASH}\\n\"\n )\n" }, { "path": "cmake/SpectreInitializeVariables.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nif(NOT CMAKE_CXX_LINK_FLAGS)\n set(CMAKE_CXX_LINK_FLAGS \"\")\nendif()\n" }, { "path": "cmake/SpectreLoadMetadata.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Read the following information from the `Metadata.yaml` file:\n# - SPECTRE_NAME: Name\n# - SPECTRE_HOMEPAGE: Homepage\n# - SPECTRE_VERSION: Version\n# - SPECTRE_DOI: Doi\n# - SPECTRE_ZENODO_ID: ZenodoId\n\nfile(READ \"${CMAKE_SOURCE_DIR}/Metadata.yaml\" SPECTRE_METADATA_FILE)\n# Split lines into cmake list\nstring(REGEX REPLACE \";\" \"\\\\\\\\;\" SPECTRE_METADATA_FILE \"${SPECTRE_METADATA_FILE}\")\nstring(REGEX REPLACE \"\\n\" \";\" SPECTRE_METADATA_FILE \"${SPECTRE_METADATA_FILE}\")\n\n# Read data from the file\nset(SPECTRE_NAME \"\")\nset(SPECTRE_HOMEPAGE \"\")\nset(SPECTRE_VERSION \"\")\nset(SPECTRE_DOI \"\")\nset(SPECTRE_ZENODO_ID \"\")\nforeach(LINE ${SPECTRE_METADATA_FILE})\n if(\"${LINE}\" MATCHES \"^Name: (.*)$\")\n set(SPECTRE_NAME ${CMAKE_MATCH_1})\n endif()\n if(\"${LINE}\" MATCHES \"^Homepage: (.*)$\")\n set(SPECTRE_HOMEPAGE ${CMAKE_MATCH_1})\n endif()\n if(\"${LINE}\" MATCHES \"^Version: (.*)$\")\n set(SPECTRE_VERSION ${CMAKE_MATCH_1})\n endif()\n if(\"${LINE}\" MATCHES \"^Doi: (.*)$\")\n set(SPECTRE_DOI ${CMAKE_MATCH_1})\n endif()\n if(\"${LINE}\" MATCHES \"^ZenodoId: (.*)$\")\n set(SPECTRE_ZENODO_ID ${CMAKE_MATCH_1})\n endif()\nendforeach()\n\n# Check we have read all required keys\nif(NOT SPECTRE_NAME)\n message(\n FATAL_ERROR \"Could not determine project name. Please check the \"\n \"Metadata.yaml file exists and has a line that matches: ^Name: (.*)$\")\nendif()\nif(NOT SPECTRE_HOMEPAGE)\n message(\n WARNING \"Could not determine project homepage. Please check the \"\n \"Metadata.yaml file exists and has a line that matches: ^Homepage: (.*)$\")\nendif()\nif(NOT SPECTRE_VERSION)\n message(\n FATAL_ERROR \"Could not determine release version. Please check the \"\n \"Metadata.yaml file exists and has a line that matches: ^Version: (.*)$\")\nendif()\nif(NOT SPECTRE_DOI)\n message(\n WARNING \"Could not determine DOI. Please check the \"\n \"Metadata.yaml file exists and has a line that matches: ^Doi: (.*)$\")\nendif()\nif(NOT SPECTRE_ZENODO_ID)\n message(\n WARNING \"Could not determine Zenodo ID. Please check the \"\n \"Metadata.yaml file exists and has a line that matches: ^ZenodoId: (.*)$\")\nendif()\n\nmessage(STATUS \"${SPECTRE_NAME} release version: ${SPECTRE_VERSION}\")\n\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"SpECTRE Version: ${SPECTRE_VERSION}\\n\"\n )\n" }, { "path": "cmake/SpectreParseTests.py", "content": "#!/usr/bin/env python\n\n# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nimport re\n\n# A list of all the allowed ctest labels/Catch tags for tests\nallowed_tags = [\n \"Actions\",\n \"Ader\",\n \"ApparentHorizonFinder\",\n \"Burgers\",\n \"Cce\",\n \"CompilationTest\",\n \"ControlSystem\",\n \"DataStructures\",\n \"Domain\",\n \"Elasticity\",\n \"Elliptic\",\n \"EquationsOfState\",\n \"ErrorHandling\",\n \"Evolution\",\n \"Fluxes\",\n \"ForceFree\",\n \"GeneralizedHarmonic\",\n \"GrMhd\",\n \"H5\",\n \"Hydro\",\n \"IO\",\n \"Informer\",\n \"Limiters\",\n \"LinearAlgebra\",\n \"LinearOperators\",\n \"LinearSolver\",\n \"M1Grey\",\n \"NumericalAlgorithms\",\n \"Observers\",\n \"Options\",\n \"Parallel\",\n \"ParallelAlgorithms\",\n \"PointwiseFunctions\",\n \"Pypp\",\n \"Python\",\n \"RelativisticEuler\",\n \"RootFinding\",\n \"ScalarAdvection\",\n \"Serialization\",\n \"Spectral\",\n \"Time\",\n \"Unit\",\n \"Utilities\",\n \"VariableFixing\",\n]\n\n# Words disallowed in tests\ndisallowed_test_name_portions = [\"Functors\"]\n\n# Allowed test attributes\nallowed_test_attributes = [\"TimeOut\", \"OutputRegex\"]\n\n# All the timeout times for the different types of tests. The order here\n# matters. Whichever time is specified last is what will be used for the\n# test if it is of multiple types.\ndefault_tag_timeouts = [(\"unit\", 5)]\n\nallowed_tags = [x.lower() for x in allowed_tags]\nallowed_test_attributes = [x.lower() for x in allowed_test_attributes]\n\n\ndef parse_source_file(file_name):\n # Read the file and remove include directives to make life easier.\n file_string = str(\n re.compile(\"#include.*\\n\").sub(\"\", str(open(file_name, \"r\").read()))\n )\n # The (.*?); part of the regex is to capture the first line of the test\n # body. However, if the test case does not (yet) contain any semicolons then\n # we accidentally fail to find a test.\n test_regex = re.compile(\n r\"(\\/\\/ \\[\\[.*?)?SPECTRE_TEST_CASE\\((.*?)\\) {(.*?);\", re.DOTALL\n )\n test_cases_found = re.findall(test_regex, file_string)\n\n if not test_cases_found and not \"static_assert\" in file_string:\n print(\n \"\\n\\nERROR!!!\\nFailed to find any test cases in the file \",\n file_name,\n )\n print(\n \"This occurs when neither a static_assert nor any \"\n \"SPECTRE_TEST_CASE are found. You may incorrectly hit this error\"\n \" message if your test case does not yet contain any code. \"\n \"Specifically, if your test case does not contain a semicolon.\"\n \"\\n\\n\\n\\n\"\n )\n sys.exit(1)\n\n for attributes, test_name, test_body_first_line in test_cases_found:\n # Capture the name of the test into the first group and the tags into\n # the second. For example,\n # \"Unit.My.Test\", \"[Unit][My]\"\n # test_name == Unit.My.Test\n # group(2) == [Unit][My]\n #\n # Also handle cases where the name is very long and goes onto multiple\n # lines,\n # \"Unit.My.Test.Name.\"\n # \"Is.Very.Long\",\n # \"[Unit][My]\"\n # test_name == Unit.My.Test.Name.Is.Very.Long\n # group(2) == [Unit][My]\n parsed_name = re.search(r'\"(.*)\",[\\s]*\"(.*)\"', test_name, re.S)\n test_name = \"\".join(parsed_name.group(1).replace('\"', \"\").split())\n for disallowed_name in disallowed_test_name_portions:\n if test_name.lower().find(disallowed_name.lower()) != -1:\n print(\n \"\\nERROR: Found disallowed portion of a test name '%s' \"\n \"the test named '%s' in the file %s.\"\n % (disallowed_name, test_name, file_name)\n )\n exit(1)\n test_tags = parsed_name.group(2).lower().replace(\"[\", \"\")[:-1]\n test_tags = test_tags.split(\"]\")\n for test_tag in test_tags:\n if not test_tag in allowed_tags:\n print(\n \"\\nERROR: The tag '%s' is not allowed but was found in \"\n \"the test '%s' in the file '%s'. To allow it add it to \"\n \"the 'allowed_tags' list in \"\n \"$SPECTRE_ROOT/cmake/SpectreParseTests.py. The currently \"\n \"allowed tags are:\\n%s\\n\\n\"\n % (test_tag, test_name, file_name, allowed_tags)\n )\n exit(1)\n test_timeout = -1\n for tag, timeout in default_tag_timeouts:\n if tag in test_tags:\n test_timeout = timeout\n\n # Parse the test attributes\n should_have_output_regex = \"OUTPUT_TEST()\" in test_body_first_line\n output_regex = \"\"\n\n all_attributes_by_name = re.findall(\n r\"\\[\\[([^,]+), (.*?)\\]\\]\", attributes, re.DOTALL\n )\n for attribute in all_attributes_by_name:\n if not attribute[0].lower() in allowed_test_attributes:\n print(\n \"\\nERROR: Found unknown test attribute '%s' applied \"\n \"to test '%s' in file %s.\"\n % (attribute[0], test_name, file_name)\n )\n exit(1)\n\n if attribute[0].lower() == \"timeout\":\n test_timeout = attribute[1]\n\n if attribute[0].lower() == \"outputregex\":\n if not should_have_output_regex:\n print(\n \"\\nERROR: The test '%s' in the file '%s' has the \"\n \"attribute OutputRegEx, but does not contain the \"\n \"macro OUTPUT_TEST() as its first line.\\n\"\n % (test_name, file_name)\n )\n exit(1)\n output_regex = attribute[1].replace(\"\\n//\", \"\")\n\n if should_have_output_regex and output_regex == \"\":\n print(\n \"\\nERROR: The test '%s' in the file '%s' was marked as an \"\n \"OUTPUT_TEST(), but \"\n \"failed to produce a parsable OutputRegex attribute! \"\n \"The syntax is // [[OutputRegex, ]] as \"\n \"a comment before the SPECTRE_TEST_CASE.\\n\"\n % (test_name, file_name)\n )\n exit(1)\n open(\"%s.timeout\" % test_name, \"w\").write(\"%s\" % test_timeout)\n open(\"%s.output_regex\" % test_name, \"w\").write(\"%s\" % output_regex)\n\n\nif __name__ == \"__main__\":\n import sys\n\n source_files = sys.argv[1:]\n for filename in source_files:\n parse_source_file(filename)\n" }, { "path": "cmake/SpectrePythonExecutable.sh", "content": "#!/bin/bash -e\n\n# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nPYTHONPATH=\"@PYTHONPATH@\" @PYTHON_EXEC_ENV_VARS@ @Python_EXECUTABLE@ \\\n @PYTHON_EXE_COMMAND@ \"$@\"\n" }, { "path": "cmake/SpectreSetSiteName.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nsite_name(HOSTNAME)\n\nfile(APPEND\n \"${CMAKE_BINARY_DIR}/BuildInfo.txt\"\n \"Hostname: ${HOSTNAME}\\n\"\n \"Host system: ${CMAKE_HOST_SYSTEM}\\n\"\n \"Host system version: ${CMAKE_HOST_SYSTEM_VERSION}\\n\"\n \"Host system processor: ${CMAKE_HOST_SYSTEM_PROCESSOR}\\n\"\n )\n" }, { "path": "cmake/SpectreSetupFlagsTarget.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# The library that contains all the flags for building SpECTRE targets.\n# Generator expressions should be used to limit flag scopes to specific\n# languages and compilers.\nadd_library(SpectreFlags INTERFACE)\n" }, { "path": "cmake/SpectreSetupPythonPackage.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nif (ENABLE_PYTHON)\n spectre_define_test_timeout_factor_option(PYTHON \"Python\")\n\n option(PY_DEV_MODE \"Enable development mode for the Python package, meaning \\\n that Python files are symlinked rather than copied to the build directory\" OFF)\n function(configure_or_symlink_py_file SOURCE_FILE TARGET_FILE)\n if(PY_DEV_MODE)\n get_filename_component(_TARGET_FILE_DIR ${TARGET_FILE} DIRECTORY)\n execute_process(COMMAND\n ${CMAKE_COMMAND} -E make_directory ${_TARGET_FILE_DIR})\n execute_process(COMMAND\n ${CMAKE_COMMAND} -E create_symlink ${SOURCE_FILE} ${TARGET_FILE})\n else()\n configure_file(${SOURCE_FILE} ${TARGET_FILE} @ONLY)\n endif()\n endfunction()\n\n set(SPECTRE_PYTHON_PREFIX \"${SPECTRE_PYTHON_PREFIX_PARENT}/spectre\")\n\n # Create the root __init__.py file\n configure_or_symlink_py_file(\n \"${CMAKE_SOURCE_DIR}/support/Python/__init__.py\"\n \"${SPECTRE_PYTHON_PREFIX}/__init__.py\"\n )\n\n # Create the root __main__.py entry point\n configure_or_symlink_py_file(\n \"${CMAKE_SOURCE_DIR}/support/Python/__main__.py\"\n \"${SPECTRE_PYTHON_PREFIX}/__main__.py\"\n )\n # Also link the main entry point to bin/\n set(PYTHON_EXE_COMMAND \"-m spectre\")\n set(PYTHON_EXEC_ENV_VARS \"\")\n # At some point we needed to preload jemalloc for the Python bindings to work,\n # otherwise we got \"cannot allocate memory in static TLS block\" errors when\n # using jemalloc. This is fixed by avoiding to link jemalloc into libraries in\n # the first place (we only dynamically link it into executables). If we want to\n # link jemalloc into libraries again (e.g. to use jemalloc features explicitly\n # in the code), the best way to do this would be to build jemalloc with a prefix\n # and use it as a custom allocator where needed, instead of generically\n # replacing the system allocator.\n #\n # ParaView needs specific environment variables set, e.g. 'LD_LIBRARY_PATH', but\n # they can interfere with simulations, e.g. when they point to ParaView's\n # bundled MPI which may be different to the MPI we built with. Therefore we\n # disable this for now. This means we can't use the pre-built ParaView binaries\n # that bundle their own MPI and Python, unless we find a way to set the needed\n # environment variables only when running ParaView. Everything should work\n # when using a ParaView built with the same MPI and Python as the rest of\n # SpECTRE.\n # if(PARAVIEW_PYTHON_ENV_VARS)\n # string(APPEND PYTHON_EXEC_ENV_VARS \" ${PARAVIEW_PYTHON_ENV_VARS}\")\n # endif()\n #\n # HDF5 file locking can be a problem when a simulation is writing data and we\n # try to read it at the same time. We disable file locking by default when\n # writing H5 files in simulations (see H5File.hpp), but readers may still have\n # file locking enabled (e.g. h5py does this by default) and this creates file\n # locks at the system level that prevent the simulation from writing to the\n # file. Therefore we disable file locking here to avoid crashing simulations.\n # Better solutions are described in H5File.hpp.\n string(APPEND PYTHON_EXEC_ENV_VARS \" HDF5_USE_FILE_LOCKING=FALSE\")\n configure_file(\n \"${CMAKE_SOURCE_DIR}/cmake/SpectrePythonExecutable.sh\"\n \"${CMAKE_BINARY_DIR}/tmp/spectre\")\n file(COPY \"${CMAKE_BINARY_DIR}/tmp/spectre\"\n DESTINATION \"${CMAKE_BINARY_DIR}/bin\"\n FILE_PERMISSIONS OWNER_READ OWNER_WRITE OWNER_EXECUTE GROUP_READ\n GROUP_EXECUTE WORLD_READ WORLD_EXECUTE)\n\n configure_file(\n \"${CMAKE_SOURCE_DIR}/cmake/SpectrePythonExecutable.sh\"\n \"${CMAKE_BINARY_DIR}/tmp/spectre\")\n file(COPY \"${CMAKE_BINARY_DIR}/tmp/spectre\"\n DESTINATION \"${CMAKE_BINARY_DIR}/bin\"\n FILE_PERMISSIONS OWNER_READ OWNER_WRITE OWNER_EXECUTE GROUP_READ\n GROUP_EXECUTE WORLD_READ WORLD_EXECUTE)\n\n # Also link the Python interpreter to bin/python-spectre as an easy way to jump\n # into a Python shell or run a script that uses pybindings\n set(PYTHON_EXE_COMMAND \"\")\n configure_file(\n \"${CMAKE_SOURCE_DIR}/cmake/SpectrePythonExecutable.sh\"\n \"${CMAKE_BINARY_DIR}/tmp/python-spectre\")\n file(COPY \"${CMAKE_BINARY_DIR}/tmp/python-spectre\"\n DESTINATION \"${CMAKE_BINARY_DIR}/bin\"\n FILE_PERMISSIONS OWNER_READ OWNER_WRITE OWNER_EXECUTE GROUP_READ\n GROUP_EXECUTE WORLD_READ WORLD_EXECUTE)\n\n # Write configuration files for installing the Python modules\n file(STRINGS\n ${CMAKE_SOURCE_DIR}/support/Python/requirements.txt\n SPECTRE_PY_DEPS)\n file(STRINGS\n ${CMAKE_SOURCE_DIR}/support/Python/dev_requirements.txt\n SPECTRE_PY_DEV_DEPS)\n list(FILTER SPECTRE_PY_DEPS EXCLUDE REGEX \"^#\")\n list(FILTER SPECTRE_PY_DEV_DEPS EXCLUDE REGEX \"^#\")\n list(REMOVE_ITEM SPECTRE_PY_DEPS \"\")\n list(REMOVE_ITEM SPECTRE_PY_DEV_DEPS \"\")\n list(JOIN SPECTRE_PY_DEPS \"\\n \" SPECTRE_PY_DEPS_OUTPUT)\n list(JOIN SPECTRE_PY_DEV_DEPS \"\\n \" SPECTRE_PY_DEV_DEPS_OUTPUT)\n configure_or_symlink_py_file(\n \"${CMAKE_SOURCE_DIR}/pyproject.toml\"\n \"${SPECTRE_PYTHON_PREFIX_PARENT}/pyproject.toml\")\n configure_or_symlink_py_file(\n \"${CMAKE_SOURCE_DIR}/setup.cfg\"\n \"${SPECTRE_PYTHON_PREFIX_PARENT}/setup.cfg\")\n\n # Write a file to be able to set up the new python path.\n file(WRITE\n \"${CMAKE_BINARY_DIR}/tmp/LoadPython.sh\"\n \"#!/bin/sh\\n\"\n \"export PYTHONPATH=${PYTHONPATH}\\n\"\n )\n configure_file(\n \"${CMAKE_BINARY_DIR}/tmp/LoadPython.sh\"\n \"${CMAKE_BINARY_DIR}/bin/LoadPython.sh\")\n\n # Install the SpECTRE Python package to the CMAKE_INSTALL_PREFIX, using pip.\n # This will install the package into the expected subdirectory, typically\n # `lib/pythonX.Y/site-packages/`. It also creates symlinks to entry points\n # specified in `setup.py`.\n install(\n CODE \"execute_process(\\\n COMMAND ${Python_EXECUTABLE} -m pip install \\\n --no-deps --no-input --no-cache-dir --no-index --ignore-installed \\\n --disable-pip-version-check --no-build-isolation \\\n --prefix ${CMAKE_INSTALL_PREFIX} ${SPECTRE_PYTHON_PREFIX_PARENT} \\\n )\"\n )\nendif()\nadd_custom_target(all-pybindings)\n\n# Add a python module, either with or without python bindings and with\n# or without additional python files. If bindings are being provided then\n# the library will be named Py${MODULE_NAME}, e.g. if MODULE_NAME is\n# DataStructures then the library name is PyDataStructures.\n#\n# - MODULE_NAME The name of the module, e.g. DataStructures.\n#\n# - MODULE_PATH Path inside the module, e.g. submodule0/submodule1 would\n# result in loading spectre.submodule0.submodule1\n#\n# - SOURCES The C++ source files for bindings. Omit if no bindings\n# are being generated.\n#\n# - LIBRARY_NAME The name of the C++ libray, e.g. PyDataStructures.\n# Required if SOURCES are specified. Must begin with \"Py\".\n#\n# - PYTHON_FILES List of the python files (relative to\n# ${CMAKE_SOURCE_DIR}/src) to add to the module. Omit if\n# no python files are to be provided.\nfunction(SPECTRE_PYTHON_ADD_MODULE MODULE_NAME)\n if (NOT ENABLE_PYTHON)\n return()\n endif()\n set(SINGLE_VALUE_ARGS MODULE_PATH LIBRARY_NAME)\n set(MULTI_VALUE_ARGS SOURCES PYTHON_FILES)\n cmake_parse_arguments(\n ARG \"\"\n \"${SINGLE_VALUE_ARGS}\"\n \"${MULTI_VALUE_ARGS}\"\n ${ARGN})\n\n set(MODULE_LOCATION\n \"${SPECTRE_PYTHON_PREFIX}/${ARG_MODULE_PATH}/${MODULE_NAME}\")\n get_filename_component(MODULE_LOCATION ${MODULE_LOCATION} ABSOLUTE)\n\n # Add our python library, if it has sources\n if(BUILD_PYTHON_BINDINGS AND NOT \"${ARG_SOURCES}\" STREQUAL \"\")\n if(\"${ARG_LIBRARY_NAME}\" STREQUAL \"\")\n message(FATAL_ERROR \"Set a LIBRARY_NAME for Python module \"\n \"'${MODULE_NAME}' that has sources.\")\n endif()\n if(NOT \"${ARG_LIBRARY_NAME}\" MATCHES \"^Py\")\n message(FATAL_ERROR \"The LIBRARY_NAME for Python module \"\n \"'${MODULE_NAME}' must begin with 'Py' but is '${ARG_LIBRARY_NAME}'.\")\n endif()\n\n Python_add_library(${ARG_LIBRARY_NAME} MODULE ${ARG_SOURCES})\n set_target_properties(\n ${ARG_LIBRARY_NAME}\n PROPERTIES\n # These can be turned on once we support them\n INTERPROCEDURAL_OPTIMIZATION OFF\n CXX__VISIBILITY_PRESET OFF\n VISIBLITY_INLINES_HIDDEN OFF\n )\n\n if (TARGET SpectrePch)\n target_precompile_headers(${ARG_LIBRARY_NAME} REUSE_FROM SpectrePch)\n target_link_libraries(${ARG_LIBRARY_NAME} PRIVATE SpectrePchFlags)\n endif()\n\n # In order to avoid runtime errors about missing compatibility functions\n # defined in the PythonBindings library, we need to link in the whole\n # archive. This is not needed on macOS.\n if (APPLE)\n target_link_libraries(\n ${ARG_LIBRARY_NAME}\n PUBLIC PythonBindings\n )\n else()\n target_link_libraries(\n ${ARG_LIBRARY_NAME}\n PUBLIC\n -Wl,--whole-archive\n PythonBindings\n -Wl,--no-whole-archive\n )\n endif()\n target_link_libraries(\n ${ARG_LIBRARY_NAME}\n PRIVATE\n CharmModuleInit\n SpectreFlags\n )\n # We don't want the 'lib' prefix for python modules, so we set the output\n # name\n set_target_properties(\n ${ARG_LIBRARY_NAME}\n PROPERTIES\n PREFIX \"\"\n LIBRARY_OUTPUT_NAME \"_Pybindings\"\n LIBRARY_OUTPUT_DIRECTORY ${MODULE_LOCATION}\n )\n # We need --no-as-needed since each python module needs to depend on all the\n # shared libraries in order to run successfully.\n set(PY_LIB_LINK_FLAGS \"${CMAKE_CXX_LINK_FLAGS}\")\n if(NOT APPLE)\n set(PY_LIB_LINK_FLAGS\n \"${CMAKE_CXX_LINK_FLAGS} -Wl,--no-as-needed\")\n endif()\n set_target_properties(\n ${ARG_LIBRARY_NAME}\n PROPERTIES\n LINK_FLAGS \"${PY_LIB_LINK_FLAGS}\"\n )\n if(BUILD_TESTING)\n add_dependencies(test-executables ${ARG_LIBRARY_NAME})\n endif()\n add_dependencies(all-pybindings ${ARG_LIBRARY_NAME})\n endif(BUILD_PYTHON_BINDINGS AND NOT \"${ARG_SOURCES}\" STREQUAL \"\")\n\n # configure the Python source files into the build directory\n foreach(PYTHON_FILE ${ARG_PYTHON_FILES})\n # Configure file\n get_filename_component(PYTHON_FILE_JUST_NAME\n \"${CMAKE_CURRENT_SOURCE_DIR}/${PYTHON_FILE}\" NAME)\n configure_or_symlink_py_file(\n \"${CMAKE_CURRENT_SOURCE_DIR}/${PYTHON_FILE}\"\n \"${MODULE_LOCATION}/${PYTHON_FILE_JUST_NAME}\"\n )\n endforeach(PYTHON_FILE ${ARG_PYTHON_FILES})\n\n # Create empty __init__.py files if none exist\n # We walk up the tree until we get to ${SPECTRE_PYTHON_PREFIX}\n set(CURRENT_MODULE ${MODULE_LOCATION})\n while(NOT ${CURRENT_MODULE} STREQUAL ${SPECTRE_PYTHON_PREFIX})\n set(INIT_FILE_LOCATION \"${CURRENT_MODULE}/__init__.py\")\n if(NOT EXISTS ${INIT_FILE_LOCATION})\n file(WRITE ${INIT_FILE_LOCATION} \"\")\n endif()\n get_filename_component(CURRENT_MODULE \"${CURRENT_MODULE}/..\" ABSOLUTE)\n endwhile()\nendfunction()\n\n# Add headers if Python bindings are being built\nfunction (spectre_python_headers LIBRARY_NAME)\n if(NOT BUILD_PYTHON_BINDINGS)\n return()\n endif()\nspectre_target_headers(\n ${LIBRARY_NAME}\n # Forward all remaining arguments\n ${ARGN}\n )\nendfunction()\n\n# Link with the LIBRARIES if Python bindings are being built\nfunction (spectre_python_link_libraries LIBRARY_NAME)\n if(NOT BUILD_PYTHON_BINDINGS)\n return()\n endif()\n target_link_libraries(\n ${LIBRARY_NAME}\n # Forward all remaining arguments\n ${ARGN}\n )\nendfunction()\n\n# Add the DEPENDENCIES if Python bindings are being built\nfunction (spectre_python_add_dependencies LIBRARY_NAME)\n if(NOT BUILD_PYTHON_BINDINGS)\n return()\n endif()\n add_dependencies(\n ${LIBRARY_NAME}\n # Forward all remaining arguments\n ${ARGN}\n )\nendfunction()\n\n# Register a python test file with ctest.\n# - TEST_NAME The name of the test,\n# e.g. \"Unit.DataStructures.Python.DataVector\"\n#\n# - FILE The file to add, e.g. Test_DataVector.py\n#\n# - TAGS A semicolon separated list of labels for the test,\n# e.g. \"Unit;DataStructures;Python\"\n# - PY_MODULE_DEPENDENCY\n# The python module that this test depends on\n# Set to None if there is no python module dependency\n#\n# Optionally:\n# - TIMEOUT secs Set the test timeout (default 2)\nfunction(SPECTRE_ADD_PYTHON_TEST TEST_NAME FILE TAGS\n PY_MODULE_DEPENDENCY)\n cmake_parse_arguments(ARG \"\" TIMEOUT \"\" ${ARGN})\n if(DEFINED ARG_TIMEOUT)\n set(TIMEOUT ${ARG_TIMEOUT})\n else()\n set(TIMEOUT 2)\n endif()\n get_filename_component(FILE \"${FILE}\" ABSOLUTE)\n string(TOLOWER \"${TAGS}\" TAGS)\n\n add_test(\n NAME \"${TEST_NAME}\"\n COMMAND\n ${Python_EXECUTABLE}\n ${FILE}\n )\n\n spectre_test_timeout(TIMEOUT PYTHON ${TIMEOUT})\n\n set(_PY_TEST_ENV_VARS \"PYTHONPATH=${PYTHONPATH}\")\n\n # The fail regular expression is what Python.unittest returns when no\n # tests are found to be run. We treat this as a test failure.\n set_tests_properties(\n \"${TEST_NAME}\"\n PROPERTIES\n FAIL_REGULAR_EXPRESSION \"Ran 0 test\"\n TIMEOUT ${TIMEOUT}\n LABELS \"${TAGS};Python\"\n ENVIRONMENT \"${_PY_TEST_ENV_VARS}\"\n )\n # check if this is a unit test, and if so add it to the dependencies\n foreach(LABEL ${TAGS})\n string(TOLOWER \"${LABEL}\" LOWER_LABEL)\n string(TOLOWER \"${PY_MODULE_DEPENDENCY}\" LOWER_DEP)\n if(\"${LOWER_LABEL}\" STREQUAL \"unit\"\n AND NOT \"${LOWER_DEP}\" STREQUAL \"none\")\n add_dependencies(unit-tests ${PY_MODULE_DEPENDENCY})\n endif()\n endforeach()\nendfunction()\n\n# Register a python test file that uses bindings with ctest.\n# - TEST_NAME The name of the test,\n# e.g. \"Unit.DataStructures.Python.DataVector\"\n#\n# - FILE The file to add, e.g. Test_DataVector.py\n#\n# - TAGS A semicolon separated list of labels for the test,\n# e.g. \"Unit;DataStructures;Python\"\n# - PY_MODULE_DEPENDENCY\n# The python module that this test depends on\n# Set to None if there is no python module dependency\n#\n# Optionally:\n# - TIMEOUT secs Set the test timeout (default 2)\nfunction(SPECTRE_ADD_PYTHON_BINDINGS_TEST TEST_NAME FILE TAGS\n PY_MODULE_DEPENDENCY)\n if(NOT BUILD_PYTHON_BINDINGS)\n return()\n endif()\n spectre_add_python_test(\n ${TEST_NAME} ${FILE} \"${TAGS}\" ${PY_MODULE_DEPENDENCY} ${ARGN})\nendfunction()\n\n# Add a convenient target name for the pybindings.\nadd_custom_target(cli)\nadd_dependencies(cli all-pybindings)\n" }, { "path": "cmake/SpectreSetupTesting.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\ninclude(CTest)\n\nset(SPECTRE_TEST_RUNNER \"\" CACHE STRING\n \"Run test executables through the given wrapper.\")\n\noption(SPECTRE_TEST_TIMEOUT_FACTOR\n \"Multiply timeout for tests by this factor\")\n\nfunction(spectre_define_test_timeout_factor_option TEST_TYPE HELP_NAME)\n option(SPECTRE_${TEST_TYPE}_TEST_TIMEOUT_FACTOR\n \"Multiply timeout for ${HELP_NAME} tests by this factor\")\nendfunction ()\n\n# Multiply BASE_TIMEOUT by the user specified option for TEST_TYPE\nfunction(spectre_test_timeout RETURN_VARIABLE TEST_TYPE BASE_TIMEOUT)\n if (SPECTRE_${TEST_TYPE}_TEST_TIMEOUT_FACTOR)\n set(FACTOR ${SPECTRE_${TEST_TYPE}_TEST_TIMEOUT_FACTOR})\n elseif (SPECTRE_TEST_TIMEOUT_FACTOR)\n set(FACTOR ${SPECTRE_TEST_TIMEOUT_FACTOR})\n else ()\n set(FACTOR 1)\n endif ()\n\n # Note: \"1\" is parsed as \"ON\" by cmake\n if (NOT \"${FACTOR}\" STREQUAL ON)\n math(EXPR RESULT \"${FACTOR} * ${BASE_TIMEOUT}\")\n else ()\n set(RESULT ${BASE_TIMEOUT})\n endif ()\n\n set(${RETURN_VARIABLE} ${RESULT} PARENT_SCOPE)\nendfunction ()\n" }, { "path": "cmake/SpectreTargetHeaders.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Add header files for CMake to track for a given library\n# or executable.\n#\n# The header and source files together are used to track dependencies between\n# targets automatically in SpECTRE. Specifically, CI checks that the\n# dependencies of a target supply all the header files used in a library.\n# While this checking still requires includes to be correct (be they checked\n# manually or automatically), it significantly lowers the burden of correct\n# dependency management on developers.\n#\n# Additionally, some IDEs perform better if the header files for libraries\n# are known.\n#\n# Usage:\n# spectre_target_headers(\n# TARGET_NAME\n# INCLUDE_DIRECTORY /path/to/include/relative/to\n# HEADERS\n# A.hpp\n# B.hpp\n# B.tpp\n# C.hpp)\n#\n# Arguments:\n# - TARGET_NAME: the name of the library or executable\n# - INCLUDE_DIRECTORY: the directory relative to which the header\n# files must be included in C++ files. E.g.\n# `${CMAKE_SOURCE_DIR}/src` if the include paths are\n# relative to `${CMAKE_SOURCE_DIR}/src`.\n# - HEADERS: the HEADERS argument is a list of all the headers files\n# to append, including tpp files, relative to the current\n# source directory.\nfunction(spectre_target_headers TARGET_NAME)\n cmake_parse_arguments(\n ARG \"\" \"INCLUDE_DIRECTORY\" \"HEADERS\"\n ${ARGN})\n\n get_target_property(\n TARGET_TYPE\n ${TARGET_NAME}\n TYPE\n )\n\n if(NOT ARG_INCLUDE_DIRECTORY)\n message(FATAL_ERROR\n \"Must specify the include directory relative to which the \"\n \"header files for a library will be included when calling \"\n \"spectre_target_headers. The named argument is INCLUDE_DIRECTORY. \"\n \"Call was made for target ${TARGET_NAME}.\")\n endif(NOT ARG_INCLUDE_DIRECTORY)\n # Note: Search the list because an empty HEADERS is okay.\n list(FIND ARGN \"HEADERS\" _FOUND_HEADERS)\n if(${_FOUND_HEADERS} EQUAL -1)\n message(FATAL_ERROR\n \"No HEADERS section specified in call to spectre_target_headers \"\n \"for target ${TARGET_NAME}. You must specificy HEADERS before \"\n \"listing the header files.\")\n endif()\n\n if(NOT ${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\n get_property(\n INCLUDE_DIRS\n TARGET ${TARGET_NAME}\n PROPERTY INCLUDE_DIRECTORIES\n )\n if(NOT ${ARG_INCLUDE_DIRECTORY} IN_LIST INCLUDE_DIRS)\n set_property(\n TARGET ${TARGET_NAME}\n APPEND\n PROPERTY INCLUDE_DIRECTORIES ${ARG_INCLUDE_DIRECTORY}\n )\n endif(NOT ${ARG_INCLUDE_DIRECTORY} IN_LIST INCLUDE_DIRS)\n endif(NOT ${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\n\n get_property(\n INTERFACE_INCLUDE_DIRS\n TARGET ${TARGET_NAME}\n PROPERTY INTERFACE_INCLUDE_DIRECTORIES\n )\n if(NOT ${ARG_INCLUDE_DIRECTORY} IN_LIST INTERFACE_INCLUDE_DIRS)\n set_property(\n TARGET ${TARGET_NAME}\n APPEND\n PROPERTY INTERFACE_INCLUDE_DIRECTORIES ${ARG_INCLUDE_DIRECTORY}\n )\n endif(NOT ${ARG_INCLUDE_DIRECTORY} IN_LIST INTERFACE_INCLUDE_DIRS)\n\n unset(_HEADER_FILES)\n foreach(HEADER ${ARG_HEADERS})\n if(NOT HEADER STREQUAL \"PRIVATE\" AND\n NOT HEADER STREQUAL \"PUBLIC\" AND\n NOT HEADER STREQUAL \"INTERFACE\" AND\n NOT IS_ABSOLUTE \"${HEADER}\")\n set(_ABSOLUTE_PATH \"${CMAKE_CURRENT_LIST_DIR}/${HEADER}\")\n file(RELATIVE_PATH HEADER ${ARG_INCLUDE_DIRECTORY} ${_ABSOLUTE_PATH})\n endif()\n list(APPEND _HEADER_FILES ${HEADER})\n endforeach()\n\n if(${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\n add_interface_lib_headers(\n TARGET ${TARGET_NAME}\n HEADERS\n ${_HEADER_FILES}\n )\n else(${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\n set_property(\n TARGET ${TARGET_NAME}\n APPEND\n PROPERTY\n PUBLIC_HEADER\n ${_HEADER_FILES}\n )\n endif(${TARGET_TYPE} STREQUAL INTERFACE_LIBRARY)\nendfunction(spectre_target_headers TARGET_NAME)\n" }, { "path": "cmake/SpectreTargetSources.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Alias for target_sources.\nfunction(spectre_target_sources TARGET)\n target_sources(${TARGET} ${ARGN})\nendfunction()\n" }, { "path": "cmake/StripSymbols.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\noption(STRIP_SYMBOLS \"Strip symbols from executables\" OFF)\n\nif (STRIP_SYMBOLS)\n if (APPLE)\n message(FATAL_ERROR \"Stripping all symbols is currently not supported on \"\n \"macOS. Please disable the `STRIP_SYMBOLS` flag.\")\n else (APPLE)\n set(CMAKE_EXE_LINKER_FLAGS \"${CMAKE_EXE_LINKER_FLAGS} -Wl,--strip-all\")\n endif (APPLE)\nendif(STRIP_SYMBOLS)\n" }, { "path": "cmake/UpdateAddExecutables.cmake", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nfunction(add_spectre_executable TARGET_NAME)\n _add_spectre_executable(${TARGET_NAME} ${ARGN})\n\n if (USE_PCH)\n get_target_property(\n TARGET_IS_IMPORTED\n ${TARGET_NAME}\n IMPORTED\n )\n if(NOT ${TARGET_IS_IMPORTED} AND TARGET SpectrePch)\n target_precompile_headers(${TARGET_NAME} REUSE_FROM SpectrePch)\n target_link_libraries(${TARGET_NAME} PRIVATE SpectrePchFlags)\n endif()\n endif (USE_PCH)\nendfunction()\n" }, { "path": "containers/Dockerfile.buildenv", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# If you change this file please push the new images to DockerHub. If you do not\n# have permission to push to DockerHub please coordinate with someone who does.\n# Since changes to this image affect our testing infrastructure it is important\n# all changes be carefully reviewed before they are pushed.\n#\n# GitHub Actions (recommended method)\n#\n# This is how you use GitHub Actions to build and push the new images:\n#\n# 1. Push your changes to the `develop` branch on your fork of the spectre\n# repository on GitHub (https://github.com/YOURNAME/spectre).\n# 2. Go to https://github.com/YOURNAME/spectre/actions/workflows/BuildDockerContainer.yaml.\n# 3. Select \"Run workflow\". Here you can select the location on DockerHub where\n# you want the new images pushed. Select `sxscollaboration/spectre` (which is\n# used by CI) or a location on your own DockerHub account. Either way, you\n# need to set the `DOCKERHUB_USERNAME` and `DOCKERHUB_TOKEN` secrets in the\n# repository to credentials that have write access.\n# 4. The images will be built and pushed to DockerHub and CI will run over them.\n# See `.github/workflows/BuildDockerContainer.yaml` for details.\n#\n# Local build & push (can be tedious and time consuming)\n#\n# What you need to push to Dockerhub is:\n#\n# Arch: linux/amd64,linux/arm64\n# # Note that cross compiling can be slow, so for testing just do amd64\n# # or arm64 depending on your CPU. Docker builds the image in a way\n# # that when someone clones it, depending on their CPU architecture,\n# # they will get either the amd64 or arm64 version.\n# Ubuntu version: 22.04 (default)\n# --platform linux/amd64,linux/arm64\n# --target dev\n# -t sxscollaboration/spectre:dev\n#\n# Arch: linux/amd64\n# Ubuntu version: 18.04\n# --platform linux/amd64\n# --target dev\n# -t sxscollaboration/spectre:dev1804\n# --build-arg UBUNTU_VERSION=18.04\n#\n# Docker must be run as root on your machine. There are 4 different images in\n# this Dockerfile, but you can ignore the 'deploy_static_execs_and_libs' since\n# it's only used in CI. Here is how to build them for x86_64 (for Apple Silicon,\n# replace linux/amd64 with linux/arm64):\n#\n# 1. `dev`\n#\n# cd $SPECTRE_HOME\n# docker build --target dev -t sxscollaboration/spectre:dev \\\n# --platform linux/amd64 \\\n# -f ./containers/Dockerfile.buildenv .\n#\n# # Cross compiling for AMD64 and ARM64:\n# #\n# # To check if you can cross compile, first run\n# # docker buildx ls\n# # This will look something like:\n# # NAME/NODE DRIVER/ENDPOINT STATUS BUILDKIT \\\n# # PLATFORMS\n# # default* docker\n# # \\_ default \\_ default running v0.13.2 \\\n# # linux/amd64, linux/amd64/v2, linux/amd64/v3, linux/386\n# #\n# # Note that the DRIVER/ENDPOINT is 'docker'. We want to instead use\n# # 'docker-container'. To do this, run\n# # docker buildx create --name mybuilder --bootstrap --use\n# # When you run 'docker buildx ls' now you should see\n# # mybuilder* docker-container\n# # The asterisk means docker will use this builder. You are now ready to\n# # cross-compile code.\n# #\n# # This is documented at:\n# # https://docs.docker.com/build/building/multi-platform/#getting-started\n#\n# docker buildx build --target dev -t sxscollaboration/spectre:dev \\\n# --platform linux/amd64,linux/arm64 \\\n# -f ./containers/Dockerfile.buildenv --push .\n#\n# You DO NOT need to push the below. CI does that automatically.\n#\n# 3. `demo` To build this, you MUST first push the `dev` images to\n# DockerHub as the `demo` image uses the remote `dev` image.\n#\n# docker push sxscollaboration/spectre:dev\n#\n# To build `demo`, you must be in $SPECTRE_ROOT and there cannot be a\n# directory named `build` in $SPECTRE_ROOT because the image will create\n# this directory (in the container).\n#\n# cd $SPECTRE_HOME\n# rm -rf build/\n# docker build --target demo -t sxscollaboration/spectre:demo \\\n# --platform linux/amd64 \\\n# -f ./containers/Dockerfile.buildenv .\n#\n# and then to push the `demo` image to DockerHub:\n#\n# docker push sxscollaboration/spectre:demo\n#\n# 4. `deploy_static_execs_and_libs` This is used for building various\n# executables and libraries with an old enough version of glibc so\n# that the resulting executables are quite portable. This must be built\n# as, but should generally only be done in CI unless you are debugging\n# the container build.\n#\n# docker build --target deploy_static_execs_and_libs --platform linux/amd64 \\\n# --build-arg UBUNTU_VERSION=18.04 -f ./containers/Dockerfile.buildenv .\n#\n# That is, it uses Ubuntu 18.04 and AMD64. There is no support for ARM and\n# newer versions of Ubuntu will limit compatibility.\nARG UBUNTU_VERSION=22.04\nFROM ubuntu:${UBUNTU_VERSION} AS base\nARG UBUNTU_VERSION=22.04\n\n# See\n# https://docs.docker.com/engine/reference/builder/#automatic-platform-args-in-the-global-scope\n# for how TARGETARCH is defined.\nARG TARGETARCH\n\n# Install add-apt-repository and basic tools\nRUN if [ ${UBUNTU_VERSION} = 18.04 ] && [ \"$TARGETARCH\" = \"arm64\" ]; then \\\n echo \"Cannot use Ubuntu 18.04 with ARM\" && exit 1; fi && apt-get update -y \\\n && apt-get install -y software-properties-common wget git file \\\n && add-apt-repository ppa:ubuntu-toolchain-r/test\n\n# Add LLVM apt repository for newer versions of clang\nRUN wget -qO- https://apt.llvm.org/llvm-snapshot.gpg.key | \\\n tee /etc/apt/trusted.gpg.d/apt.llvm.org.asc \\\n && if [ ${UBUNTU_VERSION} = 18.04 ]; then \\\n add-apt-repository -y \\\n 'deb http://apt.llvm.org/bionic/ llvm-toolchain-bionic-17 main'; \\\n elif [ ${UBUNTU_VERSION} = 22.04 ]; then \\\n add-apt-repository -y \\\n 'deb http://apt.llvm.org/jammy/ llvm-toolchain-jammy-16 main'; \\\n else \\\n exit 1; \\\n fi\n\n# Install compilers and build tools\nRUN apt-get update -y \\\n && if [ ${UBUNTU_VERSION} = 18.04 ]; then \\\n apt-get install -y gcc-10 g++-10 gfortran-10 clang-17; \\\n else \\\n apt-get install -y gcc g++ gfortran clang clang-format clang-tidy cmake; \\\n fi \\\n && apt-get install -y lld bison flex libncurses-dev gdb autoconf automake \\\n ninja-build lcov \\\n && if [ ${UBUNTU_VERSION} = 18.04 ]; then \\\n wget -O cmake-install.sh \\\n \"https://github.com/Kitware/CMake/releases/download/v3.28.1/cmake-3.28.1-linux-x86_64.sh\" \\\n && chmod +x ./cmake-install.sh && ./cmake-install.sh --skip-license \\\n --prefix=/usr/local && rm cmake-install.sh; \\\n fi\n\n# Install SpECTRE dependencies that are available through apt\n#\n# We intentionally don't install libboost-all-dev because that installs\n# Boost.MPI, which installs OpenMPI into the container. When MPI is\n# installed inside the container it makes it very difficult to use\n# Singularity on HPC systems to interface with the system MPI library.\n# The system MPI libraries are usually configured to take advantage of\n# InfiniBand or various other networking layers.\nRUN apt-get update -y \\\n && apt-get install -y \\\n libopenblas-dev liblapack-dev \\\n libgsl-dev \\\n libboost-dev libboost-program-options-dev \\\n libboost-thread-dev libboost-tools-dev libssl-dev \\\n libhdf5-dev hdf5-tools \\\n libarpack2-dev \\\n libbenchmark-dev \\\n && if [ ${UBUNTU_VERSION} = 18.04 ]; then \\\n wget https://github.com/jbeder/yaml-cpp/archive/refs/tags/0.8.0.tar.gz \\\n && tar xf 0.8.0.tar.gz && mkdir ./yaml-cpp-0.8.0/build \\\n && cd ./yaml-cpp-0.8.0/build \\\n && cmake \\\n -D CMAKE_C_COMPILER=gcc-10 \\\n -D CMAKE_CXX_COMPILER=g++-10 \\\n -D CMAKE_BUILD_TYPE=Release \\\n -D YAML_BUILD_SHARED_LIBS=OFF \\\n -D BUILD_SHARED_LIBS=OFF \\\n -D YAML_ENABLE_PIC=ON \\\n -D POSITION_INDEPENDENT_CODE=ON \\\n -D YAML_CPP_BUILD_TESTS=OFF \\\n -D YAML_CPP_BUILD_CONTRIB=OFF \\\n -D CMAKE_INSTALL_PREFIX=/usr/local \\\n .. \\\n && make ${PARALLEL_MAKE_ARG} && make install \\\n && cd ../.. && rm -rf ./0.8.0.tar.gz ./yaml-cpp-0.8.0; \\\n else \\\n apt-get install -y libjemalloc2 libjemalloc-dev libyaml-cpp-dev; \\\n fi\n\n# Install Python packages\n# We only install packages that are needed by the build system (e.g. to compile\n# Python bindings or build documentation) or used by Python code that is\n# unit-tested. Any other packages can be installed on-demand.\n# - We use python-is-python3 because on Ubuntu 20.04 /usr/bin/python was removed\n# to aid in tracking down anything that depends on python 2. However, many\n# scripts use `/usr/bin/env python` to find python so restore it.\n# - We install h5py explicitly from binary so that cross compilation is quicker.\nCOPY support/Python/requirements.txt requirements.txt\nCOPY support/Python/dev_requirements.txt dev_requirements.txt\nENV DEBIAN_FRONTEND noninteractive\nRUN apt-get update -y \\\n && if [ ${UBUNTU_VERSION} = 18.04 ]; then \\\n apt-get install -y zlib1g-dev libncurses5-dev libgdbm-dev libnss3-dev \\\n libssl-dev libreadline-dev libffi-dev libsqlite3-dev wget libbz2-dev \\\n make \\\n && wget https://www.python.org/ftp/python/3.10.1/Python-3.10.1.tgz \\\n && tar -xf Python-3.10.1.tgz && cd ./Python-3.10.1 \\\n && ./configure --enable-optimizations && make ${PARALLEL_MAKE_ARG} \\\n && make altinstall && cd ../ \\\n && rm -rf ./Python-3.10.1.tgz ./Python-3.10.1 \\\n && python3.10 -m pip install --upgrade pip \\\n && pip3.10 --no-cache-dir install --only-binary=h5py -r requirements.txt \\\n -r dev_requirements.txt; \\\n else \\\n apt-get install -y python3-pip python-is-python3 pkg-config \\\n && pip3 --no-cache-dir install --only-binary=h5py -r requirements.txt \\\n -r dev_requirements.txt; \\\n fi \\\n && rm requirements.txt dev_requirements.txt\n\n# Enable bash-completion by installing it and then adding it to the .bashrc file\nRUN apt-get update -y \\\n && apt-get install -y bash-completion \\\n && printf \"if [ -f /etc/bash_completion ] && ! shopt -oq posix; then\\n\\\n . /etc/bash_completion\\nfi\\n\\n\" >> /root/.bashrc\n\n# WARNING: We switch to an empty container briefly!!!\n#\n# Cross-compile dependencies on the host system that take a long time to build\n# when emulating the target architecture. The `xbuild` stage is an image with\n# the same architecture as the host. It compiles the packages for the target\n# architecture. Then we can copy the compiled packages into the `base` image.\n#\n# Note: because we only cross-compile the latest Ubuntu version we support,\n# we just delete the executables on Ubuntu 18.04 and disable doxygen and ccache.\nFROM --platform=$BUILDPLATFORM tonistiigi/xx AS xx\nFROM --platform=$BUILDPLATFORM ubuntu:22.04 AS xbuild\nWORKDIR /root\nCOPY --from=xx / /\nARG TARGETPLATFORM\nARG UBUNTU_VERSION=22.04\nARG PARALLEL_MAKE_ARG=-j4\n\n# Install build dependencies for the host system\nRUN apt-get update -y \\\n && apt-get install -y cmake clang lld flex bison wget git\n\n# Install build dependencies for the target architecture\n#\n# We need libstd++ to work on the target arch that we are cross-compiling for\nRUN xx-apt-get update -y \\\n && xx-apt-get install -y --no-install-recommends \\\n libc6-dev libstdc++-10-dev\n\n# - Ccache\nRUN wget https://github.com/ccache/ccache/releases/download/v4.8.2/ccache-4.8.2.tar.gz -O ccache.tar.gz \\\n && tar -xzf ccache.tar.gz \\\n && mv ccache-* ccache \\\n && cd ccache \\\n && mkdir build && cd build \\\n && cmake $(xx-clang --print-cmake-defines) \\\n -D HAVE_ASM_SSE2=OFF -D HAVE_ASM_SSE41=OFF \\\n -D HAVE_ASM_AVX2=OFF -D HAVE_ASM_AVX512=OFF \\\n -D CMAKE_BUILD_TYPE=Release .. \\\n && make $PARALLEL_MAKE_ARG\n# - Doxygen\nRUN wget https://github.com/doxygen/doxygen/archive/Release_1_14_0.tar.gz -O doxygen.tar.gz \\\n && tar -xzf doxygen.tar.gz \\\n && mv doxygen-* doxygen \\\n && cd doxygen \\\n && mkdir build && cd build \\\n && cmake $(xx-clang --print-cmake-defines) \\\n -D CMAKE_BUILD_TYPE=Release .. \\\n && make $PARALLEL_MAKE_ARG\n\n# WARNING: We now copy the things from the \"xbuild\" container/image into the\n# xbuild-test container to make sure the copying works. We do the\n# actual copy into the spectre container below.\n#\nFROM base AS xbuild-test\nARG UBUNTU_VERSION=22.04\nCOPY --from=xbuild /root/ccache/build/ccache /usr/local/bin\nRUN ccache --version\nCOPY --from=xbuild /root/doxygen/build/bin/doxygen /usr/local/bin\nRUN doxygen --version\nCOPY --from=xbuild /usr/local/bin/cmake /work/\nRUN /work/cmake --version \\\n && if [ ${UBUNTU_VERSION} = 18.04 ]; then \\\n rm /usr/local/bin/ccache /usr/local/bin/doxygen; \\\n else \\\n mv /work/cmake /usr/local/bin; \\\n fi\n\n\n# WARNING: We are now back in the spectre container. We create two base\n# images for the 2 possible target architectures and then select\n# the one we need as the `dev` container below. This is essentially an\n# `if` in the Dockerfile.\n#\n# Install software that we can't install through apt. We have to distinguish\n# between different architectures for many of those.\nFROM base AS base-amd64\nENV CHARM_ARCH=x86_64\nENV TEX_ARCH=x86_64\n\nFROM base AS base-arm64\nENV CHARM_ARCH=arm8\nENV TEX_ARCH=aarch64\n\nFROM base-${TARGETARCH} AS dev\nARG TARGETARCH\nARG UBUNTU_VERSION=22.04\n\nARG PARALLEL_MAKE_ARG=-j4\nARG DEBIAN_FRONTEND=noninteractive\n\n# We install dependencies not available through apt manually rather than using\n# Spack since Spack ends up building a lot of dependencies from scratch\n# that we don't need. Thus, not building the deps with Spack reduces total\n# build time of the Docker image.\n# - Blaze\nRUN git clone --depth 1 --branch v3.8.1 https://bitbucket.org/blaze-lib/blaze.git blaze \\\n && mv blaze/blaze /usr/local/include \\\n && rm -rf blaze*\n# - Catch2\nRUN wget https://github.com/catchorg/Catch2/archive/refs/tags/v3.14.0.tar.gz -O catch.tar.gz \\\n && tar -xzf catch.tar.gz && rm catch.tar.gz \\\n && mv Catch2-* Catch2 \\\n && cd Catch2 \\\n && cmake -B build -D BUILD_TESTING=OFF \\\n -D CMAKE_POSITION_INDEPENDENT_CODE=ON \\\n && cd build \\\n && make $PARALLEL_MAKE_ARG install \\\n && cd ../.. && rm -rf Catch2\n# - Ccache\nCOPY --from=xbuild /root/ccache/build/ccache /usr/local/bin\n# - Doxygen\nCOPY --from=xbuild /root/doxygen/build/bin/doxygen /usr/local/bin\n# - Libbacktrace\nRUN git clone https://github.com/ianlancetaylor/libbacktrace \\\n && cd libbacktrace \\\n && ./configure --prefix=/usr/local \\\n && make $PARALLEL_MAKE_ARG install \\\n && cd .. && rm -rf libbacktrace\n# - LibXSMM\nRUN if [ \"$TARGETARCH\" = \"arm64\" ] ; then \\\n git clone --single-branch --branch main --depth 1 \\\n https://github.com/libxsmm/libxsmm.git libxsmm \\\n && cd libxsmm \\\n && make $PARALLEL_MAKE_ARG PREFIX=/usr/local/ PLATFORM=1 install \\\n && cd .. \\\n && rm -rf libxsmm; \\\n else \\\n wget https://github.com/libxsmm/libxsmm/archive/1.16.1.tar.gz \\\n -O libxsmm.tar.gz \\\n && tar -xzf libxsmm.tar.gz \\\n && mv libxsmm-* libxsmm \\\n && cd libxsmm \\\n && make $PARALLEL_MAKE_ARG PREFIX=/usr/local/ install \\\n && cd .. \\\n && rm -rf libxsmm libxsmm.tar.gz; \\\n fi\n# - xsimd https://github.com/xtensor-stack/xsimd\nRUN wget http://github.com/xtensor-stack/xsimd/archive/refs/tags/11.1.0.tar.gz -O xsimd.tar.gz \\\n && tar -xzf xsimd.tar.gz && rm xsimd.tar.gz \\\n && cd ./xsimd-* \\\n && mkdir build \\\n && cd ./build \\\n && cmake -D CMAKE_BUILD_TYPE=Release \\\n -D CMAKE_INSTALL_PREFIX=/usr/local ../ \\\n && make install \\\n && cd ../.. && rm -rf xsimd-*\n\n# Update ld cache to find shared libs in /usr/local/lib/\nRUN ldconfig\n\nWORKDIR /work\n# Download and build the Charm++ version used by SpECTRE\n# We check out only a specific branch in order to reduce the repo size.\n#\n# We remove the `doc` and `example` directories since these aren't useful to us\n# in the container and we want to reduce the size of the container. We do NOT\n# remove the `tmp` directories inside the Charm++ build directories because\n# Charm++ stores non-temporary files (such as headers) that are needed when\n# building with Charm++ in the `tmp` directories.\n#\n# We build with debug symbols to make debugging Charm++-interoperability\n# easier for people, and build with O2 to reduce build size.\nRUN wget https://raw.githubusercontent.com/sxs-collaboration/spectre/develop/support/Charm/v7.0.0.patch\n\nRUN git clone --single-branch --branch v7.0.1 --depth 1 \\\n https://github.com/UIUC-PPL/charm charm_7_0_0 \\\n && cd /work/charm_7_0_0 \\\n && git checkout v7.0.1 \\\n && git apply /work/v7.0.0.patch \\\n && ./build charm++ multicore-linux-${CHARM_ARCH} gcc \\\n ${PARALLEL_MAKE_ARG} -g -O2 --build-shared --with-production \\\n && rm -r /work/charm_7_0_0/doc /work/charm_7_0_0/examples\nENV CHARM_ROOT=\"/work/charm_7_0_0/multicore-linux-${CHARM_ARCH}-gcc\"\n\n# Set the environment variable SPECTRE_CONTAINER so we can check if we are\n# inside a container (0 is true in bash)\nENV SPECTRE_CONTAINER 0\n\n# The singularity containers work better if the locale is set properly\nRUN apt-get update -y \\\n && apt-get install -y locales language-pack-fi language-pack-en \\\n && export LANGUAGE=en_US.UTF-8 \\\n && export LANG=en_US.UTF-8 \\\n && export LC_ALL=en_US.UTF-8 \\\n && locale-gen en_US.UTF-8 \\\n && dpkg-reconfigure locales\n\n# Install bibtex for Doxygen bibliography management\n# We first install the TeXLive infrastructure according to the configuration in\n# support/TeXLive/texlive.profile and then use it to install the bibtex package.\n#\n# WARNING: if you are rebuilding the container in late March/early April you\n# might have version mismatches between the TeXLive installer respositories like\n# CTAN. You can then use the previous year's TeXLive until CTAN is updated. E.g.\n# wget \\\n# ftp://tug.org/historic/systems/texlive/2025/tlnet-final/install-tl-unx.tar.gz\n# and\n# install-tl-*/install-tl -profile=texlive.profile \\\n# -repository ftp://tug.org/historic/systems/texlive/2025/tlnet-final\nRUN if [ ${UBUNTU_VERSION} = 22.04 ]; then \\\n mkdir /work/texlive && cd /work/texlive \\\n && wget http://mirror.ctan.org/systems/texlive/tlnet/install-tl-unx.tar.gz \\\n && tar -xzf install-tl-unx.tar.gz \\\n && rm install-tl-unx.tar.gz \\\n && wget https://raw.githubusercontent.com/sxs-collaboration/spectre/develop/support/TeXLive/texlive.profile \\\n && install-tl-*/install-tl -profile=texlive.profile \\\n && rm -r install-tl-* texlive.profile install-tl.log \\\n && /work/texlive/bin/${TEX_ARCH}-linux/tlmgr install bibtex \\\n ; fi\nENV PATH=\"${PATH}:/work/texlive/bin/${TEX_ARCH}-linux\"\n\n# Remove the apt-get cache in order to reduce image size\nRUN apt-get -y clean\n\nWORKDIR /work\n\n\n# Deploy compiled executables to an image that can be run on HPC systems.\n# - We could also compile in the dev container and then copy the executables to\n# a minimal deploy container to reduce its size. That requires keeping track\n# of the shared libraries that are needed to run the executables, so to make\n# things easier we just base the deploy container on the dev container.\n# - We inherit from the remote image rather than the local dev because it is\n# faster on release CI to just pull the remote dev image rather than having to\n# build the dev container again. We could pre-fetch the dev image and then\n# build from the local cache, but that didn't work right away.\nFROM sxscollaboration/spectre:dev AS deploy\nARG BUILDARCH\nARG TARGETARCH\nARG UBUNTU_VERSION=22.04\nARG PARALLEL_MAKE_ARG=-j2\n\nCOPY . spectre/\n\nRUN mkdir spectre/build && cd spectre/build \\\n && cmake \\\n -D CMAKE_C_COMPILER=clang \\\n -D CMAKE_CXX_COMPILER=clang++ \\\n -D CMAKE_Fortran_COMPILER=gfortran \\\n -D CMAKE_BUILD_TYPE=Release \\\n -D DEBUG_SYMBOLS=OFF \\\n -D BUILD_PYTHON_BINDINGS=ON \\\n -D MEMORY_ALLOCATOR=SYSTEM \\\n ..\n\n# Skip compiling the executables if we are emulating the target architecture\n# because that takes a long time. They can be compiled on-demand.\nRUN if [ \"$TARGETARCH\" = \"$BUILDARCH\" ] ; then \\\n cd spectre/build \\\n && make ${PARALLEL_MAKE_ARG} cli \\\n && make ${PARALLEL_MAKE_ARG} CharacteristicExtract \\\n && make ${PARALLEL_MAKE_ARG} PreprocessCceWorldtube \\\n && make ${PARALLEL_MAKE_ARG} WriteCceWorldtubeCoordsToFile \\\n && make ${PARALLEL_MAKE_ARG} SolveXcts \\\n ; fi\n\nENV SPECTRE_HOME /work/spectre\nENV PATH $SPECTRE_HOME/build/bin:$PATH\nENV PYTHONPATH $SPECTRE_HOME/build/bin/python:$PYTHONPATH\n\n# Set the CLI as entrypoint\nENTRYPOINT [\"spectre\"]\nCMD [\"--help\"]\n\n# Build a demo image with extra software used in the tutorials.\nFROM deploy AS demo\nARG BUILDARCH\nARG TARGETARCH\nARG UBUNTU_VERSION=22.04\nARG PARALLEL_MAKE_ARG=-j4\n\n# vim and emacs for editing files\n# Also ffmpeg for making movies with paraview output pngs\n# paraview needs curl\nRUN apt-get update -y \\\n && apt-get install -y vim emacs-nox ffmpeg curl\n\n# Install headless paraview so we can run pvserver in the container\n# Note: there is no arm64 linux binary of paraview available, so don't\n# install paraview when building for Apple Silicon. Apple Silicon users\n# should install a binary of ParaView for Mac and move data to be\n# visualized outside of the container.\nRUN if [ \"$TARGETARCH\" != \"arm64\" ] ; then \\\n wget -O paraview.tar.gz --no-check-certificate \"https://www.paraview.org/paraview-downloads/download.php?submit=Download&version=v5.10&type=binary&os=Linux&downloadFile=ParaView-5.10.1-osmesa-MPI-Linux-Python3.9-x86_64.tar.gz\" \\\n && tar -xzf paraview.tar.gz \\\n && rm paraview.tar.gz \\\n && mv ParaView-* /opt/paraview; \\\n fi\n\nENV PATH \"/opt/paraview/bin:$PATH\"\n\n# Build the executables used in the tutorial\nRUN if [ \"$TARGETARCH\" = \"$BUILDARCH\" ] ; then \\\n cd spectre/build \\\n && make ${PARALLEL_MAKE_ARG} ExportCoordinates3D \\\n && make ${PARALLEL_MAKE_ARG} EvolveScalarAdvection2D \\\n ; fi\n\nRUN pip3 --no-cache-dir install jupyterlab\n\n# Used for compiling the static executables and libraries during CI so that we\n# can release statically linked versions of our executables and libraries\n# for other groups to use.\nFROM sxscollaboration/spectre:dev1804 AS deploy_static_execs_and_libs\nARG BUILDARCH\nARG TARGETARCH\nARG UBUNTU_VERSION=18.04\nARG PARALLEL_MAKE_ARG=-j4\n\nWORKDIR /work\n\nCOPY . spectre/\n\n# Build SpECTRE with as many static libraries as possible. Because we cannot\n# statically link to glibc (it is unsupported and causes a lot of undefined\n# behavior) we build using Ubuntu 18.04 to support a fairly old version of\n# glibc.\nRUN if [ ${UBUNTU_VERSION} != 18.04 ] && [ \"$TARGETARCH\" != \"amd64\" ]; then \\\n echo \"Must use Ubuntu 18.04 with AMD64 for deploying static execs\" \\\n && exit 1; fi \\\n && mkdir spectre/build && cd spectre/build \\\n && cmake \\\n -D CMAKE_C_COMPILER=gcc-10 \\\n -D CMAKE_CXX_COMPILER=g++-10 \\\n -D CMAKE_Fortran_COMPILER=gfortran-10 \\\n -D CMAKE_BUILD_TYPE=Release \\\n -D DEBUG_SYMBOLS=OFF \\\n -D BUILD_PYTHON_BINDINGS=OFF \\\n -D MEMORY_ALLOCATOR=SYSTEM \\\n -D BUILD_SHARED_LIBS=OFF \\\n -D ENABLE_PARAVIEW=OFF \\\n -D Boost_USE_STATIC_LIBS=ON \\\n -D BLA_STATIC=ON \\\n -D GSL_STATIC=ON \\\n -D HDF5_USE_STATIC_LIBRARIES=ON \\\n -D SPECTRE_Fortran_STATIC_LIBS=ON \\\n -D YAMLCPP_STATIC_LIBRARY=ON \\\n -D USE_GIT_HOOKS=OFF \\\n -D OVERRIDE_ARCH=haswell \\\n -D USE_LD=gold \\\n -D gfortran=/usr/lib/gcc/x86_64-linux-gnu/9/libgfortran.a \\\n -D quadmath=/usr/lib/gcc/x86_64-linux-gnu/9/libquadmath.a \\\n -D BUILD_DOCS=OFF \\\n -D USE_CCACHE=OFF \\\n .. \\\n && make ${PARALLEL_MAKE_ARG} CharacteristicExtract PreprocessCceWorldtube \\\n WriteCceWorldtubeCoordsToFile \\\n && ctest -LE unit -R CharacteristicExtract -E KleinGordon\n" }, { "path": "docs/.nojekyll", "content": "" }, { "path": "docs/CODE_OF_CONDUCT.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# SpECTRE Code of Conduct {#code_of_conduct}\n\nWith the goal of supporting our community in doing the best science we\ncan, we expect that all contributors and maintainers of SpECTRE:\n\n- Behave professionally in a way that is welcoming and respectful to\nall participants.\n\n- Behave in a way that is free from any form of discrimination,\nharassment, or retaliation.\n\n- Treat each other with collegiality and respect and help to create a\nsupportive working environment.\n\nThis code of conduct is not an exhaustive list of things that you\nshould or should not do. Rather, take it in the spirit in which it’s\nintended — a guide to make it easier to communicate and participate in\nthe community.\n\nThis code of conduct applies to all spaces managed by the SpECTRE\nproject. This includes Slack channels, wikis, mailing lists, issue\ntrackers, pull request comments, SpECTRE project events, and any other\nforums created by the project for communication. It applies to all of\nyour communication and conduct in these spaces, including emails,\nchats, things you say, slides, videos, posters, signs, or even\nt-shirts you display in these spaces. In addition, violations of this\ncode outside these spaces may, in rare cases, affect a person’s\nability to participate within them, when the conduct amounts to an\negregious violation of this code.\n\nIf you believe someone is violating the code of conduct, we ask that\nyou report it by emailing conduct@spectre-code.org. For more details\nplease see our \\ref reporting_guide \"Reporting Guide\". If you would\nrather not formally report your concern, you should feel free to\ndiscuss it informally and confidentially with one of the project\nleaders.\n\nMore specifically, we expect members of the SpECTRE community to:\n\n- Be friendly and patient. During teleconferences and meetings,\nparticipants who wish to speak should feel free to type “hand up” or\nsimilar in the comment box, as needed, to get the chairs’\nattention. Meeting/teleconference chairs are encouraged to make space\nfor those unfamiliar with the topic of discussion to ask questions and\nengage.\n\n- Be welcoming. We strive to be a community that welcomes and supports\npeople of all backgrounds and identities. This includes, but is not\nlimited to members of any race, ethnicity, culture, national origin,\ncolour, immigration status, social and economic class, educational\nlevel, sex, sexual orientation, gender identity and expression, age,\nsize, family status, political belief, religion or lack thereof, and\nmental and physical ability.\n\n- Be considerate. Your work will be used by other people, and you in\nturn will depend on the work of others. Any decision you take will\naffect users and colleagues, and you should take those consequences\ninto account. Remember that we are a world-wide community, so you\nmight not be communicating in someone else’s primary language.\n\n- Be respectful. Not all of us will agree all the time, but\ndisagreement is no excuse for poor behavior and poor manners. We might\nall experience some frustration now and then, but we cannot allow that\nfrustration to turn into a personal attack. It is important to\nremember that a community where people feel uncomfortable or\nthreatened is not a productive one. Members of the SpECTRE community\nshould be respectful when dealing with other members as well as with\npeople outside the community.\n\n- Be careful in the words that you choose and be kind to others. Do\nnot insult or put down other participants. Harassment and other\nexclusionary behavior aren’t acceptable. This includes, but is not\nlimited to:\n - Violent threats or language directed against another person.\n - Discriminatory jokes and language.\n - Posting sexually explicit or violent material.\n - Posting (or threatening to post) other people’s personally\n identifying information (“doxing”).\n - Personal insults, especially those using racist or sexist terms.\n - Unwelcome sexual attention.\n - Advocating for, or encouraging, any of the above behavior. In\ngeneral, if someone asks you to stop, then stop. Persisting in such\nbehavior after being asked to stop is considered harassment.\n\n- When we disagree, try to understand why. Disagreements, both social\nand technical, happen all the time, and SpECTRE is no exception. It is\nimportant that we resolve disagreements and differing views\nconstructively. Remember that we are different. The strength of\ncommunities comes from having a varied community, people from a wide\nrange of backgrounds. Different people have different perspectives on\nissues. Being unable to understand why someone holds a viewpoint does\nnot mean that they are wrong. Do not forget that it is human to err\nand blaming each other does not get us anywhere. Instead, focus on\nhelping to resolve issues and learning from mistakes.\n\n### Attribution\n\nThis Code of Conduct is adapted from the [SXS Collaboration Code of\nConduct](https://www.black-holes.org/sxs_code_of_conduct.pdf), which\nis based on a draft of the [LLVM Code of\nConduct](https://llvm.org/docs/CodeOfConduct.html) which is adapted\nfrom [Django Project Code of\nConduct](https://www.djangoproject.com/conduct/) which used text from\nthe [Speak Up! Code of\nConduct](http://web.archive.org/web/20141109123859/http://speakup.io/coc.html).\n" }, { "path": "docs/CONTRIBUTING.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n\n# Contributing to SpECTRE {#contributing_to_spectre}\n\n\\tableofcontents\n\n# Contributing to SpECTRE {#contributing_to_spectre_2}\n\nThe following is a set of guidelines for contributing to SpECTRE,\nwhich is hosted in the [Simulating eXtreme Spacetimes\nOrganization](https://github.com/sxs-collaboration) on GitHub.\n\n## Code of Conduct\n\nThis project and everyone participating in it is governed by the \\ref\ncode_of_conduct \"SpECTRE Code of Conduct\". By participating, you are\nexpected to uphold this code. Please report possible violations of the\ncode of conduct to conduct@spectre-code.org.\n\n## What should I know before I get started? {#getting-started}\n\nSpECTRE is being developed in support of our collaborative Simulating\neXtreme Spacetimes (SXS) research program into the multi-messenger\nastrophysics of neutron star mergers, core-collapse supernovae, and\ngamma-ray bursts. As such, almost all of the current contributors to\nSpECTRE are members of SXS institutions, and a large amount of\ndiscussion about SpECTRE is done in internal SXS meetings. If you are\na member of SXS and wish to get involved, please contact one of the\nproject leaders.\n\nIn the future, we hope that SpECTRE can be applied to problems across\ndiscipline boundaries, and that it can be a true community code. At\nthe present time, however, SpECTRE cannot yet solve realistic\nproblems, and broad overview documentation is in an early, incomplete\nstage. Therefore, if you are not a member of SXS, but are interested\nin contributing to SpECTRE, we strongly encourage you to contact us at\nquestions@spectre-code.org to discuss possible contributions.\n\n## How Can I Contribute? {#how-can-i-contribute}\n\n### Reporting Bugs {#reporting-bugs}\n\nThis section guides you through submitting a bug report for\nSpECTRE. Following these guidelines helps maintainers and the\ncommunity understand your report, reproduce the behavior, and find\nrelated reports.\n\nBefore creating bug reports, please **perform a\n[search](https://github.com/sxs-collaboration/spectre/issues)** to see\nif the problem has already been reported. If it has **and the issue is\nstill open**, please add a comment to the existing issue instead of\nopening a new one.\n\n> **Note:** If you find a **Closed** issue that seems like it is the\n> same thing that you're experiencing, please open a new issue and\n> include a link to the original issue in the body of your new one.\n\n#### How Do I Submit A (Good) Bug Report? {#submit-bug-report}\n\nBugs are tracked as [GitHub\nissues](https://guides.github.com/features/issues/). When you are\ncreating a bug report, please **include as many details as\npossible**. Please fill out the template completely. The provided\ninformation helps us resolve issues faster.\n\nExplain the problem and include additional details to help maintainers\nreproduce the problem:\n\n* **Use a clear and descriptive title** for the issue to identify the\n problem.\n* **Describe the exact steps which reproduce the problem** in as much\n detail as possible. For example, start by explaining how you started\n SpECTRE, e.g. the exact command you used in the terminal, or the\n contents of the batch job script you used.\n* **Describe the behavior you observed after following the steps** and\n point out what exactly is the problem with that behavior.\n* **Explain which behavior you expected to see instead and why.**\n\nProvide more context by answering these questions:\n\n* **Can you reproduce the problem in both debug and release mode?**\n(this is controlled by the CMake flag `CMAKE_BUILD_TYPE`)\n* **Did the problem start happening recently** (e.g. after updating to\n a new version/commit of SpECTRE) or was this always a problem?\n* If the problem started happening recently, **can you reproduce the\n problem in an older version/commit?** What's the most recent\n version/commit in which the problem doesn't happen?\n* **Can you reliably reproduce the issue?** If not, provide details\n about how often the problem happens and under which conditions it\n normally happens.\n* **Can you reproduce the problem on another machine?**\n* **Can you reproduce the problem in the docker container?** (see the\n \\ref installation \"Installation notes\")\n\nInclude details about your configuration and environment:\n\n* **Add as an attachment** (or add the contents of) the following:\n - The text output by SpECTRE (including any stack trace)\n - The input file(s)\n - $SPECTRE_BUILD_DIR/BuildInfo.txt\n* **What is the name and version of the OS you're using**?\n* If possible (for SXS computers or HPC systems), a **path to a run\n directory** that is accessible by SpECTRE core developers.\n\n### Suggesting Enhancements {#suggesting-enhancements}\n\nThis section guides you through submitting an enhancement suggestion\nfor SpECTRE, including completely new features and minor improvements\nto existing functionality. Following these guidelines helps\nmaintainers and the community understand your suggestion and find\nrelated suggestions.\n\nBefore creating enhancement suggestions, please **perform a\n[search](https://github.com/sxs-collaboration/spectre/issues)** to see\nif the enhancement has already been suggested. If it has, add a\ncomment to the existing issue instead of opening a new one.\n\n#### How Do I Submit A (Good) Enhancement Suggestion? {#submit-enhancement}\n\nEnhancement suggestions are tracked as [GitHub\nissues](https://guides.github.com/features/issues/). When you are\ncreating an enhancement suggestion, please **include as many details\nas possible** as you fill in the template.\n\n* **Use a clear and descriptive title** for the issue to identify the\n suggestion.\n* **Provide a step-by-step description of the suggested enhancement**\n in as many details as possible.\n* **Explain why this enhancement would be useful** to most SpECTRE users.\n\n### Your First Code Contribution {#first-code-contribution}\n\nUnsure where to begin contributing to SpECTRE? You can start by\nlooking through these `good first issue` and `help wanted` issues:\n\n* [Good first issues][good-first-issue] - issues which should only\n require a few lines of code, and a test or two.\n* [Help wanted issues][help-wanted] - issues which should be a bit\n more involved than `good first issue`s.\n\n#### Local development {#local-development}\n\nSpECTRE can be developed locally. For instructions on how to do this,\nsee the following sections in the [SpECTRE\ndocumentation](https://spectre-code.org/):\n\n* [Installing SpECTRE](installation.html)\n* [Running Status Checks\n Locally](github_actions_guide.html#perform-checks-locally)\n\n## Pull Requests {#pull-requests}\n\nCode contributions to SpECTRE follow a [pull request\nmodel](https://help.github.com/articles/about-pull-requests/)\n\nThe process described here has several goals:\n\n- Maintain SpECTRE's code and documentation quality\n- Reach science goals in a timely manner\n- Fix problems that are important to users\n- Engage the community in working toward the best possible code\n- Enable a sustainable system for SpECTRE's maintainers to review\n contributions\n\nPlease follow these steps to have your contribution considered by the\nmaintainers:\n\n1. Follow the \\ref code_review_guide \"code review guidelines\", the\n \\ref writing_unit_tests \"guide to writing unit tests\", and the \\ref\n writing_good_dox \"guide to writing documentation\"\n2. Follow all instructions in the pull request template. Reference\n related issues and pull requests.\n3. After you submit your pull request, verify that all [status\n checks](https://help.github.com/articles/about-status-checks/) are\n passing\n\n > If a status check is failing, and you believe that the failure is\n > unrelated to your change, please leave a comment on the pull\n > request explaining why you believe the failure is unrelated. A\n > maintainer will re-run the status check for you. If we conclude\n > that the failure was a false positive, then we will open an issue\n > to track that problem with our status check suite.\n\n Only those status check failures that occur in the containerized build\n environment are your responsibility to fix. If you encounter an issue with a\n status check that runs in an environment that you do not have access to, e.g.\n on macOS or on a supercomputer, please notify\n `@sxs-collaboration/spectre-core-devs`. They will refer the issue to a person\n who has access to that environment. Unless requested by the reviewers, the PR\n will not be held up until the issue is resolved.\n\nWhile the prerequisites above must be satisfied prior to having your\npull request reviewed, the reviewers may ask you to complete\nadditional design work, tests, or other changes before your pull\nrequest can be ultimately accepted.\n\n## How SpECTRE pull request reviews are conducted {#pull-request-reviews}\n\n> Note that these are guidelines and not rigid rules.\n\nPlease make your pull requests as small as reasonably possible, as\nsmaller pull requests are easier to review. In general, longer pull\nrequests take longer to review, with the time scaling exponentially\nwith the number of lines changed. Therefore if your pull request is\ntoo large, we may ask you to break it up into several smaller pull\nrequests.\n\nIf you would like feedback on a pull request prior to it being ready\nfor formal review, please open it\n[in draft mode](https://github.blog/2019-02-14-introducing-draft-pull-requests/)\nand [request reviews][request-reviews] from whomever you wish to get feedback\nfrom. As long as the PR is in draft mode it will not be reviewed, aside from the\nfeedback requested.\n\n> Below, days mean business days, so if the time period includes the\n> weekend, add two days, and for major holidays add a day.\n> Furthermore, most of us are academics, and we occasionally go to\n> conferences which may lead to delays in the review process. Also do\n> not expect much to happen between December 20th and January 3rd.\n\nMost pull requests submitted to SpECTRE will be reviewed in the\nfollowing manner:\n\n- Within two days, one of the [SpECTRE core developers](#core-developers) will\n either review the PR or assign reviewers. If this has not happened after two\n days, please [request a review][request-reviews]\n and select the `@sxs-collaboration/spectre-core-devs` team. Also feel free to\n [ping the core developers][github-ping] (e.g\n `@sxs-collaboration/spectre-core-devs please assign reviewers`) if they fail\n to respond in a timely manner.\n- Assigned reviewers should either confirm that they are able to review (by\n reviewing or providing a reasonable timeframe for their review) or decline\n within two days so another reviewer can be assigned.\n- Anyone is welcome to self-assign themselves as a reviewer.\n- Assigned reviewers should submit their review in as timely a manner\n as possible.\n- Anyone can request changes within either the first two days of the\n pull request, or within a day after the initial reviews of the\n assigned reviewers. After this period, only the assigned reviewers\n can request changes, unless someone believes the code is wrong.\n Non-reviewers are allowed to make comments, which the pull request\n author is encouraged to address. Alternatively the author can\n create an issue with the suggested changes, assigned to themselves,\n which would then be addressed in a subsequent pull request by the\n author.\n- If any requested change is unclear to the author, they should ping\n the reviewer and ask for clarification. Authors and reviewers are\n encouraged to talk to one another (in person, via Google hangout, or\n some other verbal method if possible) to resolve any issues.\n- Reviewers are encouraged to [ping others \\@GITHUB_USERNAME][github-ping] to\n get opinions on code they are unsure about.\n- It is permissible to have a group code review led by one of the\n reviewers. The reviewer should comment on who was present at the\n group review.\n- If necessary, pull requests can also be discussed at one of the\n weekly SpECTRE meetings.\n- If changes are requested, the author should fix all of them in one\n or more fixup commits (where the first line of the commit message\n should begin with `fixup`) and push them to the PR branch.\n Fixup commits make reviews significantly faster because the reviewers don't\n have to review the full PR again, but only the parts that changed.\n- After pushing fixup commits, the author should\n [re-request reviews from the reviewers][request-reviews].\n They can also ping the reviewers that the pull request is updated.\n- Once a pull request is updated, the reviewers should either request further\n changes or approve the PR.\n- Once all reviewers have approved the PR or given the okay to squash, the\n author should [rebase on develop and then squash their\n commits](https://git-scm.com/book/en/v2/Git-Tools-Rewriting-History)\n into one or more self-contained commits (such that the code will\n compile and pass all tests after each commit). The squashed commits\n will need to be force pushed.\n- Once all reviewers have approved the pull request, someone should\n ping the `@sxs-collaboration/spectre-core-devs`. If one of the\n original reviewers is a core developer, this is not necessary and\n the core developer can merge the pull request.\n- One of the core developers will perform a final cursory review,\n requesting changes only for major problems, and commenting on other\n possible changes.\n- The pull request author should address all final requested changes\n and may either also fix final suggested changes, or create an issue\n with the suggested changes, which will be addressed in a subsequent\n pull request by the author.\n- The SpECTRE core developer will merge the pull request once all comments have\n been addressed, all reviewers have approved the PR, the code passes CI and all\n pull requests the pull request depends on have been merged. When approvals are\n dismissed by minor changes, such as rebasing, squashing fixup commits or\n adding a missing include, the core developer may merge the PR without waiting\n for all reviewers to re-approve the PR.\n\nIn addition to the guidelines above, we apply the following exceptions based on\nthe type of change:\n\n- Critical bug fixes (i.e. the code is broken) can be merged after two expedited\n reviews by SpECTRE core developers. If necessary, an issue can be created if\n further changes are desired.\n- PRs that add documentation don't need to be perfect, since having some\n docs is better than having none. Reviewers should approve after one or at most\n two rounds of review and allow further minor changes to be done in follow-ups.\n- \"Small\" or \"trivial\" PRs can be merged immediately by core developers.\n Examples for such PRs are:\n\n - Fixing typos in documentation or adding (small amounts of) documentation\n - Fixing missing includes or missing linked libraries\n - Adding Python bindings\n - Formatting code\n - Refactoring, renaming or moving files with no change in functionality\n (unless potentially controversial)\n\n It is the reviewing core developer's responsibility to decide if the PR is\n \"small\" or \"trivial\" enough to merge immediately. If they are unsure, they\n should fall back to the usual procedure of giving people two days to assign\n themselves as reviewers and/or reach out to whoever they think might want to\n review the PR.\n- Pull requests that are designated `new design` are expected to have a longer\n review period, including discussions during weekly SpECTRE meetings. SpECTRE\n core developers will provide reasonable review deadlines once the new design\n is finalized.\n\n### Git Commit Message Guidelines {#git-commit-messages}\n\n* Use the present tense (\"Add feature\" not \"Added feature\")\n* Use the imperative mood (\"Move cursor to...\" not \"Moves cursor to...\")\n* Limit the first line to 72 characters or less\n* If needed, a blank second line followed by a more complete description\n\n### SpECTRE core developers {#core-developers}\n\nSpECTRE core developers are people who are very familiar with the\nentire code, comfortable with modern C++, and willing to take the\nresponsibility of overseeing the code as a whole.\n[Current SpECTRE core\ndevelopers](https://github.com/orgs/sxs-collaboration/teams/spectre-core-devs)\ncan be pinged on GitHub at `@sxs-collaboration/spectre-core-devs`. It\nis expected that as more contributors become familiar with SpECTRE,\nadditional people will be added to the list of core developers.\n\n\n[good-first-issue]:https://github.com/sxs-collaboration/spectre/issues?q=is%3Aopen+is%3Aissue+label%3A%22good+first+issue%22+sort%3Acomments-desc\n[help-wanted]:https://github.com/sxs-collaboration/spectre/issues?q=is%3Aopen+is%3Aissue+label%3A%22help+wanted%22+sort%3Acomments-desc\n[github-ping]:https://github.blog/2011-03-23-mention-somebody-they-re-notified/\n[request-reviews]:https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/proposing-changes-to-your-work-with-pull-requests/requesting-a-pull-request-review\n" }, { "path": "docs/Changelog.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n# Changelog {#changelog}\n\nThe complete changelog for released versions of the code is available on GitHub:\n\n- [Changelog for releases on GitHub](https://github.com/sxs-collaboration/spectre/releases)\n\nChanges since the last release are printed below.\n" }, { "path": "docs/Contributing/Contributing.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Contributing to SpECTRE {#contributing_index}\n\n- \\subpage contributing_to_spectre\n- \\subpage code_of_conduct\n- \\subpage reporting_guide\n" }, { "path": "docs/Contributing/ReportingGuide.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# SpECTRE Code of Conduct - Reporting Guide {#reporting_guide}\n\n\\tableofcontents\n\nIf you believe someone is violating the code of conduct, you can\nalways file a report by emailing conduct@spectre-code.org, or discuss\nit informally and confidentially with one of the project leaders.\n**All reports will be kept confidential.**\n\nIf you believe anyone is in physical danger, please notify appropriate\nlaw enforcement first. If you are unsure what law enforcement agency\nis appropriate, please include this in your report and we will attempt\nto notify them.\n\nReports of violations of the code of conduct can be as formal or\ninformal as needed for the situation at hand. If possible, please\ninclude as much information as you can. If you feel comfortable,\nplease consider including:\n- Your contact info (so we can get in touch with you if we need to\n follow up).\n- Names (real, nicknames, or pseudonyms) of any individuals\ninvolved. If there were other witnesses besides you, please try to\ninclude them as well.\n- When and where the incident occurred. Please be as specific as\n possible.\n- Your account of what occurred. If there is a publicly available\nrecord (e.g. a mailing list archive or Slack logs) please include a\nlink.\n- Any extra context you believe existed for the incident.\n- If you believe this incident is ongoing.\n- Any other information you believe we should have.\n\n### What happens after you file a report?\n\nYou will receive an email from the Code of Conduct Committee or\nproject leader(s) you contacted, acknowledging receipt within 24 hours\n(and we will aim to respond much quicker than that). We will review\nthe incident and try to determine:\n- What happened and who was involved.\n- Whether this event constitutes a code of conduct violation.\n- Whether this is an ongoing situation, or if there is a threat to\n anyone’s physical safety.\n\nOnce the Code of Conduct Committee or contacted project leader(s) have\na complete account of the events we will make a decision on how to\nrespond, possibly in consultation with the full Executive Committee\n(excluding anyone involved in the incident). Responses may include:\n- Nothing, if we determine no violation occurred or it has already\n been appropriately resolved.\n- Providing either moderation or mediation to ongoing interactions\n (where appropriate, safe, and desired by both parties).\n- A private reprimand from the working group to the individuals\n involved.\n- An imposed vacation (i.e. asking someone to “take a week off” from a\n mailing list or Slack).\n- Escalation to the appropriate institutions.\n- Involvement of relevant law enforcement if appropriate.\n\nIf the situation is not resolved within one week, we’ll respond within\none week to the original reporter with an update and explanation.\nOnce we’ve determined our response, we will separately contact the\noriginal reporter and other individuals to let them know what actions\n(if any) we’ll be taking. We will take into account feedback from the\nindividuals involved on the appropriateness of our response, but we\ndon’t guarantee we’ll act on it.\n\n### Code of Conduct Committee\n\nThe current members of the Code of Conduct Committee (and the only\npeople that see emails sent to conduct@spectre-code.org) are:\n- Saul Teukolsky\n- Harald Pfeiffer\n\nSpECTRE is being developed in support of our collaborative Simulating\neXtreme Spacetimes (SXS) research program into the multi-messenger\nastrophysics of neutron star mergers, core-collapse supernovae, and\ngamma-ray bursts. As such, it falls under the managerial oversight of\nthe SXS Executive Committee whose current members are:\n- Matthew Duez\n- Francois Foucart\n- Lawrence Kidder\n- Geoffrey Lovelace\n- Harald Pfeiffer\n- Mark Scheel\n- Leo Stein\n- Saul Teukolsky\n- Aaron Zimmerman\n\n" }, { "path": "docs/Dependencies.bib", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# When editing this file, please follow the guidelines in\n# https://spectre-code.org/writing_good_dox.html#writing_dox_citations.\n\n@INPROCEEDINGS{Blaze1,\n author = {Iglberger, Klaus and Hager, Georg and Treibig, Jan and Rüde,\n Ulrich},\n booktitle = {2012 International Conference on High Performance Computing \\&\n Simulation (HPCS)},\n title = {High performance smart expression template math libraries},\n year = {2012},\n pages = {367-373},\n doi = {10.1109/HPCSim.2012.6266939}\n}\n\n@article{Blaze2,\n author = {Iglberger, Klaus and Hager, Georg and Treibig, Jan and\n R\\\"{u}de, Ulrich},\n title = {Expression Templates Revisited: A Performance Analysis of\n Current Methodologies},\n journal = {SIAM Journal on Scientific Computing},\n volume = {34},\n number = {2},\n pages = {C42-C69},\n year = {2012},\n doi = {10.1137/110830125},\n URL = {https://doi.org/10.1137/110830125}\n}\n\n@software{Charmpp1,\n author = {Kale, Laxmikant and Acun, Bilge and Bak, Seonmyeong and Becker,\n Aaron and Bhandarkar, Milind and Bhat, Nitin and Bhatele, Abhinav\n and Bohm, Eric and Bordage, Cyril and Brunner, Robert and Buch,\n Ronak and Chakravorty, Sayantan and Chandrasekar, Kavitha and Choi,\n Jaemin and Denardo, Michael and DeSouza, Jayant and Diener,\n Matthias and Dokania, Harshit and Dooley, Isaac and Fenton, Wayne\n and Galvez, Juan and Gioachin, Fillipo and Gupta, Abhishek and\n Gupta, Gagan and Gupta, Manish and Gursoy, Attila and Harsh, Vipul\n and Hu, Fang and Huang, Chao and Jagathesan, Narain and Jain,\n Nikhil and Jetley, Pritish and Jindal, Prateek and Kanakagiri,\n Raghavendra and Koenig, Greg and Krishnan, Sanjeev and Kumar,\n Sameer and Kunzman, David and Lang, Michael and Langer, Akhil and\n Lawlor, Orion and Wai Lee, Chee and Lifflander, Jonathan and Mahesh,\n Karthik and Mendes, Celso and Menon, Harshitha and Mei, Chao and\n Meneses, Esteban and Mikida, Eric and Miller, Phil and Mokos, Ryan\n and Narayanan, Venkatasubrahmanian and Ni, Xiang and Nomura, Kevin\n and Paranjpye, Sameer and Ramachandran, Parthasarathy and Ramkumar,\n Balkrishna and Ramos, Evan and Robson, Michael and Saboo, Neelam and\n Saletore, Vikram and Sarood, Osman and Senthil, Karthik and Shah,\n Nimish and Shu, Wennie and B. Sinha, Amitabh and Sun, Yanhua and\n Sura, Zehra and Totoni, Ehsan and Varadarajan, Krishnan and\n Venkataraman, Ramprasad and Wang, Jackie and Wesolowski, Lukasz and\n White, Sam and Wilmarth, Terry and Wright, Jeff and Yelon, Joshua\n and Zheng, Gengbin},\n doi = {10.5281/zenodo.3370873},\n month = {Aug},\n title = {{The Charm++ Parallel Programming System}},\n url = {https://charm.cs.illinois.edu},\n year = {2019}\n}\n\n@software{Charmpp2,\n author = {Laxmikant Kale and Bilge Acun and Seonmyeong Bak and Aaron\n Becker and Milind Bhandarkar and Nitin Bhat and Abhinav\n Bhatele and Eric Bohm and Cyril Bordage and Robert Brunner and\n Ronak Buch and Sayantan Chakravorty and Kavitha Chandrasekar\n and Jaemin Choi and Michael Denardo and Jayant DeSouza and\n Matthias Diener and Harshit Dokania and Isaac Dooley and Wayne\n Fenton and Zane Fink and Juan Galvez and Pathikrit Ghosh and\n Fillipo Gioachin and Abhishek Gupta and Gagan Gupta and Manish\n Gupta and Attila Gursoy and Vipul Harsh and Fang Hu and Chao\n Huang and Narain Jagathesan and Nikhil Jain and Pritish Jetley\n and Prateek Jindal and Raghavendra Kanakagiri and Greg Koenig\n and Sanjeev Krishnan and Sameer Kumar and David Kunzman and\n Michael Lang and Akhil Langer and Orion Lawlor and Chee Wai\n Lee and Jonathan Lifflander and Karthik Mahesh and Celso\n Mendes and Harshitha Menon and Chao Mei and Esteban Meneses\n and Eric Mikida and Phil Miller and Ryan Mokos and\n Venkatasubrahmanian Narayanan and Xiang Ni and Kevin Nomura\n and Sameer Paranjpye and Parthasarathy Ramachandran and\n Balkrishna Ramkumar and Evan Ramos and Michael Robson and\n Neelam Saboo and Vikram Saletore and Osman Sarood and Karthik\n Senthil and Nimish Shah and Wennie Shu and Amitabh B. Sinha\n and Yanhua Sun and Zehra Sura and Justin Szaday and Ehsan\n Totoni and Krishnan Varadarajan and Ramprasad Venkataraman and\n Jackie Wang and Lukasz Wesolowski and Sam White and Terry\n Wilmarth and Jeff Wright and Joshua Yelon and Gengbin Zheng},\n title = {{UIUC-PPL}/charm: {Charm++} version 7.0.0},\n month = oct,\n year = 2021,\n publisher = {Zenodo},\n version = {v7.0.0},\n doi = {10.5281/zenodo.5597907},\n url = {https://doi.org/10.5281/zenodo.5597907}\n}\n\n@incollection{Charmpp3,\n title = {Charm++: Parallel programming with message-driven objects},\n author = {Kale, Laxmikant V and Krishnan, Sanjeev},\n booktitle = {Parallel programming using C++},\n editor = {Gregory V. Wilson and Paul Lu},\n publisher = {The MIT Press},\n pages = {175--213},\n year = 1996,\n}\n\n@book{Gsl,\n title = {{GNU} Scientific Library Reference Manual},\n author = {Galassi, M. and others},\n publisher = {Network Theory Ltd.},\n isbn = {9780954612078},\n year = {2009},\n edition = {3}\n}\n\n@software{Hdf5,\n author = {{The HDF Group}},\n title = \"{Hierarchical Data Format, version 5}\",\n year = {1997-2023},\n note = {https://www.hdfgroup.org/HDF5/}\n}\n\n@ARTICLE{Libsharp,\n author = {{Reinecke}, M. and {Seljebotn}, D.~S.},\n title = \"{Libsharp - spherical harmonic transforms revisited}\",\n journal = {Astronomy and Astrophysics},\n keywords = {methods: numerical, cosmic background radiation, large-scale\n structure of Universe, Physics - Computational Physics},\n year = 2013,\n month = jun,\n volume = {554},\n eid = {A112},\n pages = {A112},\n doi = {10.1051/0004-6361/201321494},\n archivePrefix ={arXiv},\n eprint = {1303.4945},\n primaryClass = {physics.comp-ph},\n adsurl = {https://ui.adsabs.harvard.edu/abs/2013A&A...554A.112R},\n adsnote = {Provided by the SAO/NASA Astrophysics Data System}\n}\n\n@inproceedings{Libxsmm,\n author = {Heinecke, Alexander and Henry, Greg and Hutchinson, Maxwell\n and Pabst, Hans},\n title = {{LIBXSMM}: {Accelerating} Small Matrix Multiplications by\n Runtime Code Generation},\n year = {2016},\n isbn = {9781467388153},\n publisher = {IEEE Press},\n booktitle = {Proceedings of the International Conference for High\n Performance Computing, Networking, Storage and Analysis},\n articleno = {84},\n numpages = {11},\n pages = {1-11},\n location = {Salt Lake City, Utah},\n series = {SC '16}\n}\n\n@Article{MatplotLib1,\n Author = {Hunter, J. D.},\n Title = {Matplotlib: A 2D graphics environment},\n Journal = {Computing in Science \\& Engineering},\n Volume = {9},\n Number = {3},\n Pages = {90--95},\n abstract = {Matplotlib is a 2D graphics package used for Python for\n application development, interactive scripting, and\n publication-quality image generation across user interfaces\n and operating systems.},\n publisher = {IEEE COMPUTER SOC},\n doi = {10.1109/MCSE.2007.55},\n year = 2007\n}\n\n@software{MatplotLib2,\n author = {Thomas A Caswell and Michael Droettboom and Antony Lee and\n John Hunter and Eric Firing and Elliott Sales de Andrade and\n Tim Hoffmann and David Stansby and Jody Klymak and Nelle\n Varoquaux and Jens Hedegaard Nielsen and Benjamin Root and\n Ryan May and Phil Elson and Darren Dale and Jae-Joon Lee and\n Jouni K. Seppänen and Damon McDougall and Andrew Straw and\n Paul Hobson and Christoph Gohlke and Tony S Yu and Eric Ma and\n Adrien F. Vincent and Steven Silvester and Charlie Moad and\n Nikita Kniazev and hannah and Elan Ernest and Paul Ivanov},\n title = {matplotlib/matplotlib: {REL:} v3.3.0},\n month = jul,\n year = 2020,\n publisher = {Zenodo},\n version = {v3.3.0},\n doi = {10.5281/zenodo.3948793},\n url = {https://doi.org/10.5281/zenodo.3948793}\n}\n\n@Article{NumPy,\n title = {Array programming with {NumPy}},\n author = {Charles R. Harris and K. Jarrod Millman and St{\\'{e}}fan J.\n van der Walt and Ralf Gommers and Pauli Virtanen and David\n Cournapeau and Eric Wieser and Julian Taylor and Sebastian\n Berg and Nathaniel J. Smith and Robert Kern and Matti Picus\n and Stephan Hoyer and Marten H. van Kerkwijk and Matthew Brett\n and Allan Haldane and Jaime Fern{\\'{a}}ndez del R{\\'{i}}o and\n Mark Wiebe and Pearu Peterson and Pierre G{\\'{e}}rard-Marchant\n and Kevin Sheppard and Tyler Reddy and Warren Weckesser and\n Hameer Abbasi and Christoph Gohlke and Travis E. Oliphant},\n year = {2020},\n month = sep,\n journal = {Nature},\n volume = {585},\n number = {7825},\n pages = {357--362},\n doi = {10.1038/s41586-020-2649-2},\n publisher = {Springer Science and Business Media {LLC}},\n url = {https://doi.org/10.1038/s41586-020-2649-2}\n}\n\n@book{Paraview1,\n author = {Ayachit, Utkarsh},\n title = {The ParaView Guide: A Parallel Visualization Application},\n year = {2015},\n isbn = {1930934300},\n publisher = {Kitware, Inc.},\n address = {Clifton Park, NY, USA},\n}\n\n@book{Paraview2,\n title = {{ParaView}: {An} end-user tool for large-data visualization},\n author = {J. Ahrens and Berk Geveci and C. Law},\n publisher = {Elsevier},\n isbn = {9780123875822},\n year = {2005}\n}\n\n@software{Pybind11,\n author = {Wenzel Jakob and Jason Rhinelander and Dean Moldovan},\n year = {2017},\n note = {https://github.com/pybind/pybind11},\n title = {pybind11 -- Seamless operability between C++11 and Python}\n}\n\n@software{Yamlcpp,\n title = {yaml-cpp},\n author = {Beder, Jesse and Woehlke, Matthew and Breitbart, Jens and\n Wolchok, Scott and Hackimov, Azamat H. and Snape, Jamie and\n Hamlet, Oliver and Novotny, Paul and Tambre, Raul and\n Reinhold, Stefan and Vaucher, Alain and Zaitsev, Alexander and\n Anokhin, Alexander and Karatarakis, Alexander and Maloney,\n Andy and Polukhin, Antony and Brandenburg, Craig M. and\n Ibanez, Dan and Gladkikh, Denis and Eich, Florian and Dumont,\n Guillaume and Trigg, Haydn and King, Jim and Frederico, Joel\n and Hamilton, Jonathan and Langley, Joseph and Hämäläinen,\n Lassi and Blair, Matt and Duggan, Michael Welsh and Wang, Olli\n and Stotko, Patrick and Levine, Peter and Bena, Petr and\n Cordoba, Rodrigo Hernandez and Schmidt, Ryan and Gottlieb,\n Simon Gene and Prilmeier, Franz and Zhang, Tanki and Ishi,\n Tatsuyuki and Lyngmo, Ted and Mataré, Victor and Konečný,\n Michael and USDOE},\n abstractNote = {A {YAML} parser and emitter in {C++}.},\n doi = {10.11578/dc.20220817.13},\n url = {https://www.osti.gov/biblio/1881863},\n year = {2009},\n month = {9}\n}\n" }, { "path": "docs/DevGuide/Amr.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n# Adaptive mesh refinement (AMR) {#dev_guide_amr}\n\n\\tableofcontents\n\n### Introduction\n\nSpECTRE implements a block-based anisotropic h-p adaptive mesh\nrefinement (AMR) algorithm. Currently AMR can only occur at global\nsynchronization points, but it is planned to remove this restriction\nin the future.\n\n\\warning AMR is still under active development. The elliptic\nexecutables fully support AMR. The evolution executables currently\nonly support p-adaptivity, and only when using a global time stepper,\nand only when using a DG method. The executable will abort with an\nERROR if local time stepping or h-refinement is done.\n\nHere is an overview of what is described in detail in the sections below:\n\n- \\ref dev_guide_amr_algorithm \"AMR Algorithm\": An overview of the\n parallel phases, actions, and components that are used to do\n adaptive mesh refinement.\n- \\ref dev_guide_amr_criteria \"AMR Criteria\": Describes the\n expectations and restrictions on concrete classes implementing\n adaptive mesh refinement criteria.\n- \\ref dev_guide_amr_policies \"AMR Policies\": Describes restrictions\n and assumptions of the current algorithm, and what would be\n required to relax them.\n- \\ref dev_guide_amr_projectors \"AMR Projectors\": Describes the\n requirements on concrete classes which project data to the new or\n modified elements after mesh refinement.\n- \\ref dev_guide_amr_metavariables \"AMR Metavariables\": Describes the\n code that needs to be added to the metavariables of an executable in\n order to enable adaptive mesh refinement.\n- \\ref dev_guide_amr_input_options \"Controlling AMR\": Describes the\n options in the input file that control the behavior of adaptive mesh\n refinement.\n\n### AMR Algorithm {#dev_guide_amr_algorithm}\n\nThe AMR algorithm requires communication via simple actions between\nthe elements of the array component that are responsible for the\nElement%s of the Domain and a singleton amr::Component. See \\ref\ndev_guide_parallelization_foundations\n\"Parallelization and Core Concepts\" for an overview of phases,\nactions, metavariables, and other SpECTRE parallelization concepts.\n\nCurrently the AMR algorithm is run over several phases when a phase\nchange is triggered by an executable. See \\ref\ndev_guide_amr_input_options \"Controlling AMR\" for how to control when\nthe AMR phases are triggered.\n\n#### Evaluating refinement criteria\n\nWhen AMR is triggered, the executable should enter\nParallel::Phase::EvaluateAmrCriteria. In this phase, the\namr::Component triggers the simple action\namr::Actions::EvaluateRefinementCriteria on each element of the array\ncomponent (specified by `metavariables::amr::element_array`). Each\nelement evaluates (in order) the user-specified refinement criteria,\neach of which returns a refinement decision in each logical dimension\nof the element represented as an amr::Flag. The overall refinement\ndecision in each logical dimension is obtained by taking the highest\npriority decision in the dimension over all criteria, where\namr::Flag::Split has the highest priority and amr::Flag::Join has the\nlowest. See \\ref dev_guide_amr_criteria \"AMR Criteria\" for more\ndetails on implementing criteria. Once the overall refinement\ndecision based on the refinement criteria is made, the decision may be\nmodified to satisfy the \\ref dev_guide_amr_policies \"AMR Policies\".\nFinally, the element sends its decision (and other information in\namr::Info) to its neighbors by calling the simple action\namr::Actions::UpdateAmrDecision.\n\nIn amr::Actions::UpdateAmrDecision, an element decides whether or not it\nneeds to update its own refinement decision (or other information in\namr::Info) based on decisions (or other information in amr::Info) sent\nby its neighbor. Possible reasons to update the refinement decision\nare, e.g., if a sibling neighbor does not want to join an element that\nhad initially decided to join, or if any of the amr::Policies would\nbe violated. If the refinement decision (or other information in\namr::Info) of the element changes, the element will send its\nupdated amr::Info to its neighbors.\n\nNote that simple actions are executed asynchronusly, so both\namr::Actions::EvaluateRefinementCriteria and\namr::Actions::UpdateAmrDecision have to handle the possibility that\nthey are executed out of order. For example,\namr::Actions::UpdateAmrDecision could be executed before\namr::Actions::EvaluateRefinementCriteria. Eventually all elements\nwill reach a state where they do not need to send new information to\ntheir neighbors, thus reaching a state of quiescence. When this\nhappens Parallel::Phase::EvaluateAmrCriteria ends. At this point all\nelements have reached a consensus on how the domain should be adapted,\nbut no changes have been made to the domain. In order to adjust the\ndomain, the executable should next start\nParallel::Phase::AdjustDomain.\n\n#### Adjusting the domain\n\nAt the beginning of Parallel::Phase::AdjustDomain, the amr::Component\ncalls amr::Actions::AdjustDomain on each element of the array\ncomponent (specified by `metavariables::amr::element_array`). If the\nelement wants to split in any dimension, it will call the simple\naction amr::Actions::CreateChild on the amr::Component in order to\ncreate new refined elements that will replace the existing element.\nIf the element wants to join in any dimension, it will either call\namr::Actions::CreateParent on the amr::Component (if it is the joining\nsibling with the lowest SegmentId in each dimension being joined) or\ndo nothing in order to create a single new coarsened element that will\nreplace multiple existing elements. If the element neither wants to\nsplit nor join in any dimension, then the element mutates items in its\ndb::DataBox. First the Element, Mesh and neighbor Mesh are updated.\nThen the element calls the\n\\ref dev_guide_amr_projectors \"AMR Projectors\" that will update all\nthe mutable items in the db::DataBox.\nFinally the amr::Info of the element and its neighbors are reset and\ncleared so they are ready for a future invocation of AMR.\n\nWhen amr::Actions::CreateChild is executed by the amr::Component, it\ncreates a new element in the `metavariables::amr::element_array`\npassing a Parallel::SimpleActionCallback that will be executed after\nthe new element is created. The callback will be either to call\namr::Actions::CreateChild again for the next child to be created, or\namr::Actions::SendDataToChildren which will be invoked on the element\nthat is being split. amr::Actions::SendDataToChildren will then\ninvoke amr::Actions::InitializeChild on each new child element,\npassing along all of the mutable items in its\ndb::DataBox. amr::Actions::SendDataToChildren will then deregister and\ndelete the element being split. amr::Actions::InitializeChild will\ncreate its Element, Mesh, and neighbor Mesh, and then call the \\ref\ndev_guide_amr_projectors \"AMR Projectors\" that will update all the\nmutable items in its db::DataBox.\n\nWhen amr::Actions::CreateParent is executed by the amr::Component, it\ncreates a new element in the `metavariables::amr::element_array`\npassing a Parallel::SimpleActionCallback that will be executed after\nthe new element is created. The callback will be\namr::Actions::CollectDataFromChildren which will be invoked on one\nof the elements that are joining.\namr::Actions::CollectDataFromChildren will then invoke either itself\non another element that is joining or amr::Actions::InitializeParent\non the new parent element, collecting all of the mutable items in each\njoining element's db::DataBox. amr::Actions::CollectDataFromChildren\nwill then deregister and delete the element that is\njoining. amr::Actions::InitializeParent will create its Element, Mesh,\nand neighbor Mesh, and then call the \\ref dev_guide_amr_projectors\n\"AMR Projectors\" that will update all the mutable items in its\ndb::DataBox.\n\nWhen all of the actions finish, a state of quiescence is reached.\nWhen this happens Parallel::Phase::AdjustDomain ends. The executable\nshould now either return to the phase which triggered AMR, or enter\nParallel::Phase::CheckDomain.\n\n### AMR Criteria {#dev_guide_amr_criteria}\n\nWhen amr::Actions::EvaluateRefinementCriteria is executed, for each\nelement, it loops over a list of criteria that is specified in the\ninput file options\n(See \\ref dev_guide_amr_input_options \"Controling AMR\").\nEach criterion must be an option-creatable class derived from\namr::Criterion (see its documentation for a list of requirements for\nthe derived classes). In particular, each criterion should compute an\narray of amr::Flag%s that represent the recommended refinemenent\nchoice in each logical dimension. These choices can be computed from\nany items in the db::DataBox of the element or additional compute\nitems specified by the criterion. It is expected that a criterion\nwill compute something and then either choose to recommend refinement,\nno change, or coarsening the element either in size (h-refinement) or\npolynomial order (p-refinement). A criterion does not need to handle\nanything that is enforced by the amr::Policies such as worry about\nbounds on the refinement level or number of grid points.\n\n### AMR Policies {#dev_guide_amr_policies}\n\nThe current AMR algorithm has a set of rules that are enforced after\nthe overall refinement choice is determined from the AMR criteria.\n\nThe following rules simplify the code:\n\n- An Element cannot join if it is splitting in any dimension. Instead\n any amr::Flag::Join is changed to amr::Flag::DoNothing. Relaxing\n this restriction would be a non-trivial change that would require\n more complicated logic in determining if neighboring elements can\n join, as well as an additional code path to handle the creation and\n initialization of the new elements. This should not be a significant\n restriction as in most cases when this would occur it is unlikely\n that the siblings of the Element would agree to a valid join.\n\n- In two or three spatial dimensions, there must be a 2:1 balance\n (i.e. within one refinement level) between neighbors in the\n dimension(s) parallel to the face of the element. Relaxing this\n restriction would be a significant change to the code as the\n code for communicating boundary corrections assumes 2:1 balance. In\n order to maintain 2:1 balance with neighboring elements, a choice of\n amr::Flag::Join may be changed to amr::Flag::DoNothing, and\n amr::Flag::DoNothing may be changed to amr::Flag::Split.\n\nThe following policies are among those controlled by input file\noptions (see \\ref dev_guide_amr_input_options \"Controlling AMR\" and\nthe documentation for amr::Policies):\n\n- Whether to do isotropic or anisotropic refinement. If isotropic\n refinement is done, the AMR decision in each dimension are changed\n to the decision of the dimension with the highest priority amr::Flag\n (i.e. amr::Flag::Split has the highest priority).\n\n- Whether or not to enforce 2:1 balance for the refinement level in\n the direction perpendicular to the face.\n\n- The minimum and maximum of the refinement level and the number of\n grid points. The actual bounds on these will be the stricter of\n those specified by the input file and those set by the code. For\n the number of grid points, the code bounds are set by\n Spectral::minimum_number_of_points and\n Spectral::maximum_number_of_points for the Spectral::Basis and\n Spectral::Quadrature of the Mesh. For the refinement level, the\n minimum is zero, and the maximum is set by\n `ElementId::max_refinement_level`.\n\n### AMR Projectors {#dev_guide_amr_projectors}\n\nAfter the grid adapts, the mutable items in the DataBox of new or\nexisting elements must be updated. The Element, Mesh, neighbor Mesh,\namr::Info, and neighbor amr::Info along with the items in\n`Parallel::Tags::distributed_object_tags` are automatically updated by\nthe AMR actions, but all other items must be explicitly updated via\nprojectors that conform to amr::protocols::Projector. If any mutable\nitem has not been explicitly handled by any of the projectors, a\n`static_assert` will be triggered listing the tags for the items that\nhave not been projected.\n\nWhen a new element is created, the items in its DataBox are default\nconstructed. Their Element, Mesh, and neighbor Mesh are mutated to\ntheir desired state. Then the AMR projectors are called, passing\nalong the items in the DataBox(es) from their splitting parent element\nor joining children elements. Existing elements first mutate their\nElement, Mesh, and neighbor Mesh, and then call the AMR projectors,\npassing along the old Element and Mesh.\n\nThe `return_tags` of each projector lists the tags for the items that\nthe projector mutates. From the pre-AMR state, the projector must\ncompute the post-AMR state of these items. Typically during\nParallel::Phase::Initialization, a group of items will be initialized\nby a specific action or mutator in the action\n`Initialization::Actions::InitializeItems`. Therefore it makes sense\nto create a projector that will handle the same group of items.\nHowever some items are initialized from input file options, while\nothers are left default initialized and not mutated by any\ninitialization action. These items will still need to be handled by\nsome projector. Two convenience projectors are provided:\namr::projectors::DefaultInitialize which value initializes the items\ncorresponding to the listed tags; and\namr::projectors::CopyFromCreatorOrLeaveAsIs that will either copy the\nitem from the parent (or children, asserting that all children agree)\nof a newly created element, or leave the item unmodified for an\nexisting element for the items corresponding to the listed tags.\n\nThe list of projectors is specified in\n`metavariables::amr::projectors` in the executable, and the projectors\nare evaluated in the order in which they are specified.\n\n### Enabling AMR for an executable {#dev_guide_amr_metavariables}\n\nIn order to enable AMR for an executable, the following changes need\nto be made in the metavariables:\n\n- The addition of a struct named `amr` such as the following example:\n```\nstruct amr : tt::ConformsTo<::amr::protocols::AmrMetavariables> {\n using element_array = dg_element_array;\n using projectors = tmpl::list<::amr::projectors::DefaultInitialize<\n domain::Tags::InitialExtents,\n domain::Tags::InitialRefinementLevels,\n evolution::dg::Tags::Quadrature>>;\n static constexpr bool keep_coarse_grids = false;\n };\n```\n\n where `element_array` specifies the array component on which AMR\n will operate and `projectors` is a type list of amr::projectors\n that govern how the items in the DataBox for the `element_array` are\n updated after refinement.\n\n- The addition of amr::Component to the `component_list` of the metavariables\n\n- The addition (or modification) of the following `tmpl::pair`s in\n `factory_creation::factory_classes`:\n```\n tmpl::pair,\n tmpl::pair<\n PhaseChange,\n tmpl::list<\n PhaseControl::VisitAndReturn<\n Parallel::Phase::EvaluateAmrCriteria>,\n PhaseControl::VisitAndReturn,\n PhaseControl::VisitAndReturn>,\n```\nwhere `LIST_OF_CRITERIA` should be a list of amr::Criteria.\n\n- The addition of the following item in the list of PhaseActions for\n the component specified in `amr::element_array`:\n\n```\n Parallel::PhaseActions>,\n```\n\n- The possible addition of `PhaseControl::Actions::ExecutePhaseChange`\n to the action list for the appropriate Phase in the PhaseAction of\n the `amr::element_array`\n\n- The addition of the mutator `amr::Initialization::Initialize` to the\n list of mutators in `Initialization::Actions::InitializeItems` in\n the Parallel::PhaseActions list for Parallel::Phase::Initialization.\n\n- The appropriate includes for all of the above.\n\n### Controlling AMR {#dev_guide_amr_input_options}\n\nThere are two places in the input file that control how and when AMR happens.\n\nThe \"how\" is controlled by the option group `Amr`. Here you list the\namr::Criteria being used, the available options for the amr::Policies, and\nthe `Verbosity` of diagnostic messages that are printed. Here is an\nexample:\n```\nAmr:\n Criteria:\n - TruncationError:\n VariablesToMonitor: [Psi]\n AbsoluteTarget: 1.e-6\n RelativeTarget: 1.0\n Policies:\n EnforceTwoToOneBalanceInNormalDirection: true\n Isotropy: Anisotropic\n Limits:\n RefinementLevel: Auto\n NumGridPoints: Auto\n ErrorBeyondLimits: False\n AllowCoarsening: True\n Verbosity: Verbose\n```\n\nNote that the values `Auto` for the Limits options choose the default\nlimits set by the code. Also note that if a criterion tries to refine beyond the\nlimits, whether or not the code should error is controlled by\n`ErrorBeyondLimits`.\n\n\"When\" AMR happens is controlled by specifying a Trigger and a list of\n`PhaseChanges` in the top-level option `PhaseChangesAndTriggers`. For\nexample:\n```\nPhaseChangeAndTriggers:\n - Trigger:\n Slabs:\n EvenlySpaced:\n Interval: 10\n Offset: 0\n PhaseChanges:\n - VisitAndReturn(EvaluateAmrCriteria)\n - VisitAndReturn(AdjustDomain)\n - VisitAndReturn(CheckDomain)\n```\n\nBoth `EvaluateAmrCriteria` and `AdjustDomain` are required in order\nfor AMR to work. `VisitAndReturn(CheckDomain)` performs diagnostics\nand can be omitted. To turn off AMR, omit the three phase changes above.\n" }, { "path": "docs/DevGuide/AutomaticVersioning.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n# Automatic versioning {#dev_guide_automatic_versioning}\n\n\\tableofcontents\n\nOur automated tests can tag and publish a release automatically when requested.\nThe automation is implemented as a [GitHub\nActions](https://docs.github.com/actions) workflow in the file\n`.github/workflows/Tests.yaml`.\n\n## Creating releases\n\nThe GitHub workflow responsible for automated testing also allows creating a\nrelease when dispatched manually. To create a release (roughly on the first\nMonday of each month and/or when needed for publications), follow these\ninstructions:\n\n1. **Check for bugs on `develop`.** If you are aware of any major bugs in the\n code on `develop`, check with the (other) core developers if it would be\n better to wait with the release until those bugs are fixed.\n2. **Check the release notes.** Find the latest run of the [`Tests` workflow\n on the `develop` branch](https://github.com/sxs-collaboration/spectre/actions/workflows/Tests.yaml?query=branch%3Adevelop). Select the \"Files and formatting\" job and the\n \"Print release notes\" step within. Go through the release notes, checking\n the following in particular:\n - Label bugfix PRs with the `bugfix` label so they appear in the \"Bugfixes\"\n section and don't clutter the list.\n - Label PRs that you want to highlight with the `new feature` label, so they\n appear at the top. The selection is up to you.\n - Add upgrade instructions to PRs where they are missing, to help other\n developers with rebasing their code.\n3. **Dispatch the release.** Go to the GitHub Actions page for the [`Tests`\n workflow](https://github.com/sxs-collaboration/spectre/actions/workflows/Tests.yaml?query=branch%3Adevelop).\n [Select \"Run workflow\"](https://docs.github.com/actions/managing-workflow-runs/manually-running-a-workflow)\n and the `develop` branch. Type in a valid release version name, such as\n \"2021.05.04\", and hit \"Run workflow\". The release will only be created if\n if the version name matches the format defined in\n \\ref versioning_and_releases _and_ if it matches the current date. Therefore,\n if you wait too long with the next step, the release will fail and you have\n to dispatch it again.\n\n It is probably best to hold off merging PRs while the release workflow runs,\n to avoid possible conflicts. Therefore, warn the (other) core devs.\n4. **Ask for approval.** Once the unit tests are complete, the release workflow\n will wait for approval before publishing the release on GitHub and Zenodo.\n Notify the (other) core devs so one of them can review and approve the\n release (don't approve the release yourself). You can point them to these\n guidelines:\n\n Guidelines for reviewing a release:\n - Check for bugs on `develop` (see point 1. above).\n - Check the release notes (see point 2. above).\n\n## Release notes\n\nThe release notes are compiled automatically based on the activity in the\nrepository since the last release. They will contain a list of merged\npull-requests. Pull-requests labeled \"new feature\" or \"bugfix\" on GitHub\nwill be classified as such in the release notes.\n\nThe script `tools/CompileReleaseNotes.py` generates the release notes and can\nalso be invoked manually with a Python 3 interpreter to retrieve an overview of\nwhat happened in the repository recently. The script requires you install\n`GitPython`, `PyGithub` and `tqdm` in your Python environment.\n" }, { "path": "docs/DevGuide/Brigand.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Metaprogramming with Brigand {#brigand}\n\n\\tableofcontents\n\n\\tableofcontents{HTML:2}\n\n[comment]: # (The \\pars improve the spacing in the generated document when)\n[comment]: # (many \\snippets are involved.)\n\n\\par\nIn SpECTRE, most complex TMP is done using the [Brigand metaprogramming\nlibrary](https://github.com/edouarda/brigand). Brigand is a collection of\ntemplated classes, type aliases, and functions, primarily intended to help with\nthe manipulation and use of lists of types. This document is organized to\nroughly parallel the structure of the C++ standard, rather than following\nBrigand's classifications.\n\n\\par\nBrigand provides all of its functionality in the `brigand` namespace, but in\nSpECTRE we have aliased this namespace to `tmpl`, and the latter should be\npreferred.\n\n\\par\nAll functionality described here is provided by SpECTRE's Brigand wrapper\nheader:\n\\snippet Test_TMPLDocumentation.cpp include\n\n\\par\nExamples in this document use the following declarations and definitions:\n\\snippet Test_TMPLDocumentation.cpp example_declarations\n\n\n\\section Metafunctions\n\n\\par\nA metafunction is an analog of a familiar C++ function that is coded in the C++\ntype system. It turns out that, using metafunction programming, it is possible\nto perform arbitrary computations at compile time.\n\n\\par\nThere are multiple ways to encode a calculation in the type system. When using\nBrigand, the relevant ones are eager and lazy metafunctions.\n\n\n\\subsection lazy Eager and lazy metafunctions\n\n\\par\nMetafunctions commonly appear in two forms: eager and lazy. Lazy metafunctions\nare templated structs (or templated aliases to structs) with a `type` member\nalias that indicates the result:\n\\snippet Test_TMPLDocumentation.cpp metafunctions:lazy\nThe type traits in the standard library, such as std::is_same, are lazy\nmetafunctions.\n\n\\par\nEager metafunctions are aliases to their result types. As a trivial case,\nstruct templates can be viewed as eager metafunctions returning themselves. An\neager version of the previous example could be implemented as:\n\\snippet Test_TMPLDocumentation.cpp metafunctions:eager\nThe standard library provides eager versions of some of its metafunctions\n(generally those that modify a type, rather than predicates) using an `_t`\nsuffix. When both versions are provided, it is often convenient (and less\nerror prone!) to define the eager version in terms of the lazy version:\n\\snippet Test_TMPLDocumentation.cpp metafunctions:eager_from_lazy\nAnd the two definitions agree:\n\\snippet Test_TMPLDocumentation.cpp metafunctions:agreement\n\n\\note\nThe standard library also provides versions of many of its type traits with an\n`_v` suffix. These evaluate to compile-time *values*, rather than types. They\ncan be useful for metaprogramming, but are not the types of metafunctions being\ndiscussed here.\n\n\\par\nEager metafunctions are usually more convenient to use, so what is the point of\nadditionally creating lazy ones? The answer is that lazy metafunctions can be\nused as compile-time functors. As a simple example, we can write an (eager)\nmetafunction that calls an arbitrary lazy metafunction twice\n\\snippet Test_TMPLDocumentation.cpp metafunctions:call_lazy_metafunction\nand get the expected output:\n\\snippet Test_TMPLDocumentation.cpp metafunctions:call_lazy_metafunction_assert\nBut it fails if you try to call an arbitrary *eager* metafunction\ntwice in the same way, because the function is evaluated too early,\nresulting in the `List1` metafunction being acted upon instead of\n`eager_add_list`:\n\\snippet Test_TMPLDocumentation.cpp metafunctions:call_eager_metafunction\n\\snippet Test_TMPLDocumentation.cpp metafunctions:call_eager_metafunction_assert\n(In this simple case we could have used a template template parameter to pass\nthe eager metafunction in a form more similar to a runtime lambda, but the\npossibilities for generic manipulation of parameter lists containing template\ntemplate parameters are limited, so their use must be minimized in complex\nmetaprogramming.)\n\n\\note\nIn practice, lazy metafunctions are often implemented as empty structs\ninheriting from other lazy metafunctions. The entire inheritance chain then\ninherits a `type` alias from the ultimate base class.\n\n\\par\nMost of the standard Brigand functions are eager, but many have lazy versions\nin the nested `tmpl::lazy` namespace. These are indicated by calls to the\n`HAS_LAZY_VERSION` macro in the examples below.\n\n\n\\subsection metalambdas Brigand metalambdas\n\n\\par\nThis use of lazy metafunctions is too limited for general use, however, because\nit requires the definition of a new templated struct for every new function.\nBrigand uses a more general notation, known as metalambdas. A metalambda is a\n(possibly nested set of) lazy metafunctions with some template arguments\nreplaced by the placeholders `tmpl::_1`, `tmpl::_2`, etc. These are the first,\nsecond, etc., arguments of the metalambda, and will be replaced by the actual\narguments when the lambda is used. The lazy nature of the metafunctions\nprevents them from prematurely evaluating to results based on the literal\nplaceholder types. The \\ref apply \"tmpl::apply\" function can be used to\nevaluate a metalambda with specified arguments, and many other Brigand\nfunctions take metalambdas that are evaluated internally.\n\n\n\\subsection metalambda_structure Evaluation of metalambdas\n\n\\note\nNone of the terminology introduced in this section is standard.\n\n\\par\nWhen evaluating a metalambda, the values of any \\ref args \"arguments\"\nencountered are taken from the evaluation's argument stack. The argument stack\nis a stack (in the CS sense) of collections of zero or more arguments. The\nvalues of any \\ref args \"arguments\" that are evaluated are taken from the\ncollection at the head of the stack. The remaining collections are arguments\ncaptures in closures, and will not be present in code not using \\ref defer\n\"tmpl::defer\".\n\n\\par\nThe \\ref apply \"tmpl::apply\" metafunction is the Brigand metafunction for\nevaluating metalambdas. It can be called explicitly, and is called internally\nby many other functions. It takes a metalambda and arguments to be passed to\nthat metalambda. The argument stack for the evaluation has one entry: the\npassed arguments.\n\n\\par\nThe argument stack can gain additional entries through the creation of\nmetaclosures using \\ref defer \"tmpl::defer\". When \\ref defer \"tmpl::defer\" is\nevaluated, it produces a \\ref metalambda_metaclosure \"metaclosure\" containing a\ncopy of the current argument stack, acting as the lambda captures. When that\nmetaclosure is evaluated, the previously active stack is replaced by the stored\nstack with the head of the old stack pushed onto it.\n\n\\par\nThis makes \\ref args \"arguments\" in a \\ref metalambda_metaclosure \"metaclosure\"\nrefer to the arguments \"passed\" to it. (No explicit call syntax is used, but\nthe arguments are inherited from the calling context.) The captured arguments\nare accessible using \\ref parent \"tmpl::parent\", which pops off the last entry\nin the argument stack.\n\n\\par\nThere are eight forms that a metalambda can take: an argument, a lazy\nexpression, a bind expression, a pin expression, a defer expression, a parent\nexpression, a constant, or a metaclosure.\n\n\\subsubsection args Argument\n\n\\par\nAn argument is one of the structs `tmpl::_1`, `tmpl::_2`, or `tmpl::args`\nfor `unsigned int` n. The additional aliases `tmpl::_3`, `tmpl::_4`, ...,\n`tmpl::_9` are provided to `tmpl::args<2>`, `tmpl::args<3>`, ...,\n`tmpl::args<8>`. (The first two arguments have dedicated types in addition to\nthe general `tmpl::args<0>` and `tmpl::args<1>`. My best guess is for\nperformance reasons.)\n\\snippet Test_TMPLDocumentation.cpp tmpl::args\nWhen evaluated, they give the first (`tmpl::_1`), second (`tmpl::_2`), or\nzero-indexed Nth (`tmpl::args`) entry from the collection of arguments at\nthe top of the argument stack.\n\\snippet Test_TMPLDocumentation.cpp tmpl::args:eval\nAdditionally, `tmpl::_state` and `tmpl::_element` are aliased to `tmpl::_1` and\n`tmpl::_2`, primarily for use with \\ref fold \"tmpl::fold\".\n\n\\par\nWhen evaluating a metalambdas, the metalambda must be passed enough arguments\nto define all argument placeholders in its body. When evaluating using \\ref\napply \"tmpl::apply\", arguments are passed as template parameters after the\nmetalambda. Other Brigand functions that evaluate metalambdas pass them a\nspecified number of arguments (usually 1 or 2). Failure to pass enough\narguments may error or produce unintuitive results.\n\n\\subsubsection metalambda_lazy Lazy expression\n\n\\par\nA lazy expression is a fully-specialized struct template with only type\ntemplate parameters that is not a specialization of \\ref pin \"tmpl::pin\", \\ref\ndefer \"tmpl::defer\", or \\ref parent \"tmpl::parent\" and is not a \\ref\nmetalambda_metaclosure \"metaclosure\". When evaluated, each of its template\nparameters is evaluated as a metalambda and replaced by the result, and then\nthe struct's `type` type alias is the result of the full lazy-expression.\n\\snippet Test_TMPLDocumentation.cpp metalambda_lazy\n\n\\subsubsection bind Bind expression\n\n\\par\nA bind expression is a specialization of `tmpl::bind`. It wraps an eager\nmetafunction and its arguments. When evaluated, the arguments are each\nevaluated as metalambdas, and then the results are passed to the eager\nmetafunction.\n\\snippet Test_TMPLDocumentation.cpp tmpl::bind\n\n\\note\nThe `tmpl::bind` metafunction does not convert an eager metafunction to a lazy\none. It is handled specially in the evaluation code.\n\n\\subsubsection pin Pin expression\n\n\\par\nA pin expression is a specialization of `tmpl::pin`. Evaluating a pin\nexpression gives the (unevaluated) argument to `tmpl::pin`. This can be used\nto force a type to be treated as a \\ref metalambda_constant \"constant\", even if\nit would normally be treated as a different type of metalambda (usually a \\ref\nmetalambda_lazy \"lazy expression\").\n\\snippet Test_TMPLDocumentation.cpp tmpl::pin\n\n\\par\nPin expressions are often used to protect template arguments to eager\nmetafunctions:\n\\snippet Test_TMPLDocumentation.cpp tmpl::pin:protect_eager\n\n\\subsubsection defer Defer expression\n\n\\par\nA defer expression is a specialization of `tmpl::defer`. It does not evaluate\nits argument, but results in a \\ref metalambda_metaclosure \"metaclosure\"\ncontaining the passed metalambda and the current argument stack.\n\n\\par\nExample:\n\\snippet Test_TMPLDocumentation.cpp tmpl::defer\nThe evaluation here proceeds as follows:\n\n1. The innermost eager metafunction is the second \\ref apply \"tmpl::apply\". It\n creates an argument stack with one collection containing the single argument\n `Type1` and proceeds to evaluate `tmpl::defer`.\n\n2. Evaluating the defer expression creates a \\ref metalambda_metaclosure\n \"metaclosure\" with the contents `tmpl::_1` and the argument stack from the\n first apply. This is the result of the inner \\ref apply \"tmpl::apply\".\n\n3. Next the outer \\ref apply \"tmpl::apply\" is evaluated. It creates an\n argument stack with one collection containing the single argument`Type2`,\n and proceeds to evaluate the \\ref metalambda_metaclosure \"metaclosure\"\n created above.\n\n[comment]: # (Keep the numbering here in sync with the `parent` example.)\n\n4. Evaluating the \\ref metalambda_metaclosure \"metaclosure\" (see that section\n below) evaluates the contained `tmpl::_1` with a two-element argument stack:\n head to tail [(`Type2`), (`Type1`)].\n\n5. The first (and only) argument (`tmpl::_1`) in the head of the argument stack\n is `Type2`, which is the result of the \\ref metalambda_metaclosure\n \"metaclosure\" and the entire expression.\n\n\n\\par\nThe primary purposes for `tmpl::defer` are constructing metalambdas to pass to\nother metafunctions and preventing \"speculative\" evaluation of a portion of a\nmetalambda that is not valid for some arguments. See the examples below, in\nparticular \\ref make_subtracter, \\ref multiplication_table, \\ref maybe_first,\nand \\ref column_with_zeros.\n\n\\subsubsection parent Parent expression\n\n\\par\nA parent expression is a specialization of `tmpl::parent`. It evaluates its\nargument (treated as a metalambda) after popping the top entry off the argument\nstack. This provides access to the captured arguments in a \\ref\nmetalambda_metaclosure \"metaclosure\".\n\n\\par\nExample:\n\\snippet Test_TMPLDocumentation.cpp tmpl::parent\nThe creation of the \\ref metalambda_metaclosure \"metaclosure\" here is similar\nto the example for \\ref defer \"tmpl::defer\", except that the contained\nmetalambda is `tmpl::parent` instead of a plain `tmpl::_1`. The\nevaluation proceeds as:\n\n1. As in \\ref defer \"tmpl::defer\" example.\n\n2. As in \\ref defer \"tmpl::defer\" example.\n\n3. As in \\ref defer \"tmpl::defer\" example.\n\n4. The \\ref metalambda_metaclosure \"metaclosure\" evaluates the contained\n `tmpl::parent` with the argument stack [(`Type2`), (`Type1`)].\n\n5. Evaluating the `tmpl::parent` pops the stack, and so evaluates `tmpl::_1`\n with the stack [(`Type1`)].\n\n6. The first (and only) argument (`tmpl::_1`) in the stack's head is now\n `Type1`, which is the result of the \\ref metalambda_metaclosure\n \"metaclosure\" and the entire expression.\n\n\\warning\nDo not call `tmpl::parent` when the argument stack is empty, i.e., do not\nattempt to access more sets of captured arguments than have been captured. If\nyou want to prevent evaluation of an expression, use \\ref pin \"tmpl::pin\".\n\n\\subsubsection metalambda_constant Constant\n\n\\par\nA constant metalambda is any type that is not a struct template with only type\ntemplate parameters, a specialization of \\ref bind \"tmpl::bind\", or a\nmetaclosure. A constant metalambda evaluates to itself.\n\\snippet Test_TMPLDocumentation.cpp metalambda_constant\n\n\\subsubsection metalambda_metaclosure Metaclosure\n\n\\par\nA metaclosure is an opaque type produced by \\ref defer \"tmpl::defer\",\ncontaining a metalambda and an argument stack. When a metaclosure is\nevaluated, it evaluates the packaged metalambda with an argument stack\nconstructed by pushing the head of the current argument stack onto the argument\nstack stored in the metaclosure. See \\ref defer and \\ref parent for examples.\n\n\n\\subsection Examples\n\n\n\\subsubsection evens\n\n\\par\nFinds all numbers in a list that are even.\n\\snippet Test_TMPLDocumentation.cpp metafunctions:evens\n\\snippet Test_TMPLDocumentation.cpp metafunctions:evens:asserts\n\n\\par\nThe \\ref filter \"tmpl::filter\" metafunction takes a metalambda as its second\nargument. The \\ref integral_constant \"tmpl::integral_constant\"s have non-type\ntemplate parameters, so they are treated as constant expressions. The \\ref\nmath_comparison \"tmpl::equal_to\" and \\ref math_arithmetic \"tmpl::modulo\"\nmetafunctions are lazy, despite not being in the `tmpl::lazy` namespace.\n\n\n\\subsubsection maybe_first\n\n\\par\nReturns the first element of a list, or \\ref no_such_type_ \"tmpl::no_such_type_\"\nif the list is empty.\n\\snippet Test_TMPLDocumentation.cpp metafunctions:maybe_first\n\\snippet Test_TMPLDocumentation.cpp metafunctions:maybe_first:asserts\n\n\\par\nIn this example, the inner \\ref apply \"tmpl::apply\" call evaluates the \\ref if_\n\"tmpl::if_\" statement, returning either a \\ref metalambda_metaclosure\n\"metaclosure\" or \\ref no_such_type_ \"tmpl::no_such_type_\". The outer \\ref\napply \"tmpl::apply\" either evaluates the metaclosure, calling \\ref front\n\"tmpl::front\", or evaluates \\ref no_such_type_ \"tmpl::no_such_type_\", which is\na constant and gives itself.\n\n\\par\nThe reason for creating a metaclosure is that all the arguments to \\ref if_\n\"tmpl::if_\" are always evaluated (it is an ordinary metafunction with no\nspecial treatment during evaluation). This is a problem, because, in a naive\nattempt at this metafunction, if `L` is an empty list\n`tmpl::front>` would be evaluated for the first branch. To avoid\nthis we use \\ref defer \"tmpl::defer\" to wrap the call to \\ref front\n\"tmpl::front\" in a metaclosure, which we evaluate only if necessary.\n\n\\par\nNote that this metaclosure does not capture anything. `L` is substituted\naccording to normal C++ rules before any Brigand evaluation. This means that\nthe contents of the `tmpl::defer` are, for the first call above,\n`tmpl::bind>>`. Without the \\ref pin\n\"tmpl::pin\", the list would be interpreted as a lazy metafunction, resulting in\nan error because it does not have a `type` type alias.\n\n\\par\nThe `L` in `tmpl::size` does not need to be protected by a \\ref pin\n\"tmpl::pin\" because \\ref size \"tmpl::size\" is an eager metafunction, so that\nexpression has been converted to a \\ref integral_constant\n\"tmpl::integral_constant\" before the metalambda evaluation starts.\n\n\n\\subsubsection factorial\n\n\\par\nCalculates the factorial using a simple metalambda passed to a \\ref fold\n\"tmpl::fold\".\n\\snippet Test_TMPLDocumentation.cpp metafunctions:factorial\n\\snippet Test_TMPLDocumentation.cpp metafunctions:factorial:asserts\n\n\\par\nA nearly literal rewrite of this into runtime C++ is\n\\snippet Test_TMPLDocumentation.cpp metafunctions:factorial_cpp\n\n\\par\nThe equivalent of a range-based for loop is easier to express in functional\nprogramming (as a fold) than a standard counting for loop.\n\n\n\\subsubsection make_subtracter\n\n\\par\nDemonstrates the use of captures in metalambdas.\n\\snippet Test_TMPLDocumentation.cpp metafunctions:make_subtracter\n\\snippet Test_TMPLDocumentation.cpp metafunctions:make_subtracter:asserts\n\n\\par\nThis metafunction returns a \\ref metalambda_metaclosure \"metaclosure\" that\nsubtracts a given number from it's argument. That metaclosure uses both the\nargument passed to it (`tmpl::_1`, which is 5 in the example) and the value\ncaptured at it's creation (`tmpl::parent`, which is 3 in the\nexample).\n\n\\par\n(This `make_subtracter` could be implemented more simply as\n\\snippet Test_TMPLDocumentation.cpp metafunctions:make_subtracter_simple\nbut that doesn't demonstrate metaclosures.)\n\n\n\\subsubsection multiplication_table\n\n\\par\nConstructs a multiplication table.\n\\snippet Test_TMPLDocumentation.cpp metafunctions:multiplication_table\n\\snippet Test_TMPLDocumentation.cpp metafunctions:multiplication_table:asserts\n\n\\par\nThis demonstrates the use of \\ref defer \"tmpl::defer\" to pass a closure as an\nargument to a metafunction (\\ref transform \"tmpl::lazy::transform\"), while\ncapturing an argument from the outer context (the metalambda evaluated for the\nouter \\ref transform \"tmpl::transform\"). This is the use most similar to\ncommon uses of the C++ lambda.\n\n\\par\nThe outer (eager) \\ref transform \"tmpl::transform\" evaluates its second\nargument as a metalambda. This first evaluates the arguments to the inner \\ref\ntransform \"tmpl::lazy::transform\". The first argument is a \\ref list\n\"tmpl::list\" of \\ref integral_constant \"tmpl::integral_constant\"s (because the\n\\ref range \"tmpl::range\" is eager and has already been evaluated). This must\nbe protected by a \\ref pin \"tmpl::pin\" because it looks like a lazy\nmetafunction. The second argument gives a metaclosure, capturing the value\nfrom the outer \\ref transform \"tmpl::transform\" (available as\n`tmpl::parent`). The \\ref list \"tmpl::list\" (without the \\ref pin\n\"tmpl::pin\", which has already been evaluated) and metaclosure are then passed\nto the inner \\ref transform \"tmpl::lazy::transform\".\n\n\n\\subsubsection column_with_zeros\n\n\\par\nExtracts a column from a row-major matrix, extending any short rows with zeros.\n\\snippet Test_TMPLDocumentation.cpp metafunctions:column_with_zeros\n\\snippet Test_TMPLDocumentation.cpp metafunctions:column_with_zeros:asserts\n\n\\par\nThis example shows another use of \\ref defer \"tmpl::defer\" to avoid evaluating\nan invalid expression, similar to \\ref maybe_first. The use of an \\ref args\n\"argument\" in the deferred branch makes this case more complicated: a \\ref\nparent \"tmpl::parent\" expression is used to access arguments from where the\n\\ref defer \"tmpl::defer\" occurs to avoid having to pass the argument explicitly\nusing the \\ref apply \"tmpl::apply\" call.\n\n\\par\nThis is the \"apply-defer-parent\" pattern for lazy evaluation. A \\ref parent\n\"tmpl::parent\" is placed immediately inside a \\ref defer \"tmpl::defer\" with a\n(not immediately) surrounding \\ref apply \"tmpl::apply\". The \\ref apply\n\"tmpl::apply\" and \\ref defer \"tmpl::defer\" collectively add an (empty) element\nto the head of the argument stack, which is then popped off to restore the\noriginal value. This causes the interior metalambda to have the same result it\nwould have had without the \\ref defer \"tmpl::defer\".\n\n\n\\subsubsection factorial_recursion\n\n\\par\nAgain calculates the factorial, but using a recursive algorithm.\n\\snippet Test_TMPLDocumentation.cpp metafunctions:factorial_recursion\n\\snippet Test_TMPLDocumentation.cpp metafunctions:factorial_recursion:asserts\n\n\\par\nThis is a direct translation of the common definition \\f$f(N) = N f(N-1)\\f$ for\nnonzero \\f$N\\f$, and \\f$f(0) = 1\\f$. The metalambda is passed a copy of itself\nas the first argument and the value to take the factorial of as the second.\n\n\\par\nThis again uses the \"apply-defer-parent\" pattern to prevent \"speculative\"\nevaluation of conditional branches. In this example, speculative evaluation of\nthe branch is invalid because it would recurse infinitely.\n\n\n\\subsubsection primes\n\n\\par\nGenerates a list of prime numbers less than `N` using the sieve of\nEratosthenes. This example defines three helper metafunctions. Two, `zero`\nand `replace_at`, are defined only for clarity's sake and could be inlined.\nThe third, `range_from_types`, is not easily inlinable, and works around\nBrigand's lack of sequence generating functions without non-type template\nparameters.\n\\snippet Test_TMPLDocumentation.cpp metafunctions:primes\n\\snippet Test_TMPLDocumentation.cpp metafunctions:primes:asserts\n\n\\par\nThis is roughly equivalent to the following C++ code with loops converted to\nfold expressions over ranges.\n\\snippet Test_TMPLDocumentation.cpp metafunctions:primes_cpp\n\n\n\\section metafunction_guidelines Guidelines for writing metafunctions\n\n\\par\nThis section covers a few general guidelines for writing metafunctions in\nSpECTRE. Some of the Brigand functions mentioned below have specific advice as\nwell.\n\n1. For general metafunctions, write both lazy and eager versions. Follow the\n STL convention of `foo` being lazy, `foo_t` being eager, and `foo_v` being a\n constexpr value (if applicable). This does not apply to internal-use or\n special-purpose metafunctions.\n \\snippet Test_TMPLDocumentation.cpp guidelines:lazy_eager\n\n2. Don't perform unnecessary return-type conversions. We often recommend using\n STL types over equivalent Brigand types, but if the implementation naturally\n produces a Brigand type do not do extra work to convert it.\n\n\n\\section function_docs Brigand types and functions\n\n\\par\nIn this section, CamelCase identifiers indicate [type template\nparameters](https://en.cppreference.com/w/cpp/language/template_parameters#Type_template_parameter)\nor, occasionally, [template template\nparameters](https://en.cppreference.com/w/cpp/language/template_parameters#Template_template_parameter).\nIdentifiers in all lowercase indicate [non-type template\nparameters](https://en.cppreference.com/w/cpp/language/template_parameters#Non-type_template_parameter).\nIdentifiers in [brackets] are optional, and the default value will be\nidentified in the prose description. Identifiers with ellipses... represent\nzero or more parameters.\n\n\\par\nThe *head* of a fully specialized class template is the class template itself\n(e.g., the head of `tmpl::list` is `tmpl::list`). When taken as a\nmetafunction parameter, these are template template parameters and are usually\ncalled `Head` below.\n\n\\par\nAn identifier called `Sequence` must be a full specialization of a class\ntemplate with no non-type template parameters. Many functions do not make\nsense on sequences with a fixed length, and these require the head of their\nsequence arguments to take a variable number of template arguments. In\npractical applications, sequence arguments will usually be specializations of\n\\ref list \"tmpl::list\".\n\n\\par\nParameters called `Predicate` must be unary metalambdas returning \\ref\nintegral_constant \"tmpl::integral_constant\"s of `bool` or compatible classes.\n\n\\par\nParameters called `Comparator` must be binary metalambdas returning \\ref\nintegral_constant \"tmpl::integral_constant\"s of `bool` or compatible classes.\nThey must establish a [strict weak\nordering](https://en.wikipedia.org/wiki/Weak_ordering#Strict_weak_orderings) on\nthe types they will be applied to in the same manner as runtime comparators\nfrom the STL.\n\n\\par\nMetafunctions documented here are eager unless otherwise noted. In many cases,\nBrigand provides lazy versions of its metafunctions under the same name in the\n`tmpl::lazy` namespace. These cases are indicated by the presence of the\n`HAS_LAZY_VERSION` macro in the usage example.\n\n\n\\subsection Containers\n\n\\par\nBrigand provides container classes with the sole purpose of wrapping other\nthings.\n\n\n\\subsubsection integral_constant integral_constant\n\n\\par\nA compile-time value `value` of type `T`. Very similar to\nstd::integral_constant, except that the `constexpr` specifiers on the member\nfunctions have been omitted.\n\\snippet Test_TMPLDocumentation.cpp tmpl::integral_constant\n\n\\par\nBrigand supplies type aliases for constants of some specific types:\n\\snippet Test_TMPLDocumentation.cpp tmpl::integral_constant::abbreviations\n\n\\par\nMost metafunctions that accept integral_constants will accept any type with a\n`value` static member variable.\n\n\\par\nBecause of the `type` type alias, integral_constants behave like lazy\nmetafunctions returning themselves. Most lazy metafunctions producing an\nintegral_constant will actually inherit from their result, so `value` will be\ndirectly available without needing to go through the `type` alias.\n\n\\remark\nPrefer std::integral_constant, except for the convenience wrapper\n`tmpl::size_t` or when necessary for type equality comparison.\n\n\n\\subsubsection list list\n\n\\par\nAn empty struct templated on a parameter pack, with no additional\nfunctionality.\n\\snippet Test_TMPLDocumentation.cpp tmpl::list\n\n\\par\nMost metafunctions that operate on lists will work on any struct template.\n\n\n\\subsubsection map map\n\n\\par\nA collection of key-value \\ref pair \"tmpl::pair\"s with unique keys. See the\nsection on \\ref map_operations \"operations on maps\" for details.\n\\snippet Test_TMPLDocumentation.cpp tmpl::map\n\n\\par\nThe actual type of a map is unspecified, but it has the same template\nparameters as a call to `map` that would produce it.\n\n\\warning\nEquivalent maps may have different types, depending on the order their keys are\nstored in internally.\n\n\n\\subsubsection pair pair\n\n\\par\nA pair of types, with easy access to each type in the pair.\n\\snippet Test_TMPLDocumentation.cpp tmpl::pair\n\n\n\\subsubsection set set\n\n\\par\nAn unordered collection of distinct types. Trying to create a `set` with\nduplicate entries is an error (but \\ref set_insert \"tmpl::insert\" ignores\nduplicate entries). See the section on \\ref set_operations\n\"operations on sets\" for details.\n\\snippet Test_TMPLDocumentation.cpp tmpl::set\n\n\\par\nThe actual type of a set is unspecified, but it has the same template\nparameters as a call to `set` that would produce it.\n\n\\warning\nEquivalent sets may have different types, depending on the order their elements\nare stored in internally.\n\n\n\\subsubsection type_ type_\n\n\\par\nA struct containing a `type` alias to `T`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::type_\n\n\\par\nWhen extracting the type, programmers are encouraged to use \\ref type_from\n\"tmpl::type_from\" to make it clear that the \\c \\::type that would otherwise\nappear is not an evaluation of a lazy metafunction. See \\ref always\n\"tmpl::always\" or \\ref identity \"tmpl::identity\" for similar functionality that\nis intended for use as a metafunction.\n\n\n\\subsection Constants\n\n\\par\nBrigand defines a few concrete types and type aliases.\n\n\n\\subsubsection empty_base\n\n\\par\nAn empty struct used by \\ref inherit \"tmpl::inherit\" and \\ref inherit_linearly\n\"tmpl::inherit_linearly\". Primarily for internal use.\n\\snippet Test_TMPLDocumentation.cpp tmpl::empty_base\n\n\n\\subsubsection empty_sequence\n\n\\par\nAn empty \\ref list \"tmpl::list\".\n\\snippet Test_TMPLDocumentation.cpp tmpl::empty_sequence\n\n\\remark\nPrefer just writing `tmpl::list<>`.\n\n\n\\subsubsection false_type\n\n\\par\nA \\ref integral_constant \"tmpl::integral_constant\" representing `false`.\nSimilar to std::false_type.\n\\snippet Test_TMPLDocumentation.cpp tmpl::false_type\n\n\\remark\nPrefer std::false_type.\n\n\n\\subsubsection no_such_type_\n\n\\par\nAn empty struct returned as the failure case for various searching operations.\n\\snippet Test_TMPLDocumentation.cpp tmpl::no_such_type_\n\n\n\\subsubsection true_type\n\n\\par\nA \\ref integral_constant \"tmpl::integral_constant\" representing `true`.\nSimilar to std::true_type.\n\\snippet Test_TMPLDocumentation.cpp tmpl::true_type\n\n\\remark\nPrefer std::true_type.\n\n\n\\subsection list_constructor Constructor-like functions for lists\n\n\\par\nThese functions produce \\ref list \"tmpl::list\"s from non-list values. They are\noften similar to constructors in the STL.\n\n\n\\subsubsection filled_list filled_list\n\n\\par\nCreates a list containing `n` (passed as an `unsigned int`) of `Entry`. The\nhead of the list defaults to \\ref list \"tmpl::list\".\n\\snippet Test_TMPLDocumentation.cpp tmpl::filled_list\n\n\n\\subsubsection integral_list integral_list\n\n\\par\nShorthand for a \\ref list \"tmpl::list\" of \\ref integral_constant\n\"tmpl::integral_constant\"s of the type `T` with values `n...`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::integral_list\n\n\\remark\nPrefer std::integer_sequence when used for pack expansion. Prefer\n`tmpl::integral_list` when the contents need to be manipulated for more\ncomplicated metaprogramming.\n\n\n\\subsubsection make_sequence make_sequence\n\n\\par\nProduces a list with first element `Start` and length `n` (provided as an\n`unsigned int`). The remaining elements are obtained by repeated applications\nof the \\ref metalambdas \"metalambda\" `Next`, defaulting to \\ref next\n\"tmpl::next\". The head of the sequence can be specified, and defaults to \\ref\nlist \"tmpl::list\".\n\\snippet Test_TMPLDocumentation.cpp tmpl::make_sequence\n\n\\see \\ref range \"tmpl::range\", \\ref repeat \"tmpl::repeat\"\n\n\n\\subsubsection range range\n\n\\par\nProduces a \\ref list \"tmpl::list\" of \\ref integral_constant\n\"tmpl::integral_constant\"s of type `T` representing adjacent ascending integers\nfrom `start` to `stop`, including the starting value and excluding the ending\nvalue.\n\\snippet Test_TMPLDocumentation.cpp tmpl::range\n\n\\see \\ref reverse_range \"tmpl::reverse_range\"\n\n\n\\subsubsection reverse_range reverse_range\n\n\\par\nProduces a \\ref list \"tmpl::list\" of \\ref integral_constant\n\"tmpl::integral_constant\"s of type `T` representing adjacent descending\nintegers from `start` to `stop`, including the starting value and excluding the\nending value.\n\\snippet Test_TMPLDocumentation.cpp tmpl::reverse_range\n\n\\see \\ref range \"tmpl::range\"\n\n\n\\subsection list_query Functions for querying lists\n\n\\par\nThese tend to be similar to const member functions in the STL and the\nnon-modifying sequence operations in ``. They are most frequently\nused with \\ref list \"tmpl::list\", but similar classes will also work.\n\n\n\\subsubsection all all\n\n\\par\nChecks if `Predicate` is true for all elements of `Sequence`. The default\npredicate checks that the element's `value` is not equal to zero.\n\\snippet Test_TMPLDocumentation.cpp tmpl::all\n\n\\note\nThe predicate must return the same true value for each element for `all` to\nreturn true. This behaviour may differ by compiler, so it can't be relied upon.\n\\snippet Test_TMPLDocumentation.cpp tmpl::all:inhomogeneous\n\n\\see \\ref any \"tmpl::any\", \\ref none \"tmpl::none\"\n\n\n\\subsubsection any any\n\n\\par\nChecks if `Predicate` is true for at least one element of `Sequence`. The\ndefault predicate checks that the element's `value` is not equal to zero.\n\\snippet Test_TMPLDocumentation.cpp tmpl::any\n\n\\remark\nThe \\ref any \"tmpl::any\" and \\ref none \"tmpl::none\" metafunctions perform the\nsame tasks as \\ref found \"tmpl::found\" and \\ref not_found \"tmpl::not_found\",\nbut use different algorithms. In general, \\ref any \"tmpl::any\" and \\ref none\n\"tmpl::none\" are much faster, but \\ref found \"tmpl::found\" and \\ref not_found\n\"tmpl::not_found\" short-circuit, so they may be preferable with short lists and\nexpensive predicates.\n\n\\note\nThe predicate must return the same false value for each element for `any` to\nreturn false. This behaviour may differ by compiler, so it can't be relied upon.\n\\snippet Test_TMPLDocumentation.cpp tmpl::any:inhomogeneous\n\n\\see \\ref all \"tmpl::all\", \\ref found \"tmpl::found\", \\ref none \"tmpl::none\"\n\n\n\\subsubsection at at\n\n\\par\nRetrieves a given element of `Sequence`, similar to `operator[]` of the STL\ncontainers. The `Index` is supplied as a \\ref integral_constant\n\"tmpl::integral_constant\" or similar type.\n\\snippet Test_TMPLDocumentation.cpp tmpl::at\n\n\\par\nThis operator is \\ref map_at \"overloaded for maps\".\n\n\\see \\ref at_c \"tmpl::at_c\"\n\n\n\\subsubsection at_c at_c\n\n\\par\nRetrieves a given element of `Sequence`, similar to `operator[]` of the STL\ncontainers. The index `n` is supplied as an `unsigned int`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::at_c\n\n\\see \\ref at \"tmpl::at\"\n\n\n\\subsubsection back back\n\n\\par\nRetrieves the last element of `Sequence`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::back\n\n\n\\subsubsection count_if count_if\n\n\\par\nReturns the number of elements of `Sequence` satisfying `Predicate`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::count_if\n\n\n\\subsubsection fold fold\n\n\\par\nPerforms a [left\nfold](https://en.wikipedia.org/wiki/Fold_(higher-order_function)), i.e., given\na list `Sequence`, initial state `State`, and \\ref metalambdas \"metalambda\"\n`Functor`, updates the state by calling `Functor` on the state and the first\nelement of `Sequence`, repeats with the second, and so on, returning the final\nstate.\n\\snippet Test_TMPLDocumentation.cpp tmpl::fold\n\n\\par\nBrigand provides `tmpl::_state` and `tmpl::_element` aliases to the appropriate\n\\ref args \"arguments\" for use in folds.\n\n\\see \\ref reverse_fold \"tmpl::reverse_fold\"\n\n\n\\subsubsection found found\n\n\\par\nReturns, as a \\ref integral_constant \"tmpl::integral_constant\" of `bool`,\nwhether `Predicate` matches any element of `Sequence`. The default predicate\nchecks that the element's `value` is not equal to zero.\n\\snippet Test_TMPLDocumentation.cpp tmpl::found\n\n\\remark\nThis function performs the same operation as \\ref any \"tmpl::any\". See \\ref\nany \"tmpl::any\" for discussion.\n\n\\see \\ref any \"tmpl::any\", \\ref find \"tmpl::find\", \\ref not_found\n\"tmpl::not_found\"\n\n\n\\subsubsection front front\n\n\\par\nRetrieves the first element of `Sequence`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::front\n\n\n\\subsubsection index_if\n\n\\par\nFinds the index as a `size_t` \\ref integral_constant \"tmpl::integral_constant\"\nof the first type in `Sequence` satisfying `Predicate`. Returns `NotFound`,\ndefaulting to \\ref no_such_type_ \"tmpl::no_such_type_\" if no elements match.\n\\snippet Test_TMPLDocumentation.cpp tmpl::index_if\n\n\n\\subsubsection index_of index_of\n\n\\par\nFinds the index as a `size_t` \\ref integral_constant \"tmpl::integral_constant\"\nof the first occurrence of `T` in `Sequence`. Returns \\ref no_such_type_\n\"tmpl::no_such_type_\" if the type is not found.\n\\snippet Test_TMPLDocumentation.cpp tmpl::index_of\n\n\n\\subsubsection list_contains list_contains\n\n\\par\nChecks whether `T` is contained in `Sequence`, returning a \\ref\nintegral_constant \"tmpl::integral_constant\" of `bool`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::list_contains\n\n\\note\nThis is not a Brigand metafunction. It is implemented in SpECTRE.\n\n\n\\subsubsection none none\n\n\\par\nChecks if `Predicate` is false for all elements of `Sequence`. The default\npredicate checks that the element's `value` is not equal to zero.\n\\snippet Test_TMPLDocumentation.cpp tmpl::none\n\n\\remark\nThis function performs the same operation as \\ref not_found \"tmpl::not_found\".\nSee \\ref any \"tmpl::any\" for discussion.\n\n\\note\nThe predicate must return the same false value for each element for `none` to\nreturn true. This behaviour may differ by compiler, so it can't be relied upon.\n\\snippet Test_TMPLDocumentation.cpp tmpl::none:inhomogeneous\n\n\\see \\ref all \"tmpl::all\", \\ref any \"tmpl::any\", \\ref not_found\n\"tmpl::not_found\"\n\n\n\\subsubsection not_found not_found\n\n\\par\nReturns, as a \\ref integral_constant \"tmpl::integral_constant\" of `bool`,\nwhether `Predicate` matches no elements of `Sequence`. The default predicate\nchecks that the element's `value` is not equal to zero.\n\\snippet Test_TMPLDocumentation.cpp tmpl::not_found\n\n\\remark\nThis function performs the same operation as \\ref none \"tmpl::none\". See \\ref\nany \"tmpl::any\" for discussion.\n\n\\see \\ref find \"tmpl::find\", \\ref found \"tmpl::found\", \\ref none \"tmpl::none\"\n\n\n\\subsubsection size size\n\n\\par\nReturns the number of elements in `Sequence` as a \\ref integral_constant\n\"tmpl::integral_constant\" of type `unsigned int`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::size\n\n\\see \\ref count \"tmpl::count\"\n\n\n\\subsection list_to_list Functions producing lists from other lists\n\n\\par\nThese tend to be similar to non-const member functions in the STL and the\nmutating sequence operations in ``, but due to the nature of\nmetaprogramming all return a new list rather than modifying an argument. They\nare most frequently used with \\ref list \"tmpl::list\", but similar classes will\nalso work.\n\n\n\\subsubsection append append\n\n\\par\nConcatenates all of its arguments, keeping the head of the first (or \\ref list\n\"tmpl::list\" if passed no arguments).\n\\snippet Test_TMPLDocumentation.cpp tmpl::append\n\n\\see \\ref join \"tmpl::join\"\n\n\n\\subsubsection clear clear\n\n\\par\nProduces a list with the same head as `Sequence` but no elements.\n\\snippet Test_TMPLDocumentation.cpp tmpl::clear\n\n\\remark\nIf the head is known, prefer writing it explicitly. If the head is irrelevant,\nwrite an empty \\ref list \"tmpl::list\".\n\n\n\\subsubsection erase erase\n\n\\par\nProduces a copy of `Sequence` with the element at index `Index` (passed as a\n\\ref integral_constant \"tmpl::integral_constant\" or similar type) removed.\n\\snippet Test_TMPLDocumentation.cpp tmpl::erase\n\n\\par\nThis operator is overloaded \\ref map_erase \"for maps\" and \\ref set_erase\n\"for sets\".\n\n\\see \\ref erase_c\n\n\n\\subsubsection erase_c erase_c\n\n\\par\nProduces a copy of `Sequence` with the element at index `n` (passed as an\n`unsigned int`) removed.\n\\snippet Test_TMPLDocumentation.cpp tmpl::erase_c\n\n\n\\subsubsection filter filter\n\n\\par\nRemoves all types not matching `Predicate` from `Sequence`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::filter\n\n\\see \\ref remove_if \"tmpl::remove_if\"\n\n\n\\subsubsection find find\n\n\\par\nReturns a list containing the first element of `Sequence` for which `Predicate`\nreturns true and all subsequent elements. The default predicate checks that\nthe element's `value` is not equal to zero. Returns an empty list if the\npredicate returns false for all elements.\n\\snippet Test_TMPLDocumentation.cpp tmpl::find\n\n\\see \\ref found \"tmpl::found\", \\ref not_found \"tmpl::not_found\", \\ref\nreverse_find \"tmpl::reverse_find\"\n\n\n\\subsubsection flatten flatten\n\n\\par\nRecursively inlines the contents of elements of `Sequence` that are sequences\nwith the same head.\n\\snippet Test_TMPLDocumentation.cpp tmpl::flatten\n\n\\see \\ref join \"tmpl::join\"\n\n\n\\subsubsection join join\n\n\\par\nCombines lists in the same manner as \\ref append \"tmpl::append\", but takes a\nlist of lists instead of multiple arguments.\n\\snippet Test_TMPLDocumentation.cpp tmpl::join\n\n\n\\subsubsection list_difference list_difference\n\n\\par\nRemove all elements that occur in `Sequence2` from `Sequence1`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::list_difference\n\n\\note\nThis is not a Brigand metafunction. It is implemented in SpECTRE.\n\n\n\\subsubsection merge merge\n\n\\par\nGiven two sorted lists, returns a sorted list containing the elements of both.\nA comparator metalambda can be provided, defaulting to \\ref math_comparison\n\"tmpl::less\".\n\\snippet Test_TMPLDocumentation.cpp tmpl::merge\n\n\\note\nIf there are equivalent elements, those from the second list are placed\nearlier.\n\\snippet Test_TMPLDocumentation.cpp tmpl::merge:equiv\n\n\\see std::merge\n\n\n\\subsubsection partition partition\n\n\\par\nReturns a \\ref pair \"tmpl::pair\" containing a list of the elements of\n`Sequence` for which the `Predicate` returns true and a list of the elements of\n`Sequence` for which the `Predicate` returns false.\n\\snippet Test_TMPLDocumentation.cpp tmpl::partition\n\n\\see \\ref filter \"tmpl::filter\", \\ref remove_if \"tmpl::remove_if\"\n\n\n\\subsubsection pop_back pop_back\n\n\\par\nRemove `Count` elements from the end of `Sequence`. The number of elements to\nremove is supplied as a \\ref integral_constant \"tmpl::integral_constant\" and\ndefaults to 1.\n\\snippet Test_TMPLDocumentation.cpp tmpl::pop_back\n\n\n\\subsubsection pop_front pop_front\n\n\\par\nRemove `Count` elements from the beginning of `Sequence`. The number of\nelements to remove is supplied as a \\ref integral_constant\n\"tmpl::integral_constant\" and defaults to 1.\n\\snippet Test_TMPLDocumentation.cpp tmpl::pop_front\n\n\n\\subsubsection push_back push_back\n\n\\par\nAppends types `T...` to `Sequence`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::push_back\n\n\n\\subsubsection push_front push_front\n\n\\par\nPrepends types `T...` to `Sequence`. The order of the prepended items is\nretained: they are pushed as a unit, not one-by-one.\n\\snippet Test_TMPLDocumentation.cpp tmpl::push_front\n\n\n\\subsubsection remove remove\n\n\\par\nRemoves all occurrences of `T` from `Sequence`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::remove\n\n\n\\subsubsection remove_duplicates remove_duplicates\n\n\\par\nRemove duplicates from `Sequence`. The first occurrence of each type is kept.\n\\snippet Test_TMPLDocumentation.cpp tmpl::remove_duplicates\n\n\\note\nThis is not a Brigand metafunction. It is implemented in SpECTRE.\n\n\n\\subsubsection remove_if remove_if\n\n\\par\nRemoves all types matching `Predicate` from `Sequence`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::remove_if\n\n\\see \\ref filter \"tmpl::filter\"\n\n\n\\subsubsection replace replace\n\n\\par\nReplaces all occurrences of `Old` in `Sequence` with `New`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::replace\n\n\n\\subsubsection replace_if replace_if\n\n\\par\nReplaces all types in `Sequence` matching `Predicate` with `T`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::replace_if\n\n\n\\subsubsection reverse reverse\n\n\\par\nReverses the order of types in `Sequence`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::reverse\n\n\n\\subsubsection reverse_find reverse_find\n\n\\par\nReturns a list containing the last element of `Sequence` for which `Predicate`\nreturns true and all preceding elements. The default predicate checks that the\nelement's `value` is not equal to zero. Returns an empty list if the predicate\nreturns false for all elements.\n\\snippet Test_TMPLDocumentation.cpp tmpl::reverse_find\n\n\\see \\ref find \"tmpl::find\"\n\n\n\\subsubsection reverse_fold reverse_fold\n\n\\par\nPerforms a [right\nfold](https://en.wikipedia.org/wiki/Fold_(higher-order_function)), i.e., given\na list `Sequence`, initial state `State`, and \\ref metalambdas \"metalambda\"\n`Functor`, updates the state by calling `Functor` on the state and the last\nelement of `Sequence`, repeats with the second to last, and so on, returning\nthe final state.\n\\snippet Test_TMPLDocumentation.cpp tmpl::reverse_fold\n\n\\par\nBrigand provides `tmpl::_state` and `tmpl::_element` aliases to the appropriate\n\\ref args \"arguments\" for use in folds.\n\n\\see \\ref fold \"tmpl::fold\"\n\n\n\\subsubsection sort sort\n\n\\par\nSorts `Sequence` according to `Comparator`, which defaults to \\ref\nmath_comparison \"tmpl::less\".\n\\snippet Test_TMPLDocumentation.cpp tmpl::sort\n\n\\note\nThe sort is not stable.\n\\snippet Test_TMPLDocumentation.cpp tmpl::sort:equiv\n\n\n\\subsubsection split split\n\n\\par\nSplits `Sequence` into parts separated by `Delimiter`, discarding empty parts.\n\\snippet Test_TMPLDocumentation.cpp tmpl::split\n\n\n\\subsubsection split_at split_at\n\n\\par\nReturns a list of two of lists, the first containing the first `Index`\n(supplied as a \\ref integral_constant \"tmpl::integral_constant\") elements or\n`Sequence`, and the second containing the remaining elements.\n\\snippet Test_TMPLDocumentation.cpp tmpl::split_at\n\n\n\\subsubsection transform transform\n\n\\par\nCalls a `Functor` on each element of `Sequence`, collecting the results in a\nnew list. If additional `Sequences...` are supplied, elements from those lists\nare passed as additional arguments to `Functor`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::transform\n\n\n\\subsection map_operations Operations on maps\n\n\\par\nBrigand's \\ref map \"tmpl::map\" type can be manipulated by several\nmetafunctions.\n\n\\par\nExamples in this section use this map as an example:\n\\snippet Test_TMPLDocumentation.cpp example_map\n\n\n\\subsubsection map_at at\n\n\\par\nReturns the value associated with `Key` in `Map`. Returns \\ref\nno_such_type_ \"tmpl::no_such_type_\" if `Key` is not in the map.\n\\snippet Test_TMPLDocumentation.cpp tmpl::at:map\n\n\\par\nThis operator is \\ref at \"overloaded for lists\". When called on a \\ref map\n\"tmpl::map\", this is the same as \\ref lookup \"tmpl::lookup\".\n\n\n\\subsubsection map_erase erase\n\n\\par\nProduces a copy of `Map` with the element with the key `Key` removed. If `Key`\nis not in the map, returns `Map` unchanged.\n\\snippet Test_TMPLDocumentation.cpp tmpl::erase:map\n\n\\par\nThis operator is overloaded \\ref erase \"for lists\" and \\ref set_erase\n\"for sets\".\n\n\n\\subsubsection map_has_key has_key\n\n\\par\nReturns a \\ref integral_constant \"tmpl::integral_constant\" of `bool`\nindicating whether `Map` contains the key `Key`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::has_key:map\n\n\\par\nThis operator is \\ref set_has_key \"overloaded for sets\".\n\n\n\\subsubsection map_insert insert\n\n\\par\nReturns `Map` with `Pair` added. If the key of `Pair` is already in the map,\nthe map is returned unchanged.\n\\snippet Test_TMPLDocumentation.cpp tmpl::insert:map\n\n\\par\nThis operator is \\ref set_insert \"overloaded for sets\".\n\n\n\\subsubsection keys_as_sequence keys_as_sequence\n\n\\par\nReturns the keys from `Map` as a sequence with head `Head`, defaulting to \\ref\nset \"tmpl::set\".\n\\snippet Test_TMPLDocumentation.cpp tmpl::keys_as_sequence\n\n\\par\nIf the key-value pairs are required, they can be extracted directly from the\ntemplate arguments of the \\ref map \"tmpl::map\".\n\n\\see \\ref values_as_sequence \"tmpl::values_as_sequence\"\n\n\n\\subsubsection lookup lookup\n\n\\par\nReturns the value associated with `Key` in `Map`. Returns \\ref no_such_type_\n\"tmpl::no_such_type_\" if `Key` is not in the map.\n\\snippet Test_TMPLDocumentation.cpp tmpl::lookup\n\n\\see \\ref map_at \"tmpl::at\"\n\n\n\\subsubsection lookup_at lookup_at\n\n\\par\nReturns the value associated with `Key` in `Map`, wrapped in a \\ref type_\n\"tmpl::type_\". Returns `type_` if `Key` is not in the map.\nThis function has no eager version, but is still in the `tmpl::lazy` namespace.\n\\snippet Test_TMPLDocumentation.cpp tmpl::lookup_at\n\n\\see \\ref lookup \"tmpl::lookup\"\n\n\n\\subsubsection values_as_sequence values_as_sequence\n\n\\par\nReturns the values from `Map` as a sequence with head `Head`, defaulting to\n\\ref list \"tmpl::list\".\n\\snippet Test_TMPLDocumentation.cpp tmpl::values_as_sequence\n\n\\par\nIf the key-value pairs are required, they can be extracted directly from the\ntemplate arguments of the \\ref map \"tmpl::map\".\n\n\\see \\ref keys_as_sequence \"tmpl::keys_as_sequence\"\n\n\n\\subsection set_operations Operations on sets\n\n\\par\nBrigand's \\ref set \"tmpl::set\" type can be manipulated by several\nmetafunctions.\n\n\n\\subsubsection contains contains\n\n\\par\nReturns a \\ref integral_constant \"tmpl::integral_constant\" of `bool`\nindicating whether `Set` contains `T`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::contains\n\n\n\\subsubsection set_erase erase\n\n\\par\nProduces a copy of `Set` with the element `T` removed. If the element is not\nin the set, returns the set unchanged.\n\\snippet Test_TMPLDocumentation.cpp tmpl::erase:set\n\n\\par\nThis operator is overloaded \\ref erase \"for lists\" and \\ref map_erase\n\"for maps\".\n\n\n\\subsubsection set_has_key has_key\n\n\\par\nReturns a \\ref integral_constant \"tmpl::integral_constant\" of `bool`\nindicating whether `Set` contains `T`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::has_key:set\n\n\\par\nThis operator is \\ref map_has_key \"overloaded for maps\".\n\n\n\\subsubsection set_insert insert\n\n\\par\nReturns a copy of `Set` containing an additional element `T`. If `T` is\nalready in the set, the set is returned unchanged.\n\\snippet Test_TMPLDocumentation.cpp tmpl::insert:set\n\n\\par\nThis operator is \\ref map_insert \"overloaded for maps\".\n\n\n\\subsection math Mathematical functions\n\n\\par\nThese perform the same operations at their language counterparts, but on \\ref\nintegral_constant \"tmpl::integral_constant\"s (or anything else with a `value`\nstatic member type of type `value_type`). The results inherit from \\ref\nintegral_constant \"tmpl::integral_constant\"s of types noted below.\n\n\\par\nThese are all lazy metafunctions.\n\n\n\\subsubsection math_arithmetic Arithmetic operators\n\n\\par\nThese operations return classes inheriting from \\ref integral_constant\n\"tmpl::integral_constant\"s of the same type as the result of the language\noperator on their arguments. The integral promotion and conversion rules are\napplied. (Contrast the \\ref math_bitwise \"bitwise operators\".)\n\\snippet Test_TMPLDocumentation.cpp math_arithmetic\n\n\\par\nThe standard library runtime functors have the same names for std::plus,\nstd::minus, std::divides, and std::negate, but the other two are\nstd::multiplies and std::modulus.\n\n\n\\subsubsection math_bitwise Bitwise operators\n\n\\par\nThese operations return classes inheriting from \\ref integral_constant\n\"tmpl::integral_constant\"s of the same type as their first argument's `value`.\nThis is *not* generally the same type as the language operator, even when the\ntypes of the values of both arguments are the same. (The integer promotion and\nconversion rules are not applied.)\n\\snippet Test_TMPLDocumentation.cpp math_bitwise\n\n\\par\nThe standard library runtime functors are called std::bit_not, std::bit_and,\nstd::bit_or, and std::bit_xor.\n\n\n\\subsubsection math_comparison Comparison operators\n\n\\par\nThese operations return classes inheriting from \\ref integral_constant\n\"tmpl::integral_constant\"s of `bool`.\n\\snippet Test_TMPLDocumentation.cpp math_comparison\n\n\\par\nThe standard library runtime functors have the same names, such as\nstd::equal_to.\n\n\n\\subsubsection math_logical Logical operators\n\n\\par\nThese operations return classes inheriting from \\ref integral_constant\n\"tmpl::integral_constant\"s of `bool`. They should only be used on types\nwrapping `bool`s. The `and_` and `or_` structs can take any number of\narguments.\n\\snippet Test_TMPLDocumentation.cpp math_logical\n\n\\par\nThe standard library runtime functors are called std::logical_and,\nstd::logical_or, and std::logical_not. The xor operation is equivalent to \\ref\nmath_comparison \"tmpl::not_equal_to\".\n\n\n\\subsubsection identity identity\n\n\\par\nThe identity function. Unlike most math functions, this returns the same type\nas its argument, even if that is not a \\ref integral_constant\n\"tmpl::integral_constant\".\n\\snippet Test_TMPLDocumentation.cpp tmpl::identity\n\n\\see \\ref always \"tmpl::always\"\n\n\n\\subsubsection max max\n\n\\par\nComputes the larger of `T1` and `T2`, returning a \\ref integral_constant\n\"tmpl::integral_constant\" of the common type of its arguments.\n\\snippet Test_TMPLDocumentation.cpp tmpl::max\n\n\n\\subsubsection min min\n\n\\par\nComputes the smaller of `T1` and `T2`, returning a \\ref integral_constant\n\"tmpl::integral_constant\" of the common type of its arguments.\n\\snippet Test_TMPLDocumentation.cpp tmpl::min\n\n\n\\subsubsection next next\n\n\\par\nComputes `T` plus one, returning a \\ref integral_constant\n\"tmpl::integral_constant\" of the same type as its argument.\n\\snippet Test_TMPLDocumentation.cpp tmpl::next\n\n\n\\subsubsection prev prev\n\n\\par\nComputes `T` minus one, returning a \\ref integral_constant\n\"tmpl::integral_constant\" of the same type as its argument.\n\\snippet Test_TMPLDocumentation.cpp tmpl::prev\n\n\n\\subsection misc Miscellaneous functions\n\n\\par\nFunctions that don't fit into any of the other sections.\n\n\n\\subsubsection always always\n\n\\par\nA lazy identity function.\n\\snippet Test_TMPLDocumentation.cpp tmpl::always\n\n\\see \\ref identity \"tmpl::identity\"\n\n\n\\subsubsection apply apply\n\n\\par\nCalls a \\ref metalambdas \"metalambda\" `Lambda` with arguments `Arguments...`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::apply\n\n\n\\subsubsection count count\n\n\\par\nReturns the number of template parameters provided as a \\ref integral_constant\n\"tmpl::integral_constant\" of `unsigned int`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::count\n\n\n\\subsubsection conditional_t conditional_t\n\n\\par\nReturns `TrueResult` if the `bool` `b` is true, otherwise `FalseResult`. An\noptimized version of std::conditional_t.\n\\snippet Test_TMPLDocumentation.cpp tmpl::conditional_t\n\n\\note\nThis is not a Brigand metafunction. It is implemented in SpECTRE.\n\n\n\\subsubsection eval_if eval_if\n\n\\par\nA lazy metafunction that, if `Condition` has a true `value`, evaluates and\nreturns the result of the lazy metafunction (*not* metalambda) `TrueFunction`,\notherwise, evaluates and returns the result of the lazy metafunction\n`FalseFunction`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::eval_if\n\n\\par\nThis performs lazy evaluation of conditional branches outside of a metalambda.\n\n\n\\subsubsection eval_if_c eval_if_c\n\n\\par\nThe same as \\ref eval_if \"tmpl::eval_if\", but takes its first argument as a\n`bool` instead of a type.\n\\snippet Test_TMPLDocumentation.cpp tmpl::eval_if_c\n\n\n\\subsubsection has_type has_type\n\n\\par\nA lazy metafunction that returns `T` (defaulting to `void`), ignoring its first\nargument.\n\\snippet Test_TMPLDocumentation.cpp tmpl::has_type\n\n\\par\nThis can be used to expand a parameter pack to repetitions of the same type.\n\\snippet Test_TMPLDocumentation.cpp tmpl::has_type:pack_expansion\n\\snippet Test_TMPLDocumentation.cpp tmpl::has_type:pack_expansion:asserts\n\n\n\\subsubsection if_ if_\n\n\\par\nA lazy metafunction that returns `TrueResult` if the `value` static member\nvalue of `Condition` is true, and otherwise `FalseResult`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::if_\n\n\\warning\nThe second and third arguments are both evaluated, independent of which is\nreturned. Use \\ref defer \"tmpl::defer\" or \\ref eval_if \"tmpl::eval_if\" if this\nis undesirable.\n\n\n\\subsubsection if_c if_c\n\n\\par\nThe same as std::conditional.\n\\snippet Test_TMPLDocumentation.cpp tmpl::if_c\n\n\n\\subsubsection inherit inherit\n\n\\par\nA lazy metafunction that produces a type with all of its template arguments as\nbase classes. All the arguments must be unique.\n\\snippet Test_TMPLDocumentation.cpp tmpl::inherit\n\n\\remark\nThis task can be performed more simply than the algorithm used by Brigand by\ndirectly using pack expansions:\n\\snippet Test_TMPLDocumentation.cpp tmpl::inherit:pack:definitions\n\\snippet Test_TMPLDocumentation.cpp tmpl::inherit:pack:asserts\n\n\\note\nThe \\ref empty_base \"tmpl::empty_base\" type is used internally as a sentinel.\nThe result may or may not inherit from \\ref empty_base \"tmpl::empty_base\",\nindependently of whether it is supplied as an argument.\n\n\n\\subsubsection inherit_linearly inherit_linearly\n\n\\par\nTransforms `Sequence` into a linked list. The `NodePattern` must be a class\ntemplate (*not* a lazy metafunction) instantiated with metalambdas. The\nfunction performs a [left\nfold](https://en.wikipedia.org/wiki/Fold_(higher-order_function)), with the\n`Root` (defaulting to \\ref empty_base \"tmpl::empty_base\") as the initial state\nand the transform function evaluating the arguments to the node pattern.\n\\snippet Test_TMPLDocumentation.cpp tmpl::inherit_linearly\n\n\\remark\nThis function handles its function-like argument differently from any other\nfunction in Brigand. Prefer \\ref fold \"tmpl::fold\", which can perform the same\ntask and has a more standard interface.\n\n\n\\subsubsection is_set is_set\n\n\\par\nTests if all of its arguments are distinct, producing a \\ref integral_constant\n\"tmpl::integral_constant\" of `bool`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::is_set\n\n\\note\nThis is unrelated to the Brigand \\ref set \"tmpl::set\" type.\n\n\n\\subsubsection real_ real_\n\n\\par\nRepresents a floating point number of type `RealType` at compile time via its\ninternal memory representation. The value is stored as a \\ref\nintegral_constant \"tmpl::integral_constant\" of type `IntType` with value\n`value` (which must be the same size as `RealType`) and can be extracted at\nruntime using the conversion operator. Brigand provides the aliases\n`single_` and `double_` with `RealType` and `IntType` set to\nappropriate values.\n\\snippet Test_TMPLDocumentation.cpp tmpl::real_\n\n\\par\nThere are no compile-time mathematical functions provided for floating point\ntypes. They are opaque (or sometimes treated as integers) until runtime.\n\n\\remark\nConsider whether you really need to represent floating point values at compile\ntime.\n\n\\see std::ratio\n\n\n\\subsubsection repeat repeat\n\n\\par\nCalls a unary eager metafunction `Function` on `Initial`, then on the result of\nthat, then on the result of that, and so on, up to `Count` calls.\n\\snippet Test_TMPLDocumentation.cpp tmpl::repeat\n\n\\note\nThis function has a lazy version, but it cannot be used in a metalambda because\nthe template template parameter prevents manipulation of the parameter list.\n\\snippet Test_TMPLDocumentation.cpp tmpl::repeat:lazy\n\n\\see \\ref make_sequence \"tmpl::make_sequence\"\n\n\n\\subsubsection sizeof_ sizeof_\n\n\\par\nA lazy metafunction that computes `sizeof` its argument as an `unsigned int`\n\\ref integral_constant \"tmpl::integral_constant\".\n\\snippet Test_TMPLDocumentation.cpp tmpl::sizeof_\n\n\n\\subsubsection substitute substitute\n\n\\par\nSubstitutes values from `ArgumentList` for appearances of \\ref args\n\"tmpl::args\" (but *not* `tmpl::_1` or `tmpl::_2`) appearing in `Pattern`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::substitute\n\n\n\\subsubsection type_from type_from\n\n\\par\nExtracts the `type` from `T`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::type_from\n\n\\remark\nThis function will work on any class with a `type` type alias, but, when used\noutside of a metafunction, it should only be used with \\ref type_ \"tmpl::type_\"\nfor clarity.\n\n\n\\subsubsection wrap wrap\n\n\\par\nReplaces the head of `Sequence` with `Head`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::wrap\n\n\\note\nThis function has a lazy version, but it cannot be used in a metalambda because\nthe template template parameter prevents manipulation of the parameter list.\n\\snippet Test_TMPLDocumentation.cpp tmpl::wrap:lazy\n\n\n\\subsection runtime Runtime functionality\n\n\\par\nBrigand provides a few C++ functions that execute at runtime.\n\n\\par\nThe examples in this section use the following definition:\n\\snippet Test_TMPLDocumentation.cpp runtime_declarations\n\n\n\\subsubsection for_each_args for_each_args(functor, arguments...)\n\n\\par\nCalls `functor` on each of `arguments...`, in order. Returns `functor`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::for_each_args:defs\n\\snippet Test_TMPLDocumentation.cpp tmpl::for_each_args\n\n\n\\subsubsection for_each for_each(functor)\n\n\\par\nCalls `functor` on \\ref type_ \"tmpl::type_\" objects wrapping each type in\n`Sequence`, in order. Returns `functor`.\n\\snippet Test_TMPLDocumentation.cpp tmpl::for_each:defs\n\\snippet Test_TMPLDocumentation.cpp tmpl::for_each\n\n\\see \\ref type_from \"tmpl::type_from\"\n\n\n\\subsubsection select select(true_result, false_result)\n\n\\par\nReturns `true_result` if `Condition`'s `value` member is true,\nand `false_result` if it is false.\n\\snippet Test_TMPLDocumentation.cpp tmpl::select\n\n\n\\subsection external External integration\n\n\\par\nBrigand provides metafunctions for interfacing with some types from the\nstandard library and Boost. They usually come in pairs, with `as_X` taking a\nlist and `X_wrapper` taking a parameter pack. This makes `X_wrapper`\nequivalent to the wrapped class.\n\n\\remark\nAvoid the `*_wrapper` functions in favor of using the class directly.\n\n\n\\subsubsection boost_integration Boost\n\n\\par\nBrigand provides functions to produce the `boost::fusion` types `deque`,\n`list`, `set`, and `vector`, as well as `boost::variant`. Because we use brigand\ninstead of boost::fusion and because `std::variant` replaces `boost::variant`,\nthese are not available in SpECTRE.\n\n\\subsubsection stl_integration STL\n\n\\par\nBrigand provides functions to produce the STL types std::pair and std::tuple.\nIn addition to the usual functions, Brigand provides `pair_wrapper_`, which is\na lazy form of `pair_wrapper`. The pair functions all assert that they have\nreceived two types.\n\\snippet Test_TMPLDocumentation.cpp stl_integration\n\n\n\\subsubsection make_integral integral_constant\n\n\\par\nBrigand provides two functions for converting from std::integral_constant (or a\nsimilar class with a `value_type` and a `value`) to \\ref integral_constant\n\"tmpl::integral_constant\". The lazy metafunction `make_integral` performs this\nconversion. The `as_integral_list` eager metafunction performs this operation\non all elements of a list.\n\\snippet Test_TMPLDocumentation.cpp tmpl::make_integral\n\n\\warning\nThe standard library std::integer_sequence is not a list of types, and so\ncannot be used as input to `as_integral_list`.\n\n\n\\subsubsection as_list list\n\n\\par\nBrigand provides two metafunctions for converting types to Brigand sequences.\nThe more general function, `as_sequence`, is equivalent to \\ref wrap\n\"tmpl::wrap\". The specialized version, `tmpl::as_list`, produces a \\ref list\n\"tmpl::list\".\n\\snippet Test_TMPLDocumentation.cpp tmpl::as_list\n\n\\remark\nUsing `as_list` is often not necessary because most metafunctions operate on\narbitrary template classes.\n\n\n\\subsubsection as_set set\n\n\\par\nBrigand provides the standard two metafunctions for converting types to Brigand\n\\ref set \"tmpl::set\"s.\n\\snippet Test_TMPLDocumentation.cpp tmpl::as_set\n\n\n\\section oddities Bugs/Oddities\n\n* \\ref push_front and \\ref pop_front have lazy versions, but \\ref push_back,\n and \\ref pop_back do not.\n\n* \\ref reverse_range validates its arguments, but \\ref range does not.\n (Probably because the former is called incorrectly more often.)\n\n* Brigand inconsistently uses `unsigned int` and `size_t` for size-related\n things. (Most blatantly, the result of \\ref sizeof_ is represented as an\n `unsigned int`.)\n\n* Brigand has a file containing operator overloads for \\ref integral_constant\n \"\"s, but it is not included by the main brigand header. They work poorly,\n mostly because it inexplicably puts them all in namespace std where the\n compiler can't find them.\n" }, { "path": "docs/DevGuide/BuildOptimization.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n# Build Profiling and Optimization {#build_profiling_and_optimization}\n\n\\tableofcontents\n\n# Why is our build so expensive?\n\nSpECTRE makes heavy use of compile-time logic, which is responsible for a lot of\nthe nice type-checking, performance, and flexibility the code has to offer.\nFor instance, our central data structure, the \\ref DataBoxGroup \"DataBox\", uses\na type list of several \"tags\" to determine its contents, as well as to\nautomatically propagate dependencies in compute items.\n\nThis use of compile-time logic, however, has the trade-off of making our builds\ntake longer and use more memory than a similar implementation in runtime logic\nwould.\nThere is good reason to believe that some of these costs are payed back at\nruntime, because many of our compile-time switches permit the final runtime code\nto be more efficient or avoid unnecessary computation.\nThere is certainly room for optimization, though, either in finding better\ncompile-time implementations of the algorithms, eliminating expensive template\ninstantiations, or moving inefficient parts to runtime.\nThis guide gives a quick outline of some of the methods that can be used to\nprofile the build and possible pitfalls\n\n# Understanding template expenses\n\nThe cost of compile-time template logic is a bit non-intuitive if you are used\nto thinking only of runtime performance.\nThe main reason is that the typical unit of 'cost' in a compile-time operation\nis the number of instantiated types and functions.\nRe-using a type that has been instantiated elsewhere (in the same translation\nunit) typically has a very low compile-time cost, where instantiating a type\nwith new template parameters will incur its own cost, plus any new types that it\nrequires in e.g. type aliases or member functions.\n\nConsider a Fibonacci calculation at compile-time:\n```\ntemplate \nstruct Fibonacci {\n static constexpr size_t value =\n Fibonacci::value + Fibonacci::value;\n};\n\ntemplate <>\nstruct Fibonacci<1> {\n static constexpr size_t value = 1;\n};\n\ntemplate <>\nstruct Fibonacci<0> {\n static constexpr size_t value = 1;\n};\n```\nIf we were to write the same logic at runtime, the algorithm would be hopelessly\ninefficient; the recursive calls would cause each call to Fibonacci to make two\ncalls to the same function, resulting in an exponential time algorithm!\nHowever, the C++ language will only instantiate unique types, so only N types\nwill be created, giving a linear in compile-time operation.\n\n\nCompile-time lists and list operations frequently appear in SpECTRE, and should\nbe thought of differently from runtime list operations.\n\nIn compile-time lists, we have no access to true constant-time lookup, speedy\nalgorithms that rely on sorted structures, or more sophisticated data structures\n(balanced trees, hash tables, etc.).\nThe limitations of compile-time list techniques can cause list operations to be\nmore costly than we could achieve with runtime data structures.\n\nConsider a basic version of the compile-time list accessor:\n```\ntemplate \nstruct list_at;\n\ntemplate \nstruct list_at, 0> {\n using type = ListItem0;\n};\n\ntemplate \nstruct list_at, Index> {\n using type = typename list_at, Index - 1>::type;\n};\n```\nNow, to access the Nth item in the list, we need to instantiate \\f$O(N)\\f$\ntypes.\nThe above implementation is significantly more costly than we would find in\npractice in template metaprogramming libraries -- in particular, our chosen\nTMPL backend, [Brigand](https://github.com/edouarda/brigand), manages the task\nin \\f$O(\\log(N))\\f$ (at least in type instantiation count).\n\nMost of the list operations in SpECTRE cannot take advantage of any particular\nordering or hashing of the list, so must resort to naive list operations --\nso, searching a list (`tmpl::list_contains` or `tmpl::index_of`) is\n\\f$O(N)\\f$ cost, `tmpl::remove_duplicates` is \\f$O(N^2)\\f$, and\n`tmpl::list_difference` is similarly \\f$O(N^2)\\f$.\nSo, complicated type logic scales pretty badly with long lists, and improvements\ncan sometimes be made by reducing a list's size or avoiding the more costly list\noperations when a list is known to be long.\n\n# Profiling the build\n\nIn the current version of SpECTRE, the most expensive builds are the final\ntranslation units associated with the executables (particularly the most\ncomplicated executables, like Generalized Harmonic and Valencia), which should\nbe unsurprising from the above discussion: it is in these compilation steps that\nwe instantiate the Parallel components, and in turn, all of the \\ref\nDataBoxGroup \"DataBox\" types that will be used during the evolution.\n\nSimilarly, a number of tests have now shown that in the current version of\nSpECTRE (as of early 2021), by far the most expensive part of the build is\n\\ref DataBoxGroup \"DataBox\" operations and instantiations, and the best build\nperformance gains are available by either reducing the number of\n\\ref DataBoxGroup \"DataBox\"es that are instantiated, reducing the number of tags\n(particularly compute tags) stored in the \\ref DataBoxGroup \"DataBox\", or\noptimizing the implementations of the \\ref DataBoxGroup \"DataBox\" and its\nutilities.\nSo, generally speaking, profiling should start by focusing on the\n\\ref DataBoxGroup \"DataBox\", and move to other utilities if it becomes clear\nthat there are other parts of the code that are contributing significantly to\nthe compilation time or memory usage.\n\n\n## Specialized tests and feature exploration\n\nThis is simultaneously the most reliable and most labor-intensive strategy for\nunderstanding build costs.\nThe procedure is to identify a feature you'd like to profile and create a\nspecialized test for that feature.\nThen, you can easily include or exclude uses of functions or classes that you\nwant to profile, and compare the relative total cost of building the test\nexecutable. You may want to temporarily remove all other source files from\nthe test executable.\n\nThere are a number of tools for profiling the cost of an individual process,\nbut for compilation, the detailed tools like `perf` or hpctoolkit are unlikely\nto give useful information about what parts of our code are slow to build.\nInstead, it's best to just carefully measure the full build of the target\nin question, and rapidly iterate to include or exclude potentially expensive\nparts to understand the build costs.\n\nThere are a lot of tools that can give you the global resource usage\ninformation, including the `/proc/$PID/status` file from kernel information,\n`top`, or tools from the `sysstat` package.\nThe `time` utility is particularly user-friendly, available on ubuntu (and\ntherefore in the SpECTRE build container) via `apt-get install time`.\nThen, it can be invoked by `/usr/bin/time -v your_command` (note that simply\n`time` will route to a different alias in the default environment on ubuntu in\nthe container, so the full path `/usr/bin/time` is required).\nAfter completion, it will print a readable report of the time and memory usage.\n\nOne important feature to be aware of in profiling the build by this method is\nthe implicit memoization of many compile-time features.\nFor instance, if feature `A` and `B` both instantiate a class `C` that is\nexpensive to build, you'll see a difference in the build cost when _either_ `A`\nor `B` are included, but the cost won't be additive - the second feature will\njust 'reuse' the instantiation from the first.\nTo optimize this type of situation, either `C` must be improved to be less\ncostly to instantiate, or its use must be eliminated from _both_ `A` and `B` --\nremoving `C` from only one of the classes that use it won't help the build much\nat all.\n\n## Templight++\n\nDetailed profiling of a C++ build is a surprisingly hard task, and there are few\nuseful tools for getting a good idea for what parts of a compilation are\nexpensive. One tool that can perform some profiling of the build is\n[templight++](https://github.com/mikael-s-persson/templight).\n_It is important to note that this tool often produces build profiles that are\nmisleading or incomplete!_ It is included in this guide under the philosophy\nthat a flawed tool can be better than no tool at all in some circumstances,\nbut the templight++ profiles should be taken primarily as a loose guide for\nfeatures to investigate with more careful follow-up investigations like the\nabove suggestion of specialized tests and feature exploration.\n\nThe `templight++` build and usage instructions work nicely with the current\nSpECTRE build system, and the cmake trick suggested by the `templight++`\ndocumentation\n```bash\nexport CC=\"/path/to/llvm/build/bin/templight -Xtemplight -profiler\\\n -Xtemplight -memory\"\nexport CXX=\"/path/to/llvm/build/bin/templight++ -Xtemplight -profiler\\\n -Xtemplight -memory\"\n```\nworks well in SpECTRE. Build profiling with `templight++` are incredibly slow,\nand seem to produce increasingly misleading data for larger builds, so it is\nrecommended to avoid using the tool for our most expensive evolution\nexecutables. Experience indicates that you will likely wait for hours and be\ndisappointed by deeply flawed results.\n\n\nAfter building a target, you will find along side each `.o` file in the\n`build/src` tree an additional file that ends with `.trace.pbf`.\nThese are the `templight++` trace files, and (like many performance tool\noutputs), require post-processing to recover human-readable data.\nThe companion package\n[templight-tools](https://github.com/mikael-s-persson/templight-tools)\ncan be built to obtain the `templight-convert` utility that converts\nthe templight traces to more managable formats.\nIt is recommended to install and use\n[KCacheGrind](https://kcachegrind.github.io/html/Home.html)\n(which does, unfortunately require some KDE libraries, but doesn't require you\nto use the full KDE window system) to visualize the output -- the larger graphs\nproduced by templight are inefficient to render in the graphviz format.\n\n## Clang profiling\n\nWith `clang >= 9`, you can generate a flame graph of what the compiler is\nspending its time on, including specific function instantiations, class\ninstantiations, source file parsing, debug info generation, and function\noptimization. To do so, add `-ftime-trace` to the `cmake` option\n`-D CMAKE_CXX_FLAGS` in your `cmake` command for your build. Then, you can\nsimply `make TargetName`. This will produce a `.json` for each `.cpp.o` that\nwas compiled in the directory that the object file is stored. Note that these\nobject and `.json` files are deep within the build directory. You can then load\nyour `.json` of interest into `chrome://tracing`. Because our code base utilizes\nmany templates and some compilation targets instantiate many types, classes, and\nfunctions, note that the flame graph for a particular compilation target may be\na lot to visually navigate, click through, and analyze at a high level. Because\nof this, the tool described below can be very useful and more manageable for\nsome analyses.\n\nThe companion tool to the flame graph generation is the\n[ClangBuildAnalyzer](https://github.com/aras-p/ClangBuildAnalyzer). This is an\nopen source tool that you can clone and run to give you profiling output\nsimilar to when you profile runtime code in that it identifies compilation hot\nspots for you. It will report things like \"Here are the templates/functions\nthat took the longest to instantiate/compile.\" Note that because many of our\ntypes can have very long names due to our templating, some class and function\nsignatures will not fit in the default character limit of what is printed to the\nterminal. You can adjust the maximum character length printed by creating a\n`ClangBuildAnalyzer.ini` file in your working directory as described in the\n[ClangBuildAnalyzer](https://github.com/aras-p/ClangBuildAnalyzer) `readme.md`.\n\n## Clang AST syntax generation\n\nThere is a nice and poorly documented feature of the `clang++` compiler that it\ncan produce a rough approximation of the collection of C++ template\ninstantiations produced by a particular executable.\nAdding `-Xclang -ast-print -fsyntax-only` to the `CXX_FLAGS` will cause this\ninformation to be printed to stdout, which should probably be redirected to file\nbecause it will be an enormous output.\nImportantly, to the best of our knowledge, this tool has not yet been used to\nsuccessfully profile any SpECTRE build, but with sufficient post-processing the\nC++-syntax version of the AST might be useful to determine the number and nature\nof instantiations produced by a particular piece of code, and might offer some\nproxy for build performance.\n\nFor instance, if we put the above `Fibonacci` struct in a source file with:\n```cpp\nint main(int argc, char** argv) {\n std::cout << Fibonacci<6>::value << \"\\n\";\n}\n```\nand we compile it with\n```\nclang++-10 -Xclang -ast-print -fsyntax-only -o fib ./fib.cpp >> fib_out\n```\nwe obtain in `fib_out` (after thousands of lines of STL-generated code):\n```cpp\ntemplate struct Fibonacci {\n static constexpr size_t value =\n Fibonacci::value + Fibonacci::value;\n};\ntemplate <> struct Fibonacci<6> {\n static constexpr size_t value =\n Fibonacci<6UL - 1>::value + Fibonacci<6UL - 2>::value;\n};\ntemplate <> struct Fibonacci<5> {\n static constexpr size_t value =\n Fibonacci<5UL - 1>::value + Fibonacci<5UL - 2>::value;\n};\ntemplate <> struct Fibonacci<4> {\n static constexpr size_t value =\n Fibonacci<4UL - 1>::value + Fibonacci<4UL - 2>::value;\n};\ntemplate <> struct Fibonacci<3> {\n static constexpr size_t value =\n Fibonacci<3UL - 1>::value + Fibonacci<3UL - 2>::value;\n};\ntemplate <> struct Fibonacci<2> {\n static constexpr size_t value =\n Fibonacci<2UL - 1>::value + Fibonacci<2UL - 2>::value;\n};\ntemplate <> struct Fibonacci<1> { static constexpr size_t value = 1; };\ntemplate <> struct Fibonacci<0> { static constexpr size_t value = 1; };\nint main(int argc, char **argv) { std::cout << Fibonacci<6>::value << \"\\n\"; }\n```\nWhich is actually pretty illuminating about what the compiler decided to do in\nthis simple case.\nUnfortunately, the AST produced by `clang++` in more complicated cases produces\nextremely large outputs, so realistic cases are likely too large to be usefully\nhuman-readable.\nIt may be possible, though, to script post-processing tools to sift through the\ncollections of template instantiations for particular classes to understand\nspecific cases of template logic.\n\n" }, { "path": "docs/DevGuide/CodeReviewGuide.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Code Review Guide {#code_review_guide}\n\n\\tableofcontents\n\nCode must follow the\nC++ Core Guidelines\nand the [Google style guide](https://google.github.io/styleguide/cppguide.html).\nIf the Google style guide disagrees with the Core Guidelines, follow the Core\nGuidelines. Python code must also follow the\n[Google style guide](https://google.github.io/styleguide/pyguide.html).\n\nHere we summarize what we view as the more important portions of the guides.\n\nStylistic Items:\n\n* Adhere to [Google style](https://google.github.io/styleguide/cppguide.html).\n [Can use `clang-format -style=google`][clang_format].\n* CamelCase: class names template parameters, file names, and directory names.\n* snake_case: function, variable, metafunction and metavariable names.\n* SCREAMING_SNAKE_CASE: macros.\n* Functions or classes only used internally in a library should be in a\n namespace named `LibraryOrFile_detail`. For example, `databox_detail`,\n `Tensor_detail` or `ConstantExpressions_detail`.\n* Name unused function parameters `/*parameter_name*/` or `/*meta*/` for TMP\n cases\n* Type aliases that wrap type traits have a trailing `_t` following the STL\n* Private member variables have a [trailing underscore][variable_names].\n* Do not use\n [Hungarian notation](https://en.wikipedia.org/wiki/Hungarian_notation),\n e.g. `double* pd_blah` is bad\n* Header order:\n 1. (If a test:) `Framework/TestingFramework.hpp`, followed by one blank line\n 2. (If a cpp file with a corresponding hpp file:) hpp corresponding to cpp,\n followed by one blank line\n 3. STL and externals (in alphabetical order)\n 4. Blank line\n 5. SpECTRE includes (in alphabetical order)\n* Template definitions in header files are separated from the declaration of\n the class by the following line, which contains exactly 64 equal signs\n ``` cpp\n // ================================================================\n ```\n\n* File lists in CMake are alphabetical.\n* No blank lines surrounding Doxygen group comments\n (// \\@{ and // \\@}).\n* Use the [alternative tokens][alternative_tokens] `or`, `and`, and `not`\n instead of `||`, `&&`, and `!`.\n* Use C-style Doxygen comments (`/*! ... */`) when using multi-line math,\n otherwise C-style and C++ style comments are accepted.\n* Use the `align` environment instead of `eqnarray`. See the\n [texfaq](https://texfaq.org/FAQ-eqnarray) for an explanation as to why.\n* Multi-line equations must have a blank Doxygen line before and after the\n equation.\n* When addressing requests on a PR, the commit message must start with\n `fixup` followed by a descriptive message.\n* All python code must comply with the [black](https://github.com/psf/black)\n formatting specified by the `pyproject.toml` file.\n* Imports in Python code must be sorted to comply to the\n [isort](https://github.com/PyCQA/isort) formatting specified in the\n `pyproject.toml` file.\n\nCode Quality Items:\n\n* All code passes Clang and CppCheck static analyzers. For help\n with these tools see \\ref static_analysis_tools \"here\".\n* Almost always `auto`, except with expression templates, i.e. `DataVector`\n* All loops and if statements use braces.\n* Order of declaration in classes is `public` before `private` and member\n functions before data. See\n [Google](https://google.github.io/styleguide/cppguide.html#Declaration_Order).\n* Prefer return by value over pass-by-mutable-reference except when mutable\n reference provides superior performance (in practice if you need a mutable\n reference use `const gsl::not_null` instead of `Type&`). The mutable\n references must be the first arguments passed to the function.\n* All commits for performance changes provide quantitative evidence and the\n tests used to obtain said evidence.\n* Never include ``, use `Parallel::printf` inside\n `Parallel/Printf/Printf.hpp` instead, which is safe to use in parallel.\n* When using charm++ nodelocks include `` instead of ``.\n* Do not add anything to [the `std` namespace][extending_std].\n* Virtual functions are explicitly overridden using the `override` keyword.\n* `#%pragma once` is to be used for header guards\n* Prefer range-based for loops\n* Use `size_t` for positive integers rather than `int`, specifically when\n looping over containers. This is in compliance with what the STL uses.\n* Error messages should be helpful. An example of a bad error message is \"Size\n mismatch\". Instead this message could read \"The number of grid points in the\n matrix 'F' is not the same as the number of grid points in the determinant.\",\n along with the runtime values of the mentioned quantities if applicable.\n* Mark immutable objects as `const`\n* Make classes serializable by writing a `pup` function\n* If a class stores an object passed into a constructor the object should\n be taken by-value and `std::move`d into the member variable.\n* Definitions of function and class templates should be in `.cpp` files with\n explicit instantiations whenever possible. The macro\n `GENERATE_EXPLICIT_INSTANTIATIONS` is useful for generating many\n explicit instantiations.\n* Functions should not be marked `noexcept` unless it is part of the\n signature of an overriden function (e.g. the what() function of an exception\n derived from std::exception).\n* Variable names in macros must avoid name collisions, e.g. inside the\n `PARSE_ERROR` macro you would write\n `double variable_name_avoid_name_collisions_PARSE_ERROR = 0.0;`\n* Avoid macros if possible. Prefer `constexpr` functions, constexpr\n variables, and/or template metaprogramming\n* Explicitly specify `double`s, e.g. `sqrt(2.)` or `sqrt(2.0)` instead of\n `sqrt(2)`.\n* When the index of a `Tensor` is known at compile time, use\n `get(tensor)` instead of the member `get` function.\n* All necessary header files must be included. In header files, prefer\n forward declarations if class definitions aren't necessary.\n* Explicitly make numbers floating point, e.g. `2.` or `2.0` over `2`.\n* Avoid `mutable` member variables. If you think you really need these, discuss\n with at least 2 core developers. In a parallel environment `mutable` variables\n lead to race conditions since multiple threads can mutate a single object by\n calling a `const` member function.\n\n[alternative_tokens]:\n http://en.cppreference.com/w/cpp/language/operator_alternative\n[clang_format]: http://clang.llvm.org/docs/ClangFormat.html\n[extending_std]: http://en.cppreference.com/w/cpp/language/extending_std\n[variable_names]:\n https://google.github.io/styleguide/cppguide.html#Variable_Names\n" }, { "path": "docs/DevGuide/CompilerLinkerErrors.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n# Understanding Compiler and Linker Errors {#compiler_and_linker_errors}\n\n\\tableofcontents\n\n# Linker Errors {#understanding_linker_errors}\n\nThere are a few common mistakes that can lead to linker problems, specifically\nproblems where there is an `undefined reference`. These include:\n- forgetting to add a `.cpp` file to the list of sources of a library in a\n `CMakeLists.txt` file\n- missing an explicit instantiation of a function or class template in a `cpp`\n file\n- not including a `tpp` file inside a `cpp` file\n- the template specialization or function overload has been explicitly disabled\n via SFINAE (usually through the use of a `requires` clause)\n- not linking a library (explained below)\n\nPossibly the most difficult part of fixing linking errors is understanding what\nthey are trying to tell you. Let's take the following example\n```\nerror: undefined reference to 'Tensor >,\nbrigand::list > >\nrandom_unit_normal(gsl::not_null*>, Tensor,\nbrigand::integral_constant >,\nbrigand::list, Tensor_detail::TensorIndexType<3ul, (UpLo)1, Frame::Inertial,\n(IndexType)0> > > const&)' in\nlib/libTest_GeneralizedHarmonic.a(Test_UpwindFlux.cpp.o):\nTest_UpwindFlux.cpp:function (anonymous namespace)::test_upwind_flux_random()\n```\nWe can start by splitting out information about different parts of the\nerror. First,\n```\nerror: undefined reference to\n```\ntells us that we forgot to add a link dependency for a library or\nexecutable. The next relevant part of information is which library (executable)\nand file the missing function/class was in. This is at the end of the error\nmessage (unfortunately, where in the error message can depend on your linker,\nthese examples used `ld.lld` v9):\n```\nlib/libTest_GeneralizedHarmonic.a(Test_UpwindFlux.cpp.o):\nTest_UpwindFlux.cpp:function (anonymous namespace)::test_upwind_flux_random()\n```\nWhat this means is that the missing link dependency is used in the library\n`Test_GeneralizedHarmonic`, the file `Test_UpwindFlux.cpp`, and the function\n`test_upwind_flux_random()`.\n\nWe have now determined what the linker error is (a missing link dependency), and\nin which library, file, and function the missing link dependency is used. We now\nneed to understand what the missing link dependency is. Since SpECTRE uses a lot\nof templates, the missing reference (link dependency) can be quite\nlong. In this case it is:\n```\nTensor >,\nbrigand::list > >\nrandom_unit_normal(gsl::not_null*>, Tensor,\nbrigand::integral_constant >,\nbrigand::list, Tensor_detail::TensorIndexType<3ul, (UpLo)1, Frame::Inertial,\n(IndexType)0> > > const&)\n```\nIn order to make this easier to read, it is recommended to run the code through\nClangFormat. This can be done by copying the linker output into an empty `cpp`\nfile and running `clang-format -i EMPTY_FILE_WITH_LINKER_OUTPUT`. Keep in mind\nthat ClangFormat will only work if you have only copied the part of the linker\noutput that resembles valid C++. Doing so in this case gives:\n\\code{.cpp}\nTensor >,\n brigand::list > >\nrandom_unit_normal(\n gsl::not_null*>,\n Tensor,\n brigand::integral_constant >,\n brigand::list<\n Tensor_detail::TensorIndexType<3ul, (UpLo)1, Frame::Inertial,\n (IndexType)0>,\n Tensor_detail::TensorIndexType<3ul, (UpLo)1, Frame::Inertial,\n (IndexType)0> > > const&);\n\\endcode\nWe see that it is the function `random_unit_normal` that isn't found. Now we can\nsearch in the code base where than function is defined. Doing a\n`git grep \"random_unit_normal\"` points to\n`tests/Unit/Helpers/DataStructures/RandomUnitNormal.?pp`. Looking\nat `tests/Unit/Helpers/DataStructures/RandomUnitNormal.hpp` we see that the\nfunction `random_unit_normal` is declared there, and looking in the\ncorresponding `cpp` we see `random_unit_normal` is instantiated in the source\nfile. Opening up `tests/Unit/Helpers/DataStructures/CMakeLists.txt` we see that\nthe library name is `DataStructuresHelpers`, and `RandomUnitNormal.cpp` is in\nthe list of sources for the library. Thus, linking\n`Test_GeneralizedHarmonic` against `DataStructuresHelpers` will resolve our\nerror. To link against a library, you must add it to the\n`target_link_libraries`.\n\nIf `random_unit_normal` had been defined in the header file, then the error\nwould've indicated that we did not include the header (or `tpp`) file into\n`Test_UpwindFlux.cpp`, and so the compiler could not generate an\ninstantiation.\n\nIn summary:\n- Identify target with undefined reference, i.e. the file included in a library\n or executable.\n- Identify missing source definition (usually a function or static variable).\n- Find source declaration and definition in repository.\n- If source definition is in a `cpp` file, make sure it is in the list of\n sources in the `CMakeLists.txt` in the same directory and that the\n corresponding library is linked against by the target.\n\n If the undefined reference is a template, make sure the required instantiation\n exists.\n- If the undefined reference's definition is in a `tpp` file, make sure the\n `tpp` file is included in the target file.\n- If the undefined reference's source definition is in an `hpp` file, make sure\n the specific instantiation is possible (e.g. not forbidden by a `requires`\n clause)\n" }, { "path": "docs/DevGuide/Connectivity.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Visualisation Connectivity {#visualisation_connectivity}\n\n\\tableofcontents\n\nThis guide is split into two parts. The first part details what is meant by\n'connectivity' and how it is used to visualise SpECTRE simulations in standard\nvisualisation software such as Paraview. The second part details the\nmethodology associated with ExtendConnectivity - a post-processing executable\nthat removes gaps in the default visualisations produced by SpECTRE.\n\n# What is Connectivity?\n\nSpECTRE simulations are built on a computational grid composed of individual\ngridpoints. The 'connectivity' is a list added in the output simulation files\nthat instructs visualisation software, namely Paraview, on how to connect these\ngridpoints to create lines/surfaces/volumes (depending on the dimension of the\nsimulation) as needed. Given these instructions, Paraview interpolates the data\nover the regions between gridpoints to create line/surface/volume meshes.\n\nIn general, the connectivity list contains gridpoints in a particular sequence\nthat corresponds to a line/surface/volume mesh in Paraview. These gridpoints are\nlabelled with integers that are based on the order in which they appear in the\nh5 files output by the simulation. As one might expect, this list is structured\ndifferently depending on the dimension of the simulation. The key underlying\ndifference is the size of the smallest connected region. In 1D, our domain is\ncomposed of lines so the smallest connected region is a line made up by two\npoints. In 2D, the smallest connected region used by SpECTRE is typically a\nquadrilateral made up by four points. In 3D, the smallest connected region used\nby SpECTRE is typically a hexahedron made up by eight points. A visual\nrepresentation is illusutrated below. (Note: The numbering of points has been\nchosen arbitrarily. In reality, this numbering is determined based on the order\nof gridpoints in the h5 file(s)).\n\n\\image html ConnectivityStructure.png \"Basic connectivity in 1D, 2D, and 3D\"\n\nThe figure above shows how connectivity is defined for a region in each\ndimension. Fig (a) shows the gridpoint structure for these regions and Fig (c)\nshows how the resulting mesh appears. Fig (b) shows how a connectivity list\nshould be sequenced to create the desired mesh. Then, in 1D, our connectivity\nlist to create the line in (c) would be [1,2]. Similarly, in 2D, our\nconnectivity list would be [1,2,4,3] and in 3D, our list would be\n[1,2,4,3,5,6,8,7]. (Note that this sequencing is dictated by Paraview's\nconventions, not SpECTRE's.)\n\nThe above example illustrates how to connect the smallest connected region in\neach dimension. The complete connectivity list, detailing how the entire domain\nmesh is to be created, is made by concatenating individual connectivity lists.\nThus, in 1D, Paraview interprets the list [1,2,2,3] in blocks of 2, with the\nfirst block [1,2] representing a line between gridpoints 1 and 2, and the second\nblock [2,3] representing a line between gridpoints 2 and 3. This works similarly\nin the other dimensions.\n\n\n# How does ExtendConnectivity work?\n\nExtendConnectivity is a post-processing algorithm that looks to add more\nconnectivity entries to fill up any gaps in visualisation. These gaps have\nmultiple sources, the largest of which is the fact that SpECTRE does not add\nconnectivity between elements (as defined in\n\\ref domain_concepts \"Domain Concepts\") by default. This is important in certain\nsimulations where the endpoints of the elements do not overlap (e.g simulations\nusing Gauss quadrature), resulting in gaps between elements in visualisations.\nExtendConnectivity looks to fix this problem specifically. **Note:** The\nremainder of this guide assumes we are working with simulations whose elements\ndon't overlap.\n\n## Neighbours\n\nThe key idea in understanding how ExtendConnectivity works is understanding\nhow neighbouring elements are categorised and dealt with. The next sections\nexplain the categories of 'face neighbour', 'edge neighbour', and 'corner\nneighbour' in detail for 1D, 2D, and 3D.\n\n### 3D\n\nWe shall start in 3D because the categories are most intuitively defined in\n3D. The image below shows a typical example of SpECTRE connectivity for a 3D\nvolume element (with h-refinement 1 and p-refinement 2 in each direction),\ncoloured by their neighbour categorisation.\n\n\\image html DefaultConnectivity3D.png \"3D domain with default connectivity\"\n\nIn the above image, the grey cube is our reference element that neighbour\nelements are defined around. Then, we define any element that, if elements\noverlapped, would share a face with our reference element to be a 'face\nneighbour'. By this definition, we can see that our blue cubes in the above\nimage are our face neighbours. The definitions of the other categories are\nanalogous. We define any element that, if elements overlapped, would\nshare an edge to be an 'edge neighbour' and any element that would share a\ncorner to be a 'corner neighbour'. Hence, our red cubes are our edge neighbours\nand our green cube is our corner neighbour. In general, for a 3D simulation,\nface neighbours share a 2D region, edge neighbours share a 1D region, and corner\nneighbours share a 0D region.\n\nThese categories apply to the element as a whole. Then, after the element is\ncategorised, the gridpoints must be filtered to the particular face, edge, or\ncorner that will be connected with our reference element. Note that edge and\ncorner neighbours require gridpoints from multiple neighbours (e.g. edge\nneighbours involve connecting four edges - one from the reference element, two\nfrom face neighbours, and one from the edge neighbour). Once the correct\ngridpoints are identified, they are connected as described in the previous\nsection. The neighbour direction in particular determines the ordering of the\ngridpoints in this sequence. The image below shows the same domain after the\nmissing connectivity has been added, coloured by the type of connectivity added.\n\n\\image html ExtendedConnectivity3D.png \"3D domain with extended connectivity\"\n\nIn this image, the brown cubes are the face neighbour connections, the orange\ncubes are the edge neighbour connections, and the yellow cube is the corner\nneighbour connection. The entire process is then repeated for the next element.\n\nThis example required only one connectivity entry to be added per neighbour\nsince each element was made up of just one cube. At larger p-refinements, an\nelement consists of more cubes and consequently, more connectivity entries are\nrequired. For example, if the domain above had a p-refinement of 3 in each\ndimension instead, face connections would require adding four cubes\nand edge connections would require two cubes.\n\n### 2D\n\nWe can now generalise these definitions to other dimensions. The image below\nshows a typical example of SpECTRE connectivity for a 2D volume element (with\nh-refinement 1 and p-refinement 2 in each direction), coloured by their\nneighbour categorisation in the same colours as above.\n\n\\image html ExtendedConnectivity2D.png \"2D domain with extended connectivity\"\n\nOnce again, the grey square is our reference element. We now define our\nneighbour types to be analogous to the types in 3D but reduced by one dimension.\nThen, in a 2D simulation, face neighbours share a 1D regions, edge neighbours\nshare a 0D region, and corner neighbours do not exist. In the image above, our\nface neighbours are once again blue and our edge neighbours are once again red.\n\nOnce the elements are categorised, the relevant gridpoints are once again\nfiltered and connected according to the 2D structure explained above. In the\nimage, the face connections are coloured brown and the edge connections are\ncoloured orange again. The next element is then made the reference element and\nthe process is repeated to build up the connectivity for the entire domain.\n\n### 1D\n\nWe display the concepts in 1D for completeness. The image below shows an example\nof SpECTRE connectivity for a 1D volume element (with h-refinement 1 and\np-refinement 2), coloured by their neighbour categorisation in the same colours\nas above.\n\n\\image html ExtendedConnectivity1D.png \"1D domain with extended connectivity\"\n\nIn this image, the grey line is our reference element. In a 1D simulation, we\ncorrespondingly define face neighbours to share a 0D region and both edge and\ncorner neighbours do not exist. Then, in the image above, our face neighbour\nis once again the blue element and the face connection is coloured brown again.\n\n### Summary\n\n* Face Neighbour:
\n A neighbouring element that shares an overlap region one dimension lower than\n the dimension of the simulation.\n\n* Edge Neighbour:
\n A neighbouring element that shares an overlap region two dimensions lower than\n the dimension of the simulation.\n\n* Corner Neighbour:
\n A neighbouring element that shares an overlap region three dimensions lower\n than the dimension of the simulation.\n\n\n## Connecting elements with different p-refinements\n\nTo be added.\n" }, { "path": "docs/DevGuide/CreatingExecutables.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Creating Executables {#dev_guide_creating_executables}\n\n\\tableofcontents\n\nThere are several different types of executables that can be built:\n- An executable that uses Charm++ to run in parallel,\n e.g. `Executables/ParallelInfo`\n- An executable that does not use Charm++, does not run in parallel, and\n supplies its own `main`, e.g. `Executables/Examples/HelloWorldNoCharm`\n- An executable that uses Charm++ to run in parallel but supplies its own `main`\n- An executable that uses custom compilation or linking flags,\n e.g. `DebugPreprocessor`\n- Executables used for evolutions or elliptic solves\n\n### Executable Using Charm++ for Parallelization\n\n\\ref tutorial_minimal_parallel_executable tutorial describes how to\nadd a new parallel executable.\n\nAnother simple example of an executable using Charm++ for\nparallelization is in `src/Executables/Examples/HelloWorld`. In this\nexample, the only additional phase (besides `Initialization` and\n`Exit`) is `Execute`, and the phases are executed in order.\n`SingletonHelloWorld` defines a single component `HelloWorld`\n\n\\snippet SingletonHelloWorld.cpp executable_example_singleton\n\nwhich specifies via the `chare_type` type alias that it is a singleton\nparallel component which means that only one such object will exist\nacross all processors used by the executable. Each component must\ndefine the static function `execute_next_phase` which is executed\nduring the phases (other than `Initialization` and `Exit`) defined in\nthe metavariables struct. In `SingletonHelloWorld`, the\n`PrintMessage` action is called during the `Execute` phase.\n\n\\snippet SingletonHelloWorld.cpp executable_example_action\n\nThe `PrintMessage` action is executed on whatever process the singleton\ncomponent is created upon, and prints a message.\n\nExecutables can read in an input file (specified by the `--input-file`\nargument) that will be parsed when the executable begins. %Options\nspecified in the input file can be used to either place items in the\nParallel::GlobalCache (by specifying tags in the\n`const_global_cache_tags` type alias of the metavariables, component\nand action structs), to construct items in the db::DataBox of\ncomponents during initialization (by specifying tags in the\n`simple_tags_from_options` type alias of action struct), or be passed to\nthe `allocate_array` function of an array component (by specifying\ntags in the `array_allocation_tags` type alias of the component).\n`SingletonHelloWorld` specifies a single option\n\n\\snippet SingletonHelloWorld.cpp executable_example_options\n\nwhich a string specifying a name that will be placed into the constant global\ncache. The string is fetched when performing the `PrintMessage` action. Items\nin the constant global cache are stored once per node that the executable runs\non. An example input file for `SingletonHelloWorld` can be found in\n`tests/InputFiles/ExampleExecutables/SingletonHelloWorld.yaml` and shows how to\nspecify the options (lines beginning with a `#` are comments and can be\nignored).\n\nFurthermore among the included header files\n\n\\snippet SingletonHelloWorld.cpp executable_example_includes\n\nmust be the appropriate header for each parallel component type, which in the\n`SingletonHelloWorld` example is `AlgorithmSingleton.hpp`. Note that\nthese headers are not in the source tree, but are generated automatically when\nthe code is compiled.\n\nSee [the Parallelization documentation](group__ParallelGroup.html#details)\nfor more details.\n\n### Executable Using Charm++ with Custom main()\n\nWhile this is technically possible, it has not been tested. We recommend using\nthe Charm++ supplied main chare mechanism for the time being.\n\n### Executable Not Using Charm++\n\nAn example of an executable that does not use Charm++ for parallelization but\nstill can use all other infrastructure in SpECTRE is in\n`src/Executables/Examples/HelloWorldNoCharm`. Adding a non-Charm++ executable to\nSpECTRE mostly follows the standard way of adding an executable using CMake. The\nonly deviation is that the `CMakeLists.txt` file must tell Charm++ not to add a\n`main()` by passing the link flags `-nomain-module -nomain`. This is done using\nCMake's `set_target_properties`:\n\n```\nset_target_properties(\n ${EXECUTABLE}\n PROPERTIES LINK_FLAGS \"-nomain-module -nomain\"\n )\n```\n\nTo add the executable as a target you must use the `add_spectre_executable`\nfunction, which is a light weight wrapper around CMake's `add_executable`.\nFor example,\n\n```\nadd_spectre_executable(\n ${EXECUTABLE}\n EXCLUDE_FROM_ALL # Exclude from calls to `make` without a specified target\n HelloWorld.cpp\n )\n```\n\nYou can link in any of the SpECTRE libraries by adding them to the\n`target_link_libraries`, for example:\n\n```\ntarget_link_libraries(\n ${EXECUTABLE}\n DataStructures\n )\n```\n\nWe recommend that you add a test that the executable properly runs by adding an\ninput file to `tests/InputFiles` in an appropriate subdirectory. See\n[`tests/InputFiles/ExampleExecutables/HelloWorldNoCharm.yaml`]\n(https://github.com/sxs-collaboration/spectre/tree/develop/tests/InputFiles/\nExampleExecutables/HelloWorldNoCharm.yaml)\nfor an example.\nThe input file is passed to the executable using `--input-file\npath/to/Input.yaml`. In the case of the executable not taking any input file\nthis is just used to generate a test that runs the executable.\n\nFor these types of executables `main` can take the usual `(int argc, char\n*argv[])` and parse command line options. Executables not using Charm++ are just\nstandard executables that can link in any of the libraries in SpECTRE.\n\n\\warning\nCurrently calling `Parallel::abort` results in a segfault deep inside Charm++\ncode. However, the error messages from `ASSERT` and `ERROR` are still printed.\n\n### Executable With Custom Compilation or Linking Flags\n\nUse the CMake function `set_target_properties` to add flags to an executable. To\ncall a completely custom compiler invocation you should use the\n`add_custom_target` CMake function. The need for the `custom_target` level of\ncontrol is rare and should generally be avoided since it adds quite a bit of\ntechnical debt to the code base. Thus, it is not explained here. If you are\ncertain you need it you can see the `DebugPreprocessor` executable's\n`CMakeLists.txt` file for an example.\n\n### Executable Used for Evolution or Elliptic Solve\n\nOnce they are written, see the tutorials specific to evolution and elliptic\nsolves.\n" }, { "path": "docs/DevGuide/Databox.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Motivation for SpECTRE's DataBox {#databox_foundations}\n\n\\tableofcontents\n\n# Introduction {#databox_introduction}\nThis page walks the user through the iterative process that led to SpECTRE's\nDataBox. At each stage, it discusses the advances and challenges that result\nfrom each improvement.\n\n# Towards SpECTRE's DataBox {#databox_towards_spectres_databox}\n\n## Working without DataBoxes {#databox_working_without_databoxes}\nIn a small C++ program, it is common to use the built-in fundamental types\n(bool, int, double, etc.) in computations, and to give variable names to\nobjects of these types. For example, a section of a small program may look like\nthis:\n\n\\snippet Test_DataBoxDocumentation.cpp working_without_databoxes_small_program_1\n\nWhat changes as our program's size increases in scale? In SpECTRE, one of our\ndriving design goals is modularity. In other words, functionality should be\neasy to swap in and out as desired. These smaller modules are easier to test,\nand keep the code flexible. We could wrap our calculation in such a module,\nwhich would then allow us to decouple the initial setup of the variables from\nwhere they are used in calculations:\n\n\\snippet Test_DataBoxDocumentation.cpp working_without_databoxes_mass_compute\n\n\\snippet Test_DataBoxDocumentation.cpp working_without_databoxes_accel_compute\n\nOur small program can now be written as:\n\n\\snippet Test_DataBoxDocumentation.cpp working_without_databoxes_small_program_2\n\nOne advantage is immediate: we are free to add other computation modules that\nare independently testable and reusable. As the number of routines grows, we\ncan even begin to write routines that work on top of existing ones.\n\n\\snippet Test_DataBoxDocumentation.cpp working_without_databoxes_force_compute\n\nWhile we have made progress, two problems arise. Our first problem is that as\nthe number of quantities grows, it becomes more unwieldy to have to specify\neach function argument in our routine. The second problem is worse: the\narguments passed to functions can be transposed and the program will still\ncompile and run, but produce incorrect output. For example, the following two\nlines are equally well-formed from the point of view of the program:\n\n\\snippet Test_DataBoxDocumentation.cpp working_without_databoxes_failed_accel\n\nEvery time we call `acceleration_compute` we need to make sure we pass in the\narguments in the correct order. In large programs where `acceleration_compute`\nis called many times, it becomes inevitable that the arguments will be\naccidentally transposed. We can address the two problems described above with a\n`std::map`, the first container we'll consider in this series.\n\n##A std::map DataBox {#databox_a_std_map_databox}\nWe can encapsulate the variables we use in a `std::map`, and the first half of\nour small program example now looks like this:\n\n\\snippet Test_DataBoxDocumentation.cpp std_map_databox_small_program_1\n\nWe have not yet taken full advantage of the encapsulation that `std::map`\nprovides. We do so by rewriting our other routines to take only a single\nargument, i.e. the `std::map` itself:\n\n\\snippet Test_DataBoxDocumentation.cpp std_map_databox_mass_compute\n\n\\snippet Test_DataBoxDocumentation.cpp std_map_databox_accel_compute\n\nNotice that this solves the problem of having to provide the arguments\nin the correct order to every function call of `acceleration_compute`:\n\n\\snippet Test_DataBoxDocumentation.cpp std_map_databox_force_compute\n\n\nOur small program now looks like:\n\n\\snippet Test_DataBoxDocumentation.cpp std_map_databox_small_program_2\n\nWithin each function, we no longer need to worry about passing in the arguments\nin the correct order. This is a great improvement, but our reliance on proper\nnames does leave us open to the following mistake:\n\n~~~{.c}\n// returns 0 without emitting an error!\nreturn naive_databox[\"MisspelledKey\"];\n~~~\n\nIn the above example, the map is asked to return a value given a key\nthat does not exist! As written, however, the program is well-formed and no\nerror is emitted. (In the case of std::map, [a value is created.]\n(https://en.cppreference.com/w/cpp/container/map/operator_at)) Because the keys\nare indistinguishable from their type alone, the mistake cannot be caught at\ncompile time. In our example, the mistake won't even be caught at run time. The\nrun time portion of a SpECTRE calculation will typically be much longer (up to\nthousands of times longer!) than the compile time portion, so it is critical to\ncatch costly mistakes like this as early into the calculation as possible.\nAlthough names encoded as `std::string` cannot be distinguished by the\ncompiler, names encoded as types *can* be. This is possible with C++'s static\ntyping, and to take advantage of this we need a container that is\n*heterogeneous*, that is, capable of holding objects of different types.\n\n## A std::tuple DataBox {#databox_a_std_tuple_databox}\n\nA well-documented example of a fixed-size heterogeneous container of types is\n[std::tuple](https://en.cppreference.com/w/cpp/utility/tuple):\n\n\\snippet Test_DataBoxDocumentation.cpp std_tuple_databox_1\n\nThe contents of the `std_tuple` are obtained using\n[std::get](https://en.cppreference.com/w/cpp/utility/tuple/get):\n\n\\snippet Test_DataBoxDocumentation.cpp std_tuple_databox_2\n\nIn the above, we can see that we have promoted our keys from different values\nall of type `std::string` to different types entirely. We are not limited to\nfundamental types, we are free to make our own structs that serve as keys.\nThese user-created types are called *tags*.\n\nAs the sole purpose of the tag is to provide the compiler with a type\ndistinguishable from other types, they can be as simple as the following:\n\n\\snippet Test_DataBoxDocumentation.cpp std_tuple_tags\n\nNote that we have now promoted `Velocity`, `Radius`, etc. from being *values*\nassociated with `std::string`s at run time, to *types* distinguishable from\nother types at compile time. A large portion of SpECTRE is designed with the\nphilosophy of enlisting the help of the compiler in assuring the correctness\nof our programs. An example of a `std::tuple` making use of these tags might\nlook like:\n\n~~~{.c}\n// Note: This won't work!\nstd::tuple sophomore_databox =\n std::make_tuple(4.0, 2.0, 0.5, 10.0);\n~~~\n\nUnfortunately, this will not work. The types passed as template parameters to\n`std::tuple` must also be the types of the arguments passed to\n`std::make_tuple`. Using a `std::pair`, we could write the above as:\n\n\\snippet Test_DataBoxDocumentation.cpp std_tuple_small_program_1\n\nWhat remains is to rewrite our functions to use `std::tuple` instead of\n`std::map`. Note that since we are now using a heterogeneous container of\npotentially unknown type, our functions must be templated on the\npairs used to create the `sophomore_databox`. Our functions then look like:\n\n\\snippet Test_DataBoxDocumentation.cpp std_tuple_mass_compute\n\n\\snippet Test_DataBoxDocumentation.cpp std_tuple_acceleration_compute\n\n\\snippet Test_DataBoxDocumentation.cpp std_tuple_force_compute\n\nUsing all these `std::pair`s to get our `std::tuple` to work is a bit\ncumbersome. There is another way to package together the tagging ability\nof the struct names with the type information of the values we wish to store.\nTo do this we need to make modifications to both our tags as well as our\n%Databox implementation. This is what is done in SpECTRE's\n`tuples::TaggedTuple`, which is an improved implementation of `std::tuple` in\nterms of both performance and interface.\n\n##A TaggedTuple DataBox {#databox_a_taggedtuple_databox}\n\nTaggedTuple is an implementation of a compile time container where the keys\nare tags.\n\nTags that are compatible with SpECTRE's `tuples::TaggedTuple` must have the\ntype alias `type` in their structs. This type alias carries the type\ninformation of the data we wish to store in the databox. `tuples::TaggedTuple`\nis able to make use of this type information so we won't need auxiliary\nconstructs such as `std::pair` to package this information together anymore.\nOur new tags now look like:\n\n\\snippet Test_DataBoxDocumentation.cpp tagged_tuple_tags\n\nWe are now able to create the `junior_databox` below in the same way we\ninitially wished to create the `sophomore_databox` above:\n\n\\snippet Test_DataBoxDocumentation.cpp tagged_tuple_databox_1\n\nOur functions similarly simplify:\n\n\\snippet Test_DataBoxDocumentation.cpp tagged_tuple_mass_compute\n\n\\snippet Test_DataBoxDocumentation.cpp tagged_tuple_acceleration_compute\n\n\\snippet Test_DataBoxDocumentation.cpp tagged_tuple_force_compute\n\nIn each of these iterations of the Databox, we started with initial quantities\nand computed subsequent quantities. Let us consider again `force_compute`, in\nwhich `mass` and `acceleration` are recomputed for every call to\n`force_compute`. If `Mass` and `Acceleration` were tags somewhow, that is, if we\ncould compute them once, place them in the databox, and get them back out\nthrough the use of tags, we could get around this problem. We are now ready to\nconsider SpECTRE's DataBox, which provides the solution to this problem in the\nform of `ComputeTags`.\n\n# SpECTRE's DataBox {#databox_a_proper_databox}\n\nA brief description of SpECTRE's DataBox: a TaggedTuple with compute-on-demand.\nFor a detailed description of SpECTRE's DataBox, see the\n\\ref DataBoxGroup \"DataBox documentation\".\n\n## SimpleTags {#databox_documentation_for_simple_tags}\nJust as we needed to modify our tags to make them compatible with\n`TaggedTuple`, we need to again modify them for use with DataBox. Our ordinary\ntags become SpECTRE's SimpleTags:\n\n\\snippet Test_DataBoxDocumentation.cpp proper_databox_tags\n\nAs seen above, SimpleTags have a `type` and a `name` in their struct.\nWhen creating tags for use with a DataBox, we must make sure to the tag\ninherits from one of the existing DataBox tag types such as `db::SimpleTag`.\nWe now create our first DataBox using these `SimpleTags`:\n\n\\snippet Test_DataBoxDocumentation.cpp refined_databox\n\nWe can get our quantities out of the DataBox by using `db::get`:\n\n\\snippet Test_DataBoxDocumentation.cpp refined_databox_get\n\nSo far, the usage of DataBox has been similar to the usage of TaggedTuple. To\naddress the desire to combine the functionality of tags with the modularity of\nfunctions, DataBox provides ComputeTags.\n\n## ComputeTags {#databox_documentation_for_compute_tags}\nComputeTags are used to tag functions that are used in conjunction with a\nDataBox to produce a new quantity. ComputeTags look like:\n\n\\snippet Test_DataBoxDocumentation.cpp compute_tags\n\nComputeTags inherit from `db::ComputeTag`, and it is convenient to have them\nadditionally inherit from an existing SimpleTag (in this case `Mass`) so that\nthe quantity `MassCompute` can be obtained through the SimpleTag `Mass`.\nWe use the naming convention `TagNameCompute` so that `TagNameCompute` and\n`TagName` appear next to each other in documentation that lists tags in\nalphabetical order.\n\nWe have also added the type alias `argument_tags`, which is necessary in order\nto refer to the correct tagged quantities in the DataBox.\n\n\\note\nThe `tmpl::list` used in the type alias is a contiguous container only\nholding types. That is, there is no variable runtime data associated with it\nlike there is for `std::tuple`, which is a container associating types with\nvalues. `tmpl::list`s are useful in situations when one is working with\nmultiple tags at once.\n\nUsing nested type aliases to pass around information at compile time is a\ncommon pattern in SpECTRE. Let us see how we can compute our beloved quantity\nof mass times acceleration:\n\n\\snippet Test_DataBoxDocumentation.cpp compute_tags_force_compute\n\nAnd that's it! `db::get` utilizes the `argument_tags` specified in\n`ForceCompute` to determine which items to get out of the `refined_databox`.\nWith the corresponding quantities in hand, `db::get` passes them as arguments\nto the `function` specified in `ForceCompute`. This is why every `ComputeTag`\nmust have an `argument_tags` as well as a `function` specified; this is the\ncontract with DataBox they must satisfy in order to enjoy the full benefits of\nDataBox's generality.\n\n## Mutating DataBox items {#databox_documentation_for_mutate_tags}\nIt is reasonable to expect that in a complicated calculation, we will encounter\ntime-dependent or iteration-dependent variables. As a result, in addition to\nadding and retrieving items from our DataBox, we also need a way to *mutate*\nquantities already present in the DataBox. This can be done via\n`db::mutate_apply` and can look like the following:\n\n\\note\nThere is an alternative to `db::mutate_apply`, `db::mutate`. See the\n\\ref DataBoxGroup \"DataBox documentation\" for more details.\n\n\\snippet Test_DataBoxDocumentation.cpp mutate_tags\n\\snippet Test_DataBoxDocumentation.cpp time_dep_databox\n\n\\note\nThe `not_null`s here are used to give us the assurance that the pointers\n`time` and `falling_speed` are not null pointers. Using raw pointers alone, we\nrisk running into segmentation faults if we dereference null pointers. With\n`not_null`s we instead run into a run time error that tells us what went wrong.\nFor information on the usage of `not_null`, see the documentation for Gsl.hpp.\n\nIn the above `db::mutate_apply` example, we are changing two values in the\nDataBox using four values from the DataBox. The mutated quantities must be\npassed in as `gsl::not_null`s to the lambda. The non-mutated quantities are\npassed in as const references to the lambda.\n\n\\note\nIt is critical to guarantee that there is a strict demarcation between\npre-`db::mutate` and post-`db::mutate` quantities. `db::mutate` provides this\nguarantee via a locking mechanism; within one mutate call, all initial\npre-mutated quantities are obtained from the DataBox before performing a single\nmutation.\n\n\\note\nThe mutate functions described above are the only accepted ways to edit data\nin the Databox. It is technically possible to use pointers or references to\nedit data stored in the Databox, but this bypasses the compute tags\narchitecture. All changes to the Databox must be made by the Databox itself\nvia mutate functions.\n\nFrom the above, we can see that the different kinds of tags are provided in two\ndifferent `tmpl::list`s. The `MutateTags`, also called `ReturnTags`, refer to\nthe quantities in the DataBox we wish to mutate, and the `ArgumentTags` refer to\nadditional quantities we need from the DataBox to complete our computation. We\nnow return to the recurring question of how to make this construction more\nmodular.\n\nWe have now worked our way up to SpECTRE's DataBox, but as we can see in the\nabove `db::mutate_apply` example, the lambda used to perform the mutation ends\nup being independent of any tags or template parameters! This means we can\nfactor it out and place it in its own module, where it can be tested\nindependently of the DataBox.\n\n# Toward SpECTRE's Actions {#databox_towards_actions}\n\n## Mutators {#databox_documentation_for_mutators}\nThese constructs that exist independently of the DataBox are the precursors to\nSpECTRE's *Actions*. As they are designed to be used with `db::mutate` and\n`db::mutate_apply`, we give them the name *Mutators*. Here is the above lambda\nwritten as a Mutator-prototype, a struct-with-void-apply:\n\n\\snippet Test_DataBoxDocumentation.cpp intended_mutation\n\nThe call to `db::mutate_apply` has now been made much simpler:\n\n\\snippet Test_DataBoxDocumentation.cpp time_dep_databox2\n\nThere is a key step that we take here after this point, to make our\nstruct-with-void-apply into a proper Mutator. As we will see, this addition\nwill allow us to entirely divorce the internal details of `IntendedMutation`\nfrom the mechanism through which we update the DataBox. The key step is to\nadd type aliases to `IntendedMutation`:\n\n\\snippet Test_DataBoxDocumentation.cpp intended_mutation2\n\nWe are now able to write our call to `db::mutate_apply` in the following way:\n\n\\snippet Test_DataBoxDocumentation.cpp time_dep_databox3\n\nAs we saw earlier with `QuantityCompute`, we found that we were able to imbue\nstructs with the ability to \"read in\" types specified in other structs, through\nthe use of templates and member type aliases. This liberated us from having to\nhard-code in specific types. We notice immediately that `IntendedMutation` is a\nhard-coded type that we can factor out in favor of a template parameter:\n\n\\snippet Test_DataBoxDocumentation.cpp my_first_action\n\nNote how the `return_tags` and `argument_tags` are used as metavariables and\nare resolved by the compiler. Our call to `db::mutate_apply` has been fully\nwrapped and now takes the form:\n\n\\snippet Test_DataBoxDocumentation.cpp time_dep_databox4\n\nThe details of applying Mutators to the DataBox are entirely handled by\n`MyFirstAction`, with the details of the specific Mutator itself entirely\nencapsulated in `IntendedMutation`.\n\nSpECTRE algorithms are decomposed into Actions which can depend on more\nthings than we have considered here. Feel free to look at the\nexisting \\ref ActionsGroup \"actions that have been written.\" The intricacies of\nActions at the level that SpECTRE uses them is the subject of a future addition\nto the \\ref dev_guide \"Developer's Guide.\"\n" }, { "path": "docs/DevGuide/DebuggingTips.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n# Tips for debugging an executable {#runtime_errors}\n\nLearn how to use a debugger such as gdb.\n\nYou can debug MPI executables using the `sys::attach_debugger()` function. See\nthe documentation of that function for details.\n\n# Useful gdb commands\n\n- To break when an exception is thrown `catch throw`\n\n- To break on a specific exception type `catch throw std::out_of_range`\n (This may not work on all compilers or older versions of gdb. In this\n case you also try setting a breakpoint on the constructor of the exception\n type, `break std::out_of_range::out_of_range`)\n\n- SpECTRE has pretty printing facilities for various custom types. In order to\n enable these you must add\n `add-auto-load-safe-path /path/to/spectre/` to your `~/.gdbinit` file.\n" }, { "path": "docs/DevGuide/DevGuide.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Developer Guides {#dev_guide}\n\n### Adaptive Mesh Refinement\n- \\subpage dev_guide_amr \"Adaptive Mesh Refinement\"\n\n### Charm++ Interface\n- \\subpage load_balancing_notes \"Load Balancing Notes and Recommendations\"\n\n### Continuous Integration\nExplanations on our automated tests and deployments can be found here.\n- \\subpage dev_guide_automatic_versioning\n\n### CoordinateMap Guide\nMethods for creating custom coordinate maps are discussed here.\n- \\subpage redistributing_gridpoints \"Methods for redistributing gridpoints\"\n\n### Developing and Improving Executables\n- \\subpage dev_guide_creating_executables \"Executables and how to add them\"\n- \\subpage tutorials_parallel - A series of tutorials demonstrating how to write\n a parallel executable, and explaining some of the metaprogramming that turns\n user-provided code into a SpECTRE parallel executable\n- \\subpage dev_guide_option_parsing \"Option parsing\" to get options from input\n files\n- \\subpage dev_guide_importing \"Importing\" data from files\n- \\subpage profiling \"Profiling\" SpECTRE with a variety of different tools\n- \\subpage spectre_writing_python_bindings \"Writing Python Bindings\" to use\n SpECTRE C++ classes and functions from within python.\n- \\subpage implementing_vectors \"Implementing SpECTRE vectors\" a quick how-to\n for making new generalizations of DataVectors\n- \\subpage compiler_and_linker_errors \"How to parse linker and compiler errors\"\n- \\subpage static_analysis_tools \"Static analysis tools\"\n- \\subpage build_profiling_and_optimization - Getting started with improving\n compilation time and memory use\n- \\subpage runtime_errors \"Tips for debugging an executable\"\n\n### Foundational Concepts in SpECTRE\nDesigned to give the reader an introduction to SpECTRE's most recurring concepts\nand patterns.\n- \\subpage databox_foundations \"Towards SpECTRE's DataBox\"\n- \\subpage protocols \"Protocols: metaprogramming interfaces\"\n- \\subpage variables_foundations \"Using the Variables class\" to improve\n efficiency\n\n### GPU Support\nInformation on how to use and develop GPU support in SpECTRE.\n- \\subpage gpu_support \"GPU support\"\n\n### General SpECTRE Terminology\nTerms with SpECTRE-specific meanings are defined here.\n- \\subpage domain_concepts \"Domain Concepts\" used throughout the code are\n defined here for reference.\n- \\subpage visualisation_connectivity \"Visualisation Connectivity\" is defined\n and explained here for reference.\n\n### Having your Contributions Merged into SpECTRE\n- \\subpage writing_good_dox \"Writing good documentation\" is key for long term\n maintainability of the project.\n- \\subpage writing_unit_tests \"Writing Unit Tests\" to catch bugs and to make\n sure future changes don't cause your code to regress.\n- \\subpage github_actions_guide \"GitHub Actions\" is used to test every pull\n request.\n- \\subpage code_review_guide \"Code review guidelines.\" All code merged into\n develop must follow these requirements.\n\n### Performance and Optimization\n- \\subpage general_perf_guide \"General performance guidelines\"\n\n### Technical Documentation for Fluent Developers\nAssumes a thorough familiarity and fluency in SpECTRE's usage of TMP.\n- \\subpage DataBoxGroup \"DataBox\"\n- \\subpage observers_infrastructure_dev_guide \"Observers infrastructure\"\n- \\subpage dev_guide_parallelization_foundations - Parallelization\n infrastructure components and usage\n\n### Template Metaprogramming (TMP)\nExplanations for TMP concepts and patterns known to the greater C++ community\ncan be found here.\n- \\subpage sfinae \"SFINAE\"\n- \\subpage brigand \"The Brigand TMP library\"\n\n### Writing Tensor Equations\n- \\subpage writing_tensorexpressions\n \"Writing Tensor Equations with TensorExpressions\"\n" }, { "path": "docs/DevGuide/DomainConcepts.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Domain Concepts {#domain_concepts}\n\n\\tableofcontents\n\n* Computational Domain:
\n The region of spacetime on which a numerical simulation is performed.\n\n* Inertial Coordinate Frame:
\n A global coordinate frame covering the computational domain that is also the\n coordinate frame in which the initial (boundary) value problem that is being\n solved is specified. Denoted by Frame::Inertial.\n\n* Logical Coordinate Frame:
The coordinate frame of a reference\n cell. In the cell the logical coordinates cover the interval\n \\f$[-1, 1]\\f$ in each dimension. Currently the logical coordinates\n are Cartesian.\n\n* CoordinateMap \"Coordinate Map\":
\n A mapping between two coordinate frames. Coordinate maps are allowed to be\n time-dependent, as long as the time coordinate itself is unchanged.\n\n* Direction:
\n A logical coordinate axis and a label \"Upper\" or \"Lower\" depending on whether\n the Direction is aligned with or anti-aligned with the logical coordinate\n axis, respectively.\n\n* Block:
\n The computational domain is partitioned into a set of non-overlapping,\n distorted reference cells called Blocks. Each Block must have at most one\n neighboring Block in each Direction. The reference cell is embedded into a\n subset of the computational domain using a Coordinate Map from the\n logical frame of the Block to the global inertial frame. Blocks are\n identified by unique integral values.\n\n* Block Logical Coordinate Frame:
\n The logical coordinate frame of a Block, denoted by Frame::BlockLogical.\n The only requirement upon the logical coordinate frames of neighboring Blocks\n is that they have the same Coordinate Map from their logical coordinate frame\n to the global inertial frame on their shared boundary up to a mapping that\n swaps or negates the logical coordinate axes. In other words, at each point\n on their shared boundary, the logical coordinates of the two blocks are\n equal after possibly applying a permutation and sign flips.\n\n* Grid Coordinate Frame:
\n For time-dependent coordinate maps, it is useful (e.g. for computational\n efficiency) to split the Coordinate Map from Frame::BlockLogical to\n Frame::Inertial into a composition of two maps. This is done by introducing\n an intermediate coordinate frame (denoted by Frame::Grid) such that the\n mapping from Frame::BlockLogical to Frame::Grid is time-independent, and\n the mapping from Frame::Grid to Frame::Inertial is time-dependent.\n\n* Orientation:
\n The information of how the Block Logical Coordinates of neighboring Blocks are\n related.\n\n* \\ref BlockNeighbors \"Block Neighbors\":
\n The identity and Orientation of neighboring Blocks of a given Block.\n\n* Element:
A reference cell that is a refined subregion of a Block\n defined by its Segments in each dimension. The properties of the\n Element (e.g coordinate map) are inherited from its Block, i.e. it\n is self-similar to the Block.\n\n* Refinement Level:
\n The number of times a Block is split in half in a given dimension.\n\n* Segment:
In each dimension, the specific subset of the block\n logical coordinate interval \\f$[-1, 1]\\f$ defined by the Refinement\n Level and an integer label such that the Segment's interval is\n \\f$[-1 + 2 \\frac{i}{N}, -1 + 2 \\frac{i+1}{N}]\\f$ where \\f$i\\f$ is\n the integer label and \\f$N = 2^{(\\textrm{Refinement Level})}\\f$ is\n the number of segments on the Refinement Level.\n\n* Element Logical Coordinate Frame:
\n The logical coordinate frame of an Element. In each dimension, the Element\n Logical Coordinates are related to the Block Logical Coordinates by an affine\n mapping of the interval \\f$[-1, 1]\\f$ to the interval covered by the Segment\n in that dimension.\n\n* \\ref SegmentId \"Segment Identifier\":
\n The Refinement Level and an integer labeling a Segment.\n\n* \\ref ElementId \"Element Identifier\":
\n The Block Identifier containing the Element and a Segment Identifier\n in each dimension.\n\n* External Boundary:
\n A face of a Block or Element that has no neighbor.\n\n* Internal Boundary:
\n A boundary that is not an External Boundary.\n\n* Neighbors:
\n The identities and Orientation of the neighboring Blocks or Elements of a\n given Block or Element in a particular Direction .\n\n* External Boundary Condition:
\n A prescription for updating the solution on an External Boundary. Each\n External Boundary of a Block has exactly one External Boundary Condition\n associated with it.\n" }, { "path": "docs/DevGuide/GitHubActions.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n# GitHub Actions Continuous Integration {#github_actions_guide}\n\n\\tableofcontents\n\n# Testing SpECTRE with GitHub Actions CI {#github_actions_ci}\n\nSpECTRE uses\n[GitHub Actions](https://github.com/features/actions) for\ntesting the code. Multiple build jobs (described below) are launched\neach time a pull request is submitted or updated. GitHub Actions will also\nlaunch these build jobs each time you push to a branch on your fork of SpECTRE\nif you enable it. GitHub Actions is also used to deploy releases of the code.\n\nFor pull requests, you can view the GitHub Actions CI build by clicking on the\n`Checks` tab. Near the bottom of the `Conversation` tab a summary of the CI\nresults are presented. You can view all of the GitHub Actions runs by clicking\non the `Actions` section.\n\n## What is tested {#what-is-tested}\n\nThe GitHub Actions report lists the build jobs which will each have either a\ngreen check mark if it passes, a red `X` if it has failed, or a yellow\ndot with a circle if the build is in progress. Clicking on a build job will\ndisplay the log of the build.\n\nThe following build jobs are launched:\n* CHECK_COMMITS runs the script `tools/CheckCommits.sh` and fails the build if\n any casing of the words in the list below is the first word of the commit\n message. This allows developers to flag their commits with these keywords to\n indicate that a pull request should not be merged in its current state.\n - fixup\n - wip (for work in progress)\n - fixme\n - deleteme\n - rebaseme\n - testing\n - rebase\n* CHECK_FILES runs the script `tools/CheckFiles.sh` (which also runs the script\n `tools/FileTestDefs.sh`). The checks fail if any of the following are true:\n - Any file,\n * contains a line over 80 characters (We allow exceptions for certain file\n types and inherently long strings like URLs and include lines.\n See `tools/FileTestDefs.sh` for the full list of exceptions.)\n * is missing the license line\n * does not end with a newline\n * contains a tab character\n * contains white space at the end of a line\n * contains a carriage return character\n - A `c++` header file (i.e., `*.hpp` or `*.tpp`) is missing `#%pragma once`\n - A `c++` file (i.e., `*.hpp`, `*.tpp`, or `*.cpp`) file,\n * includes `` (useless when running in parallel)\n * includes `` (use `` instead)\n * includes `\"Utilities/TmplDebugging.hpp\"` (used only for debugging)\n * includes any non-header `*.cpp` file\n * contains a `namespace` ending in `_details` (use `_detail`)\n * contains a `struct TD` or `class TD` (used only for debugging)\n * contains `std::enable_if` (use `requires` instead)\n * contains `Ls` (use `List` instead)\n * contains additional text after `/*!` (does not render correctly in\n Doxygen)\n * contains the string `return Py_None;` (bug prone, use `Py_RETURN_NONE`\n instead)\n * contains `.ckLocal()` or `.ckLocalBranch()` (use `Parallel::local` or\n `Parallel::local_branch` instead)\n - A `c++` test,\n * uses `TEST_CASE` (use `SPECTRE_TEST_CASE` instead)\n * uses `Approx` (use `approx` instead)\n - A `CMakeLists.txt` file in `src`, but not in an Executables or\n Python-binding directory,\n * does not list a `C++` file that is present in the directory\n * lists a `C++` file that is not present in the directory\n - A `c++` or `python` file contains a `TODO` (case-insensitive) comment\n In addition, the CHECK_FILES job tests Python formatting, the release\n workflow, and other tools in `tools/`.\n* \"Check Python formatting\" runs the `black` and `isort` formatters over the\n source code.\n* RUN_CLANG_TIDY runs clang-tidy on the source code. This is done for both\n `Release` and `Debug` builds.\n* TEST_CHECK_FILES runs `tools/CheckFiles.sh --test` which tests the checks\n performed in the CHECK_FILES build.\n* The other builds compile the code and run the tests for both\n `Release` and `Debug` builds, for the `gcc` and `clang` compilers\n using a Linux OS, and the `AppleClang` compiler for `OS X`.\n* Verify the documentation builds successfully. Builds of `develop` deploy the\n documentation to GitHub pages.\n\n## How to perform the checks locally {#perform-checks-locally}\n\nBefore pushing to GitHub and waiting for GitHub Actions to perform the checks it\nis useful to perform at least the following tests locally:\n- **Unit tests:** Perform a `make unit-tests` and then execute `ctest -L Unit`\n to run all unit tests. As for `make` you can append a `-jN` flag to `ctest` to\n run in parallel on `N` cores. To run only a subset of the tests you can use\n one of the other keywords that the tests are labeled with, such as `ctest -L\n datastructures`. To run only particular tests you can also execute `ctest -R\n TEST_NAME` instead, where `TEST_NAME` is a regular expression matching the\n test identifiers such as `Unit.DataStructures.Mesh`. Pass the flag\n `--output-on-failure` to get output from failed tests. Consult `ctest -h` for\n further options.\n\n To run the input file tests you must build the executables using\n `make test-executables`. You can then run `ctest -LE unit` to run everything\n except for the unit tests, or `ctest` to run all tests.\n- **clang-tidy:** In a clang build directory, run `make clang-tidy\n FILE=SOURCE_FILE` where `SOURCE_FILE` is a relative or absolute path to a\n `.cpp` file. To perform this check for all source files that changed in your\n pull request, `make clang-tidy-hash HASH=UPSTREAM_HEAD` where `UPSTREAM_HEAD`\n is the hash of the commit that your pull request is based on, usually the\n `HEAD` of the `upstream/develop` branch.\n- **Python formatting:** Run `black --check .` and `isort --check-only .` over\n the repository. You can install these tools with `pip3 install -r\n support/Python/dev_requirements.txt`\n- **Documentation:** To render the documentation for the current state\n of the source tree the command `make doc` (or `make doc-check` to\n highlight warnings) can be used, placing its result in the `docs`\n directory in the build tree. Once code has been made into a pull\n request to GitHub, the documentation can be rendered locally using\n the `tools/pr-docs` script. To view the documentation, simply open the\n `index.html` file in the `html` subdirectory in a browser. Some functionality\n requires a web server (e.g. citation popovers), so just run a\n `python3 -m http.server` in the `html` directory to enable this.\n- The `gcc Debug` build runs code coverage for each GitHub Actions build.\n\n## Troubleshooting {#github-actions-troubleshooting}\n\n* Occasionally, a build job will fail because of a problem with GitHub Actions\n (e.g. it times out). On the `Checks` tab you can restart all or only the\n failed jobs. In the top right corner there's a `Re-run jobs` menu, which also\n has `Re-run failed jobs`. This button is `Cancel workflow` during the build\n process. Note that these buttons are only available if you have write access\n to the repository (core developer status).\n* GitHub Actions caches some things between builds. Occasionally this may\n cause a problem leading to strange build failures. For example, inexplicable\n segfaults on seemingly random tests or `Illegal instruction` failures. We have\n to be fairly lax with our caching policies, and so the cache can become stale\n and outdated when a new container is pushed, among other difficult to\n understand situations. You can rebuild the ccache by going to `Actions`, then\n select the `Tests` workflow on the left, click the `Run workflow` drop-down\n menu, and enter `yes` in the input field below the ccache discussion.\n\n If clearing the ccache doesn't help, it could be that a Docker image layer is\n not being updated. GitHub doesn't (yet) have a way to clear the cache, so\n instead we clobber it to force GitHub to eject all old caches, both ccache and\n Docker images, along with anything else. To do this go to `Actions`, select\n the `Clobber Cache` workflow, then run it on develop. This will dump 9.9GB of\n random data into the cache. The amount is specified in the `ClobberCache.yaml`\n workflow file and needs to be updated if GitHub increases their cache\n size. The current cache size limit is 10GB per repository.\n\n Note that starting these workflows is only possible if you have write access\n to the repository (core developer status).\n\n## Precompiled Headers and ccache {#precompiled-headers-ccache}\n\nGetting ccache to work with precompiled headers on GitHub Actions is a little\nchallenging. The header to be precompiled is\n`${SPECTRE_SOURCE_DIR}/tools/SpectrePch.hpp` and is symbolically linked to\n`${SPECTRE_BUILD_DIR}/SpectrePch.hpp`. The configuration that seems to work is\nspecifying the environment variables:\n\n\\code{.sh}\nCCACHE_COMPILERCHECK=content\nCCACHE_EXTRAFILES=\"${SPECTRE_SOURCE_DIR}/tools/SpectrePch.hpp\"\nCCACHE_IGNOREHEADERS=\\\n \"${SPECTRE_BUILD_DIR}/SpectrePch.hpp:${SPECTRE_BUILD_DIR}/SpectrePch.hpp.gch\"\n\\endcode\n\n## Caching Dependencies on macOS Builds {#caching-mac-os}\n\nOn macOS builds we cache all of our dependencies, like LIBXSMM and\nCharm++. These are cached in `$HOME/mac_cache`. Ultimately this saves about\n10-12 minutes even when compared to using ccache to cache the object files from\nbuilding the dependencies. We also cache `$HOME/Library/Caches/Homebrew`, which\nis where Homebrew keeps the downloaded formulas. By caching the Homebrew bottles\nwe are able to avoid brew formulas building from source because a tarball of the\npackage was not available at the time.\n" }, { "path": "docs/DevGuide/GpuSupport.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n# GPU support {#gpu_support}\n\n\\tableofcontents\n\n# Overview\n\n\\warning GPU support is experimental and this page will be updated as the\nimplementation matures.\n\nSpECTRE supports GPU acceleration through the [Kokkos](https://github.com/kokkos/kokkos)\nlibrary.\n\n## Build configuration\n\nTo enable GPU support, set the CMake option `-D SPECTRE_KOKKOS=ON` when\nconfiguring the build. Either point CMake to a Kokkos installation with\n`-D Kokkos_ROOT=path/to/kokkos` or set `-D SPECTRE_FETCH_MISSING_DEPS=ON` to\nfetch Kokkos automatically and build it as part of SpECTRE. You also have to\nselect a parallelization backend for Kokkos and possibly more configuration\noptions like the GPU architecture to build for. Read the\n[Kokkos documentation](https://kokkos.org/kokkos-core-wiki/get-started/configuration-guide.html)\nfor details on how to configure Kokkos. Here's an example for fetching Kokkos\nautomatically and building it as part of SpECTRE with the CUDA backend:\n\n```sh\ncmake -D SPECTRE_KOKKOS=ON \\\n -D SPECTRE_FETCH_MISSING_DEPS=ON \\\n -D Kokkos_ENABLE_CUDA=ON \\\n ...\n```\n\nHere's an example for using an existing Kokkos installation:\n\n```sh\ncmake -D SPECTRE_KOKKOS=ON \\\n -D Kokkos_ROOT=path/to/kokkos/build \\\n -D CMAKE_CXX_COMPILER=path/to/kokkos/bin/nvcc_wrapper \\\n ...\n```\n\nWhen building Kokkos separately with the CUDA backend, you have to set the\nfollowing configuration options:\n\n- `Kokkos_ENABLE_CUDA_CONSTEXPR=ON`\n- `Kokkos_ENABLE_CUDA_RELOCATABLE_DEVICE_CODE`\n" }, { "path": "docs/DevGuide/ImplementingVectors.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n# Implementing SpECTRE vectors {#implementing_vectors}\n\n\\tableofcontents\n\n# Overview of SpECTRE Vectors {#general_structure}\n\nIn SpECTRE, sets of contiguous or related data are stored in specializations of\nvector data types. The canonical implementation of this is the `DataVector`,\nwhich is used for storage of a contiguous sequence of doubles which support a\nwide variety of mathematical operations and represent data on a grid used during\nan evolution or elliptic solve. However, we support the ability to easily\ngenerate similar vector types which can hold data of a different type\n(e.g. `std::complex`), or support a different set of mathematical\noperations. SpECTRE vector classes are derived from the class template\n`VectorImpl`. The remainder of this brief guide gives a description of the tools\nfor defining additional vector types.\n\nFor reference, all functions described here can also be found in brief in the\nDoxygen documentation for VectorImpl.hpp, and a simple reference implementation\ncan be found in DataVector.hpp and DataVector.cpp.\n\n# The class definition {#class_definition}\n\nSpECTRE vector types inherit from vector types implemented in the\nhigh-performance arithmetic library\n[Blaze](https://bitbucket.org/blaze-lib/blaze). Using inheritance, SpECTRE\nvectors gracefully make use of the math functions defined for the Blaze types,\nbut can be customized for the specific needs in SpECTRE computations.\n\nThe trio of template parameters for `VectorImpl` are the type of the stored data\n(e.g. `double` for `DataVector`), the result type for mathematical operations,\nand the static size. The result type is used by Blaze to ensure that only\ncompatible vector types are used together in mathematical expressions. For\nexample, a vector representing `double` data on a grid (`DataVector`) cannot be\nadded to a vector representing spectral coefficients (`ModalVector`). This\navoids subtle bugs that arise when vector types are unintentionally mixed.\nIn nearly all cases the result type will be the vector type that is being\ndefined, so, for instance, `DataVector` is a derived class of\n`VectorImpl`. This template pattern is known as the\n[\"Curiously Recurring Template Pattern\"](https://en.wikipedia.org/wiki/\nCuriously_recurring_template_pattern) (CRTP).\nThe static size is used as an optimization for small vector sizes. If your\nvector is small, rather than doing heap allocations, it will use stack\nallocations in order to be efficient. The default static size is set by a global\nconstexpr bool `default_vector_impl_static_size`.\n\nFor the Blaze system to use the CRTP inheritance appropriately, it requires the\nspecification of separate type traits in the `blaze` namespace.\nThese traits can usually be declared in a standard form, so are abstracted in a\nmacro. For any new vector `MyNewVector`, the pattern that must appear at the\nbeginning of the file (i.e. before the class definition) is:\n```\n/// \\cond\nclass MyNewVector;\n/// \\endcond\nnamespace blaze {\nDECLARE_GENERAL_VECTOR_BLAZE_TRAITS(MyNewVector);\n}\n```\nThe class template `VectorImpl` defines various constructors, assignment\noperators, and iterator generation members. Most of these are inherited from\nBlaze types, but in addition, the methods `set_data_ref`, and `pup` are defined\nfor use in SpECTRE. All except for the assignment operators and constructors\nwill be implicitly inherited from `VectorImpl`. The assignment and constructors\nmay be inherited calling the following alias code in the vector class\ndefinition:\n```\nusing VectorImpl::operator=;\nusing VectorImpl::VectorImpl;\n```\n\nOnly the mathematical operations supported on the base Blaze types are supported\nby default. Those operations are determined by the storage type `T` and by the\nBlaze library. See [blaze-wiki/Vector_Operations](https://bitbucket.org/\nblaze-lib/blaze/wiki/Vector%20Operations).\n\n# Allowed operator specification {#blaze_definitions}\n\nBlaze keeps track of the return type of unary and binary operations using \"type\ntrait\" structs. These specializations for vector types should be placed in the\nheader file associated with the `VectorImpl` specialization. For `DataVector`,\nthe specializations are defined in `DataStructures/DataVector.hpp`. The presence\nor absence of template specializations of these structs also determines the set\nof allowed operations between the vector type and other types. For example, if\nadding a `double` to a `DataVector` should be allowed and the result should be\ntreated as a `DataVector` for subsequent operations, then the struct\n`blaze::AddTrait` needs to be defined as follows:\n\n```\nnamespace blaze {\n// the `template <>` head tells the compiler that\n// `AddTrait` is a class template specialization\ntemplate <>\nstruct AddTrait {\n // the `Type` alias tells blaze that the result should be treated like a\n // `DataVector` for any further operations\n using Type = DataVector;\n};\n} // namespace blaze\n```\n\nNote that this only adds support for `DataVector + double`, not `double +\nDataVector`. To get the latter the following AddTrait specialization must be\ndefined\n\n```\nnamespace blaze {\n// the `template <>` head tells the compiler that\n// `AddTrait` is a class template specialization\ntemplate <>\nstruct AddTrait {\n // the `Type` alias tells blaze that the result should be treated like a\n // `DataVector` for any further operations\n using Type = DataVector;\n};\n} // namespace blaze\n```\n\nFour helper macros are defined to assist with generating the many\nspecializations that binary operations may require. Both of these macros must be\nput inside the blaze namespace for them to work correctly.\n\nThe first of these helper macros is\n`BLAZE_TRAIT_SPECIALIZE_BINARY_TRAIT(VECTOR_TYPE, BLAZE_MATH_TRAIT)`, which will\ndefine all of the pairwise operations (`BLAZE_MATH_TRAIT`) for the vector type\n(`VECTOR_TYPE`) with itself and for the vector type with its `value_type`. This\nreduces the three specializations similar to the above code blocks to a single\nline call,\n\n```\nnamespace blaze {\nBLAZE_TRAIT_SPECIALIZE_BINARY_TRAIT(DataVector, AddTrait)\n} // namespace blaze\n```\n\nThe second helper macro is provided to easily define all of the arithmetic\noperations that will typically be supported for a vector type with its value\ntype. The macro is\n`VECTOR_BLAZE_TRAIT_SPECIALIZE_ARITHMETIC_TRAITS(VECTOR_TYPE)`, and defines all\nof:\n- `IsVector` to `std::true_type`\n- `TransposeFlag`, which informs Blaze of the interpretation of the\n data as a \"column\" or \"row\" vector\n- `AddTrait` for the `VECTOR_TYPE` and its value type (3 Blaze struct\n specializations)\n- `SubTrait` for the `VECTOR_TYPE` and its value type (3 Blaze struct\n specializations)\n- `MultTrait` for the `VECTOR_TYPE` and its value type (3 Blaze struct\n specializations)\n- `DivTrait` for the `VECTOR_TYPE` and its value type (3 Blaze struct\n specializations)\n\nThis macro is similarly intended to be used in the `blaze` namespace and can\nsubstantially simplify these specializations for new vector types. For instance,\nthe call for `DataVector` is:\n\n```\nnamespace blaze {\nVECTOR_BLAZE_TRAIT_SPECIALIZE_ARITHMETIC_TRAITS(DataVector)\n} // namespace blaze\n```\n\nThe third helper macro is provided to define a combination of Blaze traits for\nsymmetric operations of a vector type with a second type (which may or may not\nbe a vector type). The macro is\n`BLAZE_TRAIT_SPECIALIZE_COMPATIBLE_BINARY_TRAIT(VECTOR, COMPATIBLE, TRAIT)`, and\ndefines the appropriate trait for the two combinations ``\nand ``, and defines the result type to be `VECTOR`. For\ninstance, to support the multiplication of a `ComplexDataVector` with a\n`DataVector` and have the result be a `ComplexDataVector`, the following macro\ncall should be included in the `blaze` namespace:\n\n```\nnamespace blaze {\nBLAZE_TRAIT_SPECIALIZE_COMPATIBLE_BINARY_TRAIT(ComplexDataVector, DataVector,\n MultTrait);\n} // namespace blaze\n```\n\nFinally, the fourth helper macro is provided to define all of the blaze traits\nwhich are considered either unary or binary maps. This comprises most named\nunary functions (like `sin()` or `sqrt()`) and named binary functions (like\n`hypot()` and `atan2()`). The macro\n`VECTOR_BLAZE_TRAIT_SPECIALIZE_ALL_MAP_TRAITS(VECTOR_TYPE)` broadly specializes\nall blaze-defined maps in which the given `VECTOR_TYPE` as the sole argument\n(for unary maps) or both arguments (for binary maps). This macro is also\nintended to be used in the blaze namespace. The call for `DataVector` is:\n\n```\nnamespace blaze {\nVECTOR_BLAZE_TRAIT_SPECIALIZE_ALL_MAP_TRAITS(DataVector)\n} // namespace blaze\n```\n\n# Supporting operations for `std::array`s of vectors {#array_vector_definitions}\n\nIn addition to operations between SpECTRE vectors, it is useful to gracefully\nhandle operations between `std::arrays` of vectors element-wise. There are\ngeneral macros defined for handling operations between array specializations:\n`DEFINE_STD_ARRAY_BINOP` and `DEFINE_STD_ARRAY_INPLACE_BINOP` from\n`Utilities/StdArrayHelpers.hpp`.\n\nIn addition, there is a macro for rapidly generating addition and subtraction\nbetween arrays of vectors and arrays of their data types. The macro\n`MAKE_STD_ARRAY_VECTOR_BINOPS(VECTOR_TYPE)` will define:\n- the element-wise `+` and `-` with `std::array` and\n `std::array`\n- the element-wise `+` and `-` of either ordering of\n `std::array` with `std::array`\n- the `+=` and `-=` of `std::array` with a\n `std::array`\n- the `+=` and `-=` of `std::array` with a\n `std::array`.\n\n# Equivalence operators {#Vector_type_equivalence}\n\nEquivalence operators are supported by the Blaze type inheritance. The\nequivalence operator `==` evaluates to true on a pair of vectors if they are the\nsame size and contain the same values, regardless of ownership.\n\n# MakeWithValueImpl {#Vector_MakeWithValueImpl}\n\nSpECTRE offers the convenience function `make_with_value` for various types. The\ntypical behavior for a SpECTRE vector type is to create a new vector type of the\nsame type and length initialized with the value provided as the second argument\nin all entries. This behavior may be created by placing the macro\n`MAKE_WITH_VALUE_IMPL_DEFINITION_FOR(VECTOR_TYPE)` in the .hpp file. Any other\nspecializations of `MakeWithValueImpl` will need to be written manually.\n\n# Interoperability with other data types {#Vector_tensor_and_variables}\n\nWhen additional vector types are added, small changes are necessary if they are\nto be used as the base container type either for `Tensor`s or for `Variables` (a\n`Variables` contains `Tensor`s), which contain some vector type.\n\nIn `Tensor.hpp`, there is a `static_assert` which white-lists the possible types\nthat can be used as the storage type in `Tensor`s. Any new vectors must be added\nto that white-list if they are to be used within `Tensor`s.\n\n`Variables` is templated on the storage type of the stored `Tensor`s. However,\nany new data type should be appropriately tested. New vector types should be\ntested by invoking new versions of existing testing functions templated on the\nnew vector type, rather than `DataVector`.\n\n# Writing tests {#Vector_tests}\n\nIn addition to the utilities for generating new vector types, there are a number\nof convenience functions and utilities for easily generating the tests necessary\nto verify that the vectors function appropriately. These utilities are in\n`VectorImplTestHelper.hpp`, and documented individually in the\nTestingFrameworkGroup. Presented here are the salient details for rapidly\nassembling basic tests for vectors.\n\n## Utility check functions\nEach of these functions is intended to encapsulate a single frequently used unit\ntest and is templated (in order) on the vector type and the value type to be\ngenerated. The default behavior is to uniformly sample values between -100 and\n100, but alternative bounds may be passed in via the function arguments.\n\n### `TestHelpers::VectorImpl::vector_test_construct_and_assign()`\n This function tests a battery of construction and assignment operators for the\n vector type.\n\n### `TestHelpers::VectorImpl::vector_test_serialize()`\nThis function tests that vector types can be serialized and deserialized,\nretaining their data.\n\n### `TestHelpers::VectorImpl::vector_test_ref()`\nThis function tests the `set_data_ref` method of sharing data between vectors,\nand that the appropriate owning flags and move operations are handled correctly.\n\n### `TestHelpers::VectorImpl::vector_test_math_after_move()`\nTests several combinations of math operations and ownership before and after use\nof `std::move`.\n\n### `TestHelpers::VectorImpl::vector_ref_test_size_error()`\nThis function intentionally generates an error when assigning values from one\nvector to a differently sized, non-owning vector (made non-owning by use of\n`set_data_ref`). The assertion test which calls this function should search for\nthe string \"Must copy/move/assign into same size\". Three forms of the test are\nprovided, which are switched between using a value from the enum\n`RefSizeErrorTestKind` in the first function argument:\n- `RefSizeErrorTestKind::Copy`: tests that the size error is appropriately\n generated when copying to a non-owning vector of the wrong size. This has\n \"copy\" in the message.\n- `RefSizeErrorTestKind::ExpressionAssign`: tests that the size error is\n appropriately generated when assigning the result of a mathematical expression\n to a non-owning vector of the wrong size. This has \"assign\" in the message.\n- `RefSizeErrorTestKind::Move`: tests that the size error is appropriately\n generated when a vector is `std::move`d into a non-owning vector of the wrong\n size. This has \"move\" in the message.\n\n## `TestHelpers::VectorImpl::test_functions_with_vector_arguments()`\n\nThis is a general function for testing the mathematical operation of vector\ntypes with other vector types and/or their base types, with or without various\nreference wrappers. This may be used to efficiently test the full set of\npermitted math operations on a vector. See the documentation of\n`test_functions_with_vector_arguments()` for full usage details.\n\nAn example simple use case for the math test utility:\n\\snippet Test_DataVector.cpp test_functions_with_vector_arguments_example\n\nMore use cases of this functionality can be found in `Test_DataVector.cpp`.\n\n# Vector storage nuts and bolts {#Vector_storage}\n\nInternally, all vector classes inherit from the templated `VectorImpl`, which\ninherits from a `blaze::CustomVector`. Most of the mathematical operations are\nsupported through the Blaze inheritance, which ensures that the math operations\nexecute the optimized forms in Blaze.\n\nBlaze also offers the possibility of restricting operations via `groups` in the\n`blaze::CustomVector` template arguments.\nCurrently, we do not use the `blaze::GroupTag` functionality to determine\navailable operations for vectors, but in principle this feature could allow us\nto further simplify our operator choice logic in the SpECTRE vector code.\n\nSpECTRE vectors can be either \"owning\" or \"non-owning\". If a vector is owning,\nit allocates and controls the data it has access to, and is responsible for\neventually freeing that data when the vector goes out of scope. If the vector is\nnon-owning, it acts as a (possibly complete) \"view\" of otherwise allocated\nmemory. Non-owning vectors do not manage memory, nor can they change size. The\ntwo cases of data ownership cause the underlying data to be handled fairly\ndifferently, so we will discuss each in turn.\n\nWhen a SpECTRE vector is constructed as owning, or becomes owning, its memory\nis allocated in one of two ways.\n\n1. The size of the vector is larger than the `StaticSize` template parameter to\n `VectorImpl`. In that case, it allocates its own block of memory of\n appropriate size, and stores a pointer to that memory in a `std::unique_ptr`\n named `owned_data_`. The `std::unique_ptr` ensures that the SpECTRE vector\n needs to perform no further direct memory management, and that the memory\n will be appropriately managed whenever the `std::unique_ptr owned_data_`\n member is deleted or moved.\n2. The size of the vector is less than or equal to the `StaticSize` template. In\n this case, the data is stored on the stack in a `std::array`\n member variable called `static_owned_data_`. Since it is on the stack, this\n doesn't require any memory management by the user.\n\nIn either case, the base `blaze::CustomVector` must also be told about the\npointer, which is always accomplished by calling the protected function\n`VectorImpl.reset_pointer_vector(const size_t set_size)`, which sets the\n`blaze::CustomVector` internal pointer to either the pointer obtained by\n`std::unique_pointer.get()` or the pointer obtained by `std::array.data()`\ndepending on the size of the vector.\n\nWhen a SpECTRE vector is constructed as non-owning by the `VectorImpl(ValueType*\nstart, size_t set_size)` constructor, or becomes non-owning by the\n`set_data_ref` function, neither the internal `std::unique_ptr` named\n`owned_data_` nor the internal `std::array` named `static_owned_data_`\npoints to the data represented by the vector and both can be thought of as\n\"inactive\" for the purposes of computation and memory management. This behavior\nis desirable, because otherwise the `std::unique_ptr` would attempt to free\nmemory that is presumed to be also used elsewhere, causing difficult to diagnose\nmemory errors. And we needn't worry about the `std::array` because it's\nallocated on the stack. The non-owning SpECTRE vector updates the base\n`blaze::CustomVector` pointer directly by calling `blaze::CustomVector.reset`\nfrom the derived class (on itself).\n" }, { "path": "docs/DevGuide/ImportingData.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Importing data {#dev_guide_importing}\n\n\\tableofcontents\n\nThe `importers` namespace holds functionality for importing data into SpECTRE.\nWe currently support loading volume data files in the same format that is\nwritten by the `observers`.\n\n## Importing volume data\n\nThe `importers::ElementDataReader` parallel component is responsible for loading\nvolume data, interpolating it, and distributing it to elements of one or\nmultiple array parallel components. As a first step, make sure you have added\nthe `importers::ElementDataReader` to your `Metavariables::component_list`. Also\nmake sure you have a `Parallel::Phase` in which you will perform\nregistration with the importer, and another in which you want to load the data.\nHere's an example for such `Metavariables`:\n\n\\snippet Test_VolumeDataReaderAlgorithm.hpp metavars\n\nTo load volume data from a file, write an action in which you invoke\n`importers::Actions::ReadAllVolumeDataAndDistribute` on the\n`importers::ElementDataReader`. For simple use cases we provide\n`importers::Actions::ReadVolumeData`, which can be added to the\n`phase_dependent_action_list` of your element array and which will generate\ninput-file options for you. Here's an example that will be explained in more\ndetail below:\n\n\\snippet Test_VolumeDataReaderAlgorithm.hpp import_actions\n\n- The `importers::Actions::ReadVolumeData` action specifies input-file options\n and dispatches to `importers::Actions::ReadAllVolumeDataAndDistribute` on the\n `importers::ElementDataReader` nodegroup component. It loads the volume data\n file once per node on its first invocation. Subsequent invocations of these\n actions, e.g. from all other elements on the node, will do nothing. The data\n is distributed into the inboxes of all elements on the node under the\n `importers::Tags::VolumeData` tag using `Parallel::receive_data`.\n- The `importers::Actions::ReceiveVolumeData` action waits for the volume data\n to be available and directly moves it into the DataBox. If you wish to verify\n or post-process the data before populating the DataBox, use your own\n specialized action in place of `importers::Actions::ReceiveVolumeData`.\n- You need to register the elements of your array parallel component for\n receiving volume data. To do so, invoke the\n `importers::Actions::RegisterWithElementDataReader` action in an earlier\n phase, as shown in the example above.\n\nThe parameters passed to `importers::Actions::ReadAllVolumeDataAndDistribute`\nspecify the volume data to load. See the documentation of\n`importers::Actions::ReadAllVolumeDataAndDistribute` for details. In the example\nabove, we use `importers::Actions::ReadVolumeData` to generate the input-file\noptions for us and place them in an option group:\n\n\\snippet Test_VolumeDataReaderAlgorithm.hpp option_group\n\nThis results in a section in the input file that may look like this:\n\n\\snippet Test_VolumeDataReaderAlgorithm2D.yaml importer_options\n" }, { "path": "docs/DevGuide/LoadBalancingNotes.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n# Notes on SpECTRE load-balancing using Charm++'s built-in load balancers {#load_balancing_notes}\n\n\\tableofcontents\n\nThe goal of load-balancing (LB) is to ensure that HPC resources are well-used\nwhile performing large inhomogeneous simulations. In 2020-2021, Jordan Moxon\nand Francois Hebert performed a number of tests using Charm++'s built-in load\nbalancers with SpECTRE.\n\nThese notes highlight the key points and give (at the bottom) some general\nrecommendations.\n\n### Overview of how LBs work with SpECTRE\n\nIn late 2020 FH tested Charm's LBs on simple, homogeneous, SpECTRE test cases.\nThese tests reveal the following broad behavior patterns:\n- Without using any LBs (no LB command-line args, or `+balancer NullLB`),\n SpECTRE's performance depends sensitively on how the DG elements are\n distributed over the HPC system. This indicates that communication costs are\n very important in SpECTRE runs. This statement remains true for more expensive\n evolution systems like Generalized Harmonic.\n- Charm's LBs that are not communications aware (e.g., `GreedyLB`, `RefineLB`,\n ...) all result in low parallel efficiency (20-30%). This is consistent with\n the understanding that communication costs are large. A good initial\n distribution of elements over processors will be degraded by these LBs,\n leading to more complicated communication graph and loss of performance.\n- Some of Charm's communication-aware LBs perform well: they approach the\n efficiency of a \"manually tuned\" initial distribution of elements onto\n processors. This suggests these LBs do a good job of partitioning the\n communications graph. In FH's simple tests, the best results were from\n `RecBipartLB`, which came within 10-20% of a manual initial distribution.\n However, it is a slow algorithm and is best used infrequently or only a few\n times near the start of the simulation.\n\nNote that at the 2020 Charm++ Workshop, the Charm team recommended that we use\n`MetisLB`, or that we combined `MetisLB` with `RefineLB` (syntax:\n`+balancer MetisLB +balancer RefineLB`, which applies the first balancer on the\nfirst invocation and the second balancer on all subsequent invocations, to\n'polish' the results of the first LB). In practice, this failed for two reasons:\n- `MetisLB` tends to error with FPEs\n- When falling back to the pairing of `RecBipartLB` followed by `RefineLB`, the\n run starts with good performance. However, within a few applications of\n `RefineLB`, the performance is heavily degraded (down to 20-30% efficiency).\n It appears that we should stick to the comm-aware LB strategies.\n\n### Contaminated LB measurements on first invocation\n\nThere is reason to suspect that the Charm load balancing may incorrectly balance\nthe load when applied near the start of some simulations. This is because the\n'one-time' setup of the system may involve nontrivial computation, and (e.g.\nfor numeric initial data) communication patterns between components that differ\nsignificantly from the patterns during evolution. Then, the first balancer\ninvocation, based partially on the measurements taken during the\nnon-generalizable initialization phase, can give rise to a poorly-chosen balance\nand injure performance.\nThis is the suspected cause of poor performance that has been noticed\nin cases of homogeneous load and numeric initial data in Generalized Harmonic\ntests performed by Geoffrey Lovelace. JM confirmed the problem.\nIt appears that the balance is not similarly degraded when using cases that do\nnot involve numeric initial data -- some basic 2-node re-tests with Generalized\nHarmonic by JM seem to produce useful balance (improved performance) when not\nusing numeric initial data.\n\nThis issue has not been investigated to a completely satisfactory conclusion,\nthough the above explanation seems most plausible.\n\nIn cases for which it appears that the LB data is problematically impacted by\nthe set up of the evolution system, we can try two main strategies to mitigate\nthe problem:\n- Apply the load balancer at least two times near the start of the simulation,\n with sufficient gaps to collect useful balancing information. The LB database\n in Charm is cleared every time a balance is applied, so the later balances\n during the evolution should be uncontaminated. This strategy has not yet\n been carefully tested. To do this, use an input file similar to\n```\nPhaseChangeAndTriggers:\n - Trigger:\n Slabs:\n Specified:\n Values: [5, 10, 15]\n PhaseChanges:\n - VisitAndReturn(LoadBalancing)\n```\n- Use `LBTurnInstrumentOff` and `LBTurnInstrumentOn` to specifically exclude\n setup procedures from the LB instrumentation. First attempts indicate that\n this process might be challenging to accomplish correctly, and may require\n correspondence with the Charm developers to clarify at what points in the\n code execution those commands may be used, and precisely how they affect\n the load-balancing database. A first attempt by JM was to turn instrumentation\n off during array element construction, then turn instrumentation on for each\n element during the start of the `Evolve` phase, but that attempt led to a\n hang of the system, so the utility must have more constraints than were\n initially apparent.\n\n### Scotch load balancer\n\nJM tested `ScotchLB`, and found better performance than with `RecBipartLB`. The\nmargin varied a great deal among the number of nodes used, but at multiple\npoints tested, the runtime was less than 65% of the `RecBipartLB` runtime.\nThe tests were performed with homogeneous load, but starting from the\nround-robin element distribution. The indication is therefore that `ScotchLB`\nis very effective at minimizing communication costs.\n\nHowever, in practical applications, JM found that the `ScotchLB` often generates\nFPEs during the graph partition step and causes the simulation to crash.\nThe issue [charm++ issue #3401](https://github.com/UIUC-PPL/charm/issues/3401)\ntracks the progress to determine the cause of the problem and fix it in Charm.\nThe source of the problem has largely been identified, but the fix is still\npending.\n\n`ScotchLB` will likely replace `RecBipartLB` as the most-frequently recommended\ncentralized communication based balancer for SpECTRE once the FPE bugs have\nbeen fixed.\n\n### General recommendations\n\n#### Homogeneous loads\n\nFor homogeneous loads, it is likely best to omit load-balancing and just use\nthe z-curve distribution (default) to give a good initial distribution and use\nthat for the entire evolution. This means calling the SpECTRE executable with\nno LB-related command-line args, or with `+balancer NullLB`.\n\nYou may find modest gains from using a communication-based load balancer, but\nlikely only from the 'extra' parallel components of the system that cause the\nload to be not completely homogeneous (e.g., components like the interpolator\nor horizon finder).\nIf you need a very long evolution or intend to submit a large number of\nevolutions, it may be worth experimenting to see whether 1-3 applications of\n`RecBipartLB` (or `ScotchLB` once its bugs are fixed, see above) improve\nperformance for the system, for instance by using the input file:\n```\nPhaseChangeAndTriggers:\n - Trigger:\n Slabs:\n Specified:\n Values: [5, 10, 15]\n PhaseChanges:\n - VisitAndReturn(LoadBalancing)\n```\nand command-line args `+balancer RecBipartLB` (or `ScotchLB` when its\nbugs are fixed). This may be particularly relevant for cases with numeric\ninitial data or other complicated set-up procedures.\n\n#### Inhomogeneous loads\n\nBased on our experiments, we anticipate that using a load-balancer may\nsignificantly improve runtimes with inhomogeneous loads. Our testing on this\ncase is far more sparse, but for SpECTRE executables, it is probably remains\ntrue that managing communication costs will be an important goal for the\nbalancer. It is likely worth attempting the evolution with a\nperiodically-applied centralized communication-aware balancer, e.g.:\n```\nPhaseChangeAndTriggers:\n - Trigger:\n Slabs:\n EvenlySpaced:\n Interval: 1000\n Offset: 5\n PhaseChanges:\n - VisitAndReturn(LoadBalancing)\n```\npaired with command-line args `+balancer RecBipartLB` (or `ScotchLB` when its\nbugs are fixed).\n\nImportant considerations when choosing the interval with which to balance are:\n- you will want to ensure that the balancer is applied frequently enough to\n prioritize expensive parts of the simulation before any relevent features\n 'move' to other elements. For example, if a shock is moving across the\n simulation domain causing certain elements to be more expensive to compute,\n you want to balance often enough that the LB 'keeps up' with the movement of\n the shock.\n- you will want to avoid balancing so frequently that the synchronization\n and balancer calculation itself becomes a significant portion of runtime.\n\nWe have not yet taken much detailed data on using the load-balancers for\ninhomogeneous loads, so more detailed tests determining their efficacy would be\nvaluable.\n" }, { "path": "docs/DevGuide/Observers.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Observers Infrastructure {#observers_infrastructure_dev_guide}\n\n\\tableofcontents\n\nThe observers infrastructure works with two parallel components: a group and a\nnodegroup. We have two types of observations: `Reduction` and `Volume` (see the\nenum `observers::TypeOfObservation`). `Reduction` data is anything that is\nwritten once per time/integral identifier per simulation. Some examples of\nreduction data are integrals or L2 norms over the entire domain, integrals or L2\nnorms over part of the domain, and integrals over lower-dimensional surfaces\nsuch as apparent horizons or slices through the domain. Volume data is anything\nthat has physical extent, such as any of the evolved variables (or derived\nquantities thereof) across all or part of the domain, or quantities on\nlower-dimensional surfaces in the domain (e.g. the rest mass density in the\nxy-plane). Reduction and volume data both use the group and nodegroup for\nactually getting the data to disk, but do so in a slightly different manner.\n\n### Reduction Data\n\nReduction data requires combining information from many or all cores of a\nsupercomputer to get a single value. Reductions are tagged by some temporal\nvalue, which for hyperbolic systems is the time and for elliptic systems some\ncombination of linear and non-linear iteration count. The reduction data is\nstored in an object of type `Parallel::ReductionData`, which takes as template\nparameters a series of `Parallel::ReductionDatum`. A `Parallel::ReductionDatum`\ntakes as template parameters the type of the data and operators that define how\ndata from the different cores are to be combined to a single value. See the\nparagraphs below for more detail, and the documentation of\n`Parallel::ReductionDatum` for examples.\n\nAt the start of a simulation, every component and event that wants to perform a\nreduction for observation, or will be part of a reduction observation, must\nregister with the `observers::Observer` component. The `observers::Observer` is\na group, which means there is one per core. The registration is used so that the\n`Observer` knows once all data for a specific reduction (both in time and by\nname/ID) has been contributed. Reduction data is combined on each core as it is\ncontributed by using the binary operator from `Parallel::ReductionDatum`'s\nsecond template parameter. Once all the data is collected on the core, it is\ncopied to the local `observers::ObserverWriter` nodegroup, which keeps track of\nhow many of the cores on the node will be contributing to a specific\nobservation, and again combines all the data as it is being contributed. Once\nall the node's data is collected to the nodegroup, the data is sent to node `0`\nwhich combines the reduction data as it arrives using the binary operator from\n`Parallel::ReductionDatum`'s second template parameter. Using node `0` for\ncollecting the final reduction data is an arbitrary choice, but we are always\nguaranteed to have a node `0`.\n\nOnce all the reductions are received on node `0`, the `ObserverWriter` invokes\nthe `InvokeFinal` (third) template parameter on each `Parallel::ReductionDatum`\n(this is the n-ary) in order to finalize the data before writing. This is used,\nfor example, for dividing by the total number of grid points in an L1 or L2\nnorm. The reduction data is then written to an HDF5 file whose name is set in\nthe input file using the option\n`observers::Tags::ReductionFileName`. Specifically, the data is written into an\n`h5::Dat` subfile since, along with the data, the subfile name must be passed\nthrough the reductions.\n\nThe actions used for registering reductions are\n`observers::Actions::RegisterEventsWithObservers` and\n`observers::Actions::RegisterWithObservers`. There is a separate `Registration`\nphase at the beginning of all simulations where everything must register with\nthe observers. The action `observers::Actions::ContributeReductionData` is used\nto send data to the `observers::Observer` component in the case where there is a\nreduction done across an array or subset of an array. If a singleton parallel\ncomponent or a specific chare needs to write data directly to disk it should use\nthe `observers::ThreadedActions::WriteReductionDataRow` action called on the\nzeroth element of the `observers::ObserverWriter` component.\n\n### Volume Data\n\nVolume data is vaguely defined as anything that has some extent. For example, in\na 3d simulation, data on 2d surfaces is still considered volume data for the\npurposes of observing data. The spectral coefficients can also be written as\nvolume data, though some care must be taken in that case to correctly identify\nwhich mode is associated with which terms in the basis function\nexpansion. Whatever component will contribute volume data to be written must\nregister with the `observers::Observer` component (there currently isn't tested\nsupport for directly registering with the `observers::ObserverWriter`). This\nregistration is the same as in the reduction data case.\n\nOnce the observers are registered, data is contributed to the\n`observers::Observer` component using the\n`observers::Actions::ContributeVolumeData` action. The data is packed into an\n`ElementVolumeData` object that carries `TensorComponent`s on a grid.\nInformation on the grid, such as its extents, basis and quadrature, are stored\nalongside the `TensorComponent`s. Once all the elements on a single core have\ncontributed their volume data to the `observers::Observer` group, the\n`observers::Observer` group moves its data to the `observers::ObserverWriter`\ncomponent to be written. We write one file per node, appending the node ID to\nthe HDF5 file name to distinguish between files written by different nodes. The\nHDF5 file name is specified in the input file using the\n`observers::Tags::VolumeFileName` option. The data is written into a subfile of\nthe HDF5 file using the `h5::VolumeFile` class.\n\nIf a singleton parallel component or a specific chare needs to write volume data\ndirectly to disk, such as surface data from an apparent horizon, it should use\nthe `observers::ThreadedActions::WriteVolumeData` action called on the zeroth\nelement of the `observers::ObserverWriter` component. For surface data (such as\noutput from horizon finds), this data should be written to a file specified by\nthe `observers::Tags::SurfaceFileName` option.\n\n### Threading and NodeLocks\n\nSince the `observers::ObserverWriter` class is a nodegroup, its entry methods\ncan be invoked simultaneously on different cores of the node. However, this can\nlead to race conditions if care isn't taken. The biggest caution is that the\n`DataBox` cannot be mutated on one core and simultaneously accessed on\nanother. This is because in order to guarantee a reasonable state for data in\nthe `DataBox`, it must be impossible to perform a `db::get` on a `DataBox` from\ninside or while a `db::mutate` is being done. What this means in practice is\nthat all entry methods on a nodegroup must put their `DataBox` accesses inside\nof a `node_lock.lock()` and `node_lock.unlock()` block. To achieve better\nparallel performance and threading, the amount of work done while the entire\nnode is locked should be minimized. To this end, we have additional locks. One\nfor the HDF5 files because we do not require a threadsafe HDF5\n(`observers::Tags::H5FileLock`). We also have locks for the objects mutated when\ncontributing reduction data (`observers::Tags::ReductionDataLock`).\n\n### Future changes\n- It would be preferable to make the `Observer` and `ObserverWriter` parallel\n components more general and have them act as the core (node)group. Since any\n simple actions can be run on them, it should be possible to use them for most,\n if not all cases where we need a (node)group.\n" }, { "path": "docs/DevGuide/OptionParsing.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Option Parsing {#dev_guide_option_parsing}\n\n\\tableofcontents\n\nSpECTRE can read YAML configuration files at runtime to set parameters\nand choose between classes implementing an interface. %Options are\nparsed during code initialization and can be used to construct objects\nplaced in the Parallel::GlobalCache and options passed to the\nparallel components. The types necessary to mark objects for parsing\nare declared in `Options/Options.hpp`.\n\n## Metadata and options\n\nYAML input files begin with a metadata section, terminated by `---`, and\nfollowed by the executable options:\n\n```yaml\n# Metadata here\nDescription: |\n Briefly describe the configuration and link to papers for details.\n---\n# Options start here\n```\n\nThe metadata section may also be empty:\n\n```yaml\n---\n---\n# Options start here\n```\n\nYou only need the leading `---` marker if the metadata section is empty. This is\nYAML's \"document start marker\" (see the [YAML spec](https://yaml.org/spec/1.2)).\nAny metadata fields at the beginning of the file also imply the start of a\ndocument, so you don't need the first `---` marker.\n\nMetadata provide information for tools, whereas options provide information to\nthe executable. See tools like `CheckOutputFiles` for details on the metadata\nfields that they use. Metadata can also provide information on how to run the\ninput file, such as the name and version of the executable, and a description\nthat may refer to published papers for details on the configuration.\nOptions are defined by the executable and detailed below.\n\n## General option format\n\nAn option is defined by an \"option tag\", represented by a `struct`. At minimum,\nthe struct must declare the type of the object to be parsed and provide a brief\ndescription of the meaning. The name of the option in the input file\ndefaults to the name of the struct (excluding any template parameters\nand scope information), but can be overridden by providing a static\n`name()` function. Several other pieces of information, such as\nsuggestions, limits and grouping, may be provided if desired. This\ninformation is all included in the generated help output.\n\nIf an option has a suggested value, the value is specified in the\ninput file as usual, but a warning will be issued if the specified\nvalue does not match the suggestion.\n\nExamples:\n\\snippet Options/Test_Options.cpp options_example_scalar_struct\n\\snippet Options/Test_Options.cpp options_example_vector_struct\n\nThe option type can be any type understood natively by yaml-cpp\n(fundamentals, `std::string`, and `std::map`, `std::vector`,\n`std::list`, `std::array`, and `std::pair` of parsable types) and\ntypes SpECTRE adds support for. SpECTRE adds `std::unordered_map`\n(but only with ordered keys), `std::variant` (with alternatives tested\nin order), and various classes marked as constructible in their\ndeclarations.\n\nAn option tag can be placed in a group by adding a `group` type alias to the\nstruct. The alias should refer to a type that, like option tags, defines a help\nstring and may override a static `name()` function.\n\nExample:\n\\snippet Options/Test_Options.cpp options_example_group\n\n## Constructible classes\n\nA class that defines `static constexpr Options::String help` and a\ntypelist of option structs `options` can be created by the option\nparser. When the class is requested, the option parser will parse\neach of the options in the `options` list, and then supply them to the\nconstructor of the class. A class can use Options::Alternatives to\nsupport more than one possible set of options for its creation. (See\n[Custom parsing](#custom-parsing) below for more general creation\nmechanisms.)\n\nUnlike option descriptions, which should be brief, the class help\nstring has no length limits and should give a description of the class\nand any necessary discussion of its options beyond what can be\ndescribed in their individual help strings.\n\nCreatable classes must be default constructible and move assignable.\n\nThe `Options::Context` is an optional argument to the constructor that should be\nused when the constructor checks for validity of the input. If the input is\ninvalid, `PARSE_ERROR` is used to propagate the error message back through the\noptions ensuring that the error message will have a full backtrace so it is easy\nfor the user to diagnose.\n\nExample:\n\\snippet Options/Test_CustomTypeConstruction.cpp class_creation_example\n\nClasses may use the Metavariables struct, which is effectively the compile time\ninput file, in their parsing by templating the `options` type alias or by taking\nthe Metavariables as a final argument to the constructor (after the\n`Options::Context`).\n\nExample:\n\\snippet Options/Test_CustomTypeConstruction.cpp class_creation_example_with_metavariables\n\n## Factory\n\nThe factory interface creates an object of type\n`std::unique_ptr` containing a pointer to some class derived\nfrom `Base`. The list of creatable derived classes is specified in\nthe `factory_creation` struct in the metavariables, which must contain\na `factory_classes` type alias that is a `tmpl::map` from base classes\nto lists of derived classes:\n\\snippet Options/Test_Factory.cpp factory_creation\n\nWhen a `std::unique_ptr` is requested, the factory will expect a\nsingle YAML argument specifying the name of the class (as given by a\nstatic `name()` function or, lacking that, the actual class name). If\nthe derived class takes no arguments, the name can be given as a YAML\nstring, otherwise it must be given as a single key-value pair, with\nthe key the name of the class. The value portion of this pair is then\nused to create the requested derived class in the same way as an\nexplicitly constructible class. Examples:\n\\snippet Options/Test_Factory.cpp factory_without_arguments\n\\snippet Options/Test_Factory.cpp factory_with_arguments\n\n\\anchor custom-parsing\n## Custom parsing\n\nOccasionally, the requirements imposed by the default creation\nmechanism are too stringent. In these cases, the construction\nalgorithm can be overridden by providing a specialization of the\nstruct\n\\code{cpp}\ntemplate \nstruct Options::create_from_yaml {\n template \n static T create(const Options::Option& options);\n};\n\\endcode\nThe create function can perform any operations required to construct\nthe object.\n\nExample of using a specialization to parse an enum:\n\\snippet Options/Test_CustomTypeConstruction.cpp enum_creation_example\n\nNote that in the case where the `create` function does *not* need to use the\n`Metavariables` it is recommended that a general implementation forward to an\nexplicit instantiation with `void` as the `Metavariables` type. The reason for\nusing `void` specialization is to reduce compile time. Since we only need one\nfull implementation of the function independent of what type `Metavariables` is,\nwe should only parse and compile it once. By having a specialization on `void`\n(or some other non-metavariables type like `NoSuchType`) we can handle the\nmetavariables-independent case efficiently. As a concrete example, the general\ndefinition and forward declaration of the `void` specialization in the header\nfile would be:\n\n\\snippet Options/Test_CustomTypeConstruction.cpp enum_void_creation_header_example\n\nwhile in the `cpp` file the definition of the `void` specialization is:\n\n\\snippet Options/Test_CustomTypeConstruction.cpp enum_void_creation_cpp_example\n" }, { "path": "docs/DevGuide/ParallelExecutable/Concepts.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Parallelization in SpECTRE {#tutorial_parallel_concepts}\n\n\\tableofcontents\n\nThis overview describes the concepts and terminology that SpECTRE uses\nto enable parallelism. This overview is a general discussion with no\ncode examples. Subsequent tutorials will provide a more in-depth\nexploration of the parallelization infrastructure, including code\nexamples.\n\nUnlike many parallel scientific codes which use data-based\nparallelism, SpECTRE uses task-based parallelism. The classical\nstrategy for parallelism (data-based parallelism) is to assign a\nportion of the data to processes (or threads) that synchronously\nexecute compute kernels. This is implemented in many codes but it is\ndifficult to design codes with this strategy that will efficiently\nscale for complex multi-scale, multi-physics workloads. Task-based\nparallelism provides a solution: Instead of dividing work between\nparallel processes based on data ownership, there is a set of tasks\nand their inter-dependencies. Tasks are scheduled and assigned to\nprocesses dynamically, providing opportunities for load balancing and\nminimization of idle threads. By dividing the program into small\nenough tasks such that you have several tasks per thread,\ncommunication time is hidden by interleaving tasks that are ready to\nbe executed with tasks that are waiting for data.\n\nIn order to implement task-based parallelism, SpECTRE is built on top\nof the parallel programming framework of the Charm++ library, which is\ndeveloped by the [Parallel Programming\nLaboratory](http://charm.cs.illinois.edu/) at the University of\nIllinois. Charm++ is a mature parallel programming framework that\nprovides intra-node threading and can use a variety of communication\ninterfaces (including MPI) to communicate between nodes. Charm++ has\na large user base, which includes users of the cosmological\n\\f$N\\f$-body code\n[ChaNGa](https://github.com/N-BodyShop/changa/wiki/ChaNGa) and of the\nmolecular dynamics code\n[NAMD](https://www.ks.uiuc.edu/Research/namd/).\n\n## Charm++ basic concepts\n\nIn order to understand how parallelization works in SpECTRE, it is\nuseful to understand the basic concepts in the design of Charm++.\nMuch of the following is quoted verbatim from the [Charm++\ndocumentation](https://charm.readthedocs.io), interspersed with\ncomments on how SpECTRE interacts with Charm++.\n\n> Charm++ is a C++-based parallel programming system, founded on the\n> migratable-objects programming model, and supported by a novel and\n> powerful adaptive runtime system. It supports both irregular as well\n> as regular applications, and can be used to specify task-parallelism\n> as well as data parallelism in a single application. It automates\n> dynamic load balancing for task-parallel as well as data-parallel\n> applications, via separate suites of load-balancing strategies. Via\n> its message-driven execution model, it supports automatic latency\n> tolerance, modularity and parallel composition. Charm++ also supports\n> automatic checkpoint/restart, as well as fault tolerance based on\n> distributed checkpoints.\n\nSpECTRE currently wraps only some of the features of Charm++,\nprimarily the ones that support task-parallelism. We are just\nbeginning our exploration of dynamic load balancing. Coming soon we\nwill utilize automatic checkpoint/restart. At present we do not use\nCharm++ support for fault tolerance.\n\n> The key feature of the migratable-objects programming model is\n> over-decomposition: The programmer decomposes the program into a\n> large number of work units and data units, and specifies the\n> computation in terms of creation of and interactions between these\n> units, without any direct reference to the processor on which any\n> unit resides. This empowers the runtime system to assign units to\n> processors, and to change the assignment at runtime as necessary.\n\nSpECTRE's parallelization module is designed to make it easy for users\nto exploit the migratable-object model by providing a framework to\ndefine the units into which a program can be decomposed.\n\n> A basic unit of parallel computation in Charm++ programs is a\n> chare. At its most basic level, it is just a C++ object. A Charm++\n> computation consists of a large number of chares distributed on\n> available processors of the system, and interacting with each other\n> via asynchronous method invocations. Asynchronously invoking a\n> method on a remote object can also be thought of as sending a\n> “message” to it. So, these method invocations are sometimes referred\n> to as messages. (besides, in the implementation, the method\n> invocations are packaged as messages anyway). Chares can be created\n> dynamically.\n\nIn SpECTRE, we wrap Charm++ chares in struct templates that we call\n__parallel components__ that represent a collection of distributed\nobjects. We wrap the asynchronous method invocations between the\nelements of parallel components in struct templates that we call\n__actions__. Thus, each element of a parallel component can be\nthought of as a C++ object that exists on one core on the\nsupercomputer, and an action as calling a member function of that\nobject, even if the caller is on another core.\n\n> Conceptually, the system maintains a “work-pool” consisting of seeds\n> for new chares, and messages for existing chares. The Charm++\n> runtime system (Charm RTS) may pick multiple items,\n> non-deterministically, from this pool and execute them, with the\n> proviso that two different methods cannot be simultaneously\n> executing on the same chare object (say, on different\n> processors). Although one can define a reasonable theoretical\n> operational semantics of Charm++ in this fashion, a more practical\n> description of execution is useful to understand Charm++. A Charm++\n> application’s execution is distributed among Processing Elements\n> (PEs), which are OS threads or processes depending on the selected\n> Charm++ build options. On each PE, there is a scheduler operating\n> with its own private pool of messages. Each instantiated chare has\n> one PE which is where it currently resides. The pool on each PE\n> includes messages meant for chares residing on that PE, and seeds\n> for new chares that are tentatively meant to be instantiated on that\n> PE. The scheduler picks a message, creates a new chare if the\n> message is a seed (i.e. a constructor invocation) for a new chare,\n> and invokes the method specified by the message. When the method\n> returns control back to the scheduler, it repeats the cycle\n> (i.e. there is no pre-emptive scheduling of other invocations).\n\nIt is very important to keep in mind that the actions that are\nexecuted on elements of parallel components are done so\nnon-deterministically by the run-time system. Therefore it is the\nresponsibility of the programmer to ensure that actions are not called\nout of order. This means that if action B must be executed after\naction A on a given element of a parallel component, the programmer\nmust ensure that either action B is called after the completion of\naction A (i.e. it is not sufficient that action B is invoked after\naction A is invoked), or that action B checks that action A has\ncompleted before running.\n\n> When a chare method executes, it may create method invocations for\n> other chares. The Charm Runtime System (RTS) locates the PE where\n> the targeted chare resides, and delivers the invocation to the\n> scheduler on that PE.\n\nIn SpECTRE, this is done by one element of a parallel component\ncalling an action on an element of a another parallel component.\n\n> Methods of a chare that can be remotely invoked are called entry\n> methods. Entry methods may take serializable parameters, or a\n> pointer to a message object. Since chares can be created on remote\n> processors, obviously some constructor of a chare needs to be an\n> entry method. Ordinary entry methods are completely non-preemptive-\n> Charm++ will not interrupt an executing method to start any other\n> work, and all calls made are asynchronous.\n\nIn SpECTRE, the struct template that defines a parallel component has\ntaken care of creating the entry methods for the underlying chare,\nwhich are then called by invoking actions.\n\n> Charm++ provides dynamic seed-based load balancing. Thus location\n> (processor number) need not be specified while creating a remote\n> chare. The Charm RTS will then place the remote chare on a suitable\n> processor. Thus one can imagine chare creation as generating only a\n> seed for the new chare, which may take root on some specific\n> processor at a later time.\n\nWe are just in the process of beginning to explore the load-balancing\nfeatures of Charm++, but plan to have new elements of parallel\ncomponents (the wrapped chares) be creatable using actions, without\nspecifying the location on which the new element is created.\n\n> Chares can be grouped into collections. The types of collections of\n> chares supported in Charm++ are: chare-arrays, chare-groups, and\n> chare-nodegroups, referred to as arrays, groups, and nodegroups\n> throughout this manual for brevity. A Chare-array is a collection of\n> an arbitrary number of migratable chares, indexed by some index\n> type, and mapped to processors according to a user-defined map\n> group. A group (nodegroup) is a collection of chares, with exactly\n> one member element on each PE (“node”).\n\nEach of SpECTRE's parallel components has a type alias `chare_type`\ncorresponding to whether it is a chare-array, chare-group, or\nchare-nodegroup. In addition we support a singleton which is\nessentially a one-element array.\n\n> Charm++ does not allow global variables, except readonly\n> variables. A chare can normally only access its own data\n> directly. However, each chare is accessible by a globally valid\n> name. So, one can think of Charm++ as supporting a global object\n> space.\n\nSpECTRE does not use the readonly global variables provided by\nCharm++. Instead SpECTRE provides a nodegroup called the\n`GlobalCache` which provides global access to both read-only\nand writable objects, as well as a way to access every parallel component.\n\n> Every Charm++ program must have at least one mainchare. Each\n> mainchare is created by the system on processor 0 when the Charm++\n> program starts up. Execution of a Charm++ program begins with the\n> Charm RTS constructing all the designated mainchares. For a\n> mainchare named X, execution starts at constructor X() or X(CkArgMsg\n> *) which are equivalent. Typically, the mainchare constructor starts\n> the computation by creating arrays, other chares, and groups. It can\n> also be used to initialize shared readonly objects.\n\nSpECTRE provides a pre-defined mainchare called `Main` that is run\nwhen a SpECTRE executable is started. `Main` will create the other\nparallel components, and initialize items in the `GlobalCache`\nwhose items can be used by any parallel component.\n\n> Charm++ program execution is terminated by the CkExit call. Like the\n> exit system call, CkExit never returns, and it optionally accepts an\n> integer value to specify the exit code that is returned to the\n> calling shell. If no exit code is specified, a value of zero\n> (indicating successful execution) is returned. The Charm RTS ensures\n> that no more messages are processed and no entry methods are called\n> after a CkExit. CkExit need not be called on all processors; it is\n> enough to call it from just one processor at the end of the\n> computation.\n\nSpECTRE wraps `CkExit` with the function `sys::exit`. As no more\nmessages are processed by Charm++ after this call, SpECTRE also\ndefines a special `Exit` phase that is guaranteed to be executed after\nall messages and entry methods have been processed.\n\n> As described so far, the execution of individual Chares is\n> “reactive”: When method A is invoked the chare executes this code,\n> and so on. But very often, chares have specific life-cycles, and the\n> sequence of entry methods they execute can be specified in a\n> structured manner, while allowing for some localized non-determinism\n> (e.g. a pair of methods may execute in any order, but when they both\n> finish, the execution continues in a pre-determined manner, say\n> executing a 3rd entry method).\n\nCharm++ provides a special notation to simplify expression of such\ncontrol structures, but this requires writing specialized interface\nfiles that are parsed by Charm++. SpECTRE does not support this;\nrather we split the executable into a set of phases. In\neach phase, each parallel component will execute a user-defined list\nof actions.\n\n> The normal entry methods, being asynchronous, are not allowed to\n> return any value, and are declared with a void return type.\n\nSpECTRE's actions do not return any value to the calling component.\nInstead when the action is finished it can call another action to send\ndata to an element of any parallel component.\n\n> To support asynchronous method invocation and global object space,\n> the RTS needs to be able to serialize (“marshall”) the parameters,\n> and be able to generate global “names” for chares. For this purpose,\n> programmers have to declare the chare classes and the signature of\n> their entry methods in a special “.ci” file, called an interface\n> file. Other than the interface file, the rest of a Charm++ program\n> consists of just normal C++ code. The system generates several\n> classes based on the declarations in the interface file, including\n> “Proxy” classes for each chare class. Those familiar with various\n> component models (such as CORBA) in the distributed computing world\n> will recognize “proxy” to be a dummy, standin entity that refers to\n> an actual entity. For each chare type, a “proxy” class exists. The\n> methods of this “proxy” class correspond to the remote methods of\n> the actual class, and act as “forwarders”. That is, when one invokes\n> a method on a proxy to a remote object, the proxy marshalls the\n> parameters into a message, puts adequate information about the\n> target chare on the envelope of the message, and forwards it to the\n> remote object. Individual chares, chare array, groups, node-groups,\n> as well as the individual elements of these collections have a such\n> a proxy. Multiple methods for obtaining such proxies are described\n> in the manual. Proxies for each type of entity in Charm++ have some\n> differences among the features they support, but the basic syntax\n> and semantics remain the same - that of invoking methods on the\n> remote object by invoking methods on proxies.\n\nSpECTRE has wrapped all of this functionality in order to make it\neasier to use. SpECTRE automatically creates the interface files for\neach parallel component using template metaprogramming. SpECTRE\nprovides proxies for each parallel component that are all held in the\n`GlobalCache` which is available to every parallel component. In\norder for actions to be called as entry methods on remote parallel\ncomponents, the arguments to the function call must be serializable.\nCharm++ provides the `PUP` framework to serialize objects where `PUP`\nstands for pack-unpack. Since the PUP framework is used by Charm++\nfor checkpointing, load-balancing, and passing arguments when calling\nactions, all user-defined classes with member data must define a `pup`\nfunction.\n\n> In terms of physical resources, we assume the parallel machine\n> consists of one or more nodes, where a node is a largest unit over\n> which cache coherent shared memory is feasible (and therefore, the\n> maximal set of cores per which a single process can run. Each node\n> may include one or more processor chips, with shared or private\n> caches between them. Each chip may contain multiple cores, and each\n> core may support multiple hardware threads (SMT for example).\n> Charm++ recognizes two logical entities: a PE (processing element)\n> and a logical node, or simply “node”. In a Charm++ program, a PE is\n> a unit of mapping and scheduling: each PE has a scheduler with an\n> associated pool of messages. Each chare is assumed to reside on one\n> PE at a time. A logical node is implemented as an OS process. In\n> non-SMP mode there is no distinction between a PE and a logical\n> node. Otherwise, a PE takes the form of an OS thread, and a logical\n> node may contain one or more PEs. Physical nodes may be partitioned\n> into one or more logical nodes. Since PEs within a logical node\n> share the same memory address space, the Charm++ runtime system\n> optimizes communication between them by using shared\n> memory. Depending on the runtime command-line parameters, a PE may\n> optionally be associated with a subset of cores or hardware threads.\n\nIn other words, how Charm++ defines a node and a PE depends upon how\nCharm++ was installed on a system. The executable\n`Executables/ParallelInfo` can be used to determine how many nodes and\nPEs exist for a given Charm++ build and the runtime command-line\nparameters passed when calling the executable.\n\nFor more details see the [Charm++\ndocumentation](https://charm.readthedocs.io) and \\ref\ndev_guide_parallelization_foundations.\n" }, { "path": "docs/DevGuide/ParallelExecutable/MinimalExecutable.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# The minimal SpECTRE executable {#tutorial_minimal_parallel_executable}\n\n\\tableofcontents\n\nThis tutorial will illustrate what is needed to compile the minimal\nSpECTRE executable that will simply print some useful information\nabout the executable and then exit.\n\nSpecifically, this tutorial will introduce:\n- A user-provided `Metavariables`, a C++ struct that is used to\n specify the metaprogram that is converted into a C++ executable.\n- how to build a SpECTRE executable\n- how to run a SpECTRE executable\n- useful information that can be extracted from all SpECTRE executables\n- `Main`, the main parallel component that acts as the main function\n of a C++ executable.\n\nIn this tutorial, `SPECTRE_ROOT` refers to the directory in which\nSpECTRE was cloned, and `SPECTRE_BUILD_DIR` refers to the directory in\nwhich you built SpECTRE.\n\n### Creating a build target for a parallel executable\n\nThe first step is to select (or create) a directory (within\n`SPECTRE_ROOT/src`) that will hold the files from which the executable\nwill be created. For this tutorial we created the directory\n`ParallelTutorial` in `src/Executables/Examples`. If you create a new\ndirectory for the executable, you will need to edit the\n`CMakeLists.txt` file in its parent directory and add (replacing\n`ParallelTutorial` with the appropriate directory name)\n\n\\snippet Examples/CMakeLists.txt add_subdirectory\n\nThe second step is to edit (or create) the `CMakeLists.txt` file in\nthe executable directory and add a call to `add_spectre_executable` such as:\n\n\\snippet ParallelTutorial/CMakeLists.txt add_spectre_executable\n\nThe `add_spectre_executable` just forwards its arguments to CMake's\n`add_executable`. It works just like `add_executable` in that you pass it a\nsource file that defines your executable.\n\nYour source file needs a `CkRegisterMainModule()` function. This is the \"main\"\nfunction of the Charm++ program:\n\n\\snippet ParallelTutorial/MinimalExecutable.cpp main_function\n\nIt just calls `Parallel::charmxx::register_main_module()`. This\nis where SpECTRE code takes over. SpECTRE programs are defined by the\n`Metavariables` class that is passed to this function.\n\n### Writing the metavariables files\n\nThe metavariables can be thought of as a compile-time input file that defines\nwhat the executable will do:\n\n\\snippet MinimalExecutable.cpp metavariables_definition\n\nThe metavariables struct must define a `static constexpr\nstd::array default_phase_order` that is used to\ndefine the default order in which phases are executed. In this\nexample the executable will execute the `Initialization` phase\nfollowed by the `Exit` phase.\n\nThe metavariables struct must define a type alias `component_list`\nthat is a `tmpl::list` (a typelist defined in `Utilities/TMPL.hpp`) of\nthe parallel components used by the executable. In this example no\nparallel components are used.\n\nThe metavariables struct must define `help`, a `static constexpr\nOptions::String` that will be printed as part of the help message of the\nexecutable. (`Options::String` is defined in `Options/Options.hpp`.)\n\n### Building a SpECTRE executable\n\nLet `$EXECUTABLE` be the name of the executable (the first argument\npassed to the `add_spectre_executable` `CMake` function, so in this\nexample `MinimalExample`). Then the executable can be built by\nrunning the following command in `$SPECTRE_BUILD_DIR`:\n\n```\nmake $EXECUTABLE\n```\n\nwhich will produce the executable of the same name in\n`$SPECTRE_BUILD_DIR/bin`.\n\n### Running a SpECTRE executable\n\nTo run a SpECTRE executable, run the command:\n\n```\n./$SPECTRE_BUILD_DIR/bin/$EXECUTABLE \n```\n\nwhere `` must include any required command-line options. In\nthe simple example for this tutorial, no command-line options are\nrequired.\n\nOn a laptop, we get the following output:\n\n```\nCharm++: standalone mode (not using charmrun)\nCharm++> Running in Multicore mode: 1 threads\nConverse/Charm++ Commit ID: v6.8.0-0-ga36028edb\nCharmLB> Load balancer assumes all CPUs are same.\nCharm++> Running on 1 unique compute nodes (4-way SMP).\nCharm++> cpu topology info is gathered in 0.000 seconds.\n\nExecuting 'some_path/MinimalExample' using 1 processors.\nDate and time at startup: Fri Oct 25 15:03:05 2019\n\nSpECTRE Build Information:\nVersion: 0.0.0\nCompiled on host: kosh-3.local\nCompiled in directory: some_path/build\nSource directory is: some_path/parallel_tutorial\nCompiled on git branch: feature/parallel_tutorial\nCompiled with git hash: 1f4ab20cbda9ae8072a17df69de9731c43687468\nLinked on: Fri Oct 25 13:26:06 2019\n\n\nDone!\nWall time in seconds: 0.004185\nDate and time at completion: Fri Oct 25 15:03:05 2019\n\n[Partition 0][Node 0] End of program\n```\n\nwhich includes information that will be printed by every SpECTRE\nexecutable on startup and exit. First, there is information provided\nby `Charm++` that will depend upon how `Charm++` was built. Next you\nwill see information provided by SpECTRE which includes:\n\n- the name of the executable\n- how many processes the executable was run on\n- the date and time at startup\n- the version of SpECTRE that was used to compile the executable\n- where the executable was compiled\n- which git branch and hash was used to compile the executable\n- when the executable was linked\n\nOn exit, the executable will print that it is `Done!`, followed by how\nthe long the executable took to run as timed by the `Charm++`\nwall-clock timer, and the date and time at completion, followed by any\ninformation the `Charm++` provides upon exiting the program.\n\n### Extracting useful information from a SpECTRE executable\n\nEvery SpECTRE executable comes with a set of command-line options that\ncan be used to obtain useful information about the executable (and for\nexecutables expecting an input file, whether or not the input file can\nbe parsed successfully).\n\n#### Getting a list of available options\n\nTo get a list of available options for a SpECTRE executable, run\neither of the following commands:\n\n```\n./$SPECTRE_BUILD_DIR/bin/$EXECUTABLE --help\n./$SPECTRE_BUILD_DIR/bin/$EXECUTABLE -h\n```\n\nIn the middle of the `Charm++` startup information will now appear a\nlong list of `Charm++` related command-line options which we will\nignore for this tutorial. After the SpECTRE startup information,\nthere is now a list of available command-line options:\n\n```\n -h [ --help ] Describe program options\n --check-options Check input file options\n --dump-source-tree-as arg If specified, then a gzip archive of the source\n tree is dumped with the specified name. The archive\n can be expanded using 'tar -xzf ARCHIVE.tar.gz'\n --dump-paths Dump the PATH, CPATH, LD_LIBRARY_PATH,\n LIBRARY_PATH, and CMAKE_PREFIX_PATH at compile\n time.\n --dump-environment Dump the result of printenv at compile time.\n --dump-build-info Dump the contents of SpECTRE's BuildInfo.txt\n --dump-only Exit after dumping requested information.\n```\n\nwhich we will describe in detail below. This is followed by a\ndescription of the expected input-file options, which in this example\nwill simply print the `help` string from the metavariables struct, and\nthe statement that there are no options expected:\n\n```\n==== Description of expected options:\nA minimal executable\n\n\n```\n\nWe will cover input file options in a future tutorial.\n\n#### Checking options\n\nAs the minimal executable in this tutorial expects no input-file\noptions, running the command:\n\n```\n./$SPECTRE_BUILD_DIR/bin/$EXECUTABLE --check-options\n```\n\nwill print out `No options to check!` and exit the program. See a\nfuture tutorial for an example of checking input-file options.\n\n#### Dumping the source tree\n\nIn order to aid in reproducibility, all SpECTRE executables contain a\ncopy of `$SPECTRE_ROOT`. To obtain the source tree as an archive\nfile, run the command:\n\n```\n./$SPECTRE_BUILD_DIR/bin/$EXECUTABLE --dump-source-tree-as SpECTRE\n```\n\nwhich will produce the archive file `SpECTRE.tar.gz` which can be\nexpanded with the command:\n\n```\ntar -xzf SpECTRE.tar.gz\n```\n\n#### Dumping other information about a SpECTRE executable\n\nIn addition to dumping the entire source tree there are the following options:\n\n- `--dump-paths` will print out various paths from when the\n executable was compiled\n- `--dump-environment` will print the results of `printenv`\n (i.e. all of the environment variables) from when the executable was\n compiled\n- `--dump-build-info` will print the contents of SpECTRE's\n `BuildInfo.txt` which will contain the versions of libraries\n that SpECTRE linked against, as well as various `CMake` variables\n\nAlso note that the option `--dump-only` can be used to have the\nSpECTRE executable terminate immediately after dumping the\ninformation.\n\n### Behind the scenes: the main parallel component\n\nEvery Charm++ executable needs a mainchare. All SpECTRE executables\nuse `Main` (found in `src/Parallel/Main.hpp`) as the mainchare. When\na SpECTRE executable is run, the constructor of `Main` that is executed\ntakes the command line options as an argument (as type\n`CkArgMsg*`). This constructor performs the following operations:\n\n- Prints useful startup information\n- Parses the command line options, performing any requested operations\n- Parses the input file options, populating a tagged tuple with their\n values. (This is discussed in more detail in a future tutorial on\n input file options.)\n- Creates the `GlobalCache` (a nodegroup chare) that holds\n objects created from input file options that are stored\n once per Charm++ node, as well as proxies to all other parallel\n components.\n- Creates user-requested non-array parallel components, passing them\n the proxy to the `GlobalCache` as well as any items they\n request that can be created from input file options.\n- Creates empty array user-requested parallel components\n- Sends the complete list of parallel components to the\n `GlobalCache`.\n\nOnce the list of parallel components is sent to the `GlobalCache`\non each node, the `Main` member function\n`allocate_array_components_and_execute_initial_phase` will be\nexecuted. This will allocate the elements of the array parallel\ncomponents by calling the `allocate_array` member function of each\ncomponent. Then the `start_phase` member function is called on each\ncomponent, which will execute the phase action list for the\n`Initialization` phase for each component. Charm++ will execute each\nphase until it detects that nothing is happening (quiescence\ndetection). As this represents a global synchronization point, the\nnumber of phases should be minimized in order to exploit the power of\nSpECTRE. After each phase, the `execute_next_phase` member function\nof `Main` will be called. This member function first determines what\nthe next phase is. If the next phase is `Exit`, then some useful\ninformation is printed and the program exits gracefully. Otherwise the\n`execute_next_phase` member function of each parallel component is\ncalled.\n\n" }, { "path": "docs/DevGuide/Parallelization.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Parallelization, Charm++, and Core Concepts {#dev_guide_parallelization_foundations}\n\n\\tableofcontents\n\n# Introduction {#dev_guide_parallelization_introduction}\n\nSpECTRE builds a layer on top of Charm++ that performs various safety checks and\ninitialization for the user that can otherwise lead to difficult-to-debug\nundefined behavior. The central concept is what is called a %Parallel\nComponent. A %Parallel Component is a struct with several type aliases that\nis used by SpECTRE to set up the Charm++ chares and allowed communication\npatterns. %Parallel Components are input arguments to the compiler, which then\nwrites the parallelization infrastructure that you requested for the executable.\nThere is no restriction on the number of %Parallel Components, though\npractically it is best to have around 10 at most.\n\nHere is an overview of what is described in detail in the sections below:\n\n- \\ref dev_guide_parallelization_metavariables_class \"Metavariables\": Provides\n high-level configuration to the compiler, e.g. the physical system to be\n simulated.\n- \\ref dev_guide_parallelization_phases_of_execution \"Phases\": Defines distinct\n simulation phases separated by a global synchronization point,\n e.g. `Initialization`, `Evolve` and `Exit`.\n- \\ref dev_guide_parallelization_core_algorithm \"Algorithm\": In each phase,\n repeatedly iterates over a list of actions until the current phase ends.\n- \\ref dev_guide_parallelization_parallel_components \"Parallel component\":\n Maintains and executes its algorithm.\n- \\ref dev_guide_parallelization_actions \"Action\": Performs a computational\n task, e.g. evaluating the right hand side of the time evolution equations. May\n require data to be received from another action potentially being executed on\n a different core or node.\n\n# The Metavariables Class {#dev_guide_parallelization_metavariables_class}\n\nSpECTRE takes a different approach to input options passed to an executable than\nis common. SpECTRE not only reads an input file at runtime but also has many\nchoices made at compile time. The compile time options are specified by what is\nreferred to as the metavariables. What exactly the metavariables struct\nspecifies depends on the executable, but all metavariables structs must\nspecify the following:\n\n- `help`: a `static constexpr Options::String` that will be printed as part of\n the help message. It should describe the executable and basic usage of it, as\n well as any non-standard options that must be specified in the metavariables\n and their current values. An example of a help string for one of the testing\n executables is:\n \\snippet Test_AlgorithmCore.cpp help_string_example\n- `component_list`: a `tmpl::list` of the parallel components (described below)\n that are to be created. Most evolution executables will have the\n `DgElementArray` parallel component listed. An example of a `component_list`\n for one of the test executables is:\n \\snippet Test_AlgorithmCore.cpp component_list_example\n- `using const_global_cache_tags`: a `tmpl::list` of tags that are\n used to place const items in the GlobalCache. The alias may be\n omitted if the list is empty.\n- `using mutable_global_cache_tags`: a `tmpl::list` of tags that are\n used to place mutable items in the GlobalCache. The alias may be\n omitted if the list is empty.\n- `default_phase_order`: an array of Parallel::Phase that must contain at least\n `Initialization` as the first element and `Exit`as the last element. Phases\n are described in the next section.\n\nThere are also several optional members:\n\n- `input_file`: a `static constexpr Options::String` that is the default name of\n the input file that is to be read. This can be overridden at runtime by\n passing the `--input-file` argument to the executable.\n- `ignore_unrecognized_command_line_options`: a `static constexpr bool` that\n defaults to `false`. If set to `true` then unrecognized command line options\n are ignored. Ignoring unrecognized options is generally only necessary for\n tests where arguments for the testing framework,\n [Catch](https://github.com/catchorg/Catch2/), are passed to the executable.\n\n# Phases of an Execution {#dev_guide_parallelization_phases_of_execution}\n\nGlobal synchronization points, where all cores wait for each other, are\nundesirable for scalability reasons. However, they are sometimes inevitable for\nalgorithmic reasons. That is, in order to actually get a correct solution you\nneed to have a global synchronization. SpECTRE executables can have multiple\nphases, where after each phase a global synchronization occurs. By global\nsynchronization we mean that no parallel components are executing or have more\ntasks to execute: everything is waiting to be told what tasks to perform next.\n\nEvery executable must have at least two phases, `Initialization` and\n`Exit`. The next phase is decided by the member function\nParallel::Main::execute_next_phase.\nUsually the next phase is determined\nfrom the `default_phase_order` provided by the metavariables. If more\ncomplex decision making is desired, various components can send data\nto Parallel::Main via the PhaseControl infrastructure. This allows the next\nPhase to be determined dynamically. Here is an example of a\n`default_phase_order` member variable:\n\\snippet LinearSolverAlgorithmTestHelpers.hpp default_phase_order_array\n\nIn contrast, an evolution executable might have phases\n`Initialization`, `SetInitialData`, `Evolve`, and `Exit`.\nThe first phase that is entered is always\n`Initialization`. During the `Initialization` phase the\n`Parallel::GlobalCache` is created, all (node)group components are created,\nand empty array and singleton components are created. Next, the function\n`allocate_remaining_components_and_execute_initialization_phase` is called\nwhich allocates singleton components and the elements of each array component,\nand then starts the `Initialization` phase on all parallel components. Once all\nparallel components' `Initialization` phase is complete, the next\nphase is determined and the `execute_next_phase` function is called on\nall the parallel components.\n\nAt the end of an execution the `Exit` phase has the executable wait to make sure\nno \\ref dev_guide_parallelization_parallel_components \"parallel components\" are\nperforming or need to perform any more tasks, and then exits. An example where\nthis approach is important is if we are done evolving a system but still need to\nwrite data to disk. We do not want to exit the simulation until all data has\nbeen written to disk, even though we've reached the final time of the evolution.\n\nIf we reach the `Exit` phase, but some \\ref\ndev_guide_parallelization_parallel_components \"parallel components\" have not\nterminated properly, this means a deadlock has occurred. A deadlock usually\nimplies some error in the order messages have been sent/received. For example,\nif core 0 was paused and waiting to receive a message from core 1, but core 1\nwas also paused and waiting to receive a message from core 0, this would be\nconsidered a deadlock. We detect deadlocks during the `Exit` phase. All\nexecutables have the option to specify a function with the following signature\n\n\\snippet Test_DetectHangArray.cpp deadlock_analysis_function\n\nIf this function is specified in the metavariables and a deadlock occurs, this\nfunction and all the simple actions in it will run. The information printed\nduring this function call is executable dependent, but it should print enough\ninformation for you to determine why the deadlock occurred. If this function\nisn't specified and a deadlock occurs, a message about how to add this function\nto your metavariables is printed, but nothing else. After this, the executable\naborts.\n\n# The Algorithm {#dev_guide_parallelization_core_algorithm}\n\nSince most numerical algorithms repeat steps until some criterion such as the\nfinal time or convergence is met, SpECTRE's parallel components are designed to\ndo such iterations for the user. An Algorithm executes an ordered list of\nactions until one of the actions cannot be evaluated, typically because it is\nwaiting on data from elsewhere. When an algorithm can no longer evaluate actions\nit passively waits by handing control back to Charm++. Once an algorithm\nreceives data, typically done by having another parallel component call the\n`receive_data` function, the algorithm will try again to execute the next\naction. If the algorithm is still waiting on more data then the algorithm will\nagain return control to Charm++ and passively wait for more data. This is\nrepeated until all required data is available. The actions that are iterated\nover by the algorithm are called iterable actions and are described below.\nSince the action list is phase dependent we refer to them generally as\nphase-dependent action lists (PDALs, pronounced \"pedals\").\n\n# Parallel Components {#dev_guide_parallelization_parallel_components}\n\nBuilding off the introduction, a %Parallel Component is essentially a wrapper\naround Charm++ chares that makes it easy for a user to add parallel objects into\ntheir program. Charm++ chares can be confusing to work with which is why we wrap\nthem. Each parallel component runs its own \\ref\ndev_guide_parallelization_core_algorithm \"Algorithm\". Data can be sent from one\nparallel component to another and the receiving parallel components' Algorithm\nwill be able to take that data and continue the program.\n\n## 1. Types of Parallel Components {#dev_guide_parallelization_component_types}\n\nThere are four types of %Parallel Components in SpECTRE:\n\n1. `Parallel::Algorithms::Singleton`s have one object in the entire execution of\n the program. They are implemented as single element Charm++ chare arrays.\n Charm++ does offer a distributed object called a singleton, however, we\n explicitly don't use this for various reasons (see\n Parallel::Algorithms::Singleton). Henceforth and throughout SpECTRE, a\n `singleton` will refer to Parallel::Algorithms::Singleton and *not* a Charm++\n singleton.\n2. `Parallel::Algorithms::Array`s hold zero or more elements, each of which is\n an object distributed to some core. An array can grow and shrink in size\n dynamically if need be and can also be bound to another array. A bound array\n has the same number of elements as the array it is bound to, and elements\n with the same ID are on the same core. See Charm++'s chare arrays for\n details.\n3. `Parallel::Algorithms::Group`s are arrays with one element per core which are\n not able to be moved around between cores. These are typically useful for\n gathering data from elements of a Parallel::Algorithms::Array on their core,\n and then processing or reducing the data further. See\n [Charm++'s](http://charm.cs.illinois.edu/help) group chares for details.\n4. `Parallel::Algorithms::Nodegroup`s are similar to groups except that there is\n one element per node. See [parallel component\n placement](#dev_guide_parallelization_component_placement) for the definition\n of a cores and nodes. We ensure that all entry method calls done through the\n Algorithm's `simple_action` and `receive_data` functions are threadsafe.\n User-controlled threading is possible by calling the entry method member\n function `threaded_action`, which is like `simple_action` except it passes a\n node lock to the `Action`'s apply function. Note that unlike\n `simple_action`s, multiple `threaded_action`s can be executing simultaneously\n on the same chare, but on different cores of the node.\n\n\\note Technically there is a fifth type of parallel component called a MainChare\nwhich is placed and executed on the global zeroth core. However, there can only\nbe one of these in a executable, it is entirely different from a Singleton, and\nit is not specifiable by the user so we omit it from the count here.\n\n## 2. Requirements {#dev_guide_parallelization_component_requirements}\n\nEach %Parallel Component struct must have the following type aliases:\n1. `using chare_type` is set to one of the four \\ref\n dev_guide_parallelization_component_types \"types of Parallel Components\".\n2. `using metavariables` is set to the Metavariables struct that stores the\n global metavariables. It is often easiest to have the %Parallel\n Component struct have a template parameter `Metavariables` that is the\n global metavariables struct. Examples of this technique are given below.\n3. `using phase_dependent_action_list` is set to a `tmpl::list` of\n `Parallel::PhaseActions>`\n where each `PhaseAction` represents a PDAL that will be executed on\n the parallel component during the specified phase. The %Actions are\n executed in the order that they are given in the `tmpl::list`s of\n the PDALs, but the phases need not be run in linear order. However,\n `db::DataBox` types are constructed assuming the phases are\n performed from first in the `phase_dependent_action_list` to the\n last. Simple actions (described below) can be executed in any\n phase. If there are no iterable actions in a phase then a\n `PhaseAction` need not be specified for that phase. However, at\n least one `PhaseAction`, even if it is empty, must be specified.\n4. `using simple_tags_from_options` which is a `tmpl::list` of all the tags\n that will be inserted into the initial `db::DataBox` of each component.\n These tags are db::SimpleTag%s that have have a `using option_tags`\n type alias and a static function `create_from_options` (see the\n example below). This list can usually be constructed from the\n initialization actions of the component (i.e. the list of actions\n in the `PhaseAction` list for the `Initialization` phase) using the\n helper function `Parallel::get_simple_tags_from_options` (see the\n examples of components below). Each initialization action may\n specify a type alias `using simple_tags_from_options` which are a\n `tmpl::list` of tags that will be fetched from the db::DataBox by the\n action.\n5. `using const_global_cache_tags` is set to a `tmpl::list` of tags\n that are required by the `allocate_array` function of an array\n component, or simple actions called on the parallel component.\n These tags correspond to const items that are stored in the\n Parallel::GlobalCache (of which there is one copy per Charm++\n node). The alias can be omitted if the list is empty.\n6. `using mutable_global_cache_tags` is set to a `tmpl::list` of tags\n that correspond to mutable items that are stored in the\n Parallel::GlobalCache (of which there is one copy per Charm++\n core). The alias can be omitted if the list is empty.\n7. `array_allocation_tags` is set to a `tmpl::list` of tags that will be\n constructed from options and will only be used in the `allocate_array`\n function of an array component. This type alias is only required for array\n components.\n\nAdditionally, each %Parallel Component struct must define a `static constexpr\nbool checkpoint_data`, indicating whether the DataBox and inbox contents should\nbe preserved in a checkpoint. Setting this to false is intended for\norganizational components that only store registration data that can be\nregenerated during the Restart phase.\n\n\\parblock\n\\note Array parallel components must also specify the type alias `using\narray_index`, which is set to the type that indexes the %Parallel Component\nArray. Charm++ allows arrays to be 1 through 6 dimensional or be indexed by a\ncustom type. The Charm++ provided indexes are wrapped as\n`Parallel::ArrayIndex1D` through `Parallel::ArrayIndex6D`. When writing custom\narray indices, the [Charm++ manual](http://charm.cs.illinois.edu/help) tells you\nto write your own `CkArrayIndex`, but we have written a general implementation\nthat provides this functionality (see `Parallel::ArrayIndex`); all that you need\nto provide is a plain-old-data\n([POD](http://en.cppreference.com/w/cpp/concept/PODType)) struct of the size of\nat most 3 integers.\n\\endparblock\n\n\\parblock\n\\note Singletons use an `array_index` of type `int`, but users need not specify\nthis. It is already specified in the implementation of a singleton.\n\\endparblock\n\n%Parallel array components have a static `allocate_array` function\nthat is used to construct the elements of the array. The\nsignature of the `allocate_array` functions must be:\n\\code\nstatic void allocate_array(\n Parallel::CProxy_GlobalCache& global_cache,\n const tuples::tagged_tuple_from_typelist&\n initialization_items,\n const tuples::tagged_tuple_from_typelist&\n array_allocation_items,\n const std::unordered_set& procs_to_ignore);\n\\endcode\nThe `allocate_array` function is called by the Main parallel component\nwhen the execution starts and will typically insert elements into\narray parallel components. If the `allocate_array` function depends\nupon input options that are not in the GlobalCache, those tags should be\nadded to the `array_allocation_tags` type alias. A TaggedTuple is constructed\nfrom this type alias and its input options and is only available in the\n`allocate_array` function. All other tags that will be constructed from options\nand used during the %Initialization phase should be placed in the\n`simple_tags_from_options` type alias.\nThis type alias is a `tmpl::list` of tags which\nare db::SimpleTag%s that have have a `using option_tags` type alias\nand a static function `create_from_options`. They only need to be explicitly\nadded to the list if no initialization action has added them to its\n`simple_tags_from_options` type alias. If you want to ignore specific\nprocessors when placing array elements, you can pass in a\n`std::unordered_set` to `allocate_array` that contains all the\nprocessors that shouldn't have array elements on them.\n\nThe `allocate_array` functions of different\narray components are called in random order and so it is not safe to\nhave them depend on each other.\n\nEach parallel component must also decide what to do in the different phases of\nthe execution. This is controlled by an `execute_next_phase` function with\nsignature:\n\\code\nstatic void execute_next_phase(\n const Parallel::Phase next_phase,\n const Parallel::CProxy_GlobalCache& global_cache);\n\\endcode\nParallel::Main::execute_next_phase`\ndetermines the next phase, after\nwhich the `execute_next_phase` function of each component gets called. The\n`execute_next_phase` function determines what the parallel component should do\nduring the next phase. Typically the `execute_next_phase` function should just\ncall `start_phase(phase)` on the parallel component.\n\n## 3. Examples {#dev_guide_parallelization_component_examples}\n\nAn example of a singleton parallel component is:\n\\snippet Test_AlgorithmParallel.cpp singleton_parallel_component\n\nAn example of an array parallel component is:\n\\snippet Test_AlgorithmParallel.cpp array_parallel_component\n\nThere are some parallel components that are common to many executables.\n\n- Parallel::GlobalCache (a Parallel::Algorithms::Nodegroup)\n- DgElementArray (a Parallel::Algorithms::Array)\n- observers::Observer (a Parallel::Algorithms::Group)\n- observers::ObserverWriter (a Parallel::Algorithms::Nodegroup)\n\nThe MutableGlobalCache deserves special mention, which is why is has its own\nsection with instructions on how to use it. See [Mutable items in the\nGlobalCache](#dev_guide_parallelization_mutable_global_cache).\n\n## 4. Placement {#dev_guide_parallelization_component_placement}\n\nThe user has some control over where parallel components get placed on the\nresources it is running on. Here is a figure that illustrates how one may place\nparallel components.\n\n\\image html charm_node_structure.png \"Parallel component placement.\"\n\nIn this example we are running on three (3) nodes that have four (4) cores each.\nFor all our executables, we reserve one core of each node purely for\ncommunication purposes. Nothing else is run on this core. Because of this, what\nCharm++ calls a node, doesn't correspond to a full node on a supercomputer. A\ncharm-node simply corresponds to a collection of cores on a physical node. In\nour case, a charm-node is represented by the remaining cores on a node not used\nfor communication (i.e. the first charm-node corresponds to cores 1-3 on the\nfirst physical node). Also the definition of a charm-core doesn't necessarily\nhave to correspond to an actual core (it could correspond to a hyperthreaded\nvirtual core), however, for our purposes, it does.\n\nSpECTRE offers wrappers around Charm++ functions that will tell you the total\nnumber of charm-nodes/cores in an executable and what charm-node/core a parallel\ncomponent is on. (In the following examples, the type `T` is an `int` or a\n`size_t`)\n\n- `Parallel::my_node()` returns the charm-node that the parallel component is\n on. In the figure, `Sing. 4` would return `2`.\n- `Parallel::my_proc()` returns the charm-core that the parallel component is\n on. In the figure, `Sing. 4` would return `6` (*not* `9`).\n- `Parallel::number_of_nodes()` returns the total number of charm-nodes in an\n executable. The above figure would have `3` charm-nodes.\n- `Parallel::number_of_procs()` returns the total number of charm-cores in an\n executable. The above figure would have `9` charm-cores (*not* `12`).\n\n\\note For Charm++ SMP (shared memory parallelism) builds, a node corresponds to\na collection of cores on a physical node, and a core corresponds to a processor\non that physical node. However, for non-SMP builds, nodes and cores are\nequivalent. All of our builds are done with Charm++ SMP so nodes and cores have\ntheir usual definitions.\n\nThe placement of Groups and Nodegroups are determined by Charm++. This is\nbecause a Group is on every charm-core and a Nodegroup is on every charm-node.\nEven though Nodegroups are one per charm-node, the user can't choose which core\nis used on the charm-node. They run on the next available charm-core on the\ncharm-node.\n\nThe Elements of an Array, however, can be placed on specific charm-cores. They\nare inserted into the Array by using the Charm++ `insert` member function of the\nCProxy for the Array. The `insert` function is documented in the Charm++ manual.\nIn the Array example in the\n[Examples](#dev_guide_parallelization_component_examples) section, `array_proxy`\nis a `CProxy` and so all the documentation for Charm++ array proxies applies.\nSpECTRE always creates empty arrays with the constructor and requires users to\ninsert however many elements they want and on which charm-cores they want them\nto be placed. Note that load balancing calls may result in array elements being\nmoved.\n\nIn a similar fashion, Singletons can also be placed on specific charm-cores.\nThis can be specified in the input file.\n\nFrom an input file, there are two ways to specify where Array/Singleton parallel\ncomponents can be placed.\n\n```yaml\nResourceInfo:\n AvoidGlobalProc0: true\n Singletons:\n AhA:\n Proc: 12\n Exclusive: true\n AhB:\n Proc: Auto\n Exclusive: false\n```\n\nFirst is the `AvoidGlobalProc0` option. This option will tell the program to not\nput *any* Array Elements or Singletons on the global zeroth charm-core. This\ncore is sometimes used to write data to disk which is typically much slower\nthan the program execution. The second is the `Singletons:` option. You can\nset the value to `Auto`, and then each singleton will have their proc be chosen\nautomatically and they won't be exclusive. Otherwise, you must specify options\nfor each singleton as in the example above. `AhA` is the `pretty_type::name()`\nof a Singleton in the program and the user has a choice of which proc to place\nthe Singleton on (`Auto` will let the program decide) and whether to exclude\nArray Elements or other Singletons from being put on this core. This is useful\nin case the Singleton does some expensive computation that shouldn't be slowed\ndown by having lots of Array Elements on the same core. In the figure above,\n`AvoidGlobalProc0` is true, and `Sing. 2` requested to be exclusively on core\n`2`.\n\n# Actions {#dev_guide_parallelization_actions}\n\n%Actions are structs with a static `apply` method and come in five\nvariants: simple actions, iterable actions, reduction actions,\nthreaded actions, and local synchronous actions.\n\nThe signature of `apply` methods differs for the different types of\nactions, but all types have the same general form. Actions receive a\n`db::DataBox`, the Parallel::GlobalCache, and their element's index\nand parallel component, as well as arguments specific to the action\ntype.\n\nThe `db::DataBox` should be thought of as the member data of the parallel\ncomponent while the actions are the member functions. The combination of a\n`db::DataBox` and actions allows building up classes with arbitrary member data\nand methods using template parameters and invocation of actions. This approach\nallows us to eliminate the need for users to work with Charm++'s interface\nfiles, which can be error prone and difficult to use.\n\nThe Parallel::GlobalCache is passed to each action so that the\naction has access to global data and is able to invoke actions on\nother parallel components. The `ParallelComponent` template parameter\nis the tag of the parallel component that invoked the action. A proxy\nto the calling parallel component can then be retrieved from the\nParallel::GlobalCache. The remote entry method invocations are\nslightly different for different types of actions, so they will be\ndiscussed below. However, one thing that is disallowed for all actions\nis calling an action locally from within an action on the same\nparallel component. Specifically,\n\n\\snippet Test_AlgorithmNestedApply1.cpp bad_recursive_call\n\nHere `Parallel::local()` is a wrapper around `ckLocal()` which is a Charm++\nprovided method that returns a pointer to the local (currently executing)\nparallel component. See the\n[Charm++ manual](http://charm.cs.illinois.edu/help) for more\ninformation. However, you are able to queue a new action to be\nexecuted later on the same parallel component by getting your own\nparallel component from the Parallel::GlobalCache\n(`Parallel::get_parallel_component(cache)`). The\ndifference between the two calls is that by calling an action through\nthe parallel component you will first finish the series of actions you\nare in, then when they are complete Charm++ will call the next queued\naction.\n\nArray, group, and nodegroup parallel components can have actions invoked in two\nways. First is a broadcast where the action is called on all elements of the\narray:\n\n\\snippet Test_AlgorithmParallel.cpp broadcast_to_group\n\nThe second case is invoking an action on a specific array element by using the\narray element's index. The below example shows how a broadcast would be done\nmanually by looping over all elements in the array:\n\n\\snippet Test_AlgorithmParallel.cpp call_on_indexed_array\n\nNote that in general you will not know what all the elements in the array are\nand so a broadcast is the correct method of sending data to or invoking an\naction on all elements of an array parallel component.\n\nThe `array_index` argument passed to all `apply` methods is the index into the\nparallel component array. If the parallel component is not an array the value\nand type of `array_index` is implementation defined and cannot be relied on.\n\n## 1. Simple Actions {#dev_guide_parallelization_simple_actions}\n\nSimple actions can be thought of as member functions of remote objects\n(chares/parallel components). They are the direct analog of entry\nmethods in Charm++ except that the member data is stored in the\n`db::DataBox` that is passed in as the first argument. A simple action\nmust return void but can use `db::mutate` to change values of items in\nthe `db::DataBox` if the `db::DataBox` is taken as a non-const\nreference. In some cases you will need specific items to be in the\n`db::DataBox` otherwise the action won't compile. To restrict which\n`db::DataBox`es can be passed you should use `requires` in the\naction's `apply` function template parameter list. For example,\n\\snippet Test_AlgorithmCore.cpp requires_action\nchecks that `CountActionsCalled` is available in the box.\n\nSimple actions can be called using a `CProxy` (see the [Charm++\nmanual](http://charm.cs.illinois.edu/help)), which is retrieved from\nthe Parallel::GlobalCache using the parallel component struct and the\n`Parallel::get_parallel_component()` function. For example, the\naction above could be called as\n\\snippet Test_AlgorithmCore.cpp simple_action_call\nAny arguments after the proxy are passed as additional arguments to\nthe action's `apply` function.\n\n## 2. Iterable Actions {#dev_guide_parallelization_iterable_actions}\n\nIterable actions make up the algorithms described by the PDALs. These\nactions are executed one after the other until one of them cannot be\nevaluated. Their `apply` methods signature is\n\\snippet Test_AlgorithmCore.cpp apply_iterative\nThe `ActionList` type is the `tmpl::list` of iterable actions in the\ncurrent phase. That is, it is equal to the `action_list` type alias\nin the current PDAL. The `inboxes` is a collection of the tags\nspecified as `tmpl::list`s in the iterable actions' member type\naliases `inbox_tags`. This collection represents data received from\nother chares using the `receive_data` function.\n\nIterable actions can request that the algorithm be paused or halted\nfor the current phase, and control which action in the current PDAL\nwill be executed next. This is all done via the return value from the\n`apply` function. The `apply` function for iterable actions must\nreturn a Parallel::iterable_action_return_t which is a\n`std::tuple>`. The\nfirst element of the tuple controls how algorithm execution continues.\nSee the documentation of `Parallel::AlgorithmExecution` for the\nmeanings of different values of that enum. The second element of the\ntuple is usually set to `std::nullopt` in order to continue iterating\nthrough the algorithm, but can be used to jump to a different action\nin the current PDAL. Most iterable actions will simply return\n\n\\snippet Test_AlgorithmParallel.cpp iterable_action_return_continue_next_action\n\nAn action that pauses the algorithm will return\n\n\\snippet Test_AlgorithmParallel.cpp return_with_termination\n\nAfter an algorithm has been paused it can be restarted by passing\n`false` to the `set_terminate` method or by calling `receive_data(...,\ntrue)`. Since the order in which messages are received is undefined in\nmost cases the `receive_data(..., true)` call should be used to\nrestart the algorithm.\n\nThe return value `Parallel::AlgorithmExecution::Retry` deserves\nspecial mention. It is intended for use by actions that use data\nsupplied by other parallel objects to indicate that they have not\nreceived all of the data they require. The algorithm will stop until\nan operation that could supply data has occurred and then the action\nwill be retried. An example of waiting because of missing data is\n\n\\snippet Test_AlgorithmCore.cpp retry_example\n\nIn order to jump to a specific action, the metafunction\n`tmpl::index_of` can be used to get an\n`tmpl::integral_constant` with the value of the index of the element\n`element` in the typelist `list`. For example,\n\n\\snippet Test_AlgorithmCore.cpp out_of_order_action\n\nThe metafunction call `tmpl::index_of::%value` returns a `size_t` whose value is\nthat of the action `iterate_increment_int0` in the PDAL. The indexing\nof actions in the PDAL starts at `0`.\n\nIterable actions are invoked as part of the algorithm and so the only way\nto request they be invoked is by having the algorithm run on the parallel\ncomponent. The algorithm can be explicitly evaluated in a new phase by calling\n`start_phase(Phase::TheCurrentPhase)`:\n\n\\snippet Test_AlgorithmCore.cpp start_phase\n\nAlternatively, to evaluate the algorithm without changing phases the\n`perform_algorithm()` method can be used.\n\nBy passing `true` to `perform_algorithm` the algorithm will be restarted if it\nwas paused.\n\nThe algorithm is also evaluated by calling the `receive_data` function, either\non an entire array or singleton (this does a broadcast), or an on individual\nelement of the array. Here is an example of a broadcast call:\n\n\\snippet Test_AlgorithmParallel.cpp broadcast_to_group\n\nand of calling individual elements:\n\n\\snippet Test_AlgorithmParallel.cpp call_on_indexed_array\n\nThe `receive_data` function always takes a `ReceiveTag`, which is set\nin the actions' `inbox_tags` type aliases. The `inbox_tags` must have\ntwo member type aliases, a `temporal_id` which is used to identify\nwhen the data was sent, and a `type` which is the type of the data to\nbe stored in the `inboxes`. The types are typically a\n`std::unordered_map`. In the discussed scenario of\nwaiting for neighboring elements to send their data the `DATA` type\nwould be a `std::unordered_map`. Inbox tags\nmust also specify a `static bool insert_into_inbox()` function. For\nexample,\n\n\\snippet Test_AlgorithmParallel.cpp int_receive_tag\n\nThe return value indicates whether `perform_algorithm()` should be called after\ninsertion. This exists primarily to allow the communication logic used with\n`DgElementArray` to match that used with `DgElementCollection` more closely.\nIt is safe to always return `true`.\n\nFor common types of `DATA`, such as a `map`, a data structure with an `insert`\nfunction, a data structure with a `push_back` function, or copy/move assignment\nthat is used to insert the received data, inserters are available in\n`Parallel::InboxInserters`. For example, there is\n`Parallel::InboxInserters::Map` for `map` data structures. The inbox tag can\ninherit publicly off the inserters to gain the required insertion capabilities:\n\n\\snippet Test_AlgorithmCore.cpp int receive tag insert\n\nAny inbox tag that uses Charm++ messages must also specify a `message_type` type\nalias which is the object that will be sent. An example is:\n\n\\snippet Test_AlgorithmMessages.cpp charm message inbox tag\n\nThe `inbox_tags` type alias for the action is:\n\n\\snippet Test_AlgorithmParallel.cpp int_receive_tag_list\n\nAn inbox tag can also optionally specify a static function called `output_inbox`\nthat returns a `std::string`. This function can be used for printing the\ncontents of the inbox in a nice way as the types can sometimes get complicated.\nYou can also use the `Parallel::output_inbox` function to output a specific\ninbox from all the inboxes. See an above example for the signature of the\n`output_inbox` function.\n\n\\warning\nIt is the responsibility of the iterable action to remove data from the inboxes\nthat will no longer be needed.\n\nNormally when remote functions are invoked they go through the Charm++ runtime\nsystem, which adds some overhead. The `receive_data` function tries to elide\nthe call to the Charm++ RTS for calls into array components. Charm++ refers to\nthese types of remote calls as \"inline entry methods\". With the Charm++ method\nof eliding the RTS, the code becomes susceptible to stack overflows because\nof infinite recursion. The `receive_data` function is limited to at most 64 RTS\nelided calls, though in practice reaching this limit is rare. When the limit is\nreached the remote method invocation is done through the RTS instead of being\nelided.\n\n## 3. Reduction Actions {#dev_guide_parallelization_reduction_actions}\n\nReduction actions are the targets of reducing data over an array. For\nexample, you may want to know the sum of a `int` from every element in\nthe array. You can do this as follows:\n\n\\snippet Test_AlgorithmReduction.cpp contribute_to_reduction_example\n\nThis reduces over the parallel component\n`ArrayParallelComponent`, reduces to the parallel component\n`SingletonParallelComponent`, and calls the action\n`ProcessReducedSumOfInts` after the reduction has been performed. The reduction\naction is:\n\n\\snippet Test_AlgorithmReduction.cpp reduce_sum_int_action\n\nAs you can see, the last argument to the `apply` function is of type `int`, and\nis the reduced value.\n\nYou can also broadcast the result back to an array, even yourself. For example,\n\n\\snippet Test_AlgorithmReduction.cpp contribute_to_broadcast_reduction\n\nIt is often necessary to reduce custom data types, such as `std::vector` or\n`std::unordered_map`. Charm++ supports such custom reductions, and so does our\nlayer on top of Charm++.\nCustom reductions require one additional step to calling\n`contribute_to_reduction`, which is writing a reduction function to reduce the\ncustom data. We provide a generic type that can be used in custom reductions,\n`Parallel::ReductionData`, which takes a series of `Parallel::ReductionDatum` as\ntemplate parameters and `ReductionDatum::value_type`s as the arguments to the\nconstructor. Each `ReductionDatum` takes up to four template parameters (two\nare required). The first is the type of data to reduce, and the second is a\nbinary invokable that is called at each step of the reduction to combine two\nmessages. The last two template parameters are used after the reduction has\ncompleted. The third parameter is an n-ary invokable that is called once the\nreduction is complete, whose first argument is the result of the reduction. The\nadditional arguments can be any `ReductionDatum::value_type` in the\n`ReductionData` that are before the current one. The fourth template parameter\nof `ReductionDatum` is used to specify which data should be passed. It is a\n`std::index_sequence` indexing into the `ReductionData`.\n\n\\warning\nAll elements of the array must call the same reductions in the same order. It is\n*defined* behavior to do multiple reductions at once as long as all contribute\ncalls on all array elements occurred in the same order. It is **undefined**\nbehavior if the contribute calls are made in different orders on different array\nelements.\n\n## 4. Threaded Actions {#dev_guide_parallelization_threaded_actions}\n\nThreaded actions are similar to simple actions, with the difference\nbeing that multiple threaded actions may be running on the same chare\nat the same time (potentially in parallel with one simple or reduction\naction). The `apply` function for a threaded actions has the same\nsignature as that for a simple action, except that it also receives a\n`NodeLock` intended to control access to the chare's `db::DataBox`.\nAll access to the `db::DataBox`, including read-only access, must\noccur while the action owns this lock. (Simple and reduction actions\nimplicitly hold the lock for their entire execution.)\n\n\\snippet Test_AlgorithmNodelock.cpp threaded_action_example\n\nThreaded actions can only be run on nodegroup chares.\n\n## 5. Local Synchronous Actions {#dev_guide_parallelization_local_synchronous_actions}\n\nThere is limited ability to retrieve data held by another parallel component via\na direct synchronous call. Unlike the above actions, the invocation of a\nsynchronous action is precisely a call to a member function of another parallel\ncomponent; therefore, these invocations will run to completion, and return their\nresult before the calling code proceeds in execution.\n\nAside from being synchronous and being able to return data, local\nsynchronous actions behave the same as threaded actions, except that\nthey will only run on the chare of a nodegroup that is on the local\nnode.\n\nLocal synchronous actions' `apply` functions follow a signature motivated by\nthreaded actions, but take fewer arguments. This may be a bug.\n\nLocal synchronous actions must specify their return type in a\n`return_type` type alias. This is to help simplify the logic with the\nvariant `db::DataBox` held by the parallel component.\n\nAn example of a definition of a local synchronous action:\n\n\\snippet Test_AlgorithmLocalSyncAction.cpp synchronous_action_example\n\nAnd the corresponding invocation:\n\n\\snippet Test_AlgorithmLocalSyncAction.cpp synchronous_action_invocation_example\n\n\\warning Say an action is being run on a component on a node where a mutable\nitem in the GlobalCache is up-to-date. This action then calls another action on\na different component on a different node. It is **NOT** guaranteed that this\nmutable item in the GlobalCache is up-to-date on this new node. It is up to the\nuser to ensure the mutable item is up-to-date on whatever node they run an\naction on, even if it was up-to-date on the node that sent the message. The\n\\ref dev_guide_parallelization_mutable_global_cache\n\"Mutable items in the GlobalCache\" section gives details about mutable\nGlobalCache items.\n\n# Mutable items in the GlobalCache {#dev_guide_parallelization_mutable_global_cache}\n\nMost items in the GlobalCache are constant, and are specified\nby type aliases called `const_global_cache_tags` as\ndescribed above. However, the GlobalCache can also store mutable\nitems. Because of asynchronous execution, **EXTREME** care must be taken when\nmutating items in the GlobalCache, as described below.\n\nA mutable item can be of any type, as long as that type is something\nthat can be checked for whether it is \"up-to-date\". Here \"up-to-date\"\nmeans that the item can be safely used (even read-only) without\nneeding to be mutated first. For example, a mutable item might be a\nfunction of time that knows the range of times for which it is valid;\nthe mutable item is then deemed up-to-date if it will be called for a\ntime within its range of validity, and it is deemed not up-to-date if\nit will be called for a time outside its range of validity. Thus the\nup-to-date status of a mutable item is determined by both the state of\nthe item itself and by the code that wishes to use that item.\n\n## 1. Specification of mutable GlobalCache items\n\nMutable GlobalCache items are specified by a\ntype alias `mutable_global_cache_tags`, which is treated the same way\nas `const_global_cache_tags` for const items.\n\n## 2. Use of mutable GlobalCache items\n\n### 1. Checking if the item is up-to-date\n\nBecause execution is asynchronous, any code that uses a mutable item\nin the GlobalCache must first check whether that item is up-to-date.\nThe information about whether an item is up-to-date is assumed to be\nstored in the item itself. For example, a mutable object stored in\nthe GlobalCache might have type `std::map` (for some\ntype `T`), and then any code that uses the stored object can check\nwhether an entry exists for a particular `temporal_id`. To avoid\nrace conditions, it is\nimportant that up-to-date checks are based on something that is\nindependent of the order of mutation (like a `temporal_id`, and not\nlike checking the size of a vector).\n\nTo check an item, use the function\n`Parallel::mutable_cache_item_is_ready`, which returns a bool\nindicating whether the item is up-to-date. If the item is up-to-date,\nthen it can be used. `Parallel::mutable_cache_item_is_ready` takes a\nlambda as an argument. This lambda is passed a single argument: a\nconst reference to the item being retrieved. The lambda should\ndetermine whether the item is up-to-date. If so, it should return a\ndefault_constructed `std::unique_ptr`; if not, it should\nreturn a `std::unique_ptr` to a callback function that will\nbe called on the next `Parallel::mutate` of that item. The callback\nwill typically check again if the item is up-to-date and if so will\nexecute some code that gets the item via `Parallel::get`.\n\nFor the case of iterable actions,\n`Parallel::mutable_cache_item_is_ready` typically uses the callback\n`Parallel::PerformAlgorithmCallback`. In the example below, the\nvector is considered up-to-date if it is non-empty. If the vector is\nnot up-to-date, then when it becomes up-to-date the callback function\nwill be invoked; in this case the callback function re-runs\n`perform_algorithm()`, which will call the same action again.\n\n\\snippet Test_AlgorithmGlobalCache.cpp check_mutable_cache_item_is_ready\n\nNote that `Parallel::mutable_cache_item_is_ready` is called on the local\nnode and does no parallel communication.\n\n### 2. Retrieving the item\n\nThe item is retrieved using `Parallel::get` just like for constant items.\nFor example, to retrieve the item `Tags::VectorOfDoubles`:\n\\snippet Test_AlgorithmGlobalCache.cpp retrieve_mutable_cache_item\n\nNote that `Parallel::get` is called on the local node and does no\nparallel communication.\n\nWhereas we support getting *non-mutable* items in the GlobalCache from\na DataBox via `db::get`, we intentionally do not support\n`db::get` of *mutable* items in the GlobalCache from a DataBox.\nThe reason is that mutable\nitems should be retrieved only after a `Parallel::mutable_cache_item_is_ready`\ncheck, and being able to retrieve a mutable item from a DataBox makes it\ndifficult to enforce that check, especially when automatically-executing\ncompute items are considered.\n\n## 3. Modifying a mutable GlobalCache item\n\nTo modify a mutable item, pass `Parallel::mutate` two template\nparameters: the tag to mutate, and a struct with an `apply` function\nthat does the mutating. `Parallel::mutate` takes two arguments:\na reference to the local GlobalCache, and a tuple that is passed into the\nmutator function. For the following example,\n\n\\snippet Test_AlgorithmGlobalCache.cpp mutate_global_cache_item\n\nthe mutator function is defined as below:\n\\snippet Test_AlgorithmGlobalCache.cpp mutate_global_cache_item_mutator\n\n`Parallel::mutate` broadcasts to every node, where it calls the\nmutator function and then calls all the callbacks that have been set\non that node by `Parallel::mutable_cache_item_is_ready`. The\n`Parallel::mutate` operation is guaranteed to be thread-safe without\nany further action by the developer so long as the item being mutated can be\nmutated in a threadsafe way. See the `Parallel::GlobalCache` docs for more\ndetails.\n\n# Charm++ Node and Processor Level Initialization Functions {#dev_guide_parallelization_charm_node_processor_level_initialization}\n\nCharm++ allows running functions once per core and once per node before the\nconstruction of any parallel components. This is commonly used for setting up\nerror handling and enabling floating point exceptions. Other functions could\nalso be run. Which functions are run on each node and core is set by calling\n`Parallel::charmxx::register_init_node_and_proc` in `CkRegisterMainModule()`\nwith function pointers to the functions to be called. For example:\n\n\\snippet Test_AlgorithmPhaseControlNodegroup.cpp charm_init_funcs_example\n" }, { "path": "docs/DevGuide/PerformanceGuidelines.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# General Performance Guidelines {#general_perf_guide}\n\n\\tableofcontents\n\nBelow are some general guidelines for achieving decent performance.\n\n- One good measurement is worth more than a million expert opinions.\n Our testing framework [Catch2](https://github.com/catchorg/Catch2) supports\n benchmarks, so we encourage you to add benchmarks to your tests. See the\n [Catch2 benchmarks documentation](https://github.com/catchorg/Catch2/blob/devel/docs/benchmarks.md)\n for instructions. Essentially, add a `BENCHMARK` to your test case and run\n the test executable (such as `./bin/Test_LinearOperators`).\n Note that we skip benchmarks during automated unit testing with `ctest`\n because benchmarks are only meaningful in a controlled environment (such as a\n specific machine or architecture). You can keep track of the benchmark results\n you ran on specific machines in a comment in the test case (until we have a\n better way of keeping track of benchmark results).\n\n Catch2's benchmarking is not as feature-rich as Google Benchmark. We have a\n `Benchmark` executable that uses Google Benchmark so one can compare\n different implementations and see how they perform. This executable is only\n available in release builds.\n- Reduce memory allocations. On all modern hardware (many core CPUs, GPUs, and\n FPGAs), memory is almost always the bottleneck. Memory allocations are\n especially expensive since this is a quasi-serial process: the OS has to\n manage memory allocations for _all_ running threads and processes. SpECTRE has\n various classes to optimize this. For example, there are `Variables`,\n `TempBuffer`, and `DynamicBuffer` that allow making large contiguous memory\n allocations that are then used for individual tensor components.\n" }, { "path": "docs/DevGuide/Profiling.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Profiling {#profiling}\n\n\\tableofcontents\n\nThere are a number of tools available for profiling, each with their own\nstrengths and weaknesses. This makes it difficult to recommend one \"right\" way\nof analyzing performance using profilers. Instead, one should use a combination\nof the tools to discover and eliminate performance bottle necks. Common\nprofilers are Charm++ Projections (tracing-based), HPCToolkit (sampling-based,\nvery versatile), Linux perf (sampling-based, command line only), Intel VTune\n(sampling-based, works well on Intel hardware), AMD uProf (similar to Intel\nVTune), and Score-P (sampling and tracing, with MPI and pthread interfacing).\n\n## Profiling with HPCToolkit {#profiling_with_hpctoolkit}\n\nFollow the HPCToolkit installation instructions at\n[hpctoolkit.org](http://hpctoolkit.org). The Spack\ninstallation seems to work well. Once installed, compile your executable in\nRelease mode with `-D ENABLE_PROFILING=ON -D DEBUG_SYMBOLS=ON` since otherwise\nyou won't be able to get call stacks and source analysis. Using `-D\nBUILD_SHARED_LIBS=ON` is recommended since it makes HPCToolkit a lot easier to\nuse. You must also use the system allocator, `-D MEMORY_ALLOCATOR=SYSTEM`. We\nwill work from the build directory and perform all runs and performance analysis\nthere.\n\nFirst run HPCToolkit as:\n```\nhpcrun -t --event CYCLES@f200 ./bin/EXEC --input-file ./Input.yaml +p1\n```\nWe will profile on one core, but you can profile on multiple cores as well as\nmultiple nodes if using MPI as the Charm++ backend. This will generate a\n`hpctoolkit-EXEC-measurements` directory. Run\n```\nhpcstruct -jN ./hpctoolkit-EXEC-measurements\n```\nwhere `N` is the number of cores to run on. This will generate a mapping to line\nnumbers, etc. in the measurements directory.\n\n\\warning Skipping the `hpcstruct` step will make `hprprof` below run extremely\nslowly.\n\nOnce the run is complete, run\n```\nhpcprof hpctoolkit-EXEC-measurements\n```\nor if HPCToolkit version < 2024, run\n```\nhpcprof -I /path/to/spectre/src/+ hpctoolkit-EXEC-measurements\n```\nNote that the `+` is a literal `+` symbol.\n\nThis will create the directory\n```\nhpctoolkit-EXEC-database\n```\nwhich you can view using\n```\nhpcviewer ./hpctoolkit-EXEC-database\n```\n\nHPCViewer will generally start you in the `Top-down view` (callgraph of\ncallers). You can select `Bottom-up view` (callgraph of callees) to get a\ndifferent perspective. Whether you want to look at the callgraph of callers or\ncallees depends a bit on the executable, what you're looking to measure, and how\nyou like to think about things. The callees graph can give you a nice overview\nof what the low-level things taking up a lot of time are, but certainly makes\nthe call stack not look like you would expect. On the right of the callgraphs\nyou will see `CYCLES:Sum (I)` and `CYCLES:Sum (E)`. `I` means time spent\n_including_ callees, while `E` means time spent in the function itself\n(exclusive time). Sorting by exclusive gives a good idea of what the hot\nfunctions are. Here is a screenshot from HPCViewer:\n\n\\image html HpcViewerCallees.png \"HPCViewer callgraph of callees\"\n\nYou can see that 49.1% of inclusive time is spent in primitive recovery, and the\nline after the 49.1% function is a function inside the Kastaun\nrecovery scheme. The `__nss_database_lookup` is some system call,\ne.g. `__memcpy_avx_unaligned_erms` or `__memset_avx2_unaligned_erms`. Looking at\nthe calling code, e.g. `prepare_neighbor_data` gives a good hint as to what's\ngoing on. In most cases these are memory copies or memory sets (`std::vector`\ndefault initializes its memory, which is bad for performance). The way to fix\nthese bottlenecks is to avoid memory copies and `std::vector` as\nbuffers.\n\nHPCToolkit allows you to sample on a variety of different event counters instead\nof just cycles. Please see the HPCToolkit manual for details.\n\n## Profiling with AMD uProf {#profiling_with_amd_uprof}\n\n[AMD uProf](https://developer.amd.com/amd-uprof/) is AMD's sampling-based\nprofiler that makes it relatively easy to do\nquite a bit of detailed performance analysis. The uProf manual is quite good and\nextensive, so for the most part the reader is referred to that. However, we will\ngo over some basics for profiling executables and understanding the\nresults. Make sure to compile your executable in Release mode with\n`-DENABLE_PROFILING=ON -D DEBUG_SYMBOLS=ON` since otherwise you won't be able to\nget call stacks and source analysis.\n\nWhen you open uProf you may be asked to change the kernel event paranoid\nlevel. Once you have uProf open, select `PROFILE` at the top. Specify the\napplication path, options, etc. We will again run on a single core to analyze\nperformance. It's recommended that you set the Core Affinity in AMD uProf so\nthat your application isn't migrated between cores during a profiling run. Then\nchoose `Next` in the lower right corner. Make sure the `CPU Profile Type` is set\nto `CPU Profile` at the top. We will first do a `Time-based Sampling` run (on\nthe left). This means uProf will interrupt the application every `N`\nmilliseconds and see where the application is. You typically want a few thousand\ntotal samples to get something that's reasonably representative of your\napplication. Under the `Advanced %Options` make sure `Enable CSS` (on the right)\nis enabled (green) and that `Enable FPO` is also enabled. Now click `Start\nProfile` in the bottom right. Once the profile is complete you will be presented\nwith a summary outlining where your code is spending most of its time. Click\n`ANALYZE` at the top to get a more detailed view. On the left you can select\nbetween a callgraph of callees (Function HotSpots), a callgraph of callers (Call\nGraph), and a few other views. Below is an example of a result from the same run\nwe used with HPCToolkit above.\n\n\\image html AmdUprofCallgraph.png \"AMD uProf callgraph of callees\"\n\nAgain we see that most of our time is spent in primitive recovery but also that\na lot of time is spent copying memory. This was grouped into\n`__nss_database_lookup` in HPCToolkit. Unfortunately, getting a call stack out\nof the `memcpy` doesn't always work and so while you know you're spending a lot\nof time copying memory, it's not so obvious where those copies are occurring.\n\n## Profiling With Charm++ Projections {#profiling_with_projections}\n\nTo view trace data after a profiling run you must download Charm++'s\nProjections software from their [website](http://charm.cs.illinois.edu/).\nIf you encounter issues it may\nbe necessary to clone the git repository and build the correct version\nfrom scratch. Note that the version of Charm++ used to compile SpECTRE\nshould match the version of Projections used to analyze the trace data.\nYou can collect the trace data on a different machine than the one you\nwill be analyzing the data on. For example, you can collect the data on\na supercomputer and analyze it on your desktop or laptop.\n\nFor profiling you will want to use a production build of Charm++, which\nmeans compiling Charm++ with the `--with-production` flag. To enable trace\ncollecting you must build with the `--enable-tracing` flag as well. For\nexample, on a multicore 64-bit Linux machine the build command would be\n``` shell\n./build LIBS multicore-linux-x86_64 gcc -j8 --with-production --enable-tracing\n```\nYou must build your executable in Release mode as well, specifying\n`-DCMAKE_BUILD_TYPE=Release` to CMake, as well as\n```\n-DCHARM_TRACE_PROJECTIONS=ON -DCHARM_TRACE_SUMMARY=ON -DENABLE_PROFILING=ON\n```\nto enable SpECTRE to use Charm++'s tracing features.\n\n### Running SpECTRE With Trace Output\n\nWhen running SpECTRE you must specify a directory to output trace data into.\nThis is done by adding the command line argument `+traceroot DIR` where `DIR` is\nthe directory to dump the trace data into. Note that `DIR` must already exist,\nthe application will not create it.\nFor example,\n\n```shell\n./bin/EXEC --input-file ./Input.yaml +p4 +traceroot ./ExecTraces\n```\nYou might get a warning that Charm++ had to flush the log some number of times\nduring the run. Flushing the log adds overhead to the execution and so affects\ntiming measurements. While Charm++ has the ability to manually flush the log\nperiodically (and therefore exclude the time it takes to flush the log from the\ntrace), we have not yet implemented support for this. For short executable runs\nyou can increase the log size by specifying `+logsize M` when running the\nexecutable. The default log size is 1,000,000 (1000000). Note that if you\nincrease the log size too much you will run out of memory/RAM.\n\nFor more information on runtime options to\ncontrol trace data see the\n[Charm++ Projections manual](http://charm.cs.illinois.edu/manuals/html/projections/1.html).\n\n### Visualizing Trace %Data In Projections\n\nBy default Charm++ records entry method names by using the `PRETTY_FUNCTION`\nmacro. This means entry method names include all class (parallel component) and\naction template parameter names, including any template parameters of the\ntemplate parameters. This very quickly leads to incomprehensibly long names that\nare very difficult to read in the Projections interface. We include a basic\nPython executable to handle the majority of renames, but the executable supports\nadditional basic (textual find-replace) and regular expression\nreplacements via a JSON file. These additional replacements are useful for\nmaking executable-specific renames. The Python executable is\n`tools/CharmSimplifyTraces.py` and an example replacements file is\n`tools/CharmTraceReplacements.json`.\n\nSee the [Charm++ Projections manual](http://charm.cs.illinois.edu/manuals/html/projections/2.html)\nfor details.\n\n## Profiling with Score-P {#profiling_with_scorep}\n\nSee the\n[Score-P](https://www.vi-hps.org/projects/score-p/overview/overview.html)\nwebsite for installation instructions specific to Score-P.\n\nTo compile SpECTRE with Score-P you must invoke CMake with the environment\nvariable `SCOREP_WRAPPER=off` (do NOT export this variable!) and the `scorep-`\ncompiler wrappers. For example,\n```sh\nSCOREP_WRAPPER=off cmake -DCMAKE_C_COMPILER=scorep-gcc \\\n -DCMAKE_CXX_COMPILER=scorep-g++ -DCMAKE_Fortran_COMPILER=scorep-gfortran \\\n -D CMAKE_BUILD_TYPE=Release -D ENABLE_PROFILING=ON \\\n -D BUILD_DOCS=OFF -D BUILD_PYTHON_BINDINGS=OFF $SPECTRE_HOME\n```\nwhere `$SPECTRE_HOME` points to your spectre source tree. You can then compile\nthe executable you want to profile. When running the executable you will need to\nmake sure Score-P has enough memory to be able to function properly. For the\nEvolveGhSingleBlackHole, Score-P needs 1.5GB of memory. To enable profiling,\ndisable tracing, and use 1.5GB of memory for Score-P, set the environment\nvariables\n```sh\nSCOREP_ENABLE_PROFILING=1 \\\n SCOREP_ENABLE_TRACING=0 \\\n SCOREP_TOTAL_MEMORY=1536000000\n```\nWe also need to use a filter file to keep the data at all manageable and to\navoid some currently not understood interaction between Score-P and our option\nparser. The profile is in `support/Profiling/ScoreP` and named `spectre.flt`.\nThe final command should look something like:\n```sh\nSCOREP_ENABLE_PROFILING=1 SCOREP_ENABLE_TRACING=0 \\\n SCOREP_TOTAL_MEMORY=1536000000 \\\n SCOREP_FILTERING_FILE=$SPECTRE_HOME/support/Profiling/ScoreP/spectre.flt \\\n mpirun -np 2 EvolveGhSingleBlackHole --input-file ./KerrSchild.yaml +ppn 91\n```\nDepending on your profile, you might also need to increase the callpath depth by\nsetting\n```sh\nSCOREP_PROFILING_MAX_CALLPATH_DEPTH=150\n```\nOnce you've successfully run the executable you should have a directory like\n`scorep-20251006_1732_65976792745157592`. Please see the Score-P documentation\nfor how to analyze the output.\n" }, { "path": "docs/DevGuide/Protocols.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Protocols {#protocols}\n\n\\tableofcontents\n\n# Overview of protocols {#protocols_overview}\n\nProtocols are a concept we use in SpECTRE to define metaprogramming interfaces.\nA variation of this concept is built into many languages, so this is a quote\nfrom the [Swift documentation](https://docs.swift.org/swift-book/LanguageGuide/Protocols.html):\n\n> A protocol defines a blueprint of methods, properties, and other requirements\n> that suit a particular task or piece of functionality. The protocol can then\n> be adopted by a class, structure, or enumeration to provide an actual\n> implementation of those requirements. Any type that satisfies the requirements\n> of a protocol is said to conform to that protocol.\n\nYou should define a protocol when you need a template parameter to conform to an\ninterface. Here is an example of a protocol that is adapted from the [Swift\ndocumentation](https://docs.swift.org/swift-book/LanguageGuide/Protocols.html):\n\n\\snippet Utilities/Test_ProtocolHelpers.cpp named_protocol\n\nThe protocol defines an interface that any type that adopts it must implement.\nFor example, the following class conforms to the protocol we just defined:\n\n\\snippet Utilities/Test_ProtocolHelpers.cpp named_conformance\n\nThe class indicates it conforms to the protocol by (publicly) inheriting from\n`tt::ConformsTo`.\n\nOnce you have defined a protocol, you can check if a class conforms to it using\nthe `tt::assert_conforms_to` or `tt::conforms_to` metafunctions:\n\n\\snippet Utilities/Test_ProtocolHelpers.cpp conforms_to\n\nNote that checking for protocol conformance is cheap, so you may freely use\nprotocol conformance checks in your code.\n\nThis is how you can write code that relies on the interface defined by the\nprotocol:\n\n\\snippet Utilities/Test_ProtocolHelpers.cpp using_named_protocol\n\nChecking for protocol conformance here makes it clear that we are expecting\na template parameter that exposes the particular interface we have defined in\nthe protocol. Therefore, the author of the protocol and of the code that uses it\nhas explicitly defined (and documented!) the interface they expect. And the\ndeveloper who consumes the protocol by writing classes that conform to it knows\nexactly what needs to be implemented.\n\nNote that the `tt::conforms_to` metafunction is SFINAE-friendly, so you can use\nit like this:\n\n\\snippet Utilities/Test_ProtocolHelpers.cpp protocol_sfinae\n\nThe `tt::conforms_to` metafunction only checks if the class _indicates_ it\nconforms to the protocol. Where SFINAE-friendliness is not necessary prefer the\n`tt::assert_conforms_to` metafunction that triggers static asserts with\ndiagnostic messages to understand why the class does not conform to the\nprotocol.\n\nWe typically define protocols in a file named `Protocols.hpp` and within a\n`protocols` namespace, similar to how we write \\ref DataBoxTagsGroup \"tags\" in a\n`Tags.hpp` file and within a `Tags` namespace. The file should be placed in the\ndirectory associated with the code that depends on classes conforming to the\nprotocols. For example, the protocol `Named` in the example above would be\nplaced in directory that also has the `greet` function.\n\n# Protocol users: Conforming to a protocol {#protocols_conforming}\n\nTo indicate a class conforms to a protocol it (publicly) inherits from\n`tt::ConformsTo`. The class must fulfill all requirements defined\nby the protocol. The requirements are listed in the protocol's documentation.\n\nAny class that indicates it conforms to a protocol must have a unit test to\ncheck that it actually does. You can use the `tt::assert_conforms_to`\nmetafunction for the test:\n\n\\snippet Utilities/Test_ProtocolHelpers.cpp test_protocol_conformance\n\n# Protocol authors: Writing a protocol {#protocols_author}\n\nTo author a new protocol you implement a class that provides a `test`\nmetafunction and detailed documentation. The `test` metafunction takes a single\ntemplate parameter (typically named `ConformingType`) and checks that it\nconforms to the requirements laid out in the protocol's documentation. Its\npurpose is to provide diagnostic messages as compiler errors to understand why a\ntype fails to conform to the protocol. You can use `static_assert`s or trigger\nstandard compiler errors where appropriate. See the protocols defined above for\nexamples.\n\nOccasionally, you might be tempted to add template parameters to a protocol. In\nthose situations, add requirements to the protocol instead and retrieve the\nparameters from the conforming class. The reason for this guideline is that\nconforming classes will always inherit from `tt::ConformsTo`.\nTherefore, any template parameters of the protocol must also be template\nparameters of their conforming classes, which means the protocol can just\nrequire and retrieve them. For example, we could be tempted to follow this\nantipattern:\n\n\\snippet Utilities/Test_ProtocolHelpers.cpp named_antipattern\n\nHowever, instead of adding template parameters to the protocol we should add a\nrequirement to it:\n\n\\snippet Utilities/Test_ProtocolHelpers.cpp named_with_type\n\nClasses would need to specify the template parameters for any\nprotocols they conform to anyway, if the protocols had any. So they might as\nwell expose them:\n\n\\snippet Utilities/Test_ProtocolHelpers.cpp person_with_name_type\n\nThis pattern also allows us to check for protocol conformance first and then add\nfurther checks about the types if we wanted to:\n\n\\snippet Utilities/Test_ProtocolHelpers.cpp example_check_name_type\n\n# Protocol authors: Testing a protocol {#protocols_testing}\n\nProtocol authors should provide a unit test for their protocol that includes an\nexample implementation of a class that conforms to it. The protocol author\nshould add this example to the documentation of the protocol through a Doxygen\nsnippet. This gives users a convenient way to see how the author intends their\ninterface to be implemented.\n\n# Protocols and C++20 \"Constraints and concepts\" {#protocols_and_constraints}\n\nA feature related to protocols is in C++20 and goes under the name of\n[constraints and concepts](https://en.cppreference.com/w/cpp/language/constraints).\nEvery protocol defines a _concept_, but it defers checking its requirements to\nthe unit tests to save compile time. In other words, protocols provide a way to\n_indicate_ that a class fulfills a set of requirements, whereas C++20\nconstraints provide a way to _check_ that a class fulfills a set of\nrequirements. Therefore, the two features complement each other. Once C++20\nbecomes available in SpECTRE we can either gradually convert our protocols to\nconcepts and use them as constraints directly if we find the impact on compile\ntime negligible, or we can add a concept that checks protocol conformance the\nsame way that `tt::conforms_to_v` currently does (i.e. by checking inheritance).\n" }, { "path": "docs/DevGuide/PythonBindings.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Writing Python Bindings {#spectre_writing_python_bindings}\n\n\\tableofcontents\n\n## CMake and Directory Layout\n\nTo allow users to analyze output from simulations and take advantage of\nSpECTRE's data structures and functions in python, bindings must sometimes be\nwritten. SpECTRE uses [pybind11](https://pybind11.readthedocs.io/)\nto aid with generating the bindings. The C++ code for the bindings should\ngenerally go in a `Python` subdirectory. For example, the bindings for the\nDataStructures library would go in `src/DataStructures/Python/`. SpECTRE\nprovides the `spectre_python_add_module` CMake function to make adding a new\npython module, be it with or without bindings, easy. The python bindings are\nbuilt only if `-D BUILD_PYTHON_BINDINGS=ON` is passed when invoking cmake\n(enabled by default).\nYou can specify the Python version, interpreter and libraries used for compiling\nand testing the bindings by setting the `-D Python_EXECUTABLE` to an absolute\npath such as `/usr/bin/python3`.\n\nThe function `spectre_python_add_module` takes as its first argument the module,\nin our case `DataStructures`. Optionally, a list of `SOURCES` can be passed to\nthe CMake function. If you specify `SOURCES`, you must also specify a\n`LIBRARY_NAME`. A good `LIBRARY_NAME` is the name of the C++ library for which\nbindings are being built prefixed with `Py`, e.g. `PyDataStructures`. If the\nPython module will only consist of Python files, then the `SOURCES` option\nshould not be specified. Python files that should be part of the module can be\npassed with the keyword `PYTHON_FILES`. Finally, the `MODULE_PATH`\nnamed argument can be passed with a string that is the path to where the module\nshould be. For example, `MODULE_PATH \"submodule0/submodule1/\"` would mean the\nmodule is accessed from python using\n`import spectre.submodule0.submodule1.MODULE_NAME`.\n\nHere is a complete example of how to call the `spectre_python_add_module`\nfunction:\n\n\\code\nspectre_python_add_module(\n Extra\n LIBRARY_NAME \"PyExtraDataStructures\"\n MODULE_PATH \"DataStructures/\"\n SOURCES Bindings.cpp MyCoolDataStructure.cpp\n PYTHON_FILES CoolPythonDataStructure.py\n )\n\\endcode\n\nThe library that is added has the name `PyExtraDataStructures`. Make sure to\ncall `spectre_python_link_libraries` for every Python module that compiles\n`SOURCES`. For example,\n\n\\code\nspectre_python_link_libraries(\n PyExtraDataStructures\n PRIVATE\n ExtraDataStructures\n pybind11::module\n )\n\\endcode\n\nYou may also call `spectre_python_add_dependencies` for Python modules that\nhave `SOURCES`, e.g.\n\n\\code\nspectre_python_add_dependencies(\n PyExtraDataStructures\n PyDataStructures\n )\n\\endcode\n\nNote that these functions will skip adding or configure any C++ libraries if\nthe `BUILD_PYTHON_BINDINGS` flag is `OFF`.\n\n## Writing Bindings\n\nOnce a python module has been added you can write the actual bindings. You\nshould structure your bindings directory to reflect the structure of the library\nyou're writing bindings for. For example, say we want bindings for `DataVector`\nand `Matrix` then we should have one source file for each class's bindings\ninside `src/DataStructures/Python`. The functions that generate the bindings\nshould be in the `py_bindings` namespace and have a reasonable name such as\n`bind_datavector`. There should be a file named `Bindings.cpp` which calls all\nthe `bind_*` functions. The `Bindings.cpp` file is quite simple and should\n`include `, forward declare the `bind_*` functions, and\nthen have a `PYBIND11_MODULE` function. For example,\n\n\\code{.cpp}\n#include \n\nnamespace py = pybind11;\n\nnamespace py_bindings {\nvoid bind_datavector(py::module& m);\n} // namespace py_bindings\n\nPYBIND11_MODULE(_Pybindings, m) {\n py_bindings::bind_datavector(m);\n}\n\\endcode\n\nNote that the library name is passed to `PYBIND11_MODULE` and is prefixed\nwith an underscore. The underscore is important and the library name must be the\nsame that is passed as `LIBRARY_NAME` to `spectre_python_add_module` (see\nabove).\n\nThe `DataVector` bindings serve as an example with code comments on how to write\nbindings for a class. There is also extensive documentation available directly\nfrom [pybind11](https://pybind11.readthedocs.io/).\n\nIf you are binding a library full of similarly structured free functions, such\nas libraries in `src/PointwiseFunctions/`, you can bind all functions directly\nin the `Bindings.cpp` file to avoid unnecessary boilerplate code. See\n`src/PointwiseFunctions/GeneralRelativity/Python/Bindings.cpp` for an example.\n\n\\note Exceptions should be allowed to propagate through the bindings so that\nerror handling via exceptions is possible from python rather than having the\npython interpreter being killed with a call to `abort`.\n\n## Testing Python Bindings and Code\n\nAll the python bindings must be tested. SpECTRE uses the\n[unittest](https://docs.python.org/3/library/unittest.html) framework\nprovided as part of python. To register a test file with CMake use the\nSpECTRE-provided function `spectre_add_python_test` passing as the first\nargument the test name (e.g. `\"Unit.DataStructures.Python.DataVector\"`), the\nfile as the second argument (e.g. `Test_DataVector.py`), and a semicolon\nseparated list of labels as the last (e.g. `\"unit;datastructures;python\"`).\nAll the test cases should be in a single class so that the python unit testing\nframework will run all test functions on a single invocation to avoid startup\ncost.\n\nBelow is an example of registering a python test file for bindings:\n\n\\snippet tests/Unit/DataStructures/CMakeLists.txt example_add_pybindings_test\n\nPython code that does not use bindings must also be tested. You can register the\ntest file using the `spectre_add_python_test` CMake function with the same\nsignature as shown above.\n\n## Using The Bindings\n\nSee \\ref spectre_using_python \"Using SpECTRE's Python\"\n\n## Notes:\n\n- All python libraries are dynamic/shared libraries.\n- Exceptions should be allowed to propagate through the bindings so that\n error handling via exceptions is possible from python rather than having the\n python interpreter being killed with a call to `abort`.\n- All function arguments in Python bindings should be named using `py::arg`.\n See the Python bindings in `IO/H5/` for examples. Using the named arguments in\n Python code is optional, but preferred when it makes code more readable.\n In particular, use the argument names in the tests for the Python bindings so\n they are being tested as well.\n\n## Guidelines for writing command-line interfaces (CLIs)\n\n- List all CLI endpoints in `support/Python/__main__.py`.\n- Follow the recommendations in the\n [click](https://click.palletsprojects.com/en/8.1.x/) documentation.\n- Split your code into free functions that know nothing about the CLI and can\n just as well be called independently from Python, and the CLI commands that\n call the functions. Test both.\n- Take only input files that the script operates on as positional arguments\n (like H5 data files or YAML input files) and everything else as options.\n- Choose option names and shorthands consistent with other CLI endpoints in the\n repository. For example, H5 subfile names are specified with '--subfile-name'\n / '-d' and output files are specified with '--output' / '-o'. Look at other\n CLI endpoints before making choices for option names.\n- Never read or write files to or from \"default\" locations. Instead, take all\n input files as arguments and write all output files to locations specified\n explicitly by the user. This is important so users are not afraid of moving\n and renaming files, and are not left wondering where the script wrote its\n output. Examples:\n - Don't try to read a file like \"spectre.out\" from the current directory just\n because it might be there by convention. Instead, add an argument or option\n like `--out-filename` so the user can specify it.\n - Don't write a file like \"plot.pdf\" to the current directory without telling\n the user. Instead, add an option like `--output` / `-o` for the user to\n specify explicitly so they know exactly where output is written to.\n- Operate on files instead of directories when possible. For example, prefer\n taking many H5 volume data files as arguments instead of the directory that\n contains them. This helps with operating on H5 files in segments or other\n subdirectory structures. Passing many files to a script is easy for the user\n by using a glob (note: don't take the glob as a string argument, take the\n expanded list of files directly using `click.argument(..., nargs=-1,\n type=click.Path(...), required=True)`).\n Note that Click recommends to avoid `required=True` here but to [gracefully\n degrade to a noop](https://click.palletsprojects.com/en/8.1.x/arguments/#variadic-arguments)\n instead, but that's confusing for the user.\n- Never overwrite or delete files without prompting the user or asking them to\n run with `--force`.\n- When the user did not specify an option, print possible values for it and\n return instead of raising an exception. For example, print the subfile names\n in an H5 file if no subfile name was specified. This allows the user to make\n selections incrementally.\n- When the user did not specify an output file, write the output to `sys.stdout`\n if possible instead of raising an exception. This allows the user to use pipes\n and chain commands if they want, or add a quick `-o` option to write to a\n file.\n- Always use Python's `logging` module over plain `print` statements. This\n allows the user to control the verbosity.\n" }, { "path": "docs/DevGuide/QuickStartDockerVSCode.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Code development quick-start with Docker and Visual Studio Code {#dev_guide_quick_start_docker_vscode}\n\n\\tableofcontents\n\nThis page describes how to get started developing SpECTRE on Mac, Linux, or\nWindows using [Docker](https://docker.com) and the [Visual Studio\nCode](https://code.visualstudio.com) editor. This is a particularly quick way to\nget up and running with SpECTRE code development, though of course not the only\nway. If you prefer setting up your development environment differently, we\nsuggest you read the \\ref installation \"Installation\" page. If you would like to\njump right into a working development environment, read on!\n\n## Fork the SpECTRE repository on GitHub\n\nThe SpECTRE code lives on GitHub in the\n[sxs-collaboration/spectre](https://github.com/sxs-collaboration/spectre)\nrepository. Developers work on their own copy (or\n[\"fork\"](https://docs.github.com/en/github/collaborating-with-issues-and-pull-requests/about-forks))\nof the repository and contribute back to\n[sxs-collaboration/spectre](https://github.com/sxs-collaboration/spectre)\nthrough [pull requests](https://docs.github.com/en/github/collaborating-with-issues-and-pull-requests/about-pull-requests).\nFork the repository to your own account:\n\n- [Fork sxs-collaboration/spectre on GitHub](https://github.com/sxs-collaboration/spectre/fork)\n\n## Clone the SpECTRE repository to your computer\n\nTo work on SpECTRE code you will need a local copy (or \"clone\") of the\nrepository on your computer. We use SSH to communicate with GitHub, so you need\nto set up your SSH keys first. Follow GitHub's instructions to generate an SSH\nkey and add it to your GitHub account:\n\n- [Generating an SSH key and adding to to GitHub](https://docs.github.com/en/github/authenticating-to-github/generating-a-new-ssh-key-and-adding-it-to-the-ssh-agent)\n\nNow you can download the repository via SSH. Navigate to **your fork** of the\nSpECTRE repository (i.e. the repository at the URL\nhttps://github.com/YOURNAME/spectre). Follow GitHub's instructions to clone the\nrepository to your computer, selecting the SSH option:\n\n- [Cloning a repository](https://docs.github.com/en/github/creating-cloning-and-archiving-repositories/cloning-a-repository)\n\n\\note If you clone the SpECTRE repository using HTTPS instead of SSH, you won't\nbe able to push any changes you make to your fork. You'll still be able to make\nlocal changes on your computer, but you won't be able to share your changes with\nanybody.\n\n## Install Docker\n\nOn your computer you will need Docker to run the containerized development\nenvironment. Install and start Docker:\n\n- [Get Docker](https://docs.docker.com/get-docker/)\n\nIf you're new to Docker, you can read through Docker's [Getting\nstarted](https://docs.docker.com/get-started/) documentation to learn about\ntheir basic concepts. We will use Docker to download and jump into a prebuilt\ndevelopment environment that has everything installed to compile and run\nSpECTRE.\n\n## Install Visual Studio Code\n\nWe will use the Visual Studio Code editor to jump into the containerized\ndevelopment environment, edit code, compile executables and run them. Download\nand install Visual Studio Code:\n\n- [Get Visual Studio Code](https://code.visualstudio.com)\n\nMicrosoft maintains [extensive\ndocumentation](https://code.visualstudio.com/docs) for Visual Studio Code that\nyou can read to get started using the editor. We recommend you take a look\nthrough the [Tips and\nTricks](https://code.visualstudio.com/docs/getstarted/tips-and-tricks) to get an\nidea of the editor's features.\n\n## Install the \"Remote - Containers\" extension\n\nVisual Studio Code's \"Remote - Containers\" extension lets you run the editor in\na Docker container. Install the extension:\n\n- [Install the \"Remote - Containers\"\n extension](vscode:extension/ms-vscode-remote.remote-containers)\n\n## Open the SpECTRE repository in Visual Studio Code\n\nNow open the SpECTRE repository that you have cloned to your computer in Visual\nStudio Code. Depending on your operating system you can select `File > Open`,\ntype `Cmd+O` (macOS) or `Ctrl+O` (Linux or Windows), drag the repository folder\nonto the Visual Studio Code icon or any other means to open the folder in Visual\nStudio Code.\n\nNow is also time to learn how to use the single most important tool in Visual\nStudio Code, the command palette. Try it now: Hit `Cmd+P` (macOS) or `Ctrl+P`\n(Linux or Windows) and start typing the name of any file, for example\n`QuickStartDockerVSCode.md`. Hit `Enter` to open the file. This is how you can\nquickly open any file in the repository. Note that the search is fuzzy, so you\ncan type any few letters in the path to the file. In addition to opening files,\nyou can hit `Cmd+Shift+P` (macOS) or `Ctrl+Shift+P` (Linux or Windows) and type\nthe name of any command that Visual Studio Code supports (or parts of it), for\nexample `Preferences: Open User Settings`.\n\n## Reopen the SpECTRE repository in the development container\n\nOpen the command palette by hitting `Cmd+Shift+P` (macOS) or `Ctrl+Shift+P`\n(Linux or Windows) and run the command `Remote-Containers: Reopen in container`\nby starting to type a few letters of this command and then hitting `Enter`.\n\nVisual Studio Code will download and run the container and drop you into a fully\nconfigured environment where you can proceed to compile and run SpECTRE. This\nmay take a few minutes so just let VSCode run and do it's thing. There may be a\n`show logs` button somewhere on your screen if you're interested in the details\nof the download.\n\nIf you are interested to learn more about how this feature works you can\nread through the [VS Code documentation on remote containers](https://code.visualstudio.com/docs/remote/containers)\nand inspect the `.devcontainer/devcontainer.json` file that's included in the\nSpECTRE repository.\n\n\\note If you look into the `.devcontainer/devcontainer.json` file, you'll see we\nare using the `sxscollaboration/spectre:dev` container. We also offer other\ncontainers. The `sxscollaboration/spectre:ci` container has more compilers and\nthe `sxscollaboration/spectre:demo` container has a couple pre-built\nexecutables. If you'd like to build in a different container, just switch the\nimage name in the json file and reopen in the new container.\n\n## Configure, compile and run SpECTRE\n\nWith Visual Studio Code running in the development container you can now\nconfigure, compile and run SpECTRE with no additional setup. Hit `Cmd+Shift+P`\n(macOS) or `Ctrl+Shift+P` (Linux or Windows) to open the command palette and run\nthe command `CMake: Select a Kit`. You should see a `Default` kit available.\nThen, open the command palette again, run `CMake: Select Variant`, and select\neither `Release` or `Debug`. For this tutorial we recommend using `Release`. If\nyou want to actually develop SpECTRE, the `Debug` option would be better. This\nspecific kit uses `clang` to build SpECTRE along with the Python bindings.\nFinally, open the command palette once more and run `CMake: Configure` which\nwill now actually run CMake.\n\nIt will set up a build directory. You can open\nVisual Studio Code's [integrated\nterminal](https://code.visualstudio.com/docs/editor/integrated-terminal) with\nthe keyboard shortcut ``Ctrl+` `` and navigate to the newly created build\ndirectory to inspect it:\n\n```\ncd build-Default-Debug\n```\n\nFor compiling and running SpECTRE you can either use Visual Studio Code's CMake\nintegration by looking up further commands in the command palette, or use the\nterminal. We will be using the terminal from now on. Try compiling an\nexecutable, for example:\n\n```\nmake -j4 ExportCoordinates3D\n```\n\nOnce the executable has compiled successfully you can try running it:\n\n```\n./bin/ExportCoordinates3D \\\n --input-file $SPECTRE_HOME/tests/InputFiles/ExportCoordinates/Input3D.yaml\n```\n\nThis executable produced a volume data file in the `build-Default-Debug`\ndirectory that we can visualize in ParaView. Generate an XMF file from the\nvolume data file that ParaView understands:\n\n```\n./bin/spectre generate-xdmf \\\n --file-prefix ExportCoordinates3DVolume --subfile-name element_data \\\n --output ExportCoordinates3DVolume\n```\n\nSince the build directory is shared with the host file system you can now open\nParaView on your computer and load the generated XMF file as described in the\n\\ref tutorial_visualization \"visualization tutorial\".\n\n\\note If you wanted to run this executable again, you'd have to first remove the\nexisting `.h5` files, otherwise an error will occur.\n\n## Edit and contribute code to SpECTRE with VS Code\n\nYou are now ready to code! The other \\ref dev_guide \"dev guides\" will teach you\nhow to write SpECTRE code. Return to the [Visual Studio Code\ndocumentation](https://code.visualstudio.com/docs) to learn more about editing\ncode with Visual Studio Code.\n\nIn particular, the Visual Studio Code documentation can teach you how to use Git\nto commit your code changes to your repository:\n\n- [Git support in Visual Studio Code](https://code.visualstudio.com/docs/editor/versioncontrol#_git-support)\n\nSpECTRE code development follows a pull-request model. You can learn more about\nthis process in our contributing guide:\n\n- [Contributing to SpECTRE through pull requests](https://spectre-code.org/contributing_to_spectre.html#pull-requests)\n\nVisual Studio Code can also help you create and review pull requests:\n\n- [Working with pull requests in VS Code](https://code.visualstudio.com/docs/editor/github#_pull-requests)\n\n## Interactively debug a SpECTRE test with VS Code\n\nTo track down an issue with your code it can be very useful to interactively\ndebug it. First, make sure you have written a test case where the issue occurs.\nIf you have not written a test yet, this is a great time to do it. Refer to the\n\\ref writing_unit_tests \"Writing Unit Tests\" dev guide to learn how to write\ntests.\n\nTo launch the interactive debugger, hit `Cmd+Shift+P` (macOS) or `Ctrl+Shift+P`\n(Linux or Windows) to open the command palette, run the command `CMake: Set\nDebug Target` and select your test executable (e.g. `Test_LinearOperators`)\nThen run the command `CMake: Debug`.\nThe test executable will compile, run and stop on any breakpoints. Follow the\nVisual Studio Code documentation to learn how to set breakpoints in your code\nand inspect the state of your variables:\n\n- [Debug actions in VS Code](https://code.visualstudio.com/docs/editor/debugging#_debug-actions)\n\n## Real-time collaboration with Live Share\n\nYou can use the [Live\nShare](https://docs.microsoft.com/en-us/visualstudio/liveshare/) extension to\nwork together with others and edit code simultaneously. Live Share can be very\nuseful to debug code together. Follow these instructions to share a link to your\ncurrent Visual Studio Code workspace:\n\n- [Live Share Quickstart: Share your first project](https://docs.microsoft.com/en-us/visualstudio/liveshare/quickstart/share)\n\n\n## Tips and tricks\n\n- The [**GitLens extension**](https://marketplace.visualstudio.com/items?itemName=eamodio.gitlens)\n is very useful to browse your repository. Select the \"Source Control\" icon and\n explore the various panels.\n\n- When you build the **documentation** (e.g. with `make doc`), you can open it\n in a web server within VS Code:\n\n ```\n python3 -m http.server -d docs/html\n ```\n\n The web server launches on port 8000 by default, which is being forwarded\n outside the container, so you can just open http://127.0.0.1:8000 in your\n browser to view the documentation.\n\n- Instead of working in the Docker container, you can use the [Remote - SSH](https://marketplace.visualstudio.com/items?itemName=ms-vscode-remote.remote-ssh)\n extension to **work on a remote machine** such as your local supercomputing\n cluster. Ask the cluster administrators or users for suggestions concerning\n installing and running SpECTRE on the particular supercomputer.\n\n- You can work with **Jupyter notebooks in Visual Studio Code**. First, install\n Jupyter and all other Python packages you want to work with in the container:\n\n ```\n pip3 install jupyter matplotlib\n ```\n\n Any `.ipynb` notebook files you create or open will be displayed in VS Code's\n notebook editor. This is very useful for quickly plotting data from SpECTRE\n runs or using SpECTRE's Python bindings. Refer to the [VS Code documentation\n on Jupyter support](https://code.visualstudio.com/docs/python/jupyter-support)\n for more information.\n\n- Docker can quickly use up a lot of disk space. From time to time you\n can \"prune\" unneeded images and containers to reclaim disk space:\n\n - [Prune unused Docker objects](https://docs.docker.com/config/pruning/)\n\n When pruning containers, make sure no data is deleted that you care about!\n" }, { "path": "docs/DevGuide/RedistributingGridpoints.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Redistributing Gridpoints {#redistributing_gridpoints}\n\n\\tableofcontents\n\n## Introduction\nThe simplest way to construct a volume map from two parameterized surfaces is\nby linearly interpolating between them:\n\n\\f[\\vec{x}(\\xi,\\eta,\\zeta) =\n\\frac{1-\\zeta}{2}\\vec{\\sigma}_-(\\xi,\\eta)+\n\\frac{1+\\zeta}{2}\\vec{\\sigma}_+(\\xi,\\eta)\\f]\n\nIn the above example, each surface \\f$\\vec{\\sigma}_+\\f$ and\n\\f$\\vec{\\sigma}_-\\f$ is parameterized using the logical coordinates \\f$\\xi\\f$\nand \\f$\\eta\\f$, and a third coordinate \\f$\\zeta\\in[-1,1]\\f$ is used to\ninterpolate between them.\n\nWe then distribute gridpoints on this volume by specifying values of the\ncoordinates \\f$\\xi,\\eta,\\f$ and \\f$\\zeta\\f$ at which the gridpoints are located.\nIn SpECTRE these values are the locations of the quadrature nodes. The\ndistribution of the gridpoints throughout the volume depends on the\nparameterization used, and the simplest choice of parameterization does not\nnecessarily lead to the best gridpoint distribution. In this section we discuss\nsituations in which there exist better parameterizations than those obtained by\nlinear interpolation.\n\n## Generalized Logical Coordinates\n\nIn each of the following examples, we will obtain functions \\f$\\Xi(\\xi),\n\\mathrm{H}(\\eta),\\f$ and \\f$\\mathrm{Z}(\\zeta)\\f$ that give better gridpoint\ndistributions than using the logical coordinates alone. Where possible, we will\nwrite the reparameterized map such that the functional form of the map is\nunchanged when replacing \\f$\\Xi\\f$ with \\f$\\xi\\f$, etc. We therefore refer to\n\\f$\\Xi, \\mathrm{H},\\f$ and \\f$\\mathrm{Z}\\f$ as the\n*generalized logical coordinates*, as they can also refer to the logical\ncoordinates \\f$\\xi, \\eta,\\f$ and \\f$\\zeta\\f$ themselves, when the transformation\nis the identity.\n\n## Equiangular Maps\n\nThe mapping for a cubed sphere surface can be easily obtained by taking points\nthat lie on each face of a cube and normalizing them such that they lie on the\nsphere:\n\n\\f[\\vec{\\sigma}_{+z}(\\xi,\\eta) =\n\\frac{1}{\\sqrt{1 + \\xi^2 + \\eta^2}}\n\\begin{bmatrix}\n\\xi\\\\\n\\eta\\\\\n1\\\\\n\\end{bmatrix}\\f]\n\nIn the above example the parameterization used for the upper \\f$+z\\f$ surface\nof the cube is linear in \\f$\\xi\\f$ and \\f$\\eta\\f$. However, distances measured\non the surface of the sphere are not linear in \\f$\\xi\\f$ and \\f$\\eta\\f$. To see\nthis, one may compute \\f$g_{\\xi\\xi} = |\\frac{\\partial\\vec{x}}{\\partial\\xi}|^2\\f$\nto see how distances are measured in terms of \\f$\\xi\\f$:\n\n\\f[g_{\\xi,\\xi}|_{\\eta=0} = \\frac{1}{(1+\\xi^2)^2}\\f]\n\nThis metric term demonstrates that a gridpoint distribution uniform in\n\\f$\\xi\\f$ will end up being compressed near \\f$\\xi=\\pm1\\f$. Suppose we\nreparameterized the surface using the generalized logical coordinate\n\\f$\\Xi\\in[-1,1]\\f$. We would find:\n\n\\f[g_{\\xi,\\xi}|_{\\eta=0} = \\frac{\\Xi'^2}{(1+\\Xi^2)^2}\\f]\n\nIdeally, we would like distances measured along a curvilinear surface to be\nlinear in the logical coordinates. We solve the differential equation and\nobtain:\n\n\\f[\\Xi = \\tan(\\xi\\pi/4)\\f]\n\nThese two parameterizations of the cubed sphere are known as the *equidistant*\nand *equiangular* central projections of the cube onto the sphere. We now\nsummarize their usage in SpECTRE CoordinateMaps that have\n`with_equiangular_map` as a specifiable parameter:\n\nIn the case where `with_equiangular_map` is `true`, we have the\nequiangular coordinates\n\n\\f[\\textrm{equiangular xi} : \\Xi(\\xi) = \\textrm{tan}(\\xi\\pi/4)\\f]\n\n\\f[\\textrm{equiangular eta} : \\mathrm{H}(\\eta) = \\textrm{tan}(\\eta\\pi/4)\\f]\n\nwith derivatives\n\n\\f[\\Xi'(\\xi) = \\frac{\\pi}{4}(1+\\Xi^2)\\f],\n\n\\f[\\mathrm{H}'(\\eta) = \\frac{\\pi}{4}(1+\\mathrm{H}^2)\\f]\n\nIn the case where `with_equiangular_map` is `false`, we have the equidistant\ncoordinates\n\n\\f[ \\textrm{equidistant xi} : \\Xi = \\xi\\f]\n\n\\f[ \\textrm{equidistant eta} : \\mathrm{H} = \\eta\\f]\n\nwith derivatives:\n\n\\f[\\Xi'(\\xi) = 1\\f] \\f[\\mathrm{H}'(\\eta) = 1\\f]\n\n## Projective Maps\n\nThe mapping for any convex quadrilateral can be obtained by bilinearly\ninterpolating between each vertex \\f$\\vec{x}_1, \\vec{x}_2, \\vec{x}_3\\f$\nand \\f$\\vec{x}_4\\f$:\n\n\\f[\\vec{x}(\\xi,\\eta) =\n\\frac{(1-\\xi)(1-\\eta)}{4}\\vec{x}_1+\n\\frac{(1+\\xi)(1-\\eta)}{4}\\vec{x}_2+\n\\frac{(1-\\xi)(1+\\eta)}{4}\\vec{x}_3+\n\\frac{(1+\\xi)(1+\\eta)}{4}\\vec{x}_4\n\\f]\n\nIn the case of a trapezoid where two of the sides are parallel, it is\nappropriate to linearly interpolate along the parallel sides. However,\nlinearly interpolating between the two bases results in a less than\nideal gridpoint distribution. This happens in the case of SpECTRE's Frustum,\nwhere the logical coordinate \\f$\\zeta\\f$ interpolates between the bases.\n\n\\image html BilinearVProjective.png \"Comparison of mappings. (Noah Veltman)\"\n\nAs seen in Veltman's [Warp-Off]\n(https://bl.ocks.org/veltman/8f5a157276b1dc18ce2fba1bc06dfb48), linear\ninterpolation between the two bases results in a uniformly spaced grid\nbetween the bases of the frustum. This causes elements near the smaller base\nto be longer in the direction normal to the base, and elements near the larger\nbase to be shorter in the direction normal to the base. We desire elements that\nhave roughly equal sizes along each of their dimensions.\n\nWe can redistribute the gridpoints in the \\f$\\zeta\\f$ direction using a\nprojective map, moving more gridpoints toward the smaller base. We can also see\nin the figure above that a projective map can be applied incorrectly, leaving\nelements distorted at the opposite end. From this we can see that it is\nimportant to control the degree of projection.\n\nWe adapt a technique from projective geometry to obtain the desired grid\nspacing. The heart of the method lies in the fact that objects arranged in a\nline at equal distances from one another will appear to converge as they\napproach the horizon.\n\n\\image html ProjectionOntoPlane.png \"Controlling the degree of projection.\"\n\nThe above diagram demonstrates how to obtain a nonlinearly parameterized\nobject (seen in red) from a linearly parameterized one (seen in purple).\nThis is done by lifting the linearly parameterized object into a higher\nspatial dimension \\f$w\\f$, such that its projection onto the plane remains\nunchanged. As seen above, \\f$w_{\\delta}\\f$ controls the degree of projection\nof one end of the object (purple) into a higher spatial dimension \\f$w\\f$.\nIn projective geometry, these points that exist in the higher dimension are\nlabeled with *homogeneous coordinates* \\f$\\tilde{x}, \\tilde{y}, \\tilde{z}, w\\f$,\nto distinguish them from the Cartesian coordinates that label points that exist\non the \\f$w=1\\f$ hyperplane, \\f$x,y,z\\f$. The resulting grid (seen in red) is\nobtained by projecting back into the \\f$w=1\\f$ hyperplane. The Cartesian\ncoordinates are obtained by dividing each homogeneous coordinate of the\nlinearly parameterized object by its respective \\f$w\\f$ coordinate value.\n\nThe parametric equation for the purple object seen above in homogeneous\ncoordinates is:\n\\f[\\begin{bmatrix}\\tilde{x}\\\\\\tilde{y}\\\\\\tilde{z}\\\\w\\\\\\end{bmatrix}=\n\\frac{1-\\zeta}{2}\\begin{bmatrix}x_1\\\\y_1\\\\z_1\\\\1\\\\\\end{bmatrix}+\n\\frac{1+\\zeta}{2}\\begin{bmatrix}x_2w_{\\delta}\\\\y_2w_{\\delta}\\\\\nz_2w_{\\delta}\\\\w_{\\delta}\\\\\\end{bmatrix}\\f]\n\nThe equation for the projected red object in Cartesian coordinates is\nobtained by dividing by w:\n\\f[\\vec{x}(\\zeta) = \\frac{1}{w(\\zeta)}\n\\begin{bmatrix}\n\\tilde{x}(\\zeta)\\\\\n\\tilde{y}(\\zeta)\\\\\n\\tilde{z}(\\zeta)\\\\\n\\end{bmatrix}\\f]\n\nWe wish to cast our parametric equation for the surface into the form:\n\\f[\\vec{x}(\\zeta) =\n\\frac{1-\\mathrm{Z}}{2}\\vec{x}_1 + \\frac{1+\\mathrm{Z}}{2}\\vec{x}_2\\f]\nfor some appropriate choice of auxiliary variable `projective_zeta`\n\\f$ = \\mathrm{Z}(\\zeta)\\f$. We would also like for \\f$\\mathrm{Z}\\f$ to reduce to\n\\f$\\zeta\\f$ when \\f$w_{\\delta}\\ = 1\\f$.\n\nDefining the auxiliary variables \\f$w_{\\pm} := w_{\\delta}\\pm 1\\f$, the desired\n\\f$\\mathrm{Z}(\\zeta)\\f$ is given by:\n\\f[\\mathrm{Z} = \\frac{w_- + \\zeta w_+}\n{w_+ + \\zeta w_-}\\f]\n\nwith derivative:\n\\f[\\mathrm{Z}' = \\frac{\\partial\\mathrm{Z}}{\\partial \\zeta} =\n\\frac{w_+^2 - w_-^2}{(w_+ + \\zeta w_-)^2}\\f]\n\nFor SpECTRE CoordinateMaps that have `projective_scale_factor` as a specifiable\nparameter, the value \\f$w_{\\delta} = 1\\f$ should be supplied in case the user\ndoes not want to use projective scaling. If `auto_projective_scale_factor` is\nset to `true`, the map will compute a value of \\f$w_{\\delta}\\f$ that is\nappropriate.\n" }, { "path": "docs/DevGuide/StaticAnalysis.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Static Analysis Tools {#static_analysis_tools}\n\n\\tableofcontents\n\nSpECTRE code is frequently run through the\n[Clang Tidy](http://clang.llvm.org/extra/clang-tidy/) static analyzer.\nSince analyzing a single source file can take over half a minute it\nis generally not advisable to run clang-tidy over the entire code base.\nIf CMake isn't finding clang-tidy, make sure clang-tidy is installed and that\nyou have chosen clang as your compiler. To analyze a single source file\nrun, for example\n`make clang-tidy FILE=/path/to/source/src/DataStructures/DataVector.cpp`.\nTo analyze the entire code base run `make clang-tidy-all`. To analyze all\nchanged C++ source files in the commits from `FIRST_HASH` to `HEAD`, run `make\nclang-tidy-hash HASH=FIRST_HASH`.\n" }, { "path": "docs/DevGuide/TensorExpressions.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Writing Tensor Equations with TensorExpressions {#writing_tensorexpressions}\n\n\\tableofcontents\n\nSpECTRE's `TensorExpression`s interface allows you to write tensor equations in\nSpECTRE in C++ with syntax that resembles tensor index notation. To use it,\nsimply add this include to the top of your file:\n```\n#include \"DataStructures/Tensor/Tensor.hpp\"\n```\nThe following guide assumes a basic understanding of the `Tensor` class and\n\\ref tnsr \"tnsr\" type aliases. **RHS** refers to the right hand side expression\nthat we wish to compute and **LHS** refers to the resulting left hand side\ntensor that stores the result of computing the RHS expression.\n\n# Syntax {#te_syntax}\n`TensorExpression`s are arithmetic expressions of `Tensor`s that can be\nevaluated using `tenex::evaluate`. Terms used in the expression may be `Tensor`s\nor numbers (see [supported types](#te_data_type_support)).\n\nAs a simple example of how `TensorExpression`s are used, if you would like to\nraise the index of some `Tensor` `R` with some inverse spacetime metric `Tensor`\n`g`, i.e. \\f$R^c{}_b = R_{ab} g^{ac}\\f$, you can compute this with\n`TensorExpression`s by doing:\n\n\\snippet Expressions/Test_Examples.cpp te_example_evaluate_lhs_return\n\nwhere `R_up`, `R`, and `g` are rank 2 spacetime `Tensor`s and the `ti::*`\nvariables are `TensorIndex`s representing generic tensor indices. Here is a\nbreakdown of the different parts of this line:\n- the RHS expression to compute is the argument to\n\\ref tenex::evaluate \"evaluate\": `R(ti::a, ti::b) * g(ti::A, ti::C)`\n- the result LHS `Tensor` is `R_up`\n- the LHS `Tensor`'s indices are the template arguments to\n\\ref tenex::evaluate \"evaluate\": `ti::C, ti::b`\n\nThe LHS \\ref ::Symmetry \"Symmetry\" will be deduced from the RHS tensors'\nsymmetries and order of operations.\n\nAlternatively, if you already have a LHS `Tensor` variable, you can pass it into\nthe following \\ref tenex::evaluate \"evaluate\" overload, where the LHS `Tensor`\nprovided will be assigned to the result of the RHS expression:\n\n\\snippet Expressions/Test_Examples.cpp te_example_evaluate_lhs_arg\n\nNote that to use this \\ref tenex::evaluate \"evaluate\" overload, the LHS `Tensor`\ndoes not need to be previously sized unless the data type is a Blaze vector type\n(e.g. `DataVector`) *and* the RHS expression contains no `Tensor` terms\n(see [example](#te_assigning_to_a_number) where sizing is necessary). This\noverload is useful in a couple cases:\n- [Specifying the LHS symmetry](#te_specify_lhs_symmetry): One advantage of this\noverload is that it uses the \\ref ::Symmetry \"Symmetry\" of the provided LHS\ntensor instead of deducing it from the RHS expression. This enables you to\nspecify the LHS symmetry in cases where the previous\n\\ref tenex::evaluate \"evaluate\" overload does not deduce the one you want. While\nthe LHS index order in this example (`ti::C, ti::b`) could theoretically be\ndeduced from the index types of `R_up`, we still require specifying them because\nthis isn't the case for all equations and we would like to have a unified\ninterface. See [this example](#te_specify_lhs_symmetry), which demonstrates a\ncase where you might want to specify the LHS symmetry and where the LHS index\norder would not be deducible.\n- **[Using spatial and time indices on LHS spacetime indices](#te_spatial_time_index_lhs)**\n\n## Tensor indices {#te_tensor_indices}\n\n`TensorIndex`s represent generic tensor indices and are supplied as\ncomma-separated lists in two places:\n- in parentheses for each tensor in the RHS expression\n- in the template parameters of \\ref tenex::evaluate \"evaluate\" to specify the\norder of the LHS result tensor's indices.\n\nEach `TensorIndex` takes the form `ti::*` where `*` is a letter that encodes\nindex properties:\n- Uppercase letters denote upper indices and lowercase letters denote lower\nindices\n- Letters `A/a - H/h` indicate spacetime indices, `I/i - N/n` indicate spatial\nindices, and `T/t` indicates a concrete time index. This is what is currently\ndefined, but more spatial and spacetime indices (letters) can easily be added if\nneeded. Note that there is no precedence or difference between the indices of\nsome type, e.g. `ti::a`, `ti::b`, ... `ti::h` are equivalent\n\nThe properties of each `TensorIndex` and the `Tensor`'s indices (typelist of\n\\ref SpacetimeIndex \"TensorIndexType\"s) must be compatible:\n- valences (being upper or lower indices) must match\n- if a `Tensor`'s index is spacetime, you can use a spacetime `TensorIndex`,\nspatial `TensorIndex`, or concrete time `TensorIndex`\n- if a `Tensor`'s index is spatial, you must use a spatial `TensorIndex`\n\nTo demonstrate correct and incorrect usage, let's say we have tensors\n\\f$R_{ab}\\f$ (two spacetime indices, e.g. type \\ref tnsr \"tnsr::ab\") and\n\\f$S_{ij}\\f$ (two spatial indices, e.g. type \\ref tnsr \"tnsr::ij\"):\n\n```\nR(ti::c, ti::d) // OK\nR(ti::c, ti::k) // OK, can use spatial TensorIndex on spacetime index\nR(ti::c, ti::t) // OK, can use time TensorIndex on spacetime index\nR(ti::c, ti::D) // ERROR, ti::D is upper but the 2nd index is lower\nS(ti::j, ti::k) // OK\nS(ti::a, ti::k) // ERROR, can't use spacetime TensorIndex on a spatial index\nS(ti::j, ti::t) // ERROR, can't use time TensorIndex on a spatial index\n```\n\n# Examples {#te_examples}\n## Basic operations {#te_basic_operations}\n\nIn the following examples:\n- `R` is type \\ref tnsr \"tnsr::ab\"\n- `S` is type \\ref tnsr \"tnsr::ab\"\n- `T` is type \\ref Scalar \"Scalar\"\n- `U` is type \\ref tnsr \"tnsr::Ab\"\n- `V` is type \\ref tnsr \"tnsr::aBC\"\n- `G` is type \\ref tnsr \"tnsr::a\"\n- `H` is type \\ref tnsr \"tnsr::A\"\n\n### Addition and subtraction {#te_addition_and_subtraction}\n\\f$L_{ab} = R_{ab} + S_{ba}\\f$\n\n\\snippet Expressions/Test_Examples.cpp te_example_addition\n\n\\f$L = 1 - T\\f$\n\n\\snippet Expressions/Test_Examples.cpp te_example_subtraction\n\n### Contraction of a single tensor {#te_contraction}\n\\f$L = U^{a}{}_{a}\\f$\n\n\\snippet Expressions/Test_Examples.cpp te_example_contraction_to_scalar\n\n\\f$L^b = V_{a}{}^{ba}\\f$\n\n\\snippet Expressions/Test_Examples.cpp te_example_contraction_to_tensor\n\n### Inner and outer products {#te_products}\n\\f$L = G_a H^{a}\\f$\n\n\\snippet Expressions/Test_Examples.cpp te_example_inner_product\n\n\\f$L_{cb} = T G_a G_c U^{a}{}_{b}\\f$\n\n\\snippet Expressions/Test_Examples.cpp te_example_inner_and_outer_product\n\n### Division {#te_division}\n\\f$L_a = \\frac{G_a}{2}\\f$\n\n\\snippet Expressions/Test_Examples.cpp te_example_division_by_number\n\n\\f$L_{ba} = \\frac{R_{ab}}{T}\\f$\n\n\\snippet Expressions/Test_Examples.cpp te_example_division_by_tensor\n\n\\f$L = \\frac{5}{U^{a}{}_{a} + 1}\\f$\n\n\\snippet Expressions/Test_Examples.cpp te_example_division_by_tensor_expression\n\n### Square root {#te_square_root}\n\\f$L = \\sqrt{T}\\f$\n\n\\snippet Expressions/Test_Examples.cpp te_example_square_root_tensor\n\n\\f$L = \\sqrt{G_a H^a}\\f$\n\n\\snippet Expressions/Test_Examples.cpp te_example_square_root_inner_product\n\n## More features {#te_more_features}\n\n### Specifying the LHS symmetry {#te_specify_lhs_symmetry}\nWhen using the \\ref tenex::evaluate \"evaluate\" overload that returns the LHS\n`Tensor`, the \\ref ::Symmetry \"Symmetry\" of the LHS `Tensor` will be deduced\nfrom the RHS expression. However, in some cases the deduced LHS symmetry may\nnot be what you want. To specify it yourself, you can pass your LHS `Tensor`\n(that has the desired \\ref ::Symmetry \"Symmetry\") to the\n\\ref tenex::evaluate \"evaluate\" overload that takes the LHS `Tensor` as the\nfirst argument.\n\nFor example, if we have \\f$L_{ab} = R_a R_b\\f$, the indices of \\f$L\\f$ are\nsymmetric. However, when we do:\n\n\\snippet Expressions/Test_Examples.cpp te_example_deduced_lhs_symmetry_fail\n\nthe type of `L` will be \\ref tnsr \"tnsr::ab\" because it is not known at\ncompile time that the two vectors in the product are the same. To override the\ndeduced symmetry and make it a symmetric result, we can create a\n\\ref tnsr \"tnsr::aa\" and pass it into the other overload:\n\n\\snippet Expressions/Test_Examples.cpp te_example_deduced_lhs_symmetry_force\n\n### Assigning to a number {#te_assigning_to_a_number}\nYou can assign a number (e.g. `double`) to a `Tensor` of any rank to fill all\ncomponents with that value, e.g. \\f$L_{ab} = -1\\f$. How you do that is slightly\ndifferent depending on the underlying data type of your `Tensor`:\n\n- When your `Tensor`'s data type is a number type (e.g. `double`,\n`std::complex`):\n\n\\snippet Expressions/Test_Examples.cpp te_example_assign_number_to_tensor_of_numbers\n\n- When your `Tensor`'s data type is a Blaze vector type (e.g. `DataVector`,\n`ComplexDataVector`), the `Tensor` must first be sized before calling\n\\ref tenex::evaluate \"evaluate\" because there is no sizing information (from a\n`Tensor` component) in the RHS expression:\n\n\\snippet Expressions/Test_Examples.cpp te_example_assign_number_to_tensor_of_vectors\n\nSee [supported number types](#te_data_type_support) for the data types that the\nRHS number can be.\n\n### Using spatial and time indices on RHS spacetime indices {#te_spatial_time_index_rhs}\nIf a `Tensor` has spacetime indices, you can use generic spatial indices and\nconcrete time indices to refer to a subset of the components, as we see in\nliterature.\n\nLapse \\f$\\alpha\\f$ computed from the spacetime metric \\f$g_{ab}\\f$ and shift\n\\f$\\beta^i\\f$:\n\n\\f$\\alpha = \\sqrt{\\beta^i g_{it} - g_{tt}}\\f$\n\n\\snippet Expressions/Test_Examples.cpp te_example_rhs_spatial_and_time_indices\n\n### Using spatial and time indices on LHS spacetime indices {#te_spatial_time_index_lhs}\nRelated to the previous example, you can also use generic spatial indices and\nconcrete time indices for the spacetime indices of the LHS `Tensor` to assign\nsubsets of the LHS `Tensor`'s components.\n\nSpacetime metric \\f$g_{ab}\\f$ computed from the lapse \\f$\\alpha\\f$, shift\n\\f$\\beta^i\\f$, and spatial metric \\f$\\gamma_{ij}\\f$:\n\n\\f$g_{tt} = -\\alpha^2 + \\beta^m \\beta^n \\gamma_{mn}\\f$\n\n\\f$g_{ti} = \\gamma_{mi} \\beta^m\\f$\n\n\\f$g_{ij} = \\gamma_{ij}\\f$\n\n\\snippet Expressions/Test_Examples.cpp te_example_lhs_spatial_and_time_indices\n\n\\parblock\n\\note The above example is for demonstration purposes only. In practice, you\nwould want to avoid repeating computing the reused quantity\n\\f$\\beta^i \\gamma_{ij}\\f$ by e.g. storing the result of the reused quantity in\nanother variable.\n\\endparblock\n\n### Using the LHS Tensor in the RHS expression {#te_using_lhs_tensor_in_rhs}\nYou can use the LHS `Tensor` in the RHS expression to emulate operations like\n`+=`, `*=`, etc. For example, say you would like to emulate the following:\n```\n// pseudocode\nL_ab = R_ab\nL_ab += 2.0 * S_ba\n```\nYou can emulate the `+=` operation by calling \\ref tenex::update \"update\"\ninstead of \\ref tenex::evaluate \"evaluate\":\n```\nauto L = tenex::evaluate(R(ti::a, ti::b));\n// use the LHS tensor in the RHS\ntenex::update(\n make_not_null(&L), L(ti::a, ti::b) + 2.0 * S(ti::b, ti::a));\n```\nOne limitation is that when using the LHS tensor in the RHS expression, the\nLHS tensor's index order must be the same on the LHS and RHS. This means that\nthe order of the `TensorIndex` template parameters of\n\\ref tenex::update \"update\" must match the order of the `TensorIndex` arguments\nin the parentheses that come after the LHS `Tensor` in the RHS expression. For\nexample, the following is not allowed and will yield a runtime error:\n```\n// ERROR: index order for L on LHS and RHS is not the same\ntenex::update(\n make_not_null(&L), L(ti::b, ti::a) + 2.0 * S(ti::b, ti::a));\n```\n\n\\parblock\n\\note It is not advised to use very large RHS expressions with\n\\ref tenex::update \"update\" because runtime performance does not scale well as\nthe number of operations gets very large. This is because\n\\ref tenex::evaluate \"evaluate\" breaks up large expressions into smaller ones,\nbut \\ref tenex::update \"update\" cannot. One way around this is to break up the\nexpression and use more than one call to \\ref tenex::update \"update\".\n\\endparblock\n\n# Compile time math checks {#te_compile_time_math_checks}\nFor all operations, mathematical legality is checked at compile time. The\ncompiler will catch what is not sound to write on paper, which includes things\nlike no repeated indices, can't divide by a tensor with rank > 0, and that\nspatial dimensions, frames, valences, index types (spatial or spacetime), and\nranks of tensors match where they should.\n\nHere are some examples of illegal math that the compiler will catch:\n\n```\ntnsr::ab R{};\ntnsr::ab S{};\ntnsr::ab T{};\ntnsr::AB G{};\n// ERROR: LHS and RHS indices don't match\nauto result1 = tenex::evaluate(R(ti::a, ti::b) + S(ti::a, ti::b));\n// ERROR: Can't add Tensors with different indices\nauto result2 = tenex::evaluate(R(ti::a, ti::b) + S(ti::a, ti:c));\n// ERROR: Repeated index in the RHS\nauto result3 =\n tenex::evaluate(R(ti::a, ti::b) * S(ti::a, ti::c));\n// ERROR: Can't add Tensors with different Frame types\nauto result4 = tenex::evaluate(R(ti::a, ti::b) + T(ti::a, ti::b));\n// ERROR: Can't contract indices with different number of spatial dimensions\nauto result5 = tenex::evaluate(R(ti::a, ti::b) * G(ti::A, ti::B));\n// ERROR: Can't divide by a rank > 0 Tensor\nauto result6 = tenex::evaluate(R(ti::a, ti::b) / S(ti::a, ti::b));\n```\n\n# Support for data types and operations {#te_data_type_and_op_support}\n\n## Data types {#te_data_type_support}\nThe RHS expression may contain a mixture of number terms and `Tensor` terms,\ne.g. `0.5 * T(ti::a)`.\n\nCurrently supported data types for number terms:\n- `double`\n- `std::complex`\n\nCurrently supported underlying data types for `Tensor` terms:\n- `double`\n- `std::complex`\n- `DataVector`\n- `ComplexDataVector`\n\nSupport for more types can be added.\n\n## Operations {#te_operation_support}\nIt's possible for terms in the RHS expression to have different data types. The\nmixture of `double`s and `Tensor`s is shown in the\n[subtraction example](#te_addition_and_subtraction) and the\n[division examples](#te_division).\n\nIt's also possible for terms to be a mixture of both real-valued and\ncomplex-valued numbers or `Tensor`s. For example, we can compute\n\\f$z^i = x^i + i y*i\\f$, where \\f$x\\f$ and \\f$y\\f$ are real-valued `Tensor`s,\n`i` is a `std::complex`, and \\f$z\\f$ is a complex-valued `Tensor`.\n\n\\snippet Expressions/Test_Examples.cpp te_example_complex_vector\n\nIn the above example, a `std::complex` is multiplied by a\n`Tensor`, which can be thought to have an \"intermediate\" type\n`Tensor`, and then a `Tensor` is added to that\nintermediate `Tensor` to yield the resulting type,\n`Tensor`.\n\nThe following table shows the data type that results from performing a binary\noperation (`+`, `-`, `*`, `/`) between two terms of given data types:\n\n\n \n\n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n
\n Data types resulting from binary operations between supported\n TensorExpression operand types\n
doublestd::complex<double>Tensor<double>Tensor<std::complex<double>>Tensor<DataVector>Tensor<ComplexDataVector>
doubledouble-----
std::complex<double>std::complex<double>std::complex<double>----
Tensor<double>Tensor<double>Tensor<std::complex<double>>Tensor<double>---
Tensor<std::complex<double>>Tensor<std::complex<double>>Tensor<std::complex<double>>Tensor<std::complex<double>>Tensor<std::complex<double>>--
Tensor<DataVector>Tensor<DataVector>Tensor<ComplexDataVector>*Not supportedNot supportedTensor<DataVector>-
Tensor<ComplexDataVector>Tensor<ComplexDataVector>Tensor<ComplexDataVector>Not supportedNot supportedTensor<ComplexDataVector>Tensor<ComplexDataVector>
\n\n\\parblock\n\\note The only binary operation that is supported between `std::complex`\nand `Tensor` is multiplication. This is because Blaze does not\nsupport addition, subtraction, nor division between `std::complex` and\n`DataVector`.\n\\endparblock" }, { "path": "docs/DevGuide/Tmp.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# SFINAE {#sfinae}\n\n\\tableofcontents\n\nSFINAE, Substitution Failure Is Not An Error, means that if a deduced template\nsubstitution fails, compilation must continue. This can be exploited to make\ndecisions at compile time. See [here](http://nilsdeppe.com/posts/tmpl-part1)\nfor a discussion using `std::enable_if` to remove certain functions from\noverload resolution or certain template specializations from name lookup.\nAnother method of controlling name lookup resolution is using\n`std::void_t`. `void_t` is a metafunction from types to `void`, that is\n\n```cpp\ntemplate \nusing void_t = void;\n```\n\n`void_t` is useful when used in combination with `decltype` and `std::declval`\nto probe if a type has certain members. For example, we can implement a type\ntrait to check if a type `T` is iterable by first have the general definition\ninherit from `std::false_type` as follows,\n\n```cpp\ntemplate \nstruct is_iterable : std::false_type {};\n```\n\nNext we will have specialization that uses `void_t` to check if the type `T`\nhas a `begin()` and `end()` function.\n\n```cpp\ntemplate \nstruct is_iterable().begin(),\n std::declval().end())>>\n : std::true_type {};\n```\n\nWhat is happening here? Well, we use `std::declval` to convert the type `T`\nto a reference type, which allows us to call member functions inside `decltype`\nexpressions without having to construct an object. First we try to call the\nmember function `begin()` on `std::declval()`, and if that succeeds we\nthrow away the result using the comma operator. Next we try to call `end()`\non `std::declval()`, which, if it succeeds we get the return type of\nusing `decltype`. Note that `decltype` is important because we can only call\nmember functions on reference types inside of `decltype`, not just anywhere.\nFinally, if all this succeeded use `void_t` to metareturn `void`, otherwise\nthe template parameters of `void_t` fail to evaluate and the specialization\ncannot be resolved during name lookup. We could just as well use\n\n```cpp\ntemplate \nstruct is_iterable().begin()),\n decltype(std::declval().end())>>\n : std::true_type {};\n```\n\nWhich of the two implementations of the `is_iterable` is preferred is simply\na matter of taste, both behave correctly.\n\nIf you're reading closely you might wonder why the `void_t` is necessary at\nall, why not just `decltype(...)`? Well the reason is that since the default\ntemplate parameter metavalue is `void`, the specialization cannot be resolved\nduring name lookup unless the second template parameter in the specialization\nis either `void` as well or is explicitly specified when the class template\nis being invoked. Thus, the clearest implementation probably is\n\n```cpp\ntemplate >\nstruct is_iterable : std::false_type {};\n\ntemplate \nstruct is_iterable().begin(),\n std::declval().end())>>\n : std::true_type {};\n```\n\nYou could now also define a helper type alias and constexpr boolean\n\n```cpp\ntemplate \nusing is_iterable_t = typename is_iterable::type;\n\ntemplate \nconstexpr bool is_iterable_v = is_iterable::value;\n```\n" }, { "path": "docs/DevGuide/Variables.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Using Variables in SpECTRE {#variables_foundations}\n\n# What is a Variables and Why Use Them?\nVariables are a data structure that hold a contiguous memory block with Tensors\npointing to it. Variables temporaries allow you to declare temporary tensors and\nscalars so that you can do all allocations needed for a computation at one time.\nSince physical memory is shared between CPU cores, processes can't allocate in\nparallel since they might try to allocate to the same chunk of memory. As more\nCPU cores are used, this becomes a bottleneck, slowing down or stopping other\nprocesses while memory is being allocated. Using a Variables to allocate all\nmemory needed at once can improve efficiency allowing the computation to\noperate smoothly and uninterrupted.\n\n# Defining a Variables of Temporary Tags\nTo define a Variables, you'll need the TempTensor and Variables headers\n```cpp\n#include \"DataStructures/Tags/TempTensor.hpp\"\n#include \"DataStructures/Variables.hpp\"\n```\nthis will give you access to temporary Scalars and Tensors we'll need to\nallocate. You can define a Variables that allocates one Scalar with something\nlike this:\n```cpp\nVariables>>\ntemp_buffer{get<0,0>(spatial_metric).size()};\n```\nHere, the Variables we've defined `temp_buffer` provides a tmpl::list with a\nTempScalar inside as the template argument, this will allocate a single\ntemporary scalar. The size and DataType of the TempScalar is deduced by what's\ninside the {}, you can provide any tensor or std::array with the correct size\nneeded. Now, to use the allocation you've made, you can do:\n```cpp\nauto& useful_scalar = get<::Tags::TempScalar<0>>(temp_buffer);\n```\n\n# Real Use Example\nNow that we've got the basics, using them to allocate multiple Scalars and\nTensors is quite easy. For instance, let's say I need to allocate 2 scalars,\na spatial vector and 2 lower rank 2 tensors for my function.\n```cpp\nVariables, ::Tags::TempScalar<1>,\n::Tags::TempI<0, 3, Frame::Inertial>, ::Tags::Tempij<0, 3, Frame::Inertial>,\n::Tags::Tempij<1, 3, Frame::Inertial>>>\ntemp_buffer{get<0,0>(spatial_metric).size()};\n```\nHere, when we allocate for the same type of scalar or tensor (rank 2 lower) the\nway we distinguish multiple allocations is through the number within the <>.\nNow, to use each individual allocation, we can do something like:\n```cpp\nauto& cool_scalar1 = get<::Tags::TempScalar<0>>(temp_buffer);\nauto& cool_scalar2 = get<::Tags::TempScalar<1>>(temp_buffer);\nauto& cool_tensor1 = get<::Tags::Tempij<0, 3, Frame::Inertial>>(temp_buffer);\nauto& cool_tensor2 = get<::Tags::Tempij<1, 3, Frame::Inertial>>(temp_buffer);\n```\n\n# Tips\nIn the interest of reducing memory allocations, there a certain scenarios where\nyou can resuse old allocations that are no longer useful to your computation.\n\nTo see this, let's say that you're trying to make two unit vectors. You might\nstart by saying you'll need two different vectors (rank 1 upper tensors) and 2\ndifferent scalars as the magnitude of each vector.\nThe way we'd allocate for this is by doing:\n```cpp\nVariables, ::Tags::TempScalar<1>,\n::Tags::TempI<0, 3, Frame::Inertial>, ::Tags::TempI<1, 3, Frame::Inertial>>>\ntemp_buffer{get<0,0>(spatial_metric).size()};\n```\nHowever, doing this allocates more memory than we actually need. Once we finish\ncalculating the first unit vector, the memory we've allocated for the scalar\nmagnitude of the first vector will just sit there unused. We can reuse the\nallocation for the TempScalar<0> and use it when calculating the second unit\nvector without having to allocate another TempScalar. Now, allocating an extra\nscalar is not very expensive, but when using tensors, the memory required really\nadds up, so this is just another way to help make SpECTRE a bit more efficient.\n" }, { "path": "docs/DevGuide/WritingDox.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Writing Good Documentation {#writing_good_dox}\n\n\\tableofcontents\n\n# Tutorials, Instructions, and Dev Guide {#writing_dox_writing_help}\n\nAll non-code documentation such as tutorials, installation instructions, and\nthe developer guide is written inside Markdown files such as this one. These\nfiles must be placed inside `docs/Tutorials`, `docs/MainSite`, or\n`docs/DevGuide` according to what they document. Each Markdown file must start\nwith the following line\n\n``` markdown\n# The title {#the_tag}\n```\n\nwhere `The title` is replaced with your desired title, and `the_tag` with the\ntag you want to use to reference the Markdown file and documentation. Each\nmain heading of the file starts with a single octothorpe\nand can have a tag. For example,\n\n``` markdown\n# My Section {#file_name_my_section}\n```\n\nWhile the `file_name` portion is not necessary, it is useful for reducing the\nlikelihood of reference collisions. You can add a table of contents using the\nDoxygen command \\\\tableofcontents. All sections, subsections,\nsubsubsections, etc. are shown in the table of contents if they have a tag,\nif not they do not appear.\n\n# C++ Documentation {#writing_dox_cpp_dox_help}\n\nWe require you to add Doxygen documentation for any of the following\nyou may have added to the public interface in any hpp file:\n\n+ classes\n+ structs\n+ enums\n+ functions\n+ namespaces\n+ macros\n+ type aliases\n\nDocumentation begins on the line immediately above the declaration with\neither a triple slash `///` or a `/*!`.\n\nExamples:\n\\verbatim\n/// A brief description of the object to be documented\n///\n/// Doxygen comments can be made\n/// using triple slashes...\nclass ExampleClass{\n ... rest of code\n}\n\\endverbatim\n\n\\verbatim\n/*!\n * \\brief A brief description of the object to be documented\n *\n * Doxygen comments can also be made\n * using the \"slash-star, star-slash\" pattern, in this way.\n */\nclass ExampleClass{\n ... rest of code\n}\n\\endverbatim\n\nBuild your documentation by running `make doc` in your build directory.\nYou can then view it by opening `BUILD_DIR/docs/html/index.html` in a\nbrowser and using the file navigator in Doxygen to locate your file.\n\nIn addition to providing a file directory of all the source files in SpECTRE,\nDoxygen also conveniently provides two additional organizations of the files,\nModules and Namespaces. To ensure that your documentation is easily found from\nwithin Doxygen, we recommend that you add any new objects to Modules and any\nnew namespaces to Namespaces.\n\n\\note The `///` Doxygen syntax does not require a `\\brief`, while the C-style\n`/*!` does.\n\n## Add your object to an existing Module:\n\nWithin a Doxygen comment, use the Doxygen keyword\n\\verbatim\n\\ingroup\n\\endverbatim\n\nfollowed by the name of the Module (you can find the list of existing Modules in\n`docs/GroupDefs.hpp`).\n\n## Add a new Module:\n\nWithin `docs/GroupDefs.hpp`, add the name of your Module (which follows the\nnaming convention \"YourNameForModule\" followed by \"Group\") among the rest,\ntaking care to keep the list of Modules in alphabetical order.\n\n## Add a new namespace:\n\nIn the hpp file in which the namespace is declared for the first time,\nadd a Doxygen comment to the line directly above the namespace. Subsequent\nfiles which use this namespace will not need a Doxygen comment.\n\nWe also strongly encourage you to:\n\n## Put any mathematical expressions in your documentation into LaTeX form:\n\nWithin a Doxygen comment, begin and conclude your expression with\n\n\\verbatim\n\\f$\n\\endverbatim\n\nExample:\n\\verbatim\n\\\\\\ We define \\f$ \\xi : = \\eta^2 \\f$\n\\endverbatim\n\nNote that if this expression spans more than one line,\nyour Doxygen comment must of the \"slash-star, star-slash\" form shown in the\nprevious section. One can also use (within a Doxygen comment) the form\n\n\\verbatim\n\\f[ expression \\f]\n\\endverbatim\n\nto put the expression on its own line. We also encourage you to use the latex\nenv `align` for formatting these multiple-line equations. Please prefer the\n`align` environment over the `eqnarray` environment. See the\n[texfaq](https://texfaq.org/FAQ-eqnarray) for an explanation as to why. When\nusing out-of-line equations it is important to have a blank Doxygen line above\nand below the equation so that ClangFormat does not merge the equation with\nother lines. For example,\n\n\\verbatim\n * word word word\n *\n * \\f{align}{\n * a &= b \\\\\n * c &= d\n * \\f}\n *\n * word word word\n\\endverbatim\n\nprevents ClangFormat from changing the code to\n\n\\verbatim\nword word word \\f{align}{ a &= b \\\\ c &= d \\f}\n\\endverbatim\n\nwhich may not render properly and makes the source code harder to read.\n\n## Cite publications in your documentation {#writing_dox_citations}\n\nWhen you refer to publications or books in the documentation, add a\ncorresponding entry to `docs/References.bib`. Follow these guidelines when\nediting `docs/References.bib`:\n\n- Ideally, find the publication on [INSPIRE HEP](https://inspirehep.net) and\ncopy its BibTeX entry.\n- For publications that are not listed on [INSPIRE HEP](https://inspirehep.net),\nmake sure to format the new entry's key in the same style, i.e.\n`([a-zA-Z]+):([0-9]{4})([a-z]*)`. Good keys are, for\ninstance, `Einstein:1915` or `LVC:2016a`. For books you may omit the year.\n- Sort the list of BibTeX entries in the file alphabetically by their keys.\n- Provide open access or preprint information whenever possible. For\npublications available on [arXiv](https://arxiv.org), for instance, add the\nfollowing fields (filling in the correct values):\n```\narchivePrefix = {arXiv},\neprint = {1609.00098},\nprimaryClass = {astro-ph.HE},\n```\n- Provide the `url` field whenever possible. If a DOI has been issued by the\npublisher, use `https://doi.org/` and also fill the `doi` field of the\nentry. Else, use the URL provided by the publisher.\n- Make sure to wrap strings in the BibTeX entries in `{}` when capitalization is\nimportant, or when BibTeX keywords should be ignored (e.g. `and` in author\nlists).\n- Spell out journal names directly instead of using LaTeX macros such as\n `\\apj` or `\\mnras`, since Doxygen does not expand those macros in the\n generated bibliography.\n\nTo cite an entry from the `docs/References.bib` file in the documentation, use\nthe Doxygen keyword\n\\verbatim\n\\cite\n\\endverbatim\nfollowed by the BibTeX key at the place in the documentation where you want the\ncitation to appear. It will render as a numbered link to the bibliography\npage. It will also show a popover when hovering over the link, which displays\nthe bibliographic information and provides quick access to the publication.\n\n## Include any pictures that aid in the understanding of your documentation:\n\nFirst, please compress your image to be under 130kB. As most images will be\ndiagrammatical in nature this is certainly achievable!\n\nSecond, add the directory that will contain your image to the `docs/Images/`\ndirectory. Create the appropriate directories such that the directory structure\nin `docs/Images` matches that of `src` and `tests/Unit`.\n\nFinally, include the image by using the Doxygen keyword\n\n\\verbatim\n\\image html NameOfImage.png\n\\endverbatim\n\nin your hpp file.\n\n# Python Documentation {#writing_dox_python_dox_help}\n\nDocStrings...\n" }, { "path": "docs/DevGuide/WritingTests.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Writing Unit Tests {#writing_unit_tests}\n\n\\tableofcontents\n\nUnit tests are placed in the appropriate subdirectory of `tests/Unit`, which\nmirrors the directory hierarchy of `src`. Typically there should be one test\nexecutable for each production code library. For example,\nwe have a `DataStructures` library and a `Test_DataStructures` executable. When\nadding a new test there are several scenarios that can occur, which are outlined\nbelow.\n\n- You are adding a new source file to an existing test library:
\n If you are adding a new source file in a directory that already has a\n `CMakeLists.txt` simply create the source file, which should be named\n `Test_ProductionCodeFileBeingTest.cpp` and add that to the `LIBRARY_SOURCES`\n in the `CMakeLists.txt` file in the same directory you are adding the `cpp`\n file.
\n If you are adding a new source file to a library but want to place it in a\n subdirectory you must first create the subdirectory. To provide a concrete\n example, say you are adding the directory `TensorEagerMath` to\n `tests/Unit/DataStructures`. After creating the directory you must add a call\n to `add_subdirectory(TensorEagerMath)` to\n `tests/Unit/DataStructures/CMakeLists.txt` *before* the call to\n `add_test_library` and *after* the `LIBRARY_SOURCES` are set. Next add the\n file `tests/Unit/DataStructures/TensorEagerMath/CMakeLists.txt`, which should\n add the new source files by calling `set`, e.g.\n ```\n set(LIBRARY_SOURCES\n ${LIBRARY_SOURCES}\n Test_ProductionCodeFileBeingTest.cpp\n PARENT_SCOPE)\n ```\n The `PARENT_SCOPE` flag tells CMake to make the changes visible in the\n CMakeLists.txt file that called `add_subdirectory`. You can now add the\n `Test_ProductionCodeFileBeingTested.cpp` source file.\n- You are adding a new directory:
\n If the directory is a new lowest level directory you must add a\n `add_subdirectory` call to `tests/Unit/CMakeLists.txt`. If it is a new\n subdirectory you must add a `add_subdirectory` call to the\n `CMakeLists.txt` file in the directory where you are adding the\n subdirectory. Next you should read the part on adding a new test library.\n- You are adding a new test library:
\n After creating the subdirectory for the new test library you must add a\n `CMakeLists.txt` file. See `tests/Unit/DataStructures/CMakeLists.txt` for\n an example of one. The `LIBRARY` and `LIBRARY_SOURCES` variables set the name\n of the test library and the source files to be compiled into it. The library\n name should be of the format `Test_ProductionLibraryName`, for example\n `Test_DataStructures`. The library sources should be only the source files in\n the current directory. The `add_subdirectory` command can be used to add\n source files in subdirectories to the same library as is done in\n `tests/Unit/CMakeLists.txt`. The `CMakeLists.txt` in\n `tests/Unit/DataStructures/TensorEagerMath` is an example of how to add source\n files to a library from a subdirectory of the library. Note that the setting\n of `LIBRARY_SOURCES` here first includes the current `LIBRARY_SOURCES` and at\n the end specifies `PARENT_SCOPE`. The `PARENT_SCOPE` flag tells CMake to\n modify the variable in a scope that is visible to the parent directory,\n i.e. the `CMakeLists.txt` that called `add_subdirectory`.
\n Finally, in the `CMakeLists.txt` of your new library you must call\n `add_test_library`. Again, see `tests/Unit/DataStructures/CMakeLists.txt` for\n an example. The `add_test_library` function adds a test executable with the\n name of the first argument and the source files of the third argument.\n Remember to use `target_link_libraries` to link any libraries your test\n executable uses (see \\ref spectre_build_system).\n\nAll tests must start with\n```cpp\n// Distributed under the MIT License.\n// See LICENSE.txt for details.\n\n#include \"Framework/TestingFramework.hpp\"\n```\nThe file `tests/Unit/Framework/TestingFramework.hpp` must always be the first\ninclude in the test file and must be separated from the STL includes by a blank\nline. All classes and free functions should be in an anonymous/unnamed\nnamespace, e.g.\n```cpp\nnamespace {\nclass MyFreeClass {\n /* ... */\n};\n\nvoid my_free_function() {\n /* ... */\n}\n} // namespace\n```\nThis is necessary to avoid symbol redefinition errors during linking.\n\nTest cases are added by using the `SPECTRE_TEST_CASE` macro. The first argument\nto the macro is the test name, e.g. `\"Unit.DataStructures.Tensor\"`, and the\nsecond argument is a list of tags. The tags list is a string where each element\nis in square brackets. For example, `\"[Unit][DataStructures]\"`. The tags should\nonly be the type of test, in this case `Unit`, and the library being tested, in\nthis case `DataStructures`. The `SPECTRE_TEST_CASE` macro should be treated as a\nfunction, which means that it should be followed by `{ /* test code */ }`. For\nexample,\n\\snippet Test_Tensor.cpp example_spectre_test_case\nFrom within a `SPECTRE_TEST_CASE` you are able to do all the things you would\nnormally do in a C++ function, including calling other functions, setting\nvariables, using lambdas, etc.\n\nThe `CHECK` macro in the above example is provided by\n[Catch2](https://github.com/catchorg/Catch2) and is used to check conditions. We\nalso provide the `CHECK_ITERABLE_APPROX` macro which checks if two `double`s or\ntwo iterable containers of `double`s are approximately\nequal. `CHECK_ITERABLE_APPROX` is especially useful for comparing `Tensor`s,\n`DataVector`s, and `Tensor`s since it will iterate over nested\ncontainers as well.\n\n\\warning Catch's `CHECK` statement only prints numbers out to approximately 10\ndigits at most, so you should generally prefer `CHECK_ITERABLE_APPROX` for\nchecking double precision numbers, unless you want to check that two numbers are\nbitwise identical.\n\nAll unit tests must finish within a few seconds, the hard limit is 5, but having\nunit tests that long is strongly discouraged. They should typically complete in\nless than half a second. Tests that are longer are often no longer testing a\nsmall enough unit of code and should either be split into several unit tests or\nmoved to an integration test.\n\n#### Discovering New and Renamed Tests\n\nWhen you add a new test to a source file or rename an existing test the change\nneeds to be discovered by the testing infrastructure. This is done by building\nthe target `rebuild_cache`, e.g. by running `make rebuild_cache`.\n\n#### Testing Pointwise Functions\n\nPointwise functions should generally be tested in two different ways. The first\nis by taking input from an analytic solution and checking that the computed\nresult is correct. The second is to use the random number generation comparison\nwith Python infrastructure. In this approach the C++ function being tested is\nre-implemented in Python and the results are compared. Please follow these\nguidelines:\n\n- The Python implementation should be in a file with the same name as the source\n file that is being re-implemented and placed in the same directory as its\n corresponding `Test_*.cpp` source file.\n- The functions should have the same names as the C++ functions they\n re-implement.\n- If a function does sums over tensor indices then\n [`numpy.einsum`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.einsum.html)\n should be used in Python to provide an alternative implementation of the loop\n structure.\n- You can import Python functions from other re-implementations in the\n `tests/Unit/` directory to reduce code duplication. Note that the path you\n pass to `pypp::SetupLocalPythonEnvironment` determines the directory from\n which you can import Python modules. Either import modules directly from the\n `tests/Unit/` directory (e.g. `import\n PointwiseFunction.GeneralRelativity.Christoffel as christoffel`) or use\n relative imports like `from . import Christoffel as christoffel`. Don't assume\n the Python environment is set up in a subdirectory of `tests/Unit/`.\n\nIt is possible to test C++ functions that return by value and ones that return\nby `gsl::not_null`. In the latter case, since it is possible to return multiple\nvalues, one Python function taking all non-`gsl::not_null` arguments must be\nsupplied for each `gsl::not_null` argument to the C++. To perform the test the\n`pypp::check_with_random_values()` function must be called. For example, the\nfollowing checks various C++ functions by calling into `pypp`:\n\n\\snippet Test_PyppRandomValues.cpp cxx_two_not_null\n\nThe corresponding Python functions are:\n\n\\snippet PyppPyTests.py python_two_not_null\n\n#### Writing and Fixing Random-Value Based Tests\n\nMany tests in SpECTRE make use of randomly generated numbers in order to\nincrease the parameter space covered by the tests. The random number generator\nis set up using:\n```cpp\nMAKE_GENERATOR(gen);\n```\nThe generator `gen` can then be passed to distribution classes such as\n`std::uniform_real_distribution` or `UniformCustomDistribution`.\n\nEach time the test is run, a different random seed will be used. When writing a\ntest that uses random values, it is good practice to run the test at least\n\\f$10^4\\f$ times in order to set any tolerances on checks used in the test.\nThis can be done by using the following command in the build directory\n(SPECTRE_BUILD_DIR):\n```\nctest --repeat-until-fail 10000 -R TEST_NAME\n```\nwhere `TEST_NAME` is the test name passed to `SPECTRE_TEST_CASE`\n(e.g. `Unit.Evolution.Systems.CurvedScalarWave.Characteristics`).\n\nIf a test case fails when using a random number generated by `MAKE_GENERATOR`,\nas part of the output from the failed test will be the text\n```\nSeed is: SEED from FILE_NAME:LINE_NUMBER\n```\nNote that the output of tests can be found in\n`SPECTRE_BUILD_DIR/Testing/Temporary/LastTest.log`\n\nThe failing test case can then be reproduced by changing `MAKE_GENERATOR` call\nat the provided line in the given file to\n```cpp\nMAKE_GENERATOR(gen, SEED);\n```\nIf the `MAKE_GENERATOR` is within `CheckWithRandomValues.hpp`, the failing test\ncase most likely has occurred within a call to\n`pypp::check_with_random_values()`. In such a case, additional information\nshould have been printed to help you determine which call to\n`pypp::check_with_random_values()` has failed. The critical information is\nthe line\n```\nfunction: FUNCTION_NAME\n```\nwhere `FUNCTION_NAME` should correspond to the third argument of a call to\n`pypp::check_with_random_values()`. The seed that caused the test to fail can\nthen be passed as an additional argument to `pypp::check_with_random_values()`,\nwhere you may also need to pass in the default value of the comparison\ntolerance.\n\nTypically, you will need to adjust a tolerance used in a `CHECK` somewhere in\nthe test in order to get the test to succeed reliably. The function\n`pypp::check_with_random_values()` takes an argument that specifies the lower\nand upper bounds of random quantities. Typically these should be chosen to be\nof order unity in order to decrease the chance of occasionally generating large\nnumbers through multiplications which can cause an error above a reasonable\ntolerance.\n\n#### Testing Failure Cases {#testing_failure_cases}\n\n`ASSERT`s and `ERROR`s can be tested with the `CHECK_THROWS_WITH`\nmacro. This macro takes two arguments: the first is either an\nexpression or a lambda that is expected to trigger an exception (which\nnow are thrown by `ASSERT` and `ERROR` (Note: You may need to add `()`\nwrapping the lambda in order for it to compile.); the second is a\nCatch Matcher (see [Catch2](https://github.com/catchorg/Catch2) for\ncomplete documentation), usually a\n`Catch::Matchers::ContainsSubstring()` macro that matches a substring\nof the error message of the thrown exception.\n\nWhen testing `ASSERT`s the `CHECK_THROWS_WITH`\nshould be enclosed between `#%ifdef SPECTRE_DEBUG` and an `#%endif`\nIf the `#%ifdef SPECTRE_DEBUG` block is omitted then compilers will\ncorrectly flag the code as being unreachable which results in\nwarnings.\n\nAdding the \"attribute\" `// [[OutputRegex, Regular expression to match]]`\nbefore the `SPECTRE_TEST_CASE` macro will force ctest to only pass the\nparticular test if the regular expression is found in the output of the\ntest. In this case, the first line of the test should call the macro\n`OUTPUT_TEST();`.\n\n### Testing Actions\n\nThe action testing framework is documented as part of the `ActionTesting`\nnamespace.\n\n## Input file tests\n\nWe have a suite of input file tests in addition to unit tests. Every input file\nin the `tests/InputFiles/` directory is added to the test suite automatically.\nIf you don't want your input file tested at all, add the relative input file\npath to the whitelist in `cmake/AddInputFileTests.cmake`. If the input file is\nbeing tested, it must specify the `Executable` it should run with in the input\nfile metadata (above the `---` marker in the input file). Properties of the test\nare controlled by the `Testing` section in the input file metadata. The\nfollowing properties are available:\n\n- `Check`: Semicolon-separated list of checks, e.g. `parse;execute`. The\n following checks are available:\n - `parse`: Just check that the input file passes option parsing.\n - `execute`: Run the executable. If the input file metadata has an\n `ExpectedOutput` field, check that these files have been written. See\n `spectre.tools.CleanOutput` for details.\n - `execute_check_output`: In additional to `execute`, check the contents of\n some output files. The checks are defined by the `OutputFileChecks` in the\n input file metadata. See `spectre.tools.CheckOutputFiles` for details.\n- `CommandLineArgs` (optional): Additional command-line arguments passed to the\n executable.\n- `ExpectedExitCode` (optional): The expected exit code of the executable.\n Default: `0`. See `Parallel::ExitCode` for possible exit codes.\n- `Timeout` (optional): Timeout for the test. Default: 2 seconds.\n- `Priority` (optional): Priority of running this test on CI. Possible values\n are: `low` (not usually run on CI), `normal` (run at least once on CI), `high`\n (run always on CI). Default: `normal`.\n" }, { "path": "docs/Doxyfile.in", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Last updated for Doxygen 1.9.1\n# See https://www.doxygen.nl/manual/config.html\n# for documentation on the commands in this file.\n\n#---------------------------------------------------------------------------\n# Project related configuration options\n#---------------------------------------------------------------------------\n\nPROJECT_NAME = SpECTRE\n\nPROJECT_NUMBER = @SPECTRE_VERSION@\n\nOUTPUT_DIRECTORY = @PROJECT_BINARY_DIR@/docs\n\nSTRIP_FROM_PATH = @PROJECT_SOURCE_DIR@\n\nJAVADOC_AUTOBRIEF = YES\n\nMULTILINE_CPP_IS_BRIEF = YES\n\nTAB_SIZE = 2\n\nALIASES = \"spectreversion=@SPECTRE_VERSION@\" \\\n \"spectredoi=@SPECTRE_DOI@\" \\\n \"spectrezenodoid=@SPECTRE_ZENODO_ID@\" \\\n \"semantics=

Semantics:\" \\\n \"metareturns=

Returns: \" \\\n \"return=

Returns: \" \\\n \"requires=

Requires: \" \\\n \"effects=

Effects: \" \\\n \"synchronization=

Synchronization: \" \\\n \"postconditions=

Postconditions: \" \\\n \"returns=

Returns: \" \\\n \"throws=

Throws: \" \\\n \"complexity=

Complexity: \" \\\n \"remarks=

Remarks: \" \\\n \"errorconditions=

Error Conditions: \" \\\n \"notes=

Notes: \" \\\n \"details=

Details

\" \\\n \"usage=

Usage

\" \\\n \"example=

Example

\" \\\n \"derivedrequires=

Derived Class Requires:\"\n\nDISTRIBUTE_GROUP_DOC = YES\n\nSUBGROUPING = YES\n\n#---------------------------------------------------------------------------\n# Build related configuration options\n#---------------------------------------------------------------------------\n\nEXTRACT_ALL = NO\n\nEXTRACT_PRIVATE = NO\n\nEXTRACT_STATIC = NO\n\nEXTRACT_LOCAL_CLASSES = NO\n\n# We want to be able to have undocumented members, such as size() that show\n# up but what they do is rather obvious.\nWARN_IF_UNDOCUMENTED = NO\n\nCASE_SENSE_NAMES = YES\n\nGENERATE_TODOLIST = NO\n\nGENERATE_TESTLIST = NO\n\nGENERATE_BUGLIST = NO\n\nSTRIP_CODE_COMMENTS = NO\n\nSHOW_FILES = NO\n\nSHOW_USED_FILES = YES\n\nVERBATIM_HEADERS = NO\n\nCITE_BIB_FILES = @PROJECT_SOURCE_DIR@/docs/References.bib \\\n @PROJECT_SOURCE_DIR@/docs/Dependencies.bib\n\n#---------------------------------------------------------------------------\n# configuration options related to the input files\n#---------------------------------------------------------------------------\n\n# Add the documentation pages in the order they should appear in the tree view.\n# Use `\\subpage` within the pages to establish a hierarchy.\n# - We also pick up notebooks converted to markdown by the\n# `doc-notebooks-to-markdown` target (see `cmake/SetupDoxygen.cmake` for\n# details).\n# - The changelog is generated by CI (see `.github/workflows/Tests.yaml`)\nINPUT = @PROJECT_SOURCE_DIR@/docs/Installation \\\n @PROJECT_SOURCE_DIR@/docs/Tutorials \\\n @PROJECT_SOURCE_DIR@/docs/Examples \\\n @PROJECT_SOURCE_DIR@/docs/Contributing \\\n @PROJECT_SOURCE_DIR@/docs/DevGuide \\\n @PROJECT_SOURCE_DIR@/docs/Gallery.md \\\n @PROJECT_SOURCE_DIR@/docs/PublicationPolicy.md \\\n @PROJECT_SOURCE_DIR@/docs/Changelog.md \\\n @PROJECT_SOURCE_DIR@/docs \\\n @CMAKE_BINARY_DIR@/docs/tmp/notebooks_md \\\n @SPECTRE_DOXYGEN_GROUPS@ \\\n @PROJECT_SOURCE_DIR@/src \\\n @PROJECT_SOURCE_DIR@/tests/Unit/Framework \\\n @PROJECT_SOURCE_DIR@/tests/Unit/Helpers\n\nUSE_MDFILE_AS_MAINPAGE = @PROJECT_SOURCE_DIR@/docs/Main.md\n\n# We don't parse cpp files because Doxygen has trouble with some template\n# expressions and we place documentation in header files anyway.\nFILE_PATTERNS = *.hpp \\\n *.md\n\nRECURSIVE = YES\n\nEXCLUDE =\n\nEXCLUDE_SYMLINKS = NO\n\nEXCLUDE_PATTERNS =\n\nEXCLUDE_SYMBOLS = charm_init_* \\\n *detail* \\\n PUP* \\\n SPECTRE_TEST_CASE* \\\n std* \\\n YAML*\n\nEXAMPLE_PATH = @PROJECT_SOURCE_DIR@/tests/ \\\n @PROJECT_SOURCE_DIR@/src/Executables/Examples/ \\\n @PROJECT_SOURCE_DIR@/support/DevEnvironments/spack.yaml \\\n @PROJECT_SOURCE_DIR@/support/Python/dev_requirements.txt \\\n @PROJECT_SOURCE_DIR@/support/Python/requirements.txt \\\n @PROJECT_SOURCE_DIR@/citation.bib\n\nEXAMPLE_PATTERNS =\n\nEXAMPLE_RECURSIVE = NO\n\n# Input filters run over content before it is parsed by Doxygen. They are\n# invoked with a file name as additional argument. We run the following filters:\n# - Format markdown math for Doxygen. See the documentation in\n# `markdown-math-filter.pl` for details.\nINPUT_FILTER = \"@PERL_EXECUTABLE@ -0777 -p @PROJECT_SOURCE_DIR@/docs/config/markdown-math-filter.pl\"\n\n#---------------------------------------------------------------------------\n# configuration options related to the output\n#---------------------------------------------------------------------------\n\nGENERATE_HTML = @SPECTRE_DOX_GENERATE_HTML@\n\nHTML_HEADER = @PROJECT_SOURCE_DIR@/docs/config/header.html\n\nHTML_FOOTER = @PROJECT_SOURCE_DIR@/docs/config/footer.html\n\nIMAGE_PATH = @PROJECT_SOURCE_DIR@/docs/ \\\n @CMAKE_BINARY_DIR@/docs/tmp/notebooks_md\n\nGENERATE_LATEX = NO\n\nGENERATE_RTF = NO\n\nGENERATE_XML = @SPECTRE_DOX_GENERATE_XML@\n\nXML_OUTPUT = xml\n\n#---------------------------------------------------------------------------\n# Configuration options related to the preprocessor\n#---------------------------------------------------------------------------\n\nENABLE_PREPROCESSING = YES\n\nMACRO_EXPANSION = YES\n\n# Macros we actually want to expand during preprocessing\nEXPAND_AS_DEFINED = MAKE_BINARY_FUNCTIONAL \\\n MAKE_BINARY_INPLACE_OPERATOR \\\n MAKE_BINARY_OPERATOR \\\n MAKE_UNARY_FUNCTIONAL\n\nEXPAND_ONLY_PREDEF = YES\n\nSEARCH_INCLUDES = YES\n\nPREDEFINED = SPECTRE_ALWAYS_INLINE= \\\n OVERLOADER_CONSTEXPR= \\\n SPECTRE_DOXYGEN_INVOKED \\\n SPECTRE_AUTODIFF\n\n#---------------------------------------------------------------------------\n# Configuration::additions related to external references\n#---------------------------------------------------------------------------\n\n# The tag file for cppref can be updated as new features are added to the\n# standard library and to C++ by cloning\n# https://github.com/p12tic/cppreference-doc (if that is no longer\n# available there is a fork available at\n# https://github.com/nilsdeppe/cppreference-doc), entering the directory\n# and running `make doc_doxygen`. The up-to-date tag file is place in the\n# `output` subdirectory and can then be copied into the SpECTRE repo\nTAGFILES += \"@PROJECT_SOURCE_DIR@/docs/config/cppreference-doxygen-web.tag.xml=http://en.cppreference.com/w/\"\n\nALLEXTERNALS = NO\n\n#---------------------------------------------------------------------------\n# Configuration options related to the dot tool\n#---------------------------------------------------------------------------\n\nHAVE_DOT = NO\n\nCLASS_GRAPH = NO\n\nCOLLABORATION_GRAPH = NO\n\nGROUP_GRAPHS = NO\n\nUML_LOOK = NO\n\nTEMPLATE_RELATIONS = NO\n\nINCLUDE_GRAPH = NO\n\nINCLUDED_BY_GRAPH = NO\n\nCALL_GRAPH = NO\n\nCALLER_GRAPH = NO\n\nGRAPHICAL_HIERARCHY = NO\n\nDIRECTORY_GRAPH = NO\n\nDOT_IMAGE_FORMAT = svg\n\nMAX_DOT_GRAPH_DEPTH = 0\n\nGENERATE_LEGEND = NO\n\n#---------------------------------------------------------------------------\n# HTML layout file\n#---------------------------------------------------------------------------\n\nLAYOUT_FILE = @DOXYGEN_LAYOUT_FILE@\n\nHTML_EXTRA_FILES = @PROJECT_SOURCE_DIR@/docs/config/icons/octicons.eot \\\n @PROJECT_SOURCE_DIR@/docs/config/icons/octicons.svg \\\n @PROJECT_SOURCE_DIR@/docs/config/icons/octicons.ttf \\\n @PROJECT_SOURCE_DIR@/docs/config/icons/octicons.woff \\\n @PROJECT_SOURCE_DIR@/docs/config/octicons.css \\\n @PROJECT_SOURCE_DIR@/docs/config/doxygen-awesome-fragment-copy-button.js \\\n @PROJECT_SOURCE_DIR@/docs/config/doxygen-awesome-interactive-toc.js \\\n @PROJECT_SOURCE_DIR@/docs/config/doxygen-awesome-paragraph-link.js \\\n @PROJECT_SOURCE_DIR@/docs/config/js/spectre.js \\\n @PROJECT_SOURCE_DIR@/docs/config/apple-touch-icon.png \\\n @PROJECT_SOURCE_DIR@/docs/config/favicon-16x16.png \\\n @PROJECT_SOURCE_DIR@/docs/config/favicon-32x32.png \\\n @PROJECT_SOURCE_DIR@/docs/config/favicon.ico \\\n @PROJECT_SOURCE_DIR@/docs/config/safari-pinned-tab.svg \\\n @PROJECT_SOURCE_DIR@/docs/.nojekyll \\\n @PROJECT_SOURCE_DIR@/docs/config/MathJax.js \\\n @PROJECT_SOURCE_DIR@/docs/Images/banner.png \\\n @PROJECT_SOURCE_DIR@/LICENSE.txt\n\nGENERATE_TREEVIEW = YES\n\n# This width must correspond to `side-nav-fixed-width` in `custom.css`\nTREEVIEW_WIDTH = 280\n\nHTML_EXTRA_STYLESHEET = @PROJECT_SOURCE_DIR@/docs/config/doxygen-awesome.css \\\n @PROJECT_SOURCE_DIR@/docs/config/doxygen-awesome-sidebar-only.css \\\n @PROJECT_SOURCE_DIR@/docs/config/custom.css\n\nHTML_COLORSTYLE_HUE = 209\nHTML_COLORSTYLE_SAT = 255\nHTML_COLORSTYLE_GAMMA = 113\n\nUSE_MATHJAX = YES\n\n# MATHJAX_RELPATH ultimately links to docs/config/MathJax.js, which is\n# copied to docs/html/MathJax.js with the HTML_EXTRA_FILES\nMATHJAX_RELPATH = ./\n\n# Since Doxygen doesn't support MathJax 3 yet, we configure all the\n# extensions/packages through the docs/config/MathJax.js file.\nMATHJAX_EXTENSIONS =\n\nMATHJAX_CODEFILE =\n\n#---------------------------------------------------------------------------\n# Configuration::additions related to the search engine\n#---------------------------------------------------------------------------\n\nSEARCHENGINE = YES\n" }, { "path": "docs/Examples/BbhInitialData/.gitignore", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n*.yaml\n*.h5\n" }, { "path": "docs/Examples/BbhInitialData/BbhInitialData.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Binary black hole initial data {#example_bbh_id}\\n\",\n \"\\n\",\n \"In this example we run the elliptic solver to compute initial data for binary\\n\",\n \"black holes.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Distributed under the MIT License.\\n\",\n \"# See LICENSE.txt for details.\\n\",\n \"\\n\",\n \"# Dependencies:\\n\",\n \"%pip install numpy matplotlib pandas 'h5py>=3.0.0' ruamel.yaml\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import h5py\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import multiprocessing\\n\",\n \"import numpy as np\\n\",\n \"import os\\n\",\n \"import pandas as pd\\n\",\n \"from ruamel.yaml import YAML\\n\",\n \"\\n\",\n \"plt.style.use(\\\"../plots.mplstyle\\\")\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"%%bash\\n\",\n \"# Clean up output files from previous runs\\n\",\n \"rm -f Bbh*.h5\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"First, make sure you have compiled the `SolveXcts` executable. Put in the path\\n\",\n \"to your build directory below. Make sure you have compiled in `Release` mode.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"SPECTRE_BUILD_DIR = \\\"/Users/nlf/Work/spectre/build-Default-Release\\\"\\n\",\n \"SPECTRE_HOME = \\\"/Users/nlf/Projects/spectre/develop\\\"\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"\\n\",\n \"## Setup input file\\n\",\n \"\\n\",\n \"We set up an input file based on the\\n\",\n \"`tests/InputFiles/Xcts/BinaryBlackHole.yaml` example:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Load example input file\\n\",\n \"load_input_file_path = os.path.join(\\n\",\n \" SPECTRE_HOME, \\\"tests/InputFiles/Xcts/BinaryBlackHole.yaml\\\"\\n\",\n \")\\n\",\n \"yaml = YAML()\\n\",\n \"with open(load_input_file_path, \\\"r\\\") as open_input_file:\\n\",\n \" input_file = yaml.load(open_input_file)\\n\",\n \"\\n\",\n \"# Modify example input file\\n\",\n \"# - Set output file names\\n\",\n \"input_file[\\\"Observers\\\"][\\\"VolumeFileName\\\"] = \\\"BbhVolume\\\"\\n\",\n \"input_file[\\\"Observers\\\"][\\\"ReductionFileName\\\"] = \\\"BbhReductions\\\"\\n\",\n \"\\n\",\n \"# Write modified input file\\n\",\n \"with open(\\\"Bbh.yaml\\\", \\\"w\\\") as open_input_file:\\n\",\n \" yaml.dump(input_file, open_input_file)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Run executable\\n\",\n \"\\n\",\n \"We pass the input file to the `SolveXcts` executable to solve the elliptic\\n\",\n \"problem. It will take a few minutes to complete on ~10 cores. Adapt the command\\n\",\n \"below to your system, or run the `SolveXcts` executable with the `Bbh.yaml`\\n\",\n \"input file manually.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Charm++: standalone mode (not using charmrun)\\n\",\n \"Charm++> Running in Multicore mode: 12 threads (PEs)\\n\",\n \"Converse/Charm++ Commit ID: v6.10.2-0-g7bf00fa\\n\",\n \"Warning> Randomization of virtual memory (ASLR) is turned on in the kernel, thread migration may not work! Run 'echo 0 > /proc/sys/kernel/randomize_va_space' as root to disable it, or try running with '+isomalloc_sync'.\\n\",\n \"CharmLB> Load balancer assumes all CPUs are same.\\n\",\n \"Charm++> Running on 1 hosts (12 sockets x 1 cores x 1 PUs = 12-way SMP)\\n\",\n \"Charm++> cpu topology info is gathered in 0.002 seconds.\\n\",\n \"\\n\",\n \"Executing '/Users/nlf/Work/spectre/build-Default-Release/bin/SolveXcts' using 12 processors.\\n\",\n \"Charm++ startup time in seconds: 3.621687\\n\",\n \"Date and time at startup: Tue Feb 22 15:08:18 2022\\n\",\n \"\\n\",\n \"SpECTRE Build Information:\\n\",\n \"Version: 2022.02.17\\n\",\n \"Compiled on host: 98c21919c2ac\\n\",\n \"Compiled in directory: /Users/nlf/Work/spectre/build-Default-Release\\n\",\n \"Source directory is: /Users/nlf/Projects/spectre/develop\\n\",\n \"Compiled on git branch: xcts_input_files\\n\",\n \"Compiled on git revision: db7100f700b\\n\",\n \"Linked on: Thu Jan 27 17:45:20 2022\\n\",\n \"\\n\",\n \"The following options differ from their suggested values:\\n\",\n \"\\n\",\n \"Option parsing completed.\\n\",\n \"Multigrid level 0 has 232 elements in 54 blocks distributed on 12 procs.\\n\",\n \"Multigrid level 1 has 54 elements in 54 blocks distributed on 12 procs.\\n\",\n \"NewtonRaphson initialized with residual: 1.058476e+01\\n\",\n \"Gmres initialized with residual: 1.058476e+01\\n\",\n \"Gmres(1) iteration complete. Remaining residual: 2.003738e-01\\n\",\n \"Gmres(2) iteration complete. Remaining residual: 1.206809e-01\\n\",\n \"Gmres(3) iteration complete. Remaining residual: 8.694367e-02\\n\",\n \"Gmres(4) iteration complete. Remaining residual: 7.275577e-02\\n\",\n \"Gmres(5) iteration complete. Remaining residual: 4.520779e-02\\n\",\n \"Gmres(6) iteration complete. Remaining residual: 1.464362e-02\\n\",\n \"Gmres(7) iteration complete. Remaining residual: 6.754772e-03\\n\",\n \"Gmres has converged in 7 iterations: RelativeResidual - The residual magnitude has decreased to a fraction of 0.001 of its initial value or below (0.00063816).\\n\",\n \"NewtonRaphson(1) iteration complete (0 globalization steps, step length 1). Remaining residual: 2.865222e+00\\n\",\n \"Gmres initialized with residual: 2.865222e+00\\n\",\n \"Gmres(1) iteration complete. Remaining residual: 4.062729e-02\\n\",\n \"Gmres(2) iteration complete. Remaining residual: 2.455538e-02\\n\",\n \"Gmres(3) iteration complete. Remaining residual: 1.602018e-02\\n\",\n \"Gmres(4) iteration complete. Remaining residual: 1.181106e-02\\n\",\n \"Gmres(5) iteration complete. Remaining residual: 5.591212e-03\\n\",\n \"Gmres(6) iteration complete. Remaining residual: 2.012421e-03\\n\",\n \"Gmres has converged in 6 iterations: RelativeResidual - The residual magnitude has decreased to a fraction of 0.001 of its initial value or below (0.000702361).\\n\",\n \"NewtonRaphson(2) iteration complete (0 globalization steps, step length 1). Remaining residual: 8.164886e-03\\n\",\n \"Gmres initialized with residual: 8.164886e-03\\n\",\n \"Gmres(1) iteration complete. Remaining residual: 1.279278e-03\\n\",\n \"Gmres(2) iteration complete. Remaining residual: 7.680224e-04\\n\",\n \"Gmres(3) iteration complete. Remaining residual: 6.026001e-04\\n\",\n \"Gmres(4) iteration complete. Remaining residual: 5.116235e-04\\n\",\n \"Gmres(5) iteration complete. Remaining residual: 3.771227e-04\\n\",\n \"Gmres(6) iteration complete. Remaining residual: 1.521095e-04\\n\",\n \"Gmres(7) iteration complete. Remaining residual: 4.029530e-05\\n\",\n \"Gmres(8) iteration complete. Remaining residual: 1.632393e-05\\n\",\n \"Gmres(9) iteration complete. Remaining residual: 5.028700e-06\\n\",\n \"Gmres has converged in 9 iterations: RelativeResidual - The residual magnitude has decreased to a fraction of 0.001 of its initial value or below (0.000615893).\\n\",\n \"NewtonRaphson(3) iteration complete (0 globalization steps, step length 1). Remaining residual: 1.690461e-03\\n\",\n \"Gmres initialized with residual: 1.690461e-03\\n\",\n \"Gmres(1) iteration complete. Remaining residual: 6.584416e-06\\n\",\n \"Gmres(2) iteration complete. Remaining residual: 5.651935e-06\\n\",\n \"Gmres(3) iteration complete. Remaining residual: 5.288583e-06\\n\",\n \"Gmres(4) iteration complete. Remaining residual: 4.922907e-06\\n\",\n \"Gmres(5) iteration complete. Remaining residual: 4.250901e-06\\n\",\n \"Gmres(6) iteration complete. Remaining residual: 1.596286e-06\\n\",\n \"Gmres has converged in 6 iterations: RelativeResidual - The residual magnitude has decreased to a fraction of 0.001 of its initial value or below (0.00094429).\\n\",\n \"NewtonRaphson(4) iteration complete (0 globalization steps, step length 1). Remaining residual: 1.606242e-06\\n\",\n \"Gmres initialized with residual: 1.606242e-06\\n\",\n \"Gmres(1) iteration complete. Remaining residual: 7.008839e-07\\n\",\n \"Gmres(2) iteration complete. Remaining residual: 5.285042e-07\\n\",\n \"Gmres(3) iteration complete. Remaining residual: 4.919028e-07\\n\",\n \"Gmres(4) iteration complete. Remaining residual: 3.871318e-07\\n\",\n \"Gmres(5) iteration complete. Remaining residual: 1.603757e-07\\n\",\n \"Gmres(6) iteration complete. Remaining residual: 2.922369e-08\\n\",\n \"Gmres(7) iteration complete. Remaining residual: 1.438336e-08\\n\",\n \"Gmres(8) iteration complete. Remaining residual: 5.271254e-09\\n\",\n \"Gmres(9) iteration complete. Remaining residual: 2.125873e-09\\n\",\n \"Gmres(10) iteration complete. Remaining residual: 1.044162e-09\\n\",\n \"Gmres has converged in 10 iterations: RelativeResidual - The residual magnitude has decreased to a fraction of 0.001 of its initial value or below (0.000650065).\\n\",\n \"NewtonRaphson(5) iteration complete (0 globalization steps, step length 1). Remaining residual: 1.066508e-09\\n\",\n \"Gmres initialized with residual: 1.066508e-09\\n\",\n \"Gmres(1) iteration complete. Remaining residual: 8.000055e-10\\n\",\n \"Gmres(2) iteration complete. Remaining residual: 5.991477e-10\\n\",\n \"Gmres(3) iteration complete. Remaining residual: 4.073811e-10\\n\",\n \"Gmres(4) iteration complete. Remaining residual: 2.559880e-10\\n\",\n \"Gmres(5) iteration complete. Remaining residual: 1.242268e-10\\n\",\n \"Gmres(6) iteration complete. Remaining residual: 3.521815e-11\\n\",\n \"Gmres has converged in 6 iterations: AbsoluteResidual - The residual magnitude has decreased to 1e-10 or below (3.52181e-11).\\n\",\n \"NewtonRaphson(6) iteration complete (0 globalization steps, step length 1). Remaining residual: 3.589802e-11\\n\",\n \"NewtonRaphson has converged in 6 iterations: AbsoluteResidual - The residual magnitude has decreased to 1e-10 or below (3.5898e-11).\\n\",\n \"\\n\",\n \"Done!\\n\",\n \"Wall time in seconds: 769.172052\\n\",\n \"Date and time at completion: Tue Feb 22 15:21:03 2022\\n\",\n \"\\n\",\n \"[Partition 0][Node 0] End of program\\n\"\n ]\n }\n ],\n \"source\": [\n \"NUM_CORES = multiprocessing.cpu_count()\\n\",\n \"SOLVE_XCTS = os.path.join(SPECTRE_BUILD_DIR, \\\"bin/SolveXcts\\\")\\n\",\n \"!{SOLVE_XCTS} --input-file Bbh.yaml +p {NUM_CORES}\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Load initial data into evolutions\\n\",\n \"\\n\",\n \"The executable has created H5 output files with volume data and diagnostics:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"BbhReductions.h5 BbhVolume0.h5\\n\"\n ]\n }\n ],\n \"source\": [\n \"!ls *.h5\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The volume data in the `BbhVolume*.h5` files (one per node) can be imported into\\n\",\n \"evolution executables. It contains the following data:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/ Group\\n\",\n \"/VolumeData.vol Group\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626 Group\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/ConformalFactor Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/ExtrinsicCurvature_xx Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/ExtrinsicCurvature_yx Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/ExtrinsicCurvature_yy Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/ExtrinsicCurvature_zx Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/ExtrinsicCurvature_zy Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/ExtrinsicCurvature_zz Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/HamiltonianConstraint Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/InertialCoordinates_x Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/InertialCoordinates_y Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/InertialCoordinates_z Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/Lapse Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/MomentumConstraint_x Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/MomentumConstraint_y Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/MomentumConstraint_z Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/ShiftExcess_x Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/ShiftExcess_y Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/ShiftExcess_z Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/Shift_x Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/Shift_y Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/Shift_z Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/SpatialMetric_xx Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/SpatialMetric_yx Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/SpatialMetric_yy Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/SpatialMetric_zx Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/SpatialMetric_zy Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/SpatialMetric_zz Dataset {61344}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/bases Dataset {696}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/connectivity Dataset {294400}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/grid_names Dataset {5272}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/quadratures Dataset {696}\\n\",\n \"/VolumeData.vol/ObservationId1423324405707320626/total_extents Dataset {696}\\n\",\n \"/src.tar.gz Dataset {5307433}\\n\"\n ]\n }\n ],\n \"source\": [\n \"!h5ls -r BbhVolume*.h5\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"- `Lapse` ($\\\\alpha$), `Shift` ($\\\\beta^i$), `SpatialMetric` ($\\\\gamma_{ij}$) and\\n\",\n \" `ExtrinsicCurvature` ($K_{ij}$): These quantities solve the Einstein\\n\",\n \" constraint equations in \\\"corotating\\\" coordinates, such that, e.g.,\\n\",\n \" $\\\\partial_t K = 0$. The black holes remain approximately at the same\\n\",\n \" coordinate positions when starting to evolve the initial data in these\\n\",\n \" coordinates. Note that $\\\\beta^i \\\\propto r$ in these coordinates, which can be\\n\",\n \" large and hence numerically undesireable.\\n\",\n \"- `ShiftExcess` ($\\\\beta_\\\\text{excess}^i$): This shift vector excludes the\\n\",\n \" rotational part, so it is asymptotically small. Import `ShiftExcess` instead\\n\",\n \" of `Shift` in an evolution to obtain coordinates in which the black holes are\\n\",\n \" orbiting. Note that only\\n\",\n \" \\\\begin{equation}\\n\",\n \" \\\\beta^i = \\\\beta_\\\\text{background}^i + \\\\beta_\\\\text{excess}^i\\n\",\n \" \\\\end{equation}\\n\",\n \" fulfills all coordinate conditions imposed on the initial data, such as\\n\",\n \" $\\\\partial_t K = 0$. The background shift is typically\\n\",\n \" \\\\begin{equation}\\n\",\n \" \\\\beta_\\\\text{background}^i = \\\\epsilon^{ijk} \\\\Omega^{j} x^k + \\\\dot{a}_0 x^i\\n\",\n \" \\\\text{,}\\n\",\n \" \\\\end{equation}\\n\",\n \" where $\\\\Omega$ is the orbital angular velocity and $\\\\dot{a}_0$ is the\\n\",\n \" expansion parameter.\\n\",\n \" See the [Xcts::AnalyticData::Binary](https://spectre-code.org/classXcts_1_1AnalyticData_1_1Binary.html)\\n\",\n \" class for details.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Plot diagnostics\\n\",\n \"\\n\",\n \"We plot the diagnostics in `BbhReductions.h5` to see what happened during the\\n\",\n \"elliptic solve:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# These routines read the data and process them a bit. You can skip to the plot\\n\",\n \"# below to see the results.\\n\",\n \"\\n\",\n \"\\n\",\n \"def split_iteration_sequence(data):\\n\",\n \" left_bounds = np.where(data.index == 0)[0]\\n\",\n \" right_bounds = list(left_bounds[1:]) + [-1]\\n\",\n \" return [data.iloc[i:j] for i, j in zip(left_bounds, right_bounds)]\\n\",\n \"\\n\",\n \"\\n\",\n \"def load_dataset(subfile):\\n\",\n \" legend = subfile.attrs[\\\"Legend\\\"]\\n\",\n \" return pd.DataFrame(data=subfile, columns=legend).set_index(legend[0])\\n\",\n \"\\n\",\n \"\\n\",\n \"with h5py.File(\\\"BbhReductions.h5\\\", \\\"r\\\") as h5_file:\\n\",\n \" nonlinear_residuals = load_dataset(h5_file[\\\"NewtonRaphsonResiduals.dat\\\"])\\n\",\n \" all_linear_residuals = split_iteration_sequence(\\n\",\n \" load_dataset(h5_file[\\\"GmresResiduals.dat\\\"])\\n\",\n \" )\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": \"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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# Plot linear residuals\\n\",\n \"n = 0\\n\",\n \"lin_label = \\\"Linear residual\\\"\\n\",\n \"for linear_residuals in all_linear_residuals:\\n\",\n \" plt.semilogy(\\n\",\n \" linear_residuals.index + n,\\n\",\n \" linear_residuals[\\\"Residual\\\"]\\n\",\n \" / all_linear_residuals[0][\\\"Residual\\\"].iloc[0],\\n\",\n \" color=\\\"black\\\",\\n\",\n \" label=lin_label,\\n\",\n \" marker=\\\".\\\",\\n\",\n \" markersize=2.5,\\n\",\n \" zorder=30,\\n\",\n \" )\\n\",\n \" n += len(linear_residuals) - 1\\n\",\n \" lin_label = None\\n\",\n \"\\n\",\n \"# Plot nonlinear residuals\\n\",\n \"nonlin_xticks = [0] + list(\\n\",\n \" np.cumsum([len(l) - 1 for l in all_linear_residuals])\\n\",\n \")\\n\",\n \"plt.semilogy(\\n\",\n \" nonlin_xticks,\\n\",\n \" nonlinear_residuals[\\\"Residual\\\"] / nonlinear_residuals[\\\"Residual\\\"].iloc[0],\\n\",\n \" color=\\\"black\\\",\\n\",\n \" ls=\\\"dotted\\\",\\n\",\n \" marker=\\\".\\\",\\n\",\n \" label=\\\"Nonlinear residual\\\",\\n\",\n \" zorder=40,\\n\",\n \")\\n\",\n \"plt.xticks(nonlin_xticks)\\n\",\n \"xticks = (\\n\",\n \" range(len(all_linear_residuals))\\n\",\n \" if nonlinear_residuals is None\\n\",\n \" else nonlin_xticks\\n\",\n \")\\n\",\n \"\\n\",\n \"plt.xlabel(\\\"Cumulative linear solver iteration\\\")\\n\",\n \"plt.legend();\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The plot shows the convergence of the nonlinear solver (dotted line), along with\\n\",\n \"the convergence of the linear solver that runs in each nonlinear iteration\\n\",\n \"(solid line). A few things to note:\\n\",\n \"\\n\",\n \"- The residual converges down to almost machine precision, but that doesn't\\n\",\n \" reflect the discretization error of the solution. It only shows that we have\\n\",\n \" solved the discretized problem very accurately. To get an idea of the\\n\",\n \" discretization error we would have to look at quantities such as constraint\\n\",\n \" norms.\\n\",\n \"- The Newton-Raphson nonlinear solver converges slowly at first, and then begins\\n\",\n \" to converge quadratically once we are closer to the solution and hence the\\n\",\n \" linearization is more accurate.\\n\",\n \"- The linear solver needs only a few steps to converge, which is a feature of\\n\",\n \" our multigrid-Schwarz preconditioner.\\n\",\n \"\\n\",\n \"You can read more about the elliptic solver in this paper:\\n\",\n \"\\n\",\n \"- N. L. Vu _et al_., A scalable elliptic solver with task-based parallelism for\\n\",\n \" the SpECTRE numerical relativity code (2022),\\n\",\n \" [arXiv:2111.06767](https://arxiv.org/abs/2111.06767)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"interpreter\": {\n \"hash\": \"5c837ee96a6a314af6ca82ef816f2b1d9c1a2b96687b8bdeaa8036bfb18cb0dc\"\n },\n \"kernelspec\": {\n \"display_name\": \"Python 3.9.10 ('spectre')\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.9.10\"\n },\n \"orig_nbformat\": 4\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "docs/Examples/Examples.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Examples {#examples}\n\n- \\subpage example_bbh_id\n" }, { "path": "docs/Examples/plots.mplstyle", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Matplotlib style suitable for notebooks that get rendered in our documentation\n#\n# These settings configure matplotlib plots so they look good in our online\n# documentation, and have a consistent style. In a notebook, or when plotting\n# in a script, apply the style like this:\n#\n# import matplotlib.pyplot as plt\n# plt.style.use('path/to/plots.mplstyle')\n\nfigure.dpi: 150\nfigure.facecolor: white\n" }, { "path": "docs/Gallery.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n\\cond NEVER\nInstructions for adding images or videos:\n\n1. Send your media files to a SpECTRE core dev (see CONTRIBUTING.md for details\n and communication channels). They will place the files in this public Google\n Drive folder:\n https://drive.google.com/drive/folders/1xvLplF_pPlkADGfgFNaW_ByVATFv61m-\n2. Open the media files in Google Drive and get their file IDs. To do this,\n select [...] > Open in new window > Copy the in the URL of the form\n https://drive.google.com/file/d//view.\n3. Add a section to this page.\n - Embed images like this:\n &sz=w\"/>\n Replace with the width you want your image to have on the page.\n Google Drive will automatically provide an image of this size.\n - Embed videos like this:\n \\htmlonly\n \n \\endhtmlonly\n4. Open a pull request to contribute your changes (see CONTRIBUTING.md for\n details).\n\\endcond\n\n# Gallery {#gallery}\n\nThis page highlights some visualizations of SpECTRE simulations.\n\n\\note We're always happy to feature images and videos created by the SpECTRE\ncommunity on this page. See [this page on\nGitHub](https://github.com/sxs-collaboration/spectre/blob/develop/docs/Gallery.md)\nfor instructions.\n\n## Binary black hole mergers {#gallery_bbh}\n\nSpECTRE can simulate black holes that orbit each other and eventually merge,\nemitting gravitational waves.\nSpECTRE uses the Generalized Harmonic formulation of\nEinstein's equations of general relativity to solve this problem. Since we\nexpect the solution of Einstein's equations to be smooth for the BBH problem,\nwe represent our solution using the Discontinuous Galerkin (DG) method because\nof its ability to represent smooth functions to high accuracy. Also, DG allows\nSpECTRE to parallelize the BBH problem.\n\nPublications:\n\n- Lovelace, Nelli, et al. (2024). Simulating binary black hole mergers using\n discontinuous Galerkin methods. \\cite Lovelace2024wra\n\n\\htmlonly\n
\n\n
\nApparent horizons of an equal mass non-spinning BBH. The\ncolorful surface represents the lapse value in the equatorial plane and the\narrows depict the shift vector. Image credit: Alex Carpenter, CSUF\n
\n
\n\\endhtmlonly\n\n\\htmlonly\n
\n\n
\nOverview of a binary black hole simulation in SpECTRE. Upper left panel:\ncomputational grid and shape of black hole horizons during merger. A common\nhorizon has formed (blue) that envelops the two original horizons (black). Upper\nright panel: trajectories of the black holes until merger.\nThis inspiral is 18 orbits long and approximately circular.\nBottom panel: gravitational waveform extracted with CCE (see below).\nImage credit: Geoffrey Lovelace, CSUF\n
\n
\n\\endhtmlonly\n\n## Binary black hole initial data\n\nSpECTRE can generate initial data to start simulations of merging black holes.\nThis problem involves solving the elliptic constraint sector of the Einstein\nequations for a slice of spacetime that contains two black holes with the\nrequested parameters. SpECTRE uses the \\ref ::Xcts \"XCTS\" formulation with a\nnon-conformally-flat background defined by the\n\\ref ::Xcts::AnalyticData::Binary \"superposed\"\n\\ref gr::Solutions::KerrSchild \"Kerr-Schild\" formalism\nto reach high spins. Black holes are represented by excisions and\n\\ref ::Xcts::BoundaryConditions::ApparentHorizon \"boundary conditions\".\n\nPublications:\n\n- Vu et al. (2022). A scalable elliptic solver with task-based parallelism for\n the SpECTRE numerical relativity code. \\cite Vu2021coj\n- Vu (2024). A discontinuous Galerkin scheme for elliptic equations on\n extremely stretched grids. \\cite Vu2024cgf\n\n\\htmlonly\n
\n\n
\nAn initial slice of spacetime containing two black holes in orbit around each\nother. Shown is the lapse variable. The two black holes are represented as\nboundary conditions on excised regions of the computational domain.\nImage credit: Nils Vu, Caltech\n
\n
\n\\endhtmlonly\n\n## Cauchy-characteristic evolution (CCE) {#gallery_cce}\n\nSpECTRE implements a novel Cauchy-characteristic evolution (CCE) system for\nextracting gravitational waveforms from our simulations. It evolves the\nEinstein equations on null slices to infinity, which is more accurate than\nextrapolation and allows us to extract the gravitational memory effect.\nThe CCE waveform extraction is publicly available as a standalone module.\n\nTutorial:\n\n- \\ref tutorial_cce\n\nPublications:\n\n- Moxon et al. (2023). SpECTRE Cauchy-characteristic evolution system for rapid,\n precise waveform extraction. \\cite Moxon2021gbv\n- Moxon et al. (2020). Improved Cauchy-characteristic evolution system for\n high-precision numerical relativity waveforms. \\cite Moxon2020gha\n\n## Binary neutron star mergers\n\nSpECTRE can simulate merging neutron stars and other general-relativistic\nmagneto-hydrodynamic (GRMHD) problems with dynamic gravity. Our DG-FD hybrid\nscheme accelerates smooth regions of the grid with high-order spectral methods\n(see \\ref gallery_dgfd).\n\nPublications:\n\n- Deppe et al. (2024). Binary neutron star mergers using a discontinuous\n Galerkin-finite difference hybrid method. \\cite Deppe2024ckt\n\n\\htmlonly\n
\n\n
\nSimulation of two merging neutron stars. The colors show density contours.\nVideo credit: Nils Vu, Caltech\n
\n
\n\\endhtmlonly\n\n## Curved and moving meshes with control systems\n\nOur computational domains in SpECTRE are designed to adapt to the geometry of\nthe problems we want to solve. They can be curved, e.g. to wrap around excision\nregions in binary black hole problems (see \\ref gallery_bbh) or to resolve the\nwavezone in binary neutron star merger. They can also rotate and deform in time\nusing control systems, which reactively adjust coordinate maps to track the\nposition and shape of the black hole excisions or neutron stars.\n\n## Adaptive mesh refinement\n\nOur discontinuous Galerkin methods allow two types of mesh refinement: splitting\nelements in half along any dimension (h-refinement) or increasing their\npolynomial expansion order (p-refinement). The former allows us to distribute\ncomputational cost to supercomputers, while the latter allows us to use these\nresources efficiently by decreasing the numerical error exponentially with the\nnumber of grid points where the solution is smooth. Our adaptive mesh refinement\ntechnology decides which type of refinement to apply in each region of the\ndomain.\n\n## DG-FD hybrid method {#gallery_dgfd}\n\nOur hydrodynamical simulations use a discontinuous Galerkin-finite difference\n(DG-FD) hybrid method: smooth regions of the simulation are evolved with an\nefficient DG scheme and non-smooth regions fall back to a robust FD method.\nShocks and discontinuities on the grid are tracked with a troubled-cell\nindicator (TCI) to switch between DG and FD. This approach accelerates our\nsimulations by reducing the computational resources spent on smooth regions of\nthe grid, e.g. when evolving inspiral binary neutron stars and their\ngravitational radiation.\n\nPublications:\n\n- Deppe et al. (2022). A high-order shock capturing discontinuous\n Galerkin-finite difference hybrid method for GRMHD. \\cite Deppe2021ada\n- Deppe et al. (2022). Simulating magnetized neutron stars with discontinuous\n Galerkin methods. \\cite Deppe2021bhi\n\n\\htmlonly\n
\n\n
\nSimulation of the Kelvin-Helmholtz instability (KHI). Squares indicate cells\nthat have switched to a finite-difference method. They track shocks and\ndiscontinuities in the solution. The rest of the domain uses an efficient\nDG method.\nVideo credit: Nils Deppe, Cornell University\n
\n
\n\\endhtmlonly\n\n## Binary black holes in scalar Gauss-Bonnet gravity\n\nSpECTRE can generate initial data for binary black holes in scalar Gauss-Bonnet\ngravity, evolve the modified Einstein equations, and extract the gravitational\nand scalar radiation.\n\nPublications:\n\n- Nee et al. (2024). Quasistationary hair for binary black hole initial data in\n scalar Gauss-Bonnet gravity \\cite Nee2024bur\n- Lara et al. (2024). Scalarization of isolated black holes in scalar\n Gauss-Bonnet theory in the fixing-the-equations approach. \\cite Lara2024rwa\n\n\\htmlonly\n
\n\n
\nBinary black hole initial data in scalar Gauss-Bonnet gravity, in a\nconfiguration where the two black holes have opposite charge.\nThe scalar field is solved such that it is in equilibrium with the gravity\nbackground, minimizing initial transients in the evolution and giving control\nover the simulation parameters.\nImage credit: Peter James Nee, MPI for Gravitational Physics Potsdam, Germany\n
\n
\n\\endhtmlonly\n\n## Thermal noise in gravitational wave detectors\n\nWe have applied the SpECTRE technology to an interdisciplinary problem,\nsimulating the Brownian thermal noise in the mirrors of interferometric\ngravitational-wave detectors at unprecedented accuracy. It uses the SpECTRE\nelliptic solver \\cite Vu2021coj to solve an elasticity problem, which connects\nto the thermal noise problem through the fluctuation dissipation theorem.\n\nPublications:\n\n- Vu et al. (2024). High-accuracy numerical models of Brownian thermal noise in\n thin mirror coatings. \\cite Vu2023thn\n" }, { "path": "docs/GroupDefs.hpp", "content": "// Distributed under the MIT License.\n// See LICENSE.txt for details.\n\n/// \\file\n/// Defines all group definitions\n\n#pragma once\n\n/*!\n * \\defgroup ActionsGroup Actions\n * \\brief A collection of steps used in algorithms.\n */\n\n/*!\n * \\defgroup AderGroup ADER\n * \\brief Functions and classes needed for ADER (Arbitrary high-order using\n * DERivatives) time integration\n */\n\n/*!\n * \\defgroup AmrGroup Adaptive Mesh Refinement\n * \\brief Functions and classes specific to hp-adaptive mesh refinement.\n */\n\n/*!\n * \\defgroup AnalyticDataGroup Analytic Data\n * \\brief Analytic data used to specify (for example) initial data to the\n * equations implemented in \\ref EvolutionSystemsGroup.\n */\n\n/*!\n * \\defgroup AnalyticSolutionsGroup Analytic Solutions\n * \\brief Analytic solutions to the equations implemented in \\ref\n * EvolutionSystemsGroup and \\ref EllipticSystemsGroup.\n */\n\n/*!\n * \\defgroup BoundaryConditionsGroup Boundary Conditions\n * A collection of boundary conditions used for evolutions.\n */\n\n/*!\n * \\defgroup CharmExtensionsGroup Charm++ Extensions\n * \\brief Classes and functions used to make Charm++ easier and safer to use.\n */\n\n/*!\n * \\defgroup ComputationalDomainGroup Computational Domain\n * \\brief The building blocks used to describe the computational domain.\n *\n * ### Description\n * The VolumeDim-dimensional computational Domain is constructed from a set of\n * non-overlapping Block%s. Each Block is a distorted VolumeDim-dimensional\n * hypercube. Each codimension-1 boundary of a Block is either part of the\n * external boundary of the computational domain, or is identical to a boundary\n * of one other Block. Each Block is subdivided into one or more Element%s\n * that may be changed dynamically if AMR is enabled.\n */\n\n/*!\n * \\defgroup ConservativeGroup Conservative System Evolution\n * \\brief Contains generic functions used for evolving conservative\n * systems.\n */\n\n/*!\n * \\defgroup ConstantExpressionsGroup Constant Expressions\n * \\brief Contains an assortment of constexpr functions\n *\n * ### Description\n * Contains an assortment of constexpr functions that are useful for\n * metaprogramming, or efficient mathematical computations, such as\n * exponentiating to an integer power, where the power is known at compile\n * time.\n */\n\n/*!\n * \\defgroup ControlSystemGroup Control System\n * \\brief Contains control system elements\n *\n * The control system manages the time-dependent mapping between frames, such as\n * the fixed computational frame (grid frame) and the inertial frame. The\n * time-dependent parameters of the mapping are adjusted by a feedback control\n * system in order to follow the dynamical evolution of objects such as horizons\n * of black holes or surfaces of neutron stars. For example, in binary black\n * hole simulations the map is typically a composition of maps that include\n * translation, rotation, scaling, shape, etc.\n * Each map under the governance of the control system has an associated\n * time-dependent map parameter \\f$\\lambda(t)\\f$ that is a piecewise Nth order\n * polynomial. At discrete times (called reset times), the control system resets\n * the Nth time derivative of \\f$\\lambda(t)\\f$ to a new constant value, in order\n * to minimize an error function \\f$Q(t)\\f$ that is specific to each map. At\n * each reset time, the Nth derivative of \\f$\\lambda(t)\\f$ is set to a function\n * \\f$U(t)\\f$, called the control signal, that is determined by \\f$Q(t)\\f$ and\n * its time derivatives and time integral. Note that \\f$\\lambda(t)\\f$,\n * \\f$U(t)\\f$, and \\f$Q(t)\\f$ can be vectors.\n *\n * The key components of the control system are:\n * - FunctionsOfTime: each map has an associated FunctionOfTime that represents\n * the map parameter \\f$\\lambda(t)\\f$ and relevant time derivatives.\n * - ControlError: each map has an associated ControlError that computes\n * the error, \\f$Q(t)\\f$. Note that for each map, \\f$Q(t)\\f$ is defined to\n * follow the convention that \\f$dQ = -d \\lambda\\f$ as \\f$Q \\rightarrow 0\\f$.\n * - Averager: an averager can be used to average out the noise in the 'raw'\n * \\f$Q(t)\\f$ returned by the ControlError.\n * - Controller: the map controller computes the control signal \\f$U(t)\\f$ from\n * \\f$Q(t)\\f$ and its time integral and time derivatives.\n * The control is accomplished by setting the Nth derivative of\n * \\f$\\lambda(t)\\f$ to \\f$U(t)\\f$. Two common controllers are PID\n * (proportional/integral/derivative)\n * \\f[U(t) = a_{0}\\int_{t_{0}}^{t} Q(t') dt'+a_{1}Q(t)+a_{2}\\frac{dQ}{dt}\\f]\n * or\n * PND (proportional/N derivatives)\n * \\f[ U(t) = \\sum_{k=0}^{N} a_{k} \\frac{d^kQ}{dt^k} \\f]\n * The coefficients \\f$ a_{k} \\f$ in the computation of \\f$U(t)\\f$ are chosen\n * at each time such that the error \\f$Q(t)\\f$ will be critically damped\n * on a timescale of \\f$\\tau\\f$ (the damping time),\n * i.e. \\f$Q(t) \\propto e^{-t/\\tau}\\f$.\n * - TimescaleTuner: each map has a TimescaleTuner that dynamically adjusts\n * the damping timescale \\f$\\tau\\f$ appropriately to keep the error \\f$Q(t)\\f$\n * within some specified error bounds. Note that the reset time interval,\n * \\f$\\Delta t\\f$, is a constant fraction of this damping timescale,\n * i.e. \\f$\\Delta t = \\alpha \\tau\\f$ (empirically, we have found\n * \\f$\\alpha=0.3\\f$ to be a good choice).\n *\n *\n * For additional details describing our control system approach, see\n * \\cite Hemberger2012jz.\n */\n\n/*!\n * \\defgroup CoordinateMapsGroup Coordinate Maps\n * \\brief Functions for mapping coordinates between different frames\n *\n * Coordinate maps provide the maps themselves, the inverse maps, along\n * with the Jacobian and inverse Jacobian of the maps.\n */\n\n/*!\n * \\defgroup CoordMapsTimeDependentGroup Coordinate Maps, Time-dependent\n * \\brief Functions for mapping time-dependent coordinates between different\n * frames\n *\n * Coordinate maps provide the maps themselves, the inverse maps, the Jacobian\n * and inverse Jacobian of the maps, and the frame velocity (time derivative of\n * the map)\n */\n\n/*!\n * \\defgroup DataBoxGroup DataBox\n * \\brief Documentation, functions, metafunctions, and classes necessary for\n * using DataBox\n *\n * DataBox is a heterogeneous compile-time associative container with lazy\n * evaluation of functions. DataBox can not only store data, but can also store\n * functions that depend on other data inside the DataBox. The functions will be\n * evaluated when the data they return is requested. The result is cached, and\n * if a dependency of the function is modified the cache is invalidated.\n *\n * #### Simple and Compute Tags and Their Items\n *\n * The compile-time keys are `struct`s called tags, while the values are called\n * items. Tags are quite minimal, containing only the information necessary to\n * store the data and evaluate functions. There are two different types of tags\n * that a DataBox can hold: simple tags and compute tags. Simple tags are for\n * data that is inserted into the DataBox at the time of creation, while compute\n * tags are for data that will be computed from a function when the compute item\n * is retrieved. If a compute item is never retrieved from the DataBox then it\n * is never evaluated.\n *\n * Simple tags must have a member type alias `type` that is the type of the data\n * to be stored and a `static std::string name()` method that returns the name\n * of the tag. Simple tags must inherit from `db::SimpleTag`.\n *\n * Compute tags must also have a `static std::string name()` method that returns\n * the name of the tag, but they cannot have a `type` type alias. Instead,\n * compute tags must have a static member function or static member function\n * pointer named `function`. `function` can be a function template if necessary.\n * The `function` must take all its arguments by `const` reference. The\n * arguments to the function are retrieved using tags from the DataBox that the\n * compute tag is in. The tags for the arguments are set in the member type\n * alias `argument_tags`, which must be a `tmpl::list` of the tags corresponding\n * to each argument. Note that the order of the tags in the `argument_list` is\n * the order that they will be passed to the function. Compute tags must inherit\n * from `db::ComputeTag`.\n *\n * Here is an example of a simple tag:\n *\n * \\snippet Test_DataBox.cpp databox_tag_example\n *\n * and an example of a compute tag with a function pointer:\n *\n * \\snippet Test_DataBox.cpp databox_mutating_compute_item_tag\n *\n * If the compute item's tag is inline then the compute item is of the form:\n *\n * \\snippet Test_DataBox.cpp compute_item_tag_function\n *\n * Compute tags can also have their functions be overloaded on the type of its\n * arguments:\n *\n * \\snippet Test_DataBox.cpp overload_compute_tag_type\n *\n * or be overloaded on the number of arguments:\n *\n * \\snippet Test_DataBox.cpp overload_compute_tag_number_of_args\n *\n * Compute tag function templates are implemented as follows:\n *\n * \\snippet Test_DataBox.cpp overload_compute_tag_template\n *\n * Finally, overloading, function templates, and variadic functions can be\n * combined to produce extremely generic compute tags. The below compute tag\n * takes as template parameters a parameter pack of integers, which is used to\n * specify several of the arguments. The function is overloaded for the single\n * argument case, and a variadic function template is provided for the multiple\n * arguments case. Note that in practice few compute tags will be this complex.\n *\n * #### Subitems and Prefix Tags\n *\n * A simple or compute tag might also hold a collection of data, such as a\n * container of `Tensor`s. In many cases you will want to be able to retrieve\n * individual elements of the collection from the DataBox without having to\n * first retrieve the collection. The infrastructure that allows for this is\n * called *Subitems*. The subitems of the parent tag must refer to a subset of\n * the data inside the parent tag, e.g. one `Tensor` in the collection. If the\n * parent tag is `Parent` and the subitems tags are `Sub<0>, Sub<1>`, then when\n * `Parent` is added to the DataBox, so are `Sub<0>` and `Sub<1>`. This means\n * the retrieval mechanisms described below will work on `Parent`, `Sub<0>`, and\n * `Sub<1>`.\n *\n * Subitems specify requirements on the tags they act on. For example, there\n * could be a requirement that all tags with a certain type are to be treated as\n * a Subitems. Let's say that the `Parent` tag holds a `Variables`, and\n * `Variables` can be used with the Subitems infrastructure to add the nested\n * `Tensor`s. Then all tags that hold a `Variables` will have their subitems\n * added into the DataBox. To add a new type as a subitem the `db::Subitems`\n * struct must be specialized. See the documentation of `db::Subitems` for more\n * details.\n *\n * The DataBox also supports *prefix tags*, which are commonly used for items\n * that are related to a different item by some operation. Specifically, say\n * you have a tag `MyTensor` and you want to also have the time derivative of\n * `MyTensor`, then you can use the prefix tag `dt` to get `dt`. The\n * benefit of a prefix tag over, say, a separate tag `dtMyTensor` is that prefix\n * tags can be added and removed by the compute tags acting on the original tag.\n * Prefix tags can also be composed, so a second time derivative would be\n * `dt>`. The net result of the prefix tags infrastructure is that\n * the compute tag that returns `dt` only needs to know its input\n * tags, it knows how to name its output based off that. In addition to the\n * normal things a simple or a compute tag must hold, prefix tags must have a\n * nested type alias `tag`, which is the tag being prefixed. Prefix tags must\n * also inherit from `db::PrefixTag` in addition to inheriting from\n * `db::SimpleTag` or `db::ComputeTag`.\n *\n * #### Creating a DataBox\n *\n * You should never call the constructor of a DataBox directly. DataBox\n * construction is quite complicated and the helper function `db::create`\n * should be used instead. `db::create` is used to construct a\n * new DataBox. It takes two typelists as explicit template parameters, the\n * first being a list of the simple tags to add and the second being a list of\n * compute tags to add. If no compute tags are being added then only the simple\n * tags list must be specified. The tags lists should be passed as\n * `db::create,\n * db::AddComputeTags>`. The arguments to `db::create` are the\n * initial values of the simple tags and must be passed in the same order as the\n * tags in the `db::AddSimpleTags` list. If the type of an argument passed to\n * `db::create` does not match the type of the corresponding simple tag a static\n * assertion will trigger. Here is an example of how to use `db::create`:\n *\n * \\snippet Test_DataBox.cpp create_databox\n *\n * #### Accessing and Mutating Items\n *\n * To retrieve an item from a DataBox use the `db::get` function. `db::get`\n * will always return a `const` reference to the object stored in the DataBox\n * and will also have full type information available. This means you are able\n * to use `const auto&` when retrieving tags from the DataBox. For example,\n * \\snippet Test_DataBox.cpp using_db_get\n *\n * If you want to mutate the value of a simple item in the DataBox use\n * `db::mutate`. Any compute item that depends on the mutated item will have its\n * cached value invalidated and be recomputed the next time it is retrieved from\n * the DataBox. `db::mutate` takes a parameter pack of tags to mutate as\n * explicit template parameters, a `gsl::not_null` of the DataBox whose items\n * will be mutated, an invokable, and extra arguments to forward to the\n * invokable. The invokable takes the arguments passed from the DataBox by\n * `const gsl::not_null` while the extra arguments are forwarded to the\n * invokable. The invokable is not allowed to retrieve anything from the\n * DataBox, so any items must be passed as extra arguments using `db::get` to\n * retrieve them. For example,\n *\n * \\snippet Test_DataBox.cpp databox_mutate_example\n *\n * In addition to retrieving items using `db::get` and mutating them using\n * `db::mutate`, there is a facility to invoke an invokable with tags from the\n * DataBox. `db::apply` takes a `tmpl::list` of tags as an explicit template\n * parameter, will retrieve all the tags from the DataBox passed in and then\n * invoke the invokable with the items in the tag list. Similarly,\n * `db::mutate_apply` invokes the invokable but allows for mutating some of\n * the tags. See the documentation of `db::apply` and `db::mutate_apply` for\n * examples of how to use them.\n *\n */\n\n/*!\n * \\defgroup DataBoxTagsGroup DataBox Tags\n * \\brief Structures and metafunctions for labeling the contents of DataBoxes\n */\n\n/*!\n * \\defgroup DataStructuresGroup Data Structures\n * \\brief Various useful data structures used in SpECTRE\n */\n\n/*!\n * \\defgroup DgSubcellGroup DG-Subcell\n * \\brief Functions and classes specific to the discontinuous Galerkin method\n * supplemented with a finite volume or finite difference subcell limiter. Can\n * also be thought of as a DG-FD hybrid method.\n */\n\n/*!\n * \\defgroup DiscontinuousGalerkinGroup Discontinuous Galerkin\n * \\brief Functions and classes specific to the Discontinuous Galerkin\n * algorithm.\n */\n\n/*!\n * \\defgroup EllipticSystemsGroup Elliptic Systems\n * \\brief All available elliptic systems\n */\n\n/*!\n * \\defgroup EquationsOfStateGroup Equations of State\n * \\brief The various available equations of state\n */\n\n/*!\n * \\defgroup ErrorHandlingGroup Error Handling\n * Macros and functions used for handling errors\n */\n\n/*!\n * \\defgroup EventsAndTriggersGroup Events and Triggers\n * \\brief Classes and functions related to events and triggers\n */\n\n/*!\n * \\defgroup EvolutionSystemsGroup Evolution Systems\n * \\brief All available evolution systems and information on how to implement\n * evolution systems\n *\n * \\details Actions and parallel components may require an evolution system to\n * expose the following types:\n *\n * - `volume_dim`: The number of spatial dimensions\n * - `variables_tag`: The evolved variables to compute DG volume contributions\n * and fluxes for.\n * - `compute_time_derivative`: A struct that computes the bulk contribution to\n * the DG discretization of the time derivative. Must expose a `tmpl::list` of\n * `argument_tags` and a static `apply` function that takes the following\n * arguments in this order:\n * - First, the types of the tensors in\n * `db::add_tag_prefix`\n * (which represent the time derivatives of the variables) as not-null pointers.\n * - The types of the `argument_tags` as constant references.\n *\n * Actions and parallel components may also require the Metavariables to expose\n * the following types:\n *\n * - `system`: See above.\n * - `temporal_id`: A DataBox tag that identifies steps in the algorithm.\n * Generally use `Tags::TimeStepId`.\n */\n\n/*!\n * \\defgroup ExecutablesGroup Executables\n * \\brief A list of executables and how to use them\n *\n * \n * \n * \n * \n * \n * \n * \n * \n * \n * \n * \n * \n *
Executable Name Description
\\ref ParallelInfoExecutablePage \"ParallelInfo\" Executable for checking number of nodes, cores, etc.
ExportEquationOfStateForRotNS Exports a 1d equation of state in a table format that the RotNS fortran\n * code can read in.
\n */\n\n/*!\n * \\defgroup FileSystemGroup File System\n * \\brief A light-weight file system library.\n */\n\n/*!\n * \\defgroup FiniteDifferenceGroup Finite Difference\n * \\brief Functions needed for (conservative) finite difference methods.\n */\n\n/*!\n * \\defgroup GeneralRelativityGroup General Relativity\n * \\brief Contains functions used in General Relativistic simulations\n */\n\n/*!\n * \\defgroup HDF5Group HDF5\n * \\brief Functions and classes for manipulating HDF5 files\n */\n\n/*!\n * \\defgroup InitializationGroup Initialization\n * \\brief Actions and metafunctions used for initialization of parallel\n * components.\n */\n\n/*!\n * \\defgroup LimitersGroup Limiters\n * \\brief Limiters to control shocks and surfaces in the solution.\n */\n\n/*!\n * \\defgroup LinearSolverGroup Linear Solver\n * \\brief Algorithms to solve linear systems of equations\n *\n * \\details In a way, the linear solver is for elliptic systems what time\n * stepping is for the evolution code. This is because the DG scheme for an\n * elliptic system reduces to a linear system of equations of the type\n * \\f$Ax=b\\f$, where \\f$A\\f$ is a global matrix representing the DG\n * discretization of the problem. Since this is one equation for each node in\n * the computational domain it becomes unfeasible to numerically invert the\n * global matrix \\f$A\\f$. Instead, we solve the problem iteratively so that we\n * never need to construct \\f$A\\f$ globally but only need \\f$Ax\\f$ that can be\n * evaluated locally by virtue of the DG formulation. This action of the\n * operator is what we have to supply in each step of the iterative algorithms\n * implemented here. It is where most of the computational cost goes and usually\n * involves computing a volume contribution for each element and communicating\n * fluxes with neighboring elements. Since the iterative algorithms typically\n * scale badly with increasing grid size, a preconditioner \\f$P\\f$ is needed\n * in order to make \\f$P^{-1}A\\f$ easier to invert.\n *\n * \\note The smallest possible residual magnitude the linear solver can reach is\n * the product between the machine epsilon and the condition number of the\n * linear operator that is being inverted. Smaller residuals are numerical\n * artifacts. Requiring an absolute or relative residual below this limit will\n * likely make the linear solver run until it reaches its maximum number of\n * iterations.\n *\n * \\note Remember that when the linear operator \\f$A\\f$ corresponds to a PDE\n * discretization, decreasing the linear solver residual below the\n * discretization error will not improve the numerical solution any further.\n * I.e. the error \\f$e_k=x_k-x_\\mathrm{analytic}\\f$ to an analytic solution\n * will be dominated by the linear solver residual at first, but even if the\n * discretization \\f$Ax_k=b\\f$ was exactly solved after some iteration \\f$k\\f$,\n * the discretization residual\n * \\f$Ae_k=b-Ax_\\mathrm{analytic}=r_\\mathrm{discretization}\\f$ would still\n * remain. Therefore, ideally choose the absolute or relative residual criteria\n * based on an estimate of the discretization residual.\n *\n * In the iterative algorithms we usually don't work with the physical field\n * \\f$x\\f$ directly. Instead we need to apply the operator to an internal\n * variable defined by the respective algorithm. This variable is exposed as the\n * `LinearSolver::Tags::Operand` prefix, and the algorithm expects that the\n * computed operator action is written into\n * `db::add_tag_prefix>` in each step.\n */\n\n/// \\defgroup LoggingGroup Logging\n/// \\brief Functions for logging progress of running code\n\n/// \\defgroup MathFunctionsGroup Math Functions\n/// \\brief Useful analytic functions\n\n/*!\n * \\defgroup NumericalAlgorithmsGroup Numerical Algorithms\n * \\brief Generic numerical algorithms\n */\n\n/*!\n * \\defgroup NumericalFluxesGroup Numerical Fluxes\n * \\brief The set of available numerical fluxes\n */\n\n/*!\n * \\defgroup ObserversGroup Observers\n * \\brief Observing/writing data to disk.\n */\n\n/*!\n * \\defgroup OptionGroupsGroup Option Groups\n * \\brief Tags used for grouping input file options.\n *\n * An \\ref OptionTagsGroup \"option tag\" can be placed in a group with other\n * option tags to give the input file more structure. To assign a group to an\n * option tag, set its `group` type alias to a struct that provides a help\n * string and may override a static `name()` function:\n *\n * \\snippet Test_Options.cpp options_example_group\n *\n * A number of commonly used groups are listed here.\n *\n * See also the \\ref dev_guide_option_parsing \"option parsing guide\".\n */\n\n/*!\n * \\defgroup OptionParsingGroup Option Parsing\n * Things related to parsing YAML input files.\n */\n\n/*!\n * \\defgroup OptionTagsGroup Option Tags\n * \\brief Tags used for options parsed from the input file.\n *\n * These can be stored in the GlobalCache or passed to the `initialize`\n * function of a parallel component.\n */\n\n/*!\n * \\defgroup ParallelGroup Parallelization\n * \\brief Functions, classes and documentation related to parallelization and\n * Charm++\n *\n * See\n * \\ref dev_guide_parallelization_foundations \"Parallelization infrastructure\"\n * for details.\n */\n\n/*!\n * \\defgroup PeoGroup Performance, Efficiency, and Optimizations\n * \\brief Classes and functions useful for performance optimizations.\n */\n\n/*!\n * \\defgroup PrettyTypeGroup Pretty Type\n * \\brief Pretty printing of types\n */\n\n/*!\n * \\defgroup ProtocolsGroup Protocols\n * \\brief Classes that define metaprogramming interfaces\n *\n * See the \\ref protocols section of the dev guide for details.\n */\n\n/*!\n * \\defgroup PythonBindingsGroup Python Bindings\n * \\brief Classes and functions useful when writing python bindings.\n *\n * See the \\ref spectre_writing_python_bindings \"Writing Python Bindings\"\n * section of the dev guide for details on how to write python bindings.\n */\n\n/*!\n * \\defgroup SpecialRelativityGroup Special Relativity\n * \\brief Contains functions used in special relativity calculations\n */\n\n/*!\n * \\defgroup SpectralGroup Spectral\n * Things related to spectral transformations.\n */\n\n// Note: this group is ordered by how it appears in the rendered Doxygen pages\n// (i.e., \"Spin-weighted...\"), rather than the group's name (i.e., \"Swsh...\").\n/*!\n * \\defgroup SwshGroup Spin-weighted spherical harmonics\n * Utilities, tags, and metafunctions for using and manipulating spin-weighted\n * spherical harmonics\n */\n\n/*!\n * \\defgroup SurfacesGroup Surfaces\n * Things related to surfaces.\n */\n\n/*!\n * \\defgroup TensorGroup Tensor\n * Tensor use documentation.\n */\n\n/*!\n * \\defgroup TensorExpressionsGroup Tensor Expressions\n * Tensor Expressions allow writing expressions of\n * tensors in a way similar to what is used with pen and paper.\n *\n * Tensor expressions are implemented using (smart) expression templates. This\n * allows a domain specific language making expressions such as\n * \\code\n * auto T = evaluate(F(Indices::_b,\n * Indices::_a));\n * \\endcode\n * possible.\n */\n\n/*!\n * \\defgroup TestingFrameworkGroup Testing Framework\n * \\brief Classes, functions, macros, and instructions for developing tests\n *\n * \\details\n *\n * SpECTRE uses the testing framework\n * [Catch](https://github.com/philsquared/Catch). Catch supports a variety of\n * different styles of tests including BDD and fixture tests. The file\n * `cmake/SpectreAddCatchTests.cmake` parses the source files and adds the found\n * tests to ctest with the correct properties specified by tags and attributes.\n *\n * ### Usage\n *\n * To run the tests, type `ctest` in the build directory. You can specify\n * a regex to match the test name using `ctest -R Unit.Blah`, or run all\n * tests with a certain tag using `ctest -L tag`.\n *\n * ### Comparing double-precision results\n *\n * To compare two floating-point numbers that may differ by round-off, use the\n * helper object `approx`. This is an instance of Catch's comparison class\n * `Approx` in which the relative tolerance for comparisons is set to roughly\n * \\f$10^{-14}\\f$ (i.e. `std::numeric_limits::%epsilon()*100`).\n * When possible, we recommend using `approx` for fuzzy comparisons as follows:\n * \\example\n * \\snippet Test_TestingFramework.cpp approx_default\n *\n * For checks that need more control over the precision (e.g. an algorithm in\n * which round-off errors accumulate to a higher level), we recommend using\n * the `approx` helper with a one-time tolerance adjustment. A comment\n * should explain the reason for the adjustment:\n * \\example\n * \\snippet Test_TestingFramework.cpp approx_single_custom\n *\n * For tests in which the same precision adjustment is re-used many times, a new\n * helper object can be created from Catch's `Approx` with a custom precision:\n * \\example\n * \\snippet Test_TestingFramework.cpp approx_new_custom\n *\n * Note: We provide the `approx` object because Catch's `Approx` defaults to a\n * very loose tolerance (`std::numeric_limits::%epsilon()*100`, or\n * roughly \\f$10^{-5}\\f$ relative error), and so is poorly-suited to checking\n * many numerical algorithms that rely on double-precision accuracy. By\n * providing a tighter tolerance with `approx`, we avoid having to redefine the\n * tolerance in every test.\n *\n * ### Attributes\n *\n * Attributes allow you to modify properties of the test. Attributes are\n * specified as follows:\n * \\code\n * // [[TimeOut, 10]]\n * // [[OutputRegex, The error message expected from the test]]\n * SPECTRE_TEST_CASE(\"Unit.Blah\", \"[Unit]\") {\n * \\endcode\n *\n * Available attributes are:\n *\n * \n * \n * \n * \n * \n * \n * \n * \n * \n * \n * \n * \n *
Attribute Description
TimeOut override the default timeout and set the timeout to N seconds. This\n * should be set very sparingly since unit tests are designed to be\n * short. If your test is too long you should consider testing smaller\n * portions of the code if possible, or writing an integration test instead.\n *
OutputRegex \n * When testing failure modes the exact error message must be tested, not\n * just that the test failed. Since the string passed is a regular\n * expression you must escape any regex tokens. For example, to match\n * `some (word) and` you must specify the string `some \\(word\\) and`.\n * If your error message contains a newline, you can match it using the\n * dot operator `.`, which matches any character.\n *
\n *\n * ### Debugging Tests in GDB or LLDB\n *\n * Several tests fail intentionally at the executable level to test error\n * handling like ASSERT statements in the code. CTest is aware of which\n * should fail and passes them. If you want to debug an individual test\n * in a debugger you must specify the name of the test as the first argument to\n * the test executable. For example, if you want to debug the \"Unit.Gradient\"\n * test: Launch the debugger, for example if you're using LLDB then run `lldb\n * ./bin/Test_LinearOperators`. Then run the test with `run Unit.Gradient`\n * inside the debugger.\n */\n\n/*!\n * \\defgroup TimeGroup Time\n * \\brief Code related to the representation of time during simulations.\n *\n * The time covered by a simulation is divided up into a sequence of\n * adjacent, non-overlapping (except at endpoints) intervals referred\n * to as \"slabs\". The boundaries between slabs can be placed at\n * arbitrary times. Slabs, as represented in the code as the Slab\n * class, provide comparison operators comparing slabs agreeing with\n * the definition as a sequence of intervals. Slabs that do not\n * jointly belong to any such sequence should not be compared.\n *\n * The specific time is represented by the Time class, which encodes\n * the slab containing the time and the fraction of the slab that has\n * elapsed as an exact rational. Times are comparable according to\n * their natural time ordering, except for times belonging to\n * incomparable slabs.\n *\n * Differences in time within a slab are represented as exact\n * fractions of that slab by the TimeDelta class. TimeDeltas are only\n * meaningful within a single slab, with the exception that the ratio\n * of objects with different slabs may be taken, resulting in an\n * inexact floating-point result. Longer intervals of time are\n * represented using floating-point values.\n */\n\n/*!\n * \\defgroup TimeSteppersGroup Time Steppers\n * A collection of ODE integrators primarily used for time stepping.\n */\n\n/*!\n * \\defgroup TypeTraitsGroup Type Traits\n * A collection of useful type traits, including C++14 and C++17 additions to\n * the standard library.\n */\n\n/*!\n * \\defgroup UtilitiesGroup Utilities\n * \\brief A collection of useful classes, functions and metafunctions.\n */\n\n/*!\n * \\defgroup VariableFixingGroup Variable Fixing\n * \\brief A collection of different variable fixers ranging in sophistication.\n *\n * Build-up of numerical error can cause physical quantities to evolve\n * toward non-physical values. For example, pressure and density may become\n * negative. This will subsequently lead to failures in numerical inversion\n * schemes to recover the corresponding convervative values. A rough fix that\n * enforces physical quantities stay physical is to simply change them by hand\n * when needed. This can be done at various degrees of sophistication, but in\n * general the fixed quantities make up a negligible amount of the physics of\n * the simulation; a rough fix is vastly preferred to a simulation that fails\n * to complete due to nonphysical quantities.\n */\n" }, { "path": "docs/Images/Tutorials/make_multicube_figures.py", "content": "#!/usr/bin/env python\n\n# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nimport matplotlib.pyplot as plt\nimport numpy as np\nfrom mpl_toolkits.mplot3d import Axes3D\nfrom mpl_toolkits.mplot3d.art3d import Poly3DCollection\n\nplt.rcParams[\"figure.figsize\"] = (4, 4)\nplt.rcParams[\"font.size\"] = 10\n# higher-quality fonts, but much slower to render:\n# plt.rcParams['font.serif'] = 'Computer Modern'\n# plt.rcParams['text.usetex'] = True\n\n\ndef draw_basis_vectors(\n ax,\n x_origin,\n label_permutation=[0, 1, 2],\n flip_vector=[False, False, False],\n use_greek_labels=True,\n):\n from matplotlib.patches import FancyArrowPatch\n from mpl_toolkits.mplot3d import proj3d\n\n class Arrow3D(FancyArrowPatch):\n def __init__(self, xs, ys, zs, *args, **kwargs):\n FancyArrowPatch.__init__(self, (0, 0), (0, 0), *args, **kwargs)\n self._verts3d = xs, ys, zs\n\n def draw(self, renderer):\n xs3d, ys3d, zs3d = self._verts3d\n xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))\n FancyArrowPatch.draw(self, renderer)\n\n length = 0.3\n labels = (\n [r\"$\\xi$\", r\"$\\eta$\", r\"$\\zeta$\"]\n if use_greek_labels\n else [\"$x$\", \"$y$\", \"$z$\"]\n )\n arrow_props = dict(\n mutation_scale=10, arrowstyle=\"-|>\", color=\"k\", shrinkA=0, shrinkB=0\n )\n x0, y0, z0 = [\n x_origin[i] + (length if flip_vector[i] else 0.0) for i in range(3)\n ]\n dx, dy, dz = [length * (-1.0 if flip_vector[i] else 1.0) for i in range(3)]\n ax.add_artist(Arrow3D([x0, x0 + dx], [y0, y0], [z0, z0], **arrow_props))\n ax.add_artist(Arrow3D([x0, x0], [y0, y0 + dy], [z0, z0], **arrow_props))\n ax.add_artist(Arrow3D([x0, x0], [y0, y0], [z0, z0 + dz], **arrow_props))\n dxt, dyt, dzt = [\n -length - 0.15 if flip_vector[i] else length + 0.05 for i in range(3)\n ]\n dyt = dyt - (0.15 if flip_vector[1] else 0.0)\n ax.text(x0 + dxt, y0, z0, labels[label_permutation[0]])\n ax.text(x0, y0 + dyt, z0, labels[label_permutation[1]])\n ax.text(x0, y0, z0 + dzt, labels[label_permutation[2]])\n\n\ndef draw_polygon_collection(ax, polygons, face_colors, edge_colors):\n collection = Poly3DCollection(polygons)\n collection.set_color(face_colors)\n collection.set_edgecolor(edge_colors)\n collection.set_linewidth(0.6)\n ax.add_collection3d(collection)\n\n\ndef quad(p, i, j, k, l):\n return [p[i], p[j], p[k], p[l]]\n\n\ndef cube(p, index_start, strides):\n sx, sy, sz = strides\n\n def quad_x_normal(i):\n return quad(p, i, i + sy, i + sy + sz, i + sz)\n\n def quad_y_normal(i):\n return quad(p, i, i + sx, i + sx + sz, i + sz)\n\n def quad_z_normal(i):\n return quad(p, i, i + sx, i + sx + sy, i + sy)\n\n quad_lower_x = quad_x_normal(index_start)\n quad_upper_x = quad_x_normal(index_start + sx)\n quad_lower_y = quad_y_normal(index_start)\n quad_upper_y = quad_y_normal(index_start + sy)\n quad_lower_z = quad_z_normal(index_start)\n quad_upper_z = quad_z_normal(index_start + sz)\n\n return [\n quad_lower_x,\n quad_upper_x,\n quad_lower_y,\n quad_upper_y,\n quad_lower_z,\n quad_upper_z,\n ]\n\n\ndef black_color(mean_xyz):\n return \"k\"\n\n\nclass CubeManager:\n def __init__(self, point_list, strides, edge_color_function=black_color):\n self._points = point_list\n self._strides = strides\n self._ecf = edge_color_function\n self.quads = []\n self.face_colors = []\n self.edge_colors = []\n\n def add_cube(self, start_index, these_faces_transparent=[]):\n c = cube(self._points, start_index, self._strides)\n self.quads.extend(c)\n clear = (1, 1, 1, 0)\n white_semi_transparent = (1, 1, 1, 0.75)\n self.face_colors.extend(\n [\n (\n clear\n if face in these_faces_transparent\n else white_semi_transparent\n )\n for face in range(6)\n ]\n )\n self.edge_colors.extend(\n [self._ecf(np.average(face, axis=0)) for face in c]\n )\n\n\ndef one_cube_figure():\n p = np.array([[x, y, z] for z in [0, 1] for y in [0, 1] for x in [0, 1]])\n cubes = CubeManager(p, strides=[1, 2, 4])\n cubes.add_cube(0)\n\n fig = plt.figure()\n ax = Axes3D(fig)\n ax.set_aspect(\"equal\")\n ax.set_axis_off()\n ax.set_xlim(-0.5, 1.5)\n ax.set_ylim(-0.5, 1.5)\n ax.set_zlim(-0.5, 1.5)\n\n draw_polygon_collection(\n ax, cubes.quads, cubes.face_colors, cubes.edge_colors\n )\n\n draw_basis_vectors(ax, [0.1, 0.1, 0.1])\n for i in range(p.shape[0]):\n # shift labels of upper-y face to avoid overlaps\n shift_y = -0.25 if p[i, 1] < 0.5 else 0.1\n ax.text(p[i, 0], p[i, 1] + shift_y, p[i, 2], \"$\" + str(i) + \"$\")\n\n fig.savefig(\"onecube_numbered.png\")\n\n\ndef two_cube_figures():\n p = np.array([[x, y, z] for z in [0, 1] for y in [0, 1] for x in [0, 1, 2]])\n cubes = CubeManager(p, strides=[1, 3, 6])\n cubes.add_cube(0, [1])\n cubes.add_cube(1, [0])\n\n fig = plt.figure()\n ax = Axes3D(fig)\n ax.set_aspect(\"equal\")\n ax.set_axis_off()\n ax.set_xlim(0.0, 2.0)\n ax.set_ylim(-0.5, 1.5)\n ax.set_zlim(-0.5, 1.5)\n\n draw_polygon_collection(\n ax, cubes.quads, cubes.face_colors, cubes.edge_colors\n )\n\n draw_basis_vectors(ax, [0.1, 0.1, 0.1])\n draw_basis_vectors(ax, [1.1, 0.1, 0.1], label_permutation=[2, 0, 1])\n\n fig.savefig(\"twocubes.png\")\n\n for i in range(p.shape[0]):\n # shift labels of upper-y face to avoid overlaps\n shift_y = -0.25 if p[i, 1] < 0.5 else 0.1\n ax.text(p[i, 0], p[i, 1] + shift_y, p[i, 2], \"$\" + str(i) + \"$\")\n\n fig.savefig(\"twocubes_numbered.png\")\n\n\ndef eight_cube_figures():\n p = np.array(\n [[x, y, z] for z in [0, 1, 2] for y in [0, 1, 2] for x in [0, 1, 2]]\n )\n\n def red_black_blue(mean_xyz):\n r = max(1.0 - mean_xyz[1], 0.0)\n b = max(mean_xyz[1] - 1.0, 0.0)\n return [r, 0.0, b]\n\n cubes = CubeManager(\n p, strides=[1, 3, 9], edge_color_function=red_black_blue\n )\n cubes.add_cube(0, [1, 3, 5])\n cubes.add_cube(1, [0, 3, 5])\n cubes.add_cube(3, [1, 2, 5])\n cubes.add_cube(4, [0, 2, 5])\n cubes.add_cube(9, [1, 3, 4])\n cubes.add_cube(10, [0, 3, 4])\n cubes.add_cube(12, [1, 2, 4])\n cubes.add_cube(13, [0, 2, 4])\n\n fig = plt.figure()\n ax = Axes3D(fig)\n ax.set_aspect(\"equal\")\n ax.set_axis_off()\n ax.set_xlim(0.0, 2.0)\n ax.set_ylim(0.0, 2.0)\n ax.set_zlim(0.0, 2.0)\n\n draw_polygon_collection(\n ax, cubes.quads, cubes.face_colors, cubes.edge_colors\n )\n\n fig.savefig(\"eightcubes.png\")\n\n draw_basis_vectors(ax, [0.55, -0.75, 0.0], use_greek_labels=False)\n for i in range(p.shape[0]):\n # shift labels on each y=constant surface, to reduce overlaps\n shift = [0.0, 0.0, 0.0]\n if p[i, 1] == 0.0:\n shift[0] = -0.05\n shift[1] = -0.3\n elif p[i, 1] == 1.0:\n shift[0] = 0.02\n shift[2] = -0.2\n else:\n shift[1] = 0.1\n # this label needs additional manual tweaking\n if i == 15:\n shift[0] = -0.2\n shift[1] = -0.1\n # reduce R,B components so colors aren't too bright\n textcolor = red_black_blue(p[i])\n textcolor[0] /= 1.5\n textcolor[2] /= 1.5\n ax.text(\n p[i, 0] + shift[0],\n p[i, 1] + shift[1],\n p[i, 2] + shift[2],\n \"$\" + str(i) + \"$\",\n color=textcolor,\n )\n\n fig.savefig(\"eightcubes_numbered.png\")\n\n\ndef eight_cube_rotated_exploded_figure():\n p = np.array(\n [\n [x, y, z]\n for z in [0, 1, 2, 3]\n for y in [0, 1, 2, 3]\n for x in [0, 1, 2, 3]\n ]\n )\n\n def red_black_blue(mean_xyz):\n y_normalization = 1.5\n r = max(1.0 - mean_xyz[1] / y_normalization, 0.0)\n b = max(mean_xyz[1] / y_normalization - 1.0, 0.0)\n return [r, 0.0, b]\n\n cubes = CubeManager(\n p, strides=[1, 4, 16], edge_color_function=red_black_blue\n )\n cubes.add_cube(0)\n cubes.add_cube(2)\n cubes.add_cube(8)\n cubes.add_cube(10)\n cubes.add_cube(32)\n cubes.add_cube(34)\n cubes.add_cube(40)\n cubes.add_cube(42)\n\n fig = plt.figure()\n ax = Axes3D(fig)\n ax.set_aspect(\"equal\")\n ax.set_axis_off()\n ax.set_xlim(0.0, 3.0)\n ax.set_ylim(0.0, 3.0)\n ax.set_zlim(0.0, 3.0)\n\n draw_polygon_collection(\n ax, cubes.quads, cubes.face_colors, cubes.edge_colors\n )\n\n draw_basis_vectors(ax, [1.0, -0.8, 0.0], use_greek_labels=False)\n draw_basis_vectors(ax, [0.17, 0.17, 0.25])\n draw_basis_vectors(\n ax,\n [2.17, 0.17, 0.25],\n label_permutation=[2, 1, 0],\n flip_vector=[False, False, True],\n )\n draw_basis_vectors(\n ax,\n [0.17, 2.17, 0.45],\n label_permutation=[0, 2, 1],\n flip_vector=[False, False, True],\n )\n draw_basis_vectors(\n ax,\n [2.17, 2.17, 0.3],\n label_permutation=[2, 0, 1],\n flip_vector=[False, True, True],\n )\n draw_basis_vectors(\n ax,\n [0.17, 0.17, 2.25],\n label_permutation=[1, 0, 2],\n flip_vector=[False, True, False],\n )\n draw_basis_vectors(\n ax,\n [2.17, 0.17, 2.25],\n label_permutation=[1, 2, 0],\n flip_vector=[False, True, True],\n )\n draw_basis_vectors(\n ax,\n [0.17, 2.17, 2.3],\n label_permutation=[2, 0, 1],\n flip_vector=[False, True, True],\n )\n draw_basis_vectors(ax, [2.17, 2.17, 2.45])\n fig.savefig(\"eightcubes_rotated_exploded.png\")\n\n\ndef tesseract_figure():\n p = np.array(\n [\n [x, y, z]\n for z in [0, 1, 2, 3, 4]\n for y in [0, 1, 2, 3]\n for x in [0, 1, 2, 3]\n ]\n )\n\n def red_black_blue(mean_xyz):\n # note: the tesseract is a bigger domain, so mean_xyz values can be\n # larger. the factor of 1.5 normalizes R,B values back into [0,1].\n y_normalization = 1.5\n r = max(1.0 - mean_xyz[1] / y_normalization, 0.0)\n b = max(mean_xyz[1] / y_normalization - 1.0, 0.0)\n return [r, 0.0, b]\n\n cubes = CubeManager(\n p, strides=[1, 4, 16], edge_color_function=red_black_blue\n )\n cubes.add_cube(5, [5])\n cubes.add_cube(21, [4, 5])\n cubes.add_cube(33, [3])\n cubes.add_cube(36, [1])\n cubes.add_cube(38, [0])\n cubes.add_cube(41, [2])\n cubes.add_cube(53, [4])\n\n # also draw the back 3 sides of the bounding box\n box_quads = np.array(\n [quad(p, 0, 12, 76, 64), quad(p, 12, 15, 79, 76), quad(p, 0, 3, 15, 12)]\n )\n\n fig = plt.figure(figsize=(6, 6))\n ax = Axes3D(fig)\n ax.set_aspect(\"equal\")\n ax.set_axis_off()\n ax.set_xlim(-0.5, 3.5)\n ax.set_ylim(-0.5, 3.5)\n ax.set_zlim(0.0, 4.0)\n\n # draw bounding box first, else matplotlib gets the layer ordering wrong\n draw_polygon_collection(ax, box_quads, \"white\", \"lightgrey\")\n draw_polygon_collection(\n ax, cubes.quads, cubes.face_colors, cubes.edge_colors\n )\n\n # these are the visible points on the tesseract\n points_to_label = [\n 5,\n 6,\n 10,\n 21,\n 22,\n 26,\n 36,\n 33,\n 34,\n 38,\n 39,\n 43,\n 52,\n 49,\n 50,\n 53,\n 54,\n 55,\n 56,\n 58,\n 59,\n 62,\n 69,\n 70,\n 73,\n 74,\n ]\n # these are the points we want to show from the bounding box\n points_to_label.extend([0, 3, 15, 64, 76, 79])\n for i in points_to_label:\n # shift labels on each y=constant surface, to reduce overlaps\n shift = [0.0, 0.0, 0.0]\n if p[i, 1] == 0.0 or p[i, 1] == 1.0:\n shift[0] = -0.07\n shift[1] = -0.37\n else:\n shift[1] = 0.1\n # specific individual corrections at complex tesseract corners\n if i == 38:\n shift[2] = 0.27\n elif i == 39:\n shift[0] = 0.15\n shift[1] = -0.2\n elif i == 53:\n shift[0] = 0.24\n elif i == 54:\n shift[0] = 0.24\n elif i == 58:\n shift[2] = -0.3\n elif i == 69:\n shift[2] = 0.15\n # reduce R,B components so colors aren't too bright\n textcolor = red_black_blue(p[i])\n textcolor[0] /= 1.5\n textcolor[2] /= 1.5\n ax.text(\n p[i, 0] + shift[0],\n p[i, 1] + shift[1],\n p[i, 2] + shift[2],\n \"$\" + str(i) + \"$\",\n color=textcolor,\n )\n\n fig.savefig(\"tesseract_numbered.png\")\n\n\none_cube_figure()\ntwo_cube_figures()\neight_cube_figures()\neight_cube_rotated_exploded_figure()\ntesseract_figure()\n" }, { "path": "docs/Installation/BuildSystem.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Build System - CMake {#spectre_build_system}\n\n\\tableofcontents\n\nSpECTRE uses [CMake](https://cmake.org/) for the build system. In this\nguide we'll outline how to configure SpECTRE and\ndescribe some [commonly used CMake flags](#common_cmake_flags).\nWe'll also go over how to\n[add new source files](#adding_source_files),\n[libraries](#adding_libraries),\n[unit tests](#adding_unit_tests), [executables](#adding_executables), and\n[external dependencies](#adding_external_dependencies).\n\n# Configuring\n\nThe command to configure SpECTRE will look like this\n\n```\ncmake -D FLAG1=OPT1 ... -D FLAGN=OPTN \n```\n\nwhere `FLAG{1..N}` are CMake flags that are detailed in the section on\n[commonly used CMake flags](#common_cmake_flags).\n\nCMake will look in your `$PATH` environment variable for all of the\n[build dependencies](installation.html#build_dependencies) and will use the\nfirst one it finds that satisfies the requirements. However, if a dependency is\nnot in your `$PATH`, there are multiple versions of a dependency, or you just\nwant to customize your configuration, you'll have to tell CMake which dependency\nyou want to use and where it is using CMake flags. To that end, even though the\n[commonly used CMake flags](#common_cmake_flags) section has a more detailed\nlist of the flags available, the following list has the *most common* CMake\nflags you'll need to customize your configuration (e.g. compilers, charm, build\ntype, and library types):\n\n- CMAKE_C_COMPILER\n- CMAKE_CXX_COMPILER\n- CMAKE_Fortran_COMPILER\n- CHARM_ROOT\n- CMAKE_BUILD_TYPE\n- BUILD_SHARED_LIBS\n\n\\note If you are on a cluster, take a look at the\n[installation on clusters](installation_on_clusters.html)\ninstructions. If you are on a cluster we support, we will already have an\nenvironment setup and an easy way for you to configure the build without having\nto specify flags yourself.\n\n## Commonly Used CMake flags {#common_cmake_flags}\nThe following are common flags used to control building SpECTRE with CMake (in\nalphabetical order):\n- ASAN\n - Whether or not to turn on the address sanitizer compile flags\n (`-fsanitize=address`) (default is `OFF`)\n- BLAZE_USE_ALWAYS_INLINE\n - Force Blaze inlining (default is `ON`)\n - If disabled or if the platform is unable to 100% guarantee inlining,\n falls back to `BLAZE_USE_STRONG_INLINE` (see below)\n - Forced inlining reduces function call overhead, and so generally reduces\n runtime. However, it does increase compile time and compile memory usage. It\n is also easier to use a debugger when forced inlining is disabled. If you\n are encountering debugger messages like `function inlined`, then forced\n inlining should be disabled.\n- BLAZE_USE_STRONG_INLINE\n - Increase the likelihood of Blaze inlining (default is `ON`)\n - Strong inlining reduces function call overhead, and so generally reduces\n runtime. However, it does increase compile time and compile memory usage. It\n is also easier to use a debugger when strong inlining is disabled. If you\n are encountering debugger messages like `function inlined`, then strong\n inlining should be disabled.\n- BOOTSTRAP_PY_DEPS and BOOTSTRAP_PY_DEV_DEPS\n - Install missing Python dependencies into the build directory, as listed in\n `support/Python/requirements.txt` and `support/Python/dev_requirements.txt`,\n respectively. This is an alternative to creating a Python environment and\n installing the packages yourself. If you run into problems with packages\n like h5py, numpy or scipy you can/should still install them yourself to make\n sure they use the correct HDF5, BLAS, etc.\n (default is `OFF`)\n- BUILD_DOCS\n - Enable building documentation. (default is `ON`)\n- BUILD_PYTHON_BINDINGS\n - Build python libraries to call SpECTRE C++ code from python\n (default is `ON`)\n- BUILD_SHARED_LIBS\n - Whether shared libraries are built instead of static libraries\n (default is `OFF`)\n- BUILD_TESTING\n - Enable building tests. (default is `ON`)\n- CHARM_ROOT\n - The path to the build directory of `Charm++`\n- CHARM_TRACE_PROJECTIONS\n - Enables tracing with Charm++ projections. Specifically, enables the link\n flag `-tracemode projections`. (default is `OFF`)\n- CHARM_TRACE_SUMMARY\n - Enables trace summaries with Charm++ projections. Specifically, enables\n the link flag `-tracemode summary`. (default is `OFF`)\n- CMAKE_BUILD_TYPE\n - Sets the build type. Common options:\n - `Debug` (the default if the flag is not specified): sets flags\n that trigger additional error checking\n - `Release`\n- CMAKE_C_COMPILER\n - The `C` compiler used (defaults to whatever is determined by\n `CMake/Modules/CMakeDetermineCCompiler.cmake`, usually `cc`)\n- CMAKE_C_FLAGS\n - Additional flags passed to the `C` compiler.\n- CMAKE_CXX_COMPILER\n - The `C++` compiler used (defaults to whatever is determined by\n `CMake/Modules/CMakeDetermineCXXCompiler.cmake`, usually `c++`)\n- CMAKE_CXX_FLAGS\n - Additional flags passed to the `C++` compiler.\n- CMAKE_Fortran_COMPILER\n - The `Fortran` compiler used (defaults to whatever is determined by\n `CMake/Modules/CMakeDetermineFortranCompiler.cmake`)\n- CMAKE_Fortran_FLAGS\n - Additional flags passed to the `Fortran` compiler.\n- CMAKE_INSTALL_PREFIX\n - Location where the `install` target copies executables, libraries, etc. Make\n sure to set this variable before you `install`, or a default location such\n as `/usr/local` is used.\n- CMAKE_RUNTIME_OUTPUT_DIRECTORY\n - Sets the directory where the library and executables are placed.\n By default libraries end up in `/lib` and executables\n in `/bin`.\n- COVERAGE\n - Enable code coverage with GCOV and LCOV (default `OFF`)\n- DEBUG_SYMBOLS\n - Whether or not to use debug symbols (default is `ON`)\n - Disabling debug symbols will reduce compile time and total size of the build\n directory.\n- DOCS_ONLY\n - Build _only_ documentation (default is `OFF`). Requires `BUILD_DOCS=ON`.\n- ENABLE_OPENMP\n - Enable OpenMP parallelization in some parts of the code, such as Python\n bindings and interpolating volume data files. Note that simulations do not\n typically use OpenMP parallelization, so this flag only applies to tools.\n- ENABLE_PARAVIEW\n - Try to find ParaView to enable 3D rendering tools (default is `OFF`)\n- ENABLE_PROFILING\n - Enables various options to make profiling SpECTRE easier\n (default is `OFF`)\n- ENABLE_PYTHON\n - Enables Python. (default is `ON`)\n - Set to `OFF` for a minimal build on systems without a recent Python\n installation. Warning: Many things will not work!!\n - Note: Even when disabled, a minimal Python installation\n (Python ≥ 2.7) is still required.\n - BUILD_PYTHON_BINDINGS, BUILD_TESTING, BUILD_DOCS should be `OFF`.\n- ENABLE_WARNINGS\n - Whether or not warning flags are enabled (default is `ON`)\n- FUKA_ROOT\n - Set to a path to a [FUKA](https://bitbucket.org/fukaws/fuka) installation to\n enable loading FUKA initial data into SpECTRE. Can be the FUKA repository\n root or the directory where `libkadath.a` was installed. Also requires FFTW\n to be installed (see FUKA docs on dependencies).\n- GSL_STATIC\n - If set, then the GNU Scientific Library is statically linked.\n- KEEP_FRAME_POINTER\n - Whether to keep the frame pointer. Needed for profiling or other cases\n where you need to be able to figure out what the call stack is.\n (default is `OFF`)\n- MACHINE\n - Select a machine that we know how to run on, such as a particular\n supercomputer. A file named MACHINE.yaml must exist in support/Machines and\n a submit script template named MACHINE.sh must exist in\n support/SubmitScripts.\n- MEMORY_ALLOCATOR\n - Set which memory allocator to use. If there are unexplained segfaults or\n other memory issues, it would be worth setting `MEMORY_ALLOCATOR=SYSTEM` to\n see if that resolves the issue. It could be the case that different\n third-party libraries accidentally end up using different allocators, which\n is undefined behavior and will result in complete chaos.\n (default is `JEMALLOC`)\n- PY_DEV_MODE\n - Enable development mode for the Python package, meaning that Python files\n are symlinked rather than copied to the build directory. Allows to edit and\n test Python code much easier, in particular when it uses compiled Python\n bindings, but doesn't replace CMake placeholders in the Python code such as\n the project version. (default is `OFF`)\n- SPEC_ROOT\n - Set to a path to a SpEC installation (the SpEC repository root) to link in\n SpEC libraries. In particular, the SpEC::Exporter library is linked in and\n enables loading SpEC data into SpECTRE. See \\ref installation for details.\n- SPECTRE_AUTODIFF\n - Enable automatic differentation (default is `OFF`). This is required for\n computing Hessians.\n- SPECTRE_DEBUG\n - Defines `SPECTRE_DEBUG` macro to enable `ASSERT`s and other debug\n checks so they can be used in Release builds. That is, you get sanity checks\n and compiler optimizations. You cannot disable the checks in Debug builds,\n so this option has no effect in Debug builds.\n (default is `OFF` in release)\n- SPECTRE_DEBUG_Og\n - Compile Debug builds with `-Og` instead of the default `-O0`.\n `-Og` is specifically designed to preserve debuggability while enabling\n optimizations that do not interfere with source-level debugging.\n Has no effect when `SPECTRE_OPTIMIZE_SIZE=ON` (which uses `-Oz`).\n (default is `ON`)\n- SPECTRE_NAN_INIT\n - Defines `SPECTRE_NAN_INIT` macro to initialize memory to NaN in various\n places to catch use of uninitialized values.\n (default is the value of `SPECTRE_DEBUG`, or `ON` in Debug builds)\n- SPECTRE_OPTIMIZE_SIZE\n - Optimize for executable size instead of speed (adds the `-Oz` compiler\n flag). The default is `OFF`, unless on Apple Silicon machines, where the\n default is `ON`. This is because of a bug in macOS on Apple Silicon, which\n means executables larger than 2GB in size cannot run. Disabling this option\n on Apple Silicon can improve debugging tests (which are small enough so the\n bug does not affect them).\n- SPECTRE_FETCH_MISSING_DEPS\n - Download missing dependencies and build them alongside the SpECTRE source.\n (default is `OFF`)\n- SPECTRE_Fortran_STATIC_LIBS (default: `OFF`)\n - Use static version of `libgfortran` and `libquadmath`.\n- SPECTRE_INPUT_FILE_TEST_MIN_PRIORITY\n - Minimum priority of input file tests to run. Possible values are: `low` (not\n usually run on CI), `normal` (run at least once on CI), `high` (run always\n on CI). (default is `normal`)\n- SPECTRE_KOKKOS (default: `OFF`)\n - Enable Kokkos support. You must have Kokkos installed and detectable.\n- SPECTRE_LTO\n - Enable link-time optimization if the compiler supports it.\n- SPECTRE_LTO_CORES\n - Specifies the number of cores to use for parallelizing LTO. Must be a\n positive integer or \"auto\". This is only available when `SPECTRE_LTO=ON` and\n the compiler supports LTO.\n- SPECTRE_TEST_RUNNER\n - Run test executables through a wrapper. This might be `charmrun`, for\n example. (default is to not use one)\n- SPECTRE_TEST_TIMEOUT_FACTOR (and specific overrides\n SPECTRE_X_TEST_TIMEOUT_FACTOR for X one of UNIT, STANDALONE, INPUT_FILE, or\n PYTHON)\n - Multiply the timeout for the respective set of tests by this factor (default\n is `1`).\n - This is useful to run tests on slower machines.\n- SPECTRE_USE_ALWAYS_INLINE\n - Force SpECTRE inlining (default is `ON`)\n - Forced inlining reduces function call overhead, and so generally reduces\n runtime. However, it does increase compile time and compile memory usage. It\n is also easier to use a debugger when forced inlining is disabled. If you\n are encountering debugger messages like `function inlined`, then forced\n inlining should be disabled.\n- STRIP_SYMBOLS\n - Whether or not to strip all symbols (default is `OFF`)\n - If enabled strips all extraneous symbols from libraries and executables,\n further reducing the size of them.\n- STUB_EXECUTABLE_OBJECT_FILES\n - Replace object files from executables after linking with empty stubs\n (default is `OFF`)\n - This is useful for drastically reducing the build size in CI, but since the\n object files are replaced with empty stubs will generally cause linking\n problems if used during development.\n- STUB_LIBRARY_OBJECT_FILES\n - Replace object files from libraries after linking with empty stubs\n (default is `OFF`)\n - This is useful for drastically reducing the build size in CI, but since the\n object files are replaced with empty stubs will generally cause linking\n problems if used during development.\n- UBSAN_INTEGER\n - Whether or not to turn on the undefined behavior sanitizer\n [unsigned integer\n overflow](https://clang.llvm.org/docs/UndefinedBehaviorSanitizer.html) flag\n (`-fsanitize=integer`) (default is `OFF`)\n- UBSAN_UNDEFINED\n - Whether or not to turn on the undefined behavior sanitizer\n [undefined\n behavior](https://clang.llvm.org/docs/UndefinedBehaviorSanitizer.html)\n compile flags (`-fsanitize=undefined`) (default is `OFF`)\n- UNIT_TESTS_IN_TEST_EXECUTABLES\n - Whether to build the `unit-tests` target as part of the `test-executables`\n target. This is used to build only the non-unit tests in the CI build\n that doesn't use the PCH. (default is `ON`)\n- USE_CCACHE\n - Use ccache to cache build output so that rebuilding parts of the source tree\n is faster. The cache will use up space on disk, with the default being\n around 2-5GB. If you are performing a one time build to test something\n specific you should consider disabling ccache in order to avoid removing\n cached files that may be useful in other builds.\n (default is `ON`)\n- USE_FORMALINE\n - Write the source tree into HDF5 files written to disk in order to increase\n reproducibility of results.\n (default is `ON`)\n- USE_GIT_HOOKS\n - Use git hooks to perform some sanity checks so that small goofs are caught\n before they are committed. These checks are particularly useful because they\n also run automatically on \\ref github_actions_guide \"CI\" and must pass\n before pull requests are merged.\n (default is `ON`)\n- USE_LD\n - Override the automatically chosen linker. The options are `ld`, `gold`, and\n `lld`.\n (default is `OFF`)\n- USE_PCH\n - Whether or not to use pre-compiled headers (default is `ON`)\n- USE_SLEEF\n - Whether to use [Sleef](https://github.com/shibatch/sleef) with Blaze to\n vectorize addition math functions like `sin`, `cos`, and `exp`.\n (default is `OFF`)\n - \\note Blaze isn't tested super thoroughly across different architectures so\n there's unfortunately no guarantee that Blaze+Sleef will work everywhere.\n- USE_XSIMD\n - Whether to use [xsimd](https://github.com/xtensor-stack/xsimd) with Blaze to\n vectorize addition math functions like `sin`, `cos`, and `exp`.\n Defines the macro `SPECTRE_USE_XSIMD`, which can be check to enable manual\n vectorization where necessary.\n (default is `ON`)\n\n## CMake targets\n\nTo see all possible build targets, once you configure SpECTRE run\n\n```\nmake list\n```\n\nThis will be a long list of all libraries, test executables, simulation\nexecutables, and custom build targets. The custom targets that are\navailable to build with `make` or `ninja` are:\n\n- unit-tests\n - Build unit tests, which you can run with `ctest -L unit`. Available if\n `BUILD_TESTING` is `ON` (the default).\n- test-executables\n - Build all tests, including executables, so you can run all tests with\n `ctest`. Available if `BUILD_TESTING` is `ON` (the default). To compile\n `test-executables` you may have to reduce the number of cores you build on\n in parallel to avoid running out of memory.\n- all-pybindings\n - Build Python bindings. See \\ref spectre_using_python for details.\n- cli\n - Same as all-pybindings\n- install\n - Install targets that have been built to the `CMAKE_INSTALL_PREFIX`. Doesn't\n try to build anything else.\n\n# Editing the build system\n\n\\note When editing `CMakeLists.txt` files, it is conventional to\nindent multiline commands by two spaces (except for the first line),\nand to separate most commands by blank lines.\n\n## Adding Source Files {#adding_source_files}\n\nSpECTRE organizes source files into subdirectories of `src` that are\ncompiled into libraries. To add a new source file `FILE.cpp` to an\nexisting library in `src/PATH/DIR`, just edit\n`src/PATH/DIR/CMakeLists.txt` and add `FILE.cpp` to the list of files\nin\n```\nspectre_target_sources(\n ${LIBRARY}\n PRIVATE\n \n )\n```\nsuch that the resulting `` is in alphabetical order.\n\n## Adding Header Files {#adding_header_files}\n\nSimilarly to [adding new source files](#adding_source_files), you can add a new\nheader file `FILE.hpp` to a library by editing the `CMakeLists.txt` in that\ndirectory and adding `FILE.hpp` to the list of files in\n```\nspectre_target_headers(\n ${LIBRARY}\n INCLUDE_DIRECTORY ${CMAKE_SOURCE_DIR}/src\n HEADERS\n \n)\n```\n\n\\note Any `.tpp` files also go in this list of header files.\n\n## Adding Libraries {#adding_libraries}\n\nTo add a source file `FILE.cpp` that is compiled into a new library `LIB` in a\ndirectory `src/PATH/DIR` (either in a new directory, or in an existing\ndirectory that either does not have a `CMakeLists.txt` file, or does\nnot create a library in the existing `CMakeLists.txt`):\n- Create (if necessary) a `CMakeLists.txt` file in `DIR`, with the following\ntwo lines at the top:\n```\n# Distributed under the MIT License.\n# See LICENSE.txt for details.\n```\n- In the parent directory (i.e. `src/PATH`), (if necessary) add the\nfollowing line to its `CMakeLists.txt` file (if necessary, recursively\ndo the previous step and this one until you reach a `CMakeLists.txt` that\nadds the appropriate subdirectory):\n```\nadd_subdirectory(DIR)\n```\nIf there are already other `add_subdirectory()` lines in the file, place\nthe new one so that the subdirectories are in alphabetical order.\n- Add the line:\n```\nset(LIBRARY LIB)\n```\nwhere convention is that `LIB` = `DIR`. As library names must be\nunique, this is not always possible, in which case the convention is to\nprepend the parent directory to `DIR`.\n- Add the lines\n```\nadd_spectre_library(${LIBRARY})\n\nspectre_target_sources(\n ${LIBRARY}\n PRIVATE\n FILE.cpp\n )\n\nspectre_target_headers(\n ${LIBRARY}\n INCLUDE_DIRECTORY ${CMAKE_SOURCE_DIR}/src\n HEADERS\n FILE.hpp\n )\n\ntarget_link_libraries(\n ${LIBRARY}\n PUBLIC\n \n PRIVATE\n \n INTERFACE\n \n )\n```\nwhere each `` is an alphabetized list\nof libraries of the form\n```\n SomeLibrary\n SomeOtherLibrary\n YetAnotherLibrary\n```\nThe libraries listed under `INTERFACE` are those included in at\nleast one `.hpp` file in `LIB` but never used in any `.cpp` files\nin `LIB`. The libraries listed under `PRIVATE` are used in\nat least one `.cpp` file in `LIB` but not in any `.hpp` file\nin `LIB`. The libraries listed under `PUBLIC` are used in at\nleast one `.hpp` file and at least one `.cpp` file in `LIB`.\nNote that a library counts as being used in a `.cpp` file if the\ncorresponding `.hpp` file includes it. In other words, list a dependency\nas `PRIVATE` if it is needed only to compile the library, but not for\nincluding headers. List a dependency as `INTERFACE` if it is not needed\nto compile the library, but is needed for including headers. List a\ndependency as `PUBLIC` if it is needed for both.\n\n\\note If your library only contains header files, you must specify `INTERFACE`\nlike so in the `add_spectre_library(${LIBRARY} INTERFACE)` function. You should\nalso omit the `spectre_target_sources` lines as well.\n\n## Adding Unit Tests {#adding_unit_tests}\n\nWe use the [Catch](https://github.com/philsquared/Catch) testing\nframework for unit tests. All unit tests are housed in `tests/Unit`\nwith subdirectories for each subdirectory of `src`. Add the `cpp` file\nto the appropriate subdirectory and also to the `CMakeLists.txt` in\nthat subdirectory. Inside the source file you can create a new test by\nadding a `SPECTRE_TEST_CASE(\"Unit.Dir.Component\",\n\"[Unit][Dir][Tag]\")`. The `[Tag]` is optional and you can have more\nthan one, but the tags should be used quite sparingly. The purpose of\nthe tags is to be able to run all unit tests or all tests of a\nparticular set of components, e.g. `ctest -L Data` to run all tests\ninside the `Data` directory. Please see \\ref writing_unit_tests\n\"writing unit tests\", other unit tests and the [Catch\ndocumentation](https://github.com/philsquared/Catch) for more help on\nwriting tests. Unit tests should take as short a time as possible,\nwith a goal of less than two seconds. Please also limit the number of\ndistinct cases (by using `SECTION`s).\n\nYou can check the unit test coverage of your code by installing all the optional\ncomponents and then running `make unit-test-coverage` (after re-running CMake).\nThis will create the\ndirectory `BUILD_DIR/docs/html/unit-test-coverage/` which is where the coverage\ninformation is located. Open the `index.html` file in your browser and make\nsure that your tests are indeed checking all lines of your code. Your pull\nrequests might not be merged until your line coverage is over 90% (we are aiming\nfor 100% line coverage wherever possible). Unreachable lines of code can be\nexcluded from coverage analysis by adding the inline comment `LCOV_EXCL_LINE`\nor a block can be excluded using `LCOV_EXCL_START` and `LCOV_EXCL_STOP`.\nHowever, this should be used extremely sparingly since unreachable code paths\nshould be removed from the code base altogether.\n\n## Adding Executables {#adding_executables}\n\nAll general executables are found in `src/Executables`, while those\nfor specific evolution (elliptic) systems are found in\n`src/Evolution/Executables` (`src/Elliptic/Executables`). See \\ref\ndev_guide_creating_executables \"how to create executables\".\n\n## Adding External Dependencies {#adding_external_dependencies}\n\nTo add an external dependency, first add a `SetupDEPENDENCY.cmake`\nfile to the `cmake` directory. If CMake\ndoes not already support `find_package` for the library you're adding\nyou can write your own `FindDEPENDENCY.cmake` file.\nThe `SetupDEPENDENCY.cmake` file must then be included in\nthe root `spectre/CMakeLists.txt`. Be sure to test both that setting\n`LIBRARY_ROOT` works correctly for your library, and also that if the\nlibrary is required that CMake fails gracefully if the library is not\nfound.\n\n# Dependencies\n\n## Checking Dependencies\n\nGetting dependencies of libraries correct is quite difficult. SpECTRE offers the\nCMake function `check_spectre_libs_dependencies`, defined in\n`cmake/SpectreCheckDependencies.cmake`, to check the dependencies for all\nlibraries in the `libs` target. Individual target dependencies can be checked\nusing the `check_target_dependencies` CMake function defined in\n`cmake/SpectreCheckTargetDependencies.cmake`. Please see those functions in the\nsource tree for more details on how to use them.\n\n## Formaline\n\nSpECTRE's implementation of Formaline is based on, but distinct in\nimplementation from, the\n[original design](https://github.com/hypercott/formaline)\nwhich embeds an archive of the source tree into the executable. The original\ndesign creates a C/C++ file with a function that returns an array/vector of\n`char`s (a byte stream). However, this results in a very large source file (50MB\nor more), which is very slow to compile and ends up more than doubling the link\ntime. Instead, SpECTRE's Formaline implementation uses the linker `ld` to\nencode a file into an object, which means\nrather than creating a large source file, we can directly encode the source tree\narchive into the binary at the linking stage.\n\nMost of SpECTRE's Formaline is implemented\ninside the `tools/WrapExecutableLinker.sh` script. Function declarations are\nprovided in `Utilities/Formaline.hpp` and a small function that writes the\nsource file to disk is defined in `Utilities/Formaline.cpp`. The first\nFormaline-related thing done in `WrapExecutableLinker.sh` is to archive\neverything in the source directory tracked by git. Once the archive is created\nwe run `ld -r -b binary -o object.o src.tar.gz` (with unique names for\n`object.o` and `src.tar.gz` for each executable that is built to avoid name\ncollisions) to generate an object file with the source file encoded from\n`_binary_src_tar_gz_start` to `_binary_src_tar_gz_end`. Next we write a C++\nsource file that defines a function `get_archive` to convert the byte stream\ninto a `std::vector`. We also encode the output of `printenv`, the various\n`PATH` environment variables, and the CMake generated `BuildInfo.txt` file\ninto the source file. Finally, the generated source file is built during the\nlinking phase and the object file containing the source archive is linked into\nthe executable.\n\nTo further aid in reproducibility, the `printenv` output and\n`BuildInfo.txt` contents are written to HDF5 files as part of the\n`h5::Header` object. The archive of the source tree is written using the\n`h5::SourceArchive` object and can be extracted by running\n```\nh5dump -d /src.tar.gz -b LE -o src.tar.gz /path/to/hdf5/file.h5\n```\n\n# Using Kokkos\n\nKokkos support is still extremely experimental, but can be enabled by passing\n`-D SPECTRE_KOKKOS=ON` to CMake. You must pass additional CMake flags that\nKokkos will use to configure itself. For example, to enable CUDA support you\nmust pass `-D Kokkos_ENABLE_CUDA=ON`. See the\n[Kokkos documentation](https://kokkos.org/kokkos-core-wiki/keywords.html) for\ndetails.\n\n## Nvidia Compiler\n\nIf you are using CUDA to compile for Nvidia GPUs but do not have the target GPU\non the system you are compiling on then you must also tell CMake what CUDA\narchitecture to use. You can do this by passing `-D CMAKE_CUDA_ARCHITECTURES=80`\nto CMake. You must choose the architecture that will be compatible with the GPU\nyou plan to use. Note that this is actually called the compute capability\nversion by Nvidia and can be viewed\n[here](https://developer.nvidia.com/cuda-gpus).\n" }, { "path": "docs/Installation/Installation.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Installation {#installation}\n\n\\tableofcontents\n\nThis page details how to install SpECTRE on personal machines and on clusters\nthat have no official support (yet).\n\n- For details on installing SpECTRE on a number of clusters that we support\n please refer to:\n \\subpage installation_on_clusters\n- For configuring SpECTRE please refer to:\n \\subpage spectre_build_system\n- For instructions on installing SpECTRE on Apple Silicon Macs please refer to:\n \\subpage installation_on_apple_silicon\n- For information on our versioning scheme and public releases please refer to:\n \\subpage versioning_and_releases\n\n### Running containerized releases\n\n#### CLI Entrypoint\n\nA quick way to run the code without installing anything at all is with our\ncontainerized releases:\n\n```\ndocker run sxscollaboration/spectre --help\n```\n\nYou can also use [Apptainer/Singularity](https://apptainer.org) instead of\nDocker, which works better on computing clusters and is more convenient because\nit shares the host's file system:\n\n```\napptainer run docker://sxscollaboration/spectre --help\n```\n\nThe entrypoint to this container is the SpECTRE\n\\ref tutorial_cli \"command-line interface (CLI)\".\nFor example, you can generate initial data for a simulation of merging black\nholes and plot the result like this:\n\n```\napptainer run docker://sxscollaboration/spectre bbh generate-id \\\n -q 1 --chi-A 0 0 0 --chi-B 0 0 0 -D 16 -w 0.015 -a 0 -o ./bbh_id\napptainer run docker://sxscollaboration/spectre plot slice \\\n bbh_id/BbhVolume*.h5 -C 0,0,0 -n 0,0,1 -u 0,1,0 -X 24 24 \\\n -y ConformalFactor -o plot.pdf\n```\n\nThe containers currently have precompiled code only for Linux x86_64 platforms,\nand only have a limited set of executables precompiled. The supported features\navailable in the precompiled containers are:\n\n- Generating initial data\n- Running CCE (see \\ref tutorial_cce)\n- Running Python support code with the SpECTRE CLI (see \\ref tutorial_cli)\n\n#### Starting a container {#start_deploy_container}\n\nIf you'd rather use an image to start a container, you can run\n\n```\ndocker run --name spectre -i --entrypoint /bin/bash\n -t sxscollaboration/spectre:deploy\n```\n\n\\note The `--entrypoint /bin/bash` is important so you don't run the CLI.\n\n### Running static binaries\n\nAnother way of running the code without installing anything is with our\nprecompiled static binaries, which are published on GitHub:\n\n- Releases with precompiled executables:\n https://github.com/sxs-collaboration/spectre/releases\n\nThese are currently compiled only for Linux x86_64 platforms and for Intel\nHaswell architecture, so they should be compatible with machines newer than mid\n2013.\n\nWe only publish a limited set of precompiled static binaries that are useful as\nstand-alone tools, such as the CCE executables (see \\ref tutorial_cce).\n\n### Quick-start guide for code development with Docker and Visual Studio Code\n\nIf you're new to writing code for SpECTRE and would like to jump right into a\nworking development environment, a good place to start is our\n\\subpage dev_guide_quick_start_docker_vscode.\n\n### Quick-start installation {#quick_start_install}\n\nThe easiest way of installing SpECTRE natively on a new machine is this:\n\n1. Collect dependencies. You need a C++ compiler (GCC or Clang), CMake,\n BLAS/LAPACK, Boost, GSL, HDF5, and Python installed. For details on these\n required dependencies see \\ref build_dependencies. On many computing clusters\n they are available as modules. On personal machines you can install them with\n a package manager.\n\n2. Clone the SpECTRE repository:\n\n ```sh\n git clone git@github.com:sxs-collaboration/spectre.git\n export SPECTRE_HOME=$PWD/spectre\n ```\n\n3. Install Charm++:\n\n ```sh\n git clone https://github.com/UIUC-PPL/charm\n cd charm\n git checkout v8.0.0\n ./build charm++ --with-production --build-shared --disable-tls\n export CHARM_ROOT=$PWD/\n ```\n\n Choose the `` from [this list in the Charm++\n documentation](https://github.com/charmplusplus/charm?tab=readme-ov-file#how-to-choose-a-version).\n For example, choose `multicore-linux-x86_64` on a Linux laptop,\n `multicore-darwin-arm8` on an Apple Silicon laptop, and `mpi-linux-x86_64` on\n a standard computing cluster (you will also need MPI for this). See\n \\ref building-charm for details.\n\n4. Configure and build SpECTRE:\n\n ```sh\n cd $SPECTRE_HOME\n mkdir build\n cd build\n cmake \\\n -D CMAKE_C_COMPILER= \\\n -D CMAKE_CXX_COMPILER= \\\n -D CMAKE_Fortran_COMPILER=gfortran \\\n -D CMAKE_BUILD_TYPE= \\\n -D CHARM_ROOT=$CHARM_ROOT \\\n -D SPECTRE_FETCH_MISSING_DEPS=ON \\\n -D MEMORY_ALLOCATOR=SYSTEM \\\n $SPECTRE_HOME\n ```\n\n See \\ref building-spectre for details and \\ref common_cmake_flags for a list\n of possible configuration options. For example, set `-D ENABLE_OPENMP=ON`\n to enable OpenMP-parallelization for the exporter library.\n\n Now you can compile executables (again, see \\ref building-spectre for\n details). For example:\n\n ```sh\n make -j12 cli\n make -j12 BundledExporter\n ```\n\n### Installation with Spack\n\nYou can also install SpECTRE with the [Spack](https://github.com/spack/spack)\npackage manager:\n\n```sh\ngit clone https://github.com/spack/spack\nsource ./spack/share/spack/setup-env.sh\nspack compiler find\nspack external find\nspack install spectre executables=ExportCoordinates3D \\\n ^charmpp backend=multicore\n```\n\nYou probably want to customize your installation, e.g., to select a particular\nversion of SpECTRE, the executables you want to install, additional options such\nas Python bindings, or the Charm++ backend. You can display all possible options\nwith:\n\n```sh\nspack info spectre # or charmpp, etc.\n```\n\nRefer to the [Spack documentation](https://spack.readthedocs.io/en/latest/) for\nmore information.\n\n\\warning We have not found the Spack installation particularly stable since the\nSpack package manager is still in development.\n\n## Detailed installation instructions\n\nThis remainder of this page details the installation procedure for SpECTRE.\n\n### Dependencies {#build_dependencies}\n\n\\note You don't need to install any of these dependencies by hand if you\nuse a container or follow the \\ref quick_start_install.\n\n#### Required:\n\n* [GCC](https://gcc.gnu.org/) 10.0 or later,\n[Clang](https://clang.llvm.org/) 13.0 or later (see\n[here](https://apt.llvm.org/) for how to get newer versions of clang through\napt), or AppleClang 13.0.0 or later\n* [CMake](https://cmake.org/) 3.18.0 or later\n* [Git](https://git-scm.com/)\n* BLAS & LAPACK (e.g. [OpenBLAS](http://www.openblas.net))\n* [Boost](http://www.boost.org/) 1.60.0 or later\n* [GSL](https://www.gnu.org/software/gsl/) \\cite Gsl\n* [GNU make](https://www.gnu.org/software/make/)\n* [HDF5](https://support.hdfgroup.org/HDF5/) (non-mpi version on macOS)\n \\cite Hdf5\n* [Python](https://www.python.org/) 3.8 or later.\n* [Charm++](http://charm.cs.illinois.edu/) 7.0.0, or later (8 preferred).\n See also \\ref building-charm. \\cite Charmpp1 \\cite Charmpp2 \\cite Charmpp3\n\nThe following dependencies will be fetched automatically if you set\n`SPECTRE_FETCH_MISSING_DEPS=ON`:\n\n* [Blaze](https://bitbucket.org/blaze-lib/blaze/overview) v3.8.\n When installing manually, it can be beneficial to install Blaze with CMake so\n some configuration options are determined automatically, such as cache sizes.\n \\cite Blaze1 \\cite Blaze2\n* [Catch2](https://github.com/catchorg/Catch2) 3.4.0 or later.\n You can also install Catch2 from your package manager or do a standard CMake\n build and installation (as detailed in the [Catch2\n docs](https://github.com/catchorg/Catch2/blob/devel/docs/cmake-integration.md#installing-catch2-from-git-repository)).\n Compile with `CMAKE_POSITION_INDEPENDENT_CODE=ON`.\n* [LIBXSMM](https://github.com/libxsmm/libxsmm) version 1.16.1 or later. Some\n configurations of LIBXSMM build incorrectly against pthreads, causing\n ``undefined reference to 'pthread_yield'`` when building SpECTRE. It is\n unclear what conditions trigger the problem, but it is fixed in versions\n newer than 1.17. (As of this writing, there are no newer releases and\n affected systems must build from git.) \\cite Libxsmm\n* [yaml-cpp](https://github.com/jbeder/yaml-cpp) version 0.7.0 or later.\n Building with shared library support is recommended when installing from\n source. \\cite Yamlcpp\n* Python dependencies listed in `support/Python/requirements.txt`.\n Install with `pip3 install -r support/Python/requirements.txt`.\n Make sure you are working in a [Python venv](https://packaging.python.org/en/latest/guides/installing-using-pip-and-virtual-environments/#creating-a-virtual-environment)\n before installing packages.\n Alternatively, you can set `BOOTSTRAP_PY_DEPS=ON` when configuring a build\n with CMake to install missing Python packages into the build directory\n automatically.\n
\n \\include support/Python/requirements.txt\n
\n\n#### Optional:\n\n* [Pybind11](https://pybind11.readthedocs.io) 2.7.0 or later for SpECTRE Python\n bindings. Included in `support/Python/requirements.txt`. \\cite Pybind11\n* [jemalloc](https://github.com/jemalloc/jemalloc)\n* [Doxygen](https://www.doxygen.nl/index.html) 1.9.1 to 1.9.6 — to\n generate documentation\n* Python dev dependencies listed in `support/Python/dev_requirements.txt`\n — for documentation pre- and post-processing, formatting code, etc.\n Install with `pip3 install -r support/Python/dev_requirements.txt`.\n Make sure you are working in a [Python venv](https://packaging.python.org/en/latest/guides/installing-using-pip-and-virtual-environments/#creating-a-virtual-environment)\n before installing packages.\n
\n \\include support/Python/dev_requirements.txt\n
\n* [Kokkos](https://github.com/kokkos/kokkos) (experimental) - for GPU support.\n See \\ref gpu_support for details.\n* [Google Benchmark](https://github.com/google/benchmark) - to do\n microbenchmarking inside the SpECTRE framework. v1.2 or newer is required\n* [LCOV](http://ltp.sourceforge.net/coverage/lcov.php) and\n [gcov](https://gcc.gnu.org/onlinedocs/gcc/Gcov.html) — to check code test\n coverage\n* [PAPI](http://icl.utk.edu/papi/) — to access hardware performance counters\n* [ClangFormat](https://clang.llvm.org/docs/ClangFormat.html) — to format C++\n code in a clear and consistent fashion\n* [Clang-Tidy](http://clang.llvm.org/extra/clang-tidy/) — to \"lint\" C++ code\n* [Scotch](https://gitlab.inria.fr/scotch/scotch) - to build the `ScotchLB`\n graph partition based load balancer in charm++.\n* [ffmpeg](https://www.ffmpeg.org/) - for animating 1d simulations with\n matplotlib\n* [xsimd](https://github.com/xtensor-stack/xsimd) 11.0.1 or newer - for manual\n vectorization\n* [autodiff](https://github.com/autodiff/autodiff/) commit cc2aa5726fdbb258d097f87b97da3d1022f8394e\n or newer - for automatic differentiation\n* [libbacktrace](https://github.com/ianlancetaylor/libbacktrace) - to show\n source files and line numbers in backtraces of errors and asserts. Available\n by default on many systems, so you may not have to install it at all. The\n CMake configuration will tell you if you have libbacktrace installed.\n* [ParaView](https://www.paraview.org/) - for visualization \\cite Paraview1\n \\cite Paraview2 . Make sure your ParaView installation uses the same (major\n and minor) version of Python as the rest of the build.\n* [SpEC](https://www.black-holes.org/code/SpEC.html) - to load SpEC data.\n Compile the exporter in SpEC's `Support/ApplyObservers/Exporter/` directory\n (see the `Makefile` in that directory). Also make sure to compile SpEC with\n the same compiler and MPI as SpECTRE to avoid compatibility issues.\n\n#### Bundled:\n\n* [Brigand](https://github.com/edouarda/brigand)\n* [libsharp](https://github.com/Libsharp/libsharp) \\cite Libsharp\n\n## Clone the SpECTRE repository\n\nFirst, clone the [SpECTRE repository](https://github.com/sxs-collaboration/spectre)\nto a directory of your choice. In the following we will refer to it as\nSPECTRE_ROOT. You may `git clone` from GitHub, in which case SPECTRE_ROOT will\nbe `/spectre`. That is, inside SPECTRE_ROOT are `docs`,\n`src`, `support`, `tests` etc. You can also download the source and extract them\nto your desired working directory, making sure not to leave out hidden files\nwhen you `cp` or `mv` the source files.\n\n## Using Docker to obtain a SpECTRE environment {#docker_install}\n\nA [Docker](https://www.docker.com/) image is available from\n[DockerHub](https://hub.docker.com/r/sxscollaboration/spectre/) and can\nbe used to build SpECTRE on a personal machine.\n\n**Note**: If you have SELinux active\non your system you must figure out how to enable sharing files with the host\nOS. If you receive errors that you do not have permission to access a shared\ndirectory it is likely that your system has SELinux enabled. One option is to\ndisable SELinux at the expense of reducing the security of your system.\n\nTo build with the Docker image:\n\n1. Install [Docker-Desktop](https://docs.docker.com/get-docker/). For Linux, if\n you want to be able to run the following steps without `sudo`, follow the\n [post-installation-guide](https://docs.docker.com/engine/install/linux-postinstall/)\n to add a non-root user.\n\n2. Retrieve the Docker image (you may need `sudo` in front of this command)\n ```\n docker pull sxscollaboration/spectre:dev\n ```\n3. Start the Docker container (you may need `sudo`)\n ```\n docker run -v $SPECTRE_ROOT/:$SPECTRE_ROOT/ --name spectre_dev \\\n -i -t sxscollaboration/spectre:dev /bin/bash\n ```\n - `-v $SPECTRE_ROOT/:$SPECTRE_ROOT/` binds the directory `$SPECTRE_ROOT`\n (which is an environment variable you must set up or just use the actual\n path) outside the container to `$SPECTRE_ROOT` inside the container. In this\n way, files in the `$SPECTRE_ROOT` on your host system (outside the container)\n become accessible within the container through the directory SPECTRE_ROOT\n inside the container. If you wonder why the same SPECTRE_ROOT needs to be\n used for both inside and outside the container, which is why `$SPECTRE_ROOT`\n is repeated in the command above with separated by a colon, please see one of\n the notes below regarding `-v` flag.\n - The `--name spectre_dev` is optional. If you don't name your container,\n docker will generate an arbitrary name.\n - On macOS you can significantly increase the performance of file system\n operations by appending the flag `:delegated` to `-v`, e.g.\n `-v $SPECTRE_ROOT/:$SPECTRE_ROOT/:delegated` (see\n https://docs.docker.com/docker-for-mac/osxfs-caching/).\n - The `-i` flag is for interactive mode, which will drop you into the\n container.\n - It can be useful to expose a port to the host so you can run servers such\n as [Jupyter](https://jupyter.org/index.html) for accessing the Python\n bindings (see \\ref spectre_using_python) or a Python web server to view the\n documentation. To do so, append the `-p` option, e.g. `-p 8000:8000`.\n\n You will end up in a bash shell in the docker container,\n as root (you need to be root).\n Within the container, the files in `$SPECTRE_ROOT` are available and Charm++\n is installed in `/work/charm_7_0_0`. For the following steps, stay inside the\n docker container as root.\n4. Proceed with [building SpECTRE](#building-spectre).\n\n**Notes:**\n * Everything in your build directory is owned by root, and is\n accessible only within the container.\n * You should edit source files in SPECTRE_ROOT in a separate terminal\n outside the container, and use the container only for compiling and\n running the code.\n * If you exit the container (e.g. ctrl-d),\n your compilation directories are still saved, as are any other changes to\n the container that you have made.\n To restart the container, try the following commands\n (you may need `sudo`):\n 1. `docker ps -a`,\n to list all containers with their CONTAINER_IDs and CONTAINER_NAMEs,\n 2. `docker start -i CONTAINER_NAME` or `docker start -i CONTAINER_ID`,\n to restart your container (above, the CONTAINER_NAME was spectre_dev).\n * When the Docker container gets updated, you can stop it with\n `docker stop CONTAINER_NAME`, remove it with `docker rm CONTAINER_NAME`\n and then start at step 2 above to run it again.\n * You can run more than one shell in the same container, for instance\n one shell for compiling with gcc and another for compiling\n with clang.\n To add a new shell, run `docker exec -it CONTAINER_NAME /bin/bash`\n (or `docker exec -it CONTAINER_ID /bin/bash`) from\n a terminal outside the container.\n * In step 4 above, technically docker allows you to say\n `-v $SPECTRE_ROOT/:/my/new/path` to map `$SPECTRE_ROOT` outside the\n container to any path you want inside the container, but **do not do this**.\n Compiling inside the container sets up git hooks in SPECTRE_ROOT that\n contain hardcoded pathnames to SPECTRE_ROOT *as seen from inside the\n container*. So if your source paths inside and outside the container are\n different, commands like `git commit` run *from outside the container* will\n die with `No such file or directory`.\n * If you want to use Docker within VSCode, take a look at our\n [quick start guide](../DevGuide/QuickStartDockerVSCode.md) for using Docker\n with VSCode.\n\n## Using Singularity to obtain a SpECTRE environment\n\n[Singularity](https://sylabs.io) is a container alternative\nto Docker with better security and nicer integration.\n\nTo build SpECTRE with Singularity you must:\n\n1. Build [Singularity](https://sylabs.io) and add it to your\n `$PATH`\n2. `cd` to the directory where you want to store the SpECTRE Singularity image,\n source, and build directories, let's call it WORKDIR. The WORKDIR must be\n somewhere in your home directory. If this does not work for you, follow the\n Singularity instructions on setting up additional [bind\n points](https://sylabs.io/guides/3.7/user-guide/bind_paths_and_mounts.html)\n (version 3.7. For other versions, see the [docs](https://sylabs.io/docs/)).\n Once inside the WORKDIR, clone SpECTRE into `WORKDIR/SPECTRE_ROOT`.\n3. Run `sudo singularity build spectre.img\n docker://sxscollaboration/spectre:dev`.\n You can also use spectre:ci instead of spectre:dev if you want more\n compilers installed.\n\n If you get the error message that `makesquashfs` did not have enough space to\n create the image you need to set a different `SINGULARITY_TMPDIR`. This can\n be done by running: `sudo SINGULARITY_TMPDIR=/path/to/new/tmp singularity\n build spectre.img docker://sxscollaboration/spectre:dev`. Normally\n `SINGULARITY_TMPDIR` is `/tmp`, but building the image will temporarily need\n almost 8GB of space.\n\n You can control where Singularity stores the downloaded image files from\n DockerHub by specifying the `SINGULARITY_CACHEDIR` environment variable. The\n default is `$HOME/.singularity/`. Note that `$HOME` is `/root` when running\n using `sudo`.\n4. To start the container run `singularity shell spectre.img` and you\n will be dropped into a bash shell.\n5. Proceed with [building SpECTRE](#building-spectre).\n\n**Notes:**\n- You should edit source files in SPECTRE_ROOT in a separate terminal\n outside the container, and use the container only for compiling and running\n the code.\n- If you don't have the same Python version in your environment outside the\n container as the version inside the container, this will create problems\n with git hooks. The Singularity container uses python3.8 by default. Thus, it\n is up to the user to ensure that they are using the same Python version inside\n and outside the container. To use a different Python version in the container\n add `-D Python_EXECUTABLE=/path/to/python` to the cmake command where\n `/path/to/python` is usually `/usr/bin/pythonX` and `X` is the version you\n want.\n- Unlike Docker, Singularity does not keep the state between runs. However, it\n shares the home directory with the host OS so you should do all your work\n somewhere in your home directory.\n- To run more than one container just do `singularity shell spectre.img` in\n another terminal.\n- Since the data you modify lives on the host OS there is no need to worry about\n losing any data, needing to clean up old containers, or sharing data between\n containers and the host.\n\n## Using Spack to set up a SpECTRE environment\n\nSpECTRE's dependencies can be installed with\n[Spack](https://github.com/spack/spack), a package manager tailored for HPC use.\n[Install Spack](https://spack.readthedocs.io/en/latest/getting_started.html) by\ncloning it into `SPACK_DIR` (a directory of your choice). Then, enable Spack's\nshell support with `source SPACK_DIR/share/spack/setup-env.sh`. Consider adding\nthis line to your `.bash_profile`, `.bashrc`, or similar. Refer to [Spack's\ngetting started guide](https://spack.readthedocs.io/en/latest/getting_started.html)\nfor more information.\n\nOnce you have Spack installed, one way to install the SpECTRE dependencies is\nwith a [Spack environment](https://spack.readthedocs.io/en/latest/environments.html):\n\n\\include support/DevEnvironments/spack.yaml\n\nYou can also install the Spack packages listed in the environment file above\nwith a plain `spack install` if you prefer.\n\n**Notes:**\n- Spack allows very flexible configurations and we recommended you read the\n [documentation](https://spack.readthedocs.io) if you require features such as\n packages installed with different compilers.\n- For security, it is good practice to make Spack [use the system's\n OpenSSL](https://spack.readthedocs.io/en/latest/getting_started.html#openssl)\n rather than allow it to install a new copy.\n- To avoid reinstalling lots of system-provided packages with Spack, use the\n `spack external find` feature and the `--reuse` flag to `spack concretize` (or\n `spack install`). You can also install some of the dependencies with your\n system's package manager in advance, e.g., with `apt` or `brew`. If they are\n not picked up by `spack external find` automatically, register them with Spack\n manually. See the [Spack documentation on external\n packages](https://spack.readthedocs.io/en/latest/build_settings.html#external-packages)\n for details.\n- Spack works well with a module environment, such as\n [LMod](https://github.com/TACC/Lmod). See the [Spack documentation on\n modules](https://spack.readthedocs.io/en/latest/module_file_support.html) for\n details.\n\n## Building Charm++ {#building-charm}\n\nIf you are not using a container, haven't installed Charm++ with Spack, or want\nto install Charm++ manually for other reasons, follow the installation\ninstructions in the [Charm++ repository](https://github.com/UIUC-PPL/charm)\nand in their [documentation](https://charm.readthedocs.io/en/latest/quickstart.html#installing-charm).\nHere are a few notes:\n\n- Once you cloned the [Charm++ repository](https://github.com/UIUC-PPL/charm),\n run `git checkout v8.0.0` to switch to a supported, stable release of\n Charm++.\n- Apply the appropriate patch (if there is one) for the version from\n `${SPECTRE_ROOT}/support/Charm`. For example, if you have Charm++ v7.0.0\n then the patch will be `v7.0.0.patch`.\n- Choose the `LIBS` target to compile. This is needed so that we can support the\n more sophisticated load balancers in SpECTRE executables.\n- On a personal machine the correct target architecture is likely\n `multicore-linux-x86_64`, or `multicore-darwin-x86_64` on macOS. On an HPC\n system the correct Charm++ target architecture depends on the machine's\n inter-node communication architecture. It might take some experimenting to\n figure out which Charm++ configuration provides the best performance.\n- Compile Charm++ with support for shared libraries by appending the option\n `--build-shared` to the `./build` command or pass `BUILD_SHARED=ON` to the\n CMake configuration (see the [Charm++ installation\n instructions](https://github.com/UIUC-PPL/charm#building-dynamic-libraries)).\n- Passing the `--disable-tls` option to `build` or `-D DISABLE_TLS=ON` to\n cmake is required for SpECTRE's Python bindings to work.\n- When compiling Charm++ you can specify the compiler using, for example,\n ```\n ./build LIBS ARCH clang\n ```\n\n## Building SpECTRE {#building-spectre}\n\nOnce you have set up your development environment you can compile SpECTRE.\nFollow these steps:\n\n1. Create a build directory where you would like to compile SpECTRE. In the\n Docker container you could create, e.g., `/work/spectre-build`. It can be\n useful to add a descriptive label to the name of the build directory since\n you may create more later, e.g., `build-clang-Debug`. Then, `cd` into the\n build directory.\n2. Determine the location of your Charm++ installation. In the Docker container\n it is `/work/charm_7_0_0/multicore-linux-x86_64-gcc` for GCC builds and\n `/work/charm_7_0_0/mpi-linux-x86_64-smp-clang` for clang builds. For Spack\n installations you can determine it with\n `spack location --install-dir charmpp`. We refer to the install directory as\n `CHARM_ROOT` below.\n3. In your new SpECTRE build directory, configure the build with CMake:\n ```\n cmake -D CHARM_ROOT=$CHARM_ROOT SPECTRE_ROOT\n ```\n Add options to the `cmake` command to configure the build, select\n compilers, etc. For instance, to build with clang you may run:\n ```\n cmake -D CMAKE_CXX_COMPILER=clang++ \\\n -D CMAKE_C_COMPILER=clang \\\n -D CMAKE_Fortran_COMPILER=gfortran \\\n -D CHARM_ROOT=$CHARM_ROOT \\\n SPECTRE_ROOT\n ```\n See \\ref common_cmake_flags for documentation on possible configuration\n options.\n4. When cmake configuration is done, you are ready to build target executables.\n - You can see the list of available targets by running `make list` (or `ninja\n list` if you are using the Ninja generator) or by using tab completion.\n Compile targets with `make -jN TARGET` (or `ninja -jN TARGET`), where `N`\n is the number of cores to build on in parallel (e.g. `-j4`). Note that the\n Ninja generator allows you to compile individual source files too.\n - Compile the `unit-tests` target and run `ctest -L unit` to run unit tests.\n Compile `test-executables` and run `ctest` to run all tests, including\n executables. To compile `test-executables` you may have to reduce the\n number of cores you build on in parallel to avoid running out of memory.\n - To use the command-line interface (CLI), compile the `cli` target (see\n \\ref tutorial_cli).\n - To use the Python bindings, compile the `all-pybindings` target (see\n \\ref spectre_using_python).\n\n## Code Coverage Analysis\n\nFor any coverage analysis you will need to have LCOV installed on the system.\nFor documentation coverage analysis you will also need to install\n[coverxygen](https://github.com/psycofdj/coverxygen) and for test coverage\nanalysis [gcov](https://gcc.gnu.org/onlinedocs/gcc/Gcov.html).\n\nIf you have these installed (which is already done if\nyou are using the docker container), you can look at code coverage as follows:\n\n1. On a gcc build, pass `-D COVERAGE=ON` to `cmake`\n2. `make unit-test-coverage`\n3. The output is in `docs/html/unit-test-coverage`.\n" }, { "path": "docs/Installation/InstallationOnAppleSilicon.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n## Installing SpECTRE on Apple Silicon {#installation_on_apple_silicon}\n\n\\tableofcontents\n\nThe following instructions show how to install SpECTRE and its dependencies\non Apple Silicon Macs. Apple Silicon is an arm64 architecture, in contrast\nto the x86-64 architecture that SpECTRE usually targets. These instructions\nwill result in an Apple Silicon native build of SpECTRE.\n\n\\note Floating-point exception trapping is not currently\nsupported on Apple Silicon.\n\n### 0. Install the xcode command-line tools.\n\nInstall the xcode command-line tools, which include the clang compiler, etc.\nRun the following command in the terminal:\n\n```\nxcode-select --install\n```\n\n### 1. Clone spectre\n\nClone the SpECTRE repository in a directory of your choice:\n\n```sh\ngit clone git@github.com:sxs-collaboration/spectre.git\nexport SPECTRE_HOME=$PWD/spectre\n```\n\n### 2. Install python dependencies\n\nSpectre depends on python and some python packages. There are different ways to\ninstall an arm64-native python stack. The following instructions show how\nto do this using the Python 3 interpreter bundled with macOS.\n\n```sh\ncd $SPECTRE_HOME\n\n# Create a Python environment\npython3 -m venv ./env --upgrade-deps\n\n# Activate the Python environment\n. ./env/bin/activate\n\n# Install Python packages\npip install -r support/Python/requirements.txt \\\n -r support/Python/dev_requirements.txt\n\n# Optionally install additional packages you might want, like Jupyter\npip install jupyterlab\n```\n\n### 3. Install dependencies with Homebrew\n\nMost of spectre's dependencies can be installed using the\n[Homebrew](https://brew.sh) package manager. First, if you haven't already,\ninstall Homebrew by following the instructions on the\n[Homebrew](https://brew.sh) homepage. Then, run the following to install a\nFortran compiler and other dependencies:\n\n```\nbrew install gcc autoconf automake ccache cmake\nbrew install boost catch2 doxygen gsl hdf5 openblas yaml-cpp xsimd\n```\n\n\\note We use OpenBLAS instead of Apple's Accelerate framework here because\nAccelerate fails to reach the same floating point accuracy as OpenBLAS in some\nof our tests (specifically partial derivatives).\n\n### 4. Install remaining dependencies\n\nHere, install the remaining dependencies that cannot be installed with Homebrew.\nYou can install them from source manually, or use the\n[Spack](https://github.com/spack/spack) package manager (see below).\n\n#### Install manually\n\n```sh\nexport SPECTRE_DEPS_ROOT=$HOME/apps\nmkdir -p $SPECTRE_DEPS_ROOT\ncd $SPECTRE_DEPS_ROOT\n\n# Install Charm++\ngit clone https://github.com/UIUC-PPL/charm\npushd charm\ngit checkout v8.0.0\n./build charm++ multicore-darwin-arm8 --with-production -g3 -j --build-shared \\\n --disable-tls\npopd\n\n# The following dependencies are optional! They will be installed in the build\n# directory automatically if needed in the next step. You can install them\n# manually like this if you want control over where or how they are installed.\n# If you don't care, you can skip ahead.\n\n# Install Blaze\nmkdir blaze\npushd blaze\ncurl -L https://bitbucket.org/blaze-lib/blaze/downloads/blaze-3.8.tar.gz \\\n> blaze-3.8.tar.gz\ntar -xf blaze-3.8.tar.gz\nmv blaze-3.8 include\npopd\n\n# Install libxsmm\n# Need master branch of libxsmm to support Apple Silicon\ngit clone https://github.com/libxsmm/libxsmm.git\npushd libxsmm\nmake\npopd\n```\n\n#### Install with Spack\n\n```sh\n# Download spack\ncd ~\ngit clone -c feature.manyFiles=true https://github.com/spack/spack.git\ncd spack\n# Switch to latest release\ngit checkout releases/latest\n# Load shell support\n. ./share/spack/setup-env.sh\n# Find some system packages so we don't have to install them all from source\nspack external find\n# Install dependencies\nspack install \\\n charmpp@7.0.0: +shared backend=multicore build-target=charm++ \\\n blaze@3.8.2 ~blas ~lapack smp=none \\\n libxsmm@1.16.1: \\\n```\n\n### 5. Configure and build SpECTRE\n\nCreate a build directory in a location of your choice, e.g.\n\n```sh\ncd $SPECTRE_HOME\nmkdir build\ncd build\n```\n\nNext, configure SpECTRE using the following CMake command. If you installed\ndependencies with Spack, you can use `spack find -p` to retrieve the root\ndirectories of the packages and replace them in the command below.\nYou only need to specify `LIBXSMM_ROOT` and `BLAZE_ROOT` if you installed\nthose packages yourself above. The option `SPECTRE_FETCH_MISSING_DEPS` will\ntake care of downloading these if you haven't installed them above.\n\n```sh\ncmake \\\n-D CMAKE_C_COMPILER=clang \\\n-D CMAKE_CXX_COMPILER=clang++ \\\n-D CMAKE_Fortran_COMPILER=gfortran \\\n-D CMAKE_BUILD_TYPE=Debug \\\n-D BUILD_SHARED_LIBS=ON \\\n-D MEMORY_ALLOCATOR=SYSTEM \\\n-D CHARM_ROOT=${SPECTRE_DEPS_ROOT}/charm/multicore-darwin-arm8 \\\n-D SPECTRE_FETCH_MISSING_DEPS=ON \\\n-D SPECTRE_TEST_TIMEOUT_FACTOR=5 \\\n-D BLAS_ROOT=$(brew --prefix openblas) \\\n-D LAPACK_ROOT=$(brew --prefix openblas) \\\n-D LIBXSMM_ROOT=${SPECTRE_DEPS_ROOT}/libxsmm/ \\\n-D BLAZE_ROOT=${SPECTRE_DEPS_ROOT}/blaze/ \\\n..\n```\n\nFinally, build and test SpECTRE. E.g., on a Mac with 10 cores,\n\n```sh\nmake -j10 unit-tests\nmake -j10 test-executables\nctest --output-on-failure -j10\n```\n\nOptionally, to install the python bindings in your python environment,\n\n```sh\nmake -j10 all-pybindings\npip install -e ${SPECTRE_HOME}/build/bin/python\n```\n" }, { "path": "docs/Installation/InstallationOnClusters.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Installation on Clusters {#installation_on_clusters}\n\n\\tableofcontents\n\nThe installation instructions are the same for most systems because we use shell\nscripts to set up the environment for each supercomputer. We describe the\ngeneric installation instructions once, and only note special instructions if\nnecessary for the particular system. If you have already built SpECTRE and just\nwant to load the modules, source the shell file for your system and run\n`spectre_load_modules`.\n\n\\note Sample submit scripts for some systems are available in\n`support/SubmitScripts`.\n\n## General Instructions\n\n1. Run `export SPECTRE_HOME=/path/to/where/you/want/to/clone`\n2. Clone SpECTRE using `git clone SPECTRE_URL $SPECTRE_HOME` where the\n `SPECTRE_URL` is the GitHub url you want to use to clone the repo.\n3. Run `cd $SPECTRE_HOME && mkdir build && cd build`\n4. Run `. $SPECTRE_HOME/support/Environments/SYSTEM_TO_RUN_ON_gcc.sh`, where\n `SYSTEM_TO_RUN_ON` is replaced by the name of the system as described in the\n relevant section below.\n5. If you haven't already installed the dependencies, run\n `export SPECTRE_DEPS=/path/to/where/you/want/the/deps`\n Then run `spectre_setup_modules $SPECTRE_DEPS`. This\n will take a while to finish. Near the end the command will tell you how to\n make the modules available by providing a `module use` command. Make\n sure you are providing an absolute path to `spectre_setup_modules`.\n6. Run `module use $SPECTRE_DEPS/modules`\n7. Run `spectre_run_cmake`, if you get module loading errors run\n `spectre_unload_modules` and try running `spectre_run_cmake` again. CMake\n should set up successfully.\n8. Build the targets you are interested in by running, e.g.\n `make -j4 test-executables`\n\n## Anvil at Purdue University\n\nYou should build and run tests on a compute node. You can get a compute node by\nrunning\n```\nsinteractive -N1 -n 20 -p debug -t 60:00\n```\nAvoid running `module purge` because this also removes various default modules\nthat are necessary for proper operation. Instead, use `module\nrestore`. Currently the tests can only be run in serial, e.g. `ctest -j1`\nbecause all the MPI jobs end up being launched on the same core.\n\n## Frontera at TACC\n\nFollow the general instructions, using `frontera` for `SYSTEM_TO_RUN_ON`.\n\nProcesses running on the head nodes have restrictions on memory use\nthat will prevent linking the main executables. It is better to\ncompile on an interactive node. Interactive nodes can be requested\nwith the `idev` command.\n\nFor unknown reasons, incremental builds work poorly on frontera.\nRunning `make` will often unnecessarily recompile SpECTRE libraries.\n\n## CaltechHPC at Caltech\n\nCluster documentation: https://www.hpc.caltech.edu\n\nFollow the general instructions, using `caltech_hpc` for `SYSTEM_TO_RUN_ON`,\nexcept you don't need to install any dependencies, so you can skip step 5 and\nstep 6.\n\nThere are multiple types of compute nodes on CaltechHPC, which are listed on\nhttps://www.hpc.caltech.edu/resources. We compile SpECTRE to be compatible with\nall of them.\n\nWhen you go to build, you will need to get an interactive node (login nodes\nlimit the amount of memory accessible to individual users, to below the amount\nnecessary to build SpECTRE). Slurm commands are listed on\nhttps://www.hpc.caltech.edu/documentation/slurm-commands. For example to ensure\nyou get an entire node to build on, use the following command:\n\n```\nsrun [--reservation=sxs_standing] [--constraint=skylake/cascadelake/icelake] \\\n -t 02:00:00 -N 1 --exclusive -D . --pty /bin/bash\n```\n\nIf you are part of the SXS collaboration, you can use our reserved nodes by\nspecifying `--reservation=sxs_standing`. Our reserved nodes are currently\ncascadelake nodes with 56 cores each. If you want to use another type of node\nyou can specify a `--constraint`. However, note that the reservation flag won't\nwork for nodes other than cascadelake.\n\nBe sure to re-source the correct environment files once you get the interactive\nnode shell.\n\n## Ocean at Fullerton\n\nFollow the general instructions, using `ocean` for `SYSTEM_TO_RUN_ON`,\nyou do not need to install any dependencies, so you can skip steps 5 and 6.\n\n## Mbot at Cornell\n\nFollow steps 1-3 of the general instructions.\n\nThe only modules you need to load on `mbot` are `gcc/11.4.0 spectre-deps`.\nThis will load everything you need, including LLVM/Clang. You\ncan source the environment file by running\n`. $SPECTRE_HOME/support/Environments/mbot.sh` and load the modules using\n`spectre_load_modules`. This offers two functions, `spectre_run_cmake_gcc`\nand `spectre_run_cmake_clang` for the different compilers.\nThese both default to `Release` mode. If you are developing code, please use\neither `spectre_run_cmake_clang -D CMAKE_BUILD_TYPE=Debug` or\n`spectre_run_cmake_clang -D SPECTRE_DEBUG=ON` (you can also use gcc).\nThe second command with `SPECTRE_DEBUG=ON` enables sanity checks and\noptimizations. This means it can be used in production-level runs to ensure\nthere aren't any subtle bugs that might only arise after a decently\nlong simulation.\n\n## Sonic at ICTS-TIFR\n\nCluster documentation: https://it.icts.res.in/docs/sonic-cluster\n\n1. Clone the spectre source code and set `SPECTRE_HOME` to point it.\n2. Create a directory for building SpECTRE (`SPECTRE_BUILD`).\n3. Setup the software environment\n ```\n . /mnt/pfs/vaishak.p/soft/modules-5.2.0/init/bash\n ```\n Add these lines to your `.bashrc` and source it\n if you would like to make it persistent.\n4. Source the `$SPECTRE_HOME/support/Environments/Sonic.sh` script.\n5. Build SpECTRE by changing to `$SPECTRE_BUILD` and using\n one of the variants of the `spectre_run_cmake` commands.\n This by default compiles SpECTRE in Release mode,\n without debug symbols and LTO, and with system malloc.\n If you wish to compile in debug mode, with LTO/JEMALLOC, or other options,\n simply suffix the additional cmake flags to the command.\n6. Use `make` to build your targets.\n" }, { "path": "docs/Installation/VersioningAndReleases.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n# Versioning and releases {#versioning_and_releases}\n\n\\tableofcontents\n\n# Version format\n\nWe employ a date-based versioning scheme with the format `YYYY.0M.0D[.TWEAK]`,\nwhere `YYYY` is the year, `0M` the zero-padded month and `0D` the zero-padded\nday of the month when the version is released. If additional versions are\nreleased on a single day, the `TWEAK` component enumerates them. For example,\nthe first version released on May 4th, 2021 carries the name `2021.05.04`.\nAdditional versions released on May 4th, 2021 would carry the names\n`2021.05.04.1`, `2021.05.04.2`, etc.\n\nThe reason we use a date-based versioning scheme over, for example, semantic\nversioning is to avoid implying a notion of compatibility between releases (see\nsection below).\n\n# Guarantees and non-guarantees of releases\n\nEach release is **guaranteed** to pass all automated tests laid out in the\n\\ref github_actions_guide \"guide on automated tests\".\n\nWe provide **no guarantee** that releases satisfy any notion of \"compatibility\"\nwith each other. In particular, the interface of any C++ library, Python module\nor executable may change between releases. When writing code for SpECTRE we\nrecommend regularly rebasing on the latest `develop` branch of the\n[`sxs-collaboration/spectre`](https://github.com/sxs-collaboration/spectre)\nrepository and aiming to contribute your code upstream by following our \\ref\ncontributing_to_spectre \"contributing guide\" in a timely manner. That said, we\nmake an effort to retain compatibility between releases for the following\naspects of the code:\n\n- Simulation data: We try to ensure that data produced by a release remains\n compatible with future releases, in the sense that the data can be read,\n processed or converted to newer formats.\n- Python bindings: We try to offer deprecation warnings when changing the Python\n interfaces so developers of external packages that use the Python bindings\n have time to update their packages.\n\nWe may establish guarantees for specific interfaces related to these aspects.\nThese guarantees will be defined in the documentation of the respective\ninterface.\n\nWe explicitly provide **no guarantee** that input files remain compatible with\nexecutables built on different releases. Instead, we try to make input files as\nexplicit as possible by not supporting default values, so simulations don't\ncontinue with subtly changed parameters part way through. We try to reflect\nchanges that would affect running simulations in the input files, so they can\n(and often must) be reviewed before the simulation continues. Please note that\nlow-level changes or bugs may always alter results, so be advised to stick with\na particular compiled executable if a high level of reproducibility is crucial\nfor your project.\n\n# Schedule\n\nWe typically publish a release at the beginning of each month, and may publish\nadditional releases irregularly. If a major bug is discovered and fixed we will\nlikely create an unscheduled release.\n\n# How to find releases\n\nYou can find all releases on GitHub:\n\n- [sxs-collaboration/spectre releases on GitHub](https://github.com/sxs-collaboration/spectre/releases)\n\nEach release is tagged with the version name and prefixed `v` in the repository.\nFor example, this is how you can obtain the source code for the `2020.12.07`\nrelease:\n\n```sh\ngit clone -b v2020.12.07 https://github.com/sxs-collaboration/spectre\n```\n\nThe latest release is always available on the `release` branch. This is how you\ncan obtain the source code for the latest release:\n\n```sh\ngit clone -b release https://github.com/sxs-collaboration/spectre\n```\n" }, { "path": "docs/Main.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\\mainpage Introduction\n\n\\tableofcontents\n\n\\htmlonly\n

\n\n\n\n\n\n\n\n\n

\n\n\n\\endhtmlonly\n\n# What is SpECTRE? {#intro_sec}\n\nSpECTRE is an open-source code for multi-scale, multi-physics problems in\nastrophysics and gravitational physics. It is based on high-order spectral\nfinite element methods and massive parallelism. In the future, we hope that\nit can be applied to problems across discipline boundaries in fluid\ndynamics, geoscience, plasma physics, nuclear physics, and\nengineering. It runs at petascale and is designed for future exascale\ncomputers.\n\nSpECTRE is being developed in support of our collaborative Simulating\neXtreme Spacetimes (SXS) research program into the multi-messenger\nastrophysics of black hole neutron star mergers, core-collapse supernovae, and\ngamma-ray bursts.\n\n## Gallery\n\nFor an overview of some of SpECTRE's features and some simulations performed\nwith SpECTRE, visit the gallery:\n\n- Gallery: https://spectre-code.org/gallery\n\n## Citing SpECTRE\n\nPlease cite SpECTRE in any publications that make use of its code or data. Cite\nthe latest version that you use in your publication. The DOI for this version\nis:\n\n- DOI: [\\spectredoi](https://doi.org/\\spectredoi)\n\nYou can cite this BibTeX entry in your publication:\n\n\\include citation.bib\n\nTo aid reproducibility of your scientific results with SpECTRE, we recommend you\nkeep track of the version(s) you used and report this information in your\npublication. We also recommend you supply the YAML input files and, if\nappropriate, any additional C++ code you wrote to compile SpECTRE executables as\nsupplemental material to the publication.\n\nSee our [publication policy](https://spectre-code.org/publication_policies.html)\nfor more information.\n\n## Navigating the Documentation {#navigate_documentation_sec}\n\nThe SpECTRE documentation is organized into tutorials, developer guides, groups\nof related code, namespaces, and files for easier navigation. These can all be\naccessed by links in the menu bar at the top.\n\n- For instructions on **installing SpECTRE** on personal computers and clusters\n consult the \\ref installation \"Installation\" and \\ref installation_on_clusters\n \"Installation on clusters\" pages, respectively. See the\n \\ref spectre_build_system \"build system\" page for how to configure SpECTRE.\n- If you are looking to **run simulations with SpECTRE** we recommend starting\n with the \\ref tutorials \"User Tutorials\". The tutorials are designed to get\n users up and running with a simulation, as well as analyzing and visualizing\n the output.\n- For people looking to **contribute to SpECTRE** there are tutorials on the\n \\ref dev_guide \"Dev Guide\" page. For instance, the dev guide details the \\ref\n code_review_guide \"code review guidelines\", how to \\ref writing_unit_tests\n \"write unit tests\", how to \\ref writing_good_dox \"write documentation\", and\n also provides information about C++ and the philosophy behind SpECTRE\n development.\n- The [Code modules](modules.html) section contains groups of related code\n (managed through doxygen groups). For example, there is a group for all the\n data structures we use, a group for utility functions and classes, as well as\n groups for coordinate maps, domain creation, and many others. The\n [Code modules](modules.html) are designed to help developers discover existing\n functionality so that things are not re-implemented several times.\n- You can also get an overview of the code base by namespace by visiting the\n [Namespaces](namespaces.html) section.\n- To browse all files in the repository you can visit the\n [GitHub repository](https://github.com/sxs-collaboration/spectre) directly.\n\n## Logos and visuals {#logos_and_visuals}\n\nYou can find logos and other visuals (e.g. to put on slides) in various formats,\ncolors, and sizes here:\n\n- [Logos and visuals](https://drive.google.com/drive/folders/1GEvVrXNqlGojr3NBf7RMFo6BzFmf9Ww7?usp=share_link)\n" }, { "path": "docs/PublicationPolicy.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n# Publication policies {#publication_policies}\n\nSpECTRE is an open-source code that is developed and maintained by the\n[Simulating eXtreme Spacetimes (SXS) collaboration](https://black-holes.org). We\nask all authors of scientific publications that make use of SpECTRE's code or\ndata to follow the citation guidelines laid out in the section \\ref citing. An\nadditional set of guidelines, laid out in the section \\ref\nsxs_publication_policies applies to publications by members of the SXS\ncollaboration.\n\n## Citing SpECTRE {#citing}\n\nPlease cite SpECTRE in any publications that make use of its code or data. Cite\nthe latest version that you use in your publication. The DOI for this version\nis:\n\n- DOI: [\\spectredoi](https://doi.org/\\spectredoi)\n\nYou can cite this BibTeX entry in your publication:\n\n\\include citation.bib\n\nTo aid reproducibility of your scientific results with SpECTRE, we recommend you\nkeep track of the version(s) you used and report this information in your\npublication. We also recommend you supply the YAML input files and, if\nappropriate, any additional C++ code you wrote to compile SpECTRE executables as\nsupplemental material to the publication.\n\n## Policies that apply to SXS publications {#sxs_publication_policies}\n\nThese policies apply to all \"science papers\" by members of the SXS collaboration\nthat make use of SpECTRE’s code or data, as defined by the\n[SXS policies](https://github.com/sxs-collaboration/WelcomeToSXS/blob/master/SxsPolicies.md).\n\nOur publication policies have the goal that contributions to SpECTRE gain value\nin academia. For SpECTRE to be successful, it must be worth a junior\nresearcher's time to contribute to the code. Contributions are already partially\nacknowledged through authorship on the DOI, as laid out in the `Metadata.yaml`\nfile. However, authorship on the DOI alone doesn’t hold enough value in academia\nto make code contributions worthwhile that have no immediate science paper\nassociated with them, but that enable science papers down the line. Therefore,\nour policies have the purpose to grant authorship rights on science papers to\nthe developers of code that enabled them.\n\n### Guidelines for SXS paper authors\n\n- If you're a member of the SXS collaboration and use SpECTRE for your paper,\n you should probably include a list of SpECTRE developers as co-authors per the\n [SXS policies](https://github.com/sxs-collaboration/WelcomeToSXS/blob/master/SxsPolicies.md).\n- To obtain the list of co-authors, reach out to any of the people listed in the\n [SpECTRE core developers](https://github.com/orgs/sxs-collaboration/teams/spectre-core-devs/members)\n team on GitHub. Do this as early as possible, e.g., when you are setting up a\n paper repository to share early drafts and results with other co-authors.\n To contact the SpECTRE core developers, use a communication channel of your\n choice. Here are a few possibilities:\n\n - Send a message on Slack.\n - Knock on their office door.\n - Send an email to one of the core developers, or to\n [core-devs@spectre-code.org](mailto:core-devs@spectre-code.org).\n Possible wording of the email:\n\n > Dear SpECTRE core devs,\n >\n > I am / we are preparing a paper on [title or topic]. I am / we are using\n > SpECTRE in this way:\n >\n > - [Describe your use of SpECTRE briefly, e.g. as a bulleted list. Mention\n > which parts of SpECTRE you are using in particular, e.g. the initial\n > data solver, the evolution scheme, the wave extraction, etc.]\n >\n > Claims of the paper:\n >\n > - [Summarize the main claims you make in the paper. In particular, does\n > the paper make any claims about physics?]\n >\n > Please respond with the list of co-authors to include in the paper.\n >\n > Best regards,\n > [you]\n\n If you already have a draft or outline of your paper available, please feel\n free to attach it, to give the core developers a better idea of the ways you\n are using SpECTRE.\n\n The core developers will discuss among themselves, following the guidelines\n listed below, and will get back to you with a list of co-authors and their\n contributions. In the spirit of transparency within the collaboration the core\n developers will also share your description of the paper and the suggested\n list of co-authors with the\n [spectre-devel@black-holes.org](mailto:spectre-devel@black-holes.org) mailing\n list.\n- Please make the paper draft available to all co-authors as early as possible,\n e.g, by sharing access to a Git repository. This allows the co-authors to\n contribute their technical expertise to the SpECTRE-related part of the paper,\n and it also makes them aware of the ongoing work, in the spirit of\n transparency and collaboration within SXS.\n\n## Guidelines to decide who has authorship rights on SXS science papers that use SpECTRE\n\n- A contribution to SpECTRE on the order of ~500 lines of code or more should\n earn you authorship rights on the first science paper that uses the feature.\n Major contributions, such as writing a full evolution system, earns you\n authorship rights on the first three science papers that use the feature.\n \"Using the feature\" means the code contributes to the result of the paper,\n either obviously like a new coordinate map in the domain, or in a more subtle\n way like an optimization that made the simulation run faster.\n- Core developers earn authorship rights to all science papers that use SpECTRE\n for their infrastructure contributions.\n- In case of controversy, contact any person who you feel comfortable raising\n your concern with, such as one of the core developers, a member of the\n [executive committee](https://github.com/sxs-collaboration/WelcomeToSXS/blob/master/SxsPolicies.md#executive-committee),\n or the [ombudsperson](https://github.com/sxs-collaboration/WelcomeToSXS/blob/master/SxsPolicies.md#ombudsperson).\n" }, { "path": "docs/References.bib", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# When editing this file, please follow the guidelines in\n# https://spectre-code.org/writing_good_dox.html#writing_dox_citations.\n\n@article{Alcubierre2003pc,\n author = \"Alcubierre, Miguel and others\",\n title = \"{Toward standard testbeds for numerical relativity}\",\n journal = \"Class. Quant. Grav.\",\n volume = \"21\",\n year = \"2004\",\n number = \"2\",\n pages = \"589-613\",\n url = \"https://doi.org/10.1088/0264-9381/21/2/019\",\n doi = \"10.1088/0264-9381/21/2/019\",\n eprint = \"gr-qc/0305023\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n reportNumber = \"AEI-2003-041\",\n SLACcitation = \"%%CITATION = GR-QC/0305023;%%\"\n}\n\n@article{Alic2012,\n author = {Daniela Alic and Philipp Moesta and Luciano Rezzolla\n and Olindo Zanotti and Jos{\\'{e}} Luis Jaramillo},\n doi = {10.1088/0004-637x/754/1/36},\n journal = {The Astrophysical Journal},\n number = {1},\n pages = {36},\n publisher = {American Astronomical Society},\n title = {Accurate Simulations of Binary Black Hole Mergers\n in Force-free Electrodynamics},\n url = {https://doi.org/10.1088%2F0004-637x%2F754%2F1%2F36},\n volume = {754},\n year = 2012\n}\n\n@article{Anton2006,\n author = {Luis Antón and Olindo Zanotti and Juan A. Miralles\n and José M. Martí and José M. Ibáñez and José A. Font\n and José A. Pons},\n doi = {10.1086/498238},\n journal = {The Astrophysical Journal},\n month = {jan},\n pages = {296},\n title = {Numerical 3+1 General Relativistic Magnetohydrodynamics:\n A Local Characteristic Approach},\n url = {https://dx.doi.org/10.1086/498238},\n volume = {637},\n year = {2006}\n}\n\n@article{Arnold2002,\n author = \"Arnold, Douglas and Brezzi, Franco and Cockburn, Bernardo and\n L. Marini, Donatella\",\n title = \"Unified Analysis of Discontinuous {Galerkin} Methods for Elliptic\n Problems\",\n year = \"2002\",\n url = \"https://doi.org/10.1137/S0036142901384162\",\n doi = \"10.1137/S0036142901384162\",\n journal = \"SIAM Journal on Numerical Analysis\",\n number = \"5\",\n pages = \"1749--1779\",\n volume = \"39\",\n}\n\n@article{Ayachour2003,\n author = \"Ayachour, E.H.\",\n title = \"A fast implementation for {GMRES} method\",\n journal = \"Journal of Computational and Applied Mathematics\",\n volume = \"159\",\n number = \"2\",\n pages = \"269 - 283\",\n year = \"2003\",\n issn = \"0377-0427\",\n doi = \"10.1016/S0377-0427(03)00534-X\",\n url = \"http://www.sciencedirect.com/science/article/pii/S037704270300534X\",\n}\n\n@article{Balsara1999,\n author = {{Balsara}, D.~S. and {Spicer}, D.~S.},\n title = \"{A Staggered Mesh Algorithm Using High Order Godunov\n Fluxes to Ensure Solenoidal Magnetic Fields in\n Magnetohydrodynamic Simulations}\",\n journal = {Journal of Computational Physics},\n year = 1999,\n month = mar,\n volume = 149,\n pages = {270-292},\n doi = {10.1006/jcph.1998.6153},\n url = {https://doi.org/10.1006/jcph.1998.6153},\n adsurl = {http://adsabs.harvard.edu/abs/1999JCoPh.149..270B},\n adsnote = {Provided by the SAO/NASA Astrophysics Data System}\n}\n\n@article{Balsara2001,\n doi = {10.1086/318941},\n url = {https://doi.org/10.1086/318941},\n year = 2001,\n month = jan,\n publisher = {American Astronomical Society},\n volume = 132,\n number = 1,\n pages = {83--101},\n author = {Dinshaw Balsara},\n title = {Total Variation Diminishing Scheme for Relativistic\n Magnetohydrodynamics},\n journal = {Astrophysical Journal, Supplement},\n}\n\n@article{Balsara2016780,\n title = {An efficient class of WENO schemes with adaptive order},\n journal = {Journal of Computational Physics},\n volume = 326,\n pages = {780-804},\n year = 2016,\n issn = {0021-9991},\n doi = {10.1016/j.jcp.2016.09.009},\n url = {https://www.sciencedirect.com/science/article/pii/S0021999116304211},\n author = {Dinshaw S. Balsara and Sudip Garain and Chi-Wang Shu}\n}\n\n@article{Barkett2019uae,\n author = \"Barkett, Kevin and Moxon, Jordan and Scheel, Mark A. and\n Szilágyi, Béla\",\n title = \"{Spectral Cauchy-characteristic extraction of the\n gravitational wave news function}\",\n year = \"2019\",\n eprint = \"1910.09677\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = ARXIV:1910.09677;%%\"\n}\n\n@article{Barreto2004fn,\n author = {Barreto, W. and Da Silva, A. and Gomez, R. and Lehner, L.\n and Rosales, L. and Winicour, J.},\n title = {{The 3-dimensional Einstein-Klein-Gordon system in\n characteristic numerical relativity}},\n eprint = {gr-qc/0412066},\n archiveprefix = {arXiv},\n doi = {10.1103/PhysRevD.71.064028},\n journal = {Phys. Rev. D},\n volume = {71},\n pages = {064028},\n year = {2005},\n url = {https://doi.org/10.1103/PhysRevD.71.064028}\n}\n\n@article{Baumgarte1996hh,\n author = \"Baumgarte, Thomas W. and Cook, Gregory B. and Scheel,\n Mark A. and Shapiro, Stuart L. and Teukolsky, Saul A.\",\n title = \"Implementing an apparent horizon finder in\n three-dimensions\",\n journal = \"Phys. Rev.\",\n volume = \"D54\",\n year = \"1996\",\n pages = \"4849-4857\",\n doi = \"10.1103/PhysRevD.54.4849\",\n url = \"https://doi.org/10.1103/PhysRevD.54.4849\",\n eprint = \"gr-qc/9606010\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n reportNumber = \"CRSR-1115\",\n}\n\n@article{Baumgarte2006ug,\n author = \"Baumgarte, Thomas W. and Ó Murchadha, Niall and Pfeiffer,\n Harald P.\",\n title = \"The {Einstein} constraints: Uniqueness and non-uniqueness\n in the conformal thin sandwich approach\",\n journal = \"Phys. Rev.\",\n volume = \"D75\",\n year = \"2007\",\n pages = \"044009\",\n doi = \"10.1103/PhysRevD.75.044009\",\n url = \"https://doi.org/10.1103/PhysRevD.75.044009\",\n eprint = \"gr-qc/0610120\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = GR-QC/0610120;%%\"\n}\n\n@article{Baumgarte2007ht,\n author = \"Baumgarte, Thomas W. and Naculich, Stephen G.\",\n title = \"{Analytical representation of a black hole puncture solution}\",\n eprint = \"gr-qc/0701037\",\n archivePrefix = \"arXiv\",\n reportNumber = \"BOW-PH-138\",\n doi = \"10.1103/PhysRevD.75.067502\",\n url = {https://doi.org/10.1103/PhysRevD.75.067502},\n journal = \"Phys. Rev. D\",\n volume = \"75\",\n pages = \"067502\",\n year = \"2007\"\n}\n\n@book{BaumgarteShapiro,\n author = {Baumgarte, Thomas W. and Shapiro, Stuart L.},\n title = {Numerical Relativity: Solving {Einstein's} Equations on the\n Computer},\n year = {2010},\n url = {https://doi.org/10.1017/CBO9781139193344},\n doi = {10.1017/CBO9781139193344},\n publisher = {Cambridge University Press}\n}\n\n@article{BaylissTurkel,\n author = {Bayliss, Alvin and Turkel, Eli},\n title = {Radiation boundary conditions for wave-like equations},\n journal = {Communications on Pure and Applied Mathematics},\n volume = 33,\n number = 6,\n pages = {707-725},\n doi = {10.1002/cpa.3160330603},\n url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.3160330603},\n eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/cpa.3160330603},\n year = 1980\n}\n\n@article{Beckwith2011iy,\n author = \"Beckwith, Kris and Stone, James M.\",\n title = \"A Second-order {Godunov} Method for Multi-dimensional\n Relativistic Magnetohydrodynamics\",\n year = \"2011\",\n url = \"https://doi.org/10.1088/0067-0049/193/1/6\",\n doi = \"10.1088/0067-0049/193/1/6\",\n eprint = \"1101.3573\",\n archivePrefix = \"arXiv\",\n primaryClass = \"astro-ph.HE\",\n journal = \"Astrophysical Journal, Supplement\",\n number = \"1\",\n pages = \"6\",\n volume = \"193\",\n}\n\n@article{Bhagwat2017tkm,\n author = \"Bhagwat, Swetha and Okounkova, Maria and Ballmer,\n Stefan W. and Brown, Duncan A. and Giesler,\n Matthew and Scheel, Mark A. and Teukolsky, Saul A.\",\n title = \"{On choosing the start time of binary black hole\n ringdowns}\",\n eprint = \"1711.00926\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n journal = \"Phys. Rev. D\",\n volume = \"97\",\n number = \"10\",\n pages = \"104065\",\n year = \"2018\",\n doi = \"10.1103/PhysRevD.97.104065\",\n url = \"https://journals.aps.org/prd/abstract/10.1103/\n PhysRevD.97.104065\",\n}\n\n@article{Bishop1997ik,\n author = \"Bishop, Nigel T. and Gomez, Roberto and Lehner, Luis and\n Maharaj, Manoj and Winicour, Jeffrey\",\n title = \"{High powered gravitational news}\",\n journal = \"Phys. Rev.\",\n volume = \"D56\",\n year = \"1997\",\n pages = \"6298-6309\",\n doi = \"10.1103/PhysRevD.56.6298\",\n eprint = \"gr-qc/9708065\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n url = \"https://doi.org/10.1103/PhysRevD.56.6298\",\n}\n\n@incollection{Bishop1998uk,\n author = \"Bishop, Nigel T. and Gomez, Roberto and Lehner, Luis and\n Szilagyi, Bela and Winicour, Jeffrey and Isaacson,\n Richard A.\",\n title = \"{Cauchy characteristic matching}\",\n editor = \"Iyer, Bala R. and Bhawal, Biblap\",\n booktitle = \"Black Holes, Gravitational Radiation and the Universe:\n Essays in Honor of C.V. Vishveshwara\",\n journal = \"#DONE:In *Iyer, B.R. (ed.) et al.: Black holes,\n gravitational radiation and the universe* 383-408\",\n pages = \"383-408\",\n doi = \"10.1007/978-94-017-0934-7_24\",\n year = \"1998\",\n eprint = \"gr-qc/9801070\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = GR-QC/9801070;%%\"\n}\n\n@article{Bjorhus1995,\nauthor = {Bjørhus, Morten},\ntitle = {The ODE Formulation of Hyperbolic PDEs Discretized by the Spectral\n Collocation Method},\njournal = {SIAM Journal on Scientific Computing},\nvolume = {16},\nnumber = {3},\npages = {542-557},\nyear = {1995},\ndoi = {10.1137/0916035},\nURL = {https://doi.org/10.1137/0916035},\neprint = {https://doi.org/10.1137/0916035}\n}\n\n@article{Blanchet:2013haa,\n archiveprefix = {arXiv},\n author = {Blanchet, Luc},\n doi = {10.12942/lrr-2014-2},\n eprint = {1310.1528},\n journal = {Living Rev. Rel.},\n pages = {2},\n primaryclass = {gr-qc},\n title = {Gravitational Radiation from Post-Newtonian Sources and\n Inspiralling Compact Binaries},\n volume = {17},\n year = {2014}\n}\n\n@article{Bohn:2014xxa,\n author = {Bohn, Andy and Throwe, William and H\\'ebert, Fran\\c{c}ois and\n Henriksson, Katherine and Bunandar, Darius and Scheel,\n Mark A. and Taylor, Nicholas W.},\n title = {What does a binary black hole merger look like?},\n eprint = {1410.7775},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n doi = {10.1088/0264-9381/32/6/065002},\n journal = {Class. Quant. Grav.},\n volume = {32},\n number = {6},\n pages = {065002},\n year = {2015}\n}\n\n@article{Bohn:2016afc,\n author = {Bohn, Andy and Kidder, Lawrence E. and Teukolsky, Saul A.},\n title = {Parallel adaptive event horizon finder for numerical\n relativity},\n eprint = {1606.00437},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n doi = {10.1103/PhysRevD.94.064008},\n journal = {Phys. Rev. D},\n volume = {94},\n number = {6},\n pages = {064008},\n year = {2016}\n}\n\n@article{Borges20083191,\n title = {An improved weighted essentially non-oscillatory scheme for\n hyperbolic conservation laws},\n journal = {Journal of Computational Physics},\n volume = 227,\n number = 6,\n pages = {3191-3211},\n year = 2008,\n issn = {0021-9991},\n doi = {10.1016/j.jcp.2007.11.038},\n url = {https://www.sciencedirect.com/science/article/pii/S0021999107005232},\n author = {Rafael Borges and Monique Carmona and Bruno Costa and Wai Sun\n Don},\n}\n\n@article{Borrell2018,\n title = {Parallel mesh partitioning based on space filling curves},\n journal = {Computers & Fluids},\n volume = 173,\n pages = {264-272},\n year = 2018,\n issn = {0045-7930},\n doi = {10.1016/j.compfluid.2018.01.040},\n url = {https://www.sciencedirect.com/science/article/pii/S0045793018300446},\n author = {R.Borrell and J.C.Cajas and D.Mira and A.Taha and S.Koric and\n M.Vázquez and G.Houzeaux}\n}\n\n@book{Boyd2001,\n author = {Boyd, John P.},\n title = {Chebyshev and Fourier Spectral Methods},\n year = 2001,\n isbn = {0-486-41183-4},\n publisher = {Dover Publications}\n}\n\n@article{Boyle:2015nqa,\n author = \"Boyle, Michael\",\n title = \"{Transformations of asymptotic gravitational-wave data}\",\n eprint = \"1509.00862\",\n archivePrefix =\"arXiv\",\n primaryClass = \"gr-qc\",\n doi = \"10.1103/PhysRevD.93.084031\",\n journal = \"Phys.Rev.D\",\n volume = \"93\",\n number = \"8\",\n pages = \"084031\",\n year = \"2016\"\n}\n\n@article{Boyle2019kee,\n author = \"Boyle, Michael and others\",\n title = \"{The SXS Collaboration catalog of binary black hole\n simulations}\",\n year = \"2019\",\n eprint = \"1904.04831\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = ARXIV:1904.04831;%%\"\n}\n\n@article{BrandtBruegmann1997,\n title = {A Simple Construction of Initial Data for Multiple Black\n Holes},\n author = {Brandt, Steven and Br\\\"ugmann, Bernd},\n journal = {Phys. Rev. Lett.},\n volume = {78},\n issue = {19},\n pages = {3606--3609},\n numpages = {0},\n year = {1997},\n month = {May},\n publisher = {American Physical Society},\n doi = {10.1103/PhysRevLett.78.3606},\n url = {https://link.aps.org/doi/10.1103/PhysRevLett.78.3606},\n eprint = {gr-qc/0404056},\n archivePrefix = {arXiv},\n primaryClass = {gr-qc}\n}\n\n@article{Brehm2015,\n author = {Christoph Brehm and Michael F. Barad and Jeffrey A. Housman and\n Cetin C. Kiris},\n doi = {https://doi.org/10.1016/j.compfluid.2015.08.023},\n issn = {0045-7930},\n journal = {Computers & Fluids},\n keywords = {Higher order, Shock capturing, Finite difference, WENO, Localized\n artificial diffusivity, Artificial dissipation},\n pages = {184-208},\n title = {A comparison of higher-order finite-difference shock capturing\n schemes},\n url = {https://www.sciencedirect.com/science/article/pii/S0045793015002996},\n volume = {122},\n year = {2015}\n}\n\n@book{Briggs2000jp,\n title = \"A Multigrid Tutorial, Second Edition\",\n author = \"Briggs, William L and Henson, Van Emden and McCormick, Steve F\",\n year = 2000,\n url = \"http://dx.doi.org/10.1137/1.9780898719505\",\n doi = \"10.1137/1.9780898719505\",\n publisher = \"Society for Industrial and Applied Mathematics\"\n}\n\n@article{Brill1963yv,\n author = \"Brill, Dieter R. and Lindquist, Richard W.\",\n title = \"{Interaction energy in geometrostatics}\",\n url = \"https://dx.doi.org/10.1103/PhysRev.131.471\",\n doi = \"10.1103/PhysRev.131.471\",\n journal = \"Phys. Rev.\",\n volume = 131,\n pages = \"471--476\",\n year = 1963\n}\n\n@article{Brune2015,\n title = \"Composing Scalable Nonlinear Algebraic Solvers\",\n volume = \"57\",\n issn = \"1095-7200\",\n url = \"https://doi.org/10.1137/130936725\",\n doi = \"10.1137/130936725\",\n number = \"4\",\n journal = \"SIAM Review\",\n publisher = \"Society for Industrial & Applied Mathematics (SIAM)\",\n author = \"Brune, Peter R. and Knepley, Matthew G. and Smith, Barry F.\n and Tu, Xuemin\",\n year = \"2015\",\n month = \"Jan\",\n pages = \"535–565\",\n eprint = \"1607.04254\",\n archivePrefix = \"arXiv\",\n primaryClass = \"math\",\n}\n\n@article{Buchman:2012dw,\n author = \"Buchman, Luisa T. and Pfeiffer, Harald P. and Scheel, Mark A.\n and Szilagyi, Bela\",\n title = \"{Simulations of non-equal mass black hole binaries with\n spectral methods}\",\n eprint = \"1206.3015\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n doi = \"10.1103/PhysRevD.86.084033\",\n journal = \"Phys. Rev. D\",\n volume = \"86\",\n pages = \"084033\",\n year = \"2012\"\n}\n\n@article{Casoni2012,\n author = {Casoni, E. and Peraire, J. and Huerta, A.},\n title = {One-dimensional shock-capturing for high-order discontinuous\n Galerkin methods},\n journal = {International Journal for Numerical Methods in Fluids},\n volume = 71,\n number = 6,\n pages = {737-755},\n doi = {10.1002/fld.3682},\n url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.3682},\n eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.3682},\n year = 2013\n}\n\n@article{CerdaDuran2007,\n author = {{Cerd{\\'a}-Dur{\\'a}n}, P. and {Font}, J.~A. and {Dimmelmeier},\n H.},\n title = \"General relativistic simulations of\n passive-magneto-rotational core collapse with microphysics\",\n journal = {Astronomy and Astrophysics},\n year = 2007,\n month = oct,\n volume = 474,\n number = 1,\n pages = {169-191},\n doi = {10.1051/0004-6361:20077432},\n url = {https://doi.org/10.1051/0004-6361:20077432},\n archivePrefix ={arXiv},\n eprint = {astro-ph/0703597}\n}\n\n@article{CerdaDuran2008,\n author = {{Cerd{\\'a}-Dur{\\'a}n}, P. and {Font}, J.~A. and {Ant{\\'o}n},\n L. and {M{\\\"u}ller}, E.},\n title = \"A new general relativistic magnetohydrodynamics code for\n dynamical spacetimes\",\n journal = {Astronomy and Astrophysics},\n year = 2008,\n month = dec,\n volume = 492,\n number = 3,\n pages = {937-953},\n doi = {10.1051/0004-6361:200810086},\n url = {https://doi.org/10.1051/0004-6361:200810086},\n archivePrefix ={arXiv},\n eprint = {0804.4572}\n}\n\n@book{Chandrasekhar1939,\n author = \"Chandrasekhar, Subrahmanyan\",\n title = \"An introduction to the study of stellar structure\",\n year = \"1939\"\n}\n\n@article{CHEN2016604,\n title = {A fifth-order finite difference scheme for hyperbolic\n equations on block-adaptive curvilinear grids},\n journal = {Journal of Computational Physics},\n volume = 305,\n pages = {604-621},\n year = 2016,\n issn = {0021-9991},\n doi = {10.1016/j.jcp.2015.11.003},\n url = {https://www.sciencedirect.com/science/article/pii/S0021999115007378},\n author = {Yuxi Chen and Gábor Tóth and Tamas I. Gombosi},\n}\n\n@article{Cipolletta2019,\n author = {{Cipolletta}, F. and {Kalinani}, J.~V. and {Giacomazzo},\n B. and {Ciolfi}, R.},\n title = \"{Spritz: a new fully general-relativistic magnetohydrodynamic\n code}\",\n journal = {Classical and Quantum Gravity},\n year = 2020,\n month = jul,\n volume = 37,\n number = 13,\n eid = 135010,\n pages = 135010,\n doi = {10.1088/1361-6382/ab8be8},\n url = {https://doi.org/10.1088/1361-6382/ab8be8},\n archivePrefix ={arXiv},\n eprint = {1912.04794}\n}\n\n@article{CLAIN20114028,\n title = {A high-order finite volume method for systems of conservation\n laws—Multi-dimensional Optimal Order Detection (MOOD)},\n author = \"S. Clain and S. Diot and R. Loubère\",\n journal = \"Journal of Computational Physics\",\n volume = 230,\n number = 10,\n pages = \"4028 - 4050\",\n year = 2011,\n issn = \"0021-9991\",\n doi = \"10.1016/j.jcp.2011.02.026\",\n url = \"http://www.sciencedirect.com/science/article/pii/S002199911100115X\"\n}\n\n@book{Cockburn1999,\n author = \"Cockburn, Bernardo\",\n editor = \"Barth, Timothy J. and Deconinck, Herman\",\n title = \"Discontinuous Galerkin Methods for Convection-Dominated\n Problems\",\n bookTitle = \"High-Order Methods for Computational Physics\",\n year = \"1999\",\n publisher = \"Springer Berlin Heidelberg\",\n address = \"Berlin, Heidelberg\",\n pages = \"69-224\",\n isbn = \"978-3-662-03882-6\",\n doi = \"10.1007/978-3-662-03882-6_2\",\n url = \"https://doi.org/10.1007/978-3-662-03882-6_2\"\n}\n\n@ARTICLE{Cook1992,\n author = {{Cook}, Gregory B. and {Shapiro}, Stuart L. and {Teukolsky},\n Saul A.},\n title = \"{Spin-up of a Rapidly Rotating Star by Angular Momentum Loss:\n Effects of General Relativity}\",\n journal = {The Astrophysical Journal},\n year = 1992,\n month = oct,\n volume = {398},\n pages = {203},\n doi = {10.1086/171849},\n url = {https://doi.org/10.1086/171849}\n}\n\n@ARTICLE{Cook1994,\n author = {{Cook}, Gregory B. and {Shapiro}, Stuart L. and {Teukolsky},\n Saul A.},\n title = \"{Rapidly Rotating Neutron Stars in General Relativity:\n Realistic Equations of State}\",\n journal = {The Astrophysical Journal},\n year = 1994,\n month = apr,\n volume = {424},\n pages = {823},\n doi = {10.1086/173934},\n url = {https://doi.org/10.1086/173934}\n}\n\n@article{Cook1997qc,\n author = \"Cook, Gregory B. and Scheel, Mark A.\",\n title = \"{Well behaved harmonic time slices of a charged, rotating, boosted\n black hole}\",\n reportNumber = \"CRSR-1121\",\n doi = \"10.1103/PhysRevD.56.4775\",\n journal = \"Phys. Rev. D\",\n volume = \"56\",\n pages = \"4775--4781\",\n year = \"1997\",\n url = \"https://journals.aps.org/prd/abstract/10.1103/PhysRevD.56.4775\"\n}\n\n@article{Davis1988,\n author = \"Davis, S. F.\",\n title = \"Simplified Second-Order Godunov-Type Methods\",\n journal = \"SIAM J. Sci. Stat. Comput.\",\n volume = \"9\",\n year = \"1988\",\n number = \"3\",\n pages = \"445-473\",\n doi = \"10.1137/0909030\",\n url = \"https://doi.org/10.1137/0909030\"\n}\n\n@article{Deaton2013,\n author = {M. Brett Deaton and Matthew D. Duez and Francois Foucart\n and Evan O'Connor and Christian D. Ott and Lawrence E. Kidder\n and Curran D. Muhlberger and Mark A. Scheel and Bela Szilagyi},\n doi = {10.1088/0004-637X/776/1/47},\n journal = {The Astrophysical Journal},\n month = {sep},\n pages = {47},\n publisher = {The American Astronomical Society},\n title = {BLACK HOLE–NEUTRON STAR MERGERS WITH A HOT NUCLEAR EQUATION OF\n STATE: OUTFLOW AND NEUTRINO-COOLED DISK FOR A LOW-MASS,\n HIGH-SPIN CASE},\n url = {https://dx.doi.org/10.1088/0004-637X/776/1/47},\n volume = {776},\n year = {2013}\n}\n\n@article{Dedner2002,\n author = \"Dedner, A. and Kemm, F. and Kröner, D. and Munz, C.-D. and\n Schnitzer, T. and Wesenberg, M.\",\n title = \"Hyperbolic Divergence Cleaning for the {MHD} Equations\",\n year = \"2002\",\n url = \"https://doi.org/10.1006/jcph.2001.6961\",\n doi = \"10.1006/jcph.2001.6961\",\n journal = \"Journal of Computational Physics\",\n volume = \"175\",\n number = \"2\",\n pages = \"645-673\",\n}\n\n@article{DelZanna2002rv,\n author = \"Del Zanna, L. and Bucciantini, N. and Londrillo, P.\",\n title = \"{An efficient shock-capturing central-type scheme for\n multidimensional relativistic flows. II.\n Magnetohydrodynamics}\",\n journal = \"Astron. Astrophys.\",\n volume = \"400\",\n year = \"2003\",\n pages = \"397-414\",\n doi = \"10.1051/0004-6361:20021641\",\n url = \"https://doi.org/10.1051/0004-6361:20021641\",\n eprint = \"astro-ph/0210618\",\n archivePrefix = \"arXiv\",\n primaryClass = \"astro-ph\",\n SLACcitation = \"%%CITATION = ASTRO-PH/0210618;%%\"\n}\n\n@article{DelZanna2007pk,\n author = \"Del Zanna, L. and Zanotti, O. and Bucciantini, N. and\n Londrillo, P.\",\n title = \"{ECHO}: An {Eulerian Conservative High Order} scheme for\n general relativistic magnetohydrodynamics and\n magnetodynamics\",\n journal = \"Astron. Astrophys.\",\n volume = \"473\",\n year = \"2007\",\n pages = \"11-30\",\n doi = \"10.1051/0004-6361:20077093\",\n url = \"https://doi.org/10.1051/0004-6361:20077093\",\n eprint = \"0704.3206\",\n archivePrefix = \"arXiv\",\n primaryClass = \"astro-ph\",\n SLACcitation = \"%%CITATION = ARXIV:0704.3206;%%\"\n}\n\n@article{Dennison:2012vf,\n author = \"Dennison, Kenneth A. and Baumgarte, Thomas W.\",\n title = \"{Invariants for Tendex and Vortex Fields}\",\n eprint = \"1208.1218\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n doi = \"10.1103/PhysRevD.86.107503\",\n journal = \"Phys. Rev. D\",\n volume = \"86\",\n pages = \"107503\",\n year = \"2012\"\n}\n\n@book{DennisSchnabel,\n author = \"Dennis, Jr., J. E. and Schnabel, Robert B.\",\n title = \"Numerical Methods for Unconstrained Optimization and Nonlinear\n Equations\",\n doi = \"10.1137/1.9781611971200\",\n url = \"https://doi.org/10.1137/1.9781611971200\",\n year = \"1996\",\n publisher = \"Society for Industrial and Applied Mathematics\"\n}\n\n@article{Deppe2018uye,\n author = \"Deppe, Nils and Kidder, Lawrence E. and Scheel, Mark A.\n and Teukolsky, Saul A.\",\n title = \"{Critical behavior in 3D gravitational collapse of\n massless scalar fields}\",\n journal = \"Phys. Rev.\",\n volume = \"D99\",\n year = \"2019\",\n number = \"2\",\n pages = \"024018\",\n doi = \"10.1103/PhysRevD.99.024018\",\n url = \"https://doi.org/10.1103/PhysRevD.99.024018\",\n eprint = \"1802.08682\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = ARXIV:1802.08682;%%\"\n}\n\n@article{Deppe2021ada,\n author = {Deppe, Nils and H\\'ebert, Fran\\c{c}ois and Kidder, Lawrence\n E. and Teukolsky, Saul A.},\n title = {{A high-order shock capturing discontinuous\n Galerkin\\textendash{}finite difference hybrid method for\n GRMHD}},\n eprint = {2109.11645},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n doi = {10.1088/1361-6382/ac8864},\n journal = {Class. Quant. Grav.},\n volume = {39},\n number = {19},\n pages = {195001},\n year = {2022}\n}\n\n@article{Deppe2021bhi,\n author = {Deppe, Nils and others},\n title = {{Simulating magnetized neutron stars with discontinuous\n Galerkin methods}},\n eprint = {2109.12033},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n doi = {10.1103/PhysRevD.105.123031},\n journal = {Phys. Rev. D},\n volume = {105},\n number = {12},\n pages = {123031},\n year = {2022}\n}\n\n@article{Deppe2024ckt,\n author = {Deppe, Nils and others},\n title = {{Binary neutron star mergers using a discontinuous\n Galerkin-finite difference hybrid method}},\n eprint = {2406.19038},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n month = {6},\n year = {2024}\n}\n\n@article{Derry1970fk,\n author = \"Derry, L. and Isaacson, R. and Winicour, J.\",\n title = \"{Shear-free gravitational radiation}\",\n doi = \"10.1103/PhysRev.185.1647\",\n journal = \"Phys.Rev.\",\n volume = \"185\",\n pages = \"1647--1655\",\n year = \"1969\"\n}\n\n@article{Detweiler2003,\n title = {Self-force via a Green's function decomposition},\n author = {Detweiler, Steven and Whiting, Bernard F.},\n journal = {Phys. Rev. D},\n volume = {67},\n issue = {2},\n pages = {024025},\n numpages = {5},\n year = {2003},\n month = {Jan},\n publisher = {American Physical Society},\n doi = {10.1103/PhysRevD.67.024025},\n url = {https://link.aps.org/doi/10.1103/PhysRevD.67.024025}\n}\n\n@article{Diener2005tn,\n author = \"Diener, Peter and Dorband, Ernst Nils and Schnetter, Erik and\n Tiglio, Manuel\",\n title = \"{New, efficient, and accurate high order derivative and\n dissipation operators satisfying summation by parts, and\n applications in three-dimensional multi-block evolutions}\",\n eprint = \"gr-qc/0512001\",\n archivePrefix =\"arXiv\",\n doi = \"10.1007/s10915-006-9123-7\",\n journal = \"J. Sci. Comput.\",\n volume = \"32\",\n pages = \"109--145\",\n year = \"2007\"\n}\n\n@article{Dimmelmeier2001,\n doi = {10.1086/324406},\n url = {https://doi.org/10.1086%2F324406},\n year = 2001,\n month = {oct},\n publisher = {American Astronomical Society},\n volume = {560},\n number = {2},\n pages = {L163--L166},\n author = {Harald Dimmelmeier and Jose A. Font and Ewald Muller},\n title = {Gravitational Waves from Relativistic Rotational Core Collapse},\n journal = {The Astrophysical Journal}\n}\n\n@article{DIOT201243,\n title = {Improved detection criteria for the Multi-dimensional Optimal\n Order Detection (MOOD) on unstructured meshes with very\n high-order polynomials},\n author = \"S. Diot and S. Clain and R. Loubère\",\n journal = \"Computers & Fluids\",\n volume = 64,\n pages = \"43 - 63\",\n year = 2012,\n issn = \"0045-7930\",\n doi = \"10.1016/j.compfluid.2012.05.004\",\n url = {http://www.sciencedirect.com/science/article/pii/S0045793012001909},\n}\n\n@article{Diot2013,\n author = {Diot, S. and Loubère, R. and Clain, S.},\n title = {The Multidimensional Optimal Order Detection method in the\n three-dimensional case: very high-order finite volume method\n for hyperbolic systems},\n journal = {International Journal for Numerical Methods in Fluids},\n volume = 73,\n number = 4,\n pages = {362-392},\n doi = {10.1002/fld.3804},\n url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.3804},\n eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.3804},\n year = 2013\n}\n\n@article{Dumbser2007,\n author = \"Dumbser, M. and K{\\\"a}ser, M.\",\n title = \"Arbitrary high order non-oscillatory finite volume schemes on\n unstructured meshes for linear hyperbolic systems\",\n journal = \"Journal of Computational Physics\",\n volume = \"221\",\n year = \"2007\",\n pages = \"693-723\",\n doi = \"10.1016/j.jcp.2006.06.043\",\n url = \"https://doi.org/10.1016/j.jcp.2006.06.043\",\n}\n\n@article{Dumbser2013,\n author = {Michael Dumbser and Arturo Hidalgo and Olindo Zanotti},\n title = {High order space–time adaptive {ADER-WENO} finite volume schemes\n for non-conservative hyperbolic systems},\n journal = {Computer Methods in Applied Mechanics and Engineering},\n volume = {268},\n pages = {359-387},\n year = {2014},\n issn = {0045-7825},\n doi = {https://doi.org/10.1016/j.cma.2013.09.022},\n url = {https://www.sciencedirect.com/science/article/pii/S0045782513002491}\n}\n\n@article{Dumbser2014a,\n title = \"A posteriori subcell limiting of the discontinuous Galerkin\n finite element method for hyperbolic conservation laws\",\n journal = \"Journal of Computational Physics\",\n volume = \"278\",\n pages = \"47 - 75\",\n year = 2014,\n issn = \"0021-9991\",\n doi = \"10.1016/j.jcp.2014.08.009\",\n url = \"https://doi.org/10.1016/j.jcp.2014.08.009\",\n author = \"Michael Dumbser and Olindo Zanotti and Raphaël Loubère and\n Steven Diot\",\n}\n\n@article{Dumbser2017okk,\n author = \"{Dumbser, Michael and Guercilena, Federico and K\\\"oppel, Sven and\n Rezzolla, Luciano and Zanotti, Olindo}\",\n title = \"{Conformal and covariant Z4 formulation of the Einstein equations:\n strongly hyperbolic first-order reduction and solution with\n discontinuous Galerkin schemes}\",\n eprint = \"1707.09910\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n doi = \"10.1103/PhysRevD.97.084053\",\n url = \"https://doi.org/10.1103/PhysRevD.97.084053\",\n journal = \"Phys. Rev. D\",\n volume = \"97\",\n number = \"8\",\n pages = \"084053\",\n year = \"2018\"\n}\n\n@article{Estabrook1973ue,\n author = \"{Estabrook, Frank and Wahlquist, Hugo and Christensen, Steven and\n DeWitt, Bryce and Smarr, Larry and Tsiang, Elaine}\",\n title = \"{Maximally slicing a black hole}\",\n doi = \"10.1103/PhysRevD.7.2814\",\n url = \"https://doi.org/10.1103/PhysRevD.7.2814\",\n journal = \"Phys. Rev. D\",\n volume = \"7\",\n pages = \"2814--2817\",\n year = \"1973\"\n}\n\n\n@article{Etienne2008re,\n author = {Etienne, Zachariah B. and Liu, Yuk Tung and Shapiro, Stuart\n L. and Baumgarte, Thomas W.},\n title = {General relativistic simulations of black-hole-neutron-star\n mergers: Effects of black-hole spin},\n eprint = {0812.2245},\n archiveprefix = {arXiv},\n primaryclass = {astro-ph},\n doi = {10.1103/PhysRevD.79.044024},\n journal = {Phys. Rev. D},\n volume = {79},\n pages = {044024},\n year = {2009}\n}\n\n@article{Etienne2010ui,\n author = \"Etienne, Zachariah B. and Liu, Yuk Tung and Shapiro, Stuart\n L.\",\n title = \"{Relativistic magnetohydrodynamics in dynamical spacetimes: A\n new AMR implementation}\",\n journal = \"Phys. Rev.\",\n volume = \"D82\",\n year = \"2010\",\n pages = \"084031\",\n doi = \"10.1103/PhysRevD.82.084031\",\n eprint = \"1007.2848\",\n archivePrefix = \"arXiv\",\n primaryClass = \"astro-ph.HE\",\n SLACcitation = \"%%CITATION = ARXIV:1007.2848;%%\"\n}\n\n@article{Etienne2017,\n author = {Zachariah B Etienne and Mew-Bing Wan and Maria C Babiuc\n and Sean T McWilliams and Ashok Choudhary},\n doi = {10.1088/1361-6382/aa8ab3},\n journal = {Classical and Quantum Gravity},\n month = {sep},\n number = {21},\n pages = {215001},\n publisher = {{IOP} Publishing},\n title = {{GiRaFFE}: an open-source general relativistic force-free\n electrodynamics code},\n url = {https://doi.org/10.1088%2F1361-6382%2Faa8ab3},\n volume = {34},\n year = 2017\n}\n\n@article{Fischer2021voj,\n author = {Fischer, Nils L. and Pfeiffer, Harald P.},\n title = {Unified discontinuous {Galerkin} scheme for a large class of\n elliptic equations},\n year = {2022},\n month = {Jan},\n eprint = {2108.05826},\n archiveprefix = {arXiv},\n primaryclass = {math.NA},\n journal = {Phys. Rev. D},\n volume = {105},\n issue = {2},\n pages = {024034},\n numpages = {22},\n doi = {10.1103/PhysRevD.105.024034}\n}\n\n@article{Fishbone1976apj,\n author = \"Fishbone, L. G. and Moncrief, V.\",\n title = \"Relativistic Fluid Disks in Orbit Around {Kerr} Black Holes\",\n year = \"1976\",\n url = \"https://doi.org/10.1086/154565\",\n doi = \"10.1086/154565\",\n journal = \"The Astrophysical Journal\",\n number = \"1\",\n pages = \"962--976\",\n volume = \"207\",\n}\n\n@ARTICLE{Font1998,\n author = {{Font}, Jos{\\'e} A. and {Ib{\\'a}{\\~n}ez}, J.~M.},\n title = \"{A Numerical Study of Relativistic Bondi-Hoyle Accretion onto\n a Moving Black Hole: Axisymmetric Computations in a\n Schwarzschild Background}\",\n journal = {The Astrophysical Journal},\n year = 1998,\n month = \"Feb\",\n volume = 494,\n number = 1,\n pages = {297-316},\n doi = {10.1086/305205},\n adsurl = {https://ui.adsabs.harvard.edu/abs/1998ApJ...494..297F},\n}\n\n@book{Fornberg1996,\n author = {Fornberg, Bengt},\n title = {A Practical Guide to Pseudospectral Methods},\n year = 1996,\n isbn = {0-521-49582-2},\n url = {https://doi.org/10.1017/CBO9780511626357},\n doi = {10.1017/CBO9780511626357},\n publisher = {Cambridge University Press}\n}\n\n@article{Fornberg1998,\n author = {Fornberg, Bengt},\n title = {Classroom Note: Calculation of Weights in Finite\n Difference Formulas},\n journal = {SIAM Review},\n volume = 40,\n number = 3,\n pages = {685-691},\n year = 1998,\n doi = {10.1137/S0036144596322507},\n url = \"https://doi.org/10.1137/S0036144596322507\"\n}\n\n@article{Fortunato2019jl,\n title = \"Efficient Operator-Coarsening Multigrid Schemes for Local\n Discontinuous {Galerkin} Methods\",\n author = \"Fortunato, Daniel and Rycroft, Chris H and Saye, Robert\",\n journal = \"SIAM J. Sci. Comput.\",\n publisher = \"Society for Industrial and Applied Mathematics\",\n volume = 41,\n number = 6,\n pages = \"A3913--A3937\",\n month = jan,\n year = 2019,\n url = \"https://doi.org/10.1137/18M1206357\",\n issn = \"1064-8275\",\n doi = \"10.1137/18M1206357\"\n}\n\n@article{Foucart2008qt,\n author = {Foucart, Francois and Kidder, Lawrence E. and Pfeiffer,\n Harald P. and Teukolsky, Saul A.},\n title = {Initial data for black hole-neutron star binaries: A\n Flexible, high-accuracy spectral method},\n eprint = {0804.3787},\n archivePrefix = {arXiv},\n primaryClass = {gr-qc},\n doi = {10.1103/PhysRevD.77.124051},\n journal = {Phys. Rev. D},\n volume = {77},\n pages = {124051},\n year = {2008}\n}\n\n@article{Foucart2015vpa,\n author = \"Foucart, Francois and O'Connor, Evan and Roberts, Luke\n and Duez, Matthew D. and Haas, Roland and Kidder,\n Lawrence E. and Ott, Christian D. and Pfeiffer,\n Harald P. and Scheel, Mark A. and Szilagyi, Bela\",\n title = \"{Post-merger evolution of a neutron star-black hole\n binary with neutrino transport}\",\n journal = \"Phys. Rev.\",\n volume = \"D91\",\n year = \"2015\",\n number = \"12\",\n pages = \"124021\",\n doi = \"10.1103/PhysRevD.91.124021\",\n eprint = \"1502.04146\",\n archivePrefix = \"arXiv\",\n primaryClass = \"astro-ph.HE\",\n SLACcitation = \"%%CITATION = ARXIV:1502.04146;%%\"\n}\n\n@article{Foucart2017mbt,\n author = \"Foucart, Francois\",\n title = \"{Monte Carlo closure for moment-based transport schemes in\n general relativistic radiation hydrodynamic simulations}\",\n eprint = \"1708.08452\",\n archivePrefix = \"arXiv\",\n primaryClass = \"astro-ph.HE\",\n doi = \"10.1093/mnras/sty108\",\n journal = \"Mon. Not. Roy. Astron. Soc.\",\n volume = \"475\",\n number = \"3\",\n pages = \"4186--4207\",\n year = \"2018\"\n}\n\n@article{Foucart2021mcb,\n author = \"Foucart, Francois and Duez, Matthew D. and Hebert, Francois and\n Kidder, Lawrence E. and Kovarik, Phillip and Pfeiffer, Harald P.\n and Scheel, Mark A.\",\n title = \"{Implementation of Monte Carlo Transport in the General\n Relativistic SpEC Code}\",\n eprint = \"2103.16588\",\n archivePrefix = \"arXiv\",\n primaryClass = \"astro-ph.HE\",\n doi = \"10.3847/1538-4357/ac1737\",\n journal = \"Astrophys. J.\",\n volume = \"920\",\n number = \"2\",\n pages = \"82\",\n year = \"2021\"\n}\n\n@article{Galeazzi2013mia,\n author = \"Galeazzi, Filippo and Kastaun, Wolfgang and Rezzolla, Luciano and\n Font, Jos\\'e A.\",\n title = \"{Implementation of a simplified approach to radiative transfer\n in general relativity}\",\n eprint = \"1306.4953\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n doi = \"10.1103/PhysRevD.88.064009\",\n journal = \"Phys. Rev. D\",\n volume = \"88\",\n pages = \"064009\",\n year = \"2013\"\n}\n\n@article{Gammie2003,\n author = \"Gammie, Charles F. and McKinney, Jonathan C. and Tóth, Gábor\",\n title = \"{HARM}: A Numerical Scheme for General Relativistic\n Magnetohydrodynamics\",\n journal = \"The Astrophysical Journal\",\n volume = \"589\",\n number = \"1\",\n pages = \"444\",\n year = \"2003\",\n doi = \"10.1086/374594\",\n url = \"https://doi.org/10.1086/374594\",\n}\n\n@article{Gardiner2005hy,\n author = \"Gardiner, Thomas A. and Stone, James M.\",\n title = \"{An Unsplit Godunov method for ideal MHD via constrained\n transport}\",\n journal = \"J. Comput. Phys.\",\n volume = \"205\",\n year = \"2005\",\n pages = \"509-539\",\n doi = \"10.1016/j.jcp.2004.11.016\",\n url = \"https://10.1016/j.jcp.2004.11.016\",\n eprint = \"astro-ph/0501557\",\n archivePrefix = \"arXiv\",\n primaryClass = \"astro-ph\",\n SLACcitation = \"%%CITATION = ASTRO-PH/0501557;%%\"\n}\n\n@article{Gassner20114232,\n title = {Explicit one-step time discretizations for discontinuous\n Galerkin and finite volume schemes based on local predictors},\n journal = {Journal of Computational Physics},\n volume = {230},\n number = {11},\n pages = {4232-4247},\n year = {2011},\n note = {Special issue High Order Methods for CFD Problems},\n issn = {0021-9991},\n doi = {https://doi.org/10.1016/j.jcp.2010.10.024},\n url = {https://www.sciencedirect.com/science/article/pii/S0021999110005802},\n author = {Gregor Gassner and Michael Dumbser and Florian Hindenlang and\n Claus-Dieter Munz}\n}\n\n@article{Giacomazzo2006,\n author = {{Giacomazzo}, Bruno and {Rezzolla}, Luciano},\n title = \"{The exact solution of the Riemann problem in relativistic\n magnetohydrodynamics}\",\n journal = {Journal of Fluid Mechanics},\n keywords = {General Relativity and Quantum Cosmology, Astrophysics},\n year = 2006,\n month = sep,\n volume = 562,\n pages = {223-259},\n doi = {10.1017/S0022112006001145},\n url = {https://doi.org/10.1017/S0022112006001145},\n archivePrefix ={arXiv},\n eprint = {gr-qc/0507102},\n primaryClass = {gr-qc}\n}\n\n@article{Goldberg1966uu,\n author = \"Goldberg, J. N. and MacFarlane, A. J. and Newman, E. T.\n and Rohrlich, F. and Sudarshan, E. C. G.\",\n title = \"{Spin s spherical harmonics and edth}\",\n journal = \"J. Math. Phys.\",\n volume = \"8\",\n year = \"1967\",\n pages = \"2155\",\n doi = \"10.1063/1.1705135\",\n url = \"https://doi.org/10.1063/1.1705135\"\n}\n\n@article{Gundlach1997us,\n author = \"Gundlach, Carsten\",\n title = \"Pseudospectral apparent horizon finders: An Efficient\n new algorithm\",\n journal = \"Phys. Rev.\",\n volume = \"D57\",\n year = \"1998\",\n pages = \"863-875\",\n doi = \"10.1103/PhysRevD.57.863\",\n url = \"https://doi.org/10.1103/PhysRevD.57.863\",\n eprint = \"gr-qc/9707050\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n}\n\n@book{Hairer1993,\n address = {Berlin},\n author = {Hairer, E. and N{\\o}rsett, S.P. and Wanner, G.},\n keywords = {imported},\n publisher = {Springer},\n title = {Solving Ordinary Differential Equations {I} Nonstiff problems},\n year = 1993\n}\n\n@Inbook{Hairer1996,\n author=\"Hairer, Ernst and Wanner, Gerhard\",\n title=\"Solving Ordinary Differential Equations II: Stiff and\n Differential-Algebraic Problems\",\n year=\"1996\",\n publisher=\"Springer Berlin Heidelberg\",\n address=\"Berlin, Heidelberg\",\n isbn=\"978-3-642-05221-7\",\n doi=\"10.1007/978-3-642-05221-7_1\",\n url=\"https://doi.org/10.1007/978-3-642-05221-7_1\"\n}\n\n@article{Handmer2014qha,\n author = \"Handmer, Casey J. and Szilagyi, B.\",\n title = \"{Spectral Characteristic Evolution: A New Algorithm for\n Gravitational Wave Propagation}\",\n journal = \"Class. Quant. Grav.\",\n volume = \"32\",\n year = \"2015\",\n number = \"2\",\n pages = \"025008\",\n doi = \"10.1088/0264-9381/32/2/025008\",\n eprint = \"1406.7029\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n url = \"https://doi.org/10.1088/0264-9381/32/2/025008\"\n}\n\n@article{Hannam2008,\n title = {Wormholes and trumpets: Schwarzschild spacetime for\n the moving-puncture generation},\n author = {Hannam, Mark and Husa, Sascha and Ohme, Frank and\n Br\\\"ugmann, Bernd and \\'O Murchadha, Niall},\n journal = {Phys. Rev. D},\n volume = 78,\n issue = 6,\n pages = 064020,\n numpages = 19,\n year = 2008,\n month = {Sep},\n publisher = {American Physical Society},\n doi = {10.1103/PhysRevD.78.064020},\n url = {https://link.aps.org/doi/10.1103/PhysRevD.78.064020}\n}\n\n@article{Harten1983,\n author = \"Harten, A., and Lax, P. D., and B. van Leer\",\n title = \"{On Upstream Differencing and Godunov-Type Schemes\n for Hyperbolic Conservation Laws}\",\n journal = \"SIAM Review\",\n volume = \"25\",\n year = \"1983\",\n number = \"1\",\n pages = \"35-61\",\n doi = \"10.1137/1025002\",\n url = \"https://doi.org/10.1137/1025002\"\n}\n\n@article{Harten19973,\n title = {Uniformly High Order Accurate Essentially Non-oscillatory\n Schemes, III},\n author = \"Ami Harten and Bjorn Engquist and Stanley Osher and Sukumar\n R. Chakravarthy\",\n journal = \"Journal of Computational Physics\",\n volume = 131,\n number = 1,\n pages = \"3 - 47\",\n year = 1997,\n issn = \"0021-9991\",\n doi = \"10.1006/jcph.1996.5632\",\n url = {http://www.sciencedirect.com/science/article/pii/S0021999196956326}\n}\n\n@book{Hartle2003gravity,\n author = \"Hartle, J.B.\",\n title = \"Gravity: An Introduction to {Einstein's} General Relativity\",\n isbn = \"9780805386622\",\n lccn = \"2002151118\",\n year = \"2003\",\n publisher = \"Addison-Wesley\",\n url = \"https://www.pearson.com/us/higher-education/program/Hartle-Gravity-An-Introduction-to-Einstein-s-General-Relativity/PGM298455.html\",\n}\n\n@ARTICLE{Heger2005,\n author = {{Heger}, A. and {Woosley}, S.~E. and {Spruit}, H.~C.},\n title = \"{Presupernova Evolution of Differentially Rotating Massive\n Stars Including Magnetic Fields}\",\n journal = {The Astrophysical Journal},\n keywords = {Stars: Pulsars: General, Stars: Evolution, Stars: Magnetic\n Fields, Stars: Rotation, Astrophysics},\n year = 2005,\n month = jun,\n volume = {626},\n number = {1},\n pages = {350-363},\n doi = {10.1086/429868},\narchivePrefix = {arXiv},\n eprint = {astro-ph/0409422},\n primaryClass = {astro-ph},\n adsurl = {https://ui.adsabs.harvard.edu/abs/2005ApJ...626..350H},\n adsnote = {Provided by the SAO/NASA Astrophysics Data System}\n}\n\n@article{Hemberger2012jz,\n author = \"Hemberger, Daniel A. and Scheel, Mark A. and Kidder,\n Lawrence E. and Szilágyi, Béla and Lovelace, Geoffrey\n and Taylor, Nicholas W. and Teukolsky, Saul A.\",\n title = \"Dynamical Excision Boundaries in Spectral Evolutions of\n Binary Black Hole Spacetimes\",\n journal = \"Class. Quant. Grav.\",\n volume = \"30\",\n year = \"2013\",\n pages = \"115001\",\n doi = \"10.1088/0264-9381/30/11/115001\",\n url = \"https://doi.org/10.1088/0264-9381/30/11/115001\",\n eprint = \"1211.6079\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n}\n\n@book{HesthavenWarburton,\n author = \"Hesthaven, Jan S. and Warburton, Tim\",\n title = \"Nodal Discontinuous {Galerkin} Methods\",\n year = \"2008\",\n url = \"https://doi.org/10.1007/978-0-387-72067-8\",\n doi = \"10.1007/978-0-387-72067-8\",\n publisher = \"Springer\",\n}\n\n@article{Hilditch:2012fp,\n author = \"Hilditch, David and Bernuzzi, Sebastiano and Thierfelder, Marcus\n and Cao, Zhoujian and Tichy, Wolfgang and Bruegmann, Bernd\",\n title = \"{Compact binary evolutions with the Z4c formulation}\",\n eprint = \"1212.2901\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n doi = \"10.1103/PhysRevD.88.084057\",\n url = \"https://doi.org/10.1103/PhysRevD.88.084057\",\n journal = \"Phys. Rev. D\",\n volume = \"88\",\n pages = \"084057\",\n year = \"2013\"\n}\n\n@article{Holst2004wt,\n author = \"Holst, Michael and Lindblom, Lee and Owen, Robert and\n Pfeiffer, Harald P. and Scheel, Mark A. and Kidder,\n Lawrence E.\",\n title = \"Optimal constraint projection for hyperbolic evolution\n systems\",\n journal = \"Phys. Rev.\",\n volume = \"D70\",\n year = \"2004\",\n pages = \"084017\",\n doi = \"10.1103/PhysRevD.70.084017\",\n url = \"https://doi.org/10.1103/PhysRevD.70.084017\",\n eprint = \"gr-qc/0407011\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = GR-QC/0407011;%%\"\n}\n\n@Article{Hou2007,\n author = \"Hou, Songming and Liu, Xu-Dong\",\n title = \"Solutions of Multi-dimensional Hyperbolic Systems of\n Conservation Laws by Square Entropy Condition Satisfying\n Discontinuous Galerkin Method\",\n journal = \"Journal of Scientific Computing\",\n year = 2007,\n month = \"May\",\n day = 01,\n volume = 31,\n number = 1,\n pages = \"127--151\",\n issn = \"1573-7691\",\n doi = \"10.1007/s10915-006-9105-9\",\n url = \"https://doi.org/10.1007/s10915-006-9105-9\"\n}\n\n@article{Jiang1996,\n author = {Guang-Shan Jiang and Chi-Wang Shu},\n doi = {https://doi.org/10.1006/jcph.1996.0130},\n issn = {0021-9991},\n journal = {Journal of Computational Physics},\n number = {1},\n pages = {202-228},\n title = {Efficient Implementation of Weighted ENO Schemes},\n url = {https://www.sciencedirect.com/science/article/pii/S0021999196901308},\n volume = {126},\n year = {1996}\n}\n\n@article{Kastaun2020uxr,\n author = \"Kastaun, Wolfgang and Kalinani, Jay Vijay and Ciolfi,\n Riccardo\",\n title = \"{Robust Recovery of Primitive Variables in Relativistic Ideal\n Magnetohydrodynamics}\",\n eprint = \"2005.01821\",\n archivePrefix =\"arXiv\",\n primaryClass = \"gr-qc\",\n doi = \"10.1103/PhysRevD.103.023018\",\n url = \"https://doi.org/10.1103/PhysRevD.103.023018\",\n journal = \"Phys. Rev. D\",\n volume = 103,\n number = 2,\n pages = 023018,\n year = 2021\n}\n\n@article{Kennedy2003,\n author = \"Kennedy, Christopher A. and Carpenter, Mark H.\",\n title = \"Additive {Runge-Kutta} schemes for convection-diffusion-reaction\n equations\",\n journal = \"Applied Numerical Mathematics\",\n volume = \"44\",\n number = \"1\",\n pages = \"139--181\",\n year = \"2003\",\n doi = \"10.1016/S0168-9274(02)00138-1\",\n issn = \"0168-9274\",\n url = \"https://www.sciencedirect.com/science/article/pii/S0168927402001381\",\n}\n\n@techreport{Kennedy2016,\n author = \"Kennedy, Christopher A. and Carpenter, Mark H.\",\n title = \"Diagonally Implicit {Runge-Kutta} Methods for Ordinary Differential\n Equations. {A} Review\",\n number = \"20160005923\",\n institution = \"NASA STI Repository\",\n year = \"2016\",\n month = \"March\",\n url = \"https://ntrs.nasa.gov/citations/20160005923\"\n}\n\n@article{Kidder2001tz,\n author = \"Kidder, Lawrence E. and Scheel, Mark A. and\n Teukolsky, Saul A.\",\n title = \"Extending the lifetime of 3-D black hole computations with a\n new hyperbolic system of evolution equations\",\n eprint = {gr-qc/0105031},\n archiveprefix = {arXiv},\n doi = {10.1103/PhysRevD.64.064017},\n journal = {Phys. Rev. D},\n volume = {64},\n pages = {064017},\n year = {2001}\n}\n\n@article{Kidder2004rw,\n author = \"Kidder, Lawrence E. and Lindblom, Lee and\n Scheel, Mark A. and Buchman, Luisa T. and\n Pfeiffer, Harald P.\",\n title = \"{Boundary conditions for the Einstein evolution system}\",\n eprint = \"gr-qc/0412116\",\n archivePrefix = \"arXiv\",\n doi = \"10.1103/PhysRevD.71.064020\",\n journal = \"Phys. Rev. D\",\n volume = \"71\",\n pages = \"064020\",\n year = \"2005\"\n}\n\n@article{Kidder2016hev,\n author = \"Kidder, Lawrence E. and Field, Scott E. and Foucart,\n Francois and Schnetter, Erik and Teukolsky, Saul A. and\n Bohn, Andy and Deppe, Nils and Diener, Peter and Hébert,\n François and Lippuner, Jonas and Miller, Jonah and Ott,\n Christian D. and Scheel, Mark A. and Vincent, Trevor\",\n title = \"{SpECTRE}: A task-based discontinuous {Galerkin} code for\n relativistic astrophysics\",\n year = \"2017\",\n url = \"https://doi.org/10.1016/j.jcp.2016.12.059\",\n doi = \"10.1016/j.jcp.2016.12.059\",\n eprint = \"1609.00098\",\n archivePrefix = \"arXiv\",\n primaryClass = \"astro-ph.HE\",\n issn = \"0021-9991\",\n journal = \"Journal of Computational Physics\",\n pages = \"84--114\",\n volume = \"335\",\n}\n\n@article{Komissarov1999,\n author = \"Komissarov, S. S.\",\n title = \"A {Godunov}-type scheme for relativistic magnetohydrodynamics\",\n year = \"1999\",\n url = \"https://doi.org/10.1046/j.1365-8711.1999.02244.x\",\n journal = \"Monthly Notices of the Royal Astronomical Society\",\n volume = \"303\",\n number = \"2\",\n pages = \"343--366\",\n}\n\n@article{Komissarov2002,\n author = {Komissarov, S. S.},\n doi = {10.1046/j.1365-8711.2002.05313.x},\n issn = {0035-8711},\n journal = {Monthly Notices of the Royal Astronomical Society},\n number = {3},\n pages = {759-766},\n title = {{Time-dependent, force-free, degenerate electrodynamics}},\n url = {https://doi.org/10.1046/j.1365-8711.2002.05313.x},\n volume = {336},\n year = {2002}\n}\n\n@article{Komissarov2004,\n author = {Komissarov, S. S.},\n doi = {10.1111/j.1365-2966.2004.07598.x},\n issn = {0035-8711},\n journal = {Monthly Notices of the Royal Astronomical Society},\n month = may,\n number = {2},\n pages = {427--448},\n title = {Electrodynamics of black hole magnetospheres},\n url = {https://doi.org/10.1111/j.1365-2966.2004.07598.x},\n urldate = {2022-09-28},\n volume = {350},\n year = {2004}\n}\n\n@article{Komissarov2006,\n author = {Komissarov, S. S.},\n doi = {https://doi.org/10.1111/j.1365-2966.2005.09932.x},\n eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1365-2966.2005.09932.x},\n journal = {Monthly Notices of the Royal Astronomical Society},\n keywords = {MHD, relativity, pulsars: general, stars: winds and outflows},\n number = {1},\n pages = {19-31},\n title = {Simulations of the axisymmetric magnetospheres of neutron stars},\n url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1365-2966.2005.09932.x},\n volume = {367},\n year = {2006}\n}\n\n@article{Komissarov2011,\n author = {Komissarov, S. S.},\n doi = {https://doi.org/10.1111/j.1745-3933.2011.01150.x},\n eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1745-3933.2011.01150.x},\n journal = {Monthly Notices of the Royal Astronomical Society: Letters},\n keywords = {black hole physics, magnetic fields, relativistic processes},\n number = {1},\n pages = {L94-L98},\n title = {3+1 magnetodynamics},\n url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1745-3933.2011.01150.x},\n volume = {418},\n year = {2011}\n}\n\n@book{Kopriva,\n author = \"Kopriva, David A.\",\n title = \"Implementing Spectral Methods for Partial Differential\n Equations\",\n year = \"2009\",\n url = \"https://doi.org/10.1007/978-90-481-2261-5\",\n doi = \"10.1007/978-90-481-2261-5\",\n publisher = \"Springer\",\n}\n\n@article{Kozlowski1978aa,\n author = \"Kozlowski, M. and Jaroszynski, M. and Abramowicz, M. A.\",\n title = \"The analytic theory of fluid disks orbiting the {Kerr}\n black hole\",\n year = \"1978\",\n url = \"http://cdsads.u-strasbg.fr/abs/1978A%26A....63..209K\",\n journal = \"Astronomy and Astrophysics\",\n volume = \"63\",\n number = \"1-2\",\n pages = \"209--220\",\n}\n\n@inproceedings{Kreiss1973,\n title = {Methods for the approximate solution of time dependent\n problems},\n author = {Heinz-Otto Kreiss},\n year = {1973},\n volume = {10},\n series = {Global Atmospheric Research Programme},\n publisher = {International Council of Scientific Unions, World\n Meteorological Organization}\n}\n\n@article{Krivodonova2004,\n author = \"L. Krivodonova and J. Xin and J.-F. Remacle and N. Chevaugeon\n and J.E. Flaherty\",\n title = \"Shock detection and limiting with discontinuous {Galerkin} methods\n for hyperbolic conservation laws\",\n journal = \"Applied Numerical Mathematics\",\n volume = \"48\",\n number = \"3\",\n pages = \"323 - 338\",\n year = \"2004\",\n note = \"Workshop on Innovative Time Integrators for PDEs\",\n issn = \"0168-9274\",\n doi = \"https://doi.org/10.1016/j.apnum.2003.11.002\",\n url = \"http://www.sciencedirect.com/science/article/pii/S0168927403001831\",\n}\n\n@article{Krivodonova2007,\n title = \"Limiters for high-order discontinuous {Galerkin} methods\",\n journal = \"Journal of Computational Physics\",\n volume = \"226\",\n number = \"1\",\n pages = \"879 - 896\",\n year = \"2007\",\n issn = \"0021-9991\",\n url = \"https://doi.org/10.1016/j.jcp.2007.05.011\",\n doi = \"10.1016/j.jcp.2007.05.011\",\n author = \"Krivodonova, Lilia\"\n}\n\n@book{Kulikovskii2000,\n title = \"Mathematical Aspects of Numerical Solution of Hyperbolic\n Systems\",\n author = \"Kulikovskii, A. G. and Pogorelov, N. V. and Semenov, A. Y.\",\n isbn = \"9780367397739\",\n series = \"Monographs and Surveys in Pure and Applied Mathematics\",\n url = \"https://www.crcpress.com/Mathematical-Aspects-of-Numerical-Solution-of-Hyperbolic-Systems/Kulikovskii-Pogorelov-Semenov/p/book/9780367397739\",\n year = \"2000\",\n publisher = \"CRC Press\"\n}\n\n@article{Kuzmin2014,\n title = \"Hierarchical slope limiting in explicit and implicit discontinuous\n Galerkin methods\",\n author = \"Kuzmin, Dmitri\",\n journal = \"Journal of Computational Physics\",\n volume = \"257\",\n pages = \"1140-1162\",\n year = \"2014\",\n issn = \"0021-9991\",\n doi = \"https://doi.org/10.1016/j.jcp.2013.04.032\",\n url = \"https://www.sciencedirect.com/science/article/pii/S0021999113003161\",\n}\n\n@article{Lara2024rwa,\n author = {Lara, Guillermo and Pfeiffer, Harald P. and Wittek, Nikolas\n A. and Vu, Nils L. and Nelli, Kyle C. and Carpenter,\n Alexander and Lovelace, Geoffrey and Scheel, Mark A. and\n Throwe, William},\n title = {{Scalarization of isolated black holes in scalar Gauss-Bonnet\n theory in the fixing-the-equations approach}},\n eprint = {2403.08705},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n doi = {10.1103/PhysRevD.110.024033},\n journal = {Phys. Rev. D},\n volume = {110},\n number = {2},\n pages = {024033},\n year = {2024}\n}\n\n@article{Lehner2010pn,\n author = \"Lehner, Luis and Pretorius, Frans\",\n title = \"{Black Strings, Low Viscosity Fluids, and Violation of Cosmic\n Censorship}\",\n eprint = \"1006.5960\",\n archivePrefix =\"arXiv\",\n primaryClass = \"hep-th\",\n doi = \"10.1103/PhysRevLett.105.101102\",\n url = \"https://doi.org/10.1103/PhysRevLett.105.101102\",\n journal = \"Phys. Rev. Lett.\",\n volume = \"105\",\n pages = \"101102\",\n year = \"2010\"\n}\n\n@article{Liebendorfer2005,\ndoi = {10.1086/466517},\nurl = {https://dx.doi.org/10.1086/466517},\nyear = {2005},\nmonth = {nov},\npublisher = {},\nvolume = {633},\nnumber = {2},\npages = {1042},\nauthor = {Matthias Liebendörfer},\ntitle = {A Simple Parameterization of the Consequences of Deleptonization\n for Simulations of Stellar Core Collapse},\njournal = {The Astrophysical Journal}\n}\n\n@article{Lindblom1998dp,\n author = \"Lindblom, Lee\",\n title = \"Phase transitions and the mass radius curves of\n relativistic stars\",\n journal = \"Phys. Rev.\",\n volume = \"D58\",\n year = \"1998\",\n pages = \"024008\",\n doi = \"10.1103/PhysRevD.58.024008\",\n url = \"https://doi.org/10.1103/PhysRevD.58.024008\",\n eprint = \"gr-qc/9802072\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n reportNumber = \"GRP-494\",\n SLACcitation = \"%%CITATION = GR-QC/9802072;%%\"\n}\n\n@article{Lindblom2005qh,\n author = \"Lindblom, Lee and Scheel, Mark A. and Kidder,\n Lawrence E. and Owen, Robert and Rinne, Oliver\",\n title = \"A New generalized harmonic evolution system\",\n year = \"2006\",\n url = \"https://doi.org/10.1088/0264-9381/23/16/S09\",\n doi = \"10.1088/0264-9381/23/16/S09\",\n journal = \"Class. Quant. Grav.\",\n volume = \"23\",\n pages = \"S447-S462\",\n eprint = \"gr-qc/0512093\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = GR-QC/0512093;%%\"\n}\n\n@article{Loehner1987,\n title = {An adaptive finite element scheme for transient problems in CFD},\n journal = {Computer Methods in Applied Mechanics and Engineering},\n volume = {61},\n number = {3},\n pages = {323-338},\n year = {1987},\n issn = {0045-7825},\n doi = {https://doi.org/10.1016/0045-7825(87)90098-3},\n url = {https://www.sciencedirect.com/science/article/pii/0045782587900983},\n author = {Rainald Löhner}\n}\n\n@article{Loubere2014,\n title = {A New Family of High Order Unstructured MOOD and ADER Finite\n Volume Schemes for Multidimensional Systems of Hyperbolic\n Conservation Laws},\n volume = 16,\n DOI = {10.4208/cicp.181113.140314a},\n number = 3,\n journal = {Communications in Computational Physics},\n publisher = {Cambridge University Press},\n author = {Loubère, Raphaël and Dumbser, Michael and Diot, Steven},\n year = 2014,\n pages = {718–763}\n}\n\n@article{Lovelace2007tn,\n author = \"Lovelace, Geoffrey\",\n title = \"The dependence of test-mass thermal noises on beam shape\n in gravitational-wave interferometers\",\n journal = \"Class. Quant. Grav.\",\n volume = \"24\",\n year = \"2007\",\n number = \"17\",\n pages = \"4491-4512\",\n doi = \"10.1088/0264-9381/24/17/014\",\n url = \"https://doi.org/10.1088/0264-9381/24/17/014\",\n eprint = \"gr-qc/0610041\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = GR-QC/0610041;%%\"\n}\n\n@article{Lovelace2008tw,\n author = \"Lovelace, Geoffrey and Owen, Robert and Pfeiffer, Harald\n P. and Chu, Tony\",\n title = \"Binary-black-hole initial data with nearly-extremal spins\",\n journal = \"Phys. Rev.\",\n volume = \"D78\",\n year = \"2008\",\n pages = \"084017\",\n doi = \"10.1103/PhysRevD.78.084017\",\n url = \"https://doi.org/10.1103/PhysRevD.78.084017\",\n eprint = \"0805.4192\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = ARXIV:0805.4192;%%\"\n}\n\n@article{Lovelace2016uwp,\n author = \"Lovelace, Geoffrey and Lousto, Carlos O. and\n Healy, James and Scheel, Mark A. and\n Garcia, Alyssa and O'Shaughnessy, Richard and\n Boyle, Michael and Campanelli, Manuela and\n Hemberger, Daniel A. and Kidder, Lawrence E.\n and Pfeiffer, Harald P. and Szil\\'{a}gyi, B\\'{e}la\n and Teukolsky, Saul A. and Zlochower, Yosef\",\n title = \"{Modeling the source of GW150914 with targeted\n numerical-relativity simulations}\",\n journal = \"Class. Quant. Grav.\",\n volume = \"33\",\n year = \"2016\",\n number = \"24\",\n pages = \"244002\",\n doi = \"10.1088/0264-9381/33/24/244002\",\n eprint = \"1607.05377\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = ARXIV:1607.05377;%%\",\n url = \"https://doi.org/10.1088/0264-9381/33/24/244002\"\n}\n\n@article{Lovelace2017xyf,\n author = \"Lovelace, Geoffrey and Demos, Nicholas and Khan, Haroon\",\n title = \"Numerically modeling {Brownian} thermal noise in amorphous\n and crystalline thin coatings\",\n eprint = \"1707.07774\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n reportNumber = \"LIGO-P1700183\",\n doi = \"10.1088/1361-6382/aa9ccc\",\n journal = \"Class. Quant. Grav.\",\n volume = \"35\",\n number = \"2\",\n pages = \"025017\",\n year = \"2018\",\n url = \"https://doi.org/10.1088/1361-6382/aa9ccc\"\n}\n\n@article{Lovelace2024wra,\n author = {Geoffrey Lovelace and Kyle C. Nelli and Nils Deppe and Nils\n L. Vu and William Throwe and Marceline S. Bonilla and\n Alexander Carpenter and Lawrence E. Kidder and Alexandra\n Macedo and Mark A. Scheel and Azer Afram and Michael Boyle\n and Andrea Ceja and Matthew Giesler and Sarah Habib and Ken\n Z. Jones and Prayush Kumar and Guillermo Lara and Denyz\n Melchor and Iago B. Mendes and Keefe Mitman and Marlo Morales\n and Jordan Moxon and Eamonn O'Shea and Kyle Pannone and\n Harald P. Pfeiffer and Teresita Ramirez-Aguilar and Jennifer\n Sanchez and Daniel Tellez and Saul A. Teukolsky and Nikolas\n A. Wittek},\n title = {Simulating binary black hole mergers using discontinuous\n {Galerkin} methods},\n eprint = {2410.00265},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n month = {9},\n year = {2024}\n}\n\n@article{Ma2023sok,\n author = {Ma, Sizheng and Varma, Vijay and Stein, Leo C.\n and Foucart, Francois and Duez, Matthew D. and\n Kidder, Lawrence E. and Pfeiffer, Harald P. and\n Scheel, Mark A.},\n title = {{Numerical simulations of black hole-neutron star mergers\n in scalar-tensor gravity}},\n eprint = {2304.11836},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n doi = {10.1103/PhysRevD.107.124051},\n journal = {Phys. Rev. D},\n volume = {107},\n number = {12},\n pages = {124051},\n year = {2023},\n url = {https://doi.org/10.1103/PhysRevD.107.124051}\n}\n\n@article{Mathar2009,\n author = {Mathar, Richard J.},\n title = {Zernike basis to cartesian transformations},\n journal = {Serbian Astronomical Journal},\n year = 2009,\n url = {http://dx.doi.org/10.2298/SAJ0979107M},\n doi = {10.2298/saj0979107m},\n number = 179,\n pages = {107–120}\n}\n\n@article{Matsushima1995,\n author = {T. Matsushima and P.S. Marcus},\n title = {A Spectral Method for Polar Coordinates},\n journal = {Journal of Computational Physics},\n volume = 120,\n number = 2,\n pages = {365-374},\n year = 1995,\n issn = {0021-9991},\n doi = {10.1006/jcph.1995.1171},\n url = {https://doi.org/10.1006/jcph.1995.1171}\n}\n\n@Article{Michel1972,\n author = \"Michel, F. Curtis\",\n title = \"Accretion of matter by condensed objects\",\n journal = \"Astrophysics and Space Science\",\n year = \"1972\",\n month = \"Jan\",\n day = \"01\",\n volume = \"15\",\n number = \"1\",\n pages = \"153--160\",\n doi = \"10.1007/BF00649949\",\n url = \"https://doi.org/10.1007/BF00649949\"\n}\n\n@article{Mignone2010br,\n author = \"Mignone, A. and Tzeferacos, P. and Bodo, G.\",\n title = \"{High-order conservative finite difference GLM-MHD\n schemes for cell-centered MHD}\",\n journal = \"J. Comput. Phys.\",\n volume = \"229\",\n year = \"2010\",\n pages = \"5896-5920\",\n doi = \"10.1016/j.jcp.2010.04.013\",\n url = \"https://doi.org/10.1016/j.jcp.2010.04.013\",\n eprint = \"1001.2832\",\n archivePrefix = \"arXiv\",\n primaryClass = \"astro-ph.HE\",\n SLACcitation = \"%%CITATION = ARXIV:1001.2832;%%\"\n}\n\n@article{Minerbo1978,\n author = \"Minerbo, Gerald N.\",\n title = \"Maximum entropy {Eddington} factors\",\n journal = \"Journal of Quantitative Spectroscopy and Radiative Transfer\",\n volume = \"20\",\n number = \"6\",\n pages = \"541 - 545\",\n year = \"1978\",\n issn = \"0022-4073\",\n doi = \"10.1016/0022-4073(78)90024-9\",\n url = \"https://doi.org/10.1016/0022-4073(78)90024-9\"\n}\n\n@book{Misner1973,\n author = {Misner, Charles W. and Thorne, Kip S.\n and Wheeler, John Archibald},\n publisher = {W. H. Freeman},\n title = {Gravitation},\n year = {1973}\n}\n\n@article{Mitman2024review,\n author = {Keefe Mitman and Michael Boyle and Leo C. Stein and\n Nils Deppe and Lawrence E. Kidder and Jordan Moxon and\n Harald P. Pfeiffer and Mark A. Scheel and Saul A. Teukolsky\n and William Throwe and Nils L. Vu},\n title = {A Review of Gravitational Memory and BMS Frame Fixing in\n Numerical Relativity},\n eprint = {2405.08868},\n archivePrefix = {arXiv},\n primaryClass = {gr-qc},\n url = {https://doi.org/10.48550/arXiv.2405.08868},\n year = {2024}\n}\n\n@article{Moesta2013dna,\n author = {M\\\"osta, Philipp and Mundim, Bruno C. and Faber, Joshua A. and\n Haas, Roland and Noble, Scott C. and Bode, Tanja and\n L\\\"offler, Frank and Ott, Christian D. and Reisswig, Christian\n and Schnetter, Erik},\n title = \"{GRHydro: A new open source general-relativistic\n magnetohydrodynamics code for the Einstein Toolkit}\",\n eprint = \"1304.5544\",\n archivePrefix =\"arXiv\",\n primaryClass = \"gr-qc\",\n doi = \"10.1088/0264-9381/31/1/015005\",\n journal = \"Class.Quant.Grav.\",\n volume = \"31\",\n pages = \"015005\",\n year = \"2014\"\n}\n\n@article{Moesta2014,\n author = {Philipp Mösta and Bruno C Mundim and Joshua A Faber\n and Roland Haas and Scott C Noble and Tanja Bode\n and Frank Löffler and Christian D Ott and Christian Reisswig\n and Erik Schnetter},\n doi = {10.1088/0264-9381/31/1/015005},\n journal = {Classical and Quantum Gravity},\n month = {nov},\n pages = {015005},\n publisher = {IOP Publishing},\n title = {GRHydro: a new open-source general-relativistic\n magnetohydrodynamics code for the Einstein toolkit},\n url = {https://dx.doi.org/10.1088/0264-9381/31/1/015005},\n volume = {31},\n year = {2013}\n}\n\n@article{Moldenhauer2014yaa,\n author = {Moldenhauer, Niclas and Markakis, Charalampos M. and\n Johnson-McDaniel, Nathan K. and Tichy, Wolfgang and\n Br\\\"ugmann, Bernd},\n title = {Initial data for binary neutron stars with adjustable\n eccentricity},\n eprint = {1408.4136},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n doi = {10.1103/PhysRevD.90.084043},\n journal = {Phys. Rev. D},\n volume = {90},\n number = {8},\n pages = {084043},\n year = {2014}\n}\n\n@article{Most2022,\n author = {Most, Elias R and Philippov, Alexander A},\n doi = {10.1093/mnras/stac1909},\n issn = {0035-8711},\n journal = {Monthly Notices of the Royal Astronomical Society},\n month = {07},\n number = {2},\n pages = {2710-2724},\n title = {{Electromagnetic precursor flares from the late inspiral of\n neutron star binaries}},\n url = {https://doi.org/10.1093/mnras/stac1909},\n volume = {515},\n year = {2022}\n}\n\n@article{Moxon2020gha,\n author = \"Moxon, Jordan and Scheel, Mark A. and\n Teukolsky, Saul A.\",\n title = \"{Improved Cauchy-characteristic evolution system for\n high-precision numerical relativity waveforms}\",\n journal = \"Phys. Rev. D\",\n volume = \"102\",\n number = \"4\",\n pages = \"044052\",\n year = \"2020\",\n doi = \"10.1103/PhysRevD.102.044052\",\n url =\"http://dx.doi.org/10.1103/PhysRevD.102.044052\",\n eprint = \"2007.01339\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\"\n}\n\n@article{Moxon2021gbv,\n author = {Moxon, Jordan and Scheel, Mark A. and Teukolsky, Saul A. and\n Deppe, Nils and Fischer, Nils and H\\'ebert, Francois and\n Kidder, Lawrence E. and Throwe, William},\n title = {{SpECTRE Cauchy-characteristic evolution system for rapid,\n precise waveform extraction}},\n eprint = {2110.08635},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n doi = {10.1103/PhysRevD.107.064013},\n journal = {Phys. Rev. D},\n volume = {107},\n number = {6},\n pages = {064013},\n year = {2023}\n}\n\n@article{Muhlberger2014pja,\n author = \"Muhlberger, Curran D. and Nouri, Fatemeh Hossein and Duez,\n Matthew D. and Foucart, Francois and Kidder, Lawrence E. and\n Ott, Christian D. and Scheel, Mark A. and Szil\\'agyi, B\\'ela\n and Teukolsky, Saul A.\",\n title = \"{Magnetic effects on the low-T/|W| instability in\n differentially rotating neutron stars}\",\n eprint = \"1405.2144\",\n archivePrefix =\"arXiv\",\n primaryClass = \"astro-ph.HE\",\n doi = \"10.1103/PhysRevD.90.104014\",\n url = {https://journals.aps.org/prd/abstract/10.1103/PhysRevD.90.104014},\n journal = \"Phys. Rev. D\",\n volume = 90,\n number = 10,\n pages = 104014,\n year = 2014\n}\n\n@article{Nee2024bur,\n author = {Nee, Peter James and Lara, Guillermo and Pfeiffer, Harald\n P. and Vu, Nils L.},\n title = {{Quasistationary hair for binary black hole initial data\n in scalar Gauss-Bonnet gravity}},\n eprint = {2406.08410},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n month = {6},\n year = {2024}\n}\n\n@article{Nonomura2013,\n author = {Taku Nonomura and Kozo Fujii},\n doi = {https://doi.org/10.1016/j.compfluid.2012.09.001},\n issn = {0045-7930},\n journal = {Computers & Fluids},\n keywords = {Weighted compact nonlinear scheme, Robustness},\n note = {International Workshop on Future of CFD and Aerospace Sciences},\n pages = {8-18},\n title = {Robust explicit formulation of weighted compact nonlinear scheme},\n url = {https://www.sciencedirect.com/science/article/pii/S0045793012003441},\n volume = {85},\n year = {2013}\n}\n\n@book{NumericalRecipes,\n author = \"Press, William~H. and Teukolsky, Saul~A. and\n Vetterling, William~T. and Flannery, Brian~P.\",\n title = \"Numerical Recipes 3rd Edition: The Art of Scientific Computing\",\n publisher = \"Cambridge University Press\",\n year = \"2007\",\n month = \"sep\",\n url = \"{http://numerical.recipes}\",\n}\n\n@article{OBoyle2020,\n doi = {10.1103/physrevd.102.083027},\n url = {https://doi.org/10.1103%2Fphysrevd.102.083027},\n year = 2020,\n month = {oct},\n publisher = {American Physical Society ({APS})},\n volume = {102},\n number = {8},\n author = {Michael F. O'Boyle and Charalampos Markakis and Nikolaos\n Stergioulas and Jocelyn S. Read},\n title = {Parametrized equation of state for neutron star matter with\n continuous sound speed},\n journal = {Physical Review D}\n}\n\n@ARTICLE{Oconnor2015,\n author = {{O'Connor}, Evan},\n title = \"{An Open-source Neutrino Radiation Hydrodynamics Code for\n Core-collapse Supernovae}\",\n journal = {Astrophysical Journal, Supplement},\n keywords = {black hole physics, hydrodynamics, neutrinos, radiative\n transfer, stars: neutron, supernovae: general, Astrophysics - High\n Energy Astrophysical Phenomena, Nuclear Theory},\n year = 2015,\n month = aug,\n volume = {219},\n number = {2},\n eid = {24},\n pages = {24},\n doi = {10.1088/0067-0049/219/2/24},\narchivePrefix = {arXiv},\n eprint = {1411.7058},\n primaryClass = {astro-ph.HE},\n adsurl = {https://ui.adsabs.harvard.edu/abs/2015ApJS..219...24O}\n}\n\n@article{Okounkova:2019zjf,\n author = \"Okounkova, Maria and Stein, Leo C. and Moxon, Jordan and Scheel,\n Mark A. and Teukolsky, Saul A.\",\n title = \"{Numerical relativity simulation of GW150914 beyond general\n relativity}\",\n eprint = \"1911.02588\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n doi = \"10.1103/PhysRevD.101.104016\",\n journal = \"Phys. Rev. D\",\n volume = \"101\",\n number = \"10\",\n pages = \"104016\",\n year = \"2020\"\n}\n\n@article{Osburn:2022bby,\n author = {Osburn, Thomas and Nishimura, Nami},\n title = {New self-force method via elliptic partial differential\n equations for {Kerr} inspiral models},\n eprint = {2206.07031},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n doi = {10.1103/PhysRevD.106.044056},\n journal = {Phys. Rev. D},\n volume = {106},\n number = {4},\n pages = {044056},\n year = {2022}\n}\n\n@article{Ossokine2013zga,\n author = {Ossokine, Serguei and Kidder, Lawrence E. and Pfeiffer,\n Harald P.},\n title = {Precession-tracking coordinates for simulations of compact-\n object-binaries},\n eprint = {1304.3067},\n archivePrefix = {arXiv},\n primaryClass = {gr-qc},\n doi = {10.1103/PhysRevD.88.084031},\n journal = {Phys. Rev. D},\n volume = {88},\n pages = {084031},\n year = {2013}\n}\n\n@article{Ossokine2015yla,\n author = {Ossokine, Serguei and Foucart, Francois and Pfeiffer, Harald\n P. and Boyle, Michael and Szil\\'agyi, B\\'ela},\n title = {Improvements to the construction of binary black hole initial\n data},\n eprint = {1506.01689},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n doi = {10.1088/0264-9381/32/24/245010},\n journal = {Class. Quant. Grav.},\n volume = {32},\n pages = {245010},\n year = {2015}\n}\n\n@article{Owen2009sb,\n author = \"Owen, Robert\",\n title = \"The Final Remnant of Binary Black Hole Mergers:\n Multipolar Analysis\",\n journal = \"Phys. Rev.\",\n volume = \"D80\",\n year = \"2009\",\n pages = \"084012\",\n doi = \"10.1103/PhysRevD.80.084012\",\n url = \"https://doi.org/10.1103/PhysRevD.80.084012\",\n eprint = \"0907.0280\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = ARXIV:0907.0280;%%\"\n}\n\n@article{Owen2017yaj,\n author = \"Owen, Robert and Fox, Alex S. and Freiberg, John A. and\n Jacques, Terrence Pierre\",\n title = \"Black Hole Spin Axis in Numerical Relativity\",\n year = \"2017\",\n eprint = \"1708.07325\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = ARXIV:1708.07325;%%\"\n}\n\n@article{Owren1992,\n author = {Owren, Brynjulf and Zennaro, Marino},\n title = {Derivation of Efficient, Continuous, Explicit Runge–Kutta\n Methods},\n journal = {SIAM Journal on Scientific and Statistical Computing},\n volume = {13},\n number = {6},\n pages = {1488-1501},\n year = {1992},\n doi = {10.1137/0913084},\n URL = {https://epubs.siam.org/doi/10.1137/0913084}\n}\n\n@article{Pajkos2019,\n doi = {10.3847/1538-4357/ab1de2},\n url = {https://doi.org/10.3847%2F1538-4357%2Fab1de2},\n year = 2019,\n month = {jun},\n publisher = {American Astronomical Society},\n volume = {878},\n number = {1},\n pages = {13},\n author = {Michael A. Pajkos and Sean M. Couch and Kuo-Chuan Pan\n and Evan P. O'Connor},\n title = {Features of Accretion-phase Gravitational-wave Emission\n from Two-dimensional Rotating Core-collapse Supernovae},\n journal = {The Astrophysical Journal}\n}\n\n@article{Palenzuela2010,\n author = {Palenzuela, Carlos and Garrett, Travis and Lehner,\n Luis and Liebling, Steven L.},\n doi = {10.1103/PhysRevD.82.044045},\n issue = {4},\n journal = {Phys. Rev. D},\n month = {Aug},\n numpages = {14},\n pages = {044045},\n publisher = {American Physical Society},\n title = {Magnetospheres of black hole systems in force-free plasma},\n url = {https://link.aps.org/doi/10.1103/PhysRevD.82.044045},\n volume = {82},\n year = {2010}\n}\n\n@article{Palenzuela2018,\n title = \"A Simflowny-based finite-difference code for high-performance\n computing in numerical relativity\",\n volume = \"35\",\n ISSN = \"1361-6382\",\n url = \"http://dx.doi.org/10.1088/1361-6382/aad7f6\",\n DOI = \"10.1088/1361-6382/aad7f6\",\n number = \"18\",\n journal = \"Classical and Quantum Gravity\",\n publisher = \"IOP Publishing\",\n author = \"Palenzuela, Carlos and Miñano, Borja and Viganò, Daniele and\n Arbona, Antoni and Bona-Casas, Carles and Rigo, Andreu and\n Bezares, Miguel and Bona, Carles and Massó, Joan\",\n year = \"2018\",\n month = \"aug\",\n pages=\"185007\"\n}\n\n@article{Pareschi2005,\n author = {Pareschi, Lorenzo and Russo, Giovanni},\n title = {Implicit-Explicit {Runge-Kutta} Schemes and Applications to\n Hyperbolic Systems with Relaxation},\n journal = {J Sci Comput},\n volume = {25},\n year = {2005},\n pages = {129--155},\n doi = {10.1007/s10915-004-4636-4},\n url = {https://doi.org/10.1007/s10915-004-4636-4},\n archivePrefix = {arXiv},\n eprint = {1009.2757},\n primaryClass = {math.NA},\n}\n\n@article{Paschalidis2013,\n author = {Paschalidis, Vasileios and Shapiro, Stuart L.},\n doi = {10.1103/PhysRevD.88.104031},\n journal = {Physical Review D},\n month = nov,\n note = {Publisher: American Physical Society},\n number = {10},\n pages = {104031},\n title = {A new scheme for matching general relativistic ideal\n magnetohydrodynamics to its force-free limit},\n url = {https://link.aps.org/doi/10.1103/PhysRevD.88.104031},\n urldate = {2022-09-11},\n volume = {88},\n year = {2013}\n}\n\n@article{Penner2011,\n author = {{Penner}, A.~J.},\n title = \"{General relativistic magnetohydrodynamic Bondi-Hoyle\n accretion}\",\n journal = {Monthly Notices of the Royal Astronomical Society},\n year = 2011,\n month = \"Jun\",\n volume = 414,\n number = 2,\n pages = {1467-1482},\n doi = {10.1111/j.1365-2966.2011.18480.x},\n archivePrefix ={arXiv},\n eprint = {1011.2976},\n primaryClass = {astro-ph.HE},\n adsurl = {https://ui.adsabs.harvard.edu/abs/2011MNRAS.414.1467P},\n}\n\n@inproceedings{Persson2006sub,\n title = {Sub-cell shock capturing for discontinuous Galerkin methods},\n author = {Persson, Per-Olof and Peraire, Jaime},\n booktitle = {44th AIAA Aerospace Sciences Meeting and Exhibit},\n pages = 112,\n year = 2006,\n doi = {10.2514/6.2006-112}\n}\n\n@phdthesis{Pfeiffer2005zm,\n author = \"Pfeiffer, Harald Paul\",\n title = \"Initial data for black hole evolutions\",\n eprint = \"gr-qc/0510016\",\n archivePrefix = \"arXiv\",\n reportnumber = \"UMI-31-04429\",\n school = \"Cornell U.\",\n year = \"2005\"\n}\n\n@article{Porth2016rfi,\n author = \"Porth, Oliver and Olivares, Hector and Mizuno, Yosuke and\n Younsi, Ziri and Rezzolla, Luciano and Moscibrodzka,\n Monika and Falcke, Heino and Kramer, Michael\",\n title = \"The Black Hole Accretion Code\",\n url = \"https://doi.org/10.1186/s40668-017-0020-2\",\n year = \"2016\",\n eprint = \"1611.09720\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = ARXIV:1611.09720;%%\"\n}\n\n@ARTICLE{radice2022,\n author = {{Radice}, David and {Bernuzzi}, Sebastiano and {Perego},\n Albino and {Haas}, Roland},\n title = \"{A new moment-based general-relativistic neutrino-radiation\n transport code: Methods and first applications to neutron star\n mergers}\",\n journal = {Monthly Notices of the Royal Astronomical Society},\n keywords = {neutrinos, methods: numerical, neutron star mergers,\n Astrophysics - High Energy Astrophysical Phenomena, General Relativity\n and Quantum Cosmology},\n year = 2022,\n month = may,\n volume = {512},\n number = {1},\n pages = {1499-1521},\n doi = {10.1093/mnras/stac589},\narchivePrefix = {arXiv},\n eprint = {2111.14858},\n primaryClass = {astro-ph.HE},\n adsurl = {https://ui.adsabs.harvard.edu/abs/2022MNRAS.512.1499R},\n adsnote = {Provided by the SAO/NASA Astrophysics Data System}\n}\n\n@article{Renkhoff2023,\n author = {Renkhoff, Sarah and Cors, Daniela and Hilditch, David and\n Br\\\"ugmann, Bernd},\n title = {Adaptive {hp} refinement for spectral elements in numerical\n relativity},\n eprint = {2302.00575},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n doi = {10.1103/PhysRevD.107.104043},\n journal = {Phys. Rev. D},\n volume = {107},\n number = {10},\n pages = {104043},\n year = {2023}\n}\n\n@book{RezzollaBook,\n author = \"{{Rezzolla}, L. and {Zanotti}, O.}\",\n title = \"{Relativistic Hydrodynamics}\",\n publisher = \"Oxford University Press\",\n year = \"2013\",\n month = \"sep\",\n url = \"{http://adsabs.harvard.edu/abs/2013rehy.book.....R}\",\n}\n\n@ARTICLE{Richers2017,\n author = {{Richers}, Sherwood and {Ott}, Christian D. and\n {Abdikamalov}, Ernazar and {O'Connor}, Evan and {Sullivan}, Chris},\n title = \"{Equation of state effects on gravitational waves from\n rotating core collapse}\",\n journal = {Phys. Rev. D},\n keywords = {Astrophysics - High Energy Astrophysical Phenomena},\n year = 2017,\n month = mar,\n volume = {95},\n number = {6},\n eid = {063019},\n pages = {063019},\n doi = {10.1103/PhysRevD.95.063019},\narchivePrefix = {arXiv},\n eprint = {1701.02752},\n primaryClass = {astro-ph.HE},\n adsurl = {https://ui.adsabs.harvard.edu/abs/2017PhRvD..95f3019R},\n adsnote = {Provided by the SAO/NASA Astrophysics Data System}\n}\n\n@article{Rinne2007ui,\n author = \"Rinne, Oliver and Lindblom, Lee and Scheel, Mark A.\",\n title = \"{Testing outer boundary treatments for the Einstein equations}\",\n eprint = \"0704.0782\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n doi = \"10.1088/0264-9381/24/16/006\",\n journal = \"Class. Quant. Grav.\",\n volume = \"24\",\n pages = \"4053--4078\",\n year = \"2007\"\n}\n\n@book{Saad2003,\n title = \"Iterative Methods for Sparse Linear Systems: Second Edition\",\n author = \"Saad, Yousef\",\n isbn = \"978-0898715347\",\n publisher = \"Society for Industrial and Applied Mathematics\",\n year = \"2003\",\n}\n\n@article{Schaal2015,\n author = \"Schaal, K. and Bauer, A. and Chandrashekar, P. and Pakmor, R. and\n Klingenberg, C. and Springel, V.\",\n title = \"Astrophysical hydrodynamics with a high-order discontinuous\n Galerkin scheme and adaptive mesh refinement\",\n year = \"2015\",\n url = \"https://academic.oup.com/mnras/article/453/4/4278/2593686\",\n doi = \"10.1093/mnras/stv1859\",\n journal = \"MNRAS\",\n pages = \"4278--4300\",\n volume = \"453\",\n}\n\n@article{Scheel2003vs,\n author = \"Scheel, Mark A. and Erickcek, Adrienne L. and Burko, Lior M. and\n Kidder, Lawrence E. and Pfeiffer, Harald P.\n and Teukolsky, Saul A.\",\n title = \"{3-D simulations of linearized scalar fields in Kerr space-time}\",\n eprint = \"gr-qc/0305027\",\n archivePrefix = \"arXiv\",\n doi = \"10.1103/PhysRevD.69.104006\",\n journal = \"Phys. Rev. D\",\n volume = \"69\",\n pages = \"104006\",\n year = \"2004\",\n url = {https://journals.aps.org/prd/abstract/10.1103/PhysRevD.69.104006}\n}\n\n@book{Shapiro1983,\n author = \"Shapiro, Stuart L. and Teukolsky, Saul A.\",\n title = \"Black holes, white dwarfs, and neutron stars:\n the physics of compact objects\",\n year = \"1983\",\n url = {https://ui.adsabs.harvard.edu/abs/1983bhwd.book.....S},\n}\n\n@article{Shibata2003,\n title = \"Gravitational waves from axisymmetrically oscillating neutron\n stars in general relativistic simulations\",\n author = \"Shibata, Masaru and Sekiguchi, Yu-ichirou\",\n journal = \"Phys. Rev. D\",\n volume = \"68\",\n issue = \"10\",\n pages = \"104020\",\n numpages = \"14\",\n year = \"2003\",\n month = \"Nov\",\n publisher = \"American Physical Society\",\n doi = \"10.1103/PhysRevD.68.104020\",\n url = \"https://link.aps.org/doi/10.1103/PhysRevD.68.104020\"\n}\n\n@article{Shiokawa2011ih,\n author = \"Shiokawa, Hotaka and Dolence, Joshua C. and Gammie, Charles F.\n and Noble, Scott C.\",\n title = \"{Global GRMHD Simulations of Black Hole Accretion Flows:\n a Convergence Study}\",\n eprint = \"1111.0396\",\n archivePrefix = \"arXiv\",\n primaryClass = \"astro-ph.HE\",\n doi = \"10.1088/0004-637X/744/2/187\",\n journal = \"Astrophys. J.\",\n volume = \"744\",\n pages = \"187\",\n year = \"2012\"\n}\n\n@article{Shu1988439,\n title = \"Efficient implementation of essentially non-oscillatory\n shock-capturing schemes\",\n journal = \"Journal of Computational Physics\",\n volume = 77,\n number = 2,\n pages = \"439 - 471\",\n year = 1988,\n issn = \"0021-9991\",\n doi = \"10.1016/0021-9991(88)90177-5\",\n author = \"Chi-Wang Shu and Stanley Osher\",\n}\n\n@article{Sod19781,\n title = {A survey of several finite difference methods for systems of\n nonlinear hyperbolic conservation laws},\n journal = {Journal of Computational Physics},\n volume = 27,\n number = 1,\n pages = {1-31},\n year = 1978,\n issn = {0021-9991},\n doi = {https://doi.org/10.1016/0021-9991(78)90023-2},\n url = {https://www.sciencedirect.com/science/article/pii/0021999178900232},\n author = {Gary A Sod},\n}\n\n@book{Sommerfeld1949,\n author = {Sommerfeld, Arnold},\n title = {Partial Differential Equations in Physics},\n publisher = {Academic Press},\n year = 1949,\n isbn = {978-0-12-654658-3},\n doi = {10.1016/B978-0-12-654658-3.50001-X},\n url = {https://www.sciencedirect.com/science/article/pii/B978012654658350001X}\n}\n\n@InProceedings{Sonntag2014,\n author = \"Sonntag, Matthias and Munz, Claus-Dieter\",\n editor = \"Fuhrmann, J{\\\"u}rgen and Ohlberger, Mario and Rohde,\n Christian\",\n title = \"Shock Capturing for Discontinuous Galerkin Methods using\n Finite Volume Subcells\",\n booktitle = \"Finite Volumes for Complex Applications VII-Elliptic,\n Parabolic and Hyperbolic Problems\",\n year = 2014,\n publisher = \"Springer International Publishing\",\n pages = \"945--953\",\n isbn = \"978-3-319-05591-6\",\n doi = {10.1007/978-3-319-05591-6_96},\n url = {https://link.springer.com/chapter/10.1007%2F978-3-319-05591-6_96}\n}\n\n@article{Spitkovsky2006,\n author = {Anatoly Spitkovsky},\n bdsk-url-1 = {https://doi.org/10.1086/507518},\n doi = {10.1086/507518},\n journal = {The Astrophysical Journal},\n month = {aug},\n number = {1},\n pages = {L51--L54},\n publisher = {American Astronomical Society},\n title = {Time-dependent Force-free Pulsar Magnetospheres:\n Axisymmetric and Oblique Rotators},\n url = {https://doi.org/10.1086/507518},\n volume = {648},\n year = 2006\n}\n\n@article{Stamm2010,\n author = \"Stamm, Benjamin and Wihler, Thomas P.\",\n title = \"{hp-Optimal} discontinuous {Galerkin} methods for linear elliptic\n problems\",\n year = \"2010\",\n url = \"https://doi.org/10.1090/S0025-5718-10-02335-5\",\n doi = \"10.1090/S0025-5718-10-02335-5\",\n journal = \"Mathematics of Computation\",\n pages = \"2117--2133\",\n volume = \"79\",\n}\n\n@article{Stiller2016a,\n author = \"Stiller, Jörg\",\n title = \"Robust multigrid for high-order discontinuous {Galerkin}\n methods: A fast {Poisson} solver suitable for high-aspect\n ratio {Cartesian} grids\",\n volume = \"327\",\n issn = \"0021-9991\",\n url = \"https://doi.org/10.1016/j.jcp.2016.09.041\",\n doi = \"10.1016/j.jcp.2016.09.041\",\n journal = \"Journal of Computational Physics\",\n publisher = \"Elsevier BV\",\n year = \"2016\",\n eprint = \"1603.02524\",\n archivePrefix = \"arXiv\",\n primaryClass = \"cs.CE\"\n}\n\n@article{Stiller2016b,\n author = \"Stiller, Jörg\",\n title = \"Robust Multigrid for {Cartesian} Interior Penalty {DG}\n Formulations of the {Poisson} Equation in 3D\",\n year = \"2016\",\n eprint = \"1612.04796\",\n archivePrefix = \"arXiv\",\n primaryClass = \"cs.NA\"\n}\n\n@article{Suresh1997,\n author = {A. Suresh and H.T. Huynh},\n doi = {https://doi.org/10.1006/jcph.1997.5745},\n issn = {0021-9991},\n journal = {Journal of Computational Physics},\n number = {1},\n pages = {83-99},\n title = {Accurate Monotonicity-Preserving Schemes with Runge–Kutta Time\n Stepping},\n volume = {136},\n year = {1997}\n}\n\n@article{Szilagyi2009qz,\n author = \"Szilagyi, Bela and Lindblom, Lee and Scheel, Mark A.\",\n title = \"{Simulations of Binary Black Hole Mergers Using Spectral\n Methods}\",\n journal = \"Phys. Rev.\",\n volume = \"D80\",\n year = \"2009\",\n pages = \"124010\",\n doi = \"10.1103/PhysRevD.80.124010\",\n url = \"https://doi.org/10.1103/PhysRevD.80.124010\",\n eprint = \"0909.3557\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = ARXIV:0909.3557;%%\"\n}\n\n@article{Szilagyi2014fna,\n author = \"Szil\\'agyi, B\\'ela\",\n title = \"{Key Elements of Robustness in Binary Black Hole Evolutions\n using Spectral Methods}\",\n eprint = \"1405.3693\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n doi = \"10.1142/S0218271814300146\",\n journal = \"Int. J. Mod. Phys. D\",\n volume = \"23\",\n number = \"7\",\n pages = \"1430014\",\n year = \"2014\"\n}\n\n@article{Tacik2016zal,\n author = {Tacik, Nick and Foucart, Francois and Pfeiffer, Harald P.\n and Muhlberger, Curran and Kidder, Lawrence E. and Scheel,\n Mark A. and Szil\\'agyi, B.},\n title = {Initial data for black hole-neutron star binaries, with\n rotating stars},\n eprint = {1607.07962},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n doi = {10.1088/0264-9381/33/22/225012},\n journal = {Class. Quant. Grav.},\n volume = {33},\n number = {22},\n pages = {225012},\n year = {2016}\n}\n\n@article{Teukolsky1982nz,\n author = \"Teukolsky, S. A.\",\n title = \"{Linearized quadrupole waves in general relativity and the motion\n of test particles}\",\n doi = \"10.1103/PhysRevD.26.745\",\n url = \"https://doi.org/10.1103/PhysRevD.26.745\",\n journal = \"Phys.~Rev.~D\",\n volume = \"26\",\n pages = \"745--750\",\n year = \"1982\"\n}\n\n@article{Teukolsky2015ega,\n author = \"Teukolsky, Saul A.\",\n title = \"Formulation of discontinuous {Galerkin} methods for\n relativistic astrophysics\",\n journal = \"J. Comput. Phys.\",\n volume = \"312\",\n year = \"2016\",\n pages = \"333-356\",\n doi = \"10.1016/j.jcp.2016.02.031\",\n url = \"https://doi.org/10.1016/j.jcp.2016.02.031\",\n eprint = \"1510.01190\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n SLACcitation = \"%%CITATION = ARXIV:1510.01190;%%\"\n}\n\n@article{Thorne1980,\n title = {Multipole expansions of gravitational radiation},\n author = {Thorne, Kip S.},\n journal = {Rev. Mod. Phys.},\n volume = {52},\n issue = {2},\n pages = {299--339},\n numpages = {0},\n year = {1980},\n month = {Apr},\n publisher = {American Physical Society},\n doi = {10.1103/RevModPhys.52.299},\n url = {https://link.aps.org/doi/10.1103/RevModPhys.52.299}\n}\n\n@book{ThorneBlandford2017,\n author = \"Thorne, Kip S. and Blandford, Roger D.\",\n title = \"Modern Classical Physics\",\n year = \"2017\",\n url = \"https://press.princeton.edu/titles/10157.html\",\n publisher = \"Princeton University Press\",\n}\n\n@article{Toro1994,\n author = \"Toro, E. F. and Spruce, M. and Speares, W.\",\n title = \"{Restoration of the Contact Surface in the HLL–Riemann\n Solver}\",\n journal = \"Shock Waves\",\n volume = \"4\",\n year = \"1994\",\n number = \"1\",\n pages = \"25--34\",\n doi = \"10.1007/BF01414629\",\n url = \"https://doi.org/10.1007/BF01414629\"\n}\n\n@book{Toro2009,\n author = \"Toro, E. F.\",\n title = \"Riemann Solvers and Numerical Methods for Fluid Dynamics\",\n year = \"2009\",\n url = \"https://www.springer.com/us/book/9783540252023\",\n publisher = \"Springer-Verlag Berlin Heidelberg\",\n}\n\n@article{Tsitouras2011,\n author = \"Tsitouras, Ch.\",\n title = \"Runge-Kutta pairs of order 5(4) satisfying only the first column\n simplifying assumption\",\n doi = \"10.1016/j.camwa.2011.06.002\",\n journal = \"Computers & Mathematics with Applications\",\n volume = \"62\",\n number = \"2\",\n pages = \"770--775\",\n year = \"2011\",\n}\n\n@article{Varma2018sqd,\n author = \"Varma, Vijay and Scheel, Mark A. and Pfeiffer, Harald P.\",\n title = \"Comparison of binary black hole initial data sets\",\n eprint = \"1808.08228\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n doi = \"10.1103/PhysRevD.98.104011\",\n journal = \"Phys. Rev. D\",\n volume = \"98\",\n number = \"10\",\n pages = \"104011\",\n year = \"2019\"\n}\n\n@article{Vincent2019qpd,\n author = \"Vincent, Trevor and Pfeiffer, Harald P. and Fischer, Nils\n L.\",\n title = \"{hp-adaptive} discontinuous {Galerkin} solver for elliptic\n equations in numerical relativity\",\n eprint = \"1907.01572\",\n archivePrefix = \"arXiv\",\n primaryClass = \"physics.comp-ph\",\n doi = \"10.1103/PhysRevD.100.084052\",\n url = \"https://journals.aps.org/prd/abstract/10.1103/PhysRevD.100.084052\",\n journal = \"Phys. Rev. D\",\n volume = \"100\",\n number = \"8\",\n pages = \"084052\",\n year = \"2019\"\n}\n\n@article{Vu2021coj,\n author = {Vu, Nils L. and others},\n title = {A scalable elliptic solver with task-based parallelism for\n the {SpECTRE} numerical relativity code},\n eprint = {2111.06767},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n doi = {10.1103/PhysRevD.105.084027},\n journal = {Phys. Rev. D},\n volume = {105},\n number = {8},\n pages = {084027},\n year = {2022},\n month = {apr}\n}\n\n@article{Vu2023thn,\n author = {Nils L Vu and Samuel Rodriguez and Tom Włodarczyk and\n Geoffrey Lovelace and Harald P Pfeiffer and Gabriel S Bonilla\n and Nils Deppe and François Hébert and Lawrence E Kidder and\n Jordan Moxon and William Throwe},\n title = {High-accuracy numerical models of Brownian thermal noise in\n thin mirror coatings},\n eprint = {2111.06893},\n archiveprefix = {arXiv},\n primaryclass = {astro-ph.IM},\n journal = {Classical and Quantum Gravity},\n doi = {10.1088/1361-6382/acad62},\n year = {2023},\n month = {jan},\n volume = {40},\n number = {2},\n pages = {025015}\n}\n\n@article{Vu2024cgf,\n author = {Vu, Nils L.},\n title = {A discontinuous {Galerkin} scheme for elliptic equations on\n extremely stretched grids},\n eprint = {2405.06120},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n month = {5},\n year = {2024}\n}\n\n@article{Wald1974,\n author = {Wald, Robert M.},\n doi = {10.1103/PhysRevD.10.1680},\n issue = {6},\n journal = {Phys. Rev. D},\n month = {Sep},\n numpages = {0},\n pages = {1680--1685},\n publisher = {American Physical Society},\n title = {Black hole in a uniform magnetic field},\n url = {https://link.aps.org/doi/10.1103/PhysRevD.10.1680},\n volume = {10},\n year = {1974}\n}\n\n@article{Wardell:2011gb,\n author = {Wardell, Barry and Vega, Ian and Thornburg, Jonathan and\n Diener, Peter},\n title = {A Generic effective source for scalar self-force\n calculations},\n eprint = {1112.6355},\n archiveprefix = {arXiv},\n primaryclass = {gr-qc},\n doi = {10.1103/PhysRevD.85.104044},\n journal = {Phys. Rev. D},\n volume = {85},\n pages = {104044},\n year = {2012}\n}\n\n@article{White2015omx,\n author = \"White, Christopher J. and Stone, James M. and Gammie,\n Charles F.\",\n title = \"{An Extension of the Athena++ Code Framework for GRMHD\n Based on Advanced Riemann Solvers and Staggered-Mesh\n Constrained Transport}\",\n journal = \"Astrophys. J. Suppl.\",\n volume = \"225\",\n year = \"2016\",\n number = \"2\",\n pages = \"22\",\n doi = \"10.3847/0067-0049/225/2/22\",\n url = \"https://doi.org/10.3847/0067-0049/225/2/22\",\n eprint = \"1511.00943\",\n archivePrefix = \"arXiv\",\n primaryClass = \"astro-ph.HE\",\n SLACcitation = \"%%CITATION = ARXIV:1511.00943;%%\"\n}\n\n@article{Wittek:2023nyi,\n author = \"Wittek, Nikolas A. and others\",\n title = \"{Worldtube excision method for intermediate-mass-ratio\n inspirals: Scalar-field model in 3+1 dimensions}\",\n eprint = \"2304.05329\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n doi = \"10.1103/PhysRevD.108.024041\",\n journal = \"Phys. Rev. D\",\n volume = \"108\",\n number = \"2\",\n pages = \"024041\",\n year = \"2023\"\n}\n\n@article{Wittek:2024gxn,\n author = \"Wittek, Nikolas A. and Pound, Adam and Pfeiffer, Harald P.\n and Barack, Leor\",\n title = \"{Worldtube excision method for intermediate-mass-ratio\n inspirals: self-consistent evolution in a scalar-charge\n model}\",\n eprint = \"2403.08864\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n month = \"3\",\n year = \"2024\"\n}\n\n@article{Wittek:2024pis,\n author = \"Wittek, Nikolas A. and Barack, Leor and Pfeiffer, Harald P.\n and Pound, Adam and Deppe, Nils and Kidder, Lawrence E. and\n Macedo, Alexandra and Nelli, Kyle C. and Throwe, William\n and Vu, Nils L.\",\n title = \"{Relieving scale disparity in binary black hole simulations}\",\n eprint = \"2410.22290\",\n archivePrefix = \"arXiv\",\n primaryClass = \"gr-qc\",\n month = \"10\",\n year = \"2024\"\n}\n\n@article{Yee1999,\n author = \"Yee, H. C. and Sandham, N. D. and Djomehri, M. J.\",\n title = \"Low-Dissipative High-Order Shock-Capturing Methods Using\n Characteristic-Based Filters\",\n journal = \"J. Comput. Phys.\",\n volume = \"150\",\n year = \"1999\",\n pages = \"199--238\",\n doi = \"10.1006/jcph.1998.6177\",\n url = \"http://cdsads.u-strasbg.fr/abs/1999JCoPh.150..199Y\",\n}\n\n@article{Zanotti2016efficient,\n title = {Efficient conservative ADER schemes based on WENO\n reconstruction and space-time predictor in primitive\n variables},\n author = {Zanotti, Olindo and Dumbser, Michael},\n journal = {Computational astrophysics and cosmology},\n volume = 3,\n number = 1,\n pages = {1--32},\n year = 2016,\n publisher = {SpringerOpen},\n doi = \"10.1186/s40668-015-0014-x\",\n eprint = \"1511.04728\",\n archivePrefix = \"arXiv\",\n url = \"https://arxiv.org/abs/1511.04728\"\n}\n\n@article{Zhong2013,\n author = \"Zhong, Xinghui and Shu, Chi-Wang\",\n title = \"A simple weighted essentially nonoscillatory limiter for\n {Runge-Kutta} discontinuous {Galerkin} methods\",\n journal = \"Journal of Computational Physics\",\n volume = \"232\",\n year = \"2013\",\n number = \"1\",\n pages = \"397-415\",\n doi = \"10.1016/j.jcp.2012.08.028\",\n url = \"https://doi.org/10.1016/j.jcp.2012.08.028\",\n}\n\n@article{Zhu2016,\n author = \"Zhu, Jun and Zhong, Xinghui and Shu, Chi-Wang and Qiu, Jianxian\",\n title = \"{Runge-Kutta} Discontinuous {Galerkin} Method with a Simple and\n Compact {Hermite} {WENO} Limiter\",\n journal = \"Communications in Computational Physics\",\n volume = \"19\",\n year = \"2016\",\n number = \"4\",\n pages = \"944–969\",\n doi = \"10.4208/cicp.070215.200715a\",\n url = \"https://doi.org/10.4208/cicp.070215.200715a\",\n}\n\n\n# When editing this file, please follow the guidelines in\n# https://spectre-code.org/writing_good_dox.html#writing_dox_citations.\n" }, { "path": "docs/Tutorials/BeginnersTutorial.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# A Hitchhiker's Guide to Running SpECTRE {#beginners_guide}\n\n\\tableofcontents\n\nSpECTRE can be a bit complicated to get started with, especially if you aren't\nfamiliar with our core concepts of task-based parallelism and Template\nMeta-Programming (TMP). However, \nDon't Panic. This guide aims to get you introduced to running,\nvisualizing, editing, and then rebuilding SpECTRE to give you a feel for what\nSpECTRE is all about, all on your own laptop! Hopefully by the end of this guide\nyou'll feel comfortable enough to look at other executables and maybe even\nventure into the code itself!\n\n## Prerequisites\n\nTo start off, you'll need to obtain an environment to build and run SpECTRE in.\nYou could try and install all the dependencies yourself, but that is very\ntedious and very error prone. Instead, we provide a\n[Docker](https://docs.docker.com/get-docker/) container with all the\ndependencies pre-installed for you to use. The container also has the SpECTRE\nrepository cloned in it already so you don't have to worry about getting it\nyourself. To obtain the docker image, run\n\n```\ndocker pull sxscollaboration/spectre:demo\n```\n\nAnother program you will need for this tutorial is\n[Paraview](https://www.paraview.org/download/) for visualizing the output. You\nspecifically will need version 5.10.1 for this tutorial.\n\nIf you'd like to use VSCode, the tutorial also has instructions for how to start\nin VSCode as well.\n\n## Into the Container\n\nFor both a terminal and VSCode, create the container in a terminal and start it.\n\n```\ndocker create --entrypoint \"/bin/bash\" --rm --name spectre_demo -p 11111:11111 \\\n -i -t sxscollaboration/spectre:demo\n```\n```\ndocker start spectre_demo\n```\n\nWe connect port `11111` on your local machine to port `11111` of the container\nso we can use Paraview. The `--rm` will delete the container when you stop it.\nThis won't put you into the container, only start it in the background.\n\n\\note The `--entrypoint \"/bin/bash\"` is important because the default entrypoint\nof the container is the SpECTRE CLI. You can try out the default entrypoint by\nrunning `docker run sxscollaboration/spectre:demo -h` and it'll print the help\nstring for the CLI. See the [Python documentation](py/cli.html) for more.\n\nYou can also run a [Jupyter](https://jupyter.org/index.html) server for\naccessing the Python bindings (see \\ref spectre_using_python) or running Jupyter\nnotebooks. To do so, append another `-p` option with your specified port, e.g.\n`-p 8000:8000`. You can chain as many `-p` options as you want to expose more\nports.\n\nThe SpECTRE repository is located at `/work/spectre` inside the container.\n\n\n### With a Terminal {#with_terminal}\n\nTo hop in the container from a terminal, simply type\n\n```\ndocker attach spectre_demo\n```\n\nand now you're in the container!\n\n### With VSCode\n\nIf you're using VSCode, you'll need the `Remote-Containers` extension to be\nable to access the container. Once you have it, open the\n[command palette](https://code.visualstudio.com/docs/getstarted/userinterface#_command-palette)\nand run the following commands.\n\n1. `Remote-Containers: Attach to Running Container` - you should see the\n container `spectre_demo` that's currently running. Select that.\n2. `File: Open Folder` - select `/work/spectre` which is where the repo is.\n\nNow you're in the container within VSCode! The terminal in VSCode will look\nidentical to the one if you hadn't used VSCode.\n\n\\note Any changes you make inside `/work/spectre` will be lost once you stop the\ncontainer. If you'd like your changes to persist, get rid of the `--rm` flag in\nthe `docker create` command.\n\n## Compiling the code\n\n\\note From here on out, all paths are assumed to be inside the container unless\nspecified otherwise.\n\nThe container already has a SpECTRE build pre-configured. Go to the build\ndirectory and compile the executables that we will use in this tutorial:\n\n```sh\ncd /work/spectre/build\nmake -j2 ExportCoordinates3D EvolveScalarAdvection2D all-pybindings\n```\n\nThis will compile the code on two cores. If you'd like to use more cores, use\nthe `-j N` option where `N` is the number of cores.\n\nOnce the executables are compiled they will be available in the\n`/work/spectre/build/bin` directory. The container already has this directory\nadded to the `PATH` environment variable, so you can run executables from the\ncommand line right away:\n\n```sh\nspectre --help\n```\n\nIf you are not in the container but instead on a desktop or cluster you can add\nthe bin directory to your path by `cd`ing to the build directory and running\n```\nexport PATH=$PATH:`pwd`/bin\n```\nIf you log out and log back in you will need to set this again, unless you add\nit to your shell's init file.\n\n## Running ExportCoordinates3D\n\nFirst we will run the `ExportCoordinates3D` executable to visualize\nthe coordinates of a binary black hole domain.\nMake a directory where you will run everything:\n\n```\nmkdir /work/runs\ncd /work/runs\n```\n\nCopy over the input file\n`/work/spectre/tests/InputFiles/ExportCoordinates/InputTimeDependent3D.yaml`\ninto your `/work/runs` directory. To run the executable, do\n\n```\nspectre run --no-schedule -j 4 InputTimeDependent3D.yaml\n```\n\nThis will run it on 4 cores (the `--no-schedule` means it will run on the\nlogin/head node if you are using an HPC system). After this finishes you should\nsee two `H5` files in your run directory:\n\n1. ExportCoordinates3DVolume0\n2. ExportCoordinates3DReductions\n\nThe `Volume` file is where we store data from every element in our domain, like\nthe coordinates or the metric. The `Reductions` file is for more global\nquantities like the minimum grid spacing over all the elements in our domain.\n\n\\note Next time you run the executable, you will have to either move or delete\nthe existing `H5` files as SpECTRE will error if it detects that an output file\nalready exists. This is to prevent you from accidentally overwriting data.\nYou can also use the `--force / -f` and `--clean-output / -C` flags to have\n`spectre run` delete the existing files before running the executable.\n\n## Visualizing our BBH Coordinates\n\nNow it's time to use Paraview to visualize the coordinates we use for our BBH\nevolutions! SpECTRE will actually export the physical frame coordinates for\nevery executable we have because they are a really useful diagnostic to have. We\nare just using the ExportCoordinates executable here so that you don't have to\nrun a BBH evolution on your laptop which probably wouldn't work because of\nmemory requirements.\n\nBefore we get to Paraview, we have to tell paraview how to actually use the\ncoordinates in the `Volume` `H5` file. To do this we have a tool called\n`generate-xdmf` in our Python command-line interface. Inside the `runs`\ndirectory where you have the `H5` files, run\n\n```\nspectre generate-xdmf \\\n --subfile-name element_data --output BBH_Coords \\\n ExportCoordinates3DVolume*h5\n```\n\nWe output volume data per node so we append the\nnode number to each volume file we have. Since you're most likely running on a\nlaptop, you'll only be running on one node so you should only get one output\nfile for the volume. The `--subfile-name` argument is the group name inside the\n`H5` file where the data is stored (groups can be checked by\n`h5ls -r FILE_NAME`). `generate-xdmf` will generate a file called\n`BBH_Coords.xmf`. Make sure to keep this `.xmf` file next to the volume file it\nwas generated from. It uses relative paths to find the volume file which means\nif you move it, you won't be able to visualize anything.\n\n### Attaching Paraview\n\nThis is where we actually need Paraview. We have a headless (no GUI) vesion of\nparaview inside the container which we will refer to as the \"server\". To start\nthe Paraview server, run\n\n```\npvserver &\n```\n\n\\note For cluster users, check cluster-specific instructions for ParaView.\nYou may require MPI and specify which port to use.\nYou can run `mpirun -np 1 pvserver -p PARAVIEW_REMOTE_PORT` on the remote\ncluster. Here, `PARAVIEW_REMOTE_PORT` is the port that the ParaView server\nwill use on the cluster. You may choose it to be, for example, 11112.\nWith 'pvserver' running on the remote machine, open a new local terminal.\nLocally, run\n`ssh -L11111:YOUR_CLUSTER:PARAVIEW_REMOTE_PORT USERNAME@YOUR_CLUSTER`.\n\nThe `&` is so that the server runs in the background. If you hit `Enter`\na couple times you'll get back to being able to type commands. You should see\nsome output similar to\n\n```\nWaiting for client...\nConnection URL: cs://92bbb69f2af2:11111\nAccepting connection(s): 92bbb69f2af2:11111\n```\n\nThis means it's waiting for you to connect some external Paraview session (the\n\"client\") to the server. Now, ***outside*** the container, start a session of\nParaview 5.10.1. (Again, you must use this version otherwise it won't work\nproperly.)\n\n\\note For cluster users, run `mpirun -n 1 pvserver --version` to check ParaView\nversion. On your computer, download ***exactly the same*** version of Paraview.\n\nGo to `File > Connect`. Click `Add Server`. Name it whatever you\nwant, but keep the Host as `localhost`, the Server Type as `Client/Server`, the\nPort as `11111` (remember the `-p 11111:11111` flag from the docker command?).\nHere's a snapshot of what it should look like before you configure.\n\n\\image html paraview_server.png \"Paraview server settings\"\n\nHit `Configure`, then hit `Save` (we don't care about the launch configuration).\nNow you should see a list of your configured servers. Select the one you just\ncreated and hit `Connect`. It may take a minute or two to connect to the server,\nbut once you do on the left you'll see something like\n\n\\image html paraview_connect.png \"Successfully connected Paraview to a server\"\n\n\\note If you close your client, the server will stop and you won't be able to\nreconnect. You'll have to restart the server in the container.\n\n### Open the XMF File in Paraview Client {#open_xmf}\n\nNow that you have Paraview connected to the container, open the `BBH_Coords.xmf`\nfile you just generated inside Paraview (the paths you'll see are the ones in\nthe container, not your filesystem). You may be prompted to choose which XDMF\nreader to use. Choose the `XDMF Reader` option. The `Xdmf3` options won't work.\nOnce you choose a reader, on the left, you'll see\n\n\\image html beginners_paraview_left.png \"Paraview side-bar\"\n\nYou can uncheck all the boxes in the `Point Arrays` section as they aren't\nnecessary for visualizing the coordinates. Then hit `Apply`. Now you should see\na solid sphere. This isn't super helpful. In the top bar you should see a\ndropdown to change the style that the points are plotted in. Select `Surface\nWith Edges` like so. (Note: Your top bar may look slightly different from this\ndepending on what version of `Paraview` you have.)\n\n\\image html beginners_paraview_top.png \"Paraview top-bar\"\n\nNow you'll have a solid sphere with highlighted lines. To view the interior of\nthe domain, you'll need to add a filter. To access the filters, navigate to\n`Filters` on the top menu bar, hover over `Alphabetical`, and search for your\nfilter of choice. Probably the two most helpful filters\nfor viewing the domain are the `Slice` and `Clip` filters. (Note that you'll\nhave to choose the `Surface With Edges` option for each filter separately.)\n\n`Slice` is fairly self explanatory in that it will show you a single plane\nthrough the domain. Experiment with different planes to see our whole domain\nstructure!\n\nThe `Clip` filter will remove all points \"above\" a certain plane, where \"above\"\nis in the direction of the normal of that plane. If you combine two orthogonal\n`Clip`s, you can actually view a 3D wedge of our domain. Try moving the centers\nof the planes to view the domain around our excision surfaces! They have a lot\nof cool structure.\n\nIf you'd like to read more about our BBH domain, you can look at the\ndocumentation for `domain::creators::BinaryCompactObject`.\n\n## Evolution of BBH Coordinates\n\nNow that you are able to export and visualize our BBH domain coordinates at a\nsingle time, let's make a small movie of the coordinates as they evolve! To do\nthis, we'll need to edit the input file `InputTimeDependent3D.yaml`. If you\naren't familiar with YAML, it's a file type that uses key-value pairs to create\nactual objects in our C++ code. Feel free to experiment with keys and values in\nour input files. If you're unsure about what a key or value should be, we offer\nan easy way to check the options in the input file without running a whole\nsimulation. In your `/work/runs` directory, if you run\n\n```\nspectre validate InputTimeDependent3D.yaml\n```\n\nthe executable will parse and check the input file. If you made a typo, or added\nan incorrect key/value, a list of the available keys and their associated values\nwill be printed.\n\nTo change the number of times we output the coordinates, we'll need to go to the\n`%EventsAndTriggers:` block of the input file. This block is mainly where we\nspecify which quantities we want to observe in a simulation or where we\n\"Trigger\" a specific \"Event\" to happen. (For more info on `%EventsAndTriggers`,\nsee the \\ref tutorial_events_and_triggers tutorial.) Currently in this input\nfile we only have one Trigger/Event pair. The %Trigger is `TimeCompares:` and\nthe %Event is `Completion`. To have the simulation run longer, change the\n`Value:` under `TimeCompares:` to something larger. If you look at the\n`Evolution:` block above the `%EventsAndTriggers:` block, you'll see that the\ninitial time step is `0.5`. The way this executable is set up, the coordinates\nwill be exported every time step. So set the final time `Value:` under\n`TimeCompares:` to some larger multiple of `0.5` so that you'll have the\ncoordinates at a bunch of different times (a final time of `20` is reasonable.\nDepending on how many cores you run on this should take a couple minutes).\n\nThen, run the executable just like you did above (remember to move or delete the\nexisting `H5` files), run `generate-xdmf`, and open it in Paraview and apply\nsome filters of your choice. We recommend using a `Slice` filter with the normal\npointing in the `-z` direction. This is because our BBH domain rotates about the\n`z` axis. Now, in the top bar of Paraview, you should see a \"Play\" button that\nlooks like a sideways triangle (see the second image in the \\ref open_xmf\nsection). If you click this, Paraview will step through all the timesteps in the\noutput files and you'll be able to see the domain rotate a bit!\n\nNext, we encourage you to play with the other inputs that control how the domain\nevolves over time. These options are housed in the\n\n```yaml\nDomainCreator:\n BinaryCompactObject:\n ...\n TimeDependentMaps:\n ExpansionMap:\n ...\n RotationMap:\n ...\n SizeMapA:\n ...\n SizeMapB:\n ...\n```\n\nblock of the input file. Since this tutorial is more about running the code, we\nwon't go into too much detail about each option. However, in general:\n\n1. `ExpansionMap` is a global map (all parts of the domain) that controls the\n separation between the excision surfaces\n2. `RotationMap` is a global map that controls how the excision spheres rotate\n about each other\n3. `SizeMap` is a local map only around the excision spheres (not in the wave\n zone) that control the compression of grid points.\n\nPlay around with these values! You may get an error if you put something that's\ntoo unphysical, but this is a fairly consequence-free playground for you to\nexplore so just try a different value.\n\nNow you have a movie of how BBH coordinates evolve in a SpECTRE simulation!\n\n## Exploring DG+FD\n\nNow that you are able to run, and visualize SpECTRE, let's explore a feature\nthat is fairly unique to SpECTRE and is really powerful for handling\ndiscontinuities and shocks in our simulations. We call this feature `DG+FD`\n(it's also sometimes referred to as just `subcell`).\n\n### Description of DG+FD\n\n`FD` is the usual finite difference you are used to. All of the BSSN codes use\nfinite difference for solving Einstein's equations. FD is very good at capturing\nshocks and discontinuities and is a very robust method, making it well suited\nfor hydro problems and other systems that have shocks and discontinuities.\n\n`DG` stands for Discontinuous Galerkin. DG is a spectral method for representing\na solution on a grid, meaning that instead of taking the difference between the\nfunction value at two points to get the derivative, it uses known basis\nfunctions to represent the solution. Then the derivative can be known\nanalytically and you only need to supply the coefficients for the basis. DG\nworks best for representing smooth solutions; ones with very few shocks and\ndiscontinuities (like GR in vacuum). This makes DG much faster than FD for\nsmooth solutions.\n\nIn SpECTRE, we combine these two different methods into one system to take\nadvantage of the strengths of each. When we have a solution that is smooth in\nsome parts of the domain, but has shocks in other parts, using only one of these\nmethods has disadvantages. If we only used DG, we wouldn't be able to resolve\nthe shocks very well driving the errors up a lot. If we only used FD, we'd be\nable to represent the solution well, but it would be computationally\ninefficient. So we combine DG+FD so that we only do DG in the parts of the\ndomain where the solution is smooth, and switch to FD in parts where there may\nbe a shock or discontinuity. The algorithm for switching between DG and FD is\nexplained in this image.\n\n\\image html dg_fd_schematic.png \"Scheme for switching between DG and FD (credit: Nils Deppe)\"\n\nIf you'd like to learn more about how SpECTRE implements its DG+FD scheme, you\ncan read [the paper](https://arxiv.org/abs/2109.11645) on the ArXiv.\n\n### Running the Kuzmin Problem\n\nTo demonstrate DG+FD, we will be evolving the \\link\nScalarAdvection::Solutions::Kuzmin Kuzmin \\endlink problem using the\n`EvolveScalarAdvection2D` executable. This is a simple test problem that\nrotates a set of geometric shapes with uniform angular velocity, which can be\nused to evaluate how well a numerical code can handle discontinuities stably\nover time. Inside the container make a new directory `/work/runs2` where you\nwill run it. Also copy the default input file in\n`/work/spectre/tests/InputFiles/ScalarAdvection/Kuzmin2D.yaml` to this new\n`/work/runs2` directory.\n\n### Changing the Default Input File\n\nThe default input file has very low resolution so we'll need to crank that up a\nbit. The way to do this is to change the initial refinement levels and initial\nnumber of grid points which are located in\n\n```yaml\nDomainCreator:\n Rectangle:\n ...\n InitialRefinement: [x, y]\n InitialGridPoints: [x, y]\n```\n\n`InitialRefinement:` represents how many times we split a `Block` in half in\norder to create `Element`s, which are the fundamental units of our domain. So an\ninitial refinement of `[1, 1]` means we split a single Block into 4 elements\n(split in half once in each direction). For an initial refinement of `[2, 2]` we\nfirst do 1 refinement like before, and then split each of the resulting 4\nelements in half again in each direction, resulting in 16 total Elements. To\ndetermine the total number of Elements for a given refinement (same in all\ndirections), just do $2^{\\mathrm{Dim * Refinement}}$. If you're confused by\nthe terminology we use to describe the domain, we have a \\ref domain_concepts\nguide that explains all terms related to our domain.\n\n`InitialGridPoints` represents the number of grid points per dimension in each\nElement after the final refinement has been applied. So if we had an initial\nrefinement of `[2, 2]` like above and then initial grid points `[3, 3]` in each\nElement, we'd have a total of 9x16=144 grid points.\n\nAs for actual numbers to use, you can experiment to see what gives good,\nwell-resolved results. You'll definitely need more refinement than the default\ninput file, but since refinement scales exponentially, this can become very\nexpensive very quickly. On a laptop, you probably shouldn't go higher than\nrefinement `[6, 6]`. As for grid points, this will depend on how much refinement\nyou have. If you have a ton of small elements, you won't need too many grid\npoints to resolve the solution; something like `[4, 4]` would work. If you don't\nhave a lot of refinement, you may want more grid points if you still want to\nresolve your solution. For a DG scheme, increasing the number of grid points (p\nrefinement) reduces the numerical error exponentially where the solution is\nsmooth, so computational resources are used more effectively. However, to\nresolve shocks and discontinuities we have to refine the domain into more and\nsmaller elements instead (h refinement). Striking the most effective balance\nbetween h and p refinement in different parts of the domain is the job of an\nadaptive mesh refinement (AMR) algorithm.\n\nThe default input file only runs for a few time steps so we'll want to make this\nrun longer so we can actually see some evolution. From the documentation of the\n\\link ScalarAdvection::Solutions::Kuzmin Kuzmin \\endlink system, the solution\nwill rotate with an angular velocity of `1.0` (in code units). Thus, to do a\nfull orbit, it will take `6.28` code units of time. In the `%EventsAndTriggers:`\nblock of the input file, we see that the `Completion` event is triggered by the\n`Slabs` trigger. We could, in theory, calculate out how many slabs `6.28` code\nunits is using the time step, but that's super tedious. Instead let's trigger\ncompletion using the `TimeCompares` trigger instead. We used this before when\nexporting the BBH coordinates, so just copy over the yaml block and change the\n`Value:`.\n\nYour final `%EventsAndTriggers:` block should look something like this:\n\n```yaml\nEventsAndTriggers:\n - Trigger:\n TimeCompares:\n Comparison: GreaterThanOrEqualTo\n Value: 6.28\n Events:\n - Completion\n ...\n```\n\nNow you should be ready to run the executable and get some output. Here, you\nwill almost definitely benefit by running this on many cores by adding the\n`-j N` flag to the command you use to run the executable. Since we use lots\nof smaller elements, we distribute these over the available resources via a\n\\link domain::BlockZCurveProcDistribution space filling curve \\endlink to speed\nthings up.\n\n```\nspectre run --no-schedule -j 4 Kuzmin2D.yaml\n```\n\n### Visualizing the Kuzmin Problem\n\nOnce your run finishes, extract the volume data with `generate-xdmf` using\n\n```\nspectre generate-xdmf \\\n --subfile-name VolumeData --output kuzmin_problem \\\n ScalarAdvectionKuzmin2DVolume*h5\n```\n\n(Note that the `subfile-name` is different than before because it was different\nin the input file) and load it into Paraview once again. We are only interested\nin the quantity `U` which is the scalar field we were evolving. You can uncheck\nany other boxes. So now, instead of coordinates on your screen, you should see a\nlarge square colored by the solution profile described in the \\link\nScalarAdvection::Solutions::Kuzmin Kuzmin \\endlink system. You should also\nnotice that there are smaller squares that don't touch each other in the middle\nof the domain and on the edges there are large sections that are continuous.\nThese are the FD and DG grids, respectively. If you go to the top bar in\nParaview and change how you view the grid to `Surface With Edges`, this will\nbecome even more apparent.\n\nYou will notice that the FD grid is mostly around where the interesting features\nare in the solution profile; the cylinder with a wedge cut out, the cone, and\nthe hump. And then the DG grid is mostly where the solution should be zero\ntowards the boundary of the domain (i.e. the very smooth part). So right from\nthe start, you can see that we are saving computational effort by only doing the\nexpensive, yet robust, method (FD) where it is necessary and the efficient\nmethod (DG) everywhere else where the solution is smooth.\n\nNow hit the \"Play\" button in the top bar of Paraview and watch the solution\nevolve. You'll notice that the elements in the domain switch back and forth\nbetween FD and DG. They do so in such a way that the elements will switch to FD\nwhen an interesting feature enters the element and then switch back to DG once\nthe feature leaves. In this way, we are able to actually track shocks and\ndiscontinuities in real time in our solution by where the code switches to using\nFD instead of DG. This is extremely useful for expensive GRMHD simulations where\nwe only want to do FD at a shock boundary, yet that shock boundary is moving\nthrough the domain. We are able to dynamically track this shock and resolve it\nwell with FD, then switch back to DG after the shock passes through and the\nsolution has settled down again.\n\nA pretty cool filter you can add is `Warp By Scalar`. In the left panel, choose\nthe solution variable `U` as the scalar to use and hit `Apply`. In the viewing\npanel there should be a `2D` or `3D` button that you can toggle to make the view\n3D. Once you do that you should be able to see that the height of the feature is\nyour solution `U`. If you change the grid to `Surface With Edges` you can see\nthe FD or DG grids warp with the solution. And if you hit \"Play\" it'll rotate\naround and you'll see the features moving in 3D! (Don't worry if you can't find\nthis filter. Not all versions of Paraview may have it.)\n\nWe encourage you to play around with the refinement and grid points before the\nnext section to get a feel for how each changes the runtime and accuracy of\nsolution.\n\n## Editing the Kuzmin System\n\nHopefully now you feel comfortable enough running SpECTRE that you\ncan get the default input file for the pre-built executables, edit it, and run\nit. Now we are going to try our hand at actually editing some code in SpECTRE\nand then building SpECTRE. We're going to stick with the \\link\nScalarAdvection::Solutions::Kuzmin Kuzmin \\endlink system and add a new feature\nto the solution profile!\n\nYou can find the files for the Kuzmin system at\n`/work/spectre/src/PointwiseFunctions/AnalyticSolutions/ScalarAdvection/\nKuzmin.?pp`.\nIn the `hpp` file, you'll see a lot of Doxygen documentation and then the actual\nKuzmin class. The only function that you will need to care about is\n\n```cpp\ntemplate \ntuples::TaggedTuple variables(\n const tnsr::I& x, double t,\n tmpl::list /*meta*/) const;\n```\n\nAll of our analytic solutions have a function similar to this that will set the\nvalue corresponding to the tag in the return type. If you're unfamiliar with\ntags in SpECTRE, you can look at these sections for an explanation, \\ref\ndatabox_a_taggedtuple_databox and \\ref databox_a_proper_databox. However, it's\nbasically just a fancy way of doing a compile-time key/value pair. The tag is\nthe key, and the value is whatever you want it to be. In our case, the value is\na tensor, representing the solution.\n\nThe definition of this function in the `cpp` file is where you will be editing\nthe actual Kuzmin solution. Towards the bottom of this function, there is a\n`for` loop that sets the solution at every grid point. This is where you will\nadd in a new feature to the solution.\n\nYou can pick any feature you want to add, so long as it's inside the domain\nbounds of `[0,1]x[0,1]` and centered around `(0.75, 0.5)`. This is because of\nhow the kuzmin solution is set up with existing features at `(0.25, 0.5); (0.5,\n0.25); (0.5, 0.75)`. If you're having trouble thinking of a feature to add try\none of the following features:\n\n- Square centered at `(0.75, 0.5)` with solution value `1.0`\n - Side length `0.1` (any larger and it might interfere with the other\n features)\n - Circle of radius `0.045` centered on the square with value `0.0`\n- Triangle centered at `(0.75, 0.5)` with one corner facing in the `+x`\n direction with solution value `1.0`\n- Square centered at `(0.75, 0.5)`\n - Side length `0.1` (any larger and it might interfere with the other\n features)\n - Left half of the square has value `1.0` and right half of the square has\n value `0.5`\n\n\\note The more detailed you make your feature, the more resolution you will need\nto resolve it.\n\n### Re-building SpECTRE\n\nOnce you have your feature coded up, go ahead and save your changes. Now we will\nbuild SpECTRE! Go to the `/work/spectre/build` directory. This is where you have\nto be in order to build SpECTRE. We use [CMake](https://cmake.org/) to configure\nour build directory. However, since the executables are already pre-built, this\nmeans the build directory is already configured! So you don't have to worry\nabout `CMake` for now. If you wanted to reconfigure, for example using a\ndifferent compiler, then you'd have to run `CMake`. If you want to learn more\nabout how we use `CMake`, take a look at the \\ref common_cmake_flags developers\nguide.\n\nTo build the Kuzmin executable, run\n\n```\nmake EvolveScalarAdvection2D\n```\n\nThis should be very fast because you only edited a `cpp` file. Congrats! You've\njust built SpECTRE!\n\nNow re-run the executable in your `/work/runs2` directory. Hopefully everything\nworks and you get some output. When you plot it in Paraview, it should look\nalmost the same as before except your feature will be there too rotating with\nthe others! How cool! You can also see if your feature needs FD or DG more by\nhow much it switches back and forth.\n\nExperiment some more with either different features or different resolution!\n\n## Conclusions\n\nCongrats! You've made it through the tutorial! If you only want to run our\npre-built executables, you have all the tools necessary to run, visualize, and\nre-build them. If you want a full list of our executables, do\n`make list` in the build directory. This will also include our `Test_`\nexecutables which you can just ignore.\n\nIn an already configured build directory, all you have to do to build a new\nexecutable is\n\n```\nmake ExecutableName\n```\n\nand then you can copy the default input file from\n`/work/spectre/tests/InputFiles` and run it. Running an executable with the\n`--help` flag will give a description of what system is being evolved and the\ninput options necessary.\n" }, { "path": "docs/Tutorials/CCE.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# %Running CCE {#tutorial_cce}\n\n\\tableofcontents\n\n## Acquiring the CCE module {#acquiring_the_cce_module}\n\nThere are a couple different ways to acquire the CCE module/executable.\n\n### From a release {#cce_from_release}\n\nStarting from late May 2024, in every\n[Release of SpECTRE](https://github.com/sxs-collaboration/spectre/releases) we\noffer a tarball that contains everything needed to run CCE on a large number of\ndifferent systems. This will be under the `Assets` section towards the bottom\nof the release (there may be a lot of text detailing what's been updated in this\nrelease). Inside this tarball is\n\n- the CCE executable `CharacteristicExtract`\n- an example YAML input file\n- an example set of Bondi-Sachs worldtube data in the `Tests/` directory (see\n [Input worldtube data formats](#input_worldtube_data_format) section)\n- example output from CCE in the `Tests/` directory\n- a `PreprocessCceWorldtube` executable and YAML files for converting between\n [worldtube data formats](#input_worldtube_data_format) in the\n `PreprocessCceWorldtube/` directory\n- a `WriteCceWorldtubeCoordsToFile` executable that writes\n [grid points on a sphere](#spherical_nodes) to a text file in the\n `PreprocessCceWorldtube/` directory\n- a python script `CheckCceOutput.py` (meant to be run from the root of the\n tarball and after you run the example YAML input file also in the root of the\n tarball) that will check if the example output is correct\n\n\\note The tarball is `.xz` so use `tar -xf TarName.tar.xz` to extract. The `-z`\nflag to use gzip will cause an error.\n\nSee [Running the CCE executable](#running_the_cce_executable) for how to run\nCCE.\n\nWe have tested that this executable works natively on the following machines:\n\n- Expanse\n- Anvil\n- Stampede3\n- Delta (if you add\n `LD_LIBRARY_PATH=/sw/spack/deltas11-2023-03/apps/linux-rhel8-x86_64/gcc-8.5.0/gcc-11.4.0-yycklku/lib64/:$LD_LIBRARY_PATH`\n before running CCE)\n- Perlmutter\n- Ubuntu 18.04 LTS or later (LTS version only)\n\nWe have also tested that this executable works inside our\n[`dev` Docker container](https://hub.docker.com/r/sxscollaboration/spectre/tags)\non the following machines (in addition to the ones above):\n\n- Frontera\n- Delta\n\n### From Docker\n\nYou can download a docker image `sxscollaboration/spectre:deploy` which has a\nfew pre-built executables within, including the ones listed above in the\n[release](#cce_from_release) section. See the containerized releases section of\nour \\ref installation instructions for how start the container.\n\nThe input files can be found within the container at\n`/work/spectre/tests/InputFiles/`.\n\n### From source\n\nYou can clone the [spectre repo](https://github.com/sxs-collaboration/spectre)\nand follow the instructions on the \\ref installation page to obtain an\nenvironment to configure and build SpECTRE. Once you have a configured `build`\ndirectory, build the CCE executable with\n\n```\nmake CharacteristicExtract\n```\n\n\\note You may want to add the `-j4` flag to speed up compilation. However, be\nwarned that this executable will need several GB of memory to build.\n\n## Input worldtube data format {#input_worldtube_data_format}\n\nIn order to run the CCE executable, the worldtube data must be represented as\nBondi-Sachs variables decomposed as a subset of spin-weighted spherical harmonic\nmodes on a sphere of constant coordinate radius. We have chosen this format\nbecause it is far more space-efficient to store on disk than other formats. This\nsection will detail the\n[required data format](#required_h5_worldtube_data_format), provide options for\n[converting worldtube data](#converting_worldtube_data) from other NR codes into\nour format, and give insights into\n[what the worldtube data should look like](#worldtube_data_looks).\n\n### Required H5 worldtube data format {#required_h5_worldtube_data_format}\n\nWithin the H5 file that holds the worldtube data, there must be the following\ndatasets with these exact names (including the `.dat` suffix):\n\n- `Beta.dat`\n- `DrJ.dat`\n- `DuR.dat`\n- `H.dat`\n- `J.dat`\n- `Q.dat`\n- `R.dat`\n- `U.dat`\n- `W.dat`\n\nEach dataset in the file must also have an attribute named `Legend` which\nis an ASCII-encoded null-terminated variable-length string. That is, the HDF5\ntype is:\n\n```\nDATATYPE H5T_STRING {\n STRSIZE H5T_VARIABLE;\n STRPAD H5T_STR_NULLTERM;\n CSET H5T_CSET_ASCII;\n CTYPE H5T_C_S1;\n}\n```\n\nThis can be checked for a dataset by running\n\n```\nh5dump -a Beta.dat/Legend WorldtubeFile.h5\n```\n\nFor the ordering of the data, we use spherical harmonic conventions documented\nby the ylm::Spherepack class. Each row must start with the time stamp, and the\nremaining values are the complex modes in m-varies-fastest format. For\nspin-weight zero Bondi variables (`Beta`, `R`, `DuR`, `W`), we omit the\nredundant negative-m modes and imaginary parts of the m=0 modes to save space on\ndisk. Here is an example of a legend for the spin-weight zero variables:\n\n```\n\"time\", \"Re(0,0)\", \"Re(1,0)\", \"Re(1,1)\", \"Im(1,1)\", \"Re(2,0)\",\n\"Re(2,1)\", \"Im(2,1)\", \"Re(2,2)\", \"Im(2,2)\", \"Re(3,0)\", \"Re(3,1)\",\n\"Im(3,1)\", \"Re(3,2)\", \"Im(3,2)\", \"Re(3,3)\", \"Im(3,3)\", ...\n```\n\nFor non-zero spin-weight Bondi variables (`J`, `DrJ`, `H`, `Q`, `U`) we must\nstore all complex m-modes. Here is an example of a legend for variables where\nall complex m-modes must be specified:\n\n```\n\"time\", \"Re(0,0)\", \"Im(0,0)\", \"Re(1,-1)\", \"Im(1,-1)\", \"Re(1,0)\", \"Im(1,0)\",\n\"Re(1,1)\", \"Im(1,1)\", \"Re(2,-2)\", \"Im(2,-2)\", \"Re(2,-1)\", \"Im(2,-1)\", \"Re(2,0)\",\n\"Im(2,0)\", \"Re(2,1)\", \"Im(2,1)\", \"Re(2,2)\", \"Im(2,2)\", ...\n```\n\nWe don't have strict requirement on the name of the H5 file that holds the\nworldtube data. However, it is recommended to name the H5 file `...CceRXXXX.h5`,\nwhere the `XXXX` is to be replaced by the zero-padded integer for which the\nextraction radius is equal to `XXXX`M. For instance, a 100M extraction should\nhave filename `...CceR0100.h5`. If you do not adhere to this naming convention,\nyou will need to specify the extraction radius in your YAML input file.\n\n\\note This scheme of labeling files with the extraction radius is constructed\nfor compatibility with worldtube data from the SXS Collaboration's SpEC code.\n\n### Converting to the required H5 format {#converting_worldtube_data}\n\nUnless you are using worldtube data that was generated from SpECTRE (or SpEC),\nit's possible that your worldtube data is not in the correct format. We allow\nconversion into our data format from a few other data formats using the\n[`PreprocessCceWorldtube` executable provided](#acquiring_the_cce_module). These are\n\n- Nodal cartesian metric data (which we refer to as \"metric nodal\")\n- Modal cartesian metric data (which we refer to as \"metric modal\")\n- Nodal Bondi-Sachs data (which we refer to as \"bondi nodal\")\n\nRequirements for these data formats are listed below.\n\n#### Spherical harmonic modes {#spherical_modes}\n\nWhen we refer to a \"modal\" data format, we mean that the worldtube data are\nstored as spherical harmonic coefficients (a.k.a. modes). We use spherical\nharmonic conventions documented by the ylm::Spherepack class. For each dataset,\neach row must start with the time stamp, and the remaining values are the\ncomplex modes in m-varies-fastest format. That is,\n\n```\n\"time\", \"Re(0,0)\", \"Im(0,0)\", \"Re(1,-1)\", \"Im(1,-1)\", \"Re(1,0)\", \"Im(1,0)\",\n\"Re(1,1)\", \"Im(1,1)\", \"Re(2,-2)\", \"Im(2,-2)\", \"Re(2,-1)\", \"Im(2,-1)\", \"Re(2,0)\",\n\"Im(2,0)\", \"Re(2,1)\", \"Im(2,1)\", \"Re(2,2)\", \"Im(2,2)\", ...\n```\n\nEach dataset in the H5 file must also have an attribute\nnamed `Legend` which is an ASCII-encoded null-terminated variable-length string.\n\n#### Spherical harmonic nodes {#spherical_nodes}\n\nWhen we refer to a \"nodal\" data format, we mean that the worldtube data are\nstored as values at specially chosen collocation points (a.k.a. grid points or\nnodes). This allows SpECTRE to perform integrals, derivatives, and interpolation\nexactly on the input data. These grid points are Gauss-Legendre in $cos(\\theta)$\nand equally spaced in $\\phi$.\n\nBelow is a routine for computing the spherical\nharmonic $\\theta$ and $\\phi$ values. These can be used to compute the Cartesian\nlocations for a given radius using the standard transformation. The routine\nsupports \\f$\\ell\\in[4, 32]\\f$.\n\n
\n C Code for computing SpECTRE CCE gridpoint locations \n\\snippet Test_Spherepack.cpp spectre_cce_grid_point_locations\n
\n\nAlternatively, if your code can read in grid points from a text file, you can\nrun the `WriteCceWorldtubeCoordsToFile` executable like so to get a text file\nwith three columns for the x,y,z coordinates of each point.\n\n```\n./WriteCceWorldtubeCoordsToFile -r 200 -L 16 -o GridPointsR200.txt\n```\n\nEach dataset holds `1 + (l_max + 1) * (2 * l_max + 1)` columns, with the\nfirst one being the `time`. The columns must be in \\f$\\theta\\f$-varies-fastest\nordering. That is,\n\n```\n\"time\",\n\"Phi_0_Theta_0\", \"Phi_0_Theta_1\", \"Phi_0_Theta_2\", \"Phi_0_Theta_3\", \"Phi_0_Theta_4\",\n\"Phi_1_Theta_0\", \"Phi_1_Theta_1\", \"Phi_1_Theta_2\", \"Phi_1_Theta_3\", \"Phi_1_Theta_4\",\n```\n\nEach dataset in the H5 file must also have an attribute\nnamed `Legend` which is an ASCII-encoded null-terminated variable-length string.\n\n\\note Nodal data is likely the easiest to write out since no conversion to\nspherical harmonic coefficients is necessary.\n\n#### ADM Cartesian metric and derivatives {#adm_cartesian_metric_and_derivatives}\n\nFor worldtube data stored in an H5 file in the \"ADM metric nodal\" format, there\nmust be the following datasets with these exact names (including the `.dat`\nsuffix):\n\n- `gxx.dat`, `gxy.dat`, `gxz.dat`, `gyy.dat`, `gyz.dat`, `gzz.dat`\n- `Dxgxx.dat`, `Dxgxy.dat`, `Dxgxz.dat`, `Dxgyy.dat`, `Dxgyz.dat`, `Dxgzz.dat`\n- `Dygxx.dat`, `Dygxy.dat`, `Dygxz.dat`, `Dygyy.dat`, `Dygyz.dat`, `Dygzz.dat`\n- `Dzgxx.dat`, `Dzgxy.dat`, `Dzgxz.dat`, `Dzgyy.dat`, `Dzgyz.dat`, `Dzgzz.dat`\n- `Shiftx.dat`, `Shifty.dat`, `Shiftz.dat`\n- `DxShiftx.dat`, `DxShifty.dat`, `DxShiftz.dat`\n- `DyShiftx.dat`, `DyShifty.dat`, `DyShiftz.dat`\n- `DzShiftx.dat`, `DzShifty.dat`, `DzShiftz.dat`\n- `Lapse.dat`, `DxLapse.dat`, `DyLapse.dat`, `DzLapse.dat`\n- `Kxx.dat`, `Kxy.dat`, `Kxz.dat`, `Kyy.dat`, `Kyz.dat`, `Kzz.dat`\n- Either: `AuxiliaryShiftx.dat`, `AuxiliaryShifty.dat`, `AuxiliaryShiftz.dat`\n- Or: `ConformalChristoffelx.dat`, `ConformalChristoffely.dat`,\n `ConformalChristoffelz.dat`\n\nHere `g` represents the spacetime metric, but we only require the spatial\ncomponents (e.g. `gxx.dat`, `gxy.dat`, etc...) so in practice, those are the\ntensor components of the spatial metric. The temporal components of the\nspacetime metric are stored separately in the lapse and shift. Each of the\nspatial metric, lapse, and shift must also have their cartesian derivatives. `K`\nis the extrinsic curvature, `AuxiliaryShift` is the auxiliary shift vector used\nin the first-order form of the Gamma-driver condition, and\n`ConformalChristoffel` is the trace of the conformal second_order symbols.\n\nWe will compute the time derivative of the spatial metric using Eq. (2.134) of\n\\cite BaumgarteShapiro,\n\n\\begin{equation}\n\\partial_t \\gamma_{ij} = -2\\alpha K_{ij} + D_i\\beta_j + D_j\\beta_i.\n\\end{equation}\n\nThe time derivative of the lapse is computed using the `1+log` slicing condition\nfrom Eq. (4.87) of \\cite BaumgarteShapiro\n\n\\begin{equation}\n\\partial_t \\alpha = -2\\alpha K + \\beta^j\\partial_j\\alpha,\n\\end{equation}\n\nand the time derivative of the shift is computed using either the first order\nreduction form of the Gamma-driver condition from Eq. (4.89) of\n\\cite BaumgarteShapiro\n\n\\begin{equation}\n\\partial_t \\beta^i = \\eta B^i + \\beta^j\\partial_j\\beta^i,\n\\end{equation}\n\nwhere you can choose $\\eta$ (typically $\\eta=0.75$) or using the integrated\nGamma-driver condition from Eq. (12) of \\cite Hilditch:2012fp\n\n\\begin{equation}\n\\partial_t \\beta^i = \\tilde{\\Gamma}^i - \\eta\\beta^i + \\beta^j\\partial_j\\beta^i,\n\\end{equation}\n\nagain, where you can choose $\\eta$ (typically $\\eta=2/M_{\\textrm{ADM}}$).\n\n\\warning If your worldtube data is in the ADM metric nodal format but you have\nnot used `1+log` slicing and the Gamma-driver conditions specified above, your\ntime derivatives will be **wrong**. If you'd like us to support other commonly\nused gauge conditions (or variants of `1+log` or Gamma-driver), please open an\nissue on our\n[GitHub](https://github.com/sxs-collaboration/spectre).\n\nThe layout of each of these datasets must be\n[spherical harmonic nodes](#spherical_nodes).\n\n#### Cartesian metric and derivatives {#cartesian_metric_and_derivatives}\n\nFor worldtube data stored in an H5 file in either the \"metric nodal\" or \"metric\nmodal\" formats, there must be the following datasets with these exact names\n(including the `.dat` suffix):\n\n- `gxx.dat`, `gxy.dat`, `gxz.dat`, `gyy.dat`, `gyz.dat`, `gzz.dat`\n- `Drgxx.dat`, `Drgxy.dat`, `Drgxz.dat`, `Drgyy.dat`, `Drgyz.dat`, `Drgzz.dat`\n- `Dtgxx.dat`, `Dtgxy.dat`, `Dtgxz.dat`, `Dtgyy.dat`, `Dtgyz.dat`, `Dtgzz.dat`\n- `Shiftx.dat`, `Shifty.dat`, `Shiftz.dat`\n- `DrShiftx.dat`, `DrShifty.dat`, `DrShiftz.dat`\n- `DtShiftx.dat`, `DtShifty.dat`, `DtShiftz.dat`\n- `Lapse.dat`\n- `DrLapse.dat`\n- `DtLapse.dat`\n\nHere `g` represents the spacetime metric, but we only require the spatial\ncomponents (e.g. `gxx.dat`, `gxy.dat`, etc...) so in practice, those are the\ntensor components of the spatial metric. The temporal components of the\nspacetime metric are stored separately in the lapse and shift. The layout of\neach of these datasets must be in either\n[spherical harmonic modes](#spherical_modes) or\n[spherical harmonic nodes](#spherical_nodes).\n\n#### Bondi-Sachs {#bondi_sachs}\n\nIn the \"bondi nodal\" format, you must have the same Bondi variables as the\n[required format](#required_h5_worldtube_data_format), but each variable layout\nmust be the [spherical harmonic nodal layout](#spherical_nodes) with complex\nvalues interleaved as `Re`, `Im`, `Re`, `Im`, ...\n\nIf you already have data in the\n[required \"bondi modal\" format](#required_h5_worldtube_data_format), then\nnothing needs to be done.\n\n#### Running the PreprocessCceWorldtube executable\n\nThe `PreprocessCceWorldtube` executable should be run on any of the\n[allowed input formats](#converting_worldtube_data), and will produce a\ncorresponding Bondi-Sachs worldtube file that can be read in by CCE. This\nexecutable works similarly to our other executables by accepting a YAML input\nfile:\n\n```\nPreprocessCceWorldtube --input-file PreprocessCceWorldtube.yaml\n```\n\nwith a YAML file\n\n\\snippet PreprocessCceWorldtube.yaml preprocess_cce_worldtube_yaml_doxygen_example\n\nIn addition to converting worldtube data formats, `PreprocessCceWorldtube` also\naccepts multiple input worldtube H5 files that have sequential times (e.g. from\ndifferent checkpoints) and will combine the times from all H5 files alongside\nconverting the worldtube data format. If there are duplicate or overlapping\ntimes, the last/latest of the times are chosen. If you pass multiple input\nworldtube H5 files, it is assumed that they are ordered increasing in time.\n\nHere are some notes about the different options in the YAML input file:\n\n- If the extraction radius is in the `InputH5File` names, then the\n `ExtractionRadius` option can be `Auto`. Otherwise, it must be specified.\n- The option `LMaxFactor` determines the factor by which the resolution of the\n boundary computation that is run will exceed the resolution of the input and\n output files. Empirically, we have found that `LMaxFactor` of 3 is sufficient\n to achieve roundoff precision in all boundary data we have attempted, and an\n `LMaxFactor` of 2 is usually sufficient to vastly exceed the precision of the\n simulation that provided the boundary dataset.\n- `FixSpecNormalization` should always be `False` unless you are using a\n particualy old version of SpEC\n- `DescendingM` should always be `False`. This option is to support metric modal\n data from SpEC. Our [data format](#input_worldtube_data_format) is always in\n *ascending* m.\n- `BufferDepth` is an advanced option that lets you load more data into RAM at\n once so there are fewer filesystem accesses.\n- If using the ADM metric nodal input data format with a first-order form gamma\n driver, specify the `InputDataFormat:` like so:\n\\snippet AdmFirstOrderDriverPreprocessCceWorldtube.yaml first_order_input_data_format_example\n- If using the ADM metric nodal input data format with an integrated gamma\n driver, specify the `InputDataFormat:` like so:\n\\snippet AdmSecondOrderDriverPreprocessCceWorldtube.yaml second_order_input_data_format_example\n\n### What Worldtube data \"should\" look like {#worldtube_data_looks}\n\nWhile no two simulations will look exactly the same, there are some general\ntrends in the worldtube data to look for. Here is a plot of some modes of the\nBondi variable `J` from the [Bondi-Sachs](#bondi_sachs) worldtube format.\n\n\\image html worldtube_J.png \"Bondi variable J on the Worldtube\"\n\nThe 2,2 modes are oscillatory and capture the orbits of the two objects. The\nreal part of the 2,0 mode contains the gravitational memory of the system. Then\nfor this system, all the other modes are subdominant.\n\nIf you are using the [cartesian metric](#cartesian_metric_and_derivatives) or\n[adm cartesian metric](#adm_cartesian_metric_and_derivatives)\nworldtube format, here is a plot of the imaginary part of the 2,2 mode of the\nlapse and its radial and time derivative during inspiral.\n\n\\image html lapse.png \"2,2 component of lapse and its radial and time derivative\"\n\nOne thing to keep in mind with this plot is that it was produced using the\nGeneralized Harmonic formulation of Einstein's equations using the damped\nharmonic gauge. Therefore, if you are using a different formulation and gauge\n(like BSSN + moving punctures), the lapse may look different than this. One way\nto sanity check your data (regardless of what type it is or where you got it\nfrom) is to look and how the mode amplitude for a given quantity decays as you\nincrease (l,m). Here is a plot of the amplitude of the modes for the lapse in\nthe above plot.\n\n\\image html amp_lapse.png \"Amplitude of modes of Lapse\"\n\nYou'll notice that most modes are around machine precision and only the first\nfew have any real impact. This is expected.\n\n## Input file for CCE\n\nInput files for CCE are commonly named `CharacteristicExtract.yaml`. An example\ninput file with comments explaining some of the options can be found in\n`$SPECTRE_HOME/tests/InputFiles/Cce/CharacteristicExtract.yaml`. Here we expand\na bit on why we chose some of those parameters.\n\n### General options\n\n- For resolution, the example input file has lmax (`Cce.LMax`) of 20, and\n filter lmax (`Filtering.FilterLMax`) of 18; that may run a bit slow for\n basic tests, but this value yields the best precision-to-run-time ratio\n for a typical BBH system. Note that precision doesn't improve above lmax 24,\n filter 22 (be sure to update the filter as you update lmax -- the filter\n should generally be around 2 lower than the maximum l to reduce possible\n aliasing).\n- If you want to just run over all times in the worldtube H5 file, you can\n set both the `StartTime` and `EndTime` to `Auto` and it will automatically\n figure it out based on the data in the worldtube file.\n- The `ScriOutputDensity` adds extra interpolation points to the output,\n which is useful for finite-difference derivatives on the output data, but\n otherwise it'll just unnecessarily inflate the output files, so if you\n don't need the extra points, best just set it to 1.\n- For production level runs, it's recommended to have the\n `Cce.Evolution.StepChoosers.Constant` option set to 0.1 for an accurate time\n evolution. However, if you're just testing, this can be increased to 0.5 to\n speed things up.\n- We generally do not recommend extracting at less than 100M due to the CCE junk\n radiation being much worse at these smaller worldtube radii. That being said,\n we also recommend running CCE over several worldtube radii and checking which\n is the best based on the Bianchi identity violations. There isn't necessarily\n a \"best radius\" to extract waveforms at.\n- Most users will not need it, but if you want to dump data from the volume\n (instead of only on future null infinity), this is possible with the\n `ObserveFields` option to `Events` within `EventsAndTriggersAtSlabs` in the\n input file. See the input file referenced above for a (commented-out) example,\n and the documentation of the class `Cce::Events::ObserveFields` for details.\n\n### Initial data on the null hypersurface\n\nChoosing initial data on the initial null hypersurface is a non-trivial task and\nis an active area of research. We want initial data that will reduce the amount\nof CCE junk radiation as much as possible, while also having the initial data\nwork for as many cases as possible.\n\nSpECTRE currently has four different methods to choose the initial data on\nthe null hypersurface. In order from most recommended to least recommended,\nthese are:\n\n- `ConformalFactor`: Try to make initial time coordinate as inertial as\n possible at \\f$\\mathscr{I}^+\\f$ with a smart choice of the conformal factor.\n This will work for many cases, but not all. But will produce the best initial\n data when it does work.\n- `InverseCubic`: Ansatz where \\f$J = A/r + B/r^3\\f$. This is very robust and\n almost never fails, but contains a lot of CCE junk radiation compared to\n `ConformalFactor`.\n- `ZeroNonSmooth`: Make `J` vanish. Like the name says, it's not smooth.\n- `NoIncomingRadiation`: Make \\f$\\Psi_0 = 0\\f$; this does not actually lead\n to no incoming radiation, since \\f$\\Psi_0\\f$ and \\f$\\Psi_4\\f$ both include\n incoming and outgoing radiation.\n\n### Rechunking worldtube data\n\n\\note This section is less important than the others and really only matters if\nyou will be doing a large number of CCE runs like for a catalog. For only a\ncouple runs or just for testing, this part is unnecessary and can be skipped.\n\nCCE will run faster if the input worldtube hdf5 file is chunked in small numbers\nof complete rows. This is relevant because by default, SpEC and SpECTRE write\ntheir worldtube files chunked along full time-series columns, which is\nefficient for writing and compression, but not for reading in to CCE. In that\ncase, you can rechunk the input file before running CCE for maximum performance.\nThis can be done, for instance, using h5py (you will need to fill in filenames\nappropriate to your case in place of \"BondiCceR0050.h5\" and\n\"RechunkBondiCceR0050.h5\"):\n\n```py\nimport h5py\ninput_file = \"BondiCceR0050.h5\"\noutput_file = \"RechunkBondiCceR0050.h5\"\nwith h5py.File(input_file,'r') as input_h5,\\\n h5py.File(output_file, 'w') as output_h5:\n for dset in input_h5:\n if(\"Version\" in dset):\n output_h5[dset] = input_h5[dset][()]\n continue\n number_of_columns = input_h5[dset][()].shape[1]\n output_h5.create_dataset(dset, data=input_h5[dset],\n maxshape=(None, number_of_columns),\n chunks=(4, number_of_columns), dtype='d')\n for attribute in input_h5[dset].attrs.keys():\n output_h5[dset].attrs[attribute] = input_h5[dset].attrs[attribute]\n```\n\nThe rechunked data will still be in the same\n[format](#input_worldtube_data_format) as before, but will just have a\ndifferent underlying structure in the H5 file that makes it faster to read in.\n\n## Running the CCE executable {#running_the_cce_executable}\n\nOnce you have [acquired an executable](#acquiring_the_cce_module), running CCE\nin a supported environment is a simple command:\n\n```\n./CharacteristicExtract --input-file CharacteristicExtract.yaml\n```\n\nYou may notice at the beginning you get some warnings that look like\n\n```\nWarning: iterative angular solve did not reach target tolerance 1.000000e-13.\nExited after 300 iterations, achieving final maximum over collocation points\n for deviation from target of 2.073455e-08\nProceeding with evolution using the partial result from partial angular solve.\n```\n\nThis is normal and expected. All it means is that initially an angular solve\ndidn't hit a tolerance. We've found that it never really reaches the tolerance\nof 1e-13, but we still keep this tolerance so it gets as low as possible.\n\nAfter this, you'll likely see some output like\n\n```\nSimulation time: 10.000000\n Wall time: 00:00:44\nSimulation time: 20.000000\n Wall time: 00:01:14\n```\n\nwhich tells you that the simulation is proceeding as expected. When the run\nfinished, you'll see something like\n\n```\nDone!\nWall time: 06:01:41\nDate and time at completion: Thu May 23 22:31:27 2024\n\n[Partition 0][Node 0] End of program\n```\n\nIn terms of runtime, we've found that for a ~5000M long cauchy simulation, CCE\ntakes about 6 hours to run. This will vary based on a number of factors like how\nlong the cauchy evolution actually is, the desired error tolerance of your\ncharacteristic timestepper, and also how much data you output at future null\ninfinity. Therefore, take these numbers with a grain of salt and only use them\nas a rough estimate for how long a job will take.\n\n\\note CCE can technically run on two (2) cores by adding the option `++ppn 2` to\nthe above command, however, we have found in practice that this makes\nlittle-to-no difference in the runtime of the executable.\n\n## Output from CCE\n\nOnce you have the reduction data output file from a successful CCE run, you can\nconfirm the integrity of the h5 file and its contents by running\n\n```\nh5ls -r CharacteristicExtractReduction.h5\n```\n\nFor the reduction file produced by a successful run, the output of the `h5ls`\nshould resemble\n\n```\n/SpectreR0100.cce Group\n/SpectreR0100.cce/EthInertialRetardedTime Dataset {26451/Inf, 163}\n/SpectreR0100.cce/News Dataset {26451/Inf, 163}\n/SpectreR0100.cce/Psi0 Dataset {26451/Inf, 163}\n/SpectreR0100.cce/Psi1 Dataset {26451/Inf, 163}\n/SpectreR0100.cce/Psi2 Dataset {26451/Inf, 163}\n/SpectreR0100.cce/Psi3 Dataset {26451/Inf, 163}\n/SpectreR0100.cce/Psi4 Dataset {26451/Inf, 163}\n/SpectreR0100.cce/Strain Dataset {26451/Inf, 163}\n/src.tar.gz Dataset {7757329}\n```\n\nNotice that the worldtube radius will be encoded into the subfile name.\n\n\\note Prior to\n[this Pull Request](https://github.com/sxs-collaboration/spectre/pull/5985),\nmerged May 15, 2024, the output of `h5ls` looked like this\n```\n/ Group\n/Cce Group\n/Cce/EthInertialRetardedTime.dat Dataset {3995/Inf, 163}\n/Cce/News.dat Dataset {3995/Inf, 163}\n/Cce/Psi0.dat Dataset {3995/Inf, 163}\n/Cce/Psi1.dat Dataset {3995/Inf, 163}\n/Cce/Psi2.dat Dataset {3995/Inf, 163}\n/Cce/Psi3.dat Dataset {3995/Inf, 163}\n/Cce/Psi4.dat Dataset {3995/Inf, 163}\n/Cce/Strain.dat Dataset {3995/Inf, 163}\n/src.tar.gz Dataset {3750199}\n```\n\nNo matter the spin weight of the quantity, the $\\ell = 0,1$ modes will always be\noutput by CCE. Also, the `/SpectreR0100.cce` group will have a legend attribute\nthat specifies the columns.\n\n### Raw CCE output\n\nThe `Strain` represents the asymptotic transverse-traceless contribution\nto the metric scaled by the Bondi radius (to give the asymptotically leading\npart), the `News` represents the first time derivative of the strain, and each\nof the `Psi...` datasets represent the Weyl scalars, each scaled by the\nappropriate factor of the Bondi-Sachs radius to retrieve the asymptotically\nleading contribution.\n\nThe `EthInertialRetardedTime` is a diagnostic dataset that represents the\nangular derivative of the inertial retarded time, which determines the\ncoordinate transformation that is performed at future null infinity.\n\nIf you'd like to visualize the output of a CCE run, we offer a\n[CLI](py/cli.html) that will produce a plot of all of quantities except\n`EthInertialRetardedTime`. To see how to use this CLI, run\n\n```\nspectre plot cce -h\n```\n\nIf you'd like to do something more complicated than just make a quick plot,\nyou'll have to load in the output data yourself using `h5py` or our\n`spectre.IO.H5` bindings.\n\n\\note The CLI can also plot the \"old\" version of CCE output, described above.\nPass `--cce-group %Cce` to the CLI. This option is only for backwards\ncompatibility with the old CCE output and is not supported for the current\nversion of output. This options is deprecated and will be removed in the future.\n\n### Frame fixing\n\nYou may notice some odd features in some of the output quantities if you try and\nplot them. This is not a bug in CCE (not that we know of at least). This occurs\nbecause the data at future null infinity is in the wrong Bondi-Metzner-Sachs\n(BMS) frame. In order to put this data into the correct BMS frame, the\n[SXS Collaboration](https://github.com/sxs-collaboration) offers a python/numba\ncode called [scri](https://github.com/moble/scri) to do these transformations.\nSee their documentation for how to install/run/plot a waveform at future null\ninfinity in the correct BMS frame.\n\nBelow is a plot of the imaginary part of the 2,2 component for the strain when\nplotted using the raw output from SpECTRE CCE and BMS frame-fixing with scri.\nYou'll notice that there is a non-zero offset, and this component of the strain\ndoesn't decay back down to zero during the ringdown. This is because of the\nimproper BMS frame that the SpECTRE CCE waveform is in. A supertranslation must\nbe applied to transform the waveform into the correct BMS frame. See\n\\cite Mitman2024review for a review of BMS transformations and gravitational\nmemory. To perform the frame fixing, see\n[this tutorial](https://scri.readthedocs.io/en/latest/tutorial_abd.html#loading-cce-data-and-adjusting-the-bms-frame)\nin scri.\n\n\\image html im_h22.png \"Imaginary part of 2,2 component of the strain\"\n\nThe discrepancy is even more apparent if you plot the amplitude of the two\nwaveforms. It's pretty clear which waveform is the more \"physical\" one.\n\n\\image html amp_im_h22.png \"Amplitude of imaginary part of 2,2 component of the strain\"\n\nNotice that there are still some oscillations in the strain output by scri\ntowards the beginning of the waveform (up to ~1500M). This is caused by CCE junk\nradiation from imperfect initial data on the null hypersurface. In order to use\nthis waveform in analysis, the CCE junk must be cut off from the beginning.\n\nYou are also able to see gravitational memory effects with SpECTRE CCE! This\nshows up in the real part of the 2,0 mode of the strain. Though you can see the\nmemory effects in the SpECTRE CCE waveform, in order to do any analysis, you\nmust also transform the waveform to a more physically motivated BMS frame.\n\n\\image html re_h20.png \"Real part of 2,0 component of the strain\n\n## Citing CCE\n\nIf you use the SpECTRE CCE module to extract your waveforms at future null\ninfinity, please cite the following:\n\n- [SpECTRE DOI](https://zenodo.org/doi/10.5281/zenodo.4290404) (This link\n defaults to the latest release of SpECTRE. From there, you can find links to\n past releases of SpECTRE as well)\n- [SpECTRE CCE paper](https://doi.org/10.1103/PhysRevD.107.064013)\n- [CCE paper](https://doi.org/10.1103/PhysRevD.102.044052)\n\nIf you used scri to perform any frame-fixing, please also consult the\n[scri GitHub](https://github.com/moble/scri) for how you should cite it.\n\nYou can also consult our \\ref publication_policies page for further questions or\ncontact [spectre-devel@black-holes.org](mailto:spectre-devel@black-holes.org).\n" }, { "path": "docs/Tutorials/CheckpointRestart.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# %Setting up checkpoints and restarts {#tutorial_checkpoint_restart}\n\n\\tableofcontents\n\nSpECTRE executables can write checkpoints that save their instantaneous state to\ndisc; the execution can be restarted later from a saved checkpoint. This feature\nis useful for expensive simulations that would run longer than the wallclock\nlimits on a supercomputer system.\n\nExecutables can checkpoint when:\n1. The `default_phase_order` member variable in the `Metavariables` includes a\n `WriteCheckpoint` phase.\n2. The `WriteCheckpoint` phase is run by a `PhaseControl` specified in the\n `Metavariables` and the input file. The two supported ways of running the\n checkpoint phase are:\n - with `CheckpointAndExitAfterWallclock`. This is the recommended phase\n control for checkpointing, because it writes only one checkpoint before\n cleanly terminating the code.\n This reduces the disc space taken up by checkpoint files and stops using\n up the allocation's CPU-hours on work that would be redone anyway after the\n run is restarted.\n The executable will return exit code 2 when it terminates from\n `CheckpointAndExitAfterWallclock`, meaning it is incomplete and should\n continue from the checkpoint. See `Parallel::ExitCode` for a definition of\n all exit code.\n - using `VisitAndReturn(WriteCheckpoint)`. This is useful for writing more\n frequent checkpoint files, which could help when debugging a run by\n restarting it from just before the failure.\n\nTo restart an executable from a checkpoint file, run a command like this:\n```\n./MySpectreExecutable +restart Checkpoints/Checkpoint_0123\n```\nwhere the `0123` should be the number of the checkpoint to restart from. You can\nalso use the \\ref tutorial_cli \"command-line interface (CLI)\" for restarting:\n```\n./spectre run INPUT_FILE --from-last-checkpoint Checkpoints/\n```\n\nThere are a number of caveats in the current implementation of checkpointing\nand restarting:\n\n1. The same binary must be used when writing the checkpoint and when restarting\n from the checkpoint. If a different binary is used to restart the code,\n there are no guarantees that the code will restart or that the continued\n execution will be correct.\n2. The code must be restarted on the same hardware configuration used when\n writing the checkpoint --- this means the same number of nodes with the same\n number of processors per node.\n3. When using `CheckpointAndExitAfterWallclock` to trigger checkpoints, note\n that the elapsed wallclock time is checked only when the `PhaseControl` is\n run, i.e., at global synchronization points defined in the input file.\n This means that to write a checkpoint in the 30 minutes before the end of a\n job's queue time, the triggers in the input file must trigger global\n synchronizations at least once every 30 minutes (and probably 2-3 times so\n there is a margin for the time to write files to disc, etc). It is currently\n up to the user to find the balance between too-frequent synchronizations\n (that slow the code) and too-infrequent synchronizations (that won't allow\n checkpoints to be written).\n\nCertain simulation parameters can be modified when restarting from a checkpoint\nfile. This is done by parsing a new input file containing just those options to\nmodify; all other options will preserve their value from the original run.\n\nNote, however, that not all tags are permitted to be modified: in the current\nimplementation, only tags from the `const_global_cache_tags` that also have a\nmember variable `static constexpr bool is_overlayable = true;` can be modified.\nThe reason for this \"opt-in\" design is that in general, most tags interact with\npast or current simulation data in a way that would invalidate the simulation\nstate if the tag were modified on restart (example: changing the domain\ninvalidates all spatial data, changing the timestepper invalidates the history).\nOnly tags that do not interact with the state should be permitted to be updated.\nFor example: activation thresholds on various algorithms, or frequency of data\nobservation, are safe parameters to modify.\n\nThe executable will update the global cache with new input file values during\nthe phase `UpdateOptionsAtRestartFromCheckpoint`. The\n`CheckpointAndExitAfterWallclock` phase control automatically directs code flow\nto this phase after a restart.\n\nIn this option-updating phase, the code tries to read an \"overlay\" input file\nwhose name is computed from the original input file and the number of the\ncheckpoint used to restart. Say the original input file is `path/to/Input.yaml`\nand the code is restarted using a checkpoint\n`+restart Checkpoints/Checkpoint_0123`, then the overlay input file to read\nhas name `path/to/Input.overlay_0123.yaml`. If this file does not exist, the\nexecutable continues with previous parameter values.\n" }, { "path": "docs/Tutorials/Cli.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Command-line interface (CLI) {#tutorial_cli}\n\n\\tableofcontents\n\nSpECTRE has a command-line interface (CLI) that allows you to run executables,\nwork with output data, and generate plots and visualizations. To get started,\ncompile the `cli` target in your build directory. Then run:\n\n```sh\n./bin/spectre --help\n```\n\nAll available commands are listed in the [Python documentation](py/cli.html).\n\n## Autocompletion\n\nThe CLI supports autocompletion for Bash, Zsh, and Fish. Depending on your\nshell, source the corresponding file:\n\n```sh\n# In the build directory:\n# - Bash:\n. ./bin/python/shell-completion.bash\n# - Fish:\ncp ./bin/python/shell-completion.fish ~/.config/fish/completions/spectre.fish\n# - Zsh:\n. ./bin/python/shell-completion.zsh\n```\n\nYou may want to source the shell completion script on startup, e.g., in your\n`.bashrc` or `.zshrc` file.\n" }, { "path": "docs/Tutorials/DomainCreation.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# %Domain Creation {#tutorial_domain_creation}\n\n\\tableofcontents\n\n### Domain Decomposition\nThe spatial domain on which the solution is computed is divided into\nnon-overlapping cells. For 2D and 3D domains, we use curvilinear\nquadrilateral and curvilinear hexahedral elements, respectively. The\nspecification of a particular spatial domain is given by the DomainCreator.\nDomainCreators specify the properties of the initial elements (before AMR takes\nplace), which are then used by Domain to create Blocks. Each Block\nholds a CoordinateMap (described below) as well as information about its\nneighbors. For geometrical domains, (e.g. rectilinear, spherical) there are a\nfew shortcuts that can be used such that a user does not need to specify by\nhand the map and neighbor information for each %Block; these methods are\nexplained below.\n\n## CoordinateMaps\nEach Block in the Domain must hold a CoordinateMap which describes how to\nmap the logical cube (a reference cell that covers the interval \\f$[-1, 1]\\f$\nin each dimension) to the curvilinear hexahedral element the %Block describes.\nThe %CoordinateMap also provides the jacobian of the mapping.\n\n### Shortcuts for CoordinateMaps\nFor spherical domains, `Wedge<3>` implements the cubed-sphere map, and there\nexists the method `sph_wedge_coordinate_maps` in Domain/DomainHelpers.hpp to\nquickly construct six of these maps at once. For rectilinear multicube domains,\nAffine and Equiangular map the logical cubes to cartesian cubes. The method\n`maps_for_rectilinear_domains` in DomainHelpers allows the user to obtain\nthe CoordinateMaps for all of the Blocks in such a domain at once. These\ncan both be used to provide the map arguments to the Domain constructor.\n\n## Boundary Information\nEach Block must know which of the other Blocks in the Domain are its\nneighbors and which of its logical directions points to an external boundary.\n\n### Shortcuts for Boundary Information\nA quick way to encode the neighbor and boundary information for the blocks\nin a domain is through our convention of numbering and ordering the corners\nof the blocks in a well-defined way. The corner numbering scheme is described\nin the \\ref tutorial_orientations tutorial. For spherical domains,\nDomainHelpers has the methods `corners_for_radially_layered_domains` and\n`corners_for_biradially_layered_domains`, which provides the proper corner\nnumberings for the maps obtained from the method `sph_wedge_coordinate_maps`.\nThese methods are used in the\n\\ref domain::creators::Sphere \"Sphere\" DomainCreator.\nFor rectilinear multicube domains, DomainHelpers has the methods\n`corners_for_rectilinear_domains`, which provides the proper corner\nnumberings for the maps obtained from the method\n`maps_for_rectilinear_domains`.\n\n## Creating Rectilinear Domains with Shortcuts:\nThe construction of a rectilinear domain begins with the specification of\nthe total extents of the domain in each cartesian direction, in terms of\nthe number of blocks. These extents are held in an Index object.\nFor an illustrative example, we will explain how to construct a cubical\ndomain which has an extent of two blocks in each dimension:\n\n\\image html eightcubes.png \"A 2x2x2 domain.\"\n\nThe first step is to generate the corner numbering for this Domain. For\nthe purposes of this example, we will construct all blocks with their\nlogical directions aligned with one another. As each block must also have\nan associated block id, we must be aware of the order in which the corners\nfor each block are constructed.\n\nThe algorithm `corners_for_rectilinear_domains` always begins with the block\nlocated in the lowest cartesian corner of the domain. The second block is\nits immediate neighbor in the \\f$+x\\f$ direction, and so on until the block\nin this row with the highest \\f$x\\f$ coordinate is reached. The next block is\nthe the immediate neighbor of the lowest corner block in the \\f$+y\\f$\ndirection, and then continues through the neighboring blocks in the \\f$+x\\f$ as\nbefore. This is the same order in which the global corners numbers are assigned\nto the vertices of the blocks.\n\n\\image html eightcubes_numbered.png \"With global corners.\"\n\nThe block corners generated by `corners_for_rectilinear_domains` are then:\n\n```\n{0,1,3,4,9,10,12,13},\n{1,2,4,5,10,11,13,14},\n{3,4,6,7,12,13,15,16},\n{4,5,7,8,13,14,16,17},\n{9,10,12,13,18,19,21,22},\n{10,11,13,14,19,20,22,23},\n{12,13,15,16,21,22,24,25},\n{13,14,16,17,22,23,25,26}\n\n```\n\nWhat remains is to specify the CoordinateMaps that each Block will hold.\nThis is handled by `maps_for_rectilinear_domains` and currently supports\nboth Affine and Equiangular mappings. The coordinate extents of each map\nis set by the argument to `block_demarcations`. For a 2x2x1 domain, the\ncall to `maps_for_rectilinear_domains` could be:\n\n\\snippet Test_DomainHelpers.cpp show_maps_for_rectilinear_domains\n\nFor this choice of arguments we obtain the maps for a domain that extends\nfrom 0.0 to 2.0 in the \\f$x\\f$-direction, from 0.0 to 2.0 in the \\f$y\\f$\n-direction, and from -0.4 to 0.3 in the \\f$z\\f$ direction.\n\nWith the corners and maps in hand, we can pass these as arguments to the\nDomain constructor.\n\n### Non-trivial Domain Example\nThe aforementioned functions can also take an additional argument to exclude\nblocks from a domain. For this one needs to know the Index for each block\nthey wish to exclude from the domain. For the 2x2x2 domain example, the block\nindices are:\n\n```\n{0,0,0},\n{1,0,0},\n{0,1,0},\n{1,1,0},\n{0,0,1},\n{1,0,1},\n{0,1,1},\n{1,1,1}\n\n```\n\nIn this example, we construct a domain with topology \\f$S^3\\f$, which begins\nwith the net for a tesseract. We begin by specifying that the domain extents\nare three blocks along the \\f$x\\f$ and \\f$y\\f$ directions, and four blocks\nalong the \\f$z\\f$ direction. In addition, we exclude the following block\nindices:\n\n```\n{0,0,0}, //first block\n{1,0,0}, //second block\n{2,0,0}, //third block\n{0,1,0}, //fourth block\n{2,1,0}, //sixth block\n{0,2,0}, //seventh block\n{1,2,0}, //eight block\n{2,2,0}, //ninth block\n\n{0,0,1}, //10th block\n{1,0,1}, //11th block\n{2,0,1}, //12th block\n{0,1,1}, //13th block\n{2,1,1}, //15th block\n{0,2,1}, //16th block\n{1,2,1}, //17th block\n{2,2,1}, //18th block\n\n{0,0,2}, //19th block\n{2,0,2}, //21st block\n{0,2,2}, //25th block\n{2,2,2}, //27th block\n\n{0,0,2}, //28rd block\n{1,0,2}, //29th block\n{2,0,2}, //30th block\n{0,1,2}, //31th block\n{2,1,2}, //33th block\n{0,2,2}, //34th block\n{1,2,2}, //35th block\n{2,2,2}, //36th block\n\n```\nAlternatively, we can exclude none of the blocks in this way and instead\nselectively copy the block corners from the returned vector into a new vector\nthat only contains the corners for the desired blocks, if one prefers to work\nwith single-number array indices as opposed to tuples.\n\nEither way, we end up with a vector of block corners corresponding to the\nfollowing diagram:\n\n\\image html tesseract_numbered.png \"A numbered tesseract net.\"\n\nThe maps are obtained similarly. In this case we suggest using the Equiangular\nmaps for this Domain since they adapt the logical coordinates to the angular\ncoordinates on a sphere. We also need to identify corresponding faces with each\nother to obtain a domain of topology \\f$S^3\\f$, so we also need to supply the\nconstructor of Domain with PairsOfFaces. For the \\f$S^3\\f$ domain, these faces\nare:\n\n```\n\n//Folding highest cube downward:\n{{53,54,69,70},{53,54,49,50}},\n{{53,57,69,73},{53,57,52,56}},\n{{57,58,61,62},{57,58,73,74}},\n{{54,58,70,74},{54,58,55,59}},\n\n//Folding cross cubes together:\n{{54,55,38,39},{54,50,38,34}},\n{{58,59,42,43},{58,62,42,46}},\n{{53,52,37,36},{53,49,37,33}},\n{{57,56,41,40},{57,61,41,45}},\n\n//Folding second lowest cube upward:\n{{38,42,39,43},{38,42,22,26}},\n{{33,34,37,38},{21,22,37,38}},\n{{36,37,40,41},{21,37,25,41}},\n{{41,42,45,46},{41,42,25,26}},\n\n//Folding bottom cube around domain:\n{{33,34,49,50},{21,22,5,6}},\n{{39,43,55,59},{22,26,6,10}},\n{{45,46,61,62},{25,26,9,10}},\n{{36,40,52,56},{21,25,5,9}},\n{{5,6,9,10},{69,70,73,74}}\n\n```\n" }, { "path": "docs/Tutorials/EventsAndTriggers.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n\n# Events and triggers {#tutorial_events_and_triggers}\n\n\\tableofcontents\n\nThe \"events and triggers\" infrastructure (and the related \"events and\ndense triggers\") provide some control of SpECTRE executable execution\nfrom the input file contents by running user-specified code on the\nelements. It does not generally have major effects on the flow of the\n\\ref dev_guide_parallelization_core_algorithm \"algorithm\", but is\nprimarily used for observations, such as writing volume data to H5\nfiles, and minor simulation adjustments.\n\n### Events\n\nAn \\ref Event \"event\" is an input-file-creatable object that performs\nsome task that (with the exception of the \\ref Events::Completion\n\"Completion\" event) does not directly affect the execution of the\nalgorithm on the element. The effects of events are limited to\nsending messages. The most commonly used events (such as the \\ref\n::Events::ObserveNorms \"ObserveNorms\" event) send data to\nbe written to disk, but have no long-term effects on the simulation\nstate. Others (such as \\ref Events::ChangeSlabSize \"ChangeSlabSize\")\ncan have indirect effects when \\ref dev_guide_parallelization_actions\n\"actions\" react to the messages they send.\n\n### Triggers\n\nA \\ref Trigger \"trigger\" is an input-file-creatable object that\ncontrols when events are run. They are checked periodically, once per\nSlab in an evolution executable, and once per iteration in an elliptic\nsolve. At each check a trigger may fire, causing its associated\nevents to run or not. Triggers must give a consistent result over\nthe entire domain at each check, so their result must always be\nindependent of element-specific state, such as the local values of the\nsystem variables.\n\n### Dense triggers\n\nA \\ref DenseTrigger \"dense trigger\" is similar to a trigger, but uses\ntime-stepper dense output (i.e., interpolation or extrapolation) to\nprovide more precise control of the time that it fires. As a\ntime-related feature, dense triggers are only applicable to evolution\nexecutables. Dense triggers fire at a precise set of times,\nindependent of the time-step or slab state, by interpolating the\nevolved variables to the requested time before running the associated\nevents. As with normal triggers, dense triggers are required to fire\nconsistently over the entire domain.\n\n### Input file syntax\n\nThe `%EventsAndTriggers` (and `%EventsAndDenseTriggers`) sections of\nthe \\ref dev_guide_option_parsing \"input file\" are parsed as a list of\nTrigger/Events pairs:\n\n\\snippet PlaneWave1DEventsAndTriggersExample.yaml multiple_events\n\nIn this example, we are using the \\ref Triggers::Slabs \"Slabs\" trigger\nto run two events every 10 slabs: ObserveFields and\n\\ref ::Events::ObserveNorms \"ObserveNorms\". We also run the\n\\ref ::Events::Completion \"Completion\" event at the\n\\ref ::Triggers::Always \"Always\" trigger, so the run will terminate immediately.\n" }, { "path": "docs/Tutorials/Imex.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# IMEX {#tutorial_imex}\n\n\\tableofcontents\n\n### Introduction to IMEX\n\nIMEX (implicit-explicit) integration is a method for stabilizing the numerical\nevolution of stiff differential equations. While \"stiff\" is not a precisely\ndefined term, it generally refers to equations where the time step required to\nachieve numerical stability is much shorter than the timescale of the evolution\nof the solution, often by orders of magnitude. An example of a stiff equation\nis\n\n\\f{equation}\n \\label{eq:example-equation}\n \\frac{dy}{dt} = -k (y - f(t))\n\\f}\n\nwith $k$ very large. After a brief initial transient, the solution is very\nwell-approximated as $y = f(t) + O(k^{-1})$, but will be unstable if evolved\nusing an explicit time stepper with a step size larger than approximately\n$k^{-1}$, even if $f$ is slowly varying.\n\nTo see the source of the stability problem, consider evolving\n$\\eqref{eq:example-equation}$ using Euler's method. For a step from $t_0$ to\n$t_1 = t_0 + \\Delta t$, we find\n\n\\f{equation}\n \\label{eq:example-Euler}\n y_1 = y_0 + \\Delta t \\frac{dy}{dt}(y_0, t_0)\n = y_0 - k \\Delta t (y_0 - f(t_0)),\n\\f}\n\ngiving the divergence from the known infinite-$k$ solution of\n\n\\f{equation}\n y_1 - f(t_1) = y_0 - f(t_1) - k \\Delta t (y_0 - f(t_0)).\n\\f}\n\nIf $k \\Delta t$, is large, the last term will dominate and the deviation from\nthe approximate solution will increase by roughly that factor every step.\n\nTo improve this, we can evolve using an implicit time stepper. Taking the same\nstep as above with the backwards Euler method gives\n\n\\f{equation}\n \\label{eq:example-backwards-Euler}\n y_1 = y_0 + \\Delta t \\frac{dy}{dt}(y_1, t_1)\n = y_0 - k \\Delta t (y_1 - f(t_1)),\n\\f}\n\nfor a deviation of\n\n\\f{equation}\n y_1 - f(t_1) = \\frac{y_0 - f(t_1)}{1 + k \\Delta t}.\n\\f}\n\nThis goes to zero as $k \\Delta t$ becomes large, showing convergence to the\ninfinite-$k$ solution.\n\nThe unconditional (linear) stability achievable by implicit integrators allows\nthem to solve problems not feasible with explicit methods, but it comes at a\nsignificant price. While the explicit update $\\eqref{eq:example-Euler}$\ndirectly gave $y_1$, the implicit update $\\eqref{eq:example-backwards-Euler}$\nrequired the equation to be solved for the updated quantity. In this example\nthat was fairly easy, but, in a real application, finding an analytic solution\nis likely to be difficult, if not impossible. Implicit integrators are\ntherefore usually used with a numerical solve of the update equation. Even for\nsimple systems, this root-finding procedure adds significantly to the\ncomputational cost of the method, and for a system like a large PDE evolution\nit is intractable.\n\nTo mitigate this problem, we turn to the hybrid IMEX methods. The idea behind\nIMEX is to split the derivative into two terms, one without stability problems\nthat will be treated explicitly, and another that will be treated implicitly.\nNotationally, we will write\n\n\\f{equation}\n \\frac{dy}{dt}(y, t) = E(y, t) + I(y, t).\n\\f}\n\nThe simplest IMEX integrator combines the two forms of Euler's method from\nabove:\n\n\\f{equation}\n y_1 = y_0 + \\Delta t (E(y_0, t_0) + I(y_1, t_1)).\n\\f}\n\n(This integrator is not implemented in SpECTRE.) In our example above, we can,\nas an example, split $\\eqref{eq:example-equation}$ as\n\n\\f{align}\n E(y, t) &= k f(t) &\n I(y, t) &= -k y,\n\\f}\n\nwhich gives\n\n\\f{equation}\n y_1 = y_0 + k \\Delta t (f(t_0) - y_1)\n = \\frac{y_0 + k \\Delta t\\, f(t_0)}{1 + k \\Delta t}.\n\\f}\n\nIn the limit where $k \\Delta t$ goes to infinity, this gives $y_1 = f(t_0)$,\nwhich is as small a deviation from the infinite-$k$ solution as possible when\n$f$ is treated explicitly.\n\nAgain, in this simple case there is no downside to using an IMEX integrator\nover an explicit one, or an implicit method over IMEX. The gain appears in\nreal cases where the implicit-step equation cannot be solved exactly.\n\n#### Properties of IMEX time steppers\n\nAny IMEX time stepper can be used as either an implicit or an explicit time\nstepper by choosing $E$ or $I$ to be zero. As such, many significant\nproperties of an IMEX time stepper are actually properties of one or the other\npart. We won't discuss the standard properties of explicit time steppers here,\nbut most of them, such as error estimation, are used in SpECTRE ignoring the\nimplicit part.\n\nAs the entire point of using implicit methods is to increase stability, the\nmost important properties of the implicit part of a time stepper are stability\nproperties. There are many stability classifications, but we will only discuss\nthe most important here, and those only qualitatively. More information can be\nfound in \\cite Hairer1996 and \\cite Kennedy2016.\n\nThe basic desire for an implicit method is that as the equation being evolved\nbecomes increasingly stiff the evolution remains stable. (Linear) stability\nfor an infinitely large step size (or, equivalently, an infinitely stiff\nequation) is known as *A-stability*. Adams methods above second order cannot\nbe A-stable, so IMEX work generally focuses on Runge-Kutta schemes. All IMEX\ntime steppers implemented in SpECTRE are A-stable.\n\nA stronger stability condition is known as *L-stability*. L-stability is\nsimilar to A-stability, but instead of merely requiring that an analytically\ndecaying equation does not numerically diverge in the large-step-size limit, we\nrequire that the solution reaches zero in a single step. Since IMEX\napplications can take steps orders of magnitude larger than the decay timescale\nof stiff terms, this property is often desirable.\n\nIn addition to the stability properties, there is one interesting property of\nthe IMEX stepper as a whole. A wide class of time steppers, including all\nexplicit (global time-stepping) methods implementable in the current SpECTRE\ninterface, preserve (linear) conserved quantities. A linear conserved quantity\nis a linear combination of the evolved variables that is analytically constant\nunder evolution, independent of the initial conditions. In physics, a common\nexample is the integral of the density, i.e., the total mass. Such quantities\nwill be numerically preserved during evolution to the level of roundoff error,\neven if that is much smaller than the truncation error in the solution.\n\nBoth the explicit and implicit portions of all IMEX time steppers that we will\nconsider are conservative in this manner. However, the combination of the two\nparts into an IMEX scheme does not necessarily preserve this property. In\ngeneral, both the explicit and implicit parts of the split derivative must\nindividually conserve something for the full IMEX method to conserve it as\nwell. Some IMEX schemes, however, do preserve conserved quantities,\nindependent of how the derivative is split between the explicit and implicit\nparts. Such methods are termed *stiffly accurate*. (This property is also\nuseful in deriving and analyzing implicit schemes, but that is not of great\nimportance to users of the methods.)\n\n### IMEX in SpECTRE\n\nSpECTRE supports IMEX integration, with restrictions to reduce the cost of the\nsolve of the implicit equation as much as possible. Additionally, not all\nintegration schemes extend to IMEX integration, so the list of available time\nsteppers is limited for IMEX evolutions.\n\n#### Mathematical restrictions\n\nFor problems of interest to us, the evolved variables consist of several fields\ncoupled by the system derivative. The implicit solve is more expensive when\nperformed on more variables, so there is a method to restrict the solve to a\nsubset of the system if only some variables are affected by stiff terms. The\nsystem can define one or more *implicit sectors*, which are subsets of the\nevolved variables with implicit terms that can be solved independently from one\nanother. (If sectors depend on variables from other sectors, the evolution\nsystem defines the order in which the implicit updates are applied.)\n\nAs an example, for a fluid coupled to neutrinos, the neutrinos obey stiff\nequations under some conditions. If we consider neutrino flavors to be\nnon-interacting, they can each be placed in their own implicit sector and\nsolved independently. The fluid equations will usually be non-stiff, so the\nfluid variables will not be in any sector, even though they will still be used\nas arguments for computing the stiff sources.\n\nWithin each sector, restrictions are placed on the form of the implicit\nderivative (the $I$ above). When evolving a hyperbolic PDE, in general, the\nequation for an implicit step becomes an elliptic PDE. This is far too complex\nand expensive to solve for every integration substep. We therefore restrict\nthe implicit derivative to only contain source terms, i.e., terms that depend\non the sector variables only in a pointwise manner, rather than through\nderivatives or similar. (The terms may still depend on the derivatives of\nnon-sector variables.) This results in each point in the domain having an\nindependent set of algebraic equations to solve.\n\nThere is a small complexity in handling non-autonomous (time-dependent) systems\nof equations, such as those for evolutions with control systems. Some methods\nare defined in a way such that the values of time for the explicit and implicit\nparts of a substep appear to be inconsistent. SpECTRE always uses the time\nderived from the explicit portion of the method, which is equivalent to\ntreating time as an additional evolved variable with a constant explicit\nderivative of 1 and implicit derivative of 0.\n\nSpECTRE supports using an analytic solution of the implicit-step equation as\nwell as two modes for numerical root-finding: implicit and semi-implicit. The\nanalytic mode can be chosen in the definition of the implicit sector if the\nform of the implicit source allows an analytic solution. The numerical methods\ncan be toggled at runtime. The fully implicit method does a numerical\nroot-find, while the semi-implicit one linearizes the equation and solves that.\nSemi-implicit solves are faster, and, experimentally, they still stabilize the\nevolution fairly well. Using a semi-implicit solve instead of a fully implicit\none does not affect conservation properties of the method. Both numerical\nsolvers require the jacobian of the implicit source to be coded, but an\nanalytic solution does not.\n\n#### Creation of SpECTRE IMEX executables\n\nThe SpECTRE IMEX interface is defined by two protocols: \\link\nimex::protocols::ImexSystem \\endlink and \\link imex::protocols::ImplicitSector\n\\endlink. The normal evolution-system interface now only contains the explicit\nportion of the derivative, and the implicit portion is defined by the contents\nof the `implicit_sectors` typelist. See those protocols for details.\n\nIn order to use an IMEX system, various classes must be explicitly\ninstantiated. This is done in a separate source file in the system directory.\nAs an example, the instantiation file for the sectors in one of the tests is\n\n\\include tests/Unit/Helpers/Evolution/Imex/DoImplicitStepInstantiate.cpp\n\nIn the executable itself, four sets of changes are necessary. First, the\ntime-stepper type, usually defined as a type alias near the start of the\nmetavariables, must be changed from `TimeStepper` to `ImexTimeStepper`\n(IMEX-LTS is not currently supported), and an entry must be added to the\n`factory_creation` list:\n\n```\ntmpl::pair\n```\n\n(The `TimeStepper` line can be removed, although doing so is not necessary.)\n\nSecond, the IMEX actions must be added after the corresponding explicit\nactions:\n\n* In the initialization phase, the `imex::Initialize` mutator must be\n applied by adding it to the arguments of\n `Initialization::Actions::InitializeItems`. It uses objects initialized by\n `Initialization::TimeStepperHistory`, so must appear after that.\n\n* In the step actions,\n```\nimex::Actions::RecordTimeStepperData\n```\n must be added after each occurrence of `RecordTimeStepperData`,\n```\nimex::Actions::DoImplicitStep\n```\n must be added after each occurrence of `UpdateU`, and\n```\nActions::MutateApply>\n```\n must be added after each occurrence of `CleanHistory`.\n\nThird, the `imex::ImplicitDenseOutput` dense output postprocessor must\nbe added to the argument of the `evolution::Actions::RunEventsAndDenseTriggers`\naction. It must appear before any other preprocessors that use the evolved\nvariables.\n\nFinally, header includes must be added for all these things. The required\nheaders are\n```\n#include \"Evolution/Imex/Actions/DoImplicitStep.hpp\"\n#include \"Evolution/Imex/Actions/RecordTimeStepperData.hpp\"\n#include \"Evolution/Imex/CleanHistory.hpp\"\n#include \"Evolution/Imex/ImplicitDenseOutput.hpp\"\n#include \"Evolution/Imex/Initialize.hpp\"\n#include \"ParallelAlgorithms/Actions/MutateApply.hpp\"\n#include \"Time/TimeSteppers/ImexTimeStepper.hpp\"\n```\n" }, { "path": "docs/Tutorials/Orientation.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# OrientationMap {#tutorial_orientations}\n\n\\tableofcontents\n\n### Introduction\n\nThis tutorial only applies to a Domain (or a region of the Domain) that is\nconstructed from Blocks that are logical hypercubes where each Block has at\nmost a single neighboring Block in each direction.\n\nEach element in a domain has a set of internal directions which it uses\nfor computations in its own local coordinate system. These are referred to\nas the logical directions \\f$\\xi\\f$, \\f$\\eta\\f$, and \\f$\\zeta\\f$, where\n\\f$\\xi\\f$ is the first dimension, \\f$\\eta\\f$ is the second dimension, and\n\\f$\\zeta\\f$ is the third dimension. In a\ndomain with multiple Blocks, the logical directions are not necessarily\naligned on the interfaces between two Blocks, as shown in the figure below.\nAs certain operations (e.g. fluxes, limiting) communicate information across\nthe boundaries of adjacent elements, there needs to be a class that takes\ninto account the relative orientations of elements which neighbor each other.\nThis class is OrientationMap.\n\n### %OrientationMaps between %Blocks\nEach Block in a Domain has a set of BlockNeighbors, which each hold an\nOrientationMap. In this scenario, the Block is referred to as the host, and\nthe OrientationMap held by each BlockNeighbors is referred to as \"the\norientation the BlockNeighbors has with respect to the host Block.\" This is\na convention, so we give an example of constructing and assigning the correct\nOrientationMaps:\n\n\\image html twocubes.png \"Two neighboring blocks.\"\n\nIn the image above, we see a domain decomposition into two Blocks, which have\ntheir logical axes rotated relative to one another. With the left block as\nthe host Block, we see that it has a neighbor in the \\f$+\\xi\\f$ direction.\nThe host Block holds a `std::unordered_map` from Directions to BlockNeighbors;\nthe BlockNeighbors itself holds an OrientationMap that determines the mapping\nfrom each logical direction in the host Block to that in the neighboring Block.\nThat is, the OrientationMap takes as input local information (i.e. logical\ndirections in the host's coordinate system) and returns neighbor information\n(i.e. logical directions in the neighbor's coordinate system). An\nOrientationMap is constructed by passing in the block neighbor directions that\ncorrespond to the \\f$+\\xi\\f$, \\f$+\\eta\\f$, \\f$+\\zeta\\f$ directions in the host.\nIn this case, these directions in the host map to the \\f$+\\zeta\\f$,\n\\f$+\\xi\\f$, \\f$+\\eta\\f$ directions in the neighbor, respectively.\nThis BlockNeighbors thus holds the OrientationMap constructed with the list\n(\\f$+\\zeta\\f$, \\f$+\\xi\\f$, \\f$+\\eta\\f$). With the right block as the host\nblock, we see that it has a BlockNeighbors in the \\f$-\\zeta\\f$ direction, and\nthe OrientationMap held by this BlockNeighbors is the one constructed with the\narray (\\f$+\\eta\\f$, \\f$+\\zeta\\f$, \\f$+\\xi\\f$). For convenience, OrientationMap\nhas a method `inverse_map` which returns the OrientationMap that takes as input\nneighbor information and returns local information.\n\nOrientationMaps need to be provided for each BlockNeighbors in each direction\nfor each Block. This quickly becomes too large of a number to determine by\nhand as the number of Blocks and the number of dimensions increases. A remedy\nto this problem is the corner numbering scheme.\n\n### Encoding BlockNeighbors information using Corner Orderings and Numberings\nThe orientation of the \\f${dim}\\f$ logical directions within each element\ndetermines an ordering of the \\f$2^{dim}\\f$ vertices of that element. This is\ncalled the local corner numbering scheme (Local CNS) with respect to that\nelement. We give the ordering of the local corners below for the case of a\nthree-dimensional element:\n\n\\image html onecube_numbered.png \"The local corner numbering.\"\n\n```\nCorner 0 is the location of the lower xi, lower eta, lower zeta corner.\nCorner 1 is the location of the upper xi, lower eta, lower zeta corner.\nCorner 2 is the location of the lower xi, upper eta, lower zeta corner.\nCorner 3 is the location of the upper xi, upper eta, lower zeta corner.\nCorner 4 is the location of the lower xi, lower eta, upper zeta corner.\nCorner 5 is the location of the upper xi, lower eta, upper zeta corner.\nCorner 6 is the location of the lower xi, upper eta, upper zeta corner.\nCorner 7 is the location of the upper xi, upper eta, upper zeta corner.\n```\n\nWhat remains is to endow the domain decomposition with a global corner\nnumbering (Global CNS). We give an example below:\n\n\\image html twocubes_numbered.png \"A global corner numbering.\"\n\nIn the image above, we see that each vertex of the two-block domain has\nbeen assigned a number. Although each block has eight corners, four are\nshared among them, so there are only twelve unique corners in this domain.\nAny numbering may be used in the global corner numbering, so long as the\neach distinct corner is given a single distinct corner number.\n\n\\note This Global CNS assumes that there is no additional identifying of faces\nwith one another for periodic boundary conditions. That is, each element must\nhave \\f$2^{dim}\\f$ distinct corner numbers. If you wish to additionally\nidentify faces of the same block with each other, that must be done in an\nadditional step. This step is explained in the \"Setting Periodic Boundary\nConditions\" section.\n\n### The Ordered Subset of the Global CNS (Subset CNS):\nWith the Global CNS in hand, each Block inherits an ordered subset of Global\nCNS. The ordering in this set is determined by the ordering of the Local CNS,\nand the elements of the set determined by how one assigned the Global CNS to\nthe Domain. For the image above, the Subset CNS corresponding to the left block\nis {0, 1, 3, 4, 6, 7, 9, 10}, while the Subset CNS corresponding to the right\nblock is {1, 4, 7, 10, 2, 5, 8, 11}. This ordering of the Subset CNS encodes\nthe relative orientations between each Block. Subset CNSs need to be provided\nfor each Block in a Domain. It turns out that for very regular domains,\n(i.e. spherical or rectilinear) we can generate the appropriate Subset CNSs.\nAs this is a conceptual tutorial, how to construct these domains in SpECTRE\nis described in the \\ref tutorial_domain_creation tutorial.\n\n### Explanation of the Algorithms in DomainHelpers:\n\nFor illustrative purposes, we will use the following Domain composed of two\nBlocks as described above as an example.\nBecause there are 12 corners in this Domain, we will arbitrarily assign a\nunique id to each corner.\nKnowing the orientation of the logical axes within a block, we construct a\nSubset CNS for each Block.
\nHere is one possible result, given some relative orientation between the\nblocks:\n\n```\nBlock1: {0, 1, 3, 4, 6, 7, 9, 10}\nBlock2: {1, 4, 7, 10, 2, 5, 8, 11}\n```\n\nThe values of the ids only serve to identify which corners are unique and which\nare shared. This is determined by the Global CNS. The order of the ids in the\nlist is determined by the Local CNS. We take advantage of the fact that the\narray index of the global corner id is the number of the corner in the local\nCNS.\n\nThe algorithm begins by determining the shared corners between the\nBlocks:\n\n```\nresult: {1, 4, 7, 10}\n```\n\nThe next step is to determine the local ids of these shared global ids:\n\n```\nBlock1 result: {1,3,5,7}\nBlock2 result: {0,1,2,3}\n```\n\nThe next step is to convert these ids into their binary representation.\nFor reference, we give the binary representation for each number 0-7:\n\n```\nCorner 0: 000\nCorner 1: 001\nCorner 2: 010\nCorner 3: 011\nCorner 4: 100\nCorner 5: 101\nCorner 6: 110\nCorner 7: 111\n```\n\nHere 0 and 1 indicate lower and upper in the corresponding axis (zeta,\neta, xi), respectively, and the ordering has been reversed so that the\nrightmost column corresponds to the xi position and the leftmost column\nto the zeta position. Returning to the example at hand, we have:\n\n\n```\nBlock1 result: {001,011,101,111}\nBlock2 result: {000,001,010,011}\n```\n\n Note that we can now read off the shared face relative to each Block\n easily:\n\n```\nBlock1 result: Upper xi (All binary Block1 ids have a 1 in the third position)\nBlock2 result: Lower zeta (All binary Block2 ids have a 0 in the first position)\n```\n\nNow we know that `Direction<3>::%upper_xi()`\nin Block1 corresponds to `Direction<3>::%lower_zeta().%opposite()` in Block2.\n\nThe use of `.%opposite()` is a result of the Directions to a Block face being\nanti-parallel because each Block lies on the opposite side of the shared face.\n
\n\nThe remaining two correspondences are given by the alignment of the shared\nface. It is useful to know the following information:
\nIn the Local CNS, if an edge lies along the xi direction, if one takes the\ntwo corners making up that edge and takes the difference of their ids, one\n always gets the result \\f$ \\pm 1\\f$. Similarly, if the edge lies in the eta\n direction, the result will be \\f$ \\pm 2\\f$. Finally, if the edge lies in the\n zeta direction, the result will be \\f$ \\pm 4\\f$. We use this information to\n determine the alignment of the shared face:\n\n```\nBlock1: 3-1=2 => This edge is in the +eta direction.\nBlock2: 1-0=1 => This edge is in the +xi direction.\nThen, +eta in Block1 corresponds to +xi in Block2.\n\nBlock1: 5-1=4 => This edge is in the +zeta direction.\nBlock2: 2-0=2 => This edge is in the +eta direction.\nThen, +zeta in Block1 corresponds to +eta in Block2.\n```\n\nThe corresponding directions in each Block have now been deduced.\n\nTo confirm, we can use the other ids as well and arrive at the same result:
\n\n```\nBlock1: 7-5=2 => +eta\nBlock2: 3-2=1 => +xi\n\nBlock1: 7-3=4 => +zeta\nBlock2: 3-1=2 => +eta\n```\n\n### Setting Periodic Boundary Conditions\nIt is also possible to identify faces of a Block using the subset CNS. For\nexample, to identify the lower zeta face with the upper zeta face of a Block\nwhere the corners are labeled `{3,0,4,1,9,6,10,7}`, one may supply the lists\n`{3,0,4,1}` and `{9,6,10,7}` to the `set_identified_boundaries` function.\n\\note The `set_identified_boundaries` function is sensitive to the order of the\ncorners in the lists supplied as arguments. This is because the function\nidentifies corners and edges with each other as opposed to simply faces. This\nallows the user to specify more peculiar boundary conditions. For example,\nusing `{3,0,4,1}` and `{6,7,9,10}` to set the periodic boundaries will identify\nthe lower zeta face with the upper zeta face, but after a rotation of a\nquarter-turn.\n\nFor reference, here are the corners to use for each face for a Block with\ncorners labelled as `{0,1,2,3,4,5,6,7}` to set up periodic boundary conditions\nin each dimension, i.e. a \\f$\\mathrm{T}^3\\f$ topology:\n\nFace | Corners\n------|--------\nupper xi| `{1,3,5,7}`\nlower xi| `{0,2,4,6}`\nupper eta| `{2,3,6,7}`\nlower eta| `{0,1,4,5}`\nupper zeta| `{4,5,6,7}`\nlower zeta| `{0,1,2,3}`\n" }, { "path": "docs/Tutorials/ParallelExecutable/Tutorials.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Writing SpECTRE executables {#tutorials_parallel}\n\n\\tableofcontents\n\nThis set of tutorials will develop a parallel executable in stages,\nbeginning with the simplest possible executable, and then introducing\nSpECTRE's parallel features one step at a time. At each stage, the\ntutorials will illustrate what code a user needs to add in order to\nuse a particular feature, and then, for those interested, an\nexplanation of the metaprogramming that turns the user-provided code\ninto an actual SpECTRE parallel executable.\n\nPrior to going through these tutorials, you should have \\ref\ninstallation \"installed SpECTRE\" and built it successfully.\n\n| Tutorial name | Concepts introduced |\n|---------------|---------------------|\n| \\subpage tutorial_parallel_concepts \"Parallelism in SpECTRE \" | SpECTRE and Charm++ |\n| \\subpage tutorial_minimal_parallel_executable \"Minimal executable \" | Metavariables, Main component |\n\nSee also: \\subpage ParallelInfoExecutablePage\nSee also: \\subpage RandomAmrExecutablePage\n" }, { "path": "docs/Tutorials/Python.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Using SpECTRE's Python modules {#spectre_using_python}\n\n\\tableofcontents\n\nSome classes and functions from SpECTRE have Python bindings to make it easier\nto visualize data, write test code, and provide an introduction to numerical\nrelativity without needing to delve into C++.\n\n## Building the SpECTRE Python modules\n\n> tl;dr: Compile the `all-pybindings` or `cli` target.\n\nFirst, build SpECTRE with Python bindings enabled by appending the\n`-D BUILD_PYTHON_BINDINGS=ON` flag to the `cmake` command (enabled by default).\nYou can specify the\nPython version, interpreter and libraries used for compiling and testing the\nbindings by setting the `-D Python_EXECUTABLE` to an absolute path such as\n`/usr/bin/python3`. Compile the `all-pybindings` (or `cli`) target. You will\nfind that a `BUILD_DIR/bin/python` directory is created that contains the\nPython modules.\n\n## Importing the SpECTRE Python modules\n\n> tl;dr: Spin up a Jupyter notebook with `./bin/python-spectre -m jupyterlab`,\n> then `import spectre`.\n\nYou have many options for making the Python modules accessible to import in your\nscripts:\n\n- Use the `BUILD_DIR/bin/python-spectre` shortcut to run your scripts. It just\n points the `PYTHONPATH` to the modules in `BUILD_DIR/bin/python` and invokes\n the Python interpreter that you configured your build with. You can also use\n this shortcut to spin up a Jupyter server:\n\n ```sh\n BUILD_DIR/bin/python-spectre -m jupyterlab\n ```\n\n If Jupyter is not yet installed in your Python environment, you can install it\n like this:\n\n ```sh\n BUILD_DIR/bin/python-spectre -m pip install jupyterlab\n ```\n\n > Note for VSCode users: You can also select this Jupyter server as kernel for\n > notebooks running in VSCode (see [docs](https://code.visualstudio.com/docs/datascience/jupyter-notebooks#_connect-to-a-remote-jupyter-server)).\n\n- Install the modules into your Python environment:\n\n ```sh\n pip install [-e] BUILD_DIR/bin/python\n ```\n\n The optional `-e` flag installs the modules in _development mode_, which means\n they are symlinked so that changes to the modules will be reflected in your\n Python environment.\n\n You can install the Python modules like this in any Python environment that\n supports `pip`, for instance in a\n [`virtualenv`/`venv`](https://docs.python.org/3/tutorial/venv.html) or in an\n [Anaconda](https://www.anaconda.com/distribution/) environment.\n\n- You can also get access to the SpECTRE Python modules by manually adding\n `BUILD_DIR/bin/python` to your `PYTHONPATH`. This is done automatically by\n the `LoadPython.sh` script:\n\n ```sh\n . BUILD_DIR/bin/LoadPython.sh\n ```\n\nUsing any of the above options you should be able to import the `spectre` Python\nmodules in your scripts or notebooks. You can try it like this:\n\n```py\nimport spectre\n```\n\nFor an overview of all available Python modules see the\n[Python modules documentation](py/_autosummary/spectre.html). For an example\nwhat you can do with them see the tutorial on \\ref tutorial_vis_python.\n\n## Running Jupyter within the Docker container\n\nYou can run [Jupyter lab](https://jupyterlab.readthedocs.io/) in the Docker\ncontainer and access it through a browser on\nthe host for a convenient way to work with the SpECTRE Python bindings. To do\nso, make sure you have exposed a port when running the Docker container, e.g.\nby appending the option `-p 8000:8000` to the `docker run` command (see\n\\ref installation). Inside the docker container, it can be convenient to\nuse `disown` or to `apt-get install screen` and use `screen` to obtain a shell\nthat runs the Jupyter server permanently in the background. Within the shell you\nwant to run your Jupyter server, navigate to a directory that will serve as the\nroot for the file system that Jupyter has access to. Make sure it is shared with\nthe host (e.g. `SPECTRE_HOME`) so your Jupyter notebooks are not lost when the\ncontainer is deleted. Then, run the following command:\n\n```sh\nBUILD_DIR/bin/python-spectre -m jupyterlab --ip 0.0.0.0 --port 8000 --allow-root\n```\n\nCopy the token that is being displayed. Now you can open a browser on the host\nmachine, point it to `http://localhost:8000` and paste in the token. You will\nhave access to the Python environment within the Docker container.\n\n## Developing Python code\n\n> tl;dr: Set `PY_DEV_MODE=ON` in your CMake configuration so Python files are\n> symlinked to the build directory.\n\nWhen you edit any of the Python files in the repository, the changes are not\nimmediately reflected in the Python modules that you import from the build\ndirectory. You have to run `cmake .` in the build directory to update the Python\nfiles. This can be avoided by setting `cmake -D PY_DEV_MODE=ON .` in the build\ndirectory, which configures CMake to symlink the Python files rather than copy\nthem. Some features that rely on CMake variables break with this mode, e.g. the\nSpECTRE version number is not inserted into the Python modules so\n`spectre.__version__` will return nonsense. Nonetheless, enabling this mode\navoids a lot of the hassle that comes from re-configuring CMake every time you\nchange a file.\n\nFurthermore, enabling `autoreload` in Jupyter notebooks can be very helpful when\nyou are editing Python code. Add the following code before any import statements\nin your notebook:\n\n```\n%load_ext autoreload\n%autoreload 2\n```\n\nFor details on writing Python bindings for our C++ functions, rather than\nwriting Python code, see the developer guide on\n\\ref spectre_writing_python_bindings.\n" }, { "path": "docs/Tutorials/Tutorials.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# User Tutorials {#tutorials}\n\n- \\subpage beginners_guide - A brief intro to getting started with SpECTRE,\n building and rebuilding an executable with new features, and visualizing the\n output\n- \\subpage tutorial_visualization - How to run an existing executable and\n visualize its output\n- \\subpage tutorial_orientations - How to determine orientations\n- \\subpage tutorial_domain_creation - How to set up the initial domain\n- \\subpage spectre_using_python - How to install and work with the Python\n bindings and other Python modules provided by SpECTRE.\n- \\subpage tutorial_vis_python - How to visualize volume data with Python\n- \\subpage tutorial_cli - How to use the command-line interface\n- \\subpage tutorial_cce - How to get started running stand-alone CCE with\n externally produced data\n- \\subpage tutorial_checkpoint_restart - How to set up a SpECTRE executable for\n checkpointing and restarting\n- \\subpage tutorial_events_and_triggers - How to specify code to run in an input\n file\n- \\subpage tutorial_imex - How to add IMEX support to an evolution system\n" }, { "path": "docs/Tutorials/Visualization.md", "content": "\\cond NEVER\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n\\endcond\n# Running and Visualizing {#tutorial_visualization}\n\n\\tableofcontents\n\n### Building an Executable from an Existing Source File\n\nSpECTRE source files for evolution executables are located in\n`src/Evolution/Executables`. Executables can be compiled by running the command\n`make EXECUTABLE_NAME` where `EXECUTABLE_NAME` is the name of the executable\nas defined in the `CMakeLists.txt` file located in the same directory as the\nsource file. For example, to compile the executable that evolves a scalar wave\nusing a three-dimensional domain, navigate to `$SPECTRE_HOME/build/`, then\none runs the command: `make EvolveScalarWave3D`, which then results\nin an executable of the same name in the `bin` directory of the user's\nbuild directory.\n\n### Running an Evolution Executable\n\nEach SpECTRE executable reads a user-provided YAML file that specifies the\nruntime settings of the evolution. This is where options such as the Domain,\nAnalyticSolution, TimeStepper, etc are supplied. Example input files are kept\nin `tests/InputFiles`, and are written to provide a functional base input file\nwhich the user can then modify as desired. Copy the executable and YAML file\nto a directory of your choice. The YAML file is then passed as an argument to\nthe executable using the flag `--input-file`. For example, for a scalar wave\nevolution, run the command:\n\n```\n./EvolveScalarWave3D --input-file PlaneWave3D.yaml\n```\n\nYou can also use the \\ref tutorial_cli \"command-line interface (CLI)\" to run\nexecutables:\n\n```\n./spectre run PlaneWave3D.yaml\n```\n\nBy default, the example input files do not produce any output. This can be\nchanged by modifying the options passed to `EventsAndTriggers` or\n`EventsAndDenseTriggers`:\n\n\\snippet PlaneWave1DObserveExample.yaml observe_event_trigger\n\nThis will observe the norms of the errors in the system at times\n\\f$0.0\\f$ and \\f$1.0\\f$ and the field data at the start of every 50th\nslab. A successful observation will result in the creation of H5\nfiles whose names can be specified in the YAML file under the options\n`VolumeFileName` and `ReductionFileName`. One volume data file will be\nproduced from each Charm++ node that is used to run the\nexecutable. Each volume data file will have its corresponding node\nnumber appended to its file name. Visualization of the volume data\nwill be described in the next sections.\n\n### Plotting data with Python\n\nSee the tutorial on \\ref tutorial_vis_python to learn how to load and visualize\nvolume data in Python.\n\n### 3D Volume Data In ParaView\n\nA SpECTRE executable with observers produces volume and/or reduced data h5\nfiles. An XDMF file must be created from the volume data in order to do\nvisualization using ParaView. To this end we provide the tool\n`generate-xdmf` in the Python command-line interface. Run it in your build\ndirectory as `spectre generate-xdmf`. It\ntakes two required arguments which are passed to `--subfile-name`, and\n`--output`. The\nargument passed to `--subfile-name` is the name of the subfile inside the H5\nvolume data file where data is stored. In the above example, `--subfile-name`\nwould be `VolumePsiPiPhiEvery50Slabs`. The argument passed to `--output` is the\ndesired .xmf file name, also without filename extension. Use `--help` to see a\nfurther description of possible arguments.\n\nOpen the .xmf file in ParaView and select the `Xdmf Reader`, *not* the version 3\nreaders. On the left hand side of the main ParaView window is a section named\n`Properties`, here you must click the highlighted `Apply` button. ParaView will\nnow render your volume data. If you only wish to visualize a few datasets out of\na large set, we recommended unchecking the boxes for the datasets you wish to\nignore under `Point Arrays` before clicking `Apply`. Also, don't forget to check\nwhich dataset is being used for the color under `Coloring`. The default won't\nnecessarily be the dataset you want.\n\n\\note ParaView cannot understand `.xmf` files when subfile names have colons in\nthem. Please avoid subfile names like `My::Subfile:Name`.\n\n### Helpful ParaView Filters\n\nHere we describe the usage of filters we've found to better visualize our data.\nFeel free to contribute to this section!\n\n#### Removing Mesh Imprinting\nYou may notice what appears to be mesh imprinting on the data. The imprinting\neffect can be removed by applying the `Tetrahedralize` filter. To apply the\nfilter select the `Filters` menu item, then `Alphabetical` and finally\n`Tetrahedralize`.\n\n#### Creating Derived Volume Data\nNew volume data can be created from the existing volume data using the\n`Calculator` filter. In the `Calculator`'s text box, input a numerical\nexpression in terms of existing datasets evaluating to the desired\nquantity. For example, a vector-valued velocity dataset can be created\nfrom three scalar velocity component datasets using the expression\n`velocity_x * iHat + velocity_y * jHat + velocity_z * kHat` and hitting\nthe `Apply` button. By default, this will create a new dataset `Result`.\nThe name of the new dataset can be changed by changing the name provided\nto `Result Array Name` above the `Calculator` text box.\n\n#### Visualizing Vector Fields Derived From Scalar Fields\nUse the `Calculator` filter described above in \"Creating Derived Volume Data\"\nto create a new vector-valued dataset. Once this is created, use the `Glyph`\nfilter and set the `Active Attributes` to the vector you wish to visualize.\nMake sure that `Scale Mode` is set to `vector`.\n\n### Visualizing and Extracting Dat Files\n\nGlobal quantities such as error norms are stored in `h5::Dat` subfiles in the\nreduction/global HDF5 file. The command-line endpoint `spectre plot dat`\ncan be used to plot quantities, and `spectre extract-dat` can be used\nto extract them into space-separated text files. These text\nfiles can then be read with other plotting programs or viewed in an editor.\n\n### Reproducibility of Results\n\nBeing able to reproduce the results of simulations is important for scientific\nintegrity and accuracy. To this end, SpECTRE encodes the source tree,\nenvironment variables, and a record of build information (e.g., the third-party\nlibrary versions) into the executables. From most executables these can be\nretrieved using the flags `--dump-source-as filename_without_extension`,\n`--dump-paths`, `--dump-build-info`, and `--dump-environment`. The flag\n`--dump-only` will cause the program to exit after the information has been\ndumped. You can use the `--help` flag to get more details on what flags are\navailable. The flag `--dump-paths` will print to screen the environment\nvariables `PATH`, `CPATH`, `LD_LIBRARY_PATH`, `LIBRARY_PATH`, and\n`CMAKE_PREFIX_PATH` at link time. The flag `--dump-build-info` will print to\nscreen the contents of the `BuildInfo.txt` file generated by CMake. The flag\n`--dump-environment` will print to screen the output of `printenv` at link\ntime. Finally, the flag `--dump-source-as filename_without_extension` will dump\nthe archive `filename_without_extension.tar.gz`, which contains the entire\nsource tree at link time. The combined above information should be enough to\nreproduce simulations results to roundoff error as long as the third party\nlibraries used to build the executable have not changed on the system the\nsimulation was run on.\n\nOften only data from the simulation is retained, not the entire executable. In\norder to make simulations reproducible from only the HDF5 output, any HDF5 files\nwritten with SpECTRE's HDF5 wrappers contain the info about the run, output of\n`printenv` at link time, the contents of `BuildInfo.txt`, and an archive\nof the source tree. These are inside the `header.hdr` group with names\n`SimulationInfo`, `EnvironmentVariablesAtCompilation`, `BuildInfo`, and\n`src.tar.gz`. The source archive can be extracted by running the command\n```\nh5dump -d /src.tar.gz -b LE -o src.tar.gz /path/to/hdf5/file.h5\n```\nYou will need to make sure the argument to `-b` is the same endianness as your\ncomputer. In the above example little endian is used.\n" }, { "path": "docs/Tutorials/VisualizationWithPython.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Visualization with Python {#tutorial_vis_python}\\n\",\n \"\\n\",\n \"This tutorial shows you how to load 3D volume data in Python and visualize it\\n\",\n \"using `matplotlib`.\\n\",\n \"\\n\",\n \"First, you need access to the `spectre` Python bindings. A simple way to do this\\n\",\n \"is to run a Jupyter server from the build directory:\\n\",\n \"\\n\",\n \"```sh\\n\",\n \"./bin/python-spectre -m jupyterlab\\n\",\n \"```\\n\",\n \"\\n\",\n \"You can find detailed instruction in the tutorial on \\\\ref spectre_using_python.\\n\",\n \"\\n\",\n \"> Note for VSCode users: You can also select this Jupyter server as kernel for\\n\",\n \"> notebooks running in VSCode (see [docs](https://code.visualstudio.com/docs/datascience/jupyter-notebooks#_connect-to-a-remote-jupyter-server)).\\n\",\n \"\\n\",\n \"Now we can import modules from the `spectre` Python package.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Distributed under the MIT License.\\n\",\n \"# See LICENSE.txt for details.\\n\",\n \"\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import numpy as np\\n\",\n \"import os\\n\",\n \"\\n\",\n \"plt.style.use(\\\"../Examples/plots.mplstyle\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Select an observation\\n\",\n \"\\n\",\n \"First, we open the H5 volume data files from a simulation and get a list of all\\n\",\n \"available observations and their times:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"from spectre.IO.H5 import list_observations, open_volfiles\\n\",\n \"import glob\\n\",\n \"\\n\",\n \"h5files = glob.glob(\\n\",\n \" # Point this to your volume data files\\n\",\n \" \\\"BbhVolume*.h5\\\"\\n\",\n \")\\n\",\n \"subfile_name = \\\"/VolumeData\\\"\\n\",\n \"obs_ids, obs_times = list_observations(open_volfiles(h5files, subfile_name))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can also list all available variables in the volume data files:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 21,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"
ConformalFactor                 ExtrinsicCurvature_xx           ExtrinsicCurvature_yx          \\n\",\n       \"ExtrinsicCurvature_yy           ExtrinsicCurvature_zx           ExtrinsicCurvature_zy          \\n\",\n       \"ExtrinsicCurvature_zz           InertialCoordinates_x           InertialCoordinates_y          \\n\",\n       \"InertialCoordinates_z           Lapse                           RadiallyCompressedCoordinates_x\\n\",\n       \"RadiallyCompressedCoordinates_y RadiallyCompressedCoordinates_z ShiftExcess_x                  \\n\",\n       \"ShiftExcess_y                   ShiftExcess_z                   Shift_x                        \\n\",\n       \"Shift_y                         Shift_z                         SpatialMetric_xx               \\n\",\n       \"SpatialMetric_yx                SpatialMetric_yy                SpatialMetric_zx               \\n\",\n       \"SpatialMetric_zy                SpatialMetric_zz                                               \\n\",\n       \"
\\n\"\n ],\n \"text/plain\": [\n \"ConformalFactor ExtrinsicCurvature_xx ExtrinsicCurvature_yx \\n\",\n \"ExtrinsicCurvature_yy ExtrinsicCurvature_zx ExtrinsicCurvature_zy \\n\",\n \"ExtrinsicCurvature_zz InertialCoordinates_x InertialCoordinates_y \\n\",\n \"InertialCoordinates_z Lapse RadiallyCompressedCoordinates_x\\n\",\n \"RadiallyCompressedCoordinates_y RadiallyCompressedCoordinates_z ShiftExcess_x \\n\",\n \"ShiftExcess_y ShiftExcess_z Shift_x \\n\",\n \"Shift_y Shift_z SpatialMetric_xx \\n\",\n \"SpatialMetric_yx SpatialMetric_yy SpatialMetric_zx \\n\",\n \"SpatialMetric_zy SpatialMetric_zz \\n\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"import rich.columns\\n\",\n \"\\n\",\n \"for volfile in open_volfiles(h5files, subfile_name, obs_ids[-1]):\\n\",\n \" all_vars = volfile.list_tensor_components(obs_ids[-1])\\n\",\n \" # Only look into the first file. The other should have the same variables.\\n\",\n \" break\\n\",\n \"\\n\",\n \"rich.print(rich.columns.Columns(all_vars))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Interpolate to a slice\\n\",\n \"\\n\",\n \"One way of visualizing your 3D volume data in a 2D plot is with a slice. Use\\n\",\n \"`interpolate_to_points` to interpolate your volume data to any set of\\n\",\n \"coordinates:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 30,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"from spectre.IO.Exporter import interpolate_to_points\\n\",\n \"\\n\",\n \"# Coordinates of a regular grid in the xy plane\\n\",\n \"x, y = np.meshgrid(np.linspace(-15, 15, 300), np.linspace(-15, 15, 300))\\n\",\n \"z = np.zeros(x.shape)\\n\",\n \"\\n\",\n \"# Interpolation can be slow, so it's useful to cache the result. Remember to\\n\",\n \"# delete the cache file if you change anything.\\n\",\n \"cache_file = \\\"interpolated_data.npy\\\"\\n\",\n \"if os.path.isfile(cache_file):\\n\",\n \" lapse = np.load(cache_file)\\n\",\n \"else:\\n\",\n \" lapse = np.array(\\n\",\n \" interpolate_to_points(\\n\",\n \" h5files,\\n\",\n \" subfile_name=subfile_name,\\n\",\n \" observation_id=obs_ids[-1],\\n\",\n \" tensor_components=[\\\"Lapse\\\"],\\n\",\n \" target_points=[x.flatten(), y.flatten(), z.flatten()],\\n\",\n \" )\\n\",\n \" ).reshape(x.shape)\\n\",\n \" np.save(cache_file, lapse)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can plot the 2D slice with `matplotlib`:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 37,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/xp/5t2ny359187c4ljckf8sz3m80000gn/T/ipykernel_19858/3375439396.py:2: RuntimeWarning: invalid value encountered in subtract\\n\",\n \" plt.contourf(x, y, np.log(1 - lapse))\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": \"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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# Plot lapse\\n\",\n \"plt.contourf(x, y, np.log(1 - lapse))\\n\",\n \"\\n\",\n \"# Plot circles for black holes\\n\",\n \"ax = plt.gca()\\n\",\n \"for bh_pos in [-8, 8]:\\n\",\n \" ax.add_patch(\\n\",\n \" plt.Circle(xy=(bh_pos, 0), radius=0.89, color=\\\"black\\\", fill=True)\\n\",\n \" )\\n\",\n \"\\n\",\n \"# Make plot square\\n\",\n \"ax.set_aspect(\\\"equal\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Plot individual elements\\n\",\n \"\\n\",\n \"You can also iterate over elements in your volume data to plot things like\\n\",\n \"element boundaries, collocation points, etc. Use `iter_elements`:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 27,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": \"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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"from spectre.IO.H5.IterElements import iter_elements\\n\",\n \"\\n\",\n \"# Create a 3D plot\\n\",\n \"ax = plt.gcf().add_subplot(111, projection=\\\"3d\\\")\\n\",\n \"ax.axis(\\\"off\\\")\\n\",\n \"\\n\",\n \"# Iterate over elements\\n\",\n \"for element in iter_elements(\\n\",\n \" open_volfiles(h5files, subfile_name),\\n\",\n \" obs_ids=obs_ids[0],\\n\",\n \" element_patterns=[\\\"B3,*\\\"], # Only plot elements in block 3\\n\",\n \"):\\n\",\n \" # Draw outline of the element by mapping the edges of the logical cube to\\n\",\n \" # inertial coordinates using the element map\\n\",\n \" for d in range(3):\\n\",\n \" for edge in range(4):\\n\",\n \" line = np.zeros((3, 100))\\n\",\n \" line[d, :] = np.linspace(-1, 1, 100)\\n\",\n \" line[(d + 1) % 3, :] = 2 * (edge % 2) - 1\\n\",\n \" line[(d + 2) % 3, :] = 2 * (edge // 2) - 1\\n\",\n \" x, y, z = element.map(line)\\n\",\n \" ax.plot(x, y, z, color=\\\"black\\\")\\n\",\n \"\\n\",\n \"# Make plot square\\n\",\n \"ax.set_aspect(\\\"equal\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Transforming volume data\\n\",\n \"\\n\",\n \"Often you want to post-process volume data to compute derived quantities from\\n\",\n \"the ones the simulation has written out. You can sometimes do this within tools\\n\",\n \"like ParaView (e.g. using ParaView's \\\"Calculator\\\" filter) if the computation is\\n\",\n \"simple enough and pointwise (i.e., needs no derivatives or other mesh\\n\",\n \"information). If you can't get what you need in ParaView, you can use `spectre\\n\",\n \"transform-vol`. It takes any Python function (a \\\"kernel\\\"), runs it over your\\n\",\n \"volume data, and writes the result back into the files.\\n\",\n \"\\n\",\n \"For example, let's add the number of grid points in each element as a field\\n\",\n \"that we can visualize:\\n\",\n \"\\n\",\n \"```sh\\n\",\n \"spectre transform-vol BbhVolume*.h5 -d VolumeData \\\\\\n\",\n \" -k spectre.Spectral.Mesh3D:extents\\n\",\n \"```\\n\",\n \"\\n\",\n \"You will be prompted to select an output dataset name (hit enter to select the\\n\",\n \"default \\\"Extents\\\"). The result will be written back into the H5 files. If you\\n\",\n \"now regenerate an XDMF file for the volume data you will be able to see the\\n\",\n \"output in ParaView.\\n\",\n \"\\n\",\n \"The `transform-vol` tool supports arbitrary Python functions as kernels. Many\\n\",\n \"Python functions from the `spectre` module are useful kernels. For example,\\n\",\n \"here are some useful kernels:\\n\",\n \"\\n\",\n \"- p-refinement (number of grid points per dimension):\\n\",\n \" `spectre.Spectral.Mesh3D:extents`\\n\",\n \"- Relative/absolute truncation error (from power monitors):\\n\",\n \" `spectre.NumericalAlgorithms.LinearOperators:relative_truncation_error`\\n\",\n \" or `absolute_truncation_error`\\n\",\n \"- Coordinates in different frames: `Element:grid_coordinates` or\\n\",\n \" `Element:distorted_coordinates`\\n\",\n \"\\n\",\n \"You can find more useful kernels by browsing the `spectre.PointwiseFunctions`\\n\",\n \"module: https://spectre-code.org/py/_autosummary/spectre.PointwiseFunctions.html\\n\",\n \"\\n\",\n \"You can also write your own kernels. Create a Python file, e.g. `kernel.py`, and\\n\",\n \"write a function like this:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"%%file kernel.py\\n\",\n \"from spectre.DataStructures.Tensor import Scalar, DataVector\\n\",\n \"\\n\",\n \"def lapse_squared(lapse: Scalar[DataVector]) -> Scalar[DataVector]:\\n\",\n \" return np.array(lapse)**2\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now you can run this kernel over your volume data like this:\\n\",\n \"\\n\",\n \"```sh\\n\",\n \"spectre transform-vol BbhVolume*.h5 -d VolumeData \\\\\\n\",\n \" -e kernel.py -k lapse_squared\\n\",\n \"```\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"You can find more details by running `spectre transform-vol --help`.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3 (ipykernel)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.10.13\"\n },\n \"orig_nbformat\": 4\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "docs/_templates/autosummary/module.rst", "content": "{% extends \"!autosummary/module.rst\" %}\n\n.. Distributed under the MIT License.\n See LICENSE.txt for details.\n\n.. Include pybindings documentation. This won't do anything for modules that\n have no pybindings but print a warning.\n{% block modules %}\n.. automodule:: {{ fullname }}._Pybindings\n\n.. currentmodule:: {{ fullname }}\n\n{{ super() }}\n{% endblock %}\n" }, { "path": "docs/cli.rst", "content": ".. Distributed under the MIT License.\n See LICENSE.txt for details.\n\n.. click:: spectre.__main__:cli\n :prog: spectre\n :nested: full\n" }, { "path": "docs/conf.py", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Configuration file for the Sphinx documentation builder.\n#\n# This file only contains a selection of the most common options. For a full\n# list see the documentation:\n# https://www.sphinx-doc.org/en/master/usage/configuration.html\n\n# -- Path setup --------------------------------------------------------------\n\n# If extensions (or modules to document with autodoc) are in another directory,\n# add these directories to sys.path here. If the directory is relative to the\n# documentation root, use os.path.abspath to make it absolute, like shown here.\n#\nimport os\nimport sys\n\n# -- Project information -----------------------------------------------------\n\nproject = \"SpECTRE Python interface\"\ncopyright = \"2017-2026, SXS Collaboration\"\nauthor = \"SXS Collaboration\"\n\n# -- General configuration ---------------------------------------------------\n\n# Add any Sphinx extension module names here, as strings. They can be\n# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom\n# ones.\nextensions = [\n \"sphinx.ext.autodoc\",\n \"sphinx.ext.autosummary\",\n \"sphinx.ext.mathjax\",\n # Parse Numpy-style docstrings\n \"sphinx.ext.napoleon\",\n # Support markdown files\n \"myst_parser\",\n # \"breathe\",\n \"sphinx_click\",\n]\n\n# Autodoc configuration\nautodoc_default_options = {\n \"members\": True,\n \"undoc-members\": True,\n \"inherited-members\": True,\n}\nautodoc_preserve_defaults = True\n\n# Add any paths that contain templates here, relative to this directory.\ntemplates_path = [\"_templates\"]\n\n# List of patterns, relative to source directory, that match files and\n# directories to ignore when looking for source files.\n# This pattern also affects html_static_path and html_extra_path.\nexclude_patterns = [\"_build\", \"Thumbs.db\", \".DS_Store\"]\n\n# -- Options for HTML output -------------------------------------------------\n\n# The theme to use for HTML and HTML Help pages. See the documentation for\n# a list of builtin themes.\n#\nhtml_theme = \"furo\"\n\n# Add any paths that contain custom static files (such as style sheets) here,\n# relative to this directory. They are copied after the builtin static files,\n# so a file named \"default.css\" will overwrite the builtin \"default.css\".\nhtml_static_path = [\"_static\"]\n\n# -- C++ documentation with Breathe + Exhale ---------------------------------\n\n# We have also experimented with generating our C++ documentation with Sphinx.\n# See issue: https://github.com/sxs-collaboration/spectre/issues/2138\n\n# Tell sphinx what the primary language being documented is.\n# primary_domain = \"cpp\"\n\n# Tell sphinx what the pygments highlight language should be.\n# highlight_language = \"cpp\"\n\n# Configure Breathe for parsing and including C++ documentation.\n# breathe_projects = {\"SpECTRE\": \"@CMAKE_BINARY_DIR@/docs/xml\"}\n# breathe_default_project = \"SpECTRE\"\n\n# Setup the Exhale extension for automatically building namespace,\n# file, and group documentation. We have had issues with Exhale\n# failing when dealing with function overloads. To enable you must\n# add `'exhale'` to the extensions.\n#\n# exhale_args = {\n# # These arguments are required\n# \"containmentFolder\": \"./api\",\n# \"rootFileName\": \"library_root.rst\",\n# \"rootFileTitle\": \"Library API\",\n# \"doxygenStripFromPath\": \"..\",\n# # Suggested optional arguments\n# \"createTreeView\": True,\n# # TIP: if using the sphinx-bootstrap-theme, you need\n# # \"treeViewIsBootstrap\": True,\n# \"exhaleExecutesDoxygen\": False\n# # \"exhaleDoxygenStdin\": \"INPUT = ../include\"\n# }\n\n# # a simple label style which uses the bibtex keys for labels\n# class NumberedLabelStyle(BaseLabelStyle):\n# def format_labels(self, sorted_entries):\n# for entry in sorted_entries:\n# # Add one since refs usually start at 1 not 0\n# yield str(sorted_entries.index(entry) + 1)\n\n# class SpectreBibStyle(UnsrtStyle):\n# default_label_style = NumberedLabelStyle\n\n# register_plugin('pybtex.style.formatting', 'SpectreStyle', SpectreBibStyle)\n" }, { "path": "docs/config/DoxygenLayout_1_8_10.xml", "content": "\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n\n" }, { "path": "docs/config/DoxygenLayout_1_9_8.xml", "content": "\n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n\n" }, { "path": "docs/config/MathJax.js", "content": "window.MathJax = {\n tex: {\n tags: \"ams\",\n packages: ['base', 'ams', 'bbox', 'color', 'physics', 'newcommand',\n 'boldsymbol']\n },\n options: {\n ignoreHtmlClass: 'tex2jax_ignore',\n processHtmlClass: 'tex2jax_process'\n },\n loader: {\n load: ['[tex]/bbox', '[tex]/color', '[tex]/physics', '[tex]/newcommand',\n '[tex]/boldsymbol']\n }\n};\n\n(function () {\n var script = document.createElement('script');\n script.src = 'https://cdn.jsdelivr.net/npm/mathjax@3.1.0/es5/tex-chtml-full.js';\n // cryptographic hashes can be found here:\n // https://www.jsdelivr.com/package/npm/mathjax?path=es5\n script.integrity = 'sha256-HJUiQvFxmEVWZ3D0qyz7Bg0JyJ2bkriI/WHQYo1ch5Y=';\n script.crossOrigin = 'anonymous';\n script.async = true;\n document.head.appendChild(script);\n})();\n" }, { "path": "docs/config/cppreference-doxygen-web.tag.xml", "content": "\n\n \n algorithm\n cpp/header/algorithm\n std\n \n \n any\n cpp/header/any\n std\n \n \n array\n cpp/header/array\n std\n \n \n atomic\n cpp/header/atomic\n std\n \n \n bitset\n cpp/header/bitset\n std\n \n \n cassert\n cpp/header/cassert\n std\n \n \n ccomplex\n cpp/header/ccomplex\n std\n \n \n cctype\n cpp/header/cctype\n std\n \n \n cerrno\n cpp/header/cerrno\n std\n \n \n cfenv\n cpp/header/cfenv\n std\n \n \n cfloat\n cpp/header/cfloat\n std\n \n \n chrono\n cpp/header/chrono\n std\n \n \n cinttypes\n cpp/header/cinttypes\n std\n \n \n ciso646\n cpp/header/ciso646\n std\n \n \n climits\n cpp/header/climits\n std\n \n \n clocale\n cpp/header/clocale\n std\n \n \n cmath\n cpp/header/cmath\n std\n \n \n codecvt\n cpp/header/codecvt\n std\n \n \n complex\n cpp/header/complex\n std\n \n \n condition_variable\n cpp/header/condition_variable\n std\n \n \n csetjmp\n cpp/header/csetjmp\n std\n \n \n csignal\n cpp/header/csignal\n std\n \n \n cstdalign\n cpp/header/cstdalign\n std\n \n \n cstdarg\n cpp/header/cstdarg\n std\n \n \n cstdbool\n cpp/header/cstdbool\n std\n \n \n cstddef\n cpp/header/cstddef\n std\n \n \n cstdint\n cpp/header/cstdint\n std\n \n \n cstdio\n cpp/header/cstdio\n std\n \n \n cstdlib\n cpp/header/cstdlib\n std\n \n \n cstring\n cpp/header/cstring\n std\n \n \n ctgmath\n cpp/header/ctgmath\n std\n \n \n ctime\n cpp/header/ctime\n std\n \n \n cuchar\n cpp/header/cuchar\n std\n \n \n cwchar\n cpp/header/cwchar\n std\n \n \n cwctype\n cpp/header/cwctype\n std\n \n \n deque\n cpp/header/deque\n std\n \n \n exception\n cpp/header/exception\n std\n \n \n execution\n cpp/header/execution\n std\n \n \n filesystem\n cpp/header/filesystem\n std\n \n \n forward_list\n cpp/header/forward_list\n std\n \n \n fstream\n cpp/header/fstream\n std\n \n \n functional\n cpp/header/functional\n std\n \n \n future\n cpp/header/future\n std\n \n \n initializer_list\n cpp/header/initializer_list\n std\n \n \n iomanip\n cpp/header/iomanip\n std\n \n \n ios\n cpp/header/ios\n std\n \n \n iosfwd\n cpp/header/iosfwd\n std\n \n \n iostream\n cpp/header/iostream\n std\n \n \n istream\n cpp/header/istream\n std\n \n \n iterator\n cpp/header/iterator\n std\n \n \n limits\n cpp/header/limits\n std\n \n \n list\n cpp/header/list\n std\n \n \n locale\n cpp/header/locale\n std\n \n \n map\n cpp/header/map\n std\n \n \n memory\n cpp/header/memory\n std\n \n \n memory_resource\n cpp/header/memory_resource\n std\n \n \n mutex\n cpp/header/mutex\n std\n \n \n new\n cpp/header/new\n std\n \n \n numeric\n cpp/header/numeric\n std\n \n \n optional\n cpp/header/optional\n std\n \n \n ostream\n cpp/header/ostream\n std\n \n \n queue\n cpp/header/queue\n std\n \n \n random\n cpp/header/random\n std\n \n \n ratio\n cpp/header/ratio\n std\n \n \n regex\n cpp/header/regex\n std\n \n \n scoped_allocator\n cpp/header/scoped_allocator\n std\n \n \n set\n cpp/header/set\n std\n \n \n shared_mutex\n cpp/header/shared_mutex\n std\n \n \n sstream\n cpp/header/sstream\n std\n \n \n stack\n cpp/header/stack\n std\n \n \n stdexcept\n cpp/header/stdexcept\n std\n \n \n streambuf\n cpp/header/streambuf\n std\n \n \n string\n cpp/header/string\n std\n \n \n string_view\n cpp/header/string_view\n std\n \n \n strstream\n cpp/header/strstream\n std\n \n \n system_error\n cpp/header/system_error\n std\n \n \n thread\n cpp/header/thread\n std\n \n \n tuple\n cpp/header/tuple\n std\n \n \n type_traits\n cpp/header/type_traits\n std\n \n \n typeindex\n cpp/header/typeindex\n std\n \n \n typeinfo\n cpp/header/typeinfo\n std\n \n \n unordered_map\n cpp/header/unordered_map\n std\n \n \n unordered_set\n cpp/header/unordered_set\n std\n \n \n utility\n cpp/header/utility\n std\n \n \n valarray\n cpp/header/valarray\n std\n \n \n variant\n cpp/header/variant\n std\n \n \n vector\n cpp/header/vector\n std\n \n \n std\n \n std::FILE\n \n T\n _Exit\n cpp/utility/program/_Exit\n \n (T... args)\n \n \n T\n abort\n cpp/utility/program/abort\n \n (T... args)\n \n \n T\n abs(float)\n cpp/numeric/math/fabs\n \n (T... args)\n \n \n T\n abs(int)\n cpp/numeric/math/abs\n \n (T... args)\n \n \n T\n accumulate\n cpp/algorithm/accumulate\n \n (T... args)\n \n \n T\n acos\n cpp/numeric/math/acos\n \n (T... args)\n \n \n T\n acosh\n cpp/numeric/math/acosh\n \n (T... args)\n \n std::add_const\n std::add_const_t\n std::add_cv\n std::add_cv_t\n std::add_lvalue_reference\n std::add_lvalue_reference_t\n std::add_pointer\n std::add_pointer_t\n std::add_rvalue_reference\n std::add_rvalue_reference_t\n std::add_volatile\n std::add_volatile_t\n \n T\n addressof\n cpp/memory/addressof\n \n (T... args)\n \n \n T\n adjacent_difference\n cpp/algorithm/adjacent_difference\n \n (T... args)\n \n \n T\n adjacent_find\n cpp/algorithm/adjacent_find\n \n (T... args)\n \n std::adopt_lock_t\n \n T\n advance\n cpp/iterator/advance\n \n (T... args)\n \n \n T\n align\n cpp/memory/align\n \n (T... args)\n \n std::align_val_t\n \n T\n aligned_alloc\n cpp/memory/c/aligned_alloc\n \n (T... args)\n \n std::aligned_storage\n std::aligned_storage_t\n std::aligned_union\n std::aligned_union_t\n std::alignment_of\n \n T\n alignment_of_v\n cpp/types/alignment_of\n \n \n \n \n T\n all_of\n cpp/algorithm/all_any_none_of\n \n (T... args)\n \n \n T\n allocate_shared\n cpp/memory/shared_ptr/allocate_shared\n \n (T... args)\n \n std::allocator\n std::allocator_arg_t\n std::allocator_traits\n std::any\n \n T\n any_cast\n cpp/utility/any/any_cast\n \n (T... args)\n \n \n T\n any_of\n cpp/algorithm/all_any_none_of\n \n (T... args)\n \n \n T\n apply\n cpp/utility/apply\n \n (T... args)\n \n std::array\n \n T\n as_const\n cpp/utility/as_const\n \n (T... args)\n \n \n T\n asctime\n cpp/chrono/c/asctime\n \n (T... args)\n \n \n T\n asin\n cpp/numeric/math/asin\n \n (T... args)\n \n \n T\n asinh\n cpp/numeric/math/asinh\n \n (T... args)\n \n \n T\n assoc_laguerre\n cpp/numeric/special_math/assoc_laguerre\n \n (T... args)\n \n \n T\n assoc_laguerref\n cpp/numeric/special_math/assoc_laguerre\n \n (T... args)\n \n \n T\n assoc_laguerrel\n cpp/numeric/special_math/assoc_laguerre\n \n (T... args)\n \n \n T\n assoc_legendre\n cpp/numeric/special_math/assoc_legendre\n \n (T... args)\n \n \n T\n assoc_legendref\n cpp/numeric/special_math/assoc_legendre\n \n (T... args)\n \n \n T\n assoc_legendrel\n cpp/numeric/special_math/assoc_legendre\n \n (T... args)\n \n \n T\n async\n cpp/thread/async\n \n (T... args)\n \n \n T\n at_quick_exit\n cpp/utility/program/at_quick_exit\n \n (T... args)\n \n \n T\n atan\n cpp/numeric/math/atan\n \n (T... args)\n \n \n T\n atan2\n cpp/numeric/math/atan2\n \n (T... args)\n \n \n T\n atanh\n cpp/numeric/math/atanh\n \n (T... args)\n \n \n T\n atexit\n cpp/utility/program/atexit\n \n (T... args)\n \n \n T\n atof\n cpp/string/byte/atof\n \n (T... args)\n \n \n T\n atoi\n cpp/string/byte/atoi\n \n (T... args)\n \n \n T\n atol\n cpp/string/byte/atoi\n \n (T... args)\n \n \n T\n atoll\n cpp/string/byte/atoi\n \n (T... args)\n \n std::atomic\n std::atomic_bool\n std::atomic_char16_t\n std::atomic_char32_t\n \n T\n atomic_compare_exchange_strong\n cpp/atomic/atomic_compare_exchange\n \n (T... args)\n \n \n T\n atomic_compare_exchange_strong_explicit\n cpp/atomic/atomic_compare_exchange\n \n (T... args)\n \n \n T\n atomic_compare_exchange_weak\n cpp/atomic/atomic_compare_exchange\n \n (T... args)\n \n \n T\n atomic_compare_exchange_weak_explicit\n cpp/atomic/atomic_compare_exchange\n \n (T... args)\n \n \n T\n atomic_exchange\n cpp/atomic/atomic_exchange\n \n (T... args)\n \n \n T\n atomic_exchange_explicit\n cpp/atomic/atomic_exchange\n \n (T... args)\n \n \n T\n atomic_fetch_add\n cpp/atomic/atomic_fetch_add\n \n (T... args)\n \n \n T\n atomic_fetch_add_explicit\n cpp/atomic/atomic_fetch_add\n \n (T... args)\n \n \n T\n atomic_fetch_and\n cpp/atomic/atomic_fetch_sub\n \n (T... args)\n \n \n T\n atomic_fetch_and_explicit\n cpp/atomic/atomic_fetch_sub\n \n (T... args)\n \n \n T\n atomic_fetch_or\n cpp/atomic/atomic_fetch_or\n \n (T... args)\n \n \n T\n atomic_fetch_or_explicit\n cpp/atomic/atomic_fetch_or\n \n (T... args)\n \n \n T\n atomic_fetch_sub\n cpp/atomic/atomic_fetch_sub\n \n (T... args)\n \n \n T\n atomic_fetch_sub_explicit\n cpp/atomic/atomic_fetch_sub\n \n (T... args)\n \n \n T\n atomic_fetch_xor\n cpp/atomic/atomic_fetch_xor\n \n (T... args)\n \n \n T\n atomic_fetch_xor_explicit\n cpp/atomic/atomic_fetch_xor\n \n (T... args)\n \n std::atomic_flag\n \n T\n atomic_init\n cpp/atomic/atomic_init\n \n (T... args)\n \n std::atomic_int\n std::atomic_int16_t\n std::atomic_int32_t\n std::atomic_int64_t\n std::atomic_int8_t\n std::atomic_int_fast16_t\n std::atomic_int_fast32_t\n std::atomic_int_fast64_t\n std::atomic_int_fast8_t\n std::atomic_int_least16_t\n std::atomic_int_least32_t\n std::atomic_int_least64_t\n std::atomic_int_least8_t\n std::atomic_intmax_t\n std::atomic_intptr_t\n \n T\n atomic_is_lock_free\n cpp/atomic/atomic_is_lock_free\n \n (T... args)\n \n std::atomic_llong\n \n T\n atomic_load\n cpp/atomic/atomic_load\n \n (T... args)\n \n \n T\n atomic_load_explicit\n cpp/atomic/atomic_load\n \n (T... args)\n \n std::atomic_long\n std::atomic_ptrdiff_t\n std::atomic_schar\n std::atomic_short\n \n T\n atomic_signal_fence\n cpp/atomic/atomic_signal_fence\n \n (T... args)\n \n std::atomic_size_t\n \n T\n atomic_store\n cpp/atomic/atomic_store\n \n (T... args)\n \n \n T\n atomic_store_explicit\n cpp/atomic/atomic_store\n \n (T... args)\n \n \n T\n atomic_thread_fence\n cpp/atomic/atomic_thread_fence\n \n (T... args)\n \n std::atomic_uchar\n std::atomic_uint\n std::atomic_uint16_t\n std::atomic_uint32_t\n std::atomic_uint64_t\n std::atomic_uint8_t\n std::atomic_uint_fast16_t\n std::atomic_uint_fast32_t\n std::atomic_uint_fast64_t\n std::atomic_uint_fast8_t\n std::atomic_uint_least16_t\n std::atomic_uint_least32_t\n std::atomic_uint_least64_t\n std::atomic_uint_least8_t\n std::atomic_uintmax_t\n std::atomic_uintptr_t\n std::atomic_ullong\n std::atomic_ulong\n std::atomic_ushort\n std::atomic_wchar_t\n std::auto_ptr\n std::back_insert_iterator\n \n T\n back_inserter\n cpp/iterator/back_inserter\n \n (T... args)\n \n std::bad_alloc\n std::bad_any_cast\n std::bad_array_length\n std::bad_array_new_length\n std::bad_cast\n std::bad_exception\n std::bad_function_call\n std::bad_optional_access\n std::bad_typeid\n std::bad_variant_access\n std::bad_weak_ptr\n std::basic_filebuf\n std::basic_fstream\n std::basic_ifstream\n std::basic_ios\n std::basic_iostream\n std::basic_istream\n std::basic_istringstream\n std::basic_ofstream\n std::basic_ostream\n std::basic_ostringstream\n std::basic_regex\n std::basic_streambuf\n std::basic_string\n std::basic_string_view\n std::basic_stringbuf\n std::basic_stringstream\n \n T\n begin\n cpp/iterator/begin\n \n (T... args)\n \n std::bernoulli_distribution\n \n T\n beta\n cpp/numeric/special_math/beta\n \n (T... args)\n \n \n T\n betaf\n cpp/numeric/special_math/beta\n \n (T... args)\n \n \n T\n betal\n cpp/numeric/special_math/beta\n \n (T... args)\n \n std::bidirectional_iterator_tag\n std::binary_function\n std::binary_negate\n \n T\n binary_search\n cpp/algorithm/binary_search\n \n (T... args)\n \n \n T\n bind\n cpp/utility/functional/bind\n \n (T... args)\n \n std::binomial_distribution\n std::bit_and\n std::bit_not\n std::bit_or\n std::bitset\n std::bool_constant\n \n T\n boolalpha\n cpp/io/manip/boolalpha\n \n (T... args)\n \n std::boyer_moore_horspool_searcher\n std::boyer_moore_searcher\n \n T\n bsearch\n cpp/algorithm/bsearch\n \n (T... args)\n \n \n T\n btowc\n cpp/string/multibyte/btowc\n \n (T... args)\n \n \n T\n c16rtomb\n cpp/string/multibyte/c16rtomb\n \n (T... args)\n \n \n T\n c32rtomb\n cpp/string/multibyte/c32rtomb\n \n (T... args)\n \n \n T\n call_once\n cpp/thread/call_once\n \n (T... args)\n \n \n T\n calloc\n cpp/memory/c/calloc\n \n (T... args)\n \n std::cauchy_distribution\n \n T\n cbegin\n cpp/iterator/begin\n \n (T... args)\n \n \n T\n cbrt\n cpp/numeric/math/cbrt\n \n (T... args)\n \n \n T\n ceil\n cpp/numeric/math/ceil\n \n (T... args)\n \n \n T\n cend\n cpp/iterator/end\n \n (T... args)\n \n std::centi\n std::cerr\n std::char_traits\n std::chi_squared_distribution\n std::chrono\n std::cin\n \n T\n clamp\n cpp/algorithm/clamp\n \n (T... args)\n \n \n T\n clearerr\n cpp/io/c/clearerr\n \n (T... args)\n \n \n T\n clock\n cpp/chrono/c/clock\n \n (T... args)\n \n std::clock_t\n std::clog\n std::cmatch\n std::codecvt\n std::codecvt_base\n std::codecvt_byname\n std::codecvt_utf16\n std::codecvt_utf8\n std::codecvt_utf8_utf16\n std::collate\n std::collate_byname\n std::common_type\n std::common_type_t\n \n T\n comp_ellint_1\n cpp/numeric/special_math/comp_ellint_1\n \n (T... args)\n \n \n T\n comp_ellint_1f\n cpp/numeric/special_math/comp_ellint_1\n \n (T... args)\n \n \n T\n comp_ellint_1l\n cpp/numeric/special_math/comp_ellint_1\n \n (T... args)\n \n \n T\n comp_ellint_2\n cpp/numeric/special_math/comp_ellint_2\n \n (T... args)\n \n \n T\n comp_ellint_2f\n cpp/numeric/special_math/comp_ellint_2\n \n (T... args)\n \n \n T\n comp_ellint_2l\n cpp/numeric/special_math/comp_ellint_2\n \n (T... args)\n \n \n T\n comp_ellint_3\n cpp/numeric/special_math/comp_ellint_3\n \n (T... args)\n \n \n T\n comp_ellint_3f\n cpp/numeric/special_math/comp_ellint_3\n \n (T... args)\n \n \n T\n comp_ellint_3l\n cpp/numeric/special_math/comp_ellint_3\n \n (T... args)\n \n std::complex\n std::condition_variable\n std::condition_variable_any\n std::conditional\n std::conditional_t\n std::conjunction\n \n T\n conjunction_v\n cpp/types/conjunction\n \n \n \n \n T\n const_pointer_cast\n cpp/memory/shared_ptr/pointer_cast\n \n (T... args)\n \n \n T\n copy\n cpp/algorithm/copy\n \n (T... args)\n \n \n T\n copy_backward\n cpp/algorithm/copy_backward\n \n (T... args)\n \n \n T\n copy_if\n cpp/algorithm/copy\n \n (T... args)\n \n \n T\n copy_n\n cpp/algorithm/copy_n\n \n (T... args)\n \n \n T\n copysign\n cpp/numeric/math/copysign\n \n (T... args)\n \n \n T\n cos\n cpp/numeric/math/cos\n \n (T... args)\n \n \n T\n cosh\n cpp/numeric/math/cosh\n \n (T... args)\n \n \n T\n count\n cpp/algorithm/count\n \n (T... args)\n \n \n T\n count_if\n cpp/algorithm/count\n \n (T... args)\n \n std::cout\n \n T\n crbegin\n cpp/iterator/rbegin\n \n (T... args)\n \n \n T\n cref\n cpp/utility/functional/ref\n \n (T... args)\n \n std::cregex_iterator\n std::cregex_token_iterator\n \n T\n crend\n cpp/iterator/rend\n \n (T... args)\n \n std::csub_match\n \n T\n ctime\n cpp/chrono/c/ctime\n \n (T... args)\n \n std::ctype\n std::ctype_base\n std::ctype_byname\n \n T\n current_exception\n cpp/error/current_exception\n \n (T... args)\n \n \n T\n cyl_bessel_i\n cpp/numeric/special_math/cyl_bessel_i\n \n (T... args)\n \n \n T\n cyl_bessel_if\n cpp/numeric/special_math/cyl_bessel_i\n \n (T... args)\n \n \n T\n cyl_bessel_il\n cpp/numeric/special_math/cyl_bessel_i\n \n (T... args)\n \n \n T\n cyl_bessel_j\n cpp/numeric/special_math/cyl_bessel_j\n \n (T... args)\n \n \n T\n cyl_bessel_jf\n cpp/numeric/special_math/cyl_bessel_j\n \n (T... args)\n \n \n T\n cyl_bessel_jl\n cpp/numeric/special_math/cyl_bessel_j\n \n (T... args)\n \n \n T\n cyl_bessel_k\n cpp/numeric/special_math/cyl_bessel_k\n \n (T... args)\n \n \n T\n cyl_bessel_kf\n cpp/numeric/special_math/cyl_bessel_k\n \n (T... args)\n \n \n T\n cyl_bessel_kl\n cpp/numeric/special_math/cyl_bessel_k\n \n (T... args)\n \n \n T\n cyl_neumann\n cpp/numeric/special_math/cyl_neumann\n \n (T... args)\n \n \n T\n cyl_neumannf\n cpp/numeric/special_math/cyl_neumann\n \n (T... args)\n \n \n T\n cyl_neumannl\n cpp/numeric/special_math/cyl_neumann\n \n (T... args)\n \n \n T\n data\n cpp/iterator/data\n \n (T... args)\n \n \n T\n dec\n cpp/io/manip/hex\n \n (T... args)\n \n std::deca\n std::decay\n std::decay_t\n std::deci\n \n T\n declare_no_pointers\n cpp/memory/gc/declare_no_pointers\n \n (T... args)\n \n \n T\n declare_reachable\n cpp/memory/gc/declare_reachable\n \n (T... args)\n \n \n T\n declval\n cpp/utility/declval\n \n (T... args)\n \n std::default_delete\n std::default_random_engine\n std::default_searcher\n \n T\n defaultfloat\n cpp/io/manip/fixed\n \n (T... args)\n \n std::defer_lock_t\n std::deque\n \n T\n destroy\n cpp/memory/destroy\n \n (T... args)\n \n \n T\n destroy_at\n cpp/memory/destroy_at\n \n (T... args)\n \n \n T\n destroy_n\n cpp/memory/destroy_n\n \n (T... args)\n \n \n T\n difftime\n cpp/chrono/c/difftime\n \n (T... args)\n \n std::discard_block_engine\n std::discrete_distribution\n std::disjunction\n \n T\n disjunction_v\n cpp/types/disjunction\n \n \n \n \n T\n distance\n cpp/iterator/distance\n \n (T... args)\n \n \n T\n div\n cpp/numeric/math/div\n \n (T... args)\n \n std::div_t\n std::divides\n std::domain_error\n \n T\n dynamic_pointer_cast\n cpp/memory/shared_ptr/pointer_cast\n \n (T... args)\n \n \n T\n ellint_1\n cpp/numeric/special_math/ellint_1\n \n (T... args)\n \n \n T\n ellint_1f\n cpp/numeric/special_math/ellint_1\n \n (T... args)\n \n \n T\n ellint_1l\n cpp/numeric/special_math/ellint_1\n \n (T... args)\n \n \n T\n ellint_2\n cpp/numeric/special_math/ellint_2\n \n (T... args)\n \n \n T\n ellint_2f\n cpp/numeric/special_math/ellint_2\n \n (T... args)\n \n \n T\n ellint_2l\n cpp/numeric/special_math/ellint_2\n \n (T... args)\n \n \n T\n ellint_3\n cpp/numeric/special_math/ellint_3\n \n (T... args)\n \n \n T\n ellint_3f\n cpp/numeric/special_math/ellint_3\n \n (T... args)\n \n \n T\n ellint_3l\n cpp/numeric/special_math/ellint_3\n \n (T... args)\n \n \n T\n empty\n cpp/iterator/empty\n \n (T... args)\n \n std::enable_if\n std::enable_if_t\n std::enable_shared_from_this\n \n T\n end\n cpp/iterator/end\n \n (T... args)\n \n \n T\n endl\n cpp/io/manip/endl\n \n (T... args)\n \n \n T\n ends\n cpp/io/manip/ends\n \n (T... args)\n \n \n T\n equal\n cpp/algorithm/equal\n \n (T... args)\n \n \n T\n equal_range\n cpp/algorithm/equal_range\n \n (T... args)\n \n std::equal_to\n \n T\n erf\n cpp/numeric/math/erf\n \n (T... args)\n \n \n T\n erfc\n cpp/numeric/math/erfc\n \n (T... args)\n \n std::errc\n std::error_category\n std::error_code\n std::error_condition\n std::exa\n std::exception\n std::exception_ptr\n \n T\n exchange\n cpp/utility/exchange\n \n (T... args)\n \n \n T\n exclusive_scan\n cpp/algorithm/exclusive_scan\n \n (T... args)\n \n std::execution\n \n T\n exit\n cpp/utility/program/exit\n \n (T... args)\n \n \n T\n exp\n cpp/numeric/math/exp\n \n (T... args)\n \n \n T\n exp2\n cpp/numeric/math/exp2\n \n (T... args)\n \n std::experimental\n \n T\n expint\n cpp/numeric/special_math/expint\n \n (T... args)\n \n \n T\n expintf\n cpp/numeric/special_math/expint\n \n (T... args)\n \n \n T\n expintl\n cpp/numeric/special_math/expint\n \n (T... args)\n \n \n T\n expm1\n cpp/numeric/math/expm1\n \n (T... args)\n \n std::exponential_distribution\n std::extent\n \n T\n extent_v\n cpp/types/extent\n \n \n \n std::extreme_value_distribution\n \n T\n fabs\n cpp/numeric/math/fabs\n \n (T... args)\n \n std::false_type\n \n T\n fclose\n cpp/io/c/fclose\n \n (T... args)\n \n \n T\n fdim\n cpp/numeric/math/fdim\n \n (T... args)\n \n \n T\n feclearexcept\n cpp/numeric/fenv/feclearexcept\n \n (T... args)\n \n \n T\n fegetenv\n cpp/numeric/fenv/feenv\n \n (T... args)\n \n \n T\n fegetexceptflag\n cpp/numeric/fenv/feexceptflag\n \n (T... args)\n \n \n T\n fegetround\n cpp/numeric/fenv/feround\n \n (T... args)\n \n \n T\n feholdexcept\n cpp/numeric/fenv/feholdexcept\n \n (T... args)\n \n std::femto\n \n T\n feof\n cpp/io/c/feof\n \n (T... args)\n \n \n T\n feraiseexcept\n cpp/numeric/fenv/feraiseexcept\n \n (T... args)\n \n \n T\n ferror\n cpp/io/c/ferror\n \n (T... args)\n \n \n T\n fesetenv\n cpp/numeric/fenv/feenv\n \n (T... args)\n \n \n T\n fesetexceptflag\n cpp/numeric/fenv/feexceptflag\n \n (T... args)\n \n \n T\n fesetround\n cpp/numeric/fenv/feround\n \n (T... args)\n \n \n T\n fetestexcept\n cpp/numeric/fenv/fetestexcept\n \n (T... args)\n \n \n T\n feupdateenv\n cpp/numeric/fenv/feupdateenv\n \n (T... args)\n \n \n T\n fflush\n cpp/io/c/fflush\n \n (T... args)\n \n \n T\n fgetc\n cpp/io/c/fgetc\n \n (T... args)\n \n \n T\n fgetpos\n cpp/io/c/fgetpos\n \n (T... args)\n \n \n T\n fgets\n cpp/io/c/fgets\n \n (T... args)\n \n \n T\n fgetwc\n cpp/io/c/fgetwc\n \n (T... args)\n \n \n T\n fgetws\n cpp/io/c/fgetws\n \n (T... args)\n \n std::filebuf\n std::filesystem\n \n T\n fill\n cpp/algorithm/fill\n \n (T... args)\n \n \n T\n fill_n\n cpp/algorithm/fill_n\n \n (T... args)\n \n \n T\n find\n cpp/algorithm/find\n \n (T... args)\n \n \n T\n find_end\n cpp/algorithm/find_end\n \n (T... args)\n \n \n T\n find_first_of\n cpp/algorithm/find_first_of\n \n (T... args)\n \n \n T\n find_if\n cpp/algorithm/find\n \n (T... args)\n \n \n T\n find_if_not\n cpp/algorithm/find\n \n (T... args)\n \n std::fisher_f_distribution\n \n T\n fixed\n cpp/io/manip/fixed\n \n (T... args)\n \n \n T\n floor\n cpp/numeric/math/floor\n \n (T... args)\n \n \n T\n flush\n cpp/io/manip/flush\n \n (T... args)\n \n \n T\n fma\n cpp/numeric/math/fma\n \n (T... args)\n \n \n T\n fmax\n cpp/numeric/math/fmax\n \n (T... args)\n \n \n T\n fmin\n cpp/numeric/math/fmin\n \n (T... args)\n \n \n T\n fmod\n cpp/numeric/math/fmod\n \n (T... args)\n \n \n T\n fopen\n cpp/io/c/fopen\n \n (T... args)\n \n \n T\n for_each\n cpp/algorithm/for_each\n \n (T... args)\n \n \n T\n for_each_n\n cpp/algorithm/for_each_n\n \n (T... args)\n \n \n T\n forward\n cpp/utility/forward\n \n (T... args)\n \n \n T\n forward_as_tuple\n cpp/utility/tuple/forward_as_tuple\n \n (T... args)\n \n std::forward_iterator_tag\n std::forward_list\n \n T\n fpclassify\n cpp/numeric/math/fpclassify\n \n (T... args)\n \n std::fpos\n std::fpos_t\n \n T\n fprintf\n cpp/io/c/fprintf\n \n (T... args)\n \n \n T\n fputc\n cpp/io/c/fputc\n \n (T... args)\n \n \n T\n fputs\n cpp/io/c/fputs\n \n (T... args)\n \n \n T\n fputwc\n cpp/io/c/fputwc\n \n (T... args)\n \n \n T\n fputws\n cpp/io/c/fputws\n \n (T... args)\n \n \n T\n fread\n cpp/io/c/fread\n \n (T... args)\n \n \n T\n free\n cpp/memory/c/free\n \n (T... args)\n \n \n T\n freopen\n cpp/io/c/freopen\n \n (T... args)\n \n \n T\n frexp\n cpp/numeric/math/frexp\n \n (T... args)\n \n std::front_insert_iterator\n \n T\n front_inserter\n cpp/iterator/front_inserter\n \n (T... args)\n \n \n T\n fscanf\n cpp/io/c/fscanf\n \n (T... args)\n \n \n T\n fseek\n cpp/io/c/fseek\n \n (T... args)\n \n \n T\n fsetpos\n cpp/io/c/fsetpos\n \n (T... args)\n \n std::fstream\n \n T\n ftell\n cpp/io/c/ftell\n \n (T... args)\n \n std::function\n std::future\n \n T\n future_category\n cpp/thread/future/future_category\n \n (T... args)\n \n std::future_error\n \n T\n fwprintf\n cpp/io/c/fwprintf\n \n (T... args)\n \n \n T\n fwrite\n cpp/io/c/fwrite\n \n (T... args)\n \n \n T\n fwscanf\n cpp/io/c/fwscanf\n \n (T... args)\n \n std::gamma_distribution\n \n T\n gcd\n cpp/numeric/gcd\n \n (T... args)\n \n \n T\n generate\n cpp/algorithm/generate\n \n (T... args)\n \n \n T\n generate_canonical\n cpp/numeric/random/generate_canonical\n \n (T... args)\n \n \n T\n generate_n\n cpp/algorithm/generate_n\n \n (T... args)\n \n \n T\n generic_category\n cpp/error/generic_category\n \n (T... args)\n \n std::geometric_distribution\n \n T\n get_if\n cpp/utility/variant/get_if\n \n (T... args)\n \n \n T\n get_money\n cpp/io/manip/get_money\n \n (T... args)\n \n \n T\n get_new_handler\n cpp/memory/new/get_new_handler\n \n (T... args)\n \n \n T\n get_pointer_safety\n cpp/memory/gc/get_pointer_safety\n \n (T... args)\n \n \n T\n get_temporary_buffer\n cpp/memory/get_temporary_buffer\n \n (T... args)\n \n \n T\n get_terminate\n cpp/error/get_terminate\n \n (T... args)\n \n \n T\n get_time\n cpp/io/manip/get_time\n \n (T... args)\n \n \n T\n get_unexpected\n cpp/error/get_unexpected\n \n (T... args)\n \n \n T\n getc\n cpp/io/c/fgetc\n \n (T... args)\n \n \n T\n getchar\n cpp/io/c/getchar\n \n (T... args)\n \n \n T\n getenv\n cpp/utility/program/getenv\n \n (T... args)\n \n \n T\n getline\n cpp/string/basic_string/getline\n \n (T... args)\n \n \n T\n gets\n cpp/io/c/gets\n \n (T... args)\n \n \n T\n getwchar\n cpp/io/c/getwchar\n \n (T... args)\n \n std::giga\n \n T\n gmtime\n cpp/chrono/c/gmtime\n \n (T... args)\n \n std::greater\n std::greater_equal\n std::gslice\n std::gslice_array\n \n T\n has_facet\n cpp/locale/has_facet\n \n (T... args)\n \n std::has_unique_object_representations\n \n T\n has_unique_object_representations_v\n cpp/types/has_unique_object_representations\n \n \n \n std::has_virtual_destructor\n \n T\n has_virtual_destructor_v\n cpp/types/has_virtual_destructor\n \n \n \n std::hash\n std::hecto\n \n T\n hermite\n cpp/numeric/special_math/hermite\n \n (T... args)\n \n \n T\n hermitef\n cpp/numeric/special_math/hermite\n \n (T... args)\n \n \n T\n hermitel\n cpp/numeric/special_math/hermite\n \n (T... args)\n \n \n T\n hex\n cpp/io/manip/hex\n \n (T... args)\n \n \n T\n hexfloat\n cpp/io/manip/fixed\n \n (T... args)\n \n \n T\n holds_alternative\n cpp/utility/variant/holds_alternative\n \n (T... args)\n \n \n T\n hypot\n cpp/numeric/math/hypot\n \n (T... args)\n \n std::ifstream\n \n T\n ilogb\n cpp/numeric/math/ilogb\n \n (T... args)\n \n \n T\n imaxdiv\n cpp/numeric/math/div\n \n (T... args)\n \n std::imaxdiv_t\n \n T\n in_place\n cpp/utility/in_place\n \n (T... args)\n \n std::in_place_index_t\n std::in_place_t\n std::in_place_tag\n std::in_place_type_t\n \n T\n includes\n cpp/algorithm/includes\n \n (T... args)\n \n \n T\n inclusive_scan\n cpp/algorithm/inclusive_scan\n \n (T... args)\n \n std::independent_bits_engine\n std::index_sequence\n std::index_sequence_for\n std::indirect_array\n std::initializer_list\n \n T\n inner_product\n cpp/algorithm/inner_product\n \n (T... args)\n \n \n T\n inplace_merge\n cpp/algorithm/inplace_merge\n \n (T... args)\n \n std::input_iterator_tag\n std::insert_iterator\n \n T\n inserter\n cpp/iterator/inserter\n \n (T... args)\n \n std::int16_t\n std::int32_t\n std::int64_t\n std::int8_t\n std::int_fast16_t\n std::int_fast32_t\n std::int_fast64_t\n std::int_fast8_t\n std::int_least16_t\n std::int_least32_t\n std::int_least64_t\n std::int_least8_t\n std::integer_sequence\n std::integral_constant\n \n T\n internal\n cpp/io/manip/left\n \n (T... args)\n \n std::intmax_t\n std::intptr_t\n std::invalid_argument\n \n T\n invoke\n cpp/utility/functional/invoke\n \n (T... args)\n \n std::ios_base\n std::iostream\n \n T\n iostream_category\n cpp/io/iostream_category\n \n (T... args)\n \n \n T\n iota\n cpp/algorithm/iota\n \n (T... args)\n \n std::is_abstract\n \n T\n is_abstract_v\n cpp/types/is_abstract\n \n \n \n std::is_arithmetic\n \n T\n is_arithmetic_v\n cpp/types/is_arithmetic\n \n \n \n std::is_array\n \n T\n is_array_v\n cpp/types/is_array\n \n \n \n std::is_assignable\n \n T\n is_assignable_v\n cpp/types/is_assignable\n \n \n \n std::is_base_of\n \n T\n is_base_of_v\n cpp/types/is_base_of\n \n \n \n std::is_bind_expression\n \n T\n is_bind_expression_v\n cpp/utility/functional/is_bind_expression\n \n \n \n std::is_callable\n \n T\n is_callable_v\n cpp/types/is_callable\n \n \n \n std::is_class\n \n T\n is_class_v\n cpp/types/is_class\n \n \n \n std::is_compound\n \n T\n is_compound_v\n cpp/types/is_compound\n \n \n \n std::is_const\n \n T\n is_const_v\n cpp/types/is_const\n \n \n \n std::is_constructible\n \n T\n is_constructible_v\n cpp/types/is_constructible\n \n \n \n std::is_convertible\n \n T\n is_convertible_v\n cpp/types/is_convertible\n \n \n \n std::is_copy_assignable\n \n T\n is_copy_assignable_v\n cpp/types/is_copy_assignable\n \n \n \n std::is_copy_constructible\n \n T\n is_copy_constructible_v\n cpp/types/is_copy_constructible\n \n \n \n std::is_default_constructible\n \n T\n is_default_constructible_v\n cpp/types/is_default_constructible\n \n \n \n std::is_destructible\n \n T\n is_destructible_v\n cpp/types/is_destructible\n \n \n \n std::is_empty\n \n T\n is_empty_v\n cpp/types/is_empty\n \n \n \n std::is_enum\n \n T\n is_enum_v\n cpp/types/is_enum\n \n \n \n std::is_error_code_enum\n std::is_error_code_enum_v\n std::is_error_condition_enum\n \n T\n is_error_condition_enum_v\n cpp/error/error_condition/is_error_condition_enum\n \n \n \n std::is_execution_policy\n \n T\n is_execution_policy_v\n cpp/algorithm/is_execution_policy\n \n \n \n std::is_final\n \n T\n is_final_v\n cpp/types/is_final\n \n \n \n std::is_floating_point\n \n T\n is_floating_point_v\n cpp/types/is_floating_point\n \n \n \n std::is_function\n \n T\n is_function_v\n cpp/types/is_function\n \n \n \n std::is_fundamental\n \n T\n is_fundamental_v\n cpp/types/is_fundamental\n \n \n \n \n T\n is_heap\n cpp/algorithm/is_heap\n \n (T... args)\n \n \n T\n is_heap_until\n cpp/algorithm/is_heap_until\n \n (T... args)\n \n std::is_integral\n \n T\n is_integral_v\n cpp/types/is_integral\n \n \n \n std::is_literal_type\n \n T\n is_literal_type_v\n cpp/types/is_literal_type\n \n \n \n std::is_lvalue_reference\n \n T\n is_lvalue_reference_v\n cpp/types/is_lvalue_reference\n \n \n \n std::is_member_function_pointer\n \n T\n is_member_function_pointer_v\n cpp/types/is_member_function_pointer\n \n \n \n std::is_member_object_pointer\n \n T\n is_member_object_pointer_v\n cpp/types/is_member_object_pointer\n \n \n \n std::is_member_pointer\n \n T\n is_member_pointer_v\n cpp/types/is_member_pointer\n \n \n \n std::is_move_assignable\n \n T\n is_move_assignable_v\n cpp/types/is_move_assignable\n \n \n \n std::is_move_constructible\n \n T\n is_move_constructible_v\n cpp/types/is_move_constructible\n \n \n \n std::is_nothrow_assignable\n \n T\n is_nothrow_assignable_v\n cpp/types/is_assignable\n \n \n \n std::is_nothrow_callable\n \n T\n is_nothrow_callable_v\n cpp/types/is_callable\n \n \n \n std::is_nothrow_constructible\n \n T\n is_nothrow_constructible_v\n cpp/types/is_constructible\n \n \n \n std::is_nothrow_copy_assignable\n \n T\n is_nothrow_copy_assignable_v\n cpp/types/is_copy_assignable\n \n \n \n std::is_nothrow_copy_constructible\n \n T\n is_nothrow_copy_constructible_v\n cpp/types/is_copy_constructible\n \n \n \n std::is_nothrow_default_constructible\n \n T\n is_nothrow_default_constructible_v\n cpp/types/is_default_constructible\n \n \n \n std::is_nothrow_destructible\n \n T\n is_nothrow_destructible_v\n cpp/types/is_destructible\n \n \n \n std::is_nothrow_move_assignable\n \n T\n is_nothrow_move_assignable_v\n cpp/types/is_move_assignable\n \n \n \n std::is_nothrow_move_constructible\n \n T\n is_nothrow_move_constructible_v\n cpp/types/is_move_constructible\n \n \n \n std::is_nothrow_swappable\n \n T\n is_nothrow_swappable_v\n cpp/types/is_swappable\n \n \n \n std::is_nothrow_swappable_with\n \n T\n is_nothrow_swappable_with_v\n cpp/types/is_swappable_with\n \n \n \n std::is_null_pointer\n \n T\n is_null_pointer_v\n cpp/types/is_null_pointer\n \n \n \n std::is_object\n \n T\n is_object_v\n cpp/types/is_object\n \n \n \n \n T\n is_partitioned\n cpp/algorithm/is_partitioned\n \n (T... args)\n \n \n T\n is_permutation\n cpp/algorithm/is_permutation\n \n (T... args)\n \n std::is_placeholder\n \n T\n is_placeholder_v\n cpp/utility/functional/is_placeholder\n \n \n \n std::is_pod\n \n T\n is_pod_v\n cpp/types/is_pod\n \n \n \n std::is_pointer\n \n T\n is_pointer_v\n cpp/types/is_pointer\n \n \n \n std::is_polymorphic\n \n T\n is_polymorphic_v\n cpp/types/is_polymorphic\n \n \n \n std::is_reference\n \n T\n is_reference_v\n cpp/types/is_reference\n \n \n \n std::is_rvalue_reference\n \n T\n is_rvalue_reference_v\n cpp/types/is_rvalue_reference\n \n \n \n std::is_same\n \n T\n is_same_v\n cpp/types/is_same\n \n \n \n std::is_scalar\n \n T\n is_scalar_v\n cpp/types/is_scalar\n \n \n \n std::is_signed\n \n T\n is_signed_v\n cpp/types/is_signed\n \n \n \n \n T\n is_sorted\n cpp/algorithm/is_sorted\n \n (T... args)\n \n \n T\n is_sorted_until\n cpp/algorithm/is_sorted_until\n \n (T... args)\n \n std::is_standard_layout\n \n T\n is_standard_layout_v\n cpp/types/is_standard_layout\n \n \n \n std::is_swappable\n \n T\n is_swappable_v\n cpp/types/is_swappable\n \n \n \n std::is_swappable_with\n \n T\n is_swappable_with_v\n cpp/types/is_swappable_with\n \n \n \n std::is_trivial\n \n T\n is_trivial_v\n cpp/types/is_trivial\n \n \n \n std::is_trivially_assignable\n \n T\n is_trivially_assignable_v\n cpp/types/is_assignable\n \n \n \n std::is_trivially_constructible\n \n T\n is_trivially_constructible_v\n cpp/types/is_constructible\n \n \n \n std::is_trivially_copy_assignable\n \n T\n is_trivially_copy_assignable_v\n cpp/types/is_copy_assignable\n \n \n \n std::is_trivially_copy_constructible\n \n T\n is_trivially_copy_constructible_v\n cpp/types/is_copy_constructible\n \n \n \n std::is_trivially_copyable\n \n T\n is_trivially_copyable_v\n cpp/types/is_trivially_copyable\n \n \n \n std::is_trivially_default_constructible\n \n T\n is_trivially_default_constructible_v\n cpp/types/is_default_constructible\n \n \n \n std::is_trivially_destructible\n \n T\n is_trivially_destructible_v\n cpp/types/is_destructible\n \n \n \n std::is_trivially_move_assignable\n \n T\n is_trivially_move_assignable_v\n cpp/types/is_move_assignable\n \n \n \n std::is_trivially_move_constructible\n \n T\n is_trivially_move_constructible_v\n cpp/types/is_move_constructible\n \n \n \n std::is_union\n \n T\n is_union_v\n cpp/types/is_union\n \n \n \n std::is_unsigned\n \n T\n is_unsigned_v\n cpp/types/is_unsigned\n \n \n \n std::is_void\n \n T\n is_void_v\n cpp/types/is_void\n \n \n \n std::is_volatile\n \n T\n is_volatile_v\n cpp/types/is_volatile\n \n \n \n \n T\n isalnum (<cctype>)\n cpp/string/byte/isalnum\n \n (T... args)\n \n \n T\n isalnum (<clocale>)\n cpp/locale/isalnum\n \n (T... args)\n \n \n T\n isalpha (<cctype>)\n cpp/string/byte/isalpha\n \n (T... args)\n \n \n T\n isalpha (<clocale>)\n cpp/locale/isalpha\n \n (T... args)\n \n \n T\n isblank (<cctype>)\n cpp/string/byte/isblank\n \n (T... args)\n \n \n T\n isblank (<clocale>)\n cpp/locale/isblank\n \n (T... args)\n \n \n T\n iscntrl (<cctype>)\n cpp/string/byte/iscntrl\n \n (T... args)\n \n \n T\n iscntrl (<clocale>)\n cpp/locale/iscntrl\n \n (T... args)\n \n \n T\n isdigit (<cctype>)\n cpp/string/byte/isdigit\n \n (T... args)\n \n \n T\n isdigit (<clocale>)\n cpp/locale/isdigit\n \n (T... args)\n \n \n T\n isfinite\n cpp/numeric/math/isfinite\n \n (T... args)\n \n \n T\n isgraph (<cctype>)\n cpp/string/byte/isgraph\n \n (T... args)\n \n \n T\n isgraph (<clocale>)\n cpp/locale/isgraph\n \n (T... args)\n \n \n T\n isinf\n cpp/numeric/math/isinf\n \n (T... args)\n \n \n T\n islower (<cctype>)\n cpp/string/byte/islower\n \n (T... args)\n \n \n T\n islower (<clocale>)\n cpp/locale/islower\n \n (T... args)\n \n \n T\n isnan\n cpp/numeric/math/isnan\n \n (T... args)\n \n \n T\n isnormal\n cpp/numeric/math/isnormal\n \n (T... args)\n \n \n T\n isprint (<cctype>)\n cpp/string/byte/isprint\n \n (T... args)\n \n \n T\n isprint (<clocale>)\n cpp/locale/isprint\n \n (T... args)\n \n \n T\n ispunct (<cctype>)\n cpp/string/byte/ispunct\n \n (T... args)\n \n \n T\n ispunct (<clocale>)\n cpp/locale/ispunct\n \n (T... args)\n \n \n T\n isspace (<cctype>)\n cpp/string/byte/isspace\n \n (T... args)\n \n \n T\n isspace (<clocale>)\n cpp/locale/isspace\n \n (T... args)\n \n std::istream\n std::istream_iterator\n std::istreambuf_iterator\n std::istringstream\n std::istrstream\n \n T\n isupper (<cctype>)\n cpp/string/byte/isupper\n \n (T... args)\n \n \n T\n isupper (<clocale>)\n cpp/locale/isupper\n \n (T... args)\n \n \n T\n iswalnum\n cpp/string/wide/iswalnum\n \n (T... args)\n \n \n T\n iswalpha\n cpp/string/wide/iswalpha\n \n (T... args)\n \n \n T\n iswblank\n cpp/string/wide/iswblank\n \n (T... args)\n \n \n T\n iswcntrl\n cpp/string/wide/iswcntrl\n \n (T... args)\n \n \n T\n iswctype\n cpp/string/wide/iswctype\n \n (T... args)\n \n \n T\n iswdigit\n cpp/string/wide/iswdigit\n \n (T... args)\n \n \n T\n iswgraph\n cpp/string/wide/iswgraph\n \n (T... args)\n \n \n T\n iswlower\n cpp/string/wide/iswlower\n \n (T... args)\n \n \n T\n iswprint\n cpp/string/wide/iswprint\n \n (T... args)\n \n \n T\n iswpunct\n cpp/string/wide/iswpunct\n \n (T... args)\n \n \n T\n iswspace\n cpp/string/wide/iswspace\n \n (T... args)\n \n \n T\n iswupper\n cpp/string/wide/iswupper\n \n (T... args)\n \n \n T\n iswxdigit\n cpp/string/wide/iswxdigit\n \n (T... args)\n \n \n T\n isxdigit (<cctype>)\n cpp/string/byte/isxdigit\n \n (T... args)\n \n \n T\n isxdigit (<clocale>)\n cpp/locale/isxdigit\n \n (T... args)\n \n \n T\n iter_swap\n cpp/algorithm/iter_swap\n \n (T... args)\n \n std::iterator\n std::iterator_traits\n std::jmp_buf\n \n T\n kill_dependency\n cpp/atomic/kill_dependency\n \n (T... args)\n \n std::kilo\n std::knuth_b\n \n T\n labs\n cpp/numeric/math/abs\n \n (T... args)\n \n \n T\n laguerre\n cpp/numeric/special_math/laguerre\n \n (T... args)\n \n \n T\n laguerref\n cpp/numeric/special_math/laguerre\n \n (T... args)\n \n \n T\n laguerrel\n cpp/numeric/special_math/laguerre\n \n (T... args)\n \n \n T\n launder\n cpp/utility/launder\n \n (T... args)\n \n \n T\n lcm\n cpp/numeric/lcm\n \n (T... args)\n \n std::lconv\n \n T\n ldexp\n cpp/numeric/math/ldexp\n \n (T... args)\n \n \n T\n ldiv\n cpp/numeric/math/div\n \n (T... args)\n \n std::ldiv_t\n \n T\n left\n cpp/io/manip/left\n \n (T... args)\n \n \n T\n legendre\n cpp/numeric/special_math/legendre\n \n (T... args)\n \n \n T\n legendref\n cpp/numeric/special_math/legendre\n \n (T... args)\n \n \n T\n legendrel\n cpp/numeric/special_math/legendre\n \n (T... args)\n \n std::length_error\n std::less\n std::less_equal\n \n T\n lexicographical_compare\n cpp/algorithm/lexicographical_compare\n \n (T... args)\n \n \n T\n lgamma\n cpp/numeric/math/lgamma\n \n (T... args)\n \n std::linear_congruential_engine\n std::list\n \n T\n llabs\n cpp/numeric/math/abs\n \n (T... args)\n \n \n T\n lldiv\n cpp/numeric/math/div\n \n (T... args)\n \n std::lldiv_t\n \n T\n llrint\n cpp/numeric/math/rint\n \n (T... args)\n \n \n T\n llround\n cpp/numeric/math/round\n \n (T... args)\n \n std::locale\n \n T\n localeconv\n cpp/locale/localeconv\n \n (T... args)\n \n \n T\n localtime\n cpp/chrono/c/localtime\n \n (T... args)\n \n \n T\n lock\n cpp/thread/lock\n \n (T... args)\n \n std::lock_guard\n \n T\n log\n cpp/numeric/math/log\n \n (T... args)\n \n \n T\n log10\n cpp/numeric/math/log10\n \n (T... args)\n \n \n T\n log1p\n cpp/numeric/math/log1p\n \n (T... args)\n \n \n T\n logb\n cpp/numeric/math/logb\n \n (T... args)\n \n std::logic_error\n std::logical_and\n std::logical_not\n std::logical_or\n std::lognormal_distribution\n \n T\n longjmp\n cpp/utility/program/longjmp\n \n (T... args)\n \n \n T\n lower_bound\n cpp/algorithm/lower_bound\n \n (T... args)\n \n \n T\n lrint\n cpp/numeric/math/rint\n \n (T... args)\n \n \n T\n lround\n cpp/numeric/math/round\n \n (T... args)\n \n \n T\n make_any\n cpp/utility/any/make_any\n \n (T... args)\n \n std::make_boyer_moore_horspool_searcher\n std::make_boyer_moore_searcher\n std::make_default_searcher\n \n T\n make_exception_ptr\n cpp/error/make_exception_ptr\n \n (T... args)\n \n \n T\n make_from_tuple\n cpp/utility/make_from_tuple\n \n (T... args)\n \n \n T\n make_heap\n cpp/algorithm/make_heap\n \n (T... args)\n \n std::make_index_sequence\n std::make_integer_sequence\n \n T\n make_move_iterator\n cpp/iterator/make_move_iterator\n \n (T... args)\n \n \n T\n make_optional\n cpp/utility/optional/make_optional\n \n (T... args)\n \n \n T\n make_pair\n cpp/utility/pair/make_pair\n \n (T... args)\n \n \n T\n make_reverse_iterator\n cpp/iterator/make_reverse_iterator\n \n (T... args)\n \n \n T\n make_shared\n cpp/memory/shared_ptr/make_shared\n \n (T... args)\n \n std::make_signed\n std::make_signed_t\n \n T\n make_tuple\n cpp/utility/tuple/make_tuple\n \n (T... args)\n \n \n T\n make_unique\n cpp/memory/unique_ptr/make_unique\n \n (T... args)\n \n std::make_unsigned\n std::make_unsigned_t\n \n T\n malloc\n cpp/memory/c/malloc\n \n (T... args)\n \n std::map\n std::mask_array\n std::match_results\n \n T\n max\n cpp/algorithm/max\n \n (T... args)\n \n std::max_align_t\n \n T\n max_element\n cpp/algorithm/max_element\n \n (T... args)\n \n \n T\n mblen\n cpp/string/multibyte/mblen\n \n (T... args)\n \n \n T\n mbrlen\n cpp/string/multibyte/mbrlen\n \n (T... args)\n \n \n T\n mbrtoc16\n cpp/string/multibyte/mbrtoc16\n \n (T... args)\n \n \n T\n mbrtoc32\n cpp/string/multibyte/mbrtoc32\n \n (T... args)\n \n \n T\n mbrtowc\n cpp/string/multibyte/mbrtowc\n \n (T... args)\n \n \n T\n mbsinit\n cpp/string/multibyte/mbsinit\n \n (T... args)\n \n \n T\n mbsrtowcs\n cpp/string/multibyte/mbsrtowcs\n \n (T... args)\n \n std::mbstate_t\n \n T\n mbstowcs\n cpp/string/multibyte/mbstowcs\n \n (T... args)\n \n \n T\n mbtowc\n cpp/string/multibyte/mbtowc\n \n (T... args)\n \n std::mega\n \n T\n mem_fn\n cpp/utility/functional/mem_fn\n \n (T... args)\n \n \n T\n memchr\n cpp/string/byte/memchr\n \n (T... args)\n \n \n T\n memcmp\n cpp/string/byte/memcmp\n \n (T... args)\n \n \n T\n memcpy\n cpp/string/byte/memcpy\n \n (T... args)\n \n \n T\n memmove\n cpp/string/byte/memmove\n \n (T... args)\n \n \n T\n memset\n cpp/string/byte/memset\n \n (T... args)\n \n \n T\n merge\n cpp/algorithm/merge\n \n (T... args)\n \n std::mersenne_twister_engine\n std::messages\n std::messages_base\n std::messages_byname\n std::micro\n std::milli\n \n T\n min\n cpp/algorithm/min\n \n (T... args)\n \n \n T\n min_element\n cpp/algorithm/min_element\n \n (T... args)\n \n \n T\n minmax\n cpp/algorithm/minmax\n \n (T... args)\n \n \n T\n minmax_element\n cpp/algorithm/minmax_element\n \n (T... args)\n \n std::minstd_rand\n std::minstd_rand0\n std::minus\n \n T\n mismatch\n cpp/algorithm/mismatch\n \n (T... args)\n \n \n T\n mktime\n cpp/chrono/c/mktime\n \n (T... args)\n \n \n T\n modf\n cpp/numeric/math/modf\n \n (T... args)\n \n std::modulus\n std::money_base\n std::money_get\n std::money_put\n std::moneypunct\n std::moneypunct_byname\n std::monostate\n \n T\n move (algorithm)\n cpp/algorithm/move\n \n (T... args)\n \n \n T\n move (utility)\n cpp/utility/move\n \n (T... args)\n \n \n T\n move_backward\n cpp/algorithm/move_backward\n \n (T... args)\n \n \n T\n move_if_noexcept\n cpp/utility/move_if_noexcept\n \n (T... args)\n \n std::move_iterator\n std::mt19937\n std::mt19937_64\n std::multimap\n std::multiplies\n std::multiset\n std::mutex\n \n T\n nan\n cpp/numeric/math/nan\n \n (T... args)\n \n \n T\n nanf\n cpp/numeric/math/nan\n \n (T... args)\n \n \n T\n nanl\n cpp/numeric/math/nan\n \n (T... args)\n \n std::nano\n \n T\n nearbyint\n cpp/numeric/math/nearbyint\n \n (T... args)\n \n std::negate\n std::negation\n \n T\n negation_v\n cpp/types/negation\n \n \n \n std::negative_binomial_distribution\n std::nested_exception\n std::new_handler\n \n T\n next\n cpp/iterator/next\n \n (T... args)\n \n \n T\n next_permutation\n cpp/algorithm/next_permutation\n \n (T... args)\n \n \n T\n nextafter\n cpp/numeric/math/nextafter\n \n (T... args)\n \n \n T\n nexttoward\n cpp/numeric/math/nextafter\n \n (T... args)\n \n \n T\n noboolalpha\n cpp/io/manip/boolalpha\n \n (T... args)\n \n \n T\n none_of\n cpp/algorithm/all_any_none_of\n \n (T... args)\n \n std::normal_distribution\n \n T\n noshowbase\n cpp/io/manip/showbase\n \n (T... args)\n \n \n T\n noshowpoint\n cpp/io/manip/showpoint\n \n (T... args)\n \n \n T\n noshowpos\n cpp/io/manip/showpos\n \n (T... args)\n \n \n T\n noskipws\n cpp/io/manip/skipws\n \n (T... args)\n \n \n T\n not1\n cpp/utility/functional/not1\n \n (T... args)\n \n \n T\n not2\n cpp/utility/functional/not2\n \n (T... args)\n \n std::not_equal_to\n \n T\n not_fn\n cpp/utility/functional/not_fn\n \n (T... args)\n \n std::nothrow_t\n \n T\n notify_all_at_thread_exit\n cpp/thread/notify_all_at_thread_exit\n \n (T... args)\n \n \n T\n nounitbuf\n cpp/io/manip/unitbuf\n \n (T... args)\n \n \n T\n nouppercase\n cpp/io/manip/uppercase\n \n (T... args)\n \n \n T\n nth_element\n cpp/algorithm/nth_element\n \n (T... args)\n \n std::nullopt_t\n std::nullptr_t\n std::num_get\n std::num_put\n std::numeric_limits\n std::numpunct\n std::numpunct_byname\n \n T\n oct\n cpp/io/manip/hex\n \n (T... args)\n \n std::ofstream\n std::once_flag\n std::optional\n std::ostream\n std::ostream_iterator\n std::ostreambuf_iterator\n std::ostringstream\n std::ostrstream\n std::out_of_range\n std::output_iterator_tag\n std::overflow_error\n std::owner_less\n std::packaged_task\n std::pair\n \n T\n partial_sort\n cpp/algorithm/partial_sort\n \n (T... args)\n \n \n T\n partial_sort_copy\n cpp/algorithm/partial_sort_copy\n \n (T... args)\n \n \n T\n partial_sum\n cpp/algorithm/partial_sum\n \n (T... args)\n \n \n T\n partition\n cpp/algorithm/partition\n \n (T... args)\n \n \n T\n partition_copy\n cpp/algorithm/partition_copy\n \n (T... args)\n \n \n T\n partition_point\n cpp/algorithm/partition_point\n \n (T... args)\n \n \n T\n perror\n cpp/io/c/perror\n \n (T... args)\n \n std::peta\n std::pico\n std::piecewise_constant_distribution\n std::piecewise_construct_t\n std::piecewise_linear_distribution\n std::placeholders\n std::plus\n std::pmr\n std::pointer_safety\n std::pointer_traits\n std::poisson_distribution\n \n T\n pop_heap\n cpp/algorithm/pop_heap\n \n (T... args)\n \n \n T\n pow\n cpp/numeric/math/pow\n \n (T... args)\n \n \n T\n prev\n cpp/iterator/prev\n \n (T... args)\n \n \n T\n prev_permutation\n cpp/algorithm/prev_permutation\n \n (T... args)\n \n \n T\n printf\n cpp/io/c/fprintf\n \n (T... args)\n \n std::priority_queue\n std::promise\n std::ptrdiff_t\n \n T\n push_heap\n cpp/algorithm/push_heap\n \n (T... args)\n \n \n T\n put_money\n cpp/io/manip/put_money\n \n (T... args)\n \n \n T\n put_time\n cpp/io/manip/put_time\n \n (T... args)\n \n \n T\n putc\n cpp/io/c/fputc\n \n (T... args)\n \n \n T\n putchar\n cpp/io/c/putchar\n \n (T... args)\n \n \n T\n puts\n cpp/io/c/puts\n \n (T... args)\n \n \n T\n putwchar\n cpp/io/c/putwchar\n \n (T... args)\n \n \n T\n qsort\n cpp/algorithm/qsort\n \n (T... args)\n \n std::queue\n \n T\n quick_exit\n cpp/utility/program/quick_exit\n \n (T... args)\n \n \n T\n quoted\n cpp/io/manip/quoted\n \n (T... args)\n \n \n T\n raise\n cpp/utility/program/raise\n \n (T... args)\n \n \n T\n rand\n cpp/numeric/random/rand\n \n (T... args)\n \n std::random_access_iterator_tag\n std::random_device\n \n T\n random_shuffle\n cpp/algorithm/random_shuffle\n \n (T... args)\n \n std::range_error\n std::rank\n \n T\n rank_v\n cpp/types/rank\n \n \n \n std::ranlux24\n std::ranlux24_base\n std::ranlux48\n std::ranlux48_base\n std::ratio\n std::ratio_add\n std::ratio_divide\n std::ratio_equal\n \n T\n ratio_equal_v\n cpp/numeric/ratio/ratio_equal\n \n \n \n std::ratio_greater\n std::ratio_greater_equal\n \n T\n ratio_greater_equal_v\n cpp/numeric/ratio/ratio_greater_equal\n \n \n \n \n T\n ratio_greater_v\n cpp/numeric/ratio/ratio_greater\n \n \n \n std::ratio_less\n std::ratio_less_equal\n \n T\n ratio_less_equal_v\n cpp/numeric/ratio/ratio_less_equal\n \n \n \n \n T\n ratio_less_v\n cpp/numeric/ratio/ratio_less\n \n \n \n std::ratio_multiply\n std::ratio_not_equal\n \n T\n ratio_not_equal_v\n cpp/numeric/ratio/ratio_not_equal\n \n \n \n std::ratio_subtract\n std::raw_storage_iterator\n \n T\n rbegin\n cpp/iterator/rbegin\n \n (T... args)\n \n \n T\n realloc\n cpp/memory/c/realloc\n \n (T... args)\n \n std::recursive_mutex\n std::recursive_timed_mutex\n \n T\n reduce\n cpp/algorithm/reduce\n \n (T... args)\n \n \n T\n ref\n cpp/utility/functional/ref\n \n (T... args)\n \n std::reference_wrapper\n std::regex\n std::regex_constants\n std::regex_error\n std::regex_iterator\n \n T\n regex_match\n cpp/regex/regex_match\n \n (T... args)\n \n \n T\n regex_replace\n cpp/regex/regex_replace\n \n (T... args)\n \n \n T\n regex_search\n cpp/regex/regex_search\n \n (T... args)\n \n std::regex_token_iterator\n std::regex_traits\n std::rel_ops\n \n T\n remainder\n cpp/numeric/math/remainder\n \n (T... args)\n \n \n T\n remove (<algorithm>)\n cpp/algorithm/remove\n \n (T... args)\n \n \n T\n remove (<cstdio>)\n cpp/io/c/remove\n \n (T... args)\n \n std::remove_all_extents\n std::remove_all_extents_t\n std::remove_const\n std::remove_const_t\n \n T\n remove_copy\n cpp/algorithm/remove_copy\n \n (T... args)\n \n \n T\n remove_copy_if\n cpp/algorithm/remove_copy\n \n (T... args)\n \n std::remove_cv\n std::remove_cv_t\n std::remove_extent\n std::remove_extent_t\n \n T\n remove_if\n cpp/algorithm/remove\n \n (T... args)\n \n std::remove_pointer\n std::remove_pointer_t\n std::remove_reference\n std::remove_reference_t\n std::remove_volatile\n std::remove_volatile_t\n \n T\n remquo\n cpp/numeric/math/remquo\n \n (T... args)\n \n \n T\n rename\n cpp/io/c/rename\n \n (T... args)\n \n \n T\n rend\n cpp/iterator/rend\n \n (T... args)\n \n \n T\n replace\n cpp/algorithm/replace\n \n (T... args)\n \n \n T\n replace_copy\n cpp/algorithm/replace_copy\n \n (T... args)\n \n \n T\n replace_copy_if\n cpp/algorithm/replace_copy\n \n (T... args)\n \n \n T\n replace_if\n cpp/algorithm/replace\n \n (T... args)\n \n \n T\n resetiosflags\n cpp/io/manip/resetiosflags\n \n (T... args)\n \n std::result_of\n std::result_of_t\n \n T\n rethrow_exception\n cpp/error/rethrow_exception\n \n (T... args)\n \n \n T\n rethrow_if_nested\n cpp/error/rethrow_if_nested\n \n (T... args)\n \n \n T\n return_temporary_buffer\n cpp/memory/return_temporary_buffer\n \n (T... args)\n \n \n T\n reverse\n cpp/algorithm/reverse\n \n (T... args)\n \n \n T\n reverse_copy\n cpp/algorithm/reverse_copy\n \n (T... args)\n \n std::reverse_iterator\n \n T\n rewind\n cpp/io/c/rewind\n \n (T... args)\n \n \n T\n riemann_zeta\n cpp/numeric/special_math/riemann_zeta\n \n (T... args)\n \n \n T\n riemann_zetaf\n cpp/numeric/special_math/riemann_zeta\n \n (T... args)\n \n \n T\n riemann_zetal\n cpp/numeric/special_math/riemann_zeta\n \n (T... args)\n \n \n T\n right\n cpp/io/manip/left\n \n (T... args)\n \n \n T\n rint\n cpp/numeric/math/rint\n \n (T... args)\n \n \n T\n rotate\n cpp/algorithm/rotate\n \n (T... args)\n \n \n T\n rotate_copy\n cpp/algorithm/rotate_copy\n \n (T... args)\n \n \n T\n round\n cpp/numeric/math/round\n \n (T... args)\n \n std::runtime_error\n \n T\n sample\n cpp/algorithm/sample\n \n (T... args)\n \n \n T\n scalbln\n cpp/numeric/math/scalbn\n \n (T... args)\n \n \n T\n scalbn\n cpp/numeric/math/scalbn\n \n (T... args)\n \n \n T\n scanf\n cpp/io/c/fscanf\n \n (T... args)\n \n \n T\n scientific\n cpp/io/manip/fixed\n \n (T... args)\n \n std::scoped_allocator_adaptor\n \n T\n search\n cpp/algorithm/search\n \n (T... args)\n \n \n T\n search_n\n cpp/algorithm/search_n\n \n (T... args)\n \n std::seed_seq\n std::set\n \n T\n set_difference\n cpp/algorithm/set_difference\n \n (T... args)\n \n \n T\n set_intersection\n cpp/algorithm/set_intersection\n \n (T... args)\n \n \n T\n set_new_handler\n cpp/memory/new/set_new_handler\n \n (T... args)\n \n \n T\n set_symmetric_difference\n cpp/algorithm/set_symmetric_difference\n \n (T... args)\n \n \n T\n set_terminate\n cpp/error/set_terminate\n \n (T... args)\n \n \n T\n set_unexpected\n cpp/error/set_unexpected\n \n (T... args)\n \n \n T\n set_union\n cpp/algorithm/set_union\n \n (T... args)\n \n \n T\n setbase\n cpp/io/manip/setbase\n \n (T... args)\n \n \n T\n setbuf\n cpp/io/c/setbuf\n \n (T... args)\n \n \n T\n setfill\n cpp/io/manip/setfill\n \n (T... args)\n \n \n T\n setiosflags\n cpp/io/manip/setiosflags\n \n (T... args)\n \n \n T\n setlocale\n cpp/locale/setlocale\n \n (T... args)\n \n \n T\n setprecision\n cpp/io/manip/setprecision\n \n (T... args)\n \n \n T\n setvbuf\n cpp/io/c/setvbuf\n \n (T... args)\n \n \n T\n setw\n cpp/io/manip/setw\n \n (T... args)\n \n std::shared_future\n std::shared_lock\n std::shared_mutex\n std::shared_ptr\n std::shared_timed_mutex\n \n T\n showbase\n cpp/io/manip/showbase\n \n (T... args)\n \n \n T\n showpoint\n cpp/io/manip/showpoint\n \n (T... args)\n \n \n T\n showpos\n cpp/io/manip/showpos\n \n (T... args)\n \n \n T\n shuffle\n cpp/algorithm/random_shuffle\n \n (T... args)\n \n std::shuffle_order_engine\n std::sig_atomic_t\n \n T\n signal\n cpp/utility/program/signal\n \n (T... args)\n \n \n T\n signbit\n cpp/numeric/math/signbit\n \n (T... args)\n \n \n T\n sin\n cpp/numeric/math/sin\n \n (T... args)\n \n \n T\n sinh\n cpp/numeric/math/sinh\n \n (T... args)\n \n \n T\n size\n cpp/iterator/size\n \n (T... args)\n \n std::size_t\n \n T\n skipws\n cpp/io/manip/skipws\n \n (T... args)\n \n std::slice\n std::slice_array\n std::smatch\n \n T\n snprintf\n cpp/io/c/fprintf\n \n (T... args)\n \n \n T\n sort\n cpp/algorithm/sort\n \n (T... args)\n \n \n T\n sort_heap\n cpp/algorithm/sort_heap\n \n (T... args)\n \n \n T\n sph_bessel\n cpp/numeric/special_math/sph_bessel\n \n (T... args)\n \n \n T\n sph_besself\n cpp/numeric/special_math/sph_bessel\n \n (T... args)\n \n \n T\n sph_bessell\n cpp/numeric/special_math/sph_bessel\n \n (T... args)\n \n \n T\n sph_legendre\n cpp/numeric/special_math/sph_legendre\n \n (T... args)\n \n \n T\n sph_legendref\n cpp/numeric/special_math/sph_legendre\n \n (T... args)\n \n \n T\n sph_legendrel\n cpp/numeric/special_math/sph_legendre\n \n (T... args)\n \n \n T\n sph_neumann\n cpp/numeric/special_math/sph_neumann\n \n (T... args)\n \n \n T\n sph_neumannf\n cpp/numeric/special_math/sph_neumann\n \n (T... args)\n \n \n T\n sph_neumannl\n cpp/numeric/special_math/sph_neumann\n \n (T... args)\n \n \n T\n sprintf\n cpp/io/c/fprintf\n \n (T... args)\n \n \n T\n sqrt\n cpp/numeric/math/sqrt\n \n (T... args)\n \n \n T\n srand\n cpp/numeric/random/srand\n \n (T... args)\n \n std::sregex_iterator\n std::sregex_token_iterator\n \n T\n sscanf\n cpp/io/c/fscanf\n \n (T... args)\n \n std::ssub_match\n \n T\n stable_partition\n cpp/algorithm/stable_partition\n \n (T... args)\n \n \n T\n stable_sort\n cpp/algorithm/stable_sort\n \n (T... args)\n \n std::stack\n \n T\n static_pointer_cast\n cpp/memory/shared_ptr/pointer_cast\n \n (T... args)\n \n \n T\n stod\n cpp/string/basic_string/stof\n \n (T... args)\n \n \n T\n stof\n cpp/string/basic_string/stof\n \n (T... args)\n \n \n T\n stoi\n cpp/string/basic_string/stol\n \n (T... args)\n \n \n T\n stol\n cpp/string/basic_string/stol\n \n (T... args)\n \n \n T\n stold\n cpp/string/basic_string/stof\n \n (T... args)\n \n \n T\n stoll\n cpp/string/basic_string/stol\n \n (T... args)\n \n \n T\n stoul\n cpp/string/basic_string/stoul\n \n (T... args)\n \n \n T\n stoull\n cpp/string/basic_string/stoul\n \n (T... args)\n \n \n T\n strcat\n cpp/string/byte/strcat\n \n (T... args)\n \n \n T\n strchr\n cpp/string/byte/strchr\n \n (T... args)\n \n \n T\n strcmp\n cpp/string/byte/strcmp\n \n (T... args)\n \n \n T\n strcoll\n cpp/string/byte/strcoll\n \n (T... args)\n \n \n T\n strcpy\n cpp/string/byte/strcpy\n \n (T... args)\n \n \n T\n strcspn\n cpp/string/byte/strcspn\n \n (T... args)\n \n std::streambuf\n std::streamoff\n std::streampos\n std::streamsize\n \n T\n strerror\n cpp/string/byte/strerror\n \n (T... args)\n \n \n T\n strftime\n cpp/chrono/c/strftime\n \n (T... args)\n \n std::string\n std::string_view\n std::stringbuf\n std::stringstream\n \n T\n strlen\n cpp/string/byte/strlen\n \n (T... args)\n \n \n T\n strncat\n cpp/string/byte/strncat\n \n (T... args)\n \n \n T\n strncmp\n cpp/string/byte/strncmp\n \n (T... args)\n \n \n T\n strncpy\n cpp/string/byte/strncpy\n \n (T... args)\n \n \n T\n strpbrk\n cpp/string/byte/strpbrk\n \n (T... args)\n \n \n T\n strrchr\n cpp/string/byte/strrchr\n \n (T... args)\n \n \n T\n strspn\n cpp/string/byte/strspn\n \n (T... args)\n \n \n T\n strstr\n cpp/string/byte/strstr\n \n (T... args)\n \n std::strstream\n std::strstreambuf\n \n T\n strtod\n cpp/string/byte/strtof\n \n (T... args)\n \n \n T\n strtof\n cpp/string/byte/strtof\n \n (T... args)\n \n \n T\n strtoimax\n cpp/string/byte/strtoimax\n \n (T... args)\n \n \n T\n strtok\n cpp/string/byte/strtok\n \n (T... args)\n \n \n T\n strtol\n cpp/string/byte/strtol\n \n (T... args)\n \n \n T\n strtold\n cpp/string/byte/strtof\n \n (T... args)\n \n \n T\n strtoll\n cpp/string/byte/strtol\n \n (T... args)\n \n \n T\n strtoul\n cpp/string/byte/strtoul\n \n (T... args)\n \n \n T\n strtoull\n cpp/string/byte/strtoul\n \n (T... args)\n \n \n T\n strtoumax\n cpp/string/byte/strtoimax\n \n (T... args)\n \n \n T\n strxfrm\n cpp/string/byte/strxfrm\n \n (T... args)\n \n std::student_t_distribution\n std::sub_match\n std::subtract_with_carry_engine\n \n T\n swap\n cpp/algorithm/swap\n \n (T... args)\n \n \n T\n swap_ranges\n cpp/algorithm/swap_ranges\n \n (T... args)\n \n \n T\n swprintf\n cpp/io/c/fwprintf\n \n (T... args)\n \n \n T\n swscanf\n cpp/io/c/fwscanf\n \n (T... args)\n \n \n T\n system\n cpp/utility/program/system\n \n (T... args)\n \n \n T\n system_category\n cpp/error/system_category\n \n (T... args)\n \n std::system_error\n \n T\n tan\n cpp/numeric/math/tan\n \n (T... args)\n \n \n T\n tanh\n cpp/numeric/math/tanh\n \n (T... args)\n \n std::tera\n \n T\n terminate\n cpp/error/terminate\n \n (T... args)\n \n std::terminate_handler\n \n T\n tgamma\n cpp/numeric/math/tgamma\n \n (T... args)\n \n std::this_thread\n std::thread\n \n T\n throw_with_nested\n cpp/error/throw_with_nested\n \n (T... args)\n \n \n T\n tie\n cpp/utility/tuple/tie\n \n (T... args)\n \n \n T\n time\n cpp/chrono/c/time\n \n (T... args)\n \n std::time_base\n std::time_get\n std::time_get_byname\n std::time_put\n std::time_put_byname\n std::time_t\n std::timed_mutex\n \n T\n timespec\n cpp/chrono/c/timespec\n \n (T... args)\n \n \n T\n timespec_get\n cpp/chrono/c/timespec_get\n \n (T... args)\n \n std::tm\n \n T\n tmpfile\n cpp/io/c/tmpfile\n \n (T... args)\n \n \n T\n tmpnam\n cpp/io/c/tmpnam\n \n (T... args)\n \n \n T\n to_string\n cpp/string/basic_string/to_string\n \n (T... args)\n \n \n T\n to_wstring\n cpp/string/basic_string/to_wstring\n \n (T... args)\n \n \n T\n tolower (<cctype>)\n cpp/string/byte/tolower\n \n (T... args)\n \n \n T\n tolower (<clocale>)\n cpp/locale/tolower\n \n (T... args)\n \n \n T\n toupper (<cctype>)\n cpp/string/byte/toupper\n \n (T... args)\n \n \n T\n toupper (<clocale>)\n cpp/locale/toupper\n \n (T... args)\n \n \n T\n towctrans\n cpp/string/wide/towctrans\n \n (T... args)\n \n \n T\n towlower\n cpp/string/wide/towlower\n \n (T... args)\n \n \n T\n towupper\n cpp/string/wide/towupper\n \n (T... args)\n \n \n T\n transform\n cpp/algorithm/transform\n \n (T... args)\n \n \n T\n transform_exclusive_scan\n cpp/algorithm/transform_exclusive_scan\n \n (T... args)\n \n \n T\n transform_inclusive_scan\n cpp/algorithm/transform_inclusive_scan\n \n (T... args)\n \n \n T\n transform_reduce\n cpp/algorithm/transform_reduce\n \n (T... args)\n \n std::true_type\n \n T\n trunc\n cpp/numeric/math/trunc\n \n (T... args)\n \n \n T\n try_lock\n cpp/thread/try_lock\n \n (T... args)\n \n std::try_to_lock_t\n std::tuple\n \n T\n tuple_cat\n cpp/utility/tuple/tuple_cat\n \n (T... args)\n \n \n T\n tuple_size_v\n cpp/utility/tuple/tuple_size\n \n \n \n std::type_index\n std::type_info\n std::u16streampos\n std::u16string\n std::u16string_view\n std::u32streampos\n std::u32string\n std::u32string_view\n std::uint16_t\n std::uint32_t\n std::uint64_t\n std::uint8_t\n std::uint_fast16_t\n std::uint_fast32_t\n std::uint_fast64_t\n std::uint_fast8_t\n std::uint_least16_t\n std::uint_least32_t\n std::uint_least64_t\n std::uint_least8_t\n std::uintmax_t\n std::uintptr_t\n std::unary_function\n std::unary_negate\n \n T\n uncaught_exception\n cpp/error/uncaught_exception\n \n (T... args)\n \n \n T\n undeclare_no_pointers\n cpp/memory/gc/undeclare_no_pointers\n \n (T... args)\n \n \n T\n undeclare_reachable\n cpp/memory/gc/undeclare_reachable\n \n (T... args)\n \n std::underflow_error\n std::underlying_type\n std::underlying_type_t\n \n T\n unexpected\n cpp/error/unexpected\n \n (T... args)\n \n std::unexpected_handler\n \n T\n ungetc\n cpp/io/c/ungetc\n \n (T... args)\n \n \n T\n ungetwc\n cpp/io/c/ungetwc\n \n (T... args)\n \n std::uniform_int_distribution\n std::uniform_real_distribution\n \n T\n uninitialized_copy\n cpp/memory/uninitialized_copy\n \n (T... args)\n \n \n T\n uninitialized_copy_n\n cpp/memory/uninitialized_copy_n\n \n (T... args)\n \n \n T\n uninitialized_default_construct\n cpp/memory/uninitialized_default_construct\n \n (T... args)\n \n \n T\n uninitialized_default_construct_n\n cpp/memory/uninitialized_default_construct_n\n \n (T... args)\n \n \n T\n uninitialized_fill\n cpp/memory/uninitialized_fill\n \n (T... args)\n \n \n T\n uninitialized_fill_n\n cpp/memory/uninitialized_fill_n\n \n (T... args)\n \n \n T\n uninitialized_move\n cpp/memory/uninitialized_move\n \n (T... args)\n \n \n T\n uninitialized_move_n\n cpp/memory/uninitialized_move_n\n \n (T... args)\n \n \n T\n uninitialized_value_construct\n cpp/memory/uninitialized_value_construct\n \n (T... args)\n \n \n T\n uninitialized_value_construct_n\n cpp/memory/uninitialized_value_construct_n\n \n (T... args)\n \n \n T\n unique\n cpp/algorithm/unique\n \n (T... args)\n \n \n T\n unique_copy\n cpp/algorithm/unique_copy\n \n (T... args)\n \n std::unique_lock\n std::unique_ptr\n \n T\n unitbuf\n cpp/io/manip/unitbuf\n \n (T... args)\n \n std::unordered_map\n std::unordered_multimap\n std::unordered_multiset\n std::unordered_set\n \n T\n upper_bound\n cpp/algorithm/upper_bound\n \n (T... args)\n \n \n T\n uppercase\n cpp/io/manip/uppercase\n \n (T... args)\n \n \n T\n use_facet\n cpp/locale/use_facet\n \n (T... args)\n \n std::uses_allocator\n \n T\n uses_allocator_v\n cpp/memory/uses_allocator\n \n \n \n std::valarray\n std::variant\n std::variant_alternative\n std::variant_alternative_t\n std::variant_size\n \n T\n variant_size_v\n cpp/utility/variant/variant_size\n \n \n \n std::vector\n \n T\n vfprintf\n cpp/io/c/vfprintf\n \n (T... args)\n \n \n T\n vfscanf\n cpp/io/c/vfscanf\n \n (T... args)\n \n \n T\n vfwprintf\n cpp/io/c/vfwprintf\n \n (T... args)\n \n \n T\n vfwscanf\n cpp/io/c/vfwscanf\n \n (T... args)\n \n \n T\n visit\n cpp/utility/variant/visit\n \n (T... args)\n \n std::void_t\n \n T\n vprintf\n cpp/io/c/vfprintf\n \n (T... args)\n \n \n T\n vscanf\n cpp/io/c/vfscanf\n \n (T... args)\n \n \n T\n vsnprintf\n cpp/io/c/vfprintf\n \n (T... args)\n \n \n T\n vsprintf\n cpp/io/c/vfprintf\n \n (T... args)\n \n \n T\n vsscanf\n cpp/io/c/vfscanf\n \n (T... args)\n \n \n T\n vswprintf\n cpp/io/c/vfwprintf\n \n (T... args)\n \n \n T\n vswscanf\n cpp/io/c/vfwscanf\n \n (T... args)\n \n \n T\n vwprintf\n cpp/io/c/vfwprintf\n \n (T... args)\n \n \n T\n vwscanf\n cpp/io/c/vfwscanf\n \n (T... args)\n \n std::wbuffer_convert\n std::wcerr\n std::wcin\n std::wclog\n std::wcmatch\n std::wcout\n std::wcregex_iterator\n std::wcregex_token_iterator\n \n T\n wcrtomb\n cpp/string/multibyte/wcrtomb\n \n (T... args)\n \n \n T\n wcscat\n cpp/string/wide/wcscat\n \n (T... args)\n \n \n T\n wcschr\n cpp/string/wide/wcschr\n \n (T... args)\n \n \n T\n wcscmp\n cpp/string/wide/wcscmp\n \n (T... args)\n \n \n T\n wcscoll\n cpp/string/wide/wcscoll\n \n (T... args)\n \n \n T\n wcscpy\n cpp/string/wide/wcscpy\n \n (T... args)\n \n \n T\n wcscspn\n cpp/string/wide/wcscspn\n \n (T... args)\n \n \n T\n wcsftime\n cpp/chrono/c/wcsftime\n \n (T... args)\n \n \n T\n wcslen\n cpp/string/wide/wcslen\n \n (T... args)\n \n \n T\n wcsncat\n cpp/string/wide/wcsncat\n \n (T... args)\n \n \n T\n wcsncmp\n cpp/string/wide/wcsncmp\n \n (T... args)\n \n \n T\n wcsncpy\n cpp/string/wide/wcsncpy\n \n (T... args)\n \n \n T\n wcspbrk\n cpp/string/wide/wcspbrk\n \n (T... args)\n \n \n T\n wcsrchr\n cpp/string/wide/wcsrchr\n \n (T... args)\n \n \n T\n wcsrtombs\n cpp/string/multibyte/wcsrtombs\n \n (T... args)\n \n \n T\n wcsspn\n cpp/string/wide/wcsspn\n \n (T... args)\n \n \n T\n wcsstr\n cpp/string/wide/wcsstr\n \n (T... args)\n \n \n T\n wcstod\n cpp/string/wide/wcstof\n \n (T... args)\n \n \n T\n wcstof\n cpp/string/wide/wcstof\n \n (T... args)\n \n \n T\n wcstoimax\n cpp/string/wide/wcstoimax\n \n (T... args)\n \n \n T\n wcstok\n cpp/string/wide/wcstok\n \n (T... args)\n \n \n T\n wcstol\n cpp/string/wide/wcstol\n \n (T... args)\n \n \n T\n wcstold\n cpp/string/wide/wcstof\n \n (T... args)\n \n \n T\n wcstoll\n cpp/string/wide/wcstol\n \n (T... args)\n \n \n T\n wcstombs\n cpp/string/multibyte/wcstombs\n \n (T... args)\n \n \n T\n wcstoul\n cpp/string/wide/wcstoul\n \n (T... args)\n \n \n T\n wcstoull\n cpp/string/wide/wcstoul\n \n (T... args)\n \n \n T\n wcstoumax\n cpp/string/wide/wcstoimax\n \n (T... args)\n \n std::wcsub_match\n \n T\n wcsxfrm\n cpp/string/wide/wcsxfrm\n \n (T... args)\n \n \n T\n wctob\n cpp/string/multibyte/wctob\n \n (T... args)\n \n \n T\n wctomb\n cpp/string/multibyte/wctomb\n \n (T... args)\n \n \n T\n wctrans\n cpp/string/wide/wctrans\n \n (T... args)\n \n \n T\n wctype\n cpp/string/wide/wctype\n \n (T... args)\n \n std::weak_ptr\n std::weibull_distribution\n std::wfilebuf\n std::wfstream\n std::wifstream\n std::wiostream\n std::wistream\n std::wistringstream\n \n T\n wmemchr\n cpp/string/wide/wmemchr\n \n (T... args)\n \n \n T\n wmemcmp\n cpp/string/wide/wmemcmp\n \n (T... args)\n \n \n T\n wmemcpy\n cpp/string/wide/wmemcpy\n \n (T... args)\n \n \n T\n wmemmove\n cpp/string/wide/wmemmove\n \n (T... args)\n \n \n T\n wmemset\n cpp/string/wide/wmemset\n \n (T... args)\n \n std::wofstream\n std::wostream\n std::wostringstream\n \n T\n wprintf\n cpp/io/c/fwprintf\n \n (T... args)\n \n std::wregex\n \n T\n ws\n cpp/io/manip/ws\n \n (T... args)\n \n \n T\n wscanf\n cpp/io/c/fwscanf\n \n (T... args)\n \n std::wsmatch\n std::wsregex_iterator\n std::wsregex_token_iterator\n std::wssub_match\n std::wstreambuf\n std::wstreampos\n std::wstring\n std::wstring_convert\n std::wstring_view\n std::wstringbuf\n std::wstringstream\n std::yocto\n std::yotta\n std::zetta\n \n \n std::FILE\n cpp/io/c\n \n \n std::add_const\n cpp/types/add_cv\n \n \n std::add_const_t\n cpp/types/add_cv\n \n \n std::add_cv\n cpp/types/add_cv\n \n \n std::add_cv_t\n cpp/types/add_cv\n \n \n std::add_lvalue_reference\n cpp/types/add_reference\n \n \n std::add_lvalue_reference_t\n cpp/types/add_reference\n \n \n std::add_pointer\n cpp/types/add_pointer\n \n \n std::add_pointer_t\n cpp/types/add_pointer\n \n \n std::add_rvalue_reference\n cpp/types/add_reference\n \n \n std::add_rvalue_reference_t\n cpp/types/add_reference\n \n \n std::add_volatile\n cpp/types/add_cv\n \n \n std::add_volatile_t\n cpp/types/add_cv\n \n \n std::adopt_lock_t\n cpp/thread/lock_tag_t\n \n \n std::align_val_t\n cpp/memory/new/align_val_t\n \n \n std::aligned_storage\n cpp/types/aligned_storage\n \n \n std::aligned_storage_t\n cpp/types/aligned_storage\n \n \n std::aligned_union\n cpp/types/aligned_union\n \n \n std::aligned_union_t\n cpp/types/aligned_union\n \n \n std::alignment_of\n cpp/types/alignment_of\n \n \n std::allocator\n cpp/memory/allocator\n \n T\n address\n cpp/memory/allocator/address\n \n (T... args)\n \n \n T\n allocate\n cpp/memory/allocator/allocate\n \n (T... args)\n \n \n T\n allocator\n cpp/memory/allocator/allocator\n \n (T... args)\n \n \n T\n construct\n cpp/memory/allocator/construct\n \n (T... args)\n \n \n T\n deallocate\n cpp/memory/allocator/deallocate\n \n (T... args)\n \n \n T\n destroy\n cpp/memory/allocator/destroy\n \n (T... args)\n \n \n T\n max_size\n cpp/memory/allocator/max_size\n \n (T... args)\n \n \n T\n ~allocator\n cpp/memory/allocator/~allocator\n \n (T... args)\n \n \n \n std::allocator_arg_t\n cpp/memory/allocator_arg_t\n \n \n std::allocator_traits\n cpp/memory/allocator_traits\n \n T\n allocate\n cpp/memory/allocator_traits/allocate\n \n (T... args)\n \n \n T\n construct\n cpp/memory/allocator_traits/construct\n \n (T... args)\n \n \n T\n deallocate\n cpp/memory/allocator_traits/deallocate\n \n (T... args)\n \n \n T\n destroy\n cpp/memory/allocator_traits/destroy\n \n (T... args)\n \n \n T\n max_size\n cpp/memory/allocator_traits/max_size\n \n (T... args)\n \n \n T\n select_on_container_copy_construction\n cpp/memory/allocator_traits/select_on_container_copy_construction\n \n (T... args)\n \n \n \n std::any\n cpp/utility/any\n \n T\n any\n cpp/utility/any/any\n \n (T... args)\n \n \n T\n emplace\n cpp/utility/any/emplace\n \n (T... args)\n \n \n T\n has_value\n cpp/utility/any/has_value\n \n (T... args)\n \n \n T\n operator=\n cpp/utility/any/operator=\n \n (T... args)\n \n \n T\n reset\n cpp/utility/any/reset\n \n (T... args)\n \n \n T\n swap\n cpp/utility/any/swap\n \n (T... args)\n \n \n T\n type\n cpp/utility/any/type\n \n (T... args)\n \n \n T\n ~any\n cpp/utility/any/~any\n \n (T... args)\n \n \n \n std::array\n cpp/container/array\n \n T\n at\n cpp/container/array/at\n \n (T... args)\n \n \n T\n back\n cpp/container/array/back\n \n (T... args)\n \n \n T\n begin\n cpp/container/array/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/array/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/array/end\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/array/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/array/rend\n \n (T... args)\n \n \n T\n data\n cpp/container/array/data\n \n (T... args)\n \n \n T\n empty\n cpp/container/array/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/array/end\n \n (T... args)\n \n \n T\n fill\n cpp/container/array/fill\n \n (T... args)\n \n \n T\n front\n cpp/container/array/front\n \n (T... args)\n \n \n T\n max_size\n cpp/container/array/max_size\n \n (T... args)\n \n \n T\n operator[]\n cpp/container/array/operator_at\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/array/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/container/array/rend\n \n (T... args)\n \n \n T\n size\n cpp/container/array/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/array/swap\n \n (T... args)\n \n \n \n std::atomic\n cpp/atomic/atomic\n \n T\n atomic\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_bool\n cpp/atomic/atomic\n \n T\n atomic_bool\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_char16_t\n cpp/atomic/atomic\n \n T\n atomic_char16_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_char32_t\n cpp/atomic/atomic\n \n T\n atomic_char32_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_flag\n cpp/atomic/atomic_flag\n \n T\n atomic_flag\n cpp/atomic/atomic_flag/atomic_flag\n \n (T... args)\n \n \n T\n clear\n cpp/atomic/atomic_flag/clear\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic_flag/operator=\n \n (T... args)\n \n \n T\n test_and_set\n cpp/atomic/atomic_flag/test_and_set\n \n (T... args)\n \n \n \n std::atomic_int\n cpp/atomic/atomic\n \n T\n atomic_int\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_int16_t\n cpp/atomic/atomic\n \n T\n atomic_int16_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_int32_t\n cpp/atomic/atomic\n \n T\n atomic_int32_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_int64_t\n cpp/atomic/atomic\n \n T\n atomic_int64_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_int8_t\n cpp/atomic/atomic\n \n T\n atomic_int8_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_int_fast16_t\n cpp/atomic/atomic\n \n T\n atomic_int_fast16_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_int_fast32_t\n cpp/atomic/atomic\n \n T\n atomic_int_fast32_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_int_fast64_t\n cpp/atomic/atomic\n \n T\n atomic_int_fast64_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_int_fast8_t\n cpp/atomic/atomic\n \n T\n atomic_int_fast8_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_int_least16_t\n cpp/atomic/atomic\n \n T\n atomic_int_least16_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_int_least32_t\n cpp/atomic/atomic\n \n T\n atomic_int_least32_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_int_least64_t\n cpp/atomic/atomic\n \n T\n atomic_int_least64_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_int_least8_t\n cpp/atomic/atomic\n \n T\n atomic_int_least8_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_intmax_t\n cpp/atomic/atomic\n \n T\n atomic_intmax_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_intptr_t\n cpp/atomic/atomic\n \n T\n atomic_intptr_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_llong\n cpp/atomic/atomic\n \n T\n atomic_llong\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_long\n cpp/atomic/atomic\n \n T\n atomic_long\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_ptrdiff_t\n cpp/atomic/atomic\n \n T\n atomic_ptrdiff_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_schar\n cpp/atomic/atomic\n \n T\n atomic_schar\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_short\n cpp/atomic/atomic\n \n T\n atomic_short\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_size_t\n cpp/atomic/atomic\n \n T\n atomic_size_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uchar\n cpp/atomic/atomic\n \n T\n atomic_uchar\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uint\n cpp/atomic/atomic\n \n T\n atomic_uint\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uint16_t\n cpp/atomic/atomic\n \n T\n atomic_uint16_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uint32_t\n cpp/atomic/atomic\n \n T\n atomic_uint32_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uint64_t\n cpp/atomic/atomic\n \n T\n atomic_uint64_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uint8_t\n cpp/atomic/atomic\n \n T\n atomic_uint8_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uint_fast16_t\n cpp/atomic/atomic\n \n T\n atomic_uint_fast16_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uint_fast32_t\n cpp/atomic/atomic\n \n T\n atomic_uint_fast32_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uint_fast64_t\n cpp/atomic/atomic\n \n T\n atomic_uint_fast64_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uint_fast8_t\n cpp/atomic/atomic\n \n T\n atomic_uint_fast8_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uint_least16_t\n cpp/atomic/atomic\n \n T\n atomic_uint_least16_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uint_least32_t\n cpp/atomic/atomic\n \n T\n atomic_uint_least32_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uint_least64_t\n cpp/atomic/atomic\n \n T\n atomic_uint_least64_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uint_least8_t\n cpp/atomic/atomic\n \n T\n atomic_uint_least8_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uintmax_t\n cpp/atomic/atomic\n \n T\n atomic_uintmax_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_uintptr_t\n cpp/atomic/atomic\n \n T\n atomic_uintptr_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_ullong\n cpp/atomic/atomic\n \n T\n atomic_ullong\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_ulong\n cpp/atomic/atomic\n \n T\n atomic_ulong\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_ushort\n cpp/atomic/atomic\n \n T\n atomic_ushort\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::atomic_wchar_t\n cpp/atomic/atomic\n \n T\n atomic_wchar_t\n cpp/atomic/atomic/atomic\n \n (T... args)\n \n \n T\n compare_exchange_strong\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n compare_exchange_weak\n cpp/atomic/atomic/compare_exchange\n \n (T... args)\n \n \n T\n exchange\n cpp/atomic/atomic/exchange\n \n (T... args)\n \n \n T\n fetch_add\n cpp/atomic/atomic/fetch_add\n \n (T... args)\n \n \n T\n fetch_and\n cpp/atomic/atomic/fetch_and\n \n (T... args)\n \n \n T\n fetch_or\n cpp/atomic/atomic/fetch_or\n \n (T... args)\n \n \n T\n fetch_sub\n cpp/atomic/atomic/fetch_sub\n \n (T... args)\n \n \n T\n fetch_xor\n cpp/atomic/atomic/fetch_xor\n \n (T... args)\n \n \n T\n is_lock_free\n cpp/atomic/atomic/is_lock_free\n \n (T... args)\n \n \n T\n load\n cpp/atomic/atomic/load\n \n (T... args)\n \n \n T\n operator T\n cpp/atomic/atomic/operator_T\n \n (T... args)\n \n \n T\n operator&=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator++\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator--\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/atomic/atomic/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator=\n cpp/atomic/atomic/operator=\n \n (T... args)\n \n \n T\n operator^=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n operator|=\n cpp/atomic/atomic/operator_arith2\n \n (T... args)\n \n \n T\n store\n cpp/atomic/atomic/store\n \n (T... args)\n \n \n \n std::auto_ptr\n cpp/memory/auto_ptr\n \n T\n auto_ptr\n cpp/memory/auto_ptr/auto_ptr\n \n (T... args)\n \n \n T\n get\n cpp/memory/auto_ptr/get\n \n (T... args)\n \n \n T\n operator auto_ptr<Y>\n cpp/memory/auto_ptr/operator_auto_ptr\n \n (T... args)\n \n \n T\n operator*\n cpp/memory/auto_ptr/operator*\n \n (T... args)\n \n \n T\n operator->\n cpp/memory/auto_ptr/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/memory/auto_ptr/operator=\n \n (T... args)\n \n \n T\n release\n cpp/memory/auto_ptr/release\n \n (T... args)\n \n \n T\n reset\n cpp/memory/auto_ptr/reset\n \n (T... args)\n \n \n T\n ~auto_ptr\n cpp/memory/auto_ptr/~auto_ptr\n \n (T... args)\n \n \n \n std::back_insert_iterator\n cpp/iterator/back_insert_iterator\n \n \n std::bad_alloc\n cpp/memory/new/bad_alloc\n \n T\n bad_alloc\n cpp/memory/new/bad_alloc\n \n (T... args)\n \n \n T\n operator=\n cpp/memory/new/bad_alloc\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::bad_any_cast\n cpp/utility/any/bad_any_cast\n \n \n std::bad_array_length\n cpp/memory/new/bad_array_length\n \n T\n bad_array_length\n cpp/memory/new/bad_array_length\n \n (T... args)\n \n \n T\n what\n cpp/memory/new/bad_alloc\n \n (T... args)\n \n \n \n std::bad_array_new_length\n cpp/memory/new/bad_array_new_length\n \n T\n bad_array_new_length\n cpp/memory/new/bad_array_new_length/bad_array_new_length\n \n (T... args)\n \n \n T\n what\n cpp/memory/new/bad_alloc\n \n (T... args)\n \n \n \n std::bad_cast\n cpp/types/bad_cast\n \n T\n bad_cast\n cpp/types/bad_cast/bad_cast\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::bad_exception\n cpp/error/bad_exception\n \n \n std::bad_function_call\n cpp/utility/functional/bad_function_call\n \n T\n bad_function_call\n cpp/utility/functional/bad_function_call\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::bad_optional_access\n cpp/utility/optional/bad_optional_access\n \n \n std::bad_typeid\n cpp/types/bad_typeid\n \n T\n bad_typeid\n cpp/types/bad_typeid/bad_typeid\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::bad_variant_access\n cpp/utility/variant/bad_variant_access\n \n \n std::bad_weak_ptr\n cpp/memory/bad_weak_ptr\n \n T\n bad_weak_ptr\n cpp/memory/bad_weak_ptr/bad_weak_ptr\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::basic_filebuf\n cpp/io/basic_filebuf\n \n T\n basic_filebuf\n cpp/io/basic_filebuf/basic_filebuf\n \n (T... args)\n \n \n T\n close\n cpp/io/basic_filebuf/close\n \n (T... args)\n \n \n T\n eback\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n egptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n epptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n gbump\n cpp/io/basic_streambuf/gbump\n \n (T... args)\n \n \n T\n getloc\n cpp/io/basic_streambuf/getloc\n \n (T... args)\n \n \n T\n gptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n in_avail\n cpp/io/basic_streambuf/in_avail\n \n (T... args)\n \n \n T\n is_open\n cpp/io/basic_filebuf/is_open\n \n (T... args)\n \n \n T\n open\n cpp/io/basic_filebuf/open\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_filebuf/operator=\n \n (T... args)\n \n \n T\n overflow\n cpp/io/basic_streambuf/overflow\n \n (T... args)\n \n \n T\n pbackfail\n cpp/io/basic_streambuf/pbackfail\n \n (T... args)\n \n \n T\n pbase\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pbump\n cpp/io/basic_streambuf/pbump\n \n (T... args)\n \n \n T\n pptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pubimbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n pubseekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n pubseekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n pubsetbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n pubsync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n sbumpc\n cpp/io/basic_streambuf/sbumpc\n \n (T... args)\n \n \n T\n seekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n seekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n setbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n setg\n cpp/io/basic_streambuf/setg\n \n (T... args)\n \n \n T\n setp\n cpp/io/basic_streambuf/setp\n \n (T... args)\n \n \n T\n sgetc\n cpp/io/basic_streambuf/sgetc\n \n (T... args)\n \n \n T\n sgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n showmanyc\n cpp/io/basic_streambuf/showmanyc\n \n (T... args)\n \n \n T\n snextc\n cpp/io/basic_streambuf/snextc\n \n (T... args)\n \n \n T\n sputbackc\n cpp/io/basic_streambuf/sputbackc\n \n (T... args)\n \n \n T\n sputc\n cpp/io/basic_streambuf/sputc\n \n (T... args)\n \n \n T\n sputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n sungetc\n cpp/io/basic_streambuf/sungetc\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_streambuf/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n uflow\n cpp/io/basic_streambuf/uflow\n \n (T... args)\n \n \n T\n underflow\n cpp/io/basic_streambuf/underflow\n \n (T... args)\n \n \n T\n xsgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n xsputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n ~basic_filebuf\n cpp/io/basic_filebuf/~basic_filebuf\n \n (T... args)\n \n \n \n std::basic_fstream\n cpp/io/basic_fstream\n std::basic_fstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n basic_fstream\n cpp/io/basic_fstream/basic_fstream\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n close\n cpp/io/basic_fstream/close\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::basic_fstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::basic_fstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n is_open\n cpp/io/basic_fstream/is_open\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n open\n cpp/io/basic_fstream/open\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_fstream/operator=\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::basic_fstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::basic_fstream::Init\n cpp/io/ios_base/Init\n \n \n std::basic_fstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::basic_fstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::basic_fstream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::basic_ifstream\n cpp/io/basic_ifstream\n std::basic_ifstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n basic_ifstream\n cpp/io/basic_ifstream/basic_ifstream\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n close\n cpp/io/basic_ifstream/close\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::basic_ifstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::basic_ifstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n is_open\n cpp/io/basic_ifstream/is_open\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n open\n cpp/io/basic_ifstream/open\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_ifstream/operator=\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n std::basic_ifstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::basic_ifstream::Init\n cpp/io/ios_base/Init\n \n \n std::basic_ifstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::basic_ifstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::basic_ifstream::sentry\n cpp/io/basic_istream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::basic_ios\n cpp/io/basic_ios\n std::basic_ios::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n basic_ios\n cpp/io/basic_ios/basic_ios\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::basic_ios::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::basic_ios::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n imbue\n cpp/io/ios_base/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n T\n ~basic_ios\n cpp/io/basic_ios/~basic_ios\n \n (T... args)\n \n \n \n std::basic_ios::Init\n cpp/io/ios_base/Init\n \n \n std::basic_ios::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::basic_ios::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::basic_iostream\n cpp/io/basic_iostream\n std::basic_iostream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n basic_iostream\n cpp/io/basic_iostream/basic_iostream\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::basic_iostream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::basic_iostream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::basic_iostream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n T\n ~basic_iostream\n cpp/io/basic_iostream/~basic_iostream\n \n (T... args)\n \n \n \n std::basic_iostream::Init\n cpp/io/ios_base/Init\n \n \n std::basic_iostream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::basic_iostream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::basic_iostream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::basic_istream\n cpp/io/basic_istream\n std::basic_istream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n basic_istream\n cpp/io/basic_istream/basic_istream\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::basic_istream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::basic_istream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n std::basic_istream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n T\n ~basic_istream\n cpp/io/basic_istream/~basic_istream\n \n (T... args)\n \n \n \n std::basic_istream::Init\n cpp/io/ios_base/Init\n \n \n std::basic_istream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::basic_istream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::basic_istream::sentry\n cpp/io/basic_istream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::basic_istringstream\n cpp/io/basic_istringstream\n std::basic_istringstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n basic_istringstream\n cpp/io/basic_istringstream/basic_istringstream\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::basic_istringstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::basic_istringstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_istringstream/operator=\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n std::basic_istringstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n str\n cpp/io/basic_istringstream/str\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::basic_istringstream::Init\n cpp/io/ios_base/Init\n \n \n std::basic_istringstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::basic_istringstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::basic_istringstream::sentry\n cpp/io/basic_istream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::basic_ofstream\n cpp/io/basic_ofstream\n std::basic_ofstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n basic_ofstream\n cpp/io/basic_ofstream/basic_ofstream\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n close\n cpp/io/basic_ofstream/close\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::basic_ofstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::basic_ofstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n is_open\n cpp/io/basic_ofstream/is_open\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n open\n cpp/io/basic_ofstream/open\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_ofstream/operator=\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::basic_ofstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::basic_ofstream::Init\n cpp/io/ios_base/Init\n \n \n std::basic_ofstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::basic_ofstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::basic_ofstream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n \n std::basic_ostream\n cpp/io/basic_ostream\n std::basic_ostream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n basic_ostream\n cpp/io/basic_ostream/basic_ostream\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::basic_ostream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::basic_ostream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::basic_ostream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n T\n ~basic_ostream\n cpp/io/basic_ostream/~basic_ostream\n \n (T... args)\n \n \n \n std::basic_ostream::Init\n cpp/io/ios_base/Init\n \n \n std::basic_ostream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::basic_ostream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::basic_ostream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n \n std::basic_ostringstream\n cpp/io/basic_ostringstream\n std::basic_ostringstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n basic_ostringstream\n cpp/io/basic_ostringstream/basic_ostringstream\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::basic_ostringstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::basic_ostringstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_ostringstream/operator=\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::basic_ostringstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n str\n cpp/io/basic_ostringstream/str\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::basic_ostringstream::Init\n cpp/io/ios_base/Init\n \n \n std::basic_ostringstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::basic_ostringstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::basic_ostringstream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n \n std::basic_regex\n cpp/regex/basic_regex\n \n T\n assign\n cpp/regex/basic_regex/assign\n \n (T... args)\n \n \n T\n basic_regex\n cpp/regex/basic_regex/basic_regex\n \n (T... args)\n \n \n T\n flags\n cpp/regex/basic_regex/flags\n \n (T... args)\n \n \n T\n getloc\n cpp/regex/basic_regex/getloc\n \n (T... args)\n \n \n T\n imbue\n cpp/regex/basic_regex/imbue\n \n (T... args)\n \n \n T\n mark_count\n cpp/regex/basic_regex/mark_count\n \n (T... args)\n \n \n T\n operator=\n cpp/regex/basic_regex/operator=\n \n (T... args)\n \n \n T\n swap\n cpp/regex/basic_regex/swap\n \n (T... args)\n \n \n T\n ~basic_regex\n cpp/regex/basic_regex/~basic_regex\n \n (T... args)\n \n \n \n std::basic_streambuf\n cpp/io/basic_streambuf\n \n T\n basic_streambuf\n cpp/io/basic_streambuf/basic_streambuf\n \n (T... args)\n \n \n T\n eback\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n egptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n epptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n gbump\n cpp/io/basic_streambuf/gbump\n \n (T... args)\n \n \n T\n getloc\n cpp/io/basic_streambuf/getloc\n \n (T... args)\n \n \n T\n gptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n in_avail\n cpp/io/basic_streambuf/in_avail\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_streambuf/operator=\n \n (T... args)\n \n \n T\n overflow\n cpp/io/basic_streambuf/overflow\n \n (T... args)\n \n \n T\n pbackfail\n cpp/io/basic_streambuf/pbackfail\n \n (T... args)\n \n \n T\n pbase\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pbump\n cpp/io/basic_streambuf/pbump\n \n (T... args)\n \n \n T\n pptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pubimbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n pubseekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n pubseekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n pubsetbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n pubsync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n sbumpc\n cpp/io/basic_streambuf/sbumpc\n \n (T... args)\n \n \n T\n seekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n seekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n setbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n setg\n cpp/io/basic_streambuf/setg\n \n (T... args)\n \n \n T\n setp\n cpp/io/basic_streambuf/setp\n \n (T... args)\n \n \n T\n sgetc\n cpp/io/basic_streambuf/sgetc\n \n (T... args)\n \n \n T\n sgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n showmanyc\n cpp/io/basic_streambuf/showmanyc\n \n (T... args)\n \n \n T\n snextc\n cpp/io/basic_streambuf/snextc\n \n (T... args)\n \n \n T\n sputbackc\n cpp/io/basic_streambuf/sputbackc\n \n (T... args)\n \n \n T\n sputc\n cpp/io/basic_streambuf/sputc\n \n (T... args)\n \n \n T\n sputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n sungetc\n cpp/io/basic_streambuf/sungetc\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_streambuf/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n uflow\n cpp/io/basic_streambuf/uflow\n \n (T... args)\n \n \n T\n underflow\n cpp/io/basic_streambuf/underflow\n \n (T... args)\n \n \n T\n xsgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n xsputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n ~basic_streambuf\n cpp/io/basic_streambuf/~basic_streambuf\n \n (T... args)\n \n \n \n std::basic_string\n cpp/string/basic_string\n \n T\n append\n cpp/string/basic_string/append\n \n (T... args)\n \n \n T\n assign\n cpp/string/basic_string/assign\n \n (T... args)\n \n \n T\n at\n cpp/string/basic_string/at\n \n (T... args)\n \n \n T\n back\n cpp/string/basic_string/back\n \n (T... args)\n \n \n T\n basic_string\n cpp/string/basic_string/basic_string\n \n (T... args)\n \n \n T\n begin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n c_str\n cpp/string/basic_string/c_str\n \n (T... args)\n \n \n T\n capacity\n cpp/string/basic_string/capacity\n \n (T... args)\n \n \n T\n cbegin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n cend\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n clear\n cpp/string/basic_string/clear\n \n (T... args)\n \n \n T\n compare\n cpp/string/basic_string/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/basic_string/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n data\n cpp/string/basic_string/data\n \n (T... args)\n \n \n T\n empty\n cpp/string/basic_string/empty\n \n (T... args)\n \n \n T\n end\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n erase\n cpp/string/basic_string/erase\n \n (T... args)\n \n \n T\n find\n cpp/string/basic_string/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/string/basic_string/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/string/basic_string/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/string/basic_string/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/string/basic_string/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/string/basic_string/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/string/basic_string/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/string/basic_string/insert\n \n (T... args)\n \n \n T\n length\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n max_size\n cpp/string/basic_string/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/string/basic_string/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/string/basic_string/operator_at\n \n (T... args)\n \n \n T\n pop_back\n cpp/string/basic_string/pop_back\n \n (T... args)\n \n \n T\n push_back\n cpp/string/basic_string/push_back\n \n (T... args)\n \n \n T\n rbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n replace\n cpp/string/basic_string/replace\n \n (T... args)\n \n \n T\n reserve\n cpp/string/basic_string/reserve\n \n (T... args)\n \n \n T\n resize\n cpp/string/basic_string/resize\n \n (T... args)\n \n \n T\n rfind\n cpp/string/basic_string/rfind\n \n (T... args)\n \n \n T\n shrink_to_fit\n cpp/string/basic_string/shrink_to_fit\n \n (T... args)\n \n \n T\n size\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n substr\n cpp/string/basic_string/substr\n \n (T... args)\n \n \n T\n swap\n cpp/string/basic_string/swap\n \n (T... args)\n \n \n \n std::basic_string_view\n cpp/string/basic_string_view\n \n T\n at\n cpp/string/basic_string_view/at\n \n (T... args)\n \n \n T\n back\n cpp/string/basic_string_view/back\n \n (T... args)\n \n \n T\n basic_string_view\n cpp/string/basic_string_view/basic_string_view\n \n (T... args)\n \n \n T\n begin\n cpp/string/basic_string_view/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/string/basic_string_view/begin\n \n (T... args)\n \n \n T\n cend\n cpp/string/basic_string_view/end\n \n (T... args)\n \n \n T\n compare\n cpp/string/basic_string_view/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/basic_string_view/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/string/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/string/basic_string_view/rend\n \n (T... args)\n \n \n T\n data\n cpp/string/basic_string_view/data\n \n (T... args)\n \n \n T\n empty\n cpp/string/basic_string_view/empty\n \n (T... args)\n \n \n T\n end\n cpp/string/basic_string_view/end\n \n (T... args)\n \n \n T\n find\n cpp/string/basic_string_view/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/string/basic_string_view/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/string/basic_string_view/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/string/basic_string_view/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/string/basic_string_view/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/string/basic_string_view/front\n \n (T... args)\n \n \n T\n length\n cpp/string/basic_string_view/size\n \n (T... args)\n \n \n T\n max_size\n cpp/string/basic_string_view/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/string/basic_string_view/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/string/basic_string_view/operator_at\n \n (T... args)\n \n \n T\n rbegin\n cpp/string/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n remove_prefix\n cpp/string/basic_string_view/remove_prefix\n \n (T... args)\n \n \n T\n remove_suffix\n cpp/string/basic_string_view/remove_suffix\n \n (T... args)\n \n \n T\n rend\n cpp/string/basic_string_view/rend\n \n (T... args)\n \n \n T\n rfind\n cpp/string/basic_string_view/rfind\n \n (T... args)\n \n \n T\n size\n cpp/string/basic_string_view/size\n \n (T... args)\n \n \n T\n substr\n cpp/string/basic_string_view/substr\n \n (T... args)\n \n \n T\n swap\n cpp/string/basic_string_view/swap\n \n (T... args)\n \n \n \n std::basic_stringbuf\n cpp/io/basic_stringbuf\n \n T\n basic_stringbuf\n cpp/io/basic_stringbuf/basic_stringbuf\n \n (T... args)\n \n \n T\n eback\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n egptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n epptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n gbump\n cpp/io/basic_streambuf/gbump\n \n (T... args)\n \n \n T\n getloc\n cpp/io/basic_streambuf/getloc\n \n (T... args)\n \n \n T\n gptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n in_avail\n cpp/io/basic_streambuf/in_avail\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_stringbuf/operator=\n \n (T... args)\n \n \n T\n overflow\n cpp/io/basic_streambuf/overflow\n \n (T... args)\n \n \n T\n pbackfail\n cpp/io/basic_streambuf/pbackfail\n \n (T... args)\n \n \n T\n pbase\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pbump\n cpp/io/basic_streambuf/pbump\n \n (T... args)\n \n \n T\n pptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pubimbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n pubseekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n pubseekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n pubsetbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n pubsync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n sbumpc\n cpp/io/basic_streambuf/sbumpc\n \n (T... args)\n \n \n T\n seekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n seekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n setbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n setg\n cpp/io/basic_streambuf/setg\n \n (T... args)\n \n \n T\n setp\n cpp/io/basic_streambuf/setp\n \n (T... args)\n \n \n T\n sgetc\n cpp/io/basic_streambuf/sgetc\n \n (T... args)\n \n \n T\n sgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n showmanyc\n cpp/io/basic_streambuf/showmanyc\n \n (T... args)\n \n \n T\n snextc\n cpp/io/basic_streambuf/snextc\n \n (T... args)\n \n \n T\n sputbackc\n cpp/io/basic_streambuf/sputbackc\n \n (T... args)\n \n \n T\n sputc\n cpp/io/basic_streambuf/sputc\n \n (T... args)\n \n \n T\n sputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n str\n cpp/io/basic_stringbuf/str\n \n (T... args)\n \n \n T\n sungetc\n cpp/io/basic_streambuf/sungetc\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_streambuf/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n uflow\n cpp/io/basic_streambuf/uflow\n \n (T... args)\n \n \n T\n underflow\n cpp/io/basic_streambuf/underflow\n \n (T... args)\n \n \n T\n xsgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n xsputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n \n std::basic_stringstream\n cpp/io/basic_stringstream\n std::basic_stringstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n basic_stringstream\n cpp/io/basic_stringstream/basic_stringstream\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::basic_stringstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::basic_stringstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_stringstream/operator=\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::basic_stringstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n str\n cpp/io/basic_stringstream/str\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::basic_stringstream::Init\n cpp/io/ios_base/Init\n \n \n std::basic_stringstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::basic_stringstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::basic_stringstream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::bernoulli_distribution\n cpp/numeric/random/bernoulli_distribution\n \n T\n bernoulli_distribution\n cpp/numeric/random/bernoulli_distribution/bernoulli_distribution\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/bernoulli_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/bernoulli_distribution/min\n \n (T... args)\n \n \n T\n p\n cpp/numeric/random/bernoulli_distribution/p\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/bernoulli_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/bernoulli_distribution/reset\n \n (T... args)\n \n \n \n std::bidirectional_iterator_tag\n cpp/iterator/iterator_tags\n \n \n std::binary_function\n cpp/utility/functional/binary_function\n \n \n std::binary_negate\n cpp/utility/functional/binary_negate\n \n T\n binary_negate\n cpp/utility/functional/binary_negate\n \n (T... args)\n \n \n T\n operator()\n cpp/utility/functional/binary_negate\n \n (T... args)\n \n \n \n std::binomial_distribution\n cpp/numeric/random/binomial_distribution\n \n T\n binomial_distribution\n cpp/numeric/random/binomial_distribution/binomial_distribution\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/binomial_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/binomial_distribution/min\n \n (T... args)\n \n \n T\n p\n cpp/numeric/random/binomial_distribution/params\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/binomial_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/binomial_distribution/reset\n \n (T... args)\n \n \n T\n t\n cpp/numeric/random/binomial_distribution/params\n \n (T... args)\n \n \n \n std::bit_and\n cpp/utility/functional/bit_and\n \n T\n operator()\n cpp/utility/functional/bit_and\n \n (T... args)\n \n \n \n std::bit_not\n cpp/utility/functional/bit_not\n \n T\n operator()\n cpp/utility/functional/bit_not\n \n (T... args)\n \n \n \n std::bit_or\n cpp/utility/functional/bit_or\n \n T\n operator()\n cpp/utility/functional/bit_or\n \n (T... args)\n \n \n \n std::bitset\n cpp/utility/bitset\n \n T\n all\n cpp/utility/bitset/all_any_none\n \n (T... args)\n \n \n T\n any\n cpp/utility/bitset/all_any_none\n \n (T... args)\n \n \n T\n bitset\n cpp/utility/bitset/bitset\n \n (T... args)\n \n \n T\n count\n cpp/utility/bitset/count\n \n (T... args)\n \n \n T\n flip\n cpp/utility/bitset/flip\n \n (T... args)\n \n \n T\n none\n cpp/utility/bitset/all_any_none\n \n (T... args)\n \n \n T\n operator!=\n cpp/utility/bitset/operator_cmp\n \n (T... args)\n \n \n T\n operator&=\n cpp/utility/bitset/operator_logic\n \n (T... args)\n \n \n T\n operator<<\n cpp/utility/bitset/operator_ltltgtgt\n \n (T... args)\n \n \n T\n operator<<=\n cpp/utility/bitset/operator_ltltgtgt\n \n (T... args)\n \n \n T\n operator==\n cpp/utility/bitset/operator_cmp\n \n (T... args)\n \n \n T\n operator>>\n cpp/utility/bitset/operator_ltltgtgt\n \n (T... args)\n \n \n T\n operator>>=\n cpp/utility/bitset/operator_ltltgtgt\n \n (T... args)\n \n \n T\n operator[]\n cpp/utility/bitset/operator_at\n \n (T... args)\n \n \n T\n operator^=\n cpp/utility/bitset/operator_logic\n \n (T... args)\n \n \n T\n operator|=\n cpp/utility/bitset/operator_logic\n \n (T... args)\n \n \n T\n operator~\n cpp/utility/bitset/operator_logic\n \n (T... args)\n \n std::bitset::reference\n \n T\n reset\n cpp/utility/bitset/reset\n \n (T... args)\n \n \n T\n set\n cpp/utility/bitset/set\n \n (T... args)\n \n \n T\n size\n cpp/utility/bitset/size\n \n (T... args)\n \n \n T\n test\n cpp/utility/bitset/test\n \n (T... args)\n \n \n T\n to_string\n cpp/utility/bitset/to_string\n \n (T... args)\n \n \n T\n to_ullong\n cpp/utility/bitset/to_ullong\n \n (T... args)\n \n \n T\n to_ulong\n cpp/utility/bitset/to_ulong\n \n (T... args)\n \n \n \n std::bitset::reference\n cpp/utility/bitset/reference\n \n \n std::bool_constant\n cpp/types/integral_constant\n \n \n std::boyer_moore_horspool_searcher\n cpp/utility/functional/boyer_moore_horspool_searcher\n \n T\n boyer_moore_horspool_searcher\n cpp/utility/functional/boyer_moore_horspool_searcher\n \n (T... args)\n \n \n \n std::boyer_moore_searcher\n cpp/utility/functional/boyer_moore_searcher\n \n T\n boyer_moore_searcher\n cpp/utility/functional/boyer_moore_searcher\n \n (T... args)\n \n \n \n std::cauchy_distribution\n cpp/numeric/random/cauchy_distribution\n \n T\n a\n cpp/numeric/random/cauchy_distribution/params\n \n (T... args)\n \n \n T\n b\n cpp/numeric/random/cauchy_distribution/params\n \n (T... args)\n \n \n T\n cauchy_distribution\n cpp/numeric/random/cauchy_distribution/cauchy_distribution\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/cauchy_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/cauchy_distribution/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/cauchy_distribution/operator()\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/cauchy_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/cauchy_distribution/reset\n \n (T... args)\n \n \n \n std::centi\n cpp/numeric/ratio/ratio\n \n \n std::cerr\n cpp/io/cerr\n \n \n std::char_traits\n cpp/string/char_traits\n \n T\n assign\n cpp/string/char_traits/assign\n \n (T... args)\n \n \n T\n compare\n cpp/string/char_traits/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/char_traits/copy\n \n (T... args)\n \n \n T\n eof\n cpp/string/char_traits/eof\n \n (T... args)\n \n \n T\n eq\n cpp/string/char_traits/cmp\n \n (T... args)\n \n \n T\n eq_int_type\n cpp/string/char_traits/eq_int_type\n \n (T... args)\n \n \n T\n find\n cpp/string/char_traits/find\n \n (T... args)\n \n \n T\n length\n cpp/string/char_traits/length\n \n (T... args)\n \n \n T\n lt\n cpp/string/char_traits/cmp\n \n (T... args)\n \n \n T\n move\n cpp/string/char_traits/move\n \n (T... args)\n \n \n T\n not_eof\n cpp/string/char_traits/not_eof\n \n (T... args)\n \n \n T\n to_char_type\n cpp/string/char_traits/to_char_type\n \n (T... args)\n \n \n T\n to_int_type\n cpp/string/char_traits/to_int_type\n \n (T... args)\n \n \n \n std::chi_squared_distribution\n cpp/numeric/random/chi_squared_distribution\n \n T\n chi_squared_distribution\n cpp/numeric/random/chi_squared_distribution/chi_squared_distribution\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/chi_squared_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/chi_squared_distribution/min\n \n (T... args)\n \n \n T\n n\n cpp/numeric/random/chi_squared_distribution/n\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/chi_squared_distribution/operator()\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/chi_squared_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/chi_squared_distribution/reset\n \n (T... args)\n \n \n \n std::chrono\n \n std::chrono::duration\n \n T\n duration_cast\n cpp/chrono/duration/duration_cast\n \n (T... args)\n \n std::chrono::duration_values\n std::chrono::high_resolution_clock\n std::chrono::hours\n std::chrono::microseconds\n std::chrono::milliseconds\n std::chrono::minutes\n std::chrono::nanoseconds\n std::chrono::seconds\n std::chrono::steady_clock\n std::chrono::system_clock\n std::chrono::time_point\n \n T\n time_point_cast\n cpp/chrono/time_point/time_point_cast\n \n (T... args)\n \n std::chrono::treat_as_floating_point\n \n \n std::chrono::duration\n cpp/chrono/duration\n \n T\n count\n cpp/chrono/duration/count\n \n (T... args)\n \n \n T\n duration\n cpp/chrono/duration/duration\n \n (T... args)\n \n \n T\n max\n cpp/chrono/duration/max\n \n (T... args)\n \n \n T\n min\n cpp/chrono/duration/min\n \n (T... args)\n \n \n T\n operator%=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator*=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator+\n cpp/chrono/duration/operator_arith\n \n (T... args)\n \n \n T\n operator++\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator+=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator-\n cpp/chrono/duration/operator_arith\n \n (T... args)\n \n \n T\n operator--\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator-=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator/=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator=\n cpp/chrono/duration/operator=\n \n (T... args)\n \n \n T\n zero\n cpp/chrono/duration/zero\n \n (T... args)\n \n \n \n std::chrono::duration_values\n cpp/chrono/duration_values\n \n T\n max\n cpp/chrono/duration_values/max\n \n (T... args)\n \n \n T\n min\n cpp/chrono/duration_values/min\n \n (T... args)\n \n \n T\n zero\n cpp/chrono/duration_values/zero\n \n (T... args)\n \n \n \n std::chrono::high_resolution_clock\n cpp/chrono/high_resolution_clock\n \n T\n now\n cpp/chrono/high_resolution_clock/now\n \n (T... args)\n \n \n \n std::chrono::hours\n cpp/chrono/duration\n \n T\n count\n cpp/chrono/duration/count\n \n (T... args)\n \n \n T\n hours\n cpp/chrono/duration/duration\n \n (T... args)\n \n \n T\n max\n cpp/chrono/duration/max\n \n (T... args)\n \n \n T\n min\n cpp/chrono/duration/min\n \n (T... args)\n \n \n T\n operator%=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator*=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator+\n cpp/chrono/duration/operator_arith\n \n (T... args)\n \n \n T\n operator++\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator+=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator-\n cpp/chrono/duration/operator_arith\n \n (T... args)\n \n \n T\n operator--\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator-=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator/=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator=\n cpp/chrono/duration/operator=\n \n (T... args)\n \n \n T\n zero\n cpp/chrono/duration/zero\n \n (T... args)\n \n \n \n std::chrono::microseconds\n cpp/chrono/duration\n \n T\n count\n cpp/chrono/duration/count\n \n (T... args)\n \n \n T\n max\n cpp/chrono/duration/max\n \n (T... args)\n \n \n T\n microseconds\n cpp/chrono/duration/duration\n \n (T... args)\n \n \n T\n min\n cpp/chrono/duration/min\n \n (T... args)\n \n \n T\n operator%=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator*=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator+\n cpp/chrono/duration/operator_arith\n \n (T... args)\n \n \n T\n operator++\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator+=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator-\n cpp/chrono/duration/operator_arith\n \n (T... args)\n \n \n T\n operator--\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator-=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator/=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator=\n cpp/chrono/duration/operator=\n \n (T... args)\n \n \n T\n zero\n cpp/chrono/duration/zero\n \n (T... args)\n \n \n \n std::chrono::milliseconds\n cpp/chrono/duration\n \n T\n count\n cpp/chrono/duration/count\n \n (T... args)\n \n \n T\n max\n cpp/chrono/duration/max\n \n (T... args)\n \n \n T\n milliseconds\n cpp/chrono/duration/duration\n \n (T... args)\n \n \n T\n min\n cpp/chrono/duration/min\n \n (T... args)\n \n \n T\n operator%=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator*=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator+\n cpp/chrono/duration/operator_arith\n \n (T... args)\n \n \n T\n operator++\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator+=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator-\n cpp/chrono/duration/operator_arith\n \n (T... args)\n \n \n T\n operator--\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator-=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator/=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator=\n cpp/chrono/duration/operator=\n \n (T... args)\n \n \n T\n zero\n cpp/chrono/duration/zero\n \n (T... args)\n \n \n \n std::chrono::minutes\n cpp/chrono/duration\n \n T\n count\n cpp/chrono/duration/count\n \n (T... args)\n \n \n T\n max\n cpp/chrono/duration/max\n \n (T... args)\n \n \n T\n min\n cpp/chrono/duration/min\n \n (T... args)\n \n \n T\n minutes\n cpp/chrono/duration/duration\n \n (T... args)\n \n \n T\n operator%=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator*=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator+\n cpp/chrono/duration/operator_arith\n \n (T... args)\n \n \n T\n operator++\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator+=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator-\n cpp/chrono/duration/operator_arith\n \n (T... args)\n \n \n T\n operator--\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator-=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator/=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator=\n cpp/chrono/duration/operator=\n \n (T... args)\n \n \n T\n zero\n cpp/chrono/duration/zero\n \n (T... args)\n \n \n \n std::chrono::nanoseconds\n cpp/chrono/duration\n \n T\n count\n cpp/chrono/duration/count\n \n (T... args)\n \n \n T\n max\n cpp/chrono/duration/max\n \n (T... args)\n \n \n T\n min\n cpp/chrono/duration/min\n \n (T... args)\n \n \n T\n nanoseconds\n cpp/chrono/duration/duration\n \n (T... args)\n \n \n T\n operator%=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator*=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator+\n cpp/chrono/duration/operator_arith\n \n (T... args)\n \n \n T\n operator++\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator+=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator-\n cpp/chrono/duration/operator_arith\n \n (T... args)\n \n \n T\n operator--\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator-=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator/=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator=\n cpp/chrono/duration/operator=\n \n (T... args)\n \n \n T\n zero\n cpp/chrono/duration/zero\n \n (T... args)\n \n \n \n std::chrono::seconds\n cpp/chrono/duration\n \n T\n count\n cpp/chrono/duration/count\n \n (T... args)\n \n \n T\n max\n cpp/chrono/duration/max\n \n (T... args)\n \n \n T\n min\n cpp/chrono/duration/min\n \n (T... args)\n \n \n T\n operator%=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator*=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator+\n cpp/chrono/duration/operator_arith\n \n (T... args)\n \n \n T\n operator++\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator+=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator-\n cpp/chrono/duration/operator_arith\n \n (T... args)\n \n \n T\n operator--\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator--(int)\n cpp/chrono/duration/operator_arith2\n \n (T... args)\n \n \n T\n operator-=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator/=\n cpp/chrono/duration/operator_arith3\n \n (T... args)\n \n \n T\n operator=\n cpp/chrono/duration/operator=\n \n (T... args)\n \n \n T\n seconds\n cpp/chrono/duration/duration\n \n (T... args)\n \n \n T\n zero\n cpp/chrono/duration/zero\n \n (T... args)\n \n \n \n std::chrono::steady_clock\n cpp/chrono/steady_clock\n \n T\n now\n cpp/chrono/steady_clock/now\n \n (T... args)\n \n \n \n std::chrono::system_clock\n cpp/chrono/system_clock\n \n T\n from_time_t\n cpp/chrono/system_clock/from_time_t\n \n (T... args)\n \n \n T\n now\n cpp/chrono/system_clock/now\n \n (T... args)\n \n \n T\n to_time_t\n cpp/chrono/system_clock/to_time_t\n \n (T... args)\n \n \n \n std::chrono::time_point\n cpp/chrono/time_point\n \n T\n max\n cpp/chrono/time_point/max\n \n (T... args)\n \n \n T\n min\n cpp/chrono/time_point/min\n \n (T... args)\n \n \n T\n operator+\n cpp/chrono/time_point/operator_arith\n \n (T... args)\n \n \n T\n operator-\n cpp/chrono/time_point/operator_arith\n \n (T... args)\n \n \n T\n time_point\n cpp/chrono/time_point/time_point\n \n (T... args)\n \n \n T\n time_since_epoch\n cpp/chrono/time_point/time_since_epoch\n \n (T... args)\n \n \n \n std::chrono::treat_as_floating_point\n cpp/chrono/treat_as_floating_point\n \n \n std::cin\n cpp/io/cin\n \n \n std::clock_t\n cpp/chrono/c/clock_t\n \n \n std::clog\n cpp/io/clog\n \n \n std::cmatch\n cpp/regex/match_results\n \n T\n begin\n cpp/regex/match_results/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/regex/match_results/begin\n \n (T... args)\n \n \n T\n cend\n cpp/regex/match_results/end\n \n (T... args)\n \n \n T\n cmatch\n cpp/regex/match_results/match_results\n \n (T... args)\n \n \n T\n empty\n cpp/regex/match_results/empty\n \n (T... args)\n \n \n T\n end\n cpp/regex/match_results/end\n \n (T... args)\n \n \n T\n format\n cpp/regex/match_results/format\n \n (T... args)\n \n \n T\n get_allocator\n cpp/regex/match_results/get_allocator\n \n (T... args)\n \n \n T\n length\n cpp/regex/match_results/length\n \n (T... args)\n \n \n T\n max_size\n cpp/regex/match_results/max_size\n \n (T... args)\n \n \n T\n operator[]\n cpp/regex/match_results/operator_at\n \n (T... args)\n \n \n T\n position\n cpp/regex/match_results/position\n \n (T... args)\n \n \n T\n prefix\n cpp/regex/match_results/prefix\n \n (T... args)\n \n \n T\n ready\n cpp/regex/match_results/ready\n \n (T... args)\n \n \n T\n size\n cpp/regex/match_results/size\n \n (T... args)\n \n \n T\n str\n cpp/regex/match_results/str\n \n (T... args)\n \n \n T\n suffix\n cpp/regex/match_results/suffix\n \n (T... args)\n \n \n T\n swap\n cpp/regex/match_results/swap\n \n (T... args)\n \n \n T\n ~cmatch\n cpp/regex/match_results/~match_results\n \n (T... args)\n \n \n \n std::codecvt\n cpp/locale/codecvt\n \n T\n always_noconv\n cpp/locale/codecvt/always_noconv\n \n (T... args)\n \n \n T\n codecvt\n cpp/locale/codecvt/codecvt\n \n (T... args)\n \n \n T\n do_always_noconv\n cpp/locale/codecvt/always_noconv\n \n (T... args)\n \n \n T\n do_encoding\n cpp/locale/codecvt/encoding\n \n (T... args)\n \n \n T\n do_in\n cpp/locale/codecvt/in\n \n (T... args)\n \n \n T\n do_length\n cpp/locale/codecvt/length\n \n (T... args)\n \n \n T\n do_max_length\n cpp/locale/codecvt/max_length\n \n (T... args)\n \n \n T\n do_out\n cpp/locale/codecvt/out\n \n (T... args)\n \n \n T\n do_unshift\n cpp/locale/codecvt/unshift\n \n (T... args)\n \n \n T\n encoding\n cpp/locale/codecvt/encoding\n \n (T... args)\n \n std::codecvt::extern_type\n \n T\n in\n cpp/locale/codecvt/in\n \n (T... args)\n \n std::codecvt::intern_type\n \n T\n length\n cpp/locale/codecvt/length\n \n (T... args)\n \n \n T\n max_length\n cpp/locale/codecvt/max_length\n \n (T... args)\n \n \n T\n out\n cpp/locale/codecvt/out\n \n (T... args)\n \n std::codecvt::state_type\n \n T\n unshift\n cpp/locale/codecvt/unshift\n \n (T... args)\n \n \n T\n ~codecvt\n cpp/locale/codecvt/~codecvt\n \n (T... args)\n \n \n \n std::codecvt::extern_type\n cpp/locale/codecvt\n \n \n std::codecvt::intern_type\n cpp/locale/codecvt\n \n \n std::codecvt::state_type\n cpp/locale/codecvt\n \n \n std::codecvt_base\n cpp/locale/codecvt_base\n \n \n std::codecvt_byname\n cpp/locale/codecvt_byname\n \n T\n always_noconv\n cpp/locale/codecvt/always_noconv\n \n (T... args)\n \n \n T\n codecvt_byname\n cpp/locale/codecvt_byname\n \n (T... args)\n \n \n T\n do_always_noconv\n cpp/locale/codecvt/always_noconv\n \n (T... args)\n \n \n T\n do_encoding\n cpp/locale/codecvt/encoding\n \n (T... args)\n \n \n T\n do_in\n cpp/locale/codecvt/in\n \n (T... args)\n \n \n T\n do_length\n cpp/locale/codecvt/length\n \n (T... args)\n \n \n T\n do_max_length\n cpp/locale/codecvt/max_length\n \n (T... args)\n \n \n T\n do_out\n cpp/locale/codecvt/out\n \n (T... args)\n \n \n T\n do_unshift\n cpp/locale/codecvt/unshift\n \n (T... args)\n \n \n T\n encoding\n cpp/locale/codecvt/encoding\n \n (T... args)\n \n std::codecvt_byname::extern_type\n \n T\n in\n cpp/locale/codecvt/in\n \n (T... args)\n \n std::codecvt_byname::intern_type\n \n T\n length\n cpp/locale/codecvt/length\n \n (T... args)\n \n \n T\n max_length\n cpp/locale/codecvt/max_length\n \n (T... args)\n \n \n T\n out\n cpp/locale/codecvt/out\n \n (T... args)\n \n std::codecvt_byname::state_type\n \n T\n unshift\n cpp/locale/codecvt/unshift\n \n (T... args)\n \n \n T\n ~codecvt_byname\n cpp/locale/codecvt_byname\n \n (T... args)\n \n \n \n std::codecvt_byname::extern_type\n cpp/locale/codecvt\n \n \n std::codecvt_byname::intern_type\n cpp/locale/codecvt\n \n \n std::codecvt_byname::state_type\n cpp/locale/codecvt\n \n \n std::codecvt_utf16\n cpp/locale/codecvt_utf16\n \n T\n always_noconv\n cpp/locale/codecvt/always_noconv\n \n (T... args)\n \n \n T\n do_always_noconv\n cpp/locale/codecvt/always_noconv\n \n (T... args)\n \n \n T\n do_encoding\n cpp/locale/codecvt/encoding\n \n (T... args)\n \n \n T\n do_in\n cpp/locale/codecvt/in\n \n (T... args)\n \n \n T\n do_length\n cpp/locale/codecvt/length\n \n (T... args)\n \n \n T\n do_max_length\n cpp/locale/codecvt/max_length\n \n (T... args)\n \n \n T\n do_out\n cpp/locale/codecvt/out\n \n (T... args)\n \n \n T\n do_unshift\n cpp/locale/codecvt/unshift\n \n (T... args)\n \n \n T\n encoding\n cpp/locale/codecvt/encoding\n \n (T... args)\n \n std::codecvt_utf16::extern_type\n \n T\n in\n cpp/locale/codecvt/in\n \n (T... args)\n \n std::codecvt_utf16::intern_type\n \n T\n length\n cpp/locale/codecvt/length\n \n (T... args)\n \n \n T\n max_length\n cpp/locale/codecvt/max_length\n \n (T... args)\n \n \n T\n out\n cpp/locale/codecvt/out\n \n (T... args)\n \n std::codecvt_utf16::state_type\n \n T\n unshift\n cpp/locale/codecvt/unshift\n \n (T... args)\n \n \n \n std::codecvt_utf16::extern_type\n cpp/locale/codecvt\n \n \n std::codecvt_utf16::intern_type\n cpp/locale/codecvt\n \n \n std::codecvt_utf16::state_type\n cpp/locale/codecvt\n \n \n std::codecvt_utf8\n cpp/locale/codecvt_utf8\n \n T\n always_noconv\n cpp/locale/codecvt/always_noconv\n \n (T... args)\n \n \n T\n do_always_noconv\n cpp/locale/codecvt/always_noconv\n \n (T... args)\n \n \n T\n do_encoding\n cpp/locale/codecvt/encoding\n \n (T... args)\n \n \n T\n do_in\n cpp/locale/codecvt/in\n \n (T... args)\n \n \n T\n do_length\n cpp/locale/codecvt/length\n \n (T... args)\n \n \n T\n do_max_length\n cpp/locale/codecvt/max_length\n \n (T... args)\n \n \n T\n do_out\n cpp/locale/codecvt/out\n \n (T... args)\n \n \n T\n do_unshift\n cpp/locale/codecvt/unshift\n \n (T... args)\n \n \n T\n encoding\n cpp/locale/codecvt/encoding\n \n (T... args)\n \n std::codecvt_utf8::extern_type\n \n T\n in\n cpp/locale/codecvt/in\n \n (T... args)\n \n std::codecvt_utf8::intern_type\n \n T\n length\n cpp/locale/codecvt/length\n \n (T... args)\n \n \n T\n max_length\n cpp/locale/codecvt/max_length\n \n (T... args)\n \n \n T\n out\n cpp/locale/codecvt/out\n \n (T... args)\n \n std::codecvt_utf8::state_type\n \n T\n unshift\n cpp/locale/codecvt/unshift\n \n (T... args)\n \n \n \n std::codecvt_utf8::extern_type\n cpp/locale/codecvt\n \n \n std::codecvt_utf8::intern_type\n cpp/locale/codecvt\n \n \n std::codecvt_utf8::state_type\n cpp/locale/codecvt\n \n \n std::codecvt_utf8_utf16\n cpp/locale/codecvt_utf8_utf16\n \n T\n always_noconv\n cpp/locale/codecvt/always_noconv\n \n (T... args)\n \n \n T\n do_always_noconv\n cpp/locale/codecvt/always_noconv\n \n (T... args)\n \n \n T\n do_encoding\n cpp/locale/codecvt/encoding\n \n (T... args)\n \n \n T\n do_in\n cpp/locale/codecvt/in\n \n (T... args)\n \n \n T\n do_length\n cpp/locale/codecvt/length\n \n (T... args)\n \n \n T\n do_max_length\n cpp/locale/codecvt/max_length\n \n (T... args)\n \n \n T\n do_out\n cpp/locale/codecvt/out\n \n (T... args)\n \n \n T\n do_unshift\n cpp/locale/codecvt/unshift\n \n (T... args)\n \n \n T\n encoding\n cpp/locale/codecvt/encoding\n \n (T... args)\n \n std::codecvt_utf8_utf16::extern_type\n \n T\n in\n cpp/locale/codecvt/in\n \n (T... args)\n \n std::codecvt_utf8_utf16::intern_type\n \n T\n length\n cpp/locale/codecvt/length\n \n (T... args)\n \n \n T\n max_length\n cpp/locale/codecvt/max_length\n \n (T... args)\n \n \n T\n out\n cpp/locale/codecvt/out\n \n (T... args)\n \n std::codecvt_utf8_utf16::state_type\n \n T\n unshift\n cpp/locale/codecvt/unshift\n \n (T... args)\n \n \n \n std::codecvt_utf8_utf16::extern_type\n cpp/locale/codecvt\n \n \n std::codecvt_utf8_utf16::intern_type\n cpp/locale/codecvt\n \n \n std::codecvt_utf8_utf16::state_type\n cpp/locale/codecvt\n \n \n std::collate\n cpp/locale/collate\n std::collate::char_type\n \n T\n collate\n cpp/locale/collate/collate\n \n (T... args)\n \n \n T\n compare\n cpp/locale/collate/compare\n \n (T... args)\n \n \n T\n do_compare\n cpp/locale/collate/compare\n \n (T... args)\n \n \n T\n do_hash\n cpp/locale/collate/hash\n \n (T... args)\n \n \n T\n do_transform\n cpp/locale/collate/transform\n \n (T... args)\n \n \n T\n hash\n cpp/locale/collate/hash\n \n (T... args)\n \n std::collate::string_type\n \n T\n transform\n cpp/locale/collate/transform\n \n (T... args)\n \n \n T\n ~collate\n cpp/locale/collate/~collate\n \n (T... args)\n \n \n \n std::collate::char_type\n cpp/locale/collate\n \n \n std::collate::string_type\n cpp/locale/collate\n \n \n std::collate_byname\n cpp/locale/collate_byname\n std::collate_byname::char_type\n \n T\n collate_byname\n cpp/locale/collate_byname\n \n (T... args)\n \n \n T\n compare\n cpp/locale/collate/compare\n \n (T... args)\n \n \n T\n do_compare\n cpp/locale/collate/compare\n \n (T... args)\n \n \n T\n do_hash\n cpp/locale/collate/hash\n \n (T... args)\n \n \n T\n do_transform\n cpp/locale/collate/transform\n \n (T... args)\n \n \n T\n hash\n cpp/locale/collate/hash\n \n (T... args)\n \n std::collate_byname::string_type\n \n T\n transform\n cpp/locale/collate/transform\n \n (T... args)\n \n \n T\n ~collate_byname\n cpp/locale/collate_byname\n \n (T... args)\n \n \n \n std::collate_byname::char_type\n cpp/locale/collate\n \n \n std::collate_byname::string_type\n cpp/locale/collate\n \n \n std::common_type\n cpp/types/common_type\n \n \n std::common_type_t\n cpp/types/common_type\n \n \n std::complex\n cpp/numeric/complex\n \n T\n complex\n cpp/numeric/complex/complex\n \n (T... args)\n \n \n T\n imag\n cpp/numeric/complex/imag\n \n (T... args)\n \n \n T\n operator*=\n cpp/numeric/complex/operator_arith\n \n (T... args)\n \n \n T\n operator+=\n cpp/numeric/complex/operator_arith\n \n (T... args)\n \n \n T\n operator-=\n cpp/numeric/complex/operator_arith\n \n (T... args)\n \n \n T\n operator/=\n cpp/numeric/complex/operator_arith\n \n (T... args)\n \n \n T\n operator=\n cpp/numeric/complex/operator=\n \n (T... args)\n \n \n T\n real\n cpp/numeric/complex/real\n \n (T... args)\n \n \n \n std::condition_variable\n cpp/thread/condition_variable\n \n T\n condition_variable\n cpp/thread/condition_variable/condition_variable\n \n (T... args)\n \n \n T\n native_handle\n cpp/thread/condition_variable/native_handle\n \n (T... args)\n \n \n T\n notify_all\n cpp/thread/condition_variable/notify_all\n \n (T... args)\n \n \n T\n notify_one\n cpp/thread/condition_variable/notify_one\n \n (T... args)\n \n \n T\n wait\n cpp/thread/condition_variable/wait\n \n (T... args)\n \n \n T\n wait_for\n cpp/thread/condition_variable/wait_for\n \n (T... args)\n \n \n T\n wait_until\n cpp/thread/condition_variable/wait_until\n \n (T... args)\n \n \n T\n ~condition_variable\n cpp/thread/condition_variable/~condition_variable\n \n (T... args)\n \n \n \n std::condition_variable_any\n cpp/thread/condition_variable_any\n \n T\n condition_variable_any\n cpp/thread/condition_variable_any/condition_variable_any\n \n (T... args)\n \n \n T\n native_handle\n cpp/thread/condition_variable_any/native_handle\n \n (T... args)\n \n \n T\n notify_all\n cpp/thread/condition_variable_any/notify_all\n \n (T... args)\n \n \n T\n notify_one\n cpp/thread/condition_variable_any/notify_one\n \n (T... args)\n \n \n T\n wait\n cpp/thread/condition_variable_any/wait\n \n (T... args)\n \n \n T\n wait_for\n cpp/thread/condition_variable_any/wait_for\n \n (T... args)\n \n \n T\n wait_until\n cpp/thread/condition_variable_any/wait_until\n \n (T... args)\n \n \n T\n ~condition_variable_any\n cpp/thread/condition_variable_any/~condition_variable_any\n \n (T... args)\n \n \n \n std::conditional\n cpp/types/conditional\n \n \n std::conditional_t\n cpp/types/conditional\n \n \n std::conjunction\n cpp/types/conjunction\n \n \n std::cout\n cpp/io/cout\n \n \n std::cregex_iterator\n cpp/regex/regex_iterator\n \n T\n cregex_iterator\n cpp/regex/regex_iterator/regex_iterator\n \n (T... args)\n \n \n T\n operator!=\n cpp/regex/regex_iterator/operator_cmp\n \n (T... args)\n \n \n T\n operator*\n cpp/regex/regex_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/regex/regex_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/regex/regex_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator->\n cpp/regex/regex_iterator/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/regex/regex_iterator/operator=\n \n (T... args)\n \n \n T\n operator==\n cpp/regex/regex_iterator/operator_cmp\n \n (T... args)\n \n \n \n std::cregex_token_iterator\n cpp/regex/regex_token_iterator\n \n T\n cregex_token_iterator\n cpp/regex/regex_token_iterator/regex_token_iterator\n \n (T... args)\n \n \n T\n operator!=\n cpp/regex/regex_token_iterator/operator_cmp\n \n (T... args)\n \n \n T\n operator*\n cpp/regex/regex_token_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/regex/regex_token_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/regex/regex_token_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator->\n cpp/regex/regex_token_iterator/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/regex/regex_token_iterator/operator=\n \n (T... args)\n \n \n T\n operator==\n cpp/regex/regex_token_iterator/operator_cmp\n \n (T... args)\n \n \n \n std::csub_match\n cpp/regex/sub_match\n \n T\n compare\n cpp/regex/sub_match/compare\n \n (T... args)\n \n \n T\n csub_match\n cpp/regex/sub_match/sub_match\n \n (T... args)\n \n \n T\n length\n cpp/regex/sub_match/length\n \n (T... args)\n \n \n T\n operator string_type\n cpp/regex/sub_match/str\n \n (T... args)\n \n \n T\n str\n cpp/regex/sub_match/str\n \n (T... args)\n \n \n \n std::ctype\n cpp/locale/ctype\n \n T\n ctype\n cpp/locale/ctype/ctype\n \n (T... args)\n \n \n T\n do_is\n cpp/locale/ctype/is\n \n (T... args)\n \n \n T\n do_narrow\n cpp/locale/ctype/narrow\n \n (T... args)\n \n \n T\n do_scan_is\n cpp/locale/ctype/scan_is\n \n (T... args)\n \n \n T\n do_tolower\n cpp/locale/ctype/tolower\n \n (T... args)\n \n \n T\n do_toupper\n cpp/locale/ctype/toupper\n \n (T... args)\n \n \n T\n do_widen\n cpp/locale/ctype/widen\n \n (T... args)\n \n \n T\n is\n cpp/locale/ctype/is\n \n (T... args)\n \n std::ctype::mask\n \n T\n narrow\n cpp/locale/ctype/narrow\n \n (T... args)\n \n \n T\n scan_is\n cpp/locale/ctype/scan_is\n \n (T... args)\n \n \n T\n tolower\n cpp/locale/ctype/tolower\n \n (T... args)\n \n \n T\n toupper\n cpp/locale/ctype/toupper\n \n (T... args)\n \n \n T\n widen\n cpp/locale/ctype/widen\n \n (T... args)\n \n \n T\n ~ctype\n cpp/locale/ctype/~ctype\n \n (T... args)\n \n \n \n std::ctype::mask\n cpp/locale/ctype_base\n \n \n std::ctype_base\n cpp/locale/ctype_base\n std::ctype_base::mask\n \n \n std::ctype_base::mask\n cpp/locale/ctype_base\n \n \n std::ctype_byname\n cpp/locale/ctype_byname\n \n T\n ctype_byname\n cpp/locale/ctype_byname\n \n (T... args)\n \n \n T\n do_is\n cpp/locale/ctype/is\n \n (T... args)\n \n \n T\n do_narrow\n cpp/locale/ctype/narrow\n \n (T... args)\n \n \n T\n do_scan_is\n cpp/locale/ctype/scan_is\n \n (T... args)\n \n \n T\n do_tolower\n cpp/locale/ctype/tolower\n \n (T... args)\n \n \n T\n do_toupper\n cpp/locale/ctype/toupper\n \n (T... args)\n \n \n T\n do_widen\n cpp/locale/ctype/widen\n \n (T... args)\n \n \n T\n is\n cpp/locale/ctype/is\n \n (T... args)\n \n std::ctype_byname::mask\n \n T\n narrow\n cpp/locale/ctype/narrow\n \n (T... args)\n \n \n T\n scan_is\n cpp/locale/ctype/scan_is\n \n (T... args)\n \n \n T\n tolower\n cpp/locale/ctype/tolower\n \n (T... args)\n \n \n T\n toupper\n cpp/locale/ctype/toupper\n \n (T... args)\n \n \n T\n widen\n cpp/locale/ctype/widen\n \n (T... args)\n \n \n T\n ~ctype_byname\n cpp/locale/ctype_byname\n \n (T... args)\n \n \n \n std::ctype_byname::mask\n cpp/locale/ctype_base\n \n \n std::deca\n cpp/numeric/ratio/ratio\n \n \n std::decay\n cpp/types/decay\n \n \n std::decay_t\n cpp/types/decay\n \n \n std::deci\n cpp/numeric/ratio/ratio\n \n \n std::default_delete\n cpp/memory/default_delete\n \n T\n default_delete\n cpp/memory/default_delete\n \n (T... args)\n \n \n T\n operator()\n cpp/memory/default_delete\n \n (T... args)\n \n \n \n std::default_random_engine\n cpp/numeric/random\n \n \n std::default_searcher\n cpp/utility/functional/default_searcher\n \n T\n default_searcher\n cpp/utility/functional/default_searcher\n \n (T... args)\n \n \n \n std::defer_lock_t\n cpp/thread/lock_tag_t\n \n \n std::deque\n cpp/container/deque\n \n T\n assign\n cpp/container/deque/assign\n \n (T... args)\n \n \n T\n at\n cpp/container/deque/at\n \n (T... args)\n \n \n T\n back\n cpp/container/deque/back\n \n (T... args)\n \n \n T\n begin\n cpp/container/deque/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/deque/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/deque/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/deque/clear\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/deque/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/deque/rend\n \n (T... args)\n \n \n T\n deque\n cpp/container/deque/deque\n \n (T... args)\n \n \n T\n emplace\n cpp/container/deque/emplace\n \n (T... args)\n \n \n T\n emplace_back\n cpp/container/deque/emplace_back\n \n (T... args)\n \n \n T\n emplace_front\n cpp/container/deque/emplace_front\n \n (T... args)\n \n \n T\n empty\n cpp/container/deque/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/deque/end\n \n (T... args)\n \n \n T\n erase\n cpp/container/deque/erase\n \n (T... args)\n \n \n T\n front\n cpp/container/deque/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/deque/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/container/deque/insert\n \n (T... args)\n \n \n T\n max_size\n cpp/container/deque/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/container/deque/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/container/deque/operator_at\n \n (T... args)\n \n \n T\n pop_back\n cpp/container/deque/pop_back\n \n (T... args)\n \n \n T\n pop_front\n cpp/container/deque/pop_front\n \n (T... args)\n \n \n T\n push_back\n cpp/container/deque/push_back\n \n (T... args)\n \n \n T\n push_front\n cpp/container/deque/push_front\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/deque/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/container/deque/rend\n \n (T... args)\n \n \n T\n resize\n cpp/container/deque/resize\n \n (T... args)\n \n \n T\n shrink_to_fit\n cpp/container/deque/shrink_to_fit\n \n (T... args)\n \n \n T\n size\n cpp/container/deque/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/deque/swap\n \n (T... args)\n \n \n T\n ~deque\n cpp/container/deque/~deque\n \n (T... args)\n \n \n \n std::discard_block_engine\n cpp/numeric/random/discard_block_engine\n \n T\n base\n cpp/numeric/random/discard_block_engine/base\n \n (T... args)\n \n \n T\n discard\n cpp/numeric/random/discard_block_engine/discard\n \n (T... args)\n \n \n T\n discard_block_engine\n cpp/numeric/random/discard_block_engine/discard_block_engine\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/discard_block_engine/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/discard_block_engine/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/discard_block_engine/operator()\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/discard_block_engine/seed\n \n (T... args)\n \n \n \n std::discrete_distribution\n cpp/numeric/random/discrete_distribution\n \n T\n discrete_distribution\n cpp/numeric/random/discrete_distribution/discrete_distribution\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/discrete_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/discrete_distribution/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/discrete_distribution/operator()\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/discrete_distribution/param\n \n (T... args)\n \n \n T\n probabilities\n cpp/numeric/random/discrete_distribution/probabilities\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/discrete_distribution/reset\n \n (T... args)\n \n \n \n std::disjunction\n cpp/types/disjunction\n \n \n std::div_t\n cpp/numeric/math/div\n \n T\n quot\n cpp/numeric/math/div\n \n \n \n \n T\n rem\n cpp/numeric/math/div\n \n \n \n \n \n std::divides\n cpp/utility/functional/divides\n \n T\n operator()\n cpp/utility/functional/divides\n \n (T... args)\n \n \n \n std::domain_error\n cpp/error/domain_error\n \n T\n domain_error\n cpp/error/domain_error\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::enable_if\n cpp/types/enable_if\n \n \n std::enable_if_t\n cpp/types/enable_if\n \n \n std::enable_shared_from_this\n cpp/memory/enable_shared_from_this\n \n T\n enable_shared_from_this\n cpp/memory/enable_shared_from_this/enable_shared_from_this\n \n (T... args)\n \n \n T\n operator=\n cpp/memory/enable_shared_from_this/operator=\n \n (T... args)\n \n \n T\n shared_from_this\n cpp/memory/enable_shared_from_this/shared_from_this\n \n (T... args)\n \n \n T\n weak_from_this\n cpp/memory/enable_shared_from_this/weak_from_this\n \n (T... args)\n \n \n T\n ~enable_shared_from_this\n cpp/memory/enable_shared_from_this/~enable_shared_from_this\n \n (T... args)\n \n \n \n std::equal_to\n cpp/utility/functional/equal_to\n \n T\n operator()\n cpp/utility/functional/equal_to\n \n (T... args)\n \n \n \n std::errc\n cpp/error/errc\n \n \n std::error_category\n cpp/error/error_category\n \n T\n default_error_condition\n cpp/error/error_category/default_error_condition\n \n (T... args)\n \n \n T\n equivalent\n cpp/error/error_category/equivalent\n \n (T... args)\n \n \n T\n error_category\n cpp/error/error_category/error_category\n \n (T... args)\n \n \n T\n message\n cpp/error/error_category/message\n \n (T... args)\n \n \n T\n name\n cpp/error/error_category/name\n \n (T... args)\n \n \n T\n operator!=\n cpp/error/error_category/operator_cmp\n \n (T... args)\n \n \n T\n operator<\n cpp/error/error_category/operator_cmp\n \n (T... args)\n \n \n T\n operator==\n cpp/error/error_category/operator_cmp\n \n (T... args)\n \n \n T\n ~error_category\n cpp/error/error_category/~error_category\n \n (T... args)\n \n \n \n std::error_code\n cpp/error/error_code\n \n T\n assign\n cpp/error/error_code/assign\n \n (T... args)\n \n \n T\n category\n cpp/error/error_code/category\n \n (T... args)\n \n \n T\n clear\n cpp/error/error_code/clear\n \n (T... args)\n \n \n T\n default_error_condition\n cpp/error/error_code/default_error_condition\n \n (T... args)\n \n \n T\n error_code\n cpp/error/error_code/error_code\n \n (T... args)\n \n \n T\n message\n cpp/error/error_code/message\n \n (T... args)\n \n \n T\n operator bool\n cpp/error/error_code/operator_bool\n \n (T... args)\n \n \n T\n operator=\n cpp/error/error_code/operator=\n \n (T... args)\n \n \n T\n value\n cpp/error/error_code/value\n \n (T... args)\n \n \n \n std::error_condition\n cpp/error/error_condition\n \n T\n assign\n cpp/error/error_condition/assign\n \n (T... args)\n \n \n T\n category\n cpp/error/error_condition/category\n \n (T... args)\n \n \n T\n clear\n cpp/error/error_condition/clear\n \n (T... args)\n \n \n T\n error_condition\n cpp/error/error_condition/error_condition\n \n (T... args)\n \n \n T\n message\n cpp/error/error_condition/message\n \n (T... args)\n \n \n T\n operator bool\n cpp/error/error_condition/operator_bool\n \n (T... args)\n \n \n T\n operator=\n cpp/error/error_condition/operator=\n \n (T... args)\n \n \n T\n value\n cpp/error/error_condition/value\n \n (T... args)\n \n \n \n std::exa\n cpp/numeric/ratio/ratio\n \n \n std::exception\n cpp/error/exception\n \n T\n exception\n cpp/error/exception/exception\n \n (T... args)\n \n \n T\n operator=\n cpp/error/exception/operator=\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n T\n ~exception\n cpp/error/exception/~exception\n \n (T... args)\n \n \n \n std::exception_ptr\n cpp/error/exception_ptr\n \n \n std::execution\n \n std::execution::parallel_policy\n std::execution::parallel_unsequenced_policy\n std::execution::sequenced_policy\n \n \n std::execution::parallel_policy\n cpp/algorithm/execution_policy_tag_t\n \n \n std::execution::parallel_unsequenced_policy\n cpp/algorithm/execution_policy_tag_t\n \n \n std::execution::sequenced_policy\n cpp/algorithm/execution_policy_tag_t\n \n \n std::experimental\n \n \n T\n alignment_of_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n std::experimental::any\n \n T\n any_cast\n cpp/experimental/any/any_cast\n \n (T... args)\n \n \n T\n apply\n cpp/experimental/apply\n \n (T... args)\n \n std::experimental::bad_optional_access\n std::experimental::basic_string_view\n std::experimental::boyer_moore_horspool_searcher\n std::experimental::boyer_moore_searcher\n std::experimental::default_searcher\n std::experimental::detected_or\n std::experimental::detected_or_t\n std::experimental::erased_type\n \n T\n extent_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n std::experimental::filesystem\n \n T\n gcd\n cpp/experimental/gcd\n \n (T... args)\n \n \n T\n has_virtual_destructor_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n std::experimental::invocation_type\n \n T\n is_abstract_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_arithmetic_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_array_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_assignable_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_base_of_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_bind_expression_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_class_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_compound_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_const_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_constructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_convertible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_copy_assignable_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_copy_constructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_default_constructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_destructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n std::experimental::is_detected\n std::experimental::is_detected_convertible\n \n T\n is_detected_convertible_v\n cpp/experimental/is_detected\n \n \n \n std::experimental::is_detected_exact\n \n T\n is_detected_exact_v\n cpp/experimental/is_detected\n \n \n \n \n T\n is_detected_v\n cpp/experimental/is_detected\n \n \n \n \n T\n is_empty_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_enum_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_error_code_enum_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_error_condition_enum_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_final_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_floating_point_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_function_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_fundamental_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_integral_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_literal_type_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_lvalue_reference_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_member_function_pointer_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_member_object_pointer_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_member_pointer_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_move_assignable_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_move_constructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_nothrow_assignable_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_nothrow_constructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_nothrow_copy_assignable_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_nothrow_copy_constructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_nothrow_default_constructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_nothrow_destructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_nothrow_move_assignable_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_nothrow_move_constructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_null_pointer_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_object_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_placeholder_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_pod_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_pointer_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_polymorphic_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_reference_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_rvalue_reference_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_same_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_scalar_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_signed_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_standard_layout_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_trivial_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_trivially_assignable_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_trivially_constructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_trivially_copy_assignable_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_trivially_copy_constructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_trivially_copyable_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_trivially_default_constructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_trivially_destructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_trivially_move_assignable_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_trivially_move_constructible_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_union_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_unsigned_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_void_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n is_volatile_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n lcm\n cpp/experimental/lcm\n \n (T... args)\n \n \n T\n make_array\n cpp/experimental/make_array\n \n (T... args)\n \n \n T\n make_boyer_moore_horspool_searcher\n cpp/experimental/make_boyer_moore_horspool_searcher\n \n (T... args)\n \n \n T\n make_boyer_moore_searcher\n cpp/experimental/make_boyer_moore_searcher\n \n (T... args)\n \n \n T\n make_default_searcher\n cpp/experimental/make_default_searcher\n \n (T... args)\n \n \n T\n make_optional\n cpp/experimental/optional/make_optional\n \n (T... args)\n \n std::experimental::nonesuch\n \n T\n not_fn\n cpp/experimental/not_fn\n \n (T... args)\n \n std::experimental::observer_ptr\n std::experimental::optional\n std::experimental::ostream_joiner\n std::experimental::pmr\n std::experimental::propagate_const\n \n T\n randint\n cpp/experimental/randint\n \n (T... args)\n \n \n T\n rank_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n ratio_equal_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n ratio_greater_equal_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n ratio_greater_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n ratio_less_equal_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n ratio_less_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n ratio_not_equal_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n std::experimental::raw_invocation_type\n \n T\n reseed\n cpp/experimental/reseed\n \n (T... args)\n \n \n T\n sample\n cpp/experimental/sample\n \n (T... args)\n \n \n T\n search\n cpp/experimental/search\n \n (T... args)\n \n std::experimental::source_location\n std::experimental::string_view\n \n T\n to_array\n cpp/experimental/to_array\n \n (T... args)\n \n \n T\n treat_as_floating_point_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n \n T\n tuple_size_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n std::experimental::u16string_view\n std::experimental::u32string_view\n \n T\n uses_allocator_v\n cpp/experimental/type_trait_variable_templates\n \n \n \n std::experimental::wstring_view\n \n \n std::experimental::any\n cpp/experimental/any\n \n T\n any\n cpp/experimental/any/any\n \n (T... args)\n \n \n T\n clear\n cpp/experimental/any/clear\n \n (T... args)\n \n \n T\n empty\n cpp/experimental/any/empty\n \n (T... args)\n \n \n T\n operator=\n cpp/experimental/any/operator=\n \n (T... args)\n \n \n T\n swap\n cpp/experimental/any/swap\n \n (T... args)\n \n \n T\n type\n cpp/experimental/any/type\n \n (T... args)\n \n \n \n std::experimental::bad_optional_access\n cpp/utility/optional/bad_optional_access\n \n T\n bad_optional_access\n cpp/utility/optional/bad_optional_access\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::experimental::basic_string_view\n cpp/experimental/basic_string_view\n \n T\n at\n cpp/experimental/basic_string_view/at\n \n (T... args)\n \n \n T\n back\n cpp/experimental/basic_string_view/back\n \n (T... args)\n \n \n T\n basic_string_view\n cpp/experimental/basic_string_view/basic_string_view\n \n (T... args)\n \n \n T\n begin\n cpp/experimental/basic_string_view/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/experimental/basic_string_view/begin\n \n (T... args)\n \n \n T\n cend\n cpp/experimental/basic_string_view/end\n \n (T... args)\n \n \n T\n compare\n cpp/experimental/basic_string_view/compare\n \n (T... args)\n \n \n T\n copy\n cpp/experimental/basic_string_view/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/experimental/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/experimental/basic_string_view/rend\n \n (T... args)\n \n \n T\n data\n cpp/experimental/basic_string_view/data\n \n (T... args)\n \n \n T\n empty\n cpp/experimental/basic_string_view/empty\n \n (T... args)\n \n \n T\n end\n cpp/experimental/basic_string_view/end\n \n (T... args)\n \n \n T\n find\n cpp/experimental/basic_string_view/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/experimental/basic_string_view/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/experimental/basic_string_view/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/experimental/basic_string_view/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/experimental/basic_string_view/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/experimental/basic_string_view/front\n \n (T... args)\n \n \n T\n length\n cpp/experimental/basic_string_view/size\n \n (T... args)\n \n \n T\n max_size\n cpp/experimental/basic_string_view/max_size\n \n (T... args)\n \n \n T\n operator basic_string\n cpp/experimental/basic_string_view/to_string\n \n (T... args)\n \n \n T\n operator=\n cpp/experimental/basic_string_view/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/experimental/basic_string_view/operator_at\n \n (T... args)\n \n \n T\n rbegin\n cpp/experimental/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n remove_prefix\n cpp/experimental/basic_string_view/remove_prefix\n \n (T... args)\n \n \n T\n remove_suffix\n cpp/experimental/basic_string_view/remove_suffix\n \n (T... args)\n \n \n T\n rend\n cpp/experimental/basic_string_view/rend\n \n (T... args)\n \n \n T\n rfind\n cpp/experimental/basic_string_view/rfind\n \n (T... args)\n \n \n T\n size\n cpp/experimental/basic_string_view/size\n \n (T... args)\n \n \n T\n substr\n cpp/experimental/basic_string_view/substr\n \n (T... args)\n \n \n T\n swap\n cpp/experimental/basic_string_view/swap\n \n (T... args)\n \n \n T\n to_string\n cpp/experimental/basic_string_view/to_string\n \n (T... args)\n \n \n \n std::experimental::boyer_moore_horspool_searcher\n cpp/experimental/boyer_moore_horspool_searcher\n \n \n std::experimental::boyer_moore_searcher\n cpp/experimental/boyer_moore_searcher\n \n \n std::experimental::default_searcher\n cpp/experimental/default_searcher\n \n \n std::experimental::detected_or\n cpp/experimental/is_detected\n \n \n std::experimental::detected_or_t\n cpp/experimental/is_detected\n \n \n std::experimental::erased_type\n cpp/experimental/erased_type\n \n \n std::experimental::filesystem\n \n \n T\n absolute\n cpp/experimental/fs/absolute\n \n (T... args)\n \n \n T\n canonical\n cpp/experimental/fs/canonical\n \n (T... args)\n \n \n T\n copy\n cpp/experimental/fs/copy\n \n (T... args)\n \n \n T\n copy_file\n cpp/experimental/fs/copy_file\n \n (T... args)\n \n std::experimental::filesystem::copy_options\n \n T\n copy_symlink\n cpp/experimental/fs/copy_symlink\n \n (T... args)\n \n \n T\n create_directories\n cpp/experimental/fs/create_directory\n \n (T... args)\n \n \n T\n create_directory\n cpp/experimental/fs/create_directory\n \n (T... args)\n \n \n T\n create_directory_symlink\n cpp/experimental/fs/create_symlink\n \n (T... args)\n \n \n T\n create_hard_link\n cpp/experimental/fs/create_hard_link\n \n (T... args)\n \n \n T\n create_symlink\n cpp/experimental/fs/create_symlink\n \n (T... args)\n \n \n T\n current_path\n cpp/experimental/fs/current_path\n \n (T... args)\n \n std::experimental::filesystem::directory_entry\n std::experimental::filesystem::directory_iterator\n std::experimental::filesystem::directory_options\n \n T\n equivalent\n cpp/experimental/fs/equivalent\n \n (T... args)\n \n \n T\n exists\n cpp/experimental/fs/exists\n \n (T... args)\n \n \n T\n file_size\n cpp/experimental/fs/file_size\n \n (T... args)\n \n std::experimental::filesystem::file_status\n std::experimental::filesystem::file_time_type\n std::experimental::filesystem::file_type\n std::experimental::filesystem::filesystem_error\n \n T\n hard_link_count\n cpp/experimental/fs/hard_link_count\n \n (T... args)\n \n \n T\n is_block_file\n cpp/experimental/fs/is_block_file\n \n (T... args)\n \n \n T\n is_character_file\n cpp/experimental/fs/is_character_file\n \n (T... args)\n \n \n T\n is_directory\n cpp/experimental/fs/is_directory\n \n (T... args)\n \n \n T\n is_empty\n cpp/experimental/fs/is_empty\n \n (T... args)\n \n \n T\n is_fifo\n cpp/experimental/fs/is_fifo\n \n (T... args)\n \n \n T\n is_other\n cpp/experimental/fs/is_other\n \n (T... args)\n \n \n T\n is_regular_file\n cpp/experimental/fs/is_regular_file\n \n (T... args)\n \n \n T\n is_socket\n cpp/experimental/fs/is_socket\n \n (T... args)\n \n \n T\n is_symlink\n cpp/experimental/fs/is_symlink\n \n (T... args)\n \n \n T\n last_write_time\n cpp/experimental/fs/last_write_time\n \n (T... args)\n \n std::experimental::filesystem::path\n \n T\n permissions\n cpp/experimental/fs/permissions\n \n (T... args)\n \n std::experimental::filesystem::perms\n \n T\n read_symlink\n cpp/experimental/fs/read_symlink\n \n (T... args)\n \n std::experimental::filesystem::recursive_directory_iterator\n \n T\n remove\n cpp/experimental/fs/remove\n \n (T... args)\n \n \n T\n remove_all\n cpp/experimental/fs/remove\n \n (T... args)\n \n \n T\n rename\n cpp/experimental/fs/rename\n \n (T... args)\n \n \n T\n resize_file\n cpp/experimental/fs/resize_file\n \n (T... args)\n \n \n T\n space\n cpp/experimental/fs/space\n \n (T... args)\n \n std::experimental::filesystem::space_info\n \n T\n status\n cpp/experimental/fs/status\n \n (T... args)\n \n \n T\n status_known\n cpp/experimental/fs/status_known\n \n (T... args)\n \n \n T\n symlink_status\n cpp/experimental/fs/status\n \n (T... args)\n \n \n T\n system_complete\n cpp/experimental/fs/absolute\n \n (T... args)\n \n \n T\n temp_directory_path\n cpp/experimental/fs/temp_directory_path\n \n (T... args)\n \n \n \n std::experimental::filesystem::copy_options\n cpp/experimental/fs/copy_options\n \n \n std::experimental::filesystem::directory_entry\n cpp/experimental/fs/directory_entry\n \n T\n assign\n cpp/experimental/fs/directory_entry/assign\n \n (T... args)\n \n \n T\n directory_entry\n cpp/experimental/fs/directory_entry/directory_entry\n \n (T... args)\n \n \n T\n operator=\n cpp/experimental/fs/directory_entry/operator=\n \n (T... args)\n \n \n T\n path\n cpp/experimental/fs/directory_entry/path\n \n (T... args)\n \n \n T\n replace_filename\n cpp/experimental/fs/directory_entry/replace_filename\n \n (T... args)\n \n \n T\n status\n cpp/experimental/fs/directory_entry/status\n \n (T... args)\n \n \n T\n symlink_status\n cpp/experimental/fs/directory_entry/status\n \n (T... args)\n \n \n \n std::experimental::filesystem::directory_iterator\n cpp/experimental/fs/directory_iterator\n \n T\n directory_iterator\n cpp/experimental/fs/directory_iterator/directory_iterator\n \n (T... args)\n \n \n T\n increment\n cpp/experimental/fs/directory_iterator/increment\n \n (T... args)\n \n \n T\n operator*\n cpp/experimental/fs/directory_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/experimental/fs/directory_iterator/increment\n \n (T... args)\n \n \n T\n operator->\n cpp/experimental/fs/directory_iterator/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/experimental/fs/directory_iterator/operator=\n \n (T... args)\n \n \n \n std::experimental::filesystem::directory_options\n cpp/experimental/fs/directory_options\n \n \n std::experimental::filesystem::file_status\n cpp/experimental/fs/file_status\n \n T\n file_status\n cpp/experimental/fs/file_status/file_status\n \n (T... args)\n \n \n T\n operator=\n cpp/experimental/fs/file_status/operator=\n \n (T... args)\n \n \n T\n permissions\n cpp/experimental/fs/file_status/permissions\n \n (T... args)\n \n \n T\n type\n cpp/experimental/fs/file_status/type\n \n (T... args)\n \n \n \n std::experimental::filesystem::file_time_type\n cpp/experimental/fs/file_time_type\n \n \n std::experimental::filesystem::file_type\n cpp/experimental/fs/file_type\n \n \n std::experimental::filesystem::filesystem_error\n cpp/experimental/fs/filesystem_error\n \n T\n filesystem_error\n cpp/experimental/fs/filesystem_error/filesystem_error\n \n (T... args)\n \n \n T\n path1\n cpp/experimental/fs/filesystem_error/path\n \n (T... args)\n \n \n T\n path2\n cpp/experimental/fs/filesystem_error/path\n \n (T... args)\n \n \n T\n what\n cpp/experimental/fs/filesystem_error/what\n \n (T... args)\n \n \n \n std::experimental::filesystem::path\n cpp/experimental/fs/path\n \n T\n append\n cpp/experimental/fs/path/append\n \n (T... args)\n \n \n T\n assign\n cpp/experimental/fs/path/assign\n \n (T... args)\n \n \n T\n begin\n cpp/experimental/fs/path/begin\n \n (T... args)\n \n \n T\n c_str\n cpp/experimental/fs/path/native\n \n (T... args)\n \n \n T\n clear\n cpp/experimental/fs/path/clear\n \n (T... args)\n \n \n T\n compare\n cpp/experimental/fs/path/compare\n \n (T... args)\n \n \n T\n concat\n cpp/experimental/fs/path/concat\n \n (T... args)\n \n \n T\n empty\n cpp/experimental/fs/path/empty\n \n (T... args)\n \n \n T\n end\n cpp/experimental/fs/path/begin\n \n (T... args)\n \n \n T\n extension\n cpp/experimental/fs/path/extension\n \n (T... args)\n \n \n T\n filename\n cpp/experimental/fs/path/filename\n \n (T... args)\n \n \n T\n generic_string\n cpp/experimental/fs/path/generic_string\n \n (T... args)\n \n \n T\n generic_u16string\n cpp/experimental/fs/path/generic_string\n \n (T... args)\n \n \n T\n generic_u32string\n cpp/experimental/fs/path/generic_string\n \n (T... args)\n \n \n T\n generic_u8string\n cpp/experimental/fs/path/generic_string\n \n (T... args)\n \n \n T\n generic_wstring\n cpp/experimental/fs/path/generic_string\n \n (T... args)\n \n \n T\n has_extension\n cpp/experimental/fs/path/has_path\n \n (T... args)\n \n \n T\n has_filename\n cpp/experimental/fs/path/has_path\n \n (T... args)\n \n \n T\n has_parent_path\n cpp/experimental/fs/path/has_path\n \n (T... args)\n \n \n T\n has_relative_path\n cpp/experimental/fs/path/has_path\n \n (T... args)\n \n \n T\n has_root_directory\n cpp/experimental/fs/path/has_path\n \n (T... args)\n \n \n T\n has_root_name\n cpp/experimental/fs/path/has_path\n \n (T... args)\n \n \n T\n has_root_path\n cpp/experimental/fs/path/has_path\n \n (T... args)\n \n \n T\n has_stem\n cpp/experimental/fs/path/has_path\n \n (T... args)\n \n \n T\n make_preferred\n cpp/experimental/fs/path/make_preferred\n \n (T... args)\n \n \n T\n native\n cpp/experimental/fs/path/native\n \n (T... args)\n \n \n T\n operator string_type\n cpp/experimental/fs/path/native\n \n (T... args)\n \n \n T\n operator+=\n cpp/experimental/fs/path/concat\n \n (T... args)\n \n \n T\n operator/=\n cpp/experimental/fs/path/append\n \n (T... args)\n \n \n T\n operator=\n cpp/experimental/fs/path/operator=\n \n (T... args)\n \n \n T\n parent_path\n cpp/experimental/fs/path/parent_path\n \n (T... args)\n \n \n T\n path\n cpp/experimental/fs/path/path\n \n (T... args)\n \n \n T\n relative_path\n cpp/experimental/fs/path/relative_path\n \n (T... args)\n \n \n T\n remove_filename\n cpp/experimental/fs/path/remove_filename\n \n (T... args)\n \n \n T\n replace_extension\n cpp/experimental/fs/path/replace_extension\n \n (T... args)\n \n \n T\n replace_filename\n cpp/experimental/fs/path/replace_filename\n \n (T... args)\n \n \n T\n root_directory\n cpp/experimental/fs/path/root_directory\n \n (T... args)\n \n \n T\n root_name\n cpp/experimental/fs/path/root_name\n \n (T... args)\n \n \n T\n root_path\n cpp/experimental/fs/path/root_path\n \n (T... args)\n \n \n T\n stem\n cpp/experimental/fs/path/stem\n \n (T... args)\n \n \n T\n string\n cpp/experimental/fs/path/string\n \n (T... args)\n \n \n T\n swap\n cpp/experimental/fs/path/swap\n \n (T... args)\n \n \n T\n u16string\n cpp/experimental/fs/path/string\n \n (T... args)\n \n \n T\n u32string\n cpp/experimental/fs/path/string\n \n (T... args)\n \n \n T\n u8string\n cpp/experimental/fs/path/string\n \n (T... args)\n \n \n T\n wstring\n cpp/experimental/fs/path/string\n \n (T... args)\n \n \n T\n ~path\n cpp/experimental/fs/path/~path\n \n (T... args)\n \n \n \n std::experimental::filesystem::perms\n cpp/experimental/fs/perms\n \n \n std::experimental::filesystem::recursive_directory_iterator\n cpp/experimental/fs/recursive_directory_iterator\n \n T\n depth\n cpp/experimental/fs/recursive_directory_iterator/depth\n \n (T... args)\n \n \n T\n disable_recursion_pending\n cpp/experimental/fs/recursive_directory_iterator/disable_recursion_pending\n \n (T... args)\n \n \n T\n increment\n cpp/experimental/fs/recursive_directory_iterator/increment\n \n (T... args)\n \n \n T\n operator*\n cpp/experimental/fs/recursive_directory_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/experimental/fs/recursive_directory_iterator/increment\n \n (T... args)\n \n \n T\n operator->\n cpp/experimental/fs/recursive_directory_iterator/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/experimental/fs/recursive_directory_iterator/operator=\n \n (T... args)\n \n \n T\n options\n cpp/experimental/fs/recursive_directory_iterator/options\n \n (T... args)\n \n \n T\n pop\n cpp/experimental/fs/recursive_directory_iterator/pop\n \n (T... args)\n \n \n T\n recursion_pending\n cpp/experimental/fs/recursive_directory_iterator/recursion_pending\n \n (T... args)\n \n \n T\n recursive_directory_iterator\n cpp/experimental/fs/recursive_directory_iterator/recursive_directory_iterator\n \n (T... args)\n \n \n \n std::experimental::filesystem::space_info\n cpp/experimental/fs/space_info\n \n T\n available\n cpp/experimental/fs/space_info\n \n \n \n \n T\n capacity\n cpp/experimental/fs/space_info\n \n \n \n \n T\n free\n cpp/experimental/fs/space_info\n \n \n \n \n \n std::experimental::invocation_type\n cpp/experimental/invocation_type\n \n \n std::experimental::is_detected\n cpp/experimental/is_detected\n \n \n std::experimental::is_detected_convertible\n cpp/experimental/is_detected\n \n \n std::experimental::is_detected_exact\n cpp/experimental/is_detected\n \n \n std::experimental::nonesuch\n cpp/experimental/nonesuch\n \n \n std::experimental::observer_ptr\n cpp/experimental/observer_ptr\n \n \n std::experimental::optional\n cpp/experimental/optional\n \n T\n emplace\n cpp/experimental/optional/emplace\n \n (T... args)\n \n \n T\n operator bool\n cpp/experimental/optional/operator_bool\n \n (T... args)\n \n \n T\n operator*\n cpp/experimental/optional/operator*\n \n (T... args)\n \n \n T\n operator->\n cpp/experimental/optional/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/experimental/optional/operator=\n \n (T... args)\n \n \n T\n optional\n cpp/experimental/optional/optional\n \n (T... args)\n \n \n T\n swap\n cpp/experimental/optional/swap\n \n (T... args)\n \n \n T\n value\n cpp/experimental/optional/value\n \n (T... args)\n \n \n T\n value_or\n cpp/experimental/optional/value_or\n \n (T... args)\n \n \n T\n ~optional\n cpp/experimental/optional/~optional\n \n (T... args)\n \n \n \n std::experimental::ostream_joiner\n cpp/experimental/ostream_joiner\n \n \n std::experimental::pmr\n \n \n T\n get_default_resource\n cpp/experimental/get_default_resource\n \n (T... args)\n \n std::experimental::pmr::memory_resource\n std::experimental::pmr::monotonic_buffer_resource\n std::experimental::pmr::new_delete_resource\n std::experimental::pmr::null_memory_resource\n std::experimental::pmr::polymorphic_allocator\n std::experimental::pmr::resource_adaptor\n \n T\n set_default_resource\n cpp/experimental/set_default_resource\n \n (T... args)\n \n std::experimental::pmr::synchronized_pool_resource\n std::experimental::pmr::unsynchronized_pool_resource\n \n \n std::experimental::pmr::memory_resource\n cpp/experimental/memory_resource\n \n T\n allocate\n cpp/experimental/memory_resource/allocate\n \n (T... args)\n \n \n T\n deallocate\n cpp/experimental/memory_resource/deallocate\n \n (T... args)\n \n \n T\n do_allocate\n cpp/experimental/memory_resource/do_allocate\n \n (T... args)\n \n \n T\n do_deallocate\n cpp/experimental/memory_resource/do_deallocate\n \n (T... args)\n \n \n T\n do_is_equal\n cpp/experimental/memory_resource/do_is_equal\n \n (T... args)\n \n \n T\n is_equal\n cpp/experimental/memory_resource/is_equal\n \n (T... args)\n \n \n T\n memory_resource\n cpp/experimental/memory_resource/memory_resource\n \n (T... args)\n \n \n \n std::experimental::pmr::monotonic_buffer_resource\n cpp/experimental/monotonic_buffer_resource\n \n \n std::experimental::pmr::new_delete_resource\n cpp/experimental/new_delete_resource\n \n \n std::experimental::pmr::null_memory_resource\n cpp/experimental/null_Memory_resource\n \n \n std::experimental::pmr::polymorphic_allocator\n cpp/experimental/polymorphic_allocator\n \n \n std::experimental::pmr::resource_adaptor\n cpp/experimental/resource_adaptor\n \n \n std::experimental::pmr::synchronized_pool_resource\n cpp/experimental/synchronized_pool_resource\n \n \n std::experimental::pmr::unsynchronized_pool_resource\n cpp/experimental/unsynchronized_pool_resource\n \n \n std::experimental::propagate_const\n cpp/experimental/propagate_const\n \n \n std::experimental::raw_invocation_type\n cpp/experimental/raw_invocation_type\n \n \n std::experimental::source_location\n cpp/experimental/source_location\n \n \n std::experimental::string_view\n cpp/experimental/basic_string_view\n \n T\n at\n cpp/experimental/basic_string_view/at\n \n (T... args)\n \n \n T\n back\n cpp/experimental/basic_string_view/back\n \n (T... args)\n \n \n T\n begin\n cpp/experimental/basic_string_view/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/experimental/basic_string_view/begin\n \n (T... args)\n \n \n T\n cend\n cpp/experimental/basic_string_view/end\n \n (T... args)\n \n \n T\n compare\n cpp/experimental/basic_string_view/compare\n \n (T... args)\n \n \n T\n copy\n cpp/experimental/basic_string_view/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/experimental/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/experimental/basic_string_view/rend\n \n (T... args)\n \n \n T\n data\n cpp/experimental/basic_string_view/data\n \n (T... args)\n \n \n T\n empty\n cpp/experimental/basic_string_view/empty\n \n (T... args)\n \n \n T\n end\n cpp/experimental/basic_string_view/end\n \n (T... args)\n \n \n T\n find\n cpp/experimental/basic_string_view/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/experimental/basic_string_view/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/experimental/basic_string_view/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/experimental/basic_string_view/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/experimental/basic_string_view/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/experimental/basic_string_view/front\n \n (T... args)\n \n \n T\n length\n cpp/experimental/basic_string_view/size\n \n (T... args)\n \n \n T\n max_size\n cpp/experimental/basic_string_view/max_size\n \n (T... args)\n \n \n T\n operator basic_string\n cpp/experimental/basic_string_view/to_string\n \n (T... args)\n \n \n T\n operator=\n cpp/experimental/basic_string_view/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/experimental/basic_string_view/operator_at\n \n (T... args)\n \n \n T\n rbegin\n cpp/experimental/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n remove_prefix\n cpp/experimental/basic_string_view/remove_prefix\n \n (T... args)\n \n \n T\n remove_suffix\n cpp/experimental/basic_string_view/remove_suffix\n \n (T... args)\n \n \n T\n rend\n cpp/experimental/basic_string_view/rend\n \n (T... args)\n \n \n T\n rfind\n cpp/experimental/basic_string_view/rfind\n \n (T... args)\n \n \n T\n size\n cpp/experimental/basic_string_view/size\n \n (T... args)\n \n \n T\n string_view\n cpp/experimental/basic_string_view/basic_string_view\n \n (T... args)\n \n \n T\n substr\n cpp/experimental/basic_string_view/substr\n \n (T... args)\n \n \n T\n swap\n cpp/experimental/basic_string_view/swap\n \n (T... args)\n \n \n T\n to_string\n cpp/experimental/basic_string_view/to_string\n \n (T... args)\n \n \n \n std::experimental::u16string_view\n cpp/experimental/basic_string_view\n \n T\n at\n cpp/experimental/basic_string_view/at\n \n (T... args)\n \n \n T\n back\n cpp/experimental/basic_string_view/back\n \n (T... args)\n \n \n T\n begin\n cpp/experimental/basic_string_view/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/experimental/basic_string_view/begin\n \n (T... args)\n \n \n T\n cend\n cpp/experimental/basic_string_view/end\n \n (T... args)\n \n \n T\n compare\n cpp/experimental/basic_string_view/compare\n \n (T... args)\n \n \n T\n copy\n cpp/experimental/basic_string_view/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/experimental/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/experimental/basic_string_view/rend\n \n (T... args)\n \n \n T\n data\n cpp/experimental/basic_string_view/data\n \n (T... args)\n \n \n T\n empty\n cpp/experimental/basic_string_view/empty\n \n (T... args)\n \n \n T\n end\n cpp/experimental/basic_string_view/end\n \n (T... args)\n \n \n T\n find\n cpp/experimental/basic_string_view/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/experimental/basic_string_view/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/experimental/basic_string_view/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/experimental/basic_string_view/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/experimental/basic_string_view/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/experimental/basic_string_view/front\n \n (T... args)\n \n \n T\n length\n cpp/experimental/basic_string_view/size\n \n (T... args)\n \n \n T\n max_size\n cpp/experimental/basic_string_view/max_size\n \n (T... args)\n \n \n T\n operator basic_string\n cpp/experimental/basic_string_view/to_string\n \n (T... args)\n \n \n T\n operator=\n cpp/experimental/basic_string_view/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/experimental/basic_string_view/operator_at\n \n (T... args)\n \n \n T\n rbegin\n cpp/experimental/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n remove_prefix\n cpp/experimental/basic_string_view/remove_prefix\n \n (T... args)\n \n \n T\n remove_suffix\n cpp/experimental/basic_string_view/remove_suffix\n \n (T... args)\n \n \n T\n rend\n cpp/experimental/basic_string_view/rend\n \n (T... args)\n \n \n T\n rfind\n cpp/experimental/basic_string_view/rfind\n \n (T... args)\n \n \n T\n size\n cpp/experimental/basic_string_view/size\n \n (T... args)\n \n \n T\n substr\n cpp/experimental/basic_string_view/substr\n \n (T... args)\n \n \n T\n swap\n cpp/experimental/basic_string_view/swap\n \n (T... args)\n \n \n T\n to_string\n cpp/experimental/basic_string_view/to_string\n \n (T... args)\n \n \n T\n u16string_view\n cpp/experimental/basic_string_view/basic_string_view\n \n (T... args)\n \n \n \n std::experimental::u32string_view\n cpp/experimental/basic_string_view\n \n T\n at\n cpp/experimental/basic_string_view/at\n \n (T... args)\n \n \n T\n back\n cpp/experimental/basic_string_view/back\n \n (T... args)\n \n \n T\n begin\n cpp/experimental/basic_string_view/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/experimental/basic_string_view/begin\n \n (T... args)\n \n \n T\n cend\n cpp/experimental/basic_string_view/end\n \n (T... args)\n \n \n T\n compare\n cpp/experimental/basic_string_view/compare\n \n (T... args)\n \n \n T\n copy\n cpp/experimental/basic_string_view/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/experimental/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/experimental/basic_string_view/rend\n \n (T... args)\n \n \n T\n data\n cpp/experimental/basic_string_view/data\n \n (T... args)\n \n \n T\n empty\n cpp/experimental/basic_string_view/empty\n \n (T... args)\n \n \n T\n end\n cpp/experimental/basic_string_view/end\n \n (T... args)\n \n \n T\n find\n cpp/experimental/basic_string_view/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/experimental/basic_string_view/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/experimental/basic_string_view/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/experimental/basic_string_view/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/experimental/basic_string_view/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/experimental/basic_string_view/front\n \n (T... args)\n \n \n T\n length\n cpp/experimental/basic_string_view/size\n \n (T... args)\n \n \n T\n max_size\n cpp/experimental/basic_string_view/max_size\n \n (T... args)\n \n \n T\n operator basic_string\n cpp/experimental/basic_string_view/to_string\n \n (T... args)\n \n \n T\n operator=\n cpp/experimental/basic_string_view/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/experimental/basic_string_view/operator_at\n \n (T... args)\n \n \n T\n rbegin\n cpp/experimental/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n remove_prefix\n cpp/experimental/basic_string_view/remove_prefix\n \n (T... args)\n \n \n T\n remove_suffix\n cpp/experimental/basic_string_view/remove_suffix\n \n (T... args)\n \n \n T\n rend\n cpp/experimental/basic_string_view/rend\n \n (T... args)\n \n \n T\n rfind\n cpp/experimental/basic_string_view/rfind\n \n (T... args)\n \n \n T\n size\n cpp/experimental/basic_string_view/size\n \n (T... args)\n \n \n T\n substr\n cpp/experimental/basic_string_view/substr\n \n (T... args)\n \n \n T\n swap\n cpp/experimental/basic_string_view/swap\n \n (T... args)\n \n \n T\n to_string\n cpp/experimental/basic_string_view/to_string\n \n (T... args)\n \n \n T\n u32string_view\n cpp/experimental/basic_string_view/basic_string_view\n \n (T... args)\n \n \n \n std::experimental::wstring_view\n cpp/experimental/basic_string_view\n \n T\n at\n cpp/experimental/basic_string_view/at\n \n (T... args)\n \n \n T\n back\n cpp/experimental/basic_string_view/back\n \n (T... args)\n \n \n T\n begin\n cpp/experimental/basic_string_view/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/experimental/basic_string_view/begin\n \n (T... args)\n \n \n T\n cend\n cpp/experimental/basic_string_view/end\n \n (T... args)\n \n \n T\n compare\n cpp/experimental/basic_string_view/compare\n \n (T... args)\n \n \n T\n copy\n cpp/experimental/basic_string_view/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/experimental/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/experimental/basic_string_view/rend\n \n (T... args)\n \n \n T\n data\n cpp/experimental/basic_string_view/data\n \n (T... args)\n \n \n T\n empty\n cpp/experimental/basic_string_view/empty\n \n (T... args)\n \n \n T\n end\n cpp/experimental/basic_string_view/end\n \n (T... args)\n \n \n T\n find\n cpp/experimental/basic_string_view/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/experimental/basic_string_view/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/experimental/basic_string_view/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/experimental/basic_string_view/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/experimental/basic_string_view/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/experimental/basic_string_view/front\n \n (T... args)\n \n \n T\n length\n cpp/experimental/basic_string_view/size\n \n (T... args)\n \n \n T\n max_size\n cpp/experimental/basic_string_view/max_size\n \n (T... args)\n \n \n T\n operator basic_string\n cpp/experimental/basic_string_view/to_string\n \n (T... args)\n \n \n T\n operator=\n cpp/experimental/basic_string_view/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/experimental/basic_string_view/operator_at\n \n (T... args)\n \n \n T\n rbegin\n cpp/experimental/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n remove_prefix\n cpp/experimental/basic_string_view/remove_prefix\n \n (T... args)\n \n \n T\n remove_suffix\n cpp/experimental/basic_string_view/remove_suffix\n \n (T... args)\n \n \n T\n rend\n cpp/experimental/basic_string_view/rend\n \n (T... args)\n \n \n T\n rfind\n cpp/experimental/basic_string_view/rfind\n \n (T... args)\n \n \n T\n size\n cpp/experimental/basic_string_view/size\n \n (T... args)\n \n \n T\n substr\n cpp/experimental/basic_string_view/substr\n \n (T... args)\n \n \n T\n swap\n cpp/experimental/basic_string_view/swap\n \n (T... args)\n \n \n T\n to_string\n cpp/experimental/basic_string_view/to_string\n \n (T... args)\n \n \n T\n wstring_view\n cpp/experimental/basic_string_view/basic_string_view\n \n (T... args)\n \n \n \n std::exponential_distribution\n cpp/numeric/random/exponential_distribution\n \n T\n exponential_distribution\n cpp/numeric/random/exponential_distribution/exponential_distribution\n \n (T... args)\n \n \n T\n lambda\n cpp/numeric/random/exponential_distribution/lambda\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/exponential_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/exponential_distribution/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/exponential_distribution/operator()\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/exponential_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/exponential_distribution/reset\n \n (T... args)\n \n \n \n std::extent\n cpp/types/extent\n \n \n std::extreme_value_distribution\n cpp/numeric/random/extreme_value_distribution\n \n T\n a\n cpp/numeric/random/extreme_value_distribution/params\n \n (T... args)\n \n \n T\n b\n cpp/numeric/random/extreme_value_distribution/params\n \n (T... args)\n \n \n T\n extreme_value_distribution\n cpp/numeric/random/extreme_value_distribution/extreme_value_distribution\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/extreme_value_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/extreme_value_distribution/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/extreme_value_distribution/operator()\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/extreme_value_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/extreme_value_distribution/reset\n \n (T... args)\n \n \n \n std::false_type\n cpp/types/integral_constant\n \n \n std::femto\n cpp/numeric/ratio/ratio\n \n \n std::filebuf\n cpp/io/basic_filebuf\n \n T\n close\n cpp/io/basic_filebuf/close\n \n (T... args)\n \n \n T\n eback\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n egptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n epptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n filebuf\n cpp/io/basic_filebuf/basic_filebuf\n \n (T... args)\n \n \n T\n gbump\n cpp/io/basic_streambuf/gbump\n \n (T... args)\n \n \n T\n getloc\n cpp/io/basic_streambuf/getloc\n \n (T... args)\n \n \n T\n gptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n in_avail\n cpp/io/basic_streambuf/in_avail\n \n (T... args)\n \n \n T\n is_open\n cpp/io/basic_filebuf/is_open\n \n (T... args)\n \n \n T\n open\n cpp/io/basic_filebuf/open\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_filebuf/operator=\n \n (T... args)\n \n \n T\n overflow\n cpp/io/basic_streambuf/overflow\n \n (T... args)\n \n \n T\n pbackfail\n cpp/io/basic_streambuf/pbackfail\n \n (T... args)\n \n \n T\n pbase\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pbump\n cpp/io/basic_streambuf/pbump\n \n (T... args)\n \n \n T\n pptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pubimbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n pubseekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n pubseekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n pubsetbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n pubsync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n sbumpc\n cpp/io/basic_streambuf/sbumpc\n \n (T... args)\n \n \n T\n seekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n seekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n setbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n setg\n cpp/io/basic_streambuf/setg\n \n (T... args)\n \n \n T\n setp\n cpp/io/basic_streambuf/setp\n \n (T... args)\n \n \n T\n sgetc\n cpp/io/basic_streambuf/sgetc\n \n (T... args)\n \n \n T\n sgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n showmanyc\n cpp/io/basic_streambuf/showmanyc\n \n (T... args)\n \n \n T\n snextc\n cpp/io/basic_streambuf/snextc\n \n (T... args)\n \n \n T\n sputbackc\n cpp/io/basic_streambuf/sputbackc\n \n (T... args)\n \n \n T\n sputc\n cpp/io/basic_streambuf/sputc\n \n (T... args)\n \n \n T\n sputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n sungetc\n cpp/io/basic_streambuf/sungetc\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_streambuf/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n uflow\n cpp/io/basic_streambuf/uflow\n \n (T... args)\n \n \n T\n underflow\n cpp/io/basic_streambuf/underflow\n \n (T... args)\n \n \n T\n xsgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n xsputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n ~filebuf\n cpp/io/basic_filebuf/~basic_filebuf\n \n (T... args)\n \n \n \n std::filesystem\n \n \n T\n absolute\n cpp/filesystem/absolute\n \n (T... args)\n \n \n T\n canonical\n cpp/filesystem/canonical\n \n (T... args)\n \n \n T\n copy\n cpp/filesystem/copy\n \n (T... args)\n \n \n T\n copy_file\n cpp/filesystem/copy_file\n \n (T... args)\n \n std::filesystem::copy_options\n \n T\n copy_symlink\n cpp/filesystem/copy_symlink\n \n (T... args)\n \n \n T\n create_directories\n cpp/filesystem/create_directory\n \n (T... args)\n \n \n T\n create_directory\n cpp/filesystem/create_directory\n \n (T... args)\n \n \n T\n create_directory_symlink\n cpp/filesystem/create_symlink\n \n (T... args)\n \n \n T\n create_hard_link\n cpp/filesystem/create_hard_link\n \n (T... args)\n \n \n T\n create_symlink\n cpp/filesystem/create_symlink\n \n (T... args)\n \n \n T\n current_path\n cpp/filesystem/current_path\n \n (T... args)\n \n std::filesystem::directory_entry\n std::filesystem::directory_iterator\n std::filesystem::directory_options\n \n T\n equivalent\n cpp/filesystem/equivalent\n \n (T... args)\n \n \n T\n exists\n cpp/filesystem/exists\n \n (T... args)\n \n \n T\n file_size\n cpp/filesystem/file_size\n \n (T... args)\n \n std::filesystem::file_status\n std::filesystem::file_time_type\n std::filesystem::file_type\n std::filesystem::filesystem_error\n \n T\n hard_link_count\n cpp/filesystem/hard_link_count\n \n (T... args)\n \n \n T\n is_block_file\n cpp/filesystem/is_block_file\n \n (T... args)\n \n \n T\n is_character_file\n cpp/filesystem/is_character_file\n \n (T... args)\n \n \n T\n is_directory\n cpp/filesystem/is_directory\n \n (T... args)\n \n \n T\n is_empty\n cpp/filesystem/is_empty\n \n (T... args)\n \n \n T\n is_fifo\n cpp/filesystem/is_fifo\n \n (T... args)\n \n \n T\n is_other\n cpp/filesystem/is_other\n \n (T... args)\n \n \n T\n is_regular_file\n cpp/filesystem/is_regular_file\n \n (T... args)\n \n \n T\n is_socket\n cpp/filesystem/is_socket\n \n (T... args)\n \n \n T\n is_symlink\n cpp/filesystem/is_symlink\n \n (T... args)\n \n \n T\n last_write_time\n cpp/filesystem/last_write_time\n \n (T... args)\n \n std::filesystem::path\n \n T\n permissions\n cpp/filesystem/permissions\n \n (T... args)\n \n std::filesystem::perms\n \n T\n proximate\n cpp/filesystem/relative\n \n (T... args)\n \n \n T\n read_symlink\n cpp/filesystem/read_symlink\n \n (T... args)\n \n std::filesystem::recursive_directory_iterator\n \n T\n relative\n cpp/filesystem/relative\n \n (T... args)\n \n \n T\n remove\n cpp/filesystem/remove\n \n (T... args)\n \n \n T\n remove_all\n cpp/filesystem/remove\n \n (T... args)\n \n \n T\n rename\n cpp/filesystem/rename\n \n (T... args)\n \n \n T\n resize_file\n cpp/filesystem/resize_file\n \n (T... args)\n \n \n T\n space\n cpp/filesystem/space\n \n (T... args)\n \n std::filesystem::space_info\n \n T\n status\n cpp/filesystem/status\n \n (T... args)\n \n \n T\n status_known\n cpp/filesystem/status_known\n \n (T... args)\n \n \n T\n symlink_status\n cpp/filesystem/status\n \n (T... args)\n \n \n T\n system_complete\n cpp/filesystem/absolute\n \n (T... args)\n \n \n T\n temp_directory_path\n cpp/filesystem/temp_directory_path\n \n (T... args)\n \n \n T\n u8path\n cpp/filesystem/path/u8path\n \n (T... args)\n \n \n T\n weakly_canonical\n cpp/filesystem/canonical\n \n (T... args)\n \n \n \n std::filesystem::copy_options\n cpp/filesystem/copy_options\n \n \n std::filesystem::directory_entry\n cpp/filesystem/directory_entry\n \n T\n assign\n cpp/filesystem/directory_entry/assign\n \n (T... args)\n \n \n T\n directory_entry\n cpp/filesystem/directory_entry/directory_entry\n \n (T... args)\n \n \n T\n operator=\n cpp/filesystem/directory_entry/operator=\n \n (T... args)\n \n \n T\n path\n cpp/filesystem/directory_entry/path\n \n (T... args)\n \n \n T\n replace_filename\n cpp/filesystem/directory_entry/replace_filename\n \n (T... args)\n \n \n T\n status\n cpp/filesystem/directory_entry/status\n \n (T... args)\n \n \n T\n symlink_status\n cpp/filesystem/directory_entry/status\n \n (T... args)\n \n \n \n std::filesystem::directory_iterator\n cpp/filesystem/directory_iterator\n \n T\n directory_iterator\n cpp/filesystem/directory_iterator/directory_iterator\n \n (T... args)\n \n \n T\n increment\n cpp/filesystem/directory_iterator/increment\n \n (T... args)\n \n \n T\n operator*\n cpp/filesystem/directory_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/filesystem/directory_iterator/increment\n \n (T... args)\n \n \n T\n operator->\n cpp/filesystem/directory_iterator/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/filesystem/directory_iterator/operator=\n \n (T... args)\n \n \n \n std::filesystem::directory_options\n cpp/filesystem/directory_options\n \n \n std::filesystem::file_status\n cpp/filesystem/file_status\n \n T\n file_status\n cpp/filesystem/file_status/file_status\n \n (T... args)\n \n \n T\n operator=\n cpp/filesystem/file_status/operator=\n \n (T... args)\n \n \n T\n permissions\n cpp/filesystem/file_status/permissions\n \n (T... args)\n \n \n T\n type\n cpp/filesystem/file_status/type\n \n (T... args)\n \n \n T\n ~file_status\n cpp/filesystem/file_status/~file_status\n \n (T... args)\n \n \n \n std::filesystem::file_time_type\n cpp/filesystem/file_time_type\n \n \n std::filesystem::file_type\n cpp/filesystem/file_type\n \n \n std::filesystem::filesystem_error\n cpp/filesystem/filesystem_error\n \n T\n filesystem_error\n cpp/filesystem/filesystem_error/filesystem_error\n \n (T... args)\n \n \n T\n path1\n cpp/filesystem/filesystem_error/path\n \n (T... args)\n \n \n T\n path2\n cpp/filesystem/filesystem_error/path\n \n (T... args)\n \n \n T\n what\n cpp/filesystem/filesystem_error/what\n \n (T... args)\n \n \n \n std::filesystem::path\n cpp/filesystem/path\n \n T\n append\n cpp/filesystem/path/append\n \n (T... args)\n \n \n T\n assign\n cpp/filesystem/path/assign\n \n (T... args)\n \n \n T\n begin\n cpp/filesystem/path/begin\n \n (T... args)\n \n \n T\n c_str\n cpp/filesystem/path/native\n \n (T... args)\n \n \n T\n clear\n cpp/filesystem/path/clear\n \n (T... args)\n \n \n T\n compare\n cpp/filesystem/path/compare\n \n (T... args)\n \n \n T\n concat\n cpp/filesystem/path/concat\n \n (T... args)\n \n \n T\n empty\n cpp/filesystem/path/empty\n \n (T... args)\n \n \n T\n end\n cpp/filesystem/path/begin\n \n (T... args)\n \n \n T\n extension\n cpp/filesystem/path/extension\n \n (T... args)\n \n \n T\n filename\n cpp/filesystem/path/filename\n \n (T... args)\n \n \n T\n generic_string\n cpp/filesystem/path/generic_string\n \n (T... args)\n \n \n T\n generic_u16string\n cpp/filesystem/path/generic_string\n \n (T... args)\n \n \n T\n generic_u32string\n cpp/filesystem/path/generic_string\n \n (T... args)\n \n \n T\n generic_u8string\n cpp/filesystem/path/generic_string\n \n (T... args)\n \n \n T\n generic_wstring\n cpp/filesystem/path/generic_string\n \n (T... args)\n \n \n T\n has_extension\n cpp/filesystem/path/has_path\n \n (T... args)\n \n \n T\n has_filename\n cpp/filesystem/path/has_path\n \n (T... args)\n \n \n T\n has_parent_path\n cpp/filesystem/path/has_path\n \n (T... args)\n \n \n T\n has_relative_path\n cpp/filesystem/path/has_path\n \n (T... args)\n \n \n T\n has_root_directory\n cpp/filesystem/path/has_path\n \n (T... args)\n \n \n T\n has_root_name\n cpp/filesystem/path/has_path\n \n (T... args)\n \n \n T\n has_root_path\n cpp/filesystem/path/has_path\n \n (T... args)\n \n \n T\n has_stem\n cpp/filesystem/path/has_path\n \n (T... args)\n \n \n T\n is_absolute\n cpp/filesystem/path/is_absrel\n \n (T... args)\n \n \n T\n is_relative\n cpp/filesystem/path/is_absrel\n \n (T... args)\n \n \n T\n lexically_normal\n cpp/filesystem/path/lexically_normal\n \n (T... args)\n \n \n T\n lexically_proximate\n cpp/filesystem/path/lexically_normal\n \n (T... args)\n \n \n T\n lexically_relative\n cpp/filesystem/path/lexically_normal\n \n (T... args)\n \n \n T\n make_preferred\n cpp/filesystem/path/make_preferred\n \n (T... args)\n \n \n T\n native\n cpp/filesystem/path/native\n \n (T... args)\n \n \n T\n operator string_type\n cpp/filesystem/path/native\n \n (T... args)\n \n \n T\n operator+=\n cpp/filesystem/path/concat\n \n (T... args)\n \n \n T\n operator/=\n cpp/filesystem/path/append\n \n (T... args)\n \n \n T\n operator=\n cpp/filesystem/path/operator=\n \n (T... args)\n \n \n T\n parent_path\n cpp/filesystem/path/parent_path\n \n (T... args)\n \n \n T\n path\n cpp/filesystem/path/path\n \n (T... args)\n \n \n T\n relative_path\n cpp/filesystem/path/relative_path\n \n (T... args)\n \n \n T\n remove_filename\n cpp/filesystem/path/remove_filename\n \n (T... args)\n \n \n T\n replace_extension\n cpp/filesystem/path/replace_extension\n \n (T... args)\n \n \n T\n replace_filename\n cpp/filesystem/path/replace_filename\n \n (T... args)\n \n \n T\n root_directory\n cpp/filesystem/path/root_directory\n \n (T... args)\n \n \n T\n root_name\n cpp/filesystem/path/root_name\n \n (T... args)\n \n \n T\n root_path\n cpp/filesystem/path/root_path\n \n (T... args)\n \n \n T\n stem\n cpp/filesystem/path/stem\n \n (T... args)\n \n \n T\n string\n cpp/filesystem/path/string\n \n (T... args)\n \n \n T\n swap\n cpp/filesystem/path/swap\n \n (T... args)\n \n \n T\n u16string\n cpp/filesystem/path/string\n \n (T... args)\n \n \n T\n u32string\n cpp/filesystem/path/string\n \n (T... args)\n \n \n T\n u8string\n cpp/filesystem/path/string\n \n (T... args)\n \n \n T\n wstring\n cpp/filesystem/path/string\n \n (T... args)\n \n \n T\n ~path\n cpp/filesystem/path/~path\n \n (T... args)\n \n \n \n std::filesystem::perms\n cpp/filesystem/perms\n \n \n std::filesystem::recursive_directory_iterator\n cpp/filesystem/recursive_directory_iterator\n \n T\n depth\n cpp/filesystem/recursive_directory_iterator/depth\n \n (T... args)\n \n \n T\n disable_recursion_pending\n cpp/filesystem/recursive_directory_iterator/disable_recursion_pending\n \n (T... args)\n \n \n T\n increment\n cpp/filesystem/recursive_directory_iterator/increment\n \n (T... args)\n \n \n T\n operator*\n cpp/filesystem/recursive_directory_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/filesystem/recursive_directory_iterator/increment\n \n (T... args)\n \n \n T\n operator->\n cpp/filesystem/recursive_directory_iterator/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/filesystem/recursive_directory_iterator/operator=\n \n (T... args)\n \n \n T\n options\n cpp/filesystem/recursive_directory_iterator/options\n \n (T... args)\n \n \n T\n pop\n cpp/filesystem/recursive_directory_iterator/pop\n \n (T... args)\n \n \n T\n recursion_pending\n cpp/filesystem/recursive_directory_iterator/recursion_pending\n \n (T... args)\n \n \n T\n recursive_directory_iterator\n cpp/filesystem/recursive_directory_iterator/recursive_directory_iterator\n \n (T... args)\n \n \n \n std::filesystem::space_info\n cpp/filesystem/space_info\n \n T\n available\n cpp/filesystem/space_info\n \n \n \n \n T\n capacity\n cpp/filesystem/space_info\n \n \n \n \n T\n free\n cpp/filesystem/space_info\n \n \n \n \n \n std::fisher_f_distribution\n cpp/numeric/random/fisher_f_distribution\n \n T\n fisher_f_distribution\n cpp/numeric/random/fisher_f_distribution/fisher_f_distribution\n \n (T... args)\n \n \n T\n m\n cpp/numeric/random/fisher_f_distribution/params\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/fisher_f_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/fisher_f_distribution/min\n \n (T... args)\n \n \n T\n n\n cpp/numeric/random/fisher_f_distribution/params\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/fisher_f_distribution/operator()\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/fisher_f_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/fisher_f_distribution/reset\n \n (T... args)\n \n \n \n std::forward_iterator_tag\n cpp/iterator/iterator_tags\n \n \n std::forward_list\n cpp/container/forward_list\n \n T\n assign\n cpp/container/forward_list/assign\n \n (T... args)\n \n \n T\n before_begin\n cpp/container/forward_list/before_begin\n \n (T... args)\n \n \n T\n begin\n cpp/container/forward_list/begin\n \n (T... args)\n \n \n T\n cbefore_begin\n cpp/container/forward_list/before_begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/forward_list/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/forward_list/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/forward_list/clear\n \n (T... args)\n \n \n T\n emplace_after\n cpp/container/forward_list/emplace_after\n \n (T... args)\n \n \n T\n emplace_front\n cpp/container/forward_list/emplace_front\n \n (T... args)\n \n \n T\n empty\n cpp/container/forward_list/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/forward_list/end\n \n (T... args)\n \n \n T\n erase_after\n cpp/container/forward_list/erase_after\n \n (T... args)\n \n \n T\n forward_list\n cpp/container/forward_list/forward_list\n \n (T... args)\n \n \n T\n front\n cpp/container/forward_list/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/forward_list/get_allocator\n \n (T... args)\n \n \n T\n insert_after\n cpp/container/forward_list/insert_after\n \n (T... args)\n \n \n T\n max_size\n cpp/container/forward_list/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/forward_list/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/forward_list/operator=\n \n (T... args)\n \n \n T\n pop_front\n cpp/container/forward_list/pop_front\n \n (T... args)\n \n \n T\n push_front\n cpp/container/forward_list/push_front\n \n (T... args)\n \n \n T\n remove\n cpp/container/forward_list/remove\n \n (T... args)\n \n \n T\n remove_if\n cpp/container/forward_list/remove\n \n (T... args)\n \n \n T\n resize\n cpp/container/forward_list/resize\n \n (T... args)\n \n \n T\n reverse\n cpp/container/forward_list/reverse\n \n (T... args)\n \n \n T\n sort\n cpp/container/forward_list/sort\n \n (T... args)\n \n \n T\n splice_after\n cpp/container/forward_list/splice_after\n \n (T... args)\n \n \n T\n swap\n cpp/container/forward_list/swap\n \n (T... args)\n \n \n T\n unique\n cpp/container/forward_list/unique\n \n (T... args)\n \n \n T\n ~forward_list\n cpp/container/forward_list/~forward_list\n \n (T... args)\n \n \n \n std::fpos\n cpp/io/fpos\n \n T\n state\n cpp/io/fpos/state\n \n (T... args)\n \n \n \n std::fpos_t\n cpp/io/c\n \n \n std::front_insert_iterator\n cpp/iterator/front_insert_iterator\n \n \n std::fstream\n cpp/io/basic_fstream\n std::fstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n close\n cpp/io/basic_fstream/close\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::fstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::fstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n fstream\n cpp/io/basic_fstream/basic_fstream\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n is_open\n cpp/io/basic_fstream/is_open\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n open\n cpp/io/basic_fstream/open\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_fstream/operator=\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::fstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::fstream::Init\n cpp/io/ios_base/Init\n \n \n std::fstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::fstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::fstream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::function\n cpp/utility/functional/function\n \n T\n assign\n cpp/utility/functional/function/assign\n \n (T... args)\n \n \n T\n function\n cpp/utility/functional/function/function\n \n (T... args)\n \n \n T\n operator bool\n cpp/utility/functional/function/operator_bool\n \n (T... args)\n \n \n T\n operator()\n cpp/utility/functional/function/operator()\n \n (T... args)\n \n \n T\n operator=\n cpp/utility/functional/function/operator=\n \n (T... args)\n \n \n T\n swap\n cpp/utility/functional/function/swap\n \n (T... args)\n \n \n T\n target\n cpp/utility/functional/function/target\n \n (T... args)\n \n \n T\n target_type\n cpp/utility/functional/function/target_type\n \n (T... args)\n \n \n T\n ~function\n cpp/utility/functional/function/~function\n \n (T... args)\n \n \n \n std::future\n cpp/thread/future\n \n T\n future\n cpp/thread/future/future\n \n (T... args)\n \n \n T\n get\n cpp/thread/future/get\n \n (T... args)\n \n \n T\n operator=\n cpp/thread/future/operator=\n \n (T... args)\n \n \n T\n share\n cpp/thread/future/share\n \n (T... args)\n \n \n T\n valid\n cpp/thread/future/valid\n \n (T... args)\n \n \n T\n wait\n cpp/thread/future/wait\n \n (T... args)\n \n \n T\n wait_for\n cpp/thread/future/wait_for\n \n (T... args)\n \n \n T\n wait_until\n cpp/thread/future/wait_until\n \n (T... args)\n \n \n T\n ~future\n cpp/thread/future/~future\n \n (T... args)\n \n \n \n std::future_error\n cpp/thread/future_error\n \n T\n code\n cpp/thread/future_error/code\n \n (T... args)\n \n \n T\n future_error\n cpp/thread/future_error/future_error\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::gamma_distribution\n cpp/numeric/random/gamma_distribution\n \n T\n alpha\n cpp/numeric/random/gamma_distribution/params\n \n (T... args)\n \n \n T\n beta\n cpp/numeric/random/gamma_distribution/params\n \n (T... args)\n \n \n T\n gamma_distribution\n cpp/numeric/random/gamma_distribution/gamma_distribution\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/gamma_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/gamma_distribution/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/gamma_distribution/operator()\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/gamma_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/gamma_distribution/reset\n \n (T... args)\n \n \n \n std::geometric_distribution\n cpp/numeric/random/geometric_distribution\n \n T\n geometric_distribution\n cpp/numeric/random/geometric_distribution/geometric_distribution\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/geometric_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/geometric_distribution/min\n \n (T... args)\n \n \n T\n p\n cpp/numeric/random/geometric_distribution/p\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/geometric_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/geometric_distribution/reset\n \n (T... args)\n \n \n \n std::giga\n cpp/numeric/ratio/ratio\n \n \n std::greater\n cpp/utility/functional/greater\n \n T\n operator()\n cpp/utility/functional/greater\n \n (T... args)\n \n \n \n std::greater_equal\n cpp/utility/functional/greater_equal\n \n T\n operator()\n cpp/utility/functional/greater_equal\n \n (T... args)\n \n \n \n std::gslice\n cpp/numeric/valarray/gslice\n \n \n std::gslice_array\n cpp/numeric/valarray/gslice_array\n \n \n std::has_unique_object_representations\n cpp/types/has_unique_object_representations\n \n \n std::has_virtual_destructor\n cpp/types/has_virtual_destructor\n \n \n std::hash\n cpp/utility/hash\n \n T\n hash\n cpp/utility/hash/hash\n \n (T... args)\n \n \n T\n operator()\n cpp/utility/hash/operator()\n \n (T... args)\n \n \n \n std::hecto\n cpp/numeric/ratio/ratio\n \n \n std::ifstream\n cpp/io/basic_ifstream\n std::ifstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n close\n cpp/io/basic_ifstream/close\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::ifstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::ifstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ifstream\n cpp/io/basic_ifstream/basic_ifstream\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n is_open\n cpp/io/basic_ifstream/is_open\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n open\n cpp/io/basic_ifstream/open\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_ifstream/operator=\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n std::ifstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::ifstream::Init\n cpp/io/ios_base/Init\n \n \n std::ifstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::ifstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::ifstream::sentry\n cpp/io/basic_istream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::imaxdiv_t\n cpp/numeric/math/div\n \n T\n quot\n cpp/numeric/math/div\n \n \n \n \n T\n rem\n cpp/numeric/math/div\n \n \n \n \n \n std::in_place_index_t\n cpp/utility/in_place\n \n \n std::in_place_t\n cpp/utility/in_place\n \n \n std::in_place_tag\n cpp/utility/in_place_tag\n \n \n std::in_place_type_t\n cpp/utility/in_place\n \n \n std::independent_bits_engine\n cpp/numeric/random/independent_bits_engine\n \n T\n base\n cpp/numeric/random/independent_bits_engine/base\n \n (T... args)\n \n \n T\n discard\n cpp/numeric/random/independent_bits_engine/discard\n \n (T... args)\n \n \n T\n independent_bits_engine\n cpp/numeric/random/independent_bits_engine/independent_bits_engine\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/independent_bits_engine/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/independent_bits_engine/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/independent_bits_engine/operator()\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/independent_bits_engine/seed\n \n (T... args)\n \n \n \n std::index_sequence\n cpp/utility/integer_sequence\n \n \n std::index_sequence_for\n cpp/utility/integer_sequence\n \n \n std::indirect_array\n cpp/numeric/valarray/indirect_array\n \n \n std::initializer_list\n cpp/utility/initializer_list\n \n T\n begin\n cpp/utility/initializer_list/begin\n \n (T... args)\n \n \n T\n end\n cpp/utility/initializer_list/end\n \n (T... args)\n \n \n T\n initializer_list\n cpp/utility/initializer_list/initializer_list\n \n (T... args)\n \n \n T\n size\n cpp/utility/initializer_list/size\n \n (T... args)\n \n \n \n std::input_iterator_tag\n cpp/iterator/iterator_tags\n \n \n std::insert_iterator\n cpp/iterator/insert_iterator\n \n \n std::int16_t\n cpp/types/integer\n \n \n std::int32_t\n cpp/types/integer\n \n \n std::int64_t\n cpp/types/integer\n \n \n std::int8_t\n cpp/types/integer\n \n \n std::int_fast16_t\n cpp/types/integer\n \n \n std::int_fast32_t\n cpp/types/integer\n \n \n std::int_fast64_t\n cpp/types/integer\n \n \n std::int_fast8_t\n cpp/types/integer\n \n \n std::int_least16_t\n cpp/types/integer\n \n \n std::int_least32_t\n cpp/types/integer\n \n \n std::int_least64_t\n cpp/types/integer\n \n \n std::int_least8_t\n cpp/types/integer\n \n \n std::integer_sequence\n cpp/utility/integer_sequence\n \n \n std::integral_constant\n cpp/types/integral_constant\n \n \n std::intmax_t\n cpp/types/integer\n \n \n std::intptr_t\n cpp/types/integer\n \n \n std::invalid_argument\n cpp/error/invalid_argument\n \n T\n invalid_argument\n cpp/error/invalid_argument\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::ios_base\n cpp/io/ios_base\n std::ios_base::Init\n std::ios_base::event_callback\n std::ios_base::failure\n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n imbue\n cpp/io/ios_base/imbue\n \n (T... args)\n \n \n T\n ios_base\n cpp/io/ios_base/ios_base\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n T\n ~ios_base\n cpp/io/ios_base/~ios_base\n \n (T... args)\n \n \n \n std::ios_base::Init\n cpp/io/ios_base/Init\n \n \n std::ios_base::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::ios_base::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::iostream\n cpp/io/basic_iostream\n std::iostream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::iostream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::iostream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iostream\n cpp/io/basic_iostream/basic_iostream\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::iostream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n T\n ~iostream\n cpp/io/basic_iostream/~basic_iostream\n \n (T... args)\n \n \n \n std::iostream::Init\n cpp/io/ios_base/Init\n \n \n std::iostream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::iostream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::iostream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::is_abstract\n cpp/types/is_abstract\n \n \n std::is_arithmetic\n cpp/types/is_arithmetic\n \n \n std::is_array\n cpp/types/is_array\n \n \n std::is_assignable\n cpp/types/is_assignable\n \n \n std::is_base_of\n cpp/types/is_base_of\n \n \n std::is_bind_expression\n cpp/utility/functional/is_bind_expression\n \n \n std::is_callable\n cpp/types/is_callable\n \n \n std::is_class\n cpp/types/is_class\n \n \n std::is_compound\n cpp/types/is_compound\n \n \n std::is_const\n cpp/types/is_const\n \n \n std::is_constructible\n cpp/types/is_constructible\n \n \n std::is_convertible\n cpp/types/is_convertible\n \n \n std::is_copy_assignable\n cpp/types/is_copy_assignable\n \n \n std::is_copy_constructible\n cpp/types/is_copy_constructible\n \n \n std::is_default_constructible\n cpp/types/is_default_constructible\n \n \n std::is_destructible\n cpp/types/is_destructible\n \n \n std::is_empty\n cpp/types/is_empty\n \n \n std::is_enum\n cpp/types/is_enum\n \n \n std::is_error_code_enum\n cpp/error/error_code/is_error_code_enum\n \n \n std::is_error_code_enum_v\n cpp/error/error_code/is_error_code_enum\n \n \n std::is_error_condition_enum\n cpp/error/error_condition/is_error_condition_enum\n \n \n std::is_execution_policy\n cpp/algorithm/is_execution_policy\n \n \n std::is_final\n cpp/types/is_final\n \n \n std::is_floating_point\n cpp/types/is_floating_point\n \n \n std::is_function\n cpp/types/is_function\n \n \n std::is_fundamental\n cpp/types/is_fundamental\n \n \n std::is_integral\n cpp/types/is_integral\n \n \n std::is_literal_type\n cpp/types/is_literal_type\n \n \n std::is_lvalue_reference\n cpp/types/is_lvalue_reference\n \n \n std::is_member_function_pointer\n cpp/types/is_member_function_pointer\n \n \n std::is_member_object_pointer\n cpp/types/is_member_object_pointer\n \n \n std::is_member_pointer\n cpp/types/is_member_pointer\n \n \n std::is_move_assignable\n cpp/types/is_move_assignable\n \n \n std::is_move_constructible\n cpp/types/is_move_constructible\n \n \n std::is_nothrow_assignable\n cpp/types/is_assignable\n \n \n std::is_nothrow_callable\n cpp/types/is_callable\n \n \n std::is_nothrow_constructible\n cpp/types/is_constructible\n \n \n std::is_nothrow_copy_assignable\n cpp/types/is_copy_assignable\n \n \n std::is_nothrow_copy_constructible\n cpp/types/is_copy_constructible\n \n \n std::is_nothrow_default_constructible\n cpp/types/is_default_constructible\n \n \n std::is_nothrow_destructible\n cpp/types/is_destructible\n \n \n std::is_nothrow_move_assignable\n cpp/types/is_move_assignable\n \n \n std::is_nothrow_move_constructible\n cpp/types/is_move_constructible\n \n \n std::is_nothrow_swappable\n cpp/types/is_swappable\n \n \n std::is_nothrow_swappable_with\n cpp/types/is_swappable_with\n \n \n std::is_null_pointer\n cpp/types/is_null_pointer\n \n \n std::is_object\n cpp/types/is_object\n \n \n std::is_placeholder\n cpp/utility/functional/is_placeholder\n \n \n std::is_pod\n cpp/types/is_pod\n \n \n std::is_pointer\n cpp/types/is_pointer\n \n \n std::is_polymorphic\n cpp/types/is_polymorphic\n \n \n std::is_reference\n cpp/types/is_reference\n \n \n std::is_rvalue_reference\n cpp/types/is_rvalue_reference\n \n \n std::is_same\n cpp/types/is_same\n \n \n std::is_scalar\n cpp/types/is_scalar\n \n \n std::is_signed\n cpp/types/is_signed\n \n \n std::is_standard_layout\n cpp/types/is_standard_layout\n \n \n std::is_swappable\n cpp/types/is_swappable\n \n \n std::is_swappable_with\n cpp/types/is_swappable_with\n \n \n std::is_trivial\n cpp/types/is_trivial\n \n \n std::is_trivially_assignable\n cpp/types/is_assignable\n \n \n std::is_trivially_constructible\n cpp/types/is_constructible\n \n \n std::is_trivially_copy_assignable\n cpp/types/is_copy_assignable\n \n \n std::is_trivially_copy_constructible\n cpp/types/is_copy_constructible\n \n \n std::is_trivially_copyable\n cpp/types/is_trivially_copyable\n \n \n std::is_trivially_default_constructible\n cpp/types/is_default_constructible\n \n \n std::is_trivially_destructible\n cpp/types/is_destructible\n \n \n std::is_trivially_move_assignable\n cpp/types/is_move_assignable\n \n \n std::is_trivially_move_constructible\n cpp/types/is_move_constructible\n \n \n std::is_union\n cpp/types/is_union\n \n \n std::is_unsigned\n cpp/types/is_unsigned\n \n \n std::is_void\n cpp/types/is_void\n \n \n std::is_volatile\n cpp/types/is_volatile\n \n \n std::istream\n cpp/io/basic_istream\n std::istream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::istream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::istream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n istream\n cpp/io/basic_istream/basic_istream\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n std::istream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n T\n ~istream\n cpp/io/basic_istream/~basic_istream\n \n (T... args)\n \n \n \n std::istream::Init\n cpp/io/ios_base/Init\n \n \n std::istream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::istream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::istream::sentry\n cpp/io/basic_istream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::istream_iterator\n cpp/iterator/istream_iterator\n \n \n std::istreambuf_iterator\n cpp/iterator/istreambuf_iterator\n \n \n std::istringstream\n cpp/io/basic_istringstream\n std::istringstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::istringstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::istringstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n istringstream\n cpp/io/basic_istringstream/basic_istringstream\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_istringstream/operator=\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n std::istringstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n str\n cpp/io/basic_istringstream/str\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::istringstream::Init\n cpp/io/ios_base/Init\n \n \n std::istringstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::istringstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::istringstream::sentry\n cpp/io/basic_istream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::istrstream\n cpp/io/istrstream\n std::istrstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::istrstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::istrstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n istrstream\n cpp/io/istrstream/istrstream\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n std::istrstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n str\n cpp/io/istrstream/str\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n T\n ~istrstream\n cpp/io/istrstream/~istrstream\n \n (T... args)\n \n \n \n std::istrstream::Init\n cpp/io/ios_base/Init\n \n \n std::istrstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::istrstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::istrstream::sentry\n cpp/io/basic_istream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::iterator\n cpp/iterator/iterator\n \n \n std::iterator_traits\n cpp/iterator/iterator_traits\n \n \n std::jmp_buf\n cpp/utility/program/jmp_buf\n \n \n std::kilo\n cpp/numeric/ratio/ratio\n \n \n std::knuth_b\n cpp/numeric/random/shuffle_order_engine\n \n T\n base\n cpp/numeric/random/shuffle_order_engine/base\n \n (T... args)\n \n \n T\n discard\n cpp/numeric/random/shuffle_order_engine/discard\n \n (T... args)\n \n \n T\n knuth_b\n cpp/numeric/random/shuffle_order_engine/shuffle_order_engine\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/shuffle_order_engine/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/shuffle_order_engine/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/shuffle_order_engine/operator()\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/shuffle_order_engine/seed\n \n (T... args)\n \n \n \n std::lconv\n cpp/locale/lconv\n \n \n std::ldiv_t\n cpp/numeric/math/div\n \n T\n quot\n cpp/numeric/math/div\n \n \n \n \n T\n rem\n cpp/numeric/math/div\n \n \n \n \n \n std::length_error\n cpp/error/length_error\n \n T\n length_error\n cpp/error/length_error\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::less\n cpp/utility/functional/less\n \n T\n operator()\n cpp/utility/functional/less\n \n (T... args)\n \n \n \n std::less_equal\n cpp/utility/functional/less_equal\n \n T\n operator()\n cpp/utility/functional/less_equal\n \n (T... args)\n \n \n \n std::linear_congruential_engine\n cpp/numeric/random/linear_congruential_engine\n \n T\n discard\n cpp/numeric/random/linear_congruential_engine/discard\n \n (T... args)\n \n \n T\n linear_congruential_engine\n cpp/numeric/random/linear_congruential_engine/linear_congruential_engine\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/linear_congruential_engine/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/linear_congruential_engine/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/linear_congruential_engine/operator()\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/linear_congruential_engine/seed\n \n (T... args)\n \n \n \n std::list\n cpp/container/list\n \n T\n assign\n cpp/container/list/assign\n \n (T... args)\n \n \n T\n back\n cpp/container/list/back\n \n (T... args)\n \n \n T\n begin\n cpp/container/list/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/list/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/list/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/list/clear\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/list/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/list/rend\n \n (T... args)\n \n \n T\n emplace\n cpp/container/list/emplace\n \n (T... args)\n \n \n T\n emplace_back\n cpp/container/list/emplace_back\n \n (T... args)\n \n \n T\n emplace_front\n cpp/container/list/emplace_front\n \n (T... args)\n \n \n T\n empty\n cpp/container/list/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/list/end\n \n (T... args)\n \n \n T\n erase\n cpp/container/list/erase\n \n (T... args)\n \n \n T\n front\n cpp/container/list/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/list/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/container/list/insert\n \n (T... args)\n \n \n T\n list\n cpp/container/list/list\n \n (T... args)\n \n \n T\n max_size\n cpp/container/list/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/list/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/list/operator=\n \n (T... args)\n \n \n T\n pop_back\n cpp/container/list/pop_back\n \n (T... args)\n \n \n T\n pop_front\n cpp/container/list/pop_front\n \n (T... args)\n \n \n T\n push_back\n cpp/container/list/push_back\n \n (T... args)\n \n \n T\n push_front\n cpp/container/list/push_front\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/list/rbegin\n \n (T... args)\n \n \n T\n remove\n cpp/container/list/remove\n \n (T... args)\n \n \n T\n remove_if\n cpp/container/list/remove\n \n (T... args)\n \n \n T\n rend\n cpp/container/list/rend\n \n (T... args)\n \n \n T\n resize\n cpp/container/list/resize\n \n (T... args)\n \n \n T\n reverse\n cpp/container/list/reverse\n \n (T... args)\n \n \n T\n size\n cpp/container/list/size\n \n (T... args)\n \n \n T\n sort\n cpp/container/list/sort\n \n (T... args)\n \n \n T\n splice\n cpp/container/list/splice\n \n (T... args)\n \n \n T\n swap\n cpp/container/list/swap\n \n (T... args)\n \n \n T\n unique\n cpp/container/list/unique\n \n (T... args)\n \n \n T\n ~list\n cpp/container/list/~list\n \n (T... args)\n \n \n \n std::lldiv_t\n cpp/numeric/math/div\n \n T\n quot\n cpp/numeric/math/div\n \n \n \n \n T\n rem\n cpp/numeric/math/div\n \n \n \n \n \n std::locale\n cpp/locale/locale\n \n T\n classic\n cpp/locale/locale/classic\n \n (T... args)\n \n \n T\n combine\n cpp/locale/locale/combine\n \n (T... args)\n \n std::locale::facet\n \n T\n global\n cpp/locale/locale/global\n \n (T... args)\n \n std::locale::id\n \n T\n locale\n cpp/locale/locale/locale\n \n (T... args)\n \n \n T\n name\n cpp/locale/locale/name\n \n (T... args)\n \n \n T\n operator!=\n cpp/locale/locale/operator_cmp\n \n (T... args)\n \n \n T\n operator()\n cpp/locale/locale/operator()\n \n (T... args)\n \n \n T\n operator=\n cpp/locale/locale/operator=\n \n (T... args)\n \n \n T\n operator==\n cpp/locale/locale/operator_cmp\n \n (T... args)\n \n \n T\n ~locale\n cpp/locale/locale/~locale\n \n (T... args)\n \n \n \n std::locale::facet\n cpp/locale/locale/facet\n \n T\n facet\n cpp/locale/locale/facet/facet\n \n (T... args)\n \n \n \n std::locale::id\n cpp/locale/locale/id\n \n T\n id\n cpp/locale/locale/id/id\n \n (T... args)\n \n \n \n std::lock_guard\n cpp/thread/lock_guard\n \n T\n lock_guard\n cpp/thread/lock_guard/lock_guard\n \n (T... args)\n \n \n T\n ~lock_guard\n cpp/thread/lock_guard/~lock_guard\n \n (T... args)\n \n \n \n std::logic_error\n cpp/error/logic_error\n \n T\n logic_error\n cpp/error/logic_error\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::logical_and\n cpp/utility/functional/logical_and\n \n T\n operator()\n cpp/utility/functional/logical_and\n \n (T... args)\n \n \n \n std::logical_not\n cpp/utility/functional/logical_not\n \n T\n operator()\n cpp/utility/functional/logical_not\n \n (T... args)\n \n \n \n std::logical_or\n cpp/utility/functional/logical_or\n \n T\n operator()\n cpp/utility/functional/logical_or\n \n (T... args)\n \n \n \n std::lognormal_distribution\n cpp/numeric/random/lognormal_distribution\n \n T\n lognormal_distribution\n cpp/numeric/random/lognormal_distribution/lognormal_distribution\n \n (T... args)\n \n \n T\n m\n cpp/numeric/random/lognormal_distribution/params\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/lognormal_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/lognormal_distribution/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/lognormal_distribution/operator()\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/lognormal_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/lognormal_distribution/reset\n \n (T... args)\n \n \n T\n s\n cpp/numeric/random/lognormal_distribution/params\n \n (T... args)\n \n \n \n std::make_boyer_moore_horspool_searcher\n cpp/utility/functional/boyer_moore_horspool_searcher\n \n \n std::make_boyer_moore_searcher\n cpp/utility/functional/boyer_moore_searcher\n \n \n std::make_default_searcher\n cpp/utility/functional/default_searcher\n \n \n std::make_index_sequence\n cpp/utility/integer_sequence\n \n \n std::make_integer_sequence\n cpp/utility/integer_sequence\n \n \n std::make_signed\n cpp/types/make_signed\n \n \n std::make_signed_t\n cpp/types/make_signed\n \n \n std::make_unsigned\n cpp/types/make_unsigned\n \n \n std::make_unsigned_t\n cpp/types/make_unsigned\n \n \n std::map\n cpp/container/map\n \n T\n at\n cpp/container/map/at\n \n (T... args)\n \n \n T\n begin\n cpp/container/map/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/map/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/map/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/map/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/map/count\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/map/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/map/rend\n \n (T... args)\n \n \n T\n emplace\n cpp/container/map/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/map/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/map/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/map/end\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/map/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/map/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/map/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/map/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/map/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/container/map/insert\n \n (T... args)\n \n \n T\n insert_or_assign\n cpp/container/map/insert_or_assign\n \n (T... args)\n \n \n T\n key_comp\n cpp/container/map/key_comp\n \n (T... args)\n \n \n T\n lower_bound\n cpp/container/map/lower_bound\n \n (T... args)\n \n \n T\n map\n cpp/container/map/map\n \n (T... args)\n \n \n T\n max_size\n cpp/container/map/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/map/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/map/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/container/map/operator_at\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/map/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/container/map/rend\n \n (T... args)\n \n \n T\n size\n cpp/container/map/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/map/swap\n \n (T... args)\n \n \n T\n try_emplace\n cpp/container/map/try_emplace\n \n (T... args)\n \n \n T\n upper_bound\n cpp/container/map/upper_bound\n \n (T... args)\n \n \n T\n value_comp\n cpp/container/map/value_comp\n \n (T... args)\n \n std::map::value_compare\n \n T\n ~map\n cpp/container/map/~map\n \n (T... args)\n \n \n \n std::map::value_compare\n cpp/container/map/value_compare\n \n \n std::mask_array\n cpp/numeric/valarray/mask_array\n \n \n std::match_results\n cpp/regex/match_results\n \n T\n begin\n cpp/regex/match_results/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/regex/match_results/begin\n \n (T... args)\n \n \n T\n cend\n cpp/regex/match_results/end\n \n (T... args)\n \n \n T\n empty\n cpp/regex/match_results/empty\n \n (T... args)\n \n \n T\n end\n cpp/regex/match_results/end\n \n (T... args)\n \n \n T\n format\n cpp/regex/match_results/format\n \n (T... args)\n \n \n T\n get_allocator\n cpp/regex/match_results/get_allocator\n \n (T... args)\n \n \n T\n length\n cpp/regex/match_results/length\n \n (T... args)\n \n \n T\n match_results\n cpp/regex/match_results/match_results\n \n (T... args)\n \n \n T\n max_size\n cpp/regex/match_results/max_size\n \n (T... args)\n \n \n T\n operator[]\n cpp/regex/match_results/operator_at\n \n (T... args)\n \n \n T\n position\n cpp/regex/match_results/position\n \n (T... args)\n \n \n T\n prefix\n cpp/regex/match_results/prefix\n \n (T... args)\n \n \n T\n ready\n cpp/regex/match_results/ready\n \n (T... args)\n \n \n T\n size\n cpp/regex/match_results/size\n \n (T... args)\n \n \n T\n str\n cpp/regex/match_results/str\n \n (T... args)\n \n \n T\n suffix\n cpp/regex/match_results/suffix\n \n (T... args)\n \n \n T\n swap\n cpp/regex/match_results/swap\n \n (T... args)\n \n \n T\n ~match_results\n cpp/regex/match_results/~match_results\n \n (T... args)\n \n \n \n std::max_align_t\n cpp/types/max_align_t\n \n \n std::mbstate_t\n cpp/string/multibyte/mbstate_t\n \n \n std::mega\n cpp/numeric/ratio/ratio\n \n \n std::mersenne_twister_engine\n cpp/numeric/random/mersenne_twister_engine\n \n T\n discard\n cpp/numeric/random/mersenne_twister_engine/discard\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/mersenne_twister_engine/max\n \n (T... args)\n \n \n T\n mersenne_twister_engine\n cpp/numeric/random/mersenne_twister_engine/mersenne_twister_engine\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/mersenne_twister_engine/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/mersenne_twister_engine/operator()\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/mersenne_twister_engine/seed\n \n (T... args)\n \n \n \n std::messages\n cpp/locale/messages\n std::messages::catalog\n std::messages::char_type\n \n T\n close\n cpp/locale/messages/close\n \n (T... args)\n \n \n T\n do_close\n cpp/locale/messages/close\n \n (T... args)\n \n \n T\n do_get\n cpp/locale/messages/get\n \n (T... args)\n \n \n T\n do_open\n cpp/locale/messages/open\n \n (T... args)\n \n \n T\n get\n cpp/locale/messages/get\n \n (T... args)\n \n \n T\n messages\n cpp/locale/messages/messages\n \n (T... args)\n \n \n T\n open\n cpp/locale/messages/open\n \n (T... args)\n \n std::messages::string_type\n \n T\n ~messages\n cpp/locale/messages/~messages\n \n (T... args)\n \n \n \n std::messages::catalog\n cpp/locale/messages_base\n \n \n std::messages::char_type\n cpp/locale/messages\n \n \n std::messages::string_type\n cpp/locale/messages\n \n \n std::messages_base\n cpp/locale/messages_base\n std::messages_base::catalog\n \n \n std::messages_base::catalog\n cpp/locale/messages_base\n \n \n std::messages_byname\n cpp/locale/messages_byname\n std::messages_byname::catalog\n std::messages_byname::char_type\n \n T\n close\n cpp/locale/messages/close\n \n (T... args)\n \n \n T\n do_close\n cpp/locale/messages/close\n \n (T... args)\n \n \n T\n do_get\n cpp/locale/messages/get\n \n (T... args)\n \n \n T\n do_open\n cpp/locale/messages/open\n \n (T... args)\n \n \n T\n get\n cpp/locale/messages/get\n \n (T... args)\n \n \n T\n messages_byname\n cpp/locale/messages_byname\n \n (T... args)\n \n \n T\n open\n cpp/locale/messages/open\n \n (T... args)\n \n std::messages_byname::string_type\n \n T\n ~messages_byname\n cpp/locale/messages_byname\n \n (T... args)\n \n \n \n std::messages_byname::catalog\n cpp/locale/messages_base\n \n \n std::messages_byname::char_type\n cpp/locale/messages\n \n \n std::messages_byname::string_type\n cpp/locale/messages\n \n \n std::micro\n cpp/numeric/ratio/ratio\n \n \n std::milli\n cpp/numeric/ratio/ratio\n \n \n std::minstd_rand\n cpp/numeric/random/linear_congruential_engine\n \n T\n discard\n cpp/numeric/random/linear_congruential_engine/discard\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/linear_congruential_engine/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/linear_congruential_engine/min\n \n (T... args)\n \n \n T\n minstd_rand\n cpp/numeric/random/linear_congruential_engine/linear_congruential_engine\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/linear_congruential_engine/operator()\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/linear_congruential_engine/seed\n \n (T... args)\n \n \n \n std::minstd_rand0\n cpp/numeric/random/linear_congruential_engine\n \n T\n discard\n cpp/numeric/random/linear_congruential_engine/discard\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/linear_congruential_engine/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/linear_congruential_engine/min\n \n (T... args)\n \n \n T\n minstd_rand0\n cpp/numeric/random/linear_congruential_engine/linear_congruential_engine\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/linear_congruential_engine/operator()\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/linear_congruential_engine/seed\n \n (T... args)\n \n \n \n std::minus\n cpp/utility/functional/minus\n \n T\n operator()\n cpp/utility/functional/minus\n \n (T... args)\n \n \n \n std::modulus\n cpp/utility/functional/modulus\n \n T\n operator()\n cpp/utility/functional/modulus\n \n (T... args)\n \n \n \n std::money_base\n cpp/locale/money_base\n std::money_base::pattern\n \n \n std::money_base::pattern\n cpp/locale/money_base\n \n \n std::money_get\n cpp/locale/money_get\n std::money_get::char_type\n \n T\n do_get\n cpp/locale/money_get/get\n \n (T... args)\n \n \n T\n get\n cpp/locale/money_get/get\n \n (T... args)\n \n std::money_get::iter_type\n \n T\n money_get\n cpp/locale/money_get/money_get\n \n (T... args)\n \n std::money_get::pattern\n std::money_get::string_type\n \n T\n ~money_get\n cpp/locale/money_get/~money_get\n \n (T... args)\n \n \n \n std::money_get::char_type\n cpp/locale/money_get\n \n \n std::money_get::iter_type\n cpp/locale/money_get\n \n \n std::money_get::pattern\n cpp/locale/money_base\n \n \n std::money_get::string_type\n cpp/locale/money_get\n \n \n std::money_put\n cpp/locale/money_put\n std::money_put::char_type\n \n T\n do_put\n cpp/locale/money_put/put\n \n (T... args)\n \n std::money_put::iter_type\n \n T\n money_put\n cpp/locale/money_put/money_put\n \n (T... args)\n \n std::money_put::pattern\n \n T\n put\n cpp/locale/money_put/put\n \n (T... args)\n \n std::money_put::string_type\n \n T\n ~money_put\n cpp/locale/money_put/~money_put\n \n (T... args)\n \n \n \n std::money_put::char_type\n cpp/locale/money_put\n \n \n std::money_put::iter_type\n cpp/locale/money_put\n \n \n std::money_put::pattern\n cpp/locale/money_base\n \n \n std::money_put::string_type\n cpp/locale/money_put\n \n \n std::moneypunct\n cpp/locale/moneypunct\n std::moneypunct::char_type\n \n T\n curr_symbol\n cpp/locale/moneypunct/curr_symbol\n \n (T... args)\n \n \n T\n decimal_point\n cpp/locale/moneypunct/decimal_point\n \n (T... args)\n \n \n T\n do_curr_symbol\n cpp/locale/moneypunct/curr_symbol\n \n (T... args)\n \n \n T\n do_decimal_point\n cpp/locale/moneypunct/decimal_point\n \n (T... args)\n \n \n T\n do_frac_digits\n cpp/locale/moneypunct/frac_digits\n \n (T... args)\n \n \n T\n do_grouping\n cpp/locale/moneypunct/grouping\n \n (T... args)\n \n \n T\n do_neg_format\n cpp/locale/moneypunct/pos_format\n \n (T... args)\n \n \n T\n do_negative_sign\n cpp/locale/moneypunct/positive_sign\n \n (T... args)\n \n \n T\n do_pos_format\n cpp/locale/moneypunct/pos_format\n \n (T... args)\n \n \n T\n do_positive_sign\n cpp/locale/moneypunct/positive_sign\n \n (T... args)\n \n \n T\n do_thousands_sep\n cpp/locale/moneypunct/thousands_sep\n \n (T... args)\n \n \n T\n frac_digits\n cpp/locale/moneypunct/frac_digits\n \n (T... args)\n \n \n T\n grouping\n cpp/locale/moneypunct/grouping\n \n (T... args)\n \n \n T\n moneypunct\n cpp/locale/moneypunct/moneypunct\n \n (T... args)\n \n \n T\n neg_format\n cpp/locale/moneypunct/pos_format\n \n (T... args)\n \n \n T\n negative_sign\n cpp/locale/moneypunct/positive_sign\n \n (T... args)\n \n std::moneypunct::pattern\n \n T\n pos_format\n cpp/locale/moneypunct/pos_format\n \n (T... args)\n \n \n T\n positive_sign\n cpp/locale/moneypunct/positive_sign\n \n (T... args)\n \n std::moneypunct::string_type\n \n T\n thousands_sep\n cpp/locale/moneypunct/thousands_sep\n \n (T... args)\n \n \n T\n ~moneypunct\n cpp/locale/moneypunct/~moneypunct\n \n (T... args)\n \n \n \n std::moneypunct::char_type\n cpp/locale/moneypunct\n \n \n std::moneypunct::pattern\n cpp/locale/money_base\n \n \n std::moneypunct::string_type\n cpp/locale/moneypunct\n \n \n std::moneypunct_byname\n cpp/locale/moneypunct_byname\n std::moneypunct_byname::char_type\n \n T\n curr_symbol\n cpp/locale/moneypunct/curr_symbol\n \n (T... args)\n \n \n T\n decimal_point\n cpp/locale/moneypunct/decimal_point\n \n (T... args)\n \n \n T\n do_curr_symbol\n cpp/locale/moneypunct/curr_symbol\n \n (T... args)\n \n \n T\n do_decimal_point\n cpp/locale/moneypunct/decimal_point\n \n (T... args)\n \n \n T\n do_frac_digits\n cpp/locale/moneypunct/frac_digits\n \n (T... args)\n \n \n T\n do_grouping\n cpp/locale/moneypunct/grouping\n \n (T... args)\n \n \n T\n do_neg_format\n cpp/locale/moneypunct/pos_format\n \n (T... args)\n \n \n T\n do_negative_sign\n cpp/locale/moneypunct/positive_sign\n \n (T... args)\n \n \n T\n do_pos_format\n cpp/locale/moneypunct/pos_format\n \n (T... args)\n \n \n T\n do_positive_sign\n cpp/locale/moneypunct/positive_sign\n \n (T... args)\n \n \n T\n do_thousands_sep\n cpp/locale/moneypunct/thousands_sep\n \n (T... args)\n \n \n T\n frac_digits\n cpp/locale/moneypunct/frac_digits\n \n (T... args)\n \n \n T\n grouping\n cpp/locale/moneypunct/grouping\n \n (T... args)\n \n \n T\n moneypunct_byname\n cpp/locale/moneypunct_byname\n \n (T... args)\n \n \n T\n neg_format\n cpp/locale/moneypunct/pos_format\n \n (T... args)\n \n \n T\n negative_sign\n cpp/locale/moneypunct/positive_sign\n \n (T... args)\n \n std::moneypunct_byname::pattern\n \n T\n pos_format\n cpp/locale/moneypunct/pos_format\n \n (T... args)\n \n \n T\n positive_sign\n cpp/locale/moneypunct/positive_sign\n \n (T... args)\n \n std::moneypunct_byname::string_type\n \n T\n thousands_sep\n cpp/locale/moneypunct/thousands_sep\n \n (T... args)\n \n \n T\n ~moneypunct_byname\n cpp/locale/moneypunct_byname\n \n (T... args)\n \n \n \n std::moneypunct_byname::char_type\n cpp/locale/moneypunct\n \n \n std::moneypunct_byname::pattern\n cpp/locale/money_base\n \n \n std::moneypunct_byname::string_type\n cpp/locale/moneypunct\n \n \n std::monostate\n cpp/utility/variant/monostate\n \n T\n monostate\n cpp/utility/variant/monostate/monostate\n \n (T... args)\n \n \n T\n operator=\n cpp/utility/variant/monostate/operator=\n \n (T... args)\n \n \n T\n ~monostate\n cpp/utility/variant/monostate/~monostate\n \n (T... args)\n \n \n \n std::move_iterator\n cpp/iterator/move_iterator\n \n \n std::mt19937\n cpp/numeric/random/mersenne_twister_engine\n \n T\n discard\n cpp/numeric/random/mersenne_twister_engine/discard\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/mersenne_twister_engine/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/mersenne_twister_engine/min\n \n (T... args)\n \n \n T\n mt19937\n cpp/numeric/random/mersenne_twister_engine/mersenne_twister_engine\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/mersenne_twister_engine/operator()\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/mersenne_twister_engine/seed\n \n (T... args)\n \n \n \n std::mt19937_64\n cpp/numeric/random/mersenne_twister_engine\n \n T\n discard\n cpp/numeric/random/mersenne_twister_engine/discard\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/mersenne_twister_engine/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/mersenne_twister_engine/min\n \n (T... args)\n \n \n T\n mt19937_64\n cpp/numeric/random/mersenne_twister_engine/mersenne_twister_engine\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/mersenne_twister_engine/operator()\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/mersenne_twister_engine/seed\n \n (T... args)\n \n \n \n std::multimap\n cpp/container/multimap\n \n T\n begin\n cpp/container/multimap/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/multimap/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/multimap/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/multimap/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/multimap/count\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/multimap/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/multimap/rend\n \n (T... args)\n \n \n T\n emplace\n cpp/container/multimap/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/multimap/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/multimap/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/multimap/end\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/multimap/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/multimap/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/multimap/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/multimap/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/multimap/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/container/multimap/insert\n \n (T... args)\n \n \n T\n key_comp\n cpp/container/multimap/key_comp\n \n (T... args)\n \n \n T\n lower_bound\n cpp/container/multimap/lower_bound\n \n (T... args)\n \n \n T\n max_size\n cpp/container/multimap/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/multimap/merge\n \n (T... args)\n \n \n T\n multimap\n cpp/container/multimap/multimap\n \n (T... args)\n \n \n T\n operator=\n cpp/container/multimap/operator=\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/multimap/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/container/multimap/rend\n \n (T... args)\n \n \n T\n size\n cpp/container/multimap/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/multimap/swap\n \n (T... args)\n \n \n T\n upper_bound\n cpp/container/multimap/upper_bound\n \n (T... args)\n \n \n T\n value_comp\n cpp/container/multimap/value_comp\n \n (T... args)\n \n std::multimap::value_compare\n \n T\n ~multimap\n cpp/container/multimap/~multimap\n \n (T... args)\n \n \n \n std::multimap::value_compare\n cpp/container/multimap/value_compare\n \n \n std::multiplies\n cpp/utility/functional/multiplies\n \n T\n operator()\n cpp/utility/functional/multiplies\n \n (T... args)\n \n \n \n std::multiset\n cpp/container/multiset\n \n T\n begin\n cpp/container/multiset/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/multiset/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/multiset/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/multiset/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/multiset/count\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/multiset/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/multiset/rend\n \n (T... args)\n \n \n T\n emplace\n cpp/container/multiset/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/multiset/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/multiset/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/multiset/end\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/multiset/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/multiset/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/multiset/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/multiset/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/multiset/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/container/multiset/insert\n \n (T... args)\n \n \n T\n key_comp\n cpp/container/multiset/key_comp\n \n (T... args)\n \n \n T\n lower_bound\n cpp/container/multiset/lower_bound\n \n (T... args)\n \n \n T\n max_size\n cpp/container/multiset/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/multiset/merge\n \n (T... args)\n \n \n T\n multiset\n cpp/container/multiset/multiset\n \n (T... args)\n \n \n T\n operator=\n cpp/container/multiset/operator=\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/multiset/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/container/multiset/rend\n \n (T... args)\n \n \n T\n size\n cpp/container/multiset/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/multiset/swap\n \n (T... args)\n \n \n T\n upper_bound\n cpp/container/multiset/upper_bound\n \n (T... args)\n \n \n T\n value_comp\n cpp/container/multiset/value_comp\n \n (T... args)\n \n \n T\n ~multiset\n cpp/container/multiset/~multiset\n \n (T... args)\n \n \n \n std::mutex\n cpp/thread/mutex\n \n T\n lock\n cpp/thread/mutex/lock\n \n (T... args)\n \n \n T\n mutex\n cpp/thread/mutex/mutex\n \n (T... args)\n \n \n T\n native_handle\n cpp/thread/mutex/native_handle\n \n (T... args)\n \n \n T\n try_lock\n cpp/thread/mutex/try_lock\n \n (T... args)\n \n \n T\n unlock\n cpp/thread/mutex/unlock\n \n (T... args)\n \n \n \n std::nano\n cpp/numeric/ratio/ratio\n \n \n std::negate\n cpp/utility/functional/negate\n \n T\n operator()\n cpp/utility/functional/negate\n \n (T... args)\n \n \n \n std::negation\n cpp/types/negation\n \n \n std::negative_binomial_distribution\n cpp/numeric/random/negative_binomial_distribution\n \n T\n k\n cpp/numeric/random/negative_binomial_distribution/params\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/negative_binomial_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/negative_binomial_distribution/min\n \n (T... args)\n \n \n T\n negative_binomial_distribution\n cpp/numeric/random/negative_binomial_distribution/negative_binomial_distribution\n \n (T... args)\n \n \n T\n p\n cpp/numeric/random/negative_binomial_distribution/params\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/negative_binomial_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/negative_binomial_distribution/reset\n \n (T... args)\n \n \n \n std::nested_exception\n cpp/error/nested_exception\n \n T\n nested_exception\n cpp/error/nested_exception/nested_exception\n \n (T... args)\n \n \n T\n nested_ptr\n cpp/error/nested_exception/nested_ptr\n \n (T... args)\n \n \n T\n operator=\n cpp/error/nested_exception/operator=\n \n (T... args)\n \n \n T\n rethrow_nested\n cpp/error/nested_exception/rethrow_nested\n \n (T... args)\n \n \n T\n ~nested_exception\n cpp/error/nested_exception/~nested_exception\n \n (T... args)\n \n \n \n std::new_handler\n cpp/memory/new/new_handler\n \n \n std::normal_distribution\n cpp/numeric/random/normal_distribution\n \n T\n max\n cpp/numeric/random/normal_distribution/max\n \n (T... args)\n \n \n T\n mean\n cpp/numeric/random/normal_distribution/params\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/normal_distribution/min\n \n (T... args)\n \n \n T\n normal_distribution\n cpp/numeric/random/normal_distribution/normal_distribution\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/normal_distribution/operator()\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/normal_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/normal_distribution/reset\n \n (T... args)\n \n \n T\n stddev\n cpp/numeric/random/normal_distribution/params\n \n (T... args)\n \n \n \n std::not_equal_to\n cpp/utility/functional/not_equal_to\n \n T\n operator()\n cpp/utility/functional/not_equal_to\n \n (T... args)\n \n \n \n std::nothrow_t\n cpp/memory/new/nothrow_t\n \n \n std::nullopt_t\n cpp/utility/optional/nullopt_t\n \n \n std::nullptr_t\n cpp/types/nullptr_t\n \n \n std::num_get\n cpp/locale/num_get\n std::num_get::char_type\n \n T\n do_get\n cpp/locale/num_get/get\n \n (T... args)\n \n \n T\n get\n cpp/locale/num_get/get\n \n (T... args)\n \n std::num_get::iter_type\n \n T\n num_get\n cpp/locale/num_get/num_get\n \n (T... args)\n \n \n T\n ~num_get\n cpp/locale/num_get/~num_get\n \n (T... args)\n \n \n \n std::num_get::char_type\n cpp/locale/num_get\n \n \n std::num_get::iter_type\n cpp/locale/num_get\n \n \n std::num_put\n cpp/locale/num_put\n std::num_put::char_type\n \n T\n do_put\n cpp/locale/num_put/put\n \n (T... args)\n \n std::num_put::iter_type\n \n T\n num_put\n cpp/locale/num_put/num_put\n \n (T... args)\n \n \n T\n put\n cpp/locale/num_put/put\n \n (T... args)\n \n \n T\n ~num_put\n cpp/locale/num_put/~num_put\n \n (T... args)\n \n \n \n std::num_put::char_type\n cpp/locale/num_put\n \n \n std::num_put::iter_type\n cpp/locale/num_put\n \n \n std::numeric_limits\n cpp/types/numeric_limits\n \n T\n denorm_min\n cpp/types/numeric_limits/denorm_min\n \n (T... args)\n \n \n T\n epsilon\n cpp/types/numeric_limits/epsilon\n \n (T... args)\n \n \n T\n infinity\n cpp/types/numeric_limits/infinity\n \n (T... args)\n \n \n T\n lowest\n cpp/types/numeric_limits/lowest\n \n (T... args)\n \n \n T\n max\n cpp/types/numeric_limits/max\n \n (T... args)\n \n \n T\n min\n cpp/types/numeric_limits/min\n \n (T... args)\n \n \n T\n quiet_NaN\n cpp/types/numeric_limits/quiet_NaN\n \n (T... args)\n \n \n T\n round_error\n cpp/types/numeric_limits/round_error\n \n (T... args)\n \n \n T\n signaling_NaN\n cpp/types/numeric_limits/signaling_NaN\n \n (T... args)\n \n \n \n std::numpunct\n cpp/locale/numpunct\n std::numpunct::char_type\n \n T\n decimal_point\n cpp/locale/numpunct/decimal_point\n \n (T... args)\n \n \n T\n do_decimal_point\n cpp/locale/numpunct/decimal_point\n \n (T... args)\n \n \n T\n do_falsename\n cpp/locale/numpunct/truefalsename\n \n (T... args)\n \n \n T\n do_grouping\n cpp/locale/numpunct/grouping\n \n (T... args)\n \n \n T\n do_thousands_sep\n cpp/locale/numpunct/thousands_sep\n \n (T... args)\n \n \n T\n do_truename\n cpp/locale/numpunct/truefalsename\n \n (T... args)\n \n \n T\n falsename\n cpp/locale/numpunct/truefalsename\n \n (T... args)\n \n \n T\n grouping\n cpp/locale/numpunct/grouping\n \n (T... args)\n \n \n T\n numpunct\n cpp/locale/numpunct/numpunct\n \n (T... args)\n \n std::numpunct::string_type\n \n T\n thousands_sep\n cpp/locale/numpunct/thousands_sep\n \n (T... args)\n \n \n T\n truename\n cpp/locale/numpunct/truefalsename\n \n (T... args)\n \n \n T\n ~numpunct\n cpp/locale/numpunct/~numpunct\n \n (T... args)\n \n \n \n std::numpunct::char_type\n cpp/locale/numpunct\n \n \n std::numpunct::string_type\n cpp/locale/numpunct\n \n \n std::numpunct_byname\n cpp/locale/numpunct_byname\n std::numpunct_byname::char_type\n \n T\n decimal_point\n cpp/locale/numpunct/decimal_point\n \n (T... args)\n \n \n T\n do_decimal_point\n cpp/locale/numpunct/decimal_point\n \n (T... args)\n \n \n T\n do_falsename\n cpp/locale/numpunct/truefalsename\n \n (T... args)\n \n \n T\n do_grouping\n cpp/locale/numpunct/grouping\n \n (T... args)\n \n \n T\n do_thousands_sep\n cpp/locale/numpunct/thousands_sep\n \n (T... args)\n \n \n T\n do_truename\n cpp/locale/numpunct/truefalsename\n \n (T... args)\n \n \n T\n falsename\n cpp/locale/numpunct/truefalsename\n \n (T... args)\n \n \n T\n grouping\n cpp/locale/numpunct/grouping\n \n (T... args)\n \n \n T\n numpunct_byname\n cpp/locale/numpunct_byname\n \n (T... args)\n \n std::numpunct_byname::string_type\n \n T\n thousands_sep\n cpp/locale/numpunct/thousands_sep\n \n (T... args)\n \n \n T\n truename\n cpp/locale/numpunct/truefalsename\n \n (T... args)\n \n \n T\n ~numpunct_byname\n cpp/locale/numpunct_byname\n \n (T... args)\n \n \n \n std::numpunct_byname::char_type\n cpp/locale/numpunct\n \n \n std::numpunct_byname::string_type\n cpp/locale/numpunct\n \n \n std::ofstream\n cpp/io/basic_ofstream\n std::ofstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n close\n cpp/io/basic_ofstream/close\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::ofstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::ofstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n is_open\n cpp/io/basic_ofstream/is_open\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n ofstream\n cpp/io/basic_ofstream/basic_ofstream\n \n (T... args)\n \n \n T\n open\n cpp/io/basic_ofstream/open\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_ofstream/operator=\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::ofstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::ofstream::Init\n cpp/io/ios_base/Init\n \n \n std::ofstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::ofstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::ofstream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n \n std::once_flag\n cpp/thread/once_flag\n \n T\n once_flag\n cpp/thread/once_flag\n \n (T... args)\n \n \n \n std::optional\n cpp/utility/optional\n \n T\n emplace\n cpp/utility/optional/emplace\n \n (T... args)\n \n \n T\n has_value\n cpp/utility/optional/operator_bool\n \n (T... args)\n \n \n T\n operator bool\n cpp/utility/optional/operator_bool\n \n (T... args)\n \n \n T\n operator*\n cpp/utility/optional/operator*\n \n (T... args)\n \n \n T\n operator->\n cpp/utility/optional/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/utility/optional/operator=\n \n (T... args)\n \n \n T\n optional\n cpp/utility/optional/optional\n \n (T... args)\n \n \n T\n reset\n cpp/utility/optional/reset\n \n (T... args)\n \n \n T\n swap\n cpp/utility/optional/swap\n \n (T... args)\n \n \n T\n value\n cpp/utility/optional/value\n \n (T... args)\n \n \n T\n value_or\n cpp/utility/optional/value_or\n \n (T... args)\n \n \n T\n ~optional\n cpp/utility/optional/~optional\n \n (T... args)\n \n \n \n std::ostream\n cpp/io/basic_ostream\n std::ostream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::ostream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::ostream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n ostream\n cpp/io/basic_ostream/basic_ostream\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::ostream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n T\n ~ostream\n cpp/io/basic_ostream/~basic_ostream\n \n (T... args)\n \n \n \n std::ostream::Init\n cpp/io/ios_base/Init\n \n \n std::ostream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::ostream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::ostream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n \n std::ostream_iterator\n cpp/iterator/ostream_iterator\n \n \n std::ostreambuf_iterator\n cpp/iterator/ostreambuf_iterator\n \n \n std::ostringstream\n cpp/io/basic_ostringstream\n std::ostringstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::ostringstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::ostringstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_ostringstream/operator=\n \n (T... args)\n \n \n T\n ostringstream\n cpp/io/basic_ostringstream/basic_ostringstream\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::ostringstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n str\n cpp/io/basic_ostringstream/str\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::ostringstream::Init\n cpp/io/ios_base/Init\n \n \n std::ostringstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::ostringstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::ostringstream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n \n std::ostrstream\n cpp/io/ostrstream\n std::ostrstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::ostrstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::ostrstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n freeze\n cpp/io/ostrstream/freeze\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n ostrstream\n cpp/io/ostrstream/ostrstream\n \n (T... args)\n \n \n T\n pcount\n cpp/io/ostrstream/pcount\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::ostrstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n str\n cpp/io/ostrstream/str\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n T\n ~ostrstream\n cpp/io/ostrstream/~ostrstream\n \n (T... args)\n \n \n \n std::ostrstream::Init\n cpp/io/ios_base/Init\n \n \n std::ostrstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::ostrstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::ostrstream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n \n std::out_of_range\n cpp/error/out_of_range\n \n T\n out_of_range\n cpp/error/out_of_range\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::output_iterator_tag\n cpp/iterator/iterator_tags\n \n \n std::overflow_error\n cpp/error/overflow_error\n \n T\n overflow_error\n cpp/error/overflow_error\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::owner_less\n cpp/memory/owner_less\n \n T\n operator()\n cpp/memory/owner_less\n \n (T... args)\n \n \n \n std::packaged_task\n cpp/thread/packaged_task\n \n T\n get_future\n cpp/thread/packaged_task/get_future\n \n (T... args)\n \n \n T\n make_ready_at_thread_exit\n cpp/thread/packaged_task/make_ready_at_thread_exit\n \n (T... args)\n \n \n T\n operator()\n cpp/thread/packaged_task/operator()\n \n (T... args)\n \n \n T\n operator=\n cpp/thread/packaged_task/operator=\n \n (T... args)\n \n \n T\n packaged_task\n cpp/thread/packaged_task/packaged_task\n \n (T... args)\n \n \n T\n reset\n cpp/thread/packaged_task/reset\n \n (T... args)\n \n \n T\n swap\n cpp/thread/packaged_task/swap\n \n (T... args)\n \n \n T\n valid\n cpp/thread/packaged_task/valid\n \n (T... args)\n \n \n T\n ~packaged_task\n cpp/thread/packaged_task/~packaged_task\n \n (T... args)\n \n \n \n std::pair\n cpp/utility/pair\n \n T\n first\n cpp/utility/pair\n \n \n \n \n T\n operator=\n cpp/utility/pair/operator=\n \n (T... args)\n \n \n T\n pair\n cpp/utility/pair/pair\n \n (T... args)\n \n \n T\n second\n cpp/utility/pair\n \n \n \n \n T\n swap\n cpp/utility/pair/swap\n \n (T... args)\n \n \n \n std::peta\n cpp/numeric/ratio/ratio\n \n \n std::pico\n cpp/numeric/ratio/ratio\n \n \n std::piecewise_constant_distribution\n cpp/numeric/random/piecewise_constant_distribution\n \n T\n densities\n cpp/numeric/random/piecewise_constant_distribution/params\n \n (T... args)\n \n \n T\n intervals\n cpp/numeric/random/piecewise_constant_distribution/params\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/piecewise_constant_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/piecewise_constant_distribution/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/piecewise_constant_distribution/operator()\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/piecewise_constant_distribution/param\n \n (T... args)\n \n \n T\n piecewise_constant_distribution\n cpp/numeric/random/piecewise_constant_distribution/piecewise_constant_distribution\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/piecewise_constant_distribution/reset\n \n (T... args)\n \n \n \n std::piecewise_construct_t\n cpp/utility/piecewise_construct_t\n \n \n std::piecewise_linear_distribution\n cpp/numeric/random/piecewise_linear_distribution\n \n T\n densities\n cpp/numeric/random/piecewise_linear_distribution/params\n \n (T... args)\n \n \n T\n intervals\n cpp/numeric/random/piecewise_linear_distribution/params\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/piecewise_linear_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/piecewise_linear_distribution/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/piecewise_linear_distribution/operator()\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/piecewise_linear_distribution/param\n \n (T... args)\n \n \n T\n piecewise_linear_distribution\n cpp/numeric/random/piecewise_linear_distribution/piecewise_linear_distribution\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/piecewise_linear_distribution/reset\n \n (T... args)\n \n \n \n std::placeholders\n cpp/utility/functional/placeholders\n \n \n std::plus\n cpp/utility/functional/plus\n \n T\n operator()\n cpp/utility/functional/plus\n \n (T... args)\n \n \n \n std::pmr\n \n std::pmr::deque\n std::pmr::forward_list\n \n T\n get_default_resource\n cpp/memory/get_default_resource\n \n (T... args)\n \n std::pmr::list\n std::pmr::map\n std::pmr::memory_resource\n std::pmr::monotonic_buffer_resource\n std::pmr::multimap\n std::pmr::multiset\n \n T\n new_delete_resource\n cpp/memory/new_delete_resource\n \n (T... args)\n \n \n T\n null_memory_resource\n cpp/memory/null_memory_resource\n \n (T... args)\n \n std::pmr::polymorphic_allocator\n std::pmr::pool_options\n std::pmr::set\n \n T\n set_default_resource\n cpp/memory/set_default_resource\n \n (T... args)\n \n std::pmr::string\n std::pmr::synchronized_pool_resource\n std::pmr::u16string\n std::pmr::u32string\n std::pmr::unordered_map\n std::pmr::unordered_multimap\n std::pmr::unordered_multiset\n std::pmr::unordered_set\n std::pmr::unsynchronized_pool_resource\n std::pmr::vector\n std::pmr::wstring\n \n \n std::pmr::deque\n cpp/container/deque\n \n T\n assign\n cpp/container/deque/assign\n \n (T... args)\n \n \n T\n at\n cpp/container/deque/at\n \n (T... args)\n \n \n T\n back\n cpp/container/deque/back\n \n (T... args)\n \n \n T\n begin\n cpp/container/deque/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/deque/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/deque/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/deque/clear\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/deque/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/deque/rend\n \n (T... args)\n \n \n T\n deque\n cpp/container/deque/deque\n \n (T... args)\n \n \n T\n emplace\n cpp/container/deque/emplace\n \n (T... args)\n \n \n T\n emplace_back\n cpp/container/deque/emplace_back\n \n (T... args)\n \n \n T\n emplace_front\n cpp/container/deque/emplace_front\n \n (T... args)\n \n \n T\n empty\n cpp/container/deque/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/deque/end\n \n (T... args)\n \n \n T\n erase\n cpp/container/deque/erase\n \n (T... args)\n \n \n T\n front\n cpp/container/deque/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/deque/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/container/deque/insert\n \n (T... args)\n \n \n T\n max_size\n cpp/container/deque/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/container/deque/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/container/deque/operator_at\n \n (T... args)\n \n \n T\n pop_back\n cpp/container/deque/pop_back\n \n (T... args)\n \n \n T\n pop_front\n cpp/container/deque/pop_front\n \n (T... args)\n \n \n T\n push_back\n cpp/container/deque/push_back\n \n (T... args)\n \n \n T\n push_front\n cpp/container/deque/push_front\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/deque/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/container/deque/rend\n \n (T... args)\n \n \n T\n resize\n cpp/container/deque/resize\n \n (T... args)\n \n \n T\n shrink_to_fit\n cpp/container/deque/shrink_to_fit\n \n (T... args)\n \n \n T\n size\n cpp/container/deque/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/deque/swap\n \n (T... args)\n \n \n T\n ~deque\n cpp/container/deque/~deque\n \n (T... args)\n \n \n \n std::pmr::forward_list\n cpp/container/forward_list\n \n T\n assign\n cpp/container/forward_list/assign\n \n (T... args)\n \n \n T\n before_begin\n cpp/container/forward_list/before_begin\n \n (T... args)\n \n \n T\n begin\n cpp/container/forward_list/begin\n \n (T... args)\n \n \n T\n cbefore_begin\n cpp/container/forward_list/before_begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/forward_list/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/forward_list/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/forward_list/clear\n \n (T... args)\n \n \n T\n emplace_after\n cpp/container/forward_list/emplace_after\n \n (T... args)\n \n \n T\n emplace_front\n cpp/container/forward_list/emplace_front\n \n (T... args)\n \n \n T\n empty\n cpp/container/forward_list/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/forward_list/end\n \n (T... args)\n \n \n T\n erase_after\n cpp/container/forward_list/erase_after\n \n (T... args)\n \n \n T\n forward_list\n cpp/container/forward_list/forward_list\n \n (T... args)\n \n \n T\n front\n cpp/container/forward_list/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/forward_list/get_allocator\n \n (T... args)\n \n \n T\n insert_after\n cpp/container/forward_list/insert_after\n \n (T... args)\n \n \n T\n max_size\n cpp/container/forward_list/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/forward_list/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/forward_list/operator=\n \n (T... args)\n \n \n T\n pop_front\n cpp/container/forward_list/pop_front\n \n (T... args)\n \n \n T\n push_front\n cpp/container/forward_list/push_front\n \n (T... args)\n \n \n T\n remove\n cpp/container/forward_list/remove\n \n (T... args)\n \n \n T\n remove_if\n cpp/container/forward_list/remove\n \n (T... args)\n \n \n T\n resize\n cpp/container/forward_list/resize\n \n (T... args)\n \n \n T\n reverse\n cpp/container/forward_list/reverse\n \n (T... args)\n \n \n T\n sort\n cpp/container/forward_list/sort\n \n (T... args)\n \n \n T\n splice_after\n cpp/container/forward_list/splice_after\n \n (T... args)\n \n \n T\n swap\n cpp/container/forward_list/swap\n \n (T... args)\n \n \n T\n unique\n cpp/container/forward_list/unique\n \n (T... args)\n \n \n T\n ~forward_list\n cpp/container/forward_list/~forward_list\n \n (T... args)\n \n \n \n std::pmr::list\n cpp/container/list\n \n T\n assign\n cpp/container/list/assign\n \n (T... args)\n \n \n T\n back\n cpp/container/list/back\n \n (T... args)\n \n \n T\n begin\n cpp/container/list/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/list/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/list/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/list/clear\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/list/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/list/rend\n \n (T... args)\n \n \n T\n emplace\n cpp/container/list/emplace\n \n (T... args)\n \n \n T\n emplace_back\n cpp/container/list/emplace_back\n \n (T... args)\n \n \n T\n emplace_front\n cpp/container/list/emplace_front\n \n (T... args)\n \n \n T\n empty\n cpp/container/list/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/list/end\n \n (T... args)\n \n \n T\n erase\n cpp/container/list/erase\n \n (T... args)\n \n \n T\n front\n cpp/container/list/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/list/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/container/list/insert\n \n (T... args)\n \n \n T\n list\n cpp/container/list/list\n \n (T... args)\n \n \n T\n max_size\n cpp/container/list/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/list/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/list/operator=\n \n (T... args)\n \n \n T\n pop_back\n cpp/container/list/pop_back\n \n (T... args)\n \n \n T\n pop_front\n cpp/container/list/pop_front\n \n (T... args)\n \n \n T\n push_back\n cpp/container/list/push_back\n \n (T... args)\n \n \n T\n push_front\n cpp/container/list/push_front\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/list/rbegin\n \n (T... args)\n \n \n T\n remove\n cpp/container/list/remove\n \n (T... args)\n \n \n T\n remove_if\n cpp/container/list/remove\n \n (T... args)\n \n \n T\n rend\n cpp/container/list/rend\n \n (T... args)\n \n \n T\n resize\n cpp/container/list/resize\n \n (T... args)\n \n \n T\n reverse\n cpp/container/list/reverse\n \n (T... args)\n \n \n T\n size\n cpp/container/list/size\n \n (T... args)\n \n \n T\n sort\n cpp/container/list/sort\n \n (T... args)\n \n \n T\n splice\n cpp/container/list/splice\n \n (T... args)\n \n \n T\n swap\n cpp/container/list/swap\n \n (T... args)\n \n \n T\n unique\n cpp/container/list/unique\n \n (T... args)\n \n \n T\n ~list\n cpp/container/list/~list\n \n (T... args)\n \n \n \n std::pmr::map\n cpp/container/map\n \n T\n at\n cpp/container/map/at\n \n (T... args)\n \n \n T\n begin\n cpp/container/map/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/map/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/map/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/map/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/map/count\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/map/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/map/rend\n \n (T... args)\n \n \n T\n emplace\n cpp/container/map/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/map/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/map/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/map/end\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/map/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/map/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/map/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/map/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/map/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/container/map/insert\n \n (T... args)\n \n \n T\n insert_or_assign\n cpp/container/map/insert_or_assign\n \n (T... args)\n \n \n T\n key_comp\n cpp/container/map/key_comp\n \n (T... args)\n \n \n T\n lower_bound\n cpp/container/map/lower_bound\n \n (T... args)\n \n \n T\n map\n cpp/container/map/map\n \n (T... args)\n \n \n T\n max_size\n cpp/container/map/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/map/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/map/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/container/map/operator_at\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/map/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/container/map/rend\n \n (T... args)\n \n \n T\n size\n cpp/container/map/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/map/swap\n \n (T... args)\n \n \n T\n try_emplace\n cpp/container/map/try_emplace\n \n (T... args)\n \n \n T\n upper_bound\n cpp/container/map/upper_bound\n \n (T... args)\n \n \n T\n value_comp\n cpp/container/map/value_comp\n \n (T... args)\n \n std::pmr::map::value_compare\n \n T\n ~map\n cpp/container/map/~map\n \n (T... args)\n \n \n \n std::pmr::map::value_compare\n cpp/container/map/value_compare\n \n \n std::pmr::memory_resource\n cpp/memory/memory_resource\n \n T\n allocate\n cpp/memory/memory_resource/allocate\n \n (T... args)\n \n \n T\n deallocate\n cpp/memory/memory_resource/deallocate\n \n (T... args)\n \n \n T\n do_allocate\n cpp/memory/memory_resource/do_allocate\n \n (T... args)\n \n \n T\n do_deallocate\n cpp/memory/memory_resource/do_deallocate\n \n (T... args)\n \n \n T\n do_is_equal\n cpp/memory/memory_resource/do_is_equal\n \n (T... args)\n \n \n T\n is_equal\n cpp/memory/memory_resource/is_equal\n \n (T... args)\n \n \n T\n memory_resource\n cpp/memory/memory_resource/memory_resource\n \n (T... args)\n \n \n \n std::pmr::monotonic_buffer_resource\n cpp/memory/monotonic_buffer_resource\n \n T\n allocate\n cpp/memory/memory_resource/allocate\n \n (T... args)\n \n \n T\n deallocate\n cpp/memory/memory_resource/deallocate\n \n (T... args)\n \n \n T\n do_allocate\n cpp/memory/memory_resource/do_allocate\n \n (T... args)\n \n \n T\n do_deallocate\n cpp/memory/memory_resource/do_deallocate\n \n (T... args)\n \n \n T\n do_is_equal\n cpp/memory/memory_resource/do_is_equal\n \n (T... args)\n \n \n T\n is_equal\n cpp/memory/memory_resource/is_equal\n \n (T... args)\n \n \n T\n monotonic_buffer_resource\n cpp/memory/monotonic_buffer_resource/monotonic_buffer_resource\n \n (T... args)\n \n \n T\n release\n cpp/memory/monotonic_buffer_resource/release\n \n (T... args)\n \n \n T\n upstream_resource\n cpp/memory/monotonic_buffer_resource/upstream_resource\n \n (T... args)\n \n \n T\n ~monotonic_buffer_resource\n cpp/memory/monotonic_buffer_resource\n \n (T... args)\n \n \n \n std::pmr::multimap\n cpp/container/multimap\n \n T\n begin\n cpp/container/multimap/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/multimap/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/multimap/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/multimap/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/multimap/count\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/multimap/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/multimap/rend\n \n (T... args)\n \n \n T\n emplace\n cpp/container/multimap/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/multimap/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/multimap/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/multimap/end\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/multimap/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/multimap/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/multimap/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/multimap/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/multimap/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/container/multimap/insert\n \n (T... args)\n \n \n T\n key_comp\n cpp/container/multimap/key_comp\n \n (T... args)\n \n \n T\n lower_bound\n cpp/container/multimap/lower_bound\n \n (T... args)\n \n \n T\n max_size\n cpp/container/multimap/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/multimap/merge\n \n (T... args)\n \n \n T\n multimap\n cpp/container/multimap/multimap\n \n (T... args)\n \n \n T\n operator=\n cpp/container/multimap/operator=\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/multimap/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/container/multimap/rend\n \n (T... args)\n \n \n T\n size\n cpp/container/multimap/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/multimap/swap\n \n (T... args)\n \n \n T\n upper_bound\n cpp/container/multimap/upper_bound\n \n (T... args)\n \n \n T\n value_comp\n cpp/container/multimap/value_comp\n \n (T... args)\n \n std::pmr::multimap::value_compare\n \n T\n ~multimap\n cpp/container/multimap/~multimap\n \n (T... args)\n \n \n \n std::pmr::multimap::value_compare\n cpp/container/multimap/value_compare\n \n \n std::pmr::multiset\n cpp/container/multiset\n \n T\n begin\n cpp/container/multiset/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/multiset/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/multiset/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/multiset/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/multiset/count\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/multiset/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/multiset/rend\n \n (T... args)\n \n \n T\n emplace\n cpp/container/multiset/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/multiset/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/multiset/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/multiset/end\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/multiset/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/multiset/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/multiset/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/multiset/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/multiset/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/container/multiset/insert\n \n (T... args)\n \n \n T\n key_comp\n cpp/container/multiset/key_comp\n \n (T... args)\n \n \n T\n lower_bound\n cpp/container/multiset/lower_bound\n \n (T... args)\n \n \n T\n max_size\n cpp/container/multiset/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/multiset/merge\n \n (T... args)\n \n \n T\n multiset\n cpp/container/multiset/multiset\n \n (T... args)\n \n \n T\n operator=\n cpp/container/multiset/operator=\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/multiset/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/container/multiset/rend\n \n (T... args)\n \n \n T\n size\n cpp/container/multiset/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/multiset/swap\n \n (T... args)\n \n \n T\n upper_bound\n cpp/container/multiset/upper_bound\n \n (T... args)\n \n \n T\n value_comp\n cpp/container/multiset/value_comp\n \n (T... args)\n \n \n T\n ~multiset\n cpp/container/multiset/~multiset\n \n (T... args)\n \n \n \n std::pmr::polymorphic_allocator\n cpp/memory/polymorphic_allocator\n \n T\n allocate\n cpp/memory/polymorphic_allocator/allocate\n \n (T... args)\n \n \n T\n construct\n cpp/memory/polymorphic_allocator/construct\n \n (T... args)\n \n \n T\n deallocate\n cpp/memory/polymorphic_allocator/deallocate\n \n (T... args)\n \n \n T\n destroy\n cpp/memory/polymorphic_allocator/destroy\n \n (T... args)\n \n \n T\n polymorphic_allocator\n cpp/memory/polymorphic_allocator/polymorphic_allocator\n \n (T... args)\n \n \n T\n resource\n cpp/memory/polymorphic_allocator/resource\n \n (T... args)\n \n \n T\n select_on_container_copy_contruction\n cpp/memory/polymorphic_allocator/select_on_container_copy_contruction\n \n (T... args)\n \n \n T\n ~polymorphic_allocator\n cpp/memory/polymorphic_allocator\n \n (T... args)\n \n \n \n std::pmr::pool_options\n cpp/memory/pool_options\n \n T\n largest_required_pool_block\n cpp/memory/pool_options\n \n \n \n \n T\n max_blocks_per_chunk\n cpp/memory/pool_options\n \n \n \n \n \n std::pmr::set\n cpp/container/set\n \n T\n begin\n cpp/container/set/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/set/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/set/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/set/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/set/count\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/set/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/set/rend\n \n (T... args)\n \n \n T\n emplace\n cpp/container/set/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/set/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/set/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/set/end\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/set/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/set/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/set/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/set/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/set/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/container/set/insert\n \n (T... args)\n \n \n T\n key_comp\n cpp/container/set/key_comp\n \n (T... args)\n \n \n T\n lower_bound\n cpp/container/set/lower_bound\n \n (T... args)\n \n \n T\n max_size\n cpp/container/set/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/set/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/set/operator=\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/set/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/container/set/rend\n \n (T... args)\n \n \n T\n set\n cpp/container/set/set\n \n (T... args)\n \n \n T\n size\n cpp/container/set/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/set/swap\n \n (T... args)\n \n \n T\n upper_bound\n cpp/container/set/upper_bound\n \n (T... args)\n \n \n T\n value_comp\n cpp/container/set/value_comp\n \n (T... args)\n \n \n T\n ~set\n cpp/container/set/~set\n \n (T... args)\n \n \n \n std::pmr::string\n cpp/string/basic_string\n \n T\n append\n cpp/string/basic_string/append\n \n (T... args)\n \n \n T\n assign\n cpp/string/basic_string/assign\n \n (T... args)\n \n \n T\n at\n cpp/string/basic_string/at\n \n (T... args)\n \n \n T\n back\n cpp/string/basic_string/back\n \n (T... args)\n \n \n T\n begin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n c_str\n cpp/string/basic_string/c_str\n \n (T... args)\n \n \n T\n capacity\n cpp/string/basic_string/capacity\n \n (T... args)\n \n \n T\n cbegin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n cend\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n clear\n cpp/string/basic_string/clear\n \n (T... args)\n \n \n T\n compare\n cpp/string/basic_string/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/basic_string/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n data\n cpp/string/basic_string/data\n \n (T... args)\n \n \n T\n empty\n cpp/string/basic_string/empty\n \n (T... args)\n \n \n T\n end\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n erase\n cpp/string/basic_string/erase\n \n (T... args)\n \n \n T\n find\n cpp/string/basic_string/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/string/basic_string/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/string/basic_string/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/string/basic_string/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/string/basic_string/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/string/basic_string/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/string/basic_string/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/string/basic_string/insert\n \n (T... args)\n \n \n T\n length\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n max_size\n cpp/string/basic_string/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/string/basic_string/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/string/basic_string/operator_at\n \n (T... args)\n \n \n T\n pop_back\n cpp/string/basic_string/pop_back\n \n (T... args)\n \n \n T\n push_back\n cpp/string/basic_string/push_back\n \n (T... args)\n \n \n T\n rbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n replace\n cpp/string/basic_string/replace\n \n (T... args)\n \n \n T\n reserve\n cpp/string/basic_string/reserve\n \n (T... args)\n \n \n T\n resize\n cpp/string/basic_string/resize\n \n (T... args)\n \n \n T\n rfind\n cpp/string/basic_string/rfind\n \n (T... args)\n \n \n T\n shrink_to_fit\n cpp/string/basic_string/shrink_to_fit\n \n (T... args)\n \n \n T\n size\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n string\n cpp/string/basic_string/basic_string\n \n (T... args)\n \n \n T\n substr\n cpp/string/basic_string/substr\n \n (T... args)\n \n \n T\n swap\n cpp/string/basic_string/swap\n \n (T... args)\n \n \n \n std::pmr::synchronized_pool_resource\n cpp/memory/synchronized_pool_resource\n \n T\n allocate\n cpp/memory/memory_resource/allocate\n \n (T... args)\n \n \n T\n deallocate\n cpp/memory/memory_resource/deallocate\n \n (T... args)\n \n \n T\n do_allocate\n cpp/memory/memory_resource/do_allocate\n \n (T... args)\n \n \n T\n do_deallocate\n cpp/memory/memory_resource/do_deallocate\n \n (T... args)\n \n \n T\n do_is_equal\n cpp/memory/memory_resource/do_is_equal\n \n (T... args)\n \n \n T\n is_equal\n cpp/memory/memory_resource/is_equal\n \n (T... args)\n \n \n T\n options\n cpp/memory/synchronized_pool_resource/options\n \n (T... args)\n \n \n T\n release\n cpp/memory/synchronized_pool_resource/release\n \n (T... args)\n \n \n T\n synchronized_pool_resource\n cpp/memory/synchronized_pool_resource/synchronized_pool_resource\n \n (T... args)\n \n \n T\n upstream_resource\n cpp/memory/synchronized_pool_resource/upstream_resource\n \n (T... args)\n \n \n T\n ~synchronized_pool_resource\n cpp/memory/synchronized_pool_resource\n \n (T... args)\n \n \n \n std::pmr::u16string\n cpp/string/basic_string\n \n T\n append\n cpp/string/basic_string/append\n \n (T... args)\n \n \n T\n assign\n cpp/string/basic_string/assign\n \n (T... args)\n \n \n T\n at\n cpp/string/basic_string/at\n \n (T... args)\n \n \n T\n back\n cpp/string/basic_string/back\n \n (T... args)\n \n \n T\n begin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n c_str\n cpp/string/basic_string/c_str\n \n (T... args)\n \n \n T\n capacity\n cpp/string/basic_string/capacity\n \n (T... args)\n \n \n T\n cbegin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n cend\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n clear\n cpp/string/basic_string/clear\n \n (T... args)\n \n \n T\n compare\n cpp/string/basic_string/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/basic_string/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n data\n cpp/string/basic_string/data\n \n (T... args)\n \n \n T\n empty\n cpp/string/basic_string/empty\n \n (T... args)\n \n \n T\n end\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n erase\n cpp/string/basic_string/erase\n \n (T... args)\n \n \n T\n find\n cpp/string/basic_string/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/string/basic_string/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/string/basic_string/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/string/basic_string/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/string/basic_string/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/string/basic_string/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/string/basic_string/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/string/basic_string/insert\n \n (T... args)\n \n \n T\n length\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n max_size\n cpp/string/basic_string/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/string/basic_string/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/string/basic_string/operator_at\n \n (T... args)\n \n \n T\n pop_back\n cpp/string/basic_string/pop_back\n \n (T... args)\n \n \n T\n push_back\n cpp/string/basic_string/push_back\n \n (T... args)\n \n \n T\n rbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n replace\n cpp/string/basic_string/replace\n \n (T... args)\n \n \n T\n reserve\n cpp/string/basic_string/reserve\n \n (T... args)\n \n \n T\n resize\n cpp/string/basic_string/resize\n \n (T... args)\n \n \n T\n rfind\n cpp/string/basic_string/rfind\n \n (T... args)\n \n \n T\n shrink_to_fit\n cpp/string/basic_string/shrink_to_fit\n \n (T... args)\n \n \n T\n size\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n substr\n cpp/string/basic_string/substr\n \n (T... args)\n \n \n T\n swap\n cpp/string/basic_string/swap\n \n (T... args)\n \n \n T\n u16string\n cpp/string/basic_string/basic_string\n \n (T... args)\n \n \n \n std::pmr::u32string\n cpp/string/basic_string\n \n T\n append\n cpp/string/basic_string/append\n \n (T... args)\n \n \n T\n assign\n cpp/string/basic_string/assign\n \n (T... args)\n \n \n T\n at\n cpp/string/basic_string/at\n \n (T... args)\n \n \n T\n back\n cpp/string/basic_string/back\n \n (T... args)\n \n \n T\n begin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n c_str\n cpp/string/basic_string/c_str\n \n (T... args)\n \n \n T\n capacity\n cpp/string/basic_string/capacity\n \n (T... args)\n \n \n T\n cbegin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n cend\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n clear\n cpp/string/basic_string/clear\n \n (T... args)\n \n \n T\n compare\n cpp/string/basic_string/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/basic_string/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n data\n cpp/string/basic_string/data\n \n (T... args)\n \n \n T\n empty\n cpp/string/basic_string/empty\n \n (T... args)\n \n \n T\n end\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n erase\n cpp/string/basic_string/erase\n \n (T... args)\n \n \n T\n find\n cpp/string/basic_string/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/string/basic_string/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/string/basic_string/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/string/basic_string/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/string/basic_string/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/string/basic_string/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/string/basic_string/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/string/basic_string/insert\n \n (T... args)\n \n \n T\n length\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n max_size\n cpp/string/basic_string/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/string/basic_string/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/string/basic_string/operator_at\n \n (T... args)\n \n \n T\n pop_back\n cpp/string/basic_string/pop_back\n \n (T... args)\n \n \n T\n push_back\n cpp/string/basic_string/push_back\n \n (T... args)\n \n \n T\n rbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n replace\n cpp/string/basic_string/replace\n \n (T... args)\n \n \n T\n reserve\n cpp/string/basic_string/reserve\n \n (T... args)\n \n \n T\n resize\n cpp/string/basic_string/resize\n \n (T... args)\n \n \n T\n rfind\n cpp/string/basic_string/rfind\n \n (T... args)\n \n \n T\n shrink_to_fit\n cpp/string/basic_string/shrink_to_fit\n \n (T... args)\n \n \n T\n size\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n substr\n cpp/string/basic_string/substr\n \n (T... args)\n \n \n T\n swap\n cpp/string/basic_string/swap\n \n (T... args)\n \n \n T\n u32string\n cpp/string/basic_string/basic_string\n \n (T... args)\n \n \n \n std::pmr::unordered_map\n cpp/container/unordered_map\n \n T\n at\n cpp/container/unordered_map/at\n \n (T... args)\n \n \n T\n begin\n cpp/container/unordered_map/begin\n \n (T... args)\n \n \n T\n begin(int)\n cpp/container/unordered_map/begin2\n \n (T... args)\n \n \n T\n bucket\n cpp/container/unordered_map/bucket\n \n (T... args)\n \n \n T\n bucket_count\n cpp/container/unordered_map/bucket_count\n \n (T... args)\n \n \n T\n bucket_size\n cpp/container/unordered_map/bucket_size\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/unordered_map/begin\n \n (T... args)\n \n \n T\n cbegin(int)\n cpp/container/unordered_map/begin2\n \n (T... args)\n \n \n T\n cend\n cpp/container/unordered_map/end\n \n (T... args)\n \n \n T\n cend(int)\n cpp/container/unordered_map/end2\n \n (T... args)\n \n \n T\n clear\n cpp/container/unordered_map/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/unordered_map/count\n \n (T... args)\n \n \n T\n emplace\n cpp/container/unordered_map/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/unordered_map/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/unordered_map/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/unordered_map/end\n \n (T... args)\n \n \n T\n end(int)\n cpp/container/unordered_map/end2\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/unordered_map/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/unordered_map/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/unordered_map/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/unordered_map/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/unordered_map/get_allocator\n \n (T... args)\n \n \n T\n hash_function\n cpp/container/unordered_map/hash_function\n \n (T... args)\n \n \n T\n insert\n cpp/container/unordered_map/insert\n \n (T... args)\n \n \n T\n insert_or_assign\n cpp/container/unordered_map/insert_or_assign\n \n (T... args)\n \n \n T\n key_eq\n cpp/container/unordered_map/key_eq\n \n (T... args)\n \n \n T\n load_factor\n cpp/container/unordered_map/load_factor\n \n (T... args)\n \n \n T\n max_bucket_count\n cpp/container/unordered_map/max_bucket_count\n \n (T... args)\n \n \n T\n max_load_factor\n cpp/container/unordered_map/max_load_factor\n \n (T... args)\n \n \n T\n max_size\n cpp/container/unordered_map/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/unordered_map/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/unordered_map/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/container/unordered_map/operator_at\n \n (T... args)\n \n \n T\n rehash\n cpp/container/unordered_map/rehash\n \n (T... args)\n \n \n T\n reserve\n cpp/container/unordered_map/reserve\n \n (T... args)\n \n \n T\n size\n cpp/container/unordered_map/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/unordered_map/swap\n \n (T... args)\n \n \n T\n try_emplace\n cpp/container/unordered_map/try_emplace\n \n (T... args)\n \n \n T\n unordered_map\n cpp/container/unordered_map/unordered_map\n \n (T... args)\n \n \n T\n ~unordered_map\n cpp/container/unordered_map/~unordered_map\n \n (T... args)\n \n \n \n std::pmr::unordered_multimap\n cpp/container/unordered_multimap\n \n T\n begin\n cpp/container/unordered_multimap/begin\n \n (T... args)\n \n \n T\n begin(int)\n cpp/container/unordered_multimap/begin2\n \n (T... args)\n \n \n T\n bucket\n cpp/container/unordered_multimap/bucket\n \n (T... args)\n \n \n T\n bucket_count\n cpp/container/unordered_multimap/bucket_count\n \n (T... args)\n \n \n T\n bucket_size\n cpp/container/unordered_multimap/bucket_size\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/unordered_multimap/begin\n \n (T... args)\n \n \n T\n cbegin(int)\n cpp/container/unordered_multimap/begin2\n \n (T... args)\n \n \n T\n cend\n cpp/container/unordered_multimap/end\n \n (T... args)\n \n \n T\n cend(int)\n cpp/container/unordered_multimap/end2\n \n (T... args)\n \n \n T\n clear\n cpp/container/unordered_multimap/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/unordered_multimap/count\n \n (T... args)\n \n \n T\n emplace\n cpp/container/unordered_multimap/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/unordered_multimap/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/unordered_multimap/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/unordered_multimap/end\n \n (T... args)\n \n \n T\n end(int)\n cpp/container/unordered_multimap/end2\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/unordered_multimap/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/unordered_multimap/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/unordered_multimap/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/unordered_multimap/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/unordered_multimap/get_allocator\n \n (T... args)\n \n \n T\n hash_function\n cpp/container/unordered_multimap/hash_function\n \n (T... args)\n \n \n T\n insert\n cpp/container/unordered_multimap/insert\n \n (T... args)\n \n \n T\n key_eq\n cpp/container/unordered_multimap/key_eq\n \n (T... args)\n \n \n T\n load_factor\n cpp/container/unordered_multimap/load_factor\n \n (T... args)\n \n \n T\n max_bucket_count\n cpp/container/unordered_multimap/max_bucket_count\n \n (T... args)\n \n \n T\n max_load_factor\n cpp/container/unordered_multimap/max_load_factor\n \n (T... args)\n \n \n T\n max_size\n cpp/container/unordered_multimap/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/unordered_multimap/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/unordered_multimap/operator=\n \n (T... args)\n \n \n T\n rehash\n cpp/container/unordered_multimap/rehash\n \n (T... args)\n \n \n T\n reserve\n cpp/container/unordered_multimap/reserve\n \n (T... args)\n \n \n T\n size\n cpp/container/unordered_multimap/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/unordered_multimap/swap\n \n (T... args)\n \n \n T\n unordered_multimap\n cpp/container/unordered_multimap/unordered_multimap\n \n (T... args)\n \n \n T\n ~unordered_multimap\n cpp/container/unordered_multimap/~unordered_multimap\n \n (T... args)\n \n \n \n std::pmr::unordered_multiset\n cpp/container/unordered_multiset\n \n T\n begin\n cpp/container/unordered_multiset/begin\n \n (T... args)\n \n \n T\n begin(int)\n cpp/container/unordered_multiset/begin2\n \n (T... args)\n \n \n T\n bucket\n cpp/container/unordered_multiset/bucket\n \n (T... args)\n \n \n T\n bucket_count\n cpp/container/unordered_multiset/bucket_count\n \n (T... args)\n \n \n T\n bucket_size\n cpp/container/unordered_multiset/bucket_size\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/unordered_multiset/begin\n \n (T... args)\n \n \n T\n cbegin(int)\n cpp/container/unordered_multiset/begin2\n \n (T... args)\n \n \n T\n cend\n cpp/container/unordered_multiset/end\n \n (T... args)\n \n \n T\n cend(int)\n cpp/container/unordered_multiset/end2\n \n (T... args)\n \n \n T\n clear\n cpp/container/unordered_multiset/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/unordered_multiset/count\n \n (T... args)\n \n \n T\n emplace\n cpp/container/unordered_multiset/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/unordered_multiset/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/unordered_multiset/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/unordered_multiset/end\n \n (T... args)\n \n \n T\n end(int)\n cpp/container/unordered_multiset/end2\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/unordered_multiset/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/unordered_multiset/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/unordered_multiset/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/unordered_multiset/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/unordered_multiset/get_allocator\n \n (T... args)\n \n \n T\n hash_function\n cpp/container/unordered_multiset/hash_function\n \n (T... args)\n \n \n T\n insert\n cpp/container/unordered_multiset/insert\n \n (T... args)\n \n \n T\n key_eq\n cpp/container/unordered_multiset/key_eq\n \n (T... args)\n \n \n T\n load_factor\n cpp/container/unordered_multiset/load_factor\n \n (T... args)\n \n \n T\n max_bucket_count\n cpp/container/unordered_multiset/max_bucket_count\n \n (T... args)\n \n \n T\n max_load_factor\n cpp/container/unordered_multiset/max_load_factor\n \n (T... args)\n \n \n T\n max_size\n cpp/container/unordered_multiset/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/unordered_multiset/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/unordered_multiset/operator=\n \n (T... args)\n \n \n T\n rehash\n cpp/container/unordered_multiset/rehash\n \n (T... args)\n \n \n T\n reserve\n cpp/container/unordered_multiset/reserve\n \n (T... args)\n \n \n T\n size\n cpp/container/unordered_multiset/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/unordered_multiset/swap\n \n (T... args)\n \n \n T\n unordered_multiset\n cpp/container/unordered_multiset/unordered_multiset\n \n (T... args)\n \n \n T\n ~unordered_multiset\n cpp/container/unordered_multiset/~unordered_multiset\n \n (T... args)\n \n \n \n std::pmr::unordered_set\n cpp/container/unordered_set\n \n T\n begin\n cpp/container/unordered_set/begin\n \n (T... args)\n \n \n T\n begin(int)\n cpp/container/unordered_set/begin2\n \n (T... args)\n \n \n T\n bucket\n cpp/container/unordered_set/bucket\n \n (T... args)\n \n \n T\n bucket_count\n cpp/container/unordered_set/bucket_count\n \n (T... args)\n \n \n T\n bucket_size\n cpp/container/unordered_set/bucket_size\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/unordered_set/begin\n \n (T... args)\n \n \n T\n cbegin(int)\n cpp/container/unordered_set/begin2\n \n (T... args)\n \n \n T\n cend\n cpp/container/unordered_set/end\n \n (T... args)\n \n \n T\n cend(int)\n cpp/container/unordered_set/end2\n \n (T... args)\n \n \n T\n clear\n cpp/container/unordered_set/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/unordered_set/count\n \n (T... args)\n \n \n T\n emplace\n cpp/container/unordered_set/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/unordered_set/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/unordered_set/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/unordered_set/end\n \n (T... args)\n \n \n T\n end(int)\n cpp/container/unordered_set/end2\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/unordered_set/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/unordered_set/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/unordered_set/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/unordered_set/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/unordered_set/get_allocator\n \n (T... args)\n \n \n T\n hash_function\n cpp/container/unordered_set/hash_function\n \n (T... args)\n \n \n T\n insert\n cpp/container/unordered_set/insert\n \n (T... args)\n \n \n T\n key_eq\n cpp/container/unordered_set/key_eq\n \n (T... args)\n \n \n T\n load_factor\n cpp/container/unordered_set/load_factor\n \n (T... args)\n \n \n T\n max_bucket_count\n cpp/container/unordered_set/max_bucket_count\n \n (T... args)\n \n \n T\n max_load_factor\n cpp/container/unordered_set/max_load_factor\n \n (T... args)\n \n \n T\n max_size\n cpp/container/unordered_set/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/unordered_set/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/unordered_set/operator=\n \n (T... args)\n \n \n T\n rehash\n cpp/container/unordered_set/rehash\n \n (T... args)\n \n \n T\n reserve\n cpp/container/unordered_set/reserve\n \n (T... args)\n \n \n T\n size\n cpp/container/unordered_set/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/unordered_set/swap\n \n (T... args)\n \n \n T\n unordered_set\n cpp/container/unordered_set/unordered_set\n \n (T... args)\n \n \n T\n ~unordered_set\n cpp/container/unordered_set/~unordered_set\n \n (T... args)\n \n \n \n std::pmr::unsynchronized_pool_resource\n cpp/memory/unsynchronized_pool_resource\n \n T\n allocate\n cpp/memory/memory_resource/allocate\n \n (T... args)\n \n \n T\n deallocate\n cpp/memory/memory_resource/deallocate\n \n (T... args)\n \n \n T\n do_allocate\n cpp/memory/memory_resource/do_allocate\n \n (T... args)\n \n \n T\n do_deallocate\n cpp/memory/memory_resource/do_deallocate\n \n (T... args)\n \n \n T\n do_is_equal\n cpp/memory/memory_resource/do_is_equal\n \n (T... args)\n \n \n T\n is_equal\n cpp/memory/memory_resource/is_equal\n \n (T... args)\n \n \n T\n options\n cpp/memory/unsynchronized_pool_resource/options\n \n (T... args)\n \n \n T\n release\n cpp/memory/unsynchronized_pool_resource/release\n \n (T... args)\n \n \n T\n unsynchronized_pool_resource\n cpp/memory/unsynchronized_pool_resource/unsynchronized_pool_resource\n \n (T... args)\n \n \n T\n upstream_resource\n cpp/memory/unsynchronized_pool_resource/upstream_resource\n \n (T... args)\n \n \n T\n ~unsynchronized_pool_resource\n cpp/memory/unsynchronized_pool_resource\n \n (T... args)\n \n \n \n std::pmr::vector\n cpp/container/vector\n \n T\n assign\n cpp/container/vector/assign\n \n (T... args)\n \n \n T\n at\n cpp/container/vector/at\n \n (T... args)\n \n \n T\n back\n cpp/container/vector/back\n \n (T... args)\n \n \n T\n begin\n cpp/container/vector/begin\n \n (T... args)\n \n \n T\n capacity\n cpp/container/vector/capacity\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/vector/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/vector/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/vector/clear\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/vector/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/vector/rend\n \n (T... args)\n \n \n T\n data\n cpp/container/vector/data\n \n (T... args)\n \n \n T\n emplace\n cpp/container/vector/emplace\n \n (T... args)\n \n \n T\n emplace_back\n cpp/container/vector/emplace_back\n \n (T... args)\n \n \n T\n empty\n cpp/container/vector/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/vector/end\n \n (T... args)\n \n \n T\n erase\n cpp/container/vector/erase\n \n (T... args)\n \n \n T\n front\n cpp/container/vector/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/vector/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/container/vector/insert\n \n (T... args)\n \n \n T\n max_size\n cpp/container/vector/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/container/vector/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/container/vector/operator_at\n \n (T... args)\n \n \n T\n pop_back\n cpp/container/vector/pop_back\n \n (T... args)\n \n \n T\n push_back\n cpp/container/vector/push_back\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/vector/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/container/vector/rend\n \n (T... args)\n \n \n T\n reserve\n cpp/container/vector/reserve\n \n (T... args)\n \n \n T\n resize\n cpp/container/vector/resize\n \n (T... args)\n \n \n T\n shrink_to_fit\n cpp/container/vector/shrink_to_fit\n \n (T... args)\n \n \n T\n size\n cpp/container/vector/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/vector/swap\n \n (T... args)\n \n \n T\n vector\n cpp/container/vector/vector\n \n (T... args)\n \n \n T\n ~vector\n cpp/container/vector/~vector\n \n (T... args)\n \n \n \n std::pmr::wstring\n cpp/string/basic_string\n \n T\n append\n cpp/string/basic_string/append\n \n (T... args)\n \n \n T\n assign\n cpp/string/basic_string/assign\n \n (T... args)\n \n \n T\n at\n cpp/string/basic_string/at\n \n (T... args)\n \n \n T\n back\n cpp/string/basic_string/back\n \n (T... args)\n \n \n T\n begin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n c_str\n cpp/string/basic_string/c_str\n \n (T... args)\n \n \n T\n capacity\n cpp/string/basic_string/capacity\n \n (T... args)\n \n \n T\n cbegin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n cend\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n clear\n cpp/string/basic_string/clear\n \n (T... args)\n \n \n T\n compare\n cpp/string/basic_string/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/basic_string/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n data\n cpp/string/basic_string/data\n \n (T... args)\n \n \n T\n empty\n cpp/string/basic_string/empty\n \n (T... args)\n \n \n T\n end\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n erase\n cpp/string/basic_string/erase\n \n (T... args)\n \n \n T\n find\n cpp/string/basic_string/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/string/basic_string/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/string/basic_string/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/string/basic_string/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/string/basic_string/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/string/basic_string/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/string/basic_string/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/string/basic_string/insert\n \n (T... args)\n \n \n T\n length\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n max_size\n cpp/string/basic_string/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/string/basic_string/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/string/basic_string/operator_at\n \n (T... args)\n \n \n T\n pop_back\n cpp/string/basic_string/pop_back\n \n (T... args)\n \n \n T\n push_back\n cpp/string/basic_string/push_back\n \n (T... args)\n \n \n T\n rbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n replace\n cpp/string/basic_string/replace\n \n (T... args)\n \n \n T\n reserve\n cpp/string/basic_string/reserve\n \n (T... args)\n \n \n T\n resize\n cpp/string/basic_string/resize\n \n (T... args)\n \n \n T\n rfind\n cpp/string/basic_string/rfind\n \n (T... args)\n \n \n T\n shrink_to_fit\n cpp/string/basic_string/shrink_to_fit\n \n (T... args)\n \n \n T\n size\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n substr\n cpp/string/basic_string/substr\n \n (T... args)\n \n \n T\n swap\n cpp/string/basic_string/swap\n \n (T... args)\n \n \n T\n wstring\n cpp/string/basic_string/basic_string\n \n (T... args)\n \n \n \n std::pointer_safety\n cpp/memory/gc/pointer_safety\n \n \n std::pointer_traits\n cpp/memory/pointer_traits\n \n T\n pointer_to\n cpp/memory/pointer_traits/pointer_to\n \n (T... args)\n \n \n \n std::poisson_distribution\n cpp/numeric/random/poisson_distribution\n \n T\n max\n cpp/numeric/random/poisson_distribution/max\n \n (T... args)\n \n \n T\n mean\n cpp/numeric/random/poisson_distribution/mean\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/poisson_distribution/min\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/poisson_distribution/param\n \n (T... args)\n \n \n T\n poisson_distribution\n cpp/numeric/random/poisson_distribution/poisson_distribution\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/poisson_distribution/reset\n \n (T... args)\n \n \n \n std::priority_queue\n cpp/container/priority_queue\n \n T\n emplace\n cpp/container/priority_queue/emplace\n \n (T... args)\n \n \n T\n empty\n cpp/container/priority_queue/empty\n \n (T... args)\n \n \n T\n operator=\n cpp/container/priority_queue/operator=\n \n (T... args)\n \n \n T\n pop\n cpp/container/priority_queue/pop\n \n (T... args)\n \n \n T\n priority_queue\n cpp/container/priority_queue/priority_queue\n \n (T... args)\n \n \n T\n push\n cpp/container/priority_queue/push\n \n (T... args)\n \n \n T\n size\n cpp/container/priority_queue/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/priority_queue/swap\n \n (T... args)\n \n \n T\n top\n cpp/container/priority_queue/top\n \n (T... args)\n \n \n T\n ~priority_queue\n cpp/container/priority_queue/~priority_queue\n \n (T... args)\n \n \n \n std::promise\n cpp/thread/promise\n \n T\n get_future\n cpp/thread/promise/get_future\n \n (T... args)\n \n \n T\n operator=\n cpp/thread/promise/operator=\n \n (T... args)\n \n \n T\n promise\n cpp/thread/promise/promise\n \n (T... args)\n \n \n T\n set_exception\n cpp/thread/promise/set_exception\n \n (T... args)\n \n \n T\n set_exception_at_thread_exit\n cpp/thread/promise/set_exception_at_thread_exit\n \n (T... args)\n \n \n T\n set_value\n cpp/thread/promise/set_value\n \n (T... args)\n \n \n T\n set_value_at_thread_exit\n cpp/thread/promise/set_value_at_thread_exit\n \n (T... args)\n \n \n T\n swap\n cpp/thread/promise/swap\n \n (T... args)\n \n \n T\n ~promise\n cpp/thread/promise/~promise\n \n (T... args)\n \n \n \n std::ptrdiff_t\n cpp/types/ptrdiff_t\n \n \n std::queue\n cpp/container/queue\n \n T\n back\n cpp/container/queue/back\n \n (T... args)\n \n \n T\n emplace\n cpp/container/queue/emplace\n \n (T... args)\n \n \n T\n empty\n cpp/container/queue/empty\n \n (T... args)\n \n \n T\n front\n cpp/container/queue/front\n \n (T... args)\n \n \n T\n operator=\n cpp/container/queue/operator=\n \n (T... args)\n \n \n T\n pop\n cpp/container/queue/pop\n \n (T... args)\n \n \n T\n push\n cpp/container/queue/push\n \n (T... args)\n \n \n T\n queue\n cpp/container/queue/queue\n \n (T... args)\n \n \n T\n size\n cpp/container/queue/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/queue/swap\n \n (T... args)\n \n \n T\n ~queue\n cpp/container/queue/~queue\n \n (T... args)\n \n \n \n std::random_access_iterator_tag\n cpp/iterator/iterator_tags\n \n \n std::random_device\n cpp/numeric/random/random_device\n \n T\n entropy\n cpp/numeric/random/random_device/entropy\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/random_device/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/random_device/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/random_device/operator()\n \n (T... args)\n \n \n T\n random_device\n cpp/numeric/random/random_device/random_device\n \n (T... args)\n \n \n \n std::range_error\n cpp/error/range_error\n \n T\n range_error\n cpp/error/range_error\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::rank\n cpp/types/rank\n \n \n std::ranlux24\n cpp/numeric/random/discard_block_engine\n \n T\n base\n cpp/numeric/random/discard_block_engine/base\n \n (T... args)\n \n \n T\n discard\n cpp/numeric/random/discard_block_engine/discard\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/discard_block_engine/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/discard_block_engine/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/discard_block_engine/operator()\n \n (T... args)\n \n \n T\n ranlux24\n cpp/numeric/random/discard_block_engine/discard_block_engine\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/discard_block_engine/seed\n \n (T... args)\n \n \n \n std::ranlux24_base\n cpp/numeric/random/subtract_with_carry_engine\n \n T\n discard\n cpp/numeric/random/subtract_with_carry_engine/discard\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/subtract_with_carry_engine/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/subtract_with_carry_engine/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/subtract_with_carry_engine/operator()\n \n (T... args)\n \n \n T\n ranlux24_base\n cpp/numeric/random/subtract_with_carry_engine/subtract_with_carry_engine\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/subtract_with_carry_engine/seed\n \n (T... args)\n \n \n \n std::ranlux48\n cpp/numeric/random/discard_block_engine\n \n T\n base\n cpp/numeric/random/discard_block_engine/base\n \n (T... args)\n \n \n T\n discard\n cpp/numeric/random/discard_block_engine/discard\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/discard_block_engine/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/discard_block_engine/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/discard_block_engine/operator()\n \n (T... args)\n \n \n T\n ranlux48\n cpp/numeric/random/discard_block_engine/discard_block_engine\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/discard_block_engine/seed\n \n (T... args)\n \n \n \n std::ranlux48_base\n cpp/numeric/random/subtract_with_carry_engine\n \n T\n discard\n cpp/numeric/random/subtract_with_carry_engine/discard\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/subtract_with_carry_engine/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/subtract_with_carry_engine/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/subtract_with_carry_engine/operator()\n \n (T... args)\n \n \n T\n ranlux48_base\n cpp/numeric/random/subtract_with_carry_engine/subtract_with_carry_engine\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/subtract_with_carry_engine/seed\n \n (T... args)\n \n \n \n std::ratio\n cpp/numeric/ratio/ratio\n \n \n std::ratio_add\n cpp/numeric/ratio/ratio_add\n \n \n std::ratio_divide\n cpp/numeric/ratio/ratio_divide\n \n \n std::ratio_equal\n cpp/numeric/ratio/ratio_equal\n \n \n std::ratio_greater\n cpp/numeric/ratio/ratio_greater\n \n \n std::ratio_greater_equal\n cpp/numeric/ratio/ratio_greater_equal\n \n \n std::ratio_less\n cpp/numeric/ratio/ratio_less\n \n \n std::ratio_less_equal\n cpp/numeric/ratio/ratio_less_equal\n \n \n std::ratio_multiply\n cpp/numeric/ratio/ratio_multiply\n \n \n std::ratio_not_equal\n cpp/numeric/ratio/ratio_not_equal\n \n \n std::ratio_subtract\n cpp/numeric/ratio/ratio_subtract\n \n \n std::raw_storage_iterator\n cpp/memory/raw_storage_iterator\n \n T\n operator*\n cpp/memory/raw_storage_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/memory/raw_storage_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator=\n cpp/memory/raw_storage_iterator/operator=\n \n (T... args)\n \n \n T\n raw_storage_iterator\n cpp/memory/raw_storage_iterator/raw_storage_iterator\n \n (T... args)\n \n \n \n std::recursive_mutex\n cpp/thread/recursive_mutex\n \n T\n lock\n cpp/thread/recursive_mutex/lock\n \n (T... args)\n \n \n T\n native_handle\n cpp/thread/recursive_mutex/native_handle\n \n (T... args)\n \n \n T\n recursive_mutex\n cpp/thread/recursive_mutex/recursive_mutex\n \n (T... args)\n \n \n T\n try_lock\n cpp/thread/recursive_mutex/try_lock\n \n (T... args)\n \n \n T\n unlock\n cpp/thread/recursive_mutex/unlock\n \n (T... args)\n \n \n \n std::recursive_timed_mutex\n cpp/thread/recursive_timed_mutex\n \n T\n lock\n cpp/thread/recursive_timed_mutex/lock\n \n (T... args)\n \n \n T\n native_handle\n cpp/thread/recursive_timed_mutex/native_handle\n \n (T... args)\n \n \n T\n recursive_timed_mutex\n cpp/thread/recursive_timed_mutex/recursive_timed_mutex\n \n (T... args)\n \n \n T\n try_lock\n cpp/thread/recursive_timed_mutex/try_lock\n \n (T... args)\n \n \n T\n try_lock_for\n cpp/thread/recursive_timed_mutex/try_lock_for\n \n (T... args)\n \n \n T\n try_lock_until\n cpp/thread/recursive_timed_mutex/try_lock_until\n \n (T... args)\n \n \n T\n unlock\n cpp/thread/recursive_timed_mutex/unlock\n \n (T... args)\n \n \n \n std::reference_wrapper\n cpp/utility/functional/reference_wrapper\n \n T\n get\n cpp/utility/functional/reference_wrapper/get\n \n (T... args)\n \n \n T\n operator T&\n cpp/utility/functional/reference_wrapper/get\n \n (T... args)\n \n \n T\n operator()\n cpp/utility/functional/reference_wrapper/operator()\n \n (T... args)\n \n \n T\n operator=\n cpp/utility/functional/reference_wrapper/operator=\n \n (T... args)\n \n \n T\n reference_wrapper\n cpp/utility/functional/reference_wrapper/reference_wrapper\n \n (T... args)\n \n \n \n std::regex\n cpp/regex/basic_regex\n \n T\n assign\n cpp/regex/basic_regex/assign\n \n (T... args)\n \n \n T\n flags\n cpp/regex/basic_regex/flags\n \n (T... args)\n \n \n T\n getloc\n cpp/regex/basic_regex/getloc\n \n (T... args)\n \n \n T\n imbue\n cpp/regex/basic_regex/imbue\n \n (T... args)\n \n \n T\n mark_count\n cpp/regex/basic_regex/mark_count\n \n (T... args)\n \n \n T\n operator=\n cpp/regex/basic_regex/operator=\n \n (T... args)\n \n \n T\n regex\n cpp/regex/basic_regex/basic_regex\n \n (T... args)\n \n \n T\n swap\n cpp/regex/basic_regex/swap\n \n (T... args)\n \n \n T\n ~regex\n cpp/regex/basic_regex/~basic_regex\n \n (T... args)\n \n \n \n std::regex_constants\n \n \n \n std::regex_error\n cpp/regex/regex_error\n \n T\n code\n cpp/regex/regex_error/code\n \n (T... args)\n \n \n T\n regex_error\n cpp/regex/regex_error/regex_error\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::regex_iterator\n cpp/regex/regex_iterator\n \n T\n operator!=\n cpp/regex/regex_iterator/operator_cmp\n \n (T... args)\n \n \n T\n operator*\n cpp/regex/regex_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/regex/regex_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/regex/regex_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator->\n cpp/regex/regex_iterator/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/regex/regex_iterator/operator=\n \n (T... args)\n \n \n T\n operator==\n cpp/regex/regex_iterator/operator_cmp\n \n (T... args)\n \n \n T\n regex_iterator\n cpp/regex/regex_iterator/regex_iterator\n \n (T... args)\n \n \n \n std::regex_token_iterator\n cpp/regex/regex_token_iterator\n \n T\n operator!=\n cpp/regex/regex_token_iterator/operator_cmp\n \n (T... args)\n \n \n T\n operator*\n cpp/regex/regex_token_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/regex/regex_token_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/regex/regex_token_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator->\n cpp/regex/regex_token_iterator/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/regex/regex_token_iterator/operator=\n \n (T... args)\n \n \n T\n operator==\n cpp/regex/regex_token_iterator/operator_cmp\n \n (T... args)\n \n \n T\n regex_token_iterator\n cpp/regex/regex_token_iterator/regex_token_iterator\n \n (T... args)\n \n \n \n std::regex_traits\n cpp/regex/regex_traits\n \n T\n getloc\n cpp/regex/regex_traits/getloc\n \n (T... args)\n \n \n T\n imbue\n cpp/regex/regex_traits/imbue\n \n (T... args)\n \n \n T\n isctype\n cpp/regex/regex_traits/isctype\n \n (T... args)\n \n \n T\n length\n cpp/regex/regex_traits/length\n \n (T... args)\n \n \n T\n lookup_classname\n cpp/regex/regex_traits/lookup_classname\n \n (T... args)\n \n \n T\n lookup_collatename\n cpp/regex/regex_traits/lookup_collatename\n \n (T... args)\n \n \n T\n regex_traits\n cpp/regex/regex_traits/regex_traits\n \n (T... args)\n \n \n T\n transform\n cpp/regex/regex_traits/transform\n \n (T... args)\n \n \n T\n transform_primary\n cpp/regex/regex_traits/transform_primary\n \n (T... args)\n \n \n T\n translate\n cpp/regex/regex_traits/translate\n \n (T... args)\n \n \n T\n translate_nocase\n cpp/regex/regex_traits/translate_nocase\n \n (T... args)\n \n \n T\n value\n cpp/regex/regex_traits/value\n \n (T... args)\n \n \n \n std::rel_ops\n \n \n T\n operator!=\n cpp/utility/rel_ops/operator_cmp\n \n (T... args)\n \n \n T\n operator<=\n cpp/utility/rel_ops/operator_cmp\n \n (T... args)\n \n \n T\n operator>\n cpp/utility/rel_ops/operator_cmp\n \n (T... args)\n \n \n T\n operator>=\n cpp/utility/rel_ops/operator_cmp\n \n (T... args)\n \n \n \n std::remove_all_extents\n cpp/types/remove_all_extents\n \n \n std::remove_all_extents_t\n cpp/types/remove_all_extents\n \n \n std::remove_const\n cpp/types/remove_cv\n \n \n std::remove_const_t\n cpp/types/remove_cv\n \n \n std::remove_cv\n cpp/types/remove_cv\n \n \n std::remove_cv_t\n cpp/types/remove_cv\n \n \n std::remove_extent\n cpp/types/remove_extent\n \n \n std::remove_extent_t\n cpp/types/remove_extent\n \n \n std::remove_pointer\n cpp/types/remove_pointer\n \n \n std::remove_pointer_t\n cpp/types/remove_pointer\n \n \n std::remove_reference\n cpp/types/remove_reference\n \n \n std::remove_reference_t\n cpp/types/remove_reference\n \n \n std::remove_volatile\n cpp/types/remove_cv\n \n \n std::remove_volatile_t\n cpp/types/remove_cv\n \n \n std::result_of\n cpp/types/result_of\n \n \n std::result_of_t\n cpp/types/result_of\n \n \n std::reverse_iterator\n cpp/iterator/reverse_iterator\n \n \n std::runtime_error\n cpp/error/runtime_error\n \n T\n runtime_error\n cpp/error/runtime_error\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::scoped_allocator_adaptor\n cpp/memory/scoped_allocator_adaptor\n \n T\n allocate\n cpp/memory/scoped_allocator_adaptor/allocate\n \n (T... args)\n \n \n T\n construct\n cpp/memory/scoped_allocator_adaptor/construct\n \n (T... args)\n \n \n T\n deallocate\n cpp/memory/scoped_allocator_adaptor/deallocate\n \n (T... args)\n \n \n T\n destroy\n cpp/memory/scoped_allocator_adaptor/destroy\n \n (T... args)\n \n \n T\n inner_allocator\n cpp/memory/scoped_allocator_adaptor/inner_allocator\n \n (T... args)\n \n \n T\n max_size\n cpp/memory/scoped_allocator_adaptor/max_size\n \n (T... args)\n \n \n T\n outer_allocator\n cpp/memory/scoped_allocator_adaptor/outer_allocator\n \n (T... args)\n \n \n T\n scoped_allocator_adaptor\n cpp/memory/scoped_allocator_adaptor/scoped_allocator_adaptor\n \n (T... args)\n \n \n T\n select_on_container_copy_construction\n cpp/memory/scoped_allocator_adaptor/select_on_container_copy_construction\n \n (T... args)\n \n \n T\n ~scoped_allocator_adaptor\n cpp/memory/scoped_allocator_adaptor/~scoped_allocator_adaptor\n \n (T... args)\n \n \n \n std::seed_seq\n cpp/numeric/random/seed_seq\n \n T\n generate\n cpp/numeric/random/seed_seq/generate\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/seed_seq/param\n \n (T... args)\n \n \n T\n seed_seq\n cpp/numeric/random/seed_seq/seed_seq\n \n (T... args)\n \n \n T\n size\n cpp/numeric/random/seed_seq/size\n \n (T... args)\n \n \n \n std::set\n cpp/container/set\n \n T\n begin\n cpp/container/set/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/set/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/set/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/set/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/set/count\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/set/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/set/rend\n \n (T... args)\n \n \n T\n emplace\n cpp/container/set/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/set/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/set/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/set/end\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/set/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/set/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/set/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/set/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/set/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/container/set/insert\n \n (T... args)\n \n \n T\n key_comp\n cpp/container/set/key_comp\n \n (T... args)\n \n \n T\n lower_bound\n cpp/container/set/lower_bound\n \n (T... args)\n \n \n T\n max_size\n cpp/container/set/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/set/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/set/operator=\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/set/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/container/set/rend\n \n (T... args)\n \n \n T\n set\n cpp/container/set/set\n \n (T... args)\n \n \n T\n size\n cpp/container/set/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/set/swap\n \n (T... args)\n \n \n T\n upper_bound\n cpp/container/set/upper_bound\n \n (T... args)\n \n \n T\n value_comp\n cpp/container/set/value_comp\n \n (T... args)\n \n \n T\n ~set\n cpp/container/set/~set\n \n (T... args)\n \n \n \n std::shared_future\n cpp/thread/shared_future\n \n T\n get\n cpp/thread/shared_future/get\n \n (T... args)\n \n \n T\n operator=\n cpp/thread/shared_future/operator=\n \n (T... args)\n \n \n T\n shared_future\n cpp/thread/shared_future/shared_future\n \n (T... args)\n \n \n T\n valid\n cpp/thread/shared_future/valid\n \n (T... args)\n \n \n T\n wait\n cpp/thread/shared_future/wait\n \n (T... args)\n \n \n T\n wait_for\n cpp/thread/shared_future/wait_for\n \n (T... args)\n \n \n T\n wait_until\n cpp/thread/shared_future/wait_until\n \n (T... args)\n \n \n T\n ~shared_future\n cpp/thread/shared_future/~shared_future\n \n (T... args)\n \n \n \n std::shared_lock\n cpp/thread/shared_lock\n \n T\n lock\n cpp/thread/shared_lock/lock\n \n (T... args)\n \n \n T\n mutex\n cpp/thread/shared_lock/mutex\n \n (T... args)\n \n \n T\n operator bool\n cpp/thread/shared_lock/operator_bool\n \n (T... args)\n \n \n T\n operator=\n cpp/thread/shared_lock/operator=\n \n (T... args)\n \n \n T\n owns_lock\n cpp/thread/shared_lock/owns_lock\n \n (T... args)\n \n \n T\n release\n cpp/thread/shared_lock/release\n \n (T... args)\n \n \n T\n shared_lock\n cpp/thread/shared_lock/shared_lock\n \n (T... args)\n \n \n T\n swap\n cpp/thread/shared_lock/swap\n \n (T... args)\n \n \n T\n try_lock\n cpp/thread/shared_lock/try_lock\n \n (T... args)\n \n \n T\n try_lock_for\n cpp/thread/shared_lock/try_lock_for\n \n (T... args)\n \n \n T\n try_lock_until\n cpp/thread/shared_lock/try_lock_until\n \n (T... args)\n \n \n T\n unlock\n cpp/thread/shared_lock/unlock\n \n (T... args)\n \n \n T\n ~shared_lock\n cpp/thread/shared_lock/~shared_lock\n \n (T... args)\n \n \n \n std::shared_mutex\n cpp/thread/shared_mutex\n \n T\n lock\n cpp/thread/shared_mutex/lock\n \n (T... args)\n \n \n T\n lock_shared\n cpp/thread/shared_mutex/lock_shared\n \n (T... args)\n \n \n T\n native_handle\n cpp/thread/shared_mutex/native_handle\n \n (T... args)\n \n \n T\n shared_mutex\n cpp/thread/shared_mutex/shared_mutex\n \n (T... args)\n \n \n T\n try_lock\n cpp/thread/shared_mutex/try_lock\n \n (T... args)\n \n \n T\n try_lock_shared\n cpp/thread/shared_mutex/try_lock_shared\n \n (T... args)\n \n \n T\n unlock\n cpp/thread/shared_mutex/unlock\n \n (T... args)\n \n \n T\n unlock_shared\n cpp/thread/shared_mutex/unlock_shared\n \n (T... args)\n \n \n \n std::shared_ptr\n cpp/memory/shared_ptr\n \n T\n get\n cpp/memory/shared_ptr/get\n \n (T... args)\n \n \n T\n operator bool\n cpp/memory/shared_ptr/operator_bool\n \n (T... args)\n \n \n T\n operator*\n cpp/memory/shared_ptr/operator*\n \n (T... args)\n \n \n T\n operator->\n cpp/memory/shared_ptr/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/memory/shared_ptr/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/memory/shared_ptr/operator_at\n \n (T... args)\n \n \n T\n owner_before\n cpp/memory/shared_ptr/owner_before\n \n (T... args)\n \n \n T\n reset\n cpp/memory/shared_ptr/reset\n \n (T... args)\n \n \n T\n shared_ptr\n cpp/memory/shared_ptr/shared_ptr\n \n (T... args)\n \n \n T\n swap\n cpp/memory/shared_ptr/swap\n \n (T... args)\n \n \n T\n unique\n cpp/memory/shared_ptr/unique\n \n (T... args)\n \n \n T\n use_count\n cpp/memory/shared_ptr/use_count\n \n (T... args)\n \n \n T\n ~shared_ptr\n cpp/memory/shared_ptr/~shared_ptr\n \n (T... args)\n \n \n \n std::shared_timed_mutex\n cpp/thread/shared_timed_mutex\n \n T\n lock\n cpp/thread/shared_timed_mutex/lock\n \n (T... args)\n \n \n T\n lock_shared\n cpp/thread/shared_timed_mutex/lock_shared\n \n (T... args)\n \n \n T\n shared_timed_mutex\n cpp/thread/shared_timed_mutex/shared_timed_mutex\n \n (T... args)\n \n \n T\n try_lock\n cpp/thread/shared_timed_mutex/try_lock\n \n (T... args)\n \n \n T\n try_lock_for\n cpp/thread/shared_timed_mutex/try_lock_for\n \n (T... args)\n \n \n T\n try_lock_shared\n cpp/thread/shared_timed_mutex/try_lock_shared\n \n (T... args)\n \n \n T\n try_lock_shared_for\n cpp/thread/shared_timed_mutex/try_lock_shared_for\n \n (T... args)\n \n \n T\n try_lock_shared_until\n cpp/thread/shared_timed_mutex/try_lock_shared_until\n \n (T... args)\n \n \n T\n try_lock_until\n cpp/thread/shared_timed_mutex/try_lock_until\n \n (T... args)\n \n \n T\n unlock\n cpp/thread/shared_timed_mutex/unlock\n \n (T... args)\n \n \n T\n unlock_shared\n cpp/thread/shared_timed_mutex/unlock_shared\n \n (T... args)\n \n \n \n std::shuffle_order_engine\n cpp/numeric/random/shuffle_order_engine\n \n T\n base\n cpp/numeric/random/shuffle_order_engine/base\n \n (T... args)\n \n \n T\n discard\n cpp/numeric/random/shuffle_order_engine/discard\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/shuffle_order_engine/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/shuffle_order_engine/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/shuffle_order_engine/operator()\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/shuffle_order_engine/seed\n \n (T... args)\n \n \n T\n shuffle_order_engine\n cpp/numeric/random/shuffle_order_engine/shuffle_order_engine\n \n (T... args)\n \n \n \n std::sig_atomic_t\n cpp/utility/program/sig_atomic_t\n \n \n std::size_t\n cpp/types/size_t\n \n \n std::slice\n cpp/numeric/valarray/slice\n \n \n std::slice_array\n cpp/numeric/valarray/slice_array\n \n \n std::smatch\n cpp/regex/match_results\n \n T\n begin\n cpp/regex/match_results/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/regex/match_results/begin\n \n (T... args)\n \n \n T\n cend\n cpp/regex/match_results/end\n \n (T... args)\n \n \n T\n empty\n cpp/regex/match_results/empty\n \n (T... args)\n \n \n T\n end\n cpp/regex/match_results/end\n \n (T... args)\n \n \n T\n format\n cpp/regex/match_results/format\n \n (T... args)\n \n \n T\n get_allocator\n cpp/regex/match_results/get_allocator\n \n (T... args)\n \n \n T\n length\n cpp/regex/match_results/length\n \n (T... args)\n \n \n T\n max_size\n cpp/regex/match_results/max_size\n \n (T... args)\n \n \n T\n operator[]\n cpp/regex/match_results/operator_at\n \n (T... args)\n \n \n T\n position\n cpp/regex/match_results/position\n \n (T... args)\n \n \n T\n prefix\n cpp/regex/match_results/prefix\n \n (T... args)\n \n \n T\n ready\n cpp/regex/match_results/ready\n \n (T... args)\n \n \n T\n size\n cpp/regex/match_results/size\n \n (T... args)\n \n \n T\n smatch\n cpp/regex/match_results/match_results\n \n (T... args)\n \n \n T\n str\n cpp/regex/match_results/str\n \n (T... args)\n \n \n T\n suffix\n cpp/regex/match_results/suffix\n \n (T... args)\n \n \n T\n swap\n cpp/regex/match_results/swap\n \n (T... args)\n \n \n T\n ~smatch\n cpp/regex/match_results/~match_results\n \n (T... args)\n \n \n \n std::sregex_iterator\n cpp/regex/regex_iterator\n \n T\n operator!=\n cpp/regex/regex_iterator/operator_cmp\n \n (T... args)\n \n \n T\n operator*\n cpp/regex/regex_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/regex/regex_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/regex/regex_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator->\n cpp/regex/regex_iterator/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/regex/regex_iterator/operator=\n \n (T... args)\n \n \n T\n operator==\n cpp/regex/regex_iterator/operator_cmp\n \n (T... args)\n \n \n T\n sregex_iterator\n cpp/regex/regex_iterator/regex_iterator\n \n (T... args)\n \n \n \n std::sregex_token_iterator\n cpp/regex/regex_token_iterator\n \n T\n operator!=\n cpp/regex/regex_token_iterator/operator_cmp\n \n (T... args)\n \n \n T\n operator*\n cpp/regex/regex_token_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/regex/regex_token_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/regex/regex_token_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator->\n cpp/regex/regex_token_iterator/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/regex/regex_token_iterator/operator=\n \n (T... args)\n \n \n T\n operator==\n cpp/regex/regex_token_iterator/operator_cmp\n \n (T... args)\n \n \n T\n sregex_token_iterator\n cpp/regex/regex_token_iterator/regex_token_iterator\n \n (T... args)\n \n \n \n std::ssub_match\n cpp/regex/sub_match\n \n T\n compare\n cpp/regex/sub_match/compare\n \n (T... args)\n \n \n T\n length\n cpp/regex/sub_match/length\n \n (T... args)\n \n \n T\n operator string_type\n cpp/regex/sub_match/str\n \n (T... args)\n \n \n T\n ssub_match\n cpp/regex/sub_match/sub_match\n \n (T... args)\n \n \n T\n str\n cpp/regex/sub_match/str\n \n (T... args)\n \n \n \n std::stack\n cpp/container/stack\n \n T\n emplace\n cpp/container/stack/emplace\n \n (T... args)\n \n \n T\n empty\n cpp/container/stack/empty\n \n (T... args)\n \n \n T\n operator=\n cpp/container/stack/operator=\n \n (T... args)\n \n \n T\n pop\n cpp/container/stack/pop\n \n (T... args)\n \n \n T\n push\n cpp/container/stack/push\n \n (T... args)\n \n \n T\n size\n cpp/container/stack/size\n \n (T... args)\n \n \n T\n stack\n cpp/container/stack/stack\n \n (T... args)\n \n \n T\n swap\n cpp/container/stack/swap\n \n (T... args)\n \n \n T\n top\n cpp/container/stack/top\n \n (T... args)\n \n \n T\n ~stack\n cpp/container/stack/~stack\n \n (T... args)\n \n \n \n std::streambuf\n cpp/io/basic_streambuf\n \n T\n eback\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n egptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n epptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n gbump\n cpp/io/basic_streambuf/gbump\n \n (T... args)\n \n \n T\n getloc\n cpp/io/basic_streambuf/getloc\n \n (T... args)\n \n \n T\n gptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n in_avail\n cpp/io/basic_streambuf/in_avail\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_streambuf/operator=\n \n (T... args)\n \n \n T\n overflow\n cpp/io/basic_streambuf/overflow\n \n (T... args)\n \n \n T\n pbackfail\n cpp/io/basic_streambuf/pbackfail\n \n (T... args)\n \n \n T\n pbase\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pbump\n cpp/io/basic_streambuf/pbump\n \n (T... args)\n \n \n T\n pptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pubimbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n pubseekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n pubseekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n pubsetbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n pubsync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n sbumpc\n cpp/io/basic_streambuf/sbumpc\n \n (T... args)\n \n \n T\n seekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n seekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n setbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n setg\n cpp/io/basic_streambuf/setg\n \n (T... args)\n \n \n T\n setp\n cpp/io/basic_streambuf/setp\n \n (T... args)\n \n \n T\n sgetc\n cpp/io/basic_streambuf/sgetc\n \n (T... args)\n \n \n T\n sgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n showmanyc\n cpp/io/basic_streambuf/showmanyc\n \n (T... args)\n \n \n T\n snextc\n cpp/io/basic_streambuf/snextc\n \n (T... args)\n \n \n T\n sputbackc\n cpp/io/basic_streambuf/sputbackc\n \n (T... args)\n \n \n T\n sputc\n cpp/io/basic_streambuf/sputc\n \n (T... args)\n \n \n T\n sputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n streambuf\n cpp/io/basic_streambuf/basic_streambuf\n \n (T... args)\n \n \n T\n sungetc\n cpp/io/basic_streambuf/sungetc\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_streambuf/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n uflow\n cpp/io/basic_streambuf/uflow\n \n (T... args)\n \n \n T\n underflow\n cpp/io/basic_streambuf/underflow\n \n (T... args)\n \n \n T\n xsgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n xsputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n ~streambuf\n cpp/io/basic_streambuf/~basic_streambuf\n \n (T... args)\n \n \n \n std::streamoff\n cpp/io/streamoff\n \n \n std::streampos\n cpp/io/fpos\n \n T\n state\n cpp/io/fpos/state\n \n (T... args)\n \n \n \n std::streamsize\n cpp/io/streamsize\n \n \n std::string\n cpp/string/basic_string\n \n T\n append\n cpp/string/basic_string/append\n \n (T... args)\n \n \n T\n assign\n cpp/string/basic_string/assign\n \n (T... args)\n \n \n T\n at\n cpp/string/basic_string/at\n \n (T... args)\n \n \n T\n back\n cpp/string/basic_string/back\n \n (T... args)\n \n \n T\n begin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n c_str\n cpp/string/basic_string/c_str\n \n (T... args)\n \n \n T\n capacity\n cpp/string/basic_string/capacity\n \n (T... args)\n \n \n T\n cbegin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n cend\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n clear\n cpp/string/basic_string/clear\n \n (T... args)\n \n \n T\n compare\n cpp/string/basic_string/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/basic_string/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n data\n cpp/string/basic_string/data\n \n (T... args)\n \n \n T\n empty\n cpp/string/basic_string/empty\n \n (T... args)\n \n \n T\n end\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n erase\n cpp/string/basic_string/erase\n \n (T... args)\n \n \n T\n find\n cpp/string/basic_string/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/string/basic_string/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/string/basic_string/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/string/basic_string/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/string/basic_string/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/string/basic_string/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/string/basic_string/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/string/basic_string/insert\n \n (T... args)\n \n \n T\n length\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n max_size\n cpp/string/basic_string/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/string/basic_string/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/string/basic_string/operator_at\n \n (T... args)\n \n \n T\n pop_back\n cpp/string/basic_string/pop_back\n \n (T... args)\n \n \n T\n push_back\n cpp/string/basic_string/push_back\n \n (T... args)\n \n \n T\n rbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n replace\n cpp/string/basic_string/replace\n \n (T... args)\n \n \n T\n reserve\n cpp/string/basic_string/reserve\n \n (T... args)\n \n \n T\n resize\n cpp/string/basic_string/resize\n \n (T... args)\n \n \n T\n rfind\n cpp/string/basic_string/rfind\n \n (T... args)\n \n \n T\n shrink_to_fit\n cpp/string/basic_string/shrink_to_fit\n \n (T... args)\n \n \n T\n size\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n string\n cpp/string/basic_string/basic_string\n \n (T... args)\n \n \n T\n substr\n cpp/string/basic_string/substr\n \n (T... args)\n \n \n T\n swap\n cpp/string/basic_string/swap\n \n (T... args)\n \n \n \n std::string_view\n cpp/string/basic_string_view\n \n T\n at\n cpp/string/basic_string_view/at\n \n (T... args)\n \n \n T\n back\n cpp/string/basic_string_view/back\n \n (T... args)\n \n \n T\n begin\n cpp/string/basic_string_view/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/string/basic_string_view/begin\n \n (T... args)\n \n \n T\n cend\n cpp/string/basic_string_view/end\n \n (T... args)\n \n \n T\n compare\n cpp/string/basic_string_view/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/basic_string_view/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/string/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/string/basic_string_view/rend\n \n (T... args)\n \n \n T\n data\n cpp/string/basic_string_view/data\n \n (T... args)\n \n \n T\n empty\n cpp/string/basic_string_view/empty\n \n (T... args)\n \n \n T\n end\n cpp/string/basic_string_view/end\n \n (T... args)\n \n \n T\n find\n cpp/string/basic_string_view/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/string/basic_string_view/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/string/basic_string_view/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/string/basic_string_view/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/string/basic_string_view/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/string/basic_string_view/front\n \n (T... args)\n \n \n T\n length\n cpp/string/basic_string_view/size\n \n (T... args)\n \n \n T\n max_size\n cpp/string/basic_string_view/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/string/basic_string_view/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/string/basic_string_view/operator_at\n \n (T... args)\n \n \n T\n rbegin\n cpp/string/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n remove_prefix\n cpp/string/basic_string_view/remove_prefix\n \n (T... args)\n \n \n T\n remove_suffix\n cpp/string/basic_string_view/remove_suffix\n \n (T... args)\n \n \n T\n rend\n cpp/string/basic_string_view/rend\n \n (T... args)\n \n \n T\n rfind\n cpp/string/basic_string_view/rfind\n \n (T... args)\n \n \n T\n size\n cpp/string/basic_string_view/size\n \n (T... args)\n \n \n T\n string_view\n cpp/string/basic_string_view/basic_string_view\n \n (T... args)\n \n \n T\n substr\n cpp/string/basic_string_view/substr\n \n (T... args)\n \n \n T\n swap\n cpp/string/basic_string_view/swap\n \n (T... args)\n \n \n \n std::stringbuf\n cpp/io/basic_stringbuf\n \n T\n eback\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n egptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n epptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n gbump\n cpp/io/basic_streambuf/gbump\n \n (T... args)\n \n \n T\n getloc\n cpp/io/basic_streambuf/getloc\n \n (T... args)\n \n \n T\n gptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n in_avail\n cpp/io/basic_streambuf/in_avail\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_stringbuf/operator=\n \n (T... args)\n \n \n T\n overflow\n cpp/io/basic_streambuf/overflow\n \n (T... args)\n \n \n T\n pbackfail\n cpp/io/basic_streambuf/pbackfail\n \n (T... args)\n \n \n T\n pbase\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pbump\n cpp/io/basic_streambuf/pbump\n \n (T... args)\n \n \n T\n pptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pubimbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n pubseekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n pubseekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n pubsetbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n pubsync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n sbumpc\n cpp/io/basic_streambuf/sbumpc\n \n (T... args)\n \n \n T\n seekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n seekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n setbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n setg\n cpp/io/basic_streambuf/setg\n \n (T... args)\n \n \n T\n setp\n cpp/io/basic_streambuf/setp\n \n (T... args)\n \n \n T\n sgetc\n cpp/io/basic_streambuf/sgetc\n \n (T... args)\n \n \n T\n sgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n showmanyc\n cpp/io/basic_streambuf/showmanyc\n \n (T... args)\n \n \n T\n snextc\n cpp/io/basic_streambuf/snextc\n \n (T... args)\n \n \n T\n sputbackc\n cpp/io/basic_streambuf/sputbackc\n \n (T... args)\n \n \n T\n sputc\n cpp/io/basic_streambuf/sputc\n \n (T... args)\n \n \n T\n sputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n str\n cpp/io/basic_stringbuf/str\n \n (T... args)\n \n \n T\n stringbuf\n cpp/io/basic_stringbuf/basic_stringbuf\n \n (T... args)\n \n \n T\n sungetc\n cpp/io/basic_streambuf/sungetc\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_streambuf/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n uflow\n cpp/io/basic_streambuf/uflow\n \n (T... args)\n \n \n T\n underflow\n cpp/io/basic_streambuf/underflow\n \n (T... args)\n \n \n T\n xsgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n xsputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n \n std::stringstream\n cpp/io/basic_stringstream\n std::stringstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::stringstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::stringstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_stringstream/operator=\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::stringstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n str\n cpp/io/basic_stringstream/str\n \n (T... args)\n \n \n T\n stringstream\n cpp/io/basic_stringstream/basic_stringstream\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::stringstream::Init\n cpp/io/ios_base/Init\n \n \n std::stringstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::stringstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::stringstream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::strstream\n cpp/io/strstream\n std::strstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::strstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::strstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n freeze\n cpp/io/strstream/freeze\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n pcount\n cpp/io/strstream/pcount\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::strstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n str\n cpp/io/strstream/str\n \n (T... args)\n \n \n T\n strstream\n cpp/io/strstream/strstream\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n T\n ~strstream\n cpp/io/strstream/~strstream\n \n (T... args)\n \n \n \n std::strstream::Init\n cpp/io/ios_base/Init\n \n \n std::strstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::strstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::strstream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::strstreambuf\n cpp/io/strstreambuf\n \n T\n eback\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n egptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n epptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n freeze\n cpp/io/strstreambuf/freeze\n \n (T... args)\n \n \n T\n gbump\n cpp/io/basic_streambuf/gbump\n \n (T... args)\n \n \n T\n getloc\n cpp/io/basic_streambuf/getloc\n \n (T... args)\n \n \n T\n gptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n in_avail\n cpp/io/basic_streambuf/in_avail\n \n (T... args)\n \n \n T\n overflow\n cpp/io/basic_streambuf/overflow\n \n (T... args)\n \n \n T\n pbackfail\n cpp/io/basic_streambuf/pbackfail\n \n (T... args)\n \n \n T\n pbase\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pbump\n cpp/io/basic_streambuf/pbump\n \n (T... args)\n \n \n T\n pcount\n cpp/io/strstreambuf/pcount\n \n (T... args)\n \n \n T\n pptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pubimbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n pubseekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n pubseekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n pubsetbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n pubsync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n sbumpc\n cpp/io/basic_streambuf/sbumpc\n \n (T... args)\n \n \n T\n seekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n seekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n setbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n setg\n cpp/io/basic_streambuf/setg\n \n (T... args)\n \n \n T\n setp\n cpp/io/basic_streambuf/setp\n \n (T... args)\n \n \n T\n sgetc\n cpp/io/basic_streambuf/sgetc\n \n (T... args)\n \n \n T\n sgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n showmanyc\n cpp/io/basic_streambuf/showmanyc\n \n (T... args)\n \n \n T\n snextc\n cpp/io/basic_streambuf/snextc\n \n (T... args)\n \n \n T\n sputbackc\n cpp/io/basic_streambuf/sputbackc\n \n (T... args)\n \n \n T\n sputc\n cpp/io/basic_streambuf/sputc\n \n (T... args)\n \n \n T\n sputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n str\n cpp/io/strstreambuf/str\n \n (T... args)\n \n \n T\n strstreambuf\n cpp/io/strstreambuf/strstreambuf\n \n (T... args)\n \n \n T\n sungetc\n cpp/io/basic_streambuf/sungetc\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_streambuf/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n uflow\n cpp/io/basic_streambuf/uflow\n \n (T... args)\n \n \n T\n underflow\n cpp/io/basic_streambuf/underflow\n \n (T... args)\n \n \n T\n xsgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n xsputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n ~strstreambuf\n cpp/io/strstreambuf/~strstreambuf\n \n (T... args)\n \n \n \n std::student_t_distribution\n cpp/numeric/random/student_t_distribution\n \n T\n max\n cpp/numeric/random/student_t_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/student_t_distribution/min\n \n (T... args)\n \n \n T\n n\n cpp/numeric/random/student_t_distribution/n\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/student_t_distribution/operator()\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/student_t_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/student_t_distribution/reset\n \n (T... args)\n \n \n T\n student_t_distribution\n cpp/numeric/random/student_t_distribution/student_t_distribution\n \n (T... args)\n \n \n \n std::sub_match\n cpp/regex/sub_match\n \n T\n compare\n cpp/regex/sub_match/compare\n \n (T... args)\n \n \n T\n length\n cpp/regex/sub_match/length\n \n (T... args)\n \n \n T\n operator string_type\n cpp/regex/sub_match/str\n \n (T... args)\n \n \n T\n str\n cpp/regex/sub_match/str\n \n (T... args)\n \n \n T\n sub_match\n cpp/regex/sub_match/sub_match\n \n (T... args)\n \n \n \n std::subtract_with_carry_engine\n cpp/numeric/random/subtract_with_carry_engine\n \n T\n discard\n cpp/numeric/random/subtract_with_carry_engine/discard\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/subtract_with_carry_engine/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/subtract_with_carry_engine/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/subtract_with_carry_engine/operator()\n \n (T... args)\n \n \n T\n seed\n cpp/numeric/random/subtract_with_carry_engine/seed\n \n (T... args)\n \n \n T\n subtract_with_carry_engine\n cpp/numeric/random/subtract_with_carry_engine/subtract_with_carry_engine\n \n (T... args)\n \n \n \n std::system_error\n cpp/error/system_error\n \n T\n code\n cpp/error/system_error/code\n \n (T... args)\n \n \n T\n system_error\n cpp/error/system_error/system_error\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::tera\n cpp/numeric/ratio/ratio\n \n \n std::terminate_handler\n cpp/error/terminate_handler\n \n \n std::this_thread\n \n \n T\n get_id\n cpp/thread/get_id\n \n (T... args)\n \n \n T\n sleep_for\n cpp/thread/sleep_for\n \n (T... args)\n \n \n T\n sleep_until\n cpp/thread/sleep_until\n \n (T... args)\n \n \n T\n yield\n cpp/thread/yield\n \n (T... args)\n \n \n \n std::thread\n cpp/thread/thread\n \n T\n detach\n cpp/thread/thread/detach\n \n (T... args)\n \n \n T\n get_id\n cpp/thread/thread/get_id\n \n (T... args)\n \n \n T\n hardware_concurrency\n cpp/thread/thread/hardware_concurrency\n \n (T... args)\n \n std::thread::id\n \n T\n join\n cpp/thread/thread/join\n \n (T... args)\n \n \n T\n joinable\n cpp/thread/thread/joinable\n \n (T... args)\n \n \n T\n native_handle\n cpp/thread/thread/native_handle\n \n (T... args)\n \n \n T\n operator=\n cpp/thread/thread/operator=\n \n (T... args)\n \n \n T\n swap\n cpp/thread/thread/swap\n \n (T... args)\n \n \n T\n thread\n cpp/thread/thread/thread\n \n (T... args)\n \n \n T\n ~thread\n cpp/thread/thread/~thread\n \n (T... args)\n \n \n \n std::thread::id\n cpp/thread/thread/id\n \n T\n id\n cpp/thread/thread/id/id\n \n (T... args)\n \n \n T\n operator!=\n cpp/thread/thread/id/operator_cmp\n \n (T... args)\n \n \n T\n operator<\n cpp/thread/thread/id/operator_cmp\n \n (T... args)\n \n \n T\n operator<<\n cpp/thread/thread/id/operator_ltlt\n \n (T... args)\n \n \n T\n operator<=\n cpp/thread/thread/id/operator_cmp\n \n (T... args)\n \n \n T\n operator==\n cpp/thread/thread/id/operator_cmp\n \n (T... args)\n \n \n T\n operator>\n cpp/thread/thread/id/operator_cmp\n \n (T... args)\n \n \n T\n operator>=\n cpp/thread/thread/id/operator_cmp\n \n (T... args)\n \n \n \n std::time_base\n cpp/locale/time_base\n \n \n std::time_get\n cpp/locale/time_get\n std::time_get::char_type\n \n T\n date_order\n cpp/locale/time_get/date_order\n \n (T... args)\n \n \n T\n do_date_order\n cpp/locale/time_get/date_order\n \n (T... args)\n \n \n T\n do_get\n cpp/locale/time_get/get\n \n (T... args)\n \n \n T\n do_get_date\n cpp/locale/time_get/get_date\n \n (T... args)\n \n \n T\n do_get_monthname\n cpp/locale/time_get/get_monthname\n \n (T... args)\n \n \n T\n do_get_time\n cpp/locale/time_get/get_time\n \n (T... args)\n \n \n T\n do_get_weekday\n cpp/locale/time_get/get_weekday\n \n (T... args)\n \n \n T\n do_get_year\n cpp/locale/time_get/get_year\n \n (T... args)\n \n \n T\n get\n cpp/locale/time_get/get\n \n (T... args)\n \n \n T\n get_date\n cpp/locale/time_get/get_date\n \n (T... args)\n \n \n T\n get_monthname\n cpp/locale/time_get/get_monthname\n \n (T... args)\n \n \n T\n get_time\n cpp/locale/time_get/get_time\n \n (T... args)\n \n \n T\n get_weekday\n cpp/locale/time_get/get_weekday\n \n (T... args)\n \n \n T\n get_year\n cpp/locale/time_get/get_year\n \n (T... args)\n \n std::time_get::iter_type\n \n T\n time_get\n cpp/locale/time_get/time_get\n \n (T... args)\n \n \n T\n ~time_get\n cpp/locale/time_get/~time_get\n \n (T... args)\n \n \n \n std::time_get::char_type\n cpp/locale/time_get\n \n \n std::time_get::iter_type\n cpp/locale/time_get\n \n \n std::time_get_byname\n cpp/locale/time_get_byname\n std::time_get_byname::char_type\n \n T\n date_order\n cpp/locale/time_get/date_order\n \n (T... args)\n \n \n T\n do_date_order\n cpp/locale/time_get/date_order\n \n (T... args)\n \n \n T\n do_get\n cpp/locale/time_get/get\n \n (T... args)\n \n \n T\n do_get_date\n cpp/locale/time_get/get_date\n \n (T... args)\n \n \n T\n do_get_monthname\n cpp/locale/time_get/get_monthname\n \n (T... args)\n \n \n T\n do_get_time\n cpp/locale/time_get/get_time\n \n (T... args)\n \n \n T\n do_get_weekday\n cpp/locale/time_get/get_weekday\n \n (T... args)\n \n \n T\n do_get_year\n cpp/locale/time_get/get_year\n \n (T... args)\n \n \n T\n get\n cpp/locale/time_get/get\n \n (T... args)\n \n \n T\n get_date\n cpp/locale/time_get/get_date\n \n (T... args)\n \n \n T\n get_monthname\n cpp/locale/time_get/get_monthname\n \n (T... args)\n \n \n T\n get_time\n cpp/locale/time_get/get_time\n \n (T... args)\n \n \n T\n get_weekday\n cpp/locale/time_get/get_weekday\n \n (T... args)\n \n \n T\n get_year\n cpp/locale/time_get/get_year\n \n (T... args)\n \n std::time_get_byname::iter_type\n \n T\n time_get_byname\n cpp/locale/time_get_byname\n \n (T... args)\n \n \n T\n ~time_get_byname\n cpp/locale/time_get_byname\n \n (T... args)\n \n \n \n std::time_get_byname::char_type\n cpp/locale/time_get\n \n \n std::time_get_byname::iter_type\n cpp/locale/time_get\n \n \n std::time_put\n cpp/locale/time_put\n std::time_put::char_type\n \n T\n do_put\n cpp/locale/time_put/put\n \n (T... args)\n \n std::time_put::iter_type\n \n T\n put\n cpp/locale/time_put/put\n \n (T... args)\n \n \n T\n time_put\n cpp/locale/time_put/time_put\n \n (T... args)\n \n \n T\n ~time_put\n cpp/locale/time_put/~time_put\n \n (T... args)\n \n \n \n std::time_put::char_type\n cpp/locale/time_put\n \n \n std::time_put::iter_type\n cpp/locale/time_put\n \n \n std::time_put_byname\n cpp/locale/time_put_byname\n std::time_put_byname::char_type\n \n T\n do_put\n cpp/locale/time_put/put\n \n (T... args)\n \n std::time_put_byname::iter_type\n \n T\n put\n cpp/locale/time_put/put\n \n (T... args)\n \n \n T\n time_put_byname\n cpp/locale/time_put_byname\n \n (T... args)\n \n \n T\n ~time_put_byname\n cpp/locale/time_put_byname\n \n (T... args)\n \n \n \n std::time_put_byname::char_type\n cpp/locale/time_put\n \n \n std::time_put_byname::iter_type\n cpp/locale/time_put\n \n \n std::time_t\n cpp/chrono/c/time_t\n \n \n std::timed_mutex\n cpp/thread/timed_mutex\n \n T\n lock\n cpp/thread/timed_mutex/lock\n \n (T... args)\n \n \n T\n native_handle\n cpp/thread/timed_mutex/native_handle\n \n (T... args)\n \n \n T\n timed_mutex\n cpp/thread/timed_mutex/timed_mutex\n \n (T... args)\n \n \n T\n try_lock\n cpp/thread/timed_mutex/try_lock\n \n (T... args)\n \n \n T\n try_lock_for\n cpp/thread/timed_mutex/try_lock_for\n \n (T... args)\n \n \n T\n try_lock_until\n cpp/thread/timed_mutex/try_lock_until\n \n (T... args)\n \n \n T\n unlock\n cpp/thread/timed_mutex/unlock\n \n (T... args)\n \n \n \n std::tm\n cpp/chrono/c/tm\n \n \n std::true_type\n cpp/types/integral_constant\n \n \n std::try_to_lock_t\n cpp/thread/lock_tag_t\n \n \n std::tuple\n cpp/utility/tuple\n \n T\n operator=\n cpp/utility/tuple/operator=\n \n (T... args)\n \n \n T\n swap\n cpp/utility/tuple/swap\n \n (T... args)\n \n \n T\n tuple\n cpp/utility/tuple/tuple\n \n (T... args)\n \n \n \n std::type_index\n cpp/types/type_index\n \n T\n hash_code\n cpp/types/type_index/hash_code\n \n (T... args)\n \n \n T\n name\n cpp/types/type_index/name\n \n (T... args)\n \n \n T\n operator!=\n cpp/types/type_index/operator_cmp\n \n (T... args)\n \n \n T\n operator<\n cpp/types/type_index/operator_cmp\n \n (T... args)\n \n \n T\n operator<=\n cpp/types/type_index/operator_cmp\n \n (T... args)\n \n \n T\n operator==\n cpp/types/type_index/operator_cmp\n \n (T... args)\n \n \n T\n operator>\n cpp/types/type_index/operator_cmp\n \n (T... args)\n \n \n T\n operator>=\n cpp/types/type_index/operator_cmp\n \n (T... args)\n \n \n T\n type_index\n cpp/types/type_index/type_index\n \n (T... args)\n \n \n \n std::type_info\n cpp/types/type_info\n \n T\n before\n cpp/types/type_info/before\n \n (T... args)\n \n \n T\n hash_code\n cpp/types/type_info/hash_code\n \n (T... args)\n \n \n T\n name\n cpp/types/type_info/name\n \n (T... args)\n \n \n T\n operator!=\n cpp/types/type_info/operator_cmp\n \n (T... args)\n \n \n T\n operator==\n cpp/types/type_info/operator_cmp\n \n (T... args)\n \n \n \n std::u16streampos\n cpp/io/fpos\n \n T\n state\n cpp/io/fpos/state\n \n (T... args)\n \n \n \n std::u16string\n cpp/string/basic_string\n \n T\n append\n cpp/string/basic_string/append\n \n (T... args)\n \n \n T\n assign\n cpp/string/basic_string/assign\n \n (T... args)\n \n \n T\n at\n cpp/string/basic_string/at\n \n (T... args)\n \n \n T\n back\n cpp/string/basic_string/back\n \n (T... args)\n \n \n T\n begin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n c_str\n cpp/string/basic_string/c_str\n \n (T... args)\n \n \n T\n capacity\n cpp/string/basic_string/capacity\n \n (T... args)\n \n \n T\n cbegin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n cend\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n clear\n cpp/string/basic_string/clear\n \n (T... args)\n \n \n T\n compare\n cpp/string/basic_string/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/basic_string/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n data\n cpp/string/basic_string/data\n \n (T... args)\n \n \n T\n empty\n cpp/string/basic_string/empty\n \n (T... args)\n \n \n T\n end\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n erase\n cpp/string/basic_string/erase\n \n (T... args)\n \n \n T\n find\n cpp/string/basic_string/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/string/basic_string/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/string/basic_string/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/string/basic_string/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/string/basic_string/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/string/basic_string/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/string/basic_string/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/string/basic_string/insert\n \n (T... args)\n \n \n T\n length\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n max_size\n cpp/string/basic_string/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/string/basic_string/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/string/basic_string/operator_at\n \n (T... args)\n \n \n T\n pop_back\n cpp/string/basic_string/pop_back\n \n (T... args)\n \n \n T\n push_back\n cpp/string/basic_string/push_back\n \n (T... args)\n \n \n T\n rbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n replace\n cpp/string/basic_string/replace\n \n (T... args)\n \n \n T\n reserve\n cpp/string/basic_string/reserve\n \n (T... args)\n \n \n T\n resize\n cpp/string/basic_string/resize\n \n (T... args)\n \n \n T\n rfind\n cpp/string/basic_string/rfind\n \n (T... args)\n \n \n T\n shrink_to_fit\n cpp/string/basic_string/shrink_to_fit\n \n (T... args)\n \n \n T\n size\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n substr\n cpp/string/basic_string/substr\n \n (T... args)\n \n \n T\n swap\n cpp/string/basic_string/swap\n \n (T... args)\n \n \n T\n u16string\n cpp/string/basic_string/basic_string\n \n (T... args)\n \n \n \n std::u16string_view\n cpp/string/basic_string_view\n \n T\n at\n cpp/string/basic_string_view/at\n \n (T... args)\n \n \n T\n back\n cpp/string/basic_string_view/back\n \n (T... args)\n \n \n T\n begin\n cpp/string/basic_string_view/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/string/basic_string_view/begin\n \n (T... args)\n \n \n T\n cend\n cpp/string/basic_string_view/end\n \n (T... args)\n \n \n T\n compare\n cpp/string/basic_string_view/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/basic_string_view/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/string/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/string/basic_string_view/rend\n \n (T... args)\n \n \n T\n data\n cpp/string/basic_string_view/data\n \n (T... args)\n \n \n T\n empty\n cpp/string/basic_string_view/empty\n \n (T... args)\n \n \n T\n end\n cpp/string/basic_string_view/end\n \n (T... args)\n \n \n T\n find\n cpp/string/basic_string_view/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/string/basic_string_view/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/string/basic_string_view/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/string/basic_string_view/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/string/basic_string_view/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/string/basic_string_view/front\n \n (T... args)\n \n \n T\n length\n cpp/string/basic_string_view/size\n \n (T... args)\n \n \n T\n max_size\n cpp/string/basic_string_view/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/string/basic_string_view/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/string/basic_string_view/operator_at\n \n (T... args)\n \n \n T\n rbegin\n cpp/string/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n remove_prefix\n cpp/string/basic_string_view/remove_prefix\n \n (T... args)\n \n \n T\n remove_suffix\n cpp/string/basic_string_view/remove_suffix\n \n (T... args)\n \n \n T\n rend\n cpp/string/basic_string_view/rend\n \n (T... args)\n \n \n T\n rfind\n cpp/string/basic_string_view/rfind\n \n (T... args)\n \n \n T\n size\n cpp/string/basic_string_view/size\n \n (T... args)\n \n \n T\n substr\n cpp/string/basic_string_view/substr\n \n (T... args)\n \n \n T\n swap\n cpp/string/basic_string_view/swap\n \n (T... args)\n \n \n T\n u16string_view\n cpp/string/basic_string_view/basic_string_view\n \n (T... args)\n \n \n \n std::u32streampos\n cpp/io/fpos\n \n T\n state\n cpp/io/fpos/state\n \n (T... args)\n \n \n \n std::u32string\n cpp/string/basic_string\n \n T\n append\n cpp/string/basic_string/append\n \n (T... args)\n \n \n T\n assign\n cpp/string/basic_string/assign\n \n (T... args)\n \n \n T\n at\n cpp/string/basic_string/at\n \n (T... args)\n \n \n T\n back\n cpp/string/basic_string/back\n \n (T... args)\n \n \n T\n begin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n c_str\n cpp/string/basic_string/c_str\n \n (T... args)\n \n \n T\n capacity\n cpp/string/basic_string/capacity\n \n (T... args)\n \n \n T\n cbegin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n cend\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n clear\n cpp/string/basic_string/clear\n \n (T... args)\n \n \n T\n compare\n cpp/string/basic_string/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/basic_string/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n data\n cpp/string/basic_string/data\n \n (T... args)\n \n \n T\n empty\n cpp/string/basic_string/empty\n \n (T... args)\n \n \n T\n end\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n erase\n cpp/string/basic_string/erase\n \n (T... args)\n \n \n T\n find\n cpp/string/basic_string/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/string/basic_string/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/string/basic_string/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/string/basic_string/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/string/basic_string/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/string/basic_string/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/string/basic_string/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/string/basic_string/insert\n \n (T... args)\n \n \n T\n length\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n max_size\n cpp/string/basic_string/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/string/basic_string/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/string/basic_string/operator_at\n \n (T... args)\n \n \n T\n pop_back\n cpp/string/basic_string/pop_back\n \n (T... args)\n \n \n T\n push_back\n cpp/string/basic_string/push_back\n \n (T... args)\n \n \n T\n rbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n replace\n cpp/string/basic_string/replace\n \n (T... args)\n \n \n T\n reserve\n cpp/string/basic_string/reserve\n \n (T... args)\n \n \n T\n resize\n cpp/string/basic_string/resize\n \n (T... args)\n \n \n T\n rfind\n cpp/string/basic_string/rfind\n \n (T... args)\n \n \n T\n shrink_to_fit\n cpp/string/basic_string/shrink_to_fit\n \n (T... args)\n \n \n T\n size\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n substr\n cpp/string/basic_string/substr\n \n (T... args)\n \n \n T\n swap\n cpp/string/basic_string/swap\n \n (T... args)\n \n \n T\n u32string\n cpp/string/basic_string/basic_string\n \n (T... args)\n \n \n \n std::u32string_view\n cpp/string/basic_string_view\n \n T\n at\n cpp/string/basic_string_view/at\n \n (T... args)\n \n \n T\n back\n cpp/string/basic_string_view/back\n \n (T... args)\n \n \n T\n begin\n cpp/string/basic_string_view/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/string/basic_string_view/begin\n \n (T... args)\n \n \n T\n cend\n cpp/string/basic_string_view/end\n \n (T... args)\n \n \n T\n compare\n cpp/string/basic_string_view/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/basic_string_view/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/string/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/string/basic_string_view/rend\n \n (T... args)\n \n \n T\n data\n cpp/string/basic_string_view/data\n \n (T... args)\n \n \n T\n empty\n cpp/string/basic_string_view/empty\n \n (T... args)\n \n \n T\n end\n cpp/string/basic_string_view/end\n \n (T... args)\n \n \n T\n find\n cpp/string/basic_string_view/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/string/basic_string_view/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/string/basic_string_view/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/string/basic_string_view/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/string/basic_string_view/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/string/basic_string_view/front\n \n (T... args)\n \n \n T\n length\n cpp/string/basic_string_view/size\n \n (T... args)\n \n \n T\n max_size\n cpp/string/basic_string_view/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/string/basic_string_view/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/string/basic_string_view/operator_at\n \n (T... args)\n \n \n T\n rbegin\n cpp/string/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n remove_prefix\n cpp/string/basic_string_view/remove_prefix\n \n (T... args)\n \n \n T\n remove_suffix\n cpp/string/basic_string_view/remove_suffix\n \n (T... args)\n \n \n T\n rend\n cpp/string/basic_string_view/rend\n \n (T... args)\n \n \n T\n rfind\n cpp/string/basic_string_view/rfind\n \n (T... args)\n \n \n T\n size\n cpp/string/basic_string_view/size\n \n (T... args)\n \n \n T\n substr\n cpp/string/basic_string_view/substr\n \n (T... args)\n \n \n T\n swap\n cpp/string/basic_string_view/swap\n \n (T... args)\n \n \n T\n u32string_view\n cpp/string/basic_string_view/basic_string_view\n \n (T... args)\n \n \n \n std::uint16_t\n cpp/types/integer\n \n \n std::uint32_t\n cpp/types/integer\n \n \n std::uint64_t\n cpp/types/integer\n \n \n std::uint8_t\n cpp/types/integer\n \n \n std::uint_fast16_t\n cpp/types/integer\n \n \n std::uint_fast32_t\n cpp/types/integer\n \n \n std::uint_fast64_t\n cpp/types/integer\n \n \n std::uint_fast8_t\n cpp/types/integer\n \n \n std::uint_least16_t\n cpp/types/integer\n \n \n std::uint_least32_t\n cpp/types/integer\n \n \n std::uint_least64_t\n cpp/types/integer\n \n \n std::uint_least8_t\n cpp/types/integer\n \n \n std::uintmax_t\n cpp/types/integer\n \n \n std::uintptr_t\n cpp/types/integer\n \n \n std::unary_function\n cpp/utility/functional/unary_function\n \n \n std::unary_negate\n cpp/utility/functional/unary_negate\n \n T\n operator()\n cpp/utility/functional/unary_negate\n \n (T... args)\n \n \n T\n unary_negate\n cpp/utility/functional/unary_negate\n \n (T... args)\n \n \n \n std::underflow_error\n cpp/error/underflow_error\n \n T\n underflow_error\n cpp/error/underflow_error\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::underlying_type\n cpp/types/underlying_type\n \n \n std::underlying_type_t\n cpp/types/underlying_type\n \n \n std::unexpected_handler\n cpp/error/unexpected_handler\n \n \n std::uniform_int_distribution\n cpp/numeric/random/uniform_int_distribution\n \n T\n a\n cpp/numeric/random/uniform_int_distribution/params\n \n (T... args)\n \n \n T\n b\n cpp/numeric/random/uniform_int_distribution/params\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/uniform_int_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/uniform_int_distribution/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/uniform_int_distribution/operator()\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/uniform_int_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/uniform_int_distribution/reset\n \n (T... args)\n \n \n T\n uniform_int_distribution\n cpp/numeric/random/uniform_int_distribution/uniform_int_distribution\n \n (T... args)\n \n \n \n std::uniform_real_distribution\n cpp/numeric/random/uniform_real_distribution\n \n T\n a\n cpp/numeric/random/uniform_real_distribution/params\n \n (T... args)\n \n \n T\n b\n cpp/numeric/random/uniform_real_distribution/params\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/uniform_real_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/uniform_real_distribution/min\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/uniform_real_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/uniform_real_distribution/reset\n \n (T... args)\n \n \n T\n uniform_real_distribution\n cpp/numeric/random/uniform_real_distribution/uniform_real_distribution\n \n (T... args)\n \n \n \n std::unique_lock\n cpp/thread/unique_lock\n \n T\n lock\n cpp/thread/unique_lock/lock\n \n (T... args)\n \n \n T\n mutex\n cpp/thread/unique_lock/mutex\n \n (T... args)\n \n \n T\n operator bool\n cpp/thread/unique_lock/operator_bool\n \n (T... args)\n \n \n T\n operator=\n cpp/thread/unique_lock/operator=\n \n (T... args)\n \n \n T\n owns_lock\n cpp/thread/unique_lock/owns_lock\n \n (T... args)\n \n \n T\n release\n cpp/thread/unique_lock/release\n \n (T... args)\n \n \n T\n swap\n cpp/thread/unique_lock/swap\n \n (T... args)\n \n \n T\n try_lock\n cpp/thread/unique_lock/try_lock\n \n (T... args)\n \n \n T\n try_lock_for\n cpp/thread/unique_lock/try_lock_for\n \n (T... args)\n \n \n T\n try_lock_until\n cpp/thread/unique_lock/try_lock_until\n \n (T... args)\n \n \n T\n unique_lock\n cpp/thread/unique_lock/unique_lock\n \n (T... args)\n \n \n T\n unlock\n cpp/thread/unique_lock/unlock\n \n (T... args)\n \n \n T\n ~unique_lock\n cpp/thread/unique_lock/~unique_lock\n \n (T... args)\n \n \n \n std::unique_ptr\n cpp/memory/unique_ptr\n \n T\n get\n cpp/memory/unique_ptr/get\n \n (T... args)\n \n \n T\n get_deleter\n cpp/memory/unique_ptr/get_deleter\n \n (T... args)\n \n \n T\n operator bool\n cpp/memory/unique_ptr/operator_bool\n \n (T... args)\n \n \n T\n operator*\n cpp/memory/unique_ptr/operator*\n \n (T... args)\n \n \n T\n operator->\n cpp/memory/unique_ptr/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/memory/unique_ptr/operator=\n \n (T... args)\n \n \n T\n release\n cpp/memory/unique_ptr/release\n \n (T... args)\n \n \n T\n reset\n cpp/memory/unique_ptr/reset\n \n (T... args)\n \n \n T\n swap\n cpp/memory/unique_ptr/swap\n \n (T... args)\n \n \n T\n unique_ptr\n cpp/memory/unique_ptr/unique_ptr\n \n (T... args)\n \n \n T\n ~unique_ptr\n cpp/memory/unique_ptr/~unique_ptr\n \n (T... args)\n \n \n \n std::unordered_map\n cpp/container/unordered_map\n \n T\n at\n cpp/container/unordered_map/at\n \n (T... args)\n \n \n T\n begin\n cpp/container/unordered_map/begin\n \n (T... args)\n \n \n T\n begin(int)\n cpp/container/unordered_map/begin2\n \n (T... args)\n \n \n T\n bucket\n cpp/container/unordered_map/bucket\n \n (T... args)\n \n \n T\n bucket_count\n cpp/container/unordered_map/bucket_count\n \n (T... args)\n \n \n T\n bucket_size\n cpp/container/unordered_map/bucket_size\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/unordered_map/begin\n \n (T... args)\n \n \n T\n cbegin(int)\n cpp/container/unordered_map/begin2\n \n (T... args)\n \n \n T\n cend\n cpp/container/unordered_map/end\n \n (T... args)\n \n \n T\n cend(int)\n cpp/container/unordered_map/end2\n \n (T... args)\n \n \n T\n clear\n cpp/container/unordered_map/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/unordered_map/count\n \n (T... args)\n \n \n T\n emplace\n cpp/container/unordered_map/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/unordered_map/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/unordered_map/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/unordered_map/end\n \n (T... args)\n \n \n T\n end(int)\n cpp/container/unordered_map/end2\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/unordered_map/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/unordered_map/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/unordered_map/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/unordered_map/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/unordered_map/get_allocator\n \n (T... args)\n \n \n T\n hash_function\n cpp/container/unordered_map/hash_function\n \n (T... args)\n \n \n T\n insert\n cpp/container/unordered_map/insert\n \n (T... args)\n \n \n T\n insert_or_assign\n cpp/container/unordered_map/insert_or_assign\n \n (T... args)\n \n \n T\n key_eq\n cpp/container/unordered_map/key_eq\n \n (T... args)\n \n \n T\n load_factor\n cpp/container/unordered_map/load_factor\n \n (T... args)\n \n \n T\n max_bucket_count\n cpp/container/unordered_map/max_bucket_count\n \n (T... args)\n \n \n T\n max_load_factor\n cpp/container/unordered_map/max_load_factor\n \n (T... args)\n \n \n T\n max_size\n cpp/container/unordered_map/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/unordered_map/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/unordered_map/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/container/unordered_map/operator_at\n \n (T... args)\n \n \n T\n rehash\n cpp/container/unordered_map/rehash\n \n (T... args)\n \n \n T\n reserve\n cpp/container/unordered_map/reserve\n \n (T... args)\n \n \n T\n size\n cpp/container/unordered_map/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/unordered_map/swap\n \n (T... args)\n \n \n T\n try_emplace\n cpp/container/unordered_map/try_emplace\n \n (T... args)\n \n \n T\n unordered_map\n cpp/container/unordered_map/unordered_map\n \n (T... args)\n \n \n T\n ~unordered_map\n cpp/container/unordered_map/~unordered_map\n \n (T... args)\n \n \n \n std::unordered_multimap\n cpp/container/unordered_multimap\n \n T\n begin\n cpp/container/unordered_multimap/begin\n \n (T... args)\n \n \n T\n begin(int)\n cpp/container/unordered_multimap/begin2\n \n (T... args)\n \n \n T\n bucket\n cpp/container/unordered_multimap/bucket\n \n (T... args)\n \n \n T\n bucket_count\n cpp/container/unordered_multimap/bucket_count\n \n (T... args)\n \n \n T\n bucket_size\n cpp/container/unordered_multimap/bucket_size\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/unordered_multimap/begin\n \n (T... args)\n \n \n T\n cbegin(int)\n cpp/container/unordered_multimap/begin2\n \n (T... args)\n \n \n T\n cend\n cpp/container/unordered_multimap/end\n \n (T... args)\n \n \n T\n cend(int)\n cpp/container/unordered_multimap/end2\n \n (T... args)\n \n \n T\n clear\n cpp/container/unordered_multimap/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/unordered_multimap/count\n \n (T... args)\n \n \n T\n emplace\n cpp/container/unordered_multimap/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/unordered_multimap/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/unordered_multimap/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/unordered_multimap/end\n \n (T... args)\n \n \n T\n end(int)\n cpp/container/unordered_multimap/end2\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/unordered_multimap/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/unordered_multimap/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/unordered_multimap/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/unordered_multimap/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/unordered_multimap/get_allocator\n \n (T... args)\n \n \n T\n hash_function\n cpp/container/unordered_multimap/hash_function\n \n (T... args)\n \n \n T\n insert\n cpp/container/unordered_multimap/insert\n \n (T... args)\n \n \n T\n key_eq\n cpp/container/unordered_multimap/key_eq\n \n (T... args)\n \n \n T\n load_factor\n cpp/container/unordered_multimap/load_factor\n \n (T... args)\n \n \n T\n max_bucket_count\n cpp/container/unordered_multimap/max_bucket_count\n \n (T... args)\n \n \n T\n max_load_factor\n cpp/container/unordered_multimap/max_load_factor\n \n (T... args)\n \n \n T\n max_size\n cpp/container/unordered_multimap/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/unordered_multimap/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/unordered_multimap/operator=\n \n (T... args)\n \n \n T\n rehash\n cpp/container/unordered_multimap/rehash\n \n (T... args)\n \n \n T\n reserve\n cpp/container/unordered_multimap/reserve\n \n (T... args)\n \n \n T\n size\n cpp/container/unordered_multimap/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/unordered_multimap/swap\n \n (T... args)\n \n \n T\n unordered_multimap\n cpp/container/unordered_multimap/unordered_multimap\n \n (T... args)\n \n \n T\n ~unordered_multimap\n cpp/container/unordered_multimap/~unordered_multimap\n \n (T... args)\n \n \n \n std::unordered_multiset\n cpp/container/unordered_multiset\n \n T\n begin\n cpp/container/unordered_multiset/begin\n \n (T... args)\n \n \n T\n begin(int)\n cpp/container/unordered_multiset/begin2\n \n (T... args)\n \n \n T\n bucket\n cpp/container/unordered_multiset/bucket\n \n (T... args)\n \n \n T\n bucket_count\n cpp/container/unordered_multiset/bucket_count\n \n (T... args)\n \n \n T\n bucket_size\n cpp/container/unordered_multiset/bucket_size\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/unordered_multiset/begin\n \n (T... args)\n \n \n T\n cbegin(int)\n cpp/container/unordered_multiset/begin2\n \n (T... args)\n \n \n T\n cend\n cpp/container/unordered_multiset/end\n \n (T... args)\n \n \n T\n cend(int)\n cpp/container/unordered_multiset/end2\n \n (T... args)\n \n \n T\n clear\n cpp/container/unordered_multiset/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/unordered_multiset/count\n \n (T... args)\n \n \n T\n emplace\n cpp/container/unordered_multiset/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/unordered_multiset/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/unordered_multiset/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/unordered_multiset/end\n \n (T... args)\n \n \n T\n end(int)\n cpp/container/unordered_multiset/end2\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/unordered_multiset/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/unordered_multiset/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/unordered_multiset/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/unordered_multiset/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/unordered_multiset/get_allocator\n \n (T... args)\n \n \n T\n hash_function\n cpp/container/unordered_multiset/hash_function\n \n (T... args)\n \n \n T\n insert\n cpp/container/unordered_multiset/insert\n \n (T... args)\n \n \n T\n key_eq\n cpp/container/unordered_multiset/key_eq\n \n (T... args)\n \n \n T\n load_factor\n cpp/container/unordered_multiset/load_factor\n \n (T... args)\n \n \n T\n max_bucket_count\n cpp/container/unordered_multiset/max_bucket_count\n \n (T... args)\n \n \n T\n max_load_factor\n cpp/container/unordered_multiset/max_load_factor\n \n (T... args)\n \n \n T\n max_size\n cpp/container/unordered_multiset/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/unordered_multiset/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/unordered_multiset/operator=\n \n (T... args)\n \n \n T\n rehash\n cpp/container/unordered_multiset/rehash\n \n (T... args)\n \n \n T\n reserve\n cpp/container/unordered_multiset/reserve\n \n (T... args)\n \n \n T\n size\n cpp/container/unordered_multiset/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/unordered_multiset/swap\n \n (T... args)\n \n \n T\n unordered_multiset\n cpp/container/unordered_multiset/unordered_multiset\n \n (T... args)\n \n \n T\n ~unordered_multiset\n cpp/container/unordered_multiset/~unordered_multiset\n \n (T... args)\n \n \n \n std::unordered_set\n cpp/container/unordered_set\n \n T\n begin\n cpp/container/unordered_set/begin\n \n (T... args)\n \n \n T\n begin(int)\n cpp/container/unordered_set/begin2\n \n (T... args)\n \n \n T\n bucket\n cpp/container/unordered_set/bucket\n \n (T... args)\n \n \n T\n bucket_count\n cpp/container/unordered_set/bucket_count\n \n (T... args)\n \n \n T\n bucket_size\n cpp/container/unordered_set/bucket_size\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/unordered_set/begin\n \n (T... args)\n \n \n T\n cbegin(int)\n cpp/container/unordered_set/begin2\n \n (T... args)\n \n \n T\n cend\n cpp/container/unordered_set/end\n \n (T... args)\n \n \n T\n cend(int)\n cpp/container/unordered_set/end2\n \n (T... args)\n \n \n T\n clear\n cpp/container/unordered_set/clear\n \n (T... args)\n \n \n T\n count\n cpp/container/unordered_set/count\n \n (T... args)\n \n \n T\n emplace\n cpp/container/unordered_set/emplace\n \n (T... args)\n \n \n T\n emplace_hint\n cpp/container/unordered_set/emplace_hint\n \n (T... args)\n \n \n T\n empty\n cpp/container/unordered_set/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/unordered_set/end\n \n (T... args)\n \n \n T\n end(int)\n cpp/container/unordered_set/end2\n \n (T... args)\n \n \n T\n equal_range\n cpp/container/unordered_set/equal_range\n \n (T... args)\n \n \n T\n erase\n cpp/container/unordered_set/erase\n \n (T... args)\n \n \n T\n extract\n cpp/container/unordered_set/extract\n \n (T... args)\n \n \n T\n find\n cpp/container/unordered_set/find\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/unordered_set/get_allocator\n \n (T... args)\n \n \n T\n hash_function\n cpp/container/unordered_set/hash_function\n \n (T... args)\n \n \n T\n insert\n cpp/container/unordered_set/insert\n \n (T... args)\n \n \n T\n key_eq\n cpp/container/unordered_set/key_eq\n \n (T... args)\n \n \n T\n load_factor\n cpp/container/unordered_set/load_factor\n \n (T... args)\n \n \n T\n max_bucket_count\n cpp/container/unordered_set/max_bucket_count\n \n (T... args)\n \n \n T\n max_load_factor\n cpp/container/unordered_set/max_load_factor\n \n (T... args)\n \n \n T\n max_size\n cpp/container/unordered_set/max_size\n \n (T... args)\n \n \n T\n merge\n cpp/container/unordered_set/merge\n \n (T... args)\n \n \n T\n operator=\n cpp/container/unordered_set/operator=\n \n (T... args)\n \n \n T\n rehash\n cpp/container/unordered_set/rehash\n \n (T... args)\n \n \n T\n reserve\n cpp/container/unordered_set/reserve\n \n (T... args)\n \n \n T\n size\n cpp/container/unordered_set/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/unordered_set/swap\n \n (T... args)\n \n \n T\n unordered_set\n cpp/container/unordered_set/unordered_set\n \n (T... args)\n \n \n T\n ~unordered_set\n cpp/container/unordered_set/~unordered_set\n \n (T... args)\n \n \n \n std::uses_allocator\n cpp/memory/uses_allocator\n \n \n std::valarray\n cpp/numeric/valarray\n \n \n std::variant\n cpp/utility/variant\n \n T\n emplace\n cpp/utility/variant/emplace\n \n (T... args)\n \n \n T\n index\n cpp/utility/variant/index\n \n (T... args)\n \n \n T\n operator=\n cpp/utility/variant/operator=\n \n (T... args)\n \n \n T\n swap\n cpp/utility/variant/swap\n \n (T... args)\n \n \n T\n valueless_by_exception\n cpp/utility/variant/valueless_by_exception\n \n (T... args)\n \n \n T\n variant\n cpp/utility/variant/variant\n \n (T... args)\n \n \n T\n ~variant\n cpp/utility/variant/~variant\n \n (T... args)\n \n \n \n std::variant_alternative\n cpp/utility/variant/variant_alternative\n \n \n std::variant_alternative_t\n cpp/utility/variant/variant_alternative\n \n \n std::variant_size\n cpp/utility/variant/variant_size\n \n \n std::vector\n cpp/container/vector\n \n T\n assign\n cpp/container/vector/assign\n \n (T... args)\n \n \n T\n at\n cpp/container/vector/at\n \n (T... args)\n \n \n T\n back\n cpp/container/vector/back\n \n (T... args)\n \n \n T\n begin\n cpp/container/vector/begin\n \n (T... args)\n \n \n T\n capacity\n cpp/container/vector/capacity\n \n (T... args)\n \n \n T\n cbegin\n cpp/container/vector/begin\n \n (T... args)\n \n \n T\n cend\n cpp/container/vector/end\n \n (T... args)\n \n \n T\n clear\n cpp/container/vector/clear\n \n (T... args)\n \n \n T\n crbegin\n cpp/container/vector/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/container/vector/rend\n \n (T... args)\n \n \n T\n data\n cpp/container/vector/data\n \n (T... args)\n \n \n T\n emplace\n cpp/container/vector/emplace\n \n (T... args)\n \n \n T\n emplace_back\n cpp/container/vector/emplace_back\n \n (T... args)\n \n \n T\n empty\n cpp/container/vector/empty\n \n (T... args)\n \n \n T\n end\n cpp/container/vector/end\n \n (T... args)\n \n \n T\n erase\n cpp/container/vector/erase\n \n (T... args)\n \n \n T\n front\n cpp/container/vector/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/container/vector/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/container/vector/insert\n \n (T... args)\n \n \n T\n max_size\n cpp/container/vector/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/container/vector/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/container/vector/operator_at\n \n (T... args)\n \n \n T\n pop_back\n cpp/container/vector/pop_back\n \n (T... args)\n \n \n T\n push_back\n cpp/container/vector/push_back\n \n (T... args)\n \n \n T\n rbegin\n cpp/container/vector/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/container/vector/rend\n \n (T... args)\n \n \n T\n reserve\n cpp/container/vector/reserve\n \n (T... args)\n \n \n T\n resize\n cpp/container/vector/resize\n \n (T... args)\n \n \n T\n shrink_to_fit\n cpp/container/vector/shrink_to_fit\n \n (T... args)\n \n \n T\n size\n cpp/container/vector/size\n \n (T... args)\n \n \n T\n swap\n cpp/container/vector/swap\n \n (T... args)\n \n \n T\n vector\n cpp/container/vector/vector\n \n (T... args)\n \n \n T\n ~vector\n cpp/container/vector/~vector\n \n (T... args)\n \n \n \n std::void_t\n cpp/types/void_t\n \n \n std::wbuffer_convert\n cpp/locale/wbuffer_convert\n \n T\n rdbuf\n cpp/locale/wbuffer_convert/rdbuf\n \n (T... args)\n \n \n T\n state\n cpp/locale/wbuffer_convert/state\n \n (T... args)\n \n \n T\n wbuffer_convert\n cpp/locale/wbuffer_convert/wbuffer_convert\n \n (T... args)\n \n \n T\n ~wbuffer_convert\n cpp/locale/wbuffer_convert/~wbuffer_convert\n \n (T... args)\n \n \n \n std::wcerr\n cpp/io/cerr\n \n \n std::wcin\n cpp/io/cin\n \n \n std::wclog\n cpp/io/clog\n \n \n std::wcmatch\n cpp/regex/match_results\n \n T\n begin\n cpp/regex/match_results/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/regex/match_results/begin\n \n (T... args)\n \n \n T\n cend\n cpp/regex/match_results/end\n \n (T... args)\n \n \n T\n empty\n cpp/regex/match_results/empty\n \n (T... args)\n \n \n T\n end\n cpp/regex/match_results/end\n \n (T... args)\n \n \n T\n format\n cpp/regex/match_results/format\n \n (T... args)\n \n \n T\n get_allocator\n cpp/regex/match_results/get_allocator\n \n (T... args)\n \n \n T\n length\n cpp/regex/match_results/length\n \n (T... args)\n \n \n T\n max_size\n cpp/regex/match_results/max_size\n \n (T... args)\n \n \n T\n operator[]\n cpp/regex/match_results/operator_at\n \n (T... args)\n \n \n T\n position\n cpp/regex/match_results/position\n \n (T... args)\n \n \n T\n prefix\n cpp/regex/match_results/prefix\n \n (T... args)\n \n \n T\n ready\n cpp/regex/match_results/ready\n \n (T... args)\n \n \n T\n size\n cpp/regex/match_results/size\n \n (T... args)\n \n \n T\n str\n cpp/regex/match_results/str\n \n (T... args)\n \n \n T\n suffix\n cpp/regex/match_results/suffix\n \n (T... args)\n \n \n T\n swap\n cpp/regex/match_results/swap\n \n (T... args)\n \n \n T\n wcmatch\n cpp/regex/match_results/match_results\n \n (T... args)\n \n \n T\n ~wcmatch\n cpp/regex/match_results/~match_results\n \n (T... args)\n \n \n \n std::wcout\n cpp/io/cout\n \n \n std::wcregex_iterator\n cpp/regex/regex_iterator\n \n T\n operator!=\n cpp/regex/regex_iterator/operator_cmp\n \n (T... args)\n \n \n T\n operator*\n cpp/regex/regex_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/regex/regex_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/regex/regex_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator->\n cpp/regex/regex_iterator/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/regex/regex_iterator/operator=\n \n (T... args)\n \n \n T\n operator==\n cpp/regex/regex_iterator/operator_cmp\n \n (T... args)\n \n \n T\n wcregex_iterator\n cpp/regex/regex_iterator/regex_iterator\n \n (T... args)\n \n \n \n std::wcregex_token_iterator\n cpp/regex/regex_token_iterator\n \n T\n operator!=\n cpp/regex/regex_token_iterator/operator_cmp\n \n (T... args)\n \n \n T\n operator*\n cpp/regex/regex_token_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/regex/regex_token_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/regex/regex_token_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator->\n cpp/regex/regex_token_iterator/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/regex/regex_token_iterator/operator=\n \n (T... args)\n \n \n T\n operator==\n cpp/regex/regex_token_iterator/operator_cmp\n \n (T... args)\n \n \n T\n wcregex_token_iterator\n cpp/regex/regex_token_iterator/regex_token_iterator\n \n (T... args)\n \n \n \n std::wcsub_match\n cpp/regex/sub_match\n \n T\n compare\n cpp/regex/sub_match/compare\n \n (T... args)\n \n \n T\n length\n cpp/regex/sub_match/length\n \n (T... args)\n \n \n T\n operator string_type\n cpp/regex/sub_match/str\n \n (T... args)\n \n \n T\n str\n cpp/regex/sub_match/str\n \n (T... args)\n \n \n T\n wcsub_match\n cpp/regex/sub_match/sub_match\n \n (T... args)\n \n \n \n std::weak_ptr\n cpp/memory/weak_ptr\n \n T\n expired\n cpp/memory/weak_ptr/expired\n \n (T... args)\n \n \n T\n lock\n cpp/memory/weak_ptr/lock\n \n (T... args)\n \n \n T\n operator=\n cpp/memory/weak_ptr/operator=\n \n (T... args)\n \n \n T\n owner_before\n cpp/memory/weak_ptr/owner_before\n \n (T... args)\n \n \n T\n reset\n cpp/memory/weak_ptr/reset\n \n (T... args)\n \n \n T\n swap\n cpp/memory/weak_ptr/swap\n \n (T... args)\n \n \n T\n use_count\n cpp/memory/weak_ptr/use_count\n \n (T... args)\n \n \n T\n weak_ptr\n cpp/memory/weak_ptr/weak_ptr\n \n (T... args)\n \n \n T\n ~weak_ptr\n cpp/memory/weak_ptr/~weak_ptr\n \n (T... args)\n \n \n \n std::weibull_distribution\n cpp/numeric/random/weibull_distribution\n \n T\n a\n cpp/numeric/random/weibull_distribution/params\n \n (T... args)\n \n \n T\n b\n cpp/numeric/random/weibull_distribution/params\n \n (T... args)\n \n \n T\n max\n cpp/numeric/random/weibull_distribution/max\n \n (T... args)\n \n \n T\n min\n cpp/numeric/random/weibull_distribution/min\n \n (T... args)\n \n \n T\n operator()\n cpp/numeric/random/weibull_distribution/operator()\n \n (T... args)\n \n \n T\n param\n cpp/numeric/random/weibull_distribution/param\n \n (T... args)\n \n \n T\n reset\n cpp/numeric/random/weibull_distribution/reset\n \n (T... args)\n \n \n T\n weibull_distribution\n cpp/numeric/random/weibull_distribution/weibull_distribution\n \n (T... args)\n \n \n \n std::wfilebuf\n cpp/io/basic_filebuf\n \n T\n close\n cpp/io/basic_filebuf/close\n \n (T... args)\n \n \n T\n eback\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n egptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n epptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n gbump\n cpp/io/basic_streambuf/gbump\n \n (T... args)\n \n \n T\n getloc\n cpp/io/basic_streambuf/getloc\n \n (T... args)\n \n \n T\n gptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n in_avail\n cpp/io/basic_streambuf/in_avail\n \n (T... args)\n \n \n T\n is_open\n cpp/io/basic_filebuf/is_open\n \n (T... args)\n \n \n T\n open\n cpp/io/basic_filebuf/open\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_filebuf/operator=\n \n (T... args)\n \n \n T\n overflow\n cpp/io/basic_streambuf/overflow\n \n (T... args)\n \n \n T\n pbackfail\n cpp/io/basic_streambuf/pbackfail\n \n (T... args)\n \n \n T\n pbase\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pbump\n cpp/io/basic_streambuf/pbump\n \n (T... args)\n \n \n T\n pptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pubimbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n pubseekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n pubseekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n pubsetbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n pubsync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n sbumpc\n cpp/io/basic_streambuf/sbumpc\n \n (T... args)\n \n \n T\n seekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n seekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n setbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n setg\n cpp/io/basic_streambuf/setg\n \n (T... args)\n \n \n T\n setp\n cpp/io/basic_streambuf/setp\n \n (T... args)\n \n \n T\n sgetc\n cpp/io/basic_streambuf/sgetc\n \n (T... args)\n \n \n T\n sgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n showmanyc\n cpp/io/basic_streambuf/showmanyc\n \n (T... args)\n \n \n T\n snextc\n cpp/io/basic_streambuf/snextc\n \n (T... args)\n \n \n T\n sputbackc\n cpp/io/basic_streambuf/sputbackc\n \n (T... args)\n \n \n T\n sputc\n cpp/io/basic_streambuf/sputc\n \n (T... args)\n \n \n T\n sputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n sungetc\n cpp/io/basic_streambuf/sungetc\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_streambuf/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n uflow\n cpp/io/basic_streambuf/uflow\n \n (T... args)\n \n \n T\n underflow\n cpp/io/basic_streambuf/underflow\n \n (T... args)\n \n \n T\n wfilebuf\n cpp/io/basic_filebuf/basic_filebuf\n \n (T... args)\n \n \n T\n xsgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n xsputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n ~wfilebuf\n cpp/io/basic_filebuf/~basic_filebuf\n \n (T... args)\n \n \n \n std::wfstream\n cpp/io/basic_fstream\n std::wfstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n close\n cpp/io/basic_fstream/close\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::wfstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::wfstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n is_open\n cpp/io/basic_fstream/is_open\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n open\n cpp/io/basic_fstream/open\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_fstream/operator=\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::wfstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n wfstream\n cpp/io/basic_fstream/basic_fstream\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::wfstream::Init\n cpp/io/ios_base/Init\n \n \n std::wfstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::wfstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::wfstream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::wifstream\n cpp/io/basic_ifstream\n std::wifstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n close\n cpp/io/basic_ifstream/close\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::wifstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::wifstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n is_open\n cpp/io/basic_ifstream/is_open\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n open\n cpp/io/basic_ifstream/open\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_ifstream/operator=\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n std::wifstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n wifstream\n cpp/io/basic_ifstream/basic_ifstream\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::wifstream::Init\n cpp/io/ios_base/Init\n \n \n std::wifstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::wifstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::wifstream::sentry\n cpp/io/basic_istream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::wiostream\n cpp/io/basic_iostream\n std::wiostream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::wiostream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::wiostream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::wiostream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n wiostream\n cpp/io/basic_iostream/basic_iostream\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n T\n ~wiostream\n cpp/io/basic_iostream/~basic_iostream\n \n (T... args)\n \n \n \n std::wiostream::Init\n cpp/io/ios_base/Init\n \n \n std::wiostream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::wiostream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::wiostream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::wistream\n cpp/io/basic_istream\n std::wistream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::wistream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::wistream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n std::wistream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n wistream\n cpp/io/basic_istream/basic_istream\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n T\n ~wistream\n cpp/io/basic_istream/~basic_istream\n \n (T... args)\n \n \n \n std::wistream::Init\n cpp/io/ios_base/Init\n \n \n std::wistream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::wistream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::wistream::sentry\n cpp/io/basic_istream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::wistringstream\n cpp/io/basic_istringstream\n std::wistringstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::wistringstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::wistringstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_istringstream/operator=\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n std::wistringstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n str\n cpp/io/basic_istringstream/str\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n wistringstream\n cpp/io/basic_istringstream/basic_istringstream\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::wistringstream::Init\n cpp/io/ios_base/Init\n \n \n std::wistringstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::wistringstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::wistringstream::sentry\n cpp/io/basic_istream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::wofstream\n cpp/io/basic_ofstream\n std::wofstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n close\n cpp/io/basic_ofstream/close\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::wofstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::wofstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n is_open\n cpp/io/basic_ofstream/is_open\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n open\n cpp/io/basic_ofstream/open\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_ofstream/operator=\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::wofstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n wofstream\n cpp/io/basic_ofstream/basic_ofstream\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::wofstream::Init\n cpp/io/ios_base/Init\n \n \n std::wofstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::wofstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::wofstream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n \n std::wostream\n cpp/io/basic_ostream\n std::wostream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::wostream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::wostream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::wostream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n wostream\n cpp/io/basic_ostream/basic_ostream\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n T\n ~wostream\n cpp/io/basic_ostream/~basic_ostream\n \n (T... args)\n \n \n \n std::wostream::Init\n cpp/io/ios_base/Init\n \n \n std::wostream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::wostream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::wostream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n \n std::wostringstream\n cpp/io/basic_ostringstream\n std::wostringstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::wostringstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::wostringstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_ostringstream/operator=\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::wostringstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n str\n cpp/io/basic_ostringstream/str\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n wostringstream\n cpp/io/basic_ostringstream/basic_ostringstream\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::wostringstream::Init\n cpp/io/ios_base/Init\n \n \n std::wostringstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::wostringstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::wostringstream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_ostream/sentry\n \n (T... args)\n \n \n \n std::wregex\n cpp/regex/basic_regex\n \n T\n assign\n cpp/regex/basic_regex/assign\n \n (T... args)\n \n \n T\n flags\n cpp/regex/basic_regex/flags\n \n (T... args)\n \n \n T\n getloc\n cpp/regex/basic_regex/getloc\n \n (T... args)\n \n \n T\n imbue\n cpp/regex/basic_regex/imbue\n \n (T... args)\n \n \n T\n mark_count\n cpp/regex/basic_regex/mark_count\n \n (T... args)\n \n \n T\n operator=\n cpp/regex/basic_regex/operator=\n \n (T... args)\n \n \n T\n swap\n cpp/regex/basic_regex/swap\n \n (T... args)\n \n \n T\n wregex\n cpp/regex/basic_regex/basic_regex\n \n (T... args)\n \n \n T\n ~wregex\n cpp/regex/basic_regex/~basic_regex\n \n (T... args)\n \n \n \n std::wsmatch\n cpp/regex/match_results\n \n T\n begin\n cpp/regex/match_results/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/regex/match_results/begin\n \n (T... args)\n \n \n T\n cend\n cpp/regex/match_results/end\n \n (T... args)\n \n \n T\n empty\n cpp/regex/match_results/empty\n \n (T... args)\n \n \n T\n end\n cpp/regex/match_results/end\n \n (T... args)\n \n \n T\n format\n cpp/regex/match_results/format\n \n (T... args)\n \n \n T\n get_allocator\n cpp/regex/match_results/get_allocator\n \n (T... args)\n \n \n T\n length\n cpp/regex/match_results/length\n \n (T... args)\n \n \n T\n max_size\n cpp/regex/match_results/max_size\n \n (T... args)\n \n \n T\n operator[]\n cpp/regex/match_results/operator_at\n \n (T... args)\n \n \n T\n position\n cpp/regex/match_results/position\n \n (T... args)\n \n \n T\n prefix\n cpp/regex/match_results/prefix\n \n (T... args)\n \n \n T\n ready\n cpp/regex/match_results/ready\n \n (T... args)\n \n \n T\n size\n cpp/regex/match_results/size\n \n (T... args)\n \n \n T\n str\n cpp/regex/match_results/str\n \n (T... args)\n \n \n T\n suffix\n cpp/regex/match_results/suffix\n \n (T... args)\n \n \n T\n swap\n cpp/regex/match_results/swap\n \n (T... args)\n \n \n T\n wsmatch\n cpp/regex/match_results/match_results\n \n (T... args)\n \n \n T\n ~wsmatch\n cpp/regex/match_results/~match_results\n \n (T... args)\n \n \n \n std::wsregex_iterator\n cpp/regex/regex_iterator\n \n T\n operator!=\n cpp/regex/regex_iterator/operator_cmp\n \n (T... args)\n \n \n T\n operator*\n cpp/regex/regex_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/regex/regex_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/regex/regex_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator->\n cpp/regex/regex_iterator/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/regex/regex_iterator/operator=\n \n (T... args)\n \n \n T\n operator==\n cpp/regex/regex_iterator/operator_cmp\n \n (T... args)\n \n \n T\n wsregex_iterator\n cpp/regex/regex_iterator/regex_iterator\n \n (T... args)\n \n \n \n std::wsregex_token_iterator\n cpp/regex/regex_token_iterator\n \n T\n operator!=\n cpp/regex/regex_token_iterator/operator_cmp\n \n (T... args)\n \n \n T\n operator*\n cpp/regex/regex_token_iterator/operator*\n \n (T... args)\n \n \n T\n operator++\n cpp/regex/regex_token_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator++(int)\n cpp/regex/regex_token_iterator/operator_arith\n \n (T... args)\n \n \n T\n operator->\n cpp/regex/regex_token_iterator/operator*\n \n (T... args)\n \n \n T\n operator=\n cpp/regex/regex_token_iterator/operator=\n \n (T... args)\n \n \n T\n operator==\n cpp/regex/regex_token_iterator/operator_cmp\n \n (T... args)\n \n \n T\n wsregex_token_iterator\n cpp/regex/regex_token_iterator/regex_token_iterator\n \n (T... args)\n \n \n \n std::wssub_match\n cpp/regex/sub_match\n \n T\n compare\n cpp/regex/sub_match/compare\n \n (T... args)\n \n \n T\n length\n cpp/regex/sub_match/length\n \n (T... args)\n \n \n T\n operator string_type\n cpp/regex/sub_match/str\n \n (T... args)\n \n \n T\n str\n cpp/regex/sub_match/str\n \n (T... args)\n \n \n T\n wssub_match\n cpp/regex/sub_match/sub_match\n \n (T... args)\n \n \n \n std::wstreambuf\n cpp/io/basic_streambuf\n \n T\n eback\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n egptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n epptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n gbump\n cpp/io/basic_streambuf/gbump\n \n (T... args)\n \n \n T\n getloc\n cpp/io/basic_streambuf/getloc\n \n (T... args)\n \n \n T\n gptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n in_avail\n cpp/io/basic_streambuf/in_avail\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_streambuf/operator=\n \n (T... args)\n \n \n T\n overflow\n cpp/io/basic_streambuf/overflow\n \n (T... args)\n \n \n T\n pbackfail\n cpp/io/basic_streambuf/pbackfail\n \n (T... args)\n \n \n T\n pbase\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pbump\n cpp/io/basic_streambuf/pbump\n \n (T... args)\n \n \n T\n pptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pubimbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n pubseekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n pubseekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n pubsetbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n pubsync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n sbumpc\n cpp/io/basic_streambuf/sbumpc\n \n (T... args)\n \n \n T\n seekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n seekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n setbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n setg\n cpp/io/basic_streambuf/setg\n \n (T... args)\n \n \n T\n setp\n cpp/io/basic_streambuf/setp\n \n (T... args)\n \n \n T\n sgetc\n cpp/io/basic_streambuf/sgetc\n \n (T... args)\n \n \n T\n sgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n showmanyc\n cpp/io/basic_streambuf/showmanyc\n \n (T... args)\n \n \n T\n snextc\n cpp/io/basic_streambuf/snextc\n \n (T... args)\n \n \n T\n sputbackc\n cpp/io/basic_streambuf/sputbackc\n \n (T... args)\n \n \n T\n sputc\n cpp/io/basic_streambuf/sputc\n \n (T... args)\n \n \n T\n sputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n sungetc\n cpp/io/basic_streambuf/sungetc\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_streambuf/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n uflow\n cpp/io/basic_streambuf/uflow\n \n (T... args)\n \n \n T\n underflow\n cpp/io/basic_streambuf/underflow\n \n (T... args)\n \n \n T\n wstreambuf\n cpp/io/basic_streambuf/basic_streambuf\n \n (T... args)\n \n \n T\n xsgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n xsputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n ~wstreambuf\n cpp/io/basic_streambuf/~basic_streambuf\n \n (T... args)\n \n \n \n std::wstreampos\n cpp/io/fpos\n \n T\n state\n cpp/io/fpos/state\n \n (T... args)\n \n \n \n std::wstring\n cpp/string/basic_string\n \n T\n append\n cpp/string/basic_string/append\n \n (T... args)\n \n \n T\n assign\n cpp/string/basic_string/assign\n \n (T... args)\n \n \n T\n at\n cpp/string/basic_string/at\n \n (T... args)\n \n \n T\n back\n cpp/string/basic_string/back\n \n (T... args)\n \n \n T\n begin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n c_str\n cpp/string/basic_string/c_str\n \n (T... args)\n \n \n T\n capacity\n cpp/string/basic_string/capacity\n \n (T... args)\n \n \n T\n cbegin\n cpp/string/basic_string/begin\n \n (T... args)\n \n \n T\n cend\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n clear\n cpp/string/basic_string/clear\n \n (T... args)\n \n \n T\n compare\n cpp/string/basic_string/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/basic_string/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n data\n cpp/string/basic_string/data\n \n (T... args)\n \n \n T\n empty\n cpp/string/basic_string/empty\n \n (T... args)\n \n \n T\n end\n cpp/string/basic_string/end\n \n (T... args)\n \n \n T\n erase\n cpp/string/basic_string/erase\n \n (T... args)\n \n \n T\n find\n cpp/string/basic_string/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/string/basic_string/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/string/basic_string/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/string/basic_string/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/string/basic_string/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/string/basic_string/front\n \n (T... args)\n \n \n T\n get_allocator\n cpp/string/basic_string/get_allocator\n \n (T... args)\n \n \n T\n insert\n cpp/string/basic_string/insert\n \n (T... args)\n \n \n T\n length\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n max_size\n cpp/string/basic_string/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/string/basic_string/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/string/basic_string/operator_at\n \n (T... args)\n \n \n T\n pop_back\n cpp/string/basic_string/pop_back\n \n (T... args)\n \n \n T\n push_back\n cpp/string/basic_string/push_back\n \n (T... args)\n \n \n T\n rbegin\n cpp/string/basic_string/rbegin\n \n (T... args)\n \n \n T\n rend\n cpp/string/basic_string/rend\n \n (T... args)\n \n \n T\n replace\n cpp/string/basic_string/replace\n \n (T... args)\n \n \n T\n reserve\n cpp/string/basic_string/reserve\n \n (T... args)\n \n \n T\n resize\n cpp/string/basic_string/resize\n \n (T... args)\n \n \n T\n rfind\n cpp/string/basic_string/rfind\n \n (T... args)\n \n \n T\n shrink_to_fit\n cpp/string/basic_string/shrink_to_fit\n \n (T... args)\n \n \n T\n size\n cpp/string/basic_string/size\n \n (T... args)\n \n \n T\n substr\n cpp/string/basic_string/substr\n \n (T... args)\n \n \n T\n swap\n cpp/string/basic_string/swap\n \n (T... args)\n \n \n T\n wstring\n cpp/string/basic_string/basic_string\n \n (T... args)\n \n \n \n std::wstring_convert\n cpp/locale/wstring_convert\n \n T\n converted\n cpp/locale/wstring_convert/converted\n \n (T... args)\n \n \n T\n from_bytes\n cpp/locale/wstring_convert/from_bytes\n \n (T... args)\n \n \n T\n state\n cpp/locale/wstring_convert/state\n \n (T... args)\n \n \n T\n to_bytes\n cpp/locale/wstring_convert/to_bytes\n \n (T... args)\n \n \n T\n wstring_convert\n cpp/locale/wstring_convert/wstring_convert\n \n (T... args)\n \n \n T\n ~wstring_convert\n cpp/locale/wstring_convert/~wstring_convert\n \n (T... args)\n \n \n \n std::wstring_view\n cpp/string/basic_string_view\n \n T\n at\n cpp/string/basic_string_view/at\n \n (T... args)\n \n \n T\n back\n cpp/string/basic_string_view/back\n \n (T... args)\n \n \n T\n begin\n cpp/string/basic_string_view/begin\n \n (T... args)\n \n \n T\n cbegin\n cpp/string/basic_string_view/begin\n \n (T... args)\n \n \n T\n cend\n cpp/string/basic_string_view/end\n \n (T... args)\n \n \n T\n compare\n cpp/string/basic_string_view/compare\n \n (T... args)\n \n \n T\n copy\n cpp/string/basic_string_view/copy\n \n (T... args)\n \n \n T\n crbegin\n cpp/string/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n crend\n cpp/string/basic_string_view/rend\n \n (T... args)\n \n \n T\n data\n cpp/string/basic_string_view/data\n \n (T... args)\n \n \n T\n empty\n cpp/string/basic_string_view/empty\n \n (T... args)\n \n \n T\n end\n cpp/string/basic_string_view/end\n \n (T... args)\n \n \n T\n find\n cpp/string/basic_string_view/find\n \n (T... args)\n \n \n T\n find_first_not_of\n cpp/string/basic_string_view/find_first_not_of\n \n (T... args)\n \n \n T\n find_first_of\n cpp/string/basic_string_view/find_first_of\n \n (T... args)\n \n \n T\n find_last_not_of\n cpp/string/basic_string_view/find_last_not_of\n \n (T... args)\n \n \n T\n find_last_of\n cpp/string/basic_string_view/find_last_of\n \n (T... args)\n \n \n T\n front\n cpp/string/basic_string_view/front\n \n (T... args)\n \n \n T\n length\n cpp/string/basic_string_view/size\n \n (T... args)\n \n \n T\n max_size\n cpp/string/basic_string_view/max_size\n \n (T... args)\n \n \n T\n operator=\n cpp/string/basic_string_view/operator=\n \n (T... args)\n \n \n T\n operator[]\n cpp/string/basic_string_view/operator_at\n \n (T... args)\n \n \n T\n rbegin\n cpp/string/basic_string_view/rbegin\n \n (T... args)\n \n \n T\n remove_prefix\n cpp/string/basic_string_view/remove_prefix\n \n (T... args)\n \n \n T\n remove_suffix\n cpp/string/basic_string_view/remove_suffix\n \n (T... args)\n \n \n T\n rend\n cpp/string/basic_string_view/rend\n \n (T... args)\n \n \n T\n rfind\n cpp/string/basic_string_view/rfind\n \n (T... args)\n \n \n T\n size\n cpp/string/basic_string_view/size\n \n (T... args)\n \n \n T\n substr\n cpp/string/basic_string_view/substr\n \n (T... args)\n \n \n T\n swap\n cpp/string/basic_string_view/swap\n \n (T... args)\n \n \n T\n wstring_view\n cpp/string/basic_string_view/basic_string_view\n \n (T... args)\n \n \n \n std::wstringbuf\n cpp/io/basic_stringbuf\n \n T\n eback\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n egptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n epptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n gbump\n cpp/io/basic_streambuf/gbump\n \n (T... args)\n \n \n T\n getloc\n cpp/io/basic_streambuf/getloc\n \n (T... args)\n \n \n T\n gptr\n cpp/io/basic_streambuf/gptr\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n in_avail\n cpp/io/basic_streambuf/in_avail\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_stringbuf/operator=\n \n (T... args)\n \n \n T\n overflow\n cpp/io/basic_streambuf/overflow\n \n (T... args)\n \n \n T\n pbackfail\n cpp/io/basic_streambuf/pbackfail\n \n (T... args)\n \n \n T\n pbase\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pbump\n cpp/io/basic_streambuf/pbump\n \n (T... args)\n \n \n T\n pptr\n cpp/io/basic_streambuf/pptr\n \n (T... args)\n \n \n T\n pubimbue\n cpp/io/basic_streambuf/pubimbue\n \n (T... args)\n \n \n T\n pubseekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n pubseekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n pubsetbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n pubsync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n sbumpc\n cpp/io/basic_streambuf/sbumpc\n \n (T... args)\n \n \n T\n seekoff\n cpp/io/basic_streambuf/pubseekoff\n \n (T... args)\n \n \n T\n seekpos\n cpp/io/basic_streambuf/pubseekpos\n \n (T... args)\n \n \n T\n setbuf\n cpp/io/basic_streambuf/pubsetbuf\n \n (T... args)\n \n \n T\n setg\n cpp/io/basic_streambuf/setg\n \n (T... args)\n \n \n T\n setp\n cpp/io/basic_streambuf/setp\n \n (T... args)\n \n \n T\n sgetc\n cpp/io/basic_streambuf/sgetc\n \n (T... args)\n \n \n T\n sgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n showmanyc\n cpp/io/basic_streambuf/showmanyc\n \n (T... args)\n \n \n T\n snextc\n cpp/io/basic_streambuf/snextc\n \n (T... args)\n \n \n T\n sputbackc\n cpp/io/basic_streambuf/sputbackc\n \n (T... args)\n \n \n T\n sputc\n cpp/io/basic_streambuf/sputc\n \n (T... args)\n \n \n T\n sputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n T\n str\n cpp/io/basic_stringbuf/str\n \n (T... args)\n \n \n T\n sungetc\n cpp/io/basic_streambuf/sungetc\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_streambuf/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_streambuf/pubsync\n \n (T... args)\n \n \n T\n uflow\n cpp/io/basic_streambuf/uflow\n \n (T... args)\n \n \n T\n underflow\n cpp/io/basic_streambuf/underflow\n \n (T... args)\n \n \n T\n wstringbuf\n cpp/io/basic_stringbuf/basic_stringbuf\n \n (T... args)\n \n \n T\n xsgetn\n cpp/io/basic_streambuf/sgetn\n \n (T... args)\n \n \n T\n xsputn\n cpp/io/basic_streambuf/sputn\n \n (T... args)\n \n \n \n std::wstringstream\n cpp/io/basic_stringstream\n std::wstringstream::Init\n \n T\n bad\n cpp/io/basic_ios/bad\n \n (T... args)\n \n \n T\n clear\n cpp/io/basic_ios/clear\n \n (T... args)\n \n \n T\n copyfmt\n cpp/io/basic_ios/copyfmt\n \n (T... args)\n \n \n T\n eof\n cpp/io/basic_ios/eof\n \n (T... args)\n \n std::wstringstream::event_callback\n \n T\n exceptions\n cpp/io/basic_ios/exceptions\n \n (T... args)\n \n \n T\n fail\n cpp/io/basic_ios/fail\n \n (T... args)\n \n std::wstringstream::failure\n \n T\n fill\n cpp/io/basic_ios/fill\n \n (T... args)\n \n \n T\n flags\n cpp/io/ios_base/flags\n \n (T... args)\n \n \n T\n flush\n cpp/io/basic_ostream/flush\n \n (T... args)\n \n \n T\n gcount\n cpp/io/basic_istream/gcount\n \n (T... args)\n \n \n T\n get\n cpp/io/basic_istream/get\n \n (T... args)\n \n \n T\n getline\n cpp/io/basic_istream/getline\n \n (T... args)\n \n \n T\n getloc\n cpp/io/ios_base/getloc\n \n (T... args)\n \n \n T\n good\n cpp/io/basic_ios/good\n \n (T... args)\n \n \n T\n ignore\n cpp/io/basic_istream/ignore\n \n (T... args)\n \n \n T\n imbue\n cpp/io/basic_ios/imbue\n \n (T... args)\n \n \n T\n init\n cpp/io/basic_ios/init\n \n (T... args)\n \n \n T\n iword\n cpp/io/ios_base/iword\n \n (T... args)\n \n \n T\n move\n cpp/io/basic_ios/move\n \n (T... args)\n \n \n T\n narrow\n cpp/io/basic_ios/narrow\n \n (T... args)\n \n \n T\n operator bool\n cpp/io/basic_ios/operator_bool\n \n (T... args)\n \n \n T\n operator!\n cpp/io/basic_ios/operator!\n \n (T... args)\n \n \n T\n operator<<\n cpp/io/basic_ostream/operator_ltlt\n \n (T... args)\n \n \n T\n operator=\n cpp/io/basic_stringstream/operator=\n \n (T... args)\n \n \n T\n operator>>\n cpp/io/basic_istream/operator_gtgt\n \n (T... args)\n \n \n T\n peek\n cpp/io/basic_istream/peek\n \n (T... args)\n \n \n T\n precision\n cpp/io/ios_base/precision\n \n (T... args)\n \n \n T\n put\n cpp/io/basic_ostream/put\n \n (T... args)\n \n \n T\n putback\n cpp/io/basic_istream/putback\n \n (T... args)\n \n \n T\n pword\n cpp/io/ios_base/pword\n \n (T... args)\n \n \n T\n rdbuf\n cpp/io/basic_ios/rdbuf\n \n (T... args)\n \n \n T\n rdstate\n cpp/io/basic_ios/rdstate\n \n (T... args)\n \n \n T\n read\n cpp/io/basic_istream/read\n \n (T... args)\n \n \n T\n readsome\n cpp/io/basic_istream/readsome\n \n (T... args)\n \n \n T\n register_callback\n cpp/io/ios_base/register_callback\n \n (T... args)\n \n \n T\n seekg\n cpp/io/basic_istream/seekg\n \n (T... args)\n \n \n T\n seekp\n cpp/io/basic_ostream/seekp\n \n (T... args)\n \n std::wstringstream::sentry\n \n T\n set_rdbuf\n cpp/io/basic_ios/set_rdbuf\n \n (T... args)\n \n \n T\n setf\n cpp/io/ios_base/setf\n \n (T... args)\n \n \n T\n setstate\n cpp/io/basic_ios/setstate\n \n (T... args)\n \n \n T\n str\n cpp/io/basic_stringstream/str\n \n (T... args)\n \n \n T\n swap\n cpp/io/basic_ios/swap\n \n (T... args)\n \n \n T\n sync\n cpp/io/basic_istream/sync\n \n (T... args)\n \n \n T\n sync_with_stdio\n cpp/io/ios_base/sync_with_stdio\n \n (T... args)\n \n \n T\n tellg\n cpp/io/basic_istream/tellg\n \n (T... args)\n \n \n T\n tellp\n cpp/io/basic_ostream/tellp\n \n (T... args)\n \n \n T\n tie\n cpp/io/basic_ios/tie\n \n (T... args)\n \n \n T\n unget\n cpp/io/basic_istream/unget\n \n (T... args)\n \n \n T\n unsetf\n cpp/io/ios_base/unsetf\n \n (T... args)\n \n \n T\n widen\n cpp/io/basic_ios/widen\n \n (T... args)\n \n \n T\n width\n cpp/io/ios_base/width\n \n (T... args)\n \n \n T\n write\n cpp/io/basic_ostream/write\n \n (T... args)\n \n \n T\n wstringstream\n cpp/io/basic_stringstream/basic_stringstream\n \n (T... args)\n \n \n T\n xalloc\n cpp/io/ios_base/xalloc\n \n (T... args)\n \n \n \n std::wstringstream::Init\n cpp/io/ios_base/Init\n \n \n std::wstringstream::event_callback\n cpp/io/ios_base/event_callback\n \n \n std::wstringstream::failure\n cpp/io/ios_base/failure\n \n T\n failure\n cpp/io/ios_base/failure\n \n (T... args)\n \n \n T\n what\n cpp/error/exception/what\n \n (T... args)\n \n \n \n std::wstringstream::sentry\n cpp/io/basic_ostream/sentry\n \n T\n operator bool\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n T\n ~sentry\n cpp/io/basic_istream/sentry\n \n (T... args)\n \n \n \n std::yocto\n cpp/numeric/ratio/ratio\n \n \n std::yotta\n cpp/numeric/ratio/ratio\n \n \n std::zetta\n cpp/numeric/ratio/ratio\n \n \n va_list\n cpp/utility/variadic/va_list\n \n\n" }, { "path": "docs/config/custom.css", "content": "/**\nDistributed under the MIT License.\nSee LICENSE.txt for details.\n*/\n\nhtml {\n /* This width must correspond to Doxygen's `TREEVIEW_WIDTH` */\n --side-nav-fixed-width: 280px;\n}\n\n#nav-sync {\n display: none;\n}\n" }, { "path": "docs/config/doxygen-awesome-fragment-copy-button.js", "content": "/**\n\nDoxygen Awesome\nhttps://github.com/jothepro/doxygen-awesome-css\n\nMIT License\n\nCopyright (c) 2022 - 2023 jothepro\n\nPermission is hereby granted, free of charge, to any person obtaining a copy\nof this software and associated documentation files (the \"Software\"), to deal\nin the Software without restriction, including without limitation the rights\nto use, copy, modify, merge, publish, distribute, sublicense, and/or sell\ncopies of the Software, and to permit persons to whom the Software is\nfurnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in all\ncopies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\nSOFTWARE.\n\n*/\n\nclass DoxygenAwesomeFragmentCopyButton extends HTMLElement {\n constructor() {\n super();\n this.onclick=this.copyContent\n }\n static title = \"Copy to clipboard\"\n static copyIcon = ``\n static successIcon = ``\n static successDuration = 980\n static init() {\n $(function() {\n $(document).ready(function() {\n if(navigator.clipboard) {\n const fragments = document.getElementsByClassName(\"fragment\")\n for(const fragment of fragments) {\n const fragmentWrapper = document.createElement(\"div\")\n fragmentWrapper.className = \"doxygen-awesome-fragment-wrapper\"\n const fragmentCopyButton = document.createElement(\"doxygen-awesome-fragment-copy-button\")\n fragmentCopyButton.innerHTML = DoxygenAwesomeFragmentCopyButton.copyIcon\n fragmentCopyButton.title = DoxygenAwesomeFragmentCopyButton.title\n fragment.parentNode.replaceChild(fragmentWrapper, fragment)\n fragmentWrapper.appendChild(fragment)\n fragmentWrapper.appendChild(fragmentCopyButton)\n }\n }\n })\n })\n }\n\n\n copyContent() {\n const content = this.previousSibling.cloneNode(true)\n // filter out line number from file listings\n content.querySelectorAll(\".lineno, .ttc\").forEach((node) => {\n node.remove()\n })\n let textContent = content.textContent\n // remove trailing newlines that appear in file listings\n let numberOfTrailingNewlines = 0\n while(textContent.charAt(textContent.length - (numberOfTrailingNewlines + 1)) == '\\n') {\n numberOfTrailingNewlines++;\n }\n textContent = textContent.substring(0, textContent.length - numberOfTrailingNewlines)\n navigator.clipboard.writeText(textContent);\n this.classList.add(\"success\")\n this.innerHTML = DoxygenAwesomeFragmentCopyButton.successIcon\n window.setTimeout(() => {\n this.classList.remove(\"success\")\n this.innerHTML = DoxygenAwesomeFragmentCopyButton.copyIcon\n }, DoxygenAwesomeFragmentCopyButton.successDuration);\n }\n}\n\ncustomElements.define(\"doxygen-awesome-fragment-copy-button\", DoxygenAwesomeFragmentCopyButton)\n" }, { "path": "docs/config/doxygen-awesome-interactive-toc.js", "content": "/**\n\nDoxygen Awesome\nhttps://github.com/jothepro/doxygen-awesome-css\n\nMIT License\n\nCopyright (c) 2022 - 2023 jothepro\n\nPermission is hereby granted, free of charge, to any person obtaining a copy\nof this software and associated documentation files (the \"Software\"), to deal\nin the Software without restriction, including without limitation the rights\nto use, copy, modify, merge, publish, distribute, sublicense, and/or sell\ncopies of the Software, and to permit persons to whom the Software is\nfurnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in all\ncopies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\nSOFTWARE.\n\n*/\n\nclass DoxygenAwesomeInteractiveToc {\n static topOffset = 38\n static hideMobileMenu = true\n static headers = []\n\n static init() {\n window.addEventListener(\"load\", () => {\n let toc = document.querySelector(\".contents > .toc\")\n if(toc) {\n toc.classList.add(\"interactive\")\n if(!DoxygenAwesomeInteractiveToc.hideMobileMenu) {\n toc.classList.add(\"open\")\n }\n document.querySelector(\".contents > .toc > h3\")?.addEventListener(\"click\", () => {\n if(toc.classList.contains(\"open\")) {\n toc.classList.remove(\"open\")\n } else {\n toc.classList.add(\"open\")\n }\n })\n\n document.querySelectorAll(\".contents > .toc > ul a\").forEach((node) => {\n let id = node.getAttribute(\"href\").substring(1)\n DoxygenAwesomeInteractiveToc.headers.push({\n node: node,\n headerNode: document.getElementById(id)\n })\n\n document.getElementById(\"doc-content\")?.addEventListener(\"scroll\",this.throttle(DoxygenAwesomeInteractiveToc.update, 100))\n })\n DoxygenAwesomeInteractiveToc.update()\n }\n })\n }\n\n static update() {\n let active = DoxygenAwesomeInteractiveToc.headers[0]?.node\n DoxygenAwesomeInteractiveToc.headers.forEach((header) => {\n let position = header.headerNode.getBoundingClientRect().top\n header.node.classList.remove(\"active\")\n header.node.classList.remove(\"aboveActive\")\n if(position < DoxygenAwesomeInteractiveToc.topOffset) {\n active = header.node\n active?.classList.add(\"aboveActive\")\n }\n })\n active?.classList.add(\"active\")\n active?.classList.remove(\"aboveActive\")\n }\n\n static throttle(func, delay) {\n let lastCall = 0;\n return function (...args) {\n const now = new Date().getTime();\n if (now - lastCall < delay) {\n return;\n }\n lastCall = now;\n return setTimeout(() => {func(...args)}, delay);\n };\n }\n}\n" }, { "path": "docs/config/doxygen-awesome-paragraph-link.js", "content": "/**\n\nDoxygen Awesome\nhttps://github.com/jothepro/doxygen-awesome-css\n\nMIT License\n\nCopyright (c) 2022 - 2023 jothepro\n\nPermission is hereby granted, free of charge, to any person obtaining a copy\nof this software and associated documentation files (the \"Software\"), to deal\nin the Software without restriction, including without limitation the rights\nto use, copy, modify, merge, publish, distribute, sublicense, and/or sell\ncopies of the Software, and to permit persons to whom the Software is\nfurnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in all\ncopies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\nSOFTWARE.\n\n*/\n\nclass DoxygenAwesomeParagraphLink {\n // Icon from https://fonts.google.com/icons\n // Licensed under the Apache 2.0 license:\n // https://www.apache.org/licenses/LICENSE-2.0.html\n static icon = ``\n static title = \"Permanent Link\"\n static init() {\n $(function() {\n $(document).ready(function() {\n document.querySelectorAll(\".contents a.anchor[id], .contents .groupheader > a[id]\").forEach((node) => {\n let anchorlink = document.createElement(\"a\")\n anchorlink.setAttribute(\"href\", `#${node.getAttribute(\"id\")}`)\n anchorlink.setAttribute(\"title\", DoxygenAwesomeParagraphLink.title)\n anchorlink.classList.add(\"anchorlink\")\n node.classList.add(\"anchor\")\n anchorlink.innerHTML = DoxygenAwesomeParagraphLink.icon\n node.parentElement.appendChild(anchorlink)\n })\n })\n })\n }\n}\n" }, { "path": "docs/config/doxygen-awesome-sidebar-only.css", "content": "/**\n\nDoxygen Awesome\nhttps://github.com/jothepro/doxygen-awesome-css\n\nMIT License\n\nCopyright (c) 2021 - 2023 jothepro\n\nPermission is hereby granted, free of charge, to any person obtaining a copy\nof this software and associated documentation files (the \"Software\"), to deal\nin the Software without restriction, including without limitation the rights\nto use, copy, modify, merge, publish, distribute, sublicense, and/or sell\ncopies of the Software, and to permit persons to whom the Software is\nfurnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in all\ncopies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\nSOFTWARE.\n\n */\n\nhtml {\n /* side nav width. MUST be = `TREEVIEW_WIDTH`.\n * Make sure it is wide enough to contain the page title (logo + title + version)\n */\n --side-nav-fixed-width: 335px;\n --menu-display: none;\n\n --top-height: 120px;\n --toc-sticky-top: -25px;\n --toc-max-height: calc(100vh - 2 * var(--spacing-medium) - 25px);\n}\n\n#projectname {\n white-space: nowrap;\n}\n\n\n@media screen and (min-width: 768px) {\n html {\n --searchbar-background: var(--page-background-color);\n }\n\n #side-nav {\n min-width: var(--side-nav-fixed-width);\n max-width: var(--side-nav-fixed-width);\n top: var(--top-height);\n overflow: visible;\n }\n\n #nav-tree, #side-nav {\n height: calc(100vh - var(--top-height)) !important;\n }\n\n #nav-tree {\n padding: 0;\n }\n\n #top {\n display: block;\n border-bottom: none;\n height: var(--top-height);\n margin-bottom: calc(0px - var(--top-height));\n max-width: var(--side-nav-fixed-width);\n overflow: hidden;\n background: var(--side-nav-background);\n }\n #main-nav {\n float: left;\n padding-right: 0;\n }\n\n .ui-resizable-handle {\n cursor: default;\n width: 1px !important;\n background: var(--separator-color);\n box-shadow: 0 calc(-2 * var(--top-height)) 0 0 var(--separator-color);\n }\n\n #nav-path {\n position: fixed;\n right: 0;\n left: var(--side-nav-fixed-width);\n bottom: 0;\n width: auto;\n }\n\n #doc-content {\n height: calc(100vh - 31px) !important;\n padding-bottom: calc(3 * var(--spacing-large));\n padding-top: calc(var(--top-height) - 80px);\n box-sizing: border-box;\n margin-left: var(--side-nav-fixed-width) !important;\n }\n\n #MSearchBox {\n width: calc(var(--side-nav-fixed-width) - calc(2 * var(--spacing-medium)));\n }\n\n #MSearchField {\n width: calc(var(--side-nav-fixed-width) - calc(2 * var(--spacing-medium)) - 65px);\n }\n\n #MSearchResultsWindow {\n left: var(--spacing-medium) !important;\n right: auto;\n }\n}\n" }, { "path": "docs/config/doxygen-awesome.css", "content": "/**\n\nDoxygen Awesome\nhttps://github.com/jothepro/doxygen-awesome-css\n\nMIT License\n\nCopyright (c) 2021 - 2023 jothepro\n\nPermission is hereby granted, free of charge, to any person obtaining a copy\nof this software and associated documentation files (the \"Software\"), to deal\nin the Software without restriction, including without limitation the rights\nto use, copy, modify, merge, publish, distribute, sublicense, and/or sell\ncopies of the Software, and to permit persons to whom the Software is\nfurnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in all\ncopies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\nSOFTWARE.\n\n*/\n\nhtml {\n /* primary theme color. This will affect the entire websites color scheme: links, arrows, labels, ... */\n --primary-color: #1779c4;\n --primary-dark-color: #335c80;\n --primary-light-color: #70b1e9;\n\n /* page base colors */\n --page-background-color: #ffffff;\n --page-foreground-color: #2f4153;\n --page-secondary-foreground-color: #6f7e8e;\n\n /* color for all separators on the website: hr, borders, ... */\n --separator-color: #dedede;\n\n /* border radius for all rounded components. Will affect many components, like dropdowns, memitems, codeblocks, ... */\n --border-radius-large: 8px;\n --border-radius-small: 4px;\n --border-radius-medium: 6px;\n\n /* default spacings. Most components reference these values for spacing, to provide uniform spacing on the page. */\n --spacing-small: 5px;\n --spacing-medium: 10px;\n --spacing-large: 16px;\n\n /* default box shadow used for raising an element above the normal content. Used in dropdowns, search result, ... */\n --box-shadow: 0 2px 8px 0 rgba(0,0,0,.075);\n\n --odd-color: rgba(0,0,0,.028);\n\n /* font-families. will affect all text on the website\n * font-family: the normal font for text, headlines, menus\n * font-family-monospace: used for preformatted text in memtitle, code, fragments\n */\n --font-family: -apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen,Ubuntu,Cantarell,Fira Sans,Droid Sans,Helvetica Neue,sans-serif;\n --font-family-monospace: ui-monospace,SFMono-Regular,SF Mono,Menlo,Consolas,Liberation Mono,monospace;\n\n /* font sizes */\n --page-font-size: 15.6px;\n --navigation-font-size: 14.4px;\n --toc-font-size: 13.4px;\n --code-font-size: 14px; /* affects code, fragment */\n --title-font-size: 22px;\n\n /* content text properties. These only affect the page content, not the navigation or any other ui elements */\n --content-line-height: 27px;\n /* The content is centered and constraint in it's width. To make the content fill the whole page, set the variable to auto.*/\n --content-maxwidth: 1050px;\n --table-line-height: 24px;\n --toc-sticky-top: var(--spacing-medium);\n --toc-width: 200px;\n --toc-max-height: calc(100vh - 2 * var(--spacing-medium) - 85px);\n\n /* colors for various content boxes: @warning, @note, @deprecated @bug */\n --warning-color: #faf3d8;\n --warning-color-dark: #f3a600;\n --warning-color-darker: #5f4204;\n --note-color: #e4f3ff;\n --note-color-dark: #1879C4;\n --note-color-darker: #274a5c;\n --todo-color: #e4dafd;\n --todo-color-dark: #5b2bdd;\n --todo-color-darker: #2a0d72;\n --deprecated-color: #ecf0f3;\n --deprecated-color-dark: #5b6269;\n --deprecated-color-darker: #43454a;\n --bug-color: #f8d1cc;\n --bug-color-dark: #b61825;\n --bug-color-darker: #75070f;\n --invariant-color: #d8f1e3;\n --invariant-color-dark: #44b86f;\n --invariant-color-darker: #265532;\n\n /* blockquote colors */\n --blockquote-background: #f8f9fa;\n --blockquote-foreground: #636568;\n\n /* table colors */\n --tablehead-background: #f1f1f1;\n --tablehead-foreground: var(--page-foreground-color);\n\n /* menu-display: block | none\n * Visibility of the top navigation on screens >= 768px. On smaller screen the menu is always visible.\n * `GENERATE_TREEVIEW` MUST be enabled!\n */\n --menu-display: block;\n\n --menu-focus-foreground: var(--page-background-color);\n --menu-focus-background: var(--primary-color);\n --menu-selected-background: rgba(0,0,0,.05);\n\n\n --header-background: var(--page-background-color);\n --header-foreground: var(--page-foreground-color);\n\n /* searchbar colors */\n --searchbar-background: var(--side-nav-background);\n --searchbar-foreground: var(--page-foreground-color);\n\n /* searchbar size\n * (`searchbar-width` is only applied on screens >= 768px.\n * on smaller screens the searchbar will always fill the entire screen width) */\n --searchbar-height: 33px;\n --searchbar-width: 210px;\n --searchbar-border-radius: var(--searchbar-height);\n\n /* code block colors */\n --code-background: #f5f5f5;\n --code-foreground: var(--page-foreground-color);\n\n /* fragment colors */\n --fragment-background: #F8F9FA;\n --fragment-foreground: #37474F;\n --fragment-keyword: #bb6bb2;\n --fragment-keywordtype: #8258b3;\n --fragment-keywordflow: #d67c3b;\n --fragment-token: #438a59;\n --fragment-comment: #969696;\n --fragment-link: #5383d6;\n --fragment-preprocessor: #46aaa5;\n --fragment-linenumber-color: #797979;\n --fragment-linenumber-background: #f4f4f5;\n --fragment-linenumber-border: #e3e5e7;\n --fragment-lineheight: 20px;\n\n /* sidebar navigation (treeview) colors */\n --side-nav-background: #fbfbfb;\n --side-nav-foreground: var(--page-foreground-color);\n --side-nav-arrow-opacity: 0;\n --side-nav-arrow-hover-opacity: 0.9;\n\n --toc-background: var(--side-nav-background);\n --toc-foreground: var(--side-nav-foreground);\n\n /* height of an item in any tree / collapsible table */\n --tree-item-height: 30px;\n\n --memname-font-size: var(--code-font-size);\n --memtitle-font-size: 18px;\n\n --webkit-scrollbar-size: 7px;\n --webkit-scrollbar-padding: 4px;\n --webkit-scrollbar-color: var(--separator-color);\n\n --animation-duration: .12s\n}\n\n@media screen and (max-width: 767px) {\n html {\n --page-font-size: 16px;\n --navigation-font-size: 16px;\n --toc-font-size: 15px;\n --code-font-size: 15px; /* affects code, fragment */\n --title-font-size: 22px;\n }\n}\n\n@media (prefers-color-scheme: dark) {\n html:not(.light-mode) {\n color-scheme: dark;\n\n --primary-color: #1982d2;\n --primary-dark-color: #86a9c4;\n --primary-light-color: #4779ac;\n\n --box-shadow: 0 2px 8px 0 rgba(0,0,0,.35);\n\n --odd-color: rgba(100,100,100,.06);\n\n --menu-selected-background: rgba(0,0,0,.4);\n\n --page-background-color: #1C1D1F;\n --page-foreground-color: #d2dbde;\n --page-secondary-foreground-color: #859399;\n --separator-color: #38393b;\n --side-nav-background: #252628;\n\n --code-background: #2a2c2f;\n\n --tablehead-background: #2a2c2f;\n\n --blockquote-background: #222325;\n --blockquote-foreground: #7e8c92;\n\n --warning-color: #3b2e04;\n --warning-color-dark: #f1b602;\n --warning-color-darker: #ceb670;\n --note-color: #163750;\n --note-color-dark: #1982D2;\n --note-color-darker: #dcf0fa;\n --todo-color: #2a2536;\n --todo-color-dark: #7661b3;\n --todo-color-darker: #ae9ed6;\n --deprecated-color: #2e323b;\n --deprecated-color-dark: #738396;\n --deprecated-color-darker: #abb0bd;\n --bug-color: #2e1917;\n --bug-color-dark: #ad2617;\n --bug-color-darker: #f5b1aa;\n --invariant-color: #303a35;\n --invariant-color-dark: #76ce96;\n --invariant-color-darker: #cceed5;\n\n --fragment-background: #282c34;\n --fragment-foreground: #dbe4eb;\n --fragment-keyword: #cc99cd;\n --fragment-keywordtype: #ab99cd;\n --fragment-keywordflow: #e08000;\n --fragment-token: #7ec699;\n --fragment-comment: #999999;\n --fragment-link: #98c0e3;\n --fragment-preprocessor: #65cabe;\n --fragment-linenumber-color: #cccccc;\n --fragment-linenumber-background: #35393c;\n --fragment-linenumber-border: #1f1f1f;\n }\n}\n\n/* dark mode variables are defined twice, to support both the dark-mode without and with doxygen-awesome-darkmode-toggle.js */\nhtml.dark-mode {\n color-scheme: dark;\n\n --primary-color: #1982d2;\n --primary-dark-color: #86a9c4;\n --primary-light-color: #4779ac;\n\n --box-shadow: 0 2px 8px 0 rgba(0,0,0,.30);\n\n --odd-color: rgba(100,100,100,.06);\n\n --menu-selected-background: rgba(0,0,0,.4);\n\n --page-background-color: #1C1D1F;\n --page-foreground-color: #d2dbde;\n --page-secondary-foreground-color: #859399;\n --separator-color: #38393b;\n --side-nav-background: #252628;\n\n --code-background: #2a2c2f;\n\n --tablehead-background: #2a2c2f;\n\n --blockquote-background: #222325;\n --blockquote-foreground: #7e8c92;\n\n --warning-color: #3b2e04;\n --warning-color-dark: #f1b602;\n --warning-color-darker: #ceb670;\n --note-color: #163750;\n --note-color-dark: #1982D2;\n --note-color-darker: #dcf0fa;\n --todo-color: #2a2536;\n --todo-color-dark: #7661b3;\n --todo-color-darker: #ae9ed6;\n --deprecated-color: #2e323b;\n --deprecated-color-dark: #738396;\n --deprecated-color-darker: #abb0bd;\n --bug-color: #2e1917;\n --bug-color-dark: #ad2617;\n --bug-color-darker: #f5b1aa;\n --invariant-color: #303a35;\n --invariant-color-dark: #76ce96;\n --invariant-color-darker: #cceed5;\n\n --fragment-background: #282c34;\n --fragment-foreground: #dbe4eb;\n --fragment-keyword: #cc99cd;\n --fragment-keywordtype: #ab99cd;\n --fragment-keywordflow: #e08000;\n --fragment-token: #7ec699;\n --fragment-comment: #999999;\n --fragment-link: #98c0e3;\n --fragment-preprocessor: #65cabe;\n --fragment-linenumber-color: #cccccc;\n --fragment-linenumber-background: #35393c;\n --fragment-linenumber-border: #1f1f1f;\n}\n\nbody {\n color: var(--page-foreground-color);\n background-color: var(--page-background-color);\n font-size: var(--page-font-size);\n}\n\nbody, table, div, p, dl, #nav-tree .label, .title,\n.sm-dox a, .sm-dox a:hover, .sm-dox a:focus, #projectname,\n.SelectItem, #MSearchField, .navpath li.navelem a,\n.navpath li.navelem a:hover, p.reference, p.definition, div.toc li, div.toc h3 {\n font-family: var(--font-family);\n}\n\nh1, h2, h3, h4, h5 {\n margin-top: 1em;\n font-weight: 600;\n line-height: initial;\n}\n\np, div, table, dl, p.reference, p.definition {\n font-size: var(--page-font-size);\n}\n\np.reference, p.definition {\n color: var(--page-secondary-foreground-color);\n}\n\na:link, a:visited, a:hover, a:focus, a:active {\n color: var(--primary-color) !important;\n font-weight: 500;\n background: none;\n}\n\na.anchor {\n scroll-margin-top: var(--spacing-large);\n display: block;\n}\n\n/*\n Title and top navigation\n */\n\n#top {\n background: var(--header-background);\n border-bottom: 1px solid var(--separator-color);\n}\n\n@media screen and (min-width: 768px) {\n #top {\n display: flex;\n flex-wrap: wrap;\n justify-content: space-between;\n align-items: center;\n }\n}\n\n#main-nav {\n flex-grow: 5;\n padding: var(--spacing-small) var(--spacing-medium);\n}\n\n#titlearea {\n width: auto;\n padding: var(--spacing-medium) var(--spacing-large);\n background: none;\n color: var(--header-foreground);\n border-bottom: none;\n}\n\n@media screen and (max-width: 767px) {\n #titlearea {\n padding-bottom: var(--spacing-small);\n }\n}\n\n#titlearea table tbody tr {\n height: auto !important;\n}\n\n#projectname {\n font-size: var(--title-font-size);\n font-weight: 600;\n}\n\n#projectnumber {\n font-family: inherit;\n font-size: 60%;\n}\n\n#projectbrief {\n font-family: inherit;\n font-size: 80%;\n}\n\n#projectlogo {\n vertical-align: middle;\n}\n\n#projectlogo img {\n max-height: calc(var(--title-font-size) * 2);\n margin-right: var(--spacing-small);\n}\n\n.sm-dox, .tabs, .tabs2, .tabs3 {\n background: none;\n padding: 0;\n}\n\n.tabs, .tabs2, .tabs3 {\n border-bottom: 1px solid var(--separator-color);\n margin-bottom: -1px;\n}\n\n.main-menu-btn-icon, .main-menu-btn-icon:before, .main-menu-btn-icon:after {\n background: var(--page-secondary-foreground-color);\n}\n\n@media screen and (max-width: 767px) {\n .sm-dox a span.sub-arrow {\n background: var(--code-background);\n }\n\n #main-menu a.has-submenu span.sub-arrow {\n color: var(--page-secondary-foreground-color);\n border-radius: var(--border-radius-medium);\n }\n\n #main-menu a.has-submenu:hover span.sub-arrow {\n color: var(--page-foreground-color);\n }\n}\n\n@media screen and (min-width: 768px) {\n .sm-dox li, .tablist li {\n display: var(--menu-display);\n }\n\n .sm-dox a span.sub-arrow {\n border-color: var(--header-foreground) transparent transparent transparent;\n }\n\n .sm-dox a:hover span.sub-arrow {\n border-color: var(--menu-focus-foreground) transparent transparent transparent;\n }\n\n .sm-dox ul a span.sub-arrow {\n border-color: transparent transparent transparent var(--page-foreground-color);\n }\n\n .sm-dox ul a:hover span.sub-arrow {\n border-color: transparent transparent transparent var(--menu-focus-foreground);\n }\n}\n\n.sm-dox ul {\n background: var(--page-background-color);\n box-shadow: var(--box-shadow);\n border: 1px solid var(--separator-color);\n border-radius: var(--border-radius-medium) !important;\n padding: var(--spacing-small);\n animation: ease-out 150ms slideInMenu;\n}\n\n@keyframes slideInMenu {\n from {\n opacity: 0;\n transform: translate(0px, -2px);\n }\n\n to {\n opacity: 1;\n transform: translate(0px, 0px);\n }\n}\n\n.sm-dox ul a {\n color: var(--page-foreground-color) !important;\n background: var(--page-background-color);\n font-size: var(--navigation-font-size);\n}\n\n.sm-dox>li>ul:after {\n border-bottom-color: var(--page-background-color) !important;\n}\n\n.sm-dox>li>ul:before {\n border-bottom-color: var(--separator-color) !important;\n}\n\n.sm-dox ul a:hover, .sm-dox ul a:active, .sm-dox ul a:focus {\n font-size: var(--navigation-font-size) !important;\n color: var(--menu-focus-foreground) !important;\n text-shadow: none;\n background-color: var(--menu-focus-background);\n border-radius: var(--border-radius-small) !important;\n}\n\n.sm-dox a, .sm-dox a:focus, .tablist li, .tablist li a, .tablist li.current a {\n text-shadow: none;\n background: transparent;\n background-image: none !important;\n color: var(--header-foreground) !important;\n font-weight: normal;\n font-size: var(--navigation-font-size);\n border-radius: var(--border-radius-small) !important;\n}\n\n.sm-dox a:focus {\n outline: auto;\n}\n\n.sm-dox a:hover, .sm-dox a:active, .tablist li a:hover {\n text-shadow: none;\n font-weight: normal;\n background: var(--menu-focus-background);\n color: var(--menu-focus-foreground) !important;\n border-radius: var(--border-radius-small) !important;\n font-size: var(--navigation-font-size);\n}\n\n.tablist li.current {\n border-radius: var(--border-radius-small);\n background: var(--menu-selected-background);\n}\n\n.tablist li {\n margin: var(--spacing-small) 0 var(--spacing-small) var(--spacing-small);\n}\n\n.tablist a {\n padding: 0 var(--spacing-large);\n}\n\n\n/*\n Search box\n */\n\n#MSearchBox {\n height: var(--searchbar-height);\n background: var(--searchbar-background);\n border-radius: var(--searchbar-border-radius);\n border: 1px solid var(--separator-color);\n overflow: hidden;\n width: var(--searchbar-width);\n position: relative;\n box-shadow: none;\n display: block;\n margin-top: 0;\n}\n\n/* until Doxygen 1.9.4 */\n.left img#MSearchSelect {\n left: 0;\n user-select: none;\n padding-left: 8px;\n}\n\n/* Doxygen 1.9.5 */\n.left span#MSearchSelect {\n left: 0;\n user-select: none;\n margin-left: 8px;\n padding: 0;\n}\n\n.left #MSearchSelect[src$=\".png\"] {\n padding-left: 0\n}\n\n.SelectionMark {\n user-select: none;\n}\n\n.tabs .left #MSearchSelect {\n padding-left: 0;\n}\n\n.tabs #MSearchBox {\n position: absolute;\n right: var(--spacing-medium);\n}\n\n@media screen and (max-width: 767px) {\n .tabs #MSearchBox {\n position: relative;\n right: 0;\n margin-left: var(--spacing-medium);\n margin-top: 0;\n }\n}\n\n#MSearchSelectWindow, #MSearchResultsWindow {\n z-index: 9999;\n}\n\n#MSearchBox.MSearchBoxActive {\n border-color: var(--primary-color);\n box-shadow: inset 0 0 0 1px var(--primary-color);\n}\n\n#main-menu > li:last-child {\n margin-right: 0;\n}\n\n@media screen and (max-width: 767px) {\n #main-menu > li:last-child {\n height: 50px;\n }\n}\n\n#MSearchField {\n font-size: var(--navigation-font-size);\n height: calc(var(--searchbar-height) - 2px);\n background: transparent;\n width: calc(var(--searchbar-width) - 64px);\n}\n\n.MSearchBoxActive #MSearchField {\n color: var(--searchbar-foreground);\n}\n\n#MSearchSelect {\n top: calc(calc(var(--searchbar-height) / 2) - 11px);\n}\n\n#MSearchBox span.left, #MSearchBox span.right {\n background: none;\n background-image: none;\n}\n\n#MSearchBox span.right {\n padding-top: calc(calc(var(--searchbar-height) / 2) - 12px);\n position: absolute;\n right: var(--spacing-small);\n}\n\n.tabs #MSearchBox span.right {\n top: calc(calc(var(--searchbar-height) / 2) - 12px);\n}\n\n@keyframes slideInSearchResults {\n from {\n opacity: 0;\n transform: translate(0, 15px);\n }\n\n to {\n opacity: 1;\n transform: translate(0, 20px);\n }\n}\n\n#MSearchResultsWindow {\n left: auto !important;\n right: var(--spacing-medium);\n border-radius: var(--border-radius-large);\n border: 1px solid var(--separator-color);\n transform: translate(0, 20px);\n box-shadow: var(--box-shadow);\n animation: ease-out 280ms slideInSearchResults;\n background: var(--page-background-color);\n}\n\niframe#MSearchResults {\n margin: 4px;\n}\n\niframe {\n color-scheme: normal;\n}\n\n@media (prefers-color-scheme: dark) {\n html:not(.light-mode) iframe#MSearchResults {\n filter: invert() hue-rotate(180deg);\n }\n}\n\nhtml.dark-mode iframe#MSearchResults {\n filter: invert() hue-rotate(180deg);\n}\n\n#MSearchResults .SRPage {\n background-color: transparent;\n}\n\n#MSearchResults .SRPage .SREntry {\n font-size: 10pt;\n padding: var(--spacing-small) var(--spacing-medium);\n}\n\n#MSearchSelectWindow {\n border: 1px solid var(--separator-color);\n border-radius: var(--border-radius-medium);\n box-shadow: var(--box-shadow);\n background: var(--page-background-color);\n padding-top: var(--spacing-small);\n padding-bottom: var(--spacing-small);\n}\n\n#MSearchSelectWindow a.SelectItem {\n font-size: var(--navigation-font-size);\n line-height: var(--content-line-height);\n margin: 0 var(--spacing-small);\n border-radius: var(--border-radius-small);\n color: var(--page-foreground-color) !important;\n font-weight: normal;\n}\n\n#MSearchSelectWindow a.SelectItem:hover {\n background: var(--menu-focus-background);\n color: var(--menu-focus-foreground) !important;\n}\n\n@media screen and (max-width: 767px) {\n #MSearchBox {\n margin-top: var(--spacing-medium);\n margin-bottom: var(--spacing-medium);\n width: calc(100vw - 30px);\n }\n\n #main-menu > li:last-child {\n float: none !important;\n }\n\n #MSearchField {\n width: calc(100vw - 110px);\n }\n\n @keyframes slideInSearchResultsMobile {\n from {\n opacity: 0;\n transform: translate(0, 15px);\n }\n\n to {\n opacity: 1;\n transform: translate(0, 20px);\n }\n }\n\n #MSearchResultsWindow {\n left: var(--spacing-medium) !important;\n right: var(--spacing-medium);\n overflow: auto;\n transform: translate(0, 20px);\n animation: ease-out 280ms slideInSearchResultsMobile;\n width: auto !important;\n }\n\n /*\n * Overwrites for fixing the searchbox on mobile in doxygen 1.9.2\n */\n label.main-menu-btn ~ #searchBoxPos1 {\n top: 3px !important;\n right: 6px !important;\n left: 45px;\n display: flex;\n }\n\n label.main-menu-btn ~ #searchBoxPos1 > #MSearchBox {\n margin-top: 0;\n margin-bottom: 0;\n flex-grow: 2;\n float: left;\n }\n}\n\n/*\n Tree view\n */\n\n#side-nav {\n padding: 0 !important;\n background: var(--side-nav-background);\n min-width: 8px;\n max-width: 50vw;\n}\n\n@media screen and (max-width: 767px) {\n #side-nav {\n display: none;\n }\n\n #doc-content {\n margin-left: 0 !important;\n }\n}\n\n#nav-tree {\n background: transparent;\n margin-right: 1px;\n}\n\n#nav-tree .label {\n font-size: var(--navigation-font-size);\n}\n\n#nav-tree .item {\n height: var(--tree-item-height);\n line-height: var(--tree-item-height);\n overflow: hidden;\n text-overflow: ellipsis;\n}\n\n#nav-tree .item > a:focus {\n outline: none;\n}\n\n#nav-sync {\n bottom: 12px;\n right: 12px;\n top: auto !important;\n user-select: none;\n}\n\n#nav-tree .selected {\n text-shadow: none;\n background-image: none;\n background-color: transparent;\n position: relative;\n color: var(--primary-color) !important;\n font-weight: 500;\n}\n\n#nav-tree .selected::after {\n content: \"\";\n position: absolute;\n top: 1px;\n bottom: 1px;\n left: 0;\n width: 4px;\n border-radius: 0 var(--border-radius-small) var(--border-radius-small) 0;\n background: var(--primary-color);\n}\n\n\n#nav-tree a {\n color: var(--side-nav-foreground) !important;\n font-weight: normal;\n}\n\n#nav-tree a:focus {\n outline-style: auto;\n}\n\n#nav-tree .arrow {\n opacity: var(--side-nav-arrow-opacity);\n background: none;\n}\n\n.arrow {\n color: inherit;\n cursor: pointer;\n font-size: 45%;\n vertical-align: middle;\n margin-right: 2px;\n font-family: serif;\n height: auto;\n text-align: right;\n}\n\n#nav-tree div.item:hover .arrow, #nav-tree a:focus .arrow {\n opacity: var(--side-nav-arrow-hover-opacity);\n}\n\n#nav-tree .selected a {\n color: var(--primary-color) !important;\n font-weight: bolder;\n font-weight: 600;\n}\n\n.ui-resizable-e {\n width: 4px;\n background: transparent;\n box-shadow: inset -1px 0 0 0 var(--separator-color);\n}\n\n/*\n Contents\n */\n\ndiv.header {\n border-bottom: 1px solid var(--separator-color);\n background-color: var(--page-background-color);\n background-image: none;\n}\n\n@media screen and (min-width: 1000px) {\n #doc-content > div > div.contents,\n .PageDoc > div.contents {\n display: flex;\n flex-direction: row-reverse;\n flex-wrap: nowrap;\n align-items: flex-start;\n }\n\n div.contents .textblock {\n min-width: 200px;\n flex-grow: 1;\n }\n}\n\ndiv.contents, div.header .title, div.header .summary {\n max-width: var(--content-maxwidth);\n}\n\ndiv.contents, div.header .title {\n line-height: initial;\n margin: calc(var(--spacing-medium) + .2em) auto var(--spacing-medium) auto;\n}\n\ndiv.header .summary {\n margin: var(--spacing-medium) auto 0 auto;\n}\n\ndiv.headertitle {\n padding: 0;\n}\n\ndiv.header .title {\n font-weight: 600;\n font-size: 225%;\n padding: var(--spacing-medium) var(--spacing-large);\n word-break: break-word;\n}\n\ndiv.header .summary {\n width: auto;\n display: block;\n float: none;\n padding: 0 var(--spacing-large);\n}\n\ntd.memSeparator {\n border-color: var(--separator-color);\n}\n\nspan.mlabel {\n background: var(--primary-color);\n border: none;\n padding: 4px 9px;\n border-radius: 12px;\n margin-right: var(--spacing-medium);\n}\n\nspan.mlabel:last-of-type {\n margin-right: 2px;\n}\n\ndiv.contents {\n padding: 0 var(--spacing-large);\n}\n\ndiv.contents p, div.contents li {\n line-height: var(--content-line-height);\n}\n\ndiv.contents div.dyncontent {\n margin: var(--spacing-medium) 0;\n}\n\n@media (prefers-color-scheme: dark) {\n html:not(.light-mode) div.contents div.dyncontent img,\n html:not(.light-mode) div.contents center img,\n html:not(.light-mode) div.contents > table img,\n html:not(.light-mode) div.contents div.dyncontent iframe,\n html:not(.light-mode) div.contents center iframe,\n html:not(.light-mode) div.contents table iframe,\n html:not(.light-mode) div.contents .dotgraph iframe {\n filter: brightness(89%) hue-rotate(180deg) invert();\n }\n}\n\nhtml.dark-mode div.contents div.dyncontent img,\nhtml.dark-mode div.contents center img,\nhtml.dark-mode div.contents > table img,\nhtml.dark-mode div.contents div.dyncontent iframe,\nhtml.dark-mode div.contents center iframe,\nhtml.dark-mode div.contents table iframe,\nhtml.dark-mode div.contents .dotgraph iframe\n {\n filter: brightness(89%) hue-rotate(180deg) invert();\n}\n\nh2.groupheader {\n border-bottom: 0px;\n color: var(--page-foreground-color);\n box-shadow:\n 100px 0 var(--page-background-color),\n -100px 0 var(--page-background-color),\n 100px 0.75px var(--separator-color),\n -100px 0.75px var(--separator-color),\n 500px 0 var(--page-background-color),\n -500px 0 var(--page-background-color),\n 500px 0.75px var(--separator-color),\n -500px 0.75px var(--separator-color),\n 900px 0 var(--page-background-color),\n -900px 0 var(--page-background-color),\n 900px 0.75px var(--separator-color),\n -900px 0.75px var(--separator-color),\n 1400px 0 var(--page-background-color),\n -1400px 0 var(--page-background-color),\n 1400px 0.75px var(--separator-color),\n -1400px 0.75px var(--separator-color),\n 1900px 0 var(--page-background-color),\n -1900px 0 var(--page-background-color),\n 1900px 0.75px var(--separator-color),\n -1900px 0.75px var(--separator-color);\n}\n\nblockquote {\n margin: 0 var(--spacing-medium) 0 var(--spacing-medium);\n padding: var(--spacing-small) var(--spacing-large);\n background: var(--blockquote-background);\n color: var(--blockquote-foreground);\n border-left: 0;\n overflow: visible;\n border-radius: var(--border-radius-medium);\n overflow: visible;\n position: relative;\n}\n\nblockquote::before, blockquote::after {\n font-weight: bold;\n font-family: serif;\n font-size: 360%;\n opacity: .15;\n position: absolute;\n}\n\nblockquote::before {\n content: \"“\";\n left: -10px;\n top: 4px;\n}\n\nblockquote::after {\n content: \"”\";\n right: -8px;\n bottom: -25px;\n}\n\nblockquote p {\n margin: var(--spacing-small) 0 var(--spacing-medium) 0;\n}\n.paramname, .paramname em {\n font-weight: 600;\n color: var(--primary-dark-color);\n}\n\n.paramname > code {\n border: 0;\n}\n\ntable.params .paramname {\n font-weight: 600;\n font-family: var(--font-family-monospace);\n font-size: var(--code-font-size);\n padding-right: var(--spacing-small);\n line-height: var(--table-line-height);\n}\n\nh1.glow, h2.glow, h3.glow, h4.glow, h5.glow, h6.glow {\n text-shadow: 0 0 15px var(--primary-light-color);\n}\n\n.alphachar a {\n color: var(--page-foreground-color);\n}\n\n.dotgraph {\n max-width: 100%;\n overflow-x: scroll;\n}\n\n.dotgraph .caption {\n position: sticky;\n left: 0;\n}\n\n/* Wrap Graphviz graphs with the `interactive_dotgraph` class if `INTERACTIVE_SVG = YES` */\n.interactive_dotgraph .dotgraph iframe {\n max-width: 100%;\n}\n\n/*\n Table of Contents\n */\n\ndiv.contents .toc {\n max-height: var(--toc-max-height);\n min-width: var(--toc-width);\n border: 0;\n border-left: 1px solid var(--separator-color);\n border-radius: 0;\n background-color: var(--page-background-color);\n box-shadow: none;\n position: sticky;\n top: var(--toc-sticky-top);\n padding: 0 var(--spacing-large);\n margin: var(--spacing-small) 0 var(--spacing-large) var(--spacing-large);\n}\n\ndiv.toc h3 {\n color: var(--toc-foreground);\n font-size: var(--navigation-font-size);\n margin: var(--spacing-large) 0 var(--spacing-medium) 0;\n}\n\ndiv.toc li {\n padding: 0;\n background: none;\n line-height: var(--toc-font-size);\n margin: var(--toc-font-size) 0 0 0;\n}\n\ndiv.toc li::before {\n display: none;\n}\n\ndiv.toc ul {\n margin-top: 0\n}\n\ndiv.toc li a {\n font-size: var(--toc-font-size);\n color: var(--page-foreground-color) !important;\n text-decoration: none;\n}\n\ndiv.toc li a:hover, div.toc li a.active {\n color: var(--primary-color) !important;\n}\n\ndiv.toc li a.aboveActive {\n color: var(--page-secondary-foreground-color) !important;\n}\n\n\n@media screen and (max-width: 999px) {\n div.contents .toc {\n max-height: 45vh;\n float: none;\n width: auto;\n margin: 0 0 var(--spacing-medium) 0;\n position: relative;\n top: 0;\n position: relative;\n border: 1px solid var(--separator-color);\n border-radius: var(--border-radius-medium);\n background-color: var(--toc-background);\n box-shadow: var(--box-shadow);\n }\n\n div.contents .toc.interactive {\n max-height: calc(var(--navigation-font-size) + 2 * var(--spacing-large));\n overflow: hidden;\n }\n\n div.contents .toc > h3 {\n -webkit-tap-highlight-color: transparent;\n cursor: pointer;\n position: sticky;\n top: 0;\n background-color: var(--toc-background);\n margin: 0;\n padding: var(--spacing-large) 0;\n display: block;\n }\n\n div.contents .toc.interactive > h3::before {\n content: \"\";\n width: 0;\n height: 0;\n border-left: 4px solid transparent;\n border-right: 4px solid transparent;\n border-top: 5px solid var(--primary-color);\n display: inline-block;\n margin-right: var(--spacing-small);\n margin-bottom: calc(var(--navigation-font-size) / 4);\n transform: rotate(-90deg);\n transition: transform var(--animation-duration) ease-out;\n }\n\n div.contents .toc.interactive.open > h3::before {\n transform: rotate(0deg);\n }\n\n div.contents .toc.interactive.open {\n max-height: 45vh;\n overflow: auto;\n transition: max-height 0.2s ease-in-out;\n }\n\n div.contents .toc a, div.contents .toc a.active {\n color: var(--primary-color) !important;\n }\n\n div.contents .toc a:hover {\n text-decoration: underline;\n }\n}\n\n/*\n Code & Fragments\n */\n\ncode, div.fragment, pre.fragment {\n border-radius: var(--border-radius-small);\n border: 1px solid var(--separator-color);\n overflow: hidden;\n}\n\ncode {\n display: inline;\n background: var(--code-background);\n color: var(--code-foreground);\n padding: 2px 6px;\n}\n\ndiv.fragment, pre.fragment {\n margin: var(--spacing-medium) 0;\n padding: calc(var(--spacing-large) - (var(--spacing-large) / 6)) var(--spacing-large);\n background: var(--fragment-background);\n color: var(--fragment-foreground);\n overflow-x: auto;\n}\n\n@media screen and (max-width: 767px) {\n div.fragment, pre.fragment {\n border-top-right-radius: 0;\n border-bottom-right-radius: 0;\n border-right: 0;\n }\n\n .contents > div.fragment,\n .textblock > div.fragment,\n .textblock > pre.fragment,\n .textblock > .tabbed > ul > li > div.fragment,\n .textblock > .tabbed > ul > li > pre.fragment,\n .contents > .doxygen-awesome-fragment-wrapper > div.fragment,\n .textblock > .doxygen-awesome-fragment-wrapper > div.fragment,\n .textblock > .doxygen-awesome-fragment-wrapper > pre.fragment,\n .textblock > .tabbed > ul > li > .doxygen-awesome-fragment-wrapper > div.fragment,\n .textblock > .tabbed > ul > li > .doxygen-awesome-fragment-wrapper > pre.fragment {\n margin: var(--spacing-medium) calc(0px - var(--spacing-large));\n border-radius: 0;\n border-left: 0;\n }\n\n .textblock li > .fragment,\n .textblock li > .doxygen-awesome-fragment-wrapper > .fragment {\n margin: var(--spacing-medium) calc(0px - var(--spacing-large));\n }\n\n .memdoc li > .fragment,\n .memdoc li > .doxygen-awesome-fragment-wrapper > .fragment {\n margin: var(--spacing-medium) calc(0px - var(--spacing-medium));\n }\n\n .textblock ul, .memdoc ul {\n overflow: initial;\n }\n\n .memdoc > div.fragment,\n .memdoc > pre.fragment,\n dl dd > div.fragment,\n dl dd pre.fragment,\n .memdoc > .doxygen-awesome-fragment-wrapper > div.fragment,\n .memdoc > .doxygen-awesome-fragment-wrapper > pre.fragment,\n dl dd > .doxygen-awesome-fragment-wrapper > div.fragment,\n dl dd .doxygen-awesome-fragment-wrapper > pre.fragment {\n margin: var(--spacing-medium) calc(0px - var(--spacing-medium));\n border-radius: 0;\n border-left: 0;\n }\n}\n\ncode, code a, pre.fragment, div.fragment, div.fragment .line, div.fragment span, div.fragment .line a, div.fragment .line span {\n font-family: var(--font-family-monospace);\n font-size: var(--code-font-size) !important;\n}\n\ndiv.line:after {\n margin-right: var(--spacing-medium);\n}\n\ndiv.fragment .line, pre.fragment {\n white-space: pre;\n word-wrap: initial;\n line-height: var(--fragment-lineheight);\n}\n\ndiv.fragment span.keyword {\n color: var(--fragment-keyword);\n}\n\ndiv.fragment span.keywordtype {\n color: var(--fragment-keywordtype);\n}\n\ndiv.fragment span.keywordflow {\n color: var(--fragment-keywordflow);\n}\n\ndiv.fragment span.stringliteral {\n color: var(--fragment-token)\n}\n\ndiv.fragment span.comment {\n color: var(--fragment-comment);\n}\n\ndiv.fragment a.code {\n color: var(--fragment-link) !important;\n}\n\ndiv.fragment span.preprocessor {\n color: var(--fragment-preprocessor);\n}\n\ndiv.fragment span.lineno {\n display: inline-block;\n width: 27px;\n border-right: none;\n background: var(--fragment-linenumber-background);\n color: var(--fragment-linenumber-color);\n}\n\ndiv.fragment span.lineno a {\n background: none;\n color: var(--fragment-link) !important;\n}\n\ndiv.fragment > .line:first-child .lineno {\n box-shadow: -999999px 0px 0 999999px var(--fragment-linenumber-background), -999998px 0px 0 999999px var(--fragment-linenumber-border);\n background-color: var(--fragment-linenumber-background) !important;\n}\n\ndiv.line {\n border-radius: var(--border-radius-small);\n}\n\ndiv.line.glow {\n background-color: var(--primary-light-color);\n box-shadow: none;\n}\n\n/*\n dl warning, attention, note, deprecated, bug, ...\n */\n\ndl.bug dt a, dl.deprecated dt a, dl.todo dt a {\n font-weight: bold !important;\n}\n\ndl.warning, dl.attention, dl.note, dl.deprecated, dl.bug, dl.invariant, dl.pre, dl.post, dl.todo, dl.remark {\n padding: var(--spacing-medium);\n margin: var(--spacing-medium) 0;\n color: var(--page-background-color);\n overflow: hidden;\n margin-left: 0;\n border-radius: var(--border-radius-small);\n}\n\ndl.section dd {\n margin-bottom: 2px;\n}\n\ndl.warning, dl.attention {\n background: var(--warning-color);\n border-left: 8px solid var(--warning-color-dark);\n color: var(--warning-color-darker);\n}\n\ndl.warning dt, dl.attention dt {\n color: var(--warning-color-dark);\n}\n\ndl.note, dl.remark {\n background: var(--note-color);\n border-left: 8px solid var(--note-color-dark);\n color: var(--note-color-darker);\n}\n\ndl.note dt, dl.remark dt {\n color: var(--note-color-dark);\n}\n\ndl.todo {\n background: var(--todo-color);\n border-left: 8px solid var(--todo-color-dark);\n color: var(--todo-color-darker);\n}\n\ndl.todo dt a {\n color: var(--todo-color-dark) !important;\n}\n\ndl.bug dt a {\n color: var(--todo-color-dark) !important;\n}\n\ndl.bug {\n background: var(--bug-color);\n border-left: 8px solid var(--bug-color-dark);\n color: var(--bug-color-darker);\n}\n\ndl.bug dt a {\n color: var(--bug-color-dark) !important;\n}\n\ndl.deprecated {\n background: var(--deprecated-color);\n border-left: 8px solid var(--deprecated-color-dark);\n color: var(--deprecated-color-darker);\n}\n\ndl.deprecated dt a {\n color: var(--deprecated-color-dark) !important;\n}\n\ndl.section dd, dl.bug dd, dl.deprecated dd, dl.todo dd {\n margin-inline-start: 0px;\n}\n\ndl.invariant, dl.pre, dl.post {\n background: var(--invariant-color);\n border-left: 8px solid var(--invariant-color-dark);\n color: var(--invariant-color-darker);\n}\n\ndl.invariant dt, dl.pre dt, dl.post dt {\n color: var(--invariant-color-dark);\n}\n\n/*\n memitem\n */\n\ndiv.memdoc, div.memproto, h2.memtitle {\n box-shadow: none;\n background-image: none;\n border: none;\n}\n\ndiv.memdoc {\n padding: 0 var(--spacing-medium);\n background: var(--page-background-color);\n}\n\nh2.memtitle, div.memitem {\n border: 1px solid var(--separator-color);\n box-shadow: var(--box-shadow);\n}\n\nh2.memtitle {\n box-shadow: 0px var(--spacing-medium) 0 -1px var(--fragment-background), var(--box-shadow);\n}\n\ndiv.memitem {\n transition: none;\n}\n\ndiv.memproto, h2.memtitle {\n background: var(--fragment-background);\n}\n\nh2.memtitle {\n font-weight: 500;\n font-size: var(--memtitle-font-size);\n font-family: var(--font-family-monospace);\n border-bottom: none;\n border-top-left-radius: var(--border-radius-medium);\n border-top-right-radius: var(--border-radius-medium);\n word-break: break-all;\n position: relative;\n}\n\nh2.memtitle:after {\n content: \"\";\n display: block;\n background: var(--fragment-background);\n height: var(--spacing-medium);\n bottom: calc(0px - var(--spacing-medium));\n left: 0;\n right: -14px;\n position: absolute;\n border-top-right-radius: var(--border-radius-medium);\n}\n\nh2.memtitle > span.permalink {\n font-size: inherit;\n}\n\nh2.memtitle > span.permalink > a {\n text-decoration: none;\n padding-left: 3px;\n margin-right: -4px;\n user-select: none;\n display: inline-block;\n margin-top: -6px;\n}\n\nh2.memtitle > span.permalink > a:hover {\n color: var(--primary-dark-color) !important;\n}\n\na:target + h2.memtitle, a:target + h2.memtitle + div.memitem {\n border-color: var(--primary-light-color);\n}\n\ndiv.memitem {\n border-top-right-radius: var(--border-radius-medium);\n border-bottom-right-radius: var(--border-radius-medium);\n border-bottom-left-radius: var(--border-radius-medium);\n overflow: hidden;\n display: block !important;\n}\n\ndiv.memdoc {\n border-radius: 0;\n}\n\ndiv.memproto {\n border-radius: 0 var(--border-radius-small) 0 0;\n overflow: auto;\n border-bottom: 1px solid var(--separator-color);\n padding: var(--spacing-medium);\n margin-bottom: -1px;\n}\n\ndiv.memtitle {\n border-top-right-radius: var(--border-radius-medium);\n border-top-left-radius: var(--border-radius-medium);\n}\n\ndiv.memproto table.memname {\n font-family: var(--font-family-monospace);\n color: var(--page-foreground-color);\n font-size: var(--memname-font-size);\n text-shadow: none;\n}\n\ndiv.memproto div.memtemplate {\n font-family: var(--font-family-monospace);\n color: var(--primary-dark-color);\n font-size: var(--memname-font-size);\n margin-left: 2px;\n text-shadow: none;\n}\n\ntable.mlabels, table.mlabels > tbody {\n display: block;\n}\n\ntd.mlabels-left {\n width: auto;\n}\n\ntd.mlabels-right {\n margin-top: 3px;\n position: sticky;\n left: 0;\n}\n\ntable.mlabels > tbody > tr:first-child {\n display: flex;\n justify-content: space-between;\n flex-wrap: wrap;\n}\n\n.memname, .memitem span.mlabels {\n margin: 0\n}\n\n/*\n reflist\n */\n\ndl.reflist {\n box-shadow: var(--box-shadow);\n border-radius: var(--border-radius-medium);\n border: 1px solid var(--separator-color);\n overflow: hidden;\n padding: 0;\n}\n\n\ndl.reflist dt, dl.reflist dd {\n box-shadow: none;\n text-shadow: none;\n background-image: none;\n border: none;\n padding: 12px;\n}\n\n\ndl.reflist dt {\n font-weight: 500;\n border-radius: 0;\n background: var(--code-background);\n border-bottom: 1px solid var(--separator-color);\n color: var(--page-foreground-color)\n}\n\n\ndl.reflist dd {\n background: none;\n}\n\n/*\n Table\n */\n\n.contents table:not(.memberdecls):not(.mlabels):not(.fieldtable):not(.memname),\n.contents table:not(.memberdecls):not(.mlabels):not(.fieldtable):not(.memname) tbody {\n display: inline-block;\n max-width: 100%;\n}\n\n.contents > table:not(.memberdecls):not(.mlabels):not(.fieldtable):not(.memname):not(.classindex) {\n margin-left: calc(0px - var(--spacing-large));\n margin-right: calc(0px - var(--spacing-large));\n max-width: calc(100% + 2 * var(--spacing-large));\n}\n\ntable.fieldtable,\ntable.markdownTable tbody,\ntable.doxtable tbody {\n border: none;\n margin: var(--spacing-medium) 0;\n box-shadow: 0 0 0 1px var(--separator-color);\n border-radius: var(--border-radius-small);\n}\n\ntable.markdownTable, table.doxtable, table.fieldtable {\n padding: 1px;\n}\n\ntable.doxtable caption {\n display: block;\n}\n\ntable.fieldtable {\n border-collapse: collapse;\n width: 100%;\n}\n\nth.markdownTableHeadLeft,\nth.markdownTableHeadRight,\nth.markdownTableHeadCenter,\nth.markdownTableHeadNone,\ntable.doxtable th {\n background: var(--tablehead-background);\n color: var(--tablehead-foreground);\n font-weight: 600;\n font-size: var(--page-font-size);\n}\n\nth.markdownTableHeadLeft:first-child,\nth.markdownTableHeadRight:first-child,\nth.markdownTableHeadCenter:first-child,\nth.markdownTableHeadNone:first-child,\ntable.doxtable tr th:first-child {\n border-top-left-radius: var(--border-radius-small);\n}\n\nth.markdownTableHeadLeft:last-child,\nth.markdownTableHeadRight:last-child,\nth.markdownTableHeadCenter:last-child,\nth.markdownTableHeadNone:last-child,\ntable.doxtable tr th:last-child {\n border-top-right-radius: var(--border-radius-small);\n}\n\ntable.markdownTable td,\ntable.markdownTable th,\ntable.fieldtable td,\ntable.fieldtable th,\ntable.doxtable td,\ntable.doxtable th {\n border: 1px solid var(--separator-color);\n padding: var(--spacing-small) var(--spacing-medium);\n}\n\ntable.markdownTable td:last-child,\ntable.markdownTable th:last-child,\ntable.fieldtable td:last-child,\ntable.fieldtable th:last-child,\ntable.doxtable td:last-child,\ntable.doxtable th:last-child {\n border-right: none;\n}\n\ntable.markdownTable td:first-child,\ntable.markdownTable th:first-child,\ntable.fieldtable td:first-child,\ntable.fieldtable th:first-child,\ntable.doxtable td:first-child,\ntable.doxtable th:first-child {\n border-left: none;\n}\n\ntable.markdownTable tr:first-child td,\ntable.markdownTable tr:first-child th,\ntable.fieldtable tr:first-child td,\ntable.fieldtable tr:first-child th,\ntable.doxtable tr:first-child td,\ntable.doxtable tr:first-child th {\n border-top: none;\n}\n\ntable.markdownTable tr:last-child td,\ntable.markdownTable tr:last-child th,\ntable.fieldtable tr:last-child td,\ntable.fieldtable tr:last-child th,\ntable.doxtable tr:last-child td,\ntable.doxtable tr:last-child th {\n border-bottom: none;\n}\n\ntable.markdownTable tr, table.doxtable tr {\n border-bottom: 1px solid var(--separator-color);\n}\n\ntable.markdownTable tr:last-child, table.doxtable tr:last-child {\n border-bottom: none;\n}\n\n.full_width_table table:not(.memberdecls):not(.mlabels):not(.fieldtable):not(.memname) {\n display: block;\n}\n\n.full_width_table table:not(.memberdecls):not(.mlabels):not(.fieldtable):not(.memname) tbody {\n display: table;\n width: 100%;\n}\n\ntable.fieldtable th {\n font-size: var(--page-font-size);\n font-weight: 600;\n background-image: none;\n background-color: var(--tablehead-background);\n color: var(--tablehead-foreground);\n}\n\ntable.fieldtable td.fieldtype, .fieldtable td.fieldname, .fieldtable td.fieldinit, .fieldtable td.fielddoc, .fieldtable th {\n border-bottom: 1px solid var(--separator-color);\n border-right: 1px solid var(--separator-color);\n}\n\ntable.fieldtable tr:last-child td:first-child {\n border-bottom-left-radius: var(--border-radius-small);\n}\n\ntable.fieldtable tr:last-child td:last-child {\n border-bottom-right-radius: var(--border-radius-small);\n}\n\n.memberdecls td.glow, .fieldtable tr.glow {\n background-color: var(--primary-light-color);\n box-shadow: none;\n}\n\ntable.memberdecls {\n display: block;\n -webkit-tap-highlight-color: transparent;\n}\n\ntable.memberdecls tr[class^='memitem'] {\n font-family: var(--font-family-monospace);\n font-size: var(--code-font-size);\n}\n\ntable.memberdecls tr[class^='memitem'] .memTemplParams {\n font-family: var(--font-family-monospace);\n font-size: var(--code-font-size);\n color: var(--primary-dark-color);\n white-space: normal;\n}\n\ntable.memberdecls .memItemLeft,\ntable.memberdecls .memItemRight,\ntable.memberdecls .memTemplItemLeft,\ntable.memberdecls .memTemplItemRight,\ntable.memberdecls .memTemplParams {\n transition: none;\n padding-top: var(--spacing-small);\n padding-bottom: var(--spacing-small);\n border-top: 1px solid var(--separator-color);\n border-bottom: 1px solid var(--separator-color);\n background-color: var(--fragment-background);\n}\n\ntable.memberdecls .memTemplItemLeft,\ntable.memberdecls .memTemplItemRight {\n padding-top: 2px;\n}\n\ntable.memberdecls .memTemplParams {\n border-bottom: 0;\n border-left: 1px solid var(--separator-color);\n border-right: 1px solid var(--separator-color);\n border-radius: var(--border-radius-small) var(--border-radius-small) 0 0;\n padding-bottom: var(--spacing-small);\n}\n\ntable.memberdecls .memTemplItemLeft {\n border-radius: 0 0 0 var(--border-radius-small);\n border-left: 1px solid var(--separator-color);\n border-top: 0;\n}\n\ntable.memberdecls .memTemplItemRight {\n border-radius: 0 0 var(--border-radius-small) 0;\n border-right: 1px solid var(--separator-color);\n padding-left: 0;\n border-top: 0;\n}\n\ntable.memberdecls .memItemLeft {\n border-radius: var(--border-radius-small) 0 0 var(--border-radius-small);\n border-left: 1px solid var(--separator-color);\n padding-left: var(--spacing-medium);\n padding-right: 0;\n}\n\ntable.memberdecls .memItemRight {\n border-radius: 0 var(--border-radius-small) var(--border-radius-small) 0;\n border-right: 1px solid var(--separator-color);\n padding-right: var(--spacing-medium);\n padding-left: 0;\n\n}\n\ntable.memberdecls .mdescLeft, table.memberdecls .mdescRight {\n background: none;\n color: var(--page-foreground-color);\n padding: var(--spacing-small) 0;\n}\n\ntable.memberdecls .memItemLeft,\ntable.memberdecls .memTemplItemLeft {\n padding-right: var(--spacing-medium);\n}\n\ntable.memberdecls .memSeparator {\n background: var(--page-background-color);\n height: var(--spacing-large);\n border: 0;\n transition: none;\n}\n\ntable.memberdecls .groupheader {\n margin-bottom: var(--spacing-large);\n}\n\ntable.memberdecls .inherit_header td {\n padding: 0 0 var(--spacing-medium) 0;\n text-indent: -12px;\n color: var(--page-secondary-foreground-color);\n}\n\ntable.memberdecls img[src=\"closed.png\"],\ntable.memberdecls img[src=\"open.png\"],\ndiv.dynheader img[src=\"open.png\"],\ndiv.dynheader img[src=\"closed.png\"] {\n width: 0;\n height: 0;\n border-left: 4px solid transparent;\n border-right: 4px solid transparent;\n border-top: 5px solid var(--primary-color);\n margin-top: 8px;\n display: block;\n float: left;\n margin-left: -10px;\n transition: transform var(--animation-duration) ease-out;\n}\n\ntable.memberdecls img {\n margin-right: 10px;\n}\n\ntable.memberdecls img[src=\"closed.png\"],\ndiv.dynheader img[src=\"closed.png\"] {\n transform: rotate(-90deg);\n}\n\n.compoundTemplParams {\n font-family: var(--font-family-monospace);\n color: var(--primary-dark-color);\n font-size: var(--code-font-size);\n}\n\n@media screen and (max-width: 767px) {\n\n table.memberdecls .memItemLeft,\n table.memberdecls .memItemRight,\n table.memberdecls .mdescLeft,\n table.memberdecls .mdescRight,\n table.memberdecls .memTemplItemLeft,\n table.memberdecls .memTemplItemRight,\n table.memberdecls .memTemplParams {\n display: block;\n text-align: left;\n padding-left: var(--spacing-large);\n margin: 0 calc(0px - var(--spacing-large)) 0 calc(0px - var(--spacing-large));\n border-right: none;\n border-left: none;\n border-radius: 0;\n white-space: normal;\n }\n\n table.memberdecls .memItemLeft,\n table.memberdecls .mdescLeft,\n table.memberdecls .memTemplItemLeft {\n border-bottom: 0;\n padding-bottom: 0;\n }\n\n table.memberdecls .memTemplItemLeft {\n padding-top: 0;\n }\n\n table.memberdecls .mdescLeft {\n margin-bottom: calc(0px - var(--page-font-size));\n }\n\n table.memberdecls .memItemRight,\n table.memberdecls .mdescRight,\n table.memberdecls .memTemplItemRight {\n border-top: 0;\n padding-top: 0;\n padding-right: var(--spacing-large);\n overflow-x: auto;\n }\n\n table.memberdecls tr[class^='memitem']:not(.inherit) {\n display: block;\n width: calc(100vw - 2 * var(--spacing-large));\n }\n\n table.memberdecls .mdescRight {\n color: var(--page-foreground-color);\n }\n\n table.memberdecls tr.inherit {\n visibility: hidden;\n }\n\n table.memberdecls tr[style=\"display: table-row;\"] {\n display: block !important;\n visibility: visible;\n width: calc(100vw - 2 * var(--spacing-large));\n animation: fade .5s;\n }\n\n @keyframes fade {\n 0% {\n opacity: 0;\n max-height: 0;\n }\n\n 100% {\n opacity: 1;\n max-height: 200px;\n }\n }\n}\n\n\n/*\n Horizontal Rule\n */\n\nhr {\n margin-top: var(--spacing-large);\n margin-bottom: var(--spacing-large);\n height: 1px;\n background-color: var(--separator-color);\n border: 0;\n}\n\n.contents hr {\n box-shadow: 100px 0 var(--separator-color),\n -100px 0 var(--separator-color),\n 500px 0 var(--separator-color),\n -500px 0 var(--separator-color),\n 900px 0 var(--separator-color),\n -900px 0 var(--separator-color),\n 1400px 0 var(--separator-color),\n -1400px 0 var(--separator-color),\n 1900px 0 var(--separator-color),\n -1900px 0 var(--separator-color);\n}\n\n.contents img, .contents .center, .contents center, .contents div.image object {\n max-width: 100%;\n overflow: auto;\n}\n\n@media screen and (max-width: 767px) {\n .contents .dyncontent > .center, .contents > center {\n margin-left: calc(0px - var(--spacing-large));\n margin-right: calc(0px - var(--spacing-large));\n max-width: calc(100% + 2 * var(--spacing-large));\n }\n}\n\n/*\n Directories\n */\ndiv.directory {\n border-top: 1px solid var(--separator-color);\n border-bottom: 1px solid var(--separator-color);\n width: auto;\n}\n\ntable.directory {\n font-family: var(--font-family);\n font-size: var(--page-font-size);\n font-weight: normal;\n width: 100%;\n}\n\ntable.directory td.entry, table.directory td.desc {\n padding: calc(var(--spacing-small) / 2) var(--spacing-small);\n line-height: var(--table-line-height);\n}\n\ntable.directory tr.even td:last-child {\n border-radius: 0 var(--border-radius-small) var(--border-radius-small) 0;\n}\n\ntable.directory tr.even td:first-child {\n border-radius: var(--border-radius-small) 0 0 var(--border-radius-small);\n}\n\ntable.directory tr.even:last-child td:last-child {\n border-radius: 0 var(--border-radius-small) 0 0;\n}\n\ntable.directory tr.even:last-child td:first-child {\n border-radius: var(--border-radius-small) 0 0 0;\n}\n\ntable.directory td.desc {\n min-width: 250px;\n}\n\ntable.directory tr.even {\n background-color: var(--odd-color);\n}\n\ntable.directory tr.odd {\n background-color: transparent;\n}\n\n.icona {\n width: auto;\n height: auto;\n margin: 0 var(--spacing-small);\n}\n\n.icon {\n background: var(--primary-color);\n border-radius: var(--border-radius-small);\n font-size: var(--page-font-size);\n padding: calc(var(--page-font-size) / 5);\n line-height: var(--page-font-size);\n transform: scale(0.8);\n height: auto;\n width: var(--page-font-size);\n user-select: none;\n}\n\n.iconfopen, .icondoc, .iconfclosed {\n background-position: center;\n margin-bottom: 0;\n height: var(--table-line-height);\n}\n\n.icondoc {\n filter: saturate(0.2);\n}\n\n@media screen and (max-width: 767px) {\n div.directory {\n margin-left: calc(0px - var(--spacing-large));\n margin-right: calc(0px - var(--spacing-large));\n }\n}\n\n@media (prefers-color-scheme: dark) {\n html:not(.light-mode) .iconfopen, html:not(.light-mode) .iconfclosed {\n filter: hue-rotate(180deg) invert();\n }\n}\n\nhtml.dark-mode .iconfopen, html.dark-mode .iconfclosed {\n filter: hue-rotate(180deg) invert();\n}\n\n/*\n Class list\n */\n\n.classindex dl.odd {\n background: var(--odd-color);\n border-radius: var(--border-radius-small);\n}\n\n.classindex dl.even {\n background-color: transparent;\n}\n\n/*\n Class Index Doxygen 1.8\n*/\n\ntable.classindex {\n margin-left: 0;\n margin-right: 0;\n width: 100%;\n}\n\ntable.classindex table div.ah {\n background-image: none;\n background-color: initial;\n border-color: var(--separator-color);\n color: var(--page-foreground-color);\n box-shadow: var(--box-shadow);\n border-radius: var(--border-radius-large);\n padding: var(--spacing-small);\n}\n\ndiv.qindex {\n background-color: var(--odd-color);\n border-radius: var(--border-radius-small);\n border: 1px solid var(--separator-color);\n padding: var(--spacing-small) 0;\n}\n\n/*\n Footer and nav-path\n */\n\n#nav-path {\n width: 100%;\n}\n\n#nav-path ul {\n background-image: none;\n background: var(--page-background-color);\n border: none;\n border-top: 1px solid var(--separator-color);\n border-bottom: 1px solid var(--separator-color);\n border-bottom: 0;\n box-shadow: 0 0.75px 0 var(--separator-color);\n font-size: var(--navigation-font-size);\n}\n\nimg.footer {\n width: 60px;\n}\n\n.navpath li.footer {\n color: var(--page-secondary-foreground-color);\n}\n\naddress.footer {\n color: var(--page-secondary-foreground-color);\n margin-bottom: var(--spacing-large);\n}\n\n#nav-path li.navelem {\n background-image: none;\n display: flex;\n align-items: center;\n}\n\n.navpath li.navelem a {\n text-shadow: none;\n display: inline-block;\n color: var(--primary-color) !important;\n}\n\n.navpath li.navelem b {\n color: var(--primary-dark-color);\n font-weight: 500;\n}\n\nli.navelem {\n padding: 0;\n margin-left: -8px;\n}\n\nli.navelem:first-child {\n margin-left: var(--spacing-large);\n}\n\nli.navelem:first-child:before {\n display: none;\n}\n\n#nav-path li.navelem:after {\n content: '';\n border: 5px solid var(--page-background-color);\n border-bottom-color: transparent;\n border-right-color: transparent;\n border-top-color: transparent;\n transform: translateY(-1px) scaleY(4.2);\n z-index: 10;\n margin-left: 6px;\n}\n\n#nav-path li.navelem:before {\n content: '';\n border: 5px solid var(--separator-color);\n border-bottom-color: transparent;\n border-right-color: transparent;\n border-top-color: transparent;\n transform: translateY(-1px) scaleY(3.2);\n margin-right: var(--spacing-small);\n}\n\n.navpath li.navelem a:hover {\n color: var(--primary-color);\n}\n\n/*\n Scrollbars for Webkit\n*/\n\n#nav-tree::-webkit-scrollbar,\ndiv.fragment::-webkit-scrollbar,\npre.fragment::-webkit-scrollbar,\ndiv.memproto::-webkit-scrollbar,\n.contents center::-webkit-scrollbar,\n.contents .center::-webkit-scrollbar,\n.contents table:not(.memberdecls):not(.mlabels):not(.fieldtable):not(.memname) tbody::-webkit-scrollbar,\ndiv.contents .toc::-webkit-scrollbar,\n.contents .dotgraph::-webkit-scrollbar,\n.contents .tabs-overview-container::-webkit-scrollbar {\n background: transparent;\n width: calc(var(--webkit-scrollbar-size) + var(--webkit-scrollbar-padding) + var(--webkit-scrollbar-padding));\n height: calc(var(--webkit-scrollbar-size) + var(--webkit-scrollbar-padding) + var(--webkit-scrollbar-padding));\n}\n\n#nav-tree::-webkit-scrollbar-thumb,\ndiv.fragment::-webkit-scrollbar-thumb,\npre.fragment::-webkit-scrollbar-thumb,\ndiv.memproto::-webkit-scrollbar-thumb,\n.contents center::-webkit-scrollbar-thumb,\n.contents .center::-webkit-scrollbar-thumb,\n.contents table:not(.memberdecls):not(.mlabels):not(.fieldtable):not(.memname) tbody::-webkit-scrollbar-thumb,\ndiv.contents .toc::-webkit-scrollbar-thumb,\n.contents .dotgraph::-webkit-scrollbar-thumb,\n.contents .tabs-overview-container::-webkit-scrollbar-thumb {\n background-color: transparent;\n border: var(--webkit-scrollbar-padding) solid transparent;\n border-radius: calc(var(--webkit-scrollbar-padding) + var(--webkit-scrollbar-padding));\n background-clip: padding-box;\n}\n\n#nav-tree:hover::-webkit-scrollbar-thumb,\ndiv.fragment:hover::-webkit-scrollbar-thumb,\npre.fragment:hover::-webkit-scrollbar-thumb,\ndiv.memproto:hover::-webkit-scrollbar-thumb,\n.contents center:hover::-webkit-scrollbar-thumb,\n.contents .center:hover::-webkit-scrollbar-thumb,\n.contents table:not(.memberdecls):not(.mlabels):not(.fieldtable):not(.memname) tbody:hover::-webkit-scrollbar-thumb,\ndiv.contents .toc:hover::-webkit-scrollbar-thumb,\n.contents .dotgraph:hover::-webkit-scrollbar-thumb,\n.contents .tabs-overview-container:hover::-webkit-scrollbar-thumb {\n background-color: var(--webkit-scrollbar-color);\n}\n\n#nav-tree::-webkit-scrollbar-track,\ndiv.fragment::-webkit-scrollbar-track,\npre.fragment::-webkit-scrollbar-track,\ndiv.memproto::-webkit-scrollbar-track,\n.contents center::-webkit-scrollbar-track,\n.contents .center::-webkit-scrollbar-track,\n.contents table:not(.memberdecls):not(.mlabels):not(.fieldtable):not(.memname) tbody::-webkit-scrollbar-track,\ndiv.contents .toc::-webkit-scrollbar-track,\n.contents .dotgraph::-webkit-scrollbar-track,\n.contents .tabs-overview-container::-webkit-scrollbar-track {\n background: transparent;\n}\n\n#nav-tree::-webkit-scrollbar-corner {\n background-color: var(--side-nav-background);\n}\n\n#nav-tree,\ndiv.fragment,\npre.fragment,\ndiv.memproto,\n.contents center,\n.contents .center,\n.contents table:not(.memberdecls):not(.mlabels):not(.fieldtable):not(.memname) tbody,\ndiv.contents .toc {\n overflow-x: auto;\n overflow-x: overlay;\n}\n\n#nav-tree {\n overflow-x: auto;\n overflow-y: auto;\n overflow-y: overlay;\n}\n\n/*\n Scrollbars for Firefox\n*/\n\n#nav-tree,\ndiv.fragment,\npre.fragment,\ndiv.memproto,\n.contents center,\n.contents .center,\n.contents table:not(.memberdecls):not(.mlabels):not(.fieldtable):not(.memname) tbody,\ndiv.contents .toc,\n.contents .dotgraph,\n.contents .tabs-overview-container {\n scrollbar-width: thin;\n}\n\n/*\n Optional Dark mode toggle button\n*/\n\ndoxygen-awesome-dark-mode-toggle {\n display: inline-block;\n margin: 0 0 0 var(--spacing-small);\n padding: 0;\n width: var(--searchbar-height);\n height: var(--searchbar-height);\n background: none;\n border: none;\n border-radius: var(--searchbar-height);\n vertical-align: middle;\n text-align: center;\n line-height: var(--searchbar-height);\n font-size: 22px;\n display: flex;\n align-items: center;\n justify-content: center;\n user-select: none;\n cursor: pointer;\n}\n\ndoxygen-awesome-dark-mode-toggle > svg {\n transition: transform var(--animation-duration) ease-in-out;\n}\n\ndoxygen-awesome-dark-mode-toggle:active > svg {\n transform: scale(.5);\n}\n\ndoxygen-awesome-dark-mode-toggle:hover {\n background-color: rgba(0,0,0,.03);\n}\n\nhtml.dark-mode doxygen-awesome-dark-mode-toggle:hover {\n background-color: rgba(0,0,0,.18);\n}\n\n/*\n Optional fragment copy button\n*/\n.doxygen-awesome-fragment-wrapper {\n position: relative;\n}\n\ndoxygen-awesome-fragment-copy-button {\n opacity: 0;\n background: var(--fragment-background);\n width: 28px;\n height: 28px;\n position: absolute;\n right: calc(var(--spacing-large) - (var(--spacing-large) / 2.5));\n top: calc(var(--spacing-large) - (var(--spacing-large) / 2.5));\n border: 1px solid var(--fragment-foreground);\n cursor: pointer;\n border-radius: var(--border-radius-small);\n display: flex;\n justify-content: center;\n align-items: center;\n}\n\n.doxygen-awesome-fragment-wrapper:hover doxygen-awesome-fragment-copy-button, doxygen-awesome-fragment-copy-button.success {\n opacity: .28;\n}\n\ndoxygen-awesome-fragment-copy-button:hover, doxygen-awesome-fragment-copy-button.success {\n opacity: 1 !important;\n}\n\ndoxygen-awesome-fragment-copy-button:active:not([class~=success]) svg {\n transform: scale(.91);\n}\n\ndoxygen-awesome-fragment-copy-button svg {\n fill: var(--fragment-foreground);\n width: 18px;\n height: 18px;\n}\n\ndoxygen-awesome-fragment-copy-button.success svg {\n fill: rgb(14, 168, 14);\n}\n\ndoxygen-awesome-fragment-copy-button.success {\n border-color: rgb(14, 168, 14);\n}\n\n@media screen and (max-width: 767px) {\n .textblock > .doxygen-awesome-fragment-wrapper > doxygen-awesome-fragment-copy-button,\n .textblock li > .doxygen-awesome-fragment-wrapper > doxygen-awesome-fragment-copy-button,\n .memdoc li > .doxygen-awesome-fragment-wrapper > doxygen-awesome-fragment-copy-button,\n .memdoc > .doxygen-awesome-fragment-wrapper > doxygen-awesome-fragment-copy-button,\n dl dd > .doxygen-awesome-fragment-wrapper > doxygen-awesome-fragment-copy-button {\n right: 0;\n }\n}\n\n/*\n Optional paragraph link button\n*/\n\na.anchorlink {\n font-size: 90%;\n margin-left: var(--spacing-small);\n color: var(--page-foreground-color) !important;\n text-decoration: none;\n opacity: .15;\n display: none;\n transition: opacity var(--animation-duration) ease-in-out, color var(--animation-duration) ease-in-out;\n}\n\na.anchorlink svg {\n fill: var(--page-foreground-color);\n}\n\nh3 a.anchorlink svg, h4 a.anchorlink svg {\n margin-bottom: -3px;\n margin-top: -4px;\n}\n\na.anchorlink:hover {\n opacity: .45;\n}\n\nh2:hover a.anchorlink, h1:hover a.anchorlink, h3:hover a.anchorlink, h4:hover a.anchorlink {\n display: inline-block;\n}\n\n/*\n Optional tab feature\n*/\n\n.tabbed > ul {\n padding-inline-start: 0px;\n margin: 0;\n padding: var(--spacing-small) 0;\n}\n\n.tabbed > ul > li {\n display: none;\n}\n\n.tabbed > ul > li.selected {\n display: block;\n}\n\n.tabs-overview-container {\n overflow-x: auto;\n display: block;\n overflow-y: visible;\n}\n\n.tabs-overview {\n border-bottom: 1px solid var(--separator-color);\n display: flex;\n flex-direction: row;\n}\n\n@media screen and (max-width: 767px) {\n .tabs-overview-container {\n margin: 0 calc(0px - var(--spacing-large));\n }\n .tabs-overview {\n padding: 0 var(--spacing-large)\n }\n}\n\n.tabs-overview button.tab-button {\n color: var(--page-foreground-color);\n margin: 0;\n border: none;\n background: transparent;\n padding: calc(var(--spacing-large) / 2) 0;\n display: inline-block;\n font-size: var(--page-font-size);\n cursor: pointer;\n box-shadow: 0 1px 0 0 var(--separator-color);\n position: relative;\n\n -webkit-tap-highlight-color: transparent;\n}\n\n.tabs-overview button.tab-button .tab-title::before {\n display: block;\n content: attr(title);\n font-weight: 600;\n height: 0;\n overflow: hidden;\n visibility: hidden;\n}\n\n.tabs-overview button.tab-button .tab-title {\n float: left;\n white-space: nowrap;\n font-weight: normal;\n padding: calc(var(--spacing-large) / 2) var(--spacing-large);\n border-radius: var(--border-radius-medium);\n transition: background-color var(--animation-duration) ease-in-out, font-weight var(--animation-duration) ease-in-out;\n}\n\n.tabs-overview button.tab-button:not(:last-child) .tab-title {\n box-shadow: 8px 0 0 -7px var(--separator-color);\n}\n\n.tabs-overview button.tab-button:hover .tab-title {\n background: var(--separator-color);\n box-shadow: none;\n}\n\n.tabs-overview button.tab-button.active .tab-title {\n font-weight: 600;\n}\n\n.tabs-overview button.tab-button::after {\n content: '';\n display: block;\n position: absolute;\n left: 0;\n bottom: 0;\n right: 0;\n height: 0;\n width: 0%;\n margin: 0 auto;\n border-radius: var(--border-radius-small) var(--border-radius-small) 0 0;\n background-color: var(--primary-color);\n transition: width var(--animation-duration) ease-in-out, height var(--animation-duration) ease-in-out;\n}\n\n.tabs-overview button.tab-button.active::after {\n width: 100%;\n box-sizing: border-box;\n height: 3px;\n}\n\n\n/*\n Navigation Buttons\n*/\n\n.section_buttons:not(:empty) {\n margin-top: calc(var(--spacing-large) * 3);\n}\n\n.section_buttons table.markdownTable {\n display: block;\n width: 100%;\n}\n\n.section_buttons table.markdownTable tbody {\n display: table !important;\n width: 100%;\n box-shadow: none;\n border-spacing: 10px;\n}\n\n.section_buttons table.markdownTable td {\n padding: 0;\n}\n\n.section_buttons table.markdownTable th {\n display: none;\n}\n\n.section_buttons table.markdownTable tr.markdownTableHead {\n border: none;\n}\n\n.section_buttons tr th, .section_buttons tr td {\n background: none;\n border: none;\n padding: var(--spacing-large) 0 var(--spacing-small);\n}\n\n.section_buttons a {\n display: inline-block;\n border: 1px solid var(--separator-color);\n border-radius: var(--border-radius-medium);\n color: var(--page-secondary-foreground-color) !important;\n text-decoration: none;\n transition: color var(--animation-duration) ease-in-out, background-color var(--animation-duration) ease-in-out;\n}\n\n.section_buttons a:hover {\n color: var(--page-foreground-color) !important;\n background-color: var(--odd-color);\n}\n\n.section_buttons tr td.markdownTableBodyLeft a {\n padding: var(--spacing-medium) var(--spacing-large) var(--spacing-medium) calc(var(--spacing-large) / 2);\n}\n\n.section_buttons tr td.markdownTableBodyRight a {\n padding: var(--spacing-medium) calc(var(--spacing-large) / 2) var(--spacing-medium) var(--spacing-large);\n}\n\n.section_buttons tr td.markdownTableBodyLeft a::before,\n.section_buttons tr td.markdownTableBodyRight a::after {\n color: var(--page-secondary-foreground-color) !important;\n display: inline-block;\n transition: color .08s ease-in-out, transform .09s ease-in-out;\n}\n\n.section_buttons tr td.markdownTableBodyLeft a::before {\n content: '〈';\n padding-right: var(--spacing-large);\n}\n\n\n.section_buttons tr td.markdownTableBodyRight a::after {\n content: '〉';\n padding-left: var(--spacing-large);\n}\n\n\n.section_buttons tr td.markdownTableBodyLeft a:hover::before {\n color: var(--page-foreground-color) !important;\n transform: translateX(-3px);\n}\n\n.section_buttons tr td.markdownTableBodyRight a:hover::after {\n color: var(--page-foreground-color) !important;\n transform: translateX(3px);\n}\n\n@media screen and (max-width: 450px) {\n .section_buttons a {\n width: 100%;\n box-sizing: border-box;\n }\n\n .section_buttons tr td:nth-of-type(1).markdownTableBodyLeft a {\n border-radius: var(--border-radius-medium) 0 0 var(--border-radius-medium);\n border-right: none;\n }\n\n .section_buttons tr td:nth-of-type(2).markdownTableBodyRight a {\n border-radius: 0 var(--border-radius-medium) var(--border-radius-medium) 0;\n }\n}\n" }, { "path": "docs/config/footer.html", "content": "\n\n\n
\n \n
\n\n\n
\n© Copyright 2017 - 2026\nSXS Collaboration,\n\nDistributed under the\nMIT License\n
\n\n\n\n" }, { "path": "docs/config/header.html", "content": "\n\n\n \n \n \n \n \n \n $projectname: $title\n $title\n \n \n \n $treeview\n $search\n $mathjax\n \n \n \n \n \n \n $extrastylesheet\n \n \n \n \n \n \n \n \n \n
\n\n \n
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
\"Logo\"\n
\n $projectname\n  v$projectnumber\n \n
\n \n
$projectbrief
\n \n 		\n
$projectbrief
\n 		$searchbox
\n
\n \n \n" }, { "path": "docs/config/icons/octicons.css", "content": "@font-face {\n font-family: 'octicons';\n src: url('octicons.eot?#iefix') format('embedded-opentype'),\n url('octicons.woff') format('woff'),\n url('octicons.ttf') format('truetype'),\n url('octicons.svg#octicons') format('svg');\n font-weight: normal;\n font-style: normal;\n}\n\n/*\n\n.octicon is optimized for 16px.\n.mega-octicon is optimized for 32px but can be used larger.\n\n*/\n.octicon, .mega-octicon {\n font: normal normal normal 16px/1 octicons;\n display: inline-block;\n text-decoration: none;\n text-rendering: auto;\n -webkit-font-smoothing: antialiased;\n -moz-osx-font-smoothing: grayscale;\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n.mega-octicon { font-size: 32px; }\n\n.octicon-alert:before { content: '\\f02d'} /*  */\n.octicon-arrow-down:before { content: '\\f03f'} /*  */\n.octicon-arrow-left:before { content: '\\f040'} /*  */\n.octicon-arrow-right:before { content: '\\f03e'} /*  */\n.octicon-arrow-small-down:before { content: '\\f0a0'} /*  */\n.octicon-arrow-small-left:before { content: '\\f0a1'} /*  */\n.octicon-arrow-small-right:before { content: '\\f071'} /*  */\n.octicon-arrow-small-up:before { content: '\\f09f'} /*  */\n.octicon-arrow-up:before { content: '\\f03d'} /*  */\n.octicon-microscope:before,\n.octicon-beaker:before { content: '\\f0dd'} /*  */\n.octicon-bell:before { content: '\\f0de'} /*  */\n.octicon-bold:before { content: '\\f0e2'} /*  */\n.octicon-book:before { content: '\\f007'} /*  */\n.octicon-bookmark:before { content: '\\f07b'} /*  */\n.octicon-briefcase:before { content: '\\f0d3'} /*  */\n.octicon-broadcast:before { content: '\\f048'} /*  */\n.octicon-browser:before { content: '\\f0c5'} /*  */\n.octicon-bug:before { content: '\\f091'} /*  */\n.octicon-calendar:before { content: '\\f068'} /*  */\n.octicon-check:before { content: '\\f03a'} /*  */\n.octicon-checklist:before { content: '\\f076'} /*  */\n.octicon-chevron-down:before { content: '\\f0a3'} /*  */\n.octicon-chevron-left:before { content: '\\f0a4'} /*  */\n.octicon-chevron-right:before { content: '\\f078'} /*  */\n.octicon-chevron-up:before { content: '\\f0a2'} /*  */\n.octicon-circle-slash:before { content: '\\f084'} /*  */\n.octicon-circuit-board:before { content: '\\f0d6'} /*  */\n.octicon-clippy:before { content: '\\f035'} /*  */\n.octicon-clock:before { content: '\\f046'} /*  */\n.octicon-cloud-download:before { content: '\\f00b'} /*  */\n.octicon-cloud-upload:before { content: '\\f00c'} /*  */\n.octicon-code:before { content: '\\f05f'} /*  */\n.octicon-color-mode:before { content: '\\f065'} /*  */\n.octicon-comment-add:before,\n.octicon-comment:before { content: '\\f02b'} /*  */\n.octicon-comment-discussion:before { content: '\\f04f'} /*  */\n.octicon-credit-card:before { content: '\\f045'} /*  */\n.octicon-dash:before { content: '\\f0ca'} /*  */\n.octicon-dashboard:before { content: '\\f07d'} /*  */\n.octicon-database:before { content: '\\f096'} /*  */\n.octicon-clone:before,\n.octicon-desktop-download:before { content: '\\f0dc'} /*  */\n.octicon-device-camera:before { content: '\\f056'} /*  */\n.octicon-device-camera-video:before { content: '\\f057'} /*  */\n.octicon-device-desktop:before { content: '\\f27c'} /*  */\n.octicon-device-mobile:before { content: '\\f038'} /*  */\n.octicon-diff:before { content: '\\f04d'} /*  */\n.octicon-diff-added:before { content: '\\f06b'} /*  */\n.octicon-diff-ignored:before { content: '\\f099'} /*  */\n.octicon-diff-modified:before { content: '\\f06d'} /*  */\n.octicon-diff-removed:before { content: '\\f06c'} /*  */\n.octicon-diff-renamed:before { content: '\\f06e'} /*  */\n.octicon-ellipsis:before { content: '\\f09a'} /*  */\n.octicon-eye-unwatch:before,\n.octicon-eye-watch:before,\n.octicon-eye:before { content: '\\f04e'} /*  */\n.octicon-file-binary:before { content: '\\f094'} /*  */\n.octicon-file-code:before { content: '\\f010'} /*  */\n.octicon-file-directory:before { content: '\\f016'} /*  */\n.octicon-file-media:before { content: '\\f012'} /*  */\n.octicon-file-pdf:before { content: '\\f014'} /*  */\n.octicon-file-submodule:before { content: '\\f017'} /*  */\n.octicon-file-symlink-directory:before { content: '\\f0b1'} /*  */\n.octicon-file-symlink-file:before { content: '\\f0b0'} /*  */\n.octicon-file-text:before { content: '\\f011'} /*  */\n.octicon-file-zip:before { content: '\\f013'} /*  */\n.octicon-flame:before { content: '\\f0d2'} /*  */\n.octicon-fold:before { content: '\\f0cc'} /*  */\n.octicon-gear:before { content: '\\f02f'} /*  */\n.octicon-gift:before { content: '\\f042'} /*  */\n.octicon-gist:before { content: '\\f00e'} /*  */\n.octicon-gist-secret:before { content: '\\f08c'} /*  */\n.octicon-git-branch-create:before,\n.octicon-git-branch-delete:before,\n.octicon-git-branch:before { content: '\\f020'} /*  */\n.octicon-git-commit:before { content: '\\f01f'} /*  */\n.octicon-git-compare:before { content: '\\f0ac'} /*  */\n.octicon-git-merge:before { content: '\\f023'} /*  */\n.octicon-git-pull-request-abandoned:before,\n.octicon-git-pull-request:before { content: '\\f009'} /*  */\n.octicon-globe:before { content: '\\f0b6'} /*  */\n.octicon-graph:before { content: '\\f043'} /*  */\n.octicon-heart:before { content: '\\2665'} /* ♥ */\n.octicon-history:before { content: '\\f07e'} /*  */\n.octicon-home:before { content: '\\f08d'} /*  */\n.octicon-horizontal-rule:before { content: '\\f070'} /*  */\n.octicon-hubot:before { content: '\\f09d'} /*  */\n.octicon-inbox:before { content: '\\f0cf'} /*  */\n.octicon-info:before { content: '\\f059'} /*  */\n.octicon-issue-closed:before { content: '\\f028'} /*  */\n.octicon-issue-opened:before { content: '\\f026'} /*  */\n.octicon-issue-reopened:before { content: '\\f027'} /*  */\n.octicon-italic:before { content: '\\f0e4'} /*  */\n.octicon-jersey:before { content: '\\f019'} /*  */\n.octicon-key:before { content: '\\f049'} /*  */\n.octicon-keyboard:before { content: '\\f00d'} /*  */\n.octicon-law:before { content: '\\f0d8'} /*  */\n.octicon-light-bulb:before { content: '\\f000'} /*  */\n.octicon-link:before { content: '\\f05c'} /*  */\n.octicon-link-external:before { content: '\\f07f'} /*  */\n.octicon-list-ordered:before { content: '\\f062'} /*  */\n.octicon-list-unordered:before { content: '\\f061'} /*  */\n.octicon-location:before { content: '\\f060'} /*  */\n.octicon-gist-private:before,\n.octicon-mirror-private:before,\n.octicon-git-fork-private:before,\n.octicon-lock:before { content: '\\f06a'} /*  */\n.octicon-logo-gist:before { content: '\\f0ad'} /*  */\n.octicon-logo-github:before { content: '\\f092'} /*  */\n.octicon-mail:before { content: '\\f03b'} /*  */\n.octicon-mail-read:before { content: '\\f03c'} /*  */\n.octicon-mail-reply:before { content: '\\f051'} /*  */\n.octicon-mark-github:before { content: '\\f00a'} /*  */\n.octicon-markdown:before { content: '\\f0c9'} /*  */\n.octicon-megaphone:before { content: '\\f077'} /*  */\n.octicon-mention:before { content: '\\f0be'} /*  */\n.octicon-milestone:before { content: '\\f075'} /*  */\n.octicon-mirror-public:before,\n.octicon-mirror:before { content: '\\f024'} /*  */\n.octicon-mortar-board:before { content: '\\f0d7'} /*  */\n.octicon-mute:before { content: '\\f080'} /*  */\n.octicon-no-newline:before { content: '\\f09c'} /*  */\n.octicon-octoface:before { content: '\\f008'} /*  */\n.octicon-organization:before { content: '\\f037'} /*  */\n.octicon-package:before { content: '\\f0c4'} /*  */\n.octicon-paintcan:before { content: '\\f0d1'} /*  */\n.octicon-pencil:before { content: '\\f058'} /*  */\n.octicon-person-add:before,\n.octicon-person-follow:before,\n.octicon-person:before { content: '\\f018'} /*  */\n.octicon-pin:before { content: '\\f041'} /*  */\n.octicon-plug:before { content: '\\f0d4'} /*  */\n.octicon-repo-create:before,\n.octicon-gist-new:before,\n.octicon-file-directory-create:before,\n.octicon-file-add:before,\n.octicon-plus:before { content: '\\f05d'} /*  */\n.octicon-primitive-dot:before { content: '\\f052'} /*  */\n.octicon-primitive-square:before { content: '\\f053'} /*  */\n.octicon-pulse:before { content: '\\f085'} /*  */\n.octicon-question:before { content: '\\f02c'} /*  */\n.octicon-quote:before { content: '\\f063'} /*  */\n.octicon-radio-tower:before { content: '\\f030'} /*  */\n.octicon-repo-delete:before,\n.octicon-repo:before { content: '\\f001'} /*  */\n.octicon-repo-clone:before { content: '\\f04c'} /*  */\n.octicon-repo-force-push:before { content: '\\f04a'} /*  */\n.octicon-gist-fork:before,\n.octicon-repo-forked:before { content: '\\f002'} /*  */\n.octicon-repo-pull:before { content: '\\f006'} /*  */\n.octicon-repo-push:before { content: '\\f005'} /*  */\n.octicon-rocket:before { content: '\\f033'} /*  */\n.octicon-rss:before { content: '\\f034'} /*  */\n.octicon-ruby:before { content: '\\f047'} /*  */\n.octicon-search-save:before,\n.octicon-search:before { content: '\\f02e'} /*  */\n.octicon-server:before { content: '\\f097'} /*  */\n.octicon-settings:before { content: '\\f07c'} /*  */\n.octicon-shield:before { content: '\\f0e1'} /*  */\n.octicon-log-in:before,\n.octicon-sign-in:before { content: '\\f036'} /*  */\n.octicon-log-out:before,\n.octicon-sign-out:before { content: '\\f032'} /*  */\n.octicon-squirrel:before { content: '\\f0b2'} /*  */\n.octicon-star-add:before,\n.octicon-star-delete:before,\n.octicon-star:before { content: '\\f02a'} /*  */\n.octicon-stop:before { content: '\\f08f'} /*  */\n.octicon-repo-sync:before,\n.octicon-sync:before { content: '\\f087'} /*  */\n.octicon-tag-remove:before,\n.octicon-tag-add:before,\n.octicon-tag:before { content: '\\f015'} /*  */\n.octicon-tasklist:before { content: '\\f0e5'} /*  */\n.octicon-telescope:before { content: '\\f088'} /*  */\n.octicon-terminal:before { content: '\\f0c8'} /*  */\n.octicon-text-size:before { content: '\\f0e3'} /*  */\n.octicon-three-bars:before { content: '\\f05e'} /*  */\n.octicon-thumbsdown:before { content: '\\f0db'} /*  */\n.octicon-thumbsup:before { content: '\\f0da'} /*  */\n.octicon-tools:before { content: '\\f031'} /*  */\n.octicon-trashcan:before { content: '\\f0d0'} /*  */\n.octicon-triangle-down:before { content: '\\f05b'} /*  */\n.octicon-triangle-left:before { content: '\\f044'} /*  */\n.octicon-triangle-right:before { content: '\\f05a'} /*  */\n.octicon-triangle-up:before { content: '\\f0aa'} /*  */\n.octicon-unfold:before { content: '\\f039'} /*  */\n.octicon-unmute:before { content: '\\f0ba'} /*  */\n.octicon-versions:before { content: '\\f064'} /*  */\n.octicon-watch:before { content: '\\f0e0'} /*  */\n.octicon-remove-close:before,\n.octicon-x:before { content: '\\f081'} /*  */\n.octicon-zap:before { content: '\\26A1'} /* ⚡ */\n" }, { "path": "docs/config/js/doxygen-navtree-hacks.js", "content": "// Distributed under the MIT License.\n// See LICENSE.txt for details.\n\n// This file is mostly copied from:\n// https://gitlab.com/libeigen/eigen/-/blob/master/doc/eigen_navtree_hacks.js\n\nvar global_navtree_object;\n\n// Overloaded to remove links to sections/subsections\nfunction getNode(o, po) {\n po.childrenVisited = true;\n var l = po.childrenData.length - 1;\n for (var i in po.childrenData) {\n var nodeData = po.childrenData[i];\n if ((!nodeData[1]) || (nodeData[1].indexOf('#') == -1)) // <- we added this line\n po.children[i] = newNode(o, po, nodeData[0], nodeData[1], nodeData[2], i == l);\n }\n}\n\n// Overloaded to remove the animation of the sidebar\nfunction expandNode(o, node, imm, showRoot) {\n if (node.childrenData && !node.expanded) {\n if (typeof (node.childrenData) === 'string') {\n var varName = node.childrenData;\n getScript(node.relpath + varName, function () {\n node.childrenData = getData(varName);\n expandNode(o, node, imm, showRoot);\n }, showRoot);\n } else {\n if (!node.childrenVisited) {\n getNode(o, node);\n }\n $(node.getChildrenUL()).show(); // <- removed slideDown animation\n // node.plus_img.innerHTML = arrowDown; // <- removed this\n node.expanded = true;\n }\n }\n}\n\n// Overloaded to save the root node into global_navtree_object\nfunction initNavTree(toroot, relpath) {\n var o = new Object();\n global_navtree_object = o; // <- we added this line\n o.toroot = toroot;\n o.node = new Object();\n o.node.li = document.getElementById(\"nav-tree-contents\");\n o.node.childrenData = NAVTREE;\n o.node.children = new Array();\n o.node.childrenUL = document.createElement(\"ul\");\n o.node.getChildrenUL = function () { return o.node.childrenUL; };\n o.node.li.appendChild(o.node.childrenUL);\n o.node.depth = 0;\n o.node.relpath = relpath;\n o.node.expanded = false;\n o.node.isLast = true;\n o.node.plus_img = document.createElement(\"img\");\n o.node.plus_img.src = relpath + \"ftv2pnode.png\";\n o.node.plus_img.width = 16;\n o.node.plus_img.height = 22;\n\n if (localStorageSupported()) {\n var navSync = $('#nav-sync');\n if (cachedLink()) {\n showSyncOff(navSync, relpath);\n navSync.removeClass('sync');\n } else {\n showSyncOn(navSync, relpath);\n }\n navSync.click(function () { toggleSyncButton(relpath); });\n }\n\n navTo(o, toroot, window.location.hash, relpath);\n\n $(window).bind('hashchange', function () {\n if (window.location.hash && window.location.hash.length > 1) {\n var a;\n if ($(location).attr('hash')) {\n var clslink = stripPath($(location).attr('pathname')) + ':' +\n $(location).attr('hash').substring(1);\n a = $('.item a[class$=\"' + clslink + '\"]');\n }\n if (a == null || !$(a).parent().parent().hasClass('selected')) {\n $('.item').removeClass('selected');\n $('.item').removeAttr('id');\n }\n var link = stripPath2($(location).attr('pathname'));\n navTo(o, link, $(location).attr('hash'), relpath);\n } else if (!animationInProgress) {\n $('#doc-content').scrollTop(0);\n $('.item').removeClass('selected');\n $('.item').removeAttr('id');\n navTo(o, toroot, window.location.hash, relpath);\n }\n })\n\n $(window).on(\"load\", showRoot);\n}\n\n// return false if the the node has no children at all, or has only section/subsection children\nfunction checkChildrenData(node) {\n if (!(typeof (node.childrenData) === 'string')) {\n for (var i in node.childrenData) {\n var url = node.childrenData[i][1];\n if (url.indexOf(\"#\") == -1)\n return true;\n }\n return false;\n }\n return (node.childrenData);\n}\n\n// Modified to:\n// 1 - remove the root node\n// 2 - remove the section/subsection children\nfunction createIndent(o, domNode, node, level) {\n var level = -2; // <- we replaced level=-1 by level=-2\n var n = node;\n while (n.parentNode) { level++; n = n.parentNode; }\n if (checkChildrenData(node)) { // <- we modified this line to use checkChildrenData(node) instead of node.childrenData\n var imgNode = document.createElement(\"span\");\n imgNode.className = 'arrow';\n imgNode.style.paddingLeft = (16 * level).toString() + 'px';\n imgNode.innerHTML = arrowRight;\n node.plus_img = imgNode;\n node.expandToggle = document.createElement(\"a\");\n node.expandToggle.href = \"javascript:void(0)\";\n node.expandToggle.onclick = function () {\n if (node.expanded) {\n $(node.getChildrenUL()).slideUp(\"fast\");\n node.plus_img.innerHTML = arrowRight;\n node.expanded = false;\n } else {\n expandNode(o, node, false, false);\n }\n }\n node.expandToggle.appendChild(imgNode);\n domNode.appendChild(node.expandToggle);\n } else {\n var span = document.createElement(\"span\");\n span.className = 'arrow';\n span.style.width = 16 * (level + 1) + 'px';\n span.innerHTML = ' ';\n domNode.appendChild(span);\n }\n}\n\n// Overloaded to automatically expand the selected node\nfunction selectAndHighlight(hash, n) {\n var a;\n if (hash) {\n var link = stripPath($(location).attr('pathname')) + ':' + hash.substring(1);\n a = $('.item a[class$=\"' + link + '\"]');\n }\n if (a && a.length) {\n a.parent().parent().addClass('selected');\n a.parent().parent().attr('id', 'selected');\n highlightAnchor();\n } else if (n) {\n $(n.itemDiv).addClass('selected');\n $(n.itemDiv).attr('id', 'selected');\n }\n if ($('#nav-tree-contents .item:first').hasClass('selected')) {\n $('#nav-sync').css('top', '30px');\n } else {\n $('#nav-sync').css('top', '5px');\n }\n expandNode(global_navtree_object, n, true, true); // <- we added this line\n showRoot();\n}\n\n\n$(document).ready(function () {\n (function () { // wait until the first \"selected\" element has been created\n try {\n\n // this line will triger an exception if there is no #selected element, i.e., before the tree structure is complete.\n document.getElementById(\"selected\").className = \"item selected\";\n\n // ok, the default tree has been created, we can keep going...\n\n // expand the \"Code reference\" node\n var sidebar_root_items = global_navtree_object.node.children[0].children;\n expandNode(global_navtree_object, sidebar_root_items[sidebar_root_items.length - 1], true, true);\n\n // Hide the root node\n $(document.getElementsByClassName('index.html')[0]).parent().parent().css({ display: \"none\" });\n\n } catch (err) {\n setTimeout(arguments.callee, 10);\n }\n })();\n});\n\n" }, { "path": "docs/config/js/spectre.js", "content": "// Distributed under the MIT License.\n// See LICENSE.txt for details.\n\nwindow.onload = function(){\n\n // Hide type alias RHS that refers to a metafunction result in a (*_)detail namespace\n $(\"body\").children().\n find(\"td.memItemRight, td.memTemplItemRight, td.memname\").each(function () {\n $(this).html( $(this).html().replace(/( =[ ]+)[typedef ]*typename [A-Za-z0-9]*[_]?detail[s]?::[A-Za-z0-9\\-_\\.&;<> /;:\\\"=,#]+::[A-Za-z0-9_]+/g,\n \"$1implementation defined\") );\n });\n\n // Hide type alias RHS that refers to a type in a (*_)detail namespace\n // Also remove ... = decltype(something(_detail)::)\n $(\"body\").children().find(\"td.memItemRight, td.memTemplItemRight, td.memname\").each(function () {\n $(this).html( $(this).html().replace(/( =[ ]+)[typedef ]*[A-Za-z0-9\\(]*[_]?detail[s]?::[A-Za-z0-9\\-_\\.&;<> /;:\\\"=,#\\(\\)]+/g,\n \"$1implementation defined\") );\n });\n\n // Hide unnamed template parameters: , typename = void\n // Not applied to div.memitem because that causes problems with rendering\n // MathJAX\n $(\"body\").children().find(\"td.memItemRight, td.memTemplItemRight\").each(function () {\n $(this).html( $(this).html().replace(/(template[< ]+.*)(,[ ]*typename[ ]*=[ ]*void[ ]*)+/g,\n \"$1\") );\n });\n $(\"body\").children().find(\"td.memItemRight, td.memTemplItemRight, div.title\").each(function () {\n $(this).html( $(this).html().replace(/(<[A-Za-z0-9 ,]+.*)(,[ ]*typename[ ]*>)+/g,\n \"$1>\") );\n });\n\n // Hide SFINAE in template parameters\n $(\"body\").children().find(\"td.memTemplParams, div.memtemplate\").each(function () {\n $(this).html( $(this).html().replace(/(template[A-Za-z0-9&;,\\.=\\(\\) _]+)(,[ ]+typename[ ]+=[ ]+typename[ ]+std::enable_if.*::type)+/g,\n \"$1\") );\n\n });\n\n $(\"body\").children().find(\"td.memTemplParams, div.memtemplate\").each(function () {\n $(this).html( $(this).html().replace(/(template[A-Za-z0-9&;,\\.=\\(\\) _]+)(,[ ]+typename[ ]+std::enable_if.*)+>/g,\n \"$1>\") );\n\n });\n\n // Hide enable_if_t for SFINAE\n $(\"body\").children().find(\"td.memTemplParams, div.memtemplate\").each(function () {\n $(this).html( $(this).html()\n .replace(/(template[A-Za-z0-9&;,\\.=\\(\\) _]+)(,[ ]+std::enable_if_t.*)+>/g,\n \"$1>\") );\n\n });\n\n // Hide metafunctions that use only the template metaprogramming libraries\n $(\"body\").children().find(\"td.memItemRight, td.memTemplItemRight\").each(function () {\n $(this).html( $(this).html().replace(/( =[ ]+).*tmpl::(?!list\\b).*/g,\n \"$1implementation defined\") );\n });\n\n // Italicize \"implementation defined\"\n // Not applied to div.memitem because that causes problems with rendering\n // MathJAX\n $(\"body\").children().find(\"td.memItemRight, td.memTemplItemRight\").each(function () {\n $(this).html( $(this).html().replace(/implementation defined/g,\n \"implementation defined\".italics()) );\n });\n\n // Show popovers for references\n $(\"body\").children().find('a[href*=\"citelist.html#CITEREF_\"]').each(function () {\n var tooltip_base = this;\n // Get the reference id, e.g. `CITEREF_Kopriva`. This is the one used as\n // anchor on the bibliography page.\n var ref_id = $(this).attr('href').match(/CITEREF_(.*)/)[0];\n // Backslashify colons, which indicate CSS pseudo-selectors\n ref_id = ref_id.replaceAll(\":\", \"\\\\:\");\n // Load the bibliography page to retrieve the reference data as nicely\n // formatted HTML.\n // This does not work locally because it is forbidden to access files,\n // so just spin up a web server in the `html` directory with\n // `python3 -m http.server` to enable this functionality\n $.get('citelist.html', function(data) {\n // Filter the bibliography data for this particular reference\n var ref_html = $('').append($.parseHTML(data))\n .find('#' + ref_id)\n .parent()\n .next()\n .find('p.startdd')\n .html();\n // Show the reference in a tooltip\n tippy(tooltip_base, {\n content: ref_html,\n allowHTML: true,\n interactive: true,\n });\n }, 'html');\n });\n};\n" }, { "path": "docs/config/markdown-math-filter.pl", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\n# Doxygen filter to format markdown math for Doxygen\n#\n# In Doxygen documentation, including markdown files or Jupyter notebooks that\n# get converted to markdown, you can use standard $...$ syntax for inline math,\n# and \"naked LaTeX\" syntax for display-style math:\n#\n# \\begin{equation}\n# ...\n# \\end{equation}\n#\n# You can also replace `equation` with another supported environment, e.g.\n# `align`.\n#\n# This Doxygen filter formats the math for Doxygen, i.e., uses \\f$...\\f$ for\n# inline math and \\f{equation}{ ... \\f} for display-style math. This is needed\n# until Doxygen adds support for markdown-style math, see\n# https://github.com/doxygen/doxygen/issues/8009.\n\n# Wrap inline math in \\f$...\\f$\n# - Match code blocks (wrapped in ``` or \\code...\\endcode) and inline code\n# (wrapped in ` or ``), and print them directly to the output with no changes.\n# - Match display math blocks (wrapped in \\f[...\\f], \\f{...\\f}, or\n# \\begin...\\end), and print them directly to the output with no changes.\n# - Replace $...$ by \\f$...\\f$, unless already preceded by '\\f$'.\n# - The '?' makes the pattern match lazily, i.e., match as few characters as\n# possible.\n# - Modifiers:\n# s: Allow '.' to match newlines\n# g: Replace all occurences\n# e: Evaluate replacement as perl code, so we can switch between\n# replacements depending on the matched alternative, using the '//'\n# (definedness) operator.\n# x: Ignore spaces for better readability\ns{ (```.*?```)\n | (``.*?``)\n | (`.*?`)\n | (\\\\code.*?\\\\endcode)\n | (\\\\f\\[.*?\\\\f\\])\n | (\\\\f\\{.*?\\\\f\\})\n | (\\\\begin\\{(.*?)\\}(.*?)\\\\end\\{\\6\\})\n | (?\n C++ documentation \n\n\n.. toctree::\n :maxdepth: 3\n :caption: Command-line interface (CLI)\n\n cli\n\n\nPython modules\n--------------\n\n.. autosummary::\n :toctree: _autosummary\n :recursive:\n :caption: Python modules\n\n spectre\n" }, { "path": "external/CMakeLists.txt", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nadd_subdirectory(brigand)\nadd_subdirectory(EffectiveSource)\nadd_subdirectory(GravitationalEffectiveSource)\nadd_subdirectory(SPHEREPACK)\nadd_subdirectory(slatec)\n\nset(LIBRARY Libsharp)\nset(LIBSHARP_LIBDIR ${CMAKE_CURRENT_BINARY_DIR}/libsharp/auto/lib)\nset(LIBSHARP_LIB_libsharp ${LIBSHARP_LIBDIR}/libsharp.a)\nset(LIBSHARP_LIB_libfftpack ${LIBSHARP_LIBDIR}/libfftpack.a)\nset(LIBSHARP_LIB_libc_utils ${LIBSHARP_LIBDIR}/libc_utils.a)\nset(LIBSHARP_INCLUDE ${CMAKE_CURRENT_BINARY_DIR}/libsharp/auto/include)\n\nfind_program(MAKE NAMES gmake make REQUIRED)\nset(LIBSHARP_BUILD ${MAKE})\n# When using the Unix Makefile generator, verbosity is inherited from\n# the main build and works acceptably well. There's no way to\n# dynamically detect the verbosity with ninja, so silence it\n# unconditionally because ninja is quieter than make.\nif (NOT CMAKE_GENERATOR STREQUAL \"Unix Makefiles\")\n list(APPEND LIBSHARP_BUILD > /dev/null)\nendif()\n\nset(JOB_SERVER \"\")\nif (CMAKE_VERSION VERSION_GREATER_EQUAL 3.28)\n set(JOB_SERVER BUILD_JOB_SERVER_AWARE TRUE)\nendif()\n\ninclude(ExternalProject)\nExternalProject_Add(\n Libsharp-external\n PREFIX ${CMAKE_BINARY_DIR}/external/libsharp\n SOURCE_DIR ${CMAKE_CURRENT_BINARY_DIR}/libsharp\n DOWNLOAD_COMMAND\n cp -r ${CMAKE_CURRENT_SOURCE_DIR}/libsharp ${CMAKE_CURRENT_BINARY_DIR}\n # libsharp has an autoconf build system, but it doesn't do anything\n # except set CFLAGS, so we can skip it to avoid depending on\n # autoconf and set the flags below by manually writing config.auto.\n CONFIGURE_COMMAND \"\"\n # out-of-tree builds don't work\n BUILD_IN_SOURCE TRUE\n BUILD_COMMAND \"${LIBSHARP_BUILD}\"\n ${JOB_SERVER}\n BUILD_BYPRODUCTS\n ${LIBSHARP_LIB_libsharp}\n ${LIBSHARP_LIB_libfftpack}\n ${LIBSHARP_LIB_libc_utils}\n INSTALL_COMMAND \"\"\n)\n\n# Always build libsharp with optimization, since there is a big speed\n# difference and we're not interested in debugging it.\nfile(\n GENERATE OUTPUT \"libsharp/config/config.auto\"\n CONTENT\n \"CC=${CMAKE_C_COMPILER}\nCL=\\$(CC)\nSPECTRE_FLAGS=\\\\\n\\$(subst ;, ,$)\nCCFLAGS=\\$(SPECTRE_FLAGS) -fno-openmp -O3 -c\nCLFLAGS=-L. -L\\$(LIBDIR) \\$(SPECTRE_FLAGS) -fno-openmp -O3 -lm\nARCREATE=ar cr\"\n CONDITION \"$\"\n)\n\nadd_library(Libsharp::libsharp STATIC IMPORTED GLOBAL)\nset_target_properties(\n Libsharp::libsharp\n PROPERTIES\n IMPORTED_LOCATION\n ${LIBSHARP_LIB_libsharp}\n)\nadd_library(Libsharp::libfftpack STATIC IMPORTED GLOBAL)\nset_target_properties(\n Libsharp::libfftpack\n PROPERTIES\n IMPORTED_LOCATION\n ${LIBSHARP_LIB_libfftpack}\n)\nadd_library(Libsharp::libc_utils STATIC IMPORTED GLOBAL)\nset_target_properties(\n Libsharp::libc_utils\n PROPERTIES\n IMPORTED_LOCATION\n ${LIBSHARP_LIB_libc_utils}\n)\nadd_library(Libsharp INTERFACE IMPORTED GLOBAL)\ntarget_link_libraries(\n ${LIBRARY}\n INTERFACE\n Libsharp::libsharp\n Libsharp::libfftpack\n Libsharp::libc_utils\n)\n# cmake issue #15052\nfile(MAKE_DIRECTORY ${LIBSHARP_INCLUDE})\ntarget_include_directories(\n ${LIBRARY}\n SYSTEM\n INTERFACE\n ${LIBSHARP_INCLUDE}\n)\nadd_dependencies(\n ${LIBRARY}\n Libsharp-external\n)\n" }, { "path": "external/EffectiveSource/CMakeLists.txt", "content": "set(LIBRARY EffectiveSource)\n\nadd_library(${LIBRARY} kerr-circular.c)\n\ntarget_link_libraries(\n ${LIBRARY}\n PRIVATE\n GSL::gsl\n )\n\ntarget_include_directories(${LIBRARY} SYSTEM PUBLIC ${CMAKE_CURRENT_SOURCE_DIR})\n" }, { "path": "external/EffectiveSource/LICENSE.md", "content": "MIT License\n\nCopyright (c) 2025 Black Hole Perturbation Toolkit\n\nPermission is hereby granted, free of charge, to any person obtaining a copy\nof this software and associated documentation files (the \"Software\"), to deal\nin the Software without restriction, including without limitation the rights\nto use, copy, modify, merge, publish, distribute, sublicense, and/or sell\ncopies of the Software, and to permit persons to whom the Software is\nfurnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in all\ncopies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\nSOFTWARE.\n" }, { "path": "external/EffectiveSource/README.md", "content": "This is a modified version of https://github.com/barrywardell/EffectiveSource\n(revision 07a31cedfcc895fbdaab47de88825234a03f7cec).\nThis code is licensed under MIT. The license can be found in LICENSE.md.\n\nSummary of modifications:\n\n- Added CMakeLists.txt.\n- Added C++ compatibility header `effsource.hpp`.\n" }, { "path": "external/EffectiveSource/effsource.h", "content": "/*******************************************************************************\n * Copyright (C) 2011 Barry Wardell\n ******************************************************************************/\n\nstruct coordinate {\n double r;\n double theta;\n double phi;\n double t;\n};\n\nvoid effsource_init(double M, double a);\nvoid effsource_set_particle(struct coordinate * x_p, double e, double l, double ur_p);\n\nvoid effsource_PhiS(struct coordinate * x, double * PhiS);\nvoid effsource_calc(struct coordinate * x,\n double * PhiS, double * dPhiS_dx, double * d2PhiS_dx2, double * src);\n\nvoid effsource_PhiS_m(int m, struct coordinate * x, double * PhiS);\nvoid effsource_calc_m(int m, struct coordinate * x,\n double * PhiS, double * dPhiS_dx, double * d2PhiS_dx2, double * src);\n" }, { "path": "external/EffectiveSource/effsource.hpp", "content": "#pragma once\n\nextern \"C\" {\n#include \n}\n" }, { "path": "external/EffectiveSource/kerr-circular.c", "content": "/*******************************************************************************\n * Copyright (C) 2012 Barry Wardell\n ******************************************************************************/\n\n#include \n#include \n#include \"effsource.h\"\n#include \n#include \n\n/* The particle's coordinate location and 4-velocity */\nstatic struct coordinate xp;\n\n/* Mass and spin of the Kerr black hole */\nstatic double M, a;\n\n/* Static variables used to store the coefficients of the series expansions */\nstatic double A006, A008, A024, A026, A042, A044, A060, A062, A080, A106, A108, A124, A126, A142, A144, A160, A162, A180, A204, A206, A222, A224, A240, A242, A260, A304, A306, A322, A324, A340, A342, A360, A402, A404, A420, A422, A440, A502, A504, A520, A522, A540, A600, A602, A620, A700, A702, A720, A800, A900;\nstatic double alpha20, alpha02, beta;\n\n/* Numerical coefficients appearing in the elliptic integrals expressions. The\n indices here correspond to mode m, EllipticK/EllipticE, order in Sin[dphi]/Sin[dphi/2],\n term in polynomial in alpha/beta. */\nstatic const double ReEI[21][2][5][27] =\n {\n {{{0,-0.26666666666666666,-0.5333333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.4,0.13333333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,1.2666666666666666,0.5333333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-4,-6.933333333333334,-3.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,1.5333333333333334,1.5333333333333334,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,0.4666666666666667,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,-0.4666666666666667,-0.13333333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-1.5333333333333334,-1.5333333333333334,-0.5333333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,6.866666666666666,8.533333333333333,3.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,-0.4,-0.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,-0.6,-0.26666666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-1.6,-2.4,-1.0666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,9.266666666666667,14.4,6.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.3333333333333335,-24.933333333333334,-38.4,-17.066666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,1.2666666666666666,0.6,0.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,0.06666666666666667,0.7333333333333333,0.26666666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,2.6,2.933333333333333,1.0666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-3.533333333333333,-15.266666666666667,-17.6,-6.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.3333333333333333,10.2,40.93333333333333,46.93333333333333,17.066666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,0,1.6,1.0666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,5,9.066666666666666,4.266666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-7.6,-42,-59.733333333333334,-25.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,30.6,128,166.4,68.26666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.466666666666667,-73.6,-275.2,-341.3333333333333,-136.53333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,0.4666666666666667,-0.6,-2.1333333333333333,-1.0666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-1.1333333333333333,-8.733333333333333,-11.2,-4.266666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,19.8,67.06666666666666,72.53333333333333,25.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-4.2,-69.8,-198.4,-200.53333333333333,-68.26666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.06666666666666667,13.266666666666667,160,420.26666666666665,409.6,136.53333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,0.6666666666666666,-16.4,-34.13333333333333,-17.066666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,41,186.4,247.46666666666667,102.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-17.6,-204,-630.4,-716.8,-273.06666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,65.8,536,1427.2,1501.8666666666666,546.1333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.4857142857142858,-153.0857142857143,-1073.3714285714286,-2640.457142857143,-2652.647619047619,-936.2285714285714,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-0.8666666666666667,2.7333333333333334,30.266666666666666,42.666666666666664,17.066666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-3.1333333333333333,-97.4,-290.93333333333334,-298.6666666666667,-102.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,53.8,410.4,937.6,853.3333333333334,273.06666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-4.6,-177.4,-1019.2,-2075.733333333333,-1774.9333333333334,-546.1333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.02857142857142857,14.771428571428572,392.62857142857143,1984,3791.2380952380954,3120.7619047619046,936.2285714285714,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,1.6,-198.4,-814.9333333333333,-1024,-409.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,147.4,1179.7333333333333,3012.266666666667,3072,1092.2666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-31.6,-629.2,-3345.0666666666666,-7116.8,-6553.6,-2184.5333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,114.94285714285714,1556.3428571428572,6981.4857142857145,13497.295238095237,11702.857142857143,3744.9142857142856,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.492063492063492,-263.84761904761905,-3017.295238095238,-12327.009523809524,-22469.485714285714,-18724.571428571428,-5825.422222222222,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-2.7333333333333334,18.6,452.26666666666665,1250.1333333333334,1228.8,409.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-5.933333333333334,-401.26666666666665,-2212.266666666667,-4343.466666666666,-3618.133333333333,-1092.2666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,106.2,1463.3333333333333,5879.466666666666,9984,7645.866666666667,2184.5333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-4.885714285714286,-344.0857142857143,-3410.5142857142855,-11886.933333333332,-18646.55238095238,-13575.314285714287,-3744.9142857142856,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.015873015873015872,15.806349206349207,753.3714285714286,6407.466666666666,20597.02857142857,30739.504761904762,21637.28253968254,5825.422222222222,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,2.8,-970,-6314.666666666667,-14080,-13107.2,-4369.066666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,380.2,4689.866666666667,19157.333333333332,34508.8,28398.933333333334,8738.133333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-49.6,-1514.1714285714286,-12285.104761904762,-41442.74285714285,-66823.31428571428,-51180.49523809524,-14979.657142857142,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,178.05396825396826,3632.0761904761903,24604.95238095238,74800.76190476191,112737.52380952382,82388.11428571428,23301.68888888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.494949494949495,-405.9919191919192,-6920.145454545454,-42364.121212121216,-120645.81818181818,-173769.69696969696,-122863.45050505051,-33893.36565656566,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-5.133333333333334,58.2,2479.3333333333335,11306.666666666666,19814.4,15291.733333333334,4369.066666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-9.533333333333333,-1129.9333333333334,-9986.933333333332,-31906.133333333335,-47069.86666666667,-32768,-8738.133333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,178.14285714285714,3892.609523809524,24463.390476190478,66662.4,89604.87619047619,58670.32380952381,14979.657142857142,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.1079365079365076,-573.9968253968254,-8815.314285714287,-47328,-117906.28571428571,-149562.51428571428,-94038.95873015873,-23301.68888888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.010101010101010102,16.6,1251.761616161616,16279.660606060606,79786.66666666667,187671.27272727274,228846.41616161616,139810.13333333333,33893.36565656566,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,4.266666666666667,-3262.4,-30573.866666666665,-103765.33333333333,-163840,-122333.86666666667,-34952.53333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,811.4,14256.685714285713,84442.81904761905,231716.57142857142,322998.85714285716,222198.24761904762,59918.62857142857,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-71.6,-3111.35873015873,-35753.44761904762,-174188.49523809523,-426296.0761904762,-551126.5523809524,-359511.77142857143,-93206.75555555556,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,255.14487734487736,7331.7772005772,69909.00086580086,305560.71341991343,696355.4632034632,856110.1021645021,538057.1797979798,135573.46262626263,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.4965034965034967,-579.5630147630147,-13824.999533799533,-118555.33053613054,-483592.47365967365,-1.0497981165501166e6,-1.2450923412587412e6,-761297.1362859363,-187717.1020979021,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-8.066666666666666,135.93333333333334,9026.133333333333,61310.933333333334,166024.53333333333,218453.33333333334,139810.13333333333,34952.53333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-13.933333333333334,-2571.1714285714284,-33332.038095238095,-157322.3619047619,-357171.2,-422863.2380952381,-252157.5619047619,-59918.62857142857,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,270.5174603174603,8617.873015873016,78308.57142857143,312652.8,643189.0285714286,713406.1714285715,406115.1492063492,93206.75555555556,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.28975468975469,-870.3079365079365,-19227.160750360752,-147887.70909090908,-536312.6857142857,-1.0362348051948051e6,-1.0997186678210679e6,-605843.911111111,-135573.46262626263,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.006993006993006993,17.244910644910647,1895.0315462315461,35180.35244755245,245442.05874125875,836234.2041958042,1.5471995524475526e6,1.5905439527583527e6,855155.6873348873,187717.1020979021,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,6,-8800.4,-111859.80952380953,-531221.9428571429,-1.2414390857142857e6,-1.5322940952380951e6,-958698.0571428571,-239674.51428571428,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,1529,36268.93968253968,292742.09523809527,1.1256783238095238e6,2.3227830857142857e6,2.6401645714285714e6,1.557884342857143e6,372827.02222222224,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-97.6,-5729.1255411255415,-88548.89927849927,-586570.2510822511,-2.0080116917748917e6,-3.8364944623376625e6,-4.1284842943722946e6,-2.3386422303030305e6,-542293.8505050505,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,346.2218004218004,13349.73026973027,170513.0474858475,1.0105419870795871e6,3.214343297236097e6,5.829024556243756e6,6.033182035742036e6,3.3163354703962705e6,750868.4083916084,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.4974358974358974,-784.5839937839938,-25005.26247086247,-286327.7053613054,-1.5797995114219114e6,-4.77710082983683e6,-8.342656417715617e6,-8.387304409013209e6,-4.50521045034965e6,-1.0011578778554779e6,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-11.533333333333333,269.4,25857.619047619046,244643.3523809524,941524.1142857143,1.8502997333333334e6,1.9667041523809524e6,1.0785353142857142e6,239674.51428571428,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-19.133333333333333,-5094.479365079365,-91148.63492063493,-595972.8761904762,-1.9178837333333334e6,-3.3857145904761907e6,-3.3492016761904764e6,-1.744297853968254e6,-372827.02222222224,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,384.0510822510823,16824.368253968252,209062.3953823954,1.1501940363636364e6,3.3420239238095237e6,5.513081239826839e6,5.196125312554113e6,2.6097891555555556e6,542293.8505050505,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.443600843600843,-1235.5986901986903,-37219.1333999334,-389168.827972028,-1.9364873206793207e6,-5.267843912887113e6,-8.294196586702187e6,-7.550561944366745e6,-3.6917696745920745e6,-750868.4083916084,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.005128205128205128,17.78850038850039,2689.031546231546,67733.57202797203,639727.53006993,2.9806964363636365e6,7.743910966899767e6,1.1785440213830614e7,1.0452192532090131e7,5.005789389277389e6,1.0011578778554779e6,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,8,-20454.4,-338221.5111111111,-2.129646933333333e6,-6.821751466666667e6,-1.2233386666666666e7,-1.2443101866666667e7,-6.7108864e6,-1.491308088888889e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,2637,81197.69581529581,855236.9685425685,4.365921080519481e6,1.2354614081385281e7,2.0404108744588744e7,1.9569787234632034e7,1.0100222965656566e7,2.169175402020202e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-127.6,-9731.779553779554,-194743.272016872,-1.6810041968697968e6,-7.631895255677655e6,-1.9979235561238762e7,-3.121355504229104e7,-2.8716805848018646e7,-1.4349929582595183e7,-3.0034736335664336e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,451.2884670884671,22506.019314019315,371138.143989344,2.8608340821844824e6,1.2051529176956376e7,2.991034232967033e7,4.489893256254856e7,4.0046315114219114e7,1.9522578618181817e7,4.0046315114219114e6,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.4980392156862745,-1021.0684583390466,-41964.88205128205,-619011.4680926916,-4.434788679994515e6,-1.7736541547237076e7,-4.234410989606472e7,-6.1679177494547285e7,-5.3709175564952694e7,-2.5676754984999314e7,-5.182464308898944e6,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-15.533333333333333,479.4,63067.02222222222,792570.3111111111,4.1009152e6,1.1153681066666666e7,1.7336456533333335e7,1.55189248e7,7.456540444444444e6,1.491308088888889e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-25.133333333333333,-9153.99163059163,-216262.70476190475,-1.870872972005772e6,-8.079372412121212e6,-1.9716661638095237e7,-2.849857074978355e7,-2.421317832958153e7,-1.1184810666666666e7,-2.169175402020202e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,519.3591075591075,29973.258252858253,488692.7529359529,3.5444105846153847e6,1.3786808101764902e7,3.138413195977356e7,4.3162921822710626e7,3.5328619333022535e7,1.58516663993784e7,3.0034736335664336e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.576934176934177,-1672.0434454434455,-65967.23223443223,-901384.234965035,-5.895572075924076e6,-2.1422238766033966e7,-4.646431837318237e7,-6.163704083294483e7,-4.905673601491842e7,-2.1524894373892773e7,-4.0046315114219114e6,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.00392156862745098,18.25848530554413,3638.6809634809633,119650.73401892226,1.4725623786096256e6,8.997631810448375e6,3.1165726124667488e7,6.523953848801134e7,8.420522974629554e7,6.55758409995338e7,2.8267987139448788e7,5.182464308898944e6,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,10.266666666666667,-42656.4,-889373.995959596,-7.149019797979798e6,-2.9865748169696968e7,-7.235293556363636e7,-1.0554394065454546e8,-9.146124722424242e7,-4.3383508040404044e7,-8.676701608080808e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,4255.4,165053.57016317017,2.19670492991453e6,1.4330180624708625e7,5.29140260997669e7,1.1808499516270396e8,1.624359102955711e8,1.346948423011655e8,6.173806913442113e7,1.2013894534265734e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-161.6,-15539.587434787434,-390961.72201132204,-4.259990718614719e6,-2.4699115148318347e7,-8.432809336796537e7,-1.779399951088911e8,-2.3469069971592852e8,-1.8834282577156177e8,-8.409726173986015e7,-1.6018526045687646e7,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,570.3472906178788,35746.582191664544,739622.7686979687,7.187172049660143e6,3.862786977665472e7,1.249378262920452e8,2.5314112267361397e8,3.234930047362311e8,2.531309910877828e8,1.1071628296284108e8,2.0729857235595778e7,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.498452012383901,-1289.0251146857959,-66438.47422257825,-1.227617738434115e6,-1.107397992473244e7,-5.645272137256345e7,-1.7550347663965014e8,-3.4482027794523466e8,-4.29947715579034e8,-3.2974049077368206e8,-1.4183586529618162e8,-2.6185082823910456e7,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-20.066666666666666,789.9333333333333,136892.39191919193,2.2055480888888887e6,1.4743798173737373e7,5.277455204848485e7,1.1157285546666667e8,1.4395359728484848e8,1.115261196929293e8,4.7721858844444446e7,8.676701608080808e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-31.933333333333334,-15290.940326340326,-461269.8076146076,-5.10054407956488e6,-2.841850342937063e7,-9.11948410927739e7,-1.7918446766247088e8,-2.193337460960373e8,-1.6331127164320123e8,-6.7745016401554e7,-1.2013894534265734e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,676.9748695748696,49810.32203352203,1.0321920394272394e6,9.544164072727272e6,4.781388058341658e7,1.4294413774385613e8,2.6698699182559663e8,3.145956128422688e8,2.2738798300792542e8,9.210652476270397e7,1.6018526045687646e7,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.694581235757706,-2181.5221419103773,-109270.05492285492,-1.892202578033731e6,-1.5744906345607335e7,-7.356716086097433e7,-2.0929734465833253e8,-3.7668167367356825e8,-4.312426213404269e8,-3.046022843375291e8,-1.2108121158063897e8,-2.0729857235595778e7,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.0030959752321981426,18.672520393263426,4748.226915980476,197766.84242568578,3.0782871159107145e6,2.3888763615371626e7,1.062565981512135e8,2.914255876520172e8,5.098456950542433e8,5.706785877375826e8,3.9574872039228964e8,1.5492840670813686e8,2.6185082823910456e7,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,12.8,-81880,-2.1007407614607615e6,-2.095521238228438e7,-1.1023046737156177e8,-3.441285888596737e8,-6.709847600932401e8,-8.259552492307693e8,-6.240550771965812e8,-2.6430567975384617e8,-4.805557813706294e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,6520.2,311067.7942501943,5.102019779331779e6,4.133440304335664e7,1.922698987114219e8,5.530782550526806e8,1.0170620137920746e9,1.1980522605003884e9,8.746782659530692e8,3.6041683602797204e8,6.407410418275058e7,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-199.6,-23628.784478266833,-730166.5007724302,-9.797468315151514e6,-7.051502323959962e7,-3.0318843028131086e8,-8.24417740343672e8,-1.4532290842782943e9,-1.6563077409054527e9,-1.1777150141972852e9,-4.749021839427396e8,-8.291942894238311e7,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,703.3999221968262,54143.24552805296,1.3738612902969064e6,1.6423980970872264e7,1.0950013007528281e8,4.457761957446739e8,1.1633972193432798e9,1.9862208061391819e9,2.20653026587352e9,1.5363898975089884e9,6.088031756559181e8,1.0474033129564182e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.49874686716792,-1588.4598780648316,-100391.40281967774,-2.2721153274630425e6,-2.5192147588914696e7,-1.5919834323671788e8,-6.225945846062396e8,-1.5748847121862333e9,-2.622330288934644e9,-2.854181112514796e9,-1.9537500785578425e9,-7.631081280111047e8,-1.2967850541365178e8,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-25.133333333333333,1228.2,271881.5229215229,5.463605097125097e6,4.5788857465734266e7,2.0806943674778554e8,5.705886187710955e8,9.891261404195805e8,1.0929306833255634e9,7.47197496172805e8,2.883334688223776e8,4.805557813706294e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-39.53333333333333,-24135.788500388502,-905518.1986013986,-1.2458983344832946e7,-8.693429073752914e7,-3.539285428811189e8,-9.016469155505828e8,-1.4824022811648796e9,-1.5738201839888113e9,-1.0428727894327894e9,-3.9245388811934733e8,-6.407410418275058e7,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,857.3689565336624,78373.47438182733,2.0127715456099457e6,2.3112727872974087e7,1.448205784474976e8,5.48772786971836e8,1.3280004404618127e9,2.1005893010457883e9,2.16389478497818e9,1.3996187132419581e9,5.163618984139312e8,8.291942894238311e7,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.799844393652443,-2765.6909199503625,-171565.7852751995,-3.67408829080517e6,-3.790738907893345e7,-2.2126713741740116e8,-7.971567635483366e8,-1.8574286571222606e9,-2.852811286882909e9,-2.870394025251496e9,-1.8211526732190146e9,-6.61173341303739e8,-1.0474033129564182e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.002506265664160401,19.04256314720711,6021.407418450143,310071.7180627422,5.959559314048181e6,5.72743914936333e7,3.179286576710175e8,1.1032734622114787e9,2.4971591341437187e9,3.7476056187814e9,3.700130737674165e9,2.310989422798335e9,8.279473807179306e8,1.2967850541365178e8,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,15.6,-147184.4,-4.556378703962704e6,-5.516948408391608e7,-3.559327987468532e8,-1.3849838370013986e9,-3.448738599742657e9,-5.628697306405595e9,-5.996935688354312e9,-4.0186477217118883e9,-1.537778500386014e9,-2.5629641673100233e8,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,9583.4,551597.1562502857,1.092800063183875e7,1.0752849872261073e8,6.136858642814754e8,2.2008252360679007e9,5.169359078663266e9,8.074326015812789e9,8.312849426393528e9,5.419679834310819e9,2.0277569441364596e9,3.3167771576953244e8,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-241.6,-34531.581210533535,-1.2859442616457501e6,-2.0830391072875936e7,-1.8202685521436995e8,-9.600492874957876e8,-3.2540002685571485e9,-7.325356346213779e9,-1.1069155880596071e10,-1.1097453830148788e10,-7.079345431875746e9,-2.6010515605084386e9,-4.189613251825673e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,850.4475412444452,78893.74837670069,2.409665423174555e6,3.474925120193656e7,2.8114098072956973e8,1.403407938144174e9,4.564031654437904e9,9.948487456287066e9,1.4649250696397833e10,1.4378787962114319e10,9.011876808307611e9,3.2619131746357026e9,5.187140216546071e8,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.4989648033126293,-1919.3769533617697,-146019.8335099459,-3.9742071741968985e6,-5.311713496745179e7,-4.071180069944188e8,-1.951471853701304e9,-6.149049338477993e9,-1.3068470999123806e10,-1.8848566822377876e10,-1.8183385037681484e10,-1.1230798287201794e10,-4.014395471935655e9,-6.314779394056087e8,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-30.733333333333334,1824.6,503413.80792540795,1.23437348997669e7,1.2666985013706294e8,7.111014843972028e8,2.4453185536e9,5.440886345756643e9,8.003944371617716e9,7.74195386945641e9,4.739481393767832e9,1.6659267087515152e9,2.5629641673100233e8,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-47.93333333333333,-36410.112500571326,-1.6632604871154989e6,-2.7868508792540792e7,-2.3790098953758398e8,-1.1959445584594543e9,-3.819200511326039e9,-8.057472578080973e9,-1.1386686300517574e10,-1.0673579702376745e10,-6.371368734672261e9,-2.193595802021226e9,-3.3167771576953244e8,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,1060.962421067065,117999.39040993406,3.6796141928934497e6,5.137764483644158e7,3.934568326273124e8,1.8396699858694205e9,5.577640943291375e9,1.131629761773835e10,1.5511646734480068e10,1.4188707002727196e10,8.301315963658234e9,2.8105322230997224e9,4.189613251825673e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.895082488890538,-3426.029950579177,-257947.1453013447,-6.696260875827578e6,-8.390810906845228e7,-5.980646799483613e8,-2.656730813122411e9,-7.751269489416868e9,-1.5263016489000265e10,-2.042660824129106e10,-1.832174708555405e10,-1.0545574516565224e10,-3.521270185463006e9,-5.187140216546071e8,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.002070393374741201,19.377095129336347,7461.561160324547,465737.4659903026,1.0838682409513706e7,1.2638856718220124e8,8.560311134982536e8,3.660454950424734e9,1.0368589915334404e10,1.9940417844891014e10,2.6176608626888607e10,2.310528608711372e10,1.3119593909531069e10,4.330134441638459e9,6.314779394056087e8,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,18.666666666666668,-250822.4,-9.21840527146579e6,-1.3309575831290278e8,-1.0317491250125874e9,-4.880582542269025e9,-1.5029793383663677e10,-3.1108875678233482e10,-4.36671203627632e10,-4.102438746924404e10,-2.470622075987824e10,-8.623620610007843e9,-1.3267108630781298e9,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,13613,930252.8430925112,2.189775853092872e7,2.5704415869336855e8,1.7632092507090087e9,7.688769367066271e9,2.233765721776305e10,4.425202515598031e10,6.002764410921827e10,5.486875815318882e10,3.230882151159315e10,1.1067561673572819e10,1.6758453007302692e9,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-287.6,-48836.168107778016,-2.157297016025873e6,-4.150197552329858e7,-4.325356919968865e8,-2.7414740676285434e9,-1.129721454934732e10,-3.1453610225900883e10,-6.027595384543495e10,-7.961419543169162e10,-7.119894052826602e10,-4.116669092530494e10,-1.3885575348907944e10,-2.0748560866184285e9,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,1011.4910195053149,111321.75903879551,4.0295488900919873e6,6.897135012978844e7,6.652503712536638e8,3.9895117085213494e9,1.5770553504337744e10,4.2506951460346924e10,7.936585512341737e10,1.0261545331623116e11,9.014849059168524e10,5.1342279166782936e10,1.7095009931051834e10,2.5259117576224346e9,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.4991304347826087,-2281.7794378338194,-205750.77203382071,-6.631606823604064e6,-1.0514449275916624e8,-9.603493437127837e8,-5.528469326922443e9,-2.116888539068655e10,-5.561882541965658e10,-1.0169630183320364e11,-1.2921016311537668e11,-1.1184445811395491e11,-6.289520276479862e10,-2.0712476412503963e10,-3.0310941091469216e9,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-36.86666666666667,2612.733333333333,880586.5429315782,2.58769066508707e7,3.190248779785548e8,2.165737490196956e9,9.103826722266722e9,2.516944859639786e10,4.714484837223376e10,6.028345544481031e10,5.188494812822027e10,2.876927277805501e10,9.286976041546907e9,1.3267108630781298e9,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-57.13333333333333,-52928.28618502241,-2.8930003372693355e6,-5.799649101182244e7,-5.943782676834052e8,-3.6117879045470395e9,-1.4095434050579176e10,-3.694310664816257e10,-6.646474288799973e10,-8.235087355324098e10,-6.910511159213396e10,-3.752838135449264e10,-1.1905484323937954e10,-1.6758453007302692e9,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,1288.1362155560298,171329.4262403575,6.378245421382333e6,1.0642760530321938e8,9.777255230809364e8,5.52282590456045e9,2.045420469861058e10,5.153708389209838e10,8.991146463998302e10,1.0868422825737668e11,8.937325837111873e10,4.772044308351795e10,1.4923003392217157e10,2.0748560866184285e9,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.982039010629669,-4163.8773617253355,-374174.74996878806,-1.1581383324811196e7,-1.7326355869602597e8,-1.4804164912081263e9,-7.940429316689499e9,-2.828693012341041e10,-6.914758135245525e10,-1.1774449383689468e11,-1.395287760054435e11,-1.1285112004028159e11,-5.941617567775465e10,-1.8357965809863052e10,-2.5259117576224346e9,0,0,0,0,0,0,0,0,0},{0,0,0,-0.0017391304347826088,19.68235392850819,9071.70504037235,675142.9984015393,1.87165462532353e7,2.6038147706447074e8,2.1128045296213334e9,1.0902989617985832e10,3.76931192037466e10,8.995871805969456e10,1.5020871457643378e11,1.7511705338495316e11,1.3969263524174225e11,7.268311082558556e10,2.2228023467077423e10,3.0310941091469216e9,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,22,-408912.4,-1.760144321133892e7,-2.9861306666560435e8,-2.735742086051796e9,-1.5429018250372686e10,-5.7365925635849785e10,-1.459396829211136e11,-2.5834540566109332e11,-3.181407036536493e11,-2.6734969563212573e11,-1.462262308496573e11,-4.692366842044753e10,-6.703381202921077e9,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,18793,1.5042532023658487e6,4.1496704494122185e7,5.725677207573206e8,4.642875405124088e9,2.4142609768578815e10,8.469481355425212e10,2.0624416519975134e11,3.5284625417378284e11,4.227746181988333e11,3.4738564819211395e11,1.8647020933259586e11,5.8893991997092316e10,8.299424346473714e9,0,0,0,0,0,0,0,0,0,0},{0,0,0,-337.6,-67186.71908304376,-3.473936806561178e6,-7.829175553408918e7,-9.589299292985568e8,-7.183900332775953e9,-3.529847566422289e10,-1.1866407812293896e11,-2.795105576516615e11,-4.6559435752690393e11,-5.4578034888958093e11,-4.4032629265684235e11,-2.3272130603976505e11,-7.25297518974442e10,-1.0103647030489738e10,0,0,0,0,0,0,0,0,0},{0,0,0,1,1186.5310195053148,152876.8874522256,6.472435445144703e6,1.2971987635205658e8,1.4699377328144228e9,1.0417012853749659e10,4.909095266192736e10,1.5974095702715295e11,3.6655776122906323e11,5.976373260031626e11,6.881257568365696e11,5.468004776147498e11,2.8525211689964355e11,8.790172916526073e10,1.2124376436587687e10,0,0,0,0,0,0,0,0},{0,0,0,0,-3.4992592592592593,-2675.669679379713,-282242.09231669543,-1.0633815228365488e7,-1.9732870645890525e8,-2.1167235434403558e9,-1.4395851669845222e10,-6.570092170701432e10,-2.08363647527213e11,-4.6815844108415533e11,-7.499685194097299e11,-8.507323675829946e11,-6.674090341577878e11,-3.4432387109323157e11,-1.0507792911709328e11,-1.4369631332252073e10,0,0,0,0,0,0,0}},{{0.5333333333333333,-43.53333333333333,3629.4,1.4694724226778382e6,5.0982079751051836e7,7.433658698673364e8,5.9978865667303295e9,3.02094865091216e10,1.0127974704935579e11,2.3405817896550006e11,3.7868392857216315e11,4.284339090756366e11,3.3229306521589435e11,1.6843118108433334e11,5.027535902190807e10,6.703381202921077e9,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-67.13333333333334,-74599.00473169761,-4.808057892384602e6,-1.1363745491663341e8,-1.3765659670421038e9,-9.93853334295837e9,-4.646297120807411e10,-1.476455595126865e11,-3.276911350438754e11,-5.136740259640373e11,-5.665757674791024e11,-4.3035620039143896e11,-2.143610632661782e11,-6.304370417032917e10,-8.299424346473714e9,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,1539.2381660875133,241314.9715176823,1.0573575649746368e7,2.0780309906924197e8,2.255048448318664e9,1.5127647788083984e10,6.709248572068778e10,2.0490559066010007e11,4.4090160795530695e11,6.741577248596049e11,7.285603048003533e11,5.440348341050625e11,2.6709174817027032e11,7.758157541268906e10,1.0103647030489738e10,0,0,0,0,0,0,0,0,0},{0,0,0,-6.062039010629669,-4980.454188585528,-526689.1747977207,-1.9167077767400973e7,-3.374851933365408e8,-3.4042942107257743e9,-2.167534593874192e10,-9.243454922934729e10,-2.738046230308966e11,-5.748972516712766e11,-8.61570663231068e11,-9.156248791038105e11,-6.740816221370153e11,-3.269296609004137e11,-9.396391738355457e10,-1.2124376436587687e10,0,0,0,0,0,0,0,0},{0,0,0,-0.0014814814814814814,19.963062463129766,10854.591016749811,949896.1873083068,3.0939338982764497e7,5.0627985565643203e8,4.84757118825071e9,2.9683411242703876e10,1.2280305832607028e11,3.5504229585249896e11,7.308189481361008e11,1.0772753882648191e12,1.1289483918947014e12,8.212160109323472e11,3.941685297769809e11,1.1226274478321931e11,1.4369631332252073e10,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,25.6,-642174.4,-3.2001493960675444e7,-6.301171929947947e8,-6.730005930120287e9,-4.45489555789727e10,-1.9627249696235114e11,-5.995497443810022e11,-1.2980003517584287e12,-2.0066420365331858e12,-2.2010916432997065e12,-1.6733714338577625e12,-8.384014633082003e11,-2.4898273039421143e11,-3.3197697385894855e10,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,25323.4,2.3470004379713614e6,7.499139768356036e7,1.2012583049576294e9,1.1358261276733395e10,6.933205150119518e10,2.8824587254763275e11,8.428926177352782e11,1.7637070948449934e12,2.6530579083520938e12,2.8455838704309585e12,2.1231780276189883e12,1.0469973628525146e12,3.067178562827242e11,4.0414588121958954e10,0,0,0,0,0,0,0,0,0},{0,0,0,-391.6,-90283.39413633075,-5.402084146905385e6,-1.409712773254586e8,-2.0042036720084534e9,-1.7506077529181057e10,-1.009677881940971e11,-4.0223835666768646e11,-1.1377089895665e12,-2.317805564538369e12,-3.4109110612635464e12,-3.591988921734658e12,-2.6387589471896216e12,-1.2839931153068442e12,-3.718142107220224e11,-4.8497505746350746e10,0,0,0,0,0,0,0,0},{0,0,0,1,1375.5680565423518,205134.69458317457,1.00442903694642e7,2.3300366348778668e8,3.0639399202108026e9,2.531140817273939e10,1.3999475849889786e11,5.397786494220163e11,1.4872042574435613e12,2.9652929630267153e12,4.285977100720373e12,4.445188146394695e12,3.223045360499386e12,1.5505730309458252e12,4.4456046934154846e11,5.747852532900829e10,0,0,0,0,0,0,0},{0,0,0,0,-3.499361430395913,-3101.049500580224,-378382.55774830375,-1.6479398081656067e7,-3.538256790695258e8,-4.4032169385133705e9,-3.490151422566471e10,-1.869146820137703e11,-7.023015906202007e11,-1.8944051915725413e12,-3.7109112830375283e12,-5.283759154390902e12,-5.409848733761012e12,-3.8788481619419673e12,-1.8478757481648335e12,-5.2523480042024817e11,-6.7388615902975235e10,0,0,0,0,0,0}},{{0.5333333333333333,-50.733333333333334,4914.6,2.3567543213508883e6,9.531948442077139e7,1.6222566814226518e9,1.533629951143212e10,9.106927966780995e10,3.6324193033461017e11,1.0115537476095123e12,2.0078489418750176e12,2.859678973879202e12,2.902119927570143e12,2.0490001876928757e12,9.566682602454508e11,2.6558157908715884e11,3.3197697385894855e10,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-77.93333333333334,-102426.67594272287,-7.688375333570598e6,-2.1157272142042986e8,-2.9899660626777706e9,-2.5285472574644356e10,-1.39341099517905e11,-5.2671795525996155e11,-1.4085398898401514e12,-2.708603610196061e12,-3.76067732280449e12,-3.7374252386297983e12,-2.5929559786286685e12,-1.1927785557210093e12,-3.269251503437037e11,-4.0414588121958954e10,0,0,0,0,0,0,0,0,0},{0,0,0.2,1814.5882726615152,331222.3335493492,1.6875662577301286e7,3.858469039048684e8,4.882312146902555e9,3.834964651451061e10,2.0043215049773267e11,7.280122943454908e11,1.8871102433942173e12,3.5392202281469395e12,4.81403000415386e12,4.70284874154185e12,3.215586981496385e12,1.4608069383404146e12,3.9606296359519775e11,4.8497505746350746e10,0,0,0,0,0,0,0,0},{0,0,0,-6.136113084703743,-5876.883265298239,-722621.9636936528,-3.0552356959223974e7,-6.254641839081137e8,-7.35329135286915e9,-5.480054731379718e10,-2.753158133060997e11,-9.696738980136191e11,-2.4522191929156543e12,-4.506888343001096e12,-6.027500191226616e12,-5.804540636175082e12,-3.920365399720353e12,-1.7620760421174104e12,-4.732997320060526e11,-5.747852532900829e10,0,0,0,0,0,0,0},{0,0,0,-0.001277139208173691,20.222883663640623,12812.749057488787,1.302854067321981e6,4.927317433912787e7,9.370025785364087e8,1.045225177549322e10,7.488955072282285e10,3.6490079744731726e11,1.254099223039917e12,3.108551076865836e12,5.618437072552979e12,7.408490300586078e12,7.048384464155902e12,4.710622193686491e12,2.09785778289315e12,5.589291083717358e11,6.7388615902975235e10,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,29.466666666666665,-976730,-5.578954646189742e7,-1.2615869100582263e9,-1.5529302994019297e10,-1.1910193801450629e11,-6.125072742936332e11,-2.206143296031422e12,-5.709225768796877e12,-1.0749971748792695e13,-1.4747065224375662e13,-1.4582852118589701e13,-1.0122591368671906e13,-4.679251530995561e12,-1.2932668199026865e12,-1.6165835248783582e11,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,33420.2,3.550881250122197e6,1.3009442746062008e8,2.3938339984597726e9,2.6090461836376514e10,1.8454580335053577e11,8.956680843174019e11,3.088494496941551e12,7.725403893782204e12,1.415456345665883e13,1.898742633772399e13,1.842784153284401e13,1.2590136522466424e13,5.741108749446352e12,1.5680860191320073e12,1.9399002298540298e11,0,0,0,0,0,0,0,0},{0,0,0,-449.6,-118882.34141578716,-8.1507702655822905e6,-2.4382796059468478e8,-3.981492068669497e9,-4.008401440642937e10,-2.6788273341492886e11,-1.2457916692080254e12,-4.155022019169404e12,-1.011883380132408e13,-1.8137213625744375e13,-2.3887559953693965e13,-2.2825549173918258e13,-1.538763792071379e13,-6.935816898196855e12,-1.8752368888588955e12,-2.2991410131603317e11,0,0,0,0,0,0,0},{0,0,0,1,1578.6025393009725,269796.6997164444,1.5129675524776911e7,4.02205042950141e8,6.073244823885286e9,5.781867124578261e10,3.705046212385272e11,1.6674750698719607e12,5.417057116138862e12,1.2910569366340434e13,2.272747357675429e13,2.947861243273825e13,2.7800233539143176e13,1.8528636980494258e13,8.268499554905844e12,2.2158962523390093e12,2.6955446361190094e11,0,0,0,0,0,0},{0,0,0,0,-3.49944382647386,-3557.9203447280424,-497291.8376827858,-2.479476383769259e7,-6.098901382048699e8,-8.713451379196568e9,-7.957942158518886e10,-4.937089707091298e11,-2.1650359733823113e12,-6.885306538377396e12,-1.6120601827215521e13,-2.7953517732769695e13,-3.579038142482068e13,-3.3375171285503258e13,-2.2026160316691473e13,-9.744096556853e12,-2.5912009727853706e12,-3.1303099000091724e11,0,0,0,0,0}},{{0.5333333333333333,-58.46666666666667,6511.533333333334,3.65374292379483e6,1.7041039042477334e8,3.3474383786596866e9,3.6634576706844986e10,2.5307096312507574e11,1.1825685116914846e12,3.8959211372933706e12,9.271173514538479e12,1.6125338479467012e13,2.0514656081142355e13,1.8879270148820613e13,1.2234885075983668e13,5.295573999855435e12,1.3740959961466045e12,1.6165835248783582e11,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-89.53333333333333,-137512.7002443942,-1.189358210895399e7,-3.7701063823343146e8,-6.146753773932911e9,-6.016166039394057e10,-3.856178138857783e11,-1.7075189529981672e12,-5.401437822018391e12,-1.2451974168004955e13,-2.1111659790717637e13,-2.6300614293483598e13,-2.3782945860158555e13,-1.5184861333257229e13,-6.488778629702592e12,-1.665081030624709e12,-1.9399002298540298e11,0,0,0,0,0,0,0,0},{0,0,0.2,2114.4828315743325,444637.2286422091,2.6068237359630816e7,6.861001365773908e8,1.00114325811189e10,9.098481065241385e10,5.529740045299663e11,2.3523822512552803e12,7.2120144708876045e12,1.621315950309689e13,2.692705307551175e13,3.29716634138851e13,2.938224475952283e13,1.8525493900149555e13,7.830326448629547e12,1.990193939516912e12,2.2991410131603317e11,0,0,0,0,0,0,0},{0,0,0,-6.2050786019451225,-6854.203876665512,-969805.7488195399,-4.71490524203349e7,-1.110535871836198e9,-1.5050298809158161e10,-1.2973475579082533e11,-7.577552802741434e11,-3.1251463627856104e12,-9.3459380263197e12,-2.058641033023447e13,-3.3613123793561336e13,-4.056896085255746e13,-3.57073389951639e13,-2.2272676941597234e13,-9.325906219148117e12,-2.3506734841449595e12,-2.6955446361190094e11,0,0,0,0,0,0},{0,0,0,-0.0011123470522803114,20.46471615241416,14948.520395986918,1.7481414056108568e6,7.598676584469618e7,1.6618757729228277e9,2.1362875654996433e10,1.7699538829298035e11,1.0024052815552432e12,4.0333265266471006e12,1.182051050899169e13,2.5601839654882164e13,4.120957066054989e13,4.913190571704601e13,4.278719239553509e13,2.6441705068033305e13,1.0981003732620514e13,2.747716467785829e12,3.1303099000091724e11,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,33.6,-1.4449664e6,-9.378112396360818e7,-2.4134343369641385e9,-3.3903936051757397e10,-2.9801676779554596e11,-1.7669252650270583e12,-7.395409184951448e12,-2.247442917360153e13,-5.039491703618102e13,-8.391129263208694e13,-1.034420381542176e14,-9.311814740541167e13,-5.94700664214626e13,-2.5517770940204883e13,-6.595660781503701e12,-7.759600919416119e11,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,43315.4,5.230291427936181e6,2.1780053830000895e8,4.561721534340654e9,5.6748630670697624e10,4.600956128255938e11,2.574621229746886e12,1.0317263052979926e13,3.0307188769397027e13,6.613140421026188e13,1.0767812330799452e14,1.302827448528449e14,1.1543547237775336e14,7.272605132546514e13,3.083902504292948e13,7.888927601406388e12,9.196564052641327e11,0,0,0,0,0,0,0},{0,0,0,-511.6,-153795.69885244747,-1.1978643183124974e7,-4.072033459630186e8,-7.567600637131104e9,-8.695493057921883e10,-6.660723636188911e11,-3.571363466702473e12,-1.384223532826015e13,-3.9588090502665234e13,-8.450579365558694e13,-1.3509302529267044e14,-1.609267891315999e14,-1.4069221688269344e14,-8.761436750764872e13,-3.677597449159481e13,-9.323413211988104e12,-1.0782178544476038e12,0,0,0,0,0,0},{0,0,0,1,1795.6347973654888,348690.3862286264,2.2204228030820765e7,6.705854777632657e8,1.1522110280379248e10,1.2517973983561208e11,9.19332170318912e11,4.770007373158425e12,1.8007053868363406e13,5.039707192316374e13,1.056513773616503e14,1.663261076501606e14,1.955389474170697e14,1.6900738607205572e14,1.0419707990723603e14,4.335070020676101e13,1.0903912818365283e13,1.252123960003669e12,0,0,0,0,0},{0,0,0,0,-3.4995112414467253,-4046.283374356923,-642320.5204937553,-3.6354442541503884e7,-1.0156406403679376e9,-1.6508254693268639e10,-1.7202985544924103e11,-1.2230324761502656e12,-6.182633991853942e12,-2.2846441388588523e13,-6.281007640234248e13,-1.2969530267124028e14,-2.0154019556485406e14,-2.3427740497541834e14,-2.0049551613303962e14,-1.2253405597896867e14,-5.058454321247145e13,-1.2635069050946113e13,-1.4418397115193762e12,0,0,0,0}},{{0.5333333333333333,-66.73333333333333,8466.6,5.500782327216349e6,2.9307562486459124e8,6.580662628830447e9,8.25198689979895e10,6.557192881581038e11,3.544366348591472e12,1.3610364338969898e13,3.81402493752755e13,7.919889465707464e13,1.2257383139758511e14,1.4091199728388275e14,1.1864488533235611e14,7.106501175365262e13,2.8670108813717684e13,6.983640827474507e12,7.759600919416119e11,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-101.93333333333334,-181056.65587236284,-1.787733779890622e7,-6.467215044849563e8,-1.2047942031497614e10,-1.3508357853771237e11,-9.958337708633071e11,-5.100215968856238e12,-1.8803864759217754e13,-5.1043402609364266e13,-1.0331528027101834e14,-1.565720156503844e14,-1.7685958939722884e14,-1.4670592314888475e14,-8.675260770965969e13,-3.461105326764565e13,-8.348755804038454e12,-9.196564052641327e11,0,0,0,0,0,0,0},{0,0,0.2,2439.19770489493,585468.939241731,3.91400351372385e7,1.1749495789312527e9,1.958269650268004e10,2.0382117002694974e11,1.4244548817255012e12,7.007773329261644e12,2.5037504149523434e13,6.627085088332564e13,1.3138571746780752e14,1.956929732604737e14,2.1782474594777912e14,1.7841953684261428e14,1.0435529770005283e14,4.123551524987994e13,9.862522139211904e12,1.0782178544476038e12,0,0,0,0,0,0},{0,0,0,-6.2695947309773805,-7913.383352642443,-1.2767836155293747e6,-7.073831350388925e7,-1.899554623143067e9,-2.939480935713848e10,-2.901204668878392e11,-1.9481763004141086e12,-9.290239953778574e12,-3.237296296631215e13,-8.39479743534346e13,-1.6360610601542472e14,-2.401716637111394e14,-2.6402193545879147e14,-2.1393204742321744e14,-1.2394533297842339e14,-4.856788337344296e13,-1.1529974798367117e13,-1.252123960003669e12,0,0,0,0,0},{0,0,0,-0.0009775171065493646,20.69089338637782,17264.0838134564,2.3011678842776404e6,1.1394226862290737e8,2.840139762731206e9,4.167633267110191e10,3.95266965553167e11,2.5731613895229917e12,1.1969456812409002e13,4.086863287421054e13,1.0419401598474152e14,2.0016347293020044e14,2.902331341320077e14,3.156571512430503e14,2.533843334077847e14,1.4559242461110694e14,5.6631732792034625e13,1.33559889067058e13,1.4418397115193762e12,0,0,0,0}}},\n {{{0,-0.26666666666666666,38,-2.0864644e6,-1.5269386717706367e8,-4.4364839170700865e9,-7.052545524685811e10,-7.039261202593761e11,-4.761725707062858e12,-2.288315999285902e13,-8.050868479032589e13,-2.1126861740115747e14,-4.1760113688084575e14,-6.230137174218235e14,-6.97244682853531e14,-5.760027708229431e14,-3.406464803623676e14,-1.3638576338223748e14,-3.3107630589508773e13,-3.678625621056531e12,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,55257,7.524884401159955e6,3.534212218718977e8,8.358422454073611e9,1.1767720205354315e11,1.0834651446175271e12,6.917863829651936e12,3.183148547582819e13,1.0825791495805245e14,2.7646060697452588e14,5.3439199490061275e14,7.825097493435275e14,8.619879647594399e14,7.024798614322576e14,4.105674340973219e14,1.6268776314620662e14,3.913296565848068e13,4.312871417790415e12,0,0,0,0,0,0},{0,0,0,-577.6,-195891.5954785697,-1.720127764558216e7,-6.593956434546355e8,-1.3836051116645775e10,-1.7991428787352527e11,-1.5649809531653018e12,-9.574263945472568e12,-4.260947812998459e13,-1.4108556267746003e14,-3.5246266137808444e14,-6.68904000078248e14,-9.643324596899239e14,-1.0481525855129518e15,-8.443224624053235e14,-4.884650317232749e14,-1.9181971314970422e14,-4.577208698235634e13,-5.008495840014676e12,0,0,0,0,0},{0,0,0,1,2026.6651003957916,443769.2062382361,3.1848062618839644e7,1.084383682742406e9,2.1033538298344963e10,2.5857382719851614e11,2.1562791411962607e12,1.2764669581045951e13,5.532758658800373e13,1.7926934003434116e14,4.398155867559162e14,8.21954813552544e14,1.1694384435544125e15,1.2565957550652905e15,1.0021077247917248e15,5.746217280770576e14,2.2387644402300447e14,5.304452412379179e13,5.767358846077505e12,0,0,0,0},{0,0,0,0,-3.4995670995670998,-4566.139539696959,-817050.1240826164,-5.210286556396761e7,-1.6407138496930685e9,-3.010064457529331e10,-3.548915820326058e11,-2.864643885149056e12,-1.6520807008205463e13,-7.0090278456826984e13,-2.2307320285268588e14,-5.3903548690406256e14,-9.943274230202304e14,-1.3987464189591615e15,-1.488142833281783e15,-1.1763925899836822e15,-6.693106216369468e14,-2.589498048063432e14,-6.0969222087105055e13,-6.591267252660006e12,0,0,0}},{{0.5333333333333333,-75.53333333333333,10829.4,8.072048354127319e6,4.87250210500034e8,1.2400772896941032e10,1.7659692941512448e11,1.5987019273419814e12,9.889499268944688e12,4.3725671416071375e13,1.4222478427288353e14,3.464460612721393e14,6.378941277981012e14,8.892327870204825e14,9.324932431776439e14,7.236581421029889e14,4.029765524699275e14,1.5224983637304378e14,3.494694340003704e13,3.678625621056531e12,0,0,0,0,0,0,0},{0,0.13333333333333333,-115.13333333333334,-234357.4023199112,-2.6202969245825373e7,-1.0729925112854352e9,-2.264892860478733e10,-2.8833628269220435e11,-2.421334407948635e12,-1.4190732511616314e13,-6.023738501346369e13,-1.897848476488173e14,-4.506023042846216e14,-8.123862868785152e14,-1.1127081259761939e15,-1.1495259687556288e15,-8.80694584160074e14,-4.849782163048779e14,-1.8144558258461128e14,-4.128940136737588e13,-4.312871417790415e12,0,0,0,0,0,0},{0,0,0.2,2788.9909571394373,757954.1832518226,5.731896737696369e7,1.9467522753006718e9,3.6752178916813446e10,4.342367668300395e11,3.456417626472393e12,1.945586960892444e13,8.002395364327356e13,2.45820394128803e14,5.716362792738416e14,1.0128387071687611e15,1.366953901980593e15,1.394401321620245e15,1.0566084586443459e15,5.762621684739365e14,2.1376666367087962e14,4.827633490236368e13,5.008495840014676e12,0,0,0,0,0},{0,0,0,-6.330200791583441,-9055.326402164885,-1.652817817493035e6,-1.0353224612455417e8,-3.1443424489415655e9,-5.5099878956043625e10,-6.172115086692606e11,-4.719665182766741e12,-2.5747979102863504e13,-1.0327781515594061e14,-3.107840698734769e14,-7.103751521762541e14,-1.240428258290523e15,-1.6532690684504498e15,-1.6682200228770388e15,-1.2521020933688375e15,-6.771547917071688e14,-2.4931732630126084e14,-5.592820354683055e13,-5.767358846077505e12,0,0,0,0},{0,0,0,-0.0008658008658008658,20.90332181816109,19761.47677528686,2.9786440888161287e6,1.6669440060546213e8,4.697988868588864e9,7.804846936458011e10,8.399601182809939e11,6.225772187860445e12,3.3126459614313613e13,1.3018123394897244e14,3.8510657020790756e14,8.676089997567239e14,1.4962826923778152e15,1.9729018315606848e15,1.9720423433634065e15,1.4678534354359658e15,7.87971726203723e14,2.8819855324002194e14,6.4264855713435055e13,6.591267252660006e12,0,0,0}}},\n {{{0,-0.26666666666666666,42.666666666666664,-2.9489904e6,-2.4170614799515897e8,-7.873218384663625e9,-1.405806642582533e11,-1.580544280937379e12,-1.2090386727568768e13,-6.6042366119374336e13,-2.65868882310363e14,-8.051739775983438e14,-1.857133409027708e15,-3.2801533762918805e15,-4.4314102156757605e15,-4.540487334262183e15,-3.465694635513561e15,-1.9084456023722588e15,-7.161903536719025e14,-1.6388911387603578e14,-1.725148567116166e13,0,0,0,0,0,0},{0,0,-0.06666666666666667,69509,1.060304375629801e7,5.578470160261151e8,1.479270594762511e10,2.3394997790297177e11,2.4264918279035615e12,1.7521030242218191e13,9.164276368056673e13,3.5664655366664625e14,1.05113206044863e15,2.370956512005569e15,4.1103527541472025e15,5.465870295900822e15,5.524844013590857e15,4.167585692773008e15,2.2713467255841065e15,8.446251275105141e14,1.917140907650062e14,2.0033983360058703e13,0,0,0,0,0},{0,0,0,-647.6,-246094.15250627516,-2.4198988932992294e7,-1.038980191421611e9,-2.444203632713007e10,-3.570077983612116e11,-3.498184851505777e12,-2.4202280989027707e13,-1.2243539925589284e14,-4.638933812042697e14,-1.3374968892379465e15,-2.9619773218874905e15,-5.055557384458424e15,-6.63336672836086e15,-6.627413577564161e15,-4.948584988121854e15,-2.672802925395651e15,-9.85971732202283e14,-2.2219508817519653e14,-2.306943538431002e13,0,0,0,0},{0,0,0,1,2271.693671824363,557112.5844066336,4.4760097703188986e7,1.7065933499774168e9,3.710782171508295e10,5.123704928625934e11,4.812792440204033e12,3.2217907329529703e13,1.587313473404659e14,5.885027219728265e14,1.6662726075609255e15,3.6337254670711775e15,6.120647631772677e15,7.939169799895172e15,7.852589702803345e15,5.811463115882084e15,3.1140914617754305e15,1.1406361435129525e15,2.5541160604057522e14,2.6365069010640023e13,0,0,0},{0,0,0,0,-3.4996138996138995,-5117.489627447047,-1.0252931044630904e6,-7.317764631938808e7,-2.5799387735712266e9,-5.305164082877038e10,-7.024571823174719e11,-6.386343641756565e12,-4.1646702455182195e13,-2.0082495548407444e14,-7.313240134063729e14,-2.0393725447628995e15,-4.389582156680698e15,-7.310312322718411e15,-9.388355782488322e15,-9.204613694406318e15,-6.75889981067322e15,-3.596449851906305e15,-1.3090123157014138e15,-2.9144089798248025e14,-2.9927916174240027e13,0,0}},{{0.5333333333333333,-84.86666666666666,13652.733333333334,1.1580743990317933e7,7.862366731187782e8,2.251285321019336e10,3.6126970425140875e11,3.6950296972946763e12,2.591996982109244e13,1.3060390853963811e14,4.872588592243463e14,1.3728326184824732e15,2.955623641337104e15,4.887098724271143e15,6.197174104927707e15,5.97435514747484e15,4.3000613327664335e15,2.2374288971381245e15,7.949002570465775e14,1.725148567116166e14,1.725148567116166e13,0,0,0,0,0,0},{0,0.13333333333333333,-129.13333333333333,-298814.1125960173,-3.756041742575181e7,-1.7285393875937688e9,-4.103692427927973e10,-5.885977025139501e11,-5.58378211235412e12,-3.710691956026596e13,-1.7949438370340738e14,-6.486221072613646e14,-1.7811709048134368e15,-3.7547456752020125e15,-6.099911491230204e15,-7.620161622284745e15,-7.252241847091468e15,-5.161779213919494e15,-2.65959108326093e15,-9.367258010130061e14,-2.0173108244503553e14,-2.0033983360058703e13,0,0,0,0,0},{0,0,0.2,3164.105012550278,966660.7328705739,8.210917088666102e7,3.1326839561683073e9,6.649903112671311e10,8.850518794573038e11,7.957226405896327e12,5.07826266196542e13,2.3800231954847772e14,8.384811979980429e14,2.2550231205737835e15,4.671485049782065e15,7.477796091175499e15,9.223459380199674e15,8.681741711096794e15,6.119697195173343e15,3.1262899720312225e15,1.0927437571553231e15,2.3372980586735153e14,2.306943538431002e13,0,0,0,0},{0,0,0,-6.387343648726298,-10280.88273895997,-2.1078979265578426e6,-1.482407551004836e8,-5.055907877161912e9,-9.959690402930423e10,-1.2564964279090027e12,-1.0850994538243352e13,-6.710880700339022e13,-3.066885058028235e14,-1.0583451011894089e15,-2.7975704791687135e15,-5.711120851896802e15,-9.02764697095337e15,-1.10141153245736e16,-1.0268428227212878e16,-7.177155441784758e15,-3.6389915826190465e15,-1.2633984960937452e15,-2.6859414054589525e14,-2.6365069010640023e13,0,0,0},{0,0,0,-0.0007722007722007722,21.103579218418492,22442.61268540996,3.7985964582853154e6,2.3859794710035256e8,7.549734457672135e9,1.4096953641872162e11,1.7083678819651787e12,1.429842236994991e13,8.623782828471784e13,3.860843010721173e14,1.3096501921718585e15,3.4118527798952095e15,6.87871387556754e15,1.0756091873106256e16,1.2998921089798014e16,1.2017683521567574e16,8.337385441942756e15,4.199116583526632e15,1.4491212804099838e15,3.0640485606960025e14,2.9927916174240027e13,0,0}}},\n {{{0,-0.26666666666666666,47.6,-4.0895524e6,-3.731306038384463e8,-1.3541340916361624e10,-2.698066970601489e11,-3.3929623532272686e12,-2.912501505968892e13,-1.792856932147624e14,-8.178001345526671e14,-2.825665552462115e15,-7.50119392296909e15,-1.5421119083184214e16,-2.46069867650868e16,-3.036845308130471e16,-2.8690118845028184e16,-2.035084821245431e16,-1.0484659979090722e16,-3.7026001121730715e15,-8.013593344023481e14,-8.013593344023481e13,0,0,0,0,0},{0,0,-0.06666666666666667,86351.4,1.4665579721461162e7,8.590687659123018e8,2.5382910206863052e10,4.4799089906092065e11,5.197549704634442e12,4.2116936060807555e13,2.4826316584141612e14,1.0947767893988114e15,3.681377038739813e15,9.557508586062312e15,1.928610504650084e16,3.02919821648759e16,3.68806750791929e16,3.4434258261705336e16,2.417434564050942e16,1.2341328990945152e16,4.323002238921354e15,9.288483194209035e14,9.227774153724008e13,0,0,0,0},{0,0,0,-721.6,-305383.484221278,-3.3425150558028962e7,-1.5976051302013426e9,-4.187439493752403e10,-6.825325957092296e11,-7.480870721296626e12,-5.808146779339898e13,-3.311329496999199e14,-1.421626589092943e15,-4.676542004989115e15,-1.1920141073940436e16,-2.3681684177511636e16,-3.670117139829947e16,-4.416718389230369e16,-4.0819063755733816e16,-2.8399638601169932e16,-1.4382537224523932e16,-5.001926254562189e15,-1.067785294930921e15,-1.054602760425601e14,0,0,0},{0,0,0,1,2530.72069885139,690925.9210848194,6.1773305205390684e7,2.6215136024899797e9,6.350186022610584e10,9.783737218417522e11,1.0279134468481693e13,7.721651964503972e13,4.287219179136568e14,1.8010359258476095e15,5.818025681991426e15,1.460298629964141e16,2.8630185446713732e16,4.3862993135598696e16,5.225649481076826e16,4.7866759281312376e16,3.3039905722220736e16,1.6614027170527334e16,5.741105116040728e15,1.218493729951201e15,1.1971166469696011e14,0,0},{0,0,0,0,-3.4996534996535,-5700.334296291716,-1.2710928628651593e6,-1.0093436202872059e8,-3.9601706432110143e9,-9.070909301290082e10,-1.3400853937505337e12,-1.3626158227398803e13,-9.970831360069828e13,-5.418127541007572e14,-2.2355599883931558e15,-7.112384380705038e15,-1.7619359196305414e16,-3.415306825634278e16,-5.180484759888663e16,-6.1176142561382664e16,-5.559884636602166e16,-3.810791930105565e16,-1.904137287813753e16,-6.54222329112722e15,-1.3812884388110782e15,-1.350593140170832e14,0}},{{0.5333333333333333,-94.73333333333333,16992.6,1.6284696076892616e7,1.2354648054405298e9,3.953909107382076e10,7.10090176204812e11,8.145748277303172e12,6.428556882265668e13,3.6590982390426875e14,1.5502704689894388e15,4.993707604738265e15,1.2398036774129854e16,2.3903947362329856e16,3.5861500931598584e16,4.170569864198567e16,3.720611350142881e16,2.496972481358118e16,1.2193217903736838e16,4.0882542918542015e15,8.414273011224655e14,8.013593344023481e13,0,0,0,0,0},{0,0.13333333333333333,-143.93333333333334,-375927.24292232457,-5.278450853716055e7,-2.7125229474487467e9,-7.195565577844536e10,-1.1548552468425483e12,-1.2286437334588822e13,-9.185201223250092e13,-5.0188188887196794e14,-2.0594686450678228e15,-6.465664297334423e15,-1.5717197545820644e16,-2.9773055055612476e16,-4.400198164051586e16,-5.051762663082156e16,-4.456554705592129e16,-2.961652536463062e16,-1.4337322088783526e16,-4.770124322093573e15,-9.749871901895235e14,-9.227774153724008e13,0,0,0,0},{0,0,0.2,3564.768442556024,1.2164908134451648e6,1.1533096610258973e8,4.911578657437878e9,1.1646951484526044e11,1.7342546082017852e12,1.7484020896956271e13,1.2551336178335739e14,6.644159134672428e14,2.6578960250785765e15,8.171790366631361e15,1.9520413309070224e16,3.643312168795762e16,5.316310532259258e16,6.036333626184364e16,5.273684513072426e16,3.4747435047530596e16,1.6693177509884468e16,5.516045100269669e15,1.120515432952201e15,1.054602760425601e14,0,0,0},{0,0,0,-6.441397702780352,-11590.853392628731,-2.6527484863642906e6,-2.081436499095543e8,-7.921865093783669e9,-1.742928669332534e11,-2.459659492823631e12,-2.3815795421580676e13,-1.6566332438371656e14,-8.550505095885778e14,-3.35024333679381e15,-1.0123366574848608e16,-2.382922456508392e16,-4.391688037572645e16,-6.338437811869518e16,-7.128043872024897e16,-6.174789017813265e16,-4.037820760670786e16,-1.9267335122747188e16,-6.327906043885648e15,-1.2783495622996812e15,-1.1971166469696011e14,0,0},{0,0,0,-0.000693000693000693,21.292986207825482,25309.29515631317,4.780381324186655e6,3.3492374593636465e8,1.1823731636670485e10,2.4653622561126352e11,3.3416154029679727e12,3.135410116283323e13,2.126729757114602e14,1.0752440457778672e15,4.1409771925451395e15,1.233117595422076e16,2.8664288229529544e16,5.225580879389953e16,7.470388245200797e16,8.330526615716496e16,7.162566653980231e16,4.652411455487196e16,2.2066154752113164e16,7.207543889154556e15,1.4488180958196198e15,1.350593140170832e14,0}}},\n {{{0,-0.26666666666666666,52.8,-5575520,-5.632173785675783e8,-2.264573851170883e10,-5.005643706894967e11,-6.997344021760841e12,-6.694984221034684e13,-4.609967645533807e14,-2.3627840501606355e15,-9.225264284921132e15,-2.7870762591869724e16,-6.579211913432579e16,-1.219269835005012e17,-1.7736434748785085e17,-2.014372433713144e17,-1.7653028386935773e17,-1.1695051216654723e17,-5.660662707425071e16,-1.887747613881895e16,-3.8756651445640835e15,-3.691109661489603e14,0,0,0,0},{0,0,-0.06666666666666667,106080.2,1.9949649623509426e7,1.2939911180306041e9,4.2363534986906364e10,8.295293999689657e11,1.0698737964202242e13,9.66363247645834e13,6.372094391758614e14,3.1574388239306565e15,1.1998128373402768e16,3.545022868007551e16,8.214242163461622e16,1.498448307438975e17,2.1504119173799283e17,2.413696663998524e17,2.0935359957837e17,1.3743658725905952e17,6.598443928517343e16,2.1845367673730504e16,4.455696662798164e15,4.218411041702404e14,0,0,0},{0,0,0,-799.6,-374795.69873168645,-4.541501586740491e7,-2.4033232898026366e9,-6.979280795787791e10,-1.2620648339616711e12,-1.5377051478454482e13,-1.3307719247169702e14,-8.486965787241058e14,-4.0942474686362435e15,-1.521973082413072e16,-4.415040755395909e16,-1.0071975616913048e17,-1.8128971785509302e17,-2.5715892674943798e17,-2.8571552176641878e17,-2.4559351140219373e17,-1.5993872560572854e17,-7.623776610305851e16,-2.5076921618640444e16,-5.084895471889925e15,-4.7884665878784044e14,0,0},{0,0,0,1,2803.746339877031,847540.594948172,8.387088415905303e7,3.940171303117425e9,1.057365813099728e11,1.8072133228725144e12,2.1105818071761484e13,1.7671976487014494e14,1.0975457428896409e15,5.180820146125421e15,1.8912018709994548e16,5.402178465503179e16,1.2161716004687645e17,2.1639908949667334e17,3.038797903142797e17,3.3462662569227334e17,2.853611054467527e17,1.845190954017643e17,8.739229013859099e16,2.857951555540064e16,5.764577084638233e15,5.402372560683328e14,0},{0,0,0,0,-3.499687304565353,-6314.674103265669,-1.5587237516807944e6,-1.3697283658064875e8,-5.948433133232432e9,-1.5092828425611444e11,-2.4733417883407153e12,-2.7953736163984633e13,-2.2798507703929834e14,-1.3857335293027922e15,-6.424397479638844e15,-2.30959575834661e16,-6.511275177576189e16,-1.4492407203283318e17,-2.5530540726016147e17,-3.553604828117912e17,-3.882498975703751e17,-3.287640702824053e17,-2.1123805647598467e17,-9.947298157155096e16,-3.2360331425024412e16,-6.496023591260685e15,-6.06119848271788e14}},{{0.5333333333333333,-105.13333333333334,20908.2,2.2492357135156598e7,1.8958309719109235e9,6.741542072724315e10,1.3467332712719966e12,1.721588784468186e13,1.517969171625762e14,9.68623788198903e14,4.620809634242403e15,1.6852457171265348e16,4.7703107096260296e16,1.0578958618367114e17,1.8461804798071936e17,2.5344496869855994e17,2.7218267219337744e17,2.2596420895370938e17,1.4205763700894958e17,6.535328208213089e16,2.074610040494806e16,4.0602206276385635e15,3.691109661489603e14,0,0,0,0},{0,0.13333333333333333,-159.53333333333333,-467299.4470188559,-7.287456290234995e7,-4.157830371714083e9,-1.2252070190736252e11,-2.186990850552188e12,-2.5926110989630664e13,-2.1653318849256094e14,-1.326322841173958e15,-6.127978836743251e15,-2.1781741790169716e16,-6.036681088296472e16,-1.3152785185627565e17,-2.2611628841057744e17,-3.06435432704922e17,-3.2542265994529766e17,-2.6752084016889734e17,-1.667276585666764e17,-7.611122760127998e16,-2.3994120798097664e16,-4.666617214883284e15,-4.218411041702404e14,0,0,0},{0,0,0.2,3991.1974633728914,1.5126843075902709e6,1.591637552639756e8,7.523047958345665e9,1.981274589389424e11,3.28062880467928e12,3.684945335931074e13,2.9550727863338325e14,1.753482804920874e15,7.897512890513422e15,2.748953095986418e16,7.486280786775282e16,1.6070534554507542e17,2.7277027276789126e17,3.6558244328737126e17,3.8447574794727104e17,3.133601408355606e17,1.9380644168944502e17,8.786770088566074e16,2.7529585606062684e16,5.324318801283845e15,4.7884665878784044e14,0,0},{0,0,0,-6.4926797540624035,-12985.995991128793,-3.298836226795991e6,-2.871680700153716e8,-1.2127517294150885e10,-2.9628375638388446e11,-4.648967460183313e12,-5.014705791678989e13,-3.896342464153759e14,-2.254104416220173e15,-9.943117755509682e15,-3.401307144070906e16,-9.127203209515408e16,-1.934632666986177e17,-3.247778760884149e17,-4.311079790213169e17,-4.495396895431404e17,-3.636200897900059e17,-2.2336772996888845e17,-1.0065183695567805e17,-3.1360509612206944e16,-6.034695712672399e15,-5.402372560683328e14,0},{0,0,0,-0.0006253908692933083,21.472659314327856,28363.229946619325,5.944698143021086e6,4.619832444694353e8,1.809376056308954e10,4.1886637559539825e11,6.31178461726564e12,6.596977935869714e13,4.997768062476191e14,2.8319808910505985e15,1.2277848441468622e16,4.138797722399096e16,1.0967212084846331e17,2.299374395484744e17,3.823298988047106e17,5.032265327743345e17,5.208059242745585e17,4.1843448110868006e17,2.5548313610900355e17,1.1449196659647726e17,3.5494695749103796e16,6.799083515396579e15,6.06119848271788e14}}}\n};\n\nstatic const double ImEI[21][2][5][27] =\n {\n {{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.03333333333333333,-0.06666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.3,-0.26666666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.5,2.1333333333333333,1.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-1.8333333333333333,-6.133333333333334,-4.266666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.03333333333333333,4.2,12.8,8.533333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.06666666666666667,0.06666666666666667,0.06666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.1,0.43333333333333335,0.26666666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-1.2666666666666666,-2.933333333333333,-1.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.16666666666666666,4.1,8.266666666666667,4.266666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.06666666666666667,-0.4666666666666667,-9,-17.066666666666666,-8.533333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.06666666666666667,1.0666666666666667,1.0666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-2.6,-9.066666666666666,-6.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,11.6,27.733333333333334,17.066666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-3.533333333333333,-29.066666666666666,-59.733333333333334,-34.13333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.009523809523809525,8,56.68571428571428,107.27619047619048,58.51428571428571,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.13333333333333333,-0.26666666666666666,-1.6,-1.0666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.2,5.933333333333334,12.266666666666667,6.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-3.2,-22.266666666666666,-36.266666666666666,-17.066666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.06666666666666667,10.066666666666666,52.53333333333333,76.8,34.13333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.01904761904761905,-0.26666666666666666,-21.714285714285715,-99.35238095238095,-136.53333333333333,-58.51428571428571,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.1,12.6,38.4,25.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-8.9,-64.26666666666667,-123.73333333333333,-68.26666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1.5,35.2,170.13333333333333,273.06666666666666,136.53333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.271428571428571,-84,-341.9428571428571,-497.37142857142857,-234.05714285714285,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.0015873015873015873,11.88888888888889,159.4920634920635,589.6126984126984,806.1968253968254,364.0888888888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.2,-1.4,-27,-51.2,-25.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.3,24.233333333333334,113.33333333333333,157.86666666666667,68.26666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-5.4,-81.86666666666666,-281.06666666666666,-341.3333333333333,-136.53333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.04285714285714286,17.1,183.65714285714284,546.7428571428571,614.4,234.05714285714285,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.0031746031746031746,-0.15555555555555556,-36.93015873015873,-337.26984126984127,-924.4444444444445,-988.2412698412699,-364.0888888888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.13333333333333333,59.733333333333334,332.8,546.1333333333333,273.06666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-21.2,-260.26666666666665,-921.6,-1228.8,-546.1333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,2,79.88571428571429,648.5333333333333,1896.8380952380953,2262.552380952381,936.2285714285714,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-7.015873015873016,-186.48888888888888,-1262.120634920635,-3319.0603174603175,-3692.9015873015874,-1456.3555555555556,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.0005772005772005772,15.806060606060607,349.617316017316,2133.1116883116883,5241.461471861472,5560.630303030303,2118.3353535353535,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.26666666666666666,-3.7333333333333334,-149.33333333333334,-554.6666666666666,-682.6666666666666,-273.06666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.4,64.13333333333334,541.8666666666667,1433.6,1501.8666666666666,546.1333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-7.771428571428571,-209.86666666666667,-1260.4952380952382,-2852.5714285714284,-2730.6666666666665,-936.2285714285714,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.031746031746031744,24.755555555555556,462.5015873015873,2365.765079365079,4892.444444444444,4421.079365079365,1456.3555555555556,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.0011544011544011544,-0.11313131313131314,-53.58268398268398,-839.8961038961039,-3909.818181818182,-7624.588744588745,-6619.79797979798,-2118.3353535353535,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.16666666666666666,191.66666666666666,1668.2666666666667,4753.066666666667,5461.333333333333,2184.5333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-41.5,-775.8095238095239,-4313.6,-9976.685714285713,-10142.47619047619,-3744.9142857142856,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,2.5,152.63492063492063,1872.888888888889,8569.092063492064,17664.812698412698,16644.06349206349,5825.422222222222,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-8.762626262626263,-352.2020202020202,-3580.7676767676767,-14673.19595959596,-28117.59191919192,-25155.23232323232,-8473.341414141414,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.0002775002775002775,19.731934731934732,655.7495837495837,5983.52047952048,22836.666267066266,41605.430303030305,35848.75213675214,11732.318881118881,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.3333333333333333,-7.666666666666667,-528.2,-3225.6,-7074.133333333333,-6553.6,-2184.5333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.5,135.11904761904762,1809.8666666666666,7751.314285714286,14345.752380952381,12014.933333333332,3744.9142857142856,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-10.26984126984127,-436.8888888888889,-4089.930158730159,-14826.869841269841,-24894.577777777777,-19556.774603174603,-5825.422222222222,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.025252525252525252,32.86363636363637,955.6767676767677,7544.371717171717,24809.761616161617,39106.45656565657,29391.90303030303,8473.341414141414,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.000555000555000555,-0.08935508935508936,-71.26440226440226,-1727.040959040959,-12325.773426573427,-38017.645288045285,-57329.99658119658,-41714.91157731158,-11732.318881118881,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.2,489.6,6106.971428571429,26214.4,50556.34285714286,44938.97142857143,14979.657142857142,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-71.8,-1901.8920634920635,-15197.155555555555,-53000.93968253968,-90398.06984126984,-74066.08253968254,-23301.68888888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,3,260.43463203463205,4506.052525252525,29564.416738816737,91759.85685425685,144822.26608946608,112271.77373737373,33893.36565656566,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-10.51048951048951,-596.8428904428904,-8522.413053613054,-49961.41351981352,-143888.94731934732,-215275.8303030303,-160341.69137529138,-46929.275524475524,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.0001554001554001554,23.661849261849262,1106.6579642579643,14141.066045066045,77056.03978243978,210652.15602175603,303084.9044289044,219003.28578088578,62572.367365967366,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.4,-13.6,-1447.5428571428572,-13136,-44470.857142857145,-70217.14285714286,-52428.8,-14979.657142857142,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.6,247.18412698412698,4825.422222222222,30428.749206349206,86497.11746031746,123062.04444444444,85716.92698412699,23301.68888888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-12.86926406926407,-795.3656565656565,-10742.07215007215,-56978.655122655124,-146297.53535353535,-194603.1468975469,-129218.45656565657,-33893.36565656566,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.02097902097902098,41.329137529137526,1733.909557109557,19631.14219114219,94030.1724941725,225862.41491841493,286647.4368298368,183806.32913752913,46929.275524475524,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.0003108003108003108,-0.07397047397047397,-89.75540015540015,-3126.114063714064,-31870.1898989899,-142693.88282828283,-326997.6515928516,-400854.2284382284,-250289.46946386946,-62572.367365967366,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.23333333333333334,1074.7333333333333,18153.244444444445,108464.35555555555,307655.1111111111,449285.68888888886,326223.64444444445,93206.75555555556,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-114.1,-4069.7131313131313,-44104.92121212121,-214282.8606060606,-537693.0909090909,-723676.3151515152,-495690.4727272727,-135573.46262626263,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,3.5,410.27630147630146,9526.587723387724,84649.39362859362,365700.5550893551,848556.257964258,1.0798214464646464e6,709153.4968142968,187717.1020979021,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-12.25897435897436,-936.1311577311577,-17890.690287490288,-141813.89526029525,-567884.4618492619,-1.2480050523698523e6,-1.524549659052059e6,-969871.6941724942,-250289.46946386946,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.0000959824489236254,27.593994241053064,1731.1486631016044,29547.359934183463,217402.40296174414,825519.0614561909,1.7431695357191828e6,2.0641979866721514e6,1.280893167256273e6,323904.019306184,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.4666666666666667,-21.933333333333334,-3355.6222222222223,-42348.08888888889,-203582.57777777777,-479869.15555555554,-594921.2444444444,-372827.02222222224,-93206.75555555556,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.7,410.7262626262626,11022.440404040404,96074.47272727273,386563.103030303,819299.296969697,946101.5272727272,563477.2040404041,135573.46262626263,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-15.552602952602953,-1319.1589743589743,-24329.85236985237,-177655.00916860916,-643821.182905983,-1.273099178865579e6,-1.3992012382284382e6,-803012.0478632479,-187717.1020979021,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.017948717948717947,50.09052059052059,2871.1639471639473,44222.36891996892,290731.34296814294,983393.9045843045,1.851893577000777e6,1.9625562306138305e6,1.0950164289044288e6,250289.46946386946,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.0001919648978472508,-0.06315645139174551,-108.91493212669683,-5170.4839160839165,-71524.53607568901,-438562.81431509665,-1.4125950964486494e6,-2.565467062004662e6,-2.6439125666803783e6,-1.4428451769093652e6,-323904.019306184,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,2116.266666666667,46478.36998556999,367133.99595959595,1.4218853217893217e6,3.00440476998557e6,3.5321728923520925e6,2.169175402020202e6,542293.8505050505,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-170.4,-7878.639405039405,-111119.03776223776,-714162.356043956,-2.447790332334332e6,-4.76751157962038e6,-5.287365042424242e6,-3.1077609125097124e6,-750868.4083916084,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,4,609.1538683538683,18291.647552447554,211297.13166833165,1.2068968343656345e6,3.8238280972360973e6,7.039391328671329e6,7.482612264180264e6,4.254920980885781e6,1.0011578778554779e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-14.007843137254902,-1385.7954019836372,-34183.56217377394,-351855.81673751085,-1.8614895882261528e6,-5.582810520261438e6,-9.861435769605558e6,-1.0149606059509119e7,-5.624151607952831e6,-1.295616077224736e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.0000635071842502183,31.527506549178376,2558.0482279330577,56272.57883911754,537113.6969927904,2.6926125869276235e6,7.7549386769432835e6,1.3272122169070559e7,1.3318034401472213e7,7.228173904516948e6,1.6365676764944035e6,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-33.06666666666667,-6906.606637806638,-115649.93939393939,-746992.1893217893,-2.4357735803751806e6,-4.414610876767676e6,-4.515080496392496e6,-2.440322327272727e6,-542293.8505050505,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.8,636.47881007881,22496.094483294484,259039.60572760573,1.3972491252747253e6,4.090821281118881e6,6.898882843023643e6,6.700457672105672e6,3.483195116705517e6,750868.4083916084,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-18.30773670773671,-2043.3143745143745,-49402.28837828838,-475220.8388944389,-2.3042702023310023e6,-6.28517082917083e6,-1.0076758327894328e7,-9.422355652525252e6,-4.75549991981352e6,-1.0011578778554779e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.01568627450980392,59.10452945747063,4444.078065725124,89495.53131313132,773530.6577448695,3.495176651510581e6,9.067520102966314e6,1.400317438010878e7,1.2718753849005897e7,6.2719596465652e6,1.295616077224736e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.0001270143685004366,-0.05512423592918949,-128.64458637337896,-7998.43481348373,-144411.5393015653,-1.162342659386434e6,-4.9947002896331735e6,-1.2482808925253488e7,-1.8729284982381087e7,-1.6625264914387986e7,-8.04645774276415e6,-1.6365676764944035e6,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.3,3839.4,106318.05314685314,1.0702797874125873e6,5.392764956643357e6,1.5350685180419581e7,2.580816845874126e7,2.539460421818182e7,1.3515631351048952e7,3.0034736335664336e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-242.7,-14124.181152181152,-251299.74452214452,-2.0592303781551782e6,-9.185474911222111e6,-2.4106659233033635e7,-3.8236604926806524e7,-3.601039741911422e7,-1.852142074032634e7,-4.0046315114219114e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,4.5,864.0628077804548,32599.88898944193,474679.1184031655,3.455516380591957e6,1.4245058289412549e7,3.533020329192376e7,5.370181410996846e7,4.892054909771013e7,2.449892218752228e7,5.182464308898944e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-15.756965944272446,-1961.5696724328304,-60708.62697178982,-786988.0535711966,-5.303549502574206e6,-2.0688066335863516e7,-4.921807658793219e7,-7.241782910112797e7,-6.427015135233064e7,-3.1503927772517268e7,-6.546270705977614e6,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.00004422821760283061,35.461919504643966,3616.1956285200868,99702.79558212686,1.1976321362253844e6,7.643730469367165e6,2.8621924200018764e7,6.595342171821161e7,9.458539786739412e7,8.219612447821817e7,3.9589351412340805e7,8.104906588353236e6,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.6,-47.4,-13003.506293706294,-278936.1678321678,-2.3265602237762236e6,-9.980674506293707e6,-2.4597585633566435e7,-3.625286534265734e7,-3.158926858741259e7,-1.5017368167832168e7,-3.0034736335664336e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.9,935.4623043623044,42143.00606060606,619613.8922410923,4.308818503096903e6,1.6579424074592074e7,3.799234747545788e7,5.314447145174825e7,4.452023938088578e7,2.0523736496037297e7,4.0046315114219114e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-21.12561556090968,-3003.887892499657,-92251.03664962489,-1.130768793872794e6,-7.0588418527355e6,-2.5277949085518405e7,-5.502439582942548e7,-7.405439677762237e7,-6.019829813355272e7,-2.7090154341971755e7,-5.182464308898944e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.01393188854489164,68.33903526813744,6531.570529779818,166762.43296022862,1.8339761297278572e6,1.0656330035982594e7,3.6261947787464544e7,7.597502823061767e7,9.92596311986317e7,7.879468948121847e7,3.477706312550607e7,6.546270705977614e6,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.00008845643520566122,-0.04891640866873065,-148.871487026905,-11752.440015711842,-268684.86844919785,-2.74861261174986e6,-1.5174070609897017e7,-4.97030496228197e7,-1.0110656940201923e8,-1.2902029170934741e8,-1.0047113019907235e8,-4.364180470651743e7,-8.104906588353236e6,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.3333333333333333,6533.333333333333,222654.46091686093,2.778624556954157e6,1.7600566104118105e7,6.443886523574203e7,1.4451080095726496e8,2.0156645274156955e8,1.7053055852804974e8,8.009263022843823e7,1.6018526045687646e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-333,-23825.97413044472,-521880.007239819,-5.303014873879062e6,-2.974522501247772e7,-1.0042604004409708e8,-2.1250665797888386e8,-2.837202903655926e8,-2.319741694631016e8,-1.0600495177293295e8,-2.0729857235595778e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,5,1181.999610984131,54754.40911616763,980895.6130251585,8.852088141103067e6,4.5880486491885826e7,1.4637328059863028e8,2.967933223074854e8,3.832574936190464e8,3.0507729190651166e8,1.3638063970786697e8,2.6185082823910456e7,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-17.506265664160402,-2679.1916209005994,-101698.47428388605,-1.6209314727333898e6,-1.3536137961823797e7,-6.6368244028934255e7,-2.0306241420633388e8,-3.984997390155933e8,-5.012577425662849e8,-3.9049673738068247e8,-1.7144994706131846e8,-3.2419626353412945e7,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.000032049433045529426,39.39695786781532,4934.437997592661,166727.4017375813,2.460969788432378e6,1.945561056293358e7,9.154241300341979e7,2.712219032798776e8,5.1868580194167066e8,6.387408437835916e8,4.888559794904897e8,2.114323457831279e8,3.946737121285054e7,0,0,0,0,0,0,0,0,0,0,0}},{{0.6666666666666666,-65.33333333333333,-22842.255167055166,-610794.4205128205,-6.384583827195027e6,-3.4760849444599845e7,-1.1109825668873349e8,-2.199600400907537e8,-2.733161006545454e8,-2.075734000087024e8,-8.810189325128205e7,-1.6018526045687646e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,1318.9482608894373,73805.46920791626,1.3491923253530783e6,1.1743463056410257e7,5.730339427900727e7,1.7019760844996572e8,3.196860685490927e8,3.8177487075555557e8,2.810897971178939e8,1.1636988039073084e8,2.0729857235595778e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-23.999221968262216,-4237.817551557489,-161226.06704008067,-2.4533664806920635e6,-1.9149318022051428e7,-8.689604748579635e7,-2.450198244808148e8,-4.4258655082519025e8,-5.1267962114181876e8,-3.683579087309619e8,-1.4947318111982217e8,-2.6185082823910456e7,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.012531328320802004,77.76920671347916,9214.54894194213,291039.0946701733,3.9691610755076366e6,2.8811933867454045e7,1.2415265791155085e8,3.367590805724054e8,5.902267861563345e8,6.673985861532614e8,4.701430309700768e8,1.8765976023802492e8,3.2419626353412945e7,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.00006409886609105885,-0.04397182213846637,-169.53941844936594,-16578.624554339185,-468446.0812958478,-5.9377916416310035e6,-4.0923115567559e7,-1.696412196057358e8,-4.465302941617743e8,-7.640784094103152e8,-8.472253347457047e8,-5.871720202796443e8,-2.3116603138955316e8,-3.946737121285054e7,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.36666666666666664,10559.266666666666,434294.7652086476,6.574489355455003e6,5.10204267471091e7,2.3250794534097537e8,6.64917593632177e8,1.2277649331804926e9,1.4624266471674209e9,1.0850784646757164e9,4.560568591831071e8,8.291942894238311e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-443.3,-38255.76555264481,-1.0114779064221641e6,-1.2470381821703581e7,-8.571332767814559e7,-3.6026736682270384e8,-9.722698334254823e8,-1.7186034725420127e9,-1.9784568926620624e9,-1.4283144396604905e9,-5.869822733026594e8,-1.0474033129564182e8,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,5.5,1569.961476844449,87625.69572649573,1.8939060047826958e6,2.0732385792547733e7,1.3166046654165429e8,5.228893340210738e8,1.352134487330338e9,2.311593394202756e9,2.5906866318906407e9,1.8295657646295648e9,7.381699538930948e8,1.2967850541365178e8,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-19.255693581780537,-3554.4014008396293,-162426.07358635293,-3.1217844988459083e6,-3.16126055748029e7,-1.8987086397373933e8,-7.230764038384147e8,-1.809469262049569e9,-3.0129885415469217e9,-3.304452922123214e9,-2.2917775413786182e9,-9.105686358393375e8,-1.5786948485140216e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.00002397297591805601,43.33244851258581,6541.62812737135,265926.5903814425,4.731094982759278e6,4.5340842546994835e7,2.612763288477679e8,9.633487135585018e8,2.348932232111619e9,3.828700312931434e9,4.124825501869743e9,2.8177588722517457e9,1.105086393959815e9,1.894433818216826e8,0,0,0,0,0,0,0,0,0,0}},{{0.7333333333333333,-87.26666666666667,-37956.79708396179,-1.2378745500251383e6,-1.5839376732026143e7,-1.06514876608547e8,-4.268125048599296e8,-1.084457648638713e9,-1.7937872069180493e9,-1.927228914871795e9,-1.297559501340573e9,-4.9751657365429866e8,-8.291942894238311e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1.1,1798.4311052896192,122419.20256145643,2.723675026625387e6,2.8991573532491863e7,1.7462463657162815e8,6.49987059367659e8,1.5663069635696964e9,2.4893757054309864e9,2.5923743423070254e9,1.7021667641938875e9,6.393524389504802e8,1.0474033129564182e8,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-26.922953688897962,-5782.824037469239,-267059.29319830495,-4.940120546192026e6,-4.71164384933979e7,-2.6376188135589048e8,-9.316258847784076e8,-2.1581550271623797e9,-3.3260680887754226e9,-3.3792200077329974e9,-2.1743360218110523e9,-8.030092065999206e8,-1.2967850541365178e8,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.011387163561076604,87.37526544737474,12575.685027901907,481630.25459747476,7.978130346470807e6,7.071870426544951e7,3.7573583030587316e8,1.2761080113371363e9,2.867315117761134e9,4.312316120466565e9,4.2944103377974663e9,2.717461330888649e9,9.895033782650386e8,1.5786948485140216e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.00004794595183611202,-0.039938977879481315,-190.60366239225843,-22626.351358782555,-774685.3323404123,-1.1919507515836926e7,-1.0026023448105781e8,-5.122220252548393e8,-1.6875254790953407e9,-3.7006690484617324e9,-5.456117441460743e9,-5.344261556173933e9,-3.3347814351400876e9,-1.1998080848706565e9,-1.894433818216826e8,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.4,16358.4,798958.1317110135,1.4416265779644504e7,1.3432181467691442e8,7.434303361587911e8,2.626393853597904e9,6.143042747321345e9,9.628736625974842e9,1.0003891869771244e10,6.609352950962489e9,2.5137679510954037e9,4.189613251825673e8,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-575.6,-58965.4028822227,-1.851578588510492e6,-2.721337278865888e7,-2.246109735140044e8,-1.1467505597679276e9,-3.823590344956376e9,-8.562024604039784e9,-1.2971313192672047e10,-1.3113370455110611e10,-8.471497747887982e9,-3.1621604781636624e9,-5.187140216546071e8,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,6,2034.9461170318891,134714.58794018233,3.456620690885645e6,4.5099821439376034e7,3.4389086889063436e8,1.6588888433384745e9,5.299781267706849e9,1.1477806342984741e10,1.6928250138062456e10,1.6740562578044119e10,1.0617264990476751e10,3.9016315541846533e9,6.314779394056087e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-21.00521739130435,-4602.940974829003,-249320.1853983052,-5.686343886484196e6,-6.861345311881912e7,-4.947368541065237e8,-2.288195708861567e9,-7.073833639317552e9,-1.4920448268974035e10,-2.1533210358591484e10,-2.091140714317489e10,-1.3059753134332243e10,-4.736084545542065e9,-7.577735272867304e8,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.00001840349666436623,47.2682769726248,8466.622898449223,407758.88048708765,8.605464337728756e6,9.82448816901423e7,6.795288568188525e8,3.042463166214668e9,9.163485366790909e9,1.8918381774570183e10,2.681818912368284e10,2.565065895730421e10,1.5811505960561546e10,5.669268611552575e9,8.981019582657546e8,0,0,0,0,0,0,0,0,0}},{{0.8,-113.6,-60265.06342202689,-2.354631489783282e6,-3.6188869743358806e7,-2.9423519790246165e8,-1.4410252993176384e9,-4.548903494657308e9,-9.579486167460339e9,-1.3604387251458832e10,-1.2876514478657967e10,-7.78768167803846e9,-2.7232486136866875e9,-4.189613251825673e8,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1.2,2385.605764445393,194164.23206487356,5.166394900690916e6,6.6000166193341576e7,4.804116328378407e8,2.1848240357089143e9,6.539431397703931e9,1.3229596648755936e10,1.8207931242597847e10,1.6804843678929035e10,9.955319107909575e9,3.4215174889909663e9,5.187140216546071e8,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-29.892234063778012,-7677.3315851704865,-423195.2594681369,-9.353395630081888e6,-1.069960803506276e8,-7.235025322877827e8,-3.121175266299493e9,-8.978155548848114e9,-1.7608717027453564e10,-2.363934658860129e10,-2.1376840213692146e10,-1.2449678653930527e10,-4.217370523887458e9,-6.314779394056087e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.010434782608695653,97.14108009278826,16699.23576343072,762726.8199599064,1.5085840946795626e7,1.603035047267927e8,1.0283599406244267e9,4.2643450431212244e9,1.1894505365747297e10,2.2759909848626797e10,2.9943147410467827e10,2.6624309126235004e10,1.5285712870737015e10,5.114971309185431e9,7.577735272867304e8,0,0,0,0,0,0,0,0,0,0},{0,0,-0.00003680699332873246,-0.03658615136876006,-212.02777987521023,-30047.89230250005,-1.2262431435256745e6,-2.251696238611375e7,-2.2695429228591478e8,-1.3994804759815316e9,-5.627673799689461e9,-1.5316193575786037e10,-2.8723952643539726e10,-3.7161678742566864e10,-3.257762113150629e10,-1.8477746149163006e10,-6.118319590685452e9,-8.981019582657546e8,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.43333333333333335,24459.933333333334,1.39948310974227e6,2.9664356557875972e7,3.264766937613553e8,2.1527966210326242e9,9.174872352635342e9,2.63526819412877e10,5.20431450209414e10,7.080795804555496e10,6.521613086318431e10,3.8830607464800354e10,1.3486564563019785e10,2.0748560866184285e9,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-731.9,-87814.82467992813,-3.230537622359549e6,-5.578284651915676e7,-5.439079051073674e8,-3.308797228275689e9,-1.3310466229841167e10,-3.660457080636495e10,-6.987539486462099e10,-9.251142702281056e10,-8.331826353464978e10,-4.868864058693869e10,-1.6643954260047829e10,-2.5259117576224346e9,0,0,0,0,0,0,0,0,0,0,0},{0,0,6.5,2583.9516267845465,200215.24405318496,6.016616118581815e6,9.221263263214113e7,8.305750837148908e8,4.77383576908197e9,1.840021088352963e10,4.8939353849036934e10,9.094760672013042e10,1.177844008258246e11,1.0414198859975996e11,5.991259714028463e10,2.0207294060979477e10,3.0310941091469216e9,0,0,0,0,0,0,0,0,0,0},{0,0,0,-22.754814814814814,-5840.553656708876,-370080.7888040544,-9.881938796070835e6,-1.4003615801375034e8,-1.1925823709998772e9,-6.57143044116013e9,-2.4508050681444206e10,-6.348184946356478e10,-1.1543549489334048e11,-1.468037932397025e11,-1.27811573462042e11,-7.256032344847891e10,-2.4192621500783764e10,-3.5924078330630183e9,0,0,0,0,0,0,0,0,0},{0,0,0,0.00001443722583152868,51.20436448442445,10738.282242670764,604748.6713855794,1.493782547301189e7,2.0024139920202476e8,1.6355739069693673e9,8.723538381973366e9,3.1694134443060642e10,8.035017116564796e10,1.435061488294865e11,1.797385196878227e11,1.544460759994406e11,8.668740434615086e10,2.861538653232956e10,4.211788493935952e9,0,0,0,0,0,0,0,0}},{{0.8666666666666667,-144.73333333333332,-92115.75281787357,-4.24804535780092e6,-7.720394235745513e7,-7.459561839697425e8,-4.37688462512671e9,-1.675264548351156e10,-4.352291071881835e10,-7.819993218306961e10,-9.728719442636674e10,-8.229722149813876e10,-4.518485423006929e10,-1.4523992606328999e10,-2.0748560866184285e9,0,0,0,0,0,0,0,0,0,0,0,0},{0,1.3,3092.3493598562786,296618.58790897264,9.301895812628992e6,1.4042234137451884e8,1.2141829505065637e9,6.6136711412013e9,2.3997256897036137e10,5.988243978747334e10,1.0425835625270293e11,1.2646490694806935e11,1.0477864663163727e11,5.65370092624084e10,1.7906910138859047e10,2.5259117576224346e9,0,0,0,0,0,0,0,0,0,0,0},{0,0,-32.90325356909285,-9960.403453242889,-646128.1687916917,-1.6817577993811376e7,-2.272190859950398e8,-1.8244572021268456e9,-9.424164410318285e9,-3.2855536243018745e10,-7.94693874291209e10,-1.3493911256397678e11,-1.6035193404744455e11,-1.3059358460620116e11,-6.944791402530933e10,-2.1722841115552937e10,-3.0310941091469216e9,0,0,0,0,0,0,0,0,0,0},{0,0,0.00962962962962963,107.05323934367682,21670.89761846037,1.1640149545323383e6,2.7098524121223144e7,3.3995615473259085e8,2.5888012200866394e9,1.2850503978831438e10,4.34323908124913e10,1.0247227787993118e11,1.704876950572971e11,1.9917787189184882e11,1.5989240688923416e11,8.398305773017148e10,2.5988825417315273e10,3.5924078330630183e9,0,0,0,0,0,0,0,0,0},{0,0,-0.00002887445166305736,-0.033754233994114057,-233.78149683578326,-38998.16031069183,-1.8707910950575937e6,-4.041802774693853e7,-4.8079742512005436e8,-3.518362643932259e9,-1.6932117246290905e10,-5.582666431497299e10,-1.2906973332811464e11,-2.1113776786988696e11,-2.4316208621413403e11,-1.9281924836901074e11,-1.0020538726970265e11,-3.0721280779297535e10,-4.211788493935952e9,0,0,0,0,0,0,0,0}}},\n {{{0,-0.4666666666666667,35489.066666666666,2.3512673864932396e6,5.783459782554564e7,7.417629589224231e8,5.737794526335927e9,2.8958539764775536e10,9.980418605461873e10,2.4087583664136777e11,4.1111360367982263e11,4.938686168666484e11,4.0842050111710443e11,2.2130873014861176e11,7.072552921342816e10,1.0103647030489738e10,0,0,0,0,0,0,0,0,0,0,0},{0,0,-914.2,-127000.05298477177,-5.410357632421346e6,-1.084187847239819e8,-1.2320553672292948e9,-8.793144231643013e9,-4.189268519105384e10,-1.3824796054280862e11,-3.2253689193271765e11,-5.3569991047103217e11,-6.2930263262471e11,-5.107830750947536e11,-2.7241958305957956e11,-8.588099975916278e10,-1.2124376436587687e10,0,0,0,0,0,0,0,0,0,0},{0,0,7,3223.9763957964633,289078.1147930231,1.0056934701494202e7,1.7885319900918955e8,1.8774039305941489e9,1.2659112178824976e10,5.778636226399293e10,1.8443310408086594e11,4.188943611564575e11,6.80570218646967e11,7.848818851678533e11,6.271698565745526e11,3.30024403976469e11,1.028326742214289e11,1.4369631332252073e10,0,0,0,0,0,0,0,0,0},{0,0,0,-24.504469987228607,-7282.983796526446,-533794.5211804865,-1.6496528391199792e7,-2.7121016480072916e8,-2.69139348470133e9,-1.7396960801336163e10,-7.683642125146432e10,-2.388197884303981e11,-5.3073846409068134e11,-8.467207746541761e11,-9.615174725410426e11,-7.581688663491782e11,-3.943770868588842e11,-1.2164636179544427e11,-1.6847153975743809e10,0,0,0,0,0,0,0,0},{0,0,0,0.000011535450912536563,55.140655048819674,13385.468430331828,871673.8196526119,2.4913415664470177e7,3.873820740702931e8,3.686591045638684e9,2.3063912016993534e10,9.92281083489501e10,3.018436477318775e11,6.588209340059844e11,1.0351031513181844e12,1.160082623098246e12,9.043453403023804e11,4.6572230892101843e11,1.4238562392402832e11,1.9564436875057327e10,0,0,0,0,0,0,0}},{{0.9333333333333333,-181.06666666666666,-136335.83965314535,-7.327933577454448e6,-1.5542659822206742e8,-1.7593665355350988e9,-1.2169475752962036e10,-5.541107203717101e10,-1.734553628583209e11,-3.823252362645737e11,-5.987312993848872e11,-6.626663891105165e11,-5.067610463730009e11,-2.5477706093710904e11,-7.577735272867303e10,-1.0103647030489738e10,0,0,0,0,0,0,0,0,0,0,0},{0,1.4,3930.705969543536,438914.5575660432,1.6021909399733834e7,2.821148285309416e8,2.8568306121554456e9,1.834034705520107e10,7.915174003764148e10,2.3795742789826575e11,5.0818633097929156e11,7.758814204731168e11,8.410097103451432e11,6.320268394606305e11,3.130867623573008e11,9.194318797745662e10,1.2124376436587687e10,0,0,0,0,0,0,0,0,0,0},{0,0,-35.952791592926204,-12671.688278689997,-955744.668589088,-2.8937820175670214e7,-4.558361881243446e8,-4.2852364908962717e9,-2.6082358434683636e10,-1.0813493285251514e11,-3.150596210807534e11,-6.56127990059077e11,-9.812778081103854e11,-1.045448978125867e12,-7.742480850836678e11,-3.7874643521238617e11,-1.1001748988755493e11,-1.4369631332252073e10,0,0,0,0,0,0,0,0,0},{0,0,0.008939974457215836,117.10041553054182,27577.685460833156,1.7212957303475374e6,4.6594371675881036e7,6.812809157261431e8,6.07243220002907e9,3.551011349027069e10,1.4269874524439893e11,4.054913031711275e11,8.273111760165848e11,1.2162825061370105e12,1.2771474457642676e12,9.341281376272004e11,4.520414263861544e11,1.3006993878331618e11,1.6847153975743809e10,0,0,0,0,0,0,0,0},{0,0,-0.000023070901825073126,-0.031330284678449304,-255.83925591764077,-49634.48688799174,-2.765829691982738e6,-6.945891513716699e7,-9.627476140344408e8,-8.244250951607839e9,-4.673088800021546e10,-1.8316187642444714e11,-5.0994384612902716e11,-1.022841420534557e12,-1.4821974712563923e12,-1.5372206353757112e12,-1.112343356234171e12,-5.3324678896895935e11,-1.5216784236155698e11,-1.9564436875057327e10,0,0,0,0,0,0,0}}},\n {{{0,-0.5,50175,3.8110518751832955e6,1.076462696229007e8,1.5907243629794188e9,1.4251013900556408e10,8.39147841034878e10,3.408264309321651e11,9.827003704330287e11,2.041566817044961e12,3.065320744754241e12,3.2952209252682485e12,2.4722631961132183e12,1.2290545345785562e12,3.6373129309763055e11,4.8497505746350746e10,0,0,0,0,0,0,0,0,0,0},{0,0,-1124.5,-179081.18687280125,-8.746490101655236e6,-2.0128246173478386e8,-2.6356156253879805e9,-2.1787106957386932e10,-1.2111135286756642e11,-4.7103679933522406e11,-1.312930805324278e12,-2.654465838545084e12,-3.897567876302638e12,-4.1124050502739814e12,-3.036874638157322e12,-1.489333703666579e12,-4.355794497588909e11,-5.747852532900829e10,0,0,0,0,0,0,0,0,0},{0,0,7.5,3962.019044757294,407072.920718967,1.6232431369128535e7,3.3147987895103717e8,4.0090734366763234e9,3.13099625273733e10,1.6676035684980087e11,6.272725393185522e11,1.702120269314377e12,3.366309892830835e12,4.852504880352651e12,5.040497006172991e12,3.6725169792886714e12,1.7801426017692478e12,5.153247098462812e11,6.7388615902975235e10,0,0,0,0,0,0,0,0},{0,0,0,-26.25417130144605,-8945.976556539295,-751050.1272782461,-2.6597813264939196e7,-5.0203783424558866e8,-5.739732894683955e9,-4.2968855344066925e10,-2.214204398894586e11,-8.110701607930319e11,-2.1534160242155322e12,-4.1819214920925874e12,-5.935635976892781e12,-6.084107901642862e12,-4.381942913426506e12,-2.1025895514418992e12,-6.03236803647601e11,-7.825774750022931e10,0,0,0,0,0,0,0},{0,0,0,9.363190675760198e-6,59.07710774785302,16437.045563842872,1.2257532331766458e6,4.013768184797409e7,7.164271778242302e8,7.854094148649289e9,5.6903267984881676e10,2.856175070922272e11,1.0238847552212717e12,2.6698130647352876e12,5.105908405067799e12,7.152238271875518e12,7.247671528966757e12,5.167805995087918e12,2.457745328571359e12,6.99576833714171e11,9.011498196996101e10,0,0,0,0,0,0}},{{1,-223,-196278.75036659127,-1.2163480027372148e7,-2.9773689168561506e8,-3.901236201224221e9,-3.1389389329419144e10,-1.6743088681163474e11,-6.199947751483894e11,-1.6382802519391409e12,-3.132920728260574e12,-4.3465612386153613e12,-4.3323760798965054e12,-3.0231374871104106e12,-1.4018268987999307e12,-3.8798004597080597e11,-4.8497505746350746e10,0,0,0,0,0,0,0,0,0,0},{0,1.5,4912.873745602497,631897.2803378738,2.656490166119503e7,5.395585963900452e8,6.322823026301706e9,4.720796893278593e10,2.3863565691698135e11,8.485721474191187e11,2.172352790028894e12,4.049809894234472e12,5.50235200650019e12,5.38931258216232e12,3.7052589549104136e12,1.6963462050468354e12,4.643187124233951e11,5.747852532900829e10,0,0,0,0,0,0,0,0,0},{0,0,-39.038089514588414,-15851.374766259272,-1.3756719102298168e6,-4.7943245278919205e7,-8.708307769571735e8,-9.47113944257027e9,-6.703028125916526e10,-3.254547834230943e11,-1.1214448357099817e12,-2.7992820802386875e12,-5.111448386239666e12,-6.825434396193574e12,-6.587638039199097e12,-4.472282579818021e12,-2.0251695912105806e12,-5.4901901779776886e11,-6.7388615902975235e10,0,0,0,0,0,0,0,0},{0,0,0.008342602892102336,127.27291285612064,34507.8303268765,2.4771144537147037e6,7.715353799846987e7,1.3004413372683635e9,1.3407053636109262e10,9.11467268081413e10,4.288886516771684e11,1.4411578341601123e12,3.5239100414919814e12,6.3247528225204e12,8.32319236966487e12,7.933155759027074e12,5.327467452291677e12,2.3895346256094067e12,6.423656773977156e11,7.825774750022931e10,0,0,0,0,0,0,0},{0,0,-0.000018726381351520396,-0.029231881289723337,-278.179190366686,-62116.434369362025,-3.979701958366857e6,-1.1496637205380797e8,-1.8365386839217353e9,-1.8187049742974773e10,-1.198292372617549e11,-5.49880612073813e11,-1.810124500260231e12,-4.3508491817515527e12,-7.696337232599344e12,-1.000270962164139e13,-9.431448443943848e12,-6.273956282611874e12,-2.7906371863090767e12,-7.446343246991516e11,-9.011498196996101e10,0,0,0,0,0,0}}},\n {{{0,-0.5333333333333333,69358.93333333333,5.9871611113645565e6,1.924439018268767e8,3.2448156139755497e9,3.330669577632881e10,2.2601945627174777e11,1.0662940872799772e12,3.608672101565586e12,8.923743251707213e12,1.6254636226822168e13,2.1772292854629945e13,2.117283786317375e13,1.453488209257297e13,6.674693753831088e12,1.8393128105282654e12,2.2991410131603317e11,0,0,0,0,0,0,0,0,0},{0,0,-1364.8,-247010.3969398599,-1.3710914253764993e7,-3.5907586422209996e8,-5.365095399350815e9,-5.081736342983615e10,-3.255698706535722e11,-1.470867065526843e12,-4.812414875990048e12,-1.1581712843876643e13,-2.0631072691303906e13,-2.7124046546863812e13,-2.5963317717947027e13,-1.758285432472868e13,-7.979604930158186e12,-2.1762558900431414e12,-2.6955446361190094e11,0,0,0,0,0,0,0,0},{0,0,8,4805.078378923909,560851.6328710681,2.5412128545875855e7,5.904978119526415e8,8.148894279740852e9,7.291974445465744e10,4.476097728118765e11,1.955793734114073e12,6.229626820644424e12,1.4665713663876832e13,2.56478138439078e13,3.319636806334255e13,3.135144116117232e13,2.098522418302309e13,9.426637994127908e12,2.547724446396354e12,3.1303099000091724e11,0,0,0,0,0,0,0},{0,0,0,-28.003910068426197,-10845.277747543556,-1.0340539156313771e6,-4.160211107138518e7,-8.934162310823445e8,-1.1653781015963501e10,-9.995712648139485e10,-5.936175304669795e11,-2.525790561524574e12,-7.87163260522547e12,-1.819637446847215e13,-3.1333388101515715e13,-4.001900002443862e13,-3.736019485586116e13,-2.4754756721440023e13,-1.1020607767604893e13,-2.954822829857143e12,-3.6045992787984406e11,0,0,0,0,0,0},{0,0,0,7.704568327482677e-6,63.01369198098898,19921.879208008424,1.6868344786841804e6,6.273964748932823e7,1.273959927266718e9,1.593305010069684e10,1.3225038205179854e11,7.649853076246484e11,3.185325437278451e12,9.749212126813445e12,2.219341094639236e13,3.771515415332075e13,4.76205488262829e13,4.401174323403532e13,2.890378760514151e13,1.2766176186368576e13,3.3986221771528154e12,4.1195420329125037e11,0,0,0,0,0}},{{1.0666666666666667,-270.93333333333334,-275873.1560624472,-1.9526615598641343e7,-5.463067917939428e8,-8.201340252473525e9,-7.590059501108307e10,-4.682825773172421e11,-2.0210768151063833e12,-6.288523857290183e12,-1.4356521317251836e13,-2.4229695665058094e13,-3.016739913942077e13,-2.7348748241932996e13,-1.7548912264512844e13,-7.551241265098464e12,-1.9542698611862817e12,-2.2991410131603317e11,0,0,0,0,0,0,0,0,0},{0,1.6,6051.193879719814,888285.5021747415,4.261058156357549e7,9.887753453648256e8,1.327213854827666e10,1.1396014858065186e11,6.662406988329823e11,2.7610060006323486e12,8.322298591918423e12,1.852086668895058e13,3.0609487847613902e13,3.744833590963831e13,3.344798330425991e13,2.11898795413883e13,9.017191413252525e12,2.311033121849092e12,2.6955446361190094e11,0,0,0,0,0,0,0,0},{0,0,-42.156757847819044,-19540.15290525303,-1.9336304731780519e6,-7.685712819702701e7,-1.594439517783882e9,-1.9858807743317722e10,-1.6160641862808392e11,-9.073615412262385e11,-3.643384657047884e12,-1.0707067507058748e13,-2.333725913033687e13,-3.790443110434288e13,-4.569379747197401e13,-4.029844176053195e13,-2.5250191501700312e13,-1.0641806906700912e13,-2.7042399413968125e12,-3.1303099000091724e11,0,0,0,0,0,0,0},{0,0,0.007820136852394917,137.56233770685833,42550.691954386595,3.4813989145593178e6,1.2363151215452614e8,2.3794672470258155e9,2.8087829807876396e10,2.19531539097911e11,1.1943955071569575e12,4.67634681344435e12,1.34610069080083e13,2.883661986591e13,4.615458622396285e13,5.4943021866992516e13,4.792868725397259e13,2.9744824442882992e13,1.2430432946055994e13,3.135052793797065e12,3.6045992787984406e11,0,0,0,0,0,0},{0,0,-0.000015409136654965353,-0.027397444972528398,-300.78237626127407,-76605.63532406824,-5.592621537223804e6,-1.841644469419035e8,-3.3586851599070764e9,-3.807661046434377e10,-2.883838211797314e11,-1.5299369967994255e12,-5.867608218199371e12,-1.6601437441364713e13,-3.5048526877146164e13,-5.5398397289151914e13,-6.523376765866994e13,-5.636627223479088e13,-3.46882547466682e13,-1.4388245861827873e13,-3.604599278798441e12,-4.1195420329125037e11,0,0,0,0,0}}},\n {{{0,-0.5666666666666667,94002.06666666667,9.151311935305258e6,3.320851910459127e8,6.33521032186008e9,7.382275924950447e10,5.713935821593523e11,3.094041226242078e12,1.2118112094805514e13,3.5055579190329652e13,7.577080308439667e13,1.2277365554920727e14,1.4836959871768953e14,1.316939805223555e14,8.331707351347927e13,3.554854783594292e13,9.164851762804633e12,1.0782178544476038e12,0,0,0,0,0,0,0,0},{0,0,-1637.1,-334159.9205226142,-2.0918744937359024e7,-6.185177808929194e8,-1.0456566421124214e10,-1.1244319702124878e11,-8.217073662582078e11,-4.261136422965968e12,-1.613507388311211e13,-4.54274671317859e13,-9.60274321618125e13,-1.5272694341908484e14,-1.8167523305110694e14,-1.5908213959048006e14,-9.946452714264984e13,-4.200158523126891e13,-1.0730006712809219e13,-1.252123960003669e12,0,0,0,0,0,0,0},{0,0,8.5,5760.15335336423,758011.4560133434,3.872804138514868e7,1.0159241892397866e9,1.586238004713476e10,1.611446504457956e11,1.1282876946995315e12,5.658785050777512e12,2.0860295618072766e13,5.745164785582471e13,1.1922862068135155e14,1.8668579152657497e14,2.1910636544081044e14,1.8963108518772156e14,1.1735697816416962e14,4.9110491347309305e13,1.2445353299430406e13,1.4418397115193762e12,0,0,0,0,0,0},{0,0,0,-29.753679653679654,-12996.633706471774,-1.396745220816542e6,-6.3353746792567894e7,-1.5357532178764133e9,-2.2663668846309917e10,-2.2067759802151013e11,-1.4948161492516946e12,-7.300452192754711e12,-2.633115093534921e13,-7.12076759521055e13,-1.4550478401170806e14,-2.2481450876051734e14,-2.608206421034274e14,-2.2345389682757944e14,-1.3705312915212823e14,-5.689609265768836e13,-1.4315408564370951e13,-1.6478168131650015e12,0,0,0,0,0},{0,0,0,6.416135448393513e-6,66.95038440199731,23868.836113681442,2.2775814000040796e6,9.549105192520149e7,2.1884705815436573e9,3.0963237347720776e10,2.91743710502673e11,1.9247605684553428e12,9.198896562512525e12,3.258322450023937e13,8.677160313048934e13,1.749810194392509e14,2.6727116291968612e14,3.0697010372751906e14,2.6065987367419022e14,1.5860983054210656e14,6.537859338635338e13,1.6344561363015016e13,1.8704947608900017e12,0,0,0,0}},{{1.1333333333333333,-325.26666666666665,-379672.3372771824,-3.044289317860951e7,-9.653190181565726e8,-1.645654568518213e10,-1.7350035488585364e11,-1.224974862145457e12,-6.087121650396307e12,-2.198279146517062e13,-5.886931627391679e13,-1.1819629684730314e14,-1.7844037358940066e14,-2.014677026353088e14,-1.674879308472654e14,-9.947402064977933e13,-3.992880786963631e13,-9.703960690028434e12,-1.0782178544476038e12,0,0,0,0,0,0,0,0},{0,1.7,7358.141045228405,1.2228343356326213e6,6.639078335866816e7,1.7454206071277142e9,2.6599212141387142e10,2.601475592017887e11,1.740271415261319e12,8.302886018750533e12,2.904578302199949e13,7.582019351190167e13,1.490656602100751e14,2.211250836544858e14,2.4596589754150544e14,2.018771799198576e14,1.185708301208829e14,4.713181534517283e13,1.1356068692811053e13,1.252123960003669e12,0,0,0,0,0,0,0},{0,0,-45.30670672845925,-23779.18039507422,-2.661791803943833e6,-1.1969660677337208e8,-2.812574307228695e9,-3.9764345032168434e10,-3.685338752285082e11,-2.367394455421027e12,-1.0942906507013615e13,-3.73202401876562e13,-9.540709750646728e13,-1.843299072761322e14,-2.694183018006003e14,-2.9589668840921594e14,-2.401899624280804e14,-1.3971389256713602e14,-5.5062823051114625e13,-1.3166273155190094e13,-1.4418397115193762e12,0,0,0,0,0,0},{0,0,0.00735930735930736,147.96135233748615,51796.68308694178,4.792105916700205e6,1.9247997245947763e8,4.195150944550882e9,5.6203346619271835e10,5.002227932450558e11,3.113437647355672e12,1.403128377992629e13,4.686853664732211e13,1.1775423667475845e14,2.241800875868455e14,3.235464771315656e14,3.5146497769033325e14,2.825652031993201e14,1.6297151920138706e14,6.37448312874054e13,1.5139316970953451e13,1.6478168131650015e12,0,0,0,0,0},{0,0,-0.000012832270896787026,-0.025780032231645135,-323.6322744648659,-93265.65360101484,-7.69771425123931e6,-2.866519541825688e8,-5.919173280043663e9,-7.614963399570706e10,-6.566791772809753e11,-3.985094039738327e12,-1.7590885222630846e13,-5.775012578906397e13,-1.429804558962491e14,-2.6879959044347166e14,-3.8372757967297875e14,-4.1286846760141056e14,-3.291372259583687e14,-1.8840988086355138e14,-7.320015630019402e13,-1.7279808743460016e13,-1.8704947608900017e12,0,0,0,0}}},\n {{{0,-0.6,125193.6,1.3652102441336416e7,5.554014600143847e8,1.1899676153316288e10,1.56165088407177e11,1.366540496131952e12,8.40861783023701e12,3.767209777990931e13,1.2572771066140053e14,3.1699683846911475e14,6.078847468910346e14,8.864741332485448e14,9.755540111565658e14,7.962880116350478e14,4.6711589143195694e14,1.8610613034936884e14,4.507646256013208e13,5.008495840014676e12,0,0,0,0,0,0,0},{0,0,-1943.4,-444350.0575188254,-3.1158621445006426e7,-1.0328718631043336e9,-1.9611734199856762e10,-2.3751855080120044e11,-1.9624234636460256e12,-1.1564556559203219e13,-5.009287309334422e13,-1.6271440389198622e14,-4.0123038305561994e14,-7.55244323016712e14,-1.0841303144905668e15,-1.1770068866194732e15,-9.494737901060278e14,-5.512548272291732e14,-2.1763242435124375e14,-5.228566111772896e13,-5.767358846077505e12,0,0,0,0,0,0},{0,0,9,6834.2430464192685,1.0071578139815058e6,5.7630935107687674e7,1.6947655536972034e9,2.971887868603432e10,3.400242318221734e11,2.691676008673227e12,1.5341040964447729e13,6.469277318651995e13,2.0556218578916944e14,4.9764013132721725e14,9.221943510366396e14,1.306119324762518e15,1.4015595146061295e15,1.1191029056445291e15,6.438857748567351e14,2.5216204623961334e14,6.0145313680522555e13,6.591267252660006e12,0,0,0,0,0},{0,0,0,-31.503474903474903,-15415.791203007979,-1.8549118704564322e6,-9.421570811376691e7,-2.5600544123712883e9,-4.242743900283097e10,-4.6525101895250854e11,-3.5629896100471016e12,-1.977415609780622e13,-8.158625551552306e13,-2.545518754366963e14,-6.067625924438578e14,-1.1095340952535998e15,-1.553365741029738e15,-1.650033451843795e15,-1.3057251452334125e15,-7.452766846539458e14,-2.8978473074627556e14,-6.867387907839006e13,-7.481979043560007e12,0,0,0,0},{0,0,0,5.4000054000054e-6,70.88716688716688,28306.784007021753,3.0236617450400395e6,1.4194238784983155e8,3.6460856395006375e9,5.792852759286986e10,6.146661187977393e11,4.584553043233062e12,2.4898101684512574e13,1.008823224117668e14,3.099519834507942e14,7.291125023795298e14,1.3180326124569462e15,1.826761435393357e15,1.9232229378190795e15,1.5098730462049652e15,8.556875473106161e14,3.305876811925353e14,7.788932029962469e13,8.4412071260677e12,0,0,0}},{{1.2,-386.4,-512904.0826728312,-4.6250508101108156e7,-1.6498943779538748e9,-3.1693433546401592e10,-3.774969633261728e11,-3.0222573837808267e12,-1.7114252146731506e13,-7.088860314805319e13,-2.195652433185797e14,-5.154436720771549e14,-9.229759888796809e14,-1.260086991646628e15,-1.3012905395960398e15,-9.989055197138905e14,-5.52186666361618e14,-2.0770526865943212e14,-4.758071048013942e13,-5.008495840014676e12,0,0,0,0,0,0,0},{0,1.8,8846.315037650835,1.652499890670798e6,1.0081815236953616e8,2.980852295984091e9,5.117658296341241e10,5.653923499515992e11,4.2884376326036885e12,2.3314343858552824e13,9.354089348013502e13,2.8240048108547756e14,6.491502225984054e14,1.142121460503862e15,1.5361570189811522e15,1.5661512339351905e15,1.188884318540835e15,6.508081678370406e14,2.4269387512646872e14,5.516934054076771e13,5.767358846077505e12,0,0,0,0,0,0},{0,0,-48.486092838536685,-28610.053294245357,-3.5971398670573817e6,-1.8170450901651797e8,-4.800628986511418e9,-7.645048609922267e10,-8.002747183060198e11,-5.828318542596038e12,-3.0696178946402035e13,-1.2005854798795881e14,-3.549510824718861e14,-8.017723301469554e14,-1.3898631564766085e15,-1.8456808435841622e15,-1.8609896441157935e15,-1.3990467910248515e15,-7.593074829663808e14,-2.8099884047000084e14,-6.3440947306852555e13,-6.591267252660006e12,0,0,0,0,0},{0,0,0.0069498069498069494,158.46348709704054,62337.20331735644,6.475875533245151e6,2.921192897693864e8,7.157442458806223e9,1.0799555655084192e11,1.0855125833750288e12,7.659196496678287e12,3.932659690536154e13,1.5063960727715928e14,4.376723566398628e14,9.741274125347245e14,1.6673482941700252e15,2.189911586818609e15,2.1868594523613995e15,1.630061509290193e15,8.779941332352192e14,3.227187992148031e14,7.241486860017006e13,7.481979043560007e12,0,0,0,0},{0,0,-0.0000108000108000108,-0.024343224343224345,-346.71430558980086,-112261.86290506809,-1.0402072220276337e7,-4.349568507848248e8,-1.009552791463289e10,-1.4625792737830328e11,-1.4242626335574956e12,-9.797394622514166e12,-4.9269031116791766e13,-1.8547288277928522e14,-5.3100005187471706e14,-1.167000294197266e15,-1.9756813909489115e15,-2.5700586158413735e15,-2.544779679266689e15,-1.882576246583223e15,-1.007168503518773e15,-3.6794961500620994e14,-8.210992386265853e13,-8.4412071260677e12,0,0,0}}},\n {{{0,-0.6333333333333333,164158.73333333334,1.9930293177442875e7,9.033522147628825e8,2.159562943718983e10,3.1695435436427655e11,3.1117616133093535e12,2.1572888288816043e13,1.09484309701826e14,4.1677133450584825e14,1.2090804894217778e15,2.6979173704553415e15,4.645555959846248e15,6.155935299753043e15,6.217286496234509e15,4.696578395452082e15,2.568066717852626e15,9.596044046707916e14,2.191596361509452e14,2.306943538431002e13,0,0,0,0,0,0},{0,0,-2285.7,-581877.1667007137,-4.542712920857985e7,-1.6777496857464986e9,-3.554596419337812e10,-4.8146941932528937e11,-4.463236488322537e12,-2.963468073013338e13,-1.4541483616136725e14,-5.387724333982664e14,-1.528682077106105e15,-3.3483222279232085e15,-5.675362800076585e15,-7.419408932698538e15,-7.405721111493924e15,-5.536919691805194e15,-3.000077941416619e15,-1.1119673832339076e15,-2.5211597241424522e14,-2.6365069010640023e13,0,0,0,0,0},{0,0,9.5,8034.346639088207,1.3179673367617e6,8.39534763120524e7,2.750469750609688e9,5.381559497441904e10,6.886135692098751e11,6.116068398456957e12,3.927525531830635e13,1.87621875146192e14,6.800177457846064e14,1.8942591437198682e15,4.0847532803221355e15,6.831268665098625e15,8.82695090814349e15,8.720982640500069e15,6.461561639299811e15,3.4729854777955795e15,1.277987710634628e15,2.8787805081888025e14,2.9927916174240027e13,0,0,0,0},{0,0,0,-33.253291753291755,-18118.497367092852,-2.4263056561244098e6,-1.371723164151261e8,-4.1521251582654886e9,-7.677555171735455e10,-9.415385502549863e11,-8.089827546033466e12,-5.058607217578998e13,-2.364337668337472e14,-8.414253645683544e14,-2.307828334679184e15,-4.910703691264801e15,-8.118041289783834e15,-1.0383658748433438e16,-1.0167288912591014e16,-7.473149461470064e15,-3.9880042421706445e15,-1.4580506661137562e15,-3.2652123928561875e14,-3.37648285042708e13,0,0,0},{0,0,0,4.587809465858246e-6,74.82402515085442,33264.59142595566,3.9539347999028377e6,2.0657696267892247e8,5.910713251530081e9,1.0476957462492262e11,1.2431924580143315e12,1.0402955953492928e13,6.365382991017692e13,2.9216326172935256e14,1.0238733031895974e15,2.7713247980029775e15,5.829535183879195e15,9.540280533475378e15,1.209446128636118e16,1.1748726073620186e16,8.574250203286003e15,4.5463150567317e15,1.6525312353663298e15,3.6811898393680606e14,3.788249051698675e13,0,0}},{{1.2666666666666666,-454.73333333333335,-681521.0882190833,-6.866812258629e7,-2.7377423472293215e9,-5.885373059155742e10,-7.861999036201415e11,-7.081109305222594e12,-4.529513317348146e13,-2.1305179026514706e14,-7.544247442837826e14,-2.042292971648917e15,-4.264112494563583e15,-6.887192122673396e15,-8.579721224269423e15,-8.162941954518764e15,-5.819981799016939e15,-3.0089392479769985e15,-1.064858703611706e15,-2.3069435384310022e14,-2.306943538431002e13,0,0,0,0,0,0},{0,1.9,10528.43340142741,2.1966056588859563e6,1.496340808486337e8,4.94310202090654e9,9.495646973148334e10,1.1764390850983005e12,1.0037702723170137e13,6.163907586873927e13,2.808207197238787e14,9.692149606108888e14,2.56903911487428e15,5.27020715794106e15,8.385800766327233e15,1.0313148662287174e16,9.703156383423962e15,6.850671684428315e15,3.5112616134256495e15,1.2330819190015352e15,2.6529850691956525e14,2.6365069010640023e13,0,0,0,0,0},{0,0,-51.693278176413344,-34074.78014180465,-4.781836743440356e6,-2.6961591339264446e8,-7.957160824871687e9,-1.417663970015018e11,-1.6639977875868992e12,-1.3631292963271166e13,-8.108623737250361e13,-3.6010324340970756e14,-1.2170534965459422e15,-3.1699041795772295e15,-6.406817661291515e15,-1.006485817543921e16,-1.2241435673077942e16,-1.1405817498928164e16,-7.983798180042419e15,-4.0608079407256885e15,-1.4163152517613982e15,-3.0284200890600025e14,-2.9927916174240027e13,0,0,0,0},{0,0,0.006583506583506584,169.06299475396784,74264.58077013028,8.60869260141037e6,4.3336689596040046e8,1.1859561376200863e10,2.0016987814094357e11,2.255834083018215e12,1.7902005880230887e13,1.0381148852085344e14,4.5148680237416356e14,1.499482007722108e15,3.8480749449814715e15,7.679151287997549e15,1.1931083759742532e16,1.4371388164888972e16,1.3276270216445754e16,9.222548421515924e15,4.658972295533745e15,1.614980380412015e15,3.434036535377542e14,3.37648285042708e13,0,0,0},{0,0,-9.175618931716493e-6,-0.023058330375403547,-370.01552049520996,-133761.33977549043,-1.3827819745792182e7,-6.451738118427956e8,-1.6723378636699493e10,-2.709901673195793e11,-2.9584696444771226e12,-2.288771647820421e13,-1.2998082039545089e14,-5.555315701855969e14,-1.8179762075703875e15,-4.606611728235598e15,-9.092222501474912e15,-1.3990963605707124e16,-1.6709589472590812e16,-1.5319694204447672e16,-1.0570016078374418e16,-5.307109848412682e15,-1.8294877603627978e15,-3.8706022919529944e14,-3.788249051698675e13,0,0}}},\n {{{0,-0.6666666666666666,212266.66666666666,2.853599258035219e7,1.4330114863456995e9,3.800258146404937e10,6.199274770948887e11,6.782860407787912e12,5.259010470068523e13,2.998352445442762e14,1.289474302995765e15,4.256253873967506e15,1.0902678302444068e16,2.1797926698136784e16,3.403776778865586e16,4.131592071162812e16,3.85489253454479e16,2.709770607257666e16,1.3874444112447926e16,4.881180309397506e15,1.054602760425601e15,1.054602760425601e14,0,0,0,0,0},{0,0,-2666,-751541.6624389548,-6.496750631920008e7,-2.6584414136368732e9,-6.248207318933823e10,-9.406826677470544e11,-9.718503789838549e12,-7.216907849489138e13,-3.978378205026157e14,-1.6653179634893145e15,-5.376204754295016e15,-1.3518436707709178e16,-2.6605608406951144e16,-4.0986885639172104e16,-4.9169772065455784e16,-4.540651511838149e16,-3.162877001568124e16,-1.6063591016532404e16,-5.610415428520925e15,-1.204242341296801e15,-1.1971166469696011e14,0,0,0,0},{0,0,10,9367.463398770313,1.701250849010266e6,1.1998124014091475e8,4.354863213182676e9,9.45208118958657e10,1.344305113466995e12,1.3306614989260633e13,9.556877985629884e13,5.12895265809024e14,2.1002083731150322e15,6.656579614385937e15,1.6478625548324368e16,3.1999232770493936e16,4.8724507460816184e16,5.785749736908936e16,5.294839315410694e16,3.65864067552318e16,1.844784707627131e16,6.401367498840126e15,1.365940789490955e15,1.350593140170832e14,0,0,0},{0,0,0,-35.00312695434646,-21120.499631781146,-3.13075780749621e6,-1.9594466391609663e8,-6.57050375487538e9,-1.3476651743799847e11,-1.8369043800571548e12,-1.7589435314077154e13,-1.2300981206774544e14,-6.45896597792679e14,-2.5969519006174225e15,-8.1043872896729e15,-1.979717247928791e16,-3.800085757405471e16,-5.727840617892459e16,-6.7406697825393336e16,-6.119592653276693e16,-4.198322456673902e16,-2.1032687680075924e16,-7.255685440992997e15,-1.5400055927557658e15,-1.51529962067947e14,0,0},{0,0,0,3.930803703917714e-6,78.76094777966587,38771.1275913068,5.100639029001081e6,2.949841095687273e8,9.349478097378347e9,1.8381938202018082e11,2.42419630975418e12,2.2606778024802125e13,1.547013295439825e14,7.976887641336864e14,3.1582328358075825e15,9.726354425919532e15,2.3487483127377148e16,4.463176708335417e16,6.667543951844797e16,7.784411667165024e16,7.0169853688251656e16,4.78314795584771e16,2.3823442630743476e16,8.174976337050191e15,1.7267367770533495e15,1.6914972509910362e14,0}},{{1.3333333333333333,-530.6666666666666,-892251.827371045,-9.987215970701566e7,-4.424126639899304e9,-1.0578643572033942e11,-1.5747287228400437e12,-1.5845717567057562e13,-1.1362682509291195e14,-6.01771280857198e14,-2.4125671241445005e15,-7.446002113664234e15,-1.7881405459744606e16,-3.35951258854644e16,-4.9401354974251736e16,-5.657957303847233e16,-4.9900402465368104e16,-3.3212859965007824e16,-1.612718315044587e16,-5.388707887852326e15,-1.107332898446881e15,-1.054602760425601e14,0,0,0,0,0},{0,2,12417.32487790964,2.877010547668333e6,2.1757735630149266e8,7.983815399399566e9,1.7056499979904105e11,2.354551408251009e12,2.244295896408418e13,1.5448897973201038e14,7.924454954576368e14,3.09644241377513e15,9.357141993333924e15,2.2077909573687176e16,4.086271515883938e16,5.931957879239599e16,6.7183171140618856e16,5.867380519673225e16,3.8715022071894504e16,1.8654226260365056e16,6.190090662038646e15,1.2640981736452812e15,1.1971166469696011e14,0,0,0,0},{0,0,-54.92679754062404,-40215.75896837982,-6.263591942903851e6,-3.919620881744125e8,-1.2847160247073557e10,-2.5452055340858438e11,-3.3284003694315527e12,-3.045760371601915e13,-2.0308431931952872e14,-1.0153938929148701e15,-3.8851031201166525e15,-1.1535964059895936e16,-2.6816071946032308e16,-4.9000640659284456e16,-7.0346216741010216e16,-7.889814086638738e16,-6.831336974290147e16,-4.473081072704507e16,-2.1405078738350924e16,-7.0590142722074e15,-1.4334704464994968e15,-1.350593140170832e14,0,0,0},{0,0,0.006253908692933083,179.75473573239677,87672.02030488498,1.127655502867755e7,6.299257811345832e8,1.9142375540966686e10,3.592377142778432e11,4.510116251939719e12,3.997869384169198e13,2.598472460491622e14,1.2722572790529712e15,4.783417939546741e15,1.3993927307709768e16,3.2117401194767464e16,5.8041145938566104e16,8.251977130024504e16,9.176083681396456e16,7.884587952758733e16,5.127529010535035e16,2.4385985285874588e16,7.99727636948314e15,1.6157705737897392e15,1.51529962067947e14,0,0},{0,0,-7.861607407835427e-6,-0.021902438238229502,-393.52434085950074,-157932.76854200763,-1.8113190266049244e7,-9.376913624338514e8,-2.698711715217962e10,-4.86188476940676e11,-5.912673590075985e12,-5.109028982891983e13,-3.251901708214681e14,-1.5646005583864498e15,-5.796048104691107e15,-1.6742037879323554e16,-3.800261305735843e16,-6.801536029880263e16,-9.587749223709138e16,-1.0580649570083427e17,-9.029733700258528e16,-5.8363106600548536e16,-2.7603025440299108e16,-9.006629152120784e15,-1.8113116396029015e15,-1.6914972509910362e14,0}}}\n };\n\n/* Compute the singular field at the point x for the particle at xp */\nvoid effsource_PhiS(struct coordinate * x, double * PhiS)\n{\n\n double A, alpha, rho2;\n\n double r = x->r;\n double theta = x->theta;\n double phi = x->phi;\n double rp = xp.r;\n double thetap = xp.theta;\n double phip = xp.phi;\n\n double dr = r - rp;\n double dtheta = theta - thetap;\n double dphi = phi - phip;\n\n double dr2 = dr*dr;\n double dr3 = dr2*dr;\n double dr4 = dr2*dr2;\n double dr6 = dr3*dr3;\n double dr8 = dr4*dr4;\n\n double dtheta2 = dtheta*dtheta;\n double dtheta4 = dtheta2*dtheta2;\n double dtheta8 = dtheta4*dtheta4;\n \n double sindphi = sin(0.5*dphi);\n double sindphi2 = sindphi*sindphi;\n double sindphi4 = sindphi2*sindphi2;\n double sindphi8 = sindphi4*sindphi4;\n\n A = dr6*(A600 + A700*dr) + dr8*(A800 + A900*dr) + dr4*(A420 + A520*dr + dr2*(A620 + A720*dr))*dtheta2 + \n (A080 + A180*dr)*dtheta8 + dtheta4*(dr2*(A240 + A340*dr) + dr4*(A440 + A540*dr) + \n (A060 + A160*dr + dr2*(A260 + A360*dr))*dtheta2) + \n (dr4*(A402 + A502*dr + dr2*(A602 + A702*dr)) + (dr2*(A222 + A322*dr) + dr4*(A422 + A522*dr))*dtheta2 + \n dtheta4*(A042 + A142*dr + dr2*(A242 + A342*dr) + (A062 + A162*dr)*dtheta2))*sindphi2 + \n (A008 + A108*dr)*sindphi8 + sindphi4*(dr2*(A204 + A304*dr) + dr4*(A404 + A504*dr) + \n (A024 + A124*dr + dr2*(A224 + A324*dr))*dtheta2 + (A044 + A144*dr)*dtheta4 + \n (A006 + A106*dr + dr2*(A206 + A306*dr) + (A026 + A126*dr)*dtheta2)*sindphi2);\n\n alpha = alpha20*dr2 + alpha02*dtheta2;\n rho2 = alpha + beta*sindphi2;\n\n *PhiS = A/pow(rho2, 3.5);\n}\n\n/* Compute the singular field at the point x for the particle at xp */\nvoid effsource_PhiS_m(int m, struct coordinate * x, double * PhiS)\n{\n double A[5], num, alpha, ellE, ellK;\n\n double r = x->r;\n const double theta = x->theta;\n const double rp = xp.r;\n const double thetap = xp.theta;\n\n const double dr = r - rp;\n const double dtheta = theta - thetap;\n\n const double dr2 = dr*dr;\n const double dr3 = dr2*dr;\n const double dr4 = dr2*dr2;\n const double dr6 = dr3*dr3;\n const double dr8 = dr4*dr4;\n\n const double dtheta2 = dtheta*dtheta;\n const double dtheta4 = dtheta2*dtheta2;\n const double dtheta8 = dtheta4*dtheta4;\n\n A[0] = dr6*(A600 + A700*dr) + dr8*(A800 + A900*dr) + dr4*(A420 + A520*dr + dr2*(A620 + A720*dr))*dtheta2 + (A080 + A180*dr)*dtheta8 + dtheta4*(dr2*(A240 + A340*dr) + dr4*(A440 + A540*dr) + (A060 + A160*dr + dr2*(A260 + A360*dr))*dtheta2);\n A[1] = dr4*(A402 + A502*dr + dr2*(A602 + A702*dr)) + (dr2*(A222 + A322*dr) + dr4*(A422 + A522*dr))*dtheta2 + dtheta4*(A042 + A142*dr + dr2*(A242 + A342*dr) + (A062 + A162*dr)*dtheta2);\n A[2] = dr2*(A204 + A304*dr) + dr4*(A404 + A504*dr) + (A024 + A124*dr + dr2*(A224 + A324*dr))*dtheta2 + (A044 + A144*dr)*dtheta4;\n A[3] = A006 + A106*dr + dr2*(A206 + A306*dr) + (A026 + A126*dr)*dtheta2;\n A[4] = A008 + A108*dr;\n\n alpha = alpha20*dr2 + alpha02*dtheta2;\n\n const double C1 = alpha / beta;\n\n double C[27];\n C[0] = 1;\n C[1] = C1;\n C[2] = C[1]*C[1];\n C[3] = C[2]*C[1];\n C[4] = C[2]*C[2];\n C[5] = C[3]*C[2];\n C[6] = C[3]*C[3];\n C[7] = C[4]*C[3];\n C[8] = C[4]*C[4];\n C[9] = C[5]*C[4];\n C[10] = C[5]*C[5];\n C[11] = C[6]*C[5];\n C[12] = C[6]*C[6];\n C[13] = C[7]*C[6];\n C[14] = C[7]*C[7];\n C[15] = C[8]*C[7];\n C[16] = C[8]*C[8];\n C[17] = C[9]*C[8];\n C[18] = C[9]*C[9];\n C[19] = C[10]*C[9];\n C[20] = C[10]*C[10];\n C[21] = C[11]*C[10];\n C[22] = C[11]*C[11];\n C[23] = C[12]*C[11];\n C[24] = C[12]*C[12];\n C[25] = C[13]*C[12];\n C[26] = C[13]*C[13];\n\n ellE = gsl_sf_ellint_Ecomp(sqrt(1.0/(1.0+C1)), GSL_PREC_DOUBLE);\n ellK = gsl_sf_ellint_Kcomp(sqrt(1.0/(1.0+C1)), GSL_PREC_DOUBLE);\n const double ellip[2] = {ellK, ellE};\n\n if(m>20)\n {\n printf(\"Support for computing mode %d has not yet been added.\\n\", m);\n return;\n }\n\n num = 0;\n for(int i=0; i<2; i++)\n for(int j=0; j<5; j++)\n for(int k=0; k<27; k++)\n num += ReEI[m][i][j][k]*ellip[i]*A[j]*C[k];\n\n double RePhiS = 4.0*num/(beta*C[3]*pow(alpha+beta, 2.5));\n\n /* Store calculated quantities into the arrays provided by the caller,\n including the phase factor exp(-i*m*phi_p) */\n double cosmph = cos(m*xp.phi);\n double sinmph = sin(m*xp.phi);\n\n PhiS[0] = RePhiS*cosmph;\n PhiS[1] = - RePhiS*sinmph;\n}\n\n/* Compute the singular field, its derivatives and its d'Alembertian */\nvoid effsource_calc(struct coordinate * x,\n double *PhiS, double *dPhiS_dx, double *d2PhiS_dx2, double *src)\n{\n double A, dA_dr, d2A_dr2, dA_dth, d2A_dth2, dA_dR, dA_dph, d2A_dR2, d2A_dph2, dA_dt, d2A_dt2, d2A_dphdt;\n double s2, sqrts2, s2_15, s2_25, s2_35, s2_45, s2_55, ds2_dr, d2s2_dr2, ds2_dth, d2s2_dth2, ds2_dR, ds2_dph, d2s2_dR2, d2s2_dph2, ds2_dt, d2s2_dt2, d2s2_dphdt;\n\n double dPhiS_dt, dPhiS_dr, dPhiS_dth, dPhiS_dph, d2PhiS_dt2, d2PhiS_dtr, d2PhiS_dtth;\n double d2PhiS_dtph, d2PhiS_dr2, d2PhiS_drth, d2PhiS_drph, d2PhiS_dth2, d2PhiS_dthph, d2PhiS_dph2;\n\n double r = x->r;\n double theta = x->theta;\n double phi = x->phi;\n double rp = xp.r;\n double thetap = xp.theta;\n double phip = xp.phi;\n\n double dr = r - rp;\n double dtheta = theta - thetap;\n double dphi = phi - phip;\n\n double dr2 = dr*dr;\n double dr3 = dr2*dr;\n double dr4 = dr2*dr2;\n double dr5 = dr3*dr2;\n double dr6 = dr3*dr3;\n double dr7 = dr4*dr3;\n double dr8 = dr4*dr4;\n\n double dtheta2 = dtheta*dtheta;\n double dtheta3 = dtheta2*dtheta;\n double dtheta4 = dtheta2*dtheta2;\n double dtheta5 = dtheta3*dtheta2;\n double dtheta6 = dtheta3*dtheta3;\n double dtheta7 = dtheta4*dtheta3;\n double dtheta8 = dtheta4*dtheta4;\n\n double R = sin(0.5*dphi);\n double R2 = R*R;\n double R3 = R2*R;\n double R4 = R2*R2;\n double R5 = R3*R2;\n double R6 = R3*R3;\n double R7 = R4*R3;\n double R8 = R4*R4;\n double dR = 0.5*cos(0.5*dphi);\n\n double om = M / (a*M + sqrt(M*pow(rp,3)));\n\n /* A, dA/dx, d^2A/dx^2 */\n A = dr6*(A600 + A700*dr) + dr8*(A800 + A900*dr) + dr4*(A420 + A520*dr + dr2*(A620 + A720*dr))*dtheta2 + (A080 + A180*dr)*dtheta8 + dtheta4*(dr2*(A240 + A340*dr) + dr4*(A440 + A540*dr) + (A060 + A160*dr + dr2*(A260 + A360*dr))*dtheta2) + (dr4*(A402 + A502*dr + dr2*(A602 + A702*dr)) + (dr2*(A222 + A322*dr) + dr4*(A422 + A522*dr))*dtheta2 + dtheta4*(A042 + A142*dr + dr2*(A242 + A342*dr) + (A062 + A162*dr)*dtheta2))*R2 + (A008 + A108*dr)*R8 + R4*(dr2*(A204 + A304*dr) + dr4*(A404 + A504*dr) + (A024 + A124*dr + dr2*(A224 + A324*dr))*dtheta2 + (A044 + A144*dr)*dtheta4 + (A006 + A106*dr + dr2*(A206 + A306*dr) + (A026 + A126*dr)*dtheta2)*R2);;\n dA_dr = 6*(A600 + A700*dr)*dr5 + A700*dr6 + 8*(A800 + A900*dr)*dr7 + A900*dr8 + 4*(A420 + A520*dr + (A620 + A720*dr)*dr2)*dr3*dtheta2 + (A520 + 2*dr*(A620 + A720*dr) + A720*dr2)*dr4*dtheta2 + (2*dr*(A240 + A340*dr) + A340*dr2 + 4*(A440 + A540*dr)*dr3 + A540*dr4 + (A160 + 2*dr*(A260 + A360*dr) + A360*dr2)*dtheta2)*dtheta4 + A180*dtheta8 + (4*(A402 + A502*dr + (A602 + A702*dr)*dr2)*dr3 + (A502 + 2*dr*(A602 + A702*dr) + A702*dr2)*dr4 + (2*dr*(A222 + A322*dr) + A322*dr2 + 4*(A422 + A522*dr)*dr3 + A522*dr4)* dtheta2 + (A142 + 2*dr*(A242 + A342*dr) + A342*dr2 + A162*dtheta2)* dtheta4)*R2 + (2*dr*(A204 + A304*dr) + A304*dr2 + 4*(A404 + A504*dr)*dr3 + A504*dr4 + (A124 + 2*dr*(A224 + A324*dr) + A324*dr2)*dtheta2 + A144*dtheta4 + (A106 + 2*dr*(A206 + A306*dr) + A306*dr2 + A126*dtheta2)*R2)* R4 + A108*R8;\n dA_dth = 2*(A420 + A520*dr + (A620 + A720*dr)*dr2)*dr4*dtheta + 4*((A240 + A340*dr)*dr2 + (A440 + A540*dr)*dr4 + (A060 + A160*dr + (A260 + A360*dr)*dr2)*dtheta2)*dtheta3 + 2*(A060 + A160*dr + (A260 + A360*dr)*dr2)*dtheta5 + 8*(A080 + A180*dr)*dtheta7 + (2*((A222 + A322*dr)*dr2 + (A422 + A522*dr)*dr4)*dtheta + 4*(A042 + A142*dr + (A242 + A342*dr)*dr2 + (A062 + A162*dr)*dtheta2)* dtheta3 + 2*(A062 + A162*dr)*dtheta5)*R2 + (2*(A024 + A124*dr + (A224 + A324*dr)*dr2)*dtheta + 4*(A044 + A144*dr)*dtheta3 + 2*(A026 + A126*dr)*dtheta*R2)* R4;\n dA_dR = 2*((A402 + A502*dr + (A602 + A702*dr)*dr2)*dr4 + ((A222 + A322*dr)*dr2 + (A422 + A522*dr)*dr4)*dtheta2 + (A042 + A142*dr + (A242 + A342*dr)*dr2 + (A062 + A162*dr)*dtheta2)* dtheta4)*R + 4*((A204 + A304*dr)*dr2 + (A404 + A504*dr)*dr4 + (A024 + A124*dr + (A224 + A324*dr)*dr2)*dtheta2 + (A044 + A144*dr)*dtheta4 + (A006 + A106*dr + (A206 + A306*dr)*dr2 + (A026 + A126*dr)*dtheta2)* R2)*R3 + 2*(A006 + A106*dr + (A206 + A306*dr)*dr2 + (A026 + A126*dr)*dtheta2)*R5 + 8*(A008 + A108*dr)*R7;\n dA_dph = dA_dR*dR;\n dA_dt = -om*dA_dph;\n d2A_dr2 = 30*(A600 + A700*dr)*dr4 + 12*A700*dr5 + 56*(A800 + A900*dr)*dr6 + 16*A900*dr7 + 12*dr2*(A420 + A520*dr + (A620 + A720*dr)*dr2)*dtheta2 + 8*(A520 + 2*dr*(A620 + A720*dr) + A720*dr2)*dr3*dtheta2 + (4*A720*dr + 2*(A620 + A720*dr))*dr4*dtheta2 + (4*A340*dr + 2*(A240 + A340*dr) + 12*(A440 + A540*dr)*dr2 + 8*A540*dr3 + (4*A360*dr + 2*(A260 + A360*dr))*dtheta2)*dtheta4 + (12*dr2*(A402 + A502*dr + (A602 + A702*dr)*dr2) + 8*(A502 + 2*dr*(A602 + A702*dr) + A702*dr2)*dr3 + (4*A702*dr + 2*(A602 + A702*dr))*dr4 + (4*A322*dr + 2*(A222 + A322*dr) + 12*(A422 + A522*dr)*dr2 + 8*A522*dr3)*dtheta2 + (4*A342*dr + 2*(A242 + A342*dr))*dtheta4)* R2 + (4*A304*dr + 2*(A204 + A304*dr) + 12*(A404 + A504*dr)*dr2 + 8*A504*dr3 + (4*A324*dr + 2*(A224 + A324*dr))*dtheta2 + (4*A306*dr + 2*(A206 + A306*dr))*R2)*R4;\n d2A_dth2 = 2*(A420 + A520*dr + (A620 + A720*dr)*dr2)*dr4 + 12*dtheta2*((A240 + A340*dr)*dr2 + (A440 + A540*dr)*dr4 + (A060 + A160*dr + (A260 + A360*dr)*dr2)*dtheta2) + 18*(A060 + A160*dr + (A260 + A360*dr)*dr2)*dtheta4 + 56*(A080 + A180*dr)*dtheta6 + (2*((A222 + A322*dr)*dr2 + (A422 + A522*dr)*dr4) + 12*dtheta2*(A042 + A142*dr + (A242 + A342*dr)*dr2 + (A062 + A162*dr)*dtheta2) + 18*(A062 + A162*dr)*dtheta4)*R2 + (2*(A024 + A124*dr + (A224 + A324*dr)*dr2) + 12*(A044 + A144*dr)*dtheta2 + 2*(A026 + A126*dr)*R2)*R4; d2A_dR2 = 2*((A402 + A502*dr + (A602 + A702*dr)*dr2)*dr4 + ((A222 + A322*dr)*dr2 + (A422 + A522*dr)*dr4)*dtheta2 + (A042 + A142*dr + (A242 + A342*dr)*dr2 + (A062 + A162*dr)*dtheta2)* dtheta4) + 12*R2*((A204 + A304*dr)*dr2 + (A404 + A504*dr)*dr4 + (A024 + A124*dr + (A224 + A324*dr)*dr2)*dtheta2 + (A044 + A144*dr)*dtheta4 + (A006 + A106*dr + (A206 + A306*dr)*dr2 + (A026 + A126*dr)*dtheta2)* R2) + 18*(A006 + A106*dr + (A206 + A306*dr)*dr2 + (A026 + A126*dr)*dtheta2)*R4 + 56*(A008 + A108*dr)*R6;\n d2A_dph2 = - 0.25*R*dA_dR + dR*dR*d2A_dR2;\n d2A_dt2 = om*om*d2A_dph2;\n d2A_dphdt = -om*d2A_dph2;\n\n /* s, ds/dr, d^2s/dr^2 */\n s2 = alpha20*dr2 + alpha02*dtheta2 + beta*R2;\n ds2_dr = 2*alpha20*dr;\n ds2_dth = 2*alpha02*dtheta;\n ds2_dR = 2*beta*R;\n ds2_dph = ds2_dR*dR;\n ds2_dt = -om*ds2_dph;\n d2s2_dr2 = 2*alpha20;\n d2s2_dth2 = 2*alpha02;\n d2s2_dR2 = 2*beta;\n d2s2_dph2 = - 0.25*R*ds2_dR + dR*dR*d2s2_dR2;\n d2s2_dt2 = om*om*d2s2_dph2;\n d2s2_dphdt = -om*d2s2_dph2;\n sqrts2 = sqrt(s2);\n s2_15 = s2*sqrts2;\n s2_25 = s2*s2_15;\n s2_35 = s2*s2_25;\n s2_45 = s2*s2_35;\n s2_55 = s2*s2_45;\n\n /* PhiS */\n *PhiS = A/s2_35;\n\n /* First derivatives of PhiS */\n dPhiS_dt = (-7*ds2_dt*A + 2*dA_dt*s2)/(2.*s2_45);\n dPhiS_dr = (-7*ds2_dr*A + 2*dA_dr*s2) /(2.*s2_45);\n dPhiS_dth = (-7*ds2_dth*A + 2*dA_dth*s2)/(2.*s2_45);\n dPhiS_dph = (-7*ds2_dph*A + 2*dA_dph*s2)/(2.*s2_45);\n \n /* Second derivatives of PhiS */\n d2PhiS_dr2 =\n (63*ds2_dr*ds2_dr*A - 14*s2*(2*dA_dr*ds2_dr + d2s2_dr2*A) + 4*d2A_dr2*s2*s2)/(4.*s2_55);\n d2PhiS_dth2 =\n (63*ds2_dth*ds2_dth*A - 14*s2*(2*dA_dth*ds2_dth + d2s2_dth2*A) + 4*d2A_dth2*s2*s2)/(4.*s2_55);\n d2PhiS_dph2 =\n (63*ds2_dph*ds2_dph*A - 14*s2*(2*dA_dph*ds2_dph + d2s2_dph2*A) + 4*d2A_dph2*s2*s2)/(4.*s2_55);\n d2PhiS_dt2 =\n (63*ds2_dt*ds2_dt*A - 14*s2*(2*dA_dt*ds2_dt + d2s2_dt2*A) + 4*d2A_dt2*s2*s2)/(4.*s2_55);\n d2PhiS_dtph =\n (63*ds2_dph*ds2_dt*A - 14*s2*(dA_dt*ds2_dph + dA_dph*ds2_dt + d2s2_dphdt*A) + 4*d2A_dphdt*s2*s2)/(4.*s2_55);\n d2PhiS_dtr = NAN;\n d2PhiS_dtth = NAN;\n d2PhiS_drth = NAN;\n d2PhiS_drph = NAN;\n d2PhiS_dthph = NAN;\n \n \n /* Box[PhiS] */\n double sinth = sin(theta);\n double sinth2 = sinth*sinth;\n double sin2th = sin(2*theta);\n double cos2th = cos(2*theta);\n double r2 = r*r;\n double r3 = r2*r;\n double r4 = r2*r2;\n double a2 = a*a;\n double a4 = a2*a2;\n\n *src = -((2*a2*dPhiS_dr - a2*d2PhiS_dph2 - a4*d2PhiS_dr2 - a2*d2PhiS_dth2 - 4*dPhiS_dr*r - 2*a2*dPhiS_dr*r +\n 4*d2PhiS_dph2*r + 2*a*d2PhiS_dtph*r + 4*a2*d2PhiS_dr2*r + 2*d2PhiS_dth2*r + 6*dPhiS_dr*r2 - 2*d2PhiS_dph2*r2 - 4*d2PhiS_dr2*r2 -\n 2*a2*d2PhiS_dr2*r2 - d2PhiS_dth2*r2 - 2*dPhiS_dr*r3 + 4*d2PhiS_dr2*r3 - d2PhiS_dr2*r4 +\n (a4*d2PhiS_dt2 + 4*a*d2PhiS_dtph*r + 2*d2PhiS_dt2*r4 + a2*d2PhiS_dt2*r*(2 + 3*r))*sinth2 +\n cos2th*(a4*d2PhiS_dr2 - 2*a*d2PhiS_dtph*r + (-2 + r)*r*(d2PhiS_dth2 + 2*dPhiS_dr*(-1 + r) + d2PhiS_dr2*(-2 + r)*r) +\n a2*(-d2PhiS_dph2 + d2PhiS_dth2 + 2*dPhiS_dr*(-1 + r) - 4*d2PhiS_dr2*r + 2*d2PhiS_dr2*r2) +\n a2*d2PhiS_dt2*(a2 + (-2 + r)*r)*sinth2) - a2*dPhiS_dth*sin2th + 2*dPhiS_dth*r*sin2th -\n dPhiS_dth*r2*sin2th))/((sinth2*(a2 + (-2 + r)*r)*(a2 + 2*r2 + a2*cos2th)));\n\n dPhiS_dx[0] = dPhiS_dt;\n dPhiS_dx[1] = dPhiS_dr;\n dPhiS_dx[2] = dPhiS_dth;\n dPhiS_dx[3] = dPhiS_dph;\n\n d2PhiS_dx2[0] = d2PhiS_dt2;\n d2PhiS_dx2[1] = d2PhiS_dtr;\n d2PhiS_dx2[2] = d2PhiS_dtth;\n d2PhiS_dx2[3] = d2PhiS_dtph;\n d2PhiS_dx2[4] = d2PhiS_dr2;\n d2PhiS_dx2[5] = d2PhiS_drth;\n d2PhiS_dx2[6] = d2PhiS_drph;\n d2PhiS_dx2[7] = d2PhiS_dth2;\n d2PhiS_dx2[8] = d2PhiS_dthph;\n d2PhiS_dx2[9] = d2PhiS_dph2;\n}\n\n/* Compute the 2D singular field, its derivatives and its d'Alembertian */\nvoid effsource_calc_m(int m, struct coordinate * x,\n double *PhiS, double *dPhiS_dx, double *d2PhiS_dx2, double *src)\n{\n double A[5], alpha, ellE, ellK;\n double dA_dr[5], dalpha_dr, dC1_dr, dellE_dC, dellK_dC, d2ellE_dC2, d2ellK_dC2, dellE_dr, dellK_dr;\n double d2A_dr2[5], d2alpha_dr2, d2C1_dr2, d2ellE_dr2, d2ellK_dr2;\n double dA_dtheta[5], dalpha_dtheta, dC1_dtheta, dellE_dtheta, dellK_dtheta;\n double d2A_dtheta2[5], d2alpha_dtheta2, d2C1_dtheta2, d2ellE_dtheta2, d2ellK_dtheta2;\n\n double s, ds_dr, d2s_dr2, ds_dtheta, d2s_dtheta2;\n\n double dPhiS_dt, dPhiS_dr, dPhiS_dth, dPhiS_dph, d2PhiS_dt2, d2PhiS_dtr, d2PhiS_dtth;\n double d2PhiS_dtph, d2PhiS_dr2, d2PhiS_drth, d2PhiS_drph, d2PhiS_dth2, d2PhiS_dthph, d2PhiS_dph2;\n\n const double r = x->r;\n const double theta = x->theta;\n const double rp = xp.r;\n const double thetap = xp.theta;\n const double om = M / (a*M + sqrt(M*pow(rp,3)));\n\n const double dr = r - rp;\n const double dtheta = theta - thetap;\n\n const double dr2 = dr*dr;\n const double dr3 = dr2*dr;\n const double dr4 = dr2*dr2;\n const double dr5 = dr3*dr2;\n const double dr6 = dr3*dr3;\n const double dr7 = dr4*dr3;\n const double dr8 = dr4*dr4;\n\n const double dtheta2 = dtheta*dtheta;\n const double dtheta3 = dtheta2*dtheta;\n const double dtheta4 = dtheta2*dtheta2;\n const double dtheta5 = dtheta3*dtheta2;\n const double dtheta6 = dtheta3*dtheta3;\n const double dtheta7 = dtheta4*dtheta3;\n const double dtheta8 = dtheta4*dtheta4;\n\n /* Coefficients of sin(dphi) in the numerator */\n A[0] = dr6*(A600 + A700*dr) + dr8*(A800 + A900*dr) + dr4*(A420 + A520*dr + dr2*(A620 + A720*dr))*dtheta2 + (A080 + A180*dr)*dtheta8 + dtheta4*(dr2*(A240 + A340*dr) + dr4*(A440 + A540*dr) + (A060 + A160*dr + dr2*(A260 + A360*dr))*dtheta2);\n A[1] = dr4*(A402 + A502*dr + dr2*(A602 + A702*dr)) + (dr2*(A222 + A322*dr) + dr4*(A422 + A522*dr))*dtheta2 + dtheta4*(A042 + A142*dr + dr2*(A242 + A342*dr) + (A062 + A162*dr)*dtheta2);\n A[2] = dr2*(A204 + A304*dr) + dr4*(A404 + A504*dr) + (A024 + A124*dr + dr2*(A224 + A324*dr))*dtheta2 + (A044 + A144*dr)*dtheta4;\n A[3] = A006 + A106*dr + dr2*(A206 + A306*dr) + (A026 + A126*dr)*dtheta2;\n A[4] = A008 + A108*dr;\n\n /* r derivatives of coefficients */\n dA_dr[0] = 6*A600*dr5 + 7*A700*dr6 + 8*A800*dr7 + 9*A900*dr8 + 4*A420*dr3*dtheta2 + 5*A520*dr4*dtheta2 + 6*A620*dr5*dtheta2 + 7*A720*dr6*dtheta2 + 2*A240*dr*dtheta4 + 3*A340*dr2*dtheta4 + 4*A440*dr3*dtheta4 + 5*A540*dr4*dtheta4 + A160*dtheta6 + 2*A260*dr*dtheta6 + 3*A360*dr2*dtheta6 + A180*dtheta8;\n dA_dr[1] = 4*A402*dr3 + 5*A502*dr4 + 6*A602*dr5 + 7*A702*dr6 + 2*A222*dr*dtheta2 + 3*A322*dr2*dtheta2 + 4*A422*dr3*dtheta2 + 5*A522*dr4*dtheta2 + A142*dtheta4 + 2*A242*dr*dtheta4 + 3*A342*dr2*dtheta4 + A162*dtheta6;\n dA_dr[2] = 2*A204*dr + 3*A304*dr2 + 4*A404*dr3 + 5*A504*dr4 + A124*dtheta2 + 2*A224*dr*dtheta2 + 3*A324*dr2*dtheta2 + A144*dtheta4;\n dA_dr[3] = A106 + 2*A206*dr + 3*A306*dr2 + A126*dtheta2;\n dA_dr[4] = A108;\n\n /* r,r derivatives of coefficients */\n d2A_dr2[0] = 2*(15*A600*dr4 + 21*A700*dr5 + 28*A800*dr6 + 36*A900*dr7 + 6*A420*dr2*dtheta2 + 10*A520*dr3*dtheta2 + 15*A620*dr4*dtheta2 + 21*A720*dr5*dtheta2 + A240*dtheta4 + 3*A340*dr*dtheta4 + 6*A440*dr2*dtheta4 + 10*A540*dr3*dtheta4 + A260*dtheta6 + 3*A360*dr*dtheta6);\n d2A_dr2[1] = 2*(6*A402*dr2 + 10*A502*dr3 + 15*A602*dr4 + 21*A702*dr5 + A222*dtheta2 + 3*A322*dr*dtheta2 + 6*A422*dr2*dtheta2 + 10*A522*dr3*dtheta2 + A242*dtheta4 + 3*A342*dr*dtheta4);\n d2A_dr2[2] = 2*(A204 + 3*A304*dr + 6*A404*dr2 + 10*A504*dr3 + A224*dtheta2 + 3*A324*dr*dtheta2);\n d2A_dr2[3] = 2*(A206 + 3*A306*dr);\n d2A_dr2[4] = 0;\n\n /* theta derivatives of coefficients */\n dA_dtheta[0] = 2*(A420 + dr*(A520 + dr*(A620 + A720*dr)))*dr4*dtheta + 4*((A240 + A340*dr)*dr2 + (A440 + A540*dr)*dr4 + (A060 + dr*(A160 + dr*(A260 + A360*dr)))*dtheta2)*dtheta3 + 2*(A060 + dr*(A160 + dr*(A260 + A360*dr)))*dtheta5 + 8*(A080 + A180*dr)*dtheta7;\n dA_dtheta[1] = 2*dtheta*((A222 + A322*dr)*dr2 + (A422 + A522*dr)*dr4 + 2*dtheta2*(A042 + A142*dr + (A242 + A342*dr)*dr2 + (A062 + A162*dr)*dtheta2) + (A062 + A162*dr)*dtheta4);\n dA_dtheta[2] = 2*dtheta*(A024 + A124*dr + (A224 + A324*dr)*dr2 + 2*(A044 + A144*dr)*dtheta2);\n dA_dtheta[3] = 2*(A026 + A126*dr)*dtheta;\n dA_dtheta[4] = 0;\n\n /* theta,theta derivatives of coefficients */\n d2A_dtheta2[0] = 2*((A420 + dr*(A520 + dr*(A620 + A720*dr)))*dr4 + 6*dtheta2*((A240 + A340*dr)*dr2 + (A440 + A540*dr)*dr4 + (A060 + dr*(A160 + dr*(A260 + A360*dr)))*dtheta2) + 9*(A060 + dr*(A160 + dr*(A260 + A360*dr)))*dtheta4 + 28*(A080 + A180*dr)*dtheta6);\n d2A_dtheta2[1] = 2*((A222 + A322*dr)*dr2 + (A422 + A522*dr)*dr4 + 6*dtheta2*(A042 + A142*dr + (A242 + A342*dr)*dr2 + (A062 + A162*dr)*dtheta2) + 9*(A062 + A162*dr)*dtheta4);\n d2A_dtheta2[2] = 2*(A024 + A124*dr + (A224 + A324*dr)*dr2 + 6*(A044 + A144*dr)*dtheta2);\n d2A_dtheta2[3] = 2*(A026 + A126*dr);\n d2A_dtheta2[4] = 0;\n\n /* alpha term appearing in the denominator */\n alpha = alpha20*dr2 + alpha02*dtheta2;\n\n /* Derivatives of alpha */\n dalpha_dr = 2*alpha20*dr;\n d2alpha_dr2 = 2*alpha20;\n dalpha_dtheta = 2*alpha02*dtheta;\n d2alpha_dtheta2 = 2*alpha02;\n\n /* C term appearing in Elliptic integrals and related power series in numerator */\n const double C1 = alpha / beta;\n\n double C[27];\n C[0] = 1;\n C[1] = C1;\n C[2] = C1*C1;\n C[3] = C[2]*C[1];\n C[4] = C[2]*C[2];\n C[5] = C[3]*C[2];\n C[6] = C[3]*C[3];\n C[7] = C[4]*C[3];\n C[8] = C[4]*C[4];\n C[9] = C[5]*C[4];\n C[10] = C[5]*C[5];\n C[11] = C[6]*C[5];\n C[12] = C[6]*C[6];\n C[13] = C[7]*C[6];\n C[14] = C[7]*C[7];\n C[15] = C[8]*C[7];\n C[16] = C[8]*C[8];\n C[17] = C[9]*C[8];\n C[18] = C[9]*C[9];\n C[19] = C[10]*C[9];\n C[20] = C[10]*C[10];\n C[21] = C[11]*C[10];\n C[22] = C[11]*C[11];\n C[23] = C[12]*C[11];\n C[24] = C[12]*C[12];\n C[25] = C[13]*C[12];\n C[26] = C[13]*C[13];\n\n dC1_dr = dalpha_dr / beta;\n d2C1_dr2 = d2alpha_dr2 / beta;\n dC1_dtheta = dalpha_dtheta / beta;\n d2C1_dtheta2 = d2alpha_dtheta2 / beta;\n\n double dC_dr[27];\n dC_dr[0] = 0;\n dC_dr[1] = 1*C[0]*dC1_dr;\n dC_dr[2] = 2*C[1]*dC1_dr;\n dC_dr[3] = 3*C[2]*dC1_dr;\n dC_dr[4] = 4*C[3]*dC1_dr;\n dC_dr[5] = 5*C[4]*dC1_dr;\n dC_dr[6] = 6*C[5]*dC1_dr;\n dC_dr[7] = 7*C[6]*dC1_dr;\n dC_dr[8] = 8*C[7]*dC1_dr;\n dC_dr[9] = 9*C[8]*dC1_dr;\n dC_dr[10] = 10*C[9]*dC1_dr;\n dC_dr[11] = 11*C[10]*dC1_dr;\n dC_dr[12] = 12*C[11]*dC1_dr;\n dC_dr[13] = 13*C[12]*dC1_dr;\n dC_dr[14] = 14*C[13]*dC1_dr;\n dC_dr[15] = 15*C[14]*dC1_dr;\n dC_dr[16] = 16*C[15]*dC1_dr;\n dC_dr[17] = 17*C[16]*dC1_dr;\n dC_dr[18] = 18*C[17]*dC1_dr;\n dC_dr[19] = 19*C[18]*dC1_dr;\n dC_dr[20] = 20*C[19]*dC1_dr;\n dC_dr[21] = 21*C[20]*dC1_dr;\n dC_dr[22] = 22*C[21]*dC1_dr;\n dC_dr[23] = 23*C[22]*dC1_dr;\n dC_dr[24] = 24*C[23]*dC1_dr;\n dC_dr[25] = 25*C[24]*dC1_dr;\n dC_dr[26] = 26*C[25]*dC1_dr;\n\n double d2C_dr2[27];\n d2C_dr2[0] = 0;\n d2C_dr2[1] = d2C1_dr2;\n d2C_dr2[2] = 2*1*C[0]*dC1_dr*dC1_dr + 2*C[1]*d2C1_dr2;\n d2C_dr2[3] = 3*2*C[1]*dC1_dr*dC1_dr + 3*C[2]*d2C1_dr2;\n d2C_dr2[4] = 4*3*C[2]*dC1_dr*dC1_dr + 4*C[3]*d2C1_dr2;\n d2C_dr2[5] = 5*4*C[3]*dC1_dr*dC1_dr + 5*C[4]*d2C1_dr2;\n d2C_dr2[6] = 6*5*C[4]*dC1_dr*dC1_dr + 6*C[5]*d2C1_dr2;\n d2C_dr2[7] = 7*6*C[5]*dC1_dr*dC1_dr + 7*C[6]*d2C1_dr2;\n d2C_dr2[8] = 8*7*C[6]*dC1_dr*dC1_dr + 8*C[7]*d2C1_dr2;\n d2C_dr2[9] = 9*8*C[7]*dC1_dr*dC1_dr + 9*C[8]*d2C1_dr2;\n d2C_dr2[10] = 10*9*C[8]*dC1_dr*dC1_dr + 10*C[9]*d2C1_dr2;\n d2C_dr2[11] = 11*10*C[9]*dC1_dr*dC1_dr + 11*C[10]*d2C1_dr2;\n d2C_dr2[12] = 12*11*C[10]*dC1_dr*dC1_dr + 12*C[11]*d2C1_dr2;\n d2C_dr2[13] = 13*12*C[11]*dC1_dr*dC1_dr + 13*C[12]*d2C1_dr2;\n d2C_dr2[14] = 14*13*C[12]*dC1_dr*dC1_dr + 14*C[13]*d2C1_dr2;\n d2C_dr2[15] = 15*14*C[13]*dC1_dr*dC1_dr + 15*C[14]*d2C1_dr2;\n d2C_dr2[16] = 16*15*C[14]*dC1_dr*dC1_dr + 16*C[15]*d2C1_dr2;\n d2C_dr2[17] = 17*16*C[15]*dC1_dr*dC1_dr + 17*C[16]*d2C1_dr2;\n d2C_dr2[18] = 18*17*C[16]*dC1_dr*dC1_dr + 18*C[17]*d2C1_dr2;\n d2C_dr2[19] = 19*18*C[17]*dC1_dr*dC1_dr + 19*C[18]*d2C1_dr2;\n d2C_dr2[20] = 20*19*C[18]*dC1_dr*dC1_dr + 20*C[19]*d2C1_dr2;\n d2C_dr2[21] = 21*20*C[19]*dC1_dr*dC1_dr + 21*C[20]*d2C1_dr2;\n d2C_dr2[22] = 22*21*C[20]*dC1_dr*dC1_dr + 22*C[21]*d2C1_dr2;\n d2C_dr2[23] = 23*22*C[21]*dC1_dr*dC1_dr + 23*C[22]*d2C1_dr2;\n d2C_dr2[24] = 24*23*C[22]*dC1_dr*dC1_dr + 24*C[23]*d2C1_dr2;\n d2C_dr2[25] = 25*24*C[23]*dC1_dr*dC1_dr + 25*C[24]*d2C1_dr2;\n d2C_dr2[26] = 26*25*C[24]*dC1_dr*dC1_dr + 26*C[25]*d2C1_dr2;\n\n double dC_dtheta[27];\n dC_dtheta[0] = 0;\n dC_dtheta[1] = 1*C[0]*dC1_dtheta;\n dC_dtheta[2] = 2*C[1]*dC1_dtheta;\n dC_dtheta[3] = 3*C[2]*dC1_dtheta;\n dC_dtheta[4] = 4*C[3]*dC1_dtheta;\n dC_dtheta[5] = 5*C[4]*dC1_dtheta;\n dC_dtheta[6] = 6*C[5]*dC1_dtheta;\n dC_dtheta[7] = 7*C[6]*dC1_dtheta;\n dC_dtheta[8] = 8*C[7]*dC1_dtheta;\n dC_dtheta[9] = 9*C[8]*dC1_dtheta;\n dC_dtheta[10] = 10*C[9]*dC1_dtheta;\n dC_dtheta[11] = 11*C[10]*dC1_dtheta;\n dC_dtheta[12] = 12*C[11]*dC1_dtheta;\n dC_dtheta[13] = 13*C[12]*dC1_dtheta;\n dC_dtheta[14] = 14*C[13]*dC1_dtheta;\n dC_dtheta[15] = 15*C[14]*dC1_dtheta;\n dC_dtheta[16] = 16*C[15]*dC1_dtheta;\n dC_dtheta[17] = 17*C[16]*dC1_dtheta;\n dC_dtheta[18] = 18*C[17]*dC1_dtheta;\n dC_dtheta[19] = 19*C[18]*dC1_dtheta;\n dC_dtheta[20] = 20*C[19]*dC1_dtheta;\n dC_dtheta[21] = 21*C[20]*dC1_dtheta;\n dC_dtheta[22] = 22*C[21]*dC1_dtheta;\n dC_dtheta[23] = 23*C[22]*dC1_dtheta;\n dC_dtheta[24] = 24*C[23]*dC1_dtheta;\n dC_dtheta[25] = 25*C[24]*dC1_dtheta;\n dC_dtheta[26] = 26*C[25]*dC1_dtheta;\n\n double d2C_dtheta2[27];\n d2C_dtheta2[0] = 0;\n d2C_dtheta2[1] = d2C1_dtheta2;\n d2C_dtheta2[2] = 2*1*C[0]*dC1_dtheta*dC1_dtheta + 2*C[1]*d2C1_dtheta2;\n d2C_dtheta2[3] = 3*2*C[1]*dC1_dtheta*dC1_dtheta + 3*C[2]*d2C1_dtheta2;\n d2C_dtheta2[4] = 4*3*C[2]*dC1_dtheta*dC1_dtheta + 4*C[3]*d2C1_dtheta2;\n d2C_dtheta2[5] = 5*4*C[3]*dC1_dtheta*dC1_dtheta + 5*C[4]*d2C1_dtheta2;\n d2C_dtheta2[6] = 6*5*C[4]*dC1_dtheta*dC1_dtheta + 6*C[5]*d2C1_dtheta2;\n d2C_dtheta2[7] = 7*6*C[5]*dC1_dtheta*dC1_dtheta + 7*C[6]*d2C1_dtheta2;\n d2C_dtheta2[8] = 8*7*C[6]*dC1_dtheta*dC1_dtheta + 8*C[7]*d2C1_dtheta2;\n d2C_dtheta2[9] = 9*8*C[7]*dC1_dtheta*dC1_dtheta + 9*C[8]*d2C1_dtheta2;\n d2C_dtheta2[10] = 10*9*C[8]*dC1_dtheta*dC1_dtheta + 10*C[9]*d2C1_dtheta2;\n d2C_dtheta2[11] = 11*10*C[9]*dC1_dtheta*dC1_dtheta + 11*C[10]*d2C1_dtheta2;\n d2C_dtheta2[12] = 12*11*C[10]*dC1_dtheta*dC1_dtheta + 12*C[11]*d2C1_dtheta2;\n d2C_dtheta2[13] = 13*12*C[11]*dC1_dtheta*dC1_dtheta + 13*C[12]*d2C1_dtheta2;\n d2C_dtheta2[14] = 14*13*C[12]*dC1_dtheta*dC1_dtheta + 14*C[13]*d2C1_dtheta2;\n d2C_dtheta2[15] = 15*14*C[13]*dC1_dtheta*dC1_dtheta + 15*C[14]*d2C1_dtheta2;\n d2C_dtheta2[16] = 16*15*C[14]*dC1_dtheta*dC1_dtheta + 16*C[15]*d2C1_dtheta2;\n d2C_dtheta2[17] = 17*16*C[15]*dC1_dtheta*dC1_dtheta + 17*C[16]*d2C1_dtheta2;\n d2C_dtheta2[18] = 18*17*C[16]*dC1_dtheta*dC1_dtheta + 18*C[17]*d2C1_dtheta2;\n d2C_dtheta2[19] = 19*18*C[17]*dC1_dtheta*dC1_dtheta + 19*C[18]*d2C1_dtheta2;\n d2C_dtheta2[20] = 20*19*C[18]*dC1_dtheta*dC1_dtheta + 20*C[19]*d2C1_dtheta2;\n d2C_dtheta2[21] = 21*20*C[19]*dC1_dtheta*dC1_dtheta + 21*C[20]*d2C1_dtheta2;\n d2C_dtheta2[22] = 22*21*C[20]*dC1_dtheta*dC1_dtheta + 22*C[21]*d2C1_dtheta2;\n d2C_dtheta2[23] = 23*22*C[21]*dC1_dtheta*dC1_dtheta + 23*C[22]*d2C1_dtheta2;\n d2C_dtheta2[24] = 24*23*C[22]*dC1_dtheta*dC1_dtheta + 24*C[23]*d2C1_dtheta2;\n d2C_dtheta2[25] = 25*24*C[23]*dC1_dtheta*dC1_dtheta + 25*C[24]*d2C1_dtheta2;\n d2C_dtheta2[26] = 26*25*C[24]*dC1_dtheta*dC1_dtheta + 26*C[25]*d2C1_dtheta2;\n\n /* Elliptic integrals */\n ellE = gsl_sf_ellint_Ecomp(sqrt(1.0/(1.0+C1)), GSL_PREC_DOUBLE);\n ellK = gsl_sf_ellint_Kcomp(sqrt(1.0/(1.0+C1)), GSL_PREC_DOUBLE);\n const double ellip[2] = {ellK, ellE};\n\n /* Derivatives of elliptic integrals */\n dellE_dC = (ellK - ellE)/(2.*(1+C1));\n dellK_dC = (C1*ellK - (1+C1)*ellE)/(2.*C1*(1+C1));\n d2ellE_dC2 = -(2*C1*ellK - (2*C1-1)*ellE)/(4.*C1*(1+C1)*(1+C1));\n d2ellK_dC2 = -(C1*(1+2*C1)*ellK - 2*(1+C1)*(1+C1)*ellE)/(4.*C1*C1*(1+C1)*(1+C1));\n\n dellE_dr = dellE_dC * dC1_dr;\n dellE_dtheta = dellE_dC * dC1_dtheta;\n d2ellE_dr2 = d2ellE_dC2 * dC1_dr * dC1_dr + dellE_dC * d2C1_dr2;\n d2ellE_dtheta2 = d2ellE_dC2 * dC1_dtheta * dC1_dtheta + dellE_dC * d2C1_dtheta2;\n\n dellK_dr = dellK_dC * dC1_dr;\n dellK_dtheta = dellK_dC * dC1_dtheta;\n d2ellK_dr2 = d2ellK_dC2 * dC1_dr * dC1_dr + dellK_dC * d2C1_dr2;\n d2ellK_dtheta2 = d2ellK_dC2 * dC1_dtheta * dC1_dtheta + dellK_dC * d2C1_dtheta2;\n\n const double dellip_dr[2] = {dellK_dr, dellE_dr};\n const double dellip_dtheta[2] = {dellK_dtheta, dellE_dtheta};\n\n const double d2ellip_dr2[2] = {d2ellK_dr2, d2ellE_dr2};\n const double d2ellip_dtheta2[2] = {d2ellK_dtheta2, d2ellE_dtheta2};\n\n if(m>20)\n {\n printf(\"Support for computing mode %d has not yet been added.\\n\", m);\n return;\n }\n\n /* Numerator */\n double num = 0;\n for(int i=0; i<2; i++)\n for(int j=0; j<5; j++)\n for(int k=0; k<27; k++)\n num += ReEI[m][i][j][k]*ellip[i]*A[j]*C[k];\n double dnum_dr = 0;\n for(int i=0; i<2; i++)\n for(int j=0; j<5; j++)\n for(int k=0; k<27; k++)\n dnum_dr += ReEI[m][i][j][k]*\n (dellip_dr[i]*A[j]*C[k]\n + ellip[i]*dA_dr[j]*C[k]\n + ellip[i]*A[j]*dC_dr[k]);\n double d2num_dr2 = 0;\n for(int i=0; i<2; i++)\n for(int j=0; j<5; j++)\n for(int k=0; k<27; k++)\n d2num_dr2 += ReEI[m][i][j][k]*\n (d2ellip_dr2[i]*A[j]*C[k]\n + dellip_dr[i]*dA_dr[j]*C[k]\n + dellip_dr[i]*A[j]*dC_dr[k]\n + dellip_dr[i]*dA_dr[j]*C[k]\n + ellip[i]*d2A_dr2[j]*C[k]\n + ellip[i]*dA_dr[j]*dC_dr[k]\n + dellip_dr[i]*A[j]*dC_dr[k]\n + ellip[i]*dA_dr[j]*dC_dr[k]\n + ellip[i]*A[j]*d2C_dr2[k]);\n double dnum_dtheta = 0;\n for(int i=0; i<2; i++)\n for(int j=0; j<5; j++)\n for(int k=0; k<27; k++)\n dnum_dtheta += ReEI[m][i][j][k]*\n (dellip_dtheta[i]*A[j]*C[k]\n + ellip[i]*dA_dtheta[j]*C[k]\n + ellip[i]*A[j]*dC_dtheta[k]);\n double d2num_dtheta2 = 0;\n for(int i=0; i<2; i++)\n for(int j=0; j<5; j++)\n for(int k=0; k<27; k++)\n d2num_dtheta2 += ReEI[m][i][j][k]*\n (d2ellip_dtheta2[i]*A[j]*C[k]\n + dellip_dtheta[i]*dA_dtheta[j]*C[k]\n + dellip_dtheta[i]*A[j]*dC_dtheta[k]\n + dellip_dtheta[i]*dA_dtheta[j]*C[k]\n + ellip[i]*d2A_dtheta2[j]*C[k]\n + ellip[i]*dA_dtheta[j]*dC_dtheta[k]\n + dellip_dtheta[i]*A[j]*dC_dtheta[k]\n + ellip[i]*dA_dtheta[j]*dC_dtheta[k]\n + ellip[i]*A[j]*d2C_dtheta2[k]);\n\n /* Denominator */\n s = beta*C[3]*pow(alpha+beta, 2.5);\n ds_dr = beta*(3*C[2]*pow(alpha+beta, 2.5)*dC1_dr + C[3]*2.5*pow(alpha+beta, 1.5)*dalpha_dr);\n ds_dtheta = beta*(3*C[2]*pow(alpha+beta, 2.5)*dC1_dtheta + C[3]*2.5*pow(alpha+beta, 1.5)*dalpha_dtheta);\n d2s_dr2 = beta*(6*C1*pow(alpha+beta, 2.5)*dC1_dr*dC1_dr\n + 3*C[2]*2.5*pow(alpha+beta, 1.5)*dalpha_dr*dC1_dr\n + 3*C[2]*pow(alpha+beta, 2.5)*d2C1_dr2\n + 3*C[2]*dC1_dr*2.5*pow(alpha+beta, 1.5)*dalpha_dr\n + C[3]*2.5*1.5*pow(alpha+beta, 0.5)*dalpha_dr*dalpha_dr\n + C[3]*2.5*pow(alpha+beta, 1.5)*d2alpha_dr2);\n d2s_dtheta2 = beta*(6*C1*pow(alpha+beta, 2.5)*dC1_dtheta*dC1_dtheta\n + 3*C[2]*2.5*pow(alpha+beta, 1.5)*dalpha_dtheta*dC1_dtheta\n + 3*C[2]*pow(alpha+beta, 2.5)*d2C1_dtheta2\n + 3*C[2]*dC1_dtheta*2.5*pow(alpha+beta, 1.5)*dalpha_dtheta\n + C[3]*2.5*1.5*pow(alpha+beta, 0.5)*dalpha_dtheta*dalpha_dtheta\n + C[3]*2.5*pow(alpha+beta, 1.5)*d2alpha_dtheta2);\n\n /* Singular field */\n double RePhiS = 4.0*num/s;\n\n /* First derivatives of PhiS */\n dPhiS_dt = - m * om * (RePhiS); // This should be interpreted as pure-imaginary\n dPhiS_dr = 4.0*(-ds_dr*num + dnum_dr*s) /(s*s);\n dPhiS_dth = 4.0*(-ds_dtheta*num + dnum_dtheta*s)/(s*s);\n dPhiS_dph = m * (RePhiS); // This should be interpreted as pure-imaginary\n\n /* Second derivatives of PhiS */\n d2PhiS_dr2 = 4.0*(2.0*ds_dr*ds_dr*num - s*(2*dnum_dr*ds_dr + d2s_dr2*num) + d2num_dr2*s*s)/(s*s*s);\n d2PhiS_dth2 = 4.0*(2.0*ds_dtheta*ds_dtheta*num - s*(2*dnum_dtheta*ds_dtheta + d2s_dtheta2*num) + d2num_dtheta2*s*s)/(s*s*s);\n d2PhiS_dph2 = - m*m*(RePhiS);\n d2PhiS_dt2 = - m*m*om*om*(RePhiS);\n d2PhiS_dtph = m*m*om*(RePhiS);\n d2PhiS_dtr = NAN;\n d2PhiS_dtth = NAN;\n d2PhiS_drth = NAN;\n d2PhiS_drph = NAN;\n d2PhiS_dthph = NAN;\n\n /* Box[PhiS] */\n double sinth = sin(theta);\n double sinth2 = sinth*sinth;\n double sin2th = sin(2*theta);\n double cos2th = cos(2*theta);\n double r2 = r*r;\n double r3 = r2*r;\n double r4 = r2*r2;\n double a2 = a*a;\n double a4 = a2*a2;\n\n double effsrc = -((2*a2*dPhiS_dr - a2*d2PhiS_dph2 - a4*d2PhiS_dr2 - a2*d2PhiS_dth2 - 4*dPhiS_dr*r - 2*a2*dPhiS_dr*r +\n 4*d2PhiS_dph2*r + 2*a*d2PhiS_dtph*r + 4*a2*d2PhiS_dr2*r + 2*d2PhiS_dth2*r + 6*dPhiS_dr*r2 - 2*d2PhiS_dph2*r2 - 4*d2PhiS_dr2*r2 -\n 2*a2*d2PhiS_dr2*r2 - d2PhiS_dth2*r2 - 2*dPhiS_dr*r3 + 4*d2PhiS_dr2*r3 - d2PhiS_dr2*r4 +\n (a4*d2PhiS_dt2 + 4*a*d2PhiS_dtph*r + 2*d2PhiS_dt2*r4 + a2*d2PhiS_dt2*r*(2 + 3*r))*sinth2 +\n cos2th*(a4*d2PhiS_dr2 - 2*a*d2PhiS_dtph*r + (-2 + r)*r*(d2PhiS_dth2 + 2*dPhiS_dr*(-1 + r) + d2PhiS_dr2*(-2 + r)*r) +\n a2*(-d2PhiS_dph2 + d2PhiS_dth2 + 2*dPhiS_dr*(-1 + r) - 4*d2PhiS_dr2*r + 2*d2PhiS_dr2*r2) +\n a2*d2PhiS_dt2*(a2 + (-2 + r)*r)*sinth2) - a2*dPhiS_dth*sin2th + 2*dPhiS_dth*r*sin2th -\n dPhiS_dth*r2*sin2th))/((sinth2*(a2 + (-2 + r)*r)*(a2 + 2*r2 + a2*cos2th)));\n\n /* Store calculated quantities into the arrays provided by the caller,\n including the phase factor exp(-i*m*phi_p) */\n double cosmph = cos(m*xp.phi);\n double sinmph = sin(m*xp.phi);\n\n PhiS[0] = RePhiS*cosmph;\n PhiS[1] = - RePhiS*sinmph;\n\n dPhiS_dx[0] = dPhiS_dt*sinmph;\n dPhiS_dx[1] = dPhiS_dt*cosmph;\n dPhiS_dx[2] = dPhiS_dr*cosmph;\n dPhiS_dx[3] = - dPhiS_dr*sinmph;\n dPhiS_dx[4] = dPhiS_dth*cosmph;\n dPhiS_dx[5] = - dPhiS_dth*sinmph;\n dPhiS_dx[6] = dPhiS_dph*sinmph;\n dPhiS_dx[7] = dPhiS_dph*cosmph;\n\n d2PhiS_dx2[0] = d2PhiS_dt2*cosmph;\n d2PhiS_dx2[1] = - d2PhiS_dt2*sinmph;\n d2PhiS_dx2[2] = d2PhiS_dtr*cosmph;\n d2PhiS_dx2[3] = - d2PhiS_dtr*sinmph;\n d2PhiS_dx2[4] = d2PhiS_dtth*cosmph;\n d2PhiS_dx2[5] = - d2PhiS_dtth*sinmph;\n d2PhiS_dx2[6] = d2PhiS_dtph*cosmph;\n d2PhiS_dx2[7] = - d2PhiS_dtph*sinmph;\n d2PhiS_dx2[8] = d2PhiS_dr2*cosmph;\n d2PhiS_dx2[9] = - d2PhiS_dr2*sinmph;\n d2PhiS_dx2[10] = d2PhiS_drth*cosmph;\n d2PhiS_dx2[11] = - d2PhiS_drth*sinmph;\n d2PhiS_dx2[12] = d2PhiS_drph*cosmph;\n d2PhiS_dx2[13] = - d2PhiS_drph*sinmph;\n d2PhiS_dx2[14] = d2PhiS_dth2*cosmph;\n d2PhiS_dx2[15] = - d2PhiS_dth2*sinmph;\n d2PhiS_dx2[16] = d2PhiS_dthph*cosmph;\n d2PhiS_dx2[17] = - d2PhiS_dthph*sinmph;\n d2PhiS_dx2[18] = d2PhiS_dph2*cosmph;\n d2PhiS_dx2[19] = - d2PhiS_dph2*sinmph;\n\n src[0] = effsrc*cosmph;\n src[1] = - effsrc*sinmph;\n}\n\n/* Initialize array of coefficients of pows of dr, dtheta and dphi. */\nvoid effsource_init(double mass, double spin)\n{\n M = mass;\n a = spin;\n}\n\n/* Initialize array of coefficients of pows of dr, dtheta and dphi. */\nvoid effsource_set_particle(struct coordinate * x_p, double E, double L, double ur_p)\n{\n xp = *x_p;\n double r = xp.r;\n\n /* Compute A coefficients */\n {\n\tA006 = 64*pow(pow(L,2) + pow(r,2) + (pow(a,2)*(2*M + r))/r,3);\n\tA008 = (-32*pow(pow(a,2)*(2*M + r) + r*(pow(L,2) + pow(r,2)),2)*(-(pow(a,8)*pow(M,2)) + 4*pow(a,7)*E*L*pow(M,2) + 4*a*E*L*M*(2*M - 3*r)*pow(r,6) - 4*pow(a,3)*E*L*M*pow(r,3)*(22*pow(M,2) + 3*M*r + 4*pow(r,2)) - 4*pow(a,5)*E*L*M*(16*pow(M,3) + 18*pow(M,2)*r + pow(r,3)) + pow(r,6)*(2*M*pow(r,2)*(-2*M + r + 2*pow(E,2)*r) + pow(L,2)*(-16*pow(M,2) + 14*M*r - 3*pow(r,2))) + 2*pow(a,6)*M*(-2*pow(L,2)*M + 2*pow(E,2)*pow(2*M + r,3) + r*(2*pow(M,2) - M*r + pow(r,2))) + pow(a,2)*pow(r,3)*(2*M*pow(r,2)*(4*pow(M,2) + 6*(-1 + 2*pow(E,2))*M*r + 3*(1 + 2*pow(E,2))*pow(r,2)) + pow(L,2)*(32*pow(M,3) - 24*pow(M,2)*r + 16*M*pow(r,2) - 3*pow(r,3))) + pow(a,4)*M*(4*pow(L,2)*(8*pow(M,3) + 6*pow(M,2)*r - 3*M*pow(r,2) + 2*pow(r,3)) + pow(r,2)*(-4*pow(M,3) + 3*(-3 + 16*pow(E,2))*M*pow(r,2) + 6*(1 + 2*pow(E,2))*pow(r,3) + 4*pow(M,2)*(r + 12*pow(E,2)*r)))))/(3.*pow(r,8)*(pow(a,2) + r*(-2*M + r)));\n\tA024 = 48*pow(pow(a,2)*(2*M + r) + r*(pow(L,2) + pow(r,2)),2);\n\tA026 = (-16*(pow(a,2)*(2*M + r) + r*(pow(L,2) + pow(r,2)))*(-2*pow(a,7)*E*L*M*(24*pow(M,2) + 16*M*r + 3*pow(r,2)) + 2*a*E*L*M*pow(r,5)*(pow(L,2)*(10*M - 9*r) + (14*M - 15*r)*pow(r,2)) - 2*pow(a,5)*E*L*M*r*(16*pow(M,3) + 56*pow(M,2)*r + 50*M*pow(r,2) + 17*pow(r,3) + 3*pow(L,2)*(4*M + r)) + pow(a,8)*M*(6*pow(E,2)*pow(2*M + r,2) - r*(7*M + 3*r)) + pow(r,5)*(2*pow(L,2)*pow(r,2)*(-18*pow(M,2) + (21 + 2*pow(E,2))*M*r - 6*pow(r,2)) + pow(r,4)*(-8*pow(M,2) + 2*(5 + 4*pow(E,2))*M*r - 3*pow(r,2)) - 2*pow(L,4)*(8*pow(M,2) - 10*M*r + 3*pow(r,2))) + 2*pow(a,3)*E*L*M*pow(r,2)*(2*pow(L,2)*(4*pow(M,2) - 7*M*r - 6*pow(r,2)) - pow(r,2)*(16*pow(M,2) + 28*M*r + 29*pow(r,2))) + pow(a,4)*r*(12*pow(L,4)*pow(M,2) + pow(L,2)*(16*pow(M,4) - 8*(-5 + pow(E,2))*pow(M,3)*r + 16*(2 + pow(E,2))*pow(M,2)*pow(r,2) + 2*(-3 + 8*pow(E,2))*M*pow(r,3) - 9*pow(r,4)) + pow(r,2)*(4*pow(M,4) + 16*(2 + 3*pow(E,2))*pow(M,3)*r + 3*(3 + 32*pow(E,2))*pow(M,2)*pow(r,2) + 3*(-5 + 14*pow(E,2))*M*pow(r,3) - 9*pow(r,4))) + pow(a,2)*pow(r,2)*(pow(L,2)*pow(r,2)*(-4*pow(M,3) + 4*(6 + pow(E,2))*pow(M,2)*r + (33 + 14*pow(E,2))*M*pow(r,2) - 21*pow(r,3)) + pow(L,4)*(-8*pow(M,3) + 12*pow(M,2)*r + 8*M*pow(r,2) - 6*pow(r,3)) + pow(r,4)*(4*pow(M,3) + 3*(3 + 10*pow(E,2))*M*pow(r,2) - 9*pow(r,3) + 12*pow(M,2)*(r + 3*pow(E,2)*r))) + pow(a,6)*(pow(L,2)*M*(24*pow(M,2) + 4*(2 + 3*pow(E,2))*M*r + 3*(-1 + 2*pow(E,2))*pow(r,2)) + r*(-(r*(-12*pow(M,3) + 18*pow(M,2)*r + 17*M*pow(r,2) + 3*pow(r,3))) + 2*pow(E,2)*M*(8*pow(M,3) + 36*pow(M,2)*r + 42*M*pow(r,2) + 13*pow(r,3))))))/(3.*pow(r,6)*(pow(a,2) + r*(-2*M + r)));\n\tA042 = 12*pow(r,3)*(pow(a,2)*(2*M + r) + r*(pow(L,2) + pow(r,2)));\n\tA044 = (-2*(-4*pow(a,7)*E*L*M*(72*pow(M,2) + 59*M*r + 12*pow(r,2)) + 4*a*E*L*M*pow(r,3)*(pow(L,4)*(8*M - 6*r) + 6*pow(L,2)*(6*M - 5*r)*pow(r,2) + 3*(10*M - 9*r)*pow(r,4)) + pow(a,8)*(-13*pow(M,2)*r + 3*pow(r,3) + 36*pow(E,2)*M*pow(2*M + r,2)) - 4*pow(a,5)*E*L*M*r*(-48*pow(M,3) + 50*pow(M,2)*r + 140*M*pow(r,2) + 49*pow(r,3) + 6*pow(L,2)*(8*M + 3*r)) + pow(r,3)*(8*pow(L,6)*M*(-2*M + r) + pow(L,2)*pow(r,4)*(-120*pow(M,2) + 2*(71 + 12*pow(E,2))*M*r - 41*pow(r,2)) + pow(L,4)*pow(r,2)*(-100*pow(M,2) + 4*(25 + pow(E,2))*M*r - 25*pow(r,2)) + pow(r,6)*(-24*pow(M,2) + 2*(19 + 12*pow(E,2))*M*r - 13*pow(r,2))) - 4*pow(a,3)*E*L*M*pow(r,2)*(6*pow(L,4) + pow(L,2)*(-48*pow(M,2) + 36*M*r + 48*pow(r,2)) + pow(r,2)*(-66*pow(M,2) + 55*M*r + 64*pow(r,2))) + pow(a,2)*pow(r,2)*(12*pow(L,6)*M + pow(L,2)*pow(r,2)*(-192*pow(M,3) + 176*pow(M,2)*r + 12*(9 + 8*pow(E,2))*M*pow(r,2) - 73*pow(r,3)) + 2*pow(r,4)*(-12*pow(M,3) + 2*(23 + 18*pow(E,2))*pow(M,2)*r + 9*(1 + 6*pow(E,2))*M*pow(r,2) - 18*pow(r,3)) - 2*pow(L,4)*(48*pow(M,3) + 8*(-3 + pow(E,2))*pow(M,2)*r - 2*(17 + 4*pow(E,2))*M*pow(r,2) + 11*pow(r,3))) + pow(a,4)*r*(3*pow(L,4)*(32*pow(M,2) + 4*(2 + pow(E,2))*M*r + pow(r,2)) + pow(r,2)*(12*pow(M,4) + 116*pow(M,3)*r + (55 + 288*pow(E,2))*pow(M,2)*pow(r,2) + 6*(-13 + 30*pow(E,2))*M*pow(r,3) - 30*pow(r,4)) - 2*pow(L,2)*(48*pow(M,4) + 4*(-7 + 12*pow(E,2))*pow(M,3)*r - 2*(53 + 24*pow(E,2))*pow(M,2)*pow(r,2) + 4*(2 - 15*pow(E,2))*M*pow(r,3) + 13*pow(r,4))) + 2*pow(a,6)*(pow(L,2)*(72*pow(M,3) + 2*(23 + 24*pow(E,2))*pow(M,2)*r + 6*(1 + 4*pow(E,2))*M*pow(r,2) + 3*pow(r,3)) + r*(-(r*(-10*pow(M,3) + 37*pow(M,2)*r + 29*M*pow(r,2) + 2*pow(r,3))) + 6*pow(E,2)*M*(-8*pow(M,3) + 12*pow(M,2)*r + 30*M*pow(r,2) + 11*pow(r,3))))))/(3.*pow(r,3)*(pow(a,2) + r*(-2*M + r)));\n\tA060 = pow(r,6);\n\tA062 = (6*pow(a,5)*E*L*M*(12*M + 5*r) + 4*pow(a,3)*E*L*M*r*(6*pow(L,2) - 20*pow(M,2) + 11*M*r + 18*pow(r,2)) - 3*pow(a,6)*(r*(M + r) + 6*pow(E,2)*M*(2*M + r)) + 2*a*E*L*M*pow(r,2)*(-4*pow(L,2)*(4*M - 3*r) + pow(r,2)*(-26*M + 21*r)) + pow(r,2)*(8*pow(L,4)*M*(2*M - r) + 4*pow(r,4)*(2*pow(M,2) - (3 + 2*pow(E,2))*M*r + pow(r,2)) + pow(L,2)*pow(r,2)*(36*pow(M,2) - 4*(8 + pow(E,2))*M*r + 7*pow(r,2))) + pow(a,2)*r*(-12*pow(L,4)*M + 4*pow(L,2)*(10*pow(M,3) + (-3 + 4*pow(E,2))*pow(M,2)*r - 2*(3 + 2*pow(E,2))*M*pow(r,2) + pow(r,3)) + pow(r,2)*(4*pow(M,3) + 4*(-4 + pow(E,2))*pow(M,2)*r + (1 - 34*pow(E,2))*M*pow(r,2) + 5*pow(r,3))) - pow(a,4)*(3*pow(L,2)*(12*pow(M,2) + 4*(1 + pow(E,2))*M*r + pow(r,2)) + 2*r*(r*(-2*pow(M,2) - 5*M*r + pow(r,2)) + 2*pow(E,2)*M*(-10*pow(M,2) + 8*M*r + 11*pow(r,2)))))/(3.*(pow(a,2) + r*(-2*M + r)));\n\tA080 = (pow(r,3)*(r*(-3*pow(a,2) + r*(-2*M + r)) + (4*M*(-3*pow(a,4)*pow(E,2) + 6*pow(a,3)*E*L + 2*a*E*L*r*(-4*M + 3*r) + pow(a,2)*(-3*pow(L,2) + 4*pow(E,2)*(M - r)*r) - r*(pow(E,2)*pow(r,3) + pow(L,2)*(-4*M + 2*r))))/(pow(a,2) + r*(-2*M + r))))/24.;\n\tA106 = (-16*pow(pow(L,2) + pow(r,2) + (pow(a,2)*(2*M + r))/r,2)*(-2*pow(a,2)*M + 2*pow(r,3) + (4*L*(pow(a,3)*E*M - pow(a,2)*L*M + 3*a*E*M*pow(r,2) + L*pow(r,2)*(-2*M + r)))/(pow(a,2) + r*(-2*M + r))))/pow(r,2);\n\tA108 = (-16*(pow(a,2)*(2*M + r) + r*(pow(L,2) + pow(r,2)))*(2*pow(a,11)*E*L*pow(M,2)*(80*pow(M,2) + 73*M*r + 12*pow(r,2)) + 2*pow(a,9)*E*L*M*r*(32*(-1 + 6*pow(E,2))*pow(M,4) + 12*(23 + 24*pow(E,2))*pow(M,3)*r + (353 + 144*pow(E,2))*pow(M,2)*pow(r,2) + 2*(11 + 12*pow(E,2))*M*pow(r,3) - 12*pow(r,4) + 4*pow(L,2)*M*(16*M + 3*r)) + pow(a,12)*pow(M,2)*(3*r*(3*M + 2*r) - 8*pow(E,2)*(10*pow(M,2) + 11*M*r + 3*pow(r,2))) + 2*a*E*L*M*pow(r,5)*(6*pow(L,4)*pow(r,2)*(20*pow(M,2) + 4*pow(E,2)*M*r - 5*pow(r,2)) + 12*pow(L,6)*(4*pow(M,2) - pow(r,2)) + pow(L,2)*pow(r,4)*(136*pow(M,2) + 2*(-37 + 30*pow(E,2))*M*r + 3*pow(r,2)) - 2*pow(r,6)*(34*pow(M,2) - 41*M*r + 12*pow(r,2))) + 4*pow(a,3)*E*L*M*pow(r,3)*(6*pow(L,6)*(12*pow(M,2) - 2*M*r - pow(r,2)) + pow(L,2)*pow(r,3)*(-340*pow(M,3) + 6*(61 + 20*pow(E,2))*pow(M,2)*r + (-83 + 90*pow(E,2))*M*pow(r,2) - 23*pow(r,3)) + 2*pow(r,5)*(-192*pow(M,3) + 81*pow(M,2)*r + 6*(7 + pow(E,2))*M*pow(r,2) - 19*pow(r,3)) + 6*pow(L,4)*r*(20*pow(M,3) + 4*(10 + pow(E,2))*pow(M,2)*r + 2*(-5 + 2*pow(E,2))*M*pow(r,2) - 5*pow(r,3))) + 2*pow(a,5)*E*L*M*pow(r,2)*(6*pow(L,4)*(2*M + r)*(60*pow(M,2) + 2*(-5 + 2*pow(E,2))*M*r - 5*pow(r,2)) + pow(r,3)*(-420*pow(M,4) - 876*pow(M,3)*r + (907 + 144*pow(E,2))*pow(M,2)*pow(r,2) + 24*(5 + 3*pow(E,2))*M*pow(r,3) - 92*pow(r,4)) + pow(L,2)*r*(-608*pow(M,4) + 8*(13 + 30*pow(E,2))*pow(M,3)*r + 48*(17 + 10*pow(E,2))*pow(M,2)*pow(r,2) + 36*(-7 + 5*pow(E,2))*M*pow(r,3) - 79*pow(r,4))) + pow(a,2)*pow(r,3)*(48*pow(L,8)*pow(M,2)*(-2*M + r) - 24*pow(L,6)*M*pow(r,2)*(2*(5 + 4*pow(E,2))*pow(M,2) + (-5 + 4*pow(E,2))*M*r - 2*pow(E,2)*pow(r,2)) + 2*M*pow(r,7)*(60*pow(M,3) + 4*(-22 + 25*pow(E,2))*pow(M,2)*r + (51 - 86*pow(E,2))*M*pow(r,2) + (-11 + 23*pow(E,2))*pow(r,3)) + pow(L,2)*pow(r,5)*(752*pow(M,4) - 4*(197 + 66*pow(E,2))*pow(M,3)*r + 8*(28 - 11*pow(E,2))*pow(M,2)*pow(r,2) + 3*(1 + 48*pow(E,2))*M*pow(r,3) - 6*pow(r,4)) + 2*pow(L,4)*pow(r,3)*(232*pow(M,4) - 36*(9 + 10*pow(E,2))*pow(M,3)*r - 2*(-71 + 60*pow(E,2))*pow(M,2)*pow(r,2) + 5*(-5 + 18*pow(E,2))*M*pow(r,3) + 3*pow(r,4))) + 2*pow(a,7)*E*L*M*r*(2*pow(L,2)*(288*pow(M,4) + 8*(29 + 15*pow(E,2))*pow(M,3)*r + 2*(71 + 60*pow(E,2))*pow(M,2)*pow(r,2) + 2*(-26 + 15*pow(E,2))*M*pow(r,3) - 15*pow(r,4)) + r*(-256*pow(M,5) - 556*pow(M,4)*r + 8*(-7 + 36*pow(E,2))*pow(M,3)*pow(r,2) + (827 + 288*pow(E,2))*pow(M,2)*pow(r,3) + 4*(11 + 18*pow(E,2))*M*pow(r,4) - 52*pow(r,5))) - pow(a,4)*pow(r,2)*(24*pow(L,6)*M*(20*pow(M,3) + 12*pow(E,2)*pow(M,2)*r + (-5 + 2*pow(E,2))*M*pow(r,2) - pow(E,2)*pow(r,3)) + 2*pow(L,4)*M*r*(-304*pow(M,4) + 8*(11 + 60*pow(E,2))*pow(M,3)*r + 60*(5 + 14*pow(E,2))*pow(M,2)*pow(r,2) + 60*(-3 + pow(E,2))*M*pow(r,3) + (11 - 90*pow(E,2))*pow(r,4)) + M*pow(r,5)*(48*pow(M,4) - 4*(31 + 168*pow(E,2))*pow(M,3)*r - 8*(-34 + 21*pow(E,2))*pow(M,2)*pow(r,2) + (-199 + 448*pow(E,2))*M*pow(r,3) + 12*(4 - 7*pow(E,2))*pow(r,4)) + pow(L,2)*pow(r,3)*(-296*pow(M,5) - 16*(50 + 57*pow(E,2))*pow(M,4)*r + 2*(627 + 452*pow(E,2))*pow(M,3)*pow(r,2) + 2*(-215 + 12*pow(E,2))*pow(M,2)*pow(r,3) - 6*(-3 + 38*pow(E,2))*M*pow(r,4) + 3*pow(r,5))) + pow(a,6)*M*r*(-4*pow(L,4)*(96*pow(M,4) + 4*(11 + 90*pow(E,2))*pow(M,3)*r + 16*(2 + 15*pow(E,2))*pow(M,2)*pow(r,2) - 38*M*pow(r,3) - 15*pow(E,2)*pow(r,4)) + pow(r,3)*(-56*pow(M,5) + 4*(9 + 128*pow(E,2))*pow(M,4)*r + 2*(41 + 520*pow(E,2))*pow(M,3)*pow(r,2) - (157 + 464*pow(E,2))*pow(M,2)*pow(r,3) + (163 - 568*pow(E,2))*M*pow(r,4) + 4*(-13 + 19*pow(E,2))*pow(r,5)) + pow(L,2)*r*(256*pow(M,5) + 8*(47 + 76*pow(E,2))*pow(M,4)*r - 8*(-3 + 76*pow(E,2))*pow(M,3)*pow(r,2) - 2*(415 + 716*pow(E,2))*pow(M,2)*pow(r,3) + 2*(143 - 8*pow(E,2))*M*pow(r,4) + (-17 + 160*pow(E,2))*pow(r,5))) - (2*M - r)*pow(r,8)*(2*pow(E,2)*M*(12*pow(L,6) + 30*pow(L,4)*pow(r,2) + 17*pow(L,2)*pow(r,4) + 5*pow(r,6)) + (2*M - r)*r*(2*pow(L,4)*(8*M - 3*r) + 4*M*pow(r,4) + pow(L,2)*pow(r,2)*(2*M + 3*r))) - pow(a,10)*M*(2*pow(L,2)*M*(40*pow(M,2) + (29 + 32*pow(E,2))*M*r + 3*(-1 + 4*pow(E,2))*pow(r,2)) + r*(r*(50*pow(M,3) + 11*pow(M,2)*r - 19*M*pow(r,2) + 6*pow(r,3)) + pow(E,2)*(-32*pow(M,4) + 336*pow(M,3)*r + 504*pow(M,2)*pow(r,2) + 156*M*pow(r,3) - 6*pow(r,4)))) - pow(a,8)*M*r*(64*pow(L,4)*pow(M,2) + 2*pow(L,2)*(16*(-1 + 36*pow(E,2))*pow(M,4) + 4*(27 + 166*pow(E,2))*pow(M,3)*r + (141 + 364*pow(E,2))*pow(M,2)*pow(r,2) + 3*(-13 + 6*pow(E,2))*M*pow(r,3) + 3*(1 - 7*pow(E,2))*pow(r,4)) + r*(r*(-92*pow(M,4) + 20*pow(M,3)*r + 65*pow(M,2)*pow(r,2) - 63*M*pow(r,3) + 28*pow(r,4)) - 2*pow(E,2)*(128*pow(M,5) + 368*pow(M,4)*r + 120*pow(M,3)*pow(r,2) - 424*pow(M,2)*pow(r,3) - 202*M*pow(r,4) + 17*pow(r,5))))))/(3.*pow(r,10)*pow(pow(a,2) + r*(-2*M + r),2));\n\tA124 = 8*(pow(L,2) + pow(r,2) + (pow(a,2)*(2*M + r))/r)*(-(pow(a,2)*r) - pow(L,2)*r - 3*pow(r,3) - (4*L*(pow(a,3)*E*M - pow(a,2)*L*M + 3*a*E*M*pow(r,2) + L*pow(r,2)*(-2*M + r)))/(pow(a,2) + r*(-2*M + r)));\n\tA126 = (-4*(2*pow(a,11)*E*L*pow(M,2)*(-16*(-16 + 9*pow(E,2))*pow(M,2) + (293 - 144*pow(E,2))*M*r + 6*(13 - 6*pow(E,2))*pow(r,2)) + 2*a*E*L*M*pow(r,5)*(2*pow(L,4)*pow(r,2)*(328*pow(M,2) + 2*(-79 + 21*pow(E,2))*M*r - 3*pow(r,2)) + 42*pow(L,6)*(4*pow(M,2) - pow(r,2)) + 3*pow(L,2)*pow(r,4)*(128*pow(M,2) + 2*(-37 + 20*pow(E,2))*M*r + 5*pow(r,2)) - 2*pow(r,6)*(118*pow(M,2) - 125*M*r + 33*pow(r,2))) - (2*M - r)*pow(r,7)*(2*pow(r,6)*(16*pow(M,2) + 2*(-7 + 10*pow(E,2))*M*r + 3*pow(r,2)) + 4*pow(L,6)*(16*pow(M,2) + (-20 + 21*pow(E,2))*M*r + 6*pow(r,2)) + 2*pow(L,2)*pow(r,4)*(10*pow(M,2) + (-17 + 66*pow(E,2))*M*r + 6*pow(r,2)) + pow(L,4)*pow(r,2)*(88*pow(M,2) + 2*(-61 + 94*pow(E,2))*M*r + 39*pow(r,2))) + pow(a,12)*M*(3*r*(21*pow(M,2) + 23*M*r + 6*pow(r,2)) - 2*pow(E,2)*(128*pow(M,3) + 172*pow(M,2)*r + 72*M*pow(r,2) + 9*pow(r,3))) + 4*pow(a,3)*E*L*M*pow(r,3)*(21*pow(L,6)*(12*pow(M,2) - 2*M*r - pow(r,2)) + pow(r,5)*(-1104*pow(M,3) + 4*(82 + 27*pow(E,2))*pow(M,2)*r + (311 - 18*pow(E,2))*M*pow(r,2) - 103*pow(r,3)) + 2*pow(L,4)*r*(256*pow(M,3) + 2*(127 + 21*pow(E,2))*pow(M,2)*r + 6*(-24 + 7*pow(E,2))*M*pow(r,2) - 21*pow(r,3)) - 2*pow(L,2)*pow(r,3)*(102*pow(M,3) - 2*(92 + 87*pow(E,2))*pow(M,2)*r + 5*(17 - 15*pow(E,2))*M*pow(r,2) + 11*pow(r,3))) + 2*pow(a,5)*E*L*M*pow(r,2)*(2*pow(L,4)*(1224*pow(M,3) + 28*(-1 + 3*pow(E,2))*pow(M,2)*r + 2*(-95 + 21*pow(E,2))*M*pow(r,2) - 39*pow(r,3)) + pow(r,3)*(-3300*pow(M,4) + 4*(-517 + 216*pow(E,2))*pow(M,3)*r + (2435 + 504*pow(E,2))*pow(M,2)*pow(r,2) + 12*(59 - 12*pow(E,2))*M*pow(r,3) - 250*pow(r,4)) + pow(L,2)*r*(-192*pow(M,4) + 8*(169 + 114*pow(E,2))*pow(M,3)*r + 72*(4 + 17*pow(E,2))*pow(M,2)*pow(r,2) + 2*(-131 + 102*pow(E,2))*M*pow(r,3) - 131*pow(r,4))) - 2*pow(a,9)*E*L*M*(2*pow(L,2)*M*(216*pow(M,2) + 4*(2 + 9*pow(E,2))*M*r + 3*(-17 + 6*pow(E,2))*pow(r,2)) + r*(-288*(1 + 3*pow(E,2))*pow(M,4) - 4*(275 + 144*pow(E,2))*pow(M,3)*r + 3*(-403 + 72*pow(E,2))*pow(M,2)*pow(r,2) + 6*(-43 + 24*pow(E,2))*M*pow(r,3) + 36*pow(r,4))) + pow(a,2)*pow(r,3)*(-168*pow(L,8)*pow(M,2)*(2*M - r) - 2*pow(L,6)*r*(56*pow(M,4) + 12*(23 + 28*pow(E,2))*pow(M,3)*r + 14*(-13 + 12*pow(E,2))*pow(M,2)*pow(r,2) + 3*(13 - 28*pow(E,2))*M*pow(r,3) - 12*pow(r,4)) + 2*pow(r,7)*(132*pow(M,4) + 4*(-39 + 64*pow(E,2))*pow(M,3)*r + (113 - 246*pow(E,2))*pow(M,2)*pow(r,2) + (-58 + 79*pow(E,2))*M*pow(r,3) + 12*pow(r,4)) + 2*pow(L,4)*pow(r,3)*(592*pow(M,4) - 4*(139 + 329*pow(E,2))*pow(M,3)*r + 2*(91 - 22*pow(E,2))*pow(M,2)*pow(r,2) + 5*(-22 + 53*pow(E,2))*M*pow(r,3) + 42*pow(r,4)) + pow(L,2)*pow(r,5)*(2112*pow(M,4) - 4*(419 + 324*pow(E,2))*pow(M,3)*r - 4*(-73 + 4*pow(E,2))*pow(M,2)*pow(r,2) + (-93 + 464*pow(E,2))*M*pow(r,3) + 51*pow(r,4))) + 2*pow(a,7)*E*L*M*r*(-24*pow(L,4)*M*(9*M - r) + 2*pow(L,2)*(1296*pow(M,4) + 8*(35 + 51*pow(E,2))*pow(M,3)*r + 4*(-52 + 57*pow(E,2))*pow(M,2)*pow(r,2) - (19 + 6*pow(E,2))*M*pow(r,3) - 36*pow(r,4)) + r*(-1600*pow(M,5) + 4*(-515 + 216*pow(E,2))*pow(M,4)*r + 72*(13 + 22*pow(E,2))*pow(M,3)*pow(r,2) + 3*(857 + 72*pow(E,2))*pow(M,2)*pow(r,3) + 12*(43 - 18*pow(E,2))*M*pow(r,4) - 146*pow(r,5))) + pow(a,4)*pow(r,2)*(-4*pow(L,6)*M*(408*pow(M,3) + 4*(-32 + 63*pow(E,2))*pow(M,2)*r + 2*(-26 + 21*pow(E,2))*M*pow(r,2) - (5 + 21*pow(E,2))*pow(r,3)) + 2*pow(r,5)*(192*pow(M,5) + 24*(-1 + 53*pow(E,2))*pow(M,4)*r + 12*(-18 + 11*pow(E,2))*pow(M,3)*pow(r,2) + 4*(27 - 152*pow(E,2))*pow(M,2)*pow(r,3) + (-47 + 107*pow(E,2))*M*pow(r,4) + 18*pow(r,5)) + pow(L,4)*r*(1056*pow(M,5) - 80*(12 + 47*pow(E,2))*pow(M,4)*r - 8*(60 + 491*pow(E,2))*pow(M,3)*pow(r,2) + 12*(12 + 65*pow(E,2))*pow(M,2)*pow(r,3) + 2*(38 + 239*pow(E,2))*M*pow(r,4) + 45*pow(r,5)) + pow(L,2)*pow(r,3)*(3096*pow(M,5) + 12*(55 - 192*pow(E,2))*pow(M,4)*r - 2*(1367 + 788*pow(E,2))*pow(M,3)*pow(r,2) + (275 + 1116*pow(E,2))*pow(M,2)*pow(r,3) + 6*(21 + 94*pow(E,2))*M*pow(r,4) + 66*pow(r,5))) + pow(a,6)*r*(6*pow(L,6)*M*(24*pow(M,2) - 10*M*r + 3*pow(r,2)) - 2*pow(L,4)*M*(864*pow(M,4) + 8*(-1 + 306*pow(E,2))*pow(M,3)*r + 4*(-29 + 164*pow(E,2))*pow(M,2)*pow(r,2) - 32*(-2 + 9*pow(E,2))*M*pow(r,3) - (69 + 59*pow(E,2))*pow(r,4)) + pow(r,3)*(-152*pow(M,6) + 4*(23 + 800*pow(E,2))*pow(M,5)*r + 2*(-31 + 1672*pow(E,2))*pow(M,4)*pow(r,2) - (331 + 1792*pow(E,2))*pow(M,3)*pow(r,3) + (109 - 1704*pow(E,2))*pow(M,2)*pow(r,4) + 4*(8 + 19*pow(E,2))*M*pow(r,5) + 24*pow(r,6)) + pow(L,2)*r*(1600*pow(M,6) - 8*(-167 + 300*pow(E,2))*pow(M,5)*r - 4*(243 + 1228*pow(E,2))*pow(M,4)*pow(r,2) + 6*(-333 + 40*pow(E,2))*pow(M,3)*pow(r,3) + (59 + 1196*pow(E,2))*pow(M,2)*pow(r,4) + (293 + 228*pow(E,2))*M*pow(r,5) + 27*pow(r,6))) - pow(a,10)*M*(pow(L,2)*(-32*(-8 + 27*pow(E,2))*pow(M,3) + (242 - 448*pow(E,2))*pow(M,2)*r + 3*(-19 + 20*pow(E,2))*M*pow(r,2) + 18*(-3 + 2*pow(E,2))*pow(r,3)) + r*(r*(290*pow(M,3) + 165*pow(M,2)*r - 141*M*pow(r,2) - 68*pow(r,3)) + 2*pow(E,2)*(144*pow(M,4) + 680*pow(M,3)*r + 864*pow(M,2)*pow(r,2) + 358*M*pow(r,3) + 37*pow(r,4)))) + pow(a,8)*(2*pow(L,4)*M*(144*pow(M,3) + 8*(-8 + 27*pow(E,2))*pow(M,2)*r + 6*(-6 + 7*pow(E,2))*M*pow(r,2) - 9*(-3 + pow(E,2))*pow(r,3)) - pow(L,2)*M*r*(288*(1 + 18*pow(E,2))*pow(M,4) + 8*(105 + 286*pow(E,2))*pow(M,3)*r - 2*(-589 + 516*pow(E,2))*pow(M,2)*pow(r,2) + (15 - 268*pow(E,2))*M*pow(r,3) + 2*(-93 + 20*pow(E,2))*pow(r,4)) + pow(r,2)*(4*pow(E,2)*M*(400*pow(M,5) + 696*pow(M,4)*r - 12*pow(M,3)*pow(r,2) - 732*pow(M,2)*pow(r,3) - 368*M*pow(r,4) - 19*pow(r,5)) + r*(404*pow(M,5) + 8*pow(M,4)*r - 375*pow(M,3)*pow(r,2) + 103*pow(M,2)*pow(r,3) + 100*M*pow(r,4) + 6*pow(r,5))))))/(3.*pow(r,7)*pow(pow(a,2) + r*(-2*M + r),2));\n\tA142 = pow(r,2)*(2*pow(a,2)*M - 2*pow(r,3) - (4*L*(pow(a,3)*E*M - pow(a,2)*L*M + 3*a*E*M*pow(r,2) + L*pow(r,2)*(-2*M + r)))/(pow(a,2) + r*(-2*M + r)) - 4*(pow(a,2)*(2*M + r) + r*(pow(L,2) + pow(r,2))));\n\tA144 = (2*pow(a,9)*E*L*M*(16*(-16 + 9*pow(E,2))*pow(M,2) + 12*(-13 + 6*pow(E,2))*M*r - 3*pow(r,2)) + (2*M - r)*pow(r,4)*(16*pow(L,6)*M*(2*M - r) + 2*pow(L,2)*pow(r,4)*(-6*pow(M,2) + (-5 + 66*pow(E,2))*M*r + 4*pow(r,2)) + 2*pow(L,4)*pow(r,2)*(34*pow(M,2) + (-33 + 47*pow(E,2))*M*r + 8*pow(r,2)) + pow(r,6)*(48*pow(M,2) + 10*(-5 + 6*pow(E,2))*M*r + 13*pow(r,2))) - 2*a*E*L*M*pow(r,4)*(2*pow(L,4)*(200*pow(M,2) - 94*M*r - 3*pow(r,2)) + 3*pow(L,2)*pow(r,2)*(188*pow(M,2) + 4*(-27 + 5*pow(E,2))*M*r + 7*pow(r,2)) - 3*pow(r,4)*(100*pow(M,2) - 116*M*r + 33*pow(r,2))) + pow(a,10)*M*(-9*r*(13*M + 7*r) + pow(E,2)*(256*pow(M,2) + 264*M*r + 66*pow(r,2))) - 2*pow(a,3)*E*L*M*pow(r,2)*(4*pow(L,4)*(180*pow(M,2) - 92*M*r - 3*pow(r,2)) + pow(L,2)*r*(768*pow(M,3) + 4*(67 + 84*pow(E,2))*pow(M,2)*r + 4*(-149 + 9*pow(E,2))*M*pow(r,2) + 15*pow(r,3)) - 4*pow(r,3)*(426*pow(M,3) - (85 + 108*pow(E,2))*pow(M,2)*r + 12*(-13 + 3*pow(E,2))*M*pow(r,2) + 52*pow(r,3))) - 2*pow(a,5)*E*L*M*r*(-6*pow(L,4)*(18*M + r) + pow(L,2)*(1728*pow(M,3) + 24*(-33 + 10*pow(E,2))*pow(M,2)*r - 4*(83 + 15*pow(E,2))*M*pow(r,2) - 9*pow(r,3)) + 4*r*(-336*pow(M,4) + 2*(-107 + 108*pow(E,2))*pow(M,3)*r + 3*(79 + 36*pow(E,2))*pow(M,2)*pow(r,2) + (161 - 90*pow(E,2))*M*pow(r,3) - 34*pow(r,4))) - pow(a,2)*pow(r,2)*(-2*pow(L,6)*M*(240*pow(M,2) - 154*M*r + 17*pow(r,2)) + 2*pow(L,4)*r*(48*pow(M,4) - 4*(35 + 176*pow(E,2))*pow(M,3)*r + 8*(8 + 15*pow(E,2))*pow(M,2)*pow(r,2) + (-35 + 73*pow(E,2))*M*pow(r,3) + 16*pow(r,4)) + pow(r,5)*(264*pow(M,4) + 4*(-11 + 144*pow(E,2))*pow(M,3)*r + 2*(11 - 222*pow(E,2))*pow(M,2)*pow(r,2) + (-125 + 138*pow(E,2))*M*pow(r,3) + 46*pow(r,4)) + pow(L,2)*pow(r,3)*(1656*pow(M,4) - 12*(65 + 166*pow(E,2))*pow(M,3)*r + 2*(-161 + 374*pow(E,2))*pow(M,2)*pow(r,2) + (47 + 256*pow(E,2))*M*pow(r,3) + 51*pow(r,4))) - pow(a,4)*r*(6*pow(L,6)*M*(12*M + r) + 2*pow(L,4)*(-576*pow(M,4) - 36*(-9 + 20*pow(E,2))*pow(M,3)*r + 2*(-19 + 137*pow(E,2))*pow(M,2)*pow(r,2) + (47 + 29*pow(E,2))*M*pow(r,3) + 8*pow(r,4)) + pow(r,3)*(192*pow(M,5) + 4*(85 + 468*pow(E,2))*pow(M,4)*r + 228*(-1 + 2*pow(E,2))*pow(M,3)*pow(r,2) - 3*(149 + 268*pow(E,2))*pow(M,2)*pow(r,3) - 12*(-9 + pow(E,2))*M*pow(r,4) + 60*pow(r,5)) + pow(L,2)*r*(1344*pow(M,5) + 32*(13 - 105*pow(E,2))*pow(M,4)*r - 4*(243 + 280*pow(E,2))*pow(M,3)*pow(r,2) + 28*(-29 + 75*pow(E,2))*pow(M,2)*pow(r,3) + (391 + 56*pow(E,2))*M*pow(r,4) + 66*pow(r,5))) + 2*pow(a,7)*E*L*M*(4*r*(-8*(5 + 18*pow(E,2))*pow(M,3) + 3*(-59 + 12*pow(E,2))*pow(M,2)*r + (-121 + 72*pow(E,2))*M*pow(r,2) + 6*pow(r,3)) + 3*pow(L,2)*(144*pow(M,2) + pow(r,2) + 4*M*(r + 3*pow(E,2)*r))) + pow(a,8)*(pow(L,2)*M*(-32*(-8 + 27*pow(E,2))*pow(M,2) + 12*(4 - 19*pow(E,2))*M*r + 3*(-41 + 20*pow(E,2))*pow(r,2)) + r*(-(r*(-420*pow(M,3) + 115*pow(M,2)*r + 256*M*pow(r,2) + 7*pow(r,3))) + 4*pow(E,2)*M*(40*pow(M,3) + 178*pow(M,2)*r + 209*M*pow(r,2) + 60*pow(r,3)))) - pow(a,6)*(6*pow(L,4)*M*(48*pow(M,2) + 2*(-5 + 18*pow(E,2))*M*r + (11 + pow(E,2))*pow(r,2)) + pow(L,2)*r*(-32*(5 + 108*pow(E,2))*pow(M,4) + 8*(-88 + 153*pow(E,2))*pow(M,3)*r + 2*(-247 + 658*pow(E,2))*pow(M,2)*pow(r,2) + (417 - 128*pow(E,2))*M*pow(r,3) + 23*pow(r,4)) + pow(r,2)*(4*pow(E,2)*M*(336*pow(M,4) + 324*pow(M,3)*r - 128*pow(M,2)*pow(r,2) - 263*M*pow(r,3) - 66*pow(r,4)) + r*(276*pow(M,4) - 652*pow(M,3)*r - 323*pow(M,2)*pow(r,2) + 350*M*pow(r,3) + 34*pow(r,4)))))/(3.*pow(r,4)*pow(pow(a,2) + r*(-2*M + r),2));\n\tA160 = -pow(r,5)/2.;\n\tA162 = (6*pow(a,7)*E*L*M*(12*(-4 + pow(E,2))*M - 11*r) + 3*pow(a,8)*(3*r*(-3*M + r) + 2*pow(E,2)*M*(24*M + 13*r)) + 2*a*E*L*M*(2*M - r)*pow(r,3)*((82*M - 51*r)*pow(r,2) + pow(L,2)*(-124*M + 30*r)) + (2*M - r)*pow(r,3)*(8*pow(L,4)*M*(2*M - r) + pow(L,2)*pow(r,2)*(-36*pow(M,2) + 4*(8 + 11*pow(E,2))*M*r - 7*pow(r,2)) + 8*pow(r,4)*(4*pow(M,2) + (-4 + 5*pow(E,2))*M*r + pow(r,2))) - 2*pow(a,5)*E*L*M*(-12*pow(L,2)*(9*M - 2*r) + r*(8*(-11 + 15*pow(E,2))*pow(M,2) - 24*(-9 + 5*pow(E,2))*M*r + 63*pow(r,2))) - 2*pow(a,3)*E*L*M*r*(pow(L,2)*(360*pow(M,2) - 352*M*r + 54*pow(r,2)) - r*(400*pow(M,3) + 4*(19 - 54*pow(E,2))*pow(M,2)*r + 4*(-40 + 21*pow(E,2))*M*pow(r,2) + 21*pow(r,3))) - pow(a,2)*r*(-8*pow(L,4)*M*(30*pow(M,2) - 29*M*r + 7*pow(r,2)) + pow(r,3)*(88*pow(M,4) + 4*(27 + 64*pow(E,2))*pow(M,3)*r - 2*(57 + 50*pow(E,2))*pow(M,2)*pow(r,2) + (-11 + 26*pow(E,2))*M*pow(r,3) + 15*pow(r,4)) + pow(L,2)*r*(400*pow(M,4) + 8*(-26 + 63*pow(E,2))*pow(M,2)*pow(r,2) + 4*(17 + 4*pow(E,2))*M*pow(r,3) + pow(r,4) - 64*pow(M,3)*(r + 14*pow(E,2)*r))) + pow(a,6)*(-3*pow(L,2)*(24*(-2 + 3*pow(E,2))*pow(M,2) + (4 - 8*pow(E,2))*M*r - 3*pow(r,2)) + r*(r*(86*pow(M,2) - 139*M*r + 19*pow(r,2)) + 2*pow(E,2)*M*(-44*pow(M,2) + 98*M*r + 105*pow(r,2)))) + pow(a,4)*(24*pow(L,4)*M*(-3*M + r) + pow(L,2)*r*(8*(-11 + 90*pow(E,2))*pow(M,3) + 4*(59 - 178*pow(E,2))*pow(M,2)*r + 2*(-41 + 26*pow(E,2))*M*pow(r,2) + pow(r,3)) + pow(r,2)*(r*(-20*pow(M,3) + 296*pow(M,2)*r - 149*M*pow(r,2) + 3*pow(r,3)) + 2*pow(E,2)*M*(-200*pow(M,3) - 108*pow(M,2)*r + 36*M*pow(r,2) + 73*pow(r,3)))))/(12.*r*pow(pow(a,2) + r*(-2*M + r),2));\n\tA180 = -(pow(r,2)*(60*pow(a,3)*E*L*M + 4*a*E*L*M*r*(8*M + 3*r) - 3*pow(a,4)*(10*pow(E,2)*M + 3*r) + r*(8*pow(L,2)*M*(-2*M + r) + pow(r,2)*(8*pow(M,2) + 2*(-3 + 5*pow(E,2))*M*r + pow(r,2))) - 2*pow(a,2)*(15*pow(L,2)*M + r*(r*(-7*M + 4*r) + 2*pow(E,2)*M*(4*M + 5*r)))))/(48.*(pow(a,2) + r*(-2*M + r)));\n\tA204 = (48*pow(pow(a,2)*(2*M + r) + r*(pow(L,2) + pow(r,2)),2))/(pow(a,2) + r*(-2*M + r));\n\tA206 = (8*(pow(a,2)*(2*M + r) + r*(pow(L,2) + pow(r,2)))*(-4*pow(a,7)*E*L*M*(12*pow(M,2) + 23*M*r + 3*pow(r,2)) - 4*a*E*L*M*pow(r,5)*(pow(L,2)*(67*M - 36*r) + (17*M - 15*r)*pow(r,2)) - 4*pow(a,5)*E*L*M*r*(-64*pow(M,3) - 104*pow(M,2)*r + 55*M*pow(r,2) + 7*pow(r,3) + 3*pow(L,2)*(8*M + r)) + pow(a,8)*M*(-(r*(M + 6*r)) + 12*pow(E,2)*(2*pow(M,2) + 3*M*r + pow(r,2))) + 4*pow(a,3)*E*L*M*pow(r,2)*(pow(L,2)*(16*pow(M,2) - 73*M*r + 3*pow(r,2)) + pow(r,2)*(196*pow(M,2) - 17*M*r + 11*pow(r,2))) + pow(r,5)*(8*pow(L,4)*(10*pow(M,2) - 11*M*r + 3*pow(r,2)) + pow(r,4)*(40*pow(M,2) - 2*(19 + 2*pow(E,2))*M*r + 9*pow(r,2)) + 2*pow(L,2)*pow(r,2)*(54*pow(M,2) + (-57 + 2*pow(E,2))*M*r + 15*pow(r,2))) - 2*pow(a,2)*pow(r,2)*(pow(r,4)*(58*pow(M,3) + 3*(-23 + 26*pow(E,2))*pow(M,2)*r + 33*M*pow(r,2) - 6*pow(r,3)) + 2*pow(L,4)*(8*pow(M,3) - 33*pow(M,2)*r + 10*M*pow(r,2) + 3*pow(r,3)) - pow(L,2)*pow(r,2)*(-194*pow(M,3) + (171 + 104*pow(E,2))*pow(M,2)*r + (-57 + 10*pow(E,2))*M*pow(r,2) + 6*pow(r,3))) + pow(a,4)*r*(48*pow(L,4)*pow(M,2) + pow(r,2)*(4*pow(M,4) + 20*(1 - 18*pow(E,2))*pow(M,3)*r - 3*(-53 + 76*pow(E,2))*pow(M,2)*pow(r,2) + 12*(-7 + 2*pow(E,2))*M*pow(r,3) - 3*pow(r,4)) - 2*pow(L,2)*(64*pow(M,4) + 8*(11 + 2*pow(E,2))*pow(M,3)*r - (109 + 80*pow(E,2))*pow(M,2)*pow(r,2) + (51 - 14*pow(E,2))*M*pow(r,3) + 9*pow(r,4))) + 2*pow(a,6)*(pow(L,2)*M*(12*pow(M,2) + 4*(7 + 6*pow(E,2))*M*r + 3*(-1 + 2*pow(E,2))*pow(r,2)) - r*(pow(r,3)*(31*M + 3*r) + 2*pow(E,2)*M*(32*pow(M,3) + 60*pow(M,2)*r + 9*M*pow(r,2) - 8*pow(r,3))))))/(3.*pow(r,6)*pow(pow(a,2) + r*(-2*M + r),2));\n\tA222 = (24*pow(r,3)*(pow(a,2)*(2*M + r) + r*(pow(L,2) + pow(r,2))))/(pow(a,2) + r*(-2*M + r));\n\tA224 = (2*(4*pow(a,7)*E*L*M*(24*pow(M,2) + 19*M*r + 9*pow(r,2)) - 4*a*E*L*M*pow(r,3)*(4*pow(L,4)*M + 9*pow(L,2)*(12*M - 7*r)*pow(r,2) + 6*(9*M - 7*r)*pow(r,4)) + 4*pow(a,5)*E*L*M*r*(48*pow(M,3) + 142*pow(M,2)*r + 76*M*pow(r,2) + 50*pow(r,3) + pow(L,2)*(-6*M + 9*r)) - pow(a,8)*(24*pow(E,2)*pow(M,2)*(2*M + r) + r*(49*pow(M,2) + 42*M*r + 6*pow(r,2))) + pow(r,3)*(4*pow(L,6)*M*(2*M - r) + 12*pow(L,2)*pow(r,4)*(28*pow(M,2) - 32*M*r + 9*pow(r,2)) + 3*pow(r,6)*(40*pow(M,2) - 2*(23 + 2*pow(E,2))*M*r + 13*pow(r,2)) + 2*pow(L,4)*pow(r,2)*(118*pow(M,2) + (-131 + 2*pow(E,2))*M*r + 36*pow(r,2))) + 4*pow(a,3)*E*L*M*pow(r,3)*(-6*pow(L,2)*(9*M - 8*r) + r*(114*pow(M,2) + 23*M*r + 83*pow(r,2))) + 2*pow(a,2)*pow(r,3)*(pow(L,4)*(4*(18 + pow(E,2))*pow(M,2) + (-71 + 2*pow(E,2))*M*r + 15*pow(r,2)) - 3*pow(r,3)*(12*pow(M,3) + 2*(-7 + 24*pow(E,2))*pow(M,2)*r + (31 + 6*pow(E,2))*M*pow(r,2) - 15*pow(r,3)) + 3*pow(L,2)*r*(-32*pow(M,3) + 2*(19 + 9*pow(E,2))*pow(M,2)*r - 61*M*pow(r,2) + 25*pow(r,3))) + pow(a,4)*r*(6*pow(L,4)*(2*pow(M,2) - 6*M*r - pow(r,2)) - 3*pow(r,2)*(76*pow(M,4) + 12*(-1 + 16*pow(E,2))*pow(M,3)*r + 3*(-19 + 56*pow(E,2))*pow(M,2)*pow(r,2) + 4*(7 + 3*pow(E,2))*M*pow(r,3) - 19*pow(r,4)) - 2*pow(L,2)*(48*pow(M,4) + 68*pow(M,3)*r - 4*(13 + 9*pow(E,2))*pow(M,2)*pow(r,2) + 84*M*pow(r,3) - 15*pow(r,4))) - 2*pow(a,6)*(pow(L,2)*(24*pow(M,3) + (26 - 6*pow(E,2))*pow(M,2)*r + 39*M*pow(r,2) + 6*pow(r,3)) + M*r*(r*(-106*pow(M,2) - 37*M*r + 39*pow(r,2)) + 6*pow(E,2)*(8*pow(M,3) + 36*pow(M,2)*r + 20*M*pow(r,2) + pow(r,3))))))/(3.*pow(r,3)*pow(pow(a,2) + r*(-2*M + r),2));\n\tA240 = (3*pow(r,6))/(pow(a,2) + r*(-2*M + r));\n\tA242 = (24*pow(a,5)*E*L*M*(7*M + 4*r) + 12*pow(a,3)*E*L*M*r*(4*pow(L,2) - 16*pow(M,2) + 9*M*r + 23*pow(r,2)) - 12*a*E*L*M*pow(r,2)*(pow(L,2)*(8*M - 4*r) + (19*M - 13*r)*pow(r,2)) - 3*pow(a,6)*(4*pow(E,2)*M*(7*M + 3*r) + r*(10*M + 3*r)) + pow(r,2)*(24*pow(L,4)*M*(2*M - r) + pow(r,4)*(120*pow(M,2) - 2*(71 + 6*pow(E,2))*M*r + 41*pow(r,2)) + pow(L,2)*pow(r,2)*(228*pow(M,2) - 232*M*r + 59*pow(r,2))) + pow(a,2)*r*(-24*pow(L,4)*M + pow(r,2)*(-36*pow(M,3) + (22 - 84*pow(E,2))*pow(M,2)*r - 6*(19 + 10*pow(E,2))*M*pow(r,2) + 67*pow(r,3)) + 2*pow(L,2)*(48*pow(M,3) - 6*(13 + 2*pow(E,2))*M*pow(r,2) + 25*pow(r,3) + 6*pow(M,2)*(r + 4*pow(E,2)*r))) - pow(a,4)*(3*pow(L,2)*(28*pow(M,2) + 4*(5 + 2*pow(E,2))*M*r + 3*pow(r,2)) + r*(r*(-78*pow(M,2) + 14*M*r - 17*pow(r,2)) + 12*pow(E,2)*M*(-8*pow(M,2) + 10*M*r + 7*pow(r,2)))))/(6.*pow(pow(a,2) + r*(-2*M + r),2));\n\tA260 = (pow(r,3)*(48*pow(a,3)*E*L*M - 3*pow(a,4)*(8*pow(E,2)*M + r) + 16*a*E*L*M*r*(-5*M + 3*r) + r*(20*pow(L,2)*M*(2*M - r) + pow(r,2)*(40*pow(M,2) - 2*(21 + 2*pow(E,2))*M*r + 11*pow(r,2))) - 2*pow(a,2)*(12*pow(L,2)*M + r*((7*M - 4*r)*r + 2*pow(E,2)*M*(-10*M + 7*r)))))/(24.*pow(pow(a,2) + r*(-2*M + r),2));\n\tA304 = (-8*(pow(a,2)*(2*M + r) + r*(pow(L,2) + pow(r,2)))*(4*pow(a,3)*E*L*M + pow(a,4)*r + 12*a*E*L*M*pow(r,2) + pow(r,2)*(pow(r,2)*(-5*M + 2*r) + pow(L,2)*(-9*M + 4*r)) + pow(a,2)*(pow(L,2)*(-4*M + r) + r*(2*pow(M,2) - 3*M*r + 3*pow(r,2)))))/(r*pow(pow(a,2) + r*(-2*M + r),2));\n\tA306 = (4*(-4*pow(a,11)*E*L*pow(M,2)*(4*(35 + 9*pow(E,2))*pow(M,2) + (127 + 54*pow(E,2))*M*r + 3*(5 + 6*pow(E,2))*pow(r,2)) - 2*a*E*L*M*pow(r,5)*(pow(r,6)*(-184*pow(M,2) + 12*(17 + 9*pow(E,2))*M*r - 57*pow(r,2)) + pow(L,2)*pow(r,4)*(212*pow(M,2) + 4*(-23 + 57*pow(E,2))*M*r - 3*pow(r,2)) + 42*pow(L,6)*(4*pow(M,2) - pow(r,2)) + 2*pow(L,4)*pow(r,2)*(486*pow(M,2) + 2*(-170 + 21*pow(E,2))*M*r + 51*pow(r,2))) - 2*pow(a,3)*E*L*M*pow(r,3)*(4*pow(L,4)*pow(r,2)*((829 + 42*pow(E,2))*pow(M,2) + 2*(-107 + 21*pow(E,2))*M*r - 84*pow(r,2)) + 42*pow(L,6)*(12*pow(M,2) - 2*M*r - pow(r,2)) + pow(r,5)*(-3444*pow(M,3) + 2*(961 - 270*pow(E,2))*pow(M,2)*r + 4*(106 + 135*pow(E,2))*M*pow(r,2) - 257*pow(r,3)) + 2*pow(L,2)*pow(r,3)*(-3230*pow(M,3) + 3*(895 + 224*pow(E,2))*pow(M,2)*r + (-109 + 384*pow(E,2))*M*pow(r,2) - 214*pow(r,3))) + pow(r,7)*(2*pow(L,6)*(2*M - r)*(54*pow(M,2) + (-71 + 42*pow(E,2))*M*r + 24*pow(r,2)) + pow(L,4)*pow(r,2)*(272*pow(M,3) + 2*(-247 + 222*pow(E,2))*pow(M,2)*r + (311 - 226*pow(E,2))*M*pow(r,2) - 66*pow(r,3)) + pow(L,2)*pow(r,4)*(220*pow(M,3) + 340*(-1 + pow(E,2))*pow(M,2)*r + (193 - 184*pow(E,2))*M*pow(r,2) - 39*pow(r,3)) + pow(r,6)*(116*pow(M,3) + 2*(-83 + 44*pow(E,2))*pow(M,2)*r + 6*(14 - 9*pow(E,2))*M*pow(r,2) - 15*pow(r,3))) + pow(a,12)*M*(3*r*(-8*pow(M,2) - 3*M*r + 2*pow(r,2)) + pow(E,2)*(280*pow(M,3) + 308*pow(M,2)*r + 72*M*pow(r,2) - 6*pow(r,3))) - 4*pow(a,9)*E*L*M*(pow(L,2)*M*(108*pow(M,2) + 2*(137 + 24*pow(E,2))*M*r + 3*(13 + 6*pow(E,2))*pow(r,2)) + r*(24*(-1 + 12*pow(E,2))*pow(M,4) + 2*(215 + 234*pow(E,2))*pow(M,3)*r + 12*(49 + 39*pow(E,2))*pow(M,2)*pow(r,2) + 9*(-5 + 18*pow(E,2))*M*pow(r,3) - 30*pow(r,4))) - pow(a,2)*pow(r,3)*(-168*pow(L,8)*pow(M,2)*(2*M - r) + pow(L,4)*pow(r,3)*(4168*pow(M,4) - 4*(1441 + 1086*pow(E,2))*pow(M,3)*r + 4*(583 + 6*pow(E,2))*pow(M,2)*pow(r,2) + (-85 + 732*pow(E,2))*M*pow(r,3) - 81*pow(r,4)) + 2*pow(L,6)*r*(240*pow(M,4) - 4*(233 + 84*pow(E,2))*pow(M,3)*r - 6*(-83 + 28*pow(E,2))*pow(M,2)*pow(r,2) + (23 + 84*pow(E,2))*M*pow(r,3) - 36*pow(r,4)) + pow(L,2)*pow(r,5)*(3640*pow(M,4) + 12*(-413 + 58*pow(E,2))*pow(M,3)*r + 2*(1091 - 1004*pow(E,2))*pow(M,2)*pow(r,2) + (-243 + 800*pow(E,2))*M*pow(r,3) - 27*pow(r,4)) + pow(r,7)*(696*pow(M,4) + 4*(-315 + 274*pow(E,2))*pow(M,3)*r + 4*(204 - 241*pow(E,2))*pow(M,2)*pow(r,2) + (-205 + 268*pow(E,2))*M*pow(r,3) + 15*pow(r,4))) - 2*pow(a,5)*E*L*M*pow(r,2)*(2*pow(L,4)*(1008*pow(M,3) + 4*(257 + 21*pow(E,2))*pow(M,2)*r + 2*(-104 + 21*pow(E,2))*M*pow(r,2) - 87*pow(r,3)) + pow(L,2)*r*(-1888*pow(M,4) + 20*(-161 + 24*pow(E,2))*pow(M,3)*r + 288*(21 + 8*pow(E,2))*pow(M,2)*pow(r,2) + 12*(-89 + 74*pow(E,2))*M*pow(r,3) - 617*pow(r,4)) - pow(r,3)*(768*pow(M,4) + 4*(823 + 378*pow(E,2))*pow(M,3)*r + 4*(-1091 + 18*pow(E,2))*pow(M,2)*pow(r,2) - 18*(-1 + 56*pow(E,2))*M*pow(r,3) + 403*pow(r,4))) + pow(a,4)*pow(r,2)*(2*pow(L,6)*M*(672*pow(M,3) + 4*(101 + 126*pow(E,2))*pow(M,2)*r + 28*(-11 + 3*pow(E,2))*M*pow(r,2) - (31 + 42*pow(E,2))*pow(r,3)) + pow(r,5)*(180*pow(M,5) + 12*(1 - 238*pow(E,2))*pow(M,4)*r - 9*(-161 + 60*pow(E,2))*pow(M,3)*pow(r,2) + 8*(-219 + 287*pow(E,2))*pow(M,2)*pow(r,3) + (421 - 538*pow(E,2))*M*pow(r,4) + 45*pow(r,5)) + pow(L,4)*r*(-1888*pow(M,5) + 8*(-239 + 180*pow(E,2))*pow(M,4)*r + 32*(163 + 293*pow(E,2))*pow(M,3)*pow(r,2) + 12*(-223 + 58*pow(E,2))*pow(M,2)*pow(r,3) + 2*(79 - 396*pow(E,2))*M*pow(r,4) + 147*pow(r,5)) + pow(L,2)*pow(r,3)*(-364*pow(M,5) - 4*(763 + 2976*pow(E,2))*pow(M,4)*r + (6129 + 4072*pow(E,2))*pow(M,3)*pow(r,2) + 4*(-965 + 831*pow(E,2))*pow(M,2)*pow(r,3) + 3*(181 - 436*pow(E,2))*M*pow(r,4) + 171*pow(r,5))) - 2*pow(a,7)*E*L*M*r*(48*pow(L,4)*M*(6*M + r) + 2*pow(L,2)*(864*pow(M,4) + 4*(163 + 84*pow(E,2))*pow(M,3)*r + (1271 + 624*pow(E,2))*pow(M,2)*pow(r,2) + 2*(-101 + 96*pow(E,2))*M*pow(r,3) - 96*pow(r,4)) - r*(896*pow(M,5) + 1840*pow(M,4)*r + 36*(17 + 2*pow(E,2))*pow(M,3)*pow(r,2) - 4*(769 + 324*pow(E,2))*pow(M,2)*pow(r,3) + 2*(179 - 432*pow(E,2))*M*pow(r,4) + 263*pow(r,5))) + pow(a,6)*r*(6*pow(L,6)*M*(32*pow(M,2) + 2*M*r + pow(r,2)) + 4*pow(L,4)*M*(288*pow(M,4) + 4*(23 + 252*pow(E,2))*pow(M,3)*r + (389 + 1450*pow(E,2))*pow(M,2)*pow(r,2) + 2*(-125 + 69*pow(E,2))*M*pow(r,3) - (6 + 73*pow(E,2))*pow(r,4)) + pow(r,3)*(184*pow(M,6) - 4*(11 + 268*pow(E,2))*pow(M,5)*r - 6*(37 + 632*pow(E,2))*pow(M,4)*pow(r,2) + (77 + 2080*pow(E,2))*pow(M,3)*pow(r,3) + (-1231 + 2360*pow(E,2))*pow(M,2)*pow(r,4) + 3*(203 - 184*pow(E,2))*M*pow(r,5) + 75*pow(r,6)) + pow(L,2)*r*(-896*pow(M,6) - 32*(38 + 59*pow(E,2))*pow(M,5)*r - 16*(21 + 292*pow(E,2))*pow(M,4)*pow(r,2) + 2*(1643 + 4488*pow(E,2))*pow(M,3)*pow(r,3) + (-1991 + 2372*pow(E,2))*pow(M,2)*pow(r,4) + (571 - 964*pow(E,2))*M*pow(r,5) + 105*pow(r,6))) + pow(a,10)*M*(pow(L,2)*(8*(35 + 54*pow(E,2))*pow(M,3) + 8*(25 + 109*pow(E,2))*pow(M,2)*r + 3*(-7 + 76*pow(E,2))*M*pow(r,2) + 6*(3 - 2*pow(E,2))*pow(r,3)) + r*(r*(134*pow(M,3) - 21*pow(M,2)*r - 69*M*pow(r,2) + 58*pow(r,3)) + pow(E,2)*(-48*pow(M,4) + 1072*pow(M,3)*r + 1704*pow(M,2)*pow(r,2) + 452*M*pow(r,3) - 76*pow(r,4)))) + pow(a,8)*(2*pow(L,4)*M*(72*pow(M,3) + 4*(55 + 72*pow(E,2))*pow(M,2)*r + 78*pow(E,2)*M*pow(r,2) - 3*(-3 + pow(E,2))*pow(r,3)) + pow(L,2)*M*r*(48*(-1 + 72*pow(E,2))*pow(M,4) + 8*(81 + 514*pow(E,2))*pow(M,3)*r + (869 + 5400*pow(E,2))*pow(M,2)*pow(r,2) + 2*(-285 + 472*pow(E,2))*M*pow(r,3) + 4*(24 - 71*pow(E,2))*pow(r,4)) + pow(r,2)*(r*(-264*pow(M,5) + 92*pow(M,4)*r + 135*pow(M,3)*pow(r,2) - 189*pow(M,2)*pow(r,3) + 361*M*pow(r,4) + 30*pow(r,5)) - 2*pow(E,2)*M*(448*pow(M,5) + 1232*pow(M,4)*r + 680*pow(M,3)*pow(r,2) - 1460*pow(M,2)*pow(r,3) - 660*M*pow(r,4) + 149*pow(r,5))))))/(3.*pow(r,7)*pow(pow(a,2) + r*(-2*M + r),3));\n\tA322 = (-4*pow(r,2)*(2*pow(a,3)*E*L*M + 6*a*E*L*M*pow(r,2) + pow(a,4)*(3*M + 2*r) + pow(r,2)*(pow(r,2)*(-5*M + 2*r) + pow(L,2)*(-7*M + 3*r)) - 2*pow(a,2)*(pow(L,2)*(M - r) + r*(2*pow(M,2) + M*r - 2*pow(r,2)))))/pow(pow(a,2) + r*(-2*M + r),2);\n\tA324 = (4*pow(a,9)*E*L*M*(2*(-113 + 9*pow(E,2))*pow(M,2) - 57*M*r + 3*pow(r,2)) - 4*a*E*L*M*pow(r,4)*(pow(L,4)*(240*pow(M,2) - 22*M*r - 51*pow(r,2)) + pow(L,2)*pow(r,2)*(314*pow(M,2) + (-83 + 114*pow(E,2))*M*r - 42*pow(r,2)) + 3*pow(r,4)*(-84*pow(M,2) + 4*(26 + 9*pow(E,2))*M*r - 33*pow(r,2))) + pow(a,10)*M*(-21*r*(7*M + 2*r) + 4*pow(E,2)*(113*pow(M,2) + 81*M*r + 9*pow(r,2))) - 4*pow(a,7)*E*L*M*(3*pow(L,2)*(-18*pow(M,2) + 8*M*r + pow(r,2)) + r*(4*(31 + 108*pow(E,2))*pow(M,3) + 9*(109 + 30*pow(E,2))*pow(M,2)*r + (37 + 108*pow(E,2))*M*pow(r,2) - 69*pow(r,3))) - 4*pow(a,3)*E*L*M*pow(r,2)*(pow(L,4)*(612*pow(M,2) - 92*M*r - 45*pow(r,2)) + pow(r,3)*(-2250*pow(M,3) + (955 - 54*pow(E,2))*pow(M,2)*r + 9*(49 + 36*pow(E,2))*M*pow(r,2) - 211*pow(r,3)) + pow(L,2)*r*(16*pow(M,3) + 2*(409 + 114*pow(E,2))*pow(M,2)*r + 2*(-185 + 108*pow(E,2))*M*pow(r,2) - 45*pow(r,3))) + pow(r,4)*(2*pow(L,6)*M*(12*pow(M,2) - 16*M*r + 5*pow(r,2)) + pow(L,2)*pow(r,4)*(304*pow(M,3) + 2*(-243 + 340*pow(E,2))*pow(M,2)*r + (257 - 368*pow(E,2))*M*pow(r,2) - 45*pow(r,3)) + 2*pow(L,4)*pow(r,2)*(128*pow(M,3) + 2*(-113 + 111*pow(E,2))*pow(M,2)*r + (129 - 113*pow(E,2))*M*pow(r,2) - 24*pow(r,3)) + 3*pow(r,6)*(116*pow(M,3) + 2*(-85 + 44*pow(E,2))*pow(M,2)*r + 2*(41 - 27*pow(E,2))*M*pow(r,2) - 13*pow(r,3))) - 4*pow(a,5)*E*L*M*r*(6*pow(L,4)*r + pow(L,2)*(1296*pow(M,3) + 6*(47 + 34*pow(E,2))*pow(M,2)*r + (-371 + 102*pow(E,2))*M*pow(r,2) - 60*pow(r,3)) + r*(-1008*pow(M,4) + 2*(-641 + 216*pow(E,2))*pow(M,3)*r + 6*(335 + 63*pow(E,2))*pow(M,2)*pow(r,2) + (209 + 324*pow(E,2))*M*pow(r,3) - 178*pow(r,4))) + pow(a,2)*pow(r,2)*(2*pow(L,6)*M*(408*pow(M,2) - 194*M*r - 5*pow(r,2)) - 8*pow(L,4)*M*r*(104*pow(M,3) - 3*(73 + 77*pow(E,2))*pow(M,2)*r + (115 - 101*pow(E,2))*M*pow(r,2) + 17*(-1 + 3*pow(E,2))*pow(r,3)) - 3*pow(r,5)*(464*pow(M,4) + 4*(-187 + 194*pow(E,2))*pow(M,3)*r - 8*(-66 + 83*pow(E,2))*pow(M,2)*pow(r,2) + 2*(-83 + 98*pow(E,2))*M*pow(r,3) + 15*pow(r,4)) + pow(L,2)*pow(r,3)*(-4696*pow(M,4) + 8*(672 + 127*pow(E,2))*pow(M,3)*r + 6*(-347 + 324*pow(E,2))*pow(M,2)*pow(r,2) - 3*(-87 + 352*pow(E,2))*M*pow(r,3) + 15*pow(r,4))) + pow(a,4)*r*(12*pow(L,6)*M*r + 3*pow(r,3)*(60*pow(M,5) - 4*(23 + 326*pow(E,2))*pow(M,4)*r + (751 - 436*pow(E,2))*pow(M,3)*pow(r,2) + 2*(-387 + 586*pow(E,2))*pow(M,2)*pow(r,3) - 4*(-50 + 63*pow(E,2))*M*pow(r,4) + 19*pow(r,5)) + 2*pow(L,2)*r*(-1008*pow(M,5) + 4*(-227 + 328*pow(E,2))*pow(M,4)*r + 2*(1325 + 758*pow(E,2))*pow(M,3)*pow(r,2) + 14*(-95 + 6*pow(E,2))*pow(M,2)*pow(r,3) + 3*(39 - 160*pow(E,2))*M*pow(r,4) + 69*pow(r,5)) + 2*pow(L,4)*(864*pow(M,4) + 2*(-193 + 107*pow(E,2))*pow(M,2)*pow(r,2) + 17*(1 - 5*pow(E,2))*M*pow(r,3) + 24*pow(r,4) + 12*pow(M,3)*(r + 102*pow(E,2)*r))) + pow(a,8)*(2*pow(L,2)*M*((226 - 108*pow(E,2))*pow(M,2) + 24*(-2 + pow(E,2))*M*r + 3*(-15 + 8*pow(E,2))*pow(r,2)) + r*(2*pow(E,2)*M*(124*pow(M,3) + 982*pow(M,2)*r + 686*M*pow(r,2) + 3*pow(r,3)) + 3*r*(179*pow(M,3) - 70*pow(M,2)*r + 30*M*pow(r,2) + 10*pow(r,3)))) + pow(a,6)*(-12*pow(L,4)*M*(6*pow(M,2) - 4*M*r - (-3 + pow(E,2))*pow(r,2)) + 2*pow(L,2)*r*(4*(31 + 648*pow(E,2))*pow(M,4) + 28*(35 + 39*pow(E,2))*pow(M,3)*r - (361 + 140*pow(E,2))*pow(M,2)*pow(r,2) + (43 - 112*pow(E,2))*M*pow(r,3) + 39*pow(r,4)) + pow(r,2)*(3*r*(-192*pow(M,4) + 210*pow(M,3)*r - 381*pow(M,2)*pow(r,2) + 160*M*pow(r,3) + 31*pow(r,4)) - 4*pow(E,2)*M*(504*pow(M,4) + 828*pow(M,3)*r - 433*pow(M,2)*pow(r,2) - 709*M*pow(r,3) + 90*pow(r,4)))))/(3.*pow(r,4)*pow(pow(a,2) + r*(-2*M + r),3));\n\tA340 = -(pow(r,5)*(3*pow(a,2) + r*(-5*M + 2*r)))/(2.*pow(pow(a,2) + r*(-2*M + r),2));\n\tA342 = (24*pow(a,7)*E*L*M*((-25 + 3*pow(E,2))*M - 7*r) + 3*pow(a,8)*(r*(8*M + 9*r) + 2*pow(E,2)*M*(50*M + 19*r)) - 4*a*E*L*M*pow(r,3)*(3*pow(r,2)*(-76*pow(M,2) + (103 + 18*pow(E,2))*M*r - 36*pow(r,2)) + pow(L,2)*(208*pow(M,2) - 64*M*r - 27*pow(r,2))) - 12*pow(a,5)*E*L*M*(pow(L,2)*(-18*M + 8*r) + r*((4 + 48*pow(E,2))*pow(M,2) + (71 - 6*pow(E,2))*M*r + 20*pow(r,2))) - 12*pow(a,3)*E*L*M*r*(pow(L,2)*(144*pow(M,2) - 64*M*r - pow(r,2)) + 2*r*(-88*pow(M,3) + 2*(-5 + 18*pow(E,2))*pow(M,2)*r + 9*(4 + pow(E,2))*M*pow(r,2) - 13*pow(r,3))) + pow(r,3)*(-8*pow(L,4)*M*(2*pow(M,2) - 3*M*r + pow(r,2)) + pow(r,4)*(348*pow(M,3) + 8*(-64 + 33*pow(E,2))*pow(M,2)*r + (245 - 162*pow(E,2))*M*pow(r,2) - 38*pow(r,3)) + pow(L,2)*pow(r,2)*(-52*pow(M,3) + 4*(19 + 85*pow(E,2))*pow(M,2)*r - (33 + 184*pow(E,2))*M*pow(r,2) + 4*pow(r,3))) - pow(a,2)*r*(-12*pow(L,4)*M*(48*pow(M,2) - 29*M*r + pow(r,2)) + pow(L,2)*r*(1056*pow(M,4) - 16*(33 + 107*pow(E,2))*pow(M,3)*r + 4*(-35 + 16*pow(E,2))*pow(M,2)*pow(r,2) + 4*(9 + 64*pow(E,2))*M*pow(r,3) + 25*pow(r,4)) + pow(r,3)*(696*pow(M,4) + 8*(-103 + 171*pow(E,2))*pow(M,3)*r + 4*(166 - 273*pow(E,2))*pow(M,2)*pow(r,2) + 3*(-111 + 124*pow(E,2))*M*pow(r,3) + 57*pow(r,4))) + pow(a,6)*(pow(L,2)*((300 - 216*pow(E,2))*pow(M,2) + 6*(9 + 8*pow(E,2))*M*r + 27*pow(r,2)) + r*(12*pow(E,2)*M*(2*pow(M,2) + 61*M*r + 15*pow(r,2)) + r*(-312*pow(M,2) - 25*M*r + 61*pow(r,2)))) + pow(a,4)*(24*pow(L,4)*M*(-3*M + 2*r) + pow(L,2)*r*(24*(1 + 72*pow(E,2))*pow(M,3) + 12*(10 - 41*pow(E,2))*pow(M,2)*r - 3*(23 + 8*pow(E,2))*M*pow(r,2) - 2*pow(r,3)) + pow(r,2)*(-12*pow(E,2)*M*(88*pow(M,3) + 64*pow(M,2)*r - 97*M*pow(r,2) + 12*pow(r,3)) + r*(876*pow(M,3) - 512*pow(M,2)*r + 63*M*pow(r,2) + 15*pow(r,3)))))/(12.*r*pow(pow(a,2) + r*(-2*M + r),3));\n\tA360 = (pow(r,2)*(-144*pow(a,5)*E*L*M + 28*pow(a,3)*E*L*M*(4*M - 3*r)*r + 3*pow(a,6)*(24*pow(E,2)*M + 7*r) + 4*a*E*L*M*pow(r,2)*(68*pow(M,2) - 54*M*r + 15*pow(r,2)) + pow(r,2)*(-2*pow(L,2)*M*(68*pow(M,2) - 76*M*r + 21*pow(r,2)) + pow(r,2)*(116*pow(M,3) + 8*(-21 + 11*pow(E,2))*pow(M,2)*r + (83 - 54*pow(E,2))*M*pow(r,2) - 14*pow(r,3))) + pow(a,4)*(72*pow(L,2)*M + r*(r*(-53*M + 28*r) + pow(E,2)*(-56*pow(M,2) + 74*M*r))) - pow(a,2)*r*(2*pow(L,2)*M*(28*M - 5*r) + r*(r*(36*pow(M,2) - 30*M*r + 7*pow(r,2)) + 4*pow(E,2)*M*(34*pow(M,2) - 16*M*r + 13*pow(r,2))))))/(48.*pow(pow(a,2) + r*(-2*M + r),3));\n\tA402 = (12*pow(r,3)*(pow(a,2)*(2*M + r) + r*(pow(L,2) + pow(r,2))))/pow(pow(a,2) + r*(-2*M + r),2);\n\tA404 = (2*(-4*pow(a,7)*E*L*M*(48*pow(M,2) + 40*M*r + 3*pow(r,2)) - 4*pow(a,5)*E*L*M*r*(-96*pow(M,3) - 110*pow(M,2)*r + 73*M*pow(r,2) + 8*pow(r,3) + 9*pow(L,2)*(6*M + r)) + pow(a,8)*(12*pow(E,2)*M*(8*pow(M,2) + 10*M*r + 3*pow(r,2)) - r*(62*pow(M,2) + 42*M*r + 3*pow(r,2))) + pow(r,3)*(4*pow(L,6)*M*(-2*M + r) + 3*pow(r,6)*(23*pow(M,2) + 4*(-5 + pow(E,2))*M*r + 3*pow(r,2)) + 3*pow(L,2)*pow(r,4)*(42*pow(M,2) + 4*(-9 + 2*pow(E,2))*M*r + 5*pow(r,2)) + pow(L,4)*pow(r,2)*(73*pow(M,2) + 4*(-17 + 2*pow(E,2))*M*r + 12*pow(r,2))) - 4*pow(a,3)*E*L*M*pow(r,2)*(6*pow(L,4) + pow(L,2)*(-48*pow(M,2) + 81*M*r + 9*pow(r,2)) + pow(r,2)*(-234*pow(M,2) + 50*M*r + 17*pow(r,2))) + 4*a*E*L*M*pow(r,3)*(pow(L,4)*(4*M - 6*r) + 3*(M - 4*r)*pow(r,4) + pow(L,2)*(-45*M*pow(r,2) + 6*pow(r,3))) + pow(a,2)*pow(r,2)*(12*pow(L,6)*M + 6*pow(r,4)*(-16*pow(M,3) + (26 - 36*pow(E,2))*pow(M,2)*r + (-25 + 12*pow(E,2))*M*pow(r,2) + 6*pow(r,3)) + 3*pow(L,2)*pow(r,2)*(-152*pow(M,3) + 4*(35 + 9*pow(E,2))*pow(M,2)*r + 2*(-33 + 16*pow(E,2))*M*pow(r,2) + 19*pow(r,3)) + pow(L,4)*(-96*pow(M,3) + 4*(39 - 2*pow(E,2))*pow(M,2)*r + 10*(-5 + 2*pow(E,2))*M*pow(r,2) + 24*pow(r,3))) + pow(a,4)*r*(3*pow(L,4)*(36*pow(M,2) + 4*(-1 + pow(E,2))*M*r - pow(r,2)) - 2*pow(L,2)*(96*pow(M,4) + 4*(19 + 12*pow(E,2))*pow(M,3)*r - (143 + 84*pow(E,2))*pow(M,2)*pow(r,2) + 15*(3 - 4*pow(E,2))*M*pow(r,3) - 18*pow(r,4)) - 3*pow(r,2)*(36*pow(M,4) + 4*(-5 + 48*pow(E,2))*pow(M,3)*r + 9*(-5 + 8*pow(E,2))*pow(M,2)*pow(r,2) + 2*(19 - 24*pow(E,2))*M*pow(r,3) - 14*pow(r,4))) + 2*pow(a,6)*(pow(L,2)*(48*pow(M,3) + 2*(10 + 27*pow(E,2))*pow(M,2)*r + 3*(-11 + 8*pow(E,2))*M*pow(r,2) - 3*pow(r,3)) + r*(-12*pow(E,2)*M*(8*pow(M,3) + 12*pow(M,2)*r - 5*M*pow(r,2) - 5*pow(r,3)) + r*(74*pow(M,3) + 17*pow(M,2)*r - 33*M*pow(r,2) + 6*pow(r,3))))))/(3.*pow(r,3)*pow(pow(a,2) + r*(-2*M + r),3));\n\tA420 = (3*pow(r,6))/pow(pow(a,2) + r*(-2*M + r),2);\n\tA422 = (2*pow(a,5)*E*L*M*(-8*M + r) - 2*pow(a,3)*E*L*M*r*(4*pow(L,2) - 8*pow(M,2) + M*r - 7*pow(r,2)) - 2*a*E*L*M*pow(r,3)*(4*pow(L,2) + r*(3*M + 4*r)) + pow(a,6)*M*(-7*r + pow(E,2)*(8*M + 6*r)) + pow(r,4)*(pow(r,2)*(23*pow(M,2) + 2*(-11 + 2*pow(E,2))*M*r + 4*pow(r,2)) + pow(L,2)*(25*pow(M,2) + (-23 + 4*pow(E,2))*M*r + 4*pow(r,2))) + pow(a,2)*r*(4*pow(L,4)*M + pow(r,2)*(-16*pow(M,3) - 4*(-5 + 8*pow(E,2))*pow(M,2)*r + 7*(-5 + 2*pow(E,2))*M*pow(r,2) + 14*pow(r,3)) + pow(L,2)*(-8*pow(M,3) + 10*pow(M,2)*r + (-23 + 8*pow(E,2))*M*pow(r,2) + 15*pow(r,3))) + pow(a,4)*(4*pow(L,2)*M*(2*M + (-2 + pow(E,2))*r) + r*(-8*pow(E,2)*M*(pow(M,2) + M*r - 2*pow(r,2)) + r*(17*pow(M,2) - 8*M*r + 10*pow(r,2)))))/pow(pow(a,2) + r*(-2*M + r),3);\n\tA440 = (pow(r,4)*(9*pow(a,4) - 48*a*E*L*pow(M,2) + 12*pow(L,2)*M*(2*M - r) + pow(r,2)*(69*pow(M,2) + 2*(-31 + 6*pow(E,2))*M*r + 10*pow(r,2)) + 2*pow(a,2)*(6*pow(E,2)*M*(2*M + r) + r*(-30*M + 17*r))))/(24.*pow(pow(a,2) + r*(-2*M + r),3));\n\tA502 = (-2*pow(r,2)*(2*pow(a,3)*E*L*M + 6*a*E*L*M*pow(r,2) + pow(a,4)*(3*M + 2*r) + pow(r,2)*(pow(r,2)*(-4*M + r) + pow(L,2)*(-6*M + 2*r)) + pow(a,2)*(-2*pow(L,2)*(M - r) + r*(-2*pow(M,2) - 3*M*r + 3*pow(r,2)))))/pow(pow(a,2) + r*(-2*M + r),3);\n\tA504 = (-2*pow(a,9)*E*L*M*(4*(49 + 27*pow(E,2))*pow(M,2) + 6*(-7 + 12*pow(E,2))*M*r - 9*pow(r,2)) + pow(a,10)*M*(3*r*(-10*M + 7*r) + 2*pow(E,2)*(98*pow(M,2) + 30*M*r - 15*pow(r,2))) - 2*a*E*L*M*pow(r,4)*(pow(L,2)*pow(r,2)*(-725*pow(M,2) + 8*(172 + 21*pow(E,2))*M*r - 570*pow(r,2)) + 3*pow(r,4)*(-135*pow(M,2) + 4*(49 + 18*pow(E,2))*M*r - 82*pow(r,2)) + 16*pow(L,4)*(2*pow(M,2) + 15*M*r - 9*pow(r,2))) - 2*pow(a,7)*E*L*M*(pow(L,2)*(324*pow(M,2) + 12*(5 + 3*pow(E,2))*M*r + 9*pow(r,2)) + 2*r*(16*(2 + 9*pow(E,2))*pow(M,3) + 6*(94 + 57*pow(E,2))*pow(M,2)*r + 2*(-65 + 126*pow(E,2))*M*pow(r,2) - 39*pow(r,3))) + pow(r,4)*(-2*pow(L,6)*M*(44*pow(M,2) - 52*M*r + 15*pow(r,2)) + 3*M*pow(r,6)*(52*pow(M,2) + (-65 + 44*pow(E,2))*M*r + (23 - 30*pow(E,2))*pow(r,2)) + 2*pow(L,4)*pow(r,2)*(-153*pow(M,3) + (271 + 140*pow(E,2))*pow(M,2)*r - 2*(82 + 39*pow(E,2))*M*pow(r,2) + 36*pow(r,3)) + pow(L,2)*pow(r,4)*(34*pow(M,3) + (51 + 428*pow(E,2))*pow(M,2)*r - (109 + 248*pow(E,2))*M*pow(r,2) + 48*pow(r,3))) - 2*pow(a,3)*E*L*M*pow(r,2)*(2*pow(L,4)*(252*pow(M,2) + 116*M*r - 63*pow(r,2)) + pow(L,2)*r*(-784*pow(M,3) + 3*(219 + 40*pow(E,2))*pow(M,2)*r + 18*(39 + 22*pow(E,2))*M*pow(r,2) - 168*pow(r,3)) - 2*pow(r,3)*(765*pow(M,3) + 2*(8 + 135*pow(E,2))*pow(M,2)*r - 3*(89 + 132*pow(E,2))*M*pow(r,2) + 119*pow(r,3))) - 2*pow(a,5)*E*L*M*r*(18*pow(L,4)*(6*M + r) + pow(L,2)*(864*pow(M,3) + 84*(15 + 2*pow(E,2))*pow(M,2)*r + 2*(-145 + 132*pow(E,2))*M*pow(r,2) - 123*pow(r,3)) + r*(-576*pow(M,4) - 1390*pow(M,3)*r + 3*(667 + 108*pow(E,2))*pow(M,2)*pow(r,2) + 4*(89 + 252*pow(E,2))*M*pow(r,3) - 61*pow(r,4))) - pow(a,2)*pow(r,2)*(4*pow(L,6)*M*(-84*pow(M,2) + 8*M*r + 23*pow(r,2)) + 3*pow(r,5)*(210*pow(M,4) + (-355 + 484*pow(E,2))*pow(M,3)*r + 12*(23 - 33*pow(E,2))*pow(M,2)*pow(r,2) + 2*(-62 + 65*pow(E,2))*M*pow(r,3) + 21*pow(r,4)) + 2*pow(L,4)*r*(392*pow(M,4) - (409 + 196*pow(E,2))*pow(M,3)*r - (39 + 584*pow(E,2))*pow(M,2)*pow(r,2) + (-41 + 167*pow(E,2))*M*pow(r,3) + 84*pow(r,4)) + pow(L,2)*pow(r,3)*(1618*pow(M,4) + (-1559 + 2272*pow(E,2))*pow(M,3)*r + (683 - 4036*pow(E,2))*pow(M,2)*pow(r,2) + (-413 + 848*pow(E,2))*M*pow(r,3) + 165*pow(r,4))) + pow(a,4)*r*(18*pow(L,6)*M*(4*M + r) + 8*pow(L,4)*(72*pow(M,4) + 18*(4 + 7*pow(E,2))*pow(M,3)*r + (-91 + 128*pow(E,2))*pow(M,2)*pow(r,2) - 4*(-4 + 5*pow(E,2))*M*pow(r,3) + 9*pow(r,4)) + 3*pow(r,3)*(44*pow(M,5) - 56*(-1 + 8*pow(E,2))*pow(M,4)*r + 2*(233 - 192*pow(E,2))*pow(M,3)*pow(r,2) + (-499 + 736*pow(E,2))*pow(M,2)*pow(r,3) + (151 - 220*pow(E,2))*M*pow(r,4) - 27*pow(r,5)) - pow(L,2)*r*(576*pow(M,5) + 4*(263 + 196*pow(E,2))*pow(M,4)*r - 13*(215 + 88*pow(E,2))*pow(M,3)*pow(r,2) - 6*(-313 + 524*pow(E,2))*pow(M,2)*pow(r,3) + 4*(-82 + 241*pow(E,2))*M*pow(r,4) + 96*pow(r,5))) + pow(a,8)*(pow(L,2)*M*(4*(49 + 162*pow(E,2))*pow(M,2) + 12*(-12 + 23*pow(E,2))*M*r + 3*(11 - 4*pow(E,2))*pow(r,2)) + r*(2*pow(E,2)*M*(32*pow(M,3) + 608*pow(M,2)*r + 286*M*pow(r,2) - 105*pow(r,3)) + 3*r*(24*pow(M,3) + 2*pow(M,2)*r + 130*M*pow(r,2) + 15*pow(r,3)))) + pow(a,6)*(6*pow(L,4)*M*(36*pow(M,2) + 2*(-1 + 18*pow(E,2))*M*r + (5 + 3*pow(E,2))*pow(r,2)) + pow(L,2)*r*(64*(1 + 27*pow(E,2))*pow(M,4) + 16*(65 + 207*pow(E,2))*pow(M,3)*r + 68*(-14 + 17*pow(E,2))*pow(M,2)*pow(r,2) + (595 - 376*pow(E,2))*M*pow(r,3) + 117*pow(r,4)) + pow(r,2)*(3*r*(-58*pow(M,4) - 45*pow(M,3)*r - 420*pow(M,2)*pow(r,2) + 173*M*pow(r,3) + 9*pow(r,4)) - 4*pow(E,2)*M*(144*pow(M,4) + 432*pow(M,3)*r - 218*pow(M,2)*pow(r,2) - 416*M*pow(r,3) + 135*pow(r,4)))))/(3.*pow(r,4)*pow(pow(a,2) + r*(-2*M + r),4));\n\tA520 = -(pow(r,5)*(3*pow(a,2) + r*(-4*M + r)))/(2.*pow(pow(a,2) + r*(-2*M + r),3));\n\tA522 = (-6*pow(a,7)*E*L*M*(4*(14 + 3*pow(E,2))*M + 23*r) + 3*pow(a,8)*(2*pow(E,2)*M*(28*M - r) + r*(43*M + 9*r)) - 2*a*E*L*M*pow(r,3)*(pow(L,2)*(64*pow(M,2) + 344*M*r - 222*pow(r,2)) + 3*pow(r,2)*(-199*pow(M,2) + 4*(79 + 18*pow(E,2))*M*r - 134*pow(r,2))) - 6*pow(a,5)*E*L*M*(4*pow(L,2)*(9*M + 2*r) + r*(12*(7 + 6*pow(E,2))*pow(M,2) + 6*(17 + 16*pow(E,2))*M*r + 7*pow(r,2))) - 6*pow(a,3)*E*L*M*r*(2*pow(L,2)*(108*pow(M,2) + 52*M*r - 33*pow(r,2)) + r*(-272*pow(M,3) + (-73 + 72*pow(E,2))*pow(M,2)*r + 2*(103 + 78*pow(E,2))*M*pow(r,2) - 116*pow(r,3))) + pow(r,3)*(-4*pow(L,4)*M*(38*pow(M,2) - 45*M*r + 13*pow(r,2)) + 6*pow(r,4)*(52*pow(M,3) + (-63 + 44*pow(E,2))*pow(M,2)*r - 6*(-3 + 5*pow(E,2))*M*pow(r,2) + 2*pow(r,3)) + pow(L,2)*pow(r,2)*(-158*pow(M,3) + (369 + 428*pow(E,2))*pow(M,2)*r - 4*(73 + 62*pow(E,2))*M*pow(r,2) + 84*pow(r,3))) + pow(a,2)*r*(24*pow(L,4)*M*(18*pow(M,2) + M*r - 7*pow(r,2)) + pow(L,2)*r*(-816*pow(M,4) + 2*(213 + 356*pow(E,2))*pow(M,3)*r + (103 + 1444*pow(E,2))*pow(M,2)*pow(r,2) + 4*(32 - 125*pow(E,2))*M*pow(r,3) - 156*pow(r,4)) - 3*pow(r,3)*(210*pow(M,4) + (-295 + 548*pow(E,2))*pow(M,3)*r + (313 - 488*pow(E,2))*pow(M,2)*pow(r,2) + 2*(-97 + 95*pow(E,2))*M*pow(r,3) + 40*pow(r,4))) + 3*pow(a,6)*(pow(L,2)*(8*(7 + 9*pow(E,2))*pow(M,2) + 8*(6 + pow(E,2))*M*r + 9*pow(r,2)) + r*(2*pow(E,2)*M*(42*pow(M,2) + 148*M*r - 37*pow(r,2)) + r*(-240*pow(M,2) + 87*M*r + 11*pow(r,2)))) + 3*pow(a,4)*(8*pow(L,4)*M*(3*M + r) + pow(L,2)*r*(12*(7 + 36*pow(E,2))*pow(M,3) + 4*(-23 + 98*pow(E,2))*pow(M,2)*r + 4*(3 - 19*pow(E,2))*M*pow(r,2) - 13*pow(r,3)) - pow(r,2)*(r*(-385*pow(M,3) + 317*pow(M,2)*r - 120*M*pow(r,2) + 42*pow(r,3)) + 2*pow(E,2)*M*(136*pow(M,3) + 144*pow(M,2)*r - 312*M*pow(r,2) + 101*pow(r,3)))))/(12.*r*pow(pow(a,2) + r*(-2*M + r),4));\n\tA540 = (pow(r,2)*(-72*pow(a,5)*E*L*M + 9*pow(a,6)*(4*pow(E,2)*M + r) + 12*pow(a,3)*E*L*M*r*(-12*M + 11*r) + 12*a*E*L*M*pow(r,2)*(32*pow(M,2) - 42*M*r + 17*pow(r,2)) + pow(a,4)*(36*pow(L,2)*M + r*(18*pow(E,2)*M*(4*M - 3*r) + (24*M - 13*r)*r)) + pow(r,2)*(-6*pow(L,2)*M*(32*pow(M,2) - 38*M*r + 11*pow(r,2)) + pow(r,2)*(156*pow(M,3) + (-193 + 132*pow(E,2))*pow(M,2)*r + 2*(32 - 45*pow(E,2))*M*pow(r,2) + 2*pow(r,3))) - pow(a,2)*r*(pow(L,2)*(-72*pow(M,2) + 78*M*r) + r*(12*pow(E,2)*M*(16*pow(M,2) - 23*M*r + 15*pow(r,2)) + r*(183*pow(M,2) - 196*M*r + 62*pow(r,2))))))/(48.*pow(pow(a,2) + r*(-2*M + r),4));\n\tA600 = pow(r,6)/pow(pow(a,2) + r*(-2*M + r),3);\n\tA602 = (-24*pow(a,5)*E*L*M*(5*M + r) - 16*pow(a,3)*E*L*M*r*(3*pow(L,2) - 8*pow(M,2) + 2*M*r + 3*pow(r,2)) + 8*a*E*L*M*pow(r,2)*(pow(L,2)*(4*M - 6*r) + (11*M - 15*r)*pow(r,2)) + 3*pow(a,6)*(r*(-6*M + r) + 4*pow(E,2)*M*(5*M + 3*r)) + pow(r,2)*(8*pow(L,4)*M*(-2*M + r) + M*pow(r,4)*(43*M + 4*(-8 + 5*pow(E,2))*r) + pow(L,2)*pow(r,2)*(3*pow(M,2) + 4*(3 + 4*pow(E,2))*M*r - 12*pow(r,2))) + pow(a,2)*r*(24*pow(L,4)*M + pow(r,2)*(-34*pow(M,3) + (39 - 100*pow(E,2))*pow(M,2)*r + 2*(-47 + 38*pow(E,2))*M*pow(r,2) + 36*pow(r,3)) + pow(L,2)*(-64*pow(M,3) - 8*(-3 + 2*pow(E,2))*pow(M,2)*r + 10*(-3 + 4*pow(E,2))*M*pow(r,2) + 48*pow(r,3))) + pow(a,4)*(3*pow(L,2)*(20*pow(M,2) + 4*(-1 + 2*pow(E,2))*M*r + pow(r,2)) + r*(r*(32*pow(M,2) - 14*M*r + 39*pow(r,2)) + pow(E,2)*(-64*pow(M,3) + 8*pow(M,2)*r + 92*M*pow(r,2)))))/(6.*pow(pow(a,2) + r*(-2*M + r),4));\n\tA620 = (pow(r,3)*(-48*pow(a,3)*E*L*M + 16*a*E*L*M*(M - 3*r)*r + 3*pow(a,4)*(8*pow(E,2)*M + 5*r) + M*r*(pow(L,2)*(-8*M + 4*r) + pow(r,2)*(43*M + 4*(-8 + 5*pow(E,2))*r)) + pow(a,2)*(24*pow(L,2)*M + 2*r*(r*(-31*M + 18*r) + pow(E,2)*(-4*pow(M,2) + 22*M*r)))))/(24.*pow(pow(a,2) + r*(-2*M + r),4));\n\tA700 = (pow(r,5)*(-pow(a,2) + M*r))/(2.*pow(pow(a,2) + r*(-2*M + r),4));\n\tA702 = (-12*pow(a,7)*E*L*M*((2 + 6*pow(E,2))*M + 3*r) + 3*pow(a,8)*(2*pow(E,2)*M*(2*M - 7*r) + r*(26*M + 3*r)) - 4*a*E*L*M*pow(r,3)*(pow(L,2)*(-52*pow(M,2) + 144*M*r - 69*pow(r,2)) + pow(r,2)*(-85*pow(M,2) + 2*(61 + 27*pow(E,2))*M*r - 51*pow(r,2))) - 8*pow(a,5)*E*L*M*(27*pow(L,2)*M + r*((35 + 12*pow(E,2))*pow(M,2) + 3*(8 + 17*pow(E,2))*M*r - 9*pow(r,2))) + M*pow(r,3)*(-4*pow(L,4)*(26*pow(M,2) - 31*M*r + 9*pow(r,2)) + pow(L,2)*pow(r,2)*(-25*pow(M,2) + 4*(3 + 44*pow(E,2))*M*r + 2*(5 - 54*pow(E,2))*pow(r,2)) + pow(r,4)*(91*pow(M,2) + 2*(-59 + 40*pow(E,2))*M*r + 2*(23 - 29*pow(E,2))*pow(r,2))) - 4*pow(a,3)*E*L*M*r*(pow(L,2)*(72*pow(M,2) + 172*M*r - 69*pow(r,2)) + r*(-80*pow(M,3) - 65*pow(M,2)*r + 2*(64 + 69*pow(E,2))*M*pow(r,2) - 84*pow(r,3))) + pow(a,2)*r*(4*pow(L,4)*M*(24*pow(M,2) + 35*M*r - 31*pow(r,2)) + pow(L,2)*r*(-160*pow(M,4) - 52*(-1 + 2*pow(E,2))*pow(M,3)*r + (27 + 1004*pow(E,2))*pow(M,2)*pow(r,2) + 2*(51 - 130*pow(E,2))*M*pow(r,3) - 84*pow(r,4)) - pow(r,3)*(166*pow(M,4) + (-289 + 532*pow(E,2))*pow(M,3)*r + (371 - 472*pow(E,2))*pow(M,2)*pow(r,2) + 16*(-17 + 14*pow(E,2))*M*pow(r,3) + 72*pow(r,4))) + pow(a,6)*(3*pow(L,2)*((4 + 72*pow(E,2))*pow(M,2) + 26*M*r + 3*pow(r,2)) + r*(4*pow(E,2)*M*(35*pow(M,2) + 88*M*r - 48*pow(r,2)) + r*(-322*pow(M,2) + 147*M*r - 9*pow(r,2)))) + pow(a,4)*(72*pow(L,4)*pow(M,2) + pow(L,2)*r*(4*(35 + 72*pow(E,2))*pow(M,3) + 4*(-40 + 239*pow(E,2))*pow(M,2)*r + (23 - 152*pow(E,2))*M*pow(r,2) - 36*pow(r,3)) - pow(r,2)*(4*pow(E,2)*M*(40*pow(M,3) + 78*pow(M,2)*r - 195*M*pow(r,2) + 79*pow(r,3)) + r*(-376*pow(M,3) + 365*pow(M,2)*r - 205*M*pow(r,2) + 90*pow(r,3)))))/(12.*r*pow(pow(a,2) + r*(-2*M + r),5));\n\tA720 = -(pow(r,2)*(-48*pow(a,5)*E*L*M + 4*pow(a,3)*E*L*M*(68*M - 57*r)*r + 3*pow(a,6)*(8*pow(E,2)*M + 3*r) - 4*a*E*L*M*pow(r,2)*(52*pow(M,2) - 98*M*r + 45*pow(r,2)) + M*pow(r,2)*(2*pow(L,2)*(52*pow(M,2) - 64*M*r + 19*pow(r,2)) + pow(r,2)*(-91*pow(M,2) + 2*(59 - 40*pow(E,2))*M*r + 2*(-23 + 29*pow(E,2))*pow(r,2))) + pow(a,4)*(24*pow(L,2)*M + r*(-2*pow(E,2)*M*(68*M - 65*r) + r*(-79*M + 42*r))) + pow(a,2)*r*(2*pow(L,2)*M*(-68*M + 49*r) + r*(4*pow(E,2)*M*(26*pow(M,2) - 66*M*r + 41*pow(r,2)) + r*(187*pow(M,2) - 212*M*r + 72*pow(r,2))))))/(48.*pow(pow(a,2) + r*(-2*M + r),5));\n\tA800 = (pow(r,3)*(-12*pow(a,3)*E*L*M + 4*a*E*L*M*(2*M - 3*r)*r + 3*pow(a,4)*(2*pow(E,2)*M + r) + M*r*(pow(L,2)*(-4*M + 2*r) + pow(r,2)*(5*M + 4*(-1 + pow(E,2))*r)) + 2*pow(a,2)*(3*pow(L,2)*M + r*(r*(-5*M + 3*r) + pow(E,2)*M*(-2*M + 5*r)))))/(12.*pow(pow(a,2) + r*(-2*M + r),5));\n\tA900 = -(pow(r,2)*(-18*pow(a,5)*E*L*M + 2*pow(a,3)*E*L*M*(26*M - 21*r)*r + 3*pow(a,6)*(3*pow(E,2)*M + r) - 8*a*E*L*M*pow(r,2)*(2*pow(M,2) - 6*M*r + 3*pow(r,2)) + M*pow(r,2)*(pow(L,2)*(8*pow(M,2) - 10*M*r + 3*pow(r,2)) + 2*pow(r,2)*(-5*pow(M,2) + (7 - 4*pow(E,2))*M*r + 3*(-1 + pow(E,2))*pow(r,2))) + pow(a,4)*(9*pow(L,2)*M + r*(-26*pow(E,2)*M*(M - r) + r*(-17*M + 9*r))) + pow(a,2)*r*(2*pow(L,2)*M*(-13*M + 8*r) + r*(r*(30*pow(M,2) - 35*M*r + 12*pow(r,2)) + pow(E,2)*M*(8*pow(M,2) - 38*M*r + 23*pow(r,2))))))/(24.*pow(pow(a,2) + r*(-2*M + r),6));\n }\n\n /* Compute aLpha, beta coefficients */\n alpha20 = r*r/(a*a+r*(r-2*M));\n alpha02 = r*r;\n beta = 4.0*(L*L + r*r + a*a*(r+2*M)/r);\n}\n" }, { "path": "external/GravitationalEffectiveSource/CMakeLists.txt", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nset(LIBRARY GravitationalEffectiveSource)\n\nadd_library(${LIBRARY} kerr-circular.c)\n\ntarget_link_libraries(\n ${LIBRARY}\n PRIVATE\n GSL::gsl\n )\n\ntarget_include_directories(${LIBRARY} SYSTEM PUBLIC ${CMAKE_CURRENT_SOURCE_DIR})\n" }, { "path": "external/GravitationalEffectiveSource/LICENSE.md", "content": "MIT License\n\nCopyright (c) 2025 Black Hole Perturbation Toolkit\n\nPermission is hereby granted, free of charge, to any person obtaining a copy\nof this software and associated documentation files (the \"Software\"), to deal\nin the Software without restriction, including without limitation the rights\nto use, copy, modify, merge, publish, distribute, sublicense, and/or sell\ncopies of the Software, and to permit persons to whom the Software is\nfurnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in all\ncopies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\nSOFTWARE.\n" }, { "path": "external/GravitationalEffectiveSource/README.md", "content": "This is a modified version of https://github.com/barrywardell/GravitationalEffectiveSource\n(revision 4c73ea39b23bdf17bcc17dc28f980dabdd97dfec).\nThis repository is currently private (as of Jun 2025) and can be made available\nupon request by the developers of the Black Hole Perturbation Toolkit\n(https://bhptoolkit.org). A similar public repository but for the scalar (not\ngravitational) effective source with more information is available at:\nhttps://github.com/barrywardell/EffectiveSource.\nThis code is licensed under MIT. The license can be found in LICENSE.md.\n\nSummary of modifications:\n\n- Added CMakeLists.txt.\n- Renamed `effsource.h` to `effsource_gr.h`.\n- Added C++ compatibility header `effsource_gr.hpp`.\n" }, { "path": "external/GravitationalEffectiveSource/effsource_gr.h", "content": "/*******************************************************************************\n * Copyright (C) 2011 Barry Wardell\n ******************************************************************************/\n\nstruct coordinate {\n double t;\n double r;\n double theta;\n double phi;\n};\n\nvoid effsource_init(double M, double a);\nvoid effsource_set_particle(struct coordinate * x, double E, double L, double ur);\n\nvoid effsource_hS(struct coordinate * x, double * hS);\nvoid effsource_hS_m(int m, struct coordinate * x, double * hS_re, double * hS_im);\n\nvoid effsource_calc(struct coordinate * x, double *hS, double *dhS_dr, double *dhS_dth,\n double *dhS_dph, double *dhS_dt, double *src);\nvoid effsource_calc_m(int m, struct coordinate * x, double *hS_re, double *hS_im,\n double *dhS_dr_re, double *dhS_dr_im, double *dhS_dth_re, double *dhS_dth_im,\n double *dhS_dph_re, double *dhS_dph_im, double *dhS_dt_re, double *dhS_dt_im,\n double *src_re, double *src_im);\n" }, { "path": "external/GravitationalEffectiveSource/effsource_gr.hpp", "content": "#pragma once\n\nextern \"C\" {\n#include \n}\n" }, { "path": "external/GravitationalEffectiveSource/kerr-circular.c", "content": "/*******************************************************************************\n * Copyright (C) 2012-2013 Barry Wardell\n *******************************************************************************/\n\n#include \n#include \"effsource_gr.h\"\n#include \n#include \n\n/* The particle's coordinate location and 4-velocity */\nstatic struct coordinate xp;\n\n/* Mass of the black hole */\nstatic double M, a;\n\n/* Static variables used to store the coefficients of the series expansions */\nstatic double A00060, A00080, A00240, A00260, A00420, A00440, A00600, A00620, A00800, A01060, A01080, A01240, A01260, A01420, A01440, A01600, A01620, A01800, A02040, A02060, A02220, A02240, A02400, A02420, A02600, A03040, A03060, A03220, A03240, A03400, A03420, A03600, A04020, A04040, A04200, A04220, A04400, A05020, A05040, A05200, A05220, A05400, A06000, A06020, A06200, A07000, A07020, A07200, A08000, A09000;\nstatic double A10061, A10081, A10241, A10261, A10421, A10441, A10601, A10621, A10801, A11061, A11241, A11421, A11601, A12041, A12061, A12221, A12241, A12401, A12421, A12601, A13041, A13221, A13401, A14021, A14041, A14201, A14221, A14401, A15021, A15201, A16001, A16021, A16201, A17001, A18001;\nstatic double A20161, A20341, A20521, A20701, A21161, A21341, A21521, A21701, A22141, A22321, A22501, A23141, A23321, A23501, A24121, A24301, A25121, A25301, A26101, A27101;\nstatic double A30060, A30080, A30240, A30260, A30420, A30440, A30600, A30620, A30800, A31060, A31080, A31240, A31260, A31420, A31440, A31600, A31620, A31800, A32040, A32060, A32220, A32240, A32400, A32420, A32600, A33040, A33060, A33220, A33240, A33400, A33420, A33600, A34020, A34040, A34200, A34220, A34400, A35020, A35040, A35200, A35220, A35400, A36000, A36020, A36200, A37000, A37020, A37200, A38000, A39000;\nstatic double A40080, A40260, A40440, A40620, A40800, A41080, A41260, A41440, A41620, A41800, A42060, A42240, A42420, A42600, A43060, A43240, A43420, A43600, A44040, A44220, A44400, A45040, A45220, A45400, A46020, A46200, A47020, A47200, A48000, A49000;\nstatic double A50180, A50360, A50540, A50720, A50900, A52160, A52340, A52520, A52700, A54140, A54320, A54500, A56120, A56300, A58100;\nstatic double A60061, A60081, A60241, A60261, A60421, A60441, A60601, A60621, A60801, A61061, A61241, A61421, A61601, A62041, A62061, A62221, A62241, A62401, A62421, A62601, A63041, A63221, A63401, A64021, A64041, A64201, A64221, A64401, A65021, A65201, A66001, A66021, A66201, A67001, A68001;\nstatic double A70080, A70260, A70440, A70620, A70800, A71080, A71260, A71440, A71620, A71800, A72060, A72240, A72420, A72600, A73060, A73240, A73420, A73600, A74040, A74220, A74400, A75040, A75220, A75400, A76020, A76200, A77020, A77200, A78000, A79000;\nstatic double A80161, A80341, A80521, A80701, A81161, A81341, A81521, A81701, A82141, A82321, A82501, A83141, A83321, A83501, A84121, A84301, A85121, A85301, A86101, A87101;\nstatic double A90060, A90080, A90240, A90260, A90420, A90440, A90600, A90620, A90800, A91060, A91080, A91240, A91260, A91420, A91440, A91600, A91620, A91800, A92040, A92060, A92220, A92240, A92400, A92420, A92600, A93040, A93060, A93220, A93240, A93400, A93420, A93600, A94020, A94040, A94200, A94220, A94400, A95020, A95040, A95200, A95220, A95400, A96000, A96020, A96200, A97000, A97020, A97200, A98000, A99000;\nstatic double alpha20, alpha02, beta;\n\n\n/* Numerical coefficients appearing in the elliptic integrals expressions. The\n indices here correspond to mode m, EllipticK/EllipticE, order in Sin[dphi],\n term in polynomial in alpha/beta. */\nstatic const double ReEI[21][2][5][27] =\n {\n {{{0,-0.26666666666666666,-0.5333333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.4,0.13333333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,1.2666666666666666,0.5333333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-4,-6.933333333333334,-3.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,1.5333333333333334,1.5333333333333334,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,0.4666666666666667,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,-0.4666666666666667,-0.13333333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-1.5333333333333334,-1.5333333333333334,-0.5333333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,6.866666666666666,8.533333333333333,3.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,-0.4,-0.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,-0.6,-0.26666666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-1.6,-2.4,-1.0666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,9.266666666666667,14.4,6.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.3333333333333335,-24.933333333333334,-38.4,-17.066666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,1.2666666666666666,0.6,0.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,0.06666666666666667,0.7333333333333333,0.26666666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,2.6,2.933333333333333,1.0666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-3.533333333333333,-15.266666666666667,-17.6,-6.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.3333333333333333,10.2,40.93333333333333,46.93333333333333,17.066666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,0,1.6,1.0666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,5,9.066666666666666,4.266666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-7.6,-42,-59.733333333333334,-25.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,30.6,128,166.4,68.26666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.466666666666667,-73.6,-275.2,-341.3333333333333,-136.53333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,0.4666666666666667,-0.6,-2.1333333333333333,-1.0666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-1.1333333333333333,-8.733333333333333,-11.2,-4.266666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,19.8,67.06666666666666,72.53333333333333,25.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-4.2,-69.8,-198.4,-200.53333333333333,-68.26666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.06666666666666667,13.266666666666667,160,420.26666666666665,409.6,136.53333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,0.6666666666666666,-16.4,-34.13333333333333,-17.066666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,41,186.4,247.46666666666667,102.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-17.6,-204,-630.4,-716.8,-273.06666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,65.8,536,1427.2,1501.8666666666666,546.1333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.4857142857142858,-153.0857142857143,-1073.3714285714286,-2640.457142857143,-2652.647619047619,-936.2285714285714,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-0.8666666666666667,2.7333333333333334,30.266666666666666,42.666666666666664,17.066666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-3.1333333333333333,-97.4,-290.93333333333334,-298.6666666666667,-102.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,53.8,410.4,937.6,853.3333333333334,273.06666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-4.6,-177.4,-1019.2,-2075.733333333333,-1774.9333333333334,-546.1333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.02857142857142857,14.771428571428572,392.62857142857143,1984,3791.2380952380954,3120.7619047619046,936.2285714285714,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,1.6,-198.4,-814.9333333333333,-1024,-409.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,147.4,1179.7333333333333,3012.266666666667,3072,1092.2666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-31.6,-629.2,-3345.0666666666666,-7116.8,-6553.6,-2184.5333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,114.94285714285714,1556.3428571428572,6981.4857142857145,13497.295238095237,11702.857142857143,3744.9142857142856,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.492063492063492,-263.84761904761905,-3017.295238095238,-12327.009523809524,-22469.485714285714,-18724.571428571428,-5825.422222222222,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-2.7333333333333334,18.6,452.26666666666665,1250.1333333333334,1228.8,409.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-5.933333333333334,-401.26666666666665,-2212.266666666667,-4343.466666666666,-3618.133333333333,-1092.2666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,106.2,1463.3333333333333,5879.466666666666,9984,7645.866666666667,2184.5333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-4.885714285714286,-344.0857142857143,-3410.5142857142855,-11886.933333333332,-18646.55238095238,-13575.314285714287,-3744.9142857142856,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.015873015873015872,15.806349206349207,753.3714285714286,6407.466666666666,20597.02857142857,30739.504761904762,21637.28253968254,5825.422222222222,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,2.8,-970,-6314.666666666667,-14080,-13107.2,-4369.066666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,380.2,4689.866666666667,19157.333333333332,34508.8,28398.933333333334,8738.133333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-49.6,-1514.1714285714286,-12285.104761904762,-41442.74285714285,-66823.31428571428,-51180.49523809524,-14979.657142857142,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,178.05396825396826,3632.0761904761903,24604.95238095238,74800.76190476191,112737.52380952382,82388.11428571428,23301.68888888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.494949494949495,-405.9919191919192,-6920.145454545454,-42364.121212121216,-120645.81818181818,-173769.69696969696,-122863.45050505051,-33893.36565656566,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-5.133333333333334,58.2,2479.3333333333335,11306.666666666666,19814.4,15291.733333333334,4369.066666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-9.533333333333333,-1129.9333333333334,-9986.933333333332,-31906.133333333335,-47069.86666666667,-32768,-8738.133333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,178.14285714285714,3892.609523809524,24463.390476190478,66662.4,89604.87619047619,58670.32380952381,14979.657142857142,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.1079365079365076,-573.9968253968254,-8815.314285714287,-47328,-117906.28571428571,-149562.51428571428,-94038.95873015873,-23301.68888888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.010101010101010102,16.6,1251.761616161616,16279.660606060606,79786.66666666667,187671.27272727274,228846.41616161616,139810.13333333333,33893.36565656566,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,4.266666666666667,-3262.4,-30573.866666666665,-103765.33333333333,-163840,-122333.86666666667,-34952.53333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,811.4,14256.685714285713,84442.81904761905,231716.57142857142,322998.85714285716,222198.24761904762,59918.62857142857,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-71.6,-3111.35873015873,-35753.44761904762,-174188.49523809523,-426296.0761904762,-551126.5523809524,-359511.77142857143,-93206.75555555556,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,255.14487734487736,7331.7772005772,69909.00086580086,305560.71341991343,696355.4632034632,856110.1021645021,538057.1797979798,135573.46262626263,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.4965034965034967,-579.5630147630147,-13824.999533799533,-118555.33053613054,-483592.47365967365,-1.0497981165501166e6,-1.2450923412587412e6,-761297.1362859363,-187717.1020979021,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-8.066666666666666,135.93333333333334,9026.133333333333,61310.933333333334,166024.53333333333,218453.33333333334,139810.13333333333,34952.53333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-13.933333333333334,-2571.1714285714284,-33332.038095238095,-157322.3619047619,-357171.2,-422863.2380952381,-252157.5619047619,-59918.62857142857,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,270.5174603174603,8617.873015873016,78308.57142857143,312652.8,643189.0285714286,713406.1714285715,406115.1492063492,93206.75555555556,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.28975468975469,-870.3079365079365,-19227.160750360752,-147887.70909090908,-536312.6857142857,-1.0362348051948051e6,-1.0997186678210679e6,-605843.911111111,-135573.46262626263,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.006993006993006993,17.244910644910647,1895.0315462315461,35180.35244755245,245442.05874125875,836234.2041958042,1.5471995524475526e6,1.5905439527583527e6,855155.6873348873,187717.1020979021,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,6,-8800.4,-111859.80952380953,-531221.9428571429,-1.2414390857142857e6,-1.5322940952380951e6,-958698.0571428571,-239674.51428571428,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,1529,36268.93968253968,292742.09523809527,1.1256783238095238e6,2.3227830857142857e6,2.6401645714285714e6,1.557884342857143e6,372827.02222222224,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-97.6,-5729.1255411255415,-88548.89927849927,-586570.2510822511,-2.0080116917748917e6,-3.8364944623376625e6,-4.1284842943722946e6,-2.3386422303030305e6,-542293.8505050505,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,346.2218004218004,13349.73026973027,170513.0474858475,1.0105419870795871e6,3.214343297236097e6,5.829024556243756e6,6.033182035742036e6,3.3163354703962705e6,750868.4083916084,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.4974358974358974,-784.5839937839938,-25005.26247086247,-286327.7053613054,-1.5797995114219114e6,-4.77710082983683e6,-8.342656417715617e6,-8.387304409013209e6,-4.50521045034965e6,-1.0011578778554779e6,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-11.533333333333333,269.4,25857.619047619046,244643.3523809524,941524.1142857143,1.8502997333333334e6,1.9667041523809524e6,1.0785353142857142e6,239674.51428571428,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-19.133333333333333,-5094.479365079365,-91148.63492063493,-595972.8761904762,-1.9178837333333334e6,-3.3857145904761907e6,-3.3492016761904764e6,-1.744297853968254e6,-372827.02222222224,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,384.0510822510823,16824.368253968252,209062.3953823954,1.1501940363636364e6,3.3420239238095237e6,5.513081239826839e6,5.196125312554113e6,2.6097891555555556e6,542293.8505050505,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.443600843600843,-1235.5986901986903,-37219.1333999334,-389168.827972028,-1.9364873206793207e6,-5.267843912887113e6,-8.294196586702187e6,-7.550561944366745e6,-3.6917696745920745e6,-750868.4083916084,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.005128205128205128,17.78850038850039,2689.031546231546,67733.57202797203,639727.53006993,2.9806964363636365e6,7.743910966899767e6,1.1785440213830614e7,1.0452192532090131e7,5.005789389277389e6,1.0011578778554779e6,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,8,-20454.4,-338221.5111111111,-2.129646933333333e6,-6.821751466666667e6,-1.2233386666666666e7,-1.2443101866666667e7,-6.7108864e6,-1.491308088888889e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,2637,81197.69581529581,855236.9685425685,4.365921080519481e6,1.2354614081385281e7,2.0404108744588744e7,1.9569787234632034e7,1.0100222965656566e7,2.169175402020202e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-127.6,-9731.779553779554,-194743.272016872,-1.6810041968697968e6,-7.631895255677655e6,-1.9979235561238762e7,-3.121355504229104e7,-2.8716805848018646e7,-1.4349929582595183e7,-3.0034736335664336e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,451.2884670884671,22506.019314019315,371138.143989344,2.8608340821844824e6,1.2051529176956376e7,2.991034232967033e7,4.489893256254856e7,4.0046315114219114e7,1.9522578618181817e7,4.0046315114219114e6,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.4980392156862745,-1021.0684583390466,-41964.88205128205,-619011.4680926916,-4.434788679994515e6,-1.7736541547237076e7,-4.234410989606472e7,-6.1679177494547285e7,-5.3709175564952694e7,-2.5676754984999314e7,-5.182464308898944e6,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-15.533333333333333,479.4,63067.02222222222,792570.3111111111,4.1009152e6,1.1153681066666666e7,1.7336456533333335e7,1.55189248e7,7.456540444444444e6,1.491308088888889e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-25.133333333333333,-9153.99163059163,-216262.70476190475,-1.870872972005772e6,-8.079372412121212e6,-1.9716661638095237e7,-2.849857074978355e7,-2.421317832958153e7,-1.1184810666666666e7,-2.169175402020202e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,519.3591075591075,29973.258252858253,488692.7529359529,3.5444105846153847e6,1.3786808101764902e7,3.138413195977356e7,4.3162921822710626e7,3.5328619333022535e7,1.58516663993784e7,3.0034736335664336e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.576934176934177,-1672.0434454434455,-65967.23223443223,-901384.234965035,-5.895572075924076e6,-2.1422238766033966e7,-4.646431837318237e7,-6.163704083294483e7,-4.905673601491842e7,-2.1524894373892773e7,-4.0046315114219114e6,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.00392156862745098,18.25848530554413,3638.6809634809633,119650.73401892226,1.4725623786096256e6,8.997631810448375e6,3.1165726124667488e7,6.523953848801134e7,8.420522974629554e7,6.55758409995338e7,2.8267987139448788e7,5.182464308898944e6,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,10.266666666666667,-42656.4,-889373.995959596,-7.149019797979798e6,-2.9865748169696968e7,-7.235293556363636e7,-1.0554394065454546e8,-9.146124722424242e7,-4.3383508040404044e7,-8.676701608080808e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,4255.4,165053.57016317017,2.19670492991453e6,1.4330180624708625e7,5.29140260997669e7,1.1808499516270396e8,1.624359102955711e8,1.346948423011655e8,6.173806913442113e7,1.2013894534265734e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-161.6,-15539.587434787434,-390961.72201132204,-4.259990718614719e6,-2.4699115148318347e7,-8.432809336796537e7,-1.779399951088911e8,-2.3469069971592852e8,-1.8834282577156177e8,-8.409726173986015e7,-1.6018526045687646e7,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,570.3472906178788,35746.582191664544,739622.7686979687,7.187172049660143e6,3.862786977665472e7,1.249378262920452e8,2.5314112267361397e8,3.234930047362311e8,2.531309910877828e8,1.1071628296284108e8,2.0729857235595778e7,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.498452012383901,-1289.0251146857959,-66438.47422257825,-1.227617738434115e6,-1.107397992473244e7,-5.645272137256345e7,-1.7550347663965014e8,-3.4482027794523466e8,-4.29947715579034e8,-3.2974049077368206e8,-1.4183586529618162e8,-2.6185082823910456e7,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-20.066666666666666,789.9333333333333,136892.39191919193,2.2055480888888887e6,1.4743798173737373e7,5.277455204848485e7,1.1157285546666667e8,1.4395359728484848e8,1.115261196929293e8,4.7721858844444446e7,8.676701608080808e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-31.933333333333334,-15290.940326340326,-461269.8076146076,-5.10054407956488e6,-2.841850342937063e7,-9.11948410927739e7,-1.7918446766247088e8,-2.193337460960373e8,-1.6331127164320123e8,-6.7745016401554e7,-1.2013894534265734e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,676.9748695748696,49810.32203352203,1.0321920394272394e6,9.544164072727272e6,4.781388058341658e7,1.4294413774385613e8,2.6698699182559663e8,3.145956128422688e8,2.2738798300792542e8,9.210652476270397e7,1.6018526045687646e7,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.694581235757706,-2181.5221419103773,-109270.05492285492,-1.892202578033731e6,-1.5744906345607335e7,-7.356716086097433e7,-2.0929734465833253e8,-3.7668167367356825e8,-4.312426213404269e8,-3.046022843375291e8,-1.2108121158063897e8,-2.0729857235595778e7,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.0030959752321981426,18.672520393263426,4748.226915980476,197766.84242568578,3.0782871159107145e6,2.3888763615371626e7,1.062565981512135e8,2.914255876520172e8,5.098456950542433e8,5.706785877375826e8,3.9574872039228964e8,1.5492840670813686e8,2.6185082823910456e7,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,12.8,-81880,-2.1007407614607615e6,-2.095521238228438e7,-1.1023046737156177e8,-3.441285888596737e8,-6.709847600932401e8,-8.259552492307693e8,-6.240550771965812e8,-2.6430567975384617e8,-4.805557813706294e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,6520.2,311067.7942501943,5.102019779331779e6,4.133440304335664e7,1.922698987114219e8,5.530782550526806e8,1.0170620137920746e9,1.1980522605003884e9,8.746782659530692e8,3.6041683602797204e8,6.407410418275058e7,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-199.6,-23628.784478266833,-730166.5007724302,-9.797468315151514e6,-7.051502323959962e7,-3.0318843028131086e8,-8.24417740343672e8,-1.4532290842782943e9,-1.6563077409054527e9,-1.1777150141972852e9,-4.749021839427396e8,-8.291942894238311e7,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,703.3999221968262,54143.24552805296,1.3738612902969064e6,1.6423980970872264e7,1.0950013007528281e8,4.457761957446739e8,1.1633972193432798e9,1.9862208061391819e9,2.20653026587352e9,1.5363898975089884e9,6.088031756559181e8,1.0474033129564182e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.49874686716792,-1588.4598780648316,-100391.40281967774,-2.2721153274630425e6,-2.5192147588914696e7,-1.5919834323671788e8,-6.225945846062396e8,-1.5748847121862333e9,-2.622330288934644e9,-2.854181112514796e9,-1.9537500785578425e9,-7.631081280111047e8,-1.2967850541365178e8,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-25.133333333333333,1228.2,271881.5229215229,5.463605097125097e6,4.5788857465734266e7,2.0806943674778554e8,5.705886187710955e8,9.891261404195805e8,1.0929306833255634e9,7.47197496172805e8,2.883334688223776e8,4.805557813706294e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-39.53333333333333,-24135.788500388502,-905518.1986013986,-1.2458983344832946e7,-8.693429073752914e7,-3.539285428811189e8,-9.016469155505828e8,-1.4824022811648796e9,-1.5738201839888113e9,-1.0428727894327894e9,-3.9245388811934733e8,-6.407410418275058e7,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,857.3689565336624,78373.47438182733,2.0127715456099457e6,2.3112727872974087e7,1.448205784474976e8,5.48772786971836e8,1.3280004404618127e9,2.1005893010457883e9,2.16389478497818e9,1.3996187132419581e9,5.163618984139312e8,8.291942894238311e7,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.799844393652443,-2765.6909199503625,-171565.7852751995,-3.67408829080517e6,-3.790738907893345e7,-2.2126713741740116e8,-7.971567635483366e8,-1.8574286571222606e9,-2.852811286882909e9,-2.870394025251496e9,-1.8211526732190146e9,-6.61173341303739e8,-1.0474033129564182e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.002506265664160401,19.04256314720711,6021.407418450143,310071.7180627422,5.959559314048181e6,5.72743914936333e7,3.179286576710175e8,1.1032734622114787e9,2.4971591341437187e9,3.7476056187814e9,3.700130737674165e9,2.310989422798335e9,8.279473807179306e8,1.2967850541365178e8,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,15.6,-147184.4,-4.556378703962704e6,-5.516948408391608e7,-3.559327987468532e8,-1.3849838370013986e9,-3.448738599742657e9,-5.628697306405595e9,-5.996935688354312e9,-4.0186477217118883e9,-1.537778500386014e9,-2.5629641673100233e8,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,9583.4,551597.1562502857,1.092800063183875e7,1.0752849872261073e8,6.136858642814754e8,2.2008252360679007e9,5.169359078663266e9,8.074326015812789e9,8.312849426393528e9,5.419679834310819e9,2.0277569441364596e9,3.3167771576953244e8,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-241.6,-34531.581210533535,-1.2859442616457501e6,-2.0830391072875936e7,-1.8202685521436995e8,-9.600492874957876e8,-3.2540002685571485e9,-7.325356346213779e9,-1.1069155880596071e10,-1.1097453830148788e10,-7.079345431875746e9,-2.6010515605084386e9,-4.189613251825673e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,850.4475412444452,78893.74837670069,2.409665423174555e6,3.474925120193656e7,2.8114098072956973e8,1.403407938144174e9,4.564031654437904e9,9.948487456287066e9,1.4649250696397833e10,1.4378787962114319e10,9.011876808307611e9,3.2619131746357026e9,5.187140216546071e8,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.4989648033126293,-1919.3769533617697,-146019.8335099459,-3.9742071741968985e6,-5.311713496745179e7,-4.071180069944188e8,-1.951471853701304e9,-6.149049338477993e9,-1.3068470999123806e10,-1.8848566822377876e10,-1.8183385037681484e10,-1.1230798287201794e10,-4.014395471935655e9,-6.314779394056087e8,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-30.733333333333334,1824.6,503413.80792540795,1.23437348997669e7,1.2666985013706294e8,7.111014843972028e8,2.4453185536e9,5.440886345756643e9,8.003944371617716e9,7.74195386945641e9,4.739481393767832e9,1.6659267087515152e9,2.5629641673100233e8,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-47.93333333333333,-36410.112500571326,-1.6632604871154989e6,-2.7868508792540792e7,-2.3790098953758398e8,-1.1959445584594543e9,-3.819200511326039e9,-8.057472578080973e9,-1.1386686300517574e10,-1.0673579702376745e10,-6.371368734672261e9,-2.193595802021226e9,-3.3167771576953244e8,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,1060.962421067065,117999.39040993406,3.6796141928934497e6,5.137764483644158e7,3.934568326273124e8,1.8396699858694205e9,5.577640943291375e9,1.131629761773835e10,1.5511646734480068e10,1.4188707002727196e10,8.301315963658234e9,2.8105322230997224e9,4.189613251825673e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.895082488890538,-3426.029950579177,-257947.1453013447,-6.696260875827578e6,-8.390810906845228e7,-5.980646799483613e8,-2.656730813122411e9,-7.751269489416868e9,-1.5263016489000265e10,-2.042660824129106e10,-1.832174708555405e10,-1.0545574516565224e10,-3.521270185463006e9,-5.187140216546071e8,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.002070393374741201,19.377095129336347,7461.561160324547,465737.4659903026,1.0838682409513706e7,1.2638856718220124e8,8.560311134982536e8,3.660454950424734e9,1.0368589915334404e10,1.9940417844891014e10,2.6176608626888607e10,2.310528608711372e10,1.3119593909531069e10,4.330134441638459e9,6.314779394056087e8,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,18.666666666666668,-250822.4,-9.21840527146579e6,-1.3309575831290278e8,-1.0317491250125874e9,-4.880582542269025e9,-1.5029793383663677e10,-3.1108875678233482e10,-4.36671203627632e10,-4.102438746924404e10,-2.470622075987824e10,-8.623620610007843e9,-1.3267108630781298e9,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,13613,930252.8430925112,2.189775853092872e7,2.5704415869336855e8,1.7632092507090087e9,7.688769367066271e9,2.233765721776305e10,4.425202515598031e10,6.002764410921827e10,5.486875815318882e10,3.230882151159315e10,1.1067561673572819e10,1.6758453007302692e9,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-287.6,-48836.168107778016,-2.157297016025873e6,-4.150197552329858e7,-4.325356919968865e8,-2.7414740676285434e9,-1.129721454934732e10,-3.1453610225900883e10,-6.027595384543495e10,-7.961419543169162e10,-7.119894052826602e10,-4.116669092530494e10,-1.3885575348907944e10,-2.0748560866184285e9,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,1011.4910195053149,111321.75903879551,4.0295488900919873e6,6.897135012978844e7,6.652503712536638e8,3.9895117085213494e9,1.5770553504337744e10,4.2506951460346924e10,7.936585512341737e10,1.0261545331623116e11,9.014849059168524e10,5.1342279166782936e10,1.7095009931051834e10,2.5259117576224346e9,0,0,0,0,0,0,0,0,0},{0,0,0,0,-3.4991304347826087,-2281.7794378338194,-205750.77203382071,-6.631606823604064e6,-1.0514449275916624e8,-9.603493437127837e8,-5.528469326922443e9,-2.116888539068655e10,-5.561882541965658e10,-1.0169630183320364e11,-1.2921016311537668e11,-1.1184445811395491e11,-6.289520276479862e10,-2.0712476412503963e10,-3.0310941091469216e9,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-36.86666666666667,2612.733333333333,880586.5429315782,2.58769066508707e7,3.190248779785548e8,2.165737490196956e9,9.103826722266722e9,2.516944859639786e10,4.714484837223376e10,6.028345544481031e10,5.188494812822027e10,2.876927277805501e10,9.286976041546907e9,1.3267108630781298e9,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-57.13333333333333,-52928.28618502241,-2.8930003372693355e6,-5.799649101182244e7,-5.943782676834052e8,-3.6117879045470395e9,-1.4095434050579176e10,-3.694310664816257e10,-6.646474288799973e10,-8.235087355324098e10,-6.910511159213396e10,-3.752838135449264e10,-1.1905484323937954e10,-1.6758453007302692e9,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,1288.1362155560298,171329.4262403575,6.378245421382333e6,1.0642760530321938e8,9.777255230809364e8,5.52282590456045e9,2.045420469861058e10,5.153708389209838e10,8.991146463998302e10,1.0868422825737668e11,8.937325837111873e10,4.772044308351795e10,1.4923003392217157e10,2.0748560866184285e9,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.982039010629669,-4163.8773617253355,-374174.74996878806,-1.1581383324811196e7,-1.7326355869602597e8,-1.4804164912081263e9,-7.940429316689499e9,-2.828693012341041e10,-6.914758135245525e10,-1.1774449383689468e11,-1.395287760054435e11,-1.1285112004028159e11,-5.941617567775465e10,-1.8357965809863052e10,-2.5259117576224346e9,0,0,0,0,0,0,0,0,0},{0,0,0,-0.0017391304347826088,19.68235392850819,9071.70504037235,675142.9984015393,1.87165462532353e7,2.6038147706447074e8,2.1128045296213334e9,1.0902989617985832e10,3.76931192037466e10,8.995871805969456e10,1.5020871457643378e11,1.7511705338495316e11,1.3969263524174225e11,7.268311082558556e10,2.2228023467077423e10,3.0310941091469216e9,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,22,-408912.4,-1.760144321133892e7,-2.9861306666560435e8,-2.735742086051796e9,-1.5429018250372686e10,-5.7365925635849785e10,-1.459396829211136e11,-2.5834540566109332e11,-3.181407036536493e11,-2.6734969563212573e11,-1.462262308496573e11,-4.692366842044753e10,-6.703381202921077e9,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,18793,1.5042532023658487e6,4.1496704494122185e7,5.725677207573206e8,4.642875405124088e9,2.4142609768578815e10,8.469481355425212e10,2.0624416519975134e11,3.5284625417378284e11,4.227746181988333e11,3.4738564819211395e11,1.8647020933259586e11,5.8893991997092316e10,8.299424346473714e9,0,0,0,0,0,0,0,0,0,0},{0,0,0,-337.6,-67186.71908304376,-3.473936806561178e6,-7.829175553408918e7,-9.589299292985568e8,-7.183900332775953e9,-3.529847566422289e10,-1.1866407812293896e11,-2.795105576516615e11,-4.6559435752690393e11,-5.4578034888958093e11,-4.4032629265684235e11,-2.3272130603976505e11,-7.25297518974442e10,-1.0103647030489738e10,0,0,0,0,0,0,0,0,0},{0,0,0,1,1186.5310195053148,152876.8874522256,6.472435445144703e6,1.2971987635205658e8,1.4699377328144228e9,1.0417012853749659e10,4.909095266192736e10,1.5974095702715295e11,3.6655776122906323e11,5.976373260031626e11,6.881257568365696e11,5.468004776147498e11,2.8525211689964355e11,8.790172916526073e10,1.2124376436587687e10,0,0,0,0,0,0,0,0},{0,0,0,0,-3.4992592592592593,-2675.669679379713,-282242.09231669543,-1.0633815228365488e7,-1.9732870645890525e8,-2.1167235434403558e9,-1.4395851669845222e10,-6.570092170701432e10,-2.08363647527213e11,-4.6815844108415533e11,-7.499685194097299e11,-8.507323675829946e11,-6.674090341577878e11,-3.4432387109323157e11,-1.0507792911709328e11,-1.4369631332252073e10,0,0,0,0,0,0,0}},{{0.5333333333333333,-43.53333333333333,3629.4,1.4694724226778382e6,5.0982079751051836e7,7.433658698673364e8,5.9978865667303295e9,3.02094865091216e10,1.0127974704935579e11,2.3405817896550006e11,3.7868392857216315e11,4.284339090756366e11,3.3229306521589435e11,1.6843118108433334e11,5.027535902190807e10,6.703381202921077e9,0,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-67.13333333333334,-74599.00473169761,-4.808057892384602e6,-1.1363745491663341e8,-1.3765659670421038e9,-9.93853334295837e9,-4.646297120807411e10,-1.476455595126865e11,-3.276911350438754e11,-5.136740259640373e11,-5.665757674791024e11,-4.3035620039143896e11,-2.143610632661782e11,-6.304370417032917e10,-8.299424346473714e9,0,0,0,0,0,0,0,0,0,0},{0,0,0.2,1539.2381660875133,241314.9715176823,1.0573575649746368e7,2.0780309906924197e8,2.255048448318664e9,1.5127647788083984e10,6.709248572068778e10,2.0490559066010007e11,4.4090160795530695e11,6.741577248596049e11,7.285603048003533e11,5.440348341050625e11,2.6709174817027032e11,7.758157541268906e10,1.0103647030489738e10,0,0,0,0,0,0,0,0,0},{0,0,0,-6.062039010629669,-4980.454188585528,-526689.1747977207,-1.9167077767400973e7,-3.374851933365408e8,-3.4042942107257743e9,-2.167534593874192e10,-9.243454922934729e10,-2.738046230308966e11,-5.748972516712766e11,-8.61570663231068e11,-9.156248791038105e11,-6.740816221370153e11,-3.269296609004137e11,-9.396391738355457e10,-1.2124376436587687e10,0,0,0,0,0,0,0,0},{0,0,0,-0.0014814814814814814,19.963062463129766,10854.591016749811,949896.1873083068,3.0939338982764497e7,5.0627985565643203e8,4.84757118825071e9,2.9683411242703876e10,1.2280305832607028e11,3.5504229585249896e11,7.308189481361008e11,1.0772753882648191e12,1.1289483918947014e12,8.212160109323472e11,3.941685297769809e11,1.1226274478321931e11,1.4369631332252073e10,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,25.6,-642174.4,-3.2001493960675444e7,-6.301171929947947e8,-6.730005930120287e9,-4.45489555789727e10,-1.9627249696235114e11,-5.995497443810022e11,-1.2980003517584287e12,-2.0066420365331858e12,-2.2010916432997065e12,-1.6733714338577625e12,-8.384014633082003e11,-2.4898273039421143e11,-3.3197697385894855e10,0,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,25323.4,2.3470004379713614e6,7.499139768356036e7,1.2012583049576294e9,1.1358261276733395e10,6.933205150119518e10,2.8824587254763275e11,8.428926177352782e11,1.7637070948449934e12,2.6530579083520938e12,2.8455838704309585e12,2.1231780276189883e12,1.0469973628525146e12,3.067178562827242e11,4.0414588121958954e10,0,0,0,0,0,0,0,0,0},{0,0,0,-391.6,-90283.39413633075,-5.402084146905385e6,-1.409712773254586e8,-2.0042036720084534e9,-1.7506077529181057e10,-1.009677881940971e11,-4.0223835666768646e11,-1.1377089895665e12,-2.317805564538369e12,-3.4109110612635464e12,-3.591988921734658e12,-2.6387589471896216e12,-1.2839931153068442e12,-3.718142107220224e11,-4.8497505746350746e10,0,0,0,0,0,0,0,0},{0,0,0,1,1375.5680565423518,205134.69458317457,1.00442903694642e7,2.3300366348778668e8,3.0639399202108026e9,2.531140817273939e10,1.3999475849889786e11,5.397786494220163e11,1.4872042574435613e12,2.9652929630267153e12,4.285977100720373e12,4.445188146394695e12,3.223045360499386e12,1.5505730309458252e12,4.4456046934154846e11,5.747852532900829e10,0,0,0,0,0,0,0},{0,0,0,0,-3.499361430395913,-3101.049500580224,-378382.55774830375,-1.6479398081656067e7,-3.538256790695258e8,-4.4032169385133705e9,-3.490151422566471e10,-1.869146820137703e11,-7.023015906202007e11,-1.8944051915725413e12,-3.7109112830375283e12,-5.283759154390902e12,-5.409848733761012e12,-3.8788481619419673e12,-1.8478757481648335e12,-5.2523480042024817e11,-6.7388615902975235e10,0,0,0,0,0,0}},{{0.5333333333333333,-50.733333333333334,4914.6,2.3567543213508883e6,9.531948442077139e7,1.6222566814226518e9,1.533629951143212e10,9.106927966780995e10,3.6324193033461017e11,1.0115537476095123e12,2.0078489418750176e12,2.859678973879202e12,2.902119927570143e12,2.0490001876928757e12,9.566682602454508e11,2.6558157908715884e11,3.3197697385894855e10,0,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-77.93333333333334,-102426.67594272287,-7.688375333570598e6,-2.1157272142042986e8,-2.9899660626777706e9,-2.5285472574644356e10,-1.39341099517905e11,-5.2671795525996155e11,-1.4085398898401514e12,-2.708603610196061e12,-3.76067732280449e12,-3.7374252386297983e12,-2.5929559786286685e12,-1.1927785557210093e12,-3.269251503437037e11,-4.0414588121958954e10,0,0,0,0,0,0,0,0,0},{0,0,0.2,1814.5882726615152,331222.3335493492,1.6875662577301286e7,3.858469039048684e8,4.882312146902555e9,3.834964651451061e10,2.0043215049773267e11,7.280122943454908e11,1.8871102433942173e12,3.5392202281469395e12,4.81403000415386e12,4.70284874154185e12,3.215586981496385e12,1.4608069383404146e12,3.9606296359519775e11,4.8497505746350746e10,0,0,0,0,0,0,0,0},{0,0,0,-6.136113084703743,-5876.883265298239,-722621.9636936528,-3.0552356959223974e7,-6.254641839081137e8,-7.35329135286915e9,-5.480054731379718e10,-2.753158133060997e11,-9.696738980136191e11,-2.4522191929156543e12,-4.506888343001096e12,-6.027500191226616e12,-5.804540636175082e12,-3.920365399720353e12,-1.7620760421174104e12,-4.732997320060526e11,-5.747852532900829e10,0,0,0,0,0,0,0},{0,0,0,-0.001277139208173691,20.222883663640623,12812.749057488787,1.302854067321981e6,4.927317433912787e7,9.370025785364087e8,1.045225177549322e10,7.488955072282285e10,3.6490079744731726e11,1.254099223039917e12,3.108551076865836e12,5.618437072552979e12,7.408490300586078e12,7.048384464155902e12,4.710622193686491e12,2.09785778289315e12,5.589291083717358e11,6.7388615902975235e10,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,29.466666666666665,-976730,-5.578954646189742e7,-1.2615869100582263e9,-1.5529302994019297e10,-1.1910193801450629e11,-6.125072742936332e11,-2.206143296031422e12,-5.709225768796877e12,-1.0749971748792695e13,-1.4747065224375662e13,-1.4582852118589701e13,-1.0122591368671906e13,-4.679251530995561e12,-1.2932668199026865e12,-1.6165835248783582e11,0,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,33420.2,3.550881250122197e6,1.3009442746062008e8,2.3938339984597726e9,2.6090461836376514e10,1.8454580335053577e11,8.956680843174019e11,3.088494496941551e12,7.725403893782204e12,1.415456345665883e13,1.898742633772399e13,1.842784153284401e13,1.2590136522466424e13,5.741108749446352e12,1.5680860191320073e12,1.9399002298540298e11,0,0,0,0,0,0,0,0},{0,0,0,-449.6,-118882.34141578716,-8.1507702655822905e6,-2.4382796059468478e8,-3.981492068669497e9,-4.008401440642937e10,-2.6788273341492886e11,-1.2457916692080254e12,-4.155022019169404e12,-1.011883380132408e13,-1.8137213625744375e13,-2.3887559953693965e13,-2.2825549173918258e13,-1.538763792071379e13,-6.935816898196855e12,-1.8752368888588955e12,-2.2991410131603317e11,0,0,0,0,0,0,0},{0,0,0,1,1578.6025393009725,269796.6997164444,1.5129675524776911e7,4.02205042950141e8,6.073244823885286e9,5.781867124578261e10,3.705046212385272e11,1.6674750698719607e12,5.417057116138862e12,1.2910569366340434e13,2.272747357675429e13,2.947861243273825e13,2.7800233539143176e13,1.8528636980494258e13,8.268499554905844e12,2.2158962523390093e12,2.6955446361190094e11,0,0,0,0,0,0},{0,0,0,0,-3.49944382647386,-3557.9203447280424,-497291.8376827858,-2.479476383769259e7,-6.098901382048699e8,-8.713451379196568e9,-7.957942158518886e10,-4.937089707091298e11,-2.1650359733823113e12,-6.885306538377396e12,-1.6120601827215521e13,-2.7953517732769695e13,-3.579038142482068e13,-3.3375171285503258e13,-2.2026160316691473e13,-9.744096556853e12,-2.5912009727853706e12,-3.1303099000091724e11,0,0,0,0,0}},{{0.5333333333333333,-58.46666666666667,6511.533333333334,3.65374292379483e6,1.7041039042477334e8,3.3474383786596866e9,3.6634576706844986e10,2.5307096312507574e11,1.1825685116914846e12,3.8959211372933706e12,9.271173514538479e12,1.6125338479467012e13,2.0514656081142355e13,1.8879270148820613e13,1.2234885075983668e13,5.295573999855435e12,1.3740959961466045e12,1.6165835248783582e11,0,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-89.53333333333333,-137512.7002443942,-1.189358210895399e7,-3.7701063823343146e8,-6.146753773932911e9,-6.016166039394057e10,-3.856178138857783e11,-1.7075189529981672e12,-5.401437822018391e12,-1.2451974168004955e13,-2.1111659790717637e13,-2.6300614293483598e13,-2.3782945860158555e13,-1.5184861333257229e13,-6.488778629702592e12,-1.665081030624709e12,-1.9399002298540298e11,0,0,0,0,0,0,0,0},{0,0,0.2,2114.4828315743325,444637.2286422091,2.6068237359630816e7,6.861001365773908e8,1.00114325811189e10,9.098481065241385e10,5.529740045299663e11,2.3523822512552803e12,7.2120144708876045e12,1.621315950309689e13,2.692705307551175e13,3.29716634138851e13,2.938224475952283e13,1.8525493900149555e13,7.830326448629547e12,1.990193939516912e12,2.2991410131603317e11,0,0,0,0,0,0,0},{0,0,0,-6.2050786019451225,-6854.203876665512,-969805.7488195399,-4.71490524203349e7,-1.110535871836198e9,-1.5050298809158161e10,-1.2973475579082533e11,-7.577552802741434e11,-3.1251463627856104e12,-9.3459380263197e12,-2.058641033023447e13,-3.3613123793561336e13,-4.056896085255746e13,-3.57073389951639e13,-2.2272676941597234e13,-9.325906219148117e12,-2.3506734841449595e12,-2.6955446361190094e11,0,0,0,0,0,0},{0,0,0,-0.0011123470522803114,20.46471615241416,14948.520395986918,1.7481414056108568e6,7.598676584469618e7,1.6618757729228277e9,2.1362875654996433e10,1.7699538829298035e11,1.0024052815552432e12,4.0333265266471006e12,1.182051050899169e13,2.5601839654882164e13,4.120957066054989e13,4.913190571704601e13,4.278719239553509e13,2.6441705068033305e13,1.0981003732620514e13,2.747716467785829e12,3.1303099000091724e11,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,33.6,-1.4449664e6,-9.378112396360818e7,-2.4134343369641385e9,-3.3903936051757397e10,-2.9801676779554596e11,-1.7669252650270583e12,-7.395409184951448e12,-2.247442917360153e13,-5.039491703618102e13,-8.391129263208694e13,-1.034420381542176e14,-9.311814740541167e13,-5.94700664214626e13,-2.5517770940204883e13,-6.595660781503701e12,-7.759600919416119e11,0,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,43315.4,5.230291427936181e6,2.1780053830000895e8,4.561721534340654e9,5.6748630670697624e10,4.600956128255938e11,2.574621229746886e12,1.0317263052979926e13,3.0307188769397027e13,6.613140421026188e13,1.0767812330799452e14,1.302827448528449e14,1.1543547237775336e14,7.272605132546514e13,3.083902504292948e13,7.888927601406388e12,9.196564052641327e11,0,0,0,0,0,0,0},{0,0,0,-511.6,-153795.69885244747,-1.1978643183124974e7,-4.072033459630186e8,-7.567600637131104e9,-8.695493057921883e10,-6.660723636188911e11,-3.571363466702473e12,-1.384223532826015e13,-3.9588090502665234e13,-8.450579365558694e13,-1.3509302529267044e14,-1.609267891315999e14,-1.4069221688269344e14,-8.761436750764872e13,-3.677597449159481e13,-9.323413211988104e12,-1.0782178544476038e12,0,0,0,0,0,0},{0,0,0,1,1795.6347973654888,348690.3862286264,2.2204228030820765e7,6.705854777632657e8,1.1522110280379248e10,1.2517973983561208e11,9.19332170318912e11,4.770007373158425e12,1.8007053868363406e13,5.039707192316374e13,1.056513773616503e14,1.663261076501606e14,1.955389474170697e14,1.6900738607205572e14,1.0419707990723603e14,4.335070020676101e13,1.0903912818365283e13,1.252123960003669e12,0,0,0,0,0},{0,0,0,0,-3.4995112414467253,-4046.283374356923,-642320.5204937553,-3.6354442541503884e7,-1.0156406403679376e9,-1.6508254693268639e10,-1.7202985544924103e11,-1.2230324761502656e12,-6.182633991853942e12,-2.2846441388588523e13,-6.281007640234248e13,-1.2969530267124028e14,-2.0154019556485406e14,-2.3427740497541834e14,-2.0049551613303962e14,-1.2253405597896867e14,-5.058454321247145e13,-1.2635069050946113e13,-1.4418397115193762e12,0,0,0,0}},{{0.5333333333333333,-66.73333333333333,8466.6,5.500782327216349e6,2.9307562486459124e8,6.580662628830447e9,8.25198689979895e10,6.557192881581038e11,3.544366348591472e12,1.3610364338969898e13,3.81402493752755e13,7.919889465707464e13,1.2257383139758511e14,1.4091199728388275e14,1.1864488533235611e14,7.106501175365262e13,2.8670108813717684e13,6.983640827474507e12,7.759600919416119e11,0,0,0,0,0,0,0,0},{0,0.13333333333333333,-101.93333333333334,-181056.65587236284,-1.787733779890622e7,-6.467215044849563e8,-1.2047942031497614e10,-1.3508357853771237e11,-9.958337708633071e11,-5.100215968856238e12,-1.8803864759217754e13,-5.1043402609364266e13,-1.0331528027101834e14,-1.565720156503844e14,-1.7685958939722884e14,-1.4670592314888475e14,-8.675260770965969e13,-3.461105326764565e13,-8.348755804038454e12,-9.196564052641327e11,0,0,0,0,0,0,0},{0,0,0.2,2439.19770489493,585468.939241731,3.91400351372385e7,1.1749495789312527e9,1.958269650268004e10,2.0382117002694974e11,1.4244548817255012e12,7.007773329261644e12,2.5037504149523434e13,6.627085088332564e13,1.3138571746780752e14,1.956929732604737e14,2.1782474594777912e14,1.7841953684261428e14,1.0435529770005283e14,4.123551524987994e13,9.862522139211904e12,1.0782178544476038e12,0,0,0,0,0,0},{0,0,0,-6.2695947309773805,-7913.383352642443,-1.2767836155293747e6,-7.073831350388925e7,-1.899554623143067e9,-2.939480935713848e10,-2.901204668878392e11,-1.9481763004141086e12,-9.290239953778574e12,-3.237296296631215e13,-8.39479743534346e13,-1.6360610601542472e14,-2.401716637111394e14,-2.6402193545879147e14,-2.1393204742321744e14,-1.2394533297842339e14,-4.856788337344296e13,-1.1529974798367117e13,-1.252123960003669e12,0,0,0,0,0},{0,0,0,-0.0009775171065493646,20.69089338637782,17264.0838134564,2.3011678842776404e6,1.1394226862290737e8,2.840139762731206e9,4.167633267110191e10,3.95266965553167e11,2.5731613895229917e12,1.1969456812409002e13,4.086863287421054e13,1.0419401598474152e14,2.0016347293020044e14,2.902331341320077e14,3.156571512430503e14,2.533843334077847e14,1.4559242461110694e14,5.6631732792034625e13,1.33559889067058e13,1.4418397115193762e12,0,0,0,0}}},\n {{{0,-0.26666666666666666,38,-2.0864644e6,-1.5269386717706367e8,-4.4364839170700865e9,-7.052545524685811e10,-7.039261202593761e11,-4.761725707062858e12,-2.288315999285902e13,-8.050868479032589e13,-2.1126861740115747e14,-4.1760113688084575e14,-6.230137174218235e14,-6.97244682853531e14,-5.760027708229431e14,-3.406464803623676e14,-1.3638576338223748e14,-3.3107630589508773e13,-3.678625621056531e12,0,0,0,0,0,0,0},{0,0,-0.06666666666666667,55257,7.524884401159955e6,3.534212218718977e8,8.358422454073611e9,1.1767720205354315e11,1.0834651446175271e12,6.917863829651936e12,3.183148547582819e13,1.0825791495805245e14,2.7646060697452588e14,5.3439199490061275e14,7.825097493435275e14,8.619879647594399e14,7.024798614322576e14,4.105674340973219e14,1.6268776314620662e14,3.913296565848068e13,4.312871417790415e12,0,0,0,0,0,0},{0,0,0,-577.6,-195891.5954785697,-1.720127764558216e7,-6.593956434546355e8,-1.3836051116645775e10,-1.7991428787352527e11,-1.5649809531653018e12,-9.574263945472568e12,-4.260947812998459e13,-1.4108556267746003e14,-3.5246266137808444e14,-6.68904000078248e14,-9.643324596899239e14,-1.0481525855129518e15,-8.443224624053235e14,-4.884650317232749e14,-1.9181971314970422e14,-4.577208698235634e13,-5.008495840014676e12,0,0,0,0,0},{0,0,0,1,2026.6651003957916,443769.2062382361,3.1848062618839644e7,1.084383682742406e9,2.1033538298344963e10,2.5857382719851614e11,2.1562791411962607e12,1.2764669581045951e13,5.532758658800373e13,1.7926934003434116e14,4.398155867559162e14,8.21954813552544e14,1.1694384435544125e15,1.2565957550652905e15,1.0021077247917248e15,5.746217280770576e14,2.2387644402300447e14,5.304452412379179e13,5.767358846077505e12,0,0,0,0},{0,0,0,0,-3.4995670995670998,-4566.139539696959,-817050.1240826164,-5.210286556396761e7,-1.6407138496930685e9,-3.010064457529331e10,-3.548915820326058e11,-2.864643885149056e12,-1.6520807008205463e13,-7.0090278456826984e13,-2.2307320285268588e14,-5.3903548690406256e14,-9.943274230202304e14,-1.3987464189591615e15,-1.488142833281783e15,-1.1763925899836822e15,-6.693106216369468e14,-2.589498048063432e14,-6.0969222087105055e13,-6.591267252660006e12,0,0,0}},{{0.5333333333333333,-75.53333333333333,10829.4,8.072048354127319e6,4.87250210500034e8,1.2400772896941032e10,1.7659692941512448e11,1.5987019273419814e12,9.889499268944688e12,4.3725671416071375e13,1.4222478427288353e14,3.464460612721393e14,6.378941277981012e14,8.892327870204825e14,9.324932431776439e14,7.236581421029889e14,4.029765524699275e14,1.5224983637304378e14,3.494694340003704e13,3.678625621056531e12,0,0,0,0,0,0,0},{0,0.13333333333333333,-115.13333333333334,-234357.4023199112,-2.6202969245825373e7,-1.0729925112854352e9,-2.264892860478733e10,-2.8833628269220435e11,-2.421334407948635e12,-1.4190732511616314e13,-6.023738501346369e13,-1.897848476488173e14,-4.506023042846216e14,-8.123862868785152e14,-1.1127081259761939e15,-1.1495259687556288e15,-8.80694584160074e14,-4.849782163048779e14,-1.8144558258461128e14,-4.128940136737588e13,-4.312871417790415e12,0,0,0,0,0,0},{0,0,0.2,2788.9909571394373,757954.1832518226,5.731896737696369e7,1.9467522753006718e9,3.6752178916813446e10,4.342367668300395e11,3.456417626472393e12,1.945586960892444e13,8.002395364327356e13,2.45820394128803e14,5.716362792738416e14,1.0128387071687611e15,1.366953901980593e15,1.394401321620245e15,1.0566084586443459e15,5.762621684739365e14,2.1376666367087962e14,4.827633490236368e13,5.008495840014676e12,0,0,0,0,0},{0,0,0,-6.330200791583441,-9055.326402164885,-1.652817817493035e6,-1.0353224612455417e8,-3.1443424489415655e9,-5.5099878956043625e10,-6.172115086692606e11,-4.719665182766741e12,-2.5747979102863504e13,-1.0327781515594061e14,-3.107840698734769e14,-7.103751521762541e14,-1.240428258290523e15,-1.6532690684504498e15,-1.6682200228770388e15,-1.2521020933688375e15,-6.771547917071688e14,-2.4931732630126084e14,-5.592820354683055e13,-5.767358846077505e12,0,0,0,0},{0,0,0,-0.0008658008658008658,20.90332181816109,19761.47677528686,2.9786440888161287e6,1.6669440060546213e8,4.697988868588864e9,7.804846936458011e10,8.399601182809939e11,6.225772187860445e12,3.3126459614313613e13,1.3018123394897244e14,3.8510657020790756e14,8.676089997567239e14,1.4962826923778152e15,1.9729018315606848e15,1.9720423433634065e15,1.4678534354359658e15,7.87971726203723e14,2.8819855324002194e14,6.4264855713435055e13,6.591267252660006e12,0,0,0}}},\n {{{0,-0.26666666666666666,42.666666666666664,-2.9489904e6,-2.4170614799515897e8,-7.873218384663625e9,-1.405806642582533e11,-1.580544280937379e12,-1.2090386727568768e13,-6.6042366119374336e13,-2.65868882310363e14,-8.051739775983438e14,-1.857133409027708e15,-3.2801533762918805e15,-4.4314102156757605e15,-4.540487334262183e15,-3.465694635513561e15,-1.9084456023722588e15,-7.161903536719025e14,-1.6388911387603578e14,-1.725148567116166e13,0,0,0,0,0,0},{0,0,-0.06666666666666667,69509,1.060304375629801e7,5.578470160261151e8,1.479270594762511e10,2.3394997790297177e11,2.4264918279035615e12,1.7521030242218191e13,9.164276368056673e13,3.5664655366664625e14,1.05113206044863e15,2.370956512005569e15,4.1103527541472025e15,5.465870295900822e15,5.524844013590857e15,4.167585692773008e15,2.2713467255841065e15,8.446251275105141e14,1.917140907650062e14,2.0033983360058703e13,0,0,0,0,0},{0,0,0,-647.6,-246094.15250627516,-2.4198988932992294e7,-1.038980191421611e9,-2.444203632713007e10,-3.570077983612116e11,-3.498184851505777e12,-2.4202280989027707e13,-1.2243539925589284e14,-4.638933812042697e14,-1.3374968892379465e15,-2.9619773218874905e15,-5.055557384458424e15,-6.63336672836086e15,-6.627413577564161e15,-4.948584988121854e15,-2.672802925395651e15,-9.85971732202283e14,-2.2219508817519653e14,-2.306943538431002e13,0,0,0,0},{0,0,0,1,2271.693671824363,557112.5844066336,4.4760097703188986e7,1.7065933499774168e9,3.710782171508295e10,5.123704928625934e11,4.812792440204033e12,3.2217907329529703e13,1.587313473404659e14,5.885027219728265e14,1.6662726075609255e15,3.6337254670711775e15,6.120647631772677e15,7.939169799895172e15,7.852589702803345e15,5.811463115882084e15,3.1140914617754305e15,1.1406361435129525e15,2.5541160604057522e14,2.6365069010640023e13,0,0,0},{0,0,0,0,-3.4996138996138995,-5117.489627447047,-1.0252931044630904e6,-7.317764631938808e7,-2.5799387735712266e9,-5.305164082877038e10,-7.024571823174719e11,-6.386343641756565e12,-4.1646702455182195e13,-2.0082495548407444e14,-7.313240134063729e14,-2.0393725447628995e15,-4.389582156680698e15,-7.310312322718411e15,-9.388355782488322e15,-9.204613694406318e15,-6.75889981067322e15,-3.596449851906305e15,-1.3090123157014138e15,-2.9144089798248025e14,-2.9927916174240027e13,0,0}},{{0.5333333333333333,-84.86666666666666,13652.733333333334,1.1580743990317933e7,7.862366731187782e8,2.251285321019336e10,3.6126970425140875e11,3.6950296972946763e12,2.591996982109244e13,1.3060390853963811e14,4.872588592243463e14,1.3728326184824732e15,2.955623641337104e15,4.887098724271143e15,6.197174104927707e15,5.97435514747484e15,4.3000613327664335e15,2.2374288971381245e15,7.949002570465775e14,1.725148567116166e14,1.725148567116166e13,0,0,0,0,0,0},{0,0.13333333333333333,-129.13333333333333,-298814.1125960173,-3.756041742575181e7,-1.7285393875937688e9,-4.103692427927973e10,-5.885977025139501e11,-5.58378211235412e12,-3.710691956026596e13,-1.7949438370340738e14,-6.486221072613646e14,-1.7811709048134368e15,-3.7547456752020125e15,-6.099911491230204e15,-7.620161622284745e15,-7.252241847091468e15,-5.161779213919494e15,-2.65959108326093e15,-9.367258010130061e14,-2.0173108244503553e14,-2.0033983360058703e13,0,0,0,0,0},{0,0,0.2,3164.105012550278,966660.7328705739,8.210917088666102e7,3.1326839561683073e9,6.649903112671311e10,8.850518794573038e11,7.957226405896327e12,5.07826266196542e13,2.3800231954847772e14,8.384811979980429e14,2.2550231205737835e15,4.671485049782065e15,7.477796091175499e15,9.223459380199674e15,8.681741711096794e15,6.119697195173343e15,3.1262899720312225e15,1.0927437571553231e15,2.3372980586735153e14,2.306943538431002e13,0,0,0,0},{0,0,0,-6.387343648726298,-10280.88273895997,-2.1078979265578426e6,-1.482407551004836e8,-5.055907877161912e9,-9.959690402930423e10,-1.2564964279090027e12,-1.0850994538243352e13,-6.710880700339022e13,-3.066885058028235e14,-1.0583451011894089e15,-2.7975704791687135e15,-5.711120851896802e15,-9.02764697095337e15,-1.10141153245736e16,-1.0268428227212878e16,-7.177155441784758e15,-3.6389915826190465e15,-1.2633984960937452e15,-2.6859414054589525e14,-2.6365069010640023e13,0,0,0},{0,0,0,-0.0007722007722007722,21.103579218418492,22442.61268540996,3.7985964582853154e6,2.3859794710035256e8,7.549734457672135e9,1.4096953641872162e11,1.7083678819651787e12,1.429842236994991e13,8.623782828471784e13,3.860843010721173e14,1.3096501921718585e15,3.4118527798952095e15,6.87871387556754e15,1.0756091873106256e16,1.2998921089798014e16,1.2017683521567574e16,8.337385441942756e15,4.199116583526632e15,1.4491212804099838e15,3.0640485606960025e14,2.9927916174240027e13,0,0}}},\n {{{0,-0.26666666666666666,47.6,-4.0895524e6,-3.731306038384463e8,-1.3541340916361624e10,-2.698066970601489e11,-3.3929623532272686e12,-2.912501505968892e13,-1.792856932147624e14,-8.178001345526671e14,-2.825665552462115e15,-7.50119392296909e15,-1.5421119083184214e16,-2.46069867650868e16,-3.036845308130471e16,-2.8690118845028184e16,-2.035084821245431e16,-1.0484659979090722e16,-3.7026001121730715e15,-8.013593344023481e14,-8.013593344023481e13,0,0,0,0,0},{0,0,-0.06666666666666667,86351.4,1.4665579721461162e7,8.590687659123018e8,2.5382910206863052e10,4.4799089906092065e11,5.197549704634442e12,4.2116936060807555e13,2.4826316584141612e14,1.0947767893988114e15,3.681377038739813e15,9.557508586062312e15,1.928610504650084e16,3.02919821648759e16,3.68806750791929e16,3.4434258261705336e16,2.417434564050942e16,1.2341328990945152e16,4.323002238921354e15,9.288483194209035e14,9.227774153724008e13,0,0,0,0},{0,0,0,-721.6,-305383.484221278,-3.3425150558028962e7,-1.5976051302013426e9,-4.187439493752403e10,-6.825325957092296e11,-7.480870721296626e12,-5.808146779339898e13,-3.311329496999199e14,-1.421626589092943e15,-4.676542004989115e15,-1.1920141073940436e16,-2.3681684177511636e16,-3.670117139829947e16,-4.416718389230369e16,-4.0819063755733816e16,-2.8399638601169932e16,-1.4382537224523932e16,-5.001926254562189e15,-1.067785294930921e15,-1.054602760425601e14,0,0,0},{0,0,0,1,2530.72069885139,690925.9210848194,6.1773305205390684e7,2.6215136024899797e9,6.350186022610584e10,9.783737218417522e11,1.0279134468481693e13,7.721651964503972e13,4.287219179136568e14,1.8010359258476095e15,5.818025681991426e15,1.460298629964141e16,2.8630185446713732e16,4.3862993135598696e16,5.225649481076826e16,4.7866759281312376e16,3.3039905722220736e16,1.6614027170527334e16,5.741105116040728e15,1.218493729951201e15,1.1971166469696011e14,0,0},{0,0,0,0,-3.4996534996535,-5700.334296291716,-1.2710928628651593e6,-1.0093436202872059e8,-3.9601706432110143e9,-9.070909301290082e10,-1.3400853937505337e12,-1.3626158227398803e13,-9.970831360069828e13,-5.418127541007572e14,-2.2355599883931558e15,-7.112384380705038e15,-1.7619359196305414e16,-3.415306825634278e16,-5.180484759888663e16,-6.1176142561382664e16,-5.559884636602166e16,-3.810791930105565e16,-1.904137287813753e16,-6.54222329112722e15,-1.3812884388110782e15,-1.350593140170832e14,0}},{{0.5333333333333333,-94.73333333333333,16992.6,1.6284696076892616e7,1.2354648054405298e9,3.953909107382076e10,7.10090176204812e11,8.145748277303172e12,6.428556882265668e13,3.6590982390426875e14,1.5502704689894388e15,4.993707604738265e15,1.2398036774129854e16,2.3903947362329856e16,3.5861500931598584e16,4.170569864198567e16,3.720611350142881e16,2.496972481358118e16,1.2193217903736838e16,4.0882542918542015e15,8.414273011224655e14,8.013593344023481e13,0,0,0,0,0},{0,0.13333333333333333,-143.93333333333334,-375927.24292232457,-5.278450853716055e7,-2.7125229474487467e9,-7.195565577844536e10,-1.1548552468425483e12,-1.2286437334588822e13,-9.185201223250092e13,-5.0188188887196794e14,-2.0594686450678228e15,-6.465664297334423e15,-1.5717197545820644e16,-2.9773055055612476e16,-4.400198164051586e16,-5.051762663082156e16,-4.456554705592129e16,-2.961652536463062e16,-1.4337322088783526e16,-4.770124322093573e15,-9.749871901895235e14,-9.227774153724008e13,0,0,0,0},{0,0,0.2,3564.768442556024,1.2164908134451648e6,1.1533096610258973e8,4.911578657437878e9,1.1646951484526044e11,1.7342546082017852e12,1.7484020896956271e13,1.2551336178335739e14,6.644159134672428e14,2.6578960250785765e15,8.171790366631361e15,1.9520413309070224e16,3.643312168795762e16,5.316310532259258e16,6.036333626184364e16,5.273684513072426e16,3.4747435047530596e16,1.6693177509884468e16,5.516045100269669e15,1.120515432952201e15,1.054602760425601e14,0,0,0},{0,0,0,-6.441397702780352,-11590.853392628731,-2.6527484863642906e6,-2.081436499095543e8,-7.921865093783669e9,-1.742928669332534e11,-2.459659492823631e12,-2.3815795421580676e13,-1.6566332438371656e14,-8.550505095885778e14,-3.35024333679381e15,-1.0123366574848608e16,-2.382922456508392e16,-4.391688037572645e16,-6.338437811869518e16,-7.128043872024897e16,-6.174789017813265e16,-4.037820760670786e16,-1.9267335122747188e16,-6.327906043885648e15,-1.2783495622996812e15,-1.1971166469696011e14,0,0},{0,0,0,-0.000693000693000693,21.292986207825482,25309.29515631317,4.780381324186655e6,3.3492374593636465e8,1.1823731636670485e10,2.4653622561126352e11,3.3416154029679727e12,3.135410116283323e13,2.126729757114602e14,1.0752440457778672e15,4.1409771925451395e15,1.233117595422076e16,2.8664288229529544e16,5.225580879389953e16,7.470388245200797e16,8.330526615716496e16,7.162566653980231e16,4.652411455487196e16,2.2066154752113164e16,7.207543889154556e15,1.4488180958196198e15,1.350593140170832e14,0}}},\n {{{0,-0.26666666666666666,52.8,-5575520,-5.632173785675783e8,-2.264573851170883e10,-5.005643706894967e11,-6.997344021760841e12,-6.694984221034684e13,-4.609967645533807e14,-2.3627840501606355e15,-9.225264284921132e15,-2.7870762591869724e16,-6.579211913432579e16,-1.219269835005012e17,-1.7736434748785085e17,-2.014372433713144e17,-1.7653028386935773e17,-1.1695051216654723e17,-5.660662707425071e16,-1.887747613881895e16,-3.8756651445640835e15,-3.691109661489603e14,0,0,0,0},{0,0,-0.06666666666666667,106080.2,1.9949649623509426e7,1.2939911180306041e9,4.2363534986906364e10,8.295293999689657e11,1.0698737964202242e13,9.66363247645834e13,6.372094391758614e14,3.1574388239306565e15,1.1998128373402768e16,3.545022868007551e16,8.214242163461622e16,1.498448307438975e17,2.1504119173799283e17,2.413696663998524e17,2.0935359957837e17,1.3743658725905952e17,6.598443928517343e16,2.1845367673730504e16,4.455696662798164e15,4.218411041702404e14,0,0,0},{0,0,0,-799.6,-374795.69873168645,-4.541501586740491e7,-2.4033232898026366e9,-6.979280795787791e10,-1.2620648339616711e12,-1.5377051478454482e13,-1.3307719247169702e14,-8.486965787241058e14,-4.0942474686362435e15,-1.521973082413072e16,-4.415040755395909e16,-1.0071975616913048e17,-1.8128971785509302e17,-2.5715892674943798e17,-2.8571552176641878e17,-2.4559351140219373e17,-1.5993872560572854e17,-7.623776610305851e16,-2.5076921618640444e16,-5.084895471889925e15,-4.7884665878784044e14,0,0},{0,0,0,1,2803.746339877031,847540.594948172,8.387088415905303e7,3.940171303117425e9,1.057365813099728e11,1.8072133228725144e12,2.1105818071761484e13,1.7671976487014494e14,1.0975457428896409e15,5.180820146125421e15,1.8912018709994548e16,5.402178465503179e16,1.2161716004687645e17,2.1639908949667334e17,3.038797903142797e17,3.3462662569227334e17,2.853611054467527e17,1.845190954017643e17,8.739229013859099e16,2.857951555540064e16,5.764577084638233e15,5.402372560683328e14,0},{0,0,0,0,-3.499687304565353,-6314.674103265669,-1.5587237516807944e6,-1.3697283658064875e8,-5.948433133232432e9,-1.5092828425611444e11,-2.4733417883407153e12,-2.7953736163984633e13,-2.2798507703929834e14,-1.3857335293027922e15,-6.424397479638844e15,-2.30959575834661e16,-6.511275177576189e16,-1.4492407203283318e17,-2.5530540726016147e17,-3.553604828117912e17,-3.882498975703751e17,-3.287640702824053e17,-2.1123805647598467e17,-9.947298157155096e16,-3.2360331425024412e16,-6.496023591260685e15,-6.06119848271788e14}},{{0.5333333333333333,-105.13333333333334,20908.2,2.2492357135156598e7,1.8958309719109235e9,6.741542072724315e10,1.3467332712719966e12,1.721588784468186e13,1.517969171625762e14,9.68623788198903e14,4.620809634242403e15,1.6852457171265348e16,4.7703107096260296e16,1.0578958618367114e17,1.8461804798071936e17,2.5344496869855994e17,2.7218267219337744e17,2.2596420895370938e17,1.4205763700894958e17,6.535328208213089e16,2.074610040494806e16,4.0602206276385635e15,3.691109661489603e14,0,0,0,0},{0,0.13333333333333333,-159.53333333333333,-467299.4470188559,-7.287456290234995e7,-4.157830371714083e9,-1.2252070190736252e11,-2.186990850552188e12,-2.5926110989630664e13,-2.1653318849256094e14,-1.326322841173958e15,-6.127978836743251e15,-2.1781741790169716e16,-6.036681088296472e16,-1.3152785185627565e17,-2.2611628841057744e17,-3.06435432704922e17,-3.2542265994529766e17,-2.6752084016889734e17,-1.667276585666764e17,-7.611122760127998e16,-2.3994120798097664e16,-4.666617214883284e15,-4.218411041702404e14,0,0,0},{0,0,0.2,3991.1974633728914,1.5126843075902709e6,1.591637552639756e8,7.523047958345665e9,1.981274589389424e11,3.28062880467928e12,3.684945335931074e13,2.9550727863338325e14,1.753482804920874e15,7.897512890513422e15,2.748953095986418e16,7.486280786775282e16,1.6070534554507542e17,2.7277027276789126e17,3.6558244328737126e17,3.8447574794727104e17,3.133601408355606e17,1.9380644168944502e17,8.786770088566074e16,2.7529585606062684e16,5.324318801283845e15,4.7884665878784044e14,0,0},{0,0,0,-6.4926797540624035,-12985.995991128793,-3.298836226795991e6,-2.871680700153716e8,-1.2127517294150885e10,-2.9628375638388446e11,-4.648967460183313e12,-5.014705791678989e13,-3.896342464153759e14,-2.254104416220173e15,-9.943117755509682e15,-3.401307144070906e16,-9.127203209515408e16,-1.934632666986177e17,-3.247778760884149e17,-4.311079790213169e17,-4.495396895431404e17,-3.636200897900059e17,-2.2336772996888845e17,-1.0065183695567805e17,-3.1360509612206944e16,-6.034695712672399e15,-5.402372560683328e14,0},{0,0,0,-0.0006253908692933083,21.472659314327856,28363.229946619325,5.944698143021086e6,4.619832444694353e8,1.809376056308954e10,4.1886637559539825e11,6.31178461726564e12,6.596977935869714e13,4.997768062476191e14,2.8319808910505985e15,1.2277848441468622e16,4.138797722399096e16,1.0967212084846331e17,2.299374395484744e17,3.823298988047106e17,5.032265327743345e17,5.208059242745585e17,4.1843448110868006e17,2.5548313610900355e17,1.1449196659647726e17,3.5494695749103796e16,6.799083515396579e15,6.06119848271788e14}}}\n};\n\nstatic const double ImEI[21][2][5][27] =\n {\n {{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.03333333333333333,-0.06666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.3,-0.26666666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.5,2.1333333333333333,1.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-1.8333333333333333,-6.133333333333334,-4.266666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-0.03333333333333333,4.2,12.8,8.533333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.06666666666666667,0.06666666666666667,0.06666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.1,0.43333333333333335,0.26666666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-1.2666666666666666,-2.933333333333333,-1.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.16666666666666666,4.1,8.266666666666667,4.266666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.06666666666666667,-0.4666666666666667,-9,-17.066666666666666,-8.533333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.06666666666666667,1.0666666666666667,1.0666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-2.6,-9.066666666666666,-6.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,11.6,27.733333333333334,17.066666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-3.533333333333333,-29.066666666666666,-59.733333333333334,-34.13333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.009523809523809525,8,56.68571428571428,107.27619047619048,58.51428571428571,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.13333333333333333,-0.26666666666666666,-1.6,-1.0666666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.2,5.933333333333334,12.266666666666667,6.4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-3.2,-22.266666666666666,-36.266666666666666,-17.066666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.06666666666666667,10.066666666666666,52.53333333333333,76.8,34.13333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.01904761904761905,-0.26666666666666666,-21.714285714285715,-99.35238095238095,-136.53333333333333,-58.51428571428571,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.1,12.6,38.4,25.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-8.9,-64.26666666666667,-123.73333333333333,-68.26666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1.5,35.2,170.13333333333333,273.06666666666666,136.53333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-5.271428571428571,-84,-341.9428571428571,-497.37142857142857,-234.05714285714285,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.0015873015873015873,11.88888888888889,159.4920634920635,589.6126984126984,806.1968253968254,364.0888888888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.2,-1.4,-27,-51.2,-25.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.3,24.233333333333334,113.33333333333333,157.86666666666667,68.26666666666667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-5.4,-81.86666666666666,-281.06666666666666,-341.3333333333333,-136.53333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.04285714285714286,17.1,183.65714285714284,546.7428571428571,614.4,234.05714285714285,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.0031746031746031746,-0.15555555555555556,-36.93015873015873,-337.26984126984127,-924.4444444444445,-988.2412698412699,-364.0888888888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.13333333333333333,59.733333333333334,332.8,546.1333333333333,273.06666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-21.2,-260.26666666666665,-921.6,-1228.8,-546.1333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,2,79.88571428571429,648.5333333333333,1896.8380952380953,2262.552380952381,936.2285714285714,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-7.015873015873016,-186.48888888888888,-1262.120634920635,-3319.0603174603175,-3692.9015873015874,-1456.3555555555556,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.0005772005772005772,15.806060606060607,349.617316017316,2133.1116883116883,5241.461471861472,5560.630303030303,2118.3353535353535,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.26666666666666666,-3.7333333333333334,-149.33333333333334,-554.6666666666666,-682.6666666666666,-273.06666666666666,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.4,64.13333333333334,541.8666666666667,1433.6,1501.8666666666666,546.1333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-7.771428571428571,-209.86666666666667,-1260.4952380952382,-2852.5714285714284,-2730.6666666666665,-936.2285714285714,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.031746031746031744,24.755555555555556,462.5015873015873,2365.765079365079,4892.444444444444,4421.079365079365,1456.3555555555556,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.0011544011544011544,-0.11313131313131314,-53.58268398268398,-839.8961038961039,-3909.818181818182,-7624.588744588745,-6619.79797979798,-2118.3353535353535,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.16666666666666666,191.66666666666666,1668.2666666666667,4753.066666666667,5461.333333333333,2184.5333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-41.5,-775.8095238095239,-4313.6,-9976.685714285713,-10142.47619047619,-3744.9142857142856,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,2.5,152.63492063492063,1872.888888888889,8569.092063492064,17664.812698412698,16644.06349206349,5825.422222222222,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-8.762626262626263,-352.2020202020202,-3580.7676767676767,-14673.19595959596,-28117.59191919192,-25155.23232323232,-8473.341414141414,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.0002775002775002775,19.731934731934732,655.7495837495837,5983.52047952048,22836.666267066266,41605.430303030305,35848.75213675214,11732.318881118881,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.3333333333333333,-7.666666666666667,-528.2,-3225.6,-7074.133333333333,-6553.6,-2184.5333333333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.5,135.11904761904762,1809.8666666666666,7751.314285714286,14345.752380952381,12014.933333333332,3744.9142857142856,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-10.26984126984127,-436.8888888888889,-4089.930158730159,-14826.869841269841,-24894.577777777777,-19556.774603174603,-5825.422222222222,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.025252525252525252,32.86363636363637,955.6767676767677,7544.371717171717,24809.761616161617,39106.45656565657,29391.90303030303,8473.341414141414,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.000555000555000555,-0.08935508935508936,-71.26440226440226,-1727.040959040959,-12325.773426573427,-38017.645288045285,-57329.99658119658,-41714.91157731158,-11732.318881118881,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.2,489.6,6106.971428571429,26214.4,50556.34285714286,44938.97142857143,14979.657142857142,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-71.8,-1901.8920634920635,-15197.155555555555,-53000.93968253968,-90398.06984126984,-74066.08253968254,-23301.68888888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,3,260.43463203463205,4506.052525252525,29564.416738816737,91759.85685425685,144822.26608946608,112271.77373737373,33893.36565656566,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-10.51048951048951,-596.8428904428904,-8522.413053613054,-49961.41351981352,-143888.94731934732,-215275.8303030303,-160341.69137529138,-46929.275524475524,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.0001554001554001554,23.661849261849262,1106.6579642579643,14141.066045066045,77056.03978243978,210652.15602175603,303084.9044289044,219003.28578088578,62572.367365967366,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.4,-13.6,-1447.5428571428572,-13136,-44470.857142857145,-70217.14285714286,-52428.8,-14979.657142857142,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.6,247.18412698412698,4825.422222222222,30428.749206349206,86497.11746031746,123062.04444444444,85716.92698412699,23301.68888888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-12.86926406926407,-795.3656565656565,-10742.07215007215,-56978.655122655124,-146297.53535353535,-194603.1468975469,-129218.45656565657,-33893.36565656566,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.02097902097902098,41.329137529137526,1733.909557109557,19631.14219114219,94030.1724941725,225862.41491841493,286647.4368298368,183806.32913752913,46929.275524475524,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.0003108003108003108,-0.07397047397047397,-89.75540015540015,-3126.114063714064,-31870.1898989899,-142693.88282828283,-326997.6515928516,-400854.2284382284,-250289.46946386946,-62572.367365967366,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.23333333333333334,1074.7333333333333,18153.244444444445,108464.35555555555,307655.1111111111,449285.68888888886,326223.64444444445,93206.75555555556,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-114.1,-4069.7131313131313,-44104.92121212121,-214282.8606060606,-537693.0909090909,-723676.3151515152,-495690.4727272727,-135573.46262626263,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,3.5,410.27630147630146,9526.587723387724,84649.39362859362,365700.5550893551,848556.257964258,1.0798214464646464e6,709153.4968142968,187717.1020979021,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-12.25897435897436,-936.1311577311577,-17890.690287490288,-141813.89526029525,-567884.4618492619,-1.2480050523698523e6,-1.524549659052059e6,-969871.6941724942,-250289.46946386946,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.0000959824489236254,27.593994241053064,1731.1486631016044,29547.359934183463,217402.40296174414,825519.0614561909,1.7431695357191828e6,2.0641979866721514e6,1.280893167256273e6,323904.019306184,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.4666666666666667,-21.933333333333334,-3355.6222222222223,-42348.08888888889,-203582.57777777777,-479869.15555555554,-594921.2444444444,-372827.02222222224,-93206.75555555556,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.7,410.7262626262626,11022.440404040404,96074.47272727273,386563.103030303,819299.296969697,946101.5272727272,563477.2040404041,135573.46262626263,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-15.552602952602953,-1319.1589743589743,-24329.85236985237,-177655.00916860916,-643821.182905983,-1.273099178865579e6,-1.3992012382284382e6,-803012.0478632479,-187717.1020979021,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.017948717948717947,50.09052059052059,2871.1639471639473,44222.36891996892,290731.34296814294,983393.9045843045,1.851893577000777e6,1.9625562306138305e6,1.0950164289044288e6,250289.46946386946,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.0001919648978472508,-0.06315645139174551,-108.91493212669683,-5170.4839160839165,-71524.53607568901,-438562.81431509665,-1.4125950964486494e6,-2.565467062004662e6,-2.6439125666803783e6,-1.4428451769093652e6,-323904.019306184,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.26666666666666666,2116.266666666667,46478.36998556999,367133.99595959595,1.4218853217893217e6,3.00440476998557e6,3.5321728923520925e6,2.169175402020202e6,542293.8505050505,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-170.4,-7878.639405039405,-111119.03776223776,-714162.356043956,-2.447790332334332e6,-4.76751157962038e6,-5.287365042424242e6,-3.1077609125097124e6,-750868.4083916084,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,4,609.1538683538683,18291.647552447554,211297.13166833165,1.2068968343656345e6,3.8238280972360973e6,7.039391328671329e6,7.482612264180264e6,4.254920980885781e6,1.0011578778554779e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-14.007843137254902,-1385.7954019836372,-34183.56217377394,-351855.81673751085,-1.8614895882261528e6,-5.582810520261438e6,-9.861435769605558e6,-1.0149606059509119e7,-5.624151607952831e6,-1.295616077224736e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.0000635071842502183,31.527506549178376,2558.0482279330577,56272.57883911754,537113.6969927904,2.6926125869276235e6,7.7549386769432835e6,1.3272122169070559e7,1.3318034401472213e7,7.228173904516948e6,1.6365676764944035e6,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.5333333333333333,-33.06666666666667,-6906.606637806638,-115649.93939393939,-746992.1893217893,-2.4357735803751806e6,-4.414610876767676e6,-4.515080496392496e6,-2.440322327272727e6,-542293.8505050505,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.8,636.47881007881,22496.094483294484,259039.60572760573,1.3972491252747253e6,4.090821281118881e6,6.898882843023643e6,6.700457672105672e6,3.483195116705517e6,750868.4083916084,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-18.30773670773671,-2043.3143745143745,-49402.28837828838,-475220.8388944389,-2.3042702023310023e6,-6.28517082917083e6,-1.0076758327894328e7,-9.422355652525252e6,-4.75549991981352e6,-1.0011578778554779e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.01568627450980392,59.10452945747063,4444.078065725124,89495.53131313132,773530.6577448695,3.495176651510581e6,9.067520102966314e6,1.400317438010878e7,1.2718753849005897e7,6.2719596465652e6,1.295616077224736e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.0001270143685004366,-0.05512423592918949,-128.64458637337896,-7998.43481348373,-144411.5393015653,-1.162342659386434e6,-4.9947002896331735e6,-1.2482808925253488e7,-1.8729284982381087e7,-1.6625264914387986e7,-8.04645774276415e6,-1.6365676764944035e6,0,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.3,3839.4,106318.05314685314,1.0702797874125873e6,5.392764956643357e6,1.5350685180419581e7,2.580816845874126e7,2.539460421818182e7,1.3515631351048952e7,3.0034736335664336e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-242.7,-14124.181152181152,-251299.74452214452,-2.0592303781551782e6,-9.185474911222111e6,-2.4106659233033635e7,-3.8236604926806524e7,-3.601039741911422e7,-1.852142074032634e7,-4.0046315114219114e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,4.5,864.0628077804548,32599.88898944193,474679.1184031655,3.455516380591957e6,1.4245058289412549e7,3.533020329192376e7,5.370181410996846e7,4.892054909771013e7,2.449892218752228e7,5.182464308898944e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-15.756965944272446,-1961.5696724328304,-60708.62697178982,-786988.0535711966,-5.303549502574206e6,-2.0688066335863516e7,-4.921807658793219e7,-7.241782910112797e7,-6.427015135233064e7,-3.1503927772517268e7,-6.546270705977614e6,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.00004422821760283061,35.461919504643966,3616.1956285200868,99702.79558212686,1.1976321362253844e6,7.643730469367165e6,2.8621924200018764e7,6.595342171821161e7,9.458539786739412e7,8.219612447821817e7,3.9589351412340805e7,8.104906588353236e6,0,0,0,0,0,0,0,0,0,0,0,0}},{{0.6,-47.4,-13003.506293706294,-278936.1678321678,-2.3265602237762236e6,-9.980674506293707e6,-2.4597585633566435e7,-3.625286534265734e7,-3.158926858741259e7,-1.5017368167832168e7,-3.0034736335664336e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0.9,935.4623043623044,42143.00606060606,619613.8922410923,4.308818503096903e6,1.6579424074592074e7,3.799234747545788e7,5.314447145174825e7,4.452023938088578e7,2.0523736496037297e7,4.0046315114219114e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-21.12561556090968,-3003.887892499657,-92251.03664962489,-1.130768793872794e6,-7.0588418527355e6,-2.5277949085518405e7,-5.502439582942548e7,-7.405439677762237e7,-6.019829813355272e7,-2.7090154341971755e7,-5.182464308898944e6,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.01393188854489164,68.33903526813744,6531.570529779818,166762.43296022862,1.8339761297278572e6,1.0656330035982594e7,3.6261947787464544e7,7.597502823061767e7,9.92596311986317e7,7.879468948121847e7,3.477706312550607e7,6.546270705977614e6,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.00008845643520566122,-0.04891640866873065,-148.871487026905,-11752.440015711842,-268684.86844919785,-2.74861261174986e6,-1.5174070609897017e7,-4.97030496228197e7,-1.0110656940201923e8,-1.2902029170934741e8,-1.0047113019907235e8,-4.364180470651743e7,-8.104906588353236e6,0,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.3333333333333333,6533.333333333333,222654.46091686093,2.778624556954157e6,1.7600566104118105e7,6.443886523574203e7,1.4451080095726496e8,2.0156645274156955e8,1.7053055852804974e8,8.009263022843823e7,1.6018526045687646e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-333,-23825.97413044472,-521880.007239819,-5.303014873879062e6,-2.974522501247772e7,-1.0042604004409708e8,-2.1250665797888386e8,-2.837202903655926e8,-2.319741694631016e8,-1.0600495177293295e8,-2.0729857235595778e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,5,1181.999610984131,54754.40911616763,980895.6130251585,8.852088141103067e6,4.5880486491885826e7,1.4637328059863028e8,2.967933223074854e8,3.832574936190464e8,3.0507729190651166e8,1.3638063970786697e8,2.6185082823910456e7,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-17.506265664160402,-2679.1916209005994,-101698.47428388605,-1.6209314727333898e6,-1.3536137961823797e7,-6.6368244028934255e7,-2.0306241420633388e8,-3.984997390155933e8,-5.012577425662849e8,-3.9049673738068247e8,-1.7144994706131846e8,-3.2419626353412945e7,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.000032049433045529426,39.39695786781532,4934.437997592661,166727.4017375813,2.460969788432378e6,1.945561056293358e7,9.154241300341979e7,2.712219032798776e8,5.1868580194167066e8,6.387408437835916e8,4.888559794904897e8,2.114323457831279e8,3.946737121285054e7,0,0,0,0,0,0,0,0,0,0,0}},{{0.6666666666666666,-65.33333333333333,-22842.255167055166,-610794.4205128205,-6.384583827195027e6,-3.4760849444599845e7,-1.1109825668873349e8,-2.199600400907537e8,-2.733161006545454e8,-2.075734000087024e8,-8.810189325128205e7,-1.6018526045687646e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,1318.9482608894373,73805.46920791626,1.3491923253530783e6,1.1743463056410257e7,5.730339427900727e7,1.7019760844996572e8,3.196860685490927e8,3.8177487075555557e8,2.810897971178939e8,1.1636988039073084e8,2.0729857235595778e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-23.999221968262216,-4237.817551557489,-161226.06704008067,-2.4533664806920635e6,-1.9149318022051428e7,-8.689604748579635e7,-2.450198244808148e8,-4.4258655082519025e8,-5.1267962114181876e8,-3.683579087309619e8,-1.4947318111982217e8,-2.6185082823910456e7,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.012531328320802004,77.76920671347916,9214.54894194213,291039.0946701733,3.9691610755076366e6,2.8811933867454045e7,1.2415265791155085e8,3.367590805724054e8,5.902267861563345e8,6.673985861532614e8,4.701430309700768e8,1.8765976023802492e8,3.2419626353412945e7,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.00006409886609105885,-0.04397182213846637,-169.53941844936594,-16578.624554339185,-468446.0812958478,-5.9377916416310035e6,-4.0923115567559e7,-1.696412196057358e8,-4.465302941617743e8,-7.640784094103152e8,-8.472253347457047e8,-5.871720202796443e8,-2.3116603138955316e8,-3.946737121285054e7,0,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.36666666666666664,10559.266666666666,434294.7652086476,6.574489355455003e6,5.10204267471091e7,2.3250794534097537e8,6.64917593632177e8,1.2277649331804926e9,1.4624266471674209e9,1.0850784646757164e9,4.560568591831071e8,8.291942894238311e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-443.3,-38255.76555264481,-1.0114779064221641e6,-1.2470381821703581e7,-8.571332767814559e7,-3.6026736682270384e8,-9.722698334254823e8,-1.7186034725420127e9,-1.9784568926620624e9,-1.4283144396604905e9,-5.869822733026594e8,-1.0474033129564182e8,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,5.5,1569.961476844449,87625.69572649573,1.8939060047826958e6,2.0732385792547733e7,1.3166046654165429e8,5.228893340210738e8,1.352134487330338e9,2.311593394202756e9,2.5906866318906407e9,1.8295657646295648e9,7.381699538930948e8,1.2967850541365178e8,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-19.255693581780537,-3554.4014008396293,-162426.07358635293,-3.1217844988459083e6,-3.16126055748029e7,-1.8987086397373933e8,-7.230764038384147e8,-1.809469262049569e9,-3.0129885415469217e9,-3.304452922123214e9,-2.2917775413786182e9,-9.105686358393375e8,-1.5786948485140216e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.00002397297591805601,43.33244851258581,6541.62812737135,265926.5903814425,4.731094982759278e6,4.5340842546994835e7,2.612763288477679e8,9.633487135585018e8,2.348932232111619e9,3.828700312931434e9,4.124825501869743e9,2.8177588722517457e9,1.105086393959815e9,1.894433818216826e8,0,0,0,0,0,0,0,0,0,0}},{{0.7333333333333333,-87.26666666666667,-37956.79708396179,-1.2378745500251383e6,-1.5839376732026143e7,-1.06514876608547e8,-4.268125048599296e8,-1.084457648638713e9,-1.7937872069180493e9,-1.927228914871795e9,-1.297559501340573e9,-4.9751657365429866e8,-8.291942894238311e7,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1.1,1798.4311052896192,122419.20256145643,2.723675026625387e6,2.8991573532491863e7,1.7462463657162815e8,6.49987059367659e8,1.5663069635696964e9,2.4893757054309864e9,2.5923743423070254e9,1.7021667641938875e9,6.393524389504802e8,1.0474033129564182e8,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-26.922953688897962,-5782.824037469239,-267059.29319830495,-4.940120546192026e6,-4.71164384933979e7,-2.6376188135589048e8,-9.316258847784076e8,-2.1581550271623797e9,-3.3260680887754226e9,-3.3792200077329974e9,-2.1743360218110523e9,-8.030092065999206e8,-1.2967850541365178e8,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.011387163561076604,87.37526544737474,12575.685027901907,481630.25459747476,7.978130346470807e6,7.071870426544951e7,3.7573583030587316e8,1.2761080113371363e9,2.867315117761134e9,4.312316120466565e9,4.2944103377974663e9,2.717461330888649e9,9.895033782650386e8,1.5786948485140216e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,-0.00004794595183611202,-0.039938977879481315,-190.60366239225843,-22626.351358782555,-774685.3323404123,-1.1919507515836926e7,-1.0026023448105781e8,-5.122220252548393e8,-1.6875254790953407e9,-3.7006690484617324e9,-5.456117441460743e9,-5.344261556173933e9,-3.3347814351400876e9,-1.1998080848706565e9,-1.894433818216826e8,0,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.4,16358.4,798958.1317110135,1.4416265779644504e7,1.3432181467691442e8,7.434303361587911e8,2.626393853597904e9,6.143042747321345e9,9.628736625974842e9,1.0003891869771244e10,6.609352950962489e9,2.5137679510954037e9,4.189613251825673e8,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-575.6,-58965.4028822227,-1.851578588510492e6,-2.721337278865888e7,-2.246109735140044e8,-1.1467505597679276e9,-3.823590344956376e9,-8.562024604039784e9,-1.2971313192672047e10,-1.3113370455110611e10,-8.471497747887982e9,-3.1621604781636624e9,-5.187140216546071e8,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,6,2034.9461170318891,134714.58794018233,3.456620690885645e6,4.5099821439376034e7,3.4389086889063436e8,1.6588888433384745e9,5.299781267706849e9,1.1477806342984741e10,1.6928250138062456e10,1.6740562578044119e10,1.0617264990476751e10,3.9016315541846533e9,6.314779394056087e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,-21.00521739130435,-4602.940974829003,-249320.1853983052,-5.686343886484196e6,-6.861345311881912e7,-4.947368541065237e8,-2.288195708861567e9,-7.073833639317552e9,-1.4920448268974035e10,-2.1533210358591484e10,-2.091140714317489e10,-1.3059753134332243e10,-4.736084545542065e9,-7.577735272867304e8,0,0,0,0,0,0,0,0,0,0},{0,0,0,0.00001840349666436623,47.2682769726248,8466.622898449223,407758.88048708765,8.605464337728756e6,9.82448816901423e7,6.795288568188525e8,3.042463166214668e9,9.163485366790909e9,1.8918381774570183e10,2.681818912368284e10,2.565065895730421e10,1.5811505960561546e10,5.669268611552575e9,8.981019582657546e8,0,0,0,0,0,0,0,0,0}},{{0.8,-113.6,-60265.06342202689,-2.354631489783282e6,-3.6188869743358806e7,-2.9423519790246165e8,-1.4410252993176384e9,-4.548903494657308e9,-9.579486167460339e9,-1.3604387251458832e10,-1.2876514478657967e10,-7.78768167803846e9,-2.7232486136866875e9,-4.189613251825673e8,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1.2,2385.605764445393,194164.23206487356,5.166394900690916e6,6.6000166193341576e7,4.804116328378407e8,2.1848240357089143e9,6.539431397703931e9,1.3229596648755936e10,1.8207931242597847e10,1.6804843678929035e10,9.955319107909575e9,3.4215174889909663e9,5.187140216546071e8,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-29.892234063778012,-7677.3315851704865,-423195.2594681369,-9.353395630081888e6,-1.069960803506276e8,-7.235025322877827e8,-3.121175266299493e9,-8.978155548848114e9,-1.7608717027453564e10,-2.363934658860129e10,-2.1376840213692146e10,-1.2449678653930527e10,-4.217370523887458e9,-6.314779394056087e8,0,0,0,0,0,0,0,0,0,0,0},{0,0,0.010434782608695653,97.14108009278826,16699.23576343072,762726.8199599064,1.5085840946795626e7,1.603035047267927e8,1.0283599406244267e9,4.2643450431212244e9,1.1894505365747297e10,2.2759909848626797e10,2.9943147410467827e10,2.6624309126235004e10,1.5285712870737015e10,5.114971309185431e9,7.577735272867304e8,0,0,0,0,0,0,0,0,0,0},{0,0,-0.00003680699332873246,-0.03658615136876006,-212.02777987521023,-30047.89230250005,-1.2262431435256745e6,-2.251696238611375e7,-2.2695429228591478e8,-1.3994804759815316e9,-5.627673799689461e9,-1.5316193575786037e10,-2.8723952643539726e10,-3.7161678742566864e10,-3.257762113150629e10,-1.8477746149163006e10,-6.118319590685452e9,-8.981019582657546e8,0,0,0,0,0,0,0,0,0}}},\n {{{0,-0.43333333333333335,24459.933333333334,1.39948310974227e6,2.9664356557875972e7,3.264766937613553e8,2.1527966210326242e9,9.174872352635342e9,2.63526819412877e10,5.20431450209414e10,7.080795804555496e10,6.521613086318431e10,3.8830607464800354e10,1.3486564563019785e10,2.0748560866184285e9,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,-731.9,-87814.82467992813,-3.230537622359549e6,-5.578284651915676e7,-5.439079051073674e8,-3.308797228275689e9,-1.3310466229841167e10,-3.660457080636495e10,-6.987539486462099e10,-9.251142702281056e10,-8.331826353464978e10,-4.868864058693869e10,-1.6643954260047829e10,-2.5259117576224346e9,0,0,0,0,0,0,0,0,0,0,0},{0,0,6.5,2583.9516267845465,200215.24405318496,6.016616118581815e6,9.221263263214113e7,8.305750837148908e8,4.77383576908197e9,1.840021088352963e10,4.8939353849036934e10,9.094760672013042e10,1.177844008258246e11,1.0414198859975996e11,5.991259714028463e10,2.0207294060979477e10,3.0310941091469216e9,0,0,0,0,0,0,0,0,0,0},{0,0,0,-22.754814814814814,-5840.553656708876,-370080.7888040544,-9.881938796070835e6,-1.4003615801375034e8,-1.1925823709998772e9,-6.57143044116013e9,-2.4508050681444206e10,-6.348184946356478e10,-1.1543549489334048e11,-1.468037932397025e11,-1.27811573462042e11,-7.256032344847891e10,-2.4192621500783764e10,-3.5924078330630183e9,0,0,0,0,0,0,0,0,0},{0,0,0,0.00001443722583152868,51.20436448442445,10738.282242670764,604748.6713855794,1.493782547301189e7,2.0024139920202476e8,1.6355739069693673e9,8.723538381973366e9,3.1694134443060642e10,8.035017116564796e10,1.435061488294865e11,1.797385196878227e11,1.544460759994406e11,8.668740434615086e10,2.861538653232956e10,4.211788493935952e9,0,0,0,0,0,0,0,0}},{{0.8666666666666667,-144.73333333333332,-92115.75281787357,-4.24804535780092e6,-7.720394235745513e7,-7.459561839697425e8,-4.37688462512671e9,-1.675264548351156e10,-4.352291071881835e10,-7.819993218306961e10,-9.728719442636674e10,-8.229722149813876e10,-4.518485423006929e10,-1.4523992606328999e10,-2.0748560866184285e9,0,0,0,0,0,0,0,0,0,0,0,0},{0,1.3,3092.3493598562786,296618.58790897264,9.301895812628992e6,1.4042234137451884e8,1.2141829505065637e9,6.6136711412013e9,2.3997256897036137e10,5.988243978747334e10,1.0425835625270293e11,1.2646490694806935e11,1.0477864663163727e11,5.65370092624084e10,1.7906910138859047e10,2.5259117576224346e9,0,0,0,0,0,0,0,0,0,0,0},{0,0,-32.90325356909285,-9960.403453242889,-646128.1687916917,-1.6817577993811376e7,-2.272190859950398e8,-1.8244572021268456e9,-9.424164410318285e9,-3.2855536243018745e10,-7.94693874291209e10,-1.3493911256397678e11,-1.6035193404744455e11,-1.3059358460620116e11,-6.944791402530933e10,-2.1722841115552937e10,-3.0310941091469216e9,0,0,0,0,0,0,0,0,0,0},{0,0,0.00962962962962963,107.05323934367682,21670.89761846037,1.1640149545323383e6,2.7098524121223144e7,3.3995615473259085e8,2.5888012200866394e9,1.2850503978831438e10,4.34323908124913e10,1.0247227787993118e11,1.704876950572971e11,1.9917787189184882e11,1.5989240688923416e11,8.398305773017148e10,2.5988825417315273e10,3.5924078330630183e9,0,0,0,0,0,0,0,0,0},{0,0,-0.00002887445166305736,-0.033754233994114057,-233.78149683578326,-38998.16031069183,-1.8707910950575937e6,-4.041802774693853e7,-4.8079742512005436e8,-3.518362643932259e9,-1.6932117246290905e10,-5.582666431497299e10,-1.2906973332811464e11,-2.1113776786988696e11,-2.4316208621413403e11,-1.9281924836901074e11,-1.0020538726970265e11,-3.0721280779297535e10,-4.211788493935952e9,0,0,0,0,0,0,0,0}}},\n {{{0,-0.4666666666666667,35489.066666666666,2.3512673864932396e6,5.783459782554564e7,7.417629589224231e8,5.737794526335927e9,2.8958539764775536e10,9.980418605461873e10,2.4087583664136777e11,4.1111360367982263e11,4.938686168666484e11,4.0842050111710443e11,2.2130873014861176e11,7.072552921342816e10,1.0103647030489738e10,0,0,0,0,0,0,0,0,0,0,0},{0,0,-914.2,-127000.05298477177,-5.410357632421346e6,-1.084187847239819e8,-1.2320553672292948e9,-8.793144231643013e9,-4.189268519105384e10,-1.3824796054280862e11,-3.2253689193271765e11,-5.3569991047103217e11,-6.2930263262471e11,-5.107830750947536e11,-2.7241958305957956e11,-8.588099975916278e10,-1.2124376436587687e10,0,0,0,0,0,0,0,0,0,0},{0,0,7,3223.9763957964633,289078.1147930231,1.0056934701494202e7,1.7885319900918955e8,1.8774039305941489e9,1.2659112178824976e10,5.778636226399293e10,1.8443310408086594e11,4.188943611564575e11,6.80570218646967e11,7.848818851678533e11,6.271698565745526e11,3.30024403976469e11,1.028326742214289e11,1.4369631332252073e10,0,0,0,0,0,0,0,0,0},{0,0,0,-24.504469987228607,-7282.983796526446,-533794.5211804865,-1.6496528391199792e7,-2.7121016480072916e8,-2.69139348470133e9,-1.7396960801336163e10,-7.683642125146432e10,-2.388197884303981e11,-5.3073846409068134e11,-8.467207746541761e11,-9.615174725410426e11,-7.581688663491782e11,-3.943770868588842e11,-1.2164636179544427e11,-1.6847153975743809e10,0,0,0,0,0,0,0,0},{0,0,0,0.000011535450912536563,55.140655048819674,13385.468430331828,871673.8196526119,2.4913415664470177e7,3.873820740702931e8,3.686591045638684e9,2.3063912016993534e10,9.92281083489501e10,3.018436477318775e11,6.588209340059844e11,1.0351031513181844e12,1.160082623098246e12,9.043453403023804e11,4.6572230892101843e11,1.4238562392402832e11,1.9564436875057327e10,0,0,0,0,0,0,0}},{{0.9333333333333333,-181.06666666666666,-136335.83965314535,-7.327933577454448e6,-1.5542659822206742e8,-1.7593665355350988e9,-1.2169475752962036e10,-5.541107203717101e10,-1.734553628583209e11,-3.823252362645737e11,-5.987312993848872e11,-6.626663891105165e11,-5.067610463730009e11,-2.5477706093710904e11,-7.577735272867303e10,-1.0103647030489738e10,0,0,0,0,0,0,0,0,0,0,0},{0,1.4,3930.705969543536,438914.5575660432,1.6021909399733834e7,2.821148285309416e8,2.8568306121554456e9,1.834034705520107e10,7.915174003764148e10,2.3795742789826575e11,5.0818633097929156e11,7.758814204731168e11,8.410097103451432e11,6.320268394606305e11,3.130867623573008e11,9.194318797745662e10,1.2124376436587687e10,0,0,0,0,0,0,0,0,0,0},{0,0,-35.952791592926204,-12671.688278689997,-955744.668589088,-2.8937820175670214e7,-4.558361881243446e8,-4.2852364908962717e9,-2.6082358434683636e10,-1.0813493285251514e11,-3.150596210807534e11,-6.56127990059077e11,-9.812778081103854e11,-1.045448978125867e12,-7.742480850836678e11,-3.7874643521238617e11,-1.1001748988755493e11,-1.4369631332252073e10,0,0,0,0,0,0,0,0,0},{0,0,0.008939974457215836,117.10041553054182,27577.685460833156,1.7212957303475374e6,4.6594371675881036e7,6.812809157261431e8,6.07243220002907e9,3.551011349027069e10,1.4269874524439893e11,4.054913031711275e11,8.273111760165848e11,1.2162825061370105e12,1.2771474457642676e12,9.341281376272004e11,4.520414263861544e11,1.3006993878331618e11,1.6847153975743809e10,0,0,0,0,0,0,0,0},{0,0,-0.000023070901825073126,-0.031330284678449304,-255.83925591764077,-49634.48688799174,-2.765829691982738e6,-6.945891513716699e7,-9.627476140344408e8,-8.244250951607839e9,-4.673088800021546e10,-1.8316187642444714e11,-5.0994384612902716e11,-1.022841420534557e12,-1.4821974712563923e12,-1.5372206353757112e12,-1.112343356234171e12,-5.3324678896895935e11,-1.5216784236155698e11,-1.9564436875057327e10,0,0,0,0,0,0,0}}},\n {{{0,-0.5,50175,3.8110518751832955e6,1.076462696229007e8,1.5907243629794188e9,1.4251013900556408e10,8.39147841034878e10,3.408264309321651e11,9.827003704330287e11,2.041566817044961e12,3.065320744754241e12,3.2952209252682485e12,2.4722631961132183e12,1.2290545345785562e12,3.6373129309763055e11,4.8497505746350746e10,0,0,0,0,0,0,0,0,0,0},{0,0,-1124.5,-179081.18687280125,-8.746490101655236e6,-2.0128246173478386e8,-2.6356156253879805e9,-2.1787106957386932e10,-1.2111135286756642e11,-4.7103679933522406e11,-1.312930805324278e12,-2.654465838545084e12,-3.897567876302638e12,-4.1124050502739814e12,-3.036874638157322e12,-1.489333703666579e12,-4.355794497588909e11,-5.747852532900829e10,0,0,0,0,0,0,0,0,0},{0,0,7.5,3962.019044757294,407072.920718967,1.6232431369128535e7,3.3147987895103717e8,4.0090734366763234e9,3.13099625273733e10,1.6676035684980087e11,6.272725393185522e11,1.702120269314377e12,3.366309892830835e12,4.852504880352651e12,5.040497006172991e12,3.6725169792886714e12,1.7801426017692478e12,5.153247098462812e11,6.7388615902975235e10,0,0,0,0,0,0,0,0},{0,0,0,-26.25417130144605,-8945.976556539295,-751050.1272782461,-2.6597813264939196e7,-5.0203783424558866e8,-5.739732894683955e9,-4.2968855344066925e10,-2.214204398894586e11,-8.110701607930319e11,-2.1534160242155322e12,-4.1819214920925874e12,-5.935635976892781e12,-6.084107901642862e12,-4.381942913426506e12,-2.1025895514418992e12,-6.03236803647601e11,-7.825774750022931e10,0,0,0,0,0,0,0},{0,0,0,9.363190675760198e-6,59.07710774785302,16437.045563842872,1.2257532331766458e6,4.013768184797409e7,7.164271778242302e8,7.854094148649289e9,5.6903267984881676e10,2.856175070922272e11,1.0238847552212717e12,2.6698130647352876e12,5.105908405067799e12,7.152238271875518e12,7.247671528966757e12,5.167805995087918e12,2.457745328571359e12,6.99576833714171e11,9.011498196996101e10,0,0,0,0,0,0}},{{1,-223,-196278.75036659127,-1.2163480027372148e7,-2.9773689168561506e8,-3.901236201224221e9,-3.1389389329419144e10,-1.6743088681163474e11,-6.199947751483894e11,-1.6382802519391409e12,-3.132920728260574e12,-4.3465612386153613e12,-4.3323760798965054e12,-3.0231374871104106e12,-1.4018268987999307e12,-3.8798004597080597e11,-4.8497505746350746e10,0,0,0,0,0,0,0,0,0,0},{0,1.5,4912.873745602497,631897.2803378738,2.656490166119503e7,5.395585963900452e8,6.322823026301706e9,4.720796893278593e10,2.3863565691698135e11,8.485721474191187e11,2.172352790028894e12,4.049809894234472e12,5.50235200650019e12,5.38931258216232e12,3.7052589549104136e12,1.6963462050468354e12,4.643187124233951e11,5.747852532900829e10,0,0,0,0,0,0,0,0,0},{0,0,-39.038089514588414,-15851.374766259272,-1.3756719102298168e6,-4.7943245278919205e7,-8.708307769571735e8,-9.47113944257027e9,-6.703028125916526e10,-3.254547834230943e11,-1.1214448357099817e12,-2.7992820802386875e12,-5.111448386239666e12,-6.825434396193574e12,-6.587638039199097e12,-4.472282579818021e12,-2.0251695912105806e12,-5.4901901779776886e11,-6.7388615902975235e10,0,0,0,0,0,0,0,0},{0,0,0.008342602892102336,127.27291285612064,34507.8303268765,2.4771144537147037e6,7.715353799846987e7,1.3004413372683635e9,1.3407053636109262e10,9.11467268081413e10,4.288886516771684e11,1.4411578341601123e12,3.5239100414919814e12,6.3247528225204e12,8.32319236966487e12,7.933155759027074e12,5.327467452291677e12,2.3895346256094067e12,6.423656773977156e11,7.825774750022931e10,0,0,0,0,0,0,0},{0,0,-0.000018726381351520396,-0.029231881289723337,-278.179190366686,-62116.434369362025,-3.979701958366857e6,-1.1496637205380797e8,-1.8365386839217353e9,-1.8187049742974773e10,-1.198292372617549e11,-5.49880612073813e11,-1.810124500260231e12,-4.3508491817515527e12,-7.696337232599344e12,-1.000270962164139e13,-9.431448443943848e12,-6.273956282611874e12,-2.7906371863090767e12,-7.446343246991516e11,-9.011498196996101e10,0,0,0,0,0,0}}},\n {{{0,-0.5333333333333333,69358.93333333333,5.9871611113645565e6,1.924439018268767e8,3.2448156139755497e9,3.330669577632881e10,2.2601945627174777e11,1.0662940872799772e12,3.608672101565586e12,8.923743251707213e12,1.6254636226822168e13,2.1772292854629945e13,2.117283786317375e13,1.453488209257297e13,6.674693753831088e12,1.8393128105282654e12,2.2991410131603317e11,0,0,0,0,0,0,0,0,0},{0,0,-1364.8,-247010.3969398599,-1.3710914253764993e7,-3.5907586422209996e8,-5.365095399350815e9,-5.081736342983615e10,-3.255698706535722e11,-1.470867065526843e12,-4.812414875990048e12,-1.1581712843876643e13,-2.0631072691303906e13,-2.7124046546863812e13,-2.5963317717947027e13,-1.758285432472868e13,-7.979604930158186e12,-2.1762558900431414e12,-2.6955446361190094e11,0,0,0,0,0,0,0,0},{0,0,8,4805.078378923909,560851.6328710681,2.5412128545875855e7,5.904978119526415e8,8.148894279740852e9,7.291974445465744e10,4.476097728118765e11,1.955793734114073e12,6.229626820644424e12,1.4665713663876832e13,2.56478138439078e13,3.319636806334255e13,3.135144116117232e13,2.098522418302309e13,9.426637994127908e12,2.547724446396354e12,3.1303099000091724e11,0,0,0,0,0,0,0},{0,0,0,-28.003910068426197,-10845.277747543556,-1.0340539156313771e6,-4.160211107138518e7,-8.934162310823445e8,-1.1653781015963501e10,-9.995712648139485e10,-5.936175304669795e11,-2.525790561524574e12,-7.87163260522547e12,-1.819637446847215e13,-3.1333388101515715e13,-4.001900002443862e13,-3.736019485586116e13,-2.4754756721440023e13,-1.1020607767604893e13,-2.954822829857143e12,-3.6045992787984406e11,0,0,0,0,0,0},{0,0,0,7.704568327482677e-6,63.01369198098898,19921.879208008424,1.6868344786841804e6,6.273964748932823e7,1.273959927266718e9,1.593305010069684e10,1.3225038205179854e11,7.649853076246484e11,3.185325437278451e12,9.749212126813445e12,2.219341094639236e13,3.771515415332075e13,4.76205488262829e13,4.401174323403532e13,2.890378760514151e13,1.2766176186368576e13,3.3986221771528154e12,4.1195420329125037e11,0,0,0,0,0}},{{1.0666666666666667,-270.93333333333334,-275873.1560624472,-1.9526615598641343e7,-5.463067917939428e8,-8.201340252473525e9,-7.590059501108307e10,-4.682825773172421e11,-2.0210768151063833e12,-6.288523857290183e12,-1.4356521317251836e13,-2.4229695665058094e13,-3.016739913942077e13,-2.7348748241932996e13,-1.7548912264512844e13,-7.551241265098464e12,-1.9542698611862817e12,-2.2991410131603317e11,0,0,0,0,0,0,0,0,0},{0,1.6,6051.193879719814,888285.5021747415,4.261058156357549e7,9.887753453648256e8,1.327213854827666e10,1.1396014858065186e11,6.662406988329823e11,2.7610060006323486e12,8.322298591918423e12,1.852086668895058e13,3.0609487847613902e13,3.744833590963831e13,3.344798330425991e13,2.11898795413883e13,9.017191413252525e12,2.311033121849092e12,2.6955446361190094e11,0,0,0,0,0,0,0,0},{0,0,-42.156757847819044,-19540.15290525303,-1.9336304731780519e6,-7.685712819702701e7,-1.594439517783882e9,-1.9858807743317722e10,-1.6160641862808392e11,-9.073615412262385e11,-3.643384657047884e12,-1.0707067507058748e13,-2.333725913033687e13,-3.790443110434288e13,-4.569379747197401e13,-4.029844176053195e13,-2.5250191501700312e13,-1.0641806906700912e13,-2.7042399413968125e12,-3.1303099000091724e11,0,0,0,0,0,0,0},{0,0,0.007820136852394917,137.56233770685833,42550.691954386595,3.4813989145593178e6,1.2363151215452614e8,2.3794672470258155e9,2.8087829807876396e10,2.19531539097911e11,1.1943955071569575e12,4.67634681344435e12,1.34610069080083e13,2.883661986591e13,4.615458622396285e13,5.4943021866992516e13,4.792868725397259e13,2.9744824442882992e13,1.2430432946055994e13,3.135052793797065e12,3.6045992787984406e11,0,0,0,0,0,0},{0,0,-0.000015409136654965353,-0.027397444972528398,-300.78237626127407,-76605.63532406824,-5.592621537223804e6,-1.841644469419035e8,-3.3586851599070764e9,-3.807661046434377e10,-2.883838211797314e11,-1.5299369967994255e12,-5.867608218199371e12,-1.6601437441364713e13,-3.5048526877146164e13,-5.5398397289151914e13,-6.523376765866994e13,-5.636627223479088e13,-3.46882547466682e13,-1.4388245861827873e13,-3.604599278798441e12,-4.1195420329125037e11,0,0,0,0,0}}},\n {{{0,-0.5666666666666667,94002.06666666667,9.151311935305258e6,3.320851910459127e8,6.33521032186008e9,7.382275924950447e10,5.713935821593523e11,3.094041226242078e12,1.2118112094805514e13,3.5055579190329652e13,7.577080308439667e13,1.2277365554920727e14,1.4836959871768953e14,1.316939805223555e14,8.331707351347927e13,3.554854783594292e13,9.164851762804633e12,1.0782178544476038e12,0,0,0,0,0,0,0,0},{0,0,-1637.1,-334159.9205226142,-2.0918744937359024e7,-6.185177808929194e8,-1.0456566421124214e10,-1.1244319702124878e11,-8.217073662582078e11,-4.261136422965968e12,-1.613507388311211e13,-4.54274671317859e13,-9.60274321618125e13,-1.5272694341908484e14,-1.8167523305110694e14,-1.5908213959048006e14,-9.946452714264984e13,-4.200158523126891e13,-1.0730006712809219e13,-1.252123960003669e12,0,0,0,0,0,0,0},{0,0,8.5,5760.15335336423,758011.4560133434,3.872804138514868e7,1.0159241892397866e9,1.586238004713476e10,1.611446504457956e11,1.1282876946995315e12,5.658785050777512e12,2.0860295618072766e13,5.745164785582471e13,1.1922862068135155e14,1.8668579152657497e14,2.1910636544081044e14,1.8963108518772156e14,1.1735697816416962e14,4.9110491347309305e13,1.2445353299430406e13,1.4418397115193762e12,0,0,0,0,0,0},{0,0,0,-29.753679653679654,-12996.633706471774,-1.396745220816542e6,-6.3353746792567894e7,-1.5357532178764133e9,-2.2663668846309917e10,-2.2067759802151013e11,-1.4948161492516946e12,-7.300452192754711e12,-2.633115093534921e13,-7.12076759521055e13,-1.4550478401170806e14,-2.2481450876051734e14,-2.608206421034274e14,-2.2345389682757944e14,-1.3705312915212823e14,-5.689609265768836e13,-1.4315408564370951e13,-1.6478168131650015e12,0,0,0,0,0},{0,0,0,6.416135448393513e-6,66.95038440199731,23868.836113681442,2.2775814000040796e6,9.549105192520149e7,2.1884705815436573e9,3.0963237347720776e10,2.91743710502673e11,1.9247605684553428e12,9.198896562512525e12,3.258322450023937e13,8.677160313048934e13,1.749810194392509e14,2.6727116291968612e14,3.0697010372751906e14,2.6065987367419022e14,1.5860983054210656e14,6.537859338635338e13,1.6344561363015016e13,1.8704947608900017e12,0,0,0,0}},{{1.1333333333333333,-325.26666666666665,-379672.3372771824,-3.044289317860951e7,-9.653190181565726e8,-1.645654568518213e10,-1.7350035488585364e11,-1.224974862145457e12,-6.087121650396307e12,-2.198279146517062e13,-5.886931627391679e13,-1.1819629684730314e14,-1.7844037358940066e14,-2.014677026353088e14,-1.674879308472654e14,-9.947402064977933e13,-3.992880786963631e13,-9.703960690028434e12,-1.0782178544476038e12,0,0,0,0,0,0,0,0},{0,1.7,7358.141045228405,1.2228343356326213e6,6.639078335866816e7,1.7454206071277142e9,2.6599212141387142e10,2.601475592017887e11,1.740271415261319e12,8.302886018750533e12,2.904578302199949e13,7.582019351190167e13,1.490656602100751e14,2.211250836544858e14,2.4596589754150544e14,2.018771799198576e14,1.185708301208829e14,4.713181534517283e13,1.1356068692811053e13,1.252123960003669e12,0,0,0,0,0,0,0},{0,0,-45.30670672845925,-23779.18039507422,-2.661791803943833e6,-1.1969660677337208e8,-2.812574307228695e9,-3.9764345032168434e10,-3.685338752285082e11,-2.367394455421027e12,-1.0942906507013615e13,-3.73202401876562e13,-9.540709750646728e13,-1.843299072761322e14,-2.694183018006003e14,-2.9589668840921594e14,-2.401899624280804e14,-1.3971389256713602e14,-5.5062823051114625e13,-1.3166273155190094e13,-1.4418397115193762e12,0,0,0,0,0,0},{0,0,0.00735930735930736,147.96135233748615,51796.68308694178,4.792105916700205e6,1.9247997245947763e8,4.195150944550882e9,5.6203346619271835e10,5.002227932450558e11,3.113437647355672e12,1.403128377992629e13,4.686853664732211e13,1.1775423667475845e14,2.241800875868455e14,3.235464771315656e14,3.5146497769033325e14,2.825652031993201e14,1.6297151920138706e14,6.37448312874054e13,1.5139316970953451e13,1.6478168131650015e12,0,0,0,0,0},{0,0,-0.000012832270896787026,-0.025780032231645135,-323.6322744648659,-93265.65360101484,-7.69771425123931e6,-2.866519541825688e8,-5.919173280043663e9,-7.614963399570706e10,-6.566791772809753e11,-3.985094039738327e12,-1.7590885222630846e13,-5.775012578906397e13,-1.429804558962491e14,-2.6879959044347166e14,-3.8372757967297875e14,-4.1286846760141056e14,-3.291372259583687e14,-1.8840988086355138e14,-7.320015630019402e13,-1.7279808743460016e13,-1.8704947608900017e12,0,0,0,0}}},\n {{{0,-0.6,125193.6,1.3652102441336416e7,5.554014600143847e8,1.1899676153316288e10,1.56165088407177e11,1.366540496131952e12,8.40861783023701e12,3.767209777990931e13,1.2572771066140053e14,3.1699683846911475e14,6.078847468910346e14,8.864741332485448e14,9.755540111565658e14,7.962880116350478e14,4.6711589143195694e14,1.8610613034936884e14,4.507646256013208e13,5.008495840014676e12,0,0,0,0,0,0,0},{0,0,-1943.4,-444350.0575188254,-3.1158621445006426e7,-1.0328718631043336e9,-1.9611734199856762e10,-2.3751855080120044e11,-1.9624234636460256e12,-1.1564556559203219e13,-5.009287309334422e13,-1.6271440389198622e14,-4.0123038305561994e14,-7.55244323016712e14,-1.0841303144905668e15,-1.1770068866194732e15,-9.494737901060278e14,-5.512548272291732e14,-2.1763242435124375e14,-5.228566111772896e13,-5.767358846077505e12,0,0,0,0,0,0},{0,0,9,6834.2430464192685,1.0071578139815058e6,5.7630935107687674e7,1.6947655536972034e9,2.971887868603432e10,3.400242318221734e11,2.691676008673227e12,1.5341040964447729e13,6.469277318651995e13,2.0556218578916944e14,4.9764013132721725e14,9.221943510366396e14,1.306119324762518e15,1.4015595146061295e15,1.1191029056445291e15,6.438857748567351e14,2.5216204623961334e14,6.0145313680522555e13,6.591267252660006e12,0,0,0,0,0},{0,0,0,-31.503474903474903,-15415.791203007979,-1.8549118704564322e6,-9.421570811376691e7,-2.5600544123712883e9,-4.242743900283097e10,-4.6525101895250854e11,-3.5629896100471016e12,-1.977415609780622e13,-8.158625551552306e13,-2.545518754366963e14,-6.067625924438578e14,-1.1095340952535998e15,-1.553365741029738e15,-1.650033451843795e15,-1.3057251452334125e15,-7.452766846539458e14,-2.8978473074627556e14,-6.867387907839006e13,-7.481979043560007e12,0,0,0,0},{0,0,0,5.4000054000054e-6,70.88716688716688,28306.784007021753,3.0236617450400395e6,1.4194238784983155e8,3.6460856395006375e9,5.792852759286986e10,6.146661187977393e11,4.584553043233062e12,2.4898101684512574e13,1.008823224117668e14,3.099519834507942e14,7.291125023795298e14,1.3180326124569462e15,1.826761435393357e15,1.9232229378190795e15,1.5098730462049652e15,8.556875473106161e14,3.305876811925353e14,7.788932029962469e13,8.4412071260677e12,0,0,0}},{{1.2,-386.4,-512904.0826728312,-4.6250508101108156e7,-1.6498943779538748e9,-3.1693433546401592e10,-3.774969633261728e11,-3.0222573837808267e12,-1.7114252146731506e13,-7.088860314805319e13,-2.195652433185797e14,-5.154436720771549e14,-9.229759888796809e14,-1.260086991646628e15,-1.3012905395960398e15,-9.989055197138905e14,-5.52186666361618e14,-2.0770526865943212e14,-4.758071048013942e13,-5.008495840014676e12,0,0,0,0,0,0,0},{0,1.8,8846.315037650835,1.652499890670798e6,1.0081815236953616e8,2.980852295984091e9,5.117658296341241e10,5.653923499515992e11,4.2884376326036885e12,2.3314343858552824e13,9.354089348013502e13,2.8240048108547756e14,6.491502225984054e14,1.142121460503862e15,1.5361570189811522e15,1.5661512339351905e15,1.188884318540835e15,6.508081678370406e14,2.4269387512646872e14,5.516934054076771e13,5.767358846077505e12,0,0,0,0,0,0},{0,0,-48.486092838536685,-28610.053294245357,-3.5971398670573817e6,-1.8170450901651797e8,-4.800628986511418e9,-7.645048609922267e10,-8.002747183060198e11,-5.828318542596038e12,-3.0696178946402035e13,-1.2005854798795881e14,-3.549510824718861e14,-8.017723301469554e14,-1.3898631564766085e15,-1.8456808435841622e15,-1.8609896441157935e15,-1.3990467910248515e15,-7.593074829663808e14,-2.8099884047000084e14,-6.3440947306852555e13,-6.591267252660006e12,0,0,0,0,0},{0,0,0.0069498069498069494,158.46348709704054,62337.20331735644,6.475875533245151e6,2.921192897693864e8,7.157442458806223e9,1.0799555655084192e11,1.0855125833750288e12,7.659196496678287e12,3.932659690536154e13,1.5063960727715928e14,4.376723566398628e14,9.741274125347245e14,1.6673482941700252e15,2.189911586818609e15,2.1868594523613995e15,1.630061509290193e15,8.779941332352192e14,3.227187992148031e14,7.241486860017006e13,7.481979043560007e12,0,0,0,0},{0,0,-0.0000108000108000108,-0.024343224343224345,-346.71430558980086,-112261.86290506809,-1.0402072220276337e7,-4.349568507848248e8,-1.009552791463289e10,-1.4625792737830328e11,-1.4242626335574956e12,-9.797394622514166e12,-4.9269031116791766e13,-1.8547288277928522e14,-5.3100005187471706e14,-1.167000294197266e15,-1.9756813909489115e15,-2.5700586158413735e15,-2.544779679266689e15,-1.882576246583223e15,-1.007168503518773e15,-3.6794961500620994e14,-8.210992386265853e13,-8.4412071260677e12,0,0,0}}},\n {{{0,-0.6333333333333333,164158.73333333334,1.9930293177442875e7,9.033522147628825e8,2.159562943718983e10,3.1695435436427655e11,3.1117616133093535e12,2.1572888288816043e13,1.09484309701826e14,4.1677133450584825e14,1.2090804894217778e15,2.6979173704553415e15,4.645555959846248e15,6.155935299753043e15,6.217286496234509e15,4.696578395452082e15,2.568066717852626e15,9.596044046707916e14,2.191596361509452e14,2.306943538431002e13,0,0,0,0,0,0},{0,0,-2285.7,-581877.1667007137,-4.542712920857985e7,-1.6777496857464986e9,-3.554596419337812e10,-4.8146941932528937e11,-4.463236488322537e12,-2.963468073013338e13,-1.4541483616136725e14,-5.387724333982664e14,-1.528682077106105e15,-3.3483222279232085e15,-5.675362800076585e15,-7.419408932698538e15,-7.405721111493924e15,-5.536919691805194e15,-3.000077941416619e15,-1.1119673832339076e15,-2.5211597241424522e14,-2.6365069010640023e13,0,0,0,0,0},{0,0,9.5,8034.346639088207,1.3179673367617e6,8.39534763120524e7,2.750469750609688e9,5.381559497441904e10,6.886135692098751e11,6.116068398456957e12,3.927525531830635e13,1.87621875146192e14,6.800177457846064e14,1.8942591437198682e15,4.0847532803221355e15,6.831268665098625e15,8.82695090814349e15,8.720982640500069e15,6.461561639299811e15,3.4729854777955795e15,1.277987710634628e15,2.8787805081888025e14,2.9927916174240027e13,0,0,0,0},{0,0,0,-33.253291753291755,-18118.497367092852,-2.4263056561244098e6,-1.371723164151261e8,-4.1521251582654886e9,-7.677555171735455e10,-9.415385502549863e11,-8.089827546033466e12,-5.058607217578998e13,-2.364337668337472e14,-8.414253645683544e14,-2.307828334679184e15,-4.910703691264801e15,-8.118041289783834e15,-1.0383658748433438e16,-1.0167288912591014e16,-7.473149461470064e15,-3.9880042421706445e15,-1.4580506661137562e15,-3.2652123928561875e14,-3.37648285042708e13,0,0,0},{0,0,0,4.587809465858246e-6,74.82402515085442,33264.59142595566,3.9539347999028377e6,2.0657696267892247e8,5.910713251530081e9,1.0476957462492262e11,1.2431924580143315e12,1.0402955953492928e13,6.365382991017692e13,2.9216326172935256e14,1.0238733031895974e15,2.7713247980029775e15,5.829535183879195e15,9.540280533475378e15,1.209446128636118e16,1.1748726073620186e16,8.574250203286003e15,4.5463150567317e15,1.6525312353663298e15,3.6811898393680606e14,3.788249051698675e13,0,0}},{{1.2666666666666666,-454.73333333333335,-681521.0882190833,-6.866812258629e7,-2.7377423472293215e9,-5.885373059155742e10,-7.861999036201415e11,-7.081109305222594e12,-4.529513317348146e13,-2.1305179026514706e14,-7.544247442837826e14,-2.042292971648917e15,-4.264112494563583e15,-6.887192122673396e15,-8.579721224269423e15,-8.162941954518764e15,-5.819981799016939e15,-3.0089392479769985e15,-1.064858703611706e15,-2.3069435384310022e14,-2.306943538431002e13,0,0,0,0,0,0},{0,1.9,10528.43340142741,2.1966056588859563e6,1.496340808486337e8,4.94310202090654e9,9.495646973148334e10,1.1764390850983005e12,1.0037702723170137e13,6.163907586873927e13,2.808207197238787e14,9.692149606108888e14,2.56903911487428e15,5.27020715794106e15,8.385800766327233e15,1.0313148662287174e16,9.703156383423962e15,6.850671684428315e15,3.5112616134256495e15,1.2330819190015352e15,2.6529850691956525e14,2.6365069010640023e13,0,0,0,0,0},{0,0,-51.693278176413344,-34074.78014180465,-4.781836743440356e6,-2.6961591339264446e8,-7.957160824871687e9,-1.417663970015018e11,-1.6639977875868992e12,-1.3631292963271166e13,-8.108623737250361e13,-3.6010324340970756e14,-1.2170534965459422e15,-3.1699041795772295e15,-6.406817661291515e15,-1.006485817543921e16,-1.2241435673077942e16,-1.1405817498928164e16,-7.983798180042419e15,-4.0608079407256885e15,-1.4163152517613982e15,-3.0284200890600025e14,-2.9927916174240027e13,0,0,0,0},{0,0,0.006583506583506584,169.06299475396784,74264.58077013028,8.60869260141037e6,4.3336689596040046e8,1.1859561376200863e10,2.0016987814094357e11,2.255834083018215e12,1.7902005880230887e13,1.0381148852085344e14,4.5148680237416356e14,1.499482007722108e15,3.8480749449814715e15,7.679151287997549e15,1.1931083759742532e16,1.4371388164888972e16,1.3276270216445754e16,9.222548421515924e15,4.658972295533745e15,1.614980380412015e15,3.434036535377542e14,3.37648285042708e13,0,0,0},{0,0,-9.175618931716493e-6,-0.023058330375403547,-370.01552049520996,-133761.33977549043,-1.3827819745792182e7,-6.451738118427956e8,-1.6723378636699493e10,-2.709901673195793e11,-2.9584696444771226e12,-2.288771647820421e13,-1.2998082039545089e14,-5.555315701855969e14,-1.8179762075703875e15,-4.606611728235598e15,-9.092222501474912e15,-1.3990963605707124e16,-1.6709589472590812e16,-1.5319694204447672e16,-1.0570016078374418e16,-5.307109848412682e15,-1.8294877603627978e15,-3.8706022919529944e14,-3.788249051698675e13,0,0}}},\n {{{0,-0.6666666666666666,212266.66666666666,2.853599258035219e7,1.4330114863456995e9,3.800258146404937e10,6.199274770948887e11,6.782860407787912e12,5.259010470068523e13,2.998352445442762e14,1.289474302995765e15,4.256253873967506e15,1.0902678302444068e16,2.1797926698136784e16,3.403776778865586e16,4.131592071162812e16,3.85489253454479e16,2.709770607257666e16,1.3874444112447926e16,4.881180309397506e15,1.054602760425601e15,1.054602760425601e14,0,0,0,0,0},{0,0,-2666,-751541.6624389548,-6.496750631920008e7,-2.6584414136368732e9,-6.248207318933823e10,-9.406826677470544e11,-9.718503789838549e12,-7.216907849489138e13,-3.978378205026157e14,-1.6653179634893145e15,-5.376204754295016e15,-1.3518436707709178e16,-2.6605608406951144e16,-4.0986885639172104e16,-4.9169772065455784e16,-4.540651511838149e16,-3.162877001568124e16,-1.6063591016532404e16,-5.610415428520925e15,-1.204242341296801e15,-1.1971166469696011e14,0,0,0,0},{0,0,10,9367.463398770313,1.701250849010266e6,1.1998124014091475e8,4.354863213182676e9,9.45208118958657e10,1.344305113466995e12,1.3306614989260633e13,9.556877985629884e13,5.12895265809024e14,2.1002083731150322e15,6.656579614385937e15,1.6478625548324368e16,3.1999232770493936e16,4.8724507460816184e16,5.785749736908936e16,5.294839315410694e16,3.65864067552318e16,1.844784707627131e16,6.401367498840126e15,1.365940789490955e15,1.350593140170832e14,0,0,0},{0,0,0,-35.00312695434646,-21120.499631781146,-3.13075780749621e6,-1.9594466391609663e8,-6.57050375487538e9,-1.3476651743799847e11,-1.8369043800571548e12,-1.7589435314077154e13,-1.2300981206774544e14,-6.45896597792679e14,-2.5969519006174225e15,-8.1043872896729e15,-1.979717247928791e16,-3.800085757405471e16,-5.727840617892459e16,-6.7406697825393336e16,-6.119592653276693e16,-4.198322456673902e16,-2.1032687680075924e16,-7.255685440992997e15,-1.5400055927557658e15,-1.51529962067947e14,0,0},{0,0,0,3.930803703917714e-6,78.76094777966587,38771.1275913068,5.100639029001081e6,2.949841095687273e8,9.349478097378347e9,1.8381938202018082e11,2.42419630975418e12,2.2606778024802125e13,1.547013295439825e14,7.976887641336864e14,3.1582328358075825e15,9.726354425919532e15,2.3487483127377148e16,4.463176708335417e16,6.667543951844797e16,7.784411667165024e16,7.0169853688251656e16,4.78314795584771e16,2.3823442630743476e16,8.174976337050191e15,1.7267367770533495e15,1.6914972509910362e14,0}},{{1.3333333333333333,-530.6666666666666,-892251.827371045,-9.987215970701566e7,-4.424126639899304e9,-1.0578643572033942e11,-1.5747287228400437e12,-1.5845717567057562e13,-1.1362682509291195e14,-6.01771280857198e14,-2.4125671241445005e15,-7.446002113664234e15,-1.7881405459744606e16,-3.35951258854644e16,-4.9401354974251736e16,-5.657957303847233e16,-4.9900402465368104e16,-3.3212859965007824e16,-1.612718315044587e16,-5.388707887852326e15,-1.107332898446881e15,-1.054602760425601e14,0,0,0,0,0},{0,2,12417.32487790964,2.877010547668333e6,2.1757735630149266e8,7.983815399399566e9,1.7056499979904105e11,2.354551408251009e12,2.244295896408418e13,1.5448897973201038e14,7.924454954576368e14,3.09644241377513e15,9.357141993333924e15,2.2077909573687176e16,4.086271515883938e16,5.931957879239599e16,6.7183171140618856e16,5.867380519673225e16,3.8715022071894504e16,1.8654226260365056e16,6.190090662038646e15,1.2640981736452812e15,1.1971166469696011e14,0,0,0,0},{0,0,-54.92679754062404,-40215.75896837982,-6.263591942903851e6,-3.919620881744125e8,-1.2847160247073557e10,-2.5452055340858438e11,-3.3284003694315527e12,-3.045760371601915e13,-2.0308431931952872e14,-1.0153938929148701e15,-3.8851031201166525e15,-1.1535964059895936e16,-2.6816071946032308e16,-4.9000640659284456e16,-7.0346216741010216e16,-7.889814086638738e16,-6.831336974290147e16,-4.473081072704507e16,-2.1405078738350924e16,-7.0590142722074e15,-1.4334704464994968e15,-1.350593140170832e14,0,0,0},{0,0,0.006253908692933083,179.75473573239677,87672.02030488498,1.127655502867755e7,6.299257811345832e8,1.9142375540966686e10,3.592377142778432e11,4.510116251939719e12,3.997869384169198e13,2.598472460491622e14,1.2722572790529712e15,4.783417939546741e15,1.3993927307709768e16,3.2117401194767464e16,5.8041145938566104e16,8.251977130024504e16,9.176083681396456e16,7.884587952758733e16,5.127529010535035e16,2.4385985285874588e16,7.99727636948314e15,1.6157705737897392e15,1.51529962067947e14,0,0},{0,0,-7.861607407835427e-6,-0.021902438238229502,-393.52434085950074,-157932.76854200763,-1.8113190266049244e7,-9.376913624338514e8,-2.698711715217962e10,-4.86188476940676e11,-5.912673590075985e12,-5.109028982891983e13,-3.251901708214681e14,-1.5646005583864498e15,-5.796048104691107e15,-1.6742037879323554e16,-3.800261305735843e16,-6.801536029880263e16,-9.587749223709138e16,-1.0580649570083427e17,-9.029733700258528e16,-5.8363106600548536e16,-2.7603025440299108e16,-9.006629152120784e15,-1.8113116396029015e15,-1.6914972509910362e14,0}}}\n };\n\nstatic inline int max(int a, int b)\n{\n return a > b ? a : b;\n}\n\n/* Compute the singular field at the point x for the particle at xp */\nvoid effsource_hS(struct coordinate * x, double * hS)\n{\n double A[10], s2, s2_35;\n\n double r = x->r;\n double theta = x->theta;\n double phi = x->phi;\n double rp = xp.r;\n double thetap = xp.theta;\n double phip = xp.phi;\n\n double dr = r - rp;\n double dth = theta - thetap;\n double dphi = phi - phip;\n\n double dr2 = dr*dr;\n\n double dth2 = dth*dth;\n \n double Q = sin(0.5*dphi);\n double Q2 = Q*Q;\n double Q4 = Q2*Q2;\n double Q6 = Q4*Q2;\n double Q8 = Q4*Q4;\n\n double R = sin(dphi);\n\n A[0] = dth2*(dth2*(Q2*(A00420 + A00440*Q2) + dth2*(A00600 + A00800*dth2 + A00620*Q2)) + (A00240 + A00260*Q2)*Q4) + (A00060 + A00080*Q2)*Q6 + dr*(dth2*(dth2*(Q2*(A01420 + A01440*Q2) + dth2*(A01600 + A01800*dth2 + A01620*Q2)) + (A01240 + A01260*Q2)*Q4) + dr*(dth2*(Q2*(A02220 + A02240*Q2) + dth2*(A02400 + A02600*dth2 + A02420*Q2)) + (A02040 + A02060*Q2)*Q4 + dr*(dth2*(Q2*(A03220 + A03240*Q2) + dth2*(A03400 + A03600*dth2 + A03420*Q2)) + dr*(Q2*(A04020 + A04040*Q2) + dth2*(A04200 + A04400*dth2 + A04220*Q2) + dr*(Q2*(A05020 + A05040*Q2) + dth2*(A05200 + A05400*dth2 + A05220*Q2) + dr*(A06000 + A06200*dth2 + A06020*Q2 + dr*(A07000 + dr*(A08000 + A09000*dr) + A07200*dth2 + A07020*Q2)))) + (A03040 + A03060*Q2)*Q4)) + (A01060 + A01080*Q2)*Q6);\n A[1] = Q6*(A10061*R + A10081*Q2*R) + dth2*(Q4*(A10241*R + A10261*Q2*R) + dth2*(Q2*(A10421*R + A10441*Q2*R) + dth2*(A10601*R + A10801*dth2*R + A10621*Q2*R))) + dr*(A11061*Q6*R + dth2*(A11241*Q4*R + dth2*(A11601*dth2*R + A11421*Q2*R)) + dr*(Q4*(A12041*R + A12061*Q2*R) + dth2*(Q2*(A12221*R + A12241*Q2*R) + dth2*(A12401*R + A12601*dth2*R + A12421*Q2*R)) + dr*(A13041*Q4*R + dth2*(A13401*dth2*R + A13221*Q2*R) + dr*(Q2*(A14021*R + A14041*Q2*R) + dth2*(A14201*R + A14401*dth2*R + A14221*Q2*R) + dr*(A15201*dth2*R + A15021*Q2*R + dr*(A16001*R + A16201*dth2*R + A16021*Q2*R + dr*(A17001*R + A18001*dr*R)))))));\n A[2] = dth*(A20161*Q6*R + dth2*(A20341*Q4*R + dth2*(A20701*dth2*R + A20521*Q2*R))) + dr*(dth*(A21161*Q6*R + dth2*(A21341*Q4*R + dth2*(A21701*dth2*R + A21521*Q2*R))) + dr*(dth*(A22141*Q4*R + dth2*(A22501*dth2*R + A22321*Q2*R)) + dr*(dth*(A23141*Q4*R + dth2*(A23501*dth2*R + A23321*Q2*R)) + dr*(dth*(A24301*dth2*R + A24121*Q2*R) + dr*(dr*(A26101*dth*R + A27101*dr*dth*R) + dth*(A25301*dth2*R + A25121*Q2*R))))));\n A[3] = dth2*(dth2*(Q2*(A30420 + A30440*Q2) + dth2*(A30600 + A30800*dth2 + A30620*Q2)) + (A30240 + A30260*Q2)*Q4) + (A30060 + A30080*Q2)*Q6 + dr*(dth2*(dth2*(Q2*(A31420 + A31440*Q2) + dth2*(A31600 + A31800*dth2 + A31620*Q2)) + (A31240 + A31260*Q2)*Q4) + dr*(dth2*(Q2*(A32220 + A32240*Q2) + dth2*(A32400 + A32600*dth2 + A32420*Q2)) + (A32040 + A32060*Q2)*Q4 + dr*(dth2*(Q2*(A33220 + A33240*Q2) + dth2*(A33400 + A33600*dth2 + A33420*Q2)) + dr*(Q2*(A34020 + A34040*Q2) + dth2*(A34200 + A34400*dth2 + A34220*Q2) + dr*(Q2*(A35020 + A35040*Q2) + dth2*(A35200 + A35400*dth2 + A35220*Q2) + dr*(A36000 + A36200*dth2 + A36020*Q2 + dr*(A37000 + dr*(A38000 + A39000*dr) + A37200*dth2 + A37020*Q2)))) + (A33040 + A33060*Q2)*Q4)) + (A31060 + A31080*Q2)*Q6);\n A[4] = dth2*(dth2*(dth2*(A40800*dth2 + A40620*Q2) + A40440*Q4) + A40260*Q6) + A40080*Q8 + dr*(dth2*(dth2*(dth2*(A41800*dth2 + A41620*Q2) + A41440*Q4) + A41260*Q6) + dr*(dth2*(dth2*(A42600*dth2 + A42420*Q2) + A42240*Q4) + A42060*Q6 + dr*(dth2*(dth2*(A43600*dth2 + A43420*Q2) + A43240*Q4) + dr*(dth2*(A44400*dth2 + A44220*Q2) + A44040*Q4 + dr*(dth2*(A45400*dth2 + A45220*Q2) + dr*(A46200*dth2 + A46020*Q2 + dr*(dr*(A48000 + A49000*dr) + A47200*dth2 + A47020*Q2)) + A45040*Q4)) + A43060*Q6)) + A41080*Q8);\n A[5] = dr2*(dr2*(dr2*(A58100*dr2*dth + dth*(A56300*dth2 + A56120*Q2)) + dth*(dth2*(A54500*dth2 + A54320*Q2) + A54140*Q4)) + dth*(dth2*(dth2*(A52700*dth2 + A52520*Q2) + A52340*Q4) + A52160*Q6)) + dth*(dth2*(dth2*(dth2*(A50900*dth2 + A50720*Q2) + A50540*Q4) + A50360*Q6) + A50180*Q8);\n A[6] = Q6*(A60061*R + A60081*Q2*R) + dth2*(Q4*(A60241*R + A60261*Q2*R) + dth2*(Q2*(A60421*R + A60441*Q2*R) + dth2*(A60601*R + A60801*dth2*R + A60621*Q2*R))) + dr*(A61061*Q6*R + dth2*(A61241*Q4*R + dth2*(A61601*dth2*R + A61421*Q2*R)) + dr*(Q4*(A62041*R + A62061*Q2*R) + dth2*(Q2*(A62221*R + A62241*Q2*R) + dth2*(A62401*R + A62601*dth2*R + A62421*Q2*R)) + dr*(A63041*Q4*R + dth2*(A63401*dth2*R + A63221*Q2*R) + dr*(Q2*(A64021*R + A64041*Q2*R) + dth2*(A64201*R + A64401*dth2*R + A64221*Q2*R) + dr*(A65201*dth2*R + A65021*Q2*R + dr*(A66001*R + A66201*dth2*R + A66021*Q2*R + dr*(A67001*R + A68001*dr*R)))))));\n A[7] = dth2*(dth2*(dth2*(A70800*dth2 + A70620*Q2) + A70440*Q4) + A70260*Q6) + A70080*Q8 + dr*(dth2*(dth2*(dth2*(A71800*dth2 + A71620*Q2) + A71440*Q4) + A71260*Q6) + dr*(dth2*(dth2*(A72600*dth2 + A72420*Q2) + A72240*Q4) + A72060*Q6 + dr*(dth2*(dth2*(A73600*dth2 + A73420*Q2) + A73240*Q4) + dr*(dth2*(A74400*dth2 + A74220*Q2) + A74040*Q4 + dr*(dth2*(A75400*dth2 + A75220*Q2) + dr*(A76200*dth2 + A76020*Q2 + dr*(dr*(A78000 + A79000*dr) + A77200*dth2 + A77020*Q2)) + A75040*Q4)) + A73060*Q6)) + A71080*Q8);\n A[8] = dth*(A80161*Q6*R + dth2*(A80341*Q4*R + dth2*(A80701*dth2*R + A80521*Q2*R))) + dr*(dth*(A81161*Q6*R + dth2*(A81341*Q4*R + dth2*(A81701*dth2*R + A81521*Q2*R))) + dr*(dth*(A82141*Q4*R + dth2*(A82501*dth2*R + A82321*Q2*R)) + dr*(dth*(A83141*Q4*R + dth2*(A83501*dth2*R + A83321*Q2*R)) + dr*(dth*(A84301*dth2*R + A84121*Q2*R) + dr*(dr*(A86101*dth*R + A87101*dr*dth*R) + dth*(A85301*dth2*R + A85121*Q2*R))))));\n A[9] = dth2*(dth2*(Q2*(A90420 + A90440*Q2) + dth2*(A90600 + A90800*dth2 + A90620*Q2)) + (A90240 + A90260*Q2)*Q4) + (A90060 + A90080*Q2)*Q6 + dr*(dth2*(dth2*(Q2*(A91420 + A91440*Q2) + dth2*(A91600 + A91800*dth2 + A91620*Q2)) + (A91240 + A91260*Q2)*Q4) + dr*(dth2*(Q2*(A92220 + A92240*Q2) + dth2*(A92400 + A92600*dth2 + A92420*Q2)) + (A92040 + A92060*Q2)*Q4 + dr*(dth2*(Q2*(A93220 + A93240*Q2) + dth2*(A93400 + A93600*dth2 + A93420*Q2)) + dr*(Q2*(A94020 + A94040*Q2) + dth2*(A94200 + A94400*dth2 + A94220*Q2) + dr*(Q2*(A95020 + A95040*Q2) + dth2*(A95200 + A95400*dth2 + A95220*Q2) + dr*(A96000 + A96200*dth2 + A96020*Q2 + dr*(A97000 + dr*(A98000 + A99000*dr) + A97200*dth2 + A97020*Q2)))) + (A93040 + A93060*Q2)*Q4)) + (A91060 + A91080*Q2)*Q6);\n\n s2 = alpha20*dr2 + alpha02*dth2 + beta*Q2;\n s2_35 = pow(s2, 3.5);\n\n /* hS */\n for(int i=0; i<10; i++)\n {\n hS[i] = A[i]/s2_35;\n }\n}\n\n/* Compute the singular field at the point x for the particle at xp */\nvoid effsource_hS_m(int m, struct coordinate * x, double * hS_re, double * hS_im)\n{\n double A_re[10][5];\n double A_im[10][5];\n double alpha, ellE, ellK;\n\n if(m>20)\n {\n printf(\"Support for computing mode %d has not yet been added.\\n\", m);\n return;\n }\n\n const double r = x->r;\n const double theta = x->theta;\n const double rp = xp.r;\n const double thetap = xp.theta;\n\n const double dr = r - rp;\n const double dth = theta - thetap;\n\n const double dr2 = dr*dr;\n\n const double dth2 = dth*dth;\n const double dth3 = dth*dth2;\n const double dth4 = dth2*dth2;\n const double dth5 = dth3*dth2;\n const double dth6 = dth3*dth3;\n const double dth7 = dth4*dth3;\n const double dth8 = dth4*dth4;\n const double dth9 = dth5*dth4;\n\n A_re[0][0] = (A00600 + A00800*dth2)*dth6 + dr*(dr*((A02400 + A02600*dth2)*dth4 + dr*(dr*(dth2*(A04200 + A04400*dth2) + dr*(dth2*(A05200 + A05400*dth2) + dr*(A06000 + A06200*dth2 + dr*(A07000 + dr*(A08000 + A09000*dr) + A07200*dth2)))) + (A03400 + A03600*dth2)*dth4)) + (A01600 + A01800*dth2)*dth6);\n A_re[0][1] = (A00420 + A00620*dth2)*dth4 + dr*(dr*(dth2*(A02220 + A02420*dth2) + dr*(dth2*(A03220 + A03420*dth2) + dr*(A04020 + A04220*dth2 + dr*(A05020 + dr*(A06020 + A07020*dr) + A05220*dth2)))) + (A01420 + A01620*dth2)*dth4);\n A_re[0][2] = dth2*(A00240 + A00440*dth2) + dr*(dth2*(A01240 + A01440*dth2) + dr*(A02040 + A02240*dth2 + dr*(A03040 + dr*(A04040 + A05040*dr) + A03240*dth2)));\n A_re[0][3] = A00060 + A00260*dth2 + dr*(A01060 + dr*(A02060 + A03060*dr) + A01260*dth2);\n A_re[0][4] = A00080 + A01080*dr;\n A_im[0][0] = A_im[0][1] = A_im[0][2] = A_im[0][3] = A_im[0][4] = 0.0;\n\n A_re[1][0] = A_re[1][1] = A_re[1][2] = A_re[1][3] = A_re[1][4] = 0.0;\n A_im[1][0] = (A10601 + A10801*dth2)*dth6 + dr*(dr*((A12401 + A12601*dth2)*dth4 + dr*(dr*(dth2*(A14201 + A14401*dth2) + dr*(A15201*dth2 + dr*(A16001 + dr*(A17001 + A18001*dr) + A16201*dth2))) + A13401*dth4)) + A11601*dth6);\n A_im[1][1] = (A10421 + A10621*dth2)*dth4 + dr*(dr*(dth2*(A12221 + A12421*dth2) + dr*(A13221*dth2 + dr*(A14021 + dr*(A15021 + A16021*dr) + A14221*dth2))) + A11421*dth4);\n A_im[1][2] = dth2*(A10241 + A10441*dth2) + dr*(A11241*dth2 + dr*(A12041 + dr*(A13041 + A14041*dr) + A12241*dth2));\n A_im[1][3] = A10061 + dr*(A11061 + A12061*dr) + A10261*dth2;\n A_im[1][4] = A10081;\n\n A_re[2][0] = A_re[2][1] = A_re[2][2] = A_re[2][3] = A_re[2][4] = 0.0;\n A_im[2][0] = A20701*dth7 + dr*(dr*(A22501*dth5 + dr*(dr*(A24301*dth3 + dr*(dr*(A26101*dth + A27101*dr*dth) + A25301*dth3)) + A23501*dth5)) + A21701*dth7);\n A_im[2][1] = A20521*dth5 + dr*(dr*(A22321*dth3 + dr*(dr*(A24121*dth + A25121*dr*dth) + A23321*dth3)) + A21521*dth5);\n A_im[2][2] = A20341*dth3 + dr*(dr*(A22141*dth + A23141*dr*dth) + A21341*dth3);\n A_im[2][3] = A20161*dth + A21161*dr*dth;\n A_im[2][4] = 0.0;\n\n A_re[3][0] = (A30600 + A30800*dth2)*dth6 + dr*(dr*((A32400 + A32600*dth2)*dth4 + dr*(dr*(dth2*(A34200 + A34400*dth2) + dr*(dth2*(A35200 + A35400*dth2) + dr*(A36000 + A36200*dth2 + dr*(A37000 + dr*(A38000 + A39000*dr) + A37200*dth2)))) + (A33400 + A33600*dth2)*dth4)) + (A31600 + A31800*dth2)*dth6);\n A_re[3][1] = (A30420 + A30620*dth2)*dth4 + dr*(dr*(dth2*(A32220 + A32420*dth2) + dr*(dth2*(A33220 + A33420*dth2) + dr*(A34020 + A34220*dth2 + dr*(A35020 + dr*(A36020 + A37020*dr) + A35220*dth2)))) + (A31420 + A31620*dth2)*dth4);\n A_re[3][2] = dth2*(A30240 + A30440*dth2) + dr*(dth2*(A31240 + A31440*dth2) + dr*(A32040 + A32240*dth2 + dr*(A33040 + dr*(A34040 + A35040*dr) + A33240*dth2)));\n A_re[3][3] = A30060 + A30260*dth2 + dr*(A31060 + dr*(A32060 + A33060*dr) + A31260*dth2);\n A_re[3][4] = A30080 + A31080*dr;\n A_im[3][0] = A_im[3][1] = A_im[3][2] = A_im[3][3] = A_im[3][4] = 0.0;\n\n A_re[4][0] = A40800*dth8 + dr*(dr*(A42600*dth6 + dr*(dr*(A44400*dth4 + dr*(dr*(A46200*dth2 + dr*(dr*(A48000 + A49000*dr) + A47200*dth2)) + A45400*dth4)) + A43600*dth6)) + A41800*dth8);\n A_re[4][1] = A40620*dth6 + dr*(dr*(A42420*dth4 + dr*(dr*(A44220*dth2 + dr*(dr*(A46020 + A47020*dr) + A45220*dth2)) + A43420*dth4)) + A41620*dth6);\n A_re[4][2] = A40440*dth4 + dr*(dr*(A42240*dth2 + dr*(dr*(A44040 + A45040*dr) + A43240*dth2)) + A41440*dth4);\n A_re[4][3] = A40260*dth2 + dr*(dr*(A42060 + A43060*dr) + A41260*dth2);\n A_re[4][4] = A40080 + A41080*dr;\n A_im[4][0] = A_im[4][1] = A_im[4][2] = A_im[4][3] = A_im[4][4] = 0.0;\n\n A_re[5][0] = dr2*(dr2*(dr2*(A58100*dr2*dth + A56300*dth3) + A54500*dth5) + A52700*dth7) + A50900*dth9;\n A_re[5][1] = dr2*(dr2*(A56120*dr2*dth + A54320*dth3) + A52520*dth5) + A50720*dth7;\n A_re[5][2] = dr2*(A54140*dr2*dth + A52340*dth3) + A50540*dth5;\n A_re[5][3] = A52160*dr2*dth + A50360*dth3;\n A_re[5][4] = A50180*dth;\n A_im[5][0] = A_im[5][1] = A_im[5][2] = A_im[5][3] = A_im[5][4] = 0.0;\n\n A_re[6][0] = A_re[6][1] = A_re[6][2] = A_re[6][3] = A_re[6][4] = 0.0;\n A_im[6][0] = (A60601 + A60801*dth2)*dth6 + dr*(dr*((A62401 + A62601*dth2)*dth4 + dr*(dr*(dth2*(A64201 + A64401*dth2) + dr*(A65201*dth2 + dr*(A66001 + dr*(A67001 + A68001*dr) + A66201*dth2))) + A63401*dth4)) + A61601*dth6);\n A_im[6][1] = (A60421 + A60621*dth2)*dth4 + dr*(dr*(dth2*(A62221 + A62421*dth2) + dr*(A63221*dth2 + dr*(A64021 + dr*(A65021 + A66021*dr) + A64221*dth2))) + A61421*dth4);\n A_im[6][2] = dth2*(A60241 + A60441*dth2) + dr*(A61241*dth2 + dr*(A62041 + dr*(A63041 + A64041*dr) + A62241*dth2));\n A_im[6][3] = A60061 + dr*(A61061 + A62061*dr) + A60261*dth2;\n A_im[6][4] = A60081;\n\n A_re[7][0] = A70800*dth8 + dr*(dr*(A72600*dth6 + dr*(dr*(A74400*dth4 + dr*(dr*(A76200*dth2 + dr*(dr*(A78000 + A79000*dr) + A77200*dth2)) + A75400*dth4)) + A73600*dth6)) + A71800*dth8);\n A_re[7][1] = A70620*dth6 + dr*(dr*(A72420*dth4 + dr*(dr*(A74220*dth2 + dr*(dr*(A76020 + A77020*dr) + A75220*dth2)) + A73420*dth4)) + A71620*dth6);\n A_re[7][2] = A70440*dth4 + dr*(dr*(A72240*dth2 + dr*(dr*(A74040 + A75040*dr) + A73240*dth2)) + A71440*dth4);\n A_re[7][3] = A70260*dth2 + dr*(dr*(A72060 + A73060*dr) + A71260*dth2);\n A_re[7][4] = A70080 + A71080*dr;\n A_im[7][0] = A_im[7][1] = A_im[7][2] = A_im[7][3] = A_im[7][4] = 0.0;\n\n A_re[8][0] = A_re[8][1] = A_re[8][2] = A_re[8][3] = A_re[8][4] = 0.0;\n A_im[8][0] = A80701*dth7 + dr*(dr*(A82501*dth5 + dr*(dr*(A84301*dth3 + dr*(dr*(A86101*dth + A87101*dr*dth) + A85301*dth3)) + A83501*dth5)) + A81701*dth7);\n A_im[8][1] = A80521*dth5 + dr*(dr*(A82321*dth3 + dr*(dr*(A84121*dth + A85121*dr*dth) + A83321*dth3)) + A81521*dth5);\n A_im[8][2] = A80341*dth3 + dr*(dr*(A82141*dth + A83141*dr*dth) + A81341*dth3);\n A_im[8][3] = A80161*dth + A81161*dr*dth;\n A_im[8][4] = 0.0;\n\n A_re[9][0] = (A90600 + A90800*dth2)*dth6 + dr*(dr*((A92400 + A92600*dth2)*dth4 + dr*(dr*(dth2*(A94200 + A94400*dth2) + dr*(dth2*(A95200 + A95400*dth2) + dr*(A96000 + A96200*dth2 + dr*(A97000 + dr*(A98000 + A99000*dr) + A97200*dth2)))) + (A93400 + A93600*dth2)*dth4)) + (A91600 + A91800*dth2)*dth6);\n A_re[9][1] = (A90420 + A90620*dth2)*dth4 + dr*(dr*(dth2*(A92220 + A92420*dth2) + dr*(dth2*(A93220 + A93420*dth2) + dr*(A94020 + A94220*dth2 + dr*(A95020 + dr*(A96020 + A97020*dr) + A95220*dth2)))) + (A91420 + A91620*dth2)*dth4);\n A_re[9][2] = dth2*(A90240 + A90440*dth2) + dr*(dth2*(A91240 + A91440*dth2) + dr*(A92040 + A92240*dth2 + dr*(A93040 + dr*(A94040 + A95040*dr) + A93240*dth2)));\n A_re[9][3] = A90060 + A90260*dth2 + dr*(A91060 + dr*(A92060 + A93060*dr) + A91260*dth2);\n A_re[9][4] = A90080 + A91080*dr;\n A_im[9][0] = A_im[9][1] = A_im[9][2] = A_im[9][3] = A_im[9][4] = 0.0;\n\n alpha = alpha20*dr2 + alpha02*dth2;\n\n /* Powers of C = alpha / beta */\n double C[27];\n C[0] = 1;\n C[1] = alpha / beta;\n for(int i=2; i<=26; i++)\n C[i] = C[1]*C[i-1];\n\n ellE = gsl_sf_ellint_Ecomp(sqrt(1.0/(1.0+C[1])), GSL_PREC_DOUBLE);\n ellK = gsl_sf_ellint_Kcomp(sqrt(1.0/(1.0+C[1])), GSL_PREC_DOUBLE);\n\n const double fac_re = 4.0/(beta*C[3]*pow(alpha+beta, 2.5));\n const double fac_im = -32.0/(beta*beta*C[2]*pow(alpha+beta, 1.5));\n for(int l=0; l<10; l++)\n {\n hS_re[l] = 0.0;\n hS_im[l] = 0.0;\n for(int j=0; j<5; j++) {\n double fac1K = ellK*A_re[l][j];\n for(int k=max(j,0); k<=m+2+j; k++) {\n hS_re[l] += fac1K*C[k]*ReEI[m][0][j][k];\n }\n\n double fac1E = ellE*A_re[l][j];\n for(int k=max(j-1,0); k<=m+2+j; k++) {\n hS_re[l] += fac1E*C[k]*ReEI[m][1][j][k];\n }\n \n double fac2K = ellK*A_im[l][j];\n for(int k=max(j-1,0); k<=m+1+j; k++) {\n hS_im[l] += fac2K*C[k]*ImEI[m][0][j][k];\n }\n \n double fac2E = ellE*A_im[l][j];\n for(int k=max(j-2,0); k<=m+1+j; k++) {\n hS_im[l] += fac2E*C[k]*ImEI[m][1][j][k];\n }\n }\n hS_re[l] *= fac_re;\n hS_im[l] *= fac_im;\n }\n}\n\n\n/* Compute the singular field, its derivatives and its d'Alembertian */\nvoid effsource_calc(struct coordinate * x, double *hS, double *dhS_dr,\n double *dhS_dth, double *dhS_dph, double *dhS_dt, double *src)\n{\n double A[10], dA_dr[10], d2A_dr2[10], dA_dth[10], d2A_dth2[10], dA_dQ[10], dA_dR[10], dA_dph[10];\n double d2A_dQ2[10], d2A_dQR[10], d2A_dph2[10], dA_dt[10], d2A_dt2[10], d2A_dtph[10];\n\n double s2, sqrts2, s2_15, s2_25, s2_35, s2_45, s2_55, ds2_dr, d2s2_dr2, ds2_dth;\n double d2s2_dth2, ds2_dQ, ds2_dph, d2s2_dQ2, d2s2_dph2, ds2_dt, d2s2_dt2, d2s2_dtph;\n\n double d2hS_dt2[10], d2hS_dtr[10], d2hS_dtth[10];\n double d2hS_dtph[10], d2hS_dr2[10], d2hS_drth[10], d2hS_drph[10], d2hS_dth2[10], d2hS_dthph[10], d2hS_dph2[10];\n\n double r = x->r;\n double theta = x->theta;\n double phi = x->phi;\n double rp = xp.r;\n double thetap = xp.theta;\n double phip = xp.phi;\n\n double Omega = M / (a*M + sqrt(M*rp*rp*rp));\n\n double dr = r - rp;\n double dth = theta - thetap;\n double dphi = phi - phip;\n\n double dr2 = dr*dr;\n\n double dth2 = dth*dth;\n\n double Q = sin(0.5*dphi);\n double Q2 = Q*Q;\n double Q3 = Q2*Q;\n double Q4 = Q2*Q2;\n double Q5 = Q3*Q2;\n double Q6 = Q4*Q2;\n double Q7 = Q4*Q3;\n double Q8 = Q4*Q4;\n\n double R = sin(dphi);\n\n double dQ_dph = 0.5*cos(0.5*dphi);\n double dR_dph = cos(dphi);\n\n double d2Q_dph2 = -0.25*Q;\n double d2R_dph2 = -R;\n\n /* A */\n A[0] = dth2*(dth2*(Q2*(A00420 + A00440*Q2) + dth2*(A00600 + A00800*dth2 + A00620*Q2)) + (A00240 + A00260*Q2)*Q4) + (A00060 + A00080*Q2)*Q6 + dr*(dth2*(dth2*(Q2*(A01420 + A01440*Q2) + dth2*(A01600 + A01800*dth2 + A01620*Q2)) + (A01240 + A01260*Q2)*Q4) + dr*(dth2*(Q2*(A02220 + A02240*Q2) + dth2*(A02400 + A02600*dth2 + A02420*Q2)) + (A02040 + A02060*Q2)*Q4 + dr*(dth2*(Q2*(A03220 + A03240*Q2) + dth2*(A03400 + A03600*dth2 + A03420*Q2)) + dr*(Q2*(A04020 + A04040*Q2) + dth2*(A04200 + A04400*dth2 + A04220*Q2) + dr*(Q2*(A05020 + A05040*Q2) + dth2*(A05200 + A05400*dth2 + A05220*Q2) + dr*(A06000 + A06200*dth2 + A06020*Q2 + dr*(A07000 + dr*(A08000 + A09000*dr) + A07200*dth2 + A07020*Q2)))) + (A03040 + A03060*Q2)*Q4)) + (A01060 + A01080*Q2)*Q6);\n A[1] = Q6*(A10061*R + A10081*Q2*R) + dth2*(Q4*(A10241*R + A10261*Q2*R) + dth2*(Q2*(A10421*R + A10441*Q2*R) + dth2*(A10601*R + A10801*dth2*R + A10621*Q2*R))) + dr*(A11061*Q6*R + dth2*(A11241*Q4*R + dth2*(A11601*dth2*R + A11421*Q2*R)) + dr*(Q4*(A12041*R + A12061*Q2*R) + dth2*(Q2*(A12221*R + A12241*Q2*R) + dth2*(A12401*R + A12601*dth2*R + A12421*Q2*R)) + dr*(A13041*Q4*R + dth2*(A13401*dth2*R + A13221*Q2*R) + dr*(Q2*(A14021*R + A14041*Q2*R) + dth2*(A14201*R + A14401*dth2*R + A14221*Q2*R) + dr*(A15201*dth2*R + A15021*Q2*R + dr*(A16001*R + A16201*dth2*R + A16021*Q2*R + dr*(A17001*R + A18001*dr*R)))))));\n A[2] = dth*(A20161*Q6*R + dth2*(A20341*Q4*R + dth2*(A20701*dth2*R + A20521*Q2*R))) + dr*(dth*(A21161*Q6*R + dth2*(A21341*Q4*R + dth2*(A21701*dth2*R + A21521*Q2*R))) + dr*(dth*(A22141*Q4*R + dth2*(A22501*dth2*R + A22321*Q2*R)) + dr*(dth*(A23141*Q4*R + dth2*(A23501*dth2*R + A23321*Q2*R)) + dr*(dth*(A24301*dth2*R + A24121*Q2*R) + dr*(dr*(A26101*dth*R + A27101*dr*dth*R) + dth*(A25301*dth2*R + A25121*Q2*R))))));\n A[3] = dth2*(dth2*(Q2*(A30420 + A30440*Q2) + dth2*(A30600 + A30800*dth2 + A30620*Q2)) + (A30240 + A30260*Q2)*Q4) + (A30060 + A30080*Q2)*Q6 + dr*(dth2*(dth2*(Q2*(A31420 + A31440*Q2) + dth2*(A31600 + A31800*dth2 + A31620*Q2)) + (A31240 + A31260*Q2)*Q4) + dr*(dth2*(Q2*(A32220 + A32240*Q2) + dth2*(A32400 + A32600*dth2 + A32420*Q2)) + (A32040 + A32060*Q2)*Q4 + dr*(dth2*(Q2*(A33220 + A33240*Q2) + dth2*(A33400 + A33600*dth2 + A33420*Q2)) + dr*(Q2*(A34020 + A34040*Q2) + dth2*(A34200 + A34400*dth2 + A34220*Q2) + dr*(Q2*(A35020 + A35040*Q2) + dth2*(A35200 + A35400*dth2 + A35220*Q2) + dr*(A36000 + A36200*dth2 + A36020*Q2 + dr*(A37000 + dr*(A38000 + A39000*dr) + A37200*dth2 + A37020*Q2)))) + (A33040 + A33060*Q2)*Q4)) + (A31060 + A31080*Q2)*Q6);\n A[4] = dth2*(dth2*(dth2*(A40800*dth2 + A40620*Q2) + A40440*Q4) + A40260*Q6) + A40080*Q8 + dr*(dth2*(dth2*(dth2*(A41800*dth2 + A41620*Q2) + A41440*Q4) + A41260*Q6) + dr*(dth2*(dth2*(A42600*dth2 + A42420*Q2) + A42240*Q4) + A42060*Q6 + dr*(dth2*(dth2*(A43600*dth2 + A43420*Q2) + A43240*Q4) + dr*(dth2*(A44400*dth2 + A44220*Q2) + A44040*Q4 + dr*(dth2*(A45400*dth2 + A45220*Q2) + dr*(A46200*dth2 + A46020*Q2 + dr*(dr*(A48000 + A49000*dr) + A47200*dth2 + A47020*Q2)) + A45040*Q4)) + A43060*Q6)) + A41080*Q8);\n A[5] = dr2*(dr2*(dr2*(A58100*dr2*dth + dth*(A56300*dth2 + A56120*Q2)) + dth*(dth2*(A54500*dth2 + A54320*Q2) + A54140*Q4)) + dth*(dth2*(dth2*(A52700*dth2 + A52520*Q2) + A52340*Q4) + A52160*Q6)) + dth*(dth2*(dth2*(dth2*(A50900*dth2 + A50720*Q2) + A50540*Q4) + A50360*Q6) + A50180*Q8);\n A[6] = Q6*(A60061*R + A60081*Q2*R) + dth2*(Q4*(A60241*R + A60261*Q2*R) + dth2*(Q2*(A60421*R + A60441*Q2*R) + dth2*(A60601*R + A60801*dth2*R + A60621*Q2*R))) + dr*(A61061*Q6*R + dth2*(A61241*Q4*R + dth2*(A61601*dth2*R + A61421*Q2*R)) + dr*(Q4*(A62041*R + A62061*Q2*R) + dth2*(Q2*(A62221*R + A62241*Q2*R) + dth2*(A62401*R + A62601*dth2*R + A62421*Q2*R)) + dr*(A63041*Q4*R + dth2*(A63401*dth2*R + A63221*Q2*R) + dr*(Q2*(A64021*R + A64041*Q2*R) + dth2*(A64201*R + A64401*dth2*R + A64221*Q2*R) + dr*(A65201*dth2*R + A65021*Q2*R + dr*(A66001*R + A66201*dth2*R + A66021*Q2*R + dr*(A67001*R + A68001*dr*R)))))));\n A[7] = dth2*(dth2*(dth2*(A70800*dth2 + A70620*Q2) + A70440*Q4) + A70260*Q6) + A70080*Q8 + dr*(dth2*(dth2*(dth2*(A71800*dth2 + A71620*Q2) + A71440*Q4) + A71260*Q6) + dr*(dth2*(dth2*(A72600*dth2 + A72420*Q2) + A72240*Q4) + A72060*Q6 + dr*(dth2*(dth2*(A73600*dth2 + A73420*Q2) + A73240*Q4) + dr*(dth2*(A74400*dth2 + A74220*Q2) + A74040*Q4 + dr*(dth2*(A75400*dth2 + A75220*Q2) + dr*(A76200*dth2 + A76020*Q2 + dr*(dr*(A78000 + A79000*dr) + A77200*dth2 + A77020*Q2)) + A75040*Q4)) + A73060*Q6)) + A71080*Q8);\n A[8] = dth*(A80161*Q6*R + dth2*(A80341*Q4*R + dth2*(A80701*dth2*R + A80521*Q2*R))) + dr*(dth*(A81161*Q6*R + dth2*(A81341*Q4*R + dth2*(A81701*dth2*R + A81521*Q2*R))) + dr*(dth*(A82141*Q4*R + dth2*(A82501*dth2*R + A82321*Q2*R)) + dr*(dth*(A83141*Q4*R + dth2*(A83501*dth2*R + A83321*Q2*R)) + dr*(dth*(A84301*dth2*R + A84121*Q2*R) + dr*(dr*(A86101*dth*R + A87101*dr*dth*R) + dth*(A85301*dth2*R + A85121*Q2*R))))));\n A[9] = dth2*(dth2*(Q2*(A90420 + A90440*Q2) + dth2*(A90600 + A90800*dth2 + A90620*Q2)) + (A90240 + A90260*Q2)*Q4) + (A90060 + A90080*Q2)*Q6 + dr*(dth2*(dth2*(Q2*(A91420 + A91440*Q2) + dth2*(A91600 + A91800*dth2 + A91620*Q2)) + (A91240 + A91260*Q2)*Q4) + dr*(dth2*(Q2*(A92220 + A92240*Q2) + dth2*(A92400 + A92600*dth2 + A92420*Q2)) + (A92040 + A92060*Q2)*Q4 + dr*(dth2*(Q2*(A93220 + A93240*Q2) + dth2*(A93400 + A93600*dth2 + A93420*Q2)) + dr*(Q2*(A94020 + A94040*Q2) + dth2*(A94200 + A94400*dth2 + A94220*Q2) + dr*(Q2*(A95020 + A95040*Q2) + dth2*(A95200 + A95400*dth2 + A95220*Q2) + dr*(A96000 + A96200*dth2 + A96020*Q2 + dr*(A97000 + dr*(A98000 + A99000*dr) + A97200*dth2 + A97020*Q2)))) + (A93040 + A93060*Q2)*Q4)) + (A91060 + A91080*Q2)*Q6);\n\n /* dA/dx */\n dA_dr[0] = dth2*(dth2*(Q2*(A01420 + A01440*Q2) + dth2*(A01600 + A01800*dth2 + A01620*Q2)) + (A01240 + A01260*Q2)*Q4) + dr*(dth2*(Q2*(2*A02220 + 2*A02240*Q2) + dth2*(2*A02400 + 2*A02600*dth2 + 2*A02420*Q2)) + (2*A02040 + 2*A02060*Q2)*Q4 + dr*(dth2*(Q2*(3*A03220 + 3*A03240*Q2) + dth2*(3*A03400 + 3*A03600*dth2 + 3*A03420*Q2)) + dr*(Q2*(4*A04020 + 4*A04040*Q2) + dth2*(4*A04200 + 4*A04400*dth2 + 4*A04220*Q2) + dr*(Q2*(5*A05020 + 5*A05040*Q2) + dth2*(5*A05200 + 5*A05400*dth2 + 5*A05220*Q2) + dr*(6*A06000 + 6*A06200*dth2 + 6*A06020*Q2 + dr*(7*A07000 + dr*(8*A08000 + 9*A09000*dr) + 7*A07200*dth2 + 7*A07020*Q2)))) + (3*A03040 + 3*A03060*Q2)*Q4)) + (A01060 + A01080*Q2)*Q6;\n dA_dr[1] = A11061*Q6*R + dth2*(A11241*Q4*R + dth2*(A11601*dth2*R + A11421*Q2*R)) + dr*(Q4*(2*A12041*R + 2*A12061*Q2*R) + dth2*(Q2*(2*A12221*R + 2*A12241*Q2*R) + dth2*(2*A12401*R + 2*A12601*dth2*R + 2*A12421*Q2*R)) + dr*(3*A13041*Q4*R + dth2*(3*A13401*dth2*R + 3*A13221*Q2*R) + dr*(Q2*(4*A14021*R + 4*A14041*Q2*R) + dth2*(4*A14201*R + 4*A14401*dth2*R + 4*A14221*Q2*R) + dr*(5*A15201*dth2*R + 5*A15021*Q2*R + dr*(6*A16001*R + 6*A16201*dth2*R + 6*A16021*Q2*R + dr*(7*A17001*R + 8*A18001*dr*R))))));\n dA_dr[2] = dth*(A21161*Q6*R + dth2*(A21341*Q4*R + dth2*(A21701*dth2*R + A21521*Q2*R))) + dr*(dth*(2*A22141*Q4*R + dth2*(2*A22501*dth2*R + 2*A22321*Q2*R)) + dr*(dth*(3*A23141*Q4*R + dth2*(3*A23501*dth2*R + 3*A23321*Q2*R)) + dr*(dth*(4*A24301*dth2*R + 4*A24121*Q2*R) + dr*(dr*(6*A26101*dth*R + 7*A27101*dr*dth*R) + dth*(5*A25301*dth2*R + 5*A25121*Q2*R)))));\n dA_dr[3] = dth2*(dth2*(Q2*(A31420 + A31440*Q2) + dth2*(A31600 + A31800*dth2 + A31620*Q2)) + (A31240 + A31260*Q2)*Q4) + dr*(dth2*(Q2*(2*A32220 + 2*A32240*Q2) + dth2*(2*A32400 + 2*A32600*dth2 + 2*A32420*Q2)) + (2*A32040 + 2*A32060*Q2)*Q4 + dr*(dth2*(Q2*(3*A33220 + 3*A33240*Q2) + dth2*(3*A33400 + 3*A33600*dth2 + 3*A33420*Q2)) + dr*(Q2*(4*A34020 + 4*A34040*Q2) + dth2*(4*A34200 + 4*A34400*dth2 + 4*A34220*Q2) + dr*(Q2*(5*A35020 + 5*A35040*Q2) + dth2*(5*A35200 + 5*A35400*dth2 + 5*A35220*Q2) + dr*(6*A36000 + 6*A36200*dth2 + 6*A36020*Q2 + dr*(7*A37000 + dr*(8*A38000 + 9*A39000*dr) + 7*A37200*dth2 + 7*A37020*Q2)))) + (3*A33040 + 3*A33060*Q2)*Q4)) + (A31060 + A31080*Q2)*Q6;\n dA_dr[4] = dth2*(dth2*(dth2*(A41800*dth2 + A41620*Q2) + A41440*Q4) + A41260*Q6) + dr*(dth2*(dth2*(2*A42600*dth2 + 2*A42420*Q2) + 2*A42240*Q4) + 2*A42060*Q6 + dr*(dth2*(dth2*(3*A43600*dth2 + 3*A43420*Q2) + 3*A43240*Q4) + dr*(dth2*(4*A44400*dth2 + 4*A44220*Q2) + 4*A44040*Q4 + dr*(dth2*(5*A45400*dth2 + 5*A45220*Q2) + dr*(6*A46200*dth2 + 6*A46020*Q2 + dr*(dr*(8*A48000 + 9*A49000*dr) + 7*A47200*dth2 + 7*A47020*Q2)) + 5*A45040*Q4)) + 3*A43060*Q6)) + A41080*Q8;\n dA_dr[5] = dr*(dr2*(dr2*(8*A58100*dr2*dth + dth*(6*A56300*dth2 + 6*A56120*Q2)) + dth*(dth2*(4*A54500*dth2 + 4*A54320*Q2) + 4*A54140*Q4)) + dth*(dth2*(dth2*(2*A52700*dth2 + 2*A52520*Q2) + 2*A52340*Q4) + 2*A52160*Q6));\n dA_dr[6] = A61061*Q6*R + dth2*(A61241*Q4*R + dth2*(A61601*dth2*R + A61421*Q2*R)) + dr*(Q4*(2*A62041*R + 2*A62061*Q2*R) + dth2*(Q2*(2*A62221*R + 2*A62241*Q2*R) + dth2*(2*A62401*R + 2*A62601*dth2*R + 2*A62421*Q2*R)) + dr*(3*A63041*Q4*R + dth2*(3*A63401*dth2*R + 3*A63221*Q2*R) + dr*(Q2*(4*A64021*R + 4*A64041*Q2*R) + dth2*(4*A64201*R + 4*A64401*dth2*R + 4*A64221*Q2*R) + dr*(5*A65201*dth2*R + 5*A65021*Q2*R + dr*(6*A66001*R + 6*A66201*dth2*R + 6*A66021*Q2*R + dr*(7*A67001*R + 8*A68001*dr*R))))));\n dA_dr[7] = dth2*(dth2*(dth2*(A71800*dth2 + A71620*Q2) + A71440*Q4) + A71260*Q6) + dr*(dth2*(dth2*(2*A72600*dth2 + 2*A72420*Q2) + 2*A72240*Q4) + 2*A72060*Q6 + dr*(dth2*(dth2*(3*A73600*dth2 + 3*A73420*Q2) + 3*A73240*Q4) + dr*(dth2*(4*A74400*dth2 + 4*A74220*Q2) + 4*A74040*Q4 + dr*(dth2*(5*A75400*dth2 + 5*A75220*Q2) + dr*(6*A76200*dth2 + 6*A76020*Q2 + dr*(dr*(8*A78000 + 9*A79000*dr) + 7*A77200*dth2 + 7*A77020*Q2)) + 5*A75040*Q4)) + 3*A73060*Q6)) + A71080*Q8;\n dA_dr[8] = dth*(A81161*Q6*R + dth2*(A81341*Q4*R + dth2*(A81701*dth2*R + A81521*Q2*R))) + dr*(dth*(2*A82141*Q4*R + dth2*(2*A82501*dth2*R + 2*A82321*Q2*R)) + dr*(dth*(3*A83141*Q4*R + dth2*(3*A83501*dth2*R + 3*A83321*Q2*R)) + dr*(dth*(4*A84301*dth2*R + 4*A84121*Q2*R) + dr*(dr*(6*A86101*dth*R + 7*A87101*dr*dth*R) + dth*(5*A85301*dth2*R + 5*A85121*Q2*R)))));\n dA_dr[9] = dth2*(dth2*(Q2*(A91420 + A91440*Q2) + dth2*(A91600 + A91800*dth2 + A91620*Q2)) + (A91240 + A91260*Q2)*Q4) + dr*(dth2*(Q2*(2*A92220 + 2*A92240*Q2) + dth2*(2*A92400 + 2*A92600*dth2 + 2*A92420*Q2)) + (2*A92040 + 2*A92060*Q2)*Q4 + dr*(dth2*(Q2*(3*A93220 + 3*A93240*Q2) + dth2*(3*A93400 + 3*A93600*dth2 + 3*A93420*Q2)) + dr*(Q2*(4*A94020 + 4*A94040*Q2) + dth2*(4*A94200 + 4*A94400*dth2 + 4*A94220*Q2) + dr*(Q2*(5*A95020 + 5*A95040*Q2) + dth2*(5*A95200 + 5*A95400*dth2 + 5*A95220*Q2) + dr*(6*A96000 + 6*A96200*dth2 + 6*A96020*Q2 + dr*(7*A97000 + dr*(8*A98000 + 9*A99000*dr) + 7*A97200*dth2 + 7*A97020*Q2)))) + (3*A93040 + 3*A93060*Q2)*Q4)) + (A91060 + A91080*Q2)*Q6;\n dA_dth[0] = dth*(dth2*(Q2*(4*A00420 + 4*A00440*Q2) + dth2*(6*A00600 + 8*A00800*dth2 + 6*A00620*Q2)) + (2*A00240 + 2*A00260*Q2)*Q4) + dr*(dr*(dth*(Q2*(2*A02220 + 2*A02240*Q2) + dth2*(4*A02400 + 6*A02600*dth2 + 4*A02420*Q2)) + dr*(dth*(Q2*(2*A03220 + 2*A03240*Q2) + dth2*(4*A03400 + 6*A03600*dth2 + 4*A03420*Q2)) + dr*(dth*(2*A04200 + 4*A04400*dth2 + 2*A04220*Q2) + dr*(dr*(2*A06200*dth + 2*A07200*dr*dth) + dth*(2*A05200 + 4*A05400*dth2 + 2*A05220*Q2))))) + dth*(dth2*(Q2*(4*A01420 + 4*A01440*Q2) + dth2*(6*A01600 + 8*A01800*dth2 + 6*A01620*Q2)) + (2*A01240 + 2*A01260*Q2)*Q4));\n dA_dth[1] = dth*(Q4*(2*A10241*R + 2*A10261*Q2*R) + dth2*(Q2*(4*A10421*R + 4*A10441*Q2*R) + dth2*(6*A10601*R + 8*A10801*dth2*R + 6*A10621*Q2*R))) + dr*(dth*(2*A11241*Q4*R + dth2*(6*A11601*dth2*R + 4*A11421*Q2*R)) + dr*(dth*(Q2*(2*A12221*R + 2*A12241*Q2*R) + dth2*(4*A12401*R + 6*A12601*dth2*R + 4*A12421*Q2*R)) + dr*(dth*(4*A13401*dth2*R + 2*A13221*Q2*R) + dr*(dr*(2*A15201*dth*R + 2*A16201*dr*dth*R) + dth*(2*A14201*R + 4*A14401*dth2*R + 2*A14221*Q2*R)))));\n dA_dth[2] = A20161*Q6*R + dth2*(3*A20341*Q4*R + dth2*(7*A20701*dth2*R + 5*A20521*Q2*R)) + dr*(A21161*Q6*R + dth2*(3*A21341*Q4*R + dth2*(7*A21701*dth2*R + 5*A21521*Q2*R)) + dr*(A22141*Q4*R + dth2*(5*A22501*dth2*R + 3*A22321*Q2*R) + dr*(A23141*Q4*R + dth2*(5*A23501*dth2*R + 3*A23321*Q2*R) + dr*(3*A24301*dth2*R + A24121*Q2*R + dr*(3*A25301*dth2*R + A25121*Q2*R + dr*(A26101*R + A27101*dr*R))))));\n dA_dth[3] = dth*(dth2*(Q2*(4*A30420 + 4*A30440*Q2) + dth2*(6*A30600 + 8*A30800*dth2 + 6*A30620*Q2)) + (2*A30240 + 2*A30260*Q2)*Q4) + dr*(dr*(dth*(Q2*(2*A32220 + 2*A32240*Q2) + dth2*(4*A32400 + 6*A32600*dth2 + 4*A32420*Q2)) + dr*(dth*(Q2*(2*A33220 + 2*A33240*Q2) + dth2*(4*A33400 + 6*A33600*dth2 + 4*A33420*Q2)) + dr*(dth*(2*A34200 + 4*A34400*dth2 + 2*A34220*Q2) + dr*(dr*(2*A36200*dth + 2*A37200*dr*dth) + dth*(2*A35200 + 4*A35400*dth2 + 2*A35220*Q2))))) + dth*(dth2*(Q2*(4*A31420 + 4*A31440*Q2) + dth2*(6*A31600 + 8*A31800*dth2 + 6*A31620*Q2)) + (2*A31240 + 2*A31260*Q2)*Q4));\n dA_dth[4] = dth*(dth2*(dth2*(8*A40800*dth2 + 6*A40620*Q2) + 4*A40440*Q4) + 2*A40260*Q6) + dr*(dr*(dth*(dth2*(6*A42600*dth2 + 4*A42420*Q2) + 2*A42240*Q4) + dr*(dr*(dth*(4*A44400*dth2 + 2*A44220*Q2) + dr*(dr*(2*A46200*dth + 2*A47200*dr*dth) + dth*(4*A45400*dth2 + 2*A45220*Q2))) + dth*(dth2*(6*A43600*dth2 + 4*A43420*Q2) + 2*A43240*Q4))) + dth*(dth2*(dth2*(8*A41800*dth2 + 6*A41620*Q2) + 4*A41440*Q4) + 2*A41260*Q6));\n dA_dth[5] = dth2*(dth2*(dth2*(9*A50900*dth2 + 7*A50720*Q2) + 5*A50540*Q4) + 3*A50360*Q6) + dr2*(dth2*(dth2*(7*A52700*dth2 + 5*A52520*Q2) + 3*A52340*Q4) + dr2*(dth2*(5*A54500*dth2 + 3*A54320*Q2) + dr2*(A58100*dr2 + 3*A56300*dth2 + A56120*Q2) + A54140*Q4) + A52160*Q6) + A50180*Q8;\n dA_dth[6] = dth*(Q4*(2*A60241*R + 2*A60261*Q2*R) + dth2*(Q2*(4*A60421*R + 4*A60441*Q2*R) + dth2*(6*A60601*R + 8*A60801*dth2*R + 6*A60621*Q2*R))) + dr*(dth*(2*A61241*Q4*R + dth2*(6*A61601*dth2*R + 4*A61421*Q2*R)) + dr*(dth*(Q2*(2*A62221*R + 2*A62241*Q2*R) + dth2*(4*A62401*R + 6*A62601*dth2*R + 4*A62421*Q2*R)) + dr*(dth*(4*A63401*dth2*R + 2*A63221*Q2*R) + dr*(dr*(2*A65201*dth*R + 2*A66201*dr*dth*R) + dth*(2*A64201*R + 4*A64401*dth2*R + 2*A64221*Q2*R)))));\n dA_dth[7] = dth*(dth2*(dth2*(8*A70800*dth2 + 6*A70620*Q2) + 4*A70440*Q4) + 2*A70260*Q6) + dr*(dr*(dth*(dth2*(6*A72600*dth2 + 4*A72420*Q2) + 2*A72240*Q4) + dr*(dr*(dth*(4*A74400*dth2 + 2*A74220*Q2) + dr*(dr*(2*A76200*dth + 2*A77200*dr*dth) + dth*(4*A75400*dth2 + 2*A75220*Q2))) + dth*(dth2*(6*A73600*dth2 + 4*A73420*Q2) + 2*A73240*Q4))) + dth*(dth2*(dth2*(8*A71800*dth2 + 6*A71620*Q2) + 4*A71440*Q4) + 2*A71260*Q6));\n dA_dth[8] = A80161*Q6*R + dth2*(3*A80341*Q4*R + dth2*(7*A80701*dth2*R + 5*A80521*Q2*R)) + dr*(A81161*Q6*R + dth2*(3*A81341*Q4*R + dth2*(7*A81701*dth2*R + 5*A81521*Q2*R)) + dr*(A82141*Q4*R + dth2*(5*A82501*dth2*R + 3*A82321*Q2*R) + dr*(A83141*Q4*R + dth2*(5*A83501*dth2*R + 3*A83321*Q2*R) + dr*(3*A84301*dth2*R + A84121*Q2*R + dr*(3*A85301*dth2*R + A85121*Q2*R + dr*(A86101*R + A87101*dr*R))))));\n dA_dth[9] = dth*(dth2*(Q2*(4*A90420 + 4*A90440*Q2) + dth2*(6*A90600 + 8*A90800*dth2 + 6*A90620*Q2)) + (2*A90240 + 2*A90260*Q2)*Q4) + dr*(dr*(dth*(Q2*(2*A92220 + 2*A92240*Q2) + dth2*(4*A92400 + 6*A92600*dth2 + 4*A92420*Q2)) + dr*(dth*(Q2*(2*A93220 + 2*A93240*Q2) + dth2*(4*A93400 + 6*A93600*dth2 + 4*A93420*Q2)) + dr*(dth*(2*A94200 + 4*A94400*dth2 + 2*A94220*Q2) + dr*(dr*(2*A96200*dth + 2*A97200*dr*dth) + dth*(2*A95200 + 4*A95400*dth2 + 2*A95220*Q2))))) + dth*(dth2*(Q2*(4*A91420 + 4*A91440*Q2) + dth2*(6*A91600 + 8*A91800*dth2 + 6*A91620*Q2)) + (2*A91240 + 2*A91260*Q2)*Q4));\n dA_dQ[0] = dth2*(dth2*(2*A00620*dth2*Q + Q*(2*A00420 + 4*A00440*Q2)) + (4*A00240 + 6*A00260*Q2)*Q3) + (6*A00060 + 8*A00080*Q2)*Q5 + dr*(dth2*(dth2*(2*A01620*dth2*Q + Q*(2*A01420 + 4*A01440*Q2)) + (4*A01240 + 6*A01260*Q2)*Q3) + dr*(dth2*(2*A02420*dth2*Q + Q*(2*A02220 + 4*A02240*Q2)) + (4*A02040 + 6*A02060*Q2)*Q3 + dr*(dth2*(2*A03420*dth2*Q + Q*(2*A03220 + 4*A03240*Q2)) + dr*(2*A04220*dth2*Q + Q*(2*A04020 + 4*A04040*Q2) + dr*(2*A05220*dth2*Q + dr*(2*A06020*Q + 2*A07020*dr*Q) + Q*(2*A05020 + 4*A05040*Q2))) + (4*A03040 + 6*A03060*Q2)*Q3)) + (6*A01060 + 8*A01080*Q2)*Q5);\n dA_dQ[1] = Q5*(6*A10061*R + 8*A10081*Q2*R) + dth2*(Q3*(4*A10241*R + 6*A10261*Q2*R) + dth2*(2*A10621*dth2*Q*R + Q*(2*A10421*R + 4*A10441*Q2*R))) + dr*(6*A11061*Q5*R + dth2*(2*A11421*dth2*Q*R + 4*A11241*Q3*R) + dr*(Q3*(4*A12041*R + 6*A12061*Q2*R) + dth2*(2*A12421*dth2*Q*R + Q*(2*A12221*R + 4*A12241*Q2*R)) + dr*(2*A13221*dth2*Q*R + 4*A13041*Q3*R + dr*(2*A14221*dth2*Q*R + dr*(2*A15021*Q*R + 2*A16021*dr*Q*R) + Q*(2*A14021*R + 4*A14041*Q2*R)))));\n dA_dQ[2] = dth*(6*A20161*Q5*R + dth2*(2*A20521*dth2*Q*R + 4*A20341*Q3*R)) + dr*(dth*(6*A21161*Q5*R + dth2*(2*A21521*dth2*Q*R + 4*A21341*Q3*R)) + dr*(dth*(2*A22321*dth2*Q*R + 4*A22141*Q3*R) + dr*(dr*(2*A24121*dth*Q*R + 2*A25121*dr*dth*Q*R) + dth*(2*A23321*dth2*Q*R + 4*A23141*Q3*R))));\n dA_dQ[3] = dth2*(dth2*(2*A30620*dth2*Q + Q*(2*A30420 + 4*A30440*Q2)) + (4*A30240 + 6*A30260*Q2)*Q3) + (6*A30060 + 8*A30080*Q2)*Q5 + dr*(dth2*(dth2*(2*A31620*dth2*Q + Q*(2*A31420 + 4*A31440*Q2)) + (4*A31240 + 6*A31260*Q2)*Q3) + dr*(dth2*(2*A32420*dth2*Q + Q*(2*A32220 + 4*A32240*Q2)) + (4*A32040 + 6*A32060*Q2)*Q3 + dr*(dth2*(2*A33420*dth2*Q + Q*(2*A33220 + 4*A33240*Q2)) + dr*(2*A34220*dth2*Q + Q*(2*A34020 + 4*A34040*Q2) + dr*(2*A35220*dth2*Q + dr*(2*A36020*Q + 2*A37020*dr*Q) + Q*(2*A35020 + 4*A35040*Q2))) + (4*A33040 + 6*A33060*Q2)*Q3)) + (6*A31060 + 8*A31080*Q2)*Q5);\n dA_dQ[4] = dth2*(dth2*(2*A40620*dth2*Q + 4*A40440*Q3) + 6*A40260*Q5) + 8*A40080*Q7 + dr*(dth2*(dth2*(2*A41620*dth2*Q + 4*A41440*Q3) + 6*A41260*Q5) + dr*(dth2*(2*A42420*dth2*Q + 4*A42240*Q3) + 6*A42060*Q5 + dr*(dth2*(2*A43420*dth2*Q + 4*A43240*Q3) + dr*(2*A44220*dth2*Q + 4*A44040*Q3 + dr*(2*A45220*dth2*Q + dr*(2*A46020*Q + 2*A47020*dr*Q) + 4*A45040*Q3)) + 6*A43060*Q5)) + 8*A41080*Q7);\n dA_dQ[5] = dr2*(dr2*(2*A56120*dr2*dth*Q + dth*(2*A54320*dth2*Q + 4*A54140*Q3)) + dth*(dth2*(2*A52520*dth2*Q + 4*A52340*Q3) + 6*A52160*Q5)) + dth*(dth2*(dth2*(2*A50720*dth2*Q + 4*A50540*Q3) + 6*A50360*Q5) + 8*A50180*Q7);\n dA_dQ[6] = Q5*(6*A60061*R + 8*A60081*Q2*R) + dth2*(Q3*(4*A60241*R + 6*A60261*Q2*R) + dth2*(2*A60621*dth2*Q*R + Q*(2*A60421*R + 4*A60441*Q2*R))) + dr*(6*A61061*Q5*R + dth2*(2*A61421*dth2*Q*R + 4*A61241*Q3*R) + dr*(Q3*(4*A62041*R + 6*A62061*Q2*R) + dth2*(2*A62421*dth2*Q*R + Q*(2*A62221*R + 4*A62241*Q2*R)) + dr*(2*A63221*dth2*Q*R + 4*A63041*Q3*R + dr*(2*A64221*dth2*Q*R + dr*(2*A65021*Q*R + 2*A66021*dr*Q*R) + Q*(2*A64021*R + 4*A64041*Q2*R)))));\n dA_dQ[7] = dth2*(dth2*(2*A70620*dth2*Q + 4*A70440*Q3) + 6*A70260*Q5) + 8*A70080*Q7 + dr*(dth2*(dth2*(2*A71620*dth2*Q + 4*A71440*Q3) + 6*A71260*Q5) + dr*(dth2*(2*A72420*dth2*Q + 4*A72240*Q3) + 6*A72060*Q5 + dr*(dth2*(2*A73420*dth2*Q + 4*A73240*Q3) + dr*(2*A74220*dth2*Q + 4*A74040*Q3 + dr*(2*A75220*dth2*Q + dr*(2*A76020*Q + 2*A77020*dr*Q) + 4*A75040*Q3)) + 6*A73060*Q5)) + 8*A71080*Q7);\n dA_dQ[8] = dth*(6*A80161*Q5*R + dth2*(2*A80521*dth2*Q*R + 4*A80341*Q3*R)) + dr*(dth*(6*A81161*Q5*R + dth2*(2*A81521*dth2*Q*R + 4*A81341*Q3*R)) + dr*(dth*(2*A82321*dth2*Q*R + 4*A82141*Q3*R) + dr*(dr*(2*A84121*dth*Q*R + 2*A85121*dr*dth*Q*R) + dth*(2*A83321*dth2*Q*R + 4*A83141*Q3*R))));\n dA_dQ[9] = dth2*(dth2*(2*A90620*dth2*Q + Q*(2*A90420 + 4*A90440*Q2)) + (4*A90240 + 6*A90260*Q2)*Q3) + (6*A90060 + 8*A90080*Q2)*Q5 + dr*(dth2*(dth2*(2*A91620*dth2*Q + Q*(2*A91420 + 4*A91440*Q2)) + (4*A91240 + 6*A91260*Q2)*Q3) + dr*(dth2*(2*A92420*dth2*Q + Q*(2*A92220 + 4*A92240*Q2)) + (4*A92040 + 6*A92060*Q2)*Q3 + dr*(dth2*(2*A93420*dth2*Q + Q*(2*A93220 + 4*A93240*Q2)) + dr*(2*A94220*dth2*Q + Q*(2*A94020 + 4*A94040*Q2) + dr*(2*A95220*dth2*Q + dr*(2*A96020*Q + 2*A97020*dr*Q) + Q*(2*A95020 + 4*A95040*Q2))) + (4*A93040 + 6*A93060*Q2)*Q3)) + (6*A91060 + 8*A91080*Q2)*Q5);\n dA_dR[0] = 0;\n dA_dR[1] = dth2*(dth2*(Q2*(A10421 + A10441*Q2) + dth2*(A10601 + A10801*dth2 + A10621*Q2)) + (A10241 + A10261*Q2)*Q4) + (A10061 + A10081*Q2)*Q6 + dr*(dth2*(dth2*(A11601*dth2 + A11421*Q2) + A11241*Q4) + dr*(dth2*(Q2*(A12221 + A12241*Q2) + dth2*(A12401 + A12601*dth2 + A12421*Q2)) + (A12041 + A12061*Q2)*Q4 + dr*(dth2*(A13401*dth2 + A13221*Q2) + dr*(Q2*(A14021 + A14041*Q2) + dth2*(A14201 + A14401*dth2 + A14221*Q2) + dr*(A15201*dth2 + A15021*Q2 + dr*(A16001 + dr*(A17001 + A18001*dr) + A16201*dth2 + A16021*Q2))) + A13041*Q4)) + A11061*Q6);\n dA_dR[2] = dth*(dth2*(dth2*(A20701*dth2 + A20521*Q2) + A20341*Q4) + A20161*Q6) + dr*(dr*(dth*(dth2*(A22501*dth2 + A22321*Q2) + A22141*Q4) + dr*(dr*(dth*(A24301*dth2 + A24121*Q2) + dr*(dr*(A26101*dth + A27101*dr*dth) + dth*(A25301*dth2 + A25121*Q2))) + dth*(dth2*(A23501*dth2 + A23321*Q2) + A23141*Q4))) + dth*(dth2*(dth2*(A21701*dth2 + A21521*Q2) + A21341*Q4) + A21161*Q6));\n dA_dR[3] = 0;\n dA_dR[4] = 0;\n dA_dR[5] = 0;\n dA_dR[6] = dth2*(dth2*(Q2*(A60421 + A60441*Q2) + dth2*(A60601 + A60801*dth2 + A60621*Q2)) + (A60241 + A60261*Q2)*Q4) + (A60061 + A60081*Q2)*Q6 + dr*(dth2*(dth2*(A61601*dth2 + A61421*Q2) + A61241*Q4) + dr*(dth2*(Q2*(A62221 + A62241*Q2) + dth2*(A62401 + A62601*dth2 + A62421*Q2)) + (A62041 + A62061*Q2)*Q4 + dr*(dth2*(A63401*dth2 + A63221*Q2) + dr*(Q2*(A64021 + A64041*Q2) + dth2*(A64201 + A64401*dth2 + A64221*Q2) + dr*(A65201*dth2 + A65021*Q2 + dr*(A66001 + dr*(A67001 + A68001*dr) + A66201*dth2 + A66021*Q2))) + A63041*Q4)) + A61061*Q6);\n dA_dR[7] = 0;\n dA_dR[8] = dth*(dth2*(dth2*(A80701*dth2 + A80521*Q2) + A80341*Q4) + A80161*Q6) + dr*(dr*(dth*(dth2*(A82501*dth2 + A82321*Q2) + A82141*Q4) + dr*(dr*(dth*(A84301*dth2 + A84121*Q2) + dr*(dr*(A86101*dth + A87101*dr*dth) + dth*(A85301*dth2 + A85121*Q2))) + dth*(dth2*(A83501*dth2 + A83321*Q2) + A83141*Q4))) + dth*(dth2*(dth2*(A81701*dth2 + A81521*Q2) + A81341*Q4) + A81161*Q6));\n dA_dR[9] = 0;\n for(int i=0; i<10; i++)\n {\n dA_dph[i] = dA_dQ[i]*dQ_dph + dA_dR[i]*dR_dph;\n dA_dt[i] = -Omega*dA_dph[i];\n }\n\n /* d^2A/dx^2 */\n d2A_dr2[0] = dth2*(Q2*(2*A02220 + 2*A02240*Q2) + dth2*(2*A02400 + 2*A02600*dth2 + 2*A02420*Q2)) + (2*A02040 + 2*A02060*Q2)*Q4 + dr*(dth2*(Q2*(6*A03220 + 6*A03240*Q2) + dth2*(6*A03400 + 6*A03600*dth2 + 6*A03420*Q2)) + dr*(Q2*(12*A04020 + 12*A04040*Q2) + dth2*(12*A04200 + 12*A04400*dth2 + 12*A04220*Q2) + dr*(Q2*(20*A05020 + 20*A05040*Q2) + dth2*(20*A05200 + 20*A05400*dth2 + 20*A05220*Q2) + dr*(30*A06000 + 30*A06200*dth2 + 30*A06020*Q2 + dr*(42*A07000 + dr*(56*A08000 + 72*A09000*dr) + 42*A07200*dth2 + 42*A07020*Q2)))) + (6*A03040 + 6*A03060*Q2)*Q4);\n d2A_dr2[1] = Q4*(2*A12041*R + 2*A12061*Q2*R) + dth2*(Q2*(2*A12221*R + 2*A12241*Q2*R) + dth2*(2*A12401*R + 2*A12601*dth2*R + 2*A12421*Q2*R)) + dr*(6*A13041*Q4*R + dth2*(6*A13401*dth2*R + 6*A13221*Q2*R) + dr*(Q2*(12*A14021*R + 12*A14041*Q2*R) + dth2*(12*A14201*R + 12*A14401*dth2*R + 12*A14221*Q2*R) + dr*(20*A15201*dth2*R + 20*A15021*Q2*R + dr*(30*A16001*R + 30*A16201*dth2*R + 30*A16021*Q2*R + dr*(42*A17001*R + 56*A18001*dr*R)))));\n d2A_dr2[2] = dth*(2*A22141*Q4*R + dth2*(2*A22501*dth2*R + 2*A22321*Q2*R)) + dr*(dth*(6*A23141*Q4*R + dth2*(6*A23501*dth2*R + 6*A23321*Q2*R)) + dr*(dth*(12*A24301*dth2*R + 12*A24121*Q2*R) + dr*(dr*(30*A26101*dth*R + 42*A27101*dr*dth*R) + dth*(20*A25301*dth2*R + 20*A25121*Q2*R))));\n d2A_dr2[3] = dth2*(Q2*(2*A32220 + 2*A32240*Q2) + dth2*(2*A32400 + 2*A32600*dth2 + 2*A32420*Q2)) + (2*A32040 + 2*A32060*Q2)*Q4 + dr*(dth2*(Q2*(6*A33220 + 6*A33240*Q2) + dth2*(6*A33400 + 6*A33600*dth2 + 6*A33420*Q2)) + dr*(Q2*(12*A34020 + 12*A34040*Q2) + dth2*(12*A34200 + 12*A34400*dth2 + 12*A34220*Q2) + dr*(Q2*(20*A35020 + 20*A35040*Q2) + dth2*(20*A35200 + 20*A35400*dth2 + 20*A35220*Q2) + dr*(30*A36000 + 30*A36200*dth2 + 30*A36020*Q2 + dr*(42*A37000 + dr*(56*A38000 + 72*A39000*dr) + 42*A37200*dth2 + 42*A37020*Q2)))) + (6*A33040 + 6*A33060*Q2)*Q4);\n d2A_dr2[4] = dth2*(dth2*(2*A42600*dth2 + 2*A42420*Q2) + 2*A42240*Q4) + 2*A42060*Q6 + dr*(dth2*(dth2*(6*A43600*dth2 + 6*A43420*Q2) + 6*A43240*Q4) + dr*(dth2*(12*A44400*dth2 + 12*A44220*Q2) + 12*A44040*Q4 + dr*(dth2*(20*A45400*dth2 + 20*A45220*Q2) + dr*(30*A46200*dth2 + 30*A46020*Q2 + dr*(dr*(56*A48000 + 72*A49000*dr) + 42*A47200*dth2 + 42*A47020*Q2)) + 20*A45040*Q4)) + 6*A43060*Q6);\n d2A_dr2[5] = dr2*(dr2*(56*A58100*dr2*dth + dth*(30*A56300*dth2 + 30*A56120*Q2)) + dth*(dth2*(12*A54500*dth2 + 12*A54320*Q2) + 12*A54140*Q4)) + dth*(dth2*(dth2*(2*A52700*dth2 + 2*A52520*Q2) + 2*A52340*Q4) + 2*A52160*Q6);\n d2A_dr2[6] = Q4*(2*A62041*R + 2*A62061*Q2*R) + dth2*(Q2*(2*A62221*R + 2*A62241*Q2*R) + dth2*(2*A62401*R + 2*A62601*dth2*R + 2*A62421*Q2*R)) + dr*(6*A63041*Q4*R + dth2*(6*A63401*dth2*R + 6*A63221*Q2*R) + dr*(Q2*(12*A64021*R + 12*A64041*Q2*R) + dth2*(12*A64201*R + 12*A64401*dth2*R + 12*A64221*Q2*R) + dr*(20*A65201*dth2*R + 20*A65021*Q2*R + dr*(30*A66001*R + 30*A66201*dth2*R + 30*A66021*Q2*R + dr*(42*A67001*R + 56*A68001*dr*R)))));\n d2A_dr2[7] = dth2*(dth2*(2*A72600*dth2 + 2*A72420*Q2) + 2*A72240*Q4) + 2*A72060*Q6 + dr*(dth2*(dth2*(6*A73600*dth2 + 6*A73420*Q2) + 6*A73240*Q4) + dr*(dth2*(12*A74400*dth2 + 12*A74220*Q2) + 12*A74040*Q4 + dr*(dth2*(20*A75400*dth2 + 20*A75220*Q2) + dr*(30*A76200*dth2 + 30*A76020*Q2 + dr*(dr*(56*A78000 + 72*A79000*dr) + 42*A77200*dth2 + 42*A77020*Q2)) + 20*A75040*Q4)) + 6*A73060*Q6);\n d2A_dr2[8] = dth*(2*A82141*Q4*R + dth2*(2*A82501*dth2*R + 2*A82321*Q2*R)) + dr*(dth*(6*A83141*Q4*R + dth2*(6*A83501*dth2*R + 6*A83321*Q2*R)) + dr*(dth*(12*A84301*dth2*R + 12*A84121*Q2*R) + dr*(dr*(30*A86101*dth*R + 42*A87101*dr*dth*R) + dth*(20*A85301*dth2*R + 20*A85121*Q2*R))));\n d2A_dr2[9] = dth2*(Q2*(2*A92220 + 2*A92240*Q2) + dth2*(2*A92400 + 2*A92600*dth2 + 2*A92420*Q2)) + (2*A92040 + 2*A92060*Q2)*Q4 + dr*(dth2*(Q2*(6*A93220 + 6*A93240*Q2) + dth2*(6*A93400 + 6*A93600*dth2 + 6*A93420*Q2)) + dr*(Q2*(12*A94020 + 12*A94040*Q2) + dth2*(12*A94200 + 12*A94400*dth2 + 12*A94220*Q2) + dr*(Q2*(20*A95020 + 20*A95040*Q2) + dth2*(20*A95200 + 20*A95400*dth2 + 20*A95220*Q2) + dr*(30*A96000 + 30*A96200*dth2 + 30*A96020*Q2 + dr*(42*A97000 + dr*(56*A98000 + 72*A99000*dr) + 42*A97200*dth2 + 42*A97020*Q2)))) + (6*A93040 + 6*A93060*Q2)*Q4);\n d2A_dth2[0] = dth2*(Q2*(12*A00420 + 12*A00440*Q2) + dth2*(30*A00600 + 56*A00800*dth2 + 30*A00620*Q2)) + (2*A00240 + 2*A00260*Q2)*Q4 + dr*(dth2*(Q2*(12*A01420 + 12*A01440*Q2) + dth2*(30*A01600 + 56*A01800*dth2 + 30*A01620*Q2)) + dr*(Q2*(2*A02220 + 2*A02240*Q2) + dth2*(12*A02400 + 30*A02600*dth2 + 12*A02420*Q2) + dr*(Q2*(2*A03220 + 2*A03240*Q2) + dth2*(12*A03400 + 30*A03600*dth2 + 12*A03420*Q2) + dr*(2*A04200 + 12*A04400*dth2 + 2*A04220*Q2 + dr*(2*A05200 + dr*(2*A06200 + 2*A07200*dr) + 12*A05400*dth2 + 2*A05220*Q2)))) + (2*A01240 + 2*A01260*Q2)*Q4);\n d2A_dth2[1] = Q4*(2*A10241*R + 2*A10261*Q2*R) + dth2*(Q2*(12*A10421*R + 12*A10441*Q2*R) + dth2*(30*A10601*R + 56*A10801*dth2*R + 30*A10621*Q2*R)) + dr*(2*A11241*Q4*R + dth2*(30*A11601*dth2*R + 12*A11421*Q2*R) + dr*(Q2*(2*A12221*R + 2*A12241*Q2*R) + dth2*(12*A12401*R + 30*A12601*dth2*R + 12*A12421*Q2*R) + dr*(12*A13401*dth2*R + 2*A13221*Q2*R + dr*(2*A14201*R + 12*A14401*dth2*R + 2*A14221*Q2*R + dr*(2*A15201*R + 2*A16201*dr*R)))));\n d2A_dth2[2] = dth*(6*A20341*Q4*R + dth2*(42*A20701*dth2*R + 20*A20521*Q2*R)) + dr*(dth*(6*A21341*Q4*R + dth2*(42*A21701*dth2*R + 20*A21521*Q2*R)) + dr*(dth*(20*A22501*dth2*R + 6*A22321*Q2*R) + dr*(dr*(6*A24301*dth*R + 6*A25301*dr*dth*R) + dth*(20*A23501*dth2*R + 6*A23321*Q2*R))));\n d2A_dth2[3] = dth2*(Q2*(12*A30420 + 12*A30440*Q2) + dth2*(30*A30600 + 56*A30800*dth2 + 30*A30620*Q2)) + (2*A30240 + 2*A30260*Q2)*Q4 + dr*(dth2*(Q2*(12*A31420 + 12*A31440*Q2) + dth2*(30*A31600 + 56*A31800*dth2 + 30*A31620*Q2)) + dr*(Q2*(2*A32220 + 2*A32240*Q2) + dth2*(12*A32400 + 30*A32600*dth2 + 12*A32420*Q2) + dr*(Q2*(2*A33220 + 2*A33240*Q2) + dth2*(12*A33400 + 30*A33600*dth2 + 12*A33420*Q2) + dr*(2*A34200 + 12*A34400*dth2 + 2*A34220*Q2 + dr*(2*A35200 + dr*(2*A36200 + 2*A37200*dr) + 12*A35400*dth2 + 2*A35220*Q2)))) + (2*A31240 + 2*A31260*Q2)*Q4);\n d2A_dth2[4] = dth2*(dth2*(56*A40800*dth2 + 30*A40620*Q2) + 12*A40440*Q4) + 2*A40260*Q6 + dr*(dth2*(dth2*(56*A41800*dth2 + 30*A41620*Q2) + 12*A41440*Q4) + dr*(dth2*(30*A42600*dth2 + 12*A42420*Q2) + 2*A42240*Q4 + dr*(dth2*(30*A43600*dth2 + 12*A43420*Q2) + dr*(12*A44400*dth2 + 2*A44220*Q2 + dr*(dr*(2*A46200 + 2*A47200*dr) + 12*A45400*dth2 + 2*A45220*Q2)) + 2*A43240*Q4)) + 2*A41260*Q6);\n d2A_dth2[5] = dr2*(dr2*(6*A56300*dr2*dth + dth*(20*A54500*dth2 + 6*A54320*Q2)) + dth*(dth2*(42*A52700*dth2 + 20*A52520*Q2) + 6*A52340*Q4)) + dth*(dth2*(dth2*(72*A50900*dth2 + 42*A50720*Q2) + 20*A50540*Q4) + 6*A50360*Q6);\n d2A_dth2[6] = Q4*(2*A60241*R + 2*A60261*Q2*R) + dth2*(Q2*(12*A60421*R + 12*A60441*Q2*R) + dth2*(30*A60601*R + 56*A60801*dth2*R + 30*A60621*Q2*R)) + dr*(2*A61241*Q4*R + dth2*(30*A61601*dth2*R + 12*A61421*Q2*R) + dr*(Q2*(2*A62221*R + 2*A62241*Q2*R) + dth2*(12*A62401*R + 30*A62601*dth2*R + 12*A62421*Q2*R) + dr*(12*A63401*dth2*R + 2*A63221*Q2*R + dr*(2*A64201*R + 12*A64401*dth2*R + 2*A64221*Q2*R + dr*(2*A65201*R + 2*A66201*dr*R)))));\n d2A_dth2[7] = dth2*(dth2*(56*A70800*dth2 + 30*A70620*Q2) + 12*A70440*Q4) + 2*A70260*Q6 + dr*(dth2*(dth2*(56*A71800*dth2 + 30*A71620*Q2) + 12*A71440*Q4) + dr*(dth2*(30*A72600*dth2 + 12*A72420*Q2) + 2*A72240*Q4 + dr*(dth2*(30*A73600*dth2 + 12*A73420*Q2) + dr*(12*A74400*dth2 + 2*A74220*Q2 + dr*(dr*(2*A76200 + 2*A77200*dr) + 12*A75400*dth2 + 2*A75220*Q2)) + 2*A73240*Q4)) + 2*A71260*Q6);\n d2A_dth2[8] = dth*(6*A80341*Q4*R + dth2*(42*A80701*dth2*R + 20*A80521*Q2*R)) + dr*(dth*(6*A81341*Q4*R + dth2*(42*A81701*dth2*R + 20*A81521*Q2*R)) + dr*(dth*(20*A82501*dth2*R + 6*A82321*Q2*R) + dr*(dr*(6*A84301*dth*R + 6*A85301*dr*dth*R) + dth*(20*A83501*dth2*R + 6*A83321*Q2*R))));\n d2A_dth2[9] = dth2*(Q2*(12*A90420 + 12*A90440*Q2) + dth2*(30*A90600 + 56*A90800*dth2 + 30*A90620*Q2)) + (2*A90240 + 2*A90260*Q2)*Q4 + dr*(dth2*(Q2*(12*A91420 + 12*A91440*Q2) + dth2*(30*A91600 + 56*A91800*dth2 + 30*A91620*Q2)) + dr*(Q2*(2*A92220 + 2*A92240*Q2) + dth2*(12*A92400 + 30*A92600*dth2 + 12*A92420*Q2) + dr*(Q2*(2*A93220 + 2*A93240*Q2) + dth2*(12*A93400 + 30*A93600*dth2 + 12*A93420*Q2) + dr*(2*A94200 + 12*A94400*dth2 + 2*A94220*Q2 + dr*(2*A95200 + dr*(2*A96200 + 2*A97200*dr) + 12*A95400*dth2 + 2*A95220*Q2)))) + (2*A91240 + 2*A91260*Q2)*Q4);\n d2A_dQ2[0] = dth2*(Q2*(12*A00240 + 30*A00260*Q2) + dth2*(2*A00420 + 2*A00620*dth2 + 12*A00440*Q2)) + (30*A00060 + 56*A00080*Q2)*Q4 + dr*(dth2*(Q2*(12*A01240 + 30*A01260*Q2) + dth2*(2*A01420 + 2*A01620*dth2 + 12*A01440*Q2)) + dr*(Q2*(12*A02040 + 30*A02060*Q2) + dth2*(2*A02220 + 2*A02420*dth2 + 12*A02240*Q2) + dr*(Q2*(12*A03040 + 30*A03060*Q2) + dth2*(2*A03220 + 2*A03420*dth2 + 12*A03240*Q2) + dr*(2*A04020 + 2*A04220*dth2 + 12*A04040*Q2 + dr*(2*A05020 + dr*(2*A06020 + 2*A07020*dr) + 2*A05220*dth2 + 12*A05040*Q2)))) + (30*A01060 + 56*A01080*Q2)*Q4);\n d2A_dQ2[1] = Q4*(30*A10061*R + 56*A10081*Q2*R) + dth2*(Q2*(12*A10241*R + 30*A10261*Q2*R) + dth2*(2*A10421*R + 2*A10621*dth2*R + 12*A10441*Q2*R)) + dr*(30*A11061*Q4*R + dth2*(2*A11421*dth2*R + 12*A11241*Q2*R) + dr*(Q2*(12*A12041*R + 30*A12061*Q2*R) + dth2*(2*A12221*R + 2*A12421*dth2*R + 12*A12241*Q2*R) + dr*(2*A13221*dth2*R + 12*A13041*Q2*R + dr*(2*A14021*R + 2*A14221*dth2*R + 12*A14041*Q2*R + dr*(2*A15021*R + 2*A16021*dr*R)))));\n d2A_dQ2[2] = dth*(30*A20161*Q4*R + dth2*(2*A20521*dth2*R + 12*A20341*Q2*R)) + dr*(dth*(30*A21161*Q4*R + dth2*(2*A21521*dth2*R + 12*A21341*Q2*R)) + dr*(dth*(2*A22321*dth2*R + 12*A22141*Q2*R) + dr*(dr*(2*A24121*dth*R + 2*A25121*dr*dth*R) + dth*(2*A23321*dth2*R + 12*A23141*Q2*R))));\n d2A_dQ2[3] = dth2*(Q2*(12*A30240 + 30*A30260*Q2) + dth2*(2*A30420 + 2*A30620*dth2 + 12*A30440*Q2)) + (30*A30060 + 56*A30080*Q2)*Q4 + dr*(dth2*(Q2*(12*A31240 + 30*A31260*Q2) + dth2*(2*A31420 + 2*A31620*dth2 + 12*A31440*Q2)) + dr*(Q2*(12*A32040 + 30*A32060*Q2) + dth2*(2*A32220 + 2*A32420*dth2 + 12*A32240*Q2) + dr*(Q2*(12*A33040 + 30*A33060*Q2) + dth2*(2*A33220 + 2*A33420*dth2 + 12*A33240*Q2) + dr*(2*A34020 + 2*A34220*dth2 + 12*A34040*Q2 + dr*(2*A35020 + dr*(2*A36020 + 2*A37020*dr) + 2*A35220*dth2 + 12*A35040*Q2)))) + (30*A31060 + 56*A31080*Q2)*Q4);\n d2A_dQ2[4] = dth2*(dth2*(2*A40620*dth2 + 12*A40440*Q2) + 30*A40260*Q4) + 56*A40080*Q6 + dr*(dth2*(dth2*(2*A41620*dth2 + 12*A41440*Q2) + 30*A41260*Q4) + dr*(dth2*(2*A42420*dth2 + 12*A42240*Q2) + 30*A42060*Q4 + dr*(dth2*(2*A43420*dth2 + 12*A43240*Q2) + dr*(2*A44220*dth2 + 12*A44040*Q2 + dr*(dr*(2*A46020 + 2*A47020*dr) + 2*A45220*dth2 + 12*A45040*Q2)) + 30*A43060*Q4)) + 56*A41080*Q6);\n d2A_dQ2[5] = dr2*(dr2*(2*A56120*dr2*dth + dth*(2*A54320*dth2 + 12*A54140*Q2)) + dth*(dth2*(2*A52520*dth2 + 12*A52340*Q2) + 30*A52160*Q4)) + dth*(dth2*(dth2*(2*A50720*dth2 + 12*A50540*Q2) + 30*A50360*Q4) + 56*A50180*Q6);\n d2A_dQ2[6] = Q4*(30*A60061*R + 56*A60081*Q2*R) + dth2*(Q2*(12*A60241*R + 30*A60261*Q2*R) + dth2*(2*A60421*R + 2*A60621*dth2*R + 12*A60441*Q2*R)) + dr*(30*A61061*Q4*R + dth2*(2*A61421*dth2*R + 12*A61241*Q2*R) + dr*(Q2*(12*A62041*R + 30*A62061*Q2*R) + dth2*(2*A62221*R + 2*A62421*dth2*R + 12*A62241*Q2*R) + dr*(2*A63221*dth2*R + 12*A63041*Q2*R + dr*(2*A64021*R + 2*A64221*dth2*R + 12*A64041*Q2*R + dr*(2*A65021*R + 2*A66021*dr*R)))));\n d2A_dQ2[7] = dth2*(dth2*(2*A70620*dth2 + 12*A70440*Q2) + 30*A70260*Q4) + 56*A70080*Q6 + dr*(dth2*(dth2*(2*A71620*dth2 + 12*A71440*Q2) + 30*A71260*Q4) + dr*(dth2*(2*A72420*dth2 + 12*A72240*Q2) + 30*A72060*Q4 + dr*(dth2*(2*A73420*dth2 + 12*A73240*Q2) + dr*(2*A74220*dth2 + 12*A74040*Q2 + dr*(dr*(2*A76020 + 2*A77020*dr) + 2*A75220*dth2 + 12*A75040*Q2)) + 30*A73060*Q4)) + 56*A71080*Q6);\n d2A_dQ2[8] = dth*(30*A80161*Q4*R + dth2*(2*A80521*dth2*R + 12*A80341*Q2*R)) + dr*(dth*(30*A81161*Q4*R + dth2*(2*A81521*dth2*R + 12*A81341*Q2*R)) + dr*(dth*(2*A82321*dth2*R + 12*A82141*Q2*R) + dr*(dr*(2*A84121*dth*R + 2*A85121*dr*dth*R) + dth*(2*A83321*dth2*R + 12*A83141*Q2*R))));\n d2A_dQ2[9] = dth2*(Q2*(12*A90240 + 30*A90260*Q2) + dth2*(2*A90420 + 2*A90620*dth2 + 12*A90440*Q2)) + (30*A90060 + 56*A90080*Q2)*Q4 + dr*(dth2*(Q2*(12*A91240 + 30*A91260*Q2) + dth2*(2*A91420 + 2*A91620*dth2 + 12*A91440*Q2)) + dr*(Q2*(12*A92040 + 30*A92060*Q2) + dth2*(2*A92220 + 2*A92420*dth2 + 12*A92240*Q2) + dr*(Q2*(12*A93040 + 30*A93060*Q2) + dth2*(2*A93220 + 2*A93420*dth2 + 12*A93240*Q2) + dr*(2*A94020 + 2*A94220*dth2 + 12*A94040*Q2 + dr*(2*A95020 + dr*(2*A96020 + 2*A97020*dr) + 2*A95220*dth2 + 12*A95040*Q2)))) + (30*A91060 + 56*A91080*Q2)*Q4);\n d2A_dQR[0] = 0;\n d2A_dQR[1] = dth2*(dth2*(2*A10621*dth2*Q + Q*(2*A10421 + 4*A10441*Q2)) + (4*A10241 + 6*A10261*Q2)*Q3) + (6*A10061 + 8*A10081*Q2)*Q5 + dr*(dth2*(2*A11421*dth2*Q + 4*A11241*Q3) + dr*(dth2*(2*A12421*dth2*Q + Q*(2*A12221 + 4*A12241*Q2)) + (4*A12041 + 6*A12061*Q2)*Q3 + dr*(2*A13221*dth2*Q + dr*(2*A14221*dth2*Q + dr*(2*A15021*Q + 2*A16021*dr*Q) + Q*(2*A14021 + 4*A14041*Q2)) + 4*A13041*Q3)) + 6*A11061*Q5);\n d2A_dQR[2] = dth*(dth2*(2*A20521*dth2*Q + 4*A20341*Q3) + 6*A20161*Q5) + dr*(dr*(dth*(2*A22321*dth2*Q + 4*A22141*Q3) + dr*(dr*(2*A24121*dth*Q + 2*A25121*dr*dth*Q) + dth*(2*A23321*dth2*Q + 4*A23141*Q3))) + dth*(dth2*(2*A21521*dth2*Q + 4*A21341*Q3) + 6*A21161*Q5));\n d2A_dQR[3] = 0;\n d2A_dQR[4] = 0;\n d2A_dQR[5] = 0;\n d2A_dQR[6] = dth2*(dth2*(2*A60621*dth2*Q + Q*(2*A60421 + 4*A60441*Q2)) + (4*A60241 + 6*A60261*Q2)*Q3) + (6*A60061 + 8*A60081*Q2)*Q5 + dr*(dth2*(2*A61421*dth2*Q + 4*A61241*Q3) + dr*(dth2*(2*A62421*dth2*Q + Q*(2*A62221 + 4*A62241*Q2)) + (4*A62041 + 6*A62061*Q2)*Q3 + dr*(2*A63221*dth2*Q + dr*(2*A64221*dth2*Q + dr*(2*A65021*Q + 2*A66021*dr*Q) + Q*(2*A64021 + 4*A64041*Q2)) + 4*A63041*Q3)) + 6*A61061*Q5);\n d2A_dQR[7] = 0;\n d2A_dQR[8] = dth*(dth2*(2*A80521*dth2*Q + 4*A80341*Q3) + 6*A80161*Q5) + dr*(dr*(dth*(2*A82321*dth2*Q + 4*A82141*Q3) + dr*(dr*(2*A84121*dth*Q + 2*A85121*dr*dth*Q) + dth*(2*A83321*dth2*Q + 4*A83141*Q3))) + dth*(dth2*(2*A81521*dth2*Q + 4*A81341*Q3) + 6*A81161*Q5));\n d2A_dQR[9] = 0;\n for(int i=0; i<10; i++)\n {\n d2A_dph2[i] = dA_dR[i]*d2R_dph2 + dA_dQ[i]*d2Q_dph2 + 2.0*dQ_dph*dR_dph*d2A_dQR[i] + dQ_dph*dQ_dph*d2A_dQ2[i];\n d2A_dtph[i] = -Omega*d2A_dph2[i];\n d2A_dt2[i] = Omega*Omega*d2A_dph2[i];\n }\n\n /* s */\n s2 = alpha20*dr2 + alpha02*dth2 + beta*Q2;\n\n /* ds/dx */\n ds2_dr = 2*alpha20*dr;\n ds2_dth = 2*alpha02*dth;\n ds2_dQ = 2*beta*Q;\n ds2_dph = ds2_dQ*dQ_dph;\n ds2_dt = -Omega*ds2_dph;\n\n /* d^2s/dx^2 */\n d2s2_dr2 = 2*alpha20;\n d2s2_dth2 = 2*alpha02;\n d2s2_dQ2 = 2*beta;\n d2s2_dph2 = ds2_dQ*d2Q_dph2 + dQ_dph*dQ_dph*d2s2_dQ2;\n d2s2_dtph = -Omega*d2s2_dph2;\n d2s2_dt2 = Omega*Omega*d2s2_dph2;\n\n sqrts2 = sqrt(s2);\n s2_15 = s2*sqrts2;\n s2_25 = s2*s2_15;\n s2_35 = s2*s2_25;\n s2_45 = s2*s2_35;\n s2_55 = s2*s2_45;\n\n /* hS */\n for(int i=0; i<10; i++)\n {\n hS[i] = A[i]/s2_35;\n }\n\n /* First derivatives of PhiS */\n for(int i=0; i<10; i++)\n {\n dhS_dt[i] = (-7*ds2_dt*A[i] + 2*dA_dt[i]*s2)/(2.*s2_45);\n dhS_dr[i] = (-7*ds2_dr*A[i] + 2*dA_dr[i]*s2) /(2.*s2_45);\n dhS_dth[i] = (-7*ds2_dth*A[i] + 2*dA_dth[i]*s2)/(2.*s2_45);\n dhS_dph[i] = (-7*ds2_dph*A[i] + 2*dA_dph[i]*s2)/(2.*s2_45);\n }\n \n /* Second derivatives of hS */\n for(int i=0; i<10; i++)\n {\n d2hS_dr2[i] =\n (63*ds2_dr*ds2_dr*A[i] - 14*s2*(2*dA_dr[i]*ds2_dr + d2s2_dr2*A[i]) + 4*d2A_dr2[i]*s2*s2)/(4.*s2_55);\n d2hS_dth2[i] =\n (63*ds2_dth*ds2_dth*A[i] - 14*s2*(2*dA_dth[i]*ds2_dth + d2s2_dth2*A[i]) + 4*d2A_dth2[i]*s2*s2)/(4.*s2_55);\n d2hS_dph2[i] =\n (63*ds2_dph*ds2_dph*A[i] - 14*s2*(2*dA_dph[i]*ds2_dph + d2s2_dph2*A[i]) + 4*d2A_dph2[i]*s2*s2)/(4.*s2_55);\n d2hS_dt2[i] =\n (63*ds2_dt*ds2_dt*A[i] - 14*s2*(2*dA_dt[i]*ds2_dt + d2s2_dt2*A[i]) + 4*d2A_dt2[i]*s2*s2)/(4.*s2_55);\n d2hS_dtph[i] =\n (63*ds2_dph*ds2_dt*A[i] - 14*s2*(dA_dt[i]*ds2_dph + dA_dph[i]*ds2_dt + d2s2_dtph*A[i]) + 4*d2A_dtph[i]*s2*s2)/(4.*s2_55);\n d2hS_dtr[i] = NAN;\n d2hS_dtth[i] = NAN;\n d2hS_drth[i] = NAN;\n d2hS_drph[i] = NAN;\n d2hS_dthph[i] = NAN;\n }\n\n double a10, a2, a2p2r2pa2c2th2, a2p2r2pa2c2th3, a2p2r2pa2c2th4, a2p2r2pa2c2th5, a2pr2m2Mr2, a2pr2m2Mr3, a3, a4, a6, a8, costh2, costh4, M2, M3, r10, r11, r2, r2pa2cth22, r2pa2cth23, r3, r4, r5, r6, r7, r8, r9, sinth2, sinth3, sinth4, sin4th, cos2th, cos4th, cos6th, cos8th, cos10th, sin2th, r2pa2cth2, a2p2r2pa2c2th, a2pr2m2Mr, costh, sinth, tanth;\n\n M2 = M*M;\n M3 = M2*M;\n\n a2 = a*a;\n a3 = a2*a;\n a4 = a2*a2;\n a6 = a4*a2;\n a8 = a4*a4;\n a10 = a6*a4;\n\n r2 = r*r;\n r3 = r2*r;\n r4 = r2*r2;\n r5 = r3*r2;\n r6 = r3*r3;\n r7 = r4*r3;\n r8 = r4*r4;\n r9 = r5*r4;\n r10 = r5*r5;\n r11 = r6*r5;\n\n sinth = sin(theta);\n costh = cos(theta);\n tanth = sinth/costh;\n\n costh2 = costh*costh;\n costh4 = costh2*costh2;\n sinth2 = sinth*sinth;\n sinth3 = sinth2*sinth;\n sinth4 = sinth2*sinth2;\n\n cos2th = costh2 - sinth2;\n sin2th = 2.0*costh*sinth;\n sin4th = 2.0*cos2th*sin2th;\n cos4th = cos2th*cos2th - sin2th*sin2th;\n cos6th = cos2th*cos2th*cos2th - 3.0*cos2th*sin2th*sin2th;\n cos8th = cos4th*cos4th - sin4th*sin4th;\n cos10th = cos2th*cos2th*cos2th*cos2th*cos2th - 10.0*cos2th*cos2th*cos2th*sin2th*sin2th + 5.0*cos2th*sin2th*sin2th*sin2th*sin2th;\n\n r2pa2cth2 = a2*costh2 + r2;\n r2pa2cth22 = r2pa2cth2*r2pa2cth2;\n r2pa2cth23 = r2pa2cth22*r2pa2cth2;\n\n a2p2r2pa2c2th = a2 + a2*cos2th + 2*r2;\n a2p2r2pa2c2th2 = a2p2r2pa2c2th*a2p2r2pa2c2th;\n a2p2r2pa2c2th3 = a2p2r2pa2c2th2*a2p2r2pa2c2th;\n a2p2r2pa2c2th4 = a2p2r2pa2c2th2*a2p2r2pa2c2th2;\n a2p2r2pa2c2th5 = a2p2r2pa2c2th3*a2p2r2pa2c2th2;\n\n a2pr2m2Mr = a2 + r*(-2*M + r);\n a2pr2m2Mr2 = a2pr2m2Mr*a2pr2m2Mr;\n a2pr2m2Mr3 = a2pr2m2Mr2*a2pr2m2Mr;\n\n src[0] = (-8*a*d2hS_dtph[0]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (16*dhS_dt[1]*M*(a2 + a2*cos2th - 2*r2)*(a2 + r2))/a2p2r2pa2c2th3 + d2hS_dth2[0]/r2pa2cth2 + (d2hS_dr2[0]*(a2 - 2*M*r + r2))/r2pa2cth2 + (4*a*dhS_dr[3]*M*(a2*costh2 - r2))/r2pa2cth23 + (4*a*dhS_dph[1]*M*(-(a2*costh2) + r2))/r2pa2cth23 - (d2hS_dt2[0]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) + (16*hS[7]*M*r*(-9*a4 + 3*a4*cos4th + 20*a2*M*r - 2*a2*cos2th*(3*a2 + 5*r*(-2*M + r)) + 2*a2*r2 - 8*M*r3 + 4*r4))/a2p2r2pa2c2th5 + (2*dhS_dr[0]*(5*a4*M - a4*cos4th*(M - r) + 3*a4*r - 16*a2*M*r2 + 8*a2*r3 + 4*a2*cos2th*(a2*(M + r) + 2*r3) - 24*M*r4 + 8*r5))/a2p2r2pa2c2th3 - (8*a2pr2m2Mr*hS[4]*M*(3*a4*M - 27*a4*r + a4*cos4th*(M + 3*r) + 40*a2*M*r2 + 4*a2*cos2th*(a2*(M - 6*r) + (10*M - 7*r)*r2) - 4*a2*r3 - 24*M*r4 + 16*r5))/a2p2r2pa2c2th5 + (16*a*hS[3]*M2*(3*a6 + 29*a4*r2 + a4*cos4th*(a2 + 7*r2) - 80*a2*M*r3 + 32*a2*r4 + 4*a2*cos2th*(a4 + 9*a2*r2 - 20*M*r3 + 6*r4) + 32*M*r5 - 8*r6))/(a2p2r2pa2c2th5*a2pr2m2Mr) + (8*hS[0]*M2*(3*a8 + 2*a6*r2 - 20*a4*M*r3 + a4*cos4th*(a4 - 2*a2*r2 + 20*M*r3 - 3*r4) - a4*r4 + 16*a2*M*r5 + 4*a2*cos2th*(a6 - 3*a2*r4 - 2*(2*M + r)*r5) + 8*a2*r6 + 8*r8))/(a2p2r2pa2c2th5*a2pr2m2Mr) - (32*a2*dhS_dt[2]*M*r*sin2th)/a2p2r2pa2c2th3 - (96*a2*a2pr2m2Mr*hS[5]*M*(a2 + a2*cos2th - 6*r2)*sin2th)/a2p2r2pa2c2th5 + (d2hS_dph2[0]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (2*hS[9]*M*(-2*a6*M + a6*cos6th*M + 30*a6*r + 3*a6*cos6th*r - 200*a4*M*r2 + 2*a4*cos4th*(a2*(M + 9*r) + 2*(-14*M + 5*r)*r2) + 60*a4*r3 + 320*a2*M2*r3 - a2*cos2th*(a4*(M - 45*r) + 16*a2*(16*M - 5*r)*r2 - 16*(20*M2 - 11*M*r + r2)*r3) - 208*a2*M*r4 + 16*a2*r5 - 128*M2*r5 + 128*M*r6 - 32*r7))/(a2p2r2pa2c2th5*a2pr2m2Mr*sinth2) - (64*a*dhS_dph[2]*M*r)/(a2p2r2pa2c2th3*tanth) + (64*a*dhS_dth[3]*M*r)/(a2p2r2pa2c2th3*tanth) + (dhS_dth[0]*(3*a4 + a4*cos4th + 32*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-4*M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth);\n src[1] = (-8*a*d2hS_dtph[1]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dt[4]*M*(a2 + a2*cos2th - 2*r2)*(a2 + r2))/a2p2r2pa2c2th3 + d2hS_dth2[1]/r2pa2cth2 + (d2hS_dr2[1]*(a2 - 2*M*r + r2))/r2pa2cth2 - (2*dhS_dth[2]*r)/r2pa2cth22 + (2*a*dhS_dr[6]*M*(a2*costh2 - r2))/r2pa2cth23 + (2*a*dhS_dph[4]*M*(-(a2*costh2) + r2))/r2pa2cth23 - (4*a*dhS_dph[0]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (4*a*dhS_dt[3]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (d2hS_dt2[1]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) + (4*dhS_dr[1]*(-(a4*M) - a4*cos4th*(M - r) + a4*r - 6*a2*M*r2 - 2*a2*cos2th*(a2*(M - r) + (M - 3*r)*r2) + 2*a2*r3 - 4*M*r4 + 4*r5))/a2p2r2pa2c2th3 - (8*a*hS[6]*M*(3*a4*M + a4*cos4th*(M - r) - 23*a4*r + 40*a2*M*r2 + 4*a2*cos2th*(a2*(M - 6*r) + 5*(2*M - r)*r2) - 12*a2*r3 - 24*M*r4 + 16*r5))/(a2p2r2pa2c2th4*a2pr2m2Mr) - (4*dhS_dt[0]*M*(a6 + a2*(4*M - 3*r)*r3 + a2*cos2th*(a4 + 2*a2*r2 + (-4*M + r)*r3) - 2*r6))/(a2p2r2pa2c2th2*a2pr2m2Mr2) + (hS[1]*(10*a8 + a8*cos6th - 24*a6*M2 + 116*a6*M*r - 2*a6*cos6th*M*r + 22*a6*r2 + a6*cos6th*r2 - 248*a4*M2*r2 + 2*a4*cos4th*(3*a4 + 2*r2*(6*M2 - 4*M*r + r2) + a2*(-4*M2 - 10*M*r + 5*r2)) + 208*a4*M*r3 - 4*a4*r4 - 128*a2*M2*r4 + a2*cos2th*(15*a6 - 32*a2*M*(7*M - 8*r)*r2 + a4*(-32*M2 + 98*M*r + 31*r2) - 16*(20*M2 - 12*M*r + r2)*r4) + 128*a2*M*r5 - 48*a2*r6 - 64*M2*r6 + 64*M*r7 - 32*r8))/(a2p2r2pa2c2th4*a2pr2m2Mr) - (16*a2*dhS_dt[5]*M*r*sin2th)/a2p2r2pa2c2th3 - (32*a3*hS[8]*M*(a2 + a2*cos2th - 4*r2)*sin2th)/(a2p2r2pa2c2th4*a2pr2m2Mr) - (2*a2*costh*dhS_dr[2]*sinth)/r2pa2cth22 + (d2hS_dph2[1]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (dhS_dph[3]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 20*a2*M*r2 + 4*a2*cos2th*r*(a2 - 3*M*r + 2*r2) + 8*a2*r3 + 32*M2*r3 - 32*M*r4 + 8*r5))/(a2p2r2pa2c2th2*a2pr2m2Mr2*sinth2) - (32*a*dhS_dph[5]*M*r)/(a2p2r2pa2c2th3*tanth) + (32*a*dhS_dth[6]*M*r)/(a2p2r2pa2c2th3*tanth) + (dhS_dth[1]*(5*a4 - a4*cos4th + 16*a2*M*r + 4*a2*cos2th*(a2 - 4*M*r) + 16*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (4*hS[2]*(4*a6*M + 3*a6*r - 34*a4*M*r2 + a4*cos4th*(a2*(-4*M + r) + (-6*M + r)*r2) + 11*a4*r3 + 4*a2*cos2th*r*(a4 + 3*a2*r*(2*M + r) + 2*(2*M + r)*r3) - 48*a2*M*r4 + 16*a2*r5 - 16*M*r6 + 8*r7))/(a2p2r2pa2c2th4*a2pr2m2Mr*tanth);\n src[2] = (-8*a*d2hS_dtph[2]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dt[5]*M*(a2 + a2*cos2th - 2*r2)*(a2 + r2))/a2p2r2pa2c2th3 + d2hS_dth2[2]/r2pa2cth2 + (d2hS_dr2[2]*(a2 - 2*M*r + r2))/r2pa2cth2 + (2*a2pr2m2Mr*dhS_dth[1]*r)/r2pa2cth22 + (2*a*dhS_dr[8]*M*(a2*costh2 - r2))/r2pa2cth23 + (2*a*dhS_dph[5]*M*(-(a2*costh2) + r2))/r2pa2cth23 - (d2hS_dt2[2]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*a3*dhS_dph[0]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (8*a3*dhS_dt[3]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (16*a2*dhS_dt[7]*M*r*sin2th)/a2p2r2pa2c2th3 - (8*a2*dhS_dt[0]*M*r*(a2 + r2)*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (a2*a2pr2m2Mr*dhS_dr[1]*sin2th)/r2pa2cth22 + (4*a2*hS[1]*(-7*a4*M - a4*cos4th*(M - r) + 3*a4*r + 8*a2*M2*r - 4*a2*cos2th*(a2*(2*M - r) + r*(-2*M2 + 3*M*r - 2*r2)) + 28*a2*M*r2 + 8*a2*r3 - 80*M2*r3 + 32*M*r4 + 8*r5)*sin2th)/a2p2r2pa2c2th4 + (d2hS_dph2[2]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) + (8*a*hS[8]*M*r*(-a2 + 5*a2*cos4th + 4*cos2th*(a2 - r2) + 12*r2))/(a2p2r2pa2c2th4*sinth2) - (hS[2]*(15*a6 + 6*a6*cos6th + a6*cos8th + 96*a4*M*r + 16*a4*cos6th*M*r + 56*a4*r2 + 8*a4*cos6th*r2 - 160*a2*M*r3 + 8*a2*cos4th*(2*a4 + a2*r*(-12*M + 5*r) + 2*(-6*M + r)*r3) + 80*a2*r4 - 128*M*r5 + 2*cos2th*(13*a6 + a4*(-8*M*r + 44*r2) + 16*a2*(8*M + 3*r)*r3 + 64*M*r5) + 64*r6))/(4.*a2p2r2pa2c2th4*sinth2) - (8*a2*dhS_dr[2]*(-(a2*cos2th*(M - r)) + a2*(-M + r) + 2*(M + r)*r2)*sinth2)/a2p2r2pa2c2th3 - (32*a*dhS_dph[7]*M*r)/(a2p2r2pa2c2th3*tanth) + (32*a*dhS_dth[8]*M*r)/(a2p2r2pa2c2th3*tanth) - (32*a*a2pr2m2Mr*hS[6]*M*(a2 + a2*cos2th - 10*r2))/(a2p2r2pa2c2th4*tanth) + (dhS_dth[2]*(5*a4 - a4*cos4th + 16*a2*M*r + 4*a2*cos2th*(a2 - 4*M*r) + 16*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (dhS_dph[3]*(3*a4 + a4*cos4th + 4*a2*cos2th*(a2 + 2*r*(-2*M + r)) + 8*a2*r2 - 16*M*r3 + 8*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr*sinth2*tanth);\n src[3] = (-8*a*d2hS_dtph[3]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dt[6]*M*(a2 + a2*cos2th - 2*r2)*(a2 + r2))/a2p2r2pa2c2th3 + d2hS_dth2[3]/r2pa2cth2 + (d2hS_dr2[3]*(a2 - 2*M*r + r2))/r2pa2cth2 + (2*a*dhS_dr[9]*M*(a2*costh2 - r2))/r2pa2cth23 + (2*a*dhS_dph[6]*M*(-(a2*costh2) + r2))/r2pa2cth23 - (d2hS_dt2[3]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*a*hS[7]*M*r*(-3*a4 + 10*a2*M*r + 17*a2*r2 + a2*cos4th*(11*a2 - 10*M*r + 11*r2) - 8*M*r3 + 4*cos2th*(2*a4 + a2*r2 + (2*M - r)*r3) + 20*r4))/a2p2r2pa2c2th5 + (2*dhS_dph[1]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 12*a2*M*r2 + 4*a2*cos2th*r*(a2 - M*r + 2*r2) + 8*a2*r3 - 16*M*r4 + 8*r5))/a2p2r2pa2c2th3 - (4*hS[3]*M*(2*a8*M - a8*cos6th*M + 30*a8*r + 3*a8*cos6th*r - 54*a6*M*r2 - 5*a6*cos6th*M*r2 + 90*a6*r3 + 3*a6*cos6th*r3 - 80*a4*M2*r3 - 2*a4*cos4th*(a4*(M - 9*r) + a2*(21*M - 19*r)*r2 - 2*(20*M2 - 12*M*r + 5*r2)*r3) - 96*a4*M*r4 + 76*a4*r5 + 64*a2*M2*r5 + a2*cos2th*(a6*(M + 45*r) + a4*(-91*M + 125*r)*r2 + 16*a2*(-11*M + 6*r)*r4 + 16*(-4*M2 - 5*M*r + r2)*r5) + 16*a2*M*r6 - 16*a2*r7 + 64*M*r8 - 32*r9))/(a2p2r2pa2c2th5*a2pr2m2Mr) - (16*a2*dhS_dt[8]*M*r*sin2th)/a2p2r2pa2c2th3 - (16*a*a2pr2m2Mr*hS[5]*M*(-3*a4 + a4*cos4th + 26*a2*r2 - 2*a2*cos2th*(a2 + 5*r2) + 20*r4)*sin2th)/a2p2r2pa2c2th5 + (d2hS_dph2[3]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (a*hS[9]*M*(3*a6*M + a6*cos8th*(M - r) + 85*a6*r + 124*a6*cos2th*r + 4*a6*cos6th*r - 80*a4*M*r2 - 216*a4*cos2th*M*r2 - 40*a4*cos6th*M*r2 + 280*a4*r3 + 380*a4*cos2th*r3 + 4*a4*cos6th*r3 - 320*a2*M2*r3 - 4*a2*cos4th*(a4*(M - 11*r) + 2*a2*(22*M - 13*r)*r2 - 20*(4*M2 - 3*M*r + r2)*r3) - 208*a2*M*r4 - 576*a2*cos2th*M*r4 + 304*a2*r5 + 384*a2*cos2th*r5 + 256*M2*r5 - 256*cos2th*M2*r5 - 256*M*r6 - 256*cos2th*M*r6 + 64*r7 + 192*cos2th*r7))/(2.*a2p2r2pa2c2th5*a2pr2m2Mr*sinth2) - (8*a*dhS_dr[0]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*dhS_dt[1]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*a2pr2m2Mr*hS[4]*M*(3*a4*M + a4*cos4th*(M - r) - 39*a4*r + 40*a2*M*r2 + 4*a2*cos2th*(a2*(M - 10*r) + (10*M - 9*r)*r2) - 12*a2*r3 - 24*M*r4 + 32*r5)*sinth2)/a2p2r2pa2c2th5 - (8*a*hS[0]*M2*(3*a8 - 22*a6*r2 - 20*a4*M*r3 + a4*cos4th*(a4 - 10*a2*r2 + 20*M*r3 - 11*r4) - 41*a4*r4 + 16*a2*M*r5 + 4*a2*cos2th*(a6 - 8*a4*r2 - 15*a2*r4 - 2*(2*M + 3*r)*r5) + 24*a2*r6 + 40*r8)*sinth2)/(a2p2r2pa2c2th5*a2pr2m2Mr) - (32*a3*costh*dhS_dth[0]*M*r*sinth3)/a2p2r2pa2c2th3 + (32*a3*costh*dhS_dt[2]*M*r*sinth3)/a2p2r2pa2c2th3 - (2*dhS_dth[3])/(a2p2r2pa2c2th*tanth) - (32*a*dhS_dph[8]*M*r)/(a2p2r2pa2c2th3*tanth) + (32*a*dhS_dth[9]*M*r)/(a2p2r2pa2c2th3*tanth) + (2*dhS_dph[2]*(3*a4 + a4*cos4th + 8*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth);\n src[4] = (-8*a*d2hS_dtph[4]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (4*dhS_dr[4]*(3*a2*cos2th*(M - r) + a2*(3*M + r) - 2*(M + r)*r2))/a2p2r2pa2c2th2 + d2hS_dth2[4]/r2pa2cth2 + (d2hS_dr2[4]*(a2 - 2*M*r + r2))/r2pa2cth2 - (4*dhS_dth[5]*r)/r2pa2cth22 - (8*a*dhS_dph[1]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (8*a*dhS_dt[6]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (d2hS_dt2[4]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) + (2*hS[4]*(7*a6 + 3*a4*M2 + 4*a4*M*r + 10*a4*r2 - 40*a2*M2*r2 + a4*cos4th*(a2 + M2 - 4*M*r + 2*r2) + 4*a2*cos2th*(2*a4 + 2*M*(-5*M + 3*r)*r2 + a2*(M2 + r2)) + 40*a2*M*r3 - 16*a2*r4 - 56*M2*r4 + 64*M*r5 - 16*r6))/(a2p2r2pa2c2th3*a2pr2m2Mr) - (8*dhS_dt[1]*M*(a6 + a2*(4*M - 3*r)*r3 + a2*cos2th*(a4 + 2*a2*r2 + (-4*M + r)*r3) - 2*r6))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (4*a*hS[3]*M*(3*a6*M - 39*a6*r + a4*cos4th*(M - r)*(a2 - r2) + 101*a4*M*r2 - 45*a4*r3 - 48*a2*M2*r3 + 4*a2*cos2th*(a4*(M - 10*r) + a2*(25*M - 17*r)*r2 + (-12*M2 + 18*M*r - 5*r2)*r3) - 16*a2*M*r4 + 36*a2*r5 + 96*M2*r5 - 136*M*r6 + 48*r7))/(a2p2r2pa2c2th3*a2pr2m2Mr3) - (2*hS[0]*M*(3*a8*M - 27*a8*r + 62*a6*M*r2 - 58*a6*r3 - 12*a4*M2*r3 + a4*cos4th*(a4*(M + 3*r) + 2*a2*(-7*M + 3*r)*r2 + (12*M2 - 11*M*r + 3*r2)*r3) + 39*a4*M*r4 - 19*a4*r5 + 48*a2*M2*r5 + 4*a2*cos2th*(a6*(M - 6*r) + a4*(12*M - 19*r)*r2 + a2*(29*M - 20*r)*r4 + (-12*M2 + 22*M*r - 7*r2)*r5) - 56*a2*M*r6 + 28*a2*r7 - 24*M*r8 + 16*r9))/(a2p2r2pa2c2th3*a2pr2m2Mr3) - (4*a2*costh*dhS_dr[5]*sinth)/r2pa2cth22 + (d2hS_dph2[4]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (2*dhS_dph[6]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 20*a2*M*r2 + 4*a2*cos2th*r*(a2 - 3*M*r + 2*r2) + 8*a2*r3 + 32*M2*r3 - 32*M*r4 + 8*r5))/(a2p2r2pa2c2th2*a2pr2m2Mr2*sinth2) + (hS[9]*(-2*a6*M2 + a6*cos6th*M2 + 76*a6*M*r - 2*a6*cos6th*M*r + 10*a6*r2 + a6*cos6th*r2 - 248*a4*M2*r2 + 2*a4*cos4th*(a2*(M2 - 14*M*r + 3*r2) + 2*r2*(14*M2 - 12*M*r + 3*r2)) - 16*a4*M*r3 + 192*a2*M3*r3 - a2*cos2th*(a4*(M2 - 50*M*r - 15*r2) - 16*a2*r2*(-12*M2 + 2*M*r + 3*r2) - 16*r3*(12*M3 - 7*M2*r - 5*M*r2 + 3*r3)) + 36*a4*r4 + 240*a2*M2*r4 - 272*a2*M*r5 - 384*M3*r5 + 48*a2*r6 + 512*M2*r6 - 224*M*r7 + 32*r8))/(2.*a2p2r2pa2c2th3*a2pr2m2Mr3*sinth2) + (hS[7]*(3*a2*cos2th*M*r + r*(3*a2*M + 2*a2*r - 6*M*r2 + 2*r3) + 2*a4*costh2*sinth2))/(a2pr2m2Mr*r2pa2cth23) - (2*dhS_dth[4]*(-5*a2 + 3*a2*cos2th - 2*r2))/(a2p2r2pa2c2th2*tanth) + (8*hS[5]*(a2*(M - 3*r) - a2*cos2th*(M - r) + 2*(2*M - r)*r2))/(a2p2r2pa2c2th2*a2pr2m2Mr*tanth);\n src[5] = (-8*a*d2hS_dtph[5]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dr[5]*(a2*cos2th*(M - r) + a2*(M + r) - 2*M*r2))/a2p2r2pa2c2th2 + d2hS_dth2[5]/r2pa2cth2 + (d2hS_dr2[5]*(a2 - 2*M*r + r2))/r2pa2cth2 + (2*a2pr2m2Mr*dhS_dth[4]*r)/r2pa2cth22 - (2*dhS_dth[7]*r)/r2pa2cth22 - (4*a*dhS_dph[2]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (4*a*dhS_dt[8]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (d2hS_dt2[5]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (4*dhS_dt[2]*M*(a6 + a2*(4*M - 3*r)*r3 + a2*cos2th*(a4 + 2*a2*r2 + (-4*M + r)*r3) - 2*r6))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (8*a3*dhS_dph[1]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (8*a3*dhS_dt[6]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (12*a2*hS[4]*(-M + r)*sin2th)/a2p2r2pa2c2th2 - (8*a2*dhS_dt[1]*M*r*(a2 + r2)*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (a2*a2pr2m2Mr*dhS_dr[4]*sin2th)/r2pa2cth22 - (4*a2*hS[0]*M*(3*a6 - 4*a4*r*(M + 3*r) + a2*(32*M - 33*r)*r3 + a2*cos2th*(3*a4 + a2*(-4*M*r + 6*r2) + (-8*M + 3*r)*r3) + 2*(16*M - 9*r)*r5)*sin2th)/(a2p2r2pa2c2th3*a2pr2m2Mr2) - (2*a2*costh*dhS_dr[7]*sinth)/r2pa2cth22 + (d2hS_dph2[5]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (hS[5]*(a4 + 3*a4*cos4th + a4*cos6th + 8*a2*r2 - 32*M*r3 + cos2th*(3*a4 + 8*a2*r2 + 16*(2*M - r)*r3) + 24*r4))/(a2p2r2pa2c2th3*sinth2) - (dhS_dph[8]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 20*a2*M*r2 + 4*a2*cos2th*r*(a2 - 3*M*r + 2*r2) + 8*a2*r3 + 32*M2*r3 - 32*M*r4 + 8*r5))/(a2p2r2pa2c2th2*a2pr2m2Mr2*sinth2) - (8*hS[7]*r)/(a2p2r2pa2c2th2*tanth) - (2*dhS_dth[5]*(-5*a2 + 3*a2*cos2th - 2*r2))/(a2p2r2pa2c2th2*tanth) + (8*a*hS[3]*M*(-3*a6 + 5*a4*M*r + a4*cos4th*(a2 - M*r) + 20*a4*r2 - 48*a2*M*r3 - 2*a2*cos2th*(a4 - 2*a2*(M - 4*r)*r + (-16*M + 9*r)*r3) + 38*a2*r4 - 24*M*r5 + 12*r6))/(a2p2r2pa2c2th3*a2pr2m2Mr2*tanth) - (dhS_dph[6]*(3*a4 + a4*cos4th + 4*a2*cos2th*(a2 + 2*r*(-2*M + r)) + 8*a2*r2 - 16*M*r3 + 8*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr*sinth2*tanth) + (hS[9]*(-10*a6*M - a6*cos6th*M + 10*a6*r + a6*cos6th*r + 16*a4*M2*r + 92*a4*M*r2 + 36*a4*r3 - 256*a2*M2*r3 + 2*a4*cos4th*(5*a2*M + 3*a2*r - 8*M2*r - 6*M*r2 + 6*r3) + a2*cos2th*(a4*(M + 15*r) + 16*a2*(-13*M + 3*r)*r2 + 48*(8*M2 - 6*M*r + r2)*r3) + 32*a2*M*r4 + 48*a2*r5 + 128*M2*r5 - 128*M*r6 + 32*r7))/(2.*a2p2r2pa2c2th3*a2pr2m2Mr2*sinth2*tanth);\n src[6] = (-8*a*d2hS_dtph[6]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) + d2hS_dth2[6]/r2pa2cth2 + (d2hS_dr2[6]*(a2 - 2*M*r + r2))/r2pa2cth2 - (2*dhS_dth[8]*r)/r2pa2cth22 - (4*a*dhS_dph[3]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (4*a*dhS_dt[9]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (d2hS_dt2[6]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (2*dhS_dr[6]*(7*a4*M + a4*cos4th*(M - r) + a4*r - 4*a2*M*r2 + 4*a2*cos2th*(2*a2*M + (M - r)*r2) + 4*a2*r3 - 16*M*r4))/a2p2r2pa2c2th3 + (2*dhS_dph[4]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 12*a2*M*r2 + 4*a2*cos2th*r*(a2 - M*r + 2*r2) + 8*a2*r3 - 16*M*r4 + 8*r5))/a2p2r2pa2c2th3 - (4*dhS_dt[3]*M*(a6 + a2*(4*M - 3*r)*r3 + a2*cos2th*(a4 + 2*a2*r2 + (-4*M + r)*r3) - 2*r6))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (2*hS[6]*(-2*a6*M2 + a6*cos6th*M2 + 24*a6*M*r - 2*a6*cos6th*M*r + 10*a6*r2 + a6*cos6th*r2 - 40*a4*M2*r2 + 2*a4*cos4th*(a2*(M2 - 12*M*r + 3*r2) + 2*r2*(10*M2 - 9*M*r + 3*r2)) - 44*a4*M*r3 + 36*a4*r4 + 112*a2*M2*r4 - a2*cos2th*(a4*(M2 - 2*M*r - 15*r2) + 48*a2*(M - r)*r3 - 16*(M2 - 5*M*r + 3*r2)*r4) - 176*a2*M*r5 + 48*a2*r6 + 128*M2*r6 - 128*M*r7 + 32*r8))/(a2p2r2pa2c2th4*a2pr2m2Mr) + (4*a*hS[2]*M*(5*a6 - 21*a4*r2 + cos4th*(-a6 + a4*r2) - 56*a2*r4 + 4*a2*cos2th*(a4 + 3*a2*r2 + 4*r4) - 24*r6)*sin2th)/(a2p2r2pa2c2th4*a2pr2m2Mr) - (2*a2*costh*dhS_dr[8]*sinth)/r2pa2cth22 + (d2hS_dph2[6]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (dhS_dph[9]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 20*a2*M*r2 + 4*a2*cos2th*r*(a2 - 3*M*r + 2*r2) + 8*a2*r3 + 32*M2*r3 - 32*M*r4 + 8*r5))/(a2p2r2pa2c2th2*a2pr2m2Mr2*sinth2) - (8*a*dhS_dr[1]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*dhS_dt[4]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*hS[1]*M*(3*a6*M - 20*a6*r + 31*a4*M*r2 - 26*a4*r3 + a4*cos4th*(a2*M - 3*M*r2 + 2*r3) + 4*a2*cos2th*(a4*(M - 5*r) + a2*(7*M - 8*r)*r2 + (6*M - r)*r4) + 12*a2*r5 - 24*M*r6 + 24*r7)*sinth2)/(a2p2r2pa2c2th4*a2pr2m2Mr) - (32*a3*costh*dhS_dth[1]*M*r*sinth3)/a2p2r2pa2c2th3 + (32*a3*costh*dhS_dt[5]*M*r*sinth3)/a2p2r2pa2c2th3 - (dhS_dth[6]*(a4 + 3*a4*cos4th + 16*a2*M*r + 4*a2*cos2th*(a2 + 4*r*(-M + r)) + 8*r4))/(a2p2r2pa2c2th3*tanth) + (2*dhS_dph[5]*(3*a4 + a4*cos4th + 8*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (2*hS[8]*(-6*a6*M - a6*cos6th*M + 4*a6*r + a6*cos6th*r + 52*a4*M*r2 + 2*a4*cos4th*(a2*(3*M + 2*r) + (-2*M + 5*r)*r2) + 14*a4*r3 + 48*a2*M*r4 + a2*cos2th*(a4*(M + 7*r) + 8*a2*(-10*M + 3*r)*r2 + 16*(-7*M + 2*r)*r4) + 16*a2*r5 - 32*M*r6 + 16*r7))/(a2p2r2pa2c2th4*a2pr2m2Mr*tanth);\n src[7] = (-8*a*d2hS_dtph[7]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (4*dhS_dr[7]*(a2*cos2th*(M - r) + a2*(M + 3*r) + 2*(-3*M + r)*r2))/a2p2r2pa2c2th2 + d2hS_dth2[7]/r2pa2cth2 + (d2hS_dr2[7]*(a2 - 2*M*r + r2))/r2pa2cth2 + (4*a2pr2m2Mr*dhS_dth[5]*r)/r2pa2cth22 - (d2hS_dt2[7]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) + (8*a*hS[3]*M*r*(-15*a4 + a4*cos4th + 16*a2*M*r - 2*a2*cos2th*(7*a2 + r*(-8*M + 7*r)) - 2*a2*r2 - 16*M*r3 + 12*r4))/(a2p2r2pa2c2th3*a2pr2m2Mr) + (4*hS[0]*M*r*(-9*a6 + 4*a4*M*r - 7*a4*r2 + a4*cos4th*(3*a2 - 4*M*r + 3*r2) - 8*a2*M*r3 - 2*a2*cos2th*(3*a4 + 8*a2*r2 + (-4*M + 5*r)*r3) + 6*a2*r4 + 4*r6))/(a2p2r2pa2c2th3*a2pr2m2Mr) - (16*a3*dhS_dph[2]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (16*a3*dhS_dt[8]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (16*a2*hS[5]*(-M + r)*sin2th)/a2p2r2pa2c2th2 - (16*a2*dhS_dt[2]*M*r*(a2 + r2)*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (2*a2*a2pr2m2Mr*dhS_dr[5]*sin2th)/r2pa2cth22 + (d2hS_dph2[7]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (hS[7]*(6*a4 + a4*cos6th + 8*a2*r2 + 2*a2*cos4th*(5*a2 + 4*r2) + 32*M*r3 + cos2th*(15*a4 + 48*a2*r2 + 16*(-2*M + r)*r3) + 16*r4))/(2.*a2p2r2pa2c2th3*sinth2) + (a2pr2m2Mr*hS[4]*(3*a2*cos2th*M*r + r*(3*a2*M + 2*a2*r - 6*M*r2 + 2*r3) + 2*a4*costh2*sinth2))/r2pa2cth23 - (2*dhS_dth[7]*(-5*a2 + 3*a2*cos2th - 2*r2))/(a2p2r2pa2c2th2*tanth) - (2*dhS_dph[8]*(3*a4 + a4*cos4th + 4*a2*cos2th*(a2 + 2*r*(-2*M + r)) + 8*a2*r2 - 16*M*r3 + 8*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr*sinth2*tanth) + (hS[9]*(35*a6 + 8*a6*cos6th + a6*cos8th - 168*a4*M*r - 36*a4*cos6th*M*r + 120*a4*r2 + 12*a4*cos6th*r2 + 128*a2*M2*r2 + 4*a2*cos4th*(7*a4 + 2*a2*r*(5*M + 9*r) - 4*(8*M2 + M*r - 3*r2)*r2) - 48*a2*M*r3 + 144*a2*r4 - 256*M2*r4 + 64*r6 + 4*cos2th*(14*a6 + a4*r*(-23*M + 45*r) - 16*a2*(7*M - 3*r)*r3 + 16*r4*pow(-2*M + r,2))))/(8.*a2p2r2pa2c2th3*a2pr2m2Mr*sinth4);\n src[8] = (-8*a*d2hS_dtph[8]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) + d2hS_dth2[8]/r2pa2cth2 + (d2hS_dr2[8]*(a2 - 2*M*r + r2))/r2pa2cth2 + (2*a2pr2m2Mr*dhS_dth[6]*r)/r2pa2cth22 - (d2hS_dt2[8]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dr[8]*(a4*(M + r) + 3*a2*(-M + r)*r2 + a2*cos2th*(a2*(M + r) + (-M + r)*r2) + 2*(-3*M + r)*r4))/a2p2r2pa2c2th3 + (2*dhS_dph[5]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 12*a2*M*r2 + 4*a2*cos2th*r*(a2 - M*r + 2*r2) + 8*a2*r3 - 16*M*r4 + 8*r5))/a2p2r2pa2c2th3 - (8*a3*dhS_dph[3]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (8*a3*dhS_dt[9]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (8*a2*dhS_dt[3]*M*r*(a2 + r2)*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (a2*a2pr2m2Mr*dhS_dr[6]*sin2th)/r2pa2cth22 + (d2hS_dph2[8]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (hS[8]*(55*a6 + 10*a6*cos6th + a6*cos8th - 80*a4*M*r - 24*a4*cos6th*M*r + 184*a4*r2 + 16*a4*cos6th*r2 + 224*a2*M*r3 + 8*a2*cos4th*(5*a4 + a2*r*(10*M + 13*r) + 2*(2*M + 5*r)*r3) + 208*a2*r4 + 256*M*r5 + 2*cos2th*(43*a6 + 4*a4*r*(3*M + 34*r) - 16*a2*(8*M - 9*r)*r3 + 64*(-2*M + r)*r5) + 64*r6))/(4.*a2p2r2pa2c2th4*sinth2) - (8*a*dhS_dr[2]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*dhS_dt[5]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (32*a*hS[2]*M*r*(4*a4 - a2*r2 + a2*cos2th*(4*a2 + 3*r2) - 6*r4)*sinth2)/a2p2r2pa2c2th4 - (32*a3*costh*dhS_dth[2]*M*r*sinth3)/a2p2r2pa2c2th3 + (32*a3*costh*dhS_dt[7]*M*r*sinth3)/a2p2r2pa2c2th3 + (32*a2pr2m2Mr*a3*costh*hS[1]*M*(a2 + a2*cos2th - 10*r2)*sinth3)/a2p2r2pa2c2th4 - (dhS_dth[8]*(a4 + 3*a4*cos4th + 16*a2*M*r + 4*a2*cos2th*(a2 + 4*r*(-M + r)) + 8*r4))/(a2p2r2pa2c2th3*tanth) + (2*dhS_dph[7]*(3*a4 + a4*cos4th + 8*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (2*hS[6]*(-2*a6*M - a6*cos6th*M + 10*a6*r + a6*cos6th*r + 8*a4*M2*r + 60*a4*M*r2 + 2*a4*cos4th*(a2*(M + 3*r) + 2*r*(-2*M2 - 3*M*r + 3*r2)) + 36*a4*r3 - 160*a2*M2*r3 + a2*cos2th*(a4*(M + 15*r) - 16*a2*(7*M - 3*r)*r2 + 16*(10*M2 - 10*M*r + 3*r2)*r3) + 32*a2*M*r4 + 48*a2*r5 - 64*M*r6 + 32*r7))/(a2p2r2pa2c2th4*tanth) - (dhS_dph[9]*(3*a4 + a4*cos4th + 4*a2*cos2th*(a2 + 2*r*(-2*M + r)) + 8*a2*r2 - 16*M*r3 + 8*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr*sinth2*tanth);\n src[9] = (-8*a*d2hS_dtph[9]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) + d2hS_dth2[9]/r2pa2cth2 + (d2hS_dr2[9]*(a2 - 2*M*r + r2))/r2pa2cth2 - (d2hS_dt2[9]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (2*dhS_dr[9]*(5*a4*M - a4*cos4th*(M - r) + 3*a4*r - 16*a2*M*r2 + 8*a2*r3 + 4*a2*cos2th*(a2*(M + r) + 2*r3) - 24*M*r4 + 8*r5))/a2p2r2pa2c2th3 + (4*dhS_dph[6]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 12*a2*M*r2 + 4*a2*cos2th*r*(a2 - M*r + 2*r2) + 8*a2*r3 - 16*M*r4 + 8*r5))/a2p2r2pa2c2th3 + (hS[7]*(35*a8 + 8*a8*cos6th + a8*cos8th - 78*a6*M*r - 36*a6*cos6th*M*r - 2*a6*cos8th*M*r + 155*a6*r2 + 20*a6*cos6th*r2 + a6*cos8th*r2 + 80*a4*M2*r2 + 40*a4*cos6th*M2*r2 + 88*a4*M*r3 - 44*a4*cos6th*M*r3 + 264*a4*r4 + 12*a4*cos6th*r4 - 96*a2*M2*r4 + 4*a2*cos4th*(7*a6 + 5*a4*r*(4*M + 5*r) + 4*(-2*M2 + M*r + 3*r2)*r4 + a2*(-20*M2*r2 + 26*M*r3 + 30*r4)) + 304*a2*M*r5 + 208*a2*r6 + 128*M*r7 + 4*cos2th*(14*a8 + a6*r*(9*M + 59*r) + a4*r2*(-10*M2 - 37*M*r + 93*r2) + 16*a2*(2*M2 - 5*M*r + 4*r2)*r4 + 16*(-2*M + r)*r7) + 64*r8))/(2.*a2p2r2pa2c2th5) + (2*a2pr2m2Mr*hS[5]*(-10*a6*M - a6*cos6th*M + 10*a6*r + a6*cos6th*r + 140*a4*M*r2 + 2*a4*cos4th*(a2*(5*M + 3*r) + 2*(M + 3*r)*r2) + 36*a4*r3 + 160*a2*M*r4 + a2*cos2th*(a4*(M + 15*r) - 48*a2*(3*M - r)*r2 + 16*(-10*M + 3*r)*r4) + 48*a2*r5 + 32*r7)*sin2th)/a2p2r2pa2c2th5 + (d2hS_dph2[9]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) + (hS[9]*(126*a10 + a10*cos10th + 45*a10*cos6th + 10*a10*cos8th + 6*a8*M2 - a8*cos10th*M2 + 3*a8*cos6th*M2 + 2*a8*cos8th*M2 - 160*a8*M*r - 160*a8*cos6th*M*r - 32*a8*cos8th*M*r + 512*r10 + 700*a8*r2 + 160*a8*cos6th*r2 + 20*a8*cos8th*r2 - 120*a6*M2*r2 + 160*a6*cos6th*M2*r2 + 24*a6*cos8th*M2*r2 - 840*a6*M*r3 - 384*a6*cos6th*M*r3 - 24*a6*cos8th*M*r3 - 640*a4*M3*r3 - 320*a4*cos6th*M3*r3 + 1600*a6*r4 + 160*a6*cos6th*r4 - 96*a4*M2*r4 + 240*a4*cos6th*M2*r4 - 1856*a4*M*r5 - 160*a4*cos6th*M*r5 + 768*a2*M3*r5 + 8*a2*cos4th*(15*a8 - a6*(M2 + 40*M*r - 70*r2) + 4*a4*r2*(3*M2 - 37*M*r + 30*r2) + 4*a2*r3*(20*M3 + 11*M2*r - 38*M*r2 + 20*r3) + 16*M*(2*M2 + 2*M*r - r2)*r5) + 1920*a4*r6 + 768*a2*M2*r6 - 2432*a2*M*r7 + 1280*a2*r8 + 1024*M2*r8 + 2*cos2th*(105*a10 - a8*(M2 + 176*M*r - 560*r2) + 16*a6*r2*(-5*M2 - 52*M*r + 75*r2) + 8*a4*r3*(20*M3 - 31*M2*r - 182*M*r2 + 160*r3) - 128*a2*(4*M3 + 4*M2*r + 6*M*r2 - 5*r3)*r5 + 256*M*(-2*M + r)*r8) - 1536*M*r9))/(8.*a2p2r2pa2c2th5*a2pr2m2Mr*sinth2) - (16*a*dhS_dr[3]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (16*a*dhS_dt[6]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (2*a2pr2m2Mr*hS[4]*(-2*a6*M2 + a6*cos6th*M2 + 76*a6*M*r - 2*a6*cos6th*M*r + 10*a6*r2 + a6*cos6th*r2 - 40*a4*M2*r2 + 2*a4*cos4th*(a2*(M2 - 14*M*r + 3*r2) + 2*r2*(10*M2 - 8*M*r + 3*r2)) + 32*a4*M*r3 + 36*a4*r4 + 48*a2*M2*r4 - a2*cos2th*(a4*(M2 - 50*M*r - 15*r2) - 48*a2*(2*M + r)*r3 - 48*(-M2 + M*r + r2)*r4) - 144*a2*M*r5 + 48*a2*r6 - 96*M*r7 + 32*r8)*sinth2)/a2p2r2pa2c2th5 + (4*a*hS[3]*M*(2*a8*M - a8*cos6th*M + 30*a8*r + 3*a8*cos6th*r - 130*a6*M*r2 - 3*a6*cos6th*M*r2 + 70*a6*r3 + a6*cos6th*r3 - 80*a4*M2*r3 - 2*a4*cos4th*(a4*(M - 9*r) + a2*(31*M - 13*r)*r2 + 2*(-20*M2 + 14*M*r + r2)*r3) - 184*a4*M*r4 + 4*a4*r5 + 64*a2*M2*r5 + a2*cos2th*(a6*(M + 45*r) + a4*(-189*M + 95*r)*r2 - 272*a2*M*r4 - 16*(4*M2 + 3*M*r + 5*r2)*r5) + 176*a2*M*r6 - 112*a2*r7 + 256*M*r8 - 96*r9)*sinth2)/(a2p2r2pa2c2th5*a2pr2m2Mr) - (2*hS[0]*M*(-2*a10*M + a10*cos6th*M + 30*a10*r + 3*a10*cos6th*r - 32*r11 + 28*a8*M*r2 - 18*a8*cos6th*M*r2 + 120*a8*r3 + 6*a8*cos6th*r3 + 40*a6*M2*r3 + 20*a6*cos6th*M2*r3 + 46*a6*M*r4 - 15*a6*cos6th*M*r4 + 166*a6*r5 + 3*a6*cos6th*r5 - 48*a4*M2*r5 + 2*a4*cos4th*(a6*(M + 9*r) - 14*a4*(M - 2*r)*r2 + a2*(-20*M2 - 31*M*r + 29*r2)*r3 + 2*(-4*M2 - 2*M*r + 5*r2)*r5) - 152*a4*M*r6 + 60*a4*r7 - 208*a2*M*r8 + a2*cos2th*(-(a8*(M - 45*r)) + 2*a6*(9*M + 85*r)*r2 + a4*(-20*M2 + 31*M*r + 221*r2)*r3 + 16*a2*(4*M2 + 10*M*r + 7*r2)*r5 + 16*(13*M + r)*r8) - 48*a2*r9)*sinth2)/(a2p2r2pa2c2th5*a2pr2m2Mr) - (64*a3*costh*dhS_dth[3]*M*r*sinth3)/a2p2r2pa2c2th3 + (64*a3*costh*dhS_dt[8]*M*r*sinth3)/a2p2r2pa2c2th3 + (4*dhS_dph[8]*(3*a4 + a4*cos4th + 8*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (dhS_dth[9]*(9*a4 + 3*a4*cos4th + 32*a2*M*r + 24*a2*r2 + 4*a2*cos2th*(3*a2 - 8*M*r + 6*r2) + 24*r4))/(a2p2r2pa2c2th3*tanth);\n}\n\n\n/* Compute the 2D singular field, its derivatives and its d'Alembertian */\nvoid effsource_calc_m(int m, struct coordinate * x, double *hS_re, double *hS_im,\n double *dhS_dr_re, double *dhS_dr_im, double *dhS_dth_re, double *dhS_dth_im,\n double *dhS_dph_re, double *dhS_dph_im, double *dhS_dt_re, double *dhS_dt_im,\n double *src_re, double *src_im)\n{\n double A_re[10][5], A_im[10][5];\n double dA_dr_re[10][5], dA_dr_im[10][5], dA_dth_re[10][5], dA_dth_im[10][5];\n double d2A_dr2_re[10][5], d2A_dr2_im[10][5];\n double d2A_dth2_re[10][5], d2A_dth2_im[10][5];\n\n double d2hS_dt2_re[10], d2hS_dt2_im[10], d2hS_dtr_re[10], d2hS_dtr_im[10];\n double d2hS_dtth_re[10], d2hS_dtth_im[10], d2hS_dtph_re[10], d2hS_dtph_im[10];\n double d2hS_dr2_re[10], d2hS_dr2_im[10], d2hS_drth_re[10], d2hS_drth_im[10];\n double d2hS_drph_re[10], d2hS_drph_im[10], d2hS_dth2_re[10], d2hS_dth2_im[10];\n double d2hS_dthph_re[10], d2hS_dthph_im[10], d2hS_dph2_re[10], d2hS_dph2_im[10];\n\n if(m>20)\n {\n printf(\"Support for computing mode %d has not yet been added.\\n\", m);\n return;\n }\n\n const double r = x->r;\n const double theta = x->theta;\n const double rp = xp.r;\n const double thetap = xp.theta;\n\n double Omega = M / (a*M + sqrt(M*rp*rp*rp));\n\n const double dr = r - rp;\n const double dth = theta - thetap;\n\n const double dr2 = dr*dr;\n\n const double dth2 = dth*dth;\n const double dth3 = dth*dth2;\n const double dth4 = dth2*dth2;\n const double dth5 = dth3*dth2;\n const double dth6 = dth3*dth3;\n const double dth7 = dth4*dth3;\n const double dth8 = dth4*dth4;\n const double dth9 = dth5*dth4;\n\n /* A */\n A_re[0][0] = (A00600 + A00800*dth2)*dth6 + dr*(dr*((A02400 + A02600*dth2)*dth4 + dr*(dr*(dth2*(A04200 + A04400*dth2) + dr*(dth2*(A05200 + A05400*dth2) + dr*(A06000 + A06200*dth2 + dr*(A07000 + dr*(A08000 + A09000*dr) + A07200*dth2)))) + (A03400 + A03600*dth2)*dth4)) + (A01600 + A01800*dth2)*dth6);\n A_re[0][1] = (A00420 + A00620*dth2)*dth4 + dr*(dr*(dth2*(A02220 + A02420*dth2) + dr*(dth2*(A03220 + A03420*dth2) + dr*(A04020 + A04220*dth2 + dr*(A05020 + dr*(A06020 + A07020*dr) + A05220*dth2)))) + (A01420 + A01620*dth2)*dth4);\n A_re[0][2] = dth2*(A00240 + A00440*dth2) + dr*(dth2*(A01240 + A01440*dth2) + dr*(A02040 + A02240*dth2 + dr*(A03040 + dr*(A04040 + A05040*dr) + A03240*dth2)));\n A_re[0][3] = A00060 + A00260*dth2 + dr*(A01060 + dr*(A02060 + A03060*dr) + A01260*dth2);\n A_re[0][4] = A00080 + A01080*dr;\n A_im[0][0] = A_im[0][1] = A_im[0][2] = A_im[0][3] = A_im[0][4] = 0.0;\n\n A_re[1][0] = A_re[1][1] = A_re[1][2] = A_re[1][3] = A_re[1][4] = 0.0;\n A_im[1][0] = (A10601 + A10801*dth2)*dth6 + dr*(dr*((A12401 + A12601*dth2)*dth4 + dr*(dr*(dth2*(A14201 + A14401*dth2) + dr*(A15201*dth2 + dr*(A16001 + dr*(A17001 + A18001*dr) + A16201*dth2))) + A13401*dth4)) + A11601*dth6);\n A_im[1][1] = (A10421 + A10621*dth2)*dth4 + dr*(dr*(dth2*(A12221 + A12421*dth2) + dr*(A13221*dth2 + dr*(A14021 + dr*(A15021 + A16021*dr) + A14221*dth2))) + A11421*dth4);\n A_im[1][2] = dth2*(A10241 + A10441*dth2) + dr*(A11241*dth2 + dr*(A12041 + dr*(A13041 + A14041*dr) + A12241*dth2));\n A_im[1][3] = A10061 + dr*(A11061 + A12061*dr) + A10261*dth2;\n A_im[1][4] = A10081;\n\n A_re[2][0] = A_re[2][1] = A_re[2][2] = A_re[2][3] = A_re[2][4] = 0.0;\n A_im[2][0] = A20701*dth7 + dr*(dr*(A22501*dth5 + dr*(dr*(A24301*dth3 + dr*(dr*(A26101*dth + A27101*dr*dth) + A25301*dth3)) + A23501*dth5)) + A21701*dth7);\n A_im[2][1] = A20521*dth5 + dr*(dr*(A22321*dth3 + dr*(dr*(A24121*dth + A25121*dr*dth) + A23321*dth3)) + A21521*dth5);\n A_im[2][2] = A20341*dth3 + dr*(dr*(A22141*dth + A23141*dr*dth) + A21341*dth3);\n A_im[2][3] = A20161*dth + A21161*dr*dth;\n A_im[2][4] = 0.0;\n\n A_re[3][0] = (A30600 + A30800*dth2)*dth6 + dr*(dr*((A32400 + A32600*dth2)*dth4 + dr*(dr*(dth2*(A34200 + A34400*dth2) + dr*(dth2*(A35200 + A35400*dth2) + dr*(A36000 + A36200*dth2 + dr*(A37000 + dr*(A38000 + A39000*dr) + A37200*dth2)))) + (A33400 + A33600*dth2)*dth4)) + (A31600 + A31800*dth2)*dth6);\n A_re[3][1] = (A30420 + A30620*dth2)*dth4 + dr*(dr*(dth2*(A32220 + A32420*dth2) + dr*(dth2*(A33220 + A33420*dth2) + dr*(A34020 + A34220*dth2 + dr*(A35020 + dr*(A36020 + A37020*dr) + A35220*dth2)))) + (A31420 + A31620*dth2)*dth4);\n A_re[3][2] = dth2*(A30240 + A30440*dth2) + dr*(dth2*(A31240 + A31440*dth2) + dr*(A32040 + A32240*dth2 + dr*(A33040 + dr*(A34040 + A35040*dr) + A33240*dth2)));\n A_re[3][3] = A30060 + A30260*dth2 + dr*(A31060 + dr*(A32060 + A33060*dr) + A31260*dth2);\n A_re[3][4] = A30080 + A31080*dr;\n A_im[3][0] = A_im[3][1] = A_im[3][2] = A_im[3][3] = A_im[3][4] = 0.0;\n\n A_re[4][0] = A40800*dth8 + dr*(dr*(A42600*dth6 + dr*(dr*(A44400*dth4 + dr*(dr*(A46200*dth2 + dr*(dr*(A48000 + A49000*dr) + A47200*dth2)) + A45400*dth4)) + A43600*dth6)) + A41800*dth8);\n A_re[4][1] = A40620*dth6 + dr*(dr*(A42420*dth4 + dr*(dr*(A44220*dth2 + dr*(dr*(A46020 + A47020*dr) + A45220*dth2)) + A43420*dth4)) + A41620*dth6);\n A_re[4][2] = A40440*dth4 + dr*(dr*(A42240*dth2 + dr*(dr*(A44040 + A45040*dr) + A43240*dth2)) + A41440*dth4);\n A_re[4][3] = A40260*dth2 + dr*(dr*(A42060 + A43060*dr) + A41260*dth2);\n A_re[4][4] = A40080 + A41080*dr;\n A_im[4][0] = A_im[4][1] = A_im[4][2] = A_im[4][3] = A_im[4][4] = 0.0;\n\n A_re[5][0] = dr2*(dr2*(dr2*(A58100*dr2*dth + A56300*dth3) + A54500*dth5) + A52700*dth7) + A50900*dth9;\n A_re[5][1] = dr2*(dr2*(A56120*dr2*dth + A54320*dth3) + A52520*dth5) + A50720*dth7;\n A_re[5][2] = dr2*(A54140*dr2*dth + A52340*dth3) + A50540*dth5;\n A_re[5][3] = A52160*dr2*dth + A50360*dth3;\n A_re[5][4] = A50180*dth;\n A_im[5][0] = A_im[5][1] = A_im[5][2] = A_im[5][3] = A_im[5][4] = 0.0;\n\n A_re[6][0] = A_re[6][1] = A_re[6][2] = A_re[6][3] = A_re[6][4] = 0.0;\n A_im[6][0] = (A60601 + A60801*dth2)*dth6 + dr*(dr*((A62401 + A62601*dth2)*dth4 + dr*(dr*(dth2*(A64201 + A64401*dth2) + dr*(A65201*dth2 + dr*(A66001 + dr*(A67001 + A68001*dr) + A66201*dth2))) + A63401*dth4)) + A61601*dth6);\n A_im[6][1] = (A60421 + A60621*dth2)*dth4 + dr*(dr*(dth2*(A62221 + A62421*dth2) + dr*(A63221*dth2 + dr*(A64021 + dr*(A65021 + A66021*dr) + A64221*dth2))) + A61421*dth4);\n A_im[6][2] = dth2*(A60241 + A60441*dth2) + dr*(A61241*dth2 + dr*(A62041 + dr*(A63041 + A64041*dr) + A62241*dth2));\n A_im[6][3] = A60061 + dr*(A61061 + A62061*dr) + A60261*dth2;\n A_im[6][4] = A60081;\n\n A_re[7][0] = A70800*dth8 + dr*(dr*(A72600*dth6 + dr*(dr*(A74400*dth4 + dr*(dr*(A76200*dth2 + dr*(dr*(A78000 + A79000*dr) + A77200*dth2)) + A75400*dth4)) + A73600*dth6)) + A71800*dth8);\n A_re[7][1] = A70620*dth6 + dr*(dr*(A72420*dth4 + dr*(dr*(A74220*dth2 + dr*(dr*(A76020 + A77020*dr) + A75220*dth2)) + A73420*dth4)) + A71620*dth6);\n A_re[7][2] = A70440*dth4 + dr*(dr*(A72240*dth2 + dr*(dr*(A74040 + A75040*dr) + A73240*dth2)) + A71440*dth4);\n A_re[7][3] = A70260*dth2 + dr*(dr*(A72060 + A73060*dr) + A71260*dth2);\n A_re[7][4] = A70080 + A71080*dr;\n A_im[7][0] = A_im[7][1] = A_im[7][2] = A_im[7][3] = A_im[7][4] = 0.0;\n\n A_re[8][0] = A_re[8][1] = A_re[8][2] = A_re[8][3] = A_re[8][4] = 0.0;\n A_im[8][0] = A80701*dth7 + dr*(dr*(A82501*dth5 + dr*(dr*(A84301*dth3 + dr*(dr*(A86101*dth + A87101*dr*dth) + A85301*dth3)) + A83501*dth5)) + A81701*dth7);\n A_im[8][1] = A80521*dth5 + dr*(dr*(A82321*dth3 + dr*(dr*(A84121*dth + A85121*dr*dth) + A83321*dth3)) + A81521*dth5);\n A_im[8][2] = A80341*dth3 + dr*(dr*(A82141*dth + A83141*dr*dth) + A81341*dth3);\n A_im[8][3] = A80161*dth + A81161*dr*dth;\n A_im[8][4] = 0.0;\n\n A_re[9][0] = (A90600 + A90800*dth2)*dth6 + dr*(dr*((A92400 + A92600*dth2)*dth4 + dr*(dr*(dth2*(A94200 + A94400*dth2) + dr*(dth2*(A95200 + A95400*dth2) + dr*(A96000 + A96200*dth2 + dr*(A97000 + dr*(A98000 + A99000*dr) + A97200*dth2)))) + (A93400 + A93600*dth2)*dth4)) + (A91600 + A91800*dth2)*dth6);\n A_re[9][1] = (A90420 + A90620*dth2)*dth4 + dr*(dr*(dth2*(A92220 + A92420*dth2) + dr*(dth2*(A93220 + A93420*dth2) + dr*(A94020 + A94220*dth2 + dr*(A95020 + dr*(A96020 + A97020*dr) + A95220*dth2)))) + (A91420 + A91620*dth2)*dth4);\n A_re[9][2] = dth2*(A90240 + A90440*dth2) + dr*(dth2*(A91240 + A91440*dth2) + dr*(A92040 + A92240*dth2 + dr*(A93040 + dr*(A94040 + A95040*dr) + A93240*dth2)));\n A_re[9][3] = A90060 + A90260*dth2 + dr*(A91060 + dr*(A92060 + A93060*dr) + A91260*dth2);\n A_re[9][4] = A90080 + A91080*dr;\n A_im[9][0] = A_im[9][1] = A_im[9][2] = A_im[9][3] = A_im[9][4] = 0.0;\n\n\n /* dA/dr */\n dA_dr_re[0][0] = dr*((2*A02400 + 2*A02600*dth2)*dth4 + dr*(dr*(dth2*(4*A04200 + 4*A04400*dth2) + dr*(dth2*(5*A05200 + 5*A05400*dth2) + dr*(6*A06000 + 6*A06200*dth2 + dr*(7*A07000 + dr*(8*A08000 + 9*A09000*dr) + 7*A07200*dth2)))) + (3*A03400 + 3*A03600*dth2)*dth4)) + (A01600 + A01800*dth2)*dth6;\n dA_dr_re[0][1] = dr*(dth2*(2*A02220 + 2*A02420*dth2) + dr*(dth2*(3*A03220 + 3*A03420*dth2) + dr*(4*A04020 + 4*A04220*dth2 + dr*(5*A05020 + dr*(6*A06020 + 7*A07020*dr) + 5*A05220*dth2)))) + (A01420 + A01620*dth2)*dth4;\n dA_dr_re[0][2] = dth2*(A01240 + A01440*dth2) + dr*(2*A02040 + 2*A02240*dth2 + dr*(3*A03040 + dr*(4*A04040 + 5*A05040*dr) + 3*A03240*dth2));\n dA_dr_re[0][3] = A01060 + dr*(2*A02060 + 3*A03060*dr) + A01260*dth2;\n dA_dr_re[0][4] = A01080;\n dA_dr_im[0][0] = dA_dr_im[0][1] = dA_dr_im[0][2] = dA_dr_im[0][3] = dA_dr_im[0][4] = 0.0;\n\n dA_dr_re[1][0] = dA_dr_re[1][1] = dA_dr_re[1][2] = dA_dr_re[1][3] = dA_dr_re[1][4] = 0.0;\n dA_dr_im[1][0] = dr*((2*A12401 + 2*A12601*dth2)*dth4 + dr*(dr*(dth2*(4*A14201 + 4*A14401*dth2) + dr*(5*A15201*dth2 + dr*(6*A16001 + dr*(7*A17001 + 8*A18001*dr) + 6*A16201*dth2))) + 3*A13401*dth4)) + A11601*dth6;\n dA_dr_im[1][1] = dr*(dth2*(2*A12221 + 2*A12421*dth2) + dr*(3*A13221*dth2 + dr*(4*A14021 + dr*(5*A15021 + 6*A16021*dr) + 4*A14221*dth2))) + A11421*dth4;\n dA_dr_im[1][2] = A11241*dth2 + dr*(2*A12041 + dr*(3*A13041 + 4*A14041*dr) + 2*A12241*dth2);\n dA_dr_im[1][3] = A11061 + 2*A12061*dr;\n dA_dr_im[1][4] = 0.0;\n\n dA_dr_re[2][0] = dA_dr_re[2][1] = dA_dr_re[2][2] = dA_dr_re[2][3] = dA_dr_re[2][4] = 0.0;\n dA_dr_im[2][0] = dr*(2*A22501*dth5 + dr*(dr*(4*A24301*dth3 + dr*(dr*(6*A26101*dth + 7*A27101*dr*dth) + 5*A25301*dth3)) + 3*A23501*dth5)) + A21701*dth7;\n dA_dr_im[2][1] = dr*(2*A22321*dth3 + dr*(dr*(4*A24121*dth + 5*A25121*dr*dth) + 3*A23321*dth3)) + A21521*dth5;\n dA_dr_im[2][2] = dr*(2*A22141*dth + 3*A23141*dr*dth) + A21341*dth3;\n dA_dr_im[2][3] = A21161*dth;\n dA_dr_im[2][4] = 0.0;\n\n dA_dr_re[3][0] = dr*((2*A32400 + 2*A32600*dth2)*dth4 + dr*(dr*(dth2*(4*A34200 + 4*A34400*dth2) + dr*(dth2*(5*A35200 + 5*A35400*dth2) + dr*(6*A36000 + 6*A36200*dth2 + dr*(7*A37000 + dr*(8*A38000 + 9*A39000*dr) + 7*A37200*dth2)))) + (3*A33400 + 3*A33600*dth2)*dth4)) + (A31600 + A31800*dth2)*dth6;\n dA_dr_re[3][1] = dr*(dth2*(2*A32220 + 2*A32420*dth2) + dr*(dth2*(3*A33220 + 3*A33420*dth2) + dr*(4*A34020 + 4*A34220*dth2 + dr*(5*A35020 + dr*(6*A36020 + 7*A37020*dr) + 5*A35220*dth2)))) + (A31420 + A31620*dth2)*dth4;\n dA_dr_re[3][2] = dth2*(A31240 + A31440*dth2) + dr*(2*A32040 + 2*A32240*dth2 + dr*(3*A33040 + dr*(4*A34040 + 5*A35040*dr) + 3*A33240*dth2));\n dA_dr_re[3][3] = A31060 + dr*(2*A32060 + 3*A33060*dr) + A31260*dth2;\n dA_dr_re[3][4] = A31080;\n dA_dr_im[3][0] = dA_dr_im[3][1] = dA_dr_im[3][2] = dA_dr_im[3][3] = dA_dr_im[3][4] = 0.0;\n\n dA_dr_re[4][0] = dr*(2*A42600*dth6 + dr*(dr*(4*A44400*dth4 + dr*(dr*(6*A46200*dth2 + dr*(dr*(8*A48000 + 9*A49000*dr) + 7*A47200*dth2)) + 5*A45400*dth4)) + 3*A43600*dth6)) + A41800*dth8;\n dA_dr_re[4][1] = dr*(2*A42420*dth4 + dr*(dr*(4*A44220*dth2 + dr*(dr*(6*A46020 + 7*A47020*dr) + 5*A45220*dth2)) + 3*A43420*dth4)) + A41620*dth6;\n dA_dr_re[4][2] = dr*(2*A42240*dth2 + dr*(dr*(4*A44040 + 5*A45040*dr) + 3*A43240*dth2)) + A41440*dth4;\n dA_dr_re[4][3] = dr*(2*A42060 + 3*A43060*dr) + A41260*dth2;\n dA_dr_re[4][4] = A41080;\n dA_dr_im[4][0] = dA_dr_im[4][1] = dA_dr_im[4][2] = dA_dr_im[4][3] = dA_dr_im[4][4] = 0.0;\n\n dA_dr_re[5][0] = dr*(dr2*(dr2*(8*A58100*dr2*dth + 6*A56300*dth3) + 4*A54500*dth5) + 2*A52700*dth7);\n dA_dr_re[5][1] = dr*(dr2*(6*A56120*dr2*dth + 4*A54320*dth3) + 2*A52520*dth5);\n dA_dr_re[5][2] = dr*(4*A54140*dr2*dth + 2*A52340*dth3);\n dA_dr_re[5][3] = 2*A52160*dr*dth;\n dA_dr_re[5][4] = 0.0;\n dA_dr_im[5][0] = dA_dr_im[5][1] = dA_dr_im[5][2] = dA_dr_im[5][3] = dA_dr_im[5][4] = 0.0;\n\n dA_dr_re[6][0] = dA_dr_re[6][1] = dA_dr_re[6][2] = dA_dr_re[6][3] = dA_dr_re[6][4] = 0.0;\n dA_dr_im[6][0] = dr*((2*A62401 + 2*A62601*dth2)*dth4 + dr*(dr*(dth2*(4*A64201 + 4*A64401*dth2) + dr*(5*A65201*dth2 + dr*(6*A66001 + dr*(7*A67001 + 8*A68001*dr) + 6*A66201*dth2))) + 3*A63401*dth4)) + A61601*dth6;\n dA_dr_im[6][1] = dr*(dth2*(2*A62221 + 2*A62421*dth2) + dr*(3*A63221*dth2 + dr*(4*A64021 + dr*(5*A65021 + 6*A66021*dr) + 4*A64221*dth2))) + A61421*dth4;\n dA_dr_im[6][2] = A61241*dth2 + dr*(2*A62041 + dr*(3*A63041 + 4*A64041*dr) + 2*A62241*dth2);\n dA_dr_im[6][3] = A61061 + 2*A62061*dr;\n dA_dr_im[6][4] = 0.0;\n\n dA_dr_re[7][0] = dr*(2*A72600*dth6 + dr*(dr*(4*A74400*dth4 + dr*(dr*(6*A76200*dth2 + dr*(dr*(8*A78000 + 9*A79000*dr) + 7*A77200*dth2)) + 5*A75400*dth4)) + 3*A73600*dth6)) + A71800*dth8;\n dA_dr_re[7][1] = dr*(2*A72420*dth4 + dr*(dr*(4*A74220*dth2 + dr*(dr*(6*A76020 + 7*A77020*dr) + 5*A75220*dth2)) + 3*A73420*dth4)) + A71620*dth6;\n dA_dr_re[7][2] = dr*(2*A72240*dth2 + dr*(dr*(4*A74040 + 5*A75040*dr) + 3*A73240*dth2)) + A71440*dth4;\n dA_dr_re[7][3] = dr*(2*A72060 + 3*A73060*dr) + A71260*dth2;\n dA_dr_re[7][4] = A71080;\n dA_dr_im[7][0] = dA_dr_im[7][1] = dA_dr_im[7][2] = dA_dr_im[7][3] = dA_dr_im[7][4] = 0.0;\n\n dA_dr_re[8][0] = dA_dr_re[8][1] = dA_dr_re[8][2] = dA_dr_re[8][3] = dA_dr_re[8][4] = 0.0;\n dA_dr_im[8][0] = dr*(2*A82501*dth5 + dr*(dr*(4*A84301*dth3 + dr*(dr*(6*A86101*dth + 7*A87101*dr*dth) + 5*A85301*dth3)) + 3*A83501*dth5)) + A81701*dth7;\n dA_dr_im[8][1] = dr*(2*A82321*dth3 + dr*(dr*(4*A84121*dth + 5*A85121*dr*dth) + 3*A83321*dth3)) + A81521*dth5;\n dA_dr_im[8][2] = dr*(2*A82141*dth + 3*A83141*dr*dth) + A81341*dth3;\n dA_dr_im[8][3] = A81161*dth;\n dA_dr_im[8][4] = 0.0;\n\n dA_dr_re[9][0] = dr*((2*A92400 + 2*A92600*dth2)*dth4 + dr*(dr*(dth2*(4*A94200 + 4*A94400*dth2) + dr*(dth2*(5*A95200 + 5*A95400*dth2) + dr*(6*A96000 + 6*A96200*dth2 + dr*(7*A97000 + dr*(8*A98000 + 9*A99000*dr) + 7*A97200*dth2)))) + (3*A93400 + 3*A93600*dth2)*dth4)) + (A91600 + A91800*dth2)*dth6;\n dA_dr_re[9][1] = dr*(dth2*(2*A92220 + 2*A92420*dth2) + dr*(dth2*(3*A93220 + 3*A93420*dth2) + dr*(4*A94020 + 4*A94220*dth2 + dr*(5*A95020 + dr*(6*A96020 + 7*A97020*dr) + 5*A95220*dth2)))) + (A91420 + A91620*dth2)*dth4;\n dA_dr_re[9][2] = dth2*(A91240 + A91440*dth2) + dr*(2*A92040 + 2*A92240*dth2 + dr*(3*A93040 + dr*(4*A94040 + 5*A95040*dr) + 3*A93240*dth2));\n dA_dr_re[9][3] = A91060 + dr*(2*A92060 + 3*A93060*dr) + A91260*dth2;\n dA_dr_re[9][4] = A91080;\n dA_dr_im[9][0] = dA_dr_im[9][1] = dA_dr_im[9][2] = dA_dr_im[9][3] = dA_dr_im[9][4] = 0.0;\n\n\n /* dA/dth */\n dA_dth_re[0][0] = (6*A00600 + 8*A00800*dth2)*dth5 + dr*(dr*((4*A02400 + 6*A02600*dth2)*dth3 + dr*(dr*(dth*(2*A04200 + 4*A04400*dth2) + dr*(dr*(2*A06200*dth + 2*A07200*dr*dth) + dth*(2*A05200 + 4*A05400*dth2))) + (4*A03400 + 6*A03600*dth2)*dth3)) + (6*A01600 + 8*A01800*dth2)*dth5);\n dA_dth_re[0][1] = (4*A00420 + 6*A00620*dth2)*dth3 + dr*(dr*(dth*(2*A02220 + 4*A02420*dth2) + dr*(dr*(2*A04220*dth + 2*A05220*dr*dth) + dth*(2*A03220 + 4*A03420*dth2))) + (4*A01420 + 6*A01620*dth2)*dth3);\n dA_dth_re[0][2] = dth*(2*A00240 + 4*A00440*dth2) + dr*(dr*(2*A02240*dth + 2*A03240*dr*dth) + dth*(2*A01240 + 4*A01440*dth2));\n dA_dth_re[0][3] = 2*A00260*dth + 2*A01260*dr*dth;\n dA_dth_re[0][4] = 0.0;\n dA_dth_im[0][0] = dA_dth_im[0][1] = dA_dth_im[0][2] = dA_dth_im[0][3] = dA_dth_im[0][4] = 0.0;\n\n dA_dth_re[1][0] = dA_dth_re[1][1] = dA_dth_re[1][2] = dA_dth_re[1][3] = dA_dth_re[1][4] = 0.0;\n dA_dth_im[1][0] = (6*A10601 + 8*A10801*dth2)*dth5 + dr*(dr*((4*A12401 + 6*A12601*dth2)*dth3 + dr*(dr*(dr*(2*A15201*dth + 2*A16201*dr*dth) + dth*(2*A14201 + 4*A14401*dth2)) + 4*A13401*dth3)) + 6*A11601*dth5);\n dA_dth_im[1][1] = (4*A10421 + 6*A10621*dth2)*dth3 + dr*(dr*(dr*(2*A13221*dth + 2*A14221*dr*dth) + dth*(2*A12221 + 4*A12421*dth2)) + 4*A11421*dth3);\n dA_dth_im[1][2] = dr*(2*A11241*dth + 2*A12241*dr*dth) + dth*(2*A10241 + 4*A10441*dth2);\n dA_dth_im[1][3] = 2*A10261*dth;\n dA_dth_im[1][4] = 0.0;\n\n dA_dth_re[2][0] = dA_dth_re[2][1] = dA_dth_re[2][2] = dA_dth_re[2][3] = dA_dth_re[2][4] = 0.0;\n dA_dth_im[2][0] = 7*A20701*dth6 + dr*(dr*(5*A22501*dth4 + dr*(dr*(3*A24301*dth2 + dr*(dr*(A26101 + A27101*dr) + 3*A25301*dth2)) + 5*A23501*dth4)) + 7*A21701*dth6);\n dA_dth_im[2][1] = 5*A20521*dth4 + dr*(dr*(3*A22321*dth2 + dr*(dr*(A24121 + A25121*dr) + 3*A23321*dth2)) + 5*A21521*dth4);\n dA_dth_im[2][2] = 3*A20341*dth2 + dr*(dr*(A22141 + A23141*dr) + 3*A21341*dth2);\n dA_dth_im[2][3] = A20161 + A21161*dr;\n dA_dth_im[2][4] = 0.0;\n\n dA_dth_re[3][0] = (6*A30600 + 8*A30800*dth2)*dth5 + dr*(dr*((4*A32400 + 6*A32600*dth2)*dth3 + dr*(dr*(dth*(2*A34200 + 4*A34400*dth2) + dr*(dr*(2*A36200*dth + 2*A37200*dr*dth) + dth*(2*A35200 + 4*A35400*dth2))) + (4*A33400 + 6*A33600*dth2)*dth3)) + (6*A31600 + 8*A31800*dth2)*dth5);\n dA_dth_re[3][1] = (4*A30420 + 6*A30620*dth2)*dth3 + dr*(dr*(dth*(2*A32220 + 4*A32420*dth2) + dr*(dr*(2*A34220*dth + 2*A35220*dr*dth) + dth*(2*A33220 + 4*A33420*dth2))) + (4*A31420 + 6*A31620*dth2)*dth3);\n dA_dth_re[3][2] = dth*(2*A30240 + 4*A30440*dth2) + dr*(dr*(2*A32240*dth + 2*A33240*dr*dth) + dth*(2*A31240 + 4*A31440*dth2));\n dA_dth_re[3][3] = 2*A30260*dth + 2*A31260*dr*dth;\n dA_dth_re[3][4] = 0.0;\n dA_dth_im[3][0] = dA_dth_im[3][1] = dA_dth_im[3][2] = dA_dth_im[3][3] = dA_dth_im[3][4] = 0.0;\n\n dA_dth_re[4][0] = 8*A40800*dth7 + dr*(dr*(6*A42600*dth5 + dr*(dr*(4*A44400*dth3 + dr*(dr*(2*A46200*dth + 2*A47200*dr*dth) + 4*A45400*dth3)) + 6*A43600*dth5)) + 8*A41800*dth7);\n dA_dth_re[4][1] = 6*A40620*dth5 + dr*(dr*(4*A42420*dth3 + dr*(dr*(2*A44220*dth + 2*A45220*dr*dth) + 4*A43420*dth3)) + 6*A41620*dth5);\n dA_dth_re[4][2] = 4*A40440*dth3 + dr*(dr*(2*A42240*dth + 2*A43240*dr*dth) + 4*A41440*dth3);\n dA_dth_re[4][3] = 2*A40260*dth + 2*A41260*dr*dth;\n dA_dth_re[4][4] = 0.0;\n dA_dth_im[4][0] = dA_dth_im[4][1] = dA_dth_im[4][2] = dA_dth_im[4][3] = dA_dth_im[4][4] = 0.0;\n\n dA_dth_re[5][0] = dr2*(dr2*(dr2*(A58100*dr2 + 3*A56300*dth2) + 5*A54500*dth4) + 7*A52700*dth6) + 9*A50900*dth8;\n dA_dth_re[5][1] = dr2*(dr2*(A56120*dr2 + 3*A54320*dth2) + 5*A52520*dth4) + 7*A50720*dth6;\n dA_dth_re[5][2] = dr2*(A54140*dr2 + 3*A52340*dth2) + 5*A50540*dth4;\n dA_dth_re[5][3] = A52160*dr2 + 3*A50360*dth2;\n dA_dth_re[5][4] = A50180;\n dA_dth_im[5][0] = dA_dth_im[5][1] = dA_dth_im[5][2] = dA_dth_im[5][3] = dA_dth_im[5][4] = 0.0;\n\n dA_dth_re[6][0] = dA_dth_re[6][1] = dA_dth_re[6][2] = dA_dth_re[6][3] = dA_dth_re[6][4] = 0.0;\n dA_dth_im[6][0] = (6*A60601 + 8*A60801*dth2)*dth5 + dr*(dr*((4*A62401 + 6*A62601*dth2)*dth3 + dr*(dr*(dr*(2*A65201*dth + 2*A66201*dr*dth) + dth*(2*A64201 + 4*A64401*dth2)) + 4*A63401*dth3)) + 6*A61601*dth5);\n dA_dth_im[6][1] = (4*A60421 + 6*A60621*dth2)*dth3 + dr*(dr*(dr*(2*A63221*dth + 2*A64221*dr*dth) + dth*(2*A62221 + 4*A62421*dth2)) + 4*A61421*dth3);\n dA_dth_im[6][2] = dr*(2*A61241*dth + 2*A62241*dr*dth) + dth*(2*A60241 + 4*A60441*dth2);\n dA_dth_im[6][3] = 2*A60261*dth;\n dA_dth_im[6][4] = 0.0;\n\n dA_dth_re[7][0] = 8*A70800*dth7 + dr*(dr*(6*A72600*dth5 + dr*(dr*(4*A74400*dth3 + dr*(dr*(2*A76200*dth + 2*A77200*dr*dth) + 4*A75400*dth3)) + 6*A73600*dth5)) + 8*A71800*dth7);\n dA_dth_re[7][1] = 6*A70620*dth5 + dr*(dr*(4*A72420*dth3 + dr*(dr*(2*A74220*dth + 2*A75220*dr*dth) + 4*A73420*dth3)) + 6*A71620*dth5);\n dA_dth_re[7][2] = 4*A70440*dth3 + dr*(dr*(2*A72240*dth + 2*A73240*dr*dth) + 4*A71440*dth3);\n dA_dth_re[7][3] = 2*A70260*dth + 2*A71260*dr*dth;\n dA_dth_re[7][4] = 0.0;\n dA_dth_im[7][0] = dA_dth_im[7][1] = dA_dth_im[7][2] = dA_dth_im[7][3] = dA_dth_im[7][4] = 0.0;\n\n dA_dth_re[8][0] = dA_dth_re[8][1] = dA_dth_re[8][2] = dA_dth_re[8][3] = dA_dth_re[8][4] = 0.0;\n dA_dth_im[8][0] = 7*A80701*dth6 + dr*(dr*(5*A82501*dth4 + dr*(dr*(3*A84301*dth2 + dr*(dr*(A86101 + A87101*dr) + 3*A85301*dth2)) + 5*A83501*dth4)) + 7*A81701*dth6);\n dA_dth_im[8][1] = 5*A80521*dth4 + dr*(dr*(3*A82321*dth2 + dr*(dr*(A84121 + A85121*dr) + 3*A83321*dth2)) + 5*A81521*dth4);\n dA_dth_im[8][2] = 3*A80341*dth2 + dr*(dr*(A82141 + A83141*dr) + 3*A81341*dth2);\n dA_dth_im[8][3] = A80161 + A81161*dr;\n dA_dth_im[8][4] = 0.0;\n\n dA_dth_re[9][0] = (6*A90600 + 8*A90800*dth2)*dth5 + dr*(dr*((4*A92400 + 6*A92600*dth2)*dth3 + dr*(dr*(dth*(2*A94200 + 4*A94400*dth2) + dr*(dr*(2*A96200*dth + 2*A97200*dr*dth) + dth*(2*A95200 + 4*A95400*dth2))) + (4*A93400 + 6*A93600*dth2)*dth3)) + (6*A91600 + 8*A91800*dth2)*dth5);\n dA_dth_re[9][1] = (4*A90420 + 6*A90620*dth2)*dth3 + dr*(dr*(dth*(2*A92220 + 4*A92420*dth2) + dr*(dr*(2*A94220*dth + 2*A95220*dr*dth) + dth*(2*A93220 + 4*A93420*dth2))) + (4*A91420 + 6*A91620*dth2)*dth3);\n dA_dth_re[9][2] = dth*(2*A90240 + 4*A90440*dth2) + dr*(dr*(2*A92240*dth + 2*A93240*dr*dth) + dth*(2*A91240 + 4*A91440*dth2));\n dA_dth_re[9][3] = 2*A90260*dth + 2*A91260*dr*dth;\n dA_dth_re[9][4] = 0.0;\n dA_dth_im[9][0] = dA_dth_im[9][1] = dA_dth_im[9][2] = dA_dth_im[9][3] = dA_dth_im[9][4] = 0.0;\n\n\n /* d2A/dr2 */\n d2A_dr2_re[0][0] = (2*A02400 + 2*A02600*dth2)*dth4 + dr*(dr*(dth2*(12*A04200 + 12*A04400*dth2) + dr*(dth2*(20*A05200 + 20*A05400*dth2) + dr*(30*A06000 + 30*A06200*dth2 + dr*(42*A07000 + dr*(56*A08000 + 72*A09000*dr) + 42*A07200*dth2)))) + (6*A03400 + 6*A03600*dth2)*dth4);\n d2A_dr2_re[0][1] = dth2*(2*A02220 + 2*A02420*dth2) + dr*(dth2*(6*A03220 + 6*A03420*dth2) + dr*(12*A04020 + 12*A04220*dth2 + dr*(20*A05020 + dr*(30*A06020 + 42*A07020*dr) + 20*A05220*dth2)));\n d2A_dr2_re[0][2] = 2*A02040 + 2*A02240*dth2 + dr*(6*A03040 + dr*(12*A04040 + 20*A05040*dr) + 6*A03240*dth2);\n d2A_dr2_re[0][3] = 2*A02060 + 6*A03060*dr;\n d2A_dr2_re[0][4] = 0.0;\n d2A_dr2_im[0][0] = d2A_dr2_im[0][1] = d2A_dr2_im[0][2] = d2A_dr2_im[0][3] = d2A_dr2_im[0][4] = 0.0;\n\n d2A_dr2_re[1][0] = d2A_dr2_re[1][1] = d2A_dr2_re[1][2] = d2A_dr2_re[1][3] = d2A_dr2_re[1][4] = 0.0;\n d2A_dr2_im[1][0] = (2*A12401 + 2*A12601*dth2)*dth4 + dr*(dr*(dth2*(12*A14201 + 12*A14401*dth2) + dr*(20*A15201*dth2 + dr*(30*A16001 + dr*(42*A17001 + 56*A18001*dr) + 30*A16201*dth2))) + 6*A13401*dth4);\n d2A_dr2_im[1][1] = dth2*(2*A12221 + 2*A12421*dth2) + dr*(6*A13221*dth2 + dr*(12*A14021 + dr*(20*A15021 + 30*A16021*dr) + 12*A14221*dth2));\n d2A_dr2_im[1][2] = 2*A12041 + dr*(6*A13041 + 12*A14041*dr) + 2*A12241*dth2;\n d2A_dr2_im[1][3] = 2*A12061;\n d2A_dr2_im[1][4] = 0.0;\n\n d2A_dr2_re[2][0] = d2A_dr2_re[2][1] = d2A_dr2_re[2][2] = d2A_dr2_re[2][3] = d2A_dr2_re[2][4] = 0.0;\n d2A_dr2_im[2][0] = 2*A22501*dth5 + dr*(dr*(12*A24301*dth3 + dr*(dr*(30*A26101*dth + 42*A27101*dr*dth) + 20*A25301*dth3)) + 6*A23501*dth5);\n d2A_dr2_im[2][1] = 2*A22321*dth3 + dr*(dr*(12*A24121*dth + 20*A25121*dr*dth) + 6*A23321*dth3);\n d2A_dr2_im[2][2] = 2*A22141*dth + 6*A23141*dr*dth;\n d2A_dr2_im[2][3] = 0.0;\n d2A_dr2_im[2][4] = 0.0;\n\n d2A_dr2_re[3][0] = (2*A32400 + 2*A32600*dth2)*dth4 + dr*(dr*(dth2*(12*A34200 + 12*A34400*dth2) + dr*(dth2*(20*A35200 + 20*A35400*dth2) + dr*(30*A36000 + 30*A36200*dth2 + dr*(42*A37000 + dr*(56*A38000 + 72*A39000*dr) + 42*A37200*dth2)))) + (6*A33400 + 6*A33600*dth2)*dth4);\n d2A_dr2_re[3][1] = dth2*(2*A32220 + 2*A32420*dth2) + dr*(dth2*(6*A33220 + 6*A33420*dth2) + dr*(12*A34020 + 12*A34220*dth2 + dr*(20*A35020 + dr*(30*A36020 + 42*A37020*dr) + 20*A35220*dth2)));\n d2A_dr2_re[3][2] = 2*A32040 + 2*A32240*dth2 + dr*(6*A33040 + dr*(12*A34040 + 20*A35040*dr) + 6*A33240*dth2);\n d2A_dr2_re[3][3] = 2*A32060 + 6*A33060*dr;\n d2A_dr2_re[3][4] = 0.0;\n d2A_dr2_im[3][0] = d2A_dr2_im[3][1] = d2A_dr2_im[3][2] = d2A_dr2_im[3][3] = d2A_dr2_im[3][4] = 0.0;\n\n d2A_dr2_re[4][0] = 2*A42600*dth6 + dr*(dr*(12*A44400*dth4 + dr*(dr*(30*A46200*dth2 + dr*(dr*(56*A48000 + 72*A49000*dr) + 42*A47200*dth2)) + 20*A45400*dth4)) + 6*A43600*dth6);\n d2A_dr2_re[4][1] = 2*A42420*dth4 + dr*(dr*(12*A44220*dth2 + dr*(dr*(30*A46020 + 42*A47020*dr) + 20*A45220*dth2)) + 6*A43420*dth4);\n d2A_dr2_re[4][2] = 2*A42240*dth2 + dr*(dr*(12*A44040 + 20*A45040*dr) + 6*A43240*dth2);\n d2A_dr2_re[4][3] = 2*A42060 + 6*A43060*dr;\n d2A_dr2_re[4][4] = 0.0;\n d2A_dr2_im[4][0] = d2A_dr2_im[4][1] = d2A_dr2_im[4][2] = d2A_dr2_im[4][3] = d2A_dr2_im[4][4] = 0.0;\n\n d2A_dr2_re[5][0] = dr2*(dr2*(56*A58100*dr2*dth + 30*A56300*dth3) + 12*A54500*dth5) + 2*A52700*dth7;\n d2A_dr2_re[5][1] = dr2*(30*A56120*dr2*dth + 12*A54320*dth3) + 2*A52520*dth5;\n d2A_dr2_re[5][2] = 12*A54140*dr2*dth + 2*A52340*dth3;\n d2A_dr2_re[5][3] = 2*A52160*dth;\n d2A_dr2_re[5][4] = 0.0;\n d2A_dr2_im[5][0] = d2A_dr2_im[5][1] = d2A_dr2_im[5][2] = d2A_dr2_im[5][3] = d2A_dr2_im[5][4] = 0.0;\n\n d2A_dr2_re[6][0] = d2A_dr2_re[6][1] = d2A_dr2_re[6][2] = d2A_dr2_re[6][3] = d2A_dr2_re[6][4] = 0.0;\n d2A_dr2_im[6][0] = (2*A62401 + 2*A62601*dth2)*dth4 + dr*(dr*(dth2*(12*A64201 + 12*A64401*dth2) + dr*(20*A65201*dth2 + dr*(30*A66001 + dr*(42*A67001 + 56*A68001*dr) + 30*A66201*dth2))) + 6*A63401*dth4);\n d2A_dr2_im[6][1] = dth2*(2*A62221 + 2*A62421*dth2) + dr*(6*A63221*dth2 + dr*(12*A64021 + dr*(20*A65021 + 30*A66021*dr) + 12*A64221*dth2));\n d2A_dr2_im[6][2] = 2*A62041 + dr*(6*A63041 + 12*A64041*dr) + 2*A62241*dth2;\n d2A_dr2_im[6][3] = 2*A62061;\n d2A_dr2_im[6][4] = 0.0;\n\n d2A_dr2_re[7][0] = 2*A72600*dth6 + dr*(dr*(12*A74400*dth4 + dr*(dr*(30*A76200*dth2 + dr*(dr*(56*A78000 + 72*A79000*dr) + 42*A77200*dth2)) + 20*A75400*dth4)) + 6*A73600*dth6);\n d2A_dr2_re[7][1] = 2*A72420*dth4 + dr*(dr*(12*A74220*dth2 + dr*(dr*(30*A76020 + 42*A77020*dr) + 20*A75220*dth2)) + 6*A73420*dth4);\n d2A_dr2_re[7][2] = 2*A72240*dth2 + dr*(dr*(12*A74040 + 20*A75040*dr) + 6*A73240*dth2);\n d2A_dr2_re[7][3] = 2*A72060 + 6*A73060*dr;\n d2A_dr2_re[7][4] = 0.0;\n d2A_dr2_im[7][0] = d2A_dr2_im[7][1] = d2A_dr2_im[7][2] = d2A_dr2_im[7][3] = d2A_dr2_im[7][4] = 0.0;\n\n d2A_dr2_re[8][0] = d2A_dr2_re[8][1] = d2A_dr2_re[8][2] = d2A_dr2_re[8][3] = d2A_dr2_re[8][4] = 0.0;\n d2A_dr2_im[8][0] = 2*A82501*dth5 + dr*(dr*(12*A84301*dth3 + dr*(dr*(30*A86101*dth + 42*A87101*dr*dth) + 20*A85301*dth3)) + 6*A83501*dth5);\n d2A_dr2_im[8][1] = 2*A82321*dth3 + dr*(dr*(12*A84121*dth + 20*A85121*dr*dth) + 6*A83321*dth3);\n d2A_dr2_im[8][2] = 2*A82141*dth + 6*A83141*dr*dth;\n d2A_dr2_im[8][3] = 0.0;\n d2A_dr2_im[8][4] = 0.0;\n\n d2A_dr2_re[9][0] = (2*A92400 + 2*A92600*dth2)*dth4 + dr*(dr*(dth2*(12*A94200 + 12*A94400*dth2) + dr*(dth2*(20*A95200 + 20*A95400*dth2) + dr*(30*A96000 + 30*A96200*dth2 + dr*(42*A97000 + dr*(56*A98000 + 72*A99000*dr) + 42*A97200*dth2)))) + (6*A93400 + 6*A93600*dth2)*dth4);\n d2A_dr2_re[9][1] = dth2*(2*A92220 + 2*A92420*dth2) + dr*(dth2*(6*A93220 + 6*A93420*dth2) + dr*(12*A94020 + 12*A94220*dth2 + dr*(20*A95020 + dr*(30*A96020 + 42*A97020*dr) + 20*A95220*dth2)));\n d2A_dr2_re[9][2] = 2*A92040 + 2*A92240*dth2 + dr*(6*A93040 + dr*(12*A94040 + 20*A95040*dr) + 6*A93240*dth2);\n d2A_dr2_re[9][3] = 2*A92060 + 6*A93060*dr;\n d2A_dr2_re[9][4] = 0.0;\n d2A_dr2_im[9][0] = d2A_dr2_im[9][1] = d2A_dr2_im[9][2] = d2A_dr2_im[9][3] = d2A_dr2_im[9][4] = 0.0;\n\n\n /* d2A/dth2 */\n d2A_dth2_re[0][0] = (30*A00600 + 56*A00800*dth2)*dth4 + dr*(dr*(dth2*(12*A02400 + 30*A02600*dth2) + dr*(dth2*(12*A03400 + 30*A03600*dth2) + dr*(2*A04200 + 12*A04400*dth2 + dr*(2*A05200 + dr*(2*A06200 + 2*A07200*dr) + 12*A05400*dth2)))) + (30*A01600 + 56*A01800*dth2)*dth4);\n d2A_dth2_re[0][1] = dth2*(12*A00420 + 30*A00620*dth2) + dr*(dth2*(12*A01420 + 30*A01620*dth2) + dr*(2*A02220 + 12*A02420*dth2 + dr*(2*A03220 + dr*(2*A04220 + 2*A05220*dr) + 12*A03420*dth2)));\n d2A_dth2_re[0][2] = 2*A00240 + 12*A00440*dth2 + dr*(2*A01240 + dr*(2*A02240 + 2*A03240*dr) + 12*A01440*dth2);\n d2A_dth2_re[0][3] = 2*A00260 + 2*A01260*dr;\n d2A_dth2_re[0][4] = 0.0;\n d2A_dth2_im[0][0] = d2A_dth2_im[0][1] = d2A_dth2_im[0][2] = d2A_dth2_im[0][3] = d2A_dth2_im[0][4] = 0.0;\n\n d2A_dth2_re[1][0] = d2A_dth2_re[1][1] = d2A_dth2_re[1][2] = d2A_dth2_re[1][3] = d2A_dth2_re[1][4] = 0.0;\n d2A_dth2_im[1][0] = (30*A10601 + 56*A10801*dth2)*dth4 + dr*(dr*(dth2*(12*A12401 + 30*A12601*dth2) + dr*(12*A13401*dth2 + dr*(2*A14201 + dr*(2*A15201 + 2*A16201*dr) + 12*A14401*dth2))) + 30*A11601*dth4);\n d2A_dth2_im[1][1] = dth2*(12*A10421 + 30*A10621*dth2) + dr*(12*A11421*dth2 + dr*(2*A12221 + dr*(2*A13221 + 2*A14221*dr) + 12*A12421*dth2));\n d2A_dth2_im[1][2] = 2*A10241 + dr*(2*A11241 + 2*A12241*dr) + 12*A10441*dth2;\n d2A_dth2_im[1][3] = 2*A10261;\n d2A_dth2_im[1][4] = 0.0;\n\n d2A_dth2_re[2][0] = d2A_dth2_re[2][1] = d2A_dth2_re[2][2] = d2A_dth2_re[2][3] = d2A_dth2_re[2][4] = 0.0;\n d2A_dth2_im[2][0] = 42*A20701*dth5 + dr*(dr*(20*A22501*dth3 + dr*(dr*(6*A24301*dth + 6*A25301*dr*dth) + 20*A23501*dth3)) + 42*A21701*dth5);\n d2A_dth2_im[2][1] = 20*A20521*dth3 + dr*(dr*(6*A22321*dth + 6*A23321*dr*dth) + 20*A21521*dth3);\n d2A_dth2_im[2][2] = 6*A20341*dth + 6*A21341*dr*dth;\n d2A_dth2_im[2][3] = 0.0;\n d2A_dth2_im[2][4] = 0.0;\n\n d2A_dth2_re[3][0] = (30*A30600 + 56*A30800*dth2)*dth4 + dr*(dr*(dth2*(12*A32400 + 30*A32600*dth2) + dr*(dth2*(12*A33400 + 30*A33600*dth2) + dr*(2*A34200 + 12*A34400*dth2 + dr*(2*A35200 + dr*(2*A36200 + 2*A37200*dr) + 12*A35400*dth2)))) + (30*A31600 + 56*A31800*dth2)*dth4);\n d2A_dth2_re[3][1] = dth2*(12*A30420 + 30*A30620*dth2) + dr*(dth2*(12*A31420 + 30*A31620*dth2) + dr*(2*A32220 + 12*A32420*dth2 + dr*(2*A33220 + dr*(2*A34220 + 2*A35220*dr) + 12*A33420*dth2)));\n d2A_dth2_re[3][2] = 2*A30240 + 12*A30440*dth2 + dr*(2*A31240 + dr*(2*A32240 + 2*A33240*dr) + 12*A31440*dth2);\n d2A_dth2_re[3][3] = 2*A30260 + 2*A31260*dr;\n d2A_dth2_re[3][4] = 0.0;\n d2A_dth2_im[3][0] = d2A_dth2_im[3][1] = d2A_dth2_im[3][2] = d2A_dth2_im[3][3] = d2A_dth2_im[3][4] = 0.0;\n\n d2A_dth2_re[4][0] = 56*A40800*dth6 + dr*(dr*(30*A42600*dth4 + dr*(dr*(12*A44400*dth2 + dr*(dr*(2*A46200 + 2*A47200*dr) + 12*A45400*dth2)) + 30*A43600*dth4)) + 56*A41800*dth6);\n d2A_dth2_re[4][1] = 30*A40620*dth4 + dr*(dr*(12*A42420*dth2 + dr*(dr*(2*A44220 + 2*A45220*dr) + 12*A43420*dth2)) + 30*A41620*dth4);\n d2A_dth2_re[4][2] = 12*A40440*dth2 + dr*(dr*(2*A42240 + 2*A43240*dr) + 12*A41440*dth2);\n d2A_dth2_re[4][3] = 2*A40260 + 2*A41260*dr;\n d2A_dth2_re[4][4] = 0.0;\n d2A_dth2_im[4][0] = d2A_dth2_im[4][1] = d2A_dth2_im[4][2] = d2A_dth2_im[4][3] = d2A_dth2_im[4][4] = 0.0;\n\n d2A_dth2_re[5][0] = dr2*(dr2*(6*A56300*dr2*dth + 20*A54500*dth3) + 42*A52700*dth5) + 72*A50900*dth7;\n d2A_dth2_re[5][1] = dr2*(6*A54320*dr2*dth + 20*A52520*dth3) + 42*A50720*dth5;\n d2A_dth2_re[5][2] = 6*A52340*dr2*dth + 20*A50540*dth3;\n d2A_dth2_re[5][3] = 6*A50360*dth;\n d2A_dth2_re[5][4] = 0.0;\n d2A_dth2_im[5][0] = d2A_dth2_im[5][1] = d2A_dth2_im[5][2] = d2A_dth2_im[5][3] = d2A_dth2_im[5][4] = 0.0;\n\n d2A_dth2_re[6][0] = d2A_dth2_re[6][1] = d2A_dth2_re[6][2] = d2A_dth2_re[6][3] = d2A_dth2_re[6][4] = 0.0;\n d2A_dth2_im[6][0] = (30*A60601 + 56*A60801*dth2)*dth4 + dr*(dr*(dth2*(12*A62401 + 30*A62601*dth2) + dr*(12*A63401*dth2 + dr*(2*A64201 + dr*(2*A65201 + 2*A66201*dr) + 12*A64401*dth2))) + 30*A61601*dth4);\n d2A_dth2_im[6][1] = dth2*(12*A60421 + 30*A60621*dth2) + dr*(12*A61421*dth2 + dr*(2*A62221 + dr*(2*A63221 + 2*A64221*dr) + 12*A62421*dth2));\n d2A_dth2_im[6][2] = 2*A60241 + dr*(2*A61241 + 2*A62241*dr) + 12*A60441*dth2;\n d2A_dth2_im[6][3] = 2*A60261;\n d2A_dth2_im[6][4] = 0.0;\n\n d2A_dth2_re[7][0] = 56*A70800*dth6 + dr*(dr*(30*A72600*dth4 + dr*(dr*(12*A74400*dth2 + dr*(dr*(2*A76200 + 2*A77200*dr) + 12*A75400*dth2)) + 30*A73600*dth4)) + 56*A71800*dth6);\n d2A_dth2_re[7][1] = 30*A70620*dth4 + dr*(dr*(12*A72420*dth2 + dr*(dr*(2*A74220 + 2*A75220*dr) + 12*A73420*dth2)) + 30*A71620*dth4);\n d2A_dth2_re[7][2] = 12*A70440*dth2 + dr*(dr*(2*A72240 + 2*A73240*dr) + 12*A71440*dth2);\n d2A_dth2_re[7][3] = 2*A70260 + 2*A71260*dr;\n d2A_dth2_re[7][4] = 0.0;\n d2A_dth2_im[7][0] = d2A_dth2_im[7][1] = d2A_dth2_im[7][2] = d2A_dth2_im[7][3] = d2A_dth2_im[7][4] = 0.0;\n\n d2A_dth2_re[8][0] = d2A_dth2_re[8][1] = d2A_dth2_re[8][2] = d2A_dth2_re[8][3] = d2A_dth2_re[8][4] = 0.0;\n d2A_dth2_im[8][0] = 42*A80701*dth5 + dr*(dr*(20*A82501*dth3 + dr*(dr*(6*A84301*dth + 6*A85301*dr*dth) + 20*A83501*dth3)) + 42*A81701*dth5);\n d2A_dth2_im[8][1] = 20*A80521*dth3 + dr*(dr*(6*A82321*dth + 6*A83321*dr*dth) + 20*A81521*dth3);\n d2A_dth2_im[8][2] = 6*A80341*dth + 6*A81341*dr*dth;\n d2A_dth2_im[8][3] = 0.0;\n d2A_dth2_im[8][4] = 0.0;\n\n d2A_dth2_re[9][0] = (30*A90600 + 56*A90800*dth2)*dth4 + dr*(dr*(dth2*(12*A92400 + 30*A92600*dth2) + dr*(dth2*(12*A93400 + 30*A93600*dth2) + dr*(2*A94200 + 12*A94400*dth2 + dr*(2*A95200 + dr*(2*A96200 + 2*A97200*dr) + 12*A95400*dth2)))) + (30*A91600 + 56*A91800*dth2)*dth4);\n d2A_dth2_re[9][1] = dth2*(12*A90420 + 30*A90620*dth2) + dr*(dth2*(12*A91420 + 30*A91620*dth2) + dr*(2*A92220 + 12*A92420*dth2 + dr*(2*A93220 + dr*(2*A94220 + 2*A95220*dr) + 12*A93420*dth2)));\n d2A_dth2_re[9][2] = 2*A90240 + 12*A90440*dth2 + dr*(2*A91240 + dr*(2*A92240 + 2*A93240*dr) + 12*A91440*dth2);\n d2A_dth2_re[9][3] = 2*A90260 + 2*A91260*dr;\n d2A_dth2_re[9][4] = 0.0;\n d2A_dth2_im[9][0] = d2A_dth2_im[9][1] = d2A_dth2_im[9][2] = d2A_dth2_im[9][3] = d2A_dth2_im[9][4] = 0.0;\n\n /* alpha term appearing in the denominator */\n double alpha = alpha20*dr2 + alpha02*dth2;\n\n /* Derivatives of alpha */\n double dalpha_dr = 2*alpha20*dr;\n double d2alpha_dr2 = 2*alpha20;\n double dalpha_dth = 2*alpha02*dth;\n double d2alpha_dth2 = 2*alpha02;\n\n /* Powers of C = alpha / beta */\n const double beta_inv = 1.0 / beta;\n double C[27];\n C[0] = 1;\n C[1] = alpha * beta_inv;\n for(int i=2; i<=26; i++)\n C[i] = C[1]*C[i-1];\n\n double dC1_dr = dalpha_dr * beta_inv;\n double d2C1_dr2 = d2alpha_dr2 * beta_inv;\n double dC1_dth = dalpha_dth * beta_inv;\n double d2C1_dth2 = d2alpha_dth2 * beta_inv;\n\n double dC_dr[27];\n dC_dr[0] = 0;\n for(int i=1; i<=26; i++)\n dC_dr[i] = i*C[i-1]*dC1_dr;\n\n double d2C_dr2[27];\n d2C_dr2[0] = 0;\n d2C_dr2[1] = d2C1_dr2;\n for(int i=2; i<=26; i++)\n d2C_dr2[i] = i*(i-1)*C[i-2]*dC1_dr*dC1_dr + i*C[i-1]*d2C1_dr2;\n\n double dC_dth[27];\n dC_dth[0] = 0;\n for(int i=1; i<=26; i++)\n dC_dth[i] = i*C[i-1]*dC1_dth;\n\n double d2C_dth2[27];\n d2C_dth2[0] = 0;\n d2C_dth2[1] = d2C1_dth2;\n for(int i=2; i<=26; i++)\n d2C_dth2[i] = i*(i-1)*C[i-2]*dC1_dth*dC1_dth + i*C[i-1]*d2C1_dth2;\n\n /* Elliptic integrals */\n double gam = sqrt(1.0/(1.0+C[1]));\n double ellE = gsl_sf_ellint_Ecomp(gam, GSL_PREC_DOUBLE);\n double ellK = gsl_sf_ellint_Kcomp(gam, GSL_PREC_DOUBLE);\n\n /* Derivatives of elliptic integrals */\n double dellE_dC = (ellK - ellE)/(2.*(1+C[1]));\n double dellK_dC = (C[1]*ellK - (1+C[1])*ellE)/(2.*C[1]*(1+C[1]));\n double d2ellE_dC2 = -(2*C[1]*ellK - (2*C[1]-1)*ellE)/(4.*C[1]*(1+C[1])*(1+C[1]));\n double d2ellK_dC2 = -(C[1]*(1+2*C[1])*ellK - 2*(1+C[1])*(1+C[1])*ellE)/(4.*C[1]*C[1]*(1+C[1])*(1+C[1]));\n\n double dellE_dr = dellE_dC * dC1_dr;\n double dellE_dth = dellE_dC * dC1_dth;\n double d2ellE_dr2 = d2ellE_dC2 * dC1_dr * dC1_dr + dellE_dC * d2C1_dr2;\n double d2ellE_dth2 = d2ellE_dC2 * dC1_dth * dC1_dth + dellE_dC * d2C1_dth2;\n\n double dellK_dr = dellK_dC * dC1_dr;\n double dellK_dth = dellK_dC * dC1_dth;\n double d2ellK_dr2 = d2ellK_dC2 * dC1_dr * dC1_dr + dellK_dC * d2C1_dr2;\n double d2ellK_dth2 = d2ellK_dC2 * dC1_dth * dC1_dth + dellK_dC * d2C1_dth2;\n\n /* Denominator - there is a different denominator for real and imaginary parts */\n double alpha_plus_beta_10 = alpha+beta;\n double alpha_plus_beta_05 = sqrt(alpha_plus_beta_10);\n double alpha_plus_beta_15 = alpha_plus_beta_10*alpha_plus_beta_05;\n double alpha_plus_beta_20 = alpha_plus_beta_10*alpha_plus_beta_10;\n double alpha_plus_beta_25 = alpha_plus_beta_10*alpha_plus_beta_15;\n\n double beta_2 = beta*beta;\n\n double den_re = beta*C[3]*alpha_plus_beta_25/4.0;\n double dden_dr_re = beta*(6.0*C[2]*alpha_plus_beta_25*dC1_dr + C[3]*5.0*alpha_plus_beta_15*dalpha_dr)/8.0;\n double dden_dth_re = beta*(6.0*C[2]*alpha_plus_beta_25*dC1_dth + C[3]*5.0*alpha_plus_beta_15*dalpha_dth)/8.0;\n double d2den_dr2_re = beta*C[1]*alpha_plus_beta_05*(24*alpha_plus_beta_20*dC1_dr*dC1_dr + 60.0*C[1]*(alpha+beta)*dalpha_dr*dC1_dr + C[1]*(12.0*alpha_plus_beta_20*d2C1_dr2 + 5.0*C[1]*(3.0*dalpha_dr*dalpha_dr + 2.0*(alpha+beta)*d2alpha_dr2)))/16.0;\n double d2den_dth2_re = beta*C[1]*alpha_plus_beta_05*(24*alpha_plus_beta_20*dC1_dth*dC1_dth + 60.0*C[1]*(alpha+beta)*dalpha_dth*dC1_dth + C[1]*(12.0*alpha_plus_beta_20*d2C1_dth2 + 5.0*C[1]*(3.0*dalpha_dth*dalpha_dth + 2.0*(alpha+beta)*d2alpha_dth2)))/16.0;\n\n double den_im = -(beta_2*C[2]*alpha_plus_beta_15)/32.0;\n double dden_dr_im = -(beta_2*C[1]*alpha_plus_beta_05*(4.0*alpha_plus_beta_10*dC1_dr + 3*C[1]*dalpha_dr))/64.;\n double dden_dth_im = -(beta_2*C[1]*alpha_plus_beta_05*(4.0*alpha_plus_beta_10*dC1_dth + 3*C[1]*dalpha_dth))/64.;\n double d2den_dr2_im = -(beta_2*(C[1]*(8*alpha_plus_beta_20*d2C1_dr2 + 3.0*C[1]*(2.0*alpha_plus_beta_10*d2alpha_dr2 + dalpha_dr*dalpha_dr)) + 24.0*alpha_plus_beta_10*C[1]*dalpha_dr*dC1_dr + 8.0*alpha_plus_beta_20*dC1_dr*dC1_dr))/(128.*alpha_plus_beta_05);\n double d2den_dth2_im = -(beta_2*(C[1]*(8*alpha_plus_beta_20*d2C1_dth2 + 3.0*C[1]*(2.0*alpha_plus_beta_10*d2alpha_dth2 + dalpha_dth*dalpha_dth)) + 24.0*alpha_plus_beta_10*C[1]*dalpha_dth*dC1_dth + 8.0*alpha_plus_beta_20*dC1_dth*dC1_dth))/(128.*alpha_plus_beta_05);\n\n for(int l=0; l<10; l++)\n {\n /* First, compute derivatives of numerator - we will add the denominator at the end */\n\n /* hS */\n hS_re[l] = 0.0;\n hS_im[l] = 0.0;\n for(int j=0; j<5; j++) {\n double fac1K = ellK*A_re[l][j];\n for(int k=max(j,0); k<=m+2+j; k++) {\n hS_re[l] += fac1K*C[k]*ReEI[m][0][j][k];\n }\n\n double fac1E = ellE*A_re[l][j];\n for(int k=max(j-1,0); k<=m+2+j; k++) {\n hS_re[l] += fac1E*C[k]*ReEI[m][1][j][k];\n }\n \n double fac2K = ellK*A_im[l][j];\n for(int k=max(j-1,0); k<=m+1+j; k++) {\n hS_im[l] += fac2K*C[k]*ImEI[m][0][j][k];\n }\n \n double fac2E = ellE*A_im[l][j];\n for(int k=max(j-2,0); k<=m+1+j; k++) {\n hS_im[l] += fac2E*C[k]*ImEI[m][1][j][k];\n }\n }\n\n /* dhS_dr */\n dhS_dr_re[l] = 0.0;\n dhS_dr_im[l] = 0.0;\n for(int j=0; j<5; j++) {\n double fac1K = (dellK_dr*A_re[l][j] + ellK*dA_dr_re[l][j]);\n double fac2K = ellK*A_re[l][j];\n for(int k=max(j,0); k<=m+2+j; k++) {\n dhS_dr_re[l] += ReEI[m][0][j][k]*(C[k]*fac1K + fac2K*dC_dr[k]);\n }\n\n double fac1E = (dellE_dr*A_re[l][j] + ellE*dA_dr_re[l][j]);\n double fac2E = ellE*A_re[l][j];\n for(int k=max(j-1,0); k<=m+2+j; k++) {\n dhS_dr_re[l] += ReEI[m][1][j][k]*(C[k]*fac1E + fac2E*dC_dr[k]);\n }\n\n double fac3K = (dellK_dr*A_im[l][j] + ellK*dA_dr_im[l][j]);\n double fac4K = ellK*A_im[l][j];\n for(int k=max(j-1,0); k<=m+1+j; k++) {\n dhS_dr_im[l] += ImEI[m][0][j][k]*(C[k]*fac3K + fac4K*dC_dr[k]);\n }\n\n double fac3E = (dellE_dr*A_im[l][j] + ellE*dA_dr_im[l][j]);\n double fac4E = ellE*A_im[l][j];\n for(int k=max(j-2,0); k<=m+1+j; k++) {\n dhS_dr_im[l] += ImEI[m][1][j][k]*(C[k]*fac3E + fac4E*dC_dr[k]);\n }\n }\n\n /* dhS_dth */\n dhS_dth_re[l] = 0.0;\n dhS_dth_im[l] = 0.0;\n for(int j=0; j<5; j++) {\n double fac1K = (dellK_dth*A_re[l][j] + ellK*dA_dth_re[l][j]);\n double fac2K = ellK*A_re[l][j];\n for(int k=max(j,0); k<=m+2+j; k++) {\n dhS_dth_re[l] += ReEI[m][0][j][k]*(C[k]*fac1K + fac2K*dC_dth[k]);\n }\n\n double fac1E = (dellE_dth*A_re[l][j] + ellE*dA_dth_re[l][j]);\n double fac2E = ellE*A_re[l][j];\n for(int k=max(j-1,0); k<=m+2+j; k++) {\n dhS_dth_re[l] += ReEI[m][1][j][k]*(C[k]*fac1E + fac2E*dC_dth[k]);\n }\n\n double fac3K = (dellK_dth*A_im[l][j] + ellK*dA_dth_im[l][j]);\n double fac4K = ellK*A_im[l][j];\n for(int k=max(j-1,0); k<=m+1+j; k++) {\n dhS_dth_im[l] += ImEI[m][0][j][k]*(C[k]*fac3K + fac4K*dC_dth[k]);\n }\n\n double fac3E = (dellE_dth*A_im[l][j] + ellE*dA_dth_im[l][j]);\n double fac4E = ellE*A_im[l][j];\n for(int k=max(j-2,0); k<=m+1+j; k++) {\n dhS_dth_im[l] += ImEI[m][1][j][k]*(C[k]*fac3E + fac4E*dC_dth[k]);\n }\n }\n\n /* d2hS_dr2 */\n d2hS_dr2_re[l] = 0.0;\n d2hS_dr2_im[l] = 0.0;\n for(int j=0; j<5; j++) {\n double fac1K = (d2ellK_dr2*A_re[l][j] + 2.0*dellK_dr*dA_dr_re[l][j] + ellK*d2A_dr2_re[l][j]);\n double fac2K = (dellK_dr*A_re[l][j] + ellK*dA_dr_re[l][j]);\n double fac3K = ellK*A_re[l][j];\n for(int k=max(j,0); k<=m+2+j; k++) {\n d2hS_dr2_re[l] += ReEI[m][0][j][k]*(C[k]*fac1K + 2.0*dC_dr[k]*fac2K + fac3K*d2C_dr2[k]);\n }\n\n double fac1E = (d2ellE_dr2*A_re[l][j] + 2.0*dellE_dr*dA_dr_re[l][j] + ellE*d2A_dr2_re[l][j]);\n double fac2E = (dellE_dr*A_re[l][j] + ellE*dA_dr_re[l][j]);\n double fac3E = ellE*A_re[l][j];\n for(int k=max(j-1,0); k<=m+2+j; k++) {\n d2hS_dr2_re[l] += ReEI[m][1][j][k]*(C[k]*fac1E + 2.0*dC_dr[k]*fac2E + fac3E*d2C_dr2[k]);\n }\n\n double fac4K = (d2ellK_dr2*A_im[l][j] + 2.0*dellK_dr*dA_dr_im[l][j] + ellK*d2A_dr2_im[l][j]);\n double fac5K = (dellK_dr*A_im[l][j] + ellK*dA_dr_im[l][j]);\n double fac6K = ellK*A_im[l][j];\n for(int k=max(j-1,0); k<=m+1+j; k++) {\n d2hS_dr2_im[l] += ImEI[m][0][j][k]*(C[k]*fac4K + 2.0*dC_dr[k]*fac5K + fac6K*d2C_dr2[k]);\n }\n\n double fac4E = (d2ellE_dr2*A_im[l][j] + 2.0*dellE_dr*dA_dr_im[l][j] + ellE*d2A_dr2_im[l][j]);\n double fac5E = (dellE_dr*A_im[l][j] + ellE*dA_dr_im[l][j]);\n double fac6E = ellE*A_im[l][j];\n for(int k=max(j-2,0); k<=m+1+j; k++) {\n d2hS_dr2_im[l] += ImEI[m][1][j][k]*(C[k]*fac4E + 2.0*dC_dr[k]*fac5E + fac6E*d2C_dr2[k]);\n }\n }\n\n /* d2hS_dth2 */\n d2hS_dth2_re[l] = 0.0;\n d2hS_dth2_im[l] = 0.0;\n for(int j=0; j<5; j++) {\n double fac1K = (d2ellK_dth2*A_re[l][j] + 2.0*dellK_dth*dA_dth_re[l][j] + ellK*d2A_dth2_re[l][j]);\n double fac2K = (dellK_dth*A_re[l][j] + ellK*dA_dth_re[l][j]);\n double fac3K = ellK*A_re[l][j];\n for(int k=max(j,0); k<=m+2+j; k++) {\n d2hS_dth2_re[l] += ReEI[m][0][j][k]*(C[k]*fac1K + 2.0*dC_dth[k]*fac2K + fac3K*d2C_dth2[k]);\n }\n\n double fac1E = (d2ellE_dth2*A_re[l][j] + 2.0*dellE_dth*dA_dth_re[l][j] + ellE*d2A_dth2_re[l][j]);\n double fac2E = (dellE_dth*A_re[l][j] + ellE*dA_dth_re[l][j]);\n double fac3E = ellE*A_re[l][j];\n for(int k=max(j-1,0); k<=m+2+j; k++) {\n d2hS_dth2_re[l] += ReEI[m][1][j][k]*(C[k]*fac1E + 2.0*dC_dth[k]*fac2E + fac3E*d2C_dth2[k]);\n }\n\n double fac4K = (d2ellK_dth2*A_im[l][j] + 2.0*dellK_dth*dA_dth_im[l][j] + ellK*d2A_dth2_im[l][j]);\n double fac5K = (dellK_dth*A_im[l][j] + ellK*dA_dth_im[l][j]);\n double fac6K = ellK*A_im[l][j];\n for(int k=max(j-1,0); k<=m+1+j; k++) {\n d2hS_dth2_im[l] += ImEI[m][0][j][k]*(C[k]*fac4K + 2.0*dC_dth[k]*fac5K + fac6K*d2C_dth2[k]);\n }\n\n double fac4E = (d2ellE_dth2*A_im[l][j] + 2.0*dellE_dth*dA_dth_im[l][j] + ellE*d2A_dth2_im[l][j]);\n double fac5E = (dellE_dth*A_im[l][j] + ellE*dA_dth_im[l][j]);\n double fac6E = ellE*A_im[l][j];\n for(int k=max(j-2,0); k<=m+1+j; k++) {\n d2hS_dth2_im[l] += ImEI[m][1][j][k]*(C[k]*fac4E + 2.0*dC_dth[k]*fac5E + fac6E*d2C_dth2[k]);\n }\n }\n\n /* Quotient rule of differentiation to include the denominator*/\n d2hS_dr2_re[l] = (d2hS_dr2_re[l]*den_re*den_re - 2.0*dden_dr_re*den_re*dhS_dr_re[l] + 2.0*dden_dr_re*dden_dr_re*hS_re[l] - den_re*d2den_dr2_re*hS_re[l])/(den_re*den_re*den_re);\n d2hS_dr2_im[l] = (d2hS_dr2_im[l]*den_im*den_im - 2*dden_dr_im*den_im*dhS_dr_im[l] + 2*dden_dr_im*dden_dr_im*hS_im[l] - den_im*d2den_dr2_im*hS_im[l])/(den_im*den_im*den_im);\n d2hS_dth2_re[l] = (d2hS_dth2_re[l]*den_re*den_re - 2*dden_dth_re*den_re*dhS_dth_re[l] + 2*dden_dth_re*dden_dth_re*hS_re[l] - den_re*d2den_dth2_re*hS_re[l])/(den_re*den_re*den_re);\n d2hS_dth2_im[l] = (d2hS_dth2_im[l]*den_im*den_im - 2*dden_dth_im*den_im*dhS_dth_im[l] + 2*dden_dth_im*dden_dth_im*hS_im[l] - den_im*d2den_dth2_im*hS_im[l])/(den_im*den_im*den_im);\n dhS_dr_re[l] = (den_re*dhS_dr_re[l] - dden_dr_re*hS_re[l])/(den_re*den_re);\n dhS_dr_im[l] = (den_im*dhS_dr_im[l] - dden_dr_im*hS_im[l])/(den_im*den_im);\n dhS_dth_re[l] = (den_re*dhS_dth_re[l] - dden_dth_re*hS_re[l])/(den_re*den_re);\n dhS_dth_im[l] = (den_im*dhS_dth_im[l] - dden_dth_im*hS_im[l])/(den_im*den_im);\n\n hS_re[l] /= den_re;\n hS_im[l] /= den_im;\n }\n\n for(int i=0; i<10; i++)\n {\n dhS_dph_re[i] = -m*hS_im[i];\n dhS_dph_im[i] = m*hS_re[i];\n dhS_dt_re[i] = -Omega*dhS_dph_re[i];\n dhS_dt_im[i] = -Omega*dhS_dph_im[i];\n\n d2hS_dph2_re[i] = -m*dhS_dph_im[i];\n d2hS_dph2_im[i] = m*dhS_dph_re[i];\n d2hS_dtph_re[i] = -Omega*d2hS_dph2_re[i];\n d2hS_dtph_im[i] = -Omega*d2hS_dph2_im[i];\n d2hS_dt2_re[i] = -Omega*d2hS_dtph_re[i];\n d2hS_dt2_im[i] = -Omega*d2hS_dtph_im[i];\n\n d2hS_dtr_re[i] = NAN;\n d2hS_dtr_im[i] = NAN;\n d2hS_dtth_re[i] = NAN;\n d2hS_dtth_im[i] = NAN;\n d2hS_drth_re[i] = NAN;\n d2hS_drth_im[i] = NAN;\n d2hS_drph_re[i] = NAN;\n d2hS_drph_im[i] = NAN;\n d2hS_dthph_re[i] = NAN;\n d2hS_dthph_im[i] = NAN;\n }\n\n double a10, a2, a2p2r2pa2c2th2, a2p2r2pa2c2th3, a2p2r2pa2c2th4, a2p2r2pa2c2th5, a2pr2m2Mr2, a2pr2m2Mr3, a3, a4, a6, a8, costh2, costh4, M2, M3, r10, r11, r2, r2pa2cth22, r2pa2cth23, r3, r4, r5, r6, r7, r8, r9, sinth2, sinth3, sinth4, sin4th, cos2th, cos4th, cos6th, cos8th, cos10th, sin2th, r2pa2cth2, a2p2r2pa2c2th, a2pr2m2Mr, costh, sinth, tanth;\n\n M2 = M*M;\n M3 = M2*M;\n\n a2 = a*a;\n a3 = a2*a;\n a4 = a2*a2;\n a6 = a4*a2;\n a8 = a4*a4;\n a10 = a6*a4;\n\n r2 = r*r;\n r3 = r2*r;\n r4 = r2*r2;\n r5 = r3*r2;\n r6 = r3*r3;\n r7 = r4*r3;\n r8 = r4*r4;\n r9 = r5*r4;\n r10 = r5*r5;\n r11 = r6*r5;\n\n sinth = sin(theta);\n costh = cos(theta);\n tanth = sinth/costh;\n\n costh2 = costh*costh;\n costh4 = costh2*costh2;\n sinth2 = sinth*sinth;\n sinth3 = sinth2*sinth;\n sinth4 = sinth2*sinth2;\n\n cos2th = costh2 - sinth2;\n sin2th = 2.0*costh*sinth;\n sin4th = 2.0*cos2th*sin2th;\n cos4th = cos2th*cos2th - sin2th*sin2th;\n cos6th = cos2th*cos2th*cos2th - 3.0*cos2th*sin2th*sin2th;\n cos8th = cos4th*cos4th - sin4th*sin4th;\n cos10th = cos2th*cos2th*cos2th*cos2th*cos2th - 10.0*cos2th*cos2th*cos2th*sin2th*sin2th + 5.0*cos2th*sin2th*sin2th*sin2th*sin2th;\n\n r2pa2cth2 = a2*costh2 + r2;\n r2pa2cth22 = r2pa2cth2*r2pa2cth2;\n r2pa2cth23 = r2pa2cth22*r2pa2cth2;\n\n a2p2r2pa2c2th = a2 + a2*cos2th + 2*r2;\n a2p2r2pa2c2th2 = a2p2r2pa2c2th*a2p2r2pa2c2th;\n a2p2r2pa2c2th3 = a2p2r2pa2c2th2*a2p2r2pa2c2th;\n a2p2r2pa2c2th4 = a2p2r2pa2c2th2*a2p2r2pa2c2th2;\n a2p2r2pa2c2th5 = a2p2r2pa2c2th3*a2p2r2pa2c2th2;\n\n a2pr2m2Mr = a2 + r*(-2*M + r);\n a2pr2m2Mr2 = a2pr2m2Mr*a2pr2m2Mr;\n a2pr2m2Mr3 = a2pr2m2Mr2*a2pr2m2Mr;\n\n src_re[0] = (-8*a*d2hS_dtph_re[0]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (16*dhS_dt_re[1]*M*(a2 + a2*cos2th - 2*r2)*(a2 + r2))/a2p2r2pa2c2th3 + d2hS_dth2_re[0]/r2pa2cth2 + (d2hS_dr2_re[0]*(a2 - 2*M*r + r2))/r2pa2cth2 + (4*a*dhS_dr_re[3]*M*(a2*costh2 - r2))/r2pa2cth23 + (4*a*dhS_dph_re[1]*M*(-(a2*costh2) + r2))/r2pa2cth23 - (d2hS_dt2_re[0]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) + (16*hS_re[7]*M*r*(-9*a4 + 3*a4*cos4th + 20*a2*M*r - 2*a2*cos2th*(3*a2 + 5*r*(-2*M + r)) + 2*a2*r2 - 8*M*r3 + 4*r4))/a2p2r2pa2c2th5 + (2*dhS_dr_re[0]*(5*a4*M - a4*cos4th*(M - r) + 3*a4*r - 16*a2*M*r2 + 8*a2*r3 + 4*a2*cos2th*(a2*(M + r) + 2*r3) - 24*M*r4 + 8*r5))/a2p2r2pa2c2th3 - (8*a2pr2m2Mr*hS_re[4]*M*(3*a4*M - 27*a4*r + a4*cos4th*(M + 3*r) + 40*a2*M*r2 + 4*a2*cos2th*(a2*(M - 6*r) + (10*M - 7*r)*r2) - 4*a2*r3 - 24*M*r4 + 16*r5))/a2p2r2pa2c2th5 + (16*a*hS_re[3]*M2*(3*a6 + 29*a4*r2 + a4*cos4th*(a2 + 7*r2) - 80*a2*M*r3 + 32*a2*r4 + 4*a2*cos2th*(a4 + 9*a2*r2 - 20*M*r3 + 6*r4) + 32*M*r5 - 8*r6))/(a2p2r2pa2c2th5*a2pr2m2Mr) + (8*hS_re[0]*M2*(3*a8 + 2*a6*r2 - 20*a4*M*r3 + a4*cos4th*(a4 - 2*a2*r2 + 20*M*r3 - 3*r4) - a4*r4 + 16*a2*M*r5 + 4*a2*cos2th*(a6 - 3*a2*r4 - 2*(2*M + r)*r5) + 8*a2*r6 + 8*r8))/(a2p2r2pa2c2th5*a2pr2m2Mr) - (32*a2*dhS_dt_re[2]*M*r*sin2th)/a2p2r2pa2c2th3 - (96*a2*a2pr2m2Mr*hS_re[5]*M*(a2 + a2*cos2th - 6*r2)*sin2th)/a2p2r2pa2c2th5 + (d2hS_dph2_re[0]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (2*hS_re[9]*M*(-2*a6*M + a6*cos6th*M + 30*a6*r + 3*a6*cos6th*r - 200*a4*M*r2 + 2*a4*cos4th*(a2*(M + 9*r) + 2*(-14*M + 5*r)*r2) + 60*a4*r3 + 320*a2*M2*r3 - a2*cos2th*(a4*(M - 45*r) + 16*a2*(16*M - 5*r)*r2 - 16*(20*M2 - 11*M*r + r2)*r3) - 208*a2*M*r4 + 16*a2*r5 - 128*M2*r5 + 128*M*r6 - 32*r7))/(a2p2r2pa2c2th5*a2pr2m2Mr*sinth2) - (64*a*dhS_dph_re[2]*M*r)/(a2p2r2pa2c2th3*tanth) + (64*a*dhS_dth_re[3]*M*r)/(a2p2r2pa2c2th3*tanth) + (dhS_dth_re[0]*(3*a4 + a4*cos4th + 32*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-4*M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth);\n src_re[1] = (-8*a*d2hS_dtph_re[1]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dt_re[4]*M*(a2 + a2*cos2th - 2*r2)*(a2 + r2))/a2p2r2pa2c2th3 + d2hS_dth2_re[1]/r2pa2cth2 + (d2hS_dr2_re[1]*(a2 - 2*M*r + r2))/r2pa2cth2 - (2*dhS_dth_re[2]*r)/r2pa2cth22 + (2*a*dhS_dr_re[6]*M*(a2*costh2 - r2))/r2pa2cth23 + (2*a*dhS_dph_re[4]*M*(-(a2*costh2) + r2))/r2pa2cth23 - (4*a*dhS_dph_re[0]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (4*a*dhS_dt_re[3]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (d2hS_dt2_re[1]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) + (4*dhS_dr_re[1]*(-(a4*M) - a4*cos4th*(M - r) + a4*r - 6*a2*M*r2 - 2*a2*cos2th*(a2*(M - r) + (M - 3*r)*r2) + 2*a2*r3 - 4*M*r4 + 4*r5))/a2p2r2pa2c2th3 - (8*a*hS_re[6]*M*(3*a4*M + a4*cos4th*(M - r) - 23*a4*r + 40*a2*M*r2 + 4*a2*cos2th*(a2*(M - 6*r) + 5*(2*M - r)*r2) - 12*a2*r3 - 24*M*r4 + 16*r5))/(a2p2r2pa2c2th4*a2pr2m2Mr) - (4*dhS_dt_re[0]*M*(a6 + a2*(4*M - 3*r)*r3 + a2*cos2th*(a4 + 2*a2*r2 + (-4*M + r)*r3) - 2*r6))/(a2p2r2pa2c2th2*a2pr2m2Mr2) + (hS_re[1]*(10*a8 + a8*cos6th - 24*a6*M2 + 116*a6*M*r - 2*a6*cos6th*M*r + 22*a6*r2 + a6*cos6th*r2 - 248*a4*M2*r2 + 2*a4*cos4th*(3*a4 + 2*r2*(6*M2 - 4*M*r + r2) + a2*(-4*M2 - 10*M*r + 5*r2)) + 208*a4*M*r3 - 4*a4*r4 - 128*a2*M2*r4 + a2*cos2th*(15*a6 - 32*a2*M*(7*M - 8*r)*r2 + a4*(-32*M2 + 98*M*r + 31*r2) - 16*(20*M2 - 12*M*r + r2)*r4) + 128*a2*M*r5 - 48*a2*r6 - 64*M2*r6 + 64*M*r7 - 32*r8))/(a2p2r2pa2c2th4*a2pr2m2Mr) - (16*a2*dhS_dt_re[5]*M*r*sin2th)/a2p2r2pa2c2th3 - (32*a3*hS_re[8]*M*(a2 + a2*cos2th - 4*r2)*sin2th)/(a2p2r2pa2c2th4*a2pr2m2Mr) - (2*a2*costh*dhS_dr_re[2]*sinth)/r2pa2cth22 + (d2hS_dph2_re[1]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (dhS_dph_re[3]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 20*a2*M*r2 + 4*a2*cos2th*r*(a2 - 3*M*r + 2*r2) + 8*a2*r3 + 32*M2*r3 - 32*M*r4 + 8*r5))/(a2p2r2pa2c2th2*a2pr2m2Mr2*sinth2) - (32*a*dhS_dph_re[5]*M*r)/(a2p2r2pa2c2th3*tanth) + (32*a*dhS_dth_re[6]*M*r)/(a2p2r2pa2c2th3*tanth) + (dhS_dth_re[1]*(5*a4 - a4*cos4th + 16*a2*M*r + 4*a2*cos2th*(a2 - 4*M*r) + 16*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (4*hS_re[2]*(4*a6*M + 3*a6*r - 34*a4*M*r2 + a4*cos4th*(a2*(-4*M + r) + (-6*M + r)*r2) + 11*a4*r3 + 4*a2*cos2th*r*(a4 + 3*a2*r*(2*M + r) + 2*(2*M + r)*r3) - 48*a2*M*r4 + 16*a2*r5 - 16*M*r6 + 8*r7))/(a2p2r2pa2c2th4*a2pr2m2Mr*tanth);\n src_re[2] = (-8*a*d2hS_dtph_re[2]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dt_re[5]*M*(a2 + a2*cos2th - 2*r2)*(a2 + r2))/a2p2r2pa2c2th3 + d2hS_dth2_re[2]/r2pa2cth2 + (d2hS_dr2_re[2]*(a2 - 2*M*r + r2))/r2pa2cth2 + (2*a2pr2m2Mr*dhS_dth_re[1]*r)/r2pa2cth22 + (2*a*dhS_dr_re[8]*M*(a2*costh2 - r2))/r2pa2cth23 + (2*a*dhS_dph_re[5]*M*(-(a2*costh2) + r2))/r2pa2cth23 - (d2hS_dt2_re[2]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*a3*dhS_dph_re[0]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (8*a3*dhS_dt_re[3]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (16*a2*dhS_dt_re[7]*M*r*sin2th)/a2p2r2pa2c2th3 - (8*a2*dhS_dt_re[0]*M*r*(a2 + r2)*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (a2*a2pr2m2Mr*dhS_dr_re[1]*sin2th)/r2pa2cth22 + (4*a2*hS_re[1]*(-7*a4*M - a4*cos4th*(M - r) + 3*a4*r + 8*a2*M2*r - 4*a2*cos2th*(a2*(2*M - r) + r*(-2*M2 + 3*M*r - 2*r2)) + 28*a2*M*r2 + 8*a2*r3 - 80*M2*r3 + 32*M*r4 + 8*r5)*sin2th)/a2p2r2pa2c2th4 + (d2hS_dph2_re[2]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) + (8*a*hS_re[8]*M*r*(-a2 + 5*a2*cos4th + 4*cos2th*(a2 - r2) + 12*r2))/(a2p2r2pa2c2th4*sinth2) - (hS_re[2]*(15*a6 + 6*a6*cos6th + a6*cos8th + 96*a4*M*r + 16*a4*cos6th*M*r + 56*a4*r2 + 8*a4*cos6th*r2 - 160*a2*M*r3 + 8*a2*cos4th*(2*a4 + a2*r*(-12*M + 5*r) + 2*(-6*M + r)*r3) + 80*a2*r4 - 128*M*r5 + 2*cos2th*(13*a6 + a4*(-8*M*r + 44*r2) + 16*a2*(8*M + 3*r)*r3 + 64*M*r5) + 64*r6))/(4.*a2p2r2pa2c2th4*sinth2) - (8*a2*dhS_dr_re[2]*(-(a2*cos2th*(M - r)) + a2*(-M + r) + 2*(M + r)*r2)*sinth2)/a2p2r2pa2c2th3 - (32*a*dhS_dph_re[7]*M*r)/(a2p2r2pa2c2th3*tanth) + (32*a*dhS_dth_re[8]*M*r)/(a2p2r2pa2c2th3*tanth) - (32*a*a2pr2m2Mr*hS_re[6]*M*(a2 + a2*cos2th - 10*r2))/(a2p2r2pa2c2th4*tanth) + (dhS_dth_re[2]*(5*a4 - a4*cos4th + 16*a2*M*r + 4*a2*cos2th*(a2 - 4*M*r) + 16*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (dhS_dph_re[3]*(3*a4 + a4*cos4th + 4*a2*cos2th*(a2 + 2*r*(-2*M + r)) + 8*a2*r2 - 16*M*r3 + 8*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr*sinth2*tanth);\n src_re[3] = (-8*a*d2hS_dtph_re[3]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dt_re[6]*M*(a2 + a2*cos2th - 2*r2)*(a2 + r2))/a2p2r2pa2c2th3 + d2hS_dth2_re[3]/r2pa2cth2 + (d2hS_dr2_re[3]*(a2 - 2*M*r + r2))/r2pa2cth2 + (2*a*dhS_dr_re[9]*M*(a2*costh2 - r2))/r2pa2cth23 + (2*a*dhS_dph_re[6]*M*(-(a2*costh2) + r2))/r2pa2cth23 - (d2hS_dt2_re[3]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*a*hS_re[7]*M*r*(-3*a4 + 10*a2*M*r + 17*a2*r2 + a2*cos4th*(11*a2 - 10*M*r + 11*r2) - 8*M*r3 + 4*cos2th*(2*a4 + a2*r2 + (2*M - r)*r3) + 20*r4))/a2p2r2pa2c2th5 + (2*dhS_dph_re[1]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 12*a2*M*r2 + 4*a2*cos2th*r*(a2 - M*r + 2*r2) + 8*a2*r3 - 16*M*r4 + 8*r5))/a2p2r2pa2c2th3 - (4*hS_re[3]*M*(2*a8*M - a8*cos6th*M + 30*a8*r + 3*a8*cos6th*r - 54*a6*M*r2 - 5*a6*cos6th*M*r2 + 90*a6*r3 + 3*a6*cos6th*r3 - 80*a4*M2*r3 - 2*a4*cos4th*(a4*(M - 9*r) + a2*(21*M - 19*r)*r2 - 2*(20*M2 - 12*M*r + 5*r2)*r3) - 96*a4*M*r4 + 76*a4*r5 + 64*a2*M2*r5 + a2*cos2th*(a6*(M + 45*r) + a4*(-91*M + 125*r)*r2 + 16*a2*(-11*M + 6*r)*r4 + 16*(-4*M2 - 5*M*r + r2)*r5) + 16*a2*M*r6 - 16*a2*r7 + 64*M*r8 - 32*r9))/(a2p2r2pa2c2th5*a2pr2m2Mr) - (16*a2*dhS_dt_re[8]*M*r*sin2th)/a2p2r2pa2c2th3 - (16*a*a2pr2m2Mr*hS_re[5]*M*(-3*a4 + a4*cos4th + 26*a2*r2 - 2*a2*cos2th*(a2 + 5*r2) + 20*r4)*sin2th)/a2p2r2pa2c2th5 + (d2hS_dph2_re[3]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (a*hS_re[9]*M*(3*a6*M + a6*cos8th*(M - r) + 85*a6*r + 124*a6*cos2th*r + 4*a6*cos6th*r - 80*a4*M*r2 - 216*a4*cos2th*M*r2 - 40*a4*cos6th*M*r2 + 280*a4*r3 + 380*a4*cos2th*r3 + 4*a4*cos6th*r3 - 320*a2*M2*r3 - 4*a2*cos4th*(a4*(M - 11*r) + 2*a2*(22*M - 13*r)*r2 - 20*(4*M2 - 3*M*r + r2)*r3) - 208*a2*M*r4 - 576*a2*cos2th*M*r4 + 304*a2*r5 + 384*a2*cos2th*r5 + 256*M2*r5 - 256*cos2th*M2*r5 - 256*M*r6 - 256*cos2th*M*r6 + 64*r7 + 192*cos2th*r7))/(2.*a2p2r2pa2c2th5*a2pr2m2Mr*sinth2) - (8*a*dhS_dr_re[0]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*dhS_dt_re[1]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*a2pr2m2Mr*hS_re[4]*M*(3*a4*M + a4*cos4th*(M - r) - 39*a4*r + 40*a2*M*r2 + 4*a2*cos2th*(a2*(M - 10*r) + (10*M - 9*r)*r2) - 12*a2*r3 - 24*M*r4 + 32*r5)*sinth2)/a2p2r2pa2c2th5 - (8*a*hS_re[0]*M2*(3*a8 - 22*a6*r2 - 20*a4*M*r3 + a4*cos4th*(a4 - 10*a2*r2 + 20*M*r3 - 11*r4) - 41*a4*r4 + 16*a2*M*r5 + 4*a2*cos2th*(a6 - 8*a4*r2 - 15*a2*r4 - 2*(2*M + 3*r)*r5) + 24*a2*r6 + 40*r8)*sinth2)/(a2p2r2pa2c2th5*a2pr2m2Mr) - (32*a3*costh*dhS_dth_re[0]*M*r*sinth3)/a2p2r2pa2c2th3 + (32*a3*costh*dhS_dt_re[2]*M*r*sinth3)/a2p2r2pa2c2th3 - (2*dhS_dth_re[3])/(a2p2r2pa2c2th*tanth) - (32*a*dhS_dph_re[8]*M*r)/(a2p2r2pa2c2th3*tanth) + (32*a*dhS_dth_re[9]*M*r)/(a2p2r2pa2c2th3*tanth) + (2*dhS_dph_re[2]*(3*a4 + a4*cos4th + 8*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth);\n src_re[4] = (-8*a*d2hS_dtph_re[4]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (4*dhS_dr_re[4]*(3*a2*cos2th*(M - r) + a2*(3*M + r) - 2*(M + r)*r2))/a2p2r2pa2c2th2 + d2hS_dth2_re[4]/r2pa2cth2 + (d2hS_dr2_re[4]*(a2 - 2*M*r + r2))/r2pa2cth2 - (4*dhS_dth_re[5]*r)/r2pa2cth22 - (8*a*dhS_dph_re[1]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (8*a*dhS_dt_re[6]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (d2hS_dt2_re[4]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) + (2*hS_re[4]*(7*a6 + 3*a4*M2 + 4*a4*M*r + 10*a4*r2 - 40*a2*M2*r2 + a4*cos4th*(a2 + M2 - 4*M*r + 2*r2) + 4*a2*cos2th*(2*a4 + 2*M*(-5*M + 3*r)*r2 + a2*(M2 + r2)) + 40*a2*M*r3 - 16*a2*r4 - 56*M2*r4 + 64*M*r5 - 16*r6))/(a2p2r2pa2c2th3*a2pr2m2Mr) - (8*dhS_dt_re[1]*M*(a6 + a2*(4*M - 3*r)*r3 + a2*cos2th*(a4 + 2*a2*r2 + (-4*M + r)*r3) - 2*r6))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (4*a*hS_re[3]*M*(3*a6*M - 39*a6*r + a4*cos4th*(M - r)*(a2 - r2) + 101*a4*M*r2 - 45*a4*r3 - 48*a2*M2*r3 + 4*a2*cos2th*(a4*(M - 10*r) + a2*(25*M - 17*r)*r2 + (-12*M2 + 18*M*r - 5*r2)*r3) - 16*a2*M*r4 + 36*a2*r5 + 96*M2*r5 - 136*M*r6 + 48*r7))/(a2p2r2pa2c2th3*a2pr2m2Mr3) - (2*hS_re[0]*M*(3*a8*M - 27*a8*r + 62*a6*M*r2 - 58*a6*r3 - 12*a4*M2*r3 + a4*cos4th*(a4*(M + 3*r) + 2*a2*(-7*M + 3*r)*r2 + (12*M2 - 11*M*r + 3*r2)*r3) + 39*a4*M*r4 - 19*a4*r5 + 48*a2*M2*r5 + 4*a2*cos2th*(a6*(M - 6*r) + a4*(12*M - 19*r)*r2 + a2*(29*M - 20*r)*r4 + (-12*M2 + 22*M*r - 7*r2)*r5) - 56*a2*M*r6 + 28*a2*r7 - 24*M*r8 + 16*r9))/(a2p2r2pa2c2th3*a2pr2m2Mr3) - (4*a2*costh*dhS_dr_re[5]*sinth)/r2pa2cth22 + (d2hS_dph2_re[4]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (2*dhS_dph_re[6]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 20*a2*M*r2 + 4*a2*cos2th*r*(a2 - 3*M*r + 2*r2) + 8*a2*r3 + 32*M2*r3 - 32*M*r4 + 8*r5))/(a2p2r2pa2c2th2*a2pr2m2Mr2*sinth2) + (hS_re[9]*(-2*a6*M2 + a6*cos6th*M2 + 76*a6*M*r - 2*a6*cos6th*M*r + 10*a6*r2 + a6*cos6th*r2 - 248*a4*M2*r2 + 2*a4*cos4th*(a2*(M2 - 14*M*r + 3*r2) + 2*r2*(14*M2 - 12*M*r + 3*r2)) - 16*a4*M*r3 + 192*a2*M3*r3 - a2*cos2th*(a4*(M2 - 50*M*r - 15*r2) - 16*a2*r2*(-12*M2 + 2*M*r + 3*r2) - 16*r3*(12*M3 - 7*M2*r - 5*M*r2 + 3*r3)) + 36*a4*r4 + 240*a2*M2*r4 - 272*a2*M*r5 - 384*M3*r5 + 48*a2*r6 + 512*M2*r6 - 224*M*r7 + 32*r8))/(2.*a2p2r2pa2c2th3*a2pr2m2Mr3*sinth2) + (hS_re[7]*(3*a2*cos2th*M*r + r*(3*a2*M + 2*a2*r - 6*M*r2 + 2*r3) + 2*a4*costh2*sinth2))/(a2pr2m2Mr*r2pa2cth23) - (2*dhS_dth_re[4]*(-5*a2 + 3*a2*cos2th - 2*r2))/(a2p2r2pa2c2th2*tanth) + (8*hS_re[5]*(a2*(M - 3*r) - a2*cos2th*(M - r) + 2*(2*M - r)*r2))/(a2p2r2pa2c2th2*a2pr2m2Mr*tanth);\n src_re[5] = (-8*a*d2hS_dtph_re[5]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dr_re[5]*(a2*cos2th*(M - r) + a2*(M + r) - 2*M*r2))/a2p2r2pa2c2th2 + d2hS_dth2_re[5]/r2pa2cth2 + (d2hS_dr2_re[5]*(a2 - 2*M*r + r2))/r2pa2cth2 + (2*a2pr2m2Mr*dhS_dth_re[4]*r)/r2pa2cth22 - (2*dhS_dth_re[7]*r)/r2pa2cth22 - (4*a*dhS_dph_re[2]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (4*a*dhS_dt_re[8]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (d2hS_dt2_re[5]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (4*dhS_dt_re[2]*M*(a6 + a2*(4*M - 3*r)*r3 + a2*cos2th*(a4 + 2*a2*r2 + (-4*M + r)*r3) - 2*r6))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (8*a3*dhS_dph_re[1]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (8*a3*dhS_dt_re[6]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (12*a2*hS_re[4]*(-M + r)*sin2th)/a2p2r2pa2c2th2 - (8*a2*dhS_dt_re[1]*M*r*(a2 + r2)*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (a2*a2pr2m2Mr*dhS_dr_re[4]*sin2th)/r2pa2cth22 - (4*a2*hS_re[0]*M*(3*a6 - 4*a4*r*(M + 3*r) + a2*(32*M - 33*r)*r3 + a2*cos2th*(3*a4 + a2*(-4*M*r + 6*r2) + (-8*M + 3*r)*r3) + 2*(16*M - 9*r)*r5)*sin2th)/(a2p2r2pa2c2th3*a2pr2m2Mr2) - (2*a2*costh*dhS_dr_re[7]*sinth)/r2pa2cth22 + (d2hS_dph2_re[5]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (hS_re[5]*(a4 + 3*a4*cos4th + a4*cos6th + 8*a2*r2 - 32*M*r3 + cos2th*(3*a4 + 8*a2*r2 + 16*(2*M - r)*r3) + 24*r4))/(a2p2r2pa2c2th3*sinth2) - (dhS_dph_re[8]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 20*a2*M*r2 + 4*a2*cos2th*r*(a2 - 3*M*r + 2*r2) + 8*a2*r3 + 32*M2*r3 - 32*M*r4 + 8*r5))/(a2p2r2pa2c2th2*a2pr2m2Mr2*sinth2) - (8*hS_re[7]*r)/(a2p2r2pa2c2th2*tanth) - (2*dhS_dth_re[5]*(-5*a2 + 3*a2*cos2th - 2*r2))/(a2p2r2pa2c2th2*tanth) + (8*a*hS_re[3]*M*(-3*a6 + 5*a4*M*r + a4*cos4th*(a2 - M*r) + 20*a4*r2 - 48*a2*M*r3 - 2*a2*cos2th*(a4 - 2*a2*(M - 4*r)*r + (-16*M + 9*r)*r3) + 38*a2*r4 - 24*M*r5 + 12*r6))/(a2p2r2pa2c2th3*a2pr2m2Mr2*tanth) - (dhS_dph_re[6]*(3*a4 + a4*cos4th + 4*a2*cos2th*(a2 + 2*r*(-2*M + r)) + 8*a2*r2 - 16*M*r3 + 8*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr*sinth2*tanth) + (hS_re[9]*(-10*a6*M - a6*cos6th*M + 10*a6*r + a6*cos6th*r + 16*a4*M2*r + 92*a4*M*r2 + 36*a4*r3 - 256*a2*M2*r3 + 2*a4*cos4th*(5*a2*M + 3*a2*r - 8*M2*r - 6*M*r2 + 6*r3) + a2*cos2th*(a4*(M + 15*r) + 16*a2*(-13*M + 3*r)*r2 + 48*(8*M2 - 6*M*r + r2)*r3) + 32*a2*M*r4 + 48*a2*r5 + 128*M2*r5 - 128*M*r6 + 32*r7))/(2.*a2p2r2pa2c2th3*a2pr2m2Mr2*sinth2*tanth);\n src_re[6] = (-8*a*d2hS_dtph_re[6]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) + d2hS_dth2_re[6]/r2pa2cth2 + (d2hS_dr2_re[6]*(a2 - 2*M*r + r2))/r2pa2cth2 - (2*dhS_dth_re[8]*r)/r2pa2cth22 - (4*a*dhS_dph_re[3]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (4*a*dhS_dt_re[9]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (d2hS_dt2_re[6]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (2*dhS_dr_re[6]*(7*a4*M + a4*cos4th*(M - r) + a4*r - 4*a2*M*r2 + 4*a2*cos2th*(2*a2*M + (M - r)*r2) + 4*a2*r3 - 16*M*r4))/a2p2r2pa2c2th3 + (2*dhS_dph_re[4]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 12*a2*M*r2 + 4*a2*cos2th*r*(a2 - M*r + 2*r2) + 8*a2*r3 - 16*M*r4 + 8*r5))/a2p2r2pa2c2th3 - (4*dhS_dt_re[3]*M*(a6 + a2*(4*M - 3*r)*r3 + a2*cos2th*(a4 + 2*a2*r2 + (-4*M + r)*r3) - 2*r6))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (2*hS_re[6]*(-2*a6*M2 + a6*cos6th*M2 + 24*a6*M*r - 2*a6*cos6th*M*r + 10*a6*r2 + a6*cos6th*r2 - 40*a4*M2*r2 + 2*a4*cos4th*(a2*(M2 - 12*M*r + 3*r2) + 2*r2*(10*M2 - 9*M*r + 3*r2)) - 44*a4*M*r3 + 36*a4*r4 + 112*a2*M2*r4 - a2*cos2th*(a4*(M2 - 2*M*r - 15*r2) + 48*a2*(M - r)*r3 - 16*(M2 - 5*M*r + 3*r2)*r4) - 176*a2*M*r5 + 48*a2*r6 + 128*M2*r6 - 128*M*r7 + 32*r8))/(a2p2r2pa2c2th4*a2pr2m2Mr) + (4*a*hS_re[2]*M*(5*a6 - 21*a4*r2 + cos4th*(-a6 + a4*r2) - 56*a2*r4 + 4*a2*cos2th*(a4 + 3*a2*r2 + 4*r4) - 24*r6)*sin2th)/(a2p2r2pa2c2th4*a2pr2m2Mr) - (2*a2*costh*dhS_dr_re[8]*sinth)/r2pa2cth22 + (d2hS_dph2_re[6]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (dhS_dph_re[9]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 20*a2*M*r2 + 4*a2*cos2th*r*(a2 - 3*M*r + 2*r2) + 8*a2*r3 + 32*M2*r3 - 32*M*r4 + 8*r5))/(a2p2r2pa2c2th2*a2pr2m2Mr2*sinth2) - (8*a*dhS_dr_re[1]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*dhS_dt_re[4]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*hS_re[1]*M*(3*a6*M - 20*a6*r + 31*a4*M*r2 - 26*a4*r3 + a4*cos4th*(a2*M - 3*M*r2 + 2*r3) + 4*a2*cos2th*(a4*(M - 5*r) + a2*(7*M - 8*r)*r2 + (6*M - r)*r4) + 12*a2*r5 - 24*M*r6 + 24*r7)*sinth2)/(a2p2r2pa2c2th4*a2pr2m2Mr) - (32*a3*costh*dhS_dth_re[1]*M*r*sinth3)/a2p2r2pa2c2th3 + (32*a3*costh*dhS_dt_re[5]*M*r*sinth3)/a2p2r2pa2c2th3 - (dhS_dth_re[6]*(a4 + 3*a4*cos4th + 16*a2*M*r + 4*a2*cos2th*(a2 + 4*r*(-M + r)) + 8*r4))/(a2p2r2pa2c2th3*tanth) + (2*dhS_dph_re[5]*(3*a4 + a4*cos4th + 8*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (2*hS_re[8]*(-6*a6*M - a6*cos6th*M + 4*a6*r + a6*cos6th*r + 52*a4*M*r2 + 2*a4*cos4th*(a2*(3*M + 2*r) + (-2*M + 5*r)*r2) + 14*a4*r3 + 48*a2*M*r4 + a2*cos2th*(a4*(M + 7*r) + 8*a2*(-10*M + 3*r)*r2 + 16*(-7*M + 2*r)*r4) + 16*a2*r5 - 32*M*r6 + 16*r7))/(a2p2r2pa2c2th4*a2pr2m2Mr*tanth);\n src_re[7] = (-8*a*d2hS_dtph_re[7]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (4*dhS_dr_re[7]*(a2*cos2th*(M - r) + a2*(M + 3*r) + 2*(-3*M + r)*r2))/a2p2r2pa2c2th2 + d2hS_dth2_re[7]/r2pa2cth2 + (d2hS_dr2_re[7]*(a2 - 2*M*r + r2))/r2pa2cth2 + (4*a2pr2m2Mr*dhS_dth_re[5]*r)/r2pa2cth22 - (d2hS_dt2_re[7]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) + (8*a*hS_re[3]*M*r*(-15*a4 + a4*cos4th + 16*a2*M*r - 2*a2*cos2th*(7*a2 + r*(-8*M + 7*r)) - 2*a2*r2 - 16*M*r3 + 12*r4))/(a2p2r2pa2c2th3*a2pr2m2Mr) + (4*hS_re[0]*M*r*(-9*a6 + 4*a4*M*r - 7*a4*r2 + a4*cos4th*(3*a2 - 4*M*r + 3*r2) - 8*a2*M*r3 - 2*a2*cos2th*(3*a4 + 8*a2*r2 + (-4*M + 5*r)*r3) + 6*a2*r4 + 4*r6))/(a2p2r2pa2c2th3*a2pr2m2Mr) - (16*a3*dhS_dph_re[2]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (16*a3*dhS_dt_re[8]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (16*a2*hS_re[5]*(-M + r)*sin2th)/a2p2r2pa2c2th2 - (16*a2*dhS_dt_re[2]*M*r*(a2 + r2)*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (2*a2*a2pr2m2Mr*dhS_dr_re[5]*sin2th)/r2pa2cth22 + (d2hS_dph2_re[7]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (hS_re[7]*(6*a4 + a4*cos6th + 8*a2*r2 + 2*a2*cos4th*(5*a2 + 4*r2) + 32*M*r3 + cos2th*(15*a4 + 48*a2*r2 + 16*(-2*M + r)*r3) + 16*r4))/(2.*a2p2r2pa2c2th3*sinth2) + (a2pr2m2Mr*hS_re[4]*(3*a2*cos2th*M*r + r*(3*a2*M + 2*a2*r - 6*M*r2 + 2*r3) + 2*a4*costh2*sinth2))/r2pa2cth23 - (2*dhS_dth_re[7]*(-5*a2 + 3*a2*cos2th - 2*r2))/(a2p2r2pa2c2th2*tanth) - (2*dhS_dph_re[8]*(3*a4 + a4*cos4th + 4*a2*cos2th*(a2 + 2*r*(-2*M + r)) + 8*a2*r2 - 16*M*r3 + 8*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr*sinth2*tanth) + (hS_re[9]*(35*a6 + 8*a6*cos6th + a6*cos8th - 168*a4*M*r - 36*a4*cos6th*M*r + 120*a4*r2 + 12*a4*cos6th*r2 + 128*a2*M2*r2 + 4*a2*cos4th*(7*a4 + 2*a2*r*(5*M + 9*r) - 4*(8*M2 + M*r - 3*r2)*r2) - 48*a2*M*r3 + 144*a2*r4 - 256*M2*r4 + 64*r6 + 4*cos2th*(14*a6 + a4*r*(-23*M + 45*r) - 16*a2*(7*M - 3*r)*r3 + 16*r4*pow(-2*M + r,2))))/(8.*a2p2r2pa2c2th3*a2pr2m2Mr*sinth4);\n src_re[8] = (-8*a*d2hS_dtph_re[8]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) + d2hS_dth2_re[8]/r2pa2cth2 + (d2hS_dr2_re[8]*(a2 - 2*M*r + r2))/r2pa2cth2 + (2*a2pr2m2Mr*dhS_dth_re[6]*r)/r2pa2cth22 - (d2hS_dt2_re[8]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dr_re[8]*(a4*(M + r) + 3*a2*(-M + r)*r2 + a2*cos2th*(a2*(M + r) + (-M + r)*r2) + 2*(-3*M + r)*r4))/a2p2r2pa2c2th3 + (2*dhS_dph_re[5]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 12*a2*M*r2 + 4*a2*cos2th*r*(a2 - M*r + 2*r2) + 8*a2*r3 - 16*M*r4 + 8*r5))/a2p2r2pa2c2th3 - (8*a3*dhS_dph_re[3]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (8*a3*dhS_dt_re[9]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (8*a2*dhS_dt_re[3]*M*r*(a2 + r2)*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (a2*a2pr2m2Mr*dhS_dr_re[6]*sin2th)/r2pa2cth22 + (d2hS_dph2_re[8]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (hS_re[8]*(55*a6 + 10*a6*cos6th + a6*cos8th - 80*a4*M*r - 24*a4*cos6th*M*r + 184*a4*r2 + 16*a4*cos6th*r2 + 224*a2*M*r3 + 8*a2*cos4th*(5*a4 + a2*r*(10*M + 13*r) + 2*(2*M + 5*r)*r3) + 208*a2*r4 + 256*M*r5 + 2*cos2th*(43*a6 + 4*a4*r*(3*M + 34*r) - 16*a2*(8*M - 9*r)*r3 + 64*(-2*M + r)*r5) + 64*r6))/(4.*a2p2r2pa2c2th4*sinth2) - (8*a*dhS_dr_re[2]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*dhS_dt_re[5]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (32*a*hS_re[2]*M*r*(4*a4 - a2*r2 + a2*cos2th*(4*a2 + 3*r2) - 6*r4)*sinth2)/a2p2r2pa2c2th4 - (32*a3*costh*dhS_dth_re[2]*M*r*sinth3)/a2p2r2pa2c2th3 + (32*a3*costh*dhS_dt_re[7]*M*r*sinth3)/a2p2r2pa2c2th3 + (32*a2pr2m2Mr*a3*costh*hS_re[1]*M*(a2 + a2*cos2th - 10*r2)*sinth3)/a2p2r2pa2c2th4 - (dhS_dth_re[8]*(a4 + 3*a4*cos4th + 16*a2*M*r + 4*a2*cos2th*(a2 + 4*r*(-M + r)) + 8*r4))/(a2p2r2pa2c2th3*tanth) + (2*dhS_dph_re[7]*(3*a4 + a4*cos4th + 8*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (2*hS_re[6]*(-2*a6*M - a6*cos6th*M + 10*a6*r + a6*cos6th*r + 8*a4*M2*r + 60*a4*M*r2 + 2*a4*cos4th*(a2*(M + 3*r) + 2*r*(-2*M2 - 3*M*r + 3*r2)) + 36*a4*r3 - 160*a2*M2*r3 + a2*cos2th*(a4*(M + 15*r) - 16*a2*(7*M - 3*r)*r2 + 16*(10*M2 - 10*M*r + 3*r2)*r3) + 32*a2*M*r4 + 48*a2*r5 - 64*M*r6 + 32*r7))/(a2p2r2pa2c2th4*tanth) - (dhS_dph_re[9]*(3*a4 + a4*cos4th + 4*a2*cos2th*(a2 + 2*r*(-2*M + r)) + 8*a2*r2 - 16*M*r3 + 8*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr*sinth2*tanth);\n src_re[9] = (-8*a*d2hS_dtph_re[9]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) + d2hS_dth2_re[9]/r2pa2cth2 + (d2hS_dr2_re[9]*(a2 - 2*M*r + r2))/r2pa2cth2 - (d2hS_dt2_re[9]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (2*dhS_dr_re[9]*(5*a4*M - a4*cos4th*(M - r) + 3*a4*r - 16*a2*M*r2 + 8*a2*r3 + 4*a2*cos2th*(a2*(M + r) + 2*r3) - 24*M*r4 + 8*r5))/a2p2r2pa2c2th3 + (4*dhS_dph_re[6]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 12*a2*M*r2 + 4*a2*cos2th*r*(a2 - M*r + 2*r2) + 8*a2*r3 - 16*M*r4 + 8*r5))/a2p2r2pa2c2th3 + (hS_re[7]*(35*a8 + 8*a8*cos6th + a8*cos8th - 78*a6*M*r - 36*a6*cos6th*M*r - 2*a6*cos8th*M*r + 155*a6*r2 + 20*a6*cos6th*r2 + a6*cos8th*r2 + 80*a4*M2*r2 + 40*a4*cos6th*M2*r2 + 88*a4*M*r3 - 44*a4*cos6th*M*r3 + 264*a4*r4 + 12*a4*cos6th*r4 - 96*a2*M2*r4 + 4*a2*cos4th*(7*a6 + 5*a4*r*(4*M + 5*r) + 4*(-2*M2 + M*r + 3*r2)*r4 + a2*(-20*M2*r2 + 26*M*r3 + 30*r4)) + 304*a2*M*r5 + 208*a2*r6 + 128*M*r7 + 4*cos2th*(14*a8 + a6*r*(9*M + 59*r) + a4*r2*(-10*M2 - 37*M*r + 93*r2) + 16*a2*(2*M2 - 5*M*r + 4*r2)*r4 + 16*(-2*M + r)*r7) + 64*r8))/(2.*a2p2r2pa2c2th5) + (2*a2pr2m2Mr*hS_re[5]*(-10*a6*M - a6*cos6th*M + 10*a6*r + a6*cos6th*r + 140*a4*M*r2 + 2*a4*cos4th*(a2*(5*M + 3*r) + 2*(M + 3*r)*r2) + 36*a4*r3 + 160*a2*M*r4 + a2*cos2th*(a4*(M + 15*r) - 48*a2*(3*M - r)*r2 + 16*(-10*M + 3*r)*r4) + 48*a2*r5 + 32*r7)*sin2th)/a2p2r2pa2c2th5 + (d2hS_dph2_re[9]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) + (hS_re[9]*(126*a10 + a10*cos10th + 45*a10*cos6th + 10*a10*cos8th + 6*a8*M2 - a8*cos10th*M2 + 3*a8*cos6th*M2 + 2*a8*cos8th*M2 - 160*a8*M*r - 160*a8*cos6th*M*r - 32*a8*cos8th*M*r + 512*r10 + 700*a8*r2 + 160*a8*cos6th*r2 + 20*a8*cos8th*r2 - 120*a6*M2*r2 + 160*a6*cos6th*M2*r2 + 24*a6*cos8th*M2*r2 - 840*a6*M*r3 - 384*a6*cos6th*M*r3 - 24*a6*cos8th*M*r3 - 640*a4*M3*r3 - 320*a4*cos6th*M3*r3 + 1600*a6*r4 + 160*a6*cos6th*r4 - 96*a4*M2*r4 + 240*a4*cos6th*M2*r4 - 1856*a4*M*r5 - 160*a4*cos6th*M*r5 + 768*a2*M3*r5 + 8*a2*cos4th*(15*a8 - a6*(M2 + 40*M*r - 70*r2) + 4*a4*r2*(3*M2 - 37*M*r + 30*r2) + 4*a2*r3*(20*M3 + 11*M2*r - 38*M*r2 + 20*r3) + 16*M*(2*M2 + 2*M*r - r2)*r5) + 1920*a4*r6 + 768*a2*M2*r6 - 2432*a2*M*r7 + 1280*a2*r8 + 1024*M2*r8 + 2*cos2th*(105*a10 - a8*(M2 + 176*M*r - 560*r2) + 16*a6*r2*(-5*M2 - 52*M*r + 75*r2) + 8*a4*r3*(20*M3 - 31*M2*r - 182*M*r2 + 160*r3) - 128*a2*(4*M3 + 4*M2*r + 6*M*r2 - 5*r3)*r5 + 256*M*(-2*M + r)*r8) - 1536*M*r9))/(8.*a2p2r2pa2c2th5*a2pr2m2Mr*sinth2) - (16*a*dhS_dr_re[3]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (16*a*dhS_dt_re[6]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (2*a2pr2m2Mr*hS_re[4]*(-2*a6*M2 + a6*cos6th*M2 + 76*a6*M*r - 2*a6*cos6th*M*r + 10*a6*r2 + a6*cos6th*r2 - 40*a4*M2*r2 + 2*a4*cos4th*(a2*(M2 - 14*M*r + 3*r2) + 2*r2*(10*M2 - 8*M*r + 3*r2)) + 32*a4*M*r3 + 36*a4*r4 + 48*a2*M2*r4 - a2*cos2th*(a4*(M2 - 50*M*r - 15*r2) - 48*a2*(2*M + r)*r3 - 48*(-M2 + M*r + r2)*r4) - 144*a2*M*r5 + 48*a2*r6 - 96*M*r7 + 32*r8)*sinth2)/a2p2r2pa2c2th5 + (4*a*hS_re[3]*M*(2*a8*M - a8*cos6th*M + 30*a8*r + 3*a8*cos6th*r - 130*a6*M*r2 - 3*a6*cos6th*M*r2 + 70*a6*r3 + a6*cos6th*r3 - 80*a4*M2*r3 - 2*a4*cos4th*(a4*(M - 9*r) + a2*(31*M - 13*r)*r2 + 2*(-20*M2 + 14*M*r + r2)*r3) - 184*a4*M*r4 + 4*a4*r5 + 64*a2*M2*r5 + a2*cos2th*(a6*(M + 45*r) + a4*(-189*M + 95*r)*r2 - 272*a2*M*r4 - 16*(4*M2 + 3*M*r + 5*r2)*r5) + 176*a2*M*r6 - 112*a2*r7 + 256*M*r8 - 96*r9)*sinth2)/(a2p2r2pa2c2th5*a2pr2m2Mr) - (2*hS_re[0]*M*(-2*a10*M + a10*cos6th*M + 30*a10*r + 3*a10*cos6th*r - 32*r11 + 28*a8*M*r2 - 18*a8*cos6th*M*r2 + 120*a8*r3 + 6*a8*cos6th*r3 + 40*a6*M2*r3 + 20*a6*cos6th*M2*r3 + 46*a6*M*r4 - 15*a6*cos6th*M*r4 + 166*a6*r5 + 3*a6*cos6th*r5 - 48*a4*M2*r5 + 2*a4*cos4th*(a6*(M + 9*r) - 14*a4*(M - 2*r)*r2 + a2*(-20*M2 - 31*M*r + 29*r2)*r3 + 2*(-4*M2 - 2*M*r + 5*r2)*r5) - 152*a4*M*r6 + 60*a4*r7 - 208*a2*M*r8 + a2*cos2th*(-(a8*(M - 45*r)) + 2*a6*(9*M + 85*r)*r2 + a4*(-20*M2 + 31*M*r + 221*r2)*r3 + 16*a2*(4*M2 + 10*M*r + 7*r2)*r5 + 16*(13*M + r)*r8) - 48*a2*r9)*sinth2)/(a2p2r2pa2c2th5*a2pr2m2Mr) - (64*a3*costh*dhS_dth_re[3]*M*r*sinth3)/a2p2r2pa2c2th3 + (64*a3*costh*dhS_dt_re[8]*M*r*sinth3)/a2p2r2pa2c2th3 + (4*dhS_dph_re[8]*(3*a4 + a4*cos4th + 8*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (dhS_dth_re[9]*(9*a4 + 3*a4*cos4th + 32*a2*M*r + 24*a2*r2 + 4*a2*cos2th*(3*a2 - 8*M*r + 6*r2) + 24*r4))/(a2p2r2pa2c2th3*tanth);\n\n src_im[0] = (-8*a*d2hS_dtph_im[0]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (16*dhS_dt_im[1]*M*(a2 + a2*cos2th - 2*r2)*(a2 + r2))/a2p2r2pa2c2th3 + d2hS_dth2_im[0]/r2pa2cth2 + (d2hS_dr2_im[0]*(a2 - 2*M*r + r2))/r2pa2cth2 + (4*a*dhS_dr_im[3]*M*(a2*costh2 - r2))/r2pa2cth23 + (4*a*dhS_dph_im[1]*M*(-(a2*costh2) + r2))/r2pa2cth23 - (d2hS_dt2_im[0]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) + (16*hS_im[7]*M*r*(-9*a4 + 3*a4*cos4th + 20*a2*M*r - 2*a2*cos2th*(3*a2 + 5*r*(-2*M + r)) + 2*a2*r2 - 8*M*r3 + 4*r4))/a2p2r2pa2c2th5 + (2*dhS_dr_im[0]*(5*a4*M - a4*cos4th*(M - r) + 3*a4*r - 16*a2*M*r2 + 8*a2*r3 + 4*a2*cos2th*(a2*(M + r) + 2*r3) - 24*M*r4 + 8*r5))/a2p2r2pa2c2th3 - (8*a2pr2m2Mr*hS_im[4]*M*(3*a4*M - 27*a4*r + a4*cos4th*(M + 3*r) + 40*a2*M*r2 + 4*a2*cos2th*(a2*(M - 6*r) + (10*M - 7*r)*r2) - 4*a2*r3 - 24*M*r4 + 16*r5))/a2p2r2pa2c2th5 + (16*a*hS_im[3]*M2*(3*a6 + 29*a4*r2 + a4*cos4th*(a2 + 7*r2) - 80*a2*M*r3 + 32*a2*r4 + 4*a2*cos2th*(a4 + 9*a2*r2 - 20*M*r3 + 6*r4) + 32*M*r5 - 8*r6))/(a2p2r2pa2c2th5*a2pr2m2Mr) + (8*hS_im[0]*M2*(3*a8 + 2*a6*r2 - 20*a4*M*r3 + a4*cos4th*(a4 - 2*a2*r2 + 20*M*r3 - 3*r4) - a4*r4 + 16*a2*M*r5 + 4*a2*cos2th*(a6 - 3*a2*r4 - 2*(2*M + r)*r5) + 8*a2*r6 + 8*r8))/(a2p2r2pa2c2th5*a2pr2m2Mr) - (32*a2*dhS_dt_im[2]*M*r*sin2th)/a2p2r2pa2c2th3 - (96*a2*a2pr2m2Mr*hS_im[5]*M*(a2 + a2*cos2th - 6*r2)*sin2th)/a2p2r2pa2c2th5 + (d2hS_dph2_im[0]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (2*hS_im[9]*M*(-2*a6*M + a6*cos6th*M + 30*a6*r + 3*a6*cos6th*r - 200*a4*M*r2 + 2*a4*cos4th*(a2*(M + 9*r) + 2*(-14*M + 5*r)*r2) + 60*a4*r3 + 320*a2*M2*r3 - a2*cos2th*(a4*(M - 45*r) + 16*a2*(16*M - 5*r)*r2 - 16*(20*M2 - 11*M*r + r2)*r3) - 208*a2*M*r4 + 16*a2*r5 - 128*M2*r5 + 128*M*r6 - 32*r7))/(a2p2r2pa2c2th5*a2pr2m2Mr*sinth2) - (64*a*dhS_dph_im[2]*M*r)/(a2p2r2pa2c2th3*tanth) + (64*a*dhS_dth_im[3]*M*r)/(a2p2r2pa2c2th3*tanth) + (dhS_dth_im[0]*(3*a4 + a4*cos4th + 32*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-4*M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth);\n src_im[1] = (-8*a*d2hS_dtph_im[1]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dt_im[4]*M*(a2 + a2*cos2th - 2*r2)*(a2 + r2))/a2p2r2pa2c2th3 + d2hS_dth2_im[1]/r2pa2cth2 + (d2hS_dr2_im[1]*(a2 - 2*M*r + r2))/r2pa2cth2 - (2*dhS_dth_im[2]*r)/r2pa2cth22 + (2*a*dhS_dr_im[6]*M*(a2*costh2 - r2))/r2pa2cth23 + (2*a*dhS_dph_im[4]*M*(-(a2*costh2) + r2))/r2pa2cth23 - (4*a*dhS_dph_im[0]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (4*a*dhS_dt_im[3]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (d2hS_dt2_im[1]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) + (4*dhS_dr_im[1]*(-(a4*M) - a4*cos4th*(M - r) + a4*r - 6*a2*M*r2 - 2*a2*cos2th*(a2*(M - r) + (M - 3*r)*r2) + 2*a2*r3 - 4*M*r4 + 4*r5))/a2p2r2pa2c2th3 - (8*a*hS_im[6]*M*(3*a4*M + a4*cos4th*(M - r) - 23*a4*r + 40*a2*M*r2 + 4*a2*cos2th*(a2*(M - 6*r) + 5*(2*M - r)*r2) - 12*a2*r3 - 24*M*r4 + 16*r5))/(a2p2r2pa2c2th4*a2pr2m2Mr) - (4*dhS_dt_im[0]*M*(a6 + a2*(4*M - 3*r)*r3 + a2*cos2th*(a4 + 2*a2*r2 + (-4*M + r)*r3) - 2*r6))/(a2p2r2pa2c2th2*a2pr2m2Mr2) + (hS_im[1]*(10*a8 + a8*cos6th - 24*a6*M2 + 116*a6*M*r - 2*a6*cos6th*M*r + 22*a6*r2 + a6*cos6th*r2 - 248*a4*M2*r2 + 2*a4*cos4th*(3*a4 + 2*r2*(6*M2 - 4*M*r + r2) + a2*(-4*M2 - 10*M*r + 5*r2)) + 208*a4*M*r3 - 4*a4*r4 - 128*a2*M2*r4 + a2*cos2th*(15*a6 - 32*a2*M*(7*M - 8*r)*r2 + a4*(-32*M2 + 98*M*r + 31*r2) - 16*(20*M2 - 12*M*r + r2)*r4) + 128*a2*M*r5 - 48*a2*r6 - 64*M2*r6 + 64*M*r7 - 32*r8))/(a2p2r2pa2c2th4*a2pr2m2Mr) - (16*a2*dhS_dt_im[5]*M*r*sin2th)/a2p2r2pa2c2th3 - (32*a3*hS_im[8]*M*(a2 + a2*cos2th - 4*r2)*sin2th)/(a2p2r2pa2c2th4*a2pr2m2Mr) - (2*a2*costh*dhS_dr_im[2]*sinth)/r2pa2cth22 + (d2hS_dph2_im[1]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (dhS_dph_im[3]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 20*a2*M*r2 + 4*a2*cos2th*r*(a2 - 3*M*r + 2*r2) + 8*a2*r3 + 32*M2*r3 - 32*M*r4 + 8*r5))/(a2p2r2pa2c2th2*a2pr2m2Mr2*sinth2) - (32*a*dhS_dph_im[5]*M*r)/(a2p2r2pa2c2th3*tanth) + (32*a*dhS_dth_im[6]*M*r)/(a2p2r2pa2c2th3*tanth) + (dhS_dth_im[1]*(5*a4 - a4*cos4th + 16*a2*M*r + 4*a2*cos2th*(a2 - 4*M*r) + 16*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (4*hS_im[2]*(4*a6*M + 3*a6*r - 34*a4*M*r2 + a4*cos4th*(a2*(-4*M + r) + (-6*M + r)*r2) + 11*a4*r3 + 4*a2*cos2th*r*(a4 + 3*a2*r*(2*M + r) + 2*(2*M + r)*r3) - 48*a2*M*r4 + 16*a2*r5 - 16*M*r6 + 8*r7))/(a2p2r2pa2c2th4*a2pr2m2Mr*tanth);\n src_im[2] = (-8*a*d2hS_dtph_im[2]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dt_im[5]*M*(a2 + a2*cos2th - 2*r2)*(a2 + r2))/a2p2r2pa2c2th3 + d2hS_dth2_im[2]/r2pa2cth2 + (d2hS_dr2_im[2]*(a2 - 2*M*r + r2))/r2pa2cth2 + (2*a2pr2m2Mr*dhS_dth_im[1]*r)/r2pa2cth22 + (2*a*dhS_dr_im[8]*M*(a2*costh2 - r2))/r2pa2cth23 + (2*a*dhS_dph_im[5]*M*(-(a2*costh2) + r2))/r2pa2cth23 - (d2hS_dt2_im[2]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*a3*dhS_dph_im[0]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (8*a3*dhS_dt_im[3]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (16*a2*dhS_dt_im[7]*M*r*sin2th)/a2p2r2pa2c2th3 - (8*a2*dhS_dt_im[0]*M*r*(a2 + r2)*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (a2*a2pr2m2Mr*dhS_dr_im[1]*sin2th)/r2pa2cth22 + (4*a2*hS_im[1]*(-7*a4*M - a4*cos4th*(M - r) + 3*a4*r + 8*a2*M2*r - 4*a2*cos2th*(a2*(2*M - r) + r*(-2*M2 + 3*M*r - 2*r2)) + 28*a2*M*r2 + 8*a2*r3 - 80*M2*r3 + 32*M*r4 + 8*r5)*sin2th)/a2p2r2pa2c2th4 + (d2hS_dph2_im[2]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) + (8*a*hS_im[8]*M*r*(-a2 + 5*a2*cos4th + 4*cos2th*(a2 - r2) + 12*r2))/(a2p2r2pa2c2th4*sinth2) - (hS_im[2]*(15*a6 + 6*a6*cos6th + a6*cos8th + 96*a4*M*r + 16*a4*cos6th*M*r + 56*a4*r2 + 8*a4*cos6th*r2 - 160*a2*M*r3 + 8*a2*cos4th*(2*a4 + a2*r*(-12*M + 5*r) + 2*(-6*M + r)*r3) + 80*a2*r4 - 128*M*r5 + 2*cos2th*(13*a6 + a4*(-8*M*r + 44*r2) + 16*a2*(8*M + 3*r)*r3 + 64*M*r5) + 64*r6))/(4.*a2p2r2pa2c2th4*sinth2) - (8*a2*dhS_dr_im[2]*(-(a2*cos2th*(M - r)) + a2*(-M + r) + 2*(M + r)*r2)*sinth2)/a2p2r2pa2c2th3 - (32*a*dhS_dph_im[7]*M*r)/(a2p2r2pa2c2th3*tanth) + (32*a*dhS_dth_im[8]*M*r)/(a2p2r2pa2c2th3*tanth) - (32*a*a2pr2m2Mr*hS_im[6]*M*(a2 + a2*cos2th - 10*r2))/(a2p2r2pa2c2th4*tanth) + (dhS_dth_im[2]*(5*a4 - a4*cos4th + 16*a2*M*r + 4*a2*cos2th*(a2 - 4*M*r) + 16*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (dhS_dph_im[3]*(3*a4 + a4*cos4th + 4*a2*cos2th*(a2 + 2*r*(-2*M + r)) + 8*a2*r2 - 16*M*r3 + 8*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr*sinth2*tanth);\n src_im[3] = (-8*a*d2hS_dtph_im[3]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dt_im[6]*M*(a2 + a2*cos2th - 2*r2)*(a2 + r2))/a2p2r2pa2c2th3 + d2hS_dth2_im[3]/r2pa2cth2 + (d2hS_dr2_im[3]*(a2 - 2*M*r + r2))/r2pa2cth2 + (2*a*dhS_dr_im[9]*M*(a2*costh2 - r2))/r2pa2cth23 + (2*a*dhS_dph_im[6]*M*(-(a2*costh2) + r2))/r2pa2cth23 - (d2hS_dt2_im[3]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*a*hS_im[7]*M*r*(-3*a4 + 10*a2*M*r + 17*a2*r2 + a2*cos4th*(11*a2 - 10*M*r + 11*r2) - 8*M*r3 + 4*cos2th*(2*a4 + a2*r2 + (2*M - r)*r3) + 20*r4))/a2p2r2pa2c2th5 + (2*dhS_dph_im[1]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 12*a2*M*r2 + 4*a2*cos2th*r*(a2 - M*r + 2*r2) + 8*a2*r3 - 16*M*r4 + 8*r5))/a2p2r2pa2c2th3 - (4*hS_im[3]*M*(2*a8*M - a8*cos6th*M + 30*a8*r + 3*a8*cos6th*r - 54*a6*M*r2 - 5*a6*cos6th*M*r2 + 90*a6*r3 + 3*a6*cos6th*r3 - 80*a4*M2*r3 - 2*a4*cos4th*(a4*(M - 9*r) + a2*(21*M - 19*r)*r2 - 2*(20*M2 - 12*M*r + 5*r2)*r3) - 96*a4*M*r4 + 76*a4*r5 + 64*a2*M2*r5 + a2*cos2th*(a6*(M + 45*r) + a4*(-91*M + 125*r)*r2 + 16*a2*(-11*M + 6*r)*r4 + 16*(-4*M2 - 5*M*r + r2)*r5) + 16*a2*M*r6 - 16*a2*r7 + 64*M*r8 - 32*r9))/(a2p2r2pa2c2th5*a2pr2m2Mr) - (16*a2*dhS_dt_im[8]*M*r*sin2th)/a2p2r2pa2c2th3 - (16*a*a2pr2m2Mr*hS_im[5]*M*(-3*a4 + a4*cos4th + 26*a2*r2 - 2*a2*cos2th*(a2 + 5*r2) + 20*r4)*sin2th)/a2p2r2pa2c2th5 + (d2hS_dph2_im[3]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (a*hS_im[9]*M*(3*a6*M + a6*cos8th*(M - r) + 85*a6*r + 124*a6*cos2th*r + 4*a6*cos6th*r - 80*a4*M*r2 - 216*a4*cos2th*M*r2 - 40*a4*cos6th*M*r2 + 280*a4*r3 + 380*a4*cos2th*r3 + 4*a4*cos6th*r3 - 320*a2*M2*r3 - 4*a2*cos4th*(a4*(M - 11*r) + 2*a2*(22*M - 13*r)*r2 - 20*(4*M2 - 3*M*r + r2)*r3) - 208*a2*M*r4 - 576*a2*cos2th*M*r4 + 304*a2*r5 + 384*a2*cos2th*r5 + 256*M2*r5 - 256*cos2th*M2*r5 - 256*M*r6 - 256*cos2th*M*r6 + 64*r7 + 192*cos2th*r7))/(2.*a2p2r2pa2c2th5*a2pr2m2Mr*sinth2) - (8*a*dhS_dr_im[0]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*dhS_dt_im[1]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*a2pr2m2Mr*hS_im[4]*M*(3*a4*M + a4*cos4th*(M - r) - 39*a4*r + 40*a2*M*r2 + 4*a2*cos2th*(a2*(M - 10*r) + (10*M - 9*r)*r2) - 12*a2*r3 - 24*M*r4 + 32*r5)*sinth2)/a2p2r2pa2c2th5 - (8*a*hS_im[0]*M2*(3*a8 - 22*a6*r2 - 20*a4*M*r3 + a4*cos4th*(a4 - 10*a2*r2 + 20*M*r3 - 11*r4) - 41*a4*r4 + 16*a2*M*r5 + 4*a2*cos2th*(a6 - 8*a4*r2 - 15*a2*r4 - 2*(2*M + 3*r)*r5) + 24*a2*r6 + 40*r8)*sinth2)/(a2p2r2pa2c2th5*a2pr2m2Mr) - (32*a3*costh*dhS_dth_im[0]*M*r*sinth3)/a2p2r2pa2c2th3 + (32*a3*costh*dhS_dt_im[2]*M*r*sinth3)/a2p2r2pa2c2th3 - (2*dhS_dth_im[3])/(a2p2r2pa2c2th*tanth) - (32*a*dhS_dph_im[8]*M*r)/(a2p2r2pa2c2th3*tanth) + (32*a*dhS_dth_im[9]*M*r)/(a2p2r2pa2c2th3*tanth) + (2*dhS_dph_im[2]*(3*a4 + a4*cos4th + 8*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth);\n src_im[4] = (-8*a*d2hS_dtph_im[4]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (4*dhS_dr_im[4]*(3*a2*cos2th*(M - r) + a2*(3*M + r) - 2*(M + r)*r2))/a2p2r2pa2c2th2 + d2hS_dth2_im[4]/r2pa2cth2 + (d2hS_dr2_im[4]*(a2 - 2*M*r + r2))/r2pa2cth2 - (4*dhS_dth_im[5]*r)/r2pa2cth22 - (8*a*dhS_dph_im[1]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (8*a*dhS_dt_im[6]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (d2hS_dt2_im[4]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) + (2*hS_im[4]*(7*a6 + 3*a4*M2 + 4*a4*M*r + 10*a4*r2 - 40*a2*M2*r2 + a4*cos4th*(a2 + M2 - 4*M*r + 2*r2) + 4*a2*cos2th*(2*a4 + 2*M*(-5*M + 3*r)*r2 + a2*(M2 + r2)) + 40*a2*M*r3 - 16*a2*r4 - 56*M2*r4 + 64*M*r5 - 16*r6))/(a2p2r2pa2c2th3*a2pr2m2Mr) - (8*dhS_dt_im[1]*M*(a6 + a2*(4*M - 3*r)*r3 + a2*cos2th*(a4 + 2*a2*r2 + (-4*M + r)*r3) - 2*r6))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (4*a*hS_im[3]*M*(3*a6*M - 39*a6*r + a4*cos4th*(M - r)*(a2 - r2) + 101*a4*M*r2 - 45*a4*r3 - 48*a2*M2*r3 + 4*a2*cos2th*(a4*(M - 10*r) + a2*(25*M - 17*r)*r2 + (-12*M2 + 18*M*r - 5*r2)*r3) - 16*a2*M*r4 + 36*a2*r5 + 96*M2*r5 - 136*M*r6 + 48*r7))/(a2p2r2pa2c2th3*a2pr2m2Mr3) - (2*hS_im[0]*M*(3*a8*M - 27*a8*r + 62*a6*M*r2 - 58*a6*r3 - 12*a4*M2*r3 + a4*cos4th*(a4*(M + 3*r) + 2*a2*(-7*M + 3*r)*r2 + (12*M2 - 11*M*r + 3*r2)*r3) + 39*a4*M*r4 - 19*a4*r5 + 48*a2*M2*r5 + 4*a2*cos2th*(a6*(M - 6*r) + a4*(12*M - 19*r)*r2 + a2*(29*M - 20*r)*r4 + (-12*M2 + 22*M*r - 7*r2)*r5) - 56*a2*M*r6 + 28*a2*r7 - 24*M*r8 + 16*r9))/(a2p2r2pa2c2th3*a2pr2m2Mr3) - (4*a2*costh*dhS_dr_im[5]*sinth)/r2pa2cth22 + (d2hS_dph2_im[4]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (2*dhS_dph_im[6]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 20*a2*M*r2 + 4*a2*cos2th*r*(a2 - 3*M*r + 2*r2) + 8*a2*r3 + 32*M2*r3 - 32*M*r4 + 8*r5))/(a2p2r2pa2c2th2*a2pr2m2Mr2*sinth2) + (hS_im[9]*(-2*a6*M2 + a6*cos6th*M2 + 76*a6*M*r - 2*a6*cos6th*M*r + 10*a6*r2 + a6*cos6th*r2 - 248*a4*M2*r2 + 2*a4*cos4th*(a2*(M2 - 14*M*r + 3*r2) + 2*r2*(14*M2 - 12*M*r + 3*r2)) - 16*a4*M*r3 + 192*a2*M3*r3 - a2*cos2th*(a4*(M2 - 50*M*r - 15*r2) - 16*a2*r2*(-12*M2 + 2*M*r + 3*r2) - 16*r3*(12*M3 - 7*M2*r - 5*M*r2 + 3*r3)) + 36*a4*r4 + 240*a2*M2*r4 - 272*a2*M*r5 - 384*M3*r5 + 48*a2*r6 + 512*M2*r6 - 224*M*r7 + 32*r8))/(2.*a2p2r2pa2c2th3*a2pr2m2Mr3*sinth2) + (hS_im[7]*(3*a2*cos2th*M*r + r*(3*a2*M + 2*a2*r - 6*M*r2 + 2*r3) + 2*a4*costh2*sinth2))/(a2pr2m2Mr*r2pa2cth23) - (2*dhS_dth_im[4]*(-5*a2 + 3*a2*cos2th - 2*r2))/(a2p2r2pa2c2th2*tanth) + (8*hS_im[5]*(a2*(M - 3*r) - a2*cos2th*(M - r) + 2*(2*M - r)*r2))/(a2p2r2pa2c2th2*a2pr2m2Mr*tanth);\n src_im[5] = (-8*a*d2hS_dtph_im[5]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dr_im[5]*(a2*cos2th*(M - r) + a2*(M + r) - 2*M*r2))/a2p2r2pa2c2th2 + d2hS_dth2_im[5]/r2pa2cth2 + (d2hS_dr2_im[5]*(a2 - 2*M*r + r2))/r2pa2cth2 + (2*a2pr2m2Mr*dhS_dth_im[4]*r)/r2pa2cth22 - (2*dhS_dth_im[7]*r)/r2pa2cth22 - (4*a*dhS_dph_im[2]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (4*a*dhS_dt_im[8]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (d2hS_dt2_im[5]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (4*dhS_dt_im[2]*M*(a6 + a2*(4*M - 3*r)*r3 + a2*cos2th*(a4 + 2*a2*r2 + (-4*M + r)*r3) - 2*r6))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (8*a3*dhS_dph_im[1]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (8*a3*dhS_dt_im[6]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (12*a2*hS_im[4]*(-M + r)*sin2th)/a2p2r2pa2c2th2 - (8*a2*dhS_dt_im[1]*M*r*(a2 + r2)*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (a2*a2pr2m2Mr*dhS_dr_im[4]*sin2th)/r2pa2cth22 - (4*a2*hS_im[0]*M*(3*a6 - 4*a4*r*(M + 3*r) + a2*(32*M - 33*r)*r3 + a2*cos2th*(3*a4 + a2*(-4*M*r + 6*r2) + (-8*M + 3*r)*r3) + 2*(16*M - 9*r)*r5)*sin2th)/(a2p2r2pa2c2th3*a2pr2m2Mr2) - (2*a2*costh*dhS_dr_im[7]*sinth)/r2pa2cth22 + (d2hS_dph2_im[5]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (hS_im[5]*(a4 + 3*a4*cos4th + a4*cos6th + 8*a2*r2 - 32*M*r3 + cos2th*(3*a4 + 8*a2*r2 + 16*(2*M - r)*r3) + 24*r4))/(a2p2r2pa2c2th3*sinth2) - (dhS_dph_im[8]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 20*a2*M*r2 + 4*a2*cos2th*r*(a2 - 3*M*r + 2*r2) + 8*a2*r3 + 32*M2*r3 - 32*M*r4 + 8*r5))/(a2p2r2pa2c2th2*a2pr2m2Mr2*sinth2) - (8*hS_im[7]*r)/(a2p2r2pa2c2th2*tanth) - (2*dhS_dth_im[5]*(-5*a2 + 3*a2*cos2th - 2*r2))/(a2p2r2pa2c2th2*tanth) + (8*a*hS_im[3]*M*(-3*a6 + 5*a4*M*r + a4*cos4th*(a2 - M*r) + 20*a4*r2 - 48*a2*M*r3 - 2*a2*cos2th*(a4 - 2*a2*(M - 4*r)*r + (-16*M + 9*r)*r3) + 38*a2*r4 - 24*M*r5 + 12*r6))/(a2p2r2pa2c2th3*a2pr2m2Mr2*tanth) - (dhS_dph_im[6]*(3*a4 + a4*cos4th + 4*a2*cos2th*(a2 + 2*r*(-2*M + r)) + 8*a2*r2 - 16*M*r3 + 8*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr*sinth2*tanth) + (hS_im[9]*(-10*a6*M - a6*cos6th*M + 10*a6*r + a6*cos6th*r + 16*a4*M2*r + 92*a4*M*r2 + 36*a4*r3 - 256*a2*M2*r3 + 2*a4*cos4th*(5*a2*M + 3*a2*r - 8*M2*r - 6*M*r2 + 6*r3) + a2*cos2th*(a4*(M + 15*r) + 16*a2*(-13*M + 3*r)*r2 + 48*(8*M2 - 6*M*r + r2)*r3) + 32*a2*M*r4 + 48*a2*r5 + 128*M2*r5 - 128*M*r6 + 32*r7))/(2.*a2p2r2pa2c2th3*a2pr2m2Mr2*sinth2*tanth);\n src_im[6] = (-8*a*d2hS_dtph_im[6]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) + d2hS_dth2_im[6]/r2pa2cth2 + (d2hS_dr2_im[6]*(a2 - 2*M*r + r2))/r2pa2cth2 - (2*dhS_dth_im[8]*r)/r2pa2cth22 - (4*a*dhS_dph_im[3]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (4*a*dhS_dt_im[9]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 + 8*M*r3 - 6*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (d2hS_dt2_im[6]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (2*dhS_dr_im[6]*(7*a4*M + a4*cos4th*(M - r) + a4*r - 4*a2*M*r2 + 4*a2*cos2th*(2*a2*M + (M - r)*r2) + 4*a2*r3 - 16*M*r4))/a2p2r2pa2c2th3 + (2*dhS_dph_im[4]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 12*a2*M*r2 + 4*a2*cos2th*r*(a2 - M*r + 2*r2) + 8*a2*r3 - 16*M*r4 + 8*r5))/a2p2r2pa2c2th3 - (4*dhS_dt_im[3]*M*(a6 + a2*(4*M - 3*r)*r3 + a2*cos2th*(a4 + 2*a2*r2 + (-4*M + r)*r3) - 2*r6))/(a2p2r2pa2c2th2*a2pr2m2Mr2) - (2*hS_im[6]*(-2*a6*M2 + a6*cos6th*M2 + 24*a6*M*r - 2*a6*cos6th*M*r + 10*a6*r2 + a6*cos6th*r2 - 40*a4*M2*r2 + 2*a4*cos4th*(a2*(M2 - 12*M*r + 3*r2) + 2*r2*(10*M2 - 9*M*r + 3*r2)) - 44*a4*M*r3 + 36*a4*r4 + 112*a2*M2*r4 - a2*cos2th*(a4*(M2 - 2*M*r - 15*r2) + 48*a2*(M - r)*r3 - 16*(M2 - 5*M*r + 3*r2)*r4) - 176*a2*M*r5 + 48*a2*r6 + 128*M2*r6 - 128*M*r7 + 32*r8))/(a2p2r2pa2c2th4*a2pr2m2Mr) + (4*a*hS_im[2]*M*(5*a6 - 21*a4*r2 + cos4th*(-a6 + a4*r2) - 56*a2*r4 + 4*a2*cos2th*(a4 + 3*a2*r2 + 4*r4) - 24*r6)*sin2th)/(a2p2r2pa2c2th4*a2pr2m2Mr) - (2*a2*costh*dhS_dr_im[8]*sinth)/r2pa2cth22 + (d2hS_dph2_im[6]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (dhS_dph_im[9]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 20*a2*M*r2 + 4*a2*cos2th*r*(a2 - 3*M*r + 2*r2) + 8*a2*r3 + 32*M2*r3 - 32*M*r4 + 8*r5))/(a2p2r2pa2c2th2*a2pr2m2Mr2*sinth2) - (8*a*dhS_dr_im[1]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*dhS_dt_im[4]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*hS_im[1]*M*(3*a6*M - 20*a6*r + 31*a4*M*r2 - 26*a4*r3 + a4*cos4th*(a2*M - 3*M*r2 + 2*r3) + 4*a2*cos2th*(a4*(M - 5*r) + a2*(7*M - 8*r)*r2 + (6*M - r)*r4) + 12*a2*r5 - 24*M*r6 + 24*r7)*sinth2)/(a2p2r2pa2c2th4*a2pr2m2Mr) - (32*a3*costh*dhS_dth_im[1]*M*r*sinth3)/a2p2r2pa2c2th3 + (32*a3*costh*dhS_dt_im[5]*M*r*sinth3)/a2p2r2pa2c2th3 - (dhS_dth_im[6]*(a4 + 3*a4*cos4th + 16*a2*M*r + 4*a2*cos2th*(a2 + 4*r*(-M + r)) + 8*r4))/(a2p2r2pa2c2th3*tanth) + (2*dhS_dph_im[5]*(3*a4 + a4*cos4th + 8*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (2*hS_im[8]*(-6*a6*M - a6*cos6th*M + 4*a6*r + a6*cos6th*r + 52*a4*M*r2 + 2*a4*cos4th*(a2*(3*M + 2*r) + (-2*M + 5*r)*r2) + 14*a4*r3 + 48*a2*M*r4 + a2*cos2th*(a4*(M + 7*r) + 8*a2*(-10*M + 3*r)*r2 + 16*(-7*M + 2*r)*r4) + 16*a2*r5 - 32*M*r6 + 16*r7))/(a2p2r2pa2c2th4*a2pr2m2Mr*tanth);\n src_im[7] = (-8*a*d2hS_dtph_im[7]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) - (4*dhS_dr_im[7]*(a2*cos2th*(M - r) + a2*(M + 3*r) + 2*(-3*M + r)*r2))/a2p2r2pa2c2th2 + d2hS_dth2_im[7]/r2pa2cth2 + (d2hS_dr2_im[7]*(a2 - 2*M*r + r2))/r2pa2cth2 + (4*a2pr2m2Mr*dhS_dth_im[5]*r)/r2pa2cth22 - (d2hS_dt2_im[7]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) + (8*a*hS_im[3]*M*r*(-15*a4 + a4*cos4th + 16*a2*M*r - 2*a2*cos2th*(7*a2 + r*(-8*M + 7*r)) - 2*a2*r2 - 16*M*r3 + 12*r4))/(a2p2r2pa2c2th3*a2pr2m2Mr) + (4*hS_im[0]*M*r*(-9*a6 + 4*a4*M*r - 7*a4*r2 + a4*cos4th*(3*a2 - 4*M*r + 3*r2) - 8*a2*M*r3 - 2*a2*cos2th*(3*a4 + 8*a2*r2 + (-4*M + 5*r)*r3) + 6*a2*r4 + 4*r6))/(a2p2r2pa2c2th3*a2pr2m2Mr) - (16*a3*dhS_dph_im[2]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (16*a3*dhS_dt_im[8]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (16*a2*hS_im[5]*(-M + r)*sin2th)/a2p2r2pa2c2th2 - (16*a2*dhS_dt_im[2]*M*r*(a2 + r2)*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (2*a2*a2pr2m2Mr*dhS_dr_im[5]*sin2th)/r2pa2cth22 + (d2hS_dph2_im[7]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (hS_im[7]*(6*a4 + a4*cos6th + 8*a2*r2 + 2*a2*cos4th*(5*a2 + 4*r2) + 32*M*r3 + cos2th*(15*a4 + 48*a2*r2 + 16*(-2*M + r)*r3) + 16*r4))/(2.*a2p2r2pa2c2th3*sinth2) + (a2pr2m2Mr*hS_im[4]*(3*a2*cos2th*M*r + r*(3*a2*M + 2*a2*r - 6*M*r2 + 2*r3) + 2*a4*costh2*sinth2))/r2pa2cth23 - (2*dhS_dth_im[7]*(-5*a2 + 3*a2*cos2th - 2*r2))/(a2p2r2pa2c2th2*tanth) - (2*dhS_dph_im[8]*(3*a4 + a4*cos4th + 4*a2*cos2th*(a2 + 2*r*(-2*M + r)) + 8*a2*r2 - 16*M*r3 + 8*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr*sinth2*tanth) + (hS_im[9]*(35*a6 + 8*a6*cos6th + a6*cos8th - 168*a4*M*r - 36*a4*cos6th*M*r + 120*a4*r2 + 12*a4*cos6th*r2 + 128*a2*M2*r2 + 4*a2*cos4th*(7*a4 + 2*a2*r*(5*M + 9*r) - 4*(8*M2 + M*r - 3*r2)*r2) - 48*a2*M*r3 + 144*a2*r4 - 256*M2*r4 + 64*r6 + 4*cos2th*(14*a6 + a4*r*(-23*M + 45*r) - 16*a2*(7*M - 3*r)*r3 + 16*r4*pow(-2*M + r,2))))/(8.*a2p2r2pa2c2th3*a2pr2m2Mr*sinth4);\n src_im[8] = (-8*a*d2hS_dtph_im[8]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) + d2hS_dth2_im[8]/r2pa2cth2 + (d2hS_dr2_im[8]*(a2 - 2*M*r + r2))/r2pa2cth2 + (2*a2pr2m2Mr*dhS_dth_im[6]*r)/r2pa2cth22 - (d2hS_dt2_im[8]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (8*dhS_dr_im[8]*(a4*(M + r) + 3*a2*(-M + r)*r2 + a2*cos2th*(a2*(M + r) + (-M + r)*r2) + 2*(-3*M + r)*r4))/a2p2r2pa2c2th3 + (2*dhS_dph_im[5]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 12*a2*M*r2 + 4*a2*cos2th*r*(a2 - M*r + 2*r2) + 8*a2*r3 - 16*M*r4 + 8*r5))/a2p2r2pa2c2th3 - (8*a3*dhS_dph_im[3]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (8*a3*dhS_dt_im[9]*M*r*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) - (8*a2*dhS_dt_im[3]*M*r*(a2 + r2)*sin2th)/(a2p2r2pa2c2th2*a2pr2m2Mr) + (a2*a2pr2m2Mr*dhS_dr_im[6]*sin2th)/r2pa2cth22 + (d2hS_dph2_im[8]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) - (hS_im[8]*(55*a6 + 10*a6*cos6th + a6*cos8th - 80*a4*M*r - 24*a4*cos6th*M*r + 184*a4*r2 + 16*a4*cos6th*r2 + 224*a2*M*r3 + 8*a2*cos4th*(5*a4 + a2*r*(10*M + 13*r) + 2*(2*M + 5*r)*r3) + 208*a2*r4 + 256*M*r5 + 2*cos2th*(43*a6 + 4*a4*r*(3*M + 34*r) - 16*a2*(8*M - 9*r)*r3 + 64*(-2*M + r)*r5) + 64*r6))/(4.*a2p2r2pa2c2th4*sinth2) - (8*a*dhS_dr_im[2]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (8*a*dhS_dt_im[5]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (32*a*hS_im[2]*M*r*(4*a4 - a2*r2 + a2*cos2th*(4*a2 + 3*r2) - 6*r4)*sinth2)/a2p2r2pa2c2th4 - (32*a3*costh*dhS_dth_im[2]*M*r*sinth3)/a2p2r2pa2c2th3 + (32*a3*costh*dhS_dt_im[7]*M*r*sinth3)/a2p2r2pa2c2th3 + (32*a2pr2m2Mr*a3*costh*hS_im[1]*M*(a2 + a2*cos2th - 10*r2)*sinth3)/a2p2r2pa2c2th4 - (dhS_dth_im[8]*(a4 + 3*a4*cos4th + 16*a2*M*r + 4*a2*cos2th*(a2 + 4*r*(-M + r)) + 8*r4))/(a2p2r2pa2c2th3*tanth) + (2*dhS_dph_im[7]*(3*a4 + a4*cos4th + 8*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (2*hS_im[6]*(-2*a6*M - a6*cos6th*M + 10*a6*r + a6*cos6th*r + 8*a4*M2*r + 60*a4*M*r2 + 2*a4*cos4th*(a2*(M + 3*r) + 2*r*(-2*M2 - 3*M*r + 3*r2)) + 36*a4*r3 - 160*a2*M2*r3 + a2*cos2th*(a4*(M + 15*r) - 16*a2*(7*M - 3*r)*r2 + 16*(10*M2 - 10*M*r + 3*r2)*r3) + 32*a2*M*r4 + 48*a2*r5 - 64*M*r6 + 32*r7))/(a2p2r2pa2c2th4*tanth) - (dhS_dph_im[9]*(3*a4 + a4*cos4th + 4*a2*cos2th*(a2 + 2*r*(-2*M + r)) + 8*a2*r2 - 16*M*r3 + 8*r4))/(a2p2r2pa2c2th2*a2pr2m2Mr*sinth2*tanth);\n src_im[9] = (-8*a*d2hS_dtph_im[9]*M*r)/(a2p2r2pa2c2th*a2pr2m2Mr) + d2hS_dth2_im[9]/r2pa2cth2 + (d2hS_dr2_im[9]*(a2 - 2*M*r + r2))/r2pa2cth2 - (d2hS_dt2_im[9]*(a4 + a2*a2pr2m2Mr*cos2th + a2*r*(2*M + 3*r) + 2*r4))/(a2p2r2pa2c2th*a2pr2m2Mr) - (2*dhS_dr_im[9]*(5*a4*M - a4*cos4th*(M - r) + 3*a4*r - 16*a2*M*r2 + 8*a2*r3 + 4*a2*cos2th*(a2*(M + r) + 2*r3) - 24*M*r4 + 8*r5))/a2p2r2pa2c2th3 + (4*dhS_dph_im[6]*(a4*M - a4*cos4th*(M - r) + 3*a4*r - 12*a2*M*r2 + 4*a2*cos2th*r*(a2 - M*r + 2*r2) + 8*a2*r3 - 16*M*r4 + 8*r5))/a2p2r2pa2c2th3 + (hS_im[7]*(35*a8 + 8*a8*cos6th + a8*cos8th - 78*a6*M*r - 36*a6*cos6th*M*r - 2*a6*cos8th*M*r + 155*a6*r2 + 20*a6*cos6th*r2 + a6*cos8th*r2 + 80*a4*M2*r2 + 40*a4*cos6th*M2*r2 + 88*a4*M*r3 - 44*a4*cos6th*M*r3 + 264*a4*r4 + 12*a4*cos6th*r4 - 96*a2*M2*r4 + 4*a2*cos4th*(7*a6 + 5*a4*r*(4*M + 5*r) + 4*(-2*M2 + M*r + 3*r2)*r4 + a2*(-20*M2*r2 + 26*M*r3 + 30*r4)) + 304*a2*M*r5 + 208*a2*r6 + 128*M*r7 + 4*cos2th*(14*a8 + a6*r*(9*M + 59*r) + a4*r2*(-10*M2 - 37*M*r + 93*r2) + 16*a2*(2*M2 - 5*M*r + 4*r2)*r4 + 16*(-2*M + r)*r7) + 64*r8))/(2.*a2p2r2pa2c2th5) + (2*a2pr2m2Mr*hS_im[5]*(-10*a6*M - a6*cos6th*M + 10*a6*r + a6*cos6th*r + 140*a4*M*r2 + 2*a4*cos4th*(a2*(5*M + 3*r) + 2*(M + 3*r)*r2) + 36*a4*r3 + 160*a2*M*r4 + a2*cos2th*(a4*(M + 15*r) - 48*a2*(3*M - r)*r2 + 16*(-10*M + 3*r)*r4) + 48*a2*r5 + 32*r7)*sin2th)/a2p2r2pa2c2th5 + (d2hS_dph2_im[9]*(a2 + a2*cos2th + 2*r*(-2*M + r)))/(a2p2r2pa2c2th*a2pr2m2Mr*sinth2) + (hS_im[9]*(126*a10 + a10*cos10th + 45*a10*cos6th + 10*a10*cos8th + 6*a8*M2 - a8*cos10th*M2 + 3*a8*cos6th*M2 + 2*a8*cos8th*M2 - 160*a8*M*r - 160*a8*cos6th*M*r - 32*a8*cos8th*M*r + 512*r10 + 700*a8*r2 + 160*a8*cos6th*r2 + 20*a8*cos8th*r2 - 120*a6*M2*r2 + 160*a6*cos6th*M2*r2 + 24*a6*cos8th*M2*r2 - 840*a6*M*r3 - 384*a6*cos6th*M*r3 - 24*a6*cos8th*M*r3 - 640*a4*M3*r3 - 320*a4*cos6th*M3*r3 + 1600*a6*r4 + 160*a6*cos6th*r4 - 96*a4*M2*r4 + 240*a4*cos6th*M2*r4 - 1856*a4*M*r5 - 160*a4*cos6th*M*r5 + 768*a2*M3*r5 + 8*a2*cos4th*(15*a8 - a6*(M2 + 40*M*r - 70*r2) + 4*a4*r2*(3*M2 - 37*M*r + 30*r2) + 4*a2*r3*(20*M3 + 11*M2*r - 38*M*r2 + 20*r3) + 16*M*(2*M2 + 2*M*r - r2)*r5) + 1920*a4*r6 + 768*a2*M2*r6 - 2432*a2*M*r7 + 1280*a2*r8 + 1024*M2*r8 + 2*cos2th*(105*a10 - a8*(M2 + 176*M*r - 560*r2) + 16*a6*r2*(-5*M2 - 52*M*r + 75*r2) + 8*a4*r3*(20*M3 - 31*M2*r - 182*M*r2 + 160*r3) - 128*a2*(4*M3 + 4*M2*r + 6*M*r2 - 5*r3)*r5 + 256*M*(-2*M + r)*r8) - 1536*M*r9))/(8.*a2p2r2pa2c2th5*a2pr2m2Mr*sinth2) - (16*a*dhS_dr_im[3]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (16*a*dhS_dt_im[6]*M*(a4 + a2*cos2th*(a2 - r2) - 3*a2*r2 - 6*r4)*sinth2)/a2p2r2pa2c2th3 + (2*a2pr2m2Mr*hS_im[4]*(-2*a6*M2 + a6*cos6th*M2 + 76*a6*M*r - 2*a6*cos6th*M*r + 10*a6*r2 + a6*cos6th*r2 - 40*a4*M2*r2 + 2*a4*cos4th*(a2*(M2 - 14*M*r + 3*r2) + 2*r2*(10*M2 - 8*M*r + 3*r2)) + 32*a4*M*r3 + 36*a4*r4 + 48*a2*M2*r4 - a2*cos2th*(a4*(M2 - 50*M*r - 15*r2) - 48*a2*(2*M + r)*r3 - 48*(-M2 + M*r + r2)*r4) - 144*a2*M*r5 + 48*a2*r6 - 96*M*r7 + 32*r8)*sinth2)/a2p2r2pa2c2th5 + (4*a*hS_im[3]*M*(2*a8*M - a8*cos6th*M + 30*a8*r + 3*a8*cos6th*r - 130*a6*M*r2 - 3*a6*cos6th*M*r2 + 70*a6*r3 + a6*cos6th*r3 - 80*a4*M2*r3 - 2*a4*cos4th*(a4*(M - 9*r) + a2*(31*M - 13*r)*r2 + 2*(-20*M2 + 14*M*r + r2)*r3) - 184*a4*M*r4 + 4*a4*r5 + 64*a2*M2*r5 + a2*cos2th*(a6*(M + 45*r) + a4*(-189*M + 95*r)*r2 - 272*a2*M*r4 - 16*(4*M2 + 3*M*r + 5*r2)*r5) + 176*a2*M*r6 - 112*a2*r7 + 256*M*r8 - 96*r9)*sinth2)/(a2p2r2pa2c2th5*a2pr2m2Mr) - (2*hS_im[0]*M*(-2*a10*M + a10*cos6th*M + 30*a10*r + 3*a10*cos6th*r - 32*r11 + 28*a8*M*r2 - 18*a8*cos6th*M*r2 + 120*a8*r3 + 6*a8*cos6th*r3 + 40*a6*M2*r3 + 20*a6*cos6th*M2*r3 + 46*a6*M*r4 - 15*a6*cos6th*M*r4 + 166*a6*r5 + 3*a6*cos6th*r5 - 48*a4*M2*r5 + 2*a4*cos4th*(a6*(M + 9*r) - 14*a4*(M - 2*r)*r2 + a2*(-20*M2 - 31*M*r + 29*r2)*r3 + 2*(-4*M2 - 2*M*r + 5*r2)*r5) - 152*a4*M*r6 + 60*a4*r7 - 208*a2*M*r8 + a2*cos2th*(-(a8*(M - 45*r)) + 2*a6*(9*M + 85*r)*r2 + a4*(-20*M2 + 31*M*r + 221*r2)*r3 + 16*a2*(4*M2 + 10*M*r + 7*r2)*r5 + 16*(13*M + r)*r8) - 48*a2*r9)*sinth2)/(a2p2r2pa2c2th5*a2pr2m2Mr) - (64*a3*costh*dhS_dth_im[3]*M*r*sinth3)/a2p2r2pa2c2th3 + (64*a3*costh*dhS_dt_im[8]*M*r*sinth3)/a2p2r2pa2c2th3 + (4*dhS_dph_im[8]*(3*a4 + a4*cos4th + 8*a2*M*r + 4*a2*cos2th*(a2 + 2*r*(-M + r)) + 8*a2*r2 + 8*r4))/(a2p2r2pa2c2th3*tanth) - (dhS_dth_im[9]*(9*a4 + 3*a4*cos4th + 32*a2*M*r + 24*a2*r2 + 4*a2*cos2th*(3*a2 - 8*M*r + 6*r2) + 24*r4))/(a2p2r2pa2c2th3*tanth);\n}\n\n/* Initialize some constants. */\nvoid effsource_init(double mass, double spin)\n{\n M = mass;\n a = spin;\n}\n\n/* Initialize coefficients of pows of dr, dtheta and Q=sin(dphi/2), R=sin(dphi). */\nvoid effsource_set_particle(struct coordinate * x, double E, double L, double ur)\n{\n xp = *x;\n double r0 = xp.r;\n\n double E_2 = E*E;\n double E_3 = E_2*E;\n double E_4 = E_2*E_2;\n\n double L_2 = L*L;\n double L_3 = L_2*L;\n double L_4 = L_2*L_2;\n double L_6 = L_4*L_2;\n double L_8 = L_4*L_4;\n double L_10 = L_6*L_4;\n\n double r0_2 = r0*r0;\n double r0_3 = r0_2*r0;\n double r0_4 = r0_2*r0_2;\n double r0_5 = r0_3*r0_2;\n double r0_6 = r0_3*r0_3;\n double r0_7 = r0_4*r0_3;\n double r0_8 = r0_4*r0_4;\n double r0_9 = r0_5*r0_4;\n double r0_10 = r0_5*r0_5;\n double r0_11 = r0_6*r0_5;\n\n double M_2 = M*M;\n double M_3 = M_2*M;\n double M_4 = M_2*M_2;\n double M_5 = M_3*M_2;\n double M_6 = M_3*M_3;\n double M_7 = M_4*M_3;\n\n double a_2 = a*a;\n double a_3 = a_2*a;\n double a_4 = a_2*a_2;\n double a_5 = a_3*a_2;\n double a_6 = a_3*a_3;\n double a_7 = a_4*a_3;\n double a_8 = a_4*a_4;\n double a_9 = a_5*a_4;\n double a_10 = a_5*a_5;\n double a_11 = a_6*a_5;\n double a_12 = a_6*a_6;\n double a_13 = a_7*a_6;\n double a_14 = a_7*a_7;\n\n double r0_2M = r0 - 2*M;\n double r0_2M_2 = r0_2M*r0_2M;\n\n double r0_p_2M = 2*M + r0;\n double r0_p_2M_2 = r0_p_2M*r0_p_2M;\n double r0_p_2M_3 = r0_p_2M_2*r0_p_2M;\n double r0_p_2M_4 = r0_p_2M_2*r0_p_2M_2;\n\n double expr1 = a_2*(2*M + r0) + r0*(L_2 + r0_2);\n double expr1_2 = expr1*expr1;\n double expr1_3 = expr1_2*expr1;\n double expr1_4 = expr1_2*expr1_2;\n \n double expr2 = a_2 + r0*(-2*M + r0);\n double expr2_2 = expr2*expr2;\n double expr2_3 = expr2_2*expr2;\n double expr2_4 = expr2_2*expr2_2;\n double expr2_5 = expr2_3*expr2_2;\n double expr2_6 = expr2_3*expr2_3;\n double expr2_7 = expr2_4*expr2_3;\n\n double expr3 = a_3 + 3*a*r0_2;\n double expr3_2 = expr3*expr3;\n\n double expr4 = L_2 + r0_2 + (a_2*(2*M + r0))/r0;\n double expr4_2 = expr4*expr4;\n double expr4_3 = expr4_2*expr4;\n\n double expr5 = a_2*M + (2*M - r0)*r0_2;\n double expr5_2 = expr5*expr5;\n \n double expr6 = r0_3 + a_2*(2*M + r0);\n double expr6_2 = expr6*expr6;\n\n double expr7 = 2*a*E*M + L*(-2*M + r0);\n double expr7_2 = expr7*expr7;\n\n double expr8 = -2*a*L*M + E*r0_3 + a_2*E*(2*M + r0);\n double expr8_2 = expr8*expr8;\n\n /* A_{t,t} */\n {\n A00060 = 256*E_2*expr4_3;\n A00080 = (-128*expr1_2*(-(a_8*E_2*M_2*(48*M + 25*r0)) + 4*a_7*E*L*M_2*(12*M + (6 + E_2)*r0) + r0_2*(24*L_6*M*r0_2M_2 + 2*E_2*M*r0_7*(-2*M + r0 + 2*E_2*r0) + 24*L_4*M*(2*M - r0)*r0_2*(4*M - (2 + E_2)*r0) + L_2*(2*M - r0)*r0_4*(48*M_2 - 8*(3 + 4*E_2)*M*r0 + 3*E_2*r0_2)) + 4*a*E*L*M*r0_2*(12*L_4*M*(-2*M + r0) - 6*L_2*r0_2*(16*M_2 - 2*(5 + E_2)*M*r0 + r0_2) + r0_4*(-72*M_2 + 2*(24 + 7*E_2)*M*r0 - 3*(2 + E_2)*r0_2)) + 4*a_5*E*L*M*(-192*M_4 + 8*(-15 + 4*E_2)*M_3*r0 + 6*(12 + 5*E_2)*M_2*r0_2 - (6 + E_2)*r0_4 + 6*M*r0*(L_2 + 2*(3 + E_2)*r0_2)) + 4*a_3*E*L*M*r0*(-6*L_2*(24*M_3 + (2 - 4*E_2)*M_2*r0 - (9 + 2*E_2)*M*r0_2 + r0_3) + r0_2*(-240*M_3 + 2*(6 + 13*E_2)*M_2*r0 + 3*(26 + 7*E_2)*M*r0_2 - 4*(3 + E_2)*r0_3)) + 2*a_6*E_2*M*(192*M_4 + 16*(15 + E_2)*M_3*r0 + 2*(-11 + 12*E_2)*M_2*r0_2 + (1 + 2*E_2)*r0_4 + M*(-14*L_2*r0 + (-61 + 12*E_2)*r0_3)) + a_2*r0*(24*L_4*M*(4*M - (2 + E_2)*r0)*(4*M_2 - r0_2) + 2*E_2*M*r0_5*(124*M_2 + 6*(-7 + 2*E_2)*M*r0 + 3*(1 + 2*E_2)*r0_2) + L_2*r0_2*(384*M_4 + 16*(-12 + 5*E_2)*M_3*r0 - 96*(1 + E_2)*M_2*r0_2 + 16*(3 + 4*E_2)*M*r0_3 - 3*E_2*r0_4)) + a_4*M*(E_2*r0_3*(668*M_3 + 4*(61 + 12*E_2)*M_2*r0 + 3*(-59 + 16*E_2)*M*r0_2 + 6*(1 + 2*E_2)*r0_3) + 4*L_2*(96*M_4 + 8*E_2*M_3*r0 + 6*(-8 + 3*E_2)*M_2*r0_2 - 15*E_2*M*r0_3 + 2*(3 + 4*E_2)*r0_4))))/(3.*r0_9*(a_2 + r0*(-2*M + r0)));\n A00240 = 192*E_2*expr1_2;\n A00260 = (-64*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-2*a_7*E*L*M*(12*(-7 + 2*E_2)*M_2 + 2*(-33 + 8*E_2)*M*r0 + 3*(-4 + E_2)*r0_2) + a_8*E_2*M*(24*(-7 + E_2)*M_2 + (-139 + 24*E_2)*M*r0 + 3*(-9 + 2*E_2)*r0_2) + a_6*E_2*(768*M_5 + 16*(69 + E_2)*M_4*r0 + 12*(7 + 6*E_2)*M_3*r0_2 + 6*(-57 + 14*E_2)*M_2*r0_3 + (-89 + 26*E_2)*M*r0_4 - 3*r0_5 + L_2*M*(24*M_2 + 4*(-31 + 3*E_2)*M*r0 + 3*(-17 + 2*E_2)*r0_2)) + 2*a*E*L*M*r0_2*(12*L_4*(-10*M_2 + 3*M*r0 + r0_2) + L_2*r0_2*(-384*M_2 + 2*(90 + 23*E_2)*M*r0 + 3*(2 - 3*E_2)*r0_2) + r0_4*(-264*M_2 + 2*(72 + 25*E_2)*M*r0 - 3*(2 + 5*E_2)*r0_2)) - 2*a_5*E*L*M*(768*M_4 - 8*(-69 + 16*E_2)*M_3*r0 - 8*(27 + 11*E_2)*M_2*r0_2 + 2*M*r0*((-33 + 6*E_2)*L_2 + (-102 + 7*E_2)*r0_2) + r0_2*(3*(-8 + E_2)*L_2 + (-18 + 17*E_2)*r0_2)) + r0_2*(48*L_6*M*r0_2M_2 + E_2*r0_7*(-8*M_2 + 2*(5 + 4*E_2)*M*r0 - 3*r0_2) + 2*L_4*(2*M - r0)*r0_2*(96*M_2 - 2*(24 + 11*E_2)*M*r0 + 3*E_2*r0_2) + 2*L_2*r0_4*(96*M_3 - 6*(16 + 9*E_2)*M_2*r0 + (24 + 39*E_2 + 2*E_4)*M*r0_2 - 6*E_2*r0_3)) + 2*a_3*E*L*M*r0*(12*L_4*r0 + r0_2*(-912*M_3 + 4*(-15 + 32*E_2)*M_2*r0 + 2*(141 + 22*E_2)*M*r0_2 - 29*E_2*r0_3) + L_2*(-624*M_3 + 4*(-33 + 20*E_2)*M_2*r0 + 2*(105 + 11*E_2)*M*r0_2 + 6*(5 - 2*E_2)*r0_3)) + a_2*r0*(E_2*r0_5*(412*M_3 + 12*(-4 + 3*E_2)*M_2*r0 + 15*(-1 + 2*E_2)*M*r0_2 - 9*r0_3) + L_2*r0_2*(768*M_4 + 4*(-96 + 41*E_2)*M_3*r0 + 4*(-48 + 3*E_2 + E_4)*M_2*r0_2 + (96 + 57*E_2 + 14*E_4)*M*r0_3 - 21*E_2*r0_4) + 2*L_4*(384*M_4 - 4*(48 + 13*E_2)*M_3*r0 + 6*(-16 + 5*E_2)*M_2*r0_2 + 2*(24 + 5*E_2)*M*r0_3 - 3*E_2*r0_4)) + a_4*(12*E_2*L_4*M*(M - 2*r0)*r0 + E_2*r0_3*(1204*M_4 + 8*(85 + 6*E_2)*M_3*r0 + 3*(-81 + 32*E_2)*M_2*r0_2 + 3*(-29 + 14*E_2)*M*r0_3 - 9*r0_4) + L_2*(768*M_5 + 208*E_2*M_4*r0 - 8*(48 - 50*E_2 + E_4)*M_3*r0_2 + 8*E_2*(-5 + 2*E_2)*M_2*r0_3 + 2*(24 - 33*E_2 + 8*E_4)*M*r0_4 - 9*E_2*r0_5))))/(3.*r0_6*(a_2 + r0*(-2*M + r0)));\n A00420 = 48*E_2*r0_3*(a_2*(2*M + r0) + r0*(L_2 + r0_2));\n A00440 = (8*((16*a_2*E_2*L_4*M_3)/(r0*(a_2 + r0*(-2*M + r0))) - (16*a*E_3*L_3*M_2*(r0_3 + a_2*(2*M + r0)))/(r0*(a_2 + r0*(-2*M + r0))) + (4*E_4*L_2*M*expr6_2)/(r0*(a_2 + r0*(-2*M + r0))) + E_2*(-3*a_2 + r0*(-2*M + r0))*expr4_2 + (72*E_2*M_2*(a_4 + 3*a_2*r0_2)*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/r0_3 - (72*a*E*L*M*(a_2*M + (2*M - r0)*r0_2)*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/r0_3 - (48*a_2*E_2*L_2*M_3*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/(r0_2*(a_2 + r0*(-2*M + r0))) + (144*a*E*L_2*M_2*(2*a*E*M + L*(-2*M + r0))*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/(r0_2*(a_2 + r0*(-2*M + r0))) + (48*a*E_3*L*M_2*(r0_3 + a_2*(2*M + r0))*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/(r0_2*(a_2 + r0*(-2*M + r0))) - (72*E_2*L*M*(2*a*E*M + L*(-2*M + r0))*(r0_3 + a_2*(2*M + r0))*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/(r0_2*(a_2 + r0*(-2*M + r0))) - (12*E_4*M*expr6_2*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/(r0_2*(a_2 + r0*(-2*M + r0))) + (144*a_2*E_2*M*expr1_2)/r0_3 - (144*a*E*L*M*expr1_2)/r0_3 - (144*M*expr7_2*expr1_2)/(r0_3*(a_2 + r0*(-2*M + r0))) - (8*E_2*L_2*M*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/(r0_2*(a_2 + r0*(-2*M + r0))) + (12*E_2*M*expr1_2*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/(r0_3*(a_2 + r0*(-2*M + r0))) + (E_2*(a_6*M_2 - 4*a_5*E*L*M_2 + 12*a*E*L*M*r0_5 + 4*a_3*E*L*M*r0_2*(-3*M + r0) + 4*a_2*M*(M - r0)*r0_2*(2*L_2 + r0_2) + r0_5*(-2*M*r0_2 + L_2*(-8*M + 3*r0)) + a_4*M*(4*L_2*M + r0*(-2*M_2 + M*r0 - 2*r0_2))))/r0_2 + (4*E_2*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(3*a_4*M - 6*a_3*E*L*M + 6*a*E*L*M*r0_2 - (2*M - 3*r0)*r0_2*(2*L_2 + r0_2) + a_2*(6*L_2*M + r0*(2*M_2 + 7*M*r0 + 3*r0_2))))/r0_2))/3.;\n A00600 = 4*E_2*r0_6;\n A00620 = (-4*(-6*a_5*E*L*M*(2*(-13 + 6*E_2)*M + (-12 + 5*E_2)*r0) + 3*a_6*E_2*(4*(-13 + 3*E_2)*M_2 + (-23 + 6*E_2)*M*r0 + r0_2) + 2*a*E*L*M*r0*(r0_2*(-216*M_2 + 2*(24 + 19*E_2)*M*r0 + 3*(10 - 7*E_2)*r0_2) - 4*L_2*(42*M_2 - (3 + 4*E_2)*M*r0 + 3*(-3 + E_2)*r0_2)) - 4*a_3*E*L*M*(192*M_3 + (78 - 32*E_2)*M_2*r0 + (-57 + 5*E_2)*M*r0_2 + 3*r0*(2*(-3 + E_2)*L_2 + (-11 + 6*E_2)*r0_2)) + r0*(8*L_4*M*(2*M - r0)*(12*M - (6 + E_2)*r0) + 4*E_2*r0_5*(-2*M_2 + (3 + 2*E_2)*M*r0 - r0_2) + L_2*r0_2*(192*M_3 - 12*(16 + 5*E_2)*M_2*r0 + 4*(12 + 11*E_2 + E_4)*M*r0_2 - 7*E_2*r0_3)) + a_4*E_2*(3*L_2*(12*M_2 + 4*(-5 + E_2)*M*r0 + r0_2) + 2*(192*M_4 - 4*(-63 + 5*E_2)*M_3*r0 + 2*(-13 + 8*E_2)*M_2*r0_2 + 11*(-7 + 2*E_2)*M*r0_3 + r0_4)) + a_2*(12*E_2*L_4*M*r0 + E_2*r0_3*(260*M_3 - 4*(-31 + E_2)*M_2*r0 + (-73 + 34*E_2)*M*r0_2 - 5*r0_3) + 4*L_2*(96*M_4 + 2*(-24 + 7*E_2)*M_3*r0 + (-24 + 39*E_2 - 4*E_4)*M_2*r0_2 + (12 - 9*E_2 + 4*E_4)*M*r0_3 - E_2*r0_4))))/(3.*(a_2 + r0*(-2*M + r0)));\n A00800 = (r0_3*(48*a_2*E_2*M - 48*a*E*L*M + E_2*r0*(-3*a_2 + r0*(-2*M + r0)) - (24*M*expr7_2)/(a_2 + r0*(-2*M + r0)) + (4*E_2*M*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/(a_2 + r0*(-2*M + r0))))/6.;\n A01060 = (-128*E*expr1_2*(-(a_4*E*M*(8*M + 5*r0)) + 2*a_3*L*M*(4*M + (2 + E_2)*r0) + 2*a*L*M*r0*(2*L_2 + (2 + 3*E_2)*r0_2) + E*r0_3*(r0_2*(-6*M + r0) + L_2*(-8*M + 2*r0)) + a_2*E*r0*(-6*L_2*M + r0*(-6*M_2 - 9*M*r0 + r0_2))))/(r0_5*(a_2 + r0*(-2*M + r0)));\n A01080 = (-64*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(a_12*E_2*M_2*(-192*M_3 + 8*(41 - 10*E_2)*M_2*r0 + (509 - 88*E_2)*M*r0_2 + 6*(25 - 4*E_2)*r0_3) - 2*a_11*E*L*M_2*(-192*M_3 + 4*(17 + 36*E_2)*M_2*r0 + (226 + 183*E_2)*M*r0_2 + 12*(6 + 5*E_2)*r0_3) + 2*a_9*E*L*M*r0*(-768*(-5 + 4*E_2)*M_5 + 16*(359 - 236*E_2 + 12*E_4)*M_4*r0 + 4*(372 - 371*E_2 + 72*E_4)*M_3*r0_2 + (-1214 - 647*E_2 + 144*E_4)*M_2*r0_3 + 2*(-206 - 165*E_2 + 12*E_4)*M*r0_4 - 12*(-4 + E_2)*r0_5 - 2*L_2*M*(16*M_2 + (217 + 96*E_2)*M*r0 + 6*(18 + 11*E_2)*r0_2)) + 2*a*E*L*M*r0_4*(-48*L_8*r0_2M_2 - 2*(2*M - r0)*r0_7*(312*M_2 + (-170 + 37*E_2)*M*r0 + 6*(3 - 2*E_2)*r0_2) + 12*L_6*(2*M - r0)*r0*(4*M_2 - 2*(8 + 7*E_2)*M*r0 + (8 + E_2)*r0_2) + L_2*r0_5*(-2592*M_3 - 8*(-353 + 29*E_2)*M_2*r0 + 2*(-472 + 67*E_2 + 30*E_4)*M*r0_2 + 3*(30 + E_2)*r0_3) - 2*L_4*r0_3*(624*M_3 + 4*(-160 + 69*E_2)*M_2*r0 - 2*(-85 + 90*E_2 + 6*E_4)*M*r0_2 + 3*(-1 + 5*E_2)*r0_3)) + r0_5*(24*L_8*M*r0_2M_2*(6*M + (-1 + 4*E_2)*r0) - 2*E_2*M*r0_9*(16*M_2 + 2*(-6 + E_2)*M*r0 + (2 - 5*E_2)*r0_2) + 24*L_6*M*(2*M - r0)*r0_2*(40*M_2 + 4*(-7 + 3*E_2)*M*r0 - (-4 + 8*E_2 + E_4)*r0_2) + 2*L_4*(2*M - r0)*r0_4*(528*M_3 - 8*(48 + E_2)*M_2*r0 - 10*(-6 + 4*E_2 + 3*E_4)*M*r0_2 - 3*E_2*r0_3) + L_2*r0_6*(768*M_4 - 8*(120 + 23*E_2)*M_3*r0 + 4*(96 + 15*E_2 - 13*E_4)*M_2*r0_2 + 2*(-24 + 11*E_2 + 17*E_4)*M*r0_3 - 3*E_2*r0_4)) + 4*a_3*E*L*M*r0_3*(-6*L_6*(32*M_3 + 12*(-5 + 3*E_2)*M_2*r0 + 2*(1 - 7*E_2)*M*r0_2 + (8 + E_2)*r0_3) + 2*r0_5*(-1704*M_4 + 12*(57 - 47*E_2)*M_3*r0 + (702 + 151*E_2)*M_2*r0_2 + 2*(-188 + 19*E_2 + 3*E_4)*M*r0_3 + (39 - 19*E_2)*r0_4) + L_4*r0*(-1104*M_4 - 8*(-23 + 63*E_2)*M_3*r0 + 24*(62 - 11*E_2 + E_4)*M_2*r0_2 + 8*(-74 + 30*E_2 + 3*E_4)*M*r0_3 + 3*(1 - 10*E_2)*r0_4) + L_2*r0_3*(-4704*M_4 - 4*(-478 + 383*E_2)*M_3*r0 + 2*(1272 + 157*E_2 + 60*E_4)*M_2*r0_2 + 3*(-458 + 27*E_2 + 30*E_4)*M*r0_3 - 23*(-6 + E_2)*r0_4)) + a_2*r0_3*(-24*L_8*M*(2*M - r0)*(8*M_2 + (8 - 22*E_2)*M*r0 + (-3 + 4*E_2)*r0_2) + 2*E_2*M*r0_8*(1260*M_3 + 4*(-246 + 101*E_2)*M_2*r0 + (203 - 46*E_2)*M*r0_2 + (-11 + 23*E_2)*r0_3) + 24*L_6*M*r0*(184*M_4 - 4*(41 + 2*E_2)*M_3*r0 + 2*(-29 + 29*E_2 + 4*E_4)*M_2*r0_2 + (73 - 57*E_2 - 4*E_4)*M*r0_3 + (-13 + 14*E_2 + 2*E_4)*r0_4) + L_2*r0_5*(5184*M_5 + 16*(-246 + 349*E_2)*M_4*r0 + 12*(-84 - 499*E_2 + 74*E_4)*M_3*r0_2 - 24*(-53 - 69*E_2 + E_4)*M_2*r0_3 + 9*(-24 - E_2 + 16*E_4)*M*r0_4 - 6*E_2*r0_5) + 2*L_4*r0_3*(4800*M_5 + 8*(-468 + 163*E_2)*M_4*r0 + 12*(-92 - 147*E_2 + 10*E_4)*M_3*r0_2 + 2*(672 + 179*E_2 - 60*E_4)*M_2*r0_3 + (-228 + 83*E_2 + 90*E_4)*M*r0_4 + 3*E_2*r0_5)) + 2*a_5*E*L*M*r0_2*(-72*L_6*M*r0 + 2*L_4*(256*M_4 - 24*(-63 + 41*E_2)*M_3*r0 + 24*(18 - 4*E_2 + E_4)*M_2*r0_2 + 4*(-134 + 6*E_2 + 3*E_4)*M*r0_3 - 15*E_2*r0_4) + L_2*r0*(-9024*M_5 - 8*(197 + 344*E_2)*M_4*r0 + 24*(491 - 189*E_2 + 10*E_4)*M_3*r0_2 + 2*(679 + 360*E_2 + 240*E_4)*M_2*r0_3 + 4*(-714 - 91*E_2 + 45*E_4)*M*r0_4 + (282 - 79*E_2)*r0_5) + r0_3*(-12864*M_5 - 60*(46 + 71*E_2)*M_4*r0 - 92*(-114 + 37*E_2)*M_3*r0_2 + (798 + 1219*E_2 + 144*E_4)*M_2*r0_3 + 24*(-85 - 10*E_2 + 3*E_4)*M*r0_4 + 4*(63 - 23*E_2)*r0_5)) - a_10*M*(2*L_2*M*(96*M_3 + 24*(4 - 13*E_2)*M_2*r0 + (24 - 709*E_2 + 32*E_4)*M*r0_2 + 3*E_2*(-97 + 4*E_2)*r0_3) + E_2*r0*(-1280*(-3 + 2*E_2)*M_5 + 32*(269 - 125*E_2)*M_4*r0 + 2*(2021 - 888*E_2)*M_3*r0_2 + (-1429 + 88*E_2)*M_2*r0_3 + 5*(-183 + 28*E_2)*M*r0_4 - 6*(-1 + E_2)*r0_5)) + a_4*r0_2*(E_2*M*r0_6*(10848*M_4 + 4*(-149 + 984*E_2)*M_3*r0 + 4*(-1475 + 602*E_2)*M_2*r0_2 - 3*(-509 + 96*E_2)*M*r0_3 + 12*(-4 + 7*E_2)*r0_4) - 24*L_6*M*(64*M_4 - 4*(-26 + 43*E_2)*M_3*r0 - 2*(25 - 28*E_2 + 2*E_4)*M_2*r0_2 + (-27 + 21*E_2 + 2*E_4)*M*r0_3 - (-9 + 6*E_2 + E_4)*r0_4) + 2*L_4*M*r0*(5376*M_5 + 16*(-132 + 17*E_2)*M_4*r0 + 8*(-648 + 265*E_2 + 60*E_4)*M_3*r0_2 + 12*(132 - 267*E_2 + 10*E_4)*M_2*r0_3 + 4*(246 + 257*E_2 - 15*E_4)*M*r0_4 + (-276 + 43*E_2 + 90*E_4)*r0_5) + L_2*r0_3*(11520*M_6 + 8*(-384 + 1703*E_2)*M_5*r0 + 16*(-516 - 89*E_2 + 333*E_4)*M_4*r0_2 + 2*(1080 - 5793*E_2 + 1180*E_4)*M_3*r0_3 + 2*(684 + 2227*E_2 + 36*E_4)*M_2*r0_4 + 6*(-60 - 21*E_2 + 38*E_4)*M*r0_5 - 3*E_2*r0_6)) + 2*a_7*E*L*M*r0*(-8*L_4*M*r0*(26*M + 9*(3 + E_2)*r0) + 2*L_2*(512*M_5 + 16*(199 - 126*E_2)*M_4*r0 + 4*(629 - 332*E_2 + 30*E_4)*M_3*r0_2 + 2*(-329 - 83*E_2 + 60*E_4)*M_2*r0_3 + 2*(-317 - 120*E_2 + 15*E_4)*M*r0_4 + 3*(16 - 5*E_2)*r0_5) - r0*(8448*M_6 + 16*(413 + 164*E_2)*M_5*r0 + 4*(-2410 + 1699*E_2)*M_4*r0_2 - 4*(1991 - 658*E_2 + 72*E_4)*M_3*r0_3 + (1694 - 35*E_2 - 288*E_4)*M_2*r0_4 + 4*(322 + 135*E_2 - 18*E_4)*M*r0_5 + 4*(-45 + 13*E_2)*r0_6)) + a_8*M*r0*(-48*L_4*M*(4*M_2 + (2 - 19*E_2)*M*r0 - 15*E_2*r0_2) + 2*L_2*(384*(-5 + 4*E_2)*M_5 + 16*(-90 - 95*E_2 + 76*E_4)*M_4*r0 + 4*(108 - 1013*E_2 + 290*E_4)*M_3*r0_2 + (456 + 537*E_2 + 116*E_4)*M_2*r0_3 + (-12 + 1291*E_2 - 10*E_4)*M*r0_4 + 3*(-12 - 9*E_2 + 7*E_4)*r0_5) + E_2*r0*(8448*M_6 + 32*(353 + 136*E_2)*M_5*r0 + 4*(-2293 + 2744*E_2)*M_4*r0_2 + 12*(-1257 + 644*E_2)*M_3*r0_3 + 21*(-37 + 48*E_2)*M_2*r0_4 + (2167 - 324*E_2)*M*r0_5 + 2*(-14 + 17*E_2)*r0_6)) + a_6*M*r0*(-48*L_6*M*r0*(M - 6*E_2*r0) + E_2*r0_4*(16232*M_5 + 4*(2617 + 1696*E_2)*M_4*r0 + 2*(-6891 + 4840*E_2)*M_3*r0_2 + (-5661 + 2608*E_2)*M_2*r0_3 + 3*(849 - 136*E_2)*M*r0_4 + 4*(-13 + 19*E_2)*r0_5) - 4*L_4*(384*M_5 - 96*(-16 + 15*E_2)*M_4*r0 - 4*(-48 - 71*E_2 + 30*E_4)*M_3*r0_2 + 24*(-24 + 29*E_2)*M_2*r0_3 - 4*(18 + 119*E_2)*M*r0_4 + 3*(18 - 5*E_4)*r0_5) + L_2*r0*(8448*M_6 + 128*(15 + 64*E_2)*M_5*r0 + 8*(-1344 + 1249*E_2 + 620*E_4)*M_4*r0_2 + 8*(-288 - 1841*E_2 + 932*E_4)*M_3*r0_3 + 2*(1584 - 3129*E_2 + 820*E_4)*M_2*r0_4 + 2*(228 + 2435*E_2 + 24*E_4)*M*r0_5 + (-264 - 149*E_2 + 160*E_4)*r0_6))))/(3.*r0_11*expr2_2);\n A01240 = (-32*E*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(4*a_3*L*M*(6*M + (3 + E_2)*r0) + a_4*E*(-24*M_2 - 12*M*r0 + r0_2) + 12*a*L*M*r0*(L_2 + (1 + E_2)*r0_2) + E*r0_3*(3*r0_2*(-6*M + r0) + L_2*(-22*M + 5*r0)) + a_2*E*r0*(L_2*(-16*M + r0) + 2*r0*(-12*M_2 - 13*M*r0 + 2*r0_2))))/(r0_2*(a_2 + r0*(-2*M + r0)));\n A01260 = (-16*(-2*a_11*E*L*M*(192*(-7 + 3*E_2)*M_4 + 8*(17 + 132*E_2 + 18*E_4)*M_3*r0 + (1748 + 651*E_2 + 144*E_4)*M_2*r0_2 + 6*(160 + 23*E_2 + 6*E_4)*M*r0_3 + 144*r0_4) + a_12*E_2*M*(192*(-7 + 2*E_2)*M_4 + 80*(25 + 4*E_2)*M_3*r0 + (4279 - 56*E_2)*M_2*r0_2 + 3*(695 - 32*E_2)*M*r0_3 - 18*(-17 + E_2)*r0_4) + 2*a*E*L*M*r0_4*(-168*L_8*r0_2M_2 - 2*L_6*(2*M - r0)*r0*(144*M_2 + 2*(202 + 147*E_2)*M*r0 - 3*(76 + 7*E_2)*r0_2) + 2*L_4*r0_3*(-3024*M_3 - 16*(-125 + 64*E_2)*M_2*r0 + 2*(52 + 265*E_2 + 21*E_4)*M*r0_2 - 3*(58 + E_2)*r0_3) + L_2*r0_5*(-9984*M_3 - 64*(-137 + 21*E_2)*M_2*r0 + 2*(-908 + 321*E_2 + 60*E_4)*M*r0_2 + 3*(-12 + 5*E_2)*r0_3) - 2*r0_7*(2256*M_3 + 2*(-1028 + 151*E_2)*M_2*r0 + (488 - 205*E_2)*M*r0_2 + 3*(-4 + 11*E_2)*r0_3)) + r0_5*(24*L_8*M*r0_2M_2*(26*M + (-5 + 14*E_2)*r0) + 2*E_2*r0_9*(-64*M_3 + (84 - 8*E_2)*M_2*r0 + 4*(-8 + 5*E_2)*M*r0_2 + 3*r0_3) + 4*L_6*(2*M - r0)*r0_2*(1008*M_3 + 4*(-180 + 67*E_2)*M_2*r0 + (108 - 154*E_2 - 21*E_4)*M*r0_2 - 6*E_2*r0_3) + 2*L_2*r0_6*(1536*M_4 - 4*(480 + 61*E_2)*M_3*r0 + 12*(64 + 13*E_2 - 7*E_4)*M_2*r0_2 + (-96 - 29*E_2 + 66*E_4)*M*r0_3 + 6*E_2*r0_4) + L_4*r0_4*(8640*M_4 + 16*(-666 + 23*E_2)*M_3*r0 - 4*(-1044 + 177*E_2 + 86*E_4)*M_2*r0_2 + 4*(-126 + 46*E_2 + 47*E_4)*M*r0_3 + 39*E_2*r0_4)) + 4*a_3*E*L*M*r0_3*(L_6*(-896*M_3 + 12*(104 - 63*E_2)*M_2*r0 + 2*(160 + 147*E_2)*M*r0_2 - 3*(100 + 7*E_2)*r0_3) + r0_5*(-12672*M_4 - 168*(-23 + 20*E_2)*M_3*r0 + 4*(1311 + 68*E_2 + 27*E_4)*M_2*r0_2 + (-1880 + 395*E_2 - 18*E_4)*M*r0_3 - 103*E_2*r0_4) - 2*L_4*r0*(2784*M_4 + 4*(61 + 280*E_2)*M_3*r0 - 2*(1461 - 413*E_2 + 21*E_4)*M_2*r0_2 - 2*(-158 + 227*E_2 + 21*E_4)*M*r0_3 + 3*(93 + 7*E_2)*r0_4) - 2*L_2*r0_3*(9312*M_4 + 18*(-128 + 135*E_2)*M_3*r0 - 6*(822 - 66*E_2 + 29*E_4)*M_2*r0_2 + (1458 - 355*E_2 - 75*E_4)*M*r0_3 + (120 + 11*E_2)*r0_4)) + a_2*r0_3*(-24*L_8*M*(2*M - r0)*(24*M_2 + 7*(4 - 11*E_2)*M*r0 + (-11 + 14*E_2)*r0_2) + 2*E_2*r0_8*(4068*M_4 + 4*(-599 + 320*E_2)*M_3*r0 + (25 - 62*E_2)*M_2*r0_2 + (50 + 79*E_2)*M*r0_3 + 12*r0_4) + 2*L_6*r0*(8928*M_5 + 8*(-954 + 133*E_2)*M_4*r0 + 12*(-222 + 261*E_2 + 28*E_4)*M_3*r0_2 - 6*(-558 + 571*E_2 + 28*E_4)*M_2*r0_3 + 3*(-204 + 251*E_2 + 28*E_4)*M*r0_4 + 12*E_2*r0_5) + 2*L_4*r0_3*(19008*M_5 + 16*(-918 + 359*E_2)*M_4*r0 + 4*(-1044 - 635*E_2 + 143*E_4)*M_3*r0_2 + 2*(2592 - 1001*E_2 + 14*E_4)*M_2*r0_3 + (-900 + 814*E_2 + 265*E_4)*M*r0_4 + 42*E_2*r0_5) + L_2*r0_5*(20160*M_5 + 96*(-159 + 190*E_2)*M_4*r0 + 4*(-948 - 3251*E_2 + 780*E_4)*M_3*r0_2 + 4*(1218 + 57*E_2 + 116*E_4)*M_2*r0_3 + (-840 + 747*E_2 + 464*E_4)*M*r0_4 + 51*E_2*r0_5)) + a_10*M*(L_2*(192*(-7 + 6*E_2)*M_4 + 96*(-18 + 16*E_2 + 13*E_4)*M_3*r0 + 2*(-360 + 3083*E_2 + 416*E_4)*M_2*r0_2 + 3*(-32 + 1571*E_2 + 12*E_4)*M*r0_3 + 18*E_2*(51 - 2*E_2)*r0_4) + E_2*r0*(4352*(-3 + 2*E_2)*M_5 + 32*(-1134 + 439*E_2)*M_4*r0 + 2*(-11145 + 3832*E_2)*M_3*r0_2 + (6651 + 896*E_2)*M_2*r0_3 + (8285 - 412*E_2)*M*r0_4 + 2*(766 - 37*E_2)*r0_5)) - 2*a_9*E*L*M*(2*L_2*(96*M_4 + 8*(-62 + 63*E_2)*M_3*r0 + 2*(421 + 276*E_2 + 18*E_4)*M_2*r0_2 + 3*(332 + 55*E_2 + 6*E_4)*M*r0_3 + 216*r0_4) + r0*(768*(-17 + 14*E_2)*M_5 - 32*(714 - 445*E_2 + 27*E_4)*M_4*r0 - 4*(2520 - 1757*E_2 + 144*E_4)*M_3*r0_2 + (3844 + 2423*E_2 + 216*E_4)*M_2*r0_3 + 2*(1712 + 351*E_2 + 72*E_4)*M*r0_4 + 36*(14 + E_2)*r0_5)) + 2*a_5*E*L*M*r0_2*(-24*L_6*(2*M_2 + 3*M*r0 + 6*r0_2) + 2*L_4*(192*M_4 - 8*(-598 + 471*E_2)*M_3*r0 + 4*(783 - 263*E_2 + 21*E_4)*M_2*r0_2 + 2*(-638 + 105*E_2 + 21*E_4)*M*r0_3 - 3*(200 + 13*E_2)*r0_4) - r0_3*(48384*M_5 + 12*(1148 + 1219*E_2)*M_4*r0 - 4*(9036 - 3125*E_2 + 216*E_4)*M_3*r0_2 - (7716 + 1571*E_2 + 504*E_4)*M_2*r0_3 + 12*(508 - 3*E_2 + 12*E_4)*M*r0_4 + 2*(144 + 125*E_2)*r0_5) - L_2*r0*(35712*M_5 + 48*(239 + 200*E_2)*M_4*r0 - 8*(5006 - 2319*E_2 + 114*E_4)*M_3*r0_2 - 4*(3319 - 528*E_2 + 306*E_4)*M_2*r0_3 - 6*(-1328 + 39*E_2 + 34*E_4)*M*r0_4 + (1284 + 131*E_2)*r0_5)) + a_4*r0_2*(-96*L_8*M_2*r0 - 4*L_6*M*(1152*M_4 - 24*(-90 + 167*E_2)*M_3*r0 - 4*(261 - 212*E_2 + 21*E_4)*M_2*r0_2 + 2*(-243 + 506*E_2 + 21*E_4)*M*r0_3 + (198 - 299*E_2 - 21*E_4)*r0_4) + 2*E_2*r0_6*(19248*M_5 + 24*(61 + 277*E_2)*M_4*r0 + 4*(-2703 + 1021*E_2)*M_3*r0_2 + 4*(163 - 42*E_2)*M_2*r0_3 + (649 + 107*E_2)*M*r0_4 + 18*r0_5) + L_4*r0*(41472*M_6 + 96*(-156 + 85*E_2)*M_5*r0 + 16*(-2376 + 1608*E_2 + 229*E_4)*M_4*r0_2 + 8*(1476 - 2762*E_2 + 441*E_4)*M_3*r0_3 + 4*(1692 - 772*E_2 + 255*E_4)*M_2*r0_4 + 2*(-1044 + 1742*E_2 + 239*E_4)*M*r0_5 + 45*E_2*r0_6) + L_2*r0_3*(43776*M_6 + 120*(-96 + 425*E_2)*M_5*r0 + 4*(-7632 + 2413*E_2 + 3552*E_4)*M_4*r0_2 + 2*(4104 - 20579*E_2 + 5644*E_4)*M_3*r0_3 + (4872 + 3235*E_2 + 2076*E_4)*M_2*r0_4 + 6*(-228 + 585*E_2 + 94*E_4)*M*r0_5 + 66*E_2*r0_6)) + 2*a_7*E*L*M*r0*(-8*L_4*(24*M_3 + (-2 + 45*E_2)*M_2*r0 + 6*(23 + 4*E_2)*M*r0_2 + 54*r0_3) + 2*L_2*(1280*M_5 - 48*(-214 + 153*E_2)*M_4*r0 + 8*(1387 - 795*E_2 + 51*E_4)*M_3*r0_2 + 4*(109 - 414*E_2 + 57*E_4)*M_2*r0_3 - (2972 + 435*E_2 + 6*E_4)*M*r0_4 - 12*(53 + 3*E_2)*r0_5) - r0*(31488*M_6 + 32*(835 + 286*E_2)*M_5*r0 - 4*(7996 - 6067*E_2 + 216*E_4)*M_4*r0_2 - 8*(4217 - 1475*E_2 + 198*E_4)*M_3*r0_3 + (756 + 1237*E_2 - 216*E_4)*M_2*r0_4 + 4*(1444 + 227*E_2 + 54*E_4)*M*r0_5 + 2*(312 + 73*E_2)*r0_6)) + a_8*r0*(6*L_4*M*(48*(-6 + 5*E_2)*M_3 + 8*(-30 + 49*E_2 + 11*E_4)*M_2*r0 + 2*(-24 + 266*E_2 + 11*E_4)*M*r0_2 - 3*E_2*(-51 + E_2)*r0_3) + L_2*M*(768*(-17 + 16*E_2)*M_5 + 32*(-294 - 185*E_2 + 246*E_4)*M_4*r0 + 8*(276 - 4461*E_2 + 1490*E_4)*M_3*r0_2 + 6*(328 - 971*E_2 + 972*E_4)*M_2*r0_3 + (-456 + 13057*E_2 + 748*E_4)*M*r0_4 - 2*(132 - 1809*E_2 + 20*E_4)*r0_5) + E_2*r0*(31488*M_7 + 64*(721 + 233*E_2)*M_6*r0 + 4*(-7347 + 9304*E_2)*M_5*r0_2 + 24*(-2775 + 1126*E_2)*M_4*r0_3 + (-11815 + 5264*E_2)*M_3*r0_4 + (12023 - 672*E_2)*M_2*r0_5 + 4*(763 - 19*E_2)*M*r0_6 + 6*r0_7)) + a_6*r0*(6*L_6*M*r0*(24*(-5 + 3*E_2)*M_2 + 2*(-24 + 47*E_2)*M*r0 + 51*E_2*r0_2) + 2*L_4*M*(-2304*M_5 + 288*(-36 + 41*E_2)*M_4*r0 + 8*(-144 + 117*E_2 + 134*E_4)*M_3*r0_2 + 4*(864 - 1935*E_2 + 308*E_4)*M_2*r0_3 + 8*(18 + 202*E_2 + 47*E_4)*M*r0_4 + (-396 + 1473*E_2 + 59*E_4)*r0_5) + E_2*r0_4*(59816*M_6 + 20*(2283 + 1184*E_2)*M_5*r0 + 2*(-23783 + 16360*E_2)*M_4*r0_2 + (-31147 + 9920*E_2)*M_3*r0_3 + (7245 - 584*E_2)*M_2*r0_4 + 4*(740 + 19*E_2)*M*r0_5 + 24*r0_6) + L_2*r0*(31488*M_7 + 64*(114 + 521*E_2)*M_6*r0 + 8*(-4800 + 6155*E_2 + 1716*E_4)*M_5*r0_2 + 4*(-1920 - 11123*E_2 + 6356*E_4)*M_4*r0_3 + 2*(5424 - 20299*E_2 + 6552*E_4)*M_3*r0_4 + (1176 + 11723*E_2 + 2156*E_4)*M_2*r0_5 + (-984 + 5405*E_2 + 228*E_4)*M*r0_6 + 27*E_2*r0_7))))/(3.*r0_8*expr2_2);\n A01420 = (-8*E*r0*(2*a_3*L*M*(12*M + (6 + E_2)*r0) + a_4*E*(-24*M_2 - 9*M*r0 + 2*r0_2) + 6*a*L*M*r0*(2*L_2 + (2 + E_2)*r0_2) + E*r0_3*(3*r0_2*(-6*M + r0) + 4*L_2*(-5*M + r0)) + a_2*E*r0*(2*L_2*(-7*M + r0) + 5*r0*(-6*M_2 - 5*M*r0 + r0_2))))/(a_2 + r0*(-2*M + r0));\n A01440 = (-4*(a_10*E_2*M*(288*(-5 + 2*E_2)*M_3 + 4*(761 + 80*E_2)*M_2*r0 + 3*(1287 - 40*E_2)*M*r0_2 + 3*(329 - 22*E_2)*r0_3) - 2*a_9*E*L*M*(288*(-5 + 3*E_2)*M_3 + 2*(437 + 360*E_2 + 72*E_4)*M_2*r0 + 12*(144 + 11*E_2 + 6*E_4)*M*r0_2 - 3*(-154 + E_2)*r0_3) + 2*a*E*L*M*r0_3*(-8*L_6*(104*M_2 - 106*M*r0 + 27*r0_2) - 2*L_4*r0*(1104*M_3 + 4*(65 + 158*E_2)*M_2*r0 - 10*(98 + 31*E_2)*M*r0_2 + (287 + 3*E_2)*r0_3) - r0_5*(6048*M_3 + 12*(-376 + 77*E_2)*M_2*r0 + 4*(109 - 147*E_2)*M*r0_2 + 11*(14 + 9*E_2)*r0_3) + L_2*r0_3*(-8448*M_3 + 12*(424 - 129*E_2)*M_2*r0 + 4*(139 + 165*E_2 + 15*E_4)*M*r0_2 + (-494 + 21*E_2)*r0_3)) + r0_4*(8*L_6*M*(2*M - r0)*(252*M_2 + 20*(-9 + 5*E_2)*M*r0 + (27 - 52*E_2)*r0_2) + E_2*r0_7*(-192*M_3 + 12*(25 - 2*E_2)*M_2*r0 + 4*(-32 + 15*E_2)*M*r0_2 + 13*r0_3) + 2*L_2*r0_4*(2304*M_4 - 12*(240 + 7*E_2)*M_3*r0 - 12*(-96 + 7*E_4)*M_2*r0_2 + (-144 + 13*E_2 + 66*E_4)*M*r0_3 + 4*E_2*r0_4) + 2*L_4*r0_2*(4320*M_4 + 4*(-1332 + 173*E_2)*M_3*r0 - 2*(-1044 + 402*E_2 + 43*E_4)*M_2*r0_2 + (-252 + 213*E_2 + 47*E_4)*M*r0_3 + 8*E_2*r0_4)) - 2*a_7*E*L*M*(L_2*(288*M_3 + 112*(-8 + 9*E_2)*M_2*r0 + 12*(132 + 31*E_2 + 3*E_4)*M*r0_2 + 3*(308 + E_2)*r0_3) + 4*r0*(288*(-7 + 6*E_2)*M_4 - 2*(1687 - 822*E_2 + 72*E_4)*M_3*r0 + (-919 + 545*E_2 + 36*E_4)*M_2*r0_2 + (949 + 85*E_2 + 72*E_4)*M*r0_3 + 2*(185 + 3*E_2)*r0_4)) + 2*a_3*E*L*M*r0_2*(-24*L_6*M - 4*L_4*(288*M_3 + 12*(-51 + 37*E_2)*M_2*r0 - 4*(95 + 23*E_2)*M*r0_2 + (259 + 3*E_2)*r0_3) + L_2*r0*(-15840*M_4 - 48*(11 + 82*E_2)*M_3*r0 + 4*(3008 - 881*E_2 + 84*E_4)*M_2*r0_2 + 4*(174 + 217*E_2 + 9*E_4)*M*r0_3 + 5*(-374 + 3*E_2)*r0_4) - 4*r0_3*(5688*M_4 + 6*(-132 + 241*E_2)*M_3*r0 + (-2846 + 229*E_2 - 108*E_4)*M_2*r0_2 + (363 - 214*E_2 + 36*E_4)*M*r0_3 + 4*(54 + 13*E_2)*r0_4)) + a_8*(3*L_2*M*(96*(-5 + 6*E_2)*M_3 + 16*(-27 + 13*E_2 + 26*E_4)*M_2*r0 + 4*(-24 + 344*E_2 + 35*E_4)*M*r0_2 + E_2*(657 - 20*E_2)*r0_3) + E_2*r0*(2688*(-3 + 2*E_2)*M_5 + 16*(-1597 + 422*E_2)*M_4*r0 + 56*(-159 + 49*E_2)*M_3*r0_2 + (9267 - 164*E_2)*M_2*r0_3 + 12*(333 - 20*E_2)*M*r0_4 + 7*r0_5)) + a_2*r0_2*(-2*L_6*M*(576*M_3 - 48*(-12 + 47*E_2)*M_2*r0 + 2*(-396 + 743*E_2)*M*r0_2 + (180 - 199*E_2)*r0_3) + E_2*r0_6*(9672*M_4 + 12*(-269 + 240*E_2)*M_3*r0 + 6*(-403 + 14*E_2)*M_2*r0_2 + 3*(229 + 46*E_2)*M*r0_3 + 46*r0_4) + 2*L_4*r0*(9504*M_5 + 48*(-159 + 35*E_2)*M_4*r0 + 4*(-666 + 791*E_2 + 32*E_4)*M_3*r0_2 + 4*(819 - 962*E_2 + 40*E_4)*M_2*r0_3 + (-612 + 927*E_2 + 73*E_4)*M*r0_4 + 16*E_2*r0_5) + L_2*r0_3*(20160*M_5 + 24*(-636 + 553*E_2)*M_4*r0 + 4*(-1044 - 715*E_2 + 366*E_4)*M_3*r0_2 + 2*(2628 - 3105*E_2 + 614*E_4)*M_2*r0_3 + (-936 + 2087*E_2 + 256*E_4)*M*r0_4 + 51*E_2*r0_5)) + 2*a_5*E*L*M*r0*(-6*L_4*(32*M_2 + 10*(-2 + 3*E_2)*M*r0 + (77 + E_2)*r0_2) + L_2*(768*M_4 + 16*(479 - 396*E_2)*M_3*r0 + 8*(1078 - 417*E_2 + 30*E_4)*M_2*r0_2 - 4*(340 + 53*E_2 + 15*E_4)*M*r0_3 - (2300 + 9*E_2)*r0_4) - 2*r0*(10944*M_5 + 12*(403 + 244*E_2)*M_4*r0 - 4*(2437 - 1219*E_2 + 108*E_4)*M_3*r0_2 + (-5591 + 798*E_2 - 216*E_4)*M_2*r0_3 + 2*(771 - 25*E_2 + 90*E_4)*M*r0_4 + 4*(216 + 17*E_2)*r0_5)) + a_6*r0*(6*L_4*M*(24*(-9 + 10*E_2)*M_2 + 2*(-48 + 43*E_2 + 22*E_4)*M*r0 + E_2*(165 + E_2)*r0_2) + L_2*(1152*(-7 + 8*E_2)*M_5 + 288*(-5 - 5*E_2 + 8*E_4)*M_4*r0 + 8*(270 - 2368*E_2 + 633*E_4)*M_3*r0_2 + 2*(-108 + 1085*E_2 + 994*E_4)*M_2*r0_3 + (-360 + 6049*E_2 - 128*E_4)*M*r0_4 + 23*E_2*r0_5) + E_2*r0*(21888*M_6 + 48*(523 + 188*E_2)*M_5*r0 + 4*(-6059 + 3924*E_2)*M_4*r0_2 + 16*(-1991 + 436*E_2)*M_3*r0_3 + (4005 + 196*E_2)*M_2*r0_4 + 2*(2987 - 132*E_2)*M*r0_5 + 34*r0_6)) + a_4*r0*(6*L_6*M*r0*(12*(-4 + 3*E_2)*M + E_2*r0) + 3*E_2*r0_4*(9776*M_5 + 4*(923 + 828*E_2)*M_4*r0 + 8*(-958 + 307*E_2)*M_3*r0_2 + (-1373 + 116*E_2)*M_2*r0_3 - 4*(-315 + E_2)*M*r0_4 + 20*r0_5) + 2*L_4*(-1152*M_5 + 288*(-13 + 22*E_2)*M_4*r0 + 4*(414 - 231*E_2 + 28*E_4)*M_3*r0_2 + 2*(342 - 1403*E_2 + 165*E_4)*M_2*r0_3 + (-360 + 1209*E_2 + 29*E_4)*M*r0_4 + 8*E_2*r0_5) + L_2*r0*(21888*M_6 + 1920*(-3 + 8*E_2)*M_5*r0 + 32*(-576 + 629*E_2 + 99*E_4)*M_4*r0_2 + 4*(1332 - 5551*E_2 + 1448*E_4)*M_3*r0_3 + 4*(756 - 2051*E_2 + 741*E_4)*M_2*r0_4 + (-1008 + 6163*E_2 + 56*E_4)*M*r0_5 + 66*E_2*r0_6))))/(3.*r0_5*expr2_2);\n A01600 = (-2*E*r0_4*(4*a*L*M + E*r0_2*(-6*M + r0) + a_2*E*(-4*M + r0)))/(a_2 + r0*(-2*M + r0));\n A01620 = (6*a_7*E*L*M*(16*(-13 + 9*E_2)*M_2 + 4*(62 + 6*E_2 + 3*E_4)*M*r0 + (164 - 11*E_2)*r0_2) - 3*a_8*E_2*(16*(-13 + 6*E_2)*M_3 + 592*M_2*r0 + (337 - 26*E_2)*M*r0_2 - 3*r0_3) + 2*a_5*E*L*M*(12*L_2*(12*M_2 + 3*(-6 + 7*E_2)*M*r0 + (41 - 2*E_2)*r0_2) + r0*(192*(-11 + 10*E_2)*M_3 - 8*(503 - 151*E_2 + 15*E_4)*M_2*r0 + 8*(13 + 13*E_2 + 15*E_4)*M*r0_2 + (1196 - 63*E_2)*r0_3)) + 2*a*E*L*M*r0_2*(8*L_4*(52*M_2 - 56*M*r0 + 15*r0_2) + 2*L_2*r0*(1152*M_3 + 4*(-48 + 73*E_2)*M_2*r0 - 4*(137 + 23*E_2)*M*r0_2 + (178 - 15*E_2)*r0_3) + r0_3*(3552*M_3 + 4*(-476 + 157*E_2)*M_2*r0 - 8*(51 + 43*E_2)*M*r0_2 + (236 + 51*E_2)*r0_3)) + a_6*(L_2*((624 - 864*E_2)*M_3 + 24*(12 - 13*E_4)*M_2*r0 + 12*E_2*(-83 + 2*E_2)*M*r0_2 + 9*E_2*r0_3) + E_2*r0*(-704*(-3 + 2*E_2)*M_4 + 8*(1108 - 187*E_2)*M_3*r0 - 2*(229 + 150*E_2)*M_2*r0_2 + (-3107 + 210*E_2)*M*r0_3 + 19*r0_4)) + r0_3*(-8*L_4*M*(2*M - r0)*(180*M_2 + 2*(-66 + 25*E_2)*M*r0 + (21 - 29*E_2)*r0_2) - 8*E_2*r0_5*(-16*M_3 - 2*(-12 + E_2)*M_2*r0 + 5*(-2 + E_2)*M*r0_2 + r0_3) + L_2*r0_2*(-3072*M_4 + 24*(160 - 11*E_2)*M_3*r0 + 4*(-384 + 105*E_2 + 14*E_4)*M_2*r0_2 - 2*(-96 + 79*E_2 + 22*E_4)*M*r0_3 + 7*E_2*r0_4)) + 2*a_3*E*L*M*r0*(48*L_4*M + 2*L_2*(64*M_3 + 12*(-44 + 37*E_2)*M_2*r0 + 8*(-93 + 8*E_2)*M*r0_2 + (424 - 27*E_2)*r0_3) + r0*(6720*M_4 + 16*(29 + 101*E_2)*M_3*r0 - 4*(1094 - 283*E_2 + 54*E_4)*M_2*r0_2 + 4*(-250 - 54*E_2 + 21*E_4)*M*r0_3 + (940 + 21*E_2)*r0_4)) + a_4*r0*(24*L_4*M*(-3*(-4 + 5*E_2)*M + E_2*r0) + L_2*(-192*(-11 + 16*E_2)*M_4 - 8*(102 - 53*E_2 + 14*E_4)*M_3*r0 - 4*(66 - 995*E_2 + 234*E_4)*M_2*r0_2 + 2*(108 - 1081*E_2 + 26*E_4)*M*r0_3 + E_2*r0_4) + E_2*r0*(-6720*M_5 - 16*(376 + 137*E_2)*M_4*r0 + 4*(2119 - 590*E_2)*M_3*r0_2 + 24*(197 - 23*E_2)*M_2*r0_3 + (-3101 + 146*E_2)*M*r0_4 + 3*r0_5)) - a_2*r0*(-8*L_4*M*(48*M_3 + 6*(16 - 47*E_2)*M_2*r0 + (-114 + 167*E_2)*M*r0_2 + (27 - 23*E_2)*r0_3) + E_2*r0_4*(4760*M_4 + 4*(43 + 320*E_2)*M_3*r0 + 2*(-1609 + 118*E_2)*M_2*r0_2 + (925 + 26*E_2)*M*r0_3 + 15*r0_4) + L_2*r0*(6720*M_5 + 16*(-318 + 173*E_2)*M_4*r0 - 16*(111 - 168*E_2 + 4*E_4)*M_3*r0_2 + 8*(267 - 552*E_2 + 83*E_4)*M_2*r0_3 + 4*(-102 + 319*E_2 + 4*E_4)*M*r0_4 + E_2*r0_5)))/(3.*r0_2*expr2_2);\n A01800 = (r0*(12*a_5*E*L*M*(4*(-4 + 3*E_2)*M + (29 - 5*E_2)*r0) + 3*a_6*E_2*(-16*(-2 + E_2)*M_2 + 2*(-58 + 5*E_2)*M*r0 + 3*r0_2) + 8*a_3*E*L*M*(6*L_2*M + r0*(48*(-1 + E_2)*M_2 + (-134 + 19*E_2)*M*r0 + (67 - 9*E_2)*r0_2)) - r0_2*(8*L_2*M*(2*M - r0)*(48*M_2 + 2*(-18 + 5*E_2)*M*r0 + (6 - 7*E_2)*r0_2) + E_2*r0_3*(-32*M_3 - 4*(-9 + E_2)*M_2*r0 + 2*(-6 + 5*E_2)*M*r0_2 + r0_3)) + a_4*(6*L_2*M*(-8*(-2 + 3*E_2)*M + 5*E_2*r0) + E_2*r0*(-64*(-3 + 2*E_2)*M_3 - 4*(-316 + 39*E_2)*M_2*r0 + 2*(-362 + 25*E_2)*M*r0_2 + 17*r0_3)) + 4*a*E*L*M*r0*(4*L_2*(8*M_2 - 10*M*r0 + 3*r0_2) + r0*(384*M_3 + 20*(-5 + 4*E_2)*M_2*r0 - 2*(70 + 11*E_2)*M*r0_2 + (47 - 3*E_2)*r0_3)) - a_2*r0*(2*L_2*M*(96*(-1 + 2*E_2)*M_2 + (96 - 82*E_2)*M*r0 + (-24 + 13*E_2)*r0_2) + E_2*r0*(768*M_4 + 80*(7 + 2*E_2)*M_3*r0 + 4*(-293 + 26*E_2)*M_2*r0_2 + 2*(182 - 5*E_2)*M*r0_3 - 7*r0_4))))/(12.*expr2_2);\n A02040 = (192*E_2*expr1_2)/(a_2 + r0*(-2*M + r0));\n A02060 = (32*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-4*a_7*E*L*M*(48*M_3 + 12*(4 + 3*E_2)*M_2*r0 + (-12 + 35*E_2)*M*r0_2 + 3*(-4 + E_2)*r0_3) + a_8*E_2*M*(96*M_3 + 24*(4 + E_2)*M_2*r0 + (-73 + 36*E_2)*M*r0_2 + 6*(-9 + 2*E_2)*r0_3) - 4*a*E*L*M*r0_3*(-6*L_4*(20*M_2 - 21*M*r0 + 5*r0_2) + L_2*r0_2*(-384*M_2 + (348 + 139*E_2)*M*r0 - 36*(2 + E_2)*r0_2) + r0_4*(-264*M_2 + (222 + 89*E_2)*M*r0 - 3*(14 + 5*E_2)*r0_2)) + r0_3*(-96*L_6*M*r0_2M_2 + E_2*r0_7*(184*M_2 - 2*(55 + 2*E_2)*M*r0 + 9*r0_2) - 8*L_4*(2*M - r0)*r0_2*(48*M_2 - 2*(12 + 13*E_2)*M*r0 + 3*E_2*r0_2) + 2*L_2*r0_4*(-192*M_3 + 6*(32 + 49*E_2)*M_2*r0 + (-48 - 177*E_2 + 2*E_4)*M*r0_2 + 15*E_2*r0_3)) - 4*a_3*E*L*M*r0_2*(12*L_4*(2*M - r0) + L_2*(-624*M_3 + 56*(3 + E_2)*M_2*r0 + (264 + 157*E_2)*M*r0_2 - 3*(32 + E_2)*r0_3) + r0_2*(-912*M_3 + 4*(54 + 5*E_2)*M_2*r0 + (312 + 173*E_2)*M*r0_2 - (96 + 11*E_2)*r0_3)) + 2*a_2*r0_2*(12*L_6*M_2 + E_2*r0_5*(-250*M_3 + 3*(99 - 26*E_2)*M_2*r0 - 165*M*r0_2 + 6*r0_3) + L_4*(-768*M_4 + 16*(24 + 5*E_2)*M_3*r0 + 6*(36 + 49*E_2)*M_2*r0_2 - 32*(3 + 4*E_2)*M*r0_3 - 6*E_2*r0_4) + L_2*r0_2*(-768*M_4 + (384 - 98*E_2)*M_3*r0 + (204 + 627*E_2 + 104*E_4)*M_2*r0_2 + (-96 - 345*E_2 + 10*E_4)*M*r0_3 + 6*E_2*r0_4)) + 2*a_6*(L_2*M*(48*M_3 + 12*(4 + 13*E_2)*M_2*r0 + 4*(3 + 13*E_2 + 6*E_4)*M*r0_2 + 3*E_2*(-17 + 2*E_2)*r0_3) + E_2*r0*(-768*M_5 - 16*(39 + 4*E_2)*M_4*r0 - 120*(-2 + E_2)*M_3*r0_2 - 6*(-2 + 3*E_2)*M_2*r0_3 + (-139 + 16*E_2)*M*r0_4 - 3*r0_5)) + a_4*r0*(24*L_4*M*(4*M_2 + (2 + 7*E_2)*M*r0 - 2*E_2*r0_2) + E_2*r0_3*(-2108*M_4 + 20*(1 - 18*E_2)*M_3*r0 + 3*(189 - 76*E_2)*M_2*r0_2 + 12*(-37 + 2*E_2)*M*r0_3 - 3*r0_4) - 2*L_2*(768*M_5 + 256*E_2*M_4*r0 + 8*(-54 - 43*E_2 + 2*E_4)*M_3*r0_2 - (24 + 349*E_2 + 80*E_4)*M_2*r0_3 + (48 + 267*E_2 - 14*E_4)*M*r0_4 + 9*E_2*r0_5)) - 4*a_5*E*L*M*r0*(-768*M_4 + 8*(-39 + 10*E_2)*M_3*r0 + 136*(3 + E_2)*M_2*r0_2 + (78 + 151*E_2)*M*r0_3 + (-66 + 7*E_2)*r0_4 + 3*L_2*(24*M_2 + (-8 + E_2)*r0_2 + 4*M*(r0 + 3*E_2*r0)))))/(3.*r0_7*expr2_2);\n A02220 = (96*E_2*r0_3*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/(a_2 + r0*(-2*M + r0));\n A02240 = (-8*(4*a_7*E*L*M*(144*M_3 + 24*(9 + E_2)*M_2*r0 + 5*(12 + E_2)*M*r0_2 - 3*(2 + 3*E_2)*r0_3) + a_8*E_2*(-288*M_4 + 48*(-12 + E_2)*M_3*r0 + (-119 + 24*E_2)*M_2*r0_2 + 66*M*r0_3 + 6*r0_4) + 4*a*E*L*M*r0_3*(L_4*(-432*M_2 + 2*(165 + 2*E_2)*M*r0 - 48*r0_2) - 6*r0_4*(120*M_2 - 3*(29 + 11*E_2)*M*r0 + (12 + 7*E_2)*r0_2) - 3*L_2*r0_2*(384*M_2 - 4*(71 + 21*E_2)*M*r0 + (40 + 21*E_2)*r0_2)) + r0_3*(4*L_6*M*(2*M - r0)*(144*M - (72 + E_2)*r0) + 3*E_2*r0_7*(-184*M_2 + 2*(59 + 2*E_2)*M*r0 - 13*r0_2) + 36*L_2*(2*M - r0)*r0_4*(16*M_2 - 2*(4 + 11*E_2)*M*r0 + 3*E_2*r0_2) + 2*L_4*r0_2*(1152*M_3 - 2*(576 + 263*E_2)*M_2*r0 + (288 + 335*E_2 - 2*E_4)*M*r0_2 - 36*E_2*r0_3)) + 4*a_3*E*L*M*r0_2*(L_4*(60*M - 6*r0) - 6*L_2*(336*M_3 - 4*(11 + 6*E_2)*M_2*r0 - (126 + 37*E_2)*M*r0_2 + 2*(11 + 4*E_2)*r0_3) + r0_2*(-2592*M_3 + 6*(60 + 53*E_2)*M_2*r0 + (840 + 289*E_2)*M*r0_2 - (150 + 83*E_2)*r0_3)) - 2*a_2*r0_2*(36*L_6*M_2 - 3*E_2*r0_5*(108*M_3 + 2*(-77 + 24*E_2)*M_2*r0 + (143 + 6*E_2)*M*r0_2 - 15*r0_3) + L_4*(-2304*M_4 + 1152*M_3*r0 + 4*(162 + 123*E_2 + E_4)*M_2*r0_2 + (-288 - 287*E_2 + 2*E_4)*M*r0_3 + 15*E_2*r0_4) + 3*L_2*r0_2*(-768*M_4 + 384*M_3*r0 + 6*(34 + 53*E_2 + 3*E_4)*M_2*r0_2 - (96 + 277*E_2)*M*r0_3 + 25*E_2*r0_4)) - 2*a_6*(L_2*(144*M_4 + 24*(6 + 13*E_2)*M_3*r0 + 2*(18 + 95*E_2 + 3*E_4)*M_2*r0_2 - 63*E_2*M*r0_3 - 6*E_2*r0_4) - E_2*M*r0*(2304*M_4 + 48*(45 + E_2)*M_3*r0 + 2*(-149 + 108*E_2)*M_2*r0_2 + (-193 + 120*E_2)*M*r0_3 + 3*(61 + 2*E_2)*r0_4)) + 4*a_5*E*L*M*r0*(3*L_2*(64*M_2 + 10*(4 + E_2)*M*r0 - (4 + 3*E_2)*r0_2) + 2*(-1152*M_4 + 60*(-9 + 2*E_2)*M_3*r0 + (516 + 169*E_2)*M_2*r0_2 + (189 + 58*E_2)*M*r0_3 - (42 + 25*E_2)*r0_4)) + a_4*r0*(-6*L_4*(48*M_3 + 2*(12 + 23*E_2)*M_2*r0 - 10*E_2*M*r0_2 - E_2*r0_3) + 3*E_2*r0_3*(1804*M_4 + 4*(61 + 48*E_2)*M_3*r0 + (-241 + 168*E_2)*M_2*r0_2 + 4*(67 + 3*E_2)*M*r0_3 - 19*r0_4) + 2*L_2*(2304*M_5 + 1200*E_2*M_4*r0 - 4*(324 + 67*E_2)*M_3*r0_2 - 4*(18 + 121*E_2 + 9*E_4)*M_2*r0_3 + 12*(12 + 37*E_2)*M*r0_4 - 15*E_2*r0_5))))/(3.*r0_4*expr2_2);\n A02400 = (12*E_2*r0_6)/(a_2 + r0*(-2*M + r0));\n A02420 = (-2*(-24*a_5*E*L*M*(-12*M_2 + (-18 + 5*E_2)*M*r0 + 4*(-1 + E_2)*r0_2) + 3*a_6*E_2*(-48*M_3 + 4*(-30 + 7*E_2)*M_2*r0 + 2*(-11 + 6*E_2)*M*r0_2 + 3*r0_3) - 12*a_3*E*L*M*r0*(384*M_3 + 4*(3 - 10*E_2)*M_2*r0 - (134 + 19*E_2)*M*r0_2 + (-2 + 23*E_2)*r0_3 - 4*L_2*(4*M - (-2 + E_2)*r0)) + r0_2*(24*L_4*M*(2*M - r0)*(24*M - (12 + E_2)*r0) + E_2*r0_5*(-552*M_2 + 2*(179 + 6*E_2)*M*r0 - 41*r0_2) + L_2*(2*M - r0)*r0_2*(576*M_2 - 6*(48 + 71*E_2)*M*r0 + 59*E_2*r0_2)) + 12*a*E*L*M*r0_2*(-2*L_2*(84*M_2 - (47 + 4*E_2)*M*r0 + (1 + 2*E_2)*r0_2) + r0_2*(-216*M_2 + (126 + 43*E_2)*M*r0 - (6 + 13*E_2)*r0_2)) + a_4*(-3*L_2*(48*M_3 + 4*(6 + 7*E_2)*M_2*r0 + 4*E_2*(3 - 2*E_2)*M*r0_2 - 3*E_2*r0_3) + E_2*r0*(2304*M_4 - 48*(-27 + 2*E_2)*M_3*r0 + 6*(-53 + 20*E_2)*M_2*r0_2 + 2*(19 + 42*E_2)*M*r0_3 - 17*r0_4)) + a_2*r0*(24*L_4*M*(-3*M + E_2*r0) + E_2*r0_3*(900*M_3 + 2*(-167 + 42*E_2)*M_2*r0 + 30*(15 + 2*E_2)*M*r0_2 - 67*r0_3) + 2*L_2*(1152*M_4 + 48*(-12 + 5*E_2)*M_3*r0 - 6*(54 + 27*E_2 + 4*E_4)*M_2*r0_2 + 6*(24 + 31*E_2 + 2*E_4)*M*r0_3 - 25*E_2*r0_4))))/(3.*r0*expr2_2);\n A02600 = (r0_2*(24*a_3*E*L*M*(-2*M + (-3 + 2*E_2)*r0) - 3*a_4*E_2*(-8*M_2 + 8*(-3 + E_2)*M*r0 + r0_2) - 8*a*E*L*M*r0*(-96*M_2 + (39 + 10*E_2)*M*r0 - 6*(-1 + E_2)*r0_2) + r0*(-4*L_2*M*(2*M - r0)*(48*M - (24 + 5*E_2)*r0) + E_2*r0_3*(184*M_2 - 2*(57 + 2*E_2)*M*r0 + 11*r0_2)) + 2*a_2*(12*L_2*M*(M - E_2*r0) - E_2*r0*(192*M_3 - 4*(-9 + 5*E_2)*M_2*r0 + 7*(1 + 2*E_2)*M*r0_2 - 4*r0_3))))/(6.*expr2_2);\n A03040 = (-32*E*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(4*a_3*L*M*(6*M + (3 + E_2)*r0) + a_4*E*(-24*M_2 - 12*M*r0 + r0_2) + 12*a*L*M*r0*(L_2 + (1 + E_2)*r0_2) + E*r0_3*(r0_2*(-17*M + 2*r0) + L_2*(-21*M + 4*r0)) + a_2*E*r0*(L_2*(-16*M + r0) + r0*(-22*M_2 - 27*M*r0 + 3*r0_2))))/(r0_2*expr2_2);\n A03060 = (-16*(4*a_11*E*L*M*(48*(-1 + 4*E_2)*M_4 + 2*(-265 + 18*E_2 + 18*E_4)*M_3*r0 + (-421 - 189*E_2 + 54*E_4)*M_2*r0_2 + 3*(-12 - 31*E_2 + 6*E_4)*M*r0_3 + 24*r0_4) + a_12*E_2*M*(-96*(-1 + 2*E_2)*M_4 - 8*(-205 + 83*E_2)*M_3*r0 + 4*(325 - 137*E_2)*M_2*r0_2 + 3*(19 - 40*E_2)*M*r0_3 + 6*(-17 + E_2)*r0_4) + 2*a*E*L*M*r0_4*(-168*L_8*r0_2M_2 + r0_7*(-4560*M_3 - 8*(-664 + 33*E_2)*M_2*r0 + 4*(-505 + 67*E_2 + 27*E_4)*M*r0_2 + 3*(82 - 19*E_2)*r0_3) + L_2*r0_5*(-10224*M_3 + 4*(3194 - 127*E_2)*M_2*r0 + 4*(-1318 + 91*E_2 + 57*E_4)*M*r0_2 - 3*(-234 + E_2)*r0_3) - 2*L_6*r0*(360*M_3 + 4*(-44 + 147*E_2)*M_2*r0 - 28*(5 + 12*E_2)*M*r0_2 + 3*(24 + 7*E_2)*r0_3) + 2*L_4*r0_3*(-3192*M_3 + (4244 - 506*E_2)*M_2*r0 + 2*(-911 + 96*E_2 + 21*E_4)*M*r0_2 + 3*(80 + 17*E_2)*r0_3)) + r0_5*(24*L_8*M*r0_2M_2*(27*M + 2*(-3 + 7*E_2)*r0) + 3*E_2*r0_9*(-284*M_3 + (298 - 24*E_2)*M_2*r0 + 2*(-44 + 9*E_2)*M*r0_2 + 5*r0_3) + 2*L_6*(2*M - r0)*r0_2*(2088*M_3 + 2*(-774 + 143*E_2)*M_2*r0 + (252 - 169*E_2 - 42*E_4)*M*r0_2 - 24*E_2*r0_3) + L_2*r0_6*(3168*M_4 - 4*(1008 + 695*E_2)*M_3*r0 - 4*(-414 - 651*E_2 + 85*E_4)*M_2*r0_2 + (-216 - 685*E_2 + 184*E_4)*M*r0_3 + 39*E_2*r0_4) + L_4*r0_4*(8928*M_4 - 416*(27 + 5*E_2)*M_3*r0 + 2*(2268 + 867*E_2 - 230*E_4)*M_2*r0_2 + (-576 - 479*E_2 + 226*E_4)*M*r0_3 + 66*E_2*r0_4)) + 2*a_3*E*L*M*r0_3*(-2*L_6*(944*M_3 + 108*(-17 + 7*E_2)*M_2*r0 + 2*(194 - 147*E_2)*M*r0_2 + 3*(36 + 7*E_2)*r0_3) + r0_5*(-25728*M_4 + 12*(1146 - 695*E_2)*M_3*r0 + 2*(4542 + 1529*E_2 - 270*E_4)*M_2*r0_2 + 4*(-1696 + 46*E_2 + 135*E_4)*M*r0_3 + (1026 - 257*E_2)*r0_4) + 2*L_2*r0_3*(-19200*M_4 - 22*(-504 + 353*E_2)*M_3*r0 + (8880 + 3397*E_2 + 672*E_4)*M_2*r0_2 + 3*(-2270 + 69*E_2 + 128*E_4)*M*r0_3 + 2*(525 - 107*E_2)*r0_4) - 4*L_4*r0*(2976*M_4 + 2*(-751 + 718*E_2)*M_3*r0 - (3057 + 373*E_2 + 42*E_4)*M_2*r0_2 - 2*(-935 + 129*E_2 + 21*E_4)*M*r0_3 + 42*(-5 + 2*E_2)*r0_4)) - a_2*r0_3*(24*L_8*M*(48*M_3 + 2*(27 - 77*E_2)*M_2*r0 + (-62 + 105*E_2)*M*r0_2 + (11 - 14*E_2)*r0_3) - E_2*r0_8*(5880*M_4 + 4*(-1795 + 846*E_2)*M_3*r0 + 4*(1102 - 233*E_2)*M_2*r0_2 + (-1141 + 268*E_2)*M*r0_3 + 15*r0_4) + L_2*r0_5*(-20736*M_5 - 8*(-2016 + 1919*E_2)*M_4*r0 + 12*(344 + 2065*E_2 - 374*E_4)*M_3*r0_2 + 2*(-2676 - 6891*E_2 + 1052*E_4)*M_2*r0_3 + (912 + 2511*E_2 - 800*E_4)*M*r0_4 + 27*E_2*r0_5) + 2*L_6*r0*(-9216*M_5 - 64*(-126 + 25*E_2)*M_4*r0 + 4*(840 + 197*E_2 - 84*E_4)*M_3*r0_2 + 2*(-1938 + 385*E_2 + 84*E_4)*M_2*r0_3 + (648 - 419*E_2 - 84*E_4)*M*r0_4 + 36*E_2*r0_5) + L_4*r0_3*(-39168*M_5 - 24*(-1296 + 539*E_2)*M_4*r0 + 4*(2388 + 5793*E_2 + 358*E_4)*M_3*r0_2 + 4*(-2904 - 2653*E_2 + 18*E_4)*M_2*r0_3 + (1944 + 1021*E_2 - 732*E_4)*M*r0_4 + 81*E_2*r0_5)) + 4*a_9*E*L*M*(L_2*(192*M_4 + 4*(-110 + 129*E_2)*M_3*r0 + (-1037 + 114*E_2 + 48*E_4)*M_2*r0_2 + 3*(-84 - 59*E_2 + 6*E_4)*M*r0_3 + 72*r0_4) + r0*(-96*(-85 + 62*E_2)*M_5 + 8*(1302 - 899*E_2 + 36*E_4)*M_4*r0 + 2*(348 - 1145*E_2 + 234*E_4)*M_3*r0_2 + (-3053 - 736*E_2 + 468*E_4)*M_2*r0_3 + (-488 - 585*E_2 + 162*E_4)*M*r0_4 + 6*(36 - 5*E_2)*r0_5)) + a_10*M*(L_2*(-96*(-1 + 12*E_2)*M_4 - 24*(-20 - 83*E_2 + 38*E_4)*M_3*r0 + 4*(102 + 1171*E_2 - 326*E_4)*M_2*r0_2 + 3*(32 + 407*E_2 - 108*E_4)*M*r0_3 + 6*E_2*(-51 + 2*E_2)*r0_4) + E_2*r0*(64*(-255 + 148*E_2)*M_5 + 16*(-1818 + 935*E_2)*M_4*r0 + 2*(-4311 + 3016*E_2)*M_3*r0_2 + 11*(543 - 104*E_2)*M_2*r0_3 + (1397 - 676*E_2)*M*r0_4 + 2*(-329 + 38*E_2)*r0_5)) + a_4*r0_2*(-48*L_8*M_2*(M - 2*r0) - 2*L_6*M*(2304*M_4 + 24*(241 - 352*E_2)*M_3*r0 - 4*(525 - 1111*E_2 + 42*E_4)*M_2*r0_2 + 4*(-420 + 47*E_2 + 21*E_4)*M*r0_3 + (396 - 139*E_2 - 42*E_4)*r0_4) + E_2*r0_6*(34140*M_5 + 12*(-817 + 1278*E_2)*M_4*r0 + (-13965 + 8684*E_2)*M_3*r0_2 + 8*(1168 - 297*E_2)*M_2*r0_3 + (-2461 + 538*E_2)*M*r0_4 - 45*r0_5) + L_2*r0_3*(44928*M_6 + 4*(-3168 + 11983*E_2)*M_5*r0 + 4*(-8460 - 4609*E_2 + 6984*E_4)*M_4*r0_2 + (8904 - 34221*E_2 + 6296*E_4)*M_3*r0_3 + 4*(1482 + 6265*E_2 - 927*E_4)*M_2*r0_4 + 3*(-480 - 1561*E_2 + 436*E_4)*M*r0_5 - 171*E_2*r0_6) + L_4*r0*(42624*M_6 + 32*(-504 + 347*E_2)*M_5*r0 + 8*(-5532 + 1145*E_2 + 772*E_4)*M_4*r0_2 - 24*(-524 + 1207*E_2 + 148*E_4)*M_3*r0_3 + 4*(2262 + 3755*E_2 - 222*E_4)*M_2*r0_4 + 2*(-1080 - 907*E_2 + 396*E_4)*M*r0_5 - 147*E_2*r0_6)) + 2*a_7*E*L*M*r0*(8*L_4*(66*M_3 + (-133 + 75*E_2)*M_2*r0 - 3*(33 + 7*E_2)*M*r0_2 + 18*r0_3) + 2*L_2*(1088*M_5 - 96*(-139 + 87*E_2)*M_4*r0 + 4*(2231 - 1059*E_2 + 84*E_4)*M_3*r0_2 + (-4418 + 1167*E_2 + 624*E_4)*M_2*r0_3 + 2*(-1171 - 387*E_2 + 96*E_4)*M*r0_4 + 12*(41 - 8*E_2)*r0_5) - r0*(32256*M_6 + 16*(1307 + 588*E_2)*M_5*r0 + 8*(-5255 + 3282*E_2)*M_4*r0_2 + 4*(-6409 + 2653*E_2 + 18*E_4)*M_3*r0_3 - 6*(-1859 + 162*E_2 + 216*E_4)*M_2*r0_4 + 2*(2240 + 1119*E_2 - 432*E_4)*M*r0_5 + (-1254 + 263*E_2)*r0_6)) + a_8*(-6*L_4*M*(32*M_4 + 24*(-2 + 15*E_2)*M_3*r0 + 8*(-16 - 51*E_2 + 16*E_4)*M_2*r0_2 + 2*(-24 - 188*E_2 + 17*E_4)*M*r0_3 - E_2*(-51 + E_2)*r0_4) + L_2*M*r0*(192*(-85 + 76*E_2)*M_5 + 16*(-786 - 841*E_2 + 648*E_4)*M_4*r0 + 8*(594 - 3447*E_2 + 1034*E_4)*M_3*r0_2 + 3*(1768 + 2685*E_2 - 1160*E_4)*M_2*r0_3 + 2*(192 + 3881*E_2 - 664*E_4)*M*r0_4 + 4*(-66 - 438*E_2 + 71*E_4)*r0_5) + E_2*r0_2*(32256*M_7 + 32*(1091 + 468*E_2)*M_6*r0 + 8*(-4993 + 5068*E_2)*M_5*r0_2 + 20*(-2189 + 1460*E_2)*M_4*r0_3 + (5057 + 2488*E_2)*M_3*r0_4 + (5293 - 1720*E_2)*M_2*r0_5 + (-1981 + 298*E_2)*M*r0_6 - 30*r0_7)) + a_6*r0*(-6*L_6*M*(32*M_3 + 4*(-13 + 38*E_2)*M_2*r0 - 2*(24 + 91*E_2)*M*r0_2 + 17*E_2*r0_3) - 4*L_4*M*(1152*M_5 - 96*(-68 + 69*E_2)*M_4*r0 - 32*(-39 - 78*E_2 + 25*E_4)*M_3*r0_2 + (-2700 + 2937*E_2 + 770*E_4)*M_2*r0_3 + 2*(-282 - 1070*E_2 + 89*E_4)*M*r0_4 + (198 + 288*E_2 - 73*E_4)*r0_5) + E_2*r0_4*(57960*M_6 + 12*(2009 + 2004*E_2)*M_5*r0 + 14*(-3451 + 2616*E_2)*M_4*r0_2 + (-6893 + 8384*E_2)*M_3*r0_3 + (9783 - 2680*E_2)*M_2*r0_4 + 3*(-1003 + 184*E_2)*M*r0_5 - 75*r0_6) + L_2*r0*(32256*M_7 + 768*(9 + 46*E_2)*M_6*r0 + 16*(-2772 + 1921*E_2 + 1174*E_4)*M_5*r0_2 + 16*(-618 - 3587*E_2 + 2098*E_4)*M_4*r0_3 - 6*(-2316 + 1679*E_2 + 8*E_4)*M_3*r0_4 + (2520 + 19847*E_2 - 2948*E_4)*M_2*r0_5 + (-1008 - 4303*E_2 + 964*E_4)*M*r0_6 - 105*E_2*r0_7)) + 2*a_5*E*L*M*r0_2*(24*L_6*(7*M_2 - 15*M*r0 + 2*r0_2) + 2*L_4*r0*((7088 - 4128*E_2)*M_3 + 2*(561 + 428*E_2 + 42*E_4)*M_2*r0 + 2*(-1289 + 48*E_2 + 21*E_4)*M*r0_2 + 3*(84 - 29*E_2)*r0_3) - L_2*r0*(37056*M_5 + 8*(165 + 1532*E_2)*M_4*r0 - 4*(12514 - 4809*E_2 + 120*E_4)*M_3*r0_2 - 2*(-589 + 4152*E_2 + 1152*E_4)*M_2*r0_3 + 4*(3132 + 401*E_2 - 222*E_4)*M*r0_4 + (-2238 + 617*E_2)*r0_5) - r0_3*(49344*M_5 + 4*(-10362 + 3239*E_2 + 378*E_4)*M_3*r0_2 + 2*(1059 - 2746*E_2 + 36*E_4)*M_2*r0_3 + 6*(1390 + 223*E_2 - 168*E_4)*M*r0_4 + (-1650 + 403*E_2)*r0_5 + 3624*M_4*(r0 + 4*E_2*r0)))))/(3.*r0_8*expr2_3);\n A03220 = (-16*E*r0*(2*a_3*L*M*(12*M + (6 + E_2)*r0) + a_4*E*(-24*M_2 - 9*M*r0 + 2*r0_2) + 6*a*L*M*r0*(2*L_2 + (2 + E_2)*r0_2) + E*r0_3*(r0_2*(-17*M + 2*r0) + L_2*(-19*M + 3*r0)) + 2*a_2*E*r0*(L_2*(-7*M + r0) + r0*(-14*M_2 - 13*M*r0 + 2*r0_2))))/expr2_2;\n A03240 = (-4*(a_10*E_2*M*(192*(-3 + E_2)*M_3 + 4*(1033 - 89*E_2)*M_2*r0 + 3*(1201 - 108*E_2)*M*r0_2 + 6*(107 - 6*E_2)*r0_3) - 4*a_9*E*L*M*(96*(-3 + E_2)*M_3 + (973 + 258*E_2 + 18*E_4)*M_2*r0 + 15*(58 + 13*E_2)*M*r0_2 + 3*(50 + E_2)*r0_3) + 4*a*E*L*M*r0_3*(-4*L_6*(214*M_2 - 215*M*r0 + 54*r0_2) + 3*r0_5*(-2048*M_3 - 4*(-532 + 53*E_2)*M_2*r0 + 4*(-173 + 43*E_2 + 9*E_4)*M*r0_2 + (67 - 33*E_2)*r0_3) + L_2*r0_3*(-8736*M_3 + 2*(4608 - 695*E_2)*M_2*r0 + (-3036 + 817*E_2 + 114*E_4)*M*r0_2 + 6*(48 - 7*E_2)*r0_3) - L_4*r0*(2400*M_3 + 92*(-19 + 16*E_2)*M_2*r0 + 2*(8 - 423*E_2)*M*r0_2 + 3*(46 + 17*E_2)*r0_3)) + r0_4*(2*L_6*M*(2*M - r0)*(2088*M_2 + 2*(-774 + 425*E_2)*M*r0 + 7*(36 - 61*E_2)*r0_2) + 3*E_2*r0_7*(-852*M_3 + (930 - 72*E_2)*M_2*r0 + 2*(-139 + 27*E_2)*M*r0_2 + 13*r0_3) + 2*L_4*r0_2*(8928*M_4 + 312*(-36 + E_2)*M_3*r0 - 2*(-2268 + 237*E_2 + 115*E_4)*M_2*r0_2 + (-576 + 111*E_2 + 113*E_4)*M*r0_3 + 24*E_2*r0_4) + L_2*r0_4*(9504*M_4 - 112*(108 + 43*E_2)*M_3*r0 + 2*(2484 + 2283*E_2 - 340*E_4)*M_2*r0_2 + (-648 - 1169*E_2 + 368*E_4)*M*r0_3 + 45*E_2*r0_4)) + 4*a_3*E*L*M*r0_2*(-(L_4*(1344*M_3 + 12*(-316 + 163*E_2)*M_2*r0 - 8*(-62 + 97*E_2)*M*r0_2 + 3*(128 + 15*E_2)*r0_3)) + r0_3*(-23232*M_4 + (9432 - 6834*E_2)*M_3*r0 + (10068 + 815*E_2 - 54*E_4)*M_2*r0_2 + (-5208 + 505*E_2 + 324*E_4)*M*r0_3 + (456 - 211*E_2)*r0_4) + L_2*r0*(-16512*M_4 + 32*(189 - 160*E_2)*M_3*r0 + 2*(5946 - 653*E_2 + 114*E_4)*M_2*r0_2 + 2*(-2631 + 505*E_2 + 108*E_4)*M*r0_3 + 3*(58 - 15*E_2)*r0_4)) + 4*a_7*E*L*M*(L_2*(96*M_3 + 2*(-134 + 3*E_2)*M_2*r0 - 6*(189 + 38*E_2)*M*r0_2 + 3*(-100 + E_2)*r0_3) - r0*(288*(-37 + 27*E_2)*M_4 - 4*(2567 - 1443*E_2 + 108*E_4)*M_3*r0 + (1222 + 719*E_2 - 270*E_4)*M_2*r0_2 + (2784 + 811*E_2 - 108*E_4)*M*r0_3 + 3*(82 + 23*E_2)*r0_4)) + a_8*(-6*L_2*M*(96*M_3 - 2*(-20 + 233*E_2 + 14*E_4)*M_2*r0 + 4*(-1 - 233*E_2 + 2*E_4)*M*r0_2 + E_2*(-215 + 8*E_2)*r0_3) + E_2*r0*(192*(-111 + 62*E_2)*M_5 + 8*(-4474 + 1649*E_2)*M_4*r0 + (-3949 + 1972*E_2)*M_3*r0_2 - 2*(-5145 + 662*E_2)*M_2*r0_3 - 6*(-309 + E_2)*M*r0_4 - 30*r0_5)) + a_2*r0_2*(-2*L_6*M*(1152*M_3 - 24*(-80 + 197*E_2)*M_2*r0 + 2*(-1002 + 1627*E_2)*M*r0_2 + (360 - 437*E_2)*r0_3) + 3*E_2*r0_6*(4976*M_4 + 4*(-1155 + 626*E_2)*M_3*r0 - 40*(-61 + 15*E_2)*M_2*r0_2 + 2*(-353 + 98*E_2)*M*r0_3 + 15*r0_4) + 8*L_4*M*r0*(4896*M_4 + 4*(-1008 + 275*E_2)*M_3*r0 + (-1668 - 277*E_2 + 197*E_4)*M_2*r0_2 + (1896 - 454*E_2 - 105*E_4)*M*r0_3 + (-324 + 148*E_2 + 51*E_4)*r0_4) + L_2*r0_3*(41472*M_5 + 8*(-4032 + 3071*E_2)*M_4*r0 + 8*(-1188 - 3480*E_2 + 683*E_4)*M_3*r0_2 - 6*(-1956 - 1967*E_2 + 324*E_4)*M_2*r0_3 + 3*(-672 - 655*E_2 + 352*E_4)*M*r0_4 - 15*E_2*r0_5)) + 4*a_5*E*L*M*r0*(6*L_4*(14*M_2 - 44*M*r0 + (-25 + E_2)*r0_2) + L_2*(480*M_4 - 8*(-1393 + 918*E_2)*M_3*r0 + 2*(1960 - 375*E_2 + 102*E_4)*M_2*r0_2 + (-3564 - 143*E_2 + 102*E_4)*M*r0_3 - 6*(69 + 10*E_2)*r0_4) + r0*(-22464*M_5 - 12*(367 + 516*E_2)*M_4*r0 + 2*(11742 - 5065*E_2 + 216*E_4)*M_3*r0_2 + 3*(1141 + 346*E_2 + 126*E_4)*M_2*r0_3 + (-5046 - 527*E_2 + 324*E_4)*M*r0_4 + (159 - 178*E_2)*r0_5)) + a_6*(-12*L_4*M*(16*M_3 + 2*(14 + 15*E_2)*M_2*r0 - 2*(2 + 83*E_2)*M*r0_2 + E_2*(-53 + E_2)*r0_3) + 2*L_2*r0*(288*(-37 + 38*E_2)*M_5 + 12*(-220 - 585*E_2 + 296*E_4)*M_4*r0 + 4*(1044 - 2693*E_2 + 453*E_4)*M_3*r0_2 + (780 + 5621*E_2 + 140*E_4)*M_2*r0_3 + (-360 + 1217*E_2 + 112*E_4)*M*r0_4 - 39*E_2*r0_5) + E_2*r0_2*(44928*M_6 + 48*(631 + 386*E_2)*M_5*r0 + 16*(-3290 + 2187*E_2)*M_4*r0_2 + 2*(-14365 + 5518*E_2)*M_3*r0_3 + (12111 - 2644*E_2)*M_2*r0_4 + 12*(97 + 30*E_2)*M*r0_5 - 93*r0_6)) + a_4*r0*(-12*L_6*M*(8*M_2 - 2*M*r0 + E_2*r0_2) + 3*E_2*r0_4*(18292*M_5 + 4*(-253 + 1862*E_2)*M_4*r0 + (-10739 + 5140*E_2)*M_3*r0_2 + 2*(1687 - 538*E_2)*M_2*r0_3 + 12*(-37 + 21*E_2)*M*r0_4 - 19*r0_5) - 2*L_4*(2304*M_5 - 48*(-215 + 294*E_2)*M_4*r0 - 4*(846 - 1629*E_2 + 122*E_4)*M_3*r0_2 + 2*(-1392 + 541*E_2 + 111*E_4)*M_2*r0_3 + (720 - 703*E_2 - 85*E_4)*M*r0_4 + 24*E_2*r0_5) + 2*L_2*r0*(22464*M_6 + 144*(-44 + 115*E_2)*M_5*r0 + 4*(-5364 + 1699*E_2 + 1400*E_4)*M_4*r0_2 + 2*(2868 - 10673*E_2 + 2326*E_4)*M_3*r0_3 + 2*(2076 + 3331*E_2 - 42*E_4)*M_2*r0_4 + 3*(-348 + 49*E_2 + 160*E_4)*M*r0_5 - 69*E_2*r0_6))))/(3.*r0_5*expr2_3);\n A03400 = (-2*E*r0_4*(12*a*L*M + 3*a_2*E*(-4*M + r0) + E*r0_2*(-17*M + 2*r0)))/expr2_2;\n A03420 = (12*a_7*E*L*M*(4*(-27 + 20*E_2)*M_2 + 2*(132 + 11*E_2 + 3*E_4)*M*r0 + (131 - 14*E_2)*r0_2) - 3*a_8*E_2*(8*(-27 + 14*E_2)*M_3 + 4*(284 - 13*E_2)*M_2*r0 + 2*(258 - 19*E_2)*M*r0_2 - 9*r0_3) - 4*a*E*L*M*r0_2*(-12*L_4*(56*M_2 - 58*M*r0 + 15*r0_2) + r0_3*(-5448*M_3 + 12*(400 - 73*E_2)*M_2*r0 + (-1102 + 621*E_2 + 54*E_4)*M*r0_2 + (23 - 108*E_2)*r0_3) - L_2*r0*(3624*M_3 + 4*(-669 + 284*E_2)*M_2*r0 + 16*(13 - 38*E_2)*M*r0_2 + (121 + 27*E_2)*r0_3)) - 4*a_5*E*L*M*(-3*L_2*(16*M_2 + 2*(4 + 21*E_2)*M*r0 + (131 - 8*E_2)*r0_2) + r0*(-72*(-63 + 46*E_2)*M_3 + 18*(185 - 56*E_2 + 8*E_4)*M_2*r0 - (1118 + 63*E_2 + 18*E_4)*M*r0_2 + (-769 + 60*E_2)*r0_3)) + a_6*(-3*L_2*(72*(-3 + 4*E_2)*M_3 + 4*(-20 + 63*E_2 + 26*E_4)*M_2*r0 + 2*E_2*(253 - 8*E_2)*M*r0_2 - 9*E_2*r0_3) + E_2*r0*((9072 - 4800*E_2)*M_4 - 24*(-662 + 141*E_2)*M_3*r0 + 4*(-800 + 63*E_2)*M_2*r0_2 + (-4169 + 180*E_2)*M*r0_3 + 61*r0_4)) + r0_3*(-8*L_4*M*(2*M - r0)*(558*M_2 + (-423 + 169*E_2)*M*r0 + (72 - 91*E_2)*r0_2) + E_2*r0_5*(2556*M_3 + 216*(-13 + E_2)*M_2*r0 + (841 - 162*E_2)*M*r0_2 - 38*r0_3) + L_2*r0_2*(-9504*M_4 + 4*(3024 + 323*E_2)*M_3*r0 + 4*(-1242 - 243*E_2 + 85*E_4)*M_2*r0_2 + (648 + 155*E_2 - 184*E_4)*M*r0_3 + 4*E_2*r0_4)) - 4*a_3*E*L*M*r0*(-24*L_4*M + L_2*(-336*M_3 + 12*(215 - 132*E_2)*M_2*r0 + 12*(21 + 34*E_2)*M*r0_2 - (562 + 3*E_2)*r0_3) + r0*(-10368*M_4 - 36*(-71 + 74*E_2)*M_3*r0 + 2*(3095 - 612*E_2 + 108*E_4)*M_2*r0_2 + 6*(-236 + 78*E_2 + 9*E_4)*M*r0_3 - (353 + 78*E_2)*r0_4)) + a_4*(24*L_4*M*(2*M_2 - 5*(-2 + 3*E_2)*M*r0 + 2*E_2*r0_2) - L_2*r0*(144*(-63 + 76*E_2)*M_4 + 24*(107 - 245*E_2 + 40*E_4)*M_3*r0 + 12*(184 - 338*E_2 + 57*E_4)*M_2*r0_2 + (-648 + 2809*E_2 + 24*E_4)*M*r0_3 + 2*E_2*r0_4) - E_2*r0_2*(20736*M_5 + 48*(123 + 146*E_2)*M_4*r0 + 4*(-5005 + 1836*E_2)*M_3*r0_2 - 4*(422 + 147*E_2)*M_2*r0_3 + 3*(971 + 48*E_2)*M*r0_4 - 15*r0_5)) - a_2*r0*(-12*L_4*M*(96*M_3 + 4*(79 - 156*E_2)*M_2*r0 + (-296 + 419*E_2)*M*r0_2 + (54 - 59*E_2)*r0_3) + E_2*r0_4*(12216*M_4 + 24*(-289 + 203*E_2)*M_3*r0 + 4*(320 - 201*E_2)*M_2*r0_2 + 3*(-175 + 124*E_2)*M*r0_3 + 57*r0_4) + L_2*r0*(20736*M_5 + 2304*(-7 + 4*E_2)*M_4*r0 + 16*(-414 - 120*E_2 + 61*E_4)*M_3*r0_2 + 4*(1854 - 817*E_2 + 40*E_4)*M_2*r0_3 + 8*(-162 + 127*E_2 + 32*E_4)*M*r0_4 + 25*E_2*r0_5)))/(3.*r0_2*expr2_3);\n A03600 = (r0*(12*a_5*E*L*M*(4*(-7 + 6*E_2)*M + (73 - 12*E_2)*r0) + 3*a_6*E_2*(-8*(-7 + 4*E_2)*M_2 + 4*(-73 + 6*E_2)*M*r0 + 7*r0_2) + 4*a_3*E*L*M*(24*L_2*M - r0*((624 - 456*E_2)*M_2 + 40*(10 + E_2)*M*r0 + (-286 + 21*E_2)*r0_2)) + r0_2*(-6*L_2*M*(2*M - r0)*(264*M_2 + 2*(-102 + 31*E_2)*M*r0 + 3*(12 - 13*E_2)*r0_2) + E_2*r0_3*(852*M_3 + 24*(-38 + 3*E_2)*M_2*r0 + (271 - 54*E_2)*M*r0_2 - 14*r0_3)) + a_4*(-24*L_2*M*((-7 + 12*E_2)*M - 3*E_2*r0) + E_2*r0*(-32*(-39 + 19*E_2)*M_3 - 8*(-329 + 33*E_2)*M_2*r0 + (-1569 + 74*E_2)*M*r0_2 + 28*r0_3)) + 4*a*E*L*M*r0*(4*L_2*(38*M_2 - 43*M*r0 + 12*r0_2) + r0*(1584*M_3 + 4*(-268 + 93*E_2)*M_2*r0 + 2*(18 - 97*E_2)*M*r0_2 + 5*(11 + 3*E_2)*r0_3)) - a_2*r0*(2*L_2*M*(48*(-13 + 19*E_2)*M_2 + (516 - 556*E_2)*M*r0 + (-96 + 91*E_2)*r0_2) + E_2*r0*(3168*M_4 + 8*(-32 + 93*E_2)*M_3*r0 + 4*(-373 + 16*E_2)*M_2*r0_2 + 2*(211 + 26*E_2)*M*r0_3 + 7*r0_4))))/(12.*expr2_3);\n A04020 = (48*E_2*r0_3*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/expr2_2;\n A04040 = (8*(-4*a_7*E*L*M*(144*M_3 + 12*(3 + 8*E_2)*M_2*r0 + 2*(-51 + 32*E_2)*M*r0_2 + 3*(-14 + E_2)*r0_3) + a_8*E_2*(288*M_4 + 48*(-3 + 2*E_2)*M_3*r0 + 2*(-271 + 60*E_2)*M_2*r0_2 + 6*(-35 + 6*E_2)*M*r0_3 - 3*r0_4) + 4*a*E*L*M*r0_3*(L_4*(216*M_2 + 4*(-72 + E_2)*M*r0 - 6*(-13 + E_2)*r0_2) - 3*r0_4*(-120*M_2 + (124 + 35*E_2)*M*r0 + 4*(-7 + E_2)*r0_2) + 3*L_2*r0_2*(192*M_2 - (220 + 51*E_2)*M*r0 + 2*(27 + E_2)*r0_2)) - 4*a_5*E*L*M*r0*(-1152*M_4 + 24*(-7 + 2*E_2)*M_3*r0 + 2*(408 + 113*E_2)*M_2*r0_2 + 229*E_2*M*r0_3 + 8*(-21 + E_2)*r0_4 + 3*L_2*(64*M_2 + 2*(-7 + 13*E_2)*M*r0 + (-28 + 3*E_2)*r0_2)) + r0_3*(-4*L_6*M*(2*M - r0)*(72*M + (-36 + E_2)*r0) + 3*E_2*r0_7*(159*M_2 + 4*(-21 + E_2)*M*r0 + 3*r0_2) + 3*L_2*r0_4*(-192*M_3 + 2*(96 + 197*E_2)*M_2*r0 + 4*(-12 - 51*E_2 + 2*E_4)*M*r0_2 + 5*E_2*r0_3) + L_4*r0_2*(-1152*M_3 + (1152 + 721*E_2)*M_2*r0 + 4*(-72 - 95*E_2 + 2*E_4)*M*r0_2 + 12*E_2*r0_3)) - 4*a_3*E*L*M*r0_2*(6*L_4*(10*M + (-7 + E_2)*r0) + 3*L_2*(-336*M_3 + 4*(47 + 2*E_2)*M_2*r0 + (154 + 71*E_2)*M*r0_2 + (-82 + 3*E_2)*r0_3) + r0_2*(-1296*M_3 + 6*(98 + 9*E_2)*M_2*r0 + 2*(237 + 145*E_2)*M*r0_2 + (-210 + 17*E_2)*r0_3)) + a_2*r0_2*(12*L_6*M*(6*M + E_2*r0) + 6*E_2*r0_5*(40*M_3 + 2*(91 - 18*E_2)*M_2*r0 + (-149 + 12*E_2)*M*r0_2 + 6*r0_3) - 2*L_4*(1152*M_4 + 48*(-12 + E_2)*M_3*r0 + 2*(-180 - 315*E_2 + 2*E_4)*M_2*r0_2 + (144 + 265*E_2 - 10*E_4)*M*r0_3 - 12*E_2*r0_4) + 3*L_2*r0_2*(-768*M_4 + 24*(16 + 5*E_2)*M_3*r0 + 4*(54 + 205*E_2 + 9*E_4)*M_2*r0_2 + 2*(-48 - 257*E_2 + 16*E_4)*M*r0_3 + 19*E_2*r0_4)) + 2*a_6*(L_2*(144*M_4 + 48*(3 + 8*E_2)*M_3*r0 + 2*(18 - 44*E_2 + 27*E_4)*M_2*r0_2 + 3*E_2*(-67 + 8*E_2)*M*r0_3 - 3*E_2*r0_4) + E_2*r0*(-1152*M_5 - 48*(7 + 2*E_2)*M_4*r0 + 2*(313 - 72*E_2)*M_3*r0_2 + (-403 + 60*E_2)*M_2*r0_3 + 3*(-127 + 20*E_2)*M*r0_4 + 6*r0_5)) + a_4*r0*(3*L_4*(96*M_3 + 4*(12 + 31*E_2)*M_2*r0 + 4*E_2*(-15 + E_2)*M*r0_2 - E_2*r0_3) + 3*E_2*r0_3*(-740*M_4 + 4*(137 - 48*E_2)*M_3*r0 + (101 - 72*E_2)*M_2*r0_2 + 2*(-199 + 24*E_2)*M*r0_3 + 14*r0_4) - 2*L_2*(1152*M_5 + 672*E_2*M_4*r0 + 4*(-180 - 287*E_2 + 12*E_4)*M_3*r0_2 - (72 + 527*E_2 + 84*E_4)*M_2*r0_3 + 3*(24 + 211*E_2 - 20*E_4)*M*r0_4 - 18*E_2*r0_5))))/(3.*r0_4*expr2_3);\n A04200 = (12*E_2*r0_6)/expr2_2;\n A04220 = (4*(2*a_5*E*L*M*(-48*M_2 + 2*(3 - 8*E_2)*M*r0 + (20 + E_2)*r0_2) + a_6*E_2*M*(48*M_2 + 4*(-9 + 2*E_2)*M*r0 + (-47 + 6*E_2)*r0_2) - 2*a_3*E*L*M*r0*(-384*M_3 + 4*(31 + 4*E_2)*M_2*r0 + (158 + 45*E_2)*M*r0_2 - (58 + 7*E_2)*r0_3 + 4*L_2*(8*M + (-5 + E_2)*r0)) - 2*a*E*L*M*r0_2*(-4*L_2*(42*M_2 - 43*M*r0 - (-9 + E_2)*r0_2) + r0_2*(-216*M_2 + (200 + 39*E_2)*M*r0 + 2*(-19 + 2*E_2)*r0_2)) + r0_2*(-48*L_4*M*r0_2M_2 + E_2*r0_5*(159*M_2 + 2*(-43 + 2*E_2)*M*r0 + 4*r0_2) + L_2*r0_2*(-192*M_3 + 3*(64 + 67*E_2)*M_2*r0 + (-48 - 107*E_2 + 4*E_4)*M*r0_2 + 4*E_2*r0_3)) + a_4*(4*L_2*M*(12*M_2 + 2*(3 + 8*E_2)*M*r0 + E_2*(-12 + E_2)*r0_2) + E_2*r0*(-384*M_4 - 8*(-7 + E_2)*M_3*r0 + (57 - 8*E_2)*M_2*r0_2 + 8*(-19 + 2*E_2)*M*r0_3 + 10*r0_4)) + a_2*r0*(4*L_4*M*(6*M + E_2*r0) + E_2*r0_3*(-56*M_3 - 8*(-29 + 4*E_2)*M_2*r0 + 7*(-29 + 2*E_2)*M*r0_2 + 14*r0_3) + L_2*(-384*M_4 - 8*(-24 + 13*E_2)*M_3*r0 + 10*(12 + 25*E_2)*M_2*r0_2 + (-48 - 147*E_2 + 8*E_4)*M*r0_3 + 15*E_2*r0_4))))/(r0*expr2_3);\n A04400 = (r0_2*(-72*a_3*E*L*M*(2*M - r0) - 24*a*E*L*M*r0*(-48*M_2 + 2*(19 + E_2)*M*r0 - 5*r0_2) + 9*a_4*E_2*(8*M_2 - 8*M*r0 + r0_2) + r0*(-12*L_2*M*(2*M - r0)*(24*M - (12 + E_2)*r0) + E_2*r0_3*(477*M_2 + 2*(-127 + 6*E_2)*M*r0 + 10*r0_2)) + 2*a_2*(36*L_2*M_2 + E_2*r0*(-288*M_3 + 12*(14 + E_2)*M_2*r0 + 6*(-27 + E_2)*M*r0_2 + 17*r0_3))))/(6.*expr2_3);\n A05020 = (-8*E*r0*(2*a_3*L*M*(12*M + (6 + E_2)*r0) + a_4*E*(-24*M_2 - 9*M*r0 + 2*r0_2) + 6*a*L*M*r0*(2*L_2 + (2 + E_2)*r0_2) + E*r0_3*(r0_2*(-16*M + r0) + 2*L_2*(-9*M + r0)) + a_2*E*r0*(2*L_2*(-7*M + r0) + r0*(-26*M_2 - 27*M*r0 + 3*r0_2))))/expr2_3;\n A05040 = (-4*(-(a_10*E_2*M*(96*(-9 + 4*E_2)*M_3 + 4*(-272 + 169*E_2)*M_2*r0 + 6*(43 + 34*E_2)*M*r0_2 + 15*(23 - 2*E_2)*r0_3)) + 2*a_9*E*L*M*(96*(-9 + 7*E_2)*M_3 + 4*(-268 + 51*E_2 + 27*E_4)*M_2*r0 + 6*(-2 - 43*E_2 + 12*E_4)*M*r0_2 - 9*(-18 + E_2)*r0_3) + 2*a*E*L*M*r0_3*(-8*L_6*(110*M_2 - 109*M*r0 + 27*r0_2) + L_2*r0_3*(-9024*M_3 + (12900 - 2237*E_2)*M_2*r0 + 8*(-747 + 301*E_2 + 21*E_4)*M*r0_2 + 6*(141 - 95*E_2)*r0_3) + 3*r0_5*(-2080*M_3 - 5*(-538 + 51*E_2)*M_2*r0 + 4*(-287 + 81*E_2 + 18*E_4)*M*r0_2 + 2*(77 - 41*E_2)*r0_3) - 2*L_4*r0*(1296*M_3 + (-1879 + 864*E_2)*M_2*r0 + 2*(403 - 292*E_2)*M*r0_2 + 12*(-7 + 6*E_2)*r0_3)) + r0_4*(6*L_6*M*r0_2M_2*(180*M + (-48 + 77*E_2)*r0) - 3*E_2*M*r0_7*(688*M_2 + (-673 + 60*E_2)*M*r0 + (163 - 30*E_2)*r0_2) + 2*L_4*r0_2*(4608*M_4 + (-5904 + 7*E_2)*M_3*r0 - 3*(-816 + 109*E_2 + 52*E_4)*M_2*r0_2 + 2*(-162 + 118*E_2 + 39*E_4)*M*r0_3 - 36*E_2*r0_4) - L_2*r0_4*(-4896*M_4 + 2*(3168 + 1901*E_2)*M_3*r0 + (-2664 - 3213*E_2 + 524*E_4)*M_2*r0_2 + (360 + 551*E_2 - 248*E_4)*M*r0_3 + 48*E_2*r0_4)) + 2*a_3*E*L*M*r0_2*(24*L_6*M - 2*L_4*(768*M_3 + 12*(-210 + 89*E_2)*M_2*r0 + 4*(299 - 154*E_2)*M*r0_2 + 63*(-2 + E_2)*r0_3) + 2*r0_3*(-11856*M_4 + (7584 - 3525*E_2)*M_3*r0 + 2*(2298 + 218*E_2 - 135*E_4)*M_2*r0_2 + (-4356 + 467*E_2 + 396*E_4)*M*r0_3 + (786 - 119*E_2)*r0_4) + L_2*r0*(-17184*M_4 - 16*(-747 + 397*E_2)*M_3*r0 + 3*(4080 - 29*E_2 + 40*E_4)*M_2*r0_2 + 6*(-1802 + 381*E_2 + 66*E_4)*M*r0_3 + 6*(327 - 28*E_2)*r0_4)) + 2*a_7*E*L*M*(L_2*(480*M_3 + 4*(-358 + 255*E_2)*M_2*r0 + 12*(-57 - 7*E_2 + 3*E_4)*M*r0_2 + 9*(36 + E_2)*r0_3) + 2*r0*(-48*(-137 + 90*E_2)*M_4 + 4*(883 - 642*E_2 + 36*E_4)*M_3*r0 + 2*(-1495 + 172*E_2 + 171*E_4)*M_2*r0_2 + 2*(-438 - 265*E_2 + 126*E_4)*M*r0_3 + 3*(162 - 13*E_2)*r0_4)) + a_8*(-3*L_2*M*(288*(-1 + 2*E_2)*M_3 + 4*(-88 - 181*E_2 + 90*E_4)*M_2*r0 + 4*(-26 - 122*E_2 + 39*E_4)*M*r0_2 + E_2*(227 - 4*E_2)*r0_3) + E_2*r0*(96*(-137 + 68*E_2)*M_5 + 16*(-643 + 404*E_2)*M_4*r0 - 8*(-599 + 92*E_2)*M_3*r0_2 + 2*(453 - 598*E_2)*M_2*r0_3 + 6*(-359 + 35*E_2)*M*r0_4 - 45*r0_5)) + a_2*r0_2*(-4*L_6*M*(288*M_3 + 6*(111 - 206*E_2)*M_2*r0 + 8*(-75 + 112*E_2)*M*r0_2 + (90 - 131*E_2)*r0_3) + 3*E_2*r0_6*(1714*M_4 + (-3143 + 1444*E_2)*M_3*r0 + 4*(689 - 127*E_2)*M_2*r0_2 + 2*(-404 + 65*E_2)*M*r0_3 + 21*r0_4) + 2*L_4*r0*(10080*M_5 + 8*(-1062 + 343*E_2)*M_4*r0 + 3*(-1328 - 1133*E_2 + 228*E_4)*M_3*r0_2 + (4284 + 941*E_2 - 640*E_4)*M_2*r0_3 + (-684 - 233*E_2 + 167*E_4)*M*r0_4 + 84*E_2*r0_5) + L_2*r0_3*(21312*M_5 + 2*(-8496 + 5273*E_2)*M_4*r0 + (-5304 - 21071*E_2 + 5296*E_4)*M_3*r0_2 + (6456 + 14171*E_2 - 4516*E_4)*M_2*r0_3 + (-1080 - 3485*E_2 + 848*E_4)*M*r0_4 + 165*E_2*r0_5)) + 2*a_5*E*L*M*r0*(18*L_4*(20*M_2 + 2*(-18 + 5*E_2)*M*r0 + (9 + E_2)*r0_2) + L_2*(192*M_4 - 464*(-31 + 18*E_2)*M_3*r0 + 4*(-151 + 417*E_2 + 42*E_4)*M_2*r0_2 + 2*(-2814 + 59*E_2 + 132*E_4)*M*r0_3 + 3*(480 - 41*E_2)*r0_4) + r0*(-23040*M_5 + 24*(23 - 268*E_2)*M_4*r0 + 2*(13716 - 5383*E_2)*M_3*r0_2 + 3*(-1294 + 939*E_2 + 108*E_4)*M_2*r0_3 + 4*(-1752 - 53*E_2 + 252*E_4)*M*r0_4 + (1920 - 61*E_2)*r0_5)) + a_6*(-6*L_4*M*(32*M_3 + 20*(-8 + 15*E_2)*M_2*r0 + 2*(-52 - 123*E_2 + 22*E_4)*M*r0_2 + E_2*(59 + 3*E_2)*r0_3) - L_2*r0*(-96*(-137 + 132*E_2)*M_5 - 192*(-20 - 62*E_2 + 25*E_4)*M_4*r0 + 8*(-765 + 355*E_2 + 168*E_4)*M_3*r0_2 + 4*(-438 - 2108*E_2 + 457*E_4)*M_2*r0_3 + (360 + 3643*E_2 - 376*E_4)*M*r0_4 + 117*E_2*r0_5) + E_2*r0_2*(23040*M_6 + 48*(121 + 196*E_2)*M_5*r0 + 2*(-14153 + 9504*E_2)*M_4*r0_2 + (2243 + 4408*E_2)*M_3*r0_3 + 20*(387 - 136*E_2)*M_2*r0_4 + 3*(-1429 + 180*E_2)*M*r0_5 - 27*r0_6)) + a_4*r0*(-6*L_6*M*(16*M_2 + 4*(-13 + 9*E_2)*M*r0 + 3*E_2*r0_2) + 3*E_2*r0_4*(8580*M_5 + 8*(-541 + 488*E_2)*M_4*r0 + 6*(-529 + 464*E_2)*M_3*r0_2 + (4131 - 1024*E_2)*M_2*r0_3 + (-1471 + 220*E_2)*M*r0_4 + 27*r0_5) - 4*L_4*(576*M_5 - 48*(-68 + 81*E_2)*M_4*r0 - 2*(426 - 1347*E_2 + 94*E_4)*M_3*r0_2 + 2*(-519 - 371*E_2 + 144*E_4)*M_2*r0_3 - 5*(-36 - 49*E_2 + 8*E_4)*M*r0_4 + 18*E_2*r0_5) + L_2*r0*(23040*M_6 + 768*(-9 + 23*E_2)*M_5*r0 + 4*(-6096 - 1097*E_2 + 2020*E_4)*M_4*r0_2 + (6096 - 20243*E_2 + 4280*E_4)*M_3*r0_3 + 2*(2616 + 9131*E_2 - 2004*E_4)*M_2*r0_4 + 4*(-270 - 1285*E_2 + 241*E_4)*M*r0_5 + 96*E_2*r0_6))))/(3.*r0_5*expr2_4);\n A05200 = (-2*E*r0_4*(12*a*L*M + E*r0_2*(-16*M + r0) + 3*a_2*E*(-4*M + r0)))/expr2_3;\n A05220 = (-6*a_7*E*L*M*(16*(-12 + 7*E_2)*M_2 + 4*(-78 - 4*E_2 + 3*E_4)*M*r0 + (-32 + 23*E_2)*r0_2) + 3*a_8*E_2*(64*(-3 + E_2)*M_3 + 8*(-62 + 13*E_2)*M_2*r0 - (21 + 2*E_2)*M*r0_2 + 9*r0_3) - 6*a_5*E*L*M*(4*L_2*(20*M_2 + (-62 + 21*E_2)*M*r0 + 2*(-4 + E_2)*r0_2) + r0*(-64*(-61 + 39*E_2)*M_3 + 4*(119 - 45*E_2 + 18*E_4)*M_2*r0 + 2*(-688 + 39*E_2 + 48*E_4)*M*r0_2 + (148 + 7*E_2)*r0_3)) - 2*a*E*L*M*r0_2*(-360*L_4*r0_2M_2 - 2*L_2*r0*(3792*M_3 + 22*(-207 + 64*E_2)*M_2*r0 + 2*(867 - 482*E_2)*M*r0_2 + 3*(-60 + 37*E_2)*r0_3) - 3*r0_3*(3712*M_3 + (-4372 + 671*E_2)*M_2*r0 - 4*(-424 + 161*E_2 + 18*E_4)*M*r0_2 + 2*(-102 + 67*E_2)*r0_3)) + 3*a_6*(L_2*(96*(-2 + 3*E_2)*M_3 + 8*(-16 - 63*E_2 + 13*E_4)*M_2*r0 + 8*E_2*(-2 + E_2)*M*r0_2 + 9*E_2*r0_3) + E_2*r0*(-64*(-61 + 28*E_2)*M_4 + 4*(458 - 195*E_2)*M_3*r0 + 8*(-202 + 59*E_2)*M_2*r0_2 + (247 - 74*E_2)*M*r0_3 + 11*r0_4)) + r0_3*(-4*L_4*M*(2*M - r0)*(1152*M_2 + (-900 + 379*E_2)*M*r0 + (162 - 193*E_2)*r0_2) + 6*E_2*r0_5*(688*M_3 + (-679 + 60*E_2)*M_2*r0 - 6*(-27 + 5*E_2)*M*r0_2 + 2*r0_3) + L_2*r0_2*(-9792*M_4 + 2*(6336 + 1277*E_2)*M_3*r0 + (-5328 - 1863*E_2 + 524*E_4)*M_2*r0_2 + 4*(180 + 29*E_2 - 62*E_4)*M*r0_3 + 84*E_2*r0_4)) - 6*a_3*E*L*M*r0*(16*L_4*M - 2*L_2*(160*M_3 + 4*(-293 + 153*E_2)*M_2*r0 + 2*(271 - 170*E_2)*M*r0_2 + (-38 + 33*E_2)*r0_3) + r0*(-7104*M_4 - 112*(-33 + 17*E_2)*M_3*r0 + (4016 - 665*E_2 + 72*E_4)*M_2*r0_2 + 2*(-1388 + 291*E_2 + 78*E_4)*M*r0_3 + 4*(96 - 29*E_2)*r0_4)) + 3*a_4*(8*L_4*M*(4*M_2 + (-16 + 15*E_2)*M*r0 + E_2*r0_2) - L_2*r0*(64*(-61 + 66*E_2)*M_4 + 4*(220 - 841*E_2 + 132*E_4)*M_3*r0 + 4*(298 + 261*E_2 - 122*E_4)*M_2*r0_2 + 4*(-54 - 55*E_2 + 19*E_4)*M*r0_3 + 13*E_2*r0_4) - E_2*r0_2*(7104*M_5 + 144*(-12 + 17*E_2)*M_4*r0 + (-4937 + 2528*E_2)*M_3*r0_2 + (3037 - 864*E_2)*M_2*r0_3 + 2*(-460 + 101*E_2)*M*r0_4 + 42*r0_5)) - a_2*r0*(-24*L_4*M*(48*M_3 + (218 - 342*E_2)*M_2*r0 + (-180 + 253*E_2)*M*r0_2 + (27 - 37*E_2)*r0_3) + 3*E_2*r0_4*(3346*M_4 + 3*(-1429 + 620*E_2)*M_3*r0 + (3385 - 632*E_2)*M_2*r0_2 + 2*(-529 + 95*E_2)*M*r0_3 + 40*r0_4) + L_2*r0*(21312*M_5 + 48*(-354 + 209*E_2)*M_4*r0 + 2*(-3936 - 5001*E_2 + 1084*E_4)*M_3*r0_2 + (8376 + 4361*E_2 - 1732*E_4)*M_2*r0_3 + 4*(-342 - 338*E_2 + 125*E_4)*M*r0_4 + 156*E_2*r0_5)))/(3.*r0_2*expr2_4);\n A05400 = (r0*(-36*a_5*E*L*M*(-4*M + (-15 + 2*E_2)*r0) + 9*a_6*E_2*(-8*M_2 + 4*(-15 + E_2)*M*r0 + r0_2) + 4*a_3*E*L*M*r0*(12*(-107 + 66*E_2)*M_2 - 6*(-61 + 56*E_2)*M*r0 + (80 + 33*E_2)*r0_2) + a_4*(36*L_2*M*(-2*M + E_2*r0) + E_2*r0*(-24*(-107 + 44*E_2)*M_3 + 24*(19 + 5*E_2)*M_2*r0 - 2*(238 + 27*E_2)*M*r0_2 - 13*r0_3)) + r0_2*(-6*L_2*M*(2*M - r0)*(408*M_2 + 4*(-81 + 26*E_2)*M*r0 + (60 - 59*E_2)*r0_2) + E_2*r0_3*(2064*M_3 + 45*(-45 + 4*E_2)*M_2*r0 + 2*(244 - 45*E_2)*M*r0_2 + 2*r0_3)) + 4*a*E*L*M*r0*(12*L_2*(22*M_2 - 23*M*r0 + 6*r0_2) + r0*(2448*M_3 + 3*(-841 + 208*E_2)*M_2*r0 + 2*(406 - 213*E_2)*M*r0_2 + (-70 + 51*E_2)*r0_3)) - a_2*r0*(6*L_2*M*((-428 + 528*E_2)*M_2 - 4*(-80 + 97*E_2)*M*r0 + (-48 + 61*E_2)*r0_2) + E_2*r0*(4896*M_4 + 12*(-313 + 104*E_2)*M_3*r0 + (1919 - 372*E_2)*M_2*r0_2 + 60*(-11 + 3*E_2)*M*r0_3 + 62*r0_4))))/(12.*expr2_4);\n A06000 = (4*E_2*r0_6)/expr2_3;\n A06020 = (2*(-24*a_5*E*L*M*(12*M_2 + (-8 + 7*E_2)*M*r0 + (-8 + E_2)*r0_2) + 3*a_6*E_2*(48*M_3 + 4*(-22 + 5*E_2)*M_2*r0 + 2*(-35 + 6*E_2)*M*r0_2 + r0_3) - 8*a_3*E*L*M*r0*(-192*M_3 + 2*(63 - 2*E_2)*M_2*r0 + (93 + 34*E_2)*M*r0_2 + 3*(-19 + 2*E_2)*r0_3 + 6*L_2*(4*M + (-4 + E_2)*r0)) + 8*a*E*L*M*r0_2*(r0_2*(108*M_2 - (135 + 13*E_2)*M*r0 + 3*(11 - 5*E_2)*r0_2) + L_2*(84*M_2 + (-123 + 4*E_2)*M*r0 + 3*(11 - 2*E_2)*r0_2)) + r0_2*(-8*L_4*M*(2*M - r0)*(24*M + (-12 + E_2)*r0) + E_2*M*r0_5*(427*M + 20*(-10 + E_2)*r0) + L_2*r0_2*(-384*M_3 + 3*(128 + 161*E_2)*M_2*r0 + 4*(-24 - 51*E_2 + 4*E_4)*M*r0_2 - 12*E_2*r0_3)) + a_4*(3*L_2*(48*M_3 + 4*(6 + 19*E_2)*M_2*r0 + 4*E_2*(-17 + 2*E_2)*M*r0_2 + E_2*r0_3) + E_2*r0*(-768*M_4 + 16*(39 - 4*E_2)*M_3*r0 + 8*(16 + E_2)*M_2*r0_2 + 2*(-283 + 46*E_2)*M*r0_3 + 39*r0_4)) + a_2*r0*(24*L_4*M*(3*M + E_2*r0) + E_2*r0_3*(62*M_3 + (783 - 100*E_2)*M_2*r0 + 2*(-311 + 38*E_2)*M*r0_2 + 36*r0_3) + L_2*(-768*M_4 - 128*(-3 + 2*E_2)*M_3*r0 + 8*(33 + 108*E_2 - 2*E_4)*M_2*r0_2 + 2*(-48 - 219*E_2 + 20*E_4)*M*r0_3 + 48*E_2*r0_4))))/(3.*r0*expr2_4);\n A06200 = (r0_2*(-24*a_3*E*L*M*(6*M + (-7 + 2*E_2)*r0) + 3*a_4*E_2*(24*M_2 + 8*(-7 + E_2)*M*r0 + 5*r0_2) + 8*a*E*L*M*r0*(96*M_2 + (-111 + 2*E_2)*M*r0 - 6*(-4 + E_2)*r0_2) + M*r0*(-4*L_2*(2*M - r0)*(48*M + (-24 + E_2)*r0) + E_2*r0_3*(427*M + 20*(-10 + E_2)*r0)) + a_2*(24*L_2*M*(3*M + E_2*r0) + 2*E_2*r0*(-192*M_3 - 4*(-63 + E_2)*M_2*r0 + (-199 + 22*E_2)*M*r0_2 + 18*r0_3))))/(6.*expr2_4);\n A07000 = (2*E*r0_4*(-4*a*L*M + a_2*E*(4*M - r0) + 5*E*M*r0_2))/expr2_4;\n A07020 = (-12*a_7*E*L*M*(4*(-25 + 16*E_2)*M_2 + 2*(-8 + E_2 + 3*E_4)*M*r0 + 3*(11 + E_2)*r0_2) + 3*a_8*E_2*(40*(-5 + 2*E_2)*M_3 + 4*(12 + 13*E_2)*M_2*r0 - 2*(-79 + 7*E_2)*M*r0_2 + 3*r0_3) - 4*a*E*L*M*r0_2*(-4*L_4*(64*M_2 - 62*M*r0 + 15*r0_2) + L_2*r0*(-1320*M_3 + 3*(693 - 188*E_2)*M_2*r0 + 4*(-249 + 112*E_2)*M*r0_2 + 3*(44 - 23*E_2)*r0_3) + r0_3*(-1896*M_3 + (2719 - 377*E_2)*M_2*r0 + 2*(-628 + 191*E_2 + 27*E_4)*M*r0_2 + 3*(58 - 17*E_2)*r0_3)) - 4*a_5*E*L*M*(3*L_2*(32*M_2 + 2*(-40 + 21*E_2)*M*r0 + 33*r0_2) + r0*(-24*(-99 + 58*E_2)*M_3 + 2*(-302 + 67*E_2 + 12*E_4)*M_2*r0 + 2*(-499 + 64*E_2 + 51*E_4)*M*r0_2 + 3*(131 - 6*E_2)*r0_3)) + M*r0_3*(E_2*r0_5*(1799*M_2 + 2*(-843 + 80*E_2)*M*r0 + 2*(191 - 29*E_2)*r0_2) - 12*L_4*(2*M - r0)*(132*M_2 + (-106 + 47*E_2)*M*r0 + (20 - 23*E_2)*r0_2) + L_2*r0_2*(-3360*M_3 + (4416 + 1187*E_2)*M_2*r0 + 12*(-158 - 77*E_2 + 20*E_4)*M*r0_2 + 2*(132 + 77*E_2 - 54*E_4)*r0_3)) + a_6*(L_2*(24*(-25 + 36*E_2)*M_3 + 12*(-28 - 63*E_2 + 26*E_4)*M_2*r0 + 474*E_2*M*r0_2 + 9*E_2*r0_3) - E_2*r0*(16*(-297 + 124*E_2)*M_4 + 4*(382 + 113*E_2)*M_3*r0 - 54*(-39 + 16*E_2)*M_2*r0_2 + 3*(-601 + 64*E_2)*M*r0_3 + 9*r0_4)) - 4*a_3*E*L*M*r0*(24*L_4*M + L_2*(-208*M_3 - 24*(-61 + 29*E_2)*M_2*r0 + 2*(-567 + 274*E_2)*M*r0_2 + 3*(84 - 23*E_2)*r0_3) + r0*(-3648*M_4 + 2*(1387 - 500*E_2)*M_3*r0 + (1995 - 317*E_2)*M_2*r0_2 + 2*(-1124 + 234*E_2 + 69*E_4)*M*r0_3 + 12*(39 - 7*E_2)*r0_4)) + a_4*(24*L_4*M_2*(2*M + (-14 + 15*E_2)*r0) - L_2*r0*(48*(-99 + 100*E_2)*M_4 + 4*(222 - 1159*E_2 + 184*E_4)*M_3*r0 - 4*(-408 - 802*E_2 + 303*E_4)*M_2*r0_2 + (-216 - 1307*E_2 + 152*E_4)*M*r0_3 + 36*E_2*r0_4) - E_2*r0_2*(7296*M_5 + 8*(-643 + 316*E_2)*M_4*r0 + 52*(-63 + 50*E_2)*M_3*r0_2 + (6293 - 1452*E_2)*M_2*r0_3 + (-2665 + 316*E_2)*M*r0_4 + 90*r0_5)) - a_2*r0*(-4*L_4*M*(96*M_3 + 24*(23 - 31*E_2)*M_2*r0 + 35*(-12 + 17*E_2)*M*r0_2 + (54 - 91*E_2)*r0_3) + E_2*r0_4*(2654*M_4 + (-6017 + 1988*E_2)*M_3*r0 + (5939 - 856*E_2)*M_2*r0_2 + 16*(-113 + 14*E_2)*M*r0_3 + 72*r0_4) + L_2*r0*(7296*M_5 + 64*(-93 + 56*E_2)*M_4*r0 + 24*(-126 - 230*E_2 + 47*E_4)*M_3*r0_2 + (3096 + 3429*E_2 - 1228*E_4)*M_2*r0_3 + 2*(-240 - 567*E_2 + 130*E_4)*M*r0_4 + 84*E_2*r0_5)))/(3.*r0_2*expr2_5);\n A07200 = -(r0*(12*a_5*E*L*M*(4*(-11 + 6*E_2)*M + (13 - 4*E_2)*r0) - 3*a_6*E_2*(8*(-11 + 4*E_2)*M_2 + (52 - 8*E_2)*M*r0 - 3*r0_2) - 4*a_3*E*L*M*(-24*L_2*M + r0*(120*(-9 + 5*E_2)*M_2 + 20*(43 - 20*E_2)*M*r0 + 3*(-54 + 19*E_2)*r0_2)) + M*r0_2*(2*L_2*(2*M - r0)*(840*M_2 + 2*(-342 + 113*E_2)*M*r0 + (132 - 115*E_2)*r0_2) + E_2*r0_3*(-1799*M_2 - 2*(-843 + 80*E_2)*M*r0 + 2*(-191 + 29*E_2)*r0_2)) + a_4*(24*L_2*M*((11 - 12*E_2)*M + E_2*r0) + E_2*r0*(80*(-27 + 10*E_2)*M_3 - 8*(-241 + 51*E_2)*M_2*r0 + (-859 + 130*E_2)*M*r0_2 + 42*r0_3)) - 4*a*E*L*M*r0*(4*L_2*(50*M_2 - 49*M*r0 + 12*r0_2) + r0*(1680*M_3 + (-2239 + 452*E_2)*M_2*r0 + 2*(487 - 179*E_2)*M*r0_2 + 9*(-14 + 5*E_2)*r0_3)) + a_2*r0*(2*L_2*M*(120*(-9 + 10*E_2)*M_2 + (756 - 988*E_2)*M*r0 + (-96 + 145*E_2)*r0_2) + E_2*r0*(3360*M_4 + 4*(-1135 + 226*E_2)*M_3*r0 + (3707 - 520*E_2)*M_2*r0_2 + 4*(-293 + 41*E_2)*M*r0_3 + 72*r0_4))))/(12.*expr2_5);\n A08000 = (r0_2*(-12*a_3*E*L*M*(2*M + (-3 + E_2)*r0) + 3*a_4*E_2*(4*M_2 + 2*(-6 + E_2)*M*r0 + r0_2) + 4*a*E*L*M*r0*(24*M_2 + 2*(-18 + E_2)*M*r0 - 3*(-3 + E_2)*r0_2) + M*r0*(E_2*r0_3*(65*M + 4*(-7 + E_2)*r0) - 2*L_2*(2*M - r0)*(12*M + (-6 + E_2)*r0)) + 2*a_2*(3*L_2*M*(2*M + E_2*r0) + E_2*r0*(-24*M_3 - 2*(-24 + E_2)*M_2*r0 + 5*(-7 + E_2)*M*r0_2 + 3*r0_3))))/(3.*expr2_5);\n A09000 = -(r0*(6*a_5*E*L*M*(4*(-5 + 3*E_2)*M + (14 - 3*E_2)*r0) + 3*a_6*E_2*((20 - 8*E_2)*M_2 + (-28 + 3*E_2)*M*r0 + r0_2) + 2*a_3*E*L*M*(12*L_2*M + r0*((324 - 168*E_2)*M_2 + 2*(-181 + 71*E_2)*M*r0 + 3*(30 - 7*E_2)*r0_2)) + 3*M*r0_2*(L_2*(2*M - r0)*(72*M_2 + 20*(-3 + E_2)*M*r0 + 3*(4 - 3*E_2)*r0_2) + 2*E_2*r0_3*(-45*M_2 + (41 - 4*E_2)*M*r0 + (-9 + E_2)*r0_2)) + a_4*(3*L_2*M*(-4*(-5 + 6*E_2)*M + 3*E_2*r0) + E_2*r0*(4*(-81 + 28*E_2)*M_3 + (508 - 90*E_2)*M_2*r0 + (-245 + 26*E_2)*M*r0_2 + 9*r0_3)) - 4*a*E*L*M*r0*(L_2*(28*M_2 - 26*M*r0 + 6*r0_2) + r0*(216*M_3 + 4*(-86 + 15*E_2)*M_2*r0 + 13*(13 - 4*E_2)*M*r0_2 + 6*(-4 + E_2)*r0_3)) + a_2*r0*(2*L_2*M*(6*(-27 + 28*E_2)*M_2 + (108 - 149*E_2)*M*r0 + 4*(-3 + 5*E_2)*r0_2) + E_2*r0*(432*M_4 + 40*(-20 + 3*E_2)*M_3*r0 + 2*(367 - 47*E_2)*M_2*r0_2 + (-227 + 23*E_2)*M*r0_3 + 12*r0_4))))/(6.*expr2_6);\n }\n\n /* A_{t,r} */\n {\n A10061 = (-256*E*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0))*expr1_3)/(r0_5*(a_2 + r0*(-2*M + r0)));\n A10081 = (-128*expr1_2*(a_11*E_2*M_2*(312*M_2 + 289*M*r0 + 66*r0_2) + a_10*E*L*M_2*(-624*M_2 + (-589 + 32*E_2)*M*r0 + 6*(-23 + 3*E_2)*r0_2) + a_8*E*L*M*r0*(1248*M_4 + 4*(-193 + 18*E_2)*M_3*r0 + 4*(-479 + 45*E_2)*M_2*r0_2 + (-525 + 74*E_2)*M*r0_3 + 6*(5 - 3*E_2)*r0_4 - 2*L_2*M*(284*M + 3*(44 - 3*E_2)*r0)) + E*L*(2*M - r0)*r0_5*(36*L_6*M*(-2*M + r0) + 6*L_4*M*r0_2*(-26*M + (13 + 4*E_2)*r0) + 4*M*r0_6*(8*M + (-4 + 7*E_2)*r0) + L_2*r0_4*(-64*M_2 + 2*(19 + 24*E_2)*M*r0 - 3*r0_2)) + a_2*E*L*r0_3*(-12*L_6*M*(28*M_2 - 20*M*r0 + 3*r0_2) + 2*M*r0_5*(284*M_3 - 6*(-7 + 2*E_2)*M_2*r0 + 10*(-17 + 8*E_2)*M*r0_2 + 3*(13 - 17*E_2)*r0_3) - 6*L_4*M*r0*(156*M_3 - 8*(4 + E_2)*M_2*r0 - (67 + 16*E_2)*M*r0_2 + 2*(11 + 4*E_2)*r0_3) + L_2*r0_3*(-512*M_4 + 648*M_3*r0 + 2*(-43 + 108*E_2)*M_2*r0_2 - (61 + 138*E_2)*M*r0_3 + 3*r0_4)) + a_9*M*(2*L_2*M*(156*M_2 + 2*(75 + 59*E_2)*M*r0 + 3*(12 + 17*E_2)*r0_2) + E_2*r0*(-16*(39 + 14*E_2)*M_4 + 4*(169 - 84*E_2)*M_3*r0 - 7*(-187 + 24*E_2)*M_2*r0_2 + 2*(201 - 14*E_2)*M*r0_3 + 6*r0_4)) + a_6*E*L*M*r0*(-126*L_4*M*r0 + r0_2*(-68*(-39 + 4*E_2)*M_4 - 4*(-369 + 58*E_2)*M_3*r0 + (-2101 + 168*E_2)*M_2*r0_2 + 6*(-142 + 21*E_2)*M*r0_3 + 2*(53 - 41*E_2)*r0_4) + 2*L_2*(-896*M_4 + 60*(5 + 2*E_2)*M_3*r0 + 60*(-5 + 2*E_2)*M_2*r0_2 + 42*(-9 + E_2)*M*r0_3 + 3*(2 - 7*E_2)*r0_4)) - 2*a_3*M*r0_2*(E_2*r0_6*(456*M_3 + 12*(11 + 9*E_2)*M_2*r0 + (-201 + 68*E_2)*M*r0_2 - 12*r0_3) - 6*L_6*(52*M_3 + 2*(-19 + 6*E_2)*M_2*r0 - 8*E_2*M*r0_2 + (3 + 2*E_2)*r0_3) + L_2*r0_3*(96*M_4 - 4*(-60 + 83*E_2)*M_3*r0 + 48*(-3 + 2*E_2 + 3*E_4)*M_2*r0_2 + 4*(-21 + 16*E_2 + 27*E_4)*M*r0_3 + 7*(6 - 11*E_2)*r0_4) - 6*L_4*r0*(16*M_4 + 12*(-1 + 9*E_2)*M_3*r0 - 2*(9 - 5*E_2 + 4*E_4)*M_2*r0_2 + (20 - 35*E_2 - 8*E_4)*M*r0_3 + 5*(-1 + 2*E_2)*r0_4)) - a_5*M*r0*(-72*L_6*M*r0 + 3*E_2*r0_4*(364*M_4 + 4*(173 + 36*E_2)*M_3*r0 + (-221 + 200*E_2)*M_2*r0_2 + 4*(-73 + 16*E_2)*M*r0_3 - 12*r0_4) + L_2*r0_2*(-64*(-12 + 25*E_2)*M_4 + 8*(51 - 70*E_2 + 36*E_4)*M_3*r0 + 12*(-53 + 5*E_2 + 48*E_4)*M_2*r0_2 + 6*(-24 - 67*E_2 + 36*E_4)*M*r0_3 + (96 - 133*E_2)*r0_4) - 12*L_4*(56*M_4 + 2*(-25 + 42*E_2)*M_3*r0 + (3 - 6*E_2 - 8*E_4)*M_2*r0_2 - 2*(-11 + E_2 + 2*E_4)*M*r0_3 + (-3 + 5*E_2)*r0_4)) + a_7*M*r0*(12*L_4*M*(25*M + 3*(4 + E_2)*r0) - 3*E_2*r0_2*((628 + 96*E_2)*M_4 + 16*(17 + 16*E_2)*M_3*r0 + (-597 + 184*E_2)*M_2*r0_2 + 4*(-73 + 10*E_2)*M*r0_3 - 8*r0_4) + 2*L_2*(24*(-13 + 28*E_2)*M_4 + 12*(4 + 11*E_2 - 12*E_4)*M_3*r0 + 12*(25 + 23*E_2 - 12*E_4)*M_2*r0_2 + (60 + 221*E_2 - 36*E_4)*M*r0_3 + 3*(-6 + 7*E_2)*r0_4)) + a_4*E*L*M*r0_2*(-6*L_4*(264*M_3 - 24*(4 + E_2)*M_2*r0 - 2*(1 + 4*E_2)*M*r0_2 + (9 + 4*E_2)*r0_3) + r0_3*(808*M_4 - 4*(-535 + 48*E_2)*M_3*r0 + 2*(-373 + 14*E_2)*M_2*r0_2 + 3*(-247 + 58*E_2)*M*r0_3 - 138*(-1 + E_2)*r0_4) + L_2*r0*(-1232*M_4 - 8*(-73 + 21*E_2)*M_3*r0 + 8*(85 + 27*E_2)*M_2*r0_2 + 2*(-356 + 93*E_2)*M*r0_3 - 11*(1 + 12*E_2)*r0_4)) + a*M*r0_3*(36*L_8*r0_2M_2 + 6*E_2*r0_8*(-26*M_2 + (11 - 6*E_2)*M*r0 + r0_2) + 12*L_4*r0_4*(8*(-1 + 5*E_2)*M_2 - 2*(-4 + 15*E_2 + 2*E_4)*M*r0 + (-2 + 5*E_2)*r0_2) + L_2*r0_5*(-96*M_3 + 184*E_2*M_2*r0 - 2*(-36 + 109*E_2 + 36*E_4)*M*r0_2 + 3*(-8 + 21*E_2)*r0_3) + 12*L_6*(2*M - r0)*r0*(4*M_2 - (3 + 2*E_2)*r0_2 + 4*M*(r0 + 2*E_2*r0)))))/(3.*r0_11*expr2_2);\n A10241 = (-192*E*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0))*expr1_2)/(r0_2*(a_2 + r0*(-2*M + r0)));\n A10261 = (64*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(a_11*E_2*M*(12*(-55 + 2*E_2)*M_3 + (-619 + 24*E_2)*M_2*r0 + 6*(-23 + E_2)*M*r0_2 + 3*r0_3) - a_10*E*L*M*(24*(-55 + 3*E_2)*M_3 + (-1261 + 122*E_2)*M_2*r0 + 3*(-98 + 17*E_2)*M*r0_2 + 3*(1 + E_2)*r0_3) - E*L*(2*M - r0)*r0_5*(-81*L_6*M*(2*M - r0) + 2*L_4*M*r0_2*(-170*M + 85*r0 + 24*E_2*r0) + L_2*M*r0_4*(-126*M + 63*r0 + 100*E_2*r0) + r0_6*(64*M_2 - 38*M*r0 + 56*E_2*M*r0 + 3*r0_2)) + a*M*r0_3*(-72*L_8*r0_2M_2 + 3*E_2*r0_8*(104*M_2 + 2*(-25 + 12*E_2)*M*r0 - r0_2) + L_4*r0_4*(-4*(-78 + 277*E_2)*M_2 + 4*(-78 + 212*E_2 + 21*E_4)*M*r0 + 3*(26 - 49*E_2)*r0_2) - 6*L_6*(2*M - r0)*r0*(12*M_2 + 2*(7 + 20*E_2)*M*r0 - (10 + 9*E_2)*r0_2) + L_2*r0_5*(144*M_3 - 8*(-15 + 46*E_2)*M_2*r0 + 2*(-114 + 209*E_2 + 72*E_4)*M*r0_2 + 3*(22 - 39*E_2)*r0_3)) + a_9*M*(2*L_2*(6*(-55 + 6*E_2)*M_3 + (-321 - 235*E_2 + 6*E_4)*M_2*r0 + 3*(-26 - 35*E_2 + E_4)*M*r0_2 + 6*E_2*r0_3) + E_2*r0*(40*(33 + 10*E_2)*M_4 + 48*(-28 + 15*E_2)*M_3*r0 + 111*(-25 + 4*E_2)*M_2*r0_2 + 4*(-215 + 23*E_2)*M*r0_3 + 3*r0_4)) + a_2*E*L*r0_3*(6*L_6*M*(116*M_2 - 84*M*r0 + 13*r0_2) + L_4*M*r0*(1852*M_3 - 4*(127 + 3*E_2)*M_2*r0 - 3*(253 + 64*E_2)*M*r0_2 + (275 + 93*E_2)*r0_3) + L_2*r0_3*(1160*M_4 + 4*(-433 + 19*E_2)*M_3*r0 + 2*(207 - 251*E_2)*M_2*r0_2 + (75 + 287*E_2)*M*r0_3 + 3*r0_4) + r0_5*(-980*M_4 + 12*(-33 + 4*E_2)*M_3*r0 + 5*(157 - 70*E_2)*M_2*r0_2 + 21*(-9 + 10*E_2)*M*r0_3 + 9*r0_4)) + a_3*M*r0_2*(E_2*r0_6*(1680*M_3 + 44*(14 + 9*E_2)*M_2*r0 + 10*(-86 + 29*E_2)*M*r0_2 - 15*r0_3) - 12*L_6*(102*M_3 + (-77 + 30*E_2)*M_2*r0 + (3 - 19*E_2)*M*r0_2 + (5 + 4*E_2)*r0_3) + 2*L_2*r0_3*(144*M_4 + (600 - 892*E_2)*M_3*r0 + 2*(-144 + 250*E_2 + 135*E_4)*M_2*r0_2 + (-240 + 57*E_2 + 221*E_4)*M*r0_3 + (108 - 149*E_2)*r0_4) + L_4*r0*(-288*M_4 - 8*(-51 + 346*E_2)*M_3*r0 + 84*(5 + 2*E_4)*M_2*r0_2 + 4*(-156 + 223*E_2 + 42*E_4)*M*r0_3 + 3*(58 - 89*E_2)*r0_4)) + a_5*M*r0*(6*L_6*r0*(-26*M + E_2*r0) + E_2*r0_4*(2004*M_4 + 80*(53 + 9*E_2)*M_3*r0 + 27*(-43 + 44*E_2)*M_2*r0_2 + 6*(-309 + 74*E_2)*M*r0_3 - 24*r0_4) + L_4*(-1296*M_4 + 12*(107 - 176*E_2)*M_3*r0 + 2*(-75 + 188*E_2 + 84*E_4)*M_2*r0_2 + 4*(-147 - E_2 + 21*E_4)*M*r0_3 + 3*(32 - 35*E_2)*r0_4) + L_2*r0_2*(-32*(-51 + 106*E_2)*M_4 + 4*(249 - 179*E_2 + 126*E_4)*M_3*r0 + 2*(-717 + 411*E_2 + 554*E_4)*M_2*r0_2 + 2*(-180 - 557*E_2 + 229*E_4)*M*r0_3 + 13*(18 - 19*E_2)*r0_4)) - a_8*E*L*M*(L_2*(24*M_3 + 2*(-605 + 18*E_2)*M_2*r0 + 3*(-189 + 17*E_2)*M*r0_2 + 3*(3 + 2*E_2)*r0_3) + r0*(-48*(-55 + 2*E_2)*M_4 + 16*(-96 + 25*E_2)*M_3*r0 + 4*(-1028 + 157*E_2)*M_2*r0_2 + (-1144 + 177*E_2)*M*r0_3 + 3*(28 - 11*E_2)*r0_4)) + a_7*M*r0*(3*L_4*(2*(-107 + 6*E_2)*M_2 - 8*(13 + 3*E_2)*M*r0 + 5*E_2*r0_2) + E_2*r0_2*(4*(961 + 108*E_2)*M_4 + 4*(485 + 354*E_2)*M_3*r0 + 3*(-1207 + 404*E_2)*M_2*r0_2 + 6*(-311 + 52*E_2)*M*r0_3 - 12*r0_4) - 2*L_2*(12*(-55 + 112*E_2)*M_4 + 2*(48 + 19*E_2 - 130*E_4)*M_3*r0 + 2*(327 + 248*E_2 - 145*E_4)*M_2*r0_2 + (132 + 524*E_2 - 83*E_4)*M*r0_3 + 3*(-14 + 9*E_2)*r0_4)) - a_6*E*L*r0*(3*L_4*M*(4*M_2 - 91*M*r0 + (3 + E_2)*r0_2) + L_2*M*(-3488*M_4 + 8*(191 + 42*E_2)*M_3*r0 + 2*(-663 + 298*E_2)*M_2*r0_2 + 4*(-437 + 52*E_2)*M*r0_3 + 3*(22 - 25*E_2)*r0_4) + r0_2*((5476 - 904*E_2)*M_5 + 4*(863 - 119*E_2)*M_4*r0 + (-4413 + 854*E_2)*M_3*r0_2 + (-1951 + 311*E_2)*M_2*r0_3 + (260 - 173*E_2)*M*r0_4 - 3*r0_5)) + a_4*E*L*r0_2*(-3*L_6*M*r0 + 2*L_4*M*(1576*M_3 - 6*(107 + 18*E_2)*M_2*r0 + (41 - 48*E_2)*M*r0_2 + 3*(16 + 7*E_2)*r0_3) + L_2*r0*(2344*M_5 + 4*(-396 + 139*E_2)*M_4*r0 - 72*(23 + 7*E_2)*M_3*r0_2 + 17*(109 - 27*E_2)*M_2*r0_3 + (-39 + 268*E_2)*M*r0_4 + 3*r0_5) + r0_3*(-1376*M_5 + 4*(-1159 + 195*E_2)*M_4*r0 + 2*(631 - 166*E_2)*M_3*r0_2 - 9*(-194 + 47*E_2)*M_2*r0_3 + 3*(-108 + 97*E_2)*M*r0_4 + 9*r0_5))))/(3.*r0_8*expr2_2);\n A10421 = (-48*E*r0*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0))*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/(a_2 + r0*(-2*M + r0));\n A10441 = (8*(a_11*E_2*M*(72*(-29 + 2*E_2)*M_3 + (-1957 + 144*E_2)*M_2*r0 + 18*(-23 + 2*E_2)*M*r0_2 + 21*r0_3) - a_10*E*L*M*(144*(-29 + 3*E_2)*M_3 + (-4009 + 560*E_2)*M_2*r0 + 6*(-153 + 35*E_2)*M*r0_2 + 3*(7 + 6*E_2)*r0_3) - E*L*(2*M - r0)*r0_5*(-278*L_6*M*(2*M - r0) + L_4*r0_2*(-1108*M_2 + 4*(133 + 37*E_2)*M*r0 + 11*r0_2) + r0_6*(192*M_2 + 2*(-71 + 84*E_2)*M*r0 + 23*r0_2) + L_2*r0_4*(-372*M_2 + 4*(31 + 78*E_2)*M*r0 + 31*r0_2)) + a*M*r0_3*(-216*L_8*r0_2M_2 + 3*E_2*r0_8*(312*M_2 + 2*(-89 + 36*E_2)*M*r0 + 11*r0_2) - 4*L_6*(2*M - r0)*r0*(36*M_2 + 2*(27 + 115*E_2)*M*r0 - 3*(12 + 17*E_2)*r0_2) - 3*L_4*r0_4*(4*(-108 + 319*E_2)*M_2 - 4*(-108 + 243*E_2 + 19*E_4)*M*r0 + (-108 + 167*E_2)*r0_2) + 3*L_2*r0_5*(96*M_3 + 16*(15 - 23*E_2)*M_2*r0 + 2*(-156 + 187*E_2 + 72*E_4)*M*r0_2 + (84 - 95*E_2)*r0_3)) + a_2*E*L*r0_3*(8*L_6*M*(272*M_2 - 202*M*r0 + 33*r0_2) + L_4*r0*(5592*M_4 + 172*(-11 + 2*E_2)*M_3*r0 - 2*(1093 + 350*E_2)*M_2*r0_2 + (839 + 286*E_2)*M*r0_3 + 14*r0_4) + L_2*r0_3*(3840*M_4 + 16*(-391 + 36*E_2)*M_3*r0 + 10*(187 - 180*E_2)*M_2*r0_2 + (7 + 906*E_2)*M*r0_3 + 71*r0_4) + r0_5*(-2472*M_4 + 8*(-221 + 18*E_2)*M_3*r0 - 12*(-219 + 95*E_2)*M_2*r0_2 + (-707 + 648*E_2)*M*r0_3 + 72*r0_4)) + a_9*M*(2*L_2*(36*(-29 + 6*E_2)*M_3 + 2*(-513 - 341*E_2 + 24*E_4)*M_2*r0 + 3*(-84 - 101*E_2 + 8*E_4)*M*r0_2 + 39*E_2*r0_3) + E_2*r0*(48*(87 + 22*E_2)*M_4 + 4*(-1009 + 576*E_2)*M_3*r0 + (-8705 + 1656*E_2)*M_2*r0_2 + 2*(-1319 + 192*E_2)*M*r0_3 + 77*r0_4)) + a_5*M*r0*(36*L_6*r0*((-14 + E_2)*M + E_2*r0) + E_2*r0_4*(5364*M_4 + 12*(1069 + 144*E_2)*M_3*r0 + 7*(-457 + 504*E_2)*M_2*r0_2 + 108*(-53 + 14*E_2)*M*r0_3 + 162*r0_4) + L_2*r0_2*(-192*(-27 + 56*E_2)*M_4 + 8*(441 - 130*E_2 + 144*E_4)*M_3*r0 + 4*(-1197 + 1055*E_2 + 792*E_4)*M_2*r0_2 + 2*(-648 - 1993*E_2 + 768*E_4)*M*r0_3 + (828 - 581*E_2)*r0_4) + L_4*(-3744*M_4 - 72*(-57 + 94*E_2)*M_3*r0 + 4*(-171 + 486*E_2 + 104*E_4)*M_2*r0_2 + 4*(-486 - E_2 + 67*E_4)*M*r0_3 + (360 - 283*E_2)*r0_4)) + a_3*M*r0_2*(E_2*r0_6*(4608*M_3 + 12*(163 + 90*E_2)*M_2*r0 + 14*(-197 + 66*E_2)*M*r0_2 + 113*r0_3) - 4*L_6*(900*M_3 + 6*(-117 + 56*E_2)*M_2*r0 + (54 - 227*E_2)*M*r0_2 + 6*(6 + 7*E_2)*r0_3) + L_4*r0*(-576*M_4 - 48*(-33 + 191*E_2)*M_3*r0 + 4*(306 + 167*E_2 + 96*E_4)*M_2*r0_2 + 4*(-576 + 751*E_2 + 121*E_4)*M*r0_3 + (684 - 877*E_2)*r0_4) + 2*L_2*r0_3*(288*M_4 + 12*(180 - 271*E_2)*M_3*r0 + 16*(-54 + 136*E_2 + 45*E_4)*M_2*r0_2 + 4*(-234 - 5*E_2 + 174*E_4)*M*r0_3 + 3*(132 - 125*E_2)*r0_4)) + a_7*M*r0*(3*L_4*(12*(-57 + 8*E_2)*M_2 + 4*(-84 - 13*E_2 + E_4)*M*r0 + 31*E_2*r0_2) + E_2*r0_2*(12*(977 + 72*E_2)*M_4 + 16*(413 + 243*E_2)*M_3*r0 + 11*(-997 + 360*E_2)*M_2*r0_2 + 36*(-159 + 32*E_2)*M*r0_3 + 138*r0_4) - 2*L_2*(72*(-29 + 56*E_2)*M_4 - 4*(-72 + 131*E_2 + 168*E_4)*M_3*r0 + 4*(531 + 329*E_2 - 228*E_4)*M_2*r0_2 + (432 + 1729*E_2 - 312*E_4)*M*r0_3 + (-144 + 19*E_2)*r0_4)) - a_6*E*L*r0*(3*L_4*M*(32*M_2 + 2*(-143 + 6*E_2)*M*r0 + (19 + 6*E_2)*r0_2) + r0_2*((16908 - 3792*E_2)*M_5 - 12*(-979 + 126*E_2)*M_4*r0 + (-13853 + 3952*E_2)*M_3*r0_2 + 2*(-3228 + 581*E_2)*M_2*r0_3 + 2*(460 - 273*E_2)*M*r0_4 - 32*r0_5) + 2*L_2*(-5088*M_5 + 4*(691 + 54*E_2)*M_4*r0 + 24*(-91 + 48*E_2)*M_3*r0_2 + 6*(-487 + 77*E_2)*M_2*r0_3 + (167 - 105*E_2)*M*r0_4 - 3*r0_5)) - a_8*E*L*(2*L_2*M*(72*M_3 + 4*(-479 + 36*E_2)*M_2*r0 + 3*(-298 + 41*E_2)*M*r0_2 + 6*(5 + 3*E_2)*r0_3) + r0*(-288*(-29 + 2*E_2)*M_5 + 4*(-1153 + 482*E_2)*M_4*r0 + 4*(-3277 + 677*E_2)*M_3*r0_2 + 5*(-729 + 134*E_2)*M_2*r0_3 + 2*(163 - 45*E_2)*M*r0_4 - 3*r0_5)) + a_4*E*L*r0_2*(-6*L_6*M*(2*M + 3*r0) + L_4*(9456*M_4 - 48*(89 + 8*E_2)*M_3*r0 - 8*(-65 + 53*E_2)*M_2*r0_2 + 8*(32 + 15*E_2)*M*r0_3 + 3*r0_4) + L_2*r0*(6672*M_5 + 8*(-743 + 339*E_2)*M_4*r0 - 8*(710 + 207*E_2)*M_3*r0_2 + 2*(3326 - 927*E_2)*M_2*r0_3 + (-323 + 840*E_2)*M*r0_4 + 46*r0_5) + r0_3*(-3336*M_5 + 4*(-3727 + 828*E_2)*M_4*r0 + 2*(1601 - 846*E_2)*M_3*r0_2 + (5881 - 1506*E_2)*M_2*r0_3 + 54*(-21 + 17*E_2)*M*r0_4 + 78*r0_5))))/(3.*r0_5*expr2_2);\n A10601 = (-4*E*r0_4*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0)))/(a_2 + r0*(-2*M + r0));\n A10621 = (4*(6*a_9*E_2*M*((-61 + 6*E_2)*M_2 + (-26 + 3*E_2)*M*r0 + 2*r0_2) - 3*a_8*E*L*M*(4*(-61 + 9*E_2)*M_2 + (-112 + 25*E_2)*M*r0 + (4 + 3*E_2)*r0_2) - E*L*(2*M - r0)*r0_4*(-107*L_4*M*(2*M - r0) + 2*r0_4*(32*M_2 + 2*(-15 + 14*E_2)*M*r0 + 7*r0_2) + L_2*r0_2*(-186*M_2 + (71 + 52*E_2)*M*r0 + 11*r0_2)) + 2*a_7*M*(3*L_2*((-61 + 18*E_2)*M_2 + 2*(-15 - 7*E_2 + E_4)*M*r0 + 5*E_2*r0_2) + E_2*r0*((366 + 76*E_2)*M_3 + 2*(-261 + 83*E_2)*M_2*r0 + (-397 + 73*E_2)*M*r0_2 + 22*r0_3)) + 2*a_5*M*r0*(9*L_4*(2*(-5 + E_2)*M + E_2*r0) + E_2*r0_2*(18*(55 + 2*E_2)*M_3 + (-73 + 238*E_2)*M_2*r0 + (-624 + 155*E_2)*M*r0_2 + 41*r0_3) + L_2*((366 - 672*E_2)*M_3 + (-231 + 340*E_2 + 52*E_4)*M_2*r0 + 2*(-87 - 63*E_2 + 28*E_4)*M*r0_2 + (54 - 17*E_2)*r0_3)) + 2*a*M*r0_2*(-36*L_6*r0_2M_2 + 3*E_2*r0_6*(52*M_2 + 12*(-3 + E_2)*M*r0 + 5*r0_2) - L_4*(2*M - r0)*r0*(12*M_2 + 14*(-3 + 14*E_2)*M*r0 + 9*(2 - 5*E_2)*r0_2) + L_2*r0_3*(24*M_3 - 20*(-9 + 17*E_2)*M_2*r0 + 2*(-99 + 130*E_2 + 18*E_4)*M*r0_2 + 3*(17 - 15*E_2)*r0_3)) + 2*a_3*M*r0*(E_2*r0_4*(384*M_3 + 18*(21 + 5*E_2)*M_2*r0 + (-413 + 127*E_2)*M*r0_2 + 40*r0_3) + L_2*r0_2*((456 - 944*E_2)*M_3 + 2*(-36 + 155*E_2 + 18*E_4)*M_2*r0 + 2*(-144 + 90*E_2 + 43*E_4)*M*r0_2 + 7*(15 - 11*E_2)*r0_3) - 2*L_4*(150*M_3 + 3*(-55 + 46*E_2)*M_2*r0 + (63 - 104*E_2)*M*r0_2 + 9*(-1 + 2*E_2)*r0_3)) - a_6*E*L*(3*L_2*M*(12*M_2 + (-107 + 12*E_2)*M*r0 + (7 + 3*E_2)*r0_2) + r0*(-24*(-61 + 6*E_2)*M_4 + 2*(-753 + 254*E_2)*M_3*r0 + (-1183 + 284*E_2)*M_2*r0_2 - 4*(-32 + 9*E_2)*M*r0_3 - 3*r0_4)) + a_4*E*L*r0*(-3*L_4*M*(4*M + 3*r0) + L_2*(1648*M_4 - 12*(97 + 2*E_2)*M_3*r0 + 2*(321 - 116*E_2)*M_2*r0_2 + (-17 + 42*E_2)*M*r0_3 + 3*r0_4) + r0_2*(4*(-723 + 203*E_2)*M_4 + 6*(1 - 34*E_2)*M_3*r0 + (1652 - 507*E_2)*M_2*r0_2 + (-264 + 155*E_2)*M*r0_3 + 20*r0_4)) + a_2*E*L*r0_2*(2*L_4*M*(380*M_2 - 292*M*r0 + 51*r0_2) + L_2*r0*(1052*M_4 + 4*(-271 + 71*E_2)*M_3*r0 + (85 - 316*E_2)*M_2*r0_2 + (69 + 103*E_2)*M*r0_3 + 14*r0_4) + r0_3*(-412*M_4 + 4*(-247 + 68*E_2)*M_3*r0 + 5*(189 - 82*E_2)*M_2*r0_2 + 2*(-118 + 83*E_2)*M*r0_3 + 31*r0_4))))/(3.*r0_2*expr2_2);\n A10801 = (r0*(3*a_7*E_2*M*(4*(-8 + E_2)*M + 3*r0) - 3*a_6*E*L*M*(4*(-16 + 3*E_2)*M + (3 + 2*E_2)*r0) + a*M*r0*(-36*L_4*r0_2M_2 - 4*L_2*(2*M - r0)*r0_2*((-30 + 62*E_2)*M - 15*(-1 + E_2)*r0) + 3*E_2*r0_4*(52*M_2 + 4*(-11 + 3*E_2)*M*r0 + 9*r0_2)) - E*L*(2*M - r0)*r0_3*(-62*L_2*M*(2*M - r0) + r0_2*(32*M_2 - 38*M*r0 + 28*E_2*M*r0 + 11*r0_2)) + a_5*M*(12*L_2*((-8 + 3*E_2)*M + E_2*r0) + E_2*r0*(32*(6 + E_2)*M_2 + 4*(-91 + 19*E_2)*M*r0 + 29*r0_2)) + a_3*M*r0*(E_2*r0_2*(500*M_2 + 4*(-92 + 25*E_2)*M*r0 + 47*r0_2) - 4*L_2*(12*(-4 + 7*E_2)*M_2 + (54 - 71*E_2)*M*r0 + 3*(-5 + 4*E_2)*r0_2)) + a_4*E*L*(-6*L_2*M*(2*M + r0) + r0*(48*(-8 + E_2)*M_3 + 4*(145 - 46*E_2)*M_2*r0 + 2*(-37 + 12*E_2)*M*r0_2 + 3*r0_3)) + a_2*E*L*r0*(20*L_2*M*(20*M_2 - 16*M*r0 + 3*r0_2) + r0_2*(4*(-185 + 62*E_2)*M_3 + 4*(133 - 55*E_2)*M_2*r0 + (-109 + 58*E_2)*M*r0_2 + 14*r0_3))))/(6.*expr2_2);\n A11061 = (-128*expr1_2*(a_7*E_2*M*(4*M_2 + M*r0 - r0_2) + a_6*E*L*M*(-8*M_2 + (-3 + 4*E_2)*M*r0 + (1 + 3*E_2)*r0_2) + a_4*E*L*r0_2*((4 + 3*E_2)*L_2*M - 2*(15 + 2*E_2)*M_3 - (19 + 4*E_2)*M_2*r0 + (9 + 8*E_2)*M*r0_2 + 2*r0_3) + E*L*r0_3*(L_4*M*(-2*M + r0) - 2*L_2*r0_2*(6*M_2 - (5 + E_2)*M*r0 + r0_2) - r0_4*(6*M_2 - (5 + 2*E_2)*M*r0 + r0_2)) + a_5*M*(-2*E_2*r0_2*(-11*M_2 - 9*M*r0 + r0_2) + L_2*(4*M_2 + (2 - 6*E_2)*M*r0 - 7*E_2*r0_2)) + a_2*E*L*r0_2*(3*L_4*M + r0_3*(-2*(11 + 8*E_2)*M_2 + 7*(1 + E_2)*M*r0 + r0_2) + L_2*(-4*M_3 - 2*(12 + E_2)*M_2*r0 + 5*(2 + E_2)*M*r0_2 + 2*r0_3)) + a*M*r0_3*(6*E_2*(2*M - r0)*r0_4 + L_2*r0_2*((4 + 34*E_2)*M - (2 + 21*E_2)*r0) + L_4*(4*(1 + E_2)*M - 2*(r0 + 3*E_2*r0))) + a_3*M*r0*(2*L_4*(M - 3*E_2*r0) + E_2*r0_3*(6*M_2 + 17*M*r0 - 7*r0_2) + 2*L_2*r0*(4*(1 + E_2)*M_2 - (1 + 8*E_2)*r0_2 + M*(r0 + 12*E_2*r0)))))/(r0_7*expr2_2);\n A11241 = (-32*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(4*a_7*E_2*M*(3*M_2 - r0_2) + a_6*E*L*M*(-24*M_2 + 2*(-3 + 7*E_2)*M*r0 + (4 + 9*E_2)*r0_2) + 6*a*M*r0_3*(3*E_2*(2*M - r0)*r0_4 - L_2*r0_2*(-2*(1 + 7*E_2)*M + r0 + 9*E_2*r0) + L_4*(2*(1 + E_2)*M - (1 + 3*E_2)*r0)) + E*L*r0_3*(3*L_4*M*(-2*M + r0) + L_2*r0_2*(-32*M_2 + 2*(13 + 3*E_2)*M*r0 - 5*r0_2) - 3*r0_4*(6*M_2 - (5 + 2*E_2)*M*r0 + r0_2)) + 2*a_5*M*(E_2*r0_2*(36*M_2 + 22*M*r0 - 5*r0_2) + L_2*(6*M_2 + (3 - 11*E_2)*M*r0 - 11*E_2*r0_2)) + a_4*E*L*r0*(L_2*M*(2*M + (13 + 9*E_2)*r0) + r0*(-12*(8 + E_2)*M_3 - 50*M_2*r0 + 3*(9 + 8*E_2)*M*r0_2 + 5*r0_3)) + a_2*E*L*r0_2*(9*L_4*M + r0_2*(-12*M_3 - 2*(29 + 15*E_2)*M_2*r0 + (22 + 21*E_2)*M*r0_2 + 2*r0_3) + L_2*(-12*M_3 - 6*(11 + E_2)*M_2*r0 + (29 + 15*E_2)*M*r0_2 + 5*r0_3)) + 6*a_3*M*r0*(L_4*(M - 3*E_2*r0) + 2*E_2*r0_3*(3*M_2 + 4*M*r0 - 2*r0_2) + L_2*r0*(4*(1 + E_2)*M_2 - (1 + 8*E_2)*r0_2 + M*(r0 + 9*E_2*r0)))))/(r0_4*expr2_2);\n A11421 = (-8*(a_7*E_2*M*(12*M_2 - 3*M*r0 - 5*r0_2) + a_6*E*L*M*(-24*M_2 + (-3 + 16*E_2)*M*r0 + (5 + 9*E_2)*r0_2) + E*L*r0_3*(3*L_4*M*(-2*M + r0) + 2*L_2*r0_2*(-14*M_2 + (11 + 3*E_2)*M*r0 - 2*r0_2) - 3*r0_4*(6*M_2 - (5 + 2*E_2)*M*r0 + r0_2)) + a_5*M*(2*E_2*r0_2*(39*M_2 + 17*M*r0 - 7*r0_2) + L_2*(12*M_2 + (6 - 26*E_2)*M*r0 - 23*E_2*r0_2)) + a_4*E*L*r0*(L_2*M*(4*M + (14 + 9*E_2)*r0) + r0*(-6*(17 + 2*E_2)*M_3 + (-43 + 12*E_2)*M_2*r0 + 3*(9 + 8*E_2)*M*r0_2 + 4*r0_3)) + a_2*E*L*r0_2*(9*L_4*M + r0_2*(-24*M_3 - 2*(25 + 6*E_2)*M_2*r0 + (23 + 21*E_2)*M*r0_2 + r0_3) + L_2*(-12*M_3 - 6*(10 + E_2)*M_2*r0 + (28 + 15*E_2)*M*r0_2 + 4*r0_3)) + 3*a*M*r0_3*(6*E_2*(2*M - r0)*r0_4 + L_2*r0_2*((4 + 22*E_2)*M - (2 + 15*E_2)*r0) + L_4*(4*(1 + E_2)*M - 2*(r0 + 3*E_2*r0))) + 3*a_3*M*r0*(2*L_4*(M - 3*E_2*r0) + 3*E_2*r0_3*(6*M_2 + 5*M*r0 - 3*r0_2) + 2*L_2*r0*(4*(1 + E_2)*M_2 - (1 + 8*E_2)*r0_2 + M*(r0 + 6*E_2*r0)))))/(r0*expr2_2);\n A11601 = (2*r0_2*(2*a_5*E_2*M*(-M + r0) + a_4*E*L*M*(4*M - (2 + 3*E_2)*r0) - 2*a_3*M*(E_2*(7*M - 2*r0)*r0_2 + L_2*(M - 3*E_2*r0)) + 2*a*M*r0_2*(3*E_2*r0_2*(-2*M + r0) + L_2*(-2*(1 + E_2)*M + r0 + 3*E_2*r0)) - a_2*E*L*r0*(3*L_2*M + r0*(-2*(9 + E_2)*M_2 + 5*(1 + E_2)*M*r0 + r0_2)) + E*L*r0_2*(L_2*M*(2*M - r0) + r0_2*(6*M_2 - (5 + 2*E_2)*M*r0 + r0_2))))/expr2_2;\n A12041 = (-192*E*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0))*expr1_2)/(r0_2*expr2_2);\n A12061 = (-32*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(a_11*E_2*M*(24*(46 + 7*E_2)*M_3 + (1031 + 180*E_2)*M_2*r0 + 6*(41 + 8*E_2)*M*r0_2 + 6*r0_3) - a_10*E*L*M*(24*(92 + 17*E_2)*M_3 + (2087 + 296*E_2)*M_2*r0 + 6*(83 + 6*E_2)*M*r0_2 + 6*(1 + E_2)*r0_3) + E*L*r0_5*(-6*L_6*M*(102*M_2 - 103*M*r0 + 26*r0_2) + r0_6*(124*M_3 + 2*(-41 + 94*E_2)*M_2*r0 - 4*(2 + 25*E_2)*M*r0_2 + 9*r0_3) + 2*L_4*r0_2*(-734*M_3 + (791 + 102*E_2)*M_2*r0 - 2*(118 + 27*E_2)*M*r0_2 + 12*r0_3) + 2*L_2*r0_4*(-354*M_3 + 47*(9 + 4*E_2)*M_2*r0 - (153 + 100*E_2)*M*r0_2 + 15*r0_3)) + a*M*r0_3*(-3*E_2*r0_8*(116*M_2 + 4*(4 + 3*E_2)*M*r0 - 37*r0_2) + 12*L_8*(50*M_2 - 49*M*r0 + 12*r0_2) + 2*L_4*r0_4*(2*(-18 + 725*E_2)*M_2 + (18 - 1385*E_2 - 84*E_4)*M*r0 + 330*E_2*r0_2) + 12*L_6*(2*M - r0)*r0*(12*M_2 + (28 + 37*E_2)*M*r0 - (17 + 15*E_2)*r0_2) + 2*L_2*r0_5*(-144*M_3 + 614*E_2*M_2*r0 + (96 - 805*E_2 - 90*E_4)*M*r0_2 + 3*(-10 + 83*E_2)*r0_3)) - a_2*E*L*r0_3*(6*L_6*M*(244*M_2 - 193*M*r0 + 33*r0_2) + 2*L_4*r0*(1672*M_4 + (416 - 30*E_2)*M_3*r0 - 3*(478 + 87*E_2)*M_2*r0_2 + 5*(61 + 24*E_2)*M*r0_3 + 36*r0_4) + r0_5*(-1912*M_4 + 24*(7 + 4*E_2)*M_3*r0 + 14*(44 - 29*E_2)*M_2*r0_2 + 3*(-69 + 128*E_2)*M*r0_3 + 36*r0_4) + 2*L_2*r0_3*(764*M_4 + 2*(-95 + 329*E_2)*M_3*r0 - (657 + 748*E_2)*M_2*r0_2 + (153 + 308*E_2)*M*r0_3 + 48*r0_4)) + a_9*M*(2*L_2*(12*(46 + 9*E_2)*M_3 + 2*(264 + 247*E_2 + 30*E_4)*M_2*r0 + 3*(42 + 65*E_2 + 8*E_4)*M*r0_2 + 12*E_2*r0_3) + E_2*r0*(-16*(129 + 62*E_2)*M_4 + 24*(103 - 31*E_2)*M_3*r0 + 3*(1531 + 96*E_2)*M_2*r0_2 + 2*(707 + 106*E_2)*M*r0_3 + 54*r0_4)) - a_8*E*L*M*(2*L_2*(-60*M_3 + 8*(113 + 15*E_2)*M_2*r0 + 435*M*r0_2 + 3*(3 + 2*E_2)*r0_3) + r0*(-96*(43 + 3*E_2)*M_4 + 8*(363 + 125*E_2)*M_3*r0 + 2*(3311 + 734*E_2)*M_2*r0_2 + (1733 + 342*E_2)*M*r0_3 + 6*(-16 + 17*E_2)*r0_4)) - a_3*M*r0_2*(36*L_8*M + E_2*r0_6*(3084*M_3 + 2*(373 + 414*E_2)*M_2*r0 + 4*(-223 + 10*E_2)*M*r0_2 - 243*r0_3) - 12*L_6*(212*M_3 + (-133 + 66*E_2)*M_2*r0 - (19 + 60*E_2)*M*r0_2 + 4*(3 + 4*E_2)*r0_3) + 2*L_2*r0_3*(288*M_4 + (792 - 458*E_2)*M_3*r0 + (-426 - 785*E_2 + 180*E_4)*M_2*r0_2 + 2*(-135 + 414*E_2 + 113*E_4)*M*r0_3 + (132 - 391*E_2)*r0_4) - 2*L_4*r0*(288*M_4 + 8*(12 + 283*E_2)*M_3*r0 - 12*(39 - 118*E_2 + 14*E_4)*M_2*r0_2 - 2*(-135 + 773*E_2 + 84*E_4)*M*r0_3 + 9*(-8 + 37*E_2)*r0_4)) + a_7*M*(6*L_4*(-16*M_3 + 156*M_2*r0 + 6*(13 + E_2)*M*r0_2 + 5*E_2*r0_3) + E_2*r0_3*(-20*(307 + 72*E_2)*M_4 - 4*(667 + 738*E_2)*M_3*r0 + 3*(1901 - 232*E_2)*M_2*r0_2 + 78*(33 + 4*E_2)*M*r0_3 + 111*r0_4) + 2*L_2*r0*(24*(-43 + 106*E_2)*M_4 + 4*(54 + 313*E_2 - 142*E_4)*M_3*r0 + (1002 + 1583*E_2 - 220*E_4)*M_2*r0_2 + 2*(81 + 380*E_2 + E_4)*M*r0_3 + 3*(-24 + 43*E_2)*r0_4)) + a_5*M*r0*(-12*L_6*(10*M_2 + 3*(-5 + 3*E_2)*M*r0 - E_2*r0_2) + E_2*r0_4*(-3588*M_4 - 8*(832 + 279*E_2)*M_3*r0 - 3*(-749 + 544*E_2)*M_2*r0_2 + 6*(391 + 24*E_2)*M*r0_3 + 195*r0_4) + 2*L_4*(1344*M_4 + 96*(-9 + 22*E_2)*M_3*r0 - 2*(30 - 181*E_2 + 84*E_4)*M_2*r0_2 + (342 - 287*E_2 - 84*E_4)*M*r0_3 + 18*(-4 + 11*E_2)*r0_4) + 2*L_2*r0_2*(16*(-81 + 158*E_2)*M_4 - 2*(348 - 775*E_2 + 324*E_4)*M_3*r0 + 4*(267 + 261*E_2 - 139*E_4)*M_2*r0_2 + 2*(105 + 59*E_2 - 79*E_4)*M*r0_3 + (-174 + 259*E_2)*r0_4)) - a_6*E*L*r0*(-6*L_4*M*(40*M_2 + 2*(-22 + 3*E_2)*M*r0 - (3 + E_2)*r0_2) + 2*L_2*M*(3536*M_4 - 4*(121 + 108*E_2)*M_3*r0 + (933 + 250*E_2)*M_2*r0_2 + 2*(523 - 2*E_2)*M*r0_3 + 3*(1 + 40*E_2)*r0_4) + r0_2*((-8732 + 80*E_2)*M_5 + 4*(-1267 + 76*E_2)*M_4*r0 + (6519 + 2456*E_2)*M_3*r0_2 + 2*(1234 + 361*E_2)*M_2*r0_3 + (-181 + 370*E_2)*M*r0_4 + 54*r0_5)) - a_4*E*L*r0_2*(6*L_6*M*(-18*M + r0) + 2*L_4*M*(3248*M_3 - 6*(151 + 34*E_2)*M_2*r0 - (395 + 159*E_2)*M*r0_2 + 3*(50 + 23*E_2)*r0_3) + 2*L_2*r0*(2056*M_5 + 2*(9 + 44*E_2)*M_4*r0 + 3*(-359 + 236*E_2)*M_3*r0_2 + (281 - 348*E_2)*M_2*r0_3 + 2*(75 + 161*E_2)*M*r0_4 + 63*r0_5) + r0_3*(-2536*M_5 - 8*(829 + 174*E_2)*M_4*r0 + 4*(574 + 257*E_2)*M_3*r0_2 + 3*(505 + 66*E_2)*M_2*r0_3 + 6*(-49 + 93*E_2)*M*r0_4 + 99*r0_5))))/(3.*r0_8*expr2_3);\n A12221 = (-96*E*r0*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0))*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/expr2_2;\n A12241 = (-8*(a_11*E_2*M_2*(384*(9 + E_2)*M_2 + (3239 + 408*E_2)*M*r0 + 6*(125 + 18*E_2)*r0_2) - a_10*E*L*M*(48*(144 + 17*E_2)*M_3 + (6599 + 548*E_2)*M_2*r0 + 6*(261 + 14*E_2)*M*r0_2 + 18*E_2*r0_3) + E*L*r0_5*(-2*L_6*M*(1022*M_2 - 1031*M*r0 + 260*r0_2) + 3*r0_6*(124*M_3 + 2*(-57 + 94*E_2)*M_2*r0 - 4*(-6 + 25*E_2)*M*r0_2 + r0_3) + 6*L_2*r0_4*(-342*M_3 + (375 + 188*E_2)*M_2*r0 - 2*(57 + 50*E_2)*M*r0_2 + 6*r0_3) + 2*L_4*r0_2*(-2246*M_3 + 5*(469 + 58*E_2)*M_2*r0 - (647 + 154*E_2)*M*r0_2 + 18*r0_3)) + a*M*r0_3*(-9*E_2*r0_8*(116*M_2 + 12*E_2*M*r0 - 29*r0_2) + 36*L_8*(50*M_2 - 49*M*r0 + 12*r0_2) + 4*L_6*(2*M - r0)*r0*(72*M_2 + (228 + 397*E_2)*M*r0 - 3*(44 + 45*E_2)*r0_2) + 12*L_4*r0_4*((-82 + 670*E_2)*M_2 + (73 - 617*E_2 - 29*E_4)*M*r0 + (-16 + 141*E_2)*r0_2) - 12*L_2*r0_5*(48*M_3 + 6*(10 - 47*E_2)*M_2*r0 + (-90 + 361*E_2 + 36*E_4)*M*r0_2 + 2*(12 - 55*E_2)*r0_3)) + a_9*M*(2*L_2*(72*(24 + E_2)*M_3 + 2*(840 + 712*E_2 + 75*E_4)*M_2*r0 + 3*(136 + 217*E_2 + 24*E_4)*M*r0_2 + 18*E_2*r0_3) + E_2*r0*(-48*(135 + 56*E_2)*M_4 + 4*(1787 - 576*E_2)*M_3*r0 + (14027 + 336*E_2)*M_2*r0_2 + 6*(729 + 70*E_2)*M*r0_3 + 66*r0_4)) - a_2*E*L*r0_3*(2*L_6*M*(2260*M_2 - 1793*M*r0 + 309*r0_2) + 6*L_2*r0_3*(1104*M_4 + 4*(-229 + 64*E_2)*M_3*r0 - 3*(107 + 170*E_2)*M_2*r0_2 + 2*(59 + 156*E_2)*M*r0_3 + 51*r0_4) + 3*r0_5*(-1440*M_4 + 4*(-112 + 3*E_2)*M_3*r0 + 2*(431 - 207*E_2)*M_2*r0_2 + (-271 + 400*E_2)*M*r0_3 + 54*r0_4) + 2*L_4*r0*(5016*M_4 + 22*(19 + 5*E_2)*M_3*r0 - (3873 + 625*E_2)*M_2*r0_2 + 10*(95 + 34*E_2)*M*r0_3 + 87*r0_4)) + a_7*M*(-12*L_4*(28*M_3 + (-248 + 21*E_2)*M_2*r0 - (127 + 28*E_2 + 3*E_4)*M*r0_2 - 6*E_2*r0_3) + 3*E_2*r0_3*(-12*(505 + 96*E_2)*M_4 - 16*(185 + 156*E_2)*M_3*r0 + (5539 - 768*E_2)*M_2*r0_2 + 6*(459 + 28*E_2)*M*r0_3 + 51*r0_4) + 2*L_2*r0*(72*(-45 + 106*E_2)*M_4 - 8*(-75 - 268*E_2 + 192*E_4)*M_3*r0 + 2*(1635 + 1685*E_2 - 381*E_4)*M_2*r0_2 + (564 + 2791*E_2 + 48*E_4)*M*r0_3 + 3*(-82 + 127*E_2)*r0_4)) - a_3*M*r0_2*(108*L_8*M + 3*E_2*r0_6*(2520*M_3 + 4*(271 + 162*E_2)*M_2*r0 + 4*(-249 + 19*E_2)*M*r0_2 - 181*r0_3) - 4*L_6*(1872*M_3 + 3*(-411 + 230*E_2)*M_2*r0 - (114 + 535*E_2)*M*r0_2 + 3*(31 + 48*E_2)*r0_3) + 2*L_2*r0_3*(576*M_4 - 48*(-63 + 97*E_2)*M_3*r0 + 2*(-615 + 631*E_2 + 567*E_4)*M_2*r0_2 + (-1236 + 1921*E_2 + 528*E_4)*M*r0_3 + (534 - 1255*E_2)*r0_4) - 4*L_4*r0*(288*M_4 + 24*(-1 + 155*E_2)*M_3*r0 + (-714 + 965*E_2 - 228*E_4)*M_2*r0_2 + (627 - 2041*E_2 - 161*E_4)*M*r0_3 + 3*(-62 + 193*E_2)*r0_4)) - a_5*M*r0*(12*L_6*(32*M_2 + 2*(-25 + 9*E_2)*M*r0 - 3*E_2*r0_2) + 3*E_2*r0_4*(3252*M_4 + 4*(1631 + 432*E_2)*M_3*r0 + (-1615 + 1392*E_2)*M_2*r0_2 - 2*(1271 + 12*E_2)*M*r0_3 - 123*r0_4) + 4*L_4*(-1944*M_4 - 144*(-10 + 23*E_2)*M_3*r0 + 2*(6 + 87*E_2 + 110*E_4)*M_2*r0_2 + (-609 + 244*E_2 + 65*E_4)*M*r0_3 + 6*(23 - 53*E_2)*r0_4) - 2*L_2*r0_2*(48*(-84 + 173*E_2)*M_4 - 8*(327 - 559*E_2 + 216*E_4)*M_3*r0 - 6*(-598 + 164*E_2 + 349*E_4)*M_2*r0_2 + (852 + 1565*E_2 - 336*E_4)*M*r0_3 + 2*(-318 + 479*E_2)*r0_4)) - a_8*E*L*(2*L_2*M*(-312*M_3 + 2*(1421 + 129*E_2)*M_2*r0 + 3*(475 + 14*E_2)*M*r0_2 + 9*(1 + 2*E_2)*r0_3) + r0*(-288*(45 + E_2)*M_5 + 4*(2087 + 392*E_2)*M_4*r0 + 4*(5202 + 515*E_2)*M_3*r0_2 + (5761 + 898*E_2)*M_2*r0_3 + 6*(-53 + 59*E_2)*M*r0_4 + 18*r0_5)) - a_4*E*L*r0_2*(18*L_6*M*(-16*M + r0) + 2*L_4*(9696*M_4 - 12*(291 + 35*E_2)*M_3*r0 - (830 + 289*E_2)*M_2*r0_2 + 3*(157 + 65*E_2)*M*r0_3 + 9*r0_4) + 3*r0_3*(-2120*M_5 + 4*(-1739 + 102*E_2)*M_4*r0 + 2*(787 + 94*E_2)*M_3*r0_2 + (2045 + 38*E_2)*M_2*r0_3 + 6*(-62 + 101*E_2)*M*r0_4 + 117*r0_5) + 2*L_2*r0*(5880*M_5 + 4*(-163 + 246*E_2)*M_4*r0 + 2*(-2530 + 93*E_2)*M_3*r0_2 + 14*(163 - 45*E_2)*M_2*r0_3 + 6*(58 + 165*E_2)*M*r0_4 + 189*r0_5)) - a_6*E*L*r0*(6*L_4*M*(-142*M_2 + 166*M*r0 + 3*(2 + E_2)*r0_2) + 2*L_2*(10320*M_5 - 16*(167 + 54*E_2)*M_4*r0 + 12*(207 - 7*E_2)*M_3*r0_2 + (3875 + 162*E_2)*M_2*r0_3 + 3*(1 + 124*E_2)*M*r0_4 + 18*r0_5) + r0_2*(12*(-2187 + 212*E_2)*M_5 + 4*(-4325 + 666*E_2)*M_4*r0 + (19571 + 2392*E_2)*M_3*r0_2 + 2*(4349 + 803*E_2)*M_2*r0_3 + 33*(-21 + 38*E_2)*M*r0_4 + 204*r0_5))))/(3.*r0_5*expr2_3);\n A12401 = (-12*E*r0_4*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0)))/expr2_2;\n A12421 = (2*(-3*a_9*E_2*M*((600 + 44*E_2)*M_2 + 6*(45 + 4*E_2)*M*r0 - 5*r0_2) + 3*a_8*E*L*M*(4*(300 + 17*E_2)*M_2 + 2*(281 + 6*E_2)*M*r0 + (-5 + 6*E_2)*r0_2) + a_7*M*(3*L_2*(60*(-10 + E_2)*M_2 - 4*(73 + 52*E_2 + 4*E_4)*M*r0 - 7*E_2*r0_2) + 2*E_2*r0*(12*(141 + 50*E_2)*M_3 + 147*(-17 + 2*E_2)*M_2*r0 - (1871 + 66*E_2)*M*r0_2 + 8*r0_3)) + E*L*r0_4*(6*L_4*M*(386*M_2 - 389*M*r0 + 98*r0_2) + L_2*r0_2*(2352*M_3 - 4*(584 + 141*E_2)*M_2*r0 + 2*(277 + 150*E_2)*M*r0_2 + 13*r0_3) + r0_4*(-372*M_3 + (478 - 564*E_2)*M_2*r0 + 4*(-52 + 75*E_2)*M*r0_2 + 31*r0_3)) + a_5*M*(12*L_4*(16*M_2 + (-64 + 15*E_2)*M*r0 - 3*E_2*r0_2) + 2*E_2*r0_3*(6*(731 + 108*E_2)*M_3 + 2*(-199 + 453*E_2)*M_2*r0 + 3*(-837 + 10*E_2)*M*r0_2 + 40*r0_3) + L_2*r0*(-72*(-47 + 106*E_2)*M_3 + 12*(-187 + 144*E_2 + 60*E_4)*M_2*r0 + 6*(-252 - 151*E_2 + 20*E_4)*M*r0_2 + (552 - 695*E_2)*r0_3)) + a_3*M*r0*(108*L_6*M + 2*E_2*r0_4*(1890*M_3 + 3*(553 + 198*E_2)*M_2*r0 + (-1399 + 114*E_2)*M*r0_2 - 40*r0_3) + L_2*r0_2*(-48*(-87 + 188*E_2)*M_3 + 12*(-53 + 43*E_2 + 60*E_4)*M_2*r0 + 4*(-633 + 844*E_2 + 96*E_4)*M*r0_2 + (948 - 1295*E_2)*r0_3) - 12*L_4*(312*M_3 + 9*(-31 + 30*E_2)*M_2*r0 + (65 - 196*E_2)*M*r0_2 + 2*(-5 + 26*E_2)*r0_3)) - 3*a*M*r0_2*(12*L_6*(50*M_2 - 49*M*r0 + 12*r0_2) + E_2*r0_6*(-348*M_2 + 4*(17 - 9*E_2)*M*r0 + 53*r0_2) + 4*L_4*(2*M - r0)*r0*(12*M_2 + (-7 + 163*E_2)*M*r0 - (1 + 49*E_2)*r0_2) + L_2*r0_3*(-96*M_3 + 32*(-15 + 43*E_2)*M_2*r0 - 2*(-264 + 647*E_2 + 36*E_4)*M*r0_2 + 3*(-44 + 101*E_2)*r0_3)) + a_6*E*L*(3*L_2*M*(-148*M_2 + 4*(119 + 3*E_2)*M*r0 + (1 + 6*E_2)*r0_2) + r0*(144*(-47 + E_2)*M_4 + (7242 - 72*E_2)*M_3*r0 + 2*(2720 + 57*E_2)*M_2*r0_2 + (-421 + 384*E_2)*M*r0_3 + 33*r0_4)) + a_2*E*L*r0_2*(18*L_4*M*(260*M_2 - 209*M*r0 + 37*r0_2) + L_2*r0*(5592*M_4 + 12*(-247 + 73*E_2)*M_3*r0 - 2*(1082 + 591*E_2)*M_2*r0_2 + 21*(31 + 32*E_2)*M*r0_3 + 178*r0_4) + r0_3*(-2160*M_4 + 16*(-223 + 57*E_2)*M_3*r0 - 14*(-227 + 93*E_2)*M_2*r0_2 + (-941 + 948*E_2)*M*r0_3 + 221*r0_4)) + a_4*E*L*r0*(-6*L_4*M*(46*M - 3*r0) + L_2*(10032*M_4 - 24*(233 + 15*E_2)*M_3*r0 - 6*(-284 + 79*E_2)*M_2*r0_2 + 2*(136 + 195*E_2)*M*r0_3 + 33*r0_4) + r0_2*(12*(-1079 + 202*E_2)*M_4 + 2*(-55 + 162*E_2)*M_3*r0 + 2*(3133 - 330*E_2)*M_2*r0_2 + (-887 + 1014*E_2)*M*r0_3 + 223*r0_4))))/(3.*r0_2*expr2_3);\n A12601 = (r0*(-3*a_7*E_2*M*(4*(26 + E_2)*M - 3*r0) + 3*a_6*E*L*M*(208*M + (-3 + 2*E_2)*r0) + a*M*r0*(-4*L_2*(2*M - r0)*r0_2*((-90 + 203*E_2)*M + 42*r0 - 57*E_2*r0) + 3*E_2*r0_4*(116*M_2 + 4*(-13 + 3*E_2)*M*r0 - 3*r0_2) - 12*L_4*(50*M_2 - 49*M*r0 + 12*r0_2)) + a_5*M*(12*L_2*((-26 + 6*E_2)*M - E_2*r0) + E_2*r0*(4*(147 + 44*E_2)*M_2 + 4*(-268 + 7*E_2)*M*r0 + 25*r0_2)) + a_3*M*(36*L_4*M + E_2*r0_3*(16*(86 + 9*E_2)*M_2 + 4*(-219 + 19*E_2)*M*r0 + 79*r0_2) - 4*L_2*r0*(3*(-49 + 106*E_2)*M_2 + (168 - 233*E_2)*M*r0 + 3*(-17 + 20*E_2)*r0_2)) + a_4*E*L*(6*L_2*M*(-16*M + r0) + r0*(24*(-49 + 3*E_2)*M_3 + 2*(872 - 107*E_2)*M_2*r0 + 2*(-95 + 69*E_2)*M*r0_2 + 15*r0_3)) + E*L*r0_3*(2*L_2*M*(442*M_2 - 445*M*r0 + 112*r0_2) + r0_2*(-124*M_3 + 2*(109 - 94*E_2)*M_2*r0 + 4*(-32 + 25*E_2)*M*r0_2 + 25*r0_3)) + a_2*E*L*r0*(2*L_2*M*(812*M_2 - 667*M*r0 + 123*r0_2) + r0_2*(4*(-524 + 149*E_2)*M_3 + 2*(673 - 227*E_2)*M_2*r0 + (-325 + 232*E_2)*M*r0_2 + 76*r0_3))))/(6.*expr2_3);\n A13041 = (-32*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(4*a_7*E_2*M*(3*M_2 - r0_2) + a_6*E*L*M*(-24*M_2 + 2*(-3 + 7*E_2)*M*r0 + (4 + 9*E_2)*r0_2) + E*L*r0_3*(3*L_4*M*(-2*M + r0) + L_2*r0_2*(-30*M_2 + (23 + 6*E_2)*M*r0 - 4*r0_2) - 2*r0_4*(8*M_2 - 3*(2 + E_2)*M*r0 + r0_2)) + a_5*M*(E_2*r0_2*(70*M_2 + 45*M*r0 - 9*r0_2) + 2*L_2*(6*M_2 + (3 - 11*E_2)*M*r0 - 11*E_2*r0_2)) + a_3*M*r0*(6*L_4*(M - 3*E_2*r0) + 10*E_2*r0_3*(3*M_2 + 5*M*r0 - 2*r0_2) + L_2*r0*(24*(1 + E_2)*M_2 + (6 + 53*E_2)*M*r0 - (6 + 47*E_2)*r0_2)) + a_4*E*L*r0*(L_2*M*(2*M + (13 + 9*E_2)*r0) + r0*(-2*(47 + 6*E_2)*M_3 - 51*M_2*r0 + 2*(13 + 12*E_2)*M*r0_2 + 5*r0_3)) + a_2*E*L*r0_2*(9*L_4*M + r0_2*(-8*M_3 - (61 + 30*E_2)*M_2*r0 + (20 + 21*E_2)*M*r0_2 + 3*r0_3) + L_2*(-12*M_3 - (65 + 6*E_2)*M_2*r0 + (28 + 15*E_2)*M*r0_2 + 5*r0_3)) + 3*a*M*r0_3*(E_2*(11*M - 5*r0)*r0_4 + L_2*r0_2*((4 + 27*E_2)*M - (2 + 17*E_2)*r0) + L_4*(4*(1 + E_2)*M - 2*(r0 + 3*E_2*r0)))))/(r0_4*expr2_3);\n A13221 = (-16*(a_7*E_2*M*(12*M_2 - 3*M*r0 - 5*r0_2) + a_6*E*L*M*(-24*M_2 + (-3 + 16*E_2)*M*r0 + (5 + 9*E_2)*r0_2) + E*L*r0_3*(3*L_4*M*(-2*M + r0) + L_2*r0_2*(-26*M_2 + (19 + 6*E_2)*M*r0 - 3*r0_2) - 2*r0_4*(8*M_2 - 3*(2 + E_2)*M*r0 + r0_2)) + a_5*M*(E_2*r0_2*(76*M_2 + 35*M*r0 - 13*r0_2) + L_2*(12*M_2 + (6 - 26*E_2)*M*r0 - 23*E_2*r0_2)) + a_3*M*r0*(6*L_4*(M - 3*E_2*r0) + E_2*r0_3*(48*M_2 + 47*M*r0 - 23*r0_2) + L_2*r0*(24*(1 + E_2)*M_2 + (6 + 35*E_2)*M*r0 - (6 + 47*E_2)*r0_2)) + a_4*E*L*r0*(L_2*M*(4*M + (14 + 9*E_2)*r0) + 2*r0*(-2*(25 + 3*E_2)*M_3 + 2*(-11 + 3*E_2)*M_2*r0 + (13 + 12*E_2)*M*r0_2 + 2*r0_3)) + a_2*E*L*r0_2*(9*L_4*M + r0_2*(-20*M_3 - (53 + 12*E_2)*M_2*r0 + 21*(1 + E_2)*M*r0_2 + 2*r0_3) + L_2*(-12*M_3 - (59 + 6*E_2)*M_2*r0 + 3*(9 + 5*E_2)*M*r0_2 + 4*r0_3)) + 3*a*M*r0_3*(E_2*(11*M - 5*r0)*r0_4 + L_4*(4*(1 + E_2)*M - 2*(r0 + 3*E_2*r0)) + L_2*r0_2*((4 + 21*E_2)*M - 2*(r0 + 7*E_2*r0)))))/(r0*expr2_3);\n A13401 = (-2*r0_2*(6*a_5*E_2*M*(M - r0) + 3*a_4*E*L*M*(-4*M + (2 + 3*E_2)*r0) + a_3*M*(E_2*(41*M - 11*r0)*r0_2 + 6*L_2*(M - 3*E_2*r0)) + E*L*r0_2*(3*L_2*M*(-2*M + r0) - 2*r0_2*(8*M_2 - 3*(2 + E_2)*M*r0 + r0_2)) + a_2*E*L*r0*(9*L_2*M + r0*(-((53 + 6*E_2)*M_2) + (14 + 15*E_2)*M*r0 + 3*r0_2)) + 3*a*M*r0_2*(E_2*(11*M - 5*r0)*r0_2 + L_2*(4*(1 + E_2)*M - 2*(r0 + 3*E_2*r0)))))/expr2_3;\n A14021 = (-48*E*r0*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0))*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/expr2_3;\n A14041 = (-8*(a_11*E_2*M*(24*(57 + 22*E_2)*M_3 + 2*(641 + 276*E_2)*M_2*r0 + 48*(7 + 3*E_2)*M*r0_2 + 21*r0_3) - a_10*E*L*M*(48*(57 + 26*E_2)*M_3 + 2*(1295 + 554*E_2)*M_2*r0 + 6*(108 + 49*E_2)*M*r0_2 + 3*(7 + 12*E_2)*r0_3) + a*M*r0_3*(36*L_8*(26*M_2 - 25*M*r0 + 6*r0_2) + 9*E_2*r0_8*(-25*M_2 + 4*(-10 + 3*E_2)*M*r0 + 25*r0_2) + 3*L_4*r0_4*((88 + 1241*E_2)*M_2 - 4*(29 + 309*E_2 + 10*E_4)*M*r0 + 4*(9 + 74*E_2)*r0_2) - 3*L_2*r0_5*(96*M_3 + (8 - 566*E_2)*M_2*r0 + 4*(-15 + 193*E_2)*M*r0_2 + (16 - 233*E_2)*r0_3) + 4*L_6*r0*(72*M_3 + 2*(153 + 164*E_2)*M_2*r0 - (357 + 320*E_2)*M*r0_2 + 3*(31 + 25*E_2)*r0_3)) - a_2*E*L*r0_3*(8*L_6*M*(293*M_2 - 244*M*r0 + 42*r0_2) + 3*r0_5*(-632*M_4 + (103 - 132*E_2)*M_3*r0 + 2*(29 + 40*E_2)*M_2*r0_2 + (-63 + 166*E_2)*M*r0_3 + 32*r0_4) + 3*L_2*r0_3*(848*M_4 + 2*(113 + 110*E_2)*M_3*r0 - 4*(275 + 73*E_2)*M_2*r0_2 + (169 + 294*E_2)*M*r0_3 + 77*r0_4) + L_4*r0*(4392*M_4 + (2545 - 136*E_2)*M_3*r0 - 2*(2613 + 254*E_2)*M_2*r0_2 + 2*(493 + 182*E_2)*M*r0_3 + 132*r0_4)) + a_9*M*(2*L_2*(36*(19 + 8*E_2)*M_3 + 2*(327 + 371*E_2 + 99*E_4)*M_2*r0 + 12*(13 + 29*E_2 + 8*E_4)*M*r0_2 + 57*E_2*r0_3) + E_2*r0*(-48*(49 + 34*E_2)*M_4 + 3052*M_3*r0 + 8*(674 + 249*E_2)*M_2*r0_2 + 12*(150 + 67*E_2)*M*r0_3 + 153*r0_4)) + a_7*M*(3*L_4*(-112*M_3 + 4*(77 + 3*E_2)*M_2*r0 + 4*(43 + 15*E_2 + 4*E_4)*M*r0_2 + 55*E_2*r0_3) + 3*E_2*r0_3*(-4*(553 + 216*E_2)*M_4 - 24*(37 + 50*E_2)*M_3*r0 + (1975 + 552*E_2)*M_2*r0_2 + 24*(40 + 23*E_2)*M*r0_3 + 114*r0_4) + 2*L_2*r0*(24*(-49 + 150*E_2)*M_4 + 4*(78 + 661*E_2 - 216*E_4)*M_3*r0 + (1164 + 2081*E_2 + 150*E_4)*M_2*r0_2 + (138 + 1079*E_2 + 360*E_4)*M*r0_3 + 6*(-17 + 59*E_2)*r0_4)) + a_3*M*r0_2*(-108*L_8*M + 3*E_2*r0_6*(-1032*M_3 - (437 + 288*E_2)*M_2*r0 + 8*(18 + 29*E_2)*M*r0_2 + 183*r0_3) + 4*L_6*(972*M_3 + 6*(-89 + 59*E_2)*M_2*r0 - (165 + 299*E_2)*M*r0_2 + 3*(19 + 31*E_2)*r0_3) + 2*L_2*r0_3*(-288*M_4 + 48*(-19 + 20*E_2)*M_3*r0 + (408 + 1115*E_2 - 414*E_4)*M_2*r0_2 + 2*(159 - 763*E_2 + 84*E_4)*M*r0_3 + 10*(-15 + 68*E_2)*r0_4) + L_4*r0*(576*M_4 + 48*(29 + 117*E_2)*M_3*r0 + (-1560 + 4297*E_2 - 528*E_4)*M_2*r0_2 - 2*(-126 + 2329*E_2 + 80*E_4)*M*r0_3 + 12*(-7 + 106*E_2)*r0_4)) + a_5*M*r0*(-12*L_6*(32*M_2 + (-8 + 15*E_2)*M*r0 - 6*E_2*r0_2) + 3*E_2*r0_4*(-1404*M_4 - 36*(67 + 32*E_2)*M_3*r0 - 9*(-59 + 24*E_2)*M_2*r0_2 + 16*(46 + 33*E_2)*M*r0_3 + 178*r0_4) + L_4*(4032*M_4 + 24*(-71 + 270*E_2)*M_3*r0 - 4*(177 - 327*E_2 + 116*E_4)*M_2*r0_2 + 2*(258 - 487*E_2 + 4*E_4)*M*r0_3 + 3*(-64 + 309*E_2)*r0_4) + L_2*r0_2*(96*(-31 + 60*E_2)*M_4 - 8*(213 - 889*E_2 + 288*E_4)*M_3*r0 - 6*(-414 - 455*E_2 + 170*E_4)*M_2*r0_2 + 2*(210 - 155*E_2 + 432*E_4)*M*r0_3 + (-456 + 1255*E_2)*r0_4)) - a_8*E*L*(2*L_2*M*(-240*M_3 + 2*(463 + 201*E_2)*M_2*r0 + 3*(177 + 55*E_2)*M*r0_2 + 3*(13 + 12*E_2)*r0_3) + r0*(-96*(49 + 9*E_2)*M_5 + 4*(919 + 874*E_2)*M_4*r0 + 2*(3903 + 2402*E_2)*M_3*r0_2 + 2*(1096 + 775*E_2)*M_2*r0_3 + 6*(3 + 41*E_2)*M*r0_4 + 15*r0_5)) - a_6*E*L*r0*(3*L_4*M*(-252*M_2 + 2*(23 + 6*E_2)*M*r0 + (31 + 12*E_2)*r0_2) + 2*L_2*(5232*M_5 + (44 - 648*E_2)*M_4*r0 + 3*(107 + 362*E_2)*M_3*r0_2 + (991 + 624*E_2)*M_2*r0_3 + 3*(57 + 83*E_2)*M*r0_4 + 15*r0_5) + r0_2*(-108*(89 + 12*E_2)*M_5 + 20*(-293 + 42*E_2)*M_4*r0 + (6187 + 6632*E_2)*M_3*r0_2 + 2*(1246 + 1453*E_2)*M_2*r0_3 + 6*(24 + 107*E_2)*M*r0_4 + 144*r0_5)) - a_4*E*L*r0_2*(12*L_6*M*(-23*M + 3*r0) + L_4*(9936*M_4 - 12*(225 + 38*E_2)*M_3*r0 - 2*(1081 + 68*E_2)*M_2*r0_2 + 12*(55 + 21*E_2)*M*r0_3 + 15*r0_4) + 3*r0_3*(-952*M_5 - 76*(29 + 12*E_2)*M_4*r0 + 2*(277 + 418*E_2)*M_3*r0_2 + (233 + 702*E_2)*M_2*r0_3 + 2*(-13 + 135*E_2)*M*r0_4 + 78*r0_5) + L_2*r0*(5040*M_5 - 8*(-508 + 99*E_2)*M_4*r0 + 4*(-1028 + 489*E_2)*M_3*r0_2 + 2*(-788 + 405*E_2)*M_2*r0_3 + 3*(289 + 348*E_2)*M*r0_4 + 276*r0_5)) + E*L*r0_5*(-4*L_6*M*(230*M_2 - 233*M*r0 + 59*r0_2) + 3*L_2*r0_4*(-364*M_3 + 2*(203 + 80*E_2)*M_2*r0 - 2*(61 + 44*E_2)*M*r0_2 + 5*r0_3) + L_4*r0_2*(-2114*M_3 + (2213 + 272*E_2)*M_2*r0 - 2*(301 + 74*E_2)*M*r0_2 + 12*r0_3) + 3*r0_6*(18*M_3 - 4*(3 + 10*E_2)*M*r0_2 + 3*r0_3 + 3*M_2*(r0 + 24*E_2*r0)))))/(3.*r0_5*expr2_4);\n A14201 = (-12*E*r0_4*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0)))/expr2_3;\n A14221 = (-4*(a_9*E_2*M*((234 + 80*E_2)*M_2 + 6*(19 + 7*E_2)*M*r0 + 7*r0_2) - a_8*E*L*M*(4*(117 + 44*E_2)*M_2 + (226 + 87*E_2)*M*r0 + (7 + 15*E_2)*r0_2) - E*L*r0_4*(L_4*M*(340*M_2 - 344*M*r0 + 87*r0_2) + r0_4*(-18*M_3 + (17 - 72*E_2)*M_2*r0 + 8*(-1 + 5*E_2)*M*r0_2 + 2*r0_3) + L_2*r0_2*(374*M_3 - (379 + 80*E_2)*M_2*r0 + 4*(23 + 11*E_2)*M*r0_2 + 2*r0_3)) + a_7*M*(L_2*(6*(39 + 8*E_2)*M_2 + 4*(28 + 31*E_2 + 7*E_4)*M*r0 + 37*E_2*r0_2) + E_2*r0*(-4*(101 + 62*E_2)*M_3 + (625 + 136*E_2)*M_2*r0 + 2*(231 + 95*E_2)*M*r0_2 + 39*r0_3)) + a_5*M*(L_4*(-64*M_2 + 4*(19 - 6*E_2)*M*r0 + 30*E_2*r0_2) + E_2*r0_3*(-8*(124 + 45*E_2)*M_3 + (121 - 128*E_2)*M_2*r0 + 10*(48 + 29*E_2)*M*r0_2 + 57*r0_3) + L_2*r0*(4*(-101 + 300*E_2)*M_3 + 2*(145 + 56*E_2 - 68*E_4)*M_2*r0 + (160 + 55*E_2 + 72*E_4)*M*r0_2 + 2*(-38 + 93*E_2)*r0_3)) + a_3*M*r0*(-36*L_6*M + E_2*r0_4*(-516*M_3 - 9*(41 + 24*E_2)*M_2*r0 + 2*(81 + 89*E_2)*M*r0_2 + 85*r0_3) + 4*L_4*(162*M_3 + (-115 + 132*E_2)*M_2*r0 + (3 - 89*E_2)*M*r0_2 + (-1 + 31*E_2)*r0_3) + L_2*r0_2*(16*(-31 + 69*E_2)*M_3 + (80 + 393*E_2 - 168*E_4)*M_2*r0 + 4*(69 - 165*E_2 + 11*E_4)*M*r0_2 + 2*(-55 + 123*E_2)*r0_3)) + a*M*r0_2*(12*L_6*(26*M_2 - 25*M*r0 + 6*r0_2) + 3*E_2*r0_6*(-25*M_2 + 6*(-5 + 2*E_2)*M*r0 + 20*r0_2) + 2*L_4*r0*(24*M_3 + 8*(5 + 32*E_2)*M_2*r0 - 2*(31 + 113*E_2)*M*r0_2 + (18 + 47*E_2)*r0_3) + L_2*r0_3*(-48*M_3 + (-128 + 595*E_2)*M_2*r0 + 3*(48 - 205*E_2)*M*r0_2 + (-34 + 151*E_2)*r0_3)) - a_6*E*L*(L_2*M*(-112*M_2 + (155 + 48*E_2)*M*r0 + (22 + 15*E_2)*r0_2) + r0*(-8*(101 + 12*E_2)*M_4 + 5*(183 + 98*E_2)*M_3*r0 + (643 + 322*E_2)*M_2*r0_2 + 2*(-6 + 43*E_2)*M*r0_3 + 8*r0_4)) - a_2*E*L*r0_2*(2*L_4*M*(400*M_2 - 332*M*r0 + 57*r0_2) + L_2*r0*(804*M_4 + (45 + 4*E_2)*M_3*r0 - 4*(181 + 16*E_2)*M_2*r0_2 + (131 + 111*E_2)*M*r0_3 + 39*r0_4) + r0_3*(-316*M_4 - (241 + 18*E_2)*M_3*r0 + (177 + 40*E_2)*M_2*r0_2 + 8*(-12 + 17*E_2)*M*r0_3 + 42*r0_4)) - a_4*E*L*r0*(5*L_4*M*(-16*M + 3*r0) + L_2*(1696*M_4 - 6*(117 + 16*E_2)*M_3*r0 + 5*(-13 + 16*E_2)*M_2*r0_2 + 2*(51 + 41*E_2)*M*r0_3 + 8*r0_4) + r0_2*(-12*(124 + E_2)*M_4 + 12*(-2 + 25*E_2)*M_3*r0 + (505 + 323*E_2)*M_2*r0_2 + (-47 + 167*E_2)*M*r0_3 + 48*r0_4))))/(r0_2*expr2_4);\n A14401 = (r0*(-9*a_7*E_2*M*(4*(10 + 3*E_2)*M + 3*r0) + 9*a_6*E*L*M*(80*M + 24*E_2*M + 3*r0 + 6*E_2*r0) - a_5*M*(36*L_2*(10*M + 3*E_2*r0) + E_2*r0*(-48*(13 + 7*E_2)*M_2 + 12*(88 + 31*E_2)*M*r0 + 91*r0_2)) + a_3*M*(108*L_4*M + E_2*r0_3*(3*(409 + 144*E_2)*M_2 - 2*(275 + 186*E_2)*M*r0 - 22*r0_2) - 12*L_2*r0*(2*(-26 + 75*E_2)*M_2 + (61 - 88*E_2)*M*r0 + 3*(-7 + 11*E_2)*r0_2)) - 3*a*M*r0*(12*L_4*(26*M_2 - 25*M*r0 + 6*r0_2) + E_2*r0_4*(-75*M_2 + 2*(-25 + 18*E_2)*M*r0 + 40*r0_2) + 4*L_2*r0_2*(2*(-31 + 78*E_2)*M_2 + (57 - 128*E_2)*M*r0 + (-13 + 24*E_2)*r0_2)) + E*L*r0_3*(6*L_2*M*(192*M_2 - 194*M*r0 + 49*r0_2) + r0_2*(-54*M_3 + (131 - 216*E_2)*M_2*r0 + 8*(-13 + 15*E_2)*M*r0_2 + 26*r0_3)) + a_4*E*L*(-54*L_2*M*(4*M - r0) + r0*(-24*(52 + 3*E_2)*M_3 + 12*(149 + 40*E_2)*M_2*r0 + 2*(-67 + 126*E_2)*M*r0_2 + 27*r0_3)) + a_2*E*L*r0*(24*L_2*M*(103*M_2 - 86*M*r0 + 15*r0_2) + r0_2*(9*(-219 + 32*E_2)*M_3 + 1006*M_2*r0 + 6*(-58 + 53*E_2)*M*r0_2 + 134*r0_3))))/(6.*expr2_4);\n A15021 = (-8*(a_7*E_2*M*(12*M_2 - 3*M*r0 - 5*r0_2) + a_6*E*L*M*(-24*M_2 + (-3 + 16*E_2)*M*r0 + (5 + 9*E_2)*r0_2) + E*L*r0_3*(3*L_4*M*(-2*M + r0) - r0_4*(14*M_2 - 3*(3 + 2*E_2)*M*r0 + r0_2) - 2*L_2*r0_2*(12*M_2 - (8 + 3*E_2)*M*r0 + r0_2)) + a_5*M*(2*E_2*r0_2*(37*M_2 + 18*M*r0 - 6*r0_2) + L_2*(12*M_2 + (6 - 26*E_2)*M*r0 - 23*E_2*r0_2)) + a_3*M*r0*(6*L_4*(M - 3*E_2*r0) + E_2*r0_3*(42*M_2 + 49*M*r0 - 19*r0_2) + 2*L_2*r0*(12*(1 + E_2)*M_2 + (3 + 17*E_2)*M*r0 - (3 + 23*E_2)*r0_2)) + a_2*E*L*r0_2*(9*L_4*M + r0_2*(-16*M_3 - 4*(14 + 3*E_2)*M_2*r0 + (19 + 21*E_2)*M*r0_2 + 3*r0_3) + L_2*(-12*M_3 - 2*(29 + 3*E_2)*M_2*r0 + (26 + 15*E_2)*M*r0_2 + 4*r0_3)) + a_4*E*L*r0*(L_2*M*(4*M + (14 + 9*E_2)*r0) + r0*(-2*(49 + 6*E_2)*M_3 + 3*(-15 + 4*E_2)*M_2*r0 + (25 + 24*E_2)*M*r0_2 + 4*r0_3)) + 3*a*M*r0_3*(2*E_2*(5*M - 2*r0)*r0_4 + L_2*r0_2*(4*(1 + 5*E_2)*M - (2 + 13*E_2)*r0) + L_4*(4*(1 + E_2)*M - 2*(r0 + 3*E_2*r0)))))/(r0*expr2_4);\n A15201 = (-2*r0_2*(6*a_5*E_2*M*(M - r0) + 3*a_4*E*L*M*(-4*M + (2 + 3*E_2)*r0) + 2*a_3*M*(5*E_2*(4*M - r0)*r0_2 + 3*L_2*(M - 3*E_2*r0)) + 6*a*M*r0_2*(E_2*(5*M - 2*r0)*r0_2 + L_2*(2*(1 + E_2)*M - (1 + 3*E_2)*r0)) + E*L*r0_2*(3*L_2*M*(-2*M + r0) - r0_2*(14*M_2 - 3*(3 + 2*E_2)*M*r0 + r0_2)) + a_2*E*L*r0*(9*L_2*M + r0*(-2*(26 + 3*E_2)*M_2 + (13 + 15*E_2)*M*r0 + 3*r0_2))))/expr2_4;\n A16001 = (-4*E*r0_4*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0)))/expr2_4;\n A16021 = (-2*(3*a_9*E_2*M*(4*(28 + 23*E_2)*M_2 + 2*(31 + 24*E_2)*M*r0 + 11*r0_2) - 3*a_8*E*L*M*(4*(56 + 53*E_2)*M_2 + 2*(57 + 56*E_2)*M*r0 + (11 + 18*E_2)*r0_2) - E*L*r0_4*(2*L_4*M*(290*M_2 - 293*M*r0 + 74*r0_2) + M*r0_4*(26*M_2 - (53 + 92*E_2)*M*r0 + 4*(5 + 13*E_2)*r0_2) + L_2*r0_2*(654*M_3 - (639 + 124*E_2)*M_2*r0 + 4*(33 + 17*E_2)*M*r0_2 + 12*r0_3)) + a_7*M*(3*L_2*(28*(4 + 3*E_2)*M_2 + 4*(13 + 24*E_2 + 8*E_4)*M*r0 + 47*E_2*r0_2) + 2*E_2*r0*(-4*(63 + 74*E_2)*M_3 + 10*(42 + 37*E_2)*M_2*r0 + (309 + 358*E_2)*M*r0_2 + 81*r0_3)) + a*M*r0_2*(36*L_6*(18*M_2 - 17*M*r0 + 4*r0_2) + 3*E_2*r0_6*(-M_2 + 2*(-61 + 30*E_2)*M*r0 + 56*r0_2) + 4*L_4*r0*(24*M_3 + 2*(51 + 91*E_2)*M_2*r0 - (123 + 181*E_2)*M*r0_2 + 3*(11 + 13*E_2)*r0_3) + L_2*r0_3*(-96*M_3 + (-48 + 829*E_2)*M_2*r0 + 2*(36 - 451*E_2 + 36*E_4)*M*r0_2 + 12*(-1 + 17*E_2)*r0_3)) + a_3*M*r0*(-108*L_6*M + 2*E_2*r0_4*(-399*M_3 - 6*(40 + 39*E_2)*M_2*r0 + 2*(-48 + 197*E_2)*M*r0_2 + 153*r0_3) + 4*L_4*(336*M_3 + 3*(-61 + 86*E_2)*M_2*r0 - (51 + 154*E_2)*M*r0_2 + 6*(1 + 11*E_2)*r0_3) + L_2*r0_2*(16*(-39 + 86*E_2)*M_3 + (132 + 1643*E_2 - 432*E_4)*M_2*r0 + 2*(138 - 661*E_2 + 152*E_4)*M*r0_2 + 6*(-22 + 83*E_2)*r0_3)) + a_5*M*(-12*L_4*(16*M_2 + (-4 + 3*E_2)*M*r0 - 9*E_2*r0_2) + E_2*r0_3*(-6*(187 + 168*E_2)*M_3 + (195 + 92*E_2)*M_2*r0 + 118*(3 + 10*E_2)*M*r0_2 + 267*r0_3) + L_2*r0*(24*(-21 + 94*E_2)*M_3 + 4*(105 + 260*E_2 - 76*E_4)*M_2*r0 + 8*(18 - 9*E_2 + 41*E_4)*M*r0_2 + 3*(-40 + 163*E_2)*r0_3)) - a_6*E*L*(3*L_2*M*(-100*M_2 + 12*(4 + 5*E_2)*M*r0 + (29 + 18*E_2)*r0_2) + r0*(-144*(7 + 3*E_2)*M_4 + 4*(315 + 499*E_2)*M_3*r0 + 2*(392 + 625*E_2)*M_2*r0_2 + 3*(31 + 68*E_2)*M*r0_3 + 21*r0_4)) - a_2*E*L*r0_2*(2*L_4*M*(820*M_2 - 695*M*r0 + 111*r0_2) + r0_3*(-524*M_4 + (83 - 476*E_2)*M_3*r0 + (-217 + 722*E_2)*M_2*r0_2 + 40*(-2 + 5*E_2)*M*r0_3 + 84*r0_4) + L_2*r0*(1336*M_4 + (1075 - 284*E_2)*M_3*r0 + 2*(-1014 + 83*E_2)*M_2*r0_2 + 2*(141 + 100*E_2)*M*r0_3 + 84*r0_4)) - a_4*E*L*r0*(-6*L_4*M*(38*M - 9*r0) + L_2*(3440*M_4 - 12*(79 + 22*E_2)*M_3*r0 + 10*(-81 + 49*E_2)*M_2*r0_2 + 6*(51 + 31*E_2)*M*r0_3 + 21*r0_4) + r0_2*(-2*(873 + 436*E_2)*M_4 + (-49 + 1068*E_2)*M_3*r0 + 4*(17 + 396*E_2)*M_2*r0_2 + 2*(43 + 149*E_2)*M*r0_3 + 105*r0_4))))/(3.*r0_2*expr2_5);\n A16201 = (r0*(-3*a_7*E_2*M*((56 + 44*E_2)*M + 15*r0) + 3*a_6*E*L*M*(16*(7 + 6*E_2)*M + (15 + 22*E_2)*r0) - a_5*M*(12*L_2*(2*(7 + 3*E_2)*M + 11*E_2*r0) + E_2*r0*(-4*(63 + 68*E_2)*M_2 + 4*(88 + 131*E_2)*M*r0 + 141*r0_2)) + a_3*M*(108*L_4*M + E_2*r0_3*((317 + 432*E_2)*M_2 + (74 - 572*E_2)*M*r0 - 102*r0_2) - 4*L_2*r0*(3*(-21 + 94*E_2)*M_2 + (78 - 113*E_2)*M*r0 + 33*(-1 + 2*E_2)*r0_2)) + a*M*r0*(3*E_2*r0_4*(M_2 + (98 - 60*E_2)*M*r0 - 44*r0_2) - 36*L_4*(18*M_2 - 17*M*r0 + 4*r0_2) - 4*L_2*r0_2*((-72 + 214*E_2)*M_2 + 5*(12 - 37*E_2)*M*r0 + 3*(-4 + 11*E_2)*r0_2)) + E*L*r0_3*(2*L_2*M*(322*M_2 - 325*M*r0 + 82*r0_2) + r0_2*(26*M_3 - (5 + 92*E_2)*M_2*r0 + 4*(-7 + 13*E_2)*M*r0_2 + 12*r0_3)) + a_4*E*L*(6*L_2*M*(-32*M + 11*r0) + r0*(-168*(3 + E_2)*M_3 + 2*(332 + 433*E_2)*M_2*r0 + 6*(1 + 31*E_2)*M*r0_2 + 21*r0_3)) + a_2*E*L*r0*(2*L_2*M*(836*M_2 - 703*M*r0 + 111*r0_2) + r0_2*(-55*(11 + 4*E_2)*M_3 + 2*(42 + 241*E_2)*M_2*r0 + 4*(-37 + 43*E_2)*M*r0_2 + 96*r0_3))))/(6.*expr2_5);\n A17001 = (-2*r0_2*(2*a_5*E_2*M*(M - r0) + a_4*E*L*M*(-4*M + (2 + 3*E_2)*r0) + a_3*M*(E_2*(13*M - 3*r0)*r0_2 + 2*L_2*(M - 3*E_2*r0)) + E*L*M*r0_2*(L_2*(-2*M + r0) + 2*r0_2*(-2*M + r0 + E_2*r0)) + a_2*E*L*r0*(3*L_2*M + r0*(-((17 + 2*E_2)*M_2) + (4 + 5*E_2)*M*r0 + r0_2)) + a*M*r0_2*(3*E_2*(3*M - r0)*r0_2 + L_2*(4*(1 + E_2)*M - 2*(r0 + 3*E_2*r0)))))/expr2_5;\n A18001 = (r0*(-3*a_7*E_2*M*((4 + 8*E_2)*M + 3*r0) + 3*a_6*E*L*M*(2*(4 + 9*E_2)*M + (3 + 4*E_2)*r0) + E*L*M*(2*M - r0)*r0_3*(16*L_2*(2*M - r0) + r0_2*(5*M - 2*(2 + E_2)*r0)) - a*M*r0*(6*L_4*(14*M_2 - 13*M*r0 + 3*r0_2) + 3*E_2*r0_4*(5*M_2 + 4*(-5 + 3*E_2)*M*r0 + 8*r0_2) + 2*L_2*r0_2*((-6 + 28*E_2)*M_2 + (3 - 26*E_2)*M*r0 + 3*E_2*r0_2)) + a_3*M*(18*L_4*M + E_2*r0_3*((-17 + 72*E_2)*M_2 + 2*(29 - 56*E_2)*M*r0 - 24*r0_2) - 2*L_2*r0*((-6 + 66*E_2)*M_2 + (9 - 11*E_2)*M*r0 + 3*(-2 + 5*E_2)*r0_2)) + a_4*E*L*(-6*L_2*M*(5*M - 2*r0) + r0*(-12*(2 + 3*E_2)*M_3 + 2*(10 + 89*E_2)*M_2*r0 + 12*(1 + 2*E_2)*M*r0_2 + 3*r0_3)) + a_2*E*L*r0*(2*L_2*M*(106*M_2 - 89*M*r0 + 12*r0_2) + r0_2*((5 - 80*E_2)*M_3 + 2*(-27 + 62*E_2)*M_2*r0 + 2*(-4 + 7*E_2)*M*r0_2 + 12*r0_3)) - a_5*M*(6*L_2*((2 + 3*E_2)*M + 4*E_2*r0) + E_2*r0*(-4*(3 + 10*E_2)*M_2 + 27*r0_2 + 2*M*(r0 + 50*E_2*r0)))))/(3.*expr2_6);\n }\n\n /* A_{t,theta} */\n {\n A20161 = (128*E*expr1_3*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/(r0_6*(a_2 + r0*(-2*M + r0)));\n A20341 = (96*E*expr1_2*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/(r0_3*(a_2 + r0*(-2*M + r0)));\n A20521 = (24*E*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/(a_2 + r0*(-2*M + r0));\n A20701 = 2*E*r0_3*(-(E*M*(a_3 - 3*a*r0_2)) + L*(a_2*M + 2*r0_2*(-M + r0)) - (L*M*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/(a_2 + r0*(-2*M + r0)));\n A21161 = (64*expr1_2*(a_8*E*L*M*((8 - 24*E_2)*M_2 - 2*(1 + E_2)*r0_2 + M*(r0 - 11*E_2*r0)) + a_9*E_2*M*(4*(-1 + 3*E_2)*M_2 + 2*r0_2 + M*(r0 + 6*E_2*r0)) + a_6*E*L*M*(L_2*(24*M_2 + (17 + 6*E_2)*M*r0 - 2*(2 + E_2)*r0_2) + r0*(16*(-1 + 2*E_2)*M_3 - 2*(4 + 57*E_2)*M_2*r0 + (6 - 49*E_2)*M*r0_2 + (-1 + E_2)*r0_3)) - a_5*M*(2*L_4*(6*M_2 + (4 + 9*E_2)*M*r0 - 2*E_2*r0_2) + E_2*r0_3*(12*(1 + 4*E_2)*M_3 + 4*(1 - 5*E_2)*M_2*r0 - (19 + 52*E_2)*M*r0_2 - 13*r0_3) + 2*L_2*r0*(-4*M_3 - 2*(2 + 25*E_2)*M_2*r0 + (4 + 7*E_2)*M*r0_2 + (2 + E_2)*r0_3)) + a_4*E*L*r0*(2*L_4*M*(9*M - r0) + L_2*M*(-32*M_3 - 2*(17 + 4*E_2)*M_2*r0 + (39 + 10*E_2)*M*r0_2 + 5*r0_3) + r0_2*(4*(7 + 38*E_2)*M_4 - 4*(3 + 13*E_2)*M_3*r0 - (23 + 97*E_2)*M_2*r0_2 + (8 + 13*E_2)*M*r0_3 + 2*r0_4)) + a_2*E*L*r0_2*(2*L_4*M*(-12*M_2 + 9*M*r0 + r0_2) + L_2*M*r0*(56*M_3 + 4*(-11 + 2*E_2)*M_2*r0 - 2*(10 + E_2)*M*r0_2 + 3*(7 + 2*E_2)*r0_3) + r0_3*(-8*M_4 + 6*(8 + 13*E_2)*M_3*r0 - (40 + 67*E_2)*M_2*r0_2 + 3*(1 + 5*E_2)*M*r0_3 + 4*r0_4)) + a_7*M*(E_2*r0*((8 - 16*E_2)*M_3 + 44*E_2*M_2*r0 + (3 + 32*E_2)*M*r0_2 + 7*r0_3) - 2*L_2*(2*M_2 - 3*E_2*r0_2 + M*(r0 + 2*E_2*r0))) + E*L*r0_4*(4*L_4*M*(2*M_2 - 3*M*r0 + r0_2) + 2*L_2*M*r0_2*(16*M_2 - (20 + 3*E_2)*M*r0 + 2*(3 + E_2)*r0_2) + r0_4*(8*M_3 + (-4 + 5*E_2)*M*r0_2 + 2*r0_3 - 4*M_2*(r0 + 2*E_2*r0))) - a_3*M*r0*(6*L_6*M + E_2*r0_4*(4*M_3 + 4*(11 + 3*E_2)*M_2*r0 - (17 + 32*E_2)*M*r0_2 - 13*r0_3) + 2*L_2*r0_2*((8 + 80*E_2)*M_3 - 2*(5 + 19*E_2)*M_2*r0 - (3 + 34*E_2)*M*r0_2 + (4 + 15*E_2)*r0_3) + L_4*(-16*M_3 + 8*(1 + 3*E_2)*M*r0_2 + 2*(2 + E_2)*r0_3 - 4*M_2*(r0 + 6*E_2*r0))) - a*M*r0_2*(4*L_6*M*(-2*M + r0) + E_2*r0_6*(20*M_2 - 6*E_2*M*r0 - 5*r0_2) + 2*L_2*r0_4*((4 + 56*E_2)*M_2 - (6 + 47*E_2)*M*r0 + (2 + 11*E_2)*r0_2) + 2*L_4*r0_2*(2*r0*(-2*M + r0) + E_2*(8*M_2 - 7*M*r0 + 3*r0_2)))))/(r0_8*expr2_2);\n A21341 = (16*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-(a_8*E*L*M*(24*(-1 + 3*E_2)*M_2 + 44*E_2*M*r0 + (7 + 9*E_2)*r0_2)) + a_9*E_2*M*(12*(-1 + 3*E_2)*M_2 + 7*r0_2 + 6*M*(r0 + 3*E_2*r0)) + a_7*M*(L_2*(-12*M_2 + 2*(-3 + 5*E_2 + 3*E_4)*M*r0 + 25*E_2*r0_2) + 2*E_2*r0*((12 - 24*E_2)*M_3 + 6*(-1 + 11*E_2)*M_2*r0 + (1 + 48*E_2)*M*r0_2 + 10*r0_3)) + a_5*M*(-6*L_4*(6*M_2 + 2*(2 + 3*E_2)*M*r0 - 3*E_2*r0_2) + 2*E_2*r0_3*(-12*(1 + 6*E_2)*M_3 + 2*(4 + 15*E_2)*M_2*r0 + (25 + 78*E_2)*M*r0_2 + 17*r0_3) + L_2*r0*(24*M_3 - 8*(-3 - 29*E_2 + E_4)*M_2*r0 + 2*(-12 - 13*E_2 + 13*E_4)*M*r0_2 + (-12 + 7*E_2)*r0_3)) + a_2*E*L*r0_2*(L_4*M*(-64*M_2 + 48*M*r0 + 7*r0_2) + r0_4*(4*(26 + 51*E_2)*M_3 - 2*(53 + 92*E_2)*M_2*r0 + (13 + 44*E_2)*M*r0_2 + 10*r0_3) + L_2*M*r0*(144*M_3 + 40*(-3 + 2*E_2)*M_2*r0 - 2*(25 + 28*E_2)*M*r0_2 + (58 + 21*E_2)*r0_3)) - a_4*E*L*r0*(L_4*(-48*M_2 + 9*M*r0) + r0_2*(-72*(1 + 6*E_2)*M_4 + 4*(13 + 32*E_2)*M_3*r0 + 4*(10 + 69*E_2)*M_2*r0_2 - (23 + 34*E_2)*M*r0_3 - 2*r0_4) + L_2*(96*M_4 + 68*M_3*r0 + 2*(-57 + 14*E_2)*M_2*r0_2 + (-8 + E_2)*M*r0_3 + 2*r0_4)) - a_6*E*L*(L_2*M*(-72*M_2 - 40*M*r0 + (16 + 9*E_2)*r0_2) + r0*((48 - 96*E_2)*M_4 + 4*(3 + 77*E_2)*M_3*r0 + 2*(-11 + 80*E_2)*M_2*r0_2 + (9 + 4*E_2)*M*r0_3 + 2*r0_4)) + E*L*r0_4*(2*L_4*M*(16*M_2 - 22*M*r0 + 7*r0_2) + L_2*r0_2*(88*M_3 - 4*(26 + 5*E_2)*M_2*r0 + 13*(2 + E_2)*M*r0_2 + 2*r0_3) + 3*r0_4*(8*M_3 + (-4 + 5*E_2)*M*r0_2 + 2*r0_3 - 4*M_2*(r0 + 2*E_2*r0))) - a_3*M*r0*(18*L_6*M + 6*E_2*r0_4*(8*M_3 + 6*(3 + E_2)*M_2*r0 - (9 + 16*E_2)*M*r0_2 - 6*r0_3) + L_2*r0_2*(48*(1 + 9*E_2)*M_3 + 4*(-15 - 47*E_2 + 6*E_4)*M_2*r0 - 2*(9 + 91*E_2 + 13*E_4)*M*r0_2 + 3*(8 + 23*E_2)*r0_3) + L_4*(-48*M_3 + 2*(12 + 17*E_2)*M*r0_2 + 6*(2 + E_2)*r0_3 - 12*M_2*(r0 + 4*E_2*r0))) + a*M*r0_2*(12*L_6*M*(2*M - r0) + 3*E_2*r0_6*(-20*M_2 + 6*E_2*M*r0 + 5*r0_2) - 3*L_2*r0_4*(4*(2 + 25*E_2)*M_2 - 2*(6 + 39*E_2 + E_4)*M*r0 + (4 + 17*E_2)*r0_2) - 2*L_4*r0_2*(6*r0*(-2*M + r0) + E_2*(44*M_2 - 37*M*r0 + 12*r0_2)))))/(r0_5*expr2_2);\n A21521 = (4*(-(a_8*E*L*M*(24*(-1 + 3*E_2)*M_2 + (3 + 55*E_2)*M*r0 + 4*(2 + 3*E_2)*r0_2)) + a_9*E_2*M*(12*(-1 + 3*E_2)*M_2 + 8*r0_2 + 9*M*(r0 + 2*E_2*r0)) + a_7*M*(L_2*(-12*M_2 + 2*(-3 + 16*E_2 + 6*E_4)*M*r0 + 32*E_2*r0_2) + E_2*r0*((24 - 48*E_2)*M_3 + 12*(-2 + 11*E_2)*M_2*r0 + (-5 + 96*E_2)*M*r0_2 + 19*r0_3)) + a_5*M*(-6*L_4*(6*M_2 + (4 + 3*E_2)*M*r0 - 4*E_2*r0_2) + E_2*r0_3*(-12*(1 + 12*E_2)*M_3 + 4*(11 + 15*E_2)*M_2*r0 + (43 + 156*E_2)*M*r0_2 + 29*r0_3) + 2*L_2*r0*(12*M_3 + 2*(6 + 41*E_2 - 4*E_4)*M_2*r0 + (-12 - 5*E_2 + 26*E_4)*M*r0_2 + 2*(-3 + 5*E_2)*r0_3)) - a_4*E*L*r0*(-6*L_4*M*(7*M - 2*r0) + r0_2*(-12*(5 + 34*E_2)*M_4 + 4*(17 + 25*E_2)*M_3*r0 + (11 + 261*E_2)*M_2*r0_2 - (22 + 29*E_2)*M*r0_3 + 2*r0_4) + L_2*(96*M_4 + (34 - 24*E_2)*M_3*r0 + (-111 + 86*E_2)*M_2*r0_2 + (-1 + 2*E_2)*M*r0_3 + 4*r0_4)) - a_6*E*L*(L_2*M*(-72*M_2 + (-29 + 18*E_2)*M*r0 + 4*(5 + 3*E_2)*r0_2) + r0*((48 - 96*E_2)*M_4 + 274*E_2*M_3*r0 + (-26 + 173*E_2)*M_2*r0_2 + (15 + 11*E_2)*M*r0_3 + 4*r0_4)) + a_2*E*L*r0_2*(L_4*(-56*M_3 + 42*M_2*r0 + 8*M*r0_2) + L_2*M*r0*(120*M_3 + 4*(-27 + 34*E_2)*M_2*r0 - 2*(20 + 53*E_2)*M*r0_2 + (53 + 24*E_2)*r0_3) + r0_3*(24*M_4 + 2*(32 + 87*E_2)*M_3*r0 - (92 + 167*E_2)*M_2*r0_2 + (17 + 43*E_2)*M*r0_3 + 8*r0_4)) + E*L*r0_4*(4*L_4*M*(10*M_2 - 13*M*r0 + 4*r0_2) + 2*L_2*r0_2*(40*M_3 - 11*(4 + E_2)*M_2*r0 + (8 + 7*E_2)*M*r0_2 + 2*r0_3) + 3*r0_4*(8*M_3 + (-4 + 5*E_2)*M*r0_2 + 2*r0_3 - 4*M_2*(r0 + 2*E_2*r0))) + a_3*M*r0*(-18*L_6*M + 3*E_2*r0_4*(-28*M_3 - 4*(7 + 3*E_2)*M_2*r0 + (19 + 32*E_2)*M*r0_2 + 11*r0_3) - 2*L_2*r0_2*(24*(1 + 8*E_2)*M_3 + 2*(-15 - 37*E_2 + 12*E_4)*M_2*r0 - (9 + 80*E_2 + 26*E_4)*M*r0_2 + 12*(1 + 2*E_2)*r0_3) + 2*L_4*(24*M_3 + 2*(-6 + E_2)*M*r0_2 - 3*(2 + E_2)*r0_3 + 6*M_2*(r0 + 2*E_2*r0))) + a*M*r0_2*(12*L_6*M*(2*M - r0) + 3*E_2*r0_6*(-20*M_2 + 6*E_2*M*r0 + 5*r0_2) - 6*L_2*r0_4*((4 + 44*E_2)*M_2 - (6 + 31*E_2 + 2*E_4)*M*r0 + 2*(1 + 3*E_2)*r0_2) - 2*L_4*r0_2*(6*r0*(-2*M + r0) + E_2*(64*M_2 - 53*M*r0 + 15*r0_2)))))/(r0_2*expr2_2);\n A21701 = (r0*(a_7*E_2*M*((-2 + 6*E_2)*M + 3*r0) - a_6*E*L*M*(4*(-1 + 3*E_2)*M + (3 + 5*E_2)*r0) + a_5*M*(-2*L_2*(M - 5*E_2*r0) + E_2*r0*((4 - 8*E_2)*M_2 + 2*(-4 + 13*E_2)*M*r0 + 3*r0_2)) + a*M*r0*(4*L_4*M*(2*M - r0) + E_2*r0_4*(-20*M_2 + 6*E_2*M*r0 + 5*r0_2) - 2*L_2*r0_2*(4*(1 + 7*E_2)*M_2 - (6 + 23*E_2)*M*r0 + 2*(1 + 3*E_2)*r0_2)) + a_2*E*L*M*r0*(L_2*(-16*M_2 + 12*M*r0 + 3*r0_2) + r0_2*(8*(1 + 8*E_2)*M_2 - 2*(7 + 26*E_2)*M*r0 + (7 + 9*E_2)*r0_2)) + a_4*E*L*(L_2*M*(12*M - 5*r0) - r0*((8 - 16*E_2)*M_3 + 6*(-1 + 8*E_2)*M_2*r0 + E_2*M*r0_2 + 2*r0_3)) + E*L*r0_3*(2*L_2*M*(8*M_2 - 10*M*r0 + 3*r0_2) + r0_2*(8*M_3 + (-4 + 5*E_2)*M*r0_2 + 2*r0_3 - 4*M_2*(r0 + 2*E_2*r0))) + a_3*M*(-6*L_4*M + 2*L_2*r0*(2*M_2 - (2 + E_2)*r0_2 + M*(r0 + 7*E_2*r0)) + E_2*r0_3*(5*r0*(2*M + r0) + E_2*(-24*M_2 + 26*M*r0)))))/expr2_2;\n A22141 = (96*E*expr1_2*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/(r0_3*expr2_2);\n A22321 = (48*E*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/expr2_2;\n A22501 = (6*E*r0_3*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/expr2_2;\n A23141 = (16*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-(a_8*E*L*M*(24*(-1 + 3*E_2)*M_2 + 44*E_2*M*r0 + (7 + 9*E_2)*r0_2)) + a_9*E_2*M*(12*(-1 + 3*E_2)*M_2 + 7*r0_2 + 6*M*(r0 + 3*E_2*r0)) + E*L*r0_4*(2*L_4*M*(18*M_2 - 25*M*r0 + 8*r0_2) + L_2*r0_2*(88*M_3 - (100 + 21*E_2)*M_2*r0 + 2*(10 + 7*E_2)*M*r0_2 + 4*r0_3) + r0_4*(20*M_3 - (2 + 25*E_2)*M_2*r0 + 4*(-5 + 4*E_2)*M*r0_2 + 8*r0_3)) + a_7*M*(L_2*(-12*M_2 + 2*(-3 + 5*E_2 + 3*E_4)*M*r0 + 25*E_2*r0_2) + E_2*r0*((24 - 48*E_2)*M_3 + 2*(-5 + 66*E_2)*M_2*r0 + (1 + 96*E_2)*M*r0_2 + 19*r0_3)) + a_5*M*(-6*L_4*(6*M_2 + 2*(2 + 3*E_2)*M*r0 - 3*E_2*r0_2) + L_2*r0*(24*M_3 + 4*(6 + 61*E_2 - 2*E_4)*M_2*r0 + (-24 - 31*E_2 + 26*E_4)*M*r0_2 - 12*r0_3) + E_2*r0_3*(-4*(7 + 36*E_2)*M_3 + 2*(7 + 30*E_2)*M_2*r0 + (55 + 156*E_2)*M*r0_2 + 35*r0_3)) - a_6*E*L*(L_2*M*(-72*M_2 - 40*M*r0 + (16 + 9*E_2)*r0_2) + r0*((48 - 96*E_2)*M_4 + 2*(7 + 157*E_2)*M_3*r0 + (-23 + 157*E_2)*M_2*r0_2 + (8 + E_2)*M*r0_3 + 2*r0_4)) + a_4*E*L*r0*(3*L_4*M*(16*M - 3*r0) + L_2*(-96*M_4 - 74*M_3*r0 + (116 - 31*E_2)*M_2*r0_2 + 2*(6 + E_2)*M*r0_3 - 2*r0_4) + r0_2*((76 + 440*E_2)*M_4 - 4*(13 + 35*E_2)*M_3*r0 - 3*(16 + 93*E_2)*M_2*r0_2 + (25 + 41*E_2)*M*r0_3 + 4*r0_4)) + a_2*E*L*r0_2*(L_4*M*(-64*M_2 + 45*M*r0 + 10*r0_2) + L_2*r0*(152*M_4 + 42*(-3 + 2*E_2)*M_3*r0 - 8*(7 + 8*E_2)*M_2*r0_2 + 5*(12 + 5*E_2)*M*r0_3 + 2*r0_4) + r0_3*(-8*M_4 + 2*(61 + 103*E_2)*M_3*r0 - (113 + 191*E_2)*M_2*r0_2 + (6 + 49*E_2)*M*r0_3 + 14*r0_4)) - a_3*M*r0*(18*L_6*M + E_2*r0_4*(36*M_3 + 2*(61 + 18*E_2)*M_2*r0 - 3*(17 + 32*E_2)*M*r0_2 - 41*r0_3) + L_2*r0_2*(16*(3 + 28*E_2)*M_3 + 2*(-30 - 103*E_2 + 12*E_4)*M_2*r0 - 2*(9 + 95*E_2 + 13*E_4)*M*r0_2 + (24 + 79*E_2)*r0_3) - 4*L_4*(12*M_3 - (6 + 7*E_2)*M*r0_2 - 3*(1 + E_2)*r0_3 + 3*M_2*(r0 + 4*E_2*r0))) - a*M*r0_2*(12*L_6*M*(-2*M + r0) + L_2*r0_4*((24 + 302*E_2)*M_2 - (36 + 239*E_2 + 6*E_4)*M*r0 + 6*(2 + 9*E_2)*r0_2) + 9*E_2*r0_6*(6*M_2 - 2*r0_2 + M*(r0 - 2*E_2*r0)) + 2*L_4*r0_2*(6*r0*(-2*M + r0) + E_2*(48*M_2 - 44*M*r0 + 15*r0_2)))))/(r0_5*expr2_3);\n A23321 = (8*(-(a_8*E*L*M*(24*(-1 + 3*E_2)*M_2 + (3 + 55*E_2)*M*r0 + 4*(2 + 3*E_2)*r0_2)) + a_9*E_2*M*(12*(-1 + 3*E_2)*M_2 + 8*r0_2 + 9*M*(r0 + 2*E_2*r0)) - 2*a_7*M*(L_2*(6*M_2 + (3 - 16*E_2 - 6*E_4)*M*r0 - 16*E_2*r0_2) + E_2*r0*(12*(-1 + 2*E_2)*M_3 + 11*(1 - 6*E_2)*M_2*r0 + 3*(1 - 16*E_2)*M*r0_2 - 9*r0_3)) + E*L*r0_4*(2*L_4*M*(22*M_2 - 29*M*r0 + 9*r0_2) + L_2*r0_2*(80*M_3 - (84 + 23*E_2)*M_2*r0 + 5*(2 + 3*E_2)*M*r0_2 + 6*r0_3) + r0_4*(20*M_3 - (2 + 25*E_2)*M_2*r0 + 4*(-5 + 4*E_2)*M*r0_2 + 8*r0_3)) + a_5*M*(-6*L_4*(6*M_2 + (4 + 3*E_2)*M*r0 - 4*E_2*r0_2) + 2*E_2*r0_3*(-8*(1 + 9*E_2)*M_3 + 3*(7 + 10*E_2)*M_2*r0 + 6*(4 + 13*E_2)*M*r0_2 + 15*r0_3) + L_2*r0*(24*M_3 - 8*(-3 - 22*E_2 + 2*E_4)*M_2*r0 + (-24 - 15*E_2 + 52*E_4)*M*r0_2 + (-12 + 13*E_2)*r0_3)) + a_4*E*L*r0*(6*L_4*M*(7*M - 2*r0) + M*r0_2*(32*(2 + 13*E_2)*M_3 - 4*(17 + 28*E_2)*M_2*r0 - (19 + 264*E_2)*M*r0_2 + 12*(2 + 3*E_2)*r0_3) + L_2*(-96*M_4 + 8*(-5 + 3*E_2)*M_3*r0 + (113 - 89*E_2)*M_2*r0_2 + (5 + E_2)*M*r0_3 - 4*r0_4)) + a_2*E*L*r0_2*(L_4*M*(-56*M_2 + 39*M*r0 + 11*r0_2) + L_2*r0*(128*M_4 + 2*(-57 + 70*E_2)*M_3*r0 - 2*(23 + 57*E_2)*M_2*r0_2 + (55 + 28*E_2)*M*r0_3 + 2*r0_4) + r0_3*(16*M_4 + 2*(41 + 88*E_2)*M_3*r0 - 3*(33 + 58*E_2)*M_2*r0_2 + 2*(5 + 24*E_2)*M*r0_3 + 12*r0_4)) - 2*a_3*M*r0*(9*L_6*M + E_2*r0_4*(36*M_3 + (49 + 18*E_2)*M_2*r0 - 3*(9 + 16*E_2)*M*r0_2 - 19*r0_3) + L_2*r0_2*(8*(3 + 25*E_2)*M_3 + (-30 - 83*E_2 + 24*E_4)*M_2*r0 - (9 + 84*E_2 + 26*E_4)*M*r0_2 + (12 + 29*E_2)*r0_3) + L_4*(-24*M_3 + (12 - 5*E_2)*M*r0_2 + 6*(1 + E_2)*r0_3 - 6*M_2*(r0 + 2*E_2*r0))) - a_6*E*L*(L_2*M*(-72*M_2 + (-29 + 18*E_2)*M*r0 + 4*(5 + 3*E_2)*r0_2) + r0*((48 - 96*E_2)*M_4 + (-27 + 170*E_2)*M_2*r0_2 + 2*(7 + 4*E_2)*M*r0_3 + 4*r0_4 + 2*M_3*(r0 + 140*E_2*r0))) - a*M*r0_2*(12*L_6*M*(-2*M + r0) + L_2*r0_4*((24 + 266*E_2)*M_2 - (36 + 191*E_2 + 12*E_4)*M*r0 + 3*(4 + 13*E_2)*r0_2) + 9*E_2*r0_6*(6*M_2 - 2*r0_2 + M*(r0 - 2*E_2*r0)) + 4*L_4*r0_2*(3*r0*(-2*M + r0) + E_2*(34*M_2 - 30*M*r0 + 9*r0_2)))))/(r0_2*expr2_3);\n A23501 = (r0*(3*a_7*E_2*M*((-2 + 6*E_2)*M + 3*r0) - 3*a_6*E*L*M*(4*(-1 + 3*E_2)*M + (3 + 5*E_2)*r0) + a_5*M*(-6*L_2*(M - 5*E_2*r0) + E_2*r0*((12 - 24*E_2)*M_2 + (-23 + 78*E_2)*M*r0 + 8*r0_2)) + a_4*E*L*(3*L_2*M*(12*M - 5*r0) + r0*(24*(-1 + 2*E_2)*M_3 + (17 - 147*E_2)*M_2*r0 + M*r0_2 - 6*r0_3)) + a_2*E*L*r0*(3*L_2*M*(-16*M_2 + 11*M*r0 + 4*r0_2) + r0_2*(2*(13 + 98*E_2)*M_3 - (43 + 164*E_2)*M_2*r0 + (18 + 31*E_2)*M*r0_2 + 2*r0_3)) + E*L*r0_3*(2*L_2*M*(26*M_2 - 33*M*r0 + 10*r0_2) + r0_2*(20*M_3 - (2 + 25*E_2)*M_2*r0 + 4*(-5 + 4*E_2)*M*r0_2 + 8*r0_3)) - a*M*r0*(12*L_4*M*(-2*M + r0) + 2*L_2*r0_2*(4*(3 + 22*E_2)*M_2 - 2*(9 + 38*E_2)*M*r0 + 3*(2 + 7*E_2)*r0_2) + 9*E_2*r0_4*(6*M_2 - 2*r0_2 + M*(r0 - 2*E_2*r0))) + a_3*M*(-18*L_4*M + E_2*r0_3*(-2*(1 + 36*E_2)*M_2 + 6*(5 + 13*E_2)*M*r0 + 17*r0_2) + 6*L_2*r0*(2*M_2 - 2*(1 + E_2)*r0_2 + M*(r0 + 8*E_2*r0)))))/expr2_3;\n A24121 = (24*E*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/expr2_3;\n A24301 = (6*E*r0_3*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/expr2_3;\n A25121 = (4*(-(a_8*E*L*M*(24*(-1 + 3*E_2)*M_2 + (3 + 55*E_2)*M*r0 + 4*(2 + 3*E_2)*r0_2)) + a_9*E_2*M*(12*(-1 + 3*E_2)*M_2 + 8*r0_2 + 9*M*(r0 + 2*E_2*r0)) + E*L*r0_4*(4*L_4*M*(12*M_2 - 16*M*r0 + 5*r0_2) + 4*L_2*r0_2*(20*M_3 - 2*(10 + 3*E_2)*M_2*r0 + (1 + 4*E_2)*M*r0_2 + 2*r0_3) + r0_4*(16*M_3 + (8 - 26*E_2)*M_2*r0 + (-28 + 17*E_2)*M*r0_2 + 10*r0_3)) + a_7*M*(L_2*(-12*M_2 + 2*(-3 + 16*E_2 + 6*E_4)*M*r0 + 32*E_2*r0_2) + E_2*r0*((24 - 48*E_2)*M_3 + 4*(-5 + 33*E_2)*M_2*r0 + (-7 + 96*E_2)*M*r0_2 + 17*r0_3)) + a_5*M*(-6*L_4*(6*M_2 + (4 + 3*E_2)*M*r0 - 4*E_2*r0_2) + E_2*r0_3*(-4*(5 + 36*E_2)*M_3 + 20*(2 + 3*E_2)*M_2*r0 + (53 + 156*E_2)*M*r0_2 + 31*r0_3) + 2*L_2*r0*(12*M_3 + 2*(6 + 47*E_2 - 4*E_4)*M_2*r0 + 2*(-6 - 5*E_2 + 13*E_4)*M*r0_2 + 3*(-2 + E_2)*r0_3)) + a_4*E*L*r0*(6*L_4*M*(7*M - 2*r0) + L_2*(-96*M_4 + 2*(-23 + 12*E_2)*M_3*r0 - 23*(-5 + 4*E_2)*M_2*r0_2 + (9 + 4*E_2)*M*r0_3 - 4*r0_4) + r0_2*((68 + 424*E_2)*M_4 - 4*(17 + 31*E_2)*M_3*r0 - 3*(9 + 89*E_2)*M_2*r0_2 + (26 + 43*E_2)*M*r0_3 + 2*r0_4)) - a_6*E*L*(L_2*M*(-72*M_2 + (-29 + 18*E_2)*M*r0 + 4*(5 + 3*E_2)*r0_2) + r0*((48 - 96*E_2)*M_4 + 2*(2 + 143*E_2)*M_3*r0 + (-28 + 167*E_2)*M_2*r0_2 + (13 + 5*E_2)*M*r0_3 + 4*r0_4)) + a_2*E*L*r0_2*(2*L_4*M*(-28*M_2 + 18*M*r0 + 7*r0_2) + L_2*r0*(136*M_4 + 24*(-5 + 6*E_2)*M_3*r0 - 2*(26 + 61*E_2)*M_2*r0_2 + (57 + 32*E_2)*M*r0_3 + 4*r0_4) + r0_3*(8*M_4 + 2*(50 + 89*E_2)*M_3*r0 - (106 + 181*E_2)*M_2*r0_2 + (3 + 53*E_2)*M*r0_3 + 16*r0_4)) + a_3*M*r0*(-18*L_6*M + E_2*r0_4*(-60*M_3 - 4*(28 + 9*E_2)*M_2*r0 + 3*(17 + 32*E_2)*M*r0_2 + 43*r0_3) - 2*L_2*r0_2*(8*(3 + 26*E_2)*M_3 + 2*(-15 - 46*E_2 + 12*E_4)*M_2*r0 - (9 + 88*E_2 + 26*E_4)*M*r0_2 + 2*(6 + 17*E_2)*r0_3) + 2*L_4*(24*M_3 + 4*(-3 + 2*E_2)*M*r0_2 - 3*(2 + 3*E_2)*r0_3 + 6*M_2*(r0 + 2*E_2*r0))) - a*M*r0_2*(12*L_6*M*(-2*M + r0) + 3*E_2*r0_6*(16*M_2 - 6*(-1 + E_2)*M*r0 - 7*r0_2) + 2*L_2*r0_4*(2*(6 + 67*E_2)*M_2 - 2*(9 + 49*E_2 + 3*E_4)*M*r0 + 3*(2 + 7*E_2)*r0_2) + 2*L_4*r0_2*(6*r0*(-2*M + r0) + E_2*(72*M_2 - 67*M*r0 + 21*r0_2)))))/(r0_2*expr2_4);\n A25301 = (r0*(3*a_7*E_2*M*((-2 + 6*E_2)*M + 3*r0) - 3*a_6*E*L*M*(4*(-1 + 3*E_2)*M + (3 + 5*E_2)*r0) + a_5*M*(-6*L_2*(M - 5*E_2*r0) + E_2*r0*((12 - 24*E_2)*M_2 + 2*(-11 + 39*E_2)*M*r0 + 7*r0_2)) - a*M*r0*(12*L_4*M*(-2*M + r0) + 3*E_2*r0_4*(16*M_2 - 6*(-1 + E_2)*M*r0 - 7*r0_2) + 2*L_2*r0_2*(4*(3 + 23*E_2)*M_2 - (18 + 83*E_2)*M*r0 + 6*(1 + 4*E_2)*r0_2)) + a_4*E*L*(3*L_2*M*(12*M - 5*r0) + r0*(24*(-1 + 2*E_2)*M_3 - 2*(-8 + 75*E_2)*M_2*r0 + (2 + 3*E_2)*M*r0_2 - 6*r0_3)) + a_2*E*L*r0*(3*L_2*M*(-16*M_2 + 10*M*r0 + 5*r0_2) + r0_2*(4*(7 + 50*E_2)*M_3 - 4*(11 + 43*E_2)*M_2*r0 + 5*(3 + 7*E_2)*M*r0_2 + 4*r0_3)) + E*L*r0_3*(2*L_2*M*(28*M_2 - 36*M*r0 + 11*r0_2) + r0_2*(16*M_3 + (8 - 26*E_2)*M_2*r0 + (-28 + 17*E_2)*M*r0_2 + 10*r0_3)) + a_3*M*(-18*L_4*M + E_2*r0_3*(-4*(1 + 18*E_2)*M_2 + 6*(5 + 13*E_2)*M*r0 + 19*r0_2) + 6*L_2*r0*(2*M_2 - (2 + 3*E_2)*r0_2 + M*(r0 + 9*E_2*r0)))))/expr2_4;\n A26101 = (2*E*r0_3*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/expr2_4;\n A27101 = (r0*(a_7*E_2*M*((-2 + 6*E_2)*M + 3*r0) - a_6*E*L*M*(4*(-1 + 3*E_2)*M + (3 + 5*E_2)*r0) + a_5*M*(-2*L_2*(M - 5*E_2*r0) + E_2*r0*((4 - 8*E_2)*M_2 + (-7 + 26*E_2)*M*r0 + 2*r0_2)) + a_4*E*L*(L_2*M*(12*M - 5*r0) + r0*(8*(-1 + 2*E_2)*M_3 + (5 - 51*E_2)*M_2*r0 + (1 + 2*E_2)*M*r0_2 - 2*r0_3)) + E*L*r0_3*(2*L_2*M*(10*M_2 - 13*M*r0 + 4*r0_2) + r0_2*(4*M_3 + (6 - 9*E_2)*M_2*r0 + 6*(-2 + E_2)*M*r0_2 + 4*r0_3)) + a_2*E*L*r0*(L_2*M*(-16*M_2 + 9*M*r0 + 6*r0_2) + r0_2*(2*(5 + 34*E_2)*M_3 + (4 + 13*E_2)*M*r0_2 + 2*r0_3 - 15*M_2*(r0 + 4*E_2*r0))) - a*M*r0*(4*L_4*M*(-2*M + r0) + E_2*r0_4*(14*M_2 + (9 - 6*E_2)*M*r0 - 8*r0_2) + 2*L_2*r0_2*(4*(1 + 8*E_2)*M_2 + (2 + 9*E_2)*r0_2 - 6*M*(r0 + 5*E_2*r0))) + a_3*M*(-6*L_4*M + E_2*r0_3*(-2*(1 + 12*E_2)*M_2 + 2*(5 + 13*E_2)*M*r0 + 7*r0_2) + 2*L_2*r0*(2*M_2 - 2*(1 + 2*E_2)*r0_2 + M*(r0 + 10*E_2*r0)))))/expr2_5;\n }\n\n /* A_{t,phi} */\n {\n A30060 = -256*E*L*expr4_3;\n A30080 = (128*expr1_2*(-(a_8*E*L*M_2*r0) - 12*a_9*E_2*M_2*(2*M + r0) + E*L*r0_5*(36*L_4*M*(-2*M + r0) + 2*r0_4*(-2*M_2 + (-11 + 8*E_2)*M*r0 + 6*r0_2) + L_2*r0_2*(-88*M_2 + 2*(13 + 6*E_2)*M*r0 + 9*r0_2)) + 4*a*M*r0_2*(18*L_6*M*(2*M - r0) + 3*E_2*r0_7*(-2*M + 3*r0) - 3*L_4*r0_2*(-16*M_2 - 2*(-3 + E_2)*M*r0 + r0_2) + L_2*r0_4*(12*M_2 + 2*E_2*M*r0 + 3*(-1 + 2*E_2)*r0_2)) + 4*a_3*M*r0*(3*E_2*r0_5*(18*M_2 + 7*M*r0 + 7*r0_2) + 3*L_4*(40*M_3 + 2*(-1 + 2*E_2)*M_2*r0 + (-7 + 2*E_2)*M*r0_2 - r0_3) + L_2*r0_2*(72*M_3 + 2*(3 + 34*E_2)*M_2*r0 + 9*(-1 + 2*E_2)*M*r0_2 + 2*(-3 + 4*E_2)*r0_3)) + 2*a_6*E*L*M*(-384*M_4 + 64*(-6 + E_2)*M_3*r0 + 2*(-29 + 48*E_2)*M_2*r0_2 + (1 + 8*E_2)*r0_4 + M*(-2*L_2*r0 + (17 + 48*E_2)*r0_3)) + 4*a_7*M*(L_2*M*(6*M + 3*r0 - 2*E_2*r0) + 3*E_2*(32*M_4 + 52*M_3*r0 + 18*M_2*r0_2 + M*r0_3 + r0_4)) + a_4*E*L*r0*(4*L_2*M*(-208*M_3 + 6*(-17 + 2*E_2)*M_2*r0 + 12*(2 + E_2)*M*r0_2 + (11 + 3*E_2)*r0_3) + r0_2*(-916*M_4 + 4*(-95 + 48*E_2)*M_3*r0 + 3*(21 + 64*E_2)*M_2*r0_2 + 6*(5 + 8*E_2)*M*r0_3 + 12*r0_4)) + 4*a_5*M*(3*L_4*M*r0 + 3*E_2*r0_3*(60*M_3 + 46*M_2*r0 + 11*M*r0_2 + 5*r0_3) + L_2*(96*M_4 + 4*(9 + 14*E_2)*M_3*r0 + 12*(-1 + 5*E_2)*M_2*r0_2 + 6*(-1 + E_2)*M*r0_3 + (-3 + 2*E_2)*r0_4)) + a_2*E*L*r0_2*(L_4*(-240*M_3 + 36*M*r0_2) + 2*r0_4*(-128*M_3 + 12*(-1 + 4*E_2)*M_2*r0 + 3*(1 + 8*E_2)*M*r0_2 + 12*r0_3) + L_2*r0_2*(-616*M_3 + 8*(11 + 3*E_2)*M*r0_2 + 9*r0_3 + 12*M_2*(r0 + 4*E_2*r0)))))/(3.*r0_9*(a_2 + r0*(-2*M + r0)));\n A30240 = -192*E*L*expr1_2;\n A30260 = (64*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-6*a_9*E_2*M*(14*M_2 + 11*M*r0 + 2*r0_2) + a_8*E*L*M*(6*E_2*r0_p_2M_2 - r0*(7*M + 3*r0)) + E*L*r0_5*(-74*L_4*M*(2*M - r0) + 2*L_2*r0_2*(-96*M_2 + (30 + 11*E_2)*M*r0 + 9*r0_2) + r0_4*(-32*M_2 + 26*(-1 + E_2)*M*r0 + 21*r0_2)) + a_6*E*L*(-1536*M_5 + 32*(-48 + 5*E_2)*M_4*r0 + 72*(-3 + 4*E_2)*M_3*r0_2 + 12*(9 + 16*E_2)*M_2*r0_3 + (19 + 44*E_2)*M*r0_4 + 3*r0_5 + L_2*M*(24*M_2 + 4*(2 + 3*E_2)*M*r0 + 3*(-1 + 2*E_2)*r0_2)) + 2*a*M*r0_2*(3*E_2*r0_7*(-2*M + 9*r0) + 6*L_6*(22*M_2 - 13*M*r0 + r0_2) + L_4*r0_2*(192*M_2 + 2*(-51 + 20*E_2)*M*r0 + 3*(1 - 3*E_2)*r0_2) + L_2*r0_4*(60*M_2 + 2*(-12 + 19*E_2)*M*r0 + 3*(-1 + 4*E_2)*r0_2)) + a_2*E*L*r0_2*(2*L_4*M*(-232*M_2 + 6*M*r0 + 37*r0_2) + L_2*r0_2*(-1264*M_3 + 2*(15 + 38*E_2)*M_2*r0 + (189 + 50*E_2)*M*r0_2 + 21*r0_3) + r0_4*(-584*M_3 + 18*(-3 + 8*E_2)*M_2*r0 + 3*(15 + 28*E_2)*M*r0_2 + 45*r0_3)) + 2*a_3*M*r0*(6*L_6*r0 + 3*E_2*r0_5*(78*M_2 + 37*M*r0 + 19*r0_2) + L_2*r0_2*(312*M_3 + 10*(-3 + 35*E_2)*M_2*r0 + (-51 + 107*E_2)*M*r0_2 - 5*E_2*r0_3) + L_4*(456*M_3 + 2*(-33 + 34*E_2)*M_2*r0 + (-87 + 28*E_2)*M*r0_2 + 3*(5 - 6*E_2)*r0_3)) - 2*a_7*M*(L_2*(6*(-7 + 4*E_2)*M_2 + (-33 + 49*E_2)*M*r0 + 3*(-2 + 5*E_2)*r0_2) - 3*E_2*(128*M_4 + 220*M_3*r0 + 86*M_2*r0_2 - 5*M*r0_3 - 3*r0_4)) + a_4*E*L*r0*(12*L_4*M_2 + L_2*(-1664*M_4 + 32*(-25 + 2*E_2)*M_3*r0 + 22*(11 + 4*E_2)*M_2*r0_2 + 2*(48 + 17*E_2)*M*r0_3 + 3*r0_4) + r0_2*(-1844*M_4 + 8*(-104 + 33*E_2)*M_3*r0 + 3*(55 + 104*E_2)*M_2*r0_2 + 3*(31 + 32*E_2)*M*r0_3 + 27*r0_4)) + 2*a_5*M*(-3*L_4*r0*((-11 + 4*E_2)*M + (-4 + 3*E_2)*r0) + 3*E_2*r0_3*(228*M_3 + 202*M_2*r0 + 45*M*r0_2 + 9*r0_3) + L_2*(384*M_4 + 4*(27 + 74*E_2)*M_3*r0 + 14*(-6 + 23*E_2)*M_2*r0_2 + 2*(3 - 4*E_2)*M*r0_3 + (9 - 32*E_2)*r0_4))))/(3.*r0_6*(a_2 + r0*(-2*M + r0)));\n A30420 = -48*E*L*r0_3*(a_2*(2*M + r0) + r0*(L_2 + r0_2));\n A30440 = (8*(-36*a_9*E_2*M*(10*M_2 + 9*M*r0 + 2*r0_2) + a_8*E*L*(-13*M_2*r0 + 3*r0_3 + 36*E_2*M*r0_p_2M_2) + E*L*r0_3*(8*L_6*M*(-2*M + r0) + L_4*r0_2*(-460*M_2 + 4*(52 + E_2)*M*r0 + 11*r0_2) + r0_6*(-168*M_2 + 2*(-17 + 30*E_2)*M*r0 + 59*r0_2) + L_2*r0_4*(-624*M_2 + 2*(89 + 30*E_2)*M*r0 + 67*r0_2)) + 4*a*M*r0_2*(9*E_2*r0_7*(2*M + 3*r0) + 3*L_2*r0_4*(36*M_2 + 2*(-12 + 17*E_2)*M*r0 + 3*r0_2) + 3*L_4*r0_2*(96*M_2 + 6*(-11 + 5*E_2)*M*r0 + (9 - 10*E_2)*r0_2) + 2*L_6*(90*M_2 + (-63 + 4*E_2)*M*r0 - 3*(-3 + E_2)*r0_2)) + 2*a_6*E*L*(-2304*M_5 + 96*(-24 + E_2)*M_4*r0 + 2*(-157 + 144*E_2)*M_3*r0_2 + (233 + 288*E_2)*M_2*r0_3 + (79 + 84*E_2)*M*r0_4 + 16*r0_5 + L_2*(72*M_3 + 2*(23 + 24*E_2)*M_2*r0 + 6*(1 + 4*E_2)*M*r0_2 + 3*r0_3)) + a_2*E*L*r0_2*(12*L_6*M - 2*L_4*(696*M_3 + 8*(-3 + E_2)*M_2*r0 - 4*(31 + 2*E_2)*M*r0_2 - 7*r0_3) + 2*r0_4*(-984*M_3 + 4*(-29 + 36*E_2)*M_2*r0 + 9*(13 + 12*E_2)*M*r0_2 + 72*r0_3) + L_2*r0_2*(-3864*M_3 + 4*(-1 + 36*E_2)*M_2*r0 + 12*(51 + 14*E_2)*M*r0_2 + 107*r0_3)) + 4*a_3*M*r0*(-6*(-3 + E_2)*L_6*r0 + 9*E_2*r0_5*(42*M_2 + 23*M*r0 + 5*r0_2) + 3*L_4*(216*M_3 + 2*(-27 + 26*E_2)*M_2*r0 + 9*(-5 + 2*E_2)*M*r0_2 + (21 - 22*E_2)*r0_3) + L_2*r0_2*(504*M_3 + 6*(-21 + 104*E_2)*M_2*r0 + (-99 + 224*E_2)*M*r0_2 + 4*(9 - 16*E_2)*r0_3)) - 4*a_7*M*(L_2*(18*(-5 + 4*E_2)*M_2 + (-81 + 140*E_2)*M*r0 + 6*(-3 + 8*E_2)*r0_2) - 9*E_2*(64*M_4 + 116*M_3*r0 + 50*M_2*r0_2 - 7*M*r0_3 - 5*r0_4)) + a_4*E*L*r0*(3*L_4*(32*M_2 + 4*(2 + E_2)*M*r0 + r0_2) + L_2*(-4992*M_4 + 8*(-299 + 6*E_2)*M_3*r0 + 8*(103 + 30*E_2)*M_2*r0_2 + 4*(95 + 39*E_2)*M*r0_3 + 46*r0_4) + r0_2*(-5604*M_4 + 4*(-691 + 108*E_2)*M_3*r0 + (559 + 720*E_2)*M_2*r0_2 + 6*(71 + 48*E_2)*M*r0_3 + 114*r0_4)) + 4*a_5*M*(3*L_4*r0*((27 - 16*E_2)*M - 12*(-1 + E_2)*r0) + 9*E_2*r0_3*(108*M_3 + 110*M_2*r0 + 23*M*r0_2 - r0_3) + L_2*(576*M_4 + 12*(9 + 46*E_2)*M_3*r0 + 4*(-45 + 154*E_2)*M_2*r0_2 + 2*(27 - 25*E_2)*M*r0_3 + (45 - 112*E_2)*r0_4))))/(3.*r0_3*(a_2 + r0*(-2*M + r0)));\n A30600 = -4*E*L*r0_6;\n A30620 = (-4*(6*a_7*E_2*M*(13*M + 6*r0) - 3*a_6*E*L*(r0*(M + r0) + 6*E_2*M*(2*M + r0)) - E*L*r0_2*(8*L_4*M*(-2*M + r0) + 2*r0_4*(-40*M_2 + 7*E_2*M*r0 + 10*r0_2) + L_2*r0_2*(-144*M_2 + 2*(25 + 2*E_2)*M*r0 + 11*r0_2)) - 2*a*M*r0*(3*E_2*r0_5*(10*M + 3*r0) + L_2*r0_2*(84*M_2 + 4*(-18 + 17*E_2)*M*r0 + 3*(5 - 7*E_2)*r0_2) + 2*L_4*(54*M_2 + (-45 + 8*E_2)*M*r0 + 3*(3 - 2*E_2)*r0_2)) - 6*a_5*M*(L_2*((13 - 12*E_2)*M + (6 - 11*E_2)*r0) + E_2*(64*M_3 + 90*M_2*r0 + 12*M*r0_2 - 11*r0_3)) - a_2*E*L*r0*(12*L_4*M - 2*L_2*(224*M_3 + 2*(-3 + 4*E_2)*M_2*r0 - (39 + 8*E_2)*M*r0_2 - 7*r0_3) + r0_2*(-568*M_3 + 2*(-19 + 10*E_2)*M_2*r0 + (71 + 46*E_2)*M*r0_2 + 37*r0_3)) - 2*a_3*M*(-6*(-3 + 2*E_2)*L_4*r0 + 3*E_2*r0_3*(70*M_2 + 39*M*r0 - 2*r0_2) + L_2*(192*M_3 + 2*(-39 + 62*E_2)*M_2*r0 + (-39 + 56*E_2)*M*r0_2 + 3*(11 - 18*E_2)*r0_3)) - a_4*E*L*(3*L_2*(12*M_2 + 4*(1 + E_2)*M*r0 + r0_2) + 2*(-384*M_4 - 8*(24 + E_2)*M_3*r0 + (43 + 28*E_2)*M_2*r0_2 + (31 + 25*E_2)*M*r0_3 + 10*r0_4))))/(3.*(a_2 + r0*(-2*M + r0)));\n A30800 = (r0_3*(-24*a_5*E_2*M + 3*a_4*E*L*(4*E_2*M + r0) - 2*a_2*E*L*(-6*L_2*M + 96*M_3 + 8*E_2*M_2*r0 - 2*(5 + 4*E_2)*M*r0_2 - 7*r0_3) - 24*a_3*M*((-1 + E_2)*L_2 + E_2*(-4*M_2 - 4*M*r0 + r0_2)) + E*L*r0*(8*L_2*M*(-2*M + r0) + r0_2*(-52*M_2 + 4*(1 + E_2)*M*r0 + 11*r0_2)) + 8*a*M*(6*E_2*M*r0_3 + L_2*(12*M_2 + 4*(-3 + E_2)*M*r0 - 3*(-1 + E_2)*r0_2))))/(6.*(a_2 + r0*(-2*M + r0)));\n A31060 = (-128*expr1_2*(a_4*E*L*M*r0 + 2*a_5*E_2*M*(2*M + r0) + E*L*r0_3*(2*L_2*M + r0_3) - 2*a*M*r0*(L_4 + L_2*r0_2 - 3*E_2*r0_4) - 2*a_3*M*(L_2*(2*M + r0) - 2*E_2*r0_2*(3*M + 2*r0)) + a_2*E*L*r0*(2*L_2*M + r0*(-6*M_2 + 3*M*r0 + r0_2))))/(r0_5*(a_2 + r0*(-2*M + r0)));\n A31080 = (64*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(2*a_13*E_2*M_2*(-96*M_3 + 34*M_2*r0 + 113*M*r0_2 + 36*r0_3) + a_12*E*L*M_2*(384*M_3 + 16*(24 - 19*E_2)*M_2*r0 + (105 - 344*E_2)*M*r0_2 + 6*(1 - 16*E_2)*r0_3) + a_10*E*L*M*r0*(-512*(-15 + 2*E_2)*M_5 - 1920*(-7 + E_2)*M_4*r0 + 2*(3565 - 1248*E_2)*M_3*r0_2 + (695 - 2096*E_2)*M_2*r0_3 - (223 + 512*E_2)*M*r0_4 + 6*(-1 + 9*E_2)*r0_5 + 2*L_2*M*(264*M_2 - 5*(-39 + 32*E_2)*M*r0 + 3*(13 - 28*E_2)*r0_2)) + E*L*r0_6*(48*L_8*M*r0_2M_2 + 24*L_6*M*(2*M - r0)*r0_2*(11*M - (7 + 3*E_2)*r0) + 2*L_4*M*r0_4*(296*M_2 - 2*(197 + 108*E_2)*M*r0 + 3*(41 + 38*E_2)*r0_2) + L_2*r0_6*(320*M_3 - 4*(121 + 109*E_2)*M_2*r0 + 6*(26 + 41*E_2)*M*r0_2 + 3*r0_3) + 2*r0_8*(-4*M_3 + (2 - 86*E_2)*M_2*r0 + 3*(-4 + 17*E_2)*M*r0_2 + 6*r0_3)) - 2*a*M*r0_4*(24*L_10*r0_2M_2 - 6*E_2*r0_10*(-14*M_2 + (5 + 12*E_2)*M*r0 + r0_2) - 12*L_8*(2*M - r0)*r0*(14*M_2 - 2*(6 + E_2)*M*r0 + (4 + 3*E_2)*r0_2) + L_6*r0_3*(-864*M_3 + 8*(94 + 63*E_2)*M_2*r0 - 2*(101 + 258*E_2 + 36*E_4)*M*r0_2 + 3*(7 + 50*E_2)*r0_3) + L_2*r0_7*(-288*M_3 + 4*(65 + 244*E_2)*M_2*r0 - 2*(35 + 379*E_2 + 72*E_4)*M*r0_2 + 3*(2 + 53*E_2)*r0_3) + L_4*r0_5*(-816*M_3 + 4*(163 + 304*E_2)*M_2*r0 - 4*(32 + 248*E_2 + 45*E_4)*M*r0_2 + 3*(1 + 78*E_2)*r0_3)) + a_2*E*L*r0_4*(48*L_8*M*(6*M_2 - 5*M*r0 + r0_2) + 48*L_6*M*r0*(18*M_3 + (5 - 8*E_2)*M_2*r0 - 2*(7 + 3*E_2)*M*r0_2 + (5 + 3*E_2)*r0_3) + 4*L_4*M*r0_3*(124*M_3 - 48*(-3 + 4*E_2)*M_2*r0 - 6*(43 + 41*E_2)*M*r0_2 + 3*(41 + 55*E_2)*r0_3) + L_2*r0_5*(-2432*M_4 + 4*(583 + 48*E_2)*M_3*r0 - 1228*(1 + E_2)*M_2*r0_2 + 3*(153 + 308*E_2)*M*r0_3 + 6*r0_4) + 2*r0_7*(-1284*M_4 + 56*(19 + 4*E_2)*M_3*r0 - (263 + 376*E_2)*M_2*r0_2 + 3*(1 + 77*E_2)*M*r0_3 + 18*r0_4)) - 2*a_11*M*(L_2*M*(96*M_3 + (226 - 96*E_2)*M_2*r0 + (161 - 290*E_2)*M*r0_2 + 12*(3 - 10*E_2)*r0_3) - 2*E_2*r0*(320*(-3 + E_2)*M_5 + 4*(-599 + 160*E_2)*M_4*r0 + 3*(-551 + 160*E_2)*M_3*r0_2 + (-229 + 160*E_2)*M_2*r0_3 + (49 + 20*E_2)*M*r0_4 - 6*r0_5)) + a_4*E*L*r0_3*(24*L_6*M*(108*M_3 + 2*(9 - 14*E_2)*M_2*r0 - 2*(4 + 3*E_2)*M*r0_2 + 3*(1 + E_2)*r0_3) - 2*L_4*M*r0*(736*M_4 + 112*(-23 + 3*E_2)*M_3*r0 + 24*(-58 + 59*E_2)*M_2*r0_2 + 28*(7 + 15*E_2)*M*r0_3 - 3*(41 + 106*E_2)*r0_4) + L_2*r0_3*(-14144*M_5 + 48*(108 + 53*E_2)*M_4*r0 - 8*(-818 + 171*E_2)*M_3*r0_2 - 4*(356 + 351*E_2)*M_2*r0_3 + 24*(17 + 54*E_2)*M*r0_4 + 3*r0_5) + r0_5*(-14616*M_5 + 4*(691 + 516*E_2)*M_4*r0 + 2*(2735 - 4*E_2)*M_3*r0_2 - (1487 + 1288*E_2)*M_2*r0_3 + 12*(7 + 69*E_2)*M*r0_4 + 36*r0_5)) + 2*a_9*M*r0*(L_4*M*(-208*M_2 + (-313 + 168*E_2)*M*r0 + 12*(-9 + 10*E_2)*r0_2) + L_2*(-384*(5 + 6*E_2)*M_5 + 8*(-241 - 706*E_2 + 136*E_4)*M_4*r0 + 8*(-45 - 698*E_2 + 204*E_4)*M_3*r0_2 + (65 - 1270*E_2 + 816*E_4)*M_2*r0_3 + 2*(23 + 34*E_2 + 68*E_4)*M*r0_4 + 12*(2 - 9*E_2)*r0_5) + 2*E_2*r0*(2112*M_6 + 4*(893 + 144*E_2)*M_5*r0 + 2*(-695 + 896*E_2)*M_4*r0_2 + (-4079 + 1824*E_2)*M_3*r0_3 + 2*(-617 + 384*E_2)*M_2*r0_4 + (61 + 116*E_2)*M*r0_5 - 27*r0_6)) + a_6*E*L*r0_2*(72*L_6*M_2*r0 + 4*L_4*M*(1952*M_4 - 8*(-272 + 93*E_2)*M_3*r0 - 60*(-10 + 9*E_2)*M_2*r0_2 - (1 + 90*E_2)*M*r0_3 + 51*E_2*r0_4) + L_2*M*r0*(-14272*M_5 + 40*(-13 + 64*E_2)*M_4*r0 - 304*(-70 + 3*E_2)*M_3*r0_2 + 2*(3499 - 1952*E_2)*M_2*r0_3 - 2*(533 + 550*E_2)*M*r0_4 + 3*(25 + 268*E_2)*r0_5) + r0_3*(-26824*M_6 + 4*(-3273 + 424*E_2)*M_5*r0 + 2*(8659 + 1248*E_2)*M_4*r0_2 + (5521 - 2128*E_2)*M_3*r0_3 - (1759 + 1328*E_2)*M_2*r0_4 + 12*(4 + 61*E_2)*M*r0_5 + 12*r0_6)) + 2*a_7*M*r0*(-4*L_6*M*r0*(38*M - 9*(-3 + E_2)*r0) + 6*E_2*r0_4*(1460*M_5 + 12*(107 + 32*E_2)*M_4*r0 + (-893 + 736*E_2)*M_3*r0_2 + (-615 + 448*E_2)*M_2*r0_3 + 8*(5 + 11*E_2)*M*r0_4 - 14*r0_5) - 2*L_4*(704*M_5 + 8*(233 + 108*E_2)*M_4*r0 + 2*(307 + 598*E_2 - 180*E_4)*M_3*r0_2 + (-127 + 502*E_2 - 360*E_4)*M_2*r0_3 + (-31 + 84*E_2 - 90*E_4)*M*r0_4 + 3*(-8 + 35*E_2)*r0_5) + L_2*r0*(4224*M_6 + 8*(307 + 20*E_2)*M_5*r0 + 4*(-1051 - 734*E_2 + 288*E_4)*M_4*r0_2 + 2*(-1129 - 4344*E_2 + 1680*E_4)*M_3*r0_3 + (305 - 3082*E_2 + 2496*E_4)*M_2*r0_4 + 2*(122 + 53*E_2 + 276*E_4)*M*r0_5 + (66 - 449*E_2)*r0_6)) + a_8*E*L*M*r0*(72*L_4*M*r0*(4*M - (-2 + E_2)*r0) + 2*L_2*(3584*M_5 - 32*(-283 + 50*E_2)*M_4*r0 + 4*(1775 - 508*E_2)*M_3*r0_2 - 2*(-713 + 698*E_2)*M_2*r0_3 - 4*(37 + 82*E_2)*M*r0_4 + 3*(-5 + 31*E_2)*r0_5) + r0*(-16896*M_6 + 64*(-300 + 23*E_2)*M_5*r0 + 4*(3331 + 296*E_2)*M_4*r0_2 - 4*(-4751 + 280*E_2)*M_3*r0_3 + (2681 - 3424*E_2)*M_2*r0_4 - (1031 + 1036*E_2)*M*r0_5 + 6*(-2 + 53*E_2)*r0_6)) + 2*a_3*M*r0_3*(2*E_2*M*r0_8*(588*M_2 + 2*(-223 + 144*E_2)*M*r0 + (103 + 164*E_2)*r0_2) + L_2*r0_5*(2352*M_4 - 24*(47 + 68*E_2)*M_3*r0 + 36*(-13 - 39*E_2 + 24*E_4)*M_2*r0_2 + 2*(92 + 855*E_2 + 284*E_4)*M*r0_3 + (6 - 551*E_2)*r0_4) + 2*L_4*r0_3*(2160*M_4 - 4*(265 + 437*E_2)*M_3*r0 + 2*(-264 - 137*E_2 + 180*E_4)*M_2*r0_2 + (165 + 748*E_2 + 270*E_4)*M*r0_3 + (21 - 331*E_2)*r0_4) + L_6*r0*(2160*M_4 - 8*(229 + 144*E_2)*M_3*r0 + 24*(-22 + 13*E_2 + 6*E_4)*M_2*r0_2 + 4*(92 + 99*E_2 + 36*E_4)*M*r0_3 - 3*(7 + 100*E_2)*r0_4) - 12*L_8*(56*M_3 - (15 + 2*E_2)*M*r0_2 + (4 + 3*E_2)*r0_3 - 6*M_2*(r0 + 2*E_2*r0))) + 2*a_5*M*r0_2*(-36*L_8*M*r0 + E_2*r0_6*(6012*M_4 + 108*(5 + 16*E_2)*M_3*r0 + (-2601 + 2048*E_2)*M_2*r0_2 + 4*(89 + 148*E_2)*M*r0_3 - 48*r0_4) - 2*L_6*(832*M_4 + 12*(65 - 6*E_2)*M_3*r0 - 12*(16 + 3*E_2 + 6*E_4)*M_2*r0_2 - 2*(25 - 21*E_2 + 18*E_4)*M*r0_3 + 75*E_2*r0_4) + L_4*r0*(5088*M_5 - 4*(245 + 964*E_2)*M_4*r0 + 12*(-381 - 304*E_2 + 60*E_4)*M_3*r0_2 + (-41 - 504*E_2 + 1440*E_4)*M_2*r0_3 + 4*(93 + 62*E_2 + 135*E_4)*M*r0_4 + (93 - 638*E_2)*r0_5) + L_2*r0_3*(5664*M_5 + 12*(-275 - 384*E_2 + 144*E_4)*M_3*r0_2 + (-129 - 2086*E_2 + 2544*E_4)*M_2*r0_3 + 6*(46 + 185*E_2 + 140*E_4)*M*r0_4 + (54 - 733*E_2)*r0_5 + 156*M_4*(r0 + 6*E_2*r0)))))/(3.*r0_11*expr2_2);\n A31240 = (-32*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-(a_4*E*L*r0_2) + 6*a_5*E_2*M*(2*M + r0) - 6*a*M*r0*(L_4 - (-1 + E_2)*L_2*r0_2 - 3*E_2*r0_4) + E*L*r0_3*(3*r0_3 + L_2*(4*M + r0)) + 2*a_3*M*(6*E_2*r0_2*(3*M + 2*r0) + L_2*(-6*M + (-3 + E_2)*r0)) + a_2*E*L*r0*(L_2*(4*M - r0) + 2*r0*(-6*M_2 + 4*M*r0 + r0_2))))/(r0_2*(a_2 + r0*(-2*M + r0)));\n A31260 = (16*(4*a_13*E_2*M*(2*M + r0)*(24*(-7 + E_2)*M_3 + (101 + 24*E_2)*M_2*r0 + 6*(28 + E_2)*M*r0_2 + 36*r0_3) + a_12*E*L*M*(-384*(-7 + E_2)*M_4 - 128*(-27 + 10*E_2)*M_3*r0 + (1503 - 1144*E_2)*M_2*r0_2 + 3*(87 - 112*E_2)*M*r0_3 - 18*(-1 + E_2)*r0_4) + E*L*r0_6*(168*L_8*M*r0_2M_2 + 4*L_6*M*(2*M - r0)*r0_2*(220*M - 21*(7 + 3*E_2)*r0) + L_4*r0_4*(1856*M_3 - 4*(679 + 374*E_2)*M_2*r0 + 24*(38 + 33*E_2)*M*r0_2 - 9*r0_3) + 2*L_2*r0_6*(356*M_3 - 4*(172 + 195*E_2)*M_2*r0 + 3*(77 + 146*E_2)*M*r0_2 + 12*r0_3) + 2*r0_8*(-64*M_3 - 8*(-4 + 37*E_2)*M_2*r0 + 6*(-7 + 29*E_2)*M*r0_2 + 21*r0_3)) + a_2*E*L*r0_4*(168*L_8*M*(6*M_2 - 5*M*r0 + r0_2) + 2*L_6*M*r0*(968*M_3 + (676 - 672*E_2)*M_2*r0 - 2*(571 + 252*E_2)*M*r0_2 + (421 + 252*E_2)*r0_3) - 2*L_4*r0_3*(1192*M_4 + 4*(-352 + 421*E_2)*M_3*r0 + 2*(729 + 722*E_2)*M_2*r0_2 - (900 + 1127*E_2)*M*r0_3 + 12*r0_4) + L_2*r0_5*(-12672*M_4 - 12*(-647 + 88*E_2)*M_3*r0 - 4*(671 + 994*E_2)*M_2*r0_2 + (1467 + 3224*E_2)*M*r0_3 + 27*r0_4) + 2*r0_7*(-4788*M_4 + 8*(399 + 43*E_2)*M_3*r0 - (543 + 1154*E_2)*M_2*r0_2 + 5*(2 + 157*E_2)*M*r0_3 + 60*r0_4)) + 4*a_3*M*r0_3*(2*E_2*r0_8*(978*M_3 + (-631 + 486*E_2)*M_2*r0 + 2*(10 + 149*E_2)*M*r0_2 + 51*r0_3) + L_8*(-1168*M_3 + 12*(8 + 21*E_2)*M_2*r0 + 2*(218 + 21*E_2)*M*r0_2 - 9*(16 + 7*E_2)*r0_3) + L_6*r0*(4416*M_4 - 4*(925 + 404*E_2)*M_3*r0 + 2*(-519 + 290*E_2 + 126*E_4)*M_2*r0_2 + 4*(299 + 86*E_2 + 63*E_4)*M*r0_3 - 3*(93 + 142*E_2)*r0_4) + L_2*r0_5*(4608*M_4 - 12*(187 + 166*E_2)*M_3*r0 + 2*(-465 - 722*E_2 + 882*E_4)*M_2*r0_2 + (560 + 1717*E_2 + 1098*E_4)*M*r0_3 - 2*(42 + 313*E_2)*r0_4) - 2*L_4*r0_3*(-4416*M_4 + 24*(96 + 95*E_2)*M_3*r0 + (1026 + 173*E_2 - 648*E_4)*M_2*r0_2 - (639 + 801*E_2 + 443*E_4)*M*r0_3 + (105 + 457*E_2)*r0_4)) + a_4*E*L*r0_3*(4*L_6*M*(2216*M_3 + 12*(43 - 49*E_2)*M_2*r0 - 2*(76 + 63*E_2)*M*r0_2 + (68 + 63*E_2)*r0_3) + L_2*r0_3*(-59256*M_5 + 4*(1885 + 672*E_2)*M_4*r0 + 2*(13743 - 4196*E_2)*M_3*r0_2 - (1537 + 3516*E_2)*M_2*r0_3 + 438*(3 + 10*E_2)*M*r0_4 - 18*r0_5) - L_4*r0*(12576*M_5 + 16*(-886 + 227*E_2)*M_4*r0 + 8*(-1641 + 1225*E_2)*M_3*r0_2 + 4*(58 + 453*E_2)*M_2*r0_3 - 2*(468 + 1057*E_2)*M*r0_4 + 15*r0_5) + 2*r0_5*(-26472*M_5 + 24*(81 + 151*E_2)*M_4*r0 + 2*(4917 - 758*E_2)*M_3*r0_2 - 2*(723 + 904*E_2)*M_2*r0_3 + (133 + 1391*E_2)*M*r0_4 + 54*r0_5)) - 2*a_11*M*(L_2*(672*M_4 + 4*(449 + 96*E_2 + 12*E_4)*M_3*r0 + (1594 - 1063*E_2 + 48*E_4)*M_2*r0_2 + 6*(96 - 177*E_2 + 2*E_4)*M*r0_3 + 72*(1 - 3*E_2)*r0_4) - 4*E_2*r0*(544*(-3 + E_2)*M_5 + 8*(-591 + 151*E_2)*M_4*r0 + 3*(-1239 + 344*E_2)*M_3*r0_2 + 2*(-236 + 199*E_2)*M_2*r0_3 + 2*(190 + 29*E_2)*M*r0_4 + 87*r0_5)) + a_10*E*L*M*(L_2*(384*M_4 + 96*(44 + 5*E_2)*M_3*r0 + 2*(1719 - 224*E_2)*M_2*r0_2 + 3*(275 - 148*E_2)*M*r0_3 + 18*(3 - 2*E_2)*r0_4) + r0*(-512*(-51 + 8*E_2)*M_5 - 32*(-1524 + 329*E_2)*M_4*r0 - 50*(-627 + 248*E_2)*M_3*r0_2 + (7199 - 7568*E_2)*M_2*r0_3 + (329 - 1572*E_2)*M*r0_4 + 2*(22 + 53*E_2)*r0_5)) - 2*a_5*M*r0_2*(12*L_8*(2*M_2 + 11*M*r0 + 6*r0_2) - 2*E_2*r0_6*(10332*M_4 + 24*(85 + 117*E_2)*M_3*r0 + (-4857 + 3604*E_2)*M_2*r0_2 + 10*(-2 + 113*E_2)*M*r0_3 + 228*r0_4) + L_6*(5568*M_4 + 16*(349 - 45*E_2)*M_3*r0 - 4*(567 - 76*E_2 + 126*E_4)*M_2*r0_2 - 4*(86 - 201*E_2 + 63*E_4)*M*r0_3 + 6*(94 + 53*E_2)*r0_4) - L_2*r0_3*(21312*M_5 + 60*(10 + 67*E_2)*M_4*r0 + 4*(-3042 - 1595*E_2 + 1800*E_4)*M_3*r0_2 + (690 - 9047*E_2 + 9960*E_4)*M_2*r0_3 + 24*(43 + 130*E_4)*M*r0_4 - 4*(72 + 281*E_2)*r0_5) + L_4*r0*(-20160*M_5 + 24*(143 + 376*E_2)*M_4*r0 - 8*(-2141 - 830*E_2 + 342*E_4)*M_3*r0_2 - 2*(1087 - 2004*E_2 + 2488*E_4)*M_2*r0_3 - 2*(708 - 779*E_2 + 842*E_4)*M*r0_4 + (678 + 1249*E_2)*r0_5)) + a_6*E*L*r0_2*(6*L_6*M*(40*M_2 + 54*M*r0 + 3*r0_2) + 2*L_4*M*(12576*M_4 - 8*(-1887 + 674*E_2)*M_3*r0 + 4*(1433 - 814*E_2)*M_2*r0_2 + 4*(113 - 66*E_2)*M*r0_3 + (57 + 317*E_2)*r0_4) - L_2*r0*(59968*M_6 - 72*(-217 + 44*E_2)*M_5*r0 + 4*(-17777 + 3124*E_2)*M_4*r0_2 + 2*(-17037 + 7136*E_2)*M_3*r0_3 + (221 + 2012*E_2)*M_2*r0_4 - 3*(103 + 852*E_2)*M*r0_5 + 21*r0_6) + r0_3*(-99448*M_6 + 4*(-13813 + 2608*E_2)*M_5*r0 + 2*(27917 + 1752*E_2)*M_4*r0_2 + (25417 - 12128*E_2)*M_3*r0_3 - 3*(1013 + 1192*E_2)*M_2*r0_4 + 12*(12 + 199*E_2)*M*r0_5 + 24*r0_6)) - 2*a_9*M*(2*L_4*(48*M_4 + 8*(77 + 27*E_2)*M_3*r0 + (1141 + 60*E_2 + 24*E_4)*M_2*r0_2 + 3*(214 - 105*E_2 + 4*E_4)*M*r0_3 - 108*(-1 + E_2)*r0_4) + L_2*r0*(384*(17 + 18*E_2)*M_5 - 32*(-171 - 523*E_2 + 129*E_4)*M_4*r0 + 4*(192 + 5491*E_2 - 1488*E_4)*M_3*r0_2 + (1250 + 8149*E_2 - 2808*E_4)*M_2*r0_3 - 2*(-598 + 627*E_2 + 216*E_4)*M*r0_4 + 12*(20 - 49*E_2)*r0_5) - 4*E_2*r0_2*(3936*M_6 + 4*(1771 + 216*E_2)*M_5*r0 + 2*(-955 + 1492*E_2)*M_4*r0_2 + (-8261 + 3360*E_2)*M_3*r0_3 + 12*(-256 + 131*E_2)*M_2*r0_4 + (359 + 265*E_2)*M*r0_5 + 168*r0_6)) - 2*a_7*M*r0*(8*L_6*(12*M_3 + (89 + 27*E_2)*M_2*r0 + 3*(35 - 2*E_2)*M*r0_2 - 9*(-3 + E_2)*r0_3) - 12*E_2*r0_4*(2652*M_5 + 8*(323 + 75*E_2)*M_4*r0 + (-1463 + 1256*E_2)*M_3*r0_2 + (-1411 + 836*E_2)*M_2*r0_3 + 12*(2 + 15*E_2)*M*r0_4 + 58*r0_5) + 2*L_4*(2240*M_5 + 48*(133 + 45*E_2)*M_4*r0 - 4*(-341 - 936*E_2 + 322*E_4)*M_3*r0_2 - 2*(325 - 1723*E_2 + 584*E_4)*M_2*r0_3 + (694 + 577*E_2 - 250*E_4)*M*r0_4 + 12*(25 - 2*E_2)*r0_5) + L_2*r0*(-15744*M_6 - 16*(557 + 184*E_2)*M_5*r0 + 4*(3682 + 385*E_2 - 1224*E_4)*M_4*r0_2 + 4*(1543 + 6142*E_2 - 3300*E_4)*M_3*r0_3 + (-1686 + 18007*E_2 - 9288*E_4)*M_2*r0_4 - 8*(-40 - 150*E_2 + 243*E_4)*M*r0_5 + 4*(84 - 23*E_2)*r0_6)) + a_8*E*L*r0*(6*L_4*M*(112*M_3 + 8*(46 + 7*E_2)*M_2*r0 - 2*(-74 + 9*E_2)*M*r0_2 - 3*(-3 + E_2)*r0_3) + L_2*M*(22528*M_5 - 32*(-1871 + 426*E_2)*M_4*r0 - 8*(-6691 + 1994*E_2)*M_3*r0_2 - 22*(-771 + 356*E_2)*M_2*r0_3 + (1013 - 1356*E_2)*M*r0_4 + 2*(27 + 244*E_2)*r0_5) + r0*(-62976*M_7 + 64*(-1164 + 107*E_2)*M_6*r0 + 212*(193 + 8*E_2)*M_5*r0_2 - 8*(-8869 + 1698*E_2)*M_4*r0_3 + (17573 - 14832*E_2)*M_3*r0_4 - (1229 + 2912*E_2)*M_2*r0_5 + 8*(1 + 119*E_2)*M*r0_6 - 6*r0_7)) - 2*a*M*r0_4*(84*L_10*r0_2M_2 - 2*L_8*(2*M - r0)*r0*(336*M_2 - 2*(155 + 21*E_2)*M*r0 + 9*(12 + 7*E_2)*r0_2) + 2*L_6*r0_3*(-1872*M_3 + 4*(470 + 187*E_2)*M_2*r0 - 2*(341 + 385*E_2 + 63*E_4)*M*r0_2 + 21*(5 + 11*E_2)*r0_3) + 2*L_2*r0_7*(-624*M_3 + 2*(302 + 691*E_2)*M_2*r0 - (194 + 1021*E_2 + 288*E_4)*M*r0_2 + 12*(2 + 17*E_2)*r0_3) + L_4*r0_5*(-3648*M_3 + 32*(106 + 117*E_2)*M_2*r0 - 2*(518 + 1539*E_2 + 306*E_4)*M*r0_2 + 9*(14 + 83*E_2)*r0_3) - 12*E_2*r0_10*(-18*M_2 + 4*r0_2 + M*(r0 + 21*E_2*r0)))))/(3.*r0_8*expr2_2);\n A31420 = (-8*r0*(6*a_5*E_2*M*(2*M + r0) - a_4*E*L*r0*(3*M + 2*r0) - 6*a*M*r0*(L_4 + (1 - 2*E_2)*L_2*r0_2 - 3*E_2*r0_4) + E*L*r0_3*(3*r0_3 + 2*L_2*(M + r0)) + 2*a_3*M*(6*E_2*r0_2*(3*M + 2*r0) + L_2*(-6*M - 3*r0 + 2*E_2*r0)) + a_2*E*L*r0*(2*L_2*(M - r0) + r0*(-6*M_2 + 7*M*r0 + r0_2))))/(a_2 + r0*(-2*M + r0));\n A31440 = (4*(2*a_11*E_2*M*(144*(-5 + E_2)*M_3 + (437 + 144*E_2)*M_2*r0 + 36*(24 + E_2)*M*r0_2 + 231*r0_3) + a_10*E*L*M*(-576*(-5 + E_2)*M_3 + 16*(162 - 59*E_2)*M_2*r0 + 3*(231 - 160*E_2)*M*r0_2 + 3*(21 - 22*E_2)*r0_3) + E*L*r0_5*(8*L_6*M*(104*M_2 - 106*M*r0 + 27*r0_2) + 2*L_4*r0_2*(728*M_3 - 2*(512 + 157*E_2)*M_2*r0 + (352 + 159*E_2)*M*r0_2 - 11*r0_3) - 2*L_2*r0_4*(-324*M_3 + 18*(43 + 36*E_2)*M_2*r0 - 2*(154 + 177*E_2)*M*r0_2 + r0_3) + r0_6*(-336*M_3 - 24*(-7 + 31*E_2)*M_2*r0 + 2*(-59 + 216*E_2)*M*r0_2 + 59*r0_3)) - 2*a*M*r0_3*(3*E_2*r0_8*(48*M_2 + 2*(29 - 54*E_2)*M*r0 - 41*r0_2) + 4*L_8*(104*M_2 - 106*M*r0 + 27*r0_2) + L_6*r0*(-2064*M_3 + 4*(641 + 28*E_2)*M_2*r0 - 4*(317 + 80*E_2)*M*r0_2 + (251 + 138*E_2)*r0_3) + L_2*r0_5*(-2016*M_3 + 12*(172 + 209*E_2)*M_2*r0 - 2*(377 + 939*E_2 + 252*E_4)*M*r0_2 + (113 + 402*E_2)*r0_3) + L_4*r0_3*(-3984*M_3 + 24*(170 + 71*E_2)*M_2*r0 - 2*(769 + 798*E_2 + 144*E_4)*M*r0_2 + (247 + 462*E_2)*r0_3)) - a_2*E*L*r0_3*(-2*L_6*M*(592*M_2 - 482*M*r0 + 103*r0_2) + r0_5*(12936*M_4 - 12*(563 + 102*E_2)*M_3*r0 + 2*(101 + 1368*E_2)*M_2*r0_2 + (5 - 1518*E_2)*M*r0_3 - 118*r0_4) + 2*L_4*r0*(480*M_4 + 4*(-181 + 256*E_2)*M_3*r0 + 16*(37 + 26*E_2)*M_2*r0_2 - (403 + 305*E_2)*M*r0_3 + 6*r0_4) + L_2*r0_3*(11304*M_4 + 4*(-1127 + 438*E_2)*M_3*r0 + 26*(15 + 94*E_2)*M_2*r0_2 - (1153 + 1912*E_2)*M*r0_3 + 23*r0_4)) - 2*a_9*M*(L_2*(720*M_3 + (1733 + 336*E_2 + 48*E_4)*M_2*r0 + 24*(48 - 38*E_2 + E_4)*M*r0_2 + 3*(77 - 155*E_2)*r0_3) - E_2*r0*(1344*(-3 + E_2)*M_4 + 4*(-3055 + 684*E_2)*M_3*r0 + (-6107 + 1872*E_2)*M_2*r0_2 + 2*(793 + 210*E_2)*M*r0_3 + 965*r0_4)) - 2*a_3*M*r0_2*(12*L_8*M - E_2*r0_6*(5184*M_3 + 72*(-29 + 24*E_2)*M_2*r0 + 4*(-274 + 321*E_2)*M*r0_2 + 581*r0_3) + 2*L_6*(1008*M_3 - 36*(-3 + 10*E_2)*M_2*r0 + 2*(-316 + 25*E_2)*M*r0_2 + (241 + 72*E_2)*r0_3) + 2*L_2*r0_3*(-4824*M_4 + 12*(204 + 109*E_2)*M_3*r0 + 2*(503 + 13*E_2 - 540*E_4)*M_2*r0_2 - (879 + 191*E_2 + 708*E_4)*M*r0_3 + 2*(117 + 136*E_2)*r0_4) + L_4*r0*(-9360*M_4 + 24*(251 + 122*E_2)*M_3*r0 - 16*(-155 + 78*E_2 + 45*E_4)*M_2*r0_2 - 4*(699 - 64*E_2 + 130*E_4)*M*r0_3 + (863 + 592*E_2)*r0_4)) + a_8*E*L*(3*L_2*M*(192*M_3 + 16*(63 + 10*E_2)*M_2*r0 + 4*(110 - 3*E_2)*M*r0_2 + (41 - 20*E_2)*r0_3) + r0*(-768*(-21 + 4*E_2)*M_5 + 16*(1548 - 485*E_2)*M_4*r0 + 2*(5797 - 3244*E_2)*M_3*r0_2 + (1553 - 1912*E_2)*M_2*r0_3 + 2*(65 + 12*E_2)*M*r0_4 + r0_5)) + a_4*E*L*r0_2*(6*L_6*M*(20*M + r0) + 2*L_4*(4032*M_4 - 4*(-423 + 388*E_2)*M_3*r0 + 2*(131 - 25*E_2)*M_2*r0_2 + (116 + 149*E_2)*M*r0_3 + 5*r0_4) + L_2*r0*(-25248*M_5 + 16*(61 - 120*E_2)*M_4*r0 + 4*(4271 - 1696*E_2)*M_3*r0_2 + 12*(187 - 113*E_2)*M_2*r0_3 + (543 + 1640*E_2)*M*r0_4 - 10*r0_5) + r0_3*(-46632*M_5 + 12*(-353 + 492*E_2)*M_4*r0 + 2*(9973 - 1764*E_2)*M_3*r0_2 + (11 - 4032*E_2)*M_2*r0_3 + 12*(9 + 158*E_2)*M*r0_4 + 60*r0_5)) - 2*a_7*M*(2*L_4*(72*M_3 + 8*(53 + 27*E_2)*M_2*r0 + 12*(57 + 5*E_2 + E_4)*M*r0_2 + 3*(77 - 38*E_2)*r0_3) + 2*L_2*r0*(288*(7 + 6*E_2)*M_4 + 2*(41 + 1242*E_2 - 504*E_4)*M_3*r0 + (-307 + 4030*E_2 - 888*E_4)*M_2*r0_2 + (823 + 406*E_2 - 180*E_4)*M*r0_3 + 2*(176 - 295*E_2)*r0_4) - E_2*r0_2*(10944*M_5 + 12*(1315 + 144*E_2)*M_4*r0 + 8*(-1103 + 702*E_2)*M_3*r0_2 + 5*(-3001 + 1008*E_2)*M_2*r0_3 + 24*(-17 + 57*E_2)*M*r0_4 + 1572*r0_5)) + 2*a_5*M*r0*(-3*L_6*(32*M_2 + 4*(19 + 9*E_2)*M*r0 + (77 + 2*E_2)*r0_2) + E_2*r0_4*(15660*M_4 + 252*(31 + 12*E_2)*M_3*r0 + 5*(-2033 + 1008*E_2)*M_2*r0_2 + 108*(-19 + 18*E_2)*M*r0_3 + 1296*r0_4) - 2*L_4*(1248*M_4 + 2260*M_3*r0 - 4*(305 - 120*E_2 + 82*E_4)*M_2*r0_2 - 2*(19 - 441*E_2 + 52*E_4)*M*r0_3 - 49*(-11 + E_2)*r0_4) + L_2*r0*(10944*M_5 - 12*(-29 + 92*E_2)*M_4*r0 + 4*(-1955 + 244*E_2 + 576*E_4)*M_3*r0_2 + (1991 - 5956*E_2 + 3984*E_4)*M_2*r0_3 + 2*(255 - 1600*E_2 + 648*E_4)*M*r0_4 + 3*(-276 + 191*E_2)*r0_5)) + a_6*E*L*r0*(6*L_4*M*(112*M_2 + 2*(65 + 14*E_2)*M*r0 + (11 + E_2)*r0_2) + L_2*(12288*M_5 - 48*(-443 + 168*E_2)*M_4*r0 - 8*(-1748 + 573*E_2)*M_3*r0_2 + 2*(1259 - 122*E_2)*M_2*r0_3 + (189 + 376*E_2)*M*r0_4 + 11*r0_5) + r0*(-43776*M_6 + 96*(-336 + 55*E_2)*M_5*r0 - 44*(-673 + 48*E_2)*M_4*r0_2 + 8*(2774 - 1247*E_2)*M_3*r0_3 - 7*(-143 + 496*E_2)*M_2*r0_4 + 2*(31 + 450*E_2)*M*r0_5 + 2*r0_6))))/(3.*r0_5*expr2_2);\n A31600 = (-2*r0_4*(2*a_3*E_2*M - a_2*E*L*r0 + E*L*r0_3 - 2*a*M*(L_2 - 3*E_2*r0_2)))/(a_2 + r0*(-2*M + r0));\n A31620 = (12*a_9*E_2*M*(4*(-13 + 3*E_2)*M_2 + 2*(31 + 3*E_2)*M*r0 + 41*r0_2) - 3*a_8*E*L*(32*(-13 + 3*E_2)*M_3 + 96*(-2 + E_2)*M_2*r0 + (-9 + 26*E_2)*M*r0_2 + 3*r0_3) + E*L*r0_4*(16*L_4*M*(32*M_2 - 34*M*r0 + 9*r0_2) + L_2*r0_2*(408*M_3 - 4*(207 + 86*E_2)*M_2*r0 + 2*(167 + 90*E_2)*M*r0_2 - 11*r0_3) + 4*r0_4*(-80*M_3 - 20*(-2 + 5*E_2)*M_2*r0 + (-20 + 57*E_2)*M*r0_2 + 10*r0_3)) - 2*a_7*M*(3*L_2*(104*M_2 + 4*(55 + E_4)*M*r0 + (82 - 93*E_2)*r0_2) - 4*E_2*r0*(88*(-3 + E_2)*M_3 + (-947 + 178*E_2)*M_2*r0 + 4*(-23 + 19*E_2)*M*r0_2 + 202*r0_3)) - 2*a*M*r0_2*(4*L_6*(52*M_2 - 56*M*r0 + 15*r0_2) - 6*E_2*r0_6*(4*M_2 + 2*(-22 + 15*E_2)*M*r0 + 21*r0_2) + 2*L_4*r0*(-720*M_3 + 4*(204 + 19*E_2)*M_2*r0 - 2*(185 + 52*E_2)*M*r0_2 + (71 + 39*E_2)*r0_3) + L_2*r0_3*(-1440*M_3 + 4*(386 + 241*E_2)*M_2*r0 - 16*(39 + 47*E_2 + 9*E_4)*M*r0_2 + (106 + 177*E_2)*r0_3)) + a_6*E*L*(3*L_2*(96*M_3 + 8*(24 + 5*E_2)*M_2*r0 + 4*(1 - 2*E_2)*M*r0_2 - 3*r0_3) - r0*(128*(-33 + 8*E_2)*M_4 + 8*(-684 + 287*E_2)*M_3*r0 + 46*(-31 + 22*E_2)*M_2*r0_2 + (17 + 30*E_2)*M*r0_3 + 31*r0_4)) + a_2*E*L*r0_2*(8*L_4*M*(74*M_2 - 55*M*r0 + 14*r0_2) + L_2*r0*(-2992*M_4 + 16*(39 - 58*E_2)*M_3*r0 - 392*(-1 + E_2)*M_2*r0_2 + 4*(81 + 80*E_2)*M*r0_3 - 15*r0_4) + r0_3*(-7480*M_4 + 4*(673 + 200*E_2)*M_3*r0 + 2*(367 - 714*E_2)*M_2*r0_2 + (-31 + 582*E_2)*M*r0_3 + 43*r0_4)) - 2*a_5*M*(6*L_4*(12*M_2 + 6*(5 + 3*E_2)*M*r0 + (41 - 4*E_2)*r0_2) + L_2*r0*(96*(11 + 6*E_2)*M_3 - 4*(263 - 44*E_2 + 82*E_4)*M_2*r0 + 8*(11 + 155*E_2 - 13*E_4)*M*r0_2 + (562 - 469*E_2)*r0_3) - 4*E_2*r0_2*(840*M_4 + 2*(473 + 36*E_2)*M_3*r0 + 2*(-446 + 143*E_2)*M_2*r0_2 + (-491 + 170*E_2)*M*r0_3 + 245*r0_4)) - 2*a_3*M*r0*(24*L_6*M - 4*E_2*r0_4*(666*M_3 + (-37 + 126*E_2)*M_2*r0 + 4*(-90 + 37*E_2)*M*r0_2 + 136*r0_3) + 2*L_4*(272*M_3 + 12*(14 - 15*E_2)*M_2*r0 + 16*(-27 + 4*E_2)*M*r0_2 + (194 + 27*E_2)*r0_3) + L_2*r0*(-3360*M_4 + 104*(17 + 10*E_2)*M_3*r0 - 4*(-209 + 255*E_2 + 90*E_4)*M_2*r0_2 - 4*(281 - 166*E_2 + 65*E_4)*M*r0_3 + (422 - 13*E_2)*r0_4)) + a_4*E*L*r0*(24*L_4*M*(7*M - r0) + L_2*(2560*M_4 - 8*(-237 + 194*E_2)*M_3*r0 + 4*(289 + 10*E_2)*M_2*r0_2 + 2*(17 + 58*E_2)*M*r0_3 - 13*r0_4) - r0*(13440*M_5 + 16*(252 - 101*E_2)*M_4*r0 + 4*(-1827 + 422*E_2)*M_3*r0_2 + 8*(-194 + 219*E_2)*M_2*r0_3 + (43 - 402*E_2)*M*r0_4 + 19*r0_5)))/(3.*r0_2*expr2_2);\n A31800 = (r0*(6*a_7*E_2*M*(4*(-4 + E_2)*M + 29*r0) - 3*a_6*E*L*(16*(-4 + E_2)*M_2 + 10*E_2*M*r0 + 3*r0_2) - 2*a_5*M*(L_2*(48*M + 87*r0 - 30*E_2*r0) + E_2*r0*(-32*(-3 + E_2)*M_2 + (484 - 76*E_2)*M*r0 - 203*r0_2)) + E*L*r0_3*(16*L_2*M*(10*M_2 - 11*M*r0 + 3*r0_2) + r0_2*(-104*M_3 + (52 - 76*E_2)*M_2*r0 + 2*(-11 + 21*E_2)*M*r0_2 + 11*r0_3)) - a_4*E*L*(-6*L_2*M*(8*M - 5*r0) + r0*(128*(-3 + E_2)*M_3 + 20*(-24 + 11*E_2)*M_2*r0 + 2*(11 + E_2)*M*r0_2 + 23*r0_3)) + 2*a_3*M*(-12*L_4*M + 2*L_2*r0*(-48*M_2 + 2*(61 + 8*E_2)*M*r0 - 61*r0_2) + E_2*r0_2*(384*M_3 + 332*M_2*r0 + 4*(-128 + 25*E_2)*M*r0_2 + 161*r0_3)) + 2*a*M*r0*(-4*L_4*(8*M_2 - 10*M*r0 + 3*r0_2) + 9*E_2*r0_4*(4*M_2 + 4*(-3 + E_2)*M*r0 + 5*r0_2) + L_2*r0*(384*M_3 - 4*(107 + 40*E_2)*M_2*r0 + 4*(47 + 32*E_2)*M*r0_2 - 5*(7 + 6*E_2)*r0_3)) + a_2*E*L*r0*(2*L_2*M*(64*M_2 - 38*M*r0 + 13*r0_2) + r0*(-1536*M_4 + 32*(6 + 5*E_2)*M_3*r0 - 140*(-3 + 2*E_2)*M_2*r0_2 + 2*(-6 + 35*E_2)*M*r0_3 - 3*r0_4))))/(12.*expr2_2);\n A32040 = (-192*E*L*expr1_2)/(a_2 + r0*(-2*M + r0));\n A32060 = (32*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-24*a_9*E_2*M*(4*M_3 + 4*M_2*r0 - M*r0_2 - r0_3) + a_8*E*L*M*(192*M_3 + 24*(8 + E_2)*M_2*r0 + (49 - 12*E_2)*M*r0_2 + 6*(1 - 2*E_2)*r0_3) + E*L*r0_6*(-4*L_4*M*(71*M - 37*r0) + 2*L_2*r0_2*(-162*M_2 + (45 + 16*E_2)*M*r0 + 21*r0_2) + r0_4*(-52*M_2 + 2*(-23 + 20*E_2)*M*r0 + 39*r0_2)) + 2*a_6*E*L*r0*(-1536*M_5 + 208*(-6 + E_2)*M_4*r0 + 24*(7 + 20*E_2)*M_3*r0_2 + 6*(32 + 35*E_2)*M_2*r0_3 + (13 + 2*E_2)*M*r0_4 - 3*r0_5 + L_2*M*(60*M_2 + 4*(2 - 3*E_2)*M*r0 + 3*(1 - 2*E_2)*r0_2)) + 4*a*M*r0_3*(3*E_2*r0_7*(-17*M + 15*r0) + 3*L_6*(44*M_2 - 17*M*r0 - 3*r0_2) + L_4*r0_2*(192*M_2 + 2*(-27 + 8*E_2)*M*r0 + 3*(-8 + 3*E_2)*r0_2) + L_2*r0_4*(60*M_2 - (3 + 85*E_2)*M*r0 + 15*(-1 + 5*E_2)*r0_2)) + 2*a_2*E*L*r0_3*(-2*L_4*M*(220*M_2 + 9*M*r0 - 37*r0_2) + L_2*r0_2*(-1006*M_3 + (-15 + 76*E_2)*M_2*r0 + (177 + 26*E_2)*M*r0_2 + 18*r0_3) + r0_4*(-494*M_3 + 3*(-3 + 98*E_2)*M_2*r0 + 3*(17 + 18*E_2)*M*r0_2 + 36*r0_3)) + 4*a_3*M*r0_2*(-6*L_6*r0 + 3*E_2*r0_5*(36*M_2 + 9*M*r0 + 37*r0_2) + 2*L_4*(228*M_3 + 2*(3 + 11*E_2)*M_2*r0 + 2*(-24 + 7*E_2)*M*r0_2 + 9*(-2 + E_2)*r0_3) + L_2*r0_2*(312*M_3 - 4*(-9 + 7*E_2)*M_2*r0 - (60 + E_2)*M*r0_2 + (-36 + 121*E_2)*r0_3)) + 4*a_7*M*(-(L_2*(24*M_3 + 24*(1 + E_2)*M_2*r0 + (18 - 17*E_2)*M*r0_2 + 3*(2 - 5*E_2)*r0_3)) + 3*E_2*r0*(128*M_4 + 156*M_3*r0 + 24*M_2*r0_2 + 7*M*r0_3 + 11*r0_4)) + a_4*E*L*r0_2*(-24*L_4*M_2 - 2*L_2*(1616*M_4 + 8*(64 - 11*E_2)*M_3*r0 - (239 + 64*E_2)*M_2*r0_2 - (87 + 4*E_2)*M*r0_3 + 3*r0_4) + r0_2*(-3700*M_4 + 4*(-245 + 306*E_2)*M_3*r0 + 3*(183 + 340*E_2)*M_2*r0_2 + 84*(2 + E_2)*M*r0_3 + 27*r0_4)) + 4*a_5*M*r0*(-3*L_4*(4*M_2 + (6 - 4*E_2)*M*r0 + (4 - 3*E_2)*r0_2) + 3*E_2*r0_3*(204*M_3 + 108*M_2*r0 + 31*M*r0_2 + 31*r0_3) + L_2*(384*M_4 + 4*(39 + 62*E_2)*M_3*r0 + 4*(-21 + E_2)*M_2*r0_2 + (-75 + 13*E_2)*M*r0_3 + (-27 + 61*E_2)*r0_4))))/(3.*r0_7*expr2_2);\n A32220 = (-96*E*L*r0_3*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/(a_2 + r0*(-2*M + r0));\n A32240 = (8*(-12*a_9*E_2*M*(24*M_3 + 36*M_2*r0 + 10*M*r0_2 - r0_3) + a_8*E*L*(576*M_4 + 144*(4 + E_2)*M_3*r0 + (193 + 72*E_2)*M_2*r0_2 + 42*M*r0_3 + 6*r0_4) + E*L*r0_4*(4*L_6*M*(-2*M + r0) + 12*L_2*r0_4*(-90*M_2 + 2*(13 + 3*E_2)*M*r0 + 11*r0_2) + 2*L_4*r0_2*(-400*M_2 + (185 - 2*E_2)*M*r0 + 12*r0_2) + 3*r0_6*(-100*M_2 + 14*(-1 + 2*E_2)*M*r0 + 35*r0_2)) + 4*a*M*r0_3*(9*E_2*r0_7*(-11*M + 12*r0) + L_6*(360*M_2 + (-177 + 4*E_2)*M*r0 - 6*r0_2) + 3*L_4*r0_2*(192*M_2 + (-86 + 3*E_2)*M*r0 + (-8 + 15*E_2)*r0_2) + 3*L_2*r0_4*(72*M_2 - 3*(9 + 16*E_2)*M*r0 + 2*(-3 + 29*E_2)*r0_2)) + 2*a_6*E*L*r0*(-4608*M_5 + 48*(-78 + 7*E_2)*M_4*r0 + 2*(199 + 468*E_2)*M_3*r0_2 + 7*(101 + 72*E_2)*M_2*r0_3 + 3*(39 + 14*E_2)*M*r0_4 + 6*r0_5 + L_2*(264*M_3 + 2*(73 + 9*E_2)*M_2*r0 + 39*M*r0_2 + 6*r0_3)) - 2*a_2*E*L*r0_3*(L_4*(1296*M_3 + 4*(-24 + E_2)*M_2*r0 + (-221 + 2*E_2)*M*r0_2 + 9*r0_3) - 3*L_2*r0_2*(-1128*M_3 + 6*(9 + 17*E_2)*M_2*r0 + (197 + 24*E_2)*M*r0_2 + 19*r0_3) - 3*r0_4*(-588*M_3 + 2*(-5 + 96*E_2)*M_2*r0 + (85 + 42*E_2)*M*r0_2 + 35*r0_3)) - 4*a_3*M*r0_2*(3*L_6*(2*M + r0) - 9*E_2*r0_5*(36*M_2 + 19*M*r0 + 29*r0_2) + L_2*r0_2*(-1008*M_3 - 6*(-6 + 71*E_2)*M_2*r0 + (228 - 97*E_2)*M*r0_2 + (39 - 223*E_2)*r0_3) - 3*L_4*(432*M_3 + 4*(-7 + 18*E_2)*M_2*r0 + (-102 + E_2)*M*r0_2 - (10 + E_2)*r0_3)) - 4*a_7*M*(L_2*(72*M_3 + 12*(3 + 10*E_2)*M_2*r0 + (6 + 79*E_2)*M*r0_2 + 3*(1 + E_2)*r0_3) - 3*E_2*r0*(384*M_4 + 492*M_3*r0 + 128*M_2*r0_2 + 15*M*r0_3 + 17*r0_4)) + a_4*E*L*r0_2*(6*L_4*(14*M_2 + 6*M*r0 + r0_2) + L_2*(-9696*M_4 + 8*(-403 + 36*E_2)*M_3*r0 + 8*(251 + 63*E_2)*M_2*r0_2 + 24*(26 + 3*E_2)*M*r0_3 - 6*r0_4) + 3*r0_2*(-3620*M_4 + 4*(-299 + 192*E_2)*M_3*r0 + (635 + 696*E_2)*M_2*r0_2 + 4*(62 + 21*E_2)*M*r0_3 + 37*r0_4)) - 4*a_5*M*r0*(-3*E_2*r0_3*(540*M_3 + 360*M_2*r0 + 115*M*r0_2 + 67*r0_3) + L_2*(-1152*M_4 - 12*(33 + 80*E_2)*M_3*r0 + 2*(174 - 211*E_2)*M_2*r0_2 + (153 + 82*E_2)*M*r0_3 + 2*(12 - 23*E_2)*r0_4) + 6*L_4*(8*M_2 + (1 + E_2)*r0_2 + 2*M*(r0 + 2*E_2*r0)))))/(3.*r0_4*expr2_2);\n A32400 = (-12*E*L*r0_6)/(a_2 + r0*(-2*M + r0));\n A32420 = (2*(-24*a_7*E_2*M*(6*M_2 + 9*M*r0 + 2*r0_2) + 3*a_6*E*L*(96*M_3 + 12*(4 + 3*E_2)*M_2*r0 + 2*(5 + 6*E_2)*M*r0_2 + 3*r0_3) + a_4*E*L*r0*(-4608*M_4 + 48*(-30 + E_2)*M_3*r0 + 6*(167 + 68*E_2)*M_2*r0_2 + 2*(157 + 60*E_2)*M*r0_3 + 43*r0_4 + 3*L_2*(68*M_2 + 4*(5 + 2*E_2)*M*r0 + 3*r0_2)) + E*L*r0_3*(24*L_4*M*(-2*M + r0) + L_2*r0_2*(-744*M_2 + 268*M*r0 + 61*r0_2) + r0_4*(-444*M_2 + 2*(17 + 24*E_2)*M*r0 + 103*r0_2)) + 12*a*M*r0_2*(3*E_2*r0_5*(-5*M + 9*r0) + L_4*(108*M_2 + (-67 + 8*E_2)*M*r0 + (5 - 4*E_2)*r0_2) + L_2*r0_2*(84*M_2 + (-51 + 4*E_2)*M*r0 + (3 + 14*E_2)*r0_2)) + 12*a_5*M*(-2*L_2*(6*M_2 + (-3 + 11*E_2)*M*r0 + 2*(-1 + 3*E_2)*r0_2) + E_2*r0*(192*M_3 + 162*M_2*r0 + 17*M*r0_2 + 5*r0_3)) + a_2*E*L*r0_2*(24*L_4*M + L_2*(-2544*M_3 + 12*(31 - 4*E_2)*M_2*r0 + 24*(18 + E_2)*M*r0_2 + 10*r0_3) + r0_2*(-3204*M_3 + 2*(103 + 222*E_2)*M_2*r0 + 6*(79 + 22*E_2)*M*r0_2 + 137*r0_3)) + 12*a_3*M*r0*(-4*L_4*(M + (-1 + E_2)*r0) + 6*E_2*r0_3*(23*M_2 + 8*M*r0 + 6*r0_2) + L_2*(192*M_3 + 2*(-21 + 50*E_2)*M_2*r0 + (-47 + 2*E_2)*M*r0_2 + 7*(1 - 2*E_2)*r0_3))))/(3.*r0*expr2_2);\n A32600 = (r0_2*(-12*a_5*E_2*M*(2*M + 3*r0) + 3*a_4*E*L*(16*M_2 + 8*E_2*M*r0 + r0_2) + 2*a_2*E*L*r0*(12*L_2*M - 384*M_3 + 4*(18 - 5*E_2)*M_2*r0 + 7*(7 + 2*E_2)*M*r0_2 + 14*r0_3) + 12*a_3*M*(L_2*(-2*M + (3 - 4*E_2)*r0) + E_2*r0*(32*M_2 + 13*M*r0 + r0_2)) + E*L*r0_2*(20*L_2*M*(-2*M + r0) + r0_2*(-196*M_2 + 2*(15 + 2*E_2)*M*r0 + 37*r0_2)) + 4*a*M*r0*(3*E_2*r0_3*(M + 6*r0) + L_2*(96*M_2 + 5*(-15 + 4*E_2)*M*r0 - 12*(-1 + E_2)*r0_2))))/(6.*expr2_2);\n A33040 = (-32*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-(a_4*E*L*r0_2) + 6*a_5*E_2*M*(2*M + r0) - 6*a*M*r0*(L_4 - (-1 + E_2)*L_2*r0_2 - 3*E_2*r0_4) + E*L*r0_3*(L_2*(3*M + 2*r0) + r0_2*(-M + 4*r0)) + 2*a_3*M*(6*E_2*r0_2*(3*M + 2*r0) + L_2*(-6*M + (-3 + E_2)*r0)) + a_2*E*L*r0*(L_2*(4*M - r0) + r0*(-14*M_2 + 9*M*r0 + 3*r0_2))))/(r0_2*expr2_2);\n A33060 = (16*(-2*a_13*E_2*M*(2*M + r0)*(24*(-1 + E_2)*M_3 + (-253 + 36*E_2)*M_2*r0 + 12*(-7 + E_2)*M*r0_2 + 24*r0_3) + a_12*E*L*M*(192*(-1 + 2*E_2)*M_4 - 8*(120 + 73*E_2)*M_3*r0 - 4*(198 + 259*E_2)*M_2*r0_2 - 3*(61 + 104*E_2)*M*r0_3 + 6*(-1 + E_2)*r0_4) + E*L*r0_6*(168*L_8*M*r0_2M_2 + 2*L_6*M*r0_2*(908*M_2 - 14*(73 + 18*E_2)*M*r0 + (281 + 126*E_2)*r0_2) + L_4*r0_4*(1976*M_3 - 2*(1337 + 776*E_2)*M_2*r0 + (861 + 818*E_2)*M*r0_2 - 18*r0_3) + L_2*r0_6*(604*M_3 - 52*(20 + 31*E_2)*M_2*r0 + (285 + 904*E_2)*M*r0_2 + 33*r0_3) + r0_8*(-180*M_3 + 2*(95 - 294*E_2)*M_2*r0 + 2*(-73 + 175*E_2)*M*r0_2 + 45*r0_3)) + 2*a*M*r0_4*(-84*L_10*r0_2M_2 + 3*E_2*r0_10*(-180*M_2 + 2*(61 + 36*E_2)*M*r0 - 15*r0_2) + 2*L_6*r0_3*(1932*M_3 - 2*(847 + 493*E_2)*M_2*r0 + (373 + 1014*E_2 + 126*E_4)*M*r0_2 - 291*E_2*r0_3) + L_4*r0_5*(3816*M_3 - 4*(797 + 1375*E_2)*M_2*r0 + 2*(278 + 2417*E_2 + 342*E_4)*M*r0_2 + 3*(17 - 393*E_2)*r0_3) + L_2*r0_7*(1320*M_3 - 4*(296 + 957*E_2)*M_2*r0 + 2*(131 + 1562*E_2 + 306*E_4)*M*r0_2 + 3*(1 - 226*E_2)*r0_3) + 2*L_8*r0*(684*M_3 - 4*(215 + 21*E_2)*M_2*r0 + 2*(197 + 84*E_2)*M*r0_2 - 3*(22 + 21*E_2)*r0_3)) + a_2*E*L*r0_4*(168*L_8*M*(6*M_2 - 5*M*r0 + r0_2) + 2*L_6*M*r0*(1144*M_3 + (908 - 672*E_2)*M_2*r0 - 8*(167 + 63*E_2)*M*r0_2 + 3*(139 + 84*E_2)*r0_3) + L_4*r0_3*(-480*M_4 - 8*(-639 + 335*E_2)*M_3*r0 - 16*(282 + 247*E_2)*M_2*r0_2 + (1539 + 2384*E_2)*M*r0_3 + 15*r0_4) + L_2*r0_5*(-12728*M_4 + 4*(3143 + 960*E_2)*M_3*r0 - 2*(2269 + 3524*E_2)*M_2*r0_2 + (825 + 3392*E_2)*M*r0_3 + 105*r0_4) + r0_7*(-9744*M_4 + 24*(339 + 74*E_2)*M_3*r0 - 4*(415 + 671*E_2)*M_2*r0_2 + 9*(-27 + 176*E_2)*M*r0_3 + 141*r0_4)) + 2*a_3*M*r0_3*(2*E_2*r0_8*(1422*M_3 + (-1493 + 1062*E_2)*M_2*r0 + (793 + 482*E_2)*M*r0_2 - 135*r0_3) - 2*L_8*(1192*M_3 - 36*(2 + 7*E_2)*M_2*r0 - 2*(155 + 21*E_2)*M*r0_2 + 3*(20 + 21*E_2)*r0_3) + L_2*r0_5*(9600*M_4 - 12*(369 + 527*E_2)*M_3*r0 + 2*(-1251 - 3031*E_2 + 1152*E_4)*M_2*r0_2 + 2*(428 + 3823*E_2 + 1194*E_4)*M*r0_3 + (141 - 2290*E_2)*r0_4) + 2*L_4*r0_3*(9120*M_4 - 4*(1116 + 1943*E_2)*M_3*r0 + 18*(-153 - 56*E_2 + 72*E_4)*M_2*r0_2 + (843 + 3982*E_2 + 1042*E_4)*M*r0_3 + 23*(9 - 64*E_2)*r0_4) + 2*L_6*r0*(4512*M_4 - 2*(1787 + 986*E_2)*M_3*r0 + (-1461 + 470*E_2 + 252*E_4)*M_2*r0_2 + 2*(379 + 495*E_2 + 126*E_4)*M*r0_3 + 18*(4 - 33*E_2)*r0_4)) + 2*a_11*M*(L_2*(-48*(-1 + 6*E_2)*M_4 - 2*(25 - 336*E_2 + 24*E_4)*M_3*r0 + (-13 + 1315*E_2)*M_2*r0_2 + 6*(10 + 49*E_2 + 2*E_4)*M*r0_3 + 24*(1 - 3*E_2)*r0_4) + 2*E_2*r0*(16*(-255 + 74*E_2)*M_5 + 8*(-1056 + 293*E_2)*M_4*r0 + 3*(-1571 + 528*E_2)*M_3*r0_2 + 2*(-169 + 203*E_2)*M_2*r0_3 + 2*(11 + 13*E_2)*M*r0_4 - 96*r0_5)) + a_4*E*L*r0_3*(2*L_6*M*(4672*M_3 - 12*(-65 + 98*E_2)*M_2*r0 - 4*(151 + 63*E_2)*M*r0_2 + 7*(19 + 18*E_2)*r0_3) + L_4*r0*(-13088*M_5 - 8*(-3535 + 254*E_2)*M_4*r0 - 4*(-2965 + 2696*E_2)*M_3*r0_2 - 4*(1228 + 987*E_2)*M_2*r0_3 + 2*(351 + 1160*E_2)*M*r0_4 + 33*r0_5) + L_2*r0_3*(-66044*M_5 + 4*(8387 + 4320*E_2)*M_4*r0 + (28813 - 3160*E_2)*M_3*r0_2 - 2*(4883 + 4878*E_2)*M_2*r0_3 + 3*(193 + 1588*E_2)*M*r0_4 + 111*r0_5) + r0_5*(-55644*M_5 + 36*(413 + 134*E_2)*M_4*r0 + (20481 + 1156*E_2)*M_3*r0_2 - 2*(3279 + 2288*E_2)*M_2*r0_3 + (-151 + 2842*E_2)*M*r0_4 + 153*r0_5)) + 2*a_5*M*r0_2*(12*L_8*(2*M_2 - 7*M*r0 + 2*r0_2) + E_2*r0_6*(19404*M_4 + 1152*(-1 + 6*E_2)*M_3*r0 + (-6861 + 7268*E_2)*M_2*r0_2 + 2*(1267 + 842*E_2)*M*r0_3 - 660*r0_4) + 2*L_6*(-2880*M_4 + 8*(-415 + 18*E_2)*M_3*r0 + 7*(69 + 52*E_2 + 36*E_4)*M_2*r0_2 + (403 + 96*E_2 + 126*E_4)*M*r0_3 + 9*(12 - 35*E_2)*r0_4) + L_2*r0_3*(21984*M_5 + 12*(65 + 721*E_2)*M_4*r0 + 4*(-3531 - 5738*E_2 + 1116*E_4)*M_3*r0_2 + (-1143 - 7025*E_2 + 7824*E_4)*M_2*r0_3 + 6*(281 + 1112*E_2 + 584*E_4)*M*r0_4 + (429 - 3134*E_2)*r0_5) + L_4*r0*(20640*M_5 - 4*(885 + 2344*E_2)*M_4*r0 + 4*(-5035 - 5092*E_2 + 612*E_4)*M_3*r0_2 + (-1081 - 624*E_2 + 5264*E_4)*M_2*r0_3 + 2*(1248 + 1821*E_2 + 1070*E_4)*M*r0_4 + (747 - 2737*E_2)*r0_5)) + a_10*E*L*M*(L_2*(384*M_4 + 24*(-7 + 10*E_2)*M_3*r0 - 16*(57 + 85*E_2)*M_2*r0_2 - 3*(105 + 236*E_2)*M*r0_3 + 6*(-3 + 2*E_2)*r0_4) + r0*(-128*(-255 + 38*E_2)*M_5 + 16*(3192 - 445*E_2)*M_4*r0 + 2*(10011 - 3416*E_2)*M_3*r0_2 - (2713 + 6368*E_2)*M_2*r0_3 - (2041 + 1740*E_2)*M*r0_4 + 2*(-41 + 104*E_2)*r0_5)) + 2*a_9*M*(L_4*(-48*M_4 - 8*(25 + 9*E_2)*M_3*r0 + (-281 + 1116*E_2 + 48*E_4)*M_2*r0_2 + 6*(6 + 83*E_2 + 4*E_4)*M*r0_3 - 72*(-1 + E_2)*r0_4) + L_2*r0*(-96*(85 + 72*E_2)*M_5 + 16*(-540 - 1403*E_2 + 252*E_4)*M_4*r0 + 8*(-141 - 2558*E_2 + 678*E_4)*M_3*r0_2 + (1543 - 2299*E_2 + 2832*E_4)*M_2*r0_3 + 4*(220 + 75*E_2 + 147*E_4)*M*r0_4 + 12*(17 - 61*E_2)*r0_5) + E_2*r0_2*(16128*M_6 + 8*(2903 + 504*E_2)*M_5*r0 + 4*(-3431 + 3356*E_2)*M_4*r0_2 + 2*(-12925 + 6576*E_2)*M_3*r0_3 + 12*(-421 + 402*E_2)*M_2*r0_4 + 8*(55 + 68*E_2)*M*r0_5 - 567*r0_6)) - a_6*E*L*r0_2*(6*L_6*M*(40*M_2 - 6*M*r0 + r0_2) - 4*L_4*M*(6624*M_4 + 4*(2283 - 632*E_2)*M_3*r0 + (1591 - 2186*E_2)*M_2*r0_2 - 2*(304 + 243*E_2)*M*r0_3 + 2*(-12 + 95*E_2)*r0_4) + r0_3*(102120*M_6 + 4*(9595 + 132*E_2)*M_5*r0 - 2*(36117 + 3464*E_2)*M_4*r0_2 + (-15573 + 4304*E_2)*M_3*r0_3 + (9519 + 4568*E_2)*M_2*r0_4 + (227 - 2528*E_2)*M*r0_5 - 63*r0_6) - L_2*r0*(-63168*M_6 + 32*(138 + 143*E_2)*M_5*r0 + 8*(12187 + 668*E_2)*M_4*r0_2 - 2*(-9847 + 6776*E_2)*M_3*r0_3 - 5*(2017 + 1380*E_2)*M_2*r0_4 + (-219 + 2980*E_2)*M*r0_5 + 39*r0_6)) + 2*a_7*M*r0*(4*L_6*(6*M_3 + (-61 + 54*E_2)*M_2*r0 + 3*(-9 + 20*E_2)*M*r0_2 - 6*(-3 + E_2)*r0_3) + 6*E_2*r0_4*(5196*M_5 + 8*(452 + 189*E_2)*M_4*r0 + (-3323 + 2800*E_2)*M_3*r0_2 + (-1395 + 1516*E_2)*M_2*r0_3 + (291 + 236*E_2)*M*r0_4 - 139*r0_5) - 2*L_4*(2336*M_5 + 24*(323 + 108*E_2)*M_4*r0 + 2*(1597 + 2796*E_2 - 620*E_4)*M_3*r0_2 + (-857 + 824*E_2 - 1360*E_4)*M_2*r0_3 - (701 + 191*E_2 + 382*E_4)*M*r0_4 + 6*(-38 + 87*E_2)*r0_5) + L_2*r0*(16128*M_6 + 8*(1153 + 660*E_2)*M_5*r0 + 4*(-4405 - 3027*E_2 + 1152*E_4)*M_4*r0_2 + 2*(-5147 - 18986*E_2 + 5352*E_4)*M_3*r0_3 + 3*(577 - 2455*E_2 + 2784*E_4)*M_2*r0_4 + 4*(478 + 539*E_2 + 576*E_4)*M*r0_5 + (471 - 2182*E_2)*r0_6)) - a_8*E*L*r0*(6*L_4*M*(8*M_3 + 8*(8 + 7*E_2)*M_2*r0 + 2*(8 + 33*E_2)*M*r0_2 - (-3 + E_2)*r0_3) + L_2*M*(-23296*M_5 + 16*(-4603 + 792*E_2)*M_4*r0 + 8*(-6775 + 1466*E_2)*M_3*r0_2 + (-3009 + 10664*E_2)*M_2*r0_3 + 4*(1039 + 822*E_2)*M*r0_4 + 4*(69 - 179*E_2)*r0_5) + r0*(64512*M_7 - 192*(-338 + 17*E_2)*M_6*r0 - 8*(7809 + 4*E_2)*M_5*r0_2 + 4*(-17149 + 284*E_2)*M_4*r0_3 + (-1175 + 9016*E_2)*M_3*r0_4 + 3*(2223 + 1172*E_2)*M_2*r0_5 - 3*(-83 + 374*E_2)*M*r0_6 - 6*r0_7))))/(3.*r0_8*expr2_3);\n A33220 = (-16*r0*(6*a_5*E_2*M*(2*M + r0) - a_4*E*L*r0*(3*M + 2*r0) - 6*a*M*r0*(L_4 + (1 - 2*E_2)*L_2*r0_2 - 3*E_2*r0_4) + E*L*r0_3*(L_2*(M + 3*r0) + r0_2*(-M + 4*r0)) + 2*a_3*M*(6*E_2*r0_2*(3*M + 2*r0) + L_2*(-6*M - 3*r0 + 2*E_2*r0)) + 2*a_2*E*L*r0*(L_2*(M - r0) + r0*(-4*M_2 + 4*M*r0 + r0_2))))/expr2_2;\n A33240 = (4*(2*a_11*E_2*M*(48*(-6 + E_2)*M_3 + (973 + 24*E_2)*M_2*r0 + 870*M*r0_2 + 150*r0_3) + a_10*E*L*M*(1152*M_3 + 4*(120 - 331*E_2)*M_2*r0 + 9*(11 - 92*E_2)*M*r0_2 + 6*(7 - 6*E_2)*r0_3) + E*L*r0_5*(430*L_6*M*r0_2M_2 + 2*L_4*r0_2*(1548*M_3 - 26*(79 + 25*E_2)*M_2*r0 + (703 + 325*E_2)*M*r0_2 - 36*r0_3) + L_2*r0_4*(1136*M_3 - 2*(1281 + 1336*E_2)*M_2*r0 + (1015 + 1448*E_2)*M*r0_2 - 27*r0_3) + 3*r0_6*(-260*M_3 + (202 - 488*E_2)*M_2*r0 + 2*(-56 + 143*E_2)*M*r0_2 + 35*r0_3)) - 2*a*M*r0_3*(-9*E_2*r0_8*(-144*M_2 + 4*(22 + 15*E_2)*M*r0 - 7*r0_2) + 4*L_8*(214*M_2 - 215*M*r0 + 54*r0_2) + 2*L_6*r0*(-2112*M_3 + 2*(1183 + 106*E_2)*M_2*r0 - 2*(467 + 213*E_2)*M*r0_2 + 3*(45 + 53*E_2)*r0_3) + 2*L_4*r0_3*(-4128*M_3 + 4*(954 + 661*E_2)*M_2*r0 - (990 + 2569*E_2 + 324*E_4)*M*r0_2 + 3*(16 + 233*E_2)*r0_3) + 3*L_2*r0_5*(-1408*M_3 + 16*(83 + 148*E_2)*M_2*r0 - 8*(44 + 249*E_2 + 45*E_4)*M*r0_2 + (17 + 458*E_2)*r0_3)) + a_2*E*L*r0_3*(2*L_6*M*(1304*M_2 - 1102*M*r0 + 221*r0_2) + 4*L_4*r0*(-536*M_4 + 2*(981 - 433*E_2)*M_3*r0 - 6*(205 + 106*E_2)*M_2*r0_2 + (307 + 316*E_2)*M*r0_3 + 21*r0_4) + L_2*r0_3*(-23432*M_4 + 8*(2403 + 218*E_2)*M_3*r0 - 6*(831 + 1436*E_2)*M_2*r0_2 + 3*(433 + 1344*E_2)*M*r0_3 + 69*r0_4) + 3*r0_5*(-8736*M_4 + 4*(1535 + 362*E_2)*M_3*r0 - 8*(93 + 250*E_2)*M_2*r0_2 + 6*(-31 + 170*E_2)*M*r0_3 + 83*r0_4)) - 2*a_9*M*(L_2*(288*(1 + E_2)*M_3 + (1213 - 624*E_2 + 48*E_4)*M_2*r0 + 6*(141 - 208*E_2)*M*r0_2 + 6*(25 - 49*E_2)*r0_3) - E_2*r0*(96*(-111 + 31*E_2)*M_4 + 4*(-4871 + 1224*E_2)*M_3*r0 + (-6155 + 2472*E_2)*M_2*r0_2 + 6*(315 + 62*E_2)*M*r0_3 + 480*r0_4)) - 2*a_3*M*r0_2*(-3*E_2*r0_6*(2712*M_3 + 4*(-493 + 324*E_2)*M_2*r0 + 664*(1 + E_2)*M*r0_2 - 55*r0_3) + 2*L_6*(2112*M_3 + 12*(35 - 51*E_2)*M_2*r0 - 2*(467 + 64*E_2)*M*r0_2 + 9*(22 + 17*E_2)*r0_3) + 2*L_4*r0*(-9600*M_4 + 8*(729 + 388*E_2)*M_3*r0 + 2*(1779 + 631*E_2 - 324*E_4)*M_2*r0_2 - (2001 + 1864*E_2 + 640*E_4)*M*r0_3 + 39*(3 + 22*E_2)*r0_4) + 2*L_2*r0_3*(-9984*M_4 + 6*(786 + 557*E_2)*M_3*r0 + (2850 + 3865*E_2 - 1512*E_4)*M_2*r0_2 - 6*(225 + 691*E_2 + 262*E_4)*M*r0_3 + 2*(15 + 709*E_2)*r0_4)) + a_8*E*L*(6*L_2*M*(128*M_3 + 2*(107 + 30*E_2)*M_2*r0 + 4*(21 - 23*E_2)*M*r0_2 + (15 - 8*E_2)*r0_3) - r0*(384*(-111 + 19*E_2)*M_5 + 8*(-5928 + 1277*E_2)*M_4*r0 + (-8077 + 9892*E_2)*M_3*r0_2 + 4*(676 + 1043*E_2)*M_2*r0_3 - 42*(-5 + 9*E_2)*M*r0_4 + 18*r0_5)) + a_4*E*L*r0_2*(-12*L_6*M*r0 + 2*L_4*(8736*M_4 - 8*(-534 + 367*E_2)*M_3*r0 - 2*(407 + 323*E_2)*M_2*r0_2 + (61 + 301*E_2)*M*r0_3 - 18*r0_4) + 2*L_2*r0*(-26928*M_5 - 4*(-3163 + 316*E_2)*M_4*r0 + 2*(9509 - 1814*E_2)*M_3*r0_2 - 2*(1483 + 1698*E_2)*M_2*r0_3 + 3*(11 + 612*E_2)*M*r0_4 + 21*r0_5) + 3*r0_3*(-32308*M_5 + 4*(999 + 602*E_2)*M_4*r0 + (13939 - 4*E_2)*M_3*r0_2 - 4*(656 + 781*E_2)*M_2*r0_3 + 18*(-11 + 74*E_2)*M*r0_4 + 55*r0_5)) + 2*a_7*M*(-2*L_4*(72*M_3 + 2*(157 + 63*E_2)*M_2*r0 + 3*(181 - 52*E_2)*M*r0_2 + 6*(25 - 13*E_2)*r0_3) + 2*L_2*r0*(-144*(37 + 24*E_2)*M_4 + 2*(-1057 - 4032*E_2 + 984*E_4)*M_3*r0 + (937 - 4811*E_2 + 1752*E_4)*M_2*r0_2 + 2*(-33 + 151*E_2 + 246*E_4)*M*r0_3 + 3*(-43 + 10*E_2)*r0_4) + 3*E_2*r0_2*(7488*M_5 + 4*(1879 + 360*E_2)*M_4*r0 + 16*(-457 + 255*E_2)*M_3*r0_2 + 3*(-2005 + 952*E_2)*M_2*r0_3 + 2*(259 + 276*E_2)*M*r0_4 + 157*r0_5)) + 2*a_5*M*r0*(-6*L_6*(6*M_2 + 40*M*r0 + (25 - 2*E_2)*r0_2) + 3*E_2*r0_4*(10068*M_4 + 12*(145 + 216*E_2)*M_3*r0 + (-5171 + 3336*E_2)*M_2*r0_2 + 2*(289 + 456*E_2)*M*r0_3 + 13*r0_4) - 2*L_4*(2640*M_4 + 4*(1457 + 108*E_2)*M_3*r0 - 4*(247 - 315*E_2 + 158*E_4)*M_2*r0_2 + (-726 + 309*E_2 - 316*E_4)*M*r0_3 + 3*(73 + 103*E_2)*r0_4) + L_2*r0*(22464*M_5 + 12*(89 + 48*E_2)*M_4*r0 + 4*(-4749 - 3241*E_2 + 1080*E_4)*M_3*r0_2 + 3*(133 - 3800*E_2 + 2320*E_4)*M_2*r0_3 + 2*(1179 + 1276*E_2 + 1524*E_4)*M*r0_4 - (117 + 1696*E_2)*r0_5)) - a_6*E*L*r0*(-12*L_4*M*(26*M_2 + 34*M*r0 - (-3 + E_2)*r0_2) + L_2*(-25728*M_5 + 24*(-2333 + 632*E_2)*M_4*r0 + 368*(-55 + 24*E_2)*M_3*r0_2 + 142*(19 + 20*E_2)*M_2*r0_3 + 2*(241 - 520*E_2)*M*r0_4 + 54*r0_5) + r0*(89856*M_6 - 96*(-492 + 59*E_2)*M_5*r0 + 8*(-10031 + 66*E_2)*M_4*r0_2 + 2*(-15339 + 5710*E_2)*M_3*r0_3 + (8029 + 8180*E_2)*M_2*r0_4 - 48*(-13 + 46*E_2)*M*r0_5 - 3*r0_6))))/(3.*r0_5*expr2_3);\n A33400 = (2*r0_4*(-6*a_3*E_2*M + 3*a_2*E*L*r0 + E*L*(M - 4*r0)*r0_2 + 6*a*M*(L_2 - 3*E_2*r0_2)))/expr2_2;\n A33420 = (6*a_9*E_2*M*(4*(-27 + 7*E_2)*M_2 + 12*(22 + E_2)*M*r0 + 131*r0_2) - 3*a_8*E*L*(48*(-9 + 2*E_2)*M_3 + 20*(-8 + 11*E_2)*M_2*r0 + 2*(4 + 19*E_2)*M*r0_2 + 9*r0_3) + E*L*r0_4*(8*L_4*M*(194*M_2 - 201*M*r0 + 52*r0_2) + L_2*r0_2*(1132*M_3 - 4*(552 + 265*E_2)*M_2*r0 + (903 + 544*E_2)*M*r0_2 - 50*r0_3) + r0_4*(-1020*M_3 - 12*(-56 + 97*E_2)*M_2*r0 + (-299 + 666*E_2)*M*r0_2 + 100*r0_3)) - 2*a_7*M*(3*L_2*(12*(9 + 2*E_2)*M_2 + 4*(86 - 24*E_2 + E_4)*M*r0 + (131 - 159*E_2)*r0_2) - 2*E_2*r0*(12*(-189 + 50*E_2)*M_3 + 3*(-1281 + 278*E_2)*M_2*r0 + (-17 + 258*E_2)*M*r0_2 + 578*r0_3)) - 2*a*M*r0_2*(-3*E_2*r0_6*(-324*M_2 + 2*(71 + 72*E_2)*M*r0 + 13*r0_2) + 12*L_6*(56*M_2 - 58*M*r0 + 15*r0_2) + L_4*r0*(-4440*M_3 + 4*(1149 + 136*E_2)*M_2*r0 - 808*(2 + E_2)*M*r0_2 + (205 + 282*E_2)*r0_3) + L_2*r0_3*(-4488*M_3 + 12*(368 + 317*E_2)*M_2*r0 - 2*(673 + 1683*E_2 + 234*E_4)*M*r0_2 + (121 + 837*E_2)*r0_3)) + a_6*E*L*(3*L_2*(160*M_3 + 20*(9 + 2*E_2)*M_2*r0 - 2*(9 + 8*E_2)*M*r0_2 - 9*r0_3) - r0*(96*(-189 + 38*E_2)*M_4 + 48*(-256 + 93*E_2)*M_3*r0 + 12*(2 + 241*E_2)*M_2*r0_2 + (329 - 216*E_2)*M*r0_3 + 67*r0_4)) + a_2*E*L*r0_2*(12*L_4*M*(176*M_2 - 147*M*r0 + 33*r0_2) + L_2*r0*(-9936*M_4 + 16*(489 - 155*E_2)*M_3*r0 - 8*(199 + 226*E_2)*M_2*r0_2 + 4*(133 + 256*E_2)*M*r0_3 + 69*r0_4) + r0_3*(-22800*M_4 + 36*(367 + 80*E_2)*M_3*r0 - 4*(13 + 1047*E_2)*M_2*r0_2 + (-535 + 1776*E_2)*M*r0_3 + 187*r0_4)) - 2*a_5*M*(3*L_4*(36*M_2 + 4*(22 + 9*E_2)*M*r0 + (131 - 16*E_2)*r0_2) + L_2*r0*(216*(21 + 8*E_2)*M_3 - 6*(257 - 358*E_2 + 160*E_4)*M_2*r0 - 2*(257 - 567*E_2 + 210*E_4)*M*r0_2 + (757 - 493*E_2)*r0_3) - 2*E_2*r0_2*(5184*M_4 + 18*(167 + 36*E_2)*M_3*r0 + 2*(-2284 + 831*E_2)*M_2*r0_2 + 3*(-289 + 226*E_2)*M*r0_3 + 592*r0_4)) - 2*a_3*M*r0*(24*L_6*M - 2*E_2*r0_4*(3438*M_3 + 3*(-463 + 306*E_2)*M_2*r0 + (-253 + 654*E_2)*M*r0_2 + 230*r0_3) + 2*L_4*(888*M_3 + 12*(67 - 36*E_2)*M_2*r0 - 6*(163 + 8*E_2)*M*r0_2 + (275 + 117*E_2)*r0_3) + L_2*r0*(-10368*M_4 + 36*(139 + 58*E_2)*M_3*r0 + 2*(1891 + 744*E_2 - 504*E_4)*M_2*r0_2 - 4*(648 + 328*E_2 + 225*E_4)*M*r0_3 + (485 + 701*E_2)*r0_4)) - a_4*E*L*r0*(-24*L_4*M*(7*M - 2*r0) + L_2*(-8256*M_4 + 192*(-45 + 23*E_2)*M_3*r0 + 12*(-18 + 55*E_2)*M_2*r0_2 + 3*(43 - 144*E_2)*M*r0_3 + 4*r0_4) + r0*(41472*M_5 - 48*(-42 + 55*E_2)*M_4*r0 + 48*(-499 + 48*E_2)*M_3*r0_2 + 4*(293 + 1314*E_2)*M_2*r0_3 + (541 - 1440*E_2)*M*r0_4 - 47*r0_5)))/(3.*r0_2*expr2_3);\n A33600 = (r0*(6*a_7*E_2*M*(4*(-7 + 2*E_2)*M + 73*r0) - 3*a_6*E*L*(16*(-7 + 2*E_2)*M_2 + 24*E_2*M*r0 + 7*r0_2) - 2*a_5*M*(3*L_2*(28*M + (73 - 24*E_2)*r0) + E_2*r0*(-8*(-78 + 19*E_2)*M_2 - 4*(-271 + 49*E_2)*M*r0 - 463*r0_2)) + a_4*E*L*(24*L_2*M*(4*M - 3*r0) + r0*(-32*(-78 + 19*E_2)*M_3 - 8*(-84 + 71*E_2)*M_2*r0 + 5*(-29 + 14*E_2)*M*r0_2 - 46*r0_3)) + E*L*r0_3*(2*L_2*M*(300*M_2 - 328*M*r0 + 89*r0_2) + r0_2*(-420*M_3 - 32*(-8 + 9*E_2)*M_2*r0 + (-109 + 158*E_2)*M*r0_2 + 40*r0_3)) + 2*a_3*M*(-24*L_4*M - 2*L_2*r0*(312*M_2 - 2*(187 + 38*E_2)*M*r0 + (137 + 27*E_2)*r0_2) + E_2*r0_2*(1584*M_3 + 8*(34 + 9*E_2)*M_2*r0 + 8*(-114 + 35*E_2)*M*r0_2 + 325*r0_3)) - 2*a*M*r0*(4*L_4*(38*M_2 - 43*M*r0 + 12*r0_2) - 3*E_2*r0_4*(-72*M_2 + 36*E_2*M*r0 + 19*r0_2) + L_2*r0*(-1584*M_3 + 16*(101 + 33*E_2)*M_2*r0 - 4*(138 + 121*E_2)*M*r0_2 + (67 + 126*E_2)*r0_3)) + a_2*E*L*r0*(2*L_2*M*(304*M_2 - 236*M*r0 + 67*r0_2) + r0*(-6336*M_4 + 24*(112 + 13*E_2)*M_3*r0 + 4*(185 - 218*E_2)*M_2*r0_2 + 10*(-19 + 30*E_2)*M*r0_3 + 39*r0_4))))/(12.*expr2_3);\n A34020 = (-48*E*L*r0_3*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/expr2_2;\n A34040 = (8*(-12*a_9*E_2*M*(24*M_3 + 6*M_2*r0 - 17*M*r0_2 - 7*r0_3) + a_8*E*L*(576*M_4 + 576*M_3*r0 + 2*(103 - 36*E_2)*M_2*r0_2 - 6*(-7 + 6*E_2)*M*r0_3 + 3*r0_4) + E*L*r0_4*(4*L_6*M*(2*M - r0) + 3*r0_6*(-39*M_2 + 8*(-1 + E_2)*M*r0 + 17*r0_2) + 3*L_2*r0_4*(-130*M_2 + 4*(4 + E_2)*M*r0 + 31*r0_2) + L_4*r0_2*(-289*M_2 + (92 - 8*E_2)*M*r0 + 36*r0_2)) + 4*a*M*r0_3*(36*E_2*r0_7*(-3*M + 2*r0) + L_6*(180*M_2 - 2*(27 + 2*E_2)*M*r0 + 3*(-7 + 2*E_2)*r0_2) + 3*L_4*r0_2*(96*M_2 - 11*(2 + 3*E_2)*M*r0 + (-15 + 31*E_2)*r0_2) + 3*L_2*r0_4*(36*M_2 - (4 + 85*E_2)*M*r0 + (-8 + 61*E_2)*r0_2)) + 2*a_6*E*L*r0*(-2304*M_5 + 240*(-6 + E_2)*M_4*r0 + 2*(377 + 324*E_2)*M_3*r0_2 + (457 + 216*E_2)*M_2*r0_3 + 3*(1 - 14*E_2)*M*r0_4 - 18*r0_5 + L_2*(192*M_3 + 10*(10 - 3*E_2)*M_2*r0 + 3*(11 - 8*E_2)*M*r0_2 + 3*r0_3)) + a_2*E*L*r0_3*(-12*L_6*M + 3*L_2*r0_2*(-960*M_3 + 4*(32 + 39*E_2)*M_2*r0 + 2*(85 - 4*E_2)*M*r0_2 + r0_3) + 6*r0_4*(-268*M_3 + 4*(11 + 36*E_2)*M_2*r0 + (43 + 6*E_2)*M*r0_2 + 10*r0_3) - 2*L_4*(600*M_3 - 2*(45 + 2*E_2)*M_2*r0 + 5*(-17 + 2*E_2)*M*r0_2 + 24*r0_3)) - 4*a_3*M*r0_2*(3*L_6*(2*M + (7 - 2*E_2)*r0) + 3*E_2*r0_5*(6*M_2 + 17*M*r0 - 65*r0_2) + L_2*r0_2*(-504*M_3 + 6*(-13 + 36*E_2)*M_2*r0 + (123 + 121*E_2)*M*r0_2 + 23*(3 - 13*E_2)*r0_3) - 3*L_4*(216*M_3 + 2*(11 + 10*E_2)*M_2*r0 - (55 + 19*E_2)*M*r0_2 + (-29 + 23*E_2)*r0_3)) - 4*a_7*M*(L_2*(72*M_3 + 6*(21 + 8*E_2)*M_2*r0 + (87 - 61*E_2)*M*r0_2 + 3*(7 - 15*E_2)*r0_3) - 3*E_2*r0*(192*M_4 + 148*M_3*r0 - 22*M_2*r0_2 + 33*M*r0_3 + 31*r0_4)) + a_4*E*L*r0_2*(-3*L_4*(4*M_2 + 4*(-1 + E_2)*M*r0 - r0_2) - 3*r0_2*(1804*M_4 + 12*(19 - 52*E_2)*M_3*r0 - (491 + 456*E_2)*M_2*r0_2 + 2*(-41 + 6*E_2)*M*r0_3 + 10*r0_4) - 2*L_2*(2352*M_4 - 20*(-19 + 6*E_2)*M_3*r0 - (607 + 132*E_2)*M_2*r0_2 + 3*(-25 + 14*E_2)*M*r0_3 + 42*r0_4)) + 4*a_5*M*r0*(-3*L_4*(16*M_2 + (31 - 8*E_2)*M*r0 + 2*(7 - 5*E_2)*r0_2) + 3*E_2*r0_3*(228*M_3 + 34*M_2*r0 + 35*M*r0_2 + 65*r0_3) + L_2*(576*M_4 + 12*(23 + 34*E_2)*M_3*r0 - 8*(21 + 25*E_2)*M_2*r0_2 - (198 + 29*E_2)*M*r0_3 + (-66 + 161*E_2)*r0_4))))/(3.*r0_4*expr2_3);\n A34200 = (-12*E*L*r0_6)/expr2_2;\n A34220 = (4*(2*a_7*E_2*M*(-24*M_2 + 3*M*r0 + 10*r0_2) + a_6*E*L*M*(96*M_2 + 48*M*r0 + (7 - 6*E_2)*r0_2) + a_4*E*L*r0*(-768*M_4 + 32*(-3 + E_2)*M_3*r0 + (253 + 80*E_2)*M_2*r0_2 + 2*(18 - 5*E_2)*M*r0_3 - 8*r0_4 + 4*L_2*M*(8*M - (-2 + E_2)*r0)) + E*L*r0_5*(L_2*(-93*M_2 + (25 - 4*E_2)*M*r0 + 14*r0_2) + r0_2*(-63*M_2 + 2*(3 + E_2)*M*r0 + 16*r0_2)) + 2*a*M*r0_2*(3*E_2*r0_5*(-18*M + 13*r0) + 2*L_4*(54*M_2 - 23*M*r0 + (-3 + 2*E_2)*r0_2) + L_2*r0_2*(84*M_2 - (32 + 63*E_2)*M*r0 + (-7 + 52*E_2)*r0_2)) + a_2*E*L*r0_2*(-4*L_4*M + L_2*(-400*M_3 + 118*M_2*r0 + (61 - 8*E_2)*M*r0_2 - 13*r0_3) + r0_2*(-508*M_3 + 2*(61 + 64*E_2)*M_2*r0 + (83 - 2*E_2)*M*r0_2 + 8*r0_3)) - 2*a_5*M*(L_2*(24*M_2 + (27 + 8*E_2)*M*r0 + (10 - 9*E_2)*r0_2) - E_2*r0*(192*M_3 + 58*M_2*r0 - 4*M*r0_2 + 41*r0_3)) - 2*a_3*M*r0*(2*L_4*(4*M + (5 - 2*E_2)*r0) + E_2*r0_3*(-78*M_2 + 25*M*r0 - 70*r0_2) + L_2*(-192*M_3 + 2*(5 - 38*E_2)*M_2*r0 + 53*(1 + E_2)*M*r0_2 + (17 - 27*E_2)*r0_3))))/(r0*expr2_3);\n A34400 = (r0_2*(36*a_5*E_2*M*(-2*M + r0) + 9*a_4*E*L*(16*M_2 - r0_2) - 2*a_2*E*L*r0*(576*M_3 + 12*(-18 + E_2)*M_2*r0 + 6*(-14 + E_2)*M*r0_2 - r0_3) + 12*a*M*r0*(3*E_2*r0_3*(-6*M + 5*r0) + L_2*(48*M_2 + 4*(-7 + E_2)*M*r0 + r0_2)) - 12*a_3*M*(3*L_2*(2*M + r0) - 2*E_2*r0*(24*M_2 - 4*M*r0 + 7*r0_2)) + E*L*r0_2*(12*L_2*M*(-2*M + r0) + r0_2*(-261*M_2 + 2*(25 - 6*E_2)*M*r0 + 50*r0_2))))/(6.*expr2_3);\n A35020 = (-8*r0*(6*a_5*E_2*M*(2*M + r0) - a_4*E*L*r0*(3*M + 2*r0) - 6*a*M*r0*(L_4 + (1 - 2*E_2)*L_2*r0_2 - 3*E_2*r0_4) + E*L*r0_4*(4*L_2 + r0*(-2*M + 5*r0)) + 2*a_3*M*(6*E_2*r0_2*(3*M + 2*r0) + L_2*(-6*M - 3*r0 + 2*E_2*r0)) + a_2*E*L*r0*(2*L_2*(M - r0) + r0*(-10*M_2 + 9*M*r0 + 3*r0_2))))/expr2_3;\n A35040 = (4*(-2*a_11*E_2*M*(48*(-9 + 2*E_2)*M_3 + 8*(-67 + 15*E_2)*M_2*r0 + 6*(-1 + 6*E_2)*M*r0_2 + 81*r0_3) + a_10*E*L*M*(576*(-3 + E_2)*M_3 - 4*(528 + 95*E_2)*M_2*r0 - 6*(99 + 58*E_2)*M*r0_2 + 3*(-7 + 10*E_2)*r0_3) + E*L*r0_5*(2*L_6*M*(468*M_2 - 472*M*r0 + 119*r0_2) + L_2*r0_4*(578*M_3 - (1119 + 1388*E_2)*M_2*r0 + (439 + 752*E_2)*M*r0_2 - 30*r0_3) + 4*L_4*r0_2*(482*M_3 - 58*(11 + 3*E_2)*M_2*r0 + (242 + 89*E_2)*M*r0_2 - 24*r0_3) + 3*r0_6*(-138*M_3 + (131 - 236*E_2)*M_2*r0 + (-65 + 138*E_2)*M*r0_2 + 14*r0_3)) + 2*a*M*r0_3*(9*E_2*r0_8*(-113*M_2 + 2*(43 + 12*E_2)*M*r0 - 13*r0_2) - 4*L_8*(110*M_2 - 109*M*r0 + 27*r0_2) + L_4*r0_3*(4272*M_3 - 2*(1851 + 2011*E_2)*M_2*r0 + 2*(336 + 2095*E_2 + 180*E_4)*M*r0_2 + 9*(7 - 130*E_2)*r0_3) + 3*L_2*r0_5*(736*M_3 - (659 + 1437*E_2)*M_2*r0 + 2*(65 + 608*E_2 + 96*E_4)*M*r0_2 + 3*(3 - 91*E_2)*r0_3) + L_6*r0*(2160*M_3 - (2261 + 360*E_2)*M_2*r0 + 2*(371 + 314*E_2)*M*r0_2 - 12*(6 + 19*E_2)*r0_3)) + 2*a_9*M*(L_2*(-144*(-3 + 2*E_2)*M_3 + 40*(13 + 24*E_2)*M_2*r0 + 6*(51 + 56*E_2 + 4*E_4)*M*r0_2 + 9*(9 - 19*E_2)*r0_3) + E_2*r0*(48*(-137 + 34*E_2)*M_4 + 4*(-1819 + 540*E_2)*M_3*r0 + 2*(-59 + 300*E_2)*M_2*r0_2 - 6*(-49 + 8*E_2)*M*r0_3 - 477*r0_4)) + a_2*E*L*r0_3*(4*L_6*M*(356*M_2 - 322*M*r0 + 71*r0_2) + 3*r0_5*(-4606*M_4 + (4181 + 724*E_2)*M_3*r0 - 8*(101 + 94*E_2)*M_2*r0_2 + 2*(-96 + 247*E_2)*M*r0_3 + 61*r0_4) + 2*L_4*r0*(-568*M_4 + (3527 - 684*E_2)*M_3*r0 - (2279 + 916*E_2)*M_2*r0_2 + 3*(69 + 121*E_2)*M*r0_3 + 120*r0_4) + L_2*r0_3*(-13742*M_4 + (17785 + 4144*E_2)*M_3*r0 - (6037 + 6868*E_2)*M_2*r0_2 + (-47 + 2168*E_2)*M*r0_3 + 291*r0_4)) + 2*a_3*M*r0_2*(12*L_8*M + 3*E_2*r0_6*(1056*M_3 + (-1273 + 720*E_2)*M_2*r0 + 2*(465 + 118*E_2)*M*r0_2 - 203*r0_3) + L_6*(-2208*M_3 + 72*(-9 + 7*E_2)*M_2*r0 + 4*(160 + 101*E_2)*M*r0_2 + 6*(13 - 35*E_2)*r0_3) + 2*L_2*r0_3*(5160*M_4 - 3*(776 + 359*E_2)*M_3*r0 + (-1782 - 4751*E_2 + 432*E_4)*M_2*r0_2 + 6*(83 + 622*E_2 + 144*E_4)*M*r0_3 + (165 - 982*E_2)*r0_4) + L_4*r0*(9840*M_4 - 8*(729 + 416*E_2)*M_3*r0 + 2*(-2232 - 2087*E_2 + 288*E_4)*M_2*r0_2 + 2*(657 + 2230*E_2 + 380*E_4)*M*r0_3 + 21*(25 - 54*E_2)*r0_4)) + 2*a_7*M*r0*(2*L_4*(10*(11 + 9*E_2)*M_2 + 3*(47 + 72*E_2 + 4*E_4)*M*r0 + 9*(9 - 4*E_2)*r0_2) - 2*L_2*(24*(137 + 72*E_2)*M_4 + 2*(1013 + 2766*E_2 - 480*E_4)*M_3*r0 + (-629 + 889*E_2 - 864*E_4)*M_2*r0_2 - 2*(375 + 374*E_2 + 156*E_4)*M*r0_3 + 3*(-73 + 178*E_2)*r0_4) + 3*E_2*r0*(3840*M_5 + 4*(589 + 216*E_2)*M_4*r0 + 8*(-535 + 276*E_2)*M_3*r0_2 + (-1159 + 1176*E_2)*M_2*r0_3 + 4*(143 + 24*E_2)*M*r0_4 - 362*r0_5)) - a_4*E*L*r0_2*(6*L_6*M*(20*M + 3*r0) + L_4*(-9408*M_4 + 16*(-330 + 173*E_2)*M_3*r0 + 8*(287 + 155*E_2)*M_2*r0_2 - 22*(-5 + 16*E_2)*M*r0_3 + 54*r0_4) + L_2*r0*(28704*M_5 + 4*(-5923 + 140*E_2)*M_4*r0 + (-22617 + 136*E_2)*M_3*r0_2 + 30*(311 + 196*E_2)*M_2*r0_3 - 4*(-88 + 523*E_2)*M*r0_4 - 240*r0_5) + 3*r0_3*(16628*M_5 + 8*(-627 + 28*E_2)*M_4*r0 - 24*(317 + 56*E_2)*M_3*r0_2 + (2787 + 1252*E_2)*M_2*r0_3 + (191 - 664*E_2)*M*r0_4 - 71*r0_5)) - a_8*E*L*(3*L_2*M*(-64*M_3 + 20*(29 + 2*E_2)*M_2*r0 + 4*(68 + 43*E_2)*M*r0_2 + (11 - 4*E_2)*r0_3) + r0*(192*(-137 + 22*E_2)*M_5 + 16*(-1416 + 161*E_2)*M_4*r0 + 32*(104 + 103*E_2)*M_3*r0_2 + 2*(2155 + 1112*E_2)*M_2*r0_3 - 6*(-64 + 55*E_2)*M*r0_4 + 27*r0_5)) + 2*a_5*M*r0*(3*L_6*(20*M_2 + 4*(-1 + 9*E_2)*M*r0 + 3*(9 + 2*E_2)*r0_2) + 3*E_2*r0_4*(4812*M_4 + 132*(-5 + 12*E_2)*M_3*r0 + (-1843 + 1656*E_2)*M_2*r0_2 + 4*(287 + 66*E_2)*M*r0_3 - 394*r0_4) - 2*L_4*(1392*M_4 + 4*(895 + 108*E_2)*M_3*r0 + (211 + 804*E_2 - 304*E_4)*M_2*r0_2 - (699 + 603*E_2 + 212*E_4)*M*r0_3 + 24*(-13 + 15*E_2)*r0_4) + L_2*r0*(11520*M_5 + 12*(59 + 148*E_2)*M_4*r0 + 2*(-5574 - 6427*E_2 + 1008*E_4)*M_3*r0_2 + 3*(-507 - 2283*E_2 + 992*E_4)*M_2*r0_3 + 8*(225 + 722*E_2 + 219*E_4)*M*r0_4 + 2*(330 - 1021*E_2)*r0_5)) - a_6*E*L*r0*(6*L_4*M*(60*M_2 + 2*(31 + 14*E_2)*M*r0 + (5 + 3*E_2)*r0_2) + L_2*(-13440*M_5 + 48*(-723 + 148*E_2)*M_4*r0 + 32*(-203 + 132*E_2)*M_3*r0_2 + 4*(1364 + 661*E_2)*M_2*r0_3 + (763 - 688*E_2)*M*r0_4 + 81*r0_5) + r0*(46080*M_6 - 288*(-54 + E_2)*M_5*r0 - 2*(25075 + 216*E_2)*M_4*r0_2 + (-9459 + 736*E_2)*M_3*r0_3 + 4*(2231 + 1021*E_2)*M_2*r0_4 + 3*(185 - 408*E_2)*M*r0_5 - 45*r0_6))))/(3.*r0_5*expr2_4);\n A35200 = (-2*r0_4*(6*a_3*E_2*M - 3*a_2*E*L*r0 + E*L*r0_2*(-2*M + 5*r0) - 6*a*M*(L_2 - 3*E_2*r0_2)))/expr2_3;\n A35220 = (-24*a_9*E_2*M*(4*(-6 + E_2)*M_2 + 3*(-13 + E_2)*M*r0 - 4*r0_2) + 3*a_8*E*L*(96*(-4 + E_2)*M_3 - 8*(32 + 19*E_2)*M_2*r0 + (-43 + 2*E_2)*M*r0_2 - 9*r0_3) + 6*a_7*M*(L_2*(-48*(-2 + E_2)*M_2 + 4*(-7 + 48*E_2 + E_4)*M*r0 + (-16 + 39*E_2)*r0_2) + 2*E_2*r0*(16*(-61 + 14*E_2)*M_3 + (-683 + 200*E_2)*M_2*r0 + 10*(17 + 2*E_2)*M*r0_2 - 13*r0_3)) + E*L*r0_4*(4*L_4*M*(398*M_2 - 405*M*r0 + 103*r0_2) + L_2*r0_2*(1106*M_3 - 25*(81 + 44*E_2)*M_2*r0 + 28*(31 + 20*E_2)*M*r0_2 - 84*r0_3) + 6*r0_4*(-170*M_3 + (125 - 184*E_2)*M_2*r0 + 2*(-23 + 52*E_2)*M*r0_2 + 10*r0_3)) - 2*a*M*r0_2*(180*L_6*r0_2M_2 - 18*E_2*r0_6*(-97*M_2 + 2*(35 + 9*E_2)*M*r0 - 9*r0_2) - 3*L_2*r0_3*(1552*M_3 - (1438 + 1469*E_2)*M_2*r0 + 2*(166 + 663*E_2 + 84*E_4)*M*r0_2 + 2*(1 - 161*E_2)*r0_3) + 2*L_4*r0*(-2280*M_3 + (2223 + 328*E_2)*M_2*r0 - (621 + 520*E_2)*M*r0_2 + 3*(12 + 59*E_2)*r0_3)) + 6*a_5*M*r0*(4*L_4*(M + 9*E_2*M + 2*(-2 + E_2)*r0) + L_2*(-32*(61 + 18*E_2)*M_3 + 2*(-5 - 628*E_2 + 156*E_4)*M_2*r0 + 4*(105 + 121*E_2 + 44*E_4)*M*r0_2 + (46 - 139*E_2)*r0_3) + 2*E_2*r0*(1776*M_4 + 36*(5 + 8*E_2)*M_3*r0 + (-1293 + 536*E_2)*M_2*r0_2 + 8*(43 + 14*E_2)*M*r0_3 - 81*r0_4)) - 3*a_6*E*L*(L_2*(-32*M_3 + 8*(27 + 5*E_2)*M_2*r0 + 8*(6 + E_2)*M*r0_2 + 9*r0_3) + r0*(128*(-61 + 11*E_2)*M_4 + 4*(-688 + 171*E_2)*M_3*r0 + 8*(183 + 112*E_2)*M_2*r0_2 + (167 - 158*E_2)*M*r0_3 + 3*r0_4)) + a_2*E*L*r0_2*(24*L_4*M*(102*M_2 - 93*M*r0 + 20*r0_2) + 3*r0_3*(-7902*M_4 + (6345 + 796*E_2)*M_3*r0 - 7*(121 + 144*E_2)*M_2*r0_2 + 2*(-157 + 285*E_2)*M*r0_3 + 88*r0_4) + L_2*r0*(-10992*M_4 + 2*(7035 - 1076*E_2)*M_3*r0 - (4603 + 2500*E_2)*M_2*r0_2 + 4*(28 + 281*E_2)*M*r0_3 + 216*r0_4)) + 6*a_3*M*r0*(8*L_6*M + 2*E_2*r0_4*(996*M_3 + (-829 + 360*E_2)*M_2*r0 + 10*(47 + 14*E_2)*M*r0_2 - 87*r0_3) + L_4*(-640*M_3 + 4*(-185 + 54*E_2)*M_2*r0 + 2*(229 + 100*E_2)*M*r0_2 + 10*(1 - 11*E_2)*r0_3) + L_2*r0*(3552*M_4 - 8*(201 + 40*E_2)*M_3*r0 + (-1640 - 1935*E_2 + 312*E_4)*M_2*r0_2 + 2*(314 + 715*E_2 + 170*E_4)*M*r0_3 + 2*(32 - 239*E_2)*r0_4)) - 3*a_4*E*L*r0*(8*L_4*M*(7*M + r0) + L_2*(-2944*M_4 + 12*(-323 + 116*E_2)*M_3*r0 + 4*(267 + 122*E_2)*M_2*r0_2 + 12*(8 - 15*E_2)*M*r0_3 - 21*r0_4) + r0*(14208*M_5 - 16*(156 + 7*E_2)*M_4*r0 - 8923*M_3*r0_2 + (2447 + 1528*E_2)*M_2*r0_3 + 14*(20 - 37*E_2)*M*r0_4 - 74*r0_5)))/(3.*r0_2*expr2_4);\n A35400 = (r0*(18*a_7*E_2*M*(4*M + 15*r0) - 9*a_6*E*L*(16*M_2 + 4*E_2*M*r0 + r0_2) - a_4*E*L*r0*(36*L_2*M + 48*(-107 + 22*E_2)*M_3 + 24*(34 + 15*E_2)*M_2*r0 - 6*(-49 + 33*E_2)*M*r0_2 + 5*r0_3) + 2*a_5*M*(9*L_2*(4*M + (-15 + 4*E_2)*r0) + E_2*r0*(12*(-107 + 22*E_2)*M_2 + 6*(-65 + 22*E_2)*M*r0 + 197*r0_2)) + E*L*r0_3*(6*L_2*M*(136*M_2 - 146*M*r0 + 39*r0_2) + r0_2*(-606*M_3 - 9*(-43 + 44*E_2)*M_2*r0 + 2*(-68 + 105*E_2)*M*r0_2 + 38*r0_3)) + 2*a_3*M*r0*(-2*L_2*(642*M_2 - 3*(133 + 40*E_2)*M*r0 + (58 + 69*E_2)*r0_2) + E_2*r0*(2448*M_3 + 3*(-349 + 72*E_2)*M_2*r0 + 2*(73 + 120*E_2)*M*r0_2 + 62*r0_3)) - 2*a*M*r0*(12*L_4*(22*M_2 - 23*M*r0 + 6*r0_2) + 3*E_2*r0_4*(243*M_2 - 4*(38 + 9*E_2)*M*r0 + 10*r0_2) + L_2*r0*(-2448*M_3 + 3*(779 + 200*E_2)*M_2*r0 - 4*(154 + 159*E_2)*M*r0_2 + 2*(13 + 87*E_2)*r0_3)) + a_2*E*L*r0*(6*L_2*M*(176*M_2 - 156*M*r0 + 37*r0_2) + r0*(-9792*M_4 - 48*(-141 + E_2)*M_3*r0 - 3*(63 + 292*E_2)*M_2*r0_2 + 4*(-113 + 111*E_2)*M*r0_3 + 114*r0_4))))/(12.*expr2_4);\n A36000 = (-4*E*L*r0_6)/expr2_3;\n A36020 = (-2*(48*a_7*E_2*M*(3*M_2 - 2*M*r0 - 2*r0_2) + 3*a_6*E*L*(-96*M_3 + 12*(-4 + E_2)*M_2*r0 + 6*(-1 + 2*E_2)*M*r0_2 + r0_3) + E*L*r0_3*(8*L_4*M*(-2*M + r0) + L_2*r0_2*(111*M_2 + 16*E_2*M*r0 - 36*r0_2) + r0_4*(103*M_2 + 4*(-5 + 2*E_2)*M*r0 - 24*r0_2)) + a_4*E*L*r0*(1536*M_4 - 16*(6 + 7*E_2)*M_3*r0 - 8*(86 + 23*E_2)*M_2*r0_2 + 2*(-13 + 40*E_2)*M*r0_3 + 51*r0_4 - 3*L_2*(20*M_2 + (4 - 8*E_2)*M*r0 - r0_2)) - 4*a*M*r0_2*(3*E_2*r0_5*(-29*M + 15*r0) + L_4*(108*M_2 - (27 + 8*E_2)*M*r0 + 3*(-5 + 4*E_2)*r0_2) + L_2*r0_2*(84*M_2 - (15 + 133*E_2)*M*r0 + 3*(-5 + 31*E_2)*r0_2)) + 12*a_5*M*(2*L_2*(6*M_2 - (-10 + E_2)*M*r0 + (4 - 5*E_2)*r0_2) + E_2*r0*(-64*M_3 + 14*M_2*r0 + 9*M*r0_2 - 25*r0_3)) + a_2*E*L*r0_2*(24*L_4*M + r0_2*(998*M_3 - (477 + 364*E_2)*M_2*r0 + 2*(-83 + 26*E_2)*M*r0_2 + 24*r0_3) + 2*L_2*(376*M_3 - 4*(45 + 2*E_2)*M_2*r0 + 5*(-9 + 4*E_2)*M*r0_2 + 30*r0_3)) + 4*a_3*M*r0*(12*L_4*(M - (-2 + E_2)*r0) - 6*E_2*r0_3*(5*M_2 - 17*M*r0 + 16*r0_2) + L_2*(-192*M_3 - 2*(9 + 26*E_2)*M_2*r0 + (57 + 109*E_2)*M*r0_2 + 3*(13 - 23*E_2)*r0_3))))/(3.*r0*expr2_4);\n A36200 = (r0_2*(12*a_5*E_2*M*(-6*M + 7*r0) - 3*a_4*E*L*(-48*M_2 + 8*E_2*M*r0 + 5*r0_2) - 2*a_2*E*L*r0*(12*L_2*M + 384*M_3 - 4*(54 + E_2)*M_2*r0 + (-61 + 22*E_2)*M*r0_2 + 12*r0_3) - 12*a_3*M*(L_2*(6*M + (7 - 4*E_2)*r0) + E_2*r0*(-32*M_2 + 23*M*r0 - 17*r0_2)) + E*L*r0_2*(4*L_2*M*(2*M - r0) + r0_2*(-151*M_2 + 4*(11 - 5*E_2)*M*r0 + 24*r0_2)) + 4*a*M*r0*(3*E_2*r0_3*(-23*M + 12*r0) + L_2*(96*M_2 - (39 + 4*E_2)*M*r0 + 6*(-1 + 2*E_2)*r0_2))))/(6.*expr2_4);\n A37000 = (2*r0_4*(-2*a_3*E_2*M + a_2*E*L*r0 + E*L*(M - 2*r0)*r0_2 + 2*a*M*(L_2 - 3*E_2*r0_2)))/expr2_4;\n A37020 = (-6*a_9*E_2*M*(20*(-5 + E_2)*M_2 + 4*(-4 + 3*E_2)*M*r0 + 33*r0_2) + 3*a_8*E*L*(16*(-25 + 6*E_2)*M_3 - 28*(8 + E_2)*M_2*r0 + 2*(-13 + 7*E_2)*M*r0_2 - 3*r0_3) + E*L*r0_4*(4*L_4*M*(138*M_2 - 139*M*r0 + 35*r0_2) + r0_4*(-365*M_3 - 340*(-1 + E_2)*M_2*r0 + 6*(-23 + 31*E_2)*M*r0_2 + 24*r0_3) + L_2*r0_2*(247*M_3 - 6*(53 + 64*E_2)*M_2*r0 + 2*(19 + 98*E_2)*M*r0_2 + 24*r0_3)) + 2*a_7*M*(3*L_2*(-4*(-25 + 6*E_2)*M_2 + 4*(24 + 24*E_2 + E_4)*M*r0 + 3*(11 - 9*E_2)*r0_2) - 2*E_2*r0*(-4*(-297 + 62*E_2)*M_3 - 2*(-50 + 61*E_2)*M_2*r0 + (-343 + 46*E_2)*M*r0_2 + 213*r0_3)) - 2*a*M*r0_2*(4*L_6*(64*M_2 - 62*M*r0 + 15*r0_2) + 3*E_2*r0_6*(259*M_2 - 8*(26 + 3*E_2)*M*r0 + 34*r0_2) + L_4*r0*(-1560*M_3 + 3*(491 + 88*E_2)*M_2*r0 - 4*(87 + 110*E_2)*M*r0_2 + 150*E_2*r0_3) + L_2*r0_3*(-1608*M_3 + (1433 + 1459*E_2)*M_2*r0 - 4*(64 + 287*E_2 + 45*E_4)*M*r0_2 + 6*(-5 + 33*E_2)*r0_3)) + 2*a_5*M*(3*L_4*(12*M_2 + 4*(8 + 9*E_2)*M*r0 + 33*r0_2) + L_2*r0*(-72*(33 + 8*E_2)*M_3 + 4*(-130 - 449*E_2 + 76*E_4)*M_2*r0 + 2*(329 + 673*E_2 + 106*E_4)*M*r0_2 + 9*(37 - 49*E_2)*r0_3) + E_2*r0_2*(3648*M_4 + 2*(-583 + 360*E_2)*M_3*r0 + 7*(-309 + 148*E_2)*M_2*r0_2 + 2*(917 - 2*E_2)*M*r0_3 - 699*r0_4)) - a_6*E*L*(3*L_2*(32*M_3 + 4*(51 + 10*E_2)*M_2*r0 + 26*M*r0_2 + 3*r0_3) + r0*(32*(-297 + 50*E_2)*M_4 - 4*(360 + 29*E_2)*M_3*r0 + 2*(1471 + 404*E_2)*M_2*r0_2 - 3*(-63 + 76*E_2)*M*r0_3 - 27*r0_4)) + a_2*E*L*r0_2*(4*L_4*M*(232*M_2 - 227*M*r0 + 49*r0_2) + L_2*r0*(-4048*M_4 + 60*(113 - 10*E_2)*M_3*r0 - (2475 + 1084*E_2)*M_2*r0_2 + 6*(-17 + 70*E_2)*M*r0_3 + 84*r0_4) + r0_3*(-8206*M_4 + (8089 + 308*E_2)*M_3*r0 - 3*(497 + 88*E_2)*M_2*r0_2 + 12*(-36 + 43*E_2)*M*r0_3 + 96*r0_4)) + 2*a_3*M*r0*(24*L_6*M + 2*E_2*r0_4*(855*M_3 + 2*(-568 + 207*E_2)*M_2*r0 + 2*(476 + 31*E_2)*M*r0_2 - 237*r0_3) - 2*L_4*(344*M_3 + 6*(79 - 12*E_2)*M_2*r0 - 47*(3 + 4*E_2)*M*r0_2 + 3*(-32 + 25*E_2)*r0_3) + L_2*r0*(3648*M_4 + 2*(-785 + 44*E_2)*M_3*r0 + 3*(-667 - 1087*E_2 + 96*E_4)*M_2*r0_2 + 2*(208 + 1121*E_2 + 190*E_4)*M*r0_3 + 12*(22 - 57*E_2)*r0_4)) + a_4*E*L*r0*(-168*L_4*M_2 + L_2*(3136*M_4 + 4*(1221 - 328*E_2)*M_3*r0 - 4*(566 + 191*E_2)*M_2*r0_2 + (-125 + 224*E_2)*M*r0_3 + 54*r0_4) + r0*(-14592*M_5 + 16*(342 - 43*E_2)*M_4*r0 + 8*(1251 + 77*E_2)*M_3*r0_2 - 15*(293 + 72*E_2)*M_2*r0_3 + 3*(-133 + 172*E_2)*M*r0_4 + 108*r0_5)))/(3.*r0_2*expr2_5);\n A37200 = (r0*(-6*a_7*E_2*M*((-44 + 8*E_2)*M + 13*r0) + 3*a_6*E*L*(16*(-11 + 2*E_2)*M_2 + 8*E_2*M*r0 + 3*r0_2) + 2*a_5*M*(3*L_2*(44*M + (13 - 8*E_2)*r0) + E_2*r0*(40*(-27 + 5*E_2)*M_2 + 4*(134 - 5*E_2)*M*r0 - 183*r0_2)) + 2*a_3*M*(24*L_4*M - 2*L_2*r0*(540*M_2 - 4*(41 + 19*E_2)*M*r0 + 3*(-17 + 19*E_2)*r0_2) + E_2*r0_2*(1680*M_3 + (-1591 + 216*E_2)*M_2*r0 + 2*(499 + 20*E_2)*M*r0_2 - 216*r0_3)) + E*L*r0_3*(2*L_2*M*(236*M_2 - 244*M*r0 + 63*r0_2) + r0_2*(-413*M_3 - 4*(-79 + 58*E_2)*M_2*r0 + 114*(-1 + E_2)*M*r0_2 + 24*r0_3)) + a_4*E*L*(24*L_2*M*(-4*M + r0) + r0*(-160*(-27 + 5*E_2)*M_3 + 8*(-216 + 13*E_2)*M_2*r0 + (-241 + 178*E_2)*M*r0_2 + 36*r0_3)) - 2*a*M*r0*(4*L_4*(50*M_2 - 49*M*r0 + 12*r0_2) + 3*E_2*r0_4*(231*M_2 - 2*(89 + 6*E_2)*M*r0 + 26*r0_2) + L_2*r0*(-1680*M_3 + (1529 + 256*E_2)*M_2*r0 - 2*(155 + 166*E_2)*M*r0_2 + 18*(-1 + 5*E_2)*r0_3)) + a_2*E*L*r0*(2*L_2*M*(400*M_2 - 380*M*r0 + 73*r0_2) + r0*(-6720*M_4 - 8*(-780 + 49*E_2)*M_3*r0 - (909 + 256*E_2)*M_2*r0_2 + 4*(-97 + 67*E_2)*M*r0_3 + 96*r0_4))))/(12.*expr2_5);\n A38000 = (r0_2*(-6*a_5*E_2*M*(2*M - 3*r0) - 3*a_4*E*L*(-8*M_2 + 2*E_2*M*r0 + r0_2) - 2*a_2*E*L*r0*(3*L_2*M + 48*M_3 - 2*(18 + E_2)*M_2*r0 + (-8 + 5*E_2)*M*r0_2 + 3*r0_3) + E*L*M*r0_2*(L_2*(4*M - 2*r0) + r0_2*(-17*M + 2*(5 - 2*E_2)*r0)) - 6*a_3*M*(L_2*(2*M + (3 - 2*E_2)*r0) - 2*E_2*r0*(4*M_2 - 5*M*r0 + 3*r0_2)) + 2*a*M*r0*(3*E_2*r0_3*(-8*M + 3*r0) + L_2*(24*M_2 - 2*(3 + 2*E_2)*M*r0 + 3*(-1 + 2*E_2)*r0_2))))/(3.*expr2_5);\n A39000 = (r0*(-6*a_7*E_2*M*(2*(-5 + E_2)*M + 7*r0) + 3*a_6*E*L*(8*(-5 + E_2)*M_2 + 3*E_2*M*r0 + r0_2) + 2*a_5*M*(3*L_2*(10*M + (7 - 3*E_2)*r0) + E_2*r0*(2*(-81 + 14*E_2)*M_2 + (163 - 16*E_2)*M*r0 - 60*r0_2)) + E*L*M*r0_3*(L_2*(48*M_2 - 46*M*r0 + 11*r0_2) + 2*r0_2*(-27*M_2 + 2*(11 - 6*E_2)*M*r0 + 5*(-1 + E_2)*r0_2)) + 2*a_3*M*(6*L_4*M + L_2*r0*(-162*M_2 + (17 + 16*E_2)*M*r0 + 3*(11 - 5*E_2)*r0_2) + E_2*r0_2*(216*M_3 + 2*(-151 + 18*E_2)*M_2*r0 + 2*(113 - 5*E_2)*M*r0_2 - 57*r0_3)) + a_4*E*L*(3*L_2*M*(-8*M + 3*r0) + r0*(-8*(-81 + 14*E_2)*M_3 + 2*(-180 + 29*E_2)*M_2*r0 + (-35 + 26*E_2)*M*r0_2 + 9*r0_3)) - 2*a*M*r0*(3*E_2*r0_4*(36*M_2 - 31*M*r0 + 6*r0_2) + L_4*(28*M_2 - 26*M*r0 + 6*r0_2) + L_2*r0*(-216*M_3 + 2*(95 + 6*E_2)*M_2*r0 - (29 + 26*E_2)*M*r0_2 + 6*(-1 + E_2)*r0_3)) + a_2*E*L*r0*(2*L_2*M*(56*M_2 - 55*M*r0 + 8*r0_2) + r0*(-864*M_4 + 24*(41 - 4*E_2)*M_3*r0 + 2*(-100 + 7*E_2)*M_2*r0_2 + 3*(-19 + 9*E_2)*M*r0_3 + 12*r0_4))))/(6.*expr2_6);\n }\n\n /* A_{r,r} */\n {\n A40080 = (1024*expr1_3*(a_6*E_2*M*(7*M + 3*r0) - 2*a_5*E*L*M*(7*M + 3*r0) - 2*a_3*E*L*M*r0*(3*L_2 - 4*M_2 + 9*M*r0 + 5*r0_2) + 2*a*E*L*M*r0_2*(L_2*(2*M - 3*r0) - 4*M*r0_2) + r0_2*(2*E_2*M*r0_5 + L_4*M*(-2*M + r0) + L_2*r0_2*(2*M_2 + (-3 + 2*E_2)*M*r0 + r0_2)) + a_4*M*(L_2*(7*M + 3*(1 + E_2)*r0) + 2*E_2*r0*(-2*M_2 + 7*M*r0 + 4*r0_2)) + a_2*M*r0*(3*L_4 + E_2*r0_3*(11*M + 7*r0) + L_2*(-4*M_2 - 2*(-2 + E_2)*M*r0 + (2 + 5*E_2)*r0_2))))/(r0_7*expr2_2);\n A40260 = (256*expr1_2*(3*a_6*E_2*M*(9*M + 4*r0) - 6*a_5*E*L*M*(9*M + 4*r0) - 2*a_3*E*L*M*r0*(12*L_2 - 16*M_2 + 31*M*r0 + 21*r0_2) + 2*a*E*L*M*r0_2*(4*L_2*(2*M - 3*r0) - r0_2*(10*M + 3*r0)) + r0_2*(8*E_2*M*r0_5 + 4*L_4*M*(-2*M + r0) + L_2*r0_2*(4*M_2 + 8*(-1 + E_2)*M*r0 + 3*r0_2)) + a_4*M*(3*L_2*(9*M + 4*(1 + E_2)*r0) + 2*E_2*r0*(-8*M_2 + 25*M*r0 + 16*r0_2)) + a_2*M*r0*(12*L_4 + 7*E_2*r0_3*(5*M + 4*r0) - 2*L_2*(8*M_2 + 2*(-3 + 2*E_2)*M*r0 - 5*(1 + 2*E_2)*r0_2))))/(r0_4*expr2_2);\n A40440 = (192*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(a_6*E_2*M*(13*M + 6*r0) - 2*a_5*E*L*M*(13*M + 6*r0) - 2*a_3*E*L*M*r0*(6*L_2 - 8*M_2 + 13*M*r0 + 11*r0_2) + r0_2*(4*E_2*M*r0_5 + 2*L_4*M*(-2*M + r0) + L_2*r0_3*(-2*M + 4*E_2*M + r0)) + 2*a*E*L*M*r0_2*(L_2*(4*M - 6*r0) - r0_2*(2*M + 3*r0)) + a_4*M*(L_2*(13*M + 6*(1 + E_2)*r0) + 2*E_2*r0*(-4*M_2 + 11*M*r0 + 8*r0_2)) + a_2*M*r0*(6*L_4 + E_2*r0_3*(13*M + 14*r0) + L_2*(-8*M_2 - 4*(-1 + E_2)*M*r0 + 2*(3 + 5*E_2)*r0_2))))/(r0*expr2_2);\n A40620 = (16*r0_2*(E_2*M_2*expr3_2 + L_2*expr5_2 + 2*E*L*M*(a_3 + 3*a*r0_2)*(-(a_2*M) + r0_2*(-2*M + r0)) - 4*M*r0*(L_2 + r0_2 + (a_2*(2*M + r0))/r0)*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-2*M + 3*r0) + a_2*(-3*L_2 + E_2*(2*M - 5*r0)*r0) - r0*(2*E_2*r0_3 + L_2*(-2*M + r0)))))/expr2_2;\n A40800 = (-4*M*r0_5*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-2*M + 3*r0) + a_2*(-3*L_2 + E_2*(2*M - 5*r0)*r0) - r0*(2*E_2*r0_3 + L_2*(-2*M + r0))))/expr2_2;\n A41080 = (-512*expr1_2*(a_10*E_2*M*(21*M_2 + 17*M*r0 + 3*r0_2) - 2*a_9*E*L*M*((21 + 11*E_2)*M_2 + (17 + 6*E_2)*M*r0 + 3*r0_2) - 2*a*E*L*M*r0_4*(-4*L_4*M*(6*M - 5*r0) + L_2*r0_2*(-54*M_2 + (49 + 12*E_2)*M*r0 - 3*r0_2) + r0_4*(-6*M_2 + (5 + 12*E_2)*M*r0 + 3*r0_2)) + a_8*M*(L_2*(3*(7 + 22*E_2)*M_2 + (17 + 53*E_2)*M*r0 + 3*(1 + 2*E_2)*r0_2) + E_2*r0*(-94*M_3 + 5*M_2*r0 + 74*M*r0_2 + 19*r0_3)) - 2*a_7*E*L*M*(L_2*(33*M_2 + (35 + 6*E_2)*M*r0 + 6*r0_2) + r0*(-2*(47 + 4*E_2)*M_3 + (-4 + 43*E_2)*M_2*r0 + 2*(35 + 17*E_2)*M*r0_2 + 19*r0_3)) + 2*a_3*E*L*M*r0_2*(L_4*(12*M_2 - 40*M*r0 - 3*r0_2) + L_2*r0*(36*M_3 + 6*(17 + 2*E_2)*M_2*r0 - (97 + 34*E_2)*M*r0_2 - 27*r0_3) - r0_3*(36*M_3 - (88 + 15*E_2)*M_2*r0 + 2*(14 + 23*E_2)*M*r0_2 + 29*r0_3)) + a_2*r0_2*(2*L_6*M*(-4*M_2 + 6*M*r0 + r0_2) + E_2*M*r0_6*(-30*M_2 + 29*M*r0 + 22*r0_2) + L_2*r0_3*(36*M_4 - 4*(16 + 39*E_2)*M_3*r0 + (11 + 174*E_2)*M_2*r0_2 + 3*(6 + 5*E_2)*M*r0_3 - 3*r0_4) - L_4*r0*(12*M_4 + 4*(14 + 15*E_2)*M_3*r0 - (39 + 100*E_2)*M_2*r0_2 + (-16 + E_2)*M*r0_3 + 4*r0_4)) + a_6*M*(L_4*(22*M_2 + (29 + 36*E_2)*M*r0 + 3*(2 + E_2)*r0_2) + L_2*r0*(-2*(47 + 24*E_2)*M_3 + (-13 + 128*E_2)*M_2*r0 + 6*(11 + 34*E_2)*M*r0_2 + (19 + 23*E_2)*r0_3) + E_2*r0_2*(24*M_4 - 152*M_3*r0 - 123*M_2*r0_2 + 106*M*r0_3 + 43*r0_4)) + r0_4*(4*E_2*M*r0_8 - L_6*M*(12*M_2 - 8*M*r0 + r0_2) + L_4*r0_2*(-20*M_3 + 4*(5 + 3*E_2)*M_2*r0 - (9 + 2*E_2)*M*r0_2 + 2*r0_3) + L_2*r0_5*(r0*(-2*M + r0) + 2*E_2*M*(6*M + r0))) + a_4*r0*(3*L_6*M*(4*M + r0) + E_2*M*r0_4*(6*M_3 - 97*M_2*r0 + 78*M*r0_2 + 45*r0_3) + L_4*M*(-16*M_3 - 4*(11 + 6*E_2)*M_2*r0 + 2*(27 + 62*E_2)*M*r0_2 + (21 + 4*E_2)*r0_3) + L_2*r0*(24*M_5 - 2*(48 + 49*E_2)*M_3*r0_2 + 7*(10 + 39*E_2)*M_2*r0_3 + 2*(13 + 15*E_2)*M*r0_4 - 4*r0_5 - 36*M_4*(r0 + 3*E_2*r0))) + 2*a_5*E*L*M*r0*(-3*L_4*(6*M + r0) - r0*(24*M_4 - 2*(47 + 12*E_2)*M_3*r0 + (-107 + 25*E_2)*M_2*r0_2 + 2*(48 + 31*E_2)*M*r0_3 + 42*r0_4) + L_2*(24*M_3 - (95 + 28*E_2)*M*r0_2 - 22*r0_3 + M_2*(r0 + 4*E_2*r0)))))/(r0_8*expr2_3);\n A41260 = (-128*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(a_10*E_2*M*(66*M_2 + 52*M*r0 + 9*r0_2) - 2*a_9*E*L*M*((66 + 34*E_2)*M_2 + 2*(26 + 9*E_2)*M*r0 + 9*r0_2) - 2*a*E*L*M*r0_4*(L_4*(-72*M_2 + 50*M*r0 + 9*r0_2) + L_2*r0_2*(-138*M_2 + (103 + 36*E_2)*M*r0 + 15*r0_2) + r0_4*(-18*M_2 + (5 + 36*E_2)*M*r0 + 18*r0_2)) + r0_4*(16*E_2*M*r0_8 - L_6*M*(36*M_2 - 20*M*r0 + r0_2) + L_2*r0_5*(4*(-1 + 9*E_2)*M_2 + 2*(-2 + 7*E_2)*M*r0 + 3*r0_2) + L_4*r0_2*(-52*M_3 + 4*(10 + 9*E_2)*M_2*r0 - (17 + 2*E_2)*M*r0_2 + 5*r0_3)) + a_8*M*(L_2*(6*(11 + 34*E_2)*M_2 + 4*(13 + 40*E_2)*M*r0 + 9*(1 + 2*E_2)*r0_2) + E_2*r0*(-320*M_3 + 34*M_2*r0 + 253*M*r0_2 + 65*r0_3)) - 2*a_7*E*L*M*(2*L_2*(51*M_2 + (53 + 9*E_2)*M*r0 + 9*r0_2) + r0*(-8*(40 + 3*E_2)*M_3 + 2*(4 + 69*E_2)*M_2*r0 + (241 + 102*E_2)*M*r0_2 + 65*r0_3)) + 2*a_3*E*L*M*r0_2*(2*L_4*(18*M_2 - 56*M*r0 - 9*r0_2) + 2*L_2*r0*(54*M_3 + 2*(77 + 9*E_2)*M_2*r0 - (137 + 51*E_2)*M*r0_2 - 58*r0_3) - r0_3*(72*M_3 - 2*(140 + 9*E_2)*M_2*r0 + (95 + 138*E_2)*M*r0_2 + 111*r0_3)) + a_2*r0_2*(-4*L_6*M*(6*M_2 - 7*M*r0 - 4*r0_2) + E_2*M*r0_6*(-90*M_2 + 87*M*r0 + 86*r0_2) + L_4*r0*(-36*M_4 - 12*(14 + 15*E_2)*M_3*r0 + (89 + 284*E_2)*M_2*r0_2 + 9*(8 + E_2)*M*r0_3 - 11*r0_4) + L_2*r0_3*(84*M_4 - 18*(10 + 21*E_2)*M_3*r0 + (19 + 461*E_2)*M_2*r0_2 + (65 + 77*E_2)*M*r0_3 - 8*r0_4)) + 2*a_5*E*L*M*r0*(-9*L_4*(6*M + r0) + L_2*(72*M_3 + 4*(4 + 3*E_2)*M_2*r0 - (305 + 84*E_2)*M*r0_2 - 83*r0_3) - r0*(72*M_4 - 8*(44 + 9*E_2)*M_3*r0 + 2*(-164 + 51*E_2)*M_2*r0_2 + (335 + 186*E_2)*M*r0_3 + 149*r0_4)) + a_6*M*(L_4*(68*M_2 + 4*(22 + 27*E_2)*M*r0 + 9*(2 + E_2)*r0_2) + L_2*r0*(-16*(20 + 9*E_2)*M_3 + 2*(-9 + 199*E_2)*M_2*r0 + (229 + 629*E_2)*M*r0_2 + 5*(13 + 17*E_2)*r0_3) + E_2*r0_2*(72*M_4 - 556*M_3*r0 - 384*M_2*r0_2 + 381*M*r0_3 + 157*r0_4)) + a_4*r0*(9*L_6*M*(4*M + r0) + 3*E_2*M*r0_4*(-12*M_3 - 110*M_2*r0 + 89*M*r0_2 + 57*r0_3) + L_4*M*(-48*M_3 - 2*(77 + 36*E_2)*M_2*r0 + (185 + 364*E_2)*M*r0_2 + (81 + 20*E_2)*r0_3) + L_2*r0*(72*M_5 - 4*(37 + 81*E_2)*M_4*r0 - 4*(75 + 61*E_2)*M_3*r0_2 + 2*(116 + 399*E_2)*M_2*r0_3 + (97 + 130*E_2)*M*r0_4 - 11*r0_5))))/(r0_5*expr2_3);\n A41440 = (-32*(a_10*E_2*M*(69*M_2 + 53*M*r0 + 9*r0_2) - 2*a_9*E*L*M*((69 + 35*E_2)*M_2 + (53 + 18*E_2)*M*r0 + 9*r0_2) - 6*a*E*L*M*r0_4*(L_4*(-24*M_2 + 10*M*r0 + 9*r0_2) + r0_4*(-6*M_2 + (-5 + 12*E_2)*M*r0 + 12*r0_2) + L_2*r0_2*(-38*M_2 + (13 + 12*E_2)*M*r0 + 19*r0_2)) + 2*a_3*E*L*M*r0_2*(12*L_4*(3*M_2 - 8*M*r0 - 3*r0_2) + L_2*r0*(108*M_3 + 2*(175 + 18*E_2)*M_2*r0 - (257 + 102*E_2)*M*r0_2 - 187*r0_3) - 3*r0_3*(12*M_3 + (-112 + 3*E_2)*M_2*r0 + 2*(19 + 23*E_2)*M*r0_2 + 54*r0_3)) + a_8*M*(L_2*(3*(23 + 70*E_2)*M_2 + (53 + 161*E_2)*M*r0 + 9*(1 + 2*E_2)*r0_2) + E_2*r0*(-390*M_3 + 53*M_2*r0 + 308*M*r0_2 + 81*r0_3)) - 2*a_7*E*L*M*(L_2*(105*M_2 + (107 + 18*E_2)*M*r0 + 18*r0_2) + r0*(-6*(65 + 4*E_2)*M_3 + (32 + 147*E_2)*M_2*r0 + 6*(50 + 17*E_2)*M*r0_2 + 82*r0_3)) + a_2*r0_2*(12*L_6*M*(-2*M_2 + M*r0 + 3*r0_2) + 3*E_2*M*r0_6*(-30*M_2 + 29*M*r0 + 42*r0_2) + L_4*r0*(-36*M_4 - 4*(46 + 45*E_2)*M_3*r0 + 9*(5 + 28*E_2)*M_2*r0_2 + 3*(40 + 11*E_2)*M*r0_3 - 10*r0_4) + L_2*r0_3*(60*M_4 - 8*(23 + 36*E_2)*M_3*r0 + 3*(-1 + 128*E_2)*M_2*r0_2 + 3*(30 + 47*E_2)*M*r0_3 - 7*r0_4)) + a_6*M*(L_4*(70*M_2 + (89 + 108*E_2)*M*r0 + 9*(2 + E_2)*r0_2) + L_2*r0*(-6*(65 + 24*E_2)*M_3 + (11 + 380*E_2)*M_2*r0 + 2*(146 + 331*E_2)*M*r0_2 + (83 + 117*E_2)*r0_3) + 3*E_2*r0_2*(24*M_4 - 240*M_3*r0 - 149*M_2*r0_2 + 164*M*r0_3 + 71*r0_4)) + 2*a_5*E*L*M*r0*(-9*L_4*(6*M + r0) + L_2*(72*M_3 + (61 + 12*E_2)*M_2*r0 - 3*(115 + 28*E_2)*M*r0_2 - 118*r0_3) - r0*(72*M_4 - 6*(77 + 12*E_2)*M_3*r0 + (-371 + 129*E_2)*M_2*r0_2 + 2*(214 + 93*E_2)*M*r0_3 + 199*r0_4)) + a_4*r0*(9*L_6*M*(4*M + r0) + 3*E_2*M*r0_4*(-30*M_3 - 139*M_2*r0 + 108*M*r0_2 + 81*r0_3) + L_4*M*(-48*M_3 - 8*(26 + 9*E_2)*M_2*r0 + 116*(2 + 3*E_2)*M*r0_2 + (119 + 36*E_2)*r0_3) + L_2*r0*(72*M_5 - 12*(17 + 27*E_2)*M_4*r0 - 2*(176 + 129*E_2)*M_3*r0_2 + 3*(94 + 259*E_2)*M_2*r0_3 + 6*(23 + 35*E_2)*M*r0_4 - 10*r0_5)) + r0_4*(24*E_2*M*r0_8 + 3*L_6*M*(-12*M_2 + 4*M*r0 + r0_2) + 3*L_2*r0_5*(4*(-1 + 3*E_2)*M_2 + 10*E_2*M*r0 + r0_2) + L_4*r0_2*(-44*M_3 + 3*(-1 + 2*E_2)*M*r0_2 + 4*r0_3 + 12*M_2*(r0 + 3*E_2*r0)))))/(r0_2*expr2_3);\n A41620 = (-8*r0*(3*a_8*E_2*M*(4*M + r0) - 6*a_7*E*L*M*(2*(2 + E_2)*M + r0) + 2*a_5*E*L*M*(-3*L_2*(6*M + r0) + r0*((98 + 4*E_2)*M_2 - (61 + 28*E_2)*M*r0 - 42*r0_2)) + 2*a*E*L*M*r0_3*(r0_2*(6*M_2 + (25 - 12*E_2)*M*r0 - 30*r0_2) + L_2*(24*M_2 + 10*M*r0 - 27*r0_2)) + r0_3*(16*E_2*M*r0_6 + L_2*r0_3*(12*(-1 + E_2)*M_2 + 2*(2 + 5*E_2)*M*r0 + r0_2) + L_4*M*(-12*M_2 - 4*M*r0 + 5*r0_2)) + a_6*M*(3*L_2*(4*M + 12*E_2*M + r0 + E_2*r0) + E_2*r0*(-98*M_2 + 61*M*r0 + 40*r0_2)) + 2*a_3*E*L*M*r0*(2*L_2*(6*M_2 - 8*M*r0 - 15*r0_2) - r0*(12*M_3 - 4*(32 + 3*E_2)*M_2*r0 + 2*(10 + 17*E_2)*M*r0_2 + 77*r0_3)) + a_4*M*(3*L_4*(4*M + r0) + L_2*r0*(-2*(49 + 12*E_2)*M_2 + (61 + 100*E_2)*M*r0 + 4*(11 + 7*E_2)*r0_2) + E_2*r0_2*(12*M_3 - 196*M_2*r0 + 30*M*r0_2 + 87*r0_3)) - a_2*r0*(3*E_2*M*r0_4*(10*M_2 + M*r0 - 22*r0_2) + 4*L_4*M*(2*M_2 + 3*M*r0 - 8*r0_2) + L_2*r0*(-12*M_4 + 60*(1 + E_2)*M_3*r0 + (15 - 52*E_2)*M_2*r0_2 - (51 + 35*E_2)*M*r0_3 + 3*r0_4))))/expr2_3;\n A41800 = (4*M*r0_5*(4*a_4*E_2*(M - r0) + a*E*L*r0_2*(-10*M + 9*r0) + a_3*E*L*(-8*M + 9*r0) + a_2*(L_2*(4*M - 5*r0) + 2*E_2*(4*M - 3*r0)*r0_2) - r0_2*(2*E_2*r0_3 + L_2*(-2*M + r0))))/expr2_3;\n A42060 = (256*expr1_2*(3*a_6*E_2*M*(9*M + 4*r0) - 6*a_5*E*L*M*(9*M + 4*r0) - 2*a_3*E*L*M*r0*(12*L_2 - 16*M_2 + 31*M*r0 + 21*r0_2) + 2*a*E*L*M*r0_2*(4*L_2*(2*M - 3*r0) - r0_2*(10*M + 3*r0)) + r0_2*(8*E_2*M*r0_5 + 4*L_4*M*(-2*M + r0) + L_2*r0_2*(4*M_2 + 8*(-1 + E_2)*M*r0 + 3*r0_2)) + a_4*M*(3*L_2*(9*M + 4*(1 + E_2)*r0) + 2*E_2*r0*(-8*M_2 + 25*M*r0 + 16*r0_2)) + a_2*M*r0*(12*L_4 + 7*E_2*r0_3*(5*M + 4*r0) - 2*L_2*(8*M_2 + 2*(-3 + 2*E_2)*M*r0 - 5*(1 + 2*E_2)*r0_2))))/(r0_4*expr2_3);\n A42240 = (384*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(a_6*E_2*M*(13*M + 6*r0) - 2*a_5*E*L*M*(13*M + 6*r0) - 2*a_3*E*L*M*r0*(6*L_2 - 8*M_2 + 13*M*r0 + 11*r0_2) + r0_2*(4*E_2*M*r0_5 + 2*L_4*M*(-2*M + r0) + L_2*r0_3*(-2*M + 4*E_2*M + r0)) + 2*a*E*L*M*r0_2*(L_2*(4*M - 6*r0) - r0_2*(2*M + 3*r0)) + a_4*M*(L_2*(13*M + 6*(1 + E_2)*r0) + 2*E_2*r0*(-4*M_2 + 11*M*r0 + 8*r0_2)) + a_2*M*r0*(6*L_4 + E_2*r0_3*(13*M + 14*r0) + L_2*(-8*M_2 - 4*(-1 + E_2)*M*r0 + 2*(3 + 5*E_2)*r0_2))))/(r0*expr2_3);\n A42420 = (48*r0_2*(E_2*M_2*expr3_2 + L_2*expr5_2 + 2*E*L*M*(a_3 + 3*a*r0_2)*(-(a_2*M) + r0_2*(-2*M + r0)) - 4*M*r0*(L_2 + r0_2 + (a_2*(2*M + r0))/r0)*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-2*M + 3*r0) + a_2*(-3*L_2 + E_2*(2*M - 5*r0)*r0) - r0*(2*E_2*r0_3 + L_2*(-2*M + r0)))))/expr2_3;\n A42600 = (-16*M*r0_5*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-2*M + 3*r0) + a_2*(-3*L_2 + E_2*(2*M - 5*r0)*r0) - r0*(2*E_2*r0_3 + L_2*(-2*M + r0))))/expr2_3;\n A43060 = (-128*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(a_10*E_2*M*(66*M_2 + 52*M*r0 + 9*r0_2) - 2*a_9*E*L*M*((66 + 34*E_2)*M_2 + 2*(26 + 9*E_2)*M*r0 + 9*r0_2) - 2*a*E*L*M*r0_4*(4*L_2*r0_2*(-32*M_2 + 3*(7 + 3*E_2)*M*r0 + 6*r0_2) + L_4*(-70*M_2 + 45*M*r0 + 12*r0_2) + r0_4*(-10*M_2 + 9*(-1 + 4*E_2)*M*r0 + 24*r0_2)) + r0_4*(-2*E_2*M*(M - 9*r0)*r0_7 + 17*L_6*M_2*(-2*M + r0) + 2*L_4*r0_2*(-22*M_3 + (13 + 17*E_2)*M_2*r0 - 5*M*r0_2 + 2*r0_3) + L_2*r0_4*(6*M_3 + (-15 + 32*E_2)*M_2*r0 + 2*(1 + 9*E_2)*M*r0_2 + 2*r0_3)) + a_8*M*(L_2*(6*(11 + 34*E_2)*M_2 + 4*(13 + 40*E_2)*M*r0 + 9*(1 + 2*E_2)*r0_2) + E_2*r0*(-330*M_3 + 33*M_2*r0 + 261*M*r0_2 + 68*r0_3)) - 2*a_7*E*L*M*(2*L_2*(51*M_2 + (53 + 9*E_2)*M*r0 + 9*r0_2) + r0*(-6*(55 + 4*E_2)*M_3 + (7 + 138*E_2)*M_2*r0 + 3*(83 + 34*E_2)*M*r0_2 + 68*r0_3)) + 2*a_3*E*L*M*r0_2*(L_4*(36*M_2 - 109*M*r0 - 21*r0_2) + L_2*r0*(100*M_3 + (319 + 36*E_2)*M_2*r0 - 6*(44 + 17*E_2)*M*r0_2 - 129*r0_3) - r0_3*(92*M_3 - 3*(101 + 6*E_2)*M_2*r0 + (85 + 138*E_2)*M*r0_2 + 124*r0_3)) + a_2*r0_2*(L_6*M*(-24*M_2 + 25*M*r0 + 19*r0_2) + E_2*M*r0_6*(-87*M_2 + 75*M*r0 + 95*r0_2) + L_4*r0*(-28*M_4 - 2*(86 + 89*E_2)*M_3*r0 + (75 + 277*E_2)*M_2*r0_2 + 2*(41 + 7*E_2)*M*r0_3 - 11*r0_4) + L_2*r0_3*(100*M_4 - (196 + 373*E_2)*M_3*r0 + 2*(5 + 221*E_2)*M_2*r0_2 + (75 + 91*E_2)*M*r0_3 - 9*r0_4)) + 2*a_5*E*L*M*r0*(-9*L_4*(6*M + r0) + L_2*(72*M_3 + 3*(9 + 4*E_2)*M_2*r0 - 2*(155 + 42*E_2)*M*r0_2 - 89*r0_3) - r0*(80*M_4 - 6*(59 + 12*E_2)*M_3*r0 + 2*(-176 + 51*E_2)*M_2*r0_2 + (343 + 186*E_2)*M*r0_3 + 159*r0_4)) + a_6*M*(L_4*(68*M_2 + 4*(22 + 27*E_2)*M*r0 + 9*(2 + E_2)*r0_2) + L_2*r0*(-6*(55 + 24*E_2)*M_3 + (-19 + 387*E_2)*M_2*r0 + (237 + 634*E_2)*M*r0_2 + (68 + 91*E_2)*r0_3) + E_2*r0_2*(80*M_4 - 564*M_3*r0 - 407*M_2*r0_2 + 393*M*r0_3 + 168*r0_4)) + a_4*r0*(9*L_6*M*(4*M + r0) + 3*E_2*M*r0_4*(-6*M_3 - 119*M_2*r0 + 87*M*r0_2 + 62*r0_3) + L_4*M*(-48*M_3 - 3*(55 + 24*E_2)*M_2*r0 + 19*(10 + 19*E_2)*M*r0_2 + (87 + 23*E_2)*r0_3) + L_2*r0*(80*M_5 - 4*(36 + 79*E_2)*M_4*r0 - (325 + 262*E_2)*M_3*r0_2 + 4*(59 + 198*E_2)*M_2*r0_3 + 2*(53 + 73*E_2)*M*r0_4 - 11*r0_5))))/(r0_5*expr2_4);\n A43240 = (-32*(2*a_10*E_2*M*(69*M_2 + 53*M*r0 + 9*r0_2) - 4*a_9*E*L*M*((69 + 35*E_2)*M_2 + (53 + 18*E_2)*M*r0 + 9*r0_2) - 6*a*E*L*M*r0_4*(L_4*(-46*M_2 + 15*M*r0 + 21*r0_2) + 2*L_2*r0_2*(-34*M_2 + (5 + 12*E_2)*M*r0 + 23*r0_2) + r0_4*(-6*M_2 + 3*(-7 + 8*E_2)*M*r0 + 29*r0_2)) + r0_4*(-6*E_2*M*(M - 9*r0)*r0_7 + 3*L_6*M*(-22*M_2 + 5*M*r0 + 3*r0_2) + 2*L_4*r0_2*(-34*M_3 + (-5 + 33*E_2)*M_2*r0 + (5 + 9*E_2)*M*r0_2 + 3*r0_3) + L_2*r0_4*(14*M_3 + (-49 + 60*E_2)*M_2*r0 + (13 + 72*E_2)*M*r0_2 + 4*r0_3)) + a_8*M*(2*L_2*(3*(23 + 70*E_2)*M_2 + (53 + 161*E_2)*M*r0 + 9*(1 + 2*E_2)*r0_2) + E_2*r0*(-812*M_3 + 104*M_2*r0 + 641*M*r0_2 + 171*r0_3)) - 2*a_7*E*L*M*(L_2*(210*M_2 + 2*(107 + 18*E_2)*M*r0 + 36*r0_2) + r0*(-4*(203 + 12*E_2)*M_3 + 2*(31 + 147*E_2)*M_2*r0 + (625 + 204*E_2)*M*r0_2 + 173*r0_3)) + 2*a_3*E*L*M*r0_2*(3*L_4*(24*M_2 - 61*M*r0 - 27*r0_2) + 2*L_2*r0*(96*M_3 + 9*(41 + 4*E_2)*M_2*r0 - (245 + 102*E_2)*M*r0_2 - 206*r0_3) - r0_3*(120*M_3 + 2*(-367 + 9*E_2)*M_2*r0 + 69*(3 + 4*E_2)*M*r0_2 + 359*r0_3)) + a_2*r0_2*(3*L_6*M*(-16*M_2 + 5*M*r0 + 27*r0_2) + 3*E_2*M*r0_6*(-60*M_2 + 49*M*r0 + 93*r0_2) + L_4*r0*(-48*M_4 - 6*(64 + 59*E_2)*M_3*r0 + 3*(18 + 161*E_2)*M_2*r0_2 + (268 + 81*E_2)*M*r0_3 - 20*r0_4) + L_2*r0_3*(160*M_4 - 6*(68 + 95*E_2)*M_3*r0 + (-29 + 720*E_2)*M_2*r0_2 + (205 + 324*E_2)*M*r0_3 - 16*r0_4)) + 2*a_5*E*L*M*r0*(-18*L_4*(6*M + r0) + 2*L_2*(72*M_3 + 6*(13 + 2*E_2)*M_2*r0 - (353 + 84*E_2)*M*r0_2 - 127*r0_3) - r0*(168*M_4 - 4*(235 + 36*E_2)*M_3*r0 + 2*(-404 + 129*E_2)*M_2*r0_2 + 3*(295 + 124*E_2)*M*r0_3 + 427*r0_4)) + a_6*M*(2*L_4*(70*M_2 + (89 + 108*E_2)*M*r0 + 9*(2 + E_2)*r0_2) + L_2*r0*(-4*(203 + 72*E_2)*M_3 + 2*(10 + 363*E_2)*M_2*r0 + (609 + 1340*E_2)*M*r0_2 + 7*(25 + 36*E_2)*r0_3) + E_2*r0_2*(168*M_4 - 1476*M_3*r0 - 958*M_2*r0_2 + 1027*M*r0_3 + 459*r0_4)) + a_4*r0*(18*L_6*M*(4*M + r0) + 3*E_2*M*r0_4*(-48*M_3 - 304*M_2*r0 + 215*M*r0_2 + 177*r0_3) + L_4*M*(-96*M_3 - 18*(25 + 8*E_2)*M_2*r0 + 3*(160 + 229*E_2)*M*r0_2 + (256 + 81*E_2)*r0_3) + L_2*r0*(168*M_5 - 4*(101 + 156*E_2)*M_4*r0 - 4*(193 + 144*E_2)*M_3*r0_2 + 3*(193 + 514*E_2)*M_2*r0_3 + (301 + 468*E_2)*M*r0_4 - 20*r0_5))))/(r0_2*expr2_4);\n A43420 = (-8*r0*(9*a_8*E_2*M*(4*M + r0) - 18*a_7*E*L*M*(2*(2 + E_2)*M + r0) + 2*a_5*E*L*M*(-9*L_2*(6*M + r0) + r0*((311 + 12*E_2)*M_2 - (191 + 84*E_2)*M*r0 - 135*r0_2)) - 6*a*E*L*M*r0_3*(L_2*(-22*M_2 - 15*M*r0 + 30*r0_2) + r0_2*(-2*M_2 + 3*(-11 + 4*E_2)*M*r0 + 34*r0_2)) + a_6*M*(9*L_2*(4*M + 12*E_2*M + r0 + E_2*r0) + E_2*r0*(-311*M_2 + 191*M*r0 + 129*r0_2)) + r0_3*(-6*E_2*M*(M - 9*r0)*r0_5 - 3*L_4*M*(10*M_2 + 7*M*r0 - 6*r0_2) + L_2*r0_2*(10*M_3 + (-53 + 30*E_2)*M_2*r0 + 4*(5 + 9*E_2)*M*r0_2 + 2*r0_3)) + a_4*M*(9*L_4*(4*M + r0) + L_2*r0*(-((311 + 72*E_2)*M_2) + (191 + 291*E_2)*M*r0 + 3*(47 + 31*E_2)*r0_2) + 3*E_2*r0_2*(16*M_3 - 206*M_2*r0 + 28*M*r0_2 + 95*r0_3)) + 2*a_3*E*L*M*r0*(L_2*(36*M_2 - 39*M*r0 - 99*r0_2) - r0*(48*M_3 - (403 + 36*E_2)*M_2*r0 + 6*(8 + 17*E_2)*M*r0_2 + 250*r0_3)) - a_2*r0*(3*E_2*M*r0_4*(29*M_2 + 11*M*r0 - 73*r0_2) + 3*L_4*M*(8*M_2 + 15*M*r0 - 35*r0_2) + L_2*r0*(-48*M_4 + 2*(94 + 87*E_2)*M_3*r0 - 9*(-7 + 15*E_2)*M_2*r0_2 - (167 + 120*E_2)*M*r0_3 + 9*r0_4))))/expr2_4;\n A43600 = (-2*M*r0_5*(2*a_3*E*L*(35*M - 39*r0) - 35*a_4*E_2*(M - r0) - 2*a*E*L*r0*(2*M_2 - 45*M*r0 + 39*r0_2) + (M - 9*r0)*r0*(L_2*(2*M - r0) - 2*E_2*r0_3) + a_2*(L_2*(-35*M + 43*r0) + E_2*r0*(2*M_2 - 71*M*r0 + 53*r0_2))))/expr2_4;\n A44040 = (192*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(a_6*E_2*M*(13*M + 6*r0) - 2*a_5*E*L*M*(13*M + 6*r0) - 2*a_3*E*L*M*r0*(6*L_2 - 8*M_2 + 13*M*r0 + 11*r0_2) + r0_2*(4*E_2*M*r0_5 + 2*L_4*M*(-2*M + r0) + L_2*r0_3*(-2*M + 4*E_2*M + r0)) + 2*a*E*L*M*r0_2*(L_2*(4*M - 6*r0) - r0_2*(2*M + 3*r0)) + a_4*M*(L_2*(13*M + 6*(1 + E_2)*r0) + 2*E_2*r0*(-4*M_2 + 11*M*r0 + 8*r0_2)) + a_2*M*r0*(6*L_4 + E_2*r0_3*(13*M + 14*r0) + L_2*(-8*M_2 - 4*(-1 + E_2)*M*r0 + 2*(3 + 5*E_2)*r0_2))))/(r0*expr2_4);\n A44220 = (48*r0_2*(E_2*M_2*expr3_2 + L_2*expr5_2 + 2*E*L*M*(a_3 + 3*a*r0_2)*(-(a_2*M) + r0_2*(-2*M + r0)) - 4*M*r0*(L_2 + r0_2 + (a_2*(2*M + r0))/r0)*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-2*M + 3*r0) + a_2*(-3*L_2 + E_2*(2*M - 5*r0)*r0) - r0*(2*E_2*r0_3 + L_2*(-2*M + r0)))))/expr2_4;\n A44400 = (-24*M*r0_5*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-2*M + 3*r0) + a_2*(-3*L_2 + E_2*(2*M - 5*r0)*r0) - r0*(2*E_2*r0_3 + L_2*(-2*M + r0))))/expr2_4;\n A45040 = (-32*(a_10*E_2*M*(69*M_2 + 53*M*r0 + 9*r0_2) - 2*a_9*E*L*M*((69 + 35*E_2)*M_2 + (53 + 18*E_2)*M*r0 + 9*r0_2) - 6*a*E*L*M*r0_4*(r0_5*(4*(-4 + 3*E_2)*M + 17*r0) + 3*L_2*r0_2*(-10*M_2 + (-1 + 4*E_2)*M*r0 + 9*r0_2) + L_4*(-22*M_2 + 5*M*r0 + 12*r0_2)) + r0_4*(-6*E_2*M*(M - 5*r0)*r0_7 + 3*L_6*M*(-10*M_2 + M*r0 + 2*r0_2) + L_2*r0_4*(14*M_3 + (-37 + 24*E_2)*M_2*r0 + (13 + 42*E_2)*M*r0_2 + r0_3) + L_4*r0_2*(-24*M_3 + 2*(-11 + 15*E_2)*M_2*r0 + (13 + 12*E_2)*M*r0_2 + 2*r0_3)) + a_8*M*(L_2*(3*(23 + 70*E_2)*M_2 + (53 + 161*E_2)*M*r0 + 9*(1 + 2*E_2)*r0_2) + E_2*r0*(-422*M_3 + 51*M_2*r0 + 333*M*r0_2 + 90*r0_3)) - 2*a_7*E*L*M*(L_2*(105*M_2 + (107 + 18*E_2)*M*r0 + 18*r0_2) + r0*(-2*(211 + 12*E_2)*M_3 + 3*(10 + 49*E_2)*M_2*r0 + (325 + 102*E_2)*M*r0_2 + 91*r0_3)) + 2*a_3*E*L*M*r0_2*(L_4*(36*M_2 - 87*M*r0 - 45*r0_2) + L_2*r0*(84*M_3 + 4*(97 + 9*E_2)*M_2*r0 - (233 + 102*E_2)*M*r0_2 - 225*r0_3) - r0_3*(84*M_3 + (-398 + 9*E_2)*M_2*r0 + 3*(31 + 46*E_2)*M*r0_2 + 197*r0_3)) + a_2*r0_2*(3*L_6*M*(-8*M_2 + M*r0 + 15*r0_2) + 3*E_2*M*r0_6*(-30*M_2 + 20*M*r0 + 51*r0_2) + L_4*r0*(-12*M_4 - 2*(100 + 87*E_2)*M_3*r0 + 3*(3 + 77*E_2)*M_2*r0_2 + 4*(37 + 12*E_2)*M*r0_3 - 10*r0_4) + L_2*r0_3*(100*M_4 - 2*(112 + 141*E_2)*M_3*r0 + 2*(-13 + 168*E_2)*M_2*r0_2 + (115 + 183*E_2)*M*r0_3 - 9*r0_4)) + 2*a_5*E*L*M*r0*(-9*L_4*(6*M + r0) + L_2*(72*M_3 + (95 + 12*E_2)*M_2*r0 - (361 + 84*E_2)*M*r0_2 - 136*r0_3) - r0*(96*M_4 - 2*(239 + 36*E_2)*M_3*r0 + (-437 + 129*E_2)*M_2*r0_2 + (457 + 186*E_2)*M*r0_3 + 228*r0_4)) + a_6*M*(L_4*(70*M_2 + (89 + 108*E_2)*M*r0 + 9*(2 + E_2)*r0_2) + L_2*r0*(-2*(211 + 72*E_2)*M_3 + (9 + 346*E_2)*M_2*r0 + (317 + 678*E_2)*M*r0_2 + (92 + 135*E_2)*r0_3) + E_2*r0_2*(96*M_4 - 756*M_3*r0 - 511*M_2*r0_2 + 535*M*r0_3 + 246*r0_4)) + a_4*r0*(9*L_6*M*(4*M + r0) + 3*E_2*M*r0_4*(-18*M_3 - 165*M_2*r0 + 107*M*r0_2 + 96*r0_3) + L_4*M*(-48*M_3 - 2*(121 + 36*E_2)*M_2*r0 + (248 + 339*E_2)*M*r0_2 + (137 + 45*E_2)*r0_3) + L_2*r0*(96*M_5 - 100*(2 + 3*E_2)*M_4*r0 - 6*(70 + 53*E_2)*M_3*r0_2 + 9*(33 + 85*E_2)*M_2*r0_3 + (163 + 258*E_2)*M*r0_4 - 10*r0_5))))/(r0_2*expr2_5);\n A45220 = (-8*r0*(9*a_8*E_2*M*(4*M + r0) - 18*a_7*E*L*M*(2*(2 + E_2)*M + r0) + 2*a_5*E*L*M*(-9*L_2*(6*M + r0) + r0*(4*(82 + 3*E_2)*M_2 - (199 + 84*E_2)*M*r0 - 144*r0_2)) - 6*a*E*L*M*r0_3*(L_2*(-20*M_2 - 20*M*r0 + 33*r0_2) + r0_2*(2*M_2 + (-41 + 12*E_2)*M*r0 + 38*r0_2)) + a_6*M*(9*L_2*(4*M + 12*E_2*M + r0 + E_2*r0) + E_2*r0*(-328*M_2 + 199*M*r0 + 138*r0_2)) + r0_3*(-12*E_2*M*(M - 5*r0)*r0_5 - 3*L_4*M*(8*M_2 + 10*M*r0 - 7*r0_2) + L_2*r0_2*(20*M_3 + 2*(-35 + 12*E_2)*M_2*r0 + 14*(2 + 3*E_2)*M*r0_2 + r0_3)) + a_4*M*(9*L_4*(4*M + r0) + L_2*r0*(-8*(41 + 9*E_2)*M_2 + (199 + 282*E_2)*M*r0 + 6*(25 + 17*E_2)*r0_2) + 3*E_2*r0_2*(20*M_3 - 216*M_2*r0 + 26*M*r0_2 + 103*r0_3)) + 2*a_3*E*L*M*r0*(6*L_2*(6*M_2 - 5*M*r0 - 18*r0_2) - r0*(60*M_3 - 2*(211 + 18*E_2)*M_2*r0 + 6*(6 + 17*E_2)*M*r0_2 + 269*r0_3)) - a_2*r0*(3*E_2*M*r0_4*(28*M_2 + 19*M*r0 - 80*r0_2) + 6*L_4*M*(4*M_2 + 9*M*r0 - 19*r0_2) + L_2*r0*(-60*M_4 + 28*(7 + 6*E_2)*M_3*r0 + 3*(27 - 38*E_2)*M_2*r0_2 - (181 + 135*E_2)*M*r0_3 + 9*r0_4))))/expr2_5;\n A45400 = (-6*M*r0_5*(2*a_3*E*L*(19*M - 21*r0) - 19*a_4*E_2*(M - r0) - 2*a*E*L*r0*(2*M_2 - 25*M*r0 + 21*r0_2) + (M - 5*r0)*r0*(L_2*(2*M - r0) - 2*E_2*r0_3) + a_2*(L_2*(-19*M + 23*r0) + E_2*r0*(2*M_2 - 39*M*r0 + 29*r0_2))))/expr2_5;\n A46020 = (16*r0_2*(E_2*M_2*expr3_2 + L_2*expr5_2 + 2*E*L*M*(a_3 + 3*a*r0_2)*(-(a_2*M) + r0_2*(-2*M + r0)) - 4*M*r0*(L_2 + r0_2 + (a_2*(2*M + r0))/r0)*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-2*M + 3*r0) + a_2*(-3*L_2 + E_2*(2*M - 5*r0)*r0) - r0*(2*E_2*r0_3 + L_2*(-2*M + r0)))))/expr2_5;\n A46200 = (-16*M*r0_5*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-2*M + 3*r0) + a_2*(-3*L_2 + E_2*(2*M - 5*r0)*r0) - r0*(2*E_2*r0_3 + L_2*(-2*M + r0))))/expr2_5;\n A47020 = (-8*r0*(3*a_8*E_2*M*(4*M + r0) - 6*a_7*E*L*M*(2*(2 + E_2)*M + r0) + 2*a_5*E*L*M*(-3*L_2*(6*M + r0) + r0*((115 + 4*E_2)*M_2 - (69 + 28*E_2)*M*r0 - 51*r0_2)) - 2*a*E*L*M*r0_3*(L_2*(-18*M_2 - 25*M*r0 + 36*r0_2) + r0_2*(6*M_2 + (-49 + 12*E_2)*M*r0 + 42*r0_2)) + a_6*M*(3*L_2*(4*M + 12*E_2*M + r0 + E_2*r0) + E_2*r0*(-115*M_2 + 69*M*r0 + 49*r0_2)) + M*r0_3*(2*E_2*r0_5*(-3*M + 11*r0) + L_4*(-6*M_2 - 13*M*r0 + 8*r0_2) + L_2*r0_2*(10*M_2 + (-29 + 6*E_2)*M*r0 + 4*(3 + 4*E_2)*r0_2)) + 2*a_3*E*L*M*r0*(L_2*(12*M_2 - 7*M*r0 - 39*r0_2) - r0*(24*M_3 - 3*(49 + 4*E_2)*M_2*r0 + 2*(4 + 17*E_2)*M*r0_2 + 96*r0_3)) + a_4*M*(3*L_4*(4*M + r0) + L_2*r0*(-((115 + 24*E_2)*M_2) + (69 + 91*E_2)*M*r0 + (53 + 37*E_2)*r0_2) + E_2*r0_2*(24*M_3 - 226*M_2*r0 + 24*M*r0_2 + 111*r0_3)) - a_2*r0*(L_4*M*(8*M_2 + 21*M*r0 - 41*r0_2) + 3*E_2*M*r0_4*(9*M_2 + 9*M*r0 - 29*r0_2) + L_2*r0*(-24*M_4 + 2*(34 + 27*E_2)*M_3*r0 + (33 - 31*E_2)*M_2*r0_2 - 5*(13 + 10*E_2)*M*r0_3 + 3*r0_4))))/expr2_6;\n A47200 = (-2*M*r0_5*(2*a_3*E*L*(41*M - 45*r0) - 41*a_4*E_2*(M - r0) - 2*a*E*L*r0*(6*M_2 - 55*M*r0 + 45*r0_2) + (3*M - 11*r0)*r0*(L_2*(2*M - r0) - 2*E_2*r0_3) + a_2*(L_2*(-41*M + 49*r0) + E_2*r0*(6*M_2 - 85*M*r0 + 63*r0_2))))/expr2_6;\n A48000 = (-4*M*r0_5*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-2*M + 3*r0) + a_2*(-3*L_2 + E_2*(2*M - 5*r0)*r0) - r0*(2*E_2*r0_3 + L_2*(-2*M + r0))))/expr2_6;\n A49000 = (-2*M*r0_5*(2*a_3*E*L*(11*M - 12*r0) - 11*a_4*E_2*(M - r0) - 2*a*E*L*r0*(2*M_2 - 15*M*r0 + 12*r0_2) + (M - 3*r0)*r0*(L_2*(2*M - r0) - 2*E_2*r0_3) + a_2*(L_2*(-11*M + 13*r0) + E_2*r0*(2*M_2 - 23*M*r0 + 17*r0_2))))/expr2_7;\n }\n\n /* A_{r,theta} */\n {\n A50180 = (-512*expr1_3*(-(a_8*E_2*M*(7*M + 3*r0)) + a_7*E*L*M*((14 + 3*E_2)*M + 6*r0) + a*E*L*M*r0_3*(3*r0_3*((-4 + E_2)*M + 2*r0) + L_2*(-52*M_2 + 44*M*r0 - 9*r0_2)) + (2*M - r0)*r0_3*(5*L_4*M*(2*M - r0) - 3*E_2*M*r0_5 + L_2*r0_2*(2*M_2 + (3 - 4*E_2)*M*r0 - 2*r0_2)) - a_6*M*(L_2*((7 + 9*E_2)*M + 3*(1 + E_2)*r0) + E_2*r0*(-2*M_2 + 7*M*r0 + 6*r0_2)) + a_5*E*L*M*(L_2*(9*M + 6*r0) + r0*(-4*(1 + E_2)*M_2 + (8 + 13*E_2)*M*r0 + 10*r0_2)) + a_3*E*L*M*r0*(L_2*(-12*M_2 + 29*M*r0 - 3*r0_2) + r0*(-48*M_3 - 12*(-1 + E_2)*M_2*r0 + (-2 + 13*E_2)*M*r0_2 + 10*r0_3)) + a_2*r0*(3*E_2*M*r0_4*(-6*M_2 + M*r0 + 2*r0_2) + L_4*M*(4*M_2 - 8*M*r0 + 3*r0_2) + L_2*r0*(24*M_4 + 4*(-3 + 11*E_2)*M_3*r0 - 37*E_2*M_2*r0_2 + (-4 + 7*E_2)*M*r0_3 + 2*r0_4)) - a_4*M*(3*L_4*(M + r0) - 3*E_2*M*r0_2*(8*M_2 + 3*r0_2) + L_2*r0*(-2*(1 + 6*E_2)*M_2 + 4*r0_2 + M*(r0 + 34*E_2*r0)))))/(r0_8*expr2_2);\n A50360 = (384*expr1_2*(a_8*E_2*M*(9*M + 4*r0) - a_7*E*L*M*(3*(6 + E_2)*M + 8*r0) + a_5*E*L*M*(-(L_2*(9*M + 8*r0)) + r0*(4*(1 + E_2)*M_2 - (10 + 13*E_2)*M*r0 - 13*r0_2)) - (2*M - r0)*r0_3*(6*L_4*M*(2*M - r0) - 4*E_2*M*r0_5 + L_2*r0_2*(4*M_2 + (2 - 5*E_2)*M*r0 - 2*r0_2)) + a*E*L*M*r0_3*(r0_2*(8*M_2 - 3*(-2 + E_2)*M*r0 - 5*r0_2) + 10*L_2*(6*M_2 - 5*M*r0 + r0_2)) + a_6*M*((1 + E_2)*L_2*(9*M + 4*r0) + E_2*r0*(-2*M_2 + 9*M*r0 + 8*r0_2)) + a_3*E*L*M*r0*(L_2*(12*M_2 - 29*M*r0 + 2*r0_2) - r0*(-64*M_3 - 4*(-4 + 3*E_2)*M_2*r0 + (2 + 13*E_2)*M*r0_2 + 10*r0_3)) - a_2*r0*(L_4*M*(4*M_2 - 8*M*r0 + 3*r0_2) + E_2*M*r0_4*(-18*M_2 + M*r0 + 8*r0_2) + L_2*r0*(32*M_4 + 16*(-1 + 3*E_2)*M_3*r0 - (2 + 39*E_2)*M_2*r0_2 + (-3 + 8*E_2)*M*r0_3 + 2*r0_4)) + a_4*M*(L_4*(3*M + 4*r0) - E_2*M*r0_2*(32*M_2 + 9*r0_2) + L_2*r0*(-2*(1 + 6*E_2)*M_2 + (5 + E_2)*r0_2 + M*(r0 + 34*E_2*r0)))))/(r0_5*expr2_2);\n A50540 = (96*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(a_8*E_2*M*(13*M + 6*r0) - a_7*E*L*M*((26 + 3*E_2)*M + 12*r0) + a_5*E*L*M*(-3*L_2*(3*M + 4*r0) + r0*(4*(1 + E_2)*M_2 - (14 + 13*E_2)*M*r0 - 19*r0_2)) - (2*M - r0)*r0_3*(8*L_4*M*(2*M - r0) - 6*E_2*M*r0_5 + L_2*r0_2*(8*M_2 - 7*E_2*M*r0 - 2*r0_2)) + a*E*L*M*r0_3*(-3*r0_2*(-8*M_2 + (2 + E_2)*M*r0 + r0_2) + 2*L_2*(38*M_2 - 31*M*r0 + 6*r0_2)) + a_6*M*(L_2*((13 + 9*E_2)*M + 6*(1 + E_2)*r0) + E_2*r0*(-2*M_2 + 13*M*r0 + 12*r0_2)) + a_3*E*L*M*r0*(L_2*M*(12*M - 29*r0) - r0*(-96*M_3 - 12*(-2 + E_2)*M_2*r0 + (10 + 13*E_2)*M*r0_2 + 10*r0_3)) + a_2*r0*(3*E_2*M*r0_4*(6*M_2 + M*r0 - 4*r0_2) + L_4*M*(-4*M_2 + 8*M*r0 - 3*r0_2) + L_2*r0*(-48*M_4 - 8*(-3 + 7*E_2)*M_3*r0 + (6 + 43*E_2)*M_2*r0_2 + (1 - 10*E_2)*M*r0_3 - 2*r0_4)) + a_4*M*(3*L_4*(M + 2*r0) - 3*E_2*M*r0_2*(16*M_2 + 3*r0_2) + L_2*r0*(-2*(1 + 6*E_2)*M_2 + (7 + 3*E_2)*r0_2 + M*(r0 + 34*E_2*r0)))))/(r0_2*expr2_2);\n A50720 = (-8*r0*(-(a_8*E_2*M*(25*M + 12*r0)) + a_7*E*L*M*((50 + 3*E_2)*M + 24*r0) + (2*M - r0)*r0_3*(14*L_4*M*(2*M - r0) - 12*E_2*M*r0_5 - L_2*r0_2*(-20*M_2 + (6 + 13*E_2)*M*r0 + 2*r0_2)) + a*E*L*M*r0_3*(-3*r0_2*(24*M_2 - (14 + E_2)*M*r0 + r0_2) - 2*L_2*(62*M_2 - 49*M*r0 + 9*r0_2)) - a_6*M*(L_2*((25 + 9*E_2)*M + 12*(1 + E_2)*r0) + E_2*r0*(-2*M_2 + 25*M*r0 + 24*r0_2)) + a_5*E*L*M*(3*L_2*(3*M + 8*r0) + r0*(-4*(1 + E_2)*M_2 + 13*(2 + E_2)*M*r0 + 37*r0_2)) + a_3*E*L*M*r0*(L_2*(-12*M_2 + 29*M*r0 + 6*r0_2) + r0*(-192*M_3 - 12*(-4 + E_2)*M_2*r0 + (34 + 13*E_2)*M*r0_2 + 10*r0_3)) + a_2*r0*(-3*E_2*M*r0_4*(6*M_2 + 5*M*r0 - 8*r0_2) + L_4*M*(4*M_2 - 8*M*r0 + 3*r0_2) + L_2*r0*(96*M_4 + 16*(-3 + 5*E_2)*M_3*r0 - (18 + 55*E_2)*M_2*r0_2 + (5 + 16*E_2)*M*r0_3 + 2*r0_4)) - a_4*M*(3*L_4*(M + 4*r0) - 3*E_2*M*r0_2*(32*M_2 + 3*r0_2) + L_2*r0*(-2*(1 + 6*E_2)*M_2 + (13 + 9*E_2)*r0_2 + M*(r0 + 34*E_2*r0)))))/expr2_2;\n A50900 = (6*M*r0_4*(a_4*E_2 - 2*a_3*E*L + a*E*L*r0*(-4*M + r0) + a_2*(L_2 + 2*E_2*M*r0) - r0*(E_2*r0_3 + L_2*(-2*M + r0))))/(a_2 + r0*(-2*M + r0));\n A52160 = (384*expr1_2*(a_8*E_2*M*(9*M + 4*r0) - a_7*E*L*M*(3*(6 + E_2)*M + 8*r0) + a_5*E*L*M*(-(L_2*(9*M + 8*r0)) + r0*(4*(1 + E_2)*M_2 - (10 + 13*E_2)*M*r0 - 13*r0_2)) - (2*M - r0)*r0_3*(6*L_4*M*(2*M - r0) - 4*E_2*M*r0_5 + L_2*r0_2*(4*M_2 + (2 - 5*E_2)*M*r0 - 2*r0_2)) + a*E*L*M*r0_3*(r0_2*(8*M_2 - 3*(-2 + E_2)*M*r0 - 5*r0_2) + 10*L_2*(6*M_2 - 5*M*r0 + r0_2)) + a_6*M*((1 + E_2)*L_2*(9*M + 4*r0) + E_2*r0*(-2*M_2 + 9*M*r0 + 8*r0_2)) + a_3*E*L*M*r0*(L_2*(12*M_2 - 29*M*r0 + 2*r0_2) - r0*(-64*M_3 - 4*(-4 + 3*E_2)*M_2*r0 + (2 + 13*E_2)*M*r0_2 + 10*r0_3)) - a_2*r0*(L_4*M*(4*M_2 - 8*M*r0 + 3*r0_2) + E_2*M*r0_4*(-18*M_2 + M*r0 + 8*r0_2) + L_2*r0*(32*M_4 + 16*(-1 + 3*E_2)*M_3*r0 - (2 + 39*E_2)*M_2*r0_2 + (-3 + 8*E_2)*M*r0_3 + 2*r0_4)) + a_4*M*(L_4*(3*M + 4*r0) - E_2*M*r0_2*(32*M_2 + 9*r0_2) + L_2*r0*(-2*(1 + 6*E_2)*M_2 + (5 + E_2)*r0_2 + M*(r0 + 34*E_2*r0)))))/(r0_5*expr2_3);\n A52340 = (192*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(a_8*E_2*M*(13*M + 6*r0) - a_7*E*L*M*((26 + 3*E_2)*M + 12*r0) + a_5*E*L*M*(-3*L_2*(3*M + 4*r0) + r0*(4*(1 + E_2)*M_2 - (14 + 13*E_2)*M*r0 - 19*r0_2)) - (2*M - r0)*r0_3*(8*L_4*M*(2*M - r0) - 6*E_2*M*r0_5 + L_2*r0_2*(8*M_2 - 7*E_2*M*r0 - 2*r0_2)) + a*E*L*M*r0_3*(-3*r0_2*(-8*M_2 + (2 + E_2)*M*r0 + r0_2) + 2*L_2*(38*M_2 - 31*M*r0 + 6*r0_2)) + a_6*M*(L_2*((13 + 9*E_2)*M + 6*(1 + E_2)*r0) + E_2*r0*(-2*M_2 + 13*M*r0 + 12*r0_2)) + a_3*E*L*M*r0*(L_2*M*(12*M - 29*r0) - r0*(-96*M_3 - 12*(-2 + E_2)*M_2*r0 + (10 + 13*E_2)*M*r0_2 + 10*r0_3)) + a_2*r0*(3*E_2*M*r0_4*(6*M_2 + M*r0 - 4*r0_2) + L_4*M*(-4*M_2 + 8*M*r0 - 3*r0_2) + L_2*r0*(-48*M_4 - 8*(-3 + 7*E_2)*M_3*r0 + (6 + 43*E_2)*M_2*r0_2 + (1 - 10*E_2)*M*r0_3 - 2*r0_4)) + a_4*M*(3*L_4*(M + 2*r0) - 3*E_2*M*r0_2*(16*M_2 + 3*r0_2) + L_2*r0*(-2*(1 + 6*E_2)*M_2 + (7 + 3*E_2)*r0_2 + M*(r0 + 34*E_2*r0)))))/(r0_2*expr2_3);\n A52520 = (-24*r0*(-(a_8*E_2*M*(25*M + 12*r0)) + a_7*E*L*M*((50 + 3*E_2)*M + 24*r0) + (2*M - r0)*r0_3*(14*L_4*M*(2*M - r0) - 12*E_2*M*r0_5 - L_2*r0_2*(-20*M_2 + (6 + 13*E_2)*M*r0 + 2*r0_2)) + a*E*L*M*r0_3*(-3*r0_2*(24*M_2 - (14 + E_2)*M*r0 + r0_2) - 2*L_2*(62*M_2 - 49*M*r0 + 9*r0_2)) - a_6*M*(L_2*((25 + 9*E_2)*M + 12*(1 + E_2)*r0) + E_2*r0*(-2*M_2 + 25*M*r0 + 24*r0_2)) + a_5*E*L*M*(3*L_2*(3*M + 8*r0) + r0*(-4*(1 + E_2)*M_2 + 13*(2 + E_2)*M*r0 + 37*r0_2)) + a_3*E*L*M*r0*(L_2*(-12*M_2 + 29*M*r0 + 6*r0_2) + r0*(-192*M_3 - 12*(-4 + E_2)*M_2*r0 + (34 + 13*E_2)*M*r0_2 + 10*r0_3)) + a_2*r0*(-3*E_2*M*r0_4*(6*M_2 + 5*M*r0 - 8*r0_2) + L_4*M*(4*M_2 - 8*M*r0 + 3*r0_2) + L_2*r0*(96*M_4 + 16*(-3 + 5*E_2)*M_3*r0 - (18 + 55*E_2)*M_2*r0_2 + (5 + 16*E_2)*M*r0_3 + 2*r0_4)) - a_4*M*(3*L_4*(M + 4*r0) - 3*E_2*M*r0_2*(32*M_2 + 3*r0_2) + L_2*r0*(-2*(1 + 6*E_2)*M_2 + (13 + 9*E_2)*r0_2 + M*(r0 + 34*E_2*r0)))))/expr2_3;\n A52700 = (24*M*r0_4*(a_4*E_2 - 2*a_3*E*L + a*E*L*r0*(-4*M + r0) + a_2*(L_2 + 2*E_2*M*r0) - r0*(E_2*r0_3 + L_2*(-2*M + r0))))/expr2_2;\n A54140 = (96*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(a_8*E_2*M*(13*M + 6*r0) - a_7*E*L*M*((26 + 3*E_2)*M + 12*r0) + a_5*E*L*M*(-3*L_2*(3*M + 4*r0) + r0*(4*(1 + E_2)*M_2 - (14 + 13*E_2)*M*r0 - 19*r0_2)) - (2*M - r0)*r0_3*(8*L_4*M*(2*M - r0) - 6*E_2*M*r0_5 + L_2*r0_2*(8*M_2 - 7*E_2*M*r0 - 2*r0_2)) + a*E*L*M*r0_3*(-3*r0_2*(-8*M_2 + (2 + E_2)*M*r0 + r0_2) + 2*L_2*(38*M_2 - 31*M*r0 + 6*r0_2)) + a_6*M*(L_2*((13 + 9*E_2)*M + 6*(1 + E_2)*r0) + E_2*r0*(-2*M_2 + 13*M*r0 + 12*r0_2)) + a_3*E*L*M*r0*(L_2*M*(12*M - 29*r0) - r0*(-96*M_3 - 12*(-2 + E_2)*M_2*r0 + (10 + 13*E_2)*M*r0_2 + 10*r0_3)) + a_2*r0*(3*E_2*M*r0_4*(6*M_2 + M*r0 - 4*r0_2) + L_4*M*(-4*M_2 + 8*M*r0 - 3*r0_2) + L_2*r0*(-48*M_4 - 8*(-3 + 7*E_2)*M_3*r0 + (6 + 43*E_2)*M_2*r0_2 + (1 - 10*E_2)*M*r0_3 - 2*r0_4)) + a_4*M*(3*L_4*(M + 2*r0) - 3*E_2*M*r0_2*(16*M_2 + 3*r0_2) + L_2*r0*(-2*(1 + 6*E_2)*M_2 + (7 + 3*E_2)*r0_2 + M*(r0 + 34*E_2*r0)))))/(r0_2*expr2_4);\n A54320 = (-24*r0*(-(a_8*E_2*M*(25*M + 12*r0)) + a_7*E*L*M*((50 + 3*E_2)*M + 24*r0) + (2*M - r0)*r0_3*(14*L_4*M*(2*M - r0) - 12*E_2*M*r0_5 - L_2*r0_2*(-20*M_2 + (6 + 13*E_2)*M*r0 + 2*r0_2)) + a*E*L*M*r0_3*(-3*r0_2*(24*M_2 - (14 + E_2)*M*r0 + r0_2) - 2*L_2*(62*M_2 - 49*M*r0 + 9*r0_2)) - a_6*M*(L_2*((25 + 9*E_2)*M + 12*(1 + E_2)*r0) + E_2*r0*(-2*M_2 + 25*M*r0 + 24*r0_2)) + a_5*E*L*M*(3*L_2*(3*M + 8*r0) + r0*(-4*(1 + E_2)*M_2 + 13*(2 + E_2)*M*r0 + 37*r0_2)) + a_3*E*L*M*r0*(L_2*(-12*M_2 + 29*M*r0 + 6*r0_2) + r0*(-192*M_3 - 12*(-4 + E_2)*M_2*r0 + (34 + 13*E_2)*M*r0_2 + 10*r0_3)) + a_2*r0*(-3*E_2*M*r0_4*(6*M_2 + 5*M*r0 - 8*r0_2) + L_4*M*(4*M_2 - 8*M*r0 + 3*r0_2) + L_2*r0*(96*M_4 + 16*(-3 + 5*E_2)*M_3*r0 - (18 + 55*E_2)*M_2*r0_2 + (5 + 16*E_2)*M*r0_3 + 2*r0_4)) - a_4*M*(3*L_4*(M + 4*r0) - 3*E_2*M*r0_2*(32*M_2 + 3*r0_2) + L_2*r0*(-2*(1 + 6*E_2)*M_2 + (13 + 9*E_2)*r0_2 + M*(r0 + 34*E_2*r0)))))/expr2_4;\n A54500 = (36*M*r0_4*(a_4*E_2 - 2*a_3*E*L + a*E*L*r0*(-4*M + r0) + a_2*(L_2 + 2*E_2*M*r0) - r0*(E_2*r0_3 + L_2*(-2*M + r0))))/expr2_3;\n A56120 = (-8*r0*(-(a_8*E_2*M*(25*M + 12*r0)) + a_7*E*L*M*((50 + 3*E_2)*M + 24*r0) + (2*M - r0)*r0_3*(14*L_4*M*(2*M - r0) - 12*E_2*M*r0_5 - L_2*r0_2*(-20*M_2 + (6 + 13*E_2)*M*r0 + 2*r0_2)) + a*E*L*M*r0_3*(-3*r0_2*(24*M_2 - (14 + E_2)*M*r0 + r0_2) - 2*L_2*(62*M_2 - 49*M*r0 + 9*r0_2)) - a_6*M*(L_2*((25 + 9*E_2)*M + 12*(1 + E_2)*r0) + E_2*r0*(-2*M_2 + 25*M*r0 + 24*r0_2)) + a_5*E*L*M*(3*L_2*(3*M + 8*r0) + r0*(-4*(1 + E_2)*M_2 + 13*(2 + E_2)*M*r0 + 37*r0_2)) + a_3*E*L*M*r0*(L_2*(-12*M_2 + 29*M*r0 + 6*r0_2) + r0*(-192*M_3 - 12*(-4 + E_2)*M_2*r0 + (34 + 13*E_2)*M*r0_2 + 10*r0_3)) + a_2*r0*(-3*E_2*M*r0_4*(6*M_2 + 5*M*r0 - 8*r0_2) + L_4*M*(4*M_2 - 8*M*r0 + 3*r0_2) + L_2*r0*(96*M_4 + 16*(-3 + 5*E_2)*M_3*r0 - (18 + 55*E_2)*M_2*r0_2 + (5 + 16*E_2)*M*r0_3 + 2*r0_4)) - a_4*M*(3*L_4*(M + 4*r0) - 3*E_2*M*r0_2*(32*M_2 + 3*r0_2) + L_2*r0*(-2*(1 + 6*E_2)*M_2 + (13 + 9*E_2)*r0_2 + M*(r0 + 34*E_2*r0)))))/expr2_5;\n A56300 = (24*M*r0_4*(a_4*E_2 - 2*a_3*E*L + a*E*L*r0*(-4*M + r0) + a_2*(L_2 + 2*E_2*M*r0) - r0*(E_2*r0_3 + L_2*(-2*M + r0))))/expr2_4;\n A58100 = (6*M*r0_4*(a_4*E_2 - 2*a_3*E*L + a*E*L*r0*(-4*M + r0) + a_2*(L_2 + 2*E_2*M*r0) - r0*(E_2*r0_3 + L_2*(-2*M + r0))))/expr2_5;\n }\n\n /* A_{r,phi} */\n {\n A60061 = (256*L*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0))*expr1_3)/(r0_5*(a_2 + r0*(-2*M + r0)));\n A60081 = (128*expr1_2*(12*a_12*E_2*M_2*(26*M_2 + 25*M*r0 + 6*r0_2) - a_11*E*L*M_2*(624*M_2 + 611*M*r0 + 150*r0_2) - a_9*E*L*M*r0*(32*(-39 + 28*E_2)*M_4 + 4*(215 + 336*E_2)*M_3*r0 + (1739 + 672*E_2)*M_2*r0_2 + 2*(135 + 56*E_2)*M*r0_3 - 114*r0_4 + 2*L_2*M*(332*M + 165*r0)) - a*E*L*M*r0_5*(L_2*r0_4*(-112*M_2 + 2*(271 + 126*E_2)*M*r0 - 243*r0_2) + 12*L_4*r0_2*(14*M_2 + (33 + 10*E_2)*M*r0 - 20*r0_2) + 6*r0_6*(2*M_2 + (13 + 24*E_2)*M*r0 - 7*r0_2) + 60*L_6*(4*M_2 - r0_2)) - 2*a_3*E*L*M*r0_3*(30*L_6*(12*M_2 - 2*M*r0 - r0_2) + L_2*r0_3*(-8*M_3 + 42*(11 + 12*E_2)*M_2*r0 + 2*(293 + 183*E_2)*M*r0_2 - 407*r0_3) + r0_5*(-372*M_3 + 18*(13 + 24*E_2)*M_2*r0 + (219 + 272*E_2)*M*r0_2 - 144*r0_3) + 6*L_4*r0*(96*M_3 + 2*(41 + 10*E_2)*M_2*r0 + (31 + 20*E_2)*M*r0_2 - 40*r0_3)) - a_5*E*L*M*r0_2*(12*L_4*(228*M_3 + 4*(12 + 5*E_2)*M_2*r0 + (13 + 10*E_2)*M*r0_2 - 20*r0_3) + L_2*r0*(1568*M_4 + 16*(52 + 63*E_2)*M_3*r0 + 48*(41 + 40*E_2)*M_2*r0_2 + 6*(135 + 118*E_2)*M*r0_3 - 865*r0_4) + 3*r0_3*(-548*M_4 + 4*(-131 + 144*E_2)*M_3*r0 + 5*(127 + 160*E_2)*M_2*r0_2 + 4*(35 + 64*E_2)*M*r0_3 - 188*r0_4)) - a_7*E*L*M*r0*(180*L_4*M*r0 + 2*L_2*(1344*M_4 + 24*(20 + 19*E_2)*M_3*r0 + 114*(7 + 4*E_2)*M_2*r0_2 + (289 + 114*E_2)*M*r0_3 - 147*r0_4) + 3*r0_2*(12*(-81 + 32*E_2)*M_4 + 64*(-3 + 16*E_2)*M_3*r0 + (795 + 736*E_2)*M_2*r0_2 + 20*(3 + 8*E_2)*M*r0_3 - 144*r0_4)) + a_10*M*(L_2*M*(312*M_2 + (311 + 332*E_2)*M*r0 + 6*(13 + 27*E_2)*r0_2) + 12*E_2*r0*(-52*M_4 + 60*M_3*r0 + 102*M_2*r0_2 + 23*M*r0_3 - 3*r0_4)) + a_2*r0_3*(120*L_8*M_2*(2*M - r0) + 36*E_2*M*r0_8*(6*M_2 + 5*M*r0 - 5*r0_2) + 6*L_6*M*r0*(12*M_3 + 8*(3 + 10*E_2)*M_2*r0 + 5*(5 + 8*E_2)*M*r0_2 - 20*(1 + E_2)*r0_3) + L_4*r0_3*(-368*M_4 + 24*(3 + 49*E_2)*M_3*r0 + 2*(251 + 402*E_2)*M_2*r0_2 - (205 + 486*E_2)*M*r0_3 - 9*r0_4) - 2*L_2*r0_5*(100*M_4 + 6*(1 - 82*E_2)*M_3*r0 - 2*(41 + 196*E_2)*M_2*r0_2 + 3*(1 + 95*E_2)*M*r0_3 + 12*r0_4)) + a_8*M*r0*(2*L_4*M*(166*M + 84*r0 + 45*E_2*r0) - 12*E_2*r0_2*(168*M_4 + 28*M_3*r0 - 154*M_2*r0_2 - 34*M*r0_3 + 15*r0_4) + L_2*(48*(-13 + 56*E_2)*M_4 + 4*(35 + 624*E_2)*M_3*r0 + 4*(127 + 498*E_2)*M_2*r0_2 + (-9 + 578*E_2)*M*r0_3 - 6*(13 + 21*E_2)*r0_4)) + a_6*M*r0*(90*L_6*M*r0 - 24*E_2*r0_4*(66*M_4 + 66*M_3*r0 - 52*M_2*r0_2 - 13*M*r0_3 + 15*r0_4) + 2*L_4*(448*M_4 + 24*(-4 + 57*E_2)*M_3*r0 + 138*(1 + 6*E_2)*M_2*r0_2 + 6*(9 + 32*E_2)*M*r0_3 - 3*(28 + 25*E_2)*r0_4) + L_2*r0_2*(4*(-225 + 628*E_2)*M_4 + 4*(3 + 998*E_2)*M_3*r0 + (863 + 3612*E_2)*M_2*r0_2 + 6*(-10 + 149*E_2)*M*r0_3 - 2*(109 + 263*E_2)*r0_4)) + a_4*r0_2*(-36*E_2*M*r0_6*(18*M_3 - 15*M_2*r0 - 6*M*r0_2 + 10*r0_3) + 6*L_6*M*(152*M_3 + 4*(-7 + 30*E_2)*M_2*r0 + 20*E_2*M*r0_2 - 5*(3 + 2*E_2)*r0_3) + L_4*M*r0*(208*M_4 + 8*(-11 + 261*E_2)*M_3*r0 + 8*(73 + 345*E_2)*M_2*r0_2 + 2*(166 + 381*E_2)*M*r0_3 - (359 + 468*E_2)*r0_4) + L_2*r0_3*(-536*M_5 + 4*(-101 + 402*E_2)*M_4*r0 + 2*(347 + 1436*E_2)*M_3*r0_2 + 69*(3 + 14*E_2)*M_2*r0_3 - 6*(33 + 137*E_2)*M*r0_4 - 12*r0_5)) + (2*M - r0)*r0_7*(36*E_2*M*r0_7 + 30*L_6*M*(-2*M + r0 + 2*E_2*r0) + 4*L_2*r0_4*(2*M_2 + (-7 + 37*E_2)*M*r0 + 3*r0_2) + L_4*r0_2*(-64*M_2 + 9*r0_2 + 14*M*(r0 + 12*E_2*r0)))))/(3.*r0_11*expr2_2);\n A60241 = (192*L*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0))*expr1_2)/(r0_2*(a_2 + r0*(-2*M + r0)));\n A60261 = (-64*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-6*a_12*E_2*M_2*(110*M_2 + 107*M*r0 + 26*r0_2) + a_11*E*L*M*(24*(55 + E_2)*M_3 + (1307 + 24*E_2)*M_2*r0 + 6*(55 + E_2)*M*r0_2 + 3*r0_3) + a*E*L*M*r0_5*(L_4*r0_2*(80*M_2 + 2*(469 + 114*E_2)*M*r0 - 489*r0_2) + L_2*r0_4*(-476*M_2 + 2*(596 + 243*E_2)*M*r0 - 477*r0_2) + 3*r0_6*(-40*M_2 + 2*(41 + 45*E_2)*M*r0 - 31*r0_2) + 6*L_6*(64*M_2 + 10*M*r0 - 21*r0_2)) + (2*M - r0)*r0_5*(9*L_8*M*(2*M - r0) - 72*E_2*M*r0_9 + L_2*r0_6*(8*M_2 + 10*(5 - 29*E_2)*M*r0 - 27*r0_2) - 2*L_6*r0_2*(-80*M_2 + 2*(17 + 30*E_2)*M*r0 + 3*r0_2) - L_4*r0_4*(-162*M_2 + (21 + 334*E_2)*M*r0 + 30*r0_2)) + a_3*E*L*M*r0_3*(12*L_6*(114*M_2 - 17*M*r0 - 10*r0_2) + L_4*r0*(1768*M_3 + 24*(82 + 19*E_2)*M_2*r0 + 4*(241 + 114*E_2)*M*r0_2 - 975*r0_3) + r0_5*(-1668*M_3 + 2*(257 + 792*E_2)*M_2*r0 + 2*(596 + 523*E_2)*M*r0_2 - 579*r0_3) - 2*L_2*r0_3*(406*M_3 - (785 + 954*E_2)*M_2*r0 - 2*(681 + 358*E_2)*M*r0_2 + 803*r0_3)) + a_5*E*L*M*r0_2*(6*L_6*r0 + L_4*(5232*M_3 + 4*(319 + 114*E_2)*M_2*r0 + 2*(199 + 114*E_2)*M*r0_2 - 471*r0_3) + L_2*r0*(2224*M_4 + 4*(223 + 468*E_2)*M_3*r0 + 4*(1077 + 925*E_2)*M_2*r0_2 + 4*(506 + 353*E_2)*M*r0_3 - 1711*r0_4) + r0_3*(-2964*M_4 + 8*(-520 + 387*E_2)*M_3*r0 + 21*(175 + 216*E_2)*M_2*r0_2 + 6*(231 + 254*E_2)*M*r0_3 - 1104*r0_4)) + a_7*E*L*M*r0*(3*L_4*(12*M_2 + 132*M*r0 + 5*r0_2) + r0_2*(4*(-1535 + 504*E_2)*M_4 + 4*(-445 + 1434*E_2)*M_3*r0 + 3*(1753 + 1448*E_2)*M_2*r0_2 + 6*(133 + 166*E_2)*M*r0_3 - 840*r0_4) + 2*L_2*(2544*M_4 + 8*(119 + 109*E_2)*M_3*r0 + (1775 + 902*E_2)*M_2*r0_2 + (667 + 236*E_2)*M*r0_3 - 285*r0_4)) + a_9*E*L*M*(2*L_2*(36*M_3 + 2*(364 + 3*E_2)*M_2*r0 + 3*(121 + E_2)*M*r0_2 + 6*r0_3) + r0*(16*(-165 + 106*E_2)*M_4 + 888*(2 + 3*E_2)*M_3*r0 + 3*(1271 + 472*E_2)*M_2*r0_2 + 2*(344 + 127*E_2)*M*r0_3 - 219*r0_4)) - a_10*M*(L_2*(12*(55 + 6*E_2)*M_3 + (665 + 764*E_2)*M_2*r0 + 3*(58 + 121*E_2)*M*r0_2 + 3*(1 + E_2)*r0_3) + 6*E_2*r0*(-220*M_4 + 244*M_3*r0 + 438*M_2*r0_2 + 105*M*r0_3 - 12*r0_4)) - a_8*M*(L_4*(24*M_3 + 4*(179 + 9*E_2)*M_2*r0 + 9*(41 + 23*E_2)*M*r0_2 + 3*(3 + 2*E_2)*r0_3) - 12*E_2*r0_3*(348*M_4 + 86*M_3*r0 - 321*M_2*r0_2 - 84*M*r0_3 + 30*r0_4) + L_2*r0*(24*(-55 + 212*E_2)*M_4 + 4*(78 + 1237*E_2)*M_3*r0 + 2*(578 + 2141*E_2)*M_2*r0_2 + (38 + 1305*E_2)*M*r0_3 - 3*(50 + 83*E_2)*r0_4)) - a_4*r0_2*(3*L_8*M*r0 - 18*E_2*M*r0_6*(78*M_3 - 49*M_2*r0 - 34*M*r0_2 + 40*r0_3) + 2*L_6*M*(872*M_3 + 12*(-11 + 57*E_2)*M_2*r0 + 10*(1 + 12*E_2)*M*r0_2 - 3*(31 + 19*E_2)*r0_3) + L_2*r0_3*(-928*M_5 + 4*(-347 + 588*E_2)*M_4*r0 + 22*(67 + 245*E_2)*M_3*r0_2 + 3*(236 + 729*E_2)*M_2*r0_3 - 3*(150 + 547*E_2)*M*r0_4 - 45*r0_5) + L_4*r0*(104*M_5 + 4*(-96 + 923*E_2)*M_4*r0 + 72*(19 + 74*E_2)*M_3*r0_2 + (817 + 1647*E_2)*M_2*r0_3 - (753 + 934*E_2)*M*r0_4 - 15*r0_5)) - a_6*r0*(3*L_6*M*(4*M_2 + 65*M*r0 + (3 + E_2)*r0_2) - 12*E_2*M*r0_4*(246*M_4 + 294*M_3*r0 - 202*M_2*r0_2 - 73*M*r0_3 + 60*r0_4) + L_4*M*(1696*M_4 + 4*(-95 + 1308*E_2)*M_3*r0 + 76*(9 + 44*E_2)*M_2*r0_2 + 2*(128 + 425*E_2)*M*r0_3 - 3*(110 + 97*E_2)*r0_4) + L_2*r0_2*(4*(-491 + 1034*E_2)*M_5 + 4*(-58 + 1753*E_2)*M_4*r0 + 5*(405 + 1468*E_2)*M_3*r0_2 + (17 + 2063*E_2)*M_2*r0_3 - (472 + 1055*E_2)*M*r0_4 - 9*r0_5)) + a_2*r0_3*(-18*E_2*M*r0_8*(18*M_2 + 23*M*r0 - 20*r0_2) + 6*L_8*M*(-76*M_2 + 36*M*r0 + r0_2) + L_6*r0*(52*M_4 - 4*(85 + 219*E_2)*M_3*r0 - 3*(131 + 160*E_2)*M_2*r0_2 + (263 + 237*E_2)*M*r0_3 + 6*r0_4) + L_2*r0_5*(460*M_4 + 12*(19 - 140*E_2)*M_3*r0 - (535 + 1646*E_2)*M_2*r0_2 + 3*(9 + 376*E_2)*M*r0_3 + 63*r0_4) + L_4*r0_3*(944*M_4 - 8*(153 + 209*E_2)*M_2*r0_2 + (405 + 971*E_2)*M*r0_3 + 45*r0_4 - 4*M_3*(r0 + 530*E_2*r0)))))/(3.*r0_8*expr2_2);\n A60421 = (48*L*r0*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0))*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/(a_2 + r0*(-2*M + r0));\n A60441 = (-8*(-36*a_12*E_2*M_2*(58*M_2 + 57*M*r0 + 14*r0_2) + a_11*E*L*M*(144*(29 + E_2)*M_3 + (4199 + 144*E_2)*M_2*r0 + 18*(61 + 2*E_2)*M*r0_2 + 21*r0_3) + a*E*L*M*r0_5*(3*L_4*r0_2*(-196*M_2 + 20*(54 + 11*E_2)*M*r0 - 491*r0_2) + L_6*(752*M_2 + 464*M*r0 - 420*r0_2) + 3*r0_6*(-264*M_2 + 2*(163 + 126*E_2)*M*r0 - 97*r0_2) - 39*L_2*r0_4*(56*M_2 - 2*(49 + 18*E_2)*M*r0 + 35*r0_2)) + (2*M - r0)*r0_5*(62*L_8*M*(2*M - r0) - 216*E_2*M*r0_9 + L_2*r0_6*(96*M_2 - 142*(-1 + 6*E_2)*M*r0 - 95*r0_2) - L_6*r0_2*(-604*M_2 + 52*(4 + 7*E_2)*M*r0 + 47*r0_2) - L_4*r0_4*(-588*M_2 + 4*(4 + 249*E_2)*M*r0 + 139*r0_2)) + a_5*E*L*M*r0_2*(36*L_6*(M + r0) + L_4*(14832*M_3 + 160*(27 + 8*E_2)*M_2*r0 + 4*(404 + 175*E_2)*M*r0_2 - 1399*r0_3) + L_2*r0*(3936*M_4 + 16*(16 + 315*E_2)*M_3*r0 + 8*(1711 + 1332*E_2)*M_2*r0_2 + 2*(3785 + 2154*E_2)*M*r0_3 - 4973*r0_4) + r0_3*(-8028*M_4 + 12*(-1307 + 684*E_2)*M_3*r0 + (10409 + 12816*E_2)*M_2*r0_2 + 108*(55 + 42*E_2)*M*r0_3 - 3150*r0_4)) + a_7*E*L*M*r0*(3*L_4*(96*M_2 + 4*(113 + E_2)*M*r0 + 31*r0_2) + r0_2*(12*(-1615 + 432*E_2)*M_4 + 16*(-460 + 999*E_2)*M_3*r0 + (17257 + 12816*E_2)*M_2*r0_2 + 36*(109 + 86*E_2)*M*r0_3 - 2382*r0_4) + 2*L_2*(7200*M_4 + 8*(349 + 309*E_2)*M_3*r0 + 2*(2933 + 1356*E_2)*M_2*r0_2 + (2357 + 762*E_2)*M*r0_3 - 811*r0_4)) + a_9*E*L*M*(L_2*(432*M_3 + 8*(599 + 12*E_2)*M_2*r0 + 6*(403 + 8*E_2)*M*r0_2 + 78*r0_3) + r0*(96*(-87 + 50*E_2)*M_4 + 4*(1367 + 1980*E_2)*M_3*r0 + (12535 + 4464*E_2)*M_2*r0_2 + 2*(1309 + 426*E_2)*M*r0_3 - 607*r0_4)) - a_10*M*(L_2*(72*(29 + 6*E_2)*M_3 + (2147 + 2612*E_2)*M_2*r0 + 6*(99 + 203*E_2)*M*r0_2 + 3*(7 + 6*E_2)*r0_3) - 36*E_2*r0*(116*M_4 - 124*M_3*r0 - 234*M_2*r0_2 - 59*M*r0_3 + 6*r0_4)) + a_2*r0_3*(-108*E_2*M*r0_8*(6*M_2 + 13*M*r0 - 10*r0_2) - 16*L_8*M*(80*M_2 - 34*M*r0 - 3*r0_2) + L_6*r0*(840*M_4 - 4*(293 + 562*E_2)*M_3*r0 - 2*(751 + 782*E_2)*M_2*r0_2 + (839 + 718*E_2)*M*r0_3 + 50*r0_4) + L_4*r0_3*(3408*M_4 - 8*(-82 + 693*E_2)*M_3*r0 - 2*(2215 + 2646*E_2)*M_2*r0_2 + (1123 + 2922*E_2)*M*r0_3 + 251*r0_4) + L_2*r0_5*(1560*M_4 - 8*(-175 + 522*E_2)*M_3*r0 - 12*(189 + 431*E_2)*M_2*r0_2 + (85 + 3348*E_2)*M*r0_3 + 252*r0_4)) - a_4*r0_2*(6*L_8*M*(2*M + 3*r0) - 108*E_2*M*r0_6*(42*M_3 - 19*M_2*r0 - 22*M*r0_2 + 20*r0_3) + L_6*(4944*M_4 + 24*(-23 + 160*E_2)*M_3*r0 + 4*(41 + 214*E_2)*M_2*r0_2 - 4*(145 + 84*E_2)*M*r0_3 - 3*r0_4) + L_2*r0_3*(-2424*M_5 + 4*(-1493 + 1170*E_2)*M_4*r0 + 2*(2287 + 7488*E_2)*M_3*r0_2 + (3155 + 7338*E_2)*M_2*r0_3 - 18*(83 + 273*E_2)*M*r0_4 - 222*r0_5) + L_4*r0*(-624*M_5 + 8*(-229 + 1155*E_2)*M_4*r0 + 8*(566 + 1917*E_2)*M_3*r0_2 + 2*(1552 + 2763*E_2)*M_2*r0_3 - (2341 + 2820*E_2)*M*r0_4 - 118*r0_5)) - a_6*r0*(3*L_6*M*(32*M_2 + 2*(109 + 6*E_2)*M*r0 + (19 + 6*E_2)*r0_2) - 72*E_2*M*r0_4*(114*M_4 + 162*M_3*r0 - 98*M_2*r0_2 - 47*M*r0_3 + 30*r0_4) + L_2*r0_2*(12*(-535 + 812*E_2)*M_5 + 12*(-131 + 1506*E_2)*M_4*r0 + (6991 + 22204*E_2)*M_3*r0_2 + 2*(300 + 3533*E_2)*M_2*r0_3 - 2*(764 + 1587*E_2)*M*r0_4 - 68*r0_5) + 2*L_4*(2400*M_5 + 8*(-73 + 927*E_2)*M_4*r0 + 6*(203 + 858*E_2)*M_3*r0_2 + 6*(83 + 248*E_2)*M_2*r0_3 - 13*(37 + 33*E_2)*M*r0_4 - 3*r0_5)) - a_8*(2*L_4*M*(72*M_3 + 2*(581 + 72*E_2)*M_2*r0 + 3*(206 + 125*E_2)*M*r0_2 + 6*(5 + 3*E_2)*r0_3) - 72*E_2*M*r0_3*(180*M_4 + 58*M_3*r0 - 167*M_2*r0_2 - 50*M*r0_3 + 15*r0_4) + L_2*r0*(144*(-29 + 100*E_2)*M_5 + 4*(251 + 3668*E_2)*M_4*r0 + 172*(23 + 80*E_2)*M_3*r0_2 + (351 + 4414*E_2)*M_2*r0_3 - 2*(215 + 369*E_2)*M*r0_4 - 3*r0_5)) + a_3*E*L*M*r0_3*(4*L_6*(960*M_2 - 97*M*r0 - 96*r0_2) + L_4*r0*(3360*M_3 + 4*(1463 + 312*E_2)*M_2*r0 + 4*(931 + 337*E_2)*M*r0_2 - 2965*r0_3) + 2*L_2*r0_3*(-2280*M_3 + 2*(845 + 1332*E_2)*M_2*r0 + 2*(2339 + 1059*E_2)*M*r0_2 - 2319*r0_3) + r0_5*(-5544*M_3 + 2*(2257 + 1506*E_2)*M*r0_2 - 1687*r0_3 + 120*M_2*(r0 + 36*E_2*r0)))))/(3.*r0_5*expr2_2);\n A60601 = (4*L*r0_4*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0)))/(a_2 + r0*(-2*M + r0));\n A60621 = (-4*(-6*a_10*E_2*M_2*(61*M + 30*r0) + 6*a_9*E*L*M*(2*(61 + 3*E_2)*M_2 + (64 + 3*E_2)*M*r0 + 2*r0_2) + 2*a*E*L*M*r0_4*(L_2*r0_2*(-286*M_2 + (467 + 108*E_2)*M*r0 - 162*r0_2) + L_4*(40*M_2 + 142*M*r0 - 81*r0_2) + 3*r0_4*(-68*M_2 + 3*(22 + 13*E_2)*M*r0 - 16*r0_2)) + (2*M - r0)*r0_4*(35*L_6*M*(2*M - r0) - 72*E_2*M*r0_7 + 2*L_2*r0_4*(28*M_2 + (24 - 103*E_2)*M*r0 - 19*r0_2) - L_4*r0_2*(-174*M_2 + (29 + 124*E_2)*M*r0 + 29*r0_2)) + 2*a_3*E*L*M*r0_2*(L_4*(588*M_2 - 8*M*r0 - 72*r0_2) + L_2*r0*(100*M_3 + 2*(23 + 90*E_2)*M_2*r0 + 2*(408 + 115*E_2)*M*r0_2 - 347*r0_3) + r0_3*(-606*M_3 + 3*(-145 + 138*E_2)*M_2*r0 + 7*(115 + 52*E_2)*M*r0_2 - 215*r0_3)) + 2*a_5*E*L*M*r0*(9*L_4*(2*M + r0) + L_2*(1128*M_3 + 2*(125 + 98*E_2)*M_2*r0 + (501 + 128*E_2)*M*r0_2 - 170*r0_3) + 2*r0_2*(3*(-283 + 60*E_2)*M_3 + (211 + 431*E_2)*M_2*r0 + (468 + 193*E_2)*M*r0_2 - 134*r0_3)) + 2*a_7*E*L*M*(3*L_2*(18*M_2 + 2*(38 + E_2)*M*r0 + 5*r0_2) + r0*(4*(-183 + 94*E_2)*M_3 + (831 + 466*E_2)*M_2*r0 + (545 + 148*E_2)*M*r0_2 - 95*r0_3)) - 3*a_8*M*(L_2*(2*(61 + 18*E_2)*M_2 + 17*(4 + 5*E_2)*M*r0 + (4 + 3*E_2)*r0_2) + 2*E_2*r0*(-122*M_3 + 187*M_2*r0 + 125*M*r0_2 - 12*r0_3)) - a_6*(3*L_4*M*(12*M_2 + (73 + 12*E_2)*M*r0 + (7 + 3*E_2)*r0_2) + 6*E_2*M*r0_3*(-372*M_3 + 101*M_2*r0 + 203*M*r0_2 - 48*r0_3) + L_2*r0*(12*(-61 + 188*E_2)*M_4 + 4*(135 + 412*E_2)*M_3*r0 + (299 + 1010*E_2)*M_2*r0_2 - 2*(71 + 90*E_2)*M*r0_3 - 3*r0_4)) + a_4*r0*(-3*L_6*M*(4*M + 3*r0) + 18*E_2*M*r0_4*(70*M_3 + 21*M_2*r0 - 57*M*r0_2 + 24*r0_3) + L_4*(-752*M_4 - 24*(-9 + 49*E_2)*M_3*r0 - 8*(36 + 47*E_2)*M_2*r0_2 + (181 + 114*E_2)*M*r0_3 + 3*r0_4) + L_2*r0_2*(-4*(-291 + 295*E_2)*M_4 - 18*(29 + 106*E_2)*M_3*r0 - (790 + 1623*E_2)*M_2*r0_2 + (330 + 593*E_2)*M*r0_3 + 38*r0_4)) + a_2*r0_2*(2*L_6*M*(-196*M_2 + 68*M*r0 + 15*r0_2) + 18*E_2*M*r0_6*(10*M_2 - 29*M*r0 + 16*r0_2) + L_4*r0*(260*M_4 + (92 - 580*E_2)*M_3*r0 - (689 + 604*E_2)*M_2*r0_2 + (225 + 247*E_2)*M*r0_3 + 32*r0_4) + L_2*r0_3*(356*M_4 + (548 - 460*E_2)*M_3*r0 - (783 + 1280*E_2)*M_2*r0_2 + 2*(32 + 305*E_2)*M*r0_3 + 73*r0_4))))/(3.*r0_2*expr2_2);\n A60801 = -(r0*(-96*a_8*E_2*M_2 + 3*a_7*E*L*M*(4*(16 + E_2)*M + 3*r0) + a_5*E*L*M*(12*L_2*(3*M + r0) + r0*(16*(-24 + 11*E_2)*M_2 + 4*(155 + 37*E_2)*M*r0 - 91*r0_2)) + a_3*E*L*M*r0*(r0_2*(4*(-223 + 36*E_2)*M_2 + 4*(196 + 61*E_2)*M*r0 - 145*r0_2) + L_2*(528*M_2 + 68*M*r0 - 84*r0_2)) + (2*M - r0)*r0_3*(26*L_4*M*(2*M - r0) - 36*E_2*M*r0_5 + L_2*r0_2*(40*M_2 + (26 - 64*E_2)*M*r0 - 23*r0_2)) - 3*a_6*M*(L_2*(4*(8 + 3*E_2)*M + (3 + 2*E_2)*r0) - 4*E_2*r0*(16*M_2 - 32*M*r0 + 3*r0_2)) + a*E*L*M*r0_3*(3*r0_2*(-92*M_2 + 4*(19 + 9*E_2)*M*r0 - 15*r0_2) - 32*L_2*(2*M_2 - 7*M*r0 + 3*r0_2)) + a_4*(-6*L_4*M*(2*M + r0) + 36*E_2*M*r0_3*(16*M_2 - 14*M*r0 + 3*r0_2) + L_2*r0*(-48*(-4 + 11*E_2)*M_3 - 4*(59 + 64*E_2)*M_2*r0 + 10*(7 + 6*E_2)*M*r0_2 + 3*r0_3)) + a_2*r0*(-8*L_4*M*(22*M_2 - 5*M*r0 - 3*r0_2) + 36*E_2*M*r0_4*(8*M_2 - 8*M*r0 + 3*r0_2) + L_2*r0_2*(-4*(-79 + 46*E_2)*M_3 - 4*(89 + 91*E_2)*M_2*r0 + (47 + 130*E_2)*M*r0_2 + 26*r0_3))))/(6.*expr2_2);\n A61061 = (128*expr1_2*(2*a_8*E_2*M_2*(2*M + r0) - a_7*E*L*M*(8*M_2 + 5*M*r0 + r0_2) + a*E*L*M*r0_3*(L_4*(4*M - 6*r0) + L_2*(4*M - 9*r0)*r0_2 + 6*r0_4*(-3*M + r0)) - a_5*E*L*M*r0*(L_2*(12*M + 7*r0) - 2*r0*(-17*M_2 - 4*M*r0 + r0_2)) + L_2*r0_3*(2*E_2*L_2*M*r0_3 + L_4*M*(-2*M + r0) + r0_4*(6*M_2 + (-5 + 2*E_2)*M*r0 + r0_2)) - a_3*E*L*M*r0_2*(6*L_4 + r0_2*(54*M_2 + 17*M*r0 - 9*r0_2) + L_2*(-8*M_2 + 4*M*r0 + 12*r0_2)) + a_6*M*(2*E_2*M*r0_2*(12*M + 7*r0) + L_2*(4*M_2 + 3*M*r0 + 6*E_2*M*r0 + r0_2 + 3*E_2*r0_2)) + a_4*r0*(6*E_2*M_2*r0_3*(6*M + 5*r0) + L_4*M*(6*M + (4 + 3*E_2)*r0) + L_2*r0*((10 - 4*E_2)*M_3 + (-5 + 8*E_2)*M_2*r0 + (3 + 8*E_2)*M*r0_2 + 2*r0_3)) + a_2*r0_2*(3*L_6*M + 18*E_2*M_2*r0_5 + L_4*(-4*M_3 - 2*(2 + E_2)*M_2*r0 + (4 + 5*E_2)*M*r0_2 + 2*r0_3) + L_2*r0_2*(24*M_3 + 2*(-5 + E_2)*M_2*r0 + (-5 + 7*E_2)*M*r0_2 + 3*r0_3))))/(r0_7*expr2_2);\n A61241 = (32*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(6*a_8*E_2*M_2*(2*M + r0) - 2*a_7*E*L*M*(12*M_2 + 9*M*r0 + 2*r0_2) + 6*a*E*L*M*r0_3*(L_4*(2*M - 3*r0) + 3*r0_4*(-3*M + r0) - L_2*r0_2*(M + 3*r0)) - 2*a_5*E*L*M*r0*(L_2*(20*M + 11*r0) + r0*(48*M_2 + 17*M*r0 - r0_2)) + L_2*r0_3*(3*L_4*M*(-2*M + r0) + 3*r0_4*(6*M_2 + (-5 + 2*E_2)*M*r0 + r0_2) + L_2*r0_2*(4*M_2 + 2*(-2 + 3*E_2)*M*r0 + r0_2)) - 6*a_3*E*L*M*r0_2*(3*L_4 + r0_2*(24*M_2 + 9*M*r0 - 4*r0_2) + L_2*(-4*M_2 + 5*M*r0 + 6*r0_2)) + a_6*M*(6*E_2*M*r0_2*(12*M + 7*r0) + L_2*(12*M_2 + 4*(3 + 5*E_2)*M*r0 + (4 + 9*E_2)*r0_2)) + a_4*r0*(18*E_2*M_2*r0_3*(6*M + 5*r0) + L_4*M*(20*M + (13 + 9*E_2)*r0) + L_2*r0*(-12*(-2 + E_2)*M_3 + 4*(-2 + 9*E_2)*M_2*r0 + 3*(3 + 8*E_2)*M*r0_2 + 5*r0_3)) + a_2*r0_2*(9*L_6*M + 54*E_2*M_2*r0_5 + L_4*(-12*M_3 - 6*(1 + E_2)*M_2*r0 + (11 + 15*E_2)*M*r0_2 + 5*r0_3) + L_2*r0_2*(60*M_3 + 2*(-11 + 12*E_2)*M_2*r0 + 7*(-2 + 3*E_2)*M*r0_2 + 8*r0_3))))/(r0_4*expr2_2);\n A61421 = (8*(6*a_8*E_2*M_2*(2*M + r0) - a_7*E*L*M*(24*M_2 + 21*M*r0 + 5*r0_2) + 3*a*E*L*M*r0_3*(L_4*(4*M - 6*r0) + 6*r0_4*(-3*M + r0) - L_2*r0_2*(8*M + 3*r0)) - a_5*E*L*M*r0*(L_2*(44*M + 23*r0) + 2*r0*(45*M_2 + 22*M*r0 + r0_2)) + L_2*r0_3*(3*L_4*M*(-2*M + r0) + 3*r0_4*(6*M_2 + (-5 + 2*E_2)*M*r0 + r0_2) + 2*L_2*r0_2*(4*M_2 + (-4 + 3*E_2)*M*r0 + r0_2)) - 3*a_3*E*L*M*r0_2*(6*L_4 + r0_2*(42*M_2 + 19*M*r0 - 7*r0_2) + L_2*(-8*M_2 + 16*M*r0 + 12*r0_2)) + a_6*M*(6*E_2*M*r0_2*(12*M + 7*r0) + L_2*(12*M_2 + (15 + 22*E_2)*M*r0 + (5 + 9*E_2)*r0_2)) + a_4*r0*(18*E_2*M_2*r0_3*(6*M + 5*r0) + L_4*M*(22*M + (14 + 9*E_2)*r0) + L_2*r0*(-6*(-3 + 2*E_2)*M_3 + (-1 + 48*E_2)*M_2*r0 + 3*(3 + 8*E_2)*M*r0_2 + 4*r0_3)) + a_2*r0_2*(9*L_6*M + 54*E_2*M_2*r0_5 + L_4*(-12*M_3 - 6*E_2*M_2*r0 + 5*(2 + 3*E_2)*M*r0_2 + 4*r0_3) + L_2*r0_2*(48*M_3 + 14*(-1 + 3*E_2)*M_2*r0 + (-13 + 21*E_2)*M*r0_2 + 7*r0_3))))/(r0*expr2_2);\n A61601 = (2*r0_2*(2*a_6*E_2*M_2 - 2*a_5*E*L*M*(2*M + r0) - 2*a_3*E*L*M*r0*(3*L_2 + 7*M*r0) + 2*a*E*L*M*r0_2*(L_2*(2*M - 3*r0) + 3*r0_2*(-3*M + r0)) + a_4*M*(12*E_2*M*r0_2 + L_2*(2*M + 2*r0 + 3*E_2*r0)) + L_2*r0_2*(L_2*M*(-2*M + r0) + r0_2*(6*M_2 + (-5 + 2*E_2)*M*r0 + r0_2)) + a_2*r0*(3*L_4*M + 18*E_2*M_2*r0_3 + L_2*r0*(-2*(-1 + E_2)*M_2 + (-1 + 5*E_2)*M*r0 + r0_2))))/expr2_2;\n A62041 = (192*L*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0))*expr1_2)/(r0_2*expr2_2);\n A62061 = (-32*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-12*a_12*E_2*M_2*(92*M_2 + 88*M*r0 + 21*r0_2) + a_11*E*L*M*(-24*(-92 + 11*E_2)*M_3 + (2137 - 300*E_2)*M_2*r0 + 6*(85 - 14*E_2)*M*r0_2 - 6*r0_3) + a*E*L*M*r0_5*(2*L_4*r0_2*(584*M_2 + (557 + 192*E_2)*M*r0 - 474*r0_2) + 2*L_2*r0_4*(250*M_2 + (571 + 360*E_2)*M*r0 - 393*r0_2) + 3*r0_6*(-16*M_2 + 8*(14 + 15*E_2)*M*r0 - 61*r0_2) + 12*L_6*(88*M_2 - 8*M*r0 - 21*r0_2)) + a_3*E*L*M*r0_3*(12*L_6*(234*M_2 - 57*M*r0 - 22*r0_2) + 2*L_2*r0_3*(2134*M_3 + (1219 + 1800*E_2)*M_2*r0 + 10*(117 + 94*E_2)*M*r0_2 - 1459*r0_3) + r0_5*(-2820*M_3 + 2*(805 + 1818*E_2)*M_2*r0 + 4*(404 + 301*E_2)*M*r0_2 - 1227*r0_3) + 2*L_4*r0*(2704*M_3 + 12*(151 + 41*E_2)*M_2*r0 + 2*(38 + 177*E_2)*M*r0_2 - 909*r0_3)) + r0_5*(18*L_8*M_2*(-2*M + r0) + 144*E_2*M*r0_9*(-2*M + r0) + 2*L_6*M*r0_2*(158*M_2 - (167 + 210*E_2)*M*r0 + 2*(22 + 57*E_2)*r0_2) + 2*L_4*r0_4*(174*M_3 - (81 + 584*E_2)*M_2*r0 + 5*(-9 + 62*E_2)*M*r0_2 + 21*r0_3) + L_2*r0_6*(20*M_3 - 2*(-77 + 526*E_2)*M_2*r0 + 32*(-5 + 17*E_2)*M*r0_2 + 39*r0_3)) + a_5*E*L*M*r0_2*(-12*L_6*(9*M + r0) + 2*L_4*(5520*M_3 + 4*(76 + 117*E_2)*M_2*r0 + (-337 + 144*E_2)*M*r0_2 - 486*r0_3) + r0_3*(-6636*M_4 + 8*(-626 + 1035*E_2)*M_3*r0 + 3*(2363 + 2896*E_2)*M_2*r0_2 + 6*(173 + 228*E_2)*M*r0_3 - 2379*r0_4) + 2*L_2*r0*(3520*M_4 + 2*(2129 + 1080*E_2)*M_3*r0 + 4*(513 + 790*E_2)*M_2*r0_2 + 4*(77 + 185*E_2)*M*r0_3 - 1651*r0_4)) + a_7*E*L*M*r0*(-6*L_4*(120*M_2 + 6*(-8 + E_2)*M*r0 + 5*r0_2) + r0_2*((-9700 + 4896*E_2)*M_4 + 4*(-125 + 3114*E_2)*M_3*r0 + 3*(2803 + 2152*E_2)*M_2*r0_2 + 6*(-13 + 80*E_2)*M*r0_3 - 1815*r0_4) + 2*L_2*(5520*M_4 + 4*(443 + 460*E_2)*M_3*r0 + (1309 + 1240*E_2)*M_2*r0_2 + 2*(181 + 50*E_2)*M*r0_3 - 597*r0_4)) + a_9*E*L*M*(-2*L_2*(396*M_3 + 10*(-73 + 12*E_2)*M_2*r0 + 3*(-151 + 20*E_2)*M*r0_2 + 12*r0_3) + r0*(32*(-129 + 115*E_2)*M_4 + 264*(13 + 17*E_2)*M_3*r0 + 3*(1985 + 368*E_2)*M_2*r0_2 + 2*(337 - 64*E_2)*M*r0_3 - 486*r0_4)) + a_10*M*(L_2*(24*(-46 + 33*E_2)*M_3 - (1081 + 280*E_2)*M_2*r0 - 6*(43 + 54*E_2)*M*r0_2 + 6*(1 + E_2)*r0_3) + 12*E_2*r0*(172*M_4 - 228*M_3*r0 - 357*M_2*r0_2 - 74*M*r0_3 + 12*r0_4)) + a_2*r0_3*(-36*E_2*M*r0_8*(27*M_2 + 14*M*r0 - 20*r0_2) + 18*L_8*M*(-52*M_2 + 27*M*r0 + r0_2) - 2*L_6*r0*(272*M_4 + 2*(146 + 501*E_2)*M_3*r0 + 3*(64 + 105*E_2)*M_2*r0_2 - (203 + 234*E_2)*M*r0_3 - 18*r0_4) + 2*L_4*r0_3*(188*M_4 - 242*(-1 + 10*E_2)*M_3*r0 - (927 + 994*E_2)*M_2*r0_2 + (315 + 908*E_2)*M*r0_3 + 48*r0_4) + L_2*r0_5*(824*M_4 - 48*(-5 + 109*E_2)*M_3*r0 - 2*(430 + 647*E_2)*M_2*r0_2 + 3*(31 + 704*E_2)*M*r0_3 + 96*r0_4)) + a_8*M*(2*L_4*(132*M_3 + 40*(-11 + 9*E_2)*M_2*r0 + 3*(-83 + 6*E_2)*M*r0_2 + 3*(3 + 2*E_2)*r0_3) + 24*E_2*r0_3*(276*M_4 + 8*M_3*r0 - 278*M_2*r0_2 - 47*M*r0_3 + 30*r0_4) + L_2*r0*(-48*(-43 + 230*E_2)*M_4 - 8*(87 + 1063*E_2)*M_3*r0 - 2*(823 + 1786*E_2)*M_2*r0_2 + 19*(11 - 30*E_2)*M*r0_3 + 6*(56 + 83*E_2)*r0_4)) + a_6*r0*(6*L_6*M*(40*M_2 + 2*(-17 + 9*E_2)*M*r0 + (3 + E_2)*r0_2) + 24*E_2*M*r0_4*(246*M_4 + 222*M_3*r0 - 181*M_2*r0_2 - 22*M*r0_3 + 60*r0_4) - 2*L_4*M*(1840*M_4 + 4*(-59 + 1380*E_2)*M_3*r0 + (75 + 2012*E_2)*M_2*r0_2 + 2*(2 - 49*E_2)*M*r0_3 - 15*(23 + 20*E_2)*r0_4) + L_2*r0_2*(-4*(-769 + 2716*E_2)*M_5 - 4*(175 + 4916*E_2)*M_4*r0 - (3129 + 9496*E_2)*M_3*r0_2 + 2*(226 + 25*E_2)*M_2*r0_3 + (983 + 2002*E_2)*M*r0_4 + 18*r0_5)) + a_4*r0_2*(6*L_8*M*(6*M + r0) + 36*E_2*M*r0_6*(60*M_3 - 52*M_2*r0 - 7*M*r0_2 + 40*r0_3) + 2*L_6*M*(-1840*M_3 - 468*(-1 + 3*E_2)*M_2*r0 + (139 - 45*E_2)*M*r0_2 + 3*(62 + 41*E_2)*r0_3) - 2*L_4*r0*(536*M_5 + 2*(327 + 2296*E_2)*M_4*r0 + 3*(203 + 1560*E_2)*M_3*r0_2 + 5*(101 + 66*E_2)*M_2*r0_3 - 4*(177 + 223*E_2)*M*r0_4 - 27*r0_5) + L_2*r0_3*(2360*M_5 - 8*(-161 + 1434*E_2)*M_4*r0 - 4*(665 + 2563*E_2)*M_3*r0_2 + 27*(-35 + 2*E_2)*M_2*r0_3 + 6*(151 + 513*E_2)*M*r0_4 + 75*r0_5))))/(3.*r0_8*expr2_3);\n A62221 = (96*L*r0*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0))*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/expr2_2;\n A62241 = (-8*(-48*a_12*E_2*M_2*(72*M_2 + 70*M*r0 + 17*r0_2) + a_11*E*L*M_2*(-144*(-48 + 5*E_2)*M_2 + (6841 - 792*E_2)*M*r0 + 6*(283 - 36*E_2)*r0_2) + a*E*L*M*r0_5*(12*L_4*r0_2*(227*M_2 + (269 + 83*E_2)*M*r0 - 216*r0_2) + 4*L_6*(664*M_2 - 8*M*r0 - 189*r0_2) + 9*r0_6*(-112*M_2 + 12*(14 + 9*E_2)*M*r0 - 65*r0_2) - 24*L_2*r0_4*(21*M_2 - (182 + 81*E_2)*M*r0 + 97*r0_2)) + a_3*E*L*M*r0_3*(8*L_6*(1005*M_2 - 259*M*r0 - 99*r0_2) + 2*L_2*r0_3*(1896*M_3 + 2*(1897 + 2727*E_2)*M_2*r0 + (4915 + 2544*E_2)*M*r0_2 - 4447*r0_3) + 4*L_4*r0*(3192*M_3 + (3127 + 714*E_2)*M_2*r0 + (217 + 440*E_2)*M*r0_2 - 1419*r0_3) + 3*r0_5*(-3096*M_3 + 4*(181 + 756*E_2)*M_2*r0 + 20*(111 + 56*E_2)*M*r0_2 - 1213*r0_3)) + r0_5*(432*E_2*M*r0_9*(-2*M + r0) + 2*L_8*M*(50*M_2 - 77*M*r0 + 26*r0_2) + 2*L_6*r0_2*(662*M_3 - (569 + 614*E_2)*M_2*r0 + (59 + 334*E_2)*M*r0_2 + 30*r0_3) + 6*L_4*r0_4*(258*M_3 - (113 + 572*E_2)*M_2*r0 + 76*(-1 + 4*E_2)*M*r0_2 + 34*r0_3) + 3*L_2*r0_6*(116*M_3 + 2*(45 - 514*E_2)*M_2*r0 + 28*(-6 + 19*E_2)*M*r0_2 + 47*r0_3)) + a_5*E*L*M*r0_2*(-36*L_6*(12*M + r0) + 4*L_4*(7920*M_3 + 5*(159 + 134*E_2)*M_2*r0 + (-488 + 155*E_2)*M*r0_2 - 753*r0_3) + 2*L_2*r0*(7680*M_4 + 16*(523 + 378*E_2)*M_3*r0 + 6*(1360 + 1549*E_2)*M_2*r0_2 + (2077 + 1992*E_2)*M*r0_3 - 5062*r0_4) + 3*r0_3*(-5244*M_4 + 4*(-1765 + 1728*E_2)*M_3*r0 + 3*(2187 + 2504*E_2)*M_2*r0_2 + 14*(151 + 96*E_2)*M*r0_3 - 2299*r0_4)) + a_7*E*L*M*r0*(-12*L_4*(171*M_2 + 4*(-17 + 3*E_2)*M*r0 + 6*r0_2) + 2*L_2*(15696*M_4 + 32*(149 + 165*E_2)*M_3*r0 + 2*(2629 + 1821*E_2)*M_2*r0_2 + 5*(307 + 48*E_2)*M*r0_3 - 1797*r0_4) + 3*r0_2*(12*(-823 + 360*E_2)*M_4 + 16*(-140 + 687*E_2)*M_3*r0 + 21*(433 + 280*E_2)*M_2*r0_2 + 2*(415 + 276*E_2)*M*r0_3 - 1739*r0_4)) + a_9*E*L*M*(-2*L_2*(1080*M_3 + 2*(-1232 + 171*E_2)*M_2*r0 + 3*(-491 + 60*E_2)*M*r0_2 + 18*r0_3) + r0*(96*(-135 + 109*E_2)*M_4 + 44*(227 + 288*E_2)*M_3*r0 + (19657 + 3384*E_2)*M_2*r0_2 - 6*(-499 + 34*E_2)*M*r0_3 - 1374*r0_4)) + a_10*M*(L_2*(432*(-8 + 5*E_2)*M_3 - (3481 + 1276*E_2)*M_2*r0 - 18*(49 + 62*E_2)*M*r0_2 + 18*E_2*r0_3) + 12*E_2*r0*(540*M_4 - 664*M_3*r0 - 1125*M_2*r0_2 - 253*M*r0_3 + 36*r0_4)) + a_2*r0_3*(-108*E_2*M*r0_8*(21*M_2 + 17*M*r0 - 20*r0_2) + 2*L_8*M*(-1340*M_2 + 673*M*r0 + 39*r0_2) - 2*L_6*r0*(168*M_4 + 2*(613 + 1403*E_2)*M_3*r0 + (717 + 787*E_2)*M_2*r0_2 - 2*(340 + 341*E_2)*M*r0_3 - 57*r0_4) + 6*L_4*r0_3*(576*M_4 + (212 - 2450*E_2)*M_3*r0 - 3*(373 + 280*E_2)*M_2*r0_2 + 36*(9 + 25*E_2)*M*r0_3 + 71*r0_4) + 3*L_2*r0_5*(960*M_4 + (632 - 4308*E_2)*M_3*r0 - 2*(629 + 789*E_2)*M_2*r0_2 + (109 + 2092*E_2)*M*r0_3 + 130*r0_4)) + a_8*(2*L_4*M*(360*M_3 + 2*(-715 + 513*E_2)*M_2*r0 + 3*(-269 + 22*E_2)*M*r0_2 + 9*(1 + 2*E_2)*r0_3) + 48*E_2*M*r0_3*(414*M_4 + 63*M_3*r0 - 416*M_2*r0_2 - 89*M*r0_3 + 45*r0_4) + L_2*r0*(-144*(-45 + 218*E_2)*M_5 - 4*(505 + 5944*E_2)*M_4*r0 - 68*(87 + 179*E_2)*M_3*r0_2 - 7*(-43 + 350*E_2)*M_2*r0_3 + 6*(175 + 257*E_2)*M*r0_4 + 18*r0_5)) + a_4*r0_2*(18*L_8*M*(8*M + r0) + 432*E_2*M*r0_6*(15*M_3 - 10*M_2*r0 - 4*M*r0_2 + 10*r0_3) + 2*L_6*(-5280*M_4 - 6*(-171 + 670*E_2)*M_3*r0 + (388 + 53*E_2)*M_2*r0_2 + 3*(205 + 119*E_2)*M*r0_3 + 9*r0_4) - 2*L_4*r0*(600*M_5 + 4*(157 + 3066*E_2)*M_4*r0 + 2*(1462 + 7161*E_2)*M_3*r0_2 + 2*(998 + 405*E_2)*M_2*r0_3 - 6*(379 + 447*E_2)*M*r0_4 - 129*r0_5) + 3*L_2*r0_3*(1720*M_5 + 4*(685 - 2022*E_2)*M_4*r0 - 2*(1403 + 4574*E_2)*M_3*r0_2 - (1591 + 694*E_2)*M_2*r0_3 + 2*(502 + 1545*E_2)*M*r0_4 + 125*r0_5)) + a_6*r0*(6*L_6*M*(114*M_2 + 2*(-49 + 36*E_2)*M*r0 + 3*(2 + E_2)*r0_2) + 216*E_2*M*r0_4*(70*M_4 + 80*M_3*r0 - 55*M_2*r0_2 - 13*M*r0_3 + 20*r0_4) - 2*L_4*(5232*M_5 + 16*(-49 + 990*E_2)*M_4*r0 + 6*(144 + 1043*E_2)*M_3*r0_2 + (103 - 348*E_2)*M_2*r0_3 - 3*(367 + 304*E_2)*M*r0_4 - 18*r0_5) + L_2*r0_2*((9756 - 27120*E_2)*M_5 + (508 - 48456*E_2)*M_4*r0 - (11533 + 28712*E_2)*M_3*r0_2 + 2*(125 - 883*E_2)*M_2*r0_3 + 3*(1077 + 2038*E_2)*M*r0_4 + 144*r0_5))))/(3.*r0_5*expr2_3);\n A62401 = (12*L*r0_4*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0)))/expr2_2;\n A62421 = (-2*(-12*a_10*E_2*M_2*(150*M + 73*r0) - 3*a_9*E*L*M*(12*(-100 + 9*E_2)*M_2 + 6*(-101 + 10*E_2)*M*r0 - 5*r0_2) + 3*a*E*L*M*r0_4*(L_2*r0_2*(-212*M_2 + 2*(533 + 144*E_2)*M*r0 - 543*r0_2) + r0_4*(-624*M_2 + 4*(163 + 72*E_2)*M*r0 - 197*r0_2) + 4*L_4*(160*M_2 + 36*M*r0 - 67*r0_2)) + a_5*E*L*M*r0*(-36*L_4*(13*M + r0) + L_2*(14832*M_3 + 36*(9 + 70*E_2)*M_2*r0 + 6*(379 + 80*E_2)*M*r0_2 - 2231*r0_3) + 2*r0_2*(6*(-1273 + 468*E_2)*M_3 + 2*(1364 + 2253*E_2)*M_2*r0 + 3*(1317 + 286*E_2)*M*r0_2 - 1808*r0_3)) + a_3*E*L*M*r0_2*(60*L_4*(126*M_2 - 31*M*r0 - 14*r0_2) + L_2*r0*(4800*M_3 + 12*(221 + 222*E_2)*M_2*r0 + 4*(1237 + 375*E_2)*M*r0_2 - 4127*r0_3) + 2*r0_3*(-3186*M_3 + 3*(-473 + 918*E_2)*M_2*r0 + 11*(349 + 102*E_2)*M*r0_2 - 1444*r0_3)) + a_7*E*L*M*(-3*L_2*(324*M_2 + 4*(-113 + 13*E_2)*M*r0 + 7*r0_2) + 2*r0*(24*(-141 + 103*E_2)*M_3 + 3*(1393 + 578*E_2)*M_2*r0 + (2371 + 78*E_2)*M*r0_2 - 652*r0_3)) + 3*a_8*M*(L_2*(12*(-50 + 27*E_2)*M_2 - 2*(157 + 68*E_2)*M*r0 + (-5 + 6*E_2)*r0_2) + 4*E_2*r0*(282*M_3 - 463*M_2*r0 - 283*M*r0_2 + 36*r0_3)) + r0_4*(432*E_2*M*r0_7*(-2*M + r0) + 6*L_6*M*(62*M_2 - 71*M*r0 + 20*r0_2) + L_4*r0_2*(1416*M_3 - 4*(221 + 303*E_2)*M_2*r0 + 2*(-89 + 330*E_2)*M*r0_2 + 133*r0_3) + L_2*r0_4*(636*M_3 + 2*(59 - 1074*E_2)*M_2*r0 + 8*(-71 + 141*E_2)*M*r0_2 + 175*r0_3)) + a_6*(3*L_4*M*(108*M_2 + 4*(-64 + 39*E_2)*M*r0 + (1 + 6*E_2)*r0_2) + 36*E_2*M*r0_3*(276*M_3 - 109*M_2*r0 - 145*M*r0_2 + 48*r0_3) + L_2*r0*(-72*(-47 + 206*E_2)*M_4 - 6*(467 + 894*E_2)*M_3*r0 - 2*(580 + 759*E_2)*M_2*r0_2 + (1019 + 1140*E_2)*M*r0_3 + 33*r0_4)) + a_4*r0*(6*L_6*M*(26*M + 3*r0) + 108*E_2*M*r0_4*(58*M_3 + 11*M_2*r0 - 37*M*r0_2 + 24*r0_3) + L_4*(-4944*M_4 + 12*(131 - 630*E_2)*M_3*r0 + 6*(-152 + 35*E_2)*M_2*r0_2 + 2*(586 + 357*E_2)*M*r0_3 + 33*r0_4) + L_2*r0_2*(-12*(-445 + 902*E_2)*M_4 - 2*(1537 + 5850*E_2)*M_3*r0 - 2*(1931 + 1608*E_2)*M_2*r0_2 + (2053 + 3354*E_2)*M*r0_3 + 211*r0_4)) + a_2*r0_2*(-18*L_6*M*(140*M_2 - 65*M*r0 - 7*r0_2) + 108*E_2*M*r0_6*(M_2 - 20*M*r0 + 16*r0_2) + L_4*r0*(408*M_4 + 12*(3 - 413*E_2)*M_3*r0 - 2*(1448 + 753*E_2)*M_2*r0_2 + 3*(397 + 452*E_2)*M*r0_3 + 166*r0_4) + L_2*r0_3*(2016*M_4 - 28*(-86 + 213*E_2)*M_3*r0 - 2*(2017 + 1767*E_2)*M_2*r0_2 + 7*(73 + 480*E_2)*M*r0_3 + 353*r0_4))))/(3.*r0_2*expr2_3);\n A62601 = -(r0*(-312*a_8*E_2*M_2 + 3*a_7*E*L*M*(-16*(-13 + E_2)*M + 3*r0) + a_5*E*L*M*(-12*L_2*(12*M + r0) + r0*(8*(-147 + 97*E_2)*M_2 + 4*(506 + 37*E_2)*M*r0 - 419*r0_2)) + a*E*L*M*r0_3*(4*L_2*(80*M_2 + 92*M*r0 - 75*r0_2) + 3*r0_2*(-304*M_2 + 4*(65 + 21*E_2)*M*r0 - 63*r0_2)) + a_3*E*L*M*r0*(r0_2*(8*(-332 + 99*E_2)*M_2 + 28*(93 + 16*E_2)*M*r0 - 689*r0_2) + 8*L_2*(291*M_2 - 59*M*r0 - 39*r0_2)) + 3*a_6*M*(L_2*(8*(-13 + 6*E_2)*M + (-3 + 2*E_2)*r0) + 4*E_2*r0*(49*M_2 - 101*M*r0 + 12*r0_2)) + a_4*(6*L_4*M*(8*M + r0) + 72*E_2*M*r0_3*(23*M_2 - 22*M*r0 + 6*r0_2) + L_2*r0*((588 - 2328*E_2)*M_3 + 14*(-58 + E_2)*M_2*r0 + 2*(157 + 123*E_2)*M*r0_2 + 15*r0_3)) + r0_3*(144*E_2*M*r0_5*(-2*M + r0) + 2*L_4*M*(118*M_2 - 127*M*r0 + 34*r0_2) + L_2*r0_2*(308*M_3 + (2 - 404*E_2)*M_2*r0 + 4*(-56 + 55*E_2)*M*r0_2 + 73*r0_3)) + a_2*r0*(36*E_2*M*r0_4*(23*M_2 - 23*M*r0 + 12*r0_2) + L_4*(-776*M_3 + 310*M_2*r0 + 66*M*r0_2) + L_2*r0_2*(-4*(-250 + 337*E_2)*M_3 - 2*(623 + 281*E_2)*M_2*r0 + 5*(43 + 92*E_2)*M*r0_2 + 88*r0_3))))/(6.*expr2_3);\n A63041 = (32*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(6*a_8*E_2*M_2*(2*M + r0) - 2*a_7*E*L*M*(12*M_2 + 9*M*r0 + 2*r0_2) + 3*a*E*L*M*r0_3*(L_4*(4*M - 6*r0) - L_2*r0_2*(3*M + 5*r0) + r0_4*(-19*M + 7*r0)) - a_5*E*L*M*r0*(L_2*(40*M + 22*r0) + r0*(98*M_2 + 33*M*r0 - 3*r0_2)) + L_2*r0_3*(3*L_4*M*(-2*M + r0) + 2*r0_4*(10*M_2 + 3*(-3 + E_2)*M*r0 + 2*r0_2) + L_2*r0_2*(6*M_2 + (-7 + 6*E_2)*M*r0 + 2*r0_2)) - a_3*E*L*M*r0_2*(18*L_4 + 2*r0_2*(75*M_2 + 26*M*r0 - 14*r0_2) + L_2*(-24*M_2 + 31*M*r0 + 35*r0_2)) + a_6*M*(6*E_2*M*r0_2*(12*M + 7*r0) + L_2*(12*M_2 + 4*(3 + 5*E_2)*M*r0 + (4 + 9*E_2)*r0_2)) + a_4*r0*(18*E_2*M_2*r0_3*(6*M + 5*r0) + L_4*M*(20*M + (13 + 9*E_2)*r0) + L_2*r0*((26 - 12*E_2)*M_3 + 9*(-1 + 4*E_2)*M_2*r0 + 8*(1 + 3*E_2)*M*r0_2 + 5*r0_3)) + a_2*r0_2*(9*L_6*M + 54*E_2*M_2*r0_5 + L_4*(-12*M_3 - (5 + 6*E_2)*M_2*r0 + 5*(2 + 3*E_2)*M*r0_2 + 5*r0_3) + L_2*r0_2*(64*M_3 + (-25 + 24*E_2)*M_2*r0 + (-16 + 21*E_2)*M*r0_2 + 9*r0_3))))/(r0_4*expr2_3);\n A63221 = (16*(6*a_8*E_2*M_2*(2*M + r0) - a_7*E*L*M*(24*M_2 + 21*M*r0 + 5*r0_2) + 3*a*E*L*M*r0_3*(L_4*(4*M - 6*r0) - L_2*r0_2*(9*M + 2*r0) + r0_4*(-19*M + 7*r0)) - a_5*E*L*M*r0*(L_2*(44*M + 23*r0) + r0*(92*M_2 + 43*M*r0 + r0_2)) + L_2*r0_3*(3*L_4*M*(-2*M + r0) + 2*r0_4*(10*M_2 + 3*(-3 + E_2)*M*r0 + 2*r0_2) + L_2*r0_2*(10*M_2 + (-11 + 6*E_2)*M*r0 + 3*r0_2)) - a_3*E*L*M*r0_2*(18*L_4 + r0_2*(132*M_2 + 55*M*r0 - 25*r0_2) + L_2*(-24*M_2 + 49*M*r0 + 35*r0_2)) + a_6*M*(6*E_2*M*r0_2*(12*M + 7*r0) + L_2*(12*M_2 + (15 + 22*E_2)*M*r0 + (5 + 9*E_2)*r0_2)) + a_4*r0*(18*E_2*M_2*r0_3*(6*M + 5*r0) + L_4*M*(22*M + (14 + 9*E_2)*r0) + 2*L_2*r0*((10 - 6*E_2)*M_3 + (-1 + 24*E_2)*M_2*r0 + 4*(1 + 3*E_2)*M*r0_2 + 2*r0_3)) + a_2*r0_2*(9*L_6*M + 54*E_2*M_2*r0_5 + L_2*r0_2*(52*M_3 + (-17 + 42*E_2)*M_2*r0 + 3*(-5 + 7*E_2)*M*r0_2 + 8*r0_3) + L_4*(-12*M_3 + 3*(3 + 5*E_2)*M*r0_2 + 4*r0_3 + M_2*(r0 - 6*E_2*r0)))))/(r0*expr2_3);\n A63401 = (2*r0_2*(6*a_6*E_2*M_2 - 6*a_5*E*L*M*(2*M + r0) + a_3*E*L*M*r0*(-18*L_2 + r0*(-43*M + r0)) + 3*a*E*L*M*r0_2*(L_2*(4*M - 6*r0) + r0_2*(-19*M + 7*r0)) + 3*a_4*M*(12*E_2*M*r0_2 + L_2*(2*M + 2*r0 + 3*E_2*r0)) + L_2*r0_2*(3*L_2*M*(-2*M + r0) + 2*r0_2*(10*M_2 + 3*(-3 + E_2)*M*r0 + 2*r0_2)) + a_2*r0*(9*L_4*M + 54*E_2*M_2*r0_3 + L_2*r0*((7 - 6*E_2)*M_2 + (-4 + 15*E_2)*M*r0 + 3*r0_2))))/expr2_3;\n A64021 = (48*L*r0*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0))*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/expr2_3;\n A64041 = (-8*(-12*a_12*E_2*M_2*(114*M_2 + 109*M*r0 + 26*r0_2) + a_11*E*L*M*(-144*(-19 + 6*E_2)*M_3 + (2642 - 936*E_2)*M_2*r0 + 12*(50 - 21*E_2)*M*r0_2 - 21*r0_3) + a*E*L*M*r0_5*(3*L_4*r0_2*(1207*M_2 + 4*(-45 + 28*E_2)*M*r0 - 296*r0_2) + 3*L_2*r0_4*(634*M_2 + 4*(13 + 45*E_2)*M*r0 - 257*r0_2) + 4*L_6*(482*M_2 - 139*M*r0 - 75*r0_2) - 9*r0_6*(31*M_2 - 4*(17 + 6*E_2)*M*r0 + 33*r0_2)) + a_3*E*L*M*r0_3*(4*L_6*(1050*M_2 - 430*M*r0 - 93*r0_2) + L_4*r0*(9504*M_3 + (6719 + 1608*E_2)*M_2*r0 + 2*(-1583 + 206*E_2)*M*r0_2 - 2568*r0_3) + 2*L_2*r0_3*(4260*M_3 + (2059 + 2790*E_2)*M_2*r0 + 2*(61 + 213*E_2)*M*r0_2 - 2024*r0_3) + 3*r0_5*(-1440*M_3 + 3*(283 + 528*E_2)*M_2*r0 + 4*(196 + 29*E_2)*M*r0_2 - 671*r0_3)) + r0_5*(216*E_2*M*r0_9*(-2*M + r0) - 16*L_8*M*(10*M_2 - 7*M*r0 + r0_2) + 3*L_2*r0_6*(54*M_3 + (25 - 456*E_2)*M_2*r0 + 4*(-15 + 61*E_2)*M*r0_2 + 17*r0_3) + 3*L_4*r0_4*(100*M_3 + (30 - 472*E_2)*M_2*r0 + 2*(-51 + 134*E_2)*M*r0_2 + 31*r0_3) + L_6*r0_2*(26*M_3 + (55 - 488*E_2)*M_2*r0 + 2*(-53 + 146*E_2)*M*r0_2 + 36*r0_3)) + a_5*E*L*M*r0_2*(-36*L_6*(13*M + 2*r0) + L_4*(16848*M_3 + 4*(-309 + 350*E_2)*M_2*r0 - 2*(1769 + 40*E_2)*M*r0_2 - 1551*r0_3) + L_2*r0*(11520*M_4 + 8*(2075 + 882*E_2)*M_3*r0 + 6*(419 + 1322*E_2)*M_2*r0_2 - 2*(1801 + 162*E_2)*M*r0_3 - 5119*r0_4) + 3*r0_3*(-2868*M_4 + 4*(-449 + 1044*E_2)*M_3*r0 + (3421 + 3240*E_2)*M_2*r0_2 - 8*(-16 + 21*E_2)*M*r0_3 - 1290*r0_4)) + a_9*E*L*M*(-2*L_2*(1296*M_3 + 2*(-34 + 195*E_2)*M_2*r0 + 12*(-22 + 17*E_2)*M*r0_2 + 57*r0_3) + r0*(96*(-49 + 59*E_2)*M_4 + 4*(1145 + 1188*E_2)*M_3*r0 - 40*(-179 + 27*E_2)*M_2*r0_2 - 12*(-29 + 88*E_2)*M*r0_3 - 777*r0_4)) + a_10*M*(L_2*(72*(-19 + 36*E_2)*M_3 + 2*(-667 + 668*E_2)*M_2*r0 + 6*(-48 + 17*E_2)*M*r0_2 + 3*(7 + 12*E_2)*r0_3) + 12*E_2*r0*(196*M_4 - 292*M_3*r0 - 426*M_2*r0_2 - 77*M*r0_3 + 18*r0_4)) + a_2*r0_3*(-108*E_2*M*r0_8*(14*M_2 + 5*M*r0 - 10*r0_2) + 4*L_8*M*(-350*M_2 + 205*M*r0 + 3*r0_2) + L_6*r0*(-1224*M_4 - (1343 + 3376*E_2)*M_3*r0 + 2*(123 + 16*E_2)*M_2*r0_2 + 2*(241 + 308*E_2)*M*r0_3 + 36*r0_4) + 3*L_2*r0_5*(520*M_4 + 3*(13 - 980*E_2)*M_3*r0 + 2*(-237 + 94*E_2)*M_2*r0_2 + (97 + 958*E_2)*M*r0_3 + 40*r0_4) + 3*L_4*r0_3*(32*M_4 + 2*(65 - 1558*E_2)*M_3*r0 + 4*(-173 + 44*E_2)*M_2*r0_2 + (265 + 798*E_2)*M*r0_3 + 49*r0_4)) - a_7*E*L*M*r0*(3*L_4*(780*M_2 + 4*(45 + 13*E_2)*M*r0 + 55*r0_2) - 2*L_2*(8496*M_4 + 8*(241 + 351*E_2)*M_3*r0 + (-599 + 930*E_2)*M_2*r0_2 - (803 + 522*E_2)*M*r0_3 - 978*r0_4) + 3*r0_2*(-4*(-895 + 648*E_2)*M_4 - 8*(41 + 708*E_2)*M_3*r0 - 3*(1147 + 536*E_2)*M_2*r0_2 + 8*(67 + 60*E_2)*M*r0_3 + 970*r0_4)) + a_8*(2*L_4*M*(432*M_3 + 2*(-134 + 585*E_2)*M_2*r0 + 63*(-3 + 7*E_2)*M*r0_2 + 3*(13 + 12*E_2)*r0_3) + 24*E_2*M*r0_3*(300*M_4 - 46*M_3*r0 - 341*M_2*r0_2 - 32*M*r0_3 + 45*r0_4) + L_2*r0*(-48*(-49 + 354*E_2)*M_5 - 4*(269 + 2264*E_2)*M_4*r0 + 2*(-981 + 800*E_2)*M_3*r0_2 + 2*(346 + 961*E_2)*M_2*r0_3 + 6*(105 + 131*E_2)*M*r0_4 + 15*r0_5)) + a_6*r0*(3*L_6*M*(260*M_2 + 2*(11 + 78*E_2)*M*r0 + (31 + 12*E_2)*r0_2) + 24*E_2*M*r0_4*(306*M_4 + 246*M_3*r0 - 220*M_2*r0_2 + 13*M*r0_3 + 90*r0_4) + L_4*(-5664*M_5 + 16*(28 - 1053*E_2)*M_4*r0 + 6*(113 - 362*E_2)*M_3*r0_2 + 2*(397 + 1830*E_2)*M_2*r0_3 + 6*(207 + 155*E_2)*M*r0_4 + 30*r0_5) + L_2*r0_2*((3540 - 17424*E_2)*M_5 - 28*(49 + 1086*E_2)*M_4*r0 - 5*(901 + 1268*E_2)*M_3*r0_2 + 2*(508 + 2635*E_2)*M_2*r0_3 + 6*(276 + 479*E_2)*M*r0_4 + 48*r0_5)) + a_4*r0_2*(12*L_8*M*(13*M + 3*r0) + 36*E_2*M*r0_6*(66*M_3 - 67*M_2*r0 + 10*M*r0_2 + 60*r0_3) + L_6*(-5616*M_4 + 12*(129 - 350*E_2)*M_3*r0 + 2*(461 + 490*E_2)*M_2*r0_2 + 24*(26 + 15*E_2)*M*r0_3 + 15*r0_4) + 3*L_2*r0_3*(1064*M_5 + 12*(51 - 550*E_2)*M_4*r0 - 2*(703 + 2048*E_2)*M_3*r0_2 + 3*(-141 + 598*E_2)*M_2*r0_3 + 2*(253 + 711*E_2)*M*r0_4 + 34*r0_5) + L_4*r0*(-1872*M_5 - 8*(398 + 1917*E_2)*M_4*r0 - 4*(326 + 3327*E_2)*M_3*r0_2 + 2*(-308 + 2025*E_2)*M_2*r0_3 + 3*(709 + 816*E_2)*M*r0_4 + 84*r0_5))))/(3.*r0_5*expr2_4);\n A64201 = (12*L*r0_4*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0)))/expr2_3;\n A64221 = (-4*(-2*a_10*E_2*M_2*(117*M + 56*r0) + a_9*E*L*M*(-36*(-13 + 4*E_2)*M_2 + 6*(37 - 13*E_2)*M*r0 - 7*r0_2) + a*E*L*M*r0_4*(L_2*r0_2*(401*M_2 + 3*(19 + 24*E_2)*M*r0 - 181*r0_2) + 2*L_4*(284*M_2 - 80*M*r0 - 47*r0_2) + 3*r0_4*(-79*M_2 + 2*(47 + 9*E_2)*M*r0 - 34*r0_2)) + a_3*E*L*M*r0_2*(4*L_4*(336*M_2 - 154*M*r0 - 31*r0_2) + L_2*r0*(1416*M_3 + (791 + 528*E_2)*M_2*r0 + 8*(-3 + 5*E_2)*M*r0_2 - 658*r0_3) + r0_3*(-1008*M_3 + (-5 + 1008*E_2)*M_2*r0 + 2*(497 + 10*E_2)*M*r0_2 - 543*r0_3)) + a_5*E*L*M*r0*(-6*L_4*(32*M + 5*r0) + r0_2*(32*(-55 + 36*E_2)*M_3 + (1033 + 1280*E_2)*M_2*r0 - 8*(-96 + 25*E_2)*M*r0_2 - 679*r0_3) + L_2*(2688*M_3 + 4*(-103 + 112*E_2)*M_2*r0 - 3*(79 + 32*E_2)*M*r0_2 - 392*r0_3)) + a_8*M*(L_2*(18*(-13 + 24*E_2)*M_2 + (-110 + 119*E_2)*M*r0 + (7 + 15*E_2)*r0_2) + 2*E_2*r0*(202*M_3 - 367*M_2*r0 - 193*M*r0_2 + 36*r0_3)) + a_6*(L_4*M*(144*M_2 + (-37 + 192*E_2)*M*r0 + (22 + 15*E_2)*r0_2) + 2*E_2*M*r0_3*(564*M_3 - 361*M_2*r0 - 275*M*r0_2 + 144*r0_3) + L_2*r0*((404 - 2688*E_2)*M_4 - (399 + 130*E_2)*M_3*r0 + (-87 + 500*E_2)*M_2*r0_2 + 2*(99 + 97*E_2)*M*r0_3 + 8*r0_4)) + a_4*r0*(L_6*M*(64*M + 15*r0) + 6*E_2*M*r0_4*(150*M_3 + M_2*r0 - 61*M*r0_2 + 72*r0_3) + L_4*(-896*M_4 - 6*(-53 + 224*E_2)*M_3*r0 + (-19 + 452*E_2)*M_2*r0_2 + 2*(102 + 59*E_2)*M*r0_3 + 8*r0_4) + L_2*r0_2*((632 - 2436*E_2)*M_4 - 4*(134 + 495*E_2)*M_3*r0 + (-469 + 563*E_2)*M_2*r0_2 + (351 + 509*E_2)*M*r0_3 + 26*r0_4)) + a_2*r0_2*(-18*E_2*M*r0_6*(6*M_2 + 13*M*r0 - 16*r0_2) + L_6*(-448*M_3 + 260*M_2*r0 + 6*M*r0_2) + L_4*r0*(-132*M_4 - (91 + 1076*E_2)*M_3*r0 + 2*(-123 + 58*E_2)*M_2*r0_2 + (167 + 195*E_2)*M*r0_3 + 17*r0_4) + L_2*r0_3*(356*M_4 + (191 - 1542*E_2)*M_3*r0 + (-547 + 130*E_2)*M_2*r0_2 + 4*(29 + 124*E_2)*M*r0_3 + 40*r0_4)) - a_7*E*L*M*(r0*((808 - 896*E_2)*M_3 - (1133 + 224*E_2)*M_2*r0 + 2*(-247 + 122*E_2)*M*r0_2 + 245*r0_3) + L_2*(432*M_2 + 37*r0_2 + 4*M*(r0 + 16*E_2*r0))) + r0_4*(72*E_2*M*r0_7*(-2*M + r0) + L_6*M*(-20*M_2 + 4*M*r0 + 3*r0_2) + L_4*r0_2*(110*M_3 - (35 + 152*E_2)*M_2*r0 + 2*(-25 + 46*E_2)*M*r0_2 + 20*r0_3) + L_2*r0_4*(102*M_3 + 2*(-34 + 83*E_2)*M*r0_2 + 22*r0_3 - 3*M_2*(r0 + 100*E_2*r0)))))/(r0_2*expr2_4);\n A64401 = -(r0*(-360*a_8*E_2*M_2 - 9*a_7*E*L*M*(8*(-10 + 3*E_2)*M + 3*r0) + a_5*E*L*M*(-108*L_2*(6*M + r0) + r0*(24*(-52 + 53*E_2)*M_2 + 12*(197 - 37*E_2)*M*r0 - 703*r0_2)) + a_3*E*L*M*r0*(r0_2*(3*(-895 + 504*E_2)*M_2 + 10*(317 - 12*E_2)*M*r0 - 1198*r0_2) + 12*L_2*(318*M_2 - 155*M*r0 - 33*r0_2)) + 3*a*E*L*M*r0_3*(r0_2*(-381*M_2 + 350*M*r0 + 36*E_2*M*r0 - 100*r0_2) + 4*L_2*(114*M_2 - 25*M*r0 - 24*r0_2)) + 3*a_6*M*(3*L_2*(-40*M + 72*E_2*M + 3*r0 + 6*E_2*r0) + 8*E_2*r0*(26*M_2 - 56*M*r0 + 9*r0_2)) + a_4*(54*L_4*M*(4*M + r0) + 72*E_2*M*r0_3*(22*M_2 - 25*M*r0 + 9*r0_2) + L_2*r0*((624 - 3816*E_2)*M_3 + 12*(-85 + 133*E_2)*M_2*r0 + 2*(257 + 180*E_2)*M*r0_2 + 27*r0_3)) + r0_3*(216*E_2*M*r0_5*(-2*M + r0) + 6*L_4*M*(12*M_2 - 20*M*r0 + 7*r0_2) + L_2*r0_2*(450*M_3 - (73 + 432*E_2)*M_2*r0 + 8*(-31 + 33*E_2)*M*r0_2 + 86*r0_3)) + a_2*r0*(216*E_2*M*r0_4*(4*M_2 - 4*M*r0 + 3*r0_2) + 12*L_4*M*(-106*M_2 + 59*M*r0 + 3*r0_2) + L_2*r0_2*(-3*(-367 + 984*E_2)*M_3 + 2*(-799 + 270*E_2)*M_2*r0 + 6*(62 + 95*E_2)*M*r0_2 + 98*r0_3))))/(6.*expr2_4);\n A65021 = (8*(6*a_8*E_2*M_2*(2*M + r0) - a_7*E*L*M*(24*M_2 + 21*M*r0 + 5*r0_2) + 3*a*E*L*M*r0_3*(L_4*(4*M - 6*r0) - L_2*r0_2*(10*M + r0) + 4*r0_4*(-5*M + 2*r0)) - a_5*E*L*M*r0*(2*M*r0*(47*M + 21*r0) + L_2*(44*M + 23*r0)) + L_2*r0_3*(3*L_4*M*(-2*M + r0) + 2*L_2*r0_2*(6*M_2 + (-7 + 3*E_2)*M*r0 + 2*r0_2) + r0_4*(22*M_2 + 3*(-7 + 2*E_2)*M*r0 + 5*r0_2)) - a_3*E*L*M*r0_2*(18*L_4 + r0_2*(138*M_2 + 53*M*r0 - 29*r0_2) + L_2*(-24*M_2 + 50*M*r0 + 34*r0_2)) + a_6*M*(6*E_2*M*r0_2*(12*M + 7*r0) + L_2*(12*M_2 + (15 + 22*E_2)*M*r0 + (5 + 9*E_2)*r0_2)) + a_4*r0*(18*E_2*M_2*r0_3*(6*M + 5*r0) + L_4*M*(22*M + (14 + 9*E_2)*r0) + L_2*r0*((22 - 12*E_2)*M_3 + 3*(-1 + 16*E_2)*M_2*r0 + (7 + 24*E_2)*M*r0_2 + 4*r0_3)) + a_2*r0_2*(9*L_6*M + 54*E_2*M_2*r0_5 + L_4*(-12*M_3 + (2 - 6*E_2)*M_2*r0 + (8 + 15*E_2)*M*r0_2 + 4*r0_3) + L_2*r0_2*(56*M_3 + 2*(-10 + 21*E_2)*M_2*r0 + (-17 + 21*E_2)*M*r0_2 + 9*r0_3))))/(r0*expr2_4);\n A65201 = (2*r0_2*(6*a_6*E_2*M_2 - 6*a_5*E*L*M*(2*M + r0) - 2*a_3*E*L*M*r0*(9*L_2 + (22*M - r0)*r0) + 6*a*E*L*M*r0_2*(L_2*(2*M - 3*r0) + 2*r0_2*(-5*M + 2*r0)) + 3*a_4*M*(12*E_2*M*r0_2 + L_2*(2*M + 2*r0 + 3*E_2*r0)) + a_2*r0*(9*L_4*M + 54*E_2*M_2*r0_3 + L_2*r0*((8 - 6*E_2)*M_2 + 5*(-1 + 3*E_2)*M*r0 + 3*r0_2)) + L_2*r0_2*(3*L_2*M*(-2*M + r0) + r0_2*(22*M_2 + 3*(-7 + 2*E_2)*M*r0 + 5*r0_2))))/expr2_4;\n A66001 = (4*L*r0_4*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0)))/expr2_4;\n A66021 = (-2*(-12*a_10*E_2*M_2*(28*M + 13*r0) - 3*a_9*E*L*M*(4*(-56 + 39*E_2)*M_2 + 2*(-47 + 42*E_2)*M*r0 + 11*r0_2) - a*E*L*M*r0_4*(3*r0_4*(131*M_2 + 2*(-97 + 12*E_2)*M*r0 + 80*r0_2) + L_4*(-1648*M_2 + 824*M*r0 + 84*r0_2) + L_2*r0_2*(-1871*M_2 + 934*M*r0 + 132*r0_2)) + a_5*E*L*M*r0*(-36*L_4*(17*M + 3*r0) + r0_2*(6*(-349 + 456*E_2)*M_3 + (2457 + 2116*E_2)*M_2*r0 + 2*(225 - 686*E_2)*M*r0_2 - 1539*r0_3) + L_2*(5808*M_3 + 4*(-449 + 238*E_2)*M_2*r0 - 4*(423 + 136*E_2)*M*r0_2 - 801*r0_3)) + a_3*E*L*M*r0_2*(4*L_4*(714*M_2 - 467*M*r0 - 48*r0_2) + L_2*r0*(4096*M_3 + (2269 + 1224*E_2)*M_2*r0 - 10*(181 + 34*E_2)*M*r0_2 - 1218*r0_3) + 2*r0_3*(-1077*M_3 + 6*(95 + 183*E_2)*M_2*r0 + 2*(381 - 167*E_2)*M*r0_2 - 633*r0_3)) + 3*a_8*M*(L_2*(4*(-28 + 117*E_2)*M_2 + 6*(-7 + 34*E_2)*M*r0 + (11 + 18*E_2)*r0_2) + 4*E_2*r0*(42*M_3 - 91*M_2*r0 - 35*M*r0_2 + 12*r0_3)) + r0_4*(144*E_2*M*r0_7*(-2*M + r0) - 2*L_6*M*(106*M_2 - 85*M*r0 + 16*r0_2) + L_2*r0_4*(218*M_3 - (101 + 476*E_2)*M_2*r0 + 4*(-13 + 70*E_2)*M*r0_2 + 24*r0_3) + L_4*r0_2*(-42*M_3 + (165 - 196*E_2)*M_2*r0 + 4*(-36 + 35*E_2)*M*r0_2 + 36*r0_3)) - a_7*E*L*M*(3*L_2*(468*M_2 + 4*(39 + 17*E_2)*M*r0 + 47*r0_2) + 2*r0*((504 - 968*E_2)*M_3 + 2*(-441 + 65*E_2)*M_2*r0 + (-201 + 514*E_2)*M*r0_2 + 273*r0_3)) + a_6*(3*L_4*M*(156*M_2 + 12*(3 + 17*E_2)*M*r0 + (29 + 18*E_2)*r0_2) + 12*E_2*M*r0_3*(108*M_3 - 135*M_2*r0 - 43*M*r0_2 + 48*r0_3) + L_2*r0*((504 - 5808*E_2)*M_4 + 56*(-12 + 23*E_2)*M_3*r0 + 2*(20 + 1249*E_2)*M_2*r0_2 + 3*(151 + 128*E_2)*M*r0_3 + 21*r0_4)) + a_4*r0*(6*L_6*M*(34*M + 9*r0) + 36*E_2*M*r0_4*(46*M_3 - 11*M_2*r0 - 7*M*r0_2 + 24*r0_3) + L_4*(-1936*M_4 + 24*(32 - 119*E_2)*M_3*r0 + 2*(111 + 875*E_2)*M_2*r0_2 + 6*(69 + 37*E_2)*M*r0_3 + 21*r0_4) + L_2*r0_2*((798 - 6152*E_2)*M_4 - (1213 + 3996*E_2)*M_3*r0 + 4*(-133 + 837*E_2)*M_2*r0_2 + 2*(361 + 443*E_2)*M*r0_3 + 21*r0_4)) + a_2*r0_2*(-36*E_2*M*r0_6*(11*M_2 + 8*M*r0 - 16*r0_2) - 2*L_6*M*(476*M_2 - 331*M*r0 + 15*r0_2) + L_4*M*r0*(-680*M_3 - (389 + 2660*E_2)*M_2*r0 + 2*(12 + 497*E_2)*M*r0_2 + 2*(135 + 154*E_2)*r0_3) + L_2*r0_3*(868*M_4 - (229 + 4208*E_2)*M_3*r0 + (-805 + 1754*E_2)*M_2*r0_2 + 4*(85 + 209*E_2)*M*r0_3 + 24*r0_4))))/(3.*r0_2*expr2_5);\n A66201 = (r0*(168*a_8*E_2*M_2 + 3*a_7*E*L*M*(16*(-7 + 5*E_2)*M + 15*r0) - 3*a_6*M*(L_2*(8*(-7 + 30*E_2)*M + (15 + 22*E_2)*r0) + 4*E_2*r0*(21*M_2 - 49*M*r0 + 12*r0_2)) + a*E*L*M*r0_3*(L_2*(-1520*M_2 + 808*M*r0 + 60*r0_2) + 3*r0_2*(227*M_2 - 242*M*r0 + 36*E_2*M*r0 + 80*r0_2)) + a_5*E*L*M*(12*L_2*(60*M + 11*r0) + r0*((504 - 920*E_2)*M_2 + 4*(-284 + 185*E_2)*M*r0 + 513*r0_2)) + a_3*E*L*M*r0*(-8*L_2*(345*M_2 - 254*M*r0 - 24*r0_2) + r0_2*((979 - 1224*E_2)*M_2 + 2*(-841 + 304*E_2)*M*r0 + 918*r0_2)) + r0_3*(144*E_2*M*(2*M - r0)*r0_5 + 2*L_4*M*(74*M_2 - 53*M*r0 + 8*r0_2) + L_2*r0_2*(-314*M_3 + (149 + 164*E_2)*M_2*r0 + 4*(19 - 31*E_2)*M*r0_2 - 36*r0_3)) - a_4*(6*L_4*M*(40*M + 11*r0) + 72*E_2*M*r0_3*(7*M_2 - 12*M*r0 + 6*r0_2) + L_2*r0*((252 - 2760*E_2)*M_3 + 2*(-274 + 1063*E_2)*M_2*r0 + 6*(61 + 37*E_2)*M*r0_2 + 21*r0_3)) - a_2*r0*(36*E_2*M*r0_4*(11*M_2 - 11*M*r0 + 12*r0_2) - 2*L_4*M*(460*M_2 - 323*M*r0 + 15*r0_2) + L_2*r0_2*((475 - 2596*E_2)*M_3 + 10*(-90 + 131*E_2)*M_2*r0 + 8*(37 + 35*E_2)*M*r0_2 + 36*r0_3))))/(6.*expr2_5);\n A67001 = (2*r0_2*(2*a_6*E_2*M_2 - 2*a_5*E*L*M*(2*M + r0) + a_3*E*L*M*r0*(-6*L_2 + r0*(-15*M + r0)) + a*E*L*M*r0_2*(L_2*(4*M - 6*r0) + 3*r0_2*(-7*M + 3*r0)) + a_4*M*(12*E_2*M*r0_2 + L_2*(2*M + 2*r0 + 3*E_2*r0)) + L_2*r0_2*(L_2*M*(-2*M + r0) + 2*r0_2*(4*M_2 + (-4 + E_2)*M*r0 + r0_2)) + a_2*r0*(3*L_4*M + 18*E_2*M_2*r0_3 + L_2*r0*((3 - 2*E_2)*M_2 + (-2 + 5*E_2)*M*r0 + r0_2))))/expr2_5;\n A68001 = -(r0*(-12*a_8*E_2*M_2 - 3*a_7*E*L*M*(2*(-4 + 7*E_2)*M + 3*r0) + a_5*E*L*M*(-6*L_2*(21*M + 4*r0) + r0*(4*(-6 + 31*E_2)*M_2 + 4*(22 - 37*E_2)*M*r0 - 69*r0_2)) + a_3*E*L*M*r0*(r0_2*((-29 + 180*E_2)*M_2 - 2*(-83 + 71*E_2)*M*r0 - 132*r0_2) + 4*L_2*(93*M_2 - 89*M*r0 - 3*r0_2)) + 3*a_6*M*(L_2*(-4*M + 42*E_2*M + 3*r0 + 4*E_2*r0) + 2*E_2*r0*(2*M_2 - 6*M*r0 + 3*r0_2)) + a*E*L*M*r0_3*(2*L_2*(134*M_2 - 91*M*r0 + 6*r0_2) - 3*r0_2*(29*M_2 + 2*(-19 + 6*E_2)*M*r0 + 14*r0_2)) + M*r0_3*(18*E_2*r0_5*(-2*M + r0) + L_4*(-44*M_2 + 38*M*r0 - 8*r0_2) + L_2*r0_2*(46*M_2 - (43 + 4*E_2)*M*r0 + 2*(5 + 4*E_2)*r0_2)) + a_2*M*r0*(-4*L_4*(31*M_2 - 26*M*r0 + 3*r0_2) + 18*E_2*r0_4*(2*M_2 - 2*M*r0 + 3*r0_2) + L_2*r0_2*((29 - 404*E_2)*M_2 + 2*(-48 + 143*E_2)*M*r0 + 2*(23 + 10*E_2)*r0_2)) + a_4*(6*L_4*M*(7*M + 2*r0) + 18*E_2*M*r0_4*(-4*M + 3*r0) + L_2*r0*((12 - 372*E_2)*M_3 + 4*(-13 + 100*E_2)*M_2*r0 + 24*(2 + E_2)*M*r0_2 + 3*r0_3))))/(3.*expr2_6);\n }\n\n /* A_{theta,theta} */\n {\n A70080 = (1024*M*expr1_4*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/(r0_7*(a_2 + r0*(-2*M + r0)));\n A70260 = (1024*M*expr1_3*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/(r0_4*(a_2 + r0*(-2*M + r0)));\n A70440 = (384*M*r0*expr4_2*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/(a_2 + r0*(-2*M + r0));\n A70620 = (64*M*r0_3*(L_2 + r0_2 + (a_2*(2*M + r0))/r0)*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/(a_2 + r0*(-2*M + r0));\n A70800 = (4*M*r0_5*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/(a_2 + r0*(-2*M + r0));\n A71080 = (512*M*expr4_3*((-(a_2*M) + r0_3 + (2*L*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0)))/(a_2 + r0*(-2*M + r0)))*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))) - 4*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(3*a_4*E_2 - 6*a_3*E*L + 2*a*E*L*(4*M - 3*r0)*r0 + a_2*(3*L_2 + 4*E_2*r0*(-M + r0)) + r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))) + 3*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(5*a_4*E_2 - 10*a_3*E*L + 8*a*E*L*(M - r0)*r0 + r0*(E_2*r0_3 + L_2*(-4*M + 2*r0)) + a_2*(5*L_2 + 2*E_2*r0*(-2*M + 3*r0)))))/(r0_5*(a_2 + r0*(-2*M + r0)));\n A71260 = (128*M*expr4_2*(3*(-(a_2*M) + r0_3 + (2*L*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0)))/(a_2 + r0*(-2*M + r0)))*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))) - 17*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(3*a_4*E_2 - 6*a_3*E*L + 2*a*E*L*(4*M - 3*r0)*r0 + a_2*(3*L_2 + 4*E_2*r0*(-M + r0)) + r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))) + 12*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(5*a_4*E_2 - 10*a_3*E*L + 8*a*E*L*(M - r0)*r0 + r0*(E_2*r0_3 + L_2*(-4*M + 2*r0)) + a_2*(5*L_2 + 2*E_2*r0*(-2*M + 3*r0)))))/(r0_3*(a_2 + r0*(-2*M + r0)));\n A71440 = (96*M*(L_2 + r0_2 + (a_2*(2*M + r0))/r0)*(9*(L_2 + r0_2 + (a_2*(2*M + r0))/r0)*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))) + ((-(a_2*M) + r0_3 + (2*L*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0)))/(a_2 + r0*(-2*M + r0)))*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/r0 + (6*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(5*a_4*E_2 - 10*a_3*E*L + 8*a*E*L*(M - r0)*r0 + r0*(E_2*r0_3 + L_2*(-4*M + 2*r0)) + a_2*(5*L_2 + 2*E_2*r0*(-2*M + 3*r0))))/r0))/(a_2 + r0*(-2*M + r0));\n A71620 = (8*M*r0*((-(a_2*M) + r0_3 + (2*L*(a_3*E*M - a_2*L*M + 3*a*E*M*r0_2 + L*r0_2*(-2*M + r0)))/(a_2 + r0*(-2*M + r0)))*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))) - 19*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(3*a_4*E_2 - 6*a_3*E*L + 2*a*E*L*(4*M - 3*r0)*r0 + a_2*(3*L_2 + 4*E_2*r0*(-M + r0)) + r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))) + 12*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(5*a_4*E_2 - 10*a_3*E*L + 8*a*E*L*(M - r0)*r0 + r0*(E_2*r0_3 + L_2*(-4*M + 2*r0)) + a_2*(5*L_2 + 2*E_2*r0*(-2*M + 3*r0)))))/(a_2 + r0*(-2*M + r0));\n A71800 = (4*M*r0_5*(L_2*(4*M - 2*r0) + a_2*E_2*(4*M - r0) - E_2*r0_3 + a*E*L*(-8*M + 3*r0)))/(a_2 + r0*(-2*M + r0));\n A72060 = (1024*M*expr1_3*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/(r0_4*expr2_2);\n A72240 = (768*M*r0*expr4_2*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/expr2_2;\n A72420 = (192*M*r0_2*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/expr2_2;\n A72600 = (16*M*r0_5*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/expr2_2;\n A73060 = (-128*M*expr1_2*(-9*a_8*E_2*(3*M + r0) + 18*a_7*E*L*((3 + E_2)*M + r0) + r0_3*(E_2*r0_3 + L_2*(-4*M + 2*r0))*(r0_2*(-15*M + 7*r0) + L_2*(-21*M + 10*r0)) + 2*a*E*L*r0_3*(L_2*(-120*M_2 + 97*M*r0 - 18*r0_2) + r0_2*(-60*M_2 + (49 + 9*E_2)*M*r0 - 9*r0_2)) - a_6*(9*L_2*(3*M + 6*E_2*M + r0 + E_2*r0) + 4*E_2*r0*(-8*M_2 + 13*M*r0 + 4*r0_2)) + 2*a_5*E*L*(9*L_2*(3*M + r0) + r0*(-4*(8 + 3*E_2)*M_2 + (35 + 39*E_2)*M*r0 + 9*r0_2)) + a_4*(-9*L_4*(2*M + r0) + L_2*r0*(8*(4 + 9*E_2)*M_2 - (18 + 203*E_2)*M*r0 + 2*(-1 + E_2)*r0_2) + 2*E_2*r0_2*(24*M_3 + 32*M_2*r0 - 27*M*r0_2 + r0_3)) - 2*a_3*E*L*r0*(L_2*(36*M_2 - 86*M*r0 + 9*r0_2) + r0*(48*M_3 + 4*(7 + 9*E_2)*M_2*r0 - 3*(19 + 13*E_2)*M*r0_2 + 9*r0_3)) + a_2*r0*(4*E_2*r0_4*(12*M_2 - 11*M*r0 + 4*r0_2) + L_4*(24*M_2 - 47*M*r0 + 16*r0_2) + L_2*r0*(48*M_3 + 4*(-2 + 57*E_2)*M_2*r0 - (53 + 190*E_2)*M*r0_2 + 21*(1 + E_2)*r0_3))))/(r0_5*expr2_3);\n A73240 = (-96*M*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-6*a_8*E_2*(3*M + r0) + 12*a_7*E*L*((3 + E_2)*M + r0) + r0_3*(E_2*r0_3 + L_2*(-4*M + 2*r0))*(r0_2*(-15*M + 7*r0) + L_2*(-19*M + 9*r0)) + 2*a*E*L*r0_3*(L_2*(-100*M_2 + 81*M*r0 - 15*r0_2) + r0_2*(-60*M_2 + (49 + 6*E_2)*M*r0 - 9*r0_2)) + 2*a_5*E*L*(6*L_2*(3*M + r0) + r0*(-2*(1 + 4*E_2)*M_2 + (27 + 26*E_2)*M*r0 + 3*r0_2)) - a_6*(6*L_2*(3*M + 6*E_2*M + r0 + E_2*r0) + E_2*r0*(-2*M_2 + 41*M*r0 + 9*r0_2)) + a_4*(-6*L_4*(2*M + r0) + L_2*r0*((2 + 48*E_2)*M_2 - (13 + 145*E_2)*M*r0 + 3*(1 + E_2)*r0_2) + E_2*r0_2*(72*M_3 + 36*M_2*r0 - 51*M*r0_2 + 7*r0_3)) + a_2*r0*(L_4*(16*M_2 - 41*M*r0 + 15*r0_2) + E_2*r0_4*(42*M_2 - 43*M*r0 + 17*r0_2) + L_2*r0*(72*M_3 + 4*(-6 + 43*E_2)*M_2*r0 - 5*(11 + 28*E_2)*M*r0_2 + (23 + 18*E_2)*r0_3)) - 2*a_3*E*L*r0*(L_2*(24*M_2 - 67*M*r0 + 9*r0_2) + 2*r0*(36*M_3 - (29 + 13*E_2)*M*r0_2 + 6*r0_3 + 3*M_2*(r0 + 4*E_2*r0)))))/(r0_2*expr2_3);\n A73420 = (-24*M*r0*(-3*a_8*E_2*(3*M + r0) + 6*a_7*E*L*((3 + E_2)*M + r0) + r0_3*(E_2*r0_3 + L_2*(-4*M + 2*r0))*(r0_2*(-15*M + 7*r0) + L_2*(-17*M + 8*r0)) + 2*a*E*L*r0_3*(L_2*(-80*M_2 + 65*M*r0 - 12*r0_2) + r0_2*(-60*M_2 + (49 + 3*E_2)*M*r0 - 9*r0_2)) + 2*a_5*E*L*(3*L_2*(3*M + r0) + r0*(-4*(-7 + E_2)*M_2 + (19 + 13*E_2)*M*r0 - 3*r0_2)) - a_6*(3*L_2*(3*M + 6*E_2*M + r0 + E_2*r0) + 2*E_2*r0*(14*M_2 + 15*M*r0 + r0_2)) + a_4*(-3*L_4*(2*M + r0) + L_2*r0*(4*(-7 + 6*E_2)*M_2 - (8 + 87*E_2)*M*r0 + 4*(2 + E_2)*r0_2) + 4*E_2*r0_2*(24*M_3 + 2*M_2*r0 - 12*M*r0_2 + 3*r0_3)) - 2*a_3*E*L*r0*(3*L_2*(4*M_2 - 16*M*r0 + 3*r0_2) + r0*(96*M_3 + 4*(-4 + 3*E_2)*M_2*r0 - (59 + 13*E_2)*M*r0_2 + 15*r0_3)) + a_2*r0*(6*E_2*r0_4*(6*M_2 - 7*M*r0 + 3*r0_2) + L_4*(8*M_2 - 35*M*r0 + 14*r0_2) + L_2*r0*(96*M_3 + 4*(-10 + 29*E_2)*M_2*r0 - 3*(19 + 30*E_2)*M*r0_2 + 5*(5 + 3*E_2)*r0_3))))/expr2_3;\n A73600 = (-2*M*r0_5*(2*a_3*E*L*(29*M - 9*r0) + a_4*E_2*(-29*M + 5*r0) - 2*a*E*L*r0*(60*M_2 - 49*M*r0 + 9*r0_2) + (15*M - 7*r0)*r0*(L_2*(4*M - 2*r0) - E_2*r0_3) + a_2*(L_2*(-29*M + 13*r0) + 4*E_2*r0*(15*M_2 - 10*M*r0 + 3*r0_2))))/expr2_3;\n A74040 = (384*M*r0*expr4_2*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/expr2_3;\n A74220 = (192*M*r0_2*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/expr2_3;\n A74400 = (24*M*r0_5*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/expr2_3;\n A75040 = (-96*M*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-3*a_8*E_2*(3*M + r0) + 6*a_7*E*L*((3 + E_2)*M + r0) + r0_3*(E_2*r0_3 + L_2*(-4*M + 2*r0))*(r0_2*(-7*M + 3*r0) + L_2*(-9*M + 4*r0)) + a_4*(-3*L_4*(2*M + r0) + L_2*M*r0*(4*M + 24*E_2*M - 8*r0 - 71*E_2*r0) + 8*E_2*M*r0_2*(4*M_2 + 3*M*r0 - 3*r0_2)) + 2*a*E*L*r0_3*(L_2*(-48*M_2 + 37*M*r0 - 6*r0_2) + r0_2*(-28*M_2 + 3*(7 + E_2)*M*r0 - 3*r0_2)) - a_6*(3*L_2*(3*M + 6*E_2*M + r0 + E_2*r0) + 2*E_2*r0*(-2*M_2 + 11*M*r0 + 3*r0_2)) + 2*a_5*E*L*(3*L_2*(3*M + r0) + r0*(-4*(1 + E_2)*M_2 + (15 + 13*E_2)*M*r0 + 3*r0_2)) - 2*a_3*E*L*r0*(L_2*(12*M_2 - 32*M*r0 + 3*r0_2) + r0*(32*M_3 + 4*(2 + 3*E_2)*M_2*r0 - (27 + 13*E_2)*M*r0_2 + 3*r0_3)) + a_2*r0*(2*E_2*r0_4*(10*M_2 - 9*M*r0 + 3*r0_2) + L_4*(8*M_2 - 19*M*r0 + 6*r0_2) + L_2*r0*(32*M_3 + 4*(-2 + 21*E_2)*M_2*r0 - (25 + 66*E_2)*M*r0_2 + (9 + 7*E_2)*r0_3))))/(r0_2*expr2_4);\n A75220 = (-24*M*r0*(-3*a_8*E_2*(3*M + r0) + 6*a_7*E*L*((3 + E_2)*M + r0) + r0_3*(E_2*r0_3 + L_2*(-4*M + 2*r0))*(2*r0_2*(-7*M + 3*r0) + L_2*(-16*M + 7*r0)) + 2*a_5*E*L*(3*L_2*(3*M + r0) + M*r0*(22*M - 4*E_2*M + 22*r0 + 13*E_2*r0)) + 2*a*E*L*r0_3*(L_2*(-76*M_2 + 58*M*r0 - 9*r0_2) + r0_2*(-56*M_2 + 3*(14 + E_2)*M*r0 - 6*r0_2)) - a_6*(3*L_2*(3*M + 6*E_2*M + r0 + E_2*r0) + E_2*r0*(22*M_2 + 33*M*r0 + 5*r0_2)) + a_4*(-3*L_4*(2*M + r0) + L_2*r0*((-22 + 24*E_2)*M_2 - (11 + 84*E_2)*M*r0 + (5 + E_2)*r0_2) + E_2*r0_2*(88*M_3 + 20*M_2*r0 - 45*M*r0_2 + 5*r0_3)) - 2*a_3*E*L*r0*(3*L_2*(4*M_2 - 15*M*r0 + 2*r0_2) + r0*(88*M_3 + 6*(-1 + 2*E_2)*M_2*r0 - (55 + 13*E_2)*M*r0_2 + 9*r0_3)) + a_2*r0*(L_4*(8*M_2 - 32*M*r0 + 11*r0_2) + E_2*r0_4*(34*M_2 - 35*M*r0 + 13*r0_2) + L_2*r0*(88*M_3 + 16*(-2 + 7*E_2)*M_2*r0 - 2*(26 + 41*E_2)*M*r0_2 + (20 + 11*E_2)*r0_3))))/expr2_4;\n A75400 = (-6*M*r0_5*(2*a_3*E*L*(13*M - 3*r0) + a_4*E_2*(-13*M + r0) - 2*a*E*L*r0*(28*M_2 - 21*M*r0 + 3*r0_2) + (7*M - 3*r0)*r0*(L_2*(4*M - 2*r0) - E_2*r0_3) + a_2*(L_2*(-13*M + 5*r0) + 4*E_2*r0*(7*M_2 - 4*M*r0 + r0_2))))/expr2_4;\n A76020 = (64*M*r0_2*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/expr2_4;\n A76200 = (16*M*r0_5*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/expr2_4;\n A77020 = (-8*M*r0*(-3*a_8*E_2*(3*M + r0) + 6*a_7*E*L*((3 + E_2)*M + r0) + r0_3*(E_2*r0_3 + L_2*(-4*M + 2*r0))*(r0_2*(-13*M + 5*r0) + L_2*(-15*M + 6*r0)) + 2*a*E*L*r0_3*(L_2*(-72*M_2 + 51*M*r0 - 6*r0_2) + r0_2*(-52*M_2 + (35 + 3*E_2)*M*r0 - 3*r0_2)) - a_6*(3*L_2*(3*M + 6*E_2*M + r0 + E_2*r0) + 4*E_2*r0*(4*M_2 + 9*M*r0 + 2*r0_2)) + 2*a_5*E*L*(3*L_2*(3*M + r0) + r0*(-4*(-4 + E_2)*M_2 + (25 + 13*E_2)*M*r0 + 3*r0_2)) - a_4*(3*L_4*(2*M + r0) + L_2*r0*(-8*(-2 + 3*E_2)*M_2 + (14 + 81*E_2)*M*r0 + 2*(-1 + E_2)*r0_2) + 2*E_2*r0_2*(-40*M_3 - 16*M_2*r0 + 21*M*r0_2 + r0_3)) + a_2*r0*(4*E_2*r0_4*(8*M_2 - 7*M*r0 + 2*r0_2) + L_4*(8*M_2 - 29*M*r0 + 8*r0_2) + L_2*r0*(80*M_3 + 12*(-2 + 9*E_2)*M_2*r0 - (47 + 74*E_2)*M*r0_2 + (15 + 7*E_2)*r0_3)) - 2*a_3*E*L*r0*(3*L_2*(4*M_2 - 14*M*r0 + r0_2) + r0*(80*M_3 - (51 + 13*E_2)*M*r0_2 + 3*r0_3 + 4*M_2*(r0 + 3*E_2*r0)))))/expr2_5;\n A77200 = (-2*M*r0_5*(2*a_3*E*L*(23*M - 3*r0) - a_4*E_2*(23*M + r0) - 2*a*E*L*r0*(52*M_2 - 35*M*r0 + 3*r0_2) + (13*M - 5*r0)*r0*(L_2*(4*M - 2*r0) - E_2*r0_3) + a_2*(L_2*(-23*M + 7*r0) + 4*E_2*r0*(13*M_2 - 6*M*r0 + r0_2))))/expr2_5;\n A78000 = (4*M*r0_5*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/expr2_5;\n A79000 = (-2*M*r0_5*(10*a_3*E*L*M - a_4*E_2*(5*M + r0) + 2*a*E*L*M*r0*(-12*M + 7*r0) + (3*M - r0)*r0*(L_2*(4*M - 2*r0) - E_2*r0_3) + a_2*(4*E_2*M*(3*M - r0)*r0 + L_2*(-5*M + r0))))/expr2_6;\n }\n\n /* A_{theta,phi} */\n {\n A80161 = (-128*L*expr1_3*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/(r0_6*(a_2 + r0*(-2*M + r0)));\n A80341 = (-96*L*expr1_2*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/(r0_3*(a_2 + r0*(-2*M + r0)));\n A80521 = (-24*L*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/(a_2 + r0*(-2*M + r0));\n A80701 = 2*L*r0_3*(E*M*(a_3 - 3*a*r0_2) - L*(a_2*M + 2*r0_2*(-M + r0)) + (L*M*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/(a_2 + r0*(-2*M + r0)));\n A81161 = (64*expr1_2*(2*a_10*E_2*M_2*(2*M + r0) - a_9*E*L*M*(8*(1 + 3*E_2)*M_2 + (7 + 12*E_2)*M*r0 + 2*r0_2) + L_2*(2*M - r0)*r0_4*(8*L_4*M*(-2*M + r0) + 2*L_2*r0_2*(-8*M_2 + 3*E_2*M*r0 + 2*r0_2) + r0_4*(8*M_2 + (-16 + 7*E_2)*M*r0 + 6*r0_2)) + a*E*L*M*r0_4*(2*L_2*r0_2*(62*M_2 - (47 + 3*E_2)*M*r0 + 8*r0_2) + 2*L_4*(44*M_2 - 40*M*r0 + 9*r0_2) - r0_4*(40*M_2 + 6*(-11 + 2*E_2)*M*r0 + 23*r0_2)) + a_8*M*(4*E_2*M*r0*(-2*M_2 + r0_2) + L_2*((4 + 72*E_2)*M_2 + (5 + 37*E_2)*M*r0 + 2*(1 + E_2)*r0_2)) - a_7*E*L*M*(L_2*(72*M_2 + 2*(19 + 3*E_2)*M*r0 + 6*r0_2) + r0*(-16*(1 + 2*E_2)*M_3 + 8*(-1 + 11*E_2)*M_2*r0 + (15 + 64*E_2)*M*r0_2 + 9*r0_3)) + a_3*E*L*M*r0_2*(2*L_4*(12*M_2 - 33*M*r0 + 7*r0_2) + r0_3*(-116*M_3 + 12*(9 + 2*E_2)*M_2*r0 + (51 - 64*E_2)*M*r0_2 - 51*r0_3) + 2*L_2*r0*(152*M_3 + 12*(-4 + E_2)*M_2*r0 - (81 + 13*E_2)*M*r0_2 + 17*r0_3)) + a_5*E*L*M*r0*(-2*L_4*(9*M + 2*r0) + 2*L_2*(48*M_3 + 2*(-55 + 2*E_2)*M_2*r0 - (45 + 13*E_2)*M*r0_2 + 6*r0_3) - r0_2*((4 - 96*E_2)*M_3 + 4*(-21 + 10*E_2)*M_2*r0 + (23 + 104*E_2)*M*r0_2 + 35*r0_3)) + a_6*M*(-8*E_2*M*r0_4*(5*M + 2*r0) + L_4*(24*M_2 + (13 + 18*E_2)*M*r0 + 2*(2 + E_2)*r0_2) + L_2*r0*(-8*(1 + 12*E_2)*M_3 + 2*(-4 + 121*E_2)*M_2*r0 + 5*(2 + 29*E_2)*M*r0_2 - 7*(-1 + E_2)*r0_3)) + a_4*r0*(2*L_6*M*(3*M + r0) + 36*E_2*M_2*r0_4*(2*M_2 - r0_2) + L_4*M*(-32*M_3 + 6*(11 - 4*E_2)*M_2*r0 + 9*(1 + 8*E_2)*M*r0_2 - (5 + 6*E_2)*r0_3) + L_2*r0_2*((4 - 296*E_2)*M_4 + 4*(-12 + 23*E_2)*M_3*r0 + (33 + 217*E_2)*M_2*r0_2 - 3*(-4 + 9*E_2)*M*r0_3 - 6*r0_4)) - a_2*r0_2*(18*E_2*M_2*r0_6*(-2*M + r0) + 4*L_6*M*(2*M_2 - 5*M*r0 + 2*r0_2) + L_4*r0*(104*M_4 + 4*(-11 + 20*E_2)*M_3*r0 - 2*(19 + 37*E_2)*M_2*r0_2 + (9 + 14*E_2)*M*r0_3 + 4*r0_4) + L_2*r0_3*(-56*M_4 + 6*(16 + 17*E_2)*M_3*r0 - 3*(4 + 41*E_2)*M_2*r0_2 + 5*(-7 + 5*E_2)*M*r0_3 + 12*r0_4))))/(r0_8*expr2_2);\n A81341 = (16*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(6*a_10*E_2*M_2*(2*M + r0) - a_9*E*L*M*(24*(1 + 3*E_2)*M_2 + 12*(2 + 3*E_2)*M*r0 + 7*r0_2) + L_2*(2*M - r0)*r0_4*(26*L_4*M*(-2*M + r0) + 3*r0_4*(8*M_2 + (-16 + 7*E_2)*M*r0 + 6*r0_2) + L_2*r0_2*(-44*M_2 + (-6 + 19*E_2)*M*r0 + 14*r0_2)) + a*E*L*M*r0_4*(3*L_2*r0_2*(112*M_2 - 2*(39 + 4*E_2)*M*r0 + 11*r0_2) + 4*L_4*(76*M_2 - 68*M*r0 + 15*r0_2) - 3*r0_4*(40*M_2 + 6*(-11 + 2*E_2)*M*r0 + 23*r0_2)) + a_8*M*(12*E_2*M*r0*(-2*M_2 + r0_2) + L_2*(12*(1 + 18*E_2)*M_2 + 2*(9 + 61*E_2)*M*r0 + (7 + 9*E_2)*r0_2)) - a_7*E*L*M*(L_2*(216*M_2 + 8*(17 + 3*E_2)*M*r0 + 25*r0_2) + 2*r0*(-24*(1 + 2*E_2)*M_3 + 6*(-3 + 22*E_2)*M_2*r0 + (19 + 96*E_2)*M*r0_2 + 13*r0_3)) + a_5*E*L*M*r0*(-18*L_4*(4*M + r0) + L_2*(288*M_3 + 16*(-37 + 2*E_2)*M_2*r0 - 26*(11 + 4*E_2)*M*r0_2 + 23*r0_3) - 2*r0_2*((12 - 144*E_2)*M_3 + 4*(-28 + 15*E_2)*M_2*r0 + (31 + 156*E_2)*M*r0_2 + 50*r0_3)) + a_3*E*L*M*r0_2*(L_4*(96*M_2 - 236*M*r0 + 42*r0_2) - 6*r0_3*(52*M_3 - 2*(25 + 6*E_2)*M_2*r0 + (-25 + 32*E_2)*M*r0_2 + 25*r0_3) + L_2*r0*(864*M_3 + 8*(-31 + 12*E_2)*M_2*r0 - 8*(58 + 13*E_2)*M*r0_2 + 81*r0_3)) + a_6*(-24*E_2*M_2*r0_4*(5*M + 2*r0) + L_4*M*(72*M_2 + 2*(25 + 36*E_2)*M*r0 + (16 + 9*E_2)*r0_2) + L_2*r0*(-24*(1 + 12*E_2)*M_4 + 4*(-9 + 173*E_2)*M_3*r0 + 2*(13 + 224*E_2)*M_2*r0_2 + (27 - 14*E_2)*M*r0_3 + 2*r0_4)) + a_4*r0*(3*L_6*M*(8*M + 3*r0) + 108*E_2*M_2*r0_4*(2*M_2 - r0_2) + L_2*r0_2*((24 - 864*E_2)*M_4 + 8*(-16 + 31*E_2)*M_3*r0 + 2*(35 + 318*E_2)*M_2*r0_2 + (37 - 76*E_2)*M*r0_3 - 14*r0_4) + L_4*(-96*M_4 + 4*(41 - 24*E_2)*M_3*r0 + 2*(15 + 137*E_2)*M_2*r0_2 - (8 + 17*E_2)*M*r0_3 + 2*r0_4)) - a_2*r0_2*(54*E_2*M_2*r0_6*(-2*M + r0) + L_6*M*(32*M_2 - 66*M*r0 + 25*r0_2) + L_4*r0*(288*M_4 + 8*(-15 + 37*E_2)*M_3*r0 - 8*(13 + 34*E_2)*M_2*r0_2 + (22 + 45*E_2)*M*r0_3 + 12*r0_4) + L_2*r0_3*(-144*M_4 + 4*(62 + 69*E_2)*M_3*r0 - 22*(1 + 16*E_2)*M_2*r0_2 + (-101 + 74*E_2)*M*r0_3 + 34*r0_4))))/(r0_5*expr2_2);\n A81521 = (4*(6*a_10*E_2*M_2*(2*M + r0) - a_9*E*L*M*(24*(1 + 3*E_2)*M_2 + 9*(3 + 4*E_2)*M*r0 + 8*r0_2) + L_2*(2*M - r0)*r0_4*(28*L_4*M*(-2*M + r0) + 4*L_2*r0_2*(-10*M_2 + (-3 + 5*E_2)*M*r0 + 4*r0_2) + 3*r0_4*(8*M_2 + (-16 + 7*E_2)*M*r0 + 6*r0_2)) + a*E*L*M*r0_4*(6*L_2*r0_2*(50*M_2 - (31 + 5*E_2)*M*r0 + 3*r0_2) - 3*r0_4*(40*M_2 + 6*(-11 + 2*E_2)*M*r0 + 23*r0_2) + L_4*(344*M_2 - 304*M*r0 + 66*r0_2)) + a_8*M*(12*E_2*M*r0*(-2*M_2 + r0_2) + L_2*(12*(1 + 18*E_2)*M_2 + 7*(3 + 19*E_2)*M*r0 + 4*(2 + 3*E_2)*r0_2)) - a_7*E*L*M*(2*L_2*(108*M_2 + (79 + 15*E_2)*M*r0 + 16*r0_2) + r0*(-48*(1 + 2*E_2)*M_3 + 24*(-2 + 11*E_2)*M_2*r0 + (31 + 192*E_2)*M*r0_2 + 25*r0_3)) + a_3*E*L*M*r0_2*(2*L_4*(60*M_2 - 137*M*r0 + 21*r0_2) + 2*L_2*r0*(408*M_3 + 4*(-26 + 15*E_2)*M_2*r0 - 13*(17 + 5*E_2)*M*r0_2 + 30*r0_3) - 3*r0_3*(92*M_3 - 4*(23 + 6*E_2)*M_2*r0 + (-49 + 64*E_2)*M*r0_2 + 49*r0_3)) + a_5*E*L*M*r0*(-6*L_4*(15*M + 4*r0) + 2*L_2*(144*M_3 + 2*(-131 + 10*E_2)*M_2*r0 - (151 + 65*E_2)*M*r0_2 + 5*r0_3) - r0_2*(-36*(-1 + 8*E_2)*M_3 + 4*(-49 + 30*E_2)*M_2*r0 + (55 + 312*E_2)*M*r0_2 + 95*r0_3)) + a_6*(-24*E_2*M_2*r0_4*(5*M + 2*r0) + L_4*M*(72*M_2 + (61 + 90*E_2)*M*r0 + 4*(5 + 3*E_2)*r0_2) + L_2*r0*(-24*(1 + 12*E_2)*M_4 + 2*(-24 + 329*E_2)*M_3*r0 + (22 + 461*E_2)*M_2*r0_2 + (33 - 7*E_2)*M*r0_3 + 4*r0_4)) + a_4*r0*(6*L_6*M*(5*M + 2*r0) + 108*E_2*M_2*r0_4*(2*M_2 - r0_2) + L_2*r0_2*((36 - 840*E_2)*M_4 + 4*(-28 + 55*E_2)*M_3*r0 + (41 + 621*E_2)*M_2*r0_2 + (38 - 71*E_2)*M*r0_3 - 10*r0_4) + L_4*(-96*M_4 + 10*(13 - 12*E_2)*M_3*r0 + (33 + 332*E_2)*M_2*r0_2 - (1 + 16*E_2)*M*r0_3 + 4*r0_4)) - a_2*r0_2*(54*E_2*M_2*r0_6*(-2*M + r0) + 2*L_6*M*(20*M_2 - 36*M*r0 + 13*r0_2) + L_4*r0*(264*M_4 + 4*(-27 + 88*E_2)*M_3*r0 - 2*(47 + 161*E_2)*M_2*r0_2 + (17 + 48*E_2)*M*r0_3 + 12*r0_4) + L_2*r0_3*(-120*M_4 + 2*(104 + 123*E_2)*M_3*r0 - (8 + 335*E_2)*M_2*r0_2 + (-97 + 73*E_2)*M*r0_3 + 32*r0_4))))/(r0_2*expr2_2);\n A81701 = -((r0*(-2*a_8*E_2*M_2 + a_7*E*L*M*(4*(1 + 3*E_2)*M + 3*r0) - a_6*M*(2*E_2*M*r0*(-2*M + r0) + L_2*(2*M + 36*E_2*M + 3*r0 + 5*E_2*r0)) + a_5*E*L*M*(2*L_2*(18*M + 5*r0) + r0*(-8*(1 + 2*E_2)*M_2 + 2*(-3 + 26*E_2)*M*r0 + 5*r0_2)) - L_2*(2*M - r0)*r0_3*(10*L_2*M*(-2*M + r0) + r0_2*(8*M_2 + (-16 + 7*E_2)*M*r0 + 6*r0_2)) + a*E*L*M*r0_3*(-8*L_2*(16*M_2 - 14*M*r0 + 3*r0_2) + r0_2*(40*M_2 + 6*(-11 + 2*E_2)*M*r0 + 23*r0_2)) + a_3*E*L*M*r0*(-2*L_2*(24*M_2 - 52*M*r0 + 7*r0_2) + r0_2*((8 - 48*E_2)*M_2 + 4*(-7 + 13*E_2)*M*r0 + 25*r0_2)) + a_4*(18*E_2*M_2*r0_4 - L_4*M*(12*M + 5*r0) + L_2*r0*((4 + 48*E_2)*M_3 + 2*(4 - 65*E_2)*M_2*r0 + (-6 + 5*E_2)*M*r0_2 - 2*r0_3)) + a_2*r0*(18*E_2*M_2*r0_4*(-2*M + r0) + L_4*M*(16*M_2 - 26*M*r0 + 9*r0_2) + L_2*r0_2*(8*(-1 + 17*E_2)*M_3 - 2*(-9 + 62*E_2)*M_2*r0 + (-15 + 17*E_2)*M*r0_2 + 4*r0_3))))/expr2_2);\n A82141 = (-96*L*expr1_2*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/(r0_3*expr2_2);\n A82321 = (-48*L*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/expr2_2;\n A82501 = (-6*L*r0_3*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/expr2_2;\n A83141 = (-16*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-6*a_10*E_2*M_2*(2*M + r0) + a_9*E*L*M*(24*(1 + 3*E_2)*M_2 + 12*(2 + 3*E_2)*M*r0 + 7*r0_2) + a*E*L*M*r0_4*(L_4*(-312*M_2 + 286*M*r0 - 66*r0_2) + L_2*r0_2*(-338*M_2 + (239 + 24*E_2)*M*r0 - 36*r0_2) + 9*r0_4*(14*M_2 + (-23 + 4*E_2)*M*r0 + 8*r0_2)) - a_8*M*(12*E_2*M*r0*(-2*M_2 + r0_2) + L_2*(12*(1 + 18*E_2)*M_2 + 2*(9 + 61*E_2)*M*r0 + (7 + 9*E_2)*r0_2)) + L_2*r0_4*(2*L_4*M*(54*M_2 - 55*M*r0 + 14*r0_2) + L_2*r0_2*(88*M_3 - (28 + 39*E_2)*M_2*r0 + 20*(-2 + E_2)*M*r0_2 + 16*r0_3) + r0_4*(-52*M_3 + (130 - 43*E_2)*M_2*r0 + 2*(-46 + 11*E_2)*M*r0_2 + 20*r0_3)) + a_7*E*L*M*(L_2*(216*M_2 + 8*(17 + 3*E_2)*M*r0 + 25*r0_2) + r0*(-48*(1 + 2*E_2)*M_3 + 2*(-17 + 132*E_2)*M_2*r0 + (37 + 192*E_2)*M*r0_2 + 25*r0_3)) + a_5*E*L*M*r0*(18*L_4*(4*M + r0) + L_2*(-288*M_3 + 4*(151 - 8*E_2)*M_2*r0 + (281 + 104*E_2)*M*r0_2 - 30*r0_3) + r0_2*(-4*(-5 + 72*E_2)*M_3 + 2*(-113 + 60*E_2)*M_2*r0 + (67 + 312*E_2)*M*r0_2 + 101*r0_3)) + a_3*E*L*M*r0_2*(L_4*(-96*M_2 + 242*M*r0 - 48*r0_2) + L_2*r0*(-880*M_3 + (266 - 96*E_2)*M_2*r0 + 8*(59 + 13*E_2)*M*r0_2 - 91*r0_3) + r0_3*(324*M_3 - 2*(157 + 36*E_2)*M_2*r0 + 3*(-51 + 64*E_2)*M*r0_2 + 155*r0_3)) - a_6*(-24*E_2*M_2*r0_4*(5*M + 2*r0) + L_4*M*(72*M_2 + 2*(25 + 36*E_2)*M*r0 + (16 + 9*E_2)*r0_2) + L_2*r0*(-24*(1 + 12*E_2)*M_4 + 2*(-17 + 349*E_2)*M_3*r0 + 5*(5 + 89*E_2)*M_2*r0_2 + (26 - 17*E_2)*M*r0_3 + 2*r0_4)) - a_4*r0*(3*L_6*M*(8*M + 3*r0) + 108*E_2*M_2*r0_4*(2*M_2 - r0_2) + L_2*r0_2*((20 - 872*E_2)*M_4 + 4*(-32 + 65*E_2)*M_3*r0 + 3*(26 + 213*E_2)*M_2*r0_2 + (35 - 83*E_2)*M*r0_3 - 16*r0_4) + L_4*(-96*M_4 + 2*(85 - 48*E_2)*M_3*r0 + (28 + 277*E_2)*M_2*r0_2 - 4*(3 + 5*E_2)*M*r0_3 + 2*r0_4)) + a_2*r0_2*(54*E_2*M_2*r0_6*(-2*M + r0) + L_6*M*(32*M_2 - 69*M*r0 + 28*r0_2) + L_4*r0*(296*M_4 + 6*(-21 + 50*E_2)*M_3*r0 - 10*(11 + 28*E_2)*M_2*r0_2 + (24 + 49*E_2)*M*r0_3 + 14*r0_4) + L_2*r0_3*(-152*M_4 + 2*(133 + 139*E_2)*M_3*r0 - (29 + 359*E_2)*M_2*r0_2 + (-108 + 79*E_2)*M*r0_3 + 38*r0_4))))/(r0_5*expr2_3);\n A83321 = (8*(6*a_10*E_2*M_2*(2*M + r0) - a_9*E*L*M*(24*(1 + 3*E_2)*M_2 + 9*(3 + 4*E_2)*M*r0 + 8*r0_2) + a*E*L*M*r0_4*(-9*r0_4*(14*M_2 + (-23 + 4*E_2)*M*r0 + 8*r0_2) + L_2*r0_2*(302*M_2 - (191 + 30*E_2)*M*r0 + 21*r0_2) + L_4*(352*M_2 - 318*M*r0 + 72*r0_2)) + a_8*M*(12*E_2*M*r0*(-2*M_2 + r0_2) + L_2*(12*(1 + 18*E_2)*M_2 + 7*(3 + 19*E_2)*M*r0 + 4*(2 + 3*E_2)*r0_2)) + L_2*r0_4*(-2*L_4*M*(58*M_2 - 59*M*r0 + 15*r0_2) + r0_4*(52*M_3 + (-130 + 43*E_2)*M_2*r0 + 2*(46 - 11*E_2)*M*r0_2 - 20*r0_3) + L_2*r0_2*(-80*M_3 + (12 + 41*E_2)*M_2*r0 + (50 - 21*E_2)*M*r0_2 - 18*r0_3)) - 2*a_7*E*L*M*(L_2*(108*M_2 + (79 + 15*E_2)*M*r0 + 16*r0_2) + r0*(-24*(1 + 2*E_2)*M_3 + (-23 + 132*E_2)*M_2*r0 + 3*(5 + 32*E_2)*M*r0_2 + 12*r0_3)) + 2*a_3*E*L*M*r0_2*(4*L_4*(15*M_2 - 35*M*r0 + 6*r0_2) + r0_3*(-144*M_3 + (145 + 36*E_2)*M_2*r0 + 3*(25 - 32*E_2)*M*r0_2 - 76*r0_3) + L_2*r0*(416*M_3 + (-113 + 60*E_2)*M_2*r0 - 5*(45 + 13*E_2)*M*r0_2 + 35*r0_3)) + a_5*E*L*M*r0*(-6*L_4*(15*M + 4*r0) + L_2*(288*M_3 + 8*(-67 + 5*E_2)*M_2*r0 - (297 + 130*E_2)*M*r0_2 + 17*r0_3) - 2*r0_2*(-16*(-1 + 9*E_2)*M_3 + 3*(-33 + 20*E_2)*M_2*r0 + 6*(5 + 26*E_2)*M*r0_2 + 48*r0_3)) + a_6*(-24*E_2*M_2*r0_4*(5*M + 2*r0) + L_4*M*(72*M_2 + (61 + 90*E_2)*M*r0 + 4*(5 + 3*E_2)*r0_2) + L_2*r0*(-24*(1 + 12*E_2)*M_4 + 2*(-23 + 332*E_2)*M_3*r0 + (21 + 458*E_2)*M_2*r0_2 + 2*(16 - 5*E_2)*M*r0_3 + 4*r0_4)) + a_4*r0*(6*L_6*M*(5*M + 2*r0) + 108*E_2*M_2*r0_4*(2*M_2 - r0_2) + L_2*r0_2*((32 - 848*E_2)*M_4 + 8*(-14 + 29*E_2)*M_3*r0 + (49 + 624*E_2)*M_2*r0_2 + 6*(6 - 13*E_2)*M*r0_3 - 12*r0_4) + L_4*(-96*M_4 - 8*(-17 + 15*E_2)*M_3*r0 + (31 + 335*E_2)*M_2*r0_2 - (5 + 19*E_2)*M*r0_3 + 4*r0_4)) - a_2*r0_2*(54*E_2*M_2*r0_6*(-2*M + r0) + L_6*M*(40*M_2 - 75*M*r0 + 29*r0_2) + L_4*r0*(272*M_4 + 2*(-57 + 178*E_2)*M_3*r0 - 10*(10 + 33*E_2)*M_2*r0_2 + (19 + 52*E_2)*M*r0_3 + 14*r0_4) + L_2*r0_3*(-128*M_4 + 2*(113 + 124*E_2)*M_3*r0 - 3*(5 + 114*E_2)*M_2*r0_2 + 26*(-4 + 3*E_2)*M*r0_3 + 36*r0_4))))/(r0_2*expr2_3);\n A83501 = -((r0*(-6*a_8*E_2*M_2 + 3*a_7*E*L*M*(4*(1 + 3*E_2)*M + 3*r0) - 3*a_6*M*(2*E_2*M*r0*(-2*M + r0) + L_2*(2*M + 36*E_2*M + 3*r0 + 5*E_2*r0)) + a*E*L*M*r0_3*(L_2*(-392*M_2 + 350*M*r0 - 78*r0_2) + 9*r0_2*(14*M_2 + (-23 + 4*E_2)*M*r0 + 8*r0_2)) + a_5*E*L*M*(6*L_2*(18*M + 5*r0) + r0*(-24*(1 + 2*E_2)*M_2 + (-17 + 156*E_2)*M*r0 + 14*r0_2)) + a_3*E*L*M*r0*(-6*L_2*(24*M_2 - 53*M*r0 + 8*r0_2) + r0_2*((22 - 144*E_2)*M_2 + 12*(-7 + 13*E_2)*M*r0 + 77*r0_2)) + a_4*(54*E_2*M_2*r0_4 - 3*L_4*M*(12*M + 5*r0) + L_2*r0*(12*(1 + 12*E_2)*M_3 + (23 - 393*E_2)*M_2*r0 + (-17 + 18*E_2)*M*r0_2 - 6*r0_3)) + a_2*r0*(54*E_2*M_2*r0_4*(-2*M + r0) + 3*L_4*M*(16*M_2 - 27*M*r0 + 10*r0_2) + L_2*r0_2*((-22 + 412*E_2)*M_3 + (53 - 380*E_2)*M_2*r0 + (-48 + 55*E_2)*M*r0_2 + 14*r0_3)) + L_2*r0_3*(2*L_2*M*(62*M_2 - 63*M*r0 + 16*r0_2) + r0_2*(-52*M_3 + (130 - 43*E_2)*M_2*r0 + 2*(-46 + 11*E_2)*M*r0_2 + 20*r0_3))))/expr2_3);\n A84121 = (-24*L*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/expr2_3;\n A84301 = (-6*L*r0_3*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/expr2_3;\n A85121 = (-4*(-6*a_10*E_2*M_2*(2*M + r0) + a_9*E*L*M*(24*(1 + 3*E_2)*M_2 + 9*(3 + 4*E_2)*M*r0 + 8*r0_2) + a*E*L*M*r0_4*(L_4*(-360*M_2 + 332*M*r0 - 78*r0_2) + 2*L_2*r0_2*(-152*M_2 + (98 + 15*E_2)*M*r0 - 12*r0_2) + 3*r0_4*(44*M_2 + 12*(-6 + E_2)*M*r0 + 25*r0_2)) - a_8*M*(12*E_2*M*r0*(-2*M_2 + r0_2) + L_2*(12*(1 + 18*E_2)*M_2 + 7*(3 + 19*E_2)*M*r0 + 4*(2 + 3*E_2)*r0_2)) + L_2*r0_4*(4*L_4*M*(30*M_2 - 31*M*r0 + 8*r0_2) + 2*L_2*r0_2*(40*M_3 - (4 + 21*E_2)*M_2*r0 + (-28 + 11*E_2)*M*r0_2 + 10*r0_3) + r0_4*(-56*M_3 + 4*(35 - 11*E_2)*M_2*r0 + (-100 + 23*E_2)*M*r0_2 + 22*r0_3)) + a_7*E*L*M*(2*L_2*(108*M_2 + (79 + 15*E_2)*M*r0 + 16*r0_2) + r0*(-48*(1 + 2*E_2)*M_3 + 44*(-1 + 6*E_2)*M_2*r0 + (29 + 192*E_2)*M*r0_2 + 23*r0_3)) + a_5*E*L*M*r0*(6*L_4*(15*M + 4*r0) + L_2*(-288*M_3 + (548 - 40*E_2)*M_2*r0 + 2*(146 + 65*E_2)*M*r0_2 - 24*r0_3) + r0_2*(-4*(-7 + 72*E_2)*M_3 + 40*(-5 + 3*E_2)*M_2*r0 + 13*(5 + 24*E_2)*M*r0_2 + 97*r0_3)) + a_3*E*L*M*r0_2*(-2*L_4*(60*M_2 - 143*M*r0 + 27*r0_2) - 2*L_2*r0*(424*M_3 + 2*(-61 + 30*E_2)*M_2*r0 - (229 + 65*E_2)*M*r0_2 + 40*r0_3) + r0_3*(300*M_3 - 8*(38 + 9*E_2)*M_2*r0 + 3*(-51 + 64*E_2)*M*r0_2 + 157*r0_3)) - a_6*(-24*E_2*M_2*r0_4*(5*M + 2*r0) + L_4*M*(72*M_2 + (61 + 90*E_2)*M*r0 + 4*(5 + 3*E_2)*r0_2) + L_2*r0*(-24*(1 + 12*E_2)*M_4 + 2*(-22 + 335*E_2)*M_3*r0 + 5*(4 + 91*E_2)*M_2*r0_2 + (31 - 13*E_2)*M*r0_3 + 4*r0_4)) - a_4*r0*(6*L_6*M*(5*M + 2*r0) + 108*E_2*M_2*r0_4*(2*M_2 - r0_2) + L_2*r0_2*((28 - 856*E_2)*M_4 + 4*(-28 + 61*E_2)*M_3*r0 + 57*(1 + 11*E_2)*M_2*r0_2 + 17*(2 - 5*E_2)*M*r0_3 - 14*r0_4) + L_4*(-96*M_4 - 2*(-71 + 60*E_2)*M_3*r0 + (29 + 338*E_2)*M_2*r0_2 - (9 + 22*E_2)*M*r0_3 + 4*r0_4)) + a_2*r0_2*(54*E_2*M_2*r0_6*(-2*M + r0) + 2*L_6*M*(20*M_2 - 39*M*r0 + 16*r0_2) + L_4*r0*(280*M_4 + 120*(-1 + 3*E_2)*M_3*r0 - 2*(53 + 169*E_2)*M_2*r0_2 + 7*(3 + 8*E_2)*M*r0_3 + 16*r0_4) + L_2*r0_3*(-136*M_4 + 2*(122 + 125*E_2)*M_3*r0 - (22 + 349*E_2)*M_2*r0_2 + (-111 + 83*E_2)*M*r0_3 + 40*r0_4))))/(r0_2*expr2_4);\n A85301 = -((r0*(-6*a_8*E_2*M_2 + 3*a_7*E*L*M*(4*(1 + 3*E_2)*M + 3*r0) - 3*a_6*M*(2*E_2*M*r0*(-2*M + r0) + L_2*(2*M + 36*E_2*M + 3*r0 + 5*E_2*r0)) + a_5*E*L*M*(6*L_2*(18*M + 5*r0) + r0*(-24*(1 + 2*E_2)*M_2 + 4*(-4 + 39*E_2)*M*r0 + 13*r0_2)) + a*E*L*M*r0_3*(-4*L_2*(100*M_2 - 91*M*r0 + 21*r0_2) + 3*r0_2*(44*M_2 + 12*(-6 + E_2)*M*r0 + 25*r0_2)) + a_3*E*L*M*r0*(-18*L_2*(8*M_2 - 18*M*r0 + 3*r0_2) + r0_2*(-4*(-5 + 36*E_2)*M_2 + 12*(-7 + 13*E_2)*M*r0 + 79*r0_2)) + a_4*(54*E_2*M_2*r0_4 - 3*L_4*M*(12*M + 5*r0) + L_2*r0*(12*(1 + 12*E_2)*M_3 + 22*(1 - 18*E_2)*M_2*r0 + (-16 + 21*E_2)*M*r0_2 - 6*r0_3)) + a_2*r0*(54*E_2*M_2*r0_4*(-2*M + r0) + 3*L_4*M*(16*M_2 - 28*M*r0 + 11*r0_2) + L_2*r0_2*(4*(-5 + 104*E_2)*M_3 + 4*(13 - 97*E_2)*M_2*r0 + (-51 + 59*E_2)*M*r0_2 + 16*r0_3)) + L_2*r0_3*(2*L_2*M*(64*M_2 - 66*M*r0 + 17*r0_2) + r0_2*(-56*M_3 + 4*(35 - 11*E_2)*M_2*r0 + (-100 + 23*E_2)*M*r0_2 + 22*r0_3))))/expr2_4);\n A86101 = (-2*L*r0_3*(-(a_5*E*M) + a_4*(1 + 3*E_2)*L*M + a*E*M*r0*(L_2*(8*M - 6*r0) + 3*r0_2*(-2*M + r0)) + 2*a_3*E*M*(-3*L_2 + r0*(M + r0)) + L*r0*(2*L_2*M*(-2*M + r0) + r0_2*(4*M_2 + (-6 + E_2)*M*r0 + 2*r0_2)) + a_2*L*(3*L_2*M + r0*(-2*(1 + 2*E_2)*M_2 + (-1 + 4*E_2)*M*r0 + 2*r0_2))))/expr2_4;\n A87101 = -((r0*(-2*a_8*E_2*M_2 + a_7*E*L*M*(4*(1 + 3*E_2)*M + 3*r0) - a_6*M*(2*E_2*M*r0*(-2*M + r0) + L_2*(2*M + 36*E_2*M + 3*r0 + 5*E_2*r0)) + a_5*E*L*M*(2*L_2*(18*M + 5*r0) + r0*(-8*(1 + 2*E_2)*M_2 + (-5 + 52*E_2)*M*r0 + 4*r0_2)) + a*E*L*M*r0_3*(-2*L_2*(68*M_2 - 63*M*r0 + 15*r0_2) + r0_2*(46*M_2 + 3*(-25 + 4*E_2)*M*r0 + 26*r0_2)) + a_3*E*L*M*r0*(-2*L_2*(24*M_2 - 55*M*r0 + 10*r0_2) + r0_2*((6 - 48*E_2)*M_2 + 4*(-7 + 13*E_2)*M*r0 + 27*r0_2)) + a_4*(18*E_2*M_2*r0_4 - L_4*M*(12*M + 5*r0) + L_2*r0*((4 + 48*E_2)*M_3 + 7*(1 - 19*E_2)*M_2*r0 + (-5 + 8*E_2)*M*r0_2 - 2*r0_3)) + a_2*r0*(18*E_2*M_2*r0_4*(-2*M + r0) + L_4*M*(16*M_2 - 29*M*r0 + 12*r0_2) + L_2*r0_2*(2*(-3 + 70*E_2)*M_3 + (17 - 132*E_2)*M_2*r0 + 3*(-6 + 7*E_2)*M*r0_2 + 6*r0_3)) + L_2*r0_3*(2*L_2*M*(22*M_2 - 23*M*r0 + 6*r0_2) + r0_2*(-20*M_3 + 5*(10 - 3*E_2)*M_2*r0 + 4*(-9 + 2*E_2)*M*r0_2 + 8*r0_3))))/expr2_5);\n }\n\n /* A_{phi,phi} */\n {\n A90060 = 256*L_2*expr4_3;\n A90080 = (-128*expr1_2*(-24*a_9*E*L*M_2*(2*M + r0) - 4*a_7*E*L*M*(192*M_4 + 5*L_2*M*r0 + 264*M_3*r0 + 180*M_2*r0_2 + 42*M*r0_3 - 6*r0_4) - 4*a*E*L*M*r0_5*(48*L_4*M + L_2*(106*M - 15*r0)*r0_2 + 6*(10*M - 3*r0)*r0_4) + a_8*M*(24*E_2*r0_p_2M_4 + L_2*M*(48*M + 23*r0)) - 4*a_3*E*L*M*r0_2*(48*L_4*M*(2*M + r0) + L_2*r0_2*(274*M_2 + 177*M*r0 - 20*r0_2) + 6*r0_4*(30*M_2 + 17*M*r0 - 7*r0_2)) + r0_7*(24*E_2*M*r0_5 + 2*L_2*r0_2*(46*M_2 + (-47 + 38*E_2)*M*r0 + 12*r0_2) + L_4*(80*M_2 + 2*(-41 + 24*E_2)*M*r0 + 21*r0_2)) - 4*a_5*E*L*M*r0*(6*r0_2*(36*M_3 + 50*M_2*r0 + 13*M*r0_2 - 5*r0_3) + L_2*(304*M_3 + 294*M_2*r0 + 96*M*r0_2 - 5*r0_3)) + a_2*r0_2*(192*L_6*M_3 + 96*E_2*M*r0_7*(2*M + r0) + L_4*r0_2*(224*M_3 + 24*(5 + 8*E_2)*M_2*r0 + 16*(-5 + 6*E_2)*M*r0_2 + 21*r0_3) + 2*L_2*r0_4*(100*M_3 + 6*(3 + 38*E_2)*M_2*r0 + 3*(-23 + 38*E_2)*M*r0_2 + 24*r0_3)) + a_4*r0*(144*E_2*M*r0_5*r0_p_2M_2 + 4*L_4*M*(152*M_3 + 6*(11 + 8*E_2)*M_2*r0 + 3*(5 + 16*E_2)*M*r0_2 + 2*(-5 + 6*E_2)*r0_3) + L_2*r0_2*(188*M_4 + 4*(85 + 228*E_2)*M_3*r0 + 3*(5 + 304*E_2)*M_2*r0_2 + 6*(-15 + 38*E_2)*M*r0_3 + 24*r0_4)) + 2*a_6*M*(10*L_4*M*r0 + 48*E_2*r0_3*r0_p_2M_3 + L_2*(192*M_4 + 16*(9 + 19*E_2)*M_3*r0 + 2*(49 + 228*E_2)*M_2*r0_2 + (-1 + 228*E_2)*M*r0_3 + (-23 + 38*E_2)*r0_4))))/(3.*r0_9*(a_2 + r0*(-2*M + r0)));\n A90240 = 192*L_2*expr1_2;\n A90260 = (-64*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-12*a_9*E*L*M*(14*M_2 + 11*M*r0 + 2*r0_2) - 2*a*E*L*M*r0_5*(L_2*(358*M - 39*r0)*r0_2 + 6*(34*M - 9*r0)*r0_4 + L_4*(158*M + 9*r0)) - 2*a_3*E*L*M*r0_2*(6*r0_4*(114*M_2 + 59*M*r0 - 19*r0_2) + L_2*r0_2*(964*M_2 + 598*M*r0 - 19*r0_2) + 2*L_4*(164*M_2 + 79*M*r0 + 12*r0_2)) + r0_5*(48*E_2*M*r0_7 - 2*L_6*(8*M_2 + 2*M*r0 - 3*r0_2) + 2*L_4*r0_2*(54*M_2 + (-75 + 44*E_2)*M*r0 + 24*r0_2) + L_2*r0_4*(136*M_2 + 2*(-79 + 70*E_2)*M*r0 + 45*r0_2)) + a_8*M*(48*E_2*r0_p_2M_4 + L_2*(24*(7 + E_2)*M_2 + (125 + 24*E_2)*M*r0 + 3*(7 + 2*E_2)*r0_2)) - 2*a_5*E*L*M*r0*(3*L_4*(4*M + 5*r0) + 6*r0_2*(156*M_3 + 182*M_2*r0 + 51*M*r0_2 - 9*r0_3) + L_2*(1072*M_3 + 980*M_2*r0 + 386*M*r0_2 + 47*r0_3)) + a_2*r0_2*(192*E_2*M*r0_7*(2*M + r0) + L_6*(328*M_3 - 36*M_2*r0 + 32*M*r0_2 + 6*r0_3) + L_4*r0_2*(380*M_3 + 4*(12 + 85*E_2)*M_2*r0 + 7*(-9 + 26*E_2)*M*r0_2 + 63*r0_3) + L_2*r0_4*(340*M_3 + 12*(-5 + 69*E_2)*M_2*r0 + 3*(-61 + 142*E_2)*M*r0_2 + 99*r0_3)) - 2*a_7*E*L*M*(L_2*(24*M_2 + 82*M*r0 + 27*r0_2) + 6*(128*M_4 + 164*M_3*r0 + 106*M_2*r0_2 + 37*M*r0_3 + 3*r0_4)) + a_4*r0*(288*E_2*M*r0_5*r0_p_2M_2 + 12*L_6*M*(M + 2*r0) + L_4*(1072*M_4 + 8*(38 + 41*E_2)*M_3*r0 + 4*(35 + 88*E_2)*M_2*r0_2 + 2*(33 + 50*E_2)*M*r0_3 + 15*r0_4) + L_2*r0_2*(484*M_4 + 8*(43 + 204*E_2)*M_3*r0 + 3*(-1 + 560*E_2)*M_2*r0_2 + 3*(-5 + 146*E_2)*M*r0_3 + 63*r0_4)) + a_6*(192*E_2*M*r0_3*r0_p_2M_3 + L_4*M*(24*M_2 + 4*(35 + 3*E_2)*M*r0 + 3*(15 + 2*E_2)*r0_2) + L_2*(768*M_5 + 16*(27 + 67*E_2)*M_4*r0 + 36*(7 + 46*E_2)*M_3*r0_2 + 6*(29 + 146*E_2)*M_2*r0_3 + (31 + 158*E_2)*M*r0_4 + 9*r0_5))))/(3.*r0_6*(a_2 + r0*(-2*M + r0)));\n A90420 = 48*L_2*r0_3*(a_2*(2*M + r0) + r0*(L_2 + r0_2));\n A90440 = (-8*(-72*a_9*E*L*M*(10*M_2 + 9*M*r0 + 2*r0_2) + 4*a*E*L*M*r0_3*(L_6*(8*M - 6*r0) - 30*L_4*r0_2*(6*M + r0) + 18*r0_6*(-14*M + 3*r0) + 3*L_2*r0_4*(-146*M + 9*r0)) - 4*a_3*E*L*M*r0_2*(6*L_6 + 18*r0_4*(54*M_2 + 25*M*r0 - 5*r0_2) + 12*L_4*(32*M_2 + 15*M*r0 + 7*r0_2) + L_2*r0_2*(1266*M_2 + 721*M*r0 + 64*r0_2)) + r0_3*(144*E_2*M*r0_9 + 8*L_8*M*(-2*M + r0) + L_6*r0_2*(-100*M_2 + 4*(-11 + E_2)*M*r0 + 47*r0_2) + L_2*r0_6*(264*M_2 + 2*(-197 + 192*E_2)*M*r0 + 131*r0_2) + L_4*r0_4*(168*M_2 + 2*(-217 + 120*E_2)*M*r0 + 175*r0_2)) + a_8*(144*E_2*M*r0_p_2M_4 + L_2*(144*(5 + E_2)*M_3 + (635 + 144*E_2)*M_2*r0 + 36*(4 + E_2)*M*r0_2 + 3*r0_3)) - 4*a_5*E*L*M*r0*(6*L_4*(8*M + 9*r0) + 18*r0_2*(84*M_3 + 82*M_2*r0 + 25*M*r0_2 + r0_3) + L_2*(1392*M_3 + 1166*M_2*r0 + 572*M*r0_2 + 175*r0_3)) + a_2*r0_2*(12*L_8*M + 576*E_2*M*r0_7*(2*M + r0) + 2*L_6*(384*M_3 - 8*(15 + E_2)*M_2*r0 + 2*(53 + 4*E_2)*M*r0_2 + 25*r0_3) + 2*L_2*r0_4*(420*M_3 + 2*(-157 + 558*E_2)*M_2*r0 + 27*(-5 + 22*E_2)*M*r0_2 + 162*r0_3) + L_4*r0_2*(960*M_3 + 32*(-17 + 27*E_2)*M_2*r0 + 12*(9 + 44*E_2)*M*r0_2 + 287*r0_3)) - 4*a_7*E*L*M*(L_2*(72*M_2 + 221*M*r0 + 84*r0_2) + 18*(64*M_4 + 76*M_3*r0 + 46*M_2*r0_2 + 23*M*r0_3 + 5*r0_4)) + a_4*r0*(864*E_2*M*r0_5*r0_p_2M_2 + 3*L_6*(32*M_2 + 4*(14 + E_2)*M*r0 + r0_2) + 2*L_4*(1392*M_4 + 4*(25 + 96*E_2)*M_3*r0 + 2*(107 + 240*E_2)*M_2*r0_2 + 8*(44 + 21*E_2)*M*r0_3 + 59*r0_4) + L_2*r0_2*(1740*M_4 + 4*(-7 + 1080*E_2)*M_3*r0 + (-161 + 4608*E_2)*M_2*r0_2 + 6*(83 + 210*E_2)*M*r0_3 + 258*r0_4)) + 2*a_6*(288*E_2*M*r0_3*r0_p_2M_3 + L_4*(72*M_3 + 2*(185 + 24*E_2)*M_2*r0 + 6*(25 + 4*E_2)*M*r0_2 + 3*r0_3) + L_2*(1152*M_5 + 48*(9 + 29*E_2)*M_4*r0 + 2*(77 + 1116*E_2)*M_3*r0_2 + 7*(77 + 180*E_2)*M_2*r0_3 + (259 + 246*E_2)*M*r0_4 + 34*r0_5))))/(3.*r0_3*(a_2 + r0*(-2*M + r0)));\n A90600 = 4*L_2*r0_6;\n A90620 = (4*(12*a_7*E*L*M*(13*M + 6*r0) + 6*a_5*E*L*M*(128*M_3 + 76*M_2*r0 + 40*M*r0_2 + 22*r0_3 + L_2*(12*M + 17*r0)) + 2*a*E*L*M*r0_2*(-4*L_4*(4*M - 3*r0) + 6*(22*M - 3*r0)*r0_4 + L_2*r0_2*(94*M + 21*r0)) - 3*a_6*(16*E_2*M*r0_p_2M_3 + L_2*(4*(13 + 3*E_2)*M_2 + (25 + 6*E_2)*M*r0 + r0_2)) - r0_2*(48*E_2*M*r0_7 + 8*L_6*M*(-2*M + r0) + 4*L_2*r0_4*(10*M_2 + (-27 + 17*E_2)*M*r0 + 11*r0_2) + L_4*r0_2*(-36*M_2 + 4*(-10 + E_2)*M*r0 + 29*r0_2)) + 4*a_3*E*L*M*r0*(6*L_4 + 3*r0_2*(58*M_2 + 25*M*r0 + 2*r0_2) + L_2*(100*M_2 + 35*M*r0 + 36*r0_2)) - a_2*r0*(12*L_6*M + 144*E_2*M*r0_5*(2*M + r0) + 4*L_4*(50*M_3 - (33 + 4*E_2)*M_2*r0 + 4*(6 + E_2)*M*r0_2 + 8*r0_3) + L_2*r0_2*(140*M_3 + 4*(-50 + 59*E_2)*M_2*r0 + (23 + 154*E_2)*M*r0_2 + 79*r0_3)) - a_4*(144*E_2*M*r0_3*r0_p_2M_2 + 3*L_4*(12*M_2 + 4*(7 + E_2)*M*r0 + r0_2) + 2*L_2*(192*M_4 + 20*(-3 + 5*E_2)*M_3*r0 + 8*(2 + 17*E_2)*M_2*r0_2 + 13*(7 + 4*E_2)*M*r0_3 + 19*r0_4))))/(3.*(a_2 + r0*(-2*M + r0)));\n A90800 = (r0_3*(48*a_3*E*L*M - 24*L_2*(2*a_2*M + r0_3) + L_2*r0*(-3*a_2 + r0*(-2*M + r0)) - (24*M*expr8_2)/(a_2 + r0*(-2*M + r0)) + (4*L_2*M*(-3*a_4*E_2 + 6*a_3*E*L + 2*a*E*L*r0*(-4*M + 3*r0) + a_2*(-3*L_2 + 4*E_2*(M - r0)*r0) - r0*(E_2*r0_3 + L_2*(-4*M + 2*r0))))/(a_2 + r0*(-2*M + r0))))/6.;\n A91060 = (128*L*expr1_2*(4*a_5*E*M*(2*M + r0) - a_4*L*M*(8*M + 3*r0) + 6*a*E*M*r0_3*(L_2 + 2*r0_2) - L*(2*M - r0)*r0_3*(2*L_2 + 3*r0_2) + 2*a_3*E*M*r0*(L_2 + 4*r0*(3*M + 2*r0)) - a_2*L*r0*(2*L_2*M + 3*r0*(6*M_2 + M*r0 - r0_2))))/(r0_5*(a_2 + r0*(-2*M + r0)));\n A91080 = (-64*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-48*a_14*E_2*M_3*r0_p_2M_2 + 4*a_13*E*L*M_2*(96*M_3 + 226*M_2*r0 + 161*M*r0_2 + 36*r0_3) + 2*a*E*L*M*r0_6*(L_4*r0_4*(56*M_2 + 2*(313 + 222*E_2)*M*r0 - 327*r0_2) + 6*L_6*r0_2*(68*M_2 + 4*(14 + 5*E_2)*M*r0 - 45*r0_2) + 2*L_2*r0_6*(58*M_2 + (-23 + 288*E_2)*M*r0 - 3*r0_2) + 60*L_8*(4*M_2 - r0_2) + 12*r0_8*(30*M_2 + (-41 + 24*E_2)*M*r0 + 13*r0_2)) - (2*M - r0)*r0_8*(48*E_2*M*r0_9 - 24*L_8*M*(4*M - (2 + 5*E_2)*r0) + 2*L_6*r0_2*(-64*M_2 + 2*(-5 + 129*E_2)*M*r0 + 21*r0_2) + 2*L_2*r0_6*(92*M_2 + (-118 + 205*E_2)*M*r0 + 36*r0_2) + L_4*r0_4*(116*M_2 + 2*(-134 + 373*E_2)*M*r0 + 105*r0_2)) + 4*a_3*E*L*M*r0_4*(30*L_8*(12*M_2 - 2*M*r0 - r0_2) + L_4*r0_3*(244*M_3 + 2*(649 + 444*E_2)*M_2*r0 + (899 + 618*E_2)*M*r0_2 - 543*r0_3) + L_2*r0_5*(-216*M_3 + 2*(131 + 864*E_2)*M_2*r0 + 2*(337 + 518*E_2)*M*r0_2 - 177*r0_3) + 6*L_6*r0*(84*M_3 + 4*(46 + 5*E_2)*M_2*r0 + 2*(13 + 10*E_2)*M*r0_2 - 45*r0_3) + 2*r0_7*(204*M_3 + 2*(-139 + 288*E_2)*M_2*r0 + (-119 + 320*E_2)*M*r0_2 + 120*r0_3)) + a_2*r0_4*(-240*L_10*M_2*(2*M - r0) + 24*E_2*M*r0_10*(-46*M_2 + 13*M*r0 + 7*r0_2) + 24*L_8*M*r0*(32*M_3 - 2*(27 + 20*E_2)*M_2*r0 + (3 - 20*E_2)*M*r0_2 + 2*(4 + 5*E_2)*r0_3) - 2*L_2*r0_7*(804*M_4 + 4*(-304 + 685*E_2)*M_3*r0 + 5*(21 + 122*E_2)*M_2*r0_2 + (367 - 763*E_2)*M*r0_3 - 108*r0_4) + 2*L_6*r0_3*(1256*M_4 - 12*(43 + 182*E_2)*M_3*r0 - 2*(287 + 516*E_2)*M_2*r0_2 + (217 + 654*E_2)*M*r0_3 + 21*r0_4) + L_4*r0_5*(880*M_4 + 4*(383 - 1890*E_2)*M_3*r0 - 8*(160 + 361*E_2)*M_2*r0_2 + 21*(-13 + 112*E_2)*M*r0_3 + 210*r0_4)) + 2*a_5*E*L*M*r0_3*(6*L_6*(696*M_3 + 8*(39 + 5*E_2)*M_2*r0 + 20*(1 + E_2)*M*r0_2 - 45*r0_3) + L_4*r0*(32*M_4 + 24*(309 + 74*E_2)*M_3*r0 + 144*(49 + 22*E_2)*M_2*r0_2 + 4*(449 + 285*E_2)*M*r0_3 - 1149*r0_4) + L_2*r0_3*(-4236*M_4 + 4*(515 + 1728*E_2)*M_3*r0 + 3*(2395 + 2992*E_2)*M_2*r0_2 + 276*(11 + 10*E_2)*M*r0_3 - 894*r0_4) + 2*r0_5*(-2340*M_4 + 108*(-7 + 32*E_2)*M_3*r0 + (-249 + 3968*E_2)*M_2*r0_2 + 4*(131 + 280*E_2)*M*r0_3 + 240*r0_4)) + 2*a_11*E*L*M*r0*(5*L_2*M*(144*M_2 + 191*M*r0 + 60*r0_2) + 4*(64*(15 + 8*E_2)*M_5 + 4*(481 + 256*E_2)*M_4*r0 + 3*(529 + 256*E_2)*M_3*r0_2 + (683 + 256*E_2)*M_2*r0_3 + (115 + 32*E_2)*M*r0_4 - 6*r0_5)) - a_12*M*(L_2*M*(192*M_3 + 8*(89 + 90*E_2)*M_2*r0 + (587 + 696*E_2)*M*r0_2 + 6*(23 + 28*E_2)*r0_3) + 24*E_2*r0*(160*M_5 + 440*M_4*r0 + 412*M_3*r0_2 + 170*M_2*r0_3 + 33*M*r0_4 + 3*r0_5)) + 2*a_7*E*L*M*r0_2*(144*L_6*M*r0 + 2*L_4*(4128*M_4 + 8*(611 + 87*E_2)*M_3*r0 + 2*(1285 + 348*E_2)*M_2*r0_2 + 6*(90 + 29*E_2)*M*r0_3 - 195*r0_4) + L_2*r0*(-4736*M_5 + 12*(301 + 384*E_2)*M_4*r0 + 8*(1877 + 1380*E_2)*M_3*r0_2 + (12329 + 7584*E_2)*M_2*r0_3 + 8*(334 + 201*E_2)*M*r0_4 - 750*r0_5) + 12*r0_3*(-1164*M_5 + 4*(-215 + 192*E_2)*M_4*r0 + (235 + 1408*E_2)*M_3*r0_2 + (369 + 832*E_2)*M_2*r0_3 + 4*(39 + 40*E_2)*M*r0_4 + 10*r0_5)) - a_6*r0_2*(144*L_8*M_2*r0 - 48*E_2*M*r0_6*(200*M_4 + 68*M_3*r0 - 31*M_2*r0_2 + M*r0_3 - 5*r0_4) + 4*L_6*M*(1376*M_4 + 4*(353 + 522*E_2)*M_3*r0 + 168*(2 + 9*E_2)*M_2*r0_2 + 2*(29 + 156*E_2)*M*r0_3 - 3*(36 + 23*E_2)*r0_4) + L_4*M*r0*(-9344*M_5 + 8*(35 + 1732*E_2)*M_4*r0 + 8*(1095 + 4148*E_2)*M_3*r0_2 + 26*(229 + 932*E_2)*M_2*r0_3 + 2*(597 + 2624*E_2)*M*r0_4 - (1115 + 1088*E_2)*r0_5) + L_2*r0_3*(-11144*M_6 + 4*(-773 + 3824*E_2)*M_5*r0 + 2*(607 + 16744*E_2)*M_4*r0_2 + (2449 + 25488*E_2)*M_3*r0_3 + (1889 + 4936*E_2)*M_2*r0_4 - 4*(97 + 239*E_2)*M*r0_5 - 72*r0_6)) + 2*a_9*E*L*M*r0*(12*L_4*M*r0*(52*M + 31*r0) + L_2*(6144*M_5 + 32*(437 + 86*E_2)*M_4*r0 + 12*(1097 + 344*E_2)*M_3*r0_2 + 3*(2345 + 688*E_2)*M_2*r0_3 + 2*(665 + 172*E_2)*M*r0_4 - 204*r0_5) + 4*r0*(-2112*M_6 + 4*(-787 + 288*E_2)*M_5*r0 + 2*(289 + 1664*E_2)*M_4*r0_2 + (2521 + 3264*E_2)*M_3*r0_3 + 2*(733 + 672*E_2)*M_2*r0_4 + (307 + 200*E_2)*M*r0_5 - 15*r0_6)) - a_10*M*r0*(2*L_4*M*(360*M_2 + (607 + 312*E_2)*M*r0 + 3*(71 + 52*E_2)*r0_2) + L_2*(768*(5 + 16*E_2)*M_5 + 32*(151 + 821*E_2)*M_4*r0 + 2*(1505 + 13176*E_2)*M_3*r0_2 + 3*(493 + 4568*E_2)*M_2*r0_3 + (65 + 2996*E_2)*M*r0_4 + 6*(-23 + 19*E_2)*r0_5) + 24*E_2*r0*(-352*M_6 - 720*M_5*r0 + 24*M_4*r0_2 + 704*M_3*r0_3 + 450*M_2*r0_4 + 111*M*r0_5 + 13*r0_6)) - a_8*M*r0*(48*L_6*M*r0*(13*M + 3*(3 + E_2)*r0) + 48*E_2*r0_4*(-392*M_5 - 436*M_4*r0 + 68*M_3*r0_2 + 174*M_2*r0_3 + 55*M*r0_4 + 10*r0_5) + 2*L_4*(2048*M_5 + 48*(103 + 172*E_2)*M_4*r0 + 20*(153 + 554*E_2)*M_3*r0_2 + (1525 + 6532*E_2)*M_2*r0_3 + 5*(39 + 314*E_2)*M*r0_4 - 3*(71 + 19*E_2)*r0_5) + L_2*r0*(-8448*M_6 + 32*(-247 + 284*E_2)*M_5*r0 + 4*(1173 + 8392*E_2)*M_4*r0_2 + 4*(1367 + 11612*E_2)*M_3*r0_3 + (3221 + 29360*E_2)*M_2*r0_4 + (437 + 6836*E_2)*M*r0_5 + 2*(-194 + 23*E_2)*r0_6)) - a_4*r0_3*(24*E_2*M*r0_8*(28*M_3 + 42*M_2*r0 - 51*M*r0_2 - 5*r0_3) + 2*L_6*M*r0*(-2288*M_4 + 8*(233 + 396*E_2)*M_3*r0 + 12*(135 + 394*E_2)*M_2*r0_2 + 4*(97 + 267*E_2)*M*r0_3 - (443 + 534*E_2)*r0_4) + L_2*r0_5*(-1392*M_5 + 4*(-331 + 3264*E_2)*M_4*r0 + 8*(-263 + 1827*E_2)*M_3*r0_2 + (2245 + 1328*E_2)*M_2*r0_3 + 12*(18 - 167*E_2)*M*r0_4 - 216*r0_5) + L_4*r0_3*(-8008*M_5 + 80*(-1 + 201*E_2)*M_4*r0 + 2*(1439 + 9676*E_2)*M_3*r0_2 + 6*(457 + 636*E_2)*M_2*r0_3 - 6*(149 + 430*E_2)*M*r0_4 - 105*r0_5) + 24*L_8*M*(116*M_3 + (-13 + 10*E_2)*M*r0_2 - (6 + 5*E_2)*r0_3 + 20*M_2*(r0 + 3*E_2*r0)))))/(3.*r0_11*expr2_2);\n A91240 = (-32*L*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-12*a_5*E*M*(2*M + r0) + a_4*L*(24*M_2 + 12*M*r0 + r0_2) - 12*a*E*M*r0_3*(2*L_2 + 3*r0_2) - 8*a_3*E*M*r0*(L_2 + 9*M*r0 + 6*r0_2) + L*(2*M - r0)*r0_3*(7*L_2 + 9*r0_2) + a_2*L*r0*(L_2*(8*M + r0) + 2*r0*(24*M_2 + 5*M*r0 - 4*r0_2))))/(r0_2*(a_2 + r0*(-2*M + r0)));\n A91260 = (-16*(-48*a_14*E_2*M_2*r0_p_2M_2*(7*M + 2*r0) + 8*a_13*E*L*M*(2*M + r0)*(24*(7 + E_2)*M_3 + (365 + 24*E_2)*M_2*r0 + 6*(36 + E_2)*M*r0_2 + 36*r0_3) + 2*a*E*L*M*r0_6*(2*L_6*r0_2*(728*M_2 + 2*(241 + 105*E_2)*M*r0 - 423*r0_2) + 3*L_4*r0_4*(16*M_2 + 2*(283 + 256*E_2)*M*r0 - 287*r0_2) + 210*L_8*(4*M_2 - r0_2) + 24*r0_8*(40*M_2 + (-70 + 39*E_2)*M*r0 + 25*r0_2) + 2*L_2*r0_6*(130*M_2 + (-395 + 1008*E_2)*M*r0 + 165*r0_2)) - (2*M - r0)*r0_8*(192*E_2*M*r0_9 + 4*L_8*(-88*M_2 + (32 + 105*E_2)*M*r0 + 6*r0_2) + 2*L_2*r0_6*(272*M_2 + 2*(-203 + 362*E_2)*M*r0 + 135*r0_2) + L_6*r0_2*(-520*M_2 + 2*(-101 + 902*E_2)*M*r0 + 231*r0_2) + 2*L_4*r0_4*(170*M_2 + (-553 + 1314*E_2)*M*r0 + 234*r0_2)) + 4*a_3*E*L*M*r0_4*(105*L_8*(12*M_2 - 2*M*r0 - r0_2) + 2*L_4*r0_3*(-258*M_3 + 2*(1285 + 777*E_2)*M_2*r0 + (1193 + 1063*E_2)*M*r0_2 - 669*r0_3) + 2*L_6*r0*(848*M_3 + 70*(29 + 3*E_2)*M_2*r0 + 2*(53 + 105*E_2)*M*r0_2 - 393*r0_3) + L_2*r0_5*(-3216*M_3 + 4*(218 + 1503*E_2)*M_2*r0 + 21*(83 + 174*E_2)*M*r0_2 + 147*r0_3) + 4*r0_7*(66*M_3 + (-571 + 918*E_2)*M_2*r0 + (-169 + 532*E_2)*M*r0_2 + 264*r0_3)) + 2*a_5*E*L*M*r0_3*(2*L_6*(7368*M_3 + 4*(811 + 105*E_2)*M_2*r0 + 6*(-9 + 35*E_2)*M*r0_2 - 291*r0_3) + L_4*r0*(-2688*M_4 + 8*(3395 + 786*E_2)*M_3*r0 + 8*(3096 + 1379*E_2)*M_2*r0_2 + 2*(2537 + 1942*E_2)*M*r0_3 - 2151*r0_4) + L_2*r0_3*(-29172*M_4 + 4*(799 + 5976*E_2)*M_3*r0 + 3*(8421 + 10504*E_2)*M_2*r0_2 + 12*(909 + 820*E_2)*M*r0_3 - 126*r0_4) + 4*r0_5*(-5076*M_4 + 24*(-116 + 225*E_2)*M_3*r0 + (-513 + 6484*E_2)*M_2*r0_2 + 2*(680 + 961*E_2)*M*r0_3 + 744*r0_4)) + a_2*r0_4*(-840*L_10*M_2*(2*M - r0) + 24*E_2*M*r0_10*(-154*M_2 + 35*M*r0 + 29*r0_2) - 2*L_2*r0_7*(1692*M_4 + 4*(-917 + 2308*E_2)*M_3*r0 + (343 + 2102*E_2)*M_2*r0_2 - 3*(-458 + 893*E_2)*M*r0_3 - 420*r0_4) + 2*L_8*r0*(1448*M_4 - 4*(661 + 420*E_2)*M_3*r0 + 2*(271 - 420*E_2)*M_2*r0_2 + 5*(37 + 84*E_2)*M*r0_3 + 12*r0_4) + 2*L_6*r0_3*(5552*M_4 - 4*(803 + 1933*E_2)*M_3*r0 - 2*(457 + 1734*E_2)*M_2*r0_2 + (266 + 2265*E_2)*M*r0_3 + 150*r0_4) + L_4*r0_5*(6528*M_4 - 100*(-29 + 264*E_2)*M_3*r0 - 4*(715 + 2518*E_2)*M_2*r0_2 + 79*(-27 + 104*E_2)*M*r0_3 + 1011*r0_4)) - a_4*r0_3*(24*E_2*M*r0_8*(52*M_3 + 118*M_2*r0 - 141*M*r0_2 - 25*r0_3) + 4*L_8*M*(2456*M_3 + 4*(106 + 315*E_2)*M_2*r0 + 6*(-82 + 35*E_2)*M*r0_2 + 7*(1 - 15*E_2)*r0_3) + L_4*r0_3*(-37848*M_5 + 4*(1091 + 13224*E_2)*M_4*r0 + 2*(4783 + 34268*E_2)*M_3*r0_2 + 9*(685 + 1516*E_2)*M_2*r0_3 - 6*(45 + 1474*E_2)*M*r0_4 - 618*r0_5) + 2*L_2*r0_5*(-4992*M_5 + 24*(-113 + 731*E_2)*M_4*r0 + 12*(-242 + 2045*E_2)*M_3*r0_2 + 8*(452 + 341*E_2)*M_2*r0_3 + (791 - 3467*E_2)*M*r0_4 - 450*r0_5) + L_6*r0*(-18528*M_5 + 16*(1024 + 1391*E_2)*M_4*r0 + 8*(1318 + 4127*E_2)*M_3*r0_2 + 4*(-188 + 1737*E_2)*M_2*r0_3 - 22*(38 + 165*E_2)*M*r0_4 - 69*r0_5)) - a_12*M*(L_2*(192*(7 + 6*E_2)*M_4 + 16*(341 + 288*E_2)*M_3*r0 + 17*(329 + 216*E_2)*M_2*r0_2 + 3*(713 + 288*E_2)*M*r0_3 + 18*(15 + E_2)*r0_4) + 24*E_2*r0*(544*M_5 + 1640*M_4*r0 + 1684*M_3*r0_2 + 758*M_2*r0_3 + 151*M*r0_4 + 11*r0_5)) + 2*a_11*E*L*M*(L_2*(576*M_4 + 48*(78 + E_2)*M_3*r0 + (5657 + 48*E_2)*M_2*r0_2 + 6*(473 + 2*E_2)*M*r0_3 + 432*r0_4) + 8*r0*(32*(51 + 26*E_2)*M_5 + 8*(405 + 223*E_2)*M_4*r0 + 3*(1021 + 488*E_2)*M_3*r0_2 + 2*(940 + 271*E_2)*M_2*r0_3 + (647 + 76*E_2)*M*r0_4 + 84*r0_5)) + 2*a_7*E*L*M*r0_2*(-24*L_6*(3*M_2 - 20*M*r0 - 6*r0_2) + 2*L_4*(14544*M_4 + 8*(2235 + 307*E_2)*M_3*r0 + 4*(2075 + 599*E_2)*M_2*r0_2 + (2269 + 578*E_2)*M*r0_3 + 48*r0_4) + 24*r0_3*(-2116*M_5 + 168*(-11 + 7*E_2)*M_4*r0 + (181 + 2264*E_2)*M_3*r0_2 + (729 + 1412*E_2)*M_2*r0_3 + 6*(77 + 48*E_2)*M*r0_4 + 100*r0_5) + L_2*r0*(-26432*M_5 + 4*(689 + 3960*E_2)*M_4*r0 + 8*(6781 + 4830*E_2)*M_3*r0_2 + (42983 + 27000*E_2)*M_2*r0_3 + 4*(3299 + 1458*E_2)*M*r0_4 + 618*r0_5)) - a_6*r0_2*(-6*L_8*M*(8*M_2 - 82*M*r0 - 45*r0_2) - 48*E_2*M*r0_6*(728*M_4 + 356*M_3*r0 - 121*M_2*r0_2 - 43*M*r0_3 - 15*r0_4) + 2*L_6*M*(9696*M_4 + 24*(437 + 614*E_2)*M_3*r0 + 4*(59 + 2608*E_2)*M_2*r0_2 + 16*(40 + 127*E_2)*M*r0_3 + (423 - 443*E_2)*r0_4) + L_2*r0_3*(-41192*M_6 + 4*(-3823 + 6752*E_2)*M_5*r0 + 2*(2127 + 48568*E_2)*M_4*r0_2 + 3*(2001 + 30976*E_2)*M_3*r0_3 + (8091 + 20392*E_2)*M_2*r0_4 - 76*(-8 + 41*E_2)*M*r0_5 - 360*r0_6) + L_4*r0*(-40256*M_6 + 8*(-19 + 5604*E_2)*M_5*r0 + 4*(8619 + 28804*E_2)*M_4*r0_2 + 2*(5675 + 43864*E_2)*M_3*r0_3 + 3*(1895 + 6404*E_2)*M_2*r0_4 + (467 - 3516*E_2)*M*r0_5 - 75*r0_6)) - a_10*M*(L_4*(384*M_4 + 288*(12 + E_2)*M_3*r0 + 2*(3965 + 1224*E_2)*M_2*r0_2 + 3*(1597 + 404*E_2)*M*r0_3 + 18*(45 + 2*E_2)*r0_4) + L_2*r0*(768*(17 + 52*E_2)*M_5 + 32*(390 + 2897*E_2)*M_4*r0 + 2*(4257 + 50792*E_2)*M_3*r0_2 + (10973 + 55200*E_2)*M_2*r0_3 + (5755 + 12236*E_2)*M*r0_4 + 2*(410 + 253*E_2)*r0_5) + 24*E_2*r0_2*(-1312*M_6 - 2800*M_5*r0 - 216*M_4*r0_2 + 2624*M_3*r0_3 + 1894*M_2*r0_4 + 489*M*r0_5 + 47*r0_6)) + 2*a_9*E*L*M*r0*(6*L_4*(24*M_3 - 4*(-96 + E_2)*M_2*r0 + (361 - 2*E_2)*M*r0_2 + 72*r0_3) + L_2*(19968*M_5 + 32*(1559 + 303*E_2)*M_4*r0 + 12*(3933 + 1232*E_2)*M_3*r0_2 + 3*(9007 + 2520*E_2)*M_2*r0_3 + 6*(1567 + 216*E_2)*M*r0_4 + 1140*r0_5) + 8*r0*(-3936*M_6 + 4*(-1493 + 432*E_2)*M_5*r0 + 2*(161 + 2644*E_2)*M_4*r0_2 + (4231 + 5520*E_2)*M_3*r0_3 + 42*(77 + 58*E_2)*M_2*r0_4 + (1250 + 391*E_2)*M*r0_5 + 183*r0_6)) - a_8*r0*(6*L_6*M*(16*M_3 - 8*(-47 + 3*E_2)*M_2*r0 + 2*(262 + 37*E_2)*M*r0_2 + 3*(45 + E_2)*r0_3) - 48*E_2*M*r0_4*(1400*M_5 + 1724*M_4*r0 - 124*M_3*r0_2 - 722*M_2*r0_3 - 259*M*r0_4 - 35*r0_5) + L_4*M*(13312*M_5 + 96*(371 + 606*E_2)*M_4*r0 + 8*(2029 + 10014*E_2)*M_3*r0_2 + 2*(4317 + 23924*E_2)*M_2*r0_3 + 13*(627 + 892*E_2)*M*r0_4 + 14*(117 - 16*E_2)*r0_5) + L_2*r0*(-31488*M_7 + 64*(-443 + 235*E_2)*M_6*r0 + 4*(3539 + 22568*E_2)*M_5*r0_2 + 8*(1609 + 20166*E_2)*M_4*r0_3 + (10687 + 113840*E_2)*M_3*r0_4 + (7329 + 27616*E_2)*M_2*r0_5 + 36*(27 + 11*E_2)*M*r0_6 - 30*r0_7))))/(3.*r0_8*expr2_2);\n A91420 = (8*L*r0*(12*a_5*E*M*(2*M + r0) - a_4*L*(24*M_2 + 15*M*r0 + 2*r0_2) + 6*a*E*M*r0_3*(5*L_2 + 6*r0_2) - L*(2*M - r0)*r0_3*(8*L_2 + 9*r0_2) + 2*a_3*E*M*r0*(5*L_2 + 12*r0*(3*M + 2*r0)) - a_2*L*r0*(2*L_2*(5*M + r0) + r0*(42*M_2 + 11*M*r0 - 7*r0_2))))/(a_2 + r0*(-2*M + r0));\n A91440 = (-4*(-144*a_12*E_2*M_2*(10*M_2 + 9*M*r0 + 2*r0_2) + 4*a_11*E*L*M*(144*(5 + E_2)*M_3 + (1733 + 144*E_2)*M_2*r0 + 36*(32 + E_2)*M*r0_2 + 231*r0_3) - (2*M - r0)*r0_5*(288*E_2*M*r0_9 + 16*L_8*M*(-2*M + r0) + 2*L_6*r0_2*(-310*M_2 + (71 + 271*E_2)*M*r0 + 42*r0_2) + 6*L_4*r0_4*(-50*M_2 + (-115 + 298*E_2)*M*r0 + 70*r0_2) + 3*L_2*r0_6*(176*M_2 + 14*(-25 + 38*E_2)*M*r0 + 131*r0_2)) + 2*a*E*L*M*r0_5*(3*L_4*r0_2*(52*M_2 + 4*(115 + 43*E_2)*M*r0 - 243*r0_2) + 10*L_6*(104*M_2 + 2*M*r0 - 27*r0_2) + 3*L_2*r0_4*(-356*M_2 + 24*(3 + 20*E_2)*M*r0 + 53*r0_2) + 6*r0_6*(120*M_2 + 2*(-179 + 90*E_2)*M*r0 + 149*r0_2)) + 2*a_3*E*L*M*r0_3*(4*L_6*(804*M_2 - 142*M*r0 - 69*r0_2) + L_4*r0*(384*M_3 + 4*(1793 + 276*E_2)*M_2*r0 + 4*(303 + 251*E_2)*M*r0_2 - 1055*r0_3) + 4*L_2*r0_3*(-2454*M_3 + (1067 + 1404*E_2)*M_2*r0 + (895 + 996*E_2)*M*r0_2 + 104*r0_3) + 2*r0_5*(-2160*M_3 + 72*(-29 + 42*E_2)*M_2*r0 + 4*(-112 + 501*E_2)*M*r0_2 + 1373*r0_3)) - a_10*M*(L_2*(288*(5 + 6*E_2)*M_3 + 4*(1409 + 876*E_2)*M_2*r0 + 3*(1401 + 472*E_2)*M*r0_2 + 3*(287 + 22*E_2)*r0_3) + 72*E_2*r0*(112*M_4 + 324*M_3*r0 + 258*M_2*r0_2 + 71*M*r0_3 + 5*r0_4)) + a_2*r0_3*(2*L_8*M*(-1072*M_2 + 522*M*r0 + 7*r0_2) + 72*E_2*M*r0_8*(-46*M_2 + 9*M*r0 + 11*r0_2) + 2*L_6*r0*(2544*M_4 - 4*(789 + 544*E_2)*M_3*r0 + 16*(45 - 62*E_2)*M_2*r0_2 + (23 + 537*E_2)*M*r0_3 + 44*r0_4) + L_4*r0_3*(11640*M_4 - 4*(1315 + 3042*E_2)*M_3*r0 - 2*(21 + 3706*E_2)*M_2*r0_2 + (-1365 + 4216*E_2)*M*r0_3 + 623*r0_4) + L_2*r0_5*(1032*M_4 - 108*(-39 + 112*E_2)*M_3*r0 - 2*(1 + 3174*E_2)*M_2*r0_2 + (-3001 + 4554*E_2)*M*r0_3 + 910*r0_4)) + 2*a_9*E*L*M*(3*L_2*(288*M_3 + 16*(55 + E_2)*M_2*r0 + 4*(259 + 2*E_2)*M*r0_2 + 309*r0_3) + 2*r0*(192*(21 + 10*E_2)*M_4 + 4*(1409 + 900*E_2)*M_3*r0 + (5485 + 2304*E_2)*M_2*r0_2 + 2*(1891 + 246*E_2)*M*r0_3 + 929*r0_4)) + 2*a_5*E*L*M*r0_2*(-6*L_6*(6*M + r0) + L_4*(12096*M_3 + 8*(897 + 134*E_2)*M_2*r0 + 4*(107 + 119*E_2)*M*r0_2 + 133*r0_3) + 2*L_2*r0*(-6816*M_4 + 4*(743 + 684*E_2)*M_3*r0 + 10*(845 + 492*E_2)*M_2*r0_2 + 2*(1633 + 918*E_2)*M*r0_3 + 785*r0_4) + 2*r0_3*(-11988*M_4 + 36*(-167 + 156*E_2)*M_3*r0 + (491 + 8064*E_2)*M_2*r0_2 + 36*(83 + 78*E_2)*M*r0_3 + 1872*r0_4)) - a_8*(3*L_4*M*(192*M_3 + 16*(49 + 6*E_2)*M_2*r0 + 4*(412 + 65*E_2)*M*r0_2 + 5*(115 + 4*E_2)*r0_3) - 288*E_2*M*r0_2*(76*M_5 + 132*M_4*r0 - 19*M_3*r0_2 - 102*M_2*r0_3 - 41*M*r0_4 - 4*r0_5) + L_2*r0*(1152*(7 + 20*E_2)*M_5 + 16*(-49 + 2724*E_2)*M_4*r0 + 4*(689 + 9582*E_2)*M_3*r0_2 + (8609 + 12372*E_2)*M_2*r0_3 + 8*(341 + 54*E_2)*M*r0_4 + 5*r0_5)) + a_4*r0_2*(6*L_8*M*(4*M + r0) + 144*E_2*M*r0_6*(48*M_3 - 3*M_2*r0 + 4*M*r0_2 + 2*r0_3) - 2*L_6*(4032*M_4 + 12*(121 + 268*E_2)*M_3*r0 + 2*(-729 + 215*E_2)*M_2*r0_2 + (473 - 269*E_2)*M*r0_3 - 2*r0_4) + L_4*r0*(20544*M_5 - 32*(298 + 525*E_2)*M_4*r0 - 4*(1711 + 6928*E_2)*M_3*r0_2 + 4*(437 - 2283*E_2)*M_2*r0_3 + (-2197 + 3008*E_2)*M*r0_4 + 202*r0_5) + L_2*r0_3*(18528*M_5 - 36*(15 + 308*E_2)*M_4*r0 - 4*(-601 + 8034*E_2)*M_3*r0_2 - (3203 + 12948*E_2)*M_2*r0_3 + 12*(-213 + 335*E_2)*M*r0_4 + 636*r0_5)) + 2*a_7*E*L*M*r0*(3*L_4*(48*M_2 - 4*(-59 + E_2)*M*r0 + 153*r0_2) + 4*L_2*(2880*M_4 + 24*(229 + 42*E_2)*M_3*r0 + (3283 + 1068*E_2)*M_2*r0_2 + 3*(571 + 96*E_2)*M*r0_3 + 560*r0_4) + 2*r0*(-10944*M_5 + 12*(-941 + 288*E_2)*M_4*r0 + 8*(283 + 1134*E_2)*M_3*r0_2 + 25*(235 + 288*E_2)*M_2*r0_3 + 24*(208 + 75*E_2)*M*r0_4 + 1644*r0_5)) - a_6*r0*(6*L_6*M*(16*M_2 - 6*(-19 + 2*E_2)*M*r0 - (-143 + E_2)*r0_2) - 144*E_2*M*r0_4*(232*M_4 + 178*M_3*r0 - 64*M_2*r0_2 - 53*M*r0_3 - 7*r0_4) + L_4*(7680*M_5 + 1344*(11 + 18*E_2)*M_4*r0 + 8*(-356 + 2499*E_2)*M_3*r0_2 + 2*(1663 + 3038*E_2)*M_2*r0_3 + 5*(731 - 104*E_2)*M*r0_4 + r0_5) + L_2*r0*(-21888*M_6 + 48*(-149 + 148*E_2)*M_5*r0 + 60*(121 + 644*E_2)*M_4*r0_2 + 16*(-148 + 3465*E_2)*M_3*r0_3 + (6035 + 20748*E_2)*M_2*r0_4 + 6*(543 - 116*E_2)*M*r0_5 - 114*r0_6))))/(3.*r0_5*expr2_2);\n A91600 = (2*L*r0_4*(4*a_3*E*M + 12*a*E*M*r0_2 + 3*L*r0_2*(-2*M + r0) - a_2*L*(4*M + r0)))/(a_2 + r0*(-2*M + r0));\n A91620 = (48*a_10*E_2*M_2*(13*M + 6*r0) - 24*a_9*E*L*M*(4*(13 + 3*E_2)*M_2 + 2*(55 + 3*E_2)*M*r0 + 41*r0_2) - 2*a*E*L*M*r0_4*(36*r0_5*(2*(-17 + 7*E_2)*M + 17*r0) + 2*L_4*(140*M_2 + 116*M*r0 - 93*r0_2) + L_2*r0_2*(-1012*M_2 + 8*(85 + 36*E_2)*M*r0 - 87*r0_2)) + (2*M - r0)*r0_4*(-56*L_6*M*(2*M - r0) + 192*E_2*M*r0_7 + 8*L_2*r0_4*(20*M_2 + (-76 + 85*E_2)*M*r0 + 33*r0_2) + L_4*r0_2*(-420*M_2 + 4*(-12 + 79*E_2)*M*r0 + 129*r0_2)) + 3*a_8*(L_2*(16*(13 + 18*E_2)*M_3 + 16*(49 + 18*E_2)*M_2*r0 + (319 + 26*E_2)*M*r0_2 + 3*r0_3) + 8*E_2*M*r0*(88*M_3 + 262*M_2*r0 + 129*M*r0_2 + 9*r0_3)) - 2*a_7*E*L*M*(3*L_2*(144*M_2 + 4*(54 + E_2)*M*r0 + 175*r0_2) + 8*r0*(8*(33 + 14*E_2)*M_3 + (181 + 202*E_2)*M_2*r0 + (337 + 82*E_2)*M*r0_2 + 193*r0_3)) - 2*a_3*E*L*M*r0_2*(2*L_4*(804*M_2 - 64*M*r0 - 81*r0_2) + L_2*r0*(-2768*M_3 + 28*(79 + 18*E_2)*M_2*r0 + 4*(262 + 151*E_2)*M*r0_2 + 191*r0_3) + 8*r0_3*(-510*M_3 + (-169 + 198*E_2)*M_2*r0 + 5*(-9 + 38*E_2)*M*r0_2 + 205*r0_3)) + a_6*(3*L_4*(96*M_3 + 24*(8 + E_2)*M_2*r0 + 4*(81 + 2*E_2)*M*r0_2 + 3*r0_3) + 24*E_2*M*r0_2*(-280*M_4 - 380*M_3*r0 + 152*M_2*r0_2 + 197*M*r0_3 + 19*r0_4) + L_2*r0*(192*(11 + 28*E_2)*M_4 + 8*(-424 + 1049*E_2)*M_3*r0 + 2*(891 + 2434*E_2)*M_2*r0_2 + 3*(807 + 22*E_2)*M*r0_3 + 43*r0_4)) - 2*a_5*E*L*M*r0*(12*L_4*(3*M + 2*r0) + L_2*(2688*M_3 + 8*(443 + 67*E_2)*M_2*r0 + 8*(87 + 41*E_2)*M*r0_2 + 803*r0_3) + 16*r0*(-420*M_4 + (-223 + 72*E_2)*M_3*r0 + (49 + 191*E_2)*M_2*r0_2 + 2*(61 + 50*E_2)*M*r0_3 + 130*r0_4)) - a_2*r0_2*(-8*L_6*M*(134*M_2 - 57*M*r0 - 5*r0_2) + 24*E_2*M*r0_6*(-30*M_2 + M*r0 + 15*r0_2) + L_4*r0*(3920*M_4 - 32*(111 + 56*E_2)*M_3*r0 - 8*(-152 + 181*E_2)*M_2*r0_2 + 4*(-109 + 156*E_2)*M*r0_3 + 113*r0_4) + L_2*r0_3*(2840*M_4 - 4*(125 + 424*E_2)*M_3*r0 + 2*(519 - 1858*E_2)*M_2*r0_2 + (-1563 + 1450*E_2)*M*r0_3 + 407*r0_4)) + a_4*r0*(24*L_6*M*(M + r0) - 24*E_2*M*r0_4*(252*M_3 + 70*M_2*r0 - 63*M*r0_2 - 3*r0_3) + L_4*(1792*M_4 + 8*(241 + 402*E_2)*M_3*r0 + 4*(-541 + 214*E_2)*M_2*r0_2 + 2*(687 - 142*E_2)*M*r0_3 + 25*r0_4) + L_2*r0*(-6720*M_5 + 16*(124 + 43*E_2)*M_4*r0 + 4*(-145 + 1746*E_2)*M_3*r0_2 + 40*(-29 + 159*E_2)*M_2*r0_3 + (2083 - 782*E_2)*M*r0_4 - 109*r0_5)))/(3.*r0_2*expr2_2);\n A91800 = -(r0*(-96*a_8*E_2*M_2 + 12*a_7*E*L*M*(4*(4 + E_2)*M + 29*r0) + (2*M - r0)*r0_3*(40*L_4*M*(2*M - r0) - 48*E_2*M*r0_5 + L_2*r0_2*(8*M_2 + 2*(67 - 37*E_2)*M*r0 - 69*r0_2)) - 3*a_6*(16*E_2*M*r0*(4*M_2 + 14*M*r0 + r0_2) + L_2*(16*(2 + 3*E_2)*M_2 + 2*(58 + 5*E_2)*M*r0 + 3*r0_2)) + 4*a*E*L*M*r0_3*(L_2*(-80*M_2 + 106*M*r0 - 33*r0_2) + 3*r0_2*(-20*M_2 + 4*(-11 + 3*E_2)*M*r0 + 27*r0_2)) + 4*a_5*E*L*M*(3*L_2*(12*M + 5*r0) + r0*(32*(3 + E_2)*M_2 + 4*(-7 + 19*E_2)*M*r0 + 191*r0_2)) - a_4*(6*L_4*M*(8*M + 5*r0) + 48*E_2*M*r0_2*(-16*M_3 - 16*M_2*r0 + 12*M*r0_2 + r0_3) + L_2*r0*(192*(1 + 2*E_2)*M_3 + 4*(-196 + 149*E_2)*M_2*r0 + 2*(288 - 23*E_2)*M*r0_2 + 29*r0_3)) + 4*a_3*E*L*M*r0*(2*L_2*(48*M_2 + 35*M*r0 - 9*r0_2) + r0*(-384*M_3 - 4*M_2*r0 + 20*(-4 + 5*E_2)*M*r0_2 + 185*r0_3)) + a_2*r0*(48*E_2*M*r0_4*(4*M_2 - 2*M*r0 + r0_2) + 2*L_4*M*(-64*M_2 + 6*M*r0 + 13*r0_2) + L_2*r0*(768*M_4 + 16*(-47 + 10*E_2)*M_3*r0 + 4*(167 - 166*E_2)*M_2*r0_2 + 10*(-34 + 15*E_2)*M*r0_3 + 49*r0_4))))/(12.*expr2_2);\n A92040 = (192*L_2*expr1_2)/(a_2 + r0*(-2*M + r0));\n A92060 = (-32*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(-24*a_10*E_2*M_2*r0_p_2M_2 + 48*a_9*E*L*M*(4*M_3 + 4*M_2*r0 + 3*M*r0_2 + r0_3) - 4*a*E*L*M*r0_6*(L_4*(191*M - 18*r0) + L_2*(427*M - 93*r0)*r0_2 + 6*(31*M - 9*r0)*r0_4) - 4*a_3*E*L*M*r0_3*(L_2*r0_2*(1180*M_2 + 655*M*r0 - 157*r0_2) + L_4*(352*M_2 + 185*M*r0 - 27*r0_2) + 6*r0_4*(84*M_2 + 57*M*r0 - 23*r0_2)) + r0_6*(8*L_6*M*(2*M - r0) + 96*E_2*M*r0_7 + 2*L_4*r0_2*(138*M_2 + (-135 + 82*E_2)*M*r0 + 33*r0_2) + L_2*r0_4*(248*M_2 + 2*(-125 + 134*E_2)*M*r0 + 63*r0_2)) + 4*a_5*E*L*M*r0_2*(3*L_4*(4*M + 5*r0) - L_2*(1120*M_3 + 1232*M_2*r0 + 293*M*r0_2 - 91*r0_3) - 18*r0_2*(36*M_3 + 52*M_2*r0 + 13*M*r0_2 - 7*r0_3)) + 2*a_2*r0_3*(12*E_2*M*r0_7*(23*M + 16*r0) + L_6*(352*M_3 + 42*M_2*r0 - 28*M*r0_2 - 6*r0_3) + L_4*r0_2*(530*M_3 + (237 + 340*E_2)*M_2*r0 + (-183 + 158*E_2)*M*r0_2 + 18*r0_3) + L_2*r0_4*(250*M_3 + 15*(9 + 58*E_2)*M_2*r0 + 9*(-23 + 44*E_2)*M*r0_2 + 54*r0_3)) + 4*a_7*E*L*M*r0*(L_2*(12*M_2 + 47*M*r0 + 27*r0_2) - 6*(128*M_4 + 156*M_3*r0 + 88*M_2*r0_2 + 7*M*r0_3 - 9*r0_4)) - a_8*M*(L_2*(96*M_3 + 24*(4 + E_2)*M_2*r0 + (119 + 36*E_2)*M*r0_2 + 6*(7 + 2*E_2)*r0_3) - 96*E_2*r0*(16*M_4 + 26*M_3*r0 + 17*M_2*r0_2 + 6*M*r0_3 + r0_4)) + a_4*r0_2*(-24*L_6*M*(M + 2*r0) + 288*E_2*M*r0_5*(5*M_2 + 6*M*r0 + 2*r0_2) + 2*L_4*(1120*M_4 + 8*(95 + 44*E_2)*M_3*r0 + (59 + 328*E_2)*M_2*r0_2 + 7*(-27 + 10*E_2)*M*r0_3 - 15*r0_4) + L_2*r0_2*(380*M_4 + 4*(355 + 882*E_2)*M_3*r0 + 3*(51 + 1132*E_2)*M_2*r0_2 + 12*(-37 + 64*E_2)*M*r0_3 + 27*r0_4)) + 2*a_6*r0*(-(L_4*M*(12*M_2 + 4*(19 + 3*E_2)*M*r0 + 3*(15 + 2*E_2)*r0_2)) + 24*E_2*M*r0_3*(46*M_3 + 66*M_2*r0 + 37*M*r0_2 + 8*r0_3) + L_2*(768*M_5 + 16*(39 + 70*E_2)*M_4*r0 + 24*(16 + 71*E_2)*M_3*r0_2 + 6*(-26 + 135*E_2)*M_2*r0_3 + (-161 + 116*E_2)*M*r0_4 - 9*r0_5))))/(3.*r0_7*expr2_2);\n A92220 = (96*L_2*r0_3*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/(a_2 + r0*(-2*M + r0));\n A92240 = (-8*(-72*a_10*E_2*M_2*r0_p_2M_2 + 24*a_9*E*L*M*(24*M_3 + 12*M_2*r0 + 2*M*r0_2 + r0_3) + 4*a*E*L*M*r0_4*(4*L_6*M - 9*L_4*(54*M - 5*r0)*r0_2 + 18*r0_6*(-25*M + 6*r0) + 6*L_2*r0_4*(-165*M + 29*r0)) - 4*a_3*E*L*M*r0_3*(L_2*r0_2*(2778*M_2 + 1535*M*r0 - 241*r0_2) + 18*r0_4*(84*M_2 + 47*M*r0 - 15*r0_2) + 6*L_4*(144*M_2 + 78*M*r0 - r0_2)) + r0_4*(288*E_2*M*r0_9 + 4*L_8*M*(-2*M + r0) - 2*L_6*r0_2*(22*M_2 + (37 + 2*E_2)*M*r0 - 24*r0_2) + 12*L_4*r0_4*(36*M_2 + 4*(-14 + 9*E_2)*M*r0 + 19*r0_2) + 3*L_2*r0_6*(152*M_2 + 2*(-97 + 122*E_2)*M*r0 + 59*r0_2)) - 4*a_5*E*L*M*r0_2*(3*L_4*(2*M + r0) + L_2*(2928*M_3 + 2806*M_2*r0 + 784*M*r0_2 - 70*r0_3) + 6*r0_2*(396*M_3 + 432*M_2*r0 + 95*M*r0_2 - 37*r0_3)) + 2*a_2*r0_3*(36*E_2*M*r0_7*(23*M + 16*r0) + L_6*(864*M_3 - 4*(-9 + E_2)*M_2*r0 + (11 - 2*E_2)*M*r0_2 - 3*r0_3) + 9*L_4*r0_2*(128*M_3 + 2*(11 + 51*E_2)*M_2*r0 + (-25 + 48*E_2)*M*r0_2 + 13*r0_3) + 3*L_2*r0_4*(204*M_3 + 2*(-5 + 348*E_2)*M_2*r0 + 3*(-39 + 122*E_2)*M*r0_2 + 61*r0_3)) + 4*a_7*E*L*M*r0*(L_2*(24*M_2 - 19*M*r0 + 3*r0_2) - 6*(384*M_4 + 444*M_3*r0 + 208*M_2*r0_2 + 27*M*r0_3 - 11*r0_4)) + a_8*(288*E_2*M*r0*(16*M_4 + 26*M_3*r0 + 17*M_2*r0_2 + 6*M*r0_3 + r0_4) + L_2*(-288*M_4 - 48*E_2*M_3*r0 + (73 - 24*E_2)*M_2*r0_2 + 18*M*r0_3 + 6*r0_4)) + a_4*r0_2*(6*L_6*(2*M_2 + 2*M*r0 + r0_2) + 864*E_2*M*r0_5*(5*M_2 + 6*M*r0 + 2*r0_2) + 2*L_4*(2928*M_4 + 4*(341 + 216*E_2)*M_3*r0 + 4*(47 + 225*E_2)*M_2*r0_2 + 108*(-1 + 2*E_2)*M*r0_3 + 9*r0_4) + 3*L_2*r0_2*(844*M_4 + 4*(181 + 696*E_2)*M_3*r0 + (-1 + 2808*E_2)*M_2*r0_2 + 12*(-9 + 61*E_2)*M*r0_3 + 69*r0_4)) + 2*a_6*r0*(L_4*(-24*M_3 + 2*(25 + 3*E_2)*M_2*r0 + 15*M*r0_2 + 6*r0_3) + 72*E_2*M*r0_3*(46*M_3 + 66*M_2*r0 + 37*M*r0_2 + 8*r0_3) + L_2*(2304*M_5 + 48*(33 + 61*E_2)*M_4*r0 + 2*(259 + 2124*E_2)*M_3*r0_2 + (-49 + 2112*E_2)*M_2*r0_3 + 3*(-31 + 122*E_2)*M*r0_4 + 12*r0_5))))/(3.*r0_4*expr2_2);\n A92400 = (12*L_2*r0_6)/(a_2 + r0*(-2*M + r0));\n A92420 = (-2*(-72*a_8*E_2*M_2*(2*M + r0) + 48*a_7*E*L*M*(6*M_2 - 3*M*r0 - 2*r0_2) + 12*a*E*L*M*r0_3*(L_4*(8*M - 4*r0) + 6*r0_4*(-19*M + 3*r0) + L_2*r0_2*(-119*M + 5*r0)) - 24*a_5*E*L*M*r0*(192*M_3 + 114*M_2*r0 + 25*M*r0_2 + r0_3 + L_2*(5*M + 8*r0)) - 12*a_3*E*L*M*r0_2*(4*L_4 + 12*r0_2*(23*M_2 + 12*M*r0 - 2*r0_2) + L_2*(224*M_2 + 99*M*r0 + 17*r0_2)) + r0_3*(288*E_2*M*r0_7 + 24*L_6*M*(-2*M + r0) + L_4*r0_2*(-132*M_2 - 152*M*r0 + 109*r0_2) + L_2*r0_4*(168*M_2 + 62*(-7 + 6*E_2)*M*r0 + 175*r0_2)) + 3*a_6*(L_2*(-48*M_3 + 4*(18 + 5*E_2)*M_2*r0 + 6*(7 + 2*E_2)*M*r0_2 + 3*r0_3) + 24*E_2*M*r0*(32*M_3 + 36*M_2*r0 + 17*M*r0_2 + 4*r0_3)) + a_2*r0_2*(24*L_6*M + 216*E_2*M*r0_5*(5*M + 4*r0) + 2*L_4*(672*M_3 - 6*(19 + 4*E_2)*M_2*r0 + 6*(17 + 2*E_2)*M*r0_2 + 35*r0_3) + L_2*r0_2*(612*M_3 + 2*(-167 + 654*E_2)*M_2*r0 + 78*(-1 + 10*E_2)*M*r0_2 + 269*r0_3)) + a_4*r0*(3*L_4*(20*M_2 + 4*(13 + 2*E_2)*M*r0 + 3*r0_2) + 216*E_2*M*r0_3*(10*M_2 + 11*M*r0 + 4*r0_2) + L_2*(2304*M_4 + 48*(3 + 28*E_2)*M_3*r0 + 6*(3 + 236*E_2)*M_2*r0_2 + 2*(151 + 222*E_2)*M*r0_3 + 103*r0_4))))/(3.*r0*expr2_2);\n A92600 = -(r0_2*(-24*a_6*E_2*M_2 + 24*a_5*E*L*M*(2*M - 3*r0) - 24*a_3*E*L*M*r0*(2*L_2 + 32*M_2 + M*r0 + r0_2) + 8*a*E*L*M*r0_2*(2*L_2*(5*M - 3*r0) - 39*M*r0_2) + 3*a_4*(L_2*(-8*M_2 + 8*(3 + E_2)*M*r0 + r0_2) + 16*E_2*M*r0*(8*M_2 + 5*M*r0 + 2*r0_2)) + r0_2*(96*E_2*M*r0_5 + 20*L_4*M*(-2*M + r0) + L_2*r0_2*(-40*M_2 + 2*(-51 + 2*E_2)*M*r0 + 61*r0_2)) + 2*a_2*r0*(12*L_4*M + 12*E_2*M*r0_3*(7*M + 8*r0) + L_2*(192*M_3 - 4*(27 + 5*E_2)*M_2*r0 + (43 + 14*E_2)*M*r0_2 + 32*r0_3))))/(6.*expr2_2);\n A93040 = (32*L*(a_2*(2*M + r0) + r0*(L_2 + r0_2))*(12*a_5*E*M*(2*M + r0) - a_4*L*(24*M_2 + 12*M*r0 + r0_2) + 12*a*E*M*r0_3*(2*L_2 + 3*r0_2) + 8*a_3*E*M*r0*(L_2 + 9*M*r0 + 6*r0_2) + L*r0_3*(L_2*(-15*M + 8*r0) + r0_2*(-19*M + 10*r0)) - a_2*L*r0*(L_2*(8*M + r0) + r0*(50*M_2 + 9*M*r0 - 9*r0_2))))/(r0_2*expr2_2);\n A93060 = (-16*(24*a_14*E_2*M_2*r0_p_2M_2*(M + 4*r0) - 4*a_13*E*L*M*(2*M + r0)*(24*M_3 + (-37 + 24*E_2)*M_2*r0 + 12*(1 + E_2)*M*r0_2 + 24*r0_3) + 2*a*E*L*M*r0_6*(L_4*r0_4*(164*M_2 + 4*(562 + 393*E_2)*M*r0 - 1203*r0_2) + 2*L_6*r0_2*(658*M_2 + 6*(106 + 35*E_2)*M*r0 - 489*r0_2) + 210*L_8*(4*M_2 - r0_2) + 6*r0_8*(180*M_2 + 2*(-127 + 72*E_2)*M*r0 + 81*r0_2) + L_2*r0_6*(1176*M_2 + 4*(-233 + 495*E_2)*M*r0 + 141*r0_2)) + 2*a_3*E*L*M*r0_4*(210*L_8*(12*M_2 - 2*M*r0 - r0_2) + 2*L_4*r0_3*(-506*M_3 + (5351 + 3108*E_2)*M_2*r0 + (3245 + 2204*E_2)*M*r0_2 - 1998*r0_3) + L_2*r0_5*(876*M_3 + 2*(797 + 5814*E_2)*M_2*r0 + 12*(271 + 593*E_2)*M*r0_2 - 1035*r0_3) + 4*L_6*r0*(760*M_3 + (1987 + 210*E_2)*M_2*r0 + 42*(8 + 5*E_2)*M*r0_2 - 492*r0_3) + 4*r0_7*(378*M_3 + (-791 + 2088*E_2)*M_2*r0 + (-311 + 950*E_2)*M*r0_2 + 339*r0_3)) + r0_8*(24*E_2*M*r0_9*(-15*M + 7*r0) + 2*L_8*M*(2*M - r0)*(154*M - 3*(27 + 70*E_2)*r0) + L_6*r0_2*(560*M_3 + (46 - 3580*E_2)*M_2*r0 + (-487 + 1794*E_2)*M*r0_2 + 162*r0_3) + L_2*r0_6*(-1236*M_3 + (2198 - 2760*E_2)*M_2*r0 + 2*(-638 + 683*E_2)*M*r0_2 + 243*r0_3) + L_4*r0_4*(-1340*M_3 + 4*(737 - 1279*E_2)*M_2*r0 + (-1961 + 2560*E_2)*M*r0_2 + 411*r0_3)) + 2*a_5*E*L*M*r0_3*(2*L_6*(7296*M_3 + 4*(886 + 105*E_2)*M_2*r0 + 6*(44 + 35*E_2)*M*r0_2 - 531*r0_3) + L_4*r0*(-1888*M_4 + 4*(6037 + 1536*E_2)*M_3*r0 + 8*(3396 + 1397*E_2)*M_2*r0_2 + 8*(775 + 514*E_2)*M*r0_3 - 4473*r0_4) + L_2*r0_3*(-13992*M_4 + 4*(3067 + 5850*E_2)*M_3*r0 + 42*(597 + 724*E_2)*M_2*r0_2 + 6*(1415 + 1576*E_2)*M*r0_3 - 3537*r0_4) + 2*r0_5*(-9972*M_4 + 216*(-11 + 62*E_2)*M_3*r0 + (579 + 14000*E_2)*M_2*r0_2 + 2*(799 + 1634*E_2)*M*r0_3 + 468*r0_4)) + a_2*r0_4*(-840*L_10*M_2*(2*M - r0) - 72*E_2*M*r0_10*(60*M_2 - 19*M*r0 - 8*r0_2) + 2*L_8*r0*(1552*M_4 - 60*(37 + 28*E_2)*M_3*r0 - 30*(1 + 28*E_2)*M_2*r0_2 + (367 + 420*E_2)*M*r0_3 + 12*r0_4) + L_6*r0_3*(10152*M_4 - 4*(1137 + 3826*E_2)*M_3*r0 - 4*(991 + 1814*E_2)*M_2*r0_2 + (1483 + 4540*E_2)*M*r0_3 + 231*r0_4) + L_2*r0_7*(-4200*M_4 + 4*(1777 - 5538*E_2)*M_3*r0 - 4*(162 + 353*E_2)*M_2*r0_2 + (-2345 + 4988*E_2)*M*r0_3 + 723*r0_4) + L_4*r0_5*(2680*M_4 + 4*(1321 - 6546*E_2)*M_3*r0 - 10*(385 + 976*E_2)*M_2*r0_2 + (-1359 + 8000*E_2)*M*r0_3 + 861*r0_4)) - 4*a_11*E*L*M*r0*(L_2*(12*(-53 + 3*E_2)*M_3 + 2*(-404 + 15*E_2)*M_2*r0 + 3*(-33 + 2*E_2)*M*r0_2 + 72*r0_3) - 2*(80*(51 + 22*E_2)*M_5 + 8*(945 + 464*E_2)*M_4*r0 + 21*(251 + 128*E_2)*M_3*r0_2 + 8*(197 + 95*E_2)*M_2*r0_3 + 2*(-7 + 31*E_2)*M*r0_4 - 90*r0_5)) - a_12*M*(L_2*(-96*M_4 + 8*(85 + 123*E_2)*M_3*r0 + 4*(109 + 237*E_2)*M_2*r0_2 + 9*(-17 + 24*E_2)*M*r0_3 - 6*(15 + E_2)*r0_4) + 24*E_2*r0*(680*M_5 + 1604*M_4*r0 + 1314*M_3*r0_2 + 481*M_2*r0_3 + 92*M*r0_4 + 11*r0_5)) + 2*a_7*E*L*M*r0_2*(24*L_6*(3*M_2 + 19*M*r0 - 2*r0_2) + 2*L_4*(14688*M_4 + 4*(4395 + 608*E_2)*M_3*r0 + (9365 + 2492*E_2)*M_2*r0_2 + 4*(355 + 161*E_2)*M*r0_3 - 912*r0_4) + L_2*r0*(-23808*M_5 + 24*(745 + 672*E_2)*M_4*r0 + 4*(15251 + 9474*E_2)*M_3*r0_2 + 18*(2353 + 1432*E_2)*M_2*r0_3 + 2*(2963 + 2736*E_2)*M*r0_4 - 3549*r0_5) - 12*r0_3*(4452*M_5 - 120*(-25 + 24*E_2)*M_4*r0 - (1393 + 5248*E_2)*M_3*r0_2 - (1445 + 2848*E_2)*M_2*r0_3 - (351 + 452*E_2)*M*r0_4 + 43*r0_5)) + a_4*r0_3*(24*E_2*M*r0_8*(-174*M_3 - 145*M_2*r0 + 234*M*r0_2 + 15*r0_3) - 2*L_8*M*(4864*M_3 + 4*(263 + 630*E_2)*M_2*r0 + 420*(-1 + E_2)*M*r0_2 - 7*(49 + 30*E_2)*r0_3) + L_6*r0*(18016*M_5 - 8*(1311 + 2684*E_2)*M_4*r0 - 8*(1805 + 4226*E_2)*M_3*r0_2 - 4*(871 + 1914*E_2)*M_2*r0_3 + 2*(1885 + 1852*E_2)*M*r0_4 + 69*r0_5) + L_4*r0_3*(28492*M_5 + 4*(503 - 13140*E_2)*M_4*r0 - (12553 + 67264*E_2)*M_3*r0_2 - 108*(88 + 115*E_2)*M_2*r0_3 + 21*(173 + 412*E_2)*M*r0_4 + 489*r0_5) + L_2*r0_5*(8364*M_5 - 60*(-83 + 1002*E_2)*M_4*r0 - 63*(-57 + 796*E_2)*M_3*r0_2 + 20*(-349 + 158*E_2)*M_2*r0_3 + (-217 + 6298*E_2)*M*r0_4 + 711*r0_5)) + 4*a_9*E*L*M*r0*(L_4*(-108*M_3 + 6*(139 + 2*E_2)*M_2*r0 + 3*(129 + 2*E_2)*M*r0_2 - 72*r0_3) + L_2*(10560*M_5 + 8*(3409 + 612*E_2)*M_4*r0 + 6*(4067 + 1186*E_2)*M_3*r0_2 + 3*(3591 + 1156*E_2)*M_2*r0_3 + 3*(303 + 190*E_2)*M*r0_4 - 666*r0_5) + r0*(-16128*M_6 + 8*(-2749 + 936*E_2)*M_5*r0 + 4*(2017 + 5984*E_2)*M_4*r0_2 + 2*(10151 + 11760*E_2)*M_3*r0_3 + 276*(33 + 32*E_2)*M_2*r0_4 + 8*(85 + 131*E_2)*M*r0_5 - 447*r0_6)) - a_6*r0_2*(6*L_8*M*(8*M_2 + 74*M*r0 - 15*r0_2) - 24*E_2*M*r0_6*(1320*M_4 + 320*M_3*r0 - 103*M_2*r0_2 + 106*M*r0_3 - 40*r0_4) + 4*L_6*M*(4896*M_4 + 48*(109 + 152*E_2)*M_3*r0 + (1753 + 5510*E_2)*M_2*r0_2 + 2*(10 + 559*E_2)*M*r0_3 - (564 + 241*E_2)*r0_4) + L_2*r0_3*(-43656*M_6 + 4*(-3607 + 16068*E_2)*M_5*r0 + 2*(4865 + 68696*E_2)*M_4*r0_2 + (12817 + 79104*E_2)*M_3*r0_3 + 3*(1471 + 2856*E_2)*M_2*r0_4 - (2243 + 2632*E_2)*M*r0_5 - 225*r0_6) + L_4*r0*(-38784*M_6 + 16*(109 + 2906*E_2)*M_5*r0 + 64*(558 + 1775*E_2)*M_4*r0_2 + 394*(65 + 212*E_2)*M_3*r0_3 + (2097 + 17020*E_2)*M_2*r0_4 - 7*(751 + 508*E_2)*M*r0_5 - 39*r0_6)) + a_10*M*r0*(L_4*(72*(-19 + 6*E_2)*M_3 - 4*(523 + 372*E_2)*M_2*r0 - 3*(41 + 268*E_2)*M*r0_2 + 6*(45 + 2*E_2)*r0_3) - L_2*(960*(17 + 44*E_2)*M_5 + 16*(1374 + 6193*E_2)*M_4*r0 + 2*(5859 + 46232*E_2)*M_3*r0_2 + (2087 + 41976*E_2)*M_2*r0_3 + (-2105 + 8516*E_2)*M*r0_4 + 2*(-463 + 226*E_2)*r0_5) - 24*E_2*r0*(-1344*M_6 - 2416*M_5*r0 + 444*M_4*r0_2 + 2452*M_3*r0_3 + 1366*M_2*r0_4 + 327*M*r0_5 + 48*r0_6)) - a_8*r0*(-6*L_6*M*(24*M_3 - 24*(12 + E_2)*M_2*r0 - 2*(60 + 41*E_2)*M*r0_2 + (45 + E_2)*r0_3) - 24*E_2*M*r0_4*(2808*M_5 + 2772*M_4*r0 - 624*M_3*r0_2 - 1006*M_2*r0_3 - 287*M*r0_4 - 75*r0_5) + L_4*M*(14080*M_5 + 48*(827 + 1224*E_2)*M_4*r0 + 8*(3331 + 9732*E_2)*M_3*r0_2 + (10101 + 44320*E_2)*M_2*r0_3 + 2*(-987 + 5024*E_2)*M*r0_4 - 4*(624 + 89*E_2)*r0_5) + L_2*r0*(-32256*M_7 + 32*(-937 + 660*E_2)*M_6*r0 + 8*(2729 + 16220*E_2)*M_5*r0_2 + 4*(6837 + 43484*E_2)*M_4*r0_3 + (11707 + 92136*E_2)*M_3*r0_4 + (-1673 + 18680*E_2)*M_2*r0_5 + (-2227 + 502*E_2)*M*r0_6 + 6*r0_7))))/(3.*r0_8*expr2_3);\n A93220 = (16*L*r0*(12*a_5*E*M*(2*M + r0) - a_4*L*(24*M_2 + 15*M*r0 + 2*r0_2) + 6*a*E*M*r0_3*(5*L_2 + 6*r0_2) + 2*a_3*E*M*r0*(5*L_2 + 12*r0*(3*M + 2*r0)) + L*r0_3*(L_2*(-17*M + 9*r0) + r0_2*(-19*M + 10*r0)) - 2*a_2*L*r0*(L_2*(5*M + r0) + r0*(22*M_2 + 5*M*r0 - 4*r0_2))))/expr2_2;\n A93240 = (-4*(-24*a_12*E_2*M_2*(24*M_2 + 10*M*r0 - r0_2) + 4*a_11*E*L*M*(96*(3 + E_2)*M_3 + (1213 + 48*E_2)*M_2*r0 + 846*M*r0_2 + 150*r0_3) + 4*a*E*L*M*r0_5*(L_4*r0_2*(350*M_2 + (1549 + 534*E_2)*M*r0 - 888*r0_2) + L_6*(1048*M_2 + 6*M*r0 - 267*r0_2) + 3*L_2*r0_4*(-20*M_2 + 4*(5 + 117*E_2)*M*r0 - 17*r0_2) + 9*r0_6*(96*M_2 + 12*(-17 + 9*E_2)*M*r0 + 77*r0_2)) + 4*a_3*E*L*M*r0_3*(L_6*(3180*M_2 - 520*M*r0 - 261*r0_2) + L_4*r0*(928*M_3 + 6*(1057 + 178*E_2)*M_2*r0 + 2*(975 + 532*E_2)*M*r0_2 - 1479*r0_3) + L_2*r0_3*(-5322*M_3 + (4487 + 5454*E_2)*M_2*r0 + (3779 + 3828*E_2)*M*r0_2 - 921*r0_3) + 3*r0_5*(-1176*M_3 + 44*(-17 + 54*E_2)*M_2*r0 + 88*(-2 + 13*E_2)*M*r0_2 + 545*r0_3)) + r0_5*(72*E_2*M*r0_9*(-15*M + 7*r0) + 2*L_8*M*(20*M_2 - 16*M*r0 + 3*r0_2) + 2*L_6*r0_2*(912*M_3 - 10*(79 + 107*E_2)*M_2*r0 + (95 + 537*E_2)*M*r0_2 + 36*r0_3) + 3*L_2*r0_6*(-820*M_3 + 2*(853 - 1004*E_2)*M_2*r0 + 2*(-549 + 499*E_2)*M*r0_2 + 225*r0_3) + L_4*r0_4*(-112*M_3 + (2694 - 6896*E_2)*M_2*r0 + (-2657 + 3464*E_2)*M*r0_2 + 669*r0_3)) - a_10*M*(L_2*(576*(1 + 2*E_2)*M_3 + 4*(1153 + 753*E_2)*M_2*r0 + 3*(1087 + 428*E_2)*M*r0_2 + 18*(31 + 2*E_2)*r0_3) + 24*E_2*r0*(888*M_4 + 1756*M_3*r0 + 1080*M_2*r0_2 + 265*M*r0_3 + 30*r0_4)) + 4*a_5*E*L*M*r0_2*(6*L_6*r0 + L_4*(12240*M_3 + 2*(3411 + 530*E_2)*M_2*r0 + (881 + 530*E_2)*M*r0_2 - 546*r0_3) + L_2*r0*(-11664*M_4 + 2*(5207 + 2808*E_2)*M_3*r0 + 6*(3051 + 1589*E_2)*M_2*r0_2 + (5647 + 3444*E_2)*M*r0_3 - 1014*r0_4) + 3*r0_3*(-8076*M_4 + 12*(-191 + 396*E_2)*M_3*r0 + (1525 + 5784*E_2)*M_2*r0_2 + 6*(223 + 248*E_2)*M*r0_3 + 461*r0_4)) + 4*a_9*E*L*M*(3*L_2*(96*M_3 - 2*(-227 + E_2)*M_2*r0 + 465*M*r0_2 + 99*r0_3) + r0*(96*(111 + 43*E_2)*M_4 + 4*(3361 + 1764*E_2)*M_3*r0 + (7885 + 3576*E_2)*M_2*r0_2 + 6*(533 + 86*E_2)*M*r0_3 + 492*r0_4)) + a_2*r0_3*(10*L_8*M*(-424*M_2 + 210*M*r0 + r0_2) + 72*E_2*M*r0_8*(-120*M_2 + 41*M*r0 + 18*r0_2) + 8*L_6*r0*(1172*M_4 - (1181 + 1063*E_2)*M_3*r0 - (17 + 531*E_2)*M_2*r0_2 + (123 + 265*E_2)*M*r0_3 + 24*r0_4) + 3*L_2*r0_5*(304*M_4 - 4*(-637 + 2710*E_2)*M_3*r0 - 8*(32 + 257*E_2)*M_2*r0_2 + 2*(-753 + 1402*E_2)*M*r0_3 + 495*r0_4) + L_4*r0_3*(18712*M_4 - 8*(804 + 3091*E_2)*M_3*r0 - 6*(597 + 2320*E_2)*M_2*r0_2 + 3*(-223 + 2720*E_2)*M*r0_3 + 969*r0_4)) - a_8*(6*L_4*M*(64*M_3 - 6*(-73 + 2*E_2)*M_2*r0 + 4*(179 + 43*E_2)*M*r0_2 + (185 + 8*E_2)*r0_3) - 24*E_2*M*r0_2*(1872*M_5 + 2496*M_4*r0 - 1020*M_3*r0_2 - 1892*M_2*r0_3 - 623*M*r0_4 - 99*r0_5) + L_2*r0*(576*(37 + 86*E_2)*M_5 + 8*(1454 + 11103*E_2)*M_4*r0 + 3*(2035 + 21028*E_2)*M_3*r0_2 + 2*(2761 + 8838*E_2)*M_2*r0_3 + 6*(155 + 113*E_2)*M*r0_4 + 6*r0_5)) - a_4*r0_2*(12*L_8*M*r0 - 72*E_2*M*r0_6*(108*M_3 - 54*M_2*r0 + 97*M*r0_2 + 2*r0_3) + 2*L_6*(8160*M_4 + 12*(233 + 530*E_2)*M_3*r0 + 2*(-663 + 535*E_2)*M_2*r0_2 - (91 + 517*E_2)*M*r0_3 + 12*r0_4) + 3*L_2*r0_3*(-12132*M_5 + 4*(29 + 4330*E_2)*M_4*r0 + (743 + 23052*E_2)*M_3*r0_2 + 2*(1235 + 1986*E_2)*M_2*r0_3 - 4*(-92 + 603*E_2)*M*r0_4 - 313*r0_5) - 2*L_4*r0*(19440*M_5 - 4*(1853 + 4444*E_2)*M_4*r0 - 2*(4929 + 13514*E_2)*M_3*r0_2 - 6*(215 + 1322*E_2)*M_2*r0_3 + 15*(57 + 196*E_2)*M*r0_4 + 135*r0_5)) + 4*a_7*E*L*M*r0*(L_4*(-18*M_2 + 516*M*r0 + 153*r0_2) + L_2*(12384*M_4 + 12*(1937 + 340*E_2)*M_3*r0 + (13777 + 4026*E_2)*M_2*r0_2 + (4079 + 1020*E_2)*M*r0_3 + 153*r0_4) + 3*r0*(-7488*M_5 + 4*(-1601 + 648*E_2)*M_4*r0 + 32*(118 + 213*E_2)*M_3*r0_2 + 3*(1379 + 1528*E_2)*M_2*r0_3 + 6*(281 + 140*E_2)*M*r0_4 + 261*r0_5)) - a_6*r0*(-12*L_6*M*(2*M_2 - 86*M*r0 - (47 + E_2)*r0_2) - 144*E_2*M*r0_4*(444*M_4 + 226*M_3*r0 - 104*M_2*r0_2 - 39*M*r0_3 - 16*r0_4) + 2*L_4*(8256*M_5 + 12*(1349 + 2040*E_2)*M_4*r0 + 28*(113 + 675*E_2)*M_3*r0_2 + (1359 + 5128*E_2)*M_2*r0_3 - 71*(-5 + 8*E_2)*M*r0_4 + 15*r0_5) + L_2*r0*(-44928*M_6 + 48*(-353 + 486*E_2)*M_5*r0 + 16*(1403 + 6789*E_2)*M_4*r0_2 + 2*(4949 + 50898*E_2)*M_3*r0_3 + (5921 + 28164*E_2)*M_2*r0_4 - 84*(-3 + 14*E_2)*M*r0_5 - 123*r0_6))))/(3.*r0_5*expr2_3);\n A93400 = (2*L*r0_4*(12*a_3*E*M + 36*a*E*M*r0_2 - 3*a_2*L*(4*M + r0) + L*r0_2*(-19*M + 10*r0)))/expr2_2;\n A93420 = (24*a_10*E_2*M_2*(27*M + 10*r0) - 12*a_9*E*L*M*(4*(27 + 8*E_2)*M_2 + 4*(86 + 3*E_2)*M*r0 + 131*r0_2) - 4*a*E*L*M*r0_4*(L_4*(592*M_2 + 200*M*r0 - 255*r0_2) + 3*L_2*r0_2*(-268*M_2 + 3*(89 + 46*E_2)*M*r0 - 75*r0_2) + 3*r0_4*(36*M_2 + 2*(-241 + 108*E_2)*M*r0 + 229*r0_2)) + r0_4*(72*E_2*M*(15*M - 7*r0)*r0_7 - 8*L_6*M*(50*M_2 - 51*M*r0 + 13*r0_2) + L_4*r0_2*(-1684*M_3 + 4*(159 + 445*E_2)*M_2*r0 + (679 - 904*E_2)*M*r0_2 - 288*r0_3) + 3*L_2*r0_4*(404*M_3 + 8*(-158 + 157*E_2)*M_2*r0 + 15*(65 - 42*E_2)*M*r0_2 - 222*r0_3)) + 3*a_8*(L_2*(24*(9 + 16*E_2)*M_3 + 36*(36 + 13*E_2)*M_2*r0 + 38*(14 + E_2)*M*r0_2 + 9*r0_3) + 8*E_2*M*r0*(378*M_3 + 619*M_2*r0 + 244*M*r0_2 + 27*r0_3)) - 4*a_7*E*L*M*(3*L_2*(96*M_2 + 2*(99 + E_2)*M*r0 + 145*r0_2) + 2*r0*(12*(189 + 62*E_2)*M_3 + 3*(469 + 344*E_2)*M_2*r0 + 7*(169 + 42*E_2)*M*r0_2 + 572*r0_3)) - 4*a_3*E*L*M*r0_2*(3*L_4*(816*M_2 - 104*M*r0 - 77*r0_2) + L_2*r0*(-3168*M_3 + 12*(293 + 66*E_2)*M_2*r0 + 2*(842 + 423*E_2)*M*r0_2 - 347*r0_3) + 2*r0_3*(-2934*M_3 + 3*(-85 + 504*E_2)*M_2*r0 + (-1 + 906*E_2)*M*r0_2 + 716*r0_3)) + a_6*(3*L_4*(128*M_3 + 12*(31 + 2*E_2)*M_2*r0 + 2*(271 + 8*E_2)*M*r0_2 + 9*r0_3) - 72*E_2*M*r0_2*(288*M_4 + 252*M_3*r0 - 159*M_2*r0_2 - 115*M*r0_3 - 20*r0_4) + L_2*r0*(144*(63 + 124*E_2)*M_4 + 120*(-30 + 187*E_2)*M_3*r0 + 4*(668 + 2559*E_2)*M_2*r0_2 + 3*(1145 + 12*E_2)*M*r0_3 + 73*r0_4)) - 4*a_5*E*L*M*r0*(6*L_4*(3*M + 4*r0) + L_2*(4464*M_3 + 12*(419 + 68*E_2)*M_2*r0 + 3*(379 + 146*E_2)*M*r0_2 + 421*r0_3) + 2*r0*(-5184*M_4 + 54*(-33 + 20*E_2)*M_3*r0 + 8*(203 + 300*E_2)*M_2*r0_2 + 33*(33 + 26*E_2)*M*r0_3 + 748*r0_4)) - a_2*r0_2*(12*L_6*M*(-272*M_2 + 125*M*r0 + 7*r0_2) + 72*E_2*M*r0_6*(-60*M_2 + 25*M*r0 + 12*r0_2) + L_4*r0*(10656*M_4 - 16*(513 + 371*E_2)*M_3*r0 + 4*(249 - 944*E_2)*M_2*r0_2 + 16*(-15 + 112*E_2)*M*r0_3 + 305*r0_4) + L_2*r0_3*(8280*M_4 - 24*(59 + 437*E_2)*M_3*r0 + 4*(284 - 1641*E_2)*M_2*r0_2 + (-3161 + 3972*E_2)*M*r0_3 + 1013*r0_4)) + a_4*r0*(24*L_6*M*(M + 2*r0) - 72*E_2*M*r0_4*(210*M_3 + 13*M_2*r0 + 3*M*r0_2 - 6*r0_3) + L_4*(5952*M_4 + 24*(247 + 408*E_2)*M_3*r0 + 12*(-278 + 167*E_2)*M_2*r0_2 + 5*(335 - 168*E_2)*M*r0_3 + 10*r0_4) + L_2*r0*(-20736*M_5 + 144*(27 + 46*E_2)*M_4*r0 + 4*(857 + 6264*E_2)*M_3*r0_2 + 148*(-4 + 87*E_2)*M_2*r0_3 - 5*(-535 + 432*E_2)*M*r0_4 - 301*r0_5)))/(3.*r0_2*expr2_3);\n A93600 = -(r0*(-168*a_8*E_2*M_2 + 12*a_7*E*L*M*(4*(7 + 2*E_2)*M + 73*r0) - 3*a_6*(L_2*(8*(7 + 12*E_2)*M_2 + 4*(73 + 6*E_2)*M*r0 + 7*r0_2) + 8*E_2*M*r0*(52*M_2 + 71*M*r0 + 8*r0_2)) + 4*a*E*L*M*r0_3*(L_2*(-156*M_2 + 290*M*r0 - 111*r0_2) + 3*r0_2*(-72*M_2 + 4*(-31 + 9*E_2)*M*r0 + 79*r0_2)) + 4*a_5*E*L*M*(36*L_2*(2*M + r0) + r0*(8*(78 + 19*E_2)*M_2 + 4*(-16 + 49*E_2)*M*r0 + 451*r0_2)) - a_4*(24*L_4*M*(4*M + 3*r0) - 24*E_2*M*r0_2*(132*M_3 + 56*M_2*r0 - 48*M*r0_2 - 9*r0_3) + L_2*r0*(96*(13 + 19*E_2)*M_3 + 280*(-7 + 5*E_2)*M_2*r0 + (1379 - 214*E_2)*M*r0_2 + 64*r0_3)) + r0_3*(24*E_2*M*r0_5*(-15*M + 7*r0) + 2*L_4*M*(228*M_2 - 236*M*r0 + 61*r0_2) + L_2*r0_2*(12*M_3 + 8*(109 - 63*E_2)*M_2*r0 + (-907 + 262*E_2)*M*r0_2 + 234*r0_3)) + 4*a_3*E*L*M*r0*(L_2*(456*M_2 + 112*M*r0 - 75*r0_2) + r0*(-1584*M_3 + 8*(34 + 9*E_2)*M_2*r0 + 8*(-12 + 35*E_2)*M*r0_2 + 445*r0_3)) + a_2*r0*(72*E_2*M*r0_5*(3*M + 2*r0) + 2*L_4*M*(-304*M_2 + 84*M*r0 + 43*r0_2) + L_2*r0*(3168*M_4 - 8*(304 + 15*E_2)*M_3*r0 - 4*(-389 + 452*E_2)*M_2*r0_2 + 2*(-449 + 274*E_2)*M*r0_3 + 191*r0_4))))/(12.*expr2_3);\n A94020 = (48*L_2*r0_3*(a_2*(2*M + r0) + r0*(L_2 + r0_2)))/expr2_2;\n A94040 = (-8*(-72*a_10*E_2*M_2*r0_p_2M_2 + 24*a_9*E*L*M*(24*M_3 + 42*M_2*r0 + 29*M*r0_2 + 7*r0_3) - 4*a*E*L*M*r0_4*(L_6*(4*M - 6*r0) + 21*L_4*(15*M - 4*r0)*r0_2 + 3*L_2*(181*M - 46*r0)*r0_4 + 36*(5*M - r0)*r0_6) + r0_4*(4*L_8*M*(2*M - r0) + 144*E_2*M*r0_9 + L_6*r0_2*(71*M_2 - 4*(13 + 2*E_2)*M*r0 + 12*r0_2) + 3*L_2*r0_6*(57*M_2 + 4*(-13 + 29*E_2)*M*r0 + 13*r0_2) + 3*L_4*r0_4*(86*M_2 + 4*(-19 + 16*E_2)*M*r0 + 19*r0_2)) + 4*a_3*E*L*M*r0_3*(6*L_6 - 3*L_4*(160*M_2 + 97*M*r0 - 31*r0_2) + 6*r0_4*(-78*M_2 - 71*M*r0 + 23*r0_2) + L_2*r0_2*(-1494*M_2 - 820*M*r0 + 293*r0_2)) + 4*a_5*E*L*M*r0_2*(L_4*(42*M + 51*r0) - L_2*(1536*M_3 + 1634*M_2*r0 + 215*M*r0_2 - 242*r0_3) - 6*r0_2*(132*M_3 + 182*M_2*r0 + 31*M*r0_2 - 35*r0_3)) + a_2*r0_3*(-12*L_8*M + 72*E_2*M*r0_7*(7*M + 8*r0) + 2*L_6*(480*M_3 + 2*(81 + 2*E_2)*M_2*r0 - 5*(19 + 2*E_2)*M*r0_2 - 36*r0_3) + 3*L_4*r0_2*(408*M_3 + 4*(89 + 81*E_2)*M_2*r0 + 2*(-87 + 56*E_2)*M*r0_2 - 27*r0_3) + 6*L_2*r0_4*(32*M_3 + 18*(7 + 18*E_2)*M_2*r0 + 21*(-3 + 8*E_2)*M*r0_2 + 2*r0_3)) + a_4*r0_2*(864*E_2*M*r0_5*(M + r0)*(M + r0) - 3*L_6*(28*M_2 + 4*(13 + E_2)*M*r0 - r0_2) + 2*L_4*(1536*M_4 + 4*(313 + 120*E_2)*M_3*r0 + (13 + 420*E_2)*M_2*r0_2 + 3*(-161 + 16*E_2)*M*r0_3 - 66*r0_4) + 3*L_2*r0_2*(164*M_4 + 4*(191 + 336*E_2)*M_3*r0 + 3*(49 + 424*E_2)*M_2*r0_2 + 6*(-47 + 52*E_2)*M*r0_3 - 30*r0_4)) + 4*a_7*E*L*M*r0*(L_2*(96*M_2 + 202*M*r0 + 87*r0_2) - 6*(192*M_4 + 212*M_3*r0 + 70*M_2*r0_2 - 39*M*r0_3 - 25*r0_4)) + a_8*(-(L_2*(288*M_4 + 48*(15 + 4*E_2)*M_3*r0 + 2*(281 + 84*E_2)*M_2*r0_2 + 18*(7 + 2*E_2)*M*r0_3 - 3*r0_4)) + 144*E_2*M*r0*(16*M_4 + 20*M_3*r0 + 10*M_2*r0_2 + 4*M*r0_3 + r0_4)) + 2*a_6*r0*(-(L_4*(96*M_3 + 2*(160 + 21*E_2)*M_2*r0 + 3*(45 + 8*E_2)*M*r0_2 - 3*r0_3)) + 72*E_2*M*r0_3*(14*M_3 + 18*M_2*r0 + 13*M*r0_2 + 4*r0_3) + L_2*(1152*M_5 + 48*(23 + 32*E_2)*M_4*r0 + 14*(29 + 144*E_2)*M_3*r0_2 + (-569 + 852*E_2)*M_2*r0_3 + 15*(-25 + 8*E_2)*M*r0_4 - 30*r0_5))))/(3.*r0_4*expr2_3);\n A94200 = (12*L_2*r0_6)/expr2_2;\n A94220 = (-4*(-24*a_8*E_2*M_2*(2*M + r0) + 4*a_7*E*L*M*(24*M_2 + 27*M*r0 + 10*r0_2) + 2*a_5*E*L*M*r0*(-384*M_3 - 220*M_2*r0 + 16*M*r0_2 + 58*r0_3 + L_2*(16*M + 19*r0)) + 2*a*E*L*M*r0_4*(4*L_4 + 6*r0_3*(-14*M + r0) + L_2*r0*(-141*M + 28*r0)) + r0_5*(48*E_2*M*r0_5 - L_4*(9*M_2 + (9 + 4*E_2)*M*r0 - 8*r0_2) + L_2*r0_2*(9*M_2 + 2*(-13 + 28*E_2)*M*r0 + 12*r0_2)) + 2*a_3*E*L*M*r0_2*(4*L_4 + 2*r0_2*(-90*M_2 - 73*M*r0 + 22*r0_2) + L_2*(-248*M_2 - 127*M*r0 + 37*r0_2)) + a_6*M*(-(L_2*(48*M_2 + 4*(21 + 4*E_2)*M*r0 + 3*(11 + 2*E_2)*r0_2)) + 24*E_2*r0*(16*M_3 + 12*M_2*r0 + 5*M*r0_2 + 2*r0_3)) + a_2*r0_2*(-4*L_6*M + 72*E_2*M*r0_5*(M + 2*r0) + L_4*(248*M_3 + 54*M_2*r0 - (25 + 8*E_2)*M*r0_2 - 11*r0_3) + L_2*r0_2*(32*M_3 + 4*(29 + 50*E_2)*M_2*r0 + (-37 + 106*E_2)*M*r0_2 + 6*r0_3)) + a_4*r0*(-4*L_4*M*(4*M + (8 + E_2)*r0) + 72*E_2*M*r0_3*(2*M_2 + 3*M*r0 + 2*r0_2) + L_2*(384*M_4 + 8*(19 + 31*E_2)*M_3*r0 + (-13 + 200*E_2)*M_2*r0_2 + 4*(-20 + 11*E_2)*M*r0_3 - 6*r0_4))))/(r0*expr2_3);\n A94400 = (r0_2*(72*a_6*E_2*M_2 - 72*a_5*E*L*M*(2*M + r0) + 48*a_3*E*L*M*r0*(24*M_2 + M*r0 - 4*r0_2) + 24*a*E*L*M*r0_2*(-2*L_2*M + 3*r0_2*(4*M + r0)) + r0_2*(12*L_4*M*(2*M - r0) - 144*E_2*M*r0_5 + L_2*r0_2*(117*M_2 + 2*(5 + 6*E_2)*M*r0 - 38*r0_2)) + 9*a_4*(-16*E_2*M*r0*(4*M_2 + M*r0 + r0_2) + L_2*(8*M_2 + 8*M*r0 + r0_2)) - 2*a_2*r0*(-36*E_2*M*(M - 4*r0)*r0_3 + L_2*(288*M_3 - 12*(4 + E_2)*M_2*r0 - 6*(-1 + E_2)*M*r0_2 + 19*r0_3))))/(6.*expr2_3);\n A95020 = (8*L*r0*(12*a_5*E*M*(2*M + r0) - a_4*L*(24*M_2 + 15*M*r0 + 2*r0_2) + 6*a*E*M*r0_3*(5*L_2 + 6*r0_2) + 2*a_3*E*M*r0*(5*L_2 + 12*r0*(3*M + 2*r0)) + L*r0_3*(-2*L_2*(9*M - 5*r0) + r0_2*(-20*M + 11*r0)) - a_2*L*r0*(2*L_2*(5*M + r0) + r0*(46*M_2 + 9*M*r0 - 9*r0_2))))/expr2_3;\n A95040 = (-4*(24*a_12*E_2*M_2*(36*M_2 + 44*M*r0 + 13*r0_2) - 4*a_11*E*L*M*(48*(9 + E_2)*M_3 + 8*(65 + 12*E_2)*M_2*r0 + 18*(17 + 2*E_2)*M*r0_2 + 81*r0_3) + 2*a*E*L*M*r0_5*(L_4*r0_2*(457*M_2 + 4*(467 + 138*E_2)*M*r0 - 1122*r0_2) + 8*L_6*(126*M_2 + 11*M*r0 - 39*r0_2) + 3*L_2*r0_4*(501*M_2 + 4*(-79 + 114*E_2)*M*r0 + 16*r0_2) + 18*r0_6*(59*M_2 + 6*(-15 + 8*E_2)*M*r0 + 31*r0_2)) + 2*a_3*E*L*M*r0_3*(L_6*(3144*M_2 - 424*M*r0 - 294*r0_2) + L_4*r0*(1424*M_3 + (5491 + 1032*E_2)*M_2*r0 + 2*(1373 + 562*E_2)*M*r0_2 - 1884*r0_3) + 2*L_2*r0_3*(651*M_3 + 2*(755 + 1323*E_2)*M_2*r0 + (1537 + 1836*E_2)*M*r0_2 - 885*r0_3) + 6*r0_5*(-528*M_3 + (35 + 1368*E_2)*M_2*r0 + 2*(-19 + 238*E_2)*M*r0_2 + 105*r0_3)) + r0_5*(72*E_2*M*r0_9*(-7*M + 3*r0) + 2*L_8*M*(12*M_2 - 20*M*r0 + 7*r0_2) + 2*L_6*r0_2*(301*M_3 - (353 + 540*E_2)*M_2*r0 + 2*(60 + 139*E_2)*M*r0_2 - 12*r0_3) + 3*L_2*r0_6*(-476*M_3 + (837 - 940*E_2)*M_2*r0 + (-487 + 462*E_2)*M*r0_2 + 92*r0_3) + L_4*r0_4*(-946*M_3 - 7*(-291 + 476*E_2)*M_2*r0 + (-1355 + 1688*E_2)*M*r0_2 + 276*r0_3)) - 2*a_9*E*L*M*(3*L_2*(96*M_3 + 4*(-7 + 5*E_2)*M_2*r0 + 2*(53 + 4*E_2)*M*r0_2 + 111*r0_3) - 2*r0*(48*(137 + 46*E_2)*M_4 + 4*(1949 + 864*E_2)*M_3*r0 + 2*(1201 + 636*E_2)*M_2*r0_2 + 6*(-95 + 4*E_2)*M*r0_3 - 429*r0_4)) + a_10*M*(L_2*(288*(3 + 2*E_2)*M_3 + 4*(256 + 123*E_2)*M_2*r0 + 6*(157 + 22*E_2)*M*r0_2 + 3*(101 + 10*E_2)*r0_3) - 24*E_2*r0*(548*M_4 + 784*M_3*r0 + 309*M_2*r0_2 + 53*M*r0_3 + 15*r0_4)) + 2*a_5*E*L*M*r0_2*(18*L_6*(2*M + r0) + L_4*(12384*M_3 + 4*(1623 + 262*E_2)*M_2*r0 + 2*(655 + 292*E_2)*M*r0_2 - 1221*r0_3) + L_2*r0*(-9600*M_4 + 10*(1645 + 576*E_2)*M_3*r0 + 3*(6063 + 3076*E_2)*M_2*r0_2 + 4*(1087 + 804*E_2)*M*r0_3 - 3351*r0_4) - 6*r0_3*(4260*M_4 - 180*(-1 + 16*E_2)*M_3*r0 - (1489 + 3096*E_2)*M_2*r0_2 - 12*(25 + 46*E_2)*M*r0_3 + 158*r0_4)) + a_2*r0_3*(-72*E_2*M*r0_8*(71*M_2 - 29*M*r0 - 7*r0_2) + 4*L_8*M*(-524*M_2 + 252*M*r0 + 11*r0_2) + 2*L_6*r0*(2168*M_4 - (1571 + 2052*E_2)*M_3*r0 - (783 + 1192*E_2)*M_2*r0_2 + (407 + 559*E_2)*M*r0_3 + 96*r0_4) + 3*L_2*r0_5*(-78*M_4 + (1137 - 7196*E_2)*M_3*r0 + 4*(-55 + 117*E_2)*M_2*r0_2 + 2*(-268 + 633*E_2)*M*r0_3 + 189*r0_4) + L_4*r0_3*(5458*M_4 + (913 - 12344*E_2)*M_3*r0 - (3685 + 6772*E_2)*M_2*r0_2 + (175 + 3992*E_2)*M*r0_3 + 465*r0_4)) + a_8*(3*L_4*M*(64*M_3 + 4*(-23 + 30*E_2)*M_2*r0 + 12*(18 - 7*E_2)*M*r0_2 + (205 + 4*E_2)*r0_3) + 24*E_2*M*r0_2*(960*M_5 + 936*M_4*r0 - 788*M_3*r0_2 - 688*M_2*r0_3 - 139*M*r0_4 - 51*r0_5) - L_2*r0*(96*(137 + 276*E_2)*M_5 + 16*(773 + 2838*E_2)*M_4*r0 + 648*(5 + 38*E_2)*M_3*r0_2 + 2*(-1477 + 2622*E_2)*M_2*r0_3 + 6*(-287 + 45*E_2)*M*r0_4 + 9*r0_5)) - a_4*r0_2*(6*L_8*M*(4*M + 3*r0) - 72*E_2*M*r0_6*(24*M_3 - 52*M_2*r0 + 81*M*r0_2 - 2*r0_3) + 4*L_6*(2064*M_4 + 6*(113 + 262*E_2)*M_3*r0 + 2*(27 + 166*E_2)*M_2*r0_2 - 2*(137 + 68*E_2)*M*r0_3 + 9*r0_4) + L_4*r0*(-18240*M_5 + 4*(1745 + 4676*E_2)*M_4*r0 + (10747 + 26296*E_2)*M_3*r0_2 + 2*(2165 + 3444*E_2)*M_2*r0_3 - 4*(905 + 733*E_2)*M*r0_4 - 144*r0_5) - 3*L_2*r0_3*(6452*M_5 - 8*(89 + 1804*E_2)*M_4*r0 - 6*(227 + 2024*E_2)*M_3*r0_2 + (-1305 + 992*E_2)*M_2*r0_3 + (425 + 1036*E_2)*M*r0_4 + 99*r0_5)) + 2*a_7*E*L*M*r0*(-3*L_4*(60*M_2 - 4*(27 + E_2)*M*r0 + 51*r0_2) + 2*L_2*(6624*M_4 + 48*(257 + 43*E_2)*M_3*r0 + 70*(101 + 27*E_2)*M_2*r0_2 + 2*(335 + 222*E_2)*M*r0_3 - 933*r0_4) - 6*r0*(3840*M_5 - 4*(-671 + 360*E_2)*M_4*r0 - 24*(129 + 158*E_2)*M_3*r0_2 - 3*(719 + 728*E_2)*M_2*r0_3 + 20*(1 - 12*E_2)*M*r0_4 + 286*r0_5)) - a_6*r0*(-6*L_6*M*(20*M_2 - 2*(29 + 6*E_2)*M*r0 + (49 - 3*E_2)*r0_2) - 48*E_2*M*r0_4*(654*M_4 + 156*M_3*r0 - 139*M_2*r0_2 + 31*M*r0_3 - 27*r0_4) + L_4*(8832*M_5 + 96*(185 + 258*E_2)*M_4*r0 + 8*(1093 + 2229*E_2)*M_3*r0_2 + 20*(-24 + 209*E_2)*M_2*r0_3 - (2789 + 640*E_2)*M*r0_4 + 45*r0_5) + L_2*r0*(-23040*M_6 + 48*(-203 + 340*E_2)*M_5*r0 + 2*(8033 + 35712*E_2)*M_4*r0_2 + (11021 + 45528*E_2)*M_3*r0_3 + 4*(-65 + 1656*E_2)*M_2*r0_4 - 3*(947 + 132*E_2)*M*r0_5 + 3*r0_6))))/(3.*r0_5*expr2_4);\n A95200 = (2*L*r0_4*(12*a_3*E*M + 36*a*E*M*r0_2 - 3*a_2*L*(4*M + r0) + L*r0_2*(-20*M + 11*r0)))/expr2_3;\n A95220 = (-192*a_10*E_2*M_2*(3*M + 2*r0) + 48*a_9*E*L*M*(2*(12 + E_2)*M_2 + (-7 + 3*E_2)*M*r0 - 4*r0_2) + 6*a_7*E*L*M*(L_2*(48*M_2 + 4*(-36 + E_2)*M*r0 - 55*r0_2) - 4*r0*(16*(61 + 17*E_2)*M_3 + (569 + 284*E_2)*M_2*r0 + 8*(15 + 4*E_2)*M*r0_2 + r0_3)) + 3*a_8*(L_2*(-96*(2 + E_2)*M_3 + 24*(10 + 3*E_2)*M_2*r0 + (107 - 2*E_2)*M*r0_2 + 9*r0_3) + 8*E_2*M*r0*(488*M_3 + 454*M_2*r0 + 103*M*r0_2 + 27*r0_3)) - 6*a_3*E*L*M*r0_2*(2*L_4*(828*M_2 - 140*M*r0 - 77*r0_2) + L_2*r0*(-1424*M_3 + (2651 + 552*E_2)*M_2*r0 + 2*(483 + 262*E_2)*M*r0_2 - 632*r0_3) + 4*r0_3*(-972*M_3 + (215 + 612*E_2)*M_2*r0 + 8*(9 + 28*E_2)*M*r0_2 + 83*r0_3)) - r0_4*(144*E_2*M*r0_7*(-7*M + 3*r0) + 4*L_6*M*(38*M_2 - 45*M*r0 + 13*r0_2) + 6*L_2*r0_4*(-252*M_3 + (579 - 572*E_2)*M_2*r0 + 2*(-201 + 143*E_2)*M*r0_2 + 86*r0_3) + L_4*r0_2*(590*M_3 + (135 - 1676*E_2)*M_2*r0 + 4*(-161 + 218*E_2)*M*r0_2 + 204*r0_3)) + a_2*r0_2*(72*E_2*M*r0_6*(84*M_2 - 43*M*r0 - 9*r0_2) + 24*L_6*M*(138*M_2 - 67*M*r0 - 3*r0_2) + 3*L_2*r0_3*(-2642*M_4 + (543 + 5692*E_2)*M_3*r0 + (119 + 232*E_2)*M_2*r0_2 - 22*(-27 + 53*E_2)*M*r0_3 - 248*r0_4) + L_4*r0*(-9456*M_4 + 2*(3105 + 3236*E_2)*M_3*r0 + (847 + 3268*E_2)*M_2*r0_2 - 4*(154 + 437*E_2)*M*r0_3 - 228*r0_4)) - 6*a_5*E*L*M*r0*(L_4*(-12*M + 8*r0) + L_2*(3264*M_3 + 4*(793 + 138*E_2)*M_2*r0 + 2*(397 + 128*E_2)*M*r0_2 - 229*r0_3) + 4*r0*(-1776*M_4 + 12*(-25 + 36*E_2)*M_3*r0 + 11*(81 + 76*E_2)*M_2*r0_2 + 2*(109 + 86*E_2)*M*r0_3 - 11*r0_4)) - 3*a_6*(L_4*(32*M_3 + 24*(-7 + E_2)*M_2*r0 - 8*(14 + E_2)*M*r0_2 - 9*r0_3) + 8*E_2*M*r0_2*(888*M_4 + 396*M_3*r0 - 508*M_2*r0_2 - 113*M*r0_3 - 63*r0_4) - L_2*r0*(64*(61 + 102*E_2)*M_4 + 20*(46 + 329*E_2)*M_3*r0 + 8*(10 + 241*E_2)*M_2*r0_2 - (121 + 26*E_2)*M*r0_3 - 5*r0_4)) + 3*a_4*r0*(-8*L_6*M*(M - r0) - 24*E_2*M*r0_4*(180*M_3 - 46*M_2*r0 + 59*M*r0_2 - 9*r0_3) + L_4*(2176*M_4 + 4*(509 + 828*E_2)*M_3*r0 + 4*(-21 + 122*E_2)*M_2*r0_2 - 4*(59 + 71*E_2)*M*r0_3 - 29*r0_4) + L_2*r0*(-7104*M_5 + 16*(48 + 235*E_2)*M_4*r0 + (2593 + 9920*E_2)*M_3*r0_2 + (747 + 1952*E_2)*M_2*r0_3 - 2*(100 + 309*E_2)*M*r0_4 - 90*r0_5)) - 2*a*E*L*M*r0_4*(2*L_4*(752*M_2 + 76*M*r0 - 243*r0_2) + 36*r0_4*(15*M_2 + 2*(-32 + 15*E_2)*M*r0 + 29*r0_2) + 3*L_2*r0_2*(133*M_2 - 102*r0_2 + 88*M*(r0 + 3*E_2*r0))))/(3.*r0_2*expr2_4);\n A95400 = (r0*(-72*a_8*E_2*M_2 + 36*a_7*E*L*M*(4*M - 15*r0) - 4*a_5*E*L*M*r0*(18*L_2 + 12*(107 + 22*E_2)*M_2 + 6*(-7 + 22*E_2)*M*r0 + 233*r0_2) + 3*a_6*(3*L_2*(-8*M_2 + 4*(15 + E_2)*M*r0 + r0_2) + 8*E_2*M*r0*(107*M_2 + 46*M*r0 + 12*r0_2)) - 12*a*E*L*M*r0_3*(L_2*(8*M_2 + 70*M*r0 - 41*r0_2) + r0_2*(-87*M_2 + 4*(-31 + 9*E_2)*M*r0 + 86*r0_2)) + a_4*r0*(36*L_4*M - 72*E_2*M*r0*(68*M_3 - 6*M_2*r0 - 2*M*r0_2 - 5*r0_3) + L_2*(24*(107 + 132*E_2)*M_3 + 24*(-53 + 25*E_2)*M_2*r0 + 2*(388 - 171*E_2)*M*r0_2 + 23*r0_3)) - 3*r0_3*(24*E_2*M*r0_5*(-7*M + 3*r0) + 2*L_4*M*(64*M_2 - 70*M*r0 + 19*r0_2) + L_2*r0_2*(-28*M_3 + 3*(117 - 68*E_2)*M_2*r0 + 22*(-16 + 5*E_2)*M*r0_2 + 90*r0_3)) - 4*a_3*E*L*M*r0*(3*L_2*(264*M_2 - 32*M*r0 - 35*r0_2) + r0*(-2448*M_3 + 3*(287 + 72*E_2)*M_2*r0 + 2*(61 + 120*E_2)*M*r0_2 + 266*r0_3)) - a_2*r0*(72*E_2*M*r0_4*(-13*M_2 + 14*M*r0 + 2*r0_2) + 6*L_4*M*(-176*M_2 + 76*M*r0 + 13*r0_2) + L_2*r0*(4896*M_4 - 12*(251 + 112*E_2)*M_3*r0 + (991 - 1380*E_2)*M_2*r0_2 + 4*(-181 + 177*E_2)*M*r0_3 + 238*r0_4))))/(12.*expr2_4);\n A96000 = (4*L_2*r0_6)/expr2_3;\n A96020 = (2*(72*a_8*E_2*M_2*(2*M + r0) - 96*a_7*E*L*M*(3*M_2 + 5*M*r0 + 2*r0_2) + 8*a*E*L*M*r0_3*(L_4*(4*M - 6*r0) + 8*L_2*(10*M - 3*r0)*r0_2 + 3*r0_4*(7*M + 3*r0)) - 24*a_5*E*L*M*r0*(-64*M_3 - 34*M_2*r0 + 13*M*r0_2 + 19*r0_3 + L_2*(7*M + 9*r0)) + r0_3*(-96*E_2*M*r0_7 + 8*L_6*M*(-2*M + r0) + L_4*r0_2*(3*M_2 + 4*(-9 + 4*E_2)*M*r0 + 12*r0_2) + L_2*r0_4*(43*M_2 - 20*(4 + 5*E_2)*M*r0 + 24*r0_2)) - 8*a_3*E*L*M*r0_2*(6*L_4 + 6*r0_2*(-5*M_2 - 13*M*r0 + 4*r0_2) + L_2*(-136*M_2 - 77*M*r0 + 45*r0_2)) + 3*a_6*(L_2*(48*M_3 + 4*(34 + 7*E_2)*M_2*r0 + 2*(29 + 6*E_2)*M*r0_2 + r0_3) - 8*E_2*M*r0*(32*M_3 + 12*M_2*r0 + 3*M*r0_2 + 4*r0_3)) + a_2*r0_2*(24*L_6*M + 72*E_2*M*(M - 4*r0)*r0_5 - 2*L_4*(272*M_3 + 8*(18 + E_2)*M_2*r0 - (81 + 20*E_2)*M*r0_2 - 36*r0_3) + L_2*r0_2*(158*M_3 - (657 + 364*E_2)*M_2*r0 + 2*(49 - 82*E_2)*M*r0_2 + 84*r0_3)) + a_4*r0*(72*E_2*M*r0_3*(2*M_2 - M*r0 - 4*r0_2) + 3*L_4*(28*M_2 + 4*(15 + 2*E_2)*M*r0 + r0_2) - L_2*(768*M_4 + 16*(33 + 34*E_2)*M_3*r0 + 8*(-4 + 41*E_2)*M_2*r0_2 + 2*(-209 + 14*E_2)*M*r0_3 - 63*r0_4))))/(3.*r0*expr2_4);\n A96200 = (r0_2*(72*a_6*E_2*M_2 - 24*a_5*E*L*M*(6*M + 7*r0) - 24*a_3*E*L*M*r0*(2*L_2 - 32*M_2 - M*r0 + 11*r0_2) + 8*a*E*L*M*r0_2*(2*L_2*(M - 3*r0) + 3*r0_2*(M + 6*r0)) + 3*a_4*(-16*E_2*M*r0*(8*M_2 - M*r0 + 2*r0_2) + L_2*(24*M_2 + 8*(7 + E_2)*M*r0 + 5*r0_2)) + r0_2*(-96*E_2*M*r0_5 + 4*L_4*M*(-2*M + r0) + L_2*r0_2*(139*M_2 + 4*(-32 + 5*E_2)*M*r0 + 24*r0_2)) + 2*a_2*r0*(12*L_4*M + 12*E_2*M*(11*M - 8*r0)*r0_3 + L_2*(-192*M_3 - 4*(9 + E_2)*M_2*r0 + (29 + 22*E_2)*M*r0_2 + 6*r0_3))))/(6.*expr2_4);\n A97000 = (2*L*r0_4*(4*a_3*E*M + 12*a*E*M*r0_2 - a_2*L*(4*M + r0) + L*r0_2*(-7*M + 4*r0)))/expr2_4;\n A97020 = (-24*a_10*E_2*M_2*(25*M + 14*r0) + 12*a_9*E*L*M*(4*(25 + 4*E_2)*M_2 + 12*(8 + E_2)*M*r0 + 33*r0_2) - 4*a*E*L*M*r0_4*(L_4*(300*M_2 - 8*M*r0 - 81*r0_2) + 3*r0_4*(45*M_2 + 8*(-11 + 6*E_2)*M*r0 + 38*r0_2) + L_2*r0_2*(538*M_2 + 2*(-205 + 63*E_2)*M*r0 + 69*r0_2)) + r0_4*(24*E_2*M*(13*M - 5*r0)*r0_7 + 4*L_6*M*(6*M_2 - M*r0 - r0_2) + L_2*r0_4*(611*M_3 + 2*(-517 + 512*E_2)*M_2*r0 + 2*(307 - 253*E_2)*M*r0_2 - 120*r0_3) + L_4*r0_2*(335*M_3 + 24*(-27 + 22*E_2)*M_2*r0 + 2*(221 - 142*E_2)*M*r0_2 - 96*r0_3)) - 4*a_3*E*L*M*r0_2*(L_4*(840*M_2 - 172*M*r0 - 81*r0_2) + 2*L_2*r0*(-176*M_3 + 2*(395 + 72*E_2)*M_2*r0 + (131 + 121*E_2)*M*r0_2 - 246*r0_3) + 2*r0_3*(-1029*M_3 + 2*(299 + 360*E_2)*M_2*r0 + 2*(68 + 73*E_2)*M*r0_2 - 75*r0_3)) - 3*a_8*(L_2*(8*(25 + 24*E_2)*M_3 + 4*(68 + 27*E_2)*M_2*r0 + 2*(53 + 7*E_2)*M*r0_2 - 3*r0_3) - 8*E_2*M*r0*(198*M_3 + 97*M_2*r0 - 12*M*r0_2 + 9*r0_3)) + 8*a_7*E*L*M*(3*L_2*(24*M_2 + (9 + E_2)*M*r0 + 15*r0_2) + r0*(-4*(297 + 74*E_2)*M_3 - 2*(331 + 112*E_2)*M_2*r0 + (149 + 34*E_2)*M*r0_2 + 183*r0_3)) - 4*a_5*E*L*M*r0*(-18*L_4*M + L_2*(1776*M_3 + 2*(751 + 140*E_2)*M_2*r0 + 2*(201 + 55*E_2)*M*r0_2 - 363*r0_3) + r0*(-3648*M_4 + 2*(-19 + 504*E_2)*M_3*r0 + (2517 + 1744*E_2)*M_2*r0_2 + 2*(53 + 58*E_2)*M*r0_3 - 531*r0_4)) + a_2*r0_2*(4*L_6*M*(280*M_2 - 141*M*r0 - 7*r0_2) + 24*E_2*M*r0_6*(102*M_2 - 55*M*r0 - 6*r0_2) + L_2*r0_3*(-2774*M_4 + (1301 + 8284*E_2)*M_3*r0 + (209 - 2152*E_2)*M_2*r0_2 + 8*(11 - 122*E_2)*M*r0_3 - 96*r0_4) + L_4*r0*(-2720*M_4 + 24*(67 + 97*E_2)*M_3*r0 + 5*(111 + 188*E_2)*M_2*r0_2 - 10*(45 + 58*E_2)*M*r0_3 + 12*r0_4)) + a_4*r0*(-24*L_6*M_2 + 24*E_2*M*r0_4*(-162*M_3 + 107*M_2*r0 - 105*M*r0_2 + 12*r0_3) + L_4*(2368*M_4 + 4*(527 + 840*E_2)*M_3*r0 + 4*(230 + 79*E_2)*M_2*r0_2 - (1009 + 296*E_2)*M*r0_3 - 72*r0_4) + L_2*r0*(-7296*M_5 + 8*(41 + 668*E_2)*M_4*r0 + 12*(333 + 974*E_2)*M_3*r0_2 + (1451 - 660*E_2)*M_2*r0_3 - (1171 + 476*E_2)*M*r0_4 - 30*r0_5)) - a_6*(24*E_2*M*r0_2*(304*M_4 + 20*M_3*r0 - 183*M_2*r0_2 + 35*M*r0_3 - 22*r0_4) + L_2*r0*(-48*(99 + 148*E_2)*M_4 - 4*(742 + 1423*E_2)*M_3*r0 + 26*(25 - 16*E_2)*M_2*r0_2 + 3*(459 + 16*E_2)*M*r0_3 + 45*r0_4) + 3*L_4*(64*M_3 + 106*M*r0_2 - 3*r0_3 + 12*M_2*(r0 + 2*E_2*r0))))/(3.*r0_2*expr2_5);\n A97200 = -(r0*(264*a_8*E_2*M_2 - 12*a_7*E*L*M*((44 + 8*E_2)*M + 13*r0) + 3*a_6*(L_2*((88 + 96*E_2)*M_2 + 4*(13 + 2*E_2)*M*r0 + 3*r0_2) - 8*E_2*M*r0*(90*M_2 - 9*M*r0 + 8*r0_2)) + 4*a*E*L*M*r0_3*(L_2*(196*M_2 - 26*M*r0 - 45*r0_2) + 3*r0_2*(-47*M_2 + 2*(-17 + 6*E_2)*M*r0 + 34*r0_2)) + 4*a_3*E*L*M*r0*(L_2*(600*M_2 - 248*M*r0 - 57*r0_2) + r0*(-1680*M_3 + (881 + 216*E_2)*M_2*r0 + 10*(23 + 4*E_2)*M*r0_2 - 72*r0_3)) + a_4*(24*L_4*M*(4*M + r0) + 24*E_2*M*r0_2*(140*M_3 - 76*M_2*r0 + 36*M*r0_2 - 11*r0_3) + L_2*r0*(-240*(9 + 10*E_2)*M_3 + 8*(-25 + 77*E_2)*M_2*r0 + (281 + 226*E_2)*M*r0_2 + 30*r0_3)) + r0_3*(24*E_2*M*r0_5*(-13*M + 5*r0) + 2*L_4*M*(20*M_2 - 32*M*r0 + 11*r0_2) + L_2*r0_2*(-131*M_3 + (506 - 304*E_2)*M_2*r0 + 10*(-47 + 17*E_2)*M*r0_2 + 120*r0_3)) + a_2*r0*(2*L_4*M*(-400*M_2 + 228*M*r0 + r0_2) + 24*E_2*M*r0_4*(-46*M_2 + 41*M*r0 + 2*r0_2) + L_2*r0*(3360*M_4 - 4*(425 + 422*E_2)*M_3*r0 + (-77 + 8*E_2)*M_2*r0_2 + 12*(-7 + 31*E_2)*M*r0_3 + 96*r0_4)) + 4*a_5*E*L*M*(-12*L_2*(6*M + r0) + r0*(40*(27 + 5*E_2)*M_2 - 123*r0_2 - 4*M*(r0 + 5*E_2*r0)))))/(12.*expr2_5);\n A98000 = (r0_2*(12*a_6*E_2*M_2 - 12*a_5*E*L*M*(2*M + 3*r0) + 4*a*E*L*M*(2*M - 3*r0)*r0_2*(L_2 - 3*r0_2) - 12*a_3*E*L*M*r0*(L_2 - 8*M_2 + 4*r0_2) + 3*a_4*(-4*E_2*M*r0*(4*M_2 - 2*M*r0 + r0_2) + L_2*(4*M_2 + 2*(6 + E_2)*M*r0 + r0_2)) + r0_2*(-12*E_2*M*r0_5 + 2*L_4*M*(-2*M + r0) + L_2*r0_2*(29*M_2 + 4*(-10 + E_2)*M*r0 + 12*r0_2)) + 2*a_2*r0*(3*L_4*M + 6*E_2*M*(5*M - 2*r0)*r0_3 + L_2*(-24*M_3 - 2*(6 + E_2)*M_2*r0 + (7 + 5*E_2)*M*r0_2 + 3*r0_3))))/(3.*expr2_5);\n A99000 = -(r0*(60*a_8*E_2*M_2 - 12*a_7*E*L*M*(2*(5 + E_2)*M + 7*r0) + 4*a*E*L*M_2*r0_3*(L_2*(48*M - 26*r0) + 3*r0_2*(-6*M + 5*r0)) + 3*a_6*(L_2*(4*(5 + 6*E_2)*M_2 + (28 + 3*E_2)*M*r0 + r0_2) - 4*E_2*M*r0*(27*M_2 - 12*M*r0 + 2*r0_2)) - M*r0_3*(12*E_2*(3*M - r0)*r0_5 + L_4*(24*M_2 - 22*M*r0 + 5*r0_2) + 2*L_2*r0_2*(9*M_2 + (-5 + 12*E_2)*M*r0 + (1 - 7*E_2)*r0_2)) + 2*a_3*E*L*M*r0*(L_2*(168*M_2 - 110*M*r0 - 9*r0_2) + 2*r0*(-216*M_3 + 4*(37 + 9*E_2)*M_2*r0 + 2*(23 - 5*E_2)*M*r0_2 - 39*r0_3)) + a_4*(3*L_4*M*(8*M + 3*r0) + 12*E_2*M*r0_2*(36*M_3 - 34*M_2*r0 + 18*M*r0_2 - 3*r0_3) + L_2*r0*(-12*(27 + 28*E_2)*M_3 + 2*(-74 + 103*E_2)*M_2*r0 + (127 + 26*E_2)*M*r0_2 + 9*r0_3)) + a_2*M*r0*(36*E_2*M*r0_4*(-5*M + 4*r0) - 2*L_4*(56*M_2 - 39*M*r0 + 4*r0_2) + L_2*r0*(432*M_3 - 8*(23 + 39*E_2)*M_2*r0 + 2*(-45 + 61*E_2)*M*r0_2 + (41 + 31*E_2)*r0_3)) + 2*a_5*E*L*M*(-9*L_2*(4*M + r0) + 2*r0*(2*(81 + 14*E_2)*M_2 - 48*r0_2 + M*(r0 - 16*E_2*r0)))))/(6.*expr2_6);\n }\n\n /* rho */\n alpha20 = r0*r0 / (a*a + r0*(r0-2.0*M));\n alpha02 = r0*r0;\n beta = 4.0*(L*L + r0*r0 + a*a*(r0+2.0*M)/r0);\n}\n" }, { "path": "external/Licenses/BlazeCopyright.txt", "content": "Copyright (C) 2012-2020 Klaus Iglberger - All Rights Reserved\nhttps://bitbucket.org/blaze-lib/blaze/src/\n" }, { "path": "external/Licenses/BlazeLicense.txt", "content": " LICENSE OF THE BLAZE LIBRARY\n 11 November 2013\n\n\nThe Blaze library and headers are licensed under the New (Revised) BSD\nlicense. Redistribution and use in source and binary forms, with or without\nmodification, are permitted provided that the following conditions are met:\n\n* Redistributions of source code must retain the above copyright notice, this\n list of conditions and the following disclaimer.\n\n* Redistributions in binary form must reproduce the above copyright notice,\n this list of conditions and the following disclaimer in the documentation\n and/or other materials provided with the distribution.\n\n* Neither the name of the {organization} nor the names of its\n contributors may be used to endorse or promote products derived from\n this software without specific prior written permission.\n\nTHIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\"\nAND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE\nIMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\nDISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE\nFOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL\nDAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR\nSERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER\nCAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,\nOR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\nOF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n" }, { "path": "external/Licenses/BoostCopyright.txt", "content": "https://www.boost.org/\n" }, { "path": "external/Licenses/BoostLicense.txt", "content": "Boost Software License - Version 1.0 - August 17th, 2003\n\nPermission is hereby granted, free of charge, to any person or organization\nobtaining a copy of the software and accompanying documentation covered by\nthis license (the \"Software\") to use, reproduce, display, distribute,\nexecute, and transmit the Software, and to prepare derivative works of the\nSoftware, and to permit third-parties to whom the Software is furnished to\ndo so, all subject to the following:\n\nThe copyright notices in the Software and this entire statement, including\nthe above license grant, this restriction and the following disclaimer,\nmust be included in all copies of the Software, in whole or in part, and\nall derivative works of the Software, unless such copies or derivative\nworks are solely in the form of machine-executable object code generated by\na source language processor.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT\nSHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE\nFOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,\nARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\nDEALINGS IN THE SOFTWARE.\n" }, { "path": "external/Licenses/BrigandCopyright.txt", "content": "Copyright Edouard Alligand and Joel Falcou 2015-2017\nhttps://github.com/edouarda/brigand\n" }, { "path": "external/Licenses/BrigandLicense.txt", "content": "Boost Software License - Version 1.0 - August 17th, 2003\n\nPermission is hereby granted, free of charge, to any person or organization\nobtaining a copy of the software and accompanying documentation covered by\nthis license (the \"Software\") to use, reproduce, display, distribute,\nexecute, and transmit the Software, and to prepare derivative works of the\nSoftware, and to permit third-parties to whom the Software is furnished to\ndo so, all subject to the following:\n\nThe copyright notices in the Software and this entire statement, including\nthe above license grant, this restriction and the following disclaimer,\nmust be included in all copies of the Software, in whole or in part, and\nall derivative works of the Software, unless such copies or derivative\nworks are solely in the form of machine-executable object code generated by\na source language processor.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT\nSHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE\nFOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,\nARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\nDEALINGS IN THE SOFTWARE.\n" }, { "path": "external/Licenses/Catch2Copyright.txt", "content": "Copyright Catch2 Authors\nhttps://github.com/catchorg/Catch2\n" }, { "path": "external/Licenses/Catch2License.txt", "content": "Boost Software License - Version 1.0 - August 17th, 2003\n\nPermission is hereby granted, free of charge, to any person or organization\nobtaining a copy of the software and accompanying documentation covered by\nthis license (the \"Software\") to use, reproduce, display, distribute,\nexecute, and transmit the Software, and to prepare derivative works of the\nSoftware, and to permit third-parties to whom the Software is furnished to\ndo so, all subject to the following:\n\nThe copyright notices in the Software and this entire statement, including\nthe above license grant, this restriction and the following disclaimer,\nmust be included in all copies of the Software, in whole or in part, and\nall derivative works of the Software, unless such copies or derivative\nworks are solely in the form of machine-executable object code generated by\na source language processor.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT\nSHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE\nFOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,\nARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\nDEALINGS IN THE SOFTWARE.\n" }, { "path": "external/Licenses/CharmCopyright.txt", "content": "Copyright (C) 1990-present University of Illinois, Charmworks, Inc.\nhttps://github.com/charmplusplus/charm/\n" }, { "path": "external/Licenses/CharmLicense.txt", "content": " Apache License\n Version 2.0, January 2004\n http://www.apache.org/licenses/\n\n TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION\n\n 1. Definitions.\n\n \"License\" shall mean the terms and conditions for use, reproduction,\n and distribution as defined by Sections 1 through 9 of this document.\n\n \"Licensor\" shall mean the copyright owner or entity authorized by\n the copyright owner that is granting the License.\n\n \"Legal Entity\" shall mean the union of the acting entity and all\n other entities that control, are controlled by, or are under common\n control with that entity. For the purposes of this definition,\n \"control\" means (i) the power, direct or indirect, to cause the\n direction or management of such entity, whether by contract or\n otherwise, or (ii) ownership of fifty percent (50%) or more of the\n outstanding shares, or (iii) beneficial ownership of such entity.\n\n \"You\" (or \"Your\") shall mean an individual or Legal Entity\n exercising permissions granted by this License.\n\n \"Source\" form shall mean the preferred form for making modifications,\n including but not limited to software source code, documentation\n source, and configuration files.\n\n \"Object\" form shall mean any form resulting from mechanical\n transformation or translation of a Source form, including but\n not limited to compiled object code, generated documentation,\n and conversions to other media types.\n\n \"Work\" shall mean the work of authorship, whether in Source or\n Object form, made available under the License, as indicated by a\n copyright notice that is included in or attached to the work\n (an example is provided in the Appendix below).\n\n \"Derivative Works\" shall mean any work, whether in Source or Object\n form, that is based on (or derived from) the Work and for which the\n editorial revisions, annotations, elaborations, or other modifications\n represent, as a whole, an original work of authorship. For the purposes\n of this License, Derivative Works shall not include works that remain\n separable from, or merely link (or bind by name) to the interfaces of,\n the Work and Derivative Works thereof.\n\n \"Contribution\" shall mean any work of authorship, including\n the original version of the Work and any modifications or additions\n to that Work or Derivative Works thereof, that is intentionally\n submitted to Licensor for inclusion in the Work by the copyright owner\n or by an individual or Legal Entity authorized to submit on behalf of\n the copyright owner. For the purposes of this definition, \"submitted\"\n means any form of electronic, verbal, or written communication sent\n to the Licensor or its representatives, including but not limited to\n communication on electronic mailing lists, source code control systems,\n and issue tracking systems that are managed by, or on behalf of, the\n Licensor for the purpose of discussing and improving the Work, but\n excluding communication that is conspicuously marked or otherwise\n designated in writing by the copyright owner as \"Not a Contribution.\"\n\n \"Contributor\" shall mean Licensor and any individual or Legal Entity\n on behalf of whom a Contribution has been received by Licensor and\n subsequently incorporated within the Work.\n\n 2. Grant of Copyright License. Subject to the terms and conditions of\n this License, each Contributor hereby grants to You a perpetual,\n worldwide, non-exclusive, no-charge, royalty-free, irrevocable\n copyright license to reproduce, prepare Derivative Works of,\n publicly display, publicly perform, sublicense, and distribute the\n Work and such Derivative Works in Source or Object form.\n\n 3. Grant of Patent License. Subject to the terms and conditions of\n this License, each Contributor hereby grants to You a perpetual,\n worldwide, non-exclusive, no-charge, royalty-free, irrevocable\n (except as stated in this section) patent license to make, have made,\n use, offer to sell, sell, import, and otherwise transfer the Work,\n where such license applies only to those patent claims licensable\n by such Contributor that are necessarily infringed by their\n Contribution(s) alone or by combination of their Contribution(s)\n with the Work to which such Contribution(s) was submitted. If You\n institute patent litigation against any entity (including a\n cross-claim or counterclaim in a lawsuit) alleging that the Work\n or a Contribution incorporated within the Work constitutes direct\n or contributory patent infringement, then any patent licenses\n granted to You under this License for that Work shall terminate\n as of the date such litigation is filed.\n\n 4. Redistribution. You may reproduce and distribute copies of the\n Work or Derivative Works thereof in any medium, with or without\n modifications, and in Source or Object form, provided that You\n meet the following conditions:\n\n (a) You must give any other recipients of the Work or\n Derivative Works a copy of this License; and\n\n (b) You must cause any modified files to carry prominent notices\n stating that You changed the files; and\n\n (c) You must retain, in the Source form of any Derivative Works\n that You distribute, all copyright, patent, trademark, and\n attribution notices from the Source form of the Work,\n excluding those notices that do not pertain to any part of\n the Derivative Works; and\n\n (d) If the Work includes a \"NOTICE\" text file as part of its\n distribution, then any Derivative Works that You distribute must\n include a readable copy of the attribution notices contained\n within such NOTICE file, excluding those notices that do not\n pertain to any part of the Derivative Works, in at least one\n of the following places: within a NOTICE text file distributed\n as part of the Derivative Works; within the Source form or\n documentation, if provided along with the Derivative Works; or,\n within a display generated by the Derivative Works, if and\n wherever such third-party notices normally appear. The contents\n of the NOTICE file are for informational purposes only and\n do not modify the License. You may add Your own attribution\n notices within Derivative Works that You distribute, alongside\n or as an addendum to the NOTICE text from the Work, provided\n that such additional attribution notices cannot be construed\n as modifying the License.\n\n You may add Your own copyright statement to Your modifications and\n may provide additional or different license terms and conditions\n for use, reproduction, or distribution of Your modifications, or\n for any such Derivative Works as a whole, provided Your use,\n reproduction, and distribution of the Work otherwise complies with\n the conditions stated in this License.\n\n 5. Submission of Contributions. Unless You explicitly state otherwise,\n any Contribution intentionally submitted for inclusion in the Work\n by You to the Licensor shall be under the terms and conditions of\n this License, without any additional terms or conditions.\n Notwithstanding the above, nothing herein shall supersede or modify\n the terms of any separate license agreement you may have executed\n with Licensor regarding such Contributions.\n\n 6. Trademarks. This License does not grant permission to use the trade\n names, trademarks, service marks, or product names of the Licensor,\n except as required for reasonable and customary use in describing the\n origin of the Work and reproducing the content of the NOTICE file.\n\n 7. Disclaimer of Warranty. Unless required by applicable law or\n agreed to in writing, Licensor provides the Work (and each\n Contributor provides its Contributions) on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or\n implied, including, without limitation, any warranties or conditions\n of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A\n PARTICULAR PURPOSE. You are solely responsible for determining the\n appropriateness of using or redistributing the Work and assume any\n risks associated with Your exercise of permissions under this License.\n\n 8. Limitation of Liability. In no event and under no legal theory,\n whether in tort (including negligence), contract, or otherwise,\n unless required by applicable law (such as deliberate and grossly\n negligent acts) or agreed to in writing, shall any Contributor be\n liable to You for damages, including any direct, indirect, special,\n incidental, or consequential damages of any character arising as a\n result of this License or out of the use or inability to use the\n Work (including but not limited to damages for loss of goodwill,\n work stoppage, computer failure or malfunction, or any and all\n other commercial damages or losses), even if such Contributor\n has been advised of the possibility of such damages.\n\n 9. Accepting Warranty or Additional Liability. While redistributing\n the Work or Derivative Works thereof, You may choose to offer,\n and charge a fee for, acceptance of support, warranty, indemnity,\n or other liability obligations and/or rights consistent with this\n License. However, in accepting such obligations, You may act only\n on Your own behalf and on Your sole responsibility, not on behalf\n of any other Contributor, and only if You agree to indemnify,\n defend, and hold each Contributor harmless for any liability\n incurred by, or claims asserted against, such Contributor by reason\n of your accepting any such warranty or additional liability.\n\n END OF TERMS AND CONDITIONS\n\n APPENDIX: How to apply the Apache License to your work.\n\n To apply the Apache License to your work, attach the following\n boilerplate notice, with the fields enclosed by brackets \"[]\"\n replaced with your own identifying information. (Don't include\n the brackets!) The text should be enclosed in the appropriate\n comment syntax for the file format. We also recommend that a\n file or class name and description of purpose be included on the\n same \"printed page\" as the copyright notice for easier\n identification within third-party archives.\n\n Copyright [yyyy] [name of copyright owner]\n\n Licensed under the Apache License, Version 2.0 (the \"License\");\n you may not use this file except in compliance with the License.\n You may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\n Unless required by applicable law or agreed to in writing, software\n distributed under the License is distributed on an \"AS IS\" BASIS,\n WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n See the License for the specific language governing permissions and\n limitations under the License.\n\n--- LLVM Exceptions to the Apache 2.0 License ----\n\nAs an exception, if, as a result of your compiling your source code, portions\nof this Software are embedded into an Object form of such source code, you\nmay redistribute such embedded portions in such Object form without complying\nwith the conditions of Sections 4(a), 4(b) and 4(d) of the License.\n\nIn addition, if you combine or link compiled forms of this Software with\nsoftware that is licensed under the GPLv2 (\"Combined Software\") and if a\ncourt of competent jurisdiction determines that the patent provision (Section\n3), the indemnity provision (Section 9) or other Section of the License\nconflicts with the conditions of the GPLv2, you may retroactively and\nprospectively choose to deem waived or otherwise exclude such Section(s) of\nthe License, but only in their entirety and only with respect to the Combined\nSoftware.\n" }, { "path": "external/Licenses/GslCopyright.txt", "content": "Copyright (C) 2007 Free Software Foundation, Inc. \nhttps://www.gnu.org/software/gsl/\n" }, { "path": "external/Licenses/GslLicense.txt", "content": " GNU GENERAL PUBLIC LICENSE\n Version 3, 29 June 2007\n\n Copyright (C) 2007 Free Software Foundation, Inc. \n Everyone is permitted to copy and distribute verbatim copies\n of this license document, but changing it is not allowed.\n\n Preamble\n\n The GNU General Public License is a free, copyleft license for\nsoftware and other kinds of works.\n\n The licenses for most software and other practical works are designed\nto take away your freedom to share and change the works. By contrast,\nthe GNU General Public License is intended to guarantee your freedom to\nshare and change all versions of a program--to make sure it remains free\nsoftware for all its users. We, the Free Software Foundation, use the\nGNU General Public License for most of our software; it applies also to\nany other work released this way by its authors. You can apply it to\nyour programs, too.\n\n When we speak of free software, we are referring to freedom, not\nprice. Our General Public Licenses are designed to make sure that you\nhave the freedom to distribute copies of free software (and charge for\nthem if you wish), that you receive source code or can get it if you\nwant it, that you can change the software or use pieces of it in new\nfree programs, and that you know you can do these things.\n\n To protect your rights, we need to prevent others from denying you\nthese rights or asking you to surrender the rights. Therefore, you have\ncertain responsibilities if you distribute copies of the software, or if\nyou modify it: responsibilities to respect the freedom of others.\n\n For example, if you distribute copies of such a program, whether\ngratis or for a fee, you must pass on to the recipients the same\nfreedoms that you received. You must make sure that they, too, receive\nor can get the source code. And you must show them these terms so they\nknow their rights.\n\n Developers that use the GNU GPL protect your rights with two steps:\n(1) assert copyright on the software, and (2) offer you this License\ngiving you legal permission to copy, distribute and/or modify it.\n\n For the developers' and authors' protection, the GPL clearly explains\nthat there is no warranty for this free software. For both users' and\nauthors' sake, the GPL requires that modified versions be marked as\nchanged, so that their problems will not be attributed erroneously to\nauthors of previous versions.\n\n Some devices are designed to deny users access to install or run\nmodified versions of the software inside them, although the manufacturer\ncan do so. This is fundamentally incompatible with the aim of\nprotecting users' freedom to change the software. The systematic\npattern of such abuse occurs in the area of products for individuals to\nuse, which is precisely where it is most unacceptable. Therefore, we\nhave designed this version of the GPL to prohibit the practice for those\nproducts. If such problems arise substantially in other domains, we\nstand ready to extend this provision to those domains in future versions\nof the GPL, as needed to protect the freedom of users.\n\n Finally, every program is threatened constantly by software patents.\nStates should not allow patents to restrict development and use of\nsoftware on general-purpose computers, but in those that do, we wish to\navoid the special danger that patents applied to a free program could\nmake it effectively proprietary. To prevent this, the GPL assures that\npatents cannot be used to render the program non-free.\n\n The precise terms and conditions for copying, distribution and\nmodification follow.\n\n TERMS AND CONDITIONS\n\n 0. Definitions.\n\n \"This License\" refers to version 3 of the GNU General Public License.\n\n \"Copyright\" also means copyright-like laws that apply to other kinds of\nworks, such as semiconductor masks.\n\n \"The Program\" refers to any copyrightable work licensed under this\nLicense. Each licensee is addressed as \"you\". \"Licensees\" and\n\"recipients\" may be individuals or organizations.\n\n To \"modify\" a work means to copy from or adapt all or part of the work\nin a fashion requiring copyright permission, other than the making of an\nexact copy. The resulting work is called a \"modified version\" of the\nearlier work or a work \"based on\" the earlier work.\n\n A \"covered work\" means either the unmodified Program or a work based\non the Program.\n\n To \"propagate\" a work means to do anything with it that, without\npermission, would make you directly or secondarily liable for\ninfringement under applicable copyright law, except executing it on a\ncomputer or modifying a private copy. Propagation includes copying,\ndistribution (with or without modification), making available to the\npublic, and in some countries other activities as well.\n\n To \"convey\" a work means any kind of propagation that enables other\nparties to make or receive copies. Mere interaction with a user through\na computer network, with no transfer of a copy, is not conveying.\n\n An interactive user interface displays \"Appropriate Legal Notices\"\nto the extent that it includes a convenient and prominently visible\nfeature that (1) displays an appropriate copyright notice, and (2)\ntells the user that there is no warranty for the work (except to the\nextent that warranties are provided), that licensees may convey the\nwork under this License, and how to view a copy of this License. If\nthe interface presents a list of user commands or options, such as a\nmenu, a prominent item in the list meets this criterion.\n\n 1. Source Code.\n\n The \"source code\" for a work means the preferred form of the work\nfor making modifications to it. \"Object code\" means any non-source\nform of a work.\n\n A \"Standard Interface\" means an interface that either is an official\nstandard defined by a recognized standards body, or, in the case of\ninterfaces specified for a particular programming language, one that\nis widely used among developers working in that language.\n\n The \"System Libraries\" of an executable work include anything, other\nthan the work as a whole, that (a) is included in the normal form of\npackaging a Major Component, but which is not part of that Major\nComponent, and (b) serves only to enable use of the work with that\nMajor Component, or to implement a Standard Interface for which an\nimplementation is available to the public in source code form. A\n\"Major Component\", in this context, means a major essential component\n(kernel, window system, and so on) of the specific operating system\n(if any) on which the executable work runs, or a compiler used to\nproduce the work, or an object code interpreter used to run it.\n\n The \"Corresponding Source\" for a work in object code form means all\nthe source code needed to generate, install, and (for an executable\nwork) run the object code and to modify the work, including scripts to\ncontrol those activities. However, it does not include the work's\nSystem Libraries, or general-purpose tools or generally available free\nprograms which are used unmodified in performing those activities but\nwhich are not part of the work. For example, Corresponding Source\nincludes interface definition files associated with source files for\nthe work, and the source code for shared libraries and dynamically\nlinked subprograms that the work is specifically designed to require,\nsuch as by intimate data communication or control flow between those\nsubprograms and other parts of the work.\n\n The Corresponding Source need not include anything that users\ncan regenerate automatically from other parts of the Corresponding\nSource.\n\n The Corresponding Source for a work in source code form is that\nsame work.\n\n 2. Basic Permissions.\n\n All rights granted under this License are granted for the term of\ncopyright on the Program, and are irrevocable provided the stated\nconditions are met. This License explicitly affirms your unlimited\npermission to run the unmodified Program. The output from running a\ncovered work is covered by this License only if the output, given its\ncontent, constitutes a covered work. This License acknowledges your\nrights of fair use or other equivalent, as provided by copyright law.\n\n You may make, run and propagate covered works that you do not\nconvey, without conditions so long as your license otherwise remains\nin force. You may convey covered works to others for the sole purpose\nof having them make modifications exclusively for you, or provide you\nwith facilities for running those works, provided that you comply with\nthe terms of this License in conveying all material for which you do\nnot control copyright. Those thus making or running the covered works\nfor you must do so exclusively on your behalf, under your direction\nand control, on terms that prohibit them from making any copies of\nyour copyrighted material outside their relationship with you.\n\n Conveying under any other circumstances is permitted solely under\nthe conditions stated below. Sublicensing is not allowed; section 10\nmakes it unnecessary.\n\n 3. Protecting Users' Legal Rights From Anti-Circumvention Law.\n\n No covered work shall be deemed part of an effective technological\nmeasure under any applicable law fulfilling obligations under article\n11 of the WIPO copyright treaty adopted on 20 December 1996, or\nsimilar laws prohibiting or restricting circumvention of such\nmeasures.\n\n When you convey a covered work, you waive any legal power to forbid\ncircumvention of technological measures to the extent such circumvention\nis effected by exercising rights under this License with respect to\nthe covered work, and you disclaim any intention to limit operation or\nmodification of the work as a means of enforcing, against the work's\nusers, your or third parties' legal rights to forbid circumvention of\ntechnological measures.\n\n 4. Conveying Verbatim Copies.\n\n You may convey verbatim copies of the Program's source code as you\nreceive it, in any medium, provided that you conspicuously and\nappropriately publish on each copy an appropriate copyright notice;\nkeep intact all notices stating that this License and any\nnon-permissive terms added in accord with section 7 apply to the code;\nkeep intact all notices of the absence of any warranty; and give all\nrecipients a copy of this License along with the Program.\n\n You may charge any price or no price for each copy that you convey,\nand you may offer support or warranty protection for a fee.\n\n 5. Conveying Modified Source Versions.\n\n You may convey a work based on the Program, or the modifications to\nproduce it from the Program, in the form of source code under the\nterms of section 4, provided that you also meet all of these conditions:\n\n a) The work must carry prominent notices stating that you modified\n it, and giving a relevant date.\n\n b) The work must carry prominent notices stating that it is\n released under this License and any conditions added under section\n 7. This requirement modifies the requirement in section 4 to\n \"keep intact all notices\".\n\n c) You must license the entire work, as a whole, under this\n License to anyone who comes into possession of a copy. This\n License will therefore apply, along with any applicable section 7\n additional terms, to the whole of the work, and all its parts,\n regardless of how they are packaged. This License gives no\n permission to license the work in any other way, but it does not\n invalidate such permission if you have separately received it.\n\n d) If the work has interactive user interfaces, each must display\n Appropriate Legal Notices; however, if the Program has interactive\n interfaces that do not display Appropriate Legal Notices, your\n work need not make them do so.\n\n A compilation of a covered work with other separate and independent\nworks, which are not by their nature extensions of the covered work,\nand which are not combined with it such as to form a larger program,\nin or on a volume of a storage or distribution medium, is called an\n\"aggregate\" if the compilation and its resulting copyright are not\nused to limit the access or legal rights of the compilation's users\nbeyond what the individual works permit. Inclusion of a covered work\nin an aggregate does not cause this License to apply to the other\nparts of the aggregate.\n\n 6. Conveying Non-Source Forms.\n\n You may convey a covered work in object code form under the terms\nof sections 4 and 5, provided that you also convey the\nmachine-readable Corresponding Source under the terms of this License,\nin one of these ways:\n\n a) Convey the object code in, or embodied in, a physical product\n (including a physical distribution medium), accompanied by the\n Corresponding Source fixed on a durable physical medium\n customarily used for software interchange.\n\n b) Convey the object code in, or embodied in, a physical product\n (including a physical distribution medium), accompanied by a\n written offer, valid for at least three years and valid for as\n long as you offer spare parts or customer support for that product\n model, to give anyone who possesses the object code either (1) a\n copy of the Corresponding Source for all the software in the\n product that is covered by this License, on a durable physical\n medium customarily used for software interchange, for a price no\n more than your reasonable cost of physically performing this\n conveying of source, or (2) access to copy the\n Corresponding Source from a network server at no charge.\n\n c) Convey individual copies of the object code with a copy of the\n written offer to provide the Corresponding Source. This\n alternative is allowed only occasionally and noncommercially, and\n only if you received the object code with such an offer, in accord\n with subsection 6b.\n\n d) Convey the object code by offering access from a designated\n place (gratis or for a charge), and offer equivalent access to the\n Corresponding Source in the same way through the same place at no\n further charge. You need not require recipients to copy the\n Corresponding Source along with the object code. If the place to\n copy the object code is a network server, the Corresponding Source\n may be on a different server (operated by you or a third party)\n that supports equivalent copying facilities, provided you maintain\n clear directions next to the object code saying where to find the\n Corresponding Source. Regardless of what server hosts the\n Corresponding Source, you remain obligated to ensure that it is\n available for as long as needed to satisfy these requirements.\n\n e) Convey the object code using peer-to-peer transmission, provided\n you inform other peers where the object code and Corresponding\n Source of the work are being offered to the general public at no\n charge under subsection 6d.\n\n A separable portion of the object code, whose source code is excluded\nfrom the Corresponding Source as a System Library, need not be\nincluded in conveying the object code work.\n\n A \"User Product\" is either (1) a \"consumer product\", which means any\ntangible personal property which is normally used for personal, family,\nor household purposes, or (2) anything designed or sold for incorporation\ninto a dwelling. In determining whether a product is a consumer product,\ndoubtful cases shall be resolved in favor of coverage. For a particular\nproduct received by a particular user, \"normally used\" refers to a\ntypical or common use of that class of product, regardless of the status\nof the particular user or of the way in which the particular user\nactually uses, or expects or is expected to use, the product. A product\nis a consumer product regardless of whether the product has substantial\ncommercial, industrial or non-consumer uses, unless such uses represent\nthe only significant mode of use of the product.\n\n \"Installation Information\" for a User Product means any methods,\nprocedures, authorization keys, or other information required to install\nand execute modified versions of a covered work in that User Product from\na modified version of its Corresponding Source. The information must\nsuffice to ensure that the continued functioning of the modified object\ncode is in no case prevented or interfered with solely because\nmodification has been made.\n\n If you convey an object code work under this section in, or with, or\nspecifically for use in, a User Product, and the conveying occurs as\npart of a transaction in which the right of possession and use of the\nUser Product is transferred to the recipient in perpetuity or for a\nfixed term (regardless of how the transaction is characterized), the\nCorresponding Source conveyed under this section must be accompanied\nby the Installation Information. But this requirement does not apply\nif neither you nor any third party retains the ability to install\nmodified object code on the User Product (for example, the work has\nbeen installed in ROM).\n\n The requirement to provide Installation Information does not include a\nrequirement to continue to provide support service, warranty, or updates\nfor a work that has been modified or installed by the recipient, or for\nthe User Product in which it has been modified or installed. Access to a\nnetwork may be denied when the modification itself materially and\nadversely affects the operation of the network or violates the rules and\nprotocols for communication across the network.\n\n Corresponding Source conveyed, and Installation Information provided,\nin accord with this section must be in a format that is publicly\ndocumented (and with an implementation available to the public in\nsource code form), and must require no special password or key for\nunpacking, reading or copying.\n\n 7. Additional Terms.\n\n \"Additional permissions\" are terms that supplement the terms of this\nLicense by making exceptions from one or more of its conditions.\nAdditional permissions that are applicable to the entire Program shall\nbe treated as though they were included in this License, to the extent\nthat they are valid under applicable law. If additional permissions\napply only to part of the Program, that part may be used separately\nunder those permissions, but the entire Program remains governed by\nthis License without regard to the additional permissions.\n\n When you convey a copy of a covered work, you may at your option\nremove any additional permissions from that copy, or from any part of\nit. (Additional permissions may be written to require their own\nremoval in certain cases when you modify the work.) You may place\nadditional permissions on material, added by you to a covered work,\nfor which you have or can give appropriate copyright permission.\n\n Notwithstanding any other provision of this License, for material you\nadd to a covered work, you may (if authorized by the copyright holders of\nthat material) supplement the terms of this License with terms:\n\n a) Disclaiming warranty or limiting liability differently from the\n terms of sections 15 and 16 of this License; or\n\n b) Requiring preservation of specified reasonable legal notices or\n author attributions in that material or in the Appropriate Legal\n Notices displayed by works containing it; or\n\n c) Prohibiting misrepresentation of the origin of that material, or\n requiring that modified versions of such material be marked in\n reasonable ways as different from the original version; or\n\n d) Limiting the use for publicity purposes of names of licensors or\n authors of the material; or\n\n e) Declining to grant rights under trademark law for use of some\n trade names, trademarks, or service marks; or\n\n f) Requiring indemnification of licensors and authors of that\n material by anyone who conveys the material (or modified versions of\n it) with contractual assumptions of liability to the recipient, for\n any liability that these contractual assumptions directly impose on\n those licensors and authors.\n\n All other non-permissive additional terms are considered \"further\nrestrictions\" within the meaning of section 10. If the Program as you\nreceived it, or any part of it, contains a notice stating that it is\ngoverned by this License along with a term that is a further\nrestriction, you may remove that term. If a license document contains\na further restriction but permits relicensing or conveying under this\nLicense, you may add to a covered work material governed by the terms\nof that license document, provided that the further restriction does\nnot survive such relicensing or conveying.\n\n If you add terms to a covered work in accord with this section, you\nmust place, in the relevant source files, a statement of the\nadditional terms that apply to those files, or a notice indicating\nwhere to find the applicable terms.\n\n Additional terms, permissive or non-permissive, may be stated in the\nform of a separately written license, or stated as exceptions;\nthe above requirements apply either way.\n\n 8. Termination.\n\n You may not propagate or modify a covered work except as expressly\nprovided under this License. Any attempt otherwise to propagate or\nmodify it is void, and will automatically terminate your rights under\nthis License (including any patent licenses granted under the third\nparagraph of section 11).\n\n However, if you cease all violation of this License, then your\nlicense from a particular copyright holder is reinstated (a)\nprovisionally, unless and until the copyright holder explicitly and\nfinally terminates your license, and (b) permanently, if the copyright\nholder fails to notify you of the violation by some reasonable means\nprior to 60 days after the cessation.\n\n Moreover, your license from a particular copyright holder is\nreinstated permanently if the copyright holder notifies you of the\nviolation by some reasonable means, this is the first time you have\nreceived notice of violation of this License (for any work) from that\ncopyright holder, and you cure the violation prior to 30 days after\nyour receipt of the notice.\n\n Termination of your rights under this section does not terminate the\nlicenses of parties who have received copies or rights from you under\nthis License. If your rights have been terminated and not permanently\nreinstated, you do not qualify to receive new licenses for the same\nmaterial under section 10.\n\n 9. Acceptance Not Required for Having Copies.\n\n You are not required to accept this License in order to receive or\nrun a copy of the Program. Ancillary propagation of a covered work\noccurring solely as a consequence of using peer-to-peer transmission\nto receive a copy likewise does not require acceptance. However,\nnothing other than this License grants you permission to propagate or\nmodify any covered work. These actions infringe copyright if you do\nnot accept this License. Therefore, by modifying or propagating a\ncovered work, you indicate your acceptance of this License to do so.\n\n 10. Automatic Licensing of Downstream Recipients.\n\n Each time you convey a covered work, the recipient automatically\nreceives a license from the original licensors, to run, modify and\npropagate that work, subject to this License. You are not responsible\nfor enforcing compliance by third parties with this License.\n\n An \"entity transaction\" is a transaction transferring control of an\norganization, or substantially all assets of one, or subdividing an\norganization, or merging organizations. If propagation of a covered\nwork results from an entity transaction, each party to that\ntransaction who receives a copy of the work also receives whatever\nlicenses to the work the party's predecessor in interest had or could\ngive under the previous paragraph, plus a right to possession of the\nCorresponding Source of the work from the predecessor in interest, if\nthe predecessor has it or can get it with reasonable efforts.\n\n You may not impose any further restrictions on the exercise of the\nrights granted or affirmed under this License. For example, you may\nnot impose a license fee, royalty, or other charge for exercise of\nrights granted under this License, and you may not initiate litigation\n(including a cross-claim or counterclaim in a lawsuit) alleging that\nany patent claim is infringed by making, using, selling, offering for\nsale, or importing the Program or any portion of it.\n\n 11. Patents.\n\n A \"contributor\" is a copyright holder who authorizes use under this\nLicense of the Program or a work on which the Program is based. The\nwork thus licensed is called the contributor's \"contributor version\".\n\n A contributor's \"essential patent claims\" are all patent claims\nowned or controlled by the contributor, whether already acquired or\nhereafter acquired, that would be infringed by some manner, permitted\nby this License, of making, using, or selling its contributor version,\nbut do not include claims that would be infringed only as a\nconsequence of further modification of the contributor version. For\npurposes of this definition, \"control\" includes the right to grant\npatent sublicenses in a manner consistent with the requirements of\nthis License.\n\n Each contributor grants you a non-exclusive, worldwide, royalty-free\npatent license under the contributor's essential patent claims, to\nmake, use, sell, offer for sale, import and otherwise run, modify and\npropagate the contents of its contributor version.\n\n In the following three paragraphs, a \"patent license\" is any express\nagreement or commitment, however denominated, not to enforce a patent\n(such as an express permission to practice a patent or covenant not to\nsue for patent infringement). To \"grant\" such a patent license to a\nparty means to make such an agreement or commitment not to enforce a\npatent against the party.\n\n If you convey a covered work, knowingly relying on a patent license,\nand the Corresponding Source of the work is not available for anyone\nto copy, free of charge and under the terms of this License, through a\npublicly available network server or other readily accessible means,\nthen you must either (1) cause the Corresponding Source to be so\navailable, or (2) arrange to deprive yourself of the benefit of the\npatent license for this particular work, or (3) arrange, in a manner\nconsistent with the requirements of this License, to extend the patent\nlicense to downstream recipients. \"Knowingly relying\" means you have\nactual knowledge that, but for the patent license, your conveying the\ncovered work in a country, or your recipient's use of the covered work\nin a country, would infringe one or more identifiable patents in that\ncountry that you have reason to believe are valid.\n\n If, pursuant to or in connection with a single transaction or\narrangement, you convey, or propagate by procuring conveyance of, a\ncovered work, and grant a patent license to some of the parties\nreceiving the covered work authorizing them to use, propagate, modify\nor convey a specific copy of the covered work, then the patent license\nyou grant is automatically extended to all recipients of the covered\nwork and works based on it.\n\n A patent license is \"discriminatory\" if it does not include within\nthe scope of its coverage, prohibits the exercise of, or is\nconditioned on the non-exercise of one or more of the rights that are\nspecifically granted under this License. You may not convey a covered\nwork if you are a party to an arrangement with a third party that is\nin the business of distributing software, under which you make payment\nto the third party based on the extent of your activity of conveying\nthe work, and under which the third party grants, to any of the\nparties who would receive the covered work from you, a discriminatory\npatent license (a) in connection with copies of the covered work\nconveyed by you (or copies made from those copies), or (b) primarily\nfor and in connection with specific products or compilations that\ncontain the covered work, unless you entered into that arrangement,\nor that patent license was granted, prior to 28 March 2007.\n\n Nothing in this License shall be construed as excluding or limiting\nany implied license or other defenses to infringement that may\notherwise be available to you under applicable patent law.\n\n 12. No Surrender of Others' Freedom.\n\n If conditions are imposed on you (whether by court order, agreement or\notherwise) that contradict the conditions of this License, they do not\nexcuse you from the conditions of this License. If you cannot convey a\ncovered work so as to satisfy simultaneously your obligations under this\nLicense and any other pertinent obligations, then as a consequence you may\nnot convey it at all. For example, if you agree to terms that obligate you\nto collect a royalty for further conveying from those to whom you convey\nthe Program, the only way you could satisfy both those terms and this\nLicense would be to refrain entirely from conveying the Program.\n\n 13. Use with the GNU Affero General Public License.\n\n Notwithstanding any other provision of this License, you have\npermission to link or combine any covered work with a work licensed\nunder version 3 of the GNU Affero General Public License into a single\ncombined work, and to convey the resulting work. The terms of this\nLicense will continue to apply to the part which is the covered work,\nbut the special requirements of the GNU Affero General Public License,\nsection 13, concerning interaction through a network will apply to the\ncombination as such.\n\n 14. Revised Versions of this License.\n\n The Free Software Foundation may publish revised and/or new versions of\nthe GNU General Public License from time to time. Such new versions will\nbe similar in spirit to the present version, but may differ in detail to\naddress new problems or concerns.\n\n Each version is given a distinguishing version number. If the\nProgram specifies that a certain numbered version of the GNU General\nPublic License \"or any later version\" applies to it, you have the\noption of following the terms and conditions either of that numbered\nversion or of any later version published by the Free Software\nFoundation. If the Program does not specify a version number of the\nGNU General Public License, you may choose any version ever published\nby the Free Software Foundation.\n\n If the Program specifies that a proxy can decide which future\nversions of the GNU General Public License can be used, that proxy's\npublic statement of acceptance of a version permanently authorizes you\nto choose that version for the Program.\n\n Later license versions may give you additional or different\npermissions. However, no additional obligations are imposed on any\nauthor or copyright holder as a result of your choosing to follow a\nlater version.\n\n 15. Disclaimer of Warranty.\n\n THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY\nAPPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT\nHOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM \"AS IS\" WITHOUT WARRANTY\nOF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,\nTHE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR\nPURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM\nIS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF\nALL NECESSARY SERVICING, REPAIR OR CORRECTION.\n\n 16. Limitation of Liability.\n\n IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING\nWILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS\nTHE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY\nGENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE\nUSE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF\nDATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD\nPARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),\nEVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF\nSUCH DAMAGES.\n\n 17. Interpretation of Sections 15 and 16.\n\n If the disclaimer of warranty and limitation of liability provided\nabove cannot be given local legal effect according to their terms,\nreviewing courts shall apply local law that most closely approximates\nan absolute waiver of all civil liability in connection with the\nProgram, unless a warranty or assumption of liability accompanies a\ncopy of the Program in return for a fee.\n\n END OF TERMS AND CONDITIONS\n\n How to Apply These Terms to Your New Programs\n\n If you develop a new program, and you want it to be of the greatest\npossible use to the public, the best way to achieve this is to make it\nfree software which everyone can redistribute and change under these terms.\n\n To do so, attach the following notices to the program. It is safest\nto attach them to the start of each source file to most effectively\nstate the exclusion of warranty; and each file should have at least\nthe \"copyright\" line and a pointer to where the full notice is found.\n\n \n Copyright (C) \n\n This program is free software: you can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version.\n\n This program is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU General Public License for more details.\n\n You should have received a copy of the GNU General Public License\n along with this program. If not, see .\n\nAlso add information on how to contact you by electronic and paper mail.\n\n If the program does terminal interaction, make it output a short\nnotice like this when it starts in an interactive mode:\n\n Copyright (C) \n This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.\n This is free software, and you are welcome to redistribute it\n under certain conditions; type `show c' for details.\n\nThe hypothetical commands `show w' and `show c' should show the appropriate\nparts of the General Public License. Of course, your program's commands\nmight be different; for a GUI interface, you would use an \"about box\".\n\n You should also get your employer (if you work as a programmer) or school,\nif any, to sign a \"copyright disclaimer\" for the program, if necessary.\nFor more information on this, and how to apply and follow the GNU GPL, see\n.\n\n The GNU General Public License does not permit incorporating your program\ninto proprietary programs. If your program is a subroutine library, you\nmay consider it more useful to permit linking proprietary applications with\nthe library. If this is what you want to do, use the GNU Lesser General\nPublic License instead of this License. But first, please read\n.\n" }, { "path": "external/Licenses/Hdf5Copyright.txt", "content": "HDF5 (Hierarchical Data Format 5) Software Library and Utilities\nCopyright 2006 by The HDF Group.\n\nNCSA HDF5 (Hierarchical Data Format 5) Software Library and Utilities\nCopyright 1998-2006 by The Board of Trustees of the University of Illinois.\nhttps://github.com/HDFGroup/hdf5\n" }, { "path": "external/Licenses/Hdf5License.txt", "content": "Copyright Notice and License Terms for\nHDF5 (Hierarchical Data Format 5) Software Library and Utilities\n-----------------------------------------------------------------------------\n\nHDF5 (Hierarchical Data Format 5) Software Library and Utilities\nCopyright 2006 by The HDF Group.\n\nNCSA HDF5 (Hierarchical Data Format 5) Software Library and Utilities\nCopyright 1998-2006 by The Board of Trustees of the University of Illinois.\n\nAll rights reserved.\n\nRedistribution and use in source and binary forms, with or without\nmodification, are permitted for any purpose (including commercial purposes)\nprovided that the following conditions are met:\n\n1. Redistributions of source code must retain the above copyright notice,\n this list of conditions, and the following disclaimer.\n\n2. Redistributions in binary form must reproduce the above copyright notice,\n this list of conditions, and the following disclaimer in the documentation\n and/or materials provided with the distribution.\n\n3. Neither the name of The HDF Group, the name of the University, nor the\n name of any Contributor may be used to endorse or promote products derived\n from this software without specific prior written permission from\n The HDF Group, the University, or the Contributor, respectively.\n\nDISCLAIMER:\nTHIS SOFTWARE IS PROVIDED BY THE HDF GROUP AND THE CONTRIBUTORS\n\"AS IS\" WITH NO WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED. IN NO\nEVENT SHALL THE HDF GROUP OR THE CONTRIBUTORS BE LIABLE FOR ANY DAMAGES\nSUFFERED BY THE USERS ARISING OUT OF THE USE OF THIS SOFTWARE, EVEN IF\nADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\nYou are under no obligation whatsoever to provide any bug fixes, patches, or\nupgrades to the features, functionality or performance of the source code\n(\"Enhancements\") to anyone; however, if you choose to make your Enhancements\navailable either publicly, or directly to The HDF Group, without imposing a\nseparate written license agreement for such Enhancements, then you hereby\ngrant the following license: a non-exclusive, royalty-free perpetual license\nto install, use, modify, prepare derivative works, incorporate into other\ncomputer software, distribute, and sublicense such enhancements or derivative\nworks thereof, in binary and source code form.\n\n-----------------------------------------------------------------------------\n-----------------------------------------------------------------------------\n\nLimited portions of HDF5 were developed by Lawrence Berkeley National\nLaboratory (LBNL). LBNL's Copyright Notice and Licensing Terms can be\nfound here: COPYING_LBNL_HDF5 file in this directory or at\nhttps://raw.githubusercontent.com/hdfgroup/hdf5/develop/COPYING_LBNL_HDF5.\n\n-----------------------------------------------------------------------------\n-----------------------------------------------------------------------------\n\nContributors: National Center for Supercomputing Applications (NCSA) at\nthe University of Illinois, Fortner Software, Unidata Program Center\n(netCDF), The Independent JPEG Group (JPEG), Jean-loup Gailly and Mark Adler\n(gzip), and Digital Equipment Corporation (DEC).\n\n-----------------------------------------------------------------------------\n\nPortions of HDF5 were developed with support from the Lawrence Berkeley\nNational Laboratory (LBNL) and the United States Department of Energy\nunder Prime Contract No. DE-AC02-05CH11231.\n\n-----------------------------------------------------------------------------\n\nPortions of HDF5 were developed with support from Lawrence Livermore\nNational Laboratory and the United States Department of Energy under\nPrime Contract No. DE-AC52-07NA27344.\n\n-----------------------------------------------------------------------------\n\nPortions of HDF5 were developed with support from the University of\nCalifornia, Lawrence Livermore National Laboratory (UC LLNL).\nThe following statement applies to those portions of the product and must\nbe retained in any redistribution of source code, binaries, documentation,\nand/or accompanying materials:\n\n This work was partially produced at the University of California,\n Lawrence Livermore National Laboratory (UC LLNL) under contract\n no. W-7405-ENG-48 (Contract 48) between the U.S. Department of Energy\n (DOE) and The Regents of the University of California (University)\n for the operation of UC LLNL.\n\n DISCLAIMER:\n THIS WORK WAS PREPARED AS AN ACCOUNT OF WORK SPONSORED BY AN AGENCY OF\n THE UNITED STATES GOVERNMENT. NEITHER THE UNITED STATES GOVERNMENT NOR\n THE UNIVERSITY OF CALIFORNIA NOR ANY OF THEIR EMPLOYEES, MAKES ANY\n WARRANTY, EXPRESS OR IMPLIED, OR ASSUMES ANY LIABILITY OR RESPONSIBILITY\n FOR THE ACCURACY, COMPLETENESS, OR USEFULNESS OF ANY INFORMATION,\n APPARATUS, PRODUCT, OR PROCESS DISCLOSED, OR REPRESENTS THAT ITS USE\n WOULD NOT INFRINGE PRIVATELY- OWNED RIGHTS. REFERENCE HEREIN TO ANY\n SPECIFIC COMMERCIAL PRODUCTS, PROCESS, OR SERVICE BY TRADE NAME,\n TRADEMARK, MANUFACTURER, OR OTHERWISE, DOES NOT NECESSARILY CONSTITUTE\n OR IMPLY ITS ENDORSEMENT, RECOMMENDATION, OR FAVORING BY THE UNITED\n STATES GOVERNMENT OR THE UNIVERSITY OF CALIFORNIA. THE VIEWS AND\n OPINIONS OF AUTHORS EXPRESSED HEREIN DO NOT NECESSARILY STATE OR REFLECT\n THOSE OF THE UNITED STATES GOVERNMENT OR THE UNIVERSITY OF CALIFORNIA,\n AND SHALL NOT BE USED FOR ADVERTISING OR PRODUCT ENDORSEMENT PURPOSES.\n\n-----------------------------------------------------------------------------\n" }, { "path": "external/Licenses/JemallocCopyright.txt", "content": "Copyright (C) 2002-present Jason Evans .\nAll rights reserved.\nCopyright (C) 2007-2012 Mozilla Foundation. All rights reserved.\nCopyright (C) 2009-present Facebook, Inc. All rights reserved.\n" }, { "path": "external/Licenses/JemallocLicense.txt", "content": "Unless otherwise specified, files in the jemalloc source distribution are\nsubject to the following license:\n--------------------------------------------------------------------------------\nCopyright (C) 2002-present Jason Evans .\nAll rights reserved.\nCopyright (C) 2007-2012 Mozilla Foundation. All rights reserved.\nCopyright (C) 2009-present Facebook, Inc. All rights reserved.\n\nRedistribution and use in source and binary forms, with or without\nmodification, are permitted provided that the following conditions are met:\n1. Redistributions of source code must retain the above copyright notice(s),\n this list of conditions and the following disclaimer.\n2. Redistributions in binary form must reproduce the above copyright notice(s),\n this list of conditions and the following disclaimer in the documentation\n and/or other materials provided with the distribution.\n\nTHIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDER(S) ``AS IS'' AND ANY EXPRESS\nOR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF\nMERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO\nEVENT SHALL THE COPYRIGHT HOLDER(S) BE LIABLE FOR ANY DIRECT, INDIRECT,\nINCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT\nLIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR\nPROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF\nLIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE\nOR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF\nADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n--------------------------------------------------------------------------------\n" }, { "path": "external/Licenses/LibbacktraceCopyright.txt", "content": "Copyright (C) 2012-2024 Free Software Foundation, Inc.\n" }, { "path": "external/Licenses/LibbacktraceLicense.txt", "content": "Copyright (C) 2012-2024 Free Software Foundation, Inc.\n\nRedistribution and use in source and binary forms, with or without\nmodification, are permitted provided that the following conditions are\nmet:\n\n (1) Redistributions of source code must retain the above copyright\n notice, this list of conditions and the following disclaimer.\n\n (2) Redistributions in binary form must reproduce the above copyright\n notice, this list of conditions and the following disclaimer in\n the documentation and/or other materials provided with the\n distribution.\n\n (3) The name of the author may not be used to\n endorse or promote products derived from this software without\n specific prior written permission.\n\nTHIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR\nIMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\nWARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\nDISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT,\nINDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR\nSERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)\nHOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,\nSTRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING\nIN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE\nPOSSIBILITY OF SUCH DAMAGE.\n" }, { "path": "external/Licenses/LibsharpCopyright.txt", "content": "opyright (C) 2006-2013 Max-Planck-Society\nhttps://github.com/Libsharp/libsharp\n" }, { "path": "external/Licenses/LibsharpLicense.txt", "content": " GNU GENERAL PUBLIC LICENSE\n Version 2, June 1991\n\n Copyright (C) 1989, 1991 Free Software Foundation, Inc.,\n 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA\n Everyone is permitted to copy and distribute verbatim copies\n of this license document, but changing it is not allowed.\n\n Preamble\n\n The licenses for most software are designed to take away your\nfreedom to share and change it. By contrast, the GNU General Public\nLicense is intended to guarantee your freedom to share and change free\nsoftware--to make sure the software is free for all its users. This\nGeneral Public License applies to most of the Free Software\nFoundation's software and to any other program whose authors commit to\nusing it. (Some other Free Software Foundation software is covered by\nthe GNU Lesser General Public License instead.) You can apply it to\nyour programs, too.\n\n When we speak of free software, we are referring to freedom, not\nprice. Our General Public Licenses are designed to make sure that you\nhave the freedom to distribute copies of free software (and charge for\nthis service if you wish), that you receive source code or can get it\nif you want it, that you can change the software or use pieces of it\nin new free programs; and that you know you can do these things.\n\n To protect your rights, we need to make restrictions that forbid\nanyone to deny you these rights or to ask you to surrender the rights.\nThese restrictions translate to certain responsibilities for you if you\ndistribute copies of the software, or if you modify it.\n\n For example, if you distribute copies of such a program, whether\ngratis or for a fee, you must give the recipients all the rights that\nyou have. You must make sure that they, too, receive or can get the\nsource code. And you must show them these terms so they know their\nrights.\n\n We protect your rights with two steps: (1) copyright the software, and\n(2) offer you this license which gives you legal permission to copy,\ndistribute and/or modify the software.\n\n Also, for each author's protection and ours, we want to make certain\nthat everyone understands that there is no warranty for this free\nsoftware. If the software is modified by someone else and passed on, we\nwant its recipients to know that what they have is not the original, so\nthat any problems introduced by others will not reflect on the original\nauthors' reputations.\n\n Finally, any free program is threatened constantly by software\npatents. We wish to avoid the danger that redistributors of a free\nprogram will individually obtain patent licenses, in effect making the\nprogram proprietary. To prevent this, we have made it clear that any\npatent must be licensed for everyone's free use or not licensed at all.\n\n The precise terms and conditions for copying, distribution and\nmodification follow.\n\n GNU GENERAL PUBLIC LICENSE\n TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION\n\n 0. This License applies to any program or other work which contains\na notice placed by the copyright holder saying it may be distributed\nunder the terms of this General Public License. The \"Program\", below,\nrefers to any such program or work, and a \"work based on the Program\"\nmeans either the Program or any derivative work under copyright law:\nthat is to say, a work containing the Program or a portion of it,\neither verbatim or with modifications and/or translated into another\nlanguage. (Hereinafter, translation is included without limitation in\nthe term \"modification\".) Each licensee is addressed as \"you\".\n\nActivities other than copying, distribution and modification are not\ncovered by this License; they are outside its scope. The act of\nrunning the Program is not restricted, and the output from the Program\nis covered only if its contents constitute a work based on the\nProgram (independent of having been made by running the Program).\nWhether that is true depends on what the Program does.\n\n 1. You may copy and distribute verbatim copies of the Program's\nsource code as you receive it, in any medium, provided that you\nconspicuously and appropriately publish on each copy an appropriate\ncopyright notice and disclaimer of warranty; keep intact all the\nnotices that refer to this License and to the absence of any warranty;\nand give any other recipients of the Program a copy of this License\nalong with the Program.\n\nYou may charge a fee for the physical act of transferring a copy, and\nyou may at your option offer warranty protection in exchange for a fee.\n\n 2. You may modify your copy or copies of the Program or any portion\nof it, thus forming a work based on the Program, and copy and\ndistribute such modifications or work under the terms of Section 1\nabove, provided that you also meet all of these conditions:\n\n a) You must cause the modified files to carry prominent notices\n stating that you changed the files and the date of any change.\n\n b) You must cause any work that you distribute or publish, that in\n whole or in part contains or is derived from the Program or any\n part thereof, to be licensed as a whole at no charge to all third\n parties under the terms of this License.\n\n c) If the modified program normally reads commands interactively\n when run, you must cause it, when started running for such\n interactive use in the most ordinary way, to print or display an\n announcement including an appropriate copyright notice and a\n notice that there is no warranty (or else, saying that you provide\n a warranty) and that users may redistribute the program under\n these conditions, and telling the user how to view a copy of this\n License. (Exception: if the Program itself is interactive but\n does not normally print such an announcement, your work based on\n the Program is not required to print an announcement.)\n\nThese requirements apply to the modified work as a whole. If\nidentifiable sections of that work are not derived from the Program,\nand can be reasonably considered independent and separate works in\nthemselves, then this License, and its terms, do not apply to those\nsections when you distribute them as separate works. But when you\ndistribute the same sections as part of a whole which is a work based\non the Program, the distribution of the whole must be on the terms of\nthis License, whose permissions for other licensees extend to the\nentire whole, and thus to each and every part regardless of who wrote it.\n\nThus, it is not the intent of this section to claim rights or contest\nyour rights to work written entirely by you; rather, the intent is to\nexercise the right to control the distribution of derivative or\ncollective works based on the Program.\n\nIn addition, mere aggregation of another work not based on the Program\nwith the Program (or with a work based on the Program) on a volume of\na storage or distribution medium does not bring the other work under\nthe scope of this License.\n\n 3. You may copy and distribute the Program (or a work based on it,\nunder Section 2) in object code or executable form under the terms of\nSections 1 and 2 above provided that you also do one of the following:\n\n a) Accompany it with the complete corresponding machine-readable\n source code, which must be distributed under the terms of Sections\n 1 and 2 above on a medium customarily used for software interchange; or,\n\n b) Accompany it with a written offer, valid for at least three\n years, to give any third party, for a charge no more than your\n cost of physically performing source distribution, a complete\n machine-readable copy of the corresponding source code, to be\n distributed under the terms of Sections 1 and 2 above on a medium\n customarily used for software interchange; or,\n\n c) Accompany it with the information you received as to the offer\n to distribute corresponding source code. (This alternative is\n allowed only for noncommercial distribution and only if you\n received the program in object code or executable form with such\n an offer, in accord with Subsection b above.)\n\nThe source code for a work means the preferred form of the work for\nmaking modifications to it. For an executable work, complete source\ncode means all the source code for all modules it contains, plus any\nassociated interface definition files, plus the scripts used to\ncontrol compilation and installation of the executable. However, as a\nspecial exception, the source code distributed need not include\nanything that is normally distributed (in either source or binary\nform) with the major components (compiler, kernel, and so on) of the\noperating system on which the executable runs, unless that component\nitself accompanies the executable.\n\nIf distribution of executable or object code is made by offering\naccess to copy from a designated place, then offering equivalent\naccess to copy the source code from the same place counts as\ndistribution of the source code, even though third parties are not\ncompelled to copy the source along with the object code.\n\n 4. You may not copy, modify, sublicense, or distribute the Program\nexcept as expressly provided under this License. Any attempt\notherwise to copy, modify, sublicense or distribute the Program is\nvoid, and will automatically terminate your rights under this License.\nHowever, parties who have received copies, or rights, from you under\nthis License will not have their licenses terminated so long as such\nparties remain in full compliance.\n\n 5. You are not required to accept this License, since you have not\nsigned it. However, nothing else grants you permission to modify or\ndistribute the Program or its derivative works. These actions are\nprohibited by law if you do not accept this License. Therefore, by\nmodifying or distributing the Program (or any work based on the\nProgram), you indicate your acceptance of this License to do so, and\nall its terms and conditions for copying, distributing or modifying\nthe Program or works based on it.\n\n 6. Each time you redistribute the Program (or any work based on the\nProgram), the recipient automatically receives a license from the\noriginal licensor to copy, distribute or modify the Program subject to\nthese terms and conditions. You may not impose any further\nrestrictions on the recipients' exercise of the rights granted herein.\nYou are not responsible for enforcing compliance by third parties to\nthis License.\n\n 7. If, as a consequence of a court judgment or allegation of patent\ninfringement or for any other reason (not limited to patent issues),\nconditions are imposed on you (whether by court order, agreement or\notherwise) that contradict the conditions of this License, they do not\nexcuse you from the conditions of this License. If you cannot\ndistribute so as to satisfy simultaneously your obligations under this\nLicense and any other pertinent obligations, then as a consequence you\nmay not distribute the Program at all. For example, if a patent\nlicense would not permit royalty-free redistribution of the Program by\nall those who receive copies directly or indirectly through you, then\nthe only way you could satisfy both it and this License would be to\nrefrain entirely from distribution of the Program.\n\nIf any portion of this section is held invalid or unenforceable under\nany particular circumstance, the balance of the section is intended to\napply and the section as a whole is intended to apply in other\ncircumstances.\n\nIt is not the purpose of this section to induce you to infringe any\npatents or other property right claims or to contest validity of any\nsuch claims; this section has the sole purpose of protecting the\nintegrity of the free software distribution system, which is\nimplemented by public license practices. Many people have made\ngenerous contributions to the wide range of software distributed\nthrough that system in reliance on consistent application of that\nsystem; it is up to the author/donor to decide if he or she is willing\nto distribute software through any other system and a licensee cannot\nimpose that choice.\n\nThis section is intended to make thoroughly clear what is believed to\nbe a consequence of the rest of this License.\n\n 8. If the distribution and/or use of the Program is restricted in\ncertain countries either by patents or by copyrighted interfaces, the\noriginal copyright holder who places the Program under this License\nmay add an explicit geographical distribution limitation excluding\nthose countries, so that distribution is permitted only in or among\ncountries not thus excluded. In such case, this License incorporates\nthe limitation as if written in the body of this License.\n\n 9. The Free Software Foundation may publish revised and/or new versions\nof the General Public License from time to time. Such new versions will\nbe similar in spirit to the present version, but may differ in detail to\naddress new problems or concerns.\n\nEach version is given a distinguishing version number. If the Program\nspecifies a version number of this License which applies to it and \"any\nlater version\", you have the option of following the terms and conditions\neither of that version or of any later version published by the Free\nSoftware Foundation. If the Program does not specify a version number of\nthis License, you may choose any version ever published by the Free Software\nFoundation.\n\n 10. If you wish to incorporate parts of the Program into other free\nprograms whose distribution conditions are different, write to the author\nto ask for permission. For software which is copyrighted by the Free\nSoftware Foundation, write to the Free Software Foundation; we sometimes\nmake exceptions for this. Our decision will be guided by the two goals\nof preserving the free status of all derivatives of our free software and\nof promoting the sharing and reuse of software generally.\n\n NO WARRANTY\n\n 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY\nFOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN\nOTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES\nPROVIDE THE PROGRAM \"AS IS\" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED\nOR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF\nMERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS\nTO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE\nPROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,\nREPAIR OR CORRECTION.\n\n 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING\nWILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR\nREDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,\nINCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING\nOUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED\nTO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY\nYOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER\nPROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE\nPOSSIBILITY OF SUCH DAMAGES.\n\n END OF TERMS AND CONDITIONS\n\n How to Apply These Terms to Your New Programs\n\n If you develop a new program, and you want it to be of the greatest\npossible use to the public, the best way to achieve this is to make it\nfree software which everyone can redistribute and change under these terms.\n\n To do so, attach the following notices to the program. It is safest\nto attach them to the start of each source file to most effectively\nconvey the exclusion of warranty; and each file should have at least\nthe \"copyright\" line and a pointer to where the full notice is found.\n\n \n Copyright (C) \n\n This program is free software; you can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation; either version 2 of the License, or\n (at your option) any later version.\n\n This program is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU General Public License for more details.\n\n You should have received a copy of the GNU General Public License along\n with this program; if not, write to the Free Software Foundation, Inc.,\n 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.\n\nAlso add information on how to contact you by electronic and paper mail.\n\nIf the program is interactive, make it output a short notice like this\nwhen it starts in an interactive mode:\n\n Gnomovision version 69, Copyright (C) year name of author\n Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.\n This is free software, and you are welcome to redistribute it\n under certain conditions; type `show c' for details.\n\nThe hypothetical commands `show w' and `show c' should show the appropriate\nparts of the General Public License. Of course, the commands you use may\nbe called something other than `show w' and `show c'; they could even be\nmouse-clicks or menu items--whatever suits your program.\n\nYou should also get your employer (if you work as a programmer) or your\nschool, if any, to sign a \"copyright disclaimer\" for the program, if\nnecessary. Here is a sample; alter the names:\n\n Yoyodyne, Inc., hereby disclaims all copyright interest in the program\n `Gnomovision' (which makes passes at compilers) written by James Hacker.\n\n , 1 April 1989\n Ty Coon, President of Vice\n\nThis General Public License does not permit incorporating your program into\nproprietary programs. If your program is a subroutine library, you may\nconsider it more useful to permit linking proprietary applications with the\nlibrary. If this is what you want to do, use the GNU Lesser General\nPublic License instead of this License.\n" }, { "path": "external/Licenses/LibxsmmCopyright.txt", "content": "Copyright (c) 2009-2023, Intel Corporation\nCopyright (c) 2017-2022, Friedrich Schiller University Jena\nCopyright (c) 2012-2021, Technische Universitaet Muenchen\nCopyright (c) 2016-2020, Google Inc.\nhttps://github.com/libxsmm/libxsmm\n" }, { "path": "external/Licenses/LibxsmmLicense.txt", "content": "BSD 3-Clause License\n\nCopyright (c) 2009-2023, Intel Corporation\nCopyright (c) 2017-2022, Friedrich Schiller University Jena\nCopyright (c) 2012-2021, Technische Universitaet Muenchen\nCopyright (c) 2016-2020, Google Inc.\nAll rights reserved.\n\nRedistribution and use in source and binary forms, with or without modification,\nare permitted provided that the following conditions are met:\n\n Redistributions of source code must retain the above copyright notice, this\n list of conditions and the following disclaimer.\n\n Redistributions in binary form must reproduce the above copyright notice,\n this list of conditions and the following disclaimer in the documentation\n and/or other materials provided with the distribution.\n\n Neither the name of the copyright holder nor the names of its contributors\n may be used to endorse or promote products derived from this software\n without specific prior written permission.\n\nTHIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\nANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\nWARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\nDISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR\nANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\nLOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON\nANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\nSOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n" }, { "path": "external/Licenses/OpenBlasCopyright.txt", "content": "Copyright (c) 2011-2024, The OpenBLAS Project\nCopyright 2009, 2010 The University of Texas at Austin.\nhttps://github.com/OpenMathLib/OpenBLAS\n" }, { "path": "external/Licenses/OpenBlasLicense.txt", "content": "Copyright (c) 2011-2014, The OpenBLAS Project\nAll rights reserved.\n\nRedistribution and use in source and binary forms, with or without\nmodification, are permitted provided that the following conditions are\nmet:\n\n 1. Redistributions of source code must retain the above copyright\n notice, this list of conditions and the following disclaimer.\n\n 2. Redistributions in binary form must reproduce the above copyright\n notice, this list of conditions and the following disclaimer in\n the documentation and/or other materials provided with the\n distribution.\n 3. Neither the name of the OpenBLAS project nor the names of\n its contributors may be used to endorse or promote products\n derived from this software without specific prior written\n permission.\n\nTHIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\"\nAND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE\nIMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE\nARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE\nLIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL\nDAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR\nSERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER\nCAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,\nOR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE\nUSE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n" }, { "path": "external/Licenses/Pybind11Copyright.txt", "content": "Copyright (c) 2016 Wenzel Jakob , All rights reserved.\n" }, { "path": "external/Licenses/Pybind11License.txt", "content": "Copyright (c) 2016 Wenzel Jakob , All rights reserved.\n\nRedistribution and use in source and binary forms, with or without\nmodification, are permitted provided that the following conditions are met:\n\n1. Redistributions of source code must retain the above copyright notice, this\n list of conditions and the following disclaimer.\n\n2. Redistributions in binary form must reproduce the above copyright notice,\n this list of conditions and the following disclaimer in the documentation\n and/or other materials provided with the distribution.\n\n3. Neither the name of the copyright holder nor the names of its contributors\n may be used to endorse or promote products derived from this software\n without specific prior written permission.\n\nTHIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\nANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\nWARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\nDISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE\nFOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL\nDAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR\nSERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER\nCAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,\nOR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\nOF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\nPlease also refer to the file .github/CONTRIBUTING.md, which clarifies licensing of\nexternal contributions to this project including patches, pull requests, etc.\n" }, { "path": "external/Licenses/SpectreGpl3License.txt", "content": " GNU GENERAL PUBLIC LICENSE\n Version 3, 29 June 2007\n\n Copyright (C) 2007 Free Software Foundation, Inc. \n Everyone is permitted to copy and distribute verbatim copies\n of this license document, but changing it is not allowed.\n\n Preamble\n\n The GNU General Public License is a free, copyleft license for\nsoftware and other kinds of works.\n\n The licenses for most software and other practical works are designed\nto take away your freedom to share and change the works. By contrast,\nthe GNU General Public License is intended to guarantee your freedom to\nshare and change all versions of a program--to make sure it remains free\nsoftware for all its users. We, the Free Software Foundation, use the\nGNU General Public License for most of our software; it applies also to\nany other work released this way by its authors. You can apply it to\nyour programs, too.\n\n When we speak of free software, we are referring to freedom, not\nprice. Our General Public Licenses are designed to make sure that you\nhave the freedom to distribute copies of free software (and charge for\nthem if you wish), that you receive source code or can get it if you\nwant it, that you can change the software or use pieces of it in new\nfree programs, and that you know you can do these things.\n\n To protect your rights, we need to prevent others from denying you\nthese rights or asking you to surrender the rights. Therefore, you have\ncertain responsibilities if you distribute copies of the software, or if\nyou modify it: responsibilities to respect the freedom of others.\n\n For example, if you distribute copies of such a program, whether\ngratis or for a fee, you must pass on to the recipients the same\nfreedoms that you received. You must make sure that they, too, receive\nor can get the source code. And you must show them these terms so they\nknow their rights.\n\n Developers that use the GNU GPL protect your rights with two steps:\n(1) assert copyright on the software, and (2) offer you this License\ngiving you legal permission to copy, distribute and/or modify it.\n\n For the developers' and authors' protection, the GPL clearly explains\nthat there is no warranty for this free software. For both users' and\nauthors' sake, the GPL requires that modified versions be marked as\nchanged, so that their problems will not be attributed erroneously to\nauthors of previous versions.\n\n Some devices are designed to deny users access to install or run\nmodified versions of the software inside them, although the manufacturer\ncan do so. This is fundamentally incompatible with the aim of\nprotecting users' freedom to change the software. The systematic\npattern of such abuse occurs in the area of products for individuals to\nuse, which is precisely where it is most unacceptable. Therefore, we\nhave designed this version of the GPL to prohibit the practice for those\nproducts. If such problems arise substantially in other domains, we\nstand ready to extend this provision to those domains in future versions\nof the GPL, as needed to protect the freedom of users.\n\n Finally, every program is threatened constantly by software patents.\nStates should not allow patents to restrict development and use of\nsoftware on general-purpose computers, but in those that do, we wish to\navoid the special danger that patents applied to a free program could\nmake it effectively proprietary. To prevent this, the GPL assures that\npatents cannot be used to render the program non-free.\n\n The precise terms and conditions for copying, distribution and\nmodification follow.\n\n TERMS AND CONDITIONS\n\n 0. Definitions.\n\n \"This License\" refers to version 3 of the GNU General Public License.\n\n \"Copyright\" also means copyright-like laws that apply to other kinds of\nworks, such as semiconductor masks.\n\n \"The Program\" refers to any copyrightable work licensed under this\nLicense. Each licensee is addressed as \"you\". \"Licensees\" and\n\"recipients\" may be individuals or organizations.\n\n To \"modify\" a work means to copy from or adapt all or part of the work\nin a fashion requiring copyright permission, other than the making of an\nexact copy. The resulting work is called a \"modified version\" of the\nearlier work or a work \"based on\" the earlier work.\n\n A \"covered work\" means either the unmodified Program or a work based\non the Program.\n\n To \"propagate\" a work means to do anything with it that, without\npermission, would make you directly or secondarily liable for\ninfringement under applicable copyright law, except executing it on a\ncomputer or modifying a private copy. Propagation includes copying,\ndistribution (with or without modification), making available to the\npublic, and in some countries other activities as well.\n\n To \"convey\" a work means any kind of propagation that enables other\nparties to make or receive copies. Mere interaction with a user through\na computer network, with no transfer of a copy, is not conveying.\n\n An interactive user interface displays \"Appropriate Legal Notices\"\nto the extent that it includes a convenient and prominently visible\nfeature that (1) displays an appropriate copyright notice, and (2)\ntells the user that there is no warranty for the work (except to the\nextent that warranties are provided), that licensees may convey the\nwork under this License, and how to view a copy of this License. If\nthe interface presents a list of user commands or options, such as a\nmenu, a prominent item in the list meets this criterion.\n\n 1. Source Code.\n\n The \"source code\" for a work means the preferred form of the work\nfor making modifications to it. \"Object code\" means any non-source\nform of a work.\n\n A \"Standard Interface\" means an interface that either is an official\nstandard defined by a recognized standards body, or, in the case of\ninterfaces specified for a particular programming language, one that\nis widely used among developers working in that language.\n\n The \"System Libraries\" of an executable work include anything, other\nthan the work as a whole, that (a) is included in the normal form of\npackaging a Major Component, but which is not part of that Major\nComponent, and (b) serves only to enable use of the work with that\nMajor Component, or to implement a Standard Interface for which an\nimplementation is available to the public in source code form. A\n\"Major Component\", in this context, means a major essential component\n(kernel, window system, and so on) of the specific operating system\n(if any) on which the executable work runs, or a compiler used to\nproduce the work, or an object code interpreter used to run it.\n\n The \"Corresponding Source\" for a work in object code form means all\nthe source code needed to generate, install, and (for an executable\nwork) run the object code and to modify the work, including scripts to\ncontrol those activities. However, it does not include the work's\nSystem Libraries, or general-purpose tools or generally available free\nprograms which are used unmodified in performing those activities but\nwhich are not part of the work. For example, Corresponding Source\nincludes interface definition files associated with source files for\nthe work, and the source code for shared libraries and dynamically\nlinked subprograms that the work is specifically designed to require,\nsuch as by intimate data communication or control flow between those\nsubprograms and other parts of the work.\n\n The Corresponding Source need not include anything that users\ncan regenerate automatically from other parts of the Corresponding\nSource.\n\n The Corresponding Source for a work in source code form is that\nsame work.\n\n 2. Basic Permissions.\n\n All rights granted under this License are granted for the term of\ncopyright on the Program, and are irrevocable provided the stated\nconditions are met. This License explicitly affirms your unlimited\npermission to run the unmodified Program. The output from running a\ncovered work is covered by this License only if the output, given its\ncontent, constitutes a covered work. This License acknowledges your\nrights of fair use or other equivalent, as provided by copyright law.\n\n You may make, run and propagate covered works that you do not\nconvey, without conditions so long as your license otherwise remains\nin force. You may convey covered works to others for the sole purpose\nof having them make modifications exclusively for you, or provide you\nwith facilities for running those works, provided that you comply with\nthe terms of this License in conveying all material for which you do\nnot control copyright. Those thus making or running the covered works\nfor you must do so exclusively on your behalf, under your direction\nand control, on terms that prohibit them from making any copies of\nyour copyrighted material outside their relationship with you.\n\n Conveying under any other circumstances is permitted solely under\nthe conditions stated below. Sublicensing is not allowed; section 10\nmakes it unnecessary.\n\n 3. Protecting Users' Legal Rights From Anti-Circumvention Law.\n\n No covered work shall be deemed part of an effective technological\nmeasure under any applicable law fulfilling obligations under article\n11 of the WIPO copyright treaty adopted on 20 December 1996, or\nsimilar laws prohibiting or restricting circumvention of such\nmeasures.\n\n When you convey a covered work, you waive any legal power to forbid\ncircumvention of technological measures to the extent such circumvention\nis effected by exercising rights under this License with respect to\nthe covered work, and you disclaim any intention to limit operation or\nmodification of the work as a means of enforcing, against the work's\nusers, your or third parties' legal rights to forbid circumvention of\ntechnological measures.\n\n 4. Conveying Verbatim Copies.\n\n You may convey verbatim copies of the Program's source code as you\nreceive it, in any medium, provided that you conspicuously and\nappropriately publish on each copy an appropriate copyright notice;\nkeep intact all notices stating that this License and any\nnon-permissive terms added in accord with section 7 apply to the code;\nkeep intact all notices of the absence of any warranty; and give all\nrecipients a copy of this License along with the Program.\n\n You may charge any price or no price for each copy that you convey,\nand you may offer support or warranty protection for a fee.\n\n 5. Conveying Modified Source Versions.\n\n You may convey a work based on the Program, or the modifications to\nproduce it from the Program, in the form of source code under the\nterms of section 4, provided that you also meet all of these conditions:\n\n a) The work must carry prominent notices stating that you modified\n it, and giving a relevant date.\n\n b) The work must carry prominent notices stating that it is\n released under this License and any conditions added under section\n 7. This requirement modifies the requirement in section 4 to\n \"keep intact all notices\".\n\n c) You must license the entire work, as a whole, under this\n License to anyone who comes into possession of a copy. This\n License will therefore apply, along with any applicable section 7\n additional terms, to the whole of the work, and all its parts,\n regardless of how they are packaged. This License gives no\n permission to license the work in any other way, but it does not\n invalidate such permission if you have separately received it.\n\n d) If the work has interactive user interfaces, each must display\n Appropriate Legal Notices; however, if the Program has interactive\n interfaces that do not display Appropriate Legal Notices, your\n work need not make them do so.\n\n A compilation of a covered work with other separate and independent\nworks, which are not by their nature extensions of the covered work,\nand which are not combined with it such as to form a larger program,\nin or on a volume of a storage or distribution medium, is called an\n\"aggregate\" if the compilation and its resulting copyright are not\nused to limit the access or legal rights of the compilation's users\nbeyond what the individual works permit. Inclusion of a covered work\nin an aggregate does not cause this License to apply to the other\nparts of the aggregate.\n\n 6. Conveying Non-Source Forms.\n\n You may convey a covered work in object code form under the terms\nof sections 4 and 5, provided that you also convey the\nmachine-readable Corresponding Source under the terms of this License,\nin one of these ways:\n\n a) Convey the object code in, or embodied in, a physical product\n (including a physical distribution medium), accompanied by the\n Corresponding Source fixed on a durable physical medium\n customarily used for software interchange.\n\n b) Convey the object code in, or embodied in, a physical product\n (including a physical distribution medium), accompanied by a\n written offer, valid for at least three years and valid for as\n long as you offer spare parts or customer support for that product\n model, to give anyone who possesses the object code either (1) a\n copy of the Corresponding Source for all the software in the\n product that is covered by this License, on a durable physical\n medium customarily used for software interchange, for a price no\n more than your reasonable cost of physically performing this\n conveying of source, or (2) access to copy the\n Corresponding Source from a network server at no charge.\n\n c) Convey individual copies of the object code with a copy of the\n written offer to provide the Corresponding Source. This\n alternative is allowed only occasionally and noncommercially, and\n only if you received the object code with such an offer, in accord\n with subsection 6b.\n\n d) Convey the object code by offering access from a designated\n place (gratis or for a charge), and offer equivalent access to the\n Corresponding Source in the same way through the same place at no\n further charge. You need not require recipients to copy the\n Corresponding Source along with the object code. If the place to\n copy the object code is a network server, the Corresponding Source\n may be on a different server (operated by you or a third party)\n that supports equivalent copying facilities, provided you maintain\n clear directions next to the object code saying where to find the\n Corresponding Source. Regardless of what server hosts the\n Corresponding Source, you remain obligated to ensure that it is\n available for as long as needed to satisfy these requirements.\n\n e) Convey the object code using peer-to-peer transmission, provided\n you inform other peers where the object code and Corresponding\n Source of the work are being offered to the general public at no\n charge under subsection 6d.\n\n A separable portion of the object code, whose source code is excluded\nfrom the Corresponding Source as a System Library, need not be\nincluded in conveying the object code work.\n\n A \"User Product\" is either (1) a \"consumer product\", which means any\ntangible personal property which is normally used for personal, family,\nor household purposes, or (2) anything designed or sold for incorporation\ninto a dwelling. In determining whether a product is a consumer product,\ndoubtful cases shall be resolved in favor of coverage. For a particular\nproduct received by a particular user, \"normally used\" refers to a\ntypical or common use of that class of product, regardless of the status\nof the particular user or of the way in which the particular user\nactually uses, or expects or is expected to use, the product. A product\nis a consumer product regardless of whether the product has substantial\ncommercial, industrial or non-consumer uses, unless such uses represent\nthe only significant mode of use of the product.\n\n \"Installation Information\" for a User Product means any methods,\nprocedures, authorization keys, or other information required to install\nand execute modified versions of a covered work in that User Product from\na modified version of its Corresponding Source. The information must\nsuffice to ensure that the continued functioning of the modified object\ncode is in no case prevented or interfered with solely because\nmodification has been made.\n\n If you convey an object code work under this section in, or with, or\nspecifically for use in, a User Product, and the conveying occurs as\npart of a transaction in which the right of possession and use of the\nUser Product is transferred to the recipient in perpetuity or for a\nfixed term (regardless of how the transaction is characterized), the\nCorresponding Source conveyed under this section must be accompanied\nby the Installation Information. But this requirement does not apply\nif neither you nor any third party retains the ability to install\nmodified object code on the User Product (for example, the work has\nbeen installed in ROM).\n\n The requirement to provide Installation Information does not include a\nrequirement to continue to provide support service, warranty, or updates\nfor a work that has been modified or installed by the recipient, or for\nthe User Product in which it has been modified or installed. Access to a\nnetwork may be denied when the modification itself materially and\nadversely affects the operation of the network or violates the rules and\nprotocols for communication across the network.\n\n Corresponding Source conveyed, and Installation Information provided,\nin accord with this section must be in a format that is publicly\ndocumented (and with an implementation available to the public in\nsource code form), and must require no special password or key for\nunpacking, reading or copying.\n\n 7. Additional Terms.\n\n \"Additional permissions\" are terms that supplement the terms of this\nLicense by making exceptions from one or more of its conditions.\nAdditional permissions that are applicable to the entire Program shall\nbe treated as though they were included in this License, to the extent\nthat they are valid under applicable law. If additional permissions\napply only to part of the Program, that part may be used separately\nunder those permissions, but the entire Program remains governed by\nthis License without regard to the additional permissions.\n\n When you convey a copy of a covered work, you may at your option\nremove any additional permissions from that copy, or from any part of\nit. (Additional permissions may be written to require their own\nremoval in certain cases when you modify the work.) You may place\nadditional permissions on material, added by you to a covered work,\nfor which you have or can give appropriate copyright permission.\n\n Notwithstanding any other provision of this License, for material you\nadd to a covered work, you may (if authorized by the copyright holders of\nthat material) supplement the terms of this License with terms:\n\n a) Disclaiming warranty or limiting liability differently from the\n terms of sections 15 and 16 of this License; or\n\n b) Requiring preservation of specified reasonable legal notices or\n author attributions in that material or in the Appropriate Legal\n Notices displayed by works containing it; or\n\n c) Prohibiting misrepresentation of the origin of that material, or\n requiring that modified versions of such material be marked in\n reasonable ways as different from the original version; or\n\n d) Limiting the use for publicity purposes of names of licensors or\n authors of the material; or\n\n e) Declining to grant rights under trademark law for use of some\n trade names, trademarks, or service marks; or\n\n f) Requiring indemnification of licensors and authors of that\n material by anyone who conveys the material (or modified versions of\n it) with contractual assumptions of liability to the recipient, for\n any liability that these contractual assumptions directly impose on\n those licensors and authors.\n\n All other non-permissive additional terms are considered \"further\nrestrictions\" within the meaning of section 10. If the Program as you\nreceived it, or any part of it, contains a notice stating that it is\ngoverned by this License along with a term that is a further\nrestriction, you may remove that term. If a license document contains\na further restriction but permits relicensing or conveying under this\nLicense, you may add to a covered work material governed by the terms\nof that license document, provided that the further restriction does\nnot survive such relicensing or conveying.\n\n If you add terms to a covered work in accord with this section, you\nmust place, in the relevant source files, a statement of the\nadditional terms that apply to those files, or a notice indicating\nwhere to find the applicable terms.\n\n Additional terms, permissive or non-permissive, may be stated in the\nform of a separately written license, or stated as exceptions;\nthe above requirements apply either way.\n\n 8. Termination.\n\n You may not propagate or modify a covered work except as expressly\nprovided under this License. Any attempt otherwise to propagate or\nmodify it is void, and will automatically terminate your rights under\nthis License (including any patent licenses granted under the third\nparagraph of section 11).\n\n However, if you cease all violation of this License, then your\nlicense from a particular copyright holder is reinstated (a)\nprovisionally, unless and until the copyright holder explicitly and\nfinally terminates your license, and (b) permanently, if the copyright\nholder fails to notify you of the violation by some reasonable means\nprior to 60 days after the cessation.\n\n Moreover, your license from a particular copyright holder is\nreinstated permanently if the copyright holder notifies you of the\nviolation by some reasonable means, this is the first time you have\nreceived notice of violation of this License (for any work) from that\ncopyright holder, and you cure the violation prior to 30 days after\nyour receipt of the notice.\n\n Termination of your rights under this section does not terminate the\nlicenses of parties who have received copies or rights from you under\nthis License. If your rights have been terminated and not permanently\nreinstated, you do not qualify to receive new licenses for the same\nmaterial under section 10.\n\n 9. Acceptance Not Required for Having Copies.\n\n You are not required to accept this License in order to receive or\nrun a copy of the Program. Ancillary propagation of a covered work\noccurring solely as a consequence of using peer-to-peer transmission\nto receive a copy likewise does not require acceptance. However,\nnothing other than this License grants you permission to propagate or\nmodify any covered work. These actions infringe copyright if you do\nnot accept this License. Therefore, by modifying or propagating a\ncovered work, you indicate your acceptance of this License to do so.\n\n 10. Automatic Licensing of Downstream Recipients.\n\n Each time you convey a covered work, the recipient automatically\nreceives a license from the original licensors, to run, modify and\npropagate that work, subject to this License. You are not responsible\nfor enforcing compliance by third parties with this License.\n\n An \"entity transaction\" is a transaction transferring control of an\norganization, or substantially all assets of one, or subdividing an\norganization, or merging organizations. If propagation of a covered\nwork results from an entity transaction, each party to that\ntransaction who receives a copy of the work also receives whatever\nlicenses to the work the party's predecessor in interest had or could\ngive under the previous paragraph, plus a right to possession of the\nCorresponding Source of the work from the predecessor in interest, if\nthe predecessor has it or can get it with reasonable efforts.\n\n You may not impose any further restrictions on the exercise of the\nrights granted or affirmed under this License. For example, you may\nnot impose a license fee, royalty, or other charge for exercise of\nrights granted under this License, and you may not initiate litigation\n(including a cross-claim or counterclaim in a lawsuit) alleging that\nany patent claim is infringed by making, using, selling, offering for\nsale, or importing the Program or any portion of it.\n\n 11. Patents.\n\n A \"contributor\" is a copyright holder who authorizes use under this\nLicense of the Program or a work on which the Program is based. The\nwork thus licensed is called the contributor's \"contributor version\".\n\n A contributor's \"essential patent claims\" are all patent claims\nowned or controlled by the contributor, whether already acquired or\nhereafter acquired, that would be infringed by some manner, permitted\nby this License, of making, using, or selling its contributor version,\nbut do not include claims that would be infringed only as a\nconsequence of further modification of the contributor version. For\npurposes of this definition, \"control\" includes the right to grant\npatent sublicenses in a manner consistent with the requirements of\nthis License.\n\n Each contributor grants you a non-exclusive, worldwide, royalty-free\npatent license under the contributor's essential patent claims, to\nmake, use, sell, offer for sale, import and otherwise run, modify and\npropagate the contents of its contributor version.\n\n In the following three paragraphs, a \"patent license\" is any express\nagreement or commitment, however denominated, not to enforce a patent\n(such as an express permission to practice a patent or covenant not to\nsue for patent infringement). To \"grant\" such a patent license to a\nparty means to make such an agreement or commitment not to enforce a\npatent against the party.\n\n If you convey a covered work, knowingly relying on a patent license,\nand the Corresponding Source of the work is not available for anyone\nto copy, free of charge and under the terms of this License, through a\npublicly available network server or other readily accessible means,\nthen you must either (1) cause the Corresponding Source to be so\navailable, or (2) arrange to deprive yourself of the benefit of the\npatent license for this particular work, or (3) arrange, in a manner\nconsistent with the requirements of this License, to extend the patent\nlicense to downstream recipients. \"Knowingly relying\" means you have\nactual knowledge that, but for the patent license, your conveying the\ncovered work in a country, or your recipient's use of the covered work\nin a country, would infringe one or more identifiable patents in that\ncountry that you have reason to believe are valid.\n\n If, pursuant to or in connection with a single transaction or\narrangement, you convey, or propagate by procuring conveyance of, a\ncovered work, and grant a patent license to some of the parties\nreceiving the covered work authorizing them to use, propagate, modify\nor convey a specific copy of the covered work, then the patent license\nyou grant is automatically extended to all recipients of the covered\nwork and works based on it.\n\n A patent license is \"discriminatory\" if it does not include within\nthe scope of its coverage, prohibits the exercise of, or is\nconditioned on the non-exercise of one or more of the rights that are\nspecifically granted under this License. You may not convey a covered\nwork if you are a party to an arrangement with a third party that is\nin the business of distributing software, under which you make payment\nto the third party based on the extent of your activity of conveying\nthe work, and under which the third party grants, to any of the\nparties who would receive the covered work from you, a discriminatory\npatent license (a) in connection with copies of the covered work\nconveyed by you (or copies made from those copies), or (b) primarily\nfor and in connection with specific products or compilations that\ncontain the covered work, unless you entered into that arrangement,\nor that patent license was granted, prior to 28 March 2007.\n\n Nothing in this License shall be construed as excluding or limiting\nany implied license or other defenses to infringement that may\notherwise be available to you under applicable patent law.\n\n 12. No Surrender of Others' Freedom.\n\n If conditions are imposed on you (whether by court order, agreement or\notherwise) that contradict the conditions of this License, they do not\nexcuse you from the conditions of this License. If you cannot convey a\ncovered work so as to satisfy simultaneously your obligations under this\nLicense and any other pertinent obligations, then as a consequence you may\nnot convey it at all. For example, if you agree to terms that obligate you\nto collect a royalty for further conveying from those to whom you convey\nthe Program, the only way you could satisfy both those terms and this\nLicense would be to refrain entirely from conveying the Program.\n\n 13. Use with the GNU Affero General Public License.\n\n Notwithstanding any other provision of this License, you have\npermission to link or combine any covered work with a work licensed\nunder version 3 of the GNU Affero General Public License into a single\ncombined work, and to convey the resulting work. The terms of this\nLicense will continue to apply to the part which is the covered work,\nbut the special requirements of the GNU Affero General Public License,\nsection 13, concerning interaction through a network will apply to the\ncombination as such.\n\n 14. Revised Versions of this License.\n\n The Free Software Foundation may publish revised and/or new versions of\nthe GNU General Public License from time to time. Such new versions will\nbe similar in spirit to the present version, but may differ in detail to\naddress new problems or concerns.\n\n Each version is given a distinguishing version number. If the\nProgram specifies that a certain numbered version of the GNU General\nPublic License \"or any later version\" applies to it, you have the\noption of following the terms and conditions either of that numbered\nversion or of any later version published by the Free Software\nFoundation. If the Program does not specify a version number of the\nGNU General Public License, you may choose any version ever published\nby the Free Software Foundation.\n\n If the Program specifies that a proxy can decide which future\nversions of the GNU General Public License can be used, that proxy's\npublic statement of acceptance of a version permanently authorizes you\nto choose that version for the Program.\n\n Later license versions may give you additional or different\npermissions. However, no additional obligations are imposed on any\nauthor or copyright holder as a result of your choosing to follow a\nlater version.\n\n 15. Disclaimer of Warranty.\n\n THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY\nAPPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT\nHOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM \"AS IS\" WITHOUT WARRANTY\nOF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,\nTHE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR\nPURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM\nIS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF\nALL NECESSARY SERVICING, REPAIR OR CORRECTION.\n\n 16. Limitation of Liability.\n\n IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING\nWILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS\nTHE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY\nGENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE\nUSE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF\nDATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD\nPARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),\nEVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF\nSUCH DAMAGES.\n\n 17. Interpretation of Sections 15 and 16.\n\n If the disclaimer of warranty and limitation of liability provided\nabove cannot be given local legal effect according to their terms,\nreviewing courts shall apply local law that most closely approximates\nan absolute waiver of all civil liability in connection with the\nProgram, unless a warranty or assumption of liability accompanies a\ncopy of the Program in return for a fee.\n\n END OF TERMS AND CONDITIONS\n\n How to Apply These Terms to Your New Programs\n\n If you develop a new program, and you want it to be of the greatest\npossible use to the public, the best way to achieve this is to make it\nfree software which everyone can redistribute and change under these terms.\n\n To do so, attach the following notices to the program. It is safest\nto attach them to the start of each source file to most effectively\nstate the exclusion of warranty; and each file should have at least\nthe \"copyright\" line and a pointer to where the full notice is found.\n\n \n Copyright (C) \n\n This program is free software: you can redistribute it and/or modify\n it under the terms of the GNU General Public License as published by\n the Free Software Foundation, either version 3 of the License, or\n (at your option) any later version.\n\n This program is distributed in the hope that it will be useful,\n but WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n GNU General Public License for more details.\n\n You should have received a copy of the GNU General Public License\n along with this program. If not, see .\n\nAlso add information on how to contact you by electronic and paper mail.\n\n If the program does terminal interaction, make it output a short\nnotice like this when it starts in an interactive mode:\n\n Copyright (C) \n This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.\n This is free software, and you are welcome to redistribute it\n under certain conditions; type `show c' for details.\n\nThe hypothetical commands `show w' and `show c' should show the appropriate\nparts of the General Public License. Of course, your program's commands\nmight be different; for a GUI interface, you would use an \"about box\".\n\n You should also get your employer (if you work as a programmer) or school,\nif any, to sign a \"copyright disclaimer\" for the program, if necessary.\nFor more information on this, and how to apply and follow the GNU GPL, see\n.\n\n The GNU General Public License does not permit incorporating your program\ninto proprietary programs. If your program is a subroutine library, you\nmay consider it more useful to permit linking proprietary applications with\nthe library. If this is what you want to do, use the GNU Lesser General\nPublic License instead of this License. But first, please read\n.\n" }, { "path": "external/Licenses/XsimdCopyright.txt", "content": "Copyright (c) 2016, Johan Mabille, Sylvain Corlay, Wolf Vollprecht and Martin\nRenou\nCopyright (c) 2016, QuantStack\nCopyright (c) 2018, Serge Guelton\nhttps://github.com/xtensor-stack/xsimd\n" }, { "path": "external/Licenses/XsimdLicense.txt", "content": "Copyright (c) 2016, Johan Mabille, Sylvain Corlay, Wolf Vollprecht and Martin\nRenou\nCopyright (c) 2016, QuantStack\nCopyright (c) 2018, Serge Guelton\nAll rights reserved.\n\nRedistribution and use in source and binary forms, with or without\nmodification, are permitted provided that the following conditions are met:\n\n* Redistributions of source code must retain the above copyright notice, this\n list of conditions and the following disclaimer.\n\n* Redistributions in binary form must reproduce the above copyright notice,\n this list of conditions and the following disclaimer in the documentation\n and/or other materials provided with the distribution.\n\n* Neither the name of the copyright holder nor the names of its\n contributors may be used to endorse or promote products derived from\n this software without specific prior written permission.\n\nTHIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\"\nAND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE\nIMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\nDISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE\nFOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL\nDAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR\nSERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER\nCAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,\nOR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\nOF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n" }, { "path": "external/Licenses/YamlCppCopyright.txt", "content": "Copyright (c) 2008-2015 Jesse Beder.\nCopyright 2005-2010, 2013, 2015, 2017-2020 Google Inc.\nCopyright 2007 Neal Norwitz\nhttps://github.com/jbeder/yaml-cpp\n" }, { "path": "external/Licenses/YamlCppLicense.txt", "content": "Copyright (c) 2008-2015 Jesse Beder.\n\nPermission is hereby granted, free of charge, to any person obtaining a copy\nof this software and associated documentation files (the \"Software\"), to deal\nin the Software without restriction, including without limitation the rights\nto use, copy, modify, merge, publish, distribute, sublicense, and/or sell\ncopies of the Software, and to permit persons to whom the Software is\nfurnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in\nall copies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN\nTHE SOFTWARE.\n" }, { "path": "external/SPHEREPACK/CMakeLists.txt", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nset(LIBRARY SPHEREPACK)\n\nset(LIBRARY_SOURCES\n alf.f\n divgs.f\n gaqd.f\n gradgs.f\n hrfft.f\n shags.f\n shsgs.f\n slapgs.f\n sphcom.f\n vhags.f\n vhsgs.f\n vrtgs.f\n vtsgs.f\n )\n\n# Starting in gcc8, gfortran warns about instances of Fortran77 coding style in\n# certain SPHEREPACK files. The warning is:\n# Warning: Array reference at ... out of bounds ... in loop beginning ...\n#\n# Attempts to silence the warning by use of individual flags were unsuccessful,\n# so instead we silence all warnings for the problematic files.\nset(FILES_WITH_ARRAY_REFERENCES\n alf.f\n sphcom.f\n vhags.f\n vhsgs.f\n vtsgs.f\n )\nset_source_files_properties(${FILES_WITH_ARRAY_REFERENCES}\n PROPERTIES COMPILE_FLAGS -w)\n\n# Starting in gcc9, gfortran warns about deleted language features in certain\n# SPHEREPACK files. The warnings are,\n# * Warning: Fortran 2018 deleted feature: Arithmetic IF statement at ...\n# * Warning: Fortran 2018 deleted feature: Shared DO termination label at ...\n#\n# We silence these warnings too.\n# An alternative solution would be to specify the compiler flag `-std=legacy`.\nset(FILES_WITH_DELETED_FEATURES\n gradgs.f\n hrfft.f\n shags.f\n shsgs.f\n )\nset_source_files_properties(${FILES_WITH_DELETED_FEATURES}\n PROPERTIES COMPILE_FLAGS -w)\n\nadd_library(${LIBRARY} ${LIBRARY_SOURCES})\n\nif(SPECTRE_Fortran_STATIC_LIBS)\n if (NOT $gfortran)\n find_library(gfortran NAMES libgfortran.a)\n endif()\n if (NOT $quadmath)\n find_library(quadmath NAMES libquadmath.a)\n endif()\n target_link_libraries(\n ${LIBRARY}\n PRIVATE\n ${gfortran}\n ${quadmath}\n )\nendif()\n\ntarget_link_libraries(\n ${LIBRARY}\n PRIVATE\n SpectreFlags\n)\n" }, { "path": "external/SPHEREPACK/LICENSE.txt", "content": "Copyright © 2004 the University Corporation for Atmospheric Research\n(\"UCAR\"). All rights reserved. Developed by NCAR's Computational and\nInformation Systems Laboratory, UCAR, www2.cisl.ucar.edu.\n\nRedistribution and use of the Software in source and binary forms,\nwith or without modification, is permitted provided that the following\nconditions are met:\n\nNeither the names of NCAR's Computational and Information Systems\nLaboratory, the University Corporation for Atmospheric Research, nor\nthe names of its sponsors or contributors may be used to endorse or\npromote products derived from this Software without specific prior\nwritten permission. Redistributions of source code must retain the\nabove copyright notices, this list of conditions, and the disclaimer\nbelow. Redistributions in binary form must reproduce the above\ncopyright notice, this list of conditions, and the disclaimer below in\nthe documentation and/or other materials provided with the\ndistribution.\n\nTHIS SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND,\nEXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF\nMERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND\nNONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT\nHOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,\nEXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN\nACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN\nCONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE\nSOFTWARE.\n\nSPHEREPACK is a product of the Computational & Information Systems\nLaboratory at the National Center for Atmospheric Research (NCAR)\n" }, { "path": "external/SPHEREPACK/README.txt", "content": "This is a modified version of SPHEREPACK 3.2.\nThe SPHEREPACK 3.2 license can be found in LICENSE.txt.\n\nOnly 13 FORTRAN files, with the functionality we need for SpECTRE,\nhave been retained here. The unmodified SPHEREPACK contains\nadditional files with more functionality than we need, and we do not\ninclude these files, nor do we include the SPHEREPACK makefiles or\ntests.\n\nA summary of the modifications:\n\n1) We have added our own Spherepack.hpp for #including SPHEREPACK\n subroutines into C/C++.\n2) All computations were changed to double precision.\n3) divgs, gradgs, shags, shsgs, slapgs, vhags, vhsgs, vrtgs, vtsgs now\n have the ability to loop over 'offsets' and do multiple\n computations at once with a single call to a SPHEREPACK function.\n This is useful if you have a (r,theta,phi) grid, and you need to do\n spherical transforms on (theta,phi) for multiple values of r.\n4) Bugfix in vtsgs.f, where mmax was computed incorrectly if nlon is even.\n5) shsgs and shags no longer have limitations on the size of the passed-in\n coefficient arrays 'a' and 'b'. They also take additional arguments,\n 'mdabmax, 'ndabmax'. Coefficients that do not fit into the provided\n storage are ignored / treated as zero / not computed. The same holds\n for coefficients with indices above {m,n}dabmax. This allows for\n more efficient implementation of definite integrals, where now\n one can request computation of the l=0 coefficient only. This also\n helps in changing resolution, since restriction or prolongation\n of the coefficient array is no longer (explicitly) needed.\n6) Given that we so far do not need to call SPHEREPACK with symmetries\n (e.g. equatorial symmetry, octant symmetry, etc) enforced, the above\n changes were not tested with SPHEREPACK's symmetry options turned on.\n In order to avoid surprises, SPHEREPACK's symmetry options are disabled.\n If you need symmetries, please test them.\n" }, { "path": "external/SPHEREPACK/alf.f", "content": "c\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc * *\nc * copyright (c) 1998 by UCAR *\nc * *\nc * University Corporation for Atmospheric Research *\nc * *\nc * all rights reserved *\nc * *\nc * SPHEREPACK version 3.2 *\nc * *\nc * A Package of Fortran77 Subroutines and Programs *\nc * *\nc * for Modeling Geophysical Processes *\nc * *\nc * by *\nc * *\nc * John Adams and Paul Swarztrauber *\nc * *\nc * of *\nc * *\nc * the National Center for Atmospheric Research *\nc * *\nc * Boulder, Colorado (80307) U.S.A. *\nc * *\nc * which is sponsored by *\nc * *\nc * the National Science Foundation *\nc * *\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc\nc\nc\nc file alf.f contains subroutines alfk,lfim,lfim1,lfin,lfin1,lfpt\nc for computing normalized associated legendre polynomials\nc\nc subroutine alfk (n,m,cp)\nc\nc dimension of real cp(n/2 + 1)\nc arguments\nc\nc purpose routine alfk computes single precision fourier\nc coefficients in the trigonometric series\nc representation of the normalized associated\nc legendre function pbar(n,m,theta) for use by\nc routines lfp and lfpt in calculating single\nc precision pbar(n,m,theta).\nc\nc first define the normalized associated\nc legendre functions\nc\nc pbar(m,n,theta) = sqrt((2*n+1)*factorial(n-m)\nc /(2*factorial(n+m)))*sin(theta)**m/(2**n*\nc factorial(n)) times the (n+m)th derivative of\nc (x**2-1)**n with respect to x=cos(theta)\nc\nc where theta is colatitude.\nc\nc then subroutine alfk computes the coefficients\nc cp(k) in the following trigonometric\nc expansion of pbar(m,n,theta).\nc\nc 1) for n even and m even, pbar(m,n,theta) =\nc .5*cp(1) plus the sum from k=1 to k=n/2\nc of cp(k+1)*cos(2*k*th)\nc\nc 2) for n even and m odd, pbar(m,n,theta) =\nc the sum from k=1 to k=n/2 of\nc cp(k)*sin(2*k*th)\nc\nc 3) for n odd and m even, pbar(m,n,theta) =\nc the sum from k=1 to k=(n+1)/2 of\nc cp(k)*cos((2*k-1)*th)\nc\nc 4) for n odd and m odd, pbar(m,n,theta) =\nc the sum from k=1 to k=(n+1)/2 of\nc cp(k)*sin((2*k-1)*th)\nc\nc\nc usage call alfk(n,m,cp)\nc\nc arguments\nc\nc on input n\nc nonnegative integer specifying the degree of\nc pbar(n,m,theta)\nc\nc m\nc is the order of pbar(n,m,theta). m can be\nc any integer however cp is computed such that\nc pbar(n,m,theta) = 0 if abs(m) is greater\nc than n and pbar(n,m,theta) = (-1)**m*\nc pbar(n,-m,theta) for negative m.\nc\nc on output cp\nc single precision array of length (n/2)+1\nc which contains the fourier coefficients in\nc the trigonometric series representation of\nc pbar(n,m,theta)\nc\nc\nc special conditions none\nc\nc precision single\nc\nc algorithm the highest order coefficient is determined in\nc closed form and the remainig coefficients are\nc determined as the solution of a backward\nc recurrence relation.\nc\nc accuracy comparison between routines alfk and double\nc precision dalfk on the cray1 indicates\nc greater accuracy for smaller values\nc of input parameter n. agreement to 14\nc places was obtained for n=10 and to 13\nc places for n=100.\nc\n subroutine alfk (n,m,cp)\n implicit double precision (a-h,o-z)\n dimension cp(n/2+1)\n parameter (sc10=1024.d0)\n parameter (sc20=sc10*sc10)\n parameter (sc40=sc20*sc20)\nc\n cp(1) = 0.d0\n ma = iabs(m)\n if(ma .gt. n) return\n if(n-1) 2,3,5\n 2 cp(1) = dsqrt(2.d0)\n return\n 3 if(ma .ne. 0) go to 4\n cp(1) = dsqrt(1.5d0)\n return\n 4 cp(1) = dsqrt(.75d0)\n if(m .eq. -1) cp(1) = -cp(1)\n return\n 5 if(mod(n+ma,2) .ne. 0) go to 10\n nmms2 = (n-ma)/2\n fnum = n+ma+1\n fnmh = n-ma+1\n pm1 = 1.d0\n go to 15\n 10 nmms2 = (n-ma-1)/2\n fnum = n+ma+2\n fnmh = n-ma+2\n pm1 = -1.d0\n 15 t1 = 1.d0/sc20\n nex = 20\n fden = 2.d0\n if(nmms2 .lt. 1) go to 20\n do 18 i=1,nmms2\n t1 = fnum*t1/fden\n if(t1 .gt. sc20) then\n t1 = t1/sc40\n nex = nex+40\n end if\n fnum = fnum+2.d0\n fden = fden+2.d0\n 18 continue\n 20 t1 = t1/2.d0**(n-1-nex)\n if(mod(ma/2,2) .ne. 0) t1 = -t1\n t2 = 1.d0 \n if(ma .eq. 0) go to 26\n do 25 i=1,ma\n t2 = fnmh*t2/(fnmh+pm1)\n fnmh = fnmh+2.d0\n 25 continue\n 26 cp2 = t1*dsqrt((n+.5d0)*t2)\n fnnp1 = n*(n+1)\n fnmsq = fnnp1-2.d0*ma*ma\n l = (n+1)/2\n if(mod(n,2) .eq. 0 .and. mod(ma,2) .eq. 0) l = l+1\n cp(l) = cp2\n if(m .ge. 0) go to 29\n if(mod(ma,2) .ne. 0) cp(l) = -cp(l)\n 29 if(l .le. 1) return\n fk = n\n a1 = (fk-2.d0)*(fk-1.d0)-fnnp1\n b1 = 2.d0*(fk*fk-fnmsq)\n cp(l-1) = b1*cp(l)/a1\n 30 l = l-1\n if(l .le. 1) return\n fk = fk-2.d0\n a1 = (fk-2.d0)*(fk-1.d0)-fnnp1\n b1 = -2.d0*(fk*fk-fnmsq)\n c1 = (fk+1.d0)*(fk+2.d0)-fnnp1\n cp(l-1) = -(b1*cp(l)+c1*cp(l+1))/a1\n go to 30\n end\nc subroutine lfim (init,theta,l,n,nm,pb,id,wlfim)\nc\nc dimension of theta(l), pb(id,nm+1), wlfim(4*l*(nm+1))\nc arguments\nc\nc purpose given n and l, routine lfim calculates\nc the normalized associated legendre functions\nc pbar(n,m,theta) for m=0,...,n and theta(i)\nc for i=1,...,l where\nc\nc pbar(m,n,theta) = sqrt((2*n+1)*factorial(n-m)\nc /(2*factorial(n+m)))*sin(theta)**m/(2**n*\nc factorial(n)) times the (n+m)th derivative of\nc (x**2-1)**n with respect to x=cos(theta)\nc\nc usage call lfim (init,theta,l,n,nm,pb,id,wlfim)\nc\nc arguments\nc on input init\nc = 0\nc initialization only - using parameters\nc l, nm and array theta, subroutine lfim\nc initializes array wlfim for subsequent\nc use in the computation of the associated\nc legendre functions pb. initialization\nc does not have to be repeated unless\nc l, nm, or array theta are changed.\nc = 1\nc subroutine lfim uses the array wlfim that\nc was computed with init = 0 to compute pb.\nc\nc theta\nc an array that contains the colatitudes\nc at which the associated legendre functions\nc will be computed. the colatitudes must be\nc specified in radians.\nc\nc l\nc the length of the theta array. lfim is\nc vectorized with vector length l.\nc\nc n\nc nonnegative integer, less than nm, specifying\nc degree of pbar(n,m,theta). subroutine lfim\nc must be called starting with n=0. n must be\nc incremented by one in subsequent calls and\nc must not exceed nm.\nc\nc nm\nc the maximum value of n and m\nc\nc id\nc the first dimension of the two dimensional\nc array pb as it appears in the program that\nc calls lfim. (see output parameter pb)\nc\nc wlfim\nc an array with length 4*l*(nm+1) which\nc must be initialized by calling lfim\nc with init=0 (see parameter init) it\nc must not be altered between calls to\nc lfim.\nc\nc\nc on output pb\nc a two dimensional array with first\nc dimension id in the program that calls\nc lfim. the second dimension of pb must\nc be at least nm+1. starting with n=0\nc lfim is called repeatedly with n being\nc increased by one between calls. on each\nc call, subroutine lfim computes\nc = pbar(m,n,theta(i)) for m=0,...,n and\nc i=1,...l.\nc\nc wlfim\nc array containing values which must not\nc be altered unless l, nm or the array theta\nc are changed in which case lfim must be\nc called with init=0 to reinitialize the\nc wlfim array.\nc\nc special conditions n must be increased by one between calls\nc of lfim in which n is not zero.\nc\nc precision single\nc\nc\nc algorithm routine lfim calculates pbar(n,m,theta) using\nc a four term recurrence relation. (unpublished\nc notes by paul n. swarztrauber)\nc\n subroutine lfim (init,theta,l,n,nm,pb,id,wlfim)\n implicit double precision (a-h,o-z)\n dimension theta(1), pb(1) ,wlfim(1)\nc\nc total length of wlfim is 4*l*(nm+1)\nc\n lnx = l*(nm+1)\n iw1 = lnx+1\n iw2 = iw1+lnx\n iw3 = iw2+lnx\n call lfim1(init,theta,l,n,nm,id,pb,wlfim,wlfim(iw1),\n 1 wlfim(iw2),wlfim(iw3),wlfim(iw2))\n return\n end\n subroutine lfim1(init,theta,l,n,nm,id,p3,phz,ph1,p1,p2,cp)\n implicit double precision (a-h,o-z)\n dimension p1(l,*) ,p2(l,*) ,p3(id,*) ,phz(l,*) ,\n 1 ph1(l,*) ,cp(*) ,theta(*)\n nmp1 = nm+1\n if(init .ne. 0) go to 5\n ssqrt2 = 1.d0/dsqrt(2.d0)\n do 10 i=1,l\n phz(i,1) = ssqrt2\n 10 continue\n do 15 np1=2,nmp1\n nh = np1-1\n call alfk(nh,0,cp)\n do 16 i=1,l\n call lfpt(nh,0,theta(i),cp,phz(i,np1))\n 16 continue\n call alfk(nh,1,cp)\n do 17 i=1,l\n call lfpt(nh,1,theta(i),cp,ph1(i,np1))\n 17 continue\n 15 continue\n return\n 5 if(n .gt. 2) go to 60\n if(n-1)25,30,35\n 25 do 45 i=1,l\n p3(i,1)=phz(i,1)\n 45 continue\n return\n 30 do 50 i=1,l\n p3(i,1) = phz(i,2)\n p3(i,2) = ph1(i,2)\n 50 continue\n return\n 35 sq5s6 = dsqrt(5.d0/6.d0)\n sq1s6 = dsqrt(1.d0/6.d0)\n do 55 i=1,l\n p3(i,1) = phz(i,3)\n p3(i,2) = ph1(i,3)\n p3(i,3) = sq5s6*phz(i,1)-sq1s6*p3(i,1)\n p1(i,1) = phz(i,2)\n p1(i,2) = ph1(i,2)\n p2(i,1) = phz(i,3)\n p2(i,2) = ph1(i,3)\n p2(i,3) = p3(i,3)\n 55 continue\n return\n 60 nm1 = n-1\n np1 = n+1\n fn = dfloat(n)\n tn = fn+fn\n cn = (tn+1.d0)/(tn-3.d0)\n do 65 i=1,l\n p3(i,1) = phz(i,np1)\n p3(i,2) = ph1(i,np1)\n 65 continue\n if(nm1 .lt. 3) go to 71\n do 70 mp1=3,nm1\n m = mp1-1\n fm = dfloat(m)\n fnpm = fn+fm\n fnmm = fn-fm\n temp = fnpm*(fnpm-1.d0)\n cc = dsqrt(cn*(fnpm-3.d0)*(fnpm-2.d0)/temp)\n dd = dsqrt(cn*fnmm*(fnmm-1.d0)/temp)\n ee = dsqrt((fnmm+1.d0)*(fnmm+2.d0)/temp)\n do 70 i=1,l\n p3(i,mp1) = cc*p1(i,mp1-2)+dd*p1(i,mp1)-ee*p3(i,mp1-2)\n 70 continue\n 71 fnpm = fn+fn-1.d0\n temp = fnpm*(fnpm-1.d0)\n cc = dsqrt(cn*(fnpm-3.d0)*(fnpm-2.d0)/temp)\n ee = dsqrt(6.d0/temp)\n do 75 i=1,l\n p3(i,n) = cc*p1(i,n-2)-ee*p3(i,n-2)\n 75 continue\n fnpm = fn+fn\n temp = fnpm*(fnpm-1.d0)\n cc = dsqrt(cn*(fnpm-3.d0)*(fnpm-2.d0)/temp)\n ee = dsqrt(2.d0/temp)\n do 80 i=1,l\n p3(i,n+1) = cc*p1(i,n-1)-ee*p3(i,n-1)\n 80 continue\n do 90 mp1=1,np1\n do 90 i=1,l\n p1(i,mp1) = p2(i,mp1)\n p2(i,mp1) = p3(i,mp1)\n 90 continue\n return\n end\nc subroutine lfin (init,theta,l,m,nm,pb,id,wlfin)\nc\nc dimension of theta(l), pb(id,nm+1), wlfin(4*l*(nm+1))\nc arguments\nc\nc purpose given m and l, routine lfin calculates\nc the normalized associated legendre functions\nc pbar(n,m,theta) for n=m,...,nm and theta(i)\nc for i=1,...,l where\nc\nc pbar(m,n,theta) = sqrt((2*n+1)*factorial(n-m)\nc /(2*factorial(n+m)))*sin(theta)**m/(2**n*\nc factorial(n)) times the (n+m)th derivative of\nc (x**2-1)**n with respect to x=cos(theta)\nc\nc usage call lfin (init,theta,l,m,nm,pb,id,wlfin)\nc\nc arguments\nc on input init\nc = 0\nc initialization only - using parameters\nc l, nm and the array theta, subroutine lfin\nc initializes the array wlfin for subsequent\nc use in the computation of the associated\nc legendre functions pb. initialization does\nc not have to be repeated unless l, nm or\nc the array theta are changed.\nc = 1\nc subroutine lfin uses the array wlfin that\nc was computed with init = 0 to compute pb\nc\nc theta\nc an array that contains the colatitudes\nc at which the associated legendre functions\nc will be computed. the colatitudes must be\nc specified in radians.\nc\nc l\nc the length of the theta array. lfin is\nc vectorized with vector length l.\nc\nc m\nc nonnegative integer, less than nm, specifying\nc degree of pbar(n,m,theta). subroutine lfin\nc must be called starting with n=0. n must be\nc incremented by one in subsequent calls and\nc must not exceed nm.\nc\nc nm\nc the maximum value of n and m\nc\nc id\nc the first dimension of the two dimensional\nc array pb as it appears in the program that\nc calls lfin. (see output parameter pb)\nc\nc wlfin\nc an array with length 4*l*(nm+1) which\nc must be initialized by calling lfin\nc with init=0 (see parameter init) it\nc must not be altered between calls to\nc lfin.\nc\nc\nc on output pb\nc a two dimensional array with first\nc dimension id in the program that calls\nc lfin. the second dimension of pb must\nc be at least nm+1. starting with m=0\nc lfin is called repeatedly with m being\nc increased by one between calls. on each\nc call, subroutine lfin computes pb(i,n+1)\nc = pbar(m,n,theta(i)) for n=m,...,nm and\nc i=1,...l.\nc\nc wlfin\nc array containing values which must not\nc be altered unless l, nm or the array theta\nc are changed in which case lfin must be\nc called with init=0 to reinitialize the\nc wlfin array.\nc\nc special conditions m must be increased by one between calls\nc of lfin in which m is not zero.\nc\nc precision single\nc\nc algorithm routine lfin calculates pbar(n,m,theta) using\nc a four term recurrence relation. (unpublished\nc notes by paul n. swarztrauber)\nc\n subroutine lfin (init,theta,l,m,nm,pb,id,wlfin)\n implicit double precision (a-h,o-z)\n dimension theta(1), pb(1) ,wlfin(1)\nc\nc total length of wlfin is 4*l*(nm+1)\nc\n lnx = l*(nm+1)\n iw1 = lnx+1\n iw2 = iw1+lnx\n iw3 = iw2+lnx\n call lfin1(init,theta,l,m,nm,id,pb,wlfin,wlfin(iw1),\n 1 wlfin(iw2),wlfin(iw3),wlfin(iw2))\n return\n end\n subroutine lfin1(init,theta,l,m,nm,id,p3,phz,ph1,p1,p2,cp)\n implicit double precision (a-h,o-z)\n dimension p1(l,1) ,p2(l,1) ,p3(id,1) ,phz(l,1) ,\n 1 ph1(l,1) ,cp(1) ,theta(1)\n nmp1 = nm+1\n if(init .ne. 0) go to 5\n ssqrt2 = 1.d0/dsqrt(2.d0)\n do 10 i=1,l\n phz(i,1) = ssqrt2\n 10 continue\n do 15 np1=2,nmp1\n nh = np1-1\n call alfk(nh,0,cp)\n do 16 i=1,l\n call lfpt(nh,0,theta(i),cp,phz(i,np1))\n 16 continue\n call alfk(nh,1,cp)\n do 17 i=1,l\n call lfpt(nh,1,theta(i),cp,ph1(i,np1))\n 17 continue\n 15 continue\n return\n 5 mp1 = m+1\n fm = dfloat(m)\n tm = fm+fm\n if(m-1)25,30,35\n 25 do 45 np1=1,nmp1\n do 45 i=1,l\n p3(i,np1) = phz(i,np1)\n p1(i,np1) = phz(i,np1)\n 45 continue\n return\n 30 do 50 np1=2,nmp1\n do 50 i=1,l\n p3(i,np1) = ph1(i,np1)\n p2(i,np1) = ph1(i,np1)\n 50 continue\n return\n 35 temp = tm*(tm-1.d0)\n cc = dsqrt((tm+1.d0)*(tm-2.d0)/temp)\n ee = dsqrt(2.d0/temp)\n do 85 i=1,l\n p3(i,m+1) = cc*p1(i,m-1)-ee*p1(i,m+1)\n 85 continue\n if(m .eq. nm) return\n temp = tm*(tm+1.d0)\n cc = dsqrt((tm+3.d0)*(tm-2.d0)/temp)\n ee = dsqrt(6.d0/temp)\n do 70 i=1,l\n p3(i,m+2) = cc*p1(i,m)-ee*p1(i,m+2)\n 70 continue\n mp3 = m+3\n if(nmp1 .lt. mp3) go to 80\n do 75 np1=mp3,nmp1\n n = np1-1\n fn = dfloat(n)\n tn = fn+fn\n cn = (tn+1.d0)/(tn-3.d0)\n fnpm = fn+fm\n fnmm = fn-fm\n temp = fnpm*(fnpm-1.d0)\n cc = dsqrt(cn*(fnpm-3.d0)*(fnpm-2.d0)/temp)\n dd = dsqrt(cn*fnmm*(fnmm-1.d0)/temp)\n ee = dsqrt((fnmm+1.d0)*(fnmm+2.d0)/temp)\n do 75 i=1,l\n p3(i,np1) = cc*p1(i,np1-2)+dd*p3(i,np1-2)-ee*p1(i,np1)\n 75 continue\n 80 do 90 np1=m,nmp1\n do 90 i=1,l\n p1(i,np1) = p2(i,np1)\n p2(i,np1) = p3(i,np1)\n 90 continue\n return\n end\nc subroutine lfpt (n,m,theta,cp,pb)\nc\nc dimension of\nc arguments\nc cp((n/2)+1)\nc\nc purpose routine lfpt uses coefficients computed by\nc routine alfk to compute the single precision\nc normalized associated legendre function pbar(n,\nc m,theta) at colatitude theta.\nc\nc usage call lfpt(n,m,theta,cp,pb)\nc\nc arguments\nc\nc on input n\nc nonnegative integer specifying the degree of\nc pbar(n,m,theta)\nc m\nc is the order of pbar(n,m,theta). m can be\nc any integer however pbar(n,m,theta) = 0\nc if abs(m) is greater than n and\nc pbar(n,m,theta) = (-1)**m*pbar(n,-m,theta)\nc for negative m.\nc\nc theta\nc single precision colatitude in radians\nc\nc cp\nc single precision array of length (n/2)+1\nc containing coefficients computed by routine\nc alfk\nc\nc on output pb\nc single precision variable containing\nc pbar(n,m,theta)\nc\nc special conditions calls to routine lfpt must be preceded by an\nc appropriate call to routine alfk.\nc\nc precision single\nc\nc algorithm the trigonometric series formula used by\nc routine lfpt to calculate pbar(n,m,th) at\nc colatitude th depends on m and n as follows:\nc\nc 1) for n even and m even, the formula is\nc .5*cp(1) plus the sum from k=1 to k=n/2\nc of cp(k)*cos(2*k*th)\nc 2) for n even and m odd. the formula is\nc the sum from k=1 to k=n/2 of\nc cp(k)*sin(2*k*th)\nc 3) for n odd and m even, the formula is\nc the sum from k=1 to k=(n+1)/2 of\nc cp(k)*cos((2*k-1)*th)\nc 4) for n odd and m odd, the formula is\nc the sum from k=1 to k=(n+1)/2 of\nc cp(k)*sin((2*k-1)*th)\nc\nc accuracy comparison between routines lfpt and double\nc precision dlfpt on the cray1 indicates greater\nc accuracy for greater values on input parameter\nc n. agreement to 13 places was obtained for\nc n=10 and to 12 places for n=100.\nc\nc timing time per call to routine lfpt is dependent on\nc the input parameter n.\nc\n subroutine lfpt (n,m,theta,cp,pb)\n implicit double precision (a-h,o-z)\n dimension cp(1)\nc\n pb = 0.d0\n ma = iabs(m)\n if(ma .gt. n) return\n if (n) 10, 10, 30\n 10 if (ma) 20, 20, 30\n 20 pb= dsqrt(.5d0)\n go to 140\n 30 np1 = n+1\n nmod = mod(n,2)\n mmod = mod(ma,2)\n if (nmod) 40, 40, 90\n 40 if (mmod) 50, 50, 70\n 50 kdo = n/2+1\n cdt = dcos(theta+theta)\n sdt = dsin(theta+theta)\n ct = 1.d0\n st = 0.d0\n sum = .5d0*cp(1)\n do 60 kp1=2,kdo\n cth = cdt*ct-sdt*st\n st = sdt*ct+cdt*st\n ct = cth\n sum = sum+cp(kp1)*ct\n 60 continue\n pb= sum\n go to 140\n 70 kdo = n/2\n cdt = dcos(theta+theta)\n sdt = dsin(theta+theta)\n ct = 1.d0\n st = 0.d0\n sum = 0.d0\n do 80 k=1,kdo\n cth = cdt*ct-sdt*st\n st = sdt*ct+cdt*st\n ct = cth\n sum = sum+cp(k)*st\n 80 continue\n pb= sum\n go to 140\n 90 kdo = (n+1)/2\n if (mmod) 100,100,120\n 100 cdt = dcos(theta+theta)\n sdt = dsin(theta+theta)\n ct = dcos(theta)\n st = -dsin(theta)\n sum = 0.d0\n do 110 k=1,kdo\n cth = cdt*ct-sdt*st\n st = sdt*ct+cdt*st\n ct = cth\n sum = sum+cp(k)*ct\n 110 continue\n pb= sum\n go to 140\n 120 cdt = dcos(theta+theta)\n sdt = dsin(theta+theta)\n ct = dcos(theta)\n st = -dsin(theta)\n sum = 0.d0\n do 130 k=1,kdo\n cth = cdt*ct-sdt*st\n st = sdt*ct+cdt*st\n ct = cth\n sum = sum+cp(k)*st\n 130 continue\n pb= sum\n 140 return\n end\n" }, { "path": "external/SPHEREPACK/divgs.f", "content": "c\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc * *\nc * copyright (c) 1998 by UCAR *\nc * *\nc * University Corporation for Atmospheric Research *\nc * *\nc * all rights reserved *\nc * *\nc * SPHEREPACK version 3.2 *\nc * *\nc * A Package of Fortran77 Subroutines and Programs *\nc * *\nc * for Modeling Geophysical Processes *\nc * *\nc * by *\nc * *\nc * John Adams and Paul Swarztrauber *\nc * *\nc * of *\nc * *\nc * the National Center for Atmospheric Research *\nc * *\nc * Boulder, Colorado (80307) U.S.A. *\nc * *\nc * which is sponsored by *\nc * *\nc * the National Science Foundation *\nc * *\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc\nc\nc\nc\nc ... file divgs.f\nc\nc this file includes documentation and code for\nc subroutine divgs i\nc\nc ... files which must be loaded with divgs.f\nc\nc sphcom.f, hrfft.f, vhags.f, shsgs.f, gaqd.f\nc\nc\nc subroutine divgs(nstrg,nstrb,noffsg,noffsb,\nc nlat,nlon,isym,nt,divg,idiv,jdiv,br,bi,mdb,ndb,\nc + wshsgs,lshsgs,work,lwork,ierror)\nc\nc given the vector spherical harmonic coefficients br and bi, precomputed\nc by subroutine vhags for a vector field (v,w), subroutine divgs\nc computes the divergence of the vector field in the scalar array divg.\nc divg(i,j) is the divergence at the gaussian colatitude point theta(i)\nc (see nlat as input parameter) and east longitude\nc\nc lambda(j) = (j-1)*2*pi/nlon\nc\nc on the sphere. i.e.\nc\nc dv(i,j) = 1/sint*[ d(sint*v(i,j))/dtheta + d(w(i,j))/dlambda ]\nc\nc where sint = sin(theta(i)). w is the east longitudinal and v\nc is the colatitudinal component of the vector field from which\nc br,bi were precomputed\nc\nc\nc input parameters\nc\nc nstrg,nstrb strides in g,b\nc noffsg,noffsb offsets in g,b -- must be between 0 and stride-1\nc\nc nlat the number of points in the gaussian colatitude grid on the\nc full sphere. these lie in the interval (0,pi) and are computed\nc in radians in theta(1) <...< theta(nlat) by subroutine gaqd.\nc if nlat is odd the equator will be included as the grid point\nc theta((nlat+1)/2). if nlat is even the equator will be\nc excluded as a grid point and will lie half way between\nc theta(nlat/2) and theta(nlat/2+1). nlat must be at least 3.\nc note: on the half sphere, the number of grid points in the\nc colatitudinal direction is nlat/2 if nlat is even or\nc (nlat+1)/2 if nlat is odd.\nc\nc nlon the number of distinct londitude points. nlon determines\nc the grid increment in longitude as 2*pi/nlon. for example\nc nlon = 72 for a five degree grid. nlon must be greater\nc than zero. the axisymmetric case corresponds to nlon=1.\nc the efficiency of the computation is improved when nlon\nc is a product of small prime numbers.\nc\nc NOTE: this is a modified version of spherepack. Changes from\nc the original version to the current one have only been\nc tested for isym==0. For this reason an error code will\nc be returned if isym!=0.\nc\nc\nc isym a parameter which determines whether the divergence is\nc computed on the full or half sphere as follows:\nc\nc = 0\nc\nc the symmetries/antsymmetries described in isym=1,2 below\nc do not exist in (v,w) about the equator. in this case the\nc divergence is neither symmetric nor antisymmetric about\nc the equator. the divergence is computed on the entire\nc sphere. i.e., in the array divg(i,j) for i=1,...,nlat and\nc j=1,...,nlon.\nc\nc = 1\nc\nc w is antisymmetric and v is symmetric about the equator.\nc in this case the divergence is antisymmetyric about\nc the equator and is computed for the northern hemisphere\nc only. i.e., if nlat is odd the divergence is computed\nc in the array divg(i,j) for i=1,...,(nlat+1)/2 and for\nc j=1,...,nlon. if nlat is even the divergence is computed\nc in the array divg(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc\nc = 2\nc w is symmetric and v is antisymmetric about the equator\nc in this case the divergence is symmetyric about the\nc equator and is computed for the northern hemisphere\nc only. i.e., if nlat is odd the divergence is computed\nc in the array divg(i,j) for i=1,...,(nlat+1)/2 and for\nc j=1,...,nlon. if nlat is even the divergence is computed\nc in the array divg(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc\nc\nc nt nt is the number of scalar and vector fields. some\nc computational efficiency is obtained for multiple fields.\nc in the program that calls divgs, the arrays br,bi, and divg\nc can be three dimensional corresponding to an indexed multiple\nc vector field. in this case multiple scalar synthesis will\nc be performed to compute the divergence for each field. the\nc third index is the synthesis index which assumes the values\nc k=1,...,nt. for a single synthesis set nt = 1. the\nc description of the remaining parameters is simplified by\nc assuming that nt=1 or that all the arrays are two dimensional.\nc\nc idiv the first dimension of the array divg as it appears in\nc the program that calls divgs. if isym = 0 then idiv\nc must be at least nlat. if isym = 1 or 2 and nlat is\nc even then idiv must be at least nlat/2. if isym = 1 or 2\nc and nlat is odd then idiv must be at least (nlat+1)/2.\nc\nc jdiv the second dimension of the array divg as it appears in\nc the program that calls divgs. jdiv must be at least nlon.\nc\nc br,bi two or three dimensional arrays (see input parameter nt)\nc that contain vector spherical harmonic coefficients\nc of the vector field (v,w) as computed by subroutine vhags.\nc *** br and bi must be computed by vhags prior to calling\nc divgs.\nc\nc mdb the first dimension of the arrays br and bi as it\nc appears in the program that calls divgs. mdb must be at\nc least min0(nlat,nlon/2) if nlon is even or at least\nc min0(nlat,(nlon+1)/2) if nlon is odd.\nc\nc ndb the second dimension of the arrays br and bi as it\nc appears in the program that calls divgs. ndb must be at\nc least nlat.\nc\nc\nc wshsgs an array which must be intialized by subroutine shsgsi.\nc once initialized,\nc wshsgs can be used repeatedly by divgs as long as nlon\nc and nlat remain unchanged. wshsgs must not be altered\nc between calls of divgs.\nc\nc\nc lshsgs the dimension of the array wshsgs as it appears in the\nc program that calls divgs. define\nc\nc l1 = min0(nlat,(nlon+2)/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc then lshsgs must be at least\nc\nc nlat*(3*(l1+l2)-2)+(l1-1)*(l2*(2*nlat-l1)-3*l1)/2+nlon+15\nc\nc\nc work a work array that does not have to be saved.\nc\nc lwork the dimension of the array work as it appears in the\nc program that calls divgs. define\nc\nc l1 = min0(nlat,(nlon+2)/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc if isym = 0 then lwork must be at least\nc\nc nlat*((nt+1)*nlon+2*nt*l1+1)\nc\nc if isym > 0 then lwork must be at least\nc\nc (nt+1)*l2*nlon+nlat*(2*nt*l1+1)\nc\nc **************************************************************\nc\nc output parameters\nc\nc\nc divg a two or three dimensional array (see input parameter nt)\nc that contains the divergence of the vector field (v,w)\nc whose coefficients br,bi where computed by subroutine\nc vhags. divg(i,j) is the divergence at the gaussian colatitude\nc point theta(i) and longitude point lambda(j) = (j-1)*2*pi/nlon.\nc the index ranges are defined above at the input parameter\nc isym.\nc\nc\nc ierror = 0 no errors\nc = 1 error in the specification of nlat\nc = 2 error in the specification of nlon\nc = 3 error in the specification of isym\nc = 4 error in the specification of nt\nc = 5 error in the specification of idiv\nc = 6 error in the specification of jdiv\nc = 7 error in the specification of mdb\nc = 8 error in the specification of ndb\nc = 9 error in the specification of lshsgs\nc = 10 error in the specification of lwork\nc **********************************************************************\nc \nc \n subroutine divgs(nstrg,nstrb,noffsg,noffsb,\n + nlat,nlon,isym,nt,divg,idiv,jdiv,br,bi,mdb,ndb,\n + wshsgs,lshsgs,work,lwork,ierror)\n implicit double precision (a-h,o-z)\n dimension divg(nstrg,idiv,jdiv,nt),\n + br(nstrb,mdb,ndb,nt),bi(nstrb,mdb,ndb,nt)\n dimension wshsgs(lshsgs),work(lwork)\nc\nc check input parameters\nc\n ierror = 1\n if(nlat .lt. 3) return\n ierror = 2\n if(nlon .lt. 4) return\n ierror = 3\nc if (isym.lt.0 .or. isym.gt.2) return\nc see note above about symmeries\n if(isym.ne.0) return\n ierror = 4\n if(nt .lt. 0) return\n ierror = 5\n imid = (nlat+1)/2\n if((isym.eq.0 .and. idiv.lt.nlat) .or.\n 1 (isym.gt.0 .and. idiv.lt.imid)) return\n ierror = 6\n if(jdiv .lt. nlon) return\n ierror = 7\n if(mdb .lt. min0(nlat,(nlon+1)/2)) return\n mmax = min0(nlat,(nlon+2)/2)\n ierror = 8\n if(ndb .lt. nlat) return\n ierror = 9\n imid = (nlat+1)/2\n lpimn = (imid*mmax*(nlat+nlat-mmax+1))/2\nc check permanent work space length\n l2 = (nlat+1)/2\n l1 = min0((nlon+2)/2,nlat)\n lp=nlat*(3*(l1+l2)-2)+(l1-1)*(l2*(2*nlat-l1)-3*l1)/2+nlon+15\n if(lshsgs.lt.lp) return\n ierror = 10\nc\nc verify unsaved work space (add to what shses requires, file f3)\nc\n ls = nlat\n if(isym .gt. 0) ls = imid\n nln = nt*ls*nlon\nc\nc set first dimension for a,b (as requried by shses)\nc\n mab = min0(nlat,nlon/2+1)\n mn = mab*nlat*nt\n if(lwork.lt. nln+ls*nlon+2*mn+nlat) return\n ierror = 11\n if((noffsg.lt.0) .or. (noffsg.ge.nstrg)) return\n if((noffsb.lt.0) .or. (noffsb.ge.nstrb)) return\n ierror = 0\nc\nc set work space pointers\nc\n ia = 1\n ib = ia+mn\n is = ib+mn\n iwk = is+nlat\n lwk = lwork-2*mn-nlat\n call divgs1(nstrg,nstrb,noffsg,noffsb,\n + nlat,nlon,isym,nt,divg,idiv,jdiv,br,bi,mdb,ndb,\n +work(ia),work(ib),mab,work(is),wshsgs,lshsgs,work(iwk),lwk,\n +ierror)\n return\n end\n\n subroutine divgs1(nstrg,nstrb,noffsg,noffsb,\n + nlat,nlon,isym,nt,divg,idiv,jdiv,br,bi,mdb,ndb,\n + a,b,mab,sqnn,wshsgs,lshsgs,wk,lwk,ierror)\n implicit double precision (a-h,o-z)\n dimension divg(nstrg,idiv,jdiv,nt),\n + br(nstrb,mdb,ndb,nt),bi(nstrb,mdb,ndb,nt)\n dimension a(mab,nlat,nt),b(mab,nlat,nt),sqnn(nlat)\n dimension wshsgs(lshsgs),wk(lwk)\n ncb = 1+noffsb\nc\nc set coefficient multiplyers\nc\n do 1 n=2,nlat\n fn = dfloat(n-1)\n sqnn(n) = dsqrt(fn*(fn+1.))\n 1 continue\nc\nc compute divergence scalar coefficients for each vector field\nc\n do 2 k=1,nt\n do 3 n=1,nlat\n do 4 m=1,mab\n a(m,n,k) = 0.0\n b(m,n,k) = 0.0\n 4 continue\n 3 continue\nc\nc compute m=0 coefficients\nc\n do 5 n=2,nlat\n a(1,n,k) = -sqnn(n)*br(ncb,1,n,k)\n b(1,n,k) = -sqnn(n)*bi(ncb,1,n,k)\n 5 continue\nc\nc compute m>0 coefficients using vector spherepack value for mmax\nc\n mmax = min0(nlat,(nlon+1)/2)\n do 6 m=2,mmax\n do 7 n=m,nlat\n a(m,n,k) = -sqnn(n)*br(ncb,m,n,k)\n b(m,n,k) = -sqnn(n)*bi(ncb,m,n,k)\n 7 continue\n 6 continue\n 2 continue\nc\nc synthesize a,b into divg\nc\n call shsgs(nstrg,1,noffsg,0,nlat,nlon,isym,nt,divg,idiv,jdiv,a,b,\n + mab,nlat,mab,nlat,wshsgs,lshsgs,wk,lwk,ierror)\n return\n end\n" }, { "path": "external/SPHEREPACK/gaqd.f", "content": "c\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc * *\nc * copyright (c) 1998 by UCAR *\nc * *\nc * University Corporation for Atmospheric Research *\nc * *\nc * all rights reserved *\nc * *\nc * SPHEREPACK version 3.2 *\nc * *\nc * A Package of Fortran77 Subroutines and Programs *\nc * *\nc * for Modeling Geophysical Processes *\nc * *\nc * by *\nc * *\nc * John Adams and Paul Swarztrauber *\nc * *\nc * of *\nc * *\nc * the National Center for Atmospheric Research *\nc * *\nc * Boulder, Colorado (80307) U.S.A. *\nc * *\nc * which is sponsored by *\nc * *\nc * the National Science Foundation *\nc * *\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc\nc\nc\nc This version of gaqd implements the method presented in:\nc P. N. swarztrauber, Computing the points and weights for \nc Gauss-Legendre quadrature, SIAM J. Sci. Comput.,\nc 24(2002) pp. 945-954.\nc \nc The w and lwork arrays are dummy and included only to\nc permit a simple pluggable exchange with the\nc old gaqd in previous versions of SPHEREPACK\nc\nc\nc\n subroutine gaqd(nlat,theta,wts,w,lwork,ierror)\n implicit double precision (a-h,o-z)\nc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\nc\nc gauss points and weights are computed using the fourier-newton\nc described in \"on computing the points and weights for \nc gauss-legendre quadrature\", paul n. swarztrauber, siam journal \nc on scientific computing that has been accepted for publication.\nc This routine is faster and more accurate than older program \nc with the same name.\nc\nc subroutine gaqd computes the nlat gaussian colatitudes and weights\nc in double precision. the colatitudes are in radians and lie in the\nc in the interval (0,pi).\nc\nc input parameters\nc\nc nlat the number of gaussian colatitudes in the interval (0,pi)\nc (between the two poles). nlat must be greater than zero.\nc\nc w unused double precision variable that permits a simple \nc exchange with the old routine with the same name \nc in spherepack.\nc\nc lwork unused variable that permits a simple exchange with the\nc old routine with the same name in spherepack.\nc\nc output parameters\nc\nc theta a double precision array with length nlat\nc containing the gaussian colatitudes in\nc increasing radians on the interval (0,pi).\nc\nc wts a double precision array with lenght nlat\nc containing the gaussian weights.\nc\nc ierror = 0 no errors\nc = 1 if nlat.le.0\nc\nc *****************************************************************\nc\n double precision theta(nlat),wts(nlat),w,\n 1 x,pi,pis2,dtheta,dthalf,cmax,zprev,zlast,zero,\n 2 zhold,pb,dpb,dcor,sum,cz\nc\nc check work space length\nc\n ierror = 1\n if (nlat.le.0) return\n ierror = 0\nc\nc compute weights and points analytically when nlat=1,2\nc\n if (nlat.eq.1) then\n theta(1) = dacos(0.0d0)\n wts(1) = 2.0d0\n return\n end if\n if (nlat.eq.2) then\n x = dsqrt(1.0d0/3.0d0)\n theta(1) = dacos(x)\n theta(2) = dacos(-x)\n wts(1) = 1.0d0\n wts(2) = 1.0d0\n return\n end if\n eps = dsqrt(dzeps(1.0d0))\n eps = eps*dsqrt(eps)\n pis2 = 2.0d0*datan(1.0d0)\n pi = pis2+pis2 \n mnlat = mod(nlat,2)\n ns2 = nlat/2\n nhalf = (nlat+1)/2\n idx = ns2+2\nc\n call cpdp (nlat,cz,theta(ns2+1),wts(ns2+1))\nc\n dtheta = pis2/nhalf\n dthalf = dtheta/2.0d0\n cmax = .2d0*dtheta\nc\nc estimate first point next to theta = pi/2\nc\n if(mnlat.ne.0) then\n zero = pis2-dtheta\n zprev = pis2\n nix = nhalf-1\n else\n zero = pis2-dthalf\n nix = nhalf\n end if\n 9 it = 0\n 10 it = it+1\n zlast = zero\nc\nc newton iterations\nc\n call tpdp (nlat,zero,cz,theta(ns2+1),wts(ns2+1),pb,dpb)\n dcor = pb/dpb\n sgnd = 1.0d0\n if(dcor .ne. 0.0d0) sgnd = dcor/dabs(dcor)\n dcor = sgnd*min(dabs(dcor),cmax)\n zero = zero-dcor\n if(dabs(zero-zlast).gt.eps*dabs(zero)) go to 10\n theta(nix) = zero\n zhold = zero\nc wts(nix) = (nlat+nlat+1)/(dpb*dpb)\nc \nc yakimiw's formula permits using old pb and dpb\nc\n wts(nix) = (nlat+nlat+1)/(dpb+pb*dcos(zlast)/dsin(zlast))**2\n nix = nix-1\n if(nix.eq.0) go to 30\n if(nix.eq.nhalf-1) zero = 3.0d0*zero-pi\n if(nix.lt.nhalf-1) zero = zero+zero-zprev\n zprev = zhold\n go to 9\nc\nc extend points and weights via symmetries\nc\n 30 if(mnlat.ne.0) then\n theta(nhalf) = pis2\n call tpdp (nlat,pis2,cz,theta(ns2+1),wts(ns2+1),pb,dpb)\n wts(nhalf) = (nlat+nlat+1)/(dpb*dpb)\n end if\n do i=1,ns2\n wts(nlat-i+1) = wts(i)\n theta(nlat-i+1) = pi-theta(i)\n end do\n sum = 0.0d0\n do i=1,nlat\n sum = sum+wts(i)\n end do\n do i=1,nlat\n wts(i) = 2.0d0*wts(i)/sum\n end do\n return\n end\n subroutine cpdp(n,cz,cp,dcp)\n implicit double precision (a-h,o-z)\nc\nc computes the fourier coefficients of the legendre\nc polynomial p_n^0 and its derivative. \nc n is the degree and n/2 or (n+1)/2\nc coefficients are returned in cp depending on whether\nc n is even or odd. The same number of coefficients\nc are returned in dcp. For n even the constant \nc coefficient is returned in cz. \nc\n double precision cp(n/2+1),dcp(n/2+1),\n 1 t1,t2,t3,t4,cz\n ncp = (n+1)/2\n t1 = -1.0d0\n t2 = n+1.0d0\n t3 = 0.0d0\n t4 = n+n+1.0d0\n if(mod(n,2).eq.0) then\n cp(ncp) = 1.0d0\n do j = ncp,2,-1\n t1 = t1+2.0d0\n t2 = t2-1.0d0\n t3 = t3+1.0d0\n t4 = t4-2.0d0\n cp(j-1) = (t1*t2)/(t3*t4)*cp(j)\n end do\n t1 = t1+2.0d0\n t2 = t2-1.0d0\n t3 = t3+1.0d0\n t4 = t4-2.0d0\n cz = (t1*t2)/(t3*t4)*cp(1)\n do j=1,ncp\n dcp(j) = (j+j)*cp(j)\n end do\n else\n cp(ncp) = 1.0d0\n do j = ncp-1,1,-1\n t1 = t1+2.0d0\n t2 = t2-1.0d0\n t3 = t3+1.0d0\n t4 = t4-2.0d0\n cp(j) = (t1*t2)/(t3*t4)*cp(j+1)\n end do\n do j=1,ncp\n dcp(j) = (j+j-1)*cp(j)\n end do\n end if\n return\n end\n subroutine tpdp (n,theta,cz,cp,dcp,pb,dpb)\n implicit double precision (a-h,o-z)\nc\nc computes pn(theta) and its derivative dpb(theta) with \nc respect to theta\nc\n double precision cp(n/2+1),dcp(n/2+1),cz,\n 1 pb,dpb,fn,theta,cdt,sdt,cth,sth,chh\nc\n fn = n\n cdt = dcos(theta+theta)\n sdt = dsin(theta+theta)\n if(mod(n,2) .eq.0) then\nc\nc n even\nc\n kdo = n/2\n pb = .5d0*cz\n dpb = 0.0d0\n if(n .gt. 0) then\n cth = cdt\n sth = sdt\n do 170 k=1,kdo\nc pb = pb+cp(k)*cos(2*k*theta)\n pb = pb+cp(k)*cth\nc dpb = dpb-(k+k)*cp(k)*sin(2*k*theta)\n dpb = dpb-dcp(k)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 170 continue\n end if\n else\nc\nc n odd\nc\n kdo = (n+1)/2\n pb = 0.0d0\n dpb = 0.0d0\n cth = dcos(theta)\n sth = dsin(theta)\n do 190 k=1,kdo\nc pb = pb+cp(k)*cos((2*k-1)*theta)\n pb = pb+cp(k)*cth\nc dpb = dpb-(k+k-1)*cp(k)*sin((2*k-1)*theta)\n dpb = dpb-dcp(k)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 190 continue\n end if\n return\n end\n double precision function dzeps (x)\n implicit double precision (a-h,o-z)\n double precision x\nc\nc estimate unit roundoff in quantities of size x.\nc\n double precision a,b,c,eps\nc\nc this program should function properly on all systems\nc satisfying the following two assumptions,\nc 1. the base used in representing floating point\nc numbers is not a power of three.\nc 2. the quantity a in statement 10 is represented to \nc the accuracy used in floating point variables\nc that are stored in memory.\nc the statement number 10 and the go to 10 are intended to\nc force optimizing compilers to generate code satisfying \nc assumption 2.\nc under these assumptions, it should be true that,\nc a is not exactly equal to four-thirds,\nc b has a zero for its last bit or digit,\nc c is not exactly equal to one,\nc eps measures the separation of 1.0 from\nc the next larger floating point number.\nc the developers of eispack would appreciate being informed\nc about any systems where these assumptions do not hold.\nc\nc this version dated 4/6/83.\nc\n a = 4.0d0/3.0d0\n 10 b = a - 1.0d0\n c = b + b + b\n eps = abs(c-1.0d0)\n if (eps .eq. 0.0d0) go to 10\n dzeps = eps*dabs(x)\n return\n end\n" }, { "path": "external/SPHEREPACK/gradgs.f", "content": "c\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc * *\nc * copyright (c) 1998 by UCAR *\nc * *\nc * University Corporation for Atmospheric Research *\nc * *\nc * all rights reserved *\nc * *\nc * SPHEREPACK version 3.2 *\nc * *\nc * A Package of Fortran77 Subroutines and Programs *\nc * *\nc * for Modeling Geophysical Processes *\nc * *\nc * by *\nc * *\nc * John Adams and Paul Swarztrauber *\nc * *\nc * of *\nc * *\nc * the National Center for Atmospheric Research *\nc * *\nc * Boulder, Colorado (80307) U.S.A. *\nc * *\nc * which is sponsored by *\nc * *\nc * the National Science Foundation *\nc * *\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc\nc\nc ... file gradgs.f\nc\nc this file includes documentation and code for\nc subroutine gradgs i\nc\nc ... files which must be loaded with gradgec.f\nc\nc sphcom.f, hrfft.f, shags.f,vhsgs.f\nc\nc subroutine gradgs(nstrvw,nstrab,noffsvw,noffsab,\nc nlat,nlon,isym,nt,v,w,idvw,jdvw,a,b,mdab,ndab,\nc + wvhsgs,lvhsgs,work,lwork,ierror)\nc\nc given the scalar spherical harmonic coefficients a and b, precomputed\nc by subroutine shags for a scalar field sf, subroutine gradgs computes\nc an irrotational vector field (v,w) such that\nc\nc gradient(sf) = (v,w).\nc\nc v is the colatitudinal and w is the east longitudinal component\nc of the gradient. i.e.,\nc\nc v(i,j) = d(sf(i,j))/dtheta\nc\nc and\nc\nc w(i,j) = 1/sint*d(sf(i,j))/dlambda\nc\nc at the gaussian colatitude point theta(i) (see nlat as input\nc parameter) and longitude lambda(j) = (j-1)*2*pi/nlon where\nc sint = sin(theta(i)).\nc\nc\nc input parameters\nc\nc nstrvw, nstrab strides of v,w and a,b\nc noffsvw, noffsab offset of v,w and a,b -- must be between 0 and stride-1\nc Alternatively, when the two strides equal, you can set both\nc to -1 in which case the output will be computed for all\nc values of offset between 0 and stride-1.\nc\nc nlat the number of points in the gaussian colatitude grid on the\nc full sphere. these lie in the interval (0,pi) and are computed\nc in radians in theta(1) <...< theta(nlat) by subroutine gaqd.\nc if nlat is odd the equator will be included as the grid point\nc theta((nlat+1)/2). if nlat is even the equator will be\nc excluded as a grid point and will lie half way between\nc theta(nlat/2) and theta(nlat/2+1). nlat must be at least 3.\nc note: on the half sphere, the number of grid points in the\nc colatitudinal direction is nlat/2 if nlat is even or\nc (nlat+1)/2 if nlat is odd.\nc\nc nlon the number of distinct londitude points. nlon determines\nc the grid increment in longitude as 2*pi/nlon. for example\nc nlon = 72 for a five degree grid. nlon must be greater than\nc 3. the efficiency of the computation is improved when nlon\nc is a product of small prime numbers.\nc\nc NOTE: this is a modified version of spherepack. Changes from\nc the original version to the current one have only been\nc tested for isym==0. For this reason an error code will\nc be returned if isym!=0.\nc\nc\nc isym this has the same value as the isym that was input to\nc subroutine shags to compute the arrays a and b from the\nc scalar field sf. isym determines whether (v,w) are\nc computed on the full or half sphere as follows:\nc\nc = 0\nc\nc sf is not symmetric about the equator. in this case\nc the vector field (v,w) is computed on the entire sphere.\nc i.e., in the arrays v(i,j),w(i,j) for i=1,...,nlat and\nc j=1,...,nlon.\nc\nc = 1\nc\nc sf is antisymmetric about the equator. in this case w is\nc antisymmetric and v is symmetric about the equator. w\nc and v are computed on the northern hemisphere only. i.e.,\nc if nlat is odd they are computed for i=1,...,(nlat+1)/2\nc and j=1,...,nlon. if nlat is even they are computed for\nc i=1,...,nlat/2 and j=1,...,nlon.\nc\nc = 2\nc\nc sf is symmetric about the equator. in this case w is\nc symmetric and v is antisymmetric about the equator. w\nc and v are computed on the northern hemisphere only. i.e.,\nc if nlat is odd they are computed for i=1,...,(nlat+1)/2\nc and j=1,...,nlon. if nlat is even they are computed for\nc i=1,...,nlat/2 and j=1,...,nlon.\nc\nc\nc nt nt is the number of scalar and vector fields. some\nc computational efficiency is obtained for multiple fields.\nc the arrays a,b,v, and w can be three dimensional corresponding\nc to an indexed multiple array sf. in this case, multiple\nc vector synthesis will be performed to compute each vector\nc field. the third index for a,b,v, and w is the synthesis\nc index which assumes the values k = 1,...,nt. for a single\nc synthesis set nt = 1. the description of the remaining\nc parameters is simplified by assuming that nt=1 or that a,b,v,\nc and w are two dimensional arrays.\nc\nc idvw the first dimension of the arrays v,w as it appears in\nc the program that calls gradgs. if isym = 0 then idvw\nc must be at least nlat. if isym = 1 or 2 and nlat is\nc even then idvw must be at least nlat/2. if isym = 1 or 2\nc and nlat is odd then idvw must be at least (nlat+1)/2.\nc\nc jdvw the second dimension of the arrays v,w as it appears in\nc the program that calls gradgs. jdvw must be at least nlon.\nc\nc a,b two or three dimensional arrays (see input parameter nt)\nc that contain scalar spherical harmonic coefficients\nc of the scalar field array sf as computed by subroutine shags.\nc *** a,b must be computed by shags prior to calling gradgs.\nc\nc mdab the first dimension of the arrays a and b as it appears in\nc the program that calls gradgs (and shags). mdab must be at\nc least min0(nlat,(nlon+2)/2) if nlon is even or at least\nc min0(nlat,(nlon+1)/2) if nlon is odd.\nc\nc ndab the second dimension of the arrays a and b as it appears in\nc the program that calls gradgs (and shags). ndab must be at\nc least nlat.\nc\nc\nc wvhsgs an array which must be initialized by subroutine vhsgsi.\nc once initialized,\nc wvhsgs can be used repeatedly by gradgs as long as nlon\nc and nlat remain unchanged. wvhsgs must not be altered\nc between calls of gradgs.\nc\nc\nc lvhsgs the dimension of the array wvhsgs as it appears in the\nc program that calls grradgs. define\nc\nc l1 = min0(nlat,nlon/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc then lvhsgs must be at least\nc\nc l1*l2*(nlat+nlat-l1+1)+nlon+15+2*nlat\nc\nc\nc work a work array that does not have to be saved.\nc\nc lwork the dimension of the array work as it appears in the\nc program that calls gradgs. define\nc\nc l1 = min0(nlat,nlon/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc if isym = 0, lwork must be greater than or equal to\nc\nc nlat*((2*nt+1)*nlon+2*l1*nt+1).\nc\nc if isym = 1 or 2, lwork must be greater than or equal to\nc\nc (2*nt+1)*l2*nlon+nlat*(2*l1*nt+1).\nc\nc\nc **************************************************************\nc\nc output parameters\nc\nc\nc v,w two or three dimensional arrays (see input parameter nt) that\nc contain an irrotational vector field such that the gradient of\nc the scalar field sf is (v,w). w(i,j) is the east longitude\nc component and v(i,j) is the colatitudinal component of velocity\nc at gaussian colatitude and longitude lambda(j) = (j-1)*2*pi/nlon\nc the indices for v and w are defined at the input parameter\nc isym. the vorticity of (v,w) is zero. note that any nonzero\nc vector field on the sphere will be multiple valued at the poles\nc [reference swarztrauber].\nc\nc\nc ierror = 0 no errors\nc = 1 error in the specification of nlat\nc = 2 error in the specification of nlon\nc = 3 error in the specification of isym\nc = 4 error in the specification of nt\nc = 5 error in the specification of idvw\nc = 6 error in the specification of jdvw\nc = 7 error in the specification of mdab\nc = 8 error in the specification of ndab\nc = 9 error in the specification of lvhsgs\nc = 10 error in the specification of lwork\nc **********************************************************************\nc \nc \n subroutine gradgs(nstrvw,nstrab,noffsvw,noffsab,\n +nlat,nlon,isym,nt,v,w,idvw,jdvw,a,b,mdab,ndab,\n +wvhsgs,lvhsgs,work,lwork,ierror)\n implicit double precision (a-h,o-z)\n dimension v(nstrvw,idvw,jdvw,nt),w(nstrvw,idvw,jdvw,nt)\n dimension a(nstrab,mdab,ndab,nt),b(nstrab,mdab,ndab,nt)\n dimension wvhsgs(lvhsgs),work(lwork)\nc\nc check input parameters\nc\n ierror = 1\n if(nlat .lt. 3) return\n ierror = 2\n if(nlon .lt. 4) return\n ierror = 3\n if(isym.lt.0 .or. isym.gt.2) return\nc see note above about symmeries\n if(isym.ne.0) return\n ierror = 4\n if(nt .lt. 0) return\n ierror = 5\n imid = (nlat+1)/2\n if((isym.eq.0 .and. idvw.lt.nlat) .or.\n + (isym.ne.0 .and. idvw.lt.imid)) return\n ierror = 6\n if(jdvw .lt. nlon) return\n ierror = 7\n mmax = min0(nlat,(nlon+1)/2)\n if(mdab .lt. min0(nlat,(nlon+2)/2)) return\n ierror = 8\n if(ndab .lt. nlat) return\n ierror = 9\nc\nc verify minimum saved work space length\nc\n idz = (mmax*(nlat+nlat-mmax+1))/2\n lzimn = idz*imid\n lgdmin = lzimn+lzimn+nlon+15\n if(lvhsgs .lt. lgdmin) return\n ierror = 10\nc\nc verify minimum unsaved work space length\nc\n ng = 1;\n if(noffsvw.eq.-1 .and. noffsab.eq.-1) ng=nstrvw\n mn = mmax*nlat*nt*ng\n idv = nlat\n if (isym.ne.0) idv = imid\n lnl = nt*idv*nlon\n lwkmin = lnl+lnl+idv*nlon+2*mn+nlat\n if(lwork .lt. lwkmin) return\n ierror = 11\n if((noffsvw.eq.-1) .neqv. (noffsab.eq.-1)) return\n if((noffsvw.eq.-1) .and. (nstrvw.ne.nstrab)) return\n if((noffsvw.lt.-1) .or. (noffsvw.ge.nstrvw)) return\n if((noffsab.lt.-1) .or. (noffsab.ge.nstrab)) return\n ierror = 0\nc\nc set work space pointers\nc\n ibr = 1\n ibi = ibr + mn\n is = ibi + mn\n iwk = is + nlat\n liwk = lwork-2*mn-nlat\n\n call gradgs1(nstrvw,nstrab,noffsvw,noffsab,\n +nlat,nlon,isym,nt,v,w,idvw,jdvw,work(ibr),work(ibi),ng,\n +mmax,work(is),mdab,ndab,a,b,wvhsgs,lvhsgs,work(iwk),liwk,\n +ierror)\n return\n end\n\n subroutine gradgs1(nstrvw,nstrab,noffsvw,noffsab,\n +nlat,nlon,isym,nt,v,w,idvw,jdvw,br,bi,ng,mmax,\n +sqnn,mdab,ndab,a,b,wvhsgs,lvhsgs,wk,lwk,ierror)\n implicit double precision (a-h,o-z)\n dimension v(nstrvw,idvw,jdvw,nt),w(nstrvw,idvw,jdvw,nt)\n dimension br(ng,mmax,nlat,nt),bi(ng,mmax,nlat,nt),sqnn(nlat)\n dimension a(nstrab,mdab,ndab,nt),b(nstrab,mdab,ndab,nt)\n dimension wvhsgs(lvhsgs),wk(lwk)\n if(noffsab.eq.-1) then\n ncabmin=1\n ncabmax=nstrab\n else\n ncabmin=1+noffsab\n ncabmax=1+noffsab\n end if\n\n\nc\nc preset coefficient multiplyers in vector\nc\n do 1 n=2,nlat\n fn = dfloat(n-1)\n sqnn(n) = dsqrt(fn*(fn+1.d0))\n 1 continue\nc\nc compute multiple vector fields coefficients\nc\n do 2 k=1,nt\nc\nc preset br,bi to 0.0\nc\n do 3 n=1,nlat\n do 4 m=1,mmax\n do 4 ig=1,ng\n br(ig,m,n,k) = 0.0d0\n bi(ig,m,n,k) = 0.0d0\n 4 continue\n 3 continue\nc\nc compute m=0 coefficients\nc\n do 5 n=2,nlat\n do 5 ncab=ncabmin,ncabmax\n ig = ncab-ncabmin+1\n br(ig,1,n,k) = sqnn(n)*a(ncab,1,n,k)\n bi(ig,1,n,k) = sqnn(n)*b(ncab,1,n,k)\n 5 continue\nc\nc compute m>0 coefficients\nc\n do 6 m=2,mmax\n do 7 n=m,nlat\n do 7 ncab=ncabmin,ncabmax\n ig = ncab-ncabmin+1\n br(ig,m,n,k) = sqnn(n)*a(ncab,m,n,k)\n bi(ig,m,n,k) = sqnn(n)*b(ncab,m,n,k)\n 7 continue\n 6 continue\n 2 continue\nc\nc set ityp for irrotational vector synthesis to compute gradient\nc\n if (isym.eq.0) then\n ityp = 1\n else if (isym.eq.1) then\n ityp = 4\n else if (isym.eq.2) then\n ityp = 7\n end if\nc\nc vector sythesize br,bi into (v,w) (cr,ci are dummy variables)\nc\n call vhsgs(nstrvw,ng,noffsvw,noffsab,\n + nlat,nlon,ityp,nt,v,w,idvw,jdvw,br,bi,cr,ci,\n + mmax,nlat,wvhsgs,lvhsgs,wk,lwk,ierror)\n 200 continue\n return\n end\n" }, { "path": "external/SPHEREPACK/hrfft.f", "content": "c\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc * *\nc * copyright (c) 1998 by UCAR *\nc * *\nc * University Corporation for Atmospheric Research *\nc * *\nc * all rights reserved *\nc * *\nc * SPHEREPACK version 3.2 *\nc * *\nc * A Package of Fortran77 Subroutines and Programs *\nc * *\nc * for Modeling Geophysical Processes *\nc * *\nc * by *\nc * *\nc * John Adams and Paul Swarztrauber *\nc * *\nc * of *\nc * *\nc * the National Center for Atmospheric Research *\nc * *\nc * Boulder, Colorado (80307) U.S.A. *\nc * *\nc * which is sponsored by *\nc * *\nc * the National Science Foundation *\nc * *\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc\nc\nc ... file hrfft.f\nc\nc this file contains a multiple fft package for spherepack. it\nc includes code and documentation for performing fast fourier\nc transforms (see subroutines hrffti,hrfftf and hrfftb)\nc\nc **********************************************************************\nc\nc subroutine hrffti(n,wsave)\nc\nc subroutine hrffti initializes the array wsave which is used in\nc both hrfftf and hrfftb. the prime factorization of n together \nc with a tabulation of the trigonometric functions are computed and\nc stored in wsave.\nc\nc input parameter\nc\nc n the length of the sequence to be transformed.\nc\nc output parameter\nc\nc wsave a work array which must be dimensioned at least 2*n+15.\nc the same work array can be used for both hrfftf and \nc hrfftb as long as n remains unchanged. different wsave \nc arrays are required for different values of n. the \nc contents of wsave must not be changed between calls \nc of hrfftf or hrfftb.\nc\nc **********************************************************************\nc\nc subroutine hrfftf(m,n,r,mdimr,wsave,work)\nc\nc subroutine hrfftf computes the fourier coefficients of m real\nc perodic sequences (fourier analysis); i.e. hrfftf computes the\nc real fft of m sequences each with length n. the transform is \nc defined below at output parameter r.\nc\nc input parameters\nc\nc m the number of sequences.\nc\nc n the length of all m sequences. the method is most\nc efficient when n is a product of small primes. n may\nc change as long as different work arrays are provided\nc\nc r r(m,n) is a two dimensional real array that contains m\nc sequences each with length n.\nc\nc mdimr the first dimension of the r array as it appears\nc in the program that calls hrfftf. mdimr must be\nc greater than or equal to m.\nc\nc\nc wsave a work array with at least least 2*n+15 locations\nc in the program that calls hrfftf. the wsave array must be\nc initialized by calling subroutine hrffti(n,wsave) and a\nc different wsave array must be used for each different\nc value of n. this initialization does not have to be\nc repeated so long as n remains unchanged thus subsequent\nc transforms can be obtained faster than the first.\nc the same wsave array can be used by hrfftf and hrfftb.\nc\nc work a real work array with m*n locations.\nc\nc\nc output parameters\nc\nc r for all j=1,...,m\nc \nc r(j,1) = the sum from i=1 to i=n of r(j,i)\nc\nc if n is even set l =n/2 , if n is odd set l = (n+1)/2\nc\nc then for k = 2,...,l\nc\nc r(j,2*k-2) = the sum from i = 1 to i = n of\nc\nc r(j,i)*cos((k-1)*(i-1)*2*pi/n)\nc\nc r(j,2*k-1) = the sum from i = 1 to i = n of\nc\nc -r(j,i)*sin((k-1)*(i-1)*2*pi/n)\nc\nc if n is even\nc\nc r(j,n) = the sum from i = 1 to i = n of\nc\nc (-1)**(i-1)*r(j,i)\nc\nc ***** note\nc this transform is unnormalized since a call of hrfftf\nc followed by a call of hrfftb will multiply the input\nc sequence by n.\nc\nc wsave contains results which must not be destroyed between\nc calls of hrfftf or hrfftb.\nc\nc work a real work array with m*n locations that does\nc not have to be saved.\nc\nc **********************************************************************\nc\nc subroutine hrfftb(m,n,r,mdimr,wsave,work)\nc\nc subroutine hrfftb computes the real perodic sequence of m\nc sequences from their fourier coefficients (fourier synthesis). \nc the transform is defined below at output parameter r.\nc\nc input parameters\nc\nc m the number of sequences.\nc\nc n the length of all m sequences. the method is most\nc efficient when n is a product of small primes. n may\nc change as long as different work arrays are provided\nc\nc r r(m,n) is a two dimensional real array that contains\nc the fourier coefficients of m sequences each with \nc length n.\nc\nc mdimr the first dimension of the r array as it appears\nc in the program that calls hrfftb. mdimr must be\nc greater than or equal to m.\nc\nc wsave a work array which must be dimensioned at least 2*n+15.\nc in the program that calls hrfftb. the wsave array must be\nc initialized by calling subroutine hrffti(n,wsave) and a\nc different wsave array must be used for each different\nc value of n. this initialization does not have to be\nc repeated so long as n remains unchanged thus subsequent\nc transforms can be obtained faster than the first.\nc the same wsave array can be used by hrfftf and hrfftb.\nc\nc work a real work array with m*n locations.\nc\nc\nc output parameters\nc\nc r for all j=1,...,m\nc \nc for n even and for i = 1,...,n\nc\nc r(j,i) = r(j,1)+(-1)**(i-1)*r(j,n)\nc\nc plus the sum from k=2 to k=n/2 of\nc\nc 2.*r(j,2*k-2)*cos((k-1)*(i-1)*2*pi/n)\nc\nc -2.*r(j,2*k-1)*sin((k-1)*(i-1)*2*pi/n)\nc\nc for n odd and for i = 1,...,n\nc\nc r(j,i) = r(j,1) plus the sum from k=2 to k=(n+1)/2 of\nc\nc 2.*r(j,2*k-2)*cos((k-1)*(i-1)*2*pi/n)\nc\nc -2.*r(j,2*k-1)*sin((k-1)*(i-1)*2*pi/n)\nc\nc ***** note\nc this transform is unnormalized since a call of hrfftf\nc followed by a call of hrfftb will multiply the input\nc sequence by n.\nc\nc wsave contains results which must not be destroyed between\nc calls of hrfftb or hrfftf.\nc\nc work a real work array with m*n locations that does not\nc have to be saved\nc\nc **********************************************************************\nc\nc\nc\n subroutine hrffti (n,wsave)\n implicit double precision (a-h,o-z)\n dimension wsave(n+15) \n common /hrf/ tfft\n tfft = 0.d0\n if (n .eq. 1) return \n call hrfti1 (n,wsave(1),wsave(n+1))\n return \n end \n subroutine hrfti1 (n,wa,fac)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension wa(n) ,fac(15) ,ntryh(4) \n double precision tpi,argh,argld,arg\n data ntryh(1),ntryh(2),ntryh(3),ntryh(4)/4,2,3,5/ \n nl = n \n nf = 0 \n j = 0 \n 101 j = j+1 \n if (j-4) 102,102,103 \n 102 ntry = ntryh(j) \n go to 104 \n 103 ntry = ntry+2 \n 104 nq = nl/ntry \n nr = nl-ntry*nq \n if (nr) 101,105,101 \n 105 nf = nf+1 \n fac(nf+2) = ntry \n nl = nq \n if (ntry .ne. 2) go to 107 \n if (nf .eq. 1) go to 107 \n do 106 i=2,nf \n ib = nf-i+2 \n fac(ib+2) = fac(ib+1) \n 106 continue \n fac(3) = 2 \n 107 if (nl .ne. 1) go to 104 \n fac(1) = n \n fac(2) = nf \n tpi = 8.d0*datan(1.d0)\n argh = tpi/dfloat(n) \n is = 0 \n nfm1 = nf-1 \n l1 = 1 \n if (nfm1 .eq. 0) return \n do 110 k1=1,nfm1 \n ip = fac(k1+2) \n ld = 0 \n l2 = l1*ip \n ido = n/l2 \n ipm = ip-1 \n do 109 j=1,ipm \n ld = ld+l1 \n i = is \n argld = dfloat(ld)*argh \n fi = 0.d0 \n do 108 ii=3,ido,2 \n i = i+2 \n fi = fi+1.d0 \n arg = fi*argld \n\t wa(i-1) = dcos(arg)\n\t wa(i) = dsin(arg)\n 108 continue \n is = is+ido \n 109 continue \n l1 = l2 \n 110 continue \n return \n end \n subroutine hrfftf (m,n,r,mdimr,whrfft,work)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension r(mdimr,n) ,work(1) ,whrfft(n+15)\n common /hrf/ tfft\n if (n .eq. 1) return \nc tstart = second(dum)\n call hrftf1 (m,n,r,mdimr,work,whrfft,whrfft(n+1))\nc tfft = tfft+second(dum)-tstart\n return \n end \n subroutine hrftf1 (m,n,c,mdimc,ch,wa,fac)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension ch(m,n) ,c(mdimc,n) ,wa(n) ,fac(15)\n nf = fac(2) \n na = 1 \n l2 = n \n iw = n \n do 111 k1=1,nf \n kh = nf-k1 \n ip = fac(kh+3) \n l1 = l2/ip \n ido = n/l2 \n idl1 = ido*l1 \n iw = iw-(ip-1)*ido \n na = 1-na \n if (ip .ne. 4) go to 102 \n ix2 = iw+ido \n ix3 = ix2+ido \n if (na .ne. 0) go to 101 \n\t call hradf4 (m,ido,l1,c,mdimc,ch,m,wa(iw),wa(ix2),wa(ix3))\n go to 110 \n 101 call hradf4 (m,ido,l1,ch,m,c,mdimc,wa(iw),wa(ix2),wa(ix3))\n go to 110 \n 102 if (ip .ne. 2) go to 104 \n if (na .ne. 0) go to 103 \n\t call hradf2 (m,ido,l1,c,mdimc,ch,m,wa(iw))\n go to 110 \n 103 call hradf2 (m,ido,l1,ch,m,c,mdimc,wa(iw))\n go to 110 \n 104 if (ip .ne. 3) go to 106 \n ix2 = iw+ido \n if (na .ne. 0) go to 105 \n\t call hradf3 (m,ido,l1,c,mdimc,ch,m,wa(iw),wa(ix2))\n go to 110 \n 105 call hradf3 (m,ido,l1,ch,m,c,mdimc,wa(iw),wa(ix2))\n go to 110 \n 106 if (ip .ne. 5) go to 108 \n ix2 = iw+ido \n ix3 = ix2+ido \n ix4 = ix3+ido \n if (na .ne. 0) go to 107 \n call hradf5(m,ido,l1,c,mdimc,ch,m,wa(iw),wa(ix2),wa(ix3),wa(ix4))\n go to 110 \n 107 call hradf5(m,ido,l1,ch,m,c,mdimc,wa(iw),wa(ix2),wa(ix3),wa(ix4))\n go to 110 \n 108 if (ido .eq. 1) na = 1-na \n if (na .ne. 0) go to 109 \n\t call hradfg (m,ido,ip,l1,idl1,c,c,c,mdimc,ch,ch,m,wa(iw))\n na = 1 \n go to 110 \n 109 call hradfg (m,ido,ip,l1,idl1,ch,ch,ch,m,c,c,mdimc,wa(iw))\n na = 0 \n 110 l2 = l1 \n 111 continue \n if (na .eq. 1) return\n do 112 j=1,n \n do 112 i=1,m \n\t c(i,j) = ch(i,j)\n 112 continue \n return \n end \n subroutine hradf4 (mp,ido,l1,cc,mdimcc,ch,mdimch,wa1,wa2,wa3)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension cc(mdimcc,ido,l1,4) ,ch(mdimch,ido,4,l1) ,\n 1 wa1(ido) ,wa2(ido) ,wa3(ido)\n hsqt2=dsqrt(2.d0)/2.d0 \n do 101 k=1,l1 \n do 1001 m=1,mp \n ch(m,1,1,k) = (cc(m,1,k,2)+cc(m,1,k,4)) \n 1 +(cc(m,1,k,1)+cc(m,1,k,3)) \n ch(m,ido,4,k) = (cc(m,1,k,1)+cc(m,1,k,3)) \n 1 -(cc(m,1,k,2)+cc(m,1,k,4)) \n ch(m,ido,2,k) = cc(m,1,k,1)-cc(m,1,k,3) \n ch(m,1,3,k) = cc(m,1,k,4)-cc(m,1,k,2) \n 1001 continue \n 101 continue \n if (ido-2) 107,105,102 \n 102 idp2 = ido+2 \n do 104 k=1,l1 \n do 103 i=3,ido,2 \n ic = idp2-i \n do 1003 m=1,mp \n ch(m,i-1,1,k) = ((wa1(i-2)*cc(m,i-1,k,2)+wa1(i-1)* \n 1 cc(m,i,k,2))+(wa3(i-2)*cc(m,i-1,k,4)+wa3(i-1)* \n 1 cc(m,i,k,4)))+(cc(m,i-1,k,1)+(wa2(i-2)*cc(m,i-1,k,3)+ \n 1 wa2(i-1)*cc(m,i,k,3))) \n ch(m,ic-1,4,k) = (cc(m,i-1,k,1)+(wa2(i-2)*cc(m,i-1,k,3)+ \n 1 wa2(i-1)*cc(m,i,k,3)))-((wa1(i-2)*cc(m,i-1,k,2)+ \n 1 wa1(i-1)*cc(m,i,k,2))+(wa3(i-2)*cc(m,i-1,k,4)+ \n 1 wa3(i-1)*cc(m,i,k,4))) \n ch(m,i,1,k) = ((wa1(i-2)*cc(m,i,k,2)-wa1(i-1)* \n 1 cc(m,i-1,k,2))+(wa3(i-2)*cc(m,i,k,4)-wa3(i-1)* \n 1 cc(m,i-1,k,4)))+(cc(m,i,k,1)+(wa2(i-2)*cc(m,i,k,3)- \n 1 wa2(i-1)*cc(m,i-1,k,3))) \n ch(m,ic,4,k) = ((wa1(i-2)*cc(m,i,k,2)-wa1(i-1)* \n 1 cc(m,i-1,k,2))+(wa3(i-2)*cc(m,i,k,4)-wa3(i-1)* \n 1 cc(m,i-1,k,4)))-(cc(m,i,k,1)+(wa2(i-2)*cc(m,i,k,3)- \n 1 wa2(i-1)*cc(m,i-1,k,3))) \n ch(m,i-1,3,k) = ((wa1(i-2)*cc(m,i,k,2)-wa1(i-1)* \n 1 cc(m,i-1,k,2))-(wa3(i-2)*cc(m,i,k,4)-wa3(i-1)* \n 1 cc(m,i-1,k,4)))+(cc(m,i-1,k,1)-(wa2(i-2)*cc(m,i-1,k,3)+ \n 1 wa2(i-1)*cc(m,i,k,3))) \n ch(m,ic-1,2,k) = (cc(m,i-1,k,1)-(wa2(i-2)*cc(m,i-1,k,3)+ \n 1 wa2(i-1)*cc(m,i,k,3)))-((wa1(i-2)*cc(m,i,k,2)-wa1(i-1)* \n 1 cc(m,i-1,k,2))-(wa3(i-2)*cc(m,i,k,4)-wa3(i-1)* \n 1 cc(m,i-1,k,4))) \n ch(m,i,3,k) = ((wa3(i-2)*cc(m,i-1,k,4)+wa3(i-1)* \n 1 cc(m,i,k,4))-(wa1(i-2)*cc(m,i-1,k,2)+wa1(i-1)* \n 1 cc(m,i,k,2)))+(cc(m,i,k,1)-(wa2(i-2)*cc(m,i,k,3)- \n 1 wa2(i-1)*cc(m,i-1,k,3))) \n ch(m,ic,2,k) = ((wa3(i-2)*cc(m,i-1,k,4)+wa3(i-1)* \n 1 cc(m,i,k,4))-(wa1(i-2)*cc(m,i-1,k,2)+wa1(i-1)* \n 1 cc(m,i,k,2)))-(cc(m,i,k,1)-(wa2(i-2)*cc(m,i,k,3)-wa2(i-1)* \n 1 cc(m,i-1,k,3))) \n 1003 continue \n 103 continue \n 104 continue \n if (mod(ido,2) .eq. 1) return \n 105 continue \n do 106 k=1,l1 \n do 1006 m=1,mp \n ch(m,ido,1,k) = (hsqt2*(cc(m,ido,k,2)-cc(m,ido,k,4)))+ \n 1 cc(m,ido,k,1) \n ch(m,ido,3,k) = cc(m,ido,k,1)-(hsqt2*(cc(m,ido,k,2)- \n 1 cc(m,ido,k,4))) \n ch(m,1,2,k) = (-hsqt2*(cc(m,ido,k,2)+cc(m,ido,k,4)))- \n 1 cc(m,ido,k,3) \n ch(m,1,4,k) = (-hsqt2*(cc(m,ido,k,2)+cc(m,ido,k,4)))+ \n 1 cc(m,ido,k,3) \n 1006 continue \n 106 continue \n 107 return \n end \n subroutine hradf2 (mp,ido,l1,cc,mdimcc,ch,mdimch,wa1)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension ch(mdimch,ido,2,l1) ,cc(mdimcc,ido,l1,2) ,\n 1 wa1(ido) \n do 101 k=1,l1 \n do 1001 m=1,mp \n ch(m,1,1,k) = cc(m,1,k,1)+cc(m,1,k,2) \n ch(m,ido,2,k) = cc(m,1,k,1)-cc(m,1,k,2) \n 1001 continue \n 101 continue \n if (ido-2) 107,105,102 \n 102 idp2 = ido+2 \n do 104 k=1,l1 \n do 103 i=3,ido,2 \n ic = idp2-i \n do 1003 m=1,mp \n ch(m,i,1,k) = cc(m,i,k,1)+(wa1(i-2)*cc(m,i,k,2)- \n 1 wa1(i-1)*cc(m,i-1,k,2)) \n ch(m,ic,2,k) = (wa1(i-2)*cc(m,i,k,2)-wa1(i-1)* \n 1 cc(m,i-1,k,2))-cc(m,i,k,1) \n ch(m,i-1,1,k) = cc(m,i-1,k,1)+(wa1(i-2)*cc(m,i-1,k,2)+ \n 1 wa1(i-1)*cc(m,i,k,2)) \n ch(m,ic-1,2,k) = cc(m,i-1,k,1)-(wa1(i-2)*cc(m,i-1,k,2)+ \n 1 wa1(i-1)*cc(m,i,k,2)) \n 1003 continue \n 103 continue \n 104 continue \n if (mod(ido,2) .eq. 1) return \n 105 do 106 k=1,l1 \n do 1006 m=1,mp \n ch(m,1,2,k) = -cc(m,ido,k,2) \n ch(m,ido,1,k) = cc(m,ido,k,1) \n 1006 continue \n 106 continue \n 107 return \n end \n subroutine hradf3 (mp,ido,l1,cc,mdimcc,ch,mdimch,wa1,wa2)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension ch(mdimch,ido,3,l1) ,cc(mdimcc,ido,l1,3) ,\n 1 wa1(ido) ,wa2(ido) \n arg=2.d0*pimach()/3.d0 \n taur=dcos(arg) \n taui=dsin(arg) \n do 101 k=1,l1 \n do 1001 m=1,mp \n ch(m,1,1,k) = cc(m,1,k,1)+(cc(m,1,k,2)+cc(m,1,k,3)) \n ch(m,1,3,k) = taui*(cc(m,1,k,3)-cc(m,1,k,2)) \n ch(m,ido,2,k) = cc(m,1,k,1)+taur* \n 1 (cc(m,1,k,2)+cc(m,1,k,3)) \n 1001 continue \n 101 continue \n if (ido .eq. 1) return \n idp2 = ido+2 \n do 103 k=1,l1 \n do 102 i=3,ido,2 \n ic = idp2-i \n do 1002 m=1,mp \n ch(m,i-1,1,k) = cc(m,i-1,k,1)+((wa1(i-2)*cc(m,i-1,k,2)+ \n 1 wa1(i-1)*cc(m,i,k,2))+(wa2(i-2)*cc(m,i-1,k,3)+wa2(i-1)* \n 1 cc(m,i,k,3))) \n ch(m,i,1,k) = cc(m,i,k,1)+((wa1(i-2)*cc(m,i,k,2)-wa1(i-1)* \n 1 cc(m,i-1,k,2))+(wa2(i-2)*cc(m,i,k,3)-wa2(i-1)* \n 1 cc(m,i-1,k,3))) \n ch(m,i-1,3,k) = (cc(m,i-1,k,1)+taur*((wa1(i-2)* \n 1 cc(m,i-1,k,2)+wa1(i-1)*cc(m,i,k,2))+(wa2(i-2)* \n 1 cc(m,i-1,k,3)+wa2(i-1)*cc(m,i,k,3))))+(taui*((wa1(i-2)* \n 1 cc(m,i,k,2)-wa1(i-1)*cc(m,i-1,k,2))-(wa2(i-2)* \n 1 cc(m,i,k,3)-wa2(i-1)*cc(m,i-1,k,3)))) \n ch(m,ic-1,2,k) = (cc(m,i-1,k,1)+taur*((wa1(i-2)* \n 1 cc(m,i-1,k,2)+wa1(i-1)*cc(m,i,k,2))+(wa2(i-2)* \n 1 cc(m,i-1,k,3)+wa2(i-1)*cc(m,i,k,3))))-(taui*((wa1(i-2)* \n 1 cc(m,i,k,2)-wa1(i-1)*cc(m,i-1,k,2))-(wa2(i-2)* \n 1 cc(m,i,k,3)-wa2(i-1)*cc(m,i-1,k,3)))) \n ch(m,i,3,k) = (cc(m,i,k,1)+taur*((wa1(i-2)*cc(m,i,k,2)- \n 1 wa1(i-1)*cc(m,i-1,k,2))+(wa2(i-2)*cc(m,i,k,3)-wa2(i-1)* \n 1 cc(m,i-1,k,3))))+(taui*((wa2(i-2)*cc(m,i-1,k,3)+wa2(i-1)* \n 1 cc(m,i,k,3))-(wa1(i-2)*cc(m,i-1,k,2)+wa1(i-1)* \n 1 cc(m,i,k,2)))) \n ch(m,ic,2,k) = (taui*((wa2(i-2)*cc(m,i-1,k,3)+wa2(i-1)* \n 1 cc(m,i,k,3))-(wa1(i-2)*cc(m,i-1,k,2)+wa1(i-1)* \n 1 cc(m,i,k,2))))-(cc(m,i,k,1)+taur*((wa1(i-2)*cc(m,i,k,2)- \n 1 wa1(i-1)*cc(m,i-1,k,2))+(wa2(i-2)*cc(m,i,k,3)-wa2(i-1)* \n 1 cc(m,i-1,k,3)))) \n 1002 continue \n 102 continue \n 103 continue \n return \n end \n subroutine hradf5 (mp,ido,l1,cc,mdimcc,ch,mdimch,\n 1 wa1,wa2,wa3,wa4)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension cc(mdimcc,ido,l1,5) ,ch(mdimch,ido,5,l1) ,\n 1 wa1(ido) ,wa2(ido) ,wa3(ido) ,wa4(ido) \n arg=2.d0*pimach()/5.d0 \n tr11=dcos(arg) \n ti11=dsin(arg) \n tr12=dcos(2.d0*arg) \n ti12=dsin(2.d0*arg) \n do 101 k=1,l1 \n do 1001 m=1,mp \n ch(m,1,1,k) = cc(m,1,k,1)+(cc(m,1,k,5)+cc(m,1,k,2))+ \n 1 (cc(m,1,k,4)+cc(m,1,k,3)) \n ch(m,ido,2,k) = cc(m,1,k,1)+tr11*(cc(m,1,k,5)+cc(m,1,k,2))+ \n 1 tr12*(cc(m,1,k,4)+cc(m,1,k,3)) \n ch(m,1,3,k) = ti11*(cc(m,1,k,5)-cc(m,1,k,2))+ti12* \n 1 (cc(m,1,k,4)-cc(m,1,k,3)) \n ch(m,ido,4,k) = cc(m,1,k,1)+tr12*(cc(m,1,k,5)+cc(m,1,k,2))+ \n 1 tr11*(cc(m,1,k,4)+cc(m,1,k,3)) \n ch(m,1,5,k) = ti12*(cc(m,1,k,5)-cc(m,1,k,2))-ti11* \n 1 (cc(m,1,k,4)-cc(m,1,k,3)) \n 1001 continue \n 101 continue \n if (ido .eq. 1) return \n idp2 = ido+2 \n do 103 k=1,l1 \n do 102 i=3,ido,2 \n ic = idp2-i \n do 1002 m=1,mp \n ch(m,i-1,1,k) = cc(m,i-1,k,1)+((wa1(i-2)*cc(m,i-1,k,2)+ \n 1 wa1(i-1)*cc(m,i,k,2))+(wa4(i-2)*cc(m,i-1,k,5)+wa4(i-1)* \n 1 cc(m,i,k,5)))+((wa2(i-2)*cc(m,i-1,k,3)+wa2(i-1)* \n 1 cc(m,i,k,3))+(wa3(i-2)*cc(m,i-1,k,4)+wa3(i-1)*cc(m,i,k,4))) \n ch(m,i,1,k) = cc(m,i,k,1)+((wa1(i-2)*cc(m,i,k,2)-wa1(i-1)* \n 1 cc(m,i-1,k,2))+(wa4(i-2)*cc(m,i,k,5)-wa4(i-1)* \n 1 cc(m,i-1,k,5)))+((wa2(i-2)*cc(m,i,k,3)-wa2(i-1)* \n 1 cc(m,i-1,k,3))+(wa3(i-2)*cc(m,i,k,4)-wa3(i-1)* \n 1 cc(m,i-1,k,4))) \n ch(m,i-1,3,k) = cc(m,i-1,k,1)+tr11* \n 1 ( wa1(i-2)*cc(m,i-1,k,2)+wa1(i-1)*cc(m,i,k,2) \n 1 +wa4(i-2)*cc(m,i-1,k,5)+wa4(i-1)*cc(m,i,k,5))+tr12* \n 1 ( wa2(i-2)*cc(m,i-1,k,3)+wa2(i-1)*cc(m,i,k,3) \n 1 +wa3(i-2)*cc(m,i-1,k,4)+wa3(i-1)*cc(m,i,k,4))+ti11* \n 1 ( wa1(i-2)*cc(m,i,k,2)-wa1(i-1)*cc(m,i-1,k,2) \n 1 -(wa4(i-2)*cc(m,i,k,5)-wa4(i-1)*cc(m,i-1,k,5)))+ti12* \n 1 ( wa2(i-2)*cc(m,i,k,3)-wa2(i-1)*cc(m,i-1,k,3) \n 1 -(wa3(i-2)*cc(m,i,k,4)-wa3(i-1)*cc(m,i-1,k,4))) \n ch(m,ic-1,2,k) = cc(m,i-1,k,1)+tr11* \n 1 ( wa1(i-2)*cc(m,i-1,k,2)+wa1(i-1)*cc(m,i,k,2) \n 1 +wa4(i-2)*cc(m,i-1,k,5)+wa4(i-1)*cc(m,i,k,5))+tr12* \n 1 ( wa2(i-2)*cc(m,i-1,k,3)+wa2(i-1)*cc(m,i,k,3) \n 1 +wa3(i-2)*cc(m,i-1,k,4)+wa3(i-1)*cc(m,i,k,4))-(ti11* \n 1 ( wa1(i-2)*cc(m,i,k,2)-wa1(i-1)*cc(m,i-1,k,2) \n 1 -(wa4(i-2)*cc(m,i,k,5)-wa4(i-1)*cc(m,i-1,k,5)))+ti12* \n 1 ( wa2(i-2)*cc(m,i,k,3)-wa2(i-1)*cc(m,i-1,k,3) \n 1 -(wa3(i-2)*cc(m,i,k,4)-wa3(i-1)*cc(m,i-1,k,4)))) \n ch(m,i,3,k) = (cc(m,i,k,1)+tr11*((wa1(i-2)*cc(m,i,k,2)- \n 1 wa1(i-1)*cc(m,i-1,k,2))+(wa4(i-2)*cc(m,i,k,5)-wa4(i-1)* \n 1 cc(m,i-1,k,5)))+tr12*((wa2(i-2)*cc(m,i,k,3)-wa2(i-1)* \n 1 cc(m,i-1,k,3))+(wa3(i-2)*cc(m,i,k,4)-wa3(i-1)* \n 1 cc(m,i-1,k,4))))+(ti11*((wa4(i-2)*cc(m,i-1,k,5)+ \n 1 wa4(i-1)*cc(m,i,k,5))-(wa1(i-2)*cc(m,i-1,k,2)+wa1(i-1)* \n 1 cc(m,i,k,2)))+ti12*((wa3(i-2)*cc(m,i-1,k,4)+wa3(i-1)* \n 1 cc(m,i,k,4))-(wa2(i-2)*cc(m,i-1,k,3)+wa2(i-1)* \n 1 cc(m,i,k,3)))) \n ch(m,ic,2,k) = (ti11*((wa4(i-2)*cc(m,i-1,k,5)+wa4(i-1)* \n 1 cc(m,i,k,5))-(wa1(i-2)*cc(m,i-1,k,2)+wa1(i-1)* \n 1 cc(m,i,k,2)))+ti12*((wa3(i-2)*cc(m,i-1,k,4)+wa3(i-1)* \n 1 cc(m,i,k,4))-(wa2(i-2)*cc(m,i-1,k,3)+wa2(i-1)* \n 1 cc(m,i,k,3))))-(cc(m,i,k,1)+tr11*((wa1(i-2)*cc(m,i,k,2)- \n 1 wa1(i-1)*cc(m,i-1,k,2))+(wa4(i-2)*cc(m,i,k,5)-wa4(i-1)* \n 1 cc(m,i-1,k,5)))+tr12*((wa2(i-2)*cc(m,i,k,3)-wa2(i-1)* \n 1 cc(m,i-1,k,3))+(wa3(i-2)*cc(m,i,k,4)-wa3(i-1)* \n 1 cc(m,i-1,k,4)))) \n ch(m,i-1,5,k) = (cc(m,i-1,k,1)+tr12*((wa1(i-2)* \n 1 cc(m,i-1,k,2)+wa1(i-1)*cc(m,i,k,2))+(wa4(i-2)* \n 1 cc(m,i-1,k,5)+wa4(i-1)*cc(m,i,k,5)))+tr11*((wa2(i-2)* \n 1 cc(m,i-1,k,3)+wa2(i-1)*cc(m,i,k,3))+(wa3(i-2)* \n 1 cc(m,i-1,k,4)+wa3(i-1)*cc(m,i,k,4))))+(ti12*((wa1(i-2)* \n 1 cc(m,i,k,2)-wa1(i-1)*cc(m,i-1,k,2))-(wa4(i-2)*cc(m,i,k,5)- \n 1 wa4(i-1)*cc(m,i-1,k,5)))-ti11*((wa2(i-2)*cc(m,i,k,3)- \n 1 wa2(i-1)*cc(m,i-1,k,3))-(wa3(i-2)*cc(m,i,k,4)-wa3(i-1)* \n 1 cc(m,i-1,k,4)))) \n ch(m,ic-1,4,k) = (cc(m,i-1,k,1)+tr12*((wa1(i-2)* \n 1 cc(m,i-1,k,2)+wa1(i-1)*cc(m,i,k,2))+(wa4(i-2)* \n 1 cc(m,i-1,k,5)+wa4(i-1)*cc(m,i,k,5)))+tr11*((wa2(i-2)* \n 1 cc(m,i-1,k,3)+wa2(i-1)*cc(m,i,k,3))+(wa3(i-2)* \n 1 cc(m,i-1,k,4)+wa3(i-1)*cc(m,i,k,4))))-(ti12*((wa1(i-2)* \n 1 cc(m,i,k,2)-wa1(i-1)*cc(m,i-1,k,2))-(wa4(i-2)*cc(m,i,k,5)- \n 1 wa4(i-1)*cc(m,i-1,k,5)))-ti11*((wa2(i-2)*cc(m,i,k,3)- \n 1 wa2(i-1)*cc(m,i-1,k,3))-(wa3(i-2)*cc(m,i,k,4)-wa3(i-1)* \n 1 cc(m,i-1,k,4)))) \n ch(m,i,5,k) = (cc(m,i,k,1)+tr12*((wa1(i-2)*cc(m,i,k,2)- \n 1 wa1(i-1)*cc(m,i-1,k,2))+(wa4(i-2)*cc(m,i,k,5)-wa4(i-1)* \n 1 cc(m,i-1,k,5)))+tr11*((wa2(i-2)*cc(m,i,k,3)-wa2(i-1)* \n 1 cc(m,i-1,k,3))+(wa3(i-2)*cc(m,i,k,4)-wa3(i-1)* \n 1 cc(m,i-1,k,4))))+(ti12*((wa4(i-2)*cc(m,i-1,k,5)+ \n 1 wa4(i-1)*cc(m,i,k,5))-(wa1(i-2)*cc(m,i-1,k,2)+wa1(i-1)* \n 1 cc(m,i,k,2)))-ti11*((wa3(i-2)*cc(m,i-1,k,4)+wa3(i-1)* \n 1 cc(m,i,k,4))-(wa2(i-2)*cc(m,i-1,k,3)+wa2(i-1)* \n 1 cc(m,i,k,3)))) \n ch(m,ic,4,k) = (ti12*((wa4(i-2)*cc(m,i-1,k,5)+wa4(i-1)* \n 1 cc(m,i,k,5))-(wa1(i-2)*cc(m,i-1,k,2)+wa1(i-1)* \n 1 cc(m,i,k,2)))-ti11*((wa3(i-2)*cc(m,i-1,k,4)+wa3(i-1)* \n 1 cc(m,i,k,4))-(wa2(i-2)*cc(m,i-1,k,3)+wa2(i-1)* \n 1 cc(m,i,k,3))))-(cc(m,i,k,1)+tr12*((wa1(i-2)*cc(m,i,k,2)- \n 1 wa1(i-1)*cc(m,i-1,k,2))+(wa4(i-2)*cc(m,i,k,5)-wa4(i-1)* \n 1 cc(m,i-1,k,5)))+tr11*((wa2(i-2)*cc(m,i,k,3)-wa2(i-1)* \n 1 cc(m,i-1,k,3))+(wa3(i-2)*cc(m,i,k,4)-wa3(i-1)* \n 1 cc(m,i-1,k,4)))) \n 1002 continue \n 102 continue \n 103 continue \n return \n end \n subroutine hradfg (mp,ido,ip,l1,idl1,cc,c1,c2,mdimcc,\n 1 ch,ch2,mdimch,wa)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension ch(mdimch,ido,l1,ip) ,cc(mdimcc,ido,ip,l1) ,\n 1 c1(mdimcc,ido,l1,ip) ,c2(mdimcc,idl1,ip),\n 2 ch2(mdimch,idl1,ip) ,wa(ido)\n tpi=2.d0*pimach() \n arg = tpi/dfloat(ip) \n dcp = dcos(arg) \n dsp = dsin(arg) \n ipph = (ip+1)/2 \n ipp2 = ip+2 \n idp2 = ido+2 \n nbd = (ido-1)/2 \n if (ido .eq. 1) go to 119 \n do 101 ik=1,idl1 \n do 1001 m=1,mp \n ch2(m,ik,1) = c2(m,ik,1) \n 1001 continue \n 101 continue \n do 103 j=2,ip \n do 102 k=1,l1 \n do 1002 m=1,mp \n ch(m,1,k,j) = c1(m,1,k,j) \n 1002 continue \n 102 continue \n 103 continue \n if (nbd .gt. l1) go to 107 \n is = -ido \n do 106 j=2,ip \n is = is+ido \n idij = is \n do 105 i=3,ido,2 \n idij = idij+2 \n do 104 k=1,l1 \n do 1004 m=1,mp \n ch(m,i-1,k,j) = wa(idij-1)*c1(m,i-1,k,j)+wa(idij) \n 1 *c1(m,i,k,j) \n ch(m,i,k,j) = wa(idij-1)*c1(m,i,k,j)-wa(idij) \n 1 *c1(m,i-1,k,j) \n 1004 continue \n 104 continue \n 105 continue \n 106 continue \n go to 111 \n 107 is = -ido \n do 110 j=2,ip \n is = is+ido \n do 109 k=1,l1 \n idij = is \n do 108 i=3,ido,2 \n idij = idij+2 \n do 1008 m=1,mp \n ch(m,i-1,k,j) = wa(idij-1)*c1(m,i-1,k,j)+wa(idij) \n 1 *c1(m,i,k,j) \n ch(m,i,k,j) = wa(idij-1)*c1(m,i,k,j)-wa(idij) \n 1 *c1(m,i-1,k,j) \n 1008 continue \n 108 continue \n 109 continue \n 110 continue \n 111 if (nbd .lt. l1) go to 115 \n do 114 j=2,ipph \n jc = ipp2-j \n do 113 k=1,l1 \n do 112 i=3,ido,2 \n do 1012 m=1,mp \n c1(m,i-1,k,j) = ch(m,i-1,k,j)+ch(m,i-1,k,jc) \n c1(m,i-1,k,jc) = ch(m,i,k,j)-ch(m,i,k,jc) \n c1(m,i,k,j) = ch(m,i,k,j)+ch(m,i,k,jc) \n c1(m,i,k,jc) = ch(m,i-1,k,jc)-ch(m,i-1,k,j) \n 1012 continue \n 112 continue \n 113 continue \n 114 continue \n go to 121 \n 115 do 118 j=2,ipph \n jc = ipp2-j \n do 117 i=3,ido,2 \n do 116 k=1,l1 \n do 1016 m=1,mp \n c1(m,i-1,k,j) = ch(m,i-1,k,j)+ch(m,i-1,k,jc) \n c1(m,i-1,k,jc) = ch(m,i,k,j)-ch(m,i,k,jc) \n c1(m,i,k,j) = ch(m,i,k,j)+ch(m,i,k,jc) \n c1(m,i,k,jc) = ch(m,i-1,k,jc)-ch(m,i-1,k,j) \n 1016 continue \n 116 continue \n 117 continue \n 118 continue \n go to 121 \n 119 do 120 ik=1,idl1 \n do 1020 m=1,mp \n c2(m,ik,1) = ch2(m,ik,1) \n 1020 continue \n 120 continue \n 121 do 123 j=2,ipph \n jc = ipp2-j \n do 122 k=1,l1 \n do 1022 m=1,mp \n c1(m,1,k,j) = ch(m,1,k,j)+ch(m,1,k,jc) \n c1(m,1,k,jc) = ch(m,1,k,jc)-ch(m,1,k,j) \n 1022 continue \n 122 continue \n 123 continue \nc \n ar1 = 1.d0 \n ai1 = 0.d0 \n do 127 l=2,ipph \n lc = ipp2-l \n ar1h = dcp*ar1-dsp*ai1 \n ai1 = dcp*ai1+dsp*ar1 \n ar1 = ar1h \n do 124 ik=1,idl1 \n do 1024 m=1,mp \n ch2(m,ik,l) = c2(m,ik,1)+ar1*c2(m,ik,2) \n ch2(m,ik,lc) = ai1*c2(m,ik,ip) \n 1024 continue \n 124 continue \n dc2 = ar1 \n ds2 = ai1 \n ar2 = ar1 \n ai2 = ai1 \n do 126 j=3,ipph \n jc = ipp2-j \n ar2h = dc2*ar2-ds2*ai2 \n ai2 = dc2*ai2+ds2*ar2 \n ar2 = ar2h \n do 125 ik=1,idl1 \n do 1025 m=1,mp \n ch2(m,ik,l) = ch2(m,ik,l)+ar2*c2(m,ik,j) \n ch2(m,ik,lc) = ch2(m,ik,lc)+ai2*c2(m,ik,jc) \n 1025 continue \n 125 continue \n 126 continue \n 127 continue \n do 129 j=2,ipph \n do 128 ik=1,idl1 \n do 1028 m=1,mp \n ch2(m,ik,1) = ch2(m,ik,1)+c2(m,ik,j) \n 1028 continue \n 128 continue \n 129 continue \nc \n if (ido .lt. l1) go to 132 \n do 131 k=1,l1 \n do 130 i=1,ido \n do 1030 m=1,mp \n cc(m,i,1,k) = ch(m,i,k,1) \n 1030 continue \n 130 continue \n 131 continue \n go to 135 \n 132 do 134 i=1,ido \n do 133 k=1,l1 \n do 1033 m=1,mp \n cc(m,i,1,k) = ch(m,i,k,1) \n 1033 continue \n 133 continue \n 134 continue \n 135 do 137 j=2,ipph \n jc = ipp2-j \n j2 = j+j \n do 136 k=1,l1 \n do 1036 m=1,mp \n cc(m,ido,j2-2,k) = ch(m,1,k,j) \n cc(m,1,j2-1,k) = ch(m,1,k,jc) \n 1036 continue \n 136 continue \n 137 continue \n if (ido .eq. 1) return \n if (nbd .lt. l1) go to 141 \n do 140 j=2,ipph \n jc = ipp2-j \n j2 = j+j \n do 139 k=1,l1 \n do 138 i=3,ido,2 \n ic = idp2-i \n do 1038 m=1,mp \n cc(m,i-1,j2-1,k) = ch(m,i-1,k,j)+ch(m,i-1,k,jc) \n cc(m,ic-1,j2-2,k) = ch(m,i-1,k,j)-ch(m,i-1,k,jc) \n cc(m,i,j2-1,k) = ch(m,i,k,j)+ch(m,i,k,jc) \n cc(m,ic,j2-2,k) = ch(m,i,k,jc)-ch(m,i,k,j) \n 1038 continue \n 138 continue \n 139 continue \n 140 continue \n return \n 141 do 144 j=2,ipph \n jc = ipp2-j \n j2 = j+j \n do 143 i=3,ido,2 \n ic = idp2-i \n do 142 k=1,l1 \n do 1042 m=1,mp \n cc(m,i-1,j2-1,k) = ch(m,i-1,k,j)+ch(m,i-1,k,jc) \n cc(m,ic-1,j2-2,k) = ch(m,i-1,k,j)-ch(m,i-1,k,jc) \n cc(m,i,j2-1,k) = ch(m,i,k,j)+ch(m,i,k,jc) \n cc(m,ic,j2-2,k) = ch(m,i,k,jc)-ch(m,i,k,j) \n 1042 continue \n 142 continue \n 143 continue \n 144 continue \n return \n end \n double precision function pimach() \n implicit double precision (a-h,o-z) \n pimach=3.14159265358979323846264338328d0\n return \n end \n subroutine hrfftb(m,n,r,mdimr,whrfft,work)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension r(mdimr,n) ,work(1) ,whrfft(n+15)\n common /hrf/ tfft\n if (n .eq. 1) return \nc tstart = second(dum)\n call hrftb1 (m,n,r,mdimr,work,whrfft,whrfft(n+1))\nc tfft = tfft+second(dum)-tstart\n return \n end \n subroutine hrftb1 (m,n,c,mdimc,ch,wa,fac)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension ch(m,n), c(mdimc,n), wa(n) ,fac(15)\n nf = fac(2) \n na = 0 \n l1 = 1 \n iw = 1 \n do 116 k1=1,nf \n ip = fac(k1+2) \n l2 = ip*l1 \n ido = n/l2 \n idl1 = ido*l1 \n if (ip .ne. 4) go to 103 \n ix2 = iw+ido \n ix3 = ix2+ido \n if (na .ne. 0) go to 101 \n\t call hradb4 (m,ido,l1,c,mdimc,ch,m,wa(iw),wa(ix2),wa(ix3))\n go to 102 \n 101 call hradb4 (m,ido,l1,ch,m,c,mdimc,wa(iw),wa(ix2),wa(ix3))\n 102 na = 1-na \n go to 115 \n 103 if (ip .ne. 2) go to 106 \n if (na .ne. 0) go to 104 \n\t call hradb2 (m,ido,l1,c,mdimc,ch,m,wa(iw))\n go to 105 \n 104 call hradb2 (m,ido,l1,ch,m,c,mdimc,wa(iw))\n 105 na = 1-na \n go to 115 \n 106 if (ip .ne. 3) go to 109 \n ix2 = iw+ido \n if (na .ne. 0) go to 107 \n\t call hradb3 (m,ido,l1,c,mdimc,ch,m,wa(iw),wa(ix2))\n go to 108 \n 107 call hradb3 (m,ido,l1,ch,m,c,mdimc,wa(iw),wa(ix2))\n 108 na = 1-na \n go to 115 \n 109 if (ip .ne. 5) go to 112 \n ix2 = iw+ido \n ix3 = ix2+ido \n ix4 = ix3+ido \n if (na .ne. 0) go to 110 \n call hradb5 (m,ido,l1,c,mdimc,ch,m,wa(iw),wa(ix2),wa(ix3),wa(ix4))\n go to 111 \n 110 call hradb5 (m,ido,l1,ch,m,c,mdimc,wa(iw),wa(ix2),wa(ix3),wa(ix4))\n 111 na = 1-na \n go to 115 \n 112 if (na .ne. 0) go to 113 \n\t call hradbg (m,ido,ip,l1,idl1,c,c,c,mdimc,ch,ch,m,wa(iw))\n go to 114 \n 113 call hradbg (m,ido,ip,l1,idl1,ch,ch,ch,m,c,c,mdimc,wa(iw))\n 114 if (ido .eq. 1) na = 1-na \n 115 l1 = l2 \n iw = iw+(ip-1)*ido \n 116 continue \n if (na .eq. 0) return\n do 117 j=1,n \n do 117 i=1,m \n\t c(i,j) = ch(i,j)\n 117 continue \n return \n end \n subroutine hradbg (mp,ido,ip,l1,idl1,cc,c1,c2,mdimcc,\n 1 ch,ch2,mdimch,wa)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension ch(mdimch,ido,l1,ip) ,cc(mdimcc,ido,ip,l1) ,\n 1 c1(mdimcc,ido,l1,ip) ,c2(mdimcc,idl1,ip),\n 2 ch2(mdimch,idl1,ip) ,wa(ido)\n tpi=2.d0*pimach() \n arg = tpi/dfloat(ip) \n dcp = dcos(arg) \n dsp = dsin(arg) \n idp2 = ido+2 \n nbd = (ido-1)/2 \n ipp2 = ip+2 \n ipph = (ip+1)/2 \n if (ido .lt. l1) go to 103 \n do 102 k=1,l1 \n do 101 i=1,ido \n do 1001 m=1,mp \n ch(m,i,k,1) = cc(m,i,1,k) \n 1001 continue \n 101 continue \n 102 continue \n go to 106 \n 103 do 105 i=1,ido \n do 104 k=1,l1 \n do 1004 m=1,mp \n ch(m,i,k,1) = cc(m,i,1,k) \n 1004 continue \n 104 continue \n 105 continue \n 106 do 108 j=2,ipph \n jc = ipp2-j \n j2 = j+j \n do 107 k=1,l1 \n do 1007 m=1,mp \n ch(m,1,k,j) = cc(m,ido,j2-2,k)+cc(m,ido,j2-2,k) \n ch(m,1,k,jc) = cc(m,1,j2-1,k)+cc(m,1,j2-1,k) \n 1007 continue \n 107 continue \n 108 continue \n if (ido .eq. 1) go to 116 \n if (nbd .lt. l1) go to 112 \n do 111 j=2,ipph \n jc = ipp2-j \n do 110 k=1,l1 \n do 109 i=3,ido,2 \n ic = idp2-i \n do 1009 m=1,mp \n ch(m,i-1,k,j) = cc(m,i-1,2*j-1,k)+cc(m,ic-1,2*j-2,k) \n ch(m,i-1,k,jc) = cc(m,i-1,2*j-1,k)-cc(m,ic-1,2*j-2,k) \n ch(m,i,k,j) = cc(m,i,2*j-1,k)-cc(m,ic,2*j-2,k) \n ch(m,i,k,jc) = cc(m,i,2*j-1,k)+cc(m,ic,2*j-2,k) \n 1009 continue \n 109 continue \n 110 continue \n 111 continue \n go to 116 \n 112 do 115 j=2,ipph \n jc = ipp2-j \n do 114 i=3,ido,2 \n ic = idp2-i \n do 113 k=1,l1 \n do 1013 m=1,mp \n ch(m,i-1,k,j) = cc(m,i-1,2*j-1,k)+cc(m,ic-1,2*j-2,k) \n ch(m,i-1,k,jc) = cc(m,i-1,2*j-1,k)-cc(m,ic-1,2*j-2,k) \n ch(m,i,k,j) = cc(m,i,2*j-1,k)-cc(m,ic,2*j-2,k) \n ch(m,i,k,jc) = cc(m,i,2*j-1,k)+cc(m,ic,2*j-2,k) \n 1013 continue \n 113 continue \n 114 continue \n 115 continue \n 116 ar1 = 1.d0 \n ai1 = 0.d0 \n do 120 l=2,ipph \n lc = ipp2-l \n ar1h = dcp*ar1-dsp*ai1 \n ai1 = dcp*ai1+dsp*ar1 \n ar1 = ar1h \n do 117 ik=1,idl1 \n do 1017 m=1,mp \n c2(m,ik,l) = ch2(m,ik,1)+ar1*ch2(m,ik,2) \n c2(m,ik,lc) = ai1*ch2(m,ik,ip) \n 1017 continue \n 117 continue \n dc2 = ar1 \n ds2 = ai1 \n ar2 = ar1 \n ai2 = ai1 \n do 119 j=3,ipph \n jc = ipp2-j \n ar2h = dc2*ar2-ds2*ai2 \n ai2 = dc2*ai2+ds2*ar2 \n ar2 = ar2h \n do 118 ik=1,idl1 \n do 1018 m=1,mp \n c2(m,ik,l) = c2(m,ik,l)+ar2*ch2(m,ik,j) \n c2(m,ik,lc) = c2(m,ik,lc)+ai2*ch2(m,ik,jc) \n 1018 continue \n 118 continue \n 119 continue \n 120 continue \n do 122 j=2,ipph \n do 121 ik=1,idl1 \n do 1021 m=1,mp \n ch2(m,ik,1) = ch2(m,ik,1)+ch2(m,ik,j) \n 1021 continue \n 121 continue \n 122 continue \n do 124 j=2,ipph \n jc = ipp2-j \n do 123 k=1,l1 \n do 1023 m=1,mp \n ch(m,1,k,j) = c1(m,1,k,j)-c1(m,1,k,jc) \n ch(m,1,k,jc) = c1(m,1,k,j)+c1(m,1,k,jc) \n 1023 continue \n 123 continue \n 124 continue \n if (ido .eq. 1) go to 132 \n if (nbd .lt. l1) go to 128 \n do 127 j=2,ipph \n jc = ipp2-j \n do 126 k=1,l1 \n do 125 i=3,ido,2 \n do 1025 m=1,mp \n ch(m,i-1,k,j) = c1(m,i-1,k,j)-c1(m,i,k,jc) \n ch(m,i-1,k,jc) = c1(m,i-1,k,j)+c1(m,i,k,jc) \n ch(m,i,k,j) = c1(m,i,k,j)+c1(m,i-1,k,jc) \n ch(m,i,k,jc) = c1(m,i,k,j)-c1(m,i-1,k,jc) \n 1025 continue \n 125 continue \n 126 continue \n 127 continue \n go to 132 \n 128 do 131 j=2,ipph \n jc = ipp2-j \n do 130 i=3,ido,2 \n do 129 k=1,l1 \n do 1029 m=1,mp \n ch(m,i-1,k,j) = c1(m,i-1,k,j)-c1(m,i,k,jc) \n ch(m,i-1,k,jc) = c1(m,i-1,k,j)+c1(m,i,k,jc) \n ch(m,i,k,j) = c1(m,i,k,j)+c1(m,i-1,k,jc) \n ch(m,i,k,jc) = c1(m,i,k,j)-c1(m,i-1,k,jc) \n 1029 continue \n 129 continue \n 130 continue \n 131 continue \n 132 continue \n if (ido .eq. 1) return \n do 133 ik=1,idl1 \n do 1033 m=1,mp \n c2(m,ik,1) = ch2(m,ik,1) \n 1033 continue \n 133 continue \n do 135 j=2,ip \n do 134 k=1,l1 \n do 1034 m=1,mp \n c1(m,1,k,j) = ch(m,1,k,j) \n 1034 continue \n 134 continue \n 135 continue \n if (nbd .gt. l1) go to 139 \n is = -ido \n do 138 j=2,ip \n is = is+ido \n idij = is \n do 137 i=3,ido,2 \n idij = idij+2 \n do 136 k=1,l1 \n do 1036 m=1,mp \n c1(m,i-1,k,j) = wa(idij-1)*ch(m,i-1,k,j)-wa(idij)* \n 1 ch(m,i,k,j) \n c1(m,i,k,j) = wa(idij-1)*ch(m,i,k,j)+wa(idij)* \n 1 ch(m,i-1,k,j) \n 1036 continue \n 136 continue \n 137 continue \n 138 continue \n go to 143 \n 139 is = -ido \n do 142 j=2,ip \n is = is+ido \n do 141 k=1,l1 \n idij = is \n do 140 i=3,ido,2 \n idij = idij+2 \n do 1040 m=1,mp \n c1(m,i-1,k,j) = wa(idij-1)*ch(m,i-1,k,j)-wa(idij)* \n 1 ch(m,i,k,j) \n c1(m,i,k,j) = wa(idij-1)*ch(m,i,k,j)+wa(idij)* \n 1 ch(m,i-1,k,j) \n 1040 continue \n 140 continue \n 141 continue \n 142 continue \n 143 return \n end \n subroutine hradb4 (mp,ido,l1,cc,mdimcc,ch,mdimch,wa1,wa2,wa3)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension cc(mdimcc,ido,4,l1) ,ch(mdimch,ido,l1,4) ,\n 1 wa1(ido) ,wa2(ido) ,wa3(ido) \n sqrt2=dsqrt(2.d0) \n do 101 k=1,l1 \n do 1001 m=1,mp \n ch(m,1,k,3) = (cc(m,1,1,k)+cc(m,ido,4,k)) \n 1 -(cc(m,ido,2,k)+cc(m,ido,2,k)) \n ch(m,1,k,1) = (cc(m,1,1,k)+cc(m,ido,4,k)) \n 1 +(cc(m,ido,2,k)+cc(m,ido,2,k)) \n ch(m,1,k,4) = (cc(m,1,1,k)-cc(m,ido,4,k)) \n 1 +(cc(m,1,3,k)+cc(m,1,3,k)) \n ch(m,1,k,2) = (cc(m,1,1,k)-cc(m,ido,4,k)) \n 1 -(cc(m,1,3,k)+cc(m,1,3,k)) \n 1001 continue \n 101 continue \n if (ido-2) 107,105,102 \n 102 idp2 = ido+2 \n do 104 k=1,l1 \n do 103 i=3,ido,2 \n ic = idp2-i \n do 1002 m=1,mp \n ch(m,i-1,k,1) = (cc(m,i-1,1,k)+cc(m,ic-1,4,k)) \n 1 +(cc(m,i-1,3,k)+cc(m,ic-1,2,k)) \n ch(m,i,k,1) = (cc(m,i,1,k)-cc(m,ic,4,k)) \n 1 +(cc(m,i,3,k)-cc(m,ic,2,k)) \n ch(m,i-1,k,2)=wa1(i-2)*((cc(m,i-1,1,k)-cc(m,ic-1,4,k)) \n 1 -(cc(m,i,3,k)+cc(m,ic,2,k)))-wa1(i-1) \n 1 *((cc(m,i,1,k)+cc(m,ic,4,k))+(cc(m,i-1,3,k)-cc(m,ic-1,2,k))) \n ch(m,i,k,2)=wa1(i-2)*((cc(m,i,1,k)+cc(m,ic,4,k)) \n 1 +(cc(m,i-1,3,k)-cc(m,ic-1,2,k)))+wa1(i-1) \n 1 *((cc(m,i-1,1,k)-cc(m,ic-1,4,k))-(cc(m,i,3,k)+cc(m,ic,2,k))) \n ch(m,i-1,k,3)=wa2(i-2)*((cc(m,i-1,1,k)+cc(m,ic-1,4,k)) \n 1 -(cc(m,i-1,3,k)+cc(m,ic-1,2,k)))-wa2(i-1) \n 1 *((cc(m,i,1,k)-cc(m,ic,4,k))-(cc(m,i,3,k)-cc(m,ic,2,k))) \n ch(m,i,k,3)=wa2(i-2)*((cc(m,i,1,k)-cc(m,ic,4,k)) \n 1 -(cc(m,i,3,k)-cc(m,ic,2,k)))+wa2(i-1) \n 1 *((cc(m,i-1,1,k)+cc(m,ic-1,4,k))-(cc(m,i-1,3,k) \n 1 +cc(m,ic-1,2,k))) \n ch(m,i-1,k,4)=wa3(i-2)*((cc(m,i-1,1,k)-cc(m,ic-1,4,k)) \n 1 +(cc(m,i,3,k)+cc(m,ic,2,k)))-wa3(i-1) \n 1 *((cc(m,i,1,k)+cc(m,ic,4,k))-(cc(m,i-1,3,k)-cc(m,ic-1,2,k))) \n ch(m,i,k,4)=wa3(i-2)*((cc(m,i,1,k)+cc(m,ic,4,k)) \n 1 -(cc(m,i-1,3,k)-cc(m,ic-1,2,k)))+wa3(i-1) \n 1 *((cc(m,i-1,1,k)-cc(m,ic-1,4,k))+(cc(m,i,3,k)+cc(m,ic,2,k))) \n 1002 continue \n 103 continue \n 104 continue \n if (mod(ido,2) .eq. 1) return \n 105 continue \n do 106 k=1,l1 \n do 1003 m=1,mp \n ch(m,ido,k,1) = (cc(m,ido,1,k)+cc(m,ido,3,k)) \n 1 +(cc(m,ido,1,k)+cc(m,ido,3,k)) \n ch(m,ido,k,2) = sqrt2*((cc(m,ido,1,k)-cc(m,ido,3,k)) \n 1 -(cc(m,1,2,k)+cc(m,1,4,k))) \n ch(m,ido,k,3) = (cc(m,1,4,k)-cc(m,1,2,k)) \n 1 +(cc(m,1,4,k)-cc(m,1,2,k)) \n ch(m,ido,k,4) = -sqrt2*((cc(m,ido,1,k)-cc(m,ido,3,k)) \n 1 +(cc(m,1,2,k)+cc(m,1,4,k))) \n 1003 continue \n 106 continue \n 107 return \n end \n subroutine hradb2 (mp,ido,l1,cc,mdimcc,ch,mdimch,wa1)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension cc(mdimcc,ido,2,l1) ,ch(mdimch,ido,l1,2),\n 1 wa1(ido) \n do 101 k=1,l1 \n do 1001 m=1,mp \n ch(m,1,k,1) = cc(m,1,1,k)+cc(m,ido,2,k) \n ch(m,1,k,2) = cc(m,1,1,k)-cc(m,ido,2,k) \n 1001 continue \n 101 continue \n if (ido-2) 107,105,102 \n 102 idp2 = ido+2 \n do 104 k=1,l1 \n do 103 i=3,ido,2 \n ic = idp2-i \n do 1002 m=1,mp \n ch(m,i-1,k,1) = cc(m,i-1,1,k)+cc(m,ic-1,2,k) \n ch(m,i,k,1) = cc(m,i,1,k)-cc(m,ic,2,k) \n ch(m,i-1,k,2) = wa1(i-2)*(cc(m,i-1,1,k)-cc(m,ic-1,2,k)) \n 1 -wa1(i-1)*(cc(m,i,1,k)+cc(m,ic,2,k)) \n ch(m,i,k,2) = wa1(i-2)*(cc(m,i,1,k)+cc(m,ic,2,k))+wa1(i-1) \n 1 *(cc(m,i-1,1,k)-cc(m,ic-1,2,k)) \n 1002 continue \n 103 continue \n 104 continue \n if (mod(ido,2) .eq. 1) return \n 105 do 106 k=1,l1 \n do 1003 m=1,mp \n ch(m,ido,k,1) = cc(m,ido,1,k)+cc(m,ido,1,k) \n ch(m,ido,k,2) = -(cc(m,1,2,k)+cc(m,1,2,k)) \n 1003 continue \n 106 continue \n 107 return \n end \n subroutine hradb3 (mp,ido,l1,cc,mdimcc,ch,mdimch,wa1,wa2)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension cc(mdimcc,ido,3,l1) ,ch(mdimch,ido,l1,3),\n 1 wa1(ido) ,wa2(ido) \n arg=2.d0*pimach()/3.d0 \n taur=dcos(arg) \n taui=dsin(arg) \n do 101 k=1,l1 \n do 1001 m=1,mp \n ch(m,1,k,1) = cc(m,1,1,k)+2.d0*cc(m,ido,2,k) \n ch(m,1,k,2) = cc(m,1,1,k)+(2.d0*taur)*cc(m,ido,2,k) \n 1 -(2.d0*taui)*cc(m,1,3,k) \n ch(m,1,k,3) = cc(m,1,1,k)+(2.d0*taur)*cc(m,ido,2,k) \n 1 +2.d0*taui*cc(m,1,3,k) \n 1001 continue \n 101 continue \n if (ido .eq. 1) return \n idp2 = ido+2 \n do 103 k=1,l1 \n do 102 i=3,ido,2 \n ic = idp2-i \n do 1002 m=1,mp \n ch(m,i-1,k,1) = cc(m,i-1,1,k)+(cc(m,i-1,3,k)+cc(m,ic-1,2,k)) \n ch(m,i,k,1) = cc(m,i,1,k)+(cc(m,i,3,k)-cc(m,ic,2,k)) \n ch(m,i-1,k,2) = wa1(i-2)* \n 1 ((cc(m,i-1,1,k)+taur*(cc(m,i-1,3,k)+cc(m,ic-1,2,k)))- \n * (taui*(cc(m,i,3,k)+cc(m,ic,2,k)))) \n 2 -wa1(i-1)* \n 3 ((cc(m,i,1,k)+taur*(cc(m,i,3,k)-cc(m,ic,2,k)))+ \n * (taui*(cc(m,i-1,3,k)-cc(m,ic-1,2,k)))) \n ch(m,i,k,2) = wa1(i-2)* \n 4 ((cc(m,i,1,k)+taur*(cc(m,i,3,k)-cc(m,ic,2,k)))+ \n 8 (taui*(cc(m,i-1,3,k)-cc(m,ic-1,2,k)))) \n 5 +wa1(i-1)* \n 6 ((cc(m,i-1,1,k)+taur*(cc(m,i-1,3,k)+cc(m,ic-1,2,k)))- \n 8 (taui*(cc(m,i,3,k)+cc(m,ic,2,k)))) \n ch(m,i-1,k,3) = wa2(i-2)* \n 7 ((cc(m,i-1,1,k)+taur*(cc(m,i-1,3,k)+cc(m,ic-1,2,k)))+ \n 8 (taui*(cc(m,i,3,k)+cc(m,ic,2,k)))) \n 8 -wa2(i-1)* \n 9 ((cc(m,i,1,k)+taur*(cc(m,i,3,k)-cc(m,ic,2,k)))- \n 8 (taui*(cc(m,i-1,3,k)-cc(m,ic-1,2,k)))) \n ch(m,i,k,3) = wa2(i-2)* \n 1 ((cc(m,i,1,k)+taur*(cc(m,i,3,k)-cc(m,ic,2,k)))- \n 8 (taui*(cc(m,i-1,3,k)-cc(m,ic-1,2,k)))) \n 2 +wa2(i-1)* \n 3 ((cc(m,i-1,1,k)+taur*(cc(m,i-1,3,k)+cc(m,ic-1,2,k)))+ \n 8 (taui*(cc(m,i,3,k)+cc(m,ic,2,k)))) \n 1002 continue \n 102 continue \n 103 continue \n return \n end \n subroutine hradb5 (mp,ido,l1,cc,mdimcc,ch,mdimch,\n 1 wa1,wa2,wa3,wa4)\n implicit double precision (a-h,o-z)\nc \nc a multiple fft package for spherepack\nc \n dimension cc(mdimcc,ido,5,l1) ,ch(mdimch,ido,l1,5),\n 1 wa1(ido) ,wa2(ido) ,wa3(ido) ,wa4(ido) \n arg=2.d0*pimach()/5.d0 \n tr11=dcos(arg) \n ti11=dsin(arg) \n tr12=dcos(2.d0*arg) \n ti12=dsin(2.d0*arg) \n do 101 k=1,l1 \n do 1001 m=1,mp \n ch(m,1,k,1) = cc(m,1,1,k)+2.d0*cc(m,ido,2,k)+2.d0*cc(m,ido,4,k) \n ch(m,1,k,2) = (cc(m,1,1,k)+tr11*2.d0*cc(m,ido,2,k) \n 1 +tr12*2.d0*cc(m,ido,4,k))-(ti11*2.d0*cc(m,1,3,k) \n 1 +ti12*2.d0*cc(m,1,5,k)) \n ch(m,1,k,3) = (cc(m,1,1,k)+tr12*2.d0*cc(m,ido,2,k) \n 1 +tr11*2.d0*cc(m,ido,4,k))-(ti12*2.d0*cc(m,1,3,k) \n 1 -ti11*2.d0*cc(m,1,5,k)) \n ch(m,1,k,4) = (cc(m,1,1,k)+tr12*2.d0*cc(m,ido,2,k) \n 1 +tr11*2.d0*cc(m,ido,4,k))+(ti12*2.d0*cc(m,1,3,k) \n 1 -ti11*2.d0*cc(m,1,5,k)) \n ch(m,1,k,5) = (cc(m,1,1,k)+tr11*2.d0*cc(m,ido,2,k) \n 1 +tr12*2.d0*cc(m,ido,4,k))+(ti11*2.d0*cc(m,1,3,k) \n 1 +ti12*2.d0*cc(m,1,5,k)) \n 1001 continue \n 101 continue \n if (ido .eq. 1) return \n idp2 = ido+2 \n do 103 k=1,l1 \n do 102 i=3,ido,2 \n ic = idp2-i \n do 1002 m=1,mp \n ch(m,i-1,k,1) = cc(m,i-1,1,k)+(cc(m,i-1,3,k)+cc(m,ic-1,2,k)) \n 1 +(cc(m,i-1,5,k)+cc(m,ic-1,4,k)) \n ch(m,i,k,1) = cc(m,i,1,k)+(cc(m,i,3,k)-cc(m,ic,2,k)) \n 1 +(cc(m,i,5,k)-cc(m,ic,4,k)) \n ch(m,i-1,k,2) = wa1(i-2)*((cc(m,i-1,1,k)+tr11* \n 1 (cc(m,i-1,3,k)+cc(m,ic-1,2,k))+tr12 \n 1 *(cc(m,i-1,5,k)+cc(m,ic-1,4,k)))-(ti11*(cc(m,i,3,k) \n 1 +cc(m,ic,2,k))+ti12*(cc(m,i,5,k)+cc(m,ic,4,k)))) \n 1 -wa1(i-1)*((cc(m,i,1,k)+tr11*(cc(m,i,3,k)-cc(m,ic,2,k)) \n 1 +tr12*(cc(m,i,5,k)-cc(m,ic,4,k)))+(ti11*(cc(m,i-1,3,k) \n 1 -cc(m,ic-1,2,k))+ti12*(cc(m,i-1,5,k)-cc(m,ic-1,4,k)))) \n ch(m,i,k,2) = wa1(i-2)*((cc(m,i,1,k)+tr11*(cc(m,i,3,k) \n 1 -cc(m,ic,2,k))+tr12*(cc(m,i,5,k)-cc(m,ic,4,k))) \n 1 +(ti11*(cc(m,i-1,3,k)-cc(m,ic-1,2,k))+ti12 \n 1 *(cc(m,i-1,5,k)-cc(m,ic-1,4,k))))+wa1(i-1) \n 1 *((cc(m,i-1,1,k)+tr11*(cc(m,i-1,3,k) \n 1 +cc(m,ic-1,2,k))+tr12*(cc(m,i-1,5,k)+cc(m,ic-1,4,k))) \n 1 -(ti11*(cc(m,i,3,k)+cc(m,ic,2,k))+ti12 \n 1 *(cc(m,i,5,k)+cc(m,ic,4,k)))) \n ch(m,i-1,k,3) = wa2(i-2) \n 1 *((cc(m,i-1,1,k)+tr12*(cc(m,i-1,3,k)+cc(m,ic-1,2,k)) \n 1 +tr11*(cc(m,i-1,5,k)+cc(m,ic-1,4,k)))-(ti12*(cc(m,i,3,k) \n 1 +cc(m,ic,2,k))-ti11*(cc(m,i,5,k)+cc(m,ic,4,k)))) \n 1 -wa2(i-1) \n 1 *((cc(m,i,1,k)+tr12*(cc(m,i,3,k)- \n 1 cc(m,ic,2,k))+tr11*(cc(m,i,5,k)-cc(m,ic,4,k))) \n 1 +(ti12*(cc(m,i-1,3,k)-cc(m,ic-1,2,k))-ti11 \n 1 *(cc(m,i-1,5,k)-cc(m,ic-1,4,k)))) \n ch(m,i,k,3) = wa2(i-2) \n 1 *((cc(m,i,1,k)+tr12*(cc(m,i,3,k)- \n 1 cc(m,ic,2,k))+tr11*(cc(m,i,5,k)-cc(m,ic,4,k))) \n 1 +(ti12*(cc(m,i-1,3,k)-cc(m,ic-1,2,k))-ti11 \n 1 *(cc(m,i-1,5,k)-cc(m,ic-1,4,k)))) \n 1 +wa2(i-1) \n 1 *((cc(m,i-1,1,k)+tr12*(cc(m,i-1,3,k)+cc(m,ic-1,2,k)) \n 1 +tr11*(cc(m,i-1,5,k)+cc(m,ic-1,4,k)))-(ti12*(cc(m,i,3,k) \n 1 +cc(m,ic,2,k))-ti11*(cc(m,i,5,k)+cc(m,ic,4,k)))) \n ch(m,i-1,k,4) = wa3(i-2) \n 1 *((cc(m,i-1,1,k)+tr12*(cc(m,i-1,3,k)+cc(m,ic-1,2,k)) \n 1 +tr11*(cc(m,i-1,5,k)+cc(m,ic-1,4,k)))+(ti12*(cc(m,i,3,k) \n 1 +cc(m,ic,2,k))-ti11*(cc(m,i,5,k)+cc(m,ic,4,k)))) \n 1 -wa3(i-1) \n 1 *((cc(m,i,1,k)+tr12*(cc(m,i,3,k)- \n 1 cc(m,ic,2,k))+tr11*(cc(m,i,5,k)-cc(m,ic,4,k))) \n 1 -(ti12*(cc(m,i-1,3,k)-cc(m,ic-1,2,k))-ti11 \n 1 *(cc(m,i-1,5,k)-cc(m,ic-1,4,k)))) \n ch(m,i,k,4) = wa3(i-2) \n 1 *((cc(m,i,1,k)+tr12*(cc(m,i,3,k)- \n 1 cc(m,ic,2,k))+tr11*(cc(m,i,5,k)-cc(m,ic,4,k))) \n 1 -(ti12*(cc(m,i-1,3,k)-cc(m,ic-1,2,k))-ti11 \n 1 *(cc(m,i-1,5,k)-cc(m,ic-1,4,k)))) \n 1 +wa3(i-1) \n 1 *((cc(m,i-1,1,k)+tr12*(cc(m,i-1,3,k)+cc(m,ic-1,2,k)) \n 1 +tr11*(cc(m,i-1,5,k)+cc(m,ic-1,4,k)))+(ti12*(cc(m,i,3,k) \n 1 +cc(m,ic,2,k))-ti11*(cc(m,i,5,k)+cc(m,ic,4,k)))) \n ch(m,i-1,k,5) = wa4(i-2) \n 1 *((cc(m,i-1,1,k)+tr11*(cc(m,i-1,3,k)+cc(m,ic-1,2,k)) \n 1 +tr12*(cc(m,i-1,5,k)+cc(m,ic-1,4,k)))+(ti11*(cc(m,i,3,k) \n 1 +cc(m,ic,2,k))+ti12*(cc(m,i,5,k)+cc(m,ic,4,k)))) \n 1 -wa4(i-1) \n 1 *((cc(m,i,1,k)+tr11*(cc(m,i,3,k)-cc(m,ic,2,k)) \n 1 +tr12*(cc(m,i,5,k)-cc(m,ic,4,k)))-(ti11*(cc(m,i-1,3,k) \n 1 -cc(m,ic-1,2,k))+ti12*(cc(m,i-1,5,k)-cc(m,ic-1,4,k)))) \n ch(m,i,k,5) = wa4(i-2) \n 1 *((cc(m,i,1,k)+tr11*(cc(m,i,3,k)-cc(m,ic,2,k)) \n 1 +tr12*(cc(m,i,5,k)-cc(m,ic,4,k)))-(ti11*(cc(m,i-1,3,k) \n 1 -cc(m,ic-1,2,k))+ti12*(cc(m,i-1,5,k)-cc(m,ic-1,4,k)))) \n 1 +wa4(i-1) \n 1 *((cc(m,i-1,1,k)+tr11*(cc(m,i-1,3,k)+cc(m,ic-1,2,k)) \n 1 +tr12*(cc(m,i-1,5,k)+cc(m,ic-1,4,k)))+(ti11*(cc(m,i,3,k) \n 1 +cc(m,ic,2,k))+ti12*(cc(m,i,5,k)+cc(m,ic,4,k)))) \n 1002 continue \n 102 continue \n 103 continue \n return \n end \n" }, { "path": "external/SPHEREPACK/shags.f", "content": "c\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc * *\nc * copyright (c) 1998 by UCAR *\nc * *\nc * University Corporation for Atmospheric Research *\nc * *\nc * all rights reserved *\nc * *\nc * SPHEREPACK version 3.2 *\nc * *\nc * A Package of Fortran77 Subroutines and Programs *\nc * *\nc * for Modeling Geophysical Processes *\nc * *\nc * by *\nc * *\nc * John Adams and Paul Swarztrauber *\nc * *\nc * of *\nc * *\nc * the National Center for Atmospheric Research *\nc * *\nc * Boulder, Colorado (80307) U.S.A. *\nc * *\nc * which is sponsored by *\nc * *\nc * the National Science Foundation *\nc * *\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc\nc\nc\nc ... file shags.f\nc\nc this file contains code and documentation for subroutines\nc shags and shagsi\nc\nc ... files which must be loaded with shags.f\nc\nc sphcom.f, hrfft.f, gaqd.f\nc\nc subroutine shags(nstrg,nstrab,noffsg,noffsab,\nc nlat,nlon,isym,nt,g,idg,jdg,a,b,mdab,ndab,\nc 1 mdabmax,ndabmax,\nc 1 wshags,lshags,work,lwork,ierror)\nc\nc subroutine shags performs the spherical harmonic analysis\nc on the array g and stores the result in the arrays a and b.\nc the analysis is performed on a gaussian grid in colatitude\nc and an equally spaced grid in longitude. the associated\nc legendre functions are stored rather than recomputed as they\nc are in subroutine shagc. the analysis is described below\nc at output parameters a,b.\nc\nc input parameters\nc\nc nstrg,nstrab strides of g,a,b\nc noffsg,noffsab offset of g,a,b -- must be between 0 and stride-1\nc Alternatively, when the two strides equal, you can set both\nc to -1 in which case the output will be computed for all\nc values of offset between 0 and stride-1.\nc\nc nlat the number of points in the gaussian colatitude grid on the\nc full sphere. these lie in the interval (0,pi) and are compu\nc in radians in theta(1),...,theta(nlat) by subroutine gaqd.\nc if nlat is odd the equator will be included as the grid poi\nc theta((nlat+1)/2). if nlat is even the equator will be\nc excluded as a grid point and will lie half way between\nc theta(nlat/2) and theta(nlat/2+1). nlat must be at least 3.\nc note: on the half sphere, the number of grid points in the\nc colatitudinal direction is nlat/2 if nlat is even or\nc (nlat+1)/2 if nlat is odd.\nc\nc nlon the number of distinct londitude points. nlon determines\nc the grid increment in longitude as 2*pi/nlon. for example\nc nlon = 72 for a five degree grid. nlon must be greater\nc than or equal to 4. the efficiency of the computation is\nc improved when nlon is a product of small prime numbers.\nc\nc NOTE: this is a modified version of spherepack. Changes from\nc the original version to the current one have only been\nc tested for isym==0. For this reason an error code will\nc be returned if isym!=0.\nc\nc isym = 0 no symmetries exist about the equator. the analysis\nc is performed on the entire sphere. i.e. on the\nc array g(i,j) for i=1,...,nlat and j=1,...,nlon.\nc (see description of g below)\nc\nc = 1 g is antisymmetric about the equator. the analysis\nc is performed on the northern hemisphere only. i.e.\nc if nlat is odd the analysis is performed on the\nc array g(i,j) for i=1,...,(nlat+1)/2 and j=1,...,nlon.\nc if nlat is even the analysis is performed on the\nc array g(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc\nc\nc = 2 g is symmetric about the equator. the analysis is\nc performed on the northern hemisphere only. i.e.\nc if nlat is odd the analysis is performed on the\nc array g(i,j) for i=1,...,(nlat+1)/2 and j=1,...,nlon.\nc if nlat is even the analysis is performed on the\nc array g(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc\nc nt the number of analyses. in the program that calls shags,\nc the arrays g,a and b can be three dimensional in which\nc case multiple analyses will be performed. the third\nc index is the analysis index which assumes the values\nc k=1,...,nt. for a single analysis set nt=1. the\nc discription of the remaining parameters is simplified\nc by assuming that nt=1 or that the arrays g,a and b\nc have only two dimensions.\nc\nc g a two or three dimensional array (see input parameter\nc nt) that contains the discrete function to be analyzed.\nc g(i,j) contains the value of the function at the gaussian\nc point theta(i) and longitude point phi(j) = (j-1)*2*pi/nlon\nc the index ranges are defined above at the input parameter\nc isym.\nc\nc idg the first dimension of the array g as it appears in the\nc program that calls shags. if isym equals zero then idg\nc must be at least nlat. if isym is nonzero then idg must\nc be at least nlat/2 if nlat is even or at least (nlat+1)/2\nc if nlat is odd.\nc\nc jdg the second dimension of the array g as it appears in the\nc program that calls shags. jdg must be at least nlon.\nc\nc mdab the first dimension of the arrays a and b as it appears\nc in the program that calls shags. if mdab is at least\nc min0((nlon+2)/2,nlat) if nlon is even or at least\nc min0((nlon+1)/2,nlat) if nlon is odd, the output will\nc contain all coefficients. Otherwise it will be truncated.\nc\nc ndab the second dimension of the arrays a and b as it appears\nc in the program that calls shags. If ndab is at least nlat,\nc the the output will contain all coefficients. Otherwise\nc it will be truncated.\nc\nc mdabmax, ndabmax -- will only compute coefficients a,b up to these\nc\nc wshags an array which must be initialized by subroutine shagsi.\nc once initialized, wshags can be used repeatedly by shags\nc as long as nlat and nlon remain unchanged. wshags must\nc not be altered between calls of shags.\nc\nc lshags the dimension of the array wshags as it appears in the\nc program that calls shags. define\nc\nc l1 = min0(nlat,(nlon+2)/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc then lshags must be at least\nc\nc nlat*(3*(l1+l2)-2)+(l1-1)*(l2*(2*nlat-l1)-3*l1)/2+nlon+15\nc\nc work a real work space which need not be saved\nc\nc\nc lwork the dimension of the array work as it appears in the\nc program that calls shags. define\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc\nc if isym is zero then lwork must be at least\nc\nc nlat*nlon*(nt+1)\nc\nc if isym is nonzero then lwork must be at least\nc\nc l2*nlon*(nt+1)\nc\nc **************************************************************\nc\nc output parameters\nc\nc a,b both a,b are two or three dimensional arrays (see input\nc parameter nt) that contain the spherical harmonic\nc coefficients in the representation of g(i,j) given in the\nc discription of subroutine shags. for isym=0, a(m,n) and\nc b(m,n) are given by the equations listed below. symmetric\nc versions are used when isym is greater than zero.\nc\nc definitions\nc\nc 1. the normalized associated legendre functions\nc\nc pbar(m,n,theta) = dsqrt((2*n+1)*factorial(n-m)/(2*factorial(n+m)))\nc *sin(theta)**m/(2**n*factorial(n)) times the\nc (n+m)th derivative of (x**2-1)**n with respect\nc to x=cos(theta).\nc\nc 2. the fourier transform of g(i,j).\nc\nc c(m,i) = 2/nlon times the sum from j=1 to j=nlon of\nc g(i,j)*cos((m-1)*(j-1)*2*pi/nlon)\nc (the first and last terms in this sum\nc are divided by 2)\nc\nc s(m,i) = 2/nlon times the sum from j=2 to j=nlon of\nc g(i,j)*sin((m-1)*(j-1)*2*pi/nlon)\nc\nc\nc 3. the gaussian points and weights on the sphere\nc (computed by subroutine gaqd).\nc\nc theta(1),...,theta(nlat) (gaussian pts in radians)\nc wts(1),...,wts(nlat) (corresponding gaussian weights)\nc\nc\nc 4. the maximum (plus one) longitudinal wave number\nc\nc mmax = min0(nlat,(nlon+2)/2) if nlon is even or\nc mmax = min0(nlat,(nlon+1)/2) if nlon is odd.\nc\nc\nc then for m=0,...,mmax-1 and n=m,...,nlat-1 the arrays a,b\nc are given by\nc\nc a(m+1,n+1) = the sum from i=1 to i=nlat of\nc c(m+1,i)*wts(i)*pbar(m,n,theta(i))\nc\nc b(m+1,n+1) = the sum from i=1 to nlat of\nc s(m+1,i)*wts(i)*pbar(m,n,theta(i))\nc\nc ierror = 0 no errors\nc = 1 error in the specification of nlat\nc = 2 error in the specification of nlon\nc = 3 error in the specification of isym\nc = 4 error in the specification of nt\nc = 5 error in the specification of idg\nc = 6 error in the specification of jdg\nc = 9 error in the specification of lshags\nc = 10 error in the specification of lwork\nc\nc\nc ****************************************************************\nc\nc subroutine shagsi(nlat,nlon,wshags,lshags,work,lwork,dwork,ldwork,\nc + ierror)\nc\nc subroutine shagsi initializes the array wshags which can then\nc be used repeatedly by subroutines shags. it precomputes\nc and stores in wshags quantities such as gaussian weights,\nc legendre polynomial coefficients, and fft trigonometric tables.\nc\nc input parameters\nc\nc nlat the number of points in the gaussian colatitude grid on the\nc full sphere. these lie in the interval (0,pi) and are compu\nc in radians in theta(1),...,theta(nlat) by subroutine gaqd.\nc if nlat is odd the equator will be included as the grid poi\nc theta((nlat+1)/2). if nlat is even the equator will be\nc excluded as a grid point and will lie half way between\nc theta(nlat/2) and theta(nlat/2+1). nlat must be at least 3.\nc note: on the half sphere, the number of grid points in the\nc colatitudinal direction is nlat/2 if nlat is even or\nc (nlat+1)/2 if nlat is odd.\nc\nc nlon the number of distinct londitude points. nlon determines\nc the grid increment in longitude as 2*pi/nlon. for example\nc nlon = 72 for a five degree grid. nlon must be greater\nc than or equal to 4. the efficiency of the computation is\nc improved when nlon is a product of small prime numbers.\nc\nc wshags an array which must be initialized by subroutine shagsi.\nc once initialized, wshags can be used repeatedly by shags\nc as long as nlat and nlon remain unchanged. wshags must\nc not be altered between calls of shags.\nc\nc lshags the dimension of the array wshags as it appears in the\nc program that calls shags. define\nc\nc l1 = min0(nlat,(nlon+2)/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc then lshags must be at least\nc\nc nlat*(3*(l1+l2)-2)+(l1-1)*(l2*(2*nlat-l1)-3*l1)/2+nlon+15\nc\nc work a real work space which need not be saved\nc\nc lwork the dimension of the array work as it appears in the\nc program that calls shagsi. lwork must be at least\nc 4*nlat*(nlat+2)+2 in the routine calling shagsi\nc\nc dwork a double precision work array that does not have to be saved.\nc\nc ldwork the length of dwork in the calling routine. ldwork must\nc be at least nlat*(nlat+4)\nc\nc output parameter\nc\nc wshags an array which must be initialized before calling shags or\nc once initialized, wshags can be used repeatedly by shags or\nc as long as nlat and nlon remain unchanged. wshags must not\nc altered between calls of shasc.\nc\nc ierror = 0 no errors\nc = 1 error in the specification of nlat\nc = 2 error in the specification of nlon\nc = 3 error in the specification of lshags\nc = 4 error in the specification of lwork\nc = 5 error in the specification of ldwork\nc = 6 failure in gaqd to compute gaussian points\nc (due to failure in eigenvalue routine)\nc\nc\nc ****************************************************************\n subroutine shags(nstrg,nstrab,noffsg,noffsab,\n 1 nlat,nlon,mode,nt,g,idg,jdg,a,b,mdab,ndab,\n 1 mdabmax,ndabmax,wshags,lshags,work,lwork,ierror)\n implicit double precision (a-h,o-z)\nc subroutine shags performs the spherical harmonic analysis on\nc a gaussian grid on the array(s) in g and returns the coefficients\nc in array(s) a,b. the necessary legendre polynomials are fully\nc stored in this version.\nc\n dimension g(nstrg,idg,jdg,1),a(nstrab,mdab,ndab,1),\n 1 b(nstrab,mdab,ndab,1),wshags(lshags),work(lwork)\nc check input parameters\n ierror = 1\n if (nlat.lt.3) return\n ierror = 2\n if (nlon.lt.4) return\n ierror = 3\nc if (mode.lt.0 .or.mode.gt.2) return\nc see note about isym above\n if (mode.ne.0) return\nc set m limit for pmn\n l = min0((nlon+2)/2,nlat)\nc set gaussian point nearest equator pointer\n late = (nlat+mod(nlat,2))/2\nc set number of grid points for analysis/synthesis\n lat = nlat\n if (mode.ne.0) lat = late\n ierror = 4\n if (nt.lt.1) return\n ierror = 5\n if (idg.lt.lat) return\n ierror = 6\n if (jdg.lt.nlon) return\nc note that there are no requirements on the minimum values of\nc mdab, ndab\nc ierror = 7\nc if(mdab .lt. l) return\nc ierror = 8\nc if(ndab .lt. nlat) return\n l1 = l\n l2 = late\n ierror = 9\nc check permanent work space length\nc\n lp= nlat*(3*(l1+l2)-2)+(l1-1)*(l2*(2*nlat-l1)-3*l1)/2+nlon+15\n if(lshags.lt.lp) return\n ng = 1;\n if(noffsg.eq.-1 .and. noffsab.eq.-1) ng=nstrg\n ierror = 10\nc check temporary work space length\n if (mode.eq.0 .and. lwork.lt.ng*nlat*nlon*(nt+1)) return\n if (mode.ne.0 .and. lwork.lt.ng*l2*nlon*(nt+1)) return\n ierror = 11\n if((noffsg.eq.-1) .neqv. (noffsab.eq.-1)) return\n if((noffsg.eq.-1) .and. (nstrg.ne.nstrab)) return\n if((noffsg.lt.-1) .or. (noffsg.ge.nstrg)) return\n if((noffsab.lt.-1) .or. (noffsab.ge.nstrab)) return\n ierror = 0\nc set starting address for gaussian wts ,fft values,\nc and fully stored legendre polys in wshags\n iwts = 1\n ifft = nlat+2*nlat*late+3*(l*(l-1)/2+(nlat-l)*(l-1))+1\n ipmn = ifft+nlon+15\nc set pointer for internal storage of g\n iw = ng*lat*nlon*nt+1\n call shags1(nstrg,nstrab,noffsg,noffsab,nlat,\n 1nlon,l,lat,mode,g,idg,jdg,nt,a,b,mdab,ndab,mdabmax,ndabmax,\n 1wshags(iwts),wshags(ifft),wshags(ipmn),late,work,ng,work(iw))\n return\n end\n\n subroutine shags1(nstrgs,nstrab,noffsg,noffsab,\n 1 nlat,nlon,l,lat,mode,gs,idg,jdg,nt,a,b,mdab,\n 1 ndab,mdabmax,ndabmax,wts,wfft,pmn,late,g,ng,work)\n implicit double precision (a-h,o-z)\n dimension gs(nstrgs,idg,jdg,nt),a(nstrab,mdab,ndab,nt),\n 1 b(nstrab,mdab,ndab,nt),g(ng,lat,nlon,nt)\n dimension wfft(1),pmn(late,1),wts(nlat),work(1)\n nlatmax=min0(nlat,ndabmax)\n if(noffsg.eq.-1) then\n ioffset0=2\n ioffset1=1+nstrgs\n else\n ioffset0=1\n ioffset1=1\n end if\nc set gs array internally in shags1\n do 100 k=1,nt\n do 100 j=1,nlon\n do 100 i=1,lat\n do 100 ioffset=ioffset0,ioffset1\n ig=ioffset-ioffset0+1\n ncgs=noffsg+ioffset\n g(ig,i,j,k) = gs(ncgs,i,j,k)\n 100 continue\n\nc do fourier transform\n do 101 k=1,nt\n call hrfftf(ng*lat,nlon,g(1,1,1,k),ng*lat,wfft,work)\n 101 continue\n\nc scale result\n sfn = 2.0d0/dfloat(nlon)\n do 102 k=1,nt\n do 102 j=1,nlon\n do 102 i=1,lat\n do 102 ig=1,ng\n g(ig,i,j,k) = sfn*g(ig,i,j,k)\n 102 continue\n\n\nc compute using gaussian quadrature\nc a(n,m) = s (ga(theta,m)*pnm(theta)*sin(theta)*dtheta)\nc b(n,m) = s (gb(theta,m)*pnm(theta)*sin(theta)*dtheta)\nc here ga,gb are the cos(phi),sin(phi) coefficients of\nc the fourier expansion of g(theta,phi) in phi. as a result\nc of the above fourier transform they are stored in array\nc g as follows:\nc for each theta(i) and k= l-1\nc ga(0),ga(1),gb(1),ga(2),gb(2),...,ga(k-1),gb(k-1),ga(k)\nc correspond to\nc g(i,1),g(i,2),g(i,3),g(i,4),g(i,5),...,g(i,2l-4),g(i,2l-3),g(i,2l-2)\nc whenever 2*l-2 = nlon exactly\nc initialize coefficients to zero\nc do 103 k=1,nt\nc do 103 np1=1,nlat\nc do 103 mp1=1,l\nc do 103 ioffset=ioffset0,ioffset1\nc ncab=noffsab+ioffset\nc a(ncab,mp1,np1,k) = 0.0d0\nc b(ncab,mp1,np1,k) = 0.0d0\nc 103 continue\n if(noffsab.eq.-1) then\n a=0.0d0\n b=0.0d0\n else\n a(1+noffsab,:,:,:)=0.0d0\n b(1+noffsab,:,:,:)=0.0d0\n end if\nc set mp1 limit on b(mp1) calculation\n lm1 = l\n if (nlon .eq. l+l-2) lm1 = l-1\n mp1max=min0(lm1,mdabmax)\n\n if (mode.eq.0) then\nc for full sphere (mode=0) and even/odd reduction:\nc overwrite g(i) with (g(i)+g(nlat-i+1))*wts(i)\nc overwrite g(nlat-i+1) with (g(i)-g(nlat-i+1))*wts(i)\n nl2 = nlat/2\n do 104 k=1,nt\n do 104 j=1,nlon\n do 105 i=1,nl2\n do 105 ig=1,ng\n is = nlat-i+1\n t1 = g(ig,i,j,k)\n t2 = g(ig,is,j,k)\n g(ig,i,j,k) = wts(i)*(t1+t2)\n g(ig,is,j,k) = wts(i)*(t1-t2)\n 105 continue\nc adjust equator if necessary(nlat odd)\n do 104 ig=1,ng\n if (mod(nlat,2).ne.0) g(ig,late,j,k) = wts(late)*g(ig,late,j,k)\n 104 continue\nc do 201 ioffset=ioffset0,ioffset1\nc ig=ioffset-ioffset0+1\nc ncab=noffsab+ioffset\nc set m = 0 coefficients first\n mp1 = 1\n m = 0\n mml1 = m*(2*nlat-m-1)/2\n do 106 k=1,nt\n do 106 i=1,late\n is = nlat-i+1\n do 107 np1=1,nlatmax,2\n do 107 ioffset=ioffset0,ioffset1\n ig=ioffset-ioffset0+1\n ncab=noffsab+ioffset\nc n even\n a(ncab,1,np1,k) = a(ncab,1,np1,k)\n 1 +g(ig,i,1,k)*pmn(i,mml1+np1)\n 107 continue\n if(nlatmax.ge.2) then\n do 108 np1=2,nlatmax,2\n do 108 ioffset=ioffset0,ioffset1\n ig=ioffset-ioffset0+1\n ncab=noffsab+ioffset\nc n odd\n a(ncab,1,np1,k) = a(ncab,1,np1,k)\n 1 +g(ig,is,1,k)*pmn(i,mml1+np1)\n 108 continue\n end if\n 106 continue\nc compute m.ge.1 coefficients next\n if(mp1max.ge.2) then\n do 109 mp1=2,mp1max\n m = mp1-1\n mml1 = m*(2*nlat-m-1)/2\n mp2 = mp1+1\n do 110 k=1,nt\n do 111 i=1,late\n is = nlat-i+1\nc n-m even\n if(nlatmax.ge.mp1) then\n do 112 np1=mp1,nlatmax,2\n do 112 ioffset=ioffset0,ioffset1\n ig=ioffset-ioffset0+1\n ncab=noffsab+ioffset\n a(ncab,mp1,np1,k) = a(ncab,mp1,np1,k)\n 1 +g(ig,i,2*m,k)*pmn(i,mml1+np1)\n b(ncab,mp1,np1,k) = b(ncab,mp1,np1,k)\n 1 +g(ig,i,2*m+1,k)*pmn(i,mml1+np1)\n 112 continue\n end if\nc n-m odd\n if(nlatmax.ge.mp2) then\n do 113 np1=mp2,nlatmax,2\n do 113 ioffset=ioffset0,ioffset1\n ig=ioffset-ioffset0+1\n ncab=noffsab+ioffset\n a(ncab,mp1,np1,k) = a(ncab,mp1,np1,k)\n 1 +g(ig,is,2*m,k)*pmn(i,mml1+np1)\n b(ncab,mp1,np1,k) = b(ncab,mp1,np1,k)\n 1 +g(ig,is,2*m+1,k)*pmn(i,mml1+np1)\n 113 continue\n end if\n 111 continue\n 110 continue\n 109 continue\n end if\n if (nlon .eq. l+l-2) then\n if(l.le.mdabmax) then\nc compute m=l-1, n=l-1,l,...,nlat-1 coefficients\n m = l-1\n mml1 = m*(2*nlat-m-1)/2\n do 114 k=1,nt\n do 114 i=1,late\n is = nlat-i+1\n if(nlatmax.ge.l) then\n do 124 np1=l,nlatmax,2\n mn = mml1+np1\n do 124 ioffset=ioffset0,ioffset1\n ig=ioffset-ioffset0+1\n ncab=noffsab+ioffset\n a(ncab,l,np1,k) = a(ncab,l,np1,k)+0.5d0*g(ig,i,nlon,k)*pmn(i,mn)\n 124 continue\n end if\nc n-m odd\n lp1 = l+1\n if(nlatmax.ge.lp1) then\n do 125 np1=lp1,nlatmax,2\n mn = mml1+np1\n do 125 ioffset=ioffset0,ioffset1\n ig=ioffset-ioffset0+1\n ncab=noffsab+ioffset\n a(ncab,l,np1,k) = a(ncab,l,np1,k)+0.5d0*g(ig,is,nlon,k)*pmn(i,mn)\n 125 continue\n end if\n 114 continue\n end if\n end if\n\nc 201 continue\n else\n\nc do 202 ioffset=ioffset0,ioffset1\nc ig=ioffset-ioffset0+1\nc ncab=noffsab+ioffset\nc half sphere\nc overwrite g(i) with wts(i)*(g(i)+g(i)) for i=1,...,nlate/2\n nl2 = nlat/2\n do 116 k=1,nt\n do 116 j=1,nlon\n do 115 i=1,nl2\n do 115 ig=1,ng\n g(ig,i,j,k) = wts(i)*(g(ig,i,j,k)+g(ig,i,j,k))\n 115 continue\nc adjust equator separately if a grid point\n do 116 ig=1,ng\n if (nl2.lt.late) g(ig,late,j,k) = wts(late)*g(ig,late,j,k)\n 116 continue\n\nc set m = 0 coefficients first\n mp1 = 1\n m = 0\n mml1 = m*(2*nlat-m-1)/2\n ms = 1\n if (mode.eq.1) ms = 2\n do 117 k=1,nt\n do 117 i=1,late\n do 117 np1=ms,nlatmax,2\n do 117 ioffset=ioffset0,ioffset1\n ig=ioffset-ioffset0+1\n ncab=noffsab+ioffset\n a(ncab,1,np1,k) = a(ncab,1,np1,k)\n 1 +g(ig,i,1,k)*pmn(i,mml1+np1)\n 117 continue\n\nc compute m.ge.1 coefficients next\n if(mp1max.ge.2) then\n do 118 mp1=2,mp1max\n m = mp1-1\n mml1 = m*(2*nlat-m-1)/2\n ms = mp1\n if (mode.eq.1) ms = mp1+1\n if(nlatmax.ge.ms) then\n do 119 k=1,nt\n do 119 i=1,late\n do 119 np1=ms,nlatmax,2\n do 119 ioffset=ioffset0,ioffset1\n ig=ioffset-ioffset0+1\n ncab=noffsab+ioffset\n a(ncab,mp1,np1,k) = a(ncab,mp1,np1,k)\n 1 +g(ig,i,2*m,k)*pmn(i,mml1+np1)\n b(ncab,mp1,np1,k) = b(ncab,mp1,np1,k)\n 1 +g(ig,i,2*m+1,k)*pmn(i,mml1+np1)\n 119 continue\n end if\n 118 continue\n end if\n\n if (nlon.eq.l+l-2 .and. l.le.mdabmax) then\nc compute n=m=l-1 coefficients last\n m = l-1\n mml1 = m*(2*nlat-m-1)/2\nc set starting n for mode even\n ns = l\nc set starting n for mode odd\n if (mode.eq.1) ns = l+1\n if(nlatmax.ge.ns) then\n do 120 k=1,nt\n do 120 i=1,late\n do 120 np1=ns,nlatmax,2\n mn = mml1+np1\n do 120 ioffset=ioffset0,ioffset1\n ig=ioffset-ioffset0+1\n ncab=noffsab+ioffset\n a(ncab,l,np1,k) = a(ncab,l,np1,k)+0.5d0*g(ig,i,nlon,k)*pmn(i,mn)\n 120 continue\n end if\n end if\n\nc 202 continue\n end if\n\n return\n end\n subroutine shagsi(nlat,nlon,wshags,lshags,work,lwork,dwork,ldwork,\n + ierror)\n implicit double precision (a-h,o-z)\nc\nc this subroutine must be called before calling shags or shsgs with\nc fixed nlat,nlon. it precomputes the gaussian weights, points\nc and all necessary legendre polys and stores them in wshags.\nc these quantities must be preserved when calling shags or shsgs\nc repeatedly with fixed nlat,nlon. dwork must be of length at\nc least nlat*(nlat+4) in the routine calling shagsi. This is\nc not checked. undetectable errors will result if dwork is\nc smaller than nlat*(nlat+4).\nc\n dimension wshags(lshags),work(lwork)\n double precision dwork(ldwork)\n ierror = 1\n if (nlat.lt.3) return\n ierror = 2\n if (nlon.lt.4) return\nc set triangular truncation limit for spherical harmonic basis\n l = min0((nlon+2)/2,nlat)\nc set equator or nearest point (if excluded) pointer\n late = (nlat+1)/2\n l1 = l\n l2 = late\nc check permanent work space length\n ierror = 3\n lp=nlat*(3*(l1+l2)-2)+(l1-1)*(l2*(2*nlat-l1)-3*l1)/2+nlon+15\n if(lshags.lt.lp) return\n ierror = 4\nc check temporary work space\n if (lwork.lt.4*nlat*(nlat+2)+2) return\n ierror = 5\nc check double precision temporary space\n if (ldwork .lt. nlat*(nlat+4)) return\n ierror = 0\nc set preliminary quantites needed to compute and store legendre polys\n ldw = nlat*(nlat+4)\n call shagsp(nlat,nlon,wshags,lshags,dwork,ldwork,ierror)\n if (ierror.ne.0) return\nc set legendre poly pointer in wshags\n ipmnf = nlat+2*nlat*late+3*(l*(l-1)/2+(nlat-l)*(l-1))+nlon+16\n call shagss1(nlat,l,late,wshags,work,wshags(ipmnf))\n return\n end\n subroutine shagss1(nlat,l,late,w,pmn,pmnf)\n implicit double precision (a-h,o-z)\n dimension w(1),pmn(nlat,late,3),pmnf(late,1)\nc compute and store legendre polys for i=1,...,late,m=0,...,l-1\nc and n=m,...,l-1\n do i=1,nlat\n\tdo j=1,late\n\t do k=1,3\n\t pmn(i,j,k) = 0.0d0\n\t end do\n\tend do\n end do\n km0=1\n km1=2\n km2=3\n do 100 mp1=1,l\n m = mp1-1\n mml1 = m*(2*nlat-m-1)/2\nc compute pmn for n=m,...,nlat-1 and i=1,...,(l+1)/2\n mode = 0\n call legin(mode,l,nlat,m,w,pmn,km,km0,km1,km2)\nc store above in pmnf\n do 101 np1=mp1,nlat\n mn = mml1+np1\n do 102 i=1,late\n pmnf(i,mn) = pmn(np1,i,km)\n 102 continue\n 101 continue\n 100 continue\n return\n end\n subroutine shagsp(nlat,nlon,wshags,lshags,dwork,ldwork,ierror)\n implicit double precision (a-h,o-z)\n dimension wshags(lshags)\n double precision dwork(ldwork)\n ierror = 1\n if (nlat.lt.3) return\n ierror = 2\n if (nlon.lt.4) return\nc set triangular truncation limit for spherical harmonic basis\n l = min0((nlon+2)/2,nlat)\nc set equator or nearest point (if excluded) pointer\n late = (nlat+mod(nlat,2))/2\n l1 = l\n l2 = late\n ierror = 3\nc check permanent work space length\n if (lshags .lt. nlat*(2*l2+3*l1-2)+3*l1*(1-l1)/2+nlon+15)return\n ierror = 4\nc if (lwork.lt.4*nlat*(nlat+2)+2) return\n if (ldwork.lt.nlat*(nlat+4))return\n ierror = 0\nc set pointers\n i1 = 1\n i2 = i1+nlat\n i3 = i2+nlat*late\n i4 = i3+nlat*late\n i5 = i4+l*(l-1)/2 +(nlat-l)*(l-1)\n i6 = i5+l*(l-1)/2 +(nlat-l)*(l-1)\n i7 = i6+l*(l-1)/2 +(nlat-l)*(l-1)\nc set indices in temp work for double precision gaussian wts and pts\n idth = 1\nc idwts = idth+2*nlat\nc iw = idwts+2*nlat\n idwts = idth+nlat\n iw = idwts+nlat\n call shagsp1(nlat,nlon,l,late,wshags(i1),wshags(i2),wshags(i3),\n 1wshags(i4),wshags(i5),wshags(i6),wshags(i7),dwork(idth),\n 2dwork(idwts),dwork(iw),ierror)\n if (ierror.ne.0) ierror = 6\n return\n end\n\n subroutine shagsp1(nlat,nlon,l,late,wts,p0n,p1n,abel,bbel,cbel,\n + wfft,dtheta,dwts,work,ier)\n implicit double precision (a-h,o-z)\n dimension wts(nlat),p0n(nlat,late),p1n(nlat,late),abel(1),bbel(1),\n 1 cbel(1),wfft(1),dtheta(nlat),dwts(nlat)\n double precision pb,dtheta,dwts,work(*)\n indx(m,n) = (n-1)*(n-2)/2+m-1\n imndx(m,n) = l*(l-1)/2+(n-l-1)*(l-1)+m-1\n call hrffti(nlon,wfft)\n\nc compute double precision gaussian points and weights\nc lw = 4*nlat*(nlat+2)\n lw = nlat*(nlat+2)\n call gaqd(nlat,dtheta,dwts,work,lw,ier)\n if (ier.ne.0) return\n\nc store gaussian weights single precision to save computation\nc in inner loops in analysis\n do 100 i=1,nlat\n wts(i) = dwts(i)\n 100 continue\nc initialize p0n,p1n using double precision dnlfk,dnlft\n do 101 np1=1,nlat\n do 101 i=1,late\n p0n(np1,i) = 0.0d0\n p1n(np1,i) = 0.0d0\n 101 continue\nc compute m=n=0 legendre polynomials for all theta(i)\n np1 = 1\n n = 0\n m = 0\n call dnlfk(m,n,work)\n do 103 i=1,late\n call dnlft(m,n,dtheta(i),work,pb)\n p0n(1,i) = pb\n 103 continue\nc compute p0n,p1n for all theta(i) when n.gt.0\n do 104 np1=2,nlat\n n = np1-1\n m = 0\n call dnlfk(m,n,work)\n do 105 i=1,late\n call dnlft(m,n,dtheta(i),work,pb)\n p0n(np1,i) = pb\n 105 continue\nc compute m=1 legendre polynomials for all n and theta(i)\n m = 1\n call dnlfk(m,n,work)\n do 106 i=1,late\n call dnlft(m,n,dtheta(i),work,pb)\n p1n(np1,i) = pb\n 106 continue\n 104 continue\nc\nc compute and store swarztrauber recursion coefficients\nc for 2.le.m.le.n and 2.le.n.le.nlat in abel,bbel,cbel\n do 107 n=2,nlat\n mlim = min0(n,l)\n do 107 m=2,mlim\n imn = indx(m,n)\n if (n.ge.l) imn = imndx(m,n)\n abel(imn)=dsqrt(dfloat((2*n+1)*(m+n-2)*(m+n-3))/\n 1 dfloat(((2*n-3)*(m+n-1)*(m+n))))\n bbel(imn)=dsqrt(dfloat((2*n+1)*(n-m-1)*(n-m))/\n 1 dfloat(((2*n-3)*(m+n-1)*(m+n))))\n cbel(imn)=dsqrt(dfloat((n-m+1)*(n-m+2))/\n 1 dfloat(((n+m-1)*(n+m))))\n 107 continue\n return\n end\n" }, { "path": "external/SPHEREPACK/shsgs.f", "content": "c\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc * *\nc * copyright (c) 1998 by UCAR *\nc * *\nc * University Corporation for Atmospheric Research *\nc * *\nc * all rights reserved *\nc * *\nc * SPHEREPACK version 3.2 *\nc * *\nc * A Package of Fortran77 Subroutines and Programs *\nc * *\nc * for Modeling Geophysical Processes *\nc * *\nc * by *\nc * *\nc * John Adams and Paul Swarztrauber *\nc * *\nc * of *\nc * *\nc * the National Center for Atmospheric Research *\nc * *\nc * Boulder, Colorado (80307) U.S.A. *\nc * *\nc * which is sponsored by *\nc * *\nc * the National Science Foundation *\nc * *\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc\nc\nc\nc ... file shsgs.f\nc\nc this file contains code and documentation for subroutines\nc shsgs and shsgsi\nc\nc ... files which must be loaded with shsgs.f\nc\nc sphcom.f, hrfft.f, gaqd.f\nc\nc subroutine shsgs(nstrg,nstrab,noffsg,noffsab,\nc nlat,nlon,isym,nt,g,idg,jdg,a,b,mdab,ndab,\nc 1 mdabmax,ndabmax,\nc 1 wshsgs,lshsgs,work,lwork,ierror)\nc\nc subroutine shsgs performs the spherical harmonic synthesis\nc on the arrays a and b and stores the result in the array g.\nc the synthesis is performed on an equally spaced longitude grid\nc and a gaussian colatitude grid. the associated legendre functions\nc are stored rather than recomputed as they are in subroutine\nc shsgc. the synthesis is described below at output parameter\nc g.\nc\nc\nc input parameters\nc\nc nstrg,nstrab stride in g,a,b\nc noffsg,noffsab offset in g,a,b -- must be between 0 and stride-1\nc Alternatively, when the two strides equal, you can set both\nc to -1 in which case the output will be computed for all\nc values of offset between 0 and stride-1.\nc\nc nlat the number of points in the gaussian colatitude grid on the\nc full sphere. these lie in the interval (0,pi) and are compu\nc in radians in theta(1),...,theta(nlat) by subroutine gaqd.\nc if nlat is odd the equator will be included as the grid poi\nc theta((nlat+1)/2). if nlat is even the equator will be\nc excluded as a grid point and will lie half way between\nc theta(nlat/2) and theta(nlat/2+1). nlat must be at least 3.\nc note: on the half sphere, the number of grid points in the\nc colatitudinal direction is nlat/2 if nlat is even or\nc (nlat+1)/2 if nlat is odd.\nc\nc nlon the number of distinct londitude points. nlon determines\nc the grid increment in longitude as 2*pi/nlon. for example\nc nlon = 72 for a five degree grid. nlon must be greater\nc than or equal to 4. the efficiency of the computation is\nc improved when nlon is a product of small prime numbers.\nc\nc NOTE: this is a modified version of spherepack. Changes from\nc the original version to the current one have only been\nc tested for isym==0. For this reason an error code will\nc be returned if isym!=0.\nc\nc isym = 0 no symmetries exist about the equator. the synthesis\nc is performed on the entire sphere. i.e. on the\nc array g(i,j) for i=1,...,nlat and j=1,...,nlon.\nc (see description of g below)\nc\nc = 1 g is antisymmetric about the equator. the synthesis\nc is performed on the northern hemisphere only. i.e.\nc if nlat is odd the synthesis is performed on the\nc array g(i,j) for i=1,...,(nlat+1)/2 and j=1,...,nlon.\nc if nlat is even the synthesis is performed on the\nc array g(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc\nc\nc = 2 g is symmetric about the equator. the synthesis is\nc performed on the northern hemisphere only. i.e.\nc if nlat is odd the synthesis is performed on the\nc array g(i,j) for i=1,...,(nlat+1)/2 and j=1,...,nlon.\nc if nlat is even the synthesis is performed on the\nc array g(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc\nc nt the number of syntheses. in the program that calls shsgs,\nc the arrays g,a and b can be three dimensional in which\nc case multiple synthesis will be performed. the third\nc index is the synthesis index which assumes the values\nc k=1,...,nt. for a single synthesis set nt=1. the\nc discription of the remaining parameters is simplified\nc by assuming that nt=1 or that the arrays g,a and b\nc have only two dimensions.\nc\nc idg the first dimension of the array g as it appears in the\nc program that calls shagc. if isym equals zero then idg\nc must be at least nlat. if isym is nonzero then idg must\nc be at least nlat/2 if nlat is even or at least (nlat+1)/2\nc if nlat is odd.\nc\nc jdg the second dimension of the array g as it appears in the\nc program that calls shagc. jdg must be at least nlon.\nc\nc a,b two or three dimensional arrays (see the input parameter\nc nt) that contain the coefficients in the spherical harmonic\nc expansion of g(i,j) given below at the definition of the\nc output parameter g. a(m,n) and b(m,n) are defined for\nc indices m=1,...,mmax and n=m,...,nlat where mmax is the\nc maximum (plus one) longitudinal wave number given by\nc mmax = min0(nlat,(nlon+2)/2) if nlon is even or\nc mmax = min0(nlat,(nlon+1)/2) if nlon is odd.\nc\nc mdab the first dimension of the arrays a and b as it appears\nc in the program that calls shsgs. mdab must be at least\nc min0((nlon+2)/2,nlat) if nlon is even or at least\nc min0((nlon+1)/2,nlat) if nlon is odd IF IT CONTAINS\nc ALL COEFFICIENTS. If smaller, the higher coefficients\nc are ignored (i.e., treated as if they were zero).\nc\nc ndab the second dimension of the arrays a and b as it appears\nc in the program that calls shsgs. ndab must be at least nlat\nc IF IT CONTAINS ALL COEFFICIENTS. Otherwise the higher coefs\nc are ignored (i.e., treated as if they were zero).\nc\nc mdabmax, ndabmax -- will ignore coefficients a,b with index higher\nc than these\nc\nc wshsgs an array which must be initialized by subroutine shsgsi.\nc once initialized, wshsgs can be used repeatedly by shsgs\nc as long as nlat and nlon remain unchanged. wshsgs must\nc not be altered between calls of shsgs.\nc\nc lshsgs the dimension of the array wshsgs as it appears in the\nc program that calls shsgs. define\nc\nc l1 = min0(nlat,(nlon+2)/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc then lshsgs must be at least\nc\nc nlat*(3*(l1+l2)-2)+(l1-1)*(l2*(2*nlat-l1)-3*l1)/2+nlon+15\nc\nc\nc lwork the dimension of the array work as it appears in the\nc program that calls shsgs. define\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc\nc if isym is zero then lwork must be at least\nc\nc nlat*nlon*(nt+1)\nc\nc if isym is nonzero then lwork must be at least\nc\nc l2*nlon*(nt+1)\nc\nc\nc **************************************************************\nc\nc output parameters\nc\nc g a two or three dimensional array (see input parameter nt)\nc that contains the discrete function which is synthesized.\nc g(i,j) contains the value of the function at the gaussian\nc colatitude point theta(i) and longitude point\nc phi(j) = (j-1)*2*pi/nlon. the index ranges are defined\nc above at the input parameter isym. for isym=0, g(i,j)\nc is given by the the equations listed below. symmetric\nc versions are used when isym is greater than zero.\nc\nc the normalized associated legendre functions are given by\nc\nc pbar(m,n,theta) = dsqrt((2*n+1)*factorial(n-m)/(2*factorial(n+m)))\nc *sin(theta)**m/(2**n*factorial(n)) times the\nc (n+m)th derivative of (x**2-1)**n with respect\nc to x=cos(theta)\nc\nc define the maximum (plus one) longitudinal wave number\nc as mmax = min0(nlat,(nlon+2)/2) if nlon is even or\nc mmax = min0(nlat,(nlon+1)/2) if nlon is odd.\nc\nc then g(i,j) = the sum from n=0 to n=nlat-1 of\nc\nc .5*pbar(0,n,theta(i))*a(1,n+1)\nc\nc plus the sum from m=1 to m=mmax-1 of\nc\nc the sum from n=m to n=nlat-1 of\nc\nc pbar(m,n,theta(i))*(a(m+1,n+1)*cos(m*phi(j))\nc -b(m+1,n+1)*sin(m*phi(j)))\nc\nc\nc ierror = 0 no errors\nc = 1 error in the specification of nlat\nc = 2 error in the specification of nlon\nc = 3 error in the specification of isym\nc = 4 error in the specification of nt\nc = 5 error in the specification of idg\nc = 6 error in the specification of jdg\nc = 9 error in the specification of lshsgs\nc = 10 error in the specification of lwork\nc\nc\nc ****************************************************************\nc\nc subroutine shsgsi(nlat,nlon,wshsgs,lshsgs,work,lwork,dwork,ldwork,\nc + ierror)\nc\nc subroutine shsgsi initializes the array wshsgs which can then\nc be used repeatedly by subroutines shsgs. it precomputes\nc and stores in wshsgs quantities such as gaussian weights,\nc legendre polynomial coefficients, and fft trigonometric tables.\nc\nc input parameters\nc\nc nlat the number of points in the gaussian colatitude grid on the\nc full sphere. these lie in the interval (0,pi) and are compu\nc in radians in theta(1),...,theta(nlat) by subroutine gaqd.\nc if nlat is odd the equator will be included as the grid poi\nc theta((nlat+1)/2). if nlat is even the equator will be\nc excluded as a grid point and will lie half way between\nc theta(nlat/2) and theta(nlat/2+1). nlat must be at least 3.\nc note: on the half sphere, the number of grid points in the\nc colatitudinal direction is nlat/2 if nlat is even or\nc (nlat+1)/2 if nlat is odd.\nc\nc nlon the number of distinct londitude points. nlon determines\nc the grid increment in longitude as 2*pi/nlon. for example\nc nlon = 72 for a five degree grid. nlon must be greater\nc than or equal to 4. the efficiency of the computation is\nc improved when nlon is a product of small prime numbers.\nc\nc wshsgs an array which must be initialized by subroutine shsgsi.\nc once initialized, wshsgs can be used repeatedly by shsgs\nc as long as nlat and nlon remain unchanged. wshsgs must\nc not be altered between calls of shsgs.\nc\nc lshsgs the dimension of the array wshsgs as it appears in the\nc program that calls shsgs. define\nc\nc l1 = min0(nlat,(nlon+2)/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc then lshsgs must be at least\nc\nc nlat*(3*(l1+l2)-2)+(l1-1)*(l2*(2*nlat-l1)-3*l1)/2+nlon+15\nc\nc work a real work space which need not be saved\nc\nc lwork the dimension of the array work as it appears in the\nc program that calls shsgsi. lwork must be at least\nc 4*nlat*(nlat+2)+2 in the routine calling shsgsi\nc\nc dwork a double precision work array that does not have to be saved.\nc\nc ldwork the length of dwork in the calling routine. ldwork must\nc be at least nlat*(nlat+4)\nc\nc output parameter\nc\nc wshsgs an array which must be initialized before calling shsgs or\nc once initialized, wshsgs can be used repeatedly by shsgs or\nc as long as nlat and nlon remain unchanged. wshsgs must not\nc altered between calls of shsgs.\nc\nc ierror = 0 no errors\nc = 1 error in the specification of nlat\nc = 2 error in the specification of nlon\nc = 3 error in the specification of lshsgs\nc = 4 error in the specification of lwork\nc = 5 error in the specification of ldwork\nc = 5 failure in gaqd to compute gaussian points\nc (due to failure in eigenvalue routine)\nc\nc\n subroutine shsgs(nstrg,nstrab,noffsg,noffsab,\n 1 nlat,nlon,mode,nt,g,idg,jdg,a,b,mdab,ndab,\n 1 mdabmax,ndabmax,wshsgs,lshsgs,work,lwork,ierror)\n implicit double precision (a-h,o-z)\n dimension g(nstrg,idg,jdg,1),a(nstrab,mdab,ndab,1),\n 1 b(nstrab,mdab,ndab,1),wshsgs(lshsgs),work(lwork)\nc check input parameters\n ierror = 1\n if (nlat.lt.3) return\n ierror = 2\n if (nlon.lt.4) return\n ierror = 3\nc if (mode.lt.0 .or.mode.gt.2) return\nc see note about isym above\n if (mode.ne.0) return\n ierror = 4\n if (nt.lt.1) return\nc set limit on m subscript\n l = min0((nlon+2)/2,nlat)\nc set gaussian point nearest equator pointer\n late = (nlat+mod(nlat,2))/2\nc set number of grid points for analysis/synthesis\n lat = nlat\n if (mode.ne.0) lat = late\n ierror = 5\n if (idg.lt.lat) return\n ierror = 6\n if (jdg.lt.nlon) return\nc ierror = 7\nc if(mdab .lt. l) return\nc ierror = 8\nc if(ndab .lt. nlat) return\n l1 = l\n l2 = late\n ierror = 9\nc check permanent work space length\n lp=nlat*(3*(l1+l2)-2)+(l1-1)*(l2*(2*nlat-l1)-3*l1)/2+nlon+15\n if(lshsgs.lt.lp) return\nc check temporary work space length\n ng = 1;\n if(noffsg.eq.-1 .and. noffsab.eq.-1) ng=nstrg\n ierror = 10\n if (mode.eq.0 .and. lwork.lt.ng*nlat*nlon*(nt+1)) return\n if (mode.ne.0 .and. lwork.lt.ng*l2*nlon*(nt+1)) return\n ierror = 11\n if((noffsg.eq.-1) .neqv. (noffsab.eq.-1)) return\n if((noffsg.eq.-1) .and. (nstrg.ne.nstrab)) return\n if((noffsg.lt.-1) .or. (noffsg.ge.nstrg)) return\n if((noffsab.lt.-1) .or. (noffsab.ge.nstrab)) return\n ierror = 0\nc starting address for fft values and legendre polys in wshsgs\n ifft = nlat+2*nlat*late+3*(l*(l-1)/2+(nlat-l)*(l-1))+1\n ipmn = ifft+nlon+15\nc set pointer for internal storage of g\n iw = ng*lat*nlon*nt+1\n call shsgs1(nstrg,nstrab,noffsg,noffsab,\n 1 nlat,nlon,l,lat,mode,g,idg,jdg,nt,a,b,mdab,ndab,\n 1 mdabmax,ndabmax,\n 1 wshsgs(ifft),wshsgs(ipmn),late,work,ng,work(iw))\n return\n end\n\n subroutine shsgs1(nstrgs,nstrab,noffsgs,noffsab,\n 1 nlat,nlon,l,lat,mode,gs,idg,jdg,nt,a,b,mdab,\n 1 ndab,mdabmax,ndabmax,wfft,pmn,late,g,ng,work)\n implicit double precision (a-h,o-z)\n dimension gs(nstrgs,idg,jdg,nt),\n 1 a(nstrab,mdab,ndab,nt),b(nstrab,mdab,ndab,nt)\n dimension wfft(1),pmn(late,1),g(ng,lat,nlon,nt),work(1)\n nlatmax=min0(nlat,ndabmax)\n\nc ncgs=1+noffsgs\nc ncab=1+noffsab\n\n if(noffsgs.eq.-1) then\n ioffset0=2\n ioffset1=nstrgs+1\n else\n ioffset0=1\n ioffset1=1\n end if\n\n\nc reconstruct fourier coefficients in g on gaussian grid\nc using coefficients in a,b\n\nc initialize to zero\n do 100 k=1,nt\n do 100 j=1,nlon\n do 100 i=1,lat\n do 100 ig=1,ng\n g(ig,i,j,k) = 0.0d0\n 100 continue\n\n lm1 = l\n if (nlon .eq. l+l-2) lm1 = l-1\n\n mp1max = min0(lm1,mdabmax)\n\n if (mode.eq.0) then\n\nc do 201 ioffset=ioffset0,ioffset1\nc ncab=noffsab+ioffset\nc ig=ioffset-ioffset0+1\n\nc set first column in g\n m = 0\n mml1 = m*(2*nlat-m-1)/2\n do 101 k=1,nt\nc n even\n do 102 np1=1,nlatmax,2\n mn = mml1+np1\n do 102 i=1,late\n do 102 ioffset=ioffset0,ioffset1\n ncab=noffsab+ioffset\n ig=ioffset-ioffset0+1\n g(ig,i,1,k) = g(ig,i,1,k)+a(ncab,1,np1,k)*pmn(i,mn)\n 102 continue\nc n odd\n nl2 = nlat/2\n if(nlatmax.ge.2) then\n do 103 np1=2,nlatmax,2\n mn = mml1+np1\n do 103 i=1,nl2\n is = nlat-i+1\n do 103 ioffset=ioffset0,ioffset1\n ncab=noffsab+ioffset\n ig=ioffset-ioffset0+1\n g(ig,is,1,k) = g(ig,is,1,k)+a(ncab,1,np1,k)*pmn(i,mn)\n 103 continue\n end if\n 101 continue\n\nc restore m=0 coefficients from odd/even\n do 112 k=1,nt\n do 112 i=1,nl2\n do 112 ig=1,ng\n is = nlat-i+1\n t1 = g(ig,i,1,k)\n t3 = g(ig,is,1,k)\n g(ig,i,1,k) = t1+t3\n g(ig,is,1,k) = t1-t3\n 112 continue\n\nc sweep interior columns of g\n if(mp1max.ge.2) then\n do 104 mp1=2,mp1max\n m = mp1-1\n mml1 = m*(2*nlat-m-1)/2\n mp2 = m+2\n do 105 k=1,nt\nc for n-m even store (g(i,p,k)+g(nlat-i+1,p,k))/2 in g(i,p,k) p=2*m,2*m+1\nc for i=1,...,late\n if(nlatmax.ge.mp1) then\n do 106 np1=mp1,nlatmax,2\n mn = mml1+np1\n do 107 i=1,late\n do 107 ioffset=ioffset0,ioffset1\n ncab=noffsab+ioffset\n ig=ioffset-ioffset0+1\n g(ig,i,2*m,k) = g(ig,i,2*m,k)+a(ncab,mp1,np1,k)*pmn(i,mn)\n g(ig,i,2*m+1,k) = g(ig,i,2*m+1,k)+b(ncab,mp1,np1,k)*pmn(i,mn)\n 107 continue\n 106 continue\n end if\n\nc for n-m odd store g(i,p,k)-g(nlat-i+1,p,k) in g(nlat-i+1,p,k)\nc for i=1,...,nlat/2 (p=2*m,p=2*m+1)\n if(nlatmax.ge.mp2) then\n do 108 np1=mp2,nlatmax,2\n mn = mml1+np1\n do 109 i=1,nl2\n is = nlat-i+1\n do 109 ioffset=ioffset0,ioffset1\n ncab=noffsab+ioffset\n ig=ioffset-ioffset0+1\n g(ig,is,2*m,k) = g(ig,is,2*m,k)+a(ncab,mp1,np1,k)*pmn(i,mn)\n g(ig,is,2*m+1,k) = g(ig,is,2*m+1,k)+b(ncab,mp1,np1,k)*pmn(i,mn)\n 109 continue\n 108 continue\n end if\n\nc now set fourier coefficients using even-odd reduction above\n do 110 i=1,nl2\n do 110 ig=1,ng\n is = nlat-i+1\n t1 = g(ig,i,2*m,k)\n t2 = g(ig,i,2*m+1,k)\n t3 = g(ig,is,2*m,k)\n t4 = g(ig,is,2*m+1,k)\n g(ig,i,2*m,k) = t1+t3\n g(ig,i,2*m+1,k) = t2+t4\n g(ig,is,2*m,k) = t1-t3\n g(ig,is,2*m+1,k) = t2-t4\n 110 continue\n\n 105 continue\n 104 continue\n end if\n\nc set last column (using a only) if necessary\n if (nlon.eq. l+l-2) then\n if (l.le.mdabmax) then\n m = l-1\n mml1 = m*(2*nlat-m-1)/2\n do 111 k=1,nt\nc n-m even\n if(nlatmax.ge.l) then\n do 131 np1=l,nlatmax,2\n mn = mml1+np1\n do 131 i=1,late\n do 131 ioffset=ioffset0,ioffset1\n ncab=noffsab+ioffset\n ig=ioffset-ioffset0+1\n g(ig,i,nlon,k) = g(ig,i,nlon,k)+2.0d0*a(ncab,l,np1,k)*pmn(i,mn)\n\n 131 continue\n end if\n lp1 = l+1\nc n-m odd\n if(nlatmax.ge.lp1) then\n do 132 np1=lp1,nlatmax,2\n mn = mml1+np1\n do 132 i=1,nl2\n is = nlat-i+1\n do 132 ioffset=ioffset0,ioffset1\n ncab=noffsab+ioffset\n ig=ioffset-ioffset0+1\n g(ig,is,nlon,k) = g(ig,is,nlon,k)+2.0d0*a(ncab,l,np1,k)*pmn(i,mn)\n 132 continue\n end if\n do 133 i=1,nl2\n do 133 ig=1,ng\n is = nlat-i+1\n t1 = g(ig,i,nlon,k)\n t3 = g(ig,is,nlon,k)\n g(ig,i,nlon,k)= t1+t3\n g(ig,is,nlon,k)= t1-t3\n 133 continue\n 111 continue\n end if\n end if\n 201 continue\n\n else\nc half sphere (mode.ne.0)\n\nc set first column in g\n m = 0\n mml1 = m*(2*nlat-m-1)/2\n meo = 1\n if (mode.eq.1) meo = 2\n ms = m+meo\n if(nlatmax.ge.ms) then\n do 113 k=1,nt\n do 113 np1=ms,nlatmax,2\n mn = mml1+np1\n do 113 i=1,late\n do 113 ioffset=ioffset0,ioffset1\n ncab=noffsab+ioffset\n ig=ioffset-ioffset0+1\n g(ig,i,1,k) = g(ig,i,1,k)+a(ncab,1,np1,k)*pmn(i,mn)\n 113 continue\n end if\n\nc sweep interior columns of g\n\n if(mp1max.ge.2) then\n do 114 mp1=2,mp1max\n m = mp1-1\n mml1 = m*(2*nlat-m-1)/2\n ms = m+meo\n if(nlatmax.ge.ms) then\n do 115 k=1,nt\n do 115 np1=ms,nlatmax,2\n mn = mml1+np1\n do 115 i=1,late\n do 115 ioffset=ioffset0,ioffset1\n ncab=noffsab+ioffset\n ig=ioffset-ioffset0+1\n g(ig,i,2*m,k) = g(ig,i,2*m,k)+a(ncab,mp1,np1,k)*pmn(i,mn)\n g(ig,i,2*m+1,k) = g(ig,i,2*m+1,k)+b(ncab,mp1,np1,k)*pmn(i,mn)\n 115 continue\n end if\n 114 continue\n end if\n\n if (nlon.eq.l+l-2 .and. l.le.mdabmax) then\nc set last column\n m = l-1\n mml1 = m*(2*nlat-m-1)/2\n ns = l\n if (mode.eq.1) ns = l+1\n if(nlatmax.ge.ns) then\n do 116 k=1,nt\n do 116 np1=ns,nlatmax,2\n mn = mml1+np1\n do 116 i=1,late\n do 116 ioffset=ioffset0,ioffset1\n ncab=noffsab+ioffset\n ig=ioffset-ioffset0+1\n g(ig,i,nlon,k) = g(ig,i,nlon,k)+2.0d0*a(ncab,l,np1,k)*pmn(i,mn)\n 116 continue\n end if\n end if\n 202 continue\n\n end if\n\nc do inverse fourier transform\n do 120 k=1,nt\n call hrfftb(ng*lat,nlon,g(1,1,1,k),ng*lat,wfft,work)\n 120 continue\nc scale output in gs\n do 122 k=1,nt\n do 122 j=1,nlon\n do 122 i=1,lat\n do 122 ioffset=ioffset0,ioffset1\n ncgs=noffsgs+ioffset\n ig=ioffset-ioffset0+1\n gs(ncgs,i,j,k) = 0.5d0*g(ig,i,j,k)\n 122 continue\n\n return\n end\n subroutine shsgsi(nlat,nlon,wshsgs,lshsgs,work,lwork,dwork,ldwork,\n + ierror)\n implicit double precision (a-h,o-z)\nc\nc this subroutine must be called before calling shags or shsgs with\nc fixed nlat,nlon. it precomputes the gaussian weights, points\nc and all necessary legendre polys and stores them in wshsgs.\nc these quantities must be preserved when calling shsgs\nc repeatedly with fixed nlat,nlon.\nc\n dimension wshsgs(lshsgs),work(lwork)\n double precision dwork(ldwork)\n ierror = 1\n if (nlat.lt.3) return\n ierror = 2\n if (nlon.lt.4) return\nc set triangular truncation limit for spherical harmonic basis\n l = min0((nlon+2)/2,nlat)\nc set equator or nearest point (if excluded) pointer\n late = (nlat+1)/2\n l1 = l\n l2 = late\nc check permanent work space length\n ierror = 3\n lp=nlat*(3*(l1+l2)-2)+(l1-1)*(l2*(2*nlat-l1)-3*l1)/2+nlon+15\n if(lshsgs.lt.lp) return\n ierror = 4\nc check temporary work space\n if (lwork.lt.4*nlat*(nlat+2)+2) return\n ierror = 5\n if (ldwork .lt. nlat*(nlat+4)) return\n ierror = 0\nc set preliminary quantites needed to compute and store legendre polys\n ldw = nlat*(nlat+4)\n call shsgsp(nlat,nlon,wshsgs,lshsgs,dwork,ldwork,ierror)\n if (ierror.ne.0) return\nc set legendre poly pointer in wshsgs\n ipmnf = nlat+2*nlat*late+3*(l*(l-1)/2+(nlat-l)*(l-1))+nlon+16\n call shsgss1(nlat,l,late,wshsgs,work,wshsgs(ipmnf))\n return\n end\n subroutine shsgss1(nlat,l,late,w,pmn,pmnf)\n implicit double precision (a-h,o-z)\n dimension w(1),pmn(nlat,late,3),pmnf(late,1)\nc compute and store legendre polys for i=1,...,late,m=0,...,l-1\nc and n=m,...,l-1\n do i=1,nlat\n\tdo j=1,late\n\t do k=1,3\n\t pmn(i,j,k) = 0.0d0\n\t end do\n\t end do\n end do\n km0=1\n km1=2\n km2=3\n do 100 mp1=1,l\n m = mp1-1\n mml1 = m*(2*nlat-m-1)/2\nc compute pmn for n=m,...,nlat-1 and i=1,...,(l+1)/2\n mode = 0\n call legin(mode,l,nlat,m,w,pmn,km,km0,km1,km2)\nc store above in pmnf\n do 101 np1=mp1,nlat\n mn = mml1+np1\n do 102 i=1,late\n pmnf(i,mn) = pmn(np1,i,km)\n 102 continue\n 101 continue\n 100 continue\n return\n end\n subroutine shsgsp(nlat,nlon,wshsgs,lshsgs,dwork,ldwork,ierror)\n implicit double precision (a-h,o-z)\n dimension wshsgs(lshsgs)\n double precision dwork(ldwork)\n ierror = 1\n if (nlat.lt.3) return\n ierror = 2\n if (nlon.lt.4) return\nc set triangular truncation limit for spherical harmonic basis\n l = min0((nlon+2)/2,nlat)\nc set equator or nearest point (if excluded) pointer\n late = (nlat+mod(nlat,2))/2\n l1 = l\n l2 = late\n ierror = 3\nc check permanent work space length\n if (lshsgs .lt. nlat*(2*l2+3*l1-2)+3*l1*(1-l1)/2+nlon+15)return\n ierror = 4\nc if (lwork.lt.4*nlat*(nlat+2)+2) return\n if (ldwork .lt. nlat*(nlat+4)) return\n ierror = 0\nc set pointers\n i1 = 1\n i2 = i1+nlat\n i3 = i2+nlat*late\n i4 = i3+nlat*late\n i5 = i4+l*(l-1)/2 +(nlat-l)*(l-1)\n i6 = i5+l*(l-1)/2 +(nlat-l)*(l-1)\n i7 = i6+l*(l-1)/2 +(nlat-l)*(l-1)\nc set indices in temp work for double precision gaussian wts and pts\n idth = 1\nc idwts = idth+2*nlat\nc iw = idwts+2*nlat\n idwts = idth+nlat\n iw = idwts+nlat\n call shsgsp1(nlat,nlon,l,late,wshsgs(i1),wshsgs(i2),wshsgs(i3),\n 1wshsgs(i4),wshsgs(i5),wshsgs(i6),wshsgs(i7),dwork(idth),\n 2dwork(idwts),dwork(iw),ierror)\n if (ierror.ne.0) ierror = 6\n return\n end\n subroutine shsgsp1(nlat,nlon,l,late,wts,p0n,p1n,abel,bbel,cbel,\n + wfft,dtheta,dwts,work,ier)\n implicit double precision (a-h,o-z)\n dimension wts(nlat),p0n(nlat,late),p1n(nlat,late),abel(1),bbel(1),\n 1 cbel(1),wfft(1),dtheta(nlat),dwts(nlat)\n double precision pb,dtheta,dwts,work(*)\n indx(m,n) = (n-1)*(n-2)/2+m-1\n imndx(m,n) = l*(l-1)/2+(n-l-1)*(l-1)+m-1\n call hrffti(nlon,wfft)\nc\nc compute double precision gaussian points and weights\nc\n lw = nlat*(nlat+2)\n call gaqd(nlat,dtheta,dwts,work,lw,ier)\n if (ier.ne.0) return\n\nc store gaussian weights single precision to save computation\nc in inner loops in analysis\n do 100 i=1,nlat\n wts(i) = dwts(i)\n 100 continue\n\nc initialize p0n,p1n using double precision dnlfk,dnlft\n do 101 np1=1,nlat\n do 101 i=1,late\n p0n(np1,i) = 0.0d0\n p1n(np1,i) = 0.0d0\n 101 continue\nc compute m=n=0 legendre polynomials for all theta(i)\n np1 = 1\n n = 0\n m = 0\n call dnlfk(m,n,work)\n do 103 i=1,late\n call dnlft(m,n,dtheta(i),work,pb)\n p0n(1,i) = pb\n 103 continue\nc compute p0n,p1n for all theta(i) when n.gt.0\n do 104 np1=2,nlat\n n = np1-1\n m = 0\n call dnlfk(m,n,work)\n do 105 i=1,late\n call dnlft(m,n,dtheta(i),work,pb)\n p0n(np1,i) = pb\n 105 continue\nc compute m=1 legendre polynomials for all n and theta(i)\n m = 1\n call dnlfk(m,n,work)\n do 106 i=1,late\n call dnlft(m,n,dtheta(i),work,pb)\n p1n(np1,i) = pb\n 106 continue\n 104 continue\nc\nc compute and store swarztrauber recursion coefficients\nc for 2.le.m.le.n and 2.le.n.le.nlat in abel,bbel,cbel\n do 107 n=2,nlat\n mlim = min0(n,l)\n do 107 m=2,mlim\n imn = indx(m,n)\n if (n.ge.l) imn = imndx(m,n)\n abel(imn)=dsqrt(dfloat((2*n+1)*(m+n-2)*(m+n-3))/\n 1 dfloat(((2*n-3)*(m+n-1)*(m+n))))\n bbel(imn)=dsqrt(dfloat((2*n+1)*(n-m-1)*(n-m))/\n 1 dfloat(((2*n-3)*(m+n-1)*(m+n))))\n cbel(imn)=dsqrt(dfloat((n-m+1)*(n-m+2))/\n 1 dfloat(((n+m-1)*(n+m))))\n 107 continue\n return\n end\n" }, { "path": "external/SPHEREPACK/slapgs.f", "content": "c\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc * *\nc * copyright (c) 1998 by UCAR *\nc * *\nc * University Corporation for Atmospheric Research *\nc * *\nc * all rights reserved *\nc * *\nc * SPHEREPACK version 3.2 *\nc * *\nc * A Package of Fortran77 Subroutines and Programs *\nc * *\nc * for Modeling Geophysical Processes *\nc * *\nc * by *\nc * *\nc * John Adams and Paul Swarztrauber *\nc * *\nc * of *\nc * *\nc * the National Center for Atmospheric Research *\nc * *\nc * Boulder, Colorado (80307) U.S.A. *\nc * *\nc * which is sponsored by *\nc * *\nc * the National Science Foundation *\nc * *\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc\nc\nc\nc\nc ... file slapgs.f\nc\nc this file includes documentation and code for\nc subroutine slapgs i\nc\nc ... files which must be loaded with slapgs.f\nc\nc sphcom.f, hrfft.f, shags.f, shsgs.f\nc\nc\nc\nc subroutine slapgs(nstrlap,nstrab,noffslap,noffsab,\nc nlat,nlon,isym,nt,slap,ids,jds,a,b,\nc +mdab,ndab,wshsgs,lshsgs,work,lwork,ierror)\nc\nc\nc given the scalar spherical harmonic coefficients a and b, precomputed\nc by subroutine shags for a scalar field sf, subroutine slapgs computes\nc the laplacian of sf in the scalar array slap. slap(i,j) is the\nc laplacian of sf at the gaussian colatitude theta(i) (see nlat as\nc an input parameter) and east longitude lambda(j) = (j-1)*2*pi/nlon\nc on the sphere. i.e.\nc\nc slap(i,j) =\nc\nc 2 2\nc [1/sint*d (sf(i,j)/dlambda + d(sint*d(sf(i,j))/dtheta)/dtheta]/sint\nc\nc\nc where sint = sin(theta(i)). the scalar laplacian in slap has the\nc same symmetry or absence of symmetry about the equator as the scalar\nc field sf. the input parameters isym,nt,mdab,ndab must have the\nc same values used by shags to compute a and b for sf. the associated\nc legendre functions are stored rather than recomputed as they are\nc in subroutine slapgc.\nc\nc input parameters\nc\nc nstrlap, nstrab strides in lap,a,b,\nc noffslap, noffsab offset in lap,a,b, -- must be between 0 and stride-1\n\nc\nc nlat the number of points in the gaussian colatitude grid on the\nc full sphere. these lie in the interval (0,pi) and are computed\nc in radians in theta(1) <...< theta(nlat) by subroutine gaqd.\nc if nlat is odd the equator will be included as the grid point\nc theta((nlat+1)/2). if nlat is even the equator will be\nc excluded as a grid point and will lie half way between\nc theta(nlat/2) and theta(nlat/2+1). nlat must be at least 3.\nc note: on the half sphere, the number of grid points in the\nc colatitudinal direction is nlat/2 if nlat is even or\nc (nlat+1)/2 if nlat is odd.\nc\nc nlon the number of distinct longitude points. nlon determines\nc the grid increment in longitude as 2*pi/nlon. for example\nc nlon = 72 for a five degree grid. nlon must be greater\nc than zero. the axisymmetric case corresponds to nlon=1.\nc the efficiency of the computation is improved when nlon\nc is a product of small prime numbers.\nc\nc NOTE: this is a modified version of spherepack. Changes from\nc the original version to the current one have only been\nc tested for isym==0. For this reason an error code will\nc be returned if isym!=0.\nc\nc isym this parameter should have the same value input to subroutine\nc shags to compute the coefficients a and b for the scalar field\nc sf. isym is set as follows:\nc\nc = 0 no symmetries exist in sf about the equator. scalar\nc synthesis is used to compute slap on the entire sphere.\nc i.e., in the array slap(i,j) for i=1,...,nlat and\nc j=1,...,nlon.\nc\nc = 1 sf and slap are antisymmetric about the equator. the\nc synthesis used to compute slap is performed on the\nc northern hemisphere only. if nlat is odd, slap(i,j) is\nc computed for i=1,...,(nlat+1)/2 and j=1,...,nlon. if\nc nlat is even, slap(i,j) is computed for i=1,...,nlat/2\nc and j=1,...,nlon.\nc\nc\nc = 2 sf and slap are symmetric about the equator. the\nc synthesis used to compute slap is performed on the\nc northern hemisphere only. if nlat is odd, slap(i,j) is\nc computed for i=1,...,(nlat+1)/2 and j=1,...,nlon. if\nc nlat is even, slap(i,j) is computed for i=1,...,nlat/2\nc and j=1,...,nlon.\nc\nc\nc nt the number of analyses. in the program that calls slapgs\nc the arrays slap,a, and b can be three dimensional in which\nc case multiple synthesis will be performed. the third index\nc is the synthesis index which assumes the values k=1,...,nt.\nc for a single analysis set nt=1. the description of the\nc remaining parameters is simplified by assuming that nt=1\nc or that all the arrays are two dimensional.\nc\nc ids the first dimension of the array slap as it appears in the\nc program that calls slapgs. if isym = 0 then ids must be at\nc least nlat. if isym > 0 and nlat is even then ids must be\nc at least nlat/2. if isym > 0 and nlat is odd then ids must\nc be at least (nlat+1)/2.\nc\nc jds the second dimension of the array slap as it appears in the\nc program that calls slapgs. jds must be at least nlon.\nc\nc\nc a,b two or three dimensional arrays (see input parameter nt)\nc that contain scalar spherical harmonic coefficients\nc of the scalar field sf as computed by subroutine shags.\nc *** a,b must be computed by shags prior to calling slapgs.\nc\nc\nc mdab the first dimension of the arrays a and b as it appears\nc in the program that calls slapgs. mdab must be at\nc least min0(nlat,(nlon+2)/2) if nlon is even or at least\nc min0(nlat,(nlon+1)/2) if nlon is odd.\nc\nc ndab the second dimension of the arrays a and b as it appears\nc in the program that calls slapgs. ndbc must be at least\nc least nlat.\nc\nc mdab,ndab should have the same values input to shags to\nc compute the coefficients a and b.\nc\nc\nc wshsgs an array which must be initialized by subroutine slapgsi\nc (or equivalently by shsgsi). once initialized, wshsgs\nc can be used repeatedly by slapgs as long as nlat and nlon\nc remain unchanged. wshsgs must not be altered between calls\nc of slapgs.\nc\nc lshsgs the dimension of the array wshsgs as it appears in the\nc program that calls slapgs. let\nc\nc l1 = min0(nlat,(nlon+2)/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc then lshsgs must be at least\nc\nc nlat*(3*(l1+l2)-2)+(l1-1)*(l2*(2*nlat-l1)-3*l1)/2+nlon+15\nc\nc\nc work a work array that does not have to be saved.\nc\nc lwork the dimension of the array work as it appears in the\nc program that calls slapgs. define\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc l1 = min0(nlat,(nlon+2)/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc if isym is zero then lwork must be at least\nc\nc (nt+1)*nlat*nlon + nlat*(2*nt*l1+1)\nc\nc if isym is nonzero lwork must be at least\nc\nc (nt+1)*l2*nlon + nlat*(2*nt*l1+1)\nc\nc\nc **************************************************************\nc\nc output parameters\nc\nc\nc slap a two or three dimensional arrays (see input parameter nt) that\nc contain the scalar laplacian of the scalar field sf. slap(i,j)\nc is the scalar laplacian at the gaussian colatitude theta(i)\nc and longitude lambda(j) = (j-1)*2*pi/nlon for i=1,...,nlat\nc and j=1,...,nlon.\nc\nc\nc ierror a parameter which flags errors in input parameters as follows:\nc\nc = 0 no errors detected\nc\nc = 1 error in the specification of nlat\nc\nc = 2 error in the specification of nlon\nc\nc = 3 error in the specification of ityp\nc\nc = 4 error in the specification of nt\nc\nc = 5 error in the specification of ids\nc\nc = 6 error in the specification of jds\nc\nc = 7 error in the specification of mdbc\nc\nc = 8 error in the specification of ndbc\nc\nc = 9 error in the specification of lshsgs\nc\nc = 10 error in the specification of lwork\nc\nc\nc **********************************************************************\nc \nc end of documentation for slapgs\nc\nc **********************************************************************\nc\nc\n subroutine slapgs(nstrlap,nstrab,noffslap,noffsab,\n + nlat,nlon,isym,nt,slap,ids,jds,a,b,mdab,ndab,\n + wshsgs,lshsgs,work,lwork,ierror)\n implicit double precision (a-h,o-z)\n dimension slap(nstrlap,ids,jds,nt),\n + a(nstrab,mdab,ndab,nt),b(nstrab,mdab,ndab,nt)\n dimension wshsgs(lshsgs),work(lwork)\nc\nc check input parameters\nc\n ierror = 1\n if(nlat .lt. 3) return\n ierror = 2\n if(nlon .lt. 4) return\n ierror = 3\nc if (isym.lt.0 .or. isym.gt.2) return\nc see note above about symmeries\n if(isym.ne.0) return\n ierror = 4\n if(nt .lt. 0) return\n ierror = 5\n imid = (nlat+1)/2\n if((isym.eq.0 .and. ids.lt.nlat) .or.\n 1 (isym.gt.0 .and. ids.lt.imid)) return\n ierror = 6\n if(jds .lt. nlon) return\n ierror = 7\n mmax = min0(nlat,nlon/2+1)\n if(mdab .lt. mmax) return\n ierror = 8\n if(ndab .lt. nlat) return\n ierror = 9\nc\nc set and verify saved work space length\nc\n imid = (nlat+1)/2\n l2 = (nlat+mod(nlat,2))/2\n l1 = min0((nlon+2)/2,nlat)\n lp=nlat*(3*(l1+l2)-2)+(l1-1)*(l2*(2*nlat-l1)-3*l1)/2+nlon+15\n if(lshsgs.lt.lp) return\n ierror = 10\nc\nc set and verify unsaved work space length\nc\n ls = nlat\n if(isym .gt. 0) ls = imid\n nln = nt*ls*nlon\n mn = mmax*nlat*nt\nc lwkmin = nln+ls*nlon+2*mn+nlat\nc if (lwork .lt. lwkmin) return\n l2 = (nlat+1)/2\n l1 = min0(nlat,nlon/2+1)\n if (isym.eq.0) then\n\tlwkmin = (nt+1)*nlat*nlon + nlat*(2*nt*l1+1)\n else\n\tlwkmin = (nt+1)*l2*nlon + nlat*(2*nt*l1+1)\n end if\n if (lwork .lt. lwkmin) return\n ierror = 11\n if((noffslap.lt.0) .or. (noffslap.ge.nstrlap)) return\n if((noffsab.lt.0) .or. (noffsab.ge.nstrab)) return\n ierror = 0\nc\nc set work space pointers\nc\n ia = 1\n ib = ia+mn\n ifn = ib+mn\n iwk = ifn+nlat\n lwk = lwork-2*mn-nlat\n call slapgs1(nstrlap,nstrab,noffslap,noffsab,\n +nlat,nlon,isym,nt,slap,ids,jds,a,b,mdab,ndab,\n +work(ia),work(ib),mmax,work(ifn),wshsgs,lshsgs,work(iwk),lwk,\n +ierror)\n return\n end\n\n subroutine slapgs1(nstrlap,nstrab,noffslap,noffsab,\n + nlat,nlon,isym,nt,slap,ids,jds,a,b,mdab,ndab,\n + alap,blap,mmax,fnn,wsave,lsave,wk,lwk,ierror)\n implicit double precision (a-h,o-z)\n dimension slap(nstrlap,ids,jds,nt),\n + a(nstrab,mdab,ndab,nt),b(nstrab,mdab,ndab,nt)\n dimension alap(mmax,nlat,nt),blap(mmax,nlat,nt),fnn(nlat)\n dimension wsave(lsave),wk(lwk)\n ncab=1+noffsab\nc\nc set coefficient multiplyers\nc\n do 1 n=2,nlat\n fn = dfloat(n-1)\n fnn(n) = fn*(fn+1.d0)\n 1 continue\nc\nc compute scalar laplacian coefficients for each vector field\nc\n do 2 k=1,nt\n do 3 n=1,nlat\n do 4 m=1,mmax\n alap(m,n,k) = 0.0d0\n blap(m,n,k) = 0.0d0\n 4 continue\n 3 continue\nc\nc compute m=0 coefficients\nc\n do 5 n=2,nlat\n alap(1,n,k) = -fnn(n)*a(ncab,1,n,k)\n blap(1,n,k) = -fnn(n)*b(ncab,1,n,k)\n 5 continue\nc\nc compute m>0 coefficients\nc\n do 6 m=2,mmax\n do 7 n=m,nlat\n alap(m,n,k) = -fnn(n)*a(ncab,m,n,k)\n blap(m,n,k) = -fnn(n)*b(ncab,m,n,k)\n 7 continue\n 6 continue\n 2 continue\nc\nc synthesize alap,blap into slap\nc\n call shsgs(nstrlap,1,noffslap,0,\n + nlat,nlon,isym,nt,slap,ids,jds,alap,blap,\n + mmax,nlat,mmax,nlat,wsave,lsave,wk,lwk,ierror)\n return\n end\n" }, { "path": "external/SPHEREPACK/sphcom.f", "content": "c\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc * *\nc * copyright (c) 1998 by UCAR *\nc * *\nc * University Corporation for Atmospheric Research *\nc * *\nc * all rights reserved *\nc * *\nc * SPHEREPACK version 3.2 *\nc * *\nc * A Package of Fortran77 Subroutines and Programs *\nc * *\nc * for Modeling Geophysical Processes *\nc * *\nc * by *\nc * *\nc * John Adams and Paul Swarztrauber *\nc * *\nc * of *\nc * *\nc * the National Center for Atmospheric Research *\nc * *\nc * Boulder, Colorado (80307) U.S.A. *\nc * *\nc * which is sponsored by *\nc * *\nc * the National Science Foundation *\nc * *\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc\nc\nc ... file sphcom.f\nc\nc this file must be loaded with all main program files\nc in spherepack. it includes undocumented subroutines\nc called by some or all of main programs\nc\n subroutine dnlfk (m,n,cp)\n implicit double precision (a-h,o-z)\nc\nc cp requires n/2+1 double precision locations\nc\n double precision cp,fnum,fden,fnmh,a1,b1,c1,cp2,fnnp1,fnmsq,fk,\n 1 t1,t2,pm1,sc10,sc20,sc40\n dimension cp(1)\n parameter (sc10=1024.d0)\n parameter (sc20=sc10*sc10)\n parameter (sc40=sc20*sc20)\nc\n cp(1) = 0.d0\n ma = iabs(m)\n if(ma .gt. n) return\n if(n-1) 2,3,5\n 2 cp(1) = dsqrt(2.d0)\n return\n 3 if(ma .ne. 0) go to 4\n cp(1) = dsqrt(1.5d0)\n return\n 4 cp(1) = dsqrt(.75d0)\n if(m .eq. -1) cp(1) = -cp(1)\n return\n 5 if(mod(n+ma,2) .ne. 0) go to 10\n nmms2 = (n-ma)/2\n fnum = n+ma+1\n fnmh = n-ma+1\n pm1 = 1.d0\n go to 15\n 10 nmms2 = (n-ma-1)/2\n fnum = n+ma+2\n fnmh = n-ma+2\n pm1 = -1.d0\nc t1 = 1.\nc t1 = 2.d0**(n-1)\nc t1 = 1.d0/t1\n 15 t1 = 1.d0/sc20\n nex = 20\n fden = 2.d0\n if(nmms2 .lt. 1) go to 20\n do 18 i=1,nmms2\n t1 = fnum*t1/fden\n if(t1 .gt. sc20) then\n t1 = t1/sc40\n nex = nex+40\n end if\n fnum = fnum+2.d0\n fden = fden+2.d0\n 18 continue\n 20 t1 = t1/2.d0**(n-1-nex)\n if(mod(ma/2,2) .ne. 0) t1 = -t1\n t2 = 1.d0 \n if(ma .eq. 0) go to 26\n do 25 i=1,ma\n t2 = fnmh*t2/(fnmh+pm1)\n fnmh = fnmh+2.d0\n 25 continue\n 26 cp2 = t1*dsqrt((n+.5d0)*t2)\n fnnp1 = n*(n+1)\n fnmsq = fnnp1-2.d0*ma*ma\n l = (n+1)/2\n if(mod(n,2) .eq. 0 .and. mod(ma,2) .eq. 0) l = l+1\n cp(l) = cp2\n if(m .ge. 0) go to 29\n if(mod(ma,2) .ne. 0) cp(l) = -cp(l)\n 29 if(l .le. 1) return\n fk = n\n a1 = (fk-2.d0)*(fk-1.d0)-fnnp1\n b1 = 2.d0*(fk*fk-fnmsq)\n cp(l-1) = b1*cp(l)/a1\n 30 l = l-1\n if(l .le. 1) return\n fk = fk-2.d0\n a1 = (fk-2.d0)*(fk-1.d0)-fnnp1\n b1 = -2.d0*(fk*fk-fnmsq)\n c1 = (fk+1.d0)*(fk+2.d0)-fnnp1\n cp(l-1) = -(b1*cp(l)+c1*cp(l+1))/a1\n go to 30\n end\n subroutine dnlft (m,n,theta,cp,pb)\n implicit double precision (a-h,o-z)\n double precision cp(*),pb,theta,cdt,sdt,cth,sth,chh\n cdt = dcos(theta+theta)\n sdt = dsin(theta+theta)\n nmod=mod(n,2)\n mmod=mod(m,2)\n if(nmod)1,1,2\n1 if(mmod)3,3,4\nc\nc n even, m even\nc\n3 kdo=n/2\n pb = .5d0*cp(1)\n if(n .eq. 0) return\n cth = cdt\n sth = sdt\n do 170 k=1,kdo\nc pb = pb+cp(k+1)*dcos(2*k*theta)\n pb = pb+cp(k+1)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 170 continue\n return\nc\nc n even, m odd\nc\n 4 kdo = n/2\n pb = 0.d0\n cth = cdt\n sth = sdt\n do 180 k=1,kdo\nc pb = pb+cp(k)*dsin(2*k*theta)\n pb = pb+cp(k)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 180 continue\n return\n2 if(mmod)13,13,14\nc\nc n odd, m even\nc\n13 kdo = (n+1)/2\n pb = 0.d0\n cth = dcos(theta)\n sth = dsin(theta)\n do 190 k=1,kdo\nc pb = pb+cp(k)*dcos((2*k-1)*theta)\n pb = pb+cp(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 190 continue\n return\nc\nc n odd, m odd\nc\n 14 kdo = (n+1)/2\n pb = 0.d0\n cth = dcos(theta)\n sth = dsin(theta)\n do 200 k=1,kdo\nc pb = pb+cp(k)*dsin((2*k-1)*theta)\n pb = pb+cp(k)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 200 continue\n return\n end\n subroutine dnlftd (m,n,theta,cp,pb)\n implicit double precision (a-h,o-z)\nc\nc computes the derivative of pmn(theta) with respect to theta\nc\n dimension cp(1)\n double precision cp,pb,theta,cdt,sdt,cth,sth,chh\n cdt = dcos(theta+theta)\n sdt = dsin(theta+theta)\n nmod=mod(n,2)\n mmod=mod(abs(m),2)\n if(nmod)1,1,2\n1 if(mmod)3,3,4\nc\nc n even, m even\nc\n3 kdo=n/2\n pb = 0.d0\n if(n .eq. 0) return\n cth = cdt\n sth = sdt\n do 170 k=1,kdo\nc pb = pb+cp(k+1)*dcos(2*k*theta)\n pb = pb-2.d0*k*cp(k+1)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 170 continue\n return\nc\nc n even, m odd\nc\n 4 kdo = n/2\n pb = 0.d0\n cth = cdt\n sth = sdt\n do 180 k=1,kdo\nc pb = pb+cp(k)*dsin(2*k*theta)\n pb = pb+2.d0*k*cp(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 180 continue\n return\n2 if(mmod)13,13,14\nc\nc n odd, m even\nc\n13 kdo = (n+1)/2\n pb = 0.d0\n cth = dcos(theta)\n sth = dsin(theta)\n do 190 k=1,kdo\nc pb = pb+cp(k)*dcos((2*k-1)*theta)\n pb = pb-(2.d0*k-1)*cp(k)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 190 continue\n return\nc\nc n odd, m odd\nc\n 14 kdo = (n+1)/2\n pb = 0.d0\n cth = dcos(theta)\n sth = dsin(theta)\n do 200 k=1,kdo\nc pb = pb+cp(k)*dsin((2*k-1)*theta)\n pb = pb+(2.d0*k-1)*cp(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 200 continue\n return\n end\n subroutine legin(mode,l,nlat,m,w,pmn,km,km0,km1,km2)\n implicit double precision (a-h,o-z)\nc this subroutine computes legendre polynomials for n=m,...,l-1\nc and i=1,...,late (late=((nlat+mod(nlat,2))/2)gaussian grid\nc in pmn(n+1,i,km) using swarztrauber's recursion formula.\nc the vector w contains quantities precomputed in shigc.\nc legin must be called in the order m=0,1,...,l-1\nc (e.g., if m=10 is sought it must be preceded by calls with\nc m=0,1,2,...,9 in that order)\n dimension w(1),pmn(1)\nc set size of pole to equator gaussian grid\n late = (nlat+mod(nlat,2))/2\nc partition w (set pointers for p0n,p1n,abel,bbel,cbel,pmn)\n i1 = 1+nlat\n i2 = i1+nlat*late\n i3 = i2+nlat*late\n i4 = i3+(2*nlat-l)*(l-1)/2\n i5 = i4+(2*nlat-l)*(l-1)/2\n call legin1(mode,l,nlat,late,m,w(i1),w(i2),w(i3),w(i4),\n 1 w(i5),pmn,km,km0,km1,km2)\n return\n end\n subroutine legin1(mode,l,nlat,late,m,p0n,p1n,abel,bbel,cbel,\n 1 pmn,km,km0,km1,km2)\n implicit double precision (a-h,o-z)\n dimension p0n(nlat,late),p1n(nlat,late)\n dimension abel(1),bbel(1),cbel(1),pmn(nlat,late,3)\nc define index function used in storing triangular\nc arrays for recursion coefficients (functions of (m,n))\nc for 2.le.m.le.n-1 and 2.le.n.le.l-1\n indx(m,n) = (n-1)*(n-2)/2+m-1\nc for l.le.n.le.nlat and 2.le.m.le.l\n imndx(m,n) = l*(l-1)/2+(n-l-1)*(l-1)+m-1\n\nc set do loop indices for full or half sphere\n ms = m+1\n ninc = 1\n if (mode.eq.1) then\nc only compute pmn for n-m odd\n ms = m+2\n ninc = 2\n else if (mode.eq.2) then\nc only compute pmn for n-m even\n ms = m+1\n ninc = 2\n end if\n\n\n if (m.gt.1) then\n do 100 np1=ms,nlat,ninc\n n = np1-1\n imn = indx(m,n)\n if (n.ge.l) imn = imndx(m,n)\n do 100 i=1,late\n pmn(np1,i,km0) = abel(imn)*pmn(n-1,i,km2)\n 1 +bbel(imn)*pmn(n-1,i,km0)\n 2 -cbel(imn)*pmn(np1,i,km2)\n 100 continue\n\n else if (m.eq.0) then\n do 101 np1=ms,nlat,ninc\n do 101 i=1,late\n pmn(np1,i,km0) = p0n(np1,i)\n 101 continue\n\n else if (m.eq.1) then\n do 102 np1=ms,nlat,ninc\n do 102 i=1,late\n pmn(np1,i,km0) = p1n(np1,i)\n 102 continue\n end if\n\nc permute column indices\nc km0,km1,km2 store m,m-1,m-2 columns\n kmt = km0\n km0 = km2\n km2 = km1\n km1 = kmt\nc set current m index in output param km\n km = kmt\n return\n end\n\n\nc$$$ subroutine zfin (isym,nlat,nlon,m,z,i3,wzfin)\nc$$$ implicit double precision (a-h,o-z)\nc$$$ dimension z(1) ,wzfin(1)\nc$$$ imid = (nlat+1)/2\nc$$$ lim = nlat*imid\nc$$$ mmax = min0(nlat,nlon/2+1)\nc$$$ labc = ((mmax-2)*(nlat+nlat-mmax-1))/2\nc$$$ iw1 = lim+1\nc$$$ iw2 = iw1+lim\nc$$$ iw3 = iw2+labc\nc$$$ iw4 = iw3+labc\nc$$$c\nc$$$c the length of wzfin is 2*lim+3*labc\nc$$$c\nc$$$ call zfin1 (isym,nlat,m,z,imid,i3,wzfin,wzfin(iw1),wzfin(iw2),\nc$$$ 1 wzfin(iw3),wzfin(iw4))\nc$$$ return\nc$$$ end\nc$$$ subroutine zfin1 (isym,nlat,m,z,imid,i3,zz,z1,a,b,c)\nc$$$ implicit double precision (a-h,o-z)\nc$$$ dimension z(imid,nlat,3),zz(imid,1),z1(imid,1),\nc$$$ 1 a(1),b(1),c(1)\nc$$$ save i1,i2\nc$$$ ihold = i1\nc$$$ i1 = i2\nc$$$ i2 = i3\nc$$$ i3 = ihold\nc$$$ if(m-1)25,30,35\nc$$$ 25 i1 = 1\nc$$$ i2 = 2\nc$$$ i3 = 3\nc$$$ do 45 np1=1,nlat\nc$$$ do 45 i=1,imid\nc$$$ z(i,np1,i3) = zz(i,np1)\nc$$$ 45 continue\nc$$$ return\nc$$$ 30 do 50 np1=2,nlat\nc$$$ do 50 i=1,imid\nc$$$ z(i,np1,i3) = z1(i,np1)\nc$$$ 50 continue\nc$$$ return\nc$$$ 35 ns = ((m-2)*(nlat+nlat-m-1))/2+1\nc$$$ if(isym .eq. 1) go to 36\nc$$$ do 85 i=1,imid\nc$$$ z(i,m+1,i3) = a(ns)*z(i,m-1,i1)-c(ns)*z(i,m+1,i1)\nc$$$ 85 continue\nc$$$ 36 if(m .eq. nlat-1) return\nc$$$ if(isym .eq. 2) go to 71\nc$$$ ns = ns+1\nc$$$ do 70 i=1,imid\nc$$$ z(i,m+2,i3) = a(ns)*z(i,m,i1)-c(ns)*z(i,m+2,i1)\nc$$$ 70 continue\nc$$$ 71 nstrt = m+3\nc$$$ if(isym .eq. 1) nstrt = m+4\nc$$$ if(nstrt .gt. nlat) go to 80\nc$$$ nstp = 2\nc$$$ if(isym .eq. 0) nstp = 1\nc$$$ do 75 np1=nstrt,nlat,nstp\nc$$$ ns = ns+nstp\nc$$$ do 75 i=1,imid\nc$$$ z(i,np1,i3) = a(ns)*z(i,np1-2,i1)+b(ns)*z(i,np1-2,i3)\nc$$$ 1 -c(ns)*z(i,np1,i1)\nc$$$ 75 continue\nc$$$ 80 return\nc$$$ end\n subroutine zfinit (nlat,nlon,wzfin,dwork)\n implicit double precision (a-h,o-z)\n dimension wzfin(*)\n double precision dwork(*)\n imid = (nlat+1)/2\n iw1 = 2*nlat*imid+1\nc\nc the length of wzfin is 3*((l-3)*l+2)/2 + 2*l*imid\nc the length of dwork is nlat+2\nc\n call zfini1 (nlat,nlon,imid,wzfin,wzfin(iw1),dwork,\n 1 dwork(nlat/2+1))\n return\n end\n subroutine zfini1 (nlat,nlon,imid,z,abc,cz,work)\n implicit double precision (a-h,o-z)\nc\nc abc must have 3*((mmax-2)*(nlat+nlat-mmax-1))/2 locations\nc where mmax = min0(nlat,nlon/2+1)\nc cz and work must each have nlat+1 locations\nc\n dimension z(imid,nlat,2),abc(1)\n double precision pi,dt,th,zh,cz(*),work(*)\n pi = 4.d0*datan(1.d0)\n dt = pi/(nlat-1)\n do 160 mp1=1,2\n m = mp1-1\n do 160 np1=mp1,nlat\n n = np1-1\n call dnzfk(nlat,m,n,cz,work)\n do 165 i=1,imid\n th = (i-1)*dt\n call dnzft(nlat,m,n,th,cz,zh)\n z(i,np1,mp1) = zh\n 165 continue\n z(1,np1,mp1) = .5d0*z(1,np1,mp1)\n 160 continue\n call rabcp(nlat,nlon,abc)\n return\n end\n subroutine dnzfk(nlat,m,n,cz,work)\n implicit double precision (a-h,o-z)\nc\nc dnzfk computes the coefficients in the trigonometric\nc expansion of the z functions that are used in spherical\nc harmonic analysis.\nc\n dimension cz(1),work(1)\nc\nc cz and work must both have nlat/2+1 locations\nc\n double precision sum,sc1,t1,t2,work,cz\n lc = (nlat+1)/2\n sc1 = 2.d0/dfloat(nlat-1)\n call dnlfk(m,n,work)\n nmod = mod(n,2)\n mmod = mod(m,2)\n if(nmod)1,1,2\n1 if(mmod)3,3,4\nc\nc n even, m even\nc\n3 kdo = n/2+1\n do 5 idx=1,lc\n i = idx+idx-2\n sum = work(1)/(1.d0-i*i)\n if(kdo.lt.2) go to 29\n do 6 kp1=2,kdo\n k = kp1-1\n t1 = 1.d0-(k+k+i)**2\n t2 = 1.d0-(k+k-i)**2\n8 sum = sum+work(kp1)*(t1+t2)/(t1*t2)\n6 continue\n29 cz(idx) = sc1*sum\n5 continue\n return\nc\nc n even, m odd\nc\n4 kdo = n/2\n do 9 idx=1,lc\n i = idx+idx-2\n sum = 0.d0\n do 101 k=1,kdo\n t1 = 1.d0-(k+k+i)**2\n t2 = 1.d0-(k+k-i)**2\n12 sum=sum+work(k)*(t1-t2)/(t1*t2)\n101 continue\n cz(idx) = sc1*sum\n9 continue\n return\n2 if(mmod)13,13,14\nc\nc n odd, m even\nc\n13 kdo = (n+1)/2\n do 15 idx=1,lc\n i = idx+idx-1\n sum = 0.d0\n do 16 k=1,kdo\n t1 = 1.d0-(k+k-1+i)**2\n t2 = 1.d0-(k+k-1-i)**2\n18 sum=sum+work(k)*(t1+t2)/(t1*t2)\n16 continue\n cz(idx)=sc1*sum\n15 continue\n return\nc\nc n odd, m odd\nc\n14 kdo = (n+1)/2\n do 19 idx=1,lc\n i = idx+idx-3\n sum=0.d0\n do 20 k=1,kdo\n t1 = 1.d0-(k+k-1+i)**2\n t2 = 1.d0-(k+k-1-i)**2\n22 sum=sum+work(k)*(t1-t2)/(t1*t2)\n20 continue\n cz(idx)=sc1*sum\n19 continue\n return\n end\n subroutine dnzft(nlat,m,n,th,cz,zh)\n implicit double precision (a-h,o-z)\n dimension cz(1)\n double precision cz,zh,th,cdt,sdt,cth,sth,chh\n zh = 0.d0\n cdt = dcos(th+th)\n sdt = dsin(th+th)\n lmod = mod(nlat,2)\n mmod = mod(m,2)\n nmod = mod(n,2)\n if(lmod)20,20,10\n 10 lc = (nlat+1)/2\n lq = lc-1\n ls = lc-2\n if(nmod)1,1,2\n 1 if(mmod)3,3,4\nc\nc nlat odd n even m even\nc\n 3 zh = .5d0*(cz(1)+cz(lc)*dcos(2*lq*th))\n cth = cdt\n sth = sdt\n do 201 k=2,lq\nc zh = zh+cz(k)*dcos(2*(k-1)*th)\n zh = zh+cz(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 201 continue\n return\nc\nc nlat odd n even m odd\nc\n 4 cth = cdt\n sth = sdt\n do 202 k=1,ls\nc zh = zh+cz(k+1)*dsin(2*k*th)\n zh = zh+cz(k+1)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 202 continue\n return\nc\nc nlat odd n odd, m even\nc\n 2 if(mmod)5,5,6\n 5 cth = dcos(th)\n sth = dsin(th)\n do 203 k=1,lq\nc zh = zh+cz(k)*dcos((2*k-1)*th)\n zh = zh+cz(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 203 continue\n return\nc\nc nlat odd n odd m odd\nc\n 6 cth = dcos(th)\n sth = dsin(th)\n do 204 k=1,lq\nc zh = zh+cz(k+1)*dsin((2*k-1)*th)\n zh = zh+cz(k+1)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 204 continue\n return\n 20 lc = nlat/2\n lq = lc-1\n if(nmod)30,30,80\n 30 if(mmod)40,40,60\nc\nc nlat even n even m even\nc\n 40 zh = .5d0*cz(1)\n cth = cdt\n sth = sdt\n do 50 k=2,lc\nc zh = zh+cz(k)*dcos(2*(k-1)*th)\n zh = zh+cz(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 50 continue\n return\nc\nc nlat even n even m odd\nc\n 60 cth = cdt\n sth = sdt\n do 70 k=1,lq\nc zh = zh+cz(k+1)*dsin(2*k*th)\n zh = zh+cz(k+1)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 70 continue\n return\nc\nc nlat even n odd m even\nc\n 80 if(mmod)90,90,110\n 90 zh = .5d0*cz(lc)*dcos((nlat-1)*th)\n cth = dcos(th)\n sth = dsin(th)\n do 100 k=1,lq\nc zh = zh+cz(k)*dcos((2*k-1)*th)\n zh = zh+cz(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 100 continue\n return\nc\nc nlat even n odd m odd\nc\n 110 cth = dcos(th)\n sth = dsin(th)\n do 120 k=1,lq\nc zh = zh+cz(k+1)*dsin((2*k-1)*th)\n zh = zh+cz(k+1)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 120 continue\n return\n end\nc$$$ subroutine alin (isym,nlat,nlon,m,p,i3,walin)\nc$$$ implicit double precision (a-h,o-z)\nc$$$ dimension p(1) ,walin(1)\nc$$$ imid = (nlat+1)/2\nc$$$ lim = nlat*imid\nc$$$ mmax = min0(nlat,nlon/2+1)\nc$$$ labc = ((mmax-2)*(nlat+nlat-mmax-1))/2\nc$$$ iw1 = lim+1\nc$$$ iw2 = iw1+lim\nc$$$ iw3 = iw2+labc\nc$$$ iw4 = iw3+labc\nc$$$c\nc$$$c the length of walin is ((5*l-7)*l+6)/2\nc$$$c\nc$$$ call alin1 (isym,nlat,m,p,imid,i3,walin,walin(iw1),walin(iw2),\nc$$$ 1 walin(iw3),walin(iw4))\nc$$$ return\nc$$$ end\nc$$$ subroutine alin1 (isym,nlat,m,p,imid,i3,pz,p1,a,b,c)\nc$$$ implicit double precision (a-h,o-z)\nc$$$ dimension p(imid,nlat,3),pz(imid,1),p1(imid,1),\nc$$$ 1 a(1),b(1),c(1)\nc$$$ save i1,i2\nc$$$ ihold = i1\nc$$$ i1 = i2\nc$$$ i2 = i3\nc$$$ i3 = ihold\nc$$$ if(m-1)25,30,35\nc$$$ 25 i1 = 1\nc$$$ i2 = 2\nc$$$ i3 = 3\nc$$$ do 45 np1=1,nlat\nc$$$ do 45 i=1,imid\nc$$$ p(i,np1,i3) = pz(i,np1)\nc$$$ 45 continue\nc$$$ return\nc$$$ 30 do 50 np1=2,nlat\nc$$$ do 50 i=1,imid\nc$$$ p(i,np1,i3) = p1(i,np1)\nc$$$ 50 continue\nc$$$ return\nc$$$ 35 ns = ((m-2)*(nlat+nlat-m-1))/2+1\nc$$$ if(isym .eq. 1) go to 36\nc$$$ do 85 i=1,imid\nc$$$ p(i,m+1,i3) = a(ns)*p(i,m-1,i1)-c(ns)*p(i,m+1,i1)\nc$$$ 85 continue\nc$$$ 36 if(m .eq. nlat-1) return\nc$$$ if(isym .eq. 2) go to 71\nc$$$ ns = ns+1\nc$$$ do 70 i=1,imid\nc$$$ p(i,m+2,i3) = a(ns)*p(i,m,i1)-c(ns)*p(i,m+2,i1)\nc$$$ 70 continue\nc$$$ 71 nstrt = m+3\nc$$$ if(isym .eq. 1) nstrt = m+4\nc$$$ if(nstrt .gt. nlat) go to 80\nc$$$ nstp = 2\nc$$$ if(isym .eq. 0) nstp = 1\nc$$$ do 75 np1=nstrt,nlat,nstp\nc$$$ ns = ns+nstp\nc$$$ do 75 i=1,imid\nc$$$ p(i,np1,i3) = a(ns)*p(i,np1-2,i1)+b(ns)*p(i,np1-2,i3)\nc$$$ 1 -c(ns)*p(i,np1,i1)\nc$$$ 75 continue\nc$$$ 80 return\nc$$$ end\n subroutine alinit (nlat,nlon,walin,dwork)\n implicit double precision (a-h,o-z)\n dimension walin(*)\n double precision dwork(*)\n imid = (nlat+1)/2\n iw1 = 2*nlat*imid+1\nc\nc the length of walin is 3*((l-3)*l+2)/2 + 2*l*imid\nc the length of work is nlat+1\nc\n call alini1 (nlat,nlon,imid,walin,walin(iw1),dwork)\n return\n end\n subroutine alini1 (nlat,nlon,imid,p,abc,cp)\n implicit double precision (a-h,o-z)\n dimension p(imid,nlat,2),abc(1),cp(1)\n double precision pi,dt,th,cp,ph\n pi = 4.d0*datan(1.d0)\n dt = pi/(nlat-1)\n do 160 mp1=1,2\n m = mp1-1\n do 160 np1=mp1,nlat\n n = np1-1\n call dnlfk (m,n,cp)\n do 160 i=1,imid\n th = (i-1)*dt\n call dnlft (m,n,th,cp,ph)\n p(i,np1,mp1) = ph\n 160 continue\n call rabcp(nlat,nlon,abc)\n return\n end\n subroutine rabcp(nlat,nlon,abc)\n implicit double precision (a-h,o-z)\nc\nc subroutine rabcp computes the coefficients in the recurrence\nc relation for the associated legendre fuctions. array abc\nc must have 3*((mmax-2)*(nlat+nlat-mmax-1))/2 locations.\nc\n dimension abc(1)\n mmax = min0(nlat,nlon/2+1)\n labc = ((mmax-2)*(nlat+nlat-mmax-1))/2\n iw1 = labc+1\n iw2 = iw1+labc\n call rabcp1(nlat,nlon,abc,abc(iw1),abc(iw2))\n return\n end\n subroutine rabcp1(nlat,nlon,a,b,c)\n implicit double precision (a-h,o-z)\nc\nc coefficients a, b, and c for computing pbar(m,n,theta) are\nc stored in location ((m-2)*(nlat+nlat-m-1))/2+n+1\nc\n dimension a(1),b(1),c(1)\n mmax = min0(nlat,nlon/2+1)\n do 215 mp1=3,mmax\n m = mp1-1\n ns = ((m-2)*(nlat+nlat-m-1))/2+1\n fm = dfloat(m)\n tm = fm+fm\n temp = tm*(tm-1.d0)\n a(ns) = dsqrt((tm+1.d0)*(tm-2.d0)/temp)\n c(ns) = dsqrt(2.d0/temp)\n if(m .eq. nlat-1) go to 215\n ns = ns+1\n temp = tm*(tm+1.d0)\n a(ns) = dsqrt((tm+3.d0)*(tm-2.d0)/temp)\n c(ns) = dsqrt(6.d0/temp)\n mp3 = m+3\n if(mp3 .gt. nlat) go to 215\n do 210 np1=mp3,nlat\n n = np1-1\n ns = ns+1\n fn = dfloat(n)\n tn = fn+fn\n cn = (tn+1.d0)/(tn-3.d0)\n fnpm = fn+fm\n fnmm = fn-fm\n temp = fnpm*(fnpm-1.d0)\n a(ns) = dsqrt(cn*(fnpm-3.d0)*(fnpm-2.d0)/temp)\n b(ns) = dsqrt(cn*fnmm*(fnmm-1.d0)/temp)\n c(ns) = dsqrt((fnmm+1.d0)*(fnmm+2.d0)/temp)\n 210 continue\n 215 continue\n return\n end\nc$$$ subroutine sea1(nlat,nlon,imid,z,idz,zin,wzfin,dwork)\nc$$$ implicit double precision (a-h,o-z)\nc$$$ dimension z(idz,*),zin(imid,nlat,3),wzfin(*)\nc$$$ double precision dwork(*)\nc$$$ call zfinit(nlat,nlon,wzfin,dwork)\nc$$$ mmax = min0(nlat,nlon/2+1)\nc$$$ do 33 mp1=1,mmax\nc$$$ m = mp1-1\nc$$$ call zfin (0,nlat,nlon,m,zin,i3,wzfin)\nc$$$ do 33 np1=mp1,nlat\nc$$$ mn = m*(nlat-1)-(m*(m-1))/2+np1\nc$$$ do 33 i=1,imid\nc$$$ z(mn,i) = zin(i,np1,i3)\nc$$$ 33 continue\nc$$$ return\nc$$$ end\nc$$$ subroutine ses1(nlat,nlon,imid,p,pin,walin,dwork)\nc$$$ implicit double precision (a-h,o-z)\nc$$$ dimension p(imid,*),pin(imid,nlat,3),walin(*)\nc$$$ double precision dwork(*)\nc$$$ call alinit (nlat,nlon,walin,dwork)\nc$$$ mmax = min0(nlat,nlon/2+1)\nc$$$ do 10 mp1=1,mmax\nc$$$ m = mp1-1\nc$$$ call alin(0,nlat,nlon,m,pin,i3,walin)\nc$$$ do 10 np1=mp1,nlat\nc$$$ mn = m*(nlat-1)-(m*(m-1))/2+np1\nc$$$ do 10 i=1,imid\nc$$$ p(i,mn) = pin(i,np1,i3)\nc$$$ 10 continue\nc$$$ return\nc$$$ end\n subroutine zvinit (nlat,nlon,wzvin,dwork)\n implicit double precision (a-h,o-z)\n dimension wzvin(1)\n double precision dwork(*)\n imid = (nlat+1)/2\n iw1 = 2*nlat*imid+1\nc\nc the length of wzvin is \nc 2*nlat*imid +3*(max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\nc the length of dwork is nlat+2\nc\n call zvini1 (nlat,nlon,imid,wzvin,wzvin(iw1),dwork,\n 1 dwork(nlat/2+2))\n return\n end\n subroutine zvini1 (nlat,nlon,imid,zv,abc,czv,work)\n implicit double precision (a-h,o-z)\nc\nc abc must have 3*(max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\nc locations where mmax = min0(nlat,(nlon+1)/2)\nc czv and work must each have nlat/2+1 locations\nc\n dimension zv(imid,nlat,2),abc(1)\n double precision pi,dt,czv(1),zvh,th,work(1)\n pi = 4.d0*datan(1.d0)\n dt = pi/(nlat-1)\n mdo = min0(2,nlat,(nlon+1)/2)\n do 160 mp1=1,mdo\n m = mp1-1\n do 160 np1=mp1,nlat\n n = np1-1\n call dzvk(nlat,m,n,czv,work)\n do 165 i=1,imid\n th = (i-1)*dt\n call dzvt(nlat,m,n,th,czv,zvh)\n zv(i,np1,mp1) = zvh\n 165 continue\n zv(1,np1,mp1) = .5d0*zv(1,np1,mp1)\n 160 continue\n call rabcv(nlat,nlon,abc)\n return\n end\n subroutine zwinit (nlat,nlon,wzwin,dwork)\n implicit double precision (a-h,o-z)\n dimension wzwin(1)\n double precision dwork(*)\n imid = (nlat+1)/2\n iw1 = 2*nlat*imid+1\nc\nc the length of wzvin is 2*nlat*imid+3*((nlat-3)*nlat+2)/2\nc the length of dwork is nlat+2\nc\n call zwini1 (nlat,nlon,imid,wzwin,wzwin(iw1),dwork,\n 1 dwork(nlat/2+2))\n return\n end\n subroutine zwini1 (nlat,nlon,imid,zw,abc,czw,work)\n implicit double precision (a-h,o-z)\nc\nc abc must have 3*(max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\nc locations where mmax = min0(nlat,(nlon+1)/2)\nc czw and work must each have nlat+1 locations\nc\n dimension zw(imid,nlat,2),abc(1)\n double precision pi,dt,czw(1),zwh,th,work(1)\n pi = 4.d0*datan(1.d0)\n dt = pi/(nlat-1)\n mdo = min0(3,nlat,(nlon+1)/2)\n if(mdo .lt. 2) return\n do 160 mp1=2,mdo\n m = mp1-1\n do 160 np1=mp1,nlat\n n = np1-1\n call dzwk(nlat,m,n,czw,work)\n do 165 i=1,imid\n th = (i-1)*dt\n call dzwt(nlat,m,n,th,czw,zwh)\n zw(i,np1,m) = zwh\n 165 continue\n zw(1,np1,m) = .5d0*zw(1,np1,m)\n 160 continue\n call rabcw(nlat,nlon,abc)\n return\n end\nc$$$ subroutine zvin (ityp,nlat,nlon,m,zv,i3,wzvin)\nc$$$ implicit double precision (a-h,o-z)\nc$$$ dimension zv(1) ,wzvin(1)\nc$$$ imid = (nlat+1)/2\nc$$$ lim = nlat*imid\nc$$$ mmax = min0(nlat,(nlon+1)/2)\nc$$$ labc = (max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\nc$$$ iw1 = lim+1\nc$$$ iw2 = iw1+lim\nc$$$ iw3 = iw2+labc\nc$$$ iw4 = iw3+labc\nc$$$c\nc$$$c the length of wzvin is 2*lim+3*labc\nc$$$c\nc$$$ call zvin1 (ityp,nlat,m,zv,imid,i3,wzvin,wzvin(iw1),wzvin(iw2),\nc$$$ 1 wzvin(iw3),wzvin(iw4))\nc$$$ return\nc$$$ end\nc$$$ subroutine zvin1 (ityp,nlat,m,zv,imid,i3,zvz,zv1,a,b,c)\nc$$$ implicit double precision (a-h,o-z)\nc$$$ dimension zv(imid,nlat,3),zvz(imid,1),zv1(imid,1),\nc$$$ 1 a(1),b(1),c(1)\nc$$$ save i1,i2\nc$$$ ihold = i1\nc$$$ i1 = i2\nc$$$ i2 = i3\nc$$$ i3 = ihold\nc$$$ if(m-1)25,30,35\nc$$$ 25 i1 = 1\nc$$$ i2 = 2\nc$$$ i3 = 3\nc$$$ do 45 np1=1,nlat\nc$$$ do 45 i=1,imid\nc$$$ zv(i,np1,i3) = zvz(i,np1)\nc$$$ 45 continue\nc$$$ return\nc$$$ 30 do 50 np1=2,nlat\nc$$$ do 50 i=1,imid\nc$$$ zv(i,np1,i3) = zv1(i,np1)\nc$$$ 50 continue\nc$$$ return\nc$$$ 35 ns = ((m-2)*(nlat+nlat-m-1))/2+1\nc$$$ if(ityp .eq. 1) go to 36\nc$$$ do 85 i=1,imid\nc$$$ zv(i,m+1,i3) = a(ns)*zv(i,m-1,i1)-c(ns)*zv(i,m+1,i1)\nc$$$ 85 continue\nc$$$ 36 if(m .eq. nlat-1) return\nc$$$ if(ityp .eq. 2) go to 71\nc$$$ ns = ns+1\nc$$$ do 70 i=1,imid\nc$$$ zv(i,m+2,i3) = a(ns)*zv(i,m,i1)-c(ns)*zv(i,m+2,i1)\nc$$$ 70 continue\nc$$$ 71 nstrt = m+3\nc$$$ if(ityp .eq. 1) nstrt = m+4\nc$$$ if(nstrt .gt. nlat) go to 80\nc$$$ nstp = 2\nc$$$ if(ityp .eq. 0) nstp = 1\nc$$$ do 75 np1=nstrt,nlat,nstp\nc$$$ ns = ns+nstp\nc$$$ do 75 i=1,imid\nc$$$ zv(i,np1,i3) = a(ns)*zv(i,np1-2,i1)+b(ns)*zv(i,np1-2,i3)\nc$$$ 1 -c(ns)*zv(i,np1,i1)\nc$$$ 75 continue\nc$$$ 80 return\nc$$$ end\nc$$$ subroutine zwin (ityp,nlat,nlon,m,zw,i3,wzwin)\nc$$$ implicit double precision (a-h,o-z)\nc$$$ dimension zw(1) ,wzwin(1)\nc$$$ imid = (nlat+1)/2\nc$$$ lim = nlat*imid\nc$$$ mmax = min0(nlat,(nlon+1)/2)\nc$$$ labc = (max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\nc$$$ iw1 = lim+1\nc$$$ iw2 = iw1+lim\nc$$$ iw3 = iw2+labc\nc$$$ iw4 = iw3+labc\nc$$$c\nc$$$c the length of wzwin is 2*lim+3*labc\nc$$$c\nc$$$ call zwin1 (ityp,nlat,m,zw,imid,i3,wzwin,wzwin(iw1),wzwin(iw2),\nc$$$ 1 wzwin(iw3),wzwin(iw4))\nc$$$ return\nc$$$ end\nc$$$ subroutine zwin1 (ityp,nlat,m,zw,imid,i3,zw1,zw2,a,b,c)\nc$$$ implicit double precision (a-h,o-z)\nc$$$ dimension zw(imid,nlat,3),zw1(imid,1),zw2(imid,1),\nc$$$ 1 a(1),b(1),c(1)\nc$$$ save i1,i2\nc$$$ ihold = i1\nc$$$ i1 = i2\nc$$$ i2 = i3\nc$$$ i3 = ihold\nc$$$ if(m-2)25,30,35\nc$$$ 25 i1 = 1\nc$$$ i2 = 2\nc$$$ i3 = 3\nc$$$ do 45 np1=2,nlat\nc$$$ do 45 i=1,imid\nc$$$ zw(i,np1,i3) = zw1(i,np1)\nc$$$ 45 continue\nc$$$ return\nc$$$ 30 do 50 np1=3,nlat\nc$$$ do 50 i=1,imid\nc$$$ zw(i,np1,i3) = zw2(i,np1)\nc$$$ 50 continue\nc$$$ return\nc$$$ 35 ns = ((m-2)*(nlat+nlat-m-1))/2+1\nc$$$ if(ityp .eq. 1) go to 36\nc$$$ do 85 i=1,imid\nc$$$ zw(i,m+1,i3) = a(ns)*zw(i,m-1,i1)-c(ns)*zw(i,m+1,i1)\nc$$$ 85 continue\nc$$$ 36 if(m .eq. nlat-1) return\nc$$$ if(ityp .eq. 2) go to 71\nc$$$ ns = ns+1\nc$$$ do 70 i=1,imid\nc$$$ zw(i,m+2,i3) = a(ns)*zw(i,m,i1)-c(ns)*zw(i,m+2,i1)\nc$$$ 70 continue\nc$$$ 71 nstrt = m+3\nc$$$ if(ityp .eq. 1) nstrt = m+4\nc$$$ if(nstrt .gt. nlat) go to 80\nc$$$ nstp = 2\nc$$$ if(ityp .eq. 0) nstp = 1\nc$$$ do 75 np1=nstrt,nlat,nstp\nc$$$ ns = ns+nstp\nc$$$ do 75 i=1,imid\nc$$$ zw(i,np1,i3) = a(ns)*zw(i,np1-2,i1)+b(ns)*zw(i,np1-2,i3)\nc$$$ 1 -c(ns)*zw(i,np1,i1)\nc$$$ 75 continue\nc$$$ 80 return\nc$$$ end\n subroutine vbinit (nlat,nlon,wvbin,dwork)\n implicit double precision (a-h,o-z)\n dimension wvbin(1)\n double precision dwork(*)\n imid = (nlat+1)/2\n iw1 = 2*nlat*imid+1\nc\nc the length of wvbin is 2*nlat*imid+3*((nlat-3)*nlat+2)/2\nc the length of dwork is nlat+2\nc\n call vbini1 (nlat,nlon,imid,wvbin,wvbin(iw1),dwork,\n 1 dwork(nlat/2+2))\n return\n end\n subroutine vbini1 (nlat,nlon,imid,vb,abc,cvb,work)\n implicit double precision (a-h,o-z)\nc\nc abc must have 3*(max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\nc locations where mmax = min0(nlat,(nlon+1)/2)\nc cvb and work must each have nlat+1 locations\nc\n dimension vb(imid,nlat,2),abc(1)\n double precision pi,dt,cvb(1),th,vbh,work(1)\n pi = 4.d0*datan(1.d0)\n dt = pi/(nlat-1)\n mdo = min0(2,nlat,(nlon+1)/2)\n do 160 mp1=1,mdo\n m = mp1-1\n do 160 np1=mp1,nlat\n n = np1-1\n call dvbk(m,n,cvb,work)\n do 165 i=1,imid\n th = (i-1)*dt\n call dvbt(m,n,th,cvb,vbh)\n vb(i,np1,mp1) = vbh\n 165 continue\n 160 continue\n call rabcv(nlat,nlon,abc)\n return\n end\n subroutine wbinit (nlat,nlon,wwbin,dwork)\n implicit double precision (a-h,o-z)\n dimension wwbin(1)\n double precision dwork(*)\n imid = (nlat+1)/2\n iw1 = 2*nlat*imid+1\nc\nc the length of wwbin is 2*nlat*imid+3*((nlat-3)*nlat+2)/2\nc the length of dwork is nlat+2\nc\n call wbini1 (nlat,nlon,imid,wwbin,wwbin(iw1),dwork,\n 1 dwork(nlat/2+2))\n return\n end\n subroutine wbini1 (nlat,nlon,imid,wb,abc,cwb,work)\n implicit double precision (a-h,o-z)\nc\nc abc must have 3*(max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\nc locations where mmax = min0(nlat,(nlon+1)/2)\nc cwb and work must each have nlat/2+1 locations\nc\n dimension wb(imid,nlat,2),abc(1)\n double precision pi,dt,cwb(1),wbh,th,work(1)\n pi = 4.d0*datan(1.d0)\n dt = pi/(nlat-1)\n mdo = min0(3,nlat,(nlon+1)/2)\n if(mdo .lt. 2) return\n do 160 mp1=2,mdo\n m = mp1-1\n do 160 np1=mp1,nlat\n n = np1-1\n call dwbk(m,n,cwb,work)\n do 165 i=1,imid\n th = (i-1)*dt\n call dwbt(m,n,th,cwb,wbh)\n wb(i,np1,m) = wbh\n 165 continue\n 160 continue\n call rabcw(nlat,nlon,abc)\n return\n end\n subroutine vbin (ityp,nlat,nlon,m,vb,i3,wvbin,i1,i2)\n implicit double precision (a-h,o-z)\n dimension vb(1) ,wvbin(1)\n imid = (nlat+1)/2\n lim = nlat*imid\n mmax = min0(nlat,(nlon+1)/2)\n labc = (max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\n iw1 = lim+1\n iw2 = iw1+lim\n iw3 = iw2+labc\n iw4 = iw3+labc\nc\nc the length of wvbin is 2*lim+3*labc\nc\n call vbin1 (ityp,nlat,m,vb,imid,i3,wvbin,wvbin(iw1),wvbin(iw2),\n 1 wvbin(iw3),wvbin(iw4),i1,i2)\n return\n end\n subroutine vbin1 (ityp,nlat,m,vb,imid,i3,vbz,vb1,a,b,c,i1,i2)\n implicit double precision (a-h,o-z)\n dimension vb(imid,nlat,3),vbz(imid,1),vb1(imid,1),\n 1 a(1),b(1),c(1)\n ihold = i1\n i1 = i2\n i2 = i3\n i3 = ihold\n if(m-1)25,30,35\n 25 i1 = 1\n i2 = 2\n i3 = 3\n do 45 np1=1,nlat\n do 45 i=1,imid\n vb(i,np1,i3) = vbz(i,np1)\n 45 continue\n return\n 30 do 50 np1=2,nlat\n do 50 i=1,imid\n vb(i,np1,i3) = vb1(i,np1)\n 50 continue\n return\n 35 ns = ((m-2)*(nlat+nlat-m-1))/2+1\n if(ityp .eq. 1) go to 36\n do 85 i=1,imid\n vb(i,m+1,i3) = a(ns)*vb(i,m-1,i1)-c(ns)*vb(i,m+1,i1)\n 85 continue\n 36 if(m .eq. nlat-1) return\n if(ityp .eq. 2) go to 71\n ns = ns+1\n do 70 i=1,imid\n vb(i,m+2,i3) = a(ns)*vb(i,m,i1)-c(ns)*vb(i,m+2,i1)\n 70 continue\n 71 nstrt = m+3\n if(ityp .eq. 1) nstrt = m+4\n if(nstrt .gt. nlat) go to 80\n nstp = 2\n if(ityp .eq. 0) nstp = 1\n do 75 np1=nstrt,nlat,nstp\n ns = ns+nstp\n do 75 i=1,imid\n vb(i,np1,i3) = a(ns)*vb(i,np1-2,i1)+b(ns)*vb(i,np1-2,i3)\n 1 -c(ns)*vb(i,np1,i1)\n 75 continue\n 80 return\n end\n subroutine wbin (ityp,nlat,nlon,m,wb,i3,wwbin,i1,i2)\n implicit double precision (a-h,o-z)\n dimension wb(1) ,wwbin(1)\n imid = (nlat+1)/2\n lim = nlat*imid\n mmax = min0(nlat,(nlon+1)/2)\n labc = (max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\n iw1 = lim+1\n iw2 = iw1+lim\n iw3 = iw2+labc\n iw4 = iw3+labc\nc\nc the length of wwbin is 2*lim+3*labc\nc\n call wbin1 (ityp,nlat,m,wb,imid,i3,wwbin,wwbin(iw1),wwbin(iw2),\n 1 wwbin(iw3),wwbin(iw4),i1,i2)\n return\n end\n subroutine wbin1 (ityp,nlat,m,wb,imid,i3,wb1,wb2,a,b,c,i1,i2)\n implicit double precision (a-h,o-z)\n dimension wb(imid,nlat,3),wb1(imid,1),wb2(imid,1),\n 1 a(1),b(1),c(1)\n ihold = i1\n i1 = i2\n i2 = i3\n i3 = ihold\n if(m-2)25,30,35\n 25 i1 = 1\n i2 = 2\n i3 = 3\n do 45 np1=2,nlat\n do 45 i=1,imid\n wb(i,np1,i3) = wb1(i,np1)\n 45 continue\n return\n 30 do 50 np1=3,nlat\n do 50 i=1,imid\n wb(i,np1,i3) = wb2(i,np1)\n 50 continue\n return\n 35 ns = ((m-2)*(nlat+nlat-m-1))/2+1\n if(ityp .eq. 1) go to 36\n do 85 i=1,imid\n wb(i,m+1,i3) = a(ns)*wb(i,m-1,i1)-c(ns)*wb(i,m+1,i1)\n 85 continue\n 36 if(m .eq. nlat-1) return\n if(ityp .eq. 2) go to 71\n ns = ns+1\n do 70 i=1,imid\n wb(i,m+2,i3) = a(ns)*wb(i,m,i1)-c(ns)*wb(i,m+2,i1)\n 70 continue\n 71 nstrt = m+3\n if(ityp .eq. 1) nstrt = m+4\n if(nstrt .gt. nlat) go to 80\n nstp = 2\n if(ityp .eq. 0) nstp = 1\n do 75 np1=nstrt,nlat,nstp\n ns = ns+nstp\n do 75 i=1,imid\n wb(i,np1,i3) = a(ns)*wb(i,np1-2,i1)+b(ns)*wb(i,np1-2,i3)\n 1 -c(ns)*wb(i,np1,i1)\n 75 continue\n 80 return\n end\n subroutine dzvk(nlat,m,n,czv,work)\n implicit double precision (a-h,o-z)\nc\nc subroutine dzvk computes the coefficients in the trigonometric\nc expansion of the quadrature function zvbar(n,m,theta)\nc\nc input parameters\nc\nc nlat the number of colatitudes including the poles.\nc\nc n the degree (subscript) of wbarv(n,m,theta)\nc\nc m the order (superscript) of wbarv(n,m,theta)\nc\nc work a work array with at least nlat/2+1 locations\nc\nc output parameter\nc\nc czv the fourier coefficients of zvbar(n,m,theta).\nc\n dimension czv(1),work(1)\n double precision czv,sc1,sum,work,t1,t2\n if(n .le. 0) return\n lc = (nlat+1)/2\n sc1 = 2.d0/dfloat(nlat-1)\n call dvbk(m,n,work,czv)\n nmod = mod(n,2)\n mmod = mod(m,2)\n if(nmod .ne. 0) go to 1\n if(mmod .ne. 0) go to 2\nc\nc n even, m even\nc\n kdo = n/2\n do 9 id=1,lc\n i = id+id-2\n sum = 0.d0\n do 10 k=1,kdo\n t1 = 1.d0-(k+k+i)**2\n t2 = 1.d0-(k+k-i)**2\n sum = sum+work(k)*(t1-t2)/(t1*t2)\n 10 continue\n czv(id) = sc1*sum\n 9 continue\n return\nc\nc n even, m odd\nc\n 2 kdo = n/2\n do 5 id=1,lc\n i = id+id-2\n sum = 0.d0\n do 6 k=1,kdo\n t1 = 1.d0-(k+k+i)**2\n t2 = 1.d0-(k+k-i)**2\n sum = sum+work(k)*(t1+t2)/(t1*t2)\n 6 continue\n czv(id) = sc1*sum\n 5 continue\n return\n 1 if(mmod .ne. 0) go to 3\nc\nc n odd, m even\nc\n kdo = (n+1)/2\n do 19 id=1,lc\n i = id+id-3\n sum = 0.d0\n do 20 k=1,kdo\n t1 = 1.d0-(k+k-1+i)**2\n t2 = 1.d0-(k+k-1-i)**2\n sum = sum+work(k)*(t1-t2)/(t1*t2)\n 20 continue\n czv(id) = sc1*sum\n 19 continue\n return\nc\nc n odd, m odd\nc\n 3 kdo = (n+1)/2\n do 15 id=1,lc\n i = id+id-1\n sum = 0.d0\n do 16 k=1,kdo\n t1 = 1.d0-(k+k-1+i)**2\n t2 = 1.d0-(k+k-1-i)**2\n sum = sum+work(k)*(t1+t2)/(t1*t2)\n 16 continue\n czv(id) = sc1*sum\n 15 continue\n return\n end\n subroutine dzvt(nlat,m,n,th,czv,zvh)\n implicit double precision (a-h,o-z)\nc\nc subroutine dzvt tabulates the function zvbar(n,m,theta)\nc at theta = th in double precision\nc\nc input parameters\nc\nc nlat the number of colatitudes including the poles.\nc\nc n the degree (subscript) of zvbar(n,m,theta)\nc\nc m the order (superscript) of zvbar(n,m,theta)\nc\nc czv the fourier coefficients of zvbar(n,m,theta)\nc as computed by subroutine zwk.\nc\nc output parameter\nc\nc zvh zvbar(m,n,theta) evaluated at theta = th\nc\n dimension czv(1)\n double precision th,czv,zvh,cth,sth,cdt,sdt,chh\n zvh = 0.d0\n if(n .le. 0) return\n lc = (nlat+1)/2\n lq = lc-1\n ls = lc-2\n cth = dcos(th)\n sth = dsin(th)\n cdt = cth*cth-sth*sth\n sdt = 2.d0*sth*cth\n lmod = mod(nlat,2)\n mmod = mod(m,2)\n nmod = mod(n,2)\n if(lmod .eq. 0) go to 50\n if(nmod .ne. 0) go to 1\n cth = cdt\n sth = sdt\n if(mmod .ne. 0) go to 2\nc\nc nlat odd n even m even\nc\n do 10 k=1,ls\n zvh = zvh+czv(k+1)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 10 continue\n return\nc\nc nlat odd n even m odd\nc\n 2 zvh = .5d0*czv(1)\n do 20 k=2,lq\n zvh = zvh+czv(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 20 continue\n zvh = zvh+.5d0*czv(lc)*dcos((nlat-1)*th)\n return\n 1 if(mmod .ne. 0) go to 3\nc\nc nlat odd n odd m even\nc\n do 30 k=1,lq\n zvh = zvh+czv(k+1)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 30 continue\n return\nc\nc nlat odd n odd m odd\nc\n 3 do 40 k=1,lq\n zvh = zvh+czv(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 40 continue\n return\n 50 if(nmod .ne. 0) go to 51\n cth = cdt\n sth = sdt\n if(mmod .ne. 0) go to 52\nc\nc nlat even n even m even\nc\n do 55 k=1,lq\n zvh = zvh+czv(k+1)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 55 continue\n return\nc\nc nlat even n even m odd\nc\n 52 zvh = .5d0*czv(1)\n do 57 k=2,lc\n zvh = zvh+czv(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 57 continue\n return\n 51 if(mmod .ne. 0) go to 53\nc\nc nlat even n odd m even\nc\n do 58 k=1,lq\n zvh = zvh+czv(k+1)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 58 continue\n return\nc\nc nlat even n odd m odd\nc\n 53 zvh = .5d0*czv(lc)*dcos((nlat-1)*th)\n do 60 k=1,lq\n zvh = zvh+czv(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 60 continue\n return\n end\n subroutine dzwk(nlat,m,n,czw,work)\n implicit double precision (a-h,o-z)\nc\nc subroutine dzwk computes the coefficients in the trigonometric\nc expansion of the quadrature function zwbar(n,m,theta)\nc\nc input parameters\nc\nc nlat the number of colatitudes including the poles.\nc\nc n the degree (subscript) of zwbar(n,m,theta)\nc\nc m the order (superscript) of zwbar(n,m,theta)\nc\nc work a work array with at least nlat/2+1 locations\nc\nc output parameter\nc\nc czw the fourier coefficients of zwbar(n,m,theta).\nc\n dimension czw(1),work(1)\n double precision czw,work,sc1,sum,t1,t2\n if(n .le. 0) return\n lc = (nlat+1)/2\n sc1 = 2.d0/dfloat(nlat-1)\n call dwbk(m,n,work,czw)\n nmod = mod(n,2)\n mmod = mod(m,2)\n if(nmod .ne. 0) go to 1\n if(mmod .ne. 0) go to 2\nc\nc n even, m even\nc\n kdo = n/2\n do 19 id=1,lc\n i = id+id-3\n sum = 0.d0\n do 20 k=1,kdo\n t1 = 1.d0-(k+k-1+i)**2\n t2 = 1.d0-(k+k-1-i)**2\n sum = sum+work(k)*(t1-t2)/(t1*t2)\n 20 continue\n czw(id) = sc1*sum\n 19 continue\n return\nc\nc n even, m odd\nc\n 2 kdo = n/2\n do 15 id=1,lc\n i = id+id-1\n sum = 0.d0\n do 16 k=1,kdo\n t1 = 1.d0-(k+k-1+i)**2\n t2 = 1.d0-(k+k-1-i)**2\n sum = sum+work(k)*(t1+t2)/(t1*t2)\n 16 continue\n czw(id) = sc1*sum\n 15 continue\n return\n 1 if(mmod .ne. 0) go to 3\nc\nc n odd, m even\nc\n kdo = (n-1)/2\n do 9 id=1,lc\n i = id+id-2\n sum = 0.d0\n do 10 k=1,kdo\n t1 = 1.d0-(k+k+i)**2\n t2 = 1.d0-(k+k-i)**2\n sum = sum+work(k)*(t1-t2)/(t1*t2)\n 10 continue\n czw(id) = sc1*sum\n 9 continue\n return\nc\nc n odd, m odd\nc\n 3 kdo = (n+1)/2\n do 5 id=1,lc\n i = id+id-2\n sum = work(1)/(1.d0-i*i)\n if(kdo .lt. 2) go to 29\n do 6 kp1=2,kdo\n k = kp1-1\n t1 = 1.d0-(k+k+i)**2\n t2 = 1.d0-(k+k-i)**2\n sum = sum+work(kp1)*(t1+t2)/(t1*t2)\n 6 continue\n 29 czw(id) = sc1*sum\n 5 continue\n return\n end\n subroutine dzwt(nlat,m,n,th,czw,zwh)\n implicit double precision (a-h,o-z)\nc\nc subroutine dzwt tabulates the function zwbar(n,m,theta)\nc at theta = th in double precision\nc\nc input parameters\nc\nc nlat the number of colatitudes including the poles.\nc nlat must be an odd integer\nc\nc n the degree (subscript) of zwbar(n,m,theta)\nc\nc m the order (superscript) of zwbar(n,m,theta)\nc\nc czw the fourier coefficients of zwbar(n,m,theta)\nc as computed by subroutine zwk.\nc\nc output parameter\nc\nc zwh zwbar(m,n,theta) evaluated at theta = th\nc\n dimension czw(1)\n double precision czw,zwh,th,cth,sth,cdt,sdt,chh\n zwh = 0.d0\n if(n .le. 0) return\n lc = (nlat+1)/2\n lq = lc-1\n ls = lc-2\n cth = dcos(th)\n sth = dsin(th)\n cdt = cth*cth-sth*sth\n sdt = 2.d0*sth*cth\n lmod = mod(nlat,2)\n mmod = mod(m,2)\n nmod = mod(n,2)\n if(lmod .eq. 0) go to 50\n if(nmod .ne. 0) go to 1\n if(mmod .ne. 0) go to 2\nc\nc nlat odd n even m even\nc\n do 30 k=1,lq\n zwh = zwh+czw(k+1)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 30 continue\n return\nc\nc nlat odd n even m odd\nc\n 2 do 40 k=1,lq\n zwh = zwh+czw(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 40 continue\n return\n 1 cth = cdt\n sth = sdt\n if(mmod .ne. 0) go to 3\nc\nc nlat odd n odd m even\nc\n do 10 k=1,ls\n zwh = zwh+czw(k+1)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 10 continue\n return\nc\nc nlat odd n odd m odd\nc\n 3 zwh = .5d0*czw(1)\n do 20 k=2,lq\n zwh = zwh+czw(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 20 continue\n zwh = zwh+.5d0*czw(lc)*dcos((nlat-1)*th)\n return\n 50 if(nmod .ne. 0) go to 51\n if(mmod .ne. 0) go to 52\nc\nc nlat even n even m even\nc\n do 55 k=1,lq\n zwh = zwh+czw(k+1)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 55 continue\n return\nc\nc nlat even n even m odd\nc\n 52 zwh = .5d0*czw(lc)*dcos((nlat-1)*th)\n do 60 k=1,lq\n zwh = zwh+czw(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 60 continue\n return\n 51 cth = cdt\n sth = sdt\n if(mmod .ne. 0) go to 53\nc\nc nlat even n odd m even\nc\n do 65 k=1,lq\n zwh = zwh+czw(k+1)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 65 continue\n return\nc\nc nlat even n odd m odd\nc\n 53 zwh = .5d0*czw(1)\n do 70 k=2,lc\n zwh = zwh+czw(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 70 continue\n return\n end\n subroutine dvbk(m,n,cv,work)\n implicit double precision (a-h,o-z)\n double precision cv(1),work(1),fn,fk,cf\n cv(1) = 0.d0\n if(n .le. 0) return\n fn = n\n srnp1 = dsqrt(fn*(fn+1.d0))\n cf = 2.d0*m/srnp1\n modn = mod(n,2)\n modm = mod(m,2)\n call dnlfk(m,n,work)\n if(modn .ne. 0) go to 70\n ncv = n/2\n if(ncv .eq. 0) return\n fk = 0.d0\n if(modm .ne. 0) go to 60\nc\nc n even m even\nc\n do 55 l=1,ncv\n fk = fk+2.d0\n cv(l) = -fk*work(l+1)/srnp1\n 55 continue\n return\nc\nc n even m odd\nc\n 60 do 65 l=1,ncv\n fk = fk+2.d0\n cv(l) = fk*work(l)/srnp1\n 65 continue\n return\n 70 ncv = (n+1)/2\n fk = -1.d0\n if(modm .ne. 0) go to 80\nc\nc n odd m even\nc\n do 75 l=1,ncv\n fk = fk+2.d0\n cv(l) = -fk*work(l)/srnp1\n 75 continue\n return\nc\nc n odd m odd\nc\n 80 do 85 l=1,ncv\n fk = fk+2.d0\n cv(l) = fk*work(l)/srnp1\n 85 continue\n return\n end\n subroutine dwbk(m,n,cw,work)\n implicit double precision (a-h,o-z)\n double precision cw(1),work(1),fn,cf,srnp1\n cw(1) = 0.d0\n if(n.le.0 .or. m.le.0) return\n fn = n\n srnp1 = dsqrt(fn*(fn+1.d0))\n cf = 2.d0*m/srnp1\n modn = mod(n,2)\n modm = mod(m,2)\n call dnlfk(m,n,work)\n if(m .eq. 0) go to 50\n if(modn .ne. 0) go to 30\n l = n/2\n if(l .eq. 0) go to 50\n if(modm .ne. 0) go to 20\nc\nc n even m even\nc\n cw(l) = -cf*work(l+1)\n 10 l = l-1\n if(l .le. 0) go to 50\n cw(l) = cw(l+1)-cf*work(l+1)\n go to 10\nc\nc n even m odd\nc\n 20 cw(l) = cf*work(l)\n 25 l = l-1\n if(l .le. 0) go to 50\n cw(l) = cw(l+1)+cf*work(l)\n go to 25\n 30 if(modm .ne. 0) go to 40\n l = (n-1)/2\n if(l .eq. 0) go to 50\nc\nc n odd m even\nc\n cw(l) = -cf*work(l+1)\n 35 l = l-1\n if(l .le. 0) go to 50\n cw(l) = cw(l+1)-cf*work(l+1)\n go to 35\nc\nc n odd m odd\nc\n 40 l = (n+1)/2\n cw(l) = cf*work(l)\n 45 l = l-1\n if(l .le. 0) go to 50\n cw(l) = cw(l+1)+cf*work(l)\n go to 45\n 50 return\n end\n subroutine dvbt(m,n,theta,cv,vh)\n implicit double precision (a-h,o-z)\n dimension cv(1)\n double precision cv,vh,theta,cth,sth,cdt,sdt,chh\n vh = 0.d0\n if(n.eq.0) return\n cth = dcos(theta)\n sth = dsin(theta)\n cdt = cth*cth-sth*sth\n sdt = 2.d0*sth*cth\n mmod = mod(m,2)\n nmod = mod(n,2)\n if(nmod .ne. 0) go to 1\n cth = cdt\n sth = sdt\n if(mmod .ne. 0) go to 2\nc\nc n even m even\nc\n ncv = n/2\n do 10 k=1,ncv\n vh = vh+cv(k)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 10 continue\n return\nc\nc n even m odd\nc\n 2 ncv = n/2\n do 15 k=1,ncv\n vh = vh+cv(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 15 continue\n return\n 1 if(mmod .ne. 0) go to 3\nc\nc n odd m even\nc\n ncv = (n+1)/2\n do 20 k=1,ncv\n vh = vh+cv(k)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 20 continue\n return\nc\nc case m odd and n odd\nc\n 3 ncv = (n+1)/2\n do 25 k=1,ncv\n vh = vh+cv(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 25 continue\n return\n end\n subroutine dwbt(m,n,theta,cw,wh)\n implicit double precision (a-h,o-z)\n dimension cw(1)\n double precision theta,cw,wh,cth,sth,cdt,sdt,chh\n wh = 0.d0\n if(n.le.0 .or. m.le.0) return\n cth = dcos(theta)\n sth = dsin(theta)\n cdt = cth*cth-sth*sth\n sdt = 2.d0*sth*cth\n mmod=mod(m,2)\n nmod=mod(n,2)\n if(nmod .ne. 0) go to 1\n if(mmod .ne. 0) go to 2\nc\nc n even m even\nc\n ncw = n/2\n do 10 k=1,ncw\n wh = wh+cw(k)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 10 continue\n return\nc\nc n even m odd\nc\n 2 ncw = n/2\n do 8 k=1,ncw\n wh = wh+cw(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 8 continue\n return\n 1 cth = cdt\n sth = sdt\n if(mmod .ne. 0) go to 3\nc\nc n odd m even\nc\n ncw = (n-1)/2\n do 20 k=1,ncw\n wh = wh+cw(k)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 20 continue\n return\nc\nc case m odd and n odd\nc\n 3 ncw = (n+1)/2\n wh = .5d0*cw(1)\n if(ncw.lt.2) return\n do 25 k=2,ncw\n wh = wh+cw(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 25 continue\n return\n end\n subroutine rabcv(nlat,nlon,abc)\n implicit double precision (a-h,o-z)\nc\nc subroutine rabcp computes the coefficients in the recurrence\nc relation for the functions vbar(m,n,theta). array abc\nc must have 3*(max0(mmax-2,0)*(nlat+nlat-mmax-1))/2 locations.\nc\n dimension abc(1)\n mmax = min0(nlat,(nlon+1)/2)\n labc = (max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\n iw1 = labc+1\n iw2 = iw1+labc\n call rabcv1(nlat,nlon,abc,abc(iw1),abc(iw2))\n return\n end\n subroutine rabcv1(nlat,nlon,a,b,c)\n implicit double precision (a-h,o-z)\nc\nc coefficients a, b, and c for computing vbar(m,n,theta) are\nc stored in location ((m-2)*(nlat+nlat-m-1))/2+n+1\nc\n dimension a(1),b(1),c(1)\n mmax = min0(nlat,(nlon+1)/2)\n if(mmax .lt. 3) return\n do 215 mp1=3,mmax\n m = mp1-1\n ns = ((m-2)*(nlat+nlat-m-1))/2+1\n fm = dfloat(m)\n tm = fm+fm\n temp = tm*(tm-1.d0)\n tpn = (fm-2.d0)*(fm-1.d0)/(fm*(fm+1.d0))\n a(ns) = dsqrt(tpn*(tm+1.d0)*(tm-2.d0)/temp)\n c(ns) = dsqrt(2.d0/temp)\n if(m .eq. nlat-1) go to 215\n ns = ns+1\n temp = tm*(tm+1.d0)\n tpn = (fm-1.d0)*fm/((fm+1.d0)*(fm+2.d0))\n a(ns) = dsqrt(tpn*(tm+3.d0)*(tm-2.d0)/temp)\n c(ns) = dsqrt(6.d0/temp)\n mp3 = m+3\n if(mp3 .gt. nlat) go to 215\n do 210 np1=mp3,nlat\n n = np1-1\n ns = ns+1\n fn = dfloat(n)\n tn = fn+fn\n cn = (tn+1.d0)/(tn-3.d0)\n tpn = (fn-2.d0)*(fn-1.d0)/(fn*(fn+1.d0))\n fnpm = fn+fm\n fnmm = fn-fm\n temp = fnpm*(fnpm-1.d0)\n a(ns) = dsqrt(tpn*cn*(fnpm-3.d0)*(fnpm-2.d0)/temp)\n b(ns) = dsqrt(tpn*cn*fnmm*(fnmm-1.d0)/temp)\n c(ns) = dsqrt((fnmm+1.d0)*(fnmm+2.d0)/temp)\n 210 continue\n 215 continue\n return\n end\n subroutine rabcw(nlat,nlon,abc)\n implicit double precision (a-h,o-z)\nc\nc subroutine rabcw computes the coefficients in the recurrence\nc relation for the functions wbar(m,n,theta). array abc\nc must have 3*(max0(mmax-2,0)*(nlat+nlat-mmax-1))/2 locations.\nc\n dimension abc(1)\n mmax = min0(nlat,(nlon+1)/2)\n labc = (max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\n iw1 = labc+1\n iw2 = iw1+labc\n call rabcw1(nlat,nlon,abc,abc(iw1),abc(iw2))\n return\n end\n subroutine rabcw1(nlat,nlon,a,b,c)\n implicit double precision (a-h,o-z)\nc\nc coefficients a, b, and c for computing wbar(m,n,theta) are\nc stored in location ((m-2)*(nlat+nlat-m-1))/2+n+1\nc\n dimension a(1),b(1),c(1)\n mmax = min0(nlat,(nlon+1)/2)\n if(mmax .lt. 4) return\n do 215 mp1=4,mmax\n m = mp1-1\n ns = ((m-2)*(nlat+nlat-m-1))/2+1\n fm = dfloat(m)\n tm = fm+fm\n temp = tm*(tm-1.d0)\n tpn = (fm-2.d0)*(fm-1.d0)/(fm*(fm+1.d0))\n tph = fm/(fm-2.d0)\n a(ns) = tph*dsqrt(tpn*(tm+1.d0)*(tm-2.d0)/temp)\n c(ns) = tph*dsqrt(2.d0/temp)\n if(m .eq. nlat-1) go to 215\n ns = ns+1\n temp = tm*(tm+1.d0)\n tpn = (fm-1.d0)*fm/((fm+1.d0)*(fm+2.d0))\n tph = fm/(fm-2.d0)\n a(ns) = tph*dsqrt(tpn*(tm+3.d0)*(tm-2.d0)/temp)\n c(ns) = tph*dsqrt(6.d0/temp)\n mp3 = m+3\n if(mp3 .gt. nlat) go to 215\n do 210 np1=mp3,nlat\n n = np1-1\n ns = ns+1\n fn = dfloat(n)\n tn = fn+fn\n cn = (tn+1.d0)/(tn-3.d0)\n fnpm = fn+fm\n fnmm = fn-fm\n temp = fnpm*(fnpm-1.d0)\n tpn = (fn-2.d0)*(fn-1.d0)/(fn*(fn+1.d0))\n tph = fm/(fm-2.d0)\n a(ns) = tph*dsqrt(tpn*cn*(fnpm-3.d0)*(fnpm-2.d0)/temp)\n b(ns) = dsqrt(tpn*cn*fnmm*(fnmm-1.d0)/temp)\n c(ns) = tph*dsqrt((fnmm+1.d0)*(fnmm+2.d0)/temp)\n 210 continue\n 215 continue\n return\n end\n subroutine vtinit (nlat,nlon,wvbin,dwork)\n implicit double precision (a-h,o-z)\n dimension wvbin(*)\n double precision dwork(*)\n imid = (nlat+1)/2\n iw1 = 2*nlat*imid+1\nc\nc the length of wvbin is 2*nlat*imid+3*((nlat-3)*nlat+2)/2\nc the length of dwork is nlat+2\nc\n call vtini1 (nlat,nlon,imid,wvbin,wvbin(iw1),dwork,\n 1 dwork(nlat/2+2))\n return\n end\n subroutine vtini1 (nlat,nlon,imid,vb,abc,cvb,work)\n implicit double precision (a-h,o-z)\nc\nc abc must have 3*(max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\nc locations where mmax = min0(nlat,(nlon+1)/2)\nc cvb and work must each have nlat/2+1 locations\nc\n dimension vb(imid,nlat,2),abc(1),cvb(1)\n double precision pi,dt,cvb,th,vbh,work(*)\n pi = 4.d0*datan(1.d0)\n dt = pi/(nlat-1)\n mdo = min0(2,nlat,(nlon+1)/2)\n do 160 mp1=1,mdo\n m = mp1-1\n do 160 np1=mp1,nlat\n n = np1-1\n call dvtk(m,n,cvb,work)\n do 165 i=1,imid\n th = (i-1)*dt\n call dvtt(m,n,th,cvb,vbh)\n vb(i,np1,mp1) = vbh\n 165 continue\n 160 continue\n call rabcv(nlat,nlon,abc)\n return\n end\n subroutine wtinit (nlat,nlon,wwbin,dwork)\n implicit double precision (a-h,o-z)\n dimension wwbin(1)\n double precision dwork(*)\n imid = (nlat+1)/2\n iw1 = 2*nlat*imid+1\nc\nc the length of wwbin is 2*nlat*imid+3*((nlat-3)*nlat+2)/2\nc the length of dwork is nlat+2\nc\n call wtini1 (nlat,nlon,imid,wwbin,wwbin(iw1),dwork,\n 1 dwork(nlat/2+2))\n return\n end\n subroutine wtini1 (nlat,nlon,imid,wb,abc,cwb,work)\n implicit double precision (a-h,o-z)\nc\nc abc must have 3*(max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\nc locations where mmax = min0(nlat,(nlon+1)/2)\nc cwb and work must each have nlat/2+1 locations\nc\n dimension wb(imid,nlat,2),abc(1)\n double precision pi,dt,cwb(*),wbh,th,work(*)\n pi = 4.d0*datan(1.d0)\n dt = pi/(nlat-1)\n mdo = min0(3,nlat,(nlon+1)/2)\n if(mdo .lt. 2) return\n do 160 mp1=2,mdo\n m = mp1-1\n do 160 np1=mp1,nlat\n n = np1-1\n call dwtk(m,n,cwb,work)\n do 165 i=1,imid\n th = (i-1)*dt\n call dwtt(m,n,th,cwb,wbh)\n wb(i,np1,m) = wbh\n 165 continue\n 160 continue\n call rabcw(nlat,nlon,abc)\n return\n end\n subroutine vtgint (nlat,nlon,theta,wvbin,work)\n implicit double precision (a-h,o-z)\n dimension wvbin(*)\n double precision theta(*), work(*)\n imid = (nlat+1)/2\n iw1 = 2*nlat*imid+1\nc\nc theta is a double precision array with (nlat+1)/2 locations\nc nlat is the maximum value of n+1\nc the length of wvbin is 2*nlat*imid+3*((nlat-3)*nlat+2)/2\nc the length of work is nlat+2\nc\n call vtgit1 (nlat,nlon,imid,theta,wvbin,wvbin(iw1),\n + work,work(nlat/2+2))\n return\n end\n subroutine vtgit1 (nlat,nlon,imid,theta,vb,abc,cvb,work)\n implicit double precision (a-h,o-z)\nc\nc abc must have 3*(max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\nc locations where mmax = min0(nlat,(nlon+1)/2)\nc cvb and work must each have nlat/2+1 locations\nc\n dimension vb(imid,nlat,2),abc(*)\n double precision theta(*),cvb(*),work(*),vbh\n mdo = min0(2,nlat,(nlon+1)/2)\n do 160 mp1=1,mdo\n m = mp1-1\n do 160 np1=mp1,nlat\n n = np1-1\n call dvtk(m,n,cvb,work)\n do 165 i=1,imid\n call dvtt(m,n,theta(i),cvb,vbh)\n vb(i,np1,mp1) = vbh\n 165 continue\n 160 continue\n call rabcv(nlat,nlon,abc)\n return\n end\n subroutine wtgint (nlat,nlon,theta,wwbin,work)\n implicit double precision (a-h,o-z)\n dimension wwbin(*)\n double precision theta(*), work(*)\n imid = (nlat+1)/2\n iw1 = 2*nlat*imid+1\nc\nc theta is a double precision array with (nlat+1)/2 locations\nc nlat is the maximum value of n+1\nc the length of wwbin is 2*nlat*imid+3*((nlat-3)*nlat+2)/2\nc the length of work is nlat+2\nc\n call wtgit1 (nlat,nlon,imid,theta,wwbin,wwbin(iw1),\n 1 work,work(nlat/2+2))\n return\n end\n subroutine wtgit1 (nlat,nlon,imid,theta,wb,abc,cwb,work)\n implicit double precision (a-h,o-z)\nc\nc abc must have 3*((nlat-3)*nlat+2)/2 locations\nc cwb and work must each have nlat/2+1 locations\nc\n dimension wb(imid,nlat,2),abc(1)\n double precision theta(*), cwb(*), work(*), wbh\n mdo = min0(3,nlat,(nlon+1)/2)\n if(mdo .lt. 2) return\n do 160 mp1=2,mdo\n m = mp1-1\n do 160 np1=mp1,nlat\n n = np1-1\n call dwtk(m,n,cwb,work)\n do 165 i=1,imid\n call dwtt(m,n,theta(i),cwb,wbh)\n wb(i,np1,m) = wbh\n 165 continue\n 160 continue\n call rabcw(nlat,nlon,abc)\n return\n end\n subroutine dvtk(m,n,cv,work)\n implicit double precision (a-h,o-z)\n double precision cv(*),work(*),fn,fk,cf,srnp1\n cv(1) = 0.d0\n if(n .le. 0) return\n fn = n\n srnp1 = dsqrt(fn*(fn+1.d0))\n cf = 2.d0*m/srnp1\n modn = mod(n,2)\n modm = mod(m,2)\n call dnlfk(m,n,work)\n if(modn .ne. 0) go to 70\n ncv = n/2\n if(ncv .eq. 0) return\n fk = 0.d0\n if(modm .ne. 0) go to 60\nc\nc n even m even\nc\n do 55 l=1,ncv\n fk = fk+2.d0\n cv(l) = -fk*fk*work(l+1)/srnp1\n 55 continue\n return\nc\nc n even m odd\nc\n 60 do 65 l=1,ncv\n fk = fk+2.d0\n cv(l) = -fk*fk*work(l)/srnp1\n 65 continue\n return\n 70 ncv = (n+1)/2\n fk = -1.d0\n if(modm .ne. 0) go to 80\nc\nc n odd m even\nc\n do 75 l=1,ncv\n fk = fk+2.d0\n cv(l) = -fk*fk*work(l)/srnp1\n 75 continue\n return\nc\nc n odd m odd\nc\n 80 do 85 l=1,ncv\n fk = fk+2.d0\n cv(l) = -fk*fk*work(l)/srnp1\n 85 continue\n return\n end\n subroutine dwtk(m,n,cw,work)\n implicit double precision (a-h,o-z)\n double precision cw(*),work(*),fn,cf,srnp1\n cw(1) = 0.d0\n if(n.le.0 .or. m.le.0) return\n fn = n\n srnp1 = dsqrt(fn*(fn+1.d0))\n cf = 2.d0*m/srnp1\n modn = mod(n,2)\n modm = mod(m,2)\n call dnlfk(m,n,work)\n if(m .eq. 0) go to 50\n if(modn .ne. 0) go to 30\n l = n/2\n if(l .eq. 0) go to 50\n if(modm .ne. 0) go to 20\nc\nc n even m even\nc\n cw(l) = -cf*work(l+1)\n 10 l = l-1\n if(l .le. 0) go to 50\n cw(l) = cw(l+1)-cf*work(l+1)\n cw(l+1) = (l+l+1)*cw(l+1)\n go to 10\nc\nc n even m odd\nc\n 20 cw(l) = cf*work(l)\n 25 l = l-1\n if(l) 50,27,26\n 26 cw(l) = cw(l+1)+cf*work(l)\n 27 cw(l+1) = -(l+l+1)*cw(l+1)\n go to 25\n 30 if(modm .ne. 0) go to 40\n l = (n-1)/2\n if(l .eq. 0) go to 50\nc\nc n odd m even\nc\n cw(l) = -cf*work(l+1)\n 35 l = l-1\n if(l) 50,37,36\n 36 cw(l) = cw(l+1)-cf*work(l+1)\n 37 cw(l+1) = (l+l+2)*cw(l+1)\n go to 35\nc\nc n odd m odd\nc\n 40 l = (n+1)/2\n cw(l) = cf*work(l)\n 45 l = l-1\n if(l) 50,47,46\n 46 cw(l) = cw(l+1)+cf*work(l)\n 47 cw(l+1) = -(l+l)*cw(l+1)\n go to 45\n 50 return\n end\n subroutine dvtt(m,n,theta,cv,vh)\n implicit double precision (a-h,o-z)\n dimension cv(1)\n double precision cv,vh,theta,cth,sth,cdt,sdt,chh\n vh = 0.d0\n if(n.eq.0) return\n cth = dcos(theta)\n sth = dsin(theta)\n cdt = cth*cth-sth*sth\n sdt = 2.d0*sth*cth\n mmod = mod(m,2)\n nmod = mod(n,2)\n if(nmod .ne. 0) go to 1\n cth = cdt\n sth = sdt\n if(mmod .ne. 0) go to 2\nc\nc n even m even\nc\n ncv = n/2\n do 10 k=1,ncv\n vh = vh+cv(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 10 continue\n return\nc\nc n even m odd\nc\n 2 ncv = n/2\n do 15 k=1,ncv\n vh = vh+cv(k)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 15 continue\n return\n 1 if(mmod .ne. 0) go to 3\nc\nc n odd m even\nc\n ncv = (n+1)/2\n do 20 k=1,ncv\n vh = vh+cv(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 20 continue\n return\nc\nc case m odd and n odd\nc\n 3 ncv = (n+1)/2\n do 25 k=1,ncv\n vh = vh+cv(k)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 25 continue\n return\n end\n subroutine dwtt(m,n,theta,cw,wh)\n implicit double precision (a-h,o-z)\n dimension cw(1)\n double precision theta,cw,wh,cth,sth,cdt,sdt,chh\n wh = 0.d0\n if(n.le.0 .or. m.le.0) return\n cth = dcos(theta)\n sth = dsin(theta)\n cdt = cth*cth-sth*sth\n sdt = 2.d0*sth*cth\n mmod=mod(m,2)\n nmod=mod(n,2)\n if(nmod .ne. 0) go to 1\n if(mmod .ne. 0) go to 2\nc\nc n even m even\nc\n ncw = n/2\n do 10 k=1,ncw\n wh = wh+cw(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 10 continue\n return\nc\nc n even m odd\nc\n 2 ncw = n/2\n do 8 k=1,ncw\n wh = wh+cw(k)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 8 continue\n return\n 1 cth = cdt\n sth = sdt\n if(mmod .ne. 0) go to 3\nc\nc n odd m even\nc\n ncw = (n-1)/2\n do 20 k=1,ncw\n wh = wh+cw(k)*cth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 20 continue\n return\nc\nc case m odd and n odd\nc\n 3 ncw = (n+1)/2\n wh = 0.d0\n if(ncw.lt.2) return\n do 25 k=2,ncw\n wh = wh+cw(k)*sth\n chh = cdt*cth-sdt*sth\n sth = sdt*cth+cdt*sth\n cth = chh\n 25 continue\n return\n end\n subroutine vbgint (nlat,nlon,theta,wvbin,work)\n implicit double precision (a-h,o-z)\n dimension wvbin(1)\n double precision theta(*),work(*)\n imid = (nlat+1)/2\n iw1 = 2*nlat*imid+1\nc\nc theta is a double precision array with (nlat+1)/2 locations\nc nlat is the maximum value of n+1\nc the length of wvbin is 2*nlat*imid+3*((nlat-3)*nlat+2)/2\nc the length of work is nlat+2\nc\n call vbgit1 (nlat,nlon,imid,theta,wvbin,wvbin(iw1),\n + work,work(nlat/2+2))\n return\n end\n subroutine vbgit1 (nlat,nlon,imid,theta,vb,abc,cvb,work)\n implicit double precision (a-h,o-z)\nc\nc abc must have 3*(max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\nc locations where mmax = min0(nlat,(nlon+1)/2)\nc cvb and work must each have nlat/2+1 locations\nc\n dimension vb(imid,nlat,2),abc(1)\n double precision cvb(1),theta(1),vbh,work(1)\n mdo = min0(2,nlat,(nlon+1)/2)\n do 160 mp1=1,mdo\n m = mp1-1\n do 160 np1=mp1,nlat\n n = np1-1\n call dvbk(m,n,cvb,work)\n do 165 i=1,imid\n call dvbt(m,n,theta(i),cvb,vbh)\n vb(i,np1,mp1) = vbh\n 165 continue\n 160 continue\n call rabcv(nlat,nlon,abc)\n return\n end\n subroutine wbgint (nlat,nlon,theta,wwbin,work)\n implicit double precision (a-h,o-z)\n dimension wwbin(1)\n double precision work(*),theta(*)\n imid = (nlat+1)/2\n iw1 = 2*nlat*imid+1\nc\nc theta is a double precision array with (nlat+1)/2 locations\nc nlat is the maximum value of n+1\nc the length of wwbin is 2*nlat*imid+3*((nlat-3)*nlat+2)/2\nc the length of work is nlat+2\nc\n call wbgit1 (nlat,nlon,imid,theta,wwbin,wwbin(iw1),\n + work,work(nlat/2+2))\n return\n end\n subroutine wbgit1 (nlat,nlon,imid,theta,wb,abc,cwb,work)\n implicit double precision (a-h,o-z)\nc\nc abc must have 3*((nlat-3)*nlat+2)/2 locations\nc cwb and work must each have nlat/2+1 locations\nc\n dimension wb(imid,nlat,2),abc(1)\n double precision cwb(1),theta(1),wbh,work(1)\n mdo = min0(3,nlat,(nlon+1)/2)\n if(mdo .lt. 2) return\n do 160 mp1=2,mdo\n m = mp1-1\n do 160 np1=mp1,nlat\n n = np1-1\n call dwbk(m,n,cwb,work)\n do 165 i=1,imid\n call dwbt(m,n,theta(i),cwb,wbh)\n wb(i,np1,m) = wbh\n 165 continue\n 160 continue\n call rabcw(nlat,nlon,abc)\n return\n end\n\n" }, { "path": "external/SPHEREPACK/vhags.f", "content": "c\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc * *\nc * copyright (c) 1998 by UCAR *\nc * *\nc * University Corporation for Atmospheric Research *\nc * *\nc * all rights reserved *\nc * *\nc * SPHEREPACK version 3.2 *\nc * *\nc * A Package of Fortran77 Subroutines and Programs *\nc * *\nc * for Modeling Geophysical Processes *\nc * *\nc * by *\nc * *\nc * John Adams and Paul Swarztrauber *\nc * *\nc * of *\nc * *\nc * the National Center for Atmospheric Research *\nc * *\nc * Boulder, Colorado (80307) U.S.A. *\nc * *\nc * which is sponsored by *\nc * *\nc * the National Science Foundation *\nc * *\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc\nc\nc\nc ... file vhags.f\nc\nc this file contains code and documentation for subroutines\nc vhags and vhagsi\nc\nc ... files which must be loaded with vhags.f\nc\nc sphcom.f, hrfft.f, gaqd.f\nc\nc subroutine vhags(nstrvw,nstrbc,noffsvw,noffsbc,\nc nlat,nlon,ityp,nt,v,w,idvw,jdvw,br,bi,cr,ci,\nc + mdab,ndab,wvhags,lvhags,work,lwork,ierror)\nc\nc subroutine vhags performs the vector spherical harmonic analysis\nc on the vector field (v,w) and stores the result in the arrays\nc br, bi, cr, and ci. v(i,j) and w(i,j) are the colatitudinal \nc (measured from the north pole) and east longitudinal components\nc respectively, located at the gaussian colatitude point theta(i)\nc and longitude phi(j) = (j-1)*2*pi/nlon. the spectral\nc representation of (v,w) is given at output parameters v,w in \nc subroutine vhses. \nc\nc input parameters\nc\nc nstrvw,nstrbc the strides in v,w and br,bi,cr,ci\nc noffsvw,noffsbc the offset in v,w and br,bi,cr,ci\nc -- must be between 0 and stride-1\nc nlat the number of points in the gaussian colatitude grid on the\nc full sphere. these lie in the interval (0,pi) and are computed\nc in radians in theta(1) <...< theta(nlat) by subroutine gaqd.\nc if nlat is odd the equator will be included as the grid point\nc theta((nlat+1)/2). if nlat is even the equator will be\nc excluded as a grid point and will lie half way between\nc theta(nlat/2) and theta(nlat/2+1). nlat must be at least 3.\nc note: on the half sphere, the number of grid points in the\nc colatitudinal direction is nlat/2 if nlat is even or\nc (nlat+1)/2 if nlat is odd.\nc\nc\nc nlon the number of distinct londitude points. nlon determines\nc the grid increment in longitude as 2*pi/nlon. for example\nc nlon = 72 for a five degree grid. nlon must be greater\nc than zero. the axisymmetric case corresponds to nlon=1.\nc the efficiency of the computation is improved when nlon\nc is a product of small prime numbers.\nc\nc NOTE: this is a modified version of spherepack. Changes from\nc the original version to the current one have only been\nc tested for ityp=0,1,2. For this reason an error code will\nc be returned if ityp>2.\nc\nc ityp = 0 no symmetries exist about the equator. the analysis\nc is performed on the entire sphere. i.e. on the\nc arrays v(i,j),w(i,j) for i=1,...,nlat and \nc j=1,...,nlon. \nc\nc = 1 no symmetries exist about the equator. the analysis\nc is performed on the entire sphere. i.e. on the\nc arrays v(i,j),w(i,j) for i=1,...,nlat and \nc j=1,...,nlon. the curl of (v,w) is zero. that is, \nc (d/dtheta (sin(theta) w) - dv/dphi)/sin(theta) = 0. \nc the coefficients cr and ci are zero.\nc\nc = 2 no symmetries exist about the equator. the analysis\nc is performed on the entire sphere. i.e. on the\nc arrays v(i,j),w(i,j) for i=1,...,nlat and \nc j=1,...,nlon. the divergence of (v,w) is zero. i.e., \nc (d/dtheta (sin(theta) v) + dw/dphi)/sin(theta) = 0. \nc the coefficients br and bi are zero.\nc\nc = 3 v is symmetric and w is antisymmetric about the \nc equator. the analysis is performed on the northern\nc hemisphere only. i.e., if nlat is odd the analysis\nc is performed on the arrays v(i,j),w(i,j) for \nc i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the analysis is performed on the the arrays\nc v(i,j),w(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc\nc = 4 v is symmetric and w is antisymmetric about the \nc equator. the analysis is performed on the northern\nc hemisphere only. i.e., if nlat is odd the analysis\nc is performed on the arrays v(i,j),w(i,j) for \nc i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the analysis is performed on the the arrays\nc v(i,j),w(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc the curl of (v,w) is zero. that is, \nc (d/dtheta (sin(theta) w) - dv/dphi)/sin(theta) = 0. \nc the coefficients cr and ci are zero.\nc\nc = 5 v is symmetric and w is antisymmetric about the \nc equator. the analysis is performed on the northern\nc hemisphere only. i.e., if nlat is odd the analysis\nc is performed on the arrays v(i,j),w(i,j) for \nc i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the analysis is performed on the the arrays\nc v(i,j),w(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc the divergence of (v,w) is zero. i.e., \nc (d/dtheta (sin(theta) v) + dw/dphi)/sin(theta) = 0. \nc the coefficients br and bi are zero.\nc\nc = 6 v is antisymmetric and w is symmetric about the \nc equator. the analysis is performed on the northern\nc hemisphere only. i.e., if nlat is odd the analysis\nc is performed on the arrays v(i,j),w(i,j) for \nc i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the analysis is performed on the the arrays\nc v(i,j),w(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc\nc = 7 v is antisymmetric and w is symmetric about the \nc equator. the analysis is performed on the northern\nc hemisphere only. i.e., if nlat is odd the analysis\nc is performed on the arrays v(i,j),w(i,j) for \nc i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the analysis is performed on the the arrays\nc v(i,j),w(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc the curl of (v,w) is zero. that is, \nc (d/dtheta (sin(theta) w) - dv/dphi)/sin(theta) = 0. \nc the coefficients cr and ci are zero.\nc\nc = 8 v is antisymmetric and w is symmetric about the \nc equator. the analysis is performed on the northern\nc hemisphere only. i.e., if nlat is odd the analysis\nc is performed on the arrays v(i,j),w(i,j) for \nc i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the analysis is performed on the the arrays\nc v(i,j),w(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc the divergence of (v,w) is zero. i.e., \nc (d/dtheta (sin(theta) v) + dw/dphi)/sin(theta) = 0. \nc the coefficients br and bi are zero.\nc\nc\nc nt the number of analyses. in the program that calls vhags,\nc the arrays v,w,br,bi,cr, and ci can be three dimensional\nc in which case multiple analyses will be performed.\nc the third index is the analysis index which assumes the \nc values k=1,...,nt. for a single analysis set nt=1. the\nc discription of the remaining parameters is simplified\nc by assuming that nt=1 or that all the arrays are two\nc dimensional.\nc\nc v,w two or three dimensional arrays (see input parameter nt)\nc that contain the vector function to be analyzed.\nc v is the colatitudnal component and w is the east \nc longitudinal component. v(i,j),w(i,j) contain the\nc components at the gaussian colatitude point theta(i)\nc and longitude phi(j) = (j-1)*2*pi/nlon. the index ranges\nc are defined above at the input parameter ityp.\nc\nc idvw the first dimension of the arrays v,w as it appears in\nc the program that calls vhags. if ityp .le. 2 then idvw\nc must be at least nlat. if ityp .gt. 2 and nlat is\nc even then idvw must be at least nlat/2. if ityp .gt. 2\nc and nlat is odd then idvw must be at least (nlat+1)/2.\nc\nc jdvw the second dimension of the arrays v,w as it appears in\nc the program that calls vhags. jdvw must be at least nlon.\nc\nc mdab the first dimension of the arrays br,bi,cr, and ci as it\nc appears in the program that calls vhags. mdab must be at\nc least min0(nlat,nlon/2) if nlon is even or at least\nc min0(nlat,(nlon+1)/2) if nlon is odd.\nc\nc ndab the second dimension of the arrays br,bi,cr, and ci as it\nc appears in the program that calls vhags. ndab must be at\nc least nlat.\nc\nc wvhags an array which must be initialized by subroutine vhgsi.\nc once initialized, wvhags can be used repeatedly by vhags\nc as long as nlon and nlat remain unchanged. wvhags must\nc not be altered between calls of vhags.\nc\nc lvhags the dimension of the array wvhags as it appears in the\nc program that calls vhags. define\nc\nc l1 = min0(nlat,nlon/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc then lvhags must be at least\nc\nc l1*l2(nlat+nlat-l1+1)+nlon+15\nc\nc ??? (nlat+1)*(nlat+1)*nlat/2 + nlon + 15\nc\nc\nc\nc work a work array that does not have to be saved.\nc\nc lwork the dimension of the array work as it appears in the\nc program that calls vhags. define\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc if ityp .le. 2 then lwork must be at least\nc the larger of the two quantities\nc\nc 3*nlat*(nlat+1)+2 (required by vhagsi)\nc\nc and\nc\nc (2*nt+1)*nlat*nlon\nc\nc if ityp .gt. 2 then lwork must be at least\nc the larger of the two quantities\nc\nc 3*nlat*(nlat+1)+2 (required by vhagsi)\nc\nc and\nc\nc (2*nt+1)*l2*nlon\nc\nc\nc **************************************************************\nc\nc output parameters\nc\nc br,bi two or three dimensional arrays (see input parameter nt)\nc cr,ci that contain the vector spherical harmonic coefficients\nc in the spectral representation of v(i,j) and w(i,j) given \nc in the discription of subroutine vhses. br(mp1,np1),\nc bi(mp1,np1),cr(mp1,np1), and ci(mp1,np1) are computed \nc for mp1=1,...,mmax and np1=mp1,...,nlat except for np1=nlat\nc and odd mp1. mmax=min0(nlat,nlon/2) if nlon is even or \nc mmax=min0(nlat,(nlon+1)/2) if nlon is odd. \nc \nc ierror = 0 no errors\nc = 1 error in the specification of nlat\nc = 2 error in the specification of nlon\nc = 3 error in the specification of ityp\nc = 4 error in the specification of nt\nc = 5 error in the specification of idvw\nc = 6 error in the specification of jdvw\nc = 7 error in the specification of mdab\nc = 8 error in the specification of ndab\nc = 9 error in the specification of lvhags\nc = 10 error in the specification of lwork\nc\nc\nc subroutine vhagsi(nlat,nlon,wvhags,lvhags,work,lwork,ierror)\nc\nc subroutine vhagsi initializes the array wvhags which can then be\nc used repeatedly by subroutine vhags until nlat or nlon is changed.\nc\nc input parameters\nc\nc nlat the number of points in the gaussian colatitude grid on the\nc full sphere. these lie in the interval (0,pi) and are computed\nc in radians in theta(1) <...< theta(nlat) by subroutine gaqd.\nc if nlat is odd the equator will be included as the grid point\nc theta((nlat+1)/2). if nlat is even the equator will be\nc excluded as a grid point and will lie half way between\nc theta(nlat/2) and theta(nlat/2+1). nlat must be at least 3.\nc note: on the half sphere, the number of grid points in the\nc colatitudinal direction is nlat/2 if nlat is even or\nc (nlat+1)/2 if nlat is odd.\nc\nc nlon the number of distinct londitude points. nlon determines\nc the grid increment in longitude as 2*pi/nlon. for example\nc nlon = 72 for a five degree grid. nlon must be greater\nc than zero. the axisymmetric case corresponds to nlon=1.\nc the efficiency of the computation is improved when nlon\nc is a product of small prime numbers.\nc\nc lvhags the dimension of the array wvhags as it appears in the\nc program that calls vhagsi. define\nc\nc l1 = min0(nlat,nlon/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc then lvhags must be at least\nc\nc 3*nlat*(nlat+1)+2 (required by vhagsi)\nc\nc dwork a double precision work space that does not need to be saved\nc\nc ldwork the dimension of the array dwork as it appears in the\nc program that calls vhagsi. ldwork must be at least\nc\nc (3*nlat*(nlat+3)+2)/2\nc\nc **************************************************************\nc\nc output parameters\nc\nc wvhags an array which is initialized for use by subroutine vhags.\nc once initialized, wvhags can be used repeatedly by vhags\nc as long as nlat and nlon remain unchanged. wvhags must not\nc be altered between calls of vhags.\nc\nc\nc ierror = 0 no errors\nc = 1 error in the specification of nlat\nc = 2 error in the specification of nlon\nc = 3 error in the specification of lvhags\nc = 4 error in the specification of ldwork\nc\n subroutine vhags(nstrvw,nstrbc,noffsvw,noffsbc,\n 1 nlat,nlon,ityp,nt,v,w,idvw,jdvw,br,bi,cr,ci,\n 1 mdab,ndab,wvhags,lvhags,work,lwork,ierror)\n implicit double precision (a-h,o-z)\n dimension v(nstrvw,idvw,jdvw,1),w(nstrvw,idvw,jdvw,1),\n 1 br(nstrbc,mdab,ndab,1),bi(nstrbc,mdab,ndab,1),\n 1 cr(nstrbc,mdab,ndab,1),ci(nstrbc,mdab,ndab,1),\n 2 work(1),wvhags(1)\n ierror = 1\n if(nlat .lt. 3) return\n ierror = 2\n if(nlon .lt. 1) return\n ierror = 3\n if(ityp.lt.0 .or. ityp.gt.8) return\nc see note above about symmetries\n if(ityp.gt.2) return\n ierror = 4\n if(nt .lt. 0) return\n ierror = 5\n imid = (nlat+1)/2\n if((ityp.le.2 .and. idvw.lt.nlat) .or.\n 1 (ityp.gt.2 .and. idvw.lt.imid)) return\n ierror = 6\n if(jdvw .lt. nlon) return\n ierror = 7\n mmax = min0(nlat,(nlon+1)/2)\n if(mdab .lt. mmax) return\n ierror = 8\n if(ndab .lt. nlat) return\n ierror = 9\n idz = (mmax*(nlat+nlat-mmax+1))/2\n lzimn = idz*imid\n if(lvhags .lt. lzimn+lzimn+nlon+15) return\n ierror = 10\n idv = nlat\n if(ityp .gt. 2) idv = imid\n lnl = nt*idv*nlon\n if(lwork .lt. lnl+lnl+idv*nlon) return\n ierror = 11\n if((noffsvw.lt.0).or.(noffsvw.ge.nstrvw)) return\n if((noffsbc.lt.0).or.(noffsbc.ge.nstrbc)) return\n ierror = 0\n ist = 0\n if(ityp .le. 2) ist = imid\nc\nc set wvhags pointers\nc\n lmn = nlat*(nlat+1)/2\n jw1 = 1\n jw2 = jw1+imid*lmn\n jw3 = jw2+imid*lmn\nc\nc set work pointers\nc\n iw1 = ist+1\n iw2 = lnl+1\n iw3 = iw2+ist\n iw4 = iw2+lnl\n call vhags1(nstrvw,nstrbc,noffsvw,noffsbc,\n + nlat,nlon,ityp,nt,imid,idvw,jdvw,v,w,mdab,ndab,\n + br,bi,cr,ci,idv,work,work(iw1),work(iw2),work(iw3),\n + work(iw4),idz,wvhags(jw1),wvhags(jw2),wvhags(jw3))\n return\n end\n\n subroutine vhags1(nstrvw,nstrbc,noffsvw,noffsbc,\n +nlat,nlon,ityp,nt,imid,idvw,jdvw,v,w,mdab,\n +ndab,br,bi,cr,ci,idv,ve,vo,we,wo,work,idz,vb,wb,wrfft)\n implicit double precision (a-h,o-z)\n dimension v(nstrvw,idvw,jdvw,1),w(nstrvw,idvw,jdvw,1),\n 1 br(nstrbc,mdab,ndab,1),bi(nstrbc,mdab,ndab,1),\n 1 cr(nstrbc,mdab,ndab,1),ci(nstrbc,mdab,ndab,1),\n 2 ve(idv,nlon,1),vo(idv,nlon,1),we(idv,nlon,1),\n 3 wo(idv,nlon,1),work(1),\n 4 vb(imid,1),wb(imid,1),wrfft(1)\n ncvw=1+noffsvw\n ncbc=1+noffsbc\n nlp1 = nlat+1\n tsn = 2.d0/nlon\n fsn = 4.d0/nlon\n mlat = mod(nlat,2)\n mlon = mod(nlon,2)\n mmax = min0(nlat,(nlon+1)/2)\n imm1 = imid\n if(mlat .ne. 0) imm1 = imid-1\n if(ityp .gt. 2) go to 3 \n do 5 k=1,nt \n do 5 i=1,imm1\n do 5 j=1,nlon\n ve(i,j,k) = tsn*(v(ncvw,i,j,k)+v(ncvw,nlp1-i,j,k))\n vo(i,j,k) = tsn*(v(ncvw,i,j,k)-v(ncvw,nlp1-i,j,k))\n we(i,j,k) = tsn*(w(ncvw,i,j,k)+w(ncvw,nlp1-i,j,k))\n wo(i,j,k) = tsn*(w(ncvw,i,j,k)-w(ncvw,nlp1-i,j,k))\n 5 continue\n go to 2\n 3 do 8 k=1,nt\n do 8 i=1,imm1 \n do 8 j=1,nlon\n ve(i,j,k) = fsn*v(ncvw,i,j,k)\n vo(i,j,k) = fsn*v(ncvw,i,j,k)\n we(i,j,k) = fsn*w(ncvw,i,j,k)\n wo(i,j,k) = fsn*w(ncvw,i,j,k)\n 8 continue\n 2 if(mlat .eq. 0) go to 7\n do 6 k=1,nt \n do 6 j=1,nlon\n ve(imid,j,k) = tsn*v(ncvw,imid,j,k)\n we(imid,j,k) = tsn*w(ncvw,imid,j,k)\n 6 continue\n 7 do 9 k=1,nt\n call hrfftf(idv,nlon,ve(1,1,k),idv,wrfft,work)\n call hrfftf(idv,nlon,we(1,1,k),idv,wrfft,work)\n 9 continue \n ndo1 = nlat\n ndo2 = nlat\n if(mlat .ne. 0) ndo1 = nlat-1\n if(mlat .eq. 0) ndo2 = nlat-1\n if(ityp.eq.2 .or. ityp.eq.5 .or. ityp.eq.8) go to 11 \n do 10 k=1,nt\n do 10 mp1=1,mmax\n do 10 np1=mp1,nlat\n br(1,mp1,np1,k)=0.d0\n bi(1,mp1,np1,k)=0.d0\n 10 continue\n 11 if(ityp.eq.1 .or. ityp.eq.4 .or. ityp.eq.7) go to 13 \n do 12 k=1,nt\n do 12 mp1=1,mmax\n do 12 np1=mp1,nlat\n cr(ncbc,mp1,np1,k)=0.d0\n ci(ncbc,mp1,np1,k)=0.d0\n 12 continue\n 13 itypp = ityp+1\n go to (1,100,200,300,400,500,600,700,800),itypp\nc\nc case ityp=0 , no symmetries\nc\nc case m=0\nc\n 1 do 15 k=1,nt\n do 15 i=1,imid\n do 15 np1=2,ndo2,2\n br(1,1,np1,k) = br(1,1,np1,k)+vb(i,np1)*ve(i,1,k)\n cr(ncbc,1,np1,k) = cr(ncbc,1,np1,k)-vb(i,np1)*we(i,1,k)\n 15 continue\n do 16 k=1,nt\n do 16 i=1,imm1\n do 16 np1=3,ndo1,2\n br(1,1,np1,k) = br(1,1,np1,k)+vb(i,np1)*vo(i,1,k)\n cr(ncbc,1,np1,k) = cr(ncbc,1,np1,k)-vb(i,np1)*wo(i,1,k)\n 16 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) return\n do 20 mp1=2,mmax\n m = mp1-1\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 17\n do 23 k=1,nt\n do 23 i=1,imm1\n do 23 np1=mp1,ndo1,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)+vb(i,np1+mb)*vo(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*we(i,2*mp1-1,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)+vb(i,np1+mb)*vo(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*we(i,2*mp1-2,k)\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*wo(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*ve(i,2*mp1-1,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*wo(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*ve(i,2*mp1-2,k)\n 23 continue\n if(mlat .eq. 0) go to 17\n do 24 k=1,nt\n do 24 np1=mp1,ndo1,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)\n 1 +wb(imid,np1+mb)*we(imid,2*mp1-1,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)\n 1 -wb(imid,np1+mb)*we(imid,2*mp1-2,k)\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 +wb(imid,np1+mb)*ve(imid,2*mp1-1,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -wb(imid,np1+mb)*ve(imid,2*mp1-2,k)\n 24 continue\n 17 if(mp2 .gt. ndo2) go to 20\n do 21 k=1,nt\n do 21 i=1,imm1\n do 21 np1=mp2,ndo2,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)+vb(i,np1+mb)*ve(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*wo(i,2*mp1-1,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)+vb(i,np1+mb)*ve(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*wo(i,2*mp1-2,k)\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*we(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*vo(i,2*mp1-1,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*we(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*vo(i,2*mp1-2,k)\n 21 continue\n if(mlat .eq. 0) go to 20\n do 22 k=1,nt\n do 22 np1=mp2,ndo2,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)\n 1 +vb(imid,np1+mb)*ve(imid,2*mp1-2,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)\n 1 +vb(imid,np1+mb)*ve(imid,2*mp1-1,k)\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 -vb(imid,np1+mb)*we(imid,2*mp1-2,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -vb(imid,np1+mb)*we(imid,2*mp1-1,k)\n 22 continue\n 20 continue\n return\nc\nc case ityp=1 , no symmetries but cr and ci equal zero\nc\nc case m=0\nc\n 100 do 115 k=1,nt\n do 115 i=1,imid\n do 115 np1=2,ndo2,2\n br(1,1,np1,k) = br(1,1,np1,k)+vb(i,np1)*ve(i,1,k)\n 115 continue\n do 116 k=1,nt\n do 116 i=1,imm1\n do 116 np1=3,ndo1,2\n br(1,1,np1,k) = br(1,1,np1,k)+vb(i,np1)*vo(i,1,k)\n 116 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) return\n do 120 mp1=2,mmax\n m = mp1-1\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 117\n do 123 k=1,nt\n do 123 i=1,imm1\n do 123 np1=mp1,ndo1,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)+vb(i,np1+mb)*vo(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*we(i,2*mp1-1,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)+vb(i,np1+mb)*vo(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*we(i,2*mp1-2,k)\n 123 continue\n if(mlat .eq. 0) go to 117\n do 124 k=1,nt\n do 124 np1=mp1,ndo1,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)\n 1 +wb(imid,np1+mb)*we(imid,2*mp1-1,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)\n 1 -wb(imid,np1+mb)*we(imid,2*mp1-2,k)\n 124 continue\n 117 if(mp2 .gt. ndo2) go to 120\n do 121 k=1,nt\n do 121 i=1,imm1\n do 121 np1=mp2,ndo2,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)+vb(i,np1+mb)*ve(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*wo(i,2*mp1-1,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)+vb(i,np1+mb)*ve(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*wo(i,2*mp1-2,k)\n 121 continue\n if(mlat .eq. 0) go to 120\n do 122 k=1,nt\n do 122 np1=mp2,ndo2,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)\n 1 +vb(imid,np1+mb)*ve(imid,2*mp1-2,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)\n 1 +vb(imid,np1+mb)*ve(imid,2*mp1-1,k)\n 122 continue\n 120 continue\n return\nc\nc case ityp=2 , no symmetries but br and bi equal zero \nc\nc case m=0\nc\n 200 do 215 k=1,nt\n do 215 i=1,imid\n do 215 np1=2,ndo2,2\n cr(ncbc,1,np1,k) = cr(ncbc,1,np1,k)-vb(i,np1)*we(i,1,k)\n 215 continue\n do 216 k=1,nt\n do 216 i=1,imm1\n do 216 np1=3,ndo1,2\n cr(ncbc,1,np1,k) = cr(ncbc,1,np1,k)-vb(i,np1)*wo(i,1,k)\n 216 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) return\n do 220 mp1=2,mmax\n m = mp1-1\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 217\n do 223 k=1,nt\n do 223 i=1,imm1\n do 223 np1=mp1,ndo1,2\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*wo(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*ve(i,2*mp1-1,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*wo(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*ve(i,2*mp1-2,k)\n 223 continue\n if(mlat .eq. 0) go to 217\n do 224 k=1,nt\n do 224 np1=mp1,ndo1,2\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 +wb(imid,np1+mb)*ve(imid,2*mp1-1,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -wb(imid,np1+mb)*ve(imid,2*mp1-2,k)\n 224 continue\n 217 if(mp2 .gt. ndo2) go to 220\n do 221 k=1,nt\n do 221 i=1,imm1\n do 221 np1=mp2,ndo2,2\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*we(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*vo(i,2*mp1-1,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*we(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*vo(i,2*mp1-2,k)\n 221 continue\n if(mlat .eq. 0) go to 220\n do 222 k=1,nt\n do 222 np1=mp2,ndo2,2\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 -vb(imid,np1+mb)*we(imid,2*mp1-2,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -vb(imid,np1+mb)*we(imid,2*mp1-1,k)\n 222 continue\n 220 continue\n return\nc\nc case ityp=3 , v even , w odd\nc\nc case m=0\nc\n 300 do 315 k=1,nt\n do 315 i=1,imid\n do 315 np1=2,ndo2,2\n br(1,1,np1,k) = br(1,1,np1,k)+vb(i,np1)*ve(i,1,k)\n 315 continue\n do 316 k=1,nt\n do 316 i=1,imm1\n do 316 np1=3,ndo1,2\n cr(ncbc,1,np1,k) = cr(ncbc,1,np1,k)-vb(i,np1)*wo(i,1,k)\n 316 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) return\n do 320 mp1=2,mmax\n m = mp1-1\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 317\n do 323 k=1,nt\n do 323 i=1,imm1\n do 323 np1=mp1,ndo1,2\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*wo(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*ve(i,2*mp1-1,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*wo(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*ve(i,2*mp1-2,k)\n 323 continue\n if(mlat .eq. 0) go to 317\n do 324 k=1,nt\n do 324 np1=mp1,ndo1,2\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 +wb(imid,np1+mb)*ve(imid,2*mp1-1,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -wb(imid,np1+mb)*ve(imid,2*mp1-2,k)\n 324 continue\n 317 if(mp2 .gt. ndo2) go to 320\n do 321 k=1,nt\n do 321 i=1,imm1\n do 321 np1=mp2,ndo2,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)+vb(i,np1+mb)*ve(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*wo(i,2*mp1-1,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)+vb(i,np1+mb)*ve(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*wo(i,2*mp1-2,k)\n 321 continue\n if(mlat .eq. 0) go to 320\n do 322 k=1,nt\n do 322 np1=mp2,ndo2,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)\n 1 +vb(imid,np1+mb)*ve(imid,2*mp1-2,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)\n 1 +vb(imid,np1+mb)*ve(imid,2*mp1-1,k)\n 322 continue\n 320 continue\n return\nc\nc case ityp=4 , v even, w odd, and cr and ci equal 0. \nc\nc case m=0\nc\n 400 do 415 k=1,nt\n do 415 i=1,imid\n do 415 np1=2,ndo2,2\n br(1,1,np1,k) = br(1,1,np1,k)+vb(i,np1)*ve(i,1,k)\n 415 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) return\n do 420 mp1=2,mmax\n m = mp1-1\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp2 .gt. ndo2) go to 420\n do 421 k=1,nt\n do 421 i=1,imm1\n do 421 np1=mp2,ndo2,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)+vb(i,np1+mb)*ve(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*wo(i,2*mp1-1,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)+vb(i,np1+mb)*ve(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*wo(i,2*mp1-2,k)\n 421 continue\n if(mlat .eq. 0) go to 420\n do 422 k=1,nt\n do 422 np1=mp2,ndo2,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)\n 1 +vb(imid,np1+mb)*ve(imid,2*mp1-2,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)\n 1 +vb(imid,np1+mb)*ve(imid,2*mp1-1,k)\n 422 continue\n 420 continue\n return\nc\nc case ityp=5 v even, w odd, and br and bi equal zero\nc\nc case m=0\nc\n 500 do 516 k=1,nt\n do 516 i=1,imm1\n do 516 np1=3,ndo1,2\n cr(ncbc,1,np1,k) = cr(ncbc,1,np1,k)-vb(i,np1)*wo(i,1,k)\n 516 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) return\n do 520 mp1=2,mmax\n m = mp1-1\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 520\n do 523 k=1,nt\n do 523 i=1,imm1\n do 523 np1=mp1,ndo1,2\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*wo(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*ve(i,2*mp1-1,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*wo(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*ve(i,2*mp1-2,k)\n 523 continue\n if(mlat .eq. 0) go to 520\n do 524 k=1,nt\n do 524 np1=mp1,ndo1,2\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 +wb(imid,np1+mb)*ve(imid,2*mp1-1,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -wb(imid,np1+mb)*ve(imid,2*mp1-2,k)\n 524 continue\n 520 continue\n return\nc\nc case ityp=6 , v odd , w even\nc\nc case m=0\nc\n 600 do 615 k=1,nt\n do 615 i=1,imid\n do 615 np1=2,ndo2,2\n cr(ncbc,1,np1,k) = cr(ncbc,1,np1,k)-vb(i,np1)*we(i,1,k)\n 615 continue\n do 616 k=1,nt\n do 616 i=1,imm1\n do 616 np1=3,ndo1,2\n br(1,1,np1,k) = br(1,1,np1,k)+vb(i,np1)*vo(i,1,k)\n 616 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) return\n do 620 mp1=2,mmax\n m = mp1-1\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 617\n do 623 k=1,nt\n do 623 i=1,imm1\n do 623 np1=mp1,ndo1,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)+vb(i,np1+mb)*vo(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*we(i,2*mp1-1,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)+vb(i,np1+mb)*vo(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*we(i,2*mp1-2,k)\n 623 continue\n if(mlat .eq. 0) go to 617\n do 624 k=1,nt\n do 624 np1=mp1,ndo1,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)\n 1 +wb(imid,np1+mb)*we(imid,2*mp1-1,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)\n 1 -wb(imid,np1+mb)*we(imid,2*mp1-2,k)\n 624 continue\n 617 if(mp2 .gt. ndo2) go to 620\n do 621 k=1,nt\n do 621 i=1,imm1\n do 621 np1=mp2,ndo2,2\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*we(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*vo(i,2*mp1-1,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*we(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*vo(i,2*mp1-2,k)\n 621 continue\n if(mlat .eq. 0) go to 620\n do 622 k=1,nt\n do 622 np1=mp2,ndo2,2\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 -vb(imid,np1+mb)*we(imid,2*mp1-2,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -vb(imid,np1+mb)*we(imid,2*mp1-1,k)\n 622 continue\n 620 continue\n return\nc\nc case ityp=7 v odd, w even, and cr and ci equal zero\nc\nc case m=0\nc\n 700 do 716 k=1,nt\n do 716 i=1,imm1\n do 716 np1=3,ndo1,2\n br(1,1,np1,k) = br(1,1,np1,k)+vb(i,np1)*vo(i,1,k)\n 716 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) return\n do 720 mp1=2,mmax\n m = mp1-1\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 720\n do 723 k=1,nt\n do 723 i=1,imm1\n do 723 np1=mp1,ndo1,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)+vb(i,np1+mb)*vo(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*we(i,2*mp1-1,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)+vb(i,np1+mb)*vo(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*we(i,2*mp1-2,k)\n 723 continue\n if(mlat .eq. 0) go to 720\n do 724 k=1,nt\n do 724 np1=mp1,ndo1,2\n br(1,mp1,np1,k) = br(1,mp1,np1,k)\n 1 +wb(imid,np1+mb)*we(imid,2*mp1-1,k)\n bi(1,mp1,np1,k) = bi(1,mp1,np1,k)\n 1 -wb(imid,np1+mb)*we(imid,2*mp1-2,k)\n 724 continue\n 720 continue\n return\nc\nc case ityp=8 v odd, w even, and both br and bi equal zero\nc\nc case m=0\nc\n 800 do 815 k=1,nt\n do 815 i=1,imid\n do 815 np1=2,ndo2,2\n cr(ncbc,1,np1,k) = cr(ncbc,1,np1,k)-vb(i,np1)*we(i,1,k)\n 815 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) return\n do 820 mp1=2,mmax\n m = mp1-1\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp2 .gt. ndo2) go to 820\n do 821 k=1,nt\n do 821 i=1,imm1\n do 821 np1=mp2,ndo2,2\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*we(i,2*mp1-2,k)\n 1 +wb(i,np1+mb)*vo(i,2*mp1-1,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -vb(i,np1+mb)*we(i,2*mp1-1,k)\n 1 -wb(i,np1+mb)*vo(i,2*mp1-2,k)\n 821 continue\n if(mlat .eq. 0) go to 820\n do 822 k=1,nt\n do 822 np1=mp2,ndo2,2\n cr(ncbc,mp1,np1,k) = cr(ncbc,mp1,np1,k)\n 1 -vb(imid,np1+mb)*we(imid,2*mp1-2,k)\n ci(ncbc,mp1,np1,k) = ci(ncbc,mp1,np1,k)\n 1 -vb(imid,np1+mb)*we(imid,2*mp1-1,k)\n 822 continue\n 820 continue\n return\n end\n subroutine vhagsi(nlat,nlon,wvhags,lvhags,dwork,ldwork,ierror)\n implicit double precision (a-h,o-z)\n dimension wvhags(lvhags)\n double precision dwork(ldwork)\n ierror = 1\n if(nlat .lt. 3) return\n ierror = 2\n if(nlon .lt. 1) return\n ierror = 3\n imid = (nlat+1)/2\n lmn = (nlat*(nlat+1))/2\n if(lvhags .lt. 2*(imid*lmn)+nlon+15) return\n ierror = 4\nc if (ldwork.lt.nlat*(3*nlat+9)+2) return\n if (ldwork.lt.(nlat*(3*nlat+9)+2)/2) return\n ierror = 0\n jw1 = 1\n jw2 = jw1+imid*lmn\n jw3 = jw2+imid*lmn\n iw1 = 1\n iw2 = iw1+nlat\n iw3 = iw2+nlat\n iw4 = iw3+3*imid*nlat\nc iw2 = iw1+nlat+nlat\nc iw3 = iw2+nlat+nlat\nc iw4 = iw3+6*imid*nlat\n call vhgai1(nlat,imid,wvhags(jw1),wvhags(jw2),\n +dwork(iw1),dwork(iw2),dwork(iw3),dwork(iw4))\n call hrffti(nlon,wvhags(jw3))\n return\n end\n subroutine vhgai1(nlat,imid,vb,wb,dthet,dwts,dpbar,work)\n implicit double precision (a-h,o-z)\n dimension vb(imid,*),wb(imid,*)\n double precision abel,bbel,cbel,ssqr2,dcf\n double precision dpbar(imid,nlat,3), dthet(*),dwts(*),work(*)\nc lwk = 4*nlat*(nlat+2)\n lwk = nlat*(nlat+2)\n call gaqd(nlat,dthet,dwts,dpbar,lwk,ierror)\nc\nc compute associated legendre functions\nc\nc compute m=n=0 legendre polynomials for all theta(i)\nc\n ssqr2 = 1.d0/dsqrt(2.d0)\n do 90 i=1,imid\n dpbar(i,1,1) = ssqr2\n vb(i,1) = 0.d0\n wb(i,1) = 0.d0\n 90 continue\nc\nc main loop for remaining vb, and wb\nc\n do 100 n=1,nlat-1\n nm = mod(n-2,3)+1\n nz = mod(n-1,3)+1\n np = mod(n,3)+1\nc\nc compute dpbar for m=0\nc\n call dnlfk(0,n,work)\n mn = indx(0,n,nlat)\n do 105 i=1,imid\n call dnlft(0,n,dthet(i),work,dpbar(i,1,np))\n 105 continue\nc\nc compute dpbar for m=1\nc\n call dnlfk(1,n,work)\n mn = indx(1,n,nlat)\n do 106 i=1,imid\n call dnlft(1,n,dthet(i),work,dpbar(i,2,np))\nc pbar(i,mn) = dpbar(i,2,np)\n 106 continue\n 104 continue\nc\nc compute and store dpbar for m=2,n\nc\n if(n.lt.2) go to 108\n do 107 m=2,n\n abel = dsqrt(dfloat((2*n+1)*(m+n-2)*(m+n-3))/\n 1 dfloat((2*n-3)*(m+n-1)*(m+n)))\n bbel = dsqrt(dfloat((2*n+1)*(n-m-1)*(n-m))/\n 1 dfloat((2*n-3)*(m+n-1)*(m+n)))\n cbel = dsqrt(dfloat((n-m+1)*(n-m+2))/\n 1 dfloat((m+n-1)*(m+n)))\n id = indx(m,n,nlat)\n if (m.ge.n-1) go to 102\n do 103 i=1,imid\n dpbar(i,m+1,np) = abel*dpbar(i,m-1,nm)+bbel*dpbar(i,m+1,nm)\n 1 -cbel*dpbar(i,m-1,np)\n 103 continue\n go to 107\n 102 do 101 i=1,imid\n dpbar(i,m+1,np) = abel*dpbar(i,m-1,nm)-cbel*dpbar(i,m-1,np)\n 101 continue\n 107 continue\nc\nc compute the derivative of the functions\nc\n 108 continue\n ix = indx(0,n,nlat)\n iy = indx(n,n,nlat)\n do 125 i=1,imid\n vb(i,ix) = -dpbar(i,2,np)*dwts(i)\n vb(i,iy) = dpbar(i,n,np)/dsqrt(dfloat(2*(n+1)))*dwts(i)\n125 continue\nc\n if(n.eq.1) go to 131 \n dcf = dsqrt(dfloat(4*n*(n+1)))\n do 130 m=1,n-1\n ix = indx(m,n,nlat)\n abel = dsqrt(dfloat((n+m)*(n-m+1)))/dcf\n bbel = dsqrt(dfloat((n-m)*(n+m+1)))/dcf\n do 130 i=1,imid\n vb(i,ix) = (abel*dpbar(i,m,np)-bbel*dpbar(i,m+2,np))*dwts(i)\n130 continue\nc\nc compute the vector harmonic w(theta) = m*pbar/cos(theta)\nc\nc set wb=0 for m=0\nc\n 131 continue\n ix = indx(0,n,nlat)\n do 220 i=1,imid\n wb(i,ix) = 0.d0\n220 continue\nc\nc compute wb for m=1,n\nc\n dcf = dsqrt(dfloat(n+n+1)/dfloat(4*n*(n+1)*(n+n-1)))\n do 230 m=1,n\n ix = indx(m,n,nlat)\n abel = dcf*dsqrt(dfloat((n+m)*(n+m-1)))\n bbel = dcf*dsqrt(dfloat((n-m)*(n-m-1)))\n if(m.ge.n-1) go to 231\n do 229 i=1,imid\n wb(i,ix) = (abel*dpbar(i,m,nz) + bbel*dpbar(i,m+2,nz))*dwts(i)\n 229 continue\n go to 230\n 231 do 228 i=1,imid\n wb(i,ix) = abel*dpbar(i,m,nz)*dwts(i)\n 228 continue\n 230 continue\n 100 continue\n return \n end\n\n function indx(m,n,nlat)\n implicit double precision (a-h,o-z)\n integer indx\n indx = m*nlat-(m*(m+1))/2+n+1\n return\n end\n" }, { "path": "external/SPHEREPACK/vhsgs.f", "content": "c\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc * *\nc * copyright (c) 1998 by UCAR *\nc * *\nc * University Corporation for Atmospheric Research *\nc * *\nc * all rights reserved *\nc * *\nc * SPHEREPACK version 3.2 *\nc * *\nc * A Package of Fortran77 Subroutines and Programs *\nc * *\nc * for Modeling Geophysical Processes *\nc * *\nc * by *\nc * *\nc * John Adams and Paul Swarztrauber *\nc * *\nc * of *\nc * *\nc * the National Center for Atmospheric Research *\nc * *\nc * Boulder, Colorado (80307) U.S.A. *\nc * *\nc * which is sponsored by *\nc * *\nc * the National Science Foundation *\nc * *\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc\nc\nc\nc ... file vhsgs.f\nc\nc this file contains code and documentation for subroutines\nc vhsgs and vhsgsi\nc\nc ... files which must be loaded with vhsgs.f\nc\nc sphcom.f, hrfft.f, gaqd.f\nc\nc subroutine vhsgs(nstrvw,nstrbc,noffsvw,noffsbc,\nc nlat,nlon,ityp,nt,v,w,idvw,jdvw,br,bi,cr,ci,\nc + mdab,ndab,wvhsgs,lvhsgs,work,lwork,ierror)\nc \nc \nc subroutine vhsgs performs the vector spherical harmonic synthesis\nc of the arrays br, bi, cr, and ci and stores the result in the\nc arrays v and w. the synthesis is performed on an equally spaced\nc longitude grid and a gaussian colatitude grid (measured from\nc the north pole). v(i,j) and w(i,j) are the colatitudinal and\nc east longitudinal components respectively, located at the i(th)\nc colatitude gaussian point (see nlat below) and longitude\nc phi(j) = (j-1)*2*pi/nlon. the spectral respresentation of (v,w)\nc is given below at output parameters v,w.\nc\nc input parameters\nc\nc nstrvw, nstrbc strides in v,w and in br,bi,cr,ci\nc noffsvw, noffsbc offset in v,w and in br,bi,cr,ci\nc -- must be between 0 and stride-1\nc Alternatively, when the two strides equal, you can set both\nc to -1 in which case the output will be computed for all\nc values of offset between 0 and stride-1.\nc\nc nlat the number of points in the gaussian colatitude grid on the\nc full sphere. these lie in the interval (0,pi) and are computed\nc in radians in theta(1) <...< theta(nlat) by subroutine gaqd.\nc if nlat is odd the equator will be included as the grid point\nc theta((nlat+1)/2). if nlat is even the equator will be\nc excluded as a grid point and will lie half way between\nc theta(nlat/2) and theta(nlat/2+1). nlat must be at least 3.\nc note: on the half sphere, the number of grid points in the\nc colatitudinal direction is nlat/2 if nlat is even or\nc (nlat+1)/2 if nlat is odd.\nc\nc nlon the number of distinct londitude points. nlon determines\nc the grid increment in longitude as 2*pi/nlon. for example\nc nlon = 72 for a five degree grid. nlon must be greater\nc than zero. the axisymmetric case corresponds to nlon=1.\nc the efficiency of the computation is improved when nlon\nc is a product of small prime numbers.\nc\nc NOTE: this is a modified version of spherepack. Changes from\nc the original version to the current one have only been\nc tested for ityp=0,1,2. For this reason an error code will\nc be returned if ityp>2.\nc\nc ityp = 0 no symmetries exist about the equator. the synthesis\nc is performed on the entire sphere. i.e. on the\nc arrays v(i,j),w(i,j) for i=1,...,nlat and \nc j=1,...,nlon. \nc\nc = 1 no symmetries exist about the equator. the synthesis\nc is performed on the entire sphere. i.e. on the\nc arrays v(i,j),w(i,j) for i=1,...,nlat and \nc j=1,...,nlon. the curl of (v,w) is zero. that is, \nc (d/dtheta (sin(theta) w) - dv/dphi)/sin(theta) = 0. \nc the coefficients cr and ci are zero.\nc\nc = 2 no symmetries exist about the equator. the synthesis\nc is performed on the entire sphere. i.e. on the\nc arrays v(i,j),w(i,j) for i=1,...,nlat and \nc j=1,...,nlon. the divergence of (v,w) is zero. i.e., \nc (d/dtheta (sin(theta) v) + dw/dphi)/sin(theta) = 0. \nc the coefficients br and bi are zero.\nc\nc = 3 v is symmetric and w is antisymmetric about the \nc equator. the synthesis is performed on the northern\nc hemisphere only. i.e., if nlat is odd the synthesis\nc is performed on the arrays v(i,j),w(i,j) for \nc i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the synthesis is performed on the the arrays\nc v(i,j),w(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc\nc = 4 v is symmetric and w is antisymmetric about the \nc equator. the synthesis is performed on the northern\nc hemisphere only. i.e., if nlat is odd the synthesis\nc is performed on the arrays v(i,j),w(i,j) for \nc i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the synthesis is performed on the the arrays\nc v(i,j),w(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc the curl of (v,w) is zero. that is, \nc (d/dtheta (sin(theta) w) - dv/dphi)/sin(theta) = 0. \nc the coefficients cr and ci are zero.\nc\nc = 5 v is symmetric and w is antisymmetric about the \nc equator. the synthesis is performed on the northern\nc hemisphere only. i.e., if nlat is odd the synthesis\nc is performed on the arrays v(i,j),w(i,j) for \nc i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the synthesis is performed on the the arrays\nc v(i,j),w(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc the divergence of (v,w) is zero. i.e., \nc (d/dtheta (sin(theta) v) + dw/dphi)/sin(theta) = 0. \nc the coefficients br and bi are zero.\nc\nc = 6 v is antisymmetric and w is symmetric about the \nc equator. the synthesis is performed on the northern\nc hemisphere only. i.e., if nlat is odd the synthesis\nc is performed on the arrays v(i,j),w(i,j) for \nc i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the synthesis is performed on the the arrays\nc v(i,j),w(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc\nc = 7 v is antisymmetric and w is symmetric about the \nc equator. the synthesis is performed on the northern\nc hemisphere only. i.e., if nlat is odd the synthesis\nc is performed on the arrays v(i,j),w(i,j) for \nc i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the synthesis is performed on the the arrays\nc v(i,j),w(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc the curl of (v,w) is zero. that is, \nc (d/dtheta (sin(theta) w) - dv/dphi)/sin(theta) = 0. \nc the coefficients cr and ci are zero.\nc\nc = 8 v is antisymmetric and w is symmetric about the \nc equator. the synthesis is performed on the northern\nc hemisphere only. i.e., if nlat is odd the synthesis\nc is performed on the arrays v(i,j),w(i,j) for \nc i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the synthesis is performed on the the arrays\nc v(i,j),w(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc the divergence of (v,w) is zero. i.e., \nc (d/dtheta (sin(theta) v) + dw/dphi)/sin(theta) = 0. \nc the coefficients br and bi are zero.\nc\nc\nc nt the number of syntheses. in the program that calls vhsgs,\nc the arrays v,w,br,bi,cr, and ci can be three dimensional\nc in which case multiple syntheses will be performed.\nc the third index is the synthesis index which assumes the \nc values k=1,...,nt. for a single synthesis set nt=1. the\nc discription of the remaining parameters is simplified\nc by assuming that nt=1 or that all the arrays are two\nc dimensional.\nc\nc idvw the first dimension of the arrays v,w as it appears in\nc the program that calls vhags. if ityp .le. 2 then idvw\nc must be at least nlat. if ityp .gt. 2 and nlat is\nc even then idvw must be at least nlat/2. if ityp .gt. 2\nc and nlat is odd then idvw must be at least (nlat+1)/2.\nc\nc jdvw the second dimension of the arrays v,w as it appears in\nc the program that calls vhsgs. jdvw must be at least nlon.\nc\nc br,bi two or three dimensional arrays (see input parameter nt)\nc cr,ci that contain the vector spherical harmonic coefficients\nc in the spectral representation of v(i,j) and w(i,j) given\nc below at the discription of output parameters v and w.\nc\nc mdab the first dimension of the arrays br,bi,cr, and ci as it\nc appears in the program that calls vhsgs. mdab must be at\nc least min0(nlat,nlon/2) if nlon is even or at least\nc min0(nlat,(nlon+1)/2) if nlon is odd.\nc\nc ndab the second dimension of the arrays br,bi,cr, and ci as it\nc appears in the program that calls vhsgs. ndab must be at\nc least nlat.\nc\nc wvhsgs an array which must be initialized by subroutine vhsgsi.\nc once initialized, wvhsgs can be used repeatedly by vhsgs\nc as long as nlon and nlat remain unchanged. wvhsgs must\nc not be altered between calls of vhsgs.\nc\nc lvhsgs the dimension of the array wvhsgs as it appears in the\nc program that calls vhsgs. define\nc\nc l1 = min0(nlat,nlon/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc then lvhsgs must be at least\nc\nc l1*l2*(nlat+nlat-l1+1)+nlon+15+2*nlat\nc\nc\nc work a work array that does not have to be saved.\nc\nc lwork the dimension of the array work as it appears in the\nc program that calls vhsgs. define\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc if ityp .le. 2 then lwork must be at least\nc\nc (2*nt+1)*nlat*nlon\nc\nc if ityp .gt. 2 then lwork must be at least\nc\nc (2*nt+1)*l2*nlon \nc\nc **************************************************************\nc\nc output parameters\nc\nc v,w two or three dimensional arrays (see input parameter nt)\nc in which the synthesis is stored. v is the colatitudinal\nc component and w is the east longitudinal component. \nc v(i,j),w(i,j) contain the components at the guassian colatitude\nc point theta(i) and longitude phi(j) = (j-1)*2*pi/nlon.\nc the index ranges are defined above at the input parameter\nc ityp. v and w are computed from the formulas given below.\nc\nc\nc define\nc\nc 1. theta is colatitude and phi is east longitude\nc\nc 2. the normalized associated legendre funnctions\nc\nc pbar(m,n,theta) = sqrt((2*n+1)*factorial(n-m)\nc /(2*factorial(n+m)))*sin(theta)**m/(2**n*\nc factorial(n)) times the (n+m)th derivative\nc of (x**2-1)**n with respect to x=cos(theta)\nc\nc 3. vbar(m,n,theta) = the derivative of pbar(m,n,theta) with\nc respect to theta divided by the square\nc root of n(n+1).\nc\nc vbar(m,n,theta) is more easily computed in the form\nc\nc vbar(m,n,theta) = (sqrt((n+m)*(n-m+1))*pbar(m-1,n,theta)\nc -sqrt((n-m)*(n+m+1))*pbar(m+1,n,theta))/(2*sqrt(n*(n+1)))\nc\nc 4. wbar(m,n,theta) = m/(sin(theta))*pbar(m,n,theta) divided\nc by the square root of n(n+1).\nc\nc wbar(m,n,theta) is more easily computed in the form\nc\nc wbar(m,n,theta) = sqrt((2n+1)/(2n-1))*(sqrt((n+m)*(n+m-1))\nc *pbar(m-1,n-1,theta)+sqrt((n-m)*(n-m-1))*pbar(m+1,n-1,theta))\nc /(2*sqrt(n*(n+1)))\nc\nc\nc the colatitudnal dependence of the normalized surface vector\nc spherical harmonics are defined by\nc\nc 5. bbar(m,n,theta) = (vbar(m,n,theta),i*wbar(m,n,theta))\nc\nc 6. cbar(m,n,theta) = (i*wbar(m,n,theta),-vbar(m,n,theta))\nc\nc\nc the coordinate to index mappings \nc\nc 7. theta(i) = i(th) gaussian grid point and phi(j) = (j-1)*2*pi/nlon\nc\nc \nc the maximum (plus one) longitudinal wave number\nc\nc 8. mmax = min0(nlat,nlon/2) if nlon is even or\nc mmax = min0(nlat,(nlon+1)/2) if nlon is odd.\nc\nc if we further define the output vector as\nc\nc 9. h(i,j) = (v(i,j),w(i,j))\nc\nc and the complex coefficients\nc\nc 10. b(m,n) = cmplx(br(m+1,n+1),bi(m+1,n+1))\nc\nc 11. c(m,n) = cmplx(cr(m+1,n+1),ci(m+1,n+1))\nc\nc\nc then for i=1,...,nlat and j=1,...,nlon\nc\nc the expansion for real h(i,j) takes the form\nc\nc h(i,j) = the sum from n=1 to n=nlat-1 of the real part of\nc\nc .5*(b(0,n)*bbar(0,n,theta(i))+c(0,n)*cbar(0,n,theta(i)))\nc\nc plus the sum from m=1 to m=mmax-1 of the sum from n=m to \nc n=nlat-1 of the real part of\nc\nc b(m,n)*bbar(m,n,theta(i))*exp(i*m*phi(j))\nc +c(m,n)*cbar(m,n,theta(i))*exp(i*m*phi(j))\nc\nc *************************************************************\nc\nc in terms of real variables this expansion takes the form\nc\nc for i=1,...,nlat and j=1,...,nlon\nc\nc v(i,j) = the sum from n=1 to n=nlat-1 of\nc\nc .5*br(ncbc,n+1)*vbar(0,n,theta(i))\nc\nc plus the sum from m=1 to m=mmax-1 of the sum from n=m to \nc n=nlat-1 of the real part of\nc\nc (br(m+1,n+1)*vbar(m,n,theta(i))-ci(m+1,n+1)*wbar(m,n,theta(i)))\nc *cos(m*phi(j))\nc -(bi(m+1,n+1)*vbar(m,n,theta(i))+cr(m+1,n+1)*wbar(m,n,theta(i)))\nc *sin(m*phi(j))\nc\nc and for i=1,...,nlat and j=1,...,nlon\nc\nc w(i,j) = the sum from n=1 to n=nlat-1 of\nc\nc -.5*cr(1,n+1)*vbar(0,n,theta(i))\nc\nc plus the sum from m=1 to m=mmax-1 of the sum from n=m to\nc n=nlat-1 of the real part of\nc\nc -(cr(m+1,n+1)*vbar(m,n,theta(i))+bi(m+1,n+1)*wbar(m,n,theta(i)))\nc *cos(m*phi(j))\nc +(ci(m+1,n+1)*vbar(m,n,theta(i))-br(m+1,n+1)*wbar(m,n,theta(i)))\nc *sin(m*phi(j))\nc\nc\nc br(m+1,nlat),bi(m+1,nlat),cr(m+1,nlat), and ci(m+1,nlat) are\nc assumed zero for m even.\nc\nc\nc ierror = 0 no errors\nc = 1 error in the specification of nlat\nc = 2 error in the specification of nlon\nc = 3 error in the specification of ityp\nc = 4 error in the specification of nt\nc = 5 error in the specification of idvw\nc = 6 error in the specification of jdvw\nc = 7 error in the specification of mdab\nc = 8 error in the specification of ndab\nc = 9 error in the specification of lvhsgs\nc = 10 error in the specification of lwork\nc\nc\nc subroutine vhsgsi(nlat,nlon,wvhsgs,lvhsgs,dwork,ldwork,ierror)\nc\nc subroutine vhsgsi initializes the array wvhsgs which can then be\nc used repeatedly by subroutine vhsgs until nlat or nlon is changed.\nc\nc input parameters\nc\nc nlat the number of points in the gaussian colatitude grid on the\nc full sphere. these lie in the interval (0,pi) and are computed\nc in radians in theta(1) <...< theta(nlat) by subroutine gaqd.\nc if nlat is odd the equator will be included as the grid point\nc theta((nlat+1)/2). if nlat is even the equator will be\nc excluded as a grid point and will lie half way between\nc theta(nlat/2) and theta(nlat/2+1). nlat must be at least 3.\nc note: on the half sphere, the number of grid points in the\nc colatitudinal direction is nlat/2 if nlat is even or\nc (nlat+1)/2 if nlat is odd.\nc\nc nlon the number of distinct londitude points. nlon determines\nc the grid increment in longitude as 2*pi/nlon. for example\nc nlon = 72 for a five degree grid. nlon must be greater\nc than zero. the axisymmetric case corresponds to nlon=1.\nc the efficiency of the computation is improved when nlon\nc is a product of small prime numbers.\nc\nc lvhsgs the dimension of the array wvhsgs as it appears in the\nc program that calls vhsgs. define\nc\nc l1 = min0(nlat,nlon/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc then lvhsgs must be at least\nc\nc l1*l2*(nlat+nlat-l1+1)+nlon+15+2*nlat\nc\nc dwork a double precision work array that does not need to be saved\nc\nc ldwork the dimension of the array dwork as it appears in the\nc program that calls vhsgsi. ldwork must be at least\nc\nc (3*nlat*(nlat+3)+2)/2\n\nc\nc **************************************************************\nc\nc output parameters\nc\nc wvhsgs an array which is initialized for use by subroutine vhsgs.\nc once initialized, wvhsgs can be used repeatedly by vhsgs\nc as long as nlat and nlon remain unchanged. wvhsgs must not\nc be altered between calls of vhsgs.\nc\nc\nc ierror = 0 no errors\nc = 1 error in the specification of nlat\nc = 2 error in the specification of nlon\nc = 3 error in the specification of lvhsgs\nc = 4 error in the specification of lwork\nc\n subroutine vhsgs(nstrvw,nstrbc,noffsvw,noffsbc,\n + nlat,nlon,ityp,nt,v,w,idvw,jdvw,br,bi,cr,ci,\n + mdab,ndab,wvhsgs,lvhsgs,work,lwork,ierror)\n implicit double precision (a-h,o-z)\n dimension v(nstrvw,idvw,jdvw,1),w(nstrvw,idvw,jdvw,1),\n 1 br(nstrbc,mdab,ndab,1),bi(nstrbc,mdab,ndab,1),\n 1 cr(nstrbc,mdab,ndab,1),ci(nstrbc,mdab,ndab,1),\n 2 work(1),wvhsgs(1)\n ierror = 1\n if(nlat .lt. 3) return\n ierror = 2\n if(nlon .lt. 1) return\n ierror = 3\n if(ityp.lt.0 .or. ityp.gt.8) return\nc see note above about symmetries\n if(ityp.gt.2) return\n ierror = 4\n if(nt .lt. 0) return\n ierror = 5\n imid = (nlat+1)/2\n if((ityp.le.2 .and. idvw.lt.nlat) .or.\n 1 (ityp.gt.2 .and. idvw.lt.imid)) return\n ierror = 6\n if(jdvw .lt. nlon) return\n ierror = 7\n mmax = min0(nlat,(nlon+1)/2)\n if(mdab .lt. mmax) return\n ierror = 8\n if(ndab .lt. nlat) return\n ierror = 9\n idz = (mmax*(nlat+nlat-mmax+1))/2\n lzimn = idz*imid\n if(lvhsgs .lt. lzimn+lzimn+nlon+15) return\n ierror = 10\n idv = nlat\n if(ityp .gt. 2) idv = imid\n lnl = nt*idv*nlon\n ng=1\n if(noffsvw.eq.-1) ng=nstrvw\n if(lwork .lt. ng*(lnl+lnl+idv*nlon)) return\n ierror = 11\n if((noffsvw.eq.-1) .neqv. (noffsbc.eq.-1)) return\n if((noffsvw.eq.-1) .and. (nstrvw.ne.nstrbc)) return\n if((noffsvw.lt.-1) .or. (noffsvw.ge.nstrvw)) return\n if((noffsbc.lt.-1) .or. (noffsbc.ge.nstrbc)) return\n\n ierror = 0\n ist = 0\n if(ityp .le. 2) ist = imid\nc\nc set wvhsgs pointers\nc\n lmn = nlat*(nlat+1)/2\n jw1 = 1\n jw2 = jw1+imid*lmn\n jw3 = jw2+imid*lmn\nc\nc set work pointers\nc\n iw1 = ng*ist+1\n iw2 = ng*lnl+1\n iw3 = iw2+ist*ng\n iw4 = iw2+lnl*ng\n\n call vhsgs1(nstrvw,nstrbc,noffsvw,noffsbc,\n + nlat,nlon,ityp,nt,imid,idvw,jdvw,v,w,mdab,ndab,\n + br,bi,cr,ci,ng,idv,work,work(iw1),work(iw2),work(iw3),\n + work(iw4),idz,wvhsgs(jw1),wvhsgs(jw2),wvhsgs(jw3))\n return\n end\n\n subroutine vhsgs1(nstrvw,nstrbc,noffsvw,noffsbc,\n + nlat,nlon,ityp,nt,imid,idvw,jdvw,v,w,mdab,\n 1 ndab,br,bi,cr,ci,ng,idv,ve,vo,we,wo,work,idz,vb,wb,wrfft)\n implicit double precision (a-h,o-z)\n dimension v(nstrvw,idvw,jdvw,1),w(nstrvw,idvw,jdvw,1),\n 1 br(nstrbc,mdab,ndab,1),bi(nstrbc,mdab,ndab,1),\n 1 cr(nstrbc,mdab,ndab,1),ci(nstrbc,mdab,ndab,1),\n 2 ve(ng,idv,nlon,1),vo(ng,idv,nlon,1),we(ng,idv,nlon,1),\n 3 wo(ng,idv,nlon,1),work(1),wrfft(1),\n 4 vb(imid,1),wb(imid,1)\n ncvwdiff=noffsvw-noffsbc\n if(noffsbc.eq.-1) then\n ncbcmin=1\n ncbcmax=nstrbc\n else\n ncbcmin=1+noffsbc\n ncbcmax=1+noffsbc\n end if\nc do 234 ncbc=ncbcmin,ncbcmax\nc ncvw=ncvwdiff+ncbc\nc ig=ncbc-ncbcmin+1\nc ig=1\n nlp1 = nlat+1\n mlat = mod(nlat,2)\n mlon = mod(nlon,2)\n mmax = min0(nlat,(nlon+1)/2)\n imm1 = imid\n if(mlat .ne. 0) imm1 = imid-1\n do 10 k=1,nt\n do 10 j=1,nlon\n do 10 i=1,idv\n do 10 ig=1,ng\n ve(ig,i,j,k) = 0.d0\n we(ig,i,j,k) = 0.d0\n 10 continue\n ndo1 = nlat\n ndo2 = nlat\n if(mlat .ne. 0) ndo1 = nlat-1\n if(mlat .eq. 0) ndo2 = nlat-1\n 18 itypp = ityp+1\n go to (1,100,200,300,400,500,600,700,800),itypp\nc\nc case ityp=0 no symmetries\nc\nc case m = 0\nc\n 1 continue\n do 15 k=1,nt\n do 15 np1=2,ndo2,2\n do 15 i=1,imid\n do 15 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,i,1,k)=ve(ig,i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n we(ig,i,1,k)=we(ig,i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 15 continue\n do 16 k=1,nt\n do 16 np1=3,ndo1,2\n do 16 i=1,imm1\n do 16 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n vo(ig,i,1,k)=vo(ig,i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n wo(ig,i,1,k)=wo(ig,i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 16 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 30 mp1=2,mmax\n m = mp1-1\nc mb = m*(nlat-1)-(m*(m-1))/2\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 26\n do 25 k=1,nt\n do 24 np1=mp1,ndo1,2\n mn = mb+np1\n do 23 i=1,imm1\n do 23 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n vo(ig,i,2*mp1-2,k)=vo(ig,i,2*mp1-2,k)+br(ncbc,mp1,np1,k)*vb(i,mn)\n ve(ig,i,2*mp1-2,k)=ve(ig,i,2*mp1-2,k)-ci(ncbc,mp1,np1,k)*wb(i,mn)\n vo(ig,i,2*mp1-1,k)=vo(ig,i,2*mp1-1,k)+bi(ncbc,mp1,np1,k)*vb(i,mn)\n ve(ig,i,2*mp1-1,k)=ve(ig,i,2*mp1-1,k)+cr(ncbc,mp1,np1,k)*wb(i,mn)\n wo(ig,i,2*mp1-2,k)=wo(ig,i,2*mp1-2,k)-cr(ncbc,mp1,np1,k)*vb(i,mn)\n we(ig,i,2*mp1-2,k)=we(ig,i,2*mp1-2,k)-bi(ncbc,mp1,np1,k)*wb(i,mn)\n wo(ig,i,2*mp1-1,k)=wo(ig,i,2*mp1-1,k)-ci(ncbc,mp1,np1,k)*vb(i,mn)\n we(ig,i,2*mp1-1,k)=we(ig,i,2*mp1-1,k)+br(ncbc,mp1,np1,k)*wb(i,mn)\n 23 continue\n if(mlat .eq. 0) go to 24\n do 924 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,imid,2*mp1-2,k) = ve(ig,imid,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(imid,mn)\n ve(ig,imid,2*mp1-1,k) = ve(ig,imid,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(imid,mn)\n we(ig,imid,2*mp1-2,k) = we(ig,imid,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(imid,mn) \n we(ig,imid,2*mp1-1,k) = we(ig,imid,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(imid,mn)\n 924 continue\n 24 continue\n 25 continue\n 26 if(mp2 .gt. ndo2) go to 30\n do 29 k=1,nt\n do 28 np1=mp2,ndo2,2\n mn = mb+np1\n do 27 i=1,imm1\n do 27 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,i,2*mp1-2,k)=ve(ig,i,2*mp1-2,k)+br(ncbc,mp1,np1,k)*vb(i,mn)\n vo(ig,i,2*mp1-2,k)=vo(ig,i,2*mp1-2,k)-ci(ncbc,mp1,np1,k)*wb(i,mn)\n ve(ig,i,2*mp1-1,k)=ve(ig,i,2*mp1-1,k)+bi(ncbc,mp1,np1,k)*vb(i,mn)\n vo(ig,i,2*mp1-1,k)=vo(ig,i,2*mp1-1,k)+cr(ncbc,mp1,np1,k)*wb(i,mn)\n we(ig,i,2*mp1-2,k)=we(ig,i,2*mp1-2,k)-cr(ncbc,mp1,np1,k)*vb(i,mn)\n wo(ig,i,2*mp1-2,k)=wo(ig,i,2*mp1-2,k)-bi(ncbc,mp1,np1,k)*wb(i,mn)\n we(ig,i,2*mp1-1,k)=we(ig,i,2*mp1-1,k)-ci(ncbc,mp1,np1,k)*vb(i,mn)\n wo(ig,i,2*mp1-1,k)=wo(ig,i,2*mp1-1,k)+br(ncbc,mp1,np1,k)*wb(i,mn)\n 27 continue\n if(mlat .eq. 0) go to 28\n do 928 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,imid,2*mp1-2,k) = ve(ig,imid,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(imid,mn) \n ve(ig,imid,2*mp1-1,k) = ve(ig,imid,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(imid,mn)\n we(ig,imid,2*mp1-2,k) = we(ig,imid,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(imid,mn)\n we(ig,imid,2*mp1-1,k) = we(ig,imid,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(imid,mn)\n 928 continue\n 28 continue\n 29 continue\n 30 continue\n go to 950\nc\nc case ityp=1 no symmetries, cr and ci equal zero\nc\nc case m = 0\nc\n 100 continue\n do 115 k=1,nt\n do 115 np1=2,ndo2,2\n do 115 i=1,imid\n do 115 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,i,1,k)=ve(ig,i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n 115 continue\n do 116 k=1,nt\n do 116 np1=3,ndo1,2\n do 116 i=1,imm1\n do 116 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n vo(ig,i,1,k)=vo(ig,i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n 116 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 130 mp1=2,mmax\n m = mp1-1\nc mb = m*(nlat-1)-(m*(m-1))/2\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 126\n do 125 k=1,nt\n do 124 np1=mp1,ndo1,2\n mn = mb+np1\n do 123 i=1,imm1\n do 123 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n vo(ig,i,2*mp1-2,k)=vo(ig,i,2*mp1-2,k)+br(ncbc,mp1,np1,k)*vb(i,mn)\n vo(ig,i,2*mp1-1,k)=vo(ig,i,2*mp1-1,k)+bi(ncbc,mp1,np1,k)*vb(i,mn)\n we(ig,i,2*mp1-2,k)=we(ig,i,2*mp1-2,k)-bi(ncbc,mp1,np1,k)*wb(i,mn)\n we(ig,i,2*mp1-1,k)=we(ig,i,2*mp1-1,k)+br(ncbc,mp1,np1,k)*wb(i,mn)\n 123 continue\n if(mlat .eq. 0) go to 124\n do 9124 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n we(ig,imid,2*mp1-2,k) = we(ig,imid,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(imid,mn) \n we(ig,imid,2*mp1-1,k) = we(ig,imid,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(imid,mn)\n 9124 continue\n 124 continue\n 125 continue\n 126 if(mp2 .gt. ndo2) go to 130\n do 129 k=1,nt\n do 128 np1=mp2,ndo2,2\n mn = mb+np1\n do 127 i=1,imm1\n do 127 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,i,2*mp1-2,k)=ve(ig,i,2*mp1-2,k)+br(ncbc,mp1,np1,k)*vb(i,mn)\n ve(ig,i,2*mp1-1,k)=ve(ig,i,2*mp1-1,k)+bi(ncbc,mp1,np1,k)*vb(i,mn)\n wo(ig,i,2*mp1-2,k)=wo(ig,i,2*mp1-2,k)-bi(ncbc,mp1,np1,k)*wb(i,mn)\n wo(ig,i,2*mp1-1,k)=wo(ig,i,2*mp1-1,k)+br(ncbc,mp1,np1,k)*wb(i,mn)\n 127 continue\n if(mlat .eq. 0) go to 128\n do 9128 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,imid,2*mp1-2,k) = ve(ig,imid,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(imid,mn) \n ve(ig,imid,2*mp1-1,k) = ve(ig,imid,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(imid,mn)\n 9128 continue\n 128 continue\n 129 continue\n 130 continue\n go to 950\nc\nc case ityp=2 no symmetries, br and bi are equal to zero\nc\nc case m = 0\nc\n 200 do 215 k=1,nt\n do 215 np1=2,ndo2,2\n do 215 i=1,imid\n do 215 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n we(ig,i,1,k)=we(ig,i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 215 continue\n do 216 k=1,nt\n do 216 np1=3,ndo1,2\n do 216 i=1,imm1\n do 9216 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n wo(ig,i,1,k)=wo(ig,i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 9216 continue\n 216 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 230 mp1=2,mmax\n m = mp1-1\nc mb = m*(nlat-1)-(m*(m-1))/2\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 226\n do 225 k=1,nt\n do 224 np1=mp1,ndo1,2\n mn = mb+np1\n do 223 i=1,imm1\n do 223 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,i,2*mp1-2,k)=ve(ig,i,2*mp1-2,k)-ci(ncbc,mp1,np1,k)*wb(i,mn)\n ve(ig,i,2*mp1-1,k)=ve(ig,i,2*mp1-1,k)+cr(ncbc,mp1,np1,k)*wb(i,mn)\n wo(ig,i,2*mp1-2,k)=wo(ig,i,2*mp1-2,k)-cr(ncbc,mp1,np1,k)*vb(i,mn)\n wo(ig,i,2*mp1-1,k)=wo(ig,i,2*mp1-1,k)-ci(ncbc,mp1,np1,k)*vb(i,mn)\n 223 continue\n if(mlat .eq. 0) go to 224\n do 9224 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,imid,2*mp1-2,k) = ve(ig,imid,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(imid,mn)\n ve(ig,imid,2*mp1-1,k) = ve(ig,imid,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(imid,mn)\n 9224 continue\n 224 continue\n 225 continue\n 226 if(mp2 .gt. ndo2) go to 230\n do 229 k=1,nt\n do 228 np1=mp2,ndo2,2\n mn = mb+np1\n do 227 i=1,imm1\n do 227 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n vo(ig,i,2*mp1-2,k)=vo(ig,i,2*mp1-2,k)-ci(ncbc,mp1,np1,k)*wb(i,mn)\n vo(ig,i,2*mp1-1,k)=vo(ig,i,2*mp1-1,k)+cr(ncbc,mp1,np1,k)*wb(i,mn)\n we(ig,i,2*mp1-2,k)=we(ig,i,2*mp1-2,k)-cr(ncbc,mp1,np1,k)*vb(i,mn)\n we(ig,i,2*mp1-1,k)=we(ig,i,2*mp1-1,k)-ci(ncbc,mp1,np1,k)*vb(i,mn)\n 227 continue\n if(mlat .eq. 0) go to 228\n do 9228 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n we(ig,imid,2*mp1-2,k) = we(ig,imid,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(imid,mn)\n we(ig,imid,2*mp1-1,k) = we(ig,imid,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(imid,mn)\n 9228 continue\n 228 continue\n 229 continue\n 230 continue\n go to 950\nc\nc case ityp=3 v even, w odd \nc\nc case m = 0\nc\n 300 do 315 k=1,nt\n do 315 np1=2,ndo2,2\n do 315 i=1,imid\n do 315 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,i,1,k)=ve(ig,i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n 315 continue\n do 316 k=1,nt\n do 316 np1=3,ndo1,2\n do 316 i=1,imm1\n do 316 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n wo(ig,i,1,k)=wo(ig,i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 316 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 330 mp1=2,mmax\n m = mp1-1\nc mb = m*(nlat-1)-(m*(m-1))/2\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 326\n do 325 k=1,nt\n do 324 np1=mp1,ndo1,2\n mn = mb+np1\n do 323 i=1,imm1\n do 323 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,i,2*mp1-2,k)=ve(ig,i,2*mp1-2,k)-ci(ncbc,mp1,np1,k)*wb(i,mn)\n ve(ig,i,2*mp1-1,k)=ve(ig,i,2*mp1-1,k)+cr(ncbc,mp1,np1,k)*wb(i,mn)\n wo(ig,i,2*mp1-2,k)=wo(ig,i,2*mp1-2,k)-cr(ncbc,mp1,np1,k)*vb(i,mn)\n wo(ig,i,2*mp1-1,k)=wo(ig,i,2*mp1-1,k)-ci(ncbc,mp1,np1,k)*vb(i,mn)\n 323 continue\n if(mlat .eq. 0) go to 324\n do 9324 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,imid,2*mp1-2,k) = ve(ig,imid,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(imid,mn)\n ve(ig,imid,2*mp1-1,k) = ve(ig,imid,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(imid,mn)\n 9324 continue\n 324 continue\n 325 continue\n 326 if(mp2 .gt. ndo2) go to 330\n do 329 k=1,nt\n do 328 np1=mp2,ndo2,2\n mn = mb+np1\n do 327 i=1,imm1\n do 327 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,i,2*mp1-2,k)=ve(ig,i,2*mp1-2,k)+br(ncbc,mp1,np1,k)*vb(i,mn)\n ve(ig,i,2*mp1-1,k)=ve(ig,i,2*mp1-1,k)+bi(ncbc,mp1,np1,k)*vb(i,mn)\n wo(ig,i,2*mp1-2,k)=wo(ig,i,2*mp1-2,k)-bi(ncbc,mp1,np1,k)*wb(i,mn)\n wo(ig,i,2*mp1-1,k)=wo(ig,i,2*mp1-1,k)+br(ncbc,mp1,np1,k)*wb(i,mn)\n 327 continue\n if(mlat .eq. 0) go to 328\n do 9328 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,imid,2*mp1-2,k) = ve(ig,imid,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(imid,mn) \n ve(ig,imid,2*mp1-1,k) = ve(ig,imid,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(imid,mn)\n 9328 continue\n 328 continue\n 329 continue\n 330 continue\n go to 950\nc\nc case ityp=4 v even, w odd, and both cr and ci equal zero \nc\nc case m = 0\nc\n 400 do 415 k=1,nt\n do 415 np1=2,ndo2,2\n do 415 i=1,imid\n do 415 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,i,1,k)=ve(ig,i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n 415 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 430 mp1=2,mmax\n m = mp1-1\nc mb = m*(nlat-1)-(m*(m-1))/2\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp2 .gt. ndo2) go to 430\n do 429 k=1,nt\n do 428 np1=mp2,ndo2,2\n mn = mb+np1\n do 427 i=1,imm1\n do 427 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,i,2*mp1-2,k)=ve(ig,i,2*mp1-2,k)+br(ncbc,mp1,np1,k)*vb(i,mn)\n ve(ig,i,2*mp1-1,k)=ve(ig,i,2*mp1-1,k)+bi(ncbc,mp1,np1,k)*vb(i,mn)\n wo(ig,i,2*mp1-2,k)=wo(ig,i,2*mp1-2,k)-bi(ncbc,mp1,np1,k)*wb(i,mn)\n wo(ig,i,2*mp1-1,k)=wo(ig,i,2*mp1-1,k)+br(ncbc,mp1,np1,k)*wb(i,mn)\n 427 continue\n if(mlat .eq. 0) go to 428\n do 9428 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,imid,2*mp1-2,k) = ve(ig,imid,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(imid,mn) \n ve(ig,imid,2*mp1-1,k) = ve(ig,imid,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(imid,mn)\n 9428 continue\n 428 continue\n 429 continue\n 430 continue\n go to 950\nc\nc case ityp=5 v even, w odd, br and bi equal zero \nc\nc case m = 0\nc\n 500 do 516 k=1,nt\n do 516 np1=3,ndo1,2\n do 516 i=1,imm1\n do 516 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n wo(ig,i,1,k)=wo(ig,i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 516 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 530 mp1=2,mmax\n m = mp1-1\nc mb = m*(nlat-1)-(m*(m-1))/2\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 530\n do 525 k=1,nt\n do 524 np1=mp1,ndo1,2\n mn = mb+np1\n do 523 i=1,imm1\n do 523 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,i,2*mp1-2,k)=ve(ig,i,2*mp1-2,k)-ci(ncbc,mp1,np1,k)*wb(i,mn)\n ve(ig,i,2*mp1-1,k)=ve(ig,i,2*mp1-1,k)+cr(ncbc,mp1,np1,k)*wb(i,mn)\n wo(ig,i,2*mp1-2,k)=wo(ig,i,2*mp1-2,k)-cr(ncbc,mp1,np1,k)*vb(i,mn)\n wo(ig,i,2*mp1-1,k)=wo(ig,i,2*mp1-1,k)-ci(ncbc,mp1,np1,k)*vb(i,mn)\n 523 continue\n if(mlat .eq. 0) go to 524\n do 9524 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ve(ig,imid,2*mp1-2,k) = ve(ig,imid,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(imid,mn)\n ve(ig,imid,2*mp1-1,k) = ve(ig,imid,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(imid,mn)\n 9524 continue\n 524 continue\n 525 continue\n 530 continue\n go to 950\nc\nc case ityp=6 v odd , w even\nc\nc case m = 0\nc\n 600 do 615 k=1,nt\n do 615 np1=2,ndo2,2\n do 615 i=1,imid\n do 615 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n we(ig,i,1,k)=we(ig,i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 615 continue\n do 616 k=1,nt\n do 616 np1=3,ndo1,2\n do 616 i=1,imm1\n do 616 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n vo(ig,i,1,k)=vo(ig,i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n 616 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 630 mp1=2,mmax\n m = mp1-1\nc mb = m*(nlat-1)-(m*(m-1))/2\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 626\n do 625 k=1,nt\n do 624 np1=mp1,ndo1,2\n mn = mb+np1\n do 623 i=1,imm1\n do 623 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n vo(ig,i,2*mp1-2,k)=vo(ig,i,2*mp1-2,k)+br(ncbc,mp1,np1,k)*vb(i,mn)\n vo(ig,i,2*mp1-1,k)=vo(ig,i,2*mp1-1,k)+bi(ncbc,mp1,np1,k)*vb(i,mn)\n we(ig,i,2*mp1-2,k)=we(ig,i,2*mp1-2,k)-bi(ncbc,mp1,np1,k)*wb(i,mn)\n we(ig,i,2*mp1-1,k)=we(ig,i,2*mp1-1,k)+br(ncbc,mp1,np1,k)*wb(i,mn)\n 623 continue\n if(mlat .eq. 0) go to 624\n do 9624 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n we(ig,imid,2*mp1-2,k) = we(ig,imid,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(imid,mn) \n we(ig,imid,2*mp1-1,k) = we(ig,imid,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(imid,mn)\n 9624 continue\n 624 continue\n 625 continue\n 626 if(mp2 .gt. ndo2) go to 630\n do 629 k=1,nt\n do 628 np1=mp2,ndo2,2\n mn = mb+np1\n do 627 i=1,imm1\n do 627 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n vo(ig,i,2*mp1-2,k)=vo(ig,i,2*mp1-2,k)-ci(ncbc,mp1,np1,k)*wb(i,mn)\n vo(ig,i,2*mp1-1,k)=vo(ig,i,2*mp1-1,k)+cr(ncbc,mp1,np1,k)*wb(i,mn)\n we(ig,i,2*mp1-2,k)=we(ig,i,2*mp1-2,k)-cr(ncbc,mp1,np1,k)*vb(i,mn)\n we(ig,i,2*mp1-1,k)=we(ig,i,2*mp1-1,k)-ci(ncbc,mp1,np1,k)*vb(i,mn)\n 627 continue\n if(mlat .eq. 0) go to 628\n do 9628 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n we(ig,imid,2*mp1-2,k) = we(ig,imid,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(imid,mn)\n we(ig,imid,2*mp1-1,k) = we(ig,imid,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(imid,mn)\n 9628 continue\n 628 continue\n 629 continue\n 630 continue\n go to 950\nc\nc case ityp=7 v odd, w even cr and ci equal zero\nc\nc case m = 0\nc\n 700 do 716 k=1,nt\n do 716 np1=3,ndo1,2\n do 716 i=1,imm1\n do 716 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n vo(ig,i,1,k)=vo(ig,i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n 716 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 730 mp1=2,mmax\n m = mp1-1\nc mb = m*(nlat-1)-(m*(m-1))/2\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 730\n do 725 k=1,nt\n do 724 np1=mp1,ndo1,2\n mn = mb+np1\n do 723 i=1,imm1\n do 723 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n vo(ig,i,2*mp1-2,k)=vo(ig,i,2*mp1-2,k)+br(ncbc,mp1,np1,k)*vb(i,mn)\n vo(ig,i,2*mp1-1,k)=vo(ig,i,2*mp1-1,k)+bi(ncbc,mp1,np1,k)*vb(i,mn)\n we(ig,i,2*mp1-2,k)=we(ig,i,2*mp1-2,k)-bi(ncbc,mp1,np1,k)*wb(i,mn)\n we(ig,i,2*mp1-1,k)=we(ig,i,2*mp1-1,k)+br(ncbc,mp1,np1,k)*wb(i,mn)\n 723 continue\n if(mlat .eq. 0) go to 724\n do 9724 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n we(ig,imid,2*mp1-2,k) = we(ig,imid,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(imid,mn) \n we(ig,imid,2*mp1-1,k) = we(ig,imid,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(imid,mn)\n 9724 continue\n 724 continue\n 725 continue\n 730 continue\n go to 950\nc\nc case ityp=8 v odd, w even br and bi equal zero\nc\nc case m = 0\nc\n 800 do 815 k=1,nt\n do 815 np1=2,ndo2,2\n do 815 i=1,imid\n do 815 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n we(ig,i,1,k)=we(ig,i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 815 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 830 mp1=2,mmax\n m = mp1-1\nc mb = m*(nlat-1)-(m*(m-1))/2\n mb = m*nlat-(m*(m+1))/2\n mp2 = mp1+1\n if(mp2 .gt. ndo2) go to 830\n do 829 k=1,nt\n do 828 np1=mp2,ndo2,2\n mn = mb+np1\n do 827 i=1,imm1\n do 827 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n vo(ig,i,2*mp1-2,k)=vo(ig,i,2*mp1-2,k)-ci(ncbc,mp1,np1,k)*wb(i,mn)\n vo(ig,i,2*mp1-1,k)=vo(ig,i,2*mp1-1,k)+cr(ncbc,mp1,np1,k)*wb(i,mn)\n we(ig,i,2*mp1-2,k)=we(ig,i,2*mp1-2,k)-cr(ncbc,mp1,np1,k)*vb(i,mn)\n we(ig,i,2*mp1-1,k)=we(ig,i,2*mp1-1,k)-ci(ncbc,mp1,np1,k)*vb(i,mn)\n 827 continue\n if(mlat .eq. 0) go to 828\n we(ig,imid,2*mp1-2,k) = we(ig,imid,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(imid,mn)\n we(ig,imid,2*mp1-1,k) = we(ig,imid,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(imid,mn)\n 828 continue\n 829 continue\n 830 continue\n 950 continue\n do 14 k=1,nt\nc do 14 ig=1,ng\n call hrfftb(ng*idv,nlon,ve(1,1,1,k),ng*idv,wrfft,work)\n call hrfftb(ng*idv,nlon,we(1,1,1,k),ng*idv,wrfft,work)\n 14 continue\n if(ityp .gt. 2) go to 12\n do 60 k=1,nt\n do 60 j=1,nlon\n do 60 i=1,imm1\n do 60 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ncvw=ncvwdiff+ncbc\n v(ncvw,i,j,k) = .5d0*(ve(ig,i,j,k)+vo(ig,i,j,k))\n w(ncvw,i,j,k) = .5d0*(we(ig,i,j,k)+wo(ig,i,j,k))\n v(ncvw,nlp1-i,j,k) = .5d0*(ve(ig,i,j,k)-vo(ig,i,j,k))\n w(ncvw,nlp1-i,j,k) = .5d0*(we(ig,i,j,k)-wo(ig,i,j,k))\n 60 continue\n go to 13\n 12 do 11 k=1,nt\n do 11 j=1,nlon\n do 11 i=1,imm1\n do 11 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ncvw=ncvwdiff+ncbc\n v(ncvw,i,j,k) = .5d0*ve(ig,i,j,k)\n w(ncvw,i,j,k) = .5d0*we(ig,i,j,k)\n 11 continue\n 13 if(mlat .ne. 0) then\n do 65 k=1,nt\n do 65 j=1,nlon\n do 65 ncbc=ncbcmin,ncbcmax\n ig=ncbc-ncbcmin+1\n ncvw=ncvwdiff+ncbc\n ncvw=ncvwdiff+ncbc\n v(ncvw,imid,j,k) = .5d0*ve(ig,imid,j,k)\n w(ncvw,imid,j,k) = .5d0*we(ig,imid,j,k)\n 65 continue\n end if\n 234 continue\n return\n end\n subroutine vhsgsi(nlat,nlon,wvhsgs,lvhsgs,dwork,ldwork,ierror)\n implicit double precision (a-h,o-z)\nc\nc subroutine vhsfsi computes the gaussian points theta, gauss \nc weights wts, and the components vb and wb of the vector \nc harmonics. all quantities are computed internally in double \nc precision but returned in single precision and are therfore \nc accurate to single precision.\nc\nc set imid = (nlat+1)/2 and lmn=(nlat*(nlat+1))/2 then\nc wvhsgs must have 2*(imid*lmn+nlat)+nlon+15 locations\nc\nc double precision array dwork must have\nc 3*nlat*(nlat+1)+5*nlat+1 = nlat*(3*nlat+8)+1 \nc locations which is determined by the size of dthet, \nc dwts, dwork, and dpbar in vhsgs1\nc\n dimension wvhsgs(*)\n double precision dwork(*)\n ierror = 1\n if(nlat .lt. 3) return\n ierror = 2\n if(nlon .lt. 1) return\n ierror = 3\n imid = (nlat+1)/2\n lmn = (nlat*(nlat+1))/2\n if(lvhsgs .lt. 2*(imid*lmn)+nlon+15) return\n ierror = 4\n if (ldwork .lt. (nlat*3*(nlat+3)+2)/2) return\n ierror = 0\nc\nc set saved work space pointers\nc\n jw1 = 1\n jw2 = jw1+imid*lmn\n jw3 = jw2+imid*lmn\nc\nc set unsaved work space pointers\nc\n iw1 = 1\n iw2 = iw1+nlat\n iw3 = iw2+nlat\n iw4 = iw3+3*imid*nlat\nc iw2 = iw1+nlat+nlat\nc iw3 = iw2+nlat+nlat\nc iw4 = iw3+6*imid*nlat\n call vhgsi1(nlat,imid,wvhsgs(jw1),wvhsgs(jw2),\n +dwork(iw1),dwork(iw2),dwork(iw3),dwork(iw4))\n call hrffti(nlon,wvhsgs(jw3))\n return\n end\n subroutine vhgsi1(nlat,imid,vb,wb,dthet,dwts,dpbar,work)\n implicit double precision (a-h,o-z)\n dimension vb(imid,*),wb(imid,*)\n double precision abel,bbel,cbel,ssqr2,dcf\n double precision dthet(*),dwts(*),dpbar(imid,nlat,3),work(*)\nc\nc compute gauss points and weights\nc use dpbar (length 3*nnlat*(nnlat+1)) as work space for gaqd\nc\n lwk = nlat*(nlat+2)\n call gaqd(nlat,dthet,dwts,dpbar,lwk,ierror)\nc\nc compute associated legendre functions\nc\nc compute m=n=0 legendre polynomials for all theta(i)\nc\n ssqr2 = 1.d0/dsqrt(2.d0)\n do 90 i=1,imid\n dpbar(i,1,1) = ssqr2\n vb(i,1) = 0.d0\n wb(i,1) = 0.d0\n 90 continue\nc\nc main loop for remaining vb, and wb\nc\n do 100 n=1,nlat-1\n nm = mod(n-2,3)+1\n nz = mod(n-1,3)+1\n np = mod(n,3)+1\nc\nc compute dpbar for m=0\nc\n call dnlfk(0,n,work)\n mn = indx(0,n,nlat)\n do 105 i=1,imid\n call dnlft(0,n,dthet(i),work,dpbar(i,1,np))\nc pbar(i,mn) = dpbar(i,1,np)\n 105 continue\nc\nc compute dpbar for m=1\nc\n call dnlfk(1,n,work)\n mn = indx(1,n,nlat)\n do 106 i=1,imid\n call dnlft(1,n,dthet(i),work,dpbar(i,2,np))\nc pbar(i,mn) = dpbar(i,2,np)\n 106 continue\n 104 continue\nc\nc compute and store dpbar for m=2,n\nc\n if(n.lt.2) go to 108\n do 107 m=2,n\n abel = dsqrt(dfloat((2*n+1)*(m+n-2)*(m+n-3))/\n 1 dfloat((2*n-3)*(m+n-1)*(m+n)))\n bbel = dsqrt(dfloat((2*n+1)*(n-m-1)*(n-m))/\n 1 dfloat((2*n-3)*(m+n-1)*(m+n)))\n cbel = dsqrt(dfloat((n-m+1)*(n-m+2))/\n 1 dfloat((m+n-1)*(m+n)))\n id = indx(m,n,nlat)\n if (m.ge.n-1) go to 102\n do 103 i=1,imid\n dpbar(i,m+1,np) = abel*dpbar(i,m-1,nm)+bbel*dpbar(i,m+1,nm)\n 1 -cbel*dpbar(i,m-1,np)\nc pbar(i,id) = dpbar(i,m+1,np)\n 103 continue\n go to 107\n 102 do 101 i=1,imid\n dpbar(i,m+1,np) = abel*dpbar(i,m-1,nm)-cbel*dpbar(i,m-1,np)\nc pbar(i,id) = dpbar(i,m+1,np)\n 101 continue\n 107 continue\nc\nc compute the derivative of the functions\nc\n 108 ix = indx(0,n,nlat)\n iy = indx(n,n,nlat)\n do 125 i=1,imid\n vb(i,ix) = -dpbar(i,2,np)\n vb(i,iy) = dpbar(i,n,np)/dsqrt(dfloat(2*(n+1)))\n125 continue\nc\n if(n.eq.1) go to 131 \n dcf = dsqrt(dfloat(4*n*(n+1)))\n do 130 m=1,n-1\n ix = indx(m,n,nlat) \n abel = dsqrt(dfloat((n+m)*(n-m+1)))/dcf\n bbel = dsqrt(dfloat((n-m)*(n+m+1)))/dcf\n do 130 i=1,imid\n vb(i,ix) = abel*dpbar(i,m,np)-bbel*dpbar(i,m+2,np)\n130 continue\nc\nc compute the vector harmonic w(theta) = m*pbar/cos(theta)\nc\nc set wb=0 for m=0\nc\n 131 ix = indx(0,n,nlat)\n do 220 i=1,imid\n wb(i,ix) = 0.d0\n220 continue\nc\nc compute wb for m=1,n\nc\n dcf = dsqrt(dfloat(n+n+1)/dfloat(4*n*(n+1)*(n+n-1)))\n do 230 m=1,n\n ix = indx(m,n,nlat) \n abel = dcf*dsqrt(dfloat((n+m)*(n+m-1)))\n bbel = dcf*dsqrt(dfloat((n-m)*(n-m-1)))\n if(m.ge.n-1) go to 231\n do 229 i=1,imid\n wb(i,ix) = abel*dpbar(i,m,nz) + bbel*dpbar(i,m+2,nz)\n 229 continue\n go to 230\n 231 do 228 i=1,imid\n wb(i,ix) = abel*dpbar(i,m,nz)\n 228 continue\n 230 continue\n 100 continue\n return \n end\n" }, { "path": "external/SPHEREPACK/vrtgs.f", "content": "c\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc * *\nc * copyright (c) 1998 by UCAR *\nc * *\nc * University Corporation for Atmospheric Research *\nc * *\nc * all rights reserved *\nc * *\nc * SPHEREPACK version 3.2 *\nc * *\nc * A Package of Fortran77 Subroutines and Programs *\nc * *\nc * for Modeling Geophysical Processes *\nc * *\nc * by *\nc * *\nc * John Adams and Paul Swarztrauber *\nc * *\nc * of *\nc * *\nc * the National Center for Atmospheric Research *\nc * *\nc * Boulder, Colorado (80307) U.S.A. *\nc * *\nc * which is sponsored by *\nc * *\nc * the National Science Foundation *\nc * *\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc\nc\nc\nc ... file vrtgs.f\nc\nc this file includes documentation and code for\nc subroutine divgs i\nc\nc ... files which must be loaded with vrtgs.f\nc\nc sphcom.f, hrfft.f, vhgsc.f, shsgs.f, gaqd.f\nc\nc subroutine vrtgs(nstrv,nstrc,noffsv,noffsc,\nc nlat,nlon,isym,nt,vort,ivrt,jvrt,cr,ci,mdc,ndc,\nc + wshsgs,lshsgs,work,lwork,ierror)\nc\nc given the vector spherical harmonic coefficients cr and ci, precomputed\nc by subroutine vhags for a vector field (v,w), subroutine vrtgs\nc computes the vorticity of the vector field in the scalar array\nc vort. vort(i,j) is the vorticity at the gaussian colatitude\nc theta(i) (see nlat as input parameter) and longitude\nc lambda(j) = (j-1)*2*pi/nlon on the sphere. i.e.,\nc\nc vort(i,j) = [-dv/dlambda + d(sint*w)/dtheta]/sint\nc\nc where sint = sin(theta(i)). w is the east longitudinal and v\nc is the colatitudinal component of the vector field from which\nc cr,ci were precomputed. required associated legendre polynomials\nc are stored rather than recomputed as they are in subroutine vrtgc.\nc\nc\nc input parameters\nc\nc nstrv the stride in vort\nc nstrc the stride in ci,cr\nc\nc noffsv the offset in vort\nc noffsc the offset in ci,cr\nc -- must be between 0 and stride-1\nc\nc nlat the number of points in the gaussian colatitude grid on the\nc full sphere. these lie in the interval (0,pi) and are computed\nc in radians in theta(1) <...< theta(nlat) by subroutine gaqd.\nc if nlat is odd the equator will be included as the grid point\nc theta((nlat+1)/2). if nlat is even the equator will be\nc excluded as a grid point and will lie half way between\nc theta(nlat/2) and theta(nlat/2+1). nlat must be at least 3.\nc note: on the half sphere, the number of grid points in the\nc colatitudinal direction is nlat/2 if nlat is even or\nc (nlat+1)/2 if nlat is odd.\nc\nc nlon the number of distinct londitude points. nlon determines\nc the grid increment in longitude as 2*pi/nlon. for example\nc nlon = 72 for a five degree grid. nlon must be greater\nc than 3. the axisymmetric case corresponds to nlon=1.\nc the efficiency of the computation is improved when nlon\nc is a product of small prime numbers.\nc\nc NOTE: this is a modified version of spherepack. Changes from\nc the original version to the current one have only been\nc tested for isym==0. For this reason an error code will\nc be returned if isym!=0.\nc\nc\nc isym a parameter which determines whether the vorticity is\nc computed on the full or half sphere as follows:\nc\nc = 0\nc the symmetries/antsymmetries described in isym=1,2 below\nc do not exist in (v,w) about the equator. in this case the\nc vorticity is neither symmetric nor antisymmetric about\nc the equator. the vorticity is computed on the entire\nc sphere. i.e., in the array vort(i,j) for i=1,...,nlat and\nc j=1,...,nlon.\nc\nc = 1\nc w is antisymmetric and v is symmetric about the equator.\nc in this case the vorticity is symmetyric about the\nc equator and is computed for the northern hemisphere\nc only. i.e., if nlat is odd the vorticity is computed\nc in the array vort(i,j) for i=1,...,(nlat+1)/2 and for\nc j=1,...,nlon. if nlat is even the vorticity is computed\nc in the array vort(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc\nc = 2\nc w is symmetric and v is antisymmetric about the equator\nc in this case the vorticity is antisymmetric about the\nc equator and is computed for the northern hemisphere\nc only. i.e., if nlat is odd the vorticity is computed\nc in the array vort(i,j) for i=1,...,(nlat+1)/2 and for\nc j=1,...,nlon. if nlat is even the vorticity is computed\nc in the array vort(i,j) for i=1,...,nlat/2 and j=1,...,nlon.\nc\nc\nc nt nt is the number of scalar and vector fields. some\nc computational efficiency is obtained for multiple fields.\nc in the program that calls vrtgs, the arrays cr,ci, and vort\nc can be three dimensional corresponding to an indexed multiple\nc vector field. in this case multiple scalar synthesis will\nc be performed to compute the vorticity for each field. the\nc third index is the synthesis index which assumes the values\nc k=1,...,nt. for a single synthesis set nt = 1. the\nc description of the remaining parameters is simplified by\nc assuming that nt=1 or that all the arrays are two dimensional.\nc\nc ivrt the first dimension of the array vort as it appears in\nc the program that calls vrtgs. if isym = 0 then ivrt\nc must be at least nlat. if isym = 1 or 2 and nlat is\nc even then ivrt must be at least nlat/2. if isym = 1 or 2\nc and nlat is odd then ivrt must be at least (nlat+1)/2.\nc\nc jvrt the second dimension of the array vort as it appears in\nc the program that calls vrtgs. jvrt must be at least nlon.\nc\nc cr,ci two or three dimensional arrays (see input parameter nt)\nc that contain vector spherical harmonic coefficients\nc of the vector field (v,w) as computed by subroutine vhags.\nc *** cr and ci must be computed by vhags prior to calling\nc vrtgs.\nc\nc mdc the first dimension of the arrays cr and ci as it\nc appears in the program that calls vrtgs. mdc must be at\nc least min0(nlat,nlon/2) if nlon is even or at least\nc min0(nlat,(nlon+1)/2) if nlon is odd.\nc\nc ndc the second dimension of the arrays cr and ci as it\nc appears in the program that calls vrtgs. ndc must be at\nc least nlat.\nc\nc wshsgs an array which must be initialized by subroutine shsgsi.\nc once initialized,\nc wshsgs can be used repeatedly by vrtgs as long as nlon\nc and nlat remain unchanged. wshsgs must not be altered\nc between calls of vrtgs\nc\nc lshsgs the dimension of the array wshsgs as it appears in the\nc program that calls vrtgs. define\nc\nc l1 = min0(nlat,(nlon+2)/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc then lshsgs must be at least\nc\nc nlat*(3*(l1+l2)-2)+(l1-1)*(l2*(2*nlat-l1)-3*l1)/2+nlon+15\nc\nc work a work array that does not have to be saved.\nc\nc lwork the dimension of the array work as it appears in the\nc program that calls vrtgs. define\nc\nc l1 = min0(nlat,nlon/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd.\nc\nc if isym = 0 then lwork must be at least\nc\nc nlat*((nt+1)*nlon+2*nt*l1+1)\nc\nc if isym > 0 then lwork must be at least\nc\nc (nt+1)*l2*nlon+nlat*(2*nt*l1+1)\nc\nc\nc **************************************************************\nc\nc output parameters\nc\nc\nc vort a two or three dimensional array (see input parameter nt)\nc that contains the vorticity of the vector field (v,w)\nc whose coefficients cr,ci where computed by subroutine vhags.\nc vort(i,j) is the vorticity at the gaussian colatitude point\nc theta(i) and longitude point lambda(j) = (j-1)*2*pi/nlon.\nc the index ranges are defined above at the input parameter\nc isym.\nc\nc\nc ierror an error parameter which indicates fatal errors with input\nc parameters when returned positive.\nc = 0 no errors\nc = 1 error in the specification of nlat\nc = 2 error in the specification of nlon\nc = 3 error in the specification of isym\nc = 4 error in the specification of nt\nc = 5 error in the specification of ivrt\nc = 6 error in the specification of jvrt\nc = 7 error in the specification of mdc\nc = 8 error in the specification of ndc\nc = 9 error in the specification of lshsgs\nc = 10 error in the specification of lwork\nc **********************************************************************\nc \nc \n subroutine vrtgs(nstrv,nstrc,noffsv,noffsc,\n + nlat,nlon,isym,nt,vort,ivrt,jvrt,cr,ci,mdc,ndc,\n + wshsgs,lshsgs,work,lwork,ierror)\n implicit double precision (a-h,o-z)\n dimension vort(nstrv,ivrt,jvrt,nt),\n + cr(nstrc,mdc,ndc,nt),ci(nstrc,mdc,ndc,nt)\n dimension wshsgs(lshsgs),work(lwork)\nc\nc check input parameters\nc\n ierror = 1\n if(nlat .lt. 3) return\n ierror = 2\n if(nlon .lt. 4) return\n ierror = 3\nc if (isym.lt.0 .or. isym.gt.2) return\nc see note above about symmetries\n if(isym.ne.0) return\n ierror = 4\n if(nt .lt. 0) return\n ierror = 5\n imid = (nlat+1)/2\n if((isym.eq.0 .and. ivrt.lt.nlat) .or.\n 1 (isym.gt.0 .and. ivrt.lt.imid)) return\n ierror = 6\n if(jvrt .lt. nlon) return\n ierror = 7\n if(mdc .lt. min0(nlat,(nlon+1)/2)) return\n mmax = min0(nlat,(nlon+2)/2)\n ierror = 8\n if(ndc .lt. nlat) return\n ierror = 9\n imid = (nlat+1)/2\n lpimn = (imid*mmax*(nlat+nlat-mmax+1))/2\n l2 = (nlat+mod(nlat,2))/2\n l1 = min0((nlon+2)/2,nlat)\n lp=nlat*(3*(l1+l2)-2)+(l1-1)*(l2*(2*nlat-l1)-3*l1)/2+nlon+15\n if(lshsgs.lt.lp) return\n ierror = 10\nc\nc verify unsaved work space (add to what shses requires, file f3)\nc\nc\nc set first dimension for a,b (as requried by shses)\nc\n mab = min0(nlat,nlon/2+1)\n mn = mab*nlat*nt\n ls = nlat\n if(isym .gt. 0) ls = imid\n nln = nt*ls*nlon\n if(lwork.lt. nln+ls*nlon+2*mn+nlat) return\n ierror = 11\n if((noffsv.lt.0).or.(noffsv.ge.nstrv)) return\n if((noffsc.lt.0).or.(noffsc.ge.nstrc)) return\n ierror = 0\nc\nc set work space pointers\nc\n ia = 1\n ib = ia+mn\n is = ib+mn\n iwk = is+nlat\n lwk = lwork-2*mn-nlat\n call vrtgs1(nstrv,nstrc,noffsv,noffsc,\n 1 nlat,nlon,isym,nt,vort,ivrt,jvrt,cr,ci,mdc,ndc,\n +work(ia),work(ib),mab,work(is),wshsgs,lshsgs,work(iwk),lwk,\n +ierror)\n return\n end\n\n subroutine vrtgs1(nstrv,nstrc,noffsv,noffsc,\n + nlat,nlon,isym,nt,vort,ivrt,jvrt,cr,ci,mdc,ndc,\n + a,b,mab,sqnn,wsav,lwsav,wk,lwk,ierror)\n implicit double precision (a-h,o-z)\n dimension vort(nstrv,ivrt,jvrt,nt),\n + cr(nstrc,mdc,ndc,nt),ci(nstrc,mdc,ndc,nt)\n dimension a(mab,nlat,nt),b(mab,nlat,nt),sqnn(nlat)\n dimension wsav(lwsav),wk(lwk)\n ncc=noffsc+1\nc\nc set coefficient multiplyers\nc\n do 1 n=2,nlat\n fn = dfloat(n-1)\n sqnn(n) = dsqrt(fn*(fn+1.))\n 1 continue\nc\nc compute divergence scalar coefficients for each vector field\nc\n do 2 k=1,nt\n do 3 n=1,nlat\n do 4 m=1,mab\n a(m,n,k) = 0.0\n b(m,n,k) = 0.0\n 4 continue\n 3 continue\nc\nc compute m=0 coefficients\nc\n do 5 n=2,nlat\n a(1,n,k) = sqnn(n)*cr(ncc,1,n,k)\n b(1,n,k) = sqnn(n)*ci(ncc,1,n,k)\n 5 continue\nc\nc compute m>0 coefficients\nc\n mmax = min0(nlat,(nlon+1)/2)\n do 6 m=2,mmax\n do 7 n=m,nlat\n a(m,n,k) = sqnn(n)*cr(ncc,m,n,k)\n b(m,n,k) = sqnn(n)*ci(ncc,m,n,k)\n 7 continue\n 6 continue\n 2 continue\nc\nc synthesize a,b into vort\nc\n call shsgs(nstrv,1,noffsv,0,nlat,nlon,isym,nt,vort,ivrt,jvrt,a,b,\n + mab,nlat,mab,nlat,wsav,lwsav,wk,lwk,ierror)\n return\n end\n" }, { "path": "external/SPHEREPACK/vtsgs.f", "content": "c\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc * *\nc * copyright (c) 1998 by UCAR *\nc * *\nc * University Corporation for Atmospheric Research *\nc * *\nc * all rights reserved *\nc * *\nc * SPHEREPACK version 3.2 *\nc * *\nc * A Package of Fortran77 Subroutines and Programs *\nc * *\nc * for Modeling Geophysical Processes *\nc * *\nc * by *\nc * *\nc * John Adams and Paul Swarztrauber *\nc * *\nc * of *\nc * *\nc * the National Center for Atmospheric Research *\nc * *\nc * Boulder, Colorado (80307) U.S.A. *\nc * *\nc * which is sponsored by *\nc * *\nc * the National Science Foundation *\nc * *\nc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\nc\nc\nc\nc ... file vtsgs.f\nc\nc this file includes documentation and code for\nc subroutines vtsgs and vtsgsi\nc\nc ... files which must be loaded with vtsgs.f\nc\nc sphcom.f, hrfft.f, vhags.f, vhsgs.f,gaqd.f\nc \nc \nc subroutine vtsgs(nstrvw,nstrbc,noffsvw,noffsbc,\nc + nlat,nlon,ityp,nt,vt,wt,idvw,jdvw,br,bi,cr,ci,\nc + mdab,ndab,wvts,lwvts,work,lwork,ierror)\nc\nc given the vector harmonic analysis br,bi,cr, and ci (computed\nc by subroutine vhags) of some vector function (v,w), this \nc subroutine computes the vector function (vt,wt) which is\nc the derivative of (v,w) with respect to colatitude theta. vtsgs\nc is similar to vhsgs except the vector harmonics are replaced by \nc their derivative with respect to colatitude with the result that\nc (vt,wt) is computed instead of (v,w). vt(i,j) is the derivative\nc of the colatitudinal component v(i,j) at the gaussian colatitude\nc point theta(i) and longitude phi(j) = (j-1)*2*pi/nlon. the\nc spectral representation of (vt,wt) is given below at output\nc parameters vt,wt.\nc\nc input parameters\nc\nc nstrvw the stride in wt,vt\nc nstrbc the stride in bi,br,ci,cr\nc noffsvw the offset in wt,vt\nc noffsbc the offset in bi,br,ci,cr\nc -- must be between 0 and stride-1\nc\nc nlat the number of gaussian colatitudinal grid points theta(i)\nc such that 0 < theta(1) <...< theta(nlat) < pi. they are\nc computed by subroutine gaqd which is called by this\nc subroutine. if nlat is odd the equator is\nc theta((nlat+1)/2). if nlat is even the equator lies\nc half way between theta(nlat/2) and theta(nlat/2+1). nlat\nc must be at least 3. note: if (v,w) is symmetric about\nc the equator (see parameter ityp below) the number of\nc colatitudinal grid points is nlat/2 if nlat is even or\nc (nlat+1)/2 if nlat is odd.\nc\nc nlon the number of distinct londitude points. nlon determines\nc the grid increment in longitude as 2*pi/nlon. for example\nc nlon = 72 for a five degree grid. nlon must be greater\nc than zero. the axisymmetric case corresponds to nlon=1.\nc the efficiency of the computation is improved when nlon\nc is a product of small prime numbers.\nc\nc NOTE: this is a modified version of spherepack. Changes from\nc the original version to the current one have only been\nc tested for ityp=0,1,2. For this reason an error code will\nc be returned if ityp>2.\nc\nc ityp = 0 no symmetries exist about the equator. the synthesis\nc is performed on the entire sphere. i.e. the arrays\nc vt(i,j),wt(i,j) are computed for i=1,...,nlat and\nc j=1,...,nlon. \nc\nc = 1 no symmetries exist about the equator however the\nc the coefficients cr and ci are zero which implies\nc that the curl of (v,w) is zero. that is,\nc (d/dtheta (sin(theta) w) - dv/dphi)/sin(theta) = 0. \nc the calculations are performed on the entire sphere.\nc i.e. the arrays vt(i,j),wt(i,j) are computed for \nc i=1,...,nlat and j=1,...,nlon.\nc\nc = 2 no symmetries exist about the equator however the\nc the coefficients br and bi are zero which implies\nc that the divergence of (v,w) is zero. that is,\nc (d/dtheta (sin(theta) v) + dw/dphi)/sin(theta) = 0. \nc the calculations are performed on the entire sphere.\nc i.e. the arrays vt(i,j),wt(i,j) are computed for \nc i=1,...,nlat and j=1,...,nlon.\nc\nc = 3 vt is odd and wt is even about the equator. the \nc synthesis is performed on the northern hemisphere\nc only. i.e., if nlat is odd the arrays vt(i,j)\nc and wt(i,j) are computed for i=1,...,(nlat+1)/2\nc and j=1,...,nlon. if nlat is even the arrays \nc are computed for i=1,...,nlat/2 and j=1,...,nlon.\nc\nc = 4 vt is odd and wt is even about the equator and the \nc coefficients cr and ci are zero. the synthesis is\nc performed on the northern hemisphere only. i.e. if\nc nlat is odd the arrays vt(i,j),wt(i,j) are computed\nc for i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the arrays vt(i,j),wt(i,j) are computed for \nc i=1,...,nlat/2 and j=1,...,nlon.\nc\nc = 5 vt is odd and wt is even about the equator and the \nc coefficients br and bi are zero. the synthesis is\nc performed on the northern hemisphere only. i.e. if\nc nlat is odd the arrays vt(i,j),wt(i,j) are computed\nc for i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the arrays vt(i,j),wt(i,j) are computed for \nc i=1,...,nlat/2 and j=1,...,nlon.\nc\nc = 6 vt is even and wt is odd about the equator. the \nc synthesis is performed on the northern hemisphere\nc only. i.e., if nlat is odd the arrays vt(i,j),wt(i,j)\nc are computed for i=1,...,(nlat+1)/2 and j=1,...,nlon.\nc if nlat is even the arrays vt(i,j),wt(i,j) are computed \nc for i=1,...,nlat/2 and j=1,...,nlon.\nc\nc = 7 vt is even and wt is odd about the equator and the \nc coefficients cr and ci are zero. the synthesis is\nc performed on the northern hemisphere only. i.e. if\nc nlat is odd the arrays vt(i,j),wt(i,j) are computed\nc for i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the arrays vt(i,j),wt(i,j) are computed for \nc i=1,...,nlat/2 and j=1,...,nlon.\nc\nc = 8 vt is even and wt is odd about the equator and the \nc coefficients br and bi are zero. the synthesis is\nc performed on the northern hemisphere only. i.e. if\nc nlat is odd the arrays vt(i,j),wt(i,j) are computed\nc for i=1,...,(nlat+1)/2 and j=1,...,nlon. if nlat is\nc even the arrays vt(i,j),wt(i,j) are computed for \nc i=1,...,nlat/2 and j=1,...,nlon.\nc\nc nt the number of syntheses. in the program that calls vtsgs,\nc the arrays vt,wt,br,bi,cr, and ci can be three dimensional\nc in which case multiple syntheses will be performed.\nc the third index is the synthesis index which assumes the \nc values k=1,...,nt. for a single synthesis set nt=1. the\nc discription of the remaining parameters is simplified\nc by assuming that nt=1 or that all the arrays are two\nc dimensional.\nc\nc idvw the first dimension of the arrays vt,wt as it appears in\nc the program that calls vtsgs. if ityp .le. 2 then idvw\nc must be at least nlat. if ityp .gt. 2 and nlat is\nc even then idvw must be at least nlat/2. if ityp .gt. 2\nc and nlat is odd then idvw must be at least (nlat+1)/2.\nc\nc jdvw the second dimension of the arrays vt,wt as it appears in\nc the program that calls vtsgs. jdvw must be at least nlon.\nc\nc br,bi two or three dimensional arrays (see input parameter nt)\nc cr,ci that contain the vector spherical harmonic coefficients\nc of (v,w) as computed by subroutine vhags.\nc \nc mdab the first dimension of the arrays br,bi,cr, and ci as it\nc appears in the program that calls vtsgs. mdab must be at\nc least min0(nlat,nlon/2) if nlon is even or at least\nc min0(nlat,(nlon+1)/2) if nlon is odd.\nc\nc ndab the second dimension of the arrays br,bi,cr, and ci as it\nc appears in the program that calls vtsgs. ndab must be at\nc least nlat.\nc\nc wvts an array which must be initialized by subroutine vtsgsi.\nc once initialized, wvts can be used repeatedly by vtsgs\nc as long as nlon and nlat remain unchanged. wvts must\nc not be altered between calls of vtsgs.\nc\nc lwvts the dimension of the array wvts as it appears in the\nc program that calls vtsgs. define\nc\nc l1 = min0(nlat,nlon/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc then lwvts must be at least\nc\nc l1*l2*(nlat+nlat-l1+1)+nlon+15\nc\nc\nc work a work array that does not have to be saved.\nc\nc lwork the dimension of the array work as it appears in the\nc program that calls vtsgs. define\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc if ityp .le. 2 then lwork must be at least\nc\nc (2*nt+1)*nlat*nlon\nc\nc if ityp .gt. 2 then lwork must be at least\nc\nc (2*nt+1)*l2*nlon \nc\nc **************************************************************\nc\nc output parameters\nc\nc vt,wt two or three dimensional arrays (see input parameter nt)\nc in which the derivative of (v,w) with respect to \nc colatitude theta is stored. vt(i,j),wt(i,j) contain the\nc derivatives at gaussian colatitude points theta(i) for\nc i=1,...,nlat and longitude phi(j) = (j-1)*2*pi/nlon. \nc the index ranges are defined above at the input parameter\nc ityp. vt and wt are computed from the formulas for v and \nc w given in subroutine vhsgs but with vbar and wbar replaced\nc with their derivatives with respect to colatitude. these\nc derivatives are denoted by vtbar and wtbar. \nc\nc\nc *************************************************************\nc\nc in terms of real variables this expansion takes the form\nc\nc for i=1,...,nlat and j=1,...,nlon\nc\nc vt(i,j) = the sum from n=1 to n=nlat-1 of\nc\nc .5*br(1,n+1)*vtbar(0,n,theta(i))\nc\nc plus the sum from m=1 to m=mmax-1 of the sum from n=m to \nc n=nlat-1 of the real part of\nc\nc (br(m+1,n+1)*vtbar(m,n,theta(i))\nc -ci(m+1,n+1)*wtbar(m,n,theta(i)))*cos(m*phi(j))\nc -(bi(m+1,n+1)*vtbar(m,n,theta(i))\nc +cr(m+1,n+1)*wtbar(m,n,theta(i)))*sin(m*phi(j))\nc\nc and for i=1,...,nlat and j=1,...,nlon\nc\nc wt(i,j) = the sum from n=1 to n=nlat-1 of\nc\nc -.5*cr(1,n+1)*vtbar(0,n,theta(i))\nc\nc plus the sum from m=1 to m=mmax-1 of the sum from n=m to\nc n=nlat-1 of the real part of\nc\nc -(cr(m+1,n+1)*vtbar(m,n,theta(i))\nc +bi(m+1,n+1)*wtbar(m,n,theta(i)))*cos(m*phi(j))\nc +(ci(m+1,n+1)*vtbar(m,n,theta(i))\nc -br(m+1,n+1)*wtbar(m,n,theta(i)))*sin(m*phi(j))\nc\nc\nc br(m+1,nlat),bi(m+1,nlat),cr(m+1,nlat), and ci(m+1,nlat) are\nc assumed zero for m even.\nc\nc\nc ierror = 0 no errors\nc = 1 error in the specification of nlat\nc = 2 error in the specification of nlon\nc = 3 error in the specification of ityp\nc = 4 error in the specification of nt\nc = 5 error in the specification of idvw\nc = 6 error in the specification of jdvw\nc = 7 error in the specification of mdab\nc = 8 error in the specification of ndab\nc = 9 error in the specification of lwvts\nc = 10 error in the specification of lwork\nc\nc\nc *******************************************************************\nc\nc subroutine vtsgsi(nlat,nlon,wvts,lwvts,work,lwork,dwork,ldwork,\nc + ierror)\nc\nc subroutine vtsgsi initializes the array wvts which can then be\nc used repeatedly by subroutine vtsgs until nlat or nlon is changed.\nc\nc input parameters\nc\nc nlat the number of gaussian colatitudinal grid points theta(i)\nc such that 0 < theta(1) <...< theta(nlat) < pi. they are\nc computed by subroutine gaqd which is called by this\nc subroutine. if nlat is odd the equator is\nc theta((nlat+1)/2). if nlat is even the equator lies\nc half way between theta(nlat/2) and theta(nlat/2+1). nlat\nc must be at least 3. note: if (v,w) is symmetric about\nc the equator (see parameter ityp below) the number of\nc colatitudinal grid points is nlat/2 if nlat is even or\nc (nlat+1)/2 if nlat is odd.\nc\nc nlon the number of distinct londitude points. nlon determines\nc the grid increment in longitude as 2*pi/nlon. for example\nc nlon = 72 for a five degree grid. nlon must be greater\nc than zero. the axisymmetric case corresponds to nlon=1.\nc the efficiency of the computation is improved when nlon\nc is a product of small prime numbers.\nc\nc lwvts the dimension of the array wvts as it appears in the\nc program that calls vtsgs. define\nc\nc l1 = min0(nlat,nlon/2) if nlon is even or\nc l1 = min0(nlat,(nlon+1)/2) if nlon is odd\nc\nc and\nc\nc l2 = nlat/2 if nlat is even or\nc l2 = (nlat+1)/2 if nlat is odd\nc\nc then lwvts must be at least\nc\nc l1*l2*(nlat+nlat-l1+1)+nlon+15\nc\nc\nc work a work array that does not have to be saved.\nc\nc lwork the dimension of the array work as it appears in the\nc program that calls vtsgs. lwork must be at least\nc\nc 3*(max0(l1-2,0)*(nlat+nlat-l1-1))/2+(5*l2+2)*nlat\nc\nc dwork a double precision work array that does not have to be saved\nc\nc ldwork the length of dwork. ldwork must be at least\nc 3*nlat+2\nc\nc **************************************************************\nc\nc output parameters\nc\nc wvts an array which is initialized for use by subroutine vtsgs.\nc once initialized, wvts can be used repeatedly by vtsgs\nc as long as nlat or nlon remain unchanged. wvts must not\nc be altered between calls of vtsgs.\nc\nc\nc ierror = 0 no errors\nc = 1 error in the specification of nlat\nc = 2 error in the specification of nlon\nc = 3 error in the specification of lwvts\nc = 4 error in the specification of lwork\nc = 5 error in the specification of ldwork\nc\n subroutine vtsgs(nstrvw,nstrbc,noffsvw,noffsbc,\n 1 nlat,nlon,ityp,nt,vt,wt,idvw,jdvw,br,bi,cr,ci,\n 1 mdab,ndab,wvts,lwvts,work,lwork,ierror)\n implicit double precision (a-h,o-z)\nc\n dimension vt(nstrvw,idvw,jdvw,1),wt(nstrvw,idvw,jdvw,1),\n 1 br(nstrbc,mdab,ndab,1),bi(nstrbc,mdab,ndab,1),\n 1 cr(nstrbc,mdab,ndab,1),ci(nstrbc,mdab,ndab,1),\n 2 work(1),wvts(1)\n ierror = 1\n if(nlat .lt. 3) return\n ierror = 2\n if(nlon .lt. 1) return\n ierror = 3\n if(ityp.lt.0 .or. ityp.gt.8) return\n ierror = 4\nc see note above about symmetries\n if(ityp.gt.2) return\n if(nt .lt. 0) return\n ierror = 5\n imid = (nlat+1)/2\nc if((ityp.le.2 .and. idvw.lt.nlat) .or.\nc 1 (ityp.gt.2 .and. idvw.lt.imid)) return\nc see note above about symmetries\n if(ityp.ne.0) return\n ierror = 6\n if(jdvw .lt. nlon) return\n ierror = 7\n mmax = min0(nlat,(nlon+1)/2)\n if(mdab .lt. mmax) return\n ierror = 8\n if(ndab .lt. nlat) return\n ierror = 9\n idz = (mmax*(nlat+nlat-mmax+1))/2\n lzimn = idz*imid\n if(lwvts .lt. lzimn+lzimn+nlon+15) return\n ierror = 10\n idv = nlat\n if(ityp .gt. 2) idv = imid\n lnl = nt*idv*nlon\n if(lwork .lt. lnl+lnl+idv*nlon) return\n ierror = 11\n if((noffsvw.lt.0).or.(noffsvw.ge.nstrvw)) return\n if((noffsbc.lt.0).or.(noffsbc.ge.nstrbc)) return\n ierror = 0\n ist = 0\n if(ityp .le. 2) ist = imid\n iw1 = ist+1\n iw2 = lnl+1\n iw3 = iw2+ist\n iw4 = iw2+lnl\n jw1 = lzimn+1\n jw2 = jw1+lzimn\n call vtsgs1(nstrvw,nstrbc,noffsvw,noffsbc,\n 1 nlat,nlon,ityp,nt,imid,idvw,jdvw,vt,wt,mdab,ndab,\n 1 br,bi,cr,ci,idv,work,work(iw1),work(iw2),work(iw3),\n 2 work(iw4),idz,wvts,wvts(jw1),wvts(jw2))\n return\n end\n subroutine vtsgs1(nstrvw,nstrbc,noffsvw,noffsbc,\n 1 nlat,nlon,ityp,nt,imid,idvw,jdvw,vt,wt,mdab,\n 1 ndab,br,bi,cr,ci,idv,vte,vto,wte,wto,work,idz,vb,wb,wrfft)\n implicit double precision (a-h,o-z)\n dimension vt(nstrvw,idvw,jdvw,1),wt(nstrvw,idvw,jdvw,1),\n 1 br(nstrbc,mdab,ndab,1),bi(nstrbc,mdab,ndab,1),\n 1 cr(nstrbc,mdab,ndab,1),ci(nstrbc,mdab,ndab,1),\n 2 vte(idv,nlon,1),vto(idv,nlon,1),wte(idv,nlon,1),\n 3 wto(idv,nlon,1),work(1),wrfft(1),\n 4 vb(imid,1),wb(imid,1)\n ncvw = noffsvw+1\n ncbc = noffsbc+1\n nlp1 = nlat+1\n mlat = mod(nlat,2)\n mlon = mod(nlon,2)\n mmax = min0(nlat,(nlon+1)/2)\n imm1 = imid\n if(mlat .ne. 0) imm1 = imid-1\n do 10 k=1,nt\n do 10 j=1,nlon\n do 10 i=1,idv\n vte(i,j,k) = 0.d0\n wte(i,j,k) = 0.d0\n 10 continue\n ndo1 = nlat\n ndo2 = nlat\n if(mlat .ne. 0) ndo1 = nlat-1\n if(mlat .eq. 0) ndo2 = nlat-1\n 18 itypp = ityp+1\n go to (1,100,200,300,400,500,600,700,800),itypp\nc\nc case ityp=0 no symmetries\nc\nc case m = 0\nc\n 1 do 15 k=1,nt\n do 15 np1=2,ndo2,2\n do 15 i=1,imm1\n vto(i,1,k)=vto(i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n wto(i,1,k)=wto(i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 15 continue\n do 16 k=1,nt\n do 16 np1=3,ndo1,2\n do 16 i=1,imid\n vte(i,1,k)=vte(i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n wte(i,1,k)=wte(i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 16 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 30 mp1=2,mmax\n m = mp1-1\n mb = m*(nlat-1)-(m*(m-1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 26\n do 25 k=1,nt\n do 24 np1=mp1,ndo1,2\n mn = mb+np1\n do 23 i=1,imm1\n vte(i,2*mp1-2,k) = vte(i,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(i,mn)\n vto(i,2*mp1-2,k) = vto(i,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(i,mn)\n vte(i,2*mp1-1,k) = vte(i,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(i,mn)\n vto(i,2*mp1-1,k) = vto(i,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(i,mn)\n wte(i,2*mp1-2,k) = wte(i,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(i,mn)\n wto(i,2*mp1-2,k) = wto(i,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(i,mn)\n wte(i,2*mp1-1,k) = wte(i,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(i,mn)\n wto(i,2*mp1-1,k) = wto(i,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(i,mn)\n 23 continue\n if(mlat .eq. 0) go to 24\n vte(imid,2*mp1-2,k) = vte(imid,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(imid,mn)\n vte(imid,2*mp1-1,k) = vte(imid,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(imid,mn)\n wte(imid,2*mp1-2,k) = wte(imid,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(imid,mn) \n wte(imid,2*mp1-1,k) = wte(imid,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(imid,mn)\n 24 continue\n 25 continue\n 26 if(mp2 .gt. ndo2) go to 30\n do 29 k=1,nt\n do 28 np1=mp2,ndo2,2\n mn = mb+np1\n do 27 i=1,imm1\n vto(i,2*mp1-2,k) = vto(i,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(i,mn)\n vte(i,2*mp1-2,k) = vte(i,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(i,mn)\n vto(i,2*mp1-1,k) = vto(i,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(i,mn)\n vte(i,2*mp1-1,k) = vte(i,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(i,mn)\n wto(i,2*mp1-2,k) = wto(i,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(i,mn)\n wte(i,2*mp1-2,k) = wte(i,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(i,mn)\n wto(i,2*mp1-1,k) = wto(i,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(i,mn)\n wte(i,2*mp1-1,k) = wte(i,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(i,mn)\n 27 continue\n if(mlat .eq. 0) go to 28\n vte(imid,2*mp1-2,k) = vte(imid,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(imid,mn) \n vte(imid,2*mp1-1,k) = vte(imid,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(imid,mn)\n wte(imid,2*mp1-2,k) = wte(imid,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(imid,mn)\n wte(imid,2*mp1-1,k) = wte(imid,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(imid,mn)\n 28 continue\n 29 continue\n 30 continue\n go to 950\nc\nc case ityp=1 no symmetries, cr and ci equal zero\nc\nc case m = 0\nc\n 100 do 115 k=1,nt\n do 115 np1=2,ndo2,2\n do 115 i=1,imm1\n vto(i,1,k)=vto(i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n 115 continue\n do 116 k=1,nt\n do 116 np1=3,ndo1,2\n do 116 i=1,imid\n vte(i,1,k)=vte(i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n 116 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 130 mp1=2,mmax\n m = mp1-1\n mb = m*(nlat-1)-(m*(m-1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 126\n do 125 k=1,nt\n do 124 np1=mp1,ndo1,2\n mn = mb+np1\n do 123 i=1,imm1\n vte(i,2*mp1-2,k) = vte(i,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(i,mn)\n vte(i,2*mp1-1,k) = vte(i,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(i,mn)\n wto(i,2*mp1-2,k) = wto(i,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(i,mn)\n wto(i,2*mp1-1,k) = wto(i,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(i,mn)\n 123 continue\n if(mlat .eq. 0) go to 124\n vte(imid,2*mp1-2,k) = vte(imid,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(imid,mn)\n vte(imid,2*mp1-1,k) = vte(imid,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(imid,mn)\n 124 continue\n 125 continue\n 126 if(mp2 .gt. ndo2) go to 130\n do 129 k=1,nt\n do 128 np1=mp2,ndo2,2\n mn = mb+np1\n do 127 i=1,imm1\n vto(i,2*mp1-2,k) = vto(i,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(i,mn)\n vto(i,2*mp1-1,k) = vto(i,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(i,mn)\n wte(i,2*mp1-2,k) = wte(i,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(i,mn)\n wte(i,2*mp1-1,k) = wte(i,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(i,mn)\n 127 continue\n if(mlat .eq. 0) go to 128\n wte(imid,2*mp1-2,k) = wte(imid,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(imid,mn)\n wte(imid,2*mp1-1,k) = wte(imid,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(imid,mn)\n 128 continue\n 129 continue\n 130 continue\n go to 950\nc\nc case ityp=2 no symmetries, br and bi are equal to zero\nc\nc case m = 0\nc\n 200 do 215 k=1,nt\n do 215 np1=2,ndo2,2\n do 215 i=1,imm1\n wto(i,1,k)=wto(i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 215 continue\n do 216 k=1,nt\n do 216 np1=3,ndo1,2\n do 216 i=1,imid\n wte(i,1,k)=wte(i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 216 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 230 mp1=2,mmax\n m = mp1-1\n mb = m*(nlat-1)-(m*(m-1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 226\n do 225 k=1,nt\n do 224 np1=mp1,ndo1,2\n mn = mb+np1\n do 223 i=1,imm1\n vto(i,2*mp1-2,k) = vto(i,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(i,mn)\n vto(i,2*mp1-1,k) = vto(i,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(i,mn)\n wte(i,2*mp1-2,k) = wte(i,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(i,mn)\n wte(i,2*mp1-1,k) = wte(i,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(i,mn)\n 223 continue\n if(mlat .eq. 0) go to 224\n wte(imid,2*mp1-2,k) = wte(imid,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(imid,mn) \n wte(imid,2*mp1-1,k) = wte(imid,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(imid,mn)\n 224 continue\n 225 continue\n 226 if(mp2 .gt. ndo2) go to 230\n do 229 k=1,nt\n do 228 np1=mp2,ndo2,2\n mn = mb+np1\n do 227 i=1,imm1\n vte(i,2*mp1-2,k) = vte(i,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(i,mn)\n vte(i,2*mp1-1,k) = vte(i,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(i,mn)\n wto(i,2*mp1-2,k) = wto(i,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(i,mn)\n wto(i,2*mp1-1,k) = wto(i,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(i,mn)\n 227 continue\n if(mlat .eq. 0) go to 228\n vte(imid,2*mp1-2,k) = vte(imid,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(imid,mn) \n vte(imid,2*mp1-1,k) = vte(imid,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(imid,mn)\n 228 continue\n 229 continue\n 230 continue\n go to 950\nc\nc case ityp=3 v odd, w even \nc\nc case m = 0\nc\n 300 do 315 k=1,nt\n do 315 np1=2,ndo2,2\n do 315 i=1,imm1\n vto(i,1,k)=vto(i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n 315 continue\n do 316 k=1,nt\n do 316 np1=3,ndo1,2\n do 316 i=1,imid\n wte(i,1,k)=wte(i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 316 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 330 mp1=2,mmax\n m = mp1-1\n mb = m*(nlat-1)-(m*(m-1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 326\n do 325 k=1,nt\n do 324 np1=mp1,ndo1,2\n mn = mb+np1\n do 323 i=1,imm1\n vto(i,2*mp1-2,k) = vto(i,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(i,mn)\n vto(i,2*mp1-1,k) = vto(i,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(i,mn)\n wte(i,2*mp1-2,k) = wte(i,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(i,mn)\n wte(i,2*mp1-1,k) = wte(i,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(i,mn)\n 323 continue\n if(mlat .eq. 0) go to 324\n wte(imid,2*mp1-2,k) = wte(imid,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(imid,mn) \n wte(imid,2*mp1-1,k) = wte(imid,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(imid,mn)\n 324 continue\n 325 continue\n 326 if(mp2 .gt. ndo2) go to 330\n do 329 k=1,nt\n do 328 np1=mp2,ndo2,2\n mn = mb+np1\n do 327 i=1,imm1\n vto(i,2*mp1-2,k) = vto(i,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(i,mn)\n vto(i,2*mp1-1,k) = vto(i,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(i,mn)\n wte(i,2*mp1-2,k) = wte(i,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(i,mn)\n wte(i,2*mp1-1,k) = wte(i,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(i,mn)\n 327 continue\n if(mlat .eq. 0) go to 328\n wte(imid,2*mp1-2,k) = wte(imid,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(imid,mn)\n wte(imid,2*mp1-1,k) = wte(imid,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(imid,mn)\n 328 continue\n 329 continue\n 330 continue\n go to 950\nc\nc case ityp=4 v odd, w even, and both cr and ci equal zero \nc\nc case m = 0\nc\n 400 do 415 k=1,nt\n do 415 np1=2,ndo2,2\n do 415 i=1,imm1\n vto(i,1,k)=vto(i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n 415 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 430 mp1=2,mmax\n m = mp1-1\n mb = m*(nlat-1)-(m*(m-1))/2\n mp2 = mp1+1\n if(mp2 .gt. ndo2) go to 430\n do 429 k=1,nt\n do 428 np1=mp2,ndo2,2\n mn = mb+np1\n do 427 i=1,imm1\n vto(i,2*mp1-2,k) = vto(i,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(i,mn)\n vto(i,2*mp1-1,k) = vto(i,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(i,mn)\n wte(i,2*mp1-2,k) = wte(i,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(i,mn)\n wte(i,2*mp1-1,k) = wte(i,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(i,mn)\n 427 continue\n if(mlat .eq. 0) go to 428\n wte(imid,2*mp1-2,k) = wte(imid,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(imid,mn)\n wte(imid,2*mp1-1,k) = wte(imid,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(imid,mn)\n 428 continue\n 429 continue\n 430 continue\n go to 950\nc\nc case ityp=5 v odd, w even, br and bi equal zero \nc\nc case m = 0\nc\n 500 do 516 k=1,nt\n do 516 np1=3,ndo1,2\n do 516 i=1,imid\n wte(i,1,k)=wte(i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 516 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 530 mp1=2,mmax\n m = mp1-1\n mb = m*(nlat-1)-(m*(m-1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 530\n do 525 k=1,nt\n do 524 np1=mp1,ndo1,2\n mn = mb+np1\n do 523 i=1,imm1\n vto(i,2*mp1-2,k) = vto(i,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(i,mn)\n vto(i,2*mp1-1,k) = vto(i,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(i,mn)\n wte(i,2*mp1-2,k) = wte(i,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(i,mn)\n wte(i,2*mp1-1,k) = wte(i,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(i,mn)\n 523 continue\n if(mlat .eq. 0) go to 524\n wte(imid,2*mp1-2,k) = wte(imid,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(imid,mn) \n wte(imid,2*mp1-1,k) = wte(imid,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(imid,mn)\n 524 continue\n 525 continue\n 530 continue\n go to 950\nc\nc case ityp=6 v even , w odd\nc\nc case m = 0\nc\n 600 do 615 k=1,nt\n do 615 np1=2,ndo2,2\n do 615 i=1,imm1\n wto(i,1,k)=wto(i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 615 continue\n do 616 k=1,nt\n do 616 np1=3,ndo1,2\n do 616 i=1,imid\n vte(i,1,k)=vte(i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n 616 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 630 mp1=2,mmax\n m = mp1-1\n mb = m*(nlat-1)-(m*(m-1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 626\n do 625 k=1,nt\n do 624 np1=mp1,ndo1,2\n mn = mb+np1\n do 623 i=1,imm1\n vte(i,2*mp1-2,k) = vte(i,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(i,mn)\n vte(i,2*mp1-1,k) = vte(i,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(i,mn)\n wto(i,2*mp1-2,k) = wto(i,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(i,mn)\n wto(i,2*mp1-1,k) = wto(i,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(i,mn)\n 623 continue\n if(mlat .eq. 0) go to 624\n vte(imid,2*mp1-2,k) = vte(imid,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(imid,mn)\n vte(imid,2*mp1-1,k) = vte(imid,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(imid,mn)\n 624 continue\n 625 continue\n 626 if(mp2 .gt. ndo2) go to 630\n do 629 k=1,nt\n do 628 np1=mp2,ndo2,2\n mn = mb+np1\n do 627 i=1,imm1\n vte(i,2*mp1-2,k) = vte(i,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(i,mn)\n vte(i,2*mp1-1,k) = vte(i,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(i,mn)\n wto(i,2*mp1-2,k) = wto(i,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(i,mn)\n wto(i,2*mp1-1,k) = wto(i,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(i,mn)\n 627 continue\n if(mlat .eq. 0) go to 628\n vte(imid,2*mp1-2,k) = vte(imid,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(imid,mn) \n vte(imid,2*mp1-1,k) = vte(imid,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(imid,mn)\n 628 continue\n 629 continue\n 630 continue\n go to 950\nc\nc case ityp=7 v even, w odd cr and ci equal zero\nc\nc case m = 0\nc\n 700 do 716 k=1,nt\n do 716 np1=3,ndo1,2\n do 716 i=1,imid\n vte(i,1,k)=vte(i,1,k)+br(ncbc,1,np1,k)*vb(i,np1)\n 716 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 730 mp1=2,mmax\n m = mp1-1\n mb = m*(nlat-1)-(m*(m-1))/2\n mp2 = mp1+1\n if(mp1 .gt. ndo1) go to 730\n do 725 k=1,nt\n do 724 np1=mp1,ndo1,2\n mn = mb+np1\n do 723 i=1,imm1\n vte(i,2*mp1-2,k) = vte(i,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(i,mn)\n vte(i,2*mp1-1,k) = vte(i,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(i,mn)\n wto(i,2*mp1-2,k) = wto(i,2*mp1-2,k)\n 1 -bi(ncbc,mp1,np1,k)*wb(i,mn)\n wto(i,2*mp1-1,k) = wto(i,2*mp1-1,k)\n 1 +br(ncbc,mp1,np1,k)*wb(i,mn)\n 723 continue\n if(mlat .eq. 0) go to 724\n vte(imid,2*mp1-2,k) = vte(imid,2*mp1-2,k)\n 1 +br(ncbc,mp1,np1,k)*vb(imid,mn)\n vte(imid,2*mp1-1,k) = vte(imid,2*mp1-1,k)\n 1 +bi(ncbc,mp1,np1,k)*vb(imid,mn)\n 724 continue\n 725 continue\n 730 continue\n go to 950\nc\nc case ityp=8 v even, w odd, br and bi equal zero\nc\nc case m = 0\nc\n 800 do 815 k=1,nt\n do 815 np1=2,ndo2,2\n do 815 i=1,imm1\n wto(i,1,k)=wto(i,1,k)-cr(ncbc,1,np1,k)*vb(i,np1)\n 815 continue\nc\nc case m = 1 through nlat-1\nc\n if(mmax .lt. 2) go to 950\n do 830 mp1=2,mmax\n m = mp1-1\n mb = m*(nlat-1)-(m*(m-1))/2\n mp2 = mp1+1\n if(mp2 .gt. ndo2) go to 830\n do 829 k=1,nt\n do 828 np1=mp2,ndo2,2\n mn = mb+np1\n do 827 i=1,imm1\n vte(i,2*mp1-2,k) = vte(i,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(i,mn)\n vte(i,2*mp1-1,k) = vte(i,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(i,mn)\n wto(i,2*mp1-2,k) = wto(i,2*mp1-2,k)\n 1 -cr(ncbc,mp1,np1,k)*vb(i,mn)\n wto(i,2*mp1-1,k) = wto(i,2*mp1-1,k)\n 1 -ci(ncbc,mp1,np1,k)*vb(i,mn)\n 827 continue\n if(mlat .eq. 0) go to 828\n vte(imid,2*mp1-2,k) = vte(imid,2*mp1-2,k)\n 1 -ci(ncbc,mp1,np1,k)*wb(imid,mn) \n vte(imid,2*mp1-1,k) = vte(imid,2*mp1-1,k)\n 1 +cr(ncbc,mp1,np1,k)*wb(imid,mn)\n 828 continue\n 829 continue\n 830 continue\n 950 do 14 k=1,nt\n call hrfftb(idv,nlon,vte(1,1,k),idv,wrfft,work)\n call hrfftb(idv,nlon,wte(1,1,k),idv,wrfft,work)\n 14 continue\n if(ityp .gt. 2) go to 12\n do 60 k=1,nt\n do 60 j=1,nlon\n do 60 i=1,imm1\n vt(ncvw,i,j,k) = .5d0*(vte(i,j,k)+vto(i,j,k))\n wt(ncvw,i,j,k) = .5d0*(wte(i,j,k)+wto(i,j,k))\n vt(ncvw,nlp1-i,j,k) = .5d0*(vte(i,j,k)-vto(i,j,k))\n wt(ncvw,nlp1-i,j,k) = .5d0*(wte(i,j,k)-wto(i,j,k))\n 60 continue\n go to 13\n 12 do 11 k=1,nt\n do 11 j=1,nlon\n do 11 i=1,imm1\n vt(ncvw,i,j,k) = .5d0*vte(i,j,k)\n wt(ncvw,i,j,k) = .5d0*wte(i,j,k)\n 11 continue\n 13 if(mlat .eq. 0) return\n do 65 k=1,nt\n do 65 j=1,nlon\n vt(ncvw,imid,j,k) = .5d0*vte(imid,j,k)\n wt(ncvw,imid,j,k) = .5d0*wte(imid,j,k)\n 65 continue\n return\n end\n subroutine vtsgsi(nlat,nlon,wvts,lwvts,work,lwork,dwork,ldwork,\n + ierror)\n implicit double precision (a-h,o-z)\nc\nc define imid = (nlat+1)/2 and mmax = min0(nlat,(nlon+1)/2)\nc the length of wvts is imid*mmax*(nlat+nlat-mmax+1)+nlon+15\nc and the length of work is labc+5*nlat*imid+2*nlat where\nc labc = 3*(max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\nc\n dimension wvts(lwvts),work(lwork)\n double precision dwork(ldwork)\n ierror = 1\n if(nlat .lt. 3) return\n ierror = 2\n if(nlon .lt. 1) return\n ierror = 3\nc Fixed SpherePack error: was [ mmax = min0(nlat,nlon/2+1) ]\n mmax = min0(nlat,(nlon+1)/2)\nc\n imid = (nlat+1)/2\n lzimn = (imid*mmax*(nlat+nlat-mmax+1))/2\n if(lwvts .lt. lzimn+lzimn+nlon+15) return\n ierror = 4\n labc = 3*(max0(mmax-2,0)*(nlat+nlat-mmax-1))/2\n lvin = 3*nlat*imid\n lwvbin = 2*nlat*imid+labc\n ltheta = nlat+nlat\n if(lwork .lt. lvin+lwvbin+ltheta) return\n ierror = 5\n if (ldwork .lt. 3*nlat+2) return\n ierror = 0\n iw1 = lvin+1\n iw2 = iw1+lwvbin\n jw1 = nlat+1\n jw2 = jw1+nlat\n CALL VETG1(NLAT,NLON,IMID,WVTS,WVTS(LZIMN+1),WORK,work(IW1),\n 1 DWORK,DWORK(JW1),DWORK(JW2),IERROR)\n if(ierror .ne. 0) return\n call hrffti(nlon,wvts(2*lzimn+1))\n return\n end\n subroutine vetg1(nlat,nlon,imid,vb,wb,vin,wvbin,\n 1 theta,wts,dwork,ierror)\n implicit double precision (a-h,o-z)\n dimension vb(imid,*),wb(imid,*),vin(imid,nlat,3),wvbin(*)\n double precision dwork(*),theta(*),wts(*)\nc Fixed SpherePack error: was [ mmax = min0(nlat,nlon/2+1) ]\n mmax = min0(nlat,(nlon+1)/2)\nc\n ldwork = 1\n call gaqd(nlat,theta,wts,dwork,ldwork,ierr)\n if(ierr .eq. 0) go to 10\n ierror = 10+ierr\n return \n 10 call vtgint (nlat,nlon,theta,wvbin,dwork)\n i1=1\n i2=2\n do 33 mp1=1,mmax\n m = mp1-1\n call vbin (0,nlat,nlon,m,vin,i3,wvbin,i1,i2)\n do 33 np1=mp1,nlat\n mn = m*(nlat-1)-(m*(m-1))/2+np1\n do 33 i=1,imid\n vb(i,mn) = vin(i,np1,i3)\n 33 continue\n call wtgint (nlat,nlon,theta,wvbin,dwork)\n i1=1\n i2=2\n do 34 mp1=1,mmax\n m = mp1-1\n call wbin (0,nlat,nlon,m,vin,i3,wvbin,i1,i2)\n do 34 np1=mp1,nlat\n mn = m*(nlat-1)-(m*(m-1))/2+np1\n do 34 i=1,imid\n wb(i,mn) = vin(i,np1,i3)\n 34 continue\n return\n end\n\n\n\n\n\n\n\n" }, { "path": "external/brigand/CMakeLists.txt", "content": "# Distributed under the MIT License.\n# See LICENSE.txt for details.\n\nset(BRIGAND_INCLUDE_DIR ${CMAKE_SOURCE_DIR}/external/brigand/include)\n\nmessage(STATUS \"Brigand include: ${BRIGAND_INCLUDE_DIR}\")\n\nadd_library(Brigand INTERFACE IMPORTED GLOBAL)\ntarget_include_directories(Brigand SYSTEM INTERFACE ${BRIGAND_INCLUDE_DIR})\n\nadd_interface_lib_headers(\n TARGET Brigand\n HEADERS\n brigand/brigand.hpp\n)\n\nset_property(\n GLOBAL APPEND PROPERTY SPECTRE_THIRD_PARTY_LIBS\n Brigand\n)\n" }, { "path": "external/brigand/LICENSE", "content": "Boost Software License - Version 1.0 - August 17th, 2003\n\nPermission is hereby granted, free of charge, to any person or organization\nobtaining a copy of the software and accompanying documentation covered by\nthis license (the \"Software\") to use, reproduce, display, distribute,\nexecute, and transmit the Software, and to prepare derivative works of the\nSoftware, and to permit third-parties to whom the Software is furnished to\ndo so, all subject to the following:\n\nThe copyright notices in the Software and this entire statement, including\nthe above license grant, this restriction and the following disclaimer,\nmust be included in all copies of the Software, in whole or in part, and\nall derivative works of the Software, unless such copies or derivative\nworks are solely in the form of machine-executable object code generated by\na source language processor.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT\nSHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE\nFOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,\nARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\nDEALINGS IN THE SOFTWARE.\n\n" }, { "path": "external/brigand/README.md", "content": "Brigand Meta-programming library\n================================\n\n![A brigand](https://raw.githubusercontent.com/wiki/edouarda/brigand/brigand_small.jpg)\n\n[![Build Status](https://travis-ci.org/edouarda/brigand.svg?branch=master)](https://travis-ci.org/edouarda/brigand)\n\n[![Build Status](https://ci.appveyor.com/api/projects/status/github/edouarda/brigand)](https://ci.appveyor.com/project/edouarda/brigand)\n\n# Introduction\n\nBrigand is a light-weight, fully functional, instant-compile time C++ 11 meta-programming library.\n\nEverything you were doing with Boost.MPL can be done with Brigand. And if that's not the case, open an issue!\n\n# Learning\n\nShould you wish to learn more, feel free to [watch our Meeting C++ 2015 lightning talk](https://www.youtube.com/watch?v=B8XSDhWx7hY)!\n\nWant more? Our [CppCon 2016 presentation](https://www.youtube.com/watch?v=ky0JdPh_LgE) explains in details the library concepts and goes through two concrete usages.\n\nIf you are looking to learn the concepts of metaprogramming, [have a look at our free e-book](http://www.oreilly.com/programming/free/practical-c-plus-plus-metaprogramming.csp).\n\n# Tutorials\n\n * [Introduction](https://github.com/edouarda/brigand/wiki/Introduction)\n * [Algorithms](https://github.com/edouarda/brigand/wiki/Algorithms)\n * [Runtime](https://github.com/edouarda/brigand/wiki/Runtime)\n\n# Documentation\n\nThe documentation is available [here](https://github.com/edouarda/brigand/wiki).\n\n# Contributors\n\nWe'd like to thank the following contributors, in alphabetical order\n\n * Odin Holmes\n * Marek Kurdej\n * Jonathan Poelen\n\n\n# Note:\nThe copy in this directory is based on upstream hash\n9a86130c87479a38659edd7c0dda776a27f7077d.\n" }, { "path": "external/brigand/include/brigand/brigand.hpp", "content": "/*!\n@file\n@copyright Edouard Alligand and Joel Falcou 2015-2017\n(See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)\n\nEdits by SXS:\n- count_if, filter, and remove_if have an explicit empty base-case for nvcc\n support.\n*/\n#ifndef BRIGAND_HPP_INCLUDED\n#define BRIGAND_HPP_INCLUDED\nnamespace brigand\n{\ntemplate \nstruct integral_constant\n{\n static const T value = Value;\n using value_type = T;\n using type = integral_constant;\n operator value_type() const { return (value); }\n value_type operator()() const { return (value); }\n};\ntemplate \nconst T integral_constant::value;\nusing true_type = ::brigand::integral_constant;\nusing false_type = ::brigand::integral_constant;\n}\nnamespace brigand\n{\ntemplate \nstruct list\n{\n};\ntemplate \nusing integral_list = brigand::list...>;\nusing empty_sequence = brigand::list<>;\n}\nnamespace brigand\n{\nnamespace detail\n{\n template \n struct dup_append_list;\n template