[ { "path": ".codecov.yml", "content": "ignore:\n - '*/tests/*'\n" }, { "path": ".coveragerc", "content": "# this file controls the execution of coverage.py\n[run]\nomit=\n ./tests/*\n ./docs/*\n ./dev/*\n ./scripts/*\n\n[report]\n# Regexes for lines to exclude from consideration\nexclude_lines =\n # Have to re-enable the standard pragma\n pragma: no cover\n\n # Don't complain about missing debug-only code:\n def __repr__\n if self\\.debug\n\n # Don't complain if tests don't hit defensive assertion code:\n raise AssertionError\n raise NotImplementedError\n\n # Don't complain if non-runnable code isn't run:\n if 0:\n if __name__ == .__main__.:\n" }, { "path": ".github/ISSUE_TEMPLATE/bug_report.md", "content": "---\nname: Bug report\nabout: Create a report to help us improve\ntitle: ''\nlabels: potential bug\nassignees: ''\n\n---\n\n**Describe the bug**\nA clear and concise description of what the bug is.\n\n**To Reproduce**\nSteps to reproduce the behaviour.\n\nIf model related, please try and reproduce with one of the provided models (found in `/cases/`). Else, please provided the input files (a `.fem.h5`, `aero.h5` and `case.sharpy`).\n\n**Expected behavior**\nA clear and concise description of what you expected to happen.\n\n**Screenshots**\nIf applicable, add screenshots to help explain your problem.\n\n**System Info (please complete the following information):**\n - OS: [e.g. CentOS7/MacOS 13.1]\n - SHARPy Version [e.g. v1.2]\n\n**Additional context**\nAdd any other context about the problem here.\n" }, { "path": ".github/workflows/docker_build.yaml", "content": "name: Create and publish Docker image\n\non:\n push:\n branches: \n - develop\n - main\n tags:\n - 'v*'\n\nenv:\n REGISTRY: ghcr.io\n IMAGE_NAME: ${{ github.repository }}\n\njobs:\n build-and-push-image:\n runs-on: ubuntu-latest\n permissions:\n contents: read\n packages: write\n\n steps:\n - name: Checkout repository\n uses: actions/checkout@v3\n\n - name: Log in to the Container registry\n uses: docker/login-action@v2\n with:\n registry: ${{ env.REGISTRY }}\n username: ${{ github.actor }}\n password: ${{ secrets.GITHUB_TOKEN }}\n\n - name: Extract metadata (tags, labels) for Docker\n id: meta\n uses: docker/metadata-action@v4\n with:\n images: ${{ env.REGISTRY }}/${{ env.IMAGE_NAME }}\n\n - name: Build and push Docker image\n uses: docker/build-push-action@v3.2.0\n with:\n context: .\n push: true\n tags: ${{ steps.meta.outputs.tags }}\n labels: ${{ steps.meta.outputs.labels }}\n" }, { "path": ".github/workflows/docker_build_test.yaml", "content": "name: Test Docker image build\n\non:\n pull_request:\n branches:\n - main\n - develop\n - 'rc*'\n push:\n paths:\n - 'utils/*'\n - 'Dockerfile'\n - '.github/workflows/docker*'\n\nenv:\n REGISTRY: ghcr.io\n IMAGE_NAME: ${{ github.repository }}\n\njobs:\n test_image_build:\n runs-on: ubuntu-latest\n name: Test Docker image build\n permissions:\n contents: read\n packages: write\n steps:\n - name: Checkout repository\n uses: actions/checkout@v3\n\n - name: Log in to the Container registry\n uses: docker/login-action@v2\n with:\n registry: ${{ env.REGISTRY }}\n username: ${{ github.actor }}\n password: ${{ secrets.GITHUB_TOKEN }}\n\n - name: Extract metadata (tags, labels) for Docker\n id: meta\n uses: docker/metadata-action@v4\n with:\n images: ${{ env.REGISTRY }}/${{ env.IMAGE_NAME }}\n\n - name: Build Docker image\n uses: docker/build-push-action@v3.2.0\n with:\n context: .\n push: false\n tags: ${{ steps.meta.outputs.tags }}\n labels: ${{ steps.meta.outputs.labels }}\n" }, { "path": ".github/workflows/pypi_build.yaml", "content": "name: Create and publish pypi image\n\non:\n # only runs when there is a new published release\n # and for testing, pull requests to develop and main\n # and if there are changes to the build process and github action\n release:\n types: [published] \n push:\n branches: \n - develop\n - main\n paths:\n - 'setup.py'\n - '.github/workflows/pypi*' \n pull_request:\n branches:\n - main\n - develop\n - 'rc*'\n\njobs:\n create-pypi-image:\n name: >-\n Create .whl 🛞 from SHARPy distribution\n runs-on: ubuntu-20.04\n env:\n python-version-chosen: \"3.10.8\"\n permissions:\n contents: read\n packages: write\n\n steps:\n - uses: actions/checkout@v2\n - name: Set up Python ${{ env.python-version-chosen }}\n uses: actions/setup-python@v2\n with:\n python-version: ${{ env.python-version-chosen }}\n - name: Set up GCC\n uses: egor-tensin/setup-gcc@v1\n with:\n version: 7\n platform: x64\n - name: Pre-Install dependencies\n run: |\n export QT_QPA_PLATFORM='offscreen'\n sudo apt install libeigen3-dev\n git submodule init\n git submodule update\n - name: Install pypa/build\n run: >-\n python3 -m\n pip install\n build\n --user \n - name: Install wheel\n run: python3 -m pip install wheel --user\n - name: Build a source tarball\n run: python setup.py sdist\n - name: Build a binary wheel\n run: python3 setup.py bdist_wheel \n - name: Find the wheel created during pip install\n run: \n python3 -m pip cache dir\n - name: Store the distribution packages\n uses: actions/upload-artifact@v4\n with:\n name: python-package-distributions\n path: dist/\n\n publish-to-pypi:\n name: >-\n Publish Python 🐍 distribution 📦 to PyPI\n if: github.event_name == 'release' && github.event.release.action == 'published' # only publish to PyPI on tag pushes\n needs:\n - create-pypi-image\n runs-on: ubuntu-latest\n environment:\n name: pypi\n url: https://pypi.org/p/ic_sharpy # Replace with your PyPI project name\n permissions:\n id-token: write # IMPORTANT: mandatory for trusted publishing\n steps:\n - name: Download all the dists\n uses: actions/download-artifact@v4\n with:\n name: python-package-distributions\n path: dist/\n - name: Publish distribution 📦 to PyPI\n uses: pypa/gh-action-pypi-publish@release/v1\n # with:\n # path: dist/*\n" }, { "path": ".github/workflows/readme.md", "content": "# SHARPy GitHub Workflows\r\n\r\nThere are 4(+1 experimental) automated workflows for SHARPy's CI/CD.\r\n\r\n## SHARPy Tests\r\n\r\nThe related to the SHARPy tests that run the `SHARPy Tests` job are:\r\n\r\n * `sharpy_tests.yaml`: when Python or the submodules files are edited\r\n * `sharpy_no_test_needed.yaml`: otherwise\r\n\r\nThis avoids running the full set of tests for changes in the documentation etc.\r\nSince the merge to `develop` and `main` is protected by the tests passing, the \r\nsecond workflow ensures a positive result for those PRs that did not change the \r\nPython code, hence allowing the merge.\r\n\r\n## Docker\r\n\r\nTwo nearly identical workflows, the only difference is that one pushes the Docker \r\nimage to the SHARPy packages. Therefore:\r\n\r\n * `docker_build_test.yaml`: Builds the Docker image but does not push. Runs on changes to the `docker*` workflows, changes to the `utils/` directory (environments) and changes to the `Dockerfile`. Required test for PRs to merge to `develop` and `main`.\r\n * `docker_build.yaml`: Builds and pushes the Docker image. Runs on pushes to `develop`, `main` and annotated tags.\r\n\r\n## Pypi (experimental!)\r\n\r\nOne workflow with two jobs, the first creates and the second pushes the wheel \r\nartifact to ic-sharpy @ pypi. Therefore:\r\n\r\n * `pypi_build.yaml`: Builds and pushes the pypi wheel according to conditions. Runs on changes to the `pypi*` workflow, changes to the `setup.py`, and PRs and pushes to main and develop. Required test for PRs to merge to `develop` and `main`. Publishes on annotated tags. \r\n" }, { "path": ".github/workflows/sharpy_no_test_needed.yaml", "content": "name: SHARPy Tests\n\non:\n pull_request:\n branches:\n - main\n - develop\n - 'rc*'\n paths-ignore:\n - '*.py'\n - 'lib/**'\n - '.github/workflows/**'\n\njobs:\n build:\n runs-on: ubuntu-latest\n steps:\n - run: 'echo \"No changes to python files, submodules or workflows, no run required\" '\n" }, { "path": ".github/workflows/sharpy_tests.yaml", "content": "name: SHARPy Tests\n\non:\n push:\n paths:\n - '*.py'\n - 'lib/*'\n - '.github/workflows/sharpy*'\n pull_request:\n branches:\n - main\n - develop\n - 'rc*'\n\njobs:\n build:\n\n runs-on: ubuntu-latest\n strategy:\n matrix:\n python-version: [3.10.8]\n\n steps:\n - uses: actions/checkout@v4\n with:\n submodules: \"recursive\"\n fetch-tags: true\n - name: Set up Python ${{ matrix.python-version }}\n uses: actions/setup-python@v5\n with:\n python-version: ${{ matrix.python-version }}\n - name: Set up GCC\n uses: egor-tensin/setup-gcc@v1\n with:\n version: 10\n platform: x64\n - name: Check that gfortran works\n run: gfortran --version\n - name: Install build package dependencies\n run: sudo apt install libblas-dev liblapack-dev libeigen3-dev\n - name: Install sharpy and coverage using pip\n run: |\n export QT_QPA_PLATFORM='offscreen'\n pip install .\n pip install coverage\n - name: Run coverage\n run: |\n coverage run -m unittest discover\n coverage json\n - name: Upload Coverage to Codecov\n uses: codecov/codecov-action@v3\n with:\n verbose: true\n" }, { "path": ".github_changelog_generator", "content": "since-tag=1.0.0" }, { "path": ".gitignore", "content": "# Byte-compiled / optimized / DLL files\n__pycache__/\n*.py[cod]\n*$py.class\n\n# C extensions\n*.so\n\n# Distribution / packaging\n.Python\nenv/\nbuild/\ndevelop-eggs/\ndist/\ndownloads/\neggs/\n.eggs/\nparts/\nsdist/\nvar/\n*.egg-info/\n.installed.cfg\n*.egg\n\n# PyInstaller\n# Usually these files are written by a python script from a template\n# before PyInstaller builds the exe, so as to inject date/other infos into it.\n*.manifest\n*.spec\n\n# Installer logs\npip-log.txt\npip-delete-this-directory.txt\n\n# Unit test / coverage reports\nhtmlcov/\n.tox/\n.coverage\n.coverage.*\n.cache\nnosetests.xml\ncoverage.xml\n*.cover\n.hypothesis/\n\n# Translations\n*.mo\n*.pot\n\n# Django stuff:\n*.log\nlocal_settings.py\n\n# Flask stuff:\ninstance/\n.webassets-cache\n\n# Scrapy stuff:\n.scrapy\n\n# Sphinx documentation\ndocs/_build/\n\n# PyBuilder\ntarget/\n\n# IPython Notebook\n.ipynb_checkpoints\n\n# pyenv\n.python-version\n\n# celery beat schedule file\ncelerybeat-schedule\n\n# dotenv\n.env\n\n# virtualenv\nvenv/\nENV/\n\n# Spyder project settings\n.spyderproject\n\n# Rope project settings\n.ropeproject\n\n# Vim stuff\n*.*~\n*.swp\n*.h5\n\n# project dependent stuff\nlib/*.so\noutput/*\n.idea\n\n# figure folders\n*figs/*\n\n*.eps\n*.vtu\n\n\noutput*/\n\nsnapshots/\n\n# OSX files\n*.DS_Store\n\n# linear tools / tests cases\n*.prof\nfigs/*\n\n\\.spyproject/\n\n# sharpy extension\n*.sharpy\n\n# Exceptions\n# !tests/coupled/multibody/floating_wind_turbine/oc3_cs_v07.floating.h5 \n!tests/coupled/multibody/floating_wind_turbine/oc3_cs_v07.floating.h*\n" }, { "path": ".gitmodules", "content": "[submodule \"lib/UVLM\"]\n\tpath = lib/UVLM\n\turl = http://github.com/imperialcollegelondon/UVLM\n[submodule \"lib/xbeam\"]\n\tpath = lib/xbeam\n\turl = http://github.com/imperialcollegelondon/xbeam\n" }, { "path": ".readthedocs.yaml", "content": "# .readthedocs.yaml\n# Read the Docs configuration file\n# See https://docs.readthedocs.io/en/stable/config-file/v2.html for details\n\n# Required\nversion: 2\n\n# Set the version of Python and other tools you might need\nbuild:\n os: ubuntu-22.04\n tools:\n python: \"3.10\"\n\npython:\n install:\n - requirements: docs/requirements_rtd\n\n# Build documentation in the docs/ directory with Sphinx\nsphinx:\n configuration: docs/source/conf.py\n\n# We recommend specifying your dependencies to enable reproducible builds:\n# https://docs.readthedocs.io/en/stable/guides/reproducible-builds.html\n# python:\n# install:\n# - requirements: docs/requirements.txt\n" }, { "path": ".version.json", "content": "{\n \"schemaVersion\": 1,\n \"label\": \"release version\",\n \"message\": \"2.4\",\n \"color\": \"green\"\n}\n" }, { "path": ".zenodo.json", "content": "{\n \"license\": \"other-open\", \n \"title\": \"SHARPy: A dynamic aeroelastic simulation toolbox for very flexible aircraft and wind turbines\", \n \"upload_type\": \"software\", \n \"creators\": [\n {\n \"orcid\": \"0000-0002-8133-9481\", \n \"affiliation\": \"Imperial College London\", \n \"name\": \"Alfonso del Carre\"\n },\n {\n \"orcid\": \"0000-0001-7445-5970\",\n \"affiliation\": \"Imperial College London\",\n \"name\": \"Norberto Goizueta\"\n },\n {\n \"orcid\": \"0000-0003-4840-5392\", \n \"affiliation\": \"Imperial College London\", \n \"name\": \"Arturo Mu\\u00f1oz-Sim\\u00f3n\"\n }, \n {\n \"orcid\": \"0000-0002-6706-3220\", \n \"affiliation\": \"Imperial College London\",\n \"name\": \"Rafael Palacios\"\n }\n ], \n \"access_right\": \"open\"\n}\n" }, { "path": "CHANGELOG.md", "content": "# Changelog\n\n## [2.4](https://github.com/imperialcollegelondon/sharpy/tree/2.4) (2025-03-20)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/2.3...2.4)\n\n**Implemented enhancements:**\n\n- Add the automatic differentiation multibody solver based on JAX [\\#305](https://github.com/ImperialCollegeLondon/sharpy/pull/305) ([ben-l-p](https://github.com/ben-l-p))\n- Non-perpendicular hinge axis possible for multibody solver [\\#299](https://github.com/ImperialCollegeLondon/sharpy/pull/299) ([kccwing](https://github.com/kccwing))\n- Add hosting of built wheel at PyPI - develop [\\#298](https://github.com/ImperialCollegeLondon/sharpy/pull/298) ([kccwing](https://github.com/kccwing))\n- Add hosting of built wheel at PyPI - main [\\#297](https://github.com/ImperialCollegeLondon/sharpy/pull/297) ([kccwing](https://github.com/kccwing))\n\n**Fixed bugs:**\n\n- Updated docs to address issue with conda install failing [\\#290](https://github.com/ImperialCollegeLondon/sharpy/pull/290) ([ben-l-p](https://github.com/ben-l-p))\n\n**Closed issues:**\n\n- TypeError: unhashable type: 'UnstructuredGrid' [\\#313](https://github.com/ImperialCollegeLondon/sharpy/issues/313)\n- Creating aileron control surfaces to induce roll [\\#304](https://github.com/ImperialCollegeLondon/sharpy/issues/304)\n- Static Trim Routine Fails with Dynamic-Type Control Surfaces [\\#300](https://github.com/ImperialCollegeLondon/sharpy/issues/300)\n- Not a Git Repository [\\#295](https://github.com/ImperialCollegeLondon/sharpy/issues/295)\n\n**Merged pull requests:**\n\n- Merge develop into main for new version release [\\#318](https://github.com/ImperialCollegeLondon/sharpy/pull/318) ([ben-l-p](https://github.com/ben-l-p))\n- Xhale thrust node typo [\\#317](https://github.com/ImperialCollegeLondon/sharpy/pull/317) ([kccwing](https://github.com/kccwing))\n- Mayavi github dependency restored for hotfix - develop [\\#316](https://github.com/ImperialCollegeLondon/sharpy/pull/316) ([kccwing](https://github.com/kccwing))\n- Mayavi github dependency restored for hotfix [\\#311](https://github.com/ImperialCollegeLondon/sharpy/pull/311) ([kccwing](https://github.com/kccwing))\n- Update body and wake FoR multiplication [\\#309](https://github.com/ImperialCollegeLondon/sharpy/pull/309) ([kccwing](https://github.com/kccwing))\n- Bug fix for generate\\_full\\_structure [\\#306](https://github.com/ImperialCollegeLondon/sharpy/pull/306) ([kccwing](https://github.com/kccwing))\n- Fix AeroForcesCalculator giving forces in wrong frame of reference [\\#301](https://github.com/ImperialCollegeLondon/sharpy/pull/301) ([ben-l-p](https://github.com/ben-l-p))\n- Temporary Fix for NumPy 2.0 Issues \\(Develop Branch\\) [\\#293](https://github.com/ImperialCollegeLondon/sharpy/pull/293) ([ben-l-p](https://github.com/ben-l-p))\n- Temporary Fix for NumPy 2.0 Issues \\(Main Branch\\) [\\#292](https://github.com/ImperialCollegeLondon/sharpy/pull/292) ([ben-l-p](https://github.com/ben-l-p))\n\n\n## [2.3](https://github.com/imperialcollegelondon/sharpy/tree/2.3) (2024-05-10)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/2.2...2.3)\n\n**Implemented enhancements:**\n\n- Version 2.3 update [\\#289](https://github.com/ImperialCollegeLondon/sharpy/pull/289) ([ben-l-p](https://github.com/ben-l-p))\n- Update develop branch with main [\\#284](https://github.com/ImperialCollegeLondon/sharpy/pull/284) ([ben-l-p](https://github.com/ben-l-p))\n- Added pip install \\(with docs\\) [\\#280](https://github.com/ImperialCollegeLondon/sharpy/pull/280) ([ben-l-p](https://github.com/ben-l-p))\n- Update beamplot.py to have stride option, consistent with aerogridplot.py [\\#279](https://github.com/ImperialCollegeLondon/sharpy/pull/279) ([kccwing](https://github.com/kccwing))\n\n**Fixed bugs:**\n\n- Fix Github Runner Docker build failing [\\#285](https://github.com/ImperialCollegeLondon/sharpy/pull/285) ([ben-l-p](https://github.com/ben-l-p))\n- Add scipy version info to env yml [\\#277](https://github.com/ImperialCollegeLondon/sharpy/pull/277) ([SJ-Innovation](https://github.com/SJ-Innovation))\n\n**Closed issues:**\n\n- Scipy 1.12.0 Incompatible [\\#276](https://github.com/ImperialCollegeLondon/sharpy/issues/276)\n- BeamLoader postprocessor squishing answers [\\#270](https://github.com/ImperialCollegeLondon/sharpy/issues/270)\n- Solving Environment gets killed. [\\#268](https://github.com/ImperialCollegeLondon/sharpy/issues/268)\n- Error when running sharpy unittest: module scipy.sparse.\\_sputils not found [\\#227](https://github.com/ImperialCollegeLondon/sharpy/issues/227)\n- Potential bug in /sharpy/structure/utils/modalutils.py [\\#208](https://github.com/ImperialCollegeLondon/sharpy/issues/208)\n\n**Merged pull requests:**\n\n- Added ability to turn aligned grid off [\\#288](https://github.com/ImperialCollegeLondon/sharpy/pull/288) ([ben-l-p](https://github.com/ben-l-p))\n- Update with main for mamba fixes [\\#286](https://github.com/ImperialCollegeLondon/sharpy/pull/286) ([ben-l-p](https://github.com/ben-l-p))\n- Correct typos caught by Divya Sanghi [\\#283](https://github.com/ImperialCollegeLondon/sharpy/pull/283) ([bbahiam](https://github.com/bbahiam))\n- Develop: Update environment.yml to fix scipy version issue [\\#282](https://github.com/ImperialCollegeLondon/sharpy/pull/282) ([kccwing](https://github.com/kccwing))\n- Update noaero.py for consistency in function input [\\#275](https://github.com/ImperialCollegeLondon/sharpy/pull/275) ([kccwing](https://github.com/kccwing))\n- A few minor bug fixes [\\#273](https://github.com/ImperialCollegeLondon/sharpy/pull/273) ([sduess](https://github.com/sduess))\n- Update XBeam version to include compiler optimisation [\\#272](https://github.com/ImperialCollegeLondon/sharpy/pull/272) ([ben-l-p](https://github.com/ben-l-p))\n- Update XBeam version to include compiler optimisation [\\#271](https://github.com/ImperialCollegeLondon/sharpy/pull/271) ([ben-l-p](https://github.com/ben-l-p))\n- Improve docs and code of newmark\\_ss [\\#267](https://github.com/ImperialCollegeLondon/sharpy/pull/267) ([bbahiam](https://github.com/bbahiam))\n- Changed Github runner from Conda to Mamba [\\#266](https://github.com/ImperialCollegeLondon/sharpy/pull/266) ([ben-l-p](https://github.com/ben-l-p))\n- Changed Github runner from Conda to Mamba [\\#265](https://github.com/ImperialCollegeLondon/sharpy/pull/265) ([ben-l-p](https://github.com/ben-l-p))\n- Hotfix for documentation search [\\#264](https://github.com/ImperialCollegeLondon/sharpy/pull/264) ([kccwing](https://github.com/kccwing))\n- Hotfix for documentation - develop [\\#263](https://github.com/ImperialCollegeLondon/sharpy/pull/263) ([kccwing](https://github.com/kccwing))\n- Hotfix for documentation - main [\\#262](https://github.com/ImperialCollegeLondon/sharpy/pull/262) ([kccwing](https://github.com/kccwing))\n- Merging v2.2 into develop [\\#261](https://github.com/ImperialCollegeLondon/sharpy/pull/261) ([kccwing](https://github.com/kccwing))\n\n\n## [2.2](https://github.com/imperialcollegelondon/sharpy/tree/2.2) (2023-10-18)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/2.1...2.2)\n\n**Implemented enhancements:**\n\n- Added environment for Apple Silicon \\(ARM64\\) [\\#254](https://github.com/ImperialCollegeLondon/sharpy/pull/254) ([ben-l-p](https://github.com/ben-l-p))\n- New Fuselage Model plus Minor Improvements [\\#249](https://github.com/ImperialCollegeLondon/sharpy/pull/249) ([sduess](https://github.com/sduess))\n\n**Fixed bugs:**\n\n- fix polars concatenation in assembly of aeroinformation - develop [\\#253](https://github.com/ImperialCollegeLondon/sharpy/pull/253) ([kccwing](https://github.com/kccwing))\n- fix polars concatenation in assembly of aeroinformation - main [\\#252](https://github.com/ImperialCollegeLondon/sharpy/pull/252) ([kccwing](https://github.com/kccwing))\n- Minor bug fixes in aero util functions and save data postprocessor [\\#247](https://github.com/ImperialCollegeLondon/sharpy/pull/247) ([sduess](https://github.com/sduess))\n\n**Closed issues:**\n\n- Automated tests failed : UnicodeEncodeError: 'ascii' codec can't encode character '\\xe9' in position 47: ordinal not in range\\(128\\) [\\#245](https://github.com/ImperialCollegeLondon/sharpy/issues/245)\n- Wrong key in settings for /cases/templates/flying\\_wings.py [\\#205](https://github.com/ImperialCollegeLondon/sharpy/issues/205)\n\n**Merged pull requests:**\n\n- merging develop into main for v2.2 [\\#259](https://github.com/ImperialCollegeLondon/sharpy/pull/259) ([kccwing](https://github.com/kccwing))\n- fix \\[docker\\] use correct environment name in docker bashrc [\\#257](https://github.com/ImperialCollegeLondon/sharpy/pull/257) ([sduess](https://github.com/sduess))\n- Update docker environment [\\#255](https://github.com/ImperialCollegeLondon/sharpy/pull/255) ([sduess](https://github.com/sduess))\n- Update README.md [\\#246](https://github.com/ImperialCollegeLondon/sharpy/pull/246) ([rafapalacios](https://github.com/rafapalacios))\n- bringing commits to main into develop [\\#244](https://github.com/ImperialCollegeLondon/sharpy/pull/244) ([rafapalacios](https://github.com/rafapalacios))\n- Updates to plotutils.py and the cantilever\\_wing demo [\\#242](https://github.com/ImperialCollegeLondon/sharpy/pull/242) ([boltyboi](https://github.com/boltyboi))\n- Small additions to the installation guide. [\\#241](https://github.com/ImperialCollegeLondon/sharpy/pull/241) ([boltyboi](https://github.com/boltyboi))\n- Tutorial for closed-Loop Simulation with SHARPy as a hardware-in-the-loop system [\\#240](https://github.com/ImperialCollegeLondon/sharpy/pull/240) ([sduess](https://github.com/sduess))\n\n## [2.1](https://github.com/imperialcollegelondon/sharpy/tree/2.1) (2023-05-31)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/2.0...2.1)\n\n**Implemented enhancements:**\n\n- SHARPy Docker now releases to GitHub Packages [\\#218](https://github.com/ImperialCollegeLondon/sharpy/pull/218) ([ngoiz](https://github.com/ngoiz))\n- Some Enhancements and Fixes for the Polar Correction, Wake Discretisation, and Gust Velocity Field Generator [\\#217](https://github.com/ImperialCollegeLondon/sharpy/pull/217) ([sduess](https://github.com/sduess))\n- Collective blade pitch PID control of wind turbines [\\#176](https://github.com/ImperialCollegeLondon/sharpy/pull/176) ([ArturoMS13](https://github.com/ArturoMS13))\n\n**Fixed bugs:**\n\n- Handle absolute tolerance for structural convergence tests as input settings and increase default value [\\#221](https://github.com/ImperialCollegeLondon/sharpy/pull/221) ([sduess](https://github.com/sduess))\n- Fix horseshoe wake handling in UVLM [\\#204](https://github.com/ImperialCollegeLondon/sharpy/pull/204) ([sduess](https://github.com/sduess))\n\n**Closed issues:**\n\n- No such file or directory during: source bin/sharpy\\_vars.sh [\\#233](https://github.com/ImperialCollegeLondon/sharpy/issues/233)\n- Twist direction inconsistent [\\#212](https://github.com/ImperialCollegeLondon/sharpy/issues/212)\n\n**Merged pull requests:**\n\n- Version number updates for 2.1 from develop [\\#237](https://github.com/ImperialCollegeLondon/sharpy/pull/237) ([kccwing](https://github.com/kccwing))\n- Merge to main for version 2.0.1 release [\\#236](https://github.com/ImperialCollegeLondon/sharpy/pull/236) ([kccwing](https://github.com/kccwing))\n- Updates to Goland wing example [\\#234](https://github.com/ImperialCollegeLondon/sharpy/pull/234) ([rafapalacios](https://github.com/rafapalacios))\n- A bit of clean-up of the readme file of the repo [\\#231](https://github.com/ImperialCollegeLondon/sharpy/pull/231) ([rafapalacios](https://github.com/rafapalacios))\n- Dev internals [\\#223](https://github.com/ImperialCollegeLondon/sharpy/pull/223) ([ACea15](https://github.com/ACea15))\n- updating from python 3.7 to 3.10 [\\#222](https://github.com/ImperialCollegeLondon/sharpy/pull/222) ([kccwing](https://github.com/kccwing))\n- Fix typo in setting [\\#206](https://github.com/ImperialCollegeLondon/sharpy/pull/206) ([sduess](https://github.com/sduess))\n\n## [2.0](https://github.com/imperialcollegelondon/sharpy/tree/2.0) (2022-07-04)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/1.3...2.0)\n\n**Implemented enhancements:**\n\n- Plot the aeroelastic mode shape to Paraview [\\#202](https://github.com/ImperialCollegeLondon/sharpy/pull/202) ([ngoiz](https://github.com/ngoiz))\n- Enhanced linear solver [\\#196](https://github.com/ImperialCollegeLondon/sharpy/pull/196) ([ngoiz](https://github.com/ngoiz))\n- Add pip support [\\#175](https://github.com/ImperialCollegeLondon/sharpy/pull/175) ([DavidAnderegg](https://github.com/DavidAnderegg))\n\n**Fixed bugs:**\n\n- Flap inputs in state-space model not working in certain wing configurations [\\#192](https://github.com/ImperialCollegeLondon/sharpy/issues/192)\n- Fix mass matrix generation for lumped masses in case of several masses per node [\\#194](https://github.com/ImperialCollegeLondon/sharpy/pull/194) ([sduess](https://github.com/sduess))\n- Fix the sparse matrix in balancing ROM [\\#186](https://github.com/ImperialCollegeLondon/sharpy/pull/186) ([AntonioWR](https://github.com/AntonioWR))\n\n**Closed issues:**\n\n- scipy used for direct balancing method [\\#184](https://github.com/ImperialCollegeLondon/sharpy/issues/184)\n- Potential Issue in the balancing direct method [\\#183](https://github.com/ImperialCollegeLondon/sharpy/issues/183)\n- Why no pip support? [\\#171](https://github.com/ImperialCollegeLondon/sharpy/issues/171)\n\n**Merged pull requests:**\n\n- Contain write operations within with statements [\\#195](https://github.com/ImperialCollegeLondon/sharpy/pull/195) ([ngoiz](https://github.com/ngoiz))\n- Support loading/saving state-spaces and gains to h5 files [\\#188](https://github.com/ImperialCollegeLondon/sharpy/pull/188) ([ngoiz](https://github.com/ngoiz))\n- Update installation docs [\\#187](https://github.com/ImperialCollegeLondon/sharpy/pull/187) ([nacho-carnicero](https://github.com/nacho-carnicero))\n- Unittest for nonlinear dynamic solver [\\#185](https://github.com/ImperialCollegeLondon/sharpy/pull/185) ([sduess](https://github.com/sduess))\n- Change in the io-Settings to add thrust. [\\#164](https://github.com/ImperialCollegeLondon/sharpy/pull/164) ([Eriklyy](https://github.com/Eriklyy))\n- UDP-Inout change for multiply cs\\_surface\\_deflections and loads/strain [\\#162](https://github.com/ImperialCollegeLondon/sharpy/pull/162) ([Eriklyy](https://github.com/Eriklyy))\n- Update AsymptoticStability and FrequencyResponse post-processors [\\#103](https://github.com/ImperialCollegeLondon/sharpy/pull/103) ([ngoiz](https://github.com/ngoiz))\n\n## [1.3](https://github.com/imperialcollegelondon/sharpy/tree/1.3) (2021-11-11)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/v1.2.1...1.3)\n\n**Implemented enhancements:**\n\n- Include gravity direction as input for structural solvers [\\#112](https://github.com/ImperialCollegeLondon/sharpy/issues/112)\n- Simulation settings check - Unrecognised settings raise Error [\\#148](https://github.com/ImperialCollegeLondon/sharpy/pull/148) ([ngoiz](https://github.com/ngoiz))\n- Aerodynamic forces correction enhancements [\\#140](https://github.com/ImperialCollegeLondon/sharpy/pull/140) ([ngoiz](https://github.com/ngoiz))\n- New feature: apply external forces to the system at runtime [\\#125](https://github.com/ImperialCollegeLondon/sharpy/pull/125) ([ArturoMS13](https://github.com/ArturoMS13))\n- Lift distribution post-processor [\\#121](https://github.com/ImperialCollegeLondon/sharpy/pull/121) ([sduess](https://github.com/sduess))\n\n**Fixed bugs:**\n\n- Fix bug in computing total moments in A frame [\\#177](https://github.com/ImperialCollegeLondon/sharpy/pull/177) ([ngoiz](https://github.com/ngoiz))\n\n**Closed issues:**\n\n- Unrecognised model in goland test case [\\#143](https://github.com/ImperialCollegeLondon/sharpy/issues/143)\n\n**Merged pull requests:**\n\n- Implement GitHub Actions as testing suite provider [\\#179](https://github.com/ImperialCollegeLondon/sharpy/pull/179) ([ngoiz](https://github.com/ngoiz))\n- Update submodules and conda environments [\\#161](https://github.com/ImperialCollegeLondon/sharpy/pull/161) ([sduess](https://github.com/sduess))\n- Support element variables in UDP output [\\#160](https://github.com/ImperialCollegeLondon/sharpy/pull/160) ([ngoiz](https://github.com/ngoiz))\n- Output directory in the location specified in settings\\[SHARPy\\]\\[log\\_folder\\] [\\#130](https://github.com/ImperialCollegeLondon/sharpy/pull/130) ([ngoiz](https://github.com/ngoiz))\n- Update and include features in multibody [\\#126](https://github.com/ImperialCollegeLondon/sharpy/pull/126) ([ArturoMS13](https://github.com/ArturoMS13))\n- Update linear UVLM to account for CFL not equal to one in the wake convection [\\#124](https://github.com/ImperialCollegeLondon/sharpy/pull/124) ([ArturoMS13](https://github.com/ArturoMS13))\n- Minor changes [\\#123](https://github.com/ImperialCollegeLondon/sharpy/pull/123) ([ArturoMS13](https://github.com/ArturoMS13))\n\n## [v1.2.1](https://github.com/imperialcollegelondon/sharpy/tree/v1.2.1) (2021-02-09)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/v1.2...v1.2.1)\n\n**Implemented enhancements:**\n\n- Allow CFL != 1in shedding step [\\#78](https://github.com/ImperialCollegeLondon/sharpy/issues/78)\n- Vortex wake managed by SHARPy [\\#77](https://github.com/ImperialCollegeLondon/sharpy/issues/77)\n- Recover vortex core in UVLM [\\#76](https://github.com/ImperialCollegeLondon/sharpy/issues/76)\n- Include viscous drag force from airfoil properties [\\#75](https://github.com/ImperialCollegeLondon/sharpy/issues/75)\n\n**Fixed bugs:**\n\n- Bug in beamstructure.py [\\#117](https://github.com/ImperialCollegeLondon/sharpy/issues/117)\n- Definition of control surfaces and impact of node ordering in mirrored wings [\\#43](https://github.com/ImperialCollegeLondon/sharpy/issues/43)\n\n**Closed issues:**\n\n- examples refer to non-existent solver SHWUvlm [\\#119](https://github.com/ImperialCollegeLondon/sharpy/issues/119)\n- Potential bug in xbeam and cbeam interfaces [\\#89](https://github.com/ImperialCollegeLondon/sharpy/issues/89)\n- Update packages producing deprecation warnings and tackle other warnings [\\#80](https://github.com/ImperialCollegeLondon/sharpy/issues/80)\n\n**Merged pull requests:**\n\n- Rigid coupled solver [\\#120](https://github.com/ImperialCollegeLondon/sharpy/pull/120) ([ArturoMS13](https://github.com/ArturoMS13))\n- Support to save ROM projector matrices [\\#118](https://github.com/ImperialCollegeLondon/sharpy/pull/118) ([ngoiz](https://github.com/ngoiz))\n\n## [v1.2](https://github.com/imperialcollegelondon/sharpy/tree/v1.2) (2020-12-03)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/v1.1.1...v1.2)\n\n**Implemented enhancements:**\n\n- Quasi-steady solver in stepuvlm [\\#114](https://github.com/ImperialCollegeLondon/sharpy/pull/114) ([ArturoMS13](https://github.com/ArturoMS13))\n- Generator to modify structural mass at runtime [\\#107](https://github.com/ImperialCollegeLondon/sharpy/pull/107) ([ngoiz](https://github.com/ngoiz))\n- Sends simulation info to xplane via udp [\\#104](https://github.com/ImperialCollegeLondon/sharpy/pull/104) ([wong-hl](https://github.com/wong-hl))\n- Major new aerodynamic features [\\#101](https://github.com/ImperialCollegeLondon/sharpy/pull/101) ([ArturoMS13](https://github.com/ArturoMS13))\n- Simple post-processor to save simulation parameters for batch runs [\\#91](https://github.com/ImperialCollegeLondon/sharpy/pull/91) ([ngoiz](https://github.com/ngoiz))\n- SHARPy support for external inputs via UDP network [\\#90](https://github.com/ImperialCollegeLondon/sharpy/pull/90) ([ngoiz](https://github.com/ngoiz))\n- Vortex radius as input parameter [\\#86](https://github.com/ImperialCollegeLondon/sharpy/pull/86) ([ArturoMS13](https://github.com/ArturoMS13))\n- Enhanced Frequency Response post-processor and linear system input/output options [\\#83](https://github.com/ImperialCollegeLondon/sharpy/pull/83) ([ngoiz](https://github.com/ngoiz))\n- Pazi wing added to flying\\_wing template [\\#82](https://github.com/ImperialCollegeLondon/sharpy/pull/82) ([outoforderdev](https://github.com/outoforderdev))\n- Several new aerodynamic enhancements [\\#79](https://github.com/ImperialCollegeLondon/sharpy/pull/79) ([ArturoMS13](https://github.com/ArturoMS13))\n\n**Fixed bugs:**\n\n- libss.py disc2cont doesn't accept SISO systems [\\#88](https://github.com/ImperialCollegeLondon/sharpy/issues/88)\n- Dimension mismatch when assembling linear UVLM with \"shortened\" wake [\\#71](https://github.com/ImperialCollegeLondon/sharpy/issues/71)\n- Fix bug wake shape generator StaticCoupled [\\#85](https://github.com/ImperialCollegeLondon/sharpy/pull/85) ([ArturoMS13](https://github.com/ArturoMS13))\n- Rework of direct balancing [\\#74](https://github.com/ImperialCollegeLondon/sharpy/pull/74) ([outoforderdev](https://github.com/outoforderdev))\n\n**Closed issues:**\n\n- \\[develop\\] Documentation for postprocs not rendering in RTD [\\#109](https://github.com/ImperialCollegeLondon/sharpy/issues/109)\n- Numerical error in the linear UVLM output matrices when vortex radius is too small [\\#105](https://github.com/ImperialCollegeLondon/sharpy/issues/105)\n- fatal error: mkl.h: No such file or directory [\\#70](https://github.com/ImperialCollegeLondon/sharpy/issues/70)\n- lingebm.py -\\> update\\_matrices\\_time\\_scale [\\#69](https://github.com/ImperialCollegeLondon/sharpy/issues/69)\n- Missing node connectivities figure in case files documentation [\\#68](https://github.com/ImperialCollegeLondon/sharpy/issues/68)\n\n**Merged pull requests:**\n\n- \\[fix\\] Fixed bug in Gridbox class [\\#111](https://github.com/ImperialCollegeLondon/sharpy/pull/111) ([sduess](https://github.com/sduess))\n- Include linear UVLM stiffening and damping terms in the UVLM D matrix [\\#108](https://github.com/ImperialCollegeLondon/sharpy/pull/108) ([ngoiz](https://github.com/ngoiz))\n- Fix accuracy problem in UVLMLin [\\#106](https://github.com/ImperialCollegeLondon/sharpy/pull/106) ([ArturoMS13](https://github.com/ArturoMS13))\n- Minor improvements [\\#102](https://github.com/ImperialCollegeLondon/sharpy/pull/102) ([ngoiz](https://github.com/ngoiz))\n- Linearisation of externally applied follower forces [\\#100](https://github.com/ImperialCollegeLondon/sharpy/pull/100) ([ngoiz](https://github.com/ngoiz))\n- Updated docs for DataStructures and Multibody [\\#99](https://github.com/ImperialCollegeLondon/sharpy/pull/99) ([ArturoMS13](https://github.com/ArturoMS13))\n- Support linearised all-moving control surfaces [\\#97](https://github.com/ImperialCollegeLondon/sharpy/pull/97) ([ngoiz](https://github.com/ngoiz))\n- Update Linux and minimal environments [\\#96](https://github.com/ImperialCollegeLondon/sharpy/pull/96) ([ngoiz](https://github.com/ngoiz))\n- New approach to multibody computations [\\#95](https://github.com/ImperialCollegeLondon/sharpy/pull/95) ([ArturoMS13](https://github.com/ArturoMS13))\n- New SHARPy examples in the documentation [\\#94](https://github.com/ImperialCollegeLondon/sharpy/pull/94) ([ArturoMS13](https://github.com/ArturoMS13))\n- Add support for offline use of UDPout postproc [\\#93](https://github.com/ImperialCollegeLondon/sharpy/pull/93) ([ngoiz](https://github.com/ngoiz))\n- Option to transform rigid modes given at A FoR to centre of gravity and aligned with principal axes of inertia [\\#92](https://github.com/ImperialCollegeLondon/sharpy/pull/92) ([ngoiz](https://github.com/ngoiz))\n- Pazy wing modified to include the tip weight [\\#87](https://github.com/ImperialCollegeLondon/sharpy/pull/87) ([outoforderdev](https://github.com/outoforderdev))\n- Minor output clean up [\\#81](https://github.com/ImperialCollegeLondon/sharpy/pull/81) ([ngoiz](https://github.com/ngoiz))\n- Fixes assembly of linUVLM after plotting wake with minus m\\_star [\\#72](https://github.com/ImperialCollegeLondon/sharpy/pull/72) ([ngoiz](https://github.com/ngoiz))\n\n## [v1.1.1](https://github.com/imperialcollegelondon/sharpy/tree/v1.1.1) (2020-02-03)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/v1.1.0-2...v1.1.1)\n\n**Implemented enhancements:**\n\n- User-defined aerodynamic airfoil efficiency factor and constant force terms [\\#59](https://github.com/ImperialCollegeLondon/sharpy/pull/59) ([ngoiz](https://github.com/ngoiz))\n\n**Closed issues:**\n\n- Broken link on SHARPy Installation Guide [\\#67](https://github.com/ImperialCollegeLondon/sharpy/issues/67)\n- Update citation instructions [\\#62](https://github.com/ImperialCollegeLondon/sharpy/issues/62)\n- Incorrect version tag displayed when running SHARPy [\\#61](https://github.com/ImperialCollegeLondon/sharpy/issues/61)\n- Clean up SHARPy linear interface with UVLM [\\#48](https://github.com/ImperialCollegeLondon/sharpy/issues/48)\n\n**Merged pull requests:**\n\n- Documentation Improvements [\\#66](https://github.com/ImperialCollegeLondon/sharpy/pull/66) ([ngoiz](https://github.com/ngoiz))\n- Minor fixes and general code clean up of linear modules [\\#65](https://github.com/ImperialCollegeLondon/sharpy/pull/65) ([ngoiz](https://github.com/ngoiz))\n- Error log file created when program encounters exceptions [\\#64](https://github.com/ImperialCollegeLondon/sharpy/pull/64) ([ngoiz](https://github.com/ngoiz))\n- Update README.md [\\#63](https://github.com/ImperialCollegeLondon/sharpy/pull/63) ([rafapalacios](https://github.com/rafapalacios))\n- Clean up linear SHARPy's interface with UVLM [\\#60](https://github.com/ImperialCollegeLondon/sharpy/pull/60) ([ngoiz](https://github.com/ngoiz))\n\n## [v1.1.0-2](https://github.com/imperialcollegelondon/sharpy/tree/v1.1.0-2) (2019-12-12)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/v1.1.0...v1.1.0-2)\n\n## [v1.1.0](https://github.com/imperialcollegelondon/sharpy/tree/v1.1.0) (2019-12-12)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/v1.0.1...v1.1.0)\n\n**Implemented enhancements:**\n\n- Improvements to Model Reduction [\\#56](https://github.com/ImperialCollegeLondon/sharpy/pull/56) ([ngoiz](https://github.com/ngoiz))\n- Submodules and cmake build tools instead of Makefiles [\\#52](https://github.com/ImperialCollegeLondon/sharpy/pull/52) ([fonsocarre](https://github.com/fonsocarre))\n- New settings check against valid options [\\#39](https://github.com/ImperialCollegeLondon/sharpy/pull/39) ([ngoiz](https://github.com/ngoiz))\n- Default settings get type specified for the setting rather than their own type [\\#34](https://github.com/ImperialCollegeLondon/sharpy/pull/34) ([ngoiz](https://github.com/ngoiz))\n\n**Fixed bugs:**\n\n- Default value not correct in documentation when it is a numpy type. [\\#32](https://github.com/ImperialCollegeLondon/sharpy/issues/32)\n- Documentation for Postprocessors being skipped by Sphinx in RTD [\\#30](https://github.com/ImperialCollegeLondon/sharpy/issues/30)\n\n**Closed issues:**\n\n- Minor documentation issues [\\#53](https://github.com/ImperialCollegeLondon/sharpy/issues/53)\n- WindTurbine case generation script does not produce sharpy file [\\#50](https://github.com/ImperialCollegeLondon/sharpy/issues/50)\n- Considerations for building SHARPy [\\#47](https://github.com/ImperialCollegeLondon/sharpy/issues/47)\n- Installation fails on macOS with Intel compiler [\\#46](https://github.com/ImperialCollegeLondon/sharpy/issues/46)\n- run\\_theo\\_freq.py fails in Docker container [\\#37](https://github.com/ImperialCollegeLondon/sharpy/issues/37)\n- Compare to other competing software in JOSS paper [\\#36](https://github.com/ImperialCollegeLondon/sharpy/issues/36)\n\n**Merged pull requests:**\n\n- Example wind turbine [\\#58](https://github.com/ImperialCollegeLondon/sharpy/pull/58) ([ArturoMS13](https://github.com/ArturoMS13))\n- Small typo in README.md and updates to it [\\#57](https://github.com/ImperialCollegeLondon/sharpy/pull/57) ([fonsocarre](https://github.com/fonsocarre))\n- Restructuring of A Short Guide to SHARPy [\\#55](https://github.com/ImperialCollegeLondon/sharpy/pull/55) ([ngoiz](https://github.com/ngoiz))\n- JOSS Paper Minor typos fixed [\\#54](https://github.com/ImperialCollegeLondon/sharpy/pull/54) ([ngoiz](https://github.com/ngoiz))\n- Update .solver.txt extension to .sharpy [\\#51](https://github.com/ImperialCollegeLondon/sharpy/pull/51) ([ArturoMS13](https://github.com/ArturoMS13))\n- Fix typo in unittests using tearDowns instead of tearDown [\\#49](https://github.com/ImperialCollegeLondon/sharpy/pull/49) ([ngoiz](https://github.com/ngoiz))\n- Bug fixes in installation docs [\\#45](https://github.com/ImperialCollegeLondon/sharpy/pull/45) ([rafmudaf](https://github.com/rafmudaf))\n- Updated installation instructions [\\#44](https://github.com/ImperialCollegeLondon/sharpy/pull/44) ([ngoiz](https://github.com/ngoiz))\n- Travis CI now uses the minimal environment, the same as the Docker build [\\#42](https://github.com/ImperialCollegeLondon/sharpy/pull/42) ([fonsocarre](https://github.com/fonsocarre))\n- Remove calls to matplotlib \\(or wrap in try except\\) [\\#41](https://github.com/ImperialCollegeLondon/sharpy/pull/41) ([ngoiz](https://github.com/ngoiz))\n- Added information about competing software in JOSS paper [\\#40](https://github.com/ImperialCollegeLondon/sharpy/pull/40) ([fonsocarre](https://github.com/fonsocarre))\n- Removes deprecated case files from cases folder [\\#38](https://github.com/ImperialCollegeLondon/sharpy/pull/38) ([ngoiz](https://github.com/ngoiz))\n- Change position of --name argument in docs [\\#35](https://github.com/ImperialCollegeLondon/sharpy/pull/35) ([petebachant](https://github.com/petebachant))\n- Improvements in documentation [\\#31](https://github.com/ImperialCollegeLondon/sharpy/pull/31) ([ngoiz](https://github.com/ngoiz))\n\n## [v1.0.1](https://github.com/imperialcollegelondon/sharpy/tree/v1.0.1) (2019-11-17)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/1.0.0...v1.0.1)\n\n**Implemented enhancements:**\n\n- New example of linearised flying wing [\\#28](https://github.com/ImperialCollegeLondon/sharpy/pull/28) ([ngoiz](https://github.com/ngoiz))\n- SHARPy can now be obtained from a Docker Hub container [\\#27](https://github.com/ImperialCollegeLondon/sharpy/pull/27) ([fonsocarre](https://github.com/fonsocarre))\n- Improved modal solver [\\#26](https://github.com/ImperialCollegeLondon/sharpy/pull/26) ([fonsocarre](https://github.com/fonsocarre))\n- Updated function calls for latest numpy 1.17 [\\#25](https://github.com/ImperialCollegeLondon/sharpy/pull/25) ([ngoiz](https://github.com/ngoiz))\n- Examples added to documentation [\\#24](https://github.com/ImperialCollegeLondon/sharpy/pull/24) ([fonsocarre](https://github.com/fonsocarre))\n- Improved linear solver documentation and minor Krylov ROM fixes [\\#23](https://github.com/ImperialCollegeLondon/sharpy/pull/23) ([ngoiz](https://github.com/ngoiz))\n- change log generator incorporated [\\#22](https://github.com/ImperialCollegeLondon/sharpy/pull/22) ([ngoiz](https://github.com/ngoiz))\n\n**Merged pull requests:**\n\n- Version v1.0.1 released [\\#29](https://github.com/ImperialCollegeLondon/sharpy/pull/29) ([fonsocarre](https://github.com/fonsocarre))\n\n## [1.0.0](https://github.com/imperialcollegelondon/sharpy/tree/1.0.0) (2019-11-07)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/v1.0.0-rc...1.0.0)\n\n**Implemented enhancements:**\n\n- WriteVariablesTime output global beam variables and consistent out dir [\\#19](https://github.com/ImperialCollegeLondon/sharpy/pull/19) ([ngoiz](https://github.com/ngoiz))\n- Autodocumenter [\\#16](https://github.com/ImperialCollegeLondon/sharpy/pull/16) ([ngoiz](https://github.com/ngoiz))\n\n**Closed issues:**\n\n- Tests not passing due to them being outdated + test refactoring. [\\#11](https://github.com/ImperialCollegeLondon/sharpy/issues/11)\n\n**Merged pull requests:**\n\n- Release of v1.0.0!!! [\\#20](https://github.com/ImperialCollegeLondon/sharpy/pull/20) ([fonsocarre](https://github.com/fonsocarre))\n- Documentation fixes/updates [\\#18](https://github.com/ImperialCollegeLondon/sharpy/pull/18) ([ngoiz](https://github.com/ngoiz))\n- Fix dynamic control surface and settings for aerogridloader [\\#15](https://github.com/ImperialCollegeLondon/sharpy/pull/15) ([ngoiz](https://github.com/ngoiz))\n\n## [v1.0.0-rc](https://github.com/imperialcollegelondon/sharpy/tree/v1.0.0-rc) (2019-08-22)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/V0.2.1...v1.0.0-rc)\n\n**Closed issues:**\n\n- Output table [\\#10](https://github.com/ImperialCollegeLondon/sharpy/issues/10)\n\n**Merged pull requests:**\n\n- Remove H5pyDeprecationWarning [\\#14](https://github.com/ImperialCollegeLondon/sharpy/pull/14) ([ArturoMS13](https://github.com/ArturoMS13))\n- Lagrange multipliers for Catapult Take Off works + clean tests [\\#13](https://github.com/ImperialCollegeLondon/sharpy/pull/13) ([fonsocarre](https://github.com/fonsocarre))\n\n## [V0.2.1](https://github.com/imperialcollegelondon/sharpy/tree/V0.2.1) (2019-03-14)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/v0.2...V0.2.1)\n\n## [v0.2](https://github.com/imperialcollegelondon/sharpy/tree/v0.2) (2019-03-14)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/v0.1...v0.2)\n\n**Closed issues:**\n\n- Add recovery options [\\#9](https://github.com/ImperialCollegeLondon/sharpy/issues/9)\n\n## [v0.1](https://github.com/imperialcollegelondon/sharpy/tree/v0.1) (2018-09-03)\n\n[Full Changelog](https://github.com/imperialcollegelondon/sharpy/compare/bd2b65974d57d2d6486ea90cdb68ef6324efbac8...v0.1)\n\n**Implemented enhancements:**\n\n- Hinge definition for control surface [\\#8](https://github.com/ImperialCollegeLondon/sharpy/issues/8)\n- sharpy\\_main.main does not return output [\\#5](https://github.com/ImperialCollegeLondon/sharpy/issues/5)\n\n**Fixed bugs:**\n\n- Aerofoil data associated to the nodes instead of the elements [\\#6](https://github.com/ImperialCollegeLondon/sharpy/issues/6)\n\n**Merged pull requests:**\n\n- Trimming routine working [\\#4](https://github.com/ImperialCollegeLondon/sharpy/pull/4) ([fonsocarre](https://github.com/fonsocarre))\n- Feature coupled dynamic [\\#3](https://github.com/ImperialCollegeLondon/sharpy/pull/3) ([fonsocarre](https://github.com/fonsocarre))\n- Refactored storage finished [\\#2](https://github.com/ImperialCollegeLondon/sharpy/pull/2) ([fonsocarre](https://github.com/fonsocarre))\n- Settings files are ConfigObjs now, not ConfigParser anymore [\\#1](https://github.com/ImperialCollegeLondon/sharpy/pull/1) ([fonsocarre](https://github.com/fonsocarre))\n\n\n\n\\* *This Changelog was automatically generated by [github_changelog_generator](https://github.com/github-changelog-generator/github-changelog-generator)*\n" }, { "path": "CMakeLists.txt", "content": "cmake_minimum_required(VERSION 3.9)\nproject(sharpy)\n\nif(NOT CMAKE_BUILD_TYPE)\n set(CMAKE_BUILD_TYPE Release)\nendif()\n\nadd_subdirectory(lib)\n" }, { "path": "Dockerfile", "content": "FROM centos:8\n\nENV PYTHONDONTWRITEBYTECODE=true\nENV BASH_ENV ~/.bashrc\nSHELL [\"/bin/bash\", \"-c\"]\nENV PATH=${PATH}:/mamba/bin\n\n# CENTOS 8 has reached end of life - Not yet an updated Docker base for CentOS stream\n# Point to the CentOS 8 vault in order to download dependencies\nRUN cd /etc/yum.repos.d/ && \\\n sed -i 's/mirrorlist/#mirrorlist/g' /etc/yum.repos.d/CentOS-* && \\\n sed -i 's|#baseurl=http://mirror.centos.org|baseurl=http://vault.centos.org|g' /etc/yum.repos.d/CentOS-* && \\\n cd /\n\n# Development tools including compilers\nRUN yum groupinstall \"Development Tools\" -y --nogpgcheck && \\\n yum install dnf-plugins-core && \\\n yum config-manager --set-enabled powertools && \\\n yum install -y --nogpgcheck mesa-libGL libXt libXt-devel wget gcc-gfortran lapack vim tmux eigen3-devel && \\\n yum clean all\n\n# Install Mamba - swapped from Conda to Mamba due to Github runner memory constraint\n# Mambaforge is deprecated in latest miniforge https://github.com/conda-forge/miniforge/pull/704\nRUN wget --no-check-certificate https://github.com/conda-forge/miniforge/releases/download/24.7.1-0/Mambaforge-Linux-x86_64.sh -O /mamba.sh && \\\n chmod +x /mamba.sh && \\\n /mamba.sh -b -p /mamba/ && \\\n rm /mamba.sh && hash -r\n\nADD / /sharpy_dir/\n\n# Initialise mamba installation\nRUN mamba init bash && \\\n mamba update -q conda && \\\n mamba env create -f /sharpy_dir/utils/environment.yml && \\\n find /mamba/ -follow -type f -name '*.a' -delete && \\\n find /mamba/ -follow -type f -name '*.pyc' -delete && \\\n find /mamba/ -follow -type f -name '*.js.map' -delete\n\nRUN ln -s /sharpy_dir/utils/docker/* /root/\n\nRUN cd sharpy_dir && \\\n mamba activate sharpy && \\\n git submodule update --init --recursive && \\\n mkdir build && \\\n cd build && \\\n CXX=g++ FC=gfortran cmake .. && make install -j 4 && \\\n cd .. && \\\n pip install . && \\\n rm -rf build\n \nENTRYPOINT [\"/bin/bash\", \"--init-file\", \"/root/bashrc\"]\n" }, { "path": "LICENSE", "content": "BSD 3-Clause License\n\nCopyright (c) 2019, Loads Control and Aeroelastics, Imperial College London\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\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\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": "README.md", "content": "# Simulation of High Aspect Ratio aeroplanes in Python [SHARPy]\n\n![Version badge](https://img.shields.io/endpoint.svg?url=https%3A%2F%2Fraw.githubusercontent.com%2FImperialCollegeLondon%2Fsharpy%2Fmain%2F.version.json)\n![Build Status](https://github.com/ImperialCollegeLondon/sharpy/actions/workflows/sharpy_tests.yaml/badge.svg)\n[![Documentation Status](https://readthedocs.org/projects/ic-sharpy/badge/?version=main)](https://ic-sharpy.readthedocs.io/en/main/?badge=main)\n[![codecov](https://codecov.io/gh/ImperialCollegeLondon/sharpy/branch/main/graph/badge.svg)](https://codecov.io/gh/ImperialCollegeLondon/sharpy)\n[![License](https://img.shields.io/badge/License-BSD%203--Clause-blue.svg)](https://opensource.org/licenses/BSD-3-Clause)\n[![status](https://joss.theoj.org/papers/f7ccd562160f1a54f64a81e90f5d9af9/status.svg)](https://joss.theoj.org/papers/f7ccd562160f1a54f64a81e90f5d9af9)\n[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.3531965.svg)](https://doi.org/10.5281/zenodo.3531965)\n\nSHARPy is a nonlinear aeroelastic analysis package originally developed at the Department of Aeronautics, Imperial\nCollege London. It can be used for the structural, aerodynamic and aeroelastic analysis of flexible wings, aircraft and wind turbines. It is shared here under a BSD 3-Clause permissive license.\n\n![XHALE](./docs/source/_static/XHALE-render.jpg)\n\n### Contact\n\nFor more information on the [research team](http://www.imperial.ac.uk/aeroelastics/software/) developing SHARPy or to get \nin touch, [visit our homepage](http://www.imperial.ac.uk/aeroelastics).\n\n## Physical Models\n\nSHARPy is a modular aeroelastic solver that currently uses two specific models for the structural and aerodynamic response of the system.\n\nFor the structural model, SHARPy employs a geometrically-exact displacement-based composite beam formulation,\naugmented with Lagrange multipliers for additional kinematic constraints.\nThis model has the advantage of providing the solution directly in the physical problem's degrees of freedom, making the \ncoupling with the aerodynamic solver simple and not requiring any post-processing. The 1D beam formulation used limits \nthe analyses that can be done by SHARPy to slender structures, such as high aspect ratio wings.\n\nThe aerodynamic model utilises the Unsteady Vortex Lattice Method (UVLM). The aerodynamic surfaces are modelled as a thin\nvortex ring lattice with the boundary conditions enforced at the collocation points in the middle of the vortex rings.\nThe Kutta condition is also enforced at the trailing edge. The wake can be simulated by either additional vortex rings\nor by infinitely long horseshoe vortices, which are ideally suited for steady simulations only.\n\nThe aerodynamic model has recently been extended by a linear source panel method (SPM) to model nonlifting bodies for example fuselages. The SPM and UVLM can be coupled to model fuselage-wing configuration and a junction handling approach, based on phantom panels and circulation interpolation, has been added.\n\nThe input problems can be structural, aerodynamic or coupled, yielding an aeroelastic system.\n\n## [Capabilities](http://ic-sharpy.readthedocs.io/en/latest/content/capabilities.html)\n\nThe base solver SHARPy is a nonlinear aeroelastic analysis package that can be used on free-flying flexible aircraft,\nwings and wind turbines. In addition, it supports linearisation of these nonlinear systems about\narbitrary conditions and includes various tools such as: model reduction or frequency analysis.\n\nIn short, SHARPy offers (amongst others) the following solutions to the user:\n* Static aerodynamic, structural and aeroelastic solutions including fuselage effects\n* Finding trim conditions for aeroelastic configurations\n* Nonlinear, dynamic time domain simulations under a large number of conditions such as:\n + Prescribed trajectories.\n + Free flight.\n + Dynamic follower forces.\n + Control inputs in thrust, control surface deflection...\n + Arbitrary time-domain gusts, including non span-constant ones.\n + Full 3D turbulent fields.\n* Multibody dynamics with hinges, articulations and prescribed nodal motions:\n + Applicable to wind turbines.\n + Hinged aircraft.\n + Catapult assisted takeoffs.\n* Linear analysis:\n + Linearisation around a nonlinear equilibrium.\n + Frequency response analysis.\n + Asymptotic stability analysis.\n* Model order reduction:\n + Krylov-subspace reduction methods.\n + Several balancing reduction methods.\n\n## Documentation\n\nThe documentation for SHARPy can be found [here](http://ic-sharpy.readthedocs.io).\n\n## Installing SHARPy\n\nFor the latest documentation, see the \n[installation docs](https://ic-sharpy.readthedocs.io/en/latest/content/installation.html).\n\nSHARPy can also be obtained from Docker Hub to avoid compilation\nand platform-dependant issues. If you are interested, make sure you check \nthe [SHARPy Docker distribution docs](https://ic-sharpy.readthedocs.io/en/latest/content/installation.html#using-sharpy-from-a-docker-container).\n\n## Contributing and Bug reports\n\nIf you think you can add a useful feature to SHARPy, want to write documentation or you encounter a bug, by all means, \ncheck out the [collaboration guide](https://ic-sharpy.readthedocs.io/en/latest/content/contributing.html).\n\n## Citing SHARPy\n\nSHARPy has been published in the Journal of Open Source Software (JOSS) and the relevant paper can be found\n[here](https://joss.theoj.org/papers/10.21105/joss.01885).\n\nIf you are using SHARPy for your work, please remember to cite it using the paper in JOSS as:\n\n`del Carre et al., (2019). SHARPy: A dynamic aeroelastic simulation toolbox for very flexible aircraft and wind\nturbines. Journal of Open Source Software, 4(44), 1885, https://doi.org/10.21105/joss.01885`\n\nThe bibtex entry for this citation is:\n\n```\n@Article{delCarre2019,\ndoi = {10.21105/joss.01885},\nurl = {https://doi.org/10.21105/joss.01885},\nyear = {2019},\nmonth = dec,\npublisher = {The Open Journal},\nvolume = {4},\nnumber = {44},\npages = {1885},\nauthor = {Alfonso del Carre and Arturo Mu{\\~{n}}oz-Sim\\'on and Norberto Goizueta and Rafael Palacios},\ntitle = {{SHARPy}: A dynamic aeroelastic simulation toolbox for very flexible aircraft and wind turbines},\njournal = {Journal of Open Source Software}\n}\n```\n\n\n## Continuous Integration Status\n\nSHARPy uses Continuous Integration to control the integrity of its code. The status in the release and develop branches\nis:\n\nMain\n![Build Status](https://github.com/ImperialCollegeLondon/sharpy/actions/workflows/sharpy_tests.yaml/badge.svg)\n![Docker Status](https://github.com/ImperialCollegeLondon/sharpy/actions/workflows/docker_build.yaml/badge.svg)\n\nDevelop\n![Build Status](https://github.com/ImperialCollegeLondon/sharpy/actions/workflows/sharpy_tests.yaml/badge.svg?branch=develop)\n" }, { "path": "docs/.nojekyll", "content": "" }, { "path": "docs/JOSS/codemeta.json", "content": "{\n \"@context\": \"https://raw.githubusercontent.com/codemeta/codemeta/master/codemeta.jsonld\",\n \"@type\": \"Code\",\n \"author\": [\n \"Alfonso del Carre\",\n \"Arturo Muñoz-Simón\",\n \"Norberto Goizueta\",\n \"Rafael Palacios\"\n ],\n \"identifier\": \"\",\n \"codeRepository\": \"https://github.com/imperialcollegelondon/sharpy\",\n \"datePublished\": \"2019-11-04\",\n \"dateModified\": \"2019-11-04\",\n \"dateCreated\": \"2019-11-04\",\n \"description\": \"A dynamic aeroelastic simulation toolbox for very flexible aircraft and wind turbines\",\n \"keywords\": \"aeroelasticity, structural dynamics, aerodynamics, solar flight, perpetual flight, wing energy\",\n \"license\": \"BSD-3\",\n \"title\": \"SHARPy\",\n \"version\": \"v1.0.0-rc1\"\n}\n" }, { "path": "docs/JOSS/generate.rb", "content": "#!/usr/bin/ruby\n\n# For an OO language, this is distinctly procedural. Should probably fix that.\nrequire 'json'\n\ndetails = Hash.new({})\n\ncapture_params = [\n { :name => \"title\", :message => \"Enter project name.\" },\n { :name => \"url\", :message => \"Enter the URL of the project repository.\" },\n { :name => \"description\", :message => \"Enter the (short) project description.\" },\n { :name => \"license\", :message => \"Enter the license this software shared under. (hit enter to skip)\\nFor example MIT, BSD, GPL v3.0, Apache 2.0\" },\n { :name => \"doi\", :message => \"Enter the DOI of the archived version of this code. (hit enter to skip)\\nFor example http://dx.doi.org/10.6084/m9.figshare.828487\" },\n { :name => \"keywords\", :message => \"Enter keywords that should be associated with this project (hit enter to skip)\\nComma-separated, for example: turkey, chicken, pot pie\" },\n { :name => \"version\", :message => \"Enter the version of your software (hit enter to skip)\\nSEMVER preferred: http://semver.org e.g. v1.0.0\" }\n]\n\nputs \"I'm going to try and help you prepare some things for your JOSS submission\"\nputs \"If all goes well then we'll have a nice codemeta.json file soon...\"\nputs \"\"\nputs \"************************************\"\nputs \"* First, some basic details *\"\nputs \"************************************\"\nputs \"\"\n\n# Loop through the desired captures and print out for clarity\ncapture_params.each do |param|\n puts param[:message]\n print \"> \"\n input = gets\n\n details[param[:name]] = input.chomp\n\n puts \"\"\n puts \"OK, your project has #{param[:name]}: #{input}\"\n puts \"\"\nend\n\nputs \"\"\nputs \"************************************\"\nputs \"* Experimental stuff *\"\nputs \"************************************\"\nputs \"\"\n\nputs \"Would you like me to try and build a list of authors for you?\"\nputs \"(You need to be running this script in a git repository for this to work)\"\nprint \"> (Y/N)\"\nanswer = gets.chomp\n\ncase answer.downcase\nwhen \"y\", \"yes\"\n\n # Use git shortlog to extract a list of author names and commit counts.\n # Note we don't extract emails here as there's often different emails for\n # each user. Instead we capture emails at the end.\n\n git_log = `git shortlog --summary --numbered --no-merges`\n\n # [\"252\\tMichael Jackson\", \"151\\tMC Hammer\"]\n authors_and_counts = git_log.split(\"\\n\").map(&:strip)\n\n authors_and_counts.each do |author_count|\n count, author = author_count.split(\"\\t\").map(&:strip)\n\n puts \"Looks like #{author} made #{count} commits\"\n puts \"Add them to the output?\"\n print \"> (Y/N)\"\n answer = gets.chomp\n\n # If a user chooses to add this author to the output then we ask for some\n # additional information including their email, ORCID and affiliation.\n case answer.downcase\n when \"y\", \"yes\"\n puts \"What is #{author}'s email address? (hit enter to skip)\"\n print \"> \"\n email = gets.chomp\n\n puts \"What is #{author}'s ORCID? (hit enter to skip)\"\n puts \"For example: http://orcid.org/0000-0000-0000-0000\"\n print \"> \"\n orcid = gets.chomp\n\n puts \"What is #{author}'s affiliation? (hit enter to skip)\"\n print \"> \"\n affiliation = gets.chomp\n\n\n details['authors'].merge!(author => { 'commits' => count,\n 'email' => email,\n 'orcid' => orcid,\n 'affiliation' => affiliation })\n\n when \"n\", \"no\"\n puts \"OK boss...\"\n puts \"\"\n end\n end\nwhen \"n\", \"no\"\n puts \"OK boss...\"\n puts \"\"\nend\n\nputs \"Reticulating splines\"\n\n5.times do\n print \".\"\n sleep 0.5\nend\n\nputs \"\"\nputs \"Generating some JSON goodness...\"\n\n# TODO: work out how to use some kind of JSON template here.\n# Build the output list of authors from the inputs we've collected.\noutput_authors = []\n\ndetails['authors'].each do |author_name, values|\n entry = {\n \"@id\" => values['orcid'],\n \"@type\" => \"Person\",\n \"email\" => values['email'],\n \"name\" => author_name,\n \"affiliation\" => values['affiliation']\n }\n output_authors << entry\nend\n\n# TODO: this is currently a static template (written out here). It would be good\n# to do something smarter here.\noutput = {\n \"@context\" => \"https://raw.githubusercontent.com/codemeta/codemeta/master/codemeta.jsonld\",\n \"@type\" => \"Code\",\n \"author\" => output_authors,\n \"identifier\" => details['doi'],\n \"codeRepository\" => details['url'],\n \"datePublished\" => Time.now.strftime(\"%Y-%m-%d\"),\n \"dateModified\" => Time.now.strftime(\"%Y-%m-%d\"),\n \"dateCreated\" => Time.now.strftime(\"%Y-%m-%d\"),\n \"description\" => details['description'],\n \"keywords\" => details['keywords'],\n \"license\" => details['license'],\n \"title\" => details['title'],\n \"version\" => details['version']\n}\n\nFile.open('codemeta.json', 'w') {|f| f.write(JSON.pretty_generate(output)) }\n" }, { "path": "docs/JOSS/paper.bib", "content": "% Encoding: UTF-7\n@Article{Patil2001,\n author = {Mayuresh J. Patil and Dewey H. Hodges and Carlos E. S. Cesnik},\n title = {Nonlinear Aeroelasticity and Flight Dynamics of High-Altitude Long-Endurance Aircraft},\n journal = {Journal of Aircraft},\n year = {2001},\n volume = {38},\n number = {1},\n pages = {88--94},\n month = {jan},\n doi = {10.2514/2.2738},\n groups = {IFASD 2019},\n publisher = {American Institute of Aeronautics and Astronautics ({AIAA})},\n}\n\n@InProceedings{Simpson2013,\n author = {Robert J. Simpson and Rafael Palacios},\n title = {Numerical aspects of nonlinear flexible aircraft flight dynamics modeling},\n booktitle = {54th {AIAA}/{ASME}/{ASCE}/{AHS}/{ASC} Structures, Structural Dynamics, and Materials Conference},\n year = {2013},\n month = {apr},\n publisher = {American Institute of Aeronautics and Astronautics},\n doi = {10.2514/6.2013-1634},\n groups = {IFASD 2019},\n}\n\n@Article{Jones2015,\n author = {J. R. Jones and C. E. S. Cesnik},\n title = {Preliminary flight test correlations of the {X-HALE} aeroelastic experiment},\n journal = {The Aeronautical Journal},\n year = {2015},\n volume = {119},\n number = {1217},\n pages = {855--870},\n month = {jul},\n doi = {10.1017/s0001924000010952},\n groups = {IFASD 2019},\n publisher = {Cambridge University Press ({CUP})},\n}\n\n@PhdThesis{Jones2017,\n author = {Jessica Renee Jones},\n title = {Development of a Very Flexible Testbed Aircraft for the Validation of Nonlinear Aeroelastic Codes},\n school = {University of Michigan},\n year = {2017},\n groups = {IFASD 2019},\n}\n\n@InProceedings{Cesnik2011,\n author = {Carlos Cesnik and Weihua Su},\n title = {Nonlinear Aeroelastic Simulation of X-{HALE}: a Very Flexible {UAV}},\n booktitle = {49th {AIAA} Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition},\n year = {2011},\n month = {jan},\n publisher = {American Institute of Aeronautics and Astronautics},\n doi = {10.2514/6.2011-1226},\n groups = {IFASD 2019},\n}\n\n@inproceedings{Drela1999,\n doi = {10.2514/6.1999-1394},\n url = {https://doi.org/10.2514/6.1999-1394},\n year = {1999},\n month = apr,\n publisher = {American Institute of Aeronautics and Astronautics},\n author = {Mark Drela},\n title = {Integrated simulation model for preliminary aerodynamic, structural, and control-law design of aircraft},\n booktitle = {{40th Structures, Structural Dynamics, and Materials Conference and Exhibit}}\n}\n\n@PhdThesis{Shearer2006,\n author = {Christopher M. Shearer},\n title = {Coupled nonlinear flight dynamics, aeroelasticity, and control of very flexible aircraft},\n school = {University of Michigan},\n year = {2006},\n groups = {IFASD 2019},\n}\n\n@Article{Cesnik2012,\n author = {Carlos E. S. Cesnik and Patrick J. Senatore and Weihua Su and Ella M. Atkins and Christopher M. Shearer},\n title = {X-{HALE}: A Very Flexible Unmanned Aerial Vehicle for Nonlinear Aeroelastic Tests},\n journal = {{AIAA} Journal},\n year = {2012},\n volume = {50},\n number = {12},\n pages = {2820--2833},\n month = {dec},\n doi = {10.2514/1.j051392},\n groups = {IFASD 2019},\n publisher = {American Institute of Aeronautics and Astronautics ({AIAA})},\n}\n\n@Article{Cesnik2014,\n author = {Carlos E. S. Cesnik and Rafael Palacios and Eric Y. Reichenbach},\n title = {Reexamined Structural Design Procedures for Very Flexible Aircraft},\n journal = {Journal of Aircraft},\n year = {2014},\n volume = {51},\n number = {5},\n pages = {1580--1591},\n month = {sep},\n doi = {10.2514/1.c032464},\n groups = {IFASD 2019},\n publisher = {American Institute of Aeronautics and Astronautics ({AIAA})},\n}\n\n@Article{Su2011,\n author = {Weihua Su and Carlos E. S. Cesnik},\n title = {Dynamic Response of Highly Flexible Flying Wings},\n journal = {{AIAA} Journal},\n year = {2011},\n volume = {49},\n number = {2},\n pages = {324--339},\n month = {feb},\n doi = {10.2514/1.j050496},\n groups = {IFASD 2019},\n publisher = {American Institute of Aeronautics and Astronautics ({AIAA})},\n}\n\n@InProceedings{Dillsaver2013,\n author = {Matthew Dillsaver and Carlos E. S. Cesnik and Ilya Kolmanovsky},\n title = {Trajectory Control of Very Flexible Aircraft with Gust Disturbance},\n booktitle = {{AIAA} Atmospheric Flight Mechanics ({AFM}) Conference},\n year = {2013},\n month = {aug},\n publisher = {American Institute of Aeronautics and Astronautics},\n doi = {10.2514/6.2013-4745},\n groups = {IFASD 2019},\n}\n\n@article{Murua2012a,\nauthor = {Murua, Joseba and Palacios, Rafael and Graham, J. Michael R.},\ndoi = {10.1016/j.paerosci.2012.06.001},\njournal = {Progress in Aerospace Sciences},\nmonth = {nov},\npages = {46--72},\ntitle = {{Applications of the unsteady vortex-lattice method in aircraft aeroelasticity and flight dynamics}},\nvolume = {55},\nyear = {2012}\n}\n\n@ARTICLE{deskos2019,\n author = {{Deskos}, Georgios and {del Carre}, Alfonso and {Palacios}, Rafael},\n title = \"{Assessment of low-altitude atmospheric turbulence models for aircraft aeroelasticity}\",\n journal = {arXiv e-prints},\n keywords = {Physics - Fluid Dynamics},\n year = \"2019\",\n month = \"Aug\",\n eid = {arXiv:1908.00372},\n pages = {arXiv:1908.00372},\narchivePrefix = {arXiv},\n eprint = {1908.00372},\n primaryClass = {physics.flu-dyn},\n adsurl = {https://ui.adsabs.harvard.edu/abs/2019arXiv190800372D},\n adsnote = {Provided by the SAO/NASA Astrophysics Data System}\n}\n\n@Article{Palacios2010,\n author = {Rafael Palacios and Joseba Murua and Robert Cook},\n title = {Structural and Aerodynamic Models in Nonlinear Flight Dynamics of Very Flexible Aircraft},\n journal = {{AIAA} Journal},\n year = {2010},\n volume = {48},\n number = {11},\n pages = {2648--2659},\n month = {nov},\n doi = {10.2514/1.j050513},\n groups = {IFASD 2019},\n publisher = {American Institute of Aeronautics and Astronautics ({AIAA})},\n}\n\n@InProceedings{Teixeira2018,\n author = {Patricia Teixeira and Carlos E. S. Cesnik},\n title = {Propeller Effects on the Dynamic Response of {HALE} Aircraft},\n booktitle = {2018 {AIAA}/{ASCE}/{AHS}/{ASC} Structures, Structural Dynamics, and Materials Conference},\n year = {2018},\n month = {jan},\n publisher = {American Institute of Aeronautics and Astronautics},\n doi = {10.2514/6.2018-1202},\n groups = {IFASD 2019},\n}\n\n@Article{Cook2013,\n author = {Robert G. Cook and Rafael Palacios and Paul Goulart},\n title = {Robust Gust Alleviation and Stabilization of Very Flexible Aircraft},\n journal = {{AIAA} Journal},\n year = {2013},\n volume = {51},\n number = {2},\n pages = {330--340},\n month = {feb},\n doi = {10.2514/1.j051697},\n publisher = {American Institute of Aeronautics and Astronautics ({AIAA})},\n}\n\n@InProceedings{Patil2006,\n author = {Mayuresh Patil and Dana Taylor},\n title = {Gust Response of Highly Flexible Aircraft},\n booktitle = {47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference Newport, Rhode Island},\n year = {2006},\n month = {may},\n publisher = {American Institute of Aeronautics and Astronautics},\n doi = {10.2514/6.2002-1719},\n}\n\n@InProceedings{Cesnik2005,\n author = {Cesnik, Carlos E. S. and Brown, Eric L.},\n title = {Modelling of High Aspect Ratio Active Flexible Wings for Roll Control},\n booktitle = {43rd Structures, Structural Dynamics, and Material Conference},\n year = {2002},\n month = {apr},\n publisher = {American Institute of Aeronautics and Astronautics},\n doi = {10.2514/6.2006-1638},\n address = {Denver, CO},\n}\n\n@article{Hesse2014a,\nabstract = {This paper investigates the linearization, using perturbation methods, of the structural deformations in the nonlinear flight dynamic response of aircraft with slender, flexible wings. The starting point is the coupling of a displacement-based geometrically nonlinear flexible-body dynamics formulation with a three-dimensional unsteady vortex lattice method. This is followed by a linearization of the structural degrees of freedom, which are assumed to be small in a body-fixed reference frame. The translations and rotations of that reference frame and their time derivatives, which describe the vehicle flight dynamics, can still be arbitrarily large. The resulting system preserves all couplings between rigid and elastic motions and can be projected onto a few vibration modes of the unconstrained aircraft with geometrically nonlinear static deflections at a trim condition. Equally, the unsteady aerodynamics can be approximated on a fixed lattice defined by the deformed static geometry. Numerical studies on a representative highaltitude long-endurance aircraft are presented to illustrate the approach. The results show an improvement compared to those obtained using the mean-axes approximation. {\\textcopyright} 2013 by Henrik Hesse, Rafael Palacios, and Joseba Murua.},\nauthor = {Hesse, Henrik and Palacios, Rafael and Murua, Joseba},\ndoi = {10.2514/1.J052316},\njournal = {AIAA Journal},\nmonth = {mar},\nnumber = {3},\npages = {528--538},\ntitle = {Consistent Structural Linearization in Flexible Aircraft Dynamics with Large Rigid-Body Motion},\nvolume = {52},\nyear = {2014}\n}\n\n@article{Su2011b,\nabstract = {},\nauthor = {Su, Weihua and Cesnik, Carlos E. S.},\ndoi = {10.1016/j.ijsolstr.2011.04.012},\njournal = {International Journal of Solids and Structures},\npages = {2349–-2360},\ntitle = {{Strain-based Geometrically Nonlinear Beam Formulation for Modeling Very Flexible Aircraft}},\nurl = {http://arc.aiaa.org/doi/10.2514/1.C032477},\nvolume = {48},\nyear = {2012}\n}\n\n@article{Su2012,\nabstract = {A strain-based geometrically nonlinear beam formulation for structural dynamic and aeroelastic analysis of slender beams and wings has been successfully applied to study the coupled nonlinear aeroelasticity and flight dynamics of different very flexible aircraft. As an extension to the solution technique based on the nonlinear finite element developed by the authors, a modal-based approach is discussed in this paper to solve the strain-based nonlinear beam equations. The modal approach is applied to study geometrically nonlinear static and transient problems of constrained and free slender beams, subject to external structural or aero-dynamic excitations. The efficiency of the modal solution is also compared to that of the finite-element approach.},\nauthor = {Su, Weihua and Cesnik, Carlos E. S.},\ndoi = {10.2514/1.C032477},\nisbn = {9781600869372 (ISBN)},\nissn = {0021-8669},\njournal = {Journal of Aircraft},\nnumber = {3},\npages = {890--903},\ntitle = {{Strain-Based Analysis for Geometrically Nonlinear Beams: A Modal Approach}},\nurl = {http://arc.aiaa.org/doi/10.2514/1.C032477},\nvolume = {51},\nyear = {2012}\n}\n@article{Su2010,\nabstract = {Blended-wing-body (BWB) aircraft with high-aspect-ratio wings is an important configu- ration for high-altitude long-endurance unmanned aerial vehicles (HALE UAV). Recently, Northrop Grumann created a wind tunnel model under the Air Force's High Lift over Drag Active (HiLDA) Wing program to study the aeroelastic characteristics of blended-wing-body for a potential Sensorcraft concept. This paper presents a study on the coupled aeroelastic / flight dynamics stability and response of a BWB aircraft that is modified from the HiLDA experimental model. An effective method is used to model very flexible BWB vehicles based on a low-order aeroelastic formulation that is capable of capturing the important structural nonlinear effects and couplings with the flight dynamics degrees of freedom. A nonlinear strain-based beam finite element formulation is used. Finite-state unsteady subsonic aerodynamic loads are incorporated to be coupled with all lifting surfaces, including the flexible body. Based on the proposed model, body-freedom flutter is studied, and is compared with the flutter results with all or partial rigid-body degrees of freedom constrained. The applicability of wind tunnel aeroelastic results (where the rigid-body motion is limited) is discussed in view of the free flight conditions (with all 6 rigid-body degrees of freedom). Furthermore, effects of structural and aerodynamic nonlinearities as well as wing bending/torsion rigidity coupling on the stability and gust response are also studied in this paper. I.},\nauthor = {Su, Weihua and Cesnik, Carlos E. S.},\ndoi = {10.2514/1.47317},\nisbn = {9781563479731},\nissn = {0021-8669},\njournal = {Journal of Aircraft},\nnumber = {5},\npages = {1539--1553},\ntitle = {{Nonlinear Aeroelasticity of a Very Flexible Blended-Wing-Body Aircraft}},\nurl = {http://arc.aiaa.org/doi/10.2514/1.47317},\nvolume = {47},\nyear = {2010}\n}\n@article{Shearer2007,\nauthor = {Shearer, Christopher M. and Cesnik, Carlos E.S.},\ndoi = {10.2514/1.27606},\nisbn = {0021-8669},\nissn = {0021-8669},\njournal = {Journal of Aircraft},\nnumber = {5},\npages = {1528--1545},\ntitle = {{Nonlinear Flight Dynamics of Very Flexible Aircraft}},\nurl = {http://arc.aiaa.org/doi/10.2514/1.27606},\nvolume = {44},\nyear = {2007}\n}\n@article{Teixeira2017,\nauthor = {Teixeira, Patr{\\'{i}}cia C and Cesnik, Carlos E S},\njournal = {International Forum on Aeroelasticity and Structural Dynamics (IFASD)},\nkeywords = {abstract,aerodynamic propeller effects,aerovironments helios,aircraft,although propeller propulsion is,coupled nonlinear,e,etc,g,long-endurance,of such vehicles for,of the propeller slipstream,on the aeroelastic behavior,particle vortex aerodynamics,present in many high-altitude,s x-hale uas,the effect,university of michigan,very flexible wing},\nnumber = {June},\npages = {1--18},\ntitle = {{Inclusion of Propeller Effects on Aeroelastic Behavior of Very Flexible Aircraft}},\nyear = {2017}\n}\n\n@article{Peters1994,\nauthor = {A. Peters, David and J. Johnson, Mark},\nyear = {1994},\nmonth = {01},\npages = {1-28},\ntitle = {Finite-state airloads for deformable airfoils on fixed and rotating wings},\nvolume = {44},\nbooktitle = {American Society of Mechanical Engineers, Aerospace Division (Publication) AD}\n}\n@phdthesis{Skujins2012,\naddress = {Ann Arbor, MI},\nauthor = {Skujins, Torstens},\nbooktitle = {Aerospace Engineering},\npublisher = {University of Michigan},\ntitle = {{Reduced-Order Modeling of Unsteady Aerodynamics Across Multiple Mach Regimes}},\nvolume = {Ph. D.},\nyear = {2012}\n}\n\n@book{geradin2001,\n title={Flexible multibody dynamics: a finite element approach},\n author={G{\\'e}radin, M. and Cardona, A.},\n isbn={9780471489900},\n lccn={00043685},\n year={2001},\n publisher={John Wiley}\n}\n\n@phdthesis{Murua2012,\n title={Flexible aircraft dynamics with a geometrically-nonlinear description of the unsteady aerodynamics},\n author={Murua, Joseba},\n year={2012},\n school={Imperial College London}\n}\n\n@MISC{eigenweb,\n author = {Ga\\\"{e}l Guennebaud and Beno\\^{i}t Jacob and others},\n title = {Eigen v3},\n howpublished = {http://eigen.tuxfamily.org},\n year = {2010}\n }\n @article{Hesse2016,\n doi = {10.2514/1.g000715},\n url = {https://doi.org/10.2514/1.g000715},\n year = {2016},\n month = apr,\n publisher = {American Institute of Aeronautics and Astronautics ({AIAA})},\n volume = {39},\n number = {4},\n pages = {801--813},\n author = {Henrik Hesse and Rafael Palacios},\n title = {Dynamic Load Alleviation in Wake Vortex Encounters},\n journal = {Journal of Guidance, Control, and Dynamics}\n }\n\n@inproceedings{del2019efficient,\n title={Low-Altitude Dynamics of Very Flexible Aircraft},\n author={Del Carre, Alfonso and Palacios, Rafael},\n address={San Diego, California},\n year={2019},\n publisher = {American Institute of Aeronautics and Astronautics},\n doi={10.2514/6.2019-2038},\n crossref={scitech19}\n}\n\n@proceedings{scitech19,\n title={{AIAA SciTech 2019 Forum}},\n publisher = {American Institute of Aeronautics and Astronautics},\n venue={San Diego, California},\n year={2019}\n}\n\n@article{melin2013tornado,\n title={Tornado},\n author={Melin, Tomas},\n journal={KTH, Stockholm, Sweden, Masters Thesis and continued development. {http://www.flyg.kth.se/divisions/aero/software/tornado}},\n year={2013}\n}\n\n@article{Murua2012-2,\nauthor = {Murua, Joseba and Palacios, Rafael and R. Graham, J. Michael},\ntitle = {Assessment of Wake-Tail Interference Effects on the Dynamics of Flexible Aircraft},\njournal = {AIAA Journal},\nvolume = {50},\nnumber = {7},\npages = {1575-1585},\nyear = {2012},\ndoi = {10.2514/1.J051543},\nURL = { \n https://doi.org/10.2514/1.J051543\n},\neprint = { \n https://doi.org/10.2514/1.J051543\n}\n}\n\n@article{Simpson2013-2,\nauthor = {Simpson, Robert J. S. and Palacios, Rafael and Murua, Joseba},\ntitle = {Induced-Drag Calculations in the Unsteady Vortex Lattice Method},\njournal = {AIAA Journal},\nvolume = {51},\nnumber = {7},\npages = {1775-1779},\nyear = {2013},\ndoi = {10.2514/1.J052136},\n\nURL = { \n https://doi.org/10.2514/1.J052136\n \n},\neprint = { \n https://doi.org/10.2514/1.J052136\n \n}\n}\n\n@book{Katz2001,\n title={Low-Speed Aerodynamics},\n author={Katz, J. and Plotkin, A.},\n isbn={9781107717428},\n series={{Cambridge Aerospace Series}},\n year={2001},\n publisher={Cambridge University Press}\n}\n\n@book{etkin1982dynamics,\n title={Dynamics of flight: stability and control},\n author={Etkin, B.},\n isbn={9780471089360},\n lccn={81013058},\n url={https://books.google.co.uk/books?id=4n5TAAAAMAAJ},\n year={1982},\n publisher={John Wiley \\& Sons Australia, Limited}\n}\n\n@inbook{DeMarco2007,\nauthor = {Agostino De Marco and Eugene Duke and Jon Berndt},\ntitle = {A General Solution to the Aircraft Trim Problem},\nbooktitle = {AIAA Modeling and Simulation Technologies Conference and Exhibit},\nchapter = {},\nyear={2007},\npages = {},\ndoi = {10.2514/6.2007-6703},\nURL = {https://arc.aiaa.org/doi/abs/10.2514/6.2007-6703},\neprint = {https://arc.aiaa.org/doi/pdf/10.2514/6.2007-6703}\n}\n\n@book{wiener1950,\n title={Extrapolation, interpolation, and smoothing of stationary time series: with engineering applications},\n author={Wiener, Norbert and Mass.) Massachusetts Institute of Technology (Cambridge},\n year={1950},\n publisher={Technology Press}\n}\n\n@article{broyden1965class,\n title={A class of methods for solving nonlinear simultaneous equations},\n author={Broyden, Charles G},\n journal={Mathematics of computation},\n volume={19},\n number={92},\n pages={577--593},\n year={1965},\n publisher={JSTOR}\n}\n\n@Article{faa,\n title = {Dynamic Gust Loads - {AC 25.341-1}},\n author={{FAA}},\n journal = {{FAA} Advisory Circular},\n year = {2014}\n}\n\n @inproceedings{del2019ifasd,\n title={Nonlinear response of a very flexible aircraft under lateal gust},\n author={Del Carre, Alfonso and Teixeira, Patricia, and Cesnik, Carlos E. S. and Palacios, Rafael},\n booktitle={{IFASD 2019 Forum}},\n address={Savannah, Georgia},\n year={2019},\n publisher = {},\n doi={}\n}\n\n\n@Article{vonKarman1948,\n author = {von K{\\'a}rm{\\'a}n, Theodore},\n title = {Progress in the Statistical Theory of Turbulence.},\n journal = {Proceedings of the National Academy of Sciences of the United States of America},\n year = {1948},\n volume = {11},\n number = {34},\n pages = {530-539},\n issn = {0027-8424},\n}\n\n@article{KaimalEtAl1972,\nauthor = {Kaimal, J. C. and Wyngaard, J. C. and Izumi, Y. and Coté, O. R.},\ntitle = {Spectral characteristics of surface-layer turbulence},\njournal = {Quarterly Journal of the Royal Meteorological Society},\nvolume = {98},\nnumber = {417},\npages = {563-589},\ndoi = {10.1002/qj.49709841707},\nabstract = {Abstract The behaviour of spectra and cospectra of turbulence in the surface layer is described within the framework of similarity theory using wind and temperature fluctuation data obtained in the 1968 AFCRL Kansas experiments. With appropriate normalization, the spectra and cospectra are each reduced to a family of curves which spread out according to z/L at low frequencies but converge to a single universal curve in the inertial subrange. The paper compares these results with data obtained by other investigators over both land and water. Spectral constants for velocity and temperature are determined and the variability in the recent estimates of the constants is discussed. The high-frequency behaviour is consistent with local isotropy. In the inertial subrange, where the spectra fall as n−5/3, the cospectra fall faster: uω and ωθ as n−7/3, and uθ, on the average, as n−5/2. The 4/3 ratio between the transverse and longitudinal spectral levels is observed at wavelengths of the order of the height above ground under unstable conditions and at wavelengths of the order of L/10 under stable conditions. This lower isotropic limit is shown to be governed by the combined effects of shear and buoyancy on small-scale eddies.},\nyear = {1972}\n}\n\n@Article{GonzaleEtAl2018,\n author = {Jes\\'{u}s Gonzalo and Deibi L\\'{o}pez and Diego Dom\\'{i}nguez and Adri\\'{a}n Garc\\'{i}a and Alberto Escapa},\n title = {On the capabilities and limitations of high altitude pseudo-satellites},\n journal = {Progress in Aerospace Sciences},\n year = {2018},\n volume = {98},\n pages = {37 - 56},\n issn = {0376-0421},\n doi = {https://doi.org/10.1016/j.paerosci.2018.03.006},\n abstract = {The idea of self-sustaining air vehicles that excited engineers in the seventies has nowadays become a reality as proved by several initiatives worldwide. High altitude platforms, or Pseudo-satellites (HAPS), are unmanned vehicles that take advantage of weak stratospheric winds and solar energy to operate without interfering with current commercial aviation and with enough endurance to provide long-term services as satellites do. Target applications are communications, Earth observation, positioning and science among others. This paper reviews the major characteristics of stratospheric flight, where airplanes and airships will compete for best performance. The careful analysis of involved technologies and their trends allow budget models to shed light on the capabilities and limitations of each solution. Aerodynamics and aerostatics, structures and materials, propulsion, energy management, thermal control, flight management and ground infrastructures are the critical elements revisited to assess current status and expected short-term evolutions. Stratospheric airplanes require very light wing loading, which has been demonstrated to be feasible but currently limits their payload mass to few tenths of kilograms. On the other hand, airships need to be large and operationally complex but their potential to hover carrying hundreds of kilograms with reasonable power supply make them true pseudo-satellites with enormous commercial interest. This paper provides useful information on the relative importance of the technology evolutions, as well as on the selection of the proper platform for each application or set of payload requirements. The authors envisage prompt availability of both types of HAPS, aerodynamic and aerostatic, providing unprecedented services.},\n keywords = {High altitude platforms, Pseudo-satellite, HAPS, Stratospheric flight, Long endurance, Solar-powered},\n}\n\n@article{Maraniello2019,\n title = {State-Space Realizations and Internal Balancing in Potential-Flow Aerodynamics with Arbitrary Kinematics},\n year = {2019},\n journal = {AIAA Journal},\n author = {Maraniello, Salvatore and Palacios, Rafael},\n number = {6},\n pages = {1--14},\n volume = {57},\n url = {https://arc.aiaa.org/doi/10.2514/1.J058153},\n doi = {10.2514/1.J058153},\n issn = {0001-1452}\n}\n\n@misc{openfast,\n title = {{NWTC Information Portal (OpenFAST)}},\n author = {{National Wind Technology Center (NWTC)}},\n url = {https://nwtc.nrel.gov/OpenFAST},\n note = {Accessed: 2019-11-25}}\n" }, { "path": "docs/JOSS/paper.md", "content": "---\ntitle: 'SHARPy: A dynamic aeroelastic simulation toolbox for very flexible aircraft and wind turbines'\ntags:\n - aeroelasticity\n - structural dynamics\n - aerodynamics\n - solar flight\n - wind energy\nauthors:\n - name: Alfonso del Carre\n orcid: 0000-0002-8133-9481\n affiliation: 1\n - name: Arturo Muñoz-Simón\n orcid: 0000-0003-4840-5392\n affiliation: 1\n - name: Norberto Goizueta\n orcid: 0000-0001-7445-5970\n affiliation: 1\n - name: Rafael Palacios\n orcid: 0000-0002-6706-3220\n affiliation: 1\naffiliations:\n - name: Department of Aeronautics, Imperial College London. London, UK.\n index: 1\ndate: 13 August 2019\nbibliography: paper.bib\n---\n\n# Summary\n\nAeroelasticity is the study of the dynamic interaction between unsteady aerodynamics\nand structural dynamics on flexible streamlined bodies, which may include\nrigid-body dynamics. Industry standard solutions in aeronautics and wind energy\nare built on the assumption of small structural displacements, which lead to linear\nor quasi-linear theories. However, advances in areas such as energy storage and generation,\nand composite material manufacturing have fostered a new kind of aeroelastic\nstructures that may undergo large displacements under aerodynamic forces.\n\nIn particular, solar-powered High-Altitude Long-Endurance (HALE) aircraft\nhave recently seen very significant progress. New configurations\nare now able\nto stay airborne for longer than three weeks at a time.\nExtreme efficiency is achieved by reducing the total weight of the aircraft while\nincreasing the lifting surfaces' aspect ratio.\nIn a similar quest for extreme efficiency, the wind energy industry\nis also trending towards longer and more slender blades, specially for off-shore\napplications, where the largest blades are now close to 100-m long.\n\n\nThese longer and more slender structures can present large deflections and have relatively low frequency structural\nmodes which, in the case of aircraft, can interact with the flight dynamics modes with potentially unstable couplings.\nIn the case of offshore wind turbines, platform movement may generate important rotor excursions that cause complex\naeroelastic phenomena which conventional quasi-linear methods may not accurately capture.\n\n\n``SHARPy`` (Simulation of High-Aspect Ratio aeroplanes in Python) is a dynamic aeroelasticity simulation toolbox for\naircraft and wind turbines. It features a versatile interface and core code written in Python 3, while computationally\nexpensive routines are included in libraries coded in C++ and Modern Fortran. SHARPy is easily extended through a\nmodular object-oriented design, and includes tools for linear and nonlinear analysis of the time-domain aeroelastic\nresponse of flexible bodies in a large number of cases, such as 3-D discrete gust [@del2019ifasd], turbulent field\ninput [@Hesse2016; @deskos2019], control surface deflection and prescribed motion [@del2019efficient]. In addition, linearised\nstate-space models can be obtained for frequency domain analysis, controller design and model reduction.\n\n\nFew open source options are available for nonlinear aeroelastic analysis. A well known code for wind\nenergy is OpenFAST [@openfast], developed at NREL and distributed under\nApache 2.0 license. OpenFAST features a Geometrically-Exact Composite Beam structural\nmodel and an actuator-line based aerodynamic solver. The wake is modelled using\nquasi-steady Blade Element Momentum theory. To the knowledge of the authors,\nno other nonlinear aeroelasticity framework for aircraft is available\nunder open-source terms. An example of a commonly-used aircraft-oriented software\nis ASWING [@Drela1999]. It is based on geometrically nonlinear beams with approximated\nrigid body dynamics. Aerodynamic loads are calculated using a lifting-line\ntheory solver with prescribed coefficients. Lastly, UM/NAST [@del2019ifasd] is a nonlinear\naeroelastic code with GECB and UVLM solvers. However, it is a research code\nwhich has not been released as open source.\n\n\n``SHARPy`` relies only on freely-available open-source dependencies\nsuch as [Paraview](https://paraview.org) for post-processing\nThe computationally\nexpensive routines written in C++ and Fortran have been designed with Fluid-Structure\nInteraction (FSI) problems in mind, resulting in minimal overhead between\nfunction calls.\n\n## Features\nThe [structural model](https://github.com/imperialcollegelondon/xbeam)\nincluded in ``SHARPy`` is a Geometrically-Exact Composite Beam (GECB) [@geradin2001; @Hesse2014a]\nsupports multibody features\nsuch as hinges, joints and absolute and relative nodal velocity constraints through Lagrange Multipliers.\nRigid body motion can be prescribed or simulated. The structural solver supports\ndistributed and lumped mass formulation (or a combination of both). Time-integration\nis carried out using a Newmark-$\\beta$ scheme.\n\nThe [aerodynamic solver](https://github.com/imperialcollegelondon/uvlm) is an Unsteady\nVortex Lattice Method (UVLM) [@Katz2001; @Simpson2013-2].\nIt can simulate an arbitrary number of surfaces together\nwith their interactions. A non conventional force evaluation scheme is used [@Simpson2013-2] in\norder to support large sideslip angles and obtain an induced drag estimation.\nIn addition to this, added mass effects can be obtained and introduced in the\nFSI problem. This can be especially important in the case of very light flexible\naircraft flying at low altitude.\n\nThe coupling algorithm included in the code is designed to allow fully coupled\nnonlinear simulations, although weakly coupled solutions can be obtained. Independent\nstructural or aerodynamic simulation are supported natively.\nThe nonlinear system can also be linearised taking an arbitrary reference condition. The linearised system can be used\nfor frequency domain analysis, linear model order reduction methods and controller design.\n\n![Aerodynamic grid and forces in the static aeroelastic equilibrium configuration on the XHALE aircraft [@del2019ifasd]](https://github.com/ImperialCollegeLondon/sharpy/raw/main/docs/source/_static/XHALE-render.jpg)\n\n\n# Acknowledgements\nA. Carre gratefully acknowledges the support provided by Airbus Defence and Space. Norberto Goizueta's acknowledges and\nthanks the Department of Aeronautics at Imperial College for sponsoring his research.\nArturo Muñoz-Simón's research has received funding from the EU's H2020 research and innovation programme\nunder the Marie Sklodowska-Curie grant agreement 765579.\n\n# References\n" }, { "path": "docs/Makefile", "content": "# Makefile for Sphinx documentation\n#\n\n# You can set these variables from the command line.\nSPHINXOPTS =\nSPHINXBUILD = sphinx-build\nPAPER =\nBUILDDIR = build\n\n# Internal variables.\nPAPEROPT_a4 = -D latex_paper_size=a4\nPAPEROPT_letter = -D latex_paper_size=letter\nALLSPHINXOPTS = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) source\n# the i18n builder cannot share the environment and doctrees with the others\nI18NSPHINXOPTS = $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) source\n\n.PHONY: help\nhelp:\n\t@echo \"Please use \\`make ' where is one of\"\n\t@echo \" html to make standalone HTML files\"\n\t@echo \" dirhtml to make HTML files named index.html in directories\"\n\t@echo \" singlehtml to make a single large HTML file\"\n\t@echo \" pickle to make pickle files\"\n\t@echo \" json to make JSON files\"\n\t@echo \" htmlhelp to make HTML files and a HTML help project\"\n\t@echo \" qthelp to make HTML files and a qthelp project\"\n\t@echo \" applehelp to make an Apple Help Book\"\n\t@echo \" devhelp to make HTML files and a Devhelp project\"\n\t@echo \" epub to make an epub\"\n\t@echo \" epub3 to make an epub3\"\n\t@echo \" latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter\"\n\t@echo \" latexpdf to make LaTeX files and run them through pdflatex\"\n\t@echo \" latexpdfja to make LaTeX files and run them through platex/dvipdfmx\"\n\t@echo \" text to make text files\"\n\t@echo \" man to make manual pages\"\n\t@echo \" texinfo to make Texinfo files\"\n\t@echo \" info to make Texinfo files and run them through makeinfo\"\n\t@echo \" gettext to make PO message catalogs\"\n\t@echo \" changes to make an overview of all changed/added/deprecated items\"\n\t@echo \" xml to make Docutils-native XML files\"\n\t@echo \" pseudoxml to make pseudoxml-XML files for display purposes\"\n\t@echo \" linkcheck to check all external links for integrity\"\n\t@echo \" doctest to run all doctests embedded in the documentation (if enabled)\"\n\t@echo \" coverage to run coverage check of the documentation (if enabled)\"\n\t@echo \" dummy to check syntax errors of document sources\"\n\n.PHONY: clean\nclean:\n\trm -rf $(BUILDDIR)/*\n\n.PHONY: html\nhtml:\n\t$(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html\n\t@echo\n\t@echo \"Build finished. 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Dummy builder generates no files.\"\n" }, { "path": "docs/docignore.yml", "content": "# Docs to build list\n# once this is fully implemented this will become the file that specifies which packages are to be ignored for the\n# purposes of building documentation\npackages:\n - folder: 'sharpy/controllers'\n docs_folder: 'controllers'\n - folder: 'sharpy/rom'\n docs_folder: 'rom'\n\nmodules:\n - 'sharpy/postproc'\n - 'sharpy/solvers'\n - 'sharpy/linear/dev'\n - 'sharpy/linear/src/uvlmutils.py'\n - 'sharpy/aero/utils/uvlmlib.py'\n - 'sharpy/aero/utils/utils.py'\n - 'sharpy/utils/plot_utils.py'\n - 'sharpy/utils/solver_interface.py'\n - 'sharpy/linear/test'\n - 'sharpy/linear/utils'\n# - 'sharpy/generators'\n - 'sharpy/presharpy'\n - 'sharpy/lib'\n - 'sharpy/__pycache__'\n" }, { "path": "docs/requirements_rtd", "content": "sphinx>=3.0,<7\nipykernel\nnbsphinx\nsphinx-rtd-theme>=1.2.2\nrecommonmark\n" }, { "path": "docs/source/_static/.placeholder", "content": "" }, { "path": "docs/source/_static/sharpy_guide/sharpy_intro.html", "content": "\r\n\r\n\r\nsharpy_intro\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n \r\n \r\n \r\n \r\n\r\n \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
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Introduction to SHARPy

Version: June 2019

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Overview

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SHARPy (Simulation of High Aspect Ratio Planes in Python is a framework for linear and nonlinear aeroelastic analysis of flexible structures.

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It is developed by the Loads Control and Aeroelasticity lab at the Department of Aeronautics. All the code is open source and readily available in GitHub.

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Important links:

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Loads Control and Aeroelasticity lab\r\nhttps://imperial.ac.uk/aeroelastics

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Main github repository\r\nhttps://github.com/imperialcollegelondon/sharpy

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Documentation(!!!)\r\nhttps://ic-sharpy.readthedocs.io

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UVLM solver (C++)\r\nhttps://github.com/imperialcollegelondon/uvlm

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Structural solver (Fortran)\r\nhttps://github.com/imperialcollegelondon/xbeam

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SHARPy is mainly coded in Python, but the expensive routines, such as aero and structural solvers are coded in faster languages such as C++ and Fortran.

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A number of different structures and analysis methods can be run. For example:

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Very flexible aircraft nonlinear aeroelasticity (Alfonso)

The modular design of SHARPy allows to simulate complex aeroelastic cases involving very flexible aircraft. The structural solver supports very complex beam arrangements, while retaining geometrical nonlinearity. The UVLM solver features different wake modelling fidelities while supporting large lifting surface deformations in a native way.

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Among the problems studied, a few interesting ones, in no particular order are:

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  • Catapult take off of a very flexible aircraft analysis [Paper]. In this type of simulations, a PID controller was used in order to enforce displacements and velocities in a number of structural nodes (the clamping points). Then, several take off strategies were studied in order to analyse the influence of the structural stiffness in this kind of procedures. This case is a very good example of the type of problems where nonlinear aerolasticity is essential.
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  • Flight in full 3D atmospheric boundary layer (to be published). A very flexible aircraft is flown immersed in a turbulent boundary layer obtained from HPC LES simulations. The results are compared against simpler turbulence models such as von Karman and Kaimal. Intermittency and coherence features in the LES field are absent or less remarkable in the synthetic turbulence fields.
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  • Lateral gust reponse of a realistic very flexible aircraft. For this problem (to be published), a realistic very flexible aircraft (University of Michigan X-HALE) model has been created in SHARPy and validated against their own aeroelastic solver for static and dynamic cases. A set of vertical and lateral gust responses have been simulated. (Results to be presented at IFASD 2019).
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Wind turbine aeroelasticity (Arturo)

SHARPy is suitable to simulate wind turbine aeroelasticity.

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On the structural side, it accounts for material anisotropy which is needed to characterize composite blades and for geometrically non-linear deformations observed in current blades due to the increasing length and flexibility. Both rigid and flexible simulations can be performed and the structural modes can be computed accounting for rotational effects (Campbell diagrams). The rotor-tower interaction is modelled through a multibody approach based on the theory of Lagrange multipliers. Finally, he tower base can be fixed or subjected to prescribed linear and angular velocities.

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On the aerodynamic side, the use of potential flow theory allows the characterization of flow unsteadiness at a reasonable computational cost. Specifically, steady and dynamic simulations can be performed. The steady simulations are carried out in a non-inertial frame of reference linked to the rotor under uniform steady wind with the assumption of prescribed helicoidal wake. On the other hand, dynamic simulations can be enriched with a wide variety of incoming winds such as shear and yaw. Moreover, the wake shape can be freely computed under no assumptions accounting for self-induction and wake expansion or can be prescribed to an helicoidal shape for computational efficiency.

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PD: aft-loaded airfoils can be included through the definition of the camber line of the blades.

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Model Order Reduction

Numerical models of physical phenomena require fine discretisations to show convergence and agreement with their real\r\ncounterparts, and, in the case of SHARPy's aeroelastic systems, hundreds of thousands of states are not an uncommon\r\nencounter. However, modern hardware or the use of these models for other applications such as controller synthesis may limit\r\ntheir size, and we must turn to model order reduction techniques to achieve lower dimensional representations that can\r\nthen be used.

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SHARPy offers several model order reduction methods to reduce the initially large system to a lower dimension,\r\nattending to the user's requirements of numerical efficiency or global error bound.

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Krylov Methods for Model Order Reduction - Moment Matching

Model reduction by moment matching can be seen as approximating a transfer function through a power series expansion about a user defined point in the complex plane. The reduction by projection retains the moments between the full and reduced systems as long as the projection matrices span certain Krylov subspaces dependant on the expansion point and the system's matrices.\r\nThis can be taken advantage of,\r\nin particular for aeroelastic applications where the interest resides in the low frequency behaviour of the system,\r\nthe ROM can be expanded about these low frequency points discarding accuracy higher up the frequency spectrum.

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Example 1 - Aerodynamics - Frequency response of a high AR flat plate subject to a sinusoidal gust

The objective is to compare SHARPy's solution of a very high aspect ratio flat plate subject to a sinusoidal gust to\r\nthe closed form solution obtained by Sears (1944 - Ref). SHARPy's inherent 3D nature makes comparing results to the 2D\r\nsolution require very high aspect ratio wings with fine discretisations, resulting in very large state space models.\r\nIn this case, we would like to utilise a Krylov ROM to approximate the low frequency behaviour and perform a frequency\r\nresponse analysis on the reduced system, since it would represent too much computational cost if it were performed on\r\nthe full system.

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The full order model was reduced utilising Krylov methods, in particular the Arnoldi iteration, with an expansion about\r\nzero frequency to produce the following result.

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As it can be seen from the image above, the ROM approximates well the low frequency, quasi-steady state and loses\r\naccuracy as the frequency is increased, just as intended. Still, perfect matching is never achieved even at the\r\nexpansion frequency given the 3D nature of the wing compared to the 2D analytical solution.

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Example 2 - Aeroelastics - Flutter analysis of a Goland wing with modal projection

The Goland wing flutter example is presented next. The aerodynamic surface is finely discretised for the UVLM solution,\r\nresulting in not only a large state space but also in large input/output dimensionality. Therefore, to reduce the\r\nnumber of inputs and outputs, the UVLM is projected onto the structural mode shapes, the first four in this particular\r\ncase. The resulting multi input multi output system (mode shapes -> UVLM -> modal forces) was subsequently reduced using\r\nKrylov methods aimed at MIMO systems which use variations of the block Arnoldi iteration. Again, the expansion\r\nfrequency selected was the zero frequency. As a sample, the transfer function from two inputs to two outputs is\r\nshown to illustrate the performance of the reduced model against the full order UVLM.

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The reduced aerodynamic model projected onto the modal shapes was then coupled to the linearised beam model, and the\r\nstability analysed against a change in velocity. Note that the UVLM model and its ROM are actually scaled to be\r\nindependent on the freestream velocity, hence only one UVLM and ROM need to be computed. The structural model needs\r\nto be updated at each test velocity but its a lot less costly in computational terms. The resulting stability of the\r\naeroelastic system is plotted on the Argand diagram below with changing freestream velocity.

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Flutter speed [m/s]Frequency [rad/s]
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SHARPy installation

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Check https://ic-sharpy.readthedocs.io/en/latest/content/installation.html for an in-depth guide on how to install SHARPy.

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This assumes a few things about your computer:

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  • It is Linux or MacOS (definitely not Windows - if you only have Windows, check VirtualBox and make an Ubuntu or CentOS virtual machine).

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  • It has an up-to-date compiler (this might not be straightforward, run g++ --version. If lower than 5.0, you will need to update it). An up-to-date Intel Compiler for C++ and Fortran is a good option as well.

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SHARPy relies on Anaconda https://www.anaconda.com/distribution/ to handle all the python packages. Install the Python 3 version.

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You then need to download the code:

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1) Create a folder. Here it will be called code

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mkdir code\r\ncd code\r\n
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2) Clone all the necessary repos and make sure you are in the correct branch -- usually develop

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git clone https://github.com/imperialcollegelondon/sharpy --branch=develop\r\ngit clone https://github.com/imperialcollegelondon/xbeam --branch=develop\r\ngit clone https://github.com/imperialcollegelondon/uvlm --branch=develop\r\n
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3) Create the conda environment and activate it

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conda env create -f sharpy/utils/environment_linux.yml\r\n
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(or environment_macos.yml if on MacOS.

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Now activate the conda environment

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conda activate sharpy_env you are going to have to do this every time to start a new terminal and want to run SHARPy

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It sometimes fails in the pip stage when installing. If it says something about distwheel failed in mayavi, activate the environment and run pip install mayavi manually.

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4) Compile xbeam and uvlm.

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Move to the xbeam folder (cd xbeam) and run sh run_make.sh. Wait until it finishes. Please make sure your anaconda env is active before running this.

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Now the same for uvlm: cd ../uvlm and sh run_make.sh.

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5) SHARPy is now hopefully ready to go!

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Navigate to the sharpy folder: cd ../sharpy and run:

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source bin/sharpy_vars.sh\r\n
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This command is important, as it loads the program in the terminal variables.

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We can run the tests now:

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python -m unittest\r\n
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If everything has been installed properly, the tests should pass.

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----------------------------------------------------------------------\r\nRan 28 tests in 23.465s\r\n\r\nOK\r\n
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Remember to run every time you start a new terminal:

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conda activate sharpy_env\r\nsource <path-to-sharpy>/bin/sharpy_vars.sh\r\n
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Tip: edit your ~\\.bashrc (linux) or \\.bash_profile (MacOS) and add the following:

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alias load_sharpy="conda activate sharpy_env && source <path-to-sharpy>/bin/sharpy_vars.sh"\r\n# Remember to modify the <path-to-sharpy> gap with your path\r\n
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Then you just need to run in the console load_sharpy to load everything in one go.

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Basic cases

A cantilever beam (Geradin)

This case can be found in sharpy/tests/xbeam/geradin, it is part of the test suite.

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Basically, it is a 5 metres long cantilevered beam with a mass at the tip. Stiffness properties: $\\mathcal{S} = \\mathrm{diag}(EI, GA_y, GA_z, GJ, EI_y, EI_z) = \\mathrm{diag}(4.8e8, 3.231e8, 3.231e8, 1e6, 9.346e6, 9.346e6)$

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There is no distributed mass, only one at the tip. $M = 6e5/9.81$.

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The main point about the Geradin beam is that the deflections are past the linear range.

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If you open sharpy/tests/xbeam/geradin/generate_geradin.py, you are going to see a basic input file for a structural only case.

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The last part is the one that is the most important (function generate_solver_file from line 134). This is where the solver settings and the overall flow of the program is given.

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  • The flow variable controls the solvers and postprocessors that are going to be run in this simulation (and in which order). When you run sharpy with a valid header file, you will see a complete list of available solvers:
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--------------------------------------------------------------------------------\r\n            ######  ##     ##    ###    ########  ########  ##    ##\r\n           ##    ## ##     ##   ## ##   ##     ## ##     ##  ##  ##\r\n           ##       ##     ##  ##   ##  ##     ## ##     ##   ####\r\n            ######  ######### ##     ## ########  ########     ##\r\n                 ## ##     ## ######### ##   ##   ##           ##\r\n           ##    ## ##     ## ##     ## ##    ##  ##           ##\r\n            ######  ##     ## ##     ## ##     ## ##           ##\r\n--------------------------------------------------------------------------------\r\nAeroelastics Lab, Aeronautics Department.\r\n    Copyright (c), Imperial College London.\r\n    All rights reserved.\r\nRunning SHARPy from /home/ad214/run/code/sharpy/tests/xbeam/geradin\r\nSHARPy being run is in /home/ad214/run/code/sharpy\r\nThe branch being run is develop\r\nThe version and commit hash are: v0.1-731-g85eb5ab-85eb5ab\r\nThe available solvers on this session are:\r\nPreSharpy\r\nAerogridLoader\r\nBeamLoader\r\nModal\r\nNonLinearDynamic\r\nNonLinearDynamicCoupledStep\r\nNonLinearDynamicPrescribedStep\r\nNonLinearStatic\r\nPIDTrajectoryControl\r\nPrescribedUvlm\r\nStaticCoupled\r\nStaticTrim\r\nStaticUvlm\r\nStepUvlm\r\nTrim\r\nRigidDynamicPrescribedStep\r\nDynamicUVLM\r\nStepLinearUVLM\r\nStaticLinearUvlm\r\nInitializeMultibody\r\nLagrangeMultipliersTrajectoryControl\r\nNonLinearDynamicMultibody\r\nSHWUvlm\r\nStaticCoupledRBM\r\nSteadyHelicoidalWake\r\nDynamicCoupled\r\nAeroForcesCalculator\r\nAerogridPlot\r\nBeamLoads\r\nBeamPlot\r\nCleanup\r\nSaveData\r\nStallCheck\r\nWriteVariablesTime\r\nPlotFlowField\r\nCreateSnapshot\r\nLiftDistribution
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For our simple structural simulation, we only need a few blocks: BeamLoader for reading the input file and generating the beam data structure, NonLinearStatic is the structural solver for nonlinear, static beams, BeamPlot outputs the deformed shape and other quantities to a Paraview file structure (more on this later), and WriteVariablesTime outputs the data we want to text files.

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  • The case is a name for the simulation so we can identify results.

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  • The route is the path to the .sharpy file, so that SHARPy can find all the other necessary files.

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Then, the other parts of the .sharpy (or .sharpy) file are based on the following structure:

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[Header_name]\r\nvariable1 = 1\r\nvariable2 = a\r\nvariable3 = [a, a, b]
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It is important to note that you need a header per every solver indicated in flow. If that solver needs no settings, you still need to indicate the header.

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There is also a main [SHARPy] header that contains the main program settings, such as the flow and the case. It also has a setting called write_screen. It is equal to off because this is a test case, and you don't want tons of output. If you modify it to 'on', you'll be able to see what's going on on the screen.

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Simple modifications of the case

If we want to (for example), run a stiffer beam, we can do so easily:

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Open generate_geradin.py and move to line 50 more or less where there are a few lines looking like:

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ea = ...\r\nga = ...\r\n#...\r\nei = ...\r\n
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and modify them to look like:

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stiffness_multiplier = 10\r\nea = ... * stiffness_multiplier\r\nga = ... * stiffness_multiplier\r\n#...\r\nei = ... * stiffness_multiplier\r\n
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you can also change the name of the case so that the results are not overwritten:\r\nIn line 6, case_name = geradin_stiff.

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Now run again the case. First, generate the files: python generate_geradin.py, and then run the case sharpy geradin_stiff.sharpy.

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You can now have a look at the wing tip deformations for both cases in output/<case_name>/WriteVariablesTime/struct_pos_node-1.dat.

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Guide to model definition in SHARPy

This section will take a bit of time and is quite tough to follow, but keep this as a reference.

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Structural data

The case.fem.h5 file has several components. We go one by one:

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  • num_node_elem [int] is always 3 in our case (3 nodes per structural elements - quadratic beam elements).

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  • num_elem [int] number of structural elements.

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  • num_node [int] number of nodes. For simple structures, it is num_elem*(num_node_elem - 1) - 1. For more complicated ones, you need to calculate it properly.

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  • coordinates [num_node, 3] coordinates of the nodes in body-attached FoR.

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  • connectivites [num_elem, num_node_elem] a tricky one. Every row refers to an element, and the three integers in that row are the indices of the three nodes belonging to that elem. Now, the catch: the ordering is not as you'd think. Order them as $[0, 2, 1]$. That means, first one, last one, central one. The following image shows the node indices inside the circles representing the nodes, the element indices in blue and the resulting connectivities matrix next to it.\r\nConnectivities are tricky when considering complex configurations. Pay attention at the beginning and you'll save yourself a lot of trouble.

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  • stiffness_db [:, 6, 6] database of stiffness matrices. The first dimension has as many elements as different stiffness matrices are in the model.

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  • elem_stiffness [num_elem] array of indices (starting at 0). Basically, it links every element (index) to the stiffness matrix index in stiffness_db. For example elem_stiffness[0] = 0; elem_stiffness[2] = 1 means that the element 0 has a stiffness matrix equal to stiffness_db[0, :, :], and the second element has a stiffness matrix equal to stiffness_db[1, :, :].

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The shape of a stiffness matrix, $\\mathrm{S}$ is:\r\n$$\\mathrm{S} = \\begin{bmatrix}\r\nEA & & & & & \\\\\r\n & GA_y & & & & \\\\\r\n & & GA_z & & & \\\\\r\n & & & GJ & & \\\\\r\n & & & & EI_y & \\\\\r\n & & & & & EI_z \\\\\r\n\\end{bmatrix}\r\n$$\r\nwith the cross terms added if needed.

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  • mass_db and elem_mass follow the same scheme than the stiffness, but the mass matrix is given by:\r\n$$\\mathrm{M} = \\begin{bmatrix}\r\nm\\mathbf{I} & -\\tilde{\\xi}_{cg}m \\\\\r\n\\tilde{\\xi}_{cg}m & J\\\\\r\n\\end{bmatrix}\r\n$$\r\nwhere $m$ is the distributed mass per unit length [kg/m], $\\tilde{\\bullet}$ is the skew-symmetric matrix of a vector and $\\xi_{cg}$ is the location of the centre of gravity with respect to the elastic axis in MATERIAL (local) FoR.
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And what is the Material FoR? This is an important point, because all the inputs that move WITH the beam are in material FoR. For example: follower forces, stiffness, mass, lumped masses...

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The material frame of reference is noted as $B$. Essentially, the $x$ component is tangent to the beam in the increasing node ordering, $z$ looks up generally and $y$ is oriented such that the FoR is right handed.

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In the practice (vertical surfaces, structural twist effects...) it is more complicated than this. The only sure thing about $B$ is that its $x$ direction is tangent to the beam in the increasing node number direction. However, with just this, we have an infinite number of potential reference frames, with $y$ and $z$ being normal to $x$ but rotating around it. The solution is to indicate a for_delta, or frame of reference delta vector ($\\Delta$).

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Now we can define unequivocally the material frame of reference. With $x_B$ and $\\Delta$ defining a plane, $y_b$ is chosen such that the $z$ component is oriented upwards with respect to the lifting surface.

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From this definition comes the only constraint to $\\Delta$: it cannot be parallel to $x_B$.

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  • frame_fo_reference_delta [num_elem, num_node_elem, 3] contains the $\\Delta$ vector in body-attached ($A$) frame of reference. As a rule of thumb:\r\n$$\\Delta = \\left\\{ \r\n\\begin{matrix}\r\n[-1, 0, 0], \\quad \\text{if right wing} \\\\\r\n[1, 0, 0], \\quad \\text{if left wing} \\\\\r\n[0, 1, 0], \\quad \\text{if fuselage} \\\\\r\n[-1, 0, 0], \\quad \\text{if vertical fin} \\\\\r\n\\end{matrix}\r\n\\right.\r\n$$
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These rules of thumb only work if the nodes increase towards the tip of the surfaces (and the tail in the case of the fuselage).

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  • structural_twist [num_elem, num_node_elem] is technically not necessary, as the same effect can be achieved with FoR_delta. CAUTION previous versions of SHARPy had structural twist defined differently:
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structural_twist = np.zeros((num_node, num_node_elem)) # this is wrong now, and will trigger and error in SHARPy, change it!\r\nstructural_twist = np.zeros((num_elem, num_node_elem)) # this is right.\r\n
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  • boundary_conditions [num_node] is an array of integers (np.zeros((num_node, ), dtype=int)) and contains all 0 EXCEPT FOR:

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  • beam_number [num_elem] is another array of integers. Usually you don't need to modify its value. Leave it at 0.

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  • app_forces [num_elem, 6] contains the applied forces app_forces[:, 0:3] and moments app_forces[:, 3:6] in a given node. Important points: the forces are given in Material FoR (check above). That means that in a symmetrical model, a thrust force oriented upstream would have the shape $[0, T, 0, 0, 0, 0]$ in the right wing, while the left would be $[0, -T, 0, 0, 0, 0]$. Likewise, a torsional moment for twisting the wing leading edge up would be $[0, 0, 0, M, 0, 0]$ for the right, and $[0, 0, 0, -M, 0, 0]$ for the left. But careful, because an out-of-plane bending moment (wing tip up) has the same sign (think about it).

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  • lumped_mass [:] is an array with as many masses as needed (in kg this time). Their order is important, as more information is required to implement them in a model.

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  • lumped_mass_nodes [:] is an array of integers. It contains the index of the nodes related to the masses given in lumped_mass in order.

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  • lumped_mass_inertia [:, 3, 3] is an array of 3x3 inertial tensors. The relationship is set by the ordering as well.

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  • lumped_mass_position [:, 3] is the relative position of the lumped mass wrt the node (given in lumped_masss_nodes) coordinates. ATTENTION: the lumped mass is solidly attached to the node, and thus, its position is given in Material FoR.

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Aerodynamic data

All the aero data is contained in case.aero.h5.

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It is important to know that the input for aero is usually based on elements (and inside the elements, their nodes). This causes sometimes an overlap in information, as some nodes are shared by two adjacent elements (like in the connectivities graph in the previous section). The easier way of dealing with this is to make sure the data is consistent, so that the properties of the last node of the first element are the same than the first node of the second element.

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Item by item:

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  • In the aero.h5 file, there is a Group called airfoils. The airfoils are stored in this group (which acts as a folder) as a two-column matrix with $x/c$ and $y/c$ in each column. They are named '0', '1', and so on.

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  • chords [num_elem, num_node_elem] is an array with the chords of every airfoil given in an element/node basis.

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  • twist [num_elem, num_node_elem] has the twist angle in radians. It is implemented as a rotation around the local $x$ axis.

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  • sweep [num_elem, num_node_elem] same here, just a rotation around $z$.

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  • airfoil_distribution_input [num_elem, num_node_elem] contains the indices of the airfoils that you put previously in airfoils

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  • surface_distribution_input [num_elem] is an integer array. It contains the index of the surface the element belongs to. Surfaces need to be continuous, so please note that if your beam numbering is not continuous, you need to make a surface per continuous section.

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  • surface_m [num_surfaces] is an integer array with the number of chordwise panels for every surface.

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  • m_distribution [string] is a string with the chordwise panel distribution. In almost all cases, leave it at uniform.

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  • aero_node_input [num_node] is a boolean (True/False) array that indicates if that node has a lifting surface attached to it.

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  • elastic_axis [num_elem, num_node_elem] indicates the elastic axis location with respect to the leading edge as a fraction of the chord of that rib. Note that the elastic axis is already determined, as the beam is fixed now, so this settings controls the location of the lifting surface wrt the beam.

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  • control_surface [num_elem, num_node_elem] is an integer array containing -1 if that section has no control surface associated to it, and 0, 1, 2 ... if the section belongs to the control surface 0, 1, 2 ... respectively.

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  • control_surface_type [num_control_surface] contains 0 if the control surface deflection is static, and 1 is it is dynamic (if you need to run dynamic control surfaces, come see me).

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  • control_surface_chord [num_control_surface] is an INTEGER array with the number of panels belonging to the control surface. For example, if $M = 4$ and you want your control surface to be $0.25c$, you need to put 1.

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  • control_surface_hinge_coord [num_control_surface] only necessary for lifting surfaces that are deflected as a whole, like some horizontal tails in some aircraft. Leave it at 0 if you are not modelling this. If you are, come see me.

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Common solver settings

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The solver settings are covered almost entirely in the documentation (again: https://ic-sharpy.readthedocs.io). I'm going to explain in more detail the important ones. The defaults settings are generally good enough for a majority of cases.

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BeamLoader

BeamLoader reads the solver.txt and the fem.h5 files and generates the beam data structure. Its settings are simple:

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AerogridLoader

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  • mstar number of chordwise panels for the wake. A good value is $$M^* = \\frac{L_{\\mathrm{wake}}}{\\Delta t u_\\infty}$$, which means that the wake panels are the same size as the main wing ones.

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  • freestream_dir is a different approach to modifying the attitude angles. I'd leave alone unless you really need it.

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NonLinearStatic

The static beam solver settings. Important ones:

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  • max_iterations maximum number of iterations for the structural solver. These are not the same as the ones in DynamicCoupled.

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  • num_load_steps if > 1, the applied forces and gravity are applied progressively in several steps in order to avoid numerical divergence. Leave it at 1 unless you have problems with convergence of static cases.

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  • delta_curved leave it at $1e-1$.

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  • min_delta this one is more tricky. Usually $1e-6$ works well for flexible structures. If you are running more stiff stuff, you might need to lower it even more. Don't go under $1e-11$. If you don't know, start at $1e-6$, note the wing tip deflection and lower it even more. A too low value will cause the beam solver to reach max_iterations without convergence. When this happens, note the residual value and set something larger than that.

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  • gravity_on on if gravity, off if not.

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  • gravity $9.81$ if you are on Earth. Setting it to 0 is the same as gravity_on = off, but the latter is quicker.

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StaticUvlm

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  • horseshoe if this is on, mstar (in AerogridLoader) has to be 1. It controls the wake modelling. Usual wakes with mstar > 1 are discretised and are of finite length. The horsehoe modelling is derived from the analytical expansion of an discretised wake of infinite length. ATTENTION: use only in static simulations.

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  • n_rollup how many steps are carried out to convect the wake with full free-wake. This usually should be 0, but if you want a pretty picture, you can use n_rollup = int(mstar*1.5).

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  • rollup_dt if n_rollup > 0, set rollup_dt to \r\n$$\r\n\\Delta t_{\\mathrm{rollup}} = \\frac{c/M}{u_\\infty}\r\n$$

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  • 'velocity_field_generator' a few options available here. This paragraph is applicable to every aero solver that has a velocity_field_generator setting.

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    • SteadyVelocityField: quite straightforward. Give a u_inf value in u_inf and a direction in u_inf_direction.
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    • GustVelocityField: this one generate gusts in several profiles. The ones you will probably use: gust_shape: '1-cos', or 'continuous_sin'.
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      • u_inf and u_inf_direction already explained
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      • gust_length: equvalent to $2H$ in metres.
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      • gust_intensity: reference (peak) velocity of the gust, in m/s.
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      • offset x coord. of the first point of the gust with respect to the $[0, 0, 0]$ in inertial.
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      • span: span of the aircraft (you are probably not going to use this, it is implemented for DARPA gusts).
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    • VelocityFieldGenerator: a full unsteady 3D field of velocities is input. Ask me if you want to use it.
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StaticCoupled

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  • print_info: set it to on in almost all cases.
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  • structural_solver and aero_solver: these are strings with the name of the structural and aerodynamic solvers you want to use for the coupled simulation. A solver with that name needs to exist in SHARPy (check the list of available solvers at the start of a simulation).
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  • structural_solver_settings and aero_solver_settings: a dictionary (each) that is basically the same you added before if you wanted to run a standalone structural or aero simulation. A code example:
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settings = dict()\r\nsettings['NonLinearStatic'] = {\r\n    'print_info': 'on',\r\n    'max_iterations': 150\r\n    # ...\r\n}\r\nsettings['StaticUvlm'] = {\r\n    'print_info': 'on',\r\n    'horseshoe': 'off'\r\n    # ...\r\n}\r\n\r\nsettings['StaticCoupled'] = {\r\n    'structural_solver': 'NonLinearStatic',\r\n    'structural_solver_settings': settings['NonLinearStatic'],\r\n    'aero_solver': 'StaticUvlm',\r\n    'aero_solver_settings': settings['StaticUvlm'],\r\n    # ...\r\n
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  • max_iter: max number of FSI iterations
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  • n_load_steps: if > 1, it ramps the aero and gravity forces slowly to improve convergence. Leave at 0 unless you really need it, then try 4 or 5.
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  • tolerance: threshold for convergence of the FSI iteration. Make sure you are choosing a reasonable value for the case. If it converges in 1 iteration: lower it. If it takes more than 10: unless it is a very complicated case (next to flutter or overspeed conditions), lower it.
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  • relaxation_factor a real number $\\omega \\in [0, 1)$. $\\omega = 0$ means no relaxation, $\\omega \\to 1$ means every iteration affects very little to the state of the system. Usually 0.3 is a good value. If you are (again) close to overspeed, flutter... you are going to need to raise it to 0.6 or even more.
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Static trim

This solver acts like a wrapper of StaticCoupled, just like StaticCoupled is a wrap for the structural and aero solver. That means that when we initialise the StaticTrim solver, we also create a StaticCoupled, a NonlinearStatic and a StaticUvlm instance.

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It is important to know that StaticTrim only trims the longitudinal variables ($F_x, F_z, M_y$) by modifying the angle of attack, tail deflection and thrust. No lateral/directional variables are considered.

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  • solver: probably you want StaticCoupled
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  • solver_settings: most likely, something similar to settings['StaticCoupled]`.
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  • initial_alpha, initial_deflection, initial_thrust: initial values for the angle of attack, elevator deflection and thrust per engine.
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DynamicCoupled

This is where things get interesting. DynamicCoupled performs the time stepping and FSI iteration processes. Just as StaticCoupled, it requires a structural solver (for free-flight elastic aircraft it will be NonLinearDynamicCoupledStep, ask for others), and an aero solver, which will be StepUvlm.

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The structural_solver and structural_solver_settings (and the aero equivalents) are set up the same way I showed in the StaticCoupled.

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  • fsi_substeps: max iterations in FSI loop
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  • fsi_tolerance: quite descriptive. What I said for the static coupled tolerance still applies.
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  • relaxation_factor: exactly the same. There are more settings to control the relaxation, and make it vary as the simulation progresses, but you probably won't need it.
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  • minimum_steps: minimum FSI steps to run even if convergence is reached.
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  • n_time_steps: quite descriptive.
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  • dt: $\\Delta t$
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  • include_unsteady_force_contribution: this activates the added mass effects calculation. It is good to have it, but it makes the simulation a bit more challenging from a numerical point of view. Run some numbers by hand and decide if it is worth it. Removing this contribution makes the code faster.
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  • postprocessors: the fun begins. postprocessors are modules run every time step after convergence. For example, to calculate the beam loads, or output to paraview. This variable is an array of strings (['one_module', 'another_module']) and the modules are run in the order they are indicated. A typical workflow would be:
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'postprocessors': [\r\n    'BeamLoads',     # Calculate the loads at every beam element\r\n    'BeamPlot',      # Output the beam data to paraview (including the beam loads - that's why beamloads goes first)\r\n    'AerogridPlot',  # Output the aero grid to paraview\r\n]\r\n
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  • postprocessor_settings: hopefully by this time you already get the _settings thing. I won't explain the settings of the processors here, you can do it in the code.
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NonLinearDynamicCoupledStep

Almost same settings as NonLinearStatic, so I'm going to explain only the settings that are different.

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  • newmark_damp: artificial damping parameter. Increasing this damps the higher frequencies while leaving the low frequency modes relatively untouched (please note the relatively). Start with $5\\times 10^{-4}$ an increase it if needed. No more than $10^{-2}$.
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  • num_steps: number of time steps
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  • dt: $\\Delta t$
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  • initial_velocity: if you want to aircraft to fly with a velocity, this is the place to put it. Instead, you can leave it at 0 and put the velocity as a u_inf contribution. Results will be the same.
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StepUvlm

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  • convection_scheme: you probably want to leave it at 2. This convects the wake with the background flow (no influence from the aircraft). 3 is a full free-wake, which looks very good, takes very long and results don't change if compared to 2 in most of the cases.
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  • gamma_dot_filtering: if you added the unsteady_forces_contribution in DynamicCoupled, you probably want to put 7 or 9 here. If not, it won't be considered.
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A very short intro to the Command Line

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The command line is where you are going to spend quite a lot of your time. Make your life easier and learn how to use it.

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When you open a terminal, the default location to land is your HOME folder. In the terminal, your home folder is identified as ~ or $HOME.

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You can navigate to the folder of your choice using cd (change directory) for example, if you want to go to Downloads:

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cd Downloads\r\n
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Extra tip: write cd Dow and press Tab to autocomplete.

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If you haven't created the folder you want to move to, you can make dir: mkdir. For example, to create a folder called Code in you Home directory:

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# go to your home folder if you are not there yet\r\ncd ~ # or `cd ` or `cd $HOME`, all equivalent\r\n\r\n# create the dir\r\nmkdir Code\r\n
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If you have a file in Downloads called very_private_stuff.txt, you can copy it (cp) or move it (mv) to your Code folder:

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cd Code\r\n\r\n# copy it\r\ncp ../Downloads/very_private_stuff.txt ./\r\n\r\n# or move it\r\nmv  ../Downloads/very_private_stuff.txt ./\r\n
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Things that require explanation:

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  • .. denotes the parent folder of a location. For example: ../Downloads means \"go to the previous folder and then to Downloads\"
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  • . (a single period) denotes the current location. For example: ./ means \"right here\"
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You can also use mv to rename files:

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mv very_private_stuff.txt homework.txt\r\n
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If you want copy a folder, you need to add -r (this is called a flag) after cp. Example: we have a folder in Downloads called justin_bieber_complete_discography and we want to copy it to Music and call it arctic_monkeys instead:

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cd ~\r\nmkdir Music\r\n\r\n# note the space between cp and -r\r\ncp -r Downloads/justin_bieber_complete_discography Music/arctic_monkeys\r\n
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You can also delete or remove (rm) files and folders. Now you don't want your Justin Bieber tunes in your Downloads folder, so you run:

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cd ~/Downloads\r\n\r\n# note the -r here too\r\nrm -r justin_bieber_complete_discography\r\n
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ATTENTION the rm command IS NOT REVERTIBLE. No Rubbish Bin, Trash, helmet or parachute. Make sure you are very very sure you actually want to delete exactly that (and nothing else).

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A note: some files cannot be deleted with a simple rm file, and the computer will say it is protected. Then add the flag -f (force), but this makes rm even more dangerous, so try not to use it. The git internal files are sometimes protected, so if you want to delete an old copy of SHARPy, you probably will need to use it.

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These are the very basic commands for command line survival. I'm going to add a few non-essential ones, but useful nevertheless:

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  • which: it tells you which executable is running. For example which sharpy returns: /home/user/code/sharpy/bin/sharpy. It is useful for knowing which version of anything you are running and where it comes from. For example, it is useful for knowing if you are using the updated compilers (usually in /usr/local/bin) or the default ones (/usr/bin probably).
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  • top: shows you the processes running and how much RAM they're using.
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  • touch: creates and empty file with the name you tell after the command.
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  • ipython: starts a nice Python terminal with autocomplete and some colours. Much better than python.
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  • history: if you forgot that nice command that did what I wanted and now I can't remember. Extra: history | grep \"command\" (without the quotes) will only show you the history lines that contain command.
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  • *: wildcard for copying, removing, moving... Everything. Example: cp *.txt ./my_files/\". Again: careful with rm and * together. Be VERY careful with rm and -rf and * together.
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  • pwd: for when you get lost and don't know where you are in the folder structure.
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  • nano: simple text editor. Save with ctrl+o, exit with ctrl+x.
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  • more: have a look at a file quickly
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  • head: show the first lines of a file
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  • tail: show the last lines of a file
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Debugging guide

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When the program fails, there are a number of typical reasons:

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  • Did you forget conda activate sharpy_env and source bin/sharpy_vars.sh?
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    • Check my alias tip at the beginning of the document.
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    • If you do in the terminal: which sharpy, do you get the one you want?
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    • If you do which python, does the result point to anaconda3/envs/sharpy_env/bin (or similar)?
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  • Wrong input (inconsistent connectivities, mass = 0...)
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    • Sometimes not easy to detect. For the structural model, run BeamLoader and BeamPlot with no structural solver in between. Go over the structure in Paraview. Check the fem.h5 file with HDFView.
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    • Remember that connectivities are ordered as $[0, 2, 1]$ (the central node goes last).
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    • Make sure the num_elem and num_node variables are actually your correct number of elements and nodes.
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  • Not running the actual case you want to.
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    • Cleanup the folder and regenerate the case
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  • Not running the SHARPy version you want.
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    • Check at the beginning of the execution the path to the SHARPy folder.
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  • Not running the correct branch of the code.
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    • You probably want to use develop. Again, check the first few lines of SHARPy output.
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  • Very different (I'm talking orders of magnitude) stiffnesses between nodes or directions?
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  • The UVLM requires a smaller vortex core cutoff?
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  • Newmark damping is not enough for this case?
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  • Do you have an element with almost 0 mass?
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  • Have a look at the $\\dot{\\Gamma}$ filtering and numerical parameters in the settings of StepUvlm and DynamicCoupled.
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  • Add more relaxation to the StaticCoupled or DynamicCoupled solvers.
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  • The code has a bug (depending on where, it may be likely).
      \r\n
    • Go over the rest of the list. Plot the case in paraview. Go over the rest of the list again. Prepare the simplest example that reproduces the problem and come see us.
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  • The code diverges because it has to (physical unstable behaviour)
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    • Then don't complain
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  • Your model still doesn't work and you don't know why.
      \r\n
    • import pdb; pdb.set_trace() and patience
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  • If nothing else works... get a rubber duck (or a very very patient good friend) and go over every step
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If your model doesn't do what it is supposed to do:

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  • Check for symmetric response where the model is symmetric.

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      \r\n
    • If it is not, run the beam solver first and make sure your properties are correct. Make sure the matrices for mass and stiffness are rotated if they need to be (remember the Material FoR definition and the for_delta?)
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    • Now run the aerodynamic solver only and double check that the forces are symmetric.
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    • Make sure your tolerances are low enough so that at least 4 FSI iterations are performed in StaticCoupled or DynamicCoupled.
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  • Make sure your inputs are correct. For example: a dynamic case can be run with $u_\\infty = 0$ and the plane moving forwards, or $u_\\infty = $whatever and the plane velocity = 0. It is very easy to mix both, and end up with double the effective incoming speed (or none).

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  • Run simple stuff before coupling it. For example, if your wing tip deflections don't match what you'd expect, calculate the deflection under a small tip force (not too small, make sure the deflection is > 1% of the length!) by hand, and compare.

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  • It is more difficult to do the same with the UVLM, as you need a VERY VERY high aspect ratio to get close to the 2D potential solutions. You are going to have to take my word for it: the UVLM works.

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  • But check the aero grid geometry in Paraview, including chords lengths and angles.

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Other useful software

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  • HDFView for opening and inspecting the .h5 files
    • \r\n
  • Gitkraken is a good graphical interface for Git.
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  • Pycharm for editing python and running cases.
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  • Jupyter notebook (this was made with it) for results and tests.
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\r\n\r\n\r\n \r\n\r\n\r\n\r\n" }, { "path": "docs/source/conf.py", "content": "#!/usr/bin/env python3\n# -*- coding: utf-8 -*-\n#\n# SHARPy documentation build configuration file, created by\n# sphinx-quickstart on Wed Oct 19 16:40:48 2016.\n#\n# This file is execfile()d with the current directory set to its\n# containing dir.\n#\n# Note that not all possible configuration values are present in this\n# autogenerated file.\n#\n# All configuration values have a default; values that are commented out\n# serve to show the default.\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# import guzzle_sphinx_theme\n# sys.path.insert(0, os.path.abspath('../'))\nsys.path.insert(0, os.path.abspath('./../../'))\n# sys.path.insert(0, os.path.abspath('..'))\n# import recommonmark\n# from recommonmark.transform import AutoStructify\n# # Markdown Source Parsers\n# from recommonmark.parser import CommonMarkParser\n\n# print(sys.path)\n# -- General configuration ------------------------------------------------\n\n# If your documentation needs a minimal Sphinx version, state it here.\n#\nneeds_sphinx = '3.0'\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.coverage',\n 'sphinx.ext.mathjax',\n 'sphinx.ext.viewcode',\n # 'sphinx.ext.githubpages',\n 'sphinx.ext.napoleon',\n 'nbsphinx',\n 'sphinx.ext.autosectionlabel',\n 'sphinxcontrib.jquery',\n 'recommonmark'\n]\n\n# Add any paths that contain templates here, relative to this directory.\ntemplates_path = ['_templates']\n\n# Mathjax path for equation rendering\nmathjax_path = \"https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML\"\n\n# Markdown Source Parsers\nsource_parsers = {\n '.md': 'recommonmark.parser.CommonMarkParser'}\n\n# The suffix(es) of source filenames.\n# You can specify multiple suffix as a list of string:\n#\nsource_suffix = ['.rst', '.md']\n\n# The encoding of source files.\n#\n# source_encoding = 'utf-8-sig'\n\n# The master toctree document.\nmaster_doc = 'index'\n\n# General information about the project.\nproject = 'SHARPy'\ncopyright = '2025, LoCA Lab ICL'\nauthor = 'Aeroelastics Lab, Imperial College London'\n\n# The version info for the project you're documenting, acts as replacement for\n# |version| and |release|, also used in various other places throughout the\n# built documents.\n#\n# The short X.Y version.\nversion = '2.4'\n# The full version, including alpha/beta/rc tags.\nrelease = '2.4'\n\n# The language for content autogenerated by Sphinx. Refer to documentation\n# for a list of supported languages.\n#\n# This is also used if you do content translation via gettext catalogs.\n# Usually you set \"language\" from the command line for these cases.\nlanguage = None\n\n# There are two options for replacing |today|: either, you set today to some\n# non-false value, then it is used:\n#\n# today = ''\n#\n# Else, today_fmt is used as the format for a strftime call.\n#\n# today_fmt = '%B %d, %Y'\n\n# List of patterns, relative to source directory, that match files and\n# directories to ignore when looking for source files.\n# This patterns also effect to html_static_path and html_extra_path\nexclude_patterns = [\"**/.so\", \"../../lib/*\", \"../*\", \"/_static\", \"/content/\",\n '_build', '**.ipynb_checkpoints']\n\n# The reST default role (used for this markup: `text`) to use for all\n# documents.\n#\n# default_role = None\n\n# If true, '()' will be appended to :func: etc. cross-reference text.\n#\n# add_function_parentheses = True\n\n# If true, the current module name will be prepended to all description\n# unit titles (such as .. function::).\n#\n# add_module_names = True\n\n# If true, sectionauthor and moduleauthor directives will be shown in the\n# output. They are ignored by default.\n#\n# show_authors = False\n\n# The name of the Pygments (syntax highlighting) style to use.\npygments_style = 'sphinx'\n\n# A list of ignored prefixes for module index sorting.\n# modindex_common_prefix = []\n\n# If true, keep warnings as \"system message\" paragraphs in the built documents.\n# keep_warnings = False\n\n# If true, `todo` and `todoList` produce output, else they produce nothing.\ntodo_include_todos = False\n\n# Exclude matplotlib - avoids conflicts when running sphinx\n# http://www.sphinx-doc.org/en/master/usage/extensions/autodoc.html#confval-autodoc_mock_imports\nautodoc_mock_imports = [\"matplotlib\",\n \"numpy\",\n \"colorama\",\n \"h5py\",\n \"scipy\",\n \"ctypes\",\n \"tvtk\",\n \"sharpy.lib\",\n \"sharpy.utils.ctypes_utils\",\n \"sharpy.linear.src.libuvlm\",\n \"sharpy.linear.src.lib_dbiot\",\n \"pandas\",\n \"lxml\",\n 'mpl_toolkits',\n # 'sharpy.aero.utils',\n 'yaml',\n 'sharpy.aero.utils.uvlmlib',\n 'sharpy.linear.src.uvlmutils',\n 'sharpy.structure.utils.xbeamlib',\n 'sharpy.utils.constants']\n # \"interp\", \"multisurfaces\", \"assembly\", \"libss\",]\n\n # Note: N. Goizueta 3/12/18: mocking imports from sharpy.linear.src that contain numpy\n # operators outside any function definition as these are causing problems. If numpy is not\n # mocked, it doesn't build on RTD. If it is mocked, it raises an error when compiling locally\n # N. Goizueta 23/7/19 - Removing sharpy.linear until its ready to be merged. Too many errors are\n # causing a build failure on RTD.\n\n# # Exclude selected modules\n# from unittest.mock import MagicMock\n#\n# class Mock(MagicMock):\n# @classmethod\n# def __getattr__(cls, name):\n# return MagicMock()\n#\n# MOCK_MODULES = [\"matplotlib\", \"numpy\", \"colorama\", \"h5py\", \"scipy\",\n# \"sharpy.lib.libxbeam.so\", \"sharpy.utils.ctypes_utils.import_ctypes_lib\"]\n# sys.modules.update((mod_name, Mock()) for mod_name in MOCK_MODULES)\n#\n\n# Sphinx extension to execute code in the documentation\n# https://github.com/jpsenior/sphinx-execute-code\n# extensions.append('sphinx_execute_code')\n\n# -- Options for HTML output ----------------------------------------------\n\n# html_theme_path = guzzle_sphinx_theme.html_theme_path()\n# html_theme = 'guzzle_sphinx_theme'\n#\n# # Register the theme as an extension to generate a sitemap.xml\n# extensions.append(\"guzzle_sphinx_theme\")\n#\n# # Guzzle theme options (see theme.conf for more information)\n# html_theme_options = {\n# # Set the name of the project to appear in the sidebar\n# \"project_nav_name\": \"SHARPy\",\n# }\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 = 'sphinx_rtd_theme'\n\n# Theme options are theme-specific and customize the look and feel of a theme\n# further. For a list of options available for each theme, see the\n# documentation.\n#\n# html_theme_options = {}\n\n# Add any paths that contain custom themes here, relative to this directory.\n# html_theme_path = []\n\n# The name for this set of Sphinx documents.\n# \" v documentation\" by default.\n#\n# html_title = 'SHARPy v0.0'\n\n# A shorter title for the navigation bar. Default is the same as html_title.\n#\n# html_short_title = None\n\n# The name of an image file (relative to this directory) to place at the top\n# of the sidebar.\n#\n# html_logo = None\n\n# The name of an image file (relative to this directory) to use as a favicon of\n# the docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32\n# pixels large.\n#\n# html_favicon = None\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# Add any extra paths that contain custom files (such as robots.txt or\n# .htaccess) here, relative to this directory. These files are copied\n# directly to the root of the documentation.\n#\n# html_extra_path = []\n\n# If not None, a 'Last updated on:' timestamp is inserted at every page\n# bottom, using the given strftime format.\n# The empty string is equivalent to '%b %d, %Y'.\n#\n# html_last_updated_fmt = None\n\n# If true, SmartyPants will be used to convert quotes and dashes to\n# typographically correct entities.\n#\n# html_use_smartypants = True\n\n# Custom sidebar templates, maps document names to template names.\n#\n# html_sidebars = {}\n\n# Additional templates that should be rendered to pages, maps page names to\n# template names.\n#\n# html_additional_pages = {}\n\n# If false, no module index is generated.\n#\n# html_domain_indices = True\n\n# If false, no index is generated.\n#\n# html_use_index = True\n\n# If true, the index is split into individual pages for each letter.\n#\n# html_split_index = False\n\n# If true, links to the reST sources are added to the pages.\n#\n# html_show_sourcelink = True\n\n# If true, \"Created using Sphinx\" is shown in the HTML footer. Default is True.\n#\nhtml_show_sphinx = False\n\n# If true, \"(C) Copyright ...\" is shown in the HTML footer. Default is True.\n#\n# html_show_copyright = True\n\n# If true, an OpenSearch description file will be output, and all pages will\n# contain a tag referring to it. The value of this option must be the\n# base URL from which the finished HTML is served.\n#\n# html_use_opensearch = ''\n\n# This is the file name suffix for HTML files (e.g. \".xhtml\").\n# html_file_suffix = None\n\n# Language to be used for generating the HTML full-text search index.\n# Sphinx supports the following languages:\n# 'da', 'de', 'en', 'es', 'fi', 'fr', 'h', 'it', 'ja'\n# 'nl', 'no', 'pt', 'ro', 'r', 'sv', 'tr', 'zh'\n#\n# html_search_language = 'en'\n\n# A dictionary with options for the search language support, empty by default.\n# 'ja' uses this config value.\n# 'zh' user can custom change `jieba` dictionary path.\n#\n# html_search_options = {'type': 'default'}\n\n# The name of a javascript file (relative to the configuration directory) that\n# implements a search results scorer. If empty, the default will be used.\n#\n# html_search_scorer = 'scorer.js'\n\n# Output file base name for HTML help builder.\nhtmlhelp_basename = 'SHARPydoc'\n\n# -- Options for LaTeX output ---------------------------------------------\n\nlatex_elements = {\n # The paper size ('letterpaper' or 'a4paper').\n #\n 'papersize': 'a4paper',\n\n # The font size ('10pt', '11pt' or '12pt').\n #\n 'pointsize': '12pt',\n\n # Additional stuff for the LaTeX preamble.\n #\n 'preamble': r'\\setcounter{tocdepth}{2}',\n\n # Latex figure (float) alignment\n #\n 'figure_align': 'htbp',\n}\n\n# Grouping the document tree into LaTeX files. List of tuples\n# (source start file, target name, title,\n# author, documentclass [howto, manual, or own class]).\nlatex_documents = [\n (master_doc, 'SHARPy.tex', 'SHARPy Documentation',\n 'LoCA Lab ICL', 'manual'),\n]\n\n# The name of an image file (relative to this directory) to place at the top of\n# the title page.\n#\n# latex_logo = None\n\n# For \"manual\" documents, if this is true, then toplevel headings are parts,\n# not chapters.\n#\n# latex_use_parts = False\n\n# If true, show page references after internal links.\n#\n# latex_show_pagerefs = False\n\n# If true, show URL addresses after external links.\n#\n# latex_show_urls = False\n\n# Documents to append as an appendix to all manuals.\n#\n# latex_appendices = []\n\n# It false, will not define \\strong, \\code, \titleref, \\crossref ... but only\n# \\sphinxstrong, ..., \\sphinxtitleref, ... To help avoid clash with user added\n# packages.\n#\n# latex_keep_old_macro_names = True\n\n# If false, no module index is generated.\n#\n# latex_domain_indices = True\n\n\n# -- Options for manual page output ---------------------------------------\n\n# One entry per manual page. List of tuples\n# (source start file, name, description, authors, manual section).\nman_pages = [\n (master_doc, 'sharpy', 'SHARPy Documentation',\n [author], 1)\n]\n\n# If true, show URL addresses after external links.\n#\n# man_show_urls = False\n\n\n# -- Options for Texinfo output -------------------------------------------\n\n# Grouping the document tree into Texinfo files. List of tuples\n# (source start file, target name, title, author,\n# dir menu entry, description, category)\ntexinfo_documents = [\n (master_doc, 'SHARPy', 'SHARPy Documentation',\n author, 'SHARPy', 'One line description of project.',\n 'Miscellaneous'),\n]\n\n# Documents to append as an appendix to all manuals.\n#\n# texinfo_appendices = []\n\n# If false, no module index is generated.\n#\n# texinfo_domain_indices = True\n\n# How to display URL addresses: 'footnote', 'no', or 'inline'.\n#\n# texinfo_show_urls = 'footnote'\n\n# If true, do not generate a @detailmenu in the \"Top\" node's menu.\n#\n# texinfo_no_detailmenu = False\n\n# Recommonmark function\n#def setup(app):\n# app.add_config_value('recommonmark_config', {\n# 'url_resolver': lambda url: github_doc_root + url,\n# 'auto_toc_tree_section': 'Contents',\n# }, True)\n# app.add_transform(AutoStructify)\n" }, { "path": "docs/source/content/capabilities.md", "content": "# Capabilities\nThis is just the tip of the iceberg, possibilities are nearly endless and once you understand how SHARPy's modular\ninterface works, you will be capable of running very complex simulations.\n\n## Very flexible aircraft nonlinear aeroelasticity\n\nThe modular design of SHARPy allows to simulate complex aeroelastic cases involving very flexible aircraft. The\nstructural solver supports very complex beam arrangements, while retaining geometrical nonlinearity. The UVLM solver\nfeatures different wake modelling fidelities while supporting large lifting surface deformations in a native way.\n\nAmong the problems studied, a few interesting ones, in no particular order are:\n\n* Catapult take off of a very flexible aircraft analysis [\\[Paper\\]](https://arc.aiaa.org/doi/abs/10.2514/6.2019-2038). \nIn this type of simulations, a PID controller was used in order to enforce displacements and velocities in a number of\nstructural nodes (the clamping points). Then, several take off strategies were studied in order to analyse the influence\nof the structural stiffness in this kind of procedures. This case is a very good example of the type of problems where\nnonlinear aeroelasticity is essential.\n \n![_Catapult Takeoff of Flexible Aircraft_](../_static/capabilities/hale_cruise.png) \n\n* Flight in full 3D atmospheric boundary layer (to be published). A very flexible aircraft is flown immersed in a\nturbulent boundary layer obtained from HPC LES simulations. The results are compared against simpler turbulence models\nsuch as von Karman and Kaimal. Intermittency and coherence features in the LES field are absent or less remarkable in\nthe synthetic turbulence fields.\n\n![_HALE Aircraft in a Turbulent Field_](../_static/capabilities/hale_turb.jpeg)\n\n* Lateral gust reponse of a realistic very flexible aircraft. For this problem (to be published), a realistic very\nflexible aircraft (University of Michigan X-HALE) model has been created in SHARPy and validated against their own\naeroelastic solver for static and dynamic cases. A set of vertical and lateral gust responses have been simulated.\n\n![_X-HALE_](../_static/capabilities/xhale.png)\n\n## Wind turbine aeroelasticity\n\nSHARPy is suitable to simulate wind turbine aeroelasticity. \n\nOn the structural side, it accounts for material anisotropy which is needed to characterize composite blades and for\ngeometrically non-linear deformations observed in current blades due to the increasing length and flexibility. Both\nrigid and flexible simulations can be performed and the structural modes can be computed accounting for rotational\neffects (Campbell diagrams). The rotor-tower interaction is modelled through a multibody approach based on the theory\nof Lagrange multipliers. Finally, the tower base can be fixed or subjected to prescribed linear and angular velocities.\n\nOn the aerodynamic side, the use of potential flow theory allows the characterization of flow unsteadiness at a\nreasonable computational cost. Specifically, steady and dynamic simulations can be performed. The steady simulations\nare carried out in a non-inertial frame of reference linked to the rotor under uniform steady wind with the assumption\nof prescribed helicoidal wake. On the other hand, dynamic simulations can be enriched with a wide variety of incoming\nwinds such as shear and yaw. Moreover, the wake shape can be freely computed under no assumptions accounting for\nself-induction and wake expansion or can be prescribed to an helicoidal shape for computational efficiency.\n\n![Wind Turbine](../_static/capabilities/turbine.png)\n\n## Model Order Reduction\nNumerical models of physical phenomena require fine discretisations to show convergence and agreement with their real\ncounterparts, and, in the case of SHARPy's aeroelastic systems, hundreds of thousands of states are not an uncommon\nencounter. However, modern hardware or the use of these models for other applications such as controller synthesis may limit\ntheir size, and we must turn to model order reduction techniques to achieve lower dimensional representations that can\nthen be used.\n\nSHARPy offers several model order reduction methods to reduce the initially large system to a lower dimension,\nattending to the user's requirements of numerical efficiency or global error bound.\n\n### Krylov Methods for Model Order Reduction - Moment Matching\nModel reduction by moment matching can be seen as approximating a transfer function through a power series expansion \nabout a user defined point in the complex plane. The reduction by projection retains the moments between the full and \nreduced systems as long as the projection matrices span certain Krylov subspaces dependant on the expansion point and \nthe system's matrices.\nThis can be taken advantage of,\nin particular for aeroelastic applications where the interest resides in the low frequency behaviour of the system,\nthe ROM can be expanded about these low frequency points discarding accuracy higher up the frequency spectrum.\n\n#### Example 1 - Aerodynamics - Frequency response of a high AR flat plate subject to a sinusoidal gust\nThe objective is to compare SHARPy's solution of a very high aspect ratio flat plate subject to a sinusoidal gust to\nthe closed form solution obtained by Sears (1944 - Ref). SHARPy's inherent 3D nature makes comparing results to the 2D\nsolution require very high aspect ratio wings with fine discretisations, resulting in very large state space models.\nIn this case, we would like to utilise a Krylov ROM to approximate the low frequency behaviour and perform a frequency\nresponse analysis on the reduced system, since it would represent too much computational cost if it were performed on\nthe full system.\n\nThe full order model was reduced utilising Krylov methods, in particular the Arnoldi iteration, with an expansion about\nzero frequency to produce the following result.\n\n![_Sears Gust Bode Plot_](../_static/capabilities/sears.png)\n\nAs it can be seen from the image above, the ROM approximates well the low frequency, quasi-steady state and loses\naccuracy as the frequency is increased, just as intended. Still, perfect matching is never achieved even at the\nexpansion frequency given the 3D nature of the wing compared to the 2D analytical solution.\n\n#### Example 2 - Aeroelastics - Flutter analysis of a Goland wing with modal projection\nThe Goland wing flutter example is presented next. The aerodynamic surface is finely discretised for the UVLM solution,\nresulting in not only a large state space but also in large input/output dimensionality. Therefore, to reduce the\nnumber of inputs and outputs, the UVLM is projected onto the structural mode shapes, the first four in this particular\ncase. The resulting multi input multi output system (mode shapes -> UVLM -> modal forces) was subsequently reduced using\nKrylov methods aimed at MIMO systems which use variations of the block Arnoldi iteration. Again, the expansion\nfrequency selected was the zero frequency. As a sample, the transfer function from two inputs to two outputs is\nshown to illustrate the performance of the reduced model against the full order UVLM.\n\n![_Goland Reduced Order Model Transfer Functions_](../_static/capabilities/goland_rom.png)\n\nThe reduced aerodynamic model projected onto the modal shapes was then coupled to the linearised beam model, and the\nstability analysed against a change in velocity. Note that the UVLM model and its ROM are actually scaled to be\nindependent on the freestream velocity, hence only one UVLM and ROM need to be computed. The structural model needs\nto be updated at each test velocity but its a lot less costly in computational terms. The resulting stability of the\naeroelastic system is plotted on the Argand diagram below with changing freestream velocity.\n\n![_Goland Flutter_](../_static/capabilities/goland_flutter.png)\n" }, { "path": "docs/source/content/casefiles.rst", "content": "The SHARPy Case files\n=====================\n\nSHARPy takes as input a series of ``.h5`` files that contain the numerical data and a ``.sharpy`` file that contains\nthe settings for each of the solvers. How these files are generated is at the user's discretion, though templates are\nprovided, and all methods are valid as long as the required variables are provided with the appropriate format.\n\nModular Framework\n-----------------\n\nSHARPy is built with a modular framework in mind. The following diagram shows the strutuctre of a nonlinear, time\nmarching aeroelastic simulation\n\n.. image:: ../_static/case_files/sharpy_modular.png\n :target: ../_static/case_files/sharpy_modular.png\n :alt: SHARPy's modular structure\n\nEach of the blocks correspond to individual solvers with specific settings. How we choose which solvers to run,\nin which order and with what settings is done through the solver configuration file, explained in the next section.\n\n\nSolver configuration file\n-------------------------\n\nThe solver configuration file is the main input to SHARPy. It is a ConfigObj_\nformatted file with the ``.sharpy`` extension. It contains the settings for each of the solvers and the order in which\nto run them.\n\n.. _ConfigObj: http://pypi.org/project/configobj/\n\nA typical way to assemble the solver configuration file is to place all your desired settings\nin a dictionary and then convert to and write your ``ConfigObj``. If a setting is not provided the default value will be used. The settings that each solver takes, its type and default value are explained in their relevant documentation pages.\n\n.. code-block:: python\n\n import configobj\n filename = '/.sharpy'\n config = configobj.ConfigObj()\n config.filename = filename\n config['SHARPy'] = {'case': '', # an example setting\n # Rest of your settings for the PreSHARPy class\n }\n config['BeamLoader'] = {'orientation': [1., 0., 0.], # an example setting\n # Rest of settings for the BeamLoader solver\n }\n # Continue as above for the remainder of solvers that you would like to include\n\n # finally, write the config file\n config.write()\n\nThe resulting ``.sharpy`` file is a plain text file with your specified settings for each of\nthe solvers.\n\nNote that, therefore, if one of your settings is a ``np.array``, it will get transformed into\na string of plain text before being read by SHARPy. However, any setting with ``list(float)`` specified as its setting type will get converted into a ``np.array`` once it is read by SHARPy.\n\n\nFEM file\n--------\n\nThe ``case.fem.h5`` file has several components. We go one by one:\n\n* ``num_node_elem [int]`` : number of nodes per element.\n\n Always 3 in our case (3 nodes per structural elements - quadratic beam elements).\n\n\n* ``num_elem [int]`` : number of structural elements.\n\n* ``num_node [int]`` : number of nodes.\n\n For simple structures, it is ``num_elem*(num_node_elem - 1) - 1``.\n For more complicated ones, you need to calculate it properly.\n\n\n* ``coordinates [num_node, 3]``: coordinates of the nodes in body-attached FoR (A).\n\n\n* ``connectivites [num_elem, num_node_elem]`` : Beam element's connectivities.\n\n Every row refers to an element, and the three integers in that row are the indices of the three nodes\n belonging to that elem. Now, the catch: the ordering is not as you'd think. Order them as ``[0, 2, 1]``.\n That means, first one, last one, central one. The following image shows the node indices inside the\n circles representing the nodes, the element indices in blue and the resulting connectivities matrix next to it.\n Connectivities are tricky when considering complex configurations. Pay attention at the beginning and you'll\n save yourself a lot of trouble.\n\n .. image:: ./../_static/case_files/connectivities.png\n :target: ./../_static/case_files/connectivities.png\n :alt: SHARPy Beam Element Connectivities\n\n\n* ``stiffness_db [:, 6, 6]``: database of stiffness matrices.\n\n The first dimension has as many elements as different stiffness matrices are in the model.\n\n* ``elem_stiffness [num_elem]`` : array of indices (starting at 0).\n\n It links every element (index) to the stiffness matrix index in ``stiffness_db``.\n For example ``elem_stiffness[0] = 0`` ; ``elem_stiffness[2] = 1`` means that the element ``0`` has a stiffness matrix\n equal to ``stiffness_db[0, :, :]`` , and the second element has a stiffness matrix equal to\n ``stiffness_db[1, :, :]``.\n\n The shape of a stiffness matrix, :math:`\\mathrm{S}` is:\n\n .. math::\n \\mathrm{S} = \\begin{bmatrix}\n EA & & & & & \\\\\n & GA_y & & & & \\\\\n & & GA_z & & & \\\\\n & & & GJ & & \\\\\n & & & & EI_y & \\\\\n & & & & & EI_z \\\\\n \\end{bmatrix}\n\n with the cross terms added if needed.\n\n ``mass_db`` and ``elem_mass`` follow the same scheme than the stiffness, but the mass matrix is given by:\n\n .. math::\n \\mathrm{M} = \\begin{bmatrix}\n m\\mathbf{I} & -\\tilde{\\boldsymbol{\\xi}}_{cg}m \\\\\n \\tilde{\\boldsymbol{\\xi}}_{cg}m & \\mathbf{J}\\\\\n \\end{bmatrix}\n\n where :math:`m` is the distributed mass per unit length :math:`kg/m` , :math:`(\\tilde{\\bullet})` is the\n skew-symmetric matrix of a vector and :math:`\\boldsymbol{\\xi}_{cg}` is the location of the centre of gravity\n with respect to the elastic axis in MATERIAL (local) FoR. And what is the Material FoR? This is an important point,\n because all the inputs that move WITH the beam are in material FoR. For example: follower forces, stiffness, mass,\n lumped masses...\n\n .. image:: ./../_static/case_files/frames_of_reference.jpg\n :target: ./../_static/case_files/frames_of_reference.jpg\n :alt: SHARPy Frames of Reference\n\n\n The material frame of reference is noted as :math:`B`. Essentially, the :math:`x` component is tangent to the beam in the\n increasing node ordering, :math:`z` looks up generally and :math:`y` is oriented such that the FoR is right handed.\n\n In the practice (vertical surfaces, structural twist effects...) it is more complicated than this. The only\n sure thing about :math:`B` is that its :math:`x` direction is tangent to the beam in the increasing node number direction.\n However, with just this, we have an infinite number of potential reference frames, with :math:`y` and :math:`z`\n being normal to :math:`x` but rotating around it. The solution is to indicate a ``for_delta``, or frame of\n reference delta vector (:math:`\\Delta`).\n\n\n .. image:: ../_static/case_files/frame_of_reference_delta.jpg\n :target: ../_static/case_files/frame_of_reference_delta.jpg\n :alt: Frame of Reference Delta Vector\n\n\n Now we can define unequivocally the material frame of reference. With :math:`x_B` and :math:`\\Delta` defining a\n plane, :math:`y_b` is chosen such that the :math:`z` component is oriented upwards with respect to the lifting surface.\n\n From this definition comes the only constraint to :math:`\\Delta`: it cannot be parallel to :math:`x_B`.\n\n* ``frame_of_reference_delta [num_elem, num_node_elem, 3]``: rotation vector to FoR :math:`B`.\n\n contains the :math:`\\Delta` vector in body-attached (:math:`A`) frame of reference.\n\n As a rule of thumb:\n\n .. math::\n \\Delta =\n \\begin{cases}\n [-1, 0, 0], \\quad \\text{if right wing} \\\\\n [1, 0, 0], \\quad \\text{if left wing} \\\\\n [0, 1, 0], \\quad \\text{if fuselage} \\\\\n [-1, 0, 0], \\quad \\text{if vertical fin} \\\\\n \\end{cases}\n\n These rules of thumb only work if the nodes increase towards the tip of the surfaces (and the tail in the\n case of the fuselage).\n\n\n* ``structural_twist [num_elem, num_node_elem]``: Element twist.\n\n Technically not necessary, as the same effect can be achieved with ``FoR_delta``.\n\n\n* ``boundary_conditions [num_node]``: boundary conditions.\n\n An array of integers ``(np.zeros((num_node, ), dtype=int))`` and contains all ``0`` except for\n\n - One node NEEDS to have a ``1`` , this is the reference node. Usually, the first node has 1 and is located\n in ``[0, 0, 0]``. This makes things much easier.\n\n - If the node is a tip of a beam (is not attached to 2 elements, but just 1), it needs to have a ``-1``.\n\n\n* ``beam_number [num_elem]``: beam index.\n\n Is another array of integers. Usually you don't need to modify its value. Leave it at 0.\n\n\n* ``app_forces [num_elem, 6]``: applied forces and moments.\n\n Contains the applied forces ``app_forces[:, 0:3]`` and moments ``app_forces[:, 3:6]`` in a\n given node.\n\n Important points: the forces are given in Material FoR (check above). That means that in a\n symmetrical model, a thrust force oriented upstream would have the shape ``[0, T, 0, 0, 0, 0]`` in the\n right wing, while the left would be ``[0, -T, 0, 0, 0, 0]``. Likewise, a torsional moment for twisting the wing\n leading edge up would be ``[0, 0, 0, M, 0, 0]`` for the right, and ``[0, 0, 0, -M, 0, 0]`` for the left.\n But careful, because an out-of-plane bending moment (wing tip up) has the same sign (think about it).\n\n* ``lumped_mass [:]``: lumped masses.\n\n Is an array with as many masses as needed (in kg this time). Their order is important, as more\n information is required to implement them in a model.\n\n* ``lumped_mass_nodes [:]``: Lumped mass nodes.\n\n Is an array of integers. It contains the index of the nodes related to the masses given\n in lumped_mass in order.\n\n* ``lumped_mass_inertia [:, 3, 3]``: Lumped mass inertia.\n\n Is an array of ``3x3`` inertial tensors. The relationship is set by the ordering as well.\n\n* ``lumped_mass_position [:, 3]``: Lumped mass position.\n\n Is the relative position of the lumped mass with respect to the node\n (given in ``lumped_masss_nodes`` ) coordinates. ATTENTION: the lumped mass is solidly attached to the node, and\n thus, its position is given in Material FoR.\n\nAerodynamics file\n-----------------\n\nAll the aerodynamic data is contained in ``case.aero.h5``.\n\nIt is important to know that the input for aero is usually based on elements (and inside the elements, their nodes).\nThis causes sometimes an overlap in information, as some nodes are shared by two adjacent elements (like in the\nconnectivities graph in the previous section). The easier way of dealing with this is to make sure the data is\nconsistent, so that the properties of the last node of the first element are the same than the first node of the\nsecond element.\n\nItem by item:\n\n\n* ``airfoils``: Airfoil group.\n\n In the ``aero.h5`` file, there is a Group called ``airfoils``. The airfoils are stored in this group (which acts as a\n folder) as a two-column matrix with :math:`x/c` and :math:`y/c` in each column. They are named ``'0', '1'`` ,\n and so on.\n\n* ``chords [num_elem, num_node_elem]``: Chord\n\n Is an array with the chords of every airfoil given in an element/node basis.\n\n* ``twist [num_elem, num_node_elem]``: Twist.\n\n Has the twist angle in radians. It is implemented as a rotation around the local :math:`x` axis.\n\n* ``sweep [num_elem, num_node_elem]``: Sweep.\n\n Same here, just a rotation around :math:`z`.\n\n* ``airfoil_distribution [num_elem, num_node_elem]``: Airfoil distribution.\n\n Contains the indices of the airfoils that you put previously in ``airfoils``.\n\n* ``surface_distribution [num_elem]``: Surface integer array.\n\n It contains the index of the surface the element belongs\n to. Surfaces need to be continuous, so please note that if your beam numbering is not continuous, you need to make\n a surface per continuous section.\n\n* ``surface_m [num_surfaces]``: Chordwise panelling.\n\n Is an integer array with the number of chordwise panels for every surface.\n\n* ``m_distribution [string]``: Discretisation method.\n\n Is a string with the chordwise panel distribution. In almost all cases, leave it at ``uniform``.\n\n* ``aero_node [num_node]``: Aerodynamic node definition.\n\n Is a boolean (``True`` or ``False``) array that indicates if that node has a lifting\n surface attached to it.\n\n* ``elastic_axis [num_elem, num_node_elem]``: elastic axis.\n\n Indicates the elastic axis location with respect to the leading edge as a\n fraction of the chord of that rib. Note that the elastic axis is already determined, as the beam is fixed now, so\n this settings controls the location of the lifting surface wrt the beam.\n\n* ``control_surface [num_elem, num_node_elem]``: Control surface.\n\n Is an integer array containing ``-1`` if that section has no control surface associated to it, and ``0, 1, 2 ...``\n if the section belongs to the control surface ``0, 1, 2 ...`` respectively.\n\n* ``control_surface_type [num_control_surface]``: Control Surface type.\n\n Contains ``0`` if the control surface deflection is static, and ``1`` is it\n is dynamic.\n\n* ``control_surface_chord [num_control_surface]``: Control surface chord.\n\n Is an INTEGER array with the number of panels belonging to the control\n surface. For example, if ``M = 4`` and you want your control surface to be :math:`0.25c`, you need to put ``1``.\n\n* ``control_surface_hinge_coord [num_control_surface]``: Control surface hinge coordinate.\n\n Only necessary for lifting surfaces that are deflected as a\n whole, like some horizontal tails in some aircraft. Leave it at ``0`` if you are not modelling this.\n\n* ``airfoil_efficiency [num_elem, num_node_elem, 2, 3]``: Airfoil efficiency.\n\n This is an optional setting that introduces a user-defined efficiency and constant terms to the mapping\n between the aerodynamic forces calculated at the lattice grid and the structural nodes. The formatting of the\n 4-dimensional array is simple. The first two dimensions correspond to the element index and the local node index.\n The third index is whether the term is the multiplier to the force ``0`` or a constant term ``1``. The final term refers to,\n in the **local, body-attached** ``B`` frame, the factors and constant terms for: ``fy, fz, mx``.\n For more information on how these factors are included in the mapping terms\n see :func:`sharpy.aero.utils.mapping.aero2struct_force_mapping`.\n\n* ``polars`` Group (optional): Use airfoil polars to correct aerodynamic forces.\n\n This is an optional group to add if correcting the aerodynamic forces using airfoil polars is desired. A polar\n should be included for each airfoil defined. Each entry consists of a 4-column table. The first column corresponds\n to the angle of attack (in radians) and then the ``C_L``, ``C_D`` and ``C_M``.\n\nMultibody file\n--------------\n\nAll the aerodynamic data is contained in ``case.mb.h5``.\n\nThis file encapsulates both the initial conditions for the multiple bodies, and the constraints between them.\n\nItem by item:\n\n* ``num_bodies``: Number of bodies.\n\n* ``num_constraints``: Number of constraints between bodies.\n\n The initial conditions for each body and the constraint definitions are defined in groups. The body groups are named\n as ``body_xx``, where the xx is replaced with a two digit body number starting from 00, e.g. ``body_00``. Each of these\n groups should have the following items:\n\n* ``FoR_acceleration [6]``: Frame of reference initial acceleration.\n\n An array of the stacked linear and rotational initial accelerations in the inertial frame.\n\n* ``FoR_velocity [6]``: Frame of reference initial velocity.\n\n An array of the stacked linear and rotational initial velocities in the inertial frame.\n\n* ``FoR_position [6]``: Frame of reference initial position.\n\n An array of the stacked linear and rotational initial positions in the inertial frame.\n\n* ``quat [4]``: Frame of reference initial orientation.\n\n A quaternion describing the initial rotation between the body attached and inertial frames.\n\n* ``body_number``: Body number.\n\n An integer used to identify the body when creating constraints.\n\n* ``FoR_movement``: Type of frame of reference movement.\n\n Use \"free\" to include rigid body motion, or \"prescribed\" for a clamped body.\n\nThe constraint groups are named similarly to the bodies, using ``constraint_xx`` where xx is the two digit constraint number\nstarting from 00. Each of these groups should have the following items:\n\n* ``scalingFactor``: Scaling factor.\n\n This value scales the multibody equations, where generally settings to ``dt^2`` provides acceptable results.\n\n* ``behaviour``: Constraint behaviour.\n\n This string defines the type of constraint applied to a single or multiple bodies. A wide range of standard lower-pair\n kinematic joints are available, such as hinge and spherical joints, as well as prescribed rotation joints. A list of the\n available joints can be found in ``sharpy/structure/utils/lagrangeconstraints.py`` and\n ``sharpy/structure/utils/lagrangeconstraintsjax.py``, depending on the solver being used. Due to every constraint being\n different, further parameters depend upon the constraint type used. These parameters are added as variables to the constraint\n group. Some examples which may be included are listed below:\n\n* ``body_FoR``: Body frame of reference number.\n\n The number of the body which is constrained by its body attached frame of reference. For example for a double pendulum,\n this would be the lower link.\n\n* ``body``: Body number.\n\n The number of the body which is constrained by one of its nodes. For example for a double pendulum,\n this would be the upper link.\n\n* ``node_in_body``: Node in body.\n\n This is paired to the ``body`` parameter, and this indicates which node within the body is to be constrained.\n\n* ``rot_axisB [3]``: Rotation axis in the B frame.\n\n For a hinge constraint, this defines a vector for the hinge axis for the ``body``. This is defined in the material frame.\n\n* ``rot_axisA2 [3]``: Rotation axis in the A frame.\n\n For a hinge constraint, this defines a vector for the hinge axis for the ``body_FoR``. This is defined in the body attached frame.\n\n* ``controller_id``: Controller ID for using an actuated constraint.\n\n This should use the same ID as the ``MultibodyController`` used in the ``DynamicCoupled`` simulation, allowing the rotation to be controlled over time.\n\n* ``aerogrid_warp_factor [num_elem, 3]``: Aerodynamic grid warping factor.\n\n For simulating wings with dynamic sweep by a local rotation around the z axis, the aerodynamic grid needs to warp to\n account for this. To create a smooth warp, it can be preferred to gradually change the sweep (and therefore chord to\n maintain the \"same\" geometry) at elements around the discontinuity. This parameter sets the sweep per node using this\n parameter to scale the input angle. If not included, it will be ignored when generating the aerodynamic grid and have\n no effect.\n\n\nNonlifting Body file\n-----------------\n\nAll the nonlifting body data is contained in ``case.nonlifting_body.h5``.\n\nThe idea behind the structure of the model definition of nonlifting bodies in SHARPy is similiar to the aerodynamic \none for lifting surfaces. Again for each node or element we define several parameters.\n\nItem by item:\n\n* ``shape``: Type of geometrical form of 3D nonlifting body.\n\n In the ``nonlifting_body.h5`` file, there is a Group called ``shape``. The shape indicates the geometrical form of the \n nonlifting body. Common options for this parameter are ``'cylindrical'`` and ``'specific'``. For the former, SHARPy \n expects rotational symmetric cross-section for which only a radius is required for each node. For the ``'specific'`` \n option, SHARPy can create a more unique nonlifting body geometry by creating an ellipse at each fuselage defined by \n :math:`\\frac{y^2}{a^2}+\\frac{z^2}{b^2}=1` with the given ellipse axis lengths :math:`a` and :math:`b`. Further, SHARPy \n lets define the user to create a vertical offset from the node with :math:`z_0`.\n\n* ``radius [num_node]``: Cross-sectional radius.\n\n Is an array with the radius of specified for each fuselage node.\n\n* ``a_ellipse [num_node]``: Elliptical axis lengths along the local y-axis.\n\n Is an array with the length of the elliptical axis along the y-axis.\n\n* ``b_ellipse [num_node]``: Elliptical axis lengths along the local z-axis.\n\n Is an array with the length of the elliptical axis along the z-axis.\n\n* ``z_0_ellipse [num_node]``: Vertical offset of the ellipse center from the beam node.\n\n Is an array with the vertical offset of the center of the elliptical cross-section from the fuselage node.\n\n* ``surface_m [num_surfaces]``: Radial panelling.\n\n Is an integer array with the number of radial panels for every surface.\n\n* ``nonlifting_body_node [num_node]``: Nonlifting body node definition.\n\n Is a boolean (``True`` or ``False``) array that indicates if that node has a nonlifting body\n attached to it.\n \n* ``surface_distribution [num_elem]``: Nonlifting Surface integer array.\n\n It contains the index of the surface the element belongs to. Surfaces need to be continuous, so please note \n that if your beam numbering is not continuous, you need to make a surface per continuous section.\n\n\nTime-varying force input file (``.dyn.h5``)\n-------------------------------------------\n\nThe ``.dyn.h5`` file is an *optional* input file that may contain force and acceleration inputs that vary with time.\nThis is intended for use in dynamic problems. For SHARPy to look for and use this file the setting ``unsteady`` in the\n:class:`~sharpy.solvers.beamloader.BeamLoader` must be turned to ``on``.\n\nAppropriate data entries in the ``.dyn.h5`` include:\n\n* ``dynamic_forces [num_t_steps, num_node, 6]``: Dynamic forces in body attached ``B`` frame.\n\n Forces given at each time step, for each node and then for the 6 degrees of freedom (``fx, fy, fz, mx, my, mz``) in\n a body-attached (local) frame of reference ``B``.\n\n* ``for_pos [num_t_steps, 6]``: Body frame of reference (A FoR) position.\n\n Position of the reference frame A in time.\n\n* ``for_vel [num_t_steps, 6]``: Body frame of reference (A FoR) velocity.\n\n Velocity of the reference frame A in time.\n\n* ``for_acc [num_t_steps, 6]``: Body frame of reference (A FoR) acceleration.\n\n Acceleration of the reference frame A in time.\n \n If a case is restarted from a pickle file, the .dyn.h5 file should include the dynamic information for the previous simulation (that will be discarded) and the information for the new simulation. \n" }, { "path": "docs/source/content/contributing.md", "content": "# Contributing to SHARPy\n## Bug fixes and features\n\nSHARPy is a collaborative effort, and this means that some coding practices need\nto be encouraged so that the code is kept tidy and consistent. Any user is welcome\nto raise issues for bug fixes and feature proposals through Github.\n\nIf you are submitting a bug report:\n\n1. Make sure your SHARPy, xbeam and uvlm local copies are up to date and in the\nsame branch.\n\n2. Double check that your python distribution is updated by comparing with \nthe `utils/environment.yml` file.\n\n3. Try to assemble a minimal working example that can be run quickly and easily.\n\n4. Describe as accurately as possible your setup (OS, path, compilers...) and\nthe problem.\n\n5. Raise an issue with all this information in the Github repo and label it\n`potential bug`.\n\nPlease bear in mind that we do not have the resources to provide support for\nuser modifications of the code through Github. If you have doubts about how to modify certain\nparts of the code, contact us through email and we will help you as much as we can.\n\nIf you are fixing a bug:\n\n1. THANKS!\n\n2. Please create a pull request from your modified fork, and describe in a few\nlines which bug you are fixing, a minimal example that triggers the bug and how you\nare fixing it. We will review it ASAP and hopefully it will be incorporated in the\ncode!\n\nIf you have an idea for new functionality but do not know how to implement it:\n\n1. We welcome tips and suggestions from users, as it allow us to broaden the scope\nof the code. The more people using it, the better!\n\n2. Feel free to fill an issue in Github, and tag it as `feature proposal`. Please\nunderstand that the more complete the description of the potential feature, the more\nlikely it is that some of the developers will give it a go.\n\nIf you have developed new functionality and you want to share it with the world:\n\n1. AWESOME! Please follow the same instructions than for the bug fix submission.\nIf you have some peer-reviewed references related to the new code, even better, as\nit will save us some precious time.\n\n## Code formatting\n\nWe try to follow the [PEP8](https://www.python.org/dev/peps/pep-0008/) standards\n(with spaces, no tabs please!) and [Google Python Style Guide](http://google.github.io/styleguide/pyguide.html).\nWe do not ask you to freak out over formatting, but please, try to keep it tidy and\ndescriptive. A good tip is to run `pylint` [https://www.pylint.org/](https://www.pylint.org/)\nto make sure there are no obvious formatting problems.\n\n\n\n\n## Documentation\n\nContributing to SHARPy's documentation benefits everyone. As a developer, writing documentation helps you better \nunderstand what you have done and whether your functions etc make logical sense. As a user, any documentation is better \nthan digging through the code. The more we have documented, the easier the code is to use and the more users we can \nhave.\n\nIf you want to contribute by documenting code, you have come to the right place. \n\nSHARPy is documented using Sphinx and it extracts the documentation directly from the source code. It is then sorted\ninto directories automatically and a human readable website generated. The amount of work you need to do is minimal. \nThat said, the recipe for a successfully documented class, function, module is the following:\n\n1. Your documentation has to be written in ReStructuredText (rst). I know, another language... hence I will leave\n a few tips:\n \n - Inline code is written using two backticks ` `` `\n \n - Inline math is written as ``:math:`1+\\exp^{i\\pi} = 0` ``. Don't forget the backticks!\n \n - Math in a single or multiple lines is simple:\n \n ```rst\n .. math:: 1 + \\exp{i\\pi} = 0\n ``` \n \n - Lists in ReStructuredText are tricky, I must admit. Therefore, I will link to some\n [examples](http://docutils.sourceforge.net/docs/user/rst/quickref.html#enumerated-lists). The key resides in not \n forgetting the spaces, in particular when you go onto a second line!\n \n - The definite example list can be found [here](http://docutils.sourceforge.net/docs/user/rst/quickref.html).\n \n2. Titles and docstrings, the bare minimum: \n - Start docstrings with `r` such that they are interpreted raw:\n \n ```python\n r\"\"\"\n My docstring\n \"\"\"\n ```\n - All functions, modules and classes should be given a title that goes in the first line of the docstring\n \n - If you are writing a whole package with an `__init__.py` file, even if it's empty, give it a human readable\n docstring. This will then be imported into the documentation\n \n - For modules with several functions, the module docstring has to be at the very top of the file, prior to the \n `import` statements.\n \n2. We use the [Google documentation](https://google.github.io/styleguide/pyguide.html#38-comments-and-docstrings)\n style. A very good set of examples of Google style documentation for functions, modules, classes etc. can be found \n [here](https://sphinxcontrib-napoleon.readthedocs.io/en/latest/example_google.html). \n3. Function arguments and returns:\n \n - Function arguments are simple to describe:\n ```python\n def func(arg1, arg2):\n \"\"\"Summary line.\n\n Extended description of function.\n\n Args:\n arg1 (int): Description of arg1\n arg2 (str): Description of arg2\n\n Returns:\n bool: Description of return value\n\n \"\"\"\n return True\n ```\n\n4. Solver settings:\n\n - If your code has a settings dictionary, with defaults and types then make sure that:\n \n - They are defined as class variables and not instance attributes. \n \n - Define a `settings_types`, `settings_default` and `settings_description` dictionaries.\n \n - After all your settings, update the docstring with the automatically generated settings table. You will need\n to import the `sharpy.utils.settings` module\n \n ```python\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n # keep adding settings\n \n settings_table = sharpy.utils.settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default ,settings_description)\n ```\n\n5. See how your docs looks like!\n \n - Once you are done, run the following ``SHARPy`` command:\n ```bash\n sharpy any_string -d\n ```\n \n - If you are making minor updates to docstrings (i.e. you are not documenting a previously undocumented\n function/class/module) you can simply change directory to `sharpy/docs` and run \n ```bash\n make html\n ```\n \n - Your documentation will compile and warnings will appear etc. You can check the result by opening\n ```bash\n docs/build/index.html\n ```\n and navigating to your recently created page.\n \n - Make sure that **before committing** any changes in the documentation you update the entire ``docs`` directory\n by running\n ```bash\n sharpy any_string -d\n ```\n \nThank you for reading through this and contributing to make SHARPy a better documented, more user friendly code!\n\n## Git branching model\n\nFor the development of SHARPy, we try to follow [this](https://nvie.com/posts/a-successful-git-branching-model/) \nbranching model summarised by the schematic\n\n![BranchingModel](https://nvie.com/img/git-model@2x.png)\n_Credit: Vincent Driessen https://nvie.com/posts/a-successful-git-branching-model/_\n\nTherefore, attending to this model our branches have the following versions of the code:\n* `main`: latest stable release - paired with the appropriate tag.\n* `develop`: latest stable development build. Features get merged to develop.\n* `rc-**`: release candidate branch. Prior to releasing tests are performed on this branch.\n* `dev_doc`: documentation development branch. All work relating to documentation gets done here.\n* `fix_**`: hotfix branch.\n* `dev_**`: feature development branch.\n\nIf you contribute, please make sure you know what branch to work from. If in doubt please ask!\n\nCommit names are also important since they are the backbone of the code's change log. Please write concise commit titles\nand explain the main changes in the body of the commit message. An excellent guide on writing good commit messages can\nbe found [here](https://chris.beams.io/posts/git-commit/).\n\n# For developers: \n\n## Releasing a new SHARPy version\n\nIn the release candidate branch:\n\n1. Update the version number in the docs configuration file `docs/source/conf.py`. Update variables `version` and `release`\n\n2. Update `version.json` file\n\n3. Update version in `sharpy/version.py` file\n\n4. Commit, push and wait for tests to pass\n\n5. Merge release candidate branch into `main` branch\n\nIn the `main` branch:\n \n1. Create a release tag. IMPORTANT: ensure it is an *annotated* tag, otherwise the version and commit number in SHARPy will not display properly\n ```\n git tag -a \n git push origin --tags -f\n ```\n where `` is something like `2.0`.\n\n2. Run the [github_changelog_generator](https://github.com/github-changelog-generator/github-changelog-generator) tool locally with the following parameters:\n ```\n github_changelog_generator -u imperialcollegelondon -p sharpy -t --future-release \n ```\n\n3. Push the changes to the `CHANGELOG.md` file\n \n4. Create the GitHub release, choosing the newly created tag from the dropdown menu. Do not create a tag from the dropdown menu directly because it will not be an annotated tag\n\n5. (Optional) Merge `main` branch back into `develop` branch\n" }, { "path": "docs/source/content/debug.rst", "content": "A Short Debugging Guide\n-----------------------\n\nWe have put together a list of common traps you may fall into, hopefully you will find the tools here to get\nyourself out of them!\n\n* Did you forget `conda activate sharpy_env` and `source bin/sharpy_vars.sh`?\n\n - If you do in the terminal: `which sharpy`, do you get the one you want?\n - If you do `which python`, does the result point to `anaconda3/envs/sharpy_env/bin` (or similar)?\n\n* Wrong input (inconsistent connectivities, mass = 0...)\n\n * Sometimes not easy to detect. For the structural model, run `BeamLoader` and `BeamPlot` with no structural solver\n in between. Go over the structure in Paraview. Check the `fem.h5` file with HDFView.\n * Remember that connectivities are ordered as $[0, 2, 1]$ (the central node goes last).\n * Make sure the `num_elem` and `num_node` variables are actually your correct number of elements and nodes.\n\n* Not running the actual case you want to.\n\n * Cleanup the folder and regenerate the case\n\n* Not running the SHARPy version you want.\n\n * Check at the beginning of the execution the path to the SHARPy folder.\n\n* Not running the correct branch of the code.\n\n * You probably want to use `develop`. Again, check the first few lines of SHARPy output.\n\n* Very different (I'm talking orders of magnitude) stiffnesses between nodes or directions?\n\n* Maybe the UVLM requires a smaller a smaller vortex core cutoff (only for linear UVLM simulations, as the nonlinear uses another vortex core model).\n\n* Newmark damping is not enough for this case?\n\n* Do you have an element with almost 0 mass or inertia?\n\n* Are you mass matrices consistent? Check that :math:`I_{xx} = I_{yy} + I_{zz}`.\n\n* Have a look at the :math:`\\dot{\\Gamma}` filtering and numerical parameters in the settings of `StepUvlm` and\n `DynamicCoupled`.\n\n* Add more relaxation to the `StaticCoupled` or `DynamicCoupled` solvers.\n\n* The code has a bug (depending on where, it may be likely).\n\n * Go over the rest of the list. Plot the case in paraview. Go over the rest of the list again. Prepare the simplest\n example that reproduces the problem and raise an issue.\n\n* The code diverges because it has to (physical unstable behaviour)\n * Then don't complain\n* Your model still doesn't work and you don't know why.\n * `import pdb; pdb.set_trace()` and patience\n* If nothing else works... get a rubber duck (or a very very patient good friend) and go over every step\n\n\n.. image:: ../_static/debugguide/rubberduck.png\n :target: ../_static/debugguide/rubberduck.png\n :alt: A rubber duck could be a good friend\n\n\nIf your model doesn't do what it is supposed to do:\n\n* Check for symmetric response where the model is symmetric.\n\n * If it is not, run the beam solver first and make sure your properties are correct. Make sure the matrices for mass\n and stiffness are rotated if they need to be (remember the Material FoR definition and the `for_delta`?)\n\n * Now run the aerodynamic solver only and double check that the forces are symmetric.\n\n * Make sure your tolerances are low enough so that at least 4 FSI iterations are performed in `StaticCoupled` or\n `DynamicCoupled`.\n\n\n* Make sure your inputs are correct. For example: a dynamic case can be run with :math:`u_\\infty = 0` and the plane\n moving forwards, or :math:`u_\\infty = x` whatever and the plane velocity = 0. It is very easy to mix both, and end up with\n double the effective incoming speed (or none).\n\n* Run simple stuff before coupling it. For example, if your wing tip deflections don't match what you'd expect,\n calculate the deflection under a small tip force (not too small, make sure the deflection is > 1% of the length!)\n by hand, and compare.\n\n* It is more difficult to do the same with the UVLM, as you need a VERY VERY high aspect ratio to get close to the 2D\n potential solutions. You are going to have to take my word for it: the UVLM works.\n\n* But check the aero grid geometry in Paraview, including chords lengths and angles.\n" }, { "path": "docs/source/content/example_notebooks/UDP_control/control_design_script.m", "content": "function [success] = control_design_script(route_directory)\n addpath(strcat(route_directory,'/matlab_functions/'));\n success = false;\n %% Define parameters;\n case_name = 'pazy_ROM';\n output_folder = strcat(route_directory,'/output/',case_name);\n output_folder_linear = strcat(output_folder, '/linear_results/');\n complex_matrices = true;\n \n %% Reade from SHARPy generated state space model\n [state_space_system, eta_ref] = read_SHARPy_state_space_system(...\n strcat(case_name, '.linss.h5'), ...\n strcat(output_folder, '/savedata/'), ...\n complex_matrices...\n );\n \n %% Load simulation settings and store in struct\n load(strcat(output_folder_linear, 'simulation_parameters.mat'));\n n_nodes = uint8(n_nodes);\n rigid_body_motions = false;\n \n input_settings = set_input_parameters(u_inf, ...\n state_space_system.Ts, ...\n num_modes, ...\n num_aero_states, ...\n rigid_body_motions, ...\n simulation_time, ...\n num_control_surfaces, ...\n n_nodes, ...\n control_input_start, ...\n gust_input_start);\n \n %% Remove unused input and outputs from the generated ROM in SHARPy and link deflection and its rate \n state_space_system = adjust_state_space_system(state_space_system, input_settings);\n \n \n %% Get gust input\n \n gust = get_1minuscosine_gust_input(...\n gust_length, ...\n gust_intensity, ...\n state_space_system.Ts, ...\n u_inf, ...\n simulation_time);\n %% Configure Simulink Inputs\n model_name = \"PID_linear_model\";\n simIn = Simulink.SimulationInput(model_name);\n simIn = setVariable(simIn,'D_gain',0);\n simIn = setVariable(simIn,'P_gain',0);\n simIn = setVariable(simIn,'I_gain',0);\n simIn = setVariable(simIn,'state_space_system',state_space_system);\n simIn = setVariable(simIn,'input_settings',input_settings);\n simIn = setVariable(simIn,'gust', gust);\n %% Run Simulink with PID Controller \n warning('off','all');\n % open loop\n fprintf('Simulate linear open-loop gust response.')\n simIn = setVariable(simIn,'controller_on',0);\n\n out_open_loop = sim(simIn);\n % closed loop P = 5 \n simIn = setVariable(simIn,'controller_on',1);\n simIn = setVariable(simIn,'P_gain',5);\n fprintf('Simulate linear closed-loop gust response with P=5.')\n out_PID_5 = sim(simIn);\n \n % closed loop P = 10\n simIn = setVariable(simIn,'P_gain',10);\n fprintf('Simulate linear closed-loop gust response with P=10.')\n out_PID_10 = sim(simIn);\n \n %% Save results\n deflection = [out_PID_5.delta.Data(:,1)...\n out_PID_10.delta.Data(:,1)...\n zeros(size(out_PID_5.delta.Time, 1), 1)];\n deflection_rate = [out_PID_5.delta_dot.Data(:,1)...\n out_PID_10.delta_dot.Data(:,1)...\n zeros(size(out_PID_5.delta_dot.Time, 1), 1)];\n tip_deflection = [out_PID_5.actual_output.Data(:,1)...\n out_PID_10.actual_output.Data(:,1)...\n out_open_loop.actual_output.Data(:,1)];\n tip_deflection= tip_deflection + eta_ref(n_nodes/2*6-3);\n time_array = out_open_loop.tout;\n \n output_folder_linear = strcat(output_folder, '/linear_results/')\n writematrix(deflection, strcat(output_folder_linear, 'deflection.txt'),'Delimiter',',');\n writematrix(time_array, strcat(output_folder_linear, 'time_array_linear.txt'),'Delimiter',',');\n writematrix(deflection_rate,strcat(output_folder_linear, './deflection_rate.txt'),'Delimiter',',');\n writematrix(tip_deflection,strcat(output_folder_linear, './tip_deflection.txt'),'Delimiter',',');\n\n success = true\n\nend\n" }, { "path": "docs/source/content/example_notebooks/UDP_control/get_settings_udp.py", "content": "\"\"\"\r\n Script to set the required SHARPy settings for all cases within\r\n the UDP Control example notebook. \r\n\"\"\"\r\ndef get_settings_udp(model, flow, **kwargs):\r\n gust = kwargs.get('gust', False)\r\n \r\n horseshoe = kwargs.get('horseshoe', False)\r\n gravity = kwargs.get('gravity', True)\r\n wake_length_factor = kwargs.get('wake_length_factor', 10)\r\n\r\n num_cores = kwargs.get('num_cores', 2)\r\n num_modes = kwargs.get('num_modes', 20)\r\n free_flight = kwargs.get('free_flight', False)\r\n tolerance = kwargs.get('tolerance', 1e-6)\r\n n_load_steps = kwargs.get('n_load_steps', 5)\r\n fsi_tolerance = kwargs.get('fsi_tolerance', 1e-6)\r\n relaxation_factor = kwargs.get('relaxation_factor', 0.1)\r\n newmark_damp = kwargs.get('newmark_damp', 0.5e-4)\r\n output_folder = kwargs.get('output_folder', './output/')\r\n model.config['SHARPy'] = {'case': model.case_name,\r\n 'route': model.route,\r\n 'flow': flow,\r\n 'write_screen': kwargs.get('write_screen', 'on'),\r\n 'write_log': 'on',\r\n 'save_settings': 'on',\r\n 'log_folder': output_folder + '/',\r\n 'log_file': model.case_name + '.log'}\r\n\r\n\r\n model.config['BeamLoader'] = {'unsteady': 'off',\r\n 'orientation': model.quat}\r\n\r\n model.config['AerogridLoader'] = {'unsteady': 'on',\r\n 'aligned_grid': 'on',\r\n 'mstar': wake_length_factor*model.M, #int(20/tstep_factor),\r\n 'wake_shape_generator': 'StraightWake',\r\n 'wake_shape_generator_input': {\r\n 'u_inf':model.u_inf,\r\n 'u_inf_direction': [1., 0., 0.],\r\n 'dt':model.dt,\r\n },\r\n }\r\n if horseshoe:\r\n model.config['AerogridLoader']['mstar'] = 1\r\n\r\n model.config['StaticCoupled'] = {\r\n 'print_info': 'on',\r\n 'max_iter': 200,\r\n 'n_load_steps': n_load_steps,\r\n 'tolerance': 1e-5,\r\n 'relaxation_factor': relaxation_factor,\r\n 'aero_solver': 'StaticUvlm',\r\n 'aero_solver_settings': {\r\n 'rho': model.rho,\r\n 'print_info': 'off',\r\n 'horseshoe': 'on',\r\n 'num_cores': num_cores,\r\n 'n_rollup': 0,\r\n 'velocity_field_generator': 'SteadyVelocityField',\r\n 'velocity_field_input': {\r\n 'u_inf': model.u_inf,\r\n 'u_inf_direction': model.u_inf_direction},\r\n 'vortex_radius': 1e-9},\r\n 'structural_solver': 'NonLinearStatic',\r\n 'structural_solver_settings': {'print_info': 'off',\r\n 'max_iterations': 200,\r\n 'num_load_steps': 5,\r\n 'delta_curved': 1e-6,\r\n 'min_delta': 1e-8,\r\n 'gravity': gravity,\r\n 'gravity': 9.81},\r\n }\r\n\r\n\r\n model.config['AerogridPlot'] = {'include_rbm': 'off',\r\n 'include_applied_forces': 'on',\r\n 'minus_m_star': 0}\r\n model.config['BeamPlot'] = {'include_rbm': 'off',\r\n 'include_applied_forces': 'on'}\r\n \r\n model.config['WriteVariablesTime'] = {'structure_variables': ['pos'],\r\n 'structure_nodes': list(range(0, model.num_node_surf)),\r\n 'cleanup_old_solution': 'on',\r\n }\r\n \r\n \r\n \r\n model.config['DynamicCoupled'] = {'print_info': 'on',\r\n 'structural_substeps': 10,\r\n 'dynamic_relaxation': 'on',\r\n 'cleanup_previous_solution': 'on',\r\n 'structural_solver': 'NonLinearDynamicPrescribedStep',\r\n 'structural_solver_settings': {'print_info': 'off',\r\n 'max_iterations': 950,\r\n 'delta_curved': 1e-1,\r\n 'min_delta': tolerance,\r\n 'newmark_damp': newmark_damp,\r\n 'gravity': gravity,\r\n 'gravity': 9.81,\r\n 'num_steps': model.n_tstep,\r\n 'dt':model.dt,\r\n },\r\n 'aero_solver': 'StepUvlm',\r\n 'aero_solver_settings': {'print_info': 'on',\r\n 'num_cores': num_cores,\r\n 'convection_scheme': 2,\r\n 'velocity_field_generator': 'SteadyVelocityField',\r\n 'velocity_field_input': {'u_inf': model.u_inf,\r\n 'u_inf_direction': [1., 0., 0.]},\r\n 'rho': model.rho,\r\n 'n_time_steps': model.n_tstep,\r\n 'vortex_radius': 1e-9,\r\n 'dt': model.dt,\r\n 'gamma_dot_filtering': 3},\r\n 'fsi_substeps': 200,\r\n 'fsi_tolerance': fsi_tolerance,\r\n 'relaxation_factor': model.relaxation_factor,\r\n 'minimum_steps': 1,\r\n 'relaxation_steps': 150,\r\n 'final_relaxation_factor': 0.0,\r\n 'n_time_steps': model.n_tstep,\r\n 'dt': model.dt,\r\n 'include_unsteady_force_contribution': kwargs.get('unsteady_force_distribution', True),\r\n 'postprocessors': ['WriteVariablesTime', 'BeamPlot', 'AerogridPlot'],\r\n 'postprocessors_settings': {'BeamPlot': {'include_rbm': 'on',\r\n 'include_applied_forces': 'on'},\r\n 'StallCheck': {},\r\n 'AerogridPlot': {\r\n 'u_inf': model.u_inf,\r\n 'include_rbm': 'on',\r\n 'include_applied_forces': 'on',\r\n 'minus_m_star': 0},\r\n 'WriteVariablesTime': {\r\n 'structure_variables': ['pos', 'psi'],\r\n 'structure_nodes': [model.num_node_surf - 1,\r\n model.num_node_surf,\r\n model.num_node_surf + 1],\r\n },\r\n },\r\n 'network_settings': kwargs.get('network_settings', {}),\r\n }\r\n \r\n if gust:\r\n gust_settings = kwargs.get('gust_settings', {'gust_shape': '1-cos',\r\n 'gust_length': 10.,\r\n 'gust_intensity': 0.01,\r\n 'gust_offset': 0.})\r\n model.config['DynamicCoupled']['aero_solver_settings']['velocity_field_generator'] = 'GustVelocityField'\r\n model.config['DynamicCoupled']['aero_solver_settings']['velocity_field_input'] = {'u_inf': model.u_inf,\r\n 'u_inf_direction': [1., 0, 0],\r\n 'relative_motion': bool(not free_flight),\r\n 'offset': gust_settings['gust_offset'],\r\n 'gust_shape': gust_settings['gust_shape'],\r\n 'gust_parameters': {\r\n 'gust_length': gust_settings['gust_length'],\r\n 'gust_intensity': gust_settings['gust_intensity'] * model.u_inf,\r\n } \r\n }\r\n\r\n model.config['PickleData'] = {}\r\n \r\n model.config['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\r\n 'inout_coordinates': 'nodes', \r\n # 'recover_accelerations': True, \r\n 'linear_system_settings': {\r\n 'beam_settings': {'modal_projection': True,\r\n 'inout_coords': 'modes',\r\n 'discrete_time': True,\r\n 'newmark_damp': newmark_damp,\r\n 'discr_method': 'newmark',\r\n 'dt': model.dt,\r\n 'proj_modes': 'undamped',\r\n 'num_modes': num_modes,\r\n 'print_info': 'on',\r\n 'gravity': gravity,\r\n 'remove_dofs': []},\r\n 'aero_settings': {'dt': model.dt,\r\n 'integr_order': 2,\r\n 'density': model.rho,\r\n 'remove_predictor': True,\r\n 'use_sparse': 'off',\r\n 'gust_assembler': 'LeadingEdge',\r\n 'ScalingDict': kwargs.get('scaling_dict', {'length':1, 'speed': 1, 'density': 1}),\r\n },\r\n 'track_body': free_flight,\r\n 'use_euler': free_flight,\r\n }}\r\n model.config['Modal'] = {'print_info': True,\r\n 'use_undamped_modes': True,\r\n 'NumLambda': num_modes,\r\n 'rigid_body_modes': free_flight, \r\n 'write_modes_vtk': False,\r\n 'print_matrices': False,\r\n 'continuous_eigenvalues': 'off',\r\n 'dt': model.dt,\r\n 'plot_eigenvalues': False,\r\n }\r\n model.config['SaveData']['save_linear'] = True\r\n if kwargs.get('remove_gust_input_in_statespace', False):\r\n model.config['LinearAssembler']['linear_system_settings']['aero_settings']['remove_inputs'] = ['u_gust']\r\n\r\n rom_settings = kwargs.get('rom_settings', {'use': False})\r\n if rom_settings['use']:\r\n model.config['LinearAssembler']['linear_system_settings']['aero_settings']['rom_method'] = rom_settings['rom_method'],\r\n model.config['LinearAssembler']['linear_system_settings']['aero_settings']['rom_method_settings'] = rom_settings['rom_method_settings']\r\n return model.config\r\n" }, { "path": "docs/source/content/example_notebooks/UDP_control/matlab_functions/adjust_state_space_system.m", "content": "function state_space_converted = adjust_state_space_system(state_space_system, input_settings)\n%convert_state_space_for_LQR Adjust extracted state space system\n% The loaded state space system exported from SHARPy is adjusted here for\n% the closed-loop simulations. This includes:\n% - extracts the column from the B and D matrices that describe the\n% effect of the gust input to the states\n% - removing all unused inputs and rearranging for example the\n% deflection of a control surface and its rate as both depend on\n% each other\n% - removes not considered outputs\n% - assembles updated discrete state space system\n\n\n%% Reduce model by deleting unused outupts (only tip deflection relevant here)\nC_sensor = state_space_system.C(input_settings.index.tip_displacement,:);\nD_sensor = state_space_system.D(input_settings.index.tip_displacement,:);\n\n%% Reduce model with not used inputs\nidx_input_end =input_settings.index.control_input_start + 2 * input_settings.num_control_surfaces - 1;\n\nidx_inputs = [input_settings.index.control_input_start:idx_input_end];\nB_cs = state_space_system.B(:,idx_inputs);\nD_cs = D_sensor(:,idx_inputs); \n\n\n%% Extract delta to state\n\nnew_A_colum = B_cs(:,1 :input_settings.num_control_surfaces);\nA = [state_space_system.A new_A_colum; ...\n zeros(input_settings.num_control_surfaces,...\n (size(state_space_system.A,2)+ input_settings.num_control_surfaces))];\n\nfor counter = 0:1:input_settings.num_control_surfaces-1\n A(size(A,1)-counter,size(A,2)-counter) = 1; % Explain one\nend\n\n%Delete delta input and add delta_dot influence on delta \nB_cs(:,1:input_settings.num_control_surfaces) = [];\nB_cs = [B_cs; eye(input_settings.num_control_surfaces) * state_space_system.Ts]; \n\n% Adding feed through of the delta-input on the output on C and deleting \n% column added in C out of D; new column\nC = [C_sensor D_cs(:,1:input_settings.num_control_surfaces)];\nD_cs(:, 1:input_settings.num_control_surfaces) = []; \n\n\n%% Get Disturbance Matrices\nG = [state_space_system.B(:,input_settings.index.gust_input_start); ...\n zeros(input_settings.num_control_surfaces, 1)];\nH = D_sensor(:,input_settings.index.gust_input_start);\n%% Assemble final state space system\n\nstate_space_converted = ss(A,[B_cs G],C,[D_cs H],state_space_system.Ts);\n\nend" }, { "path": "docs/source/content/example_notebooks/UDP_control/matlab_functions/get_1minuscosine_gust_input.m", "content": "function gust_time_series = get_1minuscosine_gust_input(gust_length, gust_intensity, dt, u_inf, simulation_time)\n%get_1minuscosine_gust_input Gust input is generated and stored.\n\ngust_time = [0:dt:simulation_time];\noffset_gust = 0;\ngust_intensity = gust_intensity*u_inf;\n\nend_gust = gust_length/u_inf;\nx = [0:dt:end_gust]*u_inf; % spatial coordinate\n\ngust_cos = (1.0 - cos(2*pi*x/ gust_length)) * gust_intensity / 2;\ngust_vel_z = [zeros(1,offset_gust) gust_cos];\n\n%% Adjust vector length \ndelta_vector_length = size(gust_time,2) - size(gust_vel_z,2);\ngust_vel_z = [gust_vel_z zeros(1, delta_vector_length)]; \n\n%% Store gust velocities in time history\ngust_time_series = [gust_time; gust_vel_z]';\n\nend" }, { "path": "docs/source/content/example_notebooks/UDP_control/matlab_functions/read_SHARPy_state_space_system.m", "content": "function [state_space_system, eta_ref] = read_SHARPy_state_space_system(file_name_sharpy, folder, complex)\r\n%read_SHARPy_state_space_system Gets sate space model from SHARPy output\r\n\r\nabsolute_file_path = strcat(folder, file_name_sharpy);\r\n% Reference Point and Timestep\r\neta_ref = h5read(absolute_file_path, '/linearisation_vectors/eta');\r\ndt = h5read(absolute_file_path, '/ss/dt');\r\n% Read state space matrices \r\nif complex\r\n A = h5read(absolute_file_path, '/ss/A').r; \r\n B = h5read(absolute_file_path, '/ss/B').r; \r\n C = h5read(absolute_file_path, '/ss/C').r;\r\n D = h5read(absolute_file_path, '/ss/D');\r\nelse\r\n A = h5read(absolute_file_path, '/ss/A'); \r\n B = h5read(absolute_file_path, '/ss/B'); \r\n C = h5read(absolute_file_path, '/ss/C');\r\n D = h5read(absolute_file_path, '/ss/D');\r\nend\r\n\r\n% Sometimes matrices are exported transposed\r\nif size(A, 1) ~= size(B, 1)\r\n A = transpose(A); \r\n B = transpose(B); \r\nend\r\nif size(C, 1) ~= size(D, 1)\r\n C = transpose(C); \r\n D = transpose(D); \r\nend\r\n\r\n% Assemble final discrete state space system\r\nstate_space_system = ss(A, B, C, D, dt);\r\n\r\nend \r\n" }, { "path": "docs/source/content/example_notebooks/UDP_control/matlab_functions/set_input_parameters.m", "content": "function input = set_input_parameters(u_inf, ...\n dt, ...\n num_modes, ...\n num_aero_states, ...\n rbm_considered, ...\n flight_time, ...\n num_control_surfaces, ...\n n_nodes, ...\n control_input_start, ...\n gust_input_start)\n\n\n%set_input_parameters Save input settings to struct.\n% This function returns a struct that contains all necessary input\n% settings to adjust the state space model for the control design.\ninput.u_inf = u_inf;\ninput.num_modes = num_modes;\ninput.num_aero_states = num_aero_states;\ninput.rbm = rbm_considered; \ninput.flight_time = flight_time;\ninput.num_control_surfaces = num_control_surfaces;\ninput.rbm = rbm_considered;\ninput.dt = dt;\n\n%% Set indices\ninput.index.control_input_start = control_input_start;\ninput.index.gust_input_start = gust_input_start;\ninput.index.tip_displacement = n_nodes * 6 + n_nodes / 2 * 6 - 3; % forces + right wing nodes\n" }, { "path": "docs/source/content/example_notebooks/UDP_control/parameter_UDP_control_pazy_udp_closed_loop_gust_response.json", "content": "{\"server_ip_addr\": \"127.0.0.1\", \"client_ip_addr\": \"127.0.0.1\", \"port_in_network\": 64017, \"port_out_network_server\": 59017, \"port_out_network_client\": 59007, \"output_folder\": \"/home/rpalacio/sharpy/docs/source/content/example_notebooks/UDP_control/output\", \"dt\": 0.000625, \"simulation_time\": 1.0, \"num_sensors\": 1, \"initial_cs_deflection\": 0, \"reference_deflection\": 0.02290911}" }, { "path": "docs/source/content/example_notebooks/UDP_control/pazy_PID_controller_UDP.py", "content": "import socket\r\nimport logging\r\nimport struct\r\nimport sharpy.io.message_interface as message_interface\r\nimport numpy as np\r\nfrom pid_controller import PID_Controller\r\nimport json\r\nimport os\r\n\r\n\"\"\"\r\nThis script establishes a UDP connection to SHARPy from which it receives sensor measurements. \r\nBased on these measurements, a PID-Controller computes an actuator input that is feedback \r\nto SHARPy again using UDP. \r\n\r\nThe user just needs to specify the name of the case name (bottom of the script) and run the main\r\nfunction 'run_controller(case_name)'. The case name is needed to find the appropriate json input \r\nfile for all required information for the following steps:\r\n1) Load input settings \r\n2) Establish a connection to the UDP i/o network created by SHARPy (server)\r\n3) Initialise PID Controller\r\n4) Enter the time loop including: \r\n a) Sending a control input (starting with the initial value loaded from the init file)\r\n to SHARPy;\r\n b) The resulting sensor measurement for the next simulation time step is sent back to \r\n this client.\r\n c) Based on the error to the defined target value, the PID controller computes a control\r\n input.\r\n d) Both the received sensor measurement and generated control input are saved in .txt-files.\r\n a) Next step, would be a) again. But now, we send the generated control input.\r\n5) Closes UDP connections\r\n\"\"\"\r\n\r\ndef create_and_bind_client(ip_addr, port):\r\n \"\"\"\r\n Creates and bind the client to the server socket using UDP.\r\n \"\"\"\r\n sock = socket.socket(socket.AF_INET, socket.SOCK_DGRAM)\r\n sock.bind((ip_addr, port))\r\n return sock\r\n\r\ndef setup_udp_network(dict_parameters):\r\n \"\"\"\r\n This function connects the present client to two sockets, specified within the \r\n information (i.e. ip addresses and ports). Further, a timeout of 120 s are set\r\n for SHARPy's output network, i.e. if new sensor measurements are not received\r\n (normally caused by an error), the network connection is closed.\r\n \"\"\"\r\n server_ip_addr = dict_parameters[\"server_ip_addr\"] # SHARPy\r\n client_ip_addr = dict_parameters[\"client_ip_addr\"] # controller\r\n port_in_network = dict_parameters[\"port_in_network\"] \r\n port_out_network_client = dict_parameters[\"port_out_network_client\"] \r\n port_in_network_client = port_out_network_client - 8 # needs to be different from port of network client\r\n\r\n sharpy_in_network= (server_ip_addr, port_in_network)\r\n\r\n in_sock = create_and_bind_client(client_ip_addr, port_in_network_client)\r\n\r\n out_sock = create_and_bind_client(client_ip_addr, port_out_network_client)\r\n out_sock.settimeout(120)\r\n\r\n return sharpy_in_network, in_sock, out_sock\r\n\r\ndef init_logger():\r\n logging.basicConfig(format='%(asctime)s - %(name)s - %(levelname)s - %(message)s',\r\n level=20)\r\n return logging.getLogger(__name__)\r\n\r\ndef write_data_to_file(data, file_path, init_file=False):\r\n if init_file:\r\n file_mode = \"w\"\r\n else:\r\n file_mode = \"ab\"\r\n\r\n with open(file_path, file_mode) as f:\r\n np.savetxt(f, data, delimiter=',', newline='\\r\\n')\r\n\r\ndef receive_sensor_measurements(logger, out_sock, msg_len, num_sensors):\r\n \"\"\"\r\n UDP socket waits and receives sensor measurements from SHARPy. After,\r\n the message is decoded and unpacked in an appropriate format and returned\r\n to the main function.\r\n \"\"\"\r\n try:\r\n msg, conn = out_sock.recvfrom(msg_len)\r\n except socket.timeout:\r\n logger.info('Socket time out')\r\n raise\r\n logger.info('Received {}-byte long data \"{}\" from {}'.format(len(msg), msg, conn))\r\n\r\n values = message_interface.decoder(msg)\r\n logger.info('Received {}'.format(values))\r\n \r\n results = np.zeros((num_sensors,))\r\n for isensor in range(num_sensors):\r\n results[isensor] = values[isensor][1]\r\n return results\r\n\r\ndef send_control_input(logger, in_sock, sharpy_in_network, control_input_to_send):\r\n \"\"\"\r\n The generated control input is packed into a binary message readable from SHARPy.\r\n Note that, this message includes the control input twice, since the ailerons \r\n on right and left wing have different IDs. \r\n \"\"\"\r\n ctrl_value = struct.pack('<5sifif', b'RREF0', 0, control_input_to_send, 1, control_input_to_send)\r\n logger.info('Sending control input of size {} bytes.'.format(len(ctrl_value)))\r\n in_sock.sendto(ctrl_value, sharpy_in_network)\r\n logger.info('Sent control input {} to {}.'.format(control_input_to_send, sharpy_in_network))\r\n\r\ndef run_controller(case_name):\r\n \r\n # 1) Load input settings\r\n route_file_dir = os.path.abspath('')\r\n with open(route_file_dir + '/parameter_UDP_control_{}.json'.format(case_name), 'r') as fp:\r\n dict_simulation_parameters = json.load(fp)\r\n \r\n # define simulation settings\r\n curr_ts = 0\r\n num_sensors = dict_simulation_parameters[\"num_sensors\"]\r\n msg_len = 5 + 8 * num_sensors\r\n dt = dict_simulation_parameters[\"dt\"]\r\n number_timesteps = int(dict_simulation_parameters[\"simulation_time\"] / dt)\r\n output_folder = dict_simulation_parameters[\"output_folder\"]\r\n\r\n init_cs_deflection = float(dict_simulation_parameters[\"initial_cs_deflection\"])\r\n reference_deflection= dict_simulation_parameters[\"reference_deflection\"]\r\n \r\n # 2) Establish UDP connections\r\n sharpy_in_network, in_sock, out_sock = setup_udp_network(dict_simulation_parameters)\r\n\r\n # setup network and data output\r\n logger = init_logger()\r\n file_path_sensor = os.path.join(output_folder, case_name, \"{}_{}\".format(case_name, \"sensor_measurement\"))\r\n file_path_control = os.path.join(output_folder, case_name, \"{}_{}\".format(case_name, \"control_input\"))\r\n\r\n # 3) Initialise controller and control input\r\n PID = PID_Controller(10., 0., 0., target=reference_deflection)\r\n control_input = init_cs_deflection\r\n\r\n # 4) Enter time control loop\r\n while curr_ts < number_timesteps:\r\n # a)\r\n send_control_input(logger, \r\n in_sock, \r\n sharpy_in_network, \r\n control_input)\r\n\r\n # b)\r\n sensor_data = receive_sensor_measurements(logger, \r\n out_sock, \r\n msg_len,\r\n num_sensors)\r\n \r\n\r\n # c) Generate control input with PID controller\r\n if curr_ts >= 5:\r\n control_input = PID.generate_control_input(sensor_data, dt)\r\n\r\n # d) Store sensor and control input to .txt-file\r\n write_data_to_file(sensor_data,\r\n file_path_sensor, \r\n init_file= bool(curr_ts==0))\r\n\r\n write_data_to_file([control_input],\r\n file_path_control,\r\n init_file= bool(curr_ts==0))\r\n\r\n curr_ts += 1\r\n\r\n # 5) Close sockets\r\n out_sock.close()\r\n in_sock.close()\r\n logger.info('Closed input and output sockets')\r\n\r\nif __name__ == '__main__':\r\n case_name = \"pazy_udp_closed_loop_gust_response\"\r\n run_controller(case_name)" }, { "path": "docs/source/content/example_notebooks/UDP_control/pazy_network_info.yml", "content": "---\n- name: 'control_surface_deflection'\n var_type: 'control_surface'\n inout: 'in'\n position: 0\n- name: 'control_surface_deflection'\n var_type: 'control_surface'\n inout: 'in'\n position: 1\n- name: 'pos'\n inout: 'out'\n position: 8\n index: 2\n var_type: 'node'\n...\n" }, { "path": "docs/source/content/example_notebooks/UDP_control/pid_controller.py", "content": "class PID_Controller(object):\r\n def __init__(self, P_gain, I_gain, D_gain, target=0):\r\n self.P_gain = P_gain\r\n self.I_gain = I_gain\r\n self.D_gain = D_gain\r\n self.target = target\r\n\r\n self.error = 0.\r\n self.integral_error = 0.\r\n self.derivative_error = 0.\r\n self.previous_error = 0.\r\n\r\n def generate_control_input(self, sensor_measurement, dt):\r\n self.error = self.target - sensor_measurement\r\n self.integral_error += self.error * dt \r\n self.derivative_error = (self.error - self.previous_error) * dt\r\n self.previous_error = self.error\r\n \r\n return self.P_gain * self.error + self.I_gain * self.integral_error + self.derivative_error * self.D_gain" }, { "path": "docs/source/content/example_notebooks/UDP_control/tutorial_udp_control.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Closed-Loop Simulation of the Pazy wing with SHARPy as a hardware-in-the-loop system\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This tutorial exemplifies the application of an external controller on a nonlinear aeroelastic system using SHARPy as a hardware-in-the-loop system. The controller receives sensor measurements from SHARPy using an interface based on the User Datagram Protocol (UDP). After generating the control input, the control interface feeds this input back to the actuators incorporated in SHARPy again through the UDP interface. \\n\",\n \"\\n\",\n \"\\n\",\n \"The notebook includes examples of the main methods in SHARPy for controller design, including both the generation of a linearized reduced-order model (ROM) of the nonlinear aeroelastic model (around a nonlinear equilibium point) for control design and, finally, how to apply their controller on a nonlinear aeroelastic simulation. The test case is the Pazy wing as modelled by Goizueta et al (JAircraft, 2022).\\n\",\n \"\\n\",\n \"Reading material recommended are:\\n\",\n \"\\n\",\n \"[1] Artola, M., Goizueta, N., Wynn, A., and Palacios, R., “Proof of Concept for a Hardware-in-the-Loop Nonlinear ControlFramework for Very Flexible Aircraft,”AIAA Scitech 2021 Forum, 2021. https://doi.org/10.2514/6.2021-1392.\\n\",\n \"\\n\",\n \"[2] Stefanie Duessler, Thulasi Mylvaganam and Rafael Palacios. \\\"LQG-based Gust Load Alleviation Systems for Very Flexible Aircraft,\\\" AIAA 2023-2571. AIAA SCITECH 2023 Forum. January 2023. https://doi.org/10.2514/6.2023-2571.\\n\",\n \"\\n\",\n \"And other useful references for the Pazy model and Krylov-based model order reduction scheme are:\\n\",\n \"\\n\",\n \"[3] Norberto Goizueta, Andrew Wynn, Rafael Palacios, Ariel Drachinsky, and Daniella E. Raveh, \\\"Flutter Predictions for Very Flexible Wing Wind Tunnel Test\\\",\\n\",\n \"Journal of Aircraft 2022 59:4, 1082-1097. https://doi.org/10.2514/1.C036710.\\n\",\n \"\\n\",\n \"[4] Norberto Goizueta, Andrew Wynn, and Rafael Palacios, \\\"Adaptive Sampling for Interpolation of Reduced-Order Aeroelastic Systems\\\", AIAA Journal 2022 60:11, 6183-6202 https://doi.org/10.2514/1.J062050.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The notebook is structured such that first, we design the model and its operational point. Second, the model is linearized and reduced. The resulting reduced-order model (ROM) is then used for control design using Matlab. Third, we apply via a UDP Interface the designed controller on a nonlinear aeroelastic simulation performed with SHARPy.\\n\",\n \"\\n\",\n \"Please note that this notebook requires 12 hours to be completed on a standard desktop computer. The longest simulation is the open-loop nonlinear gust response simulation taking around 8 hours, while the closed-loop nonlinear gust response simulation only takes 4 hours. \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Requirements\\n\",\n \"\\n\",\n \"This notebook needs to be run within the sharpy environment. Please check if you have installed SHARPy correctly. Matlab with a version of 2022 or newer is required for the preliminary control design (the matlab engine is also available in older versions of Matlab butno through pip install).\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import matplotlib.pyplot as plt\\n\",\n \"import numpy as np\\n\",\n \"import os\\n\",\n \"import sharpy.cases.templates.flying_wings as wings\\n\",\n \"import sharpy.sharpy_main\\n\",\n \"import json\\n\",\n \"\\n\",\n \"! pip install matlabengine\\n\",\n \"import matlab.engine\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Demonstrator Model \\n\",\n \"\\n\",\n \"The very-flexible Pazy wing serves as a demonstrator model and an aileron located near the wingtip as an actuator. The control objective in this example is to alleviate the wingtip displacement due to gust-induced wing loads. As an example, we use a P-controller implemented in a Python interface with the objective to reduce the wingtip displacement induced by a gust encounter. However, the reader can test any controller run on any platform as long as a working UDP connection to SHARPy is established. \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Wind tunnel conditions\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"u_inf = 40 # m/s\\n\",\n \"alpha_deg = 1\\n\",\n \"rho = 1.225\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Wing and Wake Lattice Discretisation\\n\",\n \"\\n\",\n \"Note that for convergence, we need a finer lattice grid. However, this would unnecessarily increase this notebook's duration which is already high enough with these coarse settings.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"number_chordwise_panels = 4\\n\",\n \"number_spanwise_nodes = 16\\n\",\n \"wake_length_factor = 10\\n\",\n \"\\n\",\n \"num_control_surfaces = 2\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### General Simulation Settings\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"num_cores = 4\\n\",\n \"simulation_time =1.0\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"cases_folder = './cases/' # folder to store input files \\n\",\n \"output_folder = './output' # folder to save results\\n\",\n \"route_notebook_dir = os.path.abspath('')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Open-Loop Gust Response\\n\",\n \"After, defining the general model settings, we now simulate the open-loop response of the Pazy wing to a gust. For this, we first have to generate input files for the Pazy model aerodynamic and structural properties, giving the above-defined flight conditions, discretisation, and simulation settings.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"case_name = 'pazy_open_loop_gust_response'\\n\",\n \"pazy_model_open_loop = wings.PazyControlSurface(M=number_chordwise_panels,\\n\",\n \" N=number_spanwise_nodes,\\n\",\n \" Mstar_fact=wake_length_factor,\\n\",\n \" u_inf=u_inf,\\n\",\n \" alpha=alpha_deg,\\n\",\n \" rho=rho,\\n\",\n \" n_surfaces=2,\\n\",\n \" route=cases_folder + '/' + case_name,\\n\",\n \" case_name=case_name,\\n\",\n \" physical_time=simulation_time,)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"def generate_aero_and_fem_input_files(model):\\n\",\n \" model.clean_test_files()\\n\",\n \" model.update_derived_params()\\n\",\n \" model.generate_aero_file()\\n\",\n \" model.generate_fem_file()\\n\",\n \" \\n\",\n \"generate_aero_and_fem_input_files(pazy_model_open_loop)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Next, we define the gust shape used, i.e. a 1-cosine gust with a gust length of 10 m and intensity of 2 %.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"gust = True\\n\",\n \"gust_settings ={'gust_shape': '1-cos',\\n\",\n \" 'gust_length': 10.,\\n\",\n \" 'gust_intensity': 0.02,\\n\",\n \" 'gust_offset': 0.} \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"and create the final settings for the open-loop gust response simulation. Most importantly here, is the `flow` list which defines which solver will be run in which order. For more information about each solver, we kindly ask you to check our documentation (https://ic-sharpy.readthedocs.io/en/latest/content/solvers.html).\\n\",\n \"\\n\",\n \"We are using the `get_setttings_udp` function to create our final settings. Basic settings can be adjusted by using different inputs. Please check the function code to be aware of the parameters used here.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"flow = ['BeamLoader',\\n\",\n \" 'AerogridLoader',\\n\",\n \" 'StaticCoupled',\\n\",\n \" 'AerogridPlot',\\n\",\n \" 'BeamPlot',\\n\",\n \" 'DynamicCoupled',\\n\",\n \" ]\\n\",\n \"from get_settings_udp import get_settings_udp\\n\",\n \"\\n\",\n \"pazy_model_open_loop.set_default_config_dict()\\n\",\n \"pazy_model_open_loop.config = get_settings_udp(pazy_model_open_loop,\\n\",\n \" flow,\\n\",\n \" num_cores=num_cores,\\n\",\n \" wake_length_factor=wake_length_factor,\\n\",\n \" output_folder = output_folder,\\n\",\n \" gust=gust,\\n\",\n \" gust_settings=gust_settings)\\n\",\n \"pazy_model_open_loop.config.write()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Run SHARPy Simulation (open-loop test)\\n\",\n \"Having all input files ready, let us start the simulation. Note that this simulation takes up to eight hours. \\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"--------------------------------------------------------------------------------\\u001b[0m\\n\",\n \" ###### ## ## ### ######## ######## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ####\\u001b[0m\\n\",\n \" ###### ######### ## ## ######## ######## ##\\u001b[0m\\n\",\n \" ## ## ## ######### ## ## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \" ###### ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \"--------------------------------------------------------------------------------\\u001b[0m\\n\",\n \"Aeroelastics Lab, Aeronautics Department.\\u001b[0m\\n\",\n \" Copyright (c), Imperial College London.\\u001b[0m\\n\",\n \" All rights reserved.\\u001b[0m\\n\",\n \" License available at https://github.com/imperialcollegelondon/sharpy\\u001b[0m\\n\",\n \"\\u001b[36mRunning SHARPy from /home/rpalacio/sharpy/docs/source/content/example_notebooks/UDP_control\\u001b[0m\\n\",\n \"\\u001b[36mSHARPy being run is in /home/rpalacio/anaconda3/envs/sharpy/lib/python3.10/site-packages\\u001b[0m\\n\",\n \"SHARPy output folder set\\u001b[0m\\n\",\n \"\\u001b[34m\\t./output//pazy_open_loop_gust_response/\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of BeamLoader\\u001b[0m\\n\",\n \"Variable for_pos has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0.0, 0, 0]\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of AerogridLoader\\u001b[0m\\n\",\n \"Variable freestream_dir has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [1.0, 0.0, 0.0]\\u001b[0m\\n\",\n \"Variable control_surface_deflection has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: []\\u001b[0m\\n\",\n \"Variable control_surface_deflection_generator_settings has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n \"Variable dx1 has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: -1.0\\u001b[0m\\n\",\n \"Variable ndx1 has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n \"Variable r has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1.0\\u001b[0m\\n\",\n \"Variable dxmax has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: -1.0\\u001b[0m\\n\",\n \"\\u001b[34mThe aerodynamic grid contains 2 surfaces\\u001b[0m\\n\",\n \"\\u001b[34m Surface 0, M=4, N=8\\u001b[0m\\n\",\n \" Wake 0, M=40, N=8\\u001b[0m\\n\",\n \"\\u001b[34m Surface 1, M=4, N=8\\u001b[0m\\n\",\n \" Wake 1, M=40, N=8\\u001b[0m\\n\",\n \" In total: 64 bound panels\\u001b[0m\\n\",\n \" In total: 640 wake panels\\u001b[0m\\n\",\n \" Total number of panels = 704\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of StaticCoupled\\u001b[0m\\n\",\n \"Variable correct_forces_method has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n \"Variable correct_forces_settings has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n \"Variable runtime_generators has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of NonLinearStatic\\u001b[0m\\n\",\n \"Variable abs_threshold has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1e-13\\u001b[0m\\n\",\n \"Variable newmark_damp has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0001\\u001b[0m\\n\",\n \"Variable gravity_on has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable gravity_dir has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0.0, 0.0, 1.0]\\u001b[0m\\n\",\n \"Variable relaxation_factor has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.3\\u001b[0m\\n\",\n \"Variable dt has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.01\\u001b[0m\\n\",\n \"Variable num_steps has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 500\\u001b[0m\\n\",\n \"Variable initial_position has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0. 0. 0.]\\u001b[0m\\n\",\n \"Variable initial_velocity has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0. 0. 0. 0. 0. 0.]\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of StaticUvlm\\u001b[0m\\n\",\n \"Variable rollup_dt has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.1\\u001b[0m\\n\",\n \"Variable rollup_aic_refresh has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n \"Variable rollup_tolerance has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0001\\u001b[0m\\n\",\n \"Variable iterative_solver has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable iterative_tol has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0001\\u001b[0m\\n\",\n \"Variable iterative_precond has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable cfl1 has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"Variable vortex_radius_wake_ind has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n \"Variable rbm_vel_g has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]\\u001b[0m\\n\",\n \"Variable centre_rot_g has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0.0, 0.0, 0.0]\\u001b[0m\\n\",\n \"Variable map_forces_on_struct has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"|=====|=====|============|==========|==========|==========|==========|==========|==========|\\u001b[0m\\n\",\n \"|iter |step | log10(res) | Fx | Fy | Fz | Mx | My | Mz |\\u001b[0m\\n\",\n \"|=====|=====|============|==========|==========|==========|==========|==========|==========|\\u001b[0m\\n\"\n ]\n },\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"fatal: not a git repository (or any of the parent directories): .git\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"| 0 | 0 | 0.00000 | -0.0277 | 0.0000 | 1.9185 | 0.0000 | 0.0387 | -0.0000 |\\u001b[0m\\n\",\n \"| 1 | 0 | -6.69935 | -0.0290 | 0.0000 | 1.9636 | 0.0000 | 0.0396 | -0.0000 |\\u001b[0m\\n\",\n \"| 0 | 1 | 0.00000 | -0.0566 | 0.0000 | 3.9396 | -0.0000 | 0.0794 | -0.0000 |\\u001b[0m\\n\",\n \"| 1 | 1 | -6.06871 | -0.0592 | 0.0000 | 4.0325 | -0.0000 | 0.0812 | -0.0000 |\\u001b[0m\\n\",\n \"| 0 | 2 | 0.00000 | -0.0866 | 0.0000 | 6.0718 | -0.0000 | 0.1222 | -0.0000 |\\u001b[0m\\n\",\n \"| 1 | 2 | -5.68671 | -0.0906 | 0.0000 | 6.2157 | -0.0000 | 0.1250 | -0.0000 |\\u001b[0m\\n\",\n \"| 0 | 3 | 0.00000 | -0.1177 | 0.0000 | 8.3244 | -0.0000 | 0.1673 | -0.0000 |\\u001b[0m\\n\",\n \"| 1 | 3 | -5.40580 | -0.1233 | 0.0000 | 8.5230 | -0.0000 | 0.1712 | -0.0000 |\\u001b[0m\\n\",\n \"| 0 | 4 | 0.00000 | -0.1501 | 0.0000 | 10.7075 | -0.0000 | 0.2149 | -0.0000 |\\u001b[0m\\n\",\n \"| 1 | 4 | -5.17976 | -0.1572 | 0.0000 | 10.9648 | -0.0000 | 0.2200 | -0.0000 |\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of AerogridPlot\\u001b[0m\\n\",\n \"Variable include_forward_motion has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable include_unsteady_applied_forces has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable name_prefix has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n \"Variable u_inf has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0\\u001b[0m\\n\",\n \"Variable dt has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0\\u001b[0m\\n\",\n \"Variable include_velocities has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable include_incidence_angle has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable num_cores has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n \"Variable vortex_radius has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n \"Variable stride has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n \"Variable save_wake has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"\\u001b[34m...Finished\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of BeamPlot\\u001b[0m\\n\",\n \"Variable include_FoR has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable include_applied_moments has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"Variable name_prefix has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n \"Variable output_rbm has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"\\u001b[34m...Finished\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of DynamicCoupled\\u001b[0m\\n\",\n \"Variable controller_id has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n \"Variable controller_settings has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n \"Variable steps_without_unsteady_force has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n \"Variable pseudosteps_ramp_unsteady_force has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n \"Variable correct_forces_method has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n \"Variable correct_forces_settings has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n \"Variable runtime_generators has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of NonLinearDynamicPrescribedStep\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of StepUvlm\\u001b[0m\\n\",\n \"Variable num_load_steps has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n \"Variable abs_threshold has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1e-13\\u001b[0m\\n\",\n \"Variable gravity_on has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable gravity_dir has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0.0, 0.0, 1.0]\\u001b[0m\\n\",\n \"Variable relaxation_factor has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.3\\u001b[0m\\n\",\n \"Variable iterative_solver has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable iterative_tol has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0001\\u001b[0m\\n\",\n \"Variable iterative_precond has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable cfl1 has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"Variable vortex_radius_wake_ind has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n \"Variable interp_coords has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n \"Variable filter_method has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n \"Variable interp_method has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n \"Variable yaw_slerp has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0\\u001b[0m\\n\",\n \"Variable centre_rot has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0.0, 0.0, 0.0]\\u001b[0m\\n\",\n \"Variable quasi_steady has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable gust_component has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 2\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of WriteVariablesTime\\u001b[0m\\n\",\n \"Variable delimiter has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n \"Variable FoR_variables has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: ['']\\u001b[0m\\n\",\n \"Variable FoR_number has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0]\\u001b[0m\\n\",\n \"Variable aero_panels_variables has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: ['']\\u001b[0m\\n\",\n \"Variable aero_panels_isurf has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0]\\u001b[0m\\n\",\n \"Variable aero_panels_im has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0]\\u001b[0m\\n\",\n \"Variable aero_panels_in has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0]\\u001b[0m\\n\",\n \"Variable aero_nodes_variables has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: ['']\\u001b[0m\\n\",\n \"Variable aero_nodes_isurf has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0]\\u001b[0m\\n\",\n \"Variable aero_nodes_im has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0]\\u001b[0m\\n\",\n \"Variable aero_nodes_in has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0]\\u001b[0m\\n\",\n \"Variable cleanup_old_solution has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable vel_field_variables has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: []\\u001b[0m\\n\",\n \"Variable vel_field_points has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0. 0. 0.]\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of BeamPlot\\u001b[0m\\n\",\n \"Variable include_FoR has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable include_applied_moments has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"Variable name_prefix has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n \"Variable output_rbm has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of AerogridPlot\\u001b[0m\\n\",\n \"Variable include_forward_motion has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable include_unsteady_applied_forces has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable name_prefix has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n \"Variable dt has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0\\u001b[0m\\n\",\n \"Variable include_velocities has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable include_incidence_angle has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable num_cores has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n \"Variable vortex_radius has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n \"Variable stride has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n \"Variable save_wake has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"|=======|========|======|==============|==============|==============|==============|==============|\\u001b[0m\\n\",\n \"| ts | t | iter | struc ratio | iter time | residual vel | FoR_vel(x) | FoR_vel(z) |\\u001b[0m\\n\",\n \"|=======|========|======|==============|==============|==============|==============|==============|\\u001b[0m\\n\",\n \"| 1 | 0.0006 | 5 | 0.968365 | 18.671949 | -6.417211 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 2 | 0.0013 | 4 | 0.971972 | 15.336584 | -6.496227 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 3 | 0.0019 | 3 | 0.969326 | 12.041152 | -6.173354 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 4 | 0.0025 | 3 | 0.968342 | 10.516750 | -6.020512 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 5 | 0.0031 | 4 | 0.955032 | 9.720251 | -6.536090 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 6 | 0.0037 | 4 | 0.966989 | 13.089750 | -6.365510 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 7 | 0.0044 | 4 | 0.963588 | 12.110149 | -6.233103 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 8 | 0.0050 | 4 | 0.951098 | 9.182460 | -6.162708 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 9 | 0.0056 | 4 | 0.979628 | 28.828536 | -6.113240 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 10 | 0.0063 | 4 | 0.956612 | 13.303912 | -6.082344 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 11 | 0.0069 | 4 | 0.966229 | 12.650505 | -6.038075 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 12 | 0.0075 | 5 | 0.960982 | 14.281275 | -6.727378 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 13 | 0.0081 | 5 | 0.956631 | 12.562050 | -6.701112 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 14 | 0.0088 | 5 | 0.947390 | 10.019976 | -6.665381 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 15 | 0.0094 | 5 | 0.954709 | 11.545903 | -6.619206 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 16 | 0.0100 | 5 | 0.948316 | 9.931642 | -6.570860 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 17 | 0.0106 | 5 | 0.952382 | 11.503413 | -6.528343 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 18 | 0.0112 | 5 | 0.947785 | 10.348513 | -6.489641 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 19 | 0.0119 | 5 | 0.948694 | 9.952890 | -6.453494 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 20 | 0.0125 | 5 | 0.964102 | 15.367483 | -6.426783 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 21 | 0.0131 | 5 | 0.950298 | 10.537648 | -6.404302 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 22 | 0.0138 | 5 | 0.950145 | 10.997150 | -6.381964 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 23 | 0.0144 | 5 | 0.951866 | 10.756376 | -6.365094 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 24 | 0.0150 | 5 | 0.953387 | 11.333439 | -6.348193 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 25 | 0.0156 | 5 | 0.949008 | 10.640736 | -6.323539 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 26 | 0.0163 | 5 | 0.951558 | 11.234257 | -6.293924 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 27 | 0.0169 | 5 | 0.953764 | 11.976087 | -6.266339 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 28 | 0.0175 | 5 | 0.954230 | 12.160064 | -6.244295 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 29 | 0.0181 | 5 | 0.955667 | 11.934807 | -6.226476 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 30 | 0.0187 | 5 | 0.946544 | 9.848974 | -6.210525 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 31 | 0.0194 | 5 | 0.958163 | 12.588759 | -6.197849 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 32 | 0.0200 | 5 | 0.941142 | 9.263582 | -6.187658 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 33 | 0.0206 | 5 | 0.946805 | 10.078831 | -6.176206 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 34 | 0.0213 | 5 | 0.948141 | 10.518540 | -6.164869 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 35 | 0.0219 | 5 | 0.952281 | 11.594154 | -6.153254 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 36 | 0.0225 | 5 | 0.956436 | 12.668008 | -6.138480 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 37 | 0.0231 | 5 | 0.962601 | 14.975047 | -6.121525 | 0.000000e+00 | 0.000000e+00 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21.817333 | -6.052922 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 48 | 0.0300 | 5 | 0.948717 | 11.354869 | -6.045901 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 49 | 0.0306 | 5 | 0.948421 | 10.883957 | -6.040864 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 50 | 0.0312 | 5 | 0.948296 | 10.736110 | -6.040590 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 51 | 0.0319 | 5 | 0.948139 | 10.621232 | -6.041367 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 52 | 0.0325 | 5 | 0.948025 | 10.336440 | -6.038935 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 53 | 0.0331 | 5 | 0.952062 | 11.658173 | -6.034811 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 54 | 0.0338 | 5 | 0.952953 | 11.996480 | -6.029771 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 55 | 0.0344 | 5 | 0.952641 | 11.794019 | -6.023840 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 56 | 0.0350 | 5 | 0.948103 | 10.625961 | -6.019904 | 0.000000e+00 | 0.000000e+00 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10.962657 | -6.016870 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 67 | 0.0419 | 5 | 0.953326 | 11.602128 | -6.018436 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 68 | 0.0425 | 5 | 0.943913 | 10.217246 | -6.021504 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 69 | 0.0431 | 5 | 0.950180 | 11.015258 | -6.024162 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 70 | 0.0438 | 5 | 0.956848 | 12.476811 | -6.025761 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 71 | 0.0444 | 5 | 0.949333 | 11.022746 | -6.029208 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 72 | 0.0450 | 5 | 0.952842 | 10.957240 | -6.034612 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 73 | 0.0456 | 5 | 0.950195 | 11.372289 | -6.039117 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 74 | 0.0462 | 5 | 0.952230 | 10.951780 | -6.041620 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 75 | 0.0469 | 5 | 0.944391 | 10.321632 | -6.043629 | 0.000000e+00 | 0.000000e+00 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10.301849 | -6.110879 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 86 | 0.0537 | 5 | 0.935800 | 8.870328 | -6.115130 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 87 | 0.0544 | 5 | 0.947104 | 10.836437 | -6.120945 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 88 | 0.0550 | 5 | 0.963095 | 15.823192 | -6.127793 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 89 | 0.0556 | 5 | 0.947735 | 10.736601 | -6.135927 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 90 | 0.0563 | 5 | 0.947219 | 10.730737 | -6.144368 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 91 | 0.0569 | 5 | 0.948428 | 11.076037 | -6.150790 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 92 | 0.0575 | 5 | 0.940665 | 9.837327 | -6.155716 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 93 | 0.0581 | 5 | 0.948581 | 11.200799 | -6.161582 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 94 | 0.0588 | 5 | 0.946228 | 10.552050 | -6.168338 | 0.000000e+00 | 0.000000e+00 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| 11.989062 | -6.229463 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 105 | 0.0656 | 5 | 0.952733 | 11.871830 | -6.236478 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 106 | 0.0663 | 5 | 0.948673 | 10.807147 | -6.243449 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 107 | 0.0669 | 5 | 0.930800 | 8.894847 | -6.249473 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 108 | 0.0675 | 5 | 0.957262 | 13.341049 | -6.255890 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 109 | 0.0681 | 5 | 0.947861 | 11.027717 | -6.263542 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 110 | 0.0688 | 5 | 0.952574 | 11.537263 | -6.272266 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 111 | 0.0694 | 5 | 0.947710 | 10.136458 | -6.281527 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 112 | 0.0700 | 5 | 0.935899 | 9.226067 | -6.289751 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 113 | 0.0706 | 5 | 0.942306 | 10.016803 | -6.295951 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 114 | 0.0713 | 5 | 0.939406 | 9.518147 | -6.302064 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 115 | 0.0719 | 5 | 0.943245 | 10.038173 | -6.309255 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 116 | 0.0725 | 5 | 0.951977 | 11.464750 | -6.318358 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 117 | 0.0731 | 5 | 0.945140 | 10.013828 | -6.329243 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 118 | 0.0737 | 5 | 0.948454 | 10.736181 | -6.338812 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 119 | 0.0744 | 5 | 0.938591 | 9.071753 | -6.347747 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 120 | 0.0750 | 5 | 0.946253 | 10.567693 | -6.359016 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 121 | 0.0756 | 5 | 0.947073 | 11.273658 | -6.370755 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 122 | 0.0762 | 5 | 0.941092 | 9.599160 | -6.381991 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 123 | 0.0769 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0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 133 | 0.0831 | 5 | 0.950212 | 11.168756 | -6.489653 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 134 | 0.0838 | 5 | 0.947648 | 11.245141 | -6.496921 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 135 | 0.0844 | 5 | 0.952376 | 11.929442 | -6.503753 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 136 | 0.0850 | 5 | 0.955622 | 13.096018 | -6.511057 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 137 | 0.0856 | 5 | 0.940609 | 9.735925 | -6.520895 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 138 | 0.0863 | 5 | 0.940370 | 9.500913 | -6.533221 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 139 | 0.0869 | 5 | 0.944022 | 10.989595 | -6.543976 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 140 | 0.0875 | 5 | 0.945349 | 10.576644 | -6.550689 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 141 | 0.0881 | 5 | 0.942640 | 9.924819 | -6.556179 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n 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-6.608611 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 152 | 0.0950 | 5 | 0.937707 | 9.309265 | -6.610140 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 153 | 0.0956 | 5 | 0.945661 | 11.116661 | -6.615885 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 154 | 0.0963 | 5 | 0.947168 | 10.966585 | -6.623153 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 155 | 0.0969 | 5 | 0.947456 | 11.300364 | -6.630447 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 156 | 0.0975 | 5 | 0.943753 | 10.825258 | -6.637990 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 157 | 0.0981 | 5 | 0.963825 | 15.814815 | -6.645485 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 158 | 0.0988 | 5 | 0.945822 | 11.052504 | -6.653934 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 159 | 0.0994 | 5 | 0.948607 | 11.214047 | -6.662756 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 160 | 0.1000 | 5 | 0.946378 | 10.745310 | -6.670552 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 161 | 0.1006 | 5 | 0.947401 | 11.221507 | -6.676330 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 162 | 0.1013 | 5 | 0.944233 | 10.110627 | -6.680679 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 163 | 0.1019 | 5 | 0.947101 | 11.862333 | -6.686866 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 164 | 0.1025 | 5 | 0.967109 | 18.147130 | -6.696421 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 165 | 0.1031 | 5 | 0.940993 | 10.605252 | -6.707483 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 166 | 0.1038 | 5 | 0.955383 | 13.030459 | -6.716984 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 167 | 0.1044 | 5 | 0.948422 | 11.665669 | -6.724584 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 168 | 0.1050 | 4 | 0.955500 | 11.664639 | -6.005053 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 169 | 0.1056 | 4 | 0.951802 | 10.576800 | -6.013451 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 170 | 0.1062 | 4 | 0.951200 | 9.567037 | -6.021257 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 171 | 0.1069 | 4 | 0.968419 | 14.355263 | -6.029494 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 172 | 0.1075 | 4 | 0.966190 | 13.662715 | -6.037786 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 173 | 0.1081 | 4 | 0.956161 | 12.371329 | -6.045909 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 174 | 0.1087 | 4 | 0.951665 | 11.085254 | -6.056996 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 175 | 0.1094 | 4 | 0.953042 | 10.715927 | -6.069746 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 176 | 0.1100 | 4 | 0.958061 | 11.712813 | -6.079731 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 177 | 0.1106 | 4 | 0.960356 | 12.695643 | -6.085509 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 178 | 0.1113 | 4 | 0.954514 | 11.793410 | -6.088583 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 179 | 0.1119 | 4 | 0.950668 | 10.003142 | -6.091305 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 180 | 0.1125 | 4 | 0.946102 | 9.886626 | -6.093073 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 181 | 0.1131 | 4 | 0.949649 | 10.301983 | -6.093995 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 182 | 0.1138 | 4 | 0.953119 | 10.652363 | -6.095412 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 183 | 0.1144 | 4 | 0.951766 | 10.832586 | -6.097424 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 184 | 0.1150 | 4 | 0.955132 | 10.462639 | -6.097812 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 185 | 0.1156 | 4 | 0.960911 | 13.618529 | -6.096289 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 186 | 0.1163 | 4 | 0.956462 | 11.546490 | -6.093168 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 187 | 0.1169 | 4 | 0.962654 | 12.813508 | -6.088310 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 188 | 0.1175 | 4 | 0.968176 | 18.430304 | -6.081391 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 189 | 0.1181 | 4 | 0.946358 | 9.833844 | -6.074350 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 190 | 0.1188 | 4 | 0.947277 | 9.157477 | -6.068791 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 191 | 0.1194 | 4 | 0.968489 | 15.667897 | -6.062826 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 192 | 0.1200 | 4 | 0.950315 | 9.516710 | -6.057464 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 193 | 0.1206 | 4 | 0.940345 | 8.711639 | -6.053352 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 194 | 0.1212 | 4 | 0.950416 | 10.270131 | -6.047761 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 195 | 0.1219 | 4 | 0.949720 | 9.165432 | -6.038768 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 196 | 0.1225 | 4 | 0.943330 | 8.940929 | -6.027309 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 197 | 0.1231 | 4 | 0.945974 | 9.224462 | -6.017552 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 198 | 0.1237 | 4 | 0.938437 | 7.985228 | -6.009420 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 199 | 0.1244 | 4 | 0.949442 | 9.156467 | -6.001601 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 200 | 0.1250 | 5 | 0.948617 | 11.723775 | -6.730831 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 201 | 0.1256 | 5 | 0.936233 | 9.874182 | -6.724077 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 202 | 0.1263 | 5 | 0.948015 | 11.857640 | -6.717044 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 203 | 0.1269 | 5 | 0.937598 | 10.443674 | -6.710956 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 204 | 0.1275 | 5 | 0.950856 | 12.267857 | -6.704661 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 205 | 0.1281 | 5 | 0.949025 | 11.520669 | -6.696225 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 206 | 0.1288 | 5 | 0.952569 | 12.509402 | -6.686150 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 207 | 0.1294 | 5 | 0.945493 | 11.217238 | -6.675868 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 208 | 0.1300 | 5 | 0.943550 | 10.795355 | -6.668776 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 209 | 0.1306 | 5 | 0.963850 | 17.410402 | -6.662688 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 210 | 0.1313 | 5 | 0.964352 | 17.017205 | -6.655037 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 211 | 0.1319 | 5 | 0.944406 | 10.911295 | -6.647090 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 212 | 0.1325 | 5 | 0.941326 | 10.069910 | -6.637080 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 213 | 0.1331 | 5 | 0.949649 | 11.424372 | -6.628286 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 214 | 0.1338 | 5 | 0.948237 | 11.950824 | -6.618372 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 215 | 0.1344 | 5 | 0.933445 | 9.096234 | -6.607924 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 216 | 0.1350 | 5 | 0.954119 | 12.891909 | -6.600956 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 217 | 0.1356 | 5 | 0.949010 | 11.880124 | -6.591819 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 218 | 0.1363 | 5 | 0.946764 | 11.708015 | -6.578566 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 219 | 0.1369 | 5 | 0.939680 | 10.037507 | -6.568256 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 220 | 0.1375 | 5 | 0.949051 | 10.831389 | -6.560834 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 221 | 0.1381 | 5 | 0.951881 | 12.069925 | -6.550114 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 222 | 0.1388 | 5 | 0.946708 | 11.655207 | -6.546699 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 223 | 0.1394 | 5 | 0.945491 | 11.092597 | -6.535719 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 224 | 0.1400 | 5 | 0.942582 | 10.299325 | -6.518312 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 225 | 0.1406 | 5 | 0.943477 | 11.023694 | -6.502154 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 226 | 0.1413 | 5 | 0.941513 | 10.661141 | -6.487594 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 227 | 0.1419 | 5 | 0.944854 | 11.009248 | -6.471501 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 228 | 0.1425 | 5 | 0.947037 | 11.111865 | -6.455693 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 229 | 0.1431 | 5 | 0.943006 | 11.418393 | -6.445663 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 230 | 0.1438 | 5 | 0.937785 | 10.281053 | -6.436643 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 231 | 0.1444 | 5 | 0.953180 | 13.515919 | -6.423862 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 232 | 0.1450 | 5 | 0.942807 | 10.828190 | -6.409260 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 233 | 0.1456 | 5 | 0.947758 | 12.155366 | -6.416705 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 234 | 0.1462 | 5 | 0.947850 | 11.147242 | -6.389836 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 235 | 0.1469 | 5 | 0.949502 | 11.667867 | -6.370341 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 236 | 0.1475 | 5 | 0.941159 | 10.366536 | -6.357640 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 237 | 0.1481 | 5 | 0.941645 | 11.566625 | -6.343108 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 238 | 0.1487 | 5 | 0.943970 | 10.571422 | -6.329128 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 239 | 0.1494 | 5 | 0.948570 | 12.000235 | -6.315768 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 240 | 0.1500 | 5 | 0.956057 | 14.176120 | -6.302302 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 241 | 0.1506 | 5 | 0.941344 | 10.372841 | -6.286996 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 242 | 0.1512 | 5 | 0.944239 | 11.163841 | -6.271065 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 243 | 0.1519 | 5 | 0.941355 | 10.750759 | -6.256601 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 244 | 0.1525 | 5 | 0.946149 | 11.848520 | -6.242143 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 245 | 0.1531 | 5 | 0.953282 | 13.054623 | -6.224536 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 246 | 0.1537 | 5 | 0.939600 | 10.533198 | -6.204649 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 247 | 0.1544 | 5 | 0.950865 | 12.636092 | -6.191911 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 248 | 0.1550 | 5 | 0.939138 | 10.755056 | -6.177627 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 249 | 0.1556 | 5 | 0.941024 | 11.774469 | -6.163797 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 250 | 0.1562 | 5 | 0.945149 | 11.603998 | -6.149284 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 251 | 0.1569 | 5 | 0.944137 | 11.027009 | -6.157241 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 252 | 0.1575 | 5 | 0.945240 | 11.557927 | -6.124949 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 253 | 0.1581 | 5 | 0.946122 | 11.934396 | -6.108130 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 254 | 0.1588 | 5 | 0.935588 | 11.200220 | -6.093652 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 255 | 0.1594 | 5 | 0.948408 | 11.680672 | -6.078210 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 256 | 0.1600 | 5 | 0.943591 | 10.678600 | -6.061033 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 257 | 0.1606 | 5 | 0.945829 | 11.584085 | -6.042628 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 258 | 0.1613 | 5 | 0.947088 | 11.800646 | -6.025314 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 259 | 0.1619 | 5 | 0.944964 | 11.772600 | -6.010586 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 260 | 0.1625 | 6 | 0.945209 | 13.291276 | -6.734883 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 261 | 0.1631 | 6 | 0.943456 | 12.680267 | -6.718964 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 262 | 0.1638 | 6 | 0.944619 | 13.215398 | -6.702060 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 263 | 0.1644 | 6 | 0.947007 | 14.169829 | -6.686353 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 264 | 0.1650 | 6 | 0.938508 | 12.289283 | -6.673467 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 265 | 0.1656 | 6 | 0.951268 | 14.610949 | -6.660933 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 266 | 0.1663 | 6 | 0.935965 | 11.988576 | -6.647986 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 267 | 0.1669 | 6 | 0.946580 | 14.197086 | -6.636073 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 268 | 0.1675 | 6 | 0.942800 | 12.822154 | -6.626319 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 269 | 0.1681 | 6 | 0.947284 | 13.338966 | -6.620655 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 270 | 0.1688 | 6 | 0.939962 | 12.287910 | -6.617902 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 271 | 0.1694 | 6 | 0.949752 | 16.501225 | -6.615042 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 272 | 0.1700 | 6 | 0.939267 | 12.324404 | -6.613633 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 273 | 0.1706 | 6 | 0.944347 | 13.207239 | -6.615915 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 274 | 0.1713 | 6 | 0.942063 | 12.524115 | -6.624740 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 275 | 0.1719 | 6 | 0.945643 | 13.180858 | -6.632674 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 276 | 0.1725 | 6 | 0.936511 | 12.016970 | -6.639310 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 277 | 0.1731 | 6 | 0.947054 | 13.827464 | -6.647491 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 278 | 0.1738 | 6 | 0.935859 | 11.941455 | -6.659334 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 279 | 0.1744 | 6 | 0.939836 | 12.367750 | -6.673970 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 280 | 0.1750 | 6 | 0.936526 | 12.331560 | -6.678839 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 281 | 0.1756 | 6 | 0.938118 | 12.166943 | -6.693248 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 282 | 0.1762 | 6 | 0.935611 | 11.910315 | -6.709670 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 283 | 0.1769 | 6 | 0.944449 | 13.326162 | -6.733336 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 284 | 0.1775 | 5 | 0.939992 | 11.053350 | -6.012363 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 285 | 0.1781 | 5 | 0.948281 | 12.083963 | -6.030102 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 286 | 0.1787 | 5 | 0.948533 | 11.727205 | -6.047338 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 287 | 0.1794 | 5 | 0.939986 | 10.345996 | -6.062876 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 288 | 0.1800 | 5 | 0.945252 | 11.362258 | -6.079639 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 289 | 0.1806 | 5 | 0.947508 | 12.199549 | -6.097383 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 290 | 0.1812 | 5 | 0.933631 | 9.339983 | -6.115169 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 291 | 0.1819 | 5 | 0.940224 | 10.936754 | -6.132664 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 292 | 0.1825 | 5 | 0.939724 | 10.449330 | -6.147923 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 293 | 0.1831 | 5 | 0.948690 | 12.151484 | -6.163659 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 294 | 0.1837 | 5 | 0.942595 | 11.039602 | -6.181324 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 295 | 0.1844 | 5 | 0.945059 | 11.630183 | -6.198729 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 296 | 0.1850 | 5 | 0.945800 | 12.725906 | -6.215272 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 297 | 0.1856 | 5 | 0.942269 | 10.736765 | -6.230292 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 298 | 0.1862 | 5 | 0.942436 | 11.227497 | -6.244567 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 299 | 0.1869 | 5 | 0.939725 | 10.225151 | -6.260472 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 300 | 0.1875 | 5 | 0.944196 | 11.060303 | -6.276916 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 301 | 0.1881 | 5 | 0.960094 | 15.880141 | -6.291941 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 302 | 0.1888 | 5 | 0.948014 | 12.149703 | -6.305562 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 303 | 0.1894 | 5 | 0.941994 | 10.651260 | -6.318965 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 304 | 0.1900 | 5 | 0.950609 | 12.495602 | -6.333482 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 305 | 0.1906 | 5 | 0.940519 | 10.488050 | -6.348189 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 306 | 0.1913 | 5 | 0.947913 | 12.691566 | -6.361913 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 307 | 0.1919 | 5 | 0.942720 | 10.632595 | -6.374253 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 308 | 0.1925 | 5 | 0.956283 | 14.595177 | -6.385687 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 309 | 0.1931 | 5 | 0.938529 | 9.986877 | -6.399126 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 310 | 0.1938 | 5 | 0.941697 | 11.624213 | -6.413159 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 311 | 0.1944 | 5 | 0.947358 | 11.831380 | -6.425737 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 312 | 0.1950 | 5 | 0.940657 | 10.664760 | -6.437914 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 313 | 0.1956 | 5 | 0.945992 | 11.745995 | -6.449198 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 314 | 0.1963 | 5 | 0.945434 | 11.700196 | -6.461378 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 315 | 0.1969 | 5 | 0.952461 | 13.212226 | -6.475399 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 316 | 0.1975 | 5 | 0.946748 | 12.410715 | -6.487818 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 317 | 0.1981 | 5 | 0.942489 | 11.260109 | -6.498905 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 318 | 0.1988 | 5 | 0.954916 | 13.542801 | -6.510605 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 319 | 0.1994 | 5 | 0.951023 | 13.047720 | -6.522468 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 320 | 0.2000 | 5 | 0.941290 | 10.351259 | -6.535653 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 321 | 0.2006 | 5 | 0.949801 | 12.561128 | -6.548605 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 322 | 0.2013 | 5 | 0.933351 | 9.742402 | -6.559248 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 323 | 0.2019 | 5 | 0.945824 | 11.669179 | -6.570035 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 324 | 0.2025 | 5 | 0.940618 | 11.432235 | -6.581942 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 325 | 0.2031 | 5 | 0.943817 | 11.426316 | -6.594593 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 326 | 0.2038 | 5 | 0.953734 | 13.505159 | -6.606923 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 327 | 0.2044 | 5 | 0.931261 | 10.402201 | -6.617755 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 328 | 0.2050 | 5 | 0.949553 | 12.230616 | -6.628032 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 329 | 0.2056 | 5 | 0.943117 | 11.498853 | -6.638920 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 330 | 0.2063 | 5 | 0.943764 | 11.763657 | -6.651286 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 331 | 0.2069 | 5 | 0.943443 | 11.352340 | -6.663433 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 332 | 0.2075 | 5 | 0.939813 | 10.792876 | -6.673535 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 333 | 0.2081 | 5 | 0.939146 | 10.863336 | -6.683450 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 334 | 0.2087 | 5 | 0.942934 | 11.064193 | -6.694206 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 335 | 0.2094 | 5 | 0.947165 | 11.997910 | -6.705246 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 336 | 0.2100 | 5 | 0.951135 | 12.933304 | -6.716584 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 337 | 0.2106 | 5 | 0.946188 | 11.651776 | -6.725582 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 338 | 0.2112 | 4 | 0.947764 | 9.462267 | -6.006966 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 339 | 0.2119 | 4 | 0.945007 | 9.856144 | -6.016166 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 340 | 0.2125 | 4 | 0.952493 | 11.507456 | -6.025795 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 341 | 0.2131 | 4 | 0.950982 | 10.546667 | -6.035361 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 342 | 0.2137 | 4 | 0.952015 | 10.293428 | -6.044313 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 343 | 0.2144 | 4 | 0.947798 | 10.362436 | -6.050845 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 344 | 0.2150 | 4 | 0.947564 | 9.734232 | -6.057454 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 345 | 0.2156 | 4 | 0.942505 | 9.236773 | -6.065222 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 346 | 0.2162 | 4 | 0.947544 | 9.717363 | -6.072005 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 347 | 0.2169 | 4 | 0.938501 | 8.694150 | -6.077386 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 348 | 0.2175 | 4 | 0.949458 | 10.271883 | -6.081917 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 349 | 0.2181 | 4 | 0.938702 | 8.538571 | -6.086876 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 350 | 0.2188 | 4 | 0.939707 | 8.995470 | -6.092985 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 351 | 0.2194 | 4 | 0.946523 | 9.639948 | -6.099074 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 352 | 0.2200 | 4 | 0.935855 | 8.213983 | -6.104246 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 353 | 0.2206 | 4 | 0.944748 | 9.607103 | -6.107678 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 354 | 0.2213 | 4 | 0.956262 | 12.531544 | -6.110114 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 355 | 0.2219 | 4 | 0.942209 | 9.275017 | -6.112920 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 356 | 0.2225 | 4 | 0.946568 | 9.987548 | -6.115915 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 357 | 0.2231 | 4 | 0.935081 | 8.506918 | -6.118795 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 358 | 0.2238 | 4 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0.000000e+00 |\\u001b[0m\\n\",\n \"| 368 | 0.2300 | 4 | 0.968380 | 16.586067 | -6.106324 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 369 | 0.2306 | 4 | 0.952023 | 11.253964 | -6.100741 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 370 | 0.2313 | 4 | 0.950157 | 10.531796 | -6.094886 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 371 | 0.2319 | 4 | 0.950168 | 10.427808 | -6.088197 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 372 | 0.2325 | 4 | 0.936196 | 8.918983 | -6.080290 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 373 | 0.2331 | 4 | 0.942862 | 9.217407 | -6.071418 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 374 | 0.2338 | 4 | 0.931575 | 8.374174 | -6.062450 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 375 | 0.2344 | 4 | 0.943912 | 9.646384 | -6.054102 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 376 | 0.2350 | 4 | 0.952382 | 10.994409 | -6.045824 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 377 | 0.2356 | 4 | 0.953536 | 10.789837 | -6.037022 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 378 | 0.2363 | 4 | 0.934100 | 8.654277 | -6.028280 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 379 | 0.2369 | 4 | 0.942988 | 9.373151 | -6.019596 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 380 | 0.2375 | 4 | 0.944104 | 9.815691 | -6.010129 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 381 | 0.2381 | 4 | 0.937398 | 8.652296 | -6.000383 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 382 | 0.2388 | 5 | 0.938554 | 10.822313 | -6.725142 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 383 | 0.2394 | 5 | 0.947037 | 11.900135 | -6.714875 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 384 | 0.2400 | 5 | 0.941750 | 11.175656 | -6.704971 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 385 | 0.2406 | 5 | 0.945792 | 12.536697 | -6.695529 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 386 | 0.2412 | 5 | 0.939800 | 11.015844 | -6.686894 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 387 | 0.2419 | 5 | 0.935986 | 10.217669 | -6.678073 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 388 | 0.2425 | 5 | 0.943653 | 12.185779 | -6.668896 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 389 | 0.2431 | 5 | 0.951555 | 13.377180 | -6.660090 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 390 | 0.2437 | 5 | 0.943060 | 12.209697 | -6.651496 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 391 | 0.2444 | 5 | 0.946853 | 12.046725 | -6.642875 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 392 | 0.2450 | 5 | 0.935869 | 10.530684 | -6.634471 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 393 | 0.2456 | 5 | 0.944948 | 11.274202 | -6.626020 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 394 | 0.2462 | 5 | 0.939311 | 10.513262 | -6.617542 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 395 | 0.2469 | 5 | 0.940147 | 11.755655 | -6.609586 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 396 | 0.2475 | 5 | 0.946002 | 12.170166 | -6.601957 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 397 | 0.2481 | 5 | 0.951292 | 13.279384 | -6.594634 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 398 | 0.2487 | 5 | 0.940548 | 10.914453 | -6.586754 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 399 | 0.2494 | 5 | 0.944334 | 12.162813 | -6.577747 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 400 | 0.2500 | 5 | 0.944412 | 11.971015 | -6.567671 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 401 | 0.2506 | 5 | 0.942391 | 11.417440 | -6.556234 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 402 | 0.2513 | 5 | 0.946196 | 11.651955 | -6.544422 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 403 | 0.2519 | 5 | 0.954220 | 13.544177 | -6.532738 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 404 | 0.2525 | 5 | 0.942893 | 11.522388 | -6.520930 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 405 | 0.2531 | 5 | 0.937732 | 11.174606 | -6.508777 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 406 | 0.2538 | 5 | 0.942429 | 11.498338 | -6.496583 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 407 | 0.2544 | 5 | 0.951117 | 13.381841 | -6.484564 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 408 | 0.2550 | 5 | 0.946943 | 11.972833 | -6.472461 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 409 | 0.2556 | 5 | 0.939902 | 10.688227 | -6.459836 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 410 | 0.2562 | 5 | 0.941495 | 11.588936 | -6.446709 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 411 | 0.2569 | 5 | 0.940684 | 11.439794 | -6.433787 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 412 | 0.2575 | 5 | 0.940707 | 11.230869 | -6.420827 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 413 | 0.2581 | 5 | 0.943504 | 11.691810 | -6.407676 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 414 | 0.2587 | 5 | 0.946487 | 12.529424 | -6.394133 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 415 | 0.2594 | 5 | 0.946490 | 12.476834 | -6.380069 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 416 | 0.2600 | 5 | 0.940115 | 11.243180 | -6.365979 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 417 | 0.2606 | 5 | 0.946679 | 12.310042 | -6.351862 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 418 | 0.2612 | 5 | 0.930529 | 9.259821 | -6.337979 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 419 | 0.2619 | 5 | 0.944208 | 11.701038 | -6.324252 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 420 | 0.2625 | 5 | 0.943378 | 11.615270 | -6.310184 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 421 | 0.2631 | 5 | 0.948905 | 12.821126 | -6.295848 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 422 | 0.2637 | 5 | 0.956700 | 14.825340 | -6.281795 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 423 | 0.2644 | 5 | 0.948575 | 13.258096 | -6.268152 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 424 | 0.2650 | 5 | 0.953930 | 14.677462 | -6.254451 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 425 | 0.2656 | 5 | 0.959606 | 20.267950 | -6.240666 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 426 | 0.2662 | 5 | 0.946560 | 13.043301 | -6.226753 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 427 | 0.2669 | 5 | 0.946216 | 26.652811 | -6.213063 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 428 | 0.2675 | 5 | 0.939458 | 11.337829 | -6.199728 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 429 | 0.2681 | 5 | 0.944511 | 12.469610 | -6.186771 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 430 | 0.2687 | 5 | 0.951583 | 13.959556 | -6.173960 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 431 | 0.2694 | 5 | 0.947895 | 12.948082 | -6.161021 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 432 | 0.2700 | 5 | 0.940363 | 11.396358 | -6.148138 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 433 | 0.2706 | 5 | 0.940611 | 11.959174 | -6.135531 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 434 | 0.2712 | 5 | 0.944905 | 11.612634 | -6.123427 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 435 | 0.2719 | 5 | 0.931596 | 10.630004 | -6.111485 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 436 | 0.2725 | 5 | 0.941282 | 11.077741 | -6.099515 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 437 | 0.2731 | 5 | 0.944526 | 11.820778 | -6.087707 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 438 | 0.2737 | 5 | 0.945823 | 11.672671 | -6.076067 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 439 | 0.2744 | 5 | 0.947116 | 12.356394 | -6.064688 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 440 | 0.2750 | 5 | 0.946607 | 11.309584 | -6.053461 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 441 | 0.2756 | 5 | 0.940612 | 10.561857 | -6.042264 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 442 | 0.2762 | 5 | 0.944981 | 11.875639 | -6.030655 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 443 | 0.2769 | 5 | 0.938942 | 10.323446 | -6.018751 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 444 | 0.2775 | 5 | 0.944209 | 11.620808 | -6.006922 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 445 | 0.2781 | 6 | 0.948086 | 14.365045 | -6.736619 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 446 | 0.2787 | 6 | 0.941974 | 12.894964 | -6.724916 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 447 | 0.2794 | 6 | 0.941747 | 12.867233 | -6.712885 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 448 | 0.2800 | 6 | 0.939683 | 12.638412 | -6.700640 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 449 | 0.2806 | 6 | 0.937655 | 12.234413 | -6.688255 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 450 | 0.2812 | 6 | 0.943827 | 13.398312 | -6.676011 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 451 | 0.2819 | 6 | 0.948795 | 14.855482 | -6.663571 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 452 | 0.2825 | 6 | 0.937684 | 12.584784 | -6.650797 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 453 | 0.2831 | 6 | 0.940853 | 12.808068 | -6.637730 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 454 | 0.2838 | 6 | 0.949003 | 15.933166 | -6.624188 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 455 | 0.2844 | 6 | 0.943138 | 14.585177 | -6.610740 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 456 | 0.2850 | 6 | 0.975023 | 45.558647 | -6.597484 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 457 | 0.2856 | 6 | 0.945492 | 12.665898 | -6.583956 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 458 | 0.2863 | 6 | 0.943885 | 12.642572 | -6.570163 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 459 | 0.2869 | 6 | 0.946598 | 14.066256 | -6.556328 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 460 | 0.2875 | 6 | 0.945733 | 13.002777 | -6.542348 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 461 | 0.2881 | 6 | 0.944734 | 13.666282 | -6.528596 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 462 | 0.2888 | 6 | 0.961025 | 19.318107 | -6.515143 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 463 | 0.2894 | 6 | 0.960909 | 17.956889 | -6.501700 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 464 | 0.2900 | 6 | 0.962195 | 19.095729 | -6.488667 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 465 | 0.2906 | 6 | 0.955146 | 18.395397 | -6.475893 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 466 | 0.2913 | 6 | 0.932831 | 10.788197 | -6.463861 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 467 | 0.2919 | 6 | 0.923409 | 9.725337 | -6.452981 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 468 | 0.2925 | 6 | 0.939919 | 11.987191 | -6.442848 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 469 | 0.2931 | 6 | 0.935204 | 11.246918 | -6.433444 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 470 | 0.2938 | 6 | 0.950340 | 14.473156 | -6.425044 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 471 | 0.2944 | 6 | 0.941014 | 13.263558 | -6.417914 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 472 | 0.2950 | 6 | 0.951109 | 15.029684 | -6.412338 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 473 | 0.2956 | 6 | 0.952923 | 15.108398 | -6.408441 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 474 | 0.2963 | 6 | 0.933879 | 11.287061 | -6.406075 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 475 | 0.2969 | 6 | 0.940943 | 13.381000 | -6.405447 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 476 | 0.2975 | 6 | 0.933473 | 10.651840 | -6.406601 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 477 | 0.2981 | 6 | 0.933221 | 11.707809 | -6.409774 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 478 | 0.2988 | 6 | 0.931398 | 12.543991 | -6.415210 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 479 | 0.2994 | 6 | 0.931353 | 10.779868 | -6.422252 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 480 | 0.3000 | 6 | 0.959892 | 17.280849 | -6.430833 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 481 | 0.3006 | 6 | 0.953455 | 17.051079 | -6.440865 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 482 | 0.3013 | 6 | 0.929366 | 9.798513 | -6.452285 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 483 | 0.3019 | 6 | 0.915877 | 9.415046 | -6.465101 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 484 | 0.3025 | 6 | 0.946327 | 13.611439 | -6.479036 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 485 | 0.3031 | 6 | 0.929681 | 10.096231 | -6.493792 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 486 | 0.3038 | 6 | 0.942053 | 12.171144 | -6.509114 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 487 | 0.3044 | 6 | 0.941548 | 11.788646 | -6.524777 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 488 | 0.3050 | 6 | 0.928641 | 10.165608 | -6.540846 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 489 | 0.3056 | 6 | 0.926683 | 10.096948 | -6.557527 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 490 | 0.3063 | 6 | 0.943579 | 13.089129 | -6.574203 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 491 | 0.3069 | 6 | 0.933035 | 11.317091 | -6.590579 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 492 | 0.3075 | 6 | 0.933329 | 10.826166 | -6.606798 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 493 | 0.3081 | 6 | 0.925417 | 9.954762 | -6.622960 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 494 | 0.3088 | 6 | 0.934412 | 10.903793 | -6.639268 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 495 | 0.3094 | 6 | 0.936710 | 10.941266 | -6.655432 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 496 | 0.3100 | 6 | 0.939284 | 11.306272 | -6.671282 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 497 | 0.3106 | 6 | 0.934598 | 11.031119 | -6.686646 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 498 | 0.3113 | 6 | 0.926747 | 10.244288 | -6.701629 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 499 | 0.3119 | 6 | 0.936242 | 11.094012 | -6.716416 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 500 | 0.3125 | 6 | 0.927101 | 10.435871 | -6.731094 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 501 | 0.3131 | 5 | 0.925367 | 7.898205 | -6.003962 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 502 | 0.3138 | 5 | 0.930463 | 8.841769 | -6.017855 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 503 | 0.3144 | 5 | 0.935369 | 9.849760 | -6.031653 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 504 | 0.3150 | 5 | 0.927636 | 8.436575 | -6.045529 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 505 | 0.3156 | 5 | 0.931649 | 8.961717 | -6.059573 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 506 | 0.3163 | 5 | 0.933398 | 9.575869 | -6.073762 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 507 | 0.3169 | 5 | 0.934445 | 9.244844 | -6.088188 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 508 | 0.3175 | 5 | 0.924025 | 7.798754 | -6.102694 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 509 | 0.3181 | 5 | 0.940258 | 10.032370 | -6.117317 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 510 | 0.3188 | 5 | 0.932599 | 9.222431 | -6.132483 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 511 | 0.3194 | 5 | 0.934663 | 9.527827 | -6.148232 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 512 | 0.3200 | 5 | 0.933843 | 8.860781 | -6.164623 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 513 | 0.3206 | 5 | 0.932188 | 9.639876 | -6.181155 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 514 | 0.3212 | 5 | 0.931656 | 9.692169 | -6.197924 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 515 | 0.3219 | 5 | 0.927283 | 8.518492 | -6.215445 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 516 | 0.3225 | 5 | 0.944497 | 10.796695 | -6.233601 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 517 | 0.3231 | 5 | 0.943116 | 10.604323 | -6.252496 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 518 | 0.3237 | 5 | 0.937520 | 9.753980 | -6.271885 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 519 | 0.3244 | 5 | 0.926112 | 8.010724 | -6.291855 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 520 | 0.3250 | 5 | 0.933361 | 9.099026 | -6.312470 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 521 | 0.3256 | 5 | 0.936647 | 9.274324 | -6.334090 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 522 | 0.3262 | 5 | 0.934850 | 9.366708 | -6.356764 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 523 | 0.3269 | 5 | 0.934609 | 9.331188 | -6.380315 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 524 | 0.3275 | 5 | 0.938180 | 9.845226 | -6.404181 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 525 | 0.3281 | 5 | 0.925627 | 8.063320 | -6.428499 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 526 | 0.3287 | 5 | 0.925067 | 7.981261 | -6.453779 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 527 | 0.3294 | 5 | 0.933576 | 9.620721 | -6.479463 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 528 | 0.3300 | 5 | 0.931757 | 8.652095 | -6.506077 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 529 | 0.3306 | 5 | 0.926375 | 8.612870 | -6.533230 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 530 | 0.3312 | 5 | 0.931660 | 8.723508 | -6.560532 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 531 | 0.3319 | 5 | 0.922246 | 7.936984 | -6.588388 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 532 | 0.3325 | 5 | 0.937330 | 9.551329 | -6.616327 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 533 | 0.3331 | 5 | 0.941238 | 10.138527 | -6.645330 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 534 | 0.3337 | 5 | 0.935196 | 9.255770 | -6.675195 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 535 | 0.3344 | 5 | 0.939544 | 9.773071 | -6.704531 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 536 | 0.3350 | 5 | 0.940899 | 10.424059 | -6.733701 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 537 | 0.3356 | 4 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0.000000e+00 |\\u001b[0m\\n\",\n \"| 547 | 0.3419 | 4 | 0.958625 | 12.513767 | -6.395057 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 548 | 0.3425 | 4 | 0.950902 | 10.697214 | -6.448425 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 549 | 0.3431 | 4 | 0.947183 | 9.394122 | -6.510814 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 550 | 0.3438 | 4 | 0.949121 | 9.796854 | -6.583580 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 551 | 0.3444 | 4 | 0.946961 | 10.422144 | -6.670334 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 552 | 0.3450 | 3 | 0.952130 | 8.454171 | -6.040947 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 553 | 0.3456 | 3 | 0.958336 | 9.321894 | -6.153069 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 554 | 0.3463 | 3 | 0.954985 | 8.974295 | -6.240227 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 555 | 0.3469 | 3 | 0.918559 | 5.521563 | -6.152514 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 556 | 0.3475 | 4 | 0.926450 | 8.000008 | -6.705685 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 557 | 0.3481 | 4 | 0.928557 | 7.739259 | -6.578881 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 558 | 0.3488 | 4 | 0.925500 | 6.604689 | -6.480316 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 559 | 0.3494 | 4 | 0.929234 | 7.475034 | -6.427569 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 560 | 0.3500 | 4 | 0.929693 | 7.300120 | -6.355897 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 561 | 0.3506 | 4 | 0.936551 | 8.216637 | -6.307655 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 562 | 0.3513 | 4 | 0.932202 | 8.202960 | -6.252951 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 563 | 0.3519 | 4 | 0.931593 | 7.225138 | -6.207181 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 564 | 0.3525 | 4 | 0.933346 | 7.804957 | -6.164819 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 565 | 0.3531 | 4 | 0.935896 | 7.675990 | -6.122506 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 566 | 0.3538 | 4 | 0.921092 | 6.466938 | -6.083487 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 567 | 0.3544 | 4 | 0.932215 | 7.272089 | -6.047872 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 568 | 0.3550 | 4 | 0.934220 | 7.519600 | -6.014768 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 569 | 0.3556 | 5 | 0.928175 | 8.861348 | -6.721297 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 570 | 0.3563 | 5 | 0.942519 | 10.784671 | -6.691721 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 571 | 0.3569 | 5 | 0.921757 | 8.404438 | -6.665698 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 572 | 0.3575 | 5 | 0.938649 | 9.751264 | -6.641548 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 573 | 0.3581 | 5 | 0.929423 | 9.337398 | -6.619602 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 574 | 0.3588 | 5 | 0.931252 | 9.026243 | -6.599179 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 575 | 0.3594 | 5 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0.000000e+00 |\\u001b[0m\\n\",\n \"| 585 | 0.3656 | 5 | 0.937111 | 10.114750 | -6.442445 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 586 | 0.3663 | 5 | 0.926297 | 8.935411 | -6.431856 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 587 | 0.3669 | 5 | 0.934241 | 9.131717 | -6.421411 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 588 | 0.3675 | 5 | 0.937798 | 10.259390 | -6.410763 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 589 | 0.3681 | 5 | 0.936302 | 9.777354 | -6.400459 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 590 | 0.3688 | 5 | 0.933755 | 9.580929 | -6.390617 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 591 | 0.3694 | 5 | 0.924450 | 8.299854 | -6.381067 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 592 | 0.3700 | 5 | 0.933161 | 9.576209 | -6.371199 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 593 | 0.3706 | 5 | 0.933705 | 9.373520 | -6.361041 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 594 | 0.3713 | 5 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0.000000e+00 |\\u001b[0m\\n\",\n \"| 604 | 0.3775 | 5 | 0.924616 | 9.045664 | -6.239790 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 605 | 0.3781 | 5 | 0.920190 | 8.237810 | -6.228678 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 606 | 0.3788 | 5 | 0.938616 | 9.932866 | -6.217750 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 607 | 0.3794 | 5 | 0.928041 | 8.335514 | -6.207167 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 608 | 0.3800 | 5 | 0.942613 | 10.677613 | -6.196759 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 609 | 0.3806 | 5 | 0.931734 | 9.114785 | -6.186313 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 610 | 0.3813 | 5 | 0.930289 | 8.809337 | -6.176285 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 611 | 0.3819 | 5 | 0.920796 | 8.183632 | -6.166577 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 612 | 0.3825 | 5 | 0.936148 | 10.184320 | -6.157476 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 613 | 0.3831 | 5 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0.000000e+00 |\\u001b[0m\\n\",\n \"| 623 | 0.3894 | 5 | 0.926166 | 8.987947 | -6.081825 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 624 | 0.3900 | 5 | 0.930624 | 9.119325 | -6.077522 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 625 | 0.3906 | 5 | 0.923748 | 8.322446 | -6.072933 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 626 | 0.3912 | 5 | 0.935525 | 10.054455 | -6.068706 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 627 | 0.3919 | 5 | 0.925626 | 8.581022 | -6.064775 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 628 | 0.3925 | 5 | 0.919861 | 8.527264 | -6.061124 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 629 | 0.3931 | 5 | 0.934803 | 9.801661 | -6.057910 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 630 | 0.3937 | 5 | 0.937310 | 11.318866 | -6.054666 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 631 | 0.3944 | 5 | 0.939446 | 16.229450 | -6.051305 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 632 | 0.3950 | 5 | 0.907581 | 11.782864 | -6.048460 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 633 | 0.3956 | 5 | 0.922724 | 9.168325 | -6.045802 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 634 | 0.3962 | 5 | 0.925209 | 9.681161 | -6.043305 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 635 | 0.3969 | 5 | 0.917343 | 7.917290 | -6.041244 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 636 | 0.3975 | 5 | 0.918506 | 8.494464 | -6.038823 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 637 | 0.3981 | 5 | 0.934074 | 9.517499 | -6.036782 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 638 | 0.3987 | 5 | 0.945360 | 11.787720 | -6.035121 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 639 | 0.3994 | 5 | 0.923969 | 9.638591 | -6.033548 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 640 | 0.4000 | 5 | 0.931064 | 9.747886 | -6.032156 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 641 | 0.4006 | 5 | 0.931296 | 9.784440 | -6.030611 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 642 | 0.4012 | 5 | 0.934377 | 10.178377 | -6.029328 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 643 | 0.4019 | 5 | 0.933453 | 10.652106 | -6.028448 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 644 | 0.4025 | 5 | 0.935375 | 9.793001 | -6.027806 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 645 | 0.4031 | 5 | 0.929348 | 9.390796 | -6.027589 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 646 | 0.4037 | 5 | 0.932922 | 9.311741 | -6.027943 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 647 | 0.4044 | 5 | 0.933876 | 9.519163 | -6.028567 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 648 | 0.4050 | 5 | 0.937401 | 9.873745 | -6.029863 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 649 | 0.4056 | 5 | 0.934438 | 9.459772 | -6.031861 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 650 | 0.4062 | 5 | 0.932149 | 9.280485 | -6.034463 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 651 | 0.4069 | 5 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0.000000e+00 |\\u001b[0m\\n\",\n \"| 661 | 0.4131 | 5 | 0.925543 | 8.665427 | -6.106337 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 662 | 0.4138 | 5 | 0.935794 | 9.913590 | -6.116549 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 663 | 0.4144 | 5 | 0.924256 | 8.054446 | -6.126980 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 664 | 0.4150 | 5 | 0.926648 | 8.618163 | -6.138140 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 665 | 0.4156 | 5 | 0.923350 | 8.456890 | -6.150216 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 666 | 0.4163 | 5 | 0.934001 | 9.499949 | -6.162310 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 667 | 0.4169 | 5 | 0.947611 | 13.289274 | -6.174956 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 668 | 0.4175 | 5 | 0.927692 | 8.764567 | -6.187704 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 669 | 0.4181 | 5 | 0.922900 | 8.442053 | -6.200579 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 670 | 0.4188 | 5 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5 | 0.924880 | 8.471291 | -6.424036 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 690 | 0.4313 | 5 | 0.926839 | 9.262191 | -6.434595 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 691 | 0.4319 | 5 | 0.928622 | 9.686299 | -6.445463 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 692 | 0.4325 | 5 | 0.930559 | 8.966420 | -6.457199 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 693 | 0.4331 | 5 | 0.928816 | 9.617107 | -6.469469 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 694 | 0.4338 | 5 | 0.931878 | 9.150726 | -6.482595 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 695 | 0.4344 | 5 | 0.931842 | 9.893392 | -6.496841 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 696 | 0.4350 | 5 | 0.918096 | 7.897612 | -6.511907 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 697 | 0.4356 | 5 | 0.932114 | 9.527637 | -6.528416 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 698 | 0.4363 | 5 | 0.932973 | 9.747239 | -6.546356 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 699 | 0.4369 | 5 | 0.930940 | 9.409062 | -6.566168 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 700 | 0.4375 | 5 | 0.929531 | 8.970919 | -6.587375 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 701 | 0.4381 | 5 | 0.935546 | 10.324452 | -6.610220 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 702 | 0.4388 | 5 | 0.930878 | 9.284216 | -6.634628 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 703 | 0.4394 | 5 | 0.934634 | 10.035476 | -6.660417 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 704 | 0.4400 | 5 | 0.939653 | 11.487262 | -6.688445 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 705 | 0.4406 | 5 | 0.924306 | 8.595590 | -6.717924 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 706 | 0.4413 | 4 | 0.921074 | 6.832913 | -6.012933 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 707 | 0.4419 | 4 | 0.927642 | 7.818493 | -6.046633 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 708 | 0.4425 | 4 | 0.934645 | 7.879602 | -6.083937 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 709 | 0.4431 | 4 | 0.925286 | 7.188123 | -6.125166 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 710 | 0.4438 | 4 | 0.932295 | 8.384217 | -6.169749 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 711 | 0.4444 | 4 | 0.930219 | 7.790628 | -6.218257 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 712 | 0.4450 | 4 | 0.923999 | 6.846884 | -6.272441 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 713 | 0.4456 | 4 | 0.937155 | 8.161222 | -6.330917 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 714 | 0.4463 | 4 | 0.913784 | 6.635980 | -6.393803 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 715 | 0.4469 | 4 | 0.914941 | 6.048444 | -6.467574 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 716 | 0.4475 | 4 | 0.925868 | 7.530941 | -6.547091 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 717 | 0.4481 | 4 | 0.929802 | 7.972495 | -6.637820 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 718 | 0.4487 | 3 | 0.926613 | 5.864296 | -6.021062 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 719 | 0.4494 | 3 | 0.936496 | 6.354412 | -6.150994 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 720 | 0.4500 | 3 | 0.933876 | 6.440199 | -6.332472 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 721 | 0.4506 | 3 | 0.919855 | 5.085086 | -6.580921 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 722 | 0.4512 | 2 | 0.932419 | 5.011490 | -6.286639 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 723 | 0.4519 | 3 | 0.934949 | 6.479562 | -6.567144 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 724 | 0.4525 | 3 | 0.918759 | 4.897590 | -6.301854 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 725 | 0.4531 | 3 | 0.921584 | 5.574742 | -6.142787 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 726 | 0.4537 | 3 | 0.920810 | 5.319923 | -6.026335 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 727 | 0.4544 | 4 | 0.932090 | 8.023124 | -6.656484 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 728 | 0.4550 | 4 | 0.929770 | 7.631246 | -6.582534 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 729 | 0.4556 | 4 | 0.930141 | 7.458421 | -6.522854 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 730 | 0.4562 | 4 | 0.923609 | 7.282485 | -6.476099 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 731 | 0.4569 | 4 | 0.937906 | 8.195758 | -6.446946 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 732 | 0.4575 | 4 | 0.929661 | 7.371895 | -6.415274 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 733 | 0.4581 | 4 | 0.938033 | 8.674495 | -6.394423 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 734 | 0.4587 | 4 | 0.915943 | 6.780173 | -6.368030 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 735 | 0.4594 | 4 | 0.941495 | 9.210612 | -6.338490 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 736 | 0.4600 | 4 | 0.934103 | 8.341763 | -6.314331 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 737 | 0.4606 | 4 | 0.932541 | 8.698184 | -6.288407 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 738 | 0.4612 | 4 | 0.921989 | 7.507051 | -6.259720 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 739 | 0.4619 | 4 | 0.915109 | 7.382231 | -6.228349 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 740 | 0.4625 | 4 | 0.920841 | 7.135293 | -6.203928 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 741 | 0.4631 | 4 | 0.934369 | 8.067266 | -6.177878 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 742 | 0.4637 | 4 | 0.919072 | 6.727871 | -6.150242 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 743 | 0.4644 | 4 | 0.948047 | 10.231599 | -6.122731 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 744 | 0.4650 | 4 | 0.940385 | 9.194453 | -6.095159 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 745 | 0.4656 | 4 | 0.937440 | 9.083191 | -6.067169 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 746 | 0.4662 | 4 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0.000000e+00 |\\u001b[0m\\n\",\n \"| 756 | 0.4725 | 5 | 0.930071 | 9.035976 | -6.595895 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 757 | 0.4731 | 5 | 0.926474 | 8.695106 | -6.582927 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 758 | 0.4738 | 5 | 0.924512 | 9.216887 | -6.570494 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 759 | 0.4744 | 5 | 0.920378 | 8.357069 | -6.558830 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 760 | 0.4750 | 5 | 0.934047 | 9.965198 | -6.548863 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 761 | 0.4756 | 5 | 0.936664 | 10.491479 | -6.539285 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 762 | 0.4763 | 5 | 0.934627 | 9.910685 | -6.531018 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 763 | 0.4769 | 5 | 0.926491 | 9.685667 | -6.523587 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 764 | 0.4775 | 5 | 0.932191 | 9.751607 | -6.516481 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 765 | 0.4781 | 5 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0.000000e+00 |\\u001b[0m\\n\",\n \"| 775 | 0.4844 | 5 | 0.943513 | 11.730250 | -6.466756 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 776 | 0.4850 | 5 | 0.920746 | 8.335757 | -6.462200 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 777 | 0.4856 | 5 | 0.924331 | 9.116222 | -6.457480 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 778 | 0.4863 | 5 | 0.921914 | 8.293705 | -6.452995 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 779 | 0.4869 | 5 | 0.928560 | 8.960990 | -6.448512 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 780 | 0.4875 | 5 | 0.928040 | 9.185435 | -6.443459 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 781 | 0.4881 | 5 | 0.931650 | 10.068263 | -6.438887 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 782 | 0.4888 | 5 | 0.928517 | 9.562702 | -6.434237 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 783 | 0.4894 | 5 | 0.924984 | 8.882981 | -6.429086 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 784 | 0.4900 | 5 | 0.928633 | 8.887591 | -6.423551 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 785 | 0.4906 | 5 | 0.924556 | 8.774083 | -6.417949 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 786 | 0.4913 | 5 | 0.934734 | 10.173882 | -6.411811 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 787 | 0.4919 | 5 | 0.931321 | 9.234596 | -6.406140 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 788 | 0.4925 | 5 | 0.932815 | 9.572152 | -6.400657 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 789 | 0.4931 | 5 | 0.922462 | 8.687736 | -6.395335 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 790 | 0.4938 | 5 | 0.931916 | 9.546295 | -6.390520 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 791 | 0.4944 | 5 | 0.929535 | 9.834749 | -6.385541 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 792 | 0.4950 | 5 | 0.924741 | 9.686103 | -6.381138 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 793 | 0.4956 | 5 | 0.918371 | 8.332913 | -6.377091 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 794 | 0.4963 | 5 | 0.931072 | 9.600378 | -6.373732 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 795 | 0.4969 | 5 | 0.929066 | 9.401269 | -6.371031 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 796 | 0.4975 | 5 | 0.932095 | 9.411825 | -6.368646 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 797 | 0.4981 | 5 | 0.911633 | 8.534316 | -6.366853 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 798 | 0.4988 | 5 | 0.931736 | 9.614760 | -6.365811 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 799 | 0.4994 | 5 | 0.929255 | 9.798591 | -6.365832 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 800 | 0.5000 | 5 | 0.933150 | 10.205395 | -6.366059 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 801 | 0.5006 | 5 | 0.929677 | 9.759404 | -6.366406 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 802 | 0.5012 | 5 | 0.932164 | 9.958121 | -6.366706 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 803 | 0.5019 | 5 | 0.921897 | 8.490702 | -6.367635 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 804 | 0.5025 | 5 | 0.904407 | 6.961878 | -6.369248 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 805 | 0.5031 | 5 | 0.927244 | 9.957100 | -6.370965 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 806 | 0.5038 | 5 | 0.938502 | 10.927201 | -6.373256 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 807 | 0.5044 | 5 | 0.934453 | 10.172743 | -6.375951 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 808 | 0.5050 | 5 | 0.924405 | 9.326037 | -6.379399 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 809 | 0.5056 | 5 | 0.934565 | 9.772870 | -6.383271 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 810 | 0.5062 | 5 | 0.959726 | 16.875979 | -6.387779 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 811 | 0.5069 | 5 | 0.955313 | 16.020174 | -6.392195 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 812 | 0.5075 | 5 | 0.940828 | 11.803230 | -6.396531 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 813 | 0.5081 | 5 | 0.921266 | 8.758789 | -6.401020 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 814 | 0.5088 | 5 | 0.919964 | 8.749492 | -6.404953 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 815 | 0.5094 | 5 | 0.930982 | 9.768547 | -6.409237 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 816 | 0.5100 | 5 | 0.919187 | 8.417535 | -6.413285 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 817 | 0.5106 | 5 | 0.931183 | 9.933064 | -6.416823 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 818 | 0.5112 | 5 | 0.932770 | 9.724156 | -6.420107 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 819 | 0.5119 | 5 | 0.926745 | 10.083216 | -6.422785 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 820 | 0.5125 | 5 | 0.928231 | 9.450696 | -6.425145 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 821 | 0.5131 | 5 | 0.930732 | 10.784650 | -6.427746 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 822 | 0.5138 | 5 | 0.935950 | 11.084179 | -6.430038 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 823 | 0.5144 | 5 | 0.927837 | 9.801143 | -6.431388 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 824 | 0.5150 | 5 | 0.943368 | 12.068285 | -6.433341 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 825 | 0.5156 | 5 | 0.932240 | 10.050045 | -6.435286 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 826 | 0.5162 | 5 | 0.925537 | 8.921238 | -6.437849 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 827 | 0.5169 | 5 | 0.911140 | 7.980349 | -6.440593 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 828 | 0.5175 | 5 | 0.926102 | 8.894458 | -6.442666 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 829 | 0.5181 | 5 | 0.930764 | 10.031692 | -6.445239 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 830 | 0.5188 | 5 | 0.935228 | 10.487921 | -6.447810 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 831 | 0.5194 | 5 | 0.921017 | 8.795281 | -6.450495 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 832 | 0.5200 | 5 | 0.907694 | 7.670427 | -6.453366 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 833 | 0.5206 | 5 | 0.909943 | 7.740737 | -6.456276 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 834 | 0.5212 | 5 | 0.914818 | 8.427780 | -6.459461 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 835 | 0.5219 | 5 | 0.927102 | 9.244189 | -6.463422 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 836 | 0.5225 | 5 | 0.906902 | 8.015583 | -6.467999 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 837 | 0.5231 | 5 | 0.930278 | 9.826530 | -6.473423 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 838 | 0.5238 | 5 | 0.933573 | 9.926509 | -6.479936 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 839 | 0.5244 | 5 | 0.929016 | 10.408976 | -6.486744 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 840 | 0.5250 | 5 | 0.930422 | 9.604165 | -6.494973 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 841 | 0.5256 | 5 | 0.919496 | 8.642593 | -6.503515 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 842 | 0.5262 | 5 | 0.929341 | 9.691619 | -6.513077 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 843 | 0.5269 | 5 | 0.928971 | 9.842893 | -6.524211 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 844 | 0.5275 | 5 | 0.933453 | 11.009402 | -6.535251 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 845 | 0.5281 | 5 | 0.931839 | 9.558106 | -6.547078 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 846 | 0.5288 | 5 | 0.934031 | 9.772532 | -6.559367 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 847 | 0.5294 | 5 | 0.908875 | 7.996691 | -6.572194 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 848 | 0.5300 | 5 | 0.925056 | 8.901146 | -6.586218 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 849 | 0.5306 | 5 | 0.928417 | 9.443220 | -6.600248 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 850 | 0.5312 | 5 | 0.924937 | 9.401289 | -6.613841 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 851 | 0.5319 | 5 | 0.920601 | 8.422577 | -6.628553 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 852 | 0.5325 | 5 | 0.931052 | 9.638048 | -6.643800 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 853 | 0.5331 | 5 | 0.923216 | 9.223827 | -6.659203 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 854 | 0.5338 | 5 | 0.922922 | 8.963944 | -6.675844 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 855 | 0.5344 | 5 | 0.925591 | 9.590381 | -6.691497 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 856 | 0.5350 | 5 | 0.924429 | 8.931645 | -6.707915 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 857 | 0.5356 | 5 | 0.919343 | 8.353310 | -6.724414 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 858 | 0.5363 | 4 | 0.930092 | 7.819427 | -6.003178 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 859 | 0.5369 | 4 | 0.926550 | 7.337783 | -6.018391 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 860 | 0.5375 | 4 | 0.933688 | 8.158798 | -6.031969 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 861 | 0.5381 | 4 | 0.919090 | 6.962004 | -6.044801 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 862 | 0.5388 | 4 | 0.919216 | 6.874953 | -6.056879 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 863 | 0.5394 | 4 | 0.928819 | 8.566498 | -6.067630 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 864 | 0.5400 | 4 | 0.931326 | 8.006476 | -6.077553 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 865 | 0.5406 | 4 | 0.933139 | 8.072888 | -6.087544 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 866 | 0.5413 | 4 | 0.916050 | 6.480457 | -6.096423 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 867 | 0.5419 | 4 | 0.922485 | 7.022250 | -6.104988 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 868 | 0.5425 | 4 | 0.938603 | 9.019238 | -6.113887 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 869 | 0.5431 | 4 | 0.916699 | 6.557981 | -6.122476 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 870 | 0.5438 | 4 | 0.916775 | 7.073197 | -6.133422 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 871 | 0.5444 | 4 | 0.940131 | 9.969909 | -6.143271 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 872 | 0.5450 | 4 | 0.931838 | 8.227085 | -6.152831 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 873 | 0.5456 | 4 | 0.918185 | 6.862832 | -6.164185 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 874 | 0.5463 | 4 | 0.929651 | 7.530676 | -6.175673 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 875 | 0.5469 | 4 | 0.927331 | 7.491924 | -6.188140 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 876 | 0.5475 | 4 | 0.925307 | 7.429103 | -6.200923 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 877 | 0.5481 | 4 | 0.928364 | 8.051866 | -6.214512 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 878 | 0.5487 | 4 | 0.935477 | 8.357555 | -6.229388 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 879 | 0.5494 | 4 | 0.921338 | 7.114463 | -6.247460 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 880 | 0.5500 | 4 | 0.921997 | 7.338384 | -6.266307 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 881 | 0.5506 | 4 | 0.910171 | 7.071233 | -6.288111 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 882 | 0.5513 | 4 | 0.935646 | 8.676680 | -6.311155 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 883 | 0.5519 | 4 | 0.923082 | 7.320006 | -6.337258 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 884 | 0.5525 | 4 | 0.907399 | 6.766790 | -6.370621 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 885 | 0.5531 | 4 | 0.940883 | 9.564549 | -6.408803 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 886 | 0.5537 | 4 | 0.916768 | 6.487341 | -6.458586 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 887 | 0.5544 | 4 | 0.926042 | 7.786680 | -6.510359 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 888 | 0.5550 | 4 | 0.928651 | 7.969324 | -6.570389 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 889 | 0.5556 | 4 | 0.921681 | 7.016701 | -6.647174 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 890 | 0.5563 | 3 | 0.923542 | 5.854110 | -6.008526 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 891 | 0.5569 | 3 | 0.913919 | 5.762097 | -6.094751 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 892 | 0.5575 | 3 | 0.930279 | 6.320222 | -6.278467 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 893 | 0.5581 | 3 | 0.914855 | 5.142106 | -6.557239 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 894 | 0.5587 | 2 | 0.935250 | 4.606866 | -6.032091 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 895 | 0.5594 | 3 | 0.928966 | 6.051311 | -6.485477 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 896 | 0.5600 | 3 | 0.938568 | 7.121828 | -6.264643 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 897 | 0.5606 | 3 | 0.937551 | 7.141019 | -6.114279 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 898 | 0.5613 | 3 | 0.920823 | 5.830745 | -6.006076 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 899 | 0.5619 | 4 | 0.920828 | 7.319262 | -6.646641 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 900 | 0.5625 | 4 | 0.916745 | 7.090214 | -6.579032 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 901 | 0.5631 | 4 | 0.932117 | 8.046887 | -6.524637 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 902 | 0.5637 | 4 | 0.925768 | 7.525246 | -6.485084 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 903 | 0.5644 | 4 | 0.926730 | 7.667699 | -6.460293 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 904 | 0.5650 | 4 | 0.933479 | 8.427721 | -6.441458 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 905 | 0.5656 | 4 | 0.934279 | 8.615420 | -6.424789 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 906 | 0.5663 | 4 | 0.916425 | 6.461447 | -6.414601 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 907 | 0.5669 | 4 | 0.918330 | 7.395758 | -6.401844 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 908 | 0.5675 | 4 | 0.921588 | 7.214110 | -6.392842 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 909 | 0.5681 | 4 | 0.930740 | 7.987823 | -6.387306 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 910 | 0.5687 | 4 | 0.920880 | 7.448220 | -6.376787 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 911 | 0.5694 | 4 | 0.941468 | 9.277546 | -6.372014 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 912 | 0.5700 | 4 | 0.930895 | 8.117703 | -6.367281 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 913 | 0.5706 | 4 | 0.934344 | 8.807338 | -6.361640 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 914 | 0.5713 | 4 | 0.921214 | 7.875672 | -6.354599 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 915 | 0.5719 | 4 | 0.922923 | 7.908524 | -6.346507 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 916 | 0.5725 | 4 | 0.925797 | 7.766734 | -6.337215 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 917 | 0.5731 | 4 | 0.927046 | 7.655915 | -6.327300 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 918 | 0.5737 | 4 | 0.921664 | 7.412390 | -6.314234 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 919 | 0.5744 | 4 | 0.923584 | 7.685994 | -6.302328 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 920 | 0.5750 | 4 | 0.912803 | 7.107680 | -6.290808 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 921 | 0.5756 | 4 | 0.919204 | 6.893781 | -6.279909 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 922 | 0.5763 | 4 | 0.937091 | 9.115775 | -6.271519 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 923 | 0.5769 | 4 | 0.932698 | 9.973019 | -6.261935 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 924 | 0.5775 | 4 | 0.923969 | 7.173532 | -6.250019 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 925 | 0.5781 | 4 | 0.929120 | 8.145913 | -6.237347 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 926 | 0.5787 | 4 | 0.931338 | 8.004418 | -6.223171 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 927 | 0.5794 | 4 | 0.923704 | 7.463983 | -6.208411 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 928 | 0.5800 | 4 | 0.929193 | 8.073174 | -6.192242 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 929 | 0.5806 | 4 | 0.922863 | 7.412166 | -6.175945 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 930 | 0.5813 | 4 | 0.923749 | 7.464325 | -6.160154 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 931 | 0.5819 | 4 | 0.916635 | 6.873594 | -6.144373 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 932 | 0.5825 | 4 | 0.931041 | 8.090923 | -6.128385 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 933 | 0.5831 | 4 | 0.932154 | 8.207330 | -6.114957 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 934 | 0.5837 | 4 | 0.931573 | 8.200356 | -6.102245 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 935 | 0.5844 | 4 | 0.919409 | 7.053110 | -6.091573 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 936 | 0.5850 | 4 | 0.931813 | 8.658322 | -6.080312 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 937 | 0.5856 | 4 | 0.912471 | 7.760416 | -6.069333 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 938 | 0.5863 | 4 | 0.933213 | 8.285897 | -6.061676 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 939 | 0.5869 | 4 | 0.924844 | 7.949592 | -6.053914 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 940 | 0.5875 | 4 | 0.929657 | 7.916140 | -6.046597 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 941 | 0.5881 | 4 | 0.931614 | 8.213557 | -6.040712 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 942 | 0.5887 | 4 | 0.917494 | 6.778910 | -6.035029 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 943 | 0.5894 | 4 | 0.921157 | 7.833076 | -6.029995 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 944 | 0.5900 | 4 | 0.934626 | 8.828546 | -6.025737 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 945 | 0.5906 | 4 | 0.916082 | 7.140080 | -6.020625 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 946 | 0.5913 | 4 | 0.921550 | 7.457766 | -6.016519 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 947 | 0.5919 | 4 | 0.928874 | 8.125375 | -6.014127 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 948 | 0.5925 | 4 | 0.924238 | 8.466355 | -6.011464 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 949 | 0.5931 | 4 | 0.931175 | 8.528595 | -6.010995 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 950 | 0.5938 | 4 | 0.915849 | 6.853404 | -6.010663 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 951 | 0.5944 | 4 | 0.924345 | 7.463991 | -6.010842 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 952 | 0.5950 | 4 | 0.914219 | 6.780014 | -6.012660 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 953 | 0.5956 | 4 | 0.917663 | 7.709888 | -6.013694 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 954 | 0.5963 | 4 | 0.919802 | 7.781216 | -6.015258 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 955 | 0.5969 | 4 | 0.930770 | 8.124918 | -6.017034 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 956 | 0.5975 | 4 | 0.925433 | 7.340804 | -6.018758 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 957 | 0.5981 | 4 | 0.944448 | 10.579975 | -6.020152 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 958 | 0.5988 | 4 | 0.954444 | 13.695401 | -6.021178 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 959 | 0.5994 | 4 | 0.951249 | 11.892416 | -6.021435 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 960 | 0.6000 | 4 | 0.947216 | 11.365227 | -6.021983 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 961 | 0.6006 | 4 | 0.926662 | 7.708466 | -6.021462 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 962 | 0.6013 | 4 | 0.915030 | 6.858607 | -6.019392 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 963 | 0.6019 | 4 | 0.928690 | 8.081657 | -6.017495 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 964 | 0.6025 | 4 | 0.931064 | 8.268210 | -6.014669 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 965 | 0.6031 | 4 | 0.914736 | 6.586943 | -6.012901 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 966 | 0.6038 | 4 | 0.929174 | 8.826159 | -6.010773 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 967 | 0.6044 | 4 | 0.922514 | 7.269420 | -6.008125 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 968 | 0.6050 | 4 | 0.934059 | 8.398957 | -6.006511 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 969 | 0.6056 | 4 | 0.919612 | 7.183256 | -6.004561 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 970 | 0.6063 | 4 | 0.918401 | 7.122052 | -6.003055 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 971 | 0.6069 | 4 | 0.918601 | 7.398527 | -6.001156 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 972 | 0.6075 | 5 | 0.934709 | 10.635267 | -6.736096 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 973 | 0.6081 | 5 | 0.920950 | 9.403478 | -6.732933 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 974 | 0.6088 | 5 | 0.925128 | 9.822489 | -6.730927 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 975 | 0.6094 | 5 | 0.925081 | 9.443124 | -6.728293 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 976 | 0.6100 | 5 | 0.919867 | 8.730676 | -6.726088 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 977 | 0.6106 | 5 | 0.935123 | 11.108385 | -6.724638 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 978 | 0.6112 | 5 | 0.924291 | 9.531157 | -6.723093 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 979 | 0.6119 | 5 | 0.926213 | 9.206035 | -6.722831 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 980 | 0.6125 | 5 | 0.921258 | 9.455391 | -6.722275 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 981 | 0.6131 | 5 | 0.919319 | 9.037999 | -6.722818 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 982 | 0.6138 | 5 | 0.922101 | 9.649626 | -6.724609 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 983 | 0.6144 | 5 | 0.914127 | 9.180961 | -6.726867 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 984 | 0.6150 | 5 | 0.929605 | 9.903099 | -6.729894 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 985 | 0.6156 | 5 | 0.921145 | 8.583618 | -6.733872 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 986 | 0.6162 | 4 | 0.930872 | 8.484389 | -6.002413 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 987 | 0.6169 | 4 | 0.916844 | 7.861012 | -6.008323 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 988 | 0.6175 | 4 | 0.905383 | 6.545824 | -6.014689 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 989 | 0.6181 | 4 | 0.928213 | 8.051449 | -6.020522 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 990 | 0.6188 | 4 | 0.929307 | 7.931838 | -6.026718 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 991 | 0.6194 | 4 | 0.917231 | 7.924858 | -6.033235 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 992 | 0.6200 | 4 | 0.914644 | 7.073856 | -6.039820 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 993 | 0.6206 | 4 | 0.915804 | 7.031604 | -6.046759 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 994 | 0.6212 | 4 | 0.915532 | 6.851505 | -6.053125 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 995 | 0.6219 | 4 | 0.926133 | 7.924493 | -6.060672 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 996 | 0.6225 | 4 | 0.915122 | 6.845819 | -6.068738 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 997 | 0.6231 | 4 | 0.908980 | 7.367004 | -6.077364 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 998 | 0.6238 | 4 | 0.924743 | 7.651999 | -6.085551 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 999 | 0.6244 | 4 | 0.932288 | 8.875839 | -6.093536 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1000 | 0.6250 | 4 | 0.931087 | 8.401884 | -6.101440 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1001 | 0.6256 | 4 | 0.925997 | 7.514845 | -6.108311 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1002 | 0.6262 | 4 | 0.928103 | 8.755970 | -6.115036 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1003 | 0.6269 | 4 | 0.924007 | 7.877962 | -6.120053 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1004 | 0.6275 | 4 | 0.923370 | 7.606824 | -6.125083 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1005 | 0.6281 | 4 | 0.931847 | 8.271467 | -6.129330 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1006 | 0.6288 | 4 | 0.924153 | 7.350740 | -6.131815 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1007 | 0.6294 | 4 | 0.928794 | 9.078392 | -6.134081 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1008 | 0.6300 | 4 | 0.922034 | 7.871533 | -6.135853 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1009 | 0.6306 | 4 | 0.930759 | 8.319058 | -6.137238 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1010 | 0.6312 | 4 | 0.920082 | 7.321156 | -6.138090 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1011 | 0.6319 | 4 | 0.925351 | 7.838752 | -6.139210 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1012 | 0.6325 | 4 | 0.926898 | 7.595031 | -6.139927 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1013 | 0.6331 | 4 | 0.932205 | 8.338744 | -6.143038 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1014 | 0.6338 | 4 | 0.931919 | 8.428863 | -6.146324 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1015 | 0.6344 | 4 | 0.924758 | 7.827160 | -6.149373 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1016 | 0.6350 | 4 | 0.929116 | 8.540733 | -6.153742 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1017 | 0.6356 | 4 | 0.915126 | 7.437961 | -6.157307 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1018 | 0.6362 | 4 | 0.927702 | 8.517067 | -6.162357 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1019 | 0.6369 | 4 | 0.936099 | 9.611543 | -6.167346 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1020 | 0.6375 | 4 | 0.935214 | 9.719461 | -6.171501 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1021 | 0.6381 | 4 | 0.917992 | 7.913717 | -6.176618 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1022 | 0.6388 | 4 | 0.914312 | 6.582554 | -6.183004 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1023 | 0.6394 | 4 | 0.931955 | 8.374164 | -6.190415 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1024 | 0.6400 | 4 | 0.919650 | 7.426191 | -6.199218 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1025 | 0.6406 | 4 | 0.914648 | 7.586108 | -6.209307 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1026 | 0.6412 | 4 | 0.922771 | 7.578438 | -6.219444 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1027 | 0.6419 | 4 | 0.918334 | 7.000283 | -6.232960 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1028 | 0.6425 | 4 | 0.919806 | 7.717802 | -6.245844 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1029 | 0.6431 | 4 | 0.918627 | 7.365761 | -6.262885 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1030 | 0.6438 | 4 | 0.916576 | 7.045100 | -6.281386 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1031 | 0.6444 | 4 | 0.918363 | 7.295040 | -6.301876 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1032 | 0.6450 | 4 | 0.932141 | 8.764861 | -6.325443 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1033 | 0.6456 | 4 | 0.931872 | 8.280653 | -6.348106 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1034 | 0.6462 | 4 | 0.923205 | 7.308350 | -6.371098 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1035 | 0.6469 | 4 | 0.918940 | 7.740210 | -6.393510 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1036 | 0.6475 | 4 | 0.927996 | 8.016123 | -6.413080 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1037 | 0.6481 | 4 | 0.916981 | 7.068324 | -6.433704 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1038 | 0.6488 | 4 | 0.921732 | 8.072070 | -6.454810 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1039 | 0.6494 | 4 | 0.933029 | 8.710908 | -6.478630 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1040 | 0.6500 | 4 | 0.923166 | 7.583035 | -6.504847 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1041 | 0.6506 | 4 | 0.929650 | 7.991677 | -6.530908 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1042 | 0.6512 | 4 | 0.910652 | 7.831387 | -6.549571 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1043 | 0.6519 | 4 | 0.915165 | 7.414356 | -6.567332 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1044 | 0.6525 | 4 | 0.918041 | 7.230979 | -6.591474 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1045 | 0.6531 | 4 | 0.918513 | 7.130405 | -6.617837 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1046 | 0.6538 | 4 | 0.935045 | 10.248333 | -6.644649 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1047 | 0.6544 | 4 | 0.911800 | 7.263334 | -6.662403 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1048 | 0.6550 | 4 | 0.935323 | 8.808576 | -6.670366 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1049 | 0.6556 | 4 | 0.917601 | 7.382260 | -6.674614 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1050 | 0.6562 | 4 | 0.927703 | 8.327516 | -6.678070 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1051 | 0.6569 | 4 | 0.929240 | 8.159486 | -6.682884 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1052 | 0.6575 | 4 | 0.927343 | 8.167163 | -6.682254 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1053 | 0.6581 | 4 | 0.918255 | 7.118270 | -6.676019 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1054 | 0.6588 | 4 | 0.924514 | 7.911668 | -6.673981 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1055 | 0.6594 | 4 | 0.908841 | 7.212744 | -6.671337 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1056 | 0.6600 | 4 | 0.932677 | 8.829904 | -6.672329 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1057 | 0.6606 | 4 | 0.937924 | 9.915553 | -6.686767 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1058 | 0.6613 | 4 | 0.919435 | 7.155833 | -6.703246 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1059 | 0.6619 | 3 | 0.920376 | 5.931020 | -6.003585 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1060 | 0.6625 | 3 | 0.915874 | 5.160785 | -6.029415 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1061 | 0.6631 | 3 | 0.936080 | 7.283641 | -6.059212 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1062 | 0.6638 | 3 | 0.926326 | 6.584482 | -6.099238 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1063 | 0.6644 | 3 | 0.917920 | 5.606686 | -6.141490 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1064 | 0.6650 | 3 | 0.914574 | 5.980095 | -6.192046 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1065 | 0.6656 | 3 | 0.929508 | 7.013428 | -6.247208 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1066 | 0.6663 | 3 | 0.929459 | 6.676799 | -6.316483 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1067 | 0.6669 | 3 | 0.925459 | 6.066367 | -6.395493 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1068 | 0.6675 | 3 | 0.933261 | 7.170071 | -6.488118 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1069 | 0.6681 | 3 | 0.932382 | 7.179632 | -6.602509 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1070 | 0.6688 | 3 | 0.919540 | 6.003355 | -6.686659 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1071 | 0.6694 | 3 | 0.931598 | 6.937881 | -6.645541 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1072 | 0.6700 | 3 | 0.927833 | 6.351259 | -6.529632 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1073 | 0.6706 | 3 | 0.918263 | 5.491571 | -6.386503 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1074 | 0.6713 | 3 | 0.926692 | 6.385859 | -6.273671 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1075 | 0.6719 | 3 | 0.917119 | 5.999285 | -6.176272 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1076 | 0.6725 | 3 | 0.925408 | 5.932480 | -6.094158 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1077 | 0.6731 | 3 | 0.935232 | 7.047719 | -6.029750 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1078 | 0.6737 | 4 | 0.921706 | 8.294545 | -6.698059 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1079 | 0.6744 | 4 | 0.911691 | 7.933428 | -6.654229 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1080 | 0.6750 | 4 | 0.926209 | 7.677143 | -6.616279 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1081 | 0.6756 | 4 | 0.926396 | 8.077297 | -6.591037 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1082 | 0.6763 | 4 | 0.928085 | 8.697632 | -6.572259 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1083 | 0.6769 | 4 | 0.924713 | 8.636628 | -6.560263 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1084 | 0.6775 | 4 | 0.913943 | 6.868651 | -6.546583 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1085 | 0.6781 | 4 | 0.934523 | 9.129627 | -6.532780 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1086 | 0.6787 | 4 | 0.928840 | 8.193750 | -6.526252 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1087 | 0.6794 | 4 | 0.922079 | 7.691099 | -6.521036 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1088 | 0.6800 | 4 | 0.928793 | 9.001772 | -6.515684 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1089 | 0.6806 | 4 | 0.928990 | 8.050145 | -6.506385 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1090 | 0.6813 | 4 | 0.911485 | 7.048428 | -6.500763 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1091 | 0.6819 | 4 | 0.913823 | 6.982267 | -6.496410 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1092 | 0.6825 | 4 | 0.919510 | 7.312097 | -6.493355 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1093 | 0.6831 | 4 | 0.921880 | 8.064265 | -6.491628 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1094 | 0.6837 | 4 | 0.924319 | 8.168887 | -6.490720 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1095 | 0.6844 | 4 | 0.916849 | 8.145098 | -6.493842 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1096 | 0.6850 | 4 | 0.933056 | 9.022156 | -6.496825 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1097 | 0.6856 | 4 | 0.930876 | 9.288652 | -6.500247 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1098 | 0.6863 | 4 | 0.928344 | 8.776482 | -6.503331 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1099 | 0.6869 | 4 | 0.929797 | 8.445000 | -6.506542 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1100 | 0.6875 | 4 | 0.932857 | 8.977255 | -6.508816 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1101 | 0.6881 | 4 | 0.914474 | 6.950047 | -6.508330 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1102 | 0.6887 | 4 | 0.915831 | 6.985880 | -6.504984 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1103 | 0.6894 | 4 | 0.919720 | 7.433220 | -6.498664 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1104 | 0.6900 | 4 | 0.924345 | 8.435698 | -6.493188 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1105 | 0.6906 | 4 | 0.919239 | 7.499495 | -6.483664 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1106 | 0.6913 | 4 | 0.927702 | 8.312528 | -6.477971 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1107 | 0.6919 | 4 | 0.905430 | 7.064338 | -6.471588 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1108 | 0.6925 | 4 | 0.929447 | 8.317395 | -6.462329 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1109 | 0.6931 | 4 | 0.920270 | 7.443997 | -6.454981 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1110 | 0.6937 | 4 | 0.907604 | 7.078348 | -6.445337 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1111 | 0.6944 | 4 | 0.944930 | 11.707186 | -6.436921 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1112 | 0.6950 | 4 | 0.947047 | 12.491962 | -6.427934 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1113 | 0.6956 | 4 | 0.955191 | 13.723619 | -6.419523 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1114 | 0.6963 | 4 | 0.949932 | 12.809653 | -6.409602 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1115 | 0.6969 | 4 | 0.941285 | 10.841859 | -6.398473 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1116 | 0.6975 | 4 | 0.950025 | 12.612672 | -6.387562 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1117 | 0.6981 | 4 | 0.928513 | 9.529809 | -6.376837 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1118 | 0.6987 | 4 | 0.952280 | 13.225460 | -6.366434 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1119 | 0.6994 | 4 | 0.930254 | 8.762119 | -6.355948 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1120 | 0.7000 | 4 | 0.916934 | 7.582739 | -6.346619 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1121 | 0.7006 | 4 | 0.918606 | 8.007747 | -6.338990 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1122 | 0.7013 | 4 | 0.930048 | 8.570686 | -6.335392 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1123 | 0.7019 | 4 | 0.920564 | 8.365584 | -6.328398 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1124 | 0.7025 | 4 | 0.919386 | 7.555674 | -6.322689 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1125 | 0.7031 | 4 | 0.908091 | 7.353988 | -6.320174 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1126 | 0.7037 | 4 | 0.925578 | 7.913533 | -6.318050 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1127 | 0.7044 | 4 | 0.928327 | 8.114483 | -6.319327 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1128 | 0.7050 | 4 | 0.913671 | 7.522904 | -6.320312 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1129 | 0.7056 | 4 | 0.930980 | 8.752463 | -6.321696 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1130 | 0.7063 | 4 | 0.940251 | 10.005117 | -6.325615 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1131 | 0.7069 | 4 | 0.926527 | 8.024006 | -6.329173 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1132 | 0.7075 | 4 | 0.907798 | 7.109459 | -6.332008 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1133 | 0.7081 | 4 | 0.922298 | 8.640346 | -6.335240 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1134 | 0.7087 | 4 | 0.896194 | 6.614045 | -6.337656 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1135 | 0.7094 | 4 | 0.937337 | 9.121761 | -6.340842 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1136 | 0.7100 | 4 | 0.921886 | 8.392108 | -6.346003 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1137 | 0.7106 | 4 | 0.916224 | 7.859331 | -6.348157 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1138 | 0.7113 | 4 | 0.915565 | 8.024887 | -6.352561 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1139 | 0.7119 | 4 | 0.918944 | 8.247203 | -6.355931 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1140 | 0.7125 | 4 | 0.928581 | 8.213575 | -6.359025 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1141 | 0.7131 | 4 | 0.922211 | 7.502078 | -6.364355 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1142 | 0.7137 | 4 | 0.928090 | 8.158745 | -6.367767 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1143 | 0.7144 | 4 | 0.920783 | 8.535763 | -6.371420 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1144 | 0.7150 | 4 | 0.937610 | 9.167599 | -6.375872 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1145 | 0.7156 | 4 | 0.914974 | 7.609418 | -6.379270 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1146 | 0.7163 | 4 | 0.925423 | 8.059713 | -6.380910 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1147 | 0.7169 | 4 | 0.927696 | 8.380200 | -6.383113 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1148 | 0.7175 | 4 | 0.915872 | 8.763745 | -6.383455 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1149 | 0.7181 | 4 | 0.916754 | 7.811686 | -6.382649 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1150 | 0.7188 | 4 | 0.904398 | 7.312649 | -6.380434 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1151 | 0.7194 | 4 | 0.898388 | 6.233123 | -6.378116 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1152 | 0.7200 | 4 | 0.924043 | 8.260602 | -6.375061 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1153 | 0.7206 | 4 | 0.929171 | 8.306413 | -6.370896 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1154 | 0.7213 | 4 | 0.924714 | 7.813347 | -6.367199 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1155 | 0.7219 | 4 | 0.914168 | 7.571872 | -6.364520 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1156 | 0.7225 | 4 | 0.925041 | 8.776365 | -6.361529 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1157 | 0.7231 | 4 | 0.925620 | 8.343365 | -6.361940 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1158 | 0.7238 | 4 | 0.922507 | 7.930578 | -6.361511 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1159 | 0.7244 | 4 | 0.934175 | 8.782314 | -6.360446 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1160 | 0.7250 | 4 | 0.920790 | 7.707391 | -6.359915 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1161 | 0.7256 | 4 | 0.910863 | 7.289048 | -6.359643 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1162 | 0.7263 | 4 | 0.917009 | 7.602118 | -6.359626 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1163 | 0.7269 | 4 | 0.921294 | 8.246427 | -6.360292 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1164 | 0.7275 | 4 | 0.926745 | 8.517843 | -6.360161 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1165 | 0.7281 | 4 | 0.925840 | 8.038491 | -6.361011 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1166 | 0.7288 | 4 | 0.926431 | 8.348977 | -6.364340 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1167 | 0.7294 | 4 | 0.935242 | 10.113046 | -6.366325 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1168 | 0.7300 | 4 | 0.927744 | 8.453601 | -6.370783 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1169 | 0.7306 | 4 | 0.921554 | 7.747966 | -6.373253 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1170 | 0.7313 | 4 | 0.922679 | 8.202883 | -6.378563 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1171 | 0.7319 | 4 | 0.910188 | 7.777112 | -6.387620 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1172 | 0.7325 | 4 | 0.917733 | 7.207897 | -6.397110 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1173 | 0.7331 | 4 | 0.916014 | 7.393832 | -6.408907 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1174 | 0.7338 | 4 | 0.916073 | 7.744147 | -6.423190 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1175 | 0.7344 | 4 | 0.924179 | 7.997136 | -6.438644 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1176 | 0.7350 | 4 | 0.919824 | 8.388396 | -6.453451 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1177 | 0.7356 | 4 | 0.920209 | 7.862722 | -6.466161 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1178 | 0.7362 | 4 | 0.898070 | 7.402616 | -6.477981 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1179 | 0.7369 | 4 | 0.934894 | 9.805250 | -6.490331 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1180 | 0.7375 | 4 | 0.926073 | 7.958758 | -6.501302 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1181 | 0.7381 | 4 | 0.918172 | 7.780018 | -6.508742 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1182 | 0.7388 | 4 | 0.926471 | 9.004369 | -6.517199 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1183 | 0.7394 | 4 | 0.939136 | 10.829570 | -6.524190 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1184 | 0.7400 | 4 | 0.916182 | 8.729566 | -6.529659 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1185 | 0.7406 | 4 | 0.921064 | 8.598056 | -6.536999 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1186 | 0.7412 | 4 | 0.924541 | 7.885106 | -6.544560 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1187 | 0.7419 | 4 | 0.907229 | 6.759805 | -6.553980 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1188 | 0.7425 | 4 | 0.915924 | 7.317449 | -6.561419 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1189 | 0.7431 | 4 | 0.929004 | 8.739841 | -6.568440 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1190 | 0.7438 | 4 | 0.906303 | 7.346764 | -6.572663 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1191 | 0.7444 | 4 | 0.915393 | 8.164053 | -6.575985 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1192 | 0.7450 | 4 | 0.899735 | 7.143547 | -6.577017 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1193 | 0.7456 | 4 | 0.924635 | 8.377289 | -6.576245 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1194 | 0.7462 | 4 | 0.918561 | 7.572548 | -6.573967 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1195 | 0.7469 | 4 | 0.926113 | 7.928270 | -6.569815 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1196 | 0.7475 | 4 | 0.920556 | 7.788774 | -6.566726 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1197 | 0.7481 | 4 | 0.908997 | 6.947657 | -6.562847 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1198 | 0.7488 | 4 | 0.929165 | 8.826927 | -6.560783 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1199 | 0.7494 | 4 | 0.920913 | 7.702865 | -6.557858 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1200 | 0.7500 | 4 | 0.933831 | 8.945611 | -6.558579 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1201 | 0.7506 | 4 | 0.924699 | 8.864619 | -6.562230 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1202 | 0.7512 | 4 | 0.911546 | 7.443252 | -6.568334 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1203 | 0.7519 | 4 | 0.935485 | 9.703718 | -6.577404 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1204 | 0.7525 | 4 | 0.923595 | 8.795860 | -6.585200 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1205 | 0.7531 | 4 | 0.929596 | 8.778910 | -6.596626 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1206 | 0.7538 | 4 | 0.926712 | 8.130308 | -6.607278 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1207 | 0.7544 | 4 | 0.928199 | 8.880169 | -6.617869 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1208 | 0.7550 | 4 | 0.924128 | 7.796787 | -6.627011 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1209 | 0.7556 | 4 | 0.939659 | 9.793255 | -6.626992 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1210 | 0.7562 | 4 | 0.924773 | 8.361683 | -6.639151 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1211 | 0.7569 | 4 | 0.922705 | 7.717882 | -6.653354 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1212 | 0.7575 | 4 | 0.927571 | 8.588771 | -6.663088 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1213 | 0.7581 | 4 | 0.931787 | 8.685981 | -6.678892 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1214 | 0.7588 | 4 | 0.932016 | 8.870283 | -6.712668 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1215 | 0.7594 | 3 | 0.936448 | 7.131936 | -6.028008 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1216 | 0.7600 | 3 | 0.935406 | 7.003290 | -6.071563 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1217 | 0.7606 | 3 | 0.924934 | 6.910270 | -6.119044 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1218 | 0.7612 | 3 | 0.929694 | 6.615141 | -6.170889 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1219 | 0.7619 | 3 | 0.909327 | 5.570117 | -6.234240 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1220 | 0.7625 | 3 | 0.932986 | 7.149140 | -6.295446 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1221 | 0.7631 | 3 | 0.924188 | 6.457875 | -6.365778 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1222 | 0.7638 | 3 | 0.909953 | 5.871146 | -6.434445 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1223 | 0.7644 | 3 | 0.928547 | 6.499115 | -6.511122 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1224 | 0.7650 | 3 | 0.922555 | 6.261577 | -6.592566 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1225 | 0.7656 | 3 | 0.913798 | 6.026391 | -6.668235 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1226 | 0.7662 | 2 | 0.930050 | 5.004120 | -6.029681 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1227 | 0.7669 | 2 | 0.909977 | 4.486438 | -6.109226 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1228 | 0.7675 | 2 | 0.895722 | 3.440246 | -6.202233 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1229 | 0.7681 | 2 | 0.940644 | 5.820162 | -6.281046 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1230 | 0.7688 | 2 | 0.930324 | 5.041517 | -6.400145 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1231 | 0.7694 | 2 | 0.916581 | 4.403132 | -6.514832 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1232 | 0.7700 | 2 | 0.920085 | 4.437169 | -6.710137 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1233 | 0.7706 | 1 | 0.952456 | 4.143759 | -6.231334 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1234 | 0.7712 | 1 | 0.939911 | 3.289889 | -6.199109 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1235 | 0.7719 | 1 | 0.948967 | 3.912819 | -6.279833 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1236 | 0.7725 | 1 | 0.924042 | 3.470309 | -6.186977 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1237 | 0.7731 | 1 | 0.924761 | 3.568120 | -6.210239 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1238 | 0.7738 | 1 | 0.951496 | 4.155957 | -6.175174 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1239 | 0.7744 | 2 | 0.914439 | 4.638218 | -6.643518 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1240 | 0.7750 | 2 | 0.922798 | 4.622485 | -6.472152 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1241 | 0.7756 | 2 | 0.909284 | 4.378345 | -6.351047 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1242 | 0.7762 | 2 | 0.928217 | 4.809230 | -6.270035 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1243 | 0.7769 | 2 | 0.923236 | 4.858469 | -6.200196 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1244 | 0.7775 | 2 | 0.893751 | 4.178158 | -6.173887 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1245 | 0.7781 | 2 | 0.922553 | 4.384358 | -6.188209 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1246 | 0.7788 | 2 | 0.909896 | 4.370389 | -6.231758 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1247 | 0.7794 | 2 | 0.922965 | 4.873047 | -6.265387 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1248 | 0.7800 | 2 | 0.899864 | 4.570790 | -6.220014 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1249 | 0.7806 | 2 | 0.913468 | 4.285283 | -6.119855 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1250 | 0.7812 | 2 | 0.932397 | 5.044742 | -6.026681 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1251 | 0.7819 | 3 | 0.929710 | 7.061525 | -6.636329 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1252 | 0.7825 | 3 | 0.906493 | 5.589907 | -6.562926 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1253 | 0.7831 | 3 | 0.943008 | 8.304963 | -6.490258 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1254 | 0.7838 | 3 | 0.926622 | 6.655013 | -6.422651 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1255 | 0.7844 | 3 | 0.931639 | 6.835680 | -6.366936 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1256 | 0.7850 | 3 | 0.916696 | 6.467256 | -6.317927 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1257 | 0.7856 | 3 | 0.926912 | 6.755943 | -6.270930 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1258 | 0.7863 | 3 | 0.922191 | 6.677117 | -6.227701 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1259 | 0.7869 | 3 | 0.930687 | 7.118596 | -6.186990 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1260 | 0.7875 | 3 | 0.930117 | 6.684295 | -6.144891 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1261 | 0.7881 | 3 | 0.929701 | 7.005025 | -6.113824 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1262 | 0.7888 | 3 | 0.918863 | 6.294075 | -6.078622 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1263 | 0.7894 | 3 | 0.932202 | 6.840877 | -6.047364 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1264 | 0.7900 | 3 | 0.910877 | 5.613191 | -6.021068 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1265 | 0.7906 | 4 | 0.925607 | 8.073141 | -6.719737 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1266 | 0.7913 | 4 | 0.912307 | 7.263875 | -6.704270 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1267 | 0.7919 | 4 | 0.930200 | 8.913673 | -6.689412 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1268 | 0.7925 | 4 | 0.929462 | 8.768475 | -6.679864 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1269 | 0.7931 | 4 | 0.922741 | 8.526130 | -6.674705 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1270 | 0.7938 | 4 | 0.904746 | 7.523337 | -6.674535 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1271 | 0.7944 | 4 | 0.905644 | 7.542059 | -6.676006 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1272 | 0.7950 | 4 | 0.920402 | 7.629049 | -6.677811 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1273 | 0.7956 | 4 | 0.925692 | 9.695210 | -6.681055 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1274 | 0.7963 | 4 | 0.907982 | 7.327946 | -6.683734 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1275 | 0.7969 | 4 | 0.921152 | 7.715528 | -6.689100 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1276 | 0.7975 | 4 | 0.919780 | 7.797306 | -6.690455 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1277 | 0.7981 | 4 | 0.908231 | 6.997520 | -6.692961 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1278 | 0.7988 | 4 | 0.910907 | 6.868745 | -6.695419 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1279 | 0.7994 | 4 | 0.925940 | 8.451732 | -6.699436 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1280 | 0.8000 | 4 | 0.934993 | 10.338312 | -6.704191 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1281 | 0.8006 | 4 | 0.947827 | 13.149787 | -6.706832 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1282 | 0.8013 | 4 | 0.946172 | 12.332356 | -6.713397 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1283 | 0.8019 | 4 | 0.958371 | 15.994232 | -6.718868 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1284 | 0.8025 | 3 | 0.920216 | 6.571284 | -6.004194 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1285 | 0.8031 | 3 | 0.926825 | 6.706288 | -6.008552 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1286 | 0.8037 | 3 | 0.907671 | 5.892412 | -6.013252 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1287 | 0.8044 | 3 | 0.918813 | 6.421157 | -6.016678 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1288 | 0.8050 | 3 | 0.907797 | 5.761683 | -6.018253 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1289 | 0.8056 | 3 | 0.921126 | 6.379539 | -6.016380 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1290 | 0.8063 | 3 | 0.937599 | 7.956121 | -6.008141 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1291 | 0.8069 | 3 | 0.925893 | 6.658299 | -6.002442 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1292 | 0.8075 | 4 | 0.929607 | 9.408072 | -6.714071 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1293 | 0.8081 | 4 | 0.930463 | 8.916854 | -6.702464 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1294 | 0.8087 | 4 | 0.913496 | 8.402706 | -6.687466 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1295 | 0.8094 | 4 | 0.901661 | 7.318546 | -6.673721 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1296 | 0.8100 | 4 | 0.921061 | 8.009299 | -6.665851 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1297 | 0.8106 | 4 | 0.909855 | 7.818646 | -6.663710 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1298 | 0.8113 | 4 | 0.912429 | 7.054599 | -6.656185 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1299 | 0.8119 | 4 | 0.921310 | 8.087624 | -6.647634 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1300 | 0.8125 | 4 | 0.926882 | 8.309952 | -6.643482 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1301 | 0.8131 | 4 | 0.922634 | 8.101265 | -6.637931 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1302 | 0.8137 | 4 | 0.903305 | 7.810847 | -6.632792 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1303 | 0.8144 | 4 | 0.925649 | 8.853188 | -6.627386 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1304 | 0.8150 | 4 | 0.920076 | 8.582657 | -6.622565 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1305 | 0.8156 | 4 | 0.914099 | 7.787682 | -6.618596 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1306 | 0.8163 | 4 | 0.931229 | 9.168955 | -6.616898 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1307 | 0.8169 | 4 | 0.931456 | 10.647637 | -6.617723 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1308 | 0.8175 | 4 | 0.930434 | 8.912885 | -6.612092 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1309 | 0.8181 | 4 | 0.928742 | 8.830129 | -6.609815 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1310 | 0.8187 | 4 | 0.914587 | 7.686721 | -6.607506 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1311 | 0.8194 | 4 | 0.920700 | 9.108045 | -6.606688 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1312 | 0.8200 | 4 | 0.927001 | 8.420919 | -6.607645 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1313 | 0.8206 | 4 | 0.924258 | 8.255074 | -6.605577 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1314 | 0.8213 | 4 | 0.923330 | 8.297737 | -6.610603 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1315 | 0.8219 | 4 | 0.927977 | 9.260231 | -6.619429 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1316 | 0.8225 | 4 | 0.910872 | 7.814553 | -6.628394 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1317 | 0.8231 | 4 | 0.915706 | 8.115908 | -6.640888 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1318 | 0.8237 | 4 | 0.912054 | 7.342257 | -6.651894 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1319 | 0.8244 | 4 | 0.925312 | 8.489474 | -6.664372 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1320 | 0.8250 | 4 | 0.902651 | 7.504793 | -6.672463 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1321 | 0.8256 | 4 | 0.932649 | 9.117836 | -6.676945 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1322 | 0.8263 | 4 | 0.913811 | 7.966333 | -6.682830 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1323 | 0.8269 | 4 | 0.912447 | 8.078233 | -6.688385 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1324 | 0.8275 | 4 | 0.922237 | 8.321086 | -6.683467 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1325 | 0.8281 | 4 | 0.923167 | 8.182118 | -6.687963 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1326 | 0.8287 | 4 | 0.930753 | 9.513708 | -6.689673 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1327 | 0.8294 | 4 | 0.927944 | 8.866654 | -6.694972 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1328 | 0.8300 | 4 | 0.916398 | 8.443696 | -6.703402 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1329 | 0.8306 | 4 | 0.901440 | 7.634219 | -6.705796 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1330 | 0.8313 | 4 | 0.922754 | 8.935395 | -6.711642 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1331 | 0.8319 | 4 | 0.927116 | 8.510146 | -6.714483 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1332 | 0.8325 | 4 | 0.908065 | 7.132285 | -6.718255 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1333 | 0.8331 | 4 | 0.918213 | 8.339746 | -6.720112 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1334 | 0.8337 | 4 | 0.915420 | 7.949602 | -6.717928 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1335 | 0.8344 | 4 | 0.926254 | 8.569067 | -6.713696 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1336 | 0.8350 | 4 | 0.923414 | 9.492939 | -6.708814 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1337 | 0.8356 | 4 | 0.914152 | 8.191882 | -6.701642 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1338 | 0.8363 | 4 | 0.892766 | 6.287503 | -6.690712 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1339 | 0.8369 | 4 | 0.923519 | 8.217924 | -6.684021 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1340 | 0.8375 | 4 | 0.925387 | 8.864148 | -6.673170 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1341 | 0.8381 | 4 | 0.924136 | 8.206538 | -6.669380 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1342 | 0.8387 | 4 | 0.926988 | 9.034768 | -6.666147 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1343 | 0.8394 | 4 | 0.911987 | 7.943771 | -6.667502 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1344 | 0.8400 | 4 | 0.921000 | 8.354416 | -6.670236 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1345 | 0.8406 | 4 | 0.901436 | 6.994085 | -6.672476 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1346 | 0.8413 | 4 | 0.924168 | 8.719940 | -6.677506 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1347 | 0.8419 | 4 | 0.900978 | 7.824988 | -6.681746 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1348 | 0.8425 | 4 | 0.912713 | 7.374806 | -6.679422 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1349 | 0.8431 | 4 | 0.920766 | 8.125932 | -6.684184 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1350 | 0.8438 | 4 | 0.923853 | 8.162324 | -6.691453 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1351 | 0.8444 | 4 | 0.896098 | 6.970622 | -6.695730 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1352 | 0.8450 | 4 | 0.930811 | 9.435302 | -6.701364 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1353 | 0.8456 | 4 | 0.918538 | 8.275929 | -6.709699 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1354 | 0.8463 | 4 | 0.928470 | 8.698167 | -6.717348 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1355 | 0.8469 | 3 | 0.930309 | 7.341614 | -6.009742 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1356 | 0.8475 | 3 | 0.952561 | 11.640321 | -6.021302 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1357 | 0.8481 | 3 | 0.953932 | 12.938866 | -6.038162 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1358 | 0.8488 | 3 | 0.943049 | 9.969767 | -6.060154 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1359 | 0.8494 | 3 | 0.906790 | 5.582816 | -6.081769 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1360 | 0.8500 | 3 | 0.925486 | 6.801914 | -6.109987 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1361 | 0.8506 | 3 | 0.922876 | 6.741693 | -6.136498 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1362 | 0.8513 | 3 | 0.934594 | 7.493868 | -6.167731 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1363 | 0.8519 | 3 | 0.924786 | 7.474810 | -6.199347 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1364 | 0.8525 | 3 | 0.910837 | 5.500055 | -6.227932 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1365 | 0.8531 | 3 | 0.915531 | 5.932688 | -6.252630 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1366 | 0.8538 | 3 | 0.930793 | 7.041993 | -6.276321 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1367 | 0.8544 | 3 | 0.938088 | 8.756874 | -6.296855 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1368 | 0.8550 | 3 | 0.910723 | 6.451619 | -6.308915 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1369 | 0.8556 | 3 | 0.917983 | 7.778209 | -6.319756 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1370 | 0.8563 | 3 | 0.927807 | 7.532988 | -6.320335 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1371 | 0.8569 | 3 | 0.931662 | 7.979495 | -6.328537 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1372 | 0.8575 | 3 | 0.921234 | 6.817747 | -6.332177 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1373 | 0.8581 | 3 | 0.925978 | 6.832790 | -6.334080 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1374 | 0.8588 | 3 | 0.930740 | 7.744576 | -6.338519 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1375 | 0.8594 | 3 | 0.943918 | 9.086644 | -6.339174 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1376 | 0.8600 | 3 | 0.914050 | 5.699749 | -6.347613 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1377 | 0.8606 | 3 | 0.905264 | 6.346863 | -6.347356 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1378 | 0.8613 | 3 | 0.906315 | 5.285599 | -6.345342 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1379 | 0.8619 | 3 | 0.920860 | 7.811200 | -6.338786 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1380 | 0.8625 | 3 | 0.917868 | 6.642529 | -6.332586 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1381 | 0.8631 | 3 | 0.909967 | 5.732910 | -6.323180 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1382 | 0.8638 | 3 | 0.921635 | 6.648797 | -6.309623 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1383 | 0.8644 | 3 | 0.930756 | 7.780269 | -6.296340 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1384 | 0.8650 | 3 | 0.930719 | 7.890981 | -6.281010 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1385 | 0.8656 | 3 | 0.923992 | 6.398535 | -6.274691 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1386 | 0.8662 | 3 | 0.903839 | 6.690373 | -6.266116 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1387 | 0.8669 | 3 | 0.909279 | 6.162003 | -6.265344 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1388 | 0.8675 | 3 | 0.941367 | 8.677482 | -6.270572 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1389 | 0.8681 | 3 | 0.911446 | 6.014046 | -6.284428 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1390 | 0.8688 | 3 | 0.929819 | 6.943937 | -6.307708 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1391 | 0.8694 | 3 | 0.923763 | 6.919514 | -6.331954 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1392 | 0.8700 | 3 | 0.940189 | 8.590857 | -6.367560 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1393 | 0.8706 | 3 | 0.909837 | 6.339009 | -6.404126 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1394 | 0.8712 | 3 | 0.926164 | 6.626126 | -6.452202 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1395 | 0.8719 | 3 | 0.926851 | 6.704561 | -6.496296 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1396 | 0.8725 | 3 | 0.932812 | 8.590432 | -6.543041 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1397 | 0.8731 | 3 | 0.924830 | 6.746752 | -6.600877 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1398 | 0.8738 | 3 | 0.892529 | 5.109863 | -6.662386 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1399 | 0.8744 | 2 | 0.911400 | 4.365246 | -6.021849 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1400 | 0.8750 | 2 | 0.907444 | 4.026311 | -6.092594 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1401 | 0.8756 | 2 | 0.950411 | 7.357859 | -6.204895 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1402 | 0.8762 | 2 | 0.930811 | 5.691882 | -6.366503 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1403 | 0.8769 | 2 | 0.933039 | 5.277355 | -6.642130 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1404 | 0.8775 | 1 | 0.937317 | 3.483202 | -6.227275 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1405 | 0.8781 | 2 | 0.913230 | 5.123663 | -6.574511 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1406 | 0.8788 | 2 | 0.911899 | 6.244291 | -6.302770 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1407 | 0.8794 | 2 | 0.950953 | 7.910832 | -6.147566 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1408 | 0.8800 | 2 | 0.907901 | 4.279579 | -6.029678 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1409 | 0.8806 | 3 | 0.918393 | 6.419089 | -6.693765 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1410 | 0.8812 | 3 | 0.924358 | 6.599582 | -6.649497 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1411 | 0.8819 | 3 | 0.935163 | 8.815596 | -6.623082 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1412 | 0.8825 | 3 | 0.917370 | 6.024143 | -6.616261 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1413 | 0.8831 | 3 | 0.903074 | 5.630821 | -6.620242 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1414 | 0.8838 | 3 | 0.920935 | 6.477164 | -6.641287 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1415 | 0.8844 | 3 | 0.930969 | 7.159821 | -6.656438 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1416 | 0.8850 | 3 | 0.944903 | 9.192090 | -6.678032 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1417 | 0.8856 | 3 | 0.917504 | 6.419061 | -6.696381 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1418 | 0.8862 | 2 | 0.925873 | 4.906813 | -6.009344 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1419 | 0.8869 | 2 | 0.942563 | 6.497721 | -6.020023 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1420 | 0.8875 | 2 | 0.930500 | 6.719030 | -6.034870 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1421 | 0.8881 | 2 | 0.922138 | 4.961293 | -6.048726 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1422 | 0.8888 | 2 | 0.916820 | 4.927310 | -6.054676 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1423 | 0.8894 | 2 | 0.931824 | 5.187046 | -6.082993 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1424 | 0.8900 | 2 | 0.909958 | 4.764700 | -6.080217 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1425 | 0.8906 | 2 | 0.952513 | 8.509196 | -6.099373 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1426 | 0.8912 | 2 | 0.925765 | 5.302563 | -6.126336 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1427 | 0.8919 | 2 | 0.924751 | 4.762978 | -6.153369 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1428 | 0.8925 | 2 | 0.908702 | 4.654668 | -6.184855 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1429 | 0.8931 | 2 | 0.927439 | 4.797967 | -6.191623 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1430 | 0.8938 | 2 | 0.922327 | 4.872953 | -6.181712 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1431 | 0.8944 | 2 | 0.949224 | 7.255501 | -6.165610 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1432 | 0.8950 | 2 | 0.923494 | 4.752976 | -6.148035 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1433 | 0.8956 | 2 | 0.910790 | 4.072053 | -6.100759 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1434 | 0.8962 | 2 | 0.912764 | 4.493207 | -6.069348 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1435 | 0.8969 | 2 | 0.923236 | 4.706394 | -6.009632 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1436 | 0.8975 | 3 | 0.925365 | 7.674640 | -6.669228 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1437 | 0.8981 | 3 | 0.930127 | 8.028126 | -6.614993 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1438 | 0.8988 | 3 | 0.909886 | 5.641717 | -6.544955 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1439 | 0.8994 | 3 | 0.923842 | 6.524829 | -6.498984 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1440 | 0.9000 | 3 | 0.935796 | 9.013565 | -6.452873 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1441 | 0.9006 | 3 | 0.928812 | 7.637232 | -6.417525 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1442 | 0.9012 | 3 | 0.916514 | 6.729560 | -6.386488 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1443 | 0.9019 | 3 | 0.920521 | 6.535683 | -6.358110 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1444 | 0.9025 | 3 | 0.934488 | 8.036480 | -6.338567 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1445 | 0.9031 | 3 | 0.923621 | 8.000703 | -6.320279 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1446 | 0.9038 | 3 | 0.945605 | 10.816668 | -6.301856 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1447 | 0.9044 | 3 | 0.957473 | 13.628701 | -6.282845 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1448 | 0.9050 | 3 | 0.951944 | 10.663103 | -6.270388 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1449 | 0.9056 | 3 | 0.939845 | 8.595916 | -6.252747 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1450 | 0.9062 | 3 | 0.948901 | 9.769054 | -6.241028 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1451 | 0.9069 | 3 | 0.909184 | 6.239377 | -6.224971 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1452 | 0.9075 | 3 | 0.914978 | 6.686036 | -6.210477 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1453 | 0.9081 | 3 | 0.922125 | 6.350539 | -6.205791 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1454 | 0.9088 | 3 | 0.923767 | 7.956812 | -6.197706 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1455 | 0.9094 | 3 | 0.919677 | 6.447463 | -6.197969 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1456 | 0.9100 | 3 | 0.901075 | 5.856636 | -6.200958 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1457 | 0.9106 | 3 | 0.933259 | 7.972088 | -6.211285 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1458 | 0.9113 | 3 | 0.923401 | 6.754908 | -6.227387 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1459 | 0.9119 | 3 | 0.930110 | 7.010411 | -6.244895 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1460 | 0.9125 | 3 | 0.904108 | 5.327531 | -6.262087 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1461 | 0.9131 | 3 | 0.916977 | 6.080096 | -6.280465 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1462 | 0.9138 | 3 | 0.901609 | 6.342472 | -6.302012 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1463 | 0.9144 | 3 | 0.919275 | 6.615018 | -6.315333 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1464 | 0.9150 | 3 | 0.924563 | 6.948357 | -6.331984 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1465 | 0.9156 | 3 | 0.901309 | 6.283830 | -6.339009 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1466 | 0.9163 | 3 | 0.918418 | 6.435431 | -6.348970 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1467 | 0.9169 | 3 | 0.914044 | 6.364084 | -6.357608 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1468 | 0.9175 | 3 | 0.923417 | 6.583113 | -6.358147 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1469 | 0.9181 | 3 | 0.910274 | 6.727884 | -6.362814 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1470 | 0.9188 | 3 | 0.924321 | 6.566537 | -6.362185 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1471 | 0.9194 | 3 | 0.919724 | 6.277768 | -6.369470 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1472 | 0.9200 | 3 | 0.925420 | 7.324469 | -6.372368 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1473 | 0.9206 | 3 | 0.911357 | 6.095469 | -6.375124 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1474 | 0.9213 | 3 | 0.930778 | 8.441899 | -6.377731 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1475 | 0.9219 | 3 | 0.923867 | 7.201074 | -6.379665 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1476 | 0.9225 | 3 | 0.924486 | 6.876316 | -6.378112 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1477 | 0.9231 | 3 | 0.925674 | 7.472106 | -6.367844 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1478 | 0.9238 | 3 | 0.927625 | 7.278294 | -6.355895 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1479 | 0.9244 | 3 | 0.921834 | 7.126721 | -6.335776 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1480 | 0.9250 | 3 | 0.926204 | 6.768756 | -6.320051 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1481 | 0.9256 | 3 | 0.924415 | 6.981813 | -6.294503 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1482 | 0.9263 | 3 | 0.923252 | 8.269953 | -6.269027 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1483 | 0.9269 | 3 | 0.915274 | 6.118142 | -6.247761 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1484 | 0.9275 | 3 | 0.895026 | 5.716490 | -6.227756 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1485 | 0.9281 | 3 | 0.914148 | 5.881200 | -6.215509 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1486 | 0.9287 | 3 | 0.932979 | 7.572946 | -6.201373 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1487 | 0.9294 | 3 | 0.914681 | 6.239722 | -6.195014 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1488 | 0.9300 | 3 | 0.925638 | 6.726851 | -6.191173 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1489 | 0.9306 | 3 | 0.919700 | 6.448708 | -6.192837 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1490 | 0.9313 | 3 | 0.923637 | 7.135001 | -6.194106 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1491 | 0.9319 | 3 | 0.926781 | 6.974635 | -6.194425 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1492 | 0.9325 | 3 | 0.934381 | 8.284605 | -6.198788 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1493 | 0.9331 | 3 | 0.939366 | 8.767719 | -6.201704 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1494 | 0.9337 | 3 | 0.922030 | 6.414749 | -6.207466 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1495 | 0.9344 | 3 | 0.907948 | 5.853225 | -6.208558 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1496 | 0.9350 | 3 | 0.906547 | 5.939189 | -6.213032 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1497 | 0.9356 | 3 | 0.908636 | 5.539818 | -6.217216 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1498 | 0.9363 | 3 | 0.898894 | 6.153936 | -6.224082 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1499 | 0.9369 | 3 | 0.907490 | 5.856698 | -6.232341 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1500 | 0.9375 | 3 | 0.913808 | 6.567728 | -6.240649 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1501 | 0.9381 | 3 | 0.922514 | 6.624142 | -6.259544 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1502 | 0.9387 | 3 | 0.907688 | 5.808735 | -6.278295 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1503 | 0.9394 | 3 | 0.919367 | 6.465359 | -6.305641 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1504 | 0.9400 | 3 | 0.920099 | 6.526947 | -6.331373 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1505 | 0.9406 | 3 | 0.927817 | 7.421338 | -6.360774 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1506 | 0.9413 | 3 | 0.928545 | 8.437538 | -6.393548 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1507 | 0.9419 | 3 | 0.902386 | 6.204882 | -6.420430 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1508 | 0.9425 | 3 | 0.923993 | 6.786077 | -6.444533 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1509 | 0.9431 | 3 | 0.919801 | 6.553246 | -6.457352 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1510 | 0.9437 | 3 | 0.921803 | 6.615594 | -6.472199 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1511 | 0.9444 | 3 | 0.925004 | 7.170310 | -6.478191 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1512 | 0.9450 | 3 | 0.905564 | 6.420444 | -6.480669 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1513 | 0.9456 | 3 | 0.897894 | 5.869495 | -6.471425 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1514 | 0.9463 | 3 | 0.933066 | 7.607843 | -6.465231 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1515 | 0.9469 | 3 | 0.923439 | 6.751990 | -6.463353 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1516 | 0.9475 | 3 | 0.925066 | 7.330558 | -6.455438 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1517 | 0.9481 | 3 | 0.918668 | 6.579083 | -6.455617 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1518 | 0.9487 | 3 | 0.909436 | 6.596379 | -6.445974 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1519 | 0.9494 | 3 | 0.919355 | 6.596168 | -6.448004 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1520 | 0.9500 | 3 | 0.924505 | 6.784022 | -6.447369 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1521 | 0.9506 | 3 | 0.915205 | 7.034473 | -6.439085 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1522 | 0.9513 | 3 | 0.921929 | 7.147249 | -6.433309 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1523 | 0.9519 | 3 | 0.917739 | 6.480462 | -6.421102 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1524 | 0.9525 | 3 | 0.920645 | 7.268439 | -6.409265 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1525 | 0.9531 | 3 | 0.924978 | 6.762246 | -6.392637 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1526 | 0.9537 | 3 | 0.904161 | 5.662068 | -6.375022 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1527 | 0.9544 | 3 | 0.894575 | 5.943442 | -6.352899 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1528 | 0.9550 | 3 | 0.916485 | 6.450057 | -6.340903 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1529 | 0.9556 | 3 | 0.911471 | 5.815902 | -6.327473 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1530 | 0.9563 | 3 | 0.946163 | 10.300556 | -6.318675 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1531 | 0.9569 | 3 | 0.920140 | 6.708279 | -6.319531 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1532 | 0.9575 | 3 | 0.927131 | 7.644479 | -6.322022 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1533 | 0.9581 | 3 | 0.925872 | 7.906648 | -6.340347 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1534 | 0.9587 | 3 | 0.953359 | 12.854882 | -6.355311 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1535 | 0.9594 | 3 | 0.957625 | 12.035864 | -6.374960 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1536 | 0.9600 | 3 | 0.922788 | 6.549969 | -6.399544 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1537 | 0.9606 | 3 | 0.923255 | 7.345718 | -6.425160 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1538 | 0.9613 | 3 | 0.894928 | 5.283814 | -6.454270 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1539 | 0.9619 | 3 | 0.920838 | 6.585240 | -6.477813 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1540 | 0.9625 | 3 | 0.919923 | 6.684282 | -6.503289 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1541 | 0.9631 | 3 | 0.901987 | 6.327917 | -6.528889 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1542 | 0.9637 | 3 | 0.922220 | 6.678324 | -6.563999 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1543 | 0.9644 | 3 | 0.927326 | 7.721633 | -6.587193 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1544 | 0.9650 | 3 | 0.921554 | 6.909383 | -6.621031 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1545 | 0.9656 | 3 | 0.903761 | 5.837015 | -6.657607 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1546 | 0.9663 | 3 | 0.922861 | 6.750733 | -6.703406 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1547 | 0.9669 | 2 | 0.919500 | 4.979636 | -6.058854 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1548 | 0.9675 | 2 | 0.882183 | 4.165048 | -6.115563 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1549 | 0.9681 | 2 | 0.885237 | 4.722028 | -6.214839 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1550 | 0.9688 | 2 | 0.931076 | 5.733022 | -6.317135 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1551 | 0.9694 | 2 | 0.911807 | 4.571640 | -6.398004 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1552 | 0.9700 | 2 | 0.936105 | 6.147134 | -6.467622 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1553 | 0.9706 | 2 | 0.908700 | 4.738175 | -6.490310 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1554 | 0.9713 | 2 | 0.920402 | 5.178498 | -6.517662 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1555 | 0.9719 | 2 | 0.915520 | 4.679663 | -6.599814 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1556 | 0.9725 | 2 | 0.922605 | 4.647103 | -6.640635 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1557 | 0.9731 | 2 | 0.896298 | 4.618234 | -6.569212 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1558 | 0.9738 | 2 | 0.922466 | 4.843003 | -6.507500 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1559 | 0.9744 | 2 | 0.916682 | 4.588394 | -6.398797 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1560 | 0.9750 | 2 | 0.926053 | 5.174229 | -6.324868 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1561 | 0.9756 | 2 | 0.925270 | 5.638033 | -6.266221 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1562 | 0.9763 | 2 | 0.927981 | 5.450152 | -6.214271 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1563 | 0.9769 | 2 | 0.916252 | 4.483924 | -6.213178 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1564 | 0.9775 | 2 | 0.935426 | 6.449234 | -6.200658 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1565 | 0.9781 | 2 | 0.915920 | 4.498245 | -6.200783 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1566 | 0.9788 | 2 | 0.904817 | 4.479567 | -6.183228 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1567 | 0.9794 | 2 | 0.927257 | 5.067844 | -6.170427 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1568 | 0.9800 | 2 | 0.918439 | 4.788952 | -6.161537 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1569 | 0.9806 | 2 | 0.925997 | 5.402627 | -6.142222 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1570 | 0.9813 | 2 | 0.926460 | 5.615353 | -6.116125 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1571 | 0.9819 | 2 | 0.922461 | 4.803652 | -6.079451 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1572 | 0.9825 | 2 | 0.918388 | 5.038670 | -6.063322 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1573 | 0.9831 | 2 | 0.875533 | 3.609758 | -6.039418 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1574 | 0.9838 | 2 | 0.927343 | 6.587288 | -6.032471 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1575 | 0.9844 | 2 | 0.904182 | 4.309741 | -6.028304 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1576 | 0.9850 | 2 | 0.905156 | 4.712267 | -6.046032 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1577 | 0.9856 | 2 | 0.930125 | 5.372373 | -6.097563 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1578 | 0.9863 | 2 | 0.930499 | 5.708138 | -6.167997 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1579 | 0.9869 | 2 | 0.891846 | 4.428921 | -6.282399 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1580 | 0.9875 | 2 | 0.933033 | 5.432235 | -6.425647 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1581 | 0.9881 | 1 | 0.931325 | 3.440839 | -6.003674 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1582 | 0.9888 | 1 | 0.926261 | 3.442987 | -6.310460 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1583 | 0.9894 | 1 | 0.914095 | 3.372041 | -6.055798 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1584 | 0.9900 | 2 | 0.931821 | 5.991383 | -6.550136 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1585 | 0.9906 | 2 | 0.920986 | 4.753026 | -6.433191 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1586 | 0.9913 | 2 | 0.922951 | 5.393609 | -6.328313 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1587 | 0.9919 | 2 | 0.926422 | 5.207035 | -6.277935 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1588 | 0.9925 | 2 | 0.918221 | 4.913140 | -6.221342 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1589 | 0.9931 | 2 | 0.918656 | 5.623120 | -6.184381 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1590 | 0.9938 | 2 | 0.935746 | 6.446742 | -6.132430 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1591 | 0.9944 | 2 | 0.944267 | 6.625097 | -6.092405 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1592 | 0.9950 | 2 | 0.928395 | 5.372510 | -6.057012 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1593 | 0.9956 | 2 | 0.924128 | 5.034784 | -6.021695 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1594 | 0.9962 | 3 | 0.911149 | 6.033995 | -6.711058 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1595 | 0.9969 | 3 | 0.911349 | 6.372252 | -6.670375 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1596 | 0.9975 | 3 | 0.914314 | 6.562514 | -6.652219 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1597 | 0.9981 | 3 | 0.899058 | 5.619607 | -6.635549 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1598 | 0.9988 | 3 | 0.883084 | 6.469685 | -6.635330 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1599 | 0.9994 | 3 | 0.924483 | 7.161764 | -6.640260 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 1600 | 1.0000 | 3 | 0.928814 | 7.948421 | -6.657385 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"\\u001b[34m...Finished\\u001b[0m\\n\",\n \"\\u001b[36mFINISHED - Elapsed time = 14865.6099746 seconds\\u001b[0m\\n\",\n \"\\u001b[36mFINISHED - CPU process time = 110402.5020766 seconds\\u001b[0m\\n\"\n ]\n },\n {\n \"data\": {\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 10,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"sharpy.sharpy_main.main(['', pazy_model_open_loop.route + pazy_model_open_loop.case_name + '.sharpy'])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Plot wing tip deflection in gust response\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"To get a feeling of the gust-induced deformation at the wingtip, we now display the vertical tip deflection.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {\n \"scrolled\": true\n },\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 \"def get_resulting_vertical_tip_displacement(output_folder, model): \\n\",\n \" file_results = os.path.join(output_folder, \\n\",\n \" model.case_name, \\n\",\n \" 'WriteVariablesTime',\\n\",\n \" 'struct_pos_node{}.dat'.format(model.num_node_surf))\\n\",\n \" vertical_tip_displacement = np.loadtxt(file_results)[:,-1]\\n\",\n \" \\n\",\n \" \\n\",\n \" return vertical_tip_displacement\\n\",\n \"\\n\",\n \"\\n\",\n \"tip_displacement_open_loop = get_resulting_vertical_tip_displacement(output_folder, \\n\",\n \" pazy_model_open_loop)\\n\",\n \"\\n\",\n \"\\n\",\n \"time_array = np.arange(0, len(tip_displacement_open_loop) * pazy_model_open_loop.dt, pazy_model_open_loop.dt)\\n\",\n \"normalised_tip_displacement = tip_displacement_open_loop/ (0.5*pazy_model_open_loop.b_ref) #normalise by half wing span\\n\",\n \"normalised_tip_displacement *=100# cconvert to percentnvert to percent\\n\",\n \"plt.plot(time_array, normalised_tip_displacement)\\n\",\n \"plt.xlabel('time, sec')\\n\",\n \"plt.ylabel('$z_{tip}/(b_{ref}/2)$, %')\\n\",\n \"plt.xlim([0., simulation_time])\\n\",\n \"plt.grid()\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Generate linear ROM\\n\",\n \"\\n\",\n \"We continue with the linearization of the nonlinear aeroelastic model of the Pazy wing at the previously defined operational point and a subsequent reduction of the resulting linear state-space system. The structural and aerodynamic models are linearized and reduced separately and finally couple both resulting linear systems. Please see [2] for more details. \\n\",\n \"\\n\",\n \"The generation of the linear model for the coarse discretisation used, just takes a few seconds, as well as the execution of the linear response computation using Matlab. No need to skip anything here to save time. \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Define Simulation Settings\\n\",\n \"We can re-use the simulation settings from the open-loop case with a few exceptions. Besides the name, of course, we need to extend the simulation `flow` list by the solvers needed for the linearization and export of the resulting linear state-space system. Further, we need to change the simulation time as we need to run only on the simulation timestep of the `DynamicCoupled` solver before the linearization. Also, no gust encounter is needed as we linearise the model around its equilibrium during steady-flight conditions.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"case_name = 'pazy_ROM'\\n\",\n \"\\n\",\n \"flow = ['BeamLoader',\\n\",\n \" 'AerogridLoader',\\n\",\n \" 'StaticCoupled',\\n\",\n \" 'DynamicCoupled',\\n\",\n \" 'Modal',\\n\",\n \" 'LinearAssembler',\\n\",\n \" 'SaveData',\\n\",\n \" ]\\n\",\n \"\\n\",\n \"simulation_time_ROM = pazy_model_open_loop.dt # only one timestep has to be performed\\n\",\n \"gust = False\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We further need to define the method used to reduce the linearized aerodynamic model. Here, we are going to apply a Krylov-based model order reduction scheme for the aerodynamic system, see [4] for more information. Please note that this is only one of the reduction methods implemented in SHARPy. We also offer various reduction schemes based on balancing methods.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 17,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"use_rom = True\\n\",\n \"rom_settings = {\\n\",\n \" 'use': use_rom,\\n\",\n \" 'rom_method': 'Krylov',\\n\",\n \" 'rom_method_settings': {'Krylov': {\\n\",\n \" 'algorithm': 'mimo_rational_arnoldi',\\n\",\n \" 'r': 4, \\n\",\n \" 'frequency': np.array([0]),\\n\",\n \" 'single_side': 'observability',\\n\",\n \" },\\n\",\n \" }\\n\",\n \" }\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The linearised structural model is reduced by using modal projection and truncating non-dominant modes. Here, we keep the first 20 modes.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 18,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"num_modes = 20\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Further, we have deactivated the unsteady force contribution before generating the linear model and indicate that for the resulting linear system, we would like to retain the gust input for our preliminary control design study.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 19,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"unsteady_force_contribution = False\\n\",\n \"remove_gust_input_in_statespace = False\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Generate Input Files\\n\",\n \"As before, we generate all necessary input files for the simulation.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 20,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"pazy_model_ROM = wings.PazyControlSurface(M=number_chordwise_panels,\\n\",\n \" N=number_spanwise_nodes,\\n\",\n \" Mstar_fact=wake_length_factor,\\n\",\n \" u_inf=u_inf,\\n\",\n \" alpha=alpha_deg,\\n\",\n \" rho=rho,\\n\",\n \" n_surfaces=2,\\n\",\n \" route=cases_folder + '/' + case_name,\\n\",\n \" case_name=case_name,\\n\",\n \" physical_time=simulation_time_ROM,)\\n\",\n \"\\n\",\n \"generate_aero_and_fem_input_files(pazy_model_ROM)\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 21,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"pazy_model_ROM.set_default_config_dict()\\n\",\n \"pazy_model_ROM.config = get_settings_udp(pazy_model_ROM,\\n\",\n \" flow,\\n\",\n \" num_cores=num_cores,\\n\",\n \" wake_length_factor=wake_length_factor,\\n\",\n \" output_folder = output_folder,\\n\",\n \" gust=gust,\\n\",\n \" gust_settings=gust_settings,\\n\",\n \" num_modes = num_modes,\\n\",\n \" rom_settings = rom_settings,\\n\",\n \" remove_gust_input_in_statespace=remove_gust_input_in_statespace,\\n\",\n \" unsteady_force_distribution=unsteady_force_contribution)\\n\",\n \"pazy_model_ROM.config.write()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Run SHARPy Simulation\"]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"sharpy.sharpy_main.main(['', pazy_model_ROM.route + pazy_model_ROM.case_name + '.sharpy'])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Prepare Linear System for specific Controller\\n\",\n \"An overview of the generated linear ROM can be found near the end of the log file, including the number of states, inputs, and outputs as well as the indices mapped to each parameter. The saved linear ROM contains several unused input and output variables. The final simulation is expected to take 8 hours. Again, the results are uploaded *here* and it is still recommended to check if everything is running properly instead of skipping the entire simulation.\\n\",\n \"\\n\",\n \"We start with reading the matrices from the h5 file and get rid of all unused input and output variables that are not needed for the control design. More precisely, we keep the gust and control surface inputs as well as the vertical tip displacements as an output. \\n\",\n \"\\n\",\n \"The system input includes the control surface deflection and its rate but does not know that they are related. For small timesteps, as for this case, we can assume a linear relationship through numerical gradients $\\\\dot{\\\\delta} = \\\\frac{\\\\delta - \\\\delta^-}{dt}$ with *-* indicating the previous timestep.\\n\",\n \"\\n\",\n \"Subsequently, we simulate the open-loop and closed-loop responses for different proportional gains of the P-controller.\\n\",\n \"\\n\",\n \"But first, we save some parameters needed for this to a json file which is later loaded in the control script to avoid making changes in different files. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 25,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"folder_linear_results =os.path.join(output_folder, pazy_model_ROM.case_name,'linear_results')\\n\",\n \"if not os.path.exists(folder_linear_results):\\n\",\n \" os.makedirs(folder_linear_results)\\n\",\n \" \\n\",\n \"import scipy.io\\n\",\n \"\\n\",\n \"parameter_matlab = {'num_aero_states': 80, # see log file\\n\",\n \" 'num_modes': 20, # see log file\\n\",\n \" 'u_inf': float(pazy_model_ROM.u_inf),\\n\",\n \" 'simulation_time': simulation_time,\\n\",\n \" 'gust_length': float(gust_settings['gust_length']),\\n\",\n \" 'gust_intensity': float(gust_settings['gust_intensity']),\\n\",\n \" 'num_control_surfaces': num_control_surfaces,\\n\",\n \" 'n_nodes': number_spanwise_nodes,\\n\",\n \" 'control_input_start': 193 + 1, # see log file and + 1 for matlab indices\\n\",\n \" 'gust_input_start': 192 + 1 , # see log file and + 1 for matlab indices\\n\",\n \" }\\n\",\n \"\\n\",\n \"scipy.io.savemat(os.path.join(folder_linear_results, 'simulation_parameters.mat'), parameter_matlab)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Next, the matlab script *control_design_script.m* has to be executed which runs the linear open-loop gust response of this problem as well as two linear closed-loop gust responses using a P-controller with two different gain values. This P-controller is using the deviation of the vertical tip displacement to its reference condition as an error function. Finally, the script is saving the results as txt files in your output folder. \\n\",\n \"\\n\",\n \"Here, we use the MATLAB Engine API for Python to run the script:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 26,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"eng = matlab.engine.start_matlab()\\n\",\n \"eng.control_design_script(route_notebook_dir)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Clean Up Simulink Files\\n\",\n \"import shutil\\n\",\n \"folder_path = os.path.join(route_notebook_dir, 'slprj')\\n\",\n \"if os.path.exists(folder_path):\\n\",\n \" shutil.rmtree(folder_path)\\n\",\n \"\\n\",\n \"file_path = os.path.join(route_notebook_dir, 'PID_linear_model.slxc')\\n\",\n \"if os.path.exists(file_path):\\n\",\n \" os.remove(file_path)\\n\"\n ]\n },\n {\n \"attachments\": {},\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Postprocessing\\n\",\n \"Now, let us have a look at the linear results generated:\"\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 \"# Load linear results\\n\",\n \"tip_deflection_linear = np.loadtxt(folder_linear_results + '/tip_deflection.txt', delimiter = ',')\\n\",\n \"time_array_linear = np.loadtxt(folder_linear_results + '/time_array_linear.txt', delimiter = ',')\\n\",\n \"normalised_tip_deflection_linear = tip_deflection_linear / (0.5 *pazy_model_ROM.b_ref) * 100\\n\",\n \"control_surface_deflection_deg = np.loadtxt(folder_linear_results + '/deflection.txt', delimiter = ',')\\n\",\n \"control_surface_deflection_rate_deg = np.loadtxt(folder_linear_results + '/deflection_rate.txt', delimiter = ',')\\n\",\n \"\\n\",\n \"# Plot Data\\n\",\n \"fig, axs = plt.subplots(3, 1)\\n\",\n \"list_linestyles = ['-', '-', '--', ':']\\n\",\n \"list_labels = ['linear P=5', 'linear P=10', 'linear open-loop', 'nonlinear open-loop']\\n\",\n \"for i in range(3):\\n\",\n \" axs[0].plot(time_array_linear, normalised_tip_deflection_linear[:,i], list_linestyles[i], label=list_labels[i])\\n\",\n \"\\n\",\n \"axs[0].plot(time_array, normalised_tip_displacement, list_linestyles[-1], label=list_labels[-1])\\n\",\n \"axs[0].legend(loc ='upper right')\\n\",\n \"axs[0].set(ylabel='$z_{tip}/(b_{ref}/2)$, %')\\n\",\n \"\\n\",\n \"for i in range(3):\\n\",\n \" axs[1].plot(time_array_linear, control_surface_deflection_deg[:,i], list_linestyles[i])\\n\",\n \" \\n\",\n \"axs[1].set(ylabel='$\\\\delta$, deg')\\n\",\n \"for i in range(3):\\n\",\n \" axs[2].plot(time_array_linear, control_surface_deflection_rate_deg[:,i], list_linestyles[i])\\n\",\n \" \\n\",\n \"axs[2].set(ylabel='$\\\\dot{\\\\delta}$, deg/sec')\\n\",\n \"for ax in axs.flat:\\n\",\n \" ax.set(xlabel='time, sec')\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can see here the slightly higher peak tip deflection in the nonlinear response. Further, we see a significant reduction in tip deflection by the P-controller. Since we only have slightly higher aileron deflection and rates for the higher gain of P=10, we chose this gain value for the final control design applied to the nonlinear aeroelastic gust response simulation.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Closed-Loop Nonlinear Gust Response\\n\",\n \"Now, we need a similar simulation setup as the open-loop nonlinear response and activate the gust again.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 28,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"case_name = 'pazy_udp_closed_loop_gust_response'\\n\",\n \"gust = True\\n\",\n \"flow = ['BeamLoader',\\n\",\n \" 'AerogridLoader',\\n\",\n \" 'StaticCoupled',\\n\",\n \" 'DynamicCoupled',\\n\",\n \" ]\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"However, we need to inform SHARPy that our aileron will receive deflection values from the network which is done by setting the control surface type of both ailerons to `2`. The default value `0` would indicate a static deflection, and `1` that the control surface receives deflection inputs from the `dynamiccontrolsurface` generator. For the sake of completeness, we set the initial deflection of the ailerons to zero. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 29,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"initial_cs_deflection = [0, 0]\\n\",\n \"cs_type = 2 \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 30,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"pazy_model_closed = wings.PazyControlSurface(M=number_chordwise_panels,\\n\",\n \" N=number_spanwise_nodes,\\n\",\n \" Mstar_fact=wake_length_factor,\\n\",\n \" u_inf=u_inf,\\n\",\n \" alpha=alpha_deg,\\n\",\n \" cs_deflection=initial_cs_deflection,\\n\",\n \" rho=rho,\\n\",\n \" n_surfaces=2,\\n\",\n \" route=cases_folder + '/' + case_name,\\n\",\n \" case_name=case_name,\\n\",\n \" physical_time=simulation_time,\\n\",\n \" cs_type=cs_type)\\n\",\n \"generate_aero_and_fem_input_files(pazy_model_closed)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Next, we need to define our network settings. Therefore, we need to define the IP addresses for the server (SHARPy) and client (on whatever machine you run your computer), and the ports used. Another important input is the `variables_filename` in which we define the in and output parameters. Have a look in the file and make sure to change the position of your output node in case you make the beam discretisation finer. As we only need to measure the vertical tip displacement for our controller to work, we only have one sensor. We just save this parameter here as it is important later for the client to know, how much data it should receive from SHARPy.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 31,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Network settings for nonlinear in closed-loop simulations \\n\",\n \"server_ip_addr = '127.0.0.1' # SHARPy\\n\",\n \"client_ip_addr = '127.0.0.1' # controller\\n\",\n \"port_in_network = 64017\\n\",\n \"port_out_network_server = 59017\\n\",\n \"port_out_network_client = 59007 \\n\",\n \"num_sensors = 1 \\n\",\n \"network_settings = {'variables_filename': route_notebook_dir + '/pazy_network_info.yml', \\n\",\n \" 'send_output_to_all_clients': False,\\n\",\n \" 'byte_ordering': 'little',\\n\",\n \" 'log_name': output_folder +'/'+ case_name + '/sharpy_network.log',\\n\",\n \" 'file_log_level': 'debug',\\n\",\n \" 'console_log_level': 'error',\\n\",\n \" 'input_network_settings': {'address': server_ip_addr,\\n\",\n \" 'port': port_in_network,\\n\",\n \" },\\n\",\n \" 'output_network_settings': {'send_on_demand': False,\\n\",\n \" 'port': port_out_network_server,\\n\",\n \" 'address':server_ip_addr, \\n\",\n \" 'destination_address': [client_ip_addr],\\n\",\n \" 'destination_ports': [port_out_network_client],\\n\",\n \" }\\n\",\n \" }\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 32,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"pazy_model_closed.set_default_config_dict()\\n\",\n \"pazy_model_closed.config = get_settings_udp(pazy_model_closed,\\n\",\n \" flow,\\n\",\n \" network_settings=network_settings,\\n\",\n \" num_cores=num_cores,\\n\",\n \" wake_length_factor=wake_length_factor,\\n\",\n \" output_folder = output_folder,\\n\",\n \" gust=gust,\\n\",\n \" gust_settings=gust_settings,\\n\",\n \" write_screen = False)\\n\",\n \"pazy_model_closed.config.write()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"As before, we save some essential parameters to a json file that is loaded from the client. This is done to avoid the need of changing parameters in different files.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 33,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"\\n\",\n \"dict_parameters = {\\\"server_ip_addr\\\": server_ip_addr,\\n\",\n \" \\\"client_ip_addr\\\": client_ip_addr,\\n\",\n \" \\\"port_in_network\\\": port_in_network,\\n\",\n \" \\\"port_out_network_server\\\": port_out_network_server,\\n\",\n \" \\\"port_out_network_client\\\": port_out_network_client,\\n\",\n \" \\\"output_folder\\\": os.path.abspath(output_folder),\\n\",\n \" \\\"dt\\\": pazy_model_closed.dt,\\n\",\n \" \\\"simulation_time\\\": simulation_time,\\n\",\n \" \\\"num_sensors\\\": num_sensors,\\n\",\n \" \\\"initial_cs_deflection\\\": initial_cs_deflection[0],\\n\",\n \" \\\"reference_deflection\\\": tip_displacement_open_loop[0],\\n\",\n \" }\\n\",\n \"with open('./parameter_UDP_control_{}.json'.format(pazy_model_closed.case_name), 'w') as fp:\\n\",\n \" json.dump(dict_parameters, fp)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let us start the nonlinear gust-response simulation. Within the `DynamicCoupled` solver, the network expects an input before the actual simulation start. Hence, let the script run until you enter this solver (< 1 min) and start the controller by running *pazy_PID_controller_UDP.py* located in the notebook directory. You can double-check the *sharpy_network.log* in the output folder of this case. If the network is waiting for inputs, you are good to run the client script from your terminal using Python. \\n\",\n \"\\n\",\n \"Note that the log file is not written here on the screen as it causes errors as the amount of output characters exceeds the available buffer size of the jupyter notebook. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 34,\n \"metadata\": {\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"fatal: not a git repository (or any of the parent directories): .git\\n\"\n ]\n }\n ],\n \"source\": [\n \"sharpy.sharpy_main.main(['', pazy_model_closed.route + pazy_model_closed.case_name + '.sharpy']);\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Final Postprocessing\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 35,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"control_surface_input = np.loadtxt(os.path.join(output_folder, pazy_model_closed.case_name, \\\"pazy_udp_closed_loop_gust_response_control_input\\\"))\\n\",\n \"delta_dot = np.diff(np.rad2deg(control_surface_input))/pazy_model_closed.dt\\n\",\n \"tip_displacement_nonlinear_P10 = np.loadtxt(os.path.join(output_folder, pazy_model_closed.case_name, \\\"pazy_udp_closed_loop_gust_response_sensor_measurement\\\"))\\n\",\n \"time_array_nonlinear_closed_loop = np.arange(0, len(tip_displacement_nonlinear_P10) * pazy_model_closed.dt, pazy_model_closed.dt)\\n\",\n \"tip_displacement_nonlinear_P10 /= pazy_model_closed.b_ref/2\\n\",\n \"tip_displacement_nonlinear_P10 *= 100\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 36,\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 Data\\n\",\n \"fig, axs = plt.subplots(3, 1)\\n\",\n \"list_linestyles = ['-', '--', ':']\\n\",\n \"list_labels = ['linear P=10', 'nonlinear P=10', 'nonlinear open-loop']\\n\",\n \"axs[0].plot(time_array_linear, normalised_tip_deflection_linear[:,1], list_linestyles[0], label=list_labels[0])\\n\",\n \"axs[0].plot(time_array_nonlinear_closed_loop, \\n\",\n \" tip_displacement_nonlinear_P10, \\n\",\n \" list_linestyles[1], \\n\",\n \" label=list_labels[1])\\n\",\n \"axs[0].plot(time_array, normalised_tip_displacement, list_linestyles[-1], label=list_labels[-1])\\n\",\n \"\\n\",\n \"axs[0].legend()\\n\",\n \"axs[0].set(ylabel='$z_{tip}/(b_{ref}/2)$, %')\\n\",\n \"\\n\",\n \"\\n\",\n \"axs[1].plot(time_array_linear, control_surface_deflection_deg[:,1], list_linestyles[0])\\n\",\n \"axs[1].plot(time_array_nonlinear_closed_loop, np.rad2deg(control_surface_input), list_linestyles[1])\\n\",\n \" \\n\",\n \"axs[1].set(ylabel='$\\\\delta$, deg')\\n\",\n \"\\n\",\n \"axs[2].plot(time_array_linear, control_surface_deflection_rate_deg[:,0], list_linestyles[0])\\n\",\n \"axs[2].plot(time_array_nonlinear_closed_loop[1:], \\n\",\n \" delta_dot, \\n\",\n \" list_linestyles[1])\\n\",\n \" \\n\",\n \"axs[2].set(ylabel='$\\\\dot{\\\\delta}$, deg/sec')\\n\",\n \"for ax in axs.flat:\\n\",\n \" ax.set(xlabel='time, sec')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\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\": \"3.10.12\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "docs/source/content/example_notebooks/cantilever/model_static_cantilever.py", "content": "import h5py as h5\nimport numpy as np\nimport os\n\ndef clean_test_files(route, case_name):\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n\ndef generate_fem_file(route, case_name, num_elem, deadforce=600e3, followerforce=0):\n length = 5\n num_node_elem=3\n num_node = (num_node_elem - 1)*num_elem + 1\n angle = 0. * np.pi / 180. # Angle of the beam reference line within the x-y plane of the B frame.\n x = (np.linspace(0, length, num_node))*np.cos(angle)\n y = (np.linspace(0, length, num_node))*np.sin(angle)\n z = np.zeros((num_node,))\n\n structural_twist = np.zeros((num_elem, num_node_elem))\n\n frame_of_reference_delta = np.zeros((num_elem, num_node_elem, 3))\n for ielem in range(num_elem):\n for inode in range(num_node_elem):\n frame_of_reference_delta[ielem, inode, :] = [-np.sin(angle), np.cos(angle), 0]\n\n scale = 1\n\n x *= scale\n y *= scale\n z *= scale\n\n conn = np.zeros((num_elem, num_node_elem), dtype=int)\n for ielem in range(num_elem):\n conn[ielem, :] = (np.ones((3,)) * ielem * (num_node_elem - 1)\n + [0, 2, 1])\n\n # stiffness array\n num_stiffness = 1\n ea = 4.8e8\n ga = 3.231e8\n gj = 1.0e6\n ei = 9.346e6\n base_stiffness = np.diag([ea, ga, ga, gj, ei, ei])\n stiffness = np.zeros((num_stiffness, 6, 6))\n for i in range(num_stiffness):\n stiffness[i, :, :] = base_stiffness\n\n # element stiffness\n elem_stiffness = np.zeros((num_elem,), dtype=int)\n\n # mass array\n num_mass = 1\n m_bar = 0. # Mass is made zero for the static analysis.\n j = 10\n base_mass = np.diag([m_bar, m_bar, m_bar, j, j, j])\n mass = np.zeros((num_mass, 6, 6))\n for i in range(num_mass):\n mass[i, :, :] = base_mass\n # element masses\n elem_mass = np.zeros((num_elem,), dtype=int)\n\n # bocos\n boundary_conditions = np.zeros((num_node, 1), dtype=int)\n boundary_conditions[0] = 1 # Clamped at s=0\n boundary_conditions[-1] = -1 # Free end at s=L\n\n # beam number\n beam_number = np.zeros((num_elem, 1), dtype=int)\n\n # Applied follower forces.\n app_forces = np.zeros((num_node, 6))\n app_forces[-1, 2] = followerforce\n\n # Lmmped masses input -- Dead force is applied by a mass at the tip.\n n_lumped_mass = 1\n lumped_mass_nodes = np.array([num_node - 1], dtype=int)\n lumped_mass = np.zeros((n_lumped_mass, ))\n lumped_mass[0] = deadforce/9.81\n lumped_mass_inertia = np.zeros((n_lumped_mass, 3, 3))\n lumped_mass_position = np.zeros((n_lumped_mass, 3))\n\n #Store in h5 format.\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data = np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data = conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data = num_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data = num_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data = num_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data = stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data = elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data = mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data = elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n lumped_mass_nodes_handle = h5file.create_dataset(\n 'lumped_mass_nodes', data=lumped_mass_nodes)\n lumped_mass_handle = h5file.create_dataset(\n 'lumped_mass', data=lumped_mass)\n lumped_mass_inertia_handle = h5file.create_dataset(\n 'lumped_mass_inertia', data=lumped_mass_inertia)\n lumped_mass_position_handle = h5file.create_dataset(\n 'lumped_mass_position', data=lumped_mass_position)\n return num_node, coordinates\n\n\n# Solver options\ndef generate_solver_file (route, case_name):\n file_name = route + '/' + case_name + '.sharpy'\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n config['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': ['BeamLoader', 'NonLinearStatic'],\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n config['BeamLoader'] = {'unsteady': 'off'}\n config['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 99, # Default 99\n 'num_load_steps': 10, # Default 10\n 'delta_curved': 1e-5,\n 'min_delta': 1e-8, # Default 1e-8\n 'gravity_on': 'on',\n 'gravity': 9.81}\n config.write()\n\n# eof\n" }, { "path": "docs/source/content/example_notebooks/cantilever/static_cantilever.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# A prismatic cantilever beam under a tip load\\n\",\n \"\\n\",\n \"This is an example of the geometrically-exact beam structural solver in SHARPy.\\n\",\n \"\\n\",\n \"Reference:\\n\",\n \"Simpson R.J.S., Palacios R., “Numerical Aspects of Nonlinear Flexible Aircraft Flight Dynamics Modeling.” 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 8-11 April 2013, Boston, Massachusetts, USA [http://hdl.handle.net/10044/1/11077, http://dx.doi.org/10.2514/6.2013-1634]\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Required Packages\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import numpy as np\\n\",\n \"import os\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import sharpy.sharpy_main # used to run SHARPy from Jupyter\\n\",\n \"import model_static_cantilever as model # model definition\\n\",\n \"from IPython.display import Image\\n\",\n \"\\n\",\n \"plt.rcParams.update({'font.size': 20}) # Large fonts in all plots\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Problem 1: Tip vertical dead load\\n\",\n \"Consider first a massless beam with a heavy tip mass, such that the deformations are due to the resulting dead load P. The static equilibrium will be obtained for multiple values of P=0, 100, ..., 1000 kN\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 2,\n \"metadata\": {\n \"image/png\": {\n \"width\": 500\n }\n },\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"Image('images/cantilever.png', width=500)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Define temporary files to generate sharpy models.\\n\",\n \"case_name= 'temp'\\n\",\n \"route = './'\\n\",\n \"\\n\",\n \"Nforces=10 # Number of force steps\\n\",\n \"DeltaForce=100e3 # Increment of forces\\n\",\n \"Nelem=20 # Number of beam elements\\n\",\n \"\\n\",\n \"N=2*Nelem+1\\n\",\n \"x1=np.zeros((Nforces,N))\\n\",\n \"z1=np.zeros((Nforces,N))\\n\",\n \"\\n\",\n \"#Loop through all external forces\\n\",\n \"for jForce in range(Nforces):\\n\",\n \" model.clean_test_files(route, case_name)\\n\",\n \" model.generate_fem_file(route, case_name, Nelem, float(jForce+1)*DeltaForce)\\n\",\n \" model.generate_solver_file(route,case_name)\\n\",\n \"\\n\",\n \" case_data=sharpy.sharpy_main.main(['', route + case_name + '.sharpy'])\\n\",\n \"\\n\",\n \" x1[jForce,0:N]=case_data.structure.timestep_info[0].pos[:, 0]\\n\",\n \" z1[jForce,0:N]=case_data.structure.timestep_info[0].pos[:, 2]\\n\",\n \"\\n\",\n \"#Store initial geometry\\n\",\n \"x0=case_data.structure.ini_info.pos[:, 0]\\n\",\n \"z0=case_data.structure.ini_info.pos[:, 2]\"\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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# Plot the deformed beam shapes\\n\",\n \"fig= plt.subplots(1, 1, figsize=(15, 6))\\n\",\n \"plt.scatter(x0,z0,c='black')\\n\",\n \"plt.plot(x0,z0,c='black')\\n\",\n \"\\n\",\n \"for jForce in range(Nforces):\\n\",\n \" plt.scatter(x1[jForce,0:N],z1[jForce,0:N],c='black')\\n\",\n \" plt.plot(x1[jForce,0:N],z1[jForce,0:N],c='black')\\n\",\n \"\\n\",\n \"plt.axis('equal')\\n\",\n \"plt.grid()\\n\",\n \"plt.xlabel('x (m)')\\n\",\n \"plt.ylabel('z (m)')\\n\",\n \"plt.savefig(\\\"images/ncb1-dead-displ.eps\\\", format='eps', dpi=1000, bbox_inches='tight')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \" Force Tip z\\n\",\n \"--------------------\\n\",\n \" 100000 -0.4438\\n\",\n \" 200000 -0.8672\\n\",\n \" 300000 -1.2551\\n\",\n \" 400000 -1.5999\\n\",\n \" 500000 -1.9005\\n\",\n \" 600000 -2.1597\\n\",\n \" 700000 -2.3824\\n\",\n \" 800000 -2.5737\\n\",\n \" 900000 -2.7386\\n\",\n \" 1000000 -2.8813\\n\"\n ]\n }\n ],\n \"source\": [\n \"print('{:>8s}{:>12s}'.format('Force','Tip z'))\\n\",\n \"dash=20*'-'; print(dash)\\n\",\n \"for jForce in range(Nforces):\\n\",\n \" print('{:>8.0f}{:>12.4f}'.format((jForce+1)*DeltaForce,z1[jForce,N-1]))\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"model.clean_test_files(route, case_name)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Problem 2: Comparing follower and dead forces\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"#Loop through all external follower forces, again applied at the tip.\\n\",\n \"x2=np.zeros((Nforces,N))\\n\",\n \"z2=np.zeros((Nforces,N))\\n\",\n \"for jForce in range(Nforces):\\n\",\n \" model.clean_test_files(route, case_name)\\n\",\n \" model.generate_fem_file(route, case_name, Nelem, 0, -float(jForce+1)*DeltaForce)\\n\",\n \" model.generate_solver_file(route,case_name)\\n\",\n \"\\n\",\n \" case_foll=sharpy.sharpy_main.main(['', route + case_name + '.sharpy'])\\n\",\n \"\\n\",\n \" x2[jForce,0:N]=case_foll.structure.timestep_info[0].pos[:, 0]\\n\",\n \" z2[jForce,0:N]=case_foll.structure.timestep_info[0].pos[:, 2]\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\\n\",\n \"The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\\n\",\n \"The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\\n\",\n \"The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\\n\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"#Plot results.\\n\",\n \"fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(15, 6))\\n\",\n \"\\n\",\n \"ax0 = axs[0]\\n\",\n \"ax0.plot([0,Nforces],[0, 0],linestyle=':', c='black')\\n\",\n \"ax0.plot(range(Nforces+1), np.concatenate((5, x1[0:Nforces,-1]), axis=None)-5*np.ones(Nforces+1),linestyle='-', c='black')\\n\",\n \"ax0.plot(range(Nforces+1), np.concatenate((5, x2[0:Nforces,-1]), axis=None)-5*np.ones(Nforces+1),linestyle='--', c='black')\\n\",\n \"#ax0.axis('equal')\\n\",\n \"ax0.grid()\\n\",\n \"ax0.set_xlabel('Force (N) x 10^5')\\n\",\n \"ax0.set_ylabel('Tip horizontal displacement (m)')\\n\",\n \"ax0.set(xlim=(0, Nforces), ylim=(-6, 1))\\n\",\n \"\\n\",\n \"ax1 = axs[1]\\n\",\n \"ax1.plot([0,Nforces],np.concatenate((0, z1[0,-1]*Nforces), axis=None),linestyle=':', c='black')\\n\",\n \"ax1.plot(range(Nforces+1), np.concatenate((0, z1[0:Nforces,-1]), axis=None),linestyle='-', c='black')\\n\",\n \"ax1.plot(range(Nforces+1), np.concatenate((0, z2[0:Nforces,-1]), axis=None),linestyle='--', c='black')\\n\",\n \" \\n\",\n \" \\n\",\n \"#ax1.axis('equal')\\n\",\n \"ax1.grid()\\n\",\n \"ax1.set_xlabel('Force (N) x 10^5')\\n\",\n \"ax1.set_ylabel('Tip vertical displacement (m)')\\n\",\n \"ax1.set(xlim=(0, Nforces), ylim=(-5, 1))\\n\",\n \"\\n\",\n \"ax1.legend(['Linear','Dead','Follower'])\\n\",\n \"\\n\",\n \"fig.savefig(\\\"images/ncb1-foll-displ.eps\\\", format='eps', dpi=1000, bbox_inches=\\\"tight\\\")\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"model.clean_test_files(route, case_name)\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3\",\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\": \"3.7.5\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "docs/source/content/example_notebooks/cantilever_wing.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"tags\": []\n },\n \"source\": [\n \"# A first test case with SHARPy\\n\",\n \"This notebook explains how to create a prismatic cantilever and flexible wing in SHARPy. It aims to provide a big picture about the simulations available in SHARPy describing the very fundamental concepts. \\n\",\n \"\\n\",\n \"This notebook requires around two hours to be completed.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Generation of the aeroelastic model\\n\",\n \"This section explains how to generate the input files for SHARPy including the structure, the aerodynamics and the simulation details.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Loading of the used packages\\n\",\n \"import numpy as np # basic mathematical and array functions\\n\",\n \"import os # Functions related to the operating system\\n\",\n \"import matplotlib.pyplot as plt # Plotting library\\n\",\n \"\\n\",\n \"import sharpy.sharpy_main # Run SHARPy inside jupyter notebooks\\n\",\n \"import sharpy.utils.plotutils as pu # Plotting utilities\\n\",\n \"from sharpy.utils.constants import deg2rad # Constant to conver degrees to radians\\n\",\n \"\\n\",\n \"import sharpy.utils.generate_cases as gc\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The [generate cases](https://ic-sharpy.readthedocs.io/en/main/includes/utils/generate_cases/index.html) module of SHARPy includes a number of templates for the creation of simple cases using common parameters as inputs. It also removes clutter from this notebook.\\n\",\n \"\\n\",\n \"The following cell configures the plotting library to show the next graphics, it is not part of SHARPy.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"%%capture\\n\",\n \"! pip install plotly\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Define the problem parameters\\n\",\n \"In this section, we define the basic parameters to generate a model for the wing shown in the image below. We use SI units for all variables.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 3,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"%config InlineBackend.figure_format = 'svg'\\n\",\n \"from IPython.display import Image\\n\",\n \"url = ('https://raw.githubusercontent.com/ImperialCollegeLondon/sharpy/dev_example/docs/' + \\n\",\n \" 'source/content/example_notebooks/images/simple_wing_scheme.png')\\n\",\n \"Image(url=url, width=800)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Geometry\\n\",\n \"chord = 1. # Chord of the wing | Set to 1 by default\\n\",\n \"aspect_ratio = 16. # Ratio between lenght and chord: aspect_ratio = length/chord | Set to 16 by default\\n\",\n \"wake_length = 50 # Length of the wake in chord lengths | Set to 50 by default\\n\",\n \"\\n\",\n \"# Discretization\\n\",\n \"num_node = 21 # Number of nodes in the structural discretisation\\n\",\n \" # The number of nodes will also define the aerodynamic panels in the \\n\",\n \" # spanwise direction | Set to 21 by default\\n\",\n \"num_chord_panels = 4 # Number of aerodynamic panels in the chordwise direction | Set to 4 by default\\n\",\n \"num_points_camber = 200 # The camber line of the wing will be defined by a series of (x,y)\\n\",\n \" # coordintes. Here, we define the size of the (x,y) vectors | Set to 200 by default\\n\",\n \"\\n\",\n \"# Structural properties of the beam cross section\\n\",\n \"mass_per_unit_length = 0.75 # Mass per unit length | Set to 0.75 by default\\n\",\n \"mass_iner_x = 0.1 # Mass inertia around the local x axis | Set to 0.1 by default\\n\",\n \"mass_iner_y = 0.05 # Mass inertia around the local y axis | Set to 0.05 by default\\n\",\n \"mass_iner_z = 0.05 # Mass inertia around the local z axis | Set to 0.05 by default\\n\",\n \"pos_cg_B = np.zeros((3)) # position of the centre of mass with respect to the elastic axis\\n\",\n \"EA = 1e7 # Axial stiffness | Set to 1e7 by default\\n\",\n \"GAy = 1e6 # Shear stiffness in the local y axis | Set to 1e6 by default\\n\",\n \"GAz = 1e6 # Shear stiffness in the local z axis | Set to 1e6 by default\\n\",\n \"GJ = 1e4 # Torsional stiffness | Set to 1e4 by default\\n\",\n \"EIy = 2e4 # Bending stiffness around the flapwise direction | Set to 2e4 by default\\n\",\n \"EIz = 5e6 # Bending stiffness around the edgewise direction | Set to 5e6 by default\\n\",\n \"\\n\",\n \"# Operation\\n\",\n \"WSP = 2.0 # Wind speed | Set to 2.0 by default\\n\",\n \"air_density = 0.1 # Air density | Set to 0.1 by default\\n\",\n \"\\n\",\n \"# Time discretization\\n\",\n \"end_time = 5.0 # End time of the simulation | Set to 5.0 by default\\n\",\n \"dt = chord/num_chord_panels/WSP # Always keep one timestep per panel\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"First, we are going to compute the static equilibrium of the wing at an angle of attack (``aoa_ini_deg``). Next, we will change the angle of attack to ``aoa_end_deg`` and we will compute the dynamic response of the wing. Keep in mind we are not changing the angle of attack of the wing itself in these simulations but of the wind flowing toward it, which has the same effect.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"aoa_ini_deg = 2. # Angle of attack at the beginning of the simulation | Set to 2 by default\\n\",\n \"aoa_end_deg = 1. # Angle of attack at the end of the simulation | Set to 1 by default\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For now, we keep the size of the wake panels equal to the distance covered by the flow in one time step. \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Structural model\\n\",\n \"\\n\",\n \"This section creates a class called ``AeroelasticInformation``. This class is not directly used by SHARPy, it can be thought of as an intermediate step between common engineering inputs and the input information that SHARPy needs. \\n\",\n \"\\n\",\n \"It has many functionalities (rotate objects, assembly simple strucures together ...) which can be looked up in the [documentation](https://ic-sharpy.readthedocs.io/en/main/includes/utils/generate_cases/index.html).\\n\",\n \"\\n\",\n \"Let's initialise an Aeroelastic system that will include a ``StructuralInformation`` class and an ``AerodynamicInformation`` class:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"wing = gc.AeroelasticInformation()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The attibutes that have to be defined (not all of them are compulsory) can be displayed with the code below. They constitute the input parameters to SHARPy and their names are intuitive, however, a complete description of the input variables to SHARPy can be found in the documentation: \\n\",\n \"[structural inputs](https://ic-sharpy.readthedocs.io/en/main/content/casefiles.html#fem-file) and [aerodynamic inputs](https://ic-sharpy.readthedocs.io/en/main/content/casefiles.html#aerodynamics-file)\\n\",\n \"\\n\",\n \"For example, the structural properties are:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"dict_keys(['num_node_elem', 'num_node', 'num_elem', 'coordinates', 'connectivities', 'elem_stiffness', 'stiffness_db', 'elem_mass', 'mass_db', 'frame_of_reference_delta', 'structural_twist', 'boundary_conditions', 'beam_number', 'body_number', 'app_forces', 'lumped_mass_nodes', 'lumped_mass', 'lumped_mass_inertia', 'lumped_mass_position', 'lumped_mass_mat', 'lumped_mass_mat_nodes'])\"\n ]\n },\n \"execution_count\": 7,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"wing.StructuralInformation.__dict__.keys()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For example, the connectivities between the nodes required by the finite element solver are empty so far:\"\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 \"None\\n\"\n ]\n }\n ],\n \"source\": [\n \"print(wing.StructuralInformation.connectivities)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For a list of methods that allow us to modify the structure, Check the [documentation ](https://ic-sharpy.readthedocs.io/en/main/includes/utils/generate_cases/index.html).\\n\",\n \"\\n\",\n \"First, we need to define the basic characteristics of the equations as the number of nodes, the number of nodes per element, the number of elements and the location of the nodes in the space:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Define the number of nodes and the number of nodes per element\\n\",\n \"wing.StructuralInformation.num_node = num_node\\n\",\n \"wing.StructuralInformation.num_node_elem = 3\\n\",\n \"# Compute the number of elements assuming basic connections\\n\",\n \"wing.StructuralInformation.compute_basic_num_elem()\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[[ 0. 0. 0. ]\\n\",\n \" [ 0. 0.8 0. ]\\n\",\n \" [ 0. 1.6 0. ]\\n\",\n \" [ 0. 2.4 0. ]\\n\",\n \" [ 0. 3.2 0. ]\\n\",\n \" [ 0. 4. 0. ]\\n\",\n \" [ 0. 4.8 0. ]\\n\",\n \" [ 0. 5.6 0. ]\\n\",\n \" [ 0. 6.4 0. ]\\n\",\n \" [ 0. 7.2 0. ]\\n\",\n \" [ 0. 8. 0. ]\\n\",\n \" [ 0. 8.8 0. ]\\n\",\n \" [ 0. 9.6 0. ]\\n\",\n \" [ 0. 10.4 0. ]\\n\",\n \" [ 0. 11.2 0. ]\\n\",\n \" [ 0. 12. 0. ]\\n\",\n \" [ 0. 12.8 0. ]\\n\",\n \" [ 0. 13.6 0. ]\\n\",\n \" [ 0. 14.4 0. ]\\n\",\n \" [ 0. 15.2 0. ]\\n\",\n \" [ 0. 16. 0. ]]\\n\"\n ]\n }\n ],\n \"source\": [\n \"# Generate an array with the location of the nodes\\n\",\n \"node_r = np.zeros((num_node, 3))\\n\",\n \"node_r[:,1] = np.linspace(0, chord*aspect_ratio, num_node)\\n\",\n \"print(node_r)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The following function creates a uniform beam from the previous parameters. On top of assigning the previous parameters, it defines other variables such as the connectivities between nodes.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"wing.StructuralInformation.generate_uniform_beam(node_r,\\n\",\n \" mass_per_unit_length,\\n\",\n \" mass_iner_x,\\n\",\n \" mass_iner_y,\\n\",\n \" mass_iner_z,\\n\",\n \" pos_cg_B,\\n\",\n \" EA,\\n\",\n \" GAy,\\n\",\n \" GAz,\\n\",\n \" GJ,\\n\",\n \" EIy,\\n\",\n \" EIz,\\n\",\n \" num_node_elem = wing.StructuralInformation.num_node_elem,\\n\",\n \" y_BFoR = 'x_AFoR',\\n\",\n \" num_lumped_mass=0)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If we now show the connectivities between nodes, the function has created them for us. [Further information](https://ic-sharpy.readthedocs.io/en/main/content/casefiles.html?highlight=connectivities#fem-file)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[[ 0 2 1]\\n\",\n \" [ 2 4 3]\\n\",\n \" [ 4 6 5]\\n\",\n \" [ 6 8 7]\\n\",\n \" [ 8 10 9]\\n\",\n \" [10 12 11]\\n\",\n \" [12 14 13]\\n\",\n \" [14 16 15]\\n\",\n \" [16 18 17]\\n\",\n \" [18 20 19]]\\n\"\n ]\n }\n ],\n \"source\": [\n \"print(wing.StructuralInformation.connectivities)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's define the boundary conditions as clamped for node 0 and free for the last node (-1), where 1 denotes a clamped point and -1 denotes a free point. [Further information](https://ic-sharpy.readthedocs.io/en/main/content/casefiles.html?highlight=boundary#fem-file)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"wing.StructuralInformation.boundary_conditions[0] = 1\\n\",\n \"wing.StructuralInformation.boundary_conditions[-1] = -1\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Aerodynamics\\n\",\n \"We need to define the number of panels in the wake (``wake_panels``) and the camber line of the wing which, in this case, is flat. [Further information](https://ic-sharpy.readthedocs.io/en/main/content/casefiles.html#aerodynamics-file)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Compute the number of panels in the wake (streamwise direction) based on the previous paramete\\n\",\n \"wake_panels = int(wake_length*chord/dt)\\n\",\n \"\\n\",\n \"# Define the coordinates of the camber line of the wing\\n\",\n \"wing_camber = np.zeros((1, num_points_camber, 2))\\n\",\n \"wing_camber[0, :, 0] = np.linspace(0, 1, num_points_camber)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The following function creates an aerodynamic surface uniform on top of the beam that we have already created.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Generate blade aerodynamics\\n\",\n \"wing.AerodynamicInformation.create_one_uniform_aerodynamics(wing.StructuralInformation,\\n\",\n \" chord = chord,\\n\",\n \" twist = 0.,\\n\",\n \" sweep = 0.,\\n\",\n \" num_chord_panels = num_chord_panels,\\n\",\n \" m_distribution = 'uniform',\\n\",\n \" elastic_axis = 0.5,\\n\",\n \" num_points_camber = num_points_camber,\\n\",\n \" airfoil = wing_camber)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Summary\\n\",\n \"Now, we have all the inputs that we need for SHARPy. In this section, a first simulation with SHARPy is run. However, it will perform no computation, it will just load the data so we can plot the system we have just created.\\n\",\n \"\\n\",\n \"SHARPy runs a series of [solvers](https://ic-sharpy.readthedocs.io/en/main/content/solvers.html) and [postprocessors](https://ic-sharpy.readthedocs.io/en/main/content/postproc.html) in the order indicated by the ``flow`` variable in the ``SHARPy`` dictionary.\\n\",\n \"\\n\",\n \"The ``generate cases`` module also allows us to show all the avaiable solvers and all the parameters they accept as inputs. To do so, we need to run the following commands:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"_BaseStructural\\n\",\n \"AerogridLoader\\n\",\n \"BeamLoader\\n\",\n \"DynamicCoupled\\n\",\n \"DynamicUVLM\\n\",\n \"InitialAeroelasticLoader\\n\",\n \"LinDynamicSim\\n\",\n \"LinearAssembler\\n\",\n \"Modal\\n\",\n \"NoAero\\n\",\n \"NonLinearDynamic\\n\",\n \"NonLinearDynamicCoupledStep\\n\",\n \"NonLinearDynamicMultibody\\n\",\n \"NonLinearDynamicPrescribedStep\\n\",\n \"NonLinearStatic\\n\",\n \"NoStructural\\n\",\n \"PrescribedUvlm\\n\",\n \"RigidDynamicCoupledStep\\n\",\n \"RigidDynamicPrescribedStep\\n\",\n \"StaticCoupled\\n\",\n \"StaticTrim\\n\",\n \"StaticUvlm\\n\",\n \"StepLinearUVLM\\n\",\n \"StepUvlm\\n\",\n \"_BaseTimeIntegrator\\n\",\n \"NewmarkBeta\\n\",\n \"GeneralisedAlpha\\n\",\n \"Trim\\n\",\n \"UpdatePickle\\n\",\n \"StabilityDerivatives\\n\",\n \"WriteVariablesTime\\n\",\n \"SHARPy\\n\",\n \"SaveData\\n\",\n \"BeamLoads\\n\",\n \"UDPout\\n\",\n \"SaveParametricCase\\n\",\n \"AerogridPlot\\n\",\n \"Cleanup\\n\",\n \"PlotFlowField\\n\",\n \"FrequencyResponse\\n\",\n \"AsymptoticStability\\n\",\n \"LiftDistribution\\n\",\n \"AeroForcesCalculator\\n\",\n \"StallCheck\\n\",\n \"BeamPlot\\n\",\n \"PickleData\\n\",\n \"DynamicControlSurface\\n\",\n \"FloatingForces\\n\",\n \"TurbVelocityField\\n\",\n \"TrajectoryGenerator\\n\",\n \"PolarCorrection\\n\",\n \"EfficiencyCorrection\\n\",\n \"ModifyStructure\\n\",\n \"GustVelocityField\\n\",\n \"SteadyVelocityField\\n\",\n \"HelicoidalWake\\n\",\n \"BumpVelocityField\\n\",\n \"GridBox\\n\",\n \"StraightWake\\n\",\n \"TurbVelocityFieldBts\\n\",\n \"ShearVelocityField\\n\",\n \"BladePitchPid\\n\",\n \"ControlSurfacePidController\\n\",\n \"TakeOffTrajectoryController\\n\"\n ]\n }\n ],\n \"source\": [\n \"# Gather data about available solvers\\n\",\n \"SimInfo = gc.SimulationInformation() # Initialises the SimulationInformation class\\n\",\n \"SimInfo.set_default_values() # Assigns the default values to all the solvers\\n\",\n \"\\n\",\n \"# Print the available solvers and postprocessors\\n\",\n \"for key in SimInfo.solvers.keys():\\n\",\n \" print(key)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"As an example, let's print the input parameters of the ``BeamLoader`` solver. This solver is in charge of loading the structural infromation.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 17,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"{'unsteady': True, 'orientation': [1.0, 0, 0, 0], 'for_pos': [0.0, 0, 0]}\"\n ]\n },\n \"execution_count\": 17,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"SimInfo.solvers['BeamLoader']\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The following dictionary defines the basic inputs of SHARPy including the solvers to be run (``flow`` variable), the case name and the route in the file system. In this case we are turning off the screen output because we are not running any computation; it is useless.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 18,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\\n\",\n \" 'AerogridLoader']\\n\",\n \"\\n\",\n \"SimInfo.solvers['SHARPy']['case'] = 'plot'\\n\",\n \"SimInfo.solvers['SHARPy']['route'] = './'\\n\",\n \"SimInfo.solvers['SHARPy']['write_screen'] = 'off'\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We do not modify any of the default input paramteters in ``BeamLoader`` but we need to define the initial wake shape that we want and its size (``wake_panels``).\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 19,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"SimInfo.solvers['AerogridLoader']['unsteady'] = 'on'\\n\",\n \"SimInfo.solvers['AerogridLoader']['mstar'] = wake_panels\\n\",\n \"SimInfo.solvers['AerogridLoader']['freestream_dir'] = np.array([1.,0.,0.])\\n\",\n \"SimInfo.solvers['AerogridLoader']['wake_shape_generator'] = 'StraightWake'\\n\",\n \"SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] = {'u_inf': WSP,\\n\",\n \" 'u_inf_direction' : np.array(\\n\",\n \" [np.cos(aoa_ini_deg*deg2rad),\\n\",\n \" 0.,\\n\",\n \" np.sin(aoa_ini_deg*deg2rad)]),\\n\",\n \" 'dt': dt}\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The following functions write the input files needed by SHARPy.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 20,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\\n\",\n \"wing.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\\n\",\n \"SimInfo.generate_solver_file()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The following line of code runs SHARPy inside of jupyter notebook. It is equivalent to running this in a terminal, with: ``sharpy plot.sharpy`` being \\\"plot\\\", the case name defined above.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 21,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"fatal: not a git repository (or any of the parent directories): .git\\n\"\n ]\n }\n ],\n \"source\": [\n \"sharpy_output = sharpy.sharpy_main.main(['',\\n\",\n \" SimInfo.solvers['SHARPy']['route'] +\\n\",\n \" SimInfo.solvers['SHARPy']['case'] +\\n\",\n \" '.sharpy'])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's plot the case we have created. The function below provides a quick way of generating an interactive plot but it is not suitable for large cases. Luckily SHARPy has other more complex plotting capabilities.\\n\",\n \"\\n\",\n \"If you download the original [jupyter notebook](https://ic-sharpy.readthedocs.io/en/main/content/examples.html), change the geometric parameters above and rerun the notebook, you will see its impact on the geometry.\\n\",\n \"\\n\",\n \"In our simulations only the first 6 wake panels are plotted for the sake of efficiency. This can be changed by changing the number within ```minus_mstar```.\\n\",\n \"\\n\",\n \"Setting ```plotly``` to ```False``` will not plot a graph.\\n\",\n \"\\n\",\n \"```custom_scaling``` is a toggleable feature that realistically models the wing's aspect ratio and compresses the z axis. It is disabled by default.\\n\",\n \"\\n\",\n \"If ```custom_scaling``` is toggled on,```z_compression``` determines how compressed the z axis is. By default this is set to 0.5.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 22,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \" \\n\",\n \" \"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"data\": {\n \"application/vnd.plotly.v1+json\": {\n \"config\": {\n \"plotlyServerURL\": \"https://plot.ly\"\n },\n \"data\": [\n {\n \"line\": {\n \"color\": \"grey\"\n },\n \"mode\": \"lines\",\n \"name\": \"Aero surface\",\n \"surfaceaxis\": 2,\n \"type\": \"scatter3d\",\n \"x\": [\n -0.4375000000000001,\n -0.18750000000000006,\n -0.18750000000000006,\n -0.4375000000000001,\n -0.4375000000000001\n ],\n \"y\": [\n -7.126160546901204e-18,\n -3.054068805814802e-18,\n 0.8,\n 0.8,\n -7.126160546901204e-18\n ],\n \"z\": [\n -3.7885577460302824e-17,\n -1.6236676054415498e-17,\n -1.6236676054415498e-17,\n -3.7885577460302824e-17,\n -3.7885577460302824e-17\n ]\n },\n {\n \"line\": {\n \"color\": \"grey\"\n },\n \"mode\": \"lines\",\n \"showlegend\": false,\n \"surfaceaxis\": 2,\n \"type\": \"scatter3d\",\n \"x\": [\n -0.4375000000000001,\n -0.18750000000000006,\n -0.18750000000000006,\n -0.4375000000000001,\n -0.4375000000000001\n ],\n \"y\": [\n 0.8,\n 0.8,\n 1.6,\n 1.6,\n 0.8\n ],\n \"z\": [\n -3.7885577460302824e-17,\n -1.6236676054415498e-17,\n -1.6236676054415498e-17,\n -3.7885577460302824e-17,\n -3.7885577460302824e-17\n ]\n },\n {\n \"line\": {\n \"color\": \"grey\"\n },\n \"mode\": \"lines\",\n \"showlegend\": false,\n \"surfaceaxis\": 2,\n \"type\": \"scatter3d\",\n \"x\": [\n -0.4375000000000001,\n -0.18750000000000006,\n -0.18750000000000006,\n -0.4375000000000001,\n -0.4375000000000001\n ],\n \"y\": [\n 1.6,\n 1.6,\n 2.4000000000000004,\n 2.4000000000000004,\n 1.6\n ],\n \"z\": [\n -3.7885577460302824e-17,\n -1.6236676054415498e-17,\n -1.6236676054415498e-17,\n -3.7885577460302824e-17,\n -3.7885577460302824e-17\n ]\n },\n {\n \"line\": {\n \"color\": \"grey\"\n },\n \"mode\": \"lines\",\n \"showlegend\": false,\n \"surfaceaxis\": 2,\n \"type\": \"scatter3d\",\n \"x\": [\n -0.4375000000000001,\n -0.18750000000000006,\n -0.18750000000000006,\n -0.4375000000000001,\n -0.4375000000000001\n ],\n \"y\": [\n 2.4000000000000004,\n 2.4000000000000004,\n 3.2,\n 3.2,\n 2.4000000000000004\n ],\n \"z\": [\n -3.7885577460302824e-17,\n -1.6236676054415498e-17,\n -1.6236676054415498e-17,\n -3.7885577460302824e-17,\n -3.7885577460302824e-17\n ]\n },\n {\n \"line\": {\n \"color\": \"grey\"\n },\n \"mode\": \"lines\",\n \"showlegend\": false,\n \"surfaceaxis\": 2,\n \"type\": \"scatter3d\",\n \"x\": [\n -0.4375000000000001,\n -0.18750000000000006,\n -0.18750000000000006,\n -0.4375000000000001,\n -0.4375000000000001\n ],\n \"y\": [\n 3.2,\n 3.2,\n 4,\n 4,\n 3.2\n ],\n \"z\": [\n -3.7885577460302824e-17,\n -1.6236676054415498e-17,\n -1.6236676054415498e-17,\n -3.7885577460302824e-17,\n -3.7885577460302824e-17\n ]\n },\n {\n \"line\": {\n \"color\": \"grey\"\n },\n \"mode\": \"lines\",\n 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\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"pu.plot_timestep(sharpy_output, tstep=-1, minus_mstar=(wake_panels - 6), plotly=True,custom_scaling=False,z_compression=0.5)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Static simulation\\n\",\n \"Next, we will run a static simulation of the previous system. We have already defined the required inputs for ``BeamLoader`` and ``AerogridLoader`` but we need to define the static solvers. We are going to use an FSI solver (``StaticCoupled``) that will include a structural solver (``NonLinearStatic``) and aerodynamic solver (``StaticUvlm``). \\n\",\n \"\\n\",\n \"We will use most of the default values but redefine some of them:\\n\",\n \"- We assign the air density to all the solvers that need it\\n\",\n \"- We turn off the gravity on the structural solver\\n\",\n \"- We use a horseshoe solution without roll up for the aerodynamics\\n\",\n \"- We define the velocity field against the wing\\n\",\n \"- We do not use load steps in the FSI solver\\n\",\n \"\\n\",\n \"In the documentation you can find further information about the [modular framework](https://ic-sharpy.readthedocs.io/en/main/content/casefiles.html#modular-framework) and about the [solvers](https://ic-sharpy.readthedocs.io/en/main/content/solvers.html) and their inputs. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 23,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Define the simulation\\n\",\n \"SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\\n\",\n \" 'AerogridLoader',\\n\",\n \" 'StaticCoupled']\\n\",\n \"\\n\",\n \"SimInfo.set_variable_all_dicts('rho', air_density)\\n\",\n \"\\n\",\n \"SimInfo.solvers['SHARPy']['case'] = 'static'\\n\",\n \"SimInfo.solvers['SHARPy']['write_screen'] = 'on'\\n\",\n \"\\n\",\n \"SimInfo.solvers['NonLinearStatic']['gravity_on'] = False\\n\",\n \"\\n\",\n \"SimInfo.solvers['StaticUvlm']['horseshoe'] = True\\n\",\n \"SimInfo.solvers['StaticUvlm']['n_rollup'] = 0\\n\",\n \"SimInfo.solvers['StaticUvlm']['velocity_field_generator'] = 'SteadyVelocityField'\\n\",\n \"SimInfo.solvers['StaticUvlm']['velocity_field_input'] = {'u_inf' : WSP,\\n\",\n \" 'u_inf_direction' : np.array(\\n\",\n \" [np.cos(aoa_ini_deg*deg2rad),\\n\",\n \" 0.,\\n\",\n \" np.sin(aoa_ini_deg*deg2rad)])}\\n\",\n \"\\n\",\n \"SimInfo.solvers['StaticCoupled']['structural_solver'] = 'NonLinearStatic'\\n\",\n \"SimInfo.solvers['StaticCoupled']['structural_solver_settings'] = SimInfo.solvers['NonLinearStatic']\\n\",\n \"SimInfo.solvers['StaticCoupled']['aero_solver'] = 'StaticUvlm'\\n\",\n \"SimInfo.solvers['StaticCoupled']['aero_solver_settings'] = SimInfo.solvers['StaticUvlm']\\n\",\n \"SimInfo.solvers['StaticCoupled']['n_load_steps'] = 0\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The following functions create the input files required by SHARPy. For further information check:\\n\",\n \"- [Configuration file](https://ic-sharpy.readthedocs.io/en/main/content/casefiles.html#solver-configuration-file)\\n\",\n \"- [FEM input file](https://ic-sharpy.readthedocs.io/en/main/content/casefiles.html#fem-file)\\n\",\n \"- [Aerodynamic input file](https://ic-sharpy.readthedocs.io/en/main/content/casefiles.html#aerodynamics-file)\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 24,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\\n\",\n \"SimInfo.generate_solver_file()\\n\",\n \"wing.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 25,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"--------------------------------------------------------------------------------\\u001b[0m\\n\",\n \" ###### ## ## ### ######## ######## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ####\\u001b[0m\\n\",\n \" ###### ######### ## ## ######## ######## ##\\u001b[0m\\n\",\n \" ## ## ## ######### ## ## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \" ###### ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \"--------------------------------------------------------------------------------\\u001b[0m\\n\",\n \"Aeroelastics Lab, Aeronautics Department.\\u001b[0m\\n\",\n \" Copyright (c), Imperial College London.\\u001b[0m\\n\",\n \" All rights reserved.\\u001b[0m\\n\",\n \" License available at https://github.com/imperialcollegelondon/sharpy\\u001b[0m\\n\",\n \"\\u001b[36mRunning SHARPy from /home/loca/Downloads/sharpy copy/sharpy/docs/source/content/example_notebooks\\u001b[0m\\n\",\n \"\\u001b[36mSHARPy being run is in /home/loca/anaconda3/envs/sharpy/lib/python3.10/site-packages\\u001b[0m\\n\",\n \"SHARPy output folder set\\u001b[0m\\n\",\n \"\\u001b[34m\\t./output//static/\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of BeamLoader\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of AerogridLoader\\u001b[0m\\n\",\n \"Variable dx1 has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: -1.0\\u001b[0m\\n\",\n \"Variable ndx1 has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n \"Variable r has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1.0\\u001b[0m\\n\",\n \"Variable dxmax has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: -1.0\\u001b[0m\\n\",\n \"\\u001b[34mThe aerodynamic grid contains 1 surfaces\\u001b[0m\\n\",\n \"\\u001b[34m Surface 0, M=4, N=20\\u001b[0m\\n\",\n \" Wake 0, M=400, N=20\\u001b[0m\\n\",\n \" In total: 80 bound panels\\u001b[0m\\n\",\n \" In total: 8000 wake panels\\u001b[0m\\n\",\n \" Total number of panels = 8080\\u001b[0m\\n\"\n ]\n },\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"fatal: not a git repository (or any of the parent directories): .git\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"\\u001b[36mGenerating an instance of StaticCoupled\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of NonLinearStatic\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of StaticUvlm\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"|=====|=====|============|==========|==========|==========|==========|==========|==========|\\u001b[0m\\n\",\n \"|iter |step | log10(res) | Fx | Fy | Fz | Mx | My | Mz |\\u001b[0m\\n\",\n 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\",\n 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\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"pu.plot_timestep(sharpy_output, tstep=-1, minus_mstar=(wake_panels - 6), plotly=True,custom_scaling=False,z_compression=0.5)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Dynamic simulation\\n\",\n \"Finally, we will run a dynamic simulation after the previous static one. With that in mind, we will now include a dynamic FSI solver (``DynamicCoupled``) in the simulation.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 27,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\\n\",\n \" 'AerogridLoader',\\n\",\n \" 'StaticCoupled',\\n\",\n \" 'DynamicCoupled']\\n\",\n \"\\n\",\n \"SimInfo.solvers['SHARPy']['route'] = './'\\n\",\n \"SimInfo.solvers['SHARPy']['case'] = 'dynamic'\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We need information about the time step and the number of iterations:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 28,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Compute the number of time steps needed based on the previous parameters\\n\",\n \"time_steps = int(end_time/dt)\\n\",\n \"\\n\",\n \"# Define the time step and the number of time steps in every solver that requires them as input\\n\",\n \"SimInfo.set_variable_all_dicts('dt', dt)\\n\",\n \"SimInfo.define_num_steps(time_steps)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We define the approximation we are going to use for the wake convection (``convection_scheme``), the velocity field and deactivate the gravity.\\n\",\n \"\\n\",\n \"We are going to use an FSI solver (``DynamicCoupled``) that couples a structual solver (``NonLinearDynamicPrescribedStep``) and aerodynamic solver (``StepUvlm``).\\n\",\n \"\\n\",\n \"Moreover, the FSI solver runs a series of postprocessors after each time step. Specifically, it will save a plot of the structure (``BeamPlot``) and of the aerodynamic surfaces (``AerogridPlot``).\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 29,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"SimInfo.solvers['StepUvlm']['convection_scheme'] = 2\\n\",\n \"SimInfo.solvers['StaticUvlm']['velocity_field_generator'] = 'SteadyVelocityField'\\n\",\n \"SimInfo.solvers['StepUvlm']['velocity_field_input'] = {'u_inf' : WSP,\\n\",\n \" 'u_inf_direction' : np.array(\\n\",\n \" [np.cos(aoa_end_deg*deg2rad),\\n\",\n \" 0.,\\n\",\n \" np.sin(aoa_end_deg*deg2rad)])}\\n\",\n \"\\n\",\n \"SimInfo.solvers['NonLinearDynamicPrescribedStep']['gravity_on'] = False\\n\",\n \"\\n\",\n \"SimInfo.solvers['DynamicCoupled']['structural_solver'] = 'NonLinearDynamicPrescribedStep'\\n\",\n \"SimInfo.solvers['DynamicCoupled']['structural_solver_settings'] = SimInfo.solvers['NonLinearDynamicPrescribedStep']\\n\",\n \"SimInfo.solvers['DynamicCoupled']['aero_solver'] = 'StepUvlm'\\n\",\n \"SimInfo.solvers['DynamicCoupled']['aero_solver_settings'] = SimInfo.solvers['StepUvlm']\\n\",\n \"SimInfo.solvers['DynamicCoupled']['postprocessors'] = ['BeamPlot', 'AerogridPlot']\\n\",\n \"SimInfo.solvers['DynamicCoupled']['postprocessors_settings'] = {'BeamPlot': SimInfo.solvers['BeamPlot'],\\n\",\n \" 'AerogridPlot': SimInfo.solvers['AerogridPlot']}\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Finally, we need to define the movement of the whole wing through its velocity and acceleration. In this case we want a clamped structure so we will set every thing to zero.\\n\",\n \"\\n\",\n \"Moreover, we can define forces applied together with the aerodynamic ones. In this case they will be set to zero.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 30,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"SimInfo.with_forced_vel = True\\n\",\n \"SimInfo.for_vel = np.zeros((time_steps,6), dtype=float)\\n\",\n \"SimInfo.for_acc = np.zeros((time_steps,6), dtype=float)\\n\",\n \"SimInfo.with_dynamic_forces = True\\n\",\n \"SimInfo.dynamic_forces = np.zeros((time_steps,wing.StructuralInformation.num_node,6),\\n\",\n \" dtype=float)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We write the input files required by SHARPy again:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 31,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\\n\",\n \"wing.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\\n\",\n \"SimInfo.generate_solver_file()\\n\",\n \"SimInfo.generate_dyn_file(time_steps)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"And we run the simulation:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 32,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"--------------------------------------------------------------------------------\\u001b[0m\\n\",\n \" ###### ## ## ### ######## ######## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ####\\u001b[0m\\n\",\n \" ###### ######### ## ## ######## ######## ##\\u001b[0m\\n\",\n \" ## ## ## ######### ## ## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \" ###### ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \"--------------------------------------------------------------------------------\\u001b[0m\\n\",\n \"Aeroelastics Lab, Aeronautics Department.\\u001b[0m\\n\",\n \" Copyright (c), Imperial College London.\\u001b[0m\\n\",\n \" All rights reserved.\\u001b[0m\\n\",\n \" License available at https://github.com/imperialcollegelondon/sharpy\\u001b[0m\\n\",\n \"\\u001b[36mRunning SHARPy from /home/loca/Downloads/sharpy copy/sharpy/docs/source/content/example_notebooks\\u001b[0m\\n\",\n \"\\u001b[36mSHARPy being run is in /home/loca/anaconda3/envs/sharpy/lib/python3.10/site-packages\\u001b[0m\\n\",\n \"SHARPy output folder set\\u001b[0m\\n\",\n \"\\u001b[34m\\t./output//dynamic/\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of BeamLoader\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of AerogridLoader\\u001b[0m\\n\",\n \"Variable dx1 has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: -1.0\\u001b[0m\\n\",\n \"Variable ndx1 has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n \"Variable r has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1.0\\u001b[0m\\n\",\n \"Variable dxmax has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: -1.0\\u001b[0m\\n\",\n \"\\u001b[34mThe aerodynamic grid contains 1 surfaces\\u001b[0m\\n\",\n \"\\u001b[34m Surface 0, M=4, N=20\\u001b[0m\\n\",\n \" Wake 0, M=400, N=20\\u001b[0m\\n\",\n \" In total: 80 bound panels\\u001b[0m\\n\",\n \" In total: 8000 wake panels\\u001b[0m\\n\",\n \" Total number of panels = 8080\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of StaticCoupled\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of NonLinearStatic\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of StaticUvlm\\u001b[0m\\n\"\n ]\n },\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"fatal: not a git repository (or any of the parent directories): .git\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"|=====|=====|============|==========|==========|==========|==========|==========|==========|\\u001b[0m\\n\",\n \"|iter |step | log10(res) | Fx | Fy | Fz | Mx | My | Mz |\\u001b[0m\\n\",\n \"|=====|=====|============|==========|==========|==========|==========|==========|==========|\\u001b[0m\\n\",\n \" DeltaF DeltaX Res ResRel ResFrc ResRelFrc ResMmt ResRelMmt ErX ErPos ErPsi\\n\",\n \"LoadStep Subiter DeltaF DeltaX Res ResRel ResFrc ResRelFrc ResMmt ResRelMmt ErX ErPos ErPsi\\n\",\n \"| 0 | 0 | 0.00000 | -0.0187 | -0.0006 | 0.6029 | 4.8229 | 0.1523 | 0.1495 |\\u001b[0m\\n\",\n \" DeltaF DeltaX Res ResRel ResFrc ResRelFrc ResMmt ResRelMmt ErX ErPos ErPsi\\n\",\n \"LoadStep Subiter DeltaF DeltaX Res ResRel ResFrc ResRelFrc ResMmt ResRelMmt ErX ErPos ErPsi\\n\",\n \"| 1 | 0 | -9.22874 | -0.0188 | -0.0006 | 0.6043 | 4.8366 | 0.1526 | 0.1504 |\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of DynamicCoupled\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of NonLinearDynamicPrescribedStep\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of StepUvlm\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of BeamPlot\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of AerogridPlot\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"|=======|========|======|==============|==============|==============|==============|==============|\\u001b[0m\\n\",\n \"| ts | t | iter | struc ratio | iter time | residual vel | FoR_vel(x) | FoR_vel(z) |\\u001b[0m\\n\",\n \"|=======|========|======|==============|==============|==============|==============|==============|\\u001b[0m\\n\",\n \"| 1 | 0.1250 | 4 | 0.406694 | 2.468390 | -5.501499 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 2 | 0.2500 | 3 | 0.488530 | 2.521077 | -5.442787 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 3 | 0.3750 | 3 | 0.341496 | 1.847399 | -5.640521 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 4 | 0.5000 | 3 | 0.307099 | 1.716782 | -5.645651 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 5 | 0.6250 | 3 | 0.387260 | 1.940912 | -5.889684 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 6 | 0.7500 | 3 | 0.304108 | 1.657786 | -5.914635 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 7 | 0.8750 | 3 | 0.071527 | 1.164022 | -6.040009 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 8 | 1.0000 | 3 | 0.069586 | 1.161729 | -5.925998 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 9 | 1.1250 | 3 | 0.068879 | 1.164142 | -5.836958 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 10 | 1.2500 | 3 | 0.068450 | 1.162696 | -5.632144 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 11 | 1.3750 | 3 | 0.068106 | 1.162670 | -5.513670 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 12 | 1.5000 | 3 | 0.077652 | 1.170546 | -5.471589 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 13 | 1.6250 | 3 | 0.070499 | 1.172093 | -5.423647 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 14 | 1.7500 | 3 | 0.066050 | 1.159820 | -5.451292 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 15 | 1.8750 | 3 | 0.066831 | 1.159918 | -5.503924 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 16 | 2.0000 | 3 | 0.076779 | 1.171578 | -5.521127 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 17 | 2.1250 | 3 | 0.069862 | 1.168248 | -5.649248 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 18 | 2.2500 | 3 | 0.295345 | 1.482039 | -5.852560 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 19 | 2.3750 | 3 | 0.065010 | 1.166991 | -6.169248 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 20 | 2.5000 | 3 | 0.088990 | 1.190061 | -6.501434 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 21 | 2.6250 | 3 | 0.070542 | 1.172962 | -5.911316 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 22 | 2.7500 | 3 | 0.073701 | 1.205343 | -5.844249 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 23 | 2.8750 | 3 | 0.069573 | 1.208120 | -5.662014 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 24 | 3.0000 | 3 | 0.065514 | 1.184485 | -5.623002 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 25 | 3.1250 | 3 | 0.068776 | 1.164661 | -5.695734 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 26 | 3.2500 | 3 | 0.154359 | 1.276498 | -5.679340 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 27 | 3.3750 | 3 | 0.070216 | 1.205452 | -5.742054 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 28 | 3.5000 | 3 | 0.067111 | 1.184687 | -5.934912 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 29 | 3.6250 | 3 | 0.081985 | 1.188525 | -6.170404 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 30 | 3.7500 | 3 | 0.075176 | 1.174604 | -6.498959 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 31 | 3.8750 | 3 | 0.068256 | 1.167637 | -6.054012 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 32 | 4.0000 | 3 | 0.073072 | 1.176508 | -6.023555 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 33 | 4.1250 | 3 | 0.070665 | 1.172659 | -5.782342 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 34 | 4.2500 | 3 | 0.073685 | 1.172562 | -5.673256 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 35 | 4.3750 | 3 | 0.073392 | 1.185722 | -5.733463 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 36 | 4.5000 | 3 | 0.077823 | 1.177345 | -5.705716 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 37 | 4.6250 | 3 | 0.065806 | 1.168674 | -5.751720 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 38 | 4.7500 | 3 | 0.155288 | 1.272752 | -5.851236 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 39 | 4.8750 | 3 | 0.065315 | 1.167344 | -5.920499 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 40 | 5.0000 | 3 | 0.065910 | 1.165901 | -6.297188 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"\\u001b[34m...Finished\\u001b[0m\\n\",\n \"\\u001b[36mFINISHED - Elapsed time = 61.3302536 seconds\\u001b[0m\\n\",\n \"\\u001b[36mFINISHED - CPU process time = 205.6064506 seconds\\u001b[0m\\n\"\n ]\n }\n ],\n \"source\": [\n \"sharpy_output = sharpy.sharpy_main.main(['',\\n\",\n \" SimInfo.solvers['SHARPy']['route'] +\\n\",\n \" SimInfo.solvers['SHARPy']['case'] +\\n\",\n \" '.sharpy'])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This is the plot of the wing at the end of the simulation:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 33,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"application/vnd.plotly.v1+json\": {\n \"config\": {\n \"plotlyServerURL\": \"https://plot.ly\"\n },\n \"data\": [\n {\n \"line\": {\n \"color\": \"grey\"\n },\n \"mode\": \"lines\",\n \"name\": \"Aero surface\",\n \"surfaceaxis\": 2,\n \"type\": \"scatter3d\",\n \"x\": [\n -0.4375000000000001,\n -0.18750000000000006,\n -0.187500005737461,\n -0.4375000057285399,\n -0.4375000000000001\n ],\n \"y\": 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zG2/9rbznXj8577NmX7ZKrb7fbrz3T+rmVvv+LM53gs7d9fdcv2LmX3WRFRUV2ylE/skmvv2M/PeFie+Kuy7zgtLCu3s4/9WdWt3iJfffnZ9jl5xxtYzZYZ6XcFwSalYKRSSAAAQhAAAIQgAAEIAABCEAAAh8dgYsuusgaGxs/ugWyzHzCCSdYVVXVcu8++fxEu/e/z9jvf3u4f++U8661nb/0Odv9K5/3rz/wyPN29YXH+fcam5ptu70Ot5fHXucFlSeee8Wuueh4/95J515tY9Zfxw7+wdf870+Pm+SFEAk/0XH1Tf+yZ1+cbMf/4vu26cbrOgFFskpPx0z892N+8yd37GjvtNGICjRLnWumqbnFOWQq/HtnXHyDjVxjiP1s/71ttx8c78Sko2yTDUf59+rql9jAmv62u3v94t8cZp/9zPr+dTmI+rvzDz9onyz08nsZgSY/XhwNAQhAAAIQgAAEIAABCEAAAhD42Al80hw0x55xhUmkkXtGo6Ojw76w1WfsivOOsetv+49dccPdNmhgTTenhiVNdv+Nv3OlTONdidBUu/DXv/Dv/fT4i71r5dtf29H/PmnKu3b06ZfZY3dc2oNxu5tf8/774ee9K0aZNwd+d4+cJU4SaL607Wb23b128nNFBZraRfV2sRNY3nlvplm/ft6Fs9+3v+odOlvv8TO794Zzba0Rw3rs4fN7/sxqqqu6r7mtrd323Hlb77RZGQOBZmVQZA4IQAACEIAABCAAAQhAAAIQgEAfIaCMlq//6CQnolziyp9K/FVLQNll31/ZPdefa884F8zYJ8bb5ef+cjkit9z1sL36v7ftgtN/7t+Tg2aj9da2Q374df/7Uy+8apddd6fd4UqPso33PphjBx3zOy8GPT/hfzb9g7l2xvEH+cMvvfYOV37U4DNpJNDssO3mtu9eX/HvRQUaOWZaXcmYsnEUVKySqTXXGOoFGjlo/uCcQZtvsp4/793ps/x73zzoNLv0rCNXWklT/PoQaPrIHyAuEwIQgAAEIPBREVBXBOcSdn+56bIaMyAAAQhAAAIQWLUJqExp/CtTusubwtWqzEklRXKV7HPw6XbLFafbqLVW966Yf419xk49en+XQdNToHnwsXHeBXPzn063cpdfc9yZV9h6o0baUT/5vx4Qjz/rKvvWHjvYjl/Y3Fpc0O++h/7Gfnfaz2za+7Pttnsedeef5tt9q+33Fq4EKUmgkXijrlMHfX9PmzJ1unPt/NHv+9iff8/OvuRGv8ZZJ/zEvfeeHXLshfa4y6CR+NPsyqJ+48KQ210Gzx+u/qft9dXt/TWvjIFAszIoMgcEIAABCECgjxFoaetwf3HptKbWDhs6sNzm17XYwP5dAYLOJWzlpV12ZwYEIAABCEAAAqsegR8cdpYdsO8evjQpOh55aoL9+ab77PZrznA5M11dnCSa9K+qsNN+ub9ttflGywk0+oee0MVJ/+Dz+S029iVD6p4UHRJ5zvrD32yRc8cUub9sfHP3L9oRB3/b5ci02pGnXWqL6hpsxPAhtv7okT7IV+JKLgfNy5Pf8rk56sYkp8yuO2xtp11wnf3u1J/6ff72outNx6iblISlL23T1cVJYcV6XY6hnbbf0k46cj8/x8oYCDQrgyJzQAACEIAABFZxAvrLkxdl2jr9V4f7PYzVV6vwAk1NVamzCndYY0uHF2kqy0qcUNPPizUhyG8Vx8TlQQACEIAABCAAgV4TQKDpNTpOhAAEIAABCKzaBGTdbWtf6gSXdi/KZBuZBJrosRJrykqKbMiAcpPQg1izaj83XB0EIAABCEAAAr0jgEDTO26cBQEIQAACEFglCbS1d3oBpXZxi7V1fOiSyXWxSQJNOHfkkEqbuaDJOWqKrMy5aspKutw1DAhAAAIQgAAEIAABVybuen+n+9sXtCAAAQhAAAIQWCUJqHSpyZUlBZfMoOoyW+AEmrQjX4EmOm+xE4Mqy4pdKGARYk1a4BwHAQhAAAIQgMAqSQCBZpW8rVwUBCAAAQhAIDuBrjwZZck4YcaF/Mb/qWaYC/2d5zJl0o4VEWiia2ie+sZ276ypcKINpVBp7wDHQQACEIAABCCwKhBAoFkV7iLXAAEIQAACEEggkDZPRtNIKJmzsDk106hAo7ya1ix5NWsMrrDZtdnnja+rUigJNRWuDIoW3qlvBwdCAAIQgAAEIPApJYBA8ym9cWwbAhCAAAQgkERAokyTa4Xd7ESTtHky+Qo0CgAePqjCGprafbZM3ZK2Hh2ewh7DcbmEn1wCTmlxP6uqKLH+7osBAQhAAAIQgAAEVkUCCDSr4l3lmiAAAQhAoM8SaFrWcUklTGp7ncvRkg1SkoNGYoucLcqOKXOiTJF7odmVSulndX3SHuKlU8qaGepKp3IJNCFEONu+NH9VeYkTgVqtv/uu3JrSYre+m5sBAQhAAAIQgAAEPu0EEGg+7XeQ/UMAAhCAQJ8mEEqXJIgoUyaaJzPACTTN7rVsJUfZwGUSSuKijASZZrlz3Pd4Bo06NMlN0+66QAWxRiLOigo0EoXkpKl3bp0wQgtviUXk1vTpPwpcPAQgAAEIQOBTTwCB5lN/C7kACEAAAhDoawQkysghI3EkdF7KxKCmssSXGzW6Dk35jCDQ5BJlovNFBZr6xq4SJ51bWtLleJFYo2Bi5cjIQZOpf2SaEqiqcpdF49wyUYEmfl1aa8iAcutw4hC5NfncdY6FAAQgAAEIQKDQBBBoCn0HWB8CEIAABCCQgoDcMS3OsSKnjASQNEMCjQ5d0vyh4yTNeRJoVBolcUUikNZUG+5sI5NAEz1W4ku5c9UMrinze29r77QGtyd9D2JNmhIo5c+omimXQBOdhxbeae42x0AAAhCAAARWjMB+h5/t8u5a7a6/nL1iE32EZ0+ZOt2O+c2f7MG/X/gRrrLiUyPQrDhDZoAABCAAAQisdAJdrbA7rKSk2LWebvNCSb5DAo1GLkEjzOm7JblMF18m5BSVhQ2tfs1Mbpf4PpIEGh0vsUSZOMqPUTlSpRN/SpyjRg4giUFLO80GVZfmbO+dRnBSJs2A/qW2YHHPNuESiSrLSty65Nbk+xxxPAQgAAEIQCAbganvzrALrrjVKspL7ZD9vmFbbrpBXrA6nCu42P2/+6MeCDQfNWHmhwAEIAABCKxiBDK1wu5tmZLQqCSoxP2lZ7ETeDKNqCijnBo5ZSTKqCvT/LqW1E6dNAJNCPhd5ISfMLpEky6xprSkny9LqnN7jTprovtWpo4Y5SrZ0jWVudKqbNes+cK6EowUL0zI8Cr2B4nLgQAEIACBj43ARVfdZhuMXtPKykrtxYlv2G+PPbB77Seem2iXXHO7+/96u609cpidfeIhNmzIILvhnw/aW+98YK+/9Z59ebst7OhDvmOX//Uu++/j4/y5m49Zz379qwOsun9l91zTZ8yxg4453x69/RL/2pl/+Juf4+Y/neZ/P+LUS22fPXewbbYYYyefd429O32WcxEvtQO/u4ft/53dLCrQtLV32KHHXejXPuSHX7ds+/zYIEYWwkFTCOqsCQEIQAACEFhGQGJEq/vKlieTjwsmDjWTKJJNlIk6ZYLgkraUqrcCTXS/2utAJ5ioJCvqrImKNYOqyxK7UqXJqdG60eOUW6Ng4zInEqkUiwEBCEAAAhD4JBJ4YU6ntaWrcl6p2//CcOc+zWBykfvl6/ufZHded5ZzwRTb3gecbA/cfIEXa+bX1tleB5xiN11+qm247lp2wz8etAmT37Q/nn203XLXQ3bV3+6zW6/6tRNuhtsDj7xgf7n13+7Y06yyosxOOudqW33YYDvuF9/rcR27fvdYu/mK023E8MH2vZ+f4d+72Z1TWlpiO+5ztP37pvPt6pvus8UNjXbOSYfYjNnz/R7++/eLrHbR4u4SJ4k7HR0ddtYJP8m5z5UKMeVkCDQpQXEYBCAAAQhAYGURUOmSMl1U3pMkgih3ReVBuRwh2fal8yRqKIMmlC+pDXZovZ1t7WGuHXZtfWvi3sK6QaDRWnLIZJpXAkyFEz9yuXlChyY5XJR/47s2OdFE3aK055rK0qzzh72kFbSyHUduzcp6ypkHAhCAAARWNoHLJrVZpJHhyp4+63y/3LzUllVN9zjmyecn2r3/fcZ+/9vD/eunnHet7fylz9nuX/m8f/2BR563qy88zr/X2NRs2+11uL089jq77d5HnWvlFbvmouP9eyede7WNWX8dO/gHX/O/Pz1uknfeSPiJDs3/le23sO233tSOPO0yW2/UCPvWHjvYwJoq55q51m6/5gzntO2wdueQqSgv86dKQDr35EOd8FPuBZqDv7+njX3iRbv6ouPcPwgV59znx1F6FYeOQPOxPdYsBAEIQAACfZVAV56MOi91Be6myXUJrLJlqiSxlCBS7cQdiRwh50VlTEmCkOb1oo77G2Cb+5exNCMq0Cxe4kqUMpyn/ZS70qNseTjZnC9RsUZOlwa3r1ytw7X3Vsc5qXNVmuNCbs2Aqq4sH0qh0jwNHAMBCEAAAh8VgU+ag+bYM64wiTRyz2jIlfKFrT5jV5x3jF1/23/sihvutkEDa7pxNCxpsvtv/J0rZRpvE1+bahf++hf+vZ8ef7F9fdcv2Le/tqP/fdKUd+3o0y+zx+64tAfKu//zlL3x9vu27ZZjnBvnLVt/1EjnjKm3muoqe3/GXO+4ee2Nab5caqF7vZ/7h6o33fHX/f4Eq6qssP2PPMf9v7zIi0gXnPZzP3eufQ4dPPCjupVZ50Wg+diRsyAEIAABCPQFAspKcf+A47sOzY8F1uZz/RIJhrq20fNcJkzS6CppUqlO8bL22u2m3Ba1ts5npCklis4XFWjqm9qcQLK8sOPdMC4UOF+BJr6OBJrgrGlsdpk5ToyJrpd27+ooVd+YToRaY3CFza5t9u3CfYmYcwLRwjufJ4pjIQABCEBgVSOgMqKv/+gkJ6Jc4kuMNORe2WXfX9k9159rzzgXzNgnxtvl5/5yuUu/5a6H7dX/vW0XnN4lkshBs9F6a/s8GI2nXnjVLrvuTrvj2jN7nDvTlSwde+aVtvXmG9nWn93IRq8zwv7w539adXWl7b3bF+1L22zmHTOH/PAb9p1vfNmfu+d+J9p5pxzqBZqfHHuB3XntWe77hV7M+eqOW9u/xj6bdZ+FuGcINIWgzpoQgAAEILBKElBeSlfpUodzkSz1YbRpxZVcQIJAkOmYTKJM1CmT69xsa6YVOcL5Q5yApNImnZdNoEnKhknTQjt6LfEyqCDWKMdGgliSS0miUhrhKlv7b3JrVsk/wlwUBCAAAQikJKAypfGvTOkubwqnqQxp041H2547b2v7HHy63eIyY0attbp3xfxr7DN26tH7uwyangLNg4+Ns2tvud8F/p5u5S6/5rgzr3DlSyPtqJ/833K7UaaMypeuvfh4GzSg2vY+8FTfffIfV5/h82u++M0j7NqLTvB7kPhy9qU3uj0e4cKJB3Zn0EyY9Jb96rd/srv/eo51dnZm3WdKFCv1MASalYqTySAAAQhAoK8RSMqTGTmk0mYuaFohLHGRJUmUiS7Wm/XluslVRhS/mJUh0KTJjskmNuVbBqX9pxWu5JiRuKRMnmxD6/d3mTnlrk25StIohVqhx52TIQABCEDgU0DgB4edZQfsu4cvTYqOR56aYH92Qb3KgwndkZpbWq1/VYWd9sv9bSvnfokLNCoFD12c9A8sn99iYzvlqB8510v5ciROv+AvNmHSmz6MWOMXJ/3Bmppb7G+XneJ/v/WeR7zYU92/yrtoFtU12D0PPuUDgc+97GZ78O8X+uPUGnzWnAV26VlHZt1nIW4DAk0hqLMmBCAAAQh8agmEVtjKkpE4k+TUUODuoobMuSxpIWgOBf1KmImWL6XJlJFTZO6i5sR9RvcisUQOIHWWSjNWlkCjfJxs2TESQdT+O8n1IuFFpUu5yqCyuWIyXWsaZ0/0PDmmdA3qCKU9INakeYI4BgIQgAAEIAABEUCRcMNlAAAgAElEQVSg4TmAAAQgAAEIJBCQKKOg3WytsHOdLjdKaKOdL+jglNEH/Q4nmDQ4kSaNKBNdJ4gnacKBw3kSaHKJJfHrWBkCTVJob+hItSBHno9EHAlSyovxf8mJdYMKZVBLXUROjQv+zeWKCdeo+ycWEsjSjLgzh9yaNNQ4BgIQgAAEIAABBBqeAQhAAAIQgEAWAnLHtLj2ziFPpreg0pTuROfOVL6kD/kSZpI6E2XaY755MppjRQSabG22kzJokgQalQ4liSoScRT+mylQOV4GpfuqwOJMgcZRjpovCGNJz0CSM4cW3kkEeR8CEIAABCDQtwngoOnb95+rhwAEIACBZQS6WmGrbKnTl6ak/VCeBDBNhklUlFnqaqYkxMitE1wv+Yo80T3lmyfzUQk0SdeQ1No7qU239q1j1GFpcWNbztuivei+uFtupa4UKVM3qDBB2jBhHa85y1wr8aT1dWzIramqKLYSJz4xIAABCEAAAhCAAAINzwAEIAABCPRpAuq6pDyZaN5KkpiQD7BspTlJokx0DblP9CE+zQf/+N7ydcMEgUbfs7XEjq8RLXHK5qBJYqo5snWA0npJDpy0x+i4qFtH98e3JnfCTlysiZdMJd33pGvMdL5KopSrI2GnygUNV7q9MCAAAQhAAAIQ6JsEEGj65n3nqiEAAQhAYBkB5ZDEw3BVTjOgf6nlyjvJB2DIJclHlInOvyL7kWggp0jaDJWPUqDJtQ8JNLX12dtjpxFo0gb6qmxJQcJtLlsoOuJiTbMrcVN5WVIwcZhD8wb3U5rnQ+sNG1TenZkjB47mYEAAAhCAAAQg0DcJIND0zfvOVUMAAhCAwDICEi7qlixfEpO2DXMSSIkrQwaWWecyLUDrRcuXks7X+3JyqDtQpmyVpPN74+pIK3SEtdM6aHIFDyeVEqURmtIG+iatpeuSeKLMG4kmGrnKoAKHNPNG71fcGTXQiYJiz4AABCAAAQhAoG8SQKDpm/edq4YABCAAgWUElDuzYHHrcjwkOix2wk3cZZEGnEQZlaqED/fKlZEw05uQ37BebwWj3pRHpXGrRDl8HAKNxBd108rFMCloOF+WQdxqaXdOGpUgLRNPGt291GvRgOF8y6G0l7igNGRAmXPsUOKU5s8Yx0AAAhCAAARWRQIINKviXeWaIAABCEAgLwIzFzQtd3y+7bHjooxcMsq3kcCTxv2RtOGQVeK0nryGRCJ9KRsm7QiZLGnPiQo02crCksSTJPeJzhfTeDla9JqylS5Fj5GQMnxQV+5L0si05xBWHBdrNFe1E3DStO4O6w4bqLKuVh8G7QUet68i59xhQAACEIAABCDQNwkg0PTN+85VQwACEIBAhIBEBXVvig6VmqjMJVcwby5RJt+5km5Ibx09EhRqKvPL0ymEQDNySKVlEsoClzTtrpNEHs2VT56PBJT57tnIJopFxRoJLHLUpO3+peNHDP7wmpV1o3vMgAAEIAABCECg7xJAoOm7954rhwAEIACBZQRUyqQP1tGRrftSXJRpbe+wJU1dTplsI9tc+dyANAJFpvkkBAyuKc8r8LgrzLgktesmiEe5gpWTHDBJJVxaIym0OY1Ak0/5VtKeorx1f/o52OoEJUEnUxlU9Pi4cCb3jfgxIAABCEAAAp8GAu0dHbbFrodYaWmJ//9feVmpbTZmXfv1MQfYqLVW/zRcQo89Tpk63Y75zZ/swb9fWNC9I9AUFD+LQwACEIDAJ4FAU0u7LWxYPig4uDoksMhREzJlJMooCyWaQZJ0Hfl82M80V2/aZYd55ATJJ2BY4kGacp1okK5ECYlBKh3K5DiRQNPoOGdilqbsKI34koZx2gBkXdtQxy1NKZQ4R9024lfhsmSqKoq7xRp1hIqKePF9rFZd6nKLCAhO+nPE+xCAAAQg8MkgEASaR27/g60xbLA1NbfaBX/6u82cM9+uuej4T8Ym89gFAk0esDgUAhCAAAQg8FES6HQZILNjmST6gC7XhsQDCQ69EWWie+5thkyYozfdmMK5acSN6F6TyqKi7cLrm9q8mLPICVyDnMhQXNzP2tqXml6PijG5BJo0YkjSNaSZQ9eYJmxYxyUxiD+P2cShqFgjLq0ulFrinjo2RVtyr7Ea+TMf5Z9x5oYABCCwKhC46CLn0Gz8+K/khBPMqqp6rhsXaPTuM+Mn27mX3WQP3HyBP/iJ5ybaJdfc7v5e0G5rjxxmZ594iA0bMsj9vWqpXXDFrfbo0xOs0/287ZZj7KwTf2IlxcV21Ol/tE02WMcmTXnXpk6bYd/+2o5WUV5qTz7/qs1bsMh+/9vDbYx7PzpuumOsvfH2+9ba2mbTZ861DudqvuysI23kGkOtbvESO/MPf7PX33rP57x946vb2+EHfsuffu0t99tt9zxqAwf0tz122tbu/s9T3Q6aq2/6l9039hnvDtpuq8/YSUf80LuFdI0XXnmrX6u0pMSOP+z79uXttlhpNwUHzUpDyUQQgAAEIPBpJjBvUbP7S4J5l4zKYPQ/ZI1m94FaJVArOiT2xEWLfObMNxcmOndSvkt8H9lyWtSZSnk2Xe2y230IskY8JDiIG56fC/bVsSqzynb9EldUIpTL5ZPkjkmbLaN1osJItnuQTylUmv1rnahYU+Ser/rGtu6uVBKgGBCAAAQgAIFcBIYPN5s37+NnpDWHDu25blygaWxqtjN//zcbOmSgnXDYD2x+bZ3tdcApdtPlp9qG665lN/zjQZsw+U3749lH22PPvmyXXH273X7tmaa/bX3/F2faT3+0t3191y/4MqPmlla76vxf2XsfzLFvHnSqnXn8wV6oufJv99q8+Qvtt8cd1GMzt9z1sF1xw9123w3n2dDBA90+bnCiS7Ud89N9/c/6h7Yzjj/IGpY0+bVOPnI/L9786Ihz7P4bf2dDVhtgJ597jU3839teoJFwdOm1d9gtV5xuVZUVdsxv/2Rf+Nwmtv93dnP7Oc3OOO5A22rzjUyum7/f/bCddcJPVtpNQaBZaSiZCAIQgAAEPs0EJDrEnTJpS33SXLccMG0dS3N2Ico1T76Ojuhc+vA/1wlQ+XSACpkvoYyprKTYu4jqG9u9QBMd2bo4BUFCwo70rgV1rRmzepLElTQlUBLWSp17p76pZ5ZQnGlaFvEW2LnuTb6tzMV02KByl1PT0V0GpdcYEIAABCAAgU+bQNO/qsL/o5YEmtFrrWGXn/tLG732Gnbvf5+xBx553q6+8Dh/SXp/u70Ot5fHXuedLE3NLV780Djj4hucYDLEfrb/3l6g2daJIft9e1fvhPnsrj+xJ+/+oxdR7n/oOXvwsXH2p/N+uZxA89yLr3W/fvOdD9lrb0yz3536U9vlu7+yP55ztG228br+HDl6Wpz7ZV23x6demNR9ztPjJtk5l97kBZrTL/iLv4ZD9/uGP0dOoOv/8R+74dKT7ZDjLvTXeeD39rR11nSK2UoeCDQrGSjTQQACEIDAp5NAa3unza9r6bF5CQNDnfMln/yWbFefpitULnIrspdoO+e0d0etqNvdX4xKiou6nS9xYSbMldRmO+w9W/lTkviUxqGS1vGS5MQJ15TWaaPj8xFzdHxc0CF/Ju1TyXEQgAAE+jaBT7KDRmLKcy+9Zqecd43ded3Z9u+Hn/OulkEDa7pvmhwscqwUFRXZxVfdZu+8N9MH2M2cPd8JMl+1XxzwTS/QfGX7LbxjRmPTnQ6y8f/5sxdzHnjkBfvXQ896d010yEHzqnO/XHD6z/3L0d+3/Oohdv9N59taI4b59/562wP2xtT3bf3RI23a+7PtvFN+6l9XSdUJZ13lBZrDTr7EuWmmdgtInZ2dTiAaaLdfc4YtWLjY/nzjvfbwUy9ZTf8qO/mo/eyLn99spT2YCDQrDSUTQQACEIDAx01gcUOjXXnDPd6Kqp933WErO/fkQ3u1jTYn0GQSYlY0OyZsJkmESLPptOJCfK605VUSQsI+3d+drM6VdoUyplz7SxJodG5w5HTP78QvlRqp/Km0pMjK3Vc290uSw0bzp8noSePECdeZlHkT5ZFvh624oLO6E8MkXjEgAAEIQAACuQh80jNotPf/O+TX9vMff9NntIx9Yrx31MSHHDOtbW0+k6bY/UPQry/8q63pSo4+CoFGDprLzjrKNt9kPb+N3//5n86Z02HruE5TzzjXTNjf48++Yue7kGMJNNrPhuuuaQd8d4+cD+RTL7xqJ579Z3vmviu8K2hlDASalUGROSAAAQhAoCAEJM5ImFEtsb5/59DfeIFGYXO9GbNqm5YrA8oVbpvPGivigAnr9FYskiCgLJ1sXadCGVO56zzU4o5TGVM+HYzyEWjCtYR25Sp/anelXxLIFrtMlkwjlEple1/n6D6FAN5s90VrKsg4yRGleyWBZnZtc6pbnK9wFnU0aa0RgytTrcNBEIAABCAAgU8KgXgGjRoujHvldTvy1Eud0+RMq6musn0OPt3nuKjtthwq/3Khu6cevb93yWy56QZ20Pf39DkuR7tg4D133taO/fn3VrqD5qxLbrRO5+5RBk1d/RL7/s/P9D8Pchk1Bx9zvt33t/Ns8KABdtyZV/q9+AyaZ162q1zejUqaVML1z3897v4xqdjt8Qt28K/Ot0tdALE6V30wa57/u+dz/7oSgeaT8mCyDwhAAAIQ+OgJSHxR60b9j1P/wz/5iP1szIbr2EHuf6wSZ0Ka/2nnX2fbbDHG9vnaDr3aVG1963IZMWmcGWkXy/eDfHxefbBXt6Rou+Y0a2fLv5E4UuVaO0ugCQG+oYwpHwdJGoEm23wSKNTRSPtoaevMGCScpnwpTUmScmrKnFMnl9Ajnmk7QuV7rI4PgszMBU3+1mlP2jsDAhCAAAQg8GkiEAQadTbq+v9hka3lOjWpQ5I6ImmELk4K/ZXQcdov9/fhui9PfsuVQl3rRQ85W3bdYWs77YLrfGbMvQ8+s1JLnCTKKLw4dHH67l47eWFI4/K/3mV33P+EVfevtO9/c2e70XWDevgfv/fvXXPzv+yeB5+2dpe/pzyac0461IYPHeQ7PV1z8/3ehVNRUW5HH/J/9tUdt15ptw4HzUpDyUQQgAAEIPBREZAQI1fM4QftY488NcHOv+Lv/l81ZIcNQ/8TVZvF693rA5yI05uxpLndl/VEx8ooTQrzSchQR6h8BZZwfr6lNOE8CTRdnZc6vPgQrkkZMw3umjM5a/Lp/LQiAo32GASYFueiUZeo0pJ+tsSF/WpvCjZOI9BIvJq/uCVnELJygORATgoSzif0VwJLRVmRF87SjPjzJHFK+2JAAAIQgAAEIAABBBqeAQhAAAIQ+MQTUOr/2Nsu7hZe5JTRCHkzEmeUQyN3zSPuu1w1++yZv4tG5T0LFrcux2NFnS9hQpUaKYxYrad7M6JCSz7n67yQcZKrG1N0zo9ToIm7lCQiSSSpcsKFMnBKXD6LSqByCStpHD/iL1FKQlWukVbI0Rz5HJvp+CEDykylZQwIQAACEIAABCCAQMMzAAEIQAACBSUwwyX3y/miBP9dXMhvJmFFAs2d153V7ZhRqdNRrl75ISfaxMe4V6b4cigd35sRSk+i566o8yXMtaLlUr05X2VM1U7oUAtMlTFJHErTbjuN4BGua0UdNNmEJ5UDqfRJIshSt+k6l1GTLUcnjaCUpgxK15QmzyZcez7Hhrl1D/Tls25cQPDKChbszfPOORCAAAQgAAEIfHIIINB8cu4FO4EABCDQ5wgoW2ZfF66m0iW1KlTp0hHu57hIoxInvRZ9fbcfHG+Xn3O0z5+RyBPKnVQCddOdY30JVG/GAlcmoyyU6FhR50uYS+UwcoYo66Y3o6ucptiV0+Q+Xw4UHSdho9XVTne4EF51SUg6L7qnj1OgSXK2SASRQKOW3/HyJ+05bXemNGVQmi+ftuTiNHdRcyrRS3NHuZaXFvnuVgwIQAACEIAABCDg/07j/sLjqrsZEIAABCAAgY+fgJwzEldUkqQh94vKl+LOGJUw6Ssquijxf5cvbWUDaqrsVHfOAfvu7ueSu+YkFyK87ed618lJGTHKPokOCR0SPZLCZZMIag65OJK6CGWbJykPR+9LAIqXMel1uWjyEYYkJMyva/HZNUkjOGhyXVsuh0uSCyWavSMxRtei8ieVpKlcSQJUGq5pS9XSHpdvtyfd/2GDyru7Q+k6BrgMGgYEIAABCEAAAhBAoOEZgAAEIACBghKItskOG5EzRl2adt1xq+69SXiRiyYaDKy2hkGIGffyFHtx4hQb6UKDt3FhwtHw4HwvsKml3RbGAl/VnlkfpOWuWdGRphQn1xpyd8QFnngZk3JbokPCgESQfPafj4skCDS5WnPnEj2SWplr/tr6ngHAofxJTiFl1KhVd/yYKIO0Lpu0x2nutG27wz68eObEshAovJpr+V3pSrgYEIAABCAAAQhAAIGGZwACEIAABApKIFNejEQbCTIhADhsUG4btT884sB9bMrb071TprdlTLkuutM5RmYvbO5xyIJ5c23tNQZaY8eKl6P0tlV22FAQOiS61FSVdLtl5CTJls+iczMJO7k4BNElHwdNLoEmV8lUUneqpHIrZdj0d18a0e5PcZEqjcsmHzEuTXep6B5UyiWe6hamsYZzKZE/U9D/BLE4BCAAAQhA4BNFgBKnT9TtYDMQgAAE+h6BeABwXLRRpkxw08gp8+gzE3zuTG+6NKWlO89lirQ5R0YYb74+2V545lHb9HPb2VZbb5t2mozHDXKuiSQxJdcCEmgUMKsypmZX4iNBIo2IkiRyxNfMJxg5jYMm1/pJYlDS3kMnJZWmqWxIYk1b+1IfihxEKzltykqKEsvU8hFdkrJzMjNt9c+WBDZdFwMCEIAABCAAAQgEAgg0PAsQgAAEIFBQAvGW2RJhLnBhwaEL0+6u5Ol6F/i7ImVL+V6gwnTjrZgXzpthYx/6rxWV97cdttveRqy5Tr7T+uPl9lCsS3BRpJ1EZUw1laXOcdHlEsnVcjrTnPmWVkk0iQocufa5ogJNkrsnae9xoURlSl2BzF2uGglaTg/xI4lb3OWS67rzcUPF82q0N4l1DAhAAAIQgAAEIIBAwzMAAQhAAAKfCAIhX0Yhv8qPOd+1yN7Vtdv+sfu9UEMZLgtjnZL0gb/Y2u3uu++xdz74wAlGI2ynnXezmgED89pm2k5MmjRexrSkqcO5Q4p75cBJcqHELyKp7Ch6fJJAo+vobflTmkwYZdiE1tXx6wjByeKuY+pcCHSu9ghpW3FrnbRhwjpW+xjoSpxCftAgl2mkoGMGBCAAAQhAAAIQQKDhGYAABCAAgU8MAYk0FzhhRm234+20C7HJtvbO5YJ4JRQMda4SfcCe/MqL9tzTj1pnUYl9/vNfsM222NrKy9OVq6TJOAldl9RWWk4bCQuhjEkOHP0cd/gkccon9FdzaZ0WxyFXrk1YM41Akyv/JZd4lCTuaA9pyrEk4shFI7bx8qcou7Rts9PsKzpvKMMKDp7VB1W41ufLbD1JN4/3IQABCEAAAhDoEwQoceoTt5mLhAAEIACBfAnMqm1azmkhx8QcFyAsB4aCg8c+cJfVNbdZeVm5fXbTTVMLNZmcF6EsR2VMXQJMu8W7Meka4h/0015XGhEjOpcEGmWlSBxKGmkEmlxdpHI5UdJ0oErjDpJANd914dK9C+3KJdhI6BLr4KpJ64pRVo0EtLSt16OtxHWvRwyuTMLK+xCAAAQgAAEI9DECCDR97IZzuRCAAAQgkI5AbX3rcuJEvOynpaXZnn/qUZvy5hRbWlxqFS64d/PNt7CNxmyWs/QpKhaEMqZQglPfmDv0N58SqeiV5htOnI9TR9cjZ8hAV7YjASs+kkSWXKKIxJSK0uKcQkgaUSXTMWFu5ftIDGt1jqFs1xC/pnyyanRuVETSPdSzxIAABCAAAQhAAAJRAgg0PA8QgAAEIACBDARUWqS8kuiQaKERD5pVydOLL42z5vYOay+vsfKGuTZq3Q1t8y23zhgmLMdJqztWnZgkXoQw3jTdmIL7Y4Fzg+Qz8nHEaN40Ak3YS2lJP+twbptS1yVJLpV4WVSSQJPLAZOmq1KSgyYpx0bvh+5PnZ1mi5a0JpZ25ZNVEw8IlggkJxQDAhCAAAQgAAEIINDwDEAAAhCAAAQSCLS4FtYLFrf2OCqXOBJKnhYvafRuGo2lLqNmreHDvKtmxJprW1VlZXd5TZfQ05axjCnX1qJZOPncxDSCS3S+XMcHDuEaVJalzlcKAm5f1p482gEqV+5OUpZLkkCTdL72qGNyZeCE65ZoUu4cO/0cZIlO6pal1t2ZQoXTZtVo7i7XU5Fj1CX4DRlQ5tYpzuf2cSwEIAABCEAAAn2AAA6aPnCTuUQIQAACEOgdgZkLmpY7MVc5jUqeJox7xl6dNNE6ygf4c4tbFneVP1VW2Rc/t5ltudU2VuIya8xloaTNL4lvIk1JT/ycbO6fbGQyHR8XZoJTJp5BEz9Oa6ittESc+EgST5L2LfGnpqrEVJKWbaQtC4vmxMTLn5qdYBeuN+6ISXq6ouVQ/lwXEFwU+n4nncz7EIAABCAAAQj0GQIINH3mVnOhEIAABCCQLwGVEbW0uZqXyFDeipwQbR09X48eo5Knl5xQ07S0yJc8LS0qtX4dbVbSWu+/r73OKNtis01t6IjRqbs/RefPx70RzktyosTZRMOIswkz4ZxsIcHhvBLXrUidsTKJKEnlT0nOH4kvZa60KpfYlfbaM93bUP5U6QQmlaDJGaShkqhcolCUp/gER5EcOvqdAQEIQAACEIAABOIEEGh4JiAAAQhAAAJZCCx2GTQqcYkOhe02t3Zm7W4kwUGiQXtLg9122202d0Gtd9B0llR6saZfZ9d8FYtnWEn/QTZmg/Vt9HobZsyqyXZj8u3I5NfzZTbFGV0smdaRqCGBpbioyL8dLVmKH5/UxUlzDXC5K5naW4eW4tnEjqirJds+u3J8et6n6LFysLQ7QS2pNXmSMykIThJZ1N1qoXMEZSp/iu8zOq+EHbFgQAACEIAABCAAgTgBBBqeCQhAAAIQgEAWAk2u/fLCZbkh4RA5SyQIxB0bKrXpXyk3R7EPAFY3psampu6SJ52vsqd+nc59UznYizZy02iUO7GmvLzCNt50Cxu99tqJYk28m1SaG5gkhETn0LEDnaihLJY0gblJAo3mK3culxbnolFeTVTw0XvZyp90nAQatcGOBw+H/cph44wtplDnbENzSFDJ1TI8KUg4Orfm0zMgZ5CyiiT8ZNufnguJevPqukKdV3M/y43DgAAEIAABCEAAAnECCDQ8ExCAAAQgAIEsBDrdJ//ZsbbR8cBbtWiWK0JihlwmEgHiroo3X59szz31iO/y1FkqJ80AK25r8o6aIvc9CDcqhapYNK1LrNloYxu98eY2Yvjw5XaXVPaT6XKSSol0TrSUSSVcRRJoMuTGxOdPEmjiJUbRdSRmKY8nmwMmzJ2tw1WSw0Z7VemSHDq5umTlCjKOX29ok67XJS7p+iQSSUiK3/9oqZiOX2M18mf4Dw4EIAABCEAAApkJINDwZEAAAhCAAARyEJi3qNnlzbhP35ExckilL32qcJ14JDDkclCE0+oX19lDD9xt82pr/Uty0LT2/1B86XDCTUlLvXfXlChY2Ik15fUzrMI5crxYEymDin/oT3sDJSwEJ0f0nEwZM0nOluj5+Qo04dzg1NHvdY1tGV0o2fYc5kjjJkpqw6250ubU6NhMpVDRluPR7k9RAUkimfbCgAAEIAABCEAAApkIINDwXEAAAhCAAARyEJCDJGSXdIkWxd41IadEncuoyeXKyDStnDQT//c/X94UOj1JnFFGjbkOPxoSaVT21DJgTf9dw3k0rKqt3tYdNdo+u4Vr2z1ihHPkdOXDpB1xoSJX+O/HIdBo3+KpbBw5kDTiWTdJ4kqSOyZt6VK001IunvGSpfixIVS4vyu9UuaO2nXPcS4suar03KjciQEBCEAAAhCAAAQyEUCg4bmAAAQgAAEI5CDQ5PJF1GI5mp1S4pwQSbknuaBOe+cte+LhB3yXJw0vzrghoWZpUVc+iRw0ncWuc5Arh5JI0zRolA8WVsiwcmyqizps5JDB3lkzar0NUnWDkvNHrcOTujJp/Xwya3rroNE60TbamfaVFNybJOAktfEO90lOHAlxuXJqdKwEpRKXK5PUIj0INTUuy0edwDRvmRNryJ/hPzcQgAAEIAABCGQjgEDDswEBCEAAAhBIIKBskWgZkxwf+qCets1ypulV8vT8k/+1d6Z/4MudJMwoj0bumZBTIyEmOiTkqAwqCDdVC6b6HJuKpgU+q2akc9WMXndDGzJs+dwazSMxo31ZuVaurkxBoJEopVbjSWNFBRq5kKIdlqJCjYJ45UDJNpIEnLTdq9K2Lk/rtNF+u9Yu8tcmlur+xIAABCAAAQhAAAIINDwDEIAABCAAgV4SmFXb1CP4N60rI2k5iQt33/tve3XSxO5W3BJl5J4pdjk0KnGSaNNavbp3zeh1fZdQU9TuXu+/ulW6UOGmQaP9d4k3en1A/ypfCiV3zeChw62muqpbIJColOQS0b7ThAqH60sSaJSZo5Gp01KuwGMJHHK2yIGSSVBKU76UNlsmSeiJXmuSuBWOjYo52uuIwV1OKQYEIAABCEAAAhDIRAAHDc8FBCAAAQis0gRmzJ5vV95wj02ZOt1f57knHWpjNlwnr2vOJGroA33IFslrssjBEjYWuxyb6dOn2X8fvN93eZKTpqvUqdRKm2qtpcaJNE50kVOmtNH97kQbvd7svqvkSd8rF71njYM38L8Hd03/ea/7laqWttrIkSNsvQ02si1ddk1ze7ELPe5M3LIEhcE15SvFQZNLhMnVhSmIRBJE4u25dQFpRKQ0Ha80z1AXoJzLqROApRVydLzubxBzgtiUCJ4DIAABCEAAAhDoswQQaPrsrQ3+ZjAAACAASURBVOfCIQABCPQNArv94Hg7YN/d7cfuS0LNI09PsDuvOyuvi5fzQ4HA0aGw1zTdm3ItpDmaW7vySVTy9MQjD9isGe93Z9GE8GAJMhoSY9SeW2VQZUvm+lyaIM6ULZmzrANUvXfZSNiprHvPWlynKDlrJN7IlTNyzXVsxJpr25quHGqE+znXSOqgFM5NctAkCTQqIWt1Lpn4iAcVxzNqdLyCd3O1ApcAJL65XENpy6DyEXK0t6iYM7B/qQUnUV4PHwdDAAIQgAAEINBnCCDQ9JlbzYVCAAIQWPUJyC2jrzEbrGMDXFmPXDNHn/5HG3vbxd0Xv+lOB9lrj9+QF4wWFxK8YHFrj3Oi4bZ5TRY5ONMcL417xia4r07npFEWjZw0GnLQaJQ1zHXlUCW+vEluGZ9L01pv7WU13mmjIQHHu2xc6VOFK33S75pHrhqVS6mNd3lLnZVbuy+FklCTKWg4KYA3XMqKCDS52mRLOCl1GTT1Te09EAehRvk0CnHOFdib1OVJE6dtW55P9lC829OQAWUug6a4t48K50EAAhCAAAQg0AcIIND0gZvMJUIAAhDoCwTkjrn7wadt2y3H2PhXptjJR+5nu+ywlRdpJNhojHt5il35t3vshktPzhuJuh9FRxAJ0oToZlss2wf+WTOm22OPPeRdNQoQlggjMUYii0qg9FqHe02uGIkycsvo/aKOdmurGuydMhJwqmqn9ih90nH950/xr2nUzJnkhR85bIK7RoLNKJddUzNgoA8VTlP2syICTTg3U7vypPwYZbxUurBmBR9ny4VJcw25yqyi9y5Xlk78HkdFH5WLrT6owopcKRUDAhCAAAQgAAEIZCOAQMOzAQEIQAACn3oCixsabXdXyiSnjHfOvDXdDvrV+b6Uac01hnZf32nnX2ff2mMH2/ZzY/K+ZgkxCquNjnzySDItmCtsuKWl2R5+6D82c9pbvuSpX4cLB3bf213b7fCzDxNu7RJjJNb4kij3pbIm/R7Cg/VdjhqVPslVI+Gm2Yk1EnuqnUizZNgmtrS82qo/GO/FHzlsBlaW2aabbmbDh4/wQcPl5RVZmSUJNBJSWtu7SrniQ+fW1rf0CGEOxyQ5WzRvu8vTaXddoDJl1GieNPdILptFDW2J2TxpyqXC3qOij7o36ToZEIAABCAAAQhAIBcBBBqeDwhAAAIQ+NQTGOccM3LQRJ0xEmM0zj35UP9dIs7Bx3SJNr0ZCvNtcFk00ZH2g32u9ZIEhMmvvGjPPPukn0LiS79Ot4el5kqVhvuf5YApct9VEiUnTHe7buekKXflUPWrb+7yauZYhxN2dEy09EnOHJU/KatGgo3mD+KN1lNnKGXdVJQU2xAn0kTdNdFrCmHHg10ZTybHjcSKbDkzuRwuSQG/ccEknlHT4Zw1KqGaV5e7VXjSPQjXmrYVt46PHlvtulgNcBk0DAhAAAIQgAAEIJCLAAINzwcEIAABCHwqCEiEmTlrvu2y41beJRMdEl+23+tw76AJjhll0RzkBJmHluXPSMBRu2mFBes9lUFt48qhog6bXCCaXJDtQueyiI5oyG9vIaYReVTy9PjDD1hd84frS1zRkGtGI2TUhH1ItFHXJ70vEUbhwhoKGpYIs2ToGCuvn9H1WiSrRkKOcmt8xo0EmwVTu8ur5KypaFpgQ2uqfNCw2nivt966pgBciSHFLhNmdm3zcih6K9AklR5lK4+KZtS0OeeOunBlG2ladetcX6bkSr4yXV987vixq7kw6EoXZsyAAAQgAAEIQAACuQgg0PB8QAACEIDAJ56AhBYJKRJY7nE5M/HSJV2Ajtlnzx38VxjfOfQ3dpLLolEujUqgDj9wHxs/cYpJ7DnioH16HJsEodOV0cxe2FN8UAmOypRyhdQmzZsrJDecK8GhvKjD7v/Xffbmm290izLhfYk1EmhU8qRMGgkyKmfSUC6N8mnU7UnuGgkv6v4USpuipU8SZjSXgoRDuLAEm3JXLhXKo4qc0DNg1gS/htaq6Wy0MWOc0DVyHfv8VptZW/vyeTArItBkc97o2pIcLXLg9HdfmfYU2CnMV+6WpCyhtMdp3q6uUEW+bEpjDSfskD+T9CeB9yEAAQhAAAIQQKDhGYAABCAAgU80gUeemmA33Tm2u3zppjvG2o3uKzhjwuYl3FzhXDLR1yXa/Pg7u9uuznUjscY7aJb93puLnreo2eWUuPqiZSOfD+3Z1pOI4LQfUyvv+AhOEIlACsFVxyKVPKnTU3N7h3e4yCEjd0z4LuEk2p7bZ9Y4sUZCi4KA9T10c5LDRiVQej+UPgXHTHDVBMFGIo3WaRyygUmk0RwN7lyN8tY6s/cn2gdvTLL9DjjEdv/qLi5TZqlvTa7w31wCTa7yolA61eZyZjKNpNKkwFbnZ8uoURBxiRNpkkS2fMQ4ZePounVPde8kJDEgAAEIQAACEIBAEgEEmiRCvA8BCEAAAgUlIEFGJUnqyhTGbs4Nk8kBIxFmV9e56XDnjtE5+j0EB6sMKl4ale+FLWpodVkqPYNuRw6ptHiHp3zmlduirKSnQJBJmInOuWDeXBv7wF22eEmjf1lCjYQZZdDILaOMGgkuLa6cSaG/asEtgaV5tdH+uxw0ctR0nbO4O8vGCzCuw5NyZ4IYI8FGgo/myibSaI2yhjletHltwjirXVRvJ5x4ku22684+GLjUXV8Qa+JscmXQqPxrvgtndlpPxpHUoSkpo6bVhT5HxZRc9y2p3Cp6roSl0FWqypU2qRSOAQEIQAACEIAABJIIINAkEeJ9CEAAAhAoKIFMAcByy+gr3i5boozCgWe673LLqNxJmTMra8jBstCJNPEP4woQzubySFo72q47SZiJzqUuTy8997i9NvlVH/6rIaFEoksYEllU+uTdMU5g0ZAjJpRBhVBhhQ0rSFjv6TUJOJpLjhs5aaLCjOYKr0edNDpex1XOf9PmTH/HHnzwQdtwozF20kkn21e/urPVN7Yv5xJKyn/JJcDk6oAVrj8po0bHqfN1fVN7xg5TUd5psoLC8VFnzyBXPlXlSuEYEIAABCAAAQhAIIkAAk0SId6HAAQgAIGCE5BjRmJMCPQNocDP3X+ld8VIrIkG/q4Mt0ymi1bgbLwjUK4SpbTg9IFeOSnRUqY058rVMe6FF+zZ55+ztqYGL9SohMkLMc5JI8FFwolKmfRe6AKl173Txg3l1qjEScKOd924bk7950/x7wWBR224ozk0EmhCSVQmkab1nRettKPFOjs77YknnrANN9zQtt9+e9vvRwdYUXl/k3PFz+/UkVxdlnKVMKm8rKaqJGcAcFJGTaUrb1LAca6MmnAfksqpwnHalxwz4TlZfVCFD09mQAACEIAABCAAgSQCCDRJhHgfAhCAAAQKTkAdmOSOCS2ztSGF/l6/TLTR+yNdiHA0IPij2vSs2qYeJTfxQNh81g2OmXIXAqwSoEw5NLnmC+LQ7LkL7P67b/Vdnvp1tHlRRmVOba7VtobCgbu+O7HGiTASZJRNE9w2wWWjAGF1eOoqc+py1GgulS7pWP0soUeumiSRpsI5aZ59dKyVlJTYJptsYh988IGNHz/eDjvsMNt5191t3Q039XuSyJQtoDeXgyZTaVicVRpRRceIvTJqlBsTSpOicyUJSdFjo1k1cgiNGNzVZYsBAQhAAAIQgAAEkggg0CQR4n0IQAACECg4gdAy+9uuZEn5MuNenmKnXXDdckHBH8dG1bJZuSph5PPhPZwTL2VSTkkmYSDpehRw2+W6aTeVPE1w4cGTJ760XJen1v7Du3NmonOWN8z1Tho5ZYJLRuVN5S6Dptk5aSTSqAuUyqNCsLAyazRCGLFKopRPE3fSKLumdNF0W1I71xYtWmQvOKePuj0NHTrUJk6caBtvPMY22fSzdvDBB7k99Gybrvl1XUNdBs2cWOessP/otWfilOa+xNeQoyaTUJM2SFj7iGbVSESSQ4gBAQhAAAIQgAAE0hBAoElDiWMgAAEIQKDgBKL5MnLLyE0TSp4+zs3J5SLHRXTIhSEhIVuYbThWgoA+wMdLmXpbJiWhR+KOwovDePP1yfbcU490d3mSayaMUMqkzJlQ5lTkfpbrRkMii1wywUGj10L3J5U+Vda954UbjZo5k3y+jfJsOsoGLNfdSfP4jlBzp9r4px6zzTfv6vj0+uuv24wZM2ybbbZxolKLTZv2nhWXltn3fvBj2+Pre9nAgYP8cYFVNneNmMnxEg9tDteaiU38OelyPxX34Kdj4kJNRWlxd1empGctWlal8ik5ahgQgAAEIAABCEAgDQEEmjSUOAYCEIAABCCwjEBLW4cryekZFCyXRIMTbkK2ShyWxAblpZSVFHe3y44ek08L5+h52dp81y+us4ceuNvm1db6w0M77lDi5MuVXKmSypzkiNHrIZNGJVByzYTyJ70eSp+WDB1j5fUzvLijc0M5VLETaSTGSLBRxydl3qgFdxBp5KSZ+e5b9tprr9mIESNszTW7RB45aSTSSKyZOXOmvfjSS/aNvb5pa6412vY/4EAbufqQrBkz8Q5NceZpXC/iHkKCMz3gQagpKnJBwhlCjuPnqKRJAs3s2mb/1pABZVbuxB0GBCAAAQhAAAIQSEMAgSYNJY6BAAQgAAEIRAjE22rLzaGhUqPoSBJmwrHRTk75gJYgMNS1dI4HF2uOUPL06qSJ3VNKqJEYIxFFZU3BUaMDQkiwhBe9LueMypr0u8QclTmpNXdw10jEUTmURJoml0mjoeNV7iSRp6Sz1Zr6r2Gt1atbxaJp1vr2i9bcsNhn0ixevNjn0UiYqampsfr6epsyZYoNGTLE1l13XZs/f749++yz9uWv7OTKoLZ0zpq9be11RvVAI1FMokm27llpXElpW2dLdJE7KltGTdiY3DgShlQG58UaFxBcJAWIAQEIQAACEIAABFIQQKBJAYlDIAABCEAAAlECKrtpWdaJSK9LYKl2bgx9MNdIK8yEOXMJLUnkk4JwVfL07LNPesFGI7hpJLBIqPH7dWKNSpVUxuS/O5FFXZui34NYo2Mbho0xlUaFdtsSYCTwyFlT7UqflGcjUWfgjHHdAo/mbV8wwx5+8AFrbGy0XXbZxa8tYaa1tdU22mgjKy8v92LNiy++aFtvvbUXbxYsWGCPPfaYfeYzm9nmW25tW2/zBdv+SzvaBuus7nlLNMk0khw2OkdtuJNapEdbgWfLqAnrD6jqChpWGZyCnzU/AwIQgAAEIAABCKQlgECTlhTHQQACEIAABJYR0Id6lTRFh4SSeYtacpYy5QKYNscmPscwF6Q73wlGufJvQsnT3Lr67i5PElAk0PjyJjlqXKmTBBYJKaHESeVNctL49tsuaFjfNYpdi6h+LQ2+pEmCjVw1Kn3SXAokDlk1WiP8rDKoiqb51j7zDXt5/Av2/vvvW0VFhQ0ePNgFBm/s53311Vf995BX88Ybb3jxRm26g3jz3HPP+TKpkSNH2qj1x9guu+5mn9t62+XQymGjrKBsAo5OSGrDrWOirpiwSDahRoJMCHuWYDfAZdAwIAABCEAAAhCAQFoCCDRpSXEcBCAAAQhAYBmBppZ2W9jwYVCwHDPDBpVbZ6fKnNqsqeXDLk9poUU/3Kc9R8elcYHI4TOof5k98J//2MsvjV8mzHSVZakLk8qXQntuiSohLNj/vCwEOGTUhL1JuJFzRgHB6vYk14zO84LNkA38e77T07KsGoULSwjS62UL3rGnH37Qhg8f7h0yyp+pdXk52223nRdelEszadIkX/I0evRov6R+l1gjZ42GnDYvucwadYZasKDWRq+3gX12i628WLPp5p9NFF+izphcvHPl1MSFGolCIX9mtepSFzZMQHA+zzLHQgACEIAABPo6AQSavv4EcP0QgAAEIJA3gU5XxjLbdW2KljJ1OHVmSXNHjxbc+Uys8pjW9s68z1cpT6MTjDIFFEf3p7IsuUmmvfOW7/LUUL/YCzVyzShzRkMOmBD0qxKmDvdehSt1Clk1oSQquGokulQ6wSXk02gOCTQSZoJIo/lDDk23YOMChUtccHDdnBn28ssv+7UlxEiomTVrljU0NNimm27qX5MQ8+abb3a7ZnSshJmysrJup00Qa+S80c+1CxfaLjvvbP0HDM2YX6M5sgUsx+9ZmpyaaJiwyq50L9ZwuTXkz+TzJ4BjIQABCEAAAhBAoOEZgAAEIAABCPSCQHNrh5UUF3U7ZnrbiSksndRRKNsWM4XhSphRWK0cHHFHj4SJqrJOe+TRx+ylZeKI5m6rGuyXkKMmlC6pe5O5jNtO56SReCMxRiKNSqAkwCinRkHB8fBgHSNhR8KNukTp92YXJCz3TFSwUXDwwnlzrKNjbSe4zPQuGQkvyqORUCMhZsCAAb7ESWVNctDoGJVEyV2jod81QlmUBBqVQW2//fb+9WnTptnUqW97oWbDDTfuFmzSdHnS+SqDml/XJW7lGrp/FWVFTrQrcuVmS620xLV+YkAAAhCAAAQgAIE8CCDQ5AGLQyEAAQhAAAKBQKMrY1rU8GG77bSOjGwE40HDaUlLaJAgEzpIBTeHyrCiXaWibpqFzuWh7kezZky3xx9+wAXlNvqW2BpdLbRruvNmJNKozClk1oR9SchRWZScNvWupXaFy6BpL6txbpt277jReTUuMFhzhTIpCTYSbiTYhADi1nfm203Xfs+JNHfaXns94qYfLVnFCy8qdwrOGokua6yxhs+tkYCjEXfWhMyaINaoVGry5Mnd7huVU0mwaWxqsq98ZWcbNXpd23m3byzXISpcY7xtdq57EnXaDHTZMxJsGBCAAAQgAAEIQCAfAgg0+dDiWAhAAAIQgMAyAsqZWRgRaPTyyCGVFm/BnRaYBBRlmGRqmZ1rDgk7Vc4pI0dPV5lUh28/HXV8yGWjsFsFG8fzcSRCTBj3jKkdd2NHP58jo6wYDZUk6feS1vruVtsqYdII5U4KDu4qk+oSZpRJ01LdFSgskUbCjUqhFBKsTlASacob5naXQcmFUzTzAy/S1NYOcC6ZKueOucmLNQ0NG1h19dQeIksoZ5Kbprq62gs46vYUF2vCcaEblPYs0Udhw0Hg0TGPP/64rb/BBrbGiLVt889u6TpEfdln2GhIdBvksmTS3JNo4PAgJ9BUIdCkffQ5DgIQgAAEIACBZQQQaHgUIAABCECgTxM4/09/twHVVXb4QfvkxaHN5cXEP7inCezNtUhSy+xM50qgkbCjgOKQMxOOC26aTKJNfK7Ojlab+OKzNu6lCV6gUUmTOjv59tnudwkwS8urrcxlx7gmTi4UeIwXYdpdCLCEGYk06uSk8ie5ZnzuzMJpPjxYIcJdzpwBVlU71Xd68g4cd57ml3un+P137Z/Xt7jclnVt/vwdnVDjsmucWGP2iv3whxe6bJmtnXDzvhNixvUQWeSakTijkicJNfoup0w0UFhOmnCMXDkamQQcZeC8/fbb1l/Cz7obukDirezLX9nJRm/wmZzPRtxps/qgCisudsoXAwIQgAAEIAABCORBAIEmD1gcCgEIQAACqxaBcS9PsSv/do/NmD3fbrj0ZFtzjaF5XeCsWlf6E4kmkYNFzpUlsRbcaSfNR+CR46a/nDGlxSaBYI4LLQ5D76nMRiOp1XR0b2oL3dpUb08+8YS9POk1L5xIbNEoaa73OTUqddJQ2ZLcNP2cINOwhitxcmJM82ouZ2bZd7llJMjoGJVAScyRINPi3DT950/xrbn1uwQbiTRy1fRrXWKTXnnZPphW49wu6zt3zCAntuzlvtZets1pzlnze/ezXDMqV3rcvx7Nn5EjRkKNvpRnI0FGzpmok0ZCjEQcOWnkqNGQ0KNw4tAlSq89++yzvqSqvLzCd4naaOPP9HDYBHbR8jTdixGDuxxIDAhAAAIQgAAEIJAPAQSafGhxLAQgAAEIfKoJSIipcW4ZOWY0Tjv/OjvpyP3sAueikTiTr4tGHXtUWhSGyogUFLso0oI7H2BywijbJjpnpvPjOTNy3sxb1OIPDaJNPu2+4/NJcKibP9OefupJmzprgXfTSJCRWCPnixwwEm9Cl6dQ7qT1lS0jMabFHRPKn3SO3Dhy4kQDg717xs0tMafBiTgqpapyHZ6e+vcdtmTJEu9ykSPmpZf2dmLNIueK+aETZbbsRrLRRlc5QeV977QpK/ufDxWOCjH6XXNIhJFYo7n0u0YQdfRzvPQp22sSbDRXRUWlrTZkmG2z7fa29Tbb2pd3+KIpQ1jCnJ4B3UcGBCAAAQhAAAIQyJcAAk2+xDgeAhCAAAQ+dQQkzBx0zPlehJnpfv7xvrv7rzDC+/m6aPSBXA6VMHqbIxPOV1aMRjTcNwpbH/4z5cxEy5zi4cC5blYIDi5yto+400ZOELlwmpbU278f+I9Nfe8Da69Y5qZxgovEFd9S27lqlFOj30NLbuXM6D2JL53FXdek1tyhi5MEG3WBKm10+TXu/airRscqXLhx/gyb/cF0L7qsueaatnjxYj/PtGkHOXeM2mz/1LXl3ti5Xrq6OQ0Z8pRz19zp3TYqhZo8+WkvyCijRkNlTk84Z9C6667r59LvctcoNDgq6uh1rSkBRy6cMEJocegepdd13LDhI+yee+/13bLUXpuA4E/dfx7YMAQgAAEIQOATQwCB5hNzK9gIBCAAAQh8VAQkznx7zx3sW+4riDFHuMyZfdzvYchNk6+LpqWtw+W+fNjJSXPJzaJyo2jpU9rrkgCjrkxy5kRHtANTPGdGQbarOceGcmbU4lndmeob2xLXlxiUqQ13fK/ak0SH2kVL7MXxL9gEVy60pF9XWZAEmLKGOT5vRqVPwWkjF0317EnOZVPihRt9SZRReHBov63W3DqnbMlcL9BIsJGA41t7uzFg1gSb+e5b1tHS1F2GJAdLGHKytLZub+++2+WGmTZtJ9eau6u7k8ZOO53huje19nDXqPV2KGmSk+Zl12a8f//+/vjgsFFWTfy40LY7Ltgsqlts1998h22z5cbd93zIgDIrd2VnDAhAAAIQgAAEIJAvAQSafIlxPAQgAAEIfOoI7P6D4+36SMbMPQ8+bVfccI89dNvF3dcSd9EsbmjsLoXKdcHxrk0qb1G3JLkp8h3xVt1RYSZeshR9b9ESJ0QsWy8ILwvrW5xYEwnIWbaZ4MJpduLSkqae3Z6y7VdummEDK6zEBd/Oq6235194waZMnWpzFtVbafVqvnRJJUxyzSh3Jog15s5T622JMXLKKMdm8cjPWbkTZdTZSeHBChWWC0elTXLelCwLJpaoo6waq33f3n/3bZs4caJtvPHG3hWjETowyQUTOjpNnvwdGzXKiTyuFCrqrlH50w9/eM2y0GG5cB7vESKs+STMKIOmubm5uyRKcyubRg6bIOzIYSPBZuSa69iV191og1dbrbv7lg8LdgHBRS4DiAEBCEAAAhCAAATyJYBAky8xjocABCAAgU8dATlofvyd3W3XHbfq3vt3Dv2NL3OKu2h0wLhXptgBsTKobBctR0tLRIyRQBLySHoDKnRyiufCROfK1TZbx6nkaaALLFaeTQgszuXCybVPnafwYgk6HU7wqXbX1+CEHc07a4YrQXItuqcp/8Z1geqsGOinCh2aJNaoe5PEmSLXBUqlUBJv1BFKQ5k2Kn2SuCPnjEqb9Jrybjr6D7PmyqFdbbrffcWW1C10nZG6nCkqN9KI5sjIXTNw4EAvsEhEKS/fw4kulbbZZmt7d82CBWt1CzSjR99gu+/+nDuuK8xXnaHi82kNBQlH82vkoFEI8c8OO9qOPOYEf44cTyXOxbTYuZbKHXexYkAAAhCAAAQgAIHeEECg6Q01zoEABCAAgU8UgUeemmDjJzq3hRsK+g0hwGGTcszoSxkz2V4Lrppttxzj50jb0Wmxy6CRYyaMaEef3kBafbUK35VJQcH1jT0dLvm0zdYcg2vKXanTUi8gyTnT2NJuTU60STN0fo0TedQlaqEruVLplIYEm0HVXSG4ixpafdeqlpZmm/TyeJv0ugv7Le4qGZIQI6FFZU9yxUis8bk1Cht2rhq15NZ7Ok6vq9RJnZ3kqtHvEnSqnWCjcimVUXW2Ntv70961/736sitdGuHzYzQytcsO7hq5bSSwSFiZNu1A1777TnfeKd5dE9p4l5U1unKoX7msmg+pKFtGJU9RAUhZNU8++aQdfvRxdtyJp3UfLBatTrySGFZdUWLqhMWAAAQgAAEIQAACvSGAQNMbapwDAQhAoI8SuNKVBakUKDq+tccOtu3nxhSMyE13jPXii7oxPfr0BHvEfcXDflWuJMfMyUfs1+2imTJ1up3vujfpWF2Tri0fYSZcsEJ5F0a6NoVyoLmLPmx7nQZOcLhUlZf4DJpoJ6fQNlvf9Z5EkTRDxw8bVG4KAZaYIhEhzcjl3gnn93diRNRNo9d13vw5H9jDDz9is+YvtJaBazqlxnw77SDW6DiVQilzpnzxDC/AqLxJx2gsHrGVF2k05KpRhycdI1eOzZ5ii+bP7b6ETO2y5XrR69EW2hJXpk+fbiUlJV6wkcDz0ktHOZHmn068OdJ3hlKwsAKGa2rediVN57jzP+zEpPOnTn3bTjvjPNvz63v3QChBbX5di78nq1WX+lwfBgQgAAEIQAACEOgNAQSa3lDjHAhAAAJ9lICcKvVO7NCQwHHTnWPt+ktOLqhAE8+XUdivxrknH9rjLgWHTBBvJOxImDnZCTsrMjrdB/PZLhQ4OoYNLE8tpMRzZkqW5Zeok1OuDJpce47n0yyVeODcNCpLCiVPmc7Ptwwq6qbp6Oz0IcVRV81br0+2qdPft9kzP/CCjIQZDQkz6gjV3QlKjpmI20btuUN5VNOgUT6LRu4aiTjV89zPs9+1559/3s8Vb5ed9JrKnyZPnuxFHLlw5K4ZNWqU3Xrrie7Ue51z5mfeXTN69ERfFuV8QjZotePsln/+Vacy0QAAIABJREFU0dZeZ1QPbD5zxgk0s2u77v8a7mfyZ1bkTxPnQgACEIAABPo2AQSavn3/uXoIQAACvSIQHCm77rDVCgscvdpA5CQ5YyTGjNlgHf9qrpbZEmUUDqxjJTT98ZyjU5cy5drnPOeWiQbyDnJOiubWzh4umEznZ3KqdGe+uBInlSXl0zZba2Rzv4S22VERJbonnacSHV9a5cShtEPnqfW35ldJViYBSFk1M2e8b3eMfcJGDa2xJcPGmESYDhcurABhn0VT5vJqIi25VdakEigd59t2LyuNknCjDk/vTp5gU6ZM8W4YlTJJdFFL7WgbbOXI6PdQDqVriufXyHGjIOAlS5b4jk6ao6Zmcxs79jAn0LztztjJjj2xzZU1Lc8kWs6m+yaxhgEBCEAAAhCAAAR6SwCBprfkOA8CEIBAHyag0qDxLkj3zuvOKjiFTI6Z+GvRjkz6WeJM2oyZNBcYLx9S+Y8+sCs4Npcwo9bY8ZyZ0DZb2THKfalzGTdpWnZrPXWQ6mqznb07k/amYNs6tzd1fgrlU9qn1sqnfKqmStfZ5ZrRUB6L9r3Q/Z5tz69MGG8tDbU2bupMK+lo9s6YUOrU37lj5KyR02bJsE2sYuG0rvbbznEjh41eV9lTcNW0zppqLzz7tBdqJKyEbJpMuTRBnIkLNipfkkijTk1y18yaNcuVPE1zgk2pzZv3JeemudouubzVvvfD5cvDooHQKk2TMMeAAAQgAAEIQAACvSWAQNNbcpwHAQhAoI8SCC4UiTMrU+ToLc5Mjhl1YbrAiUjaowSZ7fc63J67/8pUbbN7sw8F70qUCCPeLju8nquEKPqehB05WRQ4W15SlLNcSs4VOV+UfRJvxZ3tWoJLR2KMfk57XpgvV0ZNyKaR2BPN0dG5YV25guYvanBdoN63yRNftA/aq1z3JRcoXFbVvWXfCarDiVPFpU6UGe4FmtCSW7k0Ko9SN6gls96x9oZFrsNUhy9bkpNG3Z7WX399L9goc0aCjVpjb7/99r6kKYxMYcA6duzYsXbyKadaQ/2xNmyNdvv2dzMLbdGW6oPcvapy94EBAQhAAAIQgAAEeksAgaa35DgPAhCAQB8kIDFEJUXnuZKiXVx50ydlyDFTU13VXW6lfR7sWmuPve1iv8Wog+aj2HNbe6fNc0Gx0RHaZQdhQm6TspLijGKInBjZBBYJHvpaWN/So4xK86YJ8810vVGBRpE3aYOH02bUhGyaqJsmXOOiJa3euRMd6gKlvJpp775l/1vQ6nJgXPep8i6xRiVOatWtIbFGocMqeaqqnepFGnWIKmucZ3WzP7Dx48f745RLI1eMnDASXPTz7rvv3kOcUamTSp+iJVFBnDnyyCPtsF+e7NuV11S6cjXXpaneiWZxV5Du8RyXP6TXVx9U4YQhB5MBAQhAAAIQgAAEekkAgaaX4DgNAhCAQF8ksNsPjrdNXH6LOiaFIWEk3tb642YTXDTKxJFwJPfMPnvuYD/ed/ePbSuzap0DJNJcaciAclMLbn3Il8CSKUsmbdvsUvfBPxryG4QSOXXSiivd9ysmBqncSe20MzleovB6IwbpuiVMtbUvdaVTuUuvwlpBrHn3vWn2Xm2D1ZUNsZqljdZavbrv9qScGpU61a++uZW71twdTrxRho3Cg99/41WrcI6jMJQt09ra6sufJNboZ7XPVhlT3E2j999++227+OKL7Rt7fdPUKEvOIolvcijJHdPoQpZDPk8oKZMwJxfTiMFdIhIDAhCAAAQgAAEI9JYAAk1vyXEeBCAAgT5GQC6Uo0//43JXve2WY3x76kIP7e/mZZ2ZtnF7kkDzcY54a2yVv0ic8aG7sUyY3rTNDoKAhIPelCVpL4P6l3k3yBIXAhzNmglztzgxIu4USeuaycQ6BA/rvUxzZ7s/YT9z59fahJdfsfdnz3XlUNOtfs2tvSgj54xChMsa5jpXTYnPpZGrpmbOJGurm2t1C+bZq6++6sub1G47DDlk3nzzTauurraGhgb/ssqgJNhIvLnvvvtstWFr+qBj8RrohCtxknilEVxQcgGp21aJE8hUjqYwZ91vBgQgAAEIQAACEFgRAgg0K0KPcyEAAQhAAALLCOhDvT7IB/EliDOLGj7ML+lt22wtIRFA3ZJUNqQxf3FL6vDgICwsrG/1IcLZRjzzpjeuGc0tR4lcORWlxbbA7VMiR64Sp+h+gjDS6HJ9oh2h6hfX2ZtTJtt056qZ/e4Uax24tnfOlLTWW2dRiZU7sUYijUqilEsz5723bdCgQd1Th3KnaFtuhQIrb2b11Ve3O++6ywYMGblc+VXI1JF7psF9lTqHjsqeSktcds+yrlUDXf6MjmNAAAIQgAAEIACBFSGAQLMi9DgXAhCAAAQgsIyASmEkfoScGeWsqMxpXl1XRklU7NAH/TSdmTR1JgdLEDsy5dJEb0hvBBYJQRIcdD1yiASBJe2NjgYBx9t1h1KtbJku4bqS1gxtuydMfd/q+1VahcugaXCtu9XtScHB/TrbrGTJAu+kaW5utkxhwBJnFBy85ZZb2pVX/dna3TzZOlhFBacQqDxsYLnPnJGQpOsqd2IUAwIQgAAEIAABCKwIAQSaFaHHuRCAAAQgAIEIAZUHRUUJCQ4SPPq5T/iZWmonwZMrQ+erTCrqJtF5cpqs5tpaa02JBNGxImVJoRRKTp18ypK0fhrhKCp2hMDgECqsnJq0bcXD9S6cN8PedAHDE157w2oHrm8lzXVWUVFhbVWDTd2ePnj7DatfuGC5MODHH3/cjjrqKDv+hJNS5/hIiBngysQ05KBRQLDcNNXuPjMgAAEIQAACEIDAihJAoFlRgpwPAQhAAAIQWEZAzo+WZR2KgkgigUVj3qKuUp80I7hQkkSdTG6V3rhmtKdMZUkqeVKZUpJTJyqwxPN2sl1vEIJ0jXIdSYCKi1BJrOKOm9dfe9Wee/55mz1zutWM2sQaB29g/ee/bksXzfZuGrXiVg6NxJmf/exnduIpp+ctCOlahw0q91uTcNbc2kn+TNKN4n0IQAACEIAABFIRQKBJhYmDIAABCEAAAskE9GF9YUOL7/qjttlBdFCnpGrntEgjdIS8GIXPSgBIGhJW5KTpElm62jwvamhNLQbp+CCWZOo0lS0TJuwrBAGrbKsp5uRJ2rsEILFxxhnL1H472/m6TJVhFbkf5LjJJHypDOpd15np1elzrL1liRXVz7NXXhxnU6ZM8Z2adt39Gz3cTkl71fty0AySa8mFLLe4sGW5Z3T9Em0YEIAABCAAAQhAYEUJINCsKEHOhwAEIAABCMQINDlhRS22o8KBPtwPdpk0C514onya+Oit80XzyEnSf1mZTT5OnXCuxKRcAklwyKjsSftXfk4QSeR+ScqMiV9rCFLudBNJYFHwbugwFe8ilelcZftkEpOyPYjzZ39gM6a/bU+88JL94qAfdXdqyufBlRNKnCV+tXUs9dc/1O1De2dAAAIQgAAEIACBlUEAgWZlUGQOCEAAAhCAQISAAnbVdjvu7AglSQ1NH+bGhJbSChhOWx4UloqXQpX/f3t3Fyrnfd8J/LGkI/lFsmUnZpcu+KYbqrIXTQw2u+BAiXfdFgpWsC+CSVoXvDd2IloIWGAnF6mztaGQoq59ZYiblFDYDXEgsE1CQqFetiTgphdltTR7Y2h2w9qxY8mW9Xa8/+/If/nR+JkzL/+ZOedInwdELJ15XuYzk4vz5fdS5tJke9KkEKj/IdVzJw3sHfpAMxMnf1Ldk41S84Qk9Xp1UPD4uUOzacafoYYk4xueZvny5blTdXOhhCvTKpnGr1croGoQdclu/2iIsoMAAQIECBAgsCwBAc2yJF2HAAECBAj0BC6UwOW1NyeHNAlG3i0zaVK9UjcDzQqYMKO2UY2fOykA6V971pXXQ89z26H9o8HFaWlKldA8xyxbmmq71XhwNMu5k56lf24qXhIuzRpMjd9XODPPJ+61BAgQIECAwDwCApp5tLyWAAECBK4qgRf/+qXuxz852d310SPd0d++Z+nvbVJIk1/6U+mSgcK/OHV25pXbecCEIwkYthogPGkr0qzDh4cg+pU+b50p81du3DeaeTPLvJt+S9MsVULj1TSpYNm7Z89M9xp/9rpJq1/RNEu1Tq4jnFn6/yVckAABAgQIENhCQEDj60GAAAEC16TAw3/4dHd3CWZ+7Vfv6J77ixdHIc3xzz60dIuENK+fOl/mlmyOhskm2NgorTFvnC5tQqXlJv8+SyVKf3X2rAN1c/0DpWIk4URCjkWqdQIyaRBwbXna6nlmqeiZhJ5nzlDetIz9v1+eneuzqcOTL5QqpUm+qdbJoN/M1hkfNlyDnVfLZq7M3Fm0cuaBR77YfebB+7YMAP/5/77a/at/+eG53p8XEyBAgAABAlefgIDm6vtMvSMCBAgQmCJw8qevdE88/Xz3zee/NHrlm6ff7vKL9GMPH11JJc1mCQkyOPhAWVk93pJ0+OClbUR1+O7Qo7cMEE5Ik3aoSXNxtqKaZRBwDWDSMjQehLS0JfXnzWS2TgKSOqB32hd8aP34VuckaDpYqppOl+1M2byVzyRHQrQcCdQyc2bPAtua8t36y//6vS7fuU8/cF9398eOXH6Uk//0Sve5L5zosgPqV0pAc/yxh7ojH7lj2tvzcwIECBAgQOAqFRDQXKUfrLdFgAABApMF8svy55480X3/r/509KJUMLz4317qXvzuS5f/bRV+qdJIADB+jFdr1J/3q2bm3ZSUa9SAJPdMCFHXfs/y3uapfKlBTm1DGt27VApttQZ7q2cYCnYS2CQ4eauEKFlzPemozz3Pe821alvYxr7rRlu2UnWUY3TfrPReIJzpP2O+YwkFUynzaAkCcyQUfOErx0ehTH6eqq76nZzlM/IaAgQIECBA4OoSENBcXZ+nd0OAAAECMwr8h099vvvzp451P3zp5e5bZRbNzQdvHFU5fPn4IyupoqmPlSqQbCEaP8ZDiQQqCTmmBRJDb3do1kydIXO2tAtNa6latPKlVqKkJWiRDU/jQc/4FqzatpT3MrQlKy1ReYZZK236dv2tVteXSqdUBF0sG5+y+WmZx4/+/uQokDlWAsK02NWwpgY2J8p3UrvTMsVdiwABAgQI7B4BAc3u+aw8KQECBAgsUSADgp974cVRe9P3SiVNApr8PWHNC392fKW/JCcgyRak8aOuc86/J5yYZQDvpKBnaDPUtACkH+yk2idByzxHDXZyzqxbkur152lLGm9JyjUWDZVy7vi943T7LdeXNdppPlr+kZDmiWcutdjle5cj38P7SmhYv4vLv6srEiBAgAABAjtdQECz0z8hz0eAAAECKxNIFU2qFRLI5Eib09PPfqO79547R5U0qzzSpnPq7SvXVNeQoSws6l4rQ3HPlwqOWY95NjTV+7xeNkjVe0waBDzL/WsrVm1p2izJTrZU1QHF45Uw49fsz5sZagEbeobakpSfXdzcHM2JGaqqmfb81a3fEpVnj9GqjrQ6HfnXd4yGB9fj6f/8je5UCWmGvnfPlJ/d/1v3mE+zqg/EdQkQIECAwA4RENDskA/CYxAgQIDA+gUy9yNVC/lFOUHN18ow18d+/2j3bNnqlF+U04KyyqOGNOPhSsadZHtRQoOhdqjxZ6qBy1DVzKTnzwajW8s9Mhg3c1daA46hlqZUBCXsqMN3h56lpfKlVrok0Mr67lnDnfocmVcT53wO75QhzjlWHc7kHpk1k9am+v3KsOCH/+jpUUXNeHvT18t3MtVeqbBJcJjzatXNKr+brk2AAAECBAisX0BAs35zdyRAgACBHSSQaoYflDk0R3/7nstBTf7tUGk9WcXa7fG3fq7MhEnlyXi4MlTZMX5uv4pkkXaoVK7cdmh/d7YMxc0Q4nmPWdZs92ffpGKotk0lXJmnymbovX/o5gOjWTcJsRK05JjVoVbt9OfVrCOcyTOmWiYhS8KWOhz490pI2K+oyevysz8oYc5X32u5S1iTP089XsLD3jaoeT83rydAgAABAgR2poCAZmd+Lp6KAAECBNYkUKtoMvujVi+k1enH/3By9At02k6yAnmVVQvvnMvWoA8GJFvNZRmawzIP2fttTudGw4ivK4lJnmGWuTPTZtkMPUfWfWf4btqqynidsrb6Uriy1UamSe9n0qamWU1qsNTfjJVqorR5reNINcyTJQTMUOr8d9a7j4czeY5U2uRIUJiWqBx5/Sq/i+t4/+5BgAABAgQIDAsIaHwzCBAgQOCaF+gPBw5GZn78z/LLc476y3DaT1Z5nC1bgzJDZTwgSRjy4RJm1O1LrVUzkwYBz9pqNM8w33Gv2laV9zjvGux6rRqu9Ofn9O8zzWf8fV7aDHWgrNMufVJrPsbDlvG/Z5jw//rfr4wqvMY3Pq35Ud2OAAECBAgQWIOAgGYNyG5BgAABAjtfoLaPZCxvqmb6g4IfeOSL3aNlNs29H79zpW/kfGl3erW0Gg2FNFn3nFaohByLrN7OgyfcyFyYbJA6M7Dqu86MyQanOpOl/4ZnaWnaCqiGIxka/G55k6+XleOzVOzUa84aItX3erAM+u3PvxkKZxJ+bexbfzgz7pQ5M/kOJghMVVda7PqVMhloffyxh1b+HVzpF9zFCRAgQIAAgS0FBDS+IAQIECBAYEwgM2ju+o0j3dHfuWf0k1TY5BfmoTaUZeNduJh5MOdGa7brUbckZW7KxbLZaSjE2eo56vmzDAKu7UP99qPa0jTL+UPPMTRvpoYlb7x1rjtXZuBMO9IiNetWqL5bnU1TNz1Vu0uVQPvLKu3VhjMJW75dwpe0yWXO0aQj1TMJBtNmV1vs+hud0u50tGxyqt/JaV5+ToAAAQIECOw+AQHN7vvMPDEBAgQIrFggv1TnqDNpjj15ovv0A/etbTBrP6TJXJRDN2xcntcyTxVJ3kMqbg7ftH+ueS+1TSihxltnLna3lkHCi86L2aolqj7bVu1O/SHDb5bKnkWO22+5VCWTyqDca13hTCpishksA4DzncrMmbrSfav3UQcH57X5DmbL0wP/8Yvd//jOc+bPLPIFcA4BAgQIENglAgKaXfJBeUwCBAgQ2B6BVDY8WFqcMkR4nUdCmnMX3u32l2ChP8w2zz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\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"pu.plot_timestep(sharpy_output, tstep=-1, minus_mstar=(wake_panels - 6), plotly=True,custom_scaling=False,z_compression=0.5)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Postprocessing\\n\",\n \"As an example, we are going to plot the evolution of the tip position along time:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 34,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/svg+xml\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" 2023-06-30T10:27:03.096903\\n\",\n \" image/svg+xml\\n\",\n \" \\n\",\n \" \\n\",\n \" Matplotlib v3.7.1, https://matplotlib.org/\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \"\\n\"\n ],\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"time = np.linspace(0, dt*time_steps, time_steps)\\n\",\n \"tip_pos = np.zeros((time_steps))\\n\",\n \"for it in range(time_steps):\\n\",\n \" tip_pos[it] = sharpy_output.structure.timestep_info[it].pos[-1, 2]\\n\",\n \"\\n\",\n \"fig, plots = plt.subplots(1, 1, figsize=(6, 3))\\n\",\n \"\\n\",\n \"plots.grid()\\n\",\n \"plots.set_xlabel(\\\"time [s]\\\")\\n\",\n \"plots.set_ylabel(\\\"tip position [m]\\\")\\n\",\n \"plots.plot(time, tip_pos, '-')\\n\",\n \"\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Conclusions\\n\",\n \"This notebook provides the big picture of the simulations with SHARPy. We recommend to go through the [documentation](https://ic-sharpy.readthedocs.io/en/main/) with special attention to the [SHARPy file description](https://ic-sharpy.readthedocs.io/en/main/content/casefiles.html) and the [examples](https://ic-sharpy.readthedocs.io/en/main/content/examples.html).\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"sharpy env)\",\n \"language\": \"python\",\n \"name\": \"sharpy\"\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\": \"3.10.12\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "docs/source/content/example_notebooks/linear_goland_flutter.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"tags\": []\n },\n \"source\": [\n \"\\n\",\n \"# Flutter Analysis of Goland's Wing\\n\",\n \"\\n\",\n \"## Description\\n\",\n \"This is simple rectangular wing with constant properties originally proposed by Martin Goland in 1945 as a flutter benchmark case. This example generates a beam/UVLM model with the original properties in SHARPy and computes flutter around an arbitrary equilibrium point using the following general process:\\n\",\n \"\\n\",\n \"* Calculate steady aerodynamic forces and deflections for a given angle of attack using a nonlinear solver\\n\",\n \"\\n\",\n \"* Linearise the dynamic aeroelastic equations about this reference condition\\n\",\n \"\\n\",\n \"* Reduce the size of the (linearized) structural subsystem using modal projection\\n\",\n \"\\n\",\n \"* Reduce the size of the (linearized) aerodyanic subsystem using a Krylov projection\\n\",\n \"\\n\",\n \"* Evaluate the stability of the linearised aeroelastic system at different velocities and plot the results.\\n\",\n \"\\n\",\n \"## Wing properties\\n\",\n \"Span: b=20 ft., chord: c=6 ft., weight: 4 psi., radius of gyration about CG: .25c, elastic axis: 0.33c, centre of gravity: 0.43c\\n\",\n \"\\n\",\n \"### References\\n\",\n \"\\n\",\n \"Goland, M. (1945). The Flutter o a Uniorm Cantilever Wing. Journal of Applied Mechanics,12(4):197-208.\\n\",\n \"\\n\",\n \"Maraniello, S., & Palacios, R. (2019). State-Space Realizations and Internal Balancing in Potential-Flow Aerodynamics with Arbitrary Kinematics. AIAA Journal, 57(6):1–14. https://doi.org/10.2514/1.J058153\\n\",\n \"\\n\",\n \"#### Latest update, RPN 14.05.2023\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Required Packages\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import numpy as np\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import os\\n\",\n \"import sys\\n\",\n \"import sharpy.cases.templates.flying_wings as wings # See this package for the Goland wing structural and aerodynamic definition\\n\",\n \"import sharpy.sharpy_main # used to run SHARPy from Jupyter\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Problem Set-up\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Operatig conditions\\n\",\n \"\\n\",\n \"The UVLM is assembled in normalised time at a velocity of $1 m/s$. The only matrices that need updating then with free stream velocity are the structural matrices, which is significantly cheaper to do than to update the UVLM.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"u_inf = 1.\\n\",\n \"alpha_deg = 2. # Define angle of attack for static aeroelastic analysis.\\n\",\n \"rho = 1.02 # Air density.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Discretisation\\n\",\n \"\\n\",\n \"Note: To achieve convergence of the flutter results with the ones found in the literature, a fine grid is needed. If you are running this notebook for the first time, set `M = 4` initially to verify that your system can perform!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"M = 16 # Number of chordwise panels\\n\",\n \"N = 32 # Number of spanwise panels\\n\",\n \"M_star_fact = 10 # Length of the wake in chords.\\n\",\n \"num_modes = 8 # Number of vibration modes retained in the structural model.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### ROM\\n\",\n \"\\n\",\n \"A moment-matching (Krylov subspace) model order reduction technique is employed. This ROM method offers the ability to interpolate the transfer functions at a desired point in the complex plane. See the ROM documentation pages for more info. Note that this ROM method matches the transfer function but does not guarantee stability. Therefore the resulting system may be unstable. These unstable modes may appear far in the right hand plane but will not affect the flutter speed calculations.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"c_ref = 1.8288 # Goland wing reference chord. Used for reduced frequency normalisation\\n\",\n \"rom_settings = dict()\\n\",\n \"rom_settings['algorithm'] = 'mimo_rational_arnoldi' # reduction algorithm\\n\",\n \"rom_settings['r'] = 6 # Krylov subspace order\\n\",\n \"frequency_continuous_k = np.array([0.]) # Interpolation point in the complex plane with reduced frequency units\\n\",\n \"frequency_continuous_w = 2 * u_inf * frequency_continuous_k / c_ref\\n\",\n \"rom_settings['frequency'] = frequency_continuous_w\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Case Admin\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The case to run will be: goland_csM16N32Ms10_nmodes8rom_MIMORA_r6_sig0000_0000j\\n\",\n \"Case files will be saved in ./cases/goland_csM16N32Ms10_nmodes8rom_MIMORA_r6_sig0000_0000j\\n\",\n \"Output files will be saved in ./output/goland_csM16N32Ms10_nmodes8rom_MIMORA_r6_sig0000_0000j/\\n\"\n ]\n }\n ],\n \"source\": [\n \"case_name = 'goland_cs'\\n\",\n \"case_nlin_info = 'M%dN%dMs%d_nmodes%d' % (M, N, M_star_fact, num_modes)\\n\",\n \"case_rom_info = 'rom_MIMORA_r%d_sig%04d_%04dj' % (rom_settings['r'], frequency_continuous_k[-1].real * 100,\\n\",\n \" frequency_continuous_k[-1].imag * 100)\\n\",\n \"\\n\",\n \"case_name += case_nlin_info + case_rom_info\\n\",\n \"route_test_dir = os.path.abspath('')\\n\",\n \"\\n\",\n \"print('The case to run will be: %s' % case_name)\\n\",\n \"print('Case files will be saved in ./cases/%s' %case_name)\\n\",\n \"print('Output files will be saved in ./output/%s/' %case_name)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Simulation Set-Up\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Goland Wing\\n\",\n \"\\n\",\n \"`ws` is an instance of a Goland wing with a control surface. Reference the template file `sharpy.cases.templates.flying_wings.GolandControlSurface` for more info on the geometrical, structural and aerodynamic definition of the Goland wing here used.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"ws = wings.GolandControlSurface(M=M,\\n\",\n \" N=N,\\n\",\n \" Mstar_fact=M_star_fact,\\n\",\n \" u_inf=u_inf,\\n\",\n \" alpha=alpha_deg,\\n\",\n \" cs_deflection=[0, 0],\\n\",\n \" rho=rho,\\n\",\n \" sweep=0,\\n\",\n \" physical_time=2,\\n\",\n \" n_surfaces=2,\\n\",\n \" route=route_test_dir + '/cases',\\n\",\n \" case_name=case_name)\\n\",\n \"\\n\",\n \"ws.clean_test_files()\\n\",\n \"ws.update_derived_params()\\n\",\n \"ws.set_default_config_dict()\\n\",\n \"\\n\",\n \"ws.generate_aero_file()\\n\",\n \"ws.generate_fem_file()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Simulation Settings\\n\",\n \"\\n\",\n \"The settings for each of the solvers are now set. For a detailed description on them please reference their respective documentation pages\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### SHARPy Settings\\n\",\n \"\\n\",\n \"The most important setting is the `flow` list. It tells SHARPy which solvers to run and in which order.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"ws.config['SHARPy'] = {\\n\",\n \" 'flow':\\n\",\n \" ['BeamLoader', 'AerogridLoader',\\n\",\n \" 'StaticCoupled',\\n\",\n \" 'AerogridPlot',\\n\",\n \" 'BeamPlot',\\n\",\n \" 'Modal',\\n\",\n \" 'LinearAssembler',\\n\",\n \" 'AsymptoticStability',\\n\",\n \" ],\\n\",\n \" 'case': ws.case_name, 'route': ws.route,\\n\",\n \" 'write_screen': 'off', 'write_log': 'on', # Change to 'on' as neded.\\n\",\n \" 'log_folder': route_test_dir + '/output/',\\n\",\n \" 'log_file': ws.case_name + '.log'}\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Beam Loader Settings\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"ws.config['BeamLoader'] = {\\n\",\n \" 'unsteady': 'off',\\n\",\n \" 'orientation': ws.quat}\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Aerogrid Loader Settings\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"ws.config['AerogridLoader'] = {\\n\",\n \" 'unsteady': 'off',\\n\",\n \" 'aligned_grid': 'on',\\n\",\n \" 'mstar': ws.Mstar_fact * ws.M,\\n\",\n \" 'freestream_dir': ws.u_inf_direction,\\n\",\n \" 'wake_shape_generator': 'StraightWake',\\n\",\n \" 'wake_shape_generator_input': {'u_inf': ws.u_inf,\\n\",\n \" 'u_inf_direction': ws.u_inf_direction,\\n\",\n \" 'dt': ws.dt}}\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Static Coupled Solver\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"ws.config['StaticCoupled'] = {\\n\",\n \" 'print_info': 'on',\\n\",\n \" 'max_iter': 200,\\n\",\n \" 'n_load_steps': 1,\\n\",\n \" 'tolerance': 1e-10,\\n\",\n \" 'relaxation_factor': 0.,\\n\",\n \" 'aero_solver': 'StaticUvlm',\\n\",\n \" 'aero_solver_settings': {\\n\",\n \" 'rho': ws.rho,\\n\",\n \" 'print_info': 'off',\\n\",\n \" 'horseshoe': 'off',\\n\",\n \" 'num_cores': 4,\\n\",\n \" 'n_rollup': 0,\\n\",\n \" 'rollup_dt': ws.dt,\\n\",\n \" 'rollup_aic_refresh': 1,\\n\",\n \" 'rollup_tolerance': 1e-4,\\n\",\n \" 'velocity_field_generator': 'SteadyVelocityField',\\n\",\n \" 'velocity_field_input': {\\n\",\n \" 'u_inf': ws.u_inf,\\n\",\n \" 'u_inf_direction': ws.u_inf_direction}},\\n\",\n \" 'structural_solver': 'NonLinearStatic',\\n\",\n \" 'structural_solver_settings': {'print_info': 'off',\\n\",\n \" 'max_iterations': 150,\\n\",\n \" 'num_load_steps': 4,\\n\",\n \" 'delta_curved': 1e-1,\\n\",\n \" 'min_delta': 1e-10,\\n\",\n \" 'gravity_on': 'on',\\n\",\n \" 'gravity': 9.81}}\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### AerogridPlot Settings\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"ws.config['AerogridPlot'] = {'include_rbm': 'off',\\n\",\n \" 'include_applied_forces': 'on',\\n\",\n \" 'minus_m_star': 0}\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### BeamPlot Settings\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"ws.config['BeamPlot'] = {'include_rbm': 'off',\\n\",\n \" 'include_applied_forces': 'on'}\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Modal Solver Settings\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"ws.config['Modal'] = {'NumLambda': 20,\\n\",\n \" 'rigid_body_modes': 'off',\\n\",\n \" 'print_matrices': 'on', # 'keep_linear_matrices': 'on', 'write_dat': 'off',\\n\",\n \" 'rigid_modes_cg': 'off',\\n\",\n \" 'continuous_eigenvalues': 'off',\\n\",\n \" 'dt': 0,\\n\",\n \" 'plot_eigenvalues': False,\\n\",\n \" 'max_rotation_deg': 15.,\\n\",\n \" 'max_displacement': 0.15,\\n\",\n \" 'write_modes_vtk': True,\\n\",\n \" 'use_undamped_modes': True}\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Linear System Assembly Settings\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"ws.config['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\\n\",\n \" 'linear_system_settings': {\\n\",\n \" 'beam_settings': {'modal_projection': 'on',\\n\",\n \" 'inout_coords': 'modes',\\n\",\n \" 'discrete_time': 'on',\\n\",\n \" 'newmark_damp': 0.5e-4,\\n\",\n \" 'discr_method': 'newmark',\\n\",\n \" 'dt': ws.dt,\\n\",\n \" 'proj_modes': 'undamped',\\n\",\n \" 'use_euler': 'off',\\n\",\n \" 'num_modes': num_modes,\\n\",\n \" 'print_info': 'on',\\n\",\n \" 'gravity': 'on',\\n\",\n \" 'remove_sym_modes': 'on',\\n\",\n \" 'remove_dofs': []},\\n\",\n \" 'aero_settings': {'dt': ws.dt,\\n\",\n \" 'ScalingDict': {'length': 0.5 * ws.c_ref,\\n\",\n \" 'speed': u_inf,\\n\",\n \" 'density': rho},\\n\",\n \" 'integr_order': 2,\\n\",\n \" 'density': ws.rho,\\n\",\n \" 'remove_predictor': 'on',\\n\",\n \" 'use_sparse': 'on',\\n\",\n \" 'remove_inputs': ['u_gust'],\\n\",\n \" 'rom_method': ['Krylov'],\\n\",\n \" 'rom_method_settings': {'Krylov': rom_settings}},\\n\",\n \" }}\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Asymptotic Stability Analysis Settings\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"ws.config['AsymptoticStability'] = {'print_info': True,\\n\",\n \" 'velocity_analysis': [100, 180, 81],\\n\",\n \" 'modes_to_plot': []}\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Write solver settings config file\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"ws.config.write()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Run SHARPy\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 17,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"fatal: not a git repository (or any of the parent directories): .git\\n\",\n \"/home/rpalacio/anaconda3/envs/sharpy/lib/python3.10/site-packages/scipy/sparse/_index.py:146: SparseEfficiencyWarning: Changing the sparsity structure of a csc_matrix is expensive. lil_matrix is more efficient.\\n\",\n \" self._set_arrayXarray(i, j, x)\\n\",\n \"/home/rpalacio/anaconda3/envs/sharpy/lib/python3.10/site-packages/sharpy/linear/src/lingebm.py:313: UserWarning: Euler parametrisation not implemented - Either rigid body modes are not being used or this method has already been called.\\n\",\n \" warnings.warn('Euler parametrisation not implemented - Either rigid body modes are not being used or this '\\n\",\n \"/home/rpalacio/anaconda3/envs/sharpy/lib/python3.10/site-packages/sharpy/rom/krylov.py:242: UserWarning: Reduced Order Model Unstable\\n\",\n \" warn.warn('Reduced Order Model Unstable')\\n\"\n ]\n },\n {\n \"data\": {\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 17,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"sharpy.sharpy_main.main(['', ws.route + ws.case_name + '.sharpy'])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Analysis\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Nonlinear equilibrium\\n\",\n \"\\n\",\n \"The nonlinear equilibrium condition can be visualised and analysed by opening, with Paraview, the files in the `/output//aero` and `/output//beam` folders to see the deflection and aerodynamic forces acting on the wing.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Stability \\n\",\n \"\\n\",\n \"The stability of the Goland wing is now analysed under changing free stream velocity. The flutter modes involves the two lowest frequency modes near the imaginary axis (1st bending and 1st torsion if aerodynamics is removed). The two modes are seen quite separated at 100 m/s. As speed is increased, the damping of the torsion mode decreases until it crosses the imaginary axis onto the right hand plane and flutter begins.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 18,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"file_name = './output/%s/stability/velocity_analysis_min1000_max1800_nvel0081.dat' % case_name\\n\",\n \"\\n\",\n \"velocity_analysis = np.loadtxt(file_name)\\n\",\n \"u_inf = velocity_analysis[:, 0]\\n\",\n \"eigs_r = velocity_analysis[:, 1]\\n\",\n \"eigs_i = velocity_analysis[:, 2]\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 23,\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 \"fig = plt.figure()\\n\",\n \"plt.scatter(eigs_r, eigs_i, c=u_inf, cmap='Blues')\\n\",\n \"cbar = plt.colorbar()\\n\",\n \"cbar.set_label('Free Stream Velocity, $u_\\\\infty$ [m/s]')\\n\",\n \"\\n\",\n \"plt.grid()\\n\",\n \"plt.xlim(-50, 5)\\n\",\n \"plt.ylim(0, 300)\\n\",\n \"plt.xlabel('Real Part, $\\\\lambda$ [rad/s]')\\n\",\n \"plt.ylabel('Imag Part, $\\\\lambda$ [rad/s]');\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 20,\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 \"fig = plt.figure()\\n\",\n \"natural_frequency = np.sqrt(eigs_r ** 2 + eigs_i ** 2)\\n\",\n \"damping_ratio = eigs_r / natural_frequency\\n\",\n \"cond = (eigs_r>-25) * (eigs_r<10) * (natural_frequency<100) # filter unwanted eigenvalues for this plot (mostly aero modes)\\n\",\n \"\\n\",\n \"plt.scatter(u_inf[cond], damping_ratio[cond], color='k', marker='s', s=9)\\n\",\n \"\\n\",\n \"plt.grid()\\n\",\n \"plt.ylim(-0.25, 0.25)\\n\",\n \"plt.xlabel('Free Stream Velocity, $u_\\\\infty$ [m/s]')\\n\",\n \"plt.ylabel('Damping Ratio, $\\\\zeta$ [-]');\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 21,\n \"metadata\": {\n \"tags\": []\n },\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 \"fig = plt.figure()\\n\",\n \"cond = (eigs_r>-25) * (eigs_r<10) # filter unwanted eigenvalues for this plot (mostly aero modes)\\n\",\n \"plt.scatter(u_inf[cond], natural_frequency[cond], color='k', marker='s', s=9)\\n\",\n \"\\n\",\n \"plt.grid()\\n\",\n \"plt.ylim(40, 100)\\n\",\n \"plt.xlabel('Free Stream Velocity, $u_\\\\infty$ [m/s]')\\n\",\n \"plt.ylabel('Natural Frequency, $\\\\omega_n$ [rad/s]');\"\n ]\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\": \"3.10.11\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "docs/source/content/example_notebooks/linear_horten.ipynb", "content": "{\n\t\"cells\": [\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"# Asymptotic Stability of a Flying Wing in Cruise Trimmed Conditions\\n\",\n\t\t\t\t\"\\n\",\n\t\t\t\t\"A Horten flying wing is analysed. The nonlinear trim condition is found and the system is linearised. The eigenvalues of the linearised system are then used to evaluate the stability at the cruise trimmed flight conditions.\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 1,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"# required packages\\n\",\n\t\t\t\t\"import sharpy.utils.algebra as algebra\\n\",\n\t\t\t\t\"import sharpy.sharpy_main\\n\",\n\t\t\t\t\"from sharpy.cases.hangar.richards_wing import Baseline\\n\",\n\t\t\t\t\"import numpy as np\\n\",\n\t\t\t\t\"import configobj\\n\",\n\t\t\t\t\"import matplotlib.pyplot as plt\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"## Flight Conditions\\n\",\n\t\t\t\t\"\\n\",\n\t\t\t\t\"Initial flight conditions. The values for angle of attack ``alpha``, control surface deflection ``cs_deflection`` and ``thrust`` are only initial values. The values required for trim will be calculated by the ``StaticTrim`` routine\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 2,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"u_inf = 28\\n\",\n\t\t\t\t\"alpha_deg = 4.5135\\n\",\n\t\t\t\t\"cs_deflection = 0.1814\\n\",\n\t\t\t\t\"thrust = 5.5129\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"## Discretisation\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 3,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"M = 4 # chordwise panels\\n\",\n\t\t\t\t\"N = 11 # spanwise panels\\n\",\n\t\t\t\t\"Msf = 5 # wake length in chord numbers\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"## Create Horten Wing\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 4,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [\n\t\t\t\t{\n\t\t\t\t\t\"name\": \"stdout\",\n\t\t\t\t\t\"output_type\": \"stream\",\n\t\t\t\t\t\"text\": [\n\t\t\t\t\t\t\"0\\n\",\n\t\t\t\t\t\t\"Section Mass: 11.88 \\n\",\n\t\t\t\t\t\t\"Linear Mass: 11.88\\n\",\n\t\t\t\t\t\t\"Section Ixx: 1.8777\\n\",\n\t\t\t\t\t\t\"Section Iyy: 1.0137\\n\",\n\t\t\t\t\t\t\"Section Izz: 2.5496\\n\",\n\t\t\t\t\t\t\"Linear Ixx: 1.88\\n\",\n\t\t\t\t\t\t\"1\\n\",\n\t\t\t\t\t\t\"Section Mass: 10.99 \\n\",\n\t\t\t\t\t\t\"Linear Mass: 10.99\\n\",\n\t\t\t\t\t\t\"Section Ixx: 1.4694\\n\",\n\t\t\t\t\t\t\"Section Iyy: 0.9345\\n\",\n\t\t\t\t\t\t\"Section Izz: 2.1501\\n\",\n\t\t\t\t\t\t\"Linear Ixx: 1.74\\n\",\n\t\t\t\t\t\t\"2\\n\",\n\t\t\t\t\t\t\"Section Mass: 10.10 \\n\",\n\t\t\t\t\t\t\"Linear Mass: 10.10\\n\",\n\t\t\t\t\t\t\"Section Ixx: 1.1257\\n\",\n\t\t\t\t\t\t\"Section Iyy: 0.8561\\n\",\n\t\t\t\t\t\t\"Section Izz: 1.7993\\n\",\n\t\t\t\t\t\t\"Linear Ixx: 1.60\\n\",\n\t\t\t\t\t\t\"3\\n\",\n\t\t\t\t\t\t\"Section Mass: 9.21 \\n\",\n\t\t\t\t\t\t\"Linear Mass: 9.21\\n\",\n\t\t\t\t\t\t\"Section Ixx: 0.8410\\n\",\n\t\t\t\t\t\t\"Section Iyy: 0.7783\\n\",\n\t\t\t\t\t\t\"Section Izz: 1.4933\\n\",\n\t\t\t\t\t\t\"Linear Ixx: 1.46\\n\",\n\t\t\t\t\t\t\"4\\n\",\n\t\t\t\t\t\t\"Section Mass: 8.32 \\n\",\n\t\t\t\t\t\t\"Linear Mass: 8.32\\n\",\n\t\t\t\t\t\t\"Section Ixx: 0.6096\\n\",\n\t\t\t\t\t\t\"Section Iyy: 0.7011\\n\",\n\t\t\t\t\t\t\"Section Izz: 1.2280\\n\",\n\t\t\t\t\t\t\"Linear Ixx: 1.31\\n\",\n\t\t\t\t\t\t\"5\\n\",\n\t\t\t\t\t\t\"Section Mass: 7.43 \\n\",\n\t\t\t\t\t\t\"Linear Mass: 7.43\\n\",\n\t\t\t\t\t\t\"Section Ixx: 0.4260\\n\",\n\t\t\t\t\t\t\"Section Iyy: 0.6246\\n\",\n\t\t\t\t\t\t\"Section Izz: 0.9996\\n\",\n\t\t\t\t\t\t\"Linear Ixx: 1.17\\n\",\n\t\t\t\t\t\t\"6\\n\",\n\t\t\t\t\t\t\"Section Mass: 6.54 \\n\",\n\t\t\t\t\t\t\"Linear Mass: 6.54\\n\",\n\t\t\t\t\t\t\"Section Ixx: 0.2845\\n\",\n\t\t\t\t\t\t\"Section Iyy: 0.5485\\n\",\n\t\t\t\t\t\t\"Section Izz: 0.8040\\n\",\n\t\t\t\t\t\t\"Linear Ixx: 1.03\\n\",\n\t\t\t\t\t\t\"7\\n\",\n\t\t\t\t\t\t\"Section Mass: 5.64 \\n\",\n\t\t\t\t\t\t\"Linear Mass: 5.64\\n\",\n\t\t\t\t\t\t\"Section Ixx: 0.1796\\n\",\n\t\t\t\t\t\t\"Section Iyy: 0.4728\\n\",\n\t\t\t\t\t\t\"Section Izz: 0.6374\\n\",\n\t\t\t\t\t\t\"Linear Ixx: 0.89\\n\",\n\t\t\t\t\t\t\"8\\n\",\n\t\t\t\t\t\t\"Section Mass: 4.75 \\n\",\n\t\t\t\t\t\t\"Linear Mass: 4.75\\n\",\n\t\t\t\t\t\t\"Section Ixx: 0.1055\\n\",\n\t\t\t\t\t\t\"Section Iyy: 0.3975\\n\",\n\t\t\t\t\t\t\"Section Izz: 0.4959\\n\",\n\t\t\t\t\t\t\"Linear Ixx: 0.75\\n\",\n\t\t\t\t\t\t\"9\\n\",\n\t\t\t\t\t\t\"Section Mass: 3.86 \\n\",\n\t\t\t\t\t\t\"Linear Mass: 3.86\\n\",\n\t\t\t\t\t\t\"Section Ixx: 0.0567\\n\",\n\t\t\t\t\t\t\"Section Iyy: 0.3226\\n\",\n\t\t\t\t\t\t\"Section Izz: 0.3753\\n\",\n\t\t\t\t\t\t\"Linear Ixx: 0.61\\n\",\n\t\t\t\t\t\t\"10\\n\",\n\t\t\t\t\t\t\"Section Mass: 2.97 \\n\",\n\t\t\t\t\t\t\"Linear Mass: 2.97\\n\",\n\t\t\t\t\t\t\"Section Ixx: 0.0275\\n\",\n\t\t\t\t\t\t\"Section Iyy: 0.2479\\n\",\n\t\t\t\t\t\t\"Section Izz: 0.2719\\n\",\n\t\t\t\t\t\t\"Linear Ixx: 0.47\\n\"\n\t\t\t\t\t]\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": [\n\t\t\t\t\"ws = Baseline(M=M,\\n\",\n\t\t\t\t\" N=N,\\n\",\n\t\t\t\t\" Mstarfactor=Msf,\\n\",\n\t\t\t\t\" u_inf=u_inf,\\n\",\n\t\t\t\t\" rho=1.02,\\n\",\n\t\t\t\t\" alpha_deg=alpha_deg,\\n\",\n\t\t\t\t\" roll_deg=0,\\n\",\n\t\t\t\t\" cs_deflection_deg=cs_deflection,\\n\",\n\t\t\t\t\" thrust=thrust,\\n\",\n\t\t\t\t\" physical_time=20,\\n\",\n\t\t\t\t\" case_name='horten',\\n\",\n\t\t\t\t\" case_name_format=4,\\n\",\n\t\t\t\t\" case_remarks='M%gN%gMsf%g' % (M, N, Msf))\\n\",\n\t\t\t\t\"\\n\",\n\t\t\t\t\"ws.set_properties()\\n\",\n\t\t\t\t\"ws.initialise()\\n\",\n\t\t\t\t\"ws.clean_test_files()\\n\",\n\t\t\t\t\"\\n\",\n\t\t\t\t\"ws.update_mass_stiffness(sigma=1., sigma_mass=2.5)\\n\",\n\t\t\t\t\"ws.update_fem_prop()\\n\",\n\t\t\t\t\"ws.generate_fem_file()\\n\",\n\t\t\t\t\"ws.update_aero_properties()\\n\",\n\t\t\t\t\"ws.generate_aero_file()\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"## Simulation Information\\n\",\n\t\t\t\t\"\\n\",\n\t\t\t\t\"The ``flow`` setting tells SHARPy which solvers to run and in which order. You may be stranged by the presence of the ``DynamicCoupled`` solver but it is necessary to give an initial speed to the structure. This will allow proper linearisation of the structural and rigid body equations.\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 5,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"flow = ['BeamLoader',\\n\",\n\t\t\t\t\" 'AerogridLoader',\\n\",\n\t\t\t\t\" 'StaticTrim',\\n\",\n\t\t\t\t\" 'BeamPlot',\\n\",\n\t\t\t\t\" 'AerogridPlot',\\n\",\n\t\t\t\t\" 'AeroForcesCalculator',\\n\",\n\t\t\t\t\" 'DynamicCoupled',\\n\",\n\t\t\t\t\" 'Modal',\\n\",\n\t\t\t\t\" 'LinearAssembler',\\n\",\n\t\t\t\t\" 'AsymptoticStability',\\n\",\n\t\t\t\t\" ]\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"### SHARPy Settings\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 6,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"settings = dict()\\n\",\n\t\t\t\t\"settings['SHARPy'] = {'case': ws.case_name,\\n\",\n\t\t\t\t\" 'route': ws.case_route,\\n\",\n\t\t\t\t\" 'flow': flow,\\n\",\n\t\t\t\t\" 'write_screen': 'on',\\n\",\n\t\t\t\t\" 'write_log': 'on',\\n\",\n\t\t\t\t\" 'log_folder': './output/',\\n\",\n\t\t\t\t\" 'log_file': ws.case_name + '.log'}\\n\",\n\t\t\t\t\"\\n\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"### Loaders\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 7,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"settings['BeamLoader'] = {'unsteady': 'off',\\n\",\n\t\t\t\t\" 'orientation': algebra.euler2quat(np.array([ws.roll,\\n\",\n\t\t\t\t\" ws.alpha,\\n\",\n\t\t\t\t\" ws.beta]))}\\n\",\n\t\t\t\t\"settings['AerogridLoader'] = {'unsteady': 'off',\\n\",\n\t\t\t\t\" 'aligned_grid': 'on',\\n\",\n\t\t\t\t\" 'mstar': int(ws.M * ws.Mstarfactor),\\n\",\n\t\t\t\t\" 'freestream_dir': ['1', '0', '0'],\\n\",\n\t\t\t\t\" 'control_surface_deflection': [''],\\n\",\n\t\t\t\t\" 'wake_shape_generator': 'StraightWake',\\n\",\n\t\t\t\t\" 'wake_shape_generator_input': {'u_inf': ws.u_inf,\\n\",\n\t\t\t\t\" 'u_inf_direction': ['1', '0', '0'],\\n\",\n\t\t\t\t\" 'dt': ws.dt}}\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"### StaticCoupled Solver\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 8,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"settings['StaticCoupled'] = {'print_info': 'on',\\n\",\n\t\t\t\t\" 'structural_solver': 'NonLinearStatic',\\n\",\n\t\t\t\t\" 'structural_solver_settings': {'print_info': 'off',\\n\",\n\t\t\t\t\" 'max_iterations': 200,\\n\",\n\t\t\t\t\" 'num_load_steps': 1,\\n\",\n\t\t\t\t\" 'delta_curved': 1e-5,\\n\",\n\t\t\t\t\" 'min_delta': ws.tolerance,\\n\",\n\t\t\t\t\" 'gravity_on': 'on',\\n\",\n\t\t\t\t\" 'gravity': 9.81},\\n\",\n\t\t\t\t\" 'aero_solver': 'StaticUvlm',\\n\",\n\t\t\t\t\" 'aero_solver_settings': {'print_info': 'on',\\n\",\n\t\t\t\t\" 'horseshoe': ws.horseshoe,\\n\",\n\t\t\t\t\" 'num_cores': 4,\\n\",\n\t\t\t\t\" 'n_rollup': int(0),\\n\",\n\t\t\t\t\" 'rollup_dt': ws.dt,\\n\",\n\t\t\t\t\" 'rollup_aic_refresh': 1,\\n\",\n\t\t\t\t\" 'rollup_tolerance': 1e-4,\\n\",\n\t\t\t\t\" 'velocity_field_generator': 'SteadyVelocityField',\\n\",\n\t\t\t\t\" 'velocity_field_input': {'u_inf': ws.u_inf,\\n\",\n\t\t\t\t\" 'u_inf_direction': [1., 0, 0]},\\n\",\n\t\t\t\t\" 'rho': ws.rho},\\n\",\n\t\t\t\t\" 'max_iter': 200,\\n\",\n\t\t\t\t\" 'n_load_steps': 1,\\n\",\n\t\t\t\t\" 'tolerance': ws.tolerance,\\n\",\n\t\t\t\t\" 'relaxation_factor': 0.2}\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"### Trim solver\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 9,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"settings['StaticTrim'] = {'solver': 'StaticCoupled',\\n\",\n\t\t\t\t\" 'solver_settings': settings['StaticCoupled'],\\n\",\n\t\t\t\t\" 'thrust_nodes': ws.thrust_nodes,\\n\",\n\t\t\t\t\" 'initial_alpha': ws.alpha,\\n\",\n\t\t\t\t\" 'initial_deflection': ws.cs_deflection,\\n\",\n\t\t\t\t\" 'initial_thrust': ws.thrust,\\n\",\n\t\t\t\t\" 'max_iter': 200,\\n\",\n\t\t\t\t\" 'fz_tolerance': 1e-2,\\n\",\n\t\t\t\t\" 'fx_tolerance': 1e-2,\\n\",\n\t\t\t\t\" 'm_tolerance': 1e-2}\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"### Nonlinear Equilibrium Post-process\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 10,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"settings['AerogridPlot'] = {\\n\",\n\t\t\t\t\" 'include_rbm': 'off',\\n\",\n\t\t\t\t\" 'include_applied_forces': 'on',\\n\",\n\t\t\t\t\" 'minus_m_star': 0,\\n\",\n\t\t\t\t\" 'u_inf': ws.u_inf\\n\",\n\t\t\t\t\" }\\n\",\n\t\t\t\t\"settings['AeroForcesCalculator'] = {\\n\",\n\t\t\t\t\" 'write_text_file': 'off',\\n\",\n\t\t\t\t\" 'text_file_name': ws.case_name + '_aeroforces.csv',\\n\",\n\t\t\t\t\" 'screen_output': 'on',\\n\",\n\t\t\t\t\" 'coefficients': True,\\n\",\n\t\t\t\t\" 'q_ref': 0.5 * ws.rho * ws.u_inf ** 2,\\n\",\n\t\t\t\t\" 'S_ref': 12.809,\\n\",\n\t\t\t\t\" }\\n\",\n\t\t\t\t\"\\n\",\n\t\t\t\t\"settings['BeamPlot'] = {\\n\",\n\t\t\t\t\" 'include_rbm': 'on',\\n\",\n\t\t\t\t\" 'include_applied_forces': 'on',\\n\",\n\t\t\t\t\" 'include_FoR': 'on'}\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"### DynamicCoupled Solver\\n\",\n\t\t\t\t\"\\n\",\n\t\t\t\t\"As mentioned before, a single time step of ``DynamicCoupled`` is required to give the structure the velocity required for the linearisation of the rigid body equations to be correct. Hence `n_time_steps = 1`\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 11,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"struct_solver_settings = {'print_info': 'off',\\n\",\n\t\t\t\t\" 'initial_velocity_direction': [-1., 0., 0.],\\n\",\n\t\t\t\t\" 'max_iterations': 950,\\n\",\n\t\t\t\t\" 'delta_curved': 1e-6,\\n\",\n\t\t\t\t\" 'min_delta': ws.tolerance,\\n\",\n\t\t\t\t\" 'newmark_damp': 5e-3,\\n\",\n\t\t\t\t\" 'gravity_on': True,\\n\",\n\t\t\t\t\" 'gravity': 9.81,\\n\",\n\t\t\t\t\" 'num_steps': ws.n_tstep,\\n\",\n\t\t\t\t\" 'dt': ws.dt,\\n\",\n\t\t\t\t\" 'initial_velocity': ws.u_inf * 1}\\n\",\n\t\t\t\t\"\\n\",\n\t\t\t\t\"step_uvlm_settings = {'print_info': 'on',\\n\",\n\t\t\t\t\" 'num_cores': 4,\\n\",\n\t\t\t\t\" 'convection_scheme': ws.wake_type,\\n\",\n\t\t\t\t\" 'velocity_field_generator': 'SteadyVelocityField',\\n\",\n\t\t\t\t\" 'velocity_field_input': {'u_inf': ws.u_inf * 0,\\n\",\n\t\t\t\t\" 'u_inf_direction': [1., 0., 0.]},\\n\",\n\t\t\t\t\" 'rho': ws.rho,\\n\",\n\t\t\t\t\" 'n_time_steps': ws.n_tstep,\\n\",\n\t\t\t\t\" 'dt': ws.dt,\\n\",\n\t\t\t\t\" 'gamma_dot_filtering': 3}\\n\",\n\t\t\t\t\"\\n\",\n\t\t\t\t\"settings['DynamicCoupled'] = {'print_info': 'on',\\n\",\n\t\t\t\t\" 'structural_solver': 'NonLinearDynamicCoupledStep',\\n\",\n\t\t\t\t\" 'structural_solver_settings': struct_solver_settings,\\n\",\n\t\t\t\t\" 'aero_solver': 'StepUvlm',\\n\",\n\t\t\t\t\" 'aero_solver_settings': step_uvlm_settings,\\n\",\n\t\t\t\t\" 'fsi_substeps': 200,\\n\",\n\t\t\t\t\" 'fsi_tolerance': ws.fsi_tolerance,\\n\",\n\t\t\t\t\" 'relaxation_factor': ws.relaxation_factor,\\n\",\n\t\t\t\t\" 'minimum_steps': 1,\\n\",\n\t\t\t\t\" 'relaxation_steps': 150,\\n\",\n\t\t\t\t\" 'final_relaxation_factor': 0.5,\\n\",\n\t\t\t\t\" 'n_time_steps': 1,\\n\",\n\t\t\t\t\" 'dt': ws.dt,\\n\",\n\t\t\t\t\" 'include_unsteady_force_contribution': 'off',\\n\",\n\t\t\t\t\" }\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"### Modal Solver Settings\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 12,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"settings['Modal'] = {'print_info': True,\\n\",\n\t\t\t\t\" 'use_undamped_modes': True,\\n\",\n\t\t\t\t\" 'NumLambda': 30,\\n\",\n\t\t\t\t\" 'rigid_body_modes': True,\\n\",\n\t\t\t\t\" 'write_modes_vtk': 'on',\\n\",\n\t\t\t\t\" 'continuous_eigenvalues': 'off',\\n\",\n\t\t\t\t\" 'dt': ws.dt,\\n\",\n\t\t\t\t\" 'plot_eigenvalues': False,\\n\",\n\t\t\t\t\" 'rigid_modes_cg': False}\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"### Linear Assembler Settings\\n\",\n\t\t\t\t\"\\n\",\n\t\t\t\t\"Note that for the assembly of the linear system, we replace the parametrisation of the orientation with Euler angles instead of quaternions.\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 13,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"settings['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\\n\",\n\t\t\t\t\" 'linear_system_settings': {\\n\",\n\t\t\t\t\" 'beam_settings': {'modal_projection': 'off',\\n\",\n\t\t\t\t\" 'inout_coords': 'modes',\\n\",\n\t\t\t\t\" 'discrete_time': True,\\n\",\n\t\t\t\t\" 'newmark_damp': 0.5e-2,\\n\",\n\t\t\t\t\" 'discr_method': 'newmark',\\n\",\n\t\t\t\t\" 'dt': ws.dt,\\n\",\n\t\t\t\t\" 'proj_modes': 'undamped',\\n\",\n\t\t\t\t\" 'num_modes': 9,\\n\",\n\t\t\t\t\" 'print_info': 'on',\\n\",\n\t\t\t\t\" 'gravity': 'on',\\n\",\n\t\t\t\t\" 'remove_dofs': []},\\n\",\n\t\t\t\t\" 'aero_settings': {'dt': ws.dt,\\n\",\n\t\t\t\t\" 'integr_order': 2,\\n\",\n\t\t\t\t\" 'density': ws.rho,\\n\",\n\t\t\t\t\" 'remove_predictor': 'off',\\n\",\n\t\t\t\t\" 'use_sparse': 'off',\\n\",\n\t\t\t\t\" 'remove_inputs': ['u_gust']},\\n\",\n\t\t\t\t\" 'track_body': 'on',\\n\",\n\t\t\t\t\" 'use_euler': 'on',\\n\",\n\t\t\t\t\" }}\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"### Asymptotic Stability Post-processor\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 14,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"settings['AsymptoticStability'] = {\\n\",\n\t\t\t\t\" 'print_info': 'on',\\n\",\n\t\t\t\t\" 'frequency_cutoff': 0,\\n\",\n\t\t\t\t\" 'export_eigenvalues': 'on',\\n\",\n\t\t\t\t\" 'num_evals': 100,\\n\",\n\t\t\t\t\" }\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"### Write solver file\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 15,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"config = configobj.ConfigObj()\\n\",\n\t\t\t\t\"np.set_printoptions(precision=16)\\n\",\n\t\t\t\t\"file_name = ws.case_route + '/' + ws.case_name + '.sharpy'\\n\",\n\t\t\t\t\"config.filename = file_name\\n\",\n\t\t\t\t\"for k, v in settings.items():\\n\",\n\t\t\t\t\" config[k] = v\\n\",\n\t\t\t\t\"config.write()\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"## Run Simulation\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 16,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [\n\t\t\t\t{\n\t\t\t\t\t\"name\": \"stdout\",\n\t\t\t\t\t\"output_type\": \"stream\",\n\t\t\t\t\t\"text\": [\n\t\t\t\t\t\t\"--------------------------------------------------------------------------------\\u001b[0m\\n\",\n\t\t\t\t\t\t\" ###### ## ## ### ######## ######## ## ##\\u001b[0m\\n\",\n\t\t\t\t\t\t\" ## ## ## ## ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n\t\t\t\t\t\t\" ## ## ## ## ## ## ## ## ## ####\\u001b[0m\\n\",\n\t\t\t\t\t\t\" ###### ######### ## ## ######## ######## ##\\u001b[0m\\n\",\n\t\t\t\t\t\t\" ## ## ## ######### ## ## ## ##\\u001b[0m\\n\",\n\t\t\t\t\t\t\" ## ## ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n\t\t\t\t\t\t\" ###### ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n\t\t\t\t\t\t\"--------------------------------------------------------------------------------\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Aeroelastics Lab, Aeronautics Department.\\u001b[0m\\n\",\n\t\t\t\t\t\t\" Copyright (c), Imperial College London.\\u001b[0m\\n\",\n\t\t\t\t\t\t\" All rights reserved.\\u001b[0m\\n\",\n\t\t\t\t\t\t\" License available at https://github.com/imperialcollegelondon/sharpy\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mRunning SHARPy from /home/ng213/2TB/pazy_code/pazy-sharpy/lib/sharpy/docs/source/content/example_notebooks\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mSHARPy being run is in /home/ng213/2TB/pazy_code/pazy-sharpy/lib/sharpy\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mThe branch being run is dev_setting_error\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mThe version and commit hash are: v1.2.1-344-g0239644-0239644\\u001b[0m\\n\",\n\t\t\t\t\t\t\"SHARPy output folder set\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m\\t./output//horten_u_inf2800_M4N11Msf5/\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of BeamLoader\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable for_pos has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: [0.0, 0, 0]\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of AerogridLoader\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable control_surface_deflection_generator_settings has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable dx1 has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: -1.0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable ndx1 has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable r has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 1.0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable dxmax has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: -1.0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34mThe aerodynamic grid contains 4 surfaces\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m Surface 0, M=4, N=2\\u001b[0m\\n\",\n\t\t\t\t\t\t\" Wake 0, M=20, N=2\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m Surface 1, M=4, N=22\\u001b[0m\\n\",\n\t\t\t\t\t\t\" Wake 1, M=20, N=22\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m Surface 2, M=4, N=2\\u001b[0m\\n\",\n\t\t\t\t\t\t\" Wake 2, M=20, N=2\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m Surface 3, M=4, N=22\\u001b[0m\\n\",\n\t\t\t\t\t\t\" Wake 3, M=20, N=22\\u001b[0m\\n\",\n\t\t\t\t\t\t\" In total: 192 bound panels\\u001b[0m\\n\",\n\t\t\t\t\t\t\" In total: 960 wake panels\\u001b[0m\\n\",\n\t\t\t\t\t\t\" Total number of panels = 1152\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of StaticTrim\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable print_info has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable tail_cs_index has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable initial_angle_eps has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0.05\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable initial_thrust_eps has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 2.0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable relaxation_factor has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0.2\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable save_info has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of StaticCoupled\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable correct_forces_method has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable runtime_generators has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of NonLinearStatic\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable newmark_damp has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0.0001\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable gravity_dir has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: [0.0, 0.0, 1.0]\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable relaxation_factor has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0.3\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable dt has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0.01\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable num_steps has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 500\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable initial_position has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: [0. 0. 0.]\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of StaticUvlm\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable iterative_solver has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable iterative_tol has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0.0001\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable iterative_precond has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable cfl1 has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable vortex_radius has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable vortex_radius_wake_ind has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable rbm_vel_g has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable centre_rot_g has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: [0.0, 0.0, 0.0]\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"|=====|=====|============|==========|==========|==========|==========|==========|==========|\\u001b[0m\\n\",\n\t\t\t\t\t\t\"|iter |step | log10(res) | Fx | Fy | Fz | Mx | My | Mz |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"|=====|=====|============|==========|==========|==========|==========|==========|==========|\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"|==========|==========|==========|==========|==========|==========|==========|==========|==========|==========|\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| iter |alpha[deg]|elev[deg] | thrust | Fx | Fy | Fz | Mx | My | Mz |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"|==========|==========|==========|==========|==========|==========|==========|==========|==========|==========|\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 0 | 0 | 0.00000 | -0.1051 | -0.0000 | 0.0598 | -0.0000 | 1.0837 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 1 | 0 | -7.62384 | -0.1284 | -0.0000 | 0.1276 | -0.0000 | 0.0045 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 2 | 0 | -8.33392 | -0.1190 | -0.0000 | 0.0397 | -0.0000 | -0.0774 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 3 | 0 | -9.30379 | -0.1133 | 0.0000 | 0.0011 | -0.0000 | -0.0070 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 4 | 0 | -10.71602 | -0.1136 | -0.0000 | 0.0032 | 0.0000 | -0.0100 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 5 | 0 | -10.88827 | -0.1138 | -0.0000 | 0.0043 | 0.0000 | -0.0119 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 6 | 0 | -11.66331 | -0.1138 | -0.0000 | 0.0042 | 0.0000 | -0.0116 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 7 | 0 | -12.88496 | -0.1138 | -0.0000 | 0.0041 | 0.0000 | -0.0116 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 0 | 4.5135 | 0.1814 | 5.5129 | -0.1138 | -0.0000 | 0.0041 | 0.0000 | -0.0116 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 0 | 0 | 0.00000 |-116.9870 | -0.0000 | 994.8063 | -0.0000 |-882.4104 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 1 | 0 | -5.79178 | -72.3841 | 0.0000 | 944.6140 | 0.0000 |-802.5912 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 2 | 0 | -6.63730 | -62.4378 | 0.0000 | 937.6662 | 0.0000 |-792.1259 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 3 | 0 | -7.22937 | -62.8923 | -0.0000 | 939.7866 | -0.0000 |-795.7093 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 4 | 0 | -8.65323 | -62.8757 | -0.0000 | 939.7100 | -0.0000 |-795.5764 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 5 | 0 | -8.81438 | -62.8640 | -0.0000 | 939.6554 | -0.0000 |-795.4837 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 6 | 0 | -9.59386 | -62.8660 | 0.0000 | 939.6644 | -0.0000 |-795.4991 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 7 | 0 | -10.80422 | -62.8661 | 0.0000 | 939.6650 | -0.0000 |-795.5000 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 8 | 0 | -11.01365 | -62.8660 | -0.0000 | 939.6647 | -0.0000 |-795.4994 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 9 | 0 | -12.15197 | -62.8660 | 0.0000 | 939.6647 | -0.0000 |-795.4995 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 0 | 7.3783 | -2.6834 | 5.5129 | -62.8660 | 0.0000 | 939.6647 | -0.0000 |-795.4995 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 0 | 0 | 0.00000 | -32.9132 | -0.0000 | 371.4715 | -0.0000 |-902.7953 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 1 | 0 | -5.48409 | -8.7241 | -0.0000 | 298.8484 | 0.0000 |-777.2938 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 2 | 0 | -6.39387 | -4.0957 | -0.0000 | 289.8092 | -0.0000 |-761.4855 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 3 | 0 | -6.85613 | -4.6263 | -0.0000 | 293.2407 | -0.0000 |-767.3376 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 4 | 0 | -8.25962 | -4.6052 | -0.0000 | 293.1048 | -0.0000 |-767.1066 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 5 | 0 | -8.44065 | -4.5914 | -0.0000 | 293.0156 | 0.0000 |-766.9545 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 6 | 0 | -9.20968 | -4.5937 | -0.0000 | 293.0308 | -0.0000 |-766.9804 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 7 | 0 | -10.44736 | -4.5939 | -0.0000 | 293.0316 | -0.0000 |-766.9819 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 8 | 0 | -10.63000 | -4.5938 | -0.0000 | 293.0311 | 0.0000 |-766.9809 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 9 | 0 | -11.74670 | -4.5938 | 0.0000 | 293.0311 | 0.0000 |-766.9810 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 10 | 0 | -12.29943 | -4.5938 | -0.0000 | 293.0311 | 0.0000 |-766.9810 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 0 | 4.5135 | 3.0462 | 5.5129 | -4.5938 | -0.0000 | 293.0311 | 0.0000 |-766.9810 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 0 | 0 | 0.00000 | -4.1051 | -0.0000 | 0.0598 | -0.0000 | 1.0834 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 1 | 0 | -7.62384 | -4.1284 | -0.0000 | 0.1276 | -0.0000 | 0.0042 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 2 | 0 | -8.33392 | -4.1190 | -0.0000 | 0.0397 | 0.0000 | -0.0778 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 3 | 0 | -9.30379 | -4.1133 | -0.0000 | 0.0011 | 0.0000 | -0.0074 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 4 | 0 | -10.71602 | -4.1136 | 0.0000 | 0.0032 | -0.0000 | -0.0104 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 5 | 0 | -10.88827 | -4.1138 | 0.0000 | 0.0043 | 0.0000 | -0.0123 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 6 | 0 | -11.66331 | -4.1138 | -0.0000 | 0.0042 | 0.0000 | -0.0119 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 7 | 0 | -12.88496 | -4.1138 | -0.0000 | 0.0041 | 0.0000 | -0.0119 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 0 | 4.5135 | 0.1814 | 7.5129 | -4.1138 | -0.0000 | 0.0041 | 0.0000 | -0.0119 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 0 | 0 | 0.00000 | 0.0095 | -0.0000 | 0.0498 | 0.0000 | 1.1013 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 1 | 0 | -7.62357 | -0.0140 | 0.0000 | 0.1189 | 0.0000 | 0.0198 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 2 | 0 | -8.33375 | -0.0046 | -0.0000 | 0.0312 | -0.0000 | -0.0624 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 3 | 0 | -9.30318 | 0.0010 | -0.0000 | -0.0075 | 0.0000 | 0.0081 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 4 | 0 | -10.71542 | 0.0007 | -0.0000 | -0.0054 | 0.0000 | 0.0051 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 5 | 0 | -10.88766 | 0.0006 | -0.0000 | -0.0043 | 0.0000 | 0.0032 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 6 | 0 | -11.66271 | 0.0006 | 0.0000 | -0.0044 | -0.0000 | 0.0035 | 0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 7 | 0 | -12.88441 | 0.0006 | -0.0000 | -0.0045 | 0.0000 | 0.0035 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 1 | 4.5135 | 0.1814 | 5.4560 | 0.0006 | -0.0000 | -0.0045 | 0.0000 | 0.0035 | -0.0000 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of BeamPlot\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable include_applied_moments has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable name_prefix has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable output_rbm has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m...Finished\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of AerogridPlot\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable include_forward_motion has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable include_unsteady_applied_forces has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable name_prefix has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable dt has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0.0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable include_velocities has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable include_incidence_angle has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable num_cores has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable vortex_radius has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m...Finished\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of AeroForcesCalculator\\u001b[0m\\n\",\n\t\t\t\t\t\t\"--------------------------------------------------------------------------------\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34mtstep | fx_g | fy_g | fz_g | Cfx_g | Cfy_g | Cfz_g \\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m 0 | 1.088e+01 | -4.476e-13 | 1.835e+03 | 2.124e-03 | -8.740e-17 | 3.583e-01\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m...Finished\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of DynamicCoupled\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable structural_substeps has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable dynamic_relaxation has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable postprocessors has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: []\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable postprocessors_settings has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable controller_id has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable controller_settings has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable cleanup_previous_solution has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable steps_without_unsteady_force has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable pseudosteps_ramp_unsteady_force has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable correct_forces_method has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable network_settings has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable runtime_generators has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of NonLinearDynamicCoupledStep\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable num_load_steps has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable gravity_dir has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: [0.0, 0.0, 1.0]\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable relaxation_factor has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0.3\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable balancing has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of StepUvlm\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable iterative_solver has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable iterative_tol has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0.0001\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable iterative_precond has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable cfl1 has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable vortex_radius has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable vortex_radius_wake_ind has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable interp_coords has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable filter_method has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable interp_method has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable yaw_slerp has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0.0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable centre_rot has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: [0.0, 0.0, 0.0]\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable quasi_steady has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"|=======|========|======|==============|==============|==============|==============|==============|\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| ts | t | iter | struc ratio | iter time | residual vel | FoR_vel(x) | FoR_vel(z) |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"|=======|========|======|==============|==============|==============|==============|==============|\\u001b[0m\\n\"\n\t\t\t\t\t]\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"name\": \"stderr\",\n\t\t\t\t\t\"output_type\": \"stream\",\n\t\t\t\t\t\"text\": [\n\t\t\t\t\t\t\"/home/ng213/2TB/pazy_code/pazy-sharpy/lib/sharpy/sharpy/aero/utils/uvlmlib.py:264: RuntimeWarning: invalid value encountered in true_divide\\n\",\n\t\t\t\t\t\t\" flightconditions.uinf_direction = np.ctypeslib.as_ctypes(ts_info.u_ext[0][:, 0, 0]/flightconditions.uinf)\\n\"\n\t\t\t\t\t]\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"name\": \"stdout\",\n\t\t\t\t\t\"output_type\": \"stream\",\n\t\t\t\t\t\"text\": [\n\t\t\t\t\t\t\"| 1 | 0.0089 | 3 | 0.877319 | 0.593232 | -10.598250 |-2.791317e+01 |-2.203426e+00 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m...Finished\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of Modal\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable keep_linear_matrices has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable write_dat has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable delta_curved has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0.01\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable max_rotation_deg has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 15.0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable max_displacement has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 0.15\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable use_custom_timestep has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: -1\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Structural eigenvalues\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"|==============|==============|==============|==============|==============|==============|==============|\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| mode | eval_real | eval_imag | freq_n (Hz) | freq_d (Hz) | damping | period (s) |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"|==============|==============|==============|==============|==============|==============|==============|\\u001b[0m\\n\"\n\t\t\t\t\t]\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"name\": \"stderr\",\n\t\t\t\t\t\"output_type\": \"stream\",\n\t\t\t\t\t\"text\": [\n\t\t\t\t\t\t\"/home/ng213/2TB/pazy_code/pazy-sharpy/lib/sharpy/sharpy/solvers/modal.py:265: UserWarning: Projecting a system with damping on undamped modal shapes\\n\",\n\t\t\t\t\t\t\" warnings.warn('Projecting a system with damping on undamped modal shapes')\\n\"\n\t\t\t\t\t]\n\t\t\t\t},\n\t\t\t\t{\n\t\t\t\t\t\"name\": \"stdout\",\n\t\t\t\t\t\"output_type\": \"stream\",\n\t\t\t\t\t\"text\": [\n\t\t\t\t\t\t\"| 0 | -0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 1 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 2 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 3 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 4 | -0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 5 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 6 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 7 | -0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 8 | -0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 9 | -0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 10 | 0.000000 | 28.293939 | 4.503120 | 4.503120 | -0.000000 | 0.222068 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 11 | 0.000000 | 29.271318 | 4.658675 | 4.658675 | -0.000000 | 0.214653 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 12 | 0.000000 | 54.780234 | 8.718545 | 8.718545 | -0.000000 | 0.114698 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 13 | 0.000000 | 58.999779 | 9.390106 | 9.390106 | -0.000000 | 0.106495 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 14 | 0.000000 | 70.520741 | 11.223724 | 11.223724 | -0.000000 | 0.089097 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 15 | 0.000000 | 76.917111 | 12.241738 | 12.241738 | -0.000000 | 0.081688 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 16 | 0.000000 | 87.324076 | 13.898058 | 13.898058 | -0.000000 | 0.071952 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 17 | 0.000000 | 108.035577 | 17.194396 | 17.194396 | -0.000000 | 0.058158 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 18 | 0.000000 | 119.692139 | 19.049596 | 19.049596 | -0.000000 | 0.052495 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 19 | 0.000000 | 133.495187 | 21.246419 | 21.246419 | -0.000000 | 0.047067 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 20 | 0.000000 | 134.444788 | 21.397553 | 21.397553 | -0.000000 | 0.046734 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 21 | 0.000000 | 151.060442 | 24.042016 | 24.042016 | -0.000000 | 0.041594 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 22 | 0.000000 | 159.369020 | 25.364367 | 25.364367 | -0.000000 | 0.039425 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 23 | 0.000000 | 171.256102 | 27.256255 | 27.256255 | -0.000000 | 0.036689 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 24 | 0.000000 | 173.895881 | 27.676389 | 27.676389 | -0.000000 | 0.036132 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 25 | 0.000000 | 199.016557 | 31.674469 | 31.674469 | -0.000000 | 0.031571 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 26 | 0.000000 | 205.412581 | 32.692428 | 32.692428 | -0.000000 | 0.030588 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 27 | 0.000000 | 205.419531 | 32.693534 | 32.693534 | -0.000000 | 0.030587 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 28 | 0.000000 | 223.563796 | 35.581283 | 35.581283 | -0.000000 | 0.028105 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 29 | 0.000000 | 227.924750 | 36.275351 | 36.275351 | -0.000000 | 0.027567 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of LinearAssembler\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable linearisation_tstep has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: -1\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable modal_tstep has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: -1\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable inout_coordinates has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable retain_inputs has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: []\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable retain_outputs has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: []\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of LinearAeroelastic\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable uvlm_filename has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of LinearUVLM\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable ScalingDict has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable gust_assembler has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable rom_method has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: []\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable rom_method_settings has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable vortex_radius has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable cfl1 has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable length has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 1.0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable speed has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 1.0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable density has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 1.0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable velocity_field_generator has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: SteadyVelocityField\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable velocity_field_input has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable physical_model has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable track_body has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable track_body_number has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: -1\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Initialising Static linear UVLM solver class...\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\t\\t\\t...done in 0.39 sec\\u001b[0m\\n\",\n\t\t\t\t\t\t\"State-space realisation of UVLM equations started...\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34mComputing wake propagation matrix with CFL1=True\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m\\tstate-space model produced in form:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m\\tx_{n+1} = A x_{n} + Bp u_{n+1}\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\t\\t\\t...done in 2.43 sec\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of LinearBeam\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable remove_sym_modes has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Warning, projecting system with damping onto undamped modes\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Linearising gravity terms...\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m\\tM = 187.12 kg\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m\\tX_CG A -> 1.19 0.00 0.01\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 1 \\t-> B 0.000 -0.089 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 0.089 0.206 0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 0.089 0.206 -0.007\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 2.6141\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 2 \\t-> B -0.010 -0.019 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 0.019 0.403 0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 0.019 0.403 -0.001\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 7.3672\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 3 \\t-> B -0.019 -0.087 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 0.234 0.800 0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 0.234 0.800 -0.018\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 5.8780\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 4 \\t-> B -0.019 -0.084 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 0.390 1.238 0.001\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 0.389 1.238 -0.030\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 2.8288\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 5 \\t-> B -0.018 -0.081 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 0.546 1.676 0.001\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 0.544 1.676 -0.041\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 5.4372\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 6 \\t-> B -0.017 -0.078 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 0.702 2.113 0.002\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 0.700 2.113 -0.053\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 2.6084\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 7 \\t-> B -0.016 -0.074 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 0.857 2.551 0.003\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 0.855 2.551 -0.064\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 4.9963\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 8 \\t-> B -0.016 -0.071 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 1.013 2.988 0.004\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 1.010 2.988 -0.076\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 2.3879\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 9 \\t-> B -0.015 -0.068 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 1.169 3.426 0.005\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 1.166 3.426 -0.087\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 4.5555\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 10 \\t-> B -0.014 -0.065 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 1.325 3.863 0.006\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 1.321 3.863 -0.098\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 2.1675\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 11 \\t-> B -0.013 -0.061 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 1.480 4.301 0.007\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 1.476 4.301 -0.109\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 4.1146\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 12 \\t-> B -0.013 -0.058 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 1.636 4.739 0.009\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 1.632 4.739 -0.120\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 1.9471\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 13 \\t-> B -0.012 -0.055 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 1.792 5.176 0.010\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 1.787 5.176 -0.131\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 3.6738\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 14 \\t-> B -0.011 -0.052 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 1.948 5.614 0.011\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 1.943 5.614 -0.142\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 1.7267\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 15 \\t-> B -0.011 -0.048 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 2.104 6.052 0.012\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 2.098 6.052 -0.153\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 3.2329\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 16 \\t-> B -0.010 -0.045 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 2.260 6.489 0.014\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 2.254 6.489 -0.164\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 1.5062\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 17 \\t-> B -0.009 -0.042 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 2.415 6.927 0.015\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 2.409 6.927 -0.175\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 2.7921\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 18 \\t-> B -0.008 -0.039 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 2.571 7.364 0.016\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 2.564 7.364 -0.186\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 1.2858\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 19 \\t-> B -0.008 -0.035 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 2.727 7.802 0.017\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 2.720 7.802 -0.197\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 2.3512\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 20 \\t-> B -0.007 -0.032 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 2.883 8.239 0.019\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 2.875 8.239 -0.208\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 1.0654\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 21 \\t-> B -0.006 -0.028 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 3.038 8.677 0.020\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 3.030 8.677 -0.219\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 1.9104\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 22 \\t-> B -0.006 -0.026 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 3.194 9.114 0.021\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 3.186 9.114 -0.230\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 0.8450\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 23 \\t-> B -0.005 -0.022 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 3.350 9.552 0.023\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 3.341 9.552 -0.241\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 1.4695\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 24 \\t-> B -0.005 -0.022 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 3.508 9.988 0.024\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 3.499 9.988 -0.252\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 0.3674\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 25 \\t-> B 0.000 0.089 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 0.089 -0.206 0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 0.089 -0.206 -0.007\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 2.6141\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 26 \\t-> B -0.010 0.019 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 0.019 -0.403 0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 0.019 -0.403 -0.001\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 7.3672\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 27 \\t-> B -0.019 0.087 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 0.234 -0.800 0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 0.234 -0.800 -0.018\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 5.8780\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 28 \\t-> B -0.019 0.084 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 0.390 -1.238 0.001\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 0.389 -1.238 -0.030\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 2.8288\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 29 \\t-> B -0.018 0.081 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 0.546 -1.676 0.001\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 0.544 -1.676 -0.041\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 5.4372\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 30 \\t-> B -0.017 0.078 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 0.702 -2.113 0.002\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 0.700 -2.113 -0.053\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 2.6084\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 31 \\t-> B -0.016 0.074 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 0.857 -2.551 0.003\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 0.855 -2.551 -0.064\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 4.9963\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 32 \\t-> B -0.016 0.071 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 1.013 -2.988 0.004\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 1.010 -2.988 -0.076\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 2.3879\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 33 \\t-> B -0.015 0.068 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 1.169 -3.426 0.005\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 1.166 -3.426 -0.087\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 4.5555\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 34 \\t-> B -0.014 0.065 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 1.325 -3.863 0.006\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 1.321 -3.863 -0.098\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 2.1675\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 35 \\t-> B -0.013 0.061 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 1.480 -4.301 0.007\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 1.476 -4.301 -0.109\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 4.1146\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 36 \\t-> B -0.013 0.058 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 1.636 -4.739 0.009\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 1.632 -4.739 -0.120\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 1.9471\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 37 \\t-> B -0.012 0.055 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 1.792 -5.176 0.010\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 1.787 -5.176 -0.131\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 3.6738\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 38 \\t-> B -0.011 0.052 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 1.948 -5.614 0.011\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 1.943 -5.614 -0.142\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 1.7267\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 39 \\t-> B -0.011 0.048 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 2.104 -6.052 0.012\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 2.098 -6.052 -0.153\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 3.2329\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 40 \\t-> B -0.010 0.045 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 2.260 -6.489 0.014\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 2.254 -6.489 -0.164\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 1.5062\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 41 \\t-> B -0.009 0.042 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 2.415 -6.927 0.015\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 2.409 -6.927 -0.175\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 2.7921\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 42 \\t-> B -0.008 0.039 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 2.571 -7.364 0.016\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 2.564 -7.364 -0.186\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 1.2858\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 43 \\t-> B -0.008 0.035 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 2.727 -7.802 0.017\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 2.720 -7.802 -0.197\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 2.3512\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 44 \\t-> B -0.007 0.032 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 2.883 -8.239 0.019\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 2.875 -8.239 -0.208\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 1.0654\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 45 \\t-> B -0.006 0.028 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 3.038 -8.677 0.020\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 3.030 -8.677 -0.219\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 1.9104\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 46 \\t-> B -0.006 0.026 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 3.194 -9.114 0.021\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 3.186 -9.114 -0.230\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 0.8450\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 47 \\t-> B -0.005 0.022 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 3.350 -9.552 0.023\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 3.341 -9.552 -0.241\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 1.4695\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mNode 48 \\t-> B -0.005 0.022 -0.000\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> A 3.508 -9.988 0.024\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\t\\t-> G 3.499 -9.988 -0.252\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\tNode mass:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36m\\t\\tMatrix: 0.3674\\u001b[0m\\n\",\n\t\t\t\t\t\t\" Updated the beam C, modal C and K matrices with the terms from the\\n\",\n\t\t\t\t\t\t\"gravity linearisation\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Aeroelastic system assembled:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m\\tAerodynamic states: 1536\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m\\tStructural states: 594\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m\\tTotal states: 2130\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m\\tInputs: 893\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m\\tOutputs: 891\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34mFinal system is:\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34mState-space system\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34mStates: 2130\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34mInputs: 893\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34mOutputs: 891\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mGenerating an instance of AsymptoticStability\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable reference_velocity has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: 1.0\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable display_root_locus has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable velocity_analysis has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: []\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable iterative_eigvals has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable modes_to_plot has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: []\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable postprocessors has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: []\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Variable postprocessors_settings has no assigned value in the settings file.\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Dynamical System Eigenvalues\\u001b[0m\\n\",\n\t\t\t\t\t\t\"Calculating eigenvalues using direct method\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[0m\\n\",\n\t\t\t\t\t\t\"|==============|==============|==============|==============|==============|==============|==============|\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| mode | eval_real | eval_imag | freq_n (Hz) | freq_d (Hz) | damping | period (s) |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"|==============|==============|==============|==============|==============|==============|==============|\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 0 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 1 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 2 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 3 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 4 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 5 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 6 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 7 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 8 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 9 | -0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 10 | -0.000884 | -0.321712 | 0.051202 | 0.051202 | 0.002747 | 19.530439 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 11 | -0.000884 | 0.321712 | 0.051202 | 0.051202 | 0.002747 | 19.530439 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 12 | -0.008470 | -0.391287 | 0.062290 | 0.062275 | 0.021642 | 16.057731 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 13 | -0.008470 | 0.391287 | 0.062290 | 0.062275 | 0.021642 | 16.057731 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 14 | -0.022506 | 0.000000 | 0.003582 | 0.000000 | 1.000000 | inf |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 15 | -0.064808 | -53.732514 | 8.551801 | 8.551795 | 0.001206 | 0.116935 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 16 | -0.064808 | 53.732514 | 8.551801 | 8.551795 | 0.001206 | 0.116935 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 17 | -0.101946 | 68.319141 | 10.873341 | 10.873329 | 0.001492 | 0.091968 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 18 | -0.101946 | -68.319141 | 10.873341 | 10.873329 | 0.001492 | 0.091968 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 19 | -0.147587 | 83.265282 | 13.252102 | 13.252081 | 0.001772 | 0.075460 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 20 | -0.147587 | -83.265282 | 13.252102 | 13.252081 | 0.001772 | 0.075460 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 21 | -0.248703 | -109.925782 | 17.495276 | 17.495232 | 0.002262 | 0.057158 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 22 | -0.248703 | 109.925782 | 17.495276 | 17.495232 | 0.002262 | 0.057158 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 23 | -0.293472 | 120.387631 | 19.160344 | 19.160287 | 0.002438 | 0.052191 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 24 | -0.293472 | -120.387631 | 19.160344 | 19.160287 | 0.002438 | 0.052191 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 25 | -0.350319 | 132.903280 | 21.152288 | 21.152214 | 0.002636 | 0.047276 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 26 | -0.350319 | -132.903280 | 21.152288 | 21.152214 | 0.002636 | 0.047276 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 27 | -0.376401 | 138.516954 | 22.045739 | 22.045658 | 0.002717 | 0.045360 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 28 | -0.376401 | -138.516954 | 22.045739 | 22.045658 | 0.002717 | 0.045360 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 29 | -0.494445 | 162.714232 | 25.896894 | 25.896774 | 0.003039 | 0.038615 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 30 | -0.494445 | -162.714232 | 25.896894 | 25.896774 | 0.003039 | 0.038615 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 31 | -0.511651 | -166.238306 | 26.457773 | 26.457648 | 0.003078 | 0.037796 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 32 | -0.511651 | 166.238306 | 26.457773 | 26.457648 | 0.003078 | 0.037796 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 33 | -0.559180 | 175.709816 | 27.965227 | 27.965086 | 0.003182 | 0.035759 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 34 | -0.559180 | -175.709816 | 27.965227 | 27.965086 | 0.003182 | 0.035759 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 35 | -0.569755 | 177.873274 | 28.309556 | 28.309411 | 0.003203 | 0.035324 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 36 | -0.569755 | -177.873274 | 28.309556 | 28.309411 | 0.003203 | 0.035324 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 37 | -0.669914 | -197.999020 | 31.512703 | 31.512523 | 0.003383 | 0.031733 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 38 | -0.669914 | 197.999020 | 31.512703 | 31.512523 | 0.003383 | 0.031733 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 39 | -0.678424 | 199.782714 | 31.796590 | 31.796406 | 0.003396 | 0.031450 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 40 | -0.678424 | -199.782714 | 31.796590 | 31.796406 | 0.003396 | 0.031450 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 41 | -0.715684 | 207.440562 | 33.015387 | 33.015191 | 0.003450 | 0.030289 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 42 | -0.715684 | -207.440562 | 33.015387 | 33.015191 | 0.003450 | 0.030289 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 43 | -0.721193 | -208.623018 | 33.203583 | 33.203385 | 0.003457 | 0.030117 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 44 | -0.721193 | 208.623018 | 33.203583 | 33.203385 | 0.003457 | 0.030117 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 45 | -0.796838 | -224.809928 | 35.779836 | 35.779611 | 0.003544 | 0.027949 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 46 | -0.796838 | 224.809928 | 35.779836 | 35.779611 | 0.003544 | 0.027949 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 47 | -0.801462 | -225.851223 | 35.945565 | 35.945339 | 0.003549 | 0.027820 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 48 | -0.801462 | 225.851223 | 35.945565 | 35.945339 | 0.003549 | 0.027820 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 49 | -0.823218 | 257.880058 | 41.043095 | 41.042886 | 0.003192 | 0.024365 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 50 | -0.823218 | -257.880058 | 41.043095 | 41.042886 | 0.003192 | 0.024365 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 51 | -0.829849 | 232.223377 | 36.959734 | 36.959498 | 0.003573 | 0.027057 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 52 | -0.829849 | -232.223377 | 36.959734 | 36.959498 | 0.003573 | 0.027057 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 53 | -0.833132 | 232.986723 | 37.081226 | 37.080989 | 0.003576 | 0.026968 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 54 | -0.833132 | -232.986723 | 37.081226 | 37.080989 | 0.003576 | 0.026968 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 55 | -0.837692 | 252.830750 | 40.239484 | 40.239264 | 0.003313 | 0.024851 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 56 | -0.837692 | -252.830750 | 40.239484 | 40.239264 | 0.003313 | 0.024851 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 57 | -0.843057 | -274.636584 | 43.709976 | 43.709770 | 0.003070 | 0.022878 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 58 | -0.843057 | 274.636584 | 43.709976 | 43.709770 | 0.003070 | 0.022878 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 59 | -0.855990 | -264.468496 | 42.091689 | 42.091468 | 0.003237 | 0.023758 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 60 | -0.855990 | 264.468496 | 42.091689 | 42.091468 | 0.003237 | 0.023758 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 61 | -0.864725 | 271.184095 | 43.160509 | 43.160289 | 0.003189 | 0.023169 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 62 | -0.864725 | -271.184095 | 43.160509 | 43.160289 | 0.003189 | 0.023169 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 63 | -0.871325 | -283.421756 | 45.108187 | 45.107973 | 0.003074 | 0.022169 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 64 | -0.871325 | 283.421756 | 45.108187 | 45.107973 | 0.003074 | 0.022169 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 65 | -0.878445 | 267.336890 | 42.548217 | 42.547987 | 0.003286 | 0.023503 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 66 | -0.878445 | -267.336890 | 42.548217 | 42.547987 | 0.003286 | 0.023503 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 67 | -0.882869 | -280.833495 | 44.696260 | 44.696039 | 0.003144 | 0.022373 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 68 | -0.882869 | 280.833495 | 44.696260 | 44.696039 | 0.003144 | 0.022373 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 69 | -0.884024 | -245.027542 | 38.997598 | 38.997344 | 0.003608 | 0.025643 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 70 | -0.884024 | 245.027542 | 38.997598 | 38.997344 | 0.003608 | 0.025643 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 71 | -0.886589 | -245.661879 | 39.098557 | 39.098302 | 0.003609 | 0.025577 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 72 | -0.886589 | 245.661879 | 39.098557 | 39.098302 | 0.003609 | 0.025577 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 73 | -0.891210 | -288.915188 | 45.982499 | 45.982280 | 0.003085 | 0.021748 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 74 | -0.891210 | 288.915188 | 45.982499 | 45.982280 | 0.003085 | 0.021748 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 75 | -0.908699 | 251.206723 | 39.981053 | 39.980792 | 0.003617 | 0.025012 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 76 | -0.908699 | -251.206723 | 39.981053 | 39.980792 | 0.003617 | 0.025012 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 77 | -0.910251 | -251.606127 | 40.044621 | 40.044359 | 0.003618 | 0.024972 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 78 | -0.910251 | 251.606127 | 40.044621 | 40.044359 | 0.003618 | 0.024972 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 79 | -0.914184 | -241.156682 | 38.381554 | 38.381278 | 0.003791 | 0.026054 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 80 | -0.914184 | 241.156682 | 38.381554 | 38.381278 | 0.003791 | 0.026054 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 81 | -0.915395 | 290.517030 | 46.237451 | 46.237221 | 0.003151 | 0.021628 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 82 | -0.915395 | -290.517030 | 46.237451 | 46.237221 | 0.003151 | 0.021628 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 83 | -0.933974 | -278.955360 | 44.397373 | 44.397124 | 0.003348 | 0.022524 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 84 | -0.933974 | 278.955360 | 44.397373 | 44.397124 | 0.003348 | 0.022524 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 85 | -0.943144 | -260.320871 | 41.431625 | 41.431353 | 0.003623 | 0.024136 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 86 | -0.943144 | 260.320871 | 41.431625 | 41.431353 | 0.003623 | 0.024136 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 87 | -0.944542 | -260.700481 | 41.492043 | 41.491770 | 0.003623 | 0.024101 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 88 | -0.944542 | 260.700481 | 41.492043 | 41.491770 | 0.003623 | 0.024101 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 89 | -0.953003 | -294.814043 | 46.921357 | 46.921112 | 0.003233 | 0.021312 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 90 | -0.953003 | 294.814043 | 46.921357 | 46.921112 | 0.003233 | 0.021312 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 91 | -0.960626 | -295.652742 | 47.054844 | 47.054595 | 0.003249 | 0.021252 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 92 | -0.960626 | 295.652742 | 47.054844 | 47.054595 | 0.003249 | 0.021252 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 93 | -0.960976 | -265.315963 | 42.226624 | 42.226347 | 0.003622 | 0.023682 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 94 | -0.960976 | 265.315963 | 42.226624 | 42.226347 | 0.003622 | 0.023682 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 95 | -0.961739 | 300.017779 | 47.749558 | 47.749313 | 0.003206 | 0.020943 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 96 | -0.961739 | -300.017779 | 47.749558 | 47.749313 | 0.003206 | 0.020943 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 97 | -0.961940 | -265.596058 | 42.271203 | 42.270925 | 0.003622 | 0.023657 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 98 | -0.961940 | 265.596058 | 42.271203 | 42.270925 | 0.003622 | 0.023657 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"| 99 | -0.965385 | -266.582863 | 42.428259 | 42.427980 | 0.003621 | 0.023569 |\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mFINISHED - Elapsed time = 16.3462206 seconds\\u001b[0m\\n\",\n\t\t\t\t\t\t\"\\u001b[36mFINISHED - CPU process time = 68.0131146 seconds\\u001b[0m\\n\"\n\t\t\t\t\t]\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": [\n\t\t\t\t\"data = sharpy.sharpy_main.main(['', ws.case_route + '/' + ws.case_name + '.sharpy'])\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"## Post-processing\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"### Nonlinear Equilibrium\\n\",\n\t\t\t\t\"\\n\",\n\t\t\t\t\"The files can be opened with Paraview to see the deformation and aerodynamic loading on the flying wing in trim conditions.\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"### Asymptotic Stability\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 17,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [],\n\t\t\t\"source\": [\n\t\t\t\t\"eigenvalues_trim = np.loadtxt('./output/horten_u_inf2800_M4N11Msf5/stability/eigenvalues.dat')\\n\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"#### Flight Dynamics modes\\n\",\n\t\t\t\t\"\\n\",\n\t\t\t\t\"The flight dynamics modes can be found close to the origin of the Argand diagram. In particular, the phugoid is the mode that is closest to the imaginary axis. An exercise is left to the user to compare this phugoid predicition with the nonlinear response!\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 18,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [\n\t\t\t\t{\n\t\t\t\t\t\"data\": {\n\t\t\t\t\t\t\"image/png\": 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xmZrk5cZiZWS5OHGZmlkvmxCHpvHRYdTMzm8DytDheBdwl6QeSFqh2LkwzM5sQMieOiPgsySROVwDnAI9I+j+SDi4oNjMzK6FcfRwREcCf0seLwN7AtZIuKSA2MzMroTwzAH4SOBt4Crgc+FREvCBpF+AR4B+KCdHMzMokU+JI+zOOAv42IrabYzwitkl6RxHBmZlZ+WQ6VZWeoppbmzSq9j9Y16jMzKy08vRx3Cbp2MIiMTOzlpBn6tj5wEclrQX6GRrk8MhCIjMzs1LKkzhOKSwKMzNrGXnmHF+b3jk+B9i9atew/R5mZjY+5bkc91ygAswCVgMnALcBJxYTmpmZlVGezvEKcCywNiLmA3OBJwuJyszMSitP4tgaEVsBJE2OiIeA1xYTlpmZlVWezvH1ktqA64CbJW0CnigmLDMzK6s8neOnp4vdkpYC04EbC4nKzMxKK0+LY1BELK93IGZm1hryXFU1Gfg7YHb16yLiop0NQtIM4Or02I8DZ0bEppoyRwPfAPYCXgL+KSKu3tn3NjOzfPJ0jl8PnEYynHp/1aMeLgBuiYg5wC3peq0twAcj4jBgAfCVtM/FzMwaKM+pqlkRsaCgOE4D5qXLVwLLgE9XF4iI31UtPyFpI/BKoK+gmMzMbBh5Why/kXREQXHMjIgNAOnzfqMVlnQcsBvwaEHxmJnZCJSMmJ6hoPQAyXAjjwHPkXOQQ0m/JJm3vNaFwJUR0VZVdlNE7D3CcfYnaZGcHRG3j1BmIbAQYObMmR2LFy/OEmKhNm/ezNSpU5sdRim4Loa4Loa4LoaUoS7mz5+/MiI6h9uXJ3EcQJosqrdHxB92NkBJDwPzImLDQGKIiJfdXChpL5Kk8c8RcU2WY3d2dsaKFSt2NsSdtmzZMubNm9fsMErBdTHEdTHEdTGkDHUhacTEMWYfh6T/jIg3AvezfdIYSCJ71SHGJSTT0l6cPl8/TBy7AT8Gvps1aZiZWf2N2ceRJg0iYlpE7FX1mBYR9UgakCSMkyU9ApycriOpU9LlaZkzgTcD50hanT6OrtP7m5lZRjt0A2C9RcSfgbcOs30FcG66fBVwVYNDMzOzGnluAFw0zOangZURsbp+IZmZWZnluRy3E/gY8Jr0sZDk3otvSfqH+odmZmZllOdU1T7AMRGxGUDSF4BrSfodVgKX1D88MzMrmzwtjgOA56vWXwAOjIhnSe7rMDOzCSBPi+P7wO2SBi6VfSfw75KmAA/UPTIzMyulPPNxfFHSDcAbSe7h+Fh61RPA+4oIzszMyifv5biPAZOA3YE9Jb05Im6tf1hmZlZWeS7HPReoALOA1cAJwG3AicWEZmZmZZSnc7wCHAusjYj5wFzgyUKiMjOz0sqTOLZGxFZIZgOMiIeAlw1EaGZm41uePo716Yx71wE3S9oEPFFMWGZmVlZ5rqo6PV3slrQUmA7cWEhUZmZWWjs0yGFELK93IGZm1hryXFXVSTJb34HVr8s6A6CZmY0PeVoc/w/4FHAvsK2YcMzMrOzyJI4nI2JJYZGYmVlLyJM4vpDOxncLVYMaRsSP6h6VmZmVVp7E8SHgdcArGDpVFYATh1lOEYGkEdfNyixP4jgqIo4oLBKzCaK7u5u+vj56enqAJGl0dXXR1tZGd3d3c4MzyyDPneO3Szq0sEjMJoCIoK+vj97eXrq6ugDo6uqit7eXvr4+IqLJEZqNLU+L443AOZIeI+njEBC+HNcsO0mDLY3e3l7a29vp7e2lUqnQ09Pj01XWEvK0ON4GHAKcDLwDeHv6bGY5VCePAU4a1krGTBySnpH0V+A+kns47ksf96fPZpbDQJ9Gta6uLp+mspYx5qmqiJjWiEDMJoKBpDFweqqjo4NKpUJvby/gloe1hh0aq8rMdowk2traBvs0li9fPnjaqq2tzUnDWoITh1mDdXd3b3ffxkCfh5OGtYo8neNmVie1ScJJw1qJE4eZmeXixGFmZrk4cZiZWS5OHGZmlosTh5mZ5eLEYdYgtXeG+05xa1VOHGYN0N3dvd2wIgN3kG/YsKHJkZnl58RhVrDaodSrhx158cUX3fKwllOKO8clzQCuBmYDjwNnRsSmEcruBTwI/DgizmtUjGY7qnYo9YFxqSqVCu3t7b75z1pOWVocFwC3RMQckjnNLxil7BeB5Q2JyqxORhpK3awVlSVxnAZcmS5fCbxruEKSOoCZwE0NisusLkYaSt2sFakM51cl9UVEW9X6pojYu6bMLsCvgA8AbwU6RzpVJWkhsBBg5syZHYsXLy4s9qw2b97M1KlTmx1GKUzEuli3bh0bN25kv/32o729fXD9oIMOYsaMGc0OrxQm4t/FSMpQF/Pnz18ZEZ3D7WtYH4ekXwKvGmbXhRkP8QnghohYN9Y54Yi4DLgMoLOzM+bNm5cj0mIsW7aMMsRRBhOxLrq7u+nr62PRokVIGmyBvPrVr55wdTGSifh3MZKy10XDEkdEnDTSPkn/JWn/iNggaX9g4zDF3gC8SdIngKnAbpI2R8Ro/SFmpTDSUOrLl7u7zlpPKa6qApYAZwMXp8/X1xaIiPcNLEs6h+RUlZOGtQwPpW7jRVk6xy8GTpb0CHByuo6kTkmXNzUyMzPbTilaHBHxZ5IO79rtK4Bzh9n+HeA7hQdmZmYvU5YWh5mZtQgnDjMzy8WJw8zMcnHiMDOzXJw4zMwsFycOMzPLxYnDzMxyceIwM7NcnDjMzCwXJw4zM8vFicPMzHJx4jAzs1ycOMzMLBcnDjMzy8WJw8zMcnHiMDOzXBQRzY6hUJKeBNY2Ow5gX+CpZgdREq6LIa6LIa6LIWWoiwMj4pXD7Rj3iaMsJK2IiM5mx1EGroshroshroshZa8Ln6oyM7NcnDjMzCwXJ47GuazZAZSI62KI62KI62JIqevCfRxmZpaLWxxmZpaLE4eZmeXixFEQSTMk3SzpkfR571HK7iXpj5K+2sgYGyVLXUg6WtJtku6XdI+kv29GrEWRtEDSw5LWSLpgmP2TJV2d7r9D0uzGR1m8DPWwSNID6d/ALZIObEacjTJWfVSVO0NSSCrFJbpOHMW5ALglIuYAt6TrI/kisLwhUTVHlrrYAnwwIg4DFgBfkdTWwBgLI2kS8DXgFOBQ4D2SDq0p9hFgU0QcAvQAX2pslMXLWA+rgM6IOBK4FriksVE2Tsb6QNI04JPAHY2NcGROHMU5DbgyXb4SeNdwhSR1ADOBmxoUVzOMWRcR8buIeCRdfgLYCAx712oLOg5YExGPRcTzwGKSOqlWXUfXAm+VpAbG2Ahj1kNELI2ILenq7cCsBsfYSFn+LiD5YXkJsLWRwY3GiaM4MyNiA0D6vF9tAUm7AP8CfKrBsTXamHVRTdJxwG7Aow2IrRFeA6yrWl+fbhu2TES8CDwN7NOQ6BonSz1U+wjw80Ijaq4x60PSXKA9In7ayMDGsmuzA2hlkn4JvGqYXRdmPMQngBsiYl2r/7isQ10MHGd/4HvA2RGxrR6xlcBw/7i118FnKdPqMn9GSe8HOoG3FBpRc41aH+kPyx7gnEYFlJUTx06IiJNG2ifpvyTtHxEb0i/DjcMUewPwJkmfAKYCu0naHBGj9YeUUh3qAkl7AT8DPhsRtxcUajOsB9qr1mcBT4xQZr2kXYHpwF8aE17DZKkHJJ1E8oPjLRHxXINia4ax6mMacDiwLP1h+SpgiaRTI2JFw6Ichk9VFWcJcHa6fDZwfW2BiHhfRBwQEbOB84HvtmLSyGDMupC0G/Bjkjq4poGxNcJdwBxJB6Wf8yySOqlWXUdnAL+K8Xd37pj1kJ6a+SZwakQM+wNjHBm1PiLi6YjYNyJmp98Rt5PUS1OTBjhxFOli4GRJjwAnp+tI6pR0eVMja7wsdXEm8GbgHEmr08fRzQm3vtI+i/OAXwAPAj+IiPslXSTp1LTYFcA+ktYAixj9KryWlLEevkzS+r4m/RuoTbDjRsb6KCUPOWJmZrm4xWFmZrk4cZiZWS5OHGZmlosTh5mZ5eLEYWZmuThxmJlZLk4cVmqSXkqv579P0k92ZsRcSZszvMc1kvbMccy29M7/LGU/KulPkn4r6VFJH8zwmj0kLU9HUkXSEZLWSvp4VZndJN2a3nFe+/rZkp6VtDrrZxohjm5J59ds+6ak/z5CzKslPS9p3515XysnJw4ru2cj4uiIOJxkCI7/WfB7PA98LMuL0tFrZ5CMOZbFkUB3RBwFvAf41wyv+TDwo4h4CSAi7iW5w3gw6aQjq94CjDSHyaMR8bKbKZXYme+A40nuZt5ORDybvt/LhhOx8cGJw1rJbaSjh0p6v6Q701+23xz4RZ7uu07SSiWTQi3M+R7/ARwy0nHSX/APSvo6cDfJHd8Hp3F8eYxjHwE8nC7/niRJDcR8kKTrJa1IP9dr013v4+VDtGwEDqvZdl1adlTDxN8+Un1JulDJJEO/BF5bc5zXA78Ddpf0s7QVdZ/G2QRcNoKI8MOP0j6AzenzJOAakkmeXg/8BHhFuu/rJJNADbxmRvq8B3AfsE/1sUZ5j11JvqQ/PtJxgNnANuCEdN9s4L6Mn2UT8GqSUVH/EfhQuv0VJC2Gg9P1vwH+L8nQ8n8a5jjXAM8BB1ZtmwQ8OUzZ7eKrjX+Uz9kB3AvsCewFrAHOr3rNIpLW0N8B36raPr1q+XFg32b/DflR/4dHx7Wy2yM9Pz8bWAncDHyc5IvtrnTU0D3YfsTdT0o6PV1uB+YAf87wHpC0OK4Y5Th/AtZGztF7JbWTjHZ6A0mr6R6gO939LpIWxA/Tz7NrGse+QF/NcRYAU0hGET4MWAsQES+lfQrTIuKZMcKpjX+4z3kC8ONIJ1UaZsyotwEfIhlX6lJJXwJ+GhH/McZ72zjgxGFl92xEHC1pOvBTkj6OAK6MiM/UFpY0DzgJeENEbJG0DNg9y3vkOE7/DnyOI4FbI+JEJXOu30cyrP5vgKOACyPiiuoXpOV2r1rfnWQmuFNJvrQPJ0lEAyaTbZa4wfjH+JwjzZWxJ9AWyUyNA7NY/g3wz5JuioiLMsRgLcx9HNYSIuJpknmXzwduBc6QtB+ApBmSDkyLTieZu3uLpNeR/HLeEVmP8wxJS2KQpFsk1c5sdwTJfNpExCbg+8Db030bgLcNdFSnV04pLTcpTRgAnyUZdv5xktNIh1e95z4kp6peqNPnvBU4Pb1CahrwzqrXzAeWpu/7amBLRFwFXAock/P9rQU5cVjLiIhVwG9Jfr1/FrhJ0j0kp6/2T4vdCOyabv8iw1z1k1Gm40TEn4Ffpx3DX06//A/h5ZMwDSaO1E9IfqUDfJvk/+KD6SmzT0fEwK/9m4A3pp3lJwNfSbdvlzhIvsyrWx9ZDfs5I+Ju4GpgNfBDklNnA05JXzfwue5M474Q+N87EIO1GA+rblZHkg4HPhwRi+p0vLnAooj4wBjlfgR8JiIertk+m6Tv4fDhXreDMd0NHD9W60bS40BnRDxVr/e2cnCLw6yOIuK+eiWN9HirgKXVlxvXUjJ73HW1SSP1EjB9Z28ArInpmNGSxsANgCRXi42XeeOtilscZmaWi1scZmaWixOHmZnl4sRhZma5OHGYmVkuThxmZpaLE4eZmeXixGFmZrk4cZiZWS7/H/gm2+tWJNTyAAAAAElFTkSuQmCC\",\n\t\t\t\t\t\t\"text/plain\": [\n\t\t\t\t\t\t\t\"
\"\n\t\t\t\t\t\t]\n\t\t\t\t\t},\n\t\t\t\t\t\"metadata\": {\n\t\t\t\t\t\t\"needs_background\": \"light\"\n\t\t\t\t\t},\n\t\t\t\t\t\"output_type\": \"display_data\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": [\n\t\t\t\t\"fig = plt.figure()\\n\",\n\t\t\t\t\"plt.scatter(eigenvalues_trim[:, 0], eigenvalues_trim[:, 1],\\n\",\n\t\t\t\t\" marker='x',\\n\",\n\t\t\t\t\" color='k')\\n\",\n\t\t\t\t\"plt.xlim(-0.5, 0.5)\\n\",\n\t\t\t\t\"plt.ylim(-0.5, 0.5)\\n\",\n\t\t\t\t\"plt.grid()\\n\",\n\t\t\t\t\"plt.xlabel('Real Part, $Re(\\\\lambda)$ [rad/s]')\\n\",\n\t\t\t\t\"plt.ylabel('Imaginary Part, $Im(\\\\lambda)$ [rad/s]');\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"markdown\",\n\t\t\t\"metadata\": {},\n\t\t\t\"source\": [\n\t\t\t\t\"#### Structural Modes\\n\",\n\t\t\t\t\"\\n\",\n\t\t\t\t\"Looking further out on the plot, the structural modes appear. There is a curve given the Newmark-$\\\\beta$ integration scheme and on top of it several modes are damped by the presence of the aerodynamics.\\n\",\n\t\t\t\t\"\\n\",\n\t\t\t\t\"Try changing `newmark_damp` in the `LinearAssembler` settings to see how this plot changes!\"\n\t\t\t]\n\t\t},\n\t\t{\n\t\t\t\"cell_type\": \"code\",\n\t\t\t\"execution_count\": 19,\n\t\t\t\"metadata\": {},\n\t\t\t\"outputs\": [\n\t\t\t\t{\n\t\t\t\t\t\"data\": {\n\t\t\t\t\t\t\"image/png\": 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\",\n\t\t\t\t\t\t\"text/plain\": [\n\t\t\t\t\t\t\t\"
\"\n\t\t\t\t\t\t]\n\t\t\t\t\t},\n\t\t\t\t\t\"metadata\": {\n\t\t\t\t\t\t\"needs_background\": \"light\"\n\t\t\t\t\t},\n\t\t\t\t\t\"output_type\": \"display_data\"\n\t\t\t\t}\n\t\t\t],\n\t\t\t\"source\": [\n\t\t\t\t\"fig = plt.figure()\\n\",\n\t\t\t\t\"plt.scatter(eigenvalues_trim[:, 0], eigenvalues_trim[:, 1],\\n\",\n\t\t\t\t\" marker='x',\\n\",\n\t\t\t\t\" color='k')\\n\",\n\t\t\t\t\"plt.xlim(-5, 0.5)\\n\",\n\t\t\t\t\"plt.ylim(-200, 200)\\n\",\n\t\t\t\t\"plt.grid()\\n\",\n\t\t\t\t\"plt.xlabel('Real Part, $Re(\\\\lambda)$ [rad/s]')\\n\",\n\t\t\t\t\"plt.ylabel('Imaginary Part, $Im(\\\\lambda)$ [rad/s]');\"\n\t\t\t]\n\t\t}\n\t],\n\t\"metadata\": {\n\t\t\"kernelspec\": {\n\t\t\t\"display_name\": \"Python 3\",\n\t\t\t\"language\": \"python\",\n\t\t\t\"name\": \"python3\"\n\t\t},\n\t\t\"language_info\": {\n\t\t\t\"codemirror_mode\": {\n\t\t\t\t\"name\": \"ipython\",\n\t\t\t\t\"version\": 3\n\t\t\t},\n\t\t\t\"file_extension\": \".py\",\n\t\t\t\"mimetype\": \"text/x-python\",\n\t\t\t\"name\": \"python\",\n\t\t\t\"nbconvert_exporter\": \"python\",\n\t\t\t\"pygments_lexer\": \"ipython3\",\n\t\t\t\"version\": \"3.7.5\"\n\t\t}\n\t},\n\t\"nbformat\": 4,\n\t\"nbformat_minor\": 4\n}\n" }, { "path": "docs/source/content/example_notebooks/nonlinear_t-tail_HALE.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"%load_ext autoreload\\n\",\n \"%autoreload 2\\n\",\n \"%matplotlib inline\\n\",\n \"%config InlineBackend.figure_format = 'svg'\\n\",\n \"import numpy as np\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"from IPython.display import Image\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# T-Tail HALE Model tutorial\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The HALE T-Tail model intends to be a representative example of a typical HALE configuration, with high flexibility and aspect-ratio.\\n\",\n \"\\n\",\n \"A geometry outline and a summary of the beam properties are given next\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 2,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"url = 'https://raw.githubusercontent.com/ImperialCollegeLondon/sharpy/dev_doc/docs/source/content/example_notebooks/images/t-tail_geometry.png'\\n\",\n \"Image(url=url, width=800)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 3,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"url = 'https://raw.githubusercontent.com/ImperialCollegeLondon/sharpy/dev_doc/docs/source/content/example_notebooks/images/t-tail_properties.png'\\n\",\n \"Image(url=url, width=500)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This case is included in `tests/coupled/simple_HALE/`. The `generate_hale.py` file in that folder is the one that, if executed, generates all the required SHARPy files. This document is a step by step guide to how to process that case.\\n\",\n \"\\n\",\n \"The T-Tail HALE model is subject to a 20% 1-cos spanwise constant gust.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"First, let's start with importing SHARPy in our Python environment.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import sharpy\\n\",\n \"import sharpy.sharpy_main as sharpy_main\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"And now the `generate_HALE.py` file needs to be executed.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"route_to_case = '../../../../sharpy/cases/coupled/simple_HALE/'\\n\",\n \"%run '../../../../sharpy/cases/coupled/simple_HALE/generate_hale.py'\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"There should be 3 new files, apart from the original `generate_hale.py`:\"\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 \"__init__.py \\u001b[34moutput\\u001b[m\\u001b[m simple_HALE.fem.h5\\n\",\n \"generate_hale.py simple_HALE.aero.h5 simple_HALE.sharpy\\n\"\n ]\n }\n ],\n \"source\": [\n \"!ls ../../../../sharpy/cases/coupled/simple_HALE/\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"SHARPy can be run now. In the terminal, doing `cd` to the `simple_HALE` folder, the command would look like:\\n\",\n \"```\\n\",\n \"sharpy simple_HALE.sharpy\\n\",\n \"```\\n\",\n \"\\n\",\n \"From a python console with `import sharpy` already run, the command is:\"\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 \"--------------------------------------------------------------------------------\\u001b[0m\\n\",\n \" ###### ## ## ### ######## ######## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ####\\u001b[0m\\n\",\n \" ###### ######### ## ## ######## ######## ##\\u001b[0m\\n\",\n \" ## ## ## ######### ## ## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \" ###### ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \"--------------------------------------------------------------------------------\\u001b[0m\\n\",\n \"Aeroelastics Lab, Aeronautics Department.\\u001b[0m\\n\",\n \" Copyright (c), Imperial College London.\\u001b[0m\\n\",\n \" All rights reserved.\\u001b[0m\\n\",\n \" License available at https://github.com/imperialcollegelondon/sharpy\\u001b[0m\\n\",\n \"\\u001b[36mRunning SHARPy from /home/ng213/2TB/pazy_code/pazy-sharpy/lib/sharpy/docs/source/content/example_notebooks\\u001b[0m\\n\",\n \"\\u001b[36mSHARPy being run is in /home/ng213/2TB/pazy_code/pazy-sharpy/lib/sharpy\\u001b[0m\\n\",\n \"\\u001b[36mThe branch being run is dev_setting_error\\u001b[0m\\n\",\n \"\\u001b[36mThe version and commit hash are: v1.2.1-348-g402e87e-402e87e\\u001b[0m\\n\",\n \"SHARPy output folder set\\u001b[0m\\n\",\n \"\\u001b[34m\\t/home/ng213/2TB/pazy_code/pazy-sharpy/lib/sharpy/cases/coupled/simple_HALE//output//simple_HALE/\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of BeamLoader\\u001b[0m\\n\",\n \"Variable for_pos has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0.0, 0, 0]\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of AerogridLoader\\u001b[0m\\n\",\n \"Variable control_surface_deflection has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: []\\u001b[0m\\n\",\n \"Variable control_surface_deflection_generator_settings has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n \"Variable dx1 has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: -1.0\\u001b[0m\\n\",\n \"Variable ndx1 has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n \"Variable r has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1.0\\u001b[0m\\n\",\n \"Variable dxmax has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: -1.0\\u001b[0m\\n\",\n \"\\u001b[34mThe aerodynamic grid contains 5 surfaces\\u001b[0m\\n\",\n \"\\u001b[34m Surface 0, M=4, N=16\\u001b[0m\\n\",\n \" Wake 0, M=20, N=16\\u001b[0m\\n\",\n \"\\u001b[34m Surface 1, M=4, N=16\\u001b[0m\\n\",\n \" Wake 1, M=20, N=16\\u001b[0m\\n\",\n \"\\u001b[34m Surface 2, M=4, N=8\\u001b[0m\\n\",\n \" Wake 2, M=20, N=8\\u001b[0m\\n\",\n \"\\u001b[34m Surface 3, M=4, N=8\\u001b[0m\\n\",\n \" Wake 3, M=20, N=8\\u001b[0m\\n\",\n \"\\u001b[34m Surface 4, M=4, N=8\\u001b[0m\\n\",\n \" Wake 4, M=20, N=8\\u001b[0m\\n\",\n \" In total: 224 bound panels\\u001b[0m\\n\",\n \" In total: 1120 wake panels\\u001b[0m\\n\",\n \" Total number of panels = 1344\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of StaticTrim\\u001b[0m\\n\",\n \"Variable print_info has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"Variable max_iter has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 100\\u001b[0m\\n\",\n \"Variable fz_tolerance has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.01\\u001b[0m\\n\",\n \"Variable fx_tolerance has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.01\\u001b[0m\\n\",\n \"Variable m_tolerance has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.01\\u001b[0m\\n\",\n \"Variable tail_cs_index has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n \"Variable thrust_nodes has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0]\\u001b[0m\\n\",\n \"Variable initial_angle_eps has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.05\\u001b[0m\\n\",\n \"Variable initial_thrust_eps has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 2.0\\u001b[0m\\n\",\n \"Variable relaxation_factor has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.2\\u001b[0m\\n\",\n \"Variable save_info has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of StaticCoupled\\u001b[0m\\n\",\n \"Variable correct_forces_method has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n \"Variable runtime_generators has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of NonLinearStatic\\u001b[0m\\n\",\n \"Variable newmark_damp has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0001\\u001b[0m\\n\",\n \"Variable gravity_dir has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0.0, 0.0, 1.0]\\u001b[0m\\n\",\n \"Variable relaxation_factor has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.3\\u001b[0m\\n\",\n \"Variable dt has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.01\\u001b[0m\\n\",\n \"Variable num_steps has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 500\\u001b[0m\\n\",\n \"Variable initial_position has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0. 0. 0.]\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of StaticUvlm\\u001b[0m\\n\",\n \"Variable iterative_solver has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable iterative_tol has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0001\\u001b[0m\\n\",\n \"Variable iterative_precond has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable cfl1 has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"Variable vortex_radius has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n \"Variable vortex_radius_wake_ind has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n \"Variable rbm_vel_g has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]\\u001b[0m\\n\",\n \"Variable centre_rot_g has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0.0, 0.0, 0.0]\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"|==========|==========|==========|==========|==========|==========|==========|==========|==========|==========|\\u001b[0m\\n\",\n \"| iter |alpha[deg]|elev[deg] | thrust | Fx | Fy | Fz | Mx | My | Mz |\\u001b[0m\\n\",\n \"|==========|==========|==========|==========|==========|==========|==========|==========|==========|==========|\\u001b[0m\\n\",\n \"| 0 | 4.3100 | -2.0800 | 6.1600 | -0.3600 | -0.0000 | 0.8010 | 0.0000 | -0.6935 | 0.0000 |\\u001b[0m\\n\",\n \"| 0 | 7.1748 | -4.9448 | 6.1600 | -27.8570 | -0.0000 | 280.1530 | 0.0000 |-105.5351 | 0.0000 |\\u001b[0m\\n\",\n \"| 0 | 4.3100 | 0.7848 | 6.1600 | -2.4506 | -0.0000 | 38.7819 | 0.0000 |-377.3661 | -0.0000 |\\u001b[0m\\n\",\n \"| 0 | 4.3100 | -2.0800 | 8.1600 | -2.3600 | -0.0000 | 0.8010 | 0.0000 | -0.6935 | 0.0000 |\\u001b[0m\\n\",\n \"| 1 | 4.3018 | -2.0771 | 5.8000 | 0.0660 | 0.0000 | -0.2782 | -0.0000 | 0.2446 | 0.0000 |\\u001b[0m\\n\",\n \"| 2 | 4.3039 | -2.0778 | 5.8558 | -0.0068 | -0.0000 | 0.0003 | 0.0000 | 0.0008 | 0.0000 |\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of BeamLoads\\u001b[0m\\n\",\n \"Variable output_file_name has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: beam_loads\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of AerogridPlot\\u001b[0m\\n\",\n \"Variable include_unsteady_applied_forces has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable name_prefix has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n \"Variable include_velocities has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable include_incidence_angle has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable num_cores has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n \"Variable vortex_radius has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n \"\\u001b[34m...Finished\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of BeamPlot\\u001b[0m\\n\",\n \"Variable include_FoR has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable include_applied_moments has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"Variable name_prefix has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n \"Variable output_rbm has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"\\u001b[34m...Finished\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of DynamicCoupled\\u001b[0m\\n\",\n \"Variable print_info has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"Variable structural_substeps has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n \"Variable dynamic_relaxation has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable controller_id has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n \"Variable controller_settings has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n \"Variable cleanup_previous_solution has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable steps_without_unsteady_force has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n \"Variable pseudosteps_ramp_unsteady_force has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n \"Variable correct_forces_method has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n \"Variable network_settings has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n \"Variable runtime_generators has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: {}\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of NonLinearDynamicCoupledStep\\u001b[0m\\n\",\n \"Variable num_load_steps has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n \"Variable gravity_dir has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0.0, 0.0, 1.0]\\u001b[0m\\n\",\n \"Variable relaxation_factor has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.3\\u001b[0m\\n\",\n \"Variable balancing has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable initial_velocity_direction has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [-1.0, 0.0, 0.0]\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of StepUvlm\\u001b[0m\\n\",\n \"Variable iterative_solver has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable iterative_tol has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0001\\u001b[0m\\n\",\n \"Variable iterative_precond has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable cfl1 has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"Variable vortex_radius has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n \"Variable vortex_radius_wake_ind has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n \"Variable interp_coords has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n \"Variable filter_method has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n \"Variable interp_method has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0\\u001b[0m\\n\",\n \"Variable yaw_slerp has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0\\u001b[0m\\n\",\n \"Variable centre_rot has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [0.0, 0.0, 0.0]\\u001b[0m\\n\",\n \"Variable quasi_steady has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"\\u001b[36mgamma_dot_filtering does not support even numbers.Changing 6 to 7\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of BeamLoads\\u001b[0m\\n\",\n \"Variable output_file_name has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: beam_loads\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of BeamPlot\\u001b[0m\\n\",\n \"Variable include_FoR has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable include_applied_moments has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"Variable name_prefix has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n \"Variable output_rbm has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: True\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of AerogridPlot\\u001b[0m\\n\",\n \"Variable include_forward_motion has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable include_unsteady_applied_forces has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable name_prefix has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: \\u001b[0m\\n\",\n \"Variable u_inf has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0\\u001b[0m\\n\",\n \"Variable dt has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0\\u001b[0m\\n\",\n \"Variable include_velocities has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable include_incidence_angle has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: False\\u001b[0m\\n\",\n \"Variable num_cores has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1\\u001b[0m\\n\",\n \"Variable vortex_radius has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1e-06\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"|=======|========|======|==============|==============|==============|==============|==============|\\u001b[0m\\n\",\n \"| ts | t | iter | struc ratio | iter time | residual vel | FoR_vel(x) | FoR_vel(z) |\\u001b[0m\\n\",\n \"|=======|========|======|==============|==============|==============|==============|==============|\\u001b[0m\\n\"\n ]\n },\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/home/ng213/2TB/pazy_code/pazy-sharpy/lib/sharpy/sharpy/aero/utils/uvlmlib.py:264: RuntimeWarning: invalid value encountered in true_divide\\n\",\n \" flightconditions.uinf_direction = np.ctypeslib.as_ctypes(ts_info.u_ext[0][:, 0, 0]/flightconditions.uinf)\\n\",\n \"/home/ng213/2TB/pazy_code/pazy-sharpy/lib/sharpy/sharpy/aero/utils/uvlmlib.py:325: RuntimeWarning: invalid value encountered in true_divide\\n\",\n \" flightconditions.uinf_direction = np.ctypeslib.as_ctypes(ts_info.u_ext[0][:, 0, 0]/flightconditions.uinf)\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"| 1 | 0.0250 | 2 | 0.660158 | 0.788767 | -4.245993 |-9.971789e+00 |-7.504783e-01 |\\u001b[0m\\n\",\n \"| 2 | 0.0500 | 3 | 0.698975 | 0.965136 | -4.635143 |-9.971745e+00 |-7.505379e-01 |\\u001b[0m\\n\",\n \"| 3 | 0.0750 | 2 | 0.699509 | 0.744684 | -4.142638 |-9.971678e+00 |-7.506741e-01 |\\u001b[0m\\n\",\n \"| 4 | 0.1000 | 2 | 0.702553 | 0.742001 | -4.583042 |-9.971654e+00 |-7.508442e-01 |\\u001b[0m\\n\",\n \"| 5 | 0.1250 | 1 | 0.705584 | 0.512845 | -4.384776 |-9.971729e+00 |-7.509873e-01 |\\u001b[0m\\n\",\n \"| 6 | 0.1500 | 2 | 0.710967 | 0.733027 | -4.729199 |-9.971808e+00 |-7.510934e-01 |\\u001b[0m\\n\",\n \"| 7 | 0.1750 | 1 | 0.717295 | 0.511901 | -4.049012 |-9.971749e+00 |-7.511575e-01 |\\u001b[0m\\n\",\n \"| 8 | 0.2000 | 1 | 0.687752 | 0.519393 | -4.147149 |-9.971609e+00 |-7.511620e-01 |\\u001b[0m\\n\",\n \"| 9 | 0.2250 | 1 | 0.657027 | 0.533608 | -4.243231 |-9.971483e+00 |-7.511461e-01 |\\u001b[0m\\n\",\n \"| 10 | 0.2500 | 1 | 0.650443 | 0.540742 | -4.352169 |-9.971378e+00 |-7.511644e-01 |\\u001b[0m\\n\",\n \"| 11 | 0.2750 | 1 | 0.656218 | 0.534101 | -4.191190 |-9.971371e+00 |-7.511728e-01 |\\u001b[0m\\n\",\n \"| 12 | 0.3000 | 1 | 0.671768 | 0.554114 | -4.122823 |-9.971442e+00 |-7.511539e-01 |\\u001b[0m\\n\",\n \"| 13 | 0.3250 | 1 | 0.656158 | 0.537498 | -4.418002 |-9.971429e+00 |-7.511300e-01 |\\u001b[0m\\n\",\n \"| 14 | 0.3500 | 1 | 0.704366 | 0.508580 | -4.678378 |-9.971349e+00 |-7.510900e-01 |\\u001b[0m\\n\",\n \"| 15 | 0.3750 | 1 | 0.719952 | 0.514705 | -4.402185 |-9.971299e+00 |-7.510668e-01 |\\u001b[0m\\n\",\n \"| 16 | 0.4000 | 1 | 0.705019 | 0.512428 | -4.448460 |-9.971290e+00 |-7.510571e-01 |\\u001b[0m\\n\",\n \"| 17 | 0.4250 | 1 | 0.713898 | 0.511336 | -4.476767 |-9.971358e+00 |-7.510533e-01 |\\u001b[0m\\n\",\n \"| 18 | 0.4500 | 1 | 0.715516 | 0.511316 | -4.534268 |-9.971488e+00 |-7.510753e-01 |\\u001b[0m\\n\",\n \"| 19 | 0.4750 | 1 | 0.709680 | 0.508300 | -4.662816 |-9.971575e+00 |-7.510784e-01 |\\u001b[0m\\n\",\n \"| 20 | 0.5000 | 2 | 0.704182 | 0.744397 | -4.812376 |-9.971586e+00 |-7.510241e-01 |\\u001b[0m\\n\",\n \"| 21 | 0.5250 | 3 | 0.708522 | 0.965943 | -4.402757 |-9.971726e+00 |-7.507397e-01 |\\u001b[0m\\n\",\n \"| 22 | 0.5500 | 4 | 0.708365 | 1.200794 | -4.475885 |-9.972374e+00 |-7.497152e-01 |\\u001b[0m\\n\",\n \"| 23 | 0.5750 | 4 | 0.708962 | 1.199187 | -4.264700 |-9.973956e+00 |-7.471042e-01 |\\u001b[0m\\n\",\n \"| 24 | 0.6000 | 4 | 0.709056 | 1.201371 | -4.148547 |-9.977005e+00 |-7.417512e-01 |\\u001b[0m\\n\",\n \"| 25 | 0.6250 | 4 | 0.707360 | 1.214448 | -4.101431 |-9.982064e+00 |-7.323149e-01 |\\u001b[0m\\n\",\n \"| 26 | 0.6500 | 4 | 0.707825 | 1.211973 | -4.083226 |-9.989506e+00 |-7.173484e-01 |\\u001b[0m\\n\",\n \"| 27 | 0.6750 | 4 | 0.705636 | 1.209574 | -4.081045 |-9.999533e+00 |-6.954412e-01 |\\u001b[0m\\n\",\n \"| 28 | 0.7000 | 4 | 0.702970 | 1.199970 | -4.095091 |-1.001216e+01 |-6.653667e-01 |\\u001b[0m\\n\",\n \"| 29 | 0.7250 | 4 | 0.705531 | 1.206136 | -4.120431 |-1.002734e+01 |-6.261403e-01 |\\u001b[0m\\n\",\n \"| 30 | 0.7500 | 4 | 0.702935 | 1.213436 | -4.153507 |-1.004515e+01 |-5.771350e-01 |\\u001b[0m\\n\",\n \"| 31 | 0.7750 | 4 | 0.698230 | 1.203890 | -4.194909 |-1.006573e+01 |-5.180671e-01 |\\u001b[0m\\n\",\n \"| 32 | 0.8000 | 4 | 0.703664 | 1.208508 | -4.236529 |-1.008907e+01 |-4.489843e-01 |\\u001b[0m\\n\",\n \"| 33 | 0.8250 | 4 | 0.701559 | 1.203176 | -4.281618 |-1.011502e+01 |-3.702984e-01 |\\u001b[0m\\n\",\n \"| 34 | 0.8500 | 4 | 0.700114 | 1.215140 | -4.272027 |-1.014323e+01 |-2.827796e-01 |\\u001b[0m\\n\",\n \"| 35 | 0.8750 | 4 | 0.701394 | 1.206869 | -4.137638 |-1.017318e+01 |-1.875441e-01 |\\u001b[0m\\n\",\n \"| 36 | 0.9000 | 4 | 0.698019 | 1.213434 | -4.087979 |-1.020434e+01 |-8.606667e-02 |\\u001b[0m\\n\",\n \"| 37 | 0.9250 | 4 | 0.697820 | 1.213205 | -4.081173 |-1.023614e+01 | 1.986601e-02 |\\u001b[0m\\n\",\n \"| 38 | 0.9500 | 4 | 0.692925 | 1.210431 | -4.067952 |-1.026798e+01 | 1.282642e-01 |\\u001b[0m\\n\",\n \"| 39 | 0.9750 | 4 | 0.692719 | 1.203242 | -4.040392 |-1.029913e+01 | 2.371167e-01 |\\u001b[0m\\n\",\n \"| 40 | 1.0000 | 4 | 0.695089 | 1.205393 | -4.023531 |-1.032875e+01 | 3.445071e-01 |\\u001b[0m\\n\",\n \"| 41 | 1.0250 | 5 | 0.696443 | 1.438348 | -4.548408 |-1.035594e+01 | 4.482817e-01 |\\u001b[0m\\n\",\n \"| 42 | 1.0500 | 5 | 0.699286 | 1.456647 | -4.496733 |-1.037989e+01 | 5.458046e-01 |\\u001b[0m\\n\",\n \"| 43 | 1.0750 | 5 | 0.693181 | 1.451422 | -4.426046 |-1.040006e+01 | 6.342879e-01 |\\u001b[0m\\n\",\n \"| 44 | 1.1000 | 5 | 0.672004 | 1.475300 | -4.379701 |-1.041606e+01 | 7.112695e-01 |\\u001b[0m\\n\",\n \"| 45 | 1.1250 | 5 | 0.672251 | 1.468131 | -4.402469 |-1.042753e+01 | 7.747229e-01 |\\u001b[0m\\n\",\n \"| 46 | 1.1500 | 5 | 0.689079 | 1.445732 | -4.477108 |-1.043429e+01 | 8.230013e-01 |\\u001b[0m\\n\",\n \"| 47 | 1.1750 | 5 | 0.690835 | 1.446807 | -4.548994 |-1.043627e+01 | 8.549797e-01 |\\u001b[0m\\n\",\n \"| 48 | 1.2000 | 5 | 0.692859 | 1.458130 | -4.602614 |-1.043347e+01 | 8.701306e-01 |\\u001b[0m\\n\",\n \"| 49 | 1.2250 | 5 | 0.692201 | 1.450715 | -4.670662 |-1.042601e+01 | 8.683187e-01 |\\u001b[0m\\n\",\n \"| 50 | 1.2500 | 4 | 0.692043 | 1.211332 | -4.009458 |-1.041409e+01 | 8.498052e-01 |\\u001b[0m\\n\",\n \"| 51 | 1.2750 | 5 | 0.691406 | 1.450458 | -4.437774 |-1.039785e+01 | 8.153184e-01 |\\u001b[0m\\n\",\n \"| 52 | 1.3000 | 5 | 0.690078 | 1.456433 | -4.400817 |-1.037756e+01 | 7.658481e-01 |\\u001b[0m\\n\",\n \"| 53 | 1.3250 | 5 | 0.642589 | 1.516374 | -4.491993 |-1.035352e+01 | 7.027470e-01 |\\u001b[0m\\n\",\n \"| 54 | 1.3500 | 5 | 0.636213 | 1.529562 | -4.660919 |-1.032602e+01 | 6.277602e-01 |\\u001b[0m\\n\",\n \"| 55 | 1.3750 | 4 | 0.654913 | 1.257229 | -4.127066 |-1.029540e+01 | 5.429281e-01 |\\u001b[0m\\n\",\n \"| 56 | 1.4000 | 4 | 0.690183 | 1.213338 | -4.180862 |-1.026211e+01 | 4.504884e-01 |\\u001b[0m\\n\",\n \"| 57 | 1.4250 | 4 | 0.690784 | 1.220024 | -4.119756 |-1.022658e+01 | 3.526569e-01 |\\u001b[0m\\n\",\n \"| 58 | 1.4500 | 4 | 0.693190 | 1.230164 | -4.115756 |-1.018920e+01 | 2.516427e-01 |\\u001b[0m\\n\",\n \"| 59 | 1.4750 | 4 | 0.689614 | 1.227466 | -4.089544 |-1.015042e+01 | 1.494680e-01 |\\u001b[0m\\n\",\n \"| 60 | 1.5000 | 4 | 0.686766 | 1.221660 | -4.073221 |-1.011070e+01 | 4.789509e-02 |\\u001b[0m\\n\",\n \"| 61 | 1.5250 | 4 | 0.688439 | 1.225181 | -4.065044 |-1.007052e+01 |-5.142849e-02 |\\u001b[0m\\n\",\n \"| 62 | 1.5500 | 4 | 0.686541 | 1.221131 | -4.066648 |-1.003034e+01 |-1.468432e-01 |\\u001b[0m\\n\",\n \"| 63 | 1.5750 | 4 | 0.649074 | 1.269069 | -4.116776 |-9.990515e+00 |-2.367221e-01 |\\u001b[0m\\n\",\n \"| 64 | 1.6000 | 4 | 0.634231 | 1.298771 | -4.232749 |-9.951260e+00 |-3.197660e-01 |\\u001b[0m\\n\",\n \"| 65 | 1.6250 | 4 | 0.631620 | 1.295939 | -4.346372 |-9.912713e+00 |-3.949816e-01 |\\u001b[0m\\n\",\n \"| 66 | 1.6500 | 4 | 0.676708 | 1.241231 | -4.462283 |-9.875008e+00 |-4.616848e-01 |\\u001b[0m\\n\",\n \"| 67 | 1.6750 | 4 | 0.690826 | 1.236500 | -4.536211 |-9.838289e+00 |-5.194903e-01 |\\u001b[0m\\n\",\n \"| 68 | 1.7000 | 4 | 0.685831 | 1.222472 | -4.557395 |-9.802717e+00 |-5.683337e-01 |\\u001b[0m\\n\",\n \"| 69 | 1.7250 | 4 | 0.683209 | 1.225972 | -4.514445 |-9.768493e+00 |-6.084703e-01 |\\u001b[0m\\n\",\n \"| 70 | 1.7500 | 4 | 0.681402 | 1.219586 | -4.515767 |-9.735644e+00 |-6.403299e-01 |\\u001b[0m\\n\",\n \"| 71 | 1.7750 | 4 | 0.679701 | 1.241776 | -4.561782 |-9.704041e+00 |-6.644313e-01 |\\u001b[0m\\n\",\n \"| 72 | 1.8000 | 4 | 0.687585 | 1.233221 | -4.576978 |-9.673585e+00 |-6.813177e-01 |\\u001b[0m\\n\",\n \"| 73 | 1.8250 | 3 | 0.685128 | 0.992525 | -4.085489 |-9.644153e+00 |-6.916357e-01 |\\u001b[0m\\n\",\n \"| 74 | 1.8500 | 3 | 0.630406 | 1.081735 | -4.228827 |-9.615525e+00 |-6.960345e-01 |\\u001b[0m\\n\",\n \"| 75 | 1.8750 | 3 | 0.633953 | 1.068277 | -4.281040 |-9.587600e+00 |-6.952011e-01 |\\u001b[0m\\n\",\n \"| 76 | 1.9000 | 3 | 0.631463 | 1.060051 | -4.298619 |-9.560401e+00 |-6.899257e-01 |\\u001b[0m\\n\",\n \"| 77 | 1.9250 | 3 | 0.641269 | 1.076329 | -4.263283 |-9.533905e+00 |-6.810428e-01 |\\u001b[0m\\n\",\n \"| 78 | 1.9500 | 3 | 0.632168 | 1.056881 | -4.172553 |-9.508183e+00 |-6.694250e-01 |\\u001b[0m\\n\",\n \"| 79 | 1.9750 | 3 | 0.644723 | 1.078860 | -4.087294 |-9.483448e+00 |-6.559401e-01 |\\u001b[0m\\n\",\n \"| 80 | 2.0000 | 3 | 0.629024 | 1.058206 | -4.017983 |-9.459903e+00 |-6.414764e-01 |\\u001b[0m\\n\",\n \"| 81 | 2.0250 | 4 | 0.641541 | 1.337528 | -4.489993 |-9.437808e+00 |-6.269365e-01 |\\u001b[0m\\n\",\n \"| 82 | 2.0500 | 4 | 0.628707 | 1.310679 | -4.470211 |-9.417538e+00 |-6.131778e-01 |\\u001b[0m\\n\",\n \"| 83 | 2.0750 | 4 | 0.628663 | 1.307533 | -4.453642 |-9.399441e+00 |-6.009539e-01 |\\u001b[0m\\n\",\n \"| 84 | 2.1000 | 4 | 0.631778 | 1.301269 | -4.451153 |-9.383802e+00 |-5.909513e-01 |\\u001b[0m\\n\",\n \"| 85 | 2.1250 | 4 | 0.629938 | 1.308679 | -4.454054 |-9.370919e+00 |-5.837527e-01 |\\u001b[0m\\n\",\n \"| 86 | 2.1500 | 4 | 0.630758 | 1.309061 | -4.489244 |-9.361058e+00 |-5.798117e-01 |\\u001b[0m\\n\",\n \"| 87 | 2.1750 | 4 | 0.630606 | 1.308830 | -4.529495 |-9.354357e+00 |-5.794602e-01 |\\u001b[0m\\n\",\n \"| 88 | 2.2000 | 4 | 0.629895 | 1.306216 | -4.555062 |-9.350910e+00 |-5.828920e-01 |\\u001b[0m\\n\",\n \"| 89 | 2.2250 | 4 | 0.627658 | 1.299544 | -4.583501 |-9.350758e+00 |-5.901807e-01 |\\u001b[0m\\n\",\n \"| 90 | 2.2500 | 4 | 0.631380 | 1.304904 | -4.577435 |-9.353747e+00 |-6.012367e-01 |\\u001b[0m\\n\",\n \"| 91 | 2.2750 | 3 | 0.632640 | 1.049719 | -4.015225 |-9.359659e+00 |-6.158432e-01 |\\u001b[0m\\n\",\n \"| 92 | 2.3000 | 3 | 0.677727 | 0.998599 | -4.029324 |-9.368239e+00 |-6.336696e-01 |\\u001b[0m\\n\",\n \"| 93 | 2.3250 | 3 | 0.681171 | 0.994001 | -4.027658 |-9.379037e+00 |-6.542748e-01 |\\u001b[0m\\n\",\n \"| 94 | 2.3500 | 3 | 0.681259 | 0.989943 | -4.032139 |-9.391519e+00 |-6.771019e-01 |\\u001b[0m\\n\",\n \"| 95 | 2.3750 | 3 | 0.662018 | 1.012158 | -4.018542 |-9.405213e+00 |-7.015133e-01 |\\u001b[0m\\n\",\n \"| 96 | 2.4000 | 4 | 0.649296 | 1.280039 | -4.507534 |-9.419633e+00 |-7.269046e-01 |\\u001b[0m\\n\",\n \"| 97 | 2.4250 | 4 | 0.643727 | 1.278447 | -4.486197 |-9.434238e+00 |-7.525958e-01 |\\u001b[0m\\n\",\n \"| 98 | 2.4500 | 4 | 0.626945 | 1.300289 | -4.469752 |-9.448552e+00 |-7.778583e-01 |\\u001b[0m\\n\",\n \"| 99 | 2.4750 | 4 | 0.630502 | 1.316456 | -4.479896 |-9.462111e+00 |-8.020210e-01 |\\u001b[0m\\n\",\n \"| 100 | 2.5000 | 4 | 0.624389 | 1.310294 | -4.502345 |-9.474427e+00 |-8.243816e-01 |\\u001b[0m\\n\",\n \"| 101 | 2.5250 | 4 | 0.631037 | 1.315843 | -4.533404 |-9.485161e+00 |-8.442818e-01 |\\u001b[0m\\n\",\n \"| 102 | 2.5500 | 4 | 0.644611 | 1.283856 | -4.554463 |-9.494088e+00 |-8.611748e-01 |\\u001b[0m\\n\",\n \"| 103 | 2.5750 | 4 | 0.680174 | 1.237591 | -4.579594 |-9.501053e+00 |-8.746547e-01 |\\u001b[0m\\n\",\n \"| 104 | 2.6000 | 4 | 0.680077 | 1.236782 | -4.596771 |-9.506032e+00 |-8.844994e-01 |\\u001b[0m\\n\",\n \"| 105 | 2.6250 | 4 | 0.675584 | 1.232872 | -4.484950 |-9.509125e+00 |-8.907008e-01 |\\u001b[0m\\n\",\n \"| 106 | 2.6500 | 4 | 0.678916 | 1.235079 | -4.463714 |-9.510468e+00 |-8.934511e-01 |\\u001b[0m\\n\",\n \"| 107 | 2.6750 | 4 | 0.677563 | 1.234071 | -4.381520 |-9.510274e+00 |-8.931021e-01 |\\u001b[0m\\n\",\n \"| 108 | 2.7000 | 4 | 0.674451 | 1.246872 | -4.443680 |-9.508969e+00 |-8.901755e-01 |\\u001b[0m\\n\",\n \"| 109 | 2.7250 | 4 | 0.680008 | 1.243277 | -4.646030 |-9.507028e+00 |-8.852282e-01 |\\u001b[0m\\n\",\n \"| 110 | 2.7500 | 3 | 0.687824 | 1.013889 | -4.095041 |-9.504803e+00 |-8.787479e-01 |\\u001b[0m\\n\",\n \"| 111 | 2.7750 | 3 | 0.678555 | 1.000272 | -4.324971 |-9.502690e+00 |-8.711948e-01 |\\u001b[0m\\n\",\n \"| 112 | 2.8000 | 3 | 0.629410 | 1.056518 | -4.391682 |-9.501123e+00 |-8.630844e-01 |\\u001b[0m\\n\",\n \"| 113 | 2.8250 | 3 | 0.631289 | 1.061790 | -4.405523 |-9.500417e+00 |-8.548953e-01 |\\u001b[0m\\n\",\n \"| 114 | 2.8500 | 3 | 0.623451 | 1.061574 | -4.405133 |-9.500842e+00 |-8.469691e-01 |\\u001b[0m\\n\",\n \"| 115 | 2.8750 | 3 | 0.629521 | 1.063894 | -4.364937 |-9.502651e+00 |-8.395888e-01 |\\u001b[0m\\n\",\n \"| 116 | 2.9000 | 3 | 0.625789 | 1.052592 | -4.333192 |-9.505900e+00 |-8.329495e-01 |\\u001b[0m\\n\",\n \"| 117 | 2.9250 | 3 | 0.634558 | 1.059645 | -4.287009 |-9.510496e+00 |-8.271466e-01 |\\u001b[0m\\n\",\n \"| 118 | 2.9500 | 3 | 0.676550 | 1.015943 | -4.245942 |-9.516385e+00 |-8.222099e-01 |\\u001b[0m\\n\",\n \"| 119 | 2.9750 | 3 | 0.680614 | 1.002676 | -4.205825 |-9.523418e+00 |-8.181140e-01 |\\u001b[0m\\n\",\n \"| 120 | 3.0000 | 3 | 0.682271 | 1.006870 | -4.188187 |-9.531318e+00 |-8.148053e-01 |\\u001b[0m\\n\",\n \"| 121 | 3.0250 | 3 | 0.680266 | 0.996102 | -4.232299 |-9.539814e+00 |-8.121677e-01 |\\u001b[0m\\n\",\n \"| 122 | 3.0500 | 3 | 0.681732 | 0.999955 | -4.231690 |-9.548602e+00 |-8.100300e-01 |\\u001b[0m\\n\",\n \"| 123 | 3.0750 | 3 | 0.682858 | 1.010936 | -4.279188 |-9.557348e+00 |-8.082342e-01 |\\u001b[0m\\n\",\n \"| 124 | 3.1000 | 3 | 0.681190 | 1.009030 | -4.271080 |-9.565764e+00 |-8.066818e-01 |\\u001b[0m\\n\",\n \"| 125 | 3.1250 | 3 | 0.683038 | 1.007188 | -4.392752 |-9.573620e+00 |-8.052156e-01 |\\u001b[0m\\n\",\n \"| 126 | 3.1500 | 3 | 0.678701 | 1.000200 | -4.449904 |-9.580739e+00 |-8.036619e-01 |\\u001b[0m\\n\",\n \"| 127 | 3.1750 | 2 | 0.676607 | 0.762312 | -4.000854 |-9.587007e+00 |-8.019792e-01 |\\u001b[0m\\n\",\n \"| 128 | 3.2000 | 3 | 0.676056 | 1.006674 | -4.538007 |-9.592408e+00 |-8.001705e-01 |\\u001b[0m\\n\",\n \"| 129 | 3.2250 | 3 | 0.675263 | 1.005720 | -4.547103 |-9.596953e+00 |-7.981922e-01 |\\u001b[0m\\n\",\n \"| 130 | 3.2500 | 3 | 0.676868 | 1.006415 | -4.525018 |-9.600665e+00 |-7.960410e-01 |\\u001b[0m\\n\",\n \"| 131 | 3.2750 | 3 | 0.675184 | 1.010851 | -4.506300 |-9.603640e+00 |-7.937587e-01 |\\u001b[0m\\n\",\n \"| 132 | 3.3000 | 3 | 0.672328 | 1.002885 | -4.509537 |-9.606035e+00 |-7.913608e-01 |\\u001b[0m\\n\",\n \"| 133 | 3.3250 | 3 | 0.671273 | 1.006276 | -4.517757 |-9.608054e+00 |-7.889411e-01 |\\u001b[0m\\n\",\n \"| 134 | 3.3500 | 2 | 0.667902 | 0.767805 | -4.004169 |-9.609914e+00 |-7.866119e-01 |\\u001b[0m\\n\",\n \"| 135 | 3.3750 | 2 | 0.672012 | 0.762166 | -4.037206 |-9.611796e+00 |-7.844475e-01 |\\u001b[0m\\n\",\n \"| 136 | 3.4000 | 2 | 0.674040 | 0.766492 | -4.091199 |-9.613836e+00 |-7.825251e-01 |\\u001b[0m\\n\",\n \"| 137 | 3.4250 | 2 | 0.677833 | 0.764682 | -4.161763 |-9.616142e+00 |-7.808889e-01 |\\u001b[0m\\n\",\n \"| 138 | 3.4500 | 2 | 0.678520 | 0.772371 | -4.208416 |-9.618837e+00 |-7.795641e-01 |\\u001b[0m\\n\",\n \"| 139 | 3.4750 | 2 | 0.675557 | 0.769200 | -4.185191 |-9.622012e+00 |-7.786017e-01 |\\u001b[0m\\n\",\n \"| 140 | 3.5000 | 2 | 0.658891 | 0.777941 | -4.143336 |-9.625717e+00 |-7.780201e-01 |\\u001b[0m\\n\",\n \"| 141 | 3.5250 | 2 | 0.670239 | 0.764967 | -4.111505 |-9.629952e+00 |-7.777878e-01 |\\u001b[0m\\n\",\n \"| 142 | 3.5500 | 2 | 0.675294 | 0.780672 | -4.095589 |-9.634644e+00 |-7.778791e-01 |\\u001b[0m\\n\",\n \"| 143 | 3.5750 | 2 | 0.674070 | 0.768821 | -4.089987 |-9.639706e+00 |-7.782389e-01 |\\u001b[0m\\n\",\n \"| 144 | 3.6000 | 2 | 0.675235 | 0.770859 | -4.092880 |-9.645044e+00 |-7.787973e-01 |\\u001b[0m\\n\",\n \"| 145 | 3.6250 | 2 | 0.667235 | 0.766770 | -4.113065 |-9.650579e+00 |-7.794970e-01 |\\u001b[0m\\n\",\n \"| 146 | 3.6500 | 2 | 0.664948 | 0.775005 | -4.162262 |-9.656221e+00 |-7.802848e-01 |\\u001b[0m\\n\",\n \"| 147 | 3.6750 | 2 | 0.669905 | 0.778505 | -4.233073 |-9.661859e+00 |-7.810839e-01 |\\u001b[0m\\n\",\n \"| 148 | 3.7000 | 2 | 0.673135 | 0.772653 | -4.300425 |-9.667393e+00 |-7.818259e-01 |\\u001b[0m\\n\",\n \"| 149 | 3.7250 | 2 | 0.668814 | 0.767011 | -4.341062 |-9.672713e+00 |-7.824584e-01 |\\u001b[0m\\n\",\n \"| 150 | 3.7500 | 2 | 0.667366 | 0.768942 | -4.347827 |-9.677758e+00 |-7.829222e-01 |\\u001b[0m\\n\",\n \"| 151 | 3.7750 | 2 | 0.671508 | 0.768175 | -4.340552 |-9.682512e+00 |-7.832059e-01 |\\u001b[0m\\n\",\n \"| 152 | 3.8000 | 2 | 0.657508 | 0.783694 | -4.331623 |-9.686971e+00 |-7.832953e-01 |\\u001b[0m\\n\",\n \"| 153 | 3.8250 | 2 | 0.672415 | 0.768370 | -4.316722 |-9.691148e+00 |-7.831777e-01 |\\u001b[0m\\n\",\n \"| 154 | 3.8500 | 2 | 0.677129 | 0.779227 | -4.299262 |-9.695058e+00 |-7.828747e-01 |\\u001b[0m\\n\",\n \"| 155 | 3.8750 | 2 | 0.673584 | 0.770337 | -4.305853 |-9.698731e+00 |-7.823999e-01 |\\u001b[0m\\n\",\n \"| 156 | 3.9000 | 2 | 0.665485 | 0.772028 | -4.334291 |-9.702215e+00 |-7.817778e-01 |\\u001b[0m\\n\",\n \"| 157 | 3.9250 | 2 | 0.666994 | 0.776969 | -4.377407 |-9.705587e+00 |-7.810551e-01 |\\u001b[0m\\n\",\n \"| 158 | 3.9500 | 2 | 0.665925 | 0.780606 | -4.439104 |-9.708933e+00 |-7.802775e-01 |\\u001b[0m\\n\",\n \"| 159 | 3.9750 | 2 | 0.670904 | 0.771282 | -4.498475 |-9.712316e+00 |-7.794772e-01 |\\u001b[0m\\n\",\n \"| 160 | 4.0000 | 1 | 0.671639 | 0.530210 | -4.008078 |-9.715787e+00 |-7.786931e-01 |\\u001b[0m\\n\",\n \"| 161 | 4.0250 | 1 | 0.670327 | 0.533749 | -4.092355 |-9.719380e+00 |-7.779506e-01 |\\u001b[0m\\n\",\n \"| 162 | 4.0500 | 1 | 0.668751 | 0.537579 | -4.156978 |-9.723116e+00 |-7.772698e-01 |\\u001b[0m\\n\",\n \"| 163 | 4.0750 | 1 | 0.663677 | 0.531485 | -4.072783 |-9.727029e+00 |-7.766788e-01 |\\u001b[0m\\n\",\n \"| 164 | 4.1000 | 2 | 0.666350 | 0.773267 | -4.569537 |-9.731146e+00 |-7.761920e-01 |\\u001b[0m\\n\",\n \"| 165 | 4.1250 | 2 | 0.682839 | 0.788505 | -4.570174 |-9.735472e+00 |-7.758138e-01 |\\u001b[0m\\n\",\n \"| 166 | 4.1500 | 2 | 0.620765 | 0.812113 | -4.549853 |-9.739981e+00 |-7.755403e-01 |\\u001b[0m\\n\",\n \"| 167 | 4.1750 | 2 | 0.618753 | 0.825905 | -4.537868 |-9.744625e+00 |-7.753472e-01 |\\u001b[0m\\n\",\n \"| 168 | 4.2000 | 2 | 0.618510 | 0.819368 | -4.524976 |-9.749356e+00 |-7.752100e-01 |\\u001b[0m\\n\",\n \"| 169 | 4.2250 | 2 | 0.613543 | 0.817032 | -4.515910 |-9.754134e+00 |-7.751152e-01 |\\u001b[0m\\n\",\n \"| 170 | 4.2500 | 2 | 0.614536 | 0.814042 | -4.538699 |-9.758943e+00 |-7.750408e-01 |\\u001b[0m\\n\",\n \"| 171 | 4.2750 | 1 | 0.625472 | 0.574294 | -4.020787 |-9.763759e+00 |-7.749700e-01 |\\u001b[0m\\n\",\n \"| 172 | 4.3000 | 1 | 0.608604 | 0.560485 | -4.061045 |-9.768537e+00 |-7.748838e-01 |\\u001b[0m\\n\",\n \"| 173 | 4.3250 | 1 | 0.613070 | 0.563931 | -4.121220 |-9.773242e+00 |-7.747597e-01 |\\u001b[0m\\n\",\n \"| 174 | 4.3500 | 1 | 0.642887 | 0.551584 | -4.110854 |-9.777831e+00 |-7.745740e-01 |\\u001b[0m\\n\",\n \"| 175 | 4.3750 | 1 | 0.666433 | 0.534772 | -4.088306 |-9.782291e+00 |-7.743221e-01 |\\u001b[0m\\n\",\n \"| 176 | 4.4000 | 1 | 0.673361 | 0.543510 | -4.077439 |-9.786631e+00 |-7.740007e-01 |\\u001b[0m\\n\",\n \"| 177 | 4.4250 | 1 | 0.675407 | 0.545999 | -4.085008 |-9.790868e+00 |-7.736116e-01 |\\u001b[0m\\n\",\n \"| 178 | 4.4500 | 1 | 0.663487 | 0.537923 | -4.084174 |-9.795016e+00 |-7.731651e-01 |\\u001b[0m\\n\",\n \"| 179 | 4.4750 | 1 | 0.656179 | 0.541705 | -4.095747 |-9.799077e+00 |-7.726600e-01 |\\u001b[0m\\n\",\n \"| 180 | 4.5000 | 1 | 0.665239 | 0.538480 | -4.143039 |-9.803063e+00 |-7.721067e-01 |\\u001b[0m\\n\",\n \"| 181 | 4.5250 | 1 | 0.671591 | 0.542443 | -4.219653 |-9.806995e+00 |-7.715207e-01 |\\u001b[0m\\n\",\n \"| 182 | 4.5500 | 1 | 0.663922 | 0.536485 | -4.324315 |-9.810904e+00 |-7.709163e-01 |\\u001b[0m\\n\",\n \"| 183 | 4.5750 | 1 | 0.657884 | 0.540013 | -4.462694 |-9.814833e+00 |-7.703121e-01 |\\u001b[0m\\n\",\n \"| 184 | 4.6000 | 1 | 0.664151 | 0.536879 | -4.555594 |-9.818801e+00 |-7.697261e-01 |\\u001b[0m\\n\",\n \"| 185 | 4.6250 | 1 | 0.664279 | 0.534583 | -4.636689 |-9.822816e+00 |-7.691634e-01 |\\u001b[0m\\n\",\n \"| 186 | 4.6500 | 1 | 0.663570 | 0.535142 | -4.623202 |-9.826877e+00 |-7.686317e-01 |\\u001b[0m\\n\",\n \"| 187 | 4.6750 | 1 | 0.654862 | 0.535068 | -4.465982 |-9.830990e+00 |-7.681383e-01 |\\u001b[0m\\n\",\n \"| 188 | 4.7000 | 1 | 0.664028 | 0.540949 | -4.338112 |-9.835165e+00 |-7.676893e-01 |\\u001b[0m\\n\",\n \"| 189 | 4.7250 | 1 | 0.663004 | 0.538335 | -4.294846 |-9.839409e+00 |-7.672874e-01 |\\u001b[0m\\n\",\n \"| 190 | 4.7500 | 1 | 0.661509 | 0.535572 | -4.283904 |-9.843723e+00 |-7.669317e-01 |\\u001b[0m\\n\",\n \"| 191 | 4.7750 | 1 | 0.667410 | 0.544977 | -4.289664 |-9.848084e+00 |-7.666140e-01 |\\u001b[0m\\n\",\n \"| 192 | 4.8000 | 1 | 0.631005 | 0.557035 | -4.285048 |-9.852468e+00 |-7.663236e-01 |\\u001b[0m\\n\",\n \"| 193 | 4.8250 | 1 | 0.655634 | 0.543174 | -4.249586 |-9.856861e+00 |-7.660553e-01 |\\u001b[0m\\n\",\n \"| 194 | 4.8500 | 1 | 0.663471 | 0.540511 | -4.240242 |-9.861248e+00 |-7.657973e-01 |\\u001b[0m\\n\",\n \"| 195 | 4.8750 | 1 | 0.663061 | 0.537256 | -4.279527 |-9.865630e+00 |-7.655457e-01 |\\u001b[0m\\n\",\n \"| 196 | 4.9000 | 1 | 0.666065 | 0.559327 | -4.341423 |-9.869997e+00 |-7.652934e-01 |\\u001b[0m\\n\",\n \"| 197 | 4.9250 | 1 | 0.655532 | 0.540197 | -4.389727 |-9.874334e+00 |-7.650274e-01 |\\u001b[0m\\n\",\n \"| 198 | 4.9500 | 1 | 0.653665 | 0.536703 | -4.392163 |-9.878621e+00 |-7.647419e-01 |\\u001b[0m\\n\",\n \"| 199 | 4.9750 | 1 | 0.643891 | 0.551159 | -4.356375 |-9.882848e+00 |-7.644317e-01 |\\u001b[0m\\n\",\n \"| 200 | 5.0000 | 1 | 0.658182 | 0.536739 | -4.357632 |-9.887023e+00 |-7.640960e-01 |\\u001b[0m\\n\",\n \"| 201 | 5.0250 | 1 | 0.666568 | 0.547456 | -4.374468 |-9.891152e+00 |-7.637354e-01 |\\u001b[0m\\n\",\n \"| 202 | 5.0500 | 1 | 0.690858 | 0.576716 | -4.405701 |-9.895246e+00 |-7.633546e-01 |\\u001b[0m\\n\",\n \"| 203 | 5.0750 | 1 | 0.648976 | 0.543039 | -4.457054 |-9.899310e+00 |-7.629532e-01 |\\u001b[0m\\n\",\n \"| 204 | 5.1000 | 1 | 0.645745 | 0.541463 | -4.487556 |-9.903338e+00 |-7.625328e-01 |\\u001b[0m\\n\",\n \"| 205 | 5.1250 | 1 | 0.591463 | 0.597350 | -4.532516 |-9.907334e+00 |-7.620999e-01 |\\u001b[0m\\n\",\n \"| 206 | 5.1500 | 1 | 0.602864 | 0.567360 | -4.584225 |-9.911313e+00 |-7.616581e-01 |\\u001b[0m\\n\",\n \"| 207 | 5.1750 | 1 | 0.607332 | 0.564882 | -4.653390 |-9.915290e+00 |-7.612183e-01 |\\u001b[0m\\n\",\n \"| 208 | 5.2000 | 1 | 0.617578 | 0.575872 | -4.738979 |-9.919278e+00 |-7.607846e-01 |\\u001b[0m\\n\",\n \"| 209 | 5.2250 | 1 | 0.608336 | 0.568334 | -4.813565 |-9.923281e+00 |-7.603606e-01 |\\u001b[0m\\n\",\n \"| 210 | 5.2500 | 1 | 0.608519 | 0.571894 | -4.767231 |-9.927295e+00 |-7.599484e-01 |\\u001b[0m\\n\",\n \"| 211 | 5.2750 | 1 | 0.611513 | 0.573648 | -4.664724 |-9.931315e+00 |-7.595504e-01 |\\u001b[0m\\n\",\n \"| 212 | 5.3000 | 1 | 0.663295 | 0.546204 | -4.542805 |-9.935346e+00 |-7.591674e-01 |\\u001b[0m\\n\",\n \"| 213 | 5.3250 | 1 | 0.653387 | 0.540858 | -4.498708 |-9.939397e+00 |-7.588020e-01 |\\u001b[0m\\n\",\n \"| 214 | 5.3500 | 1 | 0.651487 | 0.537849 | -4.514320 |-9.943465e+00 |-7.584560e-01 |\\u001b[0m\\n\",\n \"| 215 | 5.3750 | 1 | 0.662014 | 0.545498 | -4.531746 |-9.947549e+00 |-7.581246e-01 |\\u001b[0m\\n\",\n \"| 216 | 5.4000 | 1 | 0.650294 | 0.540917 | -4.526842 |-9.951634e+00 |-7.578047e-01 |\\u001b[0m\\n\",\n \"| 217 | 5.4250 | 1 | 0.653085 | 0.536544 | -4.480060 |-9.955710e+00 |-7.574922e-01 |\\u001b[0m\\n\",\n \"| 218 | 5.4500 | 1 | 0.661230 | 0.548448 | -4.442806 |-9.959772e+00 |-7.571838e-01 |\\u001b[0m\\n\",\n \"| 219 | 5.4750 | 1 | 0.655229 | 0.543616 | -4.442100 |-9.963823e+00 |-7.568782e-01 |\\u001b[0m\\n\",\n \"| 220 | 5.5000 | 1 | 0.655222 | 0.546932 | -4.480309 |-9.967864e+00 |-7.565737e-01 |\\u001b[0m\\n\",\n \"| 221 | 5.5250 | 1 | 0.650105 | 0.542159 | -4.527770 |-9.971886e+00 |-7.562652e-01 |\\u001b[0m\\n\",\n \"| 222 | 5.5500 | 1 | 0.651475 | 0.537507 | -4.542362 |-9.975885e+00 |-7.559507e-01 |\\u001b[0m\\n\",\n \"| 223 | 5.5750 | 1 | 0.659401 | 0.547510 | -4.506293 |-9.979850e+00 |-7.556271e-01 |\\u001b[0m\\n\",\n \"| 224 | 5.6000 | 1 | 0.601784 | 0.569276 | -4.504088 |-9.983780e+00 |-7.552935e-01 |\\u001b[0m\\n\",\n \"| 225 | 5.6250 | 1 | 0.623897 | 0.557574 | -4.512552 |-9.987687e+00 |-7.549518e-01 |\\u001b[0m\\n\",\n \"| 226 | 5.6500 | 1 | 0.600244 | 0.569273 | -4.550006 |-9.991573e+00 |-7.546024e-01 |\\u001b[0m\\n\",\n \"| 227 | 5.6750 | 1 | 0.624355 | 0.556274 | -4.608499 |-9.995440e+00 |-7.542473e-01 |\\u001b[0m\\n\",\n \"| 228 | 5.7000 | 1 | 0.660840 | 0.555257 | -4.628774 |-9.999287e+00 |-7.538857e-01 |\\u001b[0m\\n\",\n \"| 229 | 5.7250 | 1 | 0.648993 | 0.540272 | -4.638629 |-1.000311e+01 |-7.535194e-01 |\\u001b[0m\\n\",\n \"| 230 | 5.7500 | 1 | 0.649691 | 0.542594 | -4.620373 |-1.000691e+01 |-7.531502e-01 |\\u001b[0m\\n\",\n \"| 231 | 5.7750 | 1 | 0.654206 | 0.542916 | -4.623969 |-1.001071e+01 |-7.527814e-01 |\\u001b[0m\\n\",\n \"| 232 | 5.8000 | 1 | 0.651407 | 0.541567 | -4.658962 |-1.001450e+01 |-7.524169e-01 |\\u001b[0m\\n\",\n \"| 233 | 5.8250 | 1 | 0.634053 | 0.546768 | -4.709952 |-1.001828e+01 |-7.520571e-01 |\\u001b[0m\\n\",\n \"| 234 | 5.8500 | 1 | 0.649142 | 0.540074 | -4.711982 |-1.002206e+01 |-7.517035e-01 |\\u001b[0m\\n\",\n \"| 235 | 5.8750 | 1 | 0.651331 | 0.541255 | -4.674097 |-1.002584e+01 |-7.513553e-01 |\\u001b[0m\\n\",\n \"| 236 | 5.9000 | 1 | 0.650602 | 0.540557 | -4.609681 |-1.002960e+01 |-7.510131e-01 |\\u001b[0m\\n\",\n \"| 237 | 5.9250 | 1 | 0.625181 | 0.556794 | -4.572926 |-1.003336e+01 |-7.506790e-01 |\\u001b[0m\\n\",\n \"| 238 | 5.9500 | 1 | 0.598372 | 0.577537 | -4.593342 |-1.003712e+01 |-7.503529e-01 |\\u001b[0m\\n\",\n \"| 239 | 5.9750 | 1 | 0.597025 | 0.572500 | -4.606399 |-1.004088e+01 |-7.500343e-01 |\\u001b[0m\\n\",\n \"| 240 | 6.0000 | 1 | 0.597859 | 0.576480 | -4.633256 |-1.004462e+01 |-7.497216e-01 |\\u001b[0m\\n\",\n \"| 241 | 6.0250 | 1 | 0.598875 | 0.573635 | -4.596024 |-1.004836e+01 |-7.494121e-01 |\\u001b[0m\\n\",\n \"| 242 | 6.0500 | 1 | 0.597534 | 0.573711 | -4.557101 |-1.005207e+01 |-7.491049e-01 |\\u001b[0m\\n\",\n \"| 243 | 6.0750 | 1 | 0.615834 | 0.560475 | -4.544709 |-1.005577e+01 |-7.487993e-01 |\\u001b[0m\\n\",\n \"| 244 | 6.1000 | 1 | 0.645833 | 0.545940 | -4.560556 |-1.005945e+01 |-7.484956e-01 |\\u001b[0m\\n\",\n \"| 245 | 6.1250 | 1 | 0.641262 | 0.550605 | -4.599376 |-1.006312e+01 |-7.481921e-01 |\\u001b[0m\\n\",\n \"| 246 | 6.1500 | 1 | 0.650546 | 0.543172 | -4.621850 |-1.006677e+01 |-7.478876e-01 |\\u001b[0m\\n\",\n \"| 247 | 6.1750 | 1 | 0.650686 | 0.547601 | -4.613310 |-1.007040e+01 |-7.475803e-01 |\\u001b[0m\\n\",\n \"| 248 | 6.2000 | 1 | 0.643572 | 0.551210 | -4.588594 |-1.007400e+01 |-7.472693e-01 |\\u001b[0m\\n\",\n \"| 249 | 6.2250 | 1 | 0.643333 | 0.539960 | -4.585553 |-1.007758e+01 |-7.469564e-01 |\\u001b[0m\\n\",\n \"| 250 | 6.2500 | 1 | 0.631976 | 0.548090 | -4.600869 |-1.008114e+01 |-7.466414e-01 |\\u001b[0m\\n\",\n \"| 251 | 6.2750 | 1 | 0.647855 | 0.541747 | -4.650767 |-1.008469e+01 |-7.463261e-01 |\\u001b[0m\\n\",\n \"| 252 | 6.3000 | 1 | 0.649241 | 0.544522 | -4.672520 |-1.008821e+01 |-7.460094e-01 |\\u001b[0m\\n\",\n \"| 253 | 6.3250 | 1 | 0.643516 | 0.545110 | -4.673014 |-1.009172e+01 |-7.456916e-01 |\\u001b[0m\\n\",\n \"| 254 | 6.3500 | 1 | 0.638767 | 0.540989 | -4.653989 |-1.009520e+01 |-7.453734e-01 |\\u001b[0m\\n\",\n \"| 255 | 6.3750 | 1 | 0.631475 | 0.546431 | -4.631053 |-1.009867e+01 |-7.450557e-01 |\\u001b[0m\\n\",\n \"| 256 | 6.4000 | 1 | 0.644038 | 0.541411 | -4.653231 |-1.010213e+01 |-7.447412e-01 |\\u001b[0m\\n\",\n \"| 257 | 6.4250 | 1 | 0.645015 | 0.541870 | -4.678113 |-1.010557e+01 |-7.444295e-01 |\\u001b[0m\\n\",\n \"| 258 | 6.4500 | 1 | 0.646439 | 0.544957 | -4.706046 |-1.010900e+01 |-7.441219e-01 |\\u001b[0m\\n\",\n \"| 259 | 6.4750 | 1 | 0.636618 | 0.544506 | -4.688480 |-1.011242e+01 |-7.438168e-01 |\\u001b[0m\\n\",\n \"| 260 | 6.5000 | 1 | 0.636472 | 0.544515 | -4.660864 |-1.011582e+01 |-7.435149e-01 |\\u001b[0m\\n\",\n \"| 261 | 6.5250 | 1 | 0.642801 | 0.547305 | -4.622978 |-1.011920e+01 |-7.432168e-01 |\\u001b[0m\\n\",\n \"| 262 | 6.5500 | 1 | 0.642521 | 0.549237 | -4.634656 |-1.012258e+01 |-7.429228e-01 |\\u001b[0m\\n\",\n \"| 263 | 6.5750 | 1 | 0.640326 | 0.546690 | -4.652540 |-1.012594e+01 |-7.426333e-01 |\\u001b[0m\\n\",\n \"| 264 | 6.6000 | 1 | 0.646080 | 0.569616 | -4.675082 |-1.012928e+01 |-7.423474e-01 |\\u001b[0m\\n\",\n \"| 265 | 6.6250 | 1 | 0.637068 | 0.545332 | -4.671475 |-1.013261e+01 |-7.420636e-01 |\\u001b[0m\\n\",\n \"| 266 | 6.6500 | 1 | 0.641454 | 0.542948 | -4.635937 |-1.013592e+01 |-7.417815e-01 |\\u001b[0m\\n\",\n \"| 267 | 6.6750 | 1 | 0.648429 | 0.563219 | -4.626090 |-1.013921e+01 |-7.415010e-01 |\\u001b[0m\\n\",\n \"| 268 | 6.7000 | 1 | 0.638889 | 0.546413 | -4.619397 |-1.014248e+01 |-7.412219e-01 |\\u001b[0m\\n\",\n \"| 269 | 6.7250 | 1 | 0.645476 | 0.551120 | -4.654354 |-1.014573e+01 |-7.409449e-01 |\\u001b[0m\\n\",\n \"| 270 | 6.7500 | 1 | 0.644807 | 0.553462 | -4.677256 |-1.014897e+01 |-7.406684e-01 |\\u001b[0m\\n\",\n \"| 271 | 6.7750 | 1 | 0.643342 | 0.545453 | -4.677941 |-1.015219e+01 |-7.403922e-01 |\\u001b[0m\\n\",\n \"| 272 | 6.8000 | 1 | 0.642737 | 0.554577 | -4.663328 |-1.015538e+01 |-7.401152e-01 |\\u001b[0m\\n\",\n \"| 273 | 6.8250 | 1 | 0.636924 | 0.547193 | -4.647117 |-1.015854e+01 |-7.398382e-01 |\\u001b[0m\\n\",\n \"| 274 | 6.8500 | 1 | 0.636881 | 0.549125 | -4.652275 |-1.016169e+01 |-7.395617e-01 |\\u001b[0m\\n\",\n \"| 275 | 6.8750 | 1 | 0.642097 | 0.546781 | -4.679255 |-1.016482e+01 |-7.392860e-01 |\\u001b[0m\\n\",\n \"| 276 | 6.9000 | 1 | 0.644362 | 0.546495 | -4.710093 |-1.016793e+01 |-7.390117e-01 |\\u001b[0m\\n\",\n \"| 277 | 6.9250 | 1 | 0.636971 | 0.552398 | -4.709777 |-1.017103e+01 |-7.387375e-01 |\\u001b[0m\\n\",\n \"| 278 | 6.9500 | 1 | 0.642068 | 0.550708 | -4.702989 |-1.017410e+01 |-7.384642e-01 |\\u001b[0m\\n\",\n \"| 279 | 6.9750 | 1 | 0.636245 | 0.548906 | -4.675771 |-1.017714e+01 |-7.381918e-01 |\\u001b[0m\\n\",\n \"| 280 | 7.0000 | 1 | 0.631892 | 0.553548 | -4.683037 |-1.018018e+01 |-7.379216e-01 |\\u001b[0m\\n\",\n \"| 281 | 7.0250 | 1 | 0.636876 | 0.548173 | -4.700304 |-1.018319e+01 |-7.376540e-01 |\\u001b[0m\\n\",\n \"| 282 | 7.0500 | 1 | 0.641117 | 0.548960 | -4.723800 |-1.018619e+01 |-7.373891e-01 |\\u001b[0m\\n\",\n \"| 283 | 7.0750 | 1 | 0.639323 | 0.547961 | -4.733571 |-1.018917e+01 |-7.371265e-01 |\\u001b[0m\\n\",\n \"| 284 | 7.1000 | 1 | 0.636166 | 0.555813 | -4.706688 |-1.019212e+01 |-7.368659e-01 |\\u001b[0m\\n\",\n \"| 285 | 7.1250 | 1 | 0.634238 | 0.555710 | -4.691827 |-1.019506e+01 |-7.366075e-01 |\\u001b[0m\\n\",\n \"| 286 | 7.1500 | 1 | 0.635902 | 0.551450 | -4.681559 |-1.019798e+01 |-7.363519e-01 |\\u001b[0m\\n\",\n \"| 287 | 7.1750 | 1 | 0.637927 | 0.565596 | -4.702253 |-1.020088e+01 |-7.360992e-01 |\\u001b[0m\\n\",\n \"| 288 | 7.2000 | 1 | 0.636154 | 0.548763 | -4.718294 |-1.020377e+01 |-7.358495e-01 |\\u001b[0m\\n\",\n \"| 289 | 7.2250 | 1 | 0.635841 | 0.549645 | -4.734186 |-1.020663e+01 |-7.356017e-01 |\\u001b[0m\\n\",\n \"| 290 | 7.2500 | 1 | 0.633560 | 0.553457 | -4.709277 |-1.020948e+01 |-7.353555e-01 |\\u001b[0m\\n\",\n \"| 291 | 7.2750 | 1 | 0.633063 | 0.551744 | -4.697645 |-1.021230e+01 |-7.351108e-01 |\\u001b[0m\\n\",\n \"| 292 | 7.3000 | 1 | 0.596012 | 0.573846 | -4.690652 |-1.021510e+01 |-7.348676e-01 |\\u001b[0m\\n\",\n \"| 293 | 7.3250 | 1 | 0.628225 | 0.550297 | -4.705748 |-1.021788e+01 |-7.346267e-01 |\\u001b[0m\\n\",\n \"| 294 | 7.3500 | 1 | 0.635229 | 0.558756 | -4.733700 |-1.022064e+01 |-7.343873e-01 |\\u001b[0m\\n\",\n \"| 295 | 7.3750 | 1 | 0.633064 | 0.553635 | -4.738990 |-1.022338e+01 |-7.341492e-01 |\\u001b[0m\\n\",\n \"| 296 | 7.4000 | 1 | 0.636859 | 0.550407 | -4.735953 |-1.022610e+01 |-7.339119e-01 |\\u001b[0m\\n\",\n \"| 297 | 7.4250 | 1 | 0.623950 | 0.565263 | -4.716011 |-1.022879e+01 |-7.336753e-01 |\\u001b[0m\\n\",\n \"| 298 | 7.4500 | 1 | 0.642621 | 0.555373 | -4.714487 |-1.023146e+01 |-7.334401e-01 |\\u001b[0m\\n\",\n \"| 299 | 7.4750 | 1 | 0.631974 | 0.548812 | -4.730516 |-1.023411e+01 |-7.332063e-01 |\\u001b[0m\\n\",\n \"| 300 | 7.5000 | 1 | 0.635308 | 0.557555 | -4.753499 |-1.023674e+01 |-7.329746e-01 |\\u001b[0m\\n\",\n \"| 301 | 7.5250 | 1 | 0.629950 | 0.550125 | -4.765495 |-1.023935e+01 |-7.327439e-01 |\\u001b[0m\\n\",\n \"| 302 | 7.5500 | 1 | 0.615770 | 0.560338 | -4.762381 |-1.024194e+01 |-7.325148e-01 |\\u001b[0m\\n\",\n \"| 303 | 7.5750 | 1 | 0.584256 | 0.590264 | -4.742845 |-1.024450e+01 |-7.322869e-01 |\\u001b[0m\\n\",\n \"| 304 | 7.6000 | 1 | 0.582597 | 0.587076 | -4.737265 |-1.024704e+01 |-7.320607e-01 |\\u001b[0m\\n\",\n \"| 305 | 7.6250 | 1 | 0.584283 | 0.579482 | -4.752925 |-1.024956e+01 |-7.318370e-01 |\\u001b[0m\\n\",\n \"| 306 | 7.6500 | 1 | 0.586216 | 0.584941 | -4.767222 |-1.025207e+01 |-7.316154e-01 |\\u001b[0m\\n\",\n \"| 307 | 7.6750 | 1 | 0.585430 | 0.579851 | -4.787773 |-1.025455e+01 |-7.313962e-01 |\\u001b[0m\\n\",\n \"| 308 | 7.7000 | 1 | 0.631306 | 0.551397 | -4.774572 |-1.025701e+01 |-7.311787e-01 |\\u001b[0m\\n\",\n \"| 309 | 7.7250 | 1 | 0.634317 | 0.553543 | -4.762915 |-1.025944e+01 |-7.309630e-01 |\\u001b[0m\\n\",\n \"| 310 | 7.7500 | 1 | 0.636891 | 0.556693 | -4.750823 |-1.026186e+01 |-7.307494e-01 |\\u001b[0m\\n\",\n \"| 311 | 7.7750 | 1 | 0.639769 | 0.563616 | -4.761181 |-1.026425e+01 |-7.305383e-01 |\\u001b[0m\\n\",\n \"| 312 | 7.8000 | 1 | 0.631767 | 0.554912 | -4.781589 |-1.026663e+01 |-7.303294e-01 |\\u001b[0m\\n\",\n \"| 313 | 7.8250 | 1 | 0.634194 | 0.558768 | -4.793059 |-1.026898e+01 |-7.301229e-01 |\\u001b[0m\\n\",\n \"| 314 | 7.8500 | 1 | 0.626796 | 0.556363 | -4.791256 |-1.027131e+01 |-7.299178e-01 |\\u001b[0m\\n\",\n \"| 315 | 7.8750 | 1 | 0.625787 | 0.550935 | -4.775101 |-1.027361e+01 |-7.297145e-01 |\\u001b[0m\\n\",\n \"| 316 | 7.9000 | 1 | 0.631936 | 0.553434 | -4.770127 |-1.027590e+01 |-7.295127e-01 |\\u001b[0m\\n\",\n \"| 317 | 7.9250 | 1 | 0.632807 | 0.554769 | -4.771512 |-1.027816e+01 |-7.293129e-01 |\\u001b[0m\\n\",\n \"| 318 | 7.9500 | 1 | 0.636354 | 0.555106 | -4.801316 |-1.028040e+01 |-7.291153e-01 |\\u001b[0m\\n\",\n \"| 319 | 7.9750 | 1 | 0.651982 | 0.601691 | -4.806386 |-1.028262e+01 |-7.289192e-01 |\\u001b[0m\\n\",\n \"| 320 | 8.0000 | 1 | 0.642667 | 0.630753 | -4.813430 |-1.028481e+01 |-7.287248e-01 |\\u001b[0m\\n\",\n \"| 321 | 8.0250 | 1 | 0.638641 | 0.626061 | -4.798908 |-1.028698e+01 |-7.285314e-01 |\\u001b[0m\\n\",\n \"| 322 | 8.0500 | 1 | 0.627977 | 0.630209 | -4.790992 |-1.028913e+01 |-7.283397e-01 |\\u001b[0m\\n\",\n \"| 323 | 8.0750 | 1 | 0.615535 | 0.632846 | -4.799474 |-1.029125e+01 |-7.281498e-01 |\\u001b[0m\\n\",\n \"| 324 | 8.1000 | 1 | 0.628741 | 0.623770 | -4.816641 |-1.029336e+01 |-7.279618e-01 |\\u001b[0m\\n\",\n \"| 325 | 8.1250 | 1 | 0.646119 | 0.631292 | -4.835626 |-1.029544e+01 |-7.277758e-01 |\\u001b[0m\\n\",\n \"| 326 | 8.1500 | 1 | 0.635751 | 0.604086 | -4.834189 |-1.029750e+01 |-7.275912e-01 |\\u001b[0m\\n\",\n \"| 327 | 8.1750 | 1 | 0.635591 | 0.596375 | -4.826611 |-1.029953e+01 |-7.274083e-01 |\\u001b[0m\\n\",\n \"| 328 | 8.2000 | 1 | 0.654686 | 0.625780 | -4.815149 |-1.030154e+01 |-7.272270e-01 |\\u001b[0m\\n\",\n \"| 329 | 8.2250 | 1 | 0.631972 | 0.593750 | -4.822991 |-1.030353e+01 |-7.270479e-01 |\\u001b[0m\\n\",\n \"| 330 | 8.2500 | 1 | 0.627881 | 0.594475 | -4.835602 |-1.030549e+01 |-7.268709e-01 |\\u001b[0m\\n\",\n \"| 331 | 8.2750 | 1 | 0.632779 | 0.588022 | -4.856780 |-1.030744e+01 |-7.266960e-01 |\\u001b[0m\\n\",\n \"| 332 | 8.3000 | 1 | 0.623576 | 0.572123 | -4.856935 |-1.030936e+01 |-7.265231e-01 |\\u001b[0m\\n\",\n \"| 333 | 8.3250 | 1 | 0.616926 | 0.572569 | -4.844436 |-1.031125e+01 |-7.263517e-01 |\\u001b[0m\\n\",\n \"| 334 | 8.3500 | 1 | 0.656718 | 0.615642 | -4.841857 |-1.031313e+01 |-7.261824e-01 |\\u001b[0m\\n\",\n \"| 335 | 8.3750 | 1 | 0.647848 | 0.593447 | -4.836181 |-1.031498e+01 |-7.260150e-01 |\\u001b[0m\\n\",\n \"| 336 | 8.4000 | 1 | 0.620897 | 0.556400 | -4.858940 |-1.031681e+01 |-7.258500e-01 |\\u001b[0m\\n\",\n \"| 337 | 8.4250 | 1 | 0.636878 | 0.568918 | -4.870038 |-1.031861e+01 |-7.256870e-01 |\\u001b[0m\\n\",\n \"| 338 | 8.4500 | 1 | 0.624409 | 0.560472 | -4.878751 |-1.032040e+01 |-7.255258e-01 |\\u001b[0m\\n\",\n \"| 339 | 8.4750 | 1 | 0.626291 | 0.560779 | -4.866752 |-1.032216e+01 |-7.253663e-01 |\\u001b[0m\\n\",\n \"| 340 | 8.5000 | 1 | 0.624523 | 0.557208 | -4.860873 |-1.032389e+01 |-7.252085e-01 |\\u001b[0m\\n\",\n \"| 341 | 8.5250 | 1 | 0.621932 | 0.557273 | -4.861571 |-1.032560e+01 |-7.250526e-01 |\\u001b[0m\\n\",\n \"| 342 | 8.5500 | 1 | 0.620140 | 0.558312 | -4.876236 |-1.032729e+01 |-7.248988e-01 |\\u001b[0m\\n\",\n \"| 343 | 8.5750 | 1 | 0.618488 | 0.558703 | -4.894443 |-1.032896e+01 |-7.247469e-01 |\\u001b[0m\\n\",\n \"| 344 | 8.6000 | 1 | 0.614675 | 0.555611 | -4.898885 |-1.033060e+01 |-7.245967e-01 |\\u001b[0m\\n\",\n \"| 345 | 8.6250 | 1 | 0.608933 | 0.564743 | -4.897533 |-1.033222e+01 |-7.244482e-01 |\\u001b[0m\\n\",\n \"| 346 | 8.6500 | 1 | 0.577061 | 0.585133 | -4.881841 |-1.033381e+01 |-7.243012e-01 |\\u001b[0m\\n\",\n \"| 347 | 8.6750 | 1 | 0.608953 | 0.587979 | -4.892088 |-1.033539e+01 |-7.241562e-01 |\\u001b[0m\\n\",\n \"| 348 | 8.7000 | 1 | 0.624541 | 0.558283 | -4.899079 |-1.033693e+01 |-7.240130e-01 |\\u001b[0m\\n\",\n \"| 349 | 8.7250 | 1 | 0.625952 | 0.557111 | -4.918737 |-1.033846e+01 |-7.238720e-01 |\\u001b[0m\\n\",\n \"| 350 | 8.7500 | 1 | 0.623287 | 0.557909 | -4.928123 |-1.033996e+01 |-7.237327e-01 |\\u001b[0m\\n\",\n \"| 351 | 8.7750 | 1 | 0.622417 | 0.555740 | -4.921486 |-1.034144e+01 |-7.235950e-01 |\\u001b[0m\\n\",\n \"| 352 | 8.8000 | 1 | 0.621352 | 0.554043 | -4.914257 |-1.034289e+01 |-7.234592e-01 |\\u001b[0m\\n\",\n \"| 353 | 8.8250 | 1 | 0.625442 | 0.559248 | -4.914487 |-1.034432e+01 |-7.233251e-01 |\\u001b[0m\\n\",\n \"| 354 | 8.8500 | 1 | 0.621001 | 0.554895 | -4.927093 |-1.034573e+01 |-7.231933e-01 |\\u001b[0m\\n\",\n \"| 355 | 8.8750 | 1 | 0.616331 | 0.556795 | -4.942194 |-1.034711e+01 |-7.230634e-01 |\\u001b[0m\\n\",\n \"| 356 | 8.9000 | 1 | 0.620400 | 0.561975 | -4.953444 |-1.034848e+01 |-7.229356e-01 |\\u001b[0m\\n\",\n \"| 357 | 8.9250 | 1 | 0.617789 | 0.557966 | -4.948106 |-1.034981e+01 |-7.228093e-01 |\\u001b[0m\\n\",\n \"| 358 | 8.9500 | 1 | 0.617529 | 0.559993 | -4.942308 |-1.035113e+01 |-7.226850e-01 |\\u001b[0m\\n\",\n \"| 359 | 8.9750 | 1 | 0.618381 | 0.557392 | -4.938375 |-1.035241e+01 |-7.225625e-01 |\\u001b[0m\\n\",\n \"| 360 | 9.0000 | 1 | 0.615879 | 0.559019 | -4.952078 |-1.035368e+01 |-7.224422e-01 |\\u001b[0m\\n\",\n \"| 361 | 9.0250 | 1 | 0.619261 | 0.558077 | -4.968153 |-1.035492e+01 |-7.223238e-01 |\\u001b[0m\\n\",\n \"| 362 | 9.0500 | 1 | 0.620542 | 0.558342 | -4.974721 |-1.035614e+01 |-7.222074e-01 |\\u001b[0m\\n\",\n \"| 363 | 9.0750 | 1 | 0.620811 | 0.562190 | -4.979177 |-1.035734e+01 |-7.220928e-01 |\\u001b[0m\\n\",\n \"| 364 | 9.1000 | 1 | 0.621215 | 0.561517 | -4.966813 |-1.035851e+01 |-7.219798e-01 |\\u001b[0m\\n\",\n \"| 365 | 9.1250 | 1 | 0.619293 | 0.556963 | -4.968124 |-1.035966e+01 |-7.218687e-01 |\\u001b[0m\\n\",\n \"| 366 | 9.1500 | 1 | 0.617414 | 0.560206 | -4.976628 |-1.036079e+01 |-7.217596e-01 |\\u001b[0m\\n\",\n \"| 367 | 9.1750 | 1 | 0.617224 | 0.560026 | -4.995733 |-1.036189e+01 |-7.216525e-01 |\\u001b[0m\\n\",\n \"| 368 | 9.2000 | 1 | 0.594361 | 0.572718 | -5.002079 |-1.036297e+01 |-7.215472e-01 |\\u001b[0m\\n\",\n \"| 369 | 9.2250 | 1 | 0.591752 | 0.620408 | -5.007823 |-1.036402e+01 |-7.214437e-01 |\\u001b[0m\\n\",\n \"| 370 | 9.2500 | 1 | 0.573933 | 0.595363 | -4.998087 |-1.036505e+01 |-7.213418e-01 |\\u001b[0m\\n\",\n \"| 371 | 9.2750 | 1 | 0.574780 | 0.599225 | -4.997593 |-1.036606e+01 |-7.212418e-01 |\\u001b[0m\\n\",\n \"| 372 | 9.3000 | 1 | 0.573589 | 0.590403 | -5.006758 |-1.036704e+01 |-7.211437e-01 |\\u001b[0m\\n\",\n \"| 373 | 9.3250 | 1 | 0.609827 | 0.562178 | -5.021476 |-1.036800e+01 |-7.210476e-01 |\\u001b[0m\\n\",\n \"| 374 | 9.3500 | 1 | 0.614184 | 0.559384 | -5.036294 |-1.036894e+01 |-7.209533e-01 |\\u001b[0m\\n\",\n \"| 375 | 9.3750 | 1 | 0.613003 | 0.559421 | -5.033179 |-1.036985e+01 |-7.208608e-01 |\\u001b[0m\\n\",\n \"| 376 | 9.4000 | 1 | 0.615698 | 0.562315 | -5.033218 |-1.037074e+01 |-7.207701e-01 |\\u001b[0m\\n\",\n \"| 377 | 9.4250 | 1 | 0.614765 | 0.561798 | -5.027569 |-1.037161e+01 |-7.206811e-01 |\\u001b[0m\\n\",\n \"| 378 | 9.4500 | 1 | 0.617829 | 0.560943 | -5.035541 |-1.037245e+01 |-7.205942e-01 |\\u001b[0m\\n\",\n \"| 379 | 9.4750 | 1 | 0.618720 | 0.564336 | -5.051179 |-1.037327e+01 |-7.205092e-01 |\\u001b[0m\\n\",\n \"| 380 | 9.5000 | 1 | 0.612249 | 0.559879 | -5.064730 |-1.037407e+01 |-7.204262e-01 |\\u001b[0m\\n\",\n \"| 381 | 9.5250 | 1 | 0.616751 | 0.558819 | -5.064004 |-1.037484e+01 |-7.203449e-01 |\\u001b[0m\\n\",\n \"| 382 | 9.5500 | 1 | 0.609852 | 0.562424 | -5.062977 |-1.037559e+01 |-7.202654e-01 |\\u001b[0m\\n\",\n \"| 383 | 9.5750 | 1 | 0.610932 | 0.561283 | -5.059836 |-1.037632e+01 |-7.201877e-01 |\\u001b[0m\\n\",\n \"| 384 | 9.6000 | 1 | 0.609683 | 0.559666 | -5.063394 |-1.037702e+01 |-7.201119e-01 |\\u001b[0m\\n\",\n \"| 385 | 9.6250 | 1 | 0.614492 | 0.563530 | -5.081452 |-1.037770e+01 |-7.200382e-01 |\\u001b[0m\\n\",\n \"| 386 | 9.6500 | 1 | 0.606921 | 0.560035 | -5.090793 |-1.037835e+01 |-7.199663e-01 |\\u001b[0m\\n\",\n \"| 387 | 9.6750 | 1 | 0.614644 | 0.567031 | -5.097605 |-1.037899e+01 |-7.198962e-01 |\\u001b[0m\\n\",\n \"| 388 | 9.7000 | 1 | 0.584276 | 0.590999 | -5.091026 |-1.037960e+01 |-7.198278e-01 |\\u001b[0m\\n\",\n \"| 389 | 9.7250 | 1 | 0.567643 | 0.593811 | -5.091591 |-1.038018e+01 |-7.197613e-01 |\\u001b[0m\\n\",\n \"| 390 | 9.7500 | 1 | 0.567374 | 0.596893 | -5.095862 |-1.038075e+01 |-7.196965e-01 |\\u001b[0m\\n\",\n \"| 391 | 9.7750 | 1 | 0.572616 | 0.596802 | -5.106980 |-1.038129e+01 |-7.196338e-01 |\\u001b[0m\\n\",\n \"| 392 | 9.8000 | 1 | 0.570078 | 0.591577 | -5.123029 |-1.038181e+01 |-7.195729e-01 |\\u001b[0m\\n\",\n \"| 393 | 9.8250 | 1 | 0.568206 | 0.592200 | -5.126210 |-1.038230e+01 |-7.195138e-01 |\\u001b[0m\\n\",\n \"| 394 | 9.8500 | 1 | 0.571314 | 0.611958 | -5.123923 |-1.038277e+01 |-7.194564e-01 |\\u001b[0m\\n\",\n \"| 395 | 9.8750 | 1 | 0.567253 | 0.597897 | -5.121337 |-1.038322e+01 |-7.194006e-01 |\\u001b[0m\\n\",\n \"| 396 | 9.9000 | 1 | 0.568210 | 0.593683 | -5.128361 |-1.038365e+01 |-7.193469e-01 |\\u001b[0m\\n\",\n \"| 397 | 9.9250 | 1 | 0.565010 | 0.597851 | -5.135472 |-1.038405e+01 |-7.192949e-01 |\\u001b[0m\\n\",\n \"| 398 | 9.9500 | 1 | 0.607473 | 0.563262 | -5.151271 |-1.038443e+01 |-7.192449e-01 |\\u001b[0m\\n\",\n \"| 399 | 9.9750 | 1 | 0.611926 | 0.565768 | -5.156484 |-1.038479e+01 |-7.191966e-01 |\\u001b[0m\\n\",\n \"| 400 |10.0000 | 1 | 0.609614 | 0.566774 | -5.154040 |-1.038512e+01 |-7.191501e-01 |\\u001b[0m\\n\",\n \"| 401 |10.0250 | 1 | 0.609190 | 0.563351 | -5.151962 |-1.038543e+01 |-7.191053e-01 |\\u001b[0m\\n\",\n \"| 402 |10.0500 | 1 | 0.609842 | 0.560413 | -5.156639 |-1.038572e+01 |-7.190623e-01 |\\u001b[0m\\n\",\n \"| 403 |10.0750 | 1 | 0.608545 | 0.562862 | -5.165364 |-1.038599e+01 |-7.190212e-01 |\\u001b[0m\\n\",\n \"| 404 |10.1000 | 1 | 0.609280 | 0.574591 | -5.175709 |-1.038623e+01 |-7.189820e-01 |\\u001b[0m\\n\",\n \"| 405 |10.1250 | 1 | 0.606715 | 0.563175 | -5.184143 |-1.038645e+01 |-7.189446e-01 |\\u001b[0m\\n\",\n \"| 406 |10.1500 | 1 | 0.604479 | 0.564748 | -5.181991 |-1.038665e+01 |-7.189088e-01 |\\u001b[0m\\n\",\n \"| 407 |10.1750 | 1 | 0.606050 | 0.565112 | -5.179552 |-1.038683e+01 |-7.188749e-01 |\\u001b[0m\\n\",\n \"| 408 |10.2000 | 1 | 0.607161 | 0.564970 | -5.182516 |-1.038698e+01 |-7.188427e-01 |\\u001b[0m\\n\",\n \"| 409 |10.2250 | 1 | 0.611589 | 0.565026 | -5.191318 |-1.038711e+01 |-7.188124e-01 |\\u001b[0m\\n\",\n \"| 410 |10.2500 | 1 | 0.609824 | 0.564363 | -5.199527 |-1.038722e+01 |-7.187839e-01 |\\u001b[0m\\n\",\n \"| 411 |10.2750 | 1 | 0.608612 | 0.565428 | -5.204957 |-1.038731e+01 |-7.187572e-01 |\\u001b[0m\\n\",\n \"| 412 |10.3000 | 1 | 0.607257 | 0.561791 | -5.208673 |-1.038738e+01 |-7.187322e-01 |\\u001b[0m\\n\",\n \"| 413 |10.3250 | 1 | 0.609691 | 0.568279 | -5.201979 |-1.038742e+01 |-7.187089e-01 |\\u001b[0m\\n\",\n \"| 414 |10.3500 | 1 | 0.601743 | 0.568179 | -5.206076 |-1.038744e+01 |-7.186873e-01 |\\u001b[0m\\n\",\n \"| 415 |10.3750 | 1 | 0.601717 | 0.567023 | -5.212946 |-1.038744e+01 |-7.186677e-01 |\\u001b[0m\\n\",\n \"| 416 |10.4000 | 1 | 0.559912 | 0.595790 | -5.218419 |-1.038742e+01 |-7.186497e-01 |\\u001b[0m\\n\",\n \"| 417 |10.4250 | 1 | 0.564230 | 0.598142 | -5.224424 |-1.038737e+01 |-7.186336e-01 |\\u001b[0m\\n\",\n \"| 418 |10.4500 | 1 | 0.583181 | 0.581345 | -5.225489 |-1.038730e+01 |-7.186191e-01 |\\u001b[0m\\n\",\n \"| 419 |10.4750 | 1 | 0.602301 | 0.565017 | -5.224159 |-1.038721e+01 |-7.186063e-01 |\\u001b[0m\\n\",\n \"| 420 |10.5000 | 1 | 0.603593 | 0.566494 | -5.222729 |-1.038710e+01 |-7.185953e-01 |\\u001b[0m\\n\",\n \"| 421 |10.5250 | 1 | 0.601339 | 0.567735 | -5.228588 |-1.038697e+01 |-7.185860e-01 |\\u001b[0m\\n\",\n \"| 422 |10.5500 | 1 | 0.600440 | 0.570387 | -5.234701 |-1.038682e+01 |-7.185785e-01 |\\u001b[0m\\n\",\n \"| 423 |10.5750 | 1 | 0.578888 | 0.583202 | -5.234590 |-1.038664e+01 |-7.185728e-01 |\\u001b[0m\\n\",\n \"| 424 |10.6000 | 1 | 0.604815 | 0.565890 | -5.239249 |-1.038645e+01 |-7.185687e-01 |\\u001b[0m\\n\",\n \"| 425 |10.6250 | 1 | 0.604126 | 0.569152 | -5.236159 |-1.038623e+01 |-7.185663e-01 |\\u001b[0m\\n\",\n \"| 426 |10.6500 | 1 | 0.603547 | 0.566174 | -5.235546 |-1.038599e+01 |-7.185655e-01 |\\u001b[0m\\n\",\n \"| 427 |10.6750 | 1 | 0.602865 | 0.569464 | -5.237490 |-1.038573e+01 |-7.185666e-01 |\\u001b[0m\\n\",\n \"| 428 |10.7000 | 1 | 0.600635 | 0.568652 | -5.241270 |-1.038545e+01 |-7.185694e-01 |\\u001b[0m\\n\",\n \"| 429 |10.7250 | 1 | 0.605226 | 0.574795 | -5.242437 |-1.038514e+01 |-7.185739e-01 |\\u001b[0m\\n\",\n \"| 430 |10.7500 | 1 | 0.600788 | 0.571143 | -5.241394 |-1.038482e+01 |-7.185801e-01 |\\u001b[0m\\n\",\n \"| 431 |10.7750 | 1 | 0.577222 | 0.591226 | -5.242569 |-1.038448e+01 |-7.185880e-01 |\\u001b[0m\\n\",\n \"| 432 |10.8000 | 1 | 0.560620 | 0.597055 | -5.240958 |-1.038411e+01 |-7.185975e-01 |\\u001b[0m\\n\",\n \"| 433 |10.8250 | 1 | 0.556709 | 0.596082 | -5.238278 |-1.038372e+01 |-7.186087e-01 |\\u001b[0m\\n\",\n \"| 434 |10.8500 | 1 | 0.556684 | 0.597562 | -5.242316 |-1.038332e+01 |-7.186217e-01 |\\u001b[0m\\n\",\n \"| 435 |10.8750 | 1 | 0.559204 | 0.599864 | -5.240932 |-1.038289e+01 |-7.186363e-01 |\\u001b[0m\\n\",\n \"| 436 |10.9000 | 1 | 0.554305 | 0.620321 | -5.238040 |-1.038244e+01 |-7.186526e-01 |\\u001b[0m\\n\",\n \"| 437 |10.9250 | 1 | 0.577513 | 0.588008 | -5.241438 |-1.038197e+01 |-7.186705e-01 |\\u001b[0m\\n\",\n \"| 438 |10.9500 | 1 | 0.599971 | 0.568971 | -5.235789 |-1.038148e+01 |-7.186901e-01 |\\u001b[0m\\n\",\n \"| 439 |10.9750 | 1 | 0.599382 | 0.571610 | -5.237054 |-1.038097e+01 |-7.187113e-01 |\\u001b[0m\\n\",\n \"| 440 |11.0000 | 1 | 0.597518 | 0.569614 | -5.232763 |-1.038044e+01 |-7.187342e-01 |\\u001b[0m\\n\",\n \"| 441 |11.0250 | 1 | 0.603696 | 0.575074 | -5.233276 |-1.037989e+01 |-7.187588e-01 |\\u001b[0m\\n\",\n \"| 442 |11.0500 | 1 | 0.583094 | 0.697022 | -5.231065 |-1.037932e+01 |-7.187850e-01 |\\u001b[0m\\n\",\n \"| 443 |11.0750 | 1 | 0.619875 | 0.676204 | -5.227894 |-1.037873e+01 |-7.188128e-01 |\\u001b[0m\\n\",\n \"| 444 |11.1000 | 1 | 0.598458 | 0.604789 | -5.230200 |-1.037812e+01 |-7.188422e-01 |\\u001b[0m\\n\",\n \"| 445 |11.1250 | 1 | 0.604274 | 0.596907 | -5.223329 |-1.037749e+01 |-7.188732e-01 |\\u001b[0m\\n\",\n \"| 446 |11.1500 | 1 | 0.573906 | 0.610394 | -5.222229 |-1.037684e+01 |-7.189059e-01 |\\u001b[0m\\n\",\n \"| 447 |11.1750 | 1 | 0.561556 | 0.624831 | -5.217935 |-1.037617e+01 |-7.189403e-01 |\\u001b[0m\\n\",\n \"| 448 |11.2000 | 1 | 0.569148 | 0.626453 | -5.216896 |-1.037548e+01 |-7.189761e-01 |\\u001b[0m\\n\",\n \"| 449 |11.2250 | 1 | 0.564965 | 0.673984 | -5.213489 |-1.037477e+01 |-7.190136e-01 |\\u001b[0m\\n\",\n \"| 450 |11.2500 | 1 | 0.561458 | 0.614712 | -5.212846 |-1.037404e+01 |-7.190527e-01 |\\u001b[0m\\n\",\n \"| 451 |11.2750 | 1 | 0.573335 | 0.635211 | -5.209958 |-1.037329e+01 |-7.190933e-01 |\\u001b[0m\\n\",\n \"| 452 |11.3000 | 1 | 0.601036 | 0.589727 | -5.203174 |-1.037253e+01 |-7.191356e-01 |\\u001b[0m\\n\",\n \"| 453 |11.3250 | 1 | 0.588650 | 0.649352 | -5.201050 |-1.037174e+01 |-7.191795e-01 |\\u001b[0m\\n\",\n \"| 454 |11.3500 | 1 | 0.581506 | 0.609257 | -5.196793 |-1.037094e+01 |-7.192250e-01 |\\u001b[0m\\n\",\n \"| 455 |11.3750 | 1 | 0.589146 | 0.602935 | -5.195584 |-1.037011e+01 |-7.192719e-01 |\\u001b[0m\\n\",\n \"| 456 |11.4000 | 1 | 0.604540 | 0.602902 | -5.192228 |-1.036927e+01 |-7.193204e-01 |\\u001b[0m\\n\",\n \"| 457 |11.4250 | 1 | 0.600579 | 0.594754 | -5.191012 |-1.036841e+01 |-7.193705e-01 |\\u001b[0m\\n\",\n \"| 458 |11.4500 | 1 | 0.594932 | 0.585988 | -5.182644 |-1.036753e+01 |-7.194222e-01 |\\u001b[0m\\n\",\n \"| 459 |11.4750 | 1 | 0.594136 | 0.587465 | -5.180474 |-1.036663e+01 |-7.194754e-01 |\\u001b[0m\\n\",\n \"| 460 |11.5000 | 1 | 0.615072 | 0.617353 | -5.174101 |-1.036571e+01 |-7.195302e-01 |\\u001b[0m\\n\",\n \"| 461 |11.5250 | 1 | 0.580867 | 0.632210 | -5.174853 |-1.036478e+01 |-7.195865e-01 |\\u001b[0m\\n\",\n \"| 462 |11.5500 | 1 | 0.594978 | 0.646045 | -5.170050 |-1.036382e+01 |-7.196442e-01 |\\u001b[0m\\n\",\n \"| 463 |11.5750 | 1 | 0.578537 | 0.617545 | -5.167418 |-1.036285e+01 |-7.197035e-01 |\\u001b[0m\\n\",\n \"| 464 |11.6000 | 1 | 0.591423 | 0.656918 | -5.163354 |-1.036186e+01 |-7.197643e-01 |\\u001b[0m\\n\",\n \"| 465 |11.6250 | 1 | 0.596206 | 0.593319 | -5.154243 |-1.036085e+01 |-7.198267e-01 |\\u001b[0m\\n\",\n \"| 466 |11.6500 | 1 | 0.594452 | 0.615504 | -5.154289 |-1.035983e+01 |-7.198905e-01 |\\u001b[0m\\n\",\n \"| 467 |11.6750 | 1 | 0.585962 | 0.589556 | -5.148727 |-1.035878e+01 |-7.199559e-01 |\\u001b[0m\\n\",\n \"| 468 |11.7000 | 1 | 0.590704 | 0.592317 | -5.148438 |-1.035772e+01 |-7.200226e-01 |\\u001b[0m\\n\",\n \"| 469 |11.7250 | 1 | 0.588268 | 0.610512 | -5.143636 |-1.035664e+01 |-7.200909e-01 |\\u001b[0m\\n\",\n \"| 470 |11.7500 | 1 | 0.613000 | 0.604874 | -5.138982 |-1.035554e+01 |-7.201607e-01 |\\u001b[0m\\n\",\n \"| 471 |11.7750 | 1 | 0.597844 | 0.624120 | -5.133073 |-1.035443e+01 |-7.202319e-01 |\\u001b[0m\\n\",\n \"| 472 |11.8000 | 1 | 0.612249 | 0.607180 | -5.128111 |-1.035330e+01 |-7.203046e-01 |\\u001b[0m\\n\",\n \"| 473 |11.8250 | 1 | 0.589453 | 0.613552 | -5.126736 |-1.035215e+01 |-7.203787e-01 |\\u001b[0m\\n\",\n \"| 474 |11.8500 | 1 | 0.593775 | 0.611720 | -5.123366 |-1.035098e+01 |-7.204543e-01 |\\u001b[0m\\n\",\n \"| 475 |11.8750 | 1 | 0.589657 | 0.587944 | -5.120797 |-1.034980e+01 |-7.205313e-01 |\\u001b[0m\\n\",\n \"| 476 |11.9000 | 1 | 0.589097 | 0.606891 | -5.114568 |-1.034860e+01 |-7.206098e-01 |\\u001b[0m\\n\",\n \"| 477 |11.9250 | 1 | 0.587495 | 0.629681 | -5.110620 |-1.034739e+01 |-7.206897e-01 |\\u001b[0m\\n\",\n \"| 478 |11.9500 | 1 | 0.584468 | 0.608920 | -5.103850 |-1.034615e+01 |-7.207710e-01 |\\u001b[0m\\n\",\n \"| 479 |11.9750 | 1 | 0.590653 | 0.613406 | -5.103272 |-1.034491e+01 |-7.208537e-01 |\\u001b[0m\\n\",\n \"| 480 |12.0000 | 1 | 0.622715 | 0.666483 | -5.099819 |-1.034364e+01 |-7.209378e-01 |\\u001b[0m\\n\",\n \"| 481 |12.0250 | 1 | 0.604598 | 0.600735 | -5.096876 |-1.034236e+01 |-7.210233e-01 |\\u001b[0m\\n\",\n \"| 482 |12.0500 | 1 | 0.607466 | 0.600419 | -5.092345 |-1.034106e+01 |-7.211102e-01 |\\u001b[0m\\n\",\n \"| 483 |12.0750 | 1 | 0.611803 | 0.651007 | -5.086132 |-1.033975e+01 |-7.211985e-01 |\\u001b[0m\\n\",\n \"| 484 |12.1000 | 1 | 0.600163 | 0.604296 | -5.082930 |-1.033842e+01 |-7.212882e-01 |\\u001b[0m\\n\",\n \"| 485 |12.1250 | 1 | 0.597081 | 0.608633 | -5.078037 |-1.033707e+01 |-7.213792e-01 |\\u001b[0m\\n\",\n \"| 486 |12.1500 | 1 | 0.599493 | 0.694460 | -5.078534 |-1.033571e+01 |-7.214716e-01 |\\u001b[0m\\n\",\n \"| 487 |12.1750 | 1 | 0.569671 | 0.611804 | -5.072894 |-1.033433e+01 |-7.215653e-01 |\\u001b[0m\\n\",\n \"| 488 |12.2000 | 1 | 0.590231 | 0.592073 | -5.070548 |-1.033294e+01 |-7.216604e-01 |\\u001b[0m\\n\",\n \"| 489 |12.2250 | 1 | 0.586426 | 0.587308 | -5.063791 |-1.033153e+01 |-7.217569e-01 |\\u001b[0m\\n\",\n \"| 490 |12.2500 | 1 | 0.605616 | 0.639888 | -5.060453 |-1.033011e+01 |-7.218546e-01 |\\u001b[0m\\n\",\n \"| 491 |12.2750 | 1 | 0.601391 | 0.589785 | -5.056911 |-1.032867e+01 |-7.219537e-01 |\\u001b[0m\\n\",\n \"| 492 |12.3000 | 1 | 0.583376 | 0.588843 | -5.054795 |-1.032722e+01 |-7.220541e-01 |\\u001b[0m\\n\",\n \"| 493 |12.3250 | 1 | 0.591293 | 0.608539 | -5.052808 |-1.032575e+01 |-7.221558e-01 |\\u001b[0m\\n\",\n \"| 494 |12.3500 | 1 | 0.568992 | 0.595768 | -5.047491 |-1.032427e+01 |-7.222588e-01 |\\u001b[0m\\n\",\n \"| 495 |12.3750 | 1 | 0.563630 | 0.599818 | -5.043728 |-1.032277e+01 |-7.223631e-01 |\\u001b[0m\\n\",\n \"| 496 |12.4000 | 1 | 0.583918 | 0.582994 | -5.038711 |-1.032126e+01 |-7.224687e-01 |\\u001b[0m\\n\",\n \"| 497 |12.4250 | 1 | 0.587738 | 0.584071 | -5.036205 |-1.031973e+01 |-7.225755e-01 |\\u001b[0m\\n\",\n \"| 498 |12.4500 | 1 | 0.575600 | 0.588839 | -5.033715 |-1.031819e+01 |-7.226837e-01 |\\u001b[0m\\n\",\n \"| 499 |12.4750 | 1 | 0.586772 | 0.589606 | -5.031815 |-1.031664e+01 |-7.227930e-01 |\\u001b[0m\\n\",\n \"| 500 |12.5000 | 1 | 0.577898 | 0.602334 | -5.027416 |-1.031507e+01 |-7.229037e-01 |\\u001b[0m\\n\",\n \"| 501 |12.5250 | 1 | 0.585324 | 0.589641 | -5.023384 |-1.031348e+01 |-7.230155e-01 |\\u001b[0m\\n\",\n \"| 502 |12.5500 | 1 | 0.585512 | 0.584594 | -5.019042 |-1.031189e+01 |-7.231287e-01 |\\u001b[0m\\n\",\n \"| 503 |12.5750 | 1 | 0.583865 | 0.582880 | -5.016063 |-1.031028e+01 |-7.232430e-01 |\\u001b[0m\\n\",\n \"| 504 |12.6000 | 1 | 0.588496 | 0.592948 | -5.014501 |-1.030865e+01 |-7.233586e-01 |\\u001b[0m\\n\",\n \"| 505 |12.6250 | 1 | 0.587081 | 0.593772 | -5.011221 |-1.030702e+01 |-7.234753e-01 |\\u001b[0m\\n\",\n \"| 506 |12.6500 | 1 | 0.585744 | 0.587407 | -5.009390 |-1.030537e+01 |-7.235933e-01 |\\u001b[0m\\n\",\n \"| 507 |12.6750 | 1 | 0.584881 | 0.596360 | -5.003415 |-1.030370e+01 |-7.237125e-01 |\\u001b[0m\\n\",\n \"| 508 |12.7000 | 1 | 0.596729 | 0.591525 | -5.001095 |-1.030203e+01 |-7.238329e-01 |\\u001b[0m\\n\",\n \"| 509 |12.7250 | 1 | 0.596917 | 0.597681 | -4.997208 |-1.030034e+01 |-7.239544e-01 |\\u001b[0m\\n\",\n \"| 510 |12.7500 | 1 | 0.591709 | 0.586425 | -4.995682 |-1.029863e+01 |-7.240771e-01 |\\u001b[0m\\n\",\n \"| 511 |12.7750 | 1 | 0.587641 | 0.591100 | -4.993524 |-1.029692e+01 |-7.242010e-01 |\\u001b[0m\\n\",\n \"| 512 |12.8000 | 1 | 0.587204 | 0.586659 | -4.990360 |-1.029519e+01 |-7.243260e-01 |\\u001b[0m\\n\",\n \"| 513 |12.8250 | 1 | 0.591092 | 0.587204 | -4.986833 |-1.029345e+01 |-7.244521e-01 |\\u001b[0m\\n\",\n \"| 514 |12.8500 | 1 | 0.585463 | 0.583301 | -4.982664 |-1.029170e+01 |-7.245795e-01 |\\u001b[0m\\n\",\n \"| 515 |12.8750 | 1 | 0.589045 | 0.586801 | -4.980566 |-1.028993e+01 |-7.247079e-01 |\\u001b[0m\\n\",\n \"| 516 |12.9000 | 1 | 0.596714 | 0.601805 | -4.977829 |-1.028816e+01 |-7.248374e-01 |\\u001b[0m\\n\",\n \"| 517 |12.9250 | 1 | 0.584486 | 0.594004 | -4.976834 |-1.028637e+01 |-7.249680e-01 |\\u001b[0m\\n\",\n \"| 518 |12.9500 | 1 | 0.577005 | 0.592874 | -4.973053 |-1.028457e+01 |-7.250998e-01 |\\u001b[0m\\n\",\n \"| 519 |12.9750 | 1 | 0.576873 | 0.590686 | -4.970798 |-1.028276e+01 |-7.252326e-01 |\\u001b[0m\\n\",\n \"| 520 |13.0000 | 1 | 0.588123 | 0.584250 | -4.966119 |-1.028094e+01 |-7.253666e-01 |\\u001b[0m\\n\",\n \"| 521 |13.0250 | 1 | 0.588080 | 0.592052 | -4.964473 |-1.027910e+01 |-7.255016e-01 |\\u001b[0m\\n\",\n \"| 522 |13.0500 | 1 | 0.586211 | 0.588701 | -4.961953 |-1.027726e+01 |-7.256376e-01 |\\u001b[0m\\n\",\n \"| 523 |13.0750 | 1 | 0.582357 | 0.595669 | -4.960468 |-1.027540e+01 |-7.257747e-01 |\\u001b[0m\\n\",\n \"| 524 |13.1000 | 1 | 0.569600 | 0.594107 | -4.958069 |-1.027353e+01 |-7.259128e-01 |\\u001b[0m\\n\",\n \"| 525 |13.1250 | 1 | 0.575376 | 0.594160 | -4.954661 |-1.027165e+01 |-7.260521e-01 |\\u001b[0m\\n\",\n \"| 526 |13.1500 | 1 | 0.578324 | 0.588696 | -4.952012 |-1.026976e+01 |-7.261923e-01 |\\u001b[0m\\n\",\n \"| 527 |13.1750 | 1 | 0.587095 | 0.592266 | -4.948571 |-1.026786e+01 |-7.263335e-01 |\\u001b[0m\\n\",\n \"| 528 |13.2000 | 1 | 0.569050 | 0.599524 | -4.947926 |-1.026595e+01 |-7.264758e-01 |\\u001b[0m\\n\",\n \"| 529 |13.2250 | 1 | 0.542086 | 0.614471 | -4.945114 |-1.026403e+01 |-7.266190e-01 |\\u001b[0m\\n\",\n \"| 530 |13.2500 | 1 | 0.540521 | 0.611883 | -4.943929 |-1.026210e+01 |-7.267632e-01 |\\u001b[0m\\n\",\n \"| 531 |13.2750 | 1 | 0.543265 | 0.621184 | -4.940566 |-1.026016e+01 |-7.269084e-01 |\\u001b[0m\\n\",\n \"| 532 |13.3000 | 1 | 0.541681 | 0.615142 | -4.937617 |-1.025821e+01 |-7.270546e-01 |\\u001b[0m\\n\",\n \"| 533 |13.3250 | 1 | 0.540352 | 0.616832 | -4.935709 |-1.025625e+01 |-7.272018e-01 |\\u001b[0m\\n\",\n \"| 534 |13.3500 | 1 | 0.544213 | 0.620769 | -4.933038 |-1.025428e+01 |-7.273499e-01 |\\u001b[0m\\n\",\n \"| 535 |13.3750 | 1 | 0.580695 | 0.590777 | -4.932776 |-1.025230e+01 |-7.274989e-01 |\\u001b[0m\\n\",\n \"| 536 |13.4000 | 1 | 0.575465 | 0.596223 | -4.929595 |-1.025031e+01 |-7.276489e-01 |\\u001b[0m\\n\",\n \"| 537 |13.4250 | 1 | 0.542536 | 0.618744 | -4.928176 |-1.024831e+01 |-7.277998e-01 |\\u001b[0m\\n\",\n \"| 538 |13.4500 | 1 | 0.580911 | 0.591514 | -4.924586 |-1.024631e+01 |-7.279516e-01 |\\u001b[0m\\n\",\n \"| 539 |13.4750 | 1 | 0.581108 | 0.591034 | -4.922988 |-1.024429e+01 |-7.281044e-01 |\\u001b[0m\\n\",\n \"| 540 |13.5000 | 1 | 0.545993 | 0.614974 | -4.920767 |-1.024227e+01 |-7.282580e-01 |\\u001b[0m\\n\",\n \"| 541 |13.5250 | 1 | 0.545921 | 0.615012 | -4.919915 |-1.024023e+01 |-7.284125e-01 |\\u001b[0m\\n\",\n \"| 542 |13.5500 | 1 | 0.542495 | 0.613665 | -4.917870 |-1.023819e+01 |-7.285679e-01 |\\u001b[0m\\n\",\n \"| 543 |13.5750 | 1 | 0.536964 | 0.622532 | -4.915675 |-1.023614e+01 |-7.287241e-01 |\\u001b[0m\\n\",\n \"| 544 |13.6000 | 1 | 0.554106 | 0.603419 | -4.913529 |-1.023408e+01 |-7.288812e-01 |\\u001b[0m\\n\",\n \"| 545 |13.6250 | 1 | 0.578840 | 0.604562 | -4.910680 |-1.023202e+01 |-7.290392e-01 |\\u001b[0m\\n\",\n \"| 546 |13.6500 | 1 | 0.585058 | 0.606280 | -4.910137 |-1.022994e+01 |-7.291979e-01 |\\u001b[0m\\n\",\n \"| 547 |13.6750 | 1 | 0.579318 | 0.591994 | -4.907749 |-1.022786e+01 |-7.293575e-01 |\\u001b[0m\\n\",\n \"| 548 |13.7000 | 1 | 0.580380 | 0.589279 | -4.907371 |-1.022577e+01 |-7.295179e-01 |\\u001b[0m\\n\",\n \"| 549 |13.7250 | 1 | 0.584794 | 0.591958 | -4.904445 |-1.022367e+01 |-7.296792e-01 |\\u001b[0m\\n\",\n \"| 550 |13.7500 | 1 | 0.588687 | 0.601052 | -4.902856 |-1.022157e+01 |-7.298412e-01 |\\u001b[0m\\n\",\n \"| 551 |13.7750 | 1 | 0.579102 | 0.595429 | -4.900526 |-1.021945e+01 |-7.300040e-01 |\\u001b[0m\\n\",\n \"| 552 |13.8000 | 1 | 0.579922 | 0.596135 | -4.899156 |-1.021733e+01 |-7.301676e-01 |\\u001b[0m\\n\",\n \"| 553 |13.8250 | 1 | 0.579598 | 0.597193 | -4.898152 |-1.021521e+01 |-7.303320e-01 |\\u001b[0m\\n\",\n \"| 554 |13.8500 | 1 | 0.589419 | 0.608047 | -4.896538 |-1.021307e+01 |-7.304971e-01 |\\u001b[0m\\n\",\n \"| 555 |13.8750 | 1 | 0.584321 | 0.601955 | -4.895262 |-1.021093e+01 |-7.306629e-01 |\\u001b[0m\\n\",\n \"| 556 |13.9000 | 1 | 0.579038 | 0.593430 | -4.892631 |-1.020879e+01 |-7.308295e-01 |\\u001b[0m\\n\",\n \"| 557 |13.9250 | 1 | 0.577858 | 0.591474 | -4.891491 |-1.020663e+01 |-7.309968e-01 |\\u001b[0m\\n\",\n \"| 558 |13.9500 | 1 | 0.578370 | 0.601104 | -4.889505 |-1.020447e+01 |-7.311649e-01 |\\u001b[0m\\n\",\n \"| 559 |13.9750 | 1 | 0.574518 | 0.594961 | -4.888943 |-1.020231e+01 |-7.313336e-01 |\\u001b[0m\\n\",\n \"| 560 |14.0000 | 1 | 0.578717 | 0.588370 | -4.887586 |-1.020014e+01 |-7.315030e-01 |\\u001b[0m\\n\",\n \"| 561 |14.0250 | 1 | 0.569221 | 0.592313 | -4.886037 |-1.019796e+01 |-7.316731e-01 |\\u001b[0m\\n\",\n \"| 562 |14.0500 | 1 | 0.569323 | 0.588773 | -4.884458 |-1.019577e+01 |-7.318439e-01 |\\u001b[0m\\n\",\n \"| 563 |14.0750 | 1 | 0.575350 | 0.590234 | -4.882463 |-1.019359e+01 |-7.320154e-01 |\\u001b[0m\\n\",\n \"| 564 |14.1000 | 1 | 0.565140 | 0.597502 | -4.881607 |-1.019139e+01 |-7.321875e-01 |\\u001b[0m\\n\",\n \"| 565 |14.1250 | 1 | 0.555995 | 0.601872 | -4.880250 |-1.018919e+01 |-7.323602e-01 |\\u001b[0m\\n\",\n \"| 566 |14.1500 | 1 | 0.582065 | 0.599824 | -4.879771 |-1.018699e+01 |-7.325336e-01 |\\u001b[0m\\n\",\n \"| 567 |14.1750 | 1 | 0.573287 | 0.591480 | -4.877873 |-1.018478e+01 |-7.327076e-01 |\\u001b[0m\\n\",\n \"| 568 |14.2000 | 1 | 0.574334 | 0.602253 | -4.876963 |-1.018256e+01 |-7.328822e-01 |\\u001b[0m\\n\",\n \"| 569 |14.2250 | 1 | 0.531243 | 0.628437 | -4.874752 |-1.018034e+01 |-7.330574e-01 |\\u001b[0m\\n\",\n \"| 570 |14.2500 | 1 | 0.530046 | 0.617958 | -4.874261 |-1.017812e+01 |-7.332332e-01 |\\u001b[0m\\n\",\n \"| 571 |14.2750 | 1 | 0.533493 | 0.621578 | -4.872975 |-1.017589e+01 |-7.334095e-01 |\\u001b[0m\\n\",\n \"| 572 |14.3000 | 1 | 0.531280 | 0.620959 | -4.872344 |-1.017365e+01 |-7.335865e-01 |\\u001b[0m\\n\",\n \"| 573 |14.3250 | 1 | 0.533888 | 0.617618 | -4.871330 |-1.017142e+01 |-7.337640e-01 |\\u001b[0m\\n\",\n \"| 574 |14.3500 | 1 | 0.538329 | 0.615710 | -4.869608 |-1.016917e+01 |-7.339420e-01 |\\u001b[0m\\n\",\n \"| 575 |14.3750 | 1 | 0.538880 | 0.617203 | -4.868750 |-1.016693e+01 |-7.341206e-01 |\\u001b[0m\\n\",\n \"| 576 |14.4000 | 1 | 0.538717 | 0.619451 | -4.867217 |-1.016468e+01 |-7.342997e-01 |\\u001b[0m\\n\",\n \"| 577 |14.4250 | 1 | 0.521259 | 0.628772 | -4.866965 |-1.016243e+01 |-7.344794e-01 |\\u001b[0m\\n\",\n \"| 578 |14.4500 | 1 | 0.532905 | 0.622927 | -4.865877 |-1.016017e+01 |-7.346595e-01 |\\u001b[0m\\n\",\n \"| 579 |14.4750 | 1 | 0.533617 | 0.622496 | -4.865300 |-1.015791e+01 |-7.348401e-01 |\\u001b[0m\\n\",\n \"| 580 |14.5000 | 1 | 0.534588 | 0.619178 | -4.863812 |-1.015565e+01 |-7.350212e-01 |\\u001b[0m\\n\",\n \"| 581 |14.5250 | 1 | 0.541063 | 0.619951 | -4.862879 |-1.015338e+01 |-7.352028e-01 |\\u001b[0m\\n\",\n \"| 582 |14.5500 | 1 | 0.552002 | 0.630617 | -4.861832 |-1.015111e+01 |-7.353848e-01 |\\u001b[0m\\n\",\n \"| 583 |14.5750 | 1 | 0.534411 | 0.618651 | -4.861210 |-1.014884e+01 |-7.355673e-01 |\\u001b[0m\\n\",\n \"| 584 |14.6000 | 1 | 0.519947 | 0.634783 | -4.860831 |-1.014656e+01 |-7.357502e-01 |\\u001b[0m\\n\",\n \"| 585 |14.6250 | 1 | 0.532511 | 0.623628 | -4.859751 |-1.014429e+01 |-7.359336e-01 |\\u001b[0m\\n\",\n \"| 586 |14.6500 | 1 | 0.533837 | 0.631545 | -4.859199 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596 |14.9000 | 1 | 0.534586 | 0.618118 | -4.852261 |-1.011910e+01 |-7.379757e-01 |\\u001b[0m\\n\",\n \"| 597 |14.9250 | 1 | 0.567604 | 0.593661 | -4.852487 |-1.011680e+01 |-7.381634e-01 |\\u001b[0m\\n\",\n \"| 598 |14.9500 | 1 | 0.572954 | 0.599532 | -4.851275 |-1.011451e+01 |-7.383513e-01 |\\u001b[0m\\n\",\n \"| 599 |14.9750 | 1 | 0.562174 | 0.595357 | -4.851012 |-1.011221e+01 |-7.385395e-01 |\\u001b[0m\\n\",\n \"| 600 |15.0000 | 1 | 0.565041 | 0.594815 | -4.850216 |-1.010991e+01 |-7.387280e-01 |\\u001b[0m\\n\",\n \"| 601 |15.0250 | 1 | 0.568619 | 0.602458 | -4.849993 |-1.010761e+01 |-7.389167e-01 |\\u001b[0m\\n\",\n \"| 602 |15.0500 | 1 | 0.565685 | 0.599703 | -4.849887 |-1.010531e+01 |-7.391057e-01 |\\u001b[0m\\n\",\n \"| 603 |15.0750 | 1 | 0.559376 | 0.612765 | -4.849425 |-1.010300e+01 |-7.392949e-01 |\\u001b[0m\\n\",\n \"| 604 |15.1000 | 1 | 0.558552 | 0.602107 | -4.849206 |-1.010070e+01 |-7.394843e-01 |\\u001b[0m\\n\",\n \"| 605 |15.1250 | 1 | 0.582718 | 0.633646 | -4.848406 |-1.009840e+01 |-7.396740e-01 |\\u001b[0m\\n\",\n \"| 606 |15.1500 | 1 | 0.581577 | 0.623610 | -4.848264 |-1.009610e+01 |-7.398638e-01 |\\u001b[0m\\n\",\n \"| 607 |15.1750 | 1 | 0.565744 | 0.594525 | -4.847774 |-1.009380e+01 |-7.400538e-01 |\\u001b[0m\\n\",\n \"| 608 |15.2000 | 1 | 0.564061 | 0.594557 | -4.848037 |-1.009150e+01 |-7.402440e-01 |\\u001b[0m\\n\",\n \"| 609 |15.2250 | 1 | 0.567888 | 0.599122 | -4.847578 |-1.008921e+01 |-7.404344e-01 |\\u001b[0m\\n\",\n \"| 610 |15.2500 | 1 | 0.570234 | 0.602823 | -4.847542 |-1.008691e+01 |-7.406249e-01 |\\u001b[0m\\n\",\n \"| 611 |15.2750 | 1 | 0.561263 | 0.598452 | -4.847030 |-1.008461e+01 |-7.408156e-01 |\\u001b[0m\\n\",\n \"| 612 |15.3000 | 1 | 0.568963 | 0.599018 | -4.846710 |-1.008231e+01 |-7.410064e-01 |\\u001b[0m\\n\",\n \"| 613 |15.3250 | 1 | 0.559163 | 0.605724 | -4.846813 |-1.008002e+01 |-7.411973e-01 |\\u001b[0m\\n\",\n \"| 614 |15.3500 | 1 | 0.564462 | 0.599463 | -4.846562 |-1.007773e+01 |-7.413883e-01 |\\u001b[0m\\n\",\n \"| 615 |15.3750 | 1 | 0.580952 | 0.610074 | -4.846943 |-1.007543e+01 |-7.415794e-01 |\\u001b[0m\\n\",\n \"| 616 |15.4000 | 1 | 0.568574 | 0.597096 | -4.846413 |-1.007314e+01 |-7.417706e-01 |\\u001b[0m\\n\",\n \"| 617 |15.4250 | 1 | 0.565757 | 0.596118 | -4.846541 |-1.007085e+01 |-7.419619e-01 |\\u001b[0m\\n\",\n \"| 618 |15.4500 | 1 | 0.537671 | 0.632581 | -4.846117 |-1.006857e+01 |-7.421533e-01 |\\u001b[0m\\n\",\n \"| 619 |15.4750 | 1 | 0.561591 | 0.596576 | -4.846302 |-1.006628e+01 |-7.423447e-01 |\\u001b[0m\\n\",\n \"| 620 |15.5000 | 1 | 0.559380 | 0.594044 | -4.846417 |-1.006400e+01 |-7.425361e-01 |\\u001b[0m\\n\",\n \"| 621 |15.5250 | 1 | 0.550661 | 0.639299 | -4.846521 |-1.006172e+01 |-7.427276e-01 |\\u001b[0m\\n\",\n \"| 622 |15.5500 | 1 | 0.564344 | 0.599497 | -4.846664 |-1.005944e+01 |-7.429191e-01 |\\u001b[0m\\n\",\n \"| 623 |15.5750 | 1 | 0.564470 | 0.598390 | -4.846375 |-1.005716e+01 |-7.431107e-01 |\\u001b[0m\\n\",\n \"| 624 |15.6000 | 1 | 0.582095 | 0.621527 | -4.846646 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634 |15.8500 | 1 | 0.563058 | 0.602004 | -4.848834 |-1.003232e+01 |-7.452150e-01 |\\u001b[0m\\n\",\n \"| 635 |15.8750 | 1 | 0.565077 | 0.604592 | -4.849242 |-1.003009e+01 |-7.454058e-01 |\\u001b[0m\\n\",\n \"| 636 |15.9000 | 1 | 0.561084 | 0.613315 | -4.849257 |-1.002785e+01 |-7.455965e-01 |\\u001b[0m\\n\",\n \"| 637 |15.9250 | 1 | 0.562131 | 0.608055 | -4.849893 |-1.002562e+01 |-7.457870e-01 |\\u001b[0m\\n\",\n \"| 638 |15.9500 | 1 | 0.567037 | 0.607231 | -4.850162 |-1.002340e+01 |-7.459774e-01 |\\u001b[0m\\n\",\n \"| 639 |15.9750 | 1 | 0.559362 | 0.605681 | -4.850853 |-1.002118e+01 |-7.461676e-01 |\\u001b[0m\\n\",\n \"| 640 |16.0000 | 1 | 0.559990 | 0.606771 | -4.851290 |-1.001896e+01 |-7.463577e-01 |\\u001b[0m\\n\",\n \"| 641 |16.0250 | 1 | 0.563540 | 0.604675 | -4.851567 |-1.001675e+01 |-7.465476e-01 |\\u001b[0m\\n\",\n \"| 642 |16.0500 | 1 | 0.569776 | 0.614118 | -4.852131 |-1.001455e+01 |-7.467372e-01 |\\u001b[0m\\n\",\n \"| 643 |16.0750 | 1 | 0.526022 | 0.638151 | -4.852404 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653 |16.3250 | 1 | 0.569525 | 0.613083 | -4.857579 |-9.990618e+00 |-7.488056e-01 |\\u001b[0m\\n\",\n \"| 654 |16.3500 | 1 | 0.572920 | 0.616659 | -4.856411 |-9.988477e+00 |-7.489920e-01 |\\u001b[0m\\n\",\n \"| 655 |16.3750 | 1 | 0.565054 | 0.622951 | -4.859712 |-9.986343e+00 |-7.491781e-01 |\\u001b[0m\\n\",\n \"| 656 |16.4000 | 1 | 0.538484 | 0.637184 | -4.858656 |-9.984214e+00 |-7.493640e-01 |\\u001b[0m\\n\",\n \"| 657 |16.4250 | 1 | 0.572575 | 0.628920 | -4.863059 |-9.982092e+00 |-7.495496e-01 |\\u001b[0m\\n\",\n \"| 658 |16.4500 | 1 | 0.553086 | 0.615147 | -4.865486 |-9.979977e+00 |-7.497349e-01 |\\u001b[0m\\n\",\n \"| 659 |16.4750 | 1 | 0.554584 | 0.608671 | -4.862494 |-9.977868e+00 |-7.499197e-01 |\\u001b[0m\\n\",\n \"| 660 |16.5000 | 1 | 0.566182 | 0.632013 | -4.865031 |-9.975766e+00 |-7.501042e-01 |\\u001b[0m\\n\",\n \"| 661 |16.5250 | 1 | 0.559237 | 0.607847 | -4.864222 |-9.973671e+00 |-7.502883e-01 |\\u001b[0m\\n\",\n \"| 662 |16.5500 | 1 | 0.547495 | 0.609668 | -4.865897 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672 |16.8000 | 1 | 0.553070 | 0.605358 | -4.874922 |-9.951098e+00 |-7.522844e-01 |\\u001b[0m\\n\",\n \"| 673 |16.8250 | 1 | 0.561627 | 0.612107 | -4.876898 |-9.949092e+00 |-7.524629e-01 |\\u001b[0m\\n\",\n \"| 674 |16.8500 | 1 | 0.555659 | 0.607956 | -4.879987 |-9.947094e+00 |-7.526409e-01 |\\u001b[0m\\n\",\n \"| 675 |16.8750 | 1 | 0.553403 | 0.616417 | -4.880702 |-9.945105e+00 |-7.528184e-01 |\\u001b[0m\\n\",\n \"| 676 |16.9000 | 1 | 0.553432 | 0.612899 | -4.884087 |-9.943123e+00 |-7.529953e-01 |\\u001b[0m\\n\",\n \"| 677 |16.9250 | 1 | 0.559188 | 0.618660 | -4.883577 |-9.941150e+00 |-7.531718e-01 |\\u001b[0m\\n\",\n \"| 678 |16.9500 | 1 | 0.555787 | 0.615341 | -4.883057 |-9.939185e+00 |-7.533476e-01 |\\u001b[0m\\n\",\n \"| 679 |16.9750 | 1 | 0.558311 | 0.612354 | -4.885587 |-9.937229e+00 |-7.535229e-01 |\\u001b[0m\\n\",\n \"| 680 |17.0000 | 1 | 0.561945 | 0.618028 | -4.886378 |-9.935282e+00 |-7.536977e-01 |\\u001b[0m\\n\",\n \"| 681 |17.0250 | 1 | 0.539489 | 0.628249 | -4.890029 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691 |17.2750 | 1 | 0.520007 | 0.638176 | -4.901707 |-9.914456e+00 |-7.555791e-01 |\\u001b[0m\\n\",\n \"| 692 |17.3000 | 1 | 0.514522 | 0.638778 | -4.905930 |-9.912619e+00 |-7.557462e-01 |\\u001b[0m\\n\",\n \"| 693 |17.3250 | 1 | 0.510692 | 0.643761 | -4.907376 |-9.910792e+00 |-7.559126e-01 |\\u001b[0m\\n\",\n \"| 694 |17.3500 | 1 | 0.517713 | 0.643936 | -4.909717 |-9.908974e+00 |-7.560782e-01 |\\u001b[0m\\n\",\n \"| 695 |17.3750 | 1 | 0.541182 | 0.655376 | -4.911696 |-9.907166e+00 |-7.562432e-01 |\\u001b[0m\\n\",\n \"| 696 |17.4000 | 1 | 0.551757 | 0.611377 | -4.910876 |-9.905369e+00 |-7.564075e-01 |\\u001b[0m\\n\",\n \"| 697 |17.4250 | 1 | 0.555262 | 0.614891 | -4.913403 |-9.903581e+00 |-7.565710e-01 |\\u001b[0m\\n\",\n \"| 698 |17.4500 | 1 | 0.564454 | 0.624082 | -4.915500 |-9.901804e+00 |-7.567338e-01 |\\u001b[0m\\n\",\n \"| 699 |17.4750 | 1 | 0.553199 | 0.610732 | -4.917215 |-9.900037e+00 |-7.568959e-01 |\\u001b[0m\\n\",\n \"| 700 |17.5000 | 1 | 0.548138 | 0.608044 | -4.921356 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710 |17.7500 | 1 | 0.550066 | 0.621723 | -4.938473 |-9.881290e+00 |-7.586276e-01 |\\u001b[0m\\n\",\n \"| 711 |17.7750 | 1 | 0.547227 | 0.613100 | -4.942387 |-9.879651e+00 |-7.587801e-01 |\\u001b[0m\\n\",\n \"| 712 |17.8000 | 1 | 0.549032 | 0.607084 | -4.943841 |-9.878023e+00 |-7.589318e-01 |\\u001b[0m\\n\",\n \"| 713 |17.8250 | 1 | 0.553408 | 0.626393 | -4.946716 |-9.876405e+00 |-7.590827e-01 |\\u001b[0m\\n\",\n \"| 714 |17.8500 | 1 | 0.552940 | 0.612425 | -4.948343 |-9.874799e+00 |-7.592327e-01 |\\u001b[0m\\n\",\n \"| 715 |17.8750 | 1 | 0.547835 | 0.608350 | -4.948430 |-9.873205e+00 |-7.593819e-01 |\\u001b[0m\\n\",\n \"| 716 |17.9000 | 1 | 0.540325 | 0.615331 | -4.952754 |-9.871621e+00 |-7.595302e-01 |\\u001b[0m\\n\",\n \"| 717 |17.9250 | 1 | 0.541983 | 0.615043 | -4.954732 |-9.870049e+00 |-7.596776e-01 |\\u001b[0m\\n\",\n \"| 718 |17.9500 | 1 | 0.545322 | 0.613781 | -4.957229 |-9.868489e+00 |-7.598241e-01 |\\u001b[0m\\n\",\n \"| 719 |17.9750 | 1 | 0.550283 | 0.619134 | -4.960988 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729 |18.2250 | 1 | 0.545937 | 0.614889 | -4.984680 |-9.852095e+00 |-7.613755e-01 |\\u001b[0m\\n\",\n \"| 730 |18.2500 | 1 | 0.545980 | 0.617822 | -4.988031 |-9.850676e+00 |-7.615109e-01 |\\u001b[0m\\n\",\n \"| 731 |18.2750 | 1 | 0.542477 | 0.615399 | -4.989711 |-9.849269e+00 |-7.616453e-01 |\\u001b[0m\\n\",\n \"| 732 |18.3000 | 1 | 0.547334 | 0.637717 | -4.993188 |-9.847874e+00 |-7.617788e-01 |\\u001b[0m\\n\",\n \"| 733 |18.3250 | 1 | 0.553981 | 0.623099 | -4.994720 |-9.846492e+00 |-7.619113e-01 |\\u001b[0m\\n\",\n \"| 734 |18.3500 | 1 | 0.548177 | 0.615461 | -4.996885 |-9.845122e+00 |-7.620428e-01 |\\u001b[0m\\n\",\n \"| 735 |18.3750 | 1 | 0.541814 | 0.619284 | -5.001297 |-9.843764e+00 |-7.621732e-01 |\\u001b[0m\\n\",\n \"| 736 |18.4000 | 1 | 0.545819 | 0.612507 | -5.004011 |-9.842419e+00 |-7.623028e-01 |\\u001b[0m\\n\",\n \"| 737 |18.4250 | 1 | 0.544200 | 0.612841 | -5.007008 |-9.841085e+00 |-7.624312e-01 |\\u001b[0m\\n\",\n \"| 738 |18.4500 | 1 | 0.542160 | 0.613612 | -5.009954 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748 |18.7000 | 1 | 0.553023 | 0.625866 | -5.041104 |-9.827250e+00 |-7.637771e-01 |\\u001b[0m\\n\",\n \"| 749 |18.7250 | 1 | 0.540949 | 0.619120 | -5.044064 |-9.826069e+00 |-7.638931e-01 |\\u001b[0m\\n\",\n \"| 750 |18.7500 | 1 | 0.537734 | 0.621421 | -5.046464 |-9.824900e+00 |-7.640081e-01 |\\u001b[0m\\n\",\n \"| 751 |18.7750 | 1 | 0.538831 | 0.623689 | -5.050195 |-9.823745e+00 |-7.641221e-01 |\\u001b[0m\\n\",\n \"| 752 |18.8000 | 1 | 0.541038 | 0.621485 | -5.052620 |-9.822602e+00 |-7.642350e-01 |\\u001b[0m\\n\",\n \"| 753 |18.8250 | 1 | 0.535511 | 0.620073 | -5.056418 |-9.821472e+00 |-7.643467e-01 |\\u001b[0m\\n\",\n \"| 754 |18.8500 | 1 | 0.530924 | 0.626769 | -5.060668 |-9.820355e+00 |-7.644574e-01 |\\u001b[0m\\n\",\n \"| 755 |18.8750 | 1 | 0.537222 | 0.615511 | -5.064038 |-9.819251e+00 |-7.645670e-01 |\\u001b[0m\\n\",\n \"| 756 |18.9000 | 1 | 0.534256 | 0.619716 | -5.067645 |-9.818160e+00 |-7.646756e-01 |\\u001b[0m\\n\",\n \"| 757 |18.9250 | 1 | 0.535977 | 0.618753 | -5.070290 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767 |19.1750 | 1 | 0.535861 | 0.620145 | -5.108621 |-9.807026e+00 |-7.657963e-01 |\\u001b[0m\\n\",\n \"| 768 |19.2000 | 1 | 0.536273 | 0.636314 | -5.112126 |-9.806093e+00 |-7.658914e-01 |\\u001b[0m\\n\",\n \"| 769 |19.2250 | 1 | 0.527759 | 0.633821 | -5.115285 |-9.805173e+00 |-7.659854e-01 |\\u001b[0m\\n\",\n \"| 770 |19.2500 | 1 | 0.544239 | 0.628317 | -5.119466 |-9.804266e+00 |-7.660783e-01 |\\u001b[0m\\n\",\n \"| 771 |19.2750 | 1 | 0.537259 | 0.622405 | -5.123024 |-9.803373e+00 |-7.661701e-01 |\\u001b[0m\\n\",\n \"| 772 |19.3000 | 1 | 0.534405 | 0.621513 | -5.128168 |-9.802493e+00 |-7.662607e-01 |\\u001b[0m\\n\",\n \"| 773 |19.3250 | 1 | 0.536213 | 0.619574 | -5.132116 |-9.801626e+00 |-7.663501e-01 |\\u001b[0m\\n\",\n \"| 774 |19.3500 | 1 | 0.547262 | 0.633010 | -5.136146 |-9.800773e+00 |-7.664384e-01 |\\u001b[0m\\n\",\n \"| 775 |19.3750 | 1 | 0.532413 | 0.624157 | -5.140640 |-9.799933e+00 |-7.665256e-01 |\\u001b[0m\\n\",\n \"| 776 |19.4000 | 1 | 0.528069 | 0.631161 | -5.143361 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786 |19.6500 | 1 | 0.501214 | 0.647573 | -5.188924 |-9.791574e+00 |-7.674079e-01 |\\u001b[0m\\n\",\n \"| 787 |19.6750 | 1 | 0.495648 | 0.655176 | -5.192845 |-9.790894e+00 |-7.674811e-01 |\\u001b[0m\\n\",\n \"| 788 |19.7000 | 1 | 0.499932 | 0.647758 | -5.197708 |-9.790228e+00 |-7.675532e-01 |\\u001b[0m\\n\",\n \"| 789 |19.7250 | 1 | 0.518200 | 0.630863 | -5.201669 |-9.789575e+00 |-7.676241e-01 |\\u001b[0m\\n\",\n \"| 790 |19.7500 | 1 | 0.536332 | 0.619421 | -5.206930 |-9.788935e+00 |-7.676937e-01 |\\u001b[0m\\n\",\n \"| 791 |19.7750 | 1 | 0.531387 | 0.621932 | -5.212611 |-9.788309e+00 |-7.677623e-01 |\\u001b[0m\\n\",\n \"| 792 |19.8000 | 1 | 0.527384 | 0.622412 | -5.216559 |-9.787696e+00 |-7.678296e-01 |\\u001b[0m\\n\",\n \"| 793 |19.8250 | 1 | 0.529678 | 0.620205 | -5.221430 |-9.787096e+00 |-7.678958e-01 |\\u001b[0m\\n\",\n \"| 794 |19.8500 | 1 | 0.508913 | 0.648031 | -5.226400 |-9.786510e+00 |-7.679608e-01 |\\u001b[0m\\n\",\n \"| 795 |19.8750 | 1 | 0.504351 | 0.648719 | -5.230347 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805 |20.1250 | 1 | 0.534982 | 0.622699 | -5.281286 |-9.780938e+00 |-7.685979e-01 |\\u001b[0m\\n\",\n \"| 806 |20.1500 | 1 | 0.530764 | 0.620805 | -5.286196 |-9.780510e+00 |-7.686487e-01 |\\u001b[0m\\n\",\n \"| 807 |20.1750 | 1 | 0.511985 | 0.636388 | -5.291943 |-9.780096e+00 |-7.686984e-01 |\\u001b[0m\\n\",\n \"| 808 |20.2000 | 1 | 0.496395 | 0.650078 | -5.296389 |-9.779696e+00 |-7.687469e-01 |\\u001b[0m\\n\",\n \"| 809 |20.2250 | 1 | 0.500372 | 0.658939 | -5.302208 |-9.779308e+00 |-7.687942e-01 |\\u001b[0m\\n\",\n \"| 810 |20.2500 | 1 | 0.499443 | 0.650036 | -5.308191 |-9.778933e+00 |-7.688403e-01 |\\u001b[0m\\n\",\n \"| 811 |20.2750 | 1 | 0.507094 | 0.660675 | -5.312377 |-9.778572e+00 |-7.688852e-01 |\\u001b[0m\\n\",\n \"| 812 |20.3000 | 1 | 0.501244 | 0.655777 | -5.317533 |-9.778224e+00 |-7.689290e-01 |\\u001b[0m\\n\",\n \"| 813 |20.3250 | 1 | 0.497886 | 0.659485 | -5.322998 |-9.777888e+00 |-7.689716e-01 |\\u001b[0m\\n\",\n \"| 814 |20.3500 | 1 | 0.531331 | 0.625960 | -5.327874 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824 |20.6000 | 1 | 0.504305 | 0.636577 | -5.379300 |-9.775055e+00 |-7.693629e-01 |\\u001b[0m\\n\",\n \"| 825 |20.6250 | 1 | 0.498041 | 0.634625 | -5.383927 |-9.774875e+00 |-7.693915e-01 |\\u001b[0m\\n\",\n \"| 826 |20.6500 | 1 | 0.491458 | 0.658197 | -5.389699 |-9.774707e+00 |-7.694190e-01 |\\u001b[0m\\n\",\n \"| 827 |20.6750 | 1 | 0.496825 | 0.658731 | -5.394111 |-9.774552e+00 |-7.694452e-01 |\\u001b[0m\\n\",\n \"| 828 |20.7000 | 1 | 0.502448 | 0.654295 | -5.398969 |-9.774409e+00 |-7.694703e-01 |\\u001b[0m\\n\",\n \"| 829 |20.7250 | 1 | 0.526343 | 0.629665 | -5.404191 |-9.774279e+00 |-7.694943e-01 |\\u001b[0m\\n\",\n \"| 830 |20.7500 | 1 | 0.527985 | 0.637049 | -5.408232 |-9.774162e+00 |-7.695171e-01 |\\u001b[0m\\n\",\n \"| 831 |20.7750 | 1 | 0.526428 | 0.631766 | -5.412435 |-9.774057e+00 |-7.695388e-01 |\\u001b[0m\\n\",\n \"| 832 |20.8000 | 1 | 0.549858 | 0.656701 | -5.417086 |-9.773965e+00 |-7.695593e-01 |\\u001b[0m\\n\",\n \"| 833 |20.8250 | 1 | 0.525367 | 0.640356 | -5.421889 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843 |21.0750 | 1 | 0.514197 | 0.677148 | -5.457769 |-9.773768e+00 |-7.697103e-01 |\\u001b[0m\\n\",\n \"| 844 |21.1000 | 1 | 0.501449 | 0.669868 | -5.460336 |-9.773823e+00 |-7.697173e-01 |\\u001b[0m\\n\",\n \"| 845 |21.1250 | 1 | 0.497707 | 0.677975 | -5.463272 |-9.773890e+00 |-7.697232e-01 |\\u001b[0m\\n\",\n \"| 846 |21.1500 | 1 | 0.500228 | 0.670709 | -5.466064 |-9.773969e+00 |-7.697280e-01 |\\u001b[0m\\n\",\n \"| 847 |21.1750 | 1 | 0.504896 | 0.676630 | -5.467633 |-9.774060e+00 |-7.697316e-01 |\\u001b[0m\\n\",\n \"| 848 |21.2000 | 1 | 0.500956 | 0.671256 | -5.469894 |-9.774164e+00 |-7.697342e-01 |\\u001b[0m\\n\",\n \"| 849 |21.2250 | 1 | 0.496505 | 0.674550 | -5.472033 |-9.774278e+00 |-7.697357e-01 |\\u001b[0m\\n\",\n \"| 850 |21.2500 | 1 | 0.529665 | 0.644782 | -5.472924 |-9.774405e+00 |-7.697361e-01 |\\u001b[0m\\n\",\n \"| 851 |21.2750 | 1 | 0.528408 | 0.645465 | -5.474619 |-9.774544e+00 |-7.697354e-01 |\\u001b[0m\\n\",\n \"| 852 |21.3000 | 1 | 0.519741 | 0.635947 | -5.476252 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862 |21.5500 | 1 | 0.499270 | 0.658582 | -5.476603 |-9.776830e+00 |-7.696569e-01 |\\u001b[0m\\n\",\n \"| 863 |21.5750 | 1 | 0.519785 | 0.638694 | -5.475176 |-9.777106e+00 |-7.696434e-01 |\\u001b[0m\\n\",\n \"| 864 |21.6000 | 1 | 0.534959 | 0.658340 | -5.473925 |-9.777393e+00 |-7.696289e-01 |\\u001b[0m\\n\",\n \"| 865 |21.6250 | 1 | 0.516683 | 0.652932 | -5.472998 |-9.777691e+00 |-7.696133e-01 |\\u001b[0m\\n\",\n \"| 866 |21.6500 | 1 | 0.524993 | 0.643355 | -5.470927 |-9.778000e+00 |-7.695968e-01 |\\u001b[0m\\n\",\n \"| 867 |21.6750 | 1 | 0.521338 | 0.641387 | -5.469193 |-9.778320e+00 |-7.695792e-01 |\\u001b[0m\\n\",\n \"| 868 |21.7000 | 1 | 0.511949 | 0.650276 | -5.467707 |-9.778651e+00 |-7.695606e-01 |\\u001b[0m\\n\",\n \"| 869 |21.7250 | 1 | 0.516787 | 0.641368 | -5.465221 |-9.778993e+00 |-7.695409e-01 |\\u001b[0m\\n\",\n \"| 870 |21.7500 | 1 | 0.526370 | 0.644767 | -5.462966 |-9.779345e+00 |-7.695203e-01 |\\u001b[0m\\n\",\n \"| 871 |21.7750 | 1 | 0.527064 | 0.650980 | -5.460746 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881 |22.0250 | 1 | 0.533964 | 0.644499 | -5.431166 |-9.783921e+00 |-7.692279e-01 |\\u001b[0m\\n\",\n \"| 882 |22.0500 | 1 | 0.515048 | 0.643263 | -5.427340 |-9.784399e+00 |-7.691955e-01 |\\u001b[0m\\n\",\n \"| 883 |22.0750 | 1 | 0.528883 | 0.638636 | -5.423886 |-9.784887e+00 |-7.691622e-01 |\\u001b[0m\\n\",\n \"| 884 |22.1000 | 1 | 0.520719 | 0.634711 | -5.420468 |-9.785385e+00 |-7.691279e-01 |\\u001b[0m\\n\",\n \"| 885 |22.1250 | 1 | 0.520284 | 0.649912 | -5.416873 |-9.785892e+00 |-7.690927e-01 |\\u001b[0m\\n\",\n \"| 886 |22.1500 | 1 | 0.528762 | 0.647822 | -5.413226 |-9.786410e+00 |-7.690565e-01 |\\u001b[0m\\n\",\n \"| 887 |22.1750 | 1 | 0.509786 | 0.659574 | -5.409500 |-9.786937e+00 |-7.690194e-01 |\\u001b[0m\\n\",\n \"| 888 |22.2000 | 1 | 0.520104 | 0.640645 | -5.405926 |-9.787475e+00 |-7.689815e-01 |\\u001b[0m\\n\",\n \"| 889 |22.2250 | 1 | 0.528201 | 0.646174 | -5.401876 |-9.788022e+00 |-7.689426e-01 |\\u001b[0m\\n\",\n \"| 890 |22.2500 | 1 | 0.517401 | 0.639639 | -5.398218 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900 |22.5000 | 1 | 0.491788 | 0.670256 | -5.360229 |-9.794658e+00 |-7.684559e-01 |\\u001b[0m\\n\",\n \"| 901 |22.5250 | 1 | 0.484136 | 0.663273 | -5.356469 |-9.795316e+00 |-7.684065e-01 |\\u001b[0m\\n\",\n \"| 902 |22.5500 | 1 | 0.494571 | 0.674221 | -5.352664 |-9.795983e+00 |-7.683562e-01 |\\u001b[0m\\n\",\n \"| 903 |22.5750 | 1 | 0.484502 | 0.666114 | -5.348923 |-9.796658e+00 |-7.683051e-01 |\\u001b[0m\\n\",\n \"| 904 |22.6000 | 1 | 0.500552 | 0.659357 | -5.345406 |-9.797343e+00 |-7.682532e-01 |\\u001b[0m\\n\",\n \"| 905 |22.6250 | 1 | 0.474210 | 0.675963 | -5.341552 |-9.798036e+00 |-7.682004e-01 |\\u001b[0m\\n\",\n \"| 906 |22.6500 | 1 | 0.512181 | 0.642814 | -5.337793 |-9.798737e+00 |-7.681468e-01 |\\u001b[0m\\n\",\n \"| 907 |22.6750 | 1 | 0.530902 | 0.671671 | -5.334230 |-9.799447e+00 |-7.680925e-01 |\\u001b[0m\\n\",\n \"| 908 |22.7000 | 1 | 0.514472 | 0.642086 | -5.330476 |-9.800166e+00 |-7.680373e-01 |\\u001b[0m\\n\",\n \"| 909 |22.7250 | 1 | 0.511914 | 0.644290 | -5.326850 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919 |22.9750 | 1 | 0.518832 | 0.657375 | -5.292315 |-9.808606e+00 |-7.673791e-01 |\\u001b[0m\\n\",\n \"| 920 |23.0000 | 1 | 0.509751 | 0.646163 | -5.289145 |-9.809420e+00 |-7.673148e-01 |\\u001b[0m\\n\",\n \"| 921 |23.0250 | 1 | 0.521466 | 0.646805 | -5.285912 |-9.810242e+00 |-7.672497e-01 |\\u001b[0m\\n\",\n \"| 922 |23.0500 | 1 | 0.512008 | 0.637779 | -5.282643 |-9.811071e+00 |-7.671840e-01 |\\u001b[0m\\n\",\n \"| 923 |23.0750 | 1 | 0.517762 | 0.647592 | -5.279669 |-9.811908e+00 |-7.671175e-01 |\\u001b[0m\\n\",\n \"| 924 |23.1000 | 1 | 0.521314 | 0.644842 | -5.276377 |-9.812752e+00 |-7.670503e-01 |\\u001b[0m\\n\",\n \"| 925 |23.1250 | 1 | 0.495290 | 0.652850 | -5.273205 |-9.813603e+00 |-7.669824e-01 |\\u001b[0m\\n\",\n \"| 926 |23.1500 | 1 | 0.516843 | 0.640946 | -5.270279 |-9.814461e+00 |-7.669139e-01 |\\u001b[0m\\n\",\n \"| 927 |23.1750 | 1 | 0.511137 | 0.637577 | -5.267108 |-9.815327e+00 |-7.668446e-01 |\\u001b[0m\\n\",\n \"| 928 |23.2000 | 1 | 0.512721 | 0.636781 | -5.264265 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938 |23.4500 | 1 | 0.476561 | 0.677960 | -5.236134 |-9.825294e+00 |-7.660399e-01 |\\u001b[0m\\n\",\n \"| 939 |23.4750 | 1 | 0.479632 | 0.672821 | -5.233690 |-9.826238e+00 |-7.659630e-01 |\\u001b[0m\\n\",\n \"| 940 |23.5000 | 1 | 0.473291 | 0.676737 | -5.231094 |-9.827189e+00 |-7.658855e-01 |\\u001b[0m\\n\",\n \"| 941 |23.5250 | 1 | 0.474442 | 0.677697 | -5.228548 |-9.828146e+00 |-7.658074e-01 |\\u001b[0m\\n\",\n \"| 942 |23.5500 | 1 | 0.485998 | 0.658387 | -5.226139 |-9.829110e+00 |-7.657288e-01 |\\u001b[0m\\n\",\n \"| 943 |23.5750 | 1 | 0.514283 | 0.634293 | -5.223562 |-9.830079e+00 |-7.656495e-01 |\\u001b[0m\\n\",\n \"| 944 |23.6000 | 1 | 0.516713 | 0.646159 | -5.221143 |-9.831053e+00 |-7.655697e-01 |\\u001b[0m\\n\",\n \"| 945 |23.6250 | 1 | 0.509222 | 0.641191 | -5.218806 |-9.832034e+00 |-7.654894e-01 |\\u001b[0m\\n\",\n \"| 946 |23.6500 | 1 | 0.511243 | 0.639904 | -5.216415 |-9.833020e+00 |-7.654084e-01 |\\u001b[0m\\n\",\n \"| 947 |23.6750 | 1 | 0.504852 | 0.645054 | -5.214173 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957 |23.9250 | 1 | 0.502699 | 0.645553 | -5.192758 |-9.844224e+00 |-7.644836e-01 |\\u001b[0m\\n\",\n \"| 958 |23.9500 | 1 | 0.509565 | 0.643627 | -5.190837 |-9.845273e+00 |-7.643966e-01 |\\u001b[0m\\n\",\n \"| 959 |23.9750 | 1 | 0.505842 | 0.650800 | -5.188929 |-9.846327e+00 |-7.643091e-01 |\\u001b[0m\\n\",\n \"| 960 |24.0000 | 1 | 0.509080 | 0.639700 | -5.187018 |-9.847385e+00 |-7.642211e-01 |\\u001b[0m\\n\",\n \"| 961 |24.0250 | 1 | 0.506969 | 0.643642 | -5.185180 |-9.848448e+00 |-7.641327e-01 |\\u001b[0m\\n\",\n \"| 962 |24.0500 | 1 | 0.502202 | 0.644327 | -5.183292 |-9.849515e+00 |-7.640438e-01 |\\u001b[0m\\n\",\n \"| 963 |24.0750 | 1 | 0.504608 | 0.646704 | -5.181523 |-9.850587e+00 |-7.639545e-01 |\\u001b[0m\\n\",\n \"| 964 |24.1000 | 1 | 0.506113 | 0.640549 | -5.179790 |-9.851663e+00 |-7.638648e-01 |\\u001b[0m\\n\",\n \"| 965 |24.1250 | 1 | 0.516273 | 0.650328 | -5.178029 |-9.852743e+00 |-7.637746e-01 |\\u001b[0m\\n\",\n \"| 966 |24.1500 | 1 | 0.514624 | 0.656699 | -5.176397 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976 |24.4000 | 1 | 0.501039 | 0.644028 | -5.160961 |-9.864888e+00 |-7.627568e-01 |\\u001b[0m\\n\",\n \"| 977 |24.4250 | 1 | 0.504128 | 0.646994 | -5.159634 |-9.866014e+00 |-7.626621e-01 |\\u001b[0m\\n\",\n \"| 978 |24.4500 | 1 | 0.509705 | 0.643946 | -5.158234 |-9.867143e+00 |-7.625670e-01 |\\u001b[0m\\n\",\n \"| 979 |24.4750 | 1 | 0.504889 | 0.642303 | -5.156955 |-9.868275e+00 |-7.624717e-01 |\\u001b[0m\\n\",\n \"| 980 |24.5000 | 1 | 0.511998 | 0.654649 | -5.155620 |-9.869411e+00 |-7.623759e-01 |\\u001b[0m\\n\",\n \"| 981 |24.5250 | 1 | 0.505531 | 0.643071 | -5.154346 |-9.870549e+00 |-7.622799e-01 |\\u001b[0m\\n\",\n \"| 982 |24.5500 | 1 | 0.505855 | 0.644088 | -5.153156 |-9.871691e+00 |-7.621836e-01 |\\u001b[0m\\n\",\n \"| 983 |24.5750 | 1 | 0.503710 | 0.643562 | -5.151921 |-9.872835e+00 |-7.620870e-01 |\\u001b[0m\\n\",\n \"| 984 |24.6000 | 1 | 0.503625 | 0.652749 | -5.150775 |-9.873983e+00 |-7.619900e-01 |\\u001b[0m\\n\",\n \"| 985 |24.6250 | 1 | 0.497902 | 0.668819 | -5.149604 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995 |24.8750 | 1 | 0.487252 | 0.669019 | -5.139545 |-9.886772e+00 |-7.609062e-01 |\\u001b[0m\\n\",\n \"| 996 |24.9000 | 1 | 0.486750 | 0.677291 | -5.138686 |-9.887948e+00 |-7.608063e-01 |\\u001b[0m\\n\",\n \"| 997 |24.9250 | 1 | 0.499252 | 0.655279 | -5.137821 |-9.889126e+00 |-7.607061e-01 |\\u001b[0m\\n\",\n \"| 998 |24.9500 | 1 | 0.490417 | 0.702562 | -5.137027 |-9.890305e+00 |-7.606058e-01 |\\u001b[0m\\n\",\n \"| 999 |24.9750 | 1 | 0.503546 | 0.651132 | -5.136210 |-9.891487e+00 |-7.605052e-01 |\\u001b[0m\\n\",\n \"| 1000 |25.0000 | 1 | 0.483413 | 0.668655 | -5.135456 |-9.892670e+00 |-7.604045e-01 |\\u001b[0m\\n\",\n \"| 1001 |25.0250 | 1 | 0.493134 | 0.660787 | -5.134750 |-9.893855e+00 |-7.603035e-01 |\\u001b[0m\\n\",\n \"| 1002 |25.0500 | 1 | 0.499426 | 0.657750 | -5.134009 |-9.895041e+00 |-7.602024e-01 |\\u001b[0m\\n\",\n \"| 1003 |25.0750 | 1 | 0.494080 | 0.661456 | -5.133351 |-9.896229e+00 |-7.601011e-01 |\\u001b[0m\\n\",\n \"| 1004 |25.1000 | 1 | 0.507680 | 0.664709 | -5.132659 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|\\u001b[0m\\n\",\n \"| 1014 |25.3500 | 1 | 0.496672 | 0.655548 | -5.127374 |-9.909372e+00 |-7.589777e-01 |\\u001b[0m\\n\",\n \"| 1015 |25.3750 | 1 | 0.496958 | 0.668447 | -5.126963 |-9.910572e+00 |-7.588749e-01 |\\u001b[0m\\n\",\n \"| 1016 |25.4000 | 1 | 0.477043 | 0.671800 | -5.126575 |-9.911773e+00 |-7.587720e-01 |\\u001b[0m\\n\",\n \"| 1017 |25.4250 | 1 | 0.493859 | 0.660183 | -5.126228 |-9.912974e+00 |-7.586690e-01 |\\u001b[0m\\n\",\n \"| 1018 |25.4500 | 1 | 0.497632 | 0.654123 | -5.125876 |-9.914176e+00 |-7.585660e-01 |\\u001b[0m\\n\",\n \"| 1019 |25.4750 | 1 | 0.502519 | 0.653777 | -5.125597 |-9.915378e+00 |-7.584628e-01 |\\u001b[0m\\n\",\n \"| 1020 |25.5000 | 1 | 0.499899 | 0.652161 | -5.125308 |-9.916580e+00 |-7.583596e-01 |\\u001b[0m\\n\",\n \"| 1021 |25.5250 | 1 | 0.505590 | 0.660761 | -5.125039 |-9.917782e+00 |-7.582564e-01 |\\u001b[0m\\n\",\n \"| 1022 |25.5500 | 1 | 0.499622 | 0.658219 | -5.124808 |-9.918985e+00 |-7.581531e-01 |\\u001b[0m\\n\",\n \"| 1023 |25.5750 | 1 | 0.494296 | 0.658807 | -5.124571 |-9.920187e+00 |-7.580498e-01 |\\u001b[0m\\n\",\n \"| 1024 |25.6000 | 1 | 0.499221 | 0.654806 | -5.124375 |-9.921390e+00 |-7.579464e-01 |\\u001b[0m\\n\",\n \"| 1025 |25.6250 | 1 | 0.499540 | 0.652259 | -5.124226 |-9.922592e+00 |-7.578430e-01 |\\u001b[0m\\n\",\n \"| 1026 |25.6500 | 1 | 0.497204 | 0.653026 | -5.124062 |-9.923795e+00 |-7.577395e-01 |\\u001b[0m\\n\",\n \"| 1027 |25.6750 | 1 | 0.498324 | 0.660967 | -5.123947 |-9.924997e+00 |-7.576361e-01 |\\u001b[0m\\n\",\n \"| 1028 |25.7000 | 1 | 0.495586 | 0.657316 | -5.123838 |-9.926199e+00 |-7.575326e-01 |\\u001b[0m\\n\",\n \"| 1029 |25.7250 | 1 | 0.495336 | 0.659465 | -5.123735 |-9.927401e+00 |-7.574291e-01 |\\u001b[0m\\n\",\n \"| 1030 |25.7500 | 1 | 0.498829 | 0.654207 | -5.123691 |-9.928602e+00 |-7.573256e-01 |\\u001b[0m\\n\",\n \"| 1031 |25.7750 | 1 | 0.496229 | 0.656042 | -5.123643 |-9.929803e+00 |-7.572221e-01 |\\u001b[0m\\n\",\n \"| 1032 |25.8000 | 1 | 0.498100 | 0.658060 | -5.123639 |-9.931003e+00 |-7.571187e-01 |\\u001b[0m\\n\",\n \"| 1033 |25.8250 | 1 | 0.493844 | 0.656294 | -5.123650 |-9.932203e+00 |-7.570152e-01 |\\u001b[0m\\n\",\n \"| 1034 |25.8500 | 1 | 0.496206 | 0.652885 | -5.123656 |-9.933402e+00 |-7.569118e-01 |\\u001b[0m\\n\",\n \"| 1035 |25.8750 | 1 | 0.493092 | 0.655715 | -5.123718 |-9.934600e+00 |-7.568084e-01 |\\u001b[0m\\n\",\n \"| 1036 |25.9000 | 1 | 0.499616 | 0.658027 | -5.123774 |-9.935798e+00 |-7.567050e-01 |\\u001b[0m\\n\",\n \"| 1037 |25.9250 | 1 | 0.491226 | 0.658937 | -5.123870 |-9.936995e+00 |-7.566016e-01 |\\u001b[0m\\n\",\n \"| 1038 |25.9500 | 1 | 0.500340 | 0.653876 | -5.124001 |-9.938190e+00 |-7.564983e-01 |\\u001b[0m\\n\",\n \"| 1039 |25.9750 | 1 | 0.495677 | 0.650797 | -5.124126 |-9.939385e+00 |-7.563951e-01 |\\u001b[0m\\n\",\n \"| 1040 |26.0000 | 1 | 0.476759 | 0.680443 | -5.124280 |-9.940579e+00 |-7.562919e-01 |\\u001b[0m\\n\",\n \"| 1041 |26.0250 | 1 | 0.488234 | 0.659470 | -5.124460 |-9.941772e+00 |-7.561888e-01 |\\u001b[0m\\n\",\n \"| 1042 |26.0500 | 1 | 0.504142 | 0.662927 | -5.124649 |-9.942963e+00 |-7.560857e-01 |\\u001b[0m\\n\",\n \"| 1043 |26.0750 | 1 | 0.493124 | 0.657806 | -5.124875 |-9.944154e+00 |-7.559827e-01 |\\u001b[0m\\n\",\n \"| 1044 |26.1000 | 1 | 0.494713 | 0.663481 | -5.125130 |-9.945343e+00 |-7.558798e-01 |\\u001b[0m\\n\",\n \"| 1045 |26.1250 | 1 | 0.490307 | 0.656816 | -5.125384 |-9.946530e+00 |-7.557770e-01 |\\u001b[0m\\n\",\n \"| 1046 |26.1500 | 1 | 0.484677 | 0.662911 | -5.125675 |-9.947717e+00 |-7.556742e-01 |\\u001b[0m\\n\",\n \"| 1047 |26.1750 | 1 | 0.493045 | 0.654708 | -5.125970 |-9.948901e+00 |-7.555716e-01 |\\u001b[0m\\n\",\n \"| 1048 |26.2000 | 1 | 0.538497 | 0.726460 | -5.126294 |-9.950085e+00 |-7.554690e-01 |\\u001b[0m\\n\",\n \"| 1049 |26.2250 | 1 | 0.549513 | 0.737299 | -5.126653 |-9.951266e+00 |-7.553666e-01 |\\u001b[0m\\n\",\n \"| 1050 |26.2500 | 1 | 0.492540 | 0.664606 | -5.127014 |-9.952446e+00 |-7.552643e-01 |\\u001b[0m\\n\",\n \"| 1051 |26.2750 | 1 | 0.493577 | 0.659932 | -5.127419 |-9.953625e+00 |-7.551620e-01 |\\u001b[0m\\n\",\n \"| 1052 |26.3000 | 1 | 0.467239 | 0.712753 | -5.127825 |-9.954801e+00 |-7.550599e-01 |\\u001b[0m\\n\",\n \"| 1053 |26.3250 | 1 | 0.455075 | 0.725685 | -5.128240 |-9.955976e+00 |-7.549580e-01 |\\u001b[0m\\n\",\n \"| 1054 |26.3500 | 1 | 0.475621 | 0.676184 | -5.128711 |-9.957149e+00 |-7.548561e-01 |\\u001b[0m\\n\",\n \"| 1055 |26.3750 | 1 | 0.534025 | 0.705199 | -5.129171 |-9.958320e+00 |-7.547544e-01 |\\u001b[0m\\n\",\n \"| 1056 |26.4000 | 1 | 0.535417 | 0.733416 | -5.129674 |-9.959488e+00 |-7.546529e-01 |\\u001b[0m\\n\",\n \"| 1057 |26.4250 | 1 | 0.490559 | 0.667110 | -5.130201 |-9.960655e+00 |-7.545515e-01 |\\u001b[0m\\n\",\n \"| 1058 |26.4500 | 1 | 0.492721 | 0.667776 | -5.130724 |-9.961820e+00 |-7.544502e-01 |\\u001b[0m\\n\",\n \"| 1059 |26.4750 | 1 | 0.469686 | 0.716404 | -5.131284 |-9.962982e+00 |-7.543491e-01 |\\u001b[0m\\n\",\n \"| 1060 |26.5000 | 1 | 0.461801 | 0.727427 | -5.131858 |-9.964142e+00 |-7.542482e-01 |\\u001b[0m\\n\",\n \"| 1061 |26.5250 | 1 | 0.464589 | 0.694128 | -5.132457 |-9.965300e+00 |-7.541474e-01 |\\u001b[0m\\n\",\n \"| 1062 |26.5500 | 1 | 0.471781 | 0.706331 | -5.133085 |-9.966456e+00 |-7.540468e-01 |\\u001b[0m\\n\",\n \"| 1063 |26.5750 | 1 | 0.459214 | 0.698293 | -5.133724 |-9.967609e+00 |-7.539464e-01 |\\u001b[0m\\n\",\n \"| 1064 |26.6000 | 1 | 0.465039 | 0.701240 | -5.134387 |-9.968759e+00 |-7.538461e-01 |\\u001b[0m\\n\",\n \"| 1065 |26.6250 | 1 | 0.469236 | 0.698958 | -5.135067 |-9.969907e+00 |-7.537461e-01 |\\u001b[0m\\n\",\n \"| 1066 |26.6500 | 1 | 0.464358 | 0.702767 | -5.135759 |-9.971053e+00 |-7.536462e-01 |\\u001b[0m\\n\",\n \"| 1067 |26.6750 | 1 | 0.465766 | 0.699608 | -5.136493 |-9.972195e+00 |-7.535466e-01 |\\u001b[0m\\n\",\n \"| 1068 |26.7000 | 1 | 0.459619 | 0.698973 | -5.084913 |-9.973335e+00 |-7.534475e-01 |\\u001b[0m\\n\",\n \"| 1069 |26.7250 | 1 | 0.476216 | 0.700416 | -5.145987 |-9.974473e+00 |-7.533490e-01 |\\u001b[0m\\n\",\n \"| 1070 |26.7500 | 1 | 0.480763 | 0.738047 | -5.138887 |-9.975607e+00 |-7.532503e-01 |\\u001b[0m\\n\",\n \"| 1071 |26.7750 | 1 | 0.461171 | 0.701831 | -5.135784 |-9.976739e+00 |-7.531516e-01 |\\u001b[0m\\n\",\n \"| 1072 |26.8000 | 1 | 0.447415 | 0.732048 | -5.142042 |-9.977868e+00 |-7.530534e-01 |\\u001b[0m\\n\",\n \"| 1073 |26.8250 | 1 | 0.463453 | 0.697525 | -5.138247 |-9.978994e+00 |-7.529551e-01 |\\u001b[0m\\n\",\n \"| 1074 |26.8500 | 1 | 0.461543 | 0.697473 | -5.135863 |-9.980116e+00 |-7.528572e-01 |\\u001b[0m\\n\",\n \"| 1075 |26.8750 | 1 | 0.457196 | 0.716596 | -5.141322 |-9.981236e+00 |-7.527593e-01 |\\u001b[0m\\n\",\n \"| 1076 |26.9000 | 1 | 0.468679 | 0.696296 | -5.138910 |-9.982352e+00 |-7.526616e-01 |\\u001b[0m\\n\",\n \"| 1077 |26.9250 | 1 | 0.461713 | 0.706081 | -5.146215 |-9.983465e+00 |-7.525640e-01 |\\u001b[0m\\n\",\n \"| 1078 |26.9500 | 1 | 0.466057 | 0.697697 | -5.150453 |-9.984575e+00 |-7.524668e-01 |\\u001b[0m\\n\",\n \"| 1079 |26.9750 | 1 | 0.464665 | 0.702892 | -5.143797 |-9.985682e+00 |-7.523698e-01 |\\u001b[0m\\n\",\n \"| 1080 |27.0000 | 1 | 0.460304 | 0.700288 | -5.148337 |-9.986785e+00 |-7.522730e-01 |\\u001b[0m\\n\",\n \"| 1081 |27.0250 | 1 | 0.487071 | 0.704852 | -5.146060 |-9.987885e+00 |-7.521765e-01 |\\u001b[0m\\n\",\n \"| 1082 |27.0500 | 1 | 0.491921 | 0.701263 | -5.148301 |-9.988981e+00 |-7.520802e-01 |\\u001b[0m\\n\",\n \"| 1083 |27.0750 | 1 | 0.514891 | 0.691098 | -5.155984 |-9.990075e+00 |-7.519842e-01 |\\u001b[0m\\n\",\n \"| 1084 |27.1000 | 1 | 0.511289 | 0.700004 | -5.152389 |-9.991164e+00 |-7.518885e-01 |\\u001b[0m\\n\",\n \"| 1085 |27.1250 | 1 | 0.464907 | 0.689621 | -5.154942 |-9.992250e+00 |-7.517932e-01 |\\u001b[0m\\n\",\n \"| 1086 |27.1500 | 1 | 0.522192 | 0.703924 | -5.152321 |-9.993332e+00 |-7.516980e-01 |\\u001b[0m\\n\",\n \"| 1087 |27.1750 | 1 | 0.482099 | 0.686301 | -5.150296 |-9.994411e+00 |-7.516032e-01 |\\u001b[0m\\n\",\n \"| 1088 |27.2000 | 1 | 0.484473 | 0.666338 | -5.158286 |-9.995485e+00 |-7.515087e-01 |\\u001b[0m\\n\",\n \"| 1089 |27.2250 | 1 | 0.465606 | 0.714366 | -5.158936 |-9.996557e+00 |-7.514145e-01 |\\u001b[0m\\n\",\n \"| 1090 |27.2500 | 1 | 0.455517 | 0.696506 | -5.159762 |-9.997624e+00 |-7.513207e-01 |\\u001b[0m\\n\",\n \"| 1091 |27.2750 | 1 | 0.466815 | 0.703345 | -5.162399 |-9.998687e+00 |-7.512272e-01 |\\u001b[0m\\n\",\n \"| 1092 |27.3000 | 1 | 0.456211 | 0.701992 | -5.156860 |-9.999747e+00 |-7.511339e-01 |\\u001b[0m\\n\",\n \"| 1093 |27.3250 | 1 | 0.465226 | 0.696526 | -5.159533 |-1.000080e+01 |-7.510410e-01 |\\u001b[0m\\n\",\n \"| 1094 |27.3500 | 1 | 0.512126 | 0.700777 | -5.164709 |-1.000185e+01 |-7.509483e-01 |\\u001b[0m\\n\",\n \"| 1095 |27.3750 | 1 | 0.479834 | 0.671114 | -5.164529 |-1.000290e+01 |-7.508561e-01 |\\u001b[0m\\n\",\n \"| 1096 |27.4000 | 1 | 0.492537 | 0.673946 | -5.170199 |-1.000394e+01 |-7.507642e-01 |\\u001b[0m\\n\",\n \"| 1097 |27.4250 | 1 | 0.489561 | 0.672850 | -5.167845 |-1.000498e+01 |-7.506725e-01 |\\u001b[0m\\n\",\n \"| 1098 |27.4500 | 1 | 0.488160 | 0.668952 | -5.165967 |-1.000602e+01 |-7.505812e-01 |\\u001b[0m\\n\",\n \"| 1099 |27.4750 | 1 | 0.519246 | 0.695777 | -5.169713 |-1.000705e+01 |-7.504902e-01 |\\u001b[0m\\n\",\n \"| 1100 |27.5000 | 1 | 0.489192 | 0.667250 | -5.170115 |-1.000808e+01 |-7.503995e-01 |\\u001b[0m\\n\",\n \"| 1101 |27.5250 | 1 | 0.499167 | 0.682266 | -5.175767 |-1.000910e+01 |-7.503093e-01 |\\u001b[0m\\n\",\n \"| 1102 |27.5500 | 1 | 0.492088 | 0.672850 | -5.178382 |-1.001011e+01 |-7.502193e-01 |\\u001b[0m\\n\",\n \"| 1103 |27.5750 | 1 | 0.487768 | 0.663787 | -5.175107 |-1.001113e+01 |-7.501297e-01 |\\u001b[0m\\n\",\n \"| 1104 |27.6000 | 1 | 0.493979 | 0.674322 | -5.178327 |-1.001214e+01 |-7.500404e-01 |\\u001b[0m\\n\",\n \"| 1105 |27.6250 | 1 | 0.490692 | 0.663366 | -5.177274 |-1.001314e+01 |-7.499515e-01 |\\u001b[0m\\n\",\n \"| 1106 |27.6500 | 1 | 0.492805 | 0.674422 | -5.178603 |-1.001414e+01 |-7.498630e-01 |\\u001b[0m\\n\",\n \"| 1107 |27.6750 | 1 | 0.485858 | 0.664090 | -5.187219 |-1.001513e+01 |-7.497748e-01 |\\u001b[0m\\n\",\n \"| 1108 |27.7000 | 1 | 0.486335 | 0.663156 | -5.184418 |-1.001613e+01 |-7.496872e-01 |\\u001b[0m\\n\",\n \"| 1109 |27.7250 | 1 | 0.494404 | 0.702291 | -5.186787 |-1.001711e+01 |-7.495997e-01 |\\u001b[0m\\n\",\n \"| 1110 |27.7500 | 1 | 0.446076 | 0.705973 | -5.187599 |-1.001809e+01 |-7.495127e-01 |\\u001b[0m\\n\",\n \"| 1111 |27.7750 | 1 | 0.482750 | 0.662560 | -5.184811 |-1.001907e+01 |-7.494261e-01 |\\u001b[0m\\n\",\n \"| 1112 |27.8000 | 1 | 0.476889 | 0.669748 | -5.191664 |-1.002004e+01 |-7.493398e-01 |\\u001b[0m\\n\",\n \"| 1113 |27.8250 | 1 | 0.492741 | 0.670303 | -5.192749 |-1.002101e+01 |-7.492541e-01 |\\u001b[0m\\n\",\n \"| 1114 |27.8500 | 1 | 0.481042 | 0.663581 | -5.195669 |-1.002197e+01 |-7.491686e-01 |\\u001b[0m\\n\",\n \"| 1115 |27.8750 | 1 | 0.484773 | 0.664162 | -5.197804 |-1.002292e+01 |-7.490836e-01 |\\u001b[0m\\n\",\n \"| 1116 |27.9000 | 1 | 0.471439 | 0.679314 | -5.194899 |-1.002388e+01 |-7.489990e-01 |\\u001b[0m\\n\",\n \"| 1117 |27.9250 | 1 | 0.484387 | 0.664117 | -5.198012 |-1.002482e+01 |-7.489147e-01 |\\u001b[0m\\n\",\n \"| 1118 |27.9500 | 1 | 0.485070 | 0.664848 | -5.200681 |-1.002576e+01 |-7.488309e-01 |\\u001b[0m\\n\",\n \"| 1119 |27.9750 | 1 | 0.483672 | 0.663051 | -5.202168 |-1.002670e+01 |-7.487475e-01 |\\u001b[0m\\n\",\n \"| 1120 |28.0000 | 1 | 0.483831 | 0.665529 | -5.208302 |-1.002763e+01 |-7.486645e-01 |\\u001b[0m\\n\",\n \"| 1121 |28.0250 | 1 | 0.486482 | 0.662659 | -5.207243 |-1.002856e+01 |-7.485818e-01 |\\u001b[0m\\n\",\n \"| 1122 |28.0500 | 1 | 0.484792 | 0.665026 | -5.206583 |-1.002948e+01 |-7.484996e-01 |\\u001b[0m\\n\",\n \"| 1123 |28.0750 | 1 | 0.484451 | 0.669203 | -5.210633 |-1.003040e+01 |-7.484179e-01 |\\u001b[0m\\n\",\n \"| 1124 |28.1000 | 1 | 0.483054 | 0.665843 | -5.210285 |-1.003131e+01 |-7.483365e-01 |\\u001b[0m\\n\",\n \"| 1125 |28.1250 | 1 | 0.479900 | 0.666058 | -5.215282 |-1.003221e+01 |-7.482556e-01 |\\u001b[0m\\n\",\n \"| 1126 |28.1500 | 1 | 0.481851 | 0.666201 | -5.219299 |-1.003311e+01 |-7.481751e-01 |\\u001b[0m\\n\",\n \"| 1127 |28.1750 | 1 | 0.483100 | 0.663770 | -5.218610 |-1.003401e+01 |-7.480950e-01 |\\u001b[0m\\n\",\n \"| 1128 |28.2000 | 1 | 0.485134 | 0.663042 | -5.220768 |-1.003490e+01 |-7.480154e-01 |\\u001b[0m\\n\",\n \"| 1129 |28.2250 | 1 | 0.489655 | 0.667828 | -5.221060 |-1.003578e+01 |-7.479362e-01 |\\u001b[0m\\n\",\n \"| 1130 |28.2500 | 1 | 0.480716 | 0.672463 | -5.223165 |-1.003666e+01 |-7.478574e-01 |\\u001b[0m\\n\",\n \"| 1131 |28.2750 | 1 | 0.483455 | 0.666447 | -5.228675 |-1.003753e+01 |-7.477791e-01 |\\u001b[0m\\n\",\n \"| 1132 |28.3000 | 1 | 0.483978 | 0.671011 | -5.229529 |-1.003840e+01 |-7.477012e-01 |\\u001b[0m\\n\",\n \"| 1133 |28.3250 | 1 | 0.475710 | 0.669280 | -5.232726 |-1.003926e+01 |-7.476238e-01 |\\u001b[0m\\n\",\n \"| 1134 |28.3500 | 1 | 0.479361 | 0.669395 | -5.234044 |-1.004012e+01 |-7.475468e-01 |\\u001b[0m\\n\",\n \"| 1135 |28.3750 | 1 | 0.496386 | 0.682017 | -5.232092 |-1.004097e+01 |-7.474703e-01 |\\u001b[0m\\n\",\n \"| 1136 |28.4000 | 1 | 0.485283 | 0.674847 | -5.238405 |-1.004182e+01 |-7.473943e-01 |\\u001b[0m\\n\",\n \"| 1137 |28.4250 | 1 | 0.479666 | 0.672826 | -5.240062 |-1.004266e+01 |-7.473187e-01 |\\u001b[0m\\n\",\n \"| 1138 |28.4500 | 1 | 0.479845 | 0.676287 | -5.242591 |-1.004349e+01 |-7.472436e-01 |\\u001b[0m\\n\",\n \"| 1139 |28.4750 | 1 | 0.481158 | 0.666536 | -5.247594 |-1.004432e+01 |-7.471689e-01 |\\u001b[0m\\n\",\n \"| 1140 |28.5000 | 1 | 0.483141 | 0.667308 | -5.245477 |-1.004514e+01 |-7.470948e-01 |\\u001b[0m\\n\",\n \"| 1141 |28.5250 | 1 | 0.486443 | 0.666994 | -5.248138 |-1.004596e+01 |-7.470210e-01 |\\u001b[0m\\n\",\n \"| 1142 |28.5500 | 1 | 0.479723 | 0.665961 | -5.251076 |-1.004677e+01 |-7.469478e-01 |\\u001b[0m\\n\",\n \"| 1143 |28.5750 | 1 | 0.478889 | 0.668256 | -5.253471 |-1.004757e+01 |-7.468750e-01 |\\u001b[0m\\n\",\n \"| 1144 |28.6000 | 1 | 0.480882 | 0.666810 | -5.258529 |-1.004837e+01 |-7.468027e-01 |\\u001b[0m\\n\",\n \"| 1145 |28.6250 | 1 | 0.474088 | 0.675753 | -5.259920 |-1.004917e+01 |-7.467310e-01 |\\u001b[0m\\n\",\n \"| 1146 |28.6500 | 1 | 0.480283 | 0.668231 | -5.261212 |-1.004995e+01 |-7.466596e-01 |\\u001b[0m\\n\",\n \"| 1147 |28.6750 | 1 | 0.480788 | 0.674629 | -5.263745 |-1.005073e+01 |-7.465887e-01 |\\u001b[0m\\n\",\n \"| 1148 |28.7000 | 1 | 0.480191 | 0.669986 | -5.264326 |-1.005151e+01 |-7.465184e-01 |\\u001b[0m\\n\",\n \"| 1149 |28.7250 | 1 | 0.470319 | 0.675661 | -5.269713 |-1.005228e+01 |-7.464485e-01 |\\u001b[0m\\n\",\n \"| 1150 |28.7500 | 1 | 0.480411 | 0.673238 | -5.273651 |-1.005304e+01 |-7.463791e-01 |\\u001b[0m\\n\",\n \"| 1151 |28.7750 | 1 | 0.473258 | 0.678330 | -5.274198 |-1.005380e+01 |-7.463102e-01 |\\u001b[0m\\n\",\n \"| 1152 |28.8000 | 1 | 0.478426 | 0.670399 | -5.278360 |-1.005455e+01 |-7.462418e-01 |\\u001b[0m\\n\",\n \"| 1153 |28.8250 | 1 | 0.481835 | 0.677192 | -5.278659 |-1.005530e+01 |-7.461739e-01 |\\u001b[0m\\n\",\n \"| 1154 |28.8500 | 1 | 0.477153 | 0.671792 | -5.280378 |-1.005604e+01 |-7.461065e-01 |\\u001b[0m\\n\",\n \"| 1155 |28.8750 | 1 | 0.483710 | 0.675545 | -5.286094 |-1.005677e+01 |-7.460396e-01 |\\u001b[0m\\n\",\n \"| 1156 |28.9000 | 1 | 0.478907 | 0.667440 | -5.288677 |-1.005750e+01 |-7.459732e-01 |\\u001b[0m\\n\",\n \"| 1157 |28.9250 | 1 | 0.476032 | 0.683400 | -5.291475 |-1.005822e+01 |-7.459074e-01 |\\u001b[0m\\n\",\n \"| 1158 |28.9500 | 1 | 0.478212 | 0.670153 | -5.294549 |-1.005893e+01 |-7.458420e-01 |\\u001b[0m\\n\",\n \"| 1159 |28.9750 | 1 | 0.490696 | 0.674169 | -5.294755 |-1.005964e+01 |-7.457771e-01 |\\u001b[0m\\n\",\n \"| 1160 |29.0000 | 1 | 0.478562 | 0.668860 | -5.298482 |-1.006034e+01 |-7.457127e-01 |\\u001b[0m\\n\",\n \"| 1161 |29.0250 | 1 | 0.477472 | 0.670187 | -5.301871 |-1.006104e+01 |-7.456489e-01 |\\u001b[0m\\n\",\n \"| 1162 |29.0500 | 1 | 0.481258 | 0.684804 | -5.305298 |-1.006173e+01 |-7.455856e-01 |\\u001b[0m\\n\",\n \"| 1163 |29.0750 | 1 | 0.460059 | 0.686929 | -5.310364 |-1.006241e+01 |-7.455228e-01 |\\u001b[0m\\n\",\n \"| 1164 |29.1000 | 1 | 0.448954 | 0.699926 | -5.310048 |-1.006309e+01 |-7.454605e-01 |\\u001b[0m\\n\",\n \"| 1165 |29.1250 | 1 | 0.453478 | 0.709623 | -5.313561 |-1.006376e+01 |-7.453987e-01 |\\u001b[0m\\n\",\n \"| 1166 |29.1500 | 1 | 0.445714 | 0.707670 | -5.316738 |-1.006442e+01 |-7.453374e-01 |\\u001b[0m\\n\",\n \"| 1167 |29.1750 | 1 | 0.452987 | 0.698719 | -5.318177 |-1.006508e+01 |-7.452767e-01 |\\u001b[0m\\n\",\n \"| 1168 |29.2000 | 1 | 0.449597 | 0.705269 | -5.325022 |-1.006573e+01 |-7.452165e-01 |\\u001b[0m\\n\",\n \"| 1169 |29.2250 | 1 | 0.490915 | 0.676666 | -5.327513 |-1.006637e+01 |-7.451568e-01 |\\u001b[0m\\n\",\n \"| 1170 |29.2500 | 1 | 0.449594 | 0.712068 | -5.328948 |-1.006701e+01 |-7.450977e-01 |\\u001b[0m\\n\",\n \"| 1171 |29.2750 | 1 | 0.457821 | 0.707891 | -5.332960 |-1.006764e+01 |-7.450391e-01 |\\u001b[0m\\n\",\n \"| 1172 |29.3000 | 1 | 0.451920 | 0.700959 | -5.334478 |-1.006827e+01 |-7.449809e-01 |\\u001b[0m\\n\",\n \"| 1173 |29.3250 | 1 | 0.457635 | 0.705507 | -5.338479 |-1.006889e+01 |-7.449234e-01 |\\u001b[0m\\n\",\n \"| 1174 |29.3500 | 1 | 0.447267 | 0.700000 | -5.343494 |-1.006950e+01 |-7.448664e-01 |\\u001b[0m\\n\",\n \"| 1175 |29.3750 | 1 | 0.458476 | 0.705746 | -5.346398 |-1.007011e+01 |-7.448099e-01 |\\u001b[0m\\n\",\n \"| 1176 |29.4000 | 1 | 0.450082 | 0.701366 | -5.350024 |-1.007071e+01 |-7.447539e-01 |\\u001b[0m\\n\",\n \"| 1177 |29.4250 | 1 | 0.476268 | 0.681734 | -5.351738 |-1.007130e+01 |-7.446985e-01 |\\u001b[0m\\n\",\n \"| 1178 |29.4500 | 1 | 0.460729 | 0.691428 | -5.354504 |-1.007189e+01 |-7.446436e-01 |\\u001b[0m\\n\",\n \"| 1179 |29.4750 | 1 | 0.457731 | 0.717534 | -5.359754 |-1.007247e+01 |-7.445893e-01 |\\u001b[0m\\n\",\n \"| 1180 |29.5000 | 1 | 0.448818 | 0.702547 | -5.362285 |-1.007304e+01 |-7.445355e-01 |\\u001b[0m\\n\",\n \"| 1181 |29.5250 | 1 | 0.444427 | 0.710591 | -5.367519 |-1.007361e+01 |-7.444822e-01 |\\u001b[0m\\n\",\n \"| 1182 |29.5500 | 1 | 0.449657 | 0.703114 | -5.371200 |-1.007417e+01 |-7.444295e-01 |\\u001b[0m\\n\",\n \"| 1183 |29.5750 | 1 | 0.440618 | 0.711450 | -5.371774 |-1.007472e+01 |-7.443773e-01 |\\u001b[0m\\n\",\n \"| 1184 |29.6000 | 1 | 0.446356 | 0.706056 | -5.376509 |-1.007527e+01 |-7.443257e-01 |\\u001b[0m\\n\",\n \"| 1185 |29.6250 | 1 | 0.448475 | 0.708371 | -5.380511 |-1.007581e+01 |-7.442746e-01 |\\u001b[0m\\n\",\n \"| 1186 |29.6500 | 1 | 0.448725 | 0.706641 | -5.383604 |-1.007634e+01 |-7.442241e-01 |\\u001b[0m\\n\",\n \"| 1187 |29.6750 | 1 | 0.467714 | 0.685492 | -5.389558 |-1.007687e+01 |-7.441741e-01 |\\u001b[0m\\n\",\n \"| 1188 |29.7000 | 1 | 0.469720 | 0.679917 | -5.392343 |-1.007739e+01 |-7.441247e-01 |\\u001b[0m\\n\",\n \"| 1189 |29.7250 | 1 | 0.472234 | 0.676739 | -5.394581 |-1.007790e+01 |-7.440758e-01 |\\u001b[0m\\n\",\n \"| 1190 |29.7500 | 1 | 0.471790 | 0.681953 | -5.398936 |-1.007841e+01 |-7.440275e-01 |\\u001b[0m\\n\",\n \"| 1191 |29.7750 | 1 | 0.467655 | 0.680340 | -5.401760 |-1.007891e+01 |-7.439797e-01 |\\u001b[0m\\n\",\n \"| 1192 |29.8000 | 1 | 0.474229 | 0.672687 | -5.407802 |-1.007940e+01 |-7.439325e-01 |\\u001b[0m\\n\",\n \"| 1193 |29.8250 | 1 | 0.476449 | 0.675359 | -5.411367 |-1.007989e+01 |-7.438858e-01 |\\u001b[0m\\n\",\n \"| 1194 |29.8500 | 1 | 0.476582 | 0.678527 | -5.415002 |-1.008037e+01 |-7.438397e-01 |\\u001b[0m\\n\",\n \"| 1195 |29.8750 | 1 | 0.472185 | 0.686604 | -5.419606 |-1.008084e+01 |-7.437942e-01 |\\u001b[0m\\n\",\n \"| 1196 |29.9000 | 1 | 0.471914 | 0.678537 | -5.420797 |-1.008131e+01 |-7.437492e-01 |\\u001b[0m\\n\",\n \"| 1197 |29.9250 | 1 | 0.466368 | 0.687928 | -5.426230 |-1.008177e+01 |-7.437047e-01 |\\u001b[0m\\n\",\n \"| 1198 |29.9500 | 1 | 0.471255 | 0.677494 | -5.431831 |-1.008222e+01 |-7.436608e-01 |\\u001b[0m\\n\",\n \"| 1199 |29.9750 | 1 | 0.474277 | 0.679189 | -5.434645 |-1.008267e+01 |-7.436175e-01 |\\u001b[0m\\n\",\n \"| 1200 |30.0000 | 1 | 0.470302 | 0.680280 | -5.440101 |-1.008311e+01 |-7.435748e-01 |\\u001b[0m\\n\",\n \"\\u001b[34m...Finished\\u001b[0m\\n\",\n \"\\u001b[36mFINISHED - Elapsed time = 897.2004556 seconds\\u001b[0m\\n\",\n \"\\u001b[36mFINISHED - CPU process time = 1055.3392616 seconds\\u001b[0m\\n\"\n ]\n }\n ],\n \"source\": [\n \"case_data = sharpy_main.main(['', route_to_case + 'simple_HALE.sharpy'])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The resulting data structure that is returned from the call to `main` contains all the time-dependant variables for both the structural and aerodynamic solvers.\\n\",\n \"\\n\",\n \"`timestep_info` can be found in `case_data.structure` and `case_data.aero`. It is an array with custom-made structure to contain the data of each solver.\\n\",\n \"\\n\",\n \"In the `.sharpy` file, we can see which solvers are run:\\n\",\n \"```\\n\",\n \"flow = ['BeamLoader',\\n\",\n \" 'AerogridLoader',\\n\",\n \" 'StaticTrim',\\n\",\n \" 'BeamLoads',\\n\",\n \" 'AerogridPlot',\\n\",\n \" 'BeamPlot',\\n\",\n \" 'DynamicCoupled',\\n\",\n \" ]\\n\",\n \"```\\n\",\n \"\\n\",\n \"In order:\\n\",\n \"\\n\",\n \"* BeamLoader: reads the `fem.h5` file and generates the structure for the beam solver.\\n\",\n \"\\n\",\n \"* AerogridLoader: reads the `aero.h5` file and generates the aerodynamic grid for the aerodynamic solver.\\n\",\n \"\\n\",\n \"* StaticTrim: this solver performs a longitudinal trim (Thrust, Angle of attack and Elevator deflection) using the StaticCoupled solver.\\n\",\n \"\\n\",\n \"* BeamLoads: calculates the internal beam loads for the static solution\\n\",\n \"\\n\",\n \"* AerogridPlot: outputs the aerodynamic grid for the static solution.\\n\",\n \"\\n\",\n \"* BeamPlot: outputs the structural discretisation for the static solution.\\n\",\n \"\\n\",\n \"* DynamicCoupled: is the main driver of the dynamic simulation: executes the structural and aerodynamic solvers and couples both. Every converged time step is followed by a BeamLoads, AerogridPlot and BeamPlot execution.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Structural data organisation\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The `timestep_info` structure contains several relevant variables:\\n\",\n \"\\n\",\n \"* `for_pos`: position of the body-attached frame of reference in inertial FoR.\\n\",\n \"\\n\",\n \"* `for_vel`: velocity (in body FoR) of the body FoR wrt inertial FoR.\\n\",\n \"\\n\",\n \"* `pos`: nodal position in A FoR.\\n\",\n \"\\n\",\n \"* `psi`: nodal rotations (from the material B FoR to A FoR) in a Cartesian Rotation Vector parametrisation.\\n\",\n \"\\n\",\n \"* `applied_steady_forces`: nodal forces from the aero solver and the applied forces.\\n\",\n \"\\n\",\n \"* `postproc_cell`: is a dictionary that contains the variables generated by a postprocessor, such as the internal beam loads.\\n\",\n \"\\n\",\n \"\\n\",\n \"The structural `timestep_info` also contains some useful variables:\\n\",\n \"\\n\",\n \"* `cag` and `cga` return $C^{AG}$ and $C^{GA}$, the rotation matrices from the body-attached (A) FoR to the inertial (G).\\n\",\n \"\\n\",\n \"* `glob_pos` rotates the `pos` variable to give you the inertial nodal position. If `include_rbm = True` is passed, `for_pos` is added to it.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Aerodynamic data organisation\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The aerodynamic datastructure can be found in `case_data.aero.timestep_info`.\\n\",\n \"It contains useful variables, such as:\\n\",\n \"\\n\",\n \"* `dimensions` and `dimensions_star`: gives the dimensions of every surface and wake surface. Organised as: `dimensions[i_surf, 0] = chordwise panels`, `dimensions[i_surf, 1] = spanwise panels`.\\n\",\n \"\\n\",\n \"* `zeta` and `zeta_star`: they are the $G$ FoR coordinates of the surface vertices.\\n\",\n \"\\n\",\n \"* `gamma` and `gamma_star`: vortex ring circulations.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Structural dynamics\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can now plot the rigid body dynamics:\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"*RBM trajectory*\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/svg+xml\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \"\\n\"\n ],\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, ax = plt.subplots(1, 1, figsize=(7, 4))\\n\",\n \"\\n\",\n \"# extract information\\n\",\n \"n_tsteps = len(case_data.structure.timestep_info)\\n\",\n \"xz = np.zeros((n_tsteps, 2))\\n\",\n \"for it in range(n_tsteps):\\n\",\n \" xz[it, 0] = -case_data.structure.timestep_info[it].for_pos[0] # the - is so that increasing time -> increasing x\\n\",\n \" xz[it, 1] = case_data.structure.timestep_info[it].for_pos[2]\\n\",\n \"ax.plot(xz[:, 0], xz[:, 1])\\n\",\n \"fig.suptitle('Longitudinal trajectory of the T-Tail model in a 20% 1-cos gust encounter')\\n\",\n \"ax.set_xlabel('X [m]')\\n\",\n \"ax.set_ylabel('Z [m]');\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"*RBM velocities*\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/svg+xml\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" 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\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \"\\n\"\n ],\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, ax = plt.subplots(3, 1, figsize=(7, 6), sharex=True)\\n\",\n \"ylabels = ['Vx [m/s]', 'Vy [m/s]', 'Vz [m/s]']\\n\",\n \"\\n\",\n \"# extract information\\n\",\n \"n_tsteps = len(case_data.structure.timestep_info)\\n\",\n \"dt = case_data.settings['DynamicCoupled']['dt']\\n\",\n \"time_vec = np.linspace(0, n_tsteps*dt, n_tsteps)\\n\",\n \"for_vel = np.zeros((n_tsteps, 3))\\n\",\n \"for it in range(n_tsteps):\\n\",\n \" for_vel[it, 0:3] = case_data.structure.timestep_info[it].for_vel[0:3]\\n\",\n \" \\n\",\n \"for idim in range(3):\\n\",\n \" ax[idim].plot(time_vec, for_vel[:, idim])\\n\",\n \" ax[idim].set_ylabel(ylabels[idim])\\n\",\n \" \\n\",\n \"ax[2].set_xlabel('time [s]')\\n\",\n \"plt.subplots_adjust(hspace=0)\\n\",\n \"fig.suptitle('Linear RBM velocities. T-Tail model in a 20% 1-cos gust encounter');\\n\",\n \"# ax.set_xlabel('X [m]')\\n\",\n \"# ax.set_ylabel('Z [m]');\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/svg+xml\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, ax = plt.subplots(3, 1, figsize=(7, 6), sharex=True)\\n\",\n \"ylabels = ['Roll rate [deg/s]', 'Pitch rate [deg/s]', 'Yaw rate [deg/s]']\\n\",\n \"\\n\",\n \"# extract information\\n\",\n \"n_tsteps = len(case_data.structure.timestep_info)\\n\",\n \"dt = case_data.settings['DynamicCoupled']['dt']\\n\",\n \"time_vec = np.linspace(0, n_tsteps*dt, n_tsteps)\\n\",\n \"for_vel = np.zeros((n_tsteps, 3))\\n\",\n \"for it in range(n_tsteps):\\n\",\n \" for_vel[it, 0:3] = case_data.structure.timestep_info[it].for_vel[3:6]*180/np.pi\\n\",\n \" \\n\",\n \"for idim in range(3):\\n\",\n \" ax[idim].plot(time_vec, for_vel[:, idim])\\n\",\n \" ax[idim].set_ylabel(ylabels[idim])\\n\",\n \" \\n\",\n \"ax[2].set_xlabel('time [s]')\\n\",\n \"plt.subplots_adjust(hspace=0)\\n\",\n \"fig.suptitle('Angular RBM velocities. T-Tail model in a 20% 1-cos gust encounter');\\n\",\n \"# ax.set_xlabel('X [m]')\\n\",\n \"# ax.set_ylabel('Z [m]');\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"*Wing tip deformation*\\n\",\n \"\\n\",\n \"It is stored in `timestep_info` as `pos`. We need to find the correct node.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Wing tip node is the maximum Y one: 16\\n\"\n ]\n },\n {\n \"data\": {\n \"image/svg+xml\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \"\\n\"\n ],\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, ax = plt.subplots(1, 1, figsize=(6, 6))\\n\",\n \"ax.scatter(case_data.structure.ini_info.pos[:, 0], case_data.structure.ini_info.pos[:, 1])\\n\",\n \"ax.axis('equal')\\n\",\n \"tip_node = np.argmax(case_data.structure.ini_info.pos[:, 1])\\n\",\n \"print('Wing tip node is the maximum Y one: ', tip_node)\\n\",\n \"ax.scatter(case_data.structure.ini_info.pos[tip_node, 0], case_data.structure.ini_info.pos[tip_node, 1], color='red')\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can plot now the `pos[tip_node,:]` variable:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/svg+xml\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \"\\n\"\n ],\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, ax = plt.subplots(1, 1, figsize=(7, 3))\\n\",\n \"\\n\",\n \"# extract information\\n\",\n \"n_tsteps = len(case_data.structure.timestep_info)\\n\",\n \"xz = np.zeros((n_tsteps, 2))\\n\",\n \"for it in range(n_tsteps):\\n\",\n \" xz[it, 0] = case_data.structure.timestep_info[it].pos[tip_node, 0]\\n\",\n \" xz[it, 1] = case_data.structure.timestep_info[it].pos[tip_node, 2]\\n\",\n \"ax.plot(time_vec, xz[:, 1])\\n\",\n \"# fig.suptitle('Longitudinal trajectory of the T-Tail model in a 20% 1-cos gust encounter')\\n\",\n \"ax.set_xlabel('time [s]')\\n\",\n \"ax.set_ylabel('Vertical disp. [m]');\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/svg+xml\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \"\\n\"\n ],\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, ax = plt.subplots(1, 1, figsize=(7, 3))\\n\",\n \"\\n\",\n \"# extract information\\n\",\n \"n_tsteps = len(case_data.structure.timestep_info)\\n\",\n \"xz = np.zeros((n_tsteps, 2))\\n\",\n \"for it in range(n_tsteps):\\n\",\n \" xz[it, 0] = case_data.structure.timestep_info[it].pos[tip_node, 0]\\n\",\n \" xz[it, 1] = case_data.structure.timestep_info[it].pos[tip_node, 2]\\n\",\n \"ax.plot(time_vec, xz[:, 0])\\n\",\n \"# fig.suptitle('Longitudinal trajectory of the T-Tail model in a 20% 1-cos gust encounter')\\n\",\n \"ax.set_xlabel('time [s]')\\n\",\n \"ax.set_ylabel('Horizontal disp. [m]\\\\nPositive is aft');\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"*Wing root loads*\\n\",\n \"\\n\",\n \"The wing root loads can be extracted from the `postproc_cell` structure in `timestep_info`.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 17,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/svg+xml\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" 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\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \"\\n\"\n ],\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, ax = plt.subplots(3, 1, figsize=(7, 6), sharex=True)\\n\",\n \"ylabels = ['Torsion [Nm2]', 'OOP [Nm2]', 'IP [Nm2]']\\n\",\n \"\\n\",\n \"# extract information\\n\",\n \"n_tsteps = len(case_data.structure.timestep_info)\\n\",\n \"dt = case_data.settings['DynamicCoupled']['dt']\\n\",\n \"time_vec = np.linspace(0, n_tsteps*dt, n_tsteps)\\n\",\n \"loads = np.zeros((n_tsteps, 3))\\n\",\n \"for it in range(n_tsteps):\\n\",\n \" loads[it, 0:3] = case_data.structure.timestep_info[it].postproc_cell['loads'][0, 3:6]\\n\",\n \" \\n\",\n \"for idim in range(3):\\n\",\n \" ax[idim].plot(time_vec, loads[:, idim])\\n\",\n \" ax[idim].set_ylabel(ylabels[idim])\\n\",\n \" \\n\",\n \"ax[2].set_xlabel('time [s]')\\n\",\n \"plt.subplots_adjust(hspace=0)\\n\",\n \"fig.suptitle('Wing root loads. T-Tail model in a 20% 1-cos gust encounter');\\n\",\n \"# ax.set_xlabel('X [m]')\\n\",\n \"# ax.set_ylabel('Z [m]');\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Aerodynamic analysis\\n\",\n \"\\n\",\n \"The aerodynamic analysis can be obviously conducted using python. However, the easiest way is to run the case by yourself and open the files in `output/simple_HALE/beam` and `output/simple_HALE/aero` with [Paraview](https://www.paraview.org/).\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 18,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 18,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"url = 'https://raw.githubusercontent.com/ImperialCollegeLondon/sharpy/dev_doc/docs/source/content/example_notebooks/images/t-tail_solution.png'\\n\",\n \"Image(url=url, width=600)\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3\",\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\": \"3.7.5\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "docs/source/content/example_notebooks/wind_turbine.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Simulation NREL 5MW wind turbine\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 1,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"%config InlineBackend.figure_format = 'svg'\\n\",\n \"from IPython.display import Image\\n\",\n \"url = 'https://raw.githubusercontent.com/ImperialCollegeLondon/sharpy/dev_doc/docs/source/content/example_notebooks/images/turbulence_no_legend.png'\\n\",\n \"Image(url=url, width=800)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"In this notebook:\\n\",\n \"\\n\",\n \"The blade loads on the NREL-5MW reference wind turbine computed with SHARPy and OpenFAST will be compared. However, zero-drag airfoils have been used.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"OpenFAST: _https://openfast.readthedocs.io_\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"NREL-5MW: Jonkman, J.; Butterfield, S.; Musial, W. and Scott, G.. _Definition of a 5-MW Reference Wind Turbine for Offshore System Development_, Technical Report, NREL 2009\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Load the required packages:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Required packages\\n\",\n \"%matplotlib inline\\n\",\n \"import numpy as np\\n\",\n \"import os\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"\\n\",\n \"# Required SHARPy modules\\n\",\n \"import sharpy.sharpy_main\\n\",\n \"import sharpy.utils.algebra as algebra\\n\",\n \"import sharpy.utils.generate_cases as gc\\n\",\n \"import sharpy.cases.templates.template_wt as template_wt\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"These are the results from the OpenFAST simulation for comparison: out-of-plane `of_cNdrR` and in-plane `of_cTdrR` coefficients along the blade and thrust `of_ct` and power `of_cp` rotor coefficients\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"of_rR = np.array([0.20158356, 0.3127131, 0.40794048, 0.5984148, 0.6936519, 0.85238045, 0.899999, 0.95555407, 0.98729974, 1.0])\\n\",\n \"of_cNdrR = np.array([0.08621394, 0.14687876, 0.19345148, 0.2942731, 0.36003628, 0.43748564, 0.44762507, 0.38839236, 0.29782477, 0.0])\\n\",\n \"of_cTdrR = np.array([0.048268348, 0.051957503, 0.05304592, 0.052862607, 0.056001827, 0.0536646, 0.050112925, 0.038993906, 0.023664437, 0.0])\\n\",\n \"\\n\",\n \"of_ct = 0.69787693\\n\",\n \"of_cp = 0.48813498\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Create SHARPy case\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We define our parameters:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Mathematical constants\\n\",\n \"deg2rad = np.pi/180.\\n\",\n \"\\n\",\n \"# Case\\n\",\n \"case = 'rotor'\\n\",\n \"route = './'\\n\",\n \"\\n\",\n \"# Geometry discretization\\n\",\n \"chord_panels = np.array([8], dtype=int)\\n\",\n \"revs_in_wake = 5\\n\",\n \"\\n\",\n \"# Operation\\n\",\n \"rotation_velocity = 12.1*2*np.pi/60\\n\",\n \"pitch_deg = 0. #degrees\\n\",\n \"\\n\",\n \"# Wind\\n\",\n \"WSP = 12.\\n\",\n \"air_density = 1.225\\n\",\n \"\\n\",\n \"# Simulation\\n\",\n \"dphi = 4.*deg2rad\\n\",\n \"revs_to_simulate = 5\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Computation of associated parameters\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"dt = dphi/rotation_velocity\\n\",\n \"time_steps = int(revs_to_simulate*2.*np.pi/dphi)\\n\",\n \"mstar = int(revs_in_wake*2.*np.pi/dphi)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Generation of the rotor geometry based on information in the excel file:\"\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 \"\\u001b[33mWARNING: The poisson cofficient is assumed equal to 0.3\\u001b[0m\\n\",\n \"\\u001b[33mWARNING: Cross-section area is used as shear area\\u001b[0m\\n\",\n \"\\u001b[33mWARNING: Using perpendicular axis theorem to compute the inertia around xB\\u001b[0m\\n\",\n \"\\u001b[33mWARNING: Replacing node 29 by node 0\\u001b[0m\\n\",\n \"\\u001b[33mWARNING: Replacing node 58 by node 0\\u001b[0m\\n\"\n ]\n }\n ],\n \"source\": [\n \"op_params = {} \\n\",\n \"op_params['rotation_velocity'] = rotation_velocity \\n\",\n \"op_params['pitch_deg'] = pitch_deg \\n\",\n \"op_params['wsp'] = WSP \\n\",\n \"op_params['dt'] = dt \\n\",\n \" \\n\",\n \"geom_params = {} \\n\",\n \"geom_params['chord_panels'] = chord_panels \\n\",\n \"geom_params['tol_remove_points'] = 1e-8 \\n\",\n \"geom_params['n_points_camber'] = 100 \\n\",\n \"geom_params['h5_cross_sec_prop'] = None \\n\",\n \"geom_params['m_distribution'] = 'uniform' \\n\",\n \" \\n\",\n \"options = {} \\n\",\n \"options['camber_effect_on_twist'] = False \\n\",\n \"options['user_defined_m_distribution_type'] = None \\n\",\n \"options['include_polars'] = False \\n\",\n \"options['separate_blades'] = False \\n\",\n \" \\n\",\n \"excel_description = {} \\n\",\n \"excel_description['excel_file_name'] = 'source/type04_db_nrel5mw_oc3_v06.xlsx' \\n\",\n \"excel_description['excel_sheet_parameters'] = 'parameters' \\n\",\n \"excel_description['excel_sheet_structural_blade'] = 'structural_blade' \\n\",\n \"excel_description['excel_sheet_discretization_blade'] = 'discretization_blade' \\n\",\n \"excel_description['excel_sheet_aero_blade'] = 'aero_blade' \\n\",\n \"excel_description['excel_sheet_airfoil_info'] = 'airfoil_info' \\n\",\n \"excel_description['excel_sheet_airfoil_chord'] = 'airfoil_coord' \\n\",\n \" \\n\",\n \"rotor, hub_nodes = template_wt.rotor_from_excel_type03(op_params, \\n\",\n \" geom_params, \\n\",\n \" excel_description, \\n\",\n \" options) \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Define simulation details. The steady simulation is faster than the dynamic simulation. However, the dynamic simulation includes wake self-induction and provides more accurate results.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"steady_simulation = False\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"SimInfo = gc.SimulationInformation()\\n\",\n \"SimInfo.set_default_values()\\n\",\n \"\\n\",\n \"if steady_simulation:\\n\",\n \" SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\\n\",\n \" 'AerogridLoader',\\n\",\n \" 'StaticCoupled',\\n\",\n \" 'BeamPlot',\\n\",\n \" 'AerogridPlot', \\n\",\n \" 'SaveData'] \\n\",\n \"else:\\n\",\n \" SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\\n\",\n \" 'AerogridLoader',\\n\",\n \" 'StaticCoupled',\\n\",\n \" 'DynamicCoupled']\\n\",\n \" \\n\",\n \"SimInfo.solvers['SHARPy']['case'] = case\\n\",\n \"SimInfo.solvers['SHARPy']['route'] = route\\n\",\n \"SimInfo.solvers['SHARPy']['write_log'] = True\\n\",\n \"SimInfo.set_variable_all_dicts('dt', dt)\\n\",\n \"SimInfo.set_variable_all_dicts('rho', air_density)\\n\",\n \"\\n\",\n \"SimInfo.solvers['SteadyVelocityField']['u_inf'] = WSP\\n\",\n \"SimInfo.solvers['SteadyVelocityField']['u_inf_direction'] = np.array([0., 0., 1.])\\n\",\n \"\\n\",\n \"SimInfo.solvers['BeamLoader']['unsteady'] = 'on'\\n\",\n \"\\n\",\n \"SimInfo.solvers['AerogridLoader']['unsteady'] = 'on'\\n\",\n \"SimInfo.solvers['AerogridLoader']['mstar'] = mstar\\n\",\n \"SimInfo.solvers['AerogridLoader']['freestream_dir'] = np.array([0.,0.,0.])\\n\",\n \"SimInfo.solvers['AerogridLoader']['wake_shape_generator'] = 'HelicoidalWake'\\n\",\n \"SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] = {'u_inf': WSP,\\n\",\n \" 'u_inf_direction': SimInfo.solvers['SteadyVelocityField']['u_inf_direction'],\\n\",\n \" 'rotation_velocity': rotation_velocity*np.array([0., 0., 1.]),\\n\",\n \" 'dt': dt,\\n\",\n \" 'dphi1': dphi,\\n\",\n \" 'ndphi1': mstar,\\n\",\n \" 'r': 1.,\\n\",\n \" 'dphimax': 10*deg2rad}\\n\",\n \" \\n\",\n \"SimInfo.solvers['StaticCoupled']['structural_solver'] = 'RigidDynamicPrescribedStep'\\n\",\n \"SimInfo.solvers['StaticCoupled']['structural_solver_settings'] = SimInfo.solvers['RigidDynamicPrescribedStep']\\n\",\n \"SimInfo.solvers['StaticCoupled']['aero_solver'] = 'StaticUvlm'\\n\",\n \"SimInfo.solvers['StaticCoupled']['aero_solver_settings'] = SimInfo.solvers['StaticUvlm']\\n\",\n \"\\n\",\n \"SimInfo.solvers['StaticCoupled']['tolerance'] = 1e-8\\n\",\n \"SimInfo.solvers['StaticCoupled']['n_load_steps'] = 0\\n\",\n \"SimInfo.solvers['StaticCoupled']['relaxation_factor'] = 0.\\n\",\n \"\\n\",\n \"SimInfo.solvers['StaticUvlm']['num_cores'] = 8\\n\",\n \"SimInfo.solvers['StaticUvlm']['velocity_field_generator'] = 'SteadyVelocityField'\\n\",\n \"SimInfo.solvers['StaticUvlm']['velocity_field_input'] = SimInfo.solvers['SteadyVelocityField']\\n\",\n \"\\n\",\n \"SimInfo.solvers['SaveData']['compress_float'] = True\\n\",\n \" \\n\",\n \"# Only used for steady_simulation = False\\n\",\n \"SimInfo.solvers['StepUvlm']['convection_scheme'] = 3\\n\",\n \"SimInfo.solvers['StepUvlm']['num_cores'] = 8\\n\",\n \"SimInfo.solvers['StepUvlm']['velocity_field_generator'] = 'SteadyVelocityField'\\n\",\n \"SimInfo.solvers['StepUvlm']['velocity_field_input'] = SimInfo.solvers['SteadyVelocityField']\\n\",\n \"\\n\",\n \"SimInfo.solvers['DynamicCoupled']['structural_solver'] = 'RigidDynamicPrescribedStep'\\n\",\n \"SimInfo.solvers['DynamicCoupled']['structural_solver_settings'] = SimInfo.solvers['RigidDynamicPrescribedStep']\\n\",\n \"SimInfo.solvers['DynamicCoupled']['aero_solver'] = 'StepUvlm'\\n\",\n \"SimInfo.solvers['DynamicCoupled']['aero_solver_settings'] = SimInfo.solvers['StepUvlm']\\n\",\n \"SimInfo.solvers['DynamicCoupled']['postprocessors'] = ['BeamPlot', 'AerogridPlot', 'Cleanup', 'SaveData']\\n\",\n \"SimInfo.solvers['DynamicCoupled']['postprocessors_settings'] = {'BeamPlot': SimInfo.solvers['BeamPlot'],\\n\",\n \" 'AerogridPlot': SimInfo.solvers['AerogridPlot'],\\n\",\n \" 'Cleanup': SimInfo.solvers['Cleanup'],\\n\",\n \" 'SaveData': SimInfo.solvers['SaveData']}\\n\",\n \"SimInfo.solvers['DynamicCoupled']['minimum_steps'] = 0\\n\",\n \"SimInfo.solvers['DynamicCoupled']['include_unsteady_force_contribution'] = True\\n\",\n \"SimInfo.solvers['DynamicCoupled']['relaxation_factor'] = 0.\\n\",\n \"SimInfo.solvers['DynamicCoupled']['final_relaxation_factor'] = 0.\\n\",\n \"SimInfo.solvers['DynamicCoupled']['dynamic_relaxation'] = False\\n\",\n \"SimInfo.solvers['DynamicCoupled']['relaxation_steps'] = 0\\n\",\n \"\\n\",\n \"# Define dynamic simulation (used regardless the value of \\\"steady_simulation\\\" variable)\\n\",\n \"SimInfo.define_num_steps(time_steps)\\n\",\n \"SimInfo.with_forced_vel = True\\n\",\n \"SimInfo.for_vel = np.zeros((time_steps,6), dtype=float)\\n\",\n \"SimInfo.for_vel[:,5] = rotation_velocity\\n\",\n \"SimInfo.for_acc = np.zeros((time_steps,6), dtype=float)\\n\",\n \"SimInfo.with_dynamic_forces = True\\n\",\n \"SimInfo.dynamic_forces = np.zeros((time_steps,rotor.StructuralInformation.num_node,6), dtype=float)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Generate simulation files\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\\n\",\n \"rotor.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\\n\",\n \"SimInfo.generate_solver_file()\\n\",\n \"SimInfo.generate_dyn_file(time_steps)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Run SHARPy case\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"--------------------------------------------------------------------------------\\u001b[0m\\n\",\n \" ###### ## ## ### ######## ######## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ####\\u001b[0m\\n\",\n \" ###### ######### ## ## ######## ######## ##\\u001b[0m\\n\",\n \" ## ## ## ######### ## ## ## ##\\u001b[0m\\n\",\n \" ## ## ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \" ###### ## ## ## ## ## ## ## ##\\u001b[0m\\n\",\n \"--------------------------------------------------------------------------------\\u001b[0m\\n\",\n \"Aeroelastics Lab, Aeronautics Department.\\u001b[0m\\n\",\n \" Copyright (c), Imperial College London.\\u001b[0m\\n\",\n \" All rights reserved.\\u001b[0m\\n\",\n \" License available at https://github.com/imperialcollegelondon/sharpy\\u001b[0m\\n\",\n \"\\u001b[36mRunning SHARPy from /home/arturo/code/sharpy/docs/source/content/example_notebooks\\u001b[0m\\n\",\n \"\\u001b[36mSHARPy being run is in /home/arturo/code/sharpy\\u001b[0m\\n\",\n \"\\u001b[36mThe branch being run is dev_blade_pitch_v2\\u001b[0m\\n\",\n \"\\u001b[36mThe version and commit hash are: v1.2.1-546-g05602d1f-05602d1f\\u001b[0m\\n\",\n \"SHARPy output folder set\\u001b[0m\\n\",\n \"\\u001b[34m\\t./output//rotor/\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of BeamLoader\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of AerogridLoader\\u001b[0m\\n\",\n \"Variable shear_direction has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: [1. 0. 0.]\\u001b[0m\\n\",\n \"Variable shear_exp has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 0.0\\u001b[0m\\n\",\n \"Variable h_ref has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1.0\\u001b[0m\\n\",\n \"Variable h_corr has no assigned value in the settings file.\\u001b[0m\\n\",\n \"\\u001b[34m will default to the value: 1.0\\u001b[0m\\n\",\n \"\\u001b[34mThe aerodynamic grid contains 3 surfaces\\u001b[0m\\n\",\n \"\\u001b[34m Surface 0, M=8, N=26\\u001b[0m\\n\",\n \" Wake 0, M=450, N=26\\u001b[0m\\n\",\n \"\\u001b[34m Surface 1, M=8, N=26\\u001b[0m\\n\",\n \" Wake 1, M=450, N=26\\u001b[0m\\n\",\n \"\\u001b[34m Surface 2, M=8, N=26\\u001b[0m\\n\",\n \" Wake 2, M=450, N=26\\u001b[0m\\n\",\n \" In total: 624 bound panels\\u001b[0m\\n\",\n \" In total: 35100 wake panels\\u001b[0m\\n\",\n \" Total number of panels = 35724\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of StaticCoupled\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of RigidDynamicPrescribedStep\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of StaticUvlm\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"|=====|=====|============|==========|==========|==========|==========|==========|==========|\\u001b[0m\\n\",\n \"|iter |step | log10(res) | Fx | Fy | Fz | Mx | My | Mz |\\u001b[0m\\n\",\n \"|=====|=====|============|==========|==========|==========|==========|==========|==========|\\u001b[0m\\n\",\n \"| 0 | 0 | 0.00000 | -0.0000 | 0.0000 |21927.8250| 0.0000 | -0.0000 |5962997.5361|\\u001b[0m\\n\",\n \"| 1 | 0 | -inf | -0.0000 | 0.0000 |21927.8250| 0.0000 | -0.0000 |5962997.5361|\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of DynamicCoupled\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of RigidDynamicPrescribedStep\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of StepUvlm\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of BeamPlot\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of AerogridPlot\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of Cleanup\\u001b[0m\\n\",\n \"\\u001b[36mGenerating an instance of SaveData\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"\\u001b[0m\\n\",\n \"|=======|========|======|==============|==============|==============|==============|==============|\\u001b[0m\\n\",\n \"| ts | t | iter | struc ratio | iter time | residual vel | FoR_vel(x) | FoR_vel(z) |\\u001b[0m\\n\",\n \"|=======|========|======|==============|==============|==============|==============|==============|\\u001b[0m\\n\",\n \"| 1 | 0.0551 | 1 | 0.001471 | 11.072773 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 2 | 0.1102 | 1 | 0.001529 | 11.094774 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 3 | 0.1653 | 1 | 0.001487 | 11.017530 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 4 | 0.2204 | 1 | 0.001487 | 11.053551 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 5 | 0.2755 | 1 | 0.001495 | 10.972424 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 6 | 0.3306 | 1 | 0.001496 | 10.951425 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 7 | 0.3857 | 1 | 0.001492 | 11.018625 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 8 | 0.4408 | 1 | 0.001476 | 11.044770 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 9 | 0.4959 | 1 | 0.001478 | 11.122489 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 10 | 0.5510 | 1 | 0.001500 | 10.997606 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 11 | 0.6061 | 1 | 0.001481 | 11.076450 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 12 | 0.6612 | 1 | 0.001513 | 10.976762 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 13 | 0.7163 | 1 | 0.001489 | 11.056770 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 14 | 0.7713 | 1 | 0.001473 | 11.147662 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 15 | 0.8264 | 1 | 0.001485 | 11.047932 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 16 | 0.8815 | 1 | 0.001500 | 10.984375 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 17 | 0.9366 | 1 | 0.001492 | 10.999334 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 18 | 0.9917 | 1 | 0.001492 | 11.036468 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 19 | 1.0468 | 1 | 0.001490 | 10.989860 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 20 | 1.1019 | 1 | 0.001487 | 10.981977 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 21 | 1.1570 | 1 | 0.001480 | 11.026050 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 22 | 1.2121 | 1 | 0.001501 | 10.964416 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 23 | 1.2672 | 1 | 0.001483 | 11.061231 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 24 | 1.3223 | 1 | 0.001502 | 11.026285 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 25 | 1.3774 | 1 | 0.001497 | 10.937541 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 26 | 1.4325 | 1 | 0.001464 | 11.216671 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 27 | 1.4876 | 1 | 0.001489 | 11.077631 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 28 | 1.5427 | 1 | 0.001487 | 11.029765 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 29 | 1.5978 | 1 | 0.001484 | 11.057365 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 30 | 1.6529 | 1 | 0.001499 | 10.988523 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 31 | 1.7080 | 1 | 0.001480 | 11.082585 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 32 | 1.7631 | 1 | 0.001493 | 11.026814 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 33 | 1.8182 | 1 | 0.001500 | 10.964227 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 34 | 1.8733 | 1 | 0.001496 | 11.070894 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 35 | 1.9284 | 1 | 0.001499 | 10.991359 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 36 | 1.9835 | 1 | 0.001493 | 10.956692 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 37 | 2.0386 | 1 | 0.001489 | 11.022953 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 38 | 2.0937 | 1 | 0.001493 | 11.002933 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 39 | 2.1488 | 1 | 0.001494 | 10.971854 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 40 | 2.2039 | 1 | 0.001499 | 10.956611 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 41 | 2.2590 | 1 | 0.001484 | 11.020658 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 42 | 2.3140 | 1 | 0.001484 | 11.016274 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 43 | 2.3691 | 1 | 0.001490 | 11.171444 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 44 | 2.4242 | 1 | 0.001496 | 10.975332 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 45 | 2.4793 | 1 | 0.001479 | 11.094840 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 46 | 2.5344 | 1 | 0.001484 | 11.060059 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 47 | 2.5895 | 1 | 0.001329 | 12.309849 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 48 | 2.6446 | 1 | 0.001455 | 11.269876 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 49 | 2.6997 | 1 | 0.001489 | 11.076657 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 50 | 2.7548 | 1 | 0.001496 | 10.998456 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 51 | 2.8099 | 1 | 0.001471 | 11.215534 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 52 | 2.8650 | 1 | 0.001494 | 10.981076 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 53 | 2.9201 | 1 | 0.001476 | 11.089418 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 54 | 2.9752 | 1 | 0.001482 | 10.973016 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 55 | 3.0303 | 1 | 0.001469 | 11.115966 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 56 | 3.0854 | 1 | 0.001458 | 11.172810 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 57 | 3.1405 | 1 | 0.001496 | 10.984580 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 58 | 3.1956 | 1 | 0.001451 | 11.196615 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 59 | 3.2507 | 1 | 0.001498 | 10.961545 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 60 | 3.3058 | 1 | 0.001492 | 11.053819 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 61 | 3.3609 | 1 | 0.001492 | 11.066293 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 62 | 3.4160 | 1 | 0.001489 | 11.025009 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 63 | 3.4711 | 1 | 0.001485 | 10.999920 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 64 | 3.5262 | 1 | 0.001505 | 10.973439 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 65 | 3.5813 | 1 | 0.001495 | 10.981763 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 66 | 3.6364 | 1 | 0.001481 | 10.997240 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 67 | 3.6915 | 1 | 0.001489 | 11.030007 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 68 | 3.7466 | 1 | 0.001487 | 10.977346 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 69 | 3.8017 | 1 | 0.001490 | 11.086072 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 70 | 3.8567 | 1 | 0.001478 | 11.027897 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 71 | 3.9118 | 1 | 0.001492 | 10.997195 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 72 | 3.9669 | 1 | 0.001476 | 11.129629 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 73 | 4.0220 | 1 | 0.001491 | 10.996616 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 74 | 4.0771 | 1 | 0.001513 | 10.996785 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 75 | 4.1322 | 1 | 0.001487 | 11.010984 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 76 | 4.1873 | 1 | 0.001504 | 10.960333 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 77 | 4.2424 | 1 | 0.001483 | 11.062480 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 78 | 4.2975 | 1 | 0.001502 | 10.999189 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 79 | 4.3526 | 1 | 0.001504 | 10.989805 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 80 | 4.4077 | 1 | 0.001499 | 10.986292 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 81 | 4.4628 | 1 | 0.001471 | 11.064248 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 82 | 4.5179 | 1 | 0.001478 | 11.030763 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 83 | 4.5730 | 1 | 0.001423 | 11.418318 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 84 | 4.6281 | 1 | 0.001513 | 10.934981 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 85 | 4.6832 | 1 | 0.001477 | 10.947891 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 86 | 4.7383 | 1 | 0.001449 | 11.337449 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 87 | 4.7934 | 1 | 0.001446 | 11.356113 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 88 | 4.8485 | 1 | 0.001493 | 11.006986 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 89 | 4.9036 | 1 | 0.001508 | 10.995290 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 90 | 4.9587 | 1 | 0.001519 | 10.961908 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 91 | 5.0138 | 1 | 0.001511 | 11.004637 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 92 | 5.0689 | 1 | 0.001493 | 11.060139 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 93 | 5.1240 | 1 | 0.001475 | 11.108975 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 94 | 5.1791 | 1 | 0.001501 | 10.946505 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 95 | 5.2342 | 1 | 0.001504 | 10.936386 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 96 | 5.2893 | 1 | 0.001486 | 10.994701 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 97 | 5.3444 | 1 | 0.001483 | 11.023811 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 98 | 5.3994 | 1 | 0.001494 | 10.979126 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 99 | 5.4545 | 1 | 0.001481 | 11.163518 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 100 | 5.5096 | 1 | 0.001479 | 11.047313 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 101 | 5.5647 | 1 | 0.001473 | 11.060119 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 102 | 5.6198 | 1 | 0.001486 | 11.053105 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 103 | 5.6749 | 1 | 0.001486 | 11.092742 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 104 | 5.7300 | 1 | 0.001477 | 11.137425 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 105 | 5.7851 | 1 | 0.001491 | 11.010371 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 106 | 5.8402 | 1 | 0.001496 | 10.990369 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 107 | 5.8953 | 1 | 0.001473 | 11.243003 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 108 | 5.9504 | 1 | 0.001388 | 11.929604 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 109 | 6.0055 | 1 | 0.001458 | 11.222341 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 110 | 6.0606 | 1 | 0.001499 | 11.021925 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 111 | 6.1157 | 1 | 0.001489 | 10.988726 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 112 | 6.1708 | 1 | 0.001464 | 11.127002 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 113 | 6.2259 | 1 | 0.001490 | 10.982098 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 114 | 6.2810 | 1 | 0.001490 | 11.058744 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 115 | 6.3361 | 1 | 0.001501 | 11.036917 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 116 | 6.3912 | 1 | 0.001487 | 11.093127 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 117 | 6.4463 | 1 | 0.001511 | 10.986041 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 118 | 6.5014 | 1 | 0.001473 | 11.067499 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 119 | 6.5565 | 1 | 0.001495 | 10.978576 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 120 | 6.6116 | 1 | 0.001497 | 11.027401 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 121 | 6.6667 | 1 | 0.001487 | 11.056618 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 122 | 6.7218 | 1 | 0.001492 | 10.946566 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 123 | 6.7769 | 1 | 0.001492 | 10.977270 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 124 | 6.8320 | 1 | 0.001466 | 11.212596 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 125 | 6.8871 | 1 | 0.001493 | 10.996106 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 126 | 6.9421 | 1 | 0.001480 | 11.018607 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 127 | 6.9972 | 1 | 0.001509 | 10.976320 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 128 | 7.0523 | 1 | 0.001329 | 12.417034 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 129 | 7.1074 | 1 | 0.001510 | 10.938081 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 130 | 7.1625 | 1 | 0.001496 | 10.964072 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 131 | 7.2176 | 1 | 0.001497 | 11.006588 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 132 | 7.2727 | 1 | 0.001493 | 11.018465 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 133 | 7.3278 | 1 | 0.001493 | 11.030553 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 134 | 7.3829 | 1 | 0.001490 | 11.034491 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 135 | 7.4380 | 1 | 0.001493 | 10.942718 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 136 | 7.4931 | 1 | 0.001485 | 11.063141 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 137 | 7.5482 | 1 | 0.001490 | 10.940797 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 138 | 7.6033 | 1 | 0.001496 | 11.094267 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 139 | 7.6584 | 1 | 0.001476 | 11.092305 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 140 | 7.7135 | 1 | 0.001489 | 10.999871 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 141 | 7.7686 | 1 | 0.001486 | 10.969563 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 142 | 7.8237 | 1 | 0.001485 | 11.045270 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 143 | 7.8788 | 1 | 0.001493 | 10.999192 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 144 | 7.9339 | 1 | 0.001498 | 11.051950 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 145 | 7.9890 | 1 | 0.001489 | 11.134410 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 146 | 8.0441 | 1 | 0.001474 | 11.101941 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 147 | 8.0992 | 1 | 0.001480 | 11.063681 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 148 | 8.1543 | 1 | 0.001486 | 10.946801 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 149 | 8.2094 | 1 | 0.001484 | 11.076774 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 150 | 8.2645 | 1 | 0.001480 | 11.143664 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 151 | 8.3196 | 1 | 0.001509 | 10.947056 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 152 | 8.3747 | 1 | 0.001447 | 11.226169 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 153 | 8.4298 | 1 | 0.001479 | 11.063754 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 154 | 8.4848 | 1 | 0.001484 | 10.961506 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 155 | 8.5399 | 1 | 0.001497 | 11.050401 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 156 | 8.5950 | 1 | 0.001503 | 11.018204 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 157 | 8.6501 | 1 | 0.001472 | 11.145519 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 158 | 8.7052 | 1 | 0.001486 | 11.037257 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 159 | 8.7603 | 1 | 0.001492 | 11.036405 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 160 | 8.8154 | 1 | 0.001480 | 11.015381 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 161 | 8.8705 | 1 | 0.001498 | 10.979052 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 162 | 8.9256 | 1 | 0.001496 | 11.051611 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 163 | 8.9807 | 1 | 0.001486 | 11.052557 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 164 | 9.0358 | 1 | 0.001491 | 11.034617 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 165 | 9.0909 | 1 | 0.001488 | 11.049273 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 166 | 9.1460 | 1 | 0.001491 | 11.085268 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 167 | 9.2011 | 1 | 0.001503 | 10.958939 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 168 | 9.2562 | 1 | 0.001497 | 11.062020 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 169 | 9.3113 | 1 | 0.001518 | 10.996845 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 170 | 9.3664 | 1 | 0.001470 | 11.209611 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 171 | 9.4215 | 1 | 0.001477 | 11.023668 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 172 | 9.4766 | 1 | 0.001481 | 11.090508 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 173 | 9.5317 | 1 | 0.001512 | 10.958598 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 174 | 9.5868 | 1 | 0.001472 | 11.093911 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 175 | 9.6419 | 1 | 0.001495 | 11.022321 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 176 | 9.6970 | 1 | 0.001497 | 10.963686 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 177 | 9.7521 | 1 | 0.001495 | 11.014677 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 178 | 9.8072 | 1 | 0.001494 | 10.971079 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 179 | 9.8623 | 1 | 0.001478 | 11.075295 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 180 | 9.9174 | 1 | 0.001492 | 10.967837 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 181 | 9.9725 | 1 | 0.001502 | 11.002055 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 182 |10.0275 | 1 | 0.001478 | 11.256881 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 183 |10.0826 | 1 | 0.001503 | 10.965836 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 184 |10.1377 | 1 | 0.001492 | 11.003513 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 185 |10.1928 | 1 | 0.001499 | 11.033890 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 186 |10.2479 | 1 | 0.001477 | 11.086396 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 187 |10.3030 | 1 | 0.001494 | 11.022237 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 188 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0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 198 |10.9091 | 1 | 0.001502 | 11.026861 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 199 |10.9642 | 1 | 0.001505 | 10.987199 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 200 |11.0193 | 1 | 0.001488 | 11.061289 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 201 |11.0744 | 1 | 0.001489 | 11.049199 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 202 |11.1295 | 1 | 0.001501 | 10.973437 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 203 |11.1846 | 1 | 0.001500 | 10.937448 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 204 |11.2397 | 1 | 0.001499 | 10.940185 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 205 |11.2948 | 1 | 0.001506 | 10.956871 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 206 |11.3499 | 1 | 0.001496 | 10.959225 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 207 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0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 217 |11.9559 | 1 | 0.001484 | 11.094227 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 218 |12.0110 | 1 | 0.001465 | 11.285769 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 219 |12.0661 | 1 | 0.001472 | 11.138884 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 220 |12.1212 | 1 | 0.001462 | 11.085258 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 221 |12.1763 | 1 | 0.001506 | 10.962956 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 222 |12.2314 | 1 | 0.001481 | 11.063845 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 223 |12.2865 | 1 | 0.001490 | 10.940562 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 224 |12.3416 | 1 | 0.001487 | 11.074080 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 225 |12.3967 | 1 | 0.001500 | 10.966088 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 226 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0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 236 |13.0028 | 1 | 0.001494 | 11.034151 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 237 |13.0579 | 1 | 0.001521 | 11.393696 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 238 |13.1129 | 1 | 0.001483 | 11.187673 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 239 |13.1680 | 1 | 0.001476 | 11.165030 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 240 |13.2231 | 1 | 0.001461 | 11.121420 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 241 |13.2782 | 1 | 0.001497 | 11.077922 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 242 |13.3333 | 1 | 0.001472 | 11.274707 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 243 |13.3884 | 1 | 0.001477 | 11.087600 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 244 |13.4435 | 1 | 0.001469 | 11.061153 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 245 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0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 255 |14.0496 | 1 | 0.001498 | 10.998538 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 256 |14.1047 | 1 | 0.001490 | 10.959735 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 257 |14.1598 | 1 | 0.001497 | 11.015843 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 258 |14.2149 | 1 | 0.001442 | 11.296236 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 259 |14.2700 | 1 | 0.001470 | 11.035043 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 260 |14.3251 | 1 | 0.001499 | 11.025067 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 261 |14.3802 | 1 | 0.001483 | 11.032883 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 262 |14.4353 | 1 | 0.001450 | 11.225693 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 263 |14.4904 | 1 | 0.001490 | 11.049877 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 264 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|17.6860 | 1 | 0.001488 | 11.010496 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 322 |17.7410 | 1 | 0.001475 | 11.125369 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 323 |17.7961 | 1 | 0.001494 | 10.955690 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 324 |17.8512 | 1 | 0.001493 | 11.078510 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 325 |17.9063 | 1 | 0.001362 | 12.022863 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 326 |17.9614 | 1 | 0.001489 | 11.021870 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 327 |18.0165 | 1 | 0.001463 | 11.139775 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 328 |18.0716 | 1 | 0.001475 | 11.015395 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 329 |18.1267 | 1 | 0.001475 | 10.995628 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 330 |18.1818 | 1 | 0.001490 | 11.037015 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 331 |18.2369 | 1 | 0.001489 | 10.994272 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 332 |18.2920 | 1 | 0.001485 | 11.023925 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 333 |18.3471 | 1 | 0.001465 | 11.131615 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 334 |18.4022 | 1 | 0.001481 | 10.996215 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 335 |18.4573 | 1 | 0.001493 | 11.042847 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 336 |18.5124 | 1 | 0.001493 | 11.153712 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 337 |18.5675 | 1 | 0.001497 | 10.981005 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 338 |18.6226 | 1 | 0.001490 | 10.993124 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 339 |18.6777 | 1 | 0.001498 | 10.970379 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 340 |18.7328 | 1 | 0.001492 | 10.992345 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 341 |18.7879 | 1 | 0.001492 | 10.998224 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 342 |18.8430 | 1 | 0.001523 | 10.982035 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 343 |18.8981 | 1 | 0.001485 | 11.054384 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 344 |18.9532 | 1 | 0.001486 | 11.027520 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 345 |19.0083 | 1 | 0.001482 | 11.016985 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 346 |19.0634 | 1 | 0.001484 | 11.169659 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 347 |19.1185 | 1 | 0.001476 | 11.164135 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 348 |19.1736 | 1 | 0.001499 | 10.963815 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 349 |19.2287 | 1 | 0.001481 | 11.041115 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 350 |19.2837 | 1 | 0.001478 | 11.025983 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 351 |19.3388 | 1 | 0.001504 | 10.984140 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 352 |19.3939 | 1 | 0.001478 | 11.033161 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 353 |19.4490 | 1 | 0.001490 | 11.040692 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 354 |19.5041 | 1 | 0.001479 | 11.018249 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 355 |19.5592 | 1 | 0.001471 | 10.995813 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 356 |19.6143 | 1 | 0.001478 | 11.009744 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 357 |19.6694 | 1 | 0.001489 | 11.012060 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 358 |19.7245 | 1 | 0.001487 | 11.043458 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 359 |19.7796 | 1 | 0.001492 | 10.996924 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 360 |19.8347 | 1 | 0.001486 | 10.997914 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 361 |19.8898 | 1 | 0.001462 | 11.193126 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 362 |19.9449 | 1 | 0.001476 | 11.131790 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 363 |20.0000 | 1 | 0.001456 | 11.255347 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 364 |20.0551 | 1 | 0.001443 | 11.262457 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 365 |20.1102 | 1 | 0.001442 | 11.282331 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 366 |20.1653 | 1 | 0.001460 | 11.133270 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 367 |20.2204 | 1 | 0.001461 | 11.137590 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 368 |20.2755 | 1 | 0.001458 | 11.279287 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 369 |20.3306 | 1 | 0.001473 | 11.155934 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 370 |20.3857 | 1 | 0.001480 | 11.140440 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 371 |20.4408 | 1 | 0.001464 | 11.196868 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 372 |20.4959 | 1 | 0.001473 | 11.196430 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 373 |20.5510 | 1 | 0.001467 | 11.166742 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 374 |20.6061 | 1 | 0.001488 | 11.095840 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 375 |20.6612 | 1 | 0.001456 | 11.119288 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 376 |20.7163 | 1 | 0.001514 | 10.997535 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 377 |20.7713 | 1 | 0.001500 | 10.973636 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 378 |20.8264 | 1 | 0.001485 | 11.041631 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 379 |20.8815 | 1 | 0.001474 | 11.054704 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 380 |20.9366 | 1 | 0.001505 | 10.956344 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 381 |20.9917 | 1 | 0.001485 | 11.037928 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 382 |21.0468 | 1 | 0.001494 | 11.004072 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 383 |21.1019 | 1 | 0.001460 | 11.191711 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 384 |21.1570 | 1 | 0.001464 | 11.213192 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 385 |21.2121 | 1 | 0.001297 | 12.715977 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 386 |21.2672 | 1 | 0.001473 | 11.214244 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 387 |21.3223 | 1 | 0.001488 | 11.175076 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 388 |21.3774 | 1 | 0.001477 | 11.140157 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 389 |21.4325 | 1 | 0.001476 | 11.217773 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 390 |21.4876 | 1 | 0.001487 | 11.070076 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 391 |21.5427 | 1 | 0.001476 | 11.079977 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 392 |21.5978 | 1 | 0.001497 | 10.963420 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 393 |21.6529 | 1 | 0.001492 | 10.965270 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 394 |21.7080 | 1 | 0.001499 | 11.031488 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 395 |21.7631 | 1 | 0.001379 | 11.928026 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 396 |21.8182 | 1 | 0.001474 | 11.124487 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 397 |21.8733 | 1 | 0.001482 | 11.037149 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 398 |21.9284 | 1 | 0.001491 | 11.062619 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 399 |21.9835 | 1 | 0.001483 | 11.227740 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 400 |22.0386 | 1 | 0.001460 | 11.253708 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 401 |22.0937 | 1 | 0.001474 | 11.210907 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 402 |22.1488 | 1 | 0.001483 | 11.119041 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 403 |22.2039 | 1 | 0.001490 | 11.014906 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 404 |22.2590 | 1 | 0.001499 | 10.956471 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 405 |22.3140 | 1 | 0.001468 | 11.109550 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 406 |22.3691 | 1 | 0.001490 | 10.982853 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 407 |22.4242 | 1 | 0.001478 | 11.193154 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 408 |22.4793 | 1 | 0.001498 | 11.031459 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 409 |22.5344 | 1 | 0.001508 | 10.978516 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 410 |22.5895 | 1 | 0.001481 | 11.028180 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 411 |22.6446 | 1 | 0.001492 | 11.037275 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 412 |22.6997 | 1 | 0.001483 | 10.967960 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 413 |22.7548 | 1 | 0.001493 | 10.990911 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 414 |22.8099 | 1 | 0.001484 | 11.067482 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 415 |22.8650 | 1 | 0.001486 | 10.987234 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 416 |22.9201 | 1 | 0.001453 | 11.105183 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 417 |22.9752 | 1 | 0.001484 | 11.019325 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 418 |23.0303 | 1 | 0.001489 | 11.033711 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 419 |23.0854 | 1 | 0.001486 | 10.961752 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 420 |23.1405 | 1 | 0.001488 | 11.020402 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 421 |23.1956 | 1 | 0.001485 | 10.985927 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 422 |23.2507 | 1 | 0.001484 | 11.122986 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 423 |23.3058 | 1 | 0.001488 | 11.010117 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 424 |23.3609 | 1 | 0.001494 | 11.027276 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 425 |23.4160 | 1 | 0.001498 | 11.002853 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 426 |23.4711 | 1 | 0.001504 | 10.948009 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 427 |23.5262 | 1 | 0.001537 | 10.965587 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 428 |23.5813 | 1 | 0.001480 | 11.023513 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 429 |23.6364 | 1 | 0.001495 | 11.016430 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 430 |23.6915 | 1 | 0.001498 | 10.990407 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 431 |23.7466 | 1 | 0.001482 | 11.029547 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 432 |23.8017 | 1 | 0.001489 | 11.028503 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 433 |23.8567 | 1 | 0.001494 | 10.994521 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 434 |23.9118 | 1 | 0.001497 | 11.033860 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 435 |23.9669 | 1 | 0.001472 | 11.085127 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 436 |24.0220 | 1 | 0.001519 | 10.940756 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 437 |24.0771 | 1 | 0.001477 | 11.058848 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 438 |24.1322 | 1 | 0.001479 | 11.067911 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 439 |24.1873 | 1 | 0.001488 | 11.029004 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 440 |24.2424 | 1 | 0.001497 | 10.977903 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 441 |24.2975 | 1 | 0.001486 | 11.038936 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 442 |24.3526 | 1 | 0.001492 | 11.042946 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 443 |24.4077 | 1 | 0.001492 | 10.970813 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 444 |24.4628 | 1 | 0.001486 | 11.023437 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 445 |24.5179 | 1 | 0.001504 | 10.981979 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 446 |24.5730 | 1 | 0.001487 | 10.943550 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 447 |24.6281 | 1 | 0.001504 | 10.990585 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 448 |24.6832 | 1 | 0.001488 | 11.020756 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 449 |24.7383 | 1 | 0.001502 | 11.020719 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"| 450 |24.7934 | 1 | 0.001490 | 10.944653 | 0.000000 | 0.000000e+00 | 0.000000e+00 |\\u001b[0m\\n\",\n \"\\u001b[34m...Finished\\u001b[0m\\n\",\n \"\\u001b[36mFINISHED - Elapsed time = 5192.1956986 seconds\\u001b[0m\\n\",\n \"\\u001b[36mFINISHED - CPU process time = 38238.0321676 seconds\\u001b[0m\\n\"\n ]\n }\n ],\n \"source\": [\n \"sharpy_output = sharpy.sharpy_main.main(['', SimInfo.solvers['SHARPy']['route'] + SimInfo.solvers['SHARPy']['case'] + '.sharpy'])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Postprocessing\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This reads the structural and aerodynamic information of the last time step.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"tstep = sharpy_output.structure.timestep_info[-1]\\n\",\n \"astep = sharpy_output.aero.timestep_info[-1]\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we separate the structure into blades:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Define beams\\n\",\n \"ielem = 0\\n\",\n \"nblades = np.max(sharpy_output.structure.beam_number) + 1\\n\",\n \"nodes_blade = []\\n\",\n \"first_node = 0\\n\",\n \"for iblade in range(nblades):\\n\",\n \" nodes_blade.append(np.zeros((sharpy_output.structure.num_node,), dtype=bool))\\n\",\n \" while sharpy_output.structure.beam_number[ielem] <= iblade:\\n\",\n \" ielem += 1\\n\",\n \" if ielem == sharpy_output.structure.num_elem:\\n\",\n \" break\\n\",\n \" nodes_blade[iblade][first_node:sharpy_output.structure.connectivities[ielem-1,1]+1] = True\\n\",\n \" first_node = sharpy_output.structure.connectivities[ielem-1,1]+1\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Compute the radial position of the nodes and initialise the rest of the variables.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"r = []\\n\",\n \"c = []\\n\",\n \"dr = []\\n\",\n \"forces = []\\n\",\n \"CN_drR = []\\n\",\n \"CTan_drR = []\\n\",\n \"CP_drR = []\\n\",\n \"nodes_num = []\\n\",\n \"for iblade in range(nblades):\\n\",\n \" forces.append(tstep.steady_applied_forces[nodes_blade[iblade]].copy())\\n\",\n \"\\n\",\n \" nodes_num.append(np.arange(0, sharpy_output.structure.num_node, 1)[nodes_blade[iblade]])\\n\",\n \"\\n\",\n \" r.append(np.linalg.norm(tstep.pos[nodes_blade[iblade], :], axis=1))\\n\",\n \" dr.append(np.zeros(np.sum(nodes_blade[iblade])))\\n\",\n \" dr[iblade][0] = 0.5*(r[iblade][1]-r[iblade][0])\\n\",\n \" dr[iblade][-1] = 0.5 * (r[iblade][-1] - r[iblade][-2])\\n\",\n \" for inode in range(1,len(r[iblade]) - 1):\\n\",\n \" dr[iblade][inode] = 0.5*(r[iblade][inode+1] - r[iblade][inode-1])\\n\",\n \"\\n\",\n \" CN_drR.append(np.zeros(len(r[iblade])))\\n\",\n \" c.append(np.zeros(len(r[iblade])))\\n\",\n \" CTan_drR.append(np.zeros(len(r[iblade])))\\n\",\n \" CP_drR.append(np.zeros(len(r[iblade])))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Transform the loads computed by SHARPy into out-of-plane and in-plane components:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"rho = sharpy_output.settings['StaticCoupled']['aero_solver_settings']['rho']\\n\",\n \"uinf = sharpy_output.settings['StaticCoupled']['aero_solver_settings']['velocity_field_input']['u_inf']\\n\",\n \"R = np.max(r[0])\\n\",\n \"Cp = 0\\n\",\n \"Ct = 0\\n\",\n \"\\n\",\n \"global_force_factor = 0.5 * rho * uinf** 2 * np.pi * R**2\\n\",\n \"global_power_factor = global_force_factor*uinf\\n\",\n \"for iblade in range(nblades):\\n\",\n \" for inode in range(len(r[iblade])):\\n\",\n \" forces[iblade][inode, 0] *= 0. # Discard the spanwise component\\n\",\n \"\\n\",\n \" node_global_index = nodes_num[iblade][inode]\\n\",\n \" ielem = sharpy_output.structure.node_master_elem[node_global_index, 0]\\n\",\n \" inode_in_elem = sharpy_output.structure.node_master_elem[node_global_index, 1]\\n\",\n \" CAB = algebra.crv2rotation(tstep.psi[ielem, inode_in_elem, :])\\n\",\n \"\\n\",\n \" c[iblade][inode] = sharpy_output.aero.data_dict['chord'][ielem,inode_in_elem]\\n\",\n \"\\n\",\n \" forces_AFoR = np.dot(CAB, forces[iblade][inode, 0:3])\\n\",\n \"\\n\",\n \" CN_drR[iblade][inode] = forces_AFoR[2]/dr[iblade][inode]*R / global_force_factor\\n\",\n \" CTan_drR[iblade][inode] = np.linalg.norm(forces_AFoR[0:2])/dr[iblade][inode]*R / global_force_factor\\n\",\n \" CP_drR[iblade][inode] = np.linalg.norm(forces_AFoR[0:2])/dr[iblade][inode]*R * r[iblade][inode]*rotation_velocity / global_power_factor\\n\",\n \"\\n\",\n \" Cp += np.sum(CP_drR[iblade]*dr[iblade]/R)\\n\",\n \" Ct += np.sum(CN_drR[iblade]*dr[iblade]/R)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Results\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Plot of the loads along the blade:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/svg+xml\": [\n \"\\n\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, list_plots = plt.subplots(1, 2, figsize=(12, 3))\\n\",\n \"\\n\",\n \"list_plots[0].grid()\\n\",\n \"list_plots[0].set_xlabel(\\\"r/R [-]\\\")\\n\",\n \"list_plots[0].set_ylabel(\\\"CN/d(r/R) [-]\\\")\\n\",\n \"list_plots[0].plot(r[0]/R, CN_drR[0], '-', label='SHARPy')\\n\",\n \"list_plots[0].plot(of_rR, of_cNdrR, '-', label='OpenFAST')\\n\",\n \"list_plots[0].legend()\\n\",\n \"\\n\",\n \"list_plots[1].grid()\\n\",\n \"list_plots[1].set_xlabel(\\\"r/R [-]\\\")\\n\",\n \"list_plots[1].set_ylabel(\\\"CT/d(r/R) [-]\\\")\\n\",\n \"list_plots[1].plot(r[0]/R, CTan_drR[0], '-', label='SHARPy')\\n\",\n \"list_plots[1].plot(of_rR, of_cTdrR, '-', label='OpenFAST')\\n\",\n \"list_plots[1].legend()\\n\",\n \"\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Print the rotor thrust and power coefficients:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \" OpenFAST SHARPy\\n\",\n \"Cp[-] 0.49 0.52\\n\",\n \"Ct[-] 0.70 0.70\\n\"\n ]\n }\n ],\n \"source\": [\n \"print(\\\" OpenFAST SHARPy\\\")\\n\",\n \"print(\\\"Cp[-] %.2f %.2f\\\" % (of_cp, Cp))\\n\",\n \"print(\\\"Ct[-] %.2f %.2f\\\" % (of_ct, Ct))\"\n ]\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\": \"3.10.9\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 4\n}\n" }, { "path": "docs/source/content/examples.rst", "content": "Examples\n========\n\nA set of SHARPy examples created with Jupyter Notebooks is provided for users to interact and modify\ncases running on SHARPy.\n\n.. toctree::\n :maxdepth: 1\n :caption: SHARPy Examples\n\n example_notebooks/linear_goland_flutter\n example_notebooks/nonlinear_t-tail_HALE\n example_notebooks/linear_horten\n example_notebooks/wind_turbine\n example_notebooks/cantilever/static_cantilever\n example_notebooks/cantilever_wing\n example_notebooks/UDP_control/tutorial_udp_control\n\nDownloadable files\n------------------\n\n* :download:`./example_notebooks/linear_goland_flutter.ipynb`\n* :download:`./example_notebooks/nonlinear_t-tail_HALE.ipynb`\n* :download:`./example_notebooks/linear_horten.ipynb`\n* :download:`./example_notebooks/wind_turbine.ipynb`\n* :download:`./example_notebooks/cantilever_wing.ipynb`\n* :download:`./example_notebooks/cantilever/static_cantilever.ipynb`\n* :download:`./example_notebooks/UDP_control/tutorial_udp_control.ipynb`\n\nInput data for wind turbine: \n\n* :download:`./example_notebooks/source/type02_db_NREL5MW_v02.xlsx`\n\nInput data for static cantilever:\n\n* :download:`./example_notebooks/cantilever/model_static_cantilever.py`\n\nExternal Scripts UDP control:\n\n* :download:`./example_notebooks/UDP_control/pazy_PID_controller_UDP.py`\n* :download:`./example_notebooks/UDP_control/control_design_script.m`\n\n\n\nNote: some of these examples may need additional files which would be located in the ``./example_notebooks/`` directory. It is recommended that you run these cases directly from there rather than downloading. If you download, make sure you replicate the folder structure such that the examples are capable of finding the required files.\n\n" }, { "path": "docs/source/content/faqs.md", "content": "# Frequently Asked Questions [FAQs]\n\nOver the years, we have gathered a valuable experience running SHARPy so we would like to collect here a few of the\nmost frequently asked questions we get here to hopefully help other users.\n\nIn addition to the questions listed below, do check the [issues](https://github.com/ImperialCollegeLondon/sharpy/issues?q=is%3Aissue) page in our GitHub repo as you may find useful \ninformation there. Do also check our [Short Debugging Guide](./debug.html).\n\n* __[Q] I get a `ModuleNotFound Error` when trying to run SHARPy.__\n\n _[A]_ Make sure you have loaded the SHARPy variables using the command `source /bin_sharpy_var.sh`.\n \n* __[Q] When plotting the aerodynamic forces in Paraview from the UVLM, the forces at the boundary between two \nsurfaces (for instance at the wing root) appears halved. Is my simulation incorrect?__\n\n _[A]_ This is most likely not an issue with your simulation. We have observed over time that Paraview actually only\n plots the result from one of the surfaces, hence why it appears half of what it should be. If you extract the forces\n without using Paraview using the \n [WriteVariablesTime](https://ic-sharpy.readthedocs.io/en/master/includes/postprocs/WriteVariablesTime.html) postprocessor you will get the correct result.\n \n* __[Q] My time-domain simulation does not converge. I get a `SolverNotConverged` error. What can I do?__\n\n _[A]_ This is quite an open question and it could be for a wide variety of reasons. Things that should be in your \n First Aid kit for these situations:\n \n - Is your tolerance appropriate? If you raise the tolerance to something (maybe unreasonably) high does it \n converge?\n \n - Is your number of iterations sufficient? Increase the number of maximum allowed iterations.\n \n - Is there anything happening at all in your simulation? We have all fallen into the trap of trying to run \n a time domain simulation of something that is already in steady state. I.e. you calculate its static\n equilibrium and then try to advance in time. Since nothing is happening the convergence criteria in the solvers\n may not be triggered and reach the maximum number of iterations. Solution: make sure something happens in your time\n domain simulation: gusts, external forces, control surface deflections...\n \n - Are you giving your simulation too much of a \"kick\"? Sometimes we simulate things that dramatically change the\n state of the problem from one time step to another (like adding very large external forces at once) which may lead\n to trouble. You can choose to load the forces progressively by increasing the `num_load_steps` setting in our\n structural solvers.\n \nHopefully this list will grow over time with some of the common questions previous users encounter. If you cannot solve\nyour problem please open an [issue](https://github.com/ImperialCollegeLondon/sharpy/issues) on Github and assign it the\nlabel `label:question` so we can keep track of it and others can benefit of the discussion." }, { "path": "docs/source/content/installation.md", "content": "# SHARPy v2.3 Installation Guide\n__Last revision 10 June 2024__\n\nThe following step by step tutorial will guide you through the installation process of SHARPy. This is the updated process valid from v2.3.\n\n## Requirements\n\n__Operating System Requirements__\n\nSHARPy is being developed and tested on the following operating systems:\n* CentOS 7 and CentOS 8\n* Ubuntu 22.04 LTS\n* Debian 12\n* MacOS Mojave and Catalina (Intel)\n* MacOS Sonoma (Apple Silicon M2)\n\nWindows users can also run it by first installing the Windows Subsystem for Linux (https://learn.microsoft.com/en-us/windows/wsl/install) and a XServer such as GWSL, which can be installed through the Microsoft Store. SHARPy is also available to the vast majority of operating systems that are supported by Docker\n\n__Required Distributions__\n\n* Python 3.10 or higher\n* CMake\n* GCC 6.0 or higher, G++, GFortran (all included in Anaconda) \n* Eigen3, BLAS, MKL/LAPACK (all included in Anaconda)\n\nIf the prerequisite packages are not installed and you are not using Anaconda, they can be installed as following on Linux (with a Homebrew equivelent available for Mac installs):\n```bash\nsudo apt install -y cmake g++ gfortran libblas-dev liblapack-dev libeigen3-dev\n```\n\n__Recommended Software__\n\nYou may find the applications below useful, we recommend you use them but cannot provide any direct support.\n\n* [HDFView](https://portal.hdfgroup.org/display/HDFVIEW/HDFView) to read and view `.h5` files. HDF5 is the SHARPy\ninput file format.\n* [Paraview](https://www.paraview.org/) to visualise SHARPy's output.\n\n\nSHARPy can be installed from the source code available on GitHub or you can get it packed in a Docker container.\nIf what you want is to give it a go and run some static or simple dynamic cases (and are familiar with Docker),\nwe recommend the [Docker route](#using-sharpy-from-a-docker-container). If you want to check the code, modify it and\ncompile the libraries with custom flags, build it from source (recommended).\n\n## Building SHARPy from source (release or development builds)\n\nSHARPy can be built from source so that you can get the latest release or (stable) development build.\n\nSHARPy depends on two external libraries, [xbeam](http://github.com/imperialcollegelondon/xbeam) and\n[UVLM](http://github.com/imperialcollegelondon/UVLM). These are included as submodules to SHARPy and therefore\nonce you initialise SHARPy you will also automatically clone the relevant versions of each library.\n\n### Set up the folder structure\n\nClone `sharpy` in your desired location, if you agree with the license in `license.txt`.\n```bash\ngit clone --recursive http://github.com/ImperialCollegeLondon/sharpy\n```\nThe `--recursive` flag will also initialise and update the submodules SHARPy depends on,\n[xbeam](http://github.com/imperialcollegelondon/xbeam) and [UVLM](http://github.com/imperialcollegelondon/UVLM).\n\n\n### Quick install (Standalone)\n\nSHARPy can be installed as a standalone package, without the use of a package manager. If you wish to install using the Anaconda package manager, please use the following tutorial [HERE](#setting-up-the-python-environment-anaconda), or make a custom installation with a develop build or modified compilation settings [HERE](#custom-installation). The quick install is geared towards getting the release build of SHARPy running as quickly and simply as possible. \n\n1. Check that your Python version is 3.10 or higher. Other versions may be incompatible with the required modules.\n ```bash\n python --version\n ```\n \n2. Move into the cloned repository:\n ```bash\n cd sharpy\n ```\n\n3. Install SHARPy. This will install any required Python packages as well as building the xbeam and UVLM libraries, and may take a few minutes.\n ```bash\n pip install --user .\n ```\n The ```--user``` flag is included for systems without root access (often Linux) as the install will fail otherwise. This flag can be removed when a global install is required, and your machine allows it (works on Mac).\n \n There are options for what to install if required. For instance, to install the basic package with documentation, just do ```bash pip install --user .[docs]```. For the whole lot, ```bash pip install --user .[all]```.\n\n4. You can check the version of SHARPy you are running with:\n ```bash\n sharpy --version\n ```\n\n__You are ready to run SHARPy__. Continue reading the [Running SHARPy](#running-sharpy) section.\n\n### Setting up the Python Environment (Anaconda)\n\nSHARPy can use the Anaconda package manager to provide the necessary Python packages.\nThese are specified in an Anaconda environment that shall be activated prior to compiling the xbeam and UVLM libraries or running any SHARPy cases.\n\n1. If you still do not have it in your system, install the [Anaconda](https://conda.io/docs/) Python 3 distribution.\n\n2. Check that your Python version is at least 3.10:\n ```bash\n python --version\n ```\n3. If a specific python version is required, for example 3.10, use:\n\n ```bash\n conda install python=3.10\n ```\n \n4. Create the conda environment that SHARPy will use:\n\n ```bash\n conda env create -f environment.yml\n ```\n This should take approximately 5 minutes to complete (Tested on Ubuntu 22.04.1). For installation on Apple Silicon, use ```environment_arm64.yml```; this requires GCC and GFortran to be installed prior.\n\n Installation using Conda can be memory intensive, and will give the message ```Collecting package metadata (repodata.json): - Killed``` if all the available RAM is filled. From testing, 16GB of total system RAM is reliable for Conda install, whereas 8GB may have issues. Three solutions are available:\n * Increase available RAM (if running on a compute cluster etc)\n * Use [Mamba](https://mamba.readthedocs.io/en/latest/), a more efficient drop-in replacement for Conda\n * Create a blank conda environment and install the required packages:\n \t```bash\n conda create --name sharpy python=3.10\n conda config –add channels conda-forge\n conda install eigen libopenblas libblas libcblas liblapack libgfortran libgcc libgfortran-ng\n ```\n \n6. Activate the `sharpy` conda environment:\n ```bash\n conda activate sharpy\n ```\n You should now see ```(sharpy)``` on your command line. \n\n\n### Quick install (Anaconda)\nThe quick install is geared towards getting the release build of SHARPy running as quickly and simply as possible.\n1. Move into the cloned repository:\n ```bash\n cd sharpy\n ```\n\n2. Ensure that the SHARPy environment is active in the session. Your terminal prompt line should begin with:\n ```bash\n (sharpy) [usr@host] $\n ```\n\n3. Install SHARPy. This will install any required Python packages as well as building the xbeam and UVLM libraries, and may take a few minutes.\n ```bash\n pip install --user .\n ```\n The ```--user``` flag is included for systems without root access (often Linux) as the install will fail otherwise. This flag can be removed when a global install is required, and your machine allows it (works on Mac).\n \n There are options for what to install if required. For instance, to install the basic package with documentation, just do ```bash pip install --user .[docs]```. For the whole lot, ```bash pip install --user .[all]```.\n\n4. You can check the version of SHARPy you are running with:\n ```bash\n sharpy --version\n ```\n\nIf running SHARPy from Anaconda, you need to load the conda environment. Therefore, __before you run any SHARPy case or test__, activate the SHARPy conda environment: \n```bash\nconda activate sharpy\n```\n\n__You are ready to run SHARPy__. Continue reading the [Running SHARPy](#running-sharpy) section.\n\n### Custom installation\n\nThese steps will show you how to compile the xbeam and UVLM libraries such that you can modify the compilation settings\nto your taste. This is compatible with both standalone and Anaconda installations.\n\n1. If you want to use SHARPy's latest release, skip this step. If you would like to use the latest development work,\n you will need to checkout the `develop` branch. For more info on how we structure our development and what branches\n are used for what kind of features have a look at the [Contributing](contributing.html) page.\n ```bash\n git checkout develop\n git submodule update --recursive\n ```\n This command will check out the `develop` branch and set it to track the remote origin. It will also set the submodules (xbeam and UVLM) to the right commit.\n\n2. If using Anaconda, create the conda environment that SHARPy will use and activate the environment:\n ```bash\n conda env create -f environment.yml\n ```\n\n ```bash\n conda activate sharpy\n ```\n\n4. Create a directory `build` that will be used during CMake's building process and `cd` into it:\n ```bash\n mkdir build\n cd build\n ```\n\n5. Run CMake with custom flags:\n 1. Choose your compilers for Fortran `FC` and C++ `CXX`, for instance:\n ```bash\n FC=gfortran CXX=g++ cmake ..\n ```\n If you'd like to use the Intel compilers you can set them using:\n ```bash\n FC=ifort CXX=icpc cmake ..\n ```\n 2. Alternatively, you can build the libraries in debug mode with the following flag for cmake:\n ```bash\n -DCMAKE_BUILD_TYPE=Debug\n ```\n\n6. Compile the libraries and parallelise as you prefer.\n ```bash\n make install -j 4\n ```\n\n7. Finally, leave the build directory and install SHARPy.\n ```bash\n cd ..\n pip install .\n ```\n If you want to install it in development mode (the source files will stay\n where the are so you can modify them), you can make an editable install:\n ```\n pip install -e .\n ```\n You can obtain further information on editable installs [here](https://pip.pypa.io/en/stable/cli/pip_install/#editable-installs)\n\n8. This concludes the installation! Continue reading the [Running SHARPy](#running-sharpy) section.\n\n## Using SHARPy from a Docker container\n\n> **Tip** To install the Python environment, miniconda needs approximatelly 16GB of\n> memory. It is recommended to have at least that amount available for the\n> container in which you are building SHARPy.\n\nDocker containers are similar to lightweight virtual machines. The SHARPy container\ndistributed through [Docker Hub](https://hub.docker.com/) is a CentOS 8\nmachine with the libraries compiled with `gfortran` and `g++` and an\nAnaconda Python distribution.\n\nMake sure your machine has Docker working. The instructions are here:\n[link](https://docs.docker.com/v17.09/engine/installation/).\n\nYou might want to run a test in your terminal:\n```\ndocker pull hello-world\ndocker run hello-world\n```\nIf this works, you're good to go!\n\nFirst, obtain the SHARPy docker container:\n```\ndocker pull ghcr.io/imperialcollegelondon/sharpy:main\n```\nYou can obtain other versions as well, check those available in the [containers](https://github.com/ImperialCollegeLondon/sharpy/pkgs/container/sharpy) page.\n\nThis will donwload a Docker image of SHARPy to your machine, from where you can create and run Docker containers. To create and run a container from the downloaded image use:\n\n```\ndocker run --name sharpy -it -p 8080:8080 ghcr.io/imperialcollegelondon/sharpy:main\n```\n\nA few details about the above command, although if in doubt please check the Docker documentation. The `--name` argument gives a name to the container. Note you can create multiple containers from a single image. \n\nThe `-it` is an important command as it runs the container in interactive mode with a terminal attached. Thus you can use it an navigate it. Otherwise the container will finish as soon as it is created. \n\nThe `-p 8080:8080` argument connects the container to your machine through port `8080` (it could be any other) which may be useful for some applications. For instance, running SHARPy as hardware-in-the-loop through UDP.\n\nOnce you run it, you should see a welcome dialog such as:\n```\n>>>> docker run --name sharpy -it -p 8080:8080 ghcr.io/imperialcollegelondon/sharpy:main\nSHARPy added to PATH from the directory: /sharpy_dir/bin\n=======================================================================\nWelcome to the Docker image of SHARPy\nSHARPy is located in /sharpy_dir/ and the\nenvironment is already set up!\nCopyright Imperial College London. Released under BSD 3-Clause license.\n=======================================================================\nSHARPy>\n```\nYou are now good to go.\n\nYou can check the version of SHARPy you are running with\n```\nsharpy --version\n```\n\nIt is important to note that a docker container runs as an independent\noperating system with no access to your hard drive. If you want to copy your own\nfiles, run the container and from another terminal run:\n```\ndocker cp my_file.txt sharpy:/my_file.txt # copy from host to container\ndocker cp sharpy:/my_file.txt my_file.txt # copy from container to host\n```\nThe `sharpy:` part is the `--name` argument you wrote in the `docker run` command.\n\n**Enjoy!**\n\n## Testing with Docker\n\nYou can run the test suite once inside the container as:\n```\ncd sharpy_dir\npython -m unittest\n```\n\n**Enjoy!**\n\n## Obtain SHARPy from PyPI (experimental!)\n\nYou can obtain a built version of SHARPy, ic-sharpy, from PyPI [here](https://pypi.org/project/ic-sharpy/).\n\nTo install at default directory use\n```\npython3 -m pip install ic-sharpy\n```\nTo install at current directory use\n```\npython3 -m pip install --prefix . ic-sharpy\n```\nThe source code can be found at `/lib/python3.10/site-packages/sharpy` and the executable at `/bin/sharpy`.\n\n## Running SHARPy\n\n### Automated tests\n\nSHARPy uses unittests to verify the integrity of the code.\n\nThese tests can be run from the `./sharpy` directory.\n```bash\npython -m unittest\n```\nThe tests will run and you should see a success message. If you don't... check the following options:\n* Check you are running the latest version. Running the following from the root directory should update to the\nlatest release version:\n - `git pull`\n - `git submodule update --init --recursive`\n* If the tests don't run, make sure you have followed correctly the instructions and that you managed to compile xbeam\nand UVLM.\n* If some tests fail, i.e. you get a message after the tests run saying that certain tests did not pass, please open\nan [issue](http://www.github.com/imperialcollegelondon/sharpy/issues) with the following information:\n - Operating system\n - Whether you did a Custom/quick install\n - UVLM and xbeam compiler of choice\n - A log of the tests that failed\n\n### The SHARPy Case Structure and input files\n\n__Setting up a SHARPy case__\n\nSHARPy cases are usually structured in the following way:\n\n1. A `generate_case.py` file: contains the setup of the problem like geometry, flight conditions etc.\nThis script creates the output files that will then be used by SHARPy, namely:\n * The [structural](./casefiles.html#fem-file) `.fem.h5` file.\n * The [aerodynamic](./casefiles.html#aerodynamics-file) `.aero.h5` file.\n * [Simulation information](./casefiles.html#solver-configuration-file) and settings `.sharpy` file.\n * The dynamic forces file `.dyn.h5` (when required).\n * The linear input files `.lininput.h5` (when required).\n * The ROM settings file `.rom.h5` (when required).\n\n See the [chapter](./casefiles.html) on the case files for a detailed description on the contents of each one.\n Data is exchanged in binary format by means of `.h5` files that make the transmission efficient between the different\n languages of the required libraries. To view these `.h5` files, a viewer like [HDF5](https://portal.hdfgroup.org/display/support) is recommended.\n\n2. The `h5` files contain data of the FEM, aerodynamics, dynamic conditions. They are later read by SHARPy.\n\n3. The `.sharpy` file contains the settings for SHARPy and is the file that is parsed to SHARPy.\n\n__To run a SHARPy case__\n\nSHARPy cases are therefore usually ran in the following way:\n\n1. Create a `generate_case.py` file following the provided templates.\n\n2. Run it to produce the `.h5` files and the `.sharpy` files.\n ```bash\n python generate_case.py\n ```\n\n3. Run SHARPy (ensure the environment is activated).\n ```bash\n sharpy case.sharpy\n ```\n\n#### Output\n\nBy default, the output is located in the `output` folder.\n\nThe contents of the folder will typically be a `beam` and `aero` folders, which contain the output data that can then be\nloaded in Paraview. These are the `.vtu` format files that can be used with [Paraview](https://www.paraview.org/).\n\n\n### Running (and modifiying) a test case\n\n1. This command generates the required files for running a static, clamped beam case that is used as part of code\nverification:\n ```sh\n cd ../sharpy\n python ./tests/xbeam/geradin/generate_geradin.py\n ```\n\nNow you should see a success message, and if you check the\n`./tests/xbeam/geradin/` folder, you should see two new files:\n+ geradin_cardona.sharpy\n+ geradin_cardona.fem.h5\n\nTry to open the `sharpy` file with a plain text editor and have a quick look. The `sharpy` file is\nthe main settings file. We'll get deeper into this later.\n\nIf you try to open the `fem.h5` file, you'll get an error or something meaningless. This is because the structural data\nis stored in [HDF5](https://support.hdfgroup.org/HDF5/) format, which is compressed binary.\n\n5. Run it (part 1)\n\n The `sharpy` call is:\n ```bash\n sharpy \n ```\n\n6. Results (part 1)\n\n Since this is a test case, there is no output directly to screen.\n\n We will therefore change this setting first.\n In the `generate_geradin.py` file, look for the `SHARPy` setting `write_screen` and set it to `on`. This will\n output the progress of the execution to the terminal.\n\n We would also like to create a Paraview file to view the beam deformation. Append the post-processor `BeamPlot` to\n the end of the `SHARPy` setting `flow`, which is a list. This will run the post-processor and plot the beam in Paraview format with the settings specified in\n the `generate_geradin.py` file under `config['BeamPlot]`.\n\n7. Run (part 2)\n\n Now that we have made these modifications, run again the generation script:\n ```sh\n python ./tests/xbeam/geradin/generate_geradin.py\n ```\n\n Check the solver file `geradin.sharpy` and look for the settings we just changed. Make sure they read what we wanted.\n\n\n You are now ready to run the case again:\n ```bash\n sharpy \n ```\n\n8. Post-processing\n\n After a successful execution, you should a long display of information in the terminal as the case is being\n executed.\n\n The deformed beam will have been written in a `.vtu` file and will be located in the `output/` folder (or where\n you specified in the settings) which you can open using Paraview.\n\n In the `output` directory you will also note a folder named `WriteVariablesTime` which outputs certain variables\n as a function of time to a `.dat` file. In this case, the beam tip position deflection and rotation is written.\n Check the values of those files and look for the following result:\n ```\n\t Pos_def:\n\t\t 4.403530 0.000000 -2.159692\n\t Psi_def:\n\t\t 0.000000 0.672006 0.000000\n ```\n FYI, the correct solution for this test case by Geradin and Cardona is\n `Delta R_3 = -2.159 m` and `Psi_2 = 0.6720 rad`.\n\nCongratulations, you've run your first case. You can now check the [Examples](examples.html) section for further cases.\n" }, { "path": "docs/source/content/postproc.rst", "content": "Post-Processing\n---------------\n\n.. toctree::\n :glob:\n\n ../includes/postprocs/*" }, { "path": "docs/source/content/publications.md", "content": "# Publications\n\nSHARPy has been used in many technical papers that have been both published in Journals and presented at conferences.\nHere we present a list of past papers which have used SHARPy for research purposes:\n\n## 2022\n\n* Goizueta, N. (2022). Parametric reduced-order aeroelastic modelling for analysis, dynamic system interpolation and control of flexible aircraft. PhD Thesis. [http://doi.org/10.25560/100137](http://doi.org/10.25560/100137)\n\n* Goizueta, N., Wynn, A., & Palacios, R. (2022). Adaptive sampling for interpolation of reduced-order aeroelastic dynamical systems. AIAA Journal. Article in Advance. [https://doi.org/10.2514/1.J062050](https://doi.org/10.2514/1.J062050)\n\n* Muñoz Simón, A. (2022). Vortex-lattice-based nonlinear aeroservoelastic modelling and analysis of large floating wind turbines. PhD Thesis. [https://doi.org/10.25560/96986](https://doi.org/10.25560/96986)\n\n* Goizueta, N., Wynn, A., Palacios, R., Drachinsky, A., & Raveh, D. E. (2022). Flutter Predictions for Very Flexible Wing Wind Tunnel Test. Journal of Aircraft: 59(4), pp. 1082-1097. [https://doi.org/10.2514/1.C036710](https://doi.org/10.2514/1.C036710)\n\n* Düssler, S., Goizueta, N., Muñoz-Simón, A., & Palacios, R. (2022). Modelling and Numerical Enhancements on a UVLM for Nonlinear Aeroelastic Simulation. AIAA SciTech Forum. [https://doi.org/10.2514/6.2022-2455](https://doi.org/10.2514/6.2022-2455)\n\n* Cea, A., Palacios, R. (2022). Parametric Reduced Order Models for Aeroelastic Design of Very Flexible Aircraft. AIAA SciTech Forum. [https://doi.org/10.2514/6.2022-0727](https://doi.org/10.2514/6.2022-0727)\n\n* Wynn, A., Artola, M., Palacios, R. (2022). Nonlinear optimal control for gust load alleviation with a physics-constrained data-driven internal model. AIAA SciTech Forum. [https://doi.org/10.2514/6.2022-0442](https://doi.org/10.2514/6.2022-0442)\n\n* Goizueta, N., Wynn, A., Palacios, R. (2022). Fast flutter evaluation of very flexible wing using interpolation on an optimal training dataset. In AIAA SciTech Forum, AIAA Paper 2022-1345. [https://doi.org/10.2514/6.2022-1345](https://doi.org/10.2514/6.2022-1345)\n\n## 2021\n\n* Artola, M., Goizueta, N., Wynn, A., & Palacios, R. (2021). Aeroelastic Control and Estimation with a Minimal \nNonlinear Modal Description. AIAA Journal: 59(7), pp. 2697–2713. [https://doi.org/10.2514/1.j060018](https://doi.org/10.2514/1.j060018)\n\n* Artola, M., Goizueta, N., Wynn, A., & Palacios, R. (2021). Proof of Concept for a Hardware-in-the-Loop Nonlinear. \nIn AIAA SciTech Forum (pp. 1–26). [https://doi.org/10.2514/6.2021-1392](https://doi.org/10.2514/6.2021-1392)\n\n* Goizueta, N., Drachinsky, A., Wynn, A., Raveh, D. E., & Palacios, R. (2021). Flutter prediction for a very \nflexible wing wind tunnel test. In AIAA SciTech Forum (pp. 1–17). \n[https://doi.org/10.2514/6.2021-1711](https://doi.org/10.2514/6.2021-1711)\n\n* Goizueta, N., Wynn, A., & Palacios, R. (2021). Parametric Krylov-based order reduction of aircraft aeroelastic \nmodels. In AIAA SciTech Forum (pp. 1–25). [https://doi.org/10.2514/6.2021-1798](https://doi.org/10.2514/6.2021-1798)\n\n## 2020\n\n* del Carre, A. (2020). Aeroelasticity of very flexible aircraft at low altitudes. PhD Thesis. [https://doi.org/10.25560/88269](https://doi.org/10.25560/88269)\n\n* Muñoz-Simón, A., Palacios, R., & Wynn, A. (2020). Benchmarking different fidelities in wind turbine aerodynamics \nunder yaw. Journal of Physics: Conference Series, 1618, 42017. \n[https://doi.org/10.1088/1742-6596/1618/4/042017](https://doi.org/10.1088/1742-6596/1618/4/042017)\n\n* del Carre, A., & Palacios, R. (2020). Simulation and Optimization of Takeoff Maneuvers of Very Flexible Aircraft. \nJournal of Aircraft: 57(6)\n1097-1110. [https://doi.org/10.2514/1.C035901](https://doi.org/10.2514/1.C035901)\n\n* Maraniello, S. & Palacios, R. (2020). Parametric Reduced-Order Modeling of the Unsteady Vortex-Lattice Method. \nAIAA Journal, 58(5), 2206-2220. [https://doi.org/10.2514/1.J058894](https://doi.org/10.2514/1.J058894)\n\n* Deskos, G., del Carre, A., & Palacios, R. (2020). Assessment of low-altitude atmospheric \nturbulence models for aircraft aeroelasticity. Journal of Fluids and Structures, 95, 102981.\n[https://doi.org/10.1016/j.jfluidstructs.2020.102981](https://doi.org/10.1016/j.jfluidstructs.2020.102981)\n\n* Goizueta, Norberto, del Carre, Alfonso, Muñoz-Simón, Arturo, & Palacios, Rafael. (2020, February). \nSHARPy: from a research code to an open-source software tool for the simulation of very flexible aircraft. \nRSLondonSouthEast 2020 Conference.\nZenodo: [http://doi.org/10.5281/zenodo.3641216](http://doi.org/10.5281/zenodo.3641216)\n\n* Del Carre, A., Deskos, G., & Palacios, R. (2020). Realistic turbulence effects in low altitude dynamics of very \nflexible aircraft. In AIAA SciTech Forum (pp. 1–18). \n[https://doi.org/10.2514/6.2020-1187](https://doi.org/10.2514/6.2020-1187)\n\n* Artola, M., Goizueta, N., Wynn, A., & Palacios, R. (2020). Modal-Based Nonlinear Estimation and Control for Highly \nFlexible Aeroelastic Systems. In AIAA SciTech Forum (pp. 1–23). \n[https://doi.org/10.2514/6.2020-1192](https://doi.org/10.2514/6.2020-1192)\n\n* Muñoz-Simón, A., Wynn, A., & Palacios, R. (2020). Unsteady and three-dimensional aerodynamic effects on wind turbine \nrotor loads. In AIAA SciTech Forum. [https://doi.org/10.2514/6.2020-0991](https://doi.org/10.2514/6.2020-0991)\n\n## 2019\n\n* del Carre, A., Muñoz-Simón, A., Goizueta, N., & Palacios, R. (2019). SHARPy : A dynamic aeroelastic simulation toolbox \nfor very flexible aircraft and wind turbines. Journal of Open Source \nSoftware, 4(44), 1885. [https://doi.org/10.21105/joss.01885](https://doi.org/10.21105/joss.01885)\n\n* del Carre, A., Teixeira, P. C., Palacios, R., & Cesnik, C. E. S. (2019). Nonlinear Response of a Very Flexible \nAircraft Under Lateral Gust. In International Forum on Aeroelasticity and Structural Dynamics.\n\n* del Carre, A., & Palacios, R. (2019). Efficient Time-Domain Simulations in Nonlinear Aeroelasticity. In AIAA Scitech \nForum (pp. 1–20). [https://doi.org/10.2514/6.2019-2038](https://doi.org/10.2514/6.2019-2038)\n\n* Maraniello, S., & Palacios, R. (2019). State-Space Realizations and Internal Balancing in Potential-Flow Aerodynamics \nwith Arbitrary Kinematics. AIAA Journal, 57(6), 2308-2321. \n[https://doi.org/10.2514/1.J058153](https://doi.org/10.2514/1.J058153)\n" }, { "path": "docs/source/content/solvers.rst", "content": "SHARPy Solvers\n------------------\n\nThe available SHARPy solvers are listed below. Attending to SHARPy's modular structure, they can be run\nindependently so the order in which you desire to run them is important.\n\nThe starting point is the PreSharpy loader. It contains the simulation configuration and which solvers are to be run\nand in the order that should happen.\n\n.. toctree::\n :glob:\n\n ../includes/solvers/*\n\n" }, { "path": "docs/source/content/test_cases.rst", "content": "``SHARPy`` Test Cases\n---------------------\n\nThe following test cases are provided as a tutorial and introduction to ``SHARPy`` as well as for code validation purposes.\n\n* Geradin and Cardona Beam - See Installation_ and see test case in ``./sharpy/tests/xbeam/``\n\n.. _Installation: https://ic-sharpy.readthedocs.io/en/dev_doc/content/installation.html#running-and-modifiying-a-test-case\n\n" }, { "path": "docs/source/includes/aero/index.rst", "content": "Aerodynamic Packages\n--------------------\n\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./models/index\n\t./utils/index\n" }, { "path": "docs/source/includes/aero/models/aerogrid/AeroTimeStepInfo.rst", "content": "AeroTimeStepInfo\n----------------\n\n.. autoclass:: sharpy.aero.models.aerogrid.AeroTimeStepInfo\n\t:members:" }, { "path": "docs/source/includes/aero/models/aerogrid/Aerogrid.rst", "content": "Aerogrid\n--------\n\n.. autoclass:: sharpy.aero.models.aerogrid.Aerogrid\n\t:members:" }, { "path": "docs/source/includes/aero/models/aerogrid/generate_strip.rst", "content": "generate_strip\n--------------\n\n.. automodule:: sharpy.aero.models.aerogrid.generate_strip" }, { "path": "docs/source/includes/aero/models/aerogrid/index.rst", "content": "Aerogrid\n++++++++\n\n\nAerogrid contains all the necessary routines to generate an aerodynamic\ngrid based on the input dictionaries.\n\n\n.. toctree::\n\t:glob:\n\n\t./AeroTimeStepInfo\n\t./Aerogrid\n\t./generate_strip\n" }, { "path": "docs/source/includes/aero/models/index.rst", "content": "Models\n------\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./aerogrid/index\n" }, { "path": "docs/source/includes/aero/utils/airfoilpolars/Polar.rst", "content": "Polar\n-----\n\n.. autoclass:: sharpy.aero.utils.airfoilpolars.Polar\n\t:members:" }, { "path": "docs/source/includes/aero/utils/airfoilpolars/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./Polar\n" }, { "path": "docs/source/includes/aero/utils/index.rst", "content": "Aerodynamic Utilities\n---------------------\n\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./airfoilpolars/index\n\t./mapping/index\n" }, { "path": "docs/source/includes/aero/utils/mapping/aero2struct_force_mapping.rst", "content": "aero2struct_force_mapping\n-------------------------\n\n.. automodule:: sharpy.aero.utils.mapping.aero2struct_force_mapping" }, { "path": "docs/source/includes/aero/utils/mapping/index.rst", "content": "Force Mapping Utilities\n+++++++++++++++++++++++\n\n\n\n.. toctree::\n\t:glob:\n\n\t./aero2struct_force_mapping\n\t./total_forces_moments\n" }, { "path": "docs/source/includes/aero/utils/mapping/total_forces_moments.rst", "content": "total_forces_moments\n--------------------\n\n.. automodule:: sharpy.aero.utils.mapping.total_forces_moments" }, { "path": "docs/source/includes/cases/coupled/X-HALE/generate_xhale/generate_naca_camber.rst", "content": "generate_naca_camber\n--------------------\n\n.. automodule:: sharpy.cases.coupled.X-HALE.generate_xhale.generate_naca_camber" }, { "path": "docs/source/includes/cases/coupled/X-HALE/generate_xhale/generate_solver_file.rst", "content": "generate_solver_file\n--------------------\n\n.. automodule:: sharpy.cases.coupled.X-HALE.generate_xhale.generate_solver_file" }, { "path": "docs/source/includes/cases/coupled/X-HALE/generate_xhale/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./generate_naca_camber\n\t./generate_solver_file\n\t./read_beam_data\n" }, { "path": "docs/source/includes/cases/coupled/X-HALE/generate_xhale/read_beam_data.rst", "content": "read_beam_data\n--------------\n\n.. automodule:: sharpy.cases.coupled.X-HALE.generate_xhale.read_beam_data" }, { "path": "docs/source/includes/cases/coupled/X-HALE/index.rst", "content": "X-hale\n------\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./generate_xhale/index\n" }, { "path": "docs/source/includes/cases/coupled/index.rst", "content": "Coupled\n-------\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./X-HALE/index\n" }, { "path": "docs/source/includes/cases/hangar/horten_wing/HortenWing.rst", "content": "HortenWing\n----------\n\n.. autoclass:: sharpy.cases.hangar.horten_wing.HortenWing\n\t:members:" }, { "path": "docs/source/includes/cases/hangar/horten_wing/index.rst", "content": "Horten Wing Class Generator\n+++++++++++++++++++++++++++\n\nHorten Wing Class Generator\nN Goizueta Nov 18\n\n\n.. toctree::\n\t:glob:\n\n\t./HortenWing\n" }, { "path": "docs/source/includes/cases/hangar/index.rst", "content": "Hangar\n------\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./horten_wing/index\n\t./richards_wing/index\n\t./swept_flying_wing/index\n" }, { "path": "docs/source/includes/cases/hangar/richards_wing/HortenWing.rst", "content": "HortenWing\n----------\n\n.. autoclass:: sharpy.cases.hangar.richards_wing.HortenWing\n\t:members:" }, { "path": "docs/source/includes/cases/hangar/richards_wing/index.rst", "content": "Simple Horten Wing as used by Richards. Baseline and simplified models\n++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n\nSimple Horten Wing as used by Richards. Baseline and simplified models\n\nRichards, P. W., Yao, Y., Herd, R. A., Hodges, D. H., & Mardanpour, P. (2016). Effect of Inertial and Constitutive\nProperties on Body-Freedom Flutter for Flying Wings. Journal of Aircraft. https://doi.org/10.2514/1.C033435\n\n\n.. toctree::\n\t:glob:\n\n\t./HortenWing\n" }, { "path": "docs/source/includes/cases/hangar/swept_flying_wing/SweptWing.rst", "content": "SweptWing\n---------\n\n.. autoclass:: sharpy.cases.hangar.swept_flying_wing.SweptWing\n\t:members:" }, { "path": "docs/source/includes/cases/hangar/swept_flying_wing/index.rst", "content": "Generic Swept Flying Wing Class Generator\n+++++++++++++++++++++++++++++++++++++++++\n\nGeneric Swept Flying Wing Class Generator\nN Goizueta Nov 18\n\n\n.. toctree::\n\t:glob:\n\n\t./SweptWing\n" }, { "path": "docs/source/includes/cases/index.rst", "content": "Cases\n-----\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./coupled/index\n\t./hangar/index\n\t./templates/index\n" }, { "path": "docs/source/includes/cases/templates/Ttail/Ttail_3beams.rst", "content": "Ttail_3beams\n------------\n\n.. autoclass:: sharpy.cases.templates.Ttail.Ttail_3beams\n\t:members:" }, { "path": "docs/source/includes/cases/templates/Ttail/Ttail_canonical.rst", "content": "Ttail_canonical\n---------------\n\n.. autoclass:: sharpy.cases.templates.Ttail.Ttail_canonical\n\t:members:" }, { "path": "docs/source/includes/cases/templates/Ttail/index.rst", "content": "Templates to build T-tail models\n++++++++++++++++++++++++++++++++\n\nTemplates to build T-tail models\nS. Maraniello, Oct 2018\n\nclasses:\n- Ttail_3beam allows to generate general T-tail models with 3-beam.\n- Ttail_canonical: builds the canonical test case as per\n Murua et al., Prog. Aerosp. Sci., 71 (2014) 54-84\n\n\n.. toctree::\n\t:glob:\n\n\t./Ttail_3beams\n\t./Ttail_canonical\n" }, { "path": "docs/source/includes/cases/templates/flying_wings/FlyingWing.rst", "content": "FlyingWing\n----------\n\n.. autoclass:: sharpy.cases.templates.flying_wings.FlyingWing\n\t:members:" }, { "path": "docs/source/includes/cases/templates/flying_wings/Goland.rst", "content": "Goland\n------\n\n.. autoclass:: sharpy.cases.templates.flying_wings.Goland\n\t:members:" }, { "path": "docs/source/includes/cases/templates/flying_wings/Pazy.rst", "content": "Pazy\n----\n\n.. autoclass:: sharpy.cases.templates.flying_wings.Pazy\n\t:members:" }, { "path": "docs/source/includes/cases/templates/flying_wings/QuasiInfinite.rst", "content": "QuasiInfinite\n-------------\n\n.. autoclass:: sharpy.cases.templates.flying_wings.QuasiInfinite\n\t:members:" }, { "path": "docs/source/includes/cases/templates/flying_wings/Smith.rst", "content": "Smith\n-----\n\n.. autoclass:: sharpy.cases.templates.flying_wings.Smith\n\t:members:" }, { "path": "docs/source/includes/cases/templates/flying_wings/index.rst", "content": "Templates to build flying wing models\n+++++++++++++++++++++++++++++++++++++\n\nTemplates to build flying wing models\nS. Maraniello, Jul 2018\n\nclasses:\n- FlyingWing: generate a flying wing model from a reduced set of input. The\nbuilt in method 'update_mass_stiff' can be re-defined by the user to enter more\ncomplex inertial/stiffness properties\n- Smith(FlyingWing): generate HALE wing model\n- Goland(FlyingWing): generate Goland wing model\n\n\n.. toctree::\n\t:glob:\n\n\t./FlyingWing\n\t./Goland\n\t./Pazy\n\t./QuasiInfinite\n\t./Smith\n" }, { "path": "docs/source/includes/cases/templates/index.rst", "content": "Templates\n---------\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./Ttail/index\n\t./flying_wings/index\n\t./template_wt/index\n" }, { "path": "docs/source/includes/cases/templates/template_wt/create_blade_coordinates.rst", "content": "create_blade_coordinates\n------------------------\n\n.. automodule:: sharpy.cases.templates.template_wt.create_blade_coordinates" }, { "path": "docs/source/includes/cases/templates/template_wt/create_node_radial_pos_from_elem_centres.rst", "content": "create_node_radial_pos_from_elem_centres\n----------------------------------------\n\n.. automodule:: sharpy.cases.templates.template_wt.create_node_radial_pos_from_elem_centres" }, { "path": "docs/source/includes/cases/templates/template_wt/generate_from_excel_type03.rst", "content": "generate_from_excel_type03\n--------------------------\n\n.. automodule:: sharpy.cases.templates.template_wt.generate_from_excel_type03" }, { "path": "docs/source/includes/cases/templates/template_wt/index.rst", "content": "template_wt\n+++++++++++\n\ntemplate_wt\n\nFunctions needed to generate a wind turbines\n\nNotes:\n To load this library: import cases.templates.template_wt as template_wt\n\n\n.. toctree::\n\t:glob:\n\n\t./create_blade_coordinates\n\t./create_node_radial_pos_from_elem_centres\n\t./generate_from_excel_type03\n\t./rotor_from_excel_type03\n\t./spar_from_excel_type04\n" }, { "path": "docs/source/includes/cases/templates/template_wt/rotor_from_excel_type03.rst", "content": "rotor_from_excel_type03\n-----------------------\n\n.. automodule:: sharpy.cases.templates.template_wt.rotor_from_excel_type03" }, { "path": "docs/source/includes/cases/templates/template_wt/spar_from_excel_type04.rst", "content": "spar_from_excel_type04\n----------------------\n\n.. automodule:: sharpy.cases.templates.template_wt.spar_from_excel_type04" }, { "path": "docs/source/includes/controllers/controlsurfacepidcontroller/ControlSurfacePidController.rst", "content": "ControlSurfacePidController\n---------------------------\n\n.. autoclass:: sharpy.controllers.controlsurfacepidcontroller.ControlSurfacePidController\n\t:members:" }, { "path": "docs/source/includes/controllers/controlsurfacepidcontroller/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./ControlSurfacePidController\n" }, { "path": "docs/source/includes/controllers/index.rst", "content": "Controllers\n-----------\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./controlsurfacepidcontroller/index\n\t./takeofftrajectorycontroller/index\n" }, { "path": "docs/source/includes/controllers/takeofftrajectorycontroller/TakeOffTrajectoryController.rst", "content": "TakeOffTrajectoryController\n---------------------------\n\n.. autoclass:: sharpy.controllers.takeofftrajectorycontroller.TakeOffTrajectoryController\n\t:members:" }, { "path": "docs/source/includes/controllers/takeofftrajectorycontroller/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./TakeOffTrajectoryController\n" }, { "path": "docs/source/includes/generators/bumpvelocityfield/BumpVelocityField.rst", "content": "BumpVelocityField\n-----------------\n\n.. autoclass:: sharpy.generators.bumpvelocityfield.BumpVelocityField\n\t:members:" }, { "path": "docs/source/includes/generators/bumpvelocityfield/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./BumpVelocityField\n" }, { "path": "docs/source/includes/generators/dynamiccontrolsurface/DynamicControlSurface.rst", "content": "DynamicControlSurface\n---------------------\n\n.. autoclass:: sharpy.generators.dynamiccontrolsurface.DynamicControlSurface\n\t:members:" }, { "path": "docs/source/includes/generators/dynamiccontrolsurface/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./DynamicControlSurface\n" }, { "path": "docs/source/includes/generators/floatingforces/FloatingForces.rst", "content": "FloatingForces\n--------------\n\n.. autoclass:: sharpy.generators.floatingforces.FloatingForces\n\t:members:" }, { "path": "docs/source/includes/generators/floatingforces/change_of_to_sharpy.rst", "content": "change_of_to_sharpy\n-------------------\n\n.. automodule:: sharpy.generators.floatingforces.change_of_to_sharpy" }, { "path": "docs/source/includes/generators/floatingforces/compute_equiv_hd_added_mass.rst", "content": "compute_equiv_hd_added_mass\n---------------------------\n\n.. automodule:: sharpy.generators.floatingforces.compute_equiv_hd_added_mass" }, { "path": "docs/source/includes/generators/floatingforces/compute_jacobian.rst", "content": "compute_jacobian\n----------------\n\n.. automodule:: sharpy.generators.floatingforces.compute_jacobian" }, { "path": "docs/source/includes/generators/floatingforces/compute_xf_zf.rst", "content": "compute_xf_zf\n-------------\n\n.. automodule:: sharpy.generators.floatingforces.compute_xf_zf" }, { "path": "docs/source/includes/generators/floatingforces/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./FloatingForces\n\t./change_of_to_sharpy\n\t./compute_equiv_hd_added_mass\n\t./compute_jacobian\n\t./compute_xf_zf\n\t./jonswap_spectrum\n\t./matrix_from_rf\n\t./noise_freq_1s\n\t./quasisteady_mooring\n\t./rename_terms\n\t./response_freq_dep_matrix\n\t./rfval\n\t./time_wave_forces\n\t./wave_radiation_damping\n" }, { "path": "docs/source/includes/generators/floatingforces/jonswap_spectrum.rst", "content": "jonswap_spectrum\n----------------\n\n.. automodule:: sharpy.generators.floatingforces.jonswap_spectrum" }, { "path": "docs/source/includes/generators/floatingforces/matrix_from_rf.rst", "content": "matrix_from_rf\n--------------\n\n.. automodule:: sharpy.generators.floatingforces.matrix_from_rf" }, { "path": "docs/source/includes/generators/floatingforces/noise_freq_1s.rst", "content": "noise_freq_1s\n-------------\n\n.. automodule:: sharpy.generators.floatingforces.noise_freq_1s" }, { "path": "docs/source/includes/generators/floatingforces/quasisteady_mooring.rst", "content": "quasisteady_mooring\n-------------------\n\n.. automodule:: sharpy.generators.floatingforces.quasisteady_mooring" }, { "path": "docs/source/includes/generators/floatingforces/rename_terms.rst", "content": "rename_terms\n------------\n\n.. automodule:: sharpy.generators.floatingforces.rename_terms" }, { "path": "docs/source/includes/generators/floatingforces/response_freq_dep_matrix.rst", "content": "response_freq_dep_matrix\n------------------------\n\n.. automodule:: sharpy.generators.floatingforces.response_freq_dep_matrix" }, { "path": "docs/source/includes/generators/floatingforces/rfval.rst", "content": "rfval\n-----\n\n.. automodule:: sharpy.generators.floatingforces.rfval" }, { "path": "docs/source/includes/generators/floatingforces/time_wave_forces.rst", "content": "time_wave_forces\n----------------\n\n.. automodule:: sharpy.generators.floatingforces.time_wave_forces" }, { "path": "docs/source/includes/generators/floatingforces/wave_radiation_damping.rst", "content": "wave_radiation_damping\n----------------------\n\n.. automodule:: sharpy.generators.floatingforces.wave_radiation_damping" }, { "path": "docs/source/includes/generators/gridbox/GridBox.rst", "content": "GridBox\n-------\n\n.. autoclass:: sharpy.generators.gridbox.GridBox\n\t:members:" }, { "path": "docs/source/includes/generators/gridbox/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./GridBox\n" }, { "path": "docs/source/includes/generators/gustvelocityfield/DARPA.rst", "content": "DARPA\n-----\n\n.. autoclass:: sharpy.generators.gustvelocityfield.DARPA\n\t:members:" }, { "path": "docs/source/includes/generators/gustvelocityfield/GustVelocityField.rst", "content": "GustVelocityField\n-----------------\n\n.. autoclass:: sharpy.generators.gustvelocityfield.GustVelocityField\n\t:members:" }, { "path": "docs/source/includes/generators/gustvelocityfield/continuous_sin.rst", "content": "continuous_sin\n--------------\n\n.. autoclass:: sharpy.generators.gustvelocityfield.continuous_sin\n\t:members:" }, { "path": "docs/source/includes/generators/gustvelocityfield/index.rst", "content": "Gust Velocity Field Generators\n++++++++++++++++++++++++++++++\n\n\nThese generators are used to create a gust velocity field. :class:`.GustVelocityField` is the main class that should be\nparsed as the ``velocity_field_input`` to the desired aerodynamic solver.\n\nThe remaining classes are the specific gust profiles and parsed as ``gust_shape``.\n\nExamples:\n The typical input to the aerodynamic solver settings would therefore read similar to:\n\n >>> aero_settings = {'': '',\n >>> 'velocity_field_generator': 'GustVelocityField',\n >>> 'velocity_field_input': {'u_inf': 1,\n >>> 'gust_shape': '',\n >>> 'gust_parameters': ''}}\n\n\n\n.. toctree::\n\t:glob:\n\n\t./DARPA\n\t./GustVelocityField\n\t./continuous_sin\n\t./lateral_one_minus_cos\n\t./one_minus_cos\n\t./span_sine\n\t./time_varying\n\t./time_varying_global\n" }, { "path": "docs/source/includes/generators/gustvelocityfield/lateral_one_minus_cos.rst", "content": "lateral_one_minus_cos\n---------------------\n\n.. autoclass:: sharpy.generators.gustvelocityfield.lateral_one_minus_cos\n\t:members:" }, { "path": "docs/source/includes/generators/gustvelocityfield/one_minus_cos.rst", "content": "one_minus_cos\n-------------\n\n.. autoclass:: sharpy.generators.gustvelocityfield.one_minus_cos\n\t:members:" }, { "path": "docs/source/includes/generators/gustvelocityfield/span_sine.rst", "content": "span_sine\n---------\n\n.. autoclass:: sharpy.generators.gustvelocityfield.span_sine\n\t:members:" }, { "path": "docs/source/includes/generators/gustvelocityfield/time_varying.rst", "content": "time_varying\n------------\n\n.. autoclass:: sharpy.generators.gustvelocityfield.time_varying\n\t:members:" }, { "path": "docs/source/includes/generators/gustvelocityfield/time_varying_global.rst", "content": "time_varying_global\n-------------------\n\n.. autoclass:: sharpy.generators.gustvelocityfield.time_varying_global\n\t:members:" }, { "path": "docs/source/includes/generators/helicoidalwake/HelicoidalWake.rst", "content": "HelicoidalWake\n--------------\n\n.. autoclass:: sharpy.generators.helicoidalwake.HelicoidalWake\n\t:members:" }, { "path": "docs/source/includes/generators/helicoidalwake/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./HelicoidalWake\n" }, { "path": "docs/source/includes/generators/index.rst", "content": "Generators\n----------\n\n\nVelocity field generators prescribe the flow conditions for your problem. For instance, you can have an aircraft at\na prescribed fixed location in a velocity field towards the aircraft. Alternatively, you can have a free moving\naircraft in a static velocity field.\n\nDynamic Control Surface generators enable the user to prescribe a certain control surface deflection in time.\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./bumpvelocityfield/index\n\t./dynamiccontrolsurface/index\n\t./floatingforces/index\n\t./gridbox/index\n\t./gustvelocityfield/index\n\t./helicoidalwake/index\n\t./modifystructure/index\n\t./polaraeroforces/index\n\t./shearvelocityfield/index\n\t./steadyvelocityfield/index\n\t./straightwake/index\n\t./trajectorygenerator/index\n\t./turbvelocityfield/index\n\t./turbvelocityfieldbts/index\n" }, { "path": "docs/source/includes/generators/modifystructure/ChangeLumpedMass.rst", "content": "ChangeLumpedMass\n----------------\n\n.. autoclass:: sharpy.generators.modifystructure.ChangeLumpedMass\n\t:members:" }, { "path": "docs/source/includes/generators/modifystructure/ChangedVariable.rst", "content": "ChangedVariable\n---------------\n\n.. autoclass:: sharpy.generators.modifystructure.ChangedVariable\n\t:members:" }, { "path": "docs/source/includes/generators/modifystructure/LumpedMassControl.rst", "content": "LumpedMassControl\n-----------------\n\n.. autoclass:: sharpy.generators.modifystructure.LumpedMassControl\n\t:members:" }, { "path": "docs/source/includes/generators/modifystructure/ModifyStructure.rst", "content": "ModifyStructure\n---------------\n\n.. autoclass:: sharpy.generators.modifystructure.ModifyStructure\n\t:members:" }, { "path": "docs/source/includes/generators/modifystructure/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./ChangeLumpedMass\n\t./ChangedVariable\n\t./LumpedMassControl\n\t./ModifyStructure\n" }, { "path": "docs/source/includes/generators/polaraeroforces/EfficiencyCorrection.rst", "content": "EfficiencyCorrection\n--------------------\n\n.. autoclass:: sharpy.generators.polaraeroforces.EfficiencyCorrection\n\t:members:" }, { "path": "docs/source/includes/generators/polaraeroforces/PolarCorrection.rst", "content": "PolarCorrection\n---------------\n\n.. autoclass:: sharpy.generators.polaraeroforces.PolarCorrection\n\t:members:" }, { "path": "docs/source/includes/generators/polaraeroforces/get_aoacl0_from_camber.rst", "content": "get_aoacl0_from_camber\n----------------------\n\n.. automodule:: sharpy.generators.polaraeroforces.get_aoacl0_from_camber" }, { "path": "docs/source/includes/generators/polaraeroforces/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./EfficiencyCorrection\n\t./PolarCorrection\n\t./get_aoacl0_from_camber\n\t./local_stability_axes\n\t./magnitude_and_direction_of_relative_velocity\n\t./span_chord\n" }, { "path": "docs/source/includes/generators/polaraeroforces/local_stability_axes.rst", "content": "local_stability_axes\n--------------------\n\n.. automodule:: sharpy.generators.polaraeroforces.local_stability_axes" }, { "path": "docs/source/includes/generators/polaraeroforces/magnitude_and_direction_of_relative_velocity.rst", "content": "magnitude_and_direction_of_relative_velocity\n--------------------------------------------\n\n.. automodule:: sharpy.generators.polaraeroforces.magnitude_and_direction_of_relative_velocity" }, { "path": "docs/source/includes/generators/polaraeroforces/span_chord.rst", "content": "span_chord\n----------\n\n.. automodule:: sharpy.generators.polaraeroforces.span_chord" }, { "path": "docs/source/includes/generators/shearvelocityfield/ShearVelocityField.rst", "content": "ShearVelocityField\n------------------\n\n.. autoclass:: sharpy.generators.shearvelocityfield.ShearVelocityField\n\t:members:" }, { "path": "docs/source/includes/generators/shearvelocityfield/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./ShearVelocityField\n" }, { "path": "docs/source/includes/generators/steadyvelocityfield/SteadyVelocityField.rst", "content": "SteadyVelocityField\n-------------------\n\n.. autoclass:: sharpy.generators.steadyvelocityfield.SteadyVelocityField\n\t:members:" }, { "path": "docs/source/includes/generators/steadyvelocityfield/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./SteadyVelocityField\n" }, { "path": "docs/source/includes/generators/straightwake/StraightWake.rst", "content": "StraightWake\n------------\n\n.. autoclass:: sharpy.generators.straightwake.StraightWake\n\t:members:" }, { "path": "docs/source/includes/generators/straightwake/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./StraightWake\n" }, { "path": "docs/source/includes/generators/trajectorygenerator/TrajectoryGenerator.rst", "content": "TrajectoryGenerator\n-------------------\n\n.. autoclass:: sharpy.generators.trajectorygenerator.TrajectoryGenerator\n\t:members:" }, { "path": "docs/source/includes/generators/trajectorygenerator/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./TrajectoryGenerator\n" }, { "path": "docs/source/includes/generators/turbvelocityfield/TurbVelocityField.rst", "content": "TurbVelocityField\n-----------------\n\n.. autoclass:: sharpy.generators.turbvelocityfield.TurbVelocityField\n\t:members:" }, { "path": "docs/source/includes/generators/turbvelocityfield/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./TurbVelocityField\n" }, { "path": "docs/source/includes/generators/turbvelocityfieldbts/TurbVelocityFieldBts.rst", "content": "TurbVelocityFieldBts\n--------------------\n\n.. autoclass:: sharpy.generators.turbvelocityfieldbts.TurbVelocityFieldBts\n\t:members:" }, { "path": "docs/source/includes/generators/turbvelocityfieldbts/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./TurbVelocityFieldBts\n" }, { "path": "docs/source/includes/index.rst", "content": "SHARPy Source Code\n------------------\n\nThe core SHARPy documentation is found herein.\n\n.. note::\n\n\tThe docs are still a work in progress and therefore, most functions/classes with which there is not much user interaction are not fully documented. We would appreciate any help by means of you contributing to our growing documentation!\n\n\nIf you feel that a function/class is not well documented and, hence, you cannot use it, feel free to raise an issue so that we can improve it.\n\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./aero/index\n\t./cases/index\n\t./controllers/index\n\t./generators/index\n\t./io/index\n\t./linear/index\n\t./rom/index\n\t./structure/index\n\t./utils/index\n" }, { "path": "docs/source/includes/io/index.rst", "content": "UDP Input/Output\n----------------\n\n\n\nThis package contains the routines for the SHARPy input and output via UDP.\n\nThe main interface is performed through the :class:`~sharpy.io.network_interface.NetworkLoader`\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./inout_variables/index\n\t./network_interface/index\n" }, { "path": "docs/source/includes/io/inout_variables/SetOfVariables.rst", "content": "SetOfVariables\n--------------\n\n.. autoclass:: sharpy.io.inout_variables.SetOfVariables\n\t:members:" }, { "path": "docs/source/includes/io/inout_variables/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./SetOfVariables\n" }, { "path": "docs/source/includes/io/network_interface/InNetwork.rst", "content": "InNetwork\n---------\n\n.. autoclass:: sharpy.io.network_interface.InNetwork\n\t:members:" }, { "path": "docs/source/includes/io/network_interface/Network.rst", "content": "Network\n-------\n\n.. autoclass:: sharpy.io.network_interface.Network\n\t:members:" }, { "path": "docs/source/includes/io/network_interface/NetworkLoader.rst", "content": "NetworkLoader\n-------------\n\n.. autoclass:: sharpy.io.network_interface.NetworkLoader\n\t:members:" }, { "path": "docs/source/includes/io/network_interface/OutNetwork.rst", "content": "OutNetwork\n----------\n\n.. autoclass:: sharpy.io.network_interface.OutNetwork\n\t:members:" }, { "path": "docs/source/includes/io/network_interface/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./InNetwork\n\t./Network\n\t./NetworkLoader\n\t./OutNetwork\n" }, { "path": "docs/source/includes/linear/assembler/index.rst", "content": "Assembler\n---------\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./lincontrolsurfacedeflector/index\n\t./linearaeroelastic/index\n\t./linearbeam/index\n\t./lineargustassembler/index\n\t./linearuvlm/index\n" }, { "path": "docs/source/includes/linear/assembler/lincontrolsurfacedeflector/LinControlSurfaceDeflector.rst", "content": "LinControlSurfaceDeflector\n--------------------------\n\n.. autoclass:: sharpy.linear.assembler.lincontrolsurfacedeflector.LinControlSurfaceDeflector\n\t:members:" }, { "path": "docs/source/includes/linear/assembler/lincontrolsurfacedeflector/der_R_arbitrary_axis_times_v.rst", "content": "der_R_arbitrary_axis_times_v\n----------------------------\n\n.. automodule:: sharpy.linear.assembler.lincontrolsurfacedeflector.der_R_arbitrary_axis_times_v" }, { "path": "docs/source/includes/linear/assembler/lincontrolsurfacedeflector/index.rst", "content": "Control surface deflector for linear systems\n++++++++++++++++++++++++++++++++++++++++++++\n\nControl surface deflector for linear systems\n\n\n.. toctree::\n\t:glob:\n\n\t./LinControlSurfaceDeflector\n\t./der_R_arbitrary_axis_times_v\n" }, { "path": "docs/source/includes/linear/assembler/linearaeroelastic/LinearAeroelastic.rst", "content": "LinearAeroelastic\n-----------------\n\n.. autoclass:: sharpy.linear.assembler.linearaeroelastic.LinearAeroelastic\n\t:members:" }, { "path": "docs/source/includes/linear/assembler/linearaeroelastic/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./LinearAeroelastic\n" }, { "path": "docs/source/includes/linear/assembler/linearbeam/LinearBeam.rst", "content": "LinearBeam\n----------\n\n.. autoclass:: sharpy.linear.assembler.linearbeam.LinearBeam\n\t:members:" }, { "path": "docs/source/includes/linear/assembler/linearbeam/index.rst", "content": "Linear State Beam Element Class\n+++++++++++++++++++++++++++++++\n\nLinear State Beam Element Class\n\n\n\n.. toctree::\n\t:glob:\n\n\t./LinearBeam\n" }, { "path": "docs/source/includes/linear/assembler/lineargustassembler/LeadingEdge.rst", "content": "LeadingEdge\n-----------\n\n.. autoclass:: sharpy.linear.assembler.lineargustassembler.LeadingEdge\n\t:members:" }, { "path": "docs/source/includes/linear/assembler/lineargustassembler/MultiLeadingEdge.rst", "content": "MultiLeadingEdge\n----------------\n\n.. autoclass:: sharpy.linear.assembler.lineargustassembler.MultiLeadingEdge\n\t:members:" }, { "path": "docs/source/includes/linear/assembler/lineargustassembler/campbell.rst", "content": "campbell\n--------\n\n.. automodule:: sharpy.linear.assembler.lineargustassembler.campbell" }, { "path": "docs/source/includes/linear/assembler/lineargustassembler/gust_from_string.rst", "content": "gust_from_string\n----------------\n\n.. automodule:: sharpy.linear.assembler.lineargustassembler.gust_from_string" }, { "path": "docs/source/includes/linear/assembler/lineargustassembler/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./LeadingEdge\n\t./MultiLeadingEdge\n\t./campbell\n\t./gust_from_string\n\t./spanwise_interpolation\n" }, { "path": "docs/source/includes/linear/assembler/lineargustassembler/spanwise_interpolation.rst", "content": "spanwise_interpolation\n----------------------\n\n.. automodule:: sharpy.linear.assembler.lineargustassembler.spanwise_interpolation" }, { "path": "docs/source/includes/linear/assembler/linearuvlm/LinearUVLM.rst", "content": "LinearUVLM\n----------\n\n.. autoclass:: sharpy.linear.assembler.linearuvlm.LinearUVLM\n\t:members:" }, { "path": "docs/source/includes/linear/assembler/linearuvlm/index.rst", "content": "Linear UVLM State Space System\n++++++++++++++++++++++++++++++\n\nLinear UVLM State Space System\n\n\n.. toctree::\n\t:glob:\n\n\t./LinearUVLM\n" }, { "path": "docs/source/includes/linear/index.rst", "content": "Linear SHARPy\n-------------\n\n\nThe code included herein enables the assembly of linearised state-space systems based on the previous solution\nof a nonlinear problem that will be used as linearisation reference.\n\nThe code is structured in the following way:\n\n * Assembler: different state-spaces to assemble, from only structural/aerodynamic to fully coupled aeroelastic\n\n * Src: source code required for the linearisation and utilities for the manipulation of state-space elements\n\n\nReferences:\n\n Maraniello, S. , Palacios, R.. State-Space Realizations and Internal Balancing in Potential-Flow Aerodynamics\n with Arbitrary Kinematics. AIAA Journal, Vol. 57, No.6, June 2019\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./assembler/index\n\t./src/index\n" }, { "path": "docs/source/includes/linear/src/assembly/AICs.rst", "content": "AICs\n----\n\n.. automodule:: sharpy.linear.src.assembly.AICs" }, { "path": "docs/source/includes/linear/src/assembly/dfqsdgamma_vrel0.rst", "content": "dfqsdgamma_vrel0\n----------------\n\n.. automodule:: sharpy.linear.src.assembly.dfqsdgamma_vrel0" }, { "path": "docs/source/includes/linear/src/assembly/dfqsduinput.rst", "content": "dfqsduinput\n-----------\n\n.. automodule:: sharpy.linear.src.assembly.dfqsduinput" }, { "path": "docs/source/includes/linear/src/assembly/dfqsdvind_gamma.rst", "content": "dfqsdvind_gamma\n---------------\n\n.. automodule:: sharpy.linear.src.assembly.dfqsdvind_gamma" }, { "path": "docs/source/includes/linear/src/assembly/dfqsdvind_zeta.rst", "content": "dfqsdvind_zeta\n--------------\n\n.. automodule:: sharpy.linear.src.assembly.dfqsdvind_zeta" }, { "path": "docs/source/includes/linear/src/assembly/dfqsdzeta_omega.rst", "content": "dfqsdzeta_omega\n---------------\n\n.. automodule:: sharpy.linear.src.assembly.dfqsdzeta_omega" }, { "path": "docs/source/includes/linear/src/assembly/dfqsdzeta_vrel0.rst", "content": "dfqsdzeta_vrel0\n---------------\n\n.. automodule:: sharpy.linear.src.assembly.dfqsdzeta_vrel0" }, { "path": "docs/source/includes/linear/src/assembly/dfunstdgamma_dot.rst", "content": "dfunstdgamma_dot\n----------------\n\n.. automodule:: sharpy.linear.src.assembly.dfunstdgamma_dot" }, { "path": "docs/source/includes/linear/src/assembly/dvinddzeta.rst", "content": "dvinddzeta\n----------\n\n.. automodule:: sharpy.linear.src.assembly.dvinddzeta" }, { "path": "docs/source/includes/linear/src/assembly/dvinddzeta_cpp.rst", "content": "dvinddzeta_cpp\n--------------\n\n.. automodule:: sharpy.linear.src.assembly.dvinddzeta_cpp" }, { "path": "docs/source/includes/linear/src/assembly/eval_panel_cpp.rst", "content": "eval_panel_cpp\n--------------\n\n.. automodule:: sharpy.linear.src.assembly.eval_panel_cpp" }, { "path": "docs/source/includes/linear/src/assembly/index.rst", "content": "Assembly of linearised UVLM system\n++++++++++++++++++++++++++++++++++\n\n\nS. Maraniello, 25 May 2018\n\nIncludes:\n - Boundary conditions methods:\n - AICs: allocate aero influence coefficient matrices of multi-surfaces\n configurations\n - ``nc_dqcdzeta_Sin_to_Sout``: derivative matrix of ``nc*dQ/dzeta``\n where Q is the induced velocity at the bound collocation points of one\n surface to another.\n - ``nc_dqcdzeta_coll``: assembles ``nc_dqcdzeta_coll_Sin_to_Sout`` matrices in\n multi-surfaces configurations\n - ``uc_dncdzeta``: assemble derivative matrix dnc/dzeta*Uc at bound collocation\n points\n\n\n.. toctree::\n\t:glob:\n\n\t./AICs\n\t./dfqsdgamma_vrel0\n\t./dfqsduinput\n\t./dfqsdvind_gamma\n\t./dfqsdvind_zeta\n\t./dfqsdzeta_omega\n\t./dfqsdzeta_vrel0\n\t./dfunstdgamma_dot\n\t./dvinddzeta\n\t./dvinddzeta_cpp\n\t./eval_panel_cpp\n\t./nc_domegazetadzeta\n\t./nc_dqcdzeta\n\t./nc_dqcdzeta_Sin_to_Sout\n\t./test_wake_prop_term\n\t./uc_dncdzeta\n\t./wake_prop\n\t./wake_prop_from_dimensions\n" }, { "path": "docs/source/includes/linear/src/assembly/nc_domegazetadzeta.rst", "content": "nc_domegazetadzeta\n------------------\n\n.. automodule:: sharpy.linear.src.assembly.nc_domegazetadzeta" }, { "path": "docs/source/includes/linear/src/assembly/nc_dqcdzeta.rst", "content": "nc_dqcdzeta\n-----------\n\n.. automodule:: sharpy.linear.src.assembly.nc_dqcdzeta" }, { "path": "docs/source/includes/linear/src/assembly/nc_dqcdzeta_Sin_to_Sout.rst", "content": "nc_dqcdzeta_Sin_to_Sout\n-----------------------\n\n.. automodule:: sharpy.linear.src.assembly.nc_dqcdzeta_Sin_to_Sout" }, { "path": "docs/source/includes/linear/src/assembly/test_wake_prop_term.rst", "content": "test_wake_prop_term\n-------------------\n\n.. automodule:: sharpy.linear.src.assembly.test_wake_prop_term" }, { "path": "docs/source/includes/linear/src/assembly/uc_dncdzeta.rst", "content": "uc_dncdzeta\n-----------\n\n.. automodule:: sharpy.linear.src.assembly.uc_dncdzeta" }, { "path": "docs/source/includes/linear/src/assembly/wake_prop.rst", "content": "wake_prop\n---------\n\n.. automodule:: sharpy.linear.src.assembly.wake_prop" }, { "path": "docs/source/includes/linear/src/assembly/wake_prop_from_dimensions.rst", "content": "wake_prop_from_dimensions\n-------------------------\n\n.. automodule:: sharpy.linear.src.assembly.wake_prop_from_dimensions" }, { "path": "docs/source/includes/linear/src/gridmapping/AeroGridMap.rst", "content": "AeroGridMap\n-----------\n\n.. autoclass:: sharpy.linear.src.gridmapping.AeroGridMap\n\t:members:" }, { "path": "docs/source/includes/linear/src/gridmapping/index.rst", "content": "Mapping methods for bound surface panels\n++++++++++++++++++++++++++++++++++++++++\n\n\nS. Maraniello, 19 May 2018\n\n\n.. toctree::\n\t:glob:\n\n\t./AeroGridMap\n" }, { "path": "docs/source/includes/linear/src/index.rst", "content": "Linearised System Source Code\n-----------------------------\n\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./assembly/index\n\t./gridmapping/index\n\t./interp/index\n\t./lib_dbiot/index\n\t./lib_ucdncdzeta/index\n\t./libfit/index\n\t./libsparse/index\n\t./libss/index\n\t./lin_aeroelastic/index\n\t./lin_utils/index\n\t./lingebm/index\n\t./linuvlm/index\n\t./multisurfaces/index\n\t./surface/index\n" }, { "path": "docs/source/includes/linear/src/interp/get_Wnv_vector.rst", "content": "get_Wnv_vector\n--------------\n\n.. automodule:: sharpy.linear.src.interp.get_Wnv_vector" }, { "path": "docs/source/includes/linear/src/interp/get_Wvc_scalar.rst", "content": "get_Wvc_scalar\n--------------\n\n.. automodule:: sharpy.linear.src.interp.get_Wvc_scalar" }, { "path": "docs/source/includes/linear/src/interp/get_panel_wcv.rst", "content": "get_panel_wcv\n-------------\n\n.. automodule:: sharpy.linear.src.interp.get_panel_wcv" }, { "path": "docs/source/includes/linear/src/interp/index.rst", "content": "Defines interpolation methods (geometrically-exact) and matrices (linearisation)\n++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n\nDefines interpolation methods (geometrically-exact) and matrices (linearisation)\nS. Maraniello, 20 May 2018\n\n\n.. toctree::\n\t:glob:\n\n\t./get_Wnv_vector\n\t./get_Wvc_scalar\n\t./get_panel_wcv\n" }, { "path": "docs/source/includes/linear/src/lib_dbiot/Dvcross_by_skew3d.rst", "content": "Dvcross_by_skew3d\n-----------------\n\n.. automodule:: sharpy.linear.src.lib_dbiot.Dvcross_by_skew3d" }, { "path": "docs/source/includes/linear/src/lib_dbiot/eval_panel_comp.rst", "content": "eval_panel_comp\n---------------\n\n.. automodule:: sharpy.linear.src.lib_dbiot.eval_panel_comp" }, { "path": "docs/source/includes/linear/src/lib_dbiot/eval_panel_cpp.rst", "content": "eval_panel_cpp\n--------------\n\n.. automodule:: sharpy.linear.src.lib_dbiot.eval_panel_cpp" }, { "path": "docs/source/includes/linear/src/lib_dbiot/eval_panel_exp.rst", "content": "eval_panel_exp\n--------------\n\n.. automodule:: sharpy.linear.src.lib_dbiot.eval_panel_exp" }, { "path": "docs/source/includes/linear/src/lib_dbiot/eval_panel_fast.rst", "content": "eval_panel_fast\n---------------\n\n.. automodule:: sharpy.linear.src.lib_dbiot.eval_panel_fast" }, { "path": "docs/source/includes/linear/src/lib_dbiot/eval_panel_fast_coll.rst", "content": "eval_panel_fast_coll\n--------------------\n\n.. automodule:: sharpy.linear.src.lib_dbiot.eval_panel_fast_coll" }, { "path": "docs/source/includes/linear/src/lib_dbiot/eval_seg_comp_loop.rst", "content": "eval_seg_comp_loop\n------------------\n\n.. automodule:: sharpy.linear.src.lib_dbiot.eval_seg_comp_loop" }, { "path": "docs/source/includes/linear/src/lib_dbiot/eval_seg_exp.rst", "content": "eval_seg_exp\n------------\n\n.. automodule:: sharpy.linear.src.lib_dbiot.eval_seg_exp" }, { "path": "docs/source/includes/linear/src/lib_dbiot/eval_seg_exp_loop.rst", "content": "eval_seg_exp_loop\n-----------------\n\n.. automodule:: sharpy.linear.src.lib_dbiot.eval_seg_exp_loop" }, { "path": "docs/source/includes/linear/src/lib_dbiot/index.rst", "content": "Induced Velocity Derivatives\n++++++++++++++++++++++++++++\n\n\nCalculate derivatives of induced velocity.\n\nMethods:\n\n- eval_seg_exp and eval_seg_exp_loop: profide ders in format\n [Q_{x,y,z},ZetaPoint_{x,y,z}]\n and use fully-expanded analytical formula.\n- eval_panel_exp: iterates through whole panel\n\n- eval_seg_comp and eval_seg_comp_loop: profide ders in format\n [Q_{x,y,z},ZetaPoint_{x,y,z}]\n and use compact analytical formula.\n\n\n.. toctree::\n\t:glob:\n\n\t./Dvcross_by_skew3d\n\t./eval_panel_comp\n\t./eval_panel_cpp\n\t./eval_panel_exp\n\t./eval_panel_fast\n\t./eval_panel_fast_coll\n\t./eval_seg_comp_loop\n\t./eval_seg_exp\n\t./eval_seg_exp_loop\n" }, { "path": "docs/source/includes/linear/src/lib_ucdncdzeta/eval.rst", "content": "eval\n----\n\n.. automodule:: sharpy.linear.src.lib_ucdncdzeta.eval" }, { "path": "docs/source/includes/linear/src/lib_ucdncdzeta/index.rst", "content": "Induced Velocity Derivatives with respect to Panel Normal\n+++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n\n\nCalculate derivative of\n\n .. math:: \\boldsymbol{u}_c\\frac{\\partial\\boldsymbol{n}_c}{\\partial\\boldsymbol{zeta}}\n\nwith respect to local panel coordinates.\n\n\n.. toctree::\n\t:glob:\n\n\t./eval\n" }, { "path": "docs/source/includes/linear/src/libfit/fitfrd.rst", "content": "fitfrd\n------\n\n.. automodule:: sharpy.linear.src.libfit.fitfrd" }, { "path": "docs/source/includes/linear/src/libfit/get_rfa_res.rst", "content": "get_rfa_res\n-----------\n\n.. automodule:: sharpy.linear.src.libfit.get_rfa_res" }, { "path": "docs/source/includes/linear/src/libfit/get_rfa_res_norm.rst", "content": "get_rfa_res_norm\n----------------\n\n.. automodule:: sharpy.linear.src.libfit.get_rfa_res_norm" }, { "path": "docs/source/includes/linear/src/libfit/index.rst", "content": "Fitting Tools Library\n+++++++++++++++++++++\n\n\n@author: Salvatore Maraniello\n\n@date: 15 Jan 2018\n\n\n.. toctree::\n\t:glob:\n\n\t./fitfrd\n\t./get_rfa_res\n\t./get_rfa_res_norm\n\t./poly_fit\n\t./rfa\n\t./rfa_fit_dev\n\t./rfa_mimo\n\t./rfader\n" }, { "path": "docs/source/includes/linear/src/libfit/poly_fit.rst", "content": "poly_fit\n--------\n\n.. automodule:: sharpy.linear.src.libfit.poly_fit" }, { "path": "docs/source/includes/linear/src/libfit/rfa.rst", "content": "rfa\n---\n\n.. automodule:: sharpy.linear.src.libfit.rfa" }, { "path": "docs/source/includes/linear/src/libfit/rfa_fit_dev.rst", "content": "rfa_fit_dev\n-----------\n\n.. automodule:: sharpy.linear.src.libfit.rfa_fit_dev" }, { "path": "docs/source/includes/linear/src/libfit/rfa_mimo.rst", "content": "rfa_mimo\n--------\n\n.. automodule:: sharpy.linear.src.libfit.rfa_mimo" }, { "path": "docs/source/includes/linear/src/libfit/rfader.rst", "content": "rfader\n------\n\n.. automodule:: sharpy.linear.src.libfit.rfader" }, { "path": "docs/source/includes/linear/src/libsparse/block_dot.rst", "content": "block_dot\n---------\n\n.. automodule:: sharpy.linear.src.libsparse.block_dot" }, { "path": "docs/source/includes/linear/src/libsparse/block_matrix_dot_vector.rst", "content": "block_matrix_dot_vector\n-----------------------\n\n.. automodule:: sharpy.linear.src.libsparse.block_matrix_dot_vector" }, { "path": "docs/source/includes/linear/src/libsparse/block_sum.rst", "content": "block_sum\n---------\n\n.. automodule:: sharpy.linear.src.libsparse.block_sum" }, { "path": "docs/source/includes/linear/src/libsparse/csc_matrix.rst", "content": "csc_matrix\n----------\n\n.. autoclass:: sharpy.linear.src.libsparse.csc_matrix\n\t:members:" }, { "path": "docs/source/includes/linear/src/libsparse/dense.rst", "content": "dense\n-----\n\n.. automodule:: sharpy.linear.src.libsparse.dense" }, { "path": "docs/source/includes/linear/src/libsparse/dot.rst", "content": "dot\n---\n\n.. automodule:: sharpy.linear.src.libsparse.dot" }, { "path": "docs/source/includes/linear/src/libsparse/eye_as.rst", "content": "eye_as\n------\n\n.. automodule:: sharpy.linear.src.libsparse.eye_as" }, { "path": "docs/source/includes/linear/src/libsparse/index.rst", "content": "Collect tools to manipulate sparse and/or mixed dense/sparse matrices.\n++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n\nCollect tools to manipulate sparse and/or mixed dense/sparse matrices.\n\nauthor: S. Maraniello\ndate: Dec 2018\n\nComment: manipulating large linear system may require using both dense and sparse\nmatrices. While numpy/scipy automatically handle most operations between mixed\ndense/sparse arrays, some (e.g. dot product) require more attention. This\nlibrary collects methods to handle these situations.\n\nClasses:\nscipy.sparse matrices are wrapped so as to ensure compatibility with numpy arrays\nupon conversion to dense.\n- csc_matrix: this is a wrapper of scipy.csc_matrix.\n- SupportedTypes: types supported for operations\n- WarningTypes: due to some bugs in scipy (v.1.1.0), sum (+) operations between\nnp.ndarray and scipy.sparse matrices can result in numpy.matrixlib.defmatrix.matrix\ntypes. This list contains such undesired types that can result from dense/sparse\noperations and raises a warning if required.\n(b) convert these types into numpy.ndarrays.\n\nMethods:\n- dot: handles matrix dot products across different types.\n- solve: solves linear systems Ax=b with A and b dense, sparse or mixed.\n- dense: convert matrix to numpy array\n\nWarning:\n- only sparse types into SupportedTypes are supported!\n\nTo Do:\n- move these methods into an algebra module?\n\n\n.. toctree::\n\t:glob:\n\n\t./block_dot\n\t./block_matrix_dot_vector\n\t./block_sum\n\t./csc_matrix\n\t./dense\n\t./dot\n\t./eye_as\n\t./solve\n\t./zeros_as\n" }, { "path": "docs/source/includes/linear/src/libsparse/solve.rst", "content": "solve\n-----\n\n.. automodule:: sharpy.linear.src.libsparse.solve" }, { "path": "docs/source/includes/linear/src/libsparse/zeros_as.rst", "content": "zeros_as\n--------\n\n.. automodule:: sharpy.linear.src.libsparse.zeros_as" }, { "path": "docs/source/includes/linear/src/libss/Hnorm_from_freq_resp.rst", "content": "Hnorm_from_freq_resp\n--------------------\n\n.. automodule:: sharpy.linear.src.libss.Hnorm_from_freq_resp" }, { "path": "docs/source/includes/linear/src/libss/SSconv.rst", "content": "SSconv\n------\n\n.. automodule:: sharpy.linear.src.libss.SSconv" }, { "path": "docs/source/includes/linear/src/libss/SSderivative.rst", "content": "SSderivative\n------------\n\n.. automodule:: sharpy.linear.src.libss.SSderivative" }, { "path": "docs/source/includes/linear/src/libss/SSintegr.rst", "content": "SSintegr\n--------\n\n.. automodule:: sharpy.linear.src.libss.SSintegr" }, { "path": "docs/source/includes/linear/src/libss/StateSpace.rst", "content": "StateSpace\n----------\n\n.. autoclass:: sharpy.linear.src.libss.StateSpace\n\t:members:" }, { "path": "docs/source/includes/linear/src/libss/addGain.rst", "content": "addGain\n-------\n\n.. automodule:: sharpy.linear.src.libss.addGain" }, { "path": "docs/source/includes/linear/src/libss/adjust_phase.rst", "content": "adjust_phase\n------------\n\n.. automodule:: sharpy.linear.src.libss.adjust_phase" }, { "path": "docs/source/includes/linear/src/libss/build_SS_poly.rst", "content": "build_SS_poly\n-------------\n\n.. automodule:: sharpy.linear.src.libss.build_SS_poly" }, { "path": "docs/source/includes/linear/src/libss/butter.rst", "content": "butter\n------\n\n.. automodule:: sharpy.linear.src.libss.butter" }, { "path": "docs/source/includes/linear/src/libss/compare_ss.rst", "content": "compare_ss\n----------\n\n.. automodule:: sharpy.linear.src.libss.compare_ss" }, { "path": "docs/source/includes/linear/src/libss/couple.rst", "content": "couple\n------\n\n.. automodule:: sharpy.linear.src.libss.couple" }, { "path": "docs/source/includes/linear/src/libss/disc2cont.rst", "content": "disc2cont\n---------\n\n.. automodule:: sharpy.linear.src.libss.disc2cont" }, { "path": "docs/source/includes/linear/src/libss/eigvals.rst", "content": "eigvals\n-------\n\n.. automodule:: sharpy.linear.src.libss.eigvals" }, { "path": "docs/source/includes/linear/src/libss/freqresp.rst", "content": "freqresp\n--------\n\n.. automodule:: sharpy.linear.src.libss.freqresp" }, { "path": "docs/source/includes/linear/src/libss/get_freq_from_eigs.rst", "content": "get_freq_from_eigs\n------------------\n\n.. automodule:: sharpy.linear.src.libss.get_freq_from_eigs" }, { "path": "docs/source/includes/linear/src/libss/index.rst", "content": "Linear Time Invariant systems\n+++++++++++++++++++++++++++++\n\nLinear Time Invariant systems\nauthor: S. Maraniello\ndate: 15 Sep 2017 (still basement...)\n\nLibrary of methods to build/manipulate state-space models. The module supports\nthe sparse arrays types defined in libsparse.\n\nThe module includes:\n\nClasses:\n- StateSpace: provides a class to build DLTI/LTI systems with full and/or sparse\n\tmatrices and wraps many of the methods in these library. Methods include:\n\t- freqresp: wraps the freqresp function\n\t- addGain: adds gains in input/output. This is not a wrapper of addGain, as\n\tthe system matrices are overwritten\n\nMethods for state-space manipulation:\n- couple: feedback coupling. Does not support sparsity\n- freqresp: calculate frequency response. Supports sparsity.\n- series: series connection between systems\n- parallel: parallel connection between systems\n- SSconv: convert state-space model with predictions and delays\n- addGain: add gains to state-space model.\n- join2: merge two state-space models into one.\n- join: merge a list of state-space models into one.\n- sum state-space models and/or gains\n- scale_SS: scale state-space model\n- simulate: simulates discrete time solution\n- Hnorm_from_freq_resp: compute H norm of a frequency response\n- adjust_phase: remove discontinuities from a frequency response\n\nSpecial Models:\n- SSderivative: produces DLTI of a numerical derivative scheme\n- SSintegr: produces DLTI of an integration scheme\n- build_SS_poly: build state-space model with polynomial terms.\n\nFiltering:\n- butter\n\nUtilities:\n- get_freq_from_eigs: clculate frequency corresponding to eigenvalues\n\nComments:\n- the module supports sparse matrices hence relies on libsparse.\n\nto do:\n\t- remove unnecessary coupling routines\n\t- couple function can handle sparse matrices but only outputs dense matrices\n\t\t- verify if typical coupled systems are sparse\n\t\t- update routine\n\t\t- add method to automatically determine whether to use sparse or dense?\n\n\n.. toctree::\n\t:glob:\n\n\t./Hnorm_from_freq_resp\n\t./SSconv\n\t./SSderivative\n\t./SSintegr\n\t./StateSpace\n\t./addGain\n\t./adjust_phase\n\t./build_SS_poly\n\t./butter\n\t./compare_ss\n\t./couple\n\t./disc2cont\n\t./eigvals\n\t./freqresp\n\t./get_freq_from_eigs\n\t./join\n\t./join2\n\t./parallel\n\t./project\n\t./random_ss\n\t./retain_inout_channels\n\t./scale_SS\n\t./series\n\t./simulate\n\t./ss_block\n\t./ss_to_scipy\n\t./sum_ss\n" }, { "path": "docs/source/includes/linear/src/libss/join.rst", "content": "join\n----\n\n.. automodule:: sharpy.linear.src.libss.join" }, { "path": "docs/source/includes/linear/src/libss/join2.rst", "content": "join2\n-----\n\n.. automodule:: sharpy.linear.src.libss.join2" }, { "path": "docs/source/includes/linear/src/libss/parallel.rst", "content": "parallel\n--------\n\n.. automodule:: sharpy.linear.src.libss.parallel" }, { "path": "docs/source/includes/linear/src/libss/project.rst", "content": "project\n-------\n\n.. automodule:: sharpy.linear.src.libss.project" }, { "path": "docs/source/includes/linear/src/libss/random_ss.rst", "content": "random_ss\n---------\n\n.. automodule:: sharpy.linear.src.libss.random_ss" }, { "path": "docs/source/includes/linear/src/libss/retain_inout_channels.rst", "content": "retain_inout_channels\n---------------------\n\n.. automodule:: sharpy.linear.src.libss.retain_inout_channels" }, { "path": "docs/source/includes/linear/src/libss/scale_SS.rst", "content": "scale_SS\n--------\n\n.. automodule:: sharpy.linear.src.libss.scale_SS" }, { "path": "docs/source/includes/linear/src/libss/series.rst", "content": "series\n------\n\n.. automodule:: sharpy.linear.src.libss.series" }, { "path": "docs/source/includes/linear/src/libss/simulate.rst", "content": "simulate\n--------\n\n.. automodule:: sharpy.linear.src.libss.simulate" }, { "path": "docs/source/includes/linear/src/libss/ss_block.rst", "content": "ss_block\n--------\n\n.. autoclass:: sharpy.linear.src.libss.ss_block\n\t:members:" }, { "path": "docs/source/includes/linear/src/libss/ss_to_scipy.rst", "content": "ss_to_scipy\n-----------\n\n.. automodule:: sharpy.linear.src.libss.ss_to_scipy" }, { "path": "docs/source/includes/linear/src/libss/sum_ss.rst", "content": "sum_ss\n------\n\n.. automodule:: sharpy.linear.src.libss.sum_ss" }, { "path": "docs/source/includes/linear/src/lin_aeroelastic/LinAeroEla.rst", "content": "LinAeroEla\n----------\n\n.. autoclass:: sharpy.linear.src.lin_aeroelastic.LinAeroEla\n\t:members:" }, { "path": "docs/source/includes/linear/src/lin_aeroelastic/index.rst", "content": "Linear aeroelastic model based on coupled GEBM + UVLM\n+++++++++++++++++++++++++++++++++++++++++++++++++++++\n\nLinear aeroelastic model based on coupled GEBM + UVLM\nS. Maraniello, Jul 2018\n\n\n.. toctree::\n\t:glob:\n\n\t./LinAeroEla\n" }, { "path": "docs/source/includes/linear/src/lin_utils/Info.rst", "content": "Info\n----\n\n.. autoclass:: sharpy.linear.src.lin_utils.Info\n\t:members:" }, { "path": "docs/source/includes/linear/src/lin_utils/comp_tot_force.rst", "content": "comp_tot_force\n--------------\n\n.. automodule:: sharpy.linear.src.lin_utils.comp_tot_force" }, { "path": "docs/source/includes/linear/src/lin_utils/extract_from_data.rst", "content": "extract_from_data\n-----------------\n\n.. automodule:: sharpy.linear.src.lin_utils.extract_from_data" }, { "path": "docs/source/includes/linear/src/lin_utils/index.rst", "content": "Utilities functions for linear analysis\n+++++++++++++++++++++++++++++++++++++++\n\nUtilities functions for linear analysis\n\n\n.. toctree::\n\t:glob:\n\n\t./Info\n\t./comp_tot_force\n\t./extract_from_data\n\t./solve_linear\n" }, { "path": "docs/source/includes/linear/src/lin_utils/solve_linear.rst", "content": "solve_linear\n------------\n\n.. automodule:: sharpy.linear.src.lin_utils.solve_linear" }, { "path": "docs/source/includes/linear/src/lingebm/FlexDynamic.rst", "content": "FlexDynamic\n-----------\n\n.. autoclass:: sharpy.linear.src.lingebm.FlexDynamic\n\t:members:" }, { "path": "docs/source/includes/linear/src/lingebm/index.rst", "content": "Linear beam model class\n+++++++++++++++++++++++\n\nLinear beam model class\n\nS. Maraniello, Aug 2018\nN. Goizueta\n\n\n.. toctree::\n\t:glob:\n\n\t./FlexDynamic\n\t./newmark_ss\n\t./sort_eigvals\n" }, { "path": "docs/source/includes/linear/src/lingebm/newmark_ss.rst", "content": "newmark_ss\n----------\n\n.. autofunction:: sharpy.linear.src.lingebm.newmark_ss\n" }, { "path": "docs/source/includes/linear/src/lingebm/sort_eigvals.rst", "content": "sort_eigvals\n------------\n\n.. automodule:: sharpy.linear.src.lingebm.sort_eigvals" }, { "path": "docs/source/includes/linear/src/linuvlm/Dynamic.rst", "content": "Dynamic\n-------\n\n.. autoclass:: sharpy.linear.src.linuvlm.Dynamic\n\t:members:" }, { "path": "docs/source/includes/linear/src/linuvlm/DynamicBlock.rst", "content": "DynamicBlock\n------------\n\n.. autoclass:: sharpy.linear.src.linuvlm.DynamicBlock\n\t:members:" }, { "path": "docs/source/includes/linear/src/linuvlm/Frequency.rst", "content": "Frequency\n---------\n\n.. autoclass:: sharpy.linear.src.linuvlm.Frequency\n\t:members:" }, { "path": "docs/source/includes/linear/src/linuvlm/Static.rst", "content": "Static\n------\n\n.. autoclass:: sharpy.linear.src.linuvlm.Static\n\t:members:" }, { "path": "docs/source/includes/linear/src/linuvlm/get_Cw_cpx.rst", "content": "get_Cw_cpx\n----------\n\n.. automodule:: sharpy.linear.src.linuvlm.get_Cw_cpx" }, { "path": "docs/source/includes/linear/src/linuvlm/index.rst", "content": "Linear UVLM solver classes\n++++++++++++++++++++++++++\n\nLinear UVLM solver classes\n\nContains classes to assemble a linear UVLM system. The three main classes are:\n\n* :class:`~sharpy.linear.src.linuvlm.Static`: : for static VLM solutions.\n\n* :class:`~sharpy.linear.src.linuvlm.Dynamic`: for dynamic UVLM solutions.\n\n* :class:`~sharpy.linear.src.linuvlm.DynamicBlock`: a more efficient representation of ``Dynamic`` using lists for the\n different blocks in the UVLM equations\n\nReferences:\n\n Maraniello, S., & Palacios, R.. State-Space Realizations and Internal Balancing in Potential-Flow\n Aerodynamics with Arbitrary Kinematics. AIAA Journal, 57(6), 1–14. 2019. https://doi.org/10.2514/1.J058153\n\n\n\n.. toctree::\n\t:glob:\n\n\t./Dynamic\n\t./DynamicBlock\n\t./Frequency\n\t./Static\n\t./get_Cw_cpx\n" }, { "path": "docs/source/includes/linear/src/multisurfaces/MultiAeroGridSurfaces.rst", "content": "MultiAeroGridSurfaces\n---------------------\n\n.. autoclass:: sharpy.linear.src.multisurfaces.MultiAeroGridSurfaces\n\t:members:" }, { "path": "docs/source/includes/linear/src/multisurfaces/index.rst", "content": "Generation of multiple aerodynamic surfaces\n+++++++++++++++++++++++++++++++++++++++++++\n\n\nS. Maraniello, 25 May 2018\n\n\n.. toctree::\n\t:glob:\n\n\t./MultiAeroGridSurfaces\n" }, { "path": "docs/source/includes/linear/src/surface/AeroGridGeo.rst", "content": "AeroGridGeo\n-----------\n\n.. autoclass:: sharpy.linear.src.surface.AeroGridGeo\n\t:members:" }, { "path": "docs/source/includes/linear/src/surface/AeroGridSurface.rst", "content": "AeroGridSurface\n---------------\n\n.. autoclass:: sharpy.linear.src.surface.AeroGridSurface\n\t:members:" }, { "path": "docs/source/includes/linear/src/surface/get_aic3_cpp.rst", "content": "get_aic3_cpp\n------------\n\n.. automodule:: sharpy.linear.src.surface.get_aic3_cpp" }, { "path": "docs/source/includes/linear/src/surface/index.rst", "content": "Geometrical methods for bound surfaces\n++++++++++++++++++++++++++++++++++++++\n\nGeometrical methods for bound surfaces\n\n\nS. Maraniello, 20 May 2018\n\n\n.. toctree::\n\t:glob:\n\n\t./AeroGridGeo\n\t./AeroGridSurface\n\t./get_aic3_cpp\n" }, { "path": "docs/source/includes/postprocs/AeroForcesCalculator.rst", "content": "AeroForcesCalculator\n--------------------\n\n\n\n.. autoclass:: sharpy.postproc.aeroforcescalculator.AeroForcesCalculator\n\t:members:" }, { "path": "docs/source/includes/postprocs/AerogridPlot.rst", "content": "AerogridPlot\n------------\n\n\n\n.. autoclass:: sharpy.postproc.aerogridplot.AerogridPlot\n\t:members:" }, { "path": "docs/source/includes/postprocs/AsymptoticStability.rst", "content": "AsymptoticStability\n-------------------\n\n\n\n.. autoclass:: sharpy.postproc.asymptoticstability.AsymptoticStability\n\t:members:" }, { "path": "docs/source/includes/postprocs/BeamLoads.rst", "content": "BeamLoads\n---------\n\n\n\n.. autoclass:: sharpy.postproc.beamloads.BeamLoads\n\t:members:" }, { "path": "docs/source/includes/postprocs/BeamPlot.rst", "content": "BeamPlot\n--------\n\n\n\n.. autoclass:: sharpy.postproc.beamplot.BeamPlot\n\t:members:" }, { "path": "docs/source/includes/postprocs/Cleanup.rst", "content": "Cleanup\n-------\n\n\n\n.. autoclass:: sharpy.postproc.cleanup.Cleanup\n\t:members:" }, { "path": "docs/source/includes/postprocs/FrequencyResponse.rst", "content": "FrequencyResponse\n-----------------\n\n\n\n.. autoclass:: sharpy.postproc.frequencyresponse.FrequencyResponse\n\t:members:" }, { "path": "docs/source/includes/postprocs/LiftDistribution.rst", "content": "LiftDistribution\n----------------\n\n\n\n.. autoclass:: sharpy.postproc.liftdistribution.LiftDistribution\n\t:members:" }, { "path": "docs/source/includes/postprocs/PickleData.rst", "content": "PickleData\n----------\n\n\n\n.. autoclass:: sharpy.postproc.pickledata.PickleData\n\t:members:" }, { "path": "docs/source/includes/postprocs/PlotFlowField.rst", "content": "PlotFlowField\n-------------\n\n\n\n.. autoclass:: sharpy.postproc.plotflowfield.PlotFlowField\n\t:members:" }, { "path": "docs/source/includes/postprocs/SaveData.rst", "content": "SaveData\n--------\n\n\n\n.. autoclass:: sharpy.postproc.savedata.SaveData\n\t:members:" }, { "path": "docs/source/includes/postprocs/SaveParametricCase.rst", "content": "SaveParametricCase\n------------------\n\n\n\n.. autoclass:: sharpy.postproc.saveparametriccase.SaveParametricCase\n\t:members:" }, { "path": "docs/source/includes/postprocs/StabilityDerivatives.rst", "content": "StabilityDerivatives\n--------------------\n\n\n\n.. autoclass:: sharpy.postproc.stabilityderivatives.StabilityDerivatives\n\t:members:" }, { "path": "docs/source/includes/postprocs/StallCheck.rst", "content": "StallCheck\n----------\n\n\n\n.. autoclass:: sharpy.postproc.stallcheck.StallCheck\n\t:members:" }, { "path": "docs/source/includes/postprocs/UDPout.rst", "content": "UDPout\n------\n\n\n\n.. autoclass:: sharpy.postproc.udpout.UDPout\n\t:members:" }, { "path": "docs/source/includes/postprocs/WriteVariablesTime.rst", "content": "WriteVariablesTime\n------------------\n\n\n\n.. autoclass:: sharpy.postproc.writevariablestime.WriteVariablesTime\n\t:members:" }, { "path": "docs/source/includes/rom/balanced/Balanced.rst", "content": "Balanced\n--------\n\n.. autoclass:: sharpy.rom.balanced.Balanced\n\t:members:" }, { "path": "docs/source/includes/rom/balanced/Direct.rst", "content": "Direct\n------\n\n.. autoclass:: sharpy.rom.balanced.Direct\n\t:members:" }, { "path": "docs/source/includes/rom/balanced/FrequencyLimited.rst", "content": "FrequencyLimited\n----------------\n\n.. autoclass:: sharpy.rom.balanced.FrequencyLimited\n\t:members:" }, { "path": "docs/source/includes/rom/balanced/Iterative.rst", "content": "Iterative\n---------\n\n.. autoclass:: sharpy.rom.balanced.Iterative\n\t:members:" }, { "path": "docs/source/includes/rom/balanced/index.rst", "content": "Balancing Methods\n+++++++++++++++++\n\n\nThe following classes are available to reduce a linear system employing balancing methods.\n\nThe main class is :class:`.Balanced` and the other available classes:\n\n* :class:`.Direct`\n\n* :class:`.Iterative`\n\n* :class:`.FrequencyLimited`\n\ncorrespond to the reduction algorithm.\n\n\n\n.. toctree::\n\t:glob:\n\n\t./Balanced\n\t./Direct\n\t./FrequencyLimited\n\t./Iterative\n" }, { "path": "docs/source/includes/rom/index.rst", "content": "Model Order Reduction\n---------------------\n\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./balanced/index\n\t./krylov/index\n\t./utils/index\n" }, { "path": "docs/source/includes/rom/krylov/Krylov.rst", "content": "Krylov\n------\n\n.. autoclass:: sharpy.rom.krylov.Krylov\n\t:members:" }, { "path": "docs/source/includes/rom/krylov/index.rst", "content": "Krylov-subspaces model order reduction techniques\n+++++++++++++++++++++++++++++++++++++++++++++++++\n\n\n\n.. toctree::\n\t:glob:\n\n\t./Krylov\n" }, { "path": "docs/source/includes/rom/utils/index.rst", "content": "Utils\n-----\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./krylovutils/index\n\t./librom/index\n\t./librom_interp/index\n" }, { "path": "docs/source/includes/rom/utils/krylovutils/check_eye.rst", "content": "check_eye\n---------\n\n.. automodule:: sharpy.rom.utils.krylovutils.check_eye" }, { "path": "docs/source/includes/rom/utils/krylovutils/construct_krylov.rst", "content": "construct_krylov\n----------------\n\n.. automodule:: sharpy.rom.utils.krylovutils.construct_krylov" }, { "path": "docs/source/includes/rom/utils/krylovutils/evec.rst", "content": "evec\n----\n\n.. automodule:: sharpy.rom.utils.krylovutils.evec" }, { "path": "docs/source/includes/rom/utils/krylovutils/index.rst", "content": "Krylov Model Reduction Methods Utilities\n++++++++++++++++++++++++++++++++++++++++\n\n\n\n.. toctree::\n\t:glob:\n\n\t./check_eye\n\t./construct_krylov\n\t./evec\n\t./lu_factor\n\t./lu_solve\n\t./mgs_ortho\n\t./remove_a12\n\t./schur_ordered\n" }, { "path": "docs/source/includes/rom/utils/krylovutils/lu_factor.rst", "content": "lu_factor\n---------\n\n.. automodule:: sharpy.rom.utils.krylovutils.lu_factor" }, { "path": "docs/source/includes/rom/utils/krylovutils/lu_solve.rst", "content": "lu_solve\n--------\n\n.. automodule:: sharpy.rom.utils.krylovutils.lu_solve" }, { "path": "docs/source/includes/rom/utils/krylovutils/mgs_ortho.rst", "content": "mgs_ortho\n---------\n\n.. automodule:: sharpy.rom.utils.krylovutils.mgs_ortho" }, { "path": "docs/source/includes/rom/utils/krylovutils/remove_a12.rst", "content": "remove_a12\n----------\n\n.. automodule:: sharpy.rom.utils.krylovutils.remove_a12" }, { "path": "docs/source/includes/rom/utils/krylovutils/schur_ordered.rst", "content": "schur_ordered\n-------------\n\n.. automodule:: sharpy.rom.utils.krylovutils.schur_ordered" }, { "path": "docs/source/includes/rom/utils/librom/balfreq.rst", "content": "balfreq\n-------\n\n.. automodule:: sharpy.rom.utils.librom.balfreq" }, { "path": "docs/source/includes/rom/utils/librom/balreal_direct_py.rst", "content": "balreal_direct_py\n-----------------\n\n.. automodule:: sharpy.rom.utils.librom.balreal_direct_py" }, { "path": "docs/source/includes/rom/utils/librom/balreal_iter.rst", "content": "balreal_iter\n------------\n\n.. automodule:: sharpy.rom.utils.librom.balreal_iter" }, { "path": "docs/source/includes/rom/utils/librom/balreal_iter_old.rst", "content": "balreal_iter_old\n----------------\n\n.. automodule:: sharpy.rom.utils.librom.balreal_iter_old" }, { "path": "docs/source/includes/rom/utils/librom/check_stability.rst", "content": "check_stability\n---------------\n\n.. automodule:: sharpy.rom.utils.librom.check_stability" }, { "path": "docs/source/includes/rom/utils/librom/eigen_dec.rst", "content": "eigen_dec\n---------\n\n.. automodule:: sharpy.rom.utils.librom.eigen_dec" }, { "path": "docs/source/includes/rom/utils/librom/get_gauss_weights.rst", "content": "get_gauss_weights\n-----------------\n\n.. automodule:: sharpy.rom.utils.librom.get_gauss_weights" }, { "path": "docs/source/includes/rom/utils/librom/get_trapz_weights.rst", "content": "get_trapz_weights\n-----------------\n\n.. automodule:: sharpy.rom.utils.librom.get_trapz_weights" }, { "path": "docs/source/includes/rom/utils/librom/index.rst", "content": "General ROM utilities\n+++++++++++++++++++++\n\n\nS. Maraniello, 14 Feb 2018\n\n\n.. toctree::\n\t:glob:\n\n\t./balfreq\n\t./balreal_direct_py\n\t./balreal_iter\n\t./balreal_iter_old\n\t./check_stability\n\t./eigen_dec\n\t./get_gauss_weights\n\t./get_trapz_weights\n\t./low_rank_smith\n\t./modred\n\t./res_discrete_lyap\n\t./smith_iter\n\t./tune_rom\n" }, { "path": "docs/source/includes/rom/utils/librom/low_rank_smith.rst", "content": "low_rank_smith\n--------------\n\n.. automodule:: sharpy.rom.utils.librom.low_rank_smith" }, { "path": "docs/source/includes/rom/utils/librom/modred.rst", "content": "modred\n------\n\n.. automodule:: sharpy.rom.utils.librom.modred" }, { "path": "docs/source/includes/rom/utils/librom/res_discrete_lyap.rst", "content": "res_discrete_lyap\n-----------------\n\n.. automodule:: sharpy.rom.utils.librom.res_discrete_lyap" }, { "path": "docs/source/includes/rom/utils/librom/smith_iter.rst", "content": "smith_iter\n----------\n\n.. automodule:: sharpy.rom.utils.librom.smith_iter" }, { "path": "docs/source/includes/rom/utils/librom/tune_rom.rst", "content": "tune_rom\n--------\n\n.. automodule:: sharpy.rom.utils.librom.tune_rom" }, { "path": "docs/source/includes/rom/utils/librom_interp/FLB_transfer_function.rst", "content": "FLB_transfer_function\n---------------------\n\n.. automodule:: sharpy.rom.utils.librom_interp.FLB_transfer_function" }, { "path": "docs/source/includes/rom/utils/librom_interp/InterpROM.rst", "content": "InterpROM\n---------\n\n.. autoclass:: sharpy.rom.utils.librom_interp.InterpROM\n\t:members:" }, { "path": "docs/source/includes/rom/utils/librom_interp/index.rst", "content": "Methods for the interpolation of DLTI ROMs\n++++++++++++++++++++++++++++++++++++++++++\n\n\nThis is library for state-space models interpolation. These routines are intended\nfor small size state-space models (ROMs), hence some methods may not be optimised\nto exploit sparsity structures. For generality purposes, all methods require in\ninput interpolatory weights.\n\n\nThe module includes the methods:\n\n - :func:`~sharpy.rom.utils.librom_interp.transfer_function`: returns an interpolatory state-space model based on the\n transfer function method [1]. This method is general and is, effectively, a\n wrapper of the :func:`sharpy.linear.src.libss.join` method.\n\n - :func:`~sharpy.rom.utils.librom_interp.BT_transfer_function`: evolution of transfer function methods. The growth of\n the interpolated system size is avoided through balancing.\n\n\nReferences:\n\n [1] Benner, P., Gugercin, S. & Willcox, K., 2015. A Survey of Projection-Based\n Model Reduction Methods for Parametric Dynamical Systems. SIAM Review, 57(4),\n pp.483–531.\n\n\nAuthor: S. Maraniello\n\nDate: Mar-Apr 2019\n\n\n\n\n.. toctree::\n\t:glob:\n\n\t./FLB_transfer_function\n\t./InterpROM\n\t./transfer_function\n" }, { "path": "docs/source/includes/rom/utils/librom_interp/transfer_function.rst", "content": "transfer_function\n-----------------\n\n.. automodule:: sharpy.rom.utils.librom_interp.transfer_function" }, { "path": "docs/source/includes/solvers/aero/DynamicUVLM.rst", "content": "DynamicUVLM\n-----------\n\n\n\n.. autoclass:: sharpy.solvers.dynamicuvlm.DynamicUVLM\n\t:members:" }, { "path": "docs/source/includes/solvers/aero/NoAero.rst", "content": "NoAero\n------\n\n\n\n.. autoclass:: sharpy.solvers.noaero.NoAero\n\t:members:" }, { "path": "docs/source/includes/solvers/aero/PrescribedUvlm.rst", "content": "PrescribedUvlm\n--------------\n\n\n\n.. autoclass:: sharpy.solvers.prescribeduvlm.PrescribedUvlm\n\t:members:" }, { "path": "docs/source/includes/solvers/aero/StaticUvlm.rst", "content": "StaticUvlm\n----------\n\n\n\n.. autoclass:: sharpy.solvers.staticuvlm.StaticUvlm\n\t:members:" }, { "path": "docs/source/includes/solvers/aero/StepLinearUVLM.rst", "content": "StepLinearUVLM\n--------------\n\n\n\n.. autoclass:: sharpy.solvers.steplinearuvlm.StepLinearUVLM\n\t:members:" }, { "path": "docs/source/includes/solvers/aero/StepUvlm.rst", "content": "StepUvlm\n--------\n\n\n\n.. autoclass:: sharpy.solvers.stepuvlm.StepUvlm\n\t:members:" }, { "path": "docs/source/includes/solvers/aero_solvers.rst", "content": "Aero Solvers\n++++++++++++\n\n.. toctree::\n ./aero/DynamicUVLM\n ./aero/NoAero\n ./aero/PrescribedUvlm\n ./aero/StaticUvlm\n ./aero/StepLinearUVLM\n ./aero/StepUvlm\n" }, { "path": "docs/source/includes/solvers/coupled/DynamicCoupled.rst", "content": "DynamicCoupled\n--------------\n\n\n\n.. autoclass:: sharpy.solvers.dynamiccoupled.DynamicCoupled\n\t:members:" }, { "path": "docs/source/includes/solvers/coupled/LinDynamicSim.rst", "content": "LinDynamicSim\n-------------\n\n\n\n.. autoclass:: sharpy.solvers.lindynamicsim.LinDynamicSim\n\t:members:" }, { "path": "docs/source/includes/solvers/coupled/StaticCoupled.rst", "content": "StaticCoupled\n-------------\n\n\n\n.. autoclass:: sharpy.solvers.staticcoupled.StaticCoupled\n\t:members:" }, { "path": "docs/source/includes/solvers/coupled/StaticCoupledRBM.rst", "content": "StaticCoupledRBM\n----------------\n\n\n\n.. autoclass:: sharpy.solvers.staticcoupledrbm.StaticCoupledRBM\n\t:members:" }, { "path": "docs/source/includes/solvers/coupled_solvers.rst", "content": "Coupled Solvers\n+++++++++++++++\n\n.. toctree::\n ./coupled/DynamicCoupled\n ./coupled/LinDynamicSim\n ./coupled/StaticCoupled\n ./coupled/StaticCoupledRBM\n" }, { "path": "docs/source/includes/solvers/flight dynamics/StaticTrim.rst", "content": "StaticTrim\n----------\n\n\n\n.. autoclass:: sharpy.solvers.statictrim.StaticTrim\n\t:members:" }, { "path": "docs/source/includes/solvers/flight dynamics/Trim.rst", "content": "Trim\n----\n\n\n\n.. autoclass:: sharpy.solvers.trim.Trim\n\t:members:" }, { "path": "docs/source/includes/solvers/flight dynamics_solvers.rst", "content": "Flight dynamics Solvers\n+++++++++++++++++++++++\n\n.. toctree::\n ./flight dynamics/StaticTrim\n ./flight dynamics/Trim\n" }, { "path": "docs/source/includes/solvers/linear/LinearAssembler.rst", "content": "LinearAssembler\n---------------\n\n\n\n.. autoclass:: sharpy.solvers.linearassembler.LinearAssembler\n\t:members:" }, { "path": "docs/source/includes/solvers/linear/Modal.rst", "content": "Modal\n-----\n\n\n\n.. autoclass:: sharpy.solvers.modal.Modal\n\t:members:" }, { "path": "docs/source/includes/solvers/linear_solvers.rst", "content": "Linear Solvers\n++++++++++++++\n\n.. toctree::\n ./linear/LinearAssembler\n ./linear/Modal\n" }, { "path": "docs/source/includes/solvers/loader/AerogridLoader.rst", "content": "AerogridLoader\n--------------\n\n\n\n.. autoclass:: sharpy.solvers.aerogridloader.AerogridLoader\n\t:members:" }, { "path": "docs/source/includes/solvers/loader/BeamLoader.rst", "content": "BeamLoader\n----------\n\n\n\n.. autoclass:: sharpy.solvers.beamloader.BeamLoader\n\t:members:" }, { "path": "docs/source/includes/solvers/loader/PreSharpy.rst", "content": "PreSharpy\n---------\n\n\n\n.. autoclass:: sharpy.presharpy.presharpy.PreSharpy\n\t:members:" }, { "path": "docs/source/includes/solvers/loader_solvers.rst", "content": "Loader Solvers\n++++++++++++++\n\n.. toctree::\n ./loader/PreSharpy\n ./loader/AerogridLoader\n ./loader/BeamLoader\n" }, { "path": "docs/source/includes/solvers/structural/NonLinearDynamic.rst", "content": "NonLinearDynamic\n----------------\n\n\n\n.. autoclass:: sharpy.solvers.nonlineardynamic.NonLinearDynamic\n\t:members:" }, { "path": "docs/source/includes/solvers/structural/NonLinearDynamicCoupledStep.rst", "content": "NonLinearDynamicCoupledStep\n---------------------------\n\n\n\n.. autoclass:: sharpy.solvers.nonlineardynamiccoupledstep.NonLinearDynamicCoupledStep\n\t:members:" }, { "path": "docs/source/includes/solvers/structural/NonLinearDynamicMultibody.rst", "content": "NonLinearDynamicMultibody\n-------------------------\n\n\n\n.. autoclass:: sharpy.solvers.nonlineardynamicmultibody.NonLinearDynamicMultibody\n\t:members:" }, { "path": "docs/source/includes/solvers/structural/NonLinearDynamicPrescribedStep.rst", "content": "NonLinearDynamicPrescribedStep\n------------------------------\n\n\n\n.. autoclass:: sharpy.solvers.nonlineardynamicprescribedstep.NonLinearDynamicPrescribedStep\n\t:members:" }, { "path": "docs/source/includes/solvers/structural/NonLinearStatic.rst", "content": "NonLinearStatic\n---------------\n\n\n\n.. autoclass:: sharpy.solvers.nonlinearstatic.NonLinearStatic\n\t:members:" }, { "path": "docs/source/includes/solvers/structural/RigidDynamicCoupledStep.rst", "content": "RigidDynamicCoupledStep\n-----------------------\n\n\n\n.. autoclass:: sharpy.solvers.rigiddynamiccoupledstep.RigidDynamicCoupledStep\n\t:members:" }, { "path": "docs/source/includes/solvers/structural/RigidDynamicPrescribedStep.rst", "content": "RigidDynamicPrescribedStep\n--------------------------\n\n\n\n.. autoclass:: sharpy.solvers.rigiddynamicprescribedstep.RigidDynamicPrescribedStep\n\t:members:" }, { "path": "docs/source/includes/solvers/structural_solvers.rst", "content": "Structural Solvers\n++++++++++++++++++\n\n.. toctree::\n ./structural/NonLinearDynamic\n ./structural/NonLinearDynamicCoupledStep\n ./structural/NonLinearDynamicMultibody\n ./structural/NonLinearDynamicPrescribedStep\n ./structural/NonLinearStatic\n ./structural/RigidDynamicCoupledStep\n ./structural/RigidDynamicPrescribedStep\n" }, { "path": "docs/source/includes/solvers/time_integrator/GeneralisedAlpha.rst", "content": "GeneralisedAlpha\n----------------\n\n\n\n.. autoclass:: sharpy.solvers.generalisedalpha.GeneralisedAlpha\n\t:members:" }, { "path": "docs/source/includes/solvers/time_integrator/NewmarkBeta.rst", "content": "NewmarkBeta\n-----------\n\n\n\n.. autoclass:: sharpy.solvers.newmarkbeta.NewmarkBeta\n\t:members:" }, { "path": "docs/source/includes/solvers/time_integrator_solvers.rst", "content": "Time_integrator Solvers\n+++++++++++++++++++++++\n\n.. toctree::\n ./time_integrator/NewmarkBeta\n ./time_integrator/GeneralisedAlpha\n" }, { "path": "docs/source/includes/structure/index.rst", "content": "Structural Packages\n-------------------\n\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./models/index\n\t./utils/index\n" }, { "path": "docs/source/includes/structure/models/beam/StructTimeStepInfo.rst", "content": "StructTimeStepInfo\n------------------\n\n.. autoclass:: sharpy.structure.models.beam.StructTimeStepInfo\n\t:members:" }, { "path": "docs/source/includes/structure/models/beam/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./StructTimeStepInfo\n" }, { "path": "docs/source/includes/structure/models/beamstructures/Element.rst", "content": "Element\n-------\n\n.. autoclass:: sharpy.structure.models.beamstructures.Element\n\t:members:" }, { "path": "docs/source/includes/structure/models/beamstructures/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./Element\n" }, { "path": "docs/source/includes/structure/models/index.rst", "content": "Models\n------\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./beam/index\n\t./beamstructures/index\n" }, { "path": "docs/source/includes/structure/utils/index.rst", "content": "Utils\n-----\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./lagrangeconstraints/index\n\t./modalutils/index\n\t./xbeamlib/index\n" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/BaseLagrangeConstraint.rst", "content": "BaseLagrangeConstraint\n----------------------\n\n.. autoclass:: sharpy.structure.utils.lagrangeconstraints.BaseLagrangeConstraint\n\t:members:" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/constant_rot_vel_FoR.rst", "content": "constant_rot_vel_FoR\n--------------------\n\n.. autoclass:: sharpy.structure.utils.lagrangeconstraints.constant_rot_vel_FoR\n\t:members:" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/constant_vel_FoR.rst", "content": "constant_vel_FoR\n----------------\n\n.. autoclass:: sharpy.structure.utils.lagrangeconstraints.constant_vel_FoR\n\t:members:" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/def_rot_axis_FoR_wrt_node_general.rst", "content": "def_rot_axis_FoR_wrt_node_general\n---------------------------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.def_rot_axis_FoR_wrt_node_general" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/def_rot_axis_FoR_wrt_node_xyz.rst", "content": "def_rot_axis_FoR_wrt_node_xyz\n-----------------------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.def_rot_axis_FoR_wrt_node_xyz" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/def_rot_vect_FoR_wrt_node.rst", "content": "def_rot_vect_FoR_wrt_node\n-------------------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.def_rot_vect_FoR_wrt_node" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/def_rot_vel_FoR_wrt_node.rst", "content": "def_rot_vel_FoR_wrt_node\n------------------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.def_rot_vel_FoR_wrt_node" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/define_FoR_dof.rst", "content": "define_FoR_dof\n--------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.define_FoR_dof" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/define_node_dof.rst", "content": "define_node_dof\n---------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.define_node_dof" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/define_num_LM_eq.rst", "content": "define_num_LM_eq\n----------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.define_num_LM_eq" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/equal_lin_vel_node_FoR.rst", "content": "equal_lin_vel_node_FoR\n----------------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.equal_lin_vel_node_FoR" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/equal_pos_node_FoR.rst", "content": "equal_pos_node_FoR\n------------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.equal_pos_node_FoR" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/free.rst", "content": "free\n----\n\n.. autoclass:: sharpy.structure.utils.lagrangeconstraints.free\n\t:members:" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/fully_constrained_node_FoR.rst", "content": "fully_constrained_node_FoR\n--------------------------\n\n.. autoclass:: sharpy.structure.utils.lagrangeconstraints.fully_constrained_node_FoR\n\t:members:" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/generate_lagrange_matrix.rst", "content": "generate_lagrange_matrix\n------------------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.generate_lagrange_matrix" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/hinge_FoR.rst", "content": "hinge_FoR\n---------\n\n.. autoclass:: sharpy.structure.utils.lagrangeconstraints.hinge_FoR\n\t:members:" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/hinge_FoR_wrtG.rst", "content": "hinge_FoR_wrtG\n--------------\n\n.. autoclass:: sharpy.structure.utils.lagrangeconstraints.hinge_FoR_wrtG\n\t:members:" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/hinge_node_FoR.rst", "content": "hinge_node_FoR\n--------------\n\n.. autoclass:: sharpy.structure.utils.lagrangeconstraints.hinge_node_FoR\n\t:members:" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/hinge_node_FoR_constant_vel.rst", "content": "hinge_node_FoR_constant_vel\n---------------------------\n\n.. autoclass:: sharpy.structure.utils.lagrangeconstraints.hinge_node_FoR_constant_vel\n\t:members:" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/index.rst", "content": "LagrangeConstraints library\n+++++++++++++++++++++++++++\n\nLagrangeConstraints library\n\nLibrary used to create the matrices associated to boundary conditions through\nthe method of Lagrange Multipliers. The source code includes four different sections.\n\n* Basic structures: basic functions and variables needed to organise the library with different Lagrange Constraints to enhance the interaction with this library.\n\n* Auxiliar functions: basic queries that are performed repeatedly.\n\n* Equations: functions that generate the equations associated to the constraint of basic degrees of freedom.\n\n* Lagrange Constraints: different available Lagrange Constraints. They tipically use the basic functions in \"Equations\" to assembly the required set of equations.\n\nAttributes:\n dict_of_lc (dict): Dictionary including the available Lagrange Contraint identifier\n (``_lc_id``) and the associated ``BaseLagrangeConstraint`` class\n\nNotes:\n To use this library: import sharpy.structure.utils.lagrangeconstraints as lagrangeconstraints\n\nArgs:\n lc_list (list): list of all the defined contraints\n MBdict (dict): dictionary with the MultiBody and LagrangeMultipliers information\n MB_beam (list): list of :class:`~sharpy.structure.models.beam.Beam` of each of the bodies that form the system\n MB_tstep (list): list of :class:`~sharpy.utils.datastructures.StructTimeStepInfo` of each of the bodies that form the system\n num_LM_eq (int): number of new equations needed to define the boundary boundary conditions\n sys_size (int): total number of degrees of freedom of the multibody system\n dt (float): time step\n Lambda (np.ndarray): list of Lagrange multipliers values\n Lambda_dot (np.ndarray): list of the first derivative of the Lagrange multipliers values\n dynamic_or_static (str): string defining if the computation is dynamic or static\n LM_C (np.ndarray): Damping matrix associated to the Lagrange Multipliers equations\n LM_K (np.ndarray): Stiffness matrix associated to the Lagrange Multipliers equations\n LM_Q (np.ndarray): Vector of independent terms associated to the Lagrange Multipliers equations\n\n\n.. toctree::\n\t:glob:\n\n\t./BaseLagrangeConstraint\n\t./constant_rot_vel_FoR\n\t./constant_vel_FoR\n\t./def_rot_axis_FoR_wrt_node_general\n\t./def_rot_axis_FoR_wrt_node_xyz\n\t./def_rot_vect_FoR_wrt_node\n\t./def_rot_vel_FoR_wrt_node\n\t./define_FoR_dof\n\t./define_node_dof\n\t./define_num_LM_eq\n\t./equal_lin_vel_node_FoR\n\t./equal_pos_node_FoR\n\t./free\n\t./fully_constrained_node_FoR\n\t./generate_lagrange_matrix\n\t./hinge_FoR\n\t./hinge_FoR_wrtG\n\t./hinge_node_FoR\n\t./hinge_node_FoR_constant_vel\n\t./initialise_lc\n\t./lagrangeconstraint\n\t./lc_from_string\n\t./lin_vel_node_wrtA\n\t./lin_vel_node_wrtG\n\t./postprocess\n\t./print_available_lc\n\t./remove_constraint\n\t./spherical_FoR\n\t./spherical_node_FoR\n" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/initialise_lc.rst", "content": "initialise_lc\n-------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.initialise_lc" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/lagrangeconstraint.rst", "content": "lagrangeconstraint\n------------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.lagrangeconstraint" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/lc_from_string.rst", "content": "lc_from_string\n--------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.lc_from_string" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/lin_vel_node_wrtA.rst", "content": "lin_vel_node_wrtA\n-----------------\n\n.. autoclass:: sharpy.structure.utils.lagrangeconstraints.lin_vel_node_wrtA\n\t:members:" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/lin_vel_node_wrtG.rst", "content": "lin_vel_node_wrtG\n-----------------\n\n.. autoclass:: sharpy.structure.utils.lagrangeconstraints.lin_vel_node_wrtG\n\t:members:" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/postprocess.rst", "content": "postprocess\n-----------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.postprocess" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/print_available_lc.rst", "content": "print_available_lc\n------------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.print_available_lc" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/remove_constraint.rst", "content": "remove_constraint\n-----------------\n\n.. automodule:: sharpy.structure.utils.lagrangeconstraints.remove_constraint" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/spherical_FoR.rst", "content": "spherical_FoR\n-------------\n\n.. autoclass:: sharpy.structure.utils.lagrangeconstraints.spherical_FoR\n\t:members:" }, { "path": "docs/source/includes/structure/utils/lagrangeconstraints/spherical_node_FoR.rst", "content": "spherical_node_FoR\n------------------\n\n.. autoclass:: sharpy.structure.utils.lagrangeconstraints.spherical_node_FoR\n\t:members:" }, { "path": "docs/source/includes/structure/utils/modalutils/assert_modes_mass_normalised.rst", "content": "assert_modes_mass_normalised\n----------------------------\n\n.. automodule:: sharpy.structure.utils.modalutils.assert_modes_mass_normalised" }, { "path": "docs/source/includes/structure/utils/modalutils/assert_orthogonal_eigenvectors.rst", "content": "assert_orthogonal_eigenvectors\n------------------------------\n\n.. automodule:: sharpy.structure.utils.modalutils.assert_orthogonal_eigenvectors" }, { "path": "docs/source/includes/structure/utils/modalutils/free_modes_principal_axes.rst", "content": "free_modes_principal_axes\n-------------------------\n\n.. automodule:: sharpy.structure.utils.modalutils.free_modes_principal_axes" }, { "path": "docs/source/includes/structure/utils/modalutils/get_mode_zeta.rst", "content": "get_mode_zeta\n-------------\n\n.. automodule:: sharpy.structure.utils.modalutils.get_mode_zeta" }, { "path": "docs/source/includes/structure/utils/modalutils/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./assert_modes_mass_normalised\n\t./assert_orthogonal_eigenvectors\n\t./free_modes_principal_axes\n\t./get_mode_zeta\n\t./mode_sign_convention\n\t./modes_to_cg_ref\n\t./principal_axes_inertia\n\t./scale_mass_normalised_modes\n\t./scale_mode\n\t./write_modes_vtk\n\t./write_zeta_vtk\n" }, { "path": "docs/source/includes/structure/utils/modalutils/mode_sign_convention.rst", "content": "mode_sign_convention\n--------------------\n\n.. automodule:: sharpy.structure.utils.modalutils.mode_sign_convention" }, { "path": "docs/source/includes/structure/utils/modalutils/modes_to_cg_ref.rst", "content": "modes_to_cg_ref\n---------------\n\n.. automodule:: sharpy.structure.utils.modalutils.modes_to_cg_ref" }, { "path": "docs/source/includes/structure/utils/modalutils/principal_axes_inertia.rst", "content": "principal_axes_inertia\n----------------------\n\n.. automodule:: sharpy.structure.utils.modalutils.principal_axes_inertia" }, { "path": "docs/source/includes/structure/utils/modalutils/scale_mass_normalised_modes.rst", "content": "scale_mass_normalised_modes\n---------------------------\n\n.. automodule:: sharpy.structure.utils.modalutils.scale_mass_normalised_modes" }, { "path": "docs/source/includes/structure/utils/modalutils/scale_mode.rst", "content": "scale_mode\n----------\n\n.. automodule:: sharpy.structure.utils.modalutils.scale_mode" }, { "path": "docs/source/includes/structure/utils/modalutils/write_modes_vtk.rst", "content": "write_modes_vtk\n---------------\n\n.. automodule:: sharpy.structure.utils.modalutils.write_modes_vtk" }, { "path": "docs/source/includes/structure/utils/modalutils/write_zeta_vtk.rst", "content": "write_zeta_vtk\n--------------\n\n.. automodule:: sharpy.structure.utils.modalutils.write_zeta_vtk" }, { "path": "docs/source/includes/structure/utils/xbeamlib/Xbopts.rst", "content": "Xbopts\n------\n\n.. autoclass:: sharpy.structure.utils.xbeamlib.Xbopts\n\t:members:" }, { "path": "docs/source/includes/structure/utils/xbeamlib/cbeam3_asbly_dynamic.rst", "content": "cbeam3_asbly_dynamic\n--------------------\n\n.. automodule:: sharpy.structure.utils.xbeamlib.cbeam3_asbly_dynamic" }, { "path": "docs/source/includes/structure/utils/xbeamlib/cbeam3_asbly_static.rst", "content": "cbeam3_asbly_static\n-------------------\n\n.. automodule:: sharpy.structure.utils.xbeamlib.cbeam3_asbly_static" }, { "path": "docs/source/includes/structure/utils/xbeamlib/cbeam3_correct_gravity_forces.rst", "content": "cbeam3_correct_gravity_forces\n-----------------------------\n\n.. automodule:: sharpy.structure.utils.xbeamlib.cbeam3_correct_gravity_forces" }, { "path": "docs/source/includes/structure/utils/xbeamlib/cbeam3_loads.rst", "content": "cbeam3_loads\n------------\n\n.. automodule:: sharpy.structure.utils.xbeamlib.cbeam3_loads" }, { "path": "docs/source/includes/structure/utils/xbeamlib/cbeam3_solv_modal.rst", "content": "cbeam3_solv_modal\n-----------------\n\n.. automodule:: sharpy.structure.utils.xbeamlib.cbeam3_solv_modal" }, { "path": "docs/source/includes/structure/utils/xbeamlib/cbeam3_solv_nlnstatic.rst", "content": "cbeam3_solv_nlnstatic\n---------------------\n\n.. automodule:: sharpy.structure.utils.xbeamlib.cbeam3_solv_nlnstatic" }, { "path": "docs/source/includes/structure/utils/xbeamlib/index.rst", "content": ".. toctree::\n\t:glob:\n\n\t./Xbopts\n\t./cbeam3_asbly_dynamic\n\t./cbeam3_asbly_static\n\t./cbeam3_correct_gravity_forces\n\t./cbeam3_loads\n\t./cbeam3_solv_modal\n\t./cbeam3_solv_nlnstatic\n\t./xbeam3_asbly_dynamic\n" }, { "path": "docs/source/includes/structure/utils/xbeamlib/xbeam3_asbly_dynamic.rst", "content": "xbeam3_asbly_dynamic\n--------------------\n\n.. automodule:: sharpy.structure.utils.xbeamlib.xbeam3_asbly_dynamic" }, { "path": "docs/source/includes/utils/algebra/cross3.rst", "content": "cross3\n------\n\n.. automodule:: sharpy.utils.algebra.cross3" }, { "path": "docs/source/includes/utils/algebra/crv2quat.rst", "content": "crv2quat\n--------\n\n.. automodule:: sharpy.utils.algebra.crv2quat" }, { "path": "docs/source/includes/utils/algebra/crv2rotation.rst", "content": "crv2rotation\n------------\n\n.. automodule:: sharpy.utils.algebra.crv2rotation" }, { "path": "docs/source/includes/utils/algebra/crv2tan.rst", "content": "crv2tan\n-------\n\n.. automodule:: sharpy.utils.algebra.crv2tan" }, { "path": "docs/source/includes/utils/algebra/crv_bounds.rst", "content": "crv_bounds\n----------\n\n.. automodule:: sharpy.utils.algebra.crv_bounds" }, { "path": "docs/source/includes/utils/algebra/der_CcrvT_by_v.rst", "content": "der_CcrvT_by_v\n--------------\n\n.. automodule:: sharpy.utils.algebra.der_CcrvT_by_v" }, { "path": "docs/source/includes/utils/algebra/der_Ccrv_by_v.rst", "content": "der_Ccrv_by_v\n-------------\n\n.. automodule:: sharpy.utils.algebra.der_Ccrv_by_v" }, { "path": "docs/source/includes/utils/algebra/der_Ceuler_by_v.rst", "content": "der_Ceuler_by_v\n---------------\n\n.. automodule:: sharpy.utils.algebra.der_Ceuler_by_v" }, { "path": "docs/source/includes/utils/algebra/der_Ceuler_by_v_NED.rst", "content": "der_Ceuler_by_v_NED\n-------------------\n\n.. automodule:: sharpy.utils.algebra.der_Ceuler_by_v_NED" }, { "path": "docs/source/includes/utils/algebra/der_CquatT_by_v.rst", "content": "der_CquatT_by_v\n---------------\n\n.. automodule:: sharpy.utils.algebra.der_CquatT_by_v" }, { "path": "docs/source/includes/utils/algebra/der_Cquat_by_v.rst", "content": "der_Cquat_by_v\n--------------\n\n.. automodule:: sharpy.utils.algebra.der_Cquat_by_v" }, { "path": "docs/source/includes/utils/algebra/der_Peuler_by_v.rst", "content": "der_Peuler_by_v\n---------------\n\n.. automodule:: sharpy.utils.algebra.der_Peuler_by_v" }, { "path": "docs/source/includes/utils/algebra/der_TanT_by_xv.rst", "content": "der_TanT_by_xv\n--------------\n\n.. automodule:: sharpy.utils.algebra.der_TanT_by_xv" }, { "path": "docs/source/includes/utils/algebra/der_Tan_by_xv.rst", "content": "der_Tan_by_xv\n-------------\n\n.. automodule:: sharpy.utils.algebra.der_Tan_by_xv" }, { "path": "docs/source/includes/utils/algebra/der_Teuler_by_w.rst", "content": "der_Teuler_by_w\n---------------\n\n.. automodule:: sharpy.utils.algebra.der_Teuler_by_w" }, { "path": "docs/source/includes/utils/algebra/der_Teuler_by_w_NED.rst", "content": "der_Teuler_by_w_NED\n-------------------\n\n.. automodule:: sharpy.utils.algebra.der_Teuler_by_w_NED" }, { "path": "docs/source/includes/utils/algebra/der_quat_wrt_crv.rst", "content": "der_quat_wrt_crv\n----------------\n\n.. automodule:: sharpy.utils.algebra.der_quat_wrt_crv" }, { "path": "docs/source/includes/utils/algebra/der_skewp_skewp_v.rst", "content": "der_skewp_skewp_v\n-----------------\n\n.. automodule:: sharpy.utils.algebra.der_skewp_skewp_v" }, { "path": "docs/source/includes/utils/algebra/deuler_dt.rst", "content": "deuler_dt\n---------\n\n.. automodule:: sharpy.utils.algebra.deuler_dt" }, { "path": "docs/source/includes/utils/algebra/deuler_dt_NED.rst", "content": "deuler_dt_NED\n-------------\n\n.. automodule:: sharpy.utils.algebra.deuler_dt_NED" }, { "path": "docs/source/includes/utils/algebra/euler2quat.rst", "content": "euler2quat\n----------\n\n.. automodule:: sharpy.utils.algebra.euler2quat" }, { "path": "docs/source/includes/utils/algebra/euler2rot.rst", "content": "euler2rot\n---------\n\n.. automodule:: sharpy.utils.algebra.euler2rot" }, { "path": "docs/source/includes/utils/algebra/get_transformation_matrix.rst", "content": "get_transformation_matrix\n-------------------------\n\n.. automodule:: sharpy.utils.algebra.get_transformation_matrix" }, { "path": "docs/source/includes/utils/algebra/get_triad.rst", "content": "get_triad\n---------\n\n.. automodule:: sharpy.utils.algebra.get_triad" }, { "path": "docs/source/includes/utils/algebra/index.rst", "content": "Algebra package\n+++++++++++++++\n\nAlgebra package\n\nExtensive library with geometrical and algebraic operations\n\nNote:\n Tests can be found in ``tests/utils/algebra_test``\n\n\n.. toctree::\n\t:glob:\n\n\t./cross3\n\t./crv2quat\n\t./crv2rotation\n\t./crv2tan\n\t./crv_bounds\n\t./der_CcrvT_by_v\n\t./der_Ccrv_by_v\n\t./der_Ceuler_by_v\n\t./der_Ceuler_by_v_NED\n\t./der_CquatT_by_v\n\t./der_Cquat_by_v\n\t./der_Peuler_by_v\n\t./der_TanT_by_xv\n\t./der_Tan_by_xv\n\t./der_Teuler_by_w\n\t./der_Teuler_by_w_NED\n\t./der_quat_wrt_crv\n\t./der_skewp_skewp_v\n\t./deuler_dt\n\t./deuler_dt_NED\n\t./euler2quat\n\t./euler2rot\n\t./get_transformation_matrix\n\t./get_triad\n\t./mat2quat\n\t./multiply_matrices\n\t./norm3d\n\t./normsq3d\n\t./panel_area\n\t./quadskew\n\t./quat2euler\n\t./quat2rotation\n\t./quat_bound\n\t./rotation2crv\n\t./rotation2quat\n\t./rotation3d_x\n\t./rotation3d_y\n\t./rotation3d_z\n\t./skew\n\t./tangent_vector\n\t./triad2rotation\n\t./unit_vector\n" }, { "path": "docs/source/includes/utils/algebra/mat2quat.rst", "content": "mat2quat\n--------\n\n.. automodule:: sharpy.utils.algebra.mat2quat" }, { "path": "docs/source/includes/utils/algebra/multiply_matrices.rst", "content": "multiply_matrices\n-----------------\n\n.. automodule:: sharpy.utils.algebra.multiply_matrices" }, { "path": "docs/source/includes/utils/algebra/norm3d.rst", "content": "norm3d\n------\n\n.. automodule:: sharpy.utils.algebra.norm3d" }, { "path": "docs/source/includes/utils/algebra/normsq3d.rst", "content": "normsq3d\n--------\n\n.. automodule:: sharpy.utils.algebra.normsq3d" }, { "path": "docs/source/includes/utils/algebra/panel_area.rst", "content": "panel_area\n----------\n\n.. automodule:: sharpy.utils.algebra.panel_area" }, { "path": "docs/source/includes/utils/algebra/quadskew.rst", "content": "quadskew\n--------\n\n.. automodule:: sharpy.utils.algebra.quadskew" }, { "path": "docs/source/includes/utils/algebra/quat2euler.rst", "content": "quat2euler\n----------\n\n.. automodule:: sharpy.utils.algebra.quat2euler" }, { "path": "docs/source/includes/utils/algebra/quat2rotation.rst", "content": "quat2rotation\n-------------\n\n.. automodule:: sharpy.utils.algebra.quat2rotation" }, { "path": "docs/source/includes/utils/algebra/quat_bound.rst", "content": "quat_bound\n----------\n\n.. automodule:: sharpy.utils.algebra.quat_bound" }, { "path": "docs/source/includes/utils/algebra/rotation2crv.rst", "content": "rotation2crv\n------------\n\n.. automodule:: sharpy.utils.algebra.rotation2crv" }, { "path": "docs/source/includes/utils/algebra/rotation2quat.rst", "content": "rotation2quat\n-------------\n\n.. automodule:: sharpy.utils.algebra.rotation2quat" }, { "path": "docs/source/includes/utils/algebra/rotation3d_x.rst", "content": "rotation3d_x\n------------\n\n.. automodule:: sharpy.utils.algebra.rotation3d_x" }, { "path": "docs/source/includes/utils/algebra/rotation3d_y.rst", "content": "rotation3d_y\n------------\n\n.. automodule:: sharpy.utils.algebra.rotation3d_y" }, { "path": "docs/source/includes/utils/algebra/rotation3d_z.rst", "content": "rotation3d_z\n------------\n\n.. automodule:: sharpy.utils.algebra.rotation3d_z" }, { "path": "docs/source/includes/utils/algebra/skew.rst", "content": "skew\n----\n\n.. automodule:: sharpy.utils.algebra.skew" }, { "path": "docs/source/includes/utils/algebra/tangent_vector.rst", "content": "tangent_vector\n--------------\n\n.. automodule:: sharpy.utils.algebra.tangent_vector" }, { "path": "docs/source/includes/utils/algebra/triad2rotation.rst", "content": "triad2rotation\n--------------\n\n.. automodule:: sharpy.utils.algebra.triad2rotation" }, { "path": "docs/source/includes/utils/algebra/unit_vector.rst", "content": "unit_vector\n-----------\n\n.. automodule:: sharpy.utils.algebra.unit_vector" }, { "path": "docs/source/includes/utils/analytical/flat_plate_analytical.rst", "content": "flat_plate_analytical\n---------------------\n\n.. automodule:: sharpy.utils.analytical.flat_plate_analytical" }, { "path": "docs/source/includes/utils/analytical/garrick_drag_pitch.rst", "content": "garrick_drag_pitch\n------------------\n\n.. automodule:: sharpy.utils.analytical.garrick_drag_pitch" }, { "path": "docs/source/includes/utils/analytical/garrick_drag_plunge.rst", "content": "garrick_drag_plunge\n-------------------\n\n.. automodule:: sharpy.utils.analytical.garrick_drag_plunge" }, { "path": "docs/source/includes/utils/analytical/index.rst", "content": "Analytical Functions\n++++++++++++++++++++\n\n\nAnalytical solutions for 2D aerofoil based on thin plates theory\n\nAuthor: Salvatore Maraniello\n\nDate: 23 May 2017\n\nReferences:\n\n1. Simpson, R.J.S., Palacios, R. & Murua, J., 2013. Induced-Drag Calculations in the Unsteady Vortex Lattice Method.\n AIAA Journal, 51(7), pp.1775–1779.\n\n2. Gulcat, U., 2009. Propulsive Force of a Flexible Flapping Thin Airfoil. Journal of Aircraft, 46(2), pp.465–473.\n\n\n\n.. toctree::\n\t:glob:\n\n\t./flat_plate_analytical\n\t./garrick_drag_pitch\n\t./garrick_drag_plunge\n\t./nc_derivs\n\t./qs_derivs\n\t./sears_CL_freq_resp\n\t./sears_fun\n\t./sears_lift_sin_gust\n\t./theo_CL_freq_resp\n\t./theo_CM_freq_resp\n\t./theo_fun\n\t./theo_lift\n\t./wagner_imp_start\n" }, { "path": "docs/source/includes/utils/analytical/nc_derivs.rst", "content": "nc_derivs\n---------\n\n.. automodule:: sharpy.utils.analytical.nc_derivs" }, { "path": "docs/source/includes/utils/analytical/qs_derivs.rst", "content": "qs_derivs\n---------\n\n.. automodule:: sharpy.utils.analytical.qs_derivs" }, { "path": "docs/source/includes/utils/analytical/sears_CL_freq_resp.rst", "content": "sears_CL_freq_resp\n------------------\n\n.. automodule:: sharpy.utils.analytical.sears_CL_freq_resp" }, { "path": "docs/source/includes/utils/analytical/sears_fun.rst", "content": "sears_fun\n---------\n\n.. automodule:: sharpy.utils.analytical.sears_fun" }, { "path": "docs/source/includes/utils/analytical/sears_lift_sin_gust.rst", "content": "sears_lift_sin_gust\n-------------------\n\n.. automodule:: sharpy.utils.analytical.sears_lift_sin_gust" }, { "path": "docs/source/includes/utils/analytical/theo_CL_freq_resp.rst", "content": "theo_CL_freq_resp\n-----------------\n\n.. automodule:: sharpy.utils.analytical.theo_CL_freq_resp" }, { "path": "docs/source/includes/utils/analytical/theo_CM_freq_resp.rst", "content": "theo_CM_freq_resp\n-----------------\n\n.. automodule:: sharpy.utils.analytical.theo_CM_freq_resp" }, { "path": "docs/source/includes/utils/analytical/theo_fun.rst", "content": "theo_fun\n--------\n\n.. automodule:: sharpy.utils.analytical.theo_fun" }, { "path": "docs/source/includes/utils/analytical/theo_lift.rst", "content": "theo_lift\n---------\n\n.. automodule:: sharpy.utils.analytical.theo_lift" }, { "path": "docs/source/includes/utils/analytical/wagner_imp_start.rst", "content": "wagner_imp_start\n----------------\n\n.. automodule:: sharpy.utils.analytical.wagner_imp_start" }, { "path": "docs/source/includes/utils/control_utils/PID.rst", "content": "PID\n---\n\n.. autoclass:: sharpy.utils.control_utils.PID\n\t:members:" }, { "path": "docs/source/includes/utils/control_utils/index.rst", "content": "Controller Utilities\n++++++++++++++++++++\n\n\n\n.. toctree::\n\t:glob:\n\n\t./PID\n" }, { "path": "docs/source/includes/utils/datastructures/AeroTimeStepInfo.rst", "content": "AeroTimeStepInfo\n----------------\n\n.. autoclass:: sharpy.utils.datastructures.AeroTimeStepInfo\n\t:members:" }, { "path": "docs/source/includes/utils/datastructures/Linear.rst", "content": "Linear\n------\n\n.. autoclass:: sharpy.utils.datastructures.Linear\n\t:members:" }, { "path": "docs/source/includes/utils/datastructures/LinearTimeStepInfo.rst", "content": "LinearTimeStepInfo\n------------------\n\n.. autoclass:: sharpy.utils.datastructures.LinearTimeStepInfo\n\t:members:" }, { "path": "docs/source/includes/utils/datastructures/StructTimeStepInfo.rst", "content": "StructTimeStepInfo\n------------------\n\n.. autoclass:: sharpy.utils.datastructures.StructTimeStepInfo\n\t:members:" }, { "path": "docs/source/includes/utils/datastructures/index.rst", "content": "Data Management Structures\n++++++++++++++++++++++++++\n\n\nThese classes are responsible for storing the aerodynamic and structural time step information and relevant variables.\n\n\n\n.. toctree::\n\t:glob:\n\n\t./AeroTimeStepInfo\n\t./Linear\n\t./LinearTimeStepInfo\n\t./StructTimeStepInfo\n" }, { "path": "docs/source/includes/utils/docutils/check_folder_in_ignore.rst", "content": "check_folder_in_ignore\n----------------------\n\n.. automodule:: sharpy.utils.docutils.check_folder_in_ignore" }, { "path": "docs/source/includes/utils/docutils/generate_documentation.rst", "content": "generate_documentation\n----------------------\n\n.. automodule:: sharpy.utils.docutils.generate_documentation" }, { "path": "docs/source/includes/utils/docutils/index.rst", "content": "Documentation Generator\n+++++++++++++++++++++++\n\n\nFunctions to automatically document the code.\n\nComments and complaints: N. Goizueta\n\n\n.. toctree::\n\t:glob:\n\n\t./check_folder_in_ignore\n\t./generate_documentation\n\t./output_documentation_module_page\n\t./write_file\n\t./write_folder\n" }, { "path": "docs/source/includes/utils/docutils/output_documentation_module_page.rst", "content": "output_documentation_module_page\n--------------------------------\n\n.. automodule:: sharpy.utils.docutils.output_documentation_module_page" }, { "path": "docs/source/includes/utils/docutils/write_file.rst", "content": "write_file\n----------\n\n.. automodule:: sharpy.utils.docutils.write_file" }, { "path": "docs/source/includes/utils/docutils/write_folder.rst", "content": "write_folder\n------------\n\n.. automodule:: sharpy.utils.docutils.write_folder" }, { "path": "docs/source/includes/utils/exceptions/DocumentationError.rst", "content": "DocumentationError\n------------------\n\n.. autoclass:: sharpy.utils.exceptions.DocumentationError\n\t:members:" }, { "path": "docs/source/includes/utils/exceptions/NotConvergedSolver.rst", "content": "NotConvergedSolver\n------------------\n\n.. autoclass:: sharpy.utils.exceptions.NotConvergedSolver\n\t:members:" }, { "path": "docs/source/includes/utils/exceptions/NotRecognisedSetting.rst", "content": "NotRecognisedSetting\n--------------------\n\n.. autoclass:: sharpy.utils.exceptions.NotRecognisedSetting\n\t:members:" }, { "path": "docs/source/includes/utils/exceptions/NotValidSetting.rst", "content": "NotValidSetting\n---------------\n\n.. autoclass:: sharpy.utils.exceptions.NotValidSetting\n\t:members:" }, { "path": "docs/source/includes/utils/exceptions/index.rst", "content": "SHARPy Exception Classes\n++++++++++++++++++++++++\n\n\n\n.. toctree::\n\t:glob:\n\n\t./DocumentationError\n\t./NotConvergedSolver\n\t./NotRecognisedSetting\n\t./NotValidSetting\n" }, { "path": "docs/source/includes/utils/frequencyutils/find_limits.rst", "content": "find_limits\n-----------\n\n.. automodule:: sharpy.utils.frequencyutils.find_limits" }, { "path": "docs/source/includes/utils/frequencyutils/find_target_system.rst", "content": "find_target_system\n------------------\n\n.. automodule:: sharpy.utils.frequencyutils.find_target_system" }, { "path": "docs/source/includes/utils/frequencyutils/freqresp_relative_error.rst", "content": "freqresp_relative_error\n-----------------------\n\n.. automodule:: sharpy.utils.frequencyutils.freqresp_relative_error" }, { "path": "docs/source/includes/utils/frequencyutils/frobenius_norm.rst", "content": "frobenius_norm\n--------------\n\n.. automodule:: sharpy.utils.frequencyutils.frobenius_norm" }, { "path": "docs/source/includes/utils/frequencyutils/h_infinity_norm.rst", "content": "h_infinity_norm\n---------------\n\n.. automodule:: sharpy.utils.frequencyutils.h_infinity_norm" }, { "path": "docs/source/includes/utils/frequencyutils/hamiltonian.rst", "content": "hamiltonian\n-----------\n\n.. automodule:: sharpy.utils.frequencyutils.hamiltonian" }, { "path": "docs/source/includes/utils/frequencyutils/index.rst", "content": "Frequency Space Tools\n+++++++++++++++++++++\n\n\n\n\n.. toctree::\n\t:glob:\n\n\t./find_limits\n\t./find_target_system\n\t./freqresp_relative_error\n\t./frobenius_norm\n\t./h_infinity_norm\n\t./hamiltonian\n\t./l2norm\n\t./max_eigs\n" }, { "path": "docs/source/includes/utils/frequencyutils/l2norm.rst", "content": "l2norm\n------\n\n.. automodule:: sharpy.utils.frequencyutils.l2norm" }, { "path": "docs/source/includes/utils/frequencyutils/max_eigs.rst", "content": "max_eigs\n--------\n\n.. automodule:: sharpy.utils.frequencyutils.max_eigs" }, { "path": "docs/source/includes/utils/generate_cases/AerodynamicInformation.rst", "content": "AerodynamicInformation\n----------------------\n\n.. autoclass:: sharpy.utils.generate_cases.AerodynamicInformation\n\t:members:" }, { "path": "docs/source/includes/utils/generate_cases/AeroelasticInformation.rst", "content": "AeroelasticInformation\n----------------------\n\n.. autoclass:: sharpy.utils.generate_cases.AeroelasticInformation\n\t:members:" }, { "path": "docs/source/includes/utils/generate_cases/SimulationInformation.rst", "content": "SimulationInformation\n---------------------\n\n.. autoclass:: sharpy.utils.generate_cases.SimulationInformation\n\t:members:" }, { "path": "docs/source/includes/utils/generate_cases/StructuralInformation.rst", "content": "StructuralInformation\n---------------------\n\n.. autoclass:: sharpy.utils.generate_cases.StructuralInformation\n\t:members:" }, { "path": "docs/source/includes/utils/generate_cases/clean_test_files.rst", "content": "clean_test_files\n----------------\n\n.. automodule:: sharpy.utils.generate_cases.clean_test_files" }, { "path": "docs/source/includes/utils/generate_cases/from_node_array_to_elem_matrix.rst", "content": "from_node_array_to_elem_matrix\n------------------------------\n\n.. automodule:: sharpy.utils.generate_cases.from_node_array_to_elem_matrix" }, { "path": "docs/source/includes/utils/generate_cases/from_node_list_to_elem_matrix.rst", "content": "from_node_list_to_elem_matrix\n-----------------------------\n\n.. automodule:: sharpy.utils.generate_cases.from_node_list_to_elem_matrix" }, { "path": "docs/source/includes/utils/generate_cases/get_airfoil_camber.rst", "content": "get_airfoil_camber\n------------------\n\n.. automodule:: sharpy.utils.generate_cases.get_airfoil_camber" }, { "path": "docs/source/includes/utils/generate_cases/get_aoacl0_from_camber.rst", "content": "get_aoacl0_from_camber\n----------------------\n\n.. automodule:: sharpy.utils.generate_cases.get_aoacl0_from_camber" }, { "path": "docs/source/includes/utils/generate_cases/get_factor_geometric_progression.rst", "content": "get_factor_geometric_progression\n--------------------------------\n\n.. automodule:: sharpy.utils.generate_cases.get_factor_geometric_progression" }, { "path": "docs/source/includes/utils/generate_cases/get_mu0_from_camber.rst", "content": "get_mu0_from_camber\n-------------------\n\n.. automodule:: sharpy.utils.generate_cases.get_mu0_from_camber" }, { "path": "docs/source/includes/utils/generate_cases/index.rst", "content": "Generate cases\n++++++++++++++\n\nGenerate cases\n\nThis library provides functions and classes to help in the definition of SHARPy cases\n\nExamples:\n\n tests in: tests/utils/generate_cases\n examples: test/coupled/multibody/fix_node_velocity_wrtG/test_fix_node_velocity_wrtG\n test/coupled/multibody/fix_node_velocity_wrtA/test_fix_node_velocity_wrtA\n test/coupled/multibody/double_pendulum/test_double_pendulum_geradin\n test/coupled/prescribed/WindTurbine/test_rotor\n\nNotes:\n\n To use this library: import sharpy.utils.generate_cases as generate_cases\n\n\n\n.. toctree::\n\t:glob:\n\n\t./AerodynamicInformation\n\t./AeroelasticInformation\n\t./SimulationInformation\n\t./StructuralInformation\n\t./clean_test_files\n\t./from_node_array_to_elem_matrix\n\t./from_node_list_to_elem_matrix\n\t./get_airfoil_camber\n\t./get_aoacl0_from_camber\n\t./get_factor_geometric_progression\n\t./get_mu0_from_camber\n\t./read_column_sheet_type01\n" }, { "path": "docs/source/includes/utils/generate_cases/read_column_sheet_type01.rst", "content": "read_column_sheet_type01\n------------------------\n\n.. automodule:: sharpy.utils.generate_cases.read_column_sheet_type01" }, { "path": "docs/source/includes/utils/generator_interface/index.rst", "content": "Generator Interface\n+++++++++++++++++++\n\n\n\n.. toctree::\n\t:glob:\n\n\t./output_documentation\n" }, { "path": "docs/source/includes/utils/generator_interface/output_documentation.rst", "content": "output_documentation\n--------------------\n\n.. automodule:: sharpy.utils.generator_interface.output_documentation" }, { "path": "docs/source/includes/utils/geo_utils/generate_naca_camber.rst", "content": "generate_naca_camber\n--------------------\n\n.. automodule:: sharpy.utils.geo_utils.generate_naca_camber" }, { "path": "docs/source/includes/utils/geo_utils/index.rst", "content": "Airfoil Geometry Utils\n++++++++++++++++++++++\n\n\n\n\n.. toctree::\n\t:glob:\n\n\t./generate_naca_camber\n\t./interpolate_naca_camber\n" }, { "path": "docs/source/includes/utils/geo_utils/interpolate_naca_camber.rst", "content": "interpolate_naca_camber\n-----------------------\n\n.. automodule:: sharpy.utils.geo_utils.interpolate_naca_camber" }, { "path": "docs/source/includes/utils/h5utils/add_array_to_grp.rst", "content": "add_array_to_grp\n----------------\n\n.. automodule:: sharpy.utils.h5utils.add_array_to_grp" }, { "path": "docs/source/includes/utils/h5utils/add_as_grp.rst", "content": "add_as_grp\n----------\n\n.. automodule:: sharpy.utils.h5utils.add_as_grp" }, { "path": "docs/source/includes/utils/h5utils/check_file_exists.rst", "content": "check_file_exists\n-----------------\n\n.. automodule:: sharpy.utils.h5utils.check_file_exists" }, { "path": "docs/source/includes/utils/h5utils/index.rst", "content": "H5 File Management Utilities\n++++++++++++++++++++++++++++\n\nSet of utilities for opening/reading files\n\n\n.. toctree::\n\t:glob:\n\n\t./add_array_to_grp\n\t./add_as_grp\n\t./check_file_exists\n\t./read_group\n\t./readh5\n\t./save_list_as_array\n\t./saveh5\n" }, { "path": "docs/source/includes/utils/h5utils/read_group.rst", "content": "read_group\n----------\n\n.. automodule:: sharpy.utils.h5utils.read_group" }, { "path": "docs/source/includes/utils/h5utils/readh5.rst", "content": "readh5\n------\n\n.. automodule:: sharpy.utils.h5utils.readh5" }, { "path": "docs/source/includes/utils/h5utils/save_list_as_array.rst", "content": "save_list_as_array\n------------------\n\n.. automodule:: sharpy.utils.h5utils.save_list_as_array" }, { "path": "docs/source/includes/utils/h5utils/saveh5.rst", "content": "saveh5\n------\n\n.. automodule:: sharpy.utils.h5utils.saveh5" }, { "path": "docs/source/includes/utils/index.rst", "content": "Utilities\n---------\n\n\n.. toctree::\n\t:maxdepth: 1\n\n\t./algebra/index\n\t./analytical/index\n\t./control_utils/index\n\t./datastructures/index\n\t./docutils/index\n\t./exceptions/index\n\t./frequencyutils/index\n\t./generate_cases/index\n\t./generator_interface/index\n\t./geo_utils/index\n\t./h5utils/index\n\t./model_utils/index\n\t./multibody/index\n\t./plotutils/index\n\t./settings/index\n" }, { "path": "docs/source/includes/utils/model_utils/index.rst", "content": "Modelling Utilities\n+++++++++++++++++++\n\nModelling Utilities\n\n\n.. toctree::\n\t:glob:\n\n\t./mass_matrix_generator\n" }, { "path": "docs/source/includes/utils/model_utils/mass_matrix_generator.rst", "content": "mass_matrix_generator\n---------------------\n\n.. automodule:: sharpy.utils.model_utils.mass_matrix_generator" }, { "path": "docs/source/includes/utils/multibody/disp_and_accel2state.rst", "content": "disp_and_accel2state\n--------------------\n\n.. automodule:: sharpy.utils.multibody.disp_and_accel2state" }, { "path": "docs/source/includes/utils/multibody/get_elems_nodes_list.rst", "content": "get_elems_nodes_list\n--------------------\n\n.. automodule:: sharpy.utils.multibody.get_elems_nodes_list" }, { "path": "docs/source/includes/utils/multibody/index.rst", "content": "Multibody library\n+++++++++++++++++\n\nMultibody library\n\nLibrary used to manipulate multibody systems\n\nTo use this library: import sharpy.utils.multibody as mb\n\n\n\n.. toctree::\n\t:glob:\n\n\t./disp_and_accel2state\n\t./get_elems_nodes_list\n\t./merge_multibody\n\t./split_multibody\n\t./state2disp_and_accel\n\t./update_mb_dB_before_merge\n" }, { "path": "docs/source/includes/utils/multibody/merge_multibody.rst", "content": "merge_multibody\n---------------\n\n.. automodule:: sharpy.utils.multibody.merge_multibody" }, { "path": "docs/source/includes/utils/multibody/split_multibody.rst", "content": "split_multibody\n---------------\n\n.. automodule:: sharpy.utils.multibody.split_multibody" }, { "path": "docs/source/includes/utils/multibody/state2disp_and_accel.rst", "content": "state2disp_and_accel\n--------------------\n\n.. automodule:: sharpy.utils.multibody.state2disp_and_accel" }, { "path": "docs/source/includes/utils/multibody/update_mb_dB_before_merge.rst", "content": "update_mb_dB_before_merge\n-------------------------\n\n.. automodule:: sharpy.utils.multibody.update_mb_dB_before_merge" }, { "path": "docs/source/includes/utils/plotutils/index.rst", "content": "Plotting utilities\n++++++++++++++++++\n\n\n\n.. toctree::\n\t:glob:\n\n\t./plot_timestep\n\t./set_axes_equal\n" }, { "path": "docs/source/includes/utils/plotutils/plot_timestep.rst", "content": "plot_timestep\n-------------\n\n.. automodule:: sharpy.utils.plotutils.plot_timestep" }, { "path": "docs/source/includes/utils/plotutils/set_axes_equal.rst", "content": "set_axes_equal\n--------------\n\n.. automodule:: sharpy.utils.plotutils.set_axes_equal" }, { "path": "docs/source/includes/utils/settings/SettingsTable.rst", "content": "SettingsTable\n-------------\n\n.. autoclass:: sharpy.utils.settings.SettingsTable\n\t:members:" }, { "path": "docs/source/includes/utils/settings/check_settings_in_options.rst", "content": "check_settings_in_options\n-------------------------\n\n.. automodule:: sharpy.utils.settings.check_settings_in_options" }, { "path": "docs/source/includes/utils/settings/index.rst", "content": "Settings Generator Utilities\n++++++++++++++++++++++++++++\n\nSettings Generator Utilities\n\n\n.. toctree::\n\t:glob:\n\n\t./SettingsTable\n\t./check_settings_in_options\n\t./load_config_file\n" }, { "path": "docs/source/includes/utils/settings/load_config_file.rst", "content": "load_config_file\n----------------\n\n.. automodule:: sharpy.utils.settings.load_config_file" }, { "path": "docs/source/index.rst", "content": ".. SHARPy documentation master file, created by\n sphinx-quickstart on Wed Oct 19 16:40:48 2016.\n You can adapt this file completely to your liking, but it should at least\n contain the root `toctree` directive.\n\nSimulation of High Aspect Ratio planes in Python [SHARPy]\n=========================================================\n\n\n.. image:: https://img.shields.io/endpoint.svg?url=https%3A%2F%2Fraw.githubusercontent.com%2FImperialCollegeLondon%2Fsharpy%2Fmaster%2F.version.json\n\n.. image:: https://codecov.io/gh/ImperialCollegeLondon/sharpy/branch/main/graph/badge.svg\n :target: https://codecov.io/gh/ImperialCollegeLondon/sharpy\n\n.. image:: https://img.shields.io/badge/License-BSD%203--Clause-blue.svg\n :target: https://opensource.org/licenses/BSD-3-Clause\n\n.. image:: https://readthedocs.org/projects/ic-sharpy/badge/?version=main\n\n.. image:: https://joss.theoj.org/papers/f7ccd562160f1a54f64a81e90f5d9af9/status.svg\n :target: https://joss.theoj.org/papers/f7ccd562160f1a54f64a81e90f5d9af9\n\n.. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.3531965.svg\n :target: https://doi.org/10.5281/zenodo.3531965\n\nWelcome to SHARPy (Simulation of High Aspect Ratio aeroplanes in Python)!\n\nSHARPy is an aeroelastic analysis package currently under development at the Department of Aeronautics,\nImperial College London. It can be used for the structural, aerodynamic, aeroelastic and flight dynamics\nanalysis of flexible aircraft, flying wings and wind turbines. Amongst other capabilities_, it offers the following solutions to the user:\n\n* Static aerodynamic, structural and aeroelastic solutions including fuselage effects\n* Finding trim conditions for aeroelastic configurations\n* Nonlinear, dynamic time domain simulations under a large number of conditions such as:\n\n + Prescribed trajectories.\n + Free flight.\n + Dynamic follower forces.\n + Control inputs in thrust, control surface deflection...\n + Arbitrary time-domain gusts, including non span-constant ones.\n + Full 3D turbulent fields.\n\n* Multibody dynamics with hinges, articulations and prescribed nodal motions.\n\n + Applicable to wind turbines.\n + Hinged aircraft.\n + Catapult assisted takeoffs.\n\n* Linear analysis\n\n + Linearisation around a nonlinear equilibrium.\n + Frequency response analysis.\n + Asymptotic stability analysis.\n\n* Model order reduction\n\n + Krylov-subspace reduction methods.\n + Balancing reduction methods.\n\nThe modular design of SHARPy allows to simulate complex aeroelastic cases involving very flexible aircraft.\nThe structural solver supports very complex beam arrangements, while retaining geometrical nonlinearity.\nThe UVLM solver features different wake modelling fidelities while supporting large lifting surface deformations in a\nnative way. Detailed information on each of the solvers is presented in their respective documentation packages.\n\nContents\n--------\n\n.. toctree::\n :maxdepth: 1\n\n content/installation\n content/capabilities\n content/publications\n content/examples\n content/contributing\n content/casefiles\n content/solvers\n content/postproc\n includes/index\n content/test_cases\n content/debug\n content/faqs\n\nCiting SHARPy\n-------------\nSHARPy has been published in the Journal of Open Source Software (JOSS) and the relevant paper can be found\nhere_.\n\nIf you are using SHARPy for your work, please remember to cite it using the paper in JOSS as:\n\n del Carre et al., (2019). SHARPy: A dynamic aeroelastic simulation toolbox for very flexible aircraft and wind\n turbines. Journal of Open Source Software, 4(44), 1885, https://doi.org/10.21105/joss.01885\n\nThe bibtex entry for this citation is:\n\n.. code-block:: none\n\n @Article{delCarre2019,\n doi = {10.21105/joss.01885},\n url = {https://doi.org/10.21105/joss.01885},\n year = {2019},\n month = dec,\n publisher = {The Open Journal},\n volume = {4},\n number = {44},\n pages = {1885},\n author = {Alfonso del Carre and Arturo Mu{\\~{n}}oz-Sim\\'on and Norberto Goizueta and Rafael Palacios},\n title = {{SHARPy}: A dynamic aeroelastic simulation toolbox for very flexible aircraft and wind turbines},\n journal = {Journal of Open Source Software}\n }\n\n.. _here: https://joss.theoj.org/papers/10.21105/joss.01885\n\n\nIndices and tables\n------------------\n\n* :ref:`genindex`\n* :ref:`modindex`\n* :ref:`search`\n\nContact\n-------\n\nSHARPy is developed at the Department of Aeronautics, Imperial College London. To get in touch, visit the `Loads Control\nand Aeroelastics Lab `_ website.\n\n.. _capabilities: ./content/capabilities.html\n" }, { "path": "environment.yml", "content": "name: sharpy\nchannels:\n - conda-forge\n - defaults\ndependencies:\n - eigen\n - libopenblas\n - libblas\n - libcblas\n - liblapack\n - libgfortran\n - libgcc\n - libgfortran-ng\n - python=3.10\n" }, { "path": "environment_arm64.yml", "content": "name: sharpy\nchannels:\n - conda-forge\n - defaults\ndependencies:\n - eigen\n - libopenblas\n - libblas\n - libcblas\n - liblapack\n - libgfortran\n - python=3.10" }, { "path": "lib/.placeholder", "content": "" }, { "path": "lib/CMakeLists.txt", "content": "add_subdirectory(xbeam)\nadd_subdirectory(UVLM)\n" }, { "path": "pyproject.toml", "content": "[build-system]\nrequires = [\n \"setuptools\",\n #\"scikit-build>=0.13\",\n \"cmake>=3.14.3\"\n ]" }, { "path": "scripts/__init__.py", "content": "" }, { "path": "scripts/optimiser/__init__.py", "content": "" }, { "path": "scripts/optimiser/base_case/generate.py", "content": "#! /usr/bin/env python3\nimport os\nimport math\nimport h5py as h5\nimport numpy as np\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.generate_cases as gc\n\n\ndef generate(x_dict={}, case_name=None):\n \"\"\"\n\n \"\"\"\n if case_name is None:\n case_name = 'base'\n route = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n case_notes = str(x_dict)\n\n# EXECUTION\n flow = ['BeamLoader',\n 'AerogridLoader',\n # 'StaticTrim',\n 'StaticCoupled',\n 'BeamLoads',\n 'DynamicCoupled',\n 'PickleData'\n ]\n\n# FLIGHT CONDITIONS\n# the simulation is set such that the aircraft flies at a u_inf velocity while\n# the air is calm.\n try:\n u_inf = x_dict['release_velocity']\n except KeyError:\n print('Using default value of 10 for u_inf')\n u_inf = 10\n\n u_inf_cruise = 10\n original_u_inf = u_inf\n u_background = 0.5\n rho = 1.225\n\n# trim sigma = 1.5\n try:\n alpha_cato_delta = x_dict['dAoA']*np.pi/180\n except KeyError:\n print('Using default value of 0 for dAoA')\n alpha_cato_delta = 0*np.pi/180\n\n try:\n ramp_angle = x_dict['ramp_angle']*np.pi/180\n except KeyError:\n print('Using default value of 0 for ramp_angle')\n ramp_angle = 0.0\n\n alpha = 4.0782*np.pi/180 + alpha_cato_delta\n beta = 0\n roll = 0\n gravity = 'on'\n cs_deflection = -1.2703*np.pi/180\n rudder_static_deflection = 0.0\n # rudder_step = 0.0*np.pi/180\n thrust = 3.8682\n sigma = 1.5\n lambda_dihedral = 20*np.pi/180\n\n\n# trajectory\n t_start = 1.5\n\n try:\n acceleration = x_dict['acceleration']\n except KeyError:\n print('Using default value of 3 for acceleration')\n acceleration = 3.\n\n t_ramp = u_inf/acceleration\n t_finish = t_start + t_ramp\n t_free = 8\n controller_ramp = -1\n\n# numerics\n n_step = 1\n relaxation_factor = 0.4\n tolerance = 1e-6\n fsi_tolerance = 1e-5\n structural_substeps = 1\n\n num_cores = 4\n\n# MODEL GEOMETRY\n# beam\n span_main = 16.0\n lambda_main = 0.25\n ea_main = 0.3\n\n ea = 1e7\n ga = 1e5\n gj = 1e4\n eiy = 2e4\n eiz = 4e5\n m_bar_main = 0.75\n j_bar_main = 0.075\n\n length_fuselage = 10\n offset_fuselage = 0\n sigma_fuselage = 10\n m_bar_fuselage = 0.2\n j_bar_fuselage = 0.08\n\n span_tail = 2.5\n ea_tail = 0.5\n fin_height = 2.5\n ea_fin = 0.5\n sigma_tail = 10\n m_bar_tail = 0.3\n j_bar_tail = 0.08\n\n# lumped masses\n n_lumped_mass = 1\n lumped_mass_nodes = np.zeros((n_lumped_mass, ), dtype=int)\n lumped_mass = np.zeros((n_lumped_mass, ))\n lumped_mass[0] = 50\n lumped_mass_inertia = np.zeros((n_lumped_mass, 3, 3))\n lumped_mass_position = np.zeros((n_lumped_mass, 3))\n\n# aero\n chord_main = 1.0\n chord_tail = 0.5\n chord_fin = 0.5\n\n# DISCRETISATION\n# spatial discretisation\n# chordiwse panels\n m = 4\n# spanwise elements\n n_elem_multiplier = 2\n n_elem_main = int(4*n_elem_multiplier)\n n_elem_tail = int(2*n_elem_multiplier)\n n_elem_fin = int(2*n_elem_multiplier)\n n_elem_fuselage = int(2*n_elem_multiplier)\n n_surfaces = 5\n\n# temporal discretisation\n physical_time = t_finish + t_free\n tstep_factor = 1.\n dt = 1.0/m/u_inf_cruise*tstep_factor\n n_tstep = int(round(physical_time/dt))\n\n# END OF INPUT-----------------------------------------------------------------\n\n end_of_fuselage_node = 0\n flat_end_node = np.zeros((2, ), dtype=int) - 1\n\n# beam processing\n n_node_elem = 3\n span_main1 = (1.0 - lambda_main)*span_main\n span_main2 = lambda_main*span_main\n\n n_elem_main1 = round(n_elem_main*(1 - lambda_main))\n n_elem_main2 = n_elem_main - n_elem_main1\n\n# total number of elements\n n_elem = 0\n n_elem += n_elem_main1 + n_elem_main1\n n_elem += n_elem_main2 + n_elem_main2\n n_elem += n_elem_fuselage\n n_elem += n_elem_fin\n n_elem += n_elem_tail + n_elem_tail\n\n# number of nodes per part\n n_node_main1 = n_elem_main1*(n_node_elem - 1) + 1\n n_node_main2 = n_elem_main2*(n_node_elem - 1) + 1\n n_node_main = n_node_main1 + n_node_main2 - 1\n n_node_fuselage = n_elem_fuselage*(n_node_elem - 1) + 1\n n_node_fin = n_elem_fin*(n_node_elem - 1) + 1\n n_node_tail = n_elem_tail*(n_node_elem - 1) + 1\n\n# total number of nodes\n n_node = 0\n n_node += n_node_main1 + n_node_main1 - 1\n n_node += n_node_main2 - 1 + n_node_main2 - 1\n n_node += n_node_fuselage - 1\n n_node += n_node_fin - 1\n n_node += n_node_tail - 1\n n_node += n_node_tail - 1\n\n# stiffness and mass matrices\n n_stiffness = 3\n base_stiffness_main = sigma*np.diag([ea, ga, ga, gj, eiy, eiz])\n base_stiffness_fuselage = base_stiffness_main.copy()*sigma_fuselage\n base_stiffness_fuselage[4, 4] = base_stiffness_fuselage[5, 5]\n base_stiffness_tail = base_stiffness_main.copy()*sigma_tail\n base_stiffness_tail[4, 4] = base_stiffness_tail[5, 5]\n\n n_mass = 3\n base_mass_main = np.diag([m_bar_main, m_bar_main, m_bar_main, j_bar_main, 0.5*j_bar_main, 0.5*j_bar_main])\n base_mass_fuselage = np.diag([m_bar_fuselage,\n m_bar_fuselage,\n m_bar_fuselage,\n j_bar_fuselage,\n j_bar_fuselage*0.5,\n j_bar_fuselage*0.5])\n base_mass_tail = np.diag([m_bar_tail,\n m_bar_tail,\n m_bar_tail,\n j_bar_tail,\n j_bar_tail*0.5,\n j_bar_tail*0.5])\n\n\n# PLACEHOLDERS\n# beam\n x = np.zeros((n_node, ))\n y = np.zeros((n_node, ))\n z = np.zeros((n_node, ))\n beam_number = np.zeros((n_elem, ), dtype=int)\n frame_of_reference_delta = np.zeros((n_elem, n_node_elem, 3))\n structural_twist = np.zeros((n_elem, n_node_elem))\n conn = np.zeros((n_elem, n_node_elem), dtype=int)\n stiffness = np.zeros((n_stiffness, 6, 6))\n elem_stiffness = np.zeros((n_elem, ), dtype=int)\n mass = np.zeros((n_mass, 6, 6))\n elem_mass = np.zeros((n_elem, ), dtype=int)\n boundary_conditions = np.zeros((n_node, ), dtype=int)\n app_forces = np.zeros((n_node, 6))\n\n trajectory_file = route + '/' + case_name + '.traj.csv'\n LC = None\n first_node_centre = np.zeros((2, ), dtype=int)\n\n# aero\n airfoil_distribution = np.zeros((n_elem, n_node_elem), dtype=int)\n surface_distribution = np.zeros((n_elem,), dtype=int) - 1\n surface_m = np.zeros((n_surfaces, ), dtype=int)\n m_distribution = 'uniform'\n aero_node = np.zeros((n_node,), dtype=bool)\n twist = np.zeros((n_elem, n_node_elem))\n sweep = np.zeros((n_elem, n_node_elem))\n chord = np.zeros((n_elem, n_node_elem,))\n elastic_axis = np.zeros((n_elem, n_node_elem,))\n\n\n# FUNCTIONS-------------------------------------------------------------\n def clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n dyn_file_name = route + '/' + case_name + '.dyn.h5'\n if os.path.isfile(dyn_file_name):\n os.remove(dyn_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n traj_file_name = route + '/' + case_name + '.traj.csv'\n if os.path.isfile(traj_file_name):\n os.remove(traj_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n\n def generate_trajectory_file():\n it_start = math.ceil(t_start/dt)\n it_ramp = math.ceil(t_ramp/dt)\n it_total = it_start + it_ramp\n out_t = np.linspace(0, it_total*dt, it_total)\n out_x = np.zeros((it_total, ))\n out_y = np.zeros((it_total, ))\n out_z = np.zeros((it_total, ))\n\n t_hist_ramp = np.linspace(0, dt*it_ramp, it_ramp)\n x_ramp = -0.5*np.cos(ramp_angle)*acceleration*t_hist_ramp**2\n z_ramp = 0.5*np.sin(ramp_angle)*acceleration*t_hist_ramp**2\n\n out_x[:it_start] = 0.0\n out_x[it_start:] = x_ramp\n out_z[it_start:] = z_ramp\n\n out = np.zeros((it_total, 4))\n out[:, 0] = out_t\n out[:, 1] = out_x\n out[:, 2] = out_y\n out[:, 3] = out_z\n np.savetxt(trajectory_file, out, delimiter=',')\n\n def generate_dyn_file():\n global dt\n global n_tstep\n global route\n global case_name\n global num_elem\n global num_node_elem\n global num_node\n global amplitude\n global period\n\n dynamic_forces_time = None\n with_dynamic_forces = False\n with_forced_vel = False\n\n if with_dynamic_forces:\n f1 = 100\n dynamic_forces = np.zeros((num_node, 6))\n app_node = [int(num_node_main - 1), int(num_node_main)]\n dynamic_forces[app_node, 2] = f1\n force_time = np.zeros((n_tstep, ))\n limit = round(0.05/dt)\n force_time[50:61] = 1\n\n dynamic_forces_time = np.zeros((n_tstep, num_node, 6))\n for it in range(n_tstep):\n dynamic_forces_time[it, :, :] = force_time[it]*dynamic_forces\n\n forced_for_vel = None\n if with_forced_vel:\n forced_for_vel = np.zeros((n_tstep, 6))\n forced_for_acc = np.zeros((n_tstep, 6))\n for it in range(n_tstep):\n # if dt*it < period:\n # forced_for_vel[it, 2] = 2*np.pi/period*amplitude*np.sin(2*np.pi*dt*it/period)\n # forced_for_acc[it, 2] = (2*np.pi/period)**2*amplitude*np.cos(2*np.pi*dt*it/period)\n\n forced_for_vel[it, 3] = 2*np.pi/period*amplitude*np.sin(2*np.pi*dt*it/period)\n forced_for_acc[it, 3] = (2*np.pi/period)**2*amplitude*np.cos(2*np.pi*dt*it/period)\n\n if with_dynamic_forces or with_forced_vel:\n with h5.File(route + '/' + case_name + '.dyn.h5', 'a') as h5file:\n if with_dynamic_forces:\n h5file.create_dataset(\n 'dynamic_forces', data=dynamic_forces_time)\n if with_forced_vel:\n h5file.create_dataset(\n 'for_vel', data=forced_for_vel)\n h5file.create_dataset(\n 'for_acc', data=forced_for_acc)\n h5file.create_dataset(\n 'num_steps', data=n_tstep)\n\n def generate_fem():\n stiffness[0, ...] = base_stiffness_main\n stiffness[1, ...] = base_stiffness_fuselage\n stiffness[2, ...] = base_stiffness_tail\n\n mass[0, ...] = base_mass_main\n mass[1, ...] = base_mass_fuselage\n mass[2, ...] = base_mass_tail\n\n we = 0\n wn = 0\n # inner right wing\n beam_number[we:we + n_elem_main1] = 0\n y[wn:wn + n_node_main1] = np.linspace(0.0, span_main1, n_node_main1)\n\n for ielem in range(n_elem_main1):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n\n elem_stiffness[we:we + n_elem_main1] = 0\n elem_mass[we:we + n_elem_main1] = 0\n flat_end_node[0] = n_node_main1 - 1\n first_node_centre[0] = wn + 1 + 1\n boundary_conditions[0] = 1\n # remember this is in B FoR\n app_forces[0] = [0, thrust, 0, 0, 0, 0]\n we += n_elem_main1\n wn += n_node_main1\n\n # outer right wing\n beam_number[we:we + n_elem_main1] = 0\n y[wn:wn + n_node_main2 - 1] = y[wn - 1] + np.linspace(0.0, np.cos(lambda_dihedral)*span_main2, n_node_main2)[1:]\n z[wn:wn + n_node_main2 - 1] = z[wn - 1] + np.linspace(0.0, np.sin(lambda_dihedral)*span_main2, n_node_main2)[1:]\n for ielem in range(n_elem_main2):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_main2] = 0\n elem_mass[we:we + n_elem_main2] = 0\n boundary_conditions[wn + n_node_main2 - 2] = -1\n we += n_elem_main2\n wn += n_node_main2 - 1\n\n # inner left wing\n beam_number[we:we + n_elem_main1 - 1] = 1\n y[wn:wn + n_node_main1 - 1] = np.linspace(0.0, -span_main1, n_node_main1)[1:]\n for ielem in range(n_elem_main1):\n conn[we + ielem, :] = ((np.ones((3, ))*(we+ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = 0\n elem_stiffness[we:we + n_elem_main1] = 0\n elem_mass[we:we + n_elem_main1] = 0\n flat_end_node[1] = wn + n_node_main1 - 1 - 1\n first_node_centre[1] = wn + 1\n we += n_elem_main1\n wn += n_node_main1 - 1\n\n # outer left wing\n beam_number[we:we + n_elem_main2] = 1\n y[wn:wn + n_node_main2 - 1] = y[wn - 1] + np.linspace(0.0, -np.cos(lambda_dihedral)*span_main2, n_node_main2)[1:]\n z[wn:wn + n_node_main2 - 1] = z[wn - 1] + np.linspace(0.0, np.sin(lambda_dihedral)*span_main2, n_node_main2)[1:]\n for ielem in range(n_elem_main2):\n conn[we + ielem, :] = ((np.ones((3, ))*(we+ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_main2] = 0\n elem_mass[we:we + n_elem_main2] = 0\n boundary_conditions[wn + n_node_main2 - 2] = -1\n we += n_elem_main2\n wn += n_node_main2 - 1\n\n # fuselage\n beam_number[we:we + n_elem_fuselage] = 2\n x[wn:wn + n_node_fuselage - 1] = np.linspace(0.0, length_fuselage, n_node_fuselage)[1:]\n z[wn:wn + n_node_fuselage - 1] = np.linspace(0.0, offset_fuselage, n_node_fuselage)[1:]\n for ielem in range(n_elem_fuselage):\n conn[we + ielem, :] = ((np.ones((3,))*(we + ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [0.0, 1.0, 0.0]\n conn[we, 0] = 0\n elem_stiffness[we:we + n_elem_fuselage] = 1\n elem_mass[we:we + n_elem_fuselage] = 1\n we += n_elem_fuselage\n wn += n_node_fuselage - 1\n global end_of_fuselage_node\n end_of_fuselage_node = wn - 1\n\n # fin\n beam_number[we:we + n_elem_fin] = 3\n x[wn:wn + n_node_fin - 1] = x[end_of_fuselage_node]\n z[wn:wn + n_node_fin - 1] = z[end_of_fuselage_node] + np.linspace(0.0, fin_height, n_node_fin)[1:]\n for ielem in range(n_elem_fin):\n conn[we + ielem, :] = ((np.ones((3,))*(we + ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fuselage_node\n elem_stiffness[we:we + n_elem_fin] = 2\n elem_mass[we:we + n_elem_fin] = 2\n we += n_elem_fin\n wn += n_node_fin - 1\n end_of_fin_node = wn - 1\n\n # right tail\n beam_number[we:we + n_elem_tail] = 4\n x[wn:wn + n_node_tail - 1] = x[end_of_fin_node]\n y[wn:wn + n_node_tail - 1] = np.linspace(0.0, span_tail, n_node_tail)[1:]\n z[wn:wn + n_node_tail - 1] = z[end_of_fin_node]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fin_node\n elem_stiffness[we:we + n_elem_tail] = 2\n elem_mass[we:we + n_elem_tail] = 2\n boundary_conditions[wn + n_node_tail - 2] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n # left tail\n beam_number[we:we + n_elem_tail] = 5\n x[wn:wn + n_node_tail - 1] = x[end_of_fin_node]\n y[wn:wn + n_node_tail - 1] = np.linspace(0.0, -span_tail, n_node_tail)[1:]\n z[wn:wn + n_node_tail - 1] = z[end_of_fin_node]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fin_node\n elem_stiffness[we:we + n_elem_tail] = 2\n elem_mass[we:we + n_elem_tail] = 2\n boundary_conditions[wn + n_node_tail - 2] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=n_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=n_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=n_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n lumped_mass_nodes_handle = h5file.create_dataset(\n 'lumped_mass_nodes', data=lumped_mass_nodes)\n lumped_mass_handle = h5file.create_dataset(\n 'lumped_mass', data=lumped_mass)\n lumped_mass_inertia_handle = h5file.create_dataset(\n 'lumped_mass_inertia', data=lumped_mass_inertia)\n lumped_mass_position_handle = h5file.create_dataset(\n 'lumped_mass_position', data=lumped_mass_position)\n\n def generate_aero_file():\n global x, y, z\n # control surfaces\n n_control_surfaces = 2\n control_surface = np.zeros((n_elem, n_node_elem), dtype=int) - 1\n control_surface_type = np.zeros((n_control_surfaces, ), dtype=int)\n control_surface_deflection = np.zeros((n_control_surfaces, ))\n control_surface_chord = np.zeros((n_control_surfaces, ), dtype=int)\n control_surface_hinge_coord = np.zeros((n_control_surfaces, ), dtype=float)\n\n # control surface type 0 = static\n # control surface type 1 = dynamic\n control_surface_type[0] = 0\n control_surface_deflection[0] = cs_deflection\n control_surface_chord[0] = m\n control_surface_hinge_coord[0] = -0.25 # nondimensional wrt elastic axis (+ towards the trailing edge)\n\n control_surface_type[1] = 0\n control_surface_deflection[1] = rudder_static_deflection\n control_surface_chord[1] = 1\n control_surface_hinge_coord[1] = -0. # nondimensional wrt elastic axis (+ towards the trailing edge)\n\n we = 0\n wn = 0\n # right wing (surface 0, beam 0)\n i_surf = 0\n airfoil_distribution[we:we + n_elem_main, :] = 0\n surface_distribution[we:we + n_elem_main] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_main] = True\n temp_chord = np.linspace(chord_main, chord_main, n_node_main)\n temp_sweep = np.linspace(0.0, 0*np.pi/180, n_node_main)\n node_counter = 0\n for i_elem in range(we, we + n_elem_main):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = temp_chord[node_counter]\n elastic_axis[i_elem, i_local_node] = ea_main\n sweep[i_elem, i_local_node] = temp_sweep[node_counter]\n\n we += n_elem_main\n wn += n_node_main\n\n # left wing (surface 1, beam 1)\n i_surf = 1\n airfoil_distribution[we:we + n_elem_main, :] = 0\n # airfoil_distribution[wn:wn + n_node_main - 1] = 0\n surface_distribution[we:we + n_elem_main] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_main - 1] = True\n # chord[wn:wn + num_node_main - 1] = np.linspace(main_chord, main_tip_chord, num_node_main)[1:]\n # chord[wn:wn + num_node_main - 1] = main_chord\n # elastic_axis[wn:wn + num_node_main - 1] = main_ea\n temp_chord = np.linspace(chord_main, chord_main, n_node_main)\n node_counter = 0\n for i_elem in range(we, we + n_elem_main):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = temp_chord[node_counter]\n elastic_axis[i_elem, i_local_node] = ea_main\n sweep[i_elem, i_local_node] = -temp_sweep[node_counter]\n\n we += n_elem_main\n wn += n_node_main - 1\n\n we += n_elem_fuselage\n wn += n_node_fuselage - 1 - 1\n \n # fin (surface 2, beam 3)\n i_surf = 2\n airfoil_distribution[we:we + n_elem_fin, :] = 1\n # airfoil_distribution[wn:wn + n_node_fin] = 0\n surface_distribution[we:we + n_elem_fin] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_fin] = True\n # chord[wn:wn + num_node_fin] = fin_chord\n for i_elem in range(we, we + n_elem_fin):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_fin\n elastic_axis[i_elem, i_local_node] = ea_fin\n control_surface[i_elem, i_local_node] = 1\n # twist[end_of_fuselage_node] = 0\n # twist[wn:] = 0\n # elastic_axis[wn:wn + num_node_main] = fin_ea\n we += n_elem_fin\n wn += n_node_fin - 1\n #\n # # # right tail (surface 3, beam 4)\n i_surf = 3\n airfoil_distribution[we:we + n_elem_tail, :] = 2\n # airfoil_distribution[wn:wn + n_node_tail] = 0\n surface_distribution[we:we + n_elem_tail] = i_surf\n surface_m[i_surf] = m\n # XXX not very elegant\n aero_node[wn:] = True\n # chord[wn:wn + num_node_tail] = tail_chord\n # elastic_axis[wn:wn + num_node_main] = tail_ea\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n twist[i_elem, i_local_node] = -0\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_tail\n elastic_axis[i_elem, i_local_node] = ea_tail\n control_surface[i_elem, i_local_node] = 0\n\n we += n_elem_tail\n wn += n_node_tail\n #\n # # left tail (surface 4, beam 5)\n i_surf = 4\n airfoil_distribution[we:we + n_elem_tail, :] = 2\n # airfoil_distribution[wn:wn + n_node_tail - 1] = 0\n surface_distribution[we:we + n_elem_tail] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_tail - 1] = True\n # chord[wn:wn + num_node_tail] = tail_chord\n # elastic_axis[wn:wn + num_node_main] = tail_ea\n # twist[we:we + num_elem_tail] = -tail_twist\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n twist[i_elem, i_local_node] = -0\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_tail\n elastic_axis[i_elem, i_local_node] = ea_tail\n control_surface[i_elem, i_local_node] = 0\n we += n_elem_tail\n wn += n_node_tail\n\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n naca_airfoil_tail = airfoils_group.create_dataset('1', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n naca_airfoil_fin = airfoils_group.create_dataset('2', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input .attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # sweep\n sweep_input = h5file.create_dataset('sweep', data=sweep)\n dim_attr = sweep_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n control_surface_input = h5file.create_dataset('control_surface', data=control_surface)\n control_surface_deflection_input = h5file.create_dataset('control_surface_deflection', data=control_surface_deflection)\n control_surface_chord_input = h5file.create_dataset('control_surface_chord', data=control_surface_chord)\n control_surface_hinge_coord_input = h5file.create_dataset('control_surface_hinge_coord', data=control_surface_hinge_coord)\n control_surface_types_input = h5file.create_dataset('control_surface_type', data=control_surface_type)\n\n\n def generate_naca_camber(M=0, P=0):\n mm = M*1e-2\n p = P*1e-1\n\n def naca(x, mm, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return mm/(p*p)*(2*p*x - x*x)\n elif x > p and x < 1+1e-6:\n return mm/((1-p)*(1-p))*(1 - 2*p + 2*p*x - x*x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, mm, p) for x in x_vec])\n return x_vec, y_vec\n\n def generate_multibody_file():\n global end_of_fuselage_node\n global LC\n # LCR = gc.LagrangeConstraint()\n # LCR.behaviour = 'lin_vel_node_wrtG'\n # LCR.velocity = np.zeros((3,))\n # LCR.body_number = 0\n # LCR.node_number = flat_end_node[0]\n\n # LCL = gc.LagrangeConstraint()\n # LCL.behaviour = 'lin_vel_node_wrtG'\n # LCL.velocity = np.zeros((3,))\n # LCL.body_number = 0\n # LCL.node_number = flat_end_node[1]\n\n LCF = gc.LagrangeConstraint()\n LCF.behaviour = 'lin_vel_node_wrtG'\n LCF.velocity = np.zeros((3,))\n LCF.body_number = 0\n LCF.node_number = end_of_fuselage_node\n\n LCCR = gc.LagrangeConstraint()\n LCCR.behaviour = 'lin_vel_node_wrtG'\n LCCR.velocity = np.zeros((3,))\n LCCR.body_number = 0\n LCCR.node_number = first_node_centre[0]\n\n LCCL = gc.LagrangeConstraint()\n LCCL.behaviour = 'lin_vel_node_wrtG'\n LCCL.velocity = np.zeros((3,))\n LCCL.body_number = 0\n LCCL.node_number = first_node_centre[1]\n\n # LC = [LCR, LCL, LCF, LCCR, LCCL]\n LC = [LCF, LCCR, LCCL]\n\n MB1 = gc.BodyInformation()\n MB1.body_number = 0\n MB1.FoR_position = np.zeros((6,))\n MB1.FoR_velocity = np.zeros((6,))\n MB1.FoR_acceleration = np.zeros((6,))\n MB1.FoR_movement = 'free'\n MB1.quat = np.array([1.0, 0.0, 0.0, 0.0])\n\n MB = [MB1]\n gc.generate_multibody_file(LC, MB, route, case_name)\n\n\n def generate_solver_file():\n file_name = route + '/' + case_name + '.sharpy'\n settings = dict()\n settings['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': flow,\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n\n settings['BeamLoader'] = {'unsteady': 'on',\n 'orientation':\n algebra.euler2quat(np.array([roll,\n alpha,\n beta]))}\n settings['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n # 'mstar': int(160/tstep_factor),\n 'mstar': int(100/tstep_factor),\n 'freestream_dir': ['1', '0', '0'],\n 'control_surface_deflection': ['', ''],\n 'control_surface_deflection_generator':\n {'0': {},\n '1': {}}}\n\n settings['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'gravity_on': gravity,\n 'gravity': 0*9.81}\n\n settings['StaticUvlm'] = {'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': num_cores,\n 'n_rollup': 0,\n 'rollup_dt': dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_background,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': 0*rho}\n\n settings['StaticCoupled'] = {'print_info': 'off',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings':\n settings['NonLinearStatic'],\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': settings['StaticUvlm'],\n 'max_iter': 100,\n 'n_load_steps': n_step,\n 'tolerance': fsi_tolerance,\n 'relaxation_factor': relaxation_factor}\n\n settings['StaticTrim'] = {'solver': 'StaticCoupled',\n 'solver_settings': settings['StaticCoupled'],\n 'initial_alpha': alpha,\n 'initial_deflection': cs_deflection,\n 'initial_thrust': thrust}\n\n settings['NonLinearDynamicCoupledStep'] = {'print_info': 'off',\n 'max_iterations': 950,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'newmark_damp': 1e-2,\n 'gravity_on': gravity,\n 'gravity': 9.81,\n 'num_steps': n_tstep,\n 'dt': dt,\n 'initial_velocity': 0}\n\n settings['NonLinearDynamicMultibody'] = {'print_info': 'off',\n 'max_iterations': 950,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'newmark_damp': 1e-2,\n 'gravity_on': gravity,\n 'gravity': 9.81,\n 'num_steps': n_tstep,\n 'dt': dt}\n\n relative_motion = 'off'\n settings['StepUvlm'] = {'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': num_cores,\n 'n_rollup': 0,\n 'convection_scheme': 2,\n 'rollup_dt': dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'gamma_dot_filtering': 6,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_background,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho,\n 'n_time_steps': n_tstep,\n 'dt': dt}\n\n solver = 'NonLinearDynamicMultibody'\n settings['PickleData'] = {'folder': route + '/'}\n settings['DynamicCoupled'] = {'structural_solver': solver,\n 'structural_solver_settings': settings[solver],\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'fsi_substeps': 200,\n 'fsi_tolerance': fsi_tolerance,\n 'relaxation_factor': relaxation_factor,\n 'minimum_steps': 2,\n 'relaxation_steps': 150,\n 'dynamic_relaxation': 'off',\n 'final_relaxation_factor': 0.5,\n 'n_time_steps': n_tstep,\n 'dt': dt,\n 'structural_substeps': structural_substeps,\n 'include_unsteady_force_contribution': 'on',\n 'steps_without_unsteady_force': 9,\n 'controller_id': {#'controller_right': 'TakeOffTrajectoryController',\n # 'controller_left': 'TakeOffTrajectoryController',\n 'controller_tail': 'TakeOffTrajectoryController',\n 'controller_cright': 'TakeOffTrajectoryController',\n 'controller_cleft': 'TakeOffTrajectoryController',\n },\n 'controller_settings': {\n # 'controller_right':\n # {\n # 'trajectory_input_file': trajectory_file,\n # 'dt': dt,\n # 'trajectory_method': 'lagrange',\n # 'controlled_constraint': 'constraint_00',\n # 'initial_ramp_length_structural_substeps': controller_ramp,\n # 'write_controller_log': 'off',\n # },\n # 'controller_left':\n # {\n # 'trajectory_input_file': trajectory_file,\n # 'dt': dt,\n # 'trajectory_method': 'lagrange',\n # 'controlled_constraint': 'constraint_01',\n # 'initial_ramp_length_structural_substeps': controller_ramp,\n # 'write_controller_log': 'off',\n # },\n 'controller_tail':\n {\n 'trajectory_input_file': trajectory_file,\n 'dt': dt,\n 'trajectory_method': 'lagrange',\n 'controlled_constraint': 'constraint_00',\n 'initial_ramp_length_structural_substeps': controller_ramp,\n 'write_controller_log': 'off',\n }, 'controller_cright':\n {\n 'trajectory_input_file': trajectory_file,\n 'dt': dt,\n 'trajectory_method': 'lagrange',\n 'controlled_constraint': 'constraint_01',\n 'initial_ramp_length_structural_substeps': controller_ramp,\n 'write_controller_log': 'off',\n }, 'controller_cleft':\n {\n 'trajectory_input_file': trajectory_file,\n 'dt': dt,\n 'trajectory_method': 'lagrange',\n 'controlled_constraint': 'constraint_02',\n 'initial_ramp_length_structural_substeps': controller_ramp,\n 'write_controller_log': 'off',\n }},\n 'postprocessors': ['BeamLoads'],\n 'postprocessors_settings': {'BeamLoads': {'folder': route + '/output/',\n 'csv_output': 'off'},\n 'BeamPlot': {'folder': route + '/output/',\n 'include_rbm': 'on',\n 'include_applied_forces': 'on'},\n 'AerogridPlot': {\n 'folder': route + '/output/',\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n }\n }\n\n settings['BeamLoads'] = {'folder': route + '/output/',\n 'csv_output': 'off'}\n\n settings['BeamPlot'] = {'folder': route + '/output/',\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'include_forward_motion': 'on'}\n\n settings['AerogridPlot'] = {'folder': route + '/output/',\n 'include_rbm': 'on',\n 'include_forward_motion': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0,\n 'u_inf': 0,\n 'dt': dt}\n\n settings['Notes'] = {'note': case_notes}\n\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n for k, v in settings.items():\n config[k] = v\n config.write()\n\n gc.clean_test_files(route, case_name)\n generate_fem()\n generate_multibody_file()\n generate_aero_file()\n generate_solver_file()\n generate_dyn_file()\n if 'StaticTrim' not in flow:\n generate_trajectory_file()\n\n return {'sharpy': route + '/' + case_name + '.sharpy'}\n\n\nif __name__ == \"__main__\":\n generate()\n" }, { "path": "scripts/optimiser/optimiser.py", "content": "#! /usr/bin/env python3\n\"\"\"\nThis script is an example of the use of sharpy as a \"black box\"\nfor optimisation.\n\nIt works like this:\n\n*DRIVER\n ->\n*PARSE_INPUTS\n -> parser.input_file\n*READ_YAML\n -> yaml_dict\nOPTIMISER\n(\n -> yaml_dict, x\n *WRAPPER\n (\n -> yaml_dict, x\n *UNFOLD_X\n -> yaml_dict, x_dict\n *EVALUATE\n (\n *CASE_ID\n -> yaml_dict, case_name, x_dict\n SET_CASE\n -> file_names\n RUN_CASE\n -> data, x_dict, cost_dict\n *COST_FUNCTION\n (\n # GROUND CLEARANCE CONTRIBUTION\n *GET_GROUND_CLEARANCE\n *COST_SIGMOID\n )\n -> cost\n CLEAN_CASE\n ->\n )\n )\n)\n\n\n\n\"\"\"\n\nimport os\nimport sys\nimport glob\nimport shutil\nimport argparse\nimport warnings\nimport random\nimport pprint\nimport numpy as np\nimport scipy\nimport scipy.optimize as optimize\nfrom scipy.interpolate import Rbf\nimport yaml\nimport dill as pickle\nimport GPyOpt\n\n\nimport sharpy.sharpy_main\nimport sharpy.utils.exceptions as exc\n\ncases = list()\n\nloads_cost_array = None\nprev_result = None\n\n\ndef driver():\n # print information\n\n # parse args\n parser = parse_inputs()\n\n # read yaml\n yaml_dict = read_yaml(parser.input_file)\n pprint.pprint(yaml_dict)\n\n # get previous cases\n previous_x, previous_y = process_previous_cases(yaml_dict)\n\n # call optimiser\n optimiser(yaml_dict, previous_x, previous_y)\n\n # postprocess output\n\n return 0\n\n\ndef parse_inputs():\n parser = argparse.ArgumentParser(description=\n \"\"\"The optimiser.py script is an example of the use of SHARPy as a\nblack box for an optimiser. \"\"\")\n\n parser.add_argument('input_file', help='input file in YAML format')\n parser.add_argument(\"-v\", \"--verbosity\", action=\"count\", default=0,\n help=\"increase output verbosity\")\n parser = parser.parse_args()\n\n return parser\n\n\ndef read_yaml(file_name):\n \"\"\"read_yaml\n\n \"\"\"\n with open(file_name, 'r') as ifile:\n try:\n yaml_dict = yaml.safe_load(ifile)\n except yaml.YAMLError as exc:\n print(exc)\n\n return yaml_dict\n\n\ndef optimiser(in_dict, previous_x, previous_y):\n settings_dict = in_dict['settings']\n case_dict = in_dict['case']\n base_dict = in_dict['base']\n # create folder for cases if it doesn't exist\n try:\n os.mkdir(settings_dict['cases_folder'])\n except FileExistsError:\n pass\n # create folder for cases if it doesn't exist\n try:\n os.mkdir((settings_dict['cases_folder'] + '/' + case_dict['name'] + '/').replace('//', '/'))\n print('Folder made')\n except FileExistsError:\n print('cases_folder already exists')\n\n # clean folder for the new case to be run\n case_route = (settings_dict['cases_folder'] + '/' + case_dict['name'] + '/').replace('//', '/')\n\n # copy case\n try:\n print(base_dict['route'] + '/generate.py', case_route + 'generate.py')\n shutil.copyfile(base_dict['route'] + '/generate.py', case_route + 'generate.py')\n except IOError as error:\n print('Problem copying the case')\n print('Original error was: {}'.format(error))\n\n # add the case folder to the python path to run generate with it\n sys.path.append(case_route)\n # create folder for output if doesnt exist\n try:\n os.mkdir(in_dict['case']['output_folder'])\n except FileExistsError:\n pass\n\n output_route = in_dict['case']['output_folder'] + '/' + in_dict['case']['name'] + '/'\n if os.path.exists(output_route):\n warnings.warn('The folder ' + output_route + ' exists, cleaning it.')\n # cleanup folder\n try:\n shutil.rmtree(output_route)\n except:\n pass\n\n os.mkdir(output_route)\n\n n_params = len(in_dict['optimiser']['parameters'])\n bounds = []\n for k, v in in_dict['optimiser']['parameters_initial'].items():\n bounds.append({'name': in_dict['optimiser']['parameters'][k],\n 'type': 'continuous',\n 'domain': in_dict['optimiser']['parameters_bounds'][k]})\n pprint.pprint(bounds)\n\n constraints = list()\n try:\n length = in_dict['optimiser']['constraints']['ramp_length']\n acc_var_i = None\n release_vel_var_i = None\n for k, v in in_dict['optimiser']['parameters'].items():\n if v == 'acceleration':\n acc_var_i = k\n\n if v == 'release_velocity':\n release_vel_var_i = k\n\n # ramp_length = release_vel**2 / acceleration\n constraints.append({'name': 'length',\n 'constraint': '0.5*(x[:, ' + str(release_vel_var_i) + ']**2' +\n '/x[:, ' + str(acc_var_i) + '])' +\n ' - ' + str(length)})\n except KeyError:\n pass\n\n try:\n limit = in_dict['optimiser']['constraints']['incidence_angle']['limit']\n base_aoa = in_dict['optimiser']['constraints']['incidence_angle']['base_aoa']\n\n dAoA_var_i = None\n ramp_angle_var_i = None\n for k, v in in_dict['optimiser']['parameters'].items():\n if v == 'dAoA':\n dAoA_var_i = k\n if v == 'ramp_angle':\n ramp_angle_var_i = k\n\n # base_aoa + dAoA - ramp_angle < limit\n constraint_string = ''\n constraint_string += str(base_aoa) + ' + '\n constraint_string += 'x[:, ' + str(dAoA_var_i) + '] - '\n constraint_string += 'x[:, ' + str(ramp_angle_var_i) + '] - '\n constraint_string += str(limit)\n constraints.append({'name': 'angle',\n 'constraint': constraint_string})\n except KeyError:\n pass\n\n print(constraints)\n\n gpyopt_wrapper = lambda x: wrapper(x, in_dict)\n batch_size = in_dict['optimiser']['numerics']['batch_size']\n num_cores = in_dict['optimiser']['numerics']['n_cores']\n opt = GPyOpt.methods.BayesianOptimization(\n f=gpyopt_wrapper,\n domain=bounds,\n exact_feval=True,\n model_type='GP',\n acquisition_type='EI',\n normalize_y=False,\n initial_design_numdata=in_dict['optimiser']['numerics']['initial_design_numdata'],\n evaluator_type='local_penalization',\n batch_size=batch_size,\n num_cores=num_cores,\n acquisition_jitter=0,\n de_duplication=True,\n constraints=constraints,\n X=previous_x,\n Y=previous_y)\n\n opt.run_optimization(in_dict['optimiser']['numerics']['n_iter'],\n report_file=output_route + 'report.log',\n evaluations_file=output_route + 'evaluations.log',\n models_file=output_route + 'models.log',\n verbosity=True\n )\n\n print('*'*60)\n print('Best one cost: ', opt.fx_opt)\n print('\\tParameters: ', opt.x_opt)\n print('*'*60)\n with open(output_route + 'optimiser.pkl', 'wb') as f:\n pickle.dump(opt, f, protocol=pickle.HIGHEST_PROTOCOL)\n\n print('Running local optimisation step')\n local_x, local_cost = local_optimisation(opt, in_dict)\n\n if np.linalg.norm(opt.x_opt - local_x) < 1e-1:\n print('Results are very close, no need to dig deeper')\n else:\n new_cost = gpyopt_wrapper(local_x)\n print('New cost: ', new_cost)\n print('Improvement over the previous solution with the local min.: ',\n -(local_cost - opt.fx_opt)/opt.fx_opt*100, '%')\n print('The RBF estimation of the cost was off by: ',\n (local_cost - new_cost)/new_cost)\n\n print('FINISHED')\n\ndef local_optimisation(opt, yaml_dict=None, min_method='Powell'):\n x_in = opt.X\n y_in = opt.Y\n\n # rbf = create_rbf_surrogate(x_in, y_in)\n\n points = x_in\n values = y_in\n method = 'linear'\n options = {'eps': 0.1,\n 'gtol': 1e-3}\n # scipy.optimize\n local_opt = optimize.minimize(\n lambda x: gp_constrained(x, opt, yaml_dict),\n x0=opt.x_opt,\n method=min_method,\n options=options,\n jac='2-point')\n\n print('Local optimisation result: ')\n print('X = ', local_opt.x)\n print('f(X) = ', local_opt.fun)\n print('sucess = ', local_opt.success)\n print('n_inter = ', local_opt.nit)\n print('message = ', local_opt.message)\n return local_opt.x, local_opt.fun\n\n\n# def create_gp_surrogate(opt, yaml_dict):\n # breakpoint()\n # opt.mode\n\ndef gp_constrained(x_in, opt, yaml_dict):\n values, _ = opt.model.predict(np.atleast_2d(x_in))\n\n parameters = yaml_dict['optimiser']['parameters']\n bounds = np.zeros((len(parameters), 2))\n for k, v in parameters.items():\n bounds[k, :] = yaml_dict['optimiser']['parameters_bounds'][k]\n\n constraints_list = opt.constraints\n constraints = list()\n for v in constraints_list:\n constraints.append(v['constraint'])\n constraints[-1] = constraints[-1].replace(':,', '') + ' <= 0'\n\n multidim = True\n if len(x_in.shape) == 1:\n multidim = False\n\n if multidim:\n for i in range(x_in.shape[0]):\n for i_cons in range(len(constraints)):\n x = x_in[i, :]\n if not eval(constraints[i_cons]):\n values[i] += 15\n else:\n for i_cons in range(len(constraints)):\n x = x_in\n if not eval(constraints[i_cons]):\n values += 15\n\n return values\n\ndef rbf_constrained(x_in, rbf, yaml_dict, opt):\n parameters = yaml_dict['optimiser']['parameters']\n bounds = np.zeros((len(parameters), 2))\n for k, v in parameters.items():\n bounds[k, :] = yaml_dict['optimiser']['parameters_bounds'][k]\n\n constraints_list = opt.constraints\n constraints = list()\n for v in constraints_list:\n constraints.append(v['constraint'])\n constraints[-1] = constraints[-1].replace(':,', '') + ' <= 0'\n\n values = rbf(*x_in)\n\n multidim = True\n if len(x_in.shape) == 1:\n multidim = False\n\n if multidim:\n for i in range(x_in.shape[0]):\n for i_cons in range(len(constraints)):\n x = x_in[i, :]\n if not eval(constraints[i_cons]):\n values[i] += 15\n else:\n for i_cons in range(len(constraints)):\n x = x_in\n if not eval(constraints[i_cons]):\n values += 15\n\n return values\n\ndef create_rbf_surrogate(X, Y):\n rbf = Rbf(*(X.T), Y, function='multiquadric')\n return rbf\n\n\ndef case_id(case, x_dict):\n case_name = case\n for k, v in x_dict.items():\n case_name += f'_{k}_{v:7.5f}'\n case_name = case_name.replace('.', 'p')\n\n return case_name\n\n\ndef evaluate(x_dict, yaml_dict):\n case_name = case_id(yaml_dict['case']['name'], x_dict)\n\n print('Running ' + case_name)\n files, case_name = set_case(case_name,\n yaml_dict['base'],\n x_dict,\n yaml_dict['settings'],\n yaml_dict['case'])\n data = run_case(files)\n cost = cost_function(data, x_dict, yaml_dict['optimiser']['cost'])\n print(' Case: ' + str(case_name) + '; cost = ', cost)\n\n if data is not None:\n data.cost = cost\n\n if yaml_dict['settings']['delete_case_folders']:\n raise NotImplementedError('delete_case_folders not supported yet')\n if yaml_dict['settings']['save_data']:\n try:\n os.mkdir(yaml_dict['settings']['cases_folder'] +\n '/' + yaml_dict['case']['name'] + '/')\n except FileExistsError:\n pass\n with open(yaml_dict['settings']['cases_folder'] +\n '/' + yaml_dict['case']['name'] + '/' +\n 'data.pkl', 'wb') as data_file:\n pickle.dump(data, data_file, -1)\n\n return cost\n\n\ndef wrapper(x, yaml_dict):\n x_dict = unfold_x(x, yaml_dict['optimiser']['parameters'])\n cost = evaluate(x_dict, yaml_dict)\n return cost\n\n\ndef set_case(case_name, base_dict, x_dict, settings_dict, case_dict):\n \"\"\"set_case: takes care of the setup of the case\n\n This function copies the original case, given by route_base, then\n adds the folder to the python path, runs the generate.py file in there\n and removes the folder from the path.\n\n Args:\n case_name (str): name of the new case.\n base_dict(dict): dictionary with the base case info\n x_dict(dict): dictionary of state variables\n \"\"\"\n\n # runs the generate.py\n import generate\n file_names = generate.generate(x_dict, case_name)\n\n return file_names, case_name\n\ndef run_case(files):\n try:\n warnings.filterwarnings('ignore')\n data = sharpy.sharpy_main.main(args=['', files['sharpy']])\n except exc.NotConvergedSolver:\n print('The solver is not converged in this simulation with inputs')\n print('Returning None as data')\n data = None\n return data\n\n\ndef cost_function(data,\n x_dict,\n cost_dict,\n insight=False):\n \"\"\"\n x_dict is here to potentially impose constraints on the optimised\n parameters\n \"\"\"\n cost = 0.0\n clearance_cost = 0.0\n loading_cost = 0.0\n output_dict = dict()\n # check for data == None:\n if data is None:\n cost = 15. # need a better way\n return cost\n # ground clearance cost contribution\n try:\n cost_dict['ground_clearance']\n clearance, ts_clearance = get_ground_clearance(data)\n output_dict['ground_clearance'] = dict()\n clearance_cost = cost_sigmoid(clearance,\n **cost_dict['ground_clearance'])\n output_dict['ground_clearance']['clearance'] = clearance\n output_dict['ground_clearance']['cost'] = clearance_cost\n cost += clearance_cost\n except KeyError:\n pass\n\n # loads cost contribution\n try:\n cost_dict['loads']\n loading_cost = loads_cost(data, cost_dict['loads'])\n cost += loading_cost\n output_dict['loads'] = {'cost': loading_cost}\n except KeyError:\n pass\n\n if insight:\n return cost, output_dict\n else:\n return cost\n\n# def loads_cost(data, cost_loads_dict):\n # index2load = {0: 'Torsion',\n # 1: 'OOP',\n # 2: 'IP'}\n # try:\n # loads_array = np.loadtxt(\n # cost_loads_dict['reference_loads'],\n # skiprows=1,\n # delimiter=',')\n # except OSError:\n # try:\n # warnings.warn(\n # 'Not found reference_loads file, trying parent folder')\n # loads_array = np.loadtxt(\n # '../' + cost_loads_dict['reference_loads'],\n # skiprows=1,\n # delimiter=',')\n # except OSError:\n # warnings.warn('Not found reference_loads file, anywhere. Filling up with ones instead')\n # loads_array = np.ones((data.structure.ini_info.psi.shape[0], 4))\n\n # separate_cost = np.zeros((3,))\n\n # loads_array = np.abs(loads_array)\n # loads_array_norm = np.linalg.norm(loads_array, axis=0)\n # for row in range(loads_array.shape[0]):\n # for col in range(loads_array.shape[1]):\n # if loads_array[row, col] < loads_array_norm[col]:\n # loads_array[row, col] = loads_array_norm[col]\n\n # max_cost = np.zeros((3,))\n # for it, tstep in enumerate(data.structure.timestep_info):\n # temp = np.abs(tstep.postproc_cell['loads'][:, 3:])\n # max_vals = np.max(temp/loads_array[:, 1:] - 1.0, axis=0)\n # for i_dim in range(3):\n # max_cost[i_dim] = max(max_cost[i_dim], max_vals[i_dim])\n # separate_cost = max_cost\n\n # for k, v in index2load.items():\n # separate_cost[k] *= cost_loads_dict[v]['scale']\n # return np.sum(separate_cost)\n\ndef loads_cost(data, cost_loads_dict):\n index2load = {0: 'Torsion',\n 1: 'OOP',\n 2: 'IP'}\n try:\n loads_array = np.loadtxt(\n cost_loads_dict['reference_loads'],\n skiprows=1,\n delimiter=',')\n except OSError:\n try:\n warnings.warn(\n 'Not found reference_loads file, trying parent folder')\n loads_array = np.loadtxt(\n '../' + cost_loads_dict['reference_loads'],\n skiprows=1,\n delimiter=',')\n except OSError:\n warnings.warn('Not found reference_loads file, anywhere. Filling up with ones instead')\n loads_array = np.ones((data.structure.ini_info.psi.shape[0], 4))\n\n separate_cost = np.zeros((3,))\n\n loads_array_root = np.abs(loads_array[0, 1:])\n\n # max_cost = np.zeros((3,))\n # for it, tstep in enumerate(data.structure.timestep_info):\n # temp = np.abs(tstep.postproc_cell['loads'][:, 3:])\n # max_vals = np.max(temp/loads_array[:, 1:] - 1.0, axis=0)\n # for i_dim in range(3):\n # max_cost[i_dim] = max(max_cost[i_dim], max_vals[i_dim])\n # separate_cost = max_cost\n loads_history = np.zeros((len(data.structure.timestep_info), 3))\n for it, tstep in enumerate(data.structure.timestep_info):\n loads_history[it, :] = tstep.postproc_cell['loads'][0, 3:]/loads_array_root\n\n separate_cost = np.max(loads_history, axis=0) - 1.\n separate_cost = separate_cost*(separate_cost > 0)\n\n for k, v in index2load.items():\n separate_cost[k] *= cost_loads_dict[v]['scale']\n return np.sum(separate_cost)\n\n\ndef get_ground_clearance(data):\n \"\"\"\n Extracts the minimum value of for_pos[2] and returns that value and the\n timestep it happened at.\n \"\"\"\n structure = data.structure\n min_clear = np.PINF\n ts_min_clear = None\n for ts, tstep in enumerate(structure.timestep_info):\n try:\n tstep.mb_dict['constraint_00']\n continue\n except KeyError:\n pass\n if tstep.for_pos[2] < min_clear:\n min_clear = tstep.for_pos[2]\n ts_min_clear = ts\n return min_clear, ts_min_clear\n\n\ndef cost_sigmoid(z, z_min, z_0, x_offset=0.5, offset=0.0, scale=1.):\n # I need the input to f to be between 0 and 1 for relevant values\n def sigmoid_mod(x, c=4, x_offset=0.0, offset=0.0, scale=1.):\n return scale/(1. + np.exp(c*(x - x_offset))) + offset\n\n val = sigmoid_mod((z - z_min)/(z_0 - z_min),\n x_offset=x_offset,\n offset=offset,\n c=5,\n scale=scale)\n return val\n\n\ndef unfold_x(x, parameters_dict):\n x_dict = dict()\n for k, v in parameters_dict.items():\n x_dict[v] = x.flatten()[k]\n\n return x_dict\n\n\ndef process_previous_cases(yaml_dict):\n try:\n previous_cases_string = yaml_dict['previous_data']['cases']\n except KeyError:\n return None, None\n\n n_cases = len(glob.glob(previous_cases_string))\n x_out = np.zeros((n_cases, len(yaml_dict['optimiser']['parameters'])))\n y_out = np.zeros((n_cases, 1))\n\n for i, f in enumerate(glob.glob(previous_cases_string)):\n print('Loading ', f)\n with open(f, 'rb') as fhandle:\n data = pickle.load(fhandle)\n\n x_vec, x_dict = x_vec_from_data(data, yaml_dict['optimiser']['parameters'])\n x_out[i, :] = x_vec\n\n cost = cost_function(data, x_dict, yaml_dict['optimiser']['cost'])\n y_out[i, 0] = cost\n\n return x_out, y_out\n\n\ndef x_vec_from_data(data, param_dict):\n input_dict = eval(data.settings['Notes']['note'])\n\n x_vec = np.zeros((len(param_dict),))\n for k, v in param_dict.items():\n x_vec[k] = input_dict[v]\n return x_vec, input_dict\n\n\nif __name__ == '__main__':\n driver()\n\n\n\n" }, { "path": "scripts/optimiser/optimiser_input.yaml", "content": "case:\n name: r05_sc0p2_newcost\n output_folder: ./output/\nbase:\n name: base\n route: ./base_case/\n generate_file: generate.py\n\nsettings:\n delete_case_folders: false\n cases_folder: ./cases/\n save_data: true\n\nprevious_data:\n cases: ../../../../optimisers_postproc/cases/r10_sc0p1_newcost/*.pkl\n\noptimiser:\n numerics:\n tolerance: 0.01 \n n_iter: 30\n batch_size: 4\n n_cores: 16\n initial_design_numdata: 4\n parameters:\n 0: acceleration\n 1: dAoA\n 2: ramp_angle\n 3: release_velocity\n parameters_initial:\n 0: 2.0\n 1: 0.1\n 2: 0.0\n 3: 9.5\n parameters_bounds:\n 0: [1.0, 7.0]\n 1: [-1.0, 8.0]\n 2: [-1.0, 8.0]\n 3: [3.0, 15.0]\n cost:\n ground_clearance:\n z_min: -4\n z_0: 2\n scale: 10\n loads:\n reference_loads: 'input/cruise_loads.csv'\n Torsion:\n scale: 0.2\n OOP:\n scale: 0.2\n IP:\n scale: 0.2\n constraints:\n ramp_length: 5.0\n incidence_angle:\n limit: 9.0\n base_aoa: 4.09\n\n" }, { "path": "scripts/xplaneUDPout/HALE_varDIe.acf", "content": "I\n1004 version\nACF\n\nPROPERTIES_BEGIN\nP _cgpt/0/_name empty craft\nP _cgpt/0/_w_max 142.199996948\nP _cgpt/0/_w_now 142.199996948\nP _cgpt/0/_w_test 142.198120117\nP _cgpt/0/_z_ref 0.0\nP _cgpt/1/_name fuel tank #1\nP _cgpt/1/_w_max 0.0\nP _cgpt/1/_w_now 1.0\nP _cgpt/1/_w_test 0.0\nP _cgpt/1/_z_ref 0.0\nP _cgpt/10/_w_max 0.0\nP _cgpt/10/_w_now 1.0\nP _cgpt/10/_w_test 0.0\nP _cgpt/10/_z_ref 0.0\nP _cgpt/11/_w_max 0.0\nP _cgpt/11/_w_now 1.0\nP _cgpt/11/_w_test 0.0\nP _cgpt/11/_z_ref 0.0\nP _cgpt/12/_w_max 0.0\nP _cgpt/12/_w_now 1.0\nP _cgpt/12/_w_test 0.0\nP _cgpt/12/_z_ref 0.0\nP _cgpt/13/_w_max 0.0\nP _cgpt/13/_w_now 1.0\nP _cgpt/13/_w_test 0.0\nP _cgpt/13/_z_ref 0.0\nP _cgpt/14/_w_max 0.0\nP _cgpt/14/_w_now 1.0\nP _cgpt/14/_w_test 0.0\nP _cgpt/14/_z_ref 0.0\nP _cgpt/15/_w_max 0.0\nP _cgpt/15/_w_now 1.0\nP _cgpt/15/_w_test 0.0\nP _cgpt/15/_z_ref 0.0\nP _cgpt/16/_w_max 0.0\nP _cgpt/16/_w_now 1.0\nP _cgpt/16/_w_test 0.0\nP _cgpt/16/_z_ref 0.0\nP _cgpt/17/_w_max 0.0\nP _cgpt/17/_w_now 1.0\nP _cgpt/17/_w_test 0.0\nP _cgpt/17/_z_ref 0.0\nP _cgpt/18/_w_max 0.0\nP _cgpt/18/_w_now 1.0\nP _cgpt/18/_w_test 0.0\nP _cgpt/18/_z_ref 0.0\nP _cgpt/19/_w_max 0.0\nP _cgpt/19/_w_now 1.0\nP _cgpt/19/_w_test 0.0\nP _cgpt/19/_z_ref 0.0\nP _cgpt/2/_name fuel tank #2\nP _cgpt/2/_w_max 0.0\nP _cgpt/2/_w_now 1.0\nP _cgpt/2/_w_test 0.0\nP _cgpt/2/_z_ref 0.0\nP _cgpt/3/_name fuel tank #3\nP _cgpt/3/_w_max 0.0\nP _cgpt/3/_w_now 1.0\nP _cgpt/3/_w_test 0.0\nP _cgpt/3/_z_ref 0.0\nP _cgpt/4/_name fuel tank #4\nP _cgpt/4/_w_max 0.0\nP _cgpt/4/_w_now 1.0\nP _cgpt/4/_w_test 0.0\nP _cgpt/4/_z_ref 0.0\nP _cgpt/5/_name fuel tank #5\nP _cgpt/5/_w_max 0.0\nP _cgpt/5/_w_now 1.0\nP _cgpt/5/_w_test 0.0\nP _cgpt/5/_z_ref 0.0\nP _cgpt/6/_name fuel tank #6\nP _cgpt/6/_w_max 0.0\nP _cgpt/6/_w_now 1.0\nP _cgpt/6/_w_test 0.0\nP _cgpt/6/_z_ref 0.0\nP _cgpt/7/_name fuel tank #7\nP _cgpt/7/_w_max 0.0\nP _cgpt/7/_w_now 1.0\nP _cgpt/7/_w_test 0.0\nP _cgpt/7/_z_ref 0.0\nP _cgpt/8/_name fuel tank #8\nP _cgpt/8/_w_max 0.0\nP _cgpt/8/_w_now 1.0\nP _cgpt/8/_w_test 0.0\nP _cgpt/8/_z_ref 0.0\nP _cgpt/9/_name fuel tank #9\nP _cgpt/9/_w_max 0.0\nP _cgpt/9/_w_now 1.0\nP _cgpt/9/_w_test 0.0\nP _cgpt/9/_z_ref 0.0\nP _cgpt/count 20\nP _door/0/_type 0\nP _door/1/_type 0\nP _door/10/_type 0\nP _door/11/_type 0\nP _door/12/_type 0\nP _door/13/_type 0\nP _door/14/_type 0\nP _door/15/_type 0\nP _door/16/_type 0\nP _door/17/_type 0\nP _door/18/_type 0\nP _door/19/_type 0\nP _door/2/_type 0\nP _door/3/_type 0\nP _door/4/_type 0\nP _door/5/_type 0\nP _door/6/_type 0\nP _door/7/_type 0\nP _door/8/_type 0\nP _door/9/_type 0\nP _door/count 20\nP _engn/count 8\nP _gear/0/_axiE 0.0\nP _gear/0/_axiN 0.0\nP _gear/0/_axiR 0.0\nP _gear/0/_cyc_time 5.0\nP _gear/0/_damp -nan\nP _gear/0/_dep_rat 1.0\nP _gear/0/_eagle_claw_deg 0.0\nP _gear/0/_gear_brakes 0\nP _gear/0/_gear_can_retract 0\nP _gear/0/_gear_castors 0\nP _gear/0/_gear_def_empty 0.0\nP _gear/0/_gear_def_gross 0.0\nP _gear/0/_gear_load_fraction -nan\nP _gear/0/_gear_type 2\nP _gear/0/_gear_x 0.0\nP _gear/0/_gear_y 0.0\nP 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0\nP acf/_xmsn_of_prop/5 0\nP acf/_xmsn_of_prop/6 0\nP acf/_xmsn_of_prop/7 0\nP acf/_xmsn_of_prop/count 8\nP acf/_yawbr_cratR 0.0\nP acf/_yawbr_cratT 0.0\nP acf/_yawbr_rat1 1.0\nP acf/_yawbr_rat2 1.0\nP acf/_yawbr_ud 0.0\nP acf/_yawbr_v1 0.0\nP acf/_yawbr_v2 0.0\nP acf/_yawstring_x 512.0\nP acf/_yawstring_y 431.0\nP acf/_yel_hi_CHT 0\nP acf/_yel_hi_EGT 0\nP acf/_yel_hi_EPR 0\nP acf/_yel_hi_FF 0\nP acf/_yel_hi_ITT 0\nP acf/_yel_hi_MP 0\nP acf/_yel_hi_N1 0\nP acf/_yel_hi_N1_apu 0\nP acf/_yel_hi_N2 0\nP acf/_yel_hi_TRQ 0\nP acf/_yel_hi_bat_amp 0\nP acf/_yel_hi_bat_volt 0\nP acf/_yel_hi_fuelP 0\nP acf/_yel_hi_gen_amp 0\nP acf/_yel_hi_gen_volt 0\nP acf/_yel_hi_oilP 0\nP acf/_yel_hi_oilT 0\nP acf/_yel_hi_pwr 0\nP acf/_yel_hi_vac 0\nP acf/_yel_hi_xmsn_P 0\nP acf/_yel_hi_xmsn_T 0\nP acf/_yel_lo_CHT 0\nP acf/_yel_lo_EGT 0\nP acf/_yel_lo_EPR 0\nP acf/_yel_lo_FF 0\nP acf/_yel_lo_ITT 0\nP acf/_yel_lo_MP 0\nP acf/_yel_lo_N1 0\nP acf/_yel_lo_N1_apu 0\nP acf/_yel_lo_N2 0\nP acf/_yel_lo_TRQ 0\nP acf/_yel_lo_bat_amp 0\nP acf/_yel_lo_bat_volt 0\nP acf/_yel_lo_fuelP 0\nP acf/_yel_lo_gen_amp 0\nP acf/_yel_lo_gen_volt 0\nP acf/_yel_lo_oilP 0\nP acf/_yel_lo_oilT 0\nP acf/_yel_lo_pwr 0\nP acf/_yel_lo_vac 0\nP acf/_yel_lo_xmsn_P 0\nP acf/_yel_lo_xmsn_T 0\nPROPERTIES_END\nPANEL_2D_BEGIN\nhoriz_vac horizon_GA_vac.png\n POS 224.000000 307.000000\n DATAREF \n LIGHT_MODE MECHANICAL\n LIGHT_RHEOSTAT 0\n KEY_FRAME 0.000000 0.000000 1.000000\n KEY_FRAME 1.000000 1.000000\n\nPANEL_2D_END\nPANEL_3D_BEGIN\nhoriz_vac_adj horizon_GA_vac_adj.\n POS 294.000000 303.000000\n DATAREF \n LIGHT_MODE MECHANICAL\n LIGHT_RHEOSTAT 0\n KEY_FRAME 0.000000 0.000000 1.000000\n KEY_FRAME 1.000000 1.000000\n\nPANEL_3D_END\n" }, { "path": "scripts/xplaneUDPout/__init__.py", "content": "" }, { "path": "scripts/xplaneUDPout/variables.yaml", "content": "---\n# for_pos needs positions 0 to 2 to get the x,y,z position\n- name: 'for_pos'\n var_type: 'node'\n inout: 'out'\n position: 0\n- name: 'for_pos'\n var_type: 'node'\n inout: 'out'\n position: 1\n- name: 'for_pos'\n var_type: 'node'\n inout: 'out'\n position: 2\n# The quaternion has 4 terms. All are neeeded to carry out\n# the conversion to roll, pitch and yaw\n- name: 'quat'\n var_type: 'node'\n inout: 'out'\n position: 0\n- name: 'quat'\n var_type: 'node'\n inout: 'out'\n position: 1\n- name: 'quat'\n var_type: 'node'\n inout: 'out'\n position: 2\n- name: 'quat'\n var_type: 'node'\n inout: 'out'\n position: 3\n# Valid for simple HALE\n# Vertical tip deflection (In positive y-axis)\n- name: 'pos'\n var_type: 'node'\n inout: 'out'\n # Row\n position: 16\n # Column\n index: 2\n# Horizontal tip deflection\n- name: 'pos'\n var_type: 'node'\n inout: 'out'\n position: 16\n index: 0\n# # Simple HALE has two control surfaces\n# - name: 'control_surface_deflection' # variable name. those in the timestep_info are supported\n# var_type: 'control_surface'\n# inout: 'out' # either `in`, `out` or `inout`\n# position: 0 # control surface index\n# - name: 'control_surface_deflection' \n# var_type: 'control_surface'\n# inout: 'out' \n# position: 1 \n# - name: 'control_surface_deflection' \n# var_type: 'control_surface'\n# inout: 'out' \n# position: 2 \n...\n" }, { "path": "scripts/xplaneUDPout/xplaneUDP.py", "content": "import socket\nimport struct\nimport binascii\nimport pickle\nimport os\nimport numpy as np\n\nimport sharpy.utils.solver_interface as solver_interface\nimport sharpy.postproc\nfrom sharpy.utils.algebra import quat2euler\n\nclass XPlaneIpNotFound(Exception):\n args = \"Could not find any running XPlane instance in network.\"\n\n\nclass XPlaneTimeout(Exception):\n args = \"XPlane timeout.\"\n\n\nclass XPlaneUdp:\n \"\"\"\n Class that co-ordinates the sending of data via UDP to X-Plane\n\n ``YAML`` file assumed to be have variables in the order of, pos (x,y,z), quat (4 vars), vertical tip \n deflection, horizontal tip deflection\n\n Uses SHARPy UDPout postprocessor \n \"\"\"\n\n # Discover X-Plane via Beacon and uses multicast\n # Constants\n UDP_PORT = 49000\n MCAST_GRP = \"239.255.1.1\"\n MCAST_PORT = 49707 \n EARTH_RADIUS = 6378.137*10 ** 3 # Equatorial radius in [m]\n\n MAX_DIHEDRAL = 180 # Degrees\n MAX_SWEEP = 90 # Degrees\n\n HEIGHT_OFFSET = 100 # Meters\n DEFLECTION_ANGLE_MULTIPLICATOR = 10\n\n def __init__(self, pklFile):\n # Find location of X-Plane\n self.BeaconData = self.find_ip_xplane()\n\n self._byte_ordering = '<'\n\n _host, _port = self.find_local_ip()\n\n settings = dict()\n\n settings['UDPout'] = {\n 'output_network_settings': {\n 'destination_address': [self.BeaconData['IP']],\n 'destination_ports': [self.BeaconData['Port']],\n 'address': _host,\n 'port': _port,\n },\n 'variables_filename': os.getcwd() + '/variables.yaml',\n }\n\n self.timestep_counter = 0\n self.data = pklFile\n\n self.udpSolver = solver_interface.initialise_solver('UDPout')\n self.udpSolver.initialise(data, custom_settings=settings['UDPout'])\n\n # Longitude and Latitude of LHR (arbitrarily set) \n self.locLat = 51.470020 # 0\n self.locLon = -0.454295 # 0\n self.prevX = 0\n self.prevY = 0\n\n self.drefPaths = {}\n self.drefPaths['overrideCS'] = \"sim/operation/override/override_control_surfaces\"\n ### Ailerons ###\n self.drefPaths['leftAileronDef'] = \"sim/flightmodel/controls/wing1l_ail1def\"\n self.drefPaths['rightAileronDef'] = \"sim/flightmodel/controls/wing1r_ail1def\"\n ### Stabilisers ###\n self.drefPaths['elevatorDef'] = \"sim/flightmodel/controls/hstab1_elv1def\"\n self.drefPaths['rudderDef'] = \"sim/flightmodel/controls/vstab1_rud1def\"\n # Cockpit Panel Indicator \n # Dref for: The indicated pitch on the panel for the first vacuum instrument\n self.drefPaths['vertIndicator'] = \"sim/cockpit/gyros/the_vac_ind_deg\"\n # Dref for: The indicated roll on the panel for the first vacuum instrument\n self.drefPaths['horzIndicator'] = \"sim/cockpit/gyros/phi_vac_ind_deg\"\n # The flightmodel2 section contains data about how the actual aircraft is being drawn\n # Actual sweep in ratio (0=> no sweep, 1 => max sweep) [float, ratio]\n self.drefPaths['variableSweep'] = \"sim/flightmodel2/controls/wingsweep_ratio\"\n # Acutal dihedral [float, ratio]\n self.drefPaths['variableDihedral'] = \"sim/flightmodel2/controls/dihedral_ratio\"\n # Actual incidence [float, ratio]\n self.drefPaths['variableIncidence'] = \"sim/flightmodel2/controls/incidence_ratio\"\n # Datarefs above achieve the same\n # self.drefPaths['variableSweep'] = \"sim/flightmodel/controls/swdi\"\n # self.drefPaths['variableDihedral'] = \"sim/flightmodel/controls/dihed_rat\"\n # self.drefPaths['variableIncidence'] = \"sim/flightmodel/controls/incid_ratio\"\n\n def run(self):\n # Get values for a given time step\n vals = self.get_struct_value(\n self.data, timestep_index=self.timestep_counter)\n # Encode location information\n dvisMsg = self.encode_dvis(vals)\n # Send encoded information\n self.udpSolver.out_network.send(\n dvisMsg, self.udpSolver.out_network.clients)\n\n # Aeroelastic Information on cockpit panel \n vals = self.convert_tip_disp_to_angle(vals, [7, 8], 16)\n indicatorMsg = self.encode_dref(\n self.drefPaths['vertIndicator'], 7, lstOfVals=vals)\n self.udpSolver.out_network.send(\n indicatorMsg, self.udpSolver.out_network.clients)\n\n indicatorMsg2 = self.encode_dref(\n self.drefPaths['horzIndicator'], 8, lstOfVals=vals)\n self.udpSolver.out_network.send(\n indicatorMsg2, self.udpSolver.out_network.clients)\n\n # The simulation used here has fixed control surfaces\n vals = np.append(vals, np.asarray([-2.08, -2.08, 0]))\n\n # Send control surface information\n overrideMsg = self.encode_dref(self.drefPaths['overrideCS'], True)\n self.udpSolver.out_network.send(\n overrideMsg, self.udpSolver.out_network.clients)\n\n leftAilMsg = self.encode_dref(\n self.drefPaths['leftAileronDef'], 9, lstOfVals=vals)\n self.udpSolver.out_network.send(\n leftAilMsg, self.udpSolver.out_network.clients)\n\n rightAilMsg = self.encode_dref(\n self.drefPaths['rightAileronDef'], 10, lstOfVals=vals)\n self.udpSolver.out_network.send(\n rightAilMsg, self.udpSolver.out_network.clients)\n\n elevatorMsg = self.encode_dref(\n self.drefPaths['elevatorDef'], 11, lstOfVals=vals)\n self.udpSolver.out_network.send(\n elevatorMsg, self.udpSolver.out_network.clients)\n\n # Aeroelastic Information on wing\n vals = self.find_deflection_ratio(\n vals, [7, 8], [self.MAX_DIHEDRAL, self.MAX_SWEEP])\n dihedralMsg = self.encode_dref(\n self.drefPaths['variableDihedral'], 12, lstOfVals=vals)\n self.udpSolver.out_network.send(\n dihedralMsg, self.udpSolver.out_network.clients)\n\n sweepMsg = self.encode_dref(\n self.drefPaths['variableSweep'], 13, lstOfVals=vals)\n self.udpSolver.out_network.send(\n sweepMsg, self.udpSolver.out_network.clients)\n\n # incidenceMsg = self.encode_dref(\n # self.drefPaths['variableIncidence'], 14, lstOfVals=vals)\n # self.udpSolver.out_network.send(\n # incidenceMsg, self.udpSolver.out_network.clients)\n\n # # Incrementthe counter so it accesses the next time step values\n self.timestep_counter += 1\n\n def get_struct_value(self, data, timestep_index=-1):\n numVars = len(self.udpSolver.set_of_variables.variables)\n values = np.zeros(numVars)\n for i in range(numVars):\n try:\n values[i] = self.udpSolver.set_of_variables.variables[i].get_variable_value(\n data, timestep_index)\n except:\n # This is very dangerous!!\n # Created to handle the fact that the first control surface deflection angle is\n # not stored in the pickle (list is empty)\n values[i] = 0\n return values\n\n def encode_dref(self, drefPath, idx, lstOfVals=np.asarray([])):\n \"\"\"Sets any dataref to a given value via UDP\n\n The datarefs used by X-Plane can be found at, https://developer.x-plane.com/datarefs/\n ::\n\n struct dref_struct:\n {\n xflt var;\n xchar dref_path[strDIM];\n }\n\n N.B. Instructions in the sending data to X-Plane manually state that the dref_path needs to be \n null-terminated. However, doing so made the dataref unrecognisible to X-Plane. The issue\n was fixed by removing the null value. \n The instructions also state the the whole message should have size 509 bytes. However, this\n made X-Plane throw an error stating that the message is the incorrect length. The issue was \n resolves by changing the message length to be 512 bytes\n\n Therefore, typical message looks like,\n DREF0 + (4byte value) + dref_path + spaces to complte the whole message to 512 bytes. \n (N.B. + => append. Don't include them in the actual message)\n\n E.G. to switch on anti-ice switch\n DREF0 + (4byte value of 1) + sim/cockpit/switches/anti_ice_surf_heat_left + spaces to complete \n to 512 bytes \n\n Args:\n drefPath (str): Dataref path to the variable being set \n idx (int): Location of value to set in lstOfVals \n lstOfVals (array): All data \n\n Returns:\n Message to be sent to X-Plane in the required format\n \"\"\"\n msg = struct.pack('{}5s'.format(self._byte_ordering), b'DREF0')\n\n if lstOfVals.size == 0 and type(idx) == bool:\n # This is to send a boolean value (allows for override command to be sent)\n\n # Based on the information from XPlane dataref website, the type should be\n # int but when int is used for the format, XPlane always reads the value as\n # 0 instead of what the actual value is. Therefore, the type for packing \n # needs to be f (float) instead of int\n msg += struct.pack('{}f'.format(self._byte_ordering), int(idx))\n elif lstOfVals.size == 0:\n raise ValueError(\n \"If list of values is empty, idx must be a boolean to indicate override\")\n else:\n msg += struct.pack('{}f'.format(self._byte_ordering),\n lstOfVals[idx])\n\n # Convert dref path which is a string to bytes\n drefPath = bytes(drefPath, 'utf-8') # Add dreft path and null terminate it\n msg += struct.pack(\"{}s\".format(len(drefPath)), drefPath)\n # Find the size of the message\n msgSize = struct.calcsize('5sf' + \"{}s\".format(len(drefPath)))\n # Determine how many blank spaces to include\n remainder = 512 - msgSize\n # Append the black spaces to complete to 512 bytes\n msg += struct.pack('{}x'.format(remainder))\n\n return msg\n\n def encode_dvis(self, lstOfVals):\n \"\"\"Sends message to X-Plane to turn off flight engine and this sets location of aircraft\n\n To run X-Plane as a visual, the flight engine needs to be turned off, this is achieved by sending\n \"DVIS0\" followed by the struct:\n\n ::\n\n struct dvis_struct:\n {\n xdob lat_lon_ele[3]; # double precision for lattitude, longitude & elevation above MSL (m)\n xdob psi_the_phi[3]; # True heading, pitch up, roll right in degrees \n }\n \n Double precision is used to avoid byte-spacing confusion \n N.B. This should be sent at a higher frame rate than X-Plane for smooth animation \n\n Args:\n lstOfVals (array): Numpy array that contains all the information obtained from pickled sim \n\n Returns:\n Message to be sent to X-Plane in the required format \n \"\"\"\n msg = struct.pack('{}5s'.format(self._byte_ordering), b'DVIS0')\n lat, lon = self.convert_to_lat_lon(lstOfVals)\n msg += struct.pack(\"{}ddd\".format(self._byte_ordering),\n lat, lon, lstOfVals[2]+self.HEIGHT_OFFSET)\n # Information from pickle is in quaternion form. Therefore, this needs\n # to be converted to euler angles\n eulerAngles = quat2euler(lstOfVals[3:7])\n # Above conversion results in radians but X-Plane requires degrees\n eulerAngles = np.rad2deg(eulerAngles)\n # Individual naming for clarity\n roll, pitch, yaw = eulerAngles\n msg += struct.pack('{}ddd'.format(self._byte_ordering),\n yaw, pitch, roll)\n\n return msg\n\n def convert_to_lat_lon(self, values):\n \"\"\"Converts x, y positions[m] from simulation to latitude and logitude[degrees]\n\n This method is taken from: \n https://stackoverflow.com/questions/10122055/calculate-longitude-from-distance\n\n Args:\n values (array): Contains all simulation data for a given time step. It is assumed that \n the x, y position is in the 0th and 1st position respectively\n\n Returns:\n Local latitude [degrees], Local longitude [degrees] \n\n \"\"\"\n x = values[0]\n dx = x - self.prevX\n y = values[1]\n dy = y - self.prevY\n\n deltaLon = dx/self.EARTH_RADIUS\n deltaLat = dx/self.EARTH_RADIUS\n\n self.locLat = self.locLat + np.sign(dy)*np.rad2deg(deltaLat)\n self.locLon = self.locLon + np.sign(dx)*np.rad2deg(deltaLon*1.195)\n\n return self.locLat, self.locLon\n\n def convert_tip_disp_to_angle(self, lstOfVals, indices, arm):\n \"\"\"Converts tip displacement(m) to an angle(degrees)\n\n Sign conventions are: Positive vertical displacmenet implies up. Positive horizontal \n displacement implies aft\n\n Args:\n indices (iterable): Refers to the indices that need conversion\n arm: (float) Semi-span of the wing for tip displacement but any length along the wing can be used as \n long as it corresponds to be displacement seen \n lstOfVals (array): Numpy array that contains all the information for a given timestep\n\n Returns:\n Updated lstOfVals array\n \"\"\"\n for index in indices:\n angle = np.rad2deg(np.arctan(float(lstOfVals[index])/arm))\n lstOfVals[index] = angle\n\n return lstOfVals\n\n def find_deflection_ratio(self, lstOfVals, indices, limits):\n \"\"\"Converts an angle of deflection to ratio with respect to the maximum deflection angle\n\n N.B: This step MUST take place after the tip displacement has been converted to angles (degree) \n\n Args:\n indices (iterable): Location within origin array of vals\n limits (iterable): Value which the ratio is found with respect to (i.e. the maximum value) \n lstOfVals (array): Numpy array that contains all the information for a given timestep\n\n Returns:\n Updated lstOfVals array\n\n \"\"\"\n temp = np.zeros(len(indices))\n for i, index in enumerate(indices):\n temp[i] = float(lstOfVals[index])/limits[i]\n\n lstOfVals = np.append(lstOfVals, temp)\n\n return lstOfVals\n\n def find_local_ip(self):\n \"\"\"Finds default IP and open port\n\n This automates the process of entering an IP address and port in the settings for SHARPy UDPout\n post-processor \n\n This function has been adapted from: https://stackoverflow.com/questions/166506/finding-local-ip-addresses-using-pythons-stdlib\n\n Returns:\n Single IP address that is the default route and an open port \n \"\"\"\n s = socket.socket(socket.AF_INET, socket.SOCK_DGRAM)\n try:\n # Doesn't even have to be reachable\n s.connect(('10.255.255.255', 1))\n IP, port = s.getsockname()\n except Exception:\n IP = '127.0.0.1'\n # This is a randomly chosen number\n port = 50585\n finally:\n s.close()\n return IP, port\n\n def find_ip_xplane(self):\n \"\"\"Finds X-Plane host in network \n\n This takes the first X-Plane 10 host it can find. To prevent confusion, ensure only one is running \n\n This function is wholesale from: https://github.com/charlylima/XPlaneUDP/blob/master/XPlaneUdp.py\n\n Returns:\n Dictionary containing IP, port, hostname, X-Plane version and role\n \"\"\"\n\n self.BeaconData = {}\n\n # open socket for multicast group.\n sock = socket.socket(\n socket.AF_INET, socket.SOCK_DGRAM, socket.IPPROTO_UDP)\n sock.setsockopt(socket.SOL_SOCKET, socket.SO_REUSEADDR, 1)\n sock.bind((self.MCAST_GRP, self.MCAST_PORT))\n mreq = struct.pack(\"=4sl\", socket.inet_aton(\n self.MCAST_GRP), socket.INADDR_ANY)\n sock.setsockopt(socket.IPPROTO_IP, socket.IP_ADD_MEMBERSHIP, mreq)\n sock.settimeout(3.0)\n\n while not self.BeaconData:\n\n # receive data\n try:\n packet, sender = sock.recvfrom(15000)\n\n # decode data\n # * Header\n header = packet[0:5]\n if header != b\"BECN\\x00\":\n print(\"Unknown packet from \"+sender[0])\n print(str(len(packet)) + \" bytes\")\n print(packet)\n print(binascii.hexlify(packet))\n\n else:\n data = packet[5:21]\n # struct becn_struct\n # {\n # \tuchar beacon_major_version;\t\t// 1 at the time of X-Plane 10.40\n # \tuchar beacon_minor_version;\t\t// 1 at the time of X-Plane 10.40\n # \txint application_host_id;\t\t// 1 for X-Plane, 2 for PlaneMaker\n # \txint version_number;\t\t\t// 104014 for X-Plane 10.40b14\n # \tuint role;\t\t\t\t\t\t// 1 for master, 2 for extern visual, 3 for IOS\n # \tushort port;\t\t\t\t\t// port number X-Plane is listening on\n # \txchr\tcomputer_name[strDIM];\t// the hostname of the computer\n # };\n beacon_major_version = 0\n beacon_minor_version = 0\n application_host_id = 0\n xplane_version_number = 0\n role = 0\n port = 0\n (\n beacon_major_version, # 1 at the time of X-Plane 10.40\n beacon_minor_version, # 1 at the time of X-Plane 10.40\n application_host_id, # 1 for X-Plane, 2 for PlaneMaker\n xplane_version_number, # 104014 for X-Plane 10.40b14\n role, # 1 for master, 2 for extern visual, 3 for IOS\n port, # port number X-Plane is listening on\n ) = struct.unpack(\" -r /path/to/ \n \n To check that X-Plane is receiving all information being sent, get X-Plane to dump net data to log.txt.\n Under Settings > Operations & Warnings > Data > dumpt net data to log.txt.\n Log.txt can be found under the X-Plane 10 folder in your computer.\n\n How it works:\n\n 1. Finds X-Plane 10 via Beacon (uses multicast)\n 2. Finds default IP and an open port to send simulation information via \n 3. Initialises SHARPy UDPout post-processor \n 4. For every timestep in the simulation, send the information specified in run via UDP to the X-Plane datarefs\n\n Adapted from:\n https://github.com/charlylima/XPlaneUDP/blob/master/XPlaneUdp.py\n Original is for receiving data from X-Plane and has been adapted to send data to X-Plane\n\n See also: X-Plane Manual for sending and receiving info to X-Plane found in installed folder.\n X-Plane 10 > Instructions > Sending Data to X-plane.rtfd > TXT.rtf\n\n \"\"\"\n\n import argparse\n import time\n\n parser = argparse.ArgumentParser()\n parser.add_argument('-r', '--restart', help='restart the solution with a given snapshot', type=str,\n default=None, required=True)\n\n args = parser.parse_args()\n\n try:\n with open(args.restart, 'rb') as restart_file:\n data = pickle.load(restart_file)\n except FileNotFoundError:\n raise FileNotFoundError('The file specified for the snapshot \\\n restart (-r) does not exist. Please check.')\n\n xp = XPlaneUdp(data)\n\n for _ in range(data.ts + 1):\n xp.run()\n # Prevents all simulaiton info from being sent all at once\n time.sleep(0.03)\n" }, { "path": "setup.py", "content": "from setuptools import setup, find_packages, Extension, Command\n#from skbuild import setup\nfrom setuptools.command.build_ext import build_ext\nimport subprocess\n\nimport re\nimport os\n\nclass CMakeBuildExt(build_ext):\n \"\"\"Custom command to build Submodules packages during installation.\"\"\"\n\n # def copy_extensions_to_source(self):\n # \"Override the method to prevent copying package files\"\n # pass\n \n def finalize_options(self):\n super().finalize_options()\n # Process and use os.environ['CUSTOM_CONFIG_SETTINGS'] as needed\n self.pip_nobuild = os.environ.get('PIP_NOBUILD')\n\n def run(self):\n\n package_dir = os.path.dirname(os.path.abspath(__file__))\n build_dir = package_dir + \"/build\"\n cmake_args = []\n if self.pip_nobuild==\"yes\":\n pass\n else:\n if not os.path.isdir(build_dir):\n os.makedirs(build_dir)\n subprocess.check_call(\n [\"cmake\", \"..\"] + cmake_args, cwd=build_dir\n )\n subprocess.check_call(\n [\"make\", \"install\", \"-j4\"], cwd=build_dir\n )\n\n super().run()\n\ndef run():\n\n pip_nobuild = os.environ.get('PIP_NOBUILD')\n package_dir = os.path.dirname(os.path.abspath(__file__))\n build_dir = package_dir + \"/build\"\n cmake_args = []\n if pip_nobuild==\"yes\":\n pass\n else:\n if not os.path.isdir(build_dir):\n os.makedirs(build_dir)\n subprocess.check_call(\n [\"cmake\", \"..\"] + cmake_args, cwd=build_dir\n )\n subprocess.check_call(\n [\"make\", \"install\", \"-j4\"], cwd=build_dir\n )\n\nclass BuildCommand(Command):\n \"\"\"Custom command to build Submodules packages without installation.\"\"\"\n\n description = 'Build Submodules in lib packages'\n user_options = [\n ('cmake-args=', None, 'Additional CMake arguments'),\n ]\n\n def initialize_options(self):\n self.cmake_args = None\n\n def finalize_options(self):\n pass\n\n def run(self):\n # Run the CMake build step with additional cmake_args\n package_dir = os.path.dirname(os.path.abspath(__file__))\n build_dir = package_dir + \"/build\"\n if not os.path.isdir(build_dir):\n os.makedirs(build_dir)\n if self.cmake_args is not None:\n subprocess.check_call(\n [\"cmake\", f\"{self.cmake_args}\", \"..\"], cwd=build_dir\n )\n else:\n subprocess.check_call(\n [\"cmake\", \"..\"], cwd=build_dir\n )\n \n subprocess.check_call(\n [\"make\", \"install\", \"-j4\"], cwd=build_dir\n )\n\next_modules = [\n Extension('lib', []),\n # Add more Extension instances for additional extension modules\n]\n\nthis_directory = os.path.abspath(os.path.dirname(__file__))\n__version__ = re.findall(\n r\"\"\"__version__ = [\"']+([0-9\\.]*)[\"']+\"\"\",\n open(os.path.join(this_directory, \"sharpy/version.py\")).read(),\n)[0]\n\nwith open(os.path.join(this_directory, \"README.md\"), encoding=\"utf-8\") as f:\n long_description = f.read()\nrun()\nsetup(\n name=\"ic_sharpy\", # due to the name sharpy being taken on pypi\n version=__version__,\n description=\"\"\"SHARPy is a nonlinear aeroelastic analysis package developed\n at the Department of Aeronautics, Imperial College London. It can be used\n for the structural, aerodynamic and aeroelastic analysis of flexible\n aircraft, flying wings and wind turbines.\"\"\",\n long_description=long_description,\n long_description_content_type=\"text/markdown\",\n keywords=\"nonlinear aeroelastic structural aerodynamic analysis\",\n author=\"\",\n author_email=\"\",\n url=\"https://github.com/ImperialCollegeLondon/sharpy\",\n license=\"BSD 3-Clause License\",\n #ext_modules=ext_modules,\n cmdclass={#\"build_ext\": CMakeBuildExt,\n \"build_subm\": BuildCommand},\n packages=find_packages(\n where='./',\n include=['sharpy*'],\n exclude=['tests']\n ),\n # data_files=[\n # (\"./lib/UVLM/lib\", [\"libuvlm.so\"]),\n # (\"./lib/xbeam/lib\", [\"libxbeam.so\"])\n # ],\n python_requires=\">=3.8\",\n install_requires=[\n \"numpy<2.0\",\n \"configobj\",\n \"h5py\",\n \"scipy<1.14.0\",\n \"sympy\",\n \"matplotlib\",\n \"colorama\",\n \"dill\",\n \"jupyterlab\",\n \"pandas\",\n \"control\",\n \"openpyxl>=3.0.10\",\n \"lxml>=4.4.1\",\n \"PySocks\",\n \"PyYAML\",\n \"jax\",\n \"vtk\",\n ],\n extras_require={\n \"docs\": [\n \"sphinx\",\n \"recommonmark>=0.6.0\",\n \"sphinx_rtd_theme>=0.4.3\",\n \"nbsphinx>=0.4.3\"\n ],\n \"all\": [\n \"sphinx\",\n \"recommonmark>=0.6.0\",\n \"sphinx_rtd_theme>=0.4.3\",\n \"nbsphinx>=0.4.3\"\n ],\n },\n classifiers=[\n \"Operating System :: MacOS\",\n \"Operating System :: POSIX :: Linux\",\n \"Programming Language :: Python :: 3.10\",\n \"Programming Language :: Fortran\",\n \"Programming Language :: C++\"\n ],\n\n entry_points={\n 'console_scripts': ['sharpy=sharpy.sharpy_main:sharpy_run'],\n }\n)\n" }, { "path": "sharpy/__init__.py", "content": "from .version import __version__\n" }, { "path": "sharpy/aero/__init__.py", "content": "\"\"\"Aerodynamic Packages\"\"\"" }, { "path": "sharpy/aero/models/__init__.py", "content": "" }, { "path": "sharpy/aero/models/aerogrid.py", "content": "\"\"\"Aerogrid\n\nAerogrid contains all the necessary routines to generate an aerodynamic\ngrid based on the input dictionaries.\n\"\"\"\nimport ctypes as ct\nimport warnings\n\nimport numpy as np\nimport scipy.interpolate\n\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.cout_utils as cout\nfrom sharpy.utils.datastructures import AeroTimeStepInfo\nimport sharpy.utils.generator_interface as gen_interface\n\nfrom sharpy.aero.models.grid import Grid\n\n\nclass Aerogrid(Grid):\n \"\"\"\n ``Aerogrid`` is the main object containing information of the grid of panels\n\n It is created by the solver :class:`sharpy.solvers.aerogridloader.AerogridLoader`\n\n \"\"\"\n\n def __init__(self):\n super().__init__()\n self.dimensions_star = None\n self.airfoil_db = dict()\n\n self.grid_type = \"aero\"\n self.n_control_surfaces = 0\n\n self.cs_generators = []\n\n self.initial_strip_z_rot = None\n\n def generate(self, data_dict, beam, settings, ts):\n super().generate(data_dict, beam, settings, ts)\n\n # write grid info to screen\n self.output_info()\n\n # allocating initial grid storage\n self.ini_info = AeroTimeStepInfo(self.dimensions,\n self.dimensions_star)\n\n # Initial panel orientation, used when aligned grid is off\n self.initial_strip_z_rot = np.zeros([self.n_elem, 3])\n if not settings['aligned_grid'] and settings['initial_align']:\n for i_elem in range(self.n_elem):\n for i_local_node in range(3):\n Cab = algebra.crv2rotation(beam.ini_info.psi[i_elem, i_local_node, :])\n self.initial_strip_z_rot[i_elem, i_local_node] = \\\n algebra.angle_between_vectors_sign(settings['freestream_dir'], Cab[:, 1], Cab[:, 2])\n\n # load airfoils db\n # for i_node in range(self.n_node):\n for i_elem in range(self.n_elem):\n for i_local_node in range(self.beam.num_node_elem):\n try:\n self.airfoil_db[self.data_dict['airfoil_distribution'][i_elem, i_local_node]]\n except KeyError:\n airfoil_coords = self.data_dict['airfoils'][\n str(self.data_dict['airfoil_distribution'][i_elem, i_local_node])]\n self.airfoil_db[self.data_dict['airfoil_distribution'][i_elem, i_local_node]] = (\n scipy.interpolate.interp1d(airfoil_coords[:, 0],\n airfoil_coords[:, 1],\n kind='quadratic',\n copy=False,\n fill_value='extrapolate',\n assume_sorted=True))\n try:\n self.n_control_surfaces = np.sum(np.unique(self.data_dict['control_surface']) >= 0)\n except KeyError:\n pass\n\n # Backward compatibility: check whether control surface deflection aero_settings have been specified. If not, create\n # section with empty list, such that no cs generator is appended\n try:\n settings['control_surface_deflection']\n except KeyError:\n settings.update({'control_surface_deflection': [''] * self.n_control_surfaces})\n\n # pad ctrl surfaces dict with empty strings if not defined\n if len(settings['control_surface_deflection']) != self.n_control_surfaces:\n undef_ctrl_sfcs = [''] * (self.n_control_surfaces - len(settings['control_surface_deflection']))\n settings['control_surface_deflection'].extend(undef_ctrl_sfcs)\n\n # initialise generators\n with_error_initialising_cs = False\n for i_cs in range(self.n_control_surfaces):\n if settings['control_surface_deflection'][i_cs] == '':\n self.cs_generators.append(None)\n else:\n cout.cout_wrap('Initialising Control Surface {:g} generator'.format(i_cs), 1)\n # check that the control surface is not static\n if self.data_dict['control_surface_type'][i_cs] == 0:\n raise TypeError('Control surface {:g} is defined as static but there is a control surface generator'\n 'associated with it'.format(i_cs))\n generator_type = gen_interface.generator_from_string(\n settings['control_surface_deflection'][i_cs])\n self.cs_generators.append(generator_type())\n try:\n self.cs_generators[i_cs].initialise(\n settings['control_surface_deflection_generator_settings'][str(i_cs)])\n except KeyError:\n with_error_initialising_cs = True\n cout.cout_wrap('Error, unable to locate a settings dictionary for control surface '\n '{:g}'.format(i_cs), 4)\n\n if with_error_initialising_cs:\n raise KeyError('Unable to locate settings for at least one control surface.')\n\n self.add_timestep()\n self.generate_mapping()\n self.generate_zeta(self.beam, self.aero_settings, ts)\n\n if 'polars' in self.data_dict:\n import sharpy.aero.utils.airfoilpolars as ap\n self.polars = []\n nairfoils = np.amax(self.data_dict['airfoil_distribution']) + 1\n for iairfoil in range(nairfoils):\n new_polar = ap.Polar()\n new_polar.initialise(data_dict['polars'][str(iairfoil)])\n self.polars.append(new_polar)\n\n def output_info(self):\n cout.cout_wrap('The aerodynamic grid contains %u surfaces' % self.n_surf, 1)\n for i_surf in range(self.n_surf):\n cout.cout_wrap(' Surface %u, M=%u, N=%u' % (i_surf,\n self.dimensions[i_surf, 0],\n self.dimensions[i_surf, 1]), 1)\n cout.cout_wrap(' Wake %u, M=%u, N=%u' % (i_surf,\n self.dimensions_star[i_surf, 0],\n self.dimensions_star[i_surf, 1]))\n cout.cout_wrap(' In total: %u bound panels' % (sum(self.dimensions[:, 0] *\n self.dimensions[:, 1])))\n cout.cout_wrap(' In total: %u wake panels' % (sum(self.dimensions_star[:, 0] *\n self.dimensions_star[:, 1])))\n cout.cout_wrap(' Total number of panels = %u' % (sum(self.dimensions[:, 0] *\n self.dimensions[:, 1]) +\n sum(self.dimensions_star[:, 0] *\n self.dimensions_star[:, 1])))\n\n def calculate_dimensions(self):\n super().calculate_dimensions()\n\n self.dimensions_star = self.dimensions.copy()\n self.dimensions_star[:, 0] = self.aero_settings['mstar']\n\n def generate_zeta_timestep_info(self, structure_tstep, aero_tstep, beam, settings, it=None, dt=None):\n if it is None:\n it = len(beam.timestep_info) - 1\n global_node_in_surface = []\n for i_surf in range(self.n_surf):\n global_node_in_surface.append([])\n\n # check that we have control surface information\n try:\n self.data_dict['control_surface']\n with_control_surfaces = True\n except KeyError:\n with_control_surfaces = False\n\n # check that we have sweep information\n try:\n self.data_dict['sweep']\n except KeyError:\n self.data_dict['sweep'] = np.zeros_like(self.data_dict['twist'])\n\n # Define first_twist for backwards compatibility\n if 'first_twist' not in self.data_dict:\n self.data_dict['first_twist'] = [True] * self.data_dict['surface_m'].shape[0]\n\n # one surface per element\n for i_elem in range(self.n_elem):\n i_surf = self.data_dict['surface_distribution'][i_elem]\n # check if we have to generate a surface here\n if i_surf == -1:\n continue\n\n for i_local_node in range(len(self.beam.elements[i_elem].global_connectivities)):\n i_global_node = self.beam.elements[i_elem].global_connectivities[i_local_node]\n # i_global_node = self.beam.elements[i_elem].global_connectivities[\n # self.beam.elements[i_elem].ordering[i_local_node]]\n if not self.data_dict['aero_node'][i_global_node]:\n continue\n if i_global_node in global_node_in_surface[i_surf]:\n continue\n else:\n global_node_in_surface[i_surf].append(i_global_node)\n\n # find the i_surf and i_n data from the mapping\n i_n = -1\n ii_surf = -1\n for i in range(len(self.struct2aero_mapping[i_global_node])):\n i_n = self.struct2aero_mapping[i_global_node][i]['i_n']\n ii_surf = self.struct2aero_mapping[i_global_node][i]['i_surf']\n if ii_surf == i_surf:\n break\n # make sure it found it\n if i_n == -1 or ii_surf == -1:\n raise AssertionError('Error 12958: Something failed with the mapping in aerogrid.py. Check/report!')\n\n # control surface implementation\n control_surface_info = None\n if with_control_surfaces:\n # 1) check that this node and elem have a control surface\n if self.data_dict['control_surface'][i_elem, i_local_node] >= 0:\n i_control_surface = self.data_dict['control_surface'][i_elem, i_local_node]\n # 2) type of control surface + write info\n control_surface_info = dict()\n if self.data_dict['control_surface_type'][i_control_surface] == 0:\n control_surface_info['type'] = 'static'\n control_surface_info['deflection'] = self.data_dict['control_surface_deflection'][\n i_control_surface]\n control_surface_info['chord'] = self.data_dict['control_surface_chord'][i_control_surface]\n try:\n control_surface_info['hinge_coords'] = self.data_dict['control_surface_hinge_coords'][\n i_control_surface]\n except KeyError:\n control_surface_info['hinge_coords'] = None\n elif self.data_dict['control_surface_type'][i_control_surface] == 1:\n control_surface_info['type'] = 'dynamic'\n control_surface_info['chord'] = self.data_dict['control_surface_chord'][i_control_surface]\n try:\n control_surface_info['hinge_coords'] = self.data_dict['control_surface_hinge_coords'][\n i_control_surface]\n except KeyError:\n control_surface_info['hinge_coords'] = None\n\n params = {'it': it}\n control_surface_info['deflection'], control_surface_info['deflection_dot'] = \\\n self.cs_generators[i_control_surface](params)\n\n elif self.data_dict['control_surface_type'][i_control_surface] == 2:\n control_surface_info['type'] = 'controlled'\n\n try:\n old_deflection = self.data.aero.timestep_info[-1].control_surface_deflection[\n i_control_surface]\n except AttributeError:\n try:\n old_deflection = aero_tstep.control_surface_deflection[i_control_surface]\n except IndexError:\n old_deflection = self.data_dict['control_surface_deflection'][i_control_surface]\n\n try:\n control_surface_info['deflection'] = aero_tstep.control_surface_deflection[\n i_control_surface]\n except IndexError:\n control_surface_info['deflection'] = self.data_dict['control_surface_deflection'][\n i_control_surface]\n\n if dt is not None:\n control_surface_info['deflection_dot'] = (\n (control_surface_info['deflection'] - old_deflection) / dt)\n else:\n control_surface_info['deflection_dot'] = 0.0\n\n control_surface_info['chord'] = self.data_dict['control_surface_chord'][i_control_surface]\n\n try:\n control_surface_info['hinge_coords'] = self.data_dict['control_surface_hinge_coords'][\n i_control_surface]\n except KeyError:\n control_surface_info['hinge_coords'] = None\n else:\n raise NotImplementedError(str(self.data_dict['control_surface_type'][i_control_surface]) +\n ' control surfaces are not yet implemented')\n\n # add sweep for aerogrid warping in constraint defintition\n # if no constraint_xx.aerogrid warp factor is provided or the constraint is not an actuated type,\n # this will be ignored\n ang_warp = 0.\n if structure_tstep.mb_dict is not None and structure_tstep.mb_prescribed_dict is not None:\n for i_constraint in range(structure_tstep.mb_dict['num_constraints']):\n cst_name = f\"constraint_{i_constraint:02d}\"\n if ('controller_id' in structure_tstep.mb_dict[cst_name]\n and 'aerogrid_warp_factor' in structure_tstep.mb_dict[cst_name]):\n ctrl_id = structure_tstep.mb_dict[cst_name]['controller_id'].decode('UTF-8')\n f_warp = structure_tstep.mb_dict[cst_name]['aerogrid_warp_factor'][i_elem, i_local_node]\n ang_z = structure_tstep.mb_prescribed_dict[ctrl_id]['delta_psi'][2]\n ang_warp += f_warp * ang_z\n\n node_info = dict()\n node_info['i_node'] = i_global_node\n node_info['i_local_node'] = i_local_node\n node_info['chord'] = self.data_dict['chord'][i_elem, i_local_node] / np.cos(ang_warp)\n node_info['eaxis'] = self.data_dict['elastic_axis'][i_elem, i_local_node]\n node_info['twist'] = self.data_dict['twist'][i_elem, i_local_node]\n node_info['sweep'] = self.data_dict['sweep'][i_elem, i_local_node] + ang_warp\n node_info['M'] = self.dimensions[i_surf, 0]\n node_info['M_distribution'] = self.data_dict['m_distribution'].decode('ascii')\n node_info['airfoil'] = self.data_dict['airfoil_distribution'][i_elem, i_local_node]\n node_info['control_surface'] = control_surface_info\n node_info['beam_coord'] = structure_tstep.pos[i_global_node, :]\n node_info['pos_dot'] = structure_tstep.pos_dot[i_global_node, :]\n node_info['beam_psi'] = structure_tstep.psi[i_elem, i_local_node, :]\n node_info['psi_dot'] = structure_tstep.psi_dot[i_elem, i_local_node, :]\n node_info['for_delta'] = beam.frame_of_reference_delta[i_elem, i_local_node, :]\n node_info['elem'] = beam.elements[i_elem]\n node_info['for_pos'] = structure_tstep.for_pos\n node_info['cga'] = structure_tstep.cga()\n if node_info['M_distribution'].lower() == 'user_defined':\n ielem_in_surf = i_elem - np.sum(self.surface_distribution < i_surf)\n node_info['user_defined_m_distribution'] = self.data_dict['user_defined_m_distribution'][\n str(i_surf)][:, ielem_in_surf, i_local_node]\n (aero_tstep.zeta[i_surf][:, :, i_n],\n aero_tstep.zeta_dot[i_surf][:, :, i_n]) = (\n generate_strip(node_info,\n self.airfoil_db,\n self.aero_settings['aligned_grid'],\n initial_strip_z_rot=self.initial_strip_z_rot[i_elem, i_local_node],\n orientation_in=self.aero_settings['freestream_dir'],\n calculate_zeta_dot=True))\n # set junction boundary conditions for later phantom cell creation in UVLM\n if \"junction_boundary_condition\" in self.data_dict:\n if np.any(self.data_dict[\"junction_boundary_condition\"] >= 0):\n self.generate_phantom_panels_at_junction(aero_tstep)\n\n def generate_phantom_panels_at_junction(self, aero_tstep):\n for i_surf in range(self.n_surf):\n aero_tstep.flag_zeta_phantom[0, i_surf] = self.data_dict[\"junction_boundary_condition\"][0, i_surf]\n\n @staticmethod\n def compute_gamma_dot(dt, tstep, previous_tsteps):\n r\"\"\"\n Computes the temporal derivative of circulation (gamma) using finite differences.\n\n It will use a first order approximation for the first evaluation\n (when ``len(previous_tsteps) == 1``), and then second order ones.\n\n .. math:: \\left.\\frac{d\\Gamma}{dt}\\right|^n \\approx \\lim_{\\Delta t \\rightarrow 0}\\frac{\\Gamma^n-\\Gamma^{n-1}}{\\Delta t}\n\n For the second time step and onwards, the following second order approximation is used:\n\n .. math:: \\left.\\frac{d\\Gamma}{dt}\\right|^n \\approx \\lim_{\\Delta t \\rightarrow 0}\\frac{3\\Gamma^n -4\\Gamma^{n-1}+\\Gamma^{n-2}}{2\\Delta t}\n\n Args:\n dt (float): delta time for the finite differences\n tstep (AeroTimeStepInfo): tstep at time n (current)\n previous_tsteps (list(AeroTimeStepInfo)): previous tstep structure in order: ``[n-N,..., n-2, n-1]``\n\n Returns:\n float: first derivative of circulation with respect to time\n\n See Also:\n .. py:class:: sharpy.utils.datastructures.AeroTimeStepInfo\n \"\"\"\n # Check whether the iteration is part of FSI (ie the input is a k-step) or whether it is an only aerodynamic\n # simulation\n part_of_fsi = True\n try:\n if tstep is previous_tsteps[-1]:\n part_of_fsi = False\n except IndexError:\n for i_surf in range(tstep.n_surf):\n tstep.gamma_dot[i_surf].fill(0.0)\n return\n\n if len(previous_tsteps) == 0:\n for i_surf in range(tstep.n_surf):\n tstep.gamma_dot[i_surf].fill(0.0)\n\n if part_of_fsi:\n for i_surf in range(tstep.n_surf):\n tstep.gamma_dot[i_surf] = (tstep.gamma[i_surf] - previous_tsteps[-1].gamma[i_surf]) / dt\n else:\n for i_surf in range(tstep.n_surf):\n tstep.gamma_dot[i_surf] = (tstep.gamma[i_surf] - previous_tsteps[-2].gamma[i_surf]) / dt\n\n\ndef generate_strip(node_info, airfoil_db, aligned_grid,\n initial_strip_z_rot,\n orientation_in=np.array([1, 0, 0]),\n calculate_zeta_dot=False,\n first_twist=True):\n \"\"\"\n Returns a strip of panels in ``A`` frame of reference, it has to be then rotated to\n simulate angles of attack, etc\n \"\"\"\n strip_coordinates_a_frame = np.zeros((3, node_info['M'] + 1), dtype=ct.c_double)\n strip_coordinates_b_frame = np.zeros((3, node_info['M'] + 1), dtype=ct.c_double)\n zeta_dot_a_frame = np.zeros((3, node_info['M'] + 1), dtype=ct.c_double)\n\n # airfoil coordinates\n # we are going to store everything in the x-z plane of the b\n # FoR, so that the transformation Cab rotates everything in place.\n if node_info['M_distribution'] == 'uniform':\n strip_coordinates_b_frame[1, :] = np.linspace(0.0, 1.0, node_info['M'] + 1)\n elif node_info['M_distribution'] == '1-cos':\n domain = np.linspace(0, 1.0, node_info['M'] + 1)\n strip_coordinates_b_frame[1, :] = 0.5 * (1.0 - np.cos(domain * np.pi))\n elif node_info['M_distribution'].lower() == 'user_defined':\n strip_coordinates_b_frame[1, :] = node_info['user_defined_m_distribution']\n else:\n raise NotImplemented('M_distribution is ' + node_info['M_distribution'] +\n ' and it is not yet supported')\n strip_coordinates_b_frame[2, :] = airfoil_db[node_info['airfoil']](\n strip_coordinates_b_frame[1, :])\n\n # elastic axis correction\n for i_M in range(node_info['M'] + 1):\n strip_coordinates_b_frame[1, i_M] -= node_info['eaxis']\n\n # chord_line_b_frame = strip_coordinates_b_frame[:, -1] - strip_coordinates_b_frame[:, 0]\n cs_velocity = np.zeros_like(strip_coordinates_b_frame)\n\n # control surface deflection\n if node_info['control_surface'] is not None:\n b_frame_hinge_coords = strip_coordinates_b_frame[:, node_info['M'] - node_info['control_surface']['chord']]\n # support for different hinge location for fully articulated control surfaces\n if node_info['control_surface']['hinge_coords'] is not None:\n # make sure the hinge coordinates are only applied when M == cs_chord\n if not node_info['M'] - node_info['control_surface']['chord'] == 0:\n node_info['control_surface']['hinge_coords'] = None\n else:\n b_frame_hinge_coords = node_info['control_surface']['hinge_coords']\n\n for i_M in range(node_info['M'] - node_info['control_surface']['chord'], node_info['M'] + 1):\n relative_coords = strip_coordinates_b_frame[:, i_M] - b_frame_hinge_coords\n # rotate the control surface\n relative_coords = np.dot(algebra.rotation3d_x(-node_info['control_surface']['deflection']),\n relative_coords)\n # deflection velocity\n try:\n cs_velocity[:, i_M] += np.cross(np.array([-node_info['control_surface']['deflection_dot'], 0.0, 0.0]),\n relative_coords)\n except KeyError:\n pass\n\n # restore coordinates\n relative_coords += b_frame_hinge_coords\n\n # substitute with new coordinates\n strip_coordinates_b_frame[:, i_M] = relative_coords\n\n # chord scaling\n strip_coordinates_b_frame *= node_info['chord']\n\n # twist transformation (rotation around x_b axis)\n if np.abs(node_info['twist']) > 1e-6:\n Ctwist = algebra.rotation3d_x(node_info['twist'])\n else:\n Ctwist = np.eye(3)\n\n # Cab transformation\n Cab = algebra.crv2rotation(node_info['beam_psi'])\n\n if aligned_grid:\n rot_angle = algebra.angle_between_vectors_sign(orientation_in, Cab[:, 1], Cab[:, 2])\n else:\n rot_angle = initial_strip_z_rot\n Crot = algebra.rotation3d_z(-rot_angle)\n\n c_sweep = np.eye(3)\n if np.abs(node_info['sweep']) > 1e-6:\n c_sweep = algebra.rotation3d_z(node_info['sweep'])\n\n # transformation from beam to beam prime (with sweep and twist)\n for i_M in range(node_info['M'] + 1):\n if first_twist:\n strip_coordinates_b_frame[:, i_M] = np.dot(c_sweep, np.dot(Crot,\n np.dot(Ctwist,\n strip_coordinates_b_frame[:, i_M])))\n else:\n strip_coordinates_b_frame[:, i_M] = np.dot(Ctwist, np.dot(Crot,\n np.dot(c_sweep,\n strip_coordinates_b_frame[:, i_M])))\n strip_coordinates_a_frame[:, i_M] = np.dot(Cab, strip_coordinates_b_frame[:, i_M])\n\n cs_velocity[:, i_M] = np.dot(Cab, cs_velocity[:, i_M])\n\n # zeta_dot\n if calculate_zeta_dot:\n # velocity due to pos_dot\n for i_M in range(node_info['M'] + 1):\n zeta_dot_a_frame[:, i_M] += node_info['pos_dot']\n\n # velocity due to psi_dot\n omega_a = algebra.crv_dot2omega(node_info['beam_psi'], node_info['psi_dot'])\n for i_M in range(node_info['M'] + 1):\n zeta_dot_a_frame[:, i_M] += (\n np.dot(algebra.skew(omega_a), strip_coordinates_a_frame[:, i_M]))\n\n # control surface deflection velocity contribution\n try:\n if node_info['control_surface'] is not None:\n node_info['control_surface']['deflection_dot']\n for i_M in range(node_info['M'] + 1):\n zeta_dot_a_frame[:, i_M] += cs_velocity[:, i_M]\n except KeyError:\n pass\n\n else:\n zeta_dot_a_frame = np.zeros((3, node_info['M'] + 1), dtype=ct.c_double)\n\n # add node coords\n for i_M in range(node_info['M'] + 1):\n strip_coordinates_a_frame[:, i_M] += node_info['beam_coord']\n\n # add quarter-chord disp\n delta_c = (strip_coordinates_a_frame[:, -1] - strip_coordinates_a_frame[:, 0]) / node_info['M']\n if node_info['M_distribution'] == 'uniform':\n for i_M in range(node_info['M'] + 1):\n strip_coordinates_a_frame[:, i_M] += 0.25 * delta_c\n else:\n warnings.warn(\"No quarter chord disp of grid for non-uniform grid distributions implemented\", UserWarning)\n\n # rotation from a to g\n for i_M in range(node_info['M'] + 1):\n strip_coordinates_a_frame[:, i_M] = np.dot(node_info['cga'],\n strip_coordinates_a_frame[:, i_M])\n zeta_dot_a_frame[:, i_M] = np.dot(node_info['cga'],\n zeta_dot_a_frame[:, i_M])\n\n return strip_coordinates_a_frame, zeta_dot_a_frame\n" }, { "path": "sharpy/aero/models/grid.py", "content": "\"\"\"Grid\n\nGrid contains\n\"\"\"\nimport ctypes as ct\nimport warnings\n\nimport numpy as np\n\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.generator_interface as gen_interface\n\n\nclass Grid(object):\n \"\"\"\n ``Grid``is the parent class for the lifting surface grid and nonlifting\n body grids.\n\n It is created by the solver :class:`sharpy.solvers.aerogridloader.AerogridLoader`\n\n \"\"\"\n def __init__(self):\n self.data_dict = None\n self.beam = None\n self.aero_settings = None\n self.timestep_info = []\n self.ini_info = None\n\n self.surface_distribution = None\n self.surface_m = None\n self.dimensions = None\n self.grid_type = None\n\n self.n_node = 0\n self.n_elem = 0\n self.n_surf = 0\n self.n_aero_node = 0\n self.grid_type = None\n\n self.struct2aero_mapping = None\n self.aero2struct_mapping = []\n\n\n def generate(self, data_dict, beam, aero_settings, ts):\n\n\n self.data_dict = data_dict\n self.beam = beam\n self.aero_settings = aero_settings\n # key words = safe in aero_settings? --> grid_type\n # number of total nodes (structural + aero&struc)\n self.n_node = len(data_dict[self.grid_type + '_node']) # gridtype + '_node'\n # number of elements\n self.n_elem = len(data_dict['surface_distribution'])\n # surface distribution\n self.surface_distribution = data_dict['surface_distribution']\n # number of surfaces\n temp = set(data_dict['surface_distribution'])\n #TO-DO: improve: avoid for loops\n self.n_surf = sum(1 for i in temp if i >= 0)\n # number of chordwise panels\n self.surface_m = data_dict['surface_m']\n # number of aero nodes\n self.n_aero_node = sum(data_dict[self.grid_type + '_node'])\n\n\n # get N per surface\n self.calculate_dimensions()\n\n # write grid info to screen\n # self.output_info()\n\n def calculate_dimensions(self):\n self.dimensions = np.zeros((self.n_surf, 2), dtype=int)\n for i in range(self.n_surf):\n # adding M values\n self.dimensions[i, 0] = self.surface_m[i]\n # Improvement:\n # self.aero.dimensions[:, 0] = self.surface_m[:]\n # count N values (actually, the count result\n # will be N+1)\n nodes_in_surface = []\n\n #IMPROVEMENT\n for i_surf in range(self.n_surf):\n nodes_in_surface.append([])\n\n # Improvement!\n for i_elem in range(self.beam.num_elem):\n nodes = self.beam.elements[i_elem].global_connectivities\n i_surf = self.surface_distribution[i_elem]\n if i_surf < 0:\n continue\n for i_global_node in nodes:\n if i_global_node in nodes_in_surface[i_surf]:\n continue\n else:\n nodes_in_surface[i_surf].append(i_global_node)\n if self.data_dict[self.grid_type + '_node'][i_global_node]:\n self.dimensions[i_surf, 1] += 1\n\n # accounting for N+1 nodes -> N panels\n self.dimensions[:, 1] -= 1\n\n\n def add_timestep(self):\n try:\n self.timestep_info.append(self.timestep_info[-1].copy())\n except IndexError:\n self.timestep_info.append(self.ini_info.copy())\n\n def generate_zeta_timestep_info(self, structure_tstep, aero_tstep, beam, aero_settings, it=None, dt=None):\n if it is None:\n it = len(beam.timestep_info) - 1\n\n\n def generate_zeta(self, beam, aero_settings, ts=-1, beam_ts=-1):\n self.generate_zeta_timestep_info(beam.timestep_info[beam_ts],\n self.timestep_info[ts],\n beam,\n aero_settings)\n\n def generate_mapping(self):\n self.struct2aero_mapping = [[]]*self.n_node\n surf_n_counter = np.zeros((self.n_surf,), dtype=int)\n nodes_in_surface = []\n for i_surf in range(self.n_surf):\n nodes_in_surface.append([])\n for i_elem in range(self.n_elem):\n i_surf = self.surface_distribution[i_elem]\n if i_surf == -1:\n continue\n for i_global_node in self.beam.elements[i_elem].reordered_global_connectivities:\n if not self.data_dict[self.grid_type + '_node'][i_global_node]:\n continue\n\n if i_global_node in nodes_in_surface[i_surf]:\n continue\n else:\n nodes_in_surface[i_surf].append(i_global_node)\n surf_n_counter[i_surf] += 1\n try:\n self.struct2aero_mapping[i_global_node][0]\n except IndexError:\n self.struct2aero_mapping[i_global_node] = []\n\n i_n = surf_n_counter[i_surf] - 1\n self.struct2aero_mapping[i_global_node].append({'i_surf': i_surf,\n 'i_n': i_n})\n\n nodes_in_surface = []\n for i_surf in range(self.n_surf):\n nodes_in_surface.append([])\n\n for i_surf in range(self.n_surf):\n self.aero2struct_mapping.append([-1]*(surf_n_counter[i_surf]))\n\n for i_elem in range(self.n_elem):\n for i_global_node in self.beam.elements[i_elem].global_connectivities:\n for i in range(len(self.struct2aero_mapping[i_global_node])):\n try:\n i_surf = self.struct2aero_mapping[i_global_node][i]['i_surf']\n i_n = self.struct2aero_mapping[i_global_node][i]['i_n']\n if i_global_node in nodes_in_surface[i_surf]:\n continue\n else:\n nodes_in_surface[i_surf].append(i_global_node)\n except KeyError:\n continue\n self.aero2struct_mapping[i_surf][i_n] = i_global_node\n\n def update_orientation(self, quat, ts=-1):\n rot = algebra.quat2rotation(quat)\n self.timestep_info[ts].update_orientation(rot.T)\n" }, { "path": "sharpy/aero/models/nonliftingbodygrid.py", "content": "\"\"\"Nonlifting Body grid\n\nDescription\n\"\"\"\n\nfrom sharpy.aero.models.grid import Grid\nfrom sharpy.utils.datastructures import NonliftingBodyTimeStepInfo\nimport numpy as np\nimport sharpy.utils.algebra as algebra\n\n\nclass NonliftingBodyGrid(Grid):\n \"\"\"\n ``Nonlifting Body Grid`` is the main object containing information of the\n nonlifting bodygrid, consisting of triangular and quadrilateral panels.\n It is created by the solver :class:`sharpy.solvers.aerogridloader.AerogridLoader`\n\n \"\"\"\n def __init__(self):\n super().__init__()\n self.grid_type = 'nonlifting_body'\n\n\n def generate(self, data_dict, beam, nonlifting_body_settings, ts):\n super().generate(data_dict, beam, nonlifting_body_settings, ts)\n\n # allocating initial grid storage\n self.ini_info = NonliftingBodyTimeStepInfo(self.dimensions)\n\n self.add_timestep()\n self.generate_mapping()\n self.generate_zeta(self.beam, self.aero_settings, ts)\n\n def generate_zeta_timestep_info(self, structure_tstep, nonlifting_body_tstep, beam, aero_settings, it=None, dt=None):\n super().generate_zeta_timestep_info(structure_tstep, nonlifting_body_tstep, beam, aero_settings, it, dt)\n\n for i_surf in range(self.n_surf):\n # Get Zeta and Zeta_dot (Panel node positions in G frame)\n nonlifting_body_tstep.zeta[i_surf], nonlifting_body_tstep.zeta_dot[i_surf] = self.get_zeta_and_zeta_dot(i_surf, structure_tstep)\n\n def get_zeta_and_zeta_dot(self,i_surf, structure_tstep):\n numb_radial_nodes = self.dimensions[i_surf][0] +1\n matrix_nodes = np.zeros((3, numb_radial_nodes,\n self.dimensions[i_surf][1]+1))\n matrix_nodes_dot = matrix_nodes.copy()\n array_phi_coordinates = np.linspace(0, 2*np.pi, numb_radial_nodes)\n # cache sin and cos values\n array_sin_phi = np.sin(array_phi_coordinates)\n array_cos_phi = np.cos(array_phi_coordinates)\n\n cga_rotation_matrix = structure_tstep.cga()\n\n for node_counter, i_global_node in enumerate(self.aero2struct_mapping[i_surf]):\n # 1) Set B-Frame position\n # 1a) get cross-sectional fuselage geometry at node\n if self.data_dict[\"shape\"].decode() == 'specific':\n a_ellipse = self.data_dict[\"a_ellipse\"][i_global_node]\n b_ellipse = self.data_dict[\"b_ellipse\"][i_global_node]\n z_0 =self.data_dict[\"z_0_ellipse\"][i_global_node]\n if a_ellipse == 0. or b_ellipse == 0.:\n radius = 0\n else:\n radius = a_ellipse*b_ellipse/np.sqrt(\n (b_ellipse*array_cos_phi)**2\n +(a_ellipse*array_sin_phi)**2)\n else:\n radius = self.data_dict[\"radius\"][i_global_node]\n z_0 = 0\n \n # 1b) Get nodes position in B frame\n matrix_nodes[1, :, node_counter] = radius*array_cos_phi\n matrix_nodes[2, :, node_counter] = radius*array_sin_phi + z_0\n \n # 2) A frame\n # 2a) Convert structural position from B to A frame \n i_elem, i_local_node = self.get_elment_and_local_node_id(i_surf, i_global_node)\n psi_node = structure_tstep.psi[i_elem, i_local_node,:]\n if not (psi_node == [0, 0, 0]).all():\n # just perform roation from B to A if psi not 0\n Cab = algebra.crv2rotation(psi_node)\n for idx in range(numb_radial_nodes):\n matrix_nodes[:, idx, node_counter] = np.dot(Cab, matrix_nodes[:, idx, node_counter])\n # 2b) Add beam displacements (expressed in A-frame)\n for dim in range(3):\n matrix_nodes[dim, :, node_counter] += structure_tstep.pos[i_global_node,dim]\n\n # 2c) Add structural beam velocities (expressed in A-frame)\n for dim in range(3):\n # velocity due to pos_dot\n matrix_nodes_dot[dim, :, node_counter] += structure_tstep.pos_dot[i_global_node, dim]\n # 2d) Add effect of structural beam rotations an node velocity (expressed in A-frame)\n psi_dot_node = structure_tstep.psi_dot[i_elem, i_local_node,:]\n omega_a = algebra.crv_dot2omega(psi_node, psi_dot_node) \n for idx in range(numb_radial_nodes):\n matrix_nodes_dot[:, idx, node_counter] += (np.dot(algebra.skew(omega_a), matrix_nodes[:, idx, node_counter]))\n \n # 3) Convert position and velocities from A to G frame\n for idx in range(numb_radial_nodes):\n matrix_nodes[:, idx, node_counter] = np.dot(cga_rotation_matrix,\n matrix_nodes[:, idx, node_counter])\n matrix_nodes_dot[:, idx, node_counter] = np.dot(cga_rotation_matrix,\n matrix_nodes_dot[:, idx, node_counter])\n return matrix_nodes, matrix_nodes_dot\n\n\n def get_elment_and_local_node_id(self, i_surf, i_global_node):\n # get beam elements of surface\n idx_beam_elements_surface = np.where(self.surface_distribution == i_surf)[0]\n # find element and local node of the global node and return psi\n for i_elem in idx_beam_elements_surface:\n if i_global_node in self.beam.elements[i_elem].reordered_global_connectivities:\n i_local_node = np.where(self.beam.elements[i_elem].reordered_global_connectivities == i_global_node)[0][0]\n return i_elem, i_local_node\n raise Exception(\"The global node %u could not be assigned to any element of surface %u.\" % (i_global_node, i_surf))\n\n\n\n\n\n\n\n" }, { "path": "sharpy/aero/utils/__init__.py", "content": "\"\"\"Aerodynamic Utilities\"\"\"" }, { "path": "sharpy/aero/utils/airfoilpolars.py", "content": "import numpy as np\n# import sharpy.utils.algebra as algebra\nfrom sharpy.utils.constants import deg2rad\nfrom scipy.interpolate import interp1d\n\n\nclass Polar:\n \"\"\"\n Airfoil polar object\n \"\"\"\n\n def __init__(self):\n\n self.cm_interp = None\n self.cd_interp = None\n self.cl_interp = None\n self.table = None\n self.aoa_cl0_deg = None\n\n def initialise(self, table):\n \"\"\"\n Initialise polar\n\n Args:\n table (np.ndarray): 4-column array containing ``aoa`` (rad), ``cl``, ``cd`` and ``cm``\n\n \"\"\"\n # Store the table\n if (np.diff(table[:, 0]) > 0.).all():\n self.table = table[~np.isnan(table).any(axis=1), :]\n else:\n raise RuntimeError(\"ERROR: angles of attack not ordered\")\n\n # Look for aoa where CL=0\n npoints = self.table.shape[0]\n matches = []\n for ipoint in range(npoints - 1):\n if self.table[ipoint, 1] == 0.:\n matches.append(self.table[ipoint, 0])\n elif self.table[ipoint, 1] < 0. and self.table[ipoint + 1, 1] > 0:\n if self.table[ipoint, 0] <= 0.:\n matches.append(np.interp(0,\n self.table[ipoint:ipoint+2, 1],\n self.table[ipoint:ipoint+2, 0]))\n\n iaoacl0 = 0\n aux = np.abs(matches[0])\n for imin in range(len(matches)):\n if np.abs(matches[imin]) < aux:\n aux = np.abs(matches[imin])\n iaoacl0 = imin\n self.aoa_cl0_deg = matches[iaoacl0]\n\n self.cl_interp = interp1d(self.table[:, 0], self.table[:, 1])\n self.cd_interp = interp1d(self.table[:, 0], self.table[:, 2])\n self.cm_interp = interp1d(self.table[:, 0], self.table[:, 3])\n\n def get_coefs(self, aoa_deg):\n\n cl = self.cl_interp(aoa_deg)\n cd = self.cd_interp(aoa_deg)\n cm = self.cm_interp(aoa_deg)\n\n return cl[0], cd[0], cm[0]\n\n def get_aoa_deg_from_cl_2pi(self, cl):\n\n return cl/2/np.pi/deg2rad + self.aoa_cl0_deg\n\n\n def redefine_aoa(self, new_aoa):\n\n naoa = len(new_aoa)\n # Generate the same polar interpolated at different angles of attack\n # by linear interpolation\n table = np.zeros((naoa, 4))\n table[:, 0] = new_aoa\n for icol in range(1, 4):\n table[:, icol] = np.interp(table[:, 0],\n self.table[:, 0],\n self.table[:, icol])\n\n new_polar = Polar()\n new_polar.initialise(table)\n return new_polar\n\n def get_cdcm_from_cl(self, cl):\n # Computes the cd and cm from cl\n # It provides the first match after (or before) the AOA of CL=0\n\n cl_max = np.max(self.table[:,1]) \n cl_min = np.min(self.table[:,1])\n\n if cl_max < cl or cl_min > cl:\n print((\"cl = %.2f out of range, forces at this point will not be corrected\" % cl)) \n cd = 0.\n cm = 0. \n else: \n if cl == 0.:\n cl_new, cd, cm = self.get_coefs(self.aoa_cl0_deg)\n elif cl > 0.:\n dist = np.abs(self.table[:,0] - self.aoa_cl0_deg)\n min_dist = np.min(dist)\n i = np.where(dist == min_dist)[0][0]\n while self.table[i, 1] < cl:\n i += 1\n cd = np.interp(cl, self.table[i-1:i+1, 1], self.table[i-1:i+1, 2])\n cm = np.interp(cl, self.table[i-1:i+1, 1], self.table[i-1:i+1, 3])\n else:\n dist = np.abs(self.table[:,0] - self.aoa_cl0_deg)\n min_dist = np.min(dist)\n i = np.where(dist == min_dist)[0][0]\n while self.table[i, 1] > cl:\n i -= 1\n cd = np.interp(cl, self.table[i:i+2, 1], self.table[i:i+2, 2])\n cm = np.interp(cl, self.table[i:i+2, 1], self.table[i:i+2, 3])\n \n return float(cd), float(cm)\n\n \ndef interpolate(polar1, polar2, coef=0.5):\n\n all_aoa = np.sort(np.concatenate((polar1.table[:, 0], polar2.table[:, 0]),))\n\n different_aoa = []\n different_aoa.append(all_aoa[0])\n for iaoa in range(1, len(all_aoa)):\n if not all_aoa[iaoa] == different_aoa[-1]:\n different_aoa.append(all_aoa[iaoa])\n\n new_polar1 = polar1.redefine_aoa(different_aoa)\n new_polar2 = polar2.redefine_aoa(different_aoa)\n\n table = (1. - coef)*new_polar1.table + coef*new_polar2.table\n\n new_polar = Polar()\n new_polar.initialise(table)\n return new_polar\n" }, { "path": "sharpy/aero/utils/mapping.py", "content": "\"\"\"Force Mapping Utilities\"\"\"\nimport numpy as np\nimport sharpy.utils.algebra as algebra\n\n\ndef aero2struct_force_mapping(aero_forces,\n struct2aero_mapping,\n zeta,\n pos_def,\n psi_def,\n master,\n conn,\n cag=np.eye(3),\n data_dict=None,\n skip_moments_generated_by_forces = False):\n r\"\"\"\n Maps the aerodynamic forces at the lattice to the structural nodes\n\n The aerodynamic forces from the UVLM are always in the inertial ``G`` frame of reference and have to be transformed\n to the body or local ``B`` frame of reference in which the structural forces are defined.\n\n Since the structural nodes and aerodynamic panels are coincident in a spanwise direction, the aerodynamic forces\n that correspond to a structural node are the summation of the ``M+1`` forces defined at the lattice at that\n spanwise location.\n\n .. math::\n \\mathbf{f}_{struct}^B &= \\sum\\limits_{i=0}^{m+1}C^{BG}\\mathbf{f}_{i,aero}^G \\\\\n \\mathbf{m}_{struct}^B &= \\sum\\limits_{i=0}^{m+1}C^{BG}(\\mathbf{m}_{i,aero}^G +\n \\tilde{\\boldsymbol{\\zeta}}^G\\mathbf{f}_{i, aero}^G)\n\n where :math:`\\tilde{\\boldsymbol{\\zeta}}^G` is the skew-symmetric matrix of the vector between the lattice\n grid vertex and the structural node.\n\n Args:\n aero_forces (list): Aerodynamic forces from the UVLM in inertial frame of reference\n struct2aero_mapping (dict): Structural to aerodynamic node mapping\n zeta (list): Aerodynamic grid coordinates\n pos_def (np.ndarray): Vector of structural node displacements\n psi_def (np.ndarray): Vector of structural node rotations (CRVs)\n master: Unused\n conn (np.ndarray): Connectivities matrix\n cag (np.ndarray): Transformation matrix between inertial and body-attached reference ``A``\n data_dict (dict): Dictionary containing the grid's information.\n skip_moments_generated_by_forces (bool): Flag to skip local moment calculation.\n\n Returns:\n np.ndarray: structural forces in an ``n_node x 6`` vector\n \"\"\"\n\n n_node, _ = pos_def.shape\n n_elem, _, _ = psi_def.shape\n struct_forces = np.zeros((n_node, 6))\n\n nodes = []\n\n for i_elem in range(n_elem):\n for i_local_node in range(3):\n\n i_global_node = conn[i_elem, i_local_node]\n if i_global_node in nodes:\n continue\n\n nodes.append(i_global_node)\n for mapping in struct2aero_mapping[i_global_node]:\n i_surf = mapping['i_surf']\n i_n = mapping['i_n']\n _, n_m, _ = aero_forces[i_surf].shape\n\n crv = psi_def[i_elem, i_local_node, :]\n cab = algebra.crv2rotation(crv)\n cbg = np.dot(cab.T, cag)\n\n for i_m in range(n_m):\n struct_forces[i_global_node, 0:3] += np.dot(cbg, aero_forces[i_surf][0:3, i_m, i_n])\n struct_forces[i_global_node, 3:6] += np.dot(cbg, aero_forces[i_surf][3:6, i_m, i_n])\n \"\"\"\n The calculation of the local moment is skipped for fuselage bodies, since this \n leads to noticeably asymmetric aeroforces. This transitional solution makes \n sense since we have only considered the stiff fuselage so far and the pitching \n moment coming from the fuselage is mainly caused by the longitudinal force distribution.\n TODO: Correct the calculation of the local moment for the fuselage model.\n \"\"\"\n if not skip_moments_generated_by_forces:\n chi_g = zeta[i_surf][:, i_m, i_n] - np.dot(cag.T, pos_def[i_global_node, :])\n struct_forces[i_global_node, 3:6] += np.dot(cbg, algebra.cross3(chi_g, aero_forces[i_surf][0:3, i_m, i_n]))\n\n return struct_forces\n\n\ndef total_forces_moments(forces_nodes_a,\n pos_def,\n ref_pos=np.array([0., 0., 0.])):\n \"\"\"\n Performs a summation of the forces and moments expressed at the structural nodes in the A frame of reference.\n\n Note:\n If you need to transform forces and moments at the nodes from B to A, use the\n :func:`~sharpy.structure.models.beam.Beam.nodal_b_for_2_a_for()` function.\n\n Args:\n forces_nodes_a (np.array): ``n_node x 6`` vector of forces and moments at the nodes in A\n pos_def (np.array): ``n_node x 3`` vector of nodal positions in A\n ref_pos (np.array (optional)): Location in A about which to compute moments. Defaults to ``[0, 0, 0]``\n\n Returns:\n np.array: Vector of length 6 containing the total forces and moments expressed in A at the desired location.\n \"\"\"\n\n num_node = pos_def.shape[0]\n ra_vec = pos_def - ref_pos\n\n total_forces = np.zeros(3)\n total_moments = np.zeros(3)\n for i_global_node in range(num_node):\n total_forces += forces_nodes_a[i_global_node, :3]\n total_moments += forces_nodes_a[i_global_node, 3:] + algebra.cross3(ra_vec[i_global_node], forces_nodes_a[i_global_node, :3])\n\n return np.concatenate((total_forces, total_moments))\n" }, { "path": "sharpy/aero/utils/utils.py", "content": "\"\"\"Aero utilities functions\"\"\"\nimport numpy as np\nimport sharpy.utils.algebra as algebra\nfrom sharpy.utils import algebra as algebra\n\n\ndef flightcon_file_parser(fc_dict):\n fc = fc_dict['FlightCon']\n fc['u_inf'] = float(fc['u_inf'])\n fc['alpha'] = float(fc['alpha'])*np.pi/180.0\n fc['beta'] = float(fc['beta'])*np.pi/180.0\n fc['rho_inf'] = float(fc['rho_inf'])\n fc['c_ref'] = float(fc['c_ref'])\n fc['b_ref'] = float(fc['b_ref'])\n\n\ndef alpha_beta_to_direction(alpha, beta):\n direction = np.array([1, 0, 0])\n alpha_rot = algebra.rotation3d_y(alpha)\n beta_rot = algebra.rotation3d_z(beta)\n direction = np.dot(beta_rot, np.dot(alpha_rot, direction))\n return direction\n\n\ndef magnitude_and_direction_of_relative_velocity(displacement, displacement_vel, for_vel, cga, uext,\n add_rotation=False, rot_vel_g=np.zeros((3)), centre_rot_g=np.zeros((3))):\n r\"\"\"\n Calculates the magnitude and direction of the relative velocity ``u_rel`` at a local section of the wing.\n\n .. math::\n\n u_{rel, i}^G = \\bar{U}_{\\infty, i}^G - C^{GA}(\\chi)(\\dot{\\eta}_i^A + v^A + \\tilde{\\omega}^A\\eta_i^A\n\n where :math:`\\bar{U}_{\\infty, i}^G` is the average external velocity across all aerodynamic nodes at the\n relevant cross section.\n\n Args:\n displacement (np.array): Unit vector in the direction of the free stream velocity expressed in A frame.\n displacement_vel (np.array): Unit vector in the direction of the local chord expressed in A frame.\n for_vel (np.array): ``A`` frame of reference (FoR) velocity. Expressed in A FoR\n cga (np.array): Rotation vector from FoR ``G`` to FoR ``A``\n uext (np.array): Background flow velocity on solid grid nodes\n add_rotation (bool): Adds rotation velocity. Probalby needed in steady computations\n rot_vel_g (np.array): Rotation velocity. Only used if add_rotation = True\n centre_rot_g (np.array): Centre of rotation. Only used if add_rotation = True\n\n Returns:\n tuple: ``u_rel``, ``dir_u_rel`` expressed in the inertial, ``G`` frame.\n \"\"\"\n urel = (displacement_vel +\n for_vel[0:3] +\n algebra.cross3(for_vel[3:6], displacement))\n urel = -np.dot(cga, urel)\n urel += np.average(uext, axis=1)\n\n if add_rotation:\n urel -= algebra.cross3(rot_vel_g,\n np.dot(cga, displacement) - centre_rot_g)\n dir_urel = algebra.unit_vector(urel)\n\n return urel, dir_urel\n\n\ndef local_stability_axes(dir_urel, dir_chord):\n \"\"\"\n Rotates the body axes onto stability axes. This rotation is equivalent to the projection of a vector in S onto B.\n\n The stability axes are defined as:\n\n * ``x_s``: parallel to the free stream\n\n * ``z_s``: perpendicular to the free stream and part of the plane formed by the local chord and the vertical\n body axis ``z_b``.\n\n * ``y_s``: completes the set\n\n Args:\n dir_urel (np.array): Unit vector in the direction of the free stream velocity expressed in B frame.\n dir_chord (np.array): Unit vector in the direction of the local chord expressed in B frame.\n\n Returns:\n np.array: Rotation matrix from B to S, equivalent to the projection matrix :math:`C^{BS}` that projects a\n vector from S onto B.\n \"\"\"\n xs = dir_urel\n\n zb = np.array([0, 0, 1.])\n zs = algebra.cross3(algebra.cross3(dir_chord, zb), dir_urel)\n\n ys = -algebra.cross3(xs, zs)\n\n return algebra.triad2rotation(xs, ys, zs)\n\n\ndef span_chord(i_node_surf, zeta):\n \"\"\"\n Retrieve the local span and local chord\n\n Args:\n i_node_surf (int): Node index in aerodynamic surface\n zeta (np.array): Aerodynamic surface coordinates ``(3 x n_chord x m_span)``\n\n Returns:\n tuple: ``dir_span``, ``span``, ``dir_chord``, ``chord``\n \"\"\"\n N = zeta.shape[2] - 1 # spanwise vertices in surface (-1 for index)\n\n # Deal with the extremes\n if i_node_surf == 0:\n node_p = 1\n node_m = 0\n elif i_node_surf == N:\n node_p = N\n node_m = N - 1\n else:\n node_p = i_node_surf + 1\n node_m = i_node_surf - 1\n\n # Define the span and the span direction\n dir_span = 0.5 * (zeta[:, 0, node_p] - zeta[:, 0, node_m])\n\n span = np.linalg.norm(dir_span)\n dir_span = algebra.unit_vector(dir_span)\n\n # Define the chord and the chord direction\n dir_chord = zeta[:, -1, i_node_surf] - zeta[:, 0, i_node_surf]\n chord = np.linalg.norm(dir_chord)\n dir_chord = algebra.unit_vector(dir_chord)\n\n return dir_span, span, dir_chord, chord\n\n\ndef find_aerodynamic_solver_settings(settings):\n \"\"\"\n Retrieves the settings of the first aerodynamic solver used in the solution ``flow``. \n \n For coupled solvers, the aerodynamic solver is found in the aero solver settings. \n The StaticTrim solver can either contain a coupled or aero solver in its solver \n settings (making it into a possible 3-level Matryoshka).\n\n Args:\n settings (dict): SHARPy settings (usually found in ``data.settings`` )\n\n Returns:\n tuple: Aerodynamic solver settings\n \"\"\"\n flow = settings['SHARPy']['flow']\n for solver_name in ['StaticUvlm', 'StaticCoupled', 'StaticTrim', 'DynamicCoupled', 'StepUvlm']:\n if solver_name in flow:\n aero_solver_settings = settings[solver_name]\n if solver_name == 'StaticTrim':\n aero_solver_settings = aero_solver_settings['solver_settings']['aero_solver_settings']\n elif 'aero_solver' in settings[solver_name].keys():\n aero_solver_settings = aero_solver_settings['aero_solver_settings']\n \n return aero_solver_settings\n\n raise KeyError(\"ERROR: Aerodynamic solver not found.\")\n\ndef find_velocity_generator(settings):\n \"\"\"\n Retrieves the name and settings of the fluid velocity generator in the first aerodynamic solver used in the\n solution ``flow``.\n\n Args:\n settings (dict): SHARPy settings (usually found in ``data.settings`` )\n\n Returns:\n tuple: velocity generator name and velocity generator settings\n \"\"\"\n aero_solver_settings = find_aerodynamic_solver_settings(settings)\n\n vel_gen_name = aero_solver_settings['velocity_field_generator']\n vel_gen_settings = aero_solver_settings['velocity_field_input']\n\n return vel_gen_name, vel_gen_settings\n" }, { "path": "sharpy/aero/utils/uvlmlib.py", "content": "from sharpy.utils.sharpydir import SharpyDir\nimport sharpy.utils.ctypes_utils as ct_utils\n\nimport ctypes as ct\nfrom ctypes import *\nimport numpy as np\nfrom sharpy.utils.constants import vortex_radius_def\n\ntry:\n UvlmLib = ct_utils.import_ctypes_lib(SharpyDir + '/UVLM', 'libuvlm')\nexcept OSError:\n UvlmLib = ct_utils.import_ctypes_lib(SharpyDir + '/lib/UVLM/lib', 'libuvlm')\n\n# TODO: Combine VMOpts and UVMOpts (Class + inheritance)?\n\nclass VMopts(ct.Structure):\n \"\"\"ctypes definition for VMopts class\n struct VMopts {\n bool ImageMethod;\n unsigned int Mstar;\n bool Steady;\n bool horseshoe;\n bool KJMeth;\n bool NewAIC;\n double DelTime;\n bool Rollup;\n bool only_lifting;\n bool only_nonlifting;\n unsigned int NumCores;\n unsigned int NumSurfaces;\n unsigned int NumSurfacesNonlifting;\n double vortex_radius;\n double vortex_radius_wake_ind; \n bool u_ind_by_sources_for_lifting_forces;\n uint ignore_first_x_nodes_in_force_calculation;\n };\n \"\"\"\n _fields_ = [(\"ImageMethod\", ct.c_bool),\n (\"Steady\", ct.c_bool),\n (\"horseshoe\", ct.c_bool),\n (\"KJMeth\", ct.c_bool),\n (\"NewAIC\", ct.c_bool),\n (\"DelTime\", ct.c_double),\n (\"Rollup\", ct.c_bool),\n (\"only_lifting\", ct.c_bool),\n (\"only_nonlifting\", ct.c_bool),\n (\"phantom_wing_test\", ct.c_bool),\n (\"NumCores\", ct.c_uint),\n (\"NumSurfaces\", ct.c_uint),\n (\"NumSurfacesNonlifting\", ct.c_uint),\n (\"dt\", ct.c_double),\n (\"n_rollup\", ct.c_uint),\n (\"rollup_tolerance\", ct.c_double),\n (\"rollup_aic_refresh\", ct.c_uint),\n (\"iterative_solver\", ct.c_bool),\n (\"iterative_tol\", ct.c_double),\n (\"iterative_precond\", ct.c_bool),\n (\"vortex_radius\", ct.c_double),\n (\"vortex_radius_wake_ind\", ct.c_double),\n (\"consider_u_ind_by_sources_for_lifting_forces\", ct.c_bool),\n (\"ignore_first_x_nodes_in_force_calculation\", ct.c_uint)]\n \n\n\n def __init__(self):\n ct.Structure.__init__(self)\n self.ImageMethod = ct.c_bool(False)\n self.Steady = ct.c_bool(True)\n self.horseshoe = ct.c_bool(True)\n self.KJMeth = ct.c_bool(False) # legacy var\n self.NewAIC = ct.c_bool(False) # legacy var\n self.DelTime = ct.c_double(1.0)\n self.Rollup = ct.c_bool(False)\n self.only_lifting = ct.c_bool(False)\n self.only_nonlifting = ct.c_bool(False)\n self.NumCores = ct.c_uint(4)\n self.NumSurfaces = ct.c_uint(1)\n self.NumSurfacesNonlifting = ct.c_uint(0)\n self.dt = ct.c_double(0.01)\n self.n_rollup = ct.c_uint(0)\n self.rollup_tolerance = ct.c_double(1e-5)\n self.rollup_aic_refresh = ct.c_uint(1)\n self.iterative_solver = ct.c_bool(False)\n self.iterative_tol = ct.c_double(0)\n self.iterative_precond = ct.c_bool(False)\n self.vortex_radius = ct.c_double(vortex_radius_def)\n self.vortex_radius_wake_ind = ct.c_double(vortex_radius_def)\n self.phantom_wing_test = ct.c_bool(False)\n self.consider_u_ind_by_sources_for_lifting_forces = ct.c_bool(False)\n self.ignore_first_x_nodes_in_force_calculation = ct.c_uint(0)\n\n\n def set_options(self, options, n_surfaces = 0, n_surfaces_nonlifting = 0):\n self.Steady = ct.c_bool(True)\n self.NumSurfaces = ct.c_uint(n_surfaces)\n self.NumSurfacesNonlifting = ct.c_uint(n_surfaces_nonlifting)\n self.horseshoe = ct.c_bool(options['horseshoe'])\n self.dt = ct.c_double(options[\"rollup_dt\"])\n self.n_rollup = ct.c_uint(options[\"n_rollup\"])\n self.rollup_tolerance = ct.c_double(options[\"rollup_tolerance\"])\n self.rollup_aic_refresh = ct.c_uint(options['rollup_aic_refresh'])\n self.NumCores = ct.c_uint(options['num_cores'])\n self.iterative_solver = ct.c_bool(options['iterative_solver'])\n self.iterative_tol = ct.c_double(options['iterative_tol'])\n self.iterative_precond = ct.c_bool(options['iterative_precond'])\n self.vortex_radius = ct.c_double(options['vortex_radius'])\n self.vortex_radius_wake_ind = ct.c_double(options['vortex_radius_wake_ind'])\n\n self.only_nonlifting = ct.c_bool(options[\"only_nonlifting\"])\n self.only_lifting = ct.c_bool(not options[\"nonlifting_body_interactions\"])\n self.phantom_wing_test = ct.c_bool(options[\"phantom_wing_test\"])\n self.ignore_first_x_nodes_in_force_calculation = ct.c_uint(options[\"ignore_first_x_nodes_in_force_calculation\"])\n\n\nclass UVMopts(ct.Structure):\n _fields_ = [(\"dt\", ct.c_double),\n (\"NumCores\", ct.c_uint),\n (\"NumSurfaces\", ct.c_uint),\n (\"NumSurfacesNonlifting\", ct.c_uint), \n (\"only_lifting\", ct.c_bool),\n (\"only_nonlifting\", ct.c_bool),\n (\"phantom_wing_test\", ct.c_bool),\n (\"convection_scheme\", ct.c_uint),\n (\"ImageMethod\", ct.c_bool),\n (\"iterative_solver\", ct.c_bool),\n (\"iterative_tol\", ct.c_double),\n (\"iterative_precond\", ct.c_bool),\n (\"convect_wake\", ct.c_bool), \n (\"cfl1\", ct.c_bool),\n (\"vortex_radius\", ct.c_double),\n (\"vortex_radius_wake_ind\", ct.c_double),\n (\"interp_coords\", ct.c_uint),\n (\"filter_method\", ct.c_uint),\n (\"interp_method\", ct.c_uint),\n (\"yaw_slerp\", ct.c_double),\n (\"quasi_steady\", ct.c_bool),\n (\"num_spanwise_panels_wo_induced_velocity\", ct.c_uint),\n (\"consider_u_ind_by_sources_for_lifting_forces\", ct.c_bool),\n (\"ignore_first_x_nodes_in_force_calculation\", ct.c_uint)]\n\n def __init__(self):\n ct.Structure.__init__(self)\n self.dt = ct.c_double(0.01)\n self.NumCores = ct.c_uint(4)\n self.NumSurfaces = ct.c_uint(1)\n self.NumSurfacesNonlifting = ct.c_uint(1)\n self.convection_scheme = ct.c_uint(2)\n self.ImageMethod = ct.c_bool(False)\n self.iterative_solver = ct.c_bool(False)\n self.iterative_tol = ct.c_double(0)\n self.iterative_precond = ct.c_bool(False)\n self.convect_wake = ct.c_bool(True)\n self.cfl1 = ct.c_bool(True)\n self.vortex_radius = ct.c_double(vortex_radius_def)\n self.vortex_radius_wake_ind = ct.c_double(vortex_radius_def)\n self.yaw_slerp = ct.c_double(0.)\n self.quasi_steady = ct.c_bool(False)\n self.num_spanwise_panels_wo_induced_velocity = ct.c_uint(0)\n self.phantom_wing_test = ct.c_bool(False)\n self.consider_u_ind_by_sources_for_lifting_forces = ct.c_bool(False)\n self.ignore_first_x_nodes_in_force_calculation = ct.c_uint(0)\n\n def set_options(self, \n options, \n n_surfaces = 0, \n n_surfaces_nonlifting = 0, \n dt = None, \n convect_wake = False, \n n_span_panels_wo_u_ind = 0,\n only_lifting=True):\n if dt is None:\n self.dt = ct.c_double(options[\"dt\"])\n else:\n self.dt = ct.c_double(dt)\n self.NumCores = ct.c_uint(options[\"num_cores\"])\n self.NumSurfaces = ct.c_uint(n_surfaces)\n self.NumSurfacesNonlifting = ct.c_uint(n_surfaces_nonlifting)\n self.ImageMethod = ct.c_bool(False)\n self.convection_scheme = ct.c_uint(options[\"convection_scheme\"])\n self.iterative_solver = ct.c_bool(options['iterative_solver'])\n self.iterative_tol = ct.c_double(options['iterative_tol'])\n self.iterative_precond = ct.c_bool(options['iterative_precond'])\n self.convect_wake = ct.c_bool(convect_wake)\n self.cfl1 = ct.c_bool(options['cfl1'])\n self.vortex_radius = ct.c_double(options['vortex_radius'])\n self.vortex_radius_wake_ind = ct.c_double(options['vortex_radius_wake_ind'])\n self.interp_coords = ct.c_uint(options[\"interp_coords\"])\n self.filter_method = ct.c_uint(options[\"filter_method\"])\n self.interp_method = ct.c_uint(options[\"interp_method\"])\n self.yaw_slerp = ct.c_double(options[\"yaw_slerp\"])\n self.quasi_steady = ct.c_bool(options['quasi_steady'])\n \n self.only_nonlifting = ct.c_bool(options[\"only_nonlifting\"])\n self.only_lifting = ct.c_bool(only_lifting)\n self.phantom_wing_test = ct.c_bool(options[\"phantom_wing_test\"])\n self.ignore_first_x_nodes_in_force_calculation = ct.c_uint(options[\"ignore_first_x_nodes_in_force_calculation\"])\n self.num_spanwise_panels_wo_induced_velocity = n_span_panels_wo_u_ind\n\n\nclass FlightConditions(ct.Structure):\n _fields_ = [(\"uinf\", ct.c_double),\n (\"uinf_direction\", ct.c_double*3),\n (\"rho\", ct.c_double),\n (\"c_ref\", ct.c_double)]\n\n def __init__(self, rho, vec_u_inf):\n ct.Structure.__init__(self)\n self.set_flight_conditions(rho, vec_u_inf)\n\n def set_flight_conditions(self, rho, vec_u_inf):\n self.rho = rho\n self.uinf = np.ctypeslib.as_ctypes(np.linalg.norm(vec_u_inf))\n self.uinf_direction = np.ctypeslib.as_ctypes(vec_u_inf/self.uinf)\n\n\n# type for 2d integer matrix\nt_2int = ct.POINTER(ct.c_int)*2\n\ndef vlm_solver(ts_info, options):\n run_VLM = UvlmLib.run_VLM\n\n vmopts = VMopts()\n vmopts.set_options(options, n_surfaces = ts_info.n_surf)\n\n flightconditions = FlightConditions(options['rho'], ts_info.u_ext[0][:, 0, 0])\n\n p_rbm_vel_g = options['rbm_vel_g'].ctypes.data_as(ct.POINTER(ct.c_double))\n p_centre_rot_g = options['centre_rot_g'].ctypes.data_as(ct.POINTER(ct.c_double))\n ts_info.generate_ctypes_pointers()\n run_VLM(ct.byref(vmopts),\n ct.byref(flightconditions),\n ts_info.ct_p_dimensions,\n ts_info.ct_p_dimensions_star,\n ts_info.ct_p_zeta,\n ts_info.ct_p_zeta_star,\n ts_info.ct_p_zeta_dot,\n ts_info.ct_p_u_ext,\n ts_info.ct_p_gamma,\n ts_info.ct_p_gamma_star,\n ts_info.ct_p_forces,\n p_rbm_vel_g,\n p_centre_rot_g)\n ts_info.remove_ctypes_pointers()\n\ndef vlm_solver_nonlifting_body(ts_info, options):\n run_linear_source_panel_method = UvlmLib.run_linear_source_panel_method\n\n vmopts = VMopts()\n vmopts.set_options(options, n_surfaces_nonlifting = ts_info.n_surf)\n\n flightconditions = FlightConditions(options['rho'], ts_info.u_ext[0][:, 0, 0])\n\n ts_info.generate_ctypes_pointers()\n run_linear_source_panel_method(ct.byref(vmopts),\n ct.byref(flightconditions),\n ts_info.ct_p_dimensions,\n ts_info.ct_p_zeta,\n ts_info.ct_p_u_ext,\n ts_info.ct_p_sigma,\n ts_info.ct_p_forces,\n ts_info.ct_p_pressure_coefficients)\n ts_info.remove_ctypes_pointers()\n\ndef vlm_solver_lifting_and_nonlifting_bodies(ts_info_lifting, ts_info_nonlifting, options):\n run_VLM_coupled_with_LSPM = UvlmLib.run_VLM_coupled_with_LSPM\n\n vmopts = VMopts() \n vmopts.set_options(options, n_surfaces = ts_info_lifting.n_surf, n_surfaces_nonlifting = ts_info_nonlifting.n_surf)\n\n flightconditions = FlightConditions(options['rho'], ts_info_lifting.u_ext[0][:, 0, 0])\n\n p_rbm_vel_g = options['rbm_vel_g'].ctypes.data_as(ct.POINTER(ct.c_double))\n p_centre_rot = options['centre_rot_g'].ctypes.data_as(ct.POINTER(ct.c_double))\n ts_info_lifting.generate_ctypes_pointers()\n ts_info_nonlifting.generate_ctypes_pointers()\n run_VLM_coupled_with_LSPM(ct.byref(vmopts),\n ct.byref(flightconditions),\n ts_info_lifting.ct_p_dimensions,\n ts_info_lifting.ct_p_dimensions_star,\n ts_info_lifting.ct_p_zeta,\n ts_info_lifting.ct_p_zeta_star,\n ts_info_lifting.ct_p_zeta_dot,\n ts_info_lifting.ct_p_u_ext,\n ts_info_lifting.ct_p_gamma,\n ts_info_lifting.ct_p_gamma_star,\n ts_info_lifting.ct_p_forces,\n ts_info_lifting.ct_p_flag_zeta_phantom,\n ts_info_nonlifting.ct_p_dimensions,\n ts_info_nonlifting.ct_p_zeta,\n ts_info_nonlifting.ct_p_u_ext,\n ts_info_nonlifting.ct_p_sigma,\n ts_info_nonlifting.ct_p_forces,\n ts_info_nonlifting.ct_p_pressure_coefficients,\n p_rbm_vel_g,\n p_centre_rot)\n\n ts_info_lifting.remove_ctypes_pointers()\n ts_info_nonlifting.remove_ctypes_pointers()\n\n\ndef uvlm_solver(i_iter, ts_info, struct_ts_info, options, convect_wake=True, dt=None):\n\n p_rbm_vel = get_ctype_pointer_of_rbm_vel_in_G_frame(struct_ts_info.for_vel.copy(), struct_ts_info.cga())\n p_centre_rot = options['centre_rot'].ctypes.data_as(ct.POINTER(ct.c_double))\n\n run_UVLM = UvlmLib.run_UVLM\n\n uvmopts = UVMopts()\n uvmopts.set_options(options,\n n_surfaces = ts_info.n_surf,\n n_surfaces_nonlifting = 0, \n dt = dt, \n convect_wake = convect_wake, \n n_span_panels_wo_u_ind=0)\n\n flightconditions = FlightConditions(options['rho'], ts_info.u_ext[0][:, 0, 0])\n\n i = ct.c_uint(i_iter)\n ts_info.generate_ctypes_pointers()\n run_UVLM(ct.byref(uvmopts),\n ct.byref(flightconditions),\n ts_info.ct_p_dimensions,\n ts_info.ct_p_dimensions_star,\n ct.byref(i),\n ts_info.ct_p_u_ext,\n ts_info.ct_p_u_ext_star,\n ts_info.ct_p_zeta,\n ts_info.ct_p_zeta_star,\n ts_info.ct_p_zeta_dot,\n ts_info.ct_p_gamma,\n ts_info.ct_p_gamma_star,\n ts_info.ct_p_dist_to_orig,\n ts_info.ct_p_normals,\n ts_info.ct_p_forces,\n ts_info.ct_p_dynamic_forces,\n p_rbm_vel,\n p_centre_rot)\n ts_info.remove_ctypes_pointers()\n\ndef uvlm_solver_lifting_and_nonlifting(i_iter, ts_info, ts_info_nonlifting, struct_ts_info, options, convect_wake=True, dt=None):\n\n p_rbm_vel = get_ctype_pointer_of_rbm_vel_in_G_frame(struct_ts_info.for_vel.copy(), struct_ts_info.cga())\n p_centre_rot = options['centre_rot'].ctypes.data_as(ct.POINTER(ct.c_double))\n\n uvmopts = UVMopts()\n uvmopts.set_options(options,\n n_surfaces = ts_info.n_surf,\n n_surfaces_nonlifting = ts_info_nonlifting.n_surf, \n dt = dt, \n convect_wake = convect_wake, \n n_span_panels_wo_u_ind=4,\n only_lifting=False)\n run_UVLM = UvlmLib.run_UVLM_coupled_with_LSPM\n\n flightconditions = FlightConditions(options['rho'], ts_info.u_ext[0][:, 0, 0])\n\n i = ct.c_uint(i_iter)\n ts_info.generate_ctypes_pointers()\n ts_info_nonlifting.generate_ctypes_pointers()\n run_UVLM(ct.byref(uvmopts),\n ct.byref(flightconditions),\n ts_info.ct_p_dimensions,\n ts_info.ct_p_dimensions_star,\n ct.byref(i),\n ts_info.ct_p_u_ext,\n ts_info.ct_p_u_ext_star,\n ts_info.ct_p_zeta,\n ts_info.ct_p_zeta_star,\n ts_info.ct_p_zeta_dot,\n ts_info.ct_p_gamma,\n ts_info.ct_p_gamma_star,\n ts_info.ct_p_dist_to_orig,\n ts_info.ct_p_normals,\n ts_info.ct_p_forces,\n ts_info.ct_p_dynamic_forces,\n ts_info.ct_p_flag_zeta_phantom,\n ts_info_nonlifting.ct_p_dimensions,\n ts_info_nonlifting.ct_p_zeta,\n ts_info_nonlifting.ct_p_u_ext,\n ts_info_nonlifting.ct_p_sigma,\n ts_info_nonlifting.ct_p_forces,\n ts_info_nonlifting.ct_p_pressure_coefficients,\n p_rbm_vel,\n p_centre_rot)\n\n ts_info.remove_ctypes_pointers()\n ts_info_nonlifting.remove_ctypes_pointers()\n\ndef uvlm_calculate_unsteady_forces(ts_info,\n struct_ts_info,\n options,\n convect_wake=True,\n dt=None):\n calculate_unsteady_forces = UvlmLib.calculate_unsteady_forces\n\n uvmopts = UVMopts()\n if dt is None:\n uvmopts.dt = ct.c_double(options[\"dt\"])\n else:\n uvmopts.dt = ct.c_double(dt)\n uvmopts.NumCores = ct.c_uint(options[\"num_cores\"])\n uvmopts.NumSurfaces = ct.c_uint(ts_info.n_surf)\n uvmopts.ImageMethod = ct.c_bool(False)\n uvmopts.convection_scheme = ct.c_uint(options[\"convection_scheme\"])\n uvmopts.iterative_solver = ct.c_bool(options['iterative_solver'])\n uvmopts.iterative_tol = ct.c_double(options['iterative_tol'])\n uvmopts.iterative_precond = ct.c_bool(options['iterative_precond'])\n uvmopts.convect_wake = ct.c_bool(convect_wake)\n uvmopts.vortex_radius = ct.c_double(options['vortex_radius'])\n\n\n flightconditions = FlightConditions(options['rho'], ts_info.u_ext[0][:, 0, 0])\n\n p_rbm_vel = get_ctype_pointer_of_rbm_vel_in_G_frame(struct_ts_info.for_vel.copy(), struct_ts_info.cga())\n\n for i_surf in range(ts_info.n_surf):\n ts_info.dynamic_forces[i_surf].fill(0.0)\n\n ts_info.generate_ctypes_pointers()\n calculate_unsteady_forces(ct.byref(uvmopts),\n ct.byref(flightconditions),\n ts_info.ct_p_dimensions,\n ts_info.ct_p_dimensions_star,\n ts_info.ct_p_zeta,\n ts_info.ct_p_zeta_star,\n p_rbm_vel,\n ts_info.ct_p_gamma,\n ts_info.ct_p_gamma_star,\n ts_info.ct_p_gamma_dot,\n ts_info.ct_p_normals,\n ts_info.ct_p_dynamic_forces)\n ts_info.remove_ctypes_pointers()\n\n\ndef uvlm_calculate_incidence_angle(ts_info,\n struct_ts_info):\n calculate_incidence_angle = UvlmLib.UVLM_check_incidence_angle\n\n p_rbm_vel = get_ctype_pointer_of_rbm_vel_in_G_frame(struct_ts_info.for_vel.copy(), struct_ts_info.cga())\n\n n_surf = ct.c_uint(ts_info.n_surf)\n\n ts_info.generate_ctypes_pointers()\n calculate_incidence_angle(ct.byref(n_surf),\n ts_info.ct_p_dimensions,\n ts_info.ct_p_u_ext,\n ts_info.ct_p_zeta,\n ts_info.ct_p_zeta_dot,\n ts_info.ct_p_normals,\n p_rbm_vel,\n ts_info.postproc_cell['incidence_angle_ct_pointer'])\n ts_info.remove_ctypes_pointers()\n\n\ndef uvlm_calculate_total_induced_velocity_at_points(ts_info,\n target_triads,\n vortex_radius,\n for_pos=np.zeros((6)),\n ncores=ct.c_uint(1)):\n \"\"\"\n uvlm_calculate_total_induced_velocity_at_points\n\n Caller to the UVLM library to compute the induced velocity of all the\n surfaces and wakes at a list of points\n\n Args:\n ts_info (AeroTimeStepInfo): Time step information\n target_triads (np.array): Point coordinates, size=(npoints, 3)\n vortex_radius (float): Vortex radius threshold below which do not compute induced velocity\n uind (np.array): Induced velocity\n\n Returns:\n \tuind (np.array): Induced velocity, size=(npoints, 3)\n\n \"\"\"\n calculate_uind_at_points = UvlmLib.total_induced_velocity_at_points\n\n uvmopts = UVMopts()\n uvmopts.NumSurfaces = ct.c_uint(ts_info.n_surf)\n uvmopts.ImageMethod = ct.c_bool(False)\n uvmopts.NumCores = ct.c_uint(ncores)\n uvmopts.vortex_radius = ct.c_double(vortex_radius)\n\n npoints = target_triads.shape[0]\n uind = np.zeros((npoints, 3), dtype=ct.c_double)\n\n if type(target_triads[0,0]) == ct.c_double:\n aux_target_triads = target_triads\n else:\n aux_target_triads = target_triads.astype(dtype=ct.c_double)\n\n p_target_triads = ((ct.POINTER(ct.c_double))(* [np.ctypeslib.as_ctypes(aux_target_triads.reshape(-1))]))\n p_uind = ((ct.POINTER(ct.c_double))(* [np.ctypeslib.as_ctypes(uind.reshape(-1))]))\n\n # make a copy of ts info and add for_pos to zeta and zeta_star\n ts_info_copy = ts_info.copy()\n for i_surf in range(ts_info_copy.n_surf):\n # zeta\n for iM in range(ts_info_copy.zeta[i_surf].shape[1]):\n for iN in range(ts_info_copy.zeta[i_surf].shape[2]):\n ts_info_copy.zeta[i_surf][:, iM, iN] += for_pos[0:3]\n # zeta_star\n for iM in range(ts_info_copy.zeta_star[i_surf].shape[1]):\n for iN in range(ts_info_copy.zeta_star[i_surf].shape[2]):\n ts_info_copy.zeta_star[i_surf][:, iM, iN] += for_pos[0:3]\n\n ts_info_copy.generate_ctypes_pointers()\n calculate_uind_at_points(ct.byref(uvmopts),\n ts_info_copy.ct_p_dimensions,\n ts_info_copy.ct_p_dimensions_star,\n ts_info_copy.ct_p_zeta,\n ts_info_copy.ct_p_zeta_star,\n ts_info_copy.ct_p_gamma,\n ts_info_copy.ct_p_gamma_star,\n p_target_triads,\n p_uind,\n ct.c_uint(npoints))\n ts_info_copy.remove_ctypes_pointers()\n del p_uind\n del p_target_triads\n\n return uind\n\n\ndef biot_panel_cpp(zeta_point, zeta_panel, vortex_radius, gamma=1.0):\n \"\"\"\n Linear UVLM function\n\n Returns the induced velocity at a point ``zeta_point`` due to a panel located at ``zeta_panel`` with circulation\n ``gamma``.\n\n Args:\n zeta_point (np.ndarray): Coordinates of the point with size ``(3,)``.\n zeta_panel (np.ndarray): Panel coordinates with size ``(4, 3)``.\n gamma (float): Panel circulation.\n\n Returns:\n np.ndarray: Induced velocity at point\n\n \"\"\"\n\n assert zeta_point.flags['C_CONTIGUOUS'] and zeta_panel.flags['C_CONTIGUOUS'], \\\n 'Input not C contiguous'\n\n if type(vortex_radius) is ct.c_double:\n vortex_radius_float = vortex_radius.value\n else:\n vortex_radius_float = vortex_radius\n velP = np.zeros((3,), order='C')\n UvlmLib.call_biot_panel(\n velP.ctypes.data_as(ct.POINTER(ct.c_double)),\n zeta_point.ctypes.data_as(ct.POINTER(ct.c_double)),\n zeta_panel.ctypes.data_as(ct.POINTER(ct.c_double)),\n ct.byref(ct.c_double(gamma)),\n ct.byref(ct.c_double(vortex_radius_float)))\n\n return velP\n\n\ndef eval_panel_cpp(zeta_point, zeta_panel,\n vortex_radius, gamma_pan=1.0):\n \"\"\"\n Linear UVLM function\n\n Returns\n tuple: The derivative of the induced velocity with respect to point ``P`` and panel vertices ``ZetaP``.\n\n Warnings:\n Function may fail if zeta_point is not stored contiguously.\n\n Eg:\n\n The following will fail\n\n zeta_point=Mat[:,2,5]\n eval_panel_cpp(zeta_point,zeta_panel, vortex_radius, gamma_pan=1.0)\n\n but\n\n zeta_point=Mat[:,2,5].copy()\n eval_panel_cpp(zeta_point,zeta_panel, vortex_radius, gamma_pan=1.0)\n\n will not.\n \"\"\"\n\n assert zeta_point.flags['C_CONTIGUOUS'] and zeta_panel.flags['C_CONTIGUOUS'], \\\n 'Input not C contiguous'\n\n der_point = np.zeros((3, 3), order='C')\n der_vertices = np.zeros((4, 3, 3), order='C')\n\n if type(vortex_radius) is ct.c_double:\n vortex_radius_float = vortex_radius.value\n else:\n vortex_radius_float = vortex_radius\n UvlmLib.call_der_biot_panel(\n der_point.ctypes.data_as(ct.POINTER(ct.c_double)),\n der_vertices.ctypes.data_as(ct.POINTER(ct.c_double)),\n zeta_point.ctypes.data_as(ct.POINTER(ct.c_double)),\n zeta_panel.ctypes.data_as(ct.POINTER(ct.c_double)),\n ct.byref(ct.c_double(gamma_pan)),\n ct.byref(ct.c_double(vortex_radius_float)))\n\n return der_point, der_vertices\n\n\ndef get_induced_velocity_cpp(maps, zeta, gamma, zeta_target,\n vortex_radius):\n \"\"\"\n Linear UVLM function used in bound surfaces\n\n Computes induced velocity at a point zeta_target.\n\n Args:\n maps (sharpy.linear.src.surface.AeroGridSurface): instance of bound surface\n zeta (np.ndarray): Coordinates of panel\n gamma (float): Panel circulation strength\n zeta_target (np.ndarray): Coordinates of target point\n\n Returns:\n np.ndarray: Induced velocity by panel at target point\n\n \"\"\"\n call_ind_vel = UvlmLib.call_ind_vel\n\n assert zeta_target.flags['C_CONTIGUOUS'], \"Input not C contiguous\"\n\n M, N = maps.M, maps.N\n uind_target = np.zeros((3,), order='C')\n\n if type(vortex_radius) is ct.c_double:\n vortex_radius_float = vortex_radius.value\n else:\n vortex_radius_float = vortex_radius\n call_ind_vel(\n uind_target.ctypes.data_as(ct.POINTER(ct.c_double)),\n zeta_target.ctypes.data_as(ct.POINTER(ct.c_double)),\n zeta.ctypes.data_as(ct.POINTER(ct.c_double)),\n gamma.ctypes.data_as(ct.POINTER(ct.c_double)),\n ct.byref(ct.c_int(M)),\n ct.byref(ct.c_int(N)),\n ct.byref(ct.c_double(vortex_radius_float)))\n\n return uind_target\n\n\ndef get_aic3_cpp(maps, zeta, zeta_target, vortex_radius):\n \"\"\"\n Linear UVLM function used in bound surfaces\n\n Produces influence coefficient matrix to calculate the induced velocity\n at a target point. The aic3 matrix has shape (3,K)\n\n Args:\n maps (sharpy.linear.src.surface.AeroGridSurface): instance of linear bound surface\n zeta (np.ndarray): Coordinates of panel\n zeta_target (np.ndarray): Coordinates of target point\n\n Returns:\n np.ndarray: Aerodynamic influence coefficient\n \"\"\"\n\n assert zeta_target.flags['C_CONTIGUOUS'], \"Input not C contiguous\"\n\n K = maps.K\n aic3 = np.zeros((3, K), order='C')\n\n if type(vortex_radius) is ct.c_double:\n vortex_radius_float = vortex_radius.value\n else:\n vortex_radius_float = vortex_radius\n UvlmLib.call_aic3(\n aic3.ctypes.data_as(ct.POINTER(ct.c_double)),\n zeta_target.ctypes.data_as(ct.POINTER(ct.c_double)),\n zeta.ctypes.data_as(ct.POINTER(ct.c_double)),\n ct.byref(ct.c_int(maps.M)),\n ct.byref(ct.c_int(maps.N)),\n ct.byref(ct.c_double(vortex_radius_float)))\n\n return aic3\n\n\ndef dvinddzeta_cpp(zetac, surf_in, is_bound,\n vortex_radius, M_in_bound=None):\n \"\"\"\n Linear UVLM function used in the assembly of the linear system\n\n Produces derivatives of induced velocity by surf_in w.r.t. the zetac point.\n Derivatives are divided into those associated to the movement of zetac, and\n to the movement of the surf_in vertices (DerVert).\n\n If surf_in is bound (is_bound==True), the circulation over the TE due to the\n wake is not included in the input.\n\n If surf_in is a wake (is_bound==False), derivatives w.r.t. collocation\n points are computed ad the TE contribution on ``der_vert``. In this case, the\n chordwise paneling Min_bound of the associated input is required so as to\n calculate Kzeta and correctly allocate the derivative matrix.\n\n Returns:\n tuple: output derivatives are:\n - der_coll: 3 x 3 matrix\n - der_vert: 3 x 3*Kzeta (if surf_in is a wake, Kzeta is that of the bound)\n\n Warning:\n zetac must be contiguously stored!\n \"\"\"\n\n M_in, N_in = surf_in.maps.M, surf_in.maps.N\n Kzeta_in = surf_in.maps.Kzeta\n shape_zeta_in = (3, M_in + 1, N_in + 1)\n\n # allocate matrices\n der_coll = np.zeros((3, 3), order='C')\n\n if is_bound:\n M_in_bound = M_in\n Kzeta_in_bound = (M_in_bound + 1) * (N_in + 1)\n der_vert = np.zeros((3, 3 * Kzeta_in_bound))\n\n if type(vortex_radius) is ct.c_double:\n vortex_radius_float = vortex_radius.value\n else:\n vortex_radius_float = vortex_radius\n UvlmLib.call_dvinddzeta(\n der_coll.ctypes.data_as(ct.POINTER(ct.c_double)),\n der_vert.ctypes.data_as(ct.POINTER(ct.c_double)),\n zetac.ctypes.data_as(ct.POINTER(ct.c_double)),\n surf_in.zeta.ctypes.data_as(ct.POINTER(ct.c_double)),\n surf_in.gamma.ctypes.data_as(ct.POINTER(ct.c_double)),\n ct.byref(ct.c_int(M_in)),\n ct.byref(ct.c_int(N_in)),\n ct.byref(ct.c_bool(is_bound)),\n ct.byref(ct.c_int(M_in_bound)),\n ct.byref(ct.c_double(vortex_radius_float))\n )\n\n return der_coll, der_vert\n\ndef get_ctype_pointer_of_rbm_vel_in_G_frame(rbm_vel, cga):\n rbm_vel[0:3] = np.dot(cga, rbm_vel[0:3])\n rbm_vel[3:6] = np.dot(cga, rbm_vel[3:6])\n p_rbm_vel = rbm_vel.ctypes.data_as(ct.POINTER(ct.c_double))\n return p_rbm_vel" }, { "path": "sharpy/cases/__init__.py", "content": "" }, { "path": "sharpy/cases/coupled/WindTurbine/__init__.py", "content": "" }, { "path": "sharpy/cases/coupled/WindTurbine/generate_rotor.py", "content": "import numpy as np\nimport os\n\nimport sharpy.utils.generate_cases as gc\nimport sharpy.cases.templates.template_wt as template_wt\nfrom sharpy.utils.constants import deg2rad\nimport sharpy.utils.sharpydir as sharpydir\n\n######################################################################\n########################### PARAMETERS #############################\n######################################################################\n# Case\ncase = 'rotor'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n# Geometry discretization\nchord_panels = np.array([8], dtype=int)\nrevs_in_wake = 1\n\n# Operation\nrotation_velocity = 1.366190\npitch_deg = 0. #degrees\n\n# Wind\nWSP = 11.4\nair_density = 1.225\n\n# Simulation\ndphi = 4.*deg2rad\nrevs_to_simulate = 5\n\n######################################################################\n########################## GENERATE WT #############################\n######################################################################\ndt = dphi/rotation_velocity\n# time_steps = int(revs_to_simulate*2.*np.pi/dphi)\ntime_steps = 2 # For the test cases\n\nmstar = int(revs_in_wake*2.*np.pi/dphi)\n\nop_params = {'rotation_velocity': rotation_velocity,\n 'pitch_deg': pitch_deg,\n 'wsp': WSP,\n 'dt': dt}\n\ngeom_params = {'chord_panels':chord_panels,\n 'tol_remove_points': 1e-8,\n 'n_points_camber': 100,\n 'm_distribution': 'uniform'}\nexcel_description = {'excel_file_name': os.path.abspath(sharpydir.SharpyDir + '/docs/source/content/example_notebooks/source/type02_db_NREL5MW_v02.xlsx'),\n 'excel_sheet_parameters': 'parameters',\n 'excel_sheet_structural_blade': 'structural_blade',\n 'excel_sheet_discretization_blade': 'discretization_blade',\n 'excel_sheet_aero_blade': 'aero_blade',\n 'excel_sheet_airfoil_info': 'airfoil_info',\n 'excel_sheet_airfoil_chord': 'airfoil_coord'}\n\noptions = {'camber_effect_on_twist': False,\n 'user_defined_m_distribution_type': None,\n 'include_polars': False}\n\nrotor = template_wt.rotor_from_excel_type03(op_params,\n geom_params,\n excel_description,\n options)\n\n######################################################################\n###################### DEFINE SIMULATION ###########################\n######################################################################\nSimInfo = gc.SimulationInformation()\nSimInfo.set_default_values()\n\nSimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'BeamPlot',\n 'AerogridPlot',\n 'DynamicCoupled',\n 'SaveData']\n\nSimInfo.solvers['SHARPy']['case'] = case\nSimInfo.solvers['SHARPy']['route'] = route\nSimInfo.solvers['SHARPy']['write_log'] = True\nSimInfo.set_variable_all_dicts('dt', dt)\nSimInfo.set_variable_all_dicts('rho', air_density)\n\nSimInfo.solvers['SteadyVelocityField']['u_inf'] = WSP\nSimInfo.solvers['SteadyVelocityField']['u_inf_direction'] = np.array([0., 0., 1.])\nSimInfo.set_variable_all_dicts('velocity_field_input', SimInfo.solvers['SteadyVelocityField'])\n\nSimInfo.solvers['BeamLoader']['unsteady'] = 'on'\n\nSimInfo.solvers['AerogridLoader']['unsteady'] = 'on'\nSimInfo.solvers['AerogridLoader']['mstar'] = mstar\nSimInfo.solvers['AerogridLoader']['freestream_dir'] = np.array([0.,0.,0.])\nSimInfo.solvers['AerogridLoader']['wake_shape_generator'] = 'HelicoidalWake'\nSimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] = {'u_inf': WSP,\n 'u_inf_direction': SimInfo.solvers['SteadyVelocityField']['u_inf_direction'],\n 'rotation_velocity': rotation_velocity*np.array([0., 0., 1.]),\n 'dt': dt,\n 'dphi1': dphi,\n 'ndphi1': mstar,\n 'r': 1.,\n 'dphimax': 10*deg2rad}\n\nSimInfo.solvers['NonLinearStatic']['max_iterations'] = 200\nSimInfo.solvers['NonLinearStatic']['num_load_steps'] = 1\nSimInfo.solvers['NonLinearStatic']['min_delta'] = 1e-5\n\nSimInfo.solvers['StaticUvlm']['horseshoe'] = False\nSimInfo.solvers['StaticUvlm']['num_cores'] = 8\nSimInfo.solvers['StaticUvlm']['n_rollup'] = 0\nSimInfo.solvers['StaticUvlm']['rollup_dt'] = dt\nSimInfo.solvers['StaticUvlm']['rollup_aic_refresh'] = 1\nSimInfo.solvers['StaticUvlm']['rollup_tolerance'] = 1e-8\nSimInfo.solvers['StaticUvlm']['velocity_field_generator'] = 'SteadyVelocityField'\nSimInfo.solvers['StaticUvlm']['velocity_field_input'] = SimInfo.solvers['SteadyVelocityField']\n\nSimInfo.solvers['StaticCoupled']['structural_solver'] = 'NonLinearStatic'\nSimInfo.solvers['StaticCoupled']['structural_solver_settings'] = SimInfo.solvers['NonLinearStatic']\nSimInfo.solvers['StaticCoupled']['aero_solver'] = 'StaticUvlm'\nSimInfo.solvers['StaticCoupled']['aero_solver_settings'] = SimInfo.solvers['StaticUvlm']\n\nSimInfo.solvers['StaticCoupled']['tolerance'] = 1e-6\nSimInfo.solvers['StaticCoupled']['n_load_steps'] = 0\nSimInfo.solvers['StaticCoupled']['relaxation_factor'] = 0.\n\nSimInfo.solvers['StepUvlm']['convection_scheme'] = 2\nSimInfo.solvers['StepUvlm']['num_cores'] = 8\n\nSimInfo.solvers['WriteVariablesTime']['FoR_variables'] = ['total_forces',]\nSimInfo.solvers['WriteVariablesTime']['FoR_number'] = [0,]\n\nSimInfo.solvers['DynamicCoupled']['structural_solver'] = 'RigidDynamicPrescribedStep'\nSimInfo.solvers['DynamicCoupled']['structural_solver_settings'] = SimInfo.solvers['RigidDynamicPrescribedStep']\nSimInfo.solvers['DynamicCoupled']['aero_solver'] = 'StepUvlm'\nSimInfo.solvers['DynamicCoupled']['aero_solver_settings'] = SimInfo.solvers['StepUvlm']\nSimInfo.solvers['DynamicCoupled']['postprocessors'] = ['BeamPlot', 'AerogridPlot', 'WriteVariablesTime', 'Cleanup']\nSimInfo.solvers['DynamicCoupled']['postprocessors_settings'] = {'BeamPlot': SimInfo.solvers['BeamPlot'],\n 'AerogridPlot': SimInfo.solvers['AerogridPlot'],\n 'WriteVariablesTime': SimInfo.solvers['WriteVariablesTime'],\n 'Cleanup': SimInfo.solvers['Cleanup']}\nSimInfo.solvers['DynamicCoupled']['minimum_steps'] = 0\n\nSimInfo.define_num_steps(time_steps)\n\n# Define dynamic simulation\nSimInfo.with_forced_vel = True\nSimInfo.for_vel = np.zeros((time_steps,6), dtype=float)\nSimInfo.for_vel[:,5] = rotation_velocity\nSimInfo.for_acc = np.zeros((time_steps,6), dtype=float)\nSimInfo.with_dynamic_forces = True\nSimInfo.dynamic_forces = np.zeros((time_steps,rotor.StructuralInformation.num_node,6), dtype=float)\n\n\n######################################################################\n####################### GENERATE FILES #############################\n######################################################################\ngc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\nrotor.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\nSimInfo.generate_solver_file()\nSimInfo.generate_dyn_file(time_steps)\n" }, { "path": "sharpy/cases/coupled/X-HALE/generate_xhale.py", "content": "#!/usr/env python\n# X-HALE model for SHARPy.\n# Version 1.0\n# See IFASD 2019 paper by: del Carre, A and Teixeira, P and Palacios, R and Cesnik, C. E. S.\n#\n# Alfonso del Carre\n# June 2019\n# ============================================================================\n\nimport h5py as h5\nimport numpy as np\nimport os\nimport sharpy.utils.algebra as algebra\n\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\ncases = [\n '0', # 15%, 15 chords, lateral\n ]\n\ndata = dict()\ndata['0'] = {\n 'gust_length': 15, # in chords\n 'gust_intensity': 0.15, # in % of uinf\n 'gust_shape': 'lateral 1-cos', # '1-cos' for vertical gust\n}\n\nhorseshoe = 'off'\n\nfor case in cases:\n vertical_tail = True\n if vertical_tail:\n case_name = 'xhale_ifasd' + '_' + case\n print('Generating xhale with vertical Ctail')\n else:\n case_name = 'xhale_ifasd' + '_' + case\n print('Generating xhale with horizontal Ctail')\n\n\n flow = [\n 'BeamLoader',\n 'AerogridLoader',\n # 'StaticTrim', # uncomment for longitudinal static trim\n 'StaticCoupled', # static coupled solver with GECB and UVLM\n 'BeamLoads', # beam loads and strains computation for static\n 'BeamPlot', # beam structure and data output for static\n 'AerogridPlot', # aero grid output for static\n 'DynamicCoupled', # dynamic coupled solver. See end of file:\n # settings['DynamicCoupled']['postprocessors']\n # for the corresponding 'BeamLoads', 'BeamPlot'\n # and 'AerogridPlot' settings and calls.\n ]\n\n u_inf = 14 # free stream vel [SI]\n rho = 1.225 # density [SI]\n chord = 0.2 # main wing chord length for gust dimensioning.\n # the value used for the geometry generation is\n # given in the input/*.xslx files\n\n if vertical_tail:\n alpha = 2.4744791522743887*np.pi/180 # angle of attack [rad]\n beta = 0.*np.pi/180 # sideslip angle [rad]\n cs_deflection = 1.186515244051093*np.pi/180 # elevators deflection [rad]\n aileron_deflection = 0*0.039011*np.pi/180 # aileron deflection [rad]\n thrustC = 0.21033486522175712 # baseline thrust [N]\n differential = 0 # thrust of right side: T_R = thrustC*(1 + differential)\n # thrust of left side: T_L = thrustC*(1 - differential)\n roll = 0 # initial/static roll angle [rad]\n in_structural_twist = 5*np.pi/180\n\n\n else:\n # NOTE: These values are not the correct trim. Run StaticTrim with your\n # current discretisation\n alpha = 2.4744791522743887*np.pi/180 # angle of attack [rad]\n beta = 0.*np.pi/180 # sideslip angle [rad]\n cs_deflection = 1.186515244051093*np.pi/180 # elevators deflection [rad]\n aileron_deflection = 0*0.039011*np.pi/180 # aileron deflection [rad]\n thrustC = 0.21033486522175712 # baseline thrust [N]\n differential = 0 # thrust of right side: T_R = thrustC*(1 + differential)\n # thrust of left side: T_L = thrustC*(1 - differential)\n roll = 0 # initial/static roll angle [rad]\n in_structural_twist = 5*np.pi/180\n\n gravity = 'on'\n gravity_value = 9.807\n\n # stiffness multiplier\n sigma = 1\n # shear stiffness multipliers\n ga_mult = 0.1\n\n # spatial offset [m] for the gust. (if == 1, gust 1 m in front of reference\n # point [0, 0, 0].\n space_offset = 1.\n\n try:\n gust_intensity = data[case]['gust_intensity']\n gust_length = data[case]['gust_length']*chord\n gust_shape = data[case]['gust_shape']\n except KeyError:\n gust_intensity = 0\n gust_length = 0\n gust_shape = '1-cos'\n\n # number of load substeps in the static coupled solver.\n n_step = 1\n\n # relaxation factor for the static coupled solver\n # static relaxation factor \\in [0, 1). 0 == no relaxation\n static_relaxation_factor = 0.5\n # Dynamic relaxation parameters. Relaxation is linearly varied between\n # initial and final relaxation factor in relaxation_steps\n initial_relaxation_factor = 0.4\n final_relaxation_factor = 0.9\n relaxation_steps = 15\n\n # nonlinear beam tolerance.\n tolerance = 1e-6\n # FSI iteration tolerance\n fsi_tolerance = 1e-6\n # wake length when not running horseshoe\n wake_length = 4 # meters\n\n # geometrical data\n span_section = 1.0\n dihedral_outer = 10*np.pi/180\n\n length_centre_tail = 1.106\n length_outer_tail = 0.65\n span_tail = 0.24\n span_ctail_L = 0.145\n span_ctail_R = 0.24\n span_fin = 0.184\n span_vfin = 0.15\n\n n_sections = 3\n\n # DISCRETISATION\n # spatial discretisation\n # chordwise discretisation\n m = 8 # main wing\n m_tail = 3 # tails\n m_fin = 4 # fins and pods\n\n # number of structural elements in inner and outer sections.\n # note that you will have 2*n_elem spanwise aero panels\n n_elem_section = 4\n # structural elements in dihedral section\n n_elem_section_dihedral = 8\n # elements in central tail boom\n n_elem_centre_tail = 1\n # elements in outer tail booms\n n_elem_outer_tail = 1\n # elements in tails (per semi span)\n n_elem_tail = 1\n # elements in fins and pods\n n_elem_fin = 1\n n_elem_main = int((n_sections-1)*n_elem_section + n_elem_section_dihedral)\n # number of aero surfaces. To understand the logic of this, check SHARPy's\n # documentation\n n_surfaces = 20\n\n # temporal discretisation\n # seconds of simulation\n physical_time = 10\n # factor multiplying the theoretical timestep\n # (dt = chord/m/u_inf*tstep_factor)\n tstep_factor = 1\n dt = chord/m/u_inf*tstep_factor\n n_tstep = round(physical_time/dt)\n print('n_tstep: ', n_tstep)\n\n # if horseshoe wake (only for static) is 'on'\n # we only need one chordwise wake panel\n if horseshoe == 'on':\n mstar = 1\n else:\n # else, we put as many as we need to reach wake_length in steady conditions\n mstar = int(wake_length/(u_inf*dt))\n print('mstar = ', mstar)\n\n # beam processing\n # don't modify this\n n_node_elem = 3\n span_main = n_sections*span_section\n\n # total elements, nodes... calculation\n # total number of elements\n n_elem = 0\n n_elem += n_elem_main\n n_elem += n_elem_main\n n_elem += n_elem_centre_tail\n n_elem += n_elem_tail\n n_elem += n_elem_tail\n n_elem += n_elem_fin\n n_elem += n_elem_outer_tail\n n_elem += n_elem_tail\n n_elem += n_elem_tail\n n_elem += n_elem_fin\n n_elem += n_elem_outer_tail\n n_elem += n_elem_tail\n n_elem += n_elem_tail\n n_elem += n_elem_fin\n n_elem += n_elem_outer_tail\n n_elem += n_elem_tail\n n_elem += n_elem_tail\n n_elem += n_elem_outer_tail\n n_elem += n_elem_tail\n n_elem += n_elem_tail\n n_elem += n_elem_fin\n n_elem += n_elem_fin\n n_elem += n_elem_fin\n n_elem += n_elem_fin\n n_elem += n_elem_fin\n\n# number of nodes per part\n n_node_section = n_elem_section*(n_node_elem - 1) + 1\n n_node_section_dihedral = n_elem_section_dihedral*(n_node_elem - 1) + 1\n n_node_main = n_elem_main*(n_node_elem - 1) + 1\n n_node_centre_tail = n_elem_centre_tail*(n_node_elem - 1) + 1\n n_node_tail = n_elem_tail*(n_node_elem - 1) + 1\n n_node_outer_tail = n_elem_outer_tail*(n_node_elem - 1) + 1\n n_node_fin = n_elem_fin*(n_node_elem - 1) + 1\n\n# total number of nodes\n n_node = 0\n n_node += n_node_main + n_node_main - 1\n n_node += n_node_centre_tail - 1\n n_node += n_node_tail - 1\n n_node += n_node_tail - 1\n n_node += n_node_fin - 1\n n_node += n_node_outer_tail - 1\n n_node += n_node_tail - 1\n n_node += n_node_tail - 1\n n_node += n_node_fin - 1\n n_node += n_node_outer_tail - 1\n n_node += n_node_tail - 1\n n_node += n_node_tail - 1\n n_node += n_node_fin - 1\n n_node += n_node_outer_tail - 1\n n_node += n_node_tail - 1\n n_node += n_node_tail - 1\n n_node += n_node_outer_tail - 1\n n_node += n_node_tail - 1\n n_node += n_node_tail - 1\n n_node += n_node_fin - 1\n n_node += n_node_fin - 1\n n_node += n_node_fin - 1\n n_node += n_node_fin - 1\n n_node += n_node_fin - 1\n\n # stiffness and mass matrices\n # if you add custom stiffness/mass matrices, make sure to update this\n # number\n n_stiffness = 12\n n_mass = 17\n\n # PLACEHOLDERS\n # beam\n x = np.zeros((n_node, ))\n y = np.zeros((n_node, ))\n z = np.zeros((n_node, ))\n stiffness_db = np.zeros((n_stiffness, 6, 6))\n mass_db = np.zeros((n_mass, 6, 6))\n beam_number = np.zeros((n_elem, ), dtype=int)\n num_node_elements = np.zeros((n_elem, ), dtype=int) + 3\n frame_of_reference_delta = np.zeros((n_elem, n_node_elem, 3))\n structural_twist = np.zeros((n_elem, n_node_elem))\n conn = np.zeros((n_elem, n_node_elem), dtype=int)\n elem_stiffness = np.zeros((n_elem, ), dtype=int)\n elem_mass = np.zeros((n_elem, ), dtype=int)\n boundary_conditions = np.zeros((n_node, ), dtype=int)\n app_forces = np.zeros((n_node, 6))\n n_lumped_mass = 0\n lumped_mass_nodes = None\n lumped_mass = None\n lumped_mass_inertia = None\n lumped_mass_position = None\n\n end_nodesL = np.zeros((n_sections,), dtype=int)\n end_nodesR = np.zeros((n_sections,), dtype=int)\n end_elementsL = np.zeros((n_sections,), dtype=int)\n end_elementsR = np.zeros((n_sections,), dtype=int)\n end_tails_nodesL = np.zeros((2, ), dtype=int)\n end_tails_elementsL = np.zeros((2, ), dtype=int)\n end_tails_nodesR = np.zeros((2, ), dtype=int)\n end_tails_elementsR = np.zeros((2, ), dtype=int)\n end_of_centre_tail_node = 0\n end_of_centre_tail_elem = 0\n\n end_tip_tail_nodeC = np.zeros((2, ), dtype=int)\n end_tip_tail_elemC = np.zeros((2, ), dtype=int)\n\n tail_beam_numbersR = np.zeros((2, 3)) # 0=centre spar, 1=R tail, 2=L tail\n tail_beam_numbersL = np.zeros((2, 3)) # 0=centre spar, 1=R tail, 2=L tail\n tail_beam_numbersC = np.zeros((3, ))\n\n fin_beam_numberC = 0\n fin_beam_numberL = 0\n fin_beam_numberR = 0\n vfin_beam_numberC = 0\n vfin_beam_numberL = 0\n vfin_beam_numberR = 0\n fin_beam_numberLL = 0\n fin_beam_numberRR = 0\n\n # aero\n airfoil_distribution = np.zeros((n_elem, n_node_elem), dtype=int)\n surface_distribution = np.zeros((n_elem,), dtype=int) - 1\n surface_m = np.zeros((n_surfaces, ), dtype=int)\n # chordwise panel distribution. I'd leave there, but if you want,\n # you can try '1-cos'\n m_distribution = 'uniform'\n aero_node = np.zeros((n_node,), dtype=bool)\n twist = np.zeros((n_elem, n_node_elem))\n chord = np.zeros((n_elem, n_node_elem,))\n elastic_axis = np.zeros((n_elem, n_node_elem,))\n\n thrust_nodes = np.zeros((5,), dtype=int)\n\n# FUNCTIONS-------------------------------------------------------------\n def clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n dyn_file_name = route + '/' + case_name + '.dyn.h5'\n if os.path.isfile(dyn_file_name):\n os.remove(dyn_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n def read_beam_data(filename=route + '/inputs/beam_properties.xlsx'):\n \"\"\"\n Function reading the xlsx file with beam properties, including\n stiffness and distributed mass.\n\n Data is then processed to obtain the 6x6 mass matrices.\n \"\"\"\n import pandas as pd\n import sharpy.utils.model_utils as model_utils\n # mass\n mass_sheet = pd.read_excel(filename, sheet_name='mass', header=1, skip_rows=1, index_col=0)\n # remove units\n mass_sheet = mass_sheet.drop(['[-]'])\n mass_data = dict()\n for index, row in mass_sheet.iterrows():\n mass_data[index] = dict()\n mass_data[index]['mass'] = mass_sheet['mass'][index]\n mass_data[index]['inertia'] = np.zeros((3, 3))\n mass_data[index]['inertia'][0, 0] = mass_sheet['ixx'][index]\n mass_data[index]['inertia'][1, 1] = mass_sheet['iyy'][index]\n mass_data[index]['inertia'][2, 2] = mass_sheet['izz'][index]\n mass_data[index]['inertia'][1, 2] = mass_sheet['iyz'][index]\n mass_data[index]['inertia'][2, 1] = mass_sheet['iyz'][index]\n mass_data[index]['xcg'] = np.zeros((3,))\n mass_data[index]['xcg'][0] = mass_sheet['xcg'][index]\n mass_data[index]['xcg'][1] = mass_sheet['ycg'][index]\n mass_data[index]['xcg'][2] = mass_sheet['zcg'][index]\n\n mass_data[index]['full_matrix'] = (\n model_utils.mass_matrix_generator(mass_data[index]['mass'],\n mass_data[index]['xcg'],\n mass_data[index]['inertia']))\n # stiffness\n stiff_sheet = pd.read_excel(filename, sheet_name='stiffness', header=1, skip_rows=1, index_col=0)\n # remove units\n stiff_sheet = stiff_sheet.drop(['[-]'])\n stiff_data = dict()\n for index, row in stiff_sheet.iterrows():\n stiff_data[index] = np.zeros((6, 6))\n stiff_data[index][0, 0] = stiff_sheet['ea'][index]\n stiff_data[index][1, 1] = stiff_sheet['gay'][index]*ga_mult\n stiff_data[index][2, 2] = stiff_sheet['gaz'][index]*ga_mult\n stiff_data[index][3, 3] = stiff_sheet['gj'][index]\n stiff_data[index][4, 4] = stiff_sheet['eiy'][index]\n stiff_data[index][5, 5] = stiff_sheet['eiz'][index]\n stiff_data[index][0, 4] = stiff_sheet['k13'][index] # cross-\n stiff_data[index][4, 0] = stiff_sheet['k13'][index] # stiffness\n stiff_data[index][0, 5] = stiff_sheet['k14'][index]\n stiff_data[index][5, 0] = stiff_sheet['k14'][index] # 1-axial\n stiff_data[index][4, 5] = stiff_sheet['k34'][index] # 3-OOP\n stiff_data[index][5, 4] = stiff_sheet['k34'][index] # 4-IP\n\n return mass_data, stiff_data\n\n def read_lumped_mass_data(filename=route + '/inputs/lumped_mass.xlsx'):\n import pandas as pd\n xl = pd.ExcelFile(filename)\n sheets = {sheet_name: xl.parse(sheet_name, header=0, skiprows=(0, 2)) for sheet_name in xl.sheet_names}\n\n lumped_mass_data = dict()\n n_lumped = 0\n for sheet, val in sheets.items():\n if sheet == 'Notes':\n continue\n lumped_mass_data[sheet] = list()\n for row in range(len(val)):\n n_lumped += 1\n lumped_mass_data[sheet].append(dict())\n lumped_mass_data[sheet][row]['mass'] = 0.0\n lumped_mass_data[sheet][row]['inertia'] = np.zeros((3, 3))\n lumped_mass_data[sheet][row]['xcg'] = np.zeros((3,))\n\n lumped_mass_data[sheet][row]['mass'] = val['Mass'][row]\n lumped_mass_data[sheet][row]['inertia'][0, 0] = val['Ixx'][row]\n lumped_mass_data[sheet][row]['inertia'][1, 1] = val['Iyy'][row]\n lumped_mass_data[sheet][row]['inertia'][2, 2] = val['Izz'][row]\n lumped_mass_data[sheet][row]['inertia'][0, 1] = val['Ixy'][row]\n lumped_mass_data[sheet][row]['inertia'][1, 0] = val['Ixy'][row]\n lumped_mass_data[sheet][row]['inertia'][0, 2] = val['Ixz'][row]\n lumped_mass_data[sheet][row]['inertia'][2, 0] = val['Ixz'][row]\n lumped_mass_data[sheet][row]['inertia'][1, 2] = val['Iyz'][row]\n lumped_mass_data[sheet][row]['inertia'][2, 1] = val['Iyz'][row]\n\n # location of centre of gravity for lumped mass is given in\n # material frame of reference, which depends on the element and\n # node you are clamping it to. Check the documentation for\n # a full explanation, but as a rule of thumb: check the\n # frame_of_reference_delta vector parameter in the beam\n # definition. It usually points towards \"y\" in material FoR, and\n # \"x\" is always tangent to the beam, pointing towards increasing\n # node numbers.\n # This is valid as long as structural_twist is 0. If\n # it is not, you need to take into account that the material\n # FoR will be rotated a structrual_twist angle around\n # the material \"x\" axis.\n lumped_mass_data[sheet][row]['xcg'][0] = val['xcg'][row]\n lumped_mass_data[sheet][row]['xcg'][1] = val['ycg'][row]\n lumped_mass_data[sheet][row]['xcg'][2] = val['zcg'][row]\n\n lumped_mass_data['n_lumped_mass'] = n_lumped\n return lumped_mass_data\n\n def generate_fem():\n global end_of_centre_tail_node, end_of_centre_tail_elem\n global fin_beam_numberC, fin_beam_numberL, fin_beam_numberR\n global vfin_beam_numberC, vfin_beam_numberL, vfin_beam_numberR\n global fin_beam_numberLL, fin_beam_numberRR\n global residual_forces, residual_moments\n\n mass_data, stiff_data = read_beam_data()\n lumped_mass_data = read_lumped_mass_data()\n\n # process lumped mass\n n_lumped_mass = lumped_mass_data['n_lumped_mass']\n lumped_mass_nodes = np.zeros((n_lumped_mass, ), dtype=int)\n lumped_mass = np.zeros((n_lumped_mass, ))\n lumped_mass_inertia = np.zeros((n_lumped_mass, 3, 3))\n lumped_mass_position = np.zeros((n_lumped_mass, 3))\n lumped_mass_indices = dict()\n i_lm = 0\n for i, k in enumerate(lumped_mass_data.keys()):\n if k == 'n_lumped_mass':\n continue\n lumped_mass_indices[k] = list()\n for j in range(len(lumped_mass_data[k])):\n lumped_mass[i_lm] = lumped_mass_data[k][j]['mass']\n lumped_mass_inertia[i_lm] = lumped_mass_data[k][j]['inertia']\n lumped_mass_position[i_lm] = lumped_mass_data[k][j]['xcg']\n lumped_mass_indices[k].append(i_lm)\n i_lm += 1\n\n # process distributed mass\n mass_db[0, ...] = mass_data['Linboard']['full_matrix']\n mass_db[1, ...] = mass_data['Loutboard']['full_matrix']\n mass_db[2, ...] = mass_data['Ldihedral']['full_matrix']\n mass_db[3, ...] = mass_data['Rinboard']['full_matrix']\n mass_db[4, ...] = mass_data['Routboard']['full_matrix']\n mass_db[5, ...] = mass_data['Rdihedral']['full_matrix']\n mass_db[6, ...] = mass_data['boom']['full_matrix']\n mass_db[7, ...] = mass_data['tailL']['full_matrix']\n mass_db[8, ...] = mass_data['tailR']['full_matrix']\n mass_db[9, ...] = mass_data['Cfin']['full_matrix']\n mass_db[10, ...] = mass_data['Lfin']['full_matrix']\n mass_db[11, ...] = mass_data['Rfin']['full_matrix']\n mass_db[12, ...] = mass_data['LLfin']['full_matrix']\n mass_db[13, ...] = mass_data['RRfin']['full_matrix']\n mass_db[14, ...] = mass_data['Cvfin']['full_matrix']\n mass_db[15, ...] = mass_data['Lvfin']['full_matrix']\n mass_db[16, ...] = mass_data['Rvfin']['full_matrix']\n\n # process stiffness data\n stiffness_db[0, ...] = sigma*stiff_data['Linboard']\n stiffness_db[1, ...] = sigma*stiff_data['Loutboard']\n stiffness_db[2, ...] = sigma*stiff_data['Ldihedral']\n stiffness_db[3, ...] = sigma*stiff_data['Rinboard']\n stiffness_db[4, ...] = sigma*stiff_data['Routboard']\n stiffness_db[5, ...] = sigma*stiff_data['Rdihedral']\n stiffness_db[6, ...] = sigma*stiff_data['boom']\n stiffness_db[7, ...] = sigma*stiff_data['tailL']\n stiffness_db[8, ...] = sigma*stiff_data['tailR']\n stiffness_db[9, ...] = sigma*stiff_data['Cfin']\n stiffness_db[10, ...] = sigma*stiff_data['Lfin']\n stiffness_db[11, ...] = sigma*stiff_data['Rfin']\n\n # this matrix is useful when using symmetrical data for the mass, while\n # your local frames of reference are not.\n # For example, the right wing has a material \"y\" axis pointing fore,\n # while the left points aft due to \"x\" pointing in opposite directions.\n rotation_mat = algebra.rotation3d_z(np.pi)\n # I use this matrix to convert from the canonical material FoR to the one with\n # structural twist considered\n rotation_mat_x = algebra.rotation3d_x(-in_structural_twist)\n\n we = 0\n wn = 0\n\n # SECTION 0R\n # add the lumped mass of the pods\n lumped_mass_id = 'centre_pod'\n for i in range(len(lumped_mass_indices[lumped_mass_id])):\n lumped_mass_nodes[lumped_mass_indices[lumped_mass_id][i]] = 0\n lumped_mass_position[lumped_mass_indices[lumped_mass_id][i]] = np.dot(rotation_mat_x,\n np.dot(np.eye(3),\n lumped_mass_position[lumped_mass_indices[lumped_mass_id][i]])\n )\n\n # add thrust as applied force\n # it is necessary to rotate it in order to have a horizontal force,\n # as \"y_materal\" points 5 deg above.\n app_forces[0, 0:3] = thrustC*np.array([0.0, np.cos(in_structural_twist), -np.sin(in_structural_twist)])\n thrust_nodes[0] = 0\n\n beam_number[we:we + n_elem_section] = 0\n y[wn:wn + n_node_section] = np.linspace(0.0, span_section, n_node_section)\n structural_twist[we:we + n_elem_section, :] = in_structural_twist\n for ielem in range(n_elem_section):\n # connectivities. Order is [0, 2, 1]\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_section] = 3\n elem_mass[we:we + n_elem_section] = 3\n boundary_conditions[0] = 1\n # we: working_element\n # wn: working_node\n we += n_elem_section\n wn += n_node_section\n # keeping track of the node and element of very end of section to then\n # map the aero more easily.\n end_nodesR[0] = wn - 1\n end_elementsR[0] = we - 1\n\n # SECTION 1R\n # add the lumped mass of the pods\n lumped_mass_id = 'R_inboard_pod'\n for i in range(len(lumped_mass_indices[lumped_mass_id])):\n lumped_mass_nodes[lumped_mass_indices[lumped_mass_id][i]] = wn - 1\n lumped_mass_position[lumped_mass_indices[lumped_mass_id][i]] = np.dot(rotation_mat_x,\n np.dot(np.eye(3),\n lumped_mass_position[lumped_mass_indices[lumped_mass_id][i]])\n )\n\n app_forces[wn-1, 0:3] = thrustC*np.array([0.0, np.cos(in_structural_twist), -np.sin(in_structural_twist)])\n thrust_nodes[1] = wn - 1\n\n beam_number[we:we + n_elem_section] = 1\n y[wn:wn + n_node_section - 1] = y[wn - 1] + np.linspace(0.0, span_section, n_node_section)[1:]\n structural_twist[we:we + n_elem_section, :] = in_structural_twist\n for ielem in range(n_elem_section):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_section] = 4\n elem_mass[we:we + n_elem_section] = 4\n we += n_elem_section\n wn += n_node_section - 1\n end_nodesR[1] = wn - 1\n end_elementsR[1] = we - 1\n\n # SECTION 2R\n # add the lumped mass of the pods\n lumped_mass_id = 'R_outboard_pod'\n for i in range(len(lumped_mass_indices[lumped_mass_id])):\n lumped_mass_nodes[lumped_mass_indices[lumped_mass_id][i]] = wn - 1\n lumped_mass_position[lumped_mass_indices[lumped_mass_id][i]] = np.dot(rotation_mat_x,\n np.dot(np.eye(3),\n lumped_mass_position[lumped_mass_indices[lumped_mass_id][i]])\n )\n\n app_forces[wn-1, 0:3] = thrustC*(1 + differential)*np.array([0.0, np.cos(in_structural_twist), -np.sin(in_structural_twist)])\n thrust_nodes[2] = wn - 1\n\n beam_number[we:we + n_elem_section_dihedral] = 2\n structural_twist[we:we + n_elem_section_dihedral, :] = in_structural_twist\n y[wn:wn + n_node_section_dihedral - 1] = y[wn - 1] + np.linspace(0.0,\n np.cos(dihedral_outer)*span_section,\n n_node_section_dihedral)[1:]\n z[wn:wn + n_node_section_dihedral - 1] = z[wn - 1] + np.linspace(0.0,\n np.sin(dihedral_outer)*span_section,\n n_node_section_dihedral)[1:]\n for ielem in range(n_elem_section_dihedral):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_section_dihedral] = 5\n elem_mass[we:we + n_elem_section_dihedral] = 5\n boundary_conditions[wn + n_node_section_dihedral - 1 - 1] = -1\n we += n_elem_section_dihedral\n wn += n_node_section_dihedral - 1\n end_nodesR[2] = wn - 1\n end_elementsR[2] = we - 1\n\n # SECTION 0L\n beam_number[we:we + n_elem_section] = 3\n structural_twist[we:we + n_elem_section, :] = -in_structural_twist\n y[wn:wn + n_node_section - 1] = np.linspace(0.0, -span_section, n_node_section)[1:]\n for ielem in range(n_elem_section):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = 0\n elem_stiffness[we:we + n_elem_section] = 0\n elem_mass[we:we + n_elem_section] = 0\n we += n_elem_section\n wn += n_node_section - 1\n end_nodesL[0] = wn - 1\n end_elementsL[0] = we - 1\n\n # SECTION 1L\n # add the lumped mass of the pods\n lumped_mass_id = 'L_inboard_pod'\n for i in range(len(lumped_mass_indices[lumped_mass_id])):\n lumped_mass_nodes[lumped_mass_indices[lumped_mass_id][i]] = wn - 1\n lumped_mass_position[lumped_mass_indices[lumped_mass_id][i]] = np.dot(rotation_mat_x.T,\n np.dot(rotation_mat,\n lumped_mass_position[lumped_mass_indices[lumped_mass_id][i]])\n )\n lumped_mass_position[lumped_mass_indices[lumped_mass_id][i]][0] *= -1\n app_forces[wn-1, 0:3] = thrustC*np.array([0.0, -np.cos(in_structural_twist), -np.sin(in_structural_twist)])\n thrust_nodes[3] = wn - 1\n\n\n beam_number[we:we + n_elem_section] = 4\n structural_twist[we:we + n_elem_section, :] = -in_structural_twist\n y[wn:wn + n_node_section - 1] = y[wn - 1] + np.linspace(0.0, -span_section, n_node_section)[1:]\n for ielem in range(n_elem_section):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_section] = 1\n elem_mass[we:we + n_elem_section] = 1\n we += n_elem_section\n wn += n_node_section - 1\n end_nodesL[1] = wn - 1\n end_elementsL[1] = we - 1\n\n # SECTION 2L\n # add the lumped mass of the pods\n lumped_mass_id = 'L_outboard_pod'\n for i in range(len(lumped_mass_indices[lumped_mass_id])):\n lumped_mass_nodes[lumped_mass_indices[lumped_mass_id][i]] = wn - 1\n lumped_mass_position[lumped_mass_indices[lumped_mass_id][i]] = np.dot(rotation_mat_x.T,\n np.dot(rotation_mat,\n lumped_mass_position[lumped_mass_indices[lumped_mass_id][i]]))\n lumped_mass_position[lumped_mass_indices[lumped_mass_id][i]][0] *= -1\n app_forces[wn-1, 0:3] = thrustC*(1 - differential)*np.array([0.0, -np.cos(in_structural_twist), -np.sin(in_structural_twist)])\n thrust_nodes[4] = wn - 1\n\n beam_number[we:we + n_elem_section_dihedral] = 5\n structural_twist[we:we + n_elem_section_dihedral, :] = -in_structural_twist\n y[wn:wn + n_node_section_dihedral - 1] = y[wn - 1] + np.linspace(0.0, -np.cos(dihedral_outer)*span_section, n_node_section_dihedral)[1:]\n z[wn:wn + n_node_section_dihedral - 1] = z[wn - 1] + np.linspace(0.0, np.sin(dihedral_outer)*span_section, n_node_section_dihedral)[1:]\n for ielem in range(n_elem_section_dihedral):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_section_dihedral] = 2\n elem_mass[we:we + n_elem_section_dihedral] = 2\n boundary_conditions[wn + n_node_section_dihedral - 1 - 1] = -1\n we += n_elem_section_dihedral\n wn += n_node_section_dihedral - 1\n end_nodesL[2] = wn - 1\n end_elementsL[2] = we - 1\n\n\n # centre tail\n beam_number[we:we + n_elem_centre_tail] = 6\n tail_beam_numbersC[0] = 6\n x[wn:wn + n_node_centre_tail - 1] = np.linspace(0.0, length_centre_tail, n_node_centre_tail)[1:]\n for ielem in range(n_elem_centre_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [0.0, 1.0, 0.0]\n conn[we, 0] = 0\n elem_stiffness[we:we + n_elem_centre_tail] = 6\n elem_mass[we:we + n_elem_centre_tail] = 6\n we += n_elem_centre_tail\n wn += n_node_centre_tail - 1\n end_of_centre_tail_node = wn - 1\n end_of_centre_tail_elem = we\n\n if vertical_tail:\n beam_number[we:we + n_elem_tail] = 7\n tail_beam_numbersC[1] = 7\n x[wn:wn + n_node_tail - 1] = x[wn - 1]\n y[wn:wn + n_node_tail - 1] = y[wn - 1]\n z[wn:wn + n_node_tail - 1] = z[wn - 1] + np.linspace(0.0, span_ctail_R, n_node_tail)[1:]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_tail] = 8\n elem_mass[we:we + n_elem_tail] = 8\n boundary_conditions[wn + n_node_tail - 1 - 1] = -1\n end_tip_tail_nodeC[0] = wn + n_node_tail - 1 - 1\n end_tip_tail_elemC[0] = we + n_elem_tail - 1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n beam_number[we:we + n_elem_tail] = 8\n tail_beam_numbersC[2] = 8\n x[wn:wn + n_node_tail - 1] = x[end_of_centre_tail_node]\n y[wn:wn + n_node_tail - 1] = y[wn - 1]\n z[wn:wn + n_node_tail - 1] = z[end_of_centre_tail_node] + np.linspace(0.0, -span_ctail_L, n_node_tail)[1:]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = end_of_centre_tail_node\n elem_stiffness[we:we + n_elem_tail] = 7\n elem_mass[we:we + n_elem_tail] = 7\n boundary_conditions[wn + n_node_tail - 1 -1] = -1\n end_tip_tail_nodeC[1] = wn + n_node_tail - 1 - 1\n end_tip_tail_elemC[1] = we + n_elem_tail - 1\n we += n_elem_tail\n wn += n_node_tail - 1\n else:\n beam_number[we:we + n_elem_tail] = 7\n tail_beam_numbersC[1] = 7\n x[wn:wn + n_node_tail - 1] = x[wn - 1]\n y[wn:wn + n_node_tail - 1] = y[wn - 1] + np.linspace(0.0, span_ctail_R, n_node_tail)[1:]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_tail] = 8\n elem_mass[we:we + n_elem_tail] = 8\n boundary_conditions[wn + n_node_tail - 1 - 1] = -1\n end_tip_tail_nodeC[0] = wn + n_node_tail - 1 - 1\n end_tip_tail_elemC[0] = we + n_elem_tail - 1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n beam_number[we:we + n_elem_tail] = 8\n tail_beam_numbersC[2] = 8\n x[wn:wn + n_node_tail - 1] = x[end_of_centre_tail_node]\n y[wn:wn + n_node_tail - 1] = y[end_of_centre_tail_node] + np.linspace(0.0, -span_ctail_L, n_node_tail)[1:]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = end_of_centre_tail_node\n elem_stiffness[we:we + n_elem_tail] = 7\n elem_mass[we:we + n_elem_tail] = 7\n boundary_conditions[wn + n_node_tail - 1 -1] = -1\n end_tip_tail_nodeC[1] = wn + n_node_tail - 1 - 1\n end_tip_tail_elemC[1] = we + n_elem_tail - 1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n # outer tail 0R\n beam_number[we:we + n_elem_outer_tail] = 9\n tail_beam_numbersR[0,0] = 9\n x[wn:wn + n_node_outer_tail - 1] = np.linspace(0.0, length_outer_tail, n_node_outer_tail)[1:]\n y[wn:wn + n_node_outer_tail - 1] = y[end_nodesR[0]]\n for ielem in range(n_elem_outer_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [0.0, 1.0, 0.0]\n conn[we, 0] = end_nodesR[0]\n elem_stiffness[we:we + n_elem_outer_tail] = 6\n elem_mass[we:we + n_elem_outer_tail] = 6\n we += n_elem_outer_tail\n wn += n_node_outer_tail - 1\n end_tails_nodesR[0] = wn - 1\n end_tails_elementsR[0] = we - 1\n\n beam_number[we:we + n_elem_tail] = 10\n tail_beam_numbersR[0,1] = 10\n x[wn:wn + n_node_tail - 1] = x[end_tails_nodesR[0]]\n y[wn:wn + n_node_tail - 1] = y[end_tails_nodesR[0]] + np.linspace(0.0, span_tail, n_node_tail)[1:]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_tail] = 8\n elem_mass[we:we + n_elem_tail] = 8\n boundary_conditions[wn + n_node_tail - 1 -1] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n beam_number[we:we + n_elem_tail] = 11\n tail_beam_numbersR[0,2] = 11\n x[wn:wn + n_node_tail - 1] = x[end_tails_nodesR[0]]\n y[wn:wn + n_node_tail - 1] = y[end_tails_nodesR[0]] + np.linspace(0.0, -span_tail, n_node_tail)[1:]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = end_tails_nodesR[0]\n elem_stiffness[we:we + n_elem_tail] = 7\n elem_mass[we:we + n_elem_tail] = 7\n boundary_conditions[wn + n_node_tail - 1 -1] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n # outer tail 1R\n beam_number[we:we + n_elem_outer_tail] = 12\n tail_beam_numbersR[1,0] = 12\n x[wn:wn + n_node_outer_tail - 1] = np.linspace(0.0, length_outer_tail, n_node_outer_tail)[1:]\n y[wn:wn + n_node_outer_tail - 1] = y[end_nodesR[1]]\n for ielem in range(n_elem_outer_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [0.0, 1.0, 0.0]\n conn[we, 0] = end_nodesR[1]\n elem_stiffness[we:we + n_elem_outer_tail] = 6\n elem_mass[we:we + n_elem_outer_tail] = 6\n we += n_elem_outer_tail\n wn += n_node_outer_tail - 1\n end_tails_nodesR[1] = wn - 1\n end_tails_elementsR[1] = we - 1\n\n beam_number[we:we + n_elem_tail] = 13\n tail_beam_numbersR[1,1] = 13\n x[wn:wn + n_node_tail - 1] = x[end_tails_nodesR[1]]\n y[wn:wn + n_node_tail - 1] = y[end_tails_nodesR[1]] + np.linspace(0.0, span_tail, n_node_tail)[1:]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_tail] = 8\n elem_mass[we:we + n_elem_tail] = 8\n boundary_conditions[wn + n_node_tail - 1 -1] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n beam_number[we:we + n_elem_tail] = 14\n tail_beam_numbersR[1,2] = 14\n x[wn:wn + n_node_tail - 1] = x[end_tails_nodesR[1]]\n y[wn:wn + n_node_tail - 1] = y[end_tails_nodesR[1]] + np.linspace(0.0, -span_tail, n_node_tail)[1:]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = end_tails_nodesR[1]\n elem_stiffness[we:we + n_elem_tail] = 7\n elem_mass[we:we + n_elem_tail] = 7\n boundary_conditions[wn + n_node_tail - 1 -1] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n # outer tail 0L\n beam_number[we:we + n_elem_outer_tail] = 15\n tail_beam_numbersL[0,0] = 15\n x[wn:wn + n_node_outer_tail - 1] = np.linspace(0.0, length_outer_tail, n_node_outer_tail)[1:]\n y[wn:wn + n_node_outer_tail - 1] = y[end_nodesL[0]]\n for ielem in range(n_elem_outer_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [0.0, 1.0, 0.0]\n conn[we, 0] = end_nodesL[0]\n elem_stiffness[we:we + n_elem_outer_tail] = 6\n elem_mass[we:we + n_elem_outer_tail] = 6\n we += n_elem_outer_tail\n wn += n_node_outer_tail - 1\n end_tails_nodesL[0] = wn - 1\n end_tails_elementsL[0] = we - 1\n\n beam_number[we:we + n_elem_tail] = 16\n tail_beam_numbersL[0,1] = 16\n x[wn:wn + n_node_tail - 1] = x[end_tails_nodesL[0]]\n y[wn:wn + n_node_tail - 1] = y[end_tails_nodesL[0]] + np.linspace(0.0, span_tail, n_node_tail)[1:]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_tails_nodesL[0]\n elem_stiffness[we:we + n_elem_tail] = 8\n elem_mass[we:we + n_elem_tail] = 8\n boundary_conditions[wn + n_node_tail - 1 - 1] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n beam_number[we:we + n_elem_tail] = 17\n tail_beam_numbersL[0,2] = 17\n x[wn:wn + n_node_tail - 1] = x[end_tails_nodesL[0]]\n y[wn:wn + n_node_tail - 1] = y[end_tails_nodesL[0]] + np.linspace(0.0, -span_tail, n_node_tail)[1:]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = end_tails_nodesL[0]\n elem_stiffness[we:we + n_elem_tail] = 7\n elem_mass[we:we + n_elem_tail] = 7\n boundary_conditions[wn + n_node_tail - 1 - 1] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n # outer tail 1L\n beam_number[we:we + n_elem_outer_tail] = 18\n tail_beam_numbersL[1,0] = 18\n x[wn:wn + n_node_outer_tail - 1] = np.linspace(0.0, length_outer_tail, n_node_outer_tail)[1:]\n y[wn:wn + n_node_outer_tail - 1] = y[end_nodesL[1]]\n for ielem in range(n_elem_outer_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [0.0, 1.0, 0.0]\n conn[we, 0] = end_nodesL[1]\n elem_stiffness[we:we + n_elem_outer_tail] = 6\n elem_mass[we:we + n_elem_outer_tail] = 6\n we += n_elem_outer_tail\n wn += n_node_outer_tail - 1\n end_tails_nodesL[1] = wn - 1\n end_tails_elementsL[1] = we - 1\n\n beam_number[we:we + n_elem_tail] = 19\n tail_beam_numbersL[1,1] = 19\n x[wn:wn + n_node_tail - 1] = x[end_tails_nodesL[1]]\n y[wn:wn + n_node_tail - 1] = y[end_tails_nodesL[1]] + np.linspace(0.0, span_tail, n_node_tail)[1:]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_tail] = 8\n elem_mass[we:we + n_elem_tail] = 8\n boundary_conditions[wn + n_node_tail - 1 -1] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n beam_number[we:we + n_elem_tail] = 20\n tail_beam_numbersL[1,2] = 20\n x[wn:wn + n_node_tail - 1] = x[end_tails_nodesL[1]]\n y[wn:wn + n_node_tail - 1] = y[end_tails_nodesL[1]] + np.linspace(0.0, -span_tail, n_node_tail)[1:]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = end_tails_nodesL[1]\n elem_stiffness[we:we + n_elem_tail] = 7\n elem_mass[we:we + n_elem_tail] = 7\n boundary_conditions[wn + n_node_tail - 1 -1] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n # vertical fins (pods)\n # centre one\n beam_number[we:we + n_elem_fin] = 21\n fin_beam_numberC = 21\n x[wn:wn + n_node_fin - 1] = x[0]\n y[wn:wn + n_node_fin - 1] = y[0]\n z[wn:wn + n_node_fin - 1] = z[0] + np.linspace(0.0, -span_fin, n_node_fin)[1:]\n for ielem in range(n_elem_fin):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = 0\n elem_stiffness[we:we + n_elem_fin] = 9\n elem_mass[we:we + n_elem_fin] = 9\n boundary_conditions[wn + n_node_fin - 1 - 1] = -1\n we += n_elem_fin\n wn += n_node_fin - 1\n\n # left one\n beam_number[we:we + n_elem_fin] = 22\n fin_beam_numberL = 22\n x[wn:wn + n_node_fin - 1] = x[end_nodesL[0]]\n y[wn:wn + n_node_fin - 1] = y[end_nodesL[0]]\n z[wn:wn + n_node_fin - 1] = z[end_nodesL[0]] + np.linspace(0.0, -span_fin, n_node_fin)[1:]\n for ielem in range(n_elem_fin):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_nodesL[0]\n elem_stiffness[we:we + n_elem_fin] = 10\n elem_mass[we:we + n_elem_fin] = 10\n boundary_conditions[wn + n_node_fin - 1 - 1] = -1\n we += n_elem_fin\n wn += n_node_fin - 1\n\n # right one\n beam_number[we:we + n_elem_fin] = 23\n fin_beam_numberR = 23\n x[wn:wn + n_node_fin - 1] = x[end_nodesR[0]]\n y[wn:wn + n_node_fin - 1] = y[end_nodesR[0]]\n z[wn:wn + n_node_fin - 1] = z[end_nodesR[0]] + np.linspace(0.0, -span_fin, n_node_fin)[1:]\n for ielem in range(n_elem_fin):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_nodesR[0]\n elem_stiffness[we:we + n_elem_fin] = 11\n elem_mass[we:we + n_elem_fin] = 11\n boundary_conditions[wn + n_node_fin - 1 - 1] = -1\n we += n_elem_fin\n wn += n_node_fin - 1\n\n # left outer one\n beam_number[we:we + n_elem_fin] = 24\n fin_beam_numberLL = 24\n x[wn:wn + n_node_fin - 1] = x[end_nodesL[1]]\n y[wn:wn + n_node_fin - 1] = y[end_nodesL[1]]\n z[wn:wn + n_node_fin - 1] = z[end_nodesL[1]] + np.linspace(0.0, -span_fin, n_node_fin)[1:]\n for ielem in range(n_elem_fin):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_nodesL[1]\n elem_stiffness[we:we + n_elem_fin] = 10\n elem_mass[we:we + n_elem_fin] = 12\n boundary_conditions[wn + n_node_fin - 1 - 1] = -1\n we += n_elem_fin\n wn += n_node_fin - 1\n\n # right outer one\n beam_number[we:we + n_elem_fin] = 25\n fin_beam_numberRR = 25\n x[wn:wn + n_node_fin - 1] = x[end_nodesR[1]]\n y[wn:wn + n_node_fin - 1] = y[end_nodesR[1]]\n z[wn:wn + n_node_fin - 1] = z[end_nodesR[1]] + np.linspace(0.0, -span_fin, n_node_fin)[1:]\n for ielem in range(n_elem_fin):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_nodesR[1]\n elem_stiffness[we:we + n_elem_fin] = 11\n elem_mass[we:we + n_elem_fin] = 13\n boundary_conditions[wn + n_node_fin - 1 - 1] = -1\n we += n_elem_fin\n wn += n_node_fin - 1\n\n # vertical fins\n # centre one\n beam_number[we:we + n_elem_fin] = 26\n vfin_beam_numberC = 26\n x[wn:wn + n_node_fin - 1] = x[end_of_centre_tail_node]\n y[wn:wn + n_node_fin - 1] = y[end_of_centre_tail_node]\n z[wn:wn + n_node_fin - 1] = z[end_of_centre_tail_node] + np.linspace(0.0, -span_vfin, n_node_fin)[1:]\n for ielem in range(n_elem_fin):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_of_centre_tail_node\n elem_stiffness[we:we + n_elem_fin] = 9\n elem_mass[we:we + n_elem_fin] = 14\n boundary_conditions[wn + n_node_fin - 1 - 1] = -1\n we += n_elem_fin\n wn += n_node_fin - 1\n\n # left one\n beam_number[we:we + n_elem_fin] = 27\n vfin_beam_numberL = 27\n x[wn:wn + n_node_fin - 1] = x[end_tails_nodesL[0]]\n y[wn:wn + n_node_fin - 1] = y[end_tails_nodesL[0]]\n z[wn:wn + n_node_fin - 1] = z[end_tails_nodesL[0]] + np.linspace(0.0, -span_vfin, n_node_fin)[1:]\n for ielem in range(n_elem_fin):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_tails_nodesL[0]\n elem_stiffness[we:we + n_elem_fin] = 10\n elem_mass[we:we + n_elem_fin] = 15\n boundary_conditions[wn + n_node_fin - 1 - 1] = -1\n we += n_elem_fin\n wn += n_node_fin - 1\n\n # right one\n beam_number[we:we + n_elem_fin] = 28\n vfin_beam_numberR = 28\n x[wn:wn + n_node_fin - 1] = x[end_tails_nodesR[0]]\n y[wn:wn + n_node_fin - 1] = y[end_tails_nodesR[0]]\n z[wn:wn + n_node_fin - 1] = z[end_tails_nodesR[0]] + np.linspace(0.0, -span_vfin, n_node_fin)[1:]\n for ielem in range(n_elem_fin):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) + np.array([0, 2, 1]))\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_tails_nodesR[0]\n elem_stiffness[we:we + n_elem_fin] = 11\n elem_mass[we:we + n_elem_fin] = 16\n boundary_conditions[wn + n_node_fin - 1 - 1] = -1\n we += n_elem_fin\n wn += n_node_fin - 1\n\n\n # this output to the HDF5 file that is read by 'BeamLoader'.\n # if you want to see what's inside, check HDFView\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=n_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=n_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=n_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness_db)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass_db)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n lumped_mass_nodes_handle = h5file.create_dataset(\n 'lumped_mass_nodes', data=lumped_mass_nodes)\n lumped_mass_handle = h5file.create_dataset(\n 'lumped_mass', data=lumped_mass)\n lumped_mass_inertia_handle = h5file.create_dataset(\n 'lumped_mass_inertia', data=lumped_mass_inertia)\n lumped_mass_position_handle = h5file.create_dataset(\n 'lumped_mass_position', data=lumped_mass_position)\n\n def read_aero_data(filename=route + '/inputs/aero_properties.xlsx'):\n import pandas as pd\n\n xl = pd.ExcelFile(filename)\n sheets = {sheet_name: xl.parse(sheet_name, header=0, index_col=0) for sheet_name in xl.sheet_names}\n\n aero_data = dict()\n for sheet, val in sheets.items():\n aero_data[sheet] = dict()\n for item in val['value'].items():\n aero_data[sheet][item[0]] = item[1]\n\n return aero_data\n\n\n def generate_aero_file():\n global x, y, z\n global fin_beam_numberC, fin_beam_numberL, fin_beam_numberR\n global vfin_beam_numberC, vfin_beam_numberL, vfin_beam_numberR\n global fin_beam_numberLL, fin_beam_numberRR\n\n aero_data = read_aero_data()\n # control surfaces\n n_control_surfaces = 3\n control_surface = np.zeros((n_elem, n_node_elem), dtype=int) - 1\n control_surface_type = np.zeros((n_control_surfaces, ), dtype=int)\n control_surface_deflection = np.zeros((n_control_surfaces, ))\n control_surface_chord = np.zeros((n_control_surfaces, ), dtype=int)\n control_surface_hinge_coord = np.zeros((n_control_surfaces, ), dtype=float)\n\n # control surface type is 0 if static, 1 if dynamic\n control_surface_type[0] = 0\n control_surface_deflection[0] = cs_deflection\n # chord is given as number of panels, not length, so it has to be integer\n control_surface_chord[0] = m_tail\n # location of the hinge wrt e.axis when surface_chord == m_surface\n control_surface_hinge_coord[0] = 0\n\n control_surface_type[1] = 0\n control_surface_deflection[1] = aileron_deflection\n control_surface_chord[1] = int(m*0.25)\n control_surface_hinge_coord[1] = 0\n\n control_surface_type[2] = 0\n control_surface_deflection[2] = -aileron_deflection\n control_surface_chord[2] = int(m*0.25)\n control_surface_hinge_coord[2] = 0\n\n # right wing (surface 0, beams 0, 1, 2, 3)\n type = 'inboard'\n main_chord = aero_data[type]['chord']\n initial_node = 0\n final_node = end_nodesR[-1]\n initial_elem = 0\n final_elem = end_elementsR[-1]\n i_surf = 0\n airfoil_distribution[initial_elem: final_elem + 1, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n surface_distribution[initial_elem: final_elem + 1] = i_surf\n surface_m[i_surf] = m\n aero_node[initial_node:final_node + 1] = True\n node_counter = 0\n for i_elem in range(initial_elem, final_elem + 1):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n for i_elem in range(end_elementsR[1] + 1, end_elementsR[2] + 1):\n if i_elem == 0 or i_elem == end_elementsR[2]:\n continue\n control_surface[i_elem, :] = 1\n\n # left wing (surface 1, beams 4, 5, 6, 7)\n initial_node = end_nodesR[-1] + 1\n final_node = end_nodesL[-1]\n initial_elem = end_elementsR[-1] + 1\n final_elem = end_elementsL[-1]\n i_surf += 1\n airfoil_distribution[initial_elem: final_elem + 1, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n surface_distribution[initial_elem: final_elem + 1] = i_surf\n surface_m[i_surf] = m\n aero_node[initial_node:final_node + 1] = True\n node_counter = 0\n for i_elem in range(initial_elem, final_elem + 1):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n for i_elem in range(end_elementsL[1] + 1, end_elementsL[2] + 1):\n if i_elem == 0 or i_elem == end_elementsL[2]:\n continue\n control_surface[i_elem, :] = 2\n\n # centre tail\n type = 'Ctail'\n ctail_chord = aero_data[type]['chord']\n ctail_m = m_tail\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == tail_beam_numbersC[1]]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = ctail_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == tail_beam_numbersC[2]]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = ctail_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n\n # 0R tail\n type = '0Rtail'\n rtail_chord = aero_data[type]['chord']\n tail_m = max(3, int(m*rtail_chord/main_chord))\n tail_m = m_tail\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == tail_beam_numbersR[0,1]]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = tail_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n control_surface[i_elem, i_local_node] = 0\n\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == tail_beam_numbersR[0,2]]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = tail_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n control_surface[i_elem, i_local_node] = 0\n\n # 1R tail\n type = '0Rtail'\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == tail_beam_numbersR[1,1]]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = tail_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n control_surface[i_elem, i_local_node] = 0\n\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == tail_beam_numbersR[1,2]]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = tail_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n control_surface[i_elem, i_local_node] = 0\n\n # 0L tail\n type = '0Ltail'\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == tail_beam_numbersL[0,1]]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = tail_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n control_surface[i_elem, i_local_node] = 0\n\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == tail_beam_numbersL[0,2]]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = tail_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n control_surface[i_elem, i_local_node] = 0\n\n # 1L tail\n type = '0Ltail'\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == tail_beam_numbersL[1,1]]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = tail_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n control_surface[i_elem, i_local_node] = 0\n\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == tail_beam_numbersL[1,2]]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = tail_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n control_surface[i_elem, i_local_node] = 0\n\n type = 'Cfin'\n cfin_chord = aero_data[type]['chord']\n cfin_m = m_fin\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == fin_beam_numberC]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = cfin_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n\n type = 'Lfin'\n lfin_chord = aero_data[type]['chord']\n fin_m = m_fin\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == fin_beam_numberL]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = fin_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n\n type = 'Rfin'\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == fin_beam_numberR]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = fin_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n\n type = 'LLfin'\n lfin_chord = aero_data[type]['chord']\n fin_m = m_fin\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == fin_beam_numberLL]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = fin_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n\n type = 'RRfin'\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == fin_beam_numberRR]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = fin_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n\n type = 'Cvfin'\n cfin_chord = aero_data[type]['chord']\n cfin_m = m_fin\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == vfin_beam_numberC]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = cfin_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n\n type = 'Lvfin'\n lfin_chord = aero_data[type]['chord']\n fin_m = m_fin\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == vfin_beam_numberL]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = fin_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n\n type = 'Rvfin'\n elements = np.linspace(0, n_elem - 1, n_elem, dtype=int)[beam_number == vfin_beam_numberR]\n i_surf += 1\n for i_elem in elements:\n for i_node in range(n_node_elem):\n airfoil_distribution[i_elem, :] = aero_data['airfoil_indices'][aero_data[type]['airfoil']]\n aero_node[conn[i_elem, i_node]] = True\n surface_distribution[elements] = i_surf\n surface_m[i_surf] = fin_m\n node_counter = 0\n for i_elem in elements:\n for i_local_node in [0, 1, 2]:\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = aero_data[type]['chord']\n elastic_axis[i_elem, i_local_node] = aero_data[type]['elastic_axis']\n twist[i_elem, i_local_node] = -aero_data[type]['twist']*np.pi/180\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n emx07_main = airfoils_group.create_dataset('0', data=load_airfoil(route + '/inputs/EMX-07_camber.txt'))\n flat_tail = airfoils_group.create_dataset('1', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input .attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n control_surface_input = h5file.create_dataset('control_surface', data=control_surface)\n control_surface_deflection_input = h5file.create_dataset('control_surface_deflection', data=control_surface_deflection)\n control_surface_chord_input = h5file.create_dataset('control_surface_chord', data=control_surface_chord)\n control_surface_types_input = h5file.create_dataset('control_surface_type', data=control_surface_type)\n control_surface_hinge_coord_input = h5file.create_dataset('control_surface_hinge_coord', data=control_surface_hinge_coord)\n\n def load_airfoil(filename):\n data = np.loadtxt(filename, skiprows=1)\n return data\n\n\n def generate_naca_camber(M=0, P=0):\n \"\"\"\n https://en.wikipedia.org/wiki/NACA_airfoil\n \"\"\"\n mm = M*1e-2\n p = P*1e-1\n\n def naca(x, mm, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return mm/(p*p)*(2*p*x - x*x)\n elif x > p and x < 1+1e-6:\n return mm/((1-p)*(1-p))*(1 - 2*p + 2*p*x - x*x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, mm, p) for x in x_vec])\n return x_vec, y_vec\n\n\n def generate_solver_file():\n \"\"\"\n Main file generator. This text file contains the location of the\n case files, the case name and all the solvers to be run together\n with their settings.\n \"\"\"\n file_name = route + '/' + case_name + '.sharpy' # the extension\n # of the file is\n # not important\n settings = dict()\n settings['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': flow,\n 'write_screen': 'on',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n\n settings['BeamLoader'] = {'unsteady': 'on', # it's ok to leave it\n # 'on' for static\n # initial orientation of the aircraft,\n # this is where the trim conditions come\n 'orientation': algebra.euler2quat(np.array([roll,\n alpha,\n beta]))}\n\n settings['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n 'mstar': mstar,\n # freestream_dir only used for wake init\n 'freestream_dir': ['1', '0', '0']}\n\n settings['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 350,\n 'num_load_steps': 1,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'gravity_on': gravity,\n 'gravity': gravity_value}\n\n settings['StaticUvlm2'] = {'print_info': 'on',\n 'horseshoe': horseshoe,\n 'num_cores': 1,\n 'n_rollup': 0,\n 'rollup_dt': dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho}\n\n settings['StaticCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': settings['NonLinearStatic'],\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': settings['StaticUvlm2'],\n 'max_iter': 100,\n 'n_load_steps': n_step,\n 'tolerance': fsi_tolerance,\n 'relaxation_factor': static_relaxation_factor}\n\n settings['StaticUvlm'] = {'print_info': 'on',\n 'horseshoe': horseshoe,\n 'num_cores': 1,\n 'n_rollup': 0,\n 'rollup_dt': dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho}\n\n # this trim solver is much slower, but supports lateral trim.\n # it is based on scipy.optimize\n settings['Trim'] = {'solver': 'StaticCoupled',\n 'solver_settings': settings['StaticCoupled'],\n 'initial_alpha': alpha,\n 'initial_beta': beta,\n 'initial_roll': roll,\n 'cs_indices': 0,\n 'initial_cs_deflection': cs_deflection,\n 'initial_thrust': [],\n 'thrust_nodes': [],\n 'refine_solution': 'on',\n 'special_case': {'case_name': 'differential_thrust',\n 'initial_base_thrust': thrustC,\n 'initial_differential_parameter': differential,\n 'base_thrust_nodes': [thrust_nodes[0]],\n 'negative_thrust_nodes': [thrust_nodes[2]],\n 'positive_thrust_nodes': [thrust_nodes[1]]}}\n\n settings['NonLinearDynamicCoupledStep'] = {'print_info': 'off',\n 'max_iterations': 500,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n # newmark damping parameter.\n # it affects higher freq\n # mostly.\n 'newmark_damp': 1e-3,\n 'gravity_on': gravity,\n 'gravity': gravity_value,\n 'num_steps': n_tstep,\n 'balancing': 'off',\n 'dt': dt,\n 'initial_velocity_direction': np.array([-1.0, 0.0, 0.0]),\n 'initial_velocity': u_inf}\n\n settings['StaticTrim'] = {'solver': 'StaticCoupled',\n 'solver_settings': settings['StaticCoupled'],\n 'initial_alpha': alpha,\n 'initial_deflection': cs_deflection,\n 'initial_thrust': thrustC,\n 'thrust_nodes': thrust_nodes}\n\n settings['StepUvlm'] = {'print_info': 'off',\n 'num_cores': 6,\n 'convection_scheme': 2,\n 'gamma_dot_filtering': 6,\n # this is where the gust is input.\n 'velocity_field_generator': 'GustVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0],\n 'gust_shape': gust_shape,\n 'gust_parameters': {\n 'gust_length': gust_length,\n 'gust_intensity': gust_intensity * u_inf},\n 'offset': -space_offset},\n 'rho': rho,\n 'n_time_steps': n_tstep,\n 'dt': dt}\n\n settings['DynamicCoupled'] = {'structural_solver': 'NonLinearDynamicCoupledStep',\n 'structural_solver_settings': settings['NonLinearDynamicCoupledStep'],\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'fsi_substeps': 100,\n 'fsi_tolerance': fsi_tolerance,\n 'relaxation_factor': initial_relaxation_factor,\n 'final_relaxation_factor': final_relaxation_factor,\n 'minimum_steps': 1,\n 'relaxation_steps': relaxation_steps,\n 'n_time_steps': n_tstep,\n 'dt': dt,\n 'include_unsteady_force_contribution': 'on',\n 'cleanup_previous_solution': 'on',\n # the postprocessors in this list are\n # called every time step. Some of them\n # are the same you call in static simulations\n # and you wrote at the beginning of the\n # file\n 'postprocessors': [\n # output some variables by text\n 'WriteVariablesTime',\n # remove old timesteps\n # already output to save RAM\n 'Cleanup',\n # calculate internal\n # beam loads and strains\n 'BeamLoads',\n 'BeamPlot',\n 'AerogridPlot',\n # saves a copy of self.data\n # (the state of the simulation)\n # to restart later if needed.\n # careful, because if you don't\n # add Cleanup and don't pay attention\n # to the 'frequency' and\n # 'keep' parameters, you might\n # fill you HD for long simulations\n 'CreateSnapshot',\n ],\n 'postprocessors_settings': {'BeamLoads': {}, # you need to specify the dict even if empty\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'},\n 'AerogridPlot': {\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n 'CreateSnapshot': {# every how many tsteps if should create a snapshot\n 'frequency': 100,\n # how many old snapshots should it keep?\n # the rest will be discarded.\n 'keep': 5},\n 'Cleanup': {# keep only the last 2000 tsteps.\n # it is good to keep a relatively large number\n # in order to have a good noise filter\n # for gamma_dot\n 'remaining_steps': 2000\n },\n 'WriteVariablesTime': {\n # output a text file with\n # quat: orientation of the aircraft in quaternion\n # for_pos: FoR position in inertial FoR\n # for_vel: the derivative of the previous\n # for_acc: the derivative of the previous\n 'FoR_variables': ['quat', 'for_pos', 'for_vel', 'for_acc'],\n 'cleanup_old_solution': 'on',\n 'delimiter': ', ',\n }\n }\n }\n\n settings['Modal'] = {'print_info': 'on',\n 'use_undamped_modes': 'on',\n 'NumLambda': 100,\n 'write_modes_vtk': 'on',\n 'print_matrices': 'on',\n 'continuous_eigenvalues': 'off',\n 'dt': dt,\n 'plot_eigenvalues': 'on'}\n settings['BeamPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on'}\n\n settings['AerogridPlot'] = {'include_rbm': 'on',\n 'include_forward_motion': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0,\n 'u_inf': u_inf,\n 'dt': dt}\n settings['BeamLoads'] = dict()\n\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n for k, v in settings.items():\n config[k] = v\n config.write()\n\n\n\n clean_test_files()\n generate_fem()\n generate_aero_file()\n generate_solver_file()\n" }, { "path": "sharpy/cases/coupled/X-HALE/inputs/EMX-07_camber.txt", "content": " 0.0 0.0\n 0.3527358E-06 0.5961561E-03\n 0.2736395E-02 0.1136788E-02\n 0.1092258E-01 0.4241672E-02\n 0.2445874E-01 0.7896996E-02\n 0.4321506E-01 0.1164179E-01\n 0.6697159E-01 0.1542114E-01\n 0.9546839E-01 0.1902119E-01\n 0.1284056 0.2208612E-01\n 0.1654034 0.2422109E-01\n 0.2060818 0.2527606E-01\n 0.2499709 0.2526599E-01\n 0.2966008 0.2410581E-01\n 0.3454613 0.2209060E-01\n 0.3960123 0.1946039E-01\n 0.4477137 0.1645021E-01\n 0.4999755 0.1325003E-01\n 0.5522375 0.1003985E-01\n 0.6039397 0.6979703E-02\n 0.6544919 0.4224549E-02\n 0.7033541 0.1969342E-02\n 0.7499865 0.3292383E-03\n 0.7938786 -0.8407012E-03\n 0.8345606 -0.1650622E-02\n 0.8715624 -0.2095578E-02\n 0.9045041 -0.2160548E-02\n 0.9330056 -0.1880469E-02\n 0.9567668 -0.1405372E-02\n 0.9755279 -0.8752758E-03\n 0.9890686 -0.4201971E-03\n 0.9972590 -0.1101422E-03\n 0.9999992 0.5238689E-09\n 1.0 0.0\n" }, { "path": "sharpy/cases/coupled/__init__.py", "content": "" }, { "path": "sharpy/cases/coupled/hinged_controlled_wing/__init__.py", "content": "" }, { "path": "sharpy/cases/coupled/hinged_controlled_wing/generate_hinged_controlled_wing.py", "content": "import h5py as h5\nimport numpy as np\nimport configparser\nimport os\n\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.generate_cases as gc\n\ncase_name = 'hinged_controlled_wing'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n# m = 16 gives flutter with 165\nm_main = 4\namplitude = 5*np.pi/180\nperiod = 3\ndt_factor = 1.\nn_structural_substeps = 1\n\n# flight conditions\nu_inf = 10\nrho = 1.225\nalpha = 0.5\nbeta = 0\nc_ref = 1\nb_ref = 16\nsweep = 0*np.pi/180.\nsigma = 1\nwake_length = 10 # chords\n\nalpha_rad = alpha*np.pi/180\n\npitch_file = route + 'pitch.csv'\n\ngains = -np.array([0.9, 6.0, 0.75])\n\n# main geometry data\nmain_span = 10\nmain_chord = 2.\nmain_ea = 0.\nmain_cg = 0.3\nmain_sigma = 1\nmain_airfoil_P = 0\nmain_airfoil_M = 0\n\nn_surfaces = 1\n\ndt = main_chord/m_main/u_inf*dt_factor\nnum_steps = int(10./dt)\n\nalpha_hist = np.linspace(0, num_steps*dt, num_steps)\nalpha_hist = amplitude*np.sin(2.0*np.pi*alpha_hist/period)\nnp.savetxt(pitch_file, alpha_hist)\n\n# discretisation data\nnum_elem_main = 5\n\nnum_node_elem = 3\nnum_elem = num_elem_main\nnum_node_main = num_elem_main*(num_node_elem - 1) + 1\nnum_node = num_node_main\n\n\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n dyn_file_name = route + '/' + case_name + '.dyn.h5'\n if os.path.isfile(dyn_file_name):\n os.remove(dyn_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n\ndef generate_dyn_file():\n global dt\n global num_steps\n global route\n global case_name\n global num_elem\n global num_node_elem\n global num_node\n global amplitude\n global period\n\n dynamic_forces_time = None\n with_dynamic_forces = False\n with_forced_vel = False\n if with_dynamic_forces:\n f1 = 100\n dynamic_forces = np.zeros((num_node, 6))\n app_node = [int(num_node_main - 1), int(num_node_main)]\n dynamic_forces[app_node, 2] = f1\n force_time = np.zeros((num_steps, ))\n limit = round(0.05/dt)\n force_time[50:61] = 1\n\n dynamic_forces_time = np.zeros((num_steps, num_node, 6))\n for it in range(num_steps):\n dynamic_forces_time[it, :, :] = force_time[it]*dynamic_forces\n\n forced_for_vel = None\n if with_forced_vel:\n forced_for_vel = np.zeros((num_steps, 6))\n forced_for_acc = np.zeros((num_steps, 6))\n for it in range(num_steps):\n # if dt*it < period:\n forced_for_vel[it, 2] = 2*np.pi/period*amplitude*np.sin(2*np.pi*dt*it/period)\n forced_for_acc[it, 2] = (2*np.pi/period)**2*amplitude*np.cos(2*np.pi*dt*it/period)\n # forced_for_vel[it, 2] = 2*np.pi/period*np.pi/180*amplitude*np.cos(2*np.pi*dt*it/period)\n\n with h5.File(route + '/' + case_name + '.dyn.h5', 'a') as h5file:\n if with_dynamic_forces:\n h5file.create_dataset(\n 'dynamic_forces', data=dynamic_forces_time)\n if with_forced_vel:\n h5file.create_dataset(\n 'for_vel', data=forced_for_vel)\n h5file.create_dataset(\n 'for_acc', data=forced_for_acc)\n h5file.create_dataset(\n 'num_steps', data=num_steps)\n\n\ndef generate_fem_file():\n # placeholders\n # coordinates\n global x, y, z\n global sigma\n x = np.zeros((num_node, ))\n y = np.zeros((num_node, ))\n z = np.zeros((num_node, ))\n # struct twist\n structural_twist = np.zeros((num_elem, 3))\n # beam number\n beam_number = np.zeros((num_elem, ), dtype=int)\n # frame of reference delta\n frame_of_reference_delta = np.zeros((num_elem, num_node_elem, 3))\n # connectivities\n conn = np.zeros((num_elem, num_node_elem), dtype=int)\n # stiffness\n num_stiffness = 1\n ea = 1e5\n ga = 1e5\n gj = 0.987581e6\n eiy = 9.77221e6\n eiz = 9.77221e8\n base_stiffness = sigma*np.diag([ea, ga, ga, gj, eiy, eiz])\n stiffness = np.zeros((num_stiffness, 6, 6))\n stiffness[0, :, :] = main_sigma*base_stiffness\n elem_stiffness = np.zeros((num_elem,), dtype=int)\n # mass\n num_mass = 1\n m_base = 35.71\n j_base = 8.64\n import sharpy.utils.algebra as algebra\n # m_chi_cg = algebra.skew(m_base*np.array([0., -(main_ea - main_cg), 0.]))\n m_chi_cg = algebra.skew(m_base*np.array([0., (main_ea - main_cg), 0.]))\n base_mass = np.diag([m_base, m_base, m_base, j_base, 0.1*j_base, 0.1*j_base])\n base_mass[0:3, 3:6] = -m_chi_cg\n base_mass[3:6, 0:3] = m_chi_cg\n mass = np.zeros((num_mass, 6, 6))\n mass[0, :, :] = base_mass\n elem_mass = np.zeros((num_elem,), dtype=int)\n # boundary conditions\n boundary_conditions = np.zeros((num_node, ), dtype=int)\n boundary_conditions[0] = 1\n # applied forces\n # n_app_forces = 2\n # node_app_forces = np.zeros((n_app_forces,), dtype=int)\n app_forces = np.zeros((num_node, 6))\n\n spacing_param = 4\n\n # right wing (beam 0) --------------------------------------------------------------\n working_elem = 0\n working_node = 0\n beam_number[working_elem:working_elem + num_elem_main] = 0\n domain = np.linspace(0, 1.0, num_node_main)\n # 16 - (np.geomspace(20, 4, 10) - 4)\n x[working_node:working_node + num_node_main] = np.sin(sweep)*(main_span - (np.geomspace(main_span + spacing_param,\n 0 + spacing_param,\n num_node_main)\n - spacing_param))\n y[working_node:working_node + num_node_main] = np.abs(np.cos(sweep)*(main_span - (np.geomspace(main_span + spacing_param,\n 0 + spacing_param,\n num_node_main)\n - spacing_param)))\n y[0] = 0\n # y[working_node:working_node + num_node_main] = np.cos(sweep)*np.linspace(0.0, main_span, num_node_main)\n # x[working_node:working_node + num_node_main] = np.sin(sweep)*np.linspace(0.0, main_span, num_node_main)\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1])\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[0] = 1\n boundary_conditions[working_node + num_node_main - 1] = -1\n working_elem += num_elem_main\n working_node += num_node_main\n\n # # left wing (beam 1) --------------------------------------------------------------\n # beam_number[working_elem:working_elem + num_elem_main] = 1\n # domain = np.linspace(0.0, 1.0, num_node_main)\n # tempy = np.linspace(0.0, main_span, num_node_main)\n # # x[working_node:working_node + num_node_main - 1] = -np.sin(sweep)*tempy[0:-1]\n # # y[working_node:working_node + num_node_main - 1] = np.cos(sweep)*tempy[0:-1]\n # x[working_node:working_node + num_node_main - 1] = -np.sin(sweep)*(main_span - (np.geomspace(0 + spacing_param,\n # main_span + spacing_param,\n # num_node_main)[:-1]\n # - spacing_param))\n # y[working_node:working_node + num_node_main - 1] = -np.abs(np.cos(sweep)*(main_span - (np.geomspace(0 + spacing_param,\n # main_span + spacing_param,\n # num_node_main)[:-1]\n # - spacing_param)))\n # for ielem in range(num_elem_main):\n # for inode in range(num_node_elem):\n # frame_of_reference_delta[working_elem + ielem, inode, :] = [1, 0, 0]\n # # connectivity\n # for ielem in range(num_elem_main):\n # conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n # [0, 2, 1])\n # conn[working_elem , 0] = 0\n # elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n # elem_mass[working_elem:working_elem + num_elem_main] = 0\n # boundary_conditions[working_node + num_node_main - 1 - 1] = -1\n # working_elem += num_elem_main\n # working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=num_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=num_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=num_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n body_number_handle = h5file.create_dataset(\n 'body_number', data=np.zeros((num_elem, ), dtype=int))\n # node_app_forces_handle = h5file.create_dataset(\n # 'node_app_forces', data=node_app_forces)\n\n\ndef generate_aero_file():\n global x, y, z\n\n n_control_surfaces = 1\n control_surface = np.zeros((num_elem, num_node_elem), dtype=int)\n control_surface_type = np.zeros((n_control_surfaces,), dtype=int)\n control_surface_deflection = np.zeros((n_control_surfaces,))\n control_surface_chord = np.zeros((n_control_surfaces, ), dtype=int)\n control_surface_hinge_coord = np.zeros((n_control_surfaces, ))\n\n control_surface_type[0] = 2\n control_surface_deflection[0] = 0.0\n control_surface_chord[0] = 1\n\n airfoil_distribution = np.zeros((num_elem, num_node_elem), dtype=int)\n surface_distribution = np.zeros((num_elem,), dtype=int) - 1\n surface_m = np.zeros((n_surfaces, ), dtype=int)\n m_distribution = 'uniform'\n aero_node = np.zeros((num_node,), dtype=bool)\n twist = np.zeros((num_elem, 3))\n chord = np.zeros((num_elem, 3))\n elastic_axis = np.zeros((num_elem, 3,))\n\n working_elem = 0\n working_node = 0\n # right wing (surface 0, beam 0)\n i_surf = 0\n chord[:] = main_chord\n elastic_axis[:] = main_ea\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main] = True\n # chord[working_node:working_node + num_node_main] = main_chord\n # elastic_axis[working_node:working_node + num_node_main] = main_ea\n working_elem += num_elem_main\n working_node += num_node_main\n\n # left wing (surface 1, beam 1)\n # i_surf = 1\n # airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n # # airfoil_distribution[working_node:working_node + num_node_main - 1] = 0\n # surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n # surface_m[i_surf] = m_main\n # aero_node[working_node:working_node + num_node_main - 1] = True\n # # chord[working_node:working_node + num_node_main - 1] = main_chord\n # # elastic_axis[working_node:working_node + num_node_main - 1] = main_ea\n # working_elem += num_elem_main\n # working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n generate_naca_camber(P=main_airfoil_P, M=main_airfoil_M)))\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input .attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n control_surface_input = h5file.create_dataset('control_surface', data = control_surface)\n control_surface_input = h5file.create_dataset('control_surface_deflection', data = control_surface_deflection)\n control_surface_input = h5file.create_dataset('control_surface_chord', data = control_surface_chord)\n control_surface_input = h5file.create_dataset('control_surface_hinge_coord', data = control_surface_hinge_coord)\n control_surface_input = h5file.create_dataset('control_surface_type', data = control_surface_type)\n\n\ndef generate_naca_camber(M=0, P=0):\n m = M*1e-2\n p = P*1e-1\n\n def naca(x, m, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return m/(p*p)*(2*p*x - x*x)\n elif x > p and x < 1+1e-6:\n return m/((1-p)*(1-p))*(1 - 2*p + 2*p*x - x*x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, m, p) for x in x_vec])\n return x_vec, y_vec\n\ndef generate_multibody_file():\n LC2 = gc.LagrangeConstraint()\n LC2.behaviour = 'hinge_FoR'\n LC2.rot_axis_AFoR = np.array([0.0, 1.0, 0.0])\n LC2.body_FoR = 0\n # LC2.node_number = int(0)\n\n LC = []\n LC.append(LC2)\n\n MB1 = gc.BodyInformation()\n MB1.body_number = 0\n MB1.FoR_position = np.zeros((6,))\n MB1.FoR_velocity = np.zeros((6,))\n MB1.FoR_acceleration = np.zeros((6,))\n MB1.FoR_movement = 'free'\n MB1.quat = np.array([1.0, 0.0, 0.0, 0.0])\n\n MB = []\n MB.append(MB1)\n gc.clean_test_files(route, case_name)\n gc.generate_multibody_file(LC, MB, route, case_name)\n\ndef generate_solver_file(horseshoe=False):\n file_name = route + '/' + case_name + '.sharpy'\n # config = configparser.ConfigParser()\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n config['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'DynamicCoupled',\n # 'AerogridPlot',\n # 'BeamPlot',\n ],\n 'write_screen': 'on',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n config['BeamLoader'] = {'unsteady': 'on',\n 'orientation': algebra.euler2quat(np.array([0.0,\n alpha_rad,\n beta*np.pi/180]))}\n\n config['StaticCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-5,\n 'min_delta': 1e-13,\n 'gravity_on': 'on',\n 'gravity': 9.754},\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': main_chord/m_main/u_inf,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho},\n 'max_iter': 80,\n 'n_load_steps': 1,\n 'tolerance': 1e-5,\n 'relaxation_factor': 0.0}\n\n config['DynamicCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearDynamicMultibody',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 550,\n 'num_load_steps': 1,\n 'delta_curved': 1e-1,\n 'min_delta': 1e-4,\n 'newmark_damp': 5e-3,\n 'gravity_on': 'on',\n 'gravity': 9.754,\n 'num_steps': num_steps,\n 'dt': dt,\n 'relax_factor_lm': 0.2,\n 'time_integrator': 'NewmarkBeta',\n 'time_integrator_settings':\n {'dt': dt,\n 'newmark_damp': 5e-3,\n 'num_LM_eq': 5}},\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings':\n {'print_info': 'off',\n 'num_cores': 4,\n 'convection_scheme': 2,\n 'velocity_field_generator': 'GustVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0],\n 'gust_shape': '1-cos',\n 'gust_parameters': {\n 'gust_length': 4.0 * main_chord,\n 'gust_intensity': 0.1 * u_inf},\n 'offset': 1.0,\n 'relative_motion': 'on'},\n 'rho': rho,\n 'n_time_steps': num_steps,\n 'dt': dt},\n 'controller_id': {'controller_tip': 'ControlSurfacePidController'},\n 'controller_settings': {'controller_tip': {'P': gains[0],\n 'I': gains[1],\n 'D': gains[2],\n 'dt': dt,\n 'input_type': 'pitch',\n 'controller_log_route': './output/' + case_name + '/',\n 'controlled_surfaces': 0,\n 'time_history_input_file': 'pitch.csv'}},\n 'postprocessors': ['BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'},\n 'AerogridPlot': {\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}},\n 'fsi_substeps': 100,\n # 'fsi_substeps': 1,\n 'fsi_tolerance': 1e-5,\n 'relaxation_factor': 0.3,\n 'dynamic_relaxation': 'off',\n 'minimum_steps': 1,\n 'relaxation_steps': 25,\n 'structural_substeps': n_structural_substeps,\n 'n_time_steps': num_steps,\n 'dt': dt}\n\n config['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n 'mstar': 1,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': ['1', '0', '0'],\n 'dt': dt}}\n if not horseshoe:\n config['AerogridLoader']['mstar'] = int(m_main*wake_length)\n\n config['AerogridPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0\n }\n config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n 'unsteady': 'off'\n }\n config['BeamPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on'}\n config.write()\n\n\nclean_test_files()\ngenerate_multibody_file()\ngenerate_fem_file()\ngenerate_dyn_file()\ngenerate_solver_file(horseshoe=False)\ngenerate_aero_file()\n" }, { "path": "sharpy/cases/coupled/hinged_controlled_wing/generate_hinged_roll_controlled_wing.py", "content": "import h5py as h5\nimport numpy as np\nimport configparser\nimport os\n\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.generate_cases as gc\n\ncase_name = 'hinged_roll_controlled_wing'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n# m = 16 gives flutter with 165\nm_main = 6\namplitude = 0*np.pi/180\nperiod = 5\ndt_factor = 1.\nn_structural_substeps = 10\n\n# flight conditions\nu_inf = 10\nrho = 1.225\nalpha = 0\nbeta = 0\nc_ref = 1\nb_ref = 16\nsweep = 0*np.pi/180.\nsigma = 1\nwake_length = 10 # chords\nlambda_control_surface = 0.5\n\nalpha_rad = alpha*np.pi/180\n\nroll_file = route + 'roll.csv'\n\ngains = -np.array([45, 50.0, 1.5])\n\n# main geometry data\nmain_span = 10\nmain_chord = 2.\nmain_ea = 0.4\nmain_cg = 0.3\nmain_sigma = 1\nmain_airfoil_P = 0\nmain_airfoil_M = 0\n\nn_surfaces = 1\n\ndt = main_chord/m_main/u_inf*dt_factor\nnum_steps = int(30./dt)\n\nroll_hist = np.linspace(0, num_steps*dt, num_steps)\nroll_hist = amplitude*np.sin(2.0*np.pi*roll_hist/period)\nnp.savetxt(roll_file, roll_hist)\n\n# discretisation data\nnum_elem_main = 5\n\nnum_elem_cs = round(lambda_control_surface*num_elem_main)\n\nnum_node_elem = 3\nnum_elem = num_elem_main\nnum_node_main = num_elem_main*(num_node_elem - 1) + 1\nnum_node = num_node_main\n\n\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n dyn_file_name = route + '/' + case_name + '.dyn.h5'\n if os.path.isfile(dyn_file_name):\n os.remove(dyn_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n\ndef generate_dyn_file():\n global dt\n global num_steps\n global route\n global case_name\n global num_elem\n global num_node_elem\n global num_node\n global amplitude\n global period\n\n dynamic_forces_time = None\n with_dynamic_forces = False\n with_forced_vel = False\n if with_dynamic_forces:\n f1 = 100\n dynamic_forces = np.zeros((num_node, 6))\n app_node = [int(num_node_main - 1), int(num_node_main)]\n dynamic_forces[app_node, 2] = f1\n force_time = np.zeros((num_steps, ))\n limit = round(0.05/dt)\n force_time[50:61] = 1\n\n dynamic_forces_time = np.zeros((num_steps, num_node, 6))\n for it in range(num_steps):\n dynamic_forces_time[it, :, :] = force_time[it]*dynamic_forces\n\n forced_for_vel = None\n if with_forced_vel:\n forced_for_vel = np.zeros((num_steps, 6))\n forced_for_acc = np.zeros((num_steps, 6))\n for it in range(num_steps):\n # if dt*it < period:\n forced_for_vel[it, 2] = 2*np.pi/period*amplitude*np.sin(2*np.pi*dt*it/period)\n forced_for_acc[it, 2] = (2*np.pi/period)**2*amplitude*np.cos(2*np.pi*dt*it/period)\n # forced_for_vel[it, 2] = 2*np.pi/period*np.pi/180*amplitude*np.cos(2*np.pi*dt*it/period)\n\n with h5.File(route + '/' + case_name + '.dyn.h5', 'a') as h5file:\n if with_dynamic_forces:\n h5file.create_dataset(\n 'dynamic_forces', data=dynamic_forces_time)\n if with_forced_vel:\n h5file.create_dataset(\n 'for_vel', data=forced_for_vel)\n h5file.create_dataset(\n 'for_acc', data=forced_for_acc)\n h5file.create_dataset(\n 'num_steps', data=num_steps)\n\n\ndef generate_fem_file():\n # placeholders\n # coordinates\n global x, y, z\n global sigma\n x = np.zeros((num_node, ))\n y = np.zeros((num_node, ))\n z = np.zeros((num_node, ))\n # struct twist\n structural_twist = np.zeros((num_elem, 3))\n # beam number\n beam_number = np.zeros((num_elem, ), dtype=int)\n # frame of reference delta\n frame_of_reference_delta = np.zeros((num_elem, num_node_elem, 3))\n # connectivities\n conn = np.zeros((num_elem, num_node_elem), dtype=int)\n # stiffness\n num_stiffness = 1\n ea = 1e5\n ga = 1e5\n gj = 0.987581e6\n eiy = 9.77221e6\n eiz = 9.77221e8\n base_stiffness = sigma*np.diag([ea, ga, ga, gj, eiy, eiz])\n stiffness = np.zeros((num_stiffness, 6, 6))\n stiffness[0, :, :] = main_sigma*base_stiffness\n elem_stiffness = np.zeros((num_elem,), dtype=int)\n # mass\n num_mass = 1\n m_base = 1\n j_base = 0.5\n import sharpy.utils.algebra as algebra\n # m_chi_cg = algebra.skew(m_base*np.array([0., -(main_ea - main_cg), 0.]))\n m_chi_cg = algebra.skew(m_base*np.array([0., (main_ea - main_cg), 0.]))\n base_mass = np.diag([m_base, m_base, m_base, j_base, 0.5*j_base, 0.5*j_base])\n base_mass[0:3, 3:6] = -m_chi_cg\n base_mass[3:6, 0:3] = m_chi_cg\n mass = np.zeros((num_mass, 6, 6))\n mass[0, :, :] = base_mass\n elem_mass = np.zeros((num_elem,), dtype=int)\n # boundary conditions\n boundary_conditions = np.zeros((num_node, ), dtype=int)\n boundary_conditions[0] = 1\n # applied forces\n # n_app_forces = 2\n # node_app_forces = np.zeros((n_app_forces,), dtype=int)\n app_forces = np.zeros((num_node, 6))\n\n spacing_param = 10\n\n # right wing (beam 0) --------------------------------------------------------------\n working_elem = 0\n working_node = 0\n beam_number[working_elem:working_elem + num_elem_main] = 0\n domain = np.linspace(0, 1.0, num_node_main)\n # 16 - (np.geomspace(20, 4, 10) - 4)\n x[working_node:working_node + num_node_main] = np.sin(sweep)*(main_span - (np.geomspace(main_span + spacing_param,\n 0 + spacing_param,\n num_node_main)\n - spacing_param))\n y[working_node:working_node + num_node_main] = np.abs(np.cos(sweep)*(main_span - (np.geomspace(main_span + spacing_param,\n 0 + spacing_param,\n num_node_main)\n - spacing_param)))\n y[0] = 0\n # y[working_node:working_node + num_node_main] = np.cos(sweep)*np.linspace(0.0, main_span, num_node_main)\n # x[working_node:working_node + num_node_main] = np.sin(sweep)*np.linspace(0.0, main_span, num_node_main)\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1])\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[0] = 1\n boundary_conditions[working_node + num_node_main - 1] = -1\n working_elem += num_elem_main\n working_node += num_node_main\n\n # # left wing (beam 1) --------------------------------------------------------------\n # beam_number[working_elem:working_elem + num_elem_main] = 1\n # domain = np.linspace(0.0, 1.0, num_node_main)\n # tempy = np.linspace(0.0, main_span, num_node_main)\n # # x[working_node:working_node + num_node_main - 1] = -np.sin(sweep)*tempy[0:-1]\n # # y[working_node:working_node + num_node_main - 1] = np.cos(sweep)*tempy[0:-1]\n # x[working_node:working_node + num_node_main - 1] = -np.sin(sweep)*(main_span - (np.geomspace(0 + spacing_param,\n # main_span + spacing_param,\n # num_node_main)[:-1]\n # - spacing_param))\n # y[working_node:working_node + num_node_main - 1] = -np.abs(np.cos(sweep)*(main_span - (np.geomspace(0 + spacing_param,\n # main_span + spacing_param,\n # num_node_main)[:-1]\n # - spacing_param)))\n # for ielem in range(num_elem_main):\n # for inode in range(num_node_elem):\n # frame_of_reference_delta[working_elem + ielem, inode, :] = [1, 0, 0]\n # # connectivity\n # for ielem in range(num_elem_main):\n # conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n # [0, 2, 1])\n # conn[working_elem , 0] = 0\n # elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n # elem_mass[working_elem:working_elem + num_elem_main] = 0\n # boundary_conditions[working_node + num_node_main - 1 - 1] = -1\n # working_elem += num_elem_main\n # working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=num_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=num_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=num_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n body_number_handle = h5file.create_dataset(\n 'body_number', data=np.zeros((num_elem, ), dtype=int))\n # node_app_forces_handle = h5file.create_dataset(\n # 'node_app_forces', data=node_app_forces)\n\n\ndef generate_aero_file():\n global x, y, z\n\n n_control_surfaces = 1\n control_surface = np.zeros((num_elem, num_node_elem), dtype=int) - 1\n control_surface_type = np.zeros((n_control_surfaces,), dtype=int)\n control_surface_deflection = np.zeros((n_control_surfaces,))\n control_surface_chord = np.zeros((n_control_surfaces, ), dtype=int)\n control_surface_hinge_coord = np.zeros((n_control_surfaces, ))\n\n control_surface[-num_elem_cs:, :] = 0\n control_surface_type[0] = 2\n control_surface_deflection[0] = 0.0\n control_surface_chord[0] = int(0.35*m_main)\n\n airfoil_distribution = np.zeros((num_elem, num_node_elem), dtype=int)\n surface_distribution = np.zeros((num_elem,), dtype=int) - 1\n surface_m = np.zeros((n_surfaces, ), dtype=int)\n m_distribution = 'uniform'\n aero_node = np.zeros((num_node,), dtype=bool)\n twist = np.zeros((num_elem, 3))\n chord = np.zeros((num_elem, 3))\n elastic_axis = np.zeros((num_elem, 3,))\n\n working_elem = 0\n working_node = 0\n # right wing (surface 0, beam 0)\n i_surf = 0\n chord[:] = main_chord\n elastic_axis[:] = main_ea\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main] = True\n # chord[working_node:working_node + num_node_main] = main_chord\n # elastic_axis[working_node:working_node + num_node_main] = main_ea\n working_elem += num_elem_main\n working_node += num_node_main\n\n # left wing (surface 1, beam 1)\n # i_surf = 1\n # airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n # # airfoil_distribution[working_node:working_node + num_node_main - 1] = 0\n # surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n # surface_m[i_surf] = m_main\n # aero_node[working_node:working_node + num_node_main - 1] = True\n # # chord[working_node:working_node + num_node_main - 1] = main_chord\n # # elastic_axis[working_node:working_node + num_node_main - 1] = main_ea\n # working_elem += num_elem_main\n # working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n generate_naca_camber(P=main_airfoil_P, M=main_airfoil_M)))\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input .attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n control_surface_input = h5file.create_dataset('control_surface', data = control_surface)\n control_surface_input = h5file.create_dataset('control_surface_deflection', data = control_surface_deflection)\n control_surface_input = h5file.create_dataset('control_surface_chord', data = control_surface_chord)\n control_surface_input = h5file.create_dataset('control_surface_hinge_coord', data = control_surface_hinge_coord)\n control_surface_input = h5file.create_dataset('control_surface_type', data = control_surface_type)\n\n\ndef generate_naca_camber(M=0, P=0):\n m = M*1e-2\n p = P*1e-1\n\n def naca(x, m, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return m/(p*p)*(2*p*x - x*x)\n elif x > p and x < 1+1e-6:\n return m/((1-p)*(1-p))*(1 - 2*p + 2*p*x - x*x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, m, p) for x in x_vec])\n return x_vec, y_vec\n\ndef generate_multibody_file():\n LC2 = gc.LagrangeConstraint()\n LC2.behaviour = 'hinge_FoR'\n LC2.rot_axis_AFoR = np.array([1.0, 0.0, 0.0])\n LC2.body_FoR = 0\n # LC2.node_number = int(0)\n\n LC = []\n LC.append(LC2)\n\n MB1 = gc.BodyInformation()\n MB1.body_number = 0\n MB1.FoR_position = np.zeros((6,))\n MB1.FoR_velocity = np.zeros((6,))\n MB1.FoR_acceleration = np.zeros((6,))\n MB1.FoR_movement = 'free'\n MB1.quat = np.array([1.0, 0.0, 0.0, 0.0])\n\n MB = []\n MB.append(MB1)\n gc.clean_test_files(route, case_name)\n gc.generate_multibody_file(LC, MB, route, case_name)\n\ndef generate_solver_file(horseshoe=False):\n file_name = route + '/' + case_name + '.sharpy'\n # config = configparser.ConfigParser()\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n config['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'DynamicCoupled',\n # 'AerogridPlot',\n # 'BeamPlot',\n ],\n 'write_screen': 'on',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n config['BeamLoader'] = {'unsteady': 'on',\n 'orientation': algebra.euler2quat(np.array([0.0,\n alpha_rad,\n beta*np.pi/180]))}\n\n config['StaticCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-5,\n 'min_delta': 1e-13,\n 'gravity_on': 'on',\n 'gravity': 9.754},\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho},\n 'max_iter': 80,\n 'n_load_steps': 1,\n 'tolerance': 1e-5,\n 'relaxation_factor': 0.0}\n config['DynamicCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearDynamicMultibody',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 550,\n 'num_load_steps': 1,\n 'delta_curved': 1e-1,\n 'min_delta': 1e-6,\n 'newmark_damp': 1e-2,\n 'gravity_on': 'on',\n 'gravity': 9.754,\n 'num_steps': num_steps,\n 'time_integrator': 'NewmarkBeta',\n 'time_integrator_settings':\n {'dt': dt,\n 'newmark_damp': 5e-3,\n 'num_LM_eq': 5},\n },\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': {'print_info': 'off',\n 'num_cores': 4,\n 'convection_scheme': 3,\n 'gamma_dot_filtering': 9,\n 'velocity_field_generator': 'GustVelocityField',\n 'velocity_field_input':\n {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0],\n 'gust_shape': '1-cos',\n 'gust_parameters': {\n 'gust_length': 10.0 * main_chord,\n 'gust_intensity': 0.15 * u_inf},\n 'offset': 20.0,\n 'relative_motion': 'on'},\n 'rho': rho,\n 'n_time_steps': num_steps,\n 'dt': dt},\n 'controller_id': {'controller_tip': 'ControlSurfacePidController'},\n 'controller_settings': {'controller_tip': {'P': gains[0],\n 'I': gains[1],\n 'D': gains[2],\n 'dt': dt,\n 'input_type': 'roll',\n 'controller_log_route': './output/' + case_name + '/',\n 'controlled_surfaces': 0,\n 'time_history_input_file': 'roll.csv'}},\n 'postprocessors': ['BeamLoads', 'BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'BeamLoads': {},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'},\n 'AerogridPlot': {\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}},\n 'fsi_substeps': 100,\n # 'fsi_substeps': 1,\n 'fsi_tolerance': 1e-5,\n 'relaxation_factor': 0.2,\n 'dynamic_relaxation': 'off',\n 'minimum_steps': 1,\n 'relaxation_steps': 25,\n 'include_unsteady_force_contribution': 'off',\n 'steps_without_unsteady_force': 10,\n 'pseudosteps_ramp_unsteady_force': 6,\n 'structural_substeps': n_structural_substeps,\n 'n_time_steps': num_steps,\n 'dt': dt,\n 'structural_substeps': 0}\n\n if horseshoe is True:\n config['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n 'mstar': 1,\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {\n 'u_inf': u_inf,\n 'u_inf_direction': [1., 0., 0.],\n 'dt': dt,\n },\n 'freestream_dir': ['1', '0', '0']}\n else:\n config['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {\n 'u_inf': u_inf,\n 'u_inf_direction': [1., 0., 0.],\n 'dt': dt,\n },\n 'mstar': int(m_main * wake_length),\n 'freestream_dir': ['1', '0', '0']}\n\n config['AerogridPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0\n }\n config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n 'unsteady': 'off'\n }\n config['BeamPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on'}\n config.write()\n\n\nclean_test_files()\ngenerate_multibody_file()\ngenerate_fem_file()\ngenerate_dyn_file()\ngenerate_solver_file(horseshoe=False)\ngenerate_aero_file()\n" }, { "path": "sharpy/cases/coupled/linear_horten/__init__.py", "content": "" }, { "path": "sharpy/cases/coupled/multibody_takeoff/__init__.py", "content": "" }, { "path": "sharpy/cases/coupled/multibody_takeoff/generate_hale.py", "content": "#! /usr/bin/env python3\nimport h5py as h5\nimport numpy as np\nimport os\nimport sharpy.utils.algebra as algebra\n\ncase_name = 'simple_HALE_cato'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n# EXECUTION\nflow = ['BeamLoader',\n 'AerogridLoader',\n # 'NonLinearStatic',\n # 'StaticUvlm',\n # 'StaticTrim',\n 'StaticCoupled',\n 'BeamLoads',\n 'AerogridPlot',\n 'BeamPlot',\n 'DynamicCoupled',\n ]\n\n# if free_flight is False, the motion of the centre of the wing is prescribed.\nfree_flight = True\n\n# FLIGHT CONDITIONS\n# the simulation is set such that the aircraft flies at a u_inf velocity while\n# the air is calm.\nu_inf = 10\nrho = 1.225\n\n# trim sigma = 1.5\nalpha = 4.281820969436041*np.pi/180\nbeta = 0\nroll = 0\ngravity = 'on'\ncs_deflection = -1.588626664555141*np.pi/180\nrudder_static_deflection = 0.0\nrudder_step = 0.0*np.pi/180\nthrust = 8.482569525210431\nsigma = 100\nlambda_dihedral = 20*np.pi/180\n\n# gust settings\ngust_intensity = 0.00\ngust_length = 1*u_inf\ngust_offset = 0.5*u_inf\n\n# numerics\nn_step = 1\nrelaxation_factor = 0.5\ntolerance = 1e-7\nfsi_tolerance = 1e-6\n\nnum_cores = 2\n\n# MODEL GEOMETRY\n# beam\nspan_main = 16.0\nlambda_main = 0.25\nea_main = 0.3\n\nea = 1e7\nga = 1e7\ngj = 1e4\neiy = 2e4\neiz = 4e6\nm_bar_main = 0.75\nj_bar_main = 0.075\n\nlength_fuselage = 10\noffset_fuselage = 0\nsigma_fuselage = 100\nm_bar_fuselage = 0.2\nj_bar_fuselage = 0.08\n\nspan_tail = 2.5\nea_tail = 0.5\nfin_height = 2.5\nea_fin = 0.5\nsigma_tail = 100\nm_bar_tail = 0.3\nj_bar_tail = 0.08\n\n# lumped masses\nn_lumped_mass = 1\nlumped_mass_nodes = np.zeros((n_lumped_mass, ), dtype=int)\nlumped_mass = np.zeros((n_lumped_mass, ))\nlumped_mass[0] = 50\nlumped_mass_inertia = np.zeros((n_lumped_mass, 3, 3))\nlumped_mass_position = np.zeros((n_lumped_mass, 3))\n\n# aero\nchord_main = 1.0\nchord_tail = 0.5\nchord_fin = 0.5\n\n# DISCRETISATION\n# spatial discretisation\n# chordiwse panels\nm = 8\n# spanwise elements\nn_elem_multiplier = 2\nn_elem_main = int(4*n_elem_multiplier)\nn_elem_tail = int(2*n_elem_multiplier)\nn_elem_fin = int(2*n_elem_multiplier)\nn_elem_fuselage = int(2*n_elem_multiplier)\nn_surfaces = 5\n\n# temporal discretisation\nphysical_time = 30\ntstep_factor = 1.\ndt = 1.0/m/u_inf*tstep_factor\nn_tstep = round(physical_time/dt)\n\n# END OF INPUT-----------------------------------------------------------------\n\n# beam processing\nn_node_elem = 3\nspan_main1 = (1.0 - lambda_main)*span_main\nspan_main2 = lambda_main*span_main\n\nn_elem_main1 = round(n_elem_main*(1 - lambda_main))\nn_elem_main2 = n_elem_main - n_elem_main1\n\n# total number of elements\nn_elem = 0\nn_elem += n_elem_main1 + n_elem_main1\nn_elem += n_elem_main2 + n_elem_main2\nn_elem += n_elem_fuselage\nn_elem += n_elem_fin\nn_elem += n_elem_tail + n_elem_tail\n\n# number of nodes per part\nn_node_main1 = n_elem_main1*(n_node_elem - 1) + 1\nn_node_main2 = n_elem_main2*(n_node_elem - 1) + 1\nn_node_main = n_node_main1 + n_node_main2 - 1\nn_node_fuselage = n_elem_fuselage*(n_node_elem - 1) + 1\nn_node_fin = n_elem_fin*(n_node_elem - 1) + 1\nn_node_tail = n_elem_tail*(n_node_elem - 1) + 1\n\n# total number of nodes\nn_node = 0\nn_node += n_node_main1 + n_node_main1 - 1\nn_node += n_node_main2 - 1 + n_node_main2 - 1\nn_node += n_node_fuselage - 1\nn_node += n_node_fin - 1\nn_node += n_node_tail - 1\nn_node += n_node_tail - 1\n\n# stiffness and mass matrices\nn_stiffness = 3\nbase_stiffness_main = sigma*np.diag([ea, ga, ga, gj, eiy, eiz])\nbase_stiffness_fuselage = base_stiffness_main.copy()*sigma_fuselage\nbase_stiffness_fuselage[4, 4] = base_stiffness_fuselage[5, 5]\nbase_stiffness_tail = base_stiffness_main.copy()*sigma_tail\nbase_stiffness_tail[4, 4] = base_stiffness_tail[5, 5]\n\nn_mass = 3\nbase_mass_main = np.diag([m_bar_main, m_bar_main, m_bar_main, j_bar_main, 0.5*j_bar_main, 0.5*j_bar_main])\nbase_mass_fuselage = np.diag([m_bar_fuselage,\n m_bar_fuselage,\n m_bar_fuselage,\n j_bar_fuselage,\n j_bar_fuselage*0.5,\n j_bar_fuselage*0.5])\nbase_mass_tail = np.diag([m_bar_tail,\n m_bar_tail,\n m_bar_tail,\n j_bar_tail,\n j_bar_tail*0.5,\n j_bar_tail*0.5])\n\n\n# PLACEHOLDERS\n# beam\nx = np.zeros((n_node, ))\ny = np.zeros((n_node, ))\nz = np.zeros((n_node, ))\nbeam_number = np.zeros((n_elem, ), dtype=int)\nframe_of_reference_delta = np.zeros((n_elem, n_node_elem, 3))\nstructural_twist = np.zeros((n_elem, 3))\nconn = np.zeros((n_elem, n_node_elem), dtype=int)\nstiffness = np.zeros((n_stiffness, 6, 6))\nelem_stiffness = np.zeros((n_elem, ), dtype=int)\nmass = np.zeros((n_mass, 6, 6))\nelem_mass = np.zeros((n_elem, ), dtype=int)\nboundary_conditions = np.zeros((n_node, ), dtype=int)\napp_forces = np.zeros((n_node, 6))\n\n\n# aero\nairfoil_distribution = np.zeros((n_elem, n_node_elem), dtype=int)\nsurface_distribution = np.zeros((n_elem,), dtype=int) - 1\nsurface_m = np.zeros((n_surfaces, ), dtype=int)\nm_distribution = 'uniform'\naero_node = np.zeros((n_node,), dtype=bool)\ntwist = np.zeros((n_elem, n_node_elem))\nsweep = np.zeros((n_elem, n_node_elem))\nchord = np.zeros((n_elem, n_node_elem,))\nelastic_axis = np.zeros((n_elem, n_node_elem,))\n\n\n# FUNCTIONS-------------------------------------------------------------\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n dyn_file_name = route + '/' + case_name + '.dyn.h5'\n if os.path.isfile(dyn_file_name):\n os.remove(dyn_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\ndef generate_dyn_file():\n global dt\n global n_tstep\n global route\n global case_name\n global num_elem\n global num_node_elem\n global num_node\n global amplitude\n global period\n\n dynamic_forces_time = None\n with_dynamic_forces = False\n with_forced_vel = False\n\n if with_dynamic_forces:\n f1 = 100\n dynamic_forces = np.zeros((num_node, 6))\n app_node = [int(num_node_main - 1), int(num_node_main)]\n dynamic_forces[app_node, 2] = f1\n force_time = np.zeros((n_tstep, ))\n limit = round(0.05/dt)\n force_time[50:61] = 1\n\n dynamic_forces_time = np.zeros((n_tstep, num_node, 6))\n for it in range(n_tstep):\n dynamic_forces_time[it, :, :] = force_time[it]*dynamic_forces\n\n forced_for_vel = None\n if with_forced_vel:\n forced_for_vel = np.zeros((n_tstep, 6))\n forced_for_acc = np.zeros((n_tstep, 6))\n for it in range(n_tstep):\n # if dt*it < period:\n # forced_for_vel[it, 2] = 2*np.pi/period*amplitude*np.sin(2*np.pi*dt*it/period)\n # forced_for_acc[it, 2] = (2*np.pi/period)**2*amplitude*np.cos(2*np.pi*dt*it/period)\n\n forced_for_vel[it, 3] = 2*np.pi/period*amplitude*np.sin(2*np.pi*dt*it/period)\n forced_for_acc[it, 3] = (2*np.pi/period)**2*amplitude*np.cos(2*np.pi*dt*it/period)\n\n if with_dynamic_forces or with_forced_vel:\n with h5.File(route + '/' + case_name + '.dyn.h5', 'a') as h5file:\n if with_dynamic_forces:\n h5file.create_dataset(\n 'dynamic_forces', data=dynamic_forces_time)\n if with_forced_vel:\n h5file.create_dataset(\n 'for_vel', data=forced_for_vel)\n h5file.create_dataset(\n 'for_acc', data=forced_for_acc)\n h5file.create_dataset(\n 'num_steps', data=n_tstep)\n\ndef generate_fem():\n stiffness[0, ...] = base_stiffness_main\n stiffness[1, ...] = base_stiffness_fuselage\n stiffness[2, ...] = base_stiffness_tail\n\n mass[0, ...] = base_mass_main\n mass[1, ...] = base_mass_fuselage\n mass[2, ...] = base_mass_tail\n\n we = 0\n wn = 0\n # inner right wing\n beam_number[we:we + n_elem_main1] = 0\n y[wn:wn + n_node_main1] = np.linspace(0.0, span_main1, n_node_main1)\n\n for ielem in range(n_elem_main1):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n\n elem_stiffness[we:we + n_elem_main1] = 0\n elem_mass[we:we + n_elem_main1] = 0\n boundary_conditions[0] = 1\n # remember this is in B FoR\n app_forces[0] = [0, thrust, 0, 0, 0, 0]\n we += n_elem_main1\n wn += n_node_main1\n\n # outer right wing\n beam_number[we:we + n_elem_main1] = 0\n y[wn:wn + n_node_main2 - 1] = y[wn - 1] + np.linspace(0.0, np.cos(lambda_dihedral)*span_main2, n_node_main2)[1:]\n z[wn:wn + n_node_main2 - 1] = z[wn - 1] + np.linspace(0.0, np.sin(lambda_dihedral)*span_main2, n_node_main2)[1:]\n for ielem in range(n_elem_main2):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_main2] = 0\n elem_mass[we:we + n_elem_main2] = 0\n boundary_conditions[wn + n_node_main2 - 2] = -1\n we += n_elem_main2\n wn += n_node_main2 - 1\n\n # inner left wing\n beam_number[we:we + n_elem_main1 - 1] = 1\n y[wn:wn + n_node_main1 - 1] = np.linspace(0.0, -span_main1, n_node_main1)[1:]\n for ielem in range(n_elem_main1):\n conn[we + ielem, :] = ((np.ones((3, ))*(we+ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = 0\n elem_stiffness[we:we + n_elem_main1] = 0\n elem_mass[we:we + n_elem_main1] = 0\n we += n_elem_main1\n wn += n_node_main1 - 1\n\n # outer left wing\n beam_number[we:we + n_elem_main2] = 1\n y[wn:wn + n_node_main2 - 1] = y[wn - 1] + np.linspace(0.0, -np.cos(lambda_dihedral)*span_main2, n_node_main2)[1:]\n z[wn:wn + n_node_main2 - 1] = z[wn - 1] + np.linspace(0.0, np.sin(lambda_dihedral)*span_main2, n_node_main2)[1:]\n for ielem in range(n_elem_main2):\n conn[we + ielem, :] = ((np.ones((3, ))*(we+ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_main2] = 0\n elem_mass[we:we + n_elem_main2] = 0\n boundary_conditions[wn + n_node_main2 - 2] = -1\n we += n_elem_main2\n wn += n_node_main2 - 1\n\n # fuselage\n beam_number[we:we + n_elem_fuselage] = 2\n x[wn:wn + n_node_fuselage - 1] = np.linspace(0.0, length_fuselage, n_node_fuselage)[1:]\n z[wn:wn + n_node_fuselage - 1] = np.linspace(0.0, offset_fuselage, n_node_fuselage)[1:]\n for ielem in range(n_elem_fuselage):\n conn[we + ielem, :] = ((np.ones((3,))*(we + ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [0.0, 1.0, 0.0]\n conn[we, 0] = 0\n elem_stiffness[we:we + n_elem_fuselage] = 1\n elem_mass[we:we + n_elem_fuselage] = 1\n we += n_elem_fuselage\n wn += n_node_fuselage - 1\n global end_of_fuselage_node\n end_of_fuselage_node = wn - 1\n\n # fin\n beam_number[we:we + n_elem_fin] = 3\n x[wn:wn + n_node_fin - 1] = x[end_of_fuselage_node]\n z[wn:wn + n_node_fin - 1] = z[end_of_fuselage_node] + np.linspace(0.0, fin_height, n_node_fin)[1:]\n for ielem in range(n_elem_fin):\n conn[we + ielem, :] = ((np.ones((3,))*(we + ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fuselage_node\n elem_stiffness[we:we + n_elem_fin] = 2\n elem_mass[we:we + n_elem_fin] = 2\n we += n_elem_fin\n wn += n_node_fin - 1\n end_of_fin_node = wn - 1\n\n # right tail\n beam_number[we:we + n_elem_tail] = 4\n x[wn:wn + n_node_tail - 1] = x[end_of_fin_node]\n y[wn:wn + n_node_tail - 1] = np.linspace(0.0, span_tail, n_node_tail)[1:]\n z[wn:wn + n_node_tail - 1] = z[end_of_fin_node]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fin_node\n elem_stiffness[we:we + n_elem_tail] = 2\n elem_mass[we:we + n_elem_tail] = 2\n boundary_conditions[wn + n_node_tail - 2] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n # left tail\n beam_number[we:we + n_elem_tail] = 5\n x[wn:wn + n_node_tail - 1] = x[end_of_fin_node]\n y[wn:wn + n_node_tail - 1] = np.linspace(0.0, -span_tail, n_node_tail)[1:]\n z[wn:wn + n_node_tail - 1] = z[end_of_fin_node]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3, ))*(we + ielem)*(n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fin_node\n elem_stiffness[we:we + n_elem_tail] = 2\n elem_mass[we:we + n_elem_tail] = 2\n boundary_conditions[wn + n_node_tail - 2] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=n_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=n_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=n_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n lumped_mass_nodes_handle = h5file.create_dataset(\n 'lumped_mass_nodes', data=lumped_mass_nodes)\n lumped_mass_handle = h5file.create_dataset(\n 'lumped_mass', data=lumped_mass)\n lumped_mass_inertia_handle = h5file.create_dataset(\n 'lumped_mass_inertia', data=lumped_mass_inertia)\n lumped_mass_position_handle = h5file.create_dataset(\n 'lumped_mass_position', data=lumped_mass_position)\n\ndef generate_aero_file():\n global x, y, z\n # control surfaces\n n_control_surfaces = 2\n control_surface = np.zeros((n_elem, n_node_elem), dtype=int) - 1\n control_surface_type = np.zeros((n_control_surfaces, ), dtype=int)\n control_surface_deflection = np.zeros((n_control_surfaces, ))\n control_surface_chord = np.zeros((n_control_surfaces, ), dtype=int)\n control_surface_hinge_coord = np.zeros((n_control_surfaces, ), dtype=float)\n\n # control surface type 0 = static\n # control surface type 1 = dynamic\n control_surface_type[0] = 0\n control_surface_deflection[0] = cs_deflection\n control_surface_chord[0] = m\n control_surface_hinge_coord[0] = -0.25 # nondimensional wrt elastic axis (+ towards the trailing edge)\n\n control_surface_type[1] = 0\n control_surface_deflection[1] = rudder_static_deflection\n control_surface_chord[1] = 1\n control_surface_hinge_coord[1] = -0. # nondimensional wrt elastic axis (+ towards the trailing edge)\n\n we = 0\n wn = 0\n # right wing (surface 0, beam 0)\n i_surf = 0\n airfoil_distribution[we:we + n_elem_main, :] = 0\n surface_distribution[we:we + n_elem_main] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_main] = True\n temp_chord = np.linspace(chord_main, chord_main, n_node_main)\n temp_sweep = np.linspace(0.0, 0*np.pi/180, n_node_main)\n node_counter = 0\n for i_elem in range(we, we + n_elem_main):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = temp_chord[node_counter]\n elastic_axis[i_elem, i_local_node] = ea_main\n sweep[i_elem, i_local_node] = temp_sweep[node_counter]\n\n we += n_elem_main\n wn += n_node_main\n\n # left wing (surface 1, beam 1)\n i_surf = 1\n airfoil_distribution[we:we + n_elem_main, :] = 0\n # airfoil_distribution[wn:wn + n_node_main - 1] = 0\n surface_distribution[we:we + n_elem_main] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_main - 1] = True\n # chord[wn:wn + num_node_main - 1] = np.linspace(main_chord, main_tip_chord, num_node_main)[1:]\n # chord[wn:wn + num_node_main - 1] = main_chord\n # elastic_axis[wn:wn + num_node_main - 1] = main_ea\n temp_chord = np.linspace(chord_main, chord_main, n_node_main)\n node_counter = 0\n for i_elem in range(we, we + n_elem_main):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = temp_chord[node_counter]\n elastic_axis[i_elem, i_local_node] = ea_main\n sweep[i_elem, i_local_node] = -temp_sweep[node_counter]\n\n we += n_elem_main\n wn += n_node_main - 1\n\n we += n_elem_fuselage\n wn += n_node_fuselage - 1 - 1\n #\n # # fin (surface 2, beam 3)\n i_surf = 2\n airfoil_distribution[we:we + n_elem_fin, :] = 1\n # airfoil_distribution[wn:wn + n_node_fin] = 0\n surface_distribution[we:we + n_elem_fin] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_fin] = True\n # chord[wn:wn + num_node_fin] = fin_chord\n for i_elem in range(we, we + n_elem_fin):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_fin\n elastic_axis[i_elem, i_local_node] = ea_fin\n control_surface[i_elem, i_local_node] = 1\n # twist[end_of_fuselage_node] = 0\n # twist[wn:] = 0\n # elastic_axis[wn:wn + num_node_main] = fin_ea\n we += n_elem_fin\n wn += n_node_fin - 1\n #\n # # # right tail (surface 3, beam 4)\n i_surf = 3\n airfoil_distribution[we:we + n_elem_tail, :] = 2\n # airfoil_distribution[wn:wn + n_node_tail] = 0\n surface_distribution[we:we + n_elem_tail] = i_surf\n surface_m[i_surf] = m\n # XXX not very elegant\n aero_node[wn:] = True\n # chord[wn:wn + num_node_tail] = tail_chord\n # elastic_axis[wn:wn + num_node_main] = tail_ea\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n twist[i_elem, i_local_node] = -0\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_tail\n elastic_axis[i_elem, i_local_node] = ea_tail\n control_surface[i_elem, i_local_node] = 0\n\n we += n_elem_tail\n wn += n_node_tail\n #\n # # left tail (surface 4, beam 5)\n i_surf = 4\n airfoil_distribution[we:we + n_elem_tail, :] = 2\n # airfoil_distribution[wn:wn + n_node_tail - 1] = 0\n surface_distribution[we:we + n_elem_tail] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_tail - 1] = True\n # chord[wn:wn + num_node_tail] = tail_chord\n # elastic_axis[wn:wn + num_node_main] = tail_ea\n # twist[we:we + num_elem_tail] = -tail_twist\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n twist[i_elem, i_local_node] = -0\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_tail\n elastic_axis[i_elem, i_local_node] = ea_tail\n control_surface[i_elem, i_local_node] = 0\n we += n_elem_tail\n wn += n_node_tail\n\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n naca_airfoil_tail = airfoils_group.create_dataset('1', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n naca_airfoil_fin = airfoils_group.create_dataset('2', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input .attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # sweep\n sweep_input = h5file.create_dataset('sweep', data=sweep)\n dim_attr = sweep_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n control_surface_input = h5file.create_dataset('control_surface', data=control_surface)\n control_surface_deflection_input = h5file.create_dataset('control_surface_deflection', data=control_surface_deflection)\n control_surface_chord_input = h5file.create_dataset('control_surface_chord', data=control_surface_chord)\n control_surface_hinge_coord_input = h5file.create_dataset('control_surface_hinge_coord', data=control_surface_hinge_coord)\n control_surface_types_input = h5file.create_dataset('control_surface_type', data=control_surface_type)\n\n\ndef generate_naca_camber(M=0, P=0):\n mm = M*1e-2\n p = P*1e-1\n\n def naca(x, mm, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return mm/(p*p)*(2*p*x - x*x)\n elif x > p and x < 1+1e-6:\n return mm/((1-p)*(1-p))*(1 - 2*p + 2*p*x - x*x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, mm, p) for x in x_vec])\n return x_vec, y_vec\n\n\ndef generate_solver_file():\n file_name = route + '/' + case_name + '.sharpy'\n settings = dict()\n settings['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': flow,\n 'write_screen': 'on',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n\n settings['BeamLoader'] = {'unsteady': 'on',\n 'orientation': algebra.euler2quat(np.array([roll,\n alpha,\n beta]))}\n\n settings['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n 'mstar': int(20 / tstep_factor),\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {\n 'u_inf': u_inf,\n 'u_inf_direction': [1., 0., 0.],\n 'dt': dt,\n },\n 'control_surface_deflection': ['', ''],\n 'control_surface_deflection_generator_settings':\n {'0': {},\n '1': {}}}\n\n settings['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'gravity_on': gravity,\n 'gravity': 9.81}\n\n settings['StaticUvlm'] = {'print_info': 'on',\n 'horseshoe': 'off',\n 'num_cores': num_cores,\n 'n_rollup': 0,\n 'rollup_dt': dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho}\n\n settings['StaticCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': settings['NonLinearStatic'],\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': settings['StaticUvlm'],\n 'max_iter': 100,\n 'n_load_steps': n_step,\n 'tolerance': fsi_tolerance,\n 'relaxation_factor': relaxation_factor}\n\n settings['StaticTrim'] = {'solver': 'StaticCoupled',\n 'solver_settings': settings['StaticCoupled'],\n 'initial_alpha': alpha,\n 'initial_deflection': cs_deflection,\n 'initial_thrust': thrust}\n\n settings['NonLinearDynamicCoupledStep'] = {'print_info': 'off',\n 'max_iterations': 950,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'newmark_damp': 5e-3,\n 'gravity_on': gravity,\n 'gravity': 9.81,\n 'num_steps': n_tstep,\n 'dt': dt,\n 'initial_velocity': u_inf}\n\n settings['NonLinearDynamicPrescribedStep'] = {'print_info': 'off',\n 'max_iterations': 950,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'newmark_damp': 5e-3,\n 'gravity_on': gravity,\n 'gravity': 9.81,\n 'num_steps': n_tstep,\n 'dt': dt,\n 'initial_velocity': u_inf}\n\n relative_motion = 'off'\n settings['StepUvlm'] = {'print_info': 'off',\n 'num_cores': num_cores,\n 'convection_scheme': 2,\n 'gamma_dot_filtering': 6,\n 'velocity_field_generator': 'GustVelocityField',\n 'velocity_field_input': {'u_inf': 0,\n 'u_inf_direction': [1., 0, 0],\n 'gust_shape': '1-cos',\n 'gust_parameters': {\n 'gust_length': gust_length,\n 'gust_intensity': gust_intensity * u_inf},\n 'offset': gust_offset,\n 'relative_motion': relative_motion},\n 'rho': rho,\n 'n_time_steps': n_tstep,\n 'dt': dt}\n\n solver = 'NonLinearDynamicCoupledStep'\n settings['DynamicCoupled'] = {'structural_solver': solver,\n 'structural_solver_settings': settings[solver],\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'fsi_substeps': 200,\n 'fsi_tolerance': fsi_tolerance,\n 'relaxation_factor': relaxation_factor,\n 'minimum_steps': 1,\n 'relaxation_steps': 150,\n 'final_relaxation_factor': 0.5,\n 'n_time_steps': n_tstep,\n 'dt': dt,\n 'include_unsteady_force_contribution': 'on',\n 'postprocessors': ['BeamLoads', 'BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'BeamLoads': {'csv_output': 'off'},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'},\n 'AerogridPlot': {\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n }}\n\n settings['BeamLoads'] = {'csv_output': 'off'}\n\n settings['BeamPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on'}\n\n settings['AerogridPlot'] = {'include_rbm': 'on',\n 'include_forward_motion': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0,\n 'u_inf': u_inf,\n 'dt': dt}\n\n\n\n\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n for k, v in settings.items():\n config[k] = v\n config.write()\n\n\n\nclean_test_files()\ngenerate_fem()\ngenerate_aero_file()\ngenerate_solver_file()\ngenerate_dyn_file()\n" }, { "path": "sharpy/cases/coupled/simple_HALE/__init__.py", "content": "" }, { "path": "sharpy/cases/coupled/simple_HALE/generate_hale.py", "content": "#! /usr/bin/env python3\nimport h5py as h5\nimport numpy as np\nimport os\nimport sharpy.utils.algebra as algebra\n\ncase_name = 'simple_HALE'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n# EXECUTION\nflow = ['BeamLoader',\n 'AerogridLoader',\n # 'NonLinearStatic',\n # 'StaticUvlm',\n 'StaticTrim',\n # 'StaticCoupled',\n 'BeamLoads',\n 'AerogridPlot',\n 'BeamPlot',\n 'DynamicCoupled',\n # 'Modal',\n # 'LinearAssember',\n # 'AsymptoticStability',\n ]\n\n# if free_flight is False, the motion of the centre of the wing is prescribed.\nfree_flight = True\nif not free_flight:\n case_name += '_prescribed'\n amplitude = 0 * np.pi / 180\n period = 3\n case_name += '_amp_' + str(amplitude).replace('.', '') + '_period_' + str(period)\n\n# FLIGHT CONDITIONS\n# the simulation is set such that the aircraft flies at a u_inf velocity while\n# the air is calm.\nu_inf = 10\nrho = 1.225\n\n# trim sigma = 1.5\nalpha = 4.31 * np.pi / 180\nbeta = 0\nroll = 0\ngravity = 'on'\ncs_deflection = -2.08 * np.pi / 180\nrudder_static_deflection = 0.0\nrudder_step = 0.0 * np.pi / 180\nthrust = 6.16\nsigma = 1.5\nlambda_dihedral = 20 * np.pi / 180\n\n# gust settings\ngust_intensity = 0.20\ngust_length = 1 * u_inf\ngust_offset = 0.5 * u_inf\n\n# numerics\nn_step = 5\nstructural_relaxation_factor = 0.6\nrelaxation_factor = 0.35\ntolerance = 1e-6\nfsi_tolerance = 1e-4\n\nnum_cores = 2\n\n# MODEL GEOMETRY\n# beam\nspan_main = 16.0\nlambda_main = 0.25\nea_main = 0.3\n\nea = 1e7\nga = 1e5\ngj = 1e4\neiy = 2e4\neiz = 4e6\nm_bar_main = 0.75\nj_bar_main = 0.075\n\nlength_fuselage = 10\noffset_fuselage = 0\nsigma_fuselage = 10\nm_bar_fuselage = 0.2\nj_bar_fuselage = 0.08\n\nspan_tail = 2.5\nea_tail = 0.5\nfin_height = 2.5\nea_fin = 0.5\nsigma_tail = 100\nm_bar_tail = 0.3\nj_bar_tail = 0.08\n\n# lumped masses\nn_lumped_mass = 1\nlumped_mass_nodes = np.zeros((n_lumped_mass,), dtype=int)\nlumped_mass = np.zeros((n_lumped_mass,))\nlumped_mass[0] = 50\nlumped_mass_inertia = np.zeros((n_lumped_mass, 3, 3))\nlumped_mass_position = np.zeros((n_lumped_mass, 3))\n\n# aero\nchord_main = 1.0\nchord_tail = 0.5\nchord_fin = 0.5\n\n# DISCRETISATION\n# spatial discretisation\n# chordiwse panels\nm = 4\n# spanwise elements\nn_elem_multiplier = 2\nn_elem_main = int(4 * n_elem_multiplier)\nn_elem_tail = int(2 * n_elem_multiplier)\nn_elem_fin = int(2 * n_elem_multiplier)\nn_elem_fuselage = int(2 * n_elem_multiplier)\nn_surfaces = 5\n\n# temporal discretisation\nphysical_time = 30\ntstep_factor = 1.\ndt = 1.0 / m / u_inf * tstep_factor\nn_tstep = round(physical_time / dt)\n\n# END OF INPUT-----------------------------------------------------------------\n\n# beam processing\nn_node_elem = 3\nspan_main1 = (1.0 - lambda_main) * span_main\nspan_main2 = lambda_main * span_main\n\nn_elem_main1 = round(n_elem_main * (1 - lambda_main))\nn_elem_main2 = n_elem_main - n_elem_main1\n\n# total number of elements\nn_elem = 0\nn_elem += n_elem_main1 + n_elem_main1\nn_elem += n_elem_main2 + n_elem_main2\nn_elem += n_elem_fuselage\nn_elem += n_elem_fin\nn_elem += n_elem_tail + n_elem_tail\n\n# number of nodes per part\nn_node_main1 = n_elem_main1 * (n_node_elem - 1) + 1\nn_node_main2 = n_elem_main2 * (n_node_elem - 1) + 1\nn_node_main = n_node_main1 + n_node_main2 - 1\nn_node_fuselage = n_elem_fuselage * (n_node_elem - 1) + 1\nn_node_fin = n_elem_fin * (n_node_elem - 1) + 1\nn_node_tail = n_elem_tail * (n_node_elem - 1) + 1\n\n# total number of nodes\nn_node = 0\nn_node += n_node_main1 + n_node_main1 - 1\nn_node += n_node_main2 - 1 + n_node_main2 - 1\nn_node += n_node_fuselage - 1\nn_node += n_node_fin - 1\nn_node += n_node_tail - 1\nn_node += n_node_tail - 1\n\n# stiffness and mass matrices\nn_stiffness = 3\nbase_stiffness_main = sigma * np.diag([ea, ga, ga, gj, eiy, eiz])\nbase_stiffness_fuselage = base_stiffness_main.copy() * sigma_fuselage\nbase_stiffness_fuselage[4, 4] = base_stiffness_fuselage[5, 5]\nbase_stiffness_tail = base_stiffness_main.copy() * sigma_tail\nbase_stiffness_tail[4, 4] = base_stiffness_tail[5, 5]\n\nn_mass = 3\nbase_mass_main = np.diag([m_bar_main, m_bar_main, m_bar_main, j_bar_main, 0.5 * j_bar_main, 0.5 * j_bar_main])\nbase_mass_fuselage = np.diag([m_bar_fuselage,\n m_bar_fuselage,\n m_bar_fuselage,\n j_bar_fuselage,\n j_bar_fuselage * 0.5,\n j_bar_fuselage * 0.5])\nbase_mass_tail = np.diag([m_bar_tail,\n m_bar_tail,\n m_bar_tail,\n j_bar_tail,\n j_bar_tail * 0.5,\n j_bar_tail * 0.5])\n\n# PLACEHOLDERS\n# beam\nx = np.zeros((n_node,))\ny = np.zeros((n_node,))\nz = np.zeros((n_node,))\nbeam_number = np.zeros((n_elem,), dtype=int)\nframe_of_reference_delta = np.zeros((n_elem, n_node_elem, 3))\nstructural_twist = np.zeros((n_elem, 3))\nconn = np.zeros((n_elem, n_node_elem), dtype=int)\nstiffness = np.zeros((n_stiffness, 6, 6))\nelem_stiffness = np.zeros((n_elem,), dtype=int)\nmass = np.zeros((n_mass, 6, 6))\nelem_mass = np.zeros((n_elem,), dtype=int)\nboundary_conditions = np.zeros((n_node,), dtype=int)\napp_forces = np.zeros((n_node, 6))\n\n# aero\nairfoil_distribution = np.zeros((n_elem, n_node_elem), dtype=int)\nsurface_distribution = np.zeros((n_elem,), dtype=int) - 1\nsurface_m = np.zeros((n_surfaces,), dtype=int)\nm_distribution = 'uniform'\naero_node = np.zeros((n_node,), dtype=bool)\ntwist = np.zeros((n_elem, n_node_elem))\nsweep = np.zeros((n_elem, n_node_elem))\nchord = np.zeros((n_elem, n_node_elem,))\nelastic_axis = np.zeros((n_elem, n_node_elem,))\n\n\n# FUNCTIONS-------------------------------------------------------------\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n dyn_file_name = route + '/' + case_name + '.dyn.h5'\n if os.path.isfile(dyn_file_name):\n os.remove(dyn_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n\ndef generate_dyn_file():\n global dt\n global n_tstep\n global route\n global case_name\n global num_elem\n global num_node_elem\n global num_node\n global amplitude\n global period\n global free_flight\n\n dynamic_forces_time = None\n with_dynamic_forces = False\n with_forced_vel = False\n if not free_flight:\n with_forced_vel = True\n\n if with_dynamic_forces:\n f1 = 100\n dynamic_forces = np.zeros((num_node, 6))\n app_node = [int(num_node_main - 1), int(num_node_main)]\n dynamic_forces[app_node, 2] = f1\n force_time = np.zeros((n_tstep,))\n limit = round(0.05 / dt)\n force_time[50:61] = 1\n\n dynamic_forces_time = np.zeros((n_tstep, num_node, 6))\n for it in range(n_tstep):\n dynamic_forces_time[it, :, :] = force_time[it] * dynamic_forces\n\n forced_for_vel = None\n if with_forced_vel:\n forced_for_vel = np.zeros((n_tstep, 6))\n forced_for_acc = np.zeros((n_tstep, 6))\n for it in range(n_tstep):\n # if dt*it < period:\n # forced_for_vel[it, 2] = 2*np.pi/period*amplitude*np.sin(2*np.pi*dt*it/period)\n # forced_for_acc[it, 2] = (2*np.pi/period)**2*amplitude*np.cos(2*np.pi*dt*it/period)\n\n forced_for_vel[it, 3] = 2 * np.pi / period * amplitude * np.sin(2 * np.pi * dt * it / period)\n forced_for_acc[it, 3] = (2 * np.pi / period) ** 2 * amplitude * np.cos(2 * np.pi * dt * it / period)\n\n if with_dynamic_forces or with_forced_vel:\n with h5.File(route + '/' + case_name + '.dyn.h5', 'a') as h5file:\n if with_dynamic_forces:\n h5file.create_dataset(\n 'dynamic_forces', data=dynamic_forces_time)\n if with_forced_vel:\n h5file.create_dataset(\n 'for_vel', data=forced_for_vel)\n h5file.create_dataset(\n 'for_acc', data=forced_for_acc)\n h5file.create_dataset(\n 'num_steps', data=n_tstep)\n\n\ndef generate_fem():\n stiffness[0, ...] = base_stiffness_main\n stiffness[1, ...] = base_stiffness_fuselage\n stiffness[2, ...] = base_stiffness_tail\n\n mass[0, ...] = base_mass_main\n mass[1, ...] = base_mass_fuselage\n mass[2, ...] = base_mass_tail\n\n we = 0\n wn = 0\n # inner right wing\n beam_number[we:we + n_elem_main1] = 0\n y[wn:wn + n_node_main1] = np.linspace(0.0, span_main1, n_node_main1)\n\n for ielem in range(n_elem_main1):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n\n elem_stiffness[we:we + n_elem_main1] = 0\n elem_mass[we:we + n_elem_main1] = 0\n boundary_conditions[0] = 1\n # remember this is in B FoR\n app_forces[0] = [0, thrust, 0, 0, 0, 0]\n we += n_elem_main1\n wn += n_node_main1\n\n # outer right wing\n beam_number[we:we + n_elem_main1] = 0\n y[wn:wn + n_node_main2 - 1] = y[wn - 1] + np.linspace(0.0, np.cos(lambda_dihedral) * span_main2, n_node_main2)[1:]\n z[wn:wn + n_node_main2 - 1] = z[wn - 1] + np.linspace(0.0, np.sin(lambda_dihedral) * span_main2, n_node_main2)[1:]\n for ielem in range(n_elem_main2):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_main2] = 0\n elem_mass[we:we + n_elem_main2] = 0\n boundary_conditions[wn + n_node_main2 - 2] = -1\n we += n_elem_main2\n wn += n_node_main2 - 1\n\n # inner left wing\n beam_number[we:we + n_elem_main1 - 1] = 1\n y[wn:wn + n_node_main1 - 1] = np.linspace(0.0, -span_main1, n_node_main1)[1:]\n for ielem in range(n_elem_main1):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = 0\n elem_stiffness[we:we + n_elem_main1] = 0\n elem_mass[we:we + n_elem_main1] = 0\n we += n_elem_main1\n wn += n_node_main1 - 1\n\n # outer left wing\n beam_number[we:we + n_elem_main2] = 1\n y[wn:wn + n_node_main2 - 1] = y[wn - 1] + np.linspace(0.0, -np.cos(lambda_dihedral) * span_main2, n_node_main2)[1:]\n z[wn:wn + n_node_main2 - 1] = z[wn - 1] + np.linspace(0.0, np.sin(lambda_dihedral) * span_main2, n_node_main2)[1:]\n for ielem in range(n_elem_main2):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_main2] = 0\n elem_mass[we:we + n_elem_main2] = 0\n boundary_conditions[wn + n_node_main2 - 2] = -1\n we += n_elem_main2\n wn += n_node_main2 - 1\n\n # fuselage\n beam_number[we:we + n_elem_fuselage] = 2\n x[wn:wn + n_node_fuselage - 1] = np.linspace(0.0, length_fuselage, n_node_fuselage)[1:]\n z[wn:wn + n_node_fuselage - 1] = np.linspace(0.0, offset_fuselage, n_node_fuselage)[1:]\n for ielem in range(n_elem_fuselage):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [0.0, 1.0, 0.0]\n conn[we, 0] = 0\n elem_stiffness[we:we + n_elem_fuselage] = 1\n elem_mass[we:we + n_elem_fuselage] = 1\n we += n_elem_fuselage\n wn += n_node_fuselage - 1\n global end_of_fuselage_node\n end_of_fuselage_node = wn - 1\n\n # fin\n beam_number[we:we + n_elem_fin] = 3\n x[wn:wn + n_node_fin - 1] = x[end_of_fuselage_node]\n z[wn:wn + n_node_fin - 1] = z[end_of_fuselage_node] + np.linspace(0.0, fin_height, n_node_fin)[1:]\n for ielem in range(n_elem_fin):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fuselage_node\n elem_stiffness[we:we + n_elem_fin] = 2\n elem_mass[we:we + n_elem_fin] = 2\n we += n_elem_fin\n wn += n_node_fin - 1\n end_of_fin_node = wn - 1\n\n # right tail\n beam_number[we:we + n_elem_tail] = 4\n x[wn:wn + n_node_tail - 1] = x[end_of_fin_node]\n y[wn:wn + n_node_tail - 1] = np.linspace(0.0, span_tail, n_node_tail)[1:]\n z[wn:wn + n_node_tail - 1] = z[end_of_fin_node]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fin_node\n elem_stiffness[we:we + n_elem_tail] = 2\n elem_mass[we:we + n_elem_tail] = 2\n boundary_conditions[wn + n_node_tail - 2] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n # left tail\n beam_number[we:we + n_elem_tail] = 5\n x[wn:wn + n_node_tail - 1] = x[end_of_fin_node]\n y[wn:wn + n_node_tail - 1] = np.linspace(0.0, -span_tail, n_node_tail)[1:]\n z[wn:wn + n_node_tail - 1] = z[end_of_fin_node]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fin_node\n elem_stiffness[we:we + n_elem_tail] = 2\n elem_mass[we:we + n_elem_tail] = 2\n boundary_conditions[wn + n_node_tail - 2] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=n_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=n_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=n_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n lumped_mass_nodes_handle = h5file.create_dataset(\n 'lumped_mass_nodes', data=lumped_mass_nodes)\n lumped_mass_handle = h5file.create_dataset(\n 'lumped_mass', data=lumped_mass)\n lumped_mass_inertia_handle = h5file.create_dataset(\n 'lumped_mass_inertia', data=lumped_mass_inertia)\n lumped_mass_position_handle = h5file.create_dataset(\n 'lumped_mass_position', data=lumped_mass_position)\n\n\ndef generate_aero_file():\n global x, y, z\n # control surfaces\n n_control_surfaces = 2\n control_surface = np.zeros((n_elem, n_node_elem), dtype=int) - 1\n control_surface_type = np.zeros((n_control_surfaces,), dtype=int)\n control_surface_deflection = np.zeros((n_control_surfaces,))\n control_surface_chord = np.zeros((n_control_surfaces,), dtype=int)\n control_surface_hinge_coord = np.zeros((n_control_surfaces,), dtype=float)\n\n # control surface type 0 = static\n # control surface type 1 = dynamic\n control_surface_type[0] = 0\n control_surface_deflection[0] = cs_deflection\n control_surface_chord[0] = m\n control_surface_hinge_coord[0] = -0.25 # nondimensional wrt elastic axis (+ towards the trailing edge)\n\n control_surface_type[1] = 0\n control_surface_deflection[1] = rudder_static_deflection\n control_surface_chord[1] = 1\n control_surface_hinge_coord[1] = -0. # nondimensional wrt elastic axis (+ towards the trailing edge)\n\n we = 0\n wn = 0\n # right wing (surface 0, beam 0)\n i_surf = 0\n airfoil_distribution[we:we + n_elem_main, :] = 0\n surface_distribution[we:we + n_elem_main] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_main] = True\n temp_chord = np.linspace(chord_main, chord_main, n_node_main)\n temp_sweep = np.linspace(0.0, 0 * np.pi / 180, n_node_main)\n node_counter = 0\n for i_elem in range(we, we + n_elem_main):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = temp_chord[node_counter]\n elastic_axis[i_elem, i_local_node] = ea_main\n sweep[i_elem, i_local_node] = temp_sweep[node_counter]\n\n we += n_elem_main\n wn += n_node_main\n\n # left wing (surface 1, beam 1)\n i_surf = 1\n airfoil_distribution[we:we + n_elem_main, :] = 0\n # airfoil_distribution[wn:wn + n_node_main - 1] = 0\n surface_distribution[we:we + n_elem_main] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_main - 1] = True\n # chord[wn:wn + num_node_main - 1] = np.linspace(main_chord, main_tip_chord, num_node_main)[1:]\n # chord[wn:wn + num_node_main - 1] = main_chord\n # elastic_axis[wn:wn + num_node_main - 1] = main_ea\n temp_chord = np.linspace(chord_main, chord_main, n_node_main)\n node_counter = 0\n for i_elem in range(we, we + n_elem_main):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = temp_chord[node_counter]\n elastic_axis[i_elem, i_local_node] = ea_main\n sweep[i_elem, i_local_node] = -temp_sweep[node_counter]\n\n we += n_elem_main\n wn += n_node_main - 1\n\n we += n_elem_fuselage\n wn += n_node_fuselage - 1 - 1\n #\n # # fin (surface 2, beam 3)\n i_surf = 2\n airfoil_distribution[we:we + n_elem_fin, :] = 1\n # airfoil_distribution[wn:wn + n_node_fin] = 0\n surface_distribution[we:we + n_elem_fin] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_fin] = True\n # chord[wn:wn + num_node_fin] = fin_chord\n for i_elem in range(we, we + n_elem_fin):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_fin\n elastic_axis[i_elem, i_local_node] = ea_fin\n control_surface[i_elem, i_local_node] = 1\n # twist[end_of_fuselage_node] = 0\n # twist[wn:] = 0\n # elastic_axis[wn:wn + num_node_main] = fin_ea\n we += n_elem_fin\n wn += n_node_fin - 1\n #\n # # # right tail (surface 3, beam 4)\n i_surf = 3\n airfoil_distribution[we:we + n_elem_tail, :] = 2\n # airfoil_distribution[wn:wn + n_node_tail] = 0\n surface_distribution[we:we + n_elem_tail] = i_surf\n surface_m[i_surf] = m\n # XXX not very elegant\n aero_node[wn:] = True\n # chord[wn:wn + num_node_tail] = tail_chord\n # elastic_axis[wn:wn + num_node_main] = tail_ea\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n twist[i_elem, i_local_node] = -0\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_tail\n elastic_axis[i_elem, i_local_node] = ea_tail\n control_surface[i_elem, i_local_node] = 0\n\n we += n_elem_tail\n wn += n_node_tail\n #\n # # left tail (surface 4, beam 5)\n i_surf = 4\n airfoil_distribution[we:we + n_elem_tail, :] = 2\n # airfoil_distribution[wn:wn + n_node_tail - 1] = 0\n surface_distribution[we:we + n_elem_tail] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_tail - 1] = True\n # chord[wn:wn + num_node_tail] = tail_chord\n # elastic_axis[wn:wn + num_node_main] = tail_ea\n # twist[we:we + num_elem_tail] = -tail_twist\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n twist[i_elem, i_local_node] = -0\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_tail\n elastic_axis[i_elem, i_local_node] = ea_tail\n control_surface[i_elem, i_local_node] = 0\n we += n_elem_tail\n wn += n_node_tail\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n naca_airfoil_tail = airfoils_group.create_dataset('1', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n naca_airfoil_fin = airfoils_group.create_dataset('2', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input.attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # sweep\n sweep_input = h5file.create_dataset('sweep', data=sweep)\n dim_attr = sweep_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n control_surface_input = h5file.create_dataset('control_surface', data=control_surface)\n control_surface_deflection_input = h5file.create_dataset('control_surface_deflection',\n data=control_surface_deflection)\n control_surface_chord_input = h5file.create_dataset('control_surface_chord', data=control_surface_chord)\n control_surface_hinge_coord_input = h5file.create_dataset('control_surface_hinge_coord',\n data=control_surface_hinge_coord)\n control_surface_types_input = h5file.create_dataset('control_surface_type', data=control_surface_type)\n\n\ndef generate_naca_camber(M=0, P=0):\n mm = M * 1e-2\n p = P * 1e-1\n\n def naca(x, mm, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return mm / (p * p) * (2 * p * x - x * x)\n elif x > p and x < 1 + 1e-6:\n return mm / ((1 - p) * (1 - p)) * (1 - 2 * p + 2 * p * x - x * x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, mm, p) for x in x_vec])\n return x_vec, y_vec\n\n\ndef generate_solver_file():\n file_name = route + '/' + case_name + '.sharpy'\n settings = dict()\n settings['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': flow,\n 'write_screen': 'on',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n\n settings['BeamLoader'] = {'unsteady': 'on',\n 'orientation': algebra.euler2quat(np.array([roll,\n alpha,\n beta]))}\n settings['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n 'mstar': int(20 / tstep_factor),\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': ['1', '0', '0'],\n 'dt': dt}}\n\n settings['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'gravity_on': gravity,\n 'gravity': 9.81}\n\n settings['StaticUvlm'] = {'print_info': 'on',\n 'horseshoe': 'off',\n 'num_cores': num_cores,\n 'n_rollup': 0,\n 'rollup_dt': dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho}\n\n settings['StaticCoupled'] = {'print_info': 'off',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': settings['NonLinearStatic'],\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': settings['StaticUvlm'],\n 'max_iter': 100,\n 'n_load_steps': n_step,\n 'tolerance': fsi_tolerance,\n 'relaxation_factor': structural_relaxation_factor}\n\n settings['StaticTrim'] = {'solver': 'StaticCoupled',\n 'solver_settings': settings['StaticCoupled'],\n 'initial_alpha': alpha,\n 'initial_deflection': cs_deflection,\n 'initial_thrust': thrust}\n\n settings['NonLinearDynamicCoupledStep'] = {'print_info': 'off',\n 'max_iterations': 950,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'newmark_damp': 5e-3,\n 'gravity_on': gravity,\n 'gravity': 9.81,\n 'num_steps': n_tstep,\n 'dt': dt,\n 'initial_velocity': u_inf}\n\n settings['NonLinearDynamicPrescribedStep'] = {'print_info': 'off',\n 'max_iterations': 950,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'newmark_damp': 5e-3,\n 'gravity_on': gravity,\n 'gravity': 9.81,\n 'num_steps': n_tstep,\n 'dt': dt,\n 'initial_velocity': u_inf * int(free_flight)}\n\n relative_motion = 'off'\n if not free_flight:\n relative_motion = 'on'\n settings['StepUvlm'] = {'print_info': 'off',\n 'num_cores': num_cores,\n 'convection_scheme': 2,\n 'gamma_dot_filtering': 6,\n 'velocity_field_generator': 'GustVelocityField',\n 'velocity_field_input': {'u_inf': int(not free_flight) * u_inf,\n 'u_inf_direction': [1., 0, 0],\n 'gust_shape': '1-cos',\n 'gust_parameters': {'gust_length': gust_length,\n 'gust_intensity': gust_intensity * u_inf},\n 'offset': gust_offset,\n 'relative_motion': relative_motion},\n 'rho': rho,\n 'n_time_steps': n_tstep,\n 'dt': dt}\n\n if free_flight:\n solver = 'NonLinearDynamicCoupledStep'\n else:\n solver = 'NonLinearDynamicPrescribedStep'\n settings['DynamicCoupled'] = {'structural_solver': solver,\n 'structural_solver_settings': settings[solver],\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'fsi_substeps': 200,\n 'fsi_tolerance': fsi_tolerance,\n 'relaxation_factor': relaxation_factor,\n 'minimum_steps': 1,\n 'relaxation_steps': 150,\n 'final_relaxation_factor': 0.5,\n 'n_time_steps': n_tstep,\n 'dt': dt,\n 'include_unsteady_force_contribution': 'on',\n 'postprocessors': ['BeamLoads', 'BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'BeamLoads': {'csv_output': 'off'},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'},\n 'AerogridPlot': {\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n }}\n\n settings['BeamLoads'] = {'csv_output': 'off'}\n\n settings['BeamPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on'}\n\n\n settings['AerogridPlot'] = {'include_rbm': 'on',\n 'include_forward_motion': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0,\n 'u_inf': u_inf,\n 'dt': dt}\n\n settings['Modal'] = {'print_info': True,\n 'use_undamped_modes': True,\n 'NumLambda': 30,\n 'rigid_body_modes': True,\n 'write_modes_vtk': 'on',\n 'print_matrices': 'on',\n 'continuous_eigenvalues': 'off',\n 'dt': dt,\n 'plot_eigenvalues': False}\n\n settings['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n 'linear_system_settings': {\n 'beam_settings': {'modal_projection': False,\n 'inout_coords': 'nodes',\n 'discrete_time': True,\n 'newmark_damp': 0.05,\n 'discr_method': 'newmark',\n 'dt': dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'off',\n 'num_modes': 40,\n 'print_info': 'on',\n 'gravity': 'on',\n 'remove_dofs': []},\n 'aero_settings': {'dt': dt,\n 'integr_order': 2,\n 'density': rho,\n 'remove_predictor': False,\n 'use_sparse': True,\n 'remove_inputs': ['u_gust']}\n }}\n\n settings['AsymptoticStability'] = {'print_info': 'on',\n 'modes_to_plot': [],\n 'display_root_locus': 'off',\n 'frequency_cutoff': 0,\n 'export_eigenvalues': 'off',\n 'num_evals': 40}\n\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n for k, v in settings.items():\n config[k] = v\n config.write()\n\n\nclean_test_files()\ngenerate_fem()\ngenerate_aero_file()\ngenerate_solver_file()\ngenerate_dyn_file()\n" }, { "path": "sharpy/cases/hangar/__init__.py", "content": "" }, { "path": "sharpy/cases/hangar/horten_wing.py", "content": "\"\"\"\nHorten Wing Class Generator\nN Goizueta Nov 18\n\"\"\"\n\nimport numpy as np\nimport os\nimport h5py as h5\nimport sharpy.utils.geo_utils as geo_utils\nimport sharpy.utils.algebra as algebra\nimport configobj\nimport scipy.linalg as sclalg\n\n\nclass HortenWing:\n \"\"\"\n Horten Wing Class Generator\n\n A ``HortenWing`` class contains the basic geometry and properties of a simplified Horten wing, as\n described by Richards (2016)\n\n This class allows the user to quickly obtain SHARPy cases for the purposes of parametric analyses.\n\n \"\"\"\n\n def __init__(self,\n M,\n N,\n Mstarfactor,\n u_inf,\n rho=1.225,\n alpha_deg=0.,\n beta_deg=0.,\n roll_deg=0.,\n cs_deflection_deg=0.,\n thrust=5.,\n physical_time=10,\n case_name_format=2,\n case_remarks=None,\n case_route='./cases/',\n case_name='horten'):\n\n # Discretisation\n self.M = M\n self.N = N\n self.Mstarfactor = Mstarfactor\n\n self.n_node_elem = 3\n self.n_elem_wing = N\n self.n_elem_fuselage = 1\n self.n_surfaces = 4\n\n # Case admin\n if case_name_format == 0:\n self.case_name = case_name + '_u_inf%.4d_a%.4d' % (int(u_inf*100), int(alpha_deg * 100))\n elif case_name_format == 1:\n self.case_name = case_name + '_u_inf%.4d' % int(u_inf*100)\n elif case_name_format == 2:\n self.case_name = case_name\n else:\n self.case_name = case_name + '_u_inf%.4d_%s' % (int(u_inf*100), case_remarks)\n\n self.case_route = os.path.abspath(case_route + self.case_name + '/')\n\n self.config = None\n\n # Flight conditions\n self.u_inf = u_inf\n self.rho = rho\n self.alpha = alpha_deg * np.pi / 180\n self.roll = roll_deg * np.pi / 180\n self.beta = beta_deg * np.pi / 180\n self.cs_deflection = cs_deflection_deg * np.pi / 180\n self.thrust = thrust\n\n # Compute number of nodes\n n_node = 0\n self.n_node_wing = self.n_elem_wing * (self.n_node_elem - 1)\n self.n_node_fuselage = self.n_elem_fuselage * self.n_node_elem\n n_node += 2 * self.n_node_fuselage - 1 + 2 * self.n_node_wing\n self.n_node = n_node\n\n # Compute number of elements\n self.n_elem = 2 * (self.n_elem_wing + self.n_elem_fuselage)\n\n # Wing geometry\n self.span = 20.0 # [m]\n self.sweep_LE = 20 * np.pi / 180 # [rad] Leading Edge Sweep\n # self.c_root = 1.0 # [m] Root chord - Richards\n self.c_root = 1.5819 # [m] Root chord - Mardanpour 2014\n self.taper_ratio = 0.17 # Mardanpour 2014\n # self.taper_ratio = 0.25 # Richards\n self.thrust_nodes = [self.n_node_fuselage - 1,\n self.n_node_fuselage + self.n_node_wing + 1]\n\n self.loc_cg = 0.45 # CG position wrt to LE (from sectional analysis)\n # EA is the reference in NATASHA - defined with respect to the midchord. SHARPy is wrt to LE and as a pct of\n # local chord\n self.main_ea_root = 0.5 + 0.15*0.0254 / self.c_root\n self.main_ea_tip = 0.5 + 0.21*0.0254 / (self.c_root*self.taper_ratio)\n\n # FUSELAGE GEOMETRY\n # self.fuselage_width = 1.\n self.fuselage_width = 0.8248\n self.c_fuselage = 84*0.0254\n\n # WASH OUT\n self.washout_root = 0*np.pi/180\n self.washout_tip = -2 * np.pi / 180\n\n # Horseshoe wake\n self.horseshoe = False\n self.wake_type = 2\n self.dt_factor = 1\n self.dt = 1 / self.M / self.u_inf * self.dt_factor\n\n # Dynamics\n self.physical_time = physical_time\n self.n_tstep = int(physical_time/self.dt)\n self.gust_intensity = 0.05\n\n # Numerics\n self.tolerance = 1e-12\n self.fsi_tolerance = 1e-10\n self.relaxation_factor = 0.2\n\n # H5 Variables initialisation as class attributes\n # coordinates\n self.x = np.zeros((n_node,))\n self.y = np.zeros((n_node,))\n self.z = np.zeros((n_node,))\n # beam number\n self.beam_number = np.zeros(self.n_elem, dtype=int)\n # frame of reference delta\n self.frame_of_reference_delta = np.zeros((self.n_elem, self.n_node_elem, 3))\n # connectivity of beams\n self.connectivities = np.zeros((self.n_elem, self.n_node_elem), dtype=int)\n # stiffness\n self.n_stiffness = self.n_elem_wing + self.n_elem_fuselage\n self.base_stiffness = np.zeros((self.n_stiffness, 6, 6))\n self.elem_stiffness = np.zeros((self.n_elem,), dtype=int)\n # mass\n self.n_mass = self.n_elem_wing * 2 // 2\n self.base_mass = np.zeros((self.n_mass, 6, 6))\n self.elem_mass = np.zeros(self.n_elem, dtype=int)\n # boundary conditions\n self.boundary_conditions = np.zeros((n_node,), dtype=int)\n # applied forces\n self.app_forces = np.zeros((n_node, 6))\n self.n_lumped_mass = 3\n\n self.lumped_mass_nodes = np.zeros((self.n_lumped_mass), dtype=int)\n self.lumped_mass = np.zeros(self.n_lumped_mass)\n self.lumped_mass_inertia = np.zeros((self.n_lumped_mass, 3, 3))\n self.lumped_mass_position = np.zeros((self.n_lumped_mass, 3))\n\n # Aerodynamic properties\n # H5 AERO FILE VARIABLES INITIALISATION\n # airfoil distribution\n self.airfoil_distribution = np.zeros((self.n_elem, self.n_node_elem), dtype=int)\n # surface distribution\n self.surface_distribution = np.zeros((self.n_elem,), dtype=int) - 1\n self.surface_m = np.zeros((self.n_surfaces,), dtype=int)\n self.m_distribution = 'uniform'\n # aerodynamic nodes boolean\n self.aero_nodes = np.zeros((self.n_node,), dtype=bool)\n # aero twist\n self.twist = np.zeros((self.n_elem, self.n_node_elem))\n # chord\n self.chord = np.zeros((self.n_elem, self.n_node_elem))\n # elastic axis\n self.elastic_axis = np.zeros((self.n_elem, self.n_node_elem))\n\n # control surfaces attributes initialisation\n self.n_control_surfaces = 1\n self.control_surface = np.zeros((self.n_elem, self.n_node_elem), dtype=int) - 1\n self.control_surface_type = np.zeros((self.n_control_surfaces,), dtype=int)\n self.control_surface_deflection = np.zeros((self.n_control_surfaces,))\n self.control_surface_chord = np.zeros((self.n_control_surfaces,), dtype=int)\n self.control_surface_hinge_coord = np.zeros((self.n_control_surfaces,), dtype=float)\n\n self.settings = dict()\n\n def initialise(self):\n\n if not os.path.exists(self.case_route):\n os.makedirs(self.case_route)\n\n # Compute number of nodes\n n_node = 0\n self.n_node_wing = self.n_elem_wing * (self.n_node_elem - 1)\n self.n_node_fuselage = self.n_elem_fuselage * self.n_node_elem\n n_node += 2 * self.n_node_fuselage - 1 + 2 * self.n_node_wing\n self.n_node = n_node\n\n # Compute number of elements\n self.n_elem = 2 * (self.n_elem_wing + self.n_elem_fuselage)\n\n self.dt = 1 / self.M / self.u_inf * self.dt_factor\n\n # H5 Variables initialisation as class attributes\n # coordinates\n self.x = np.zeros((n_node,))\n self.y = np.zeros((n_node,))\n self.z = np.zeros((n_node,))\n # beam number\n self.beam_number = np.zeros(self.n_elem, dtype=int)\n # frame of reference delta\n self.frame_of_reference_delta = np.zeros((self.n_elem, self.n_node_elem, 3))\n # connectivity of beams\n self.connectivities = np.zeros((self.n_elem, self.n_node_elem), dtype=int)\n # stiffness\n self.n_stiffness = self.n_elem_wing + self.n_elem_fuselage\n self.base_stiffness = np.zeros((self.n_stiffness, 6, 6))\n self.elem_stiffness = np.zeros((self.n_elem,), dtype=int)\n # mass\n self.base_mass = np.zeros((self.n_mass, 6, 6))\n self.elem_mass = np.zeros(self.n_elem, dtype=int)\n # boundary conditions\n self.boundary_conditions = np.zeros((n_node,), dtype=int)\n # applied forces\n self.app_forces = np.zeros((n_node, 6))\n self.n_lumped_mass = 3\n\n self.lumped_mass_nodes = np.zeros((self.n_lumped_mass), dtype=int)\n self.lumped_mass = np.zeros(self.n_lumped_mass)\n self.lumped_mass_inertia = np.zeros((self.n_lumped_mass, 3, 3))\n self.lumped_mass_position = np.zeros((self.n_lumped_mass, 3))\n\n # Aerodynamic properties\n # H5 AERO FILE VARIABLES INITIALISATION\n # airfoil distribution\n self.airfoil_distribution = np.zeros((self.n_elem, self.n_node_elem), dtype=int)\n # surface distribution\n self.surface_distribution = np.zeros((self.n_elem,), dtype=int) - 1\n self.surface_m = np.zeros((self.n_surfaces,), dtype=int)\n self.m_distribution = 'uniform'\n # aerodynamic nodes boolean\n self.aero_nodes = np.zeros((self.n_node,), dtype=bool)\n # aero twist\n self.twist = np.zeros((self.n_elem, self.n_node_elem))\n # chord\n self.chord = np.zeros((self.n_elem, self.n_node_elem))\n # elastic axis\n self.elastic_axis = np.zeros((self.n_elem, self.n_node_elem))\n\n # control surfaces attributes initialisation\n self.n_control_surfaces = 1\n self.control_surface = np.zeros((self.n_elem, self.n_node_elem), dtype=int) - 1\n self.control_surface_type = np.zeros((self.n_control_surfaces,), dtype=int)\n self.control_surface_deflection = np.zeros((self.n_control_surfaces,))\n self.control_surface_chord = np.zeros((self.n_control_surfaces,), dtype=int)\n self.control_surface_hinge_coord = np.zeros((self.n_control_surfaces,), dtype=float)\n\n self.settings = dict()\n\n def dynamic_control_surface(self, *delta):\n \"\"\"\n Generate dynamic control surface input files\n\n Args:\n delta (list): list of numpy arrays containing deflection time history\n\n Returns:\n\n \"\"\"\n i = 0\n for cs in delta:\n self.control_surface_type[i] = 1\n np.savetxt(self.case_route + '/' + self.case_name + '.input.txt', cs)\n i += 1\n\n def planform_area(self):\n S_fus = 0.5 * (self.c_fuselage + self.c_root) * self.fuselage_width\n S_wing = 0.5 * (self.c_root + self.c_root*self.taper_ratio) * self.span / 2\n return 2*S_fus + 2*S_wing\n\n def update_mass_stiffness(self, sigma=1.):\n r\"\"\"\n The mass and stiffness matrices are computed. Both vary over the span of the wing, hence a\n dictionary is created that acts as a database of the different properties along the wing.\n\n The variation of the stiffness is cubic along the span:\n\n .. math:: \\mathbf{K} = \\mathbf{K}_0\\bar{c}^3\n\n where :math:`\\mathbf{K}_0 is the stiffness of the wing root section and :math:`\\bar{c}` is\n the ratio between the local chord and the root chord.\n\n The variation of the sectional mass is quadratic along the span:\n\n .. math:: \\mu = \\mu_0\\,\\bar{c}^2\n\n where :math:`\\mu` is the mass per unit span and the zero subscript denotes the root value.\n\n The sectional inertia is varied linearly along the span, based on the information by Mardanpour 2013.\n\n Three lumped masses are included with the following properties (Richards, 2013)\n\n ===== ===== ================= ========= =============================== ============\n No Node Relative Position Mass [kg] Inertia [kg m^2] Description\n ===== ===== ================= ========= =============================== ============\n ``0`` ``2`` ``[0,0,0]`` ``5.24`` ``[0.29547, 0.29322, 0.29547]`` Right Engine\n ``1`` ``S`` ``[0,0,0]`` ``5.24`` ``[0.29547, 0.29322, 0.29547]`` Left Engine\n ``2`` ``0`` ``[0,0,0]`` ``15.29`` ``[0.5, 1.0, 1.0]*15.29`` Fuselage\n ===== ===== ================= ========= =============================== ============\n\n\n Args:\n sigma (float): stiffening factor\n\n Returns:\n\n \"\"\"\n\n n_elem_fuselage = self.n_elem_fuselage\n n_elem_wing = self.n_elem_wing\n n_node_wing = self.n_node_wing\n n_node_fuselage = self.n_node_fuselage\n c_root = self.c_root\n taper_ratio = self.taper_ratio\n\n # Local chord to root chord initialisation\n c_bar_temp = np.linspace(c_root, taper_ratio * c_root, n_elem_wing)\n\n # Structural properties at the wing root section from Richards 2016\n ea = 1e6\n ga = 1e6\n gj = 4.24e5\n eiy = 3.84e5\n eiz = 2.46e7\n\n # Sectional mass from Richards 2016\n mu_0 = 9.761\n # Bending inertia properties from Mardanpour 2013\n j_root = 0.303\n j_tip = 0.2e-2 * 4.448 / 9.81\n\n # Number of stiffnesses used\n n_stiffness = self.n_stiffness\n\n # Initialise the stiffness database\n base_stiffness = self.base_stiffness\n\n # Wing root section stiffness properties\n # stiffness_root = sigma * np.diag([ea, ga, ga, gj, eiy, eiz])\n stiffness_root = np.array([[3.23624595e+09, 0.00000000e+00, 0.00000000e+00,\n 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n [0.00000000e+00, 1.00000000e+14, 0.00000000e+00,\n 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n [0.00000000e+00, 0.00000000e+00, 1.00000000e+14,\n 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n [0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n 8.04987046e+07, -1.69971789e+05, 5.69905411e+07],\n [0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n -1.69971789e+05, 5.03651190e+07, -6.70649560e+06],\n [0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n 5.69905411e+07, -6.70649560e+06, 2.24864852e+09]]) * sigma\n\n stiffness_tip = np.array([[5.86034256e+07, 0.00000000e+00, 0.00000000e+00,\n 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n [0.00000000e+00, 1.00000000e+15, 0.00000000e+00,\n 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n [0.00000000e+00, 0.00000000e+00, 1.00000000e+15,\n 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],\n [0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n 2.93227100e+04, -2.11280834e+03, 2.52782426e+04],\n [0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n -2.11280834e+03, 1.44883639e+05, -2.52913470e+04],\n [0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n 2.52782426e+04, -2.52913470e+04, 3.02592902e+05]]) * sigma\n\n\n stiffness_root = np.diag(np.diag(stiffness_root))\n stiffness_tip = np.diag(np.diag(stiffness_tip))\n\n # Rigid fuselage\n sigma_fuselage = 1000\n base_stiffness[0, :, :] = sigma_fuselage * stiffness_root\n\n # Cubic variation of the stiffness along the span - Richards\n # for stiff_entry in range(1, n_stiffness):\n # base_stiffness[stiff_entry, :, :] = stiffness_root * c_bar_temp[stiff_entry - 1] ** 3\n\n # Linear variation between root an tip as per Mardanpour 2014\n alpha = np.linspace(0, 1, self.n_elem_wing)\n for i_elem in range(0, self.n_elem_wing):\n base_stiffness[i_elem + 1, :, :] = stiffness_root*(1-alpha[i_elem]) + stiffness_tip*alpha[i_elem]\n\n # Mass variation along the span\n n_mass = self.n_mass\n sigma_mass = 1\n\n # Initialise database\n base_mass = self.base_mass\n\n mu_root = 2.784472 * sigma_mass\n chi_root_right = np.array([0, -5.29, 0.594]) * 0.0254 * 0\n chi_root_left = np.array([0, +5.29, 0.594]) * 0.0254 * 0\n m_root = np.eye(3) * mu_root\n j_root = np.array([[0.30378797, 0., 0.],\n [0., 0.0122422, 0.],\n [0., 0., 0.30016065]])\n\n j_root = np.diag([0.1, 0.1, 0.2])\n mass_root_right = sclalg.block_diag(np.diag([mu_root, mu_root, mu_root]), j_root)\n mass_root_left = sclalg.block_diag(np.diag([mu_root, mu_root, mu_root]), j_root)\n\n mass_root_right[:3, -3:] = -mu_root * algebra.skew(chi_root_right)\n mass_root_right[-3:, :3] = mu_root * algebra.skew(chi_root_right)\n\n mass_root_left[:3, -3:] = -mu_root * algebra.skew(chi_root_left)\n mass_root_left[-3:, :3] = mu_root * algebra.skew(chi_root_left)\n\n mu_tip = 0.284084 * sigma_mass\n chi_tip_right = np.array([0, -1.644, +0.563]) * 0.0254 * 0\n chi_tip_left = np.array([0, +1.644, +0.563]) * 0.0254 * 0\n j_tip = np.array([[9.06829766e-04, 0.00000000e+00, 0.00000000e+00],\n [0.00000000e+00, 6.34780836e-05, 0.00000000e+00],\n [0.00000000e+00, 0.00000000e+00, 8.16146789e-04]])\n j_tip = np.diag([0.1, 0.1, 0.2])\n mass_tip_right = sclalg.block_diag(np.diag([mu_tip, mu_tip, mu_tip]), j_tip)\n mass_tip_left = sclalg.block_diag(np.diag([mu_tip, mu_tip, mu_tip]), j_tip)\n mass_tip_right[:3, -3:] += -algebra.skew(chi_tip_right) * mu_tip\n mass_tip_right[-3:, :3] += algebra.skew(chi_tip_right) * mu_tip\n\n mass_tip_left[:3, -3:] += -algebra.skew(chi_tip_right) * mu_tip\n mass_tip_left[-3:, :3] += algebra.skew(chi_tip_right) * mu_tip\n\n mass_tip_left = mass_tip_right\n mass_root_left = mass_root_right\n\n for i_elem in range(self.n_elem_wing):\n base_mass[i_elem, :, :] = mass_root_right*(1-alpha[i_elem]) + mass_tip_right*alpha[i_elem]\n\n # for i_elem in range(self.n_elem_wing, 2*self.n_elem_wing):\n # base_mass[i_elem, :, :] = mass_root_left*(1-alpha[i_elem-self.n_elem_wing]) + mass_tip_left*alpha[i_elem-self.n_elem_wing]\n\n # Quadratic variation in the mass per unit span - Richards\n # mu_temp = mu_0 * np.ones_like(c_bar_temp)\n # j_temp = np.linspace(j_root, j_tip, n_elem_wing)\n\n # for mass_entry in range(n_mass):\n # base_mass[mass_entry, :, :] = np.diag([\n # mu_temp[mass_entry],\n # mu_temp[mass_entry],\n # mu_temp[mass_entry],\n # j_temp[mass_entry],\n # j_temp[mass_entry],\n # j_temp[mass_entry]\n # ])\n\n # Lumped mass initialisation\n # 0 - Right engine\n # 1 - Left engine\n # 2 - Fuselage\n\n lumped_mass_nodes = self.lumped_mass_nodes\n lumped_mass = self.lumped_mass\n lumped_mass_inertia = self.lumped_mass_inertia\n lumped_mass_position = self.lumped_mass_position\n\n # Lumped masses nodal position\n lumped_mass_nodes[0] = 2\n lumped_mass_nodes[1] = n_node_fuselage + n_node_wing + 1\n lumped_mass_nodes[2] = 0\n\n # Lumped mass value from Richards 2013\n # lumped_mass[0:2] = 51.445 / 9.81\n # lumped_mass[2] = 150 / 9.81\n\n # Lumped masses from Mardanpour\n # Pilot mass\n lumped_mass[2] = 16.06\n lumped_mass_position[2] = np.array([0., -0.254, -0.254])\n\n # Engine mass\n lumped_mass[0:2] = 0.535\n lumped_mass_inertia[0, :, :] = np.diag([0.02994352, 0.02994352, 0.02994352])\n lumped_mass_inertia[1, :, :] = np.diag([0.02994352, 0.02994352, 0.02994352])\n\n # Lumped mass inertia\n # lumped_mass_inertia[0, :, :] = np.diag([0.29547, 0.29322, 0.29547])\n # lumped_mass_inertia[1, :, :] = np.diag([0.29547, 0.29322, 0.29547])\n # lumped_mass_inertia[2, :, :] = np.diag([0.5, 1, 1]) * lumped_mass[2]\n\n # Define class attributes\n self.lumped_mass = lumped_mass * 0\n self.lumped_mass_nodes = lumped_mass_nodes * 0\n self.lumped_mass_inertia = lumped_mass_inertia * 0\n self.lumped_mass_position = lumped_mass_position * 0\n\n self.base_stiffness = base_stiffness\n self.base_mass = base_mass\n\n def update_fem_prop(self):\n \"\"\"\n Computes the FEM properties prior to analysis such as the connectivity matrix, coordinates, etc\n\n Returns:\n\n \"\"\"\n # Obtain class attributes\n n_node_elem = self.n_node_elem\n n_elem = self.n_elem\n n_elem_wing = self.n_elem_wing\n n_elem_fuselage = self.n_elem_fuselage\n n_node = self.n_node\n n_node_wing = self.n_node_wing\n n_node_fuselage = self.n_node_fuselage\n fuselage_width = self.fuselage_width\n thrust = self.thrust\n thrust_nodes = self.thrust_nodes\n span = self.span\n sweep_LE = self.sweep_LE\n\n # mass and stiffness matrices\n stiffness = self.base_stiffness\n mass = self.base_mass\n n_stiffness = stiffness.shape[0]\n n_mass = mass.shape[0]\n\n # H5 FEM FILE VARIABLES INITIALISATION\n # coordinates\n x = np.zeros((n_node,))\n y = np.zeros((n_node,))\n z = np.zeros((n_node,))\n # twist\n structural_twist = np.zeros_like(x)\n # beam number\n beam_number = np.zeros(n_elem, dtype=int)\n # frame of reference delta\n frame_of_reference_delta = np.zeros((n_elem, n_node_elem, 3))\n # connectivity of beams\n conn = np.zeros((n_elem, n_node_elem), dtype=int)\n # stiffness\n stiffness = np.zeros((n_stiffness, 6, 6))\n elem_stiffness = np.zeros((n_elem,), dtype=int)\n # mass\n mass = np.zeros((n_mass, 6, 6))\n elem_mass = np.zeros(n_elem, dtype=int)\n # boundary conditions\n boundary_conditions = np.zeros((n_node,), dtype=int)\n # applied forces\n app_forces = np.zeros((n_node, 6))\n\n # assemble connectivites\n # worked elements\n we = 0\n # worked nodes\n wn = 0\n\n # RIGHT RIGID FUSELAGE\n beam_number[we:we + 1] = 0\n # coordinates\n x[wn:wn + n_node_fuselage] = 0\n y[wn:wn + n_node_fuselage] = np.linspace(0, fuselage_width / 2, n_node_fuselage)\n\n # connectivities\n elem_mass[0] = 0\n conn[we, :] = [0, 2, 1]\n\n # frame of reference change\n frame_of_reference_delta[0, 0, :] = [-1.0, 0.0, 0.0]\n frame_of_reference_delta[0, 1, :] = [-1.0, 0.0, 0.0]\n frame_of_reference_delta[0, 2, :] = [-1.0, 0.0, 0.0]\n\n # element stiffness\n elem_stiffness[0] = 0\n elem_mass[0] = 0\n\n # boundary conditions\n boundary_conditions[0] = 1\n\n # applied forces - engine 1\n app_forces[thrust_nodes[0]] = [0, thrust, 0,\n 0, 0, 0]\n\n # updated worked nodes and elements\n we += n_elem_fuselage\n wn += n_node_fuselage\n\n # RIGHT WING\n beam_number[we:we + n_elem_wing] = 1\n # y coordinate (positive right)\n y[wn:wn + n_node_wing] = np.linspace(fuselage_width / 2,\n span / 2,\n n_node_wing + 1)[1:]\n x[wn:wn + n_node_wing] = 0 + (y[wn:wn + n_node_wing] - fuselage_width / 2) * np.tan(sweep_LE)\n\n # connectivities\n for ielem in range(n_elem_wing):\n conn[we + ielem, :] = (np.ones(n_node_elem) * (we + ielem) * (n_node_elem - 1) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n\n elem_mass[we + ielem] = ielem\n elem_stiffness[we + ielem] = ielem + 1\n\n # element stiffness and mass\n # elem_stiffness[we:we+n_elem_wing] = 0\n # elem_mass[we:we+n_elem_wing] = 0\n\n # boundary conditions of free end\n boundary_conditions[wn + n_node_wing - 1] = -1\n\n # update worked elements and nodes\n we += n_elem_wing\n wn += n_node_wing\n\n # LEFT FUSELAGE\n beam_number[we:we + n_elem_fuselage] = 2\n # coordinates\n y[wn:wn + n_node_fuselage - 1] = np.linspace(0,\n -fuselage_width / 2,\n n_node_fuselage)[1:]\n x[wn:wn + n_node_fuselage - 1] = 0\n\n # connectivity\n conn[we, :] = [0, wn + 1, wn]\n\n # frame of reference delta\n for ielem in range(n_elem_fuselage):\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n\n # element stiffness and mass\n elem_stiffness[we:we + n_elem_fuselage] = 0\n elem_mass[we:we + n_elem_fuselage] = self.n_elem_wing\n\n # applied forces - engine 2\n app_forces[thrust_nodes[1]] = [0, -thrust, 0,\n 0, 0, 0]\n\n # update worked elements and nodes\n we += n_elem_fuselage\n wn += n_node_fuselage - 1\n\n # LEFT WING\n # coordinates\n beam_number[we:we + n_elem_wing] = 3\n y[wn:wn + n_node_wing] = np.linspace(-fuselage_width / 2,\n -span / 2,\n n_node_wing + 1)[1:]\n x[wn:wn + n_node_wing] = 0 + -1 * (y[wn:wn + n_node_wing] + fuselage_width / 2) * np.tan(sweep_LE)\n\n # left wing connectivities\n for ielem in range(n_elem_wing):\n conn[we + ielem, :] = np.ones(n_node_elem) * (we + ielem) * (n_node_elem - 1) + [0, 2, 1]\n\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n\n elem_mass[we + ielem] = ielem + self.n_elem_wing\n elem_stiffness[we + ielem] = ielem + 1\n\n # element stiffness and mass\n # elem_stiffness[we:we+n_node_wing] = 0\n\n # boundary conditions at the free end\n boundary_conditions[wn + n_node_wing - 1] = -1\n\n # update worked elements and nodes\n we += n_elem_wing\n wn += n_node_wing\n\n # set attributes\n self.x = x\n self.y = y\n self.z = z\n self.connectivities = conn\n self.elem_stiffness = elem_stiffness\n self.elem_mass = elem_mass\n self.frame_of_reference_delta = frame_of_reference_delta\n self.boundary_conditions = boundary_conditions\n self.beam_number = beam_number\n self.app_forces = app_forces\n\n def generate_fem_file(self):\n \"\"\"\n Generates the ``.fem.h5`` folder containing the structural information of the problem\n\n The file is written to ``self.case_route / self.case_name .fem.h5``\n\n \"\"\"\n\n\n with h5.File(self.case_route + '/' + self.case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates',\n data=np.column_stack((self.x, self.y, self.z)))\n connectivities = h5file.create_dataset('connectivities', data=self.connectivities)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=self.n_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=self.n_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=self.n_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=self.base_stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=self.elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=self.base_mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=self.elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=self.frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=np.zeros((self.n_elem, self.n_node_elem)))\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=self.boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=self.beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=self.app_forces)\n lumped_mass_nodes_handle = h5file.create_dataset(\n 'lumped_mass_nodes', data=self.lumped_mass_nodes)\n lumped_mass_handle = h5file.create_dataset(\n 'lumped_mass', data=self.lumped_mass)\n lumped_mass_inertia_handle = h5file.create_dataset(\n 'lumped_mass_inertia', data=self.lumped_mass_inertia)\n lumped_mass_position_handle = h5file.create_dataset(\n 'lumped_mass_position', data=self.lumped_mass_position)\n\n def create_linear_simulation(self, delta_e=None, delta_dot=None):\n\n Kpanels = self.M * (self.n_node - 1)\n Kvertices = (self.M + 1) * self.n_node\n Kpanels_wake = Kpanels * self.Mstarfactor\n n_states_aero = 3 * Kpanels + Kpanels_wake\n # n_inputs_aero = 2 * 3 * Kvertices\n\n n_states_struct = 2*(6 * (self.n_node - 1) + 9)\n n_inputs_struct = n_states_struct // 2\n\n x0 = np.zeros((n_states_aero + n_states_struct))\n # x0[-7] = 0.05\n # x0[-4:] = (algebra.euler2quat([ -5*np.pi/180, 0, 0]))\n u = np.zeros((self.n_tstep, n_states_struct + n_inputs_struct + 2 * self.n_control_surfaces))\n # u[0:3, -7] = -1000\n if delta_e is not None:\n u[:, n_states_struct:n_states_struct+self.n_control_surfaces] = delta_e\n u[:, n_states_struct + self.n_control_surfaces:n_states_struct+self.n_control_surfaces + self.n_control_surfaces] = delta_dot\n\n # u[10:15, -8] = 100\n\n self.generate_linear_sim_files(x0, u)\n\n def generate_linear_sim_files(self, x0, input_vec):\n if not os.path.exists(self.case_route):\n os.makedirs(self.case_route)\n\n with h5.File(self.case_route + '/' + self.case_name + '.lininput.h5', 'a') as h5file:\n x0 = h5file.create_dataset(\n 'x0', data=x0)\n u = h5file.create_dataset(\n 'u', data=input_vec)\n\n def clean_test_files(self):\n \"\"\"\n Clears previously generated files\n \"\"\"\n\n case_name = self.case_name\n route = self.case_route\n\n # FEM\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n # Dynamics File\n dyn_file_name = route + '/' + case_name + '.dyn.h5'\n if os.path.isfile(dyn_file_name):\n os.remove(dyn_file_name)\n\n # Aerodynamics File\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n # Solver file\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n # Flight conditions file\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n # Linear inputs file\n lin_file_name = self.case_route + '/' + self.case_name + '.lininput.h5'\n if os.path.isfile(lin_file_name):\n os.remove(lin_file_name)\n\n # if os.path.isdir(route):\n # os.system('rm -r %s' %route)\n\n def update_aero_properties(self):\n \"\"\"\n Updates the aerodynamic properties of the horten wing\n\n \"\"\"\n\n # Retrieve attributes\n n_elem = self.n_elem\n n_node_elem = self.n_node_elem\n n_node_wing = self.n_node_wing\n n_node_fuselage = self.n_node_fuselage\n n_elem_fuselage = self.n_elem_fuselage\n n_elem_wing = self.n_elem_wing\n c_root = self.c_root\n taper_ratio = self.taper_ratio\n washout_root = self.washout_root\n washout_tip = self.washout_tip\n n_control_surfaces = self.n_control_surfaces\n cs_deflection = self.cs_deflection\n m = self.M\n main_ea_root = self.main_ea_root\n main_ea_tip = self.main_ea_tip\n airfoil_distribution = self.airfoil_distribution\n chord = self.chord\n surface_distribution = self.surface_distribution\n surface_m = self.surface_m\n aero_nodes = self.aero_nodes\n elastic_axis = self.elastic_axis\n twist = self.twist\n\n control_surface = self.control_surface\n control_surface_type = self.control_surface_type\n control_surface_deflection = self.control_surface_deflection\n control_surface_chord = self.control_surface_chord\n control_surface_hinge_coord = self.control_surface_hinge_coord\n\n self.dt = 1 / self.M / self.u_inf\n\n # control surface type: 0 = static\n # control surface type: 1 = dynamic\n control_surface_type[0] = self.control_surface_type[0]\n control_surface_deflection[0] = cs_deflection\n control_surface_chord[0] = 2 # m\n control_surface_hinge_coord[0] = 0.25\n\n # RIGHT FUSELAGE (Surface 0, Beam 0)\n we = 0\n wn = 0\n\n i_surf = 0\n airfoil_distribution[we:we + n_elem_fuselage] = 0\n surface_distribution[we:we + n_elem_fuselage] = i_surf\n surface_m[i_surf] = m\n\n aero_nodes[wn:wn + n_node_fuselage] = True\n\n temp_chord = np.linspace(self.c_fuselage, self.c_root, self.n_node_fuselage)\n temp_washout = washout_root\n\n # apply chord and elastic axis at each node\n node_counter = 0\n for ielem in range(we, we + n_elem_fuselage):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[ielem, i_local_node] = temp_chord[node_counter]\n elastic_axis[ielem, i_local_node] = main_ea_root\n twist[ielem, i_local_node] = -temp_washout\n\n we += n_elem_fuselage\n wn += n_node_fuselage\n\n # RIGHT WING (Surface 1, Beam 1)\n # surface_id\n i_surf = 1\n airfoil_distribution[we:we + n_elem_wing, :] = 0\n surface_distribution[we:we + n_elem_wing] = i_surf\n surface_m[i_surf] = m\n\n # specify aerodynamic characteristics of wing nodes\n aero_nodes[wn:wn + n_node_wing - 1] = True\n\n # linear taper initialisation\n temp_chord = np.linspace(c_root, taper_ratio * c_root, n_node_wing + 1)\n\n # linear wash out initialisation\n temp_washout = np.linspace(washout_root, washout_tip, n_node_wing + 1)\n\n # elastic axis variation\n temp_ea = np.linspace(main_ea_root, main_ea_tip, n_node_wing + 1)\n\n # apply chord and elastic axis at each node\n node_counter = 0\n for ielem in range(we, we + n_elem_wing):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[ielem, i_local_node] = temp_chord[node_counter]\n elastic_axis[ielem, i_local_node] = temp_ea[node_counter]\n twist[ielem, i_local_node] = -temp_washout[node_counter]\n if ielem >= round(((we + n_elem_wing) / 2)):\n control_surface[ielem, i_local_node] = 0\n\n # update working element and node\n we += n_elem_wing\n wn += n_node_wing - 1\n\n # LEFT FUSELAGE (Surface 2, Beam 2)\n i_surf = 2\n airfoil_distribution[we:we + n_elem_fuselage] = 0\n surface_distribution[we:we + n_elem_fuselage] = i_surf\n surface_m[i_surf] = m\n\n aero_nodes[wn:wn + n_node_fuselage] = True\n\n temp_chord = np.linspace(self.c_fuselage, self.c_root, self.n_node_fuselage)\n temp_washout = washout_root\n\n # apply chord and elastic axis at each node\n node_counter = 0\n for ielem in range(we, we + n_elem_fuselage):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[ielem, i_local_node] = temp_chord[node_counter]\n elastic_axis[ielem, i_local_node] = main_ea_root\n twist[ielem, i_local_node] = -temp_washout\n\n we += n_elem_fuselage\n wn += n_node_fuselage\n\n # LEFT WING (Surface 3, Beam 3)\n i_surf = 3\n airfoil_distribution[we:we + n_elem_wing, :] = 0\n surface_distribution[we: we + n_elem_wing] = i_surf\n surface_m[i_surf] = m\n\n # linear taper initialisation\n temp_chord = np.linspace(c_root, taper_ratio * c_root, n_node_wing + 1)\n\n # linear wash out initialisation\n temp_washout = np.linspace(washout_root, washout_tip, n_node_wing + 1)\n\n # specify aerodynamic characterisics of wing nodes\n aero_nodes[wn:wn + n_node_wing] = True\n\n # linear taper initialisation\n # apply chord and elastic axis at each node\n node_counter = 0\n for ielem in range(we, we + n_elem_wing):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[ielem, i_local_node] = temp_chord[node_counter]\n elastic_axis[ielem, i_local_node] = temp_ea[node_counter]\n twist[ielem, i_local_node] = -temp_washout[node_counter]\n if ielem >= round((we + n_elem_wing / 2)):\n control_surface[ielem, i_local_node] = 0\n\n # update working element and node\n we += n_elem_wing\n wn += n_node_wing\n\n # end node is the middle node\n mid_chord = np.array(chord[:, 1], copy=True)\n chord[:, 1] = chord[:, 2]\n chord[:, 2] = mid_chord\n\n mid_ea = np.array(elastic_axis[:, 1], copy=True)\n elastic_axis[:, 1] = elastic_axis[:, 2]\n elastic_axis[:, 2] = mid_ea\n\n # Update aerodynamic attributes of class\n self.chord = chord\n self.twist = twist\n self.aero_nodes = aero_nodes\n self.elastic_axis = elastic_axis\n self.control_surface = control_surface\n\n def generate_aero_file(self, route=None, case_name=None):\n \"\"\"\n Generates the ``.aero.h5`` file with the aerodynamic properties of the wing\n\n Args:\n route (str): route to write case file. If None is specified the default will be used\n case_name (str): name of file. If None is specified the default will be used\n\n \"\"\"\n\n if not route:\n route = self.case_route\n\n if not case_name:\n case_name = self.case_name\n\n if not os.path.isdir(self.case_route):\n os.makedirs(self.case_route)\n\n chord = self.chord\n twist = self.twist\n airfoil_distribution = self.airfoil_distribution\n surface_distribution = self.surface_distribution\n surface_m = self.surface_m\n m_distribution = self.m_distribution\n aero_nodes = self.aero_nodes\n elastic_axis = self.elastic_axis\n control_surface = self.control_surface\n control_surface_deflection = self.control_surface_deflection\n control_surface_chord = self.control_surface_chord\n control_surface_hinge_coord = self.control_surface_hinge_coord\n control_surface_type = self.control_surface_type\n\n control_surface_deflection[0] = self.cs_deflection\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n geo_utils.generate_naca_camber(P=0, M=0)))\n naca_airfoil_tail = airfoils_group.create_dataset('1', data=np.column_stack(\n geo_utils.generate_naca_camber(P=0, M=0)))\n naca_airfoil_fin = airfoils_group.create_dataset('2', data=np.column_stack(\n geo_utils.generate_naca_camber(P=0, M=0)))\n\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input.attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution',\n data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_nodes)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n control_surface_input = h5file.create_dataset('control_surface', data=control_surface)\n control_surface_deflection_input = h5file.create_dataset('control_surface_deflection',\n data=control_surface_deflection)\n control_surface_chord_input = h5file.create_dataset('control_surface_chord', data=control_surface_chord)\n control_surface_hinge_coord_input = h5file.create_dataset('control_surface_hinge_coord',\n data=control_surface_hinge_coord)\n control_surface_types_input = h5file.create_dataset('control_surface_type', data=control_surface_type)\n\n def set_default_config_dict(self, route=None, case_name=None):\n \"\"\"\n Generates default solver configuration file\n Returns:\n\n \"\"\"\n\n if not route:\n route = self.case_route\n\n if not case_name:\n case_name = self.case_name\n\n u_inf = self.u_inf\n rho = self.rho\n dt = self.dt\n tolerance = self.tolerance\n alpha = self.alpha\n beta = self.beta\n thrust = self.thrust\n thrust_nodes = self.thrust_nodes\n cs_deflection = self.cs_deflection\n fsi_tolerance = self.fsi_tolerance\n n_tstep = self.n_tstep\n gust_intensity = self.gust_intensity\n relaxation_factor = self.relaxation_factor\n\n file_name = route + '/' + case_name + '.sharpy'\n\n settings = dict()\n settings['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'Modal',\n 'AerogridPlot',\n 'BeamPlot',\n 'SaveData'],\n 'write_screen': 'on',\n 'write_log': 'on',\n 'log_folder': route + '/output/' + case_name + '/',\n 'log_file': case_name + '.log'}\n\n settings['BeamLoader'] = {'unsteady': 'off',\n 'orientation': algebra.euler2quat(np.array([self.roll,\n self.alpha,\n self.beta]))}\n\n settings['StaticUvlm'] = {'print_info': 'on',\n 'horseshoe': self.horseshoe,\n 'num_cores': 4,\n 'n_rollup': 1,\n 'rollup_dt': dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho}\n\n settings['StaticCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 200,\n 'num_load_steps': 1,\n 'delta_curved': 1e-5,\n 'min_delta': tolerance,\n 'gravity_on': 'on',\n 'gravity': 9.81},\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {'print_info': 'on',\n 'horseshoe': self.horseshoe,\n 'num_cores': 4,\n 'n_rollup': int(0),\n 'rollup_dt': dt, #self.c_root / self.M / self.u_inf,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho},\n 'max_iter': 200,\n 'n_load_steps': 1,\n 'tolerance': tolerance,\n 'relaxation_factor': 0.2}\n\n if self.horseshoe is True:\n settings['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 1,\n 'freestream_dir': ['1', '0', '0'],\n 'control_surface_deflection': ['']}\n else:\n settings['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': int(self.M * self.Mstarfactor),\n 'freestream_dir': ['1', '0', '0'],\n 'control_surface_deflection': ['']}\n\n settings['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-8,\n 'min_delta': tolerance,\n 'gravity_on': True,\n 'gravity': 9.81}\n\n settings['StaticTrim'] = {'solver': 'StaticCoupled',\n 'solver_settings': settings['StaticCoupled'],\n 'thrust_nodes': thrust_nodes,\n 'initial_alpha': alpha,\n 'initial_deflection': cs_deflection,\n 'initial_thrust': thrust,\n 'max_iter': 200,\n 'fz_tolerance': 1e-2,\n 'fx_tolerance': 1e-2,\n 'm_tolerance': 1e-2}\n\n settings['Trim'] = {'solver': 'StaticCoupled',\n 'solver_settings': settings['StaticCoupled'],\n 'initial_alpha': alpha,\n 'initial_beta': beta,\n 'cs_indices': [0],\n 'initial_cs_deflection': [cs_deflection],\n 'thrust_nodes': thrust_nodes,\n 'initial_thrust': [thrust, thrust]}\n\n settings['NonLinearDynamicCoupledStep'] = {'print_info': 'off',\n 'initial_velocity_direction': [-1., 0., 0.],\n 'max_iterations': 950,\n 'delta_curved': 1e-6,\n 'min_delta': tolerance,\n 'newmark_damp': 5e-3,\n 'gravity_on': True,\n 'gravity': 9.81,\n 'num_steps': n_tstep,\n 'dt': dt,\n 'initial_velocity': u_inf * 1}\n\n settings['NonLinearDynamicPrescribedStep'] = {'print_info': 'on',\n 'initial_velocity_direction': [-1., 0., 0.],\n 'max_iterations': 950,\n 'delta_curved': 1e-6,\n 'min_delta': self.tolerance,\n 'newmark_damp': 5e-3,\n 'gravity_on': True,\n 'gravity': 9.81,\n 'num_steps': self.n_tstep,\n 'dt': self.dt}\n\n settings['StepLinearUVLM'] = {'dt': self.dt,\n 'integr_order': 1,\n 'remove_predictor': True,\n 'use_sparse': True,\n 'velocity_field_generator': 'GustVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0., 0.],\n 'gust_shape': '1-cos',\n 'gust_length': 1.,\n 'gust_intensity': self.gust_intensity * u_inf,\n 'offset': 30.,\n 'span': self.span}}\n\n settings['StepUvlm'] = {'print_info': 'on',\n 'horseshoe': self.horseshoe,\n 'num_cores': 4,\n 'n_rollup': 1,\n 'convection_scheme': self.wake_type,\n 'rollup_dt': dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'GustVelocityField',\n 'velocity_field_input': {'u_inf': u_inf * 0,\n 'u_inf_direction': [1., 0, 0],\n 'gust_shape': '1-cos',\n 'gust_length': 5.,\n 'gust_intensity': gust_intensity * u_inf,\n 'offset': 15.0,\n 'span': self.span,\n 'relative_motion': True},\n # 'velocity_field_generator': 'SteadyVelocityField',\n # 'velocity_field_input': {'u_inf': u_inf*1,\n # 'u_inf_direction': [1., 0., 0.]},\n 'rho': rho,\n 'n_time_steps': n_tstep,\n 'dt': dt,\n 'gamma_dot_filtering': 3}\n\n settings['DynamicCoupled'] = {'print_info': 'on',\n # 'structural_substeps': 1,\n # 'dynamic_relaxation': 'on',\n # 'clean_up_previous_solution': 'on',\n 'structural_solver': 'NonLinearDynamicCoupledStep',\n 'structural_solver_settings': settings['NonLinearDynamicCoupledStep'],\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'fsi_substeps': 200,\n 'fsi_tolerance': fsi_tolerance,\n 'relaxation_factor': relaxation_factor,\n 'minimum_steps': 1,\n 'relaxation_steps': 150,\n 'final_relaxation_factor': 0.5,\n 'n_time_steps': n_tstep,\n 'dt': dt,\n 'include_unsteady_force_contribution': 'off',\n 'postprocessors': ['BeamLoads', 'StallCheck', 'BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'BeamLoads': {'csv_output': 'off'},\n 'StallCheck': {'output_degrees': True,\n 'stall_angles': {\n '0': [-12 * np.pi / 180,\n 6 * np.pi / 180],\n '1': [-12 * np.pi / 180,\n 6 * np.pi / 180],\n '2': [-12 * np.pi / 180,\n 6 * np.pi / 180]}},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'},\n 'AerogridPlot': {\n 'u_inf': u_inf,\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n # 'WriteVariablesTime': {\n # # 'delimeter': ',',\n # # 'structure_nodes': [0],\n # # 'structure_variables': ['Z']\n # # settings['WriteVariablesTime'] = {'delimiter': ' ',\n # 'FoR_variables': ['GFoR_pos', 'GFoR_vel', 'GFoR_acc'],\n # 'FoR_number': [],\n # 'structure_variables': ['AFoR_steady_forces', 'AFoR_unsteady_forces','AFoR_position'],\n # 'structure_nodes': [0,-1],\n # 'aero_panels_variables': ['gamma', 'gamma_dot'],\n # 'aero_panels_isurf': [0,1,2],\n # 'aero_panels_im': [1,1,1],\n # 'aero_panels_in': [-2,-2,-2],\n # 'aero_nodes_variables': ['GFoR_steady_force', 'GFoR_unsteady_force'],\n # 'aero_nodes_isurf': [0,1,2],\n # 'aero_nodes_im': [1,1,1],\n # 'aero_nodes_in': [-2,-2,-2]\n # }}}\n }}\n\n settings['Modal'] = {'print_info': True,\n 'use_undamped_modes': True,\n 'NumLambda': 30,\n 'rigid_body_modes': True,\n 'write_modes_vtk': 'on',\n 'print_matrices': 'on',\n 'save_data': 'on',\n 'continuous_eigenvalues': 'off',\n 'dt': dt,\n 'plot_eigenvalues': False}\n\n settings['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n 'linear_system_settings': {\n 'beam_settings': {'modal_projection': False,\n 'inout_coords': 'nodes',\n 'discrete_time': True,\n 'newmark_damp': 0.5,\n 'discr_method': 'newmark',\n 'dt': dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'off',\n 'num_modes': 40,\n 'print_info': 'on',\n 'gravity': 'on',\n 'remove_dofs': []},\n 'aero_settings': {'dt': dt,\n 'integr_order': 2,\n 'density': rho,\n 'remove_predictor': False,\n 'use_sparse': True,\n 'rigid_body_motion': True,\n 'use_euler': False,\n 'remove_inputs': ['u_gust']},\n 'rigid_body_motion': True}}\n\n settings['AsymptoticStability'] = {'sys_id': 'LinearAeroelastic',\n 'print_info': 'on',\n 'display_root_locus':'off',\n 'frequency_cutoff': 0,\n 'export_eigenvalues': 'on',\n 'num_evals':100}\n\n settings['LinDynamicSim'] = {'dt': dt,\n 'n_tsteps': self.n_tstep,\n 'sys_id': 'LinearAeroelastic',\n 'postprocessors': ['BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'AerogridPlot': {\n 'u_inf': u_inf,\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'}}}\n\n settings['AerogridPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0,\n 'u_inf': u_inf\n }\n settings['AeroForcesCalculator'] = {'write_text_file': 'off',\n 'text_file_name': case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n 'unsteady': 'off',\n 'coefficients': True,\n 'q_ref': 0.5 * rho * u_inf ** 2,\n 'S_ref': self.planform_area()\n }\n settings['BeamPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'include_FoR': 'on'}\n\n settings['BeamLoads'] = {'csv_output': 'off'}\n\n settings['SaveData'] = {'save_aero': 'on',\n 'save_structure': 'on',\n 'save_linear': 'off'}\n\n settings['StabilityDerivatives'] = {'u_inf': self.u_inf,\n 'S_ref': 12.809,\n 'b_ref': self.span,\n 'c_ref': 0.719}\n\n config = configobj.ConfigObj()\n config.filename = file_name\n for k, v in settings.items():\n config[k] = v\n config.write()\n self.settings = settings\n\n self.config = config\n\nif __name__=='__main__':\n\n ws = HortenWing(M=4,\n N=11,\n Mstarfactor=5,\n u_inf=28,\n rho=1.225,\n alpha_deg=4)\n" }, { "path": "sharpy/cases/hangar/richards_wing.py", "content": "\"\"\"\nSimple Horten Wing as used by Richards. Baseline and simplified models\n\nRichards, P. W., Yao, Y., Herd, R. A., Hodges, D. H., & Mardanpour, P. (2016). Effect of Inertial and Constitutive\nProperties on Body-Freedom Flutter for Flying Wings. Journal of Aircraft. https://doi.org/10.2514/1.C033435\n\"\"\"\nimport numpy as np\nfrom sharpy.cases.hangar.horten_wing import HortenWing\nimport sharpy.utils.algebra as algebra\n\n\nclass Baseline(HortenWing):\n\n def set_properties(self):\n\n # Wing geometry\n self.span = 20.0 # [m]\n self.sweep_LE = 20 * np.pi / 180 # [rad] Leading Edge Sweep\n self.c_root = 1.0 # [m] Root chord - Richards\n self.taper_ratio = 0.25 # Richards\n self.thrust_nodes = [self.n_node_fuselage - 1,\n self.n_node_fuselage + self.n_node_wing + 1]\n\n self.loc_cg = 0.45 # CG position wrt to LE (from sectional analysis)\n # EA is the reference in NATASHA - defined with respect to the midchord. SHARPy is wrt to LE and as a pct of\n # local chord\n self.main_ea_root = 0.33\n self.main_ea_tip = 0.33\n self.n_mass = 2 * self.n_elem_wing\n\n # FUSELAGE GEOMETRY\n self.fuselage_width = 1.65/2\n self.c_fuselage = self.c_root\n\n # WASH OUT\n self.washout_root = 0*np.pi/180\n self.washout_tip = -2 * np.pi / 180\n\n # Horseshoe wake\n self.horseshoe = False\n self.wake_type = 2\n self.dt_factor = 1\n self.dt = 1 / self.M / self.u_inf * self.dt_factor\n\n # Dynamics\n self.n_tstep = int(self.physical_time/self.dt)\n self.gust_intensity = 0.1\n\n # Numerics\n self.tolerance = 1e-12\n self.fsi_tolerance = 1e-10\n self.relaxation_factor = 0.2\n\n def update_mass_stiffness(self, sigma=1., sigma_mass=1., payload=0):\n \"\"\"\n Sets the mass and stiffness properties of the default wing\n\n Returns:\n\n \"\"\"\n\n n_elem_fuselage = self.n_elem_fuselage\n n_elem_wing = self.n_elem_wing\n n_node_wing = self.n_node_wing\n n_node_fuselage = self.n_node_fuselage\n c_root = self.c_root\n taper_ratio = self.taper_ratio\n\n # Local chord to root chord initialisation\n c_bar_temp = np.linspace(c_root, taper_ratio * c_root, n_elem_wing)\n\n # Structural properties at the wing root section from Richards 2016\n ea = 1e6\n ga = 1e6\n gj = 4.24e5\n eiy = 3.84e5\n eiz = 2.46e7\n\n root_i_beam = IBeam()\n root_i_beam.build(c_root)\n root_i_beam.rotation_axes = np.array([0, self.main_ea_root-0.25, 0])\n\n root_airfoil = Airfoil()\n root_airfoil.build(c_root)\n root_i_beam.rotation_axes = np.array([0, self.main_ea_root-0.25, 0])\n\n mu_0 = root_i_beam.mass + root_airfoil.mass\n j_xx = root_i_beam.ixx + root_airfoil.ixx\n j_yy = root_i_beam.iyy + root_airfoil.iyy\n j_zz = root_i_beam.izz + root_airfoil.izz\n\n # Number of stiffnesses used\n n_stiffness = self.n_stiffness\n\n # Initialise the stiffness database\n base_stiffness = self.base_stiffness\n\n stiffness_root = sigma * np.diag([ea, ga, ga, gj, eiy, eiz])\n stiffness_tip = taper_ratio ** 2 * stiffness_root\n\n # Assume a linear variation in the stiffness. Richards et al. use VABS on the linearly tapered wing to find the\n # spanwise properties\n alpha = np.linspace(0, 1, self.n_elem_wing)\n for i_elem in range(0, self.n_elem_wing):\n base_stiffness[i_elem + 1, :, :] = stiffness_root*(1-alpha[i_elem]**2) + stiffness_tip*alpha[i_elem]**2\n base_stiffness[0] = base_stiffness[1]\n\n # Mass variation along the span\n # Right wing centre of mass - wrt to 0.25c\n cm = (root_airfoil.centre_mass * root_airfoil.mass + root_i_beam.centre_mass * root_i_beam.mass) \\\n / np.sum(root_airfoil.mass + root_i_beam.mass)\n cg = np.array([0, -(cm[0] + 0.25 * self.c_root - self.main_ea_root), 0]) * 1\n n_mass = self.n_mass\n # sigma_mass = 1.25\n\n # Initialise database\n base_mass = self.base_mass\n\n mass_root_right = np.diag([mu_0, mu_0, mu_0, j_xx, j_yy, j_zz]) * sigma_mass\n mass_root_right[:3, -3:] = -algebra.skew(cg) * mu_0\n mass_root_right[-3:, :3] = algebra.skew(cg) * mu_0\n\n mass_root_left = np.diag([mu_0, mu_0, mu_0, j_xx, j_yy, j_zz]) * sigma_mass\n mass_root_left[:3, -3:] = -algebra.skew(-cg) * mu_0\n mass_root_left[-3:, :3] = algebra.skew(-cg) * mu_0\n\n mass_tip_right = taper_ratio * mass_root_right\n mass_tip_left = taper_ratio * mass_root_left\n\n ixx_dummy = []\n iyy_dummy = []\n izz_dummy = []\n\n for i_elem in range(self.n_elem_wing):\n # Create full cross section\n c_bar = self.c_root * ((1-alpha[i_elem]) + self.taper_ratio * alpha[i_elem])\n x_section = WingCrossSection(c_bar)\n # print(i_elem)\n # print('Section Mass: %.2f ' %x_section.mass)\n # print('Linear Mass: %.2f' % (mu_0 * (1-alpha[i_elem]) + mu_0 * self.taper_ratio * alpha[i_elem]))\n # print('Section Ixx: %.4f' % x_section.ixx)\n # print('Section Iyy: %.4f' % x_section.iyy)\n # print('Section Izz: %.4f' % x_section.izz)\n # print('Linear Ixx: %.2f' % (j_xx * (1-alpha[i_elem]) + j_xx * self.taper_ratio * alpha[i_elem]))\n # base_mass[i_elem, :, :] = mass_root_right*(1-alpha[i_elem]) + mass_tip_right*alpha[i_elem]\n # base_mass[i_elem + self.n_elem_wing + self.n_elem_fuselage - 1] = mass_root_left*(1-alpha[i_elem]) + mass_tip_left*alpha[i_elem]\n\n base_mass[i_elem, :, :] = np.diag([x_section.mass, x_section.mass, x_section.mass,\n x_section.ixx, x_section.iyy, x_section.izz])\n cg = np.array([0, -(x_section.centre_mass[0] + (0.25 - self.main_ea_root) * c_bar / self.c_root), 0]) * 1\n base_mass[i_elem, :3, -3:] = -algebra.skew(cg) * x_section.mass\n base_mass[i_elem, -3:, :3] = algebra.skew(cg) * x_section.mass\n\n base_mass[i_elem + self.n_elem_wing + self.n_elem_fuselage - 1, :, :] = np.diag([x_section.mass, x_section.mass, x_section.mass,\n x_section.ixx, x_section.iyy, x_section.izz])\n cg = np.array([0, -(x_section.centre_mass[0] + (0.25 - self.main_ea_root) * c_bar / self.c_root), 0]) * 1\n base_mass[i_elem + self.n_elem_wing + self.n_elem_fuselage - 1, :3, -3:] = -algebra.skew(-cg) * x_section.mass\n base_mass[i_elem + self.n_elem_wing + self.n_elem_fuselage - 1, -3:, :3] = algebra.skew(-cg) * x_section.mass\n\n ixx_dummy.append(x_section.ixx)\n iyy_dummy.append(x_section.iyy)\n izz_dummy.append(x_section.izz)\n\n # for item in x_section.items:\n # plt.plot(item.y, item.z)\n # plt.scatter(x_section.centre_mass[0], x_section.centre_mass[1])\n # plt.show()\n # print(x_section.centre_mass)\n # print(cg)\n\n # plt.plot(range(self.n_elem_wing), ixx_dummy)\n # plt.plot(range(self.n_elem_wing), iyy_dummy)\n # plt.plot(range(self.n_elem_wing), izz_dummy)\n # plt.show()\n # Lumped mass initialisation\n lumped_mass_nodes = self.lumped_mass_nodes\n lumped_mass = self.lumped_mass\n lumped_mass_inertia = self.lumped_mass_inertia\n lumped_mass_position = self.lumped_mass_position\n\n # Lumped masses nodal position\n # 0 - Right engine\n # 1 - Left engine\n # 2 - Fuselage\n lumped_mass_nodes[0] = 2\n lumped_mass_nodes[1] = n_node_fuselage + n_node_wing + 1\n lumped_mass_nodes[2] = 0\n\n # Lumped mass value from Richards 2013\n lumped_mass[0:2] = 51.445 / 9.81\n lumped_mass[2] = 150 / 9.81 + payload\n # lumped_mass_position[2] = [0, 0, -10.]\n\n # Lumped mass inertia\n lumped_mass_inertia[0, :, :] = np.diag([0.29547, 0.29322, 0.29547])\n lumped_mass_inertia[1, :, :] = np.diag([0.29547, 0.29322, 0.29547])\n lumped_mass_inertia[2, :, :] = np.diag([0.5, 1, 1]) * lumped_mass[2]\n\n # Define class attributes\n self.lumped_mass = lumped_mass * 1\n self.lumped_mass_nodes = lumped_mass_nodes * 1\n self.lumped_mass_inertia = lumped_mass_inertia * 1\n self.lumped_mass_position = lumped_mass_position * 1\n\n self.base_stiffness = base_stiffness\n self.base_mass = base_mass\n\n\nclass CrossSection(object):\n def __init__(self):\n self.rho = 2770\n\n self.rotation_axes = np.array([0, 0.33-0.25, 0])\n\n self.y = np.ndarray((2,))\n self.z = np.ndarray((2,))\n self.t = np.ndarray((2,))\n\n @property\n def mass(self):\n \"\"\"\n Mass of the I beam per unit length\n \"\"\"\n return np.sum(self.t * self.elem_length) * self.rho\n\n @property\n def ixx(self):\n ixx_ = np.sum(self.elem_length * self.t * self.rho * (self.elem_cm_y ** 2 + self.elem_cm_z ** 2))\n return ixx_ + self.mass * (self.centre_mass[0] - self.rotation_axes[1]) ** 2\n\n @property\n def elem_length(self):\n elem_length = np.sqrt(np.diff(self.y) ** 2 + np.diff(self.z) ** 2)\n return elem_length\n\n @property\n def elem_cm_y(self):\n elem_cm_y_ = np.ndarray((self.n_elem, ))\n elem_cm_y_[:] = 0.5 * (self.y[:-1] + self.y[1:])\n return elem_cm_y_\n\n @property\n def elem_cm_z(self):\n elem_cm_z_ = np.ndarray((self.n_elem, ))\n elem_cm_z_[:] = 0.5 * (self.z[:-1] + self.z[1:])\n return elem_cm_z_\n\n @property\n def centre_mass(self):\n y_cm = np.sum(self.elem_cm_y * self.elem_length) / np.sum(self.elem_length)\n z_cm = np.sum(self.elem_cm_z * self.elem_length) / np.sum(self.elem_length)\n\n return np.array([y_cm, z_cm])\n\n @property\n def iyy(self):\n x_dom = np.linspace(-0.5, 0.5, 100)\n x_cg = 0.5 * (x_dom[:-1].copy() + x_dom[1:].copy())\n dx = np.diff(x_dom)[0]\n iyy_ = 0\n for elem in range(len(self.elem_length)):\n z_cg = np.ones_like(x_cg) * self.elem_cm_z[elem]\n iyy_ += np.sum(self.elem_length[elem] * self.t[elem] * dx * self.rho * (x_cg ** 2 + z_cg ** 2))\n return iyy_ #np.sum(self.elem_length * self.t * self.rho * 1 * self.elem_cm_z ** 2)\n\n @property\n def izz(self):\n x_dom = np.linspace(-0.5, 0.5, 100)\n x_cg = 0.5 * (x_dom[:-1].copy() + x_dom[1:].copy())\n dx = np.diff(x_dom)[0]\n iyy_ = 0\n izz_ = 0\n for elem in range(len(self.elem_length)):\n y_cg = np.ones_like(x_cg) * self.elem_cm_y[elem]\n izz_ += np.sum(self.elem_length[elem] * self.t[elem] * dx * self.rho * (x_cg ** 2 + y_cg ** 2))\n return izz_ #np.sum(self.elem_length * self.t * self.rho * 1 * self.elem_cm_y ** 2)\n\n @property\n def n_node(self):\n return self.y.shape[0]\n\n @property\n def n_elem(self):\n return self.n_node - 1\n\n def build(self, y, z, t):\n self.y = y\n self.z = z\n self.t = t\n\n\nclass IBeam(CrossSection):\n\n def build(self, c_root):\n t_skin = 0.127e-2\n t_c = 0.12\n w_I = 10e-2 * c_root # Width of the Ibeam\n\n self.rho = 2770\n\n self.y = np.ndarray((self.n_node, ))\n self.z = np.ndarray((self.n_node, ))\n self.t = np.ndarray((self.n_node, ))\n\n z_max = t_c * c_root\n y = np.array([-w_I/2, w_I/2, 0, 0, -w_I/2, w_I/2])\n z = np.array([z_max/2, z_max/2, z_max/2, -z_max/2, -z_max/2, -z_max/2])\n t = np.array([t_skin, 0, t_skin, 0, t_skin])\n\n self.y = y\n self.z = z\n self.t = t\n\n\nclass Airfoil(CrossSection):\n\n def build(self, c_root):\n t_c = 0.12\n t_skin = 0.127e-2 * 1.5\n\n y_dom = np.linspace(0, c_root, 100)\n y = np.concatenate((y_dom, y_dom[:-1][::-1]))\n z_dom = 5 * t_c * (0.2969 * np.sqrt(y_dom/c_root) -\n 0.1260 * y_dom/c_root -\n 0.3516 * (y_dom/c_root) ** 2 +\n 0.2843 * (y_dom/c_root) ** 3 -\n 0.1015 * (y_dom/c_root) ** 4) * c_root\n z = np.concatenate((z_dom, -z_dom[:-1][::-1]))\n\n self.y = y - 0.25 * c_root\n self.z = z\n self.t = t_skin * np.ones(self.n_elem)\n\n\nclass WingCrossSection:\n\n def __init__(self, chord):\n self.chord = chord\n\n self.items = list()\n\n self.items.append(Airfoil())\n self.items.append(IBeam())\n\n for item in self.items:\n item.build(chord)\n\n @property\n def mass(self):\n return np.sum([item.mass for item in self.items])\n\n @property\n def centre_mass(self):\n y = np.sum([item.mass * item.centre_mass[0] for item in self.items]) / self.mass\n z = np.sum([item.mass * item.centre_mass[1] for item in self.items]) / self.mass\n return np.array([y, z])\n\n @property\n def ixx(self):\n return np.sum([item.ixx for item in self.items])\n\n @property\n def iyy(self):\n return np.sum([item.iyy for item in self.items])\n\n @property\n def izz(self):\n return np.sum([item.izz for item in self.items])\n\n\nif __name__ == '__main__':\n\n ws = Baseline(M=4,\n N=11,\n Mstarfactor=5,\n u_inf=28,\n rho=1.225,\n alpha_deg=4)\n\n # ws.clean_test_files()\n ws.update_mass_stiffness()\n ws.update_fem_prop()\n # ws.generate_fem_file()\n ws.update_aero_properties()\n # ws.generate_aero_file()\n # ws.set_default_config_dict()\n" }, { "path": "sharpy/cases/hangar/swept_flying_wing.py", "content": "\"\"\"\nGeneric Swept Flying Wing Class Generator\nN Goizueta Nov 18\n\"\"\"\n\nimport numpy as np\nimport os\nimport h5py as h5\nimport sharpy.utils.geo_utils as geo_utils\nimport sharpy.utils.algebra as algebra\nimport configobj\nimport scipy.linalg as sclalg\n\n\nclass SweptWing:\n \"\"\"\n Generic Swept Flying Wing Wing Class Generator\n\n A ``HortenWing`` class contains the basic geometry and properties of a simplified swept flying wing, as\n described by Simpson.\n\n This class allows the user to quickly obtain SHARPy cases for the purposes of parametric analyses.\n\n \"\"\"\n\n def __init__(self,\n M,\n N,\n Mstarfactor,\n u_inf,\n rho=1.225,\n alpha_deg=0.,\n beta_deg=0.,\n cs_deflection_deg=0.,\n thrust=5.,\n physical_time=10,\n case_name_format=0,\n case_remarks=None,\n case_route='./cases/',\n case_name='swf'):\n\n # Discretisation\n self.M = M\n self.N = N\n self.Mstarfactor = Mstarfactor\n\n self.n_node_elem = 3\n self.n_elem_wing = 11\n self.n_elem_fuselage = 0\n self.n_surfaces = 4\n\n # Case admin\n if case_name_format == 0:\n self.case_name = case_name + '_u_inf%.4d_a%.4d' % (int(u_inf), int(alpha_deg * 100))\n elif case_name_format == 1:\n self.case_name = case_name + '_u_inf%.4d' % int(u_inf*100)\n elif case_name_format == 2:\n self.case_name = case_name\n else:\n self.case_name = case_name + '_u_inf%.4d_%s' % (int(u_inf), case_remarks)\n\n self.case_route = os.path.abspath(case_route + self.case_name + '/')\n\n self.config = None\n\n # Flight conditions\n self.u_inf = u_inf\n self.rho = rho\n self.alpha = alpha_deg * np.pi / 180\n self.beta = beta_deg * np.pi / 180\n self.cs_deflection = cs_deflection_deg * np.pi / 180\n self.thrust = thrust\n\n # Compute number of nodes\n n_node = 0\n self.n_node_wing = self.n_elem_wing * (self.n_node_elem - 1)\n self.n_node_fuselage = self.n_elem_fuselage * self.n_node_elem\n n_node += 2 * self.n_node_wing + 1\n self.n_node = n_node\n\n # Compute number of elements\n self.n_elem = 2 * (self.n_elem_wing + self.n_elem_fuselage)\n\n # Wing geometry\n self.span = 8 # [m]\n self.sweep_LE = 20 * np.pi / 180 # [rad] Leading Edge Sweep\n self.c_root = 1.15 # [m] Root chord\n self.taper_ratio = 0.65 * self.c_root\n self.thrust_nodes = [self.n_node_fuselage + 2,\n self.n_node_fuselage + self.n_node_wing + 2]\n # self.thrust_nodes = [1]\n\n self.loc_cg = 0.45 # CG position wrt to LE (from sectional analysis)\n self.ea_offset_root = 0.13 # from Mardanpour\n self.ea_offset_tip = -1.644 * 0.0254\n self.main_ea_root = 0.25\n self.main_ea_tip = 0.25\n\n # FUSELAGE GEOMETRY\n self.fuselage_width = 0\n # self.fuselage_width = 0.8248\n # self.c_fuselage = 84*0.0254\n\n # WASH OUT\n self.washout_root = 0*np.pi/180\n self.washout_tip = -2 * np.pi / 180\n\n # Horseshoe wake\n self.horseshoe = False\n self.wake_type = 2\n self.dt_factor = 1\n self.dt = 1 / self.M / self.u_inf * self.dt_factor\n\n # Dynamics\n self.n_tstep = int(physical_time/self.dt)\n self.gust_intensity = 0.1\n\n # Numerics\n self.tolerance = 1e-12\n self.fsi_tolerance = 1e-10\n self.relaxation_factor = 0.2\n\n # H5 Variables initialisation as class attributes\n # coordinates\n self.x = np.zeros((n_node,))\n self.y = np.zeros((n_node,))\n self.z = np.zeros((n_node,))\n # beam number\n self.beam_number = np.zeros(self.n_elem, dtype=int)\n # frame of reference delta\n self.frame_of_reference_delta = np.zeros((self.n_elem, self.n_node_elem, 3))\n # connectivity of beams\n self.connectivities = np.zeros((self.n_elem, self.n_node_elem), dtype=int)\n # stiffness\n self.n_stiffness = self.n_elem_wing + self.n_elem_fuselage\n self.base_stiffness = np.zeros((self.n_stiffness, 6, 6))\n self.elem_stiffness = np.zeros((self.n_elem,), dtype=int)\n # mass\n self.n_mass = self.n_elem_wing\n self.base_mass = np.zeros((self.n_mass, 6, 6))\n self.elem_mass = np.zeros(self.n_elem, dtype=int)\n # boundary conditions\n self.boundary_conditions = np.zeros((n_node,), dtype=int)\n # applied forces\n self.app_forces = np.zeros((n_node, 6))\n self.n_lumped_mass = 3\n\n self.lumped_mass_nodes = np.zeros((self.n_lumped_mass), dtype=int)\n self.lumped_mass = np.zeros(self.n_lumped_mass)\n self.lumped_mass_inertia = np.zeros((self.n_lumped_mass, 3, 3))\n self.lumped_mass_position = np.zeros((self.n_lumped_mass, 3))\n\n # Aerodynamic properties\n # H5 AERO FILE VARIABLES INITIALISATION\n # airfoil distribution\n self.airfoil_distribution = np.zeros((self.n_elem, self.n_node_elem), dtype=int)\n # surface distribution\n self.surface_distribution = np.zeros((self.n_elem,), dtype=int) - 1\n self.surface_m = np.zeros((self.n_surfaces,), dtype=int)\n self.m_distribution = 'uniform'\n # aerodynamic nodes boolean\n self.aero_nodes = np.zeros((self.n_node,), dtype=bool)\n # aero twist\n self.twist = np.zeros((self.n_elem, self.n_node_elem))\n # chord\n self.chord = np.zeros((self.n_elem, self.n_node_elem))\n # elastic axis\n self.elastic_axis = np.zeros((self.n_elem, self.n_node_elem))\n\n # control surfaces attributes initialisation\n self.n_control_surfaces = 1\n self.control_surface = np.zeros((self.n_elem, self.n_node_elem), dtype=int) - 1\n self.control_surface_type = np.zeros((self.n_control_surfaces,), dtype=int)\n self.control_surface_deflection = np.zeros((self.n_control_surfaces,))\n self.control_surface_chord = np.zeros((self.n_control_surfaces,), dtype=int)\n self.control_surface_hinge_coord = np.zeros((self.n_control_surfaces,), dtype=float)\n\n self.settings = dict()\n\n def update_mass_stiffness(self, sigma=1.):\n r\"\"\"\n The mass and stiffness matrices are computed. Both vary over the span of the wing, hence a\n dictionary is created that acts as a database of the different properties along the wing.\n\n The variation of the stiffness is cubic along the span:\n\n .. math:: \\mathbf{K} = \\mathbf{K}_0\\bar{c}^3\n\n where :math:`\\mathbf{K}_0 is the stiffness of the wing root section and :math:`\\bar{c}` is\n the ratio between the local chord and the root chord.\n\n The variation of the sectional mass is quadratic along the span:\n\n .. math:: \\mu = \\mu_0\\,\\bar{c}^2\n\n where :math:`\\mu` is the mass per unit span and the zero subscript denotes the root value.\n\n The sectional inertia is varied linearly along the span, based on the information by Mardanpour 2013.\n\n Three lumped masses are included with the following properties (Richards, 2013)\n\n ===== ===== ================= ========= =============================== ============\n No Node Relative Position Mass [kg] Inertia [kg m^2] Description\n ===== ===== ================= ========= =============================== ============\n ``0`` ``2`` ``[0,0,0]`` ``5.24`` ``[0.29547, 0.29322, 0.29547]`` Right Engine\n ``1`` ``S`` ``[0,0,0]`` ``5.24`` ``[0.29547, 0.29322, 0.29547]`` Left Engine\n ``2`` ``0`` ``[0,0,0]`` ``15.29`` ``[0.5, 1.0, 1.0]*15.29`` Fuselage\n ===== ===== ================= ========= =============================== ============\n\n\n Args:\n sigma (float): stiffening factor\n\n Returns:\n\n \"\"\"\n\n n_elem_fuselage = self.n_elem_fuselage\n n_elem_wing = self.n_elem_wing\n n_node_wing = self.n_node_wing\n n_node_fuselage = self.n_node_fuselage\n c_root = self.c_root\n taper_ratio = self.taper_ratio\n\n # Local chord to root chord initialisation\n c_bar_temp = np.linspace(c_root, taper_ratio * c_root, n_elem_wing)\n\n # Structural properties at the wing root section from Richards 2016\n ea = 1e7\n ga = 1e9\n gj = 7.5e4\n eiy = 4.5e4\n eiz = 2.4e6\n\n ea_t = 1e7\n ga_t = 1e9\n gj_t = 3e4\n eiy_t = 2e4\n eiz_t = 1e6\n\n # Sectional mass from Richards 2016\n mu_r = 15\n mu_t = 2\n j_r = 0.5\n j_t = 0.1\n\n # Number of stiffnesses used\n n_stiffness = self.n_stiffness\n\n # Initialise the stiffness database\n base_stiffness = self.base_stiffness\n\n # Wing root section stiffness properties\n stiffness_root = sigma * np.diag([ea, ga, ga, gj, eiy, eiz])\n stiffness_tip = sigma * np.diag([ea_t, ga_t, ga_t, gj_t, eiy_t, eiz_t])\n\n # Linear variation between root and tip\n alpha = np.linspace(0, 1, self.n_elem_wing)\n for i_elem in range(0, self.n_elem_wing):\n base_stiffness[i_elem, :, :] = stiffness_root*(1-alpha[i_elem]) + stiffness_tip*alpha[i_elem]\n\n # Mass variation along the span\n n_mass = self.n_mass\n sigma_mass = 1\n\n # Initialise database\n base_mass = self.base_mass\n\n chi_root = np.array([0, 5.29, 0*-0.594]) * 0\n m_root = np.eye(3) * mu_r\n j_root = np.array([[j_r, 0., 0.],\n [0., j_r, 0.],\n [0., 0., 2*j_r]])\n\n mass_root = sclalg.block_diag(m_root, j_root)\n mass_root[:3, -3:] = -mu_r * algebra.skew(chi_root)\n mass_root[-3:, :3] = mu_r * algebra.skew(chi_root)\n\n chi_tip = chi_root # np.array([0, -1.644, -0.563])\n j_tip = np.array([[j_t, 0.00000000e+00, 0.00000000e+00],\n [0.00000000e+00, j_t, 0.00000000e+00],\n [0.00000000e+00, 0.00000000e+00, 2*j_t]])\n mass_tip = sclalg.block_diag(np.diag([mu_t, mu_t, mu_t]), j_tip)\n mass_tip[:3, -3:] += -algebra.skew(chi_tip) * mu_t\n mass_tip[-3:, :3] += -algebra.skew(chi_tip) * mu_t\n\n for i_elem in range(self.n_elem_wing):\n base_mass[i_elem, :, :] = mass_root*(1-alpha[i_elem]) + mass_tip*alpha[i_elem]\n\n # Lumped mass initialisation\n # 0 - Right engine\n # 1 - Left engine\n\n lumped_mass_nodes = self.lumped_mass_nodes\n lumped_mass = self.lumped_mass\n lumped_mass_inertia = self.lumped_mass_inertia\n lumped_mass_position = self.lumped_mass_position\n\n # Lumped masses nodal position\n lumped_mass_nodes[0] = 2\n lumped_mass_nodes[1] = n_node_fuselage + n_node_wing + 2\n\n # Engine mass\n lumped_mass[0:2] = 40\n lumped_mass_inertia[0, :, :] = np.diag([5, 5, 5])\n lumped_mass_inertia[1, :, :] = np.diag([5, 5, 5])\n\n lumped_mass_position[0] = np.array([0, -0.1, 0])\n lumped_mass_position[1] = np.array([0, 0.1, 0])\n\n # Define class attributes\n self.lumped_mass = lumped_mass\n self.lumped_mass_nodes = lumped_mass_nodes\n self.lumped_mass_inertia = lumped_mass_inertia\n self.lumped_mass_position = lumped_mass_position\n\n self.base_stiffness = base_stiffness\n self.base_mass = base_mass\n\n def update_fem_prop(self):\n \"\"\"\n Computes the FEM properties prior to analysis such as the connectivity matrix, coordinates, etc\n\n Returns:\n\n \"\"\"\n # Obtain class attributes\n n_node_elem = self.n_node_elem\n n_elem = self.n_elem\n n_elem_wing = self.n_elem_wing\n n_elem_fuselage = self.n_elem_fuselage\n n_node = self.n_node\n n_node_wing = self.n_node_wing\n n_node_fuselage = self.n_node_fuselage\n fuselage_width = self.fuselage_width\n thrust = self.thrust\n thrust_nodes = self.thrust_nodes\n span = self.span\n sweep_LE = self.sweep_LE\n\n # mass and stiffness matrices\n stiffness = self.base_stiffness\n mass = self.base_mass\n n_stiffness = stiffness.shape[0]\n n_mass = mass.shape[0]\n\n # H5 FEM FILE VARIABLES INITIALISATION\n # coordinates\n x = np.zeros((n_node,))\n y = np.zeros((n_node,))\n z = np.zeros((n_node,))\n # twist\n structural_twist = np.zeros_like(x)\n # beam number\n beam_number = np.zeros(n_elem, dtype=int)\n # frame of reference delta\n frame_of_reference_delta = np.zeros((n_elem, n_node_elem, 3))\n # connectivity of beams\n conn = np.zeros((n_elem, n_node_elem), dtype=int)\n # stiffness\n stiffness = np.zeros((n_stiffness, 6, 6))\n elem_stiffness = np.zeros((n_elem,), dtype=int)\n # mass\n mass = np.zeros((n_mass, 6, 6))\n elem_mass = np.zeros(n_elem, dtype=int)\n # boundary conditions\n boundary_conditions = np.zeros((n_node,), dtype=int)\n # applied forces\n app_forces = np.zeros((n_node, 6))\n\n # assemble connectivites\n # worked elements\n we = 0\n # worked nodes\n wn = 0\n\n # # RIGHT RIGID FUSELAGE\n # beam_number[we:we + 1] = 0\n # # coordinates\n # x[wn:wn + n_node_fuselage] = 0\n # y[wn:wn + n_node_fuselage] = np.linspace(0, fuselage_width / 2, n_node_fuselage)\n #\n # # connectivities\n # elem_mass[0] = 0\n # conn[we, :] = [0, 2, 1]\n #\n # # frame of reference change\n # frame_of_reference_delta[0, 0, :] = [-1.0, 0.0, 0.0]\n # frame_of_reference_delta[0, 1, :] = [-1.0, 0.0, 0.0]\n # frame_of_reference_delta[0, 2, :] = [-1.0, 0.0, 0.0]\n #\n # # element stiffness\n # elem_stiffness[0] = 0\n # elem_mass[0] = 0\n #\n # # boundary conditions\n # boundary_conditions[0] = 1\n #\n # # applied forces - engine 1\n # app_forces[thrust_nodes[0]] = [0, thrust, 0,\n # 0, 0, 0]\n #\n # # updated worked nodes and elements\n # we += n_elem_fuselage\n # wn += n_node_fuselage\n\n # RIGHT WING\n beam_number[we:we + n_elem_wing] = 0\n # y coordinate (positive right)\n y[wn:wn + n_node_wing + 1] = np.linspace(0,\n span / 2,\n n_node_wing + 1)\n x[wn:wn + n_node_wing + 1] = y[wn:wn + n_node_wing + 1] * np.tan(sweep_LE)\n\n # connectivities\n for ielem in range(n_elem_wing):\n conn[we + ielem, :] = (np.ones(n_node_elem) * (we + ielem) * (n_node_elem - 1) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n\n elem_mass[we + ielem] = ielem\n elem_stiffness[we + ielem] = ielem\n\n # element stiffness and mass\n # elem_stiffness[we:we+n_elem_wing] = 0\n # elem_mass[we:we+n_elem_wing] = 0\n\n # boundary conditions of free end\n boundary_conditions[wn + n_node_wing - 1] = -1\n # Clamped end\n boundary_conditions[0] = 1\n\n # applied forces - engine 1\n app_forces[thrust_nodes[0]] = [-thrust * np.sin(sweep_LE), thrust * np.cos(sweep_LE), 0,\n 0, 0, 0]\n\n # update worked elements and nodes\n we += n_elem_wing\n wn += n_node_wing + 1\n\n # # LEFT FUSELAGE\n # beam_number[we:we + n_elem_fuselage] = 2\n # # coordinates\n # y[wn:wn + n_node_fuselage - 1] = np.linspace(0,\n # -fuselage_width / 2,\n # n_node_fuselage)[1:]\n # x[wn:wn + n_node_fuselage - 1] = 0\n #\n # # connectivity\n # conn[we, :] = [0, wn + 1, wn]\n #\n # # frame of reference delta\n # for ielem in range(n_elem_fuselage):\n # for inode in range(n_node_elem):\n # frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n #\n # # element stiffness and mass\n # elem_stiffness[we:we + n_elem_fuselage] = 0\n # elem_mass[we:we + n_elem_fuselage] = 0\n #\n # # applied forces - engine 2\n # app_forces[thrust_nodes[1]] = [0, -thrust, 0,\n # 0, 0, 0]\n #\n # # update worked elements and nodes\n # we += n_elem_fuselage\n # wn += n_node_fuselage - 1\n\n # LEFT WING\n # coordinates\n beam_number[we:we + n_elem_wing] = 1\n y[wn:wn + n_node_wing] = np.linspace(0,\n -span / 2,\n n_node_wing + 1)[1:]\n x[wn:wn + n_node_wing] = -1 * y[wn:wn + n_node_wing] * np.tan(sweep_LE)\n\n # left wing connectivities\n for ielem in range(n_elem_wing):\n conn[we + ielem, :] = np.ones(n_node_elem) * (we + ielem) * (n_node_elem - 1) + [0, 2, 1]\n\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n\n elem_mass[we + ielem] = ielem\n elem_stiffness[we + ielem] = ielem\n\n # element stiffness and mass\n # elem_stiffness[we:we+n_node_wing] = 0\n conn[we, 0] = 0\n\n # boundary conditions at the free end\n boundary_conditions[wn + n_node_wing - 1] = -1\n\n # applied forces - engine 2\n app_forces[thrust_nodes[1]] = [-thrust * np.sin(sweep_LE), -thrust * np.cos(sweep_LE), 0,\n 0, 0, 0]\n\n # update worked elements and nodes\n we += n_elem_wing\n wn += n_node_wing\n\n # set attributes\n self.x = x\n self.y = y\n self.z = z\n self.connectivities = conn\n self.elem_stiffness = elem_stiffness\n self.elem_mass = elem_mass\n self.frame_of_reference_delta = frame_of_reference_delta\n self.boundary_conditions = boundary_conditions\n self.beam_number = beam_number\n self.app_forces = app_forces\n\n def generate_fem_file(self):\n \"\"\"\n Generates the ``.fem.h5`` folder containing the structural information of the problem\n\n The file is written to ``self.case_route / self.case_name .fem.h5``\n\n \"\"\"\n\n if not os.path.exists(self.case_route):\n os.makedirs(self.case_route)\n\n with h5.File(self.case_route + '/' + self.case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates',\n data=np.column_stack((self.x, self.y, self.z)))\n connectivities = h5file.create_dataset('connectivities', data=self.connectivities)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=self.n_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=self.n_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=self.n_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=self.base_stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=self.elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=self.base_mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=self.elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=self.frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=np.zeros((self.n_elem, self.n_node_elem)))\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=self.boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=self.beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=self.app_forces)\n lumped_mass_nodes_handle = h5file.create_dataset(\n 'lumped_mass_nodes', data=self.lumped_mass_nodes)\n lumped_mass_handle = h5file.create_dataset(\n 'lumped_mass', data=self.lumped_mass)\n lumped_mass_inertia_handle = h5file.create_dataset(\n 'lumped_mass_inertia', data=self.lumped_mass_inertia)\n lumped_mass_position_handle = h5file.create_dataset(\n 'lumped_mass_position', data=self.lumped_mass_position)\n\n def clean_test_files(self):\n \"\"\"\n Clears previously generated files\n \"\"\"\n\n case_name = self.case_name\n route = self.case_route\n\n # FEM\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n # Dynamics File\n dyn_file_name = route + '/' + case_name + '.dyn.h5'\n if os.path.isfile(dyn_file_name):\n os.remove(dyn_file_name)\n\n # Aerodynamics File\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n # Solver file\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n # Flight conditions file\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n # if os.path.isdir(route):\n # os.system('rm -r %s' %route)\n\n def update_aero_properties(self):\n \"\"\"\n Updates the aerodynamic properties of the horten wing\n\n \"\"\"\n\n # Retrieve attributes\n n_elem = self.n_elem\n n_node_elem = self.n_node_elem\n n_node_wing = self.n_node_wing\n n_node_fuselage = self.n_node_fuselage\n n_elem_fuselage = self.n_elem_fuselage\n n_elem_wing = self.n_elem_wing\n c_root = self.c_root\n taper_ratio = self.taper_ratio\n washout_root = self.washout_root\n washout_tip = self.washout_tip\n n_control_surfaces = self.n_control_surfaces\n cs_deflection = self.cs_deflection\n m = self.M\n main_ea_root = self.main_ea_root\n main_ea_tip = self.main_ea_tip\n airfoil_distribution = self.airfoil_distribution\n chord = self.chord\n surface_distribution = self.surface_distribution\n surface_m = self.surface_m\n aero_nodes = self.aero_nodes\n elastic_axis = self.elastic_axis\n twist = self.twist\n\n control_surface = self.control_surface\n control_surface_type = self.control_surface_type\n control_surface_deflection = self.control_surface_deflection\n control_surface_chord = self.control_surface_chord\n control_surface_hinge_coord = self.control_surface_hinge_coord\n\n self.dt = 1 / self.M / self.u_inf\n\n # control surface type: 0 = static\n # control surface type: 1 = dynamic\n control_surface_type[0] = 0\n control_surface_deflection[0] = cs_deflection\n control_surface_chord[0] = 2 # m\n control_surface_hinge_coord[0] = 0.25\n\n # # RIGHT FUSELAGE (Surface 0, Beam 0)\n we = 0\n wn = 0\n #\n # i_surf = 0\n # airfoil_distribution[we:we + n_elem_fuselage] = 0\n # surface_distribution[we:we + n_elem_fuselage] = i_surf\n # surface_m[i_surf] = m\n #\n # aero_nodes[wn:wn + n_node_fuselage] = True\n #\n # temp_chord = np.linspace(self.c_fuselage, self.c_root, self.n_node_fuselage)\n # temp_washout = washout_root\n #\n # # apply chord and elastic axis at each node\n # node_counter = 0\n # for ielem in range(we, we + n_elem_fuselage):\n # for i_local_node in range(n_node_elem):\n # if not i_local_node == 0:\n # node_counter += 1\n # chord[ielem, i_local_node] = temp_chord[node_counter]\n # elastic_axis[ielem, i_local_node] = main_ea_root\n # twist[ielem, i_local_node] = -temp_washout\n #\n # we += n_elem_fuselage\n # wn += n_node_fuselage\n\n # RIGHT WING (Surface 1, Beam 1)\n # surface_id\n i_surf = 0\n airfoil_distribution[we:we + n_elem_wing, :] = 0\n surface_distribution[we:we + n_elem_wing] = i_surf\n surface_m[i_surf] = m\n\n # specify aerodynamic characteristics of wing nodes\n aero_nodes[wn:wn + n_node_wing + 1] = True\n\n # linear taper initialisation\n temp_chord = np.linspace(c_root, taper_ratio * c_root, n_node_wing + 1)\n\n # linear wash out initialisation\n temp_washout = np.linspace(washout_root, washout_tip, n_node_wing + 1)\n\n # elastic axis variation\n temp_ea = np.linspace(main_ea_root, main_ea_tip, n_node_wing + 1)\n\n # apply chord and elastic axis at each node\n node_counter = 0\n for ielem in range(we, we + n_elem_wing):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[ielem, i_local_node] = temp_chord[node_counter]\n elastic_axis[ielem, i_local_node] = temp_ea[node_counter]\n twist[ielem, i_local_node] = -temp_washout[node_counter]\n if ielem >= round((we + n_elem_wing // 2)):\n control_surface[ielem, i_local_node] = 0\n\n # update working element and node\n we += n_elem_wing\n wn += n_node_wing + 1\n\n # # LEFT FUSELAGE (Surface 2, Beam 2)\n # i_surf = 2\n # airfoil_distribution[we:we + n_elem_fuselage] = 0\n # surface_distribution[we:we + n_elem_fuselage] = i_surf\n # surface_m[i_surf] = m\n #\n # aero_nodes[wn:wn + n_node_fuselage] = True\n #\n # temp_chord = np.linspace(self.c_fuselage, self.c_root, self.n_node_fuselage)\n # temp_washout = washout_root\n #\n # # apply chord and elastic axis at each node\n # node_counter = 0\n # for ielem in range(we, we + n_elem_fuselage):\n # for i_local_node in range(n_node_elem):\n # if not i_local_node == 0:\n # node_counter += 1\n # chord[ielem, i_local_node] = temp_chord[node_counter]\n # elastic_axis[ielem, i_local_node] = main_ea_root\n # twist[ielem, i_local_node] = -temp_washout\n #\n # we += n_elem_fuselage\n # wn += n_node_fuselage\n\n # LEFT WING (Surface 3, Beam 3)\n i_surf = 1\n airfoil_distribution[we:we + n_elem_wing, :] = 0\n surface_distribution[we: we + n_elem_wing] = i_surf\n surface_m[i_surf] = m\n\n # linear taper initialisation\n temp_chord = np.linspace(c_root, taper_ratio * c_root, n_node_wing + 1)\n\n # linear wash out initialisation\n temp_washout = np.linspace(washout_root, washout_tip, n_node_wing + 1)\n\n # specify aerodynamic characterisics of wing nodes\n aero_nodes[wn:wn + n_node_wing] = True\n\n # linear taper initialisation\n # apply chord and elastic axis at each node\n node_counter = 0\n for ielem in range(we, we + n_elem_wing):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[ielem, i_local_node] = temp_chord[node_counter]\n elastic_axis[ielem, i_local_node] = temp_ea[node_counter]\n twist[ielem, i_local_node] = -temp_washout[node_counter]\n if ielem >= round((we + n_elem_wing // 2)):\n control_surface[ielem, i_local_node] = 0\n\n # update working element and node\n we += n_elem_wing\n wn += n_node_wing\n\n # end node is the middle node\n mid_chord = np.array(chord[:, 1], copy=True)\n chord[:, 1] = chord[:, 2]\n chord[:, 2] = mid_chord\n\n mid_ea = np.array(elastic_axis[:, 1], copy=True)\n elastic_axis[:, 1] = elastic_axis[:, 2]\n elastic_axis[:, 2] = mid_ea\n\n # Update aerodynamic attributes of class\n self.chord = chord\n self.twist = twist\n self.aero_nodes = aero_nodes\n self.elastic_axis = elastic_axis\n self.control_surface = control_surface\n\n def generate_aero_file(self, route=None, case_name=None):\n \"\"\"\n Generates the ``.aero.h5`` file with the aerodynamic properties of the wing\n\n Args:\n route (str): route to write case file. If None is specified the default will be used\n case_name (str): name of file. If None is specified the default will be used\n\n \"\"\"\n\n if not route:\n route = self.case_route\n\n if not case_name:\n case_name = self.case_name\n\n if not os.path.isdir(self.case_route):\n os.makedirs(self.case_route)\n\n chord = self.chord\n twist = self.twist\n airfoil_distribution = self.airfoil_distribution\n surface_distribution = self.surface_distribution\n surface_m = self.surface_m\n m_distribution = self.m_distribution\n aero_nodes = self.aero_nodes\n elastic_axis = self.elastic_axis\n control_surface = self.control_surface\n control_surface_deflection = self.control_surface_deflection\n control_surface_chord = self.control_surface_chord\n control_surface_hinge_coord = self.control_surface_hinge_coord\n control_surface_type = self.control_surface_type\n\n control_surface_deflection[0] = self.cs_deflection\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n geo_utils.generate_naca_camber(P=0, M=0)))\n naca_airfoil_tail = airfoils_group.create_dataset('1', data=np.column_stack(\n geo_utils.generate_naca_camber(P=0, M=0)))\n naca_airfoil_fin = airfoils_group.create_dataset('2', data=np.column_stack(\n geo_utils.generate_naca_camber(P=0, M=0)))\n\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input.attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution',\n data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_nodes)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n control_surface_input = h5file.create_dataset('control_surface', data=control_surface)\n control_surface_deflection_input = h5file.create_dataset('control_surface_deflection',\n data=control_surface_deflection)\n control_surface_chord_input = h5file.create_dataset('control_surface_chord', data=control_surface_chord)\n control_surface_hinge_coord_input = h5file.create_dataset('control_surface_hinge_coord',\n data=control_surface_hinge_coord)\n control_surface_types_input = h5file.create_dataset('control_surface_type', data=control_surface_type)\n\n def set_default_config_dict(self, route=None, case_name=None):\n \"\"\"\n Generates default solver configuration file\n Returns:\n\n \"\"\"\n\n if not route:\n route = self.case_route\n\n if not case_name:\n case_name = self.case_name\n\n u_inf = self.u_inf\n rho = self.rho\n dt = self.dt\n tolerance = self.tolerance\n alpha = self.alpha\n beta = self.beta\n thrust = self.thrust\n thrust_nodes = self.thrust_nodes\n cs_deflection = self.cs_deflection\n fsi_tolerance = self.fsi_tolerance\n n_tstep = self.n_tstep\n gust_intensity = self.gust_intensity\n relaxation_factor = self.relaxation_factor\n\n file_name = route + '/' + case_name + '.sharpy'\n\n settings = dict()\n settings['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'Modal',\n 'AerogridPlot',\n 'BeamPlot',\n 'SaveData'],\n 'write_screen': 'on',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n\n settings['BeamLoader'] = {'unsteady': 'off',\n 'orientation': algebra.euler2quat(np.array([0.0,\n self.alpha,\n self.beta]))}\n\n settings['StaticUvlm'] = {'print_info': 'on',\n 'horseshoe': self.horseshoe,\n 'num_cores': 4,\n 'n_rollup': 1,\n 'rollup_dt': dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho}\n\n settings['StaticCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 200,\n 'num_load_steps': 1,\n 'delta_curved': 1e-5,\n 'min_delta': tolerance,\n 'gravity_on': 'on',\n 'gravity': 9.81},\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {'print_info': 'on',\n 'horseshoe': self.horseshoe,\n 'num_cores': 4,\n 'n_rollup': int(1),\n 'rollup_dt': dt, #self.c_root / self.M / self.u_inf,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho},\n 'max_iter': 200,\n 'n_load_steps': 1,\n 'tolerance': tolerance,\n 'relaxation_factor': 0.2}\n\n if self.horseshoe is True:\n settings['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 1,\n 'freestream_dir': ['1', '0', '0'],\n 'control_surface_deflection': ['']}\n else:\n settings['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': int(self.M * self.Mstarfactor),\n 'freestream_dir': ['1', '0', '0'],\n 'control_surface_deflection': ['']}\n\n settings['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-8,\n 'min_delta': tolerance,\n 'gravity_on': True,\n 'gravity': 9.81}\n\n settings['StaticTrim'] = {'solver': 'StaticCoupled',\n 'solver_settings': settings['StaticCoupled'],\n 'thrust_nodes': thrust_nodes,\n 'initial_alpha': alpha,\n 'initial_deflection': cs_deflection,\n 'initial_thrust': thrust,\n 'max_iter': 200,\n 'fz_tolerance': 1e-2,\n 'fx_tolerance': 1e-2,\n 'm_tolerance': 1e-2}\n\n settings['Trim'] = {'solver': 'StaticCoupled',\n 'solver_settings': settings['StaticCoupled'],\n 'initial_alpha': alpha,\n 'initial_beta': beta,\n 'cs_indices': [0],\n 'initial_cs_deflection': [cs_deflection],\n 'thrust_nodes': thrust_nodes,\n 'initial_thrust': [thrust, thrust]}\n\n settings['NonLinearDynamicCoupledStep'] = {'print_info': 'off',\n 'initial_velocity_direction': [-1., 0., 0.],\n 'max_iterations': 950,\n 'delta_curved': 1e-6,\n 'min_delta': tolerance,\n 'newmark_damp': 5e-3,\n 'gravity_on': True,\n 'gravity': 9.81,\n 'num_steps': n_tstep,\n 'dt': dt,\n 'initial_velocity': u_inf * 0}\n\n settings['NonLinearDynamicPrescribedStep'] = {'print_info': 'off',\n 'initial_velocity_direction': [-1., 0., 0.],\n 'max_iterations': 950,\n 'delta_curved': 1e-6,\n 'min_delta': self.tolerance,\n 'newmark_damp': 5e-3,\n 'gravity_on': True,\n 'gravity': 9.81,\n 'num_steps': self.n_tstep,\n 'dt': self.dt}\n\n settings['StepLinearUVLM'] = {'dt': self.dt,\n 'integr_order': 1,\n 'remove_predictor': True,\n 'use_sparse': True,\n 'velocity_field_generator': 'GustVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0., 0.],\n 'gust_shape': '1-cos',\n 'gust_length': 1.,\n 'gust_intensity': self.gust_intensity * u_inf,\n 'offset': 30.,\n 'span': self.span}}\n\n settings['StepUvlm'] = {'print_info': 'off',\n 'horseshoe': self.horseshoe,\n 'num_cores': 4,\n 'n_rollup': 100,\n 'convection_scheme': self.wake_type,\n 'rollup_dt': dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'GustVelocityField',\n 'velocity_field_input': {'u_inf': u_inf * 1,\n 'u_inf_direction': [1., 0, 0],\n 'gust_shape': '1-cos',\n 'gust_length': 1.,\n 'gust_intensity': gust_intensity * u_inf,\n 'offset': 30.0,\n 'span': self.span},\n # 'velocity_field_generator': 'SteadyVelocityField',\n # 'velocity_field_input': {'u_inf': u_inf*1,\n # 'u_inf_direction': [1., 0., 0.]},\n 'rho': rho,\n 'n_time_steps': n_tstep,\n 'dt': dt,\n 'gamma_dot_filtering': 3}\n\n settings['DynamicCoupled'] = {'print_info': 'on',\n 'structural_substeps': 1,\n 'dynamic_relaxation': 'on',\n 'clean_up_previous_solution': 'on',\n 'structural_solver': 'NonLinearDynamicCoupledStep',\n 'structural_solver_settings': settings['NonLinearDynamicCoupledStep'],\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'fsi_substeps': 200,\n 'fsi_tolerance': fsi_tolerance,\n 'relaxation_factor': relaxation_factor,\n 'minimum_steps': 1,\n 'relaxation_steps': 150,\n 'final_relaxation_factor': 0.0,\n 'n_time_steps': n_tstep,\n 'dt': dt,\n 'include_unsteady_force_contribution': 'off',\n 'postprocessors': ['BeamLoads', 'StallCheck', 'BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'BeamLoads': {'csv_output': 'off'},\n 'StallCheck': {'output_degrees': True,\n 'stall_angles': {\n '0': [-12 * np.pi / 180,\n 6 * np.pi / 180],\n '1': [-12 * np.pi / 180,\n 6 * np.pi / 180],\n '2': [-12 * np.pi / 180,\n 6 * np.pi / 180]}},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'},\n 'AerogridPlot': {\n 'u_inf': u_inf,\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n # 'WriteVariablesTime': {\n # # 'delimeter': ',',\n # # 'structure_nodes': [0],\n # # 'structure_variables': ['Z']\n # # settings['WriteVariablesTime'] = {'delimiter': ' ',\n # 'FoR_variables': ['GFoR_pos', 'GFoR_vel', 'GFoR_acc'],\n # 'FoR_number': [],\n # 'structure_variables': ['AFoR_steady_forces', 'AFoR_unsteady_forces','AFoR_position'],\n # 'structure_nodes': [0,-1],\n # 'aero_panels_variables': ['gamma', 'gamma_dot'],\n # 'aero_panels_isurf': [0,1,2],\n # 'aero_panels_im': [1,1,1],\n # 'aero_panels_in': [-2,-2,-2],\n # 'aero_nodes_variables': ['GFoR_steady_force', 'GFoR_unsteady_force'],\n # 'aero_nodes_isurf': [0,1,2],\n # 'aero_nodes_im': [1,1,1],\n # 'aero_nodes_in': [-2,-2,-2]\n # }}}\n }}\n\n settings['Modal'] = {'print_info': True,\n 'use_undamped_modes': True,\n 'NumLambda': 20,\n 'rigid_body_modes': True,\n 'write_modes_vtk': 'on',\n 'print_matrices': 'on',\n 'save_data': 'on',\n 'continuous_eigenvalues': 'off',\n 'dt': dt,\n 'plot_eigenvalues': False}\n\n settings['LinearAssembler'] = {'flow': ['LinearAeroelastic'],\n 'LinearAeroelastic': {\n 'beam_settings': {'modal_projection': False,\n 'inout_coords': 'nodes',\n 'discrete_time': True,\n 'newmark_damp': 0.015,\n 'discr_method': 'newmark',\n 'dt': dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'off',\n 'num_modes': 40,\n 'print_info': 'on',\n 'gravity': 'on',\n 'remove_dofs': []},\n 'aero_settings': {'dt': dt,\n 'integr_order': 2,\n 'density': rho,\n 'remove_predictor': False,\n 'use_sparse': True,\n 'rigid_body_motion': True,\n 'use_euler': False,\n 'remove_inputs': []},\n 'rigid_body_motion': True}}\n\n settings['AsymptoticStability'] = {'sys_id': 'LinearAeroelastic',\n 'print_info': 'on',\n 'frequency_cutoff': 0,\n 'export_eigenvalues': 'on'}\n\n settings['AerogridPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0,\n 'u_inf': u_inf\n }\n settings['AeroForcesCalculator'] = {'write_text_file': 'off',\n 'text_file_name': case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n 'unsteady': 'off'\n }\n settings['BeamPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on'}\n\n settings['BeamLoads'] = {'csv_output': 'off'}\n\n settings['SaveData'] = {}\n\n config = configobj.ConfigObj()\n config.filename = file_name\n for k, v in settings.items():\n config[k] = v\n config.write()\n self.settings = settings\n\n self.config = config\n\nif __name__=='__main__':\n\n import sharpy.sharpy_main\n\n ws = SweptWing(M=6,\n N=11,\n Mstarfactor=1,\n u_inf=22,\n rho=1.225,\n alpha_deg=0,\n cs_deflection_deg=-10,\n thrust=5,\n case_name_format=1)\n ws.horseshoe = True\n\n ws.clean_test_files()\n ws.update_mass_stiffness()\n ws.update_fem_prop()\n ws.update_aero_properties()\n ws.generate_fem_file()\n ws.generate_aero_file()\n ws.set_default_config_dict()\n\n ws.config['SHARPy']['flow'] = ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'AeroForcesCalculator',\n # 'StaticTrim',\n # 'AeroForcesCalculator',\n 'Modal',\n 'LinearAssembler',\n 'AsymptoticStability',\n # 'BeamPlot',\n # 'AerogridPlot']\n]\n ws.config.write()\n\n sharpy.sharpy_main.main(['', ws.config['SHARPy']['route'] + '/' + ws.config['SHARPy']['case'] + '.sharpy'])\n" }, { "path": "sharpy/cases/templates/Ttail.py", "content": "'''\nTemplates to build T-tail models\nS. Maraniello, Oct 2018\n\nclasses:\n- Ttail_3beam allows to generate general T-tail models with 3-beam.\n- Ttail_canonical: builds the canonical test case as per\n Murua et al., Prog. Aerosp. Sci., 71 (2014) 54-84\n'''\n\nimport h5py as h5\nimport numpy as np\nimport configobj\nimport os\nfrom IPython import embed\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.geo_utils as geo_utils\n\n\nclass Ttail_3beams():\n '''\n Produces a relatively general geometry of a 3 beams T-tail.\n By default, quadratic beam elements are used. Three beams, sharing one node,\n are used to model the system. VTP and HPT can be tapered, but they have the\n same chord at the intersection. The time-step is automatically defined based\n on the HTP root chord, the panelling M and the incoming flow speed.\n\n Input:\n - M: chordwise panelling of surfaces (same for HTP and VTP)\n - Nv: vertical panelling of VTP. Nv must be divisible by 2.\n - Nh: span-wise panelling of HTP. Nh refers to the full number of\n panels on the HTP (left and right) and must be divisible by 4.\n - Mstar_fact: wake length to chord ratio\n - u_inf: wind-speed\n - rho: air density\n - chord_htp_root: chord length at the htp-vtp interspection\n - chord_htp_tip: tip chord of the HPT (at the root, vtp and htp)\n - chord_vtp_root: chord at the vtp base.\n - span_htp: total span of the HTP (left and right)\n - height_vtp: vertical distance between first and last node of the vtp. Note\n that, in case of sweep angle, this is not the VTP length.\n - alpha_htp_deg=0.0: HTP incidence in degrees, positive if upward. Note that\n if non-zero, both UVLM grid and structural properties are rotated.\n - sweep_htp_deg=0.0: sweep angle, positive if backward\n - sweep_vtp_deg=0.0: sweep angle, positive if backward\n - main_ea: chord-normalised distance of elastic axis from leading edge. Must\n be the same for HTP and VTP\n - alpha_inf_deg: angle of attach of incoming flow [deg]. This is obtained\n rotating the local frame A in which the geometry is defined if\n rotate_frame_A is True, otherwise the incoming flow is tilted.\n - beta_inf_deg: sideslip angle of incoming flow [deg]. This is obtained\n rotating the local frame A in which the geometry is defined if\n rotate_frame_A is True, otherwise the incoming flow is tilted.\n - rotate_frame_A: determines whether the angles alpha_inf_deg and\n beta_inf_deg are obtained through rotation of the T-tail or rotation of\n the incoming flow.\n\n Usage:\n - generate class instance:\n ws=Ttail_3beams(...)\n - manually define mass/stiffness properties in update_mass_stiff method\n - def ws.update_mass_stiff:\n ...\n - run:\n ws.clean_test_files()\n ws.update_derived_params()\n ws.generate_fem_file()\n ws.generate_aero_file()\n ws.set_default_config_dict()\n\n Warning:\n - cambred aerofoils not implemented in the model\n - as the mass/structural properties are not generated by this class, to\n produce a *fem.h5 input file one needs to manually define the\n update_mass_stiff method. (see Ttail_canonical)\n '''\n\n def __init__(self,\n M, # chordwise panelling\n Nv, # panelling VTP\n Nh, # panelling HTP (total, not half)\n Mstar_fact,\n u_inf, # flight cond\n rho,\n # size\n chord_htp_root,\n chord_htp_tip,\n chord_vtp_root,\n span_htp,\n height_vtp,\n # elastic axis\n main_ea, # from LE.\n # angles\n alpha_htp_deg=0.0, # positive if upward\n sweep_htp_deg=0.0, # positive if backward\n sweep_vtp_deg=0.0, # positive if backward\n # others\n alpha_inf_deg=0.0,\n beta_inf_deg=0.0,\n rotate_frame_A=True,\n route='.', # saving\n case_name='Ttail'):\n\n\n ### parametrisation\n assert Nv%2 != 1,\\\n 'vertical panelling of VTP must be divisible by 2 (using 3-noded FEs!)'\n assert Nh%4 != 1,\\\n 'spanwise panelling of full HTP must be divisible by 4 (using 3-noded FEs!)'\n\n # chordwise\n self.M=M\n # vtp\n self.Nv=Nv\n # htp\n self.Nh=Nh\n self.Nh_semi=Nh//2\n # wake\n self.Mstar_fact=Mstar_fact # wake chord-wise panel factor\n\n # beam elements\n self.n_surfaces=3\n self.num_nodes_elem=3\n self.num_elem_vtp=self.Nv//2\n self.num_elem_htpL=self.Nh_semi//2 # port\n self.num_elem_htpR=self.Nh_semi//2 # starboard\n self.num_elem_tot=self.num_elem_vtp+self.num_elem_htpL+self.num_elem_htpR\n\n self.num_nodes_vtp =2*self.num_elem_vtp +1\n self.num_nodes_htpL=2*self.num_elem_htpL+1\n self.num_nodes_htpR=2*self.num_elem_htpR+1\n self.num_nodes_tot=2*self.num_elem_vtp+2*self.num_elem_htpL+2*self.num_elem_htpR+1\n\n ### store input\n self.u_inf=u_inf # flight cond\n self.rho=rho\n\n self.chord_htp_root=chord_htp_root\n self.chord_htp_tip=chord_htp_tip\n self.chord_vtp_root=chord_vtp_root\n self.span_htp=span_htp\n self.height_vtp=height_vtp\n self.main_ea=main_ea\n\n self.alpha_htp_deg=alpha_htp_deg\n self.sweep_htp_deg=sweep_htp_deg\n self.sweep_vtp_deg=sweep_vtp_deg\n\n # FoR A orientation\n self.alpha_inf_deg=alpha_inf_deg\n self.beta_inf_deg=beta_inf_deg\n self.rotate_frame_A=rotate_frame_A\n\n if self.rotate_frame_A:\n self.quat=algebra.euler2quat(\n np.pi/180.*np.array([0.0,alpha_inf_deg,beta_inf_deg]))\n self.u_inf_direction=np.array([1.,0.,0.])\n else:\n self.quat=algebra.euler2quat(np.array([0.,0.,0.]))\n self.u_inf_direction=np.dot(algebra.euler2rot(\n np.pi/180.*np.array([0.0,alpha_inf_deg,beta_inf_deg])),\n np.array([1.,0.,0.]))\n\n # time-step\n self.dt=self.chord_htp_root/self.M/self.u_inf\n\n self.route=route + '/'\n self.case_name=case_name\n\n # # Aerofoil shape: root and tip\n # self.root_airfoil_P = 0\n # self.root_airfoil_M = 0\n # self.tip_airfoil_P = 0\n # self.tip_airfoil_M = 0\n\n\n\n def update_fem_prop(self):\n '''\n Produce FEM connectivity, coordinates, mapping and BCs.\n\n Elements are numbered globally starting from:\n - vtp: bottom to top\n - htpL: tip to middle\n - htpR: middle to tip\n\n The node at which VTP and HPT intersect is number (global)\n 2*num_elem_vtp+1\n '''\n\n num_nodes_elem=self.num_nodes_elem\n num_elem_vtp=self.num_elem_vtp\n num_elem_htpL=self.num_elem_htpL\n num_elem_htpR=self.num_elem_htpR\n num_elem_tot=self.num_elem_tot\n\n num_nodes_vtp =self.num_nodes_vtp\n num_nodes_htpL=self.num_nodes_htpL\n num_nodes_htpR=self.num_nodes_htpR\n num_nodes_tot=self.num_nodes_tot\n\n\n ### beam number\n # used by both fem and aero (surface_number)\n # for each element (global number) allocate beam\n # vtp: 0\n # htpL: 1\n # htpR: 2\n beam_number=np.zeros((num_elem_tot),dtype=np.int)\n beam_number[ :num_elem_vtp]=0 # vtp\n beam_number[num_elem_vtp:num_elem_vtp+num_elem_htpL]=1 # htp L\n beam_number[-num_elem_htpR:]=2 # htp R\n\n\n ### Connectivity\n # surface: for each surface, specity the elements global no.\n # global: for each element, specify the local-global node number.\n conn_loc=np.array([0, 2, 1],dtype=int)\n\n conn_surf_vtp=[ee for ee in range(num_elem_vtp)]\n conn_surf_htpL=[num_elem_vtp+ee for ee in range(num_elem_htpL)]\n conn_surf_htpR=[num_elem_vtp+num_elem_htpL+ee for ee in range(num_elem_htpR)]\n\n conn_glob=np.zeros((num_elem_tot,num_nodes_elem),dtype=int)\n # add vtp\n node_here=0\n for ee in conn_surf_vtp:\n conn_glob[ee,:]=node_here+conn_loc\n node_here+=2\n node_intersection=node_here\n # add htp left\n node_here+=1\n node_free_htpL=node_here\n for ee in conn_surf_htpL:#range(num_elem_htpL):\n conn_glob[ee,:]=node_here+conn_loc\n node_here+=2\n conn_glob[num_elem_vtp+num_elem_htpL-1,1]=node_intersection\n node_here-=1\n # add htp right\n for ee in conn_surf_htpR:\n conn_glob[ee,:]=node_here+conn_loc\n node_here+=2\n conn_glob[num_elem_vtp+num_elem_htpL,0]=node_intersection\n node_free_htpR=node_here\n\n\n ### Nodal coordinates\n sweep_htp=np.pi/180.*self.sweep_htp_deg\n sweep_vtp=np.pi/180.*self.sweep_vtp_deg\n xv = np.zeros((num_nodes_tot,))\n yv = np.zeros((num_nodes_tot,))\n zv = np.zeros((num_nodes_tot,))\n # vtp\n nnvec=range(num_nodes_vtp)\n zv[nnvec]=np.linspace(0,self.height_vtp,num_nodes_vtp)\n xv[nnvec]=zv[nnvec]*np.tan( sweep_vtp )\n # increment all other nodes\n xv[node_intersection:]=xv[node_intersection]\n zv[node_intersection:]=zv[node_intersection]\n # htpL\n nnvec=[1+node_intersection+nn for nn in range(num_nodes_htpL)]\n nnvec[-1]=node_intersection\n yv[nnvec]=np.linspace(-.5*self.span_htp,0.,num_nodes_htpL)\n xv[nnvec]-=yv[nnvec]*np.tan(sweep_htp)\n # htpR\n nnvec=[node_free_htpR-nn for nn in range(num_nodes_htpR)][::-1]\n nnvec[0]=node_intersection\n yv[nnvec]=np.linspace(0.,.5*self.span_htp,num_nodes_htpR)\n xv[nnvec]+=yv[nnvec]*np.tan(sweep_htp)\n\n\n ### boundary conditions\n boundary_conditions=np.zeros((num_nodes_tot,), dtype=int)\n boundary_conditions[0]=1 # clamp\n boundary_conditions[node_free_htpL]=-1 # free-end htpL\n boundary_conditions[node_free_htpR]=-1 # free end htpR\n\n\n ### Define yB, where yB points to the LE.\n # account for HTP incidence\n frame_of_reference_delta = np.zeros((num_elem_tot, num_nodes_elem, 3))\n for ielem in range(num_elem_tot):\n for inode in range(num_nodes_elem):\n frame_of_reference_delta[ielem, inode, :] = [-1, 0, 0]\n\n self.frame_of_reference_delta=frame_of_reference_delta\n self.boundary_conditions=boundary_conditions\n self.beam_number=beam_number\n\n self.conn_loc=conn_loc\n self.conn_surf_vtp=conn_surf_vtp\n self.conn_surf_htpL=conn_surf_htpL\n self.conn_surf_htpR=conn_surf_htpR\n self.conn_glob=conn_glob\n\n self.x=xv\n self.y=yv\n self.z=zv\n\n\n\n\n def update_aero_prop(self):\n assert hasattr(self,'conn_glob'),\\\n 'Run \"update_derived_params\" before generating files'\n\n num_nodes_elem=self.num_nodes_elem\n num_elem_vtp=self.num_elem_vtp\n num_elem_htpL=self.num_elem_htpL\n num_elem_htpR=self.num_elem_htpR\n num_elem_tot=self.num_elem_tot\n\n num_nodes_vtp =self.num_nodes_vtp\n num_nodes_htpL=self.num_nodes_htpL\n num_nodes_htpR=self.num_nodes_htpR\n num_nodes_tot=self.num_nodes_tot\n\n\n ### Generate aerofoil profiles.\n # only flat plate\n airfoil_distribution=np.zeros((num_elem_tot,3),dtype=np.int)\n Airfoils_surf=[]\n Airfoils_surf.append(np.column_stack(geo_utils.generate_naca_camber(0,2)))\n # # vtp\n # # Airfoils_surf.append(geo_utils.generate_naca_camber(0,2))\n # # Na=1\n # for ee in self.conn_surf_vtp:\n # for nn_loc in [0,2]:\n # node_glob=self.conn_glob[ee,nn_loc]\n # eta=xxx\n # Airfoils_surf.append(\n # np.column_stack(\n # geo_utils.interpolate_naca_camber(\n # eta,\n # 0,self.root_airfoil_P,\n # self.tip_airfoil_M,self.tip_airfoil_P)))\n\n\n ### Define aerodynamic nodes\n aero_node=np.ones((num_nodes_tot,),dtype=bool)\n\n\n ### Define chord-wise panelling\n surface_m=self.M*np.ones((3,),dtype=int)\n\n\n ### Define chord-length, sweep, twist\n chord=np.zeros((num_elem_tot, 3))\n twist=np.zeros((num_elem_tot, 3))\n sweep=np.zeros((num_elem_tot, 3))\n # vtp\n nn_count=0\n for ee in self.conn_surf_vtp:\n for nn in [0,1,2]:\n nn_loc=self.conn_loc[nn]\n eta=np.float(nn_count+nn)/(num_nodes_vtp-1)\n chord[ee,nn_loc]=(1.-eta)*self.chord_vtp_root+eta*self.chord_htp_root\n sweep[ee,nn_loc]=eta*np.pi/180.*(-self.alpha_htp_deg)\n nn_count+=2\n # htpL\n twist[self.conn_surf_htpL,:]=-np.pi/180.*self.alpha_htp_deg\n nn_count=0\n for ee in self.conn_surf_htpL:\n for nn in [0,1,2]:\n nn_loc=self.conn_loc[nn]\n eta=np.float(nn_count+nn)/(num_nodes_htpL-1)\n chord[ee,nn_loc]=(1.-eta)*self.chord_htp_tip+eta*self.chord_htp_root\n nn_count+=1\n # htpR\n twist[self.conn_surf_htpR,:]=-np.pi/180.*self.alpha_htp_deg\n nn_count=0\n for ee in self.conn_surf_htpR:\n for nn in [0,1,2]:\n nn_loc=self.conn_loc[nn]\n eta=np.float(nn_count+nn)/(num_nodes_htpR-1)\n chord[ee,nn_loc]=(1.-eta)*self.chord_htp_root+eta*self.chord_htp_tip\n nn_count+=1\n\n ### Define chord elastic axis position\n elastic_axis=self.main_ea*np.ones((num_elem_tot, 3,))\n\n ### store\n self.Airfoils_surf=Airfoils_surf\n self.airfoil_distribution=airfoil_distribution\n\n self.aero_node=aero_node\n self.surface_m=surface_m\n\n self.twist=twist\n self.sweep=sweep\n self.chord=chord\n self.elastic_axis=elastic_axis\n\n\n def update_mass_stiff(self):\n '''\n This method can be substituted to produce different wing configs\n '''\n\n # uniform mass/stiffness on HTP/VTP\n ea,ga=1e7,1e7\n gj, eiy,eiz=1e6,2e5,5e6\n self.stiffness=np.zeros((1, 6, 6))\n self.stiffness[0]=np.diag([ea, ga, ga, gj, eiy, eiz])\n self.mass=np.zeros((1, 6, 6))\n self.mass[0, :, :]=np.diag([1., 1., 1., .1, .1, .1])\n self.elem_stiffness=np.zeros((self.num_elem_tot,), dtype=int)\n self.elem_mass=np.zeros((self.num_elem_tot,), dtype=int)\n\n\n def update_derived_params(self):\n # FEM connectivity, coords definition and mapping\n self.update_fem_prop()\n # Mass/stiffness properties\n self.update_mass_stiff()\n # Aero props\n self.update_aero_prop()\n\n\n def generate_fem_file(self):\n\n assert hasattr(self,'conn_glob'),\\\n 'Run \"update_derived_params\" before generating files'\n\n with h5.File(self.route+'/'+self.case_name+'.fem.h5','a') as h5file:\n\n coordinates = h5file.create_dataset(\n 'coordinates',data=np.column_stack((self.x, self.y, self.z)))\n conectivities = h5file.create_dataset(\n 'connectivities', data=self.conn_glob)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=self.num_nodes_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=self.num_nodes_tot)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=self.num_elem_tot)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=self.stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=self.elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=self.mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=self.elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=self.frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=np.zeros((self.num_elem_tot,3)))\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=self.boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=self.beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=np.zeros((self.num_nodes_tot,6)))\n\n\n\n def set_default_config_dict(self):\n\n if self.rotate_frame_A:\n alpha_aero=np.pi/180.*self.alpha_inf_deg\n beta_aero=np.pi/180.*self.beta_inf_deg\n else:\n alpha_aero=0.\n beta_aero=0.\n str_u_inf_direction=[str(self.u_inf_direction[cc]) for cc in range(3)]\n\n\n config=configobj.ConfigObj()\n config.filename=self.route+'/'+self.case_name+'.sharpy'\n\n config['SHARPy']={\n 'flow':['BeamLoader', 'AerogridLoader',\n 'StaticCoupled', #'StaticUvlm',\n 'AerogridPlot', 'BeamPlot', 'SaveData'],\n 'case': self.case_name, 'route': self.route,\n 'write_screen': 'off', 'write_log': 'on',\n 'log_folder': self.route+'/output/',\n 'log_file': self.case_name+'.log'}\n\n config['BeamLoader']={\n 'unsteady': 'off',\n 'orientation': self.quat}\n\n config['AerogridLoader']={\n 'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': self.Mstar_fact*self.M,\n 'freestream_dir':str_u_inf_direction\n }\n config['StaticUvlm']={\n 'rho': self.rho,\n 'velocity_field_generator':'SteadyVelocityField',\n 'velocity_field_input':{\n 'u_inf': self.u_inf,\n 'u_inf_direction':self.u_inf_direction},\n 'rollup_dt': self.dt,\n 'print_info': 'on',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup' : 0,\n 'rollup_aic_refresh': 0,\n 'rollup_tolerance': 1e-4}\n\n config['StaticCoupled']={\n 'print_info': 'on',\n 'max_iter': 50,\n 'n_load_steps': 1,\n 'tolerance': 1e-6,\n 'relaxation_factor': 0.,\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings':{\n 'rho': self.rho,\n 'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': self.dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': self.u_inf,\n 'u_inf_direction': str_u_inf_direction}},\n #\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 4,\n 'delta_curved': 1e-5,\n 'min_delta': 1e-5,\n 'gravity_on': 'on',\n 'gravity': 9.754,\n 'orientation': self.quat},}\n\n\n config['LinearUvlm'] = { 'dt': self.dt,\n 'integr_order': 2,\n 'density': self.rho,\n 'remove_predictor': True,\n 'use_sparse': True,\n 'ScalingDict':{'length': 1.,\n 'speed': 1.,\n 'density':1.}}\n\n config['AerogridPlot']={'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}\n\n config['AeroForcesCalculator']={'write_text_file': 'on',\n 'text_file_name': self.case_name+'_aeroforces.csv',\n 'screen_output': 'on',\n 'unsteady': 'off'}\n\n config['BeamPlot']={'include_rbm': 'off',\n 'include_applied_forces': 'on'}\n\n config['SaveData'] = {}\n\n config['Modal'] = {'NumLambda': 60,\n 'print_matrices': 'off',\n 'write_modes_vtk': True,\n 'use_undamped_modes': True}\n\n config.write()\n self.config=config\n\n\n\n def generate_aero_file(self):\n\n with h5.File(self.route+'/'+self.case_name+'.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n for aa in range(len(self.Airfoils_surf)):\n airfoils_group.create_dataset('%d'%aa,data=self.Airfoils_surf[aa])\n\n chord_input = h5file.create_dataset('chord', data=self.chord)\n dim_attr = chord_input.attrs['units'] = 'm'\n twist_input = h5file.create_dataset('twist', data=self.twist)\n dim_attr=twist_input.attrs['units']='rad'\n sweep_input = h5file.create_dataset('sweep', data=self.sweep)\n dim_attr=sweep_input.attrs['units']='rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset(\n 'airfoil_distribution', data=self.airfoil_distribution)\n surface_distribution_input = h5file.create_dataset(\n 'surface_distribution', data=self.beam_number)\n surface_m_input = h5file.create_dataset(\n 'surface_m', data=self.surface_m)\n m_distribution_input = h5file.create_dataset(\n 'm_distribution', data='uniform'.encode('ascii', 'ignore'))\n aero_node_input = h5file.create_dataset(\n 'aero_node', data=self.aero_node)\n elastic_axis_input = h5file.create_dataset(\n 'elastic_axis', data=self.elastic_axis)\n\n\n\n def clean_test_files(self):\n fem_file_name = self.route+'/'+self.case_name+'.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n aero_file_name = self.route+'/'+self.case_name+'.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = self.route+'/'+self.case_name+'.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = self.route+'/'+self.case_name+'.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n\n\nclass Ttail_canonical(Ttail_3beams):\n '''\n Produces a model of the Canonical T-tail test case proposed by\n Murua et al., Prog. Aerosp. Sci., 71 (2014) 54-84\n starting from the Ttail_3beam class.\n '''\n\n def __init__(self,\n M,Nv,Nh,Mstar_fact,\n u_inf,rho,\n alpha_htp_deg,\n kv,kh,\n alpha_inf_deg=0.,\n beta_inf_deg=0.,\n rotate_frame_A=True,\n route='.',case_name='Ttail_can'):\n\n super().__init__( M=M, Nv=Nv, Nh=Nh, Mstar_fact=Mstar_fact,\n u_inf=u_inf, rho=rho,\n # size\n chord_htp_root=2.,\n chord_htp_tip=2.,\n chord_vtp_root=2.,\n span_htp=4.*2.,\n height_vtp=6.,\n # ea\n main_ea=.25,\n # angles\n alpha_htp_deg=alpha_htp_deg,\n sweep_htp_deg=0.0,\n sweep_vtp_deg=0.0,\n # flow\n alpha_inf_deg=alpha_inf_deg,\n beta_inf_deg=beta_inf_deg,\n rotate_frame_A=rotate_frame_A,\n # other\n route=route,\n case_name=case_name)\n self.kv=kv\n self.kh=kh\n self.main_cg=.35\n\n\n def update_mass_stiff(self):\n '''\n This method can be substituted to produce different wing configs.\n\n Remind: the delta_frame_of_reference is chosen such that the B FoR axis\n are:\n - xb: along the wing span\n - yb: pointing towards the leading edge\n - zb: accordingly\n '''\n\n ### mass matrix\n # identical for vtp/htp\n m_unit = 35.\n j_tors = 8.\n pos_cg_b=np.array([0.,self.chord_vtp_root*(self.main_cg-self.main_ea), 0.])\n m_chi_cg=algebra.skew(m_unit*pos_cg_b)\n self.mass=np.zeros((2, 6, 6))\n self.mass[0, :, :]=np.diag([ m_unit, m_unit, m_unit,\n j_tors, .1*j_tors, .9*j_tors])\n self.mass[0,:3,3:]=+m_chi_cg\n self.mass[0,3:,:3]=-m_chi_cg\n self.elem_mass=np.zeros((self.num_elem_tot,), dtype=int)\n\n\n ### stiffness\n ea,ga=1e9,1e9\n # vtp\n Kvtp=np.diag([ea, ga, ga, 1e6*self.kv, 1e7, 1e9])\n # htp\n Khtp=np.diag([ea, ga, ga, 1e7*self.kh, 1e7*self.kh, 1e9])\n\n self.stiffness=np.zeros((2, 6, 6))\n self.stiffness[0,:,:]=Kvtp\n self.stiffness[1,:,:]=Khtp\n self.elem_stiffness=np.zeros((self.num_elem_tot,), dtype=int)\n self.elem_stiffness[self.conn_surf_vtp] =0\n self.elem_stiffness[self.conn_surf_htpL]=1\n self.elem_stiffness[self.conn_surf_htpR]=1\n\n\n\n\nif __name__=='__main__':\n\n import os\n os.system('mkdir -p %s' %'./test' )\n\n ws=Ttail_3beams(M=4,\n Nv=6, # panelling VTP\n Nh=8, # panelling HTP (total, not half)\n Mstar_fact=7.,\n u_inf=30., # flight cond\n rho=1.225,\n # size\n chord_htp_root=2.,\n chord_htp_tip=2.,\n chord_vtp_root=2.,\n span_htp=4.*2.,\n height_vtp=6.,\n # ea\n main_ea=.25,\n # angles\n alpha_htp_deg=5.0, # positive if upward\n sweep_htp_deg=60.0, # positive if backward\n sweep_vtp_deg=30.0, # positive if backward\n #\n alpha_inf_deg=0.0,\n beta_inf_deg=0.0,\n rotate_frame_A=True,\n route='./test/',\n case_name='Ttail')\n ws.clean_test_files()\n ws.update_derived_params()\n ws.generate_fem_file()\n ws.generate_aero_file()\n ws.set_default_config_dict()\n\n\n wc=Ttail_canonical(\n M=4,Nv=6,Nh=8,Mstar_fact=6,\n u_inf=30.,rho=1.225,\n alpha_htp_deg=2.,\n kv=1.,kh=10.,\n alpha_inf_deg=0.,\n beta_inf_deg=0.,\n rotate_frame_A=True,\n route='./test/',case_name='Tcanonical')\n wc.clean_test_files()\n wc.update_derived_params()\n wc.generate_fem_file()\n wc.generate_aero_file()\n wc.set_default_config_dict()\n" }, { "path": "sharpy/cases/templates/__init__.py", "content": "" }, { "path": "sharpy/cases/templates/flying_wings.py", "content": "'''\nTemplates to build flying wing models\nS. Maraniello, Jul 2018\n\nclasses:\n- FlyingWing: generate a flying wing model from a reduced set of input. The\nbuilt in method 'update_mass_stiff' can be re-defined by the user to enter more\ncomplex inertial/stiffness properties\n- Smith(FlyingWing): generate HALE wing model\n- Goland(FlyingWing): generate Goland wing model\n'''\n\nimport warnings\nimport h5py as h5\nimport numpy as np\nimport configobj\nimport os\n# from IPython import embed\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.geo_utils as geo_utils\n\nnp.set_printoptions(linewidth=120)\n\n\nclass FlyingWing():\n '''\n Flying wing template.\n - discretisation, and basic geometry/flight conditions can be passed in input\n - stiffness/mass properties must defined within the \"update_mass_stiffness\"\n method.\n - other aeroelastic params are attached as attributes to the class.\n - the method update_config_dict provides default setting for solver. These\n can be modified after an instance of the FlyingWing class is created.\n\n Args:\n M,N: chord/span-wise discretisations\n Mstar_fact: wake\n u_inf: flow speed\n alpha: FoR A pitch angle [deg]\n rho: density\n b_ref: geometry\n main_chord: main chord\n aspect_ratio:\n roll=0.: FoR A roll angle [deg] (see RollNodes flag)\n beta=0@ FoR A side angle [deg]\n sweep=0: sweep angle [deg]\n n_surfaces=2:\n physical_time=2:\n route='.': saving route\n case_name='flying_wing':\n RollNodes=False : If true, the wing nodes are rolled insted of the FoR A\n\n Usage:\n ws=flying_wings.FlyingWing(*args)\n ws.clean_test_files()\n ws.update_derived_params()\n ws.generate_fem_file()\n ws.generate_aero_file()\n ws.set_default_config_dict()\n ws.config['SHARPy']= bla bla bla\n ws.config.write()\n '''\n\n def __init__(self,\n M, N,\n Mstar_fact,\n u_inf,\n alpha,\n rho,\n b_ref,\n main_chord,\n aspect_ratio,\n roll=0.,\n yaw=0.,\n beta=0,\n sweep=0,\n n_surfaces=2,\n physical_time=2,\n route='.',\n case_name='flying_wing',\n RollNodes=False,\n polar_file=None):\n\n ### parametrisation\n assert n_surfaces < 3, \"use 1 or 2 surfaces only!\"\n assert N % 2 != 1, \\\n 'UVLM spanwise panels must be even when using 3-noded FEs!'\n self.M = M # chord-wise panels\n self.N = N # total spanwise panels (over all surfaces)\n self.Mstar_fact = Mstar_fact # wake chord-wise panel factor\n self.n_surfaces = n_surfaces\n self.num_node_elem = 3\n\n ### store input\n self.u_inf = u_inf # flight cond\n self.rho = rho\n self.alpha = alpha # angles\n self.beta = beta\n self.roll = roll\n self.yaw = yaw\n self.sweep = sweep\n self.b_ref = b_ref # geometry\n self.main_chord = main_chord\n self.aspect_ratio = aspect_ratio\n self.route = route + '/'\n self.case_name = case_name\n self.RollNodes = RollNodes\n\n # Verify that the route exists and create directory if necessary\n try:\n os.makedirs(self.route)\n except FileExistsError:\n pass\n\n ### other params\n self.u_inf_direction = np.array([1., np.sin(beta * np.pi / 180), 0.])\n self.gravity_on = True\n\n # aeroelasticity\n self.sigma = 1\n self.main_ea = 0.2\n self.main_cg = 0.5\n self.c_ref = 1. # ref. chord\n\n # Aerofoil shape: root and tip\n self.root_airfoil_P = 0\n self.root_airfoil_M = 0\n self.tip_airfoil_P = 0\n self.tip_airfoil_M = 0\n\n self.polars = None # list of polar for each airfoil\n if polar_file is not None:\n self.load_polar(polar_file)\n\n # Numerics for dynamic simulations\n self.dt_factor = 1\n self.n_tstep = None\n self.physical_time = physical_time\n self.horseshoe = False\n self.fsi_tolerance = 1e-10\n self.relaxation_factor = 0.2\n self.gust_intensity = 0.01\n self.gust_length = 5\n self.tolerance = 1e-6\n\n n_lumped_mass = 1\n self.lumped_mass = np.zeros((n_lumped_mass))\n self.lumped_mass_position = np.zeros((n_lumped_mass, 3))\n self.lumped_mass_inertia = np.zeros((n_lumped_mass, 3, 3))\n self.lumped_mass_nodes = np.zeros((n_lumped_mass), dtype=int)\n\n # Control surface initialisation\n self.n_control_surfaces = 0\n self.control_surface = np.zeros((N + 1, 3), dtype=int) - 1\n self.control_surface_type = np.zeros((self.n_control_surfaces), dtype=int)\n self.control_surface_deflection = np.zeros((self.n_control_surfaces,))\n self.control_surface_chord = np.array([M//2], dtype=int)\n self.control_surface_hinge_coord = np.zeros_like(self.control_surface_type, dtype=float)\n\n def settings_to_config(self, settings):\n file_name = self.route + '/' + self.case_name + '.sharpy'\n config = configobj.ConfigObj()\n config.filename = file_name\n for k, v in settings.items():\n config[k] = v\n config.write()\n\n return file_name\n\n def update_mass_stiff(self):\n '''This method can be substituted to produce different wing configs'''\n # uniform mass/stiffness\n\n ea, ga = 1e7, 1e7\n gj, eiy, eiz = 1e6, 2e5, 5e6\n base_stiffness = np.diag([ea, ga, ga, gj, eiy, eiz])\n\n self.stiffness = np.zeros((1, 6, 6))\n self.stiffness[0] = self.sigma * base_stiffness\n\n self.mass = np.zeros((1, 6, 6))\n self.mass[0, :, :] = np.diag([1., 1., 1., .1, .1, .1])\n\n self.elem_stiffness = np.zeros((self.num_elem_tot,), dtype=int)\n self.elem_mass = np.zeros((self.num_elem_tot,), dtype=int)\n\n n_lumped_mass = 1\n self.lumped_mass = np.zeros((n_lumped_mass))\n self.lumped_mass_position = np.zeros((n_lumped_mass, 3))\n self.lumped_mass_inertia = np.zeros((n_lumped_mass, 3, 3))\n self.lumped_mass_nodes = np.zeros((n_lumped_mass), dtype=int)\n\n self.lumped_mass[0] = 5.\n self.lumped_mass_position[0] = np.array([0, 0.25, 0])\n\n def load_polar(self, file):\n \"\"\"\n Read polar from Airfoil Tools polar txt file\n\n Args:\n file (str):\n \"\"\"\n polar_raw_data = np.loadtxt(file, skiprows=12)\n self.polars = np.column_stack((polar_raw_data[:, 0] * np.pi / 180, # aoa\n polar_raw_data[:, 1], # cl\n polar_raw_data[:, 2], # cd\n polar_raw_data[:, 4])) #cm\n\n def update_derived_params(self):\n ### Derived\n\n # time-step\n self.dt = self.main_chord / self.M / self.u_inf * self.dt_factor\n self.n_tstep = int(np.round(self.physical_time / self.dt))\n\n # angles\n self.alpha_rad = self.alpha * np.pi / 180.\n self.roll_rad = self.roll * np.pi / 180.\n self.beta_rad = self.beta * np.pi / 180.\n self.sweep_rad = self.sweep * np.pi / 180.\n self.yaw_rad = self.yaw * np.pi / 180.\n\n # FoR A orientation\n # if self.RollNodes:\n self.quat = algebra.euler2quat(np.array([self.roll_rad, self.alpha_rad, self.yaw_rad]))\n # else:\n # if np.abs(self.roll)>1e-3:\n # warnings.warn(\n # 'FoR A quaternion will be built with inverted '+\\\n # 'roll angle sign to compensate bug in algebra.euler2quat')\n # self.quat=algebra.euler2quat(np.array([-self.roll_rad,self.alpha_rad,self.beta_rad]))\n\n # geometry\n self.wing_span = self.aspect_ratio * self.main_chord # /np.cos(self.sweep_rad)\n self.S = self.wing_span * self.main_chord\n\n # discretisation\n assert self.n_surfaces < 3, \"use 1 or 2 surfaces only!\"\n assert self.N % 2 != 1, \\\n 'UVLM spanwise panels must be even when using 3-noded FEs!'\n self.num_elem_tot = self.N // 2\n\n assert self.num_elem_tot % self.n_surfaces != 1, \\\n \"Can't distribute equally FEM elements over surfaces\"\n self.num_elem_surf = self.num_elem_tot // self.n_surfaces\n self.num_node_surf = self.N // self.n_surfaces + 1\n self.num_node_tot = self.N + 1\n\n self.control_surface = np.zeros((self.num_elem_tot, self.num_node_elem), dtype=int) - 1\n\n # FEM connectivity, coords definition and mapping\n self.update_fem_prop()\n\n # Mass/stiffness properties\n self.update_mass_stiff()\n\n # Aero props\n self.update_aero_prop()\n\n def update_fem_prop(self):\n ''' Produce FEM connectivity, coordinates, mapping and BCs'''\n\n n_surfaces = self.n_surfaces\n num_node_elem = self.num_node_elem\n num_node_surf = self.num_node_surf\n num_node_tot = self.num_node_tot\n num_elem_surf = self.num_elem_surf\n num_elem_tot = self.num_elem_tot\n sweep_rad = self.sweep_rad\n half_span = 0.5 * self.wing_span\n\n #### Connectivity and nodal coordinates\n # Warning: the elements direction determines the xB axis direction.\n # Hence, to avoid accidentally rotating aerofoil profiles, if a wing is\n # defined through multiple surfaces, nodes should be oriented in the\n # same direction.\n\n # generate connectivity. Mid node at the end of array.\n conn_loc = np.array([0, 2, 1], dtype=int)\n conn_surf = np.zeros((num_elem_surf, num_node_elem), dtype=int)\n conn_glob = np.zeros((num_elem_tot, num_node_elem), dtype=int)\n\n # connectivity surface 01\n for ielem in range(num_elem_surf):\n conn_surf[ielem, :] = conn_loc + ielem * (num_node_elem - 1)\n # global connectivity. Multiple surfaces merge at node 0.\n\n conn_glob[:num_elem_surf, :] = conn_surf\n for ss in range(1, n_surfaces):\n conn_glob[ss * num_elem_surf:(ss + 1) * num_elem_surf, :] = \\\n conn_surf + ss * (num_node_surf - 1) + 1\n conn_glob[(ss + 1) * num_elem_surf - 1, 1] = 0\n\n ### Nodal coordinates\n z = np.zeros((num_node_tot,))\n if n_surfaces == 1:\n ### Local coord from half surface\n x01 = np.sin(sweep_rad) * np.linspace(0., half_span, (num_node_surf + 1) // 2)\n y01 = np.cos(sweep_rad) * np.linspace(0., half_span, (num_node_surf + 1) // 2)\n # and mirrow\n x = np.concatenate([x01[-1:0:-1], x01])\n y = np.concatenate([-y01[-1:0:-1], y01])\n if n_surfaces == 2:\n ### Local coord for surface 00\n x01 = np.sin(sweep_rad) * np.linspace(0., half_span, num_node_surf)\n y01 = np.cos(sweep_rad) * np.linspace(0., half_span, num_node_surf)\n # and mirrow\n x = np.concatenate([x01, x01[-1:0:-1]])\n y = np.concatenate([y01, -y01[-1:0:-1]])\n if n_surfaces > 2:\n raise NameError(\n 'Geometry not implemented for multiple surfaces! Rotate them.')\n\n if self.RollNodes:\n sr, cr = np.sin(self.roll_rad), np.cos(self.roll_rad)\n yold = y.copy()\n y = cr * yold\n z = sr * yold\n\n ### surface/beam to element mapping\n # beam_number and surface_distribution in fem/aero files\n surface_number = np.zeros((num_elem_tot,), dtype=int)\n for ss in range(n_surfaces):\n surface_number[ss * num_elem_surf:(ss + 1) * num_elem_surf] = ss\n\n ##### boundary conditions\n boundary_conditions = np.zeros((num_node_tot,), dtype=int)\n if n_surfaces == 1:\n boundary_conditions[[0, -1]] = -1 # free-ends\n boundary_conditions[(num_node_surf - 1) // 2] = 1 # mid-clamp\n if n_surfaces == 2:\n boundary_conditions[0] = 1 # clamp at root (node 0)\n boundary_conditions[num_node_surf - 1] = -1 # free surf 00\n boundary_conditions[num_node_surf] = -1 # free surf 01\n if n_surfaces > 2:\n raise NameError('BCs not implemented for more than 2 surfaces')\n\n ### Define yB, where yB points to the LE.\n frame_of_reference_delta = np.zeros((num_elem_tot, num_node_elem, 3))\n for ielem in range(num_elem_tot):\n for inode in range(num_node_elem):\n frame_of_reference_delta[ielem, inode, :] = [-1, 0, 0]\n\n self.frame_of_reference_delta = frame_of_reference_delta\n self.boundary_conditions = boundary_conditions\n self.conn_glob = conn_glob\n self.conn_surf = conn_surf\n self.surface_number = surface_number\n self.x = x\n self.y = y\n self.z = z\n\n\n def update_aero_prop(self):\n assert hasattr(self, 'conn_glob'), \\\n 'Run \"update_derived_params\" before generating files'\n\n n_surfaces = self.n_surfaces\n num_node_surf = self.num_node_surf\n num_node_tot = self.num_node_tot\n num_elem_surf = self.num_elem_surf\n num_elem_tot = self.num_elem_tot\n\n ### Generate aerofoil profiles. Only on surf 0.\n Airfoils_surf = []\n if n_surfaces == 2:\n for inode in range(num_node_surf):\n eta = inode / num_node_surf\n Airfoils_surf.append(\n np.column_stack(\n geo_utils.interpolate_naca_camber(\n eta,\n self.root_airfoil_M, self.root_airfoil_P,\n self.tip_airfoil_M, self.tip_airfoil_P)))\n airfoil_distribution_surf = self.conn_surf\n airfoil_distribution = np.concatenate([airfoil_distribution_surf,\n airfoil_distribution_surf[::-1, [1, 0, 2]]])\n if n_surfaces == 1:\n num_node_half = (num_node_surf + 1) // 2\n for inode in range(num_node_half):\n eta = inode / num_node_half\n Airfoils_surf.append(\n np.column_stack(\n geo_utils.interpolate_naca_camber(\n eta,\n self.root_airfoil_M, self.root_airfoil_P,\n self.tip_airfoil_M, self.tip_airfoil_P)))\n airfoil_distribution_surf = self.conn_surf[:num_elem_surf // 2, :]\n airfoil_distribution = np.concatenate([\n airfoil_distribution_surf[::-1, [1, 0, 2]],\n airfoil_distribution_surf])\n\n self.Airfoils_surf = Airfoils_surf\n self.airfoil_distribution = airfoil_distribution\n\n ### others\n self.aero_node = np.ones((num_node_tot,), dtype=bool)\n self.surface_m = self.M * np.ones((n_surfaces,), dtype=int)\n\n self.twist = np.zeros((num_elem_tot, 3))\n self.chord = self.main_chord * np.ones((num_elem_tot, 3))\n self.elastic_axis = self.main_ea * np.ones((num_elem_tot, 3,))\n\n def set_default_config_dict(self):\n\n str_u_inf_direction = [str(self.u_inf_direction[cc]) for cc in range(3)]\n\n config = configobj.ConfigObj()\n config.filename = self.route + '/' + self.case_name + '.sharpy'\n settings = dict()\n\n config['SHARPy'] = {\n 'flow': ['BeamLoader', 'AerogridLoader',\n # 'StaticUvlm',\n 'StaticCoupled',\n 'AerogridPlot', 'BeamPlot', 'SaveData'],\n 'case': self.case_name, 'route': self.route,\n 'write_screen': 'on', 'write_log': 'on',\n 'log_folder': './output/' + self.case_name + '/',\n 'log_file': self.case_name + '.log'}\n\n config['BeamLoader'] = {\n 'unsteady': 'off',\n 'orientation': self.quat}\n\n config['AerogridLoader'] = {\n 'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': self.Mstar_fact * self.M,\n 'freestream_dir': str_u_inf_direction\n }\n config['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 0,\n 'delta_curved': 1e-5,\n 'min_delta': 1e-5,\n 'gravity_on': self.gravity_on,\n 'gravity': 9.754,\n 'orientation': self.quat}\n config['StaticUvlm'] = {\n 'rho': self.rho,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': self.u_inf,\n 'u_inf_direction': self.u_inf_direction},\n 'rollup_dt': self.dt,\n 'print_info': 'on',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_aic_refresh': 0,\n 'rollup_tolerance': 1e-4}\n\n config['StaticCoupled'] = {\n 'print_info': 'on',\n 'max_iter': 200,\n 'n_load_steps': 1,\n 'tolerance': 1e-10,\n 'relaxation_factor': 0.,\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {\n 'rho': self.rho,\n 'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': self.dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': self.u_inf,\n 'u_inf_direction': str_u_inf_direction}},\n #\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 0,\n 'delta_curved': 1e-1,\n 'min_delta': 1e-10,\n 'gravity_on': self.gravity_on,\n 'gravity': 9.81}}\n\n config['LinearUvlm'] = {'dt': self.dt,\n 'integr_order': 2,\n 'density': self.rho,\n 'remove_predictor': True,\n 'use_sparse': True,\n 'ScalingDict': {'length': 1.,\n 'speed': 1.,\n 'density': 1.}}\n\n settings['StepLinearUVLM'] = {'dt': self.dt,\n 'solution_method': 'direct',\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': self.u_inf,\n 'u_inf_direction': self.u_inf_direction}}\n\n settings['NonLinearDynamicPrescribedStep'] = {'print_info': 'off',\n 'max_iterations': 950,\n 'delta_curved': 1e-1,\n 'min_delta': self.tolerance*1e3,\n 'newmark_damp': 5e-3,\n 'gravity_on': self.gravity_on,\n 'gravity': 9.81,\n 'num_steps': self.n_tstep,\n 'dt': self.dt}\n\n settings['StepUvlm'] = {'print_info': 'on',\n 'horseshoe': self.horseshoe,\n 'num_cores': 4,\n 'n_rollup': 100,\n 'convection_scheme': 0,\n 'rollup_dt': self.dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n # 'velocity_field_generator': 'TurbSimVelocityField',\n # 'velocity_field_input': {'turbulent_field': '/2TB/turbsim_fields/TurbSim_wide_long_A_low.h5',\n # 'offset': [30., 0., -10],\n # 'u_inf': 0.},\n # 'velocity_field_generator': 'GustVelocityField',\n # 'velocity_field_input': {'u_inf': self.u_inf,\n # 'u_inf_direction': self.u_inf_direction,\n # 'gust_shape': 'continuous_sin',\n # 'gust_length': self.gust_length,\n # 'gust_intensity': self.gust_intensity * self.u_inf,\n # 'offset': 15.0,\n # 'span': self.main_chord * self.aspect_ratio},\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': self.u_inf*1,\n 'u_inf_direction': [1., 0., 0.]},\n 'rho': self.rho,\n 'n_time_steps': self.n_tstep,\n 'dt': self.dt,\n 'gamma_dot_filtering': 3}\n\n config['DynamicCoupled'] = {'print_info': 'on',\n 'structural_substeps': 0,\n 'dynamic_relaxation': 'on',\n 'cleanup_previous_solution': 'on',\n 'structural_solver': 'NonLinearDynamicPrescribedStep',\n 'structural_solver_settings': settings['NonLinearDynamicPrescribedStep'],\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'fsi_substeps': 200,\n 'fsi_tolerance': self.fsi_tolerance,\n 'relaxation_factor': self.relaxation_factor,\n 'minimum_steps': 1,\n 'relaxation_steps': 150,\n 'final_relaxation_factor': 0.0,\n 'n_time_steps': self.n_tstep,\n 'dt': self.dt,\n 'include_unsteady_force_contribution': 'off',\n 'postprocessors': ['BeamLoads', 'StallCheck', 'BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'BeamLoads': {'csv_output': 'off'},\n 'StallCheck': {'output_degrees': True,\n 'stall_angles': {\n '0': [-12 * np.pi / 180,\n 6 * np.pi / 180],\n '1': [-12 * np.pi / 180,\n 6 * np.pi / 180],\n '2': [-12 * np.pi / 180,\n 6 * np.pi / 180]}},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'},\n 'AerogridPlot': {\n 'u_inf': self.u_inf,\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}}}\n\n config['DynamicUVLM'] = {'print_info': 'on',\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'n_time_steps': self.n_tstep,\n 'dt': self.dt,\n 'include_unsteady_force_contribution': 'on',\n 'postprocessors': ['AerogridPlot'],\n 'postprocessors_settings': {'AerogridPlot': {'u_inf': self.u_inf,\n 'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}}\n }\n\n config['AerogridPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}\n\n config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': self.case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n 'unsteady': 'off'}\n\n config['BeamPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on'}\n\n config['SaveData'] = {}\n\n config['Modal'] = {'NumLambda': 20,\n 'rigid_body_modes': 'off',\n 'print_matrices': 'off',\n 'save_data': 'off',\n 'continuous_eigenvalues': 'off',\n 'dt': 0,\n 'plot_eigenvalues': False,\n 'max_rotation_deg': 15.,\n 'max_displacement': 0.15,\n 'write_modes_vtk': True,\n 'use_undamped_modes': True}\n\n config['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n 'linear_system_settings': {\n 'beam_settings': {'modal_projection': False,\n 'inout_coords': 'nodes',\n 'discrete_time': True,\n 'newmark_damp': 0.5,\n 'discr_method': 'newmark',\n 'dt': self.dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'off',\n 'num_modes': 40,\n 'print_info': 'on',\n 'gravity': 'on',\n 'remove_dofs': []},\n 'aero_settings': {'dt': self.dt,\n 'integr_order': 2,\n 'density': self.rho,\n 'remove_predictor': False,\n 'use_sparse': True,\n 'rigid_body_motion': False,\n 'use_euler': False,\n 'remove_inputs': ['u_gust']},\n 'rigid_body_motion': False}}\n\n config['AsymptoticStability'] = {'print_info': True,\n 'velocity_analysis': [30, 180, 151]}\n\n config['LinDynamicSim'] = {'dt': self.dt,\n 'n_tsteps': self.n_tstep,\n 'sys_id': 'LinearAeroelastic',\n 'postprocessors': ['BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'AerogridPlot': {\n 'u_inf': self.u_inf,\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'}}}\n\n config['FrequencyResponse'] = {'compute_fom': 'on',\n 'frequency_unit': 'k',\n 'frequency_bounds': [0.0001, 1.0],\n 'quick_plot': 'on'}\n\n\n config.write()\n self.config = config\n # print('config dictionary set-up with flow:')\n # print(config['SHARPy']['flow'])\n\n def generate_aero_file(self, airfoil_efficiency=None):\n\n with h5.File(self.route + '/' + self.case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n for aa in range(len(self.Airfoils_surf)):\n airfoils_group.create_dataset('%d' % aa, data=self.Airfoils_surf[aa])\n\n chord_input = h5file.create_dataset('chord', data=self.chord)\n dim_attr = chord_input.attrs['units'] = 'm'\n\n twist_input = h5file.create_dataset('twist', data=self.twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset(\n 'airfoil_distribution', data=self.airfoil_distribution)\n surface_distribution_input = h5file.create_dataset(\n 'surface_distribution', data=self.surface_number)\n surface_m_input = h5file.create_dataset(\n 'surface_m', data=self.surface_m)\n m_distribution_input = h5file.create_dataset(\n 'm_distribution', data='uniform'.encode('ascii', 'ignore'))\n aero_node_input = h5file.create_dataset(\n 'aero_node', data=self.aero_node)\n elastic_axis_input = h5file.create_dataset(\n 'elastic_axis', data=self.elastic_axis)\n control_surface_input = h5file.create_dataset(\n 'control_surface', data=self.control_surface)\n control_surface_type_input = h5file.create_dataset(\n 'control_surface_type', data=self.control_surface_type)\n control_surface_deflection_input = h5file.create_dataset(\n 'control_surface_deflection', data=self.control_surface_deflection)\n control_surface_chord_input = h5file.create_dataset(\n 'control_surface_chord', data=self.control_surface_chord)\n if airfoil_efficiency is not None:\n a_eff_handle = h5file.create_dataset(\n 'airfoil_efficiency', data=airfoil_efficiency)\n\n if self.control_surface_hinge_coord is not None:\n cs_hinge = h5file.create_dataset(\n 'control_surface_hinge_coord', data=self.control_surface_hinge_coord\n )\n\n if self.polars is not None:\n polars_group = h5file.create_group('polars')\n for i_airfoil in range(len(self.Airfoils_surf)):\n polars_group.create_dataset('{:g}'.format(i_airfoil), data=self.polars)\n\n def generate_fem_file(self):\n\n assert hasattr(self, 'conn_glob'), \\\n 'Run \"update_derived_params\" before generating files'\n\n with h5.File(self.route + '/' + self.case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset(\n 'coordinates', data=np.column_stack((self.x, self.y, self.z)))\n conectivities = h5file.create_dataset(\n 'connectivities', data=self.conn_glob)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=self.num_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=self.num_node_tot)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=self.num_elem_tot)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=self.stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=self.elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=self.mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=self.elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=self.frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=np.zeros((self.num_elem_tot, 3)))\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=self.boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=self.surface_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=np.zeros((self.num_node_tot, 6)))\n lumped_mass_handle = h5file.create_dataset(\n 'lumped_mass', data=self.lumped_mass)\n lumped_mass_inertia_handle = h5file.create_dataset(\n 'lumped_mass_inertia', data=self.lumped_mass_inertia)\n lumped_mass_position_handle = h5file.create_dataset(\n 'lumped_mass_position', data=self.lumped_mass_position)\n lumped_mass__nodes_handle = h5file.create_dataset(\n 'lumped_mass_nodes', data=self.lumped_mass_nodes)\n\n def generate_rom_files(self, left_tangent, right_tangent, ro, rc, fo, fc):\n with h5.File(self.route + '/' + self.case_name + '.rom.h5', 'a') as h5file:\n lt_handle = h5file.create_dataset('left_tangent',\n data=left_tangent)\n rt_handle = h5file.create_dataset('right_tangent',\n data=right_tangent)\n ro_h = h5file.create_dataset('ro', data=ro)\n fo_h = h5file.create_dataset('fo', data=fo)\n fc_h = h5file.create_dataset('fc', data=fc)\n rc_h = h5file.create_dataset('rc', data=rc)\n\n def clean_test_files(self):\n fem_file_name = self.route + '/' + self.case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n aero_file_name = self.route + '/' + self.case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = self.route + '/' + self.case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = self.route + '/' + self.case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n lininput_file_name = self.route + '/' + self.case_name + '.lininput.h5'\n if os.path.isfile(lininput_file_name):\n os.remove(lininput_file_name)\n\n rom_file = self.route + '/' + self.case_name + '.rom.h5'\n if os.path.isfile(rom_file):\n os.remove(rom_file)\n\nclass Smith(FlyingWing):\n '''\n Build Smith HALE wing.\n This class is nothing but a FlyingWing with pre-defined geometry properties\n and mass/stiffness data (\"update_mass_stiffness\" method)\n '''\n\n def __init__(self,\n M, N, # chord/span-wise discretisations\n Mstar_fact,\n u_inf, # flight cond\n alpha,\n rho=0.08891,\n b_ref=32., # geometry\n main_chord=1.,\n aspect_ratio=32,\n roll=0.,\n beta=0.,\n sweep=0.,\n n_surfaces=2,\n route='.',\n case_name='smith',\n RollNodes=False):\n super().__init__(M=M, N=N,\n Mstar_fact=Mstar_fact,\n u_inf=u_inf,\n alpha=alpha,\n rho=rho,\n b_ref=b_ref,\n main_chord=main_chord,\n aspect_ratio=aspect_ratio,\n roll=roll,\n beta=beta,\n sweep=sweep,\n n_surfaces=n_surfaces,\n route=route,\n case_name=case_name,\n RollNodes=RollNodes)\n self.c_ref = 1.\n\n def update_mass_stiff(self):\n '''This method can be substituted to produce different wing configs'''\n # uniform mass/stiffness\n\n ea, ga = 1e5, 1e5\n gj, eiy, eiz = 1e4, 2e4, 5e6\n base_stiffness = np.diag([ea, ga, ga, gj, eiy, eiz])\n\n self.stiffness = np.zeros((1, 6, 6))\n self.stiffness[0] = self.sigma * base_stiffness\n\n self.mass = np.zeros((1, 6, 6))\n self.mass[0, :, :] = np.diag([0.75, 0.75, 0.75, .1, .1, .1])\n\n self.elem_stiffness = np.zeros((self.num_elem_tot,), dtype=int)\n self.elem_mass = np.zeros((self.num_elem_tot,), dtype=int)\n\n\nclass Goland(FlyingWing):\n '''\n Build a Goland wing.\n This class is nothing but a FlyingWing with pre-defined geometry properties\n and mass/stiffness data (\"update_mass_stiffness\" method)\n '''\n\n def __init__(self,\n M, N, # chord/span-wise discretisations\n Mstar_fact,\n u_inf, # flight cond\n alpha,\n rho=1.02,\n b_ref=2. * 6.096, # geometry\n main_chord=1.8288,\n aspect_ratio=(2. * 6.096) / 1.8288,\n roll=0.,\n yaw=0.,\n beta=0.,\n sweep=0.,\n n_surfaces=1,\n physical_time=2,\n route='.',\n case_name='goland',\n RollNodes=False):\n super().__init__(M=M, N=N,\n Mstar_fact=Mstar_fact,\n u_inf=u_inf,\n alpha=alpha,\n rho=rho,\n b_ref=b_ref,\n main_chord=main_chord,\n aspect_ratio=aspect_ratio,\n roll=roll,\n beta=beta,\n yaw=yaw,\n sweep=sweep,\n physical_time=physical_time,\n n_surfaces=n_surfaces,\n route=route,\n case_name=case_name,\n RollNodes=RollNodes)\n\n # aeroelasticity parameters\n self.main_ea = 0.33\n self.main_cg = 0.43\n self.sigma = 1\n\n # other\n self.c_ref = 1.8288\n\n def update_mass_stiff(self):\n '''\n This method can be substituted to produce different wing configs.\n\n Forthis model, remind that the delta_frame_of_reference is chosen such\n that the B FoR axis are:\n - xb: along the wing span\n - yb: pointing towards the leading edge (i.e. roughly opposite than xa)\n - zb: upward as za\n '''\n # uniform mass/stiffness\n\n # ea,ga=1e7,1e6\n ea, ga = 1e9, 1e9\n gj = 0.987581e6\n eiy = 9.77221e6\n eiz = 1e2 * eiy\n base_stiffness = np.diag([ea, ga, ga, self.sigma * gj, self.sigma * eiy, eiz])\n\n self.stiffness = np.zeros((1, 6, 6))\n self.stiffness[0] = base_stiffness\n\n m_unit = 35.71\n j_tors = 8.64\n pos_cg_b = np.array([0., self.c_ref * (self.main_cg - self.main_ea), 0.])\n m_chi_cg = algebra.skew(m_unit * pos_cg_b)\n self.mass = np.zeros((1, 6, 6))\n self.mass[0, :, :] = np.diag([m_unit, m_unit, m_unit,\n j_tors, .1 * j_tors, .9 * j_tors])\n\n self.mass[0, :3, 3:] = m_chi_cg\n self.mass[0, 3:, :3] = -m_chi_cg\n\n self.elem_stiffness = np.zeros((self.num_elem_tot,), dtype=int)\n self.elem_mass = np.zeros((self.num_elem_tot,), dtype=int)\n\n\nclass GolandControlSurface(Goland):\n\n def __init__(self,\n M, N, # chord/span-wise discretisations\n Mstar_fact,\n u_inf, # flight cond\n alpha,\n cs_deflection=[0,0],\n n_control_surfaces=2,\n rho=1.02,\n b_ref=2. * 6.096, # geometry\n main_chord=1.8288,\n pct_flap=0.2,\n aspect_ratio=(2. * 6.096) / 1.8288,\n roll=0.,\n yaw=0.,\n beta=0.,\n sweep=0.,\n n_surfaces=1,\n physical_time=2,\n cs_type=0,\n route='.',\n case_name='goland',\n RollNodes=False):\n\n super().__init__(M=M, N=N,\n Mstar_fact=Mstar_fact,\n u_inf=u_inf,\n alpha=alpha,\n rho=rho,\n b_ref=b_ref,\n main_chord=main_chord,\n aspect_ratio=aspect_ratio,\n roll=roll,\n beta=beta,\n yaw=yaw,\n sweep=sweep,\n physical_time=physical_time,\n n_surfaces=n_surfaces,\n route=route,\n case_name=case_name,\n RollNodes=RollNodes)\n\n # aeroelasticity parameters\n self.main_ea = 0.33\n self.main_cg = 0.43\n self.sigma = 1\n\n self.n_control_surfaces = n_control_surfaces\n self.control_surface_deflection = np.zeros(self.n_control_surfaces, dtype=float)\n self.control_surface_deflection[:] = np.deg2rad(cs_deflection)\n self.control_surface_chord = M // 2 * np.ones(self.n_control_surfaces, dtype=int)\n self.control_surface_type = np.zeros(self.n_control_surfaces, dtype=int) + cs_type\n self.control_surface_hinge_coord = np.zeros_like(self.control_surface_type, dtype=int)\n # other\n self.c_ref = 1.8288\n self.pct_flap = pct_flap\n\n def update_aero_prop(self):\n assert hasattr(self, 'conn_glob'), \\\n 'Run \"update_derived_params\" before generating files'\n\n n_surfaces = self.n_surfaces\n num_node_surf = self.num_node_surf\n num_node_tot = self.num_node_tot\n num_elem_surf = self.num_elem_surf\n num_elem_tot = self.num_elem_tot\n pct_flap = self.pct_flap\n\n control_surface = self.control_surface\n\n ### Generate aerofoil profiles. Only on surf 0.\n Airfoils_surf = []\n if n_surfaces == 2:\n for inode in range(num_node_surf):\n eta = inode / num_node_surf\n Airfoils_surf.append(\n np.column_stack(\n geo_utils.interpolate_naca_camber(\n eta,\n self.root_airfoil_M, self.root_airfoil_P,\n self.tip_airfoil_M, self.tip_airfoil_P)))\n # if inode >= num_node_surf // 2:\n ws_elem = 0\n for i_surf in range(2):\n # print('Surface' + str(i_surf))\n for i_elem in range(num_elem_surf):\n for i_local_node in range(self.num_node_elem):\n if i_elem >= int(num_elem_surf *(1- pct_flap)):\n if i_surf == 0:\n control_surface[ws_elem + i_elem, i_local_node] = 0 # Right flap\n else:\n control_surface[ws_elem + i_elem, i_local_node] = 1 # Left flap\n ws_elem += num_elem_surf\n # control_surface[i_elem, i_local_node] = 0\n\n airfoil_distribution_surf = self.conn_surf\n airfoil_distribution = np.concatenate([airfoil_distribution_surf,\n airfoil_distribution_surf[::-1, [1, 0, 2]]])\n control_surface[-num_elem_surf:] = control_surface[-num_elem_surf:, :][::-1]\n\n if n_surfaces == 1:\n num_node_half = (num_node_surf + 1) // 2\n for inode in range(num_node_half):\n eta = inode / num_node_half\n Airfoils_surf.append(\n np.column_stack(\n geo_utils.interpolate_naca_camber(\n eta,\n self.root_airfoil_M, self.root_airfoil_P,\n self.tip_airfoil_M, self.tip_airfoil_P)))\n airfoil_distribution_surf = self.conn_surf[:num_elem_surf // 2, :]\n airfoil_distribution = np.concatenate([\n airfoil_distribution_surf[::-1, [1, 0, 2]],\n airfoil_distribution_surf])\n\n self.Airfoils_surf = Airfoils_surf\n self.airfoil_distribution = airfoil_distribution\n\n ### others\n self.aero_node = np.ones((num_node_tot,), dtype=bool)\n self.surface_m = self.M * np.ones((n_surfaces,), dtype=int)\n\n self.twist = np.zeros((num_elem_tot, 3))\n self.chord = self.main_chord * np.ones((num_elem_tot, 3))\n self.elastic_axis = self.main_ea * np.ones((num_elem_tot, 3,))\n self.control_surface = control_surface\n\n def create_linear_files(self, x0, input_vec):\n with h5.File(self.route + '/' + self.case_name + '.lininput.h5', 'a') as h5file:\n x0 = h5file.create_dataset(\n 'x0', data=x0)\n u = h5file.create_dataset(\n 'u', data=input_vec)\n\nclass QuasiInfinite(FlyingWing):\n '''\n Builds a very high aspect ratio wing, for simulating 2D aerodynamics\n This class is nothing but a FlyingWing with pre-defined geometry properties\n and mass/stiffness data (\"update_mass_stiffness\" method)\n '''\n\n def __init__(self,\n M, N,\n Mstar_fact,\n u_inf,\n alpha,\n aspect_ratio,\n rho=0.08891,\n b_ref=32.,\n main_chord=3.,\n roll=0.,\n beta=0.,\n sweep=0.,\n n_surfaces=1,\n route='.',\n case_name='qsinf',\n RollNodes=False,\n polar_file=None):\n super().__init__(M=M, N=N,\n Mstar_fact=Mstar_fact,\n u_inf=u_inf,\n alpha=alpha,\n rho=rho,\n b_ref=b_ref,\n main_chord=main_chord,\n aspect_ratio=aspect_ratio,\n roll=roll,\n beta=beta,\n sweep=sweep,\n n_surfaces=n_surfaces,\n route=route,\n case_name=case_name,\n RollNodes=RollNodes,\n polar_file=polar_file)\n self.c_ref = main_chord\n self.main_ea = 0.5\n self.main_cg = 0.5\n\n def update_mass_stiff(self):\n '''This method can be substituted to produce different wing configs'''\n # uniform mass/stiffness\n\n ea, ga = 1e9, 1e9\n gj = 2e8\n eiy = 1e8\n eiz = 1e8\n base_stiffness = np.diag([ea, ga, ga, gj, eiy, eiz])\n self.stiffness = np.zeros((1, 6, 6))\n self.stiffness[0] = self.sigma * base_stiffness\n\n m_unit = 1.\n self.mass = np.zeros((1, 6, 6))\n self.mass[0, :, :] = np.diag([m_unit, m_unit, m_unit, 1., .5, .5])\n self.elem_stiffness = np.zeros((self.num_elem_tot,), dtype=int)\n self.elem_mass = np.zeros((self.num_elem_tot,), dtype=int)\n\nclass Pazy(FlyingWing):\n '''\n Build a Pazy wing.\n\n The Pazy wing is a highly flexible wing designed and developed at Technion University as an aeroelastic\n test case.\n\n '''\n\n def __init__(self,\n M, N, # chord/span-wise discretisations\n Mstar_fact,\n u_inf, # flight cond\n alpha,\n rho=1.225,\n tip_rod=True,\n b_ref=2. * 0.55, # geometry\n main_chord=0.1,\n aspect_ratio=(2. * 0.55) / 0.1,\n roll=0.,\n yaw=0.,\n beta=0.,\n sweep=0.,\n n_surfaces=1,\n physical_time=2,\n route='.',\n case_name='pazy',\n RollNodes=False):\n\n super().__init__(M=M, N=N,\n Mstar_fact=Mstar_fact,\n u_inf=u_inf,\n alpha=alpha,\n rho=rho,\n b_ref=b_ref,\n main_chord=main_chord,\n aspect_ratio=aspect_ratio,\n roll=roll,\n beta=beta,\n yaw=yaw,\n sweep=sweep,\n physical_time=physical_time,\n n_surfaces=n_surfaces,\n route=route,\n case_name=case_name,\n RollNodes=RollNodes)\n\n # aeroelasticity parameters\n# self.main_ea = 0.3\n self.main_ea = 0.4475\n self.main_cg = 0.4510\n self.sigma = 1\n\n # other\n self.c_ref = main_chord\n\n self.tip_rod = tip_rod\n\n def update_mass_stiff(self):\n '''\n This method can be substituted to produce different wing configs.\n\n For this model, remind that the delta_frame_of_reference is chosen such\n that the B FoR axis are:\n - xb: along the wing span\n - yb: pointing towards the leading edge (i.e. roughly opposite than xa)\n - zb: upward as za\n '''\n # uniform mass/stiffness\n\n # Scaling factors (for debugging):\n sigma_scale_stiff = 1\n sigma_scale_I = 1\n\n # Pulling:\n ea = 7.12E+06\n\n # In-plane bending:\n ga_inp = 3.31E+06\n ei_inp = 3.11E+03\n\n # Out-of-plane bending:\n # Original:\n # ga_oup = -4.16E+03\n ei_oup = 4.67E+00\n\n # Adjusted:\n # Adjusted to become non-negative\n ga_oup = 1E+06\n\n # Torsion:\n gj = 7.20E+00\n\n base_stiffness = np.diag([ea, ga_oup, ga_inp, gj, ei_oup, ei_inp]) * sigma_scale_stiff\n\n self.stiffness = np.zeros((1, 6, 6))\n self.stiffness[0] = base_stiffness\n\n m_unit = 5.50E-01 # kg/m\n\n # Test cases to confirm properties:\n # Tests in vacuum, AoA=0 deg, analysed with NonLinearStatic beam solver. Verification displacements taken from\n # full 3D non-linear analysis in Abaqus.\n\n # Bending:\n # 5 N load at the tip. Expected deflection of about 62.6 mm at the tip (no gravity)\n # Tip coordinate in beam-fitted coordinates: X = 0.55m, Y = 0.m, Z = 0.m\n # m_unit = 0.001 # negligible mass distribution to mimic no-gravity FEA analysis\n # self.lumped_mass[0] = 5.2866 / 9.81\n # self.lumped_mass_position[0] = np.array([0, 0, 0])\n # self.lumped_mass_nodes[0] = self.N // 2\n # self.lumped_mass_inertia[0, :, :] = np.diag([1e-1, 1e-1, 1e-1])\n\n # Alternative bending:\n # self.app_forces[self.N//2, :] = [0, 0, 5.2866, 0, 0, 0]\n\n # Torsion:\n # Torsion of 0.3275 Nm, difference in tip LE/TE height: 1.130498767 + 1.361232758 = 2.49 mm\n # self.app_forces[self.N // 2, :] = [0, 0, 0, 0.3275, 0, 0]\n\n pos_cg_b = np.array([0., self.c_ref * (self.main_cg - self.main_ea), 0.])*sigma_scale_I\n m_chi_cg = algebra.skew(m_unit * pos_cg_b)\n self.mass = np.zeros((1, 6, 6))\n\n Js = 3.03E-04 # kg.m2/m\n\n # Mass matrix J components: torsion, out of plane bending, in-plane bending\n # Torsion: increasing J decreases natural frequency\n # Bending: increasing J increases natural frequency\n # Chosen experimentally to match natural frequencies from Abaqus analysis\n self.mass[0, :, :] = np.diag([m_unit, m_unit, m_unit, Js, 0.5*Js, 12*Js])*sigma_scale_I\n self.mass[0, :3, 3:] = m_chi_cg\n self.mass[0, 3:, :3] = -m_chi_cg\n\n self.elem_stiffness = np.zeros((self.num_elem_tot,), dtype=int)\n self.elem_mass = np.zeros((self.num_elem_tot,), dtype=int)\n\n if self.tip_rod:\n n_lumped_mass = 2\n self.lumped_mass = np.zeros((n_lumped_mass))\n self.lumped_mass_position = np.zeros((n_lumped_mass, 3))\n self.lumped_mass_inertia = np.zeros((n_lumped_mass, 3, 3))\n self.lumped_mass_nodes = np.zeros((n_lumped_mass), dtype=int)\n\n # Lumped mass for approximating the wingtip weight (1):\n self.lumped_mass[0] = 19.95 / 1E3 # mass in kg\n # self.lumped_mass[0] = 1 # mass in kg - just to visually check\n self.lumped_mass_position[0] = np.array([0.005, -0.005, 0])\n self.lumped_mass_nodes[0] = self.N // 2\n self.lumped_mass_inertia[0, :, :] = np.diag([1.2815E-04, 2.87E-07, 1.17E-04])\n\n # Lumped mass for approximating the wingtip weight (2):\n self.lumped_mass[1] = 19.95 / 1E3 # mass in kg\n # self.lumped_mass[1] = 1 # mass in kg - just to visually check\n self.lumped_mass_position[1] = np.array([-0.005, -0.005, 0]) # positive x now ascending towards root\n self.lumped_mass_nodes[1] = self.N // 2 + 1\n self.lumped_mass_inertia[1, :, :] = np.diag([1.2815E-04, 2.87E-07, 1.17E-04])\n\n\n\nclass PazyControlSurface(Pazy):\n\n def __init__(self,\n M, N, # chord/span-wise discretisations\n Mstar_fact,\n u_inf, # flight cond\n alpha,\n cs_deflection=0,\n n_control_surfaces=2,\n rho=1.225,\n tip_rod=True,\n b_ref= 2. * 0.55, # geometry\n main_chord= 0.1,\n pct_flap= 0.2,\n aspect_ratio= (2. * 0.55) / 0.1,\n roll=0.,\n yaw=0.,\n beta=0.,\n sweep=0.,\n n_surfaces=1,\n physical_time=2,\n route='.',\n case_name='pazy',\n RollNodes=False,\n cs_type=0):\n\n super().__init__(M=M, N=N,\n Mstar_fact=Mstar_fact,\n u_inf=u_inf,\n alpha=alpha,\n rho=rho,\n tip_rod=tip_rod,\n b_ref=b_ref,\n main_chord=main_chord,\n aspect_ratio=aspect_ratio,\n roll=roll,\n beta=beta,\n yaw=yaw,\n sweep=sweep,\n physical_time=physical_time,\n n_surfaces=n_surfaces,\n route=route,\n case_name=case_name,\n RollNodes=RollNodes)\n\n # aeroelasticity parameters\n# self.main_ea = 0.3\n self.main_ea = 0.4475\n self.main_cg = 0.4510\n self.sigma = 1\n\n self.n_control_surfaces = self.n_surfaces\n self.control_surface_deflection = np.zeros(self.n_control_surfaces, dtype=float)\n self.control_surface_deflection[:] = np.deg2rad(cs_deflection)\n self.control_surface_chord = M // 2 * np.ones(self.n_control_surfaces, dtype=int)\n self.control_surface_type = np.zeros(self.n_control_surfaces, dtype=int) + cs_type\n self.control_surface_hinge_coord = np.zeros_like(self.control_surface_type, dtype=int)\n # other\n self.c_ref = main_chord\n self.pct_flap = pct_flap\n\n def update_aero_prop(self):\n assert hasattr(self, 'conn_glob'), \\\n 'Run \"update_derived_params\" before generating files'\n\n n_surfaces = self.n_surfaces\n num_node_surf = self.num_node_surf\n num_node_tot = self.num_node_tot\n num_elem_surf = self.num_elem_surf\n num_elem_tot = self.num_elem_tot\n pct_flap = self.pct_flap\n\n control_surface = self.control_surface\n\n ### Generate aerofoil profiles. Only on surf 0.\n Airfoils_surf = []\n if n_surfaces == 2:\n for inode in range(num_node_surf):\n eta = inode / num_node_surf\n Airfoils_surf.append(\n np.column_stack(\n geo_utils.interpolate_naca_camber(\n eta,\n self.root_airfoil_M, self.root_airfoil_P,\n self.tip_airfoil_M, self.tip_airfoil_P)))\n # if inode >= num_node_surf // 2:\n ws_elem = 0\n for i_surf in range(2):\n for i_elem in range(num_elem_surf):\n for i_local_node in range(self.num_node_elem):\n if i_elem >= int(num_elem_surf *(1- pct_flap)):\n if i_surf == 0:\n control_surface[ws_elem + i_elem, i_local_node] = 0 # Right flap\n else:\n control_surface[ws_elem + i_elem, i_local_node] = 1 # Left flap\n ws_elem += num_elem_surf\n # control_surface[i_elem, i_local_node] = 0\n\n airfoil_distribution_surf = self.conn_surf\n airfoil_distribution = np.concatenate([airfoil_distribution_surf,\n airfoil_distribution_surf[::-1, [1, 0, 2]]])\n control_surface[-num_elem_surf:] = control_surface[-num_elem_surf:, :][::-1]\n\n if n_surfaces == 1:\n num_node_half = (num_node_surf + 1) // 2\n for inode in range(num_node_half):\n eta = inode / num_node_half\n Airfoils_surf.append(\n np.column_stack(\n geo_utils.interpolate_naca_camber(\n eta,\n self.root_airfoil_M, self.root_airfoil_P,\n self.tip_airfoil_M, self.tip_airfoil_P)))\n airfoil_distribution_surf = self.conn_surf[:num_elem_surf // 2, :]\n airfoil_distribution = np.concatenate([\n airfoil_distribution_surf[::-1, [1, 0, 2]],\n airfoil_distribution_surf])\n\n self.Airfoils_surf = Airfoils_surf\n self.airfoil_distribution = airfoil_distribution\n\n ### others\n self.aero_node = np.ones((num_node_tot,), dtype=bool)\n self.surface_m = self.M * np.ones((n_surfaces,), dtype=int)\n\n self.twist = np.zeros((num_elem_tot, 3))\n self.chord = self.main_chord * np.ones((num_elem_tot, 3))\n self.elastic_axis = self.main_ea * np.ones((num_elem_tot, 3,))\n self.control_surface = control_surface\n\n def create_linear_files(self, x0, input_vec):\n with h5.File(self.route + '/' + self.case_name + '.lininput.h5', 'a') as h5file:\n x0 = h5file.create_dataset(\n 'x0', data=x0)\n u = h5file.create_dataset(\n 'u', data=input_vec)\n\n\n\nif __name__ == '__main__':\n import os\n\n os.system('mkdir -p %s' % './test')\n\n ws = Goland(M=4, N=20, Mstar_fact=12, u_inf=25., alpha=2.0, route='./test')\n ws.clean_test_files()\n ws.update_derived_params()\n ws.generate_fem_file()\n ws.generate_aero_file()\n" }, { "path": "sharpy/cases/templates/fuselage_wing_configuration/__init__.py", "content": "" }, { "path": "sharpy/cases/templates/fuselage_wing_configuration/fuselage_wing_configuration.py", "content": "import configobj\nfrom .fwc_structure import FWC_Structure\nfrom .fwc_aero import FWC_Aero\nfrom .fwc_fuselage import FWC_Fuselage\nimport os\nimport sharpy.sharpy_main\n\n\nclass Fuselage_Wing_Configuration:\n \"\"\"\n Fuselage_Wing_Configuration is a template class to create an \n aircraft model of a simple wing-fuselage configuration within\n SHARPy. \n \n \"\"\"\n\n def __init__(self, case_name, case_route, output_route):\n self.case_name = case_name\n self.case_route = case_route\n self.output_route = output_route\n\n self.structure = None\n self.aero = None\n self.fuselage = None\n\n self.settings = None\n\n def init_aeroelastic(self, **kwargs):\n self.clean()\n self.init_structure(**kwargs)\n self.init_aero(**kwargs)\n if not kwargs.get('lifting_only', True):\n self.init_fuselage(**kwargs)\n\n def init_structure(self, **kwargs):\n self.structure = FWC_Structure(self.case_name, self.case_route, **kwargs)\n\n def init_aero(self, **kwargs):\n self.aero = FWC_Aero(self.structure, self.case_name, self.case_route,**kwargs)\n\n def init_fuselage(self, **kwargs):\n self.fuselage = FWC_Fuselage(self.structure, self.case_name, self.case_route,**kwargs)\n def generate(self):\n if not os.path.isdir(self.case_route):\n os.makedirs(self.case_route)\n self.structure.generate()\n self.aero.generate()\n if self.fuselage is not None:\n self.fuselage.generate()\n\n def create_settings(self, settings):\n file_name = self.case_route + '/' + self.case_name + '.sharpy'\n config = configobj.ConfigObj()\n config.filename = file_name\n for k, v in settings.items():\n config[k] = v\n config.write()\n self.settings = settings\n\n def clean(self):\n list_files = ['.fem.h5', '.aero.h5', '.nonlifting_body.h5', '.dyn.h5', '.mb.h5', '.sharpy', '.flightcon.txt']\n for file in list_files:\n path_file = self.case_route + '/' + self.case_name + file\n if os.path.isfile(path_file):\n os.remove(path_file)\n\n def run(self):\n sharpy.sharpy_main.main(['', self.case_route + '/' + self.case_name + '.sharpy'])\n\n" }, { "path": "sharpy/cases/templates/fuselage_wing_configuration/fwc_aero.py", "content": "import h5py as h5\nimport numpy as np\n\n\nclass FWC_Aero:\n \"\"\"\n FWC_Aero contains all attributes to define the aerodynamic grid and makes it accessible for SHARPy.\n \"\"\"\n def __init__(self, structure, case_name, case_route, **kwargs):\n \"\"\" \n Key-Word Arguments:\n - structure: structural object of BFF model\n \"\"\"\n self.structure = structure\n\n self.route = case_route\n self.case_name = case_name\n\n self.ea_wing = kwargs.get('elastic_axis',0.5)\n self.num_chordwise_panels = kwargs.get('num_chordwise_panels', 4)\n self.chord_wing = kwargs.get('chord', 1.)\n self.alpha_zero_deg = kwargs.get('alpha_zero_deg', 0.)\n self.n_surfaces = 2\n self.radius_fuselage = kwargs.get('max_radius', 0.5)\n self.lifting_only = kwargs.get('lifting_only', True)\n \n\n def generate(self):\n \"\"\"\n Function to set up all necessary parameter inputs to define the geometry and discretisation\n of the lifting surfaces. Finally, informations are saved to an .h5 file serving as an input\n file for SHARPy.\n \"\"\"\n self.initialize_attributes()\n self.set_wing_properties()\n self.set_junction_boundary_conditions()\n self.write_input_file()\n\n def initialize_attributes(self):\n \"\"\"\n Initilializes all necessary attributes for the aero.h5 input file based on the number of \n nodes, elements, and surfaces of the model.\n \"\"\"\n self.airfoil_distribution = np.zeros((self.structure.n_elem, self.structure.n_node_elem), dtype=int)\n self.surface_distribution = np.zeros((self.structure.n_elem,), dtype=int)\n self.surface_m = np.zeros((self.n_surfaces, ), dtype=int) + self.num_chordwise_panels\n self.aero_node = np.zeros((self.structure.n_node,), dtype=bool)\n\n self.twist = np.zeros((self.structure.n_elem, self.structure.n_node_elem))\n self.sweep = np.zeros_like(self.twist)\n self.chord = np.zeros_like(self.twist)\n self.elastic_axis = np.zeros_like(self.twist)\n\n self.junction_boundary_condition_aero = np.zeros((1, self.n_surfaces), dtype=int) - 1\n \n def get_y_junction(self):\n if self.structure.vertical_wing_position == 0:\n return self.radius_fuselage\n else:\n return np.sqrt(self.radius_fuselage**2-self.structure.vertical_wing_position**2)\n def set_wing_properties(self):\n \"\"\"\n Sets necessary parameters to define the lifting surfaces of one wing (right).\n \"\"\"\n \n if not self.lifting_only:\n self.aero_node[:self.structure.n_node_right_wing] = abs(self.structure.y[:self.structure.n_node_right_wing]) > self.get_y_junction() - 0.05\n self.aero_node[self.structure.n_node_right_wing:self.structure.n_node_wing_total] = self.aero_node[1:self.structure.n_node_right_wing]\n else:\n self.aero_node[:self.structure.n_node_wing_total] = True\n self.chord[:2*self.structure.n_elem_per_wing, :] = self.chord_wing\n self.elastic_axis[:2*self.structure.n_elem_per_wing, :] = self.ea_wing\n self.twist[:2*self.structure.n_elem_per_wing, :] = -np.deg2rad(self.alpha_zero_deg)\n # surf distribution 0 for right and 1 for left wing\n self.surface_distribution[self.structure.n_elem_per_wing:2*self.structure.n_elem_per_wing] = 1\n\n def set_junction_boundary_conditions(self):\n \"\"\"\n Sets the boundary conditions for the fuselage-wing junction. These BCs\n define the partner surface.\n \"\"\"\n # Right wing (surface 0) has the left wing (surface 1) as a partner surface.\n self.junction_boundary_condition_aero[0, 0] = 1\n # Left wing (surface 1) has the left wing (surface 0) as a partner surface.\n self.junction_boundary_condition_aero[0, 1] = 0\n\n def write_input_file(self):\n \"\"\"\n Writes previously defined parameters to an .h5 file which serves later as an \n input file for SHARPy.\n \"\"\"\n \n with h5.File(self.route + '/' + self.case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n airfoils_group.create_dataset('0', \n data=np.column_stack(\n self.generate_naca_camber(P=0, M=0)\n ))\n\n h5file.create_dataset('chord', data=self.chord)\n h5file.create_dataset('twist', data=self.twist)\n h5file.create_dataset('sweep', data=self.sweep)\n\n # airfoil distribution\n h5file.create_dataset('airfoil_distribution', data=self.airfoil_distribution)\n h5file.create_dataset('surface_distribution', data=self.surface_distribution)\n h5file.create_dataset('surface_m', data=self.surface_m)\n h5file.create_dataset('m_distribution', data='uniform')\n h5file.create_dataset('aero_node', data=self.aero_node)\n h5file.create_dataset('elastic_axis', data=self.elastic_axis)\n h5file.create_dataset('junction_boundary_condition', data=self.junction_boundary_condition_aero)\n \n\n def generate_naca_camber(self,M=0, P=0):\n \"\"\"\n Generates the camber line coordinates of a specified NACA airfoil.\n # TODO: needed?\n \"\"\"\n mm = M*1e-2\n p = P*1e-1\n\n def naca(x, mm, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return mm/(p*p)*(2*p*x - x*x)\n elif x > p and x < 1+1e-6:\n return mm/((1-p)*(1-p))*(1 - 2*p + 2*p*x - x*x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, mm, p) for x in x_vec])\n \n return x_vec, y_vec\n" }, { "path": "sharpy/cases/templates/fuselage_wing_configuration/fwc_fuselage.py", "content": "#! /usr/bin/env python3\nimport h5py as h5\nimport numpy as np\nimport matplotlib.pyplot as plt\n \n\nclass FWC_Fuselage:\n \"\"\"\n FWC_Fuselage contains all attributes to define the nonlifting body grid \n representing the fuselage shape and makes it accessible for SHARPy.\n \"\"\"\n def __init__(self, structure, case_name, case_route, **kwargs):\n \"\"\" \n Key-Word Arguments:\n - structure: structural object of BFF model\n \"\"\"\n self.num_radial_panels = kwargs.get('num_radial_panels', 12)\n self.max_radius = kwargs.get('max_radius')\n self.fuselage_shape = kwargs.get('fuselage_shape','cylindrical')\n self.flag_plot_radius = kwargs.get('flag_plot_radius', False)\n self.structure = structure\n\n self.route = case_route\n self.case_name = case_name\n self.n_nonlifting_bodies = 1\n\n def generate(self): \n \"\"\"\n Function to set up all necessary parameter inputs to define the geometry and discretisation\n of the nonlifting surfaces. Finally, informations are saved to an .h5 file serving as an input\n file for SHARPy.\n \"\"\"\n\n self.initialize_parameters()\n\n self.nonlifting_body_node[self.structure.n_node_wing_total:self.structure.n_node_fuselage_tail] = True\n if self.structure.vertical_wing_position == 0:\n self.nonlifting_body_node[0] = True\n self.nonlifting_body_distribution[self.structure.n_elem_per_wing*2:self.structure.n_elem_per_wing*2+self.structure.n_elem_fuselage] = 0\n self.nonlifting_body_m[0] = self.num_radial_panels\n\n self.get_fuselage_geometry()\n\n self.write_fuselage_input_file()\n \n\n def initialize_parameters(self): \n \"\"\"\n Initilializes all necessary attributes for the nonlifting.h5 input file based on the number of \n nodes, elements, and surfaces of the nonlifting model.\n \"\"\" \n self.nonlifting_body_node = np.zeros((self.structure.n_node,), dtype=bool)\n self.nonlifting_body_distribution = np.zeros((self.structure.n_elem,), dtype=int) - 1\n self.nonlifting_body_m = np.zeros((self.n_nonlifting_bodies, ), dtype=int)\n self.radius = np.zeros((self.structure.n_node,))\n\n def get_fuselage_geometry(self):\n x_coord_fuselage_sorted = np.sort(self.get_values_at_fuselage_nodes(self.structure.x))\n if self.fuselage_shape == 'cylindrical':\n radius_fuselage = self.create_fuselage_geometry(x_coord_fuselage_sorted.copy(), 0.2*self.structure.fuselage_length, 0.8*self.structure.fuselage_length) \n elif self.fuselage_shape == 'ellipsoid':\n radius_fuselage = self.get_radius_ellipsoid(x_coord_fuselage_sorted.copy(), self.structure.fuselage_length/2, self.max_radius)\n else:\n raise \"ERROR Fuselage shape {} unknown.\".format(self.fuselage_shape)\n if self.structure.vertical_wing_position == 0:\n self.radius[0] = radius_fuselage[self.structure.idx_junction]\n self.radius[self.structure.n_node_wing_total:] =np.delete(radius_fuselage, self.structure.idx_junction)\n else:\n self.radius[self.structure.n_node_wing_total:self.structure.n_node_fuselage_tail] = radius_fuselage\n if self.flag_plot_radius:\n self.plot_fuselage_radius(self.get_values_at_fuselage_nodes(self.structure.x), self.get_values_at_fuselage_nodes(self.radius))\n self.plot_fuselage_radius(x_coord_fuselage_sorted, radius_fuselage)\n\n def get_values_at_fuselage_nodes(self, array):\n return array[self.nonlifting_body_node]\n \n def plot_fuselage_radius(self, x, radius):\n plt.scatter(x,\n radius)\n plt.grid()\n plt.xlabel(\"x, m\")\n plt.ylabel(\"r, m\")\n plt.gca().set_aspect('equal')\n plt.show()\n\n def write_fuselage_input_file(self):\n with h5.File(self.route + '/' + self.case_name + '.nonlifting_body.h5', 'a') as h5file:\n h5file.create_dataset('shape', data='cylindrical')\n h5file.create_dataset('surface_m', data=self.nonlifting_body_m)\n h5file.create_dataset('nonlifting_body_node', data=self.nonlifting_body_node)\n h5file.create_dataset('surface_distribution', data=self.nonlifting_body_distribution)\n h5file.create_dataset('radius', data=self.radius)\n\n def get_radius_ellipsoid(self, x_coordinates, a, b):\n x_coordinates[:] -= x_coordinates[-1] - a\n y_coordinates = b*np.sqrt(1-(x_coordinates/a)**2)\n return y_coordinates\n\n def find_index_of_closest_entry(self, array_values, target_value):\n return np.argmin(np.abs(array_values - target_value))\n\n\n def create_fuselage_geometry(self, x_coord_fuselage, x_nose_end, x_tail_start):\n array_radius = np.zeros_like(x_coord_fuselage)\n # start with nose at zero to get indices of nose and tail correct\n x_coord_fuselage[:] -= x_coord_fuselage[0]\n idx_cylinder_start = self.find_index_of_closest_entry(x_coord_fuselage, x_nose_end)\n idx_cylinder_end = self.find_index_of_closest_entry(x_coord_fuselage, x_tail_start)\n\n # set constant radius of cylinder\n array_radius[idx_cylinder_start:idx_cylinder_end] = self.max_radius\n # get ellipsoidal nose and tail shape\n array_radius[:idx_cylinder_start+1] = self.get_nose_shape(x_coord_fuselage[:idx_cylinder_start+1],\n self.max_radius)\n \n array_radius[idx_cylinder_end-1:] = np.flip(self.get_nose_shape(x_coord_fuselage[idx_cylinder_end-1:],\n self.max_radius))\n \n return array_radius\n \n def get_nose_shape(self, x_coord, radius):\n n_nodes = len(x_coord)\n x_coord[:] -= x_coord[-1]\n x_coord = np.concatenate((x_coord, np.flip(x_coord[:-1]))) \n radius = self.get_radius_ellipsoid(x_coord, x_coord[0], radius)\n return radius[:n_nodes]\n" }, { "path": "sharpy/cases/templates/fuselage_wing_configuration/fwc_get_settings.py", "content": "import numpy as np\nimport sharpy.utils.algebra as algebra\n\ndef define_simulation_settings(flow, model, alpha_deg, u_inf, \n dt=1,\n rho = 1.225, \n lifting_only=True, \n nonlifting_only=False, \n phantom_test=False,\n horseshoe=False, **kwargs):\n gravity = kwargs.get('gravity',True)\n nonlifting_body_interactions = not lifting_only and not nonlifting_only\n wake_length = kwargs.get('wake_length', 10)\n # Other parameters\n if horseshoe:\n mstar = 1 \n else:\n mstar = wake_length*model.aero.num_chordwise_panels\n # numerics\n n_step = kwargs.get('n_step', 5)\n structural_relaxation_factor = kwargs.get('structural_relaxation_factor', 0.6)\n tolerance = kwargs.get('tolerance', 1e-6)\n fsi_tolerance = kwargs.get('fsi_tolerance', 1e-6)\n num_cores = kwargs.get('num_cores',2)\n\n if not lifting_only:\n nonlifting_body_interactions = True\n else:\n nonlifting_body_interactions = False\n settings = {}\n settings['SHARPy'] = {'case': model.case_name,\n 'route': model.case_route,\n 'flow': flow,\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': model.output_route,\n 'log_file': model.case_name + '.log'}\n\n\n settings['BeamLoader'] = {'unsteady': 'on',\n 'orientation': algebra.euler2quat(np.array([0.,\n np.deg2rad(alpha_deg),\n 0.]))}\n\n settings['BeamLoads'] = {}\n settings['LiftDistribution'] = {'coefficients': True}\n \n settings['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'gravity_on': gravity,\n 'gravity': 9.81}\n\n settings['StaticUvlm'] = {'print_info': 'on',\n 'horseshoe': horseshoe,\n 'num_cores': num_cores,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho,\n 'nonlifting_body_interactions': nonlifting_body_interactions,\n 'only_nonlifting': nonlifting_only,\n 'phantom_wing_test': phantom_test,\n 'ignore_first_x_nodes_in_force_calculation': kwargs.get('ignore_first_x_nodes_in_force_calculation', 0),\n }\n\n settings['StaticCoupled'] = {'print_info': 'off',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': settings['NonLinearStatic'],\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': settings['StaticUvlm'],\n 'max_iter': 100,\n 'n_load_steps': n_step,\n 'tolerance': fsi_tolerance,\n 'relaxation_factor': structural_relaxation_factor,\n 'nonlifting_body_interactions': nonlifting_body_interactions}\n\n settings['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n 'mstar': mstar, #int(20/tstep_factor),\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {\n 'u_inf': u_inf,\n 'u_inf_direction': [1., 0., 0.],\n 'dt': dt,\n },\n }\n if 'WriteVariablesTime' in flow:\n settings['WriteVariablesTime'] = {'cleanup_old_solution': True}\n if kwargs.get('writeCpVariables', False):\n settings['WriteVariablesTime']['nonlifting_nodes_variables'] = ['pressure_coefficients'] \n settings['WriteVariablesTime']['nonlifting_nodes_isurf'] = np.zeros((model.structure.n_node_fuselage,))\n settings['WriteVariablesTime']['nonlifting_nodes_im'] = np.zeros((model.structure.n_node_fuselage))\n settings['WriteVariablesTime']['nonlifting_nodes_in'] = list(range(model.structure.n_node_fuselage))\n if kwargs.get('writeWingPosVariables', False):\n settings['WriteVariablesTime']['structure_variables'] = ['pos']\n settings['WriteVariablesTime']['structure_nodes'] = list(range(model.structure.n_node-2))\n\n settings['NonliftingbodygridLoader'] = {}\n\n settings['AeroForcesCalculator'] = {'coefficients': False}\n settings['AerogridPlot'] = {'plot_nonlifting_surfaces': nonlifting_body_interactions}\n settings['BeamPlot'] = {}\n\n settings['NoStructural'] = {}\n settings['NonLinearDynamicPrescribedStep'] = {'print_info': 'off',\n 'max_iterations': 950,\n 'delta_curved': 1e-1,\n 'min_delta': 1e-6,\n 'newmark_damp': 1e-4,\n 'gravity_on': gravity,\n 'gravity': 9.81,\n 'num_steps': kwargs.get('n_tsteps',10),\n 'dt': dt,\n }\n settings['StepUvlm'] = {'print_info': 'on',\n 'num_cores': 4,\n 'convection_scheme': 3,\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0., 0.]},\n 'rho': rho,\n 'n_time_steps': kwargs.get('n_tsteps',10),\n 'dt': dt,\n 'phantom_wing_test': phantom_test,\n 'nonlifting_body_interactions': not lifting_only,\n 'gamma_dot_filtering': 3, \n 'ignore_first_x_nodes_in_force_calculation': kwargs.get('ignore_first_x_nodes_in_force_calculation', 0),}\n \n dynamic_structural_solver = kwargs.get('structural_solver','NonLinearDynamicPrescribedStep')\n settings['DynamicCoupled'] = {'structural_solver': dynamic_structural_solver,\n 'structural_solver_settings': settings[dynamic_structural_solver],\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'fsi_substeps': kwargs.get('fsi_substeps', 200),\n 'fsi_tolerance': fsi_tolerance,\n 'relaxation_factor': kwargs.get('relaxation_factor',0.1),\n 'minimum_steps': 1,\n 'relaxation_steps': 150,\n 'final_relaxation_factor': kwargs.get('final_relaxation_factor', 0.05),\n 'n_time_steps': kwargs.get('n_tsteps',10),\n 'dt': dt,\n 'nonlifting_body_interactions': not lifting_only,\n 'include_unsteady_force_contribution': kwargs.get('unsteady_force_distribution', True), \n 'postprocessors': ['BeamLoads'],\n 'postprocessors_settings': {\n 'BeamLoads': {'csv_output': 'off'},\n },\n }\n\n\n return settings" }, { "path": "sharpy/cases/templates/fuselage_wing_configuration/fwc_structure.py", "content": "import numpy as np\nimport h5py as h5\n\n\nclass FWC_Structure:\n\n \"\"\"\n FWC_Structure contains all attributes to define the beam geometriy \n and discretisation and makes it accessible for SHARPy.\n \"\"\"\n def __init__(self, case_name, case_route, **kwargs):\n self.n_elem_multiplier = kwargs.get('n_elem_multiplier', 1)\n\n self.route = case_route\n self.case_name = case_name\n\n self.n_node_elem = 3\n self.n_surfaces = 2\n self.n_material = 2 # wing + fuselage\n \n self.half_wingspan = kwargs.get('half_wingspan', 2)\n self.fuselage_length = kwargs.get('fuselage_length', 10)\n self.offset_nose_wing_beam = kwargs.get('offset_nose_wing', self.fuselage_length/2)\n self.vertical_wing_position = kwargs.get('vertical_wing_position', 0.)\n self.n_elem_per_wing = kwargs.get('n_elem_per_wing', 10)\n self.n_elem_fuselage = kwargs.get('n_elem_fuselage', 10)\n\n self.sigma = kwargs.get('sigma', 10)\n self.sigma_fuselage = kwargs.get('sigma_fuselage', 100.)\n\n\n\n self.enforce_uniform_fuselage_discretisation = kwargs.get(\n 'enforce_uniform_fuselage_discretisation', False\n )\n self.fuselage_discretisation = kwargs.get('fuselage_discretisation', 'uniform')\n\n self.thrust = 0.\n\n def generate(self):\n \"\"\"\n Function to set up all necessary parameter inputs to define the geometry and discretisation\n of the beam. Finally, informations are saved to an .h5 file serving as an input\n file for SHARPy.\n \"\"\"\n self.set_element_and_nodes()\n self.initialize_parameters()\n\n self.set_stiffness_and_mass_propoerties()\n self.set_beam_properties_right_wing()\n self.mirror_wing_beam() \n self.app_forces[0] = [0, self.thrust, 0, 0, 0, 0]\n \n self.set_beam_properties_fuselage()\n self.write_input_file()\n\n def set_element_and_nodes(self):\n \"\"\"\n Based on the specified number of elements of the wing and fuselage, the number of nodes of each \n component and the total number of elements and nodes are defined here.\n \"\"\"\n\n self.n_node_fuselage = self.n_elem_fuselage*(self.n_node_elem - 1)\n self.n_node_right_wing = self.n_elem_per_wing*(self.n_node_elem - 1) + 1\n # the left wing beam has one node less than the right one, since they shares the center node\n self.n_node_left_wing = self.n_node_right_wing - 1 \n\n self.n_node_wing_total = self.n_node_right_wing + self.n_node_left_wing\n self.n_node_fuselage_tail = self.n_node_wing_total + self.n_node_fuselage\n self.n_node = self.n_node_fuselage + self.n_node_wing_total\n self.n_elem =self.n_elem_fuselage + 2 * self.n_elem_per_wing\n\n # vertical wing offset requires a connection element between wing and fuselage beam\n if not self.vertical_wing_position == 0:\n self.n_elem += 1\n self.n_node += 1\n\n def initialize_parameters(self):\n self.x = np.zeros((self.n_node, ))\n self.y = np.zeros((self.n_node, ))\n self.z = np.zeros((self.n_node, ))\n\n self.frame_of_reference_delta = np.zeros((self.n_elem, self.n_node_elem, 3))\n self.conn = np.zeros((self.n_elem, self.n_node_elem), dtype=int)\n\n self.beam_number = np.zeros((self.n_elem, ), dtype=int)\n self.boundary_conditions = np.zeros((self.n_node, ), dtype=int)\n self.structural_twist = np.zeros((self.n_elem, self.n_node_elem))\n\n self.app_forces = np.zeros((self.n_node, 6))\n\n\n self.stiffness = np.zeros((self.n_material, 6, 6))\n self.mass = np.zeros((self.n_material, 6, 6))\n self.elem_stiffness = np.zeros((self.n_elem, ), dtype=int)\n self.mass = np.zeros((self.n_material, 6, 6))\n self.elem_mass = np.zeros((self.n_elem, ), dtype=int)\n\n def set_stiffness_and_mass_propoerties(self):\n # Define aeroelastic properties\n ea = 1e7\n ga = 1e5\n gj = 1e4\n eiy = 2e4\n eiz = 4e6\n m_bar_main = 0.75\n j_bar_main = 0.075\n\n m_bar_fuselage = 0.3*1.5\n j_bar_fuselage = 0.08\n\n base_stiffness_main = self.sigma*np.diag([ea, ga, ga, gj, eiy, eiz])\n base_stiffness_fuselage = base_stiffness_main.copy()*self.sigma_fuselage\n base_stiffness_fuselage[4, 4] = base_stiffness_fuselage[5, 5]\n\n self.stiffness[0, ...] = base_stiffness_main\n self.stiffness[1, ...] = base_stiffness_fuselage\n\n self.mass[0, ...] = self.generate_mass_matrix(m_bar_main, j_bar_main)\n self.mass[1, ...] = self.generate_mass_matrix(m_bar_fuselage, j_bar_fuselage)\n \n def generate_mass_matrix(self, m_bar, j_bar):\n return np.diag([m_bar, m_bar, m_bar, \n j_bar, 0.5*j_bar, 0.5*j_bar])\n\n def set_beam_properties_right_wing(self):\n \"\"\"\n Defines all necessary parameters to define the beam including node coordinate,\n elements with their associated nodes, frame of reference delta, boundary conditions\n such as reference node and free tips, stiffness and mass property ID for each element,\n and twist.\n \"\"\" \n self.y[:self.n_node_right_wing] = np.linspace(0, self.half_wingspan, self.n_node_right_wing)\n self.z[:self.n_node_right_wing] += self.vertical_wing_position\n for ielem in range(self.n_elem_per_wing):\n self.conn[ielem, :] = ((np.ones((3, )) * ielem * (self.n_node_elem - 1)) +\n [0, 2, 1]) \n for ilocalnode in range(self.n_node_elem):\n self.frame_of_reference_delta[ielem, ilocalnode, :] = [-1.0, 0.0, 0.0] \n \n self.boundary_conditions[0] = 1\n self.boundary_conditions[self.n_node_right_wing-1] = -1 # free tip\n\n def mirror_wing_beam(self):\n \"\"\"\n Mirrors the parameters from the beam representing the right free-flying wing\n for the left one.\n \"\"\"\n\n self.x[self.n_node_right_wing:self.n_node_wing_total] = self.x[1:self.n_node_right_wing]\n self.y[self.n_node_right_wing:self.n_node_wing_total] = - self.y[1:self.n_node_right_wing]\n self.z[self.n_node_right_wing:self.n_node_wing_total] = self.z[1:self.n_node_right_wing]\n self.frame_of_reference_delta[self.n_elem_per_wing:2*self.n_elem_per_wing, :, :] = self.frame_of_reference_delta[:self.n_elem_per_wing, :, :] * (-1)\n self.elem_stiffness[self.n_elem_per_wing:2*self.n_elem_per_wing] = self.elem_stiffness[:self.n_elem_per_wing]\n self.elem_mass[self.n_elem_per_wing:2*self.n_elem_per_wing] = self.elem_mass[:self.n_elem_per_wing]\n\n self.beam_number[self.n_elem_per_wing:2*self.n_elem_per_wing] = 1\n self.boundary_conditions[self.n_node_wing_total-1] = -1 # free tip\n self.conn[self.n_elem_per_wing:2*self.n_elem_per_wing, :] = self.conn[:self.n_elem_per_wing, :] + self.n_node_right_wing - 1\n self.conn[self.n_elem_per_wing, 0] = 0\n\n def set_x_coordinate_fuselage(self):\n if self.vertical_wing_position == 0:\n n_nodes_fuselage = self.n_node_fuselage + 1\n else:\n n_nodes_fuselage = self.n_node_fuselage\n if self.fuselage_discretisation == 'uniform':\n x_coord_fuselage = np.linspace(0, self.fuselage_length, n_nodes_fuselage) - self.offset_nose_wing_beam\n elif self.fuselage_discretisation == '1-cosine':\n x_coord_fuselage = np.linspace(0, 1, n_nodes_fuselage) \n x_coord_fuselage = 0.5*(1.0 - np.cos(x_coord_fuselage*np.pi))\n x_coord_fuselage *= self.fuselage_length\n x_coord_fuselage -= self.offset_nose_wing_beam\n else:\n raise \"ERROR Specified fuselage discretisation '{}' unknown\".format(self.fuselage_discretisation)\n self.idx_junction = self.find_index_of_closest_entry(x_coord_fuselage, self.x[0])\n \n self.idx_junction_global = self.idx_junction + self.n_node_wing_total\n if self.vertical_wing_position == 0:\n if self.enforce_uniform_fuselage_discretisation:\n self.x[:self.n_node_wing_total] += x_coord_fuselage[self.idx_junction]\n x_coord_fuselage = np.delete(x_coord_fuselage, self.idx_junction)\n self.x[self.n_node_wing_total:self.n_node_fuselage_tail] = x_coord_fuselage\n\n def adjust_fuselage_connectivities(self):\n idx_in_conn = np.where(self.conn == self.idx_junction_global)\n self.conn[idx_in_conn[0][0]+1:, :] -= 1\n\n if idx_in_conn[0][0] == 2:\n # if middle node, correct end node of element \n self.conn[idx_in_conn[0][0], 1] -= 1\n for i_match in range(np.shape(idx_in_conn)[1]):\n #several matches possible if junction node is not middle node\n self.conn[idx_in_conn[0][i_match], idx_in_conn[1][i_match]] = 0\n\n def add_additional_element_for_low_wing(self):\n self.x[-1] = self.x[0]\n self.y[-1] = self.y[0]\n self.z[-1] = self.vertical_wing_position / 2\n self.conn[-1, 0] = 0\n self.conn[-1, 1] = self.idx_junction_global\n self.conn[-1, 2] = self.n_node - 1\n self.elem_stiffness[-1] = 1\n self.elem_mass[-1] = 1\n self.beam_number[-1] = 3\n \n \n def set_beam_properties_fuselage(self):\n self.set_x_coordinate_fuselage()\n self.beam_number[self.n_elem_per_wing*2:] = 2\n for ielem in range(self.n_elem_per_wing * 2,self.n_elem):\n self.conn[ielem, :] = ((np.ones((3, )) * (ielem-self.n_elem_per_wing * 2) * (self.n_node_elem - 1)) +\n [0, 2, 1]) + self.n_node_wing_total\n for ilocalnode in range(self.n_node_elem):\n self.frame_of_reference_delta[ielem, ilocalnode, :] = [0.0, 1.0, 0.0] \n self.elem_stiffness[self.n_elem_per_wing*2:] = 1\n self.elem_mass[self.n_elem_per_wing*2:] = 1\n \n if self.vertical_wing_position == 0:\n self.adjust_fuselage_connectivities()\n else:\n self.add_additional_element_for_low_wing()\n self.boundary_conditions[self.n_node_wing_total] = -1 # fuselage nose\n self.boundary_conditions[self.n_node_wing_total + self.n_node_fuselage - 1] = -1 # fuselage tail\n\n def find_index_of_closest_entry(self, array_values, target_value):\n return np.argmin(np.abs(array_values - target_value))\n\n def set_thrust(self, value):\n self.thrust = value\n\n def write_input_file(self):\n \"\"\"\n Writes previously defined parameters to an .h5 file which serves later as an \n input file for SHARPy.\n \"\"\" \n with h5.File(self.route + '/' + self.case_name + '.fem.h5', 'a') as h5file:\n h5file.create_dataset('coordinates', data=np.column_stack((self.x, self.y, self.z)))\n h5file.create_dataset('connectivities', data=self.conn)\n h5file.create_dataset('num_node_elem', data=self.n_node_elem)\n h5file.create_dataset('num_node', data=self.n_node)\n h5file.create_dataset('num_elem', data=self.n_elem)\n h5file.create_dataset('stiffness_db', data=self.stiffness)\n h5file.create_dataset('elem_stiffness', data=self.elem_stiffness)\n h5file.create_dataset('mass_db', data=self.mass)\n h5file.create_dataset('elem_mass', data=self.elem_mass)\n h5file.create_dataset('frame_of_reference_delta', data=self.frame_of_reference_delta)\n h5file.create_dataset('boundary_conditions', data=self.boundary_conditions)\n h5file.create_dataset('beam_number', data=self.beam_number)\n\n h5file.create_dataset('structural_twist', data=self.structural_twist)\n h5file.create_dataset('app_forces', data=self.app_forces)\n" }, { "path": "sharpy/cases/templates/template_wt.py", "content": "\"\"\"\ntemplate_wt\n\nFunctions needed to generate a wind turbines\n\nNotes:\n To load this library: import sharpy.cases.templates.template_wt as template_wt\n\"\"\"\n\n\nimport pandas as pd\nimport numpy as np\nimport scipy.interpolate as scint\nimport math\nimport sys\n\nimport sharpy.utils.generate_cases as gc\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.h5utils as h5\nfrom sharpy.utils.constants import deg2rad\nimport sharpy.aero.utils.airfoilpolars as ap\nimport sharpy.utils.cout_utils as cout\n\nif not cout.check_running_unittest():\n cout.cout_wrap.print_screen = True\n cout.cout_wrap.print_file = False\n\n\n######################################################################\n# AUX FUNCTIONS\n######################################################################\ndef create_node_radial_pos_from_elem_centres(root_elem_centres_tip, num_node, num_elem, num_node_elem):\n \"\"\"\n create_node_radial_pos_from_elem_centres\n\n Define the position of the nodes adn the elements in the blade from the list of element centres\n\n Args:\n root_elem_centres_tip (np.array):\n - First value: Radial position of the beginning of the blade\n - Last value: Radial position of the tip of the blade\n - Rest of the values: Radial position the rest of the strucutral element centres\n num_node (int): number of nodes\n num_elem (int): number of elements\n num_node_elem (int): number of nodes in each element\n\n Returns:\n node_r (np.array): Radial position of the nodes\n elem_r (np.array): Radial position of the elements\n\n Notes:\n Radial positions are measured from the hub centre and measured in the rotation plane\n \"\"\"\n\n elem_r = root_elem_centres_tip[1:-1]\n node_r = np.zeros((num_node, ), )\n node_r[0] = root_elem_centres_tip[0]\n node_r[-2] = root_elem_centres_tip[-2]\n node_r[-1] = root_elem_centres_tip[-1]\n\n for ielem in range(num_elem-1):\n node_r[ielem*(num_node_elem-1)+1] = elem_r[ielem]\n node_r[ielem*(num_node_elem-1)+2] = 0.5*(elem_r[ielem]+elem_r[ielem+1])\n\n return node_r, elem_r\n\n\ndef create_blade_coordinates(num_node, node_r, node_y, node_z):\n \"\"\"\n create_blade_coordinates\n\n Creates SHARPy format of the nodes coordinates and\n applies prebending and presweept to node radial position\n\n Args:\n num_node (int): number of nodes\n node_r (np.array): Radial position of the nodes\n node_y (np.array): Displacement of each point IN the rotation plane\n node_z (np.array): Displacement of each point OUT OF the rotation plane\n\n Returns:\n coordinates (np.array): nodes coordinates\n \"\"\"\n coordinates = np.zeros((num_node, 3),)\n coordinates[:, 0] = node_r\n coordinates[:, 1] = node_y\n coordinates[:, 2] = node_z\n return coordinates\n\n\n######################################################################\n# FROM excel type04\n######################################################################\ndef spar_from_excel_type04(op_params,\n geom_params,\n excel_description,\n options):\n \"\"\"\n spar_from_excel_type04\n\n Function needed to generate a spar floating wind turbine rotor from an excel database type04.\n Rotor + tower + floating spar\n\n Args:\n op_param (dict): Dictionary with operating parameters\n geom_param (dict): Dictionray with geometical parameters\n excel_description (dict): Dictionary describing the sheets of the excel file\n option (dict): Dictionary with the different options for the wind turbine generation\n\n Returns:\n floating (sharpy.utils.generate_cases.AeroelasticInfromation): Aeroelastic information of the spar floating wind turbine\n \"\"\"\n\n # Generate the tower + rotor\n wt, LC, MB, hub_nodes = generate_from_excel_type03(op_params,\n geom_params,\n excel_description,\n options)\n # Remove base clam\n wt.StructuralInformation.boundary_conditions[0] = 0\n\n excel_file_name = excel_description['excel_file_name']\n excel_sheet_parameters = excel_description['excel_sheet_parameters']\n excel_sheet_structural_spar = excel_description['excel_sheet_structural_spar']\n tol_remove_points = geom_params['tol_remove_points']\n\n TowerBaseHeight = gc.read_column_sheet_type01(excel_file_name,\n excel_sheet_parameters,\n 'TowerBaseHeight')\n\n # Generate the spar\n if options['concentrate_spar']:\n mtower = wt.StructuralInformation.mass_db[0, 0, 0]\n\n PlatformTotalMass = gc.read_column_sheet_type01(excel_file_name,\n excel_sheet_parameters,\n 'PlatformTotalMass')\n PlatformIrollCM = gc.read_column_sheet_type01(excel_file_name,\n excel_sheet_parameters,\n 'PlatformIrollCM')\n PlatformIpitchCM = gc.read_column_sheet_type01(excel_file_name,\n excel_sheet_parameters,\n 'PlatformIpitchCM')\n PlatformIyawCM = gc.read_column_sheet_type01(excel_file_name,\n excel_sheet_parameters,\n 'PlatformIyawCM')\n PlatformCMbelowSWL = gc.read_column_sheet_type01(excel_file_name,\n excel_sheet_parameters,\n 'PlatformCMbelowSWL')\n\n mpoint = PlatformTotalMass - mtower*TowerBaseHeight\n IyawPoint = PlatformIyawCM - (1./6)*mtower*TowerBaseHeight**3\n IpitchPoint = PlatformIpitchCM + PlatformTotalMass*PlatformCMbelowSWL**2 - (1./3)*mtower*TowerBaseHeight**3\n IrollPoint = PlatformIrollCM + PlatformTotalMass*PlatformCMbelowSWL**2 - (1./3)*mtower*TowerBaseHeight**3\n xpoint = (PlatformTotalMass*PlatformCMbelowSWL + 0.5*mtower*TowerBaseHeight**2)/mpoint\n\n iner_mat = np.zeros((6,6))\n iner_mat[0:3, 0:3] = mpoint*np.eye(3)\n iner_mat[0:3, 3:6] = -mpoint*algebra.skew(np.array([-xpoint, 0, 0]))\n iner_mat[3:6, 0:3] = -iner_mat[0:3, 3:6]\n iner_mat[3, 3] = IyawPoint\n iner_mat[4, 4] = IpitchPoint\n iner_mat[5, 5] = IrollPoint\n\n base_stiffness_top = wt.StructuralInformation.stiffness_db[0, :, :]\n base_mass_top = wt.StructuralInformation.mass_db[0, :, :]\n base_stiffness_bot = 100*base_stiffness_top\n base_mass_bot = base_mass_top\n\n num_lumped_mass_mat = 1\n\n else:\n SparHeight = gc.read_column_sheet_type01(excel_file_name,\n excel_sheet_parameters,\n 'SparHeight')\n SparBallastMass = gc.read_column_sheet_type01(excel_file_name,\n excel_sheet_parameters,\n 'SparBallastMass')\n SparBallastDepth = gc.read_column_sheet_type01(excel_file_name,\n excel_sheet_parameters,\n 'SparBallastDepth')\n\n # Read from excel file\n SparHtFract = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_spar, 'SparHtFract')\n SparMassDen = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_spar, 'SparMassDen')\n SparFAStif = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_spar, 'SparFAStif')\n SparSSStif = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_spar, 'SparSSStif')\n SparGJStif = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_spar, 'SparGJStif')\n SparEAStif = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_spar, 'SparEAStif')\n SparFAIner = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_spar, 'SparFAIner')\n SparSSIner = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_spar, 'SparSSIner')\n SparFAcgOf = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_spar, 'SparFAcgOf')\n SparSScgOf = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_spar, 'SparSScgOf')\n\n ElevationSpar = SparHtFract*SparHeight\n spar = gc.AeroelasticInformation()\n spar.StructuralInformation.num_elem = len(ElevationSpar) - 2\n spar.StructuralInformation.num_node_elem = 3\n spar.StructuralInformation.compute_basic_num_node()\n\n # Interpolate excel variables into the correct locations\n node_r, elem_r = create_node_radial_pos_from_elem_centres(ElevationSpar,\n spar.StructuralInformation.num_node,\n spar.StructuralInformation.num_elem,\n spar.StructuralInformation.num_node_elem)\n\n # Stiffness\n elem_EA = np.interp(elem_r, ElevationSpar, SparEAStif)\n elem_EIz = np.interp(elem_r, ElevationSpar, SparSSStif)\n elem_EIy = np.interp(elem_r, ElevationSpar, SparFAStif)\n elem_GJ = np.interp(elem_r, ElevationSpar, SparGJStif)\n # Stiffness: estimate unknown properties\n cout.cout_wrap.print_file = False\n cout.cout_wrap('WARNING: The poisson cofficient is assumed equal to 0.3', 3)\n cout.cout_wrap('WARNING: Cross-section area is used as shear area', 3)\n poisson_coef = 0.3\n elem_GAy = elem_EA/2.0/(1.0+poisson_coef)\n elem_GAz = elem_EA/2.0/(1.0+poisson_coef)\n\n # Inertia\n elem_mass_per_unit_length = np.interp(elem_r, ElevationSpar, SparMassDen)\n elem_mass_iner_y = np.interp(elem_r, ElevationSpar, SparFAIner)\n elem_mass_iner_z = np.interp(elem_r, ElevationSpar, SparSSIner)\n # TODO: check yz axis and Flap-edge\n elem_pos_cg_B = np.zeros((spar.StructuralInformation.num_elem, 3),)\n elem_pos_cg_B[:, 1] = np.interp(elem_r, ElevationSpar, SparSScgOf)\n elem_pos_cg_B[:, 2] = np.interp(elem_r, ElevationSpar, SparFAcgOf)\n\n # Stiffness: estimate unknown properties\n cout.cout_wrap('WARNING: Using perpendicular axis theorem to compute the inertia around xB', 3)\n elem_mass_iner_x = elem_mass_iner_y + elem_mass_iner_z\n\n # Create the tower\n spar.StructuralInformation.create_mass_db_from_vector(elem_mass_per_unit_length, elem_mass_iner_x, elem_mass_iner_y, elem_mass_iner_z, elem_pos_cg_B)\n spar.StructuralInformation.create_stiff_db_from_vector(elem_EA, elem_GAy, elem_GAz, elem_GJ, elem_EIy, elem_EIz)\n\n coordinates = np.zeros((spar.StructuralInformation.num_node, 3),)\n coordinates[:, 0] = node_r\n\n spar.StructuralInformation.generate_1to1_from_vectors(\n num_node_elem=spar.StructuralInformation.num_node_elem,\n num_node=spar.StructuralInformation.num_node,\n num_elem=spar.StructuralInformation.num_elem,\n coordinates=coordinates,\n stiffness_db=spar.StructuralInformation.stiffness_db,\n mass_db=spar.StructuralInformation.mass_db,\n frame_of_reference_delta='y_AFoR',\n vec_node_structural_twist=np.zeros((spar.StructuralInformation.num_node,),),\n num_lumped_mass=1)\n\n spar.StructuralInformation.boundary_conditions[0] = -1\n spar.StructuralInformation.boundary_conditions[-1] = 1\n\n # Include ballast mass\n dist = np.abs(coordinates[:, 0] + SparBallastDepth)\n min_dist = np.amin(dist)\n loc_min = np.where(dist == min_dist)[0]\n\n cout.cout_wrap(\"Ballast at node %d at position %f\" % (loc_min, coordinates[loc_min, 0]), 2)\n\n spar.StructuralInformation.lumped_mass_nodes[0] = loc_min\n spar.StructuralInformation.lumped_mass[0] = SparBallastMass\n spar.StructuralInformation.lumped_mass_inertia[0] = np.zeros((3,3))\n spar.StructuralInformation.lumped_mass_position[0] = np.zeros((3,))\n\n spar.AerodynamicInformation.set_to_zero(spar.StructuralInformation.num_node_elem,\n spar.StructuralInformation.num_node,\n spar.StructuralInformation.num_elem)\n\n base_stiffness_bot = spar.StructuralInformation.stiffness_db[-1, :, :]\n base_mass_bot = spar.StructuralInformation.mass_db[-1, :, :]\n base_stiffness_top = base_stiffness_bot\n base_mass_top = base_mass_bot\n\n num_lumped_mass_mat = 0\n\n # Generate tower base\n NodesBase = gc.read_column_sheet_type01(excel_file_name,\n excel_sheet_parameters,\n 'NodesBase')\n\n base = gc.AeroelasticInformation()\n base.StructuralInformation.num_node = NodesBase\n base.StructuralInformation.num_node_elem = 3\n base.StructuralInformation.compute_basic_num_elem()\n\n node_coord = np.zeros((base.StructuralInformation.num_node, 3))\n node_coord[:, 0] = np.linspace(0., TowerBaseHeight, base.StructuralInformation.num_node)\n\n base_stiffness_db = np.zeros((base.StructuralInformation.num_elem, 6, 6))\n base_mass_db = np.zeros((base.StructuralInformation.num_elem, 6, 6))\n vec_node_structural_twist = np.zeros((base.StructuralInformation.num_node,))\n\n # for ielem in range(base.StructuralInformation.num_elem):\n # base_stiffness_db[ielem, :, :] = base_stiffness.copy()\n # base_mass_db[ielem, :, :] = base_mass.copy()\n for ielem in range(base.StructuralInformation.num_elem):\n inode_cent = 2*ielem + 1\n rel_dist_to_bot = node_coord[inode_cent, 0]/TowerBaseHeight\n rel_dist_to_top = (node_coord[-1, 0] - node_coord[inode_cent, 0])/TowerBaseHeight\n base_stiffness_db[ielem, :, :] = (base_stiffness_bot*rel_dist_to_top +\n base_stiffness_top*rel_dist_to_bot)\n base_mass_db[ielem, :, :] = (base_mass_bot*rel_dist_to_top +\n base_mass_top*rel_dist_to_bot)\n\n base.StructuralInformation.generate_1to1_from_vectors(\n base.StructuralInformation.num_node_elem,\n base.StructuralInformation.num_node,\n base.StructuralInformation.num_elem,\n node_coord,\n base_stiffness_db,\n base_mass_db,\n 'y_AFoR',\n vec_node_structural_twist,\n num_lumped_mass=0,\n num_lumped_mass_mat=num_lumped_mass_mat)\n\n base.StructuralInformation.boundary_conditions[0] = 1\n base.StructuralInformation.body_number *= 0\n\n base.AerodynamicInformation.set_to_zero(base.StructuralInformation.num_node_elem,\n base.StructuralInformation.num_node,\n base.StructuralInformation.num_elem)\n\n if options['concentrate_spar']:\n base.StructuralInformation.lumped_mass_mat_nodes = np.array([0], dtype=int)\n base.StructuralInformation.lumped_mass_mat = np.zeros((1, 6, 6))\n base.StructuralInformation.lumped_mass_mat[0, :, :] = iner_mat\n\n nodes_base = base.StructuralInformation.num_node + 0\n for inode in range(len(hub_nodes)):\n hub_nodes[inode] += nodes_base\n wt.StructuralInformation.coordinates[:, 0] += TowerBaseHeight\n base.assembly(wt)\n base.remove_duplicated_points(1e-6, skip=hub_nodes)\n for ielem in range(base.StructuralInformation.num_elem):\n if not base.StructuralInformation.body_number[ielem] == 0:\n base.StructuralInformation.body_number[ielem] -= 1\n for ilc in range(len(LC)):\n LC[ilc].node_in_body += nodes_base - 1\n spar = base # Just a rename for the return\n else:\n # Assembly\n spar.assembly(base)\n spar.remove_duplicated_points(1e-6)\n spar.StructuralInformation.body_number *= 0\n nodes_spar = spar.StructuralInformation.num_node + 0\n for inode in range(len(hub_nodes)):\n hub_nodes[inode] += nodes_spar\n\n wt.StructuralInformation.coordinates[:, 0] += TowerBaseHeight\n spar.assembly(wt)\n spar.remove_duplicated_points(1e-6, skip=hub_nodes)\n for ielem in range(spar.StructuralInformation.num_elem):\n if not spar.StructuralInformation.body_number[ielem] == 0:\n spar.StructuralInformation.body_number[ielem] -= 1\n\n # Update Lagrange Constraints and Multibody information\n for ilc in range(len(LC)):\n LC[ilc].node_in_body += nodes_spar - 1\n\n MB[0].FoR_movement = 'free'\n for ibody in range(1, len(MB)):\n MB[ibody].FoR_position[0] += TowerBaseHeight\n\n return spar, LC, MB\n\n######################################################################\n# FROM excel type03\n######################################################################\ndef rotor_from_excel_type03(in_op_params,\n in_geom_params,\n in_excel_description,\n in_options):\n \"\"\"\n rotor_from_excel_type03\n\n Function needed to generate a wind turbine rotor from an excel database type03\n\n Args:\n op_param (dict): Dictionary with operating parameters\n geom_param (dict): Dictionray with geometical parameters\n excel_description (dict): Dictionary describing the sheets of the excel file\n option (dict): Dictionary with the different options for the wind turbine generation\n\n Returns:\n rotor (sharpy.utils.generate_cases.AeroelasticInfromation): Aeroelastic information of the rotor\n \"\"\"\n # Default values\n op_params = {}\n op_params['rotation_velocity'] = None # Rotation velocity of the rotor\n op_params['pitch_deg'] = None # pitch angle in degrees\n op_params['wsp'] = 0. # wind speed (It may be needed for discretisation purposes)\n op_params['dt'] = 0. # time step (It may be needed for discretisation purposes)\n\n geom_params = {}\n geom_params['chord_panels'] = None # Number of panels on the blade surface in the chord direction\n geom_params['tol_remove_points'] = 1e-3 # maximum distance to remove adjacent points\n geom_params['n_points_camber'] = 100 # number of points to define the camber of the airfoil\n geom_params['h5_cross_sec_prop'] = None # h5 containing mass and stiffness matrices along the blade\n geom_params['m_distribution'] = 'uniform' #\n\n options = {}\n options['camber_effect_on_twist'] = False # When true plain airfoils are used and the blade is twisted and preloaded based on thin airfoil theory\n options['user_defined_m_distribution_type'] = None # type of distribution of the chordwise panels when 'm_distribution' == 'user_defined'\n options['include_polars'] = False #\n options['separate_blades'] = False # Keep blades as different bodies\n options['twist_in_aero'] = False # Twist the aerodynamic surface instead of the structure\n\n excel_description = {}\n excel_description['excel_file_name'] = 'database_excel_type02.xlsx'\n excel_description['excel_sheet_parameters'] = 'parameters'\n excel_description['excel_sheet_structural_blade'] = 'structural_blade'\n excel_description['excel_sheet_discretization_blade'] = 'discretization_blade'\n excel_description['excel_sheet_aero_blade'] = 'aero_blade'\n excel_description['excel_sheet_airfoil_info'] = 'airfoil_info'\n excel_description['excel_sheet_airfoil_chord'] = 'airfoil_coord'\n\n # Overwrite the default values with the values of the input arguments\n for key in in_op_params:\n op_params[key] = in_op_params[key]\n for key in in_geom_params:\n geom_params[key] = in_geom_params[key]\n for key in in_options:\n options[key] = in_options[key]\n for key in in_excel_description:\n excel_description[key] = in_excel_description[key]\n\n # Put the dictionaries information into variables (to avoid changing the function)\n rotation_velocity = op_params['rotation_velocity']\n pitch_deg = op_params['pitch_deg']\n wsp = op_params['wsp']\n dt = op_params['dt']\n\n chord_panels = geom_params['chord_panels']\n tol_remove_points = geom_params['tol_remove_points']\n n_points_camber = geom_params['n_points_camber']\n h5_cross_sec_prop = geom_params['h5_cross_sec_prop']\n m_distribution = geom_params['m_distribution']\n\n camber_effect_on_twist = options['camber_effect_on_twist']\n user_defined_m_distribution_type = options['user_defined_m_distribution_type']\n include_polars = options['include_polars']\n\n excel_file_name = excel_description['excel_file_name']\n excel_sheet_parameters = excel_description['excel_sheet_parameters']\n excel_sheet_structural_blade = excel_description['excel_sheet_structural_blade']\n excel_sheet_discretization_blade = excel_description['excel_sheet_discretization_blade']\n excel_sheet_aero_blade = excel_description['excel_sheet_aero_blade']\n excel_sheet_airfoil_info = excel_description['excel_sheet_airfoil_info']\n excel_sheet_airfoil_coord = excel_description['excel_sheet_airfoil_chord']\n\n ######################################################################\n ## BLADE\n ######################################################################\n blade = gc.AeroelasticInformation()\n\n ######################################################################\n ### STRUCTURE\n ######################################################################\n # Read blade structural information from excel file\n rR_structural = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'rR')\n OutPElAxis = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'OutPElAxis')\n InPElAxis = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'InPElAxis')\n ElAxisAftLEc = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'ElAxisAftLEc')\n StrcTwst = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'StrcTwst')*deg2rad\n BMassDen = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'BMassDen')\n FlpStff = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'FlpStff')\n EdgStff = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'EdgStff')\n FlapEdgeStiff = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'FlapEdgeStiff')\n GJStff = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'GJStff')\n EAStff = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'EAStff')\n FlpIner = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'FlpIner')\n EdgIner = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'EdgIner')\n FlapEdgeIner = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'FlapEdgeIner')\n PrebendRef = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'PrebendRef')\n PreswpRef = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'PreswpRef')\n OutPcg = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'OutPcg')\n InPcg = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_blade, 'InPcg')\n\n # Blade parameters\n TipRad = gc.read_column_sheet_type01(excel_file_name, excel_sheet_parameters, 'TipRad')\n # HubRad = gc.read_column_sheet_type01(excel_file_name, excel_sheet_parameters, 'HubRad')\n\n # Discretization points\n rR = gc.read_column_sheet_type01(excel_file_name, excel_sheet_discretization_blade, 'rR')\n\n # Interpolate excel variables into the correct locations\n # Geometry\n if rR[0] < rR_structural[0]:\n rR_structural = np.concatenate((np.array([0.]), rR_structural),)\n OutPElAxis = np.concatenate((np.array([OutPElAxis[0]]), OutPElAxis),)\n InPElAxis = np.concatenate((np.array([InPElAxis[0]]), InPElAxis),)\n ElAxisAftLEc = np.concatenate((np.array([ElAxisAftLEc[0]]), ElAxisAftLEc),)\n StrcTwst = np.concatenate((np.array([StrcTwst[0]]), StrcTwst),)\n BMassDen = np.concatenate((np.array([BMassDen[0]]), BMassDen),)\n FlpStff = np.concatenate((np.array([FlpStff[0]]), FlpStff),)\n EdgStff = np.concatenate((np.array([EdgStff[0]]), EdgStff),)\n FlapEdgeStiff = np.concatenate((np.array([FlapEdgeStiff[0]]), FlapEdgeStiff),)\n GJStff = np.concatenate((np.array([GJStff[0]]), GJStff),)\n EAStff = np.concatenate((np.array([EAStff[0]]), EAStff),)\n FlpIner = np.concatenate((np.array([FlpIner[0]]), FlpIner),)\n EdgIner = np.concatenate((np.array([EdgIner[0]]), EdgIner),)\n FlapEdgeIner = np.concatenate((np.array([FlapEdgeIner[0]]), FlapEdgeIner),)\n PrebendRef = np.concatenate((np.array([PrebendRef[0]]), PrebendRef),)\n PreswpRef = np.concatenate((np.array([PreswpRef[0]]), PreswpRef),)\n OutPcg = np.concatenate((np.array([OutPcg[0]]), OutPcg),)\n InPcg = np.concatenate((np.array([InPcg[0]]), InPcg),)\n\n # Base parameters\n use_excel_struct_as_elem = False\n if use_excel_struct_as_elem:\n blade.StructuralInformation.num_node_elem = 3\n blade.StructuralInformation.num_elem = len(rR) - 2\n blade.StructuralInformation.compute_basic_num_node()\n\n node_r, elem_r = create_node_radial_pos_from_elem_centres(rR*TipRad,\n blade.StructuralInformation.num_node,\n blade.StructuralInformation.num_elem,\n blade.StructuralInformation.num_node_elem)\n else:\n # Use excel struct as nodes\n # Check the number of nodes\n blade.StructuralInformation.num_node_elem = 3\n blade.StructuralInformation.num_node = len(rR)\n if ((len(rR) - 1) % (blade.StructuralInformation.num_node_elem - 1)) == 0:\n blade.StructuralInformation.num_elem = int((len(rR) - 1)/(blade.StructuralInformation.num_node_elem - 1))\n node_r = rR*TipRad\n elem_rR = rR[1::2] + 0.\n elem_r = rR[1::2]*TipRad + 0.\n else:\n raise RuntimeError((\"ERROR: Cannot build %d-noded elements from %d nodes\" % (blade.StructuralInformation.num_node_elem, blade.StructuralInformation.num_node)))\n\n node_y = np.interp(rR, rR_structural, InPElAxis) + np.interp(rR, rR_structural, PreswpRef)\n node_z = -np.interp(rR, rR_structural, OutPElAxis) - np.interp(rR, rR_structural, PrebendRef)\n node_twist = -1.0*np.interp(rR, rR_structural, StrcTwst)\n\n coordinates = create_blade_coordinates(blade.StructuralInformation.num_node, node_r, node_y, node_z)\n\n if h5_cross_sec_prop is None:\n # Stiffness\n elem_EA = np.interp(elem_rR, rR_structural, EAStff)\n elem_EIy = np.interp(elem_rR, rR_structural, FlpStff)\n elem_EIz = np.interp(elem_rR, rR_structural, EdgStff)\n elem_EIyz = np.interp(elem_rR, rR_structural, FlapEdgeStiff)\n elem_GJ = np.interp(elem_rR, rR_structural, GJStff)\n\n # Stiffness: estimate unknown properties\n cout.cout_wrap.print_file = False\n cout.cout_wrap('WARNING: The poisson cofficient is assumed equal to 0.3', 3)\n cout.cout_wrap('WARNING: Cross-section area is used as shear area', 3)\n poisson_coef = 0.3\n elem_GAy = elem_EA/2.0/(1.0+poisson_coef)\n elem_GAz = elem_EA/2.0/(1.0+poisson_coef)\n # Inertia\n elem_pos_cg_B = np.zeros((blade.StructuralInformation.num_elem, 3),)\n elem_pos_cg_B[:, 1] = np.interp(elem_rR, rR_structural, InPcg)\n elem_pos_cg_B[:, 2] = -np.interp(elem_rR, rR_structural, OutPcg)\n\n elem_mass_per_unit_length = np.interp(elem_rR, rR_structural, BMassDen)\n elem_mass_iner_y = np.interp(elem_rR, rR_structural, FlpIner)\n elem_mass_iner_z = np.interp(elem_rR, rR_structural, EdgIner)\n elem_mass_iner_yz = np.interp(elem_rR, rR_structural, FlapEdgeIner)\n\n # Inertia: estimate unknown properties\n cout.cout_wrap('WARNING: Using perpendicular axis theorem to compute the inertia around xB', 3)\n elem_mass_iner_x = elem_mass_iner_y + elem_mass_iner_z\n\n # Generate blade structural properties\n blade.StructuralInformation.create_mass_db_from_vector(elem_mass_per_unit_length, elem_mass_iner_x, elem_mass_iner_y, elem_mass_iner_z, elem_pos_cg_B, elem_mass_iner_yz)\n blade.StructuralInformation.create_stiff_db_from_vector(elem_EA, elem_GAy, elem_GAz, elem_GJ, elem_EIy, elem_EIz, elem_EIyz)\n\n else:\n # read Mass/Stiffness from database\n cross_prop = h5.readh5(h5_cross_sec_prop).str_prop\n\n # create mass_db/stiffness_db (interpolate at mid-node of each element)\n blade.StructuralInformation.mass_db = scint.interp1d(\n cross_prop.radius, cross_prop.M, kind='cubic', copy=False, assume_sorted=True, axis=0,\n bounds_error=False, fill_value='extrapolate')(node_r[1::2])\n blade.StructuralInformation.stiffness_db = scint.interp1d(\n cross_prop.radius, cross_prop.K, kind='cubic', copy=False, assume_sorted=True, axis=0,\n bounds_error=False, fill_value='extrapolate')(node_r[1::2])\n\n blade.StructuralInformation.generate_1to1_from_vectors(\n num_node_elem=blade.StructuralInformation.num_node_elem,\n num_node=blade.StructuralInformation.num_node,\n num_elem=blade.StructuralInformation.num_elem,\n coordinates=coordinates,\n stiffness_db=blade.StructuralInformation.stiffness_db,\n mass_db=blade.StructuralInformation.mass_db,\n frame_of_reference_delta='y_AFoR',\n vec_node_structural_twist=np.zeros_like(node_twist) if options['twist_in_aero'] else node_twist,\n num_lumped_mass=0)\n\n # Boundary conditions\n blade.StructuralInformation.boundary_conditions = np.zeros((blade.StructuralInformation.num_node), dtype=int)\n blade.StructuralInformation.boundary_conditions[0] = 1\n blade.StructuralInformation.boundary_conditions[-1] = -1\n\n ######################################################################\n ### AERODYNAMICS\n ######################################################################\n # Read blade aerodynamic information from excel file\n rR_aero = gc.read_column_sheet_type01(excel_file_name, excel_sheet_aero_blade, 'rR')\n chord_aero = gc.read_column_sheet_type01(excel_file_name, excel_sheet_aero_blade, 'BlChord')\n thickness_aero = gc.read_column_sheet_type01(excel_file_name, excel_sheet_aero_blade, 'BlThickness')\n\n pure_airfoils_names = gc.read_column_sheet_type01(excel_file_name, excel_sheet_airfoil_info, 'Name')\n pure_airfoils_thickness = gc.read_column_sheet_type01(excel_file_name, excel_sheet_airfoil_info, 'Thickness')\n\n node_ElAxisAftLEc = np.interp(node_r, rR_structural*TipRad, ElAxisAftLEc)\n\n # Read coordinates of the pure airfoils\n n_pure_airfoils = len(pure_airfoils_names)\n\n pure_airfoils_camber = np.zeros((n_pure_airfoils, n_points_camber, 2),)\n xls = pd.ExcelFile(excel_file_name)\n excel_db = pd.read_excel(xls, sheet_name=excel_sheet_airfoil_coord)\n for iairfoil in range(n_pure_airfoils):\n # Look for the NaN\n icoord = 2\n while(not(math.isnan(excel_db[\"%s_x\" % pure_airfoils_names[iairfoil]][icoord]))):\n icoord += 1\n if(icoord == len(excel_db[\"%s_x\" % pure_airfoils_names[iairfoil]])):\n break\n\n # Compute the camber of the airfoils at the defined chord points\n pure_airfoils_camber[iairfoil, :, 0], pure_airfoils_camber[iairfoil, :, 1] = gc.get_airfoil_camber(excel_db[\"%s_x\" % pure_airfoils_names[iairfoil]][2:icoord],\n excel_db[\"%s_y\" % pure_airfoils_names[iairfoil]][2:icoord],\n n_points_camber)\n\n # Basic variables\n surface_distribution = np.zeros((blade.StructuralInformation.num_elem), dtype=int)\n\n\n # Interpolate in the correct positions\n node_chord = np.interp(node_r, rR_aero*TipRad, chord_aero)\n\n # Define the nodes with aerodynamic properties\n # Look for the first element that is goint to be aerodynamic\n first_aero_elem = 0\n while (elem_r[first_aero_elem] <= rR_aero[0]*TipRad):\n first_aero_elem += 1\n first_aero_node = first_aero_elem*(blade.StructuralInformation.num_node_elem - 1)\n aero_node = np.zeros((blade.StructuralInformation.num_node,), dtype=bool)\n aero_node[first_aero_node:] = np.ones((blade.StructuralInformation.num_node-first_aero_node,), dtype=bool)\n\n # Define the airfoil at each stage\n # airfoils = blade.AerodynamicInformation.interpolate_airfoils_camber(pure_airfoils_camber,excel_aero_r, node_r, n_points_camber)\n\n node_thickness = np.interp(node_r, rR_aero*TipRad, thickness_aero)\n\n airfoils = blade.AerodynamicInformation.interpolate_airfoils_camber_thickness(pure_airfoils_camber, pure_airfoils_thickness, node_thickness, n_points_camber)\n airfoil_distribution = np.linspace(0, blade.StructuralInformation.num_node - 1, blade.StructuralInformation.num_node, dtype=int)\n\n # User defined m distribution\n if (m_distribution == 'user_defined') and (user_defined_m_distribution_type == 'last_geometric'):\n blade_nodes = blade.StructuralInformation.num_node\n udmd_by_nodes = np.zeros((blade_nodes, chord_panels[0] + 1))\n for inode in range(blade_nodes):\n r = np.linalg.norm(blade.StructuralInformation.coordinates[inode, :])\n vrel = np.sqrt(rotation_velocity**2*r**2 + wsp**2)\n last_length = vrel*dt/node_chord[inode]\n last_length = np.minimum(last_length, 0.5)\n if last_length <= 0.5:\n ratio = gc.get_factor_geometric_progression(last_length, 1., chord_panels)\n udmd_by_nodes[inode, -1] = 1.\n udmd_by_nodes[inode, 0] = 0.\n for im in range(chord_panels[0] - 1, 0, -1):\n udmd_by_nodes[inode, im] = udmd_by_nodes[inode, im + 1] - last_length\n last_length *= ratio\n # Check\n if (np.diff(udmd_by_nodes[inode, :]) < 0.).any():\n sys.error(\"ERROR in the panel discretization of the blade in node %d\" % (inode))\n else:\n raise RuntimeError((\"ERROR: cannot match the last panel size for node: %d\" % inode))\n udmd_by_nodes[inode, :] = np.linspace(0, 1, chord_panels + 1)\n else:\n udmd_by_nodes = None\n\n node_twist_aero = np.zeros_like(node_chord)\n if camber_effect_on_twist:\n cout.cout_wrap(\"WARNING: The steady applied Mx should be manually multiplied by the density\", 3)\n for inode in range(blade.StructuralInformation.num_node):\n node_twist_aero[inode] = gc.get_aoacl0_from_camber(airfoils[inode, :, 0], airfoils[inode, :, 1])\n mu0 = gc.get_mu0_from_camber(airfoils[inode, :, 0], airfoils[inode, :, 1])\n r = np.linalg.norm(blade.StructuralInformation.coordinates[inode, :])\n vrel = np.sqrt(rotation_velocity**2*r**2 + wsp**2)\n if inode == 0:\n dr = 0.5*np.linalg.norm(blade.StructuralInformation.coordinates[1, :] - blade.StructuralInformation.coordinates[0, :])\n elif inode == len(blade.StructuralInformation.coordinates[:, 0]) - 1:\n dr = 0.5*np.linalg.norm(blade.StructuralInformation.coordinates[-1, :] - blade.StructuralInformation.coordinates[-2, :])\n else:\n dr = 0.5*np.linalg.norm(blade.StructuralInformation.coordinates[inode + 1, :] - blade.StructuralInformation.coordinates[inode - 1, :])\n moment_factor = 0.5*vrel**2*node_chord[inode]**2*dr\n # print(\"node\", inode, \"mu0\", mu0, \"CMc/4\", 2.*mu0 + np.pi/2*node_twist_struct[inode])\n blade.StructuralInformation.app_forces[inode, 3] = (2.*mu0 + np.pi/2*node_twist_aero[inode])*moment_factor\n airfoils[inode, :, 1] *= 0.\n\n # Write SHARPy format\n blade.AerodynamicInformation.create_aerodynamics_from_vec(blade.StructuralInformation,\n aero_node,\n node_chord,\n (node_twist + node_twist_aero) if options['twist_in_aero'] else node_twist_aero,\n np.pi*np.ones_like(node_chord),\n chord_panels,\n surface_distribution,\n m_distribution,\n node_ElAxisAftLEc,\n airfoil_distribution,\n airfoils,\n udmd_by_nodes,\n first_twist=False)\n\n # Read the polars of the pure airfoils\n if include_polars:\n pure_polars = [None]*n_pure_airfoils\n for iairfoil in range(n_pure_airfoils):\n excel_sheet_polar = pure_airfoils_names[iairfoil]\n aoa = gc.read_column_sheet_type01(excel_file_name, excel_sheet_polar, 'AoA')\n cl = gc.read_column_sheet_type01(excel_file_name, excel_sheet_polar, 'CL')\n cd = gc.read_column_sheet_type01(excel_file_name, excel_sheet_polar, 'CD')\n cm = gc.read_column_sheet_type01(excel_file_name, excel_sheet_polar, 'CM')\n polar = ap.Polar()\n polar.initialise(np.column_stack((aoa, cl, cd, cm)))\n pure_polars[iairfoil] = polar\n\n # Generate the polars for each airfoil\n blade.AerodynamicInformation.polars = [None]*blade.StructuralInformation.num_node\n for inode in range(blade.StructuralInformation.num_node):\n # Find the airfoils between which the node is;\n ipure = 0\n while pure_airfoils_thickness[ipure] > node_thickness[inode]:\n ipure += 1\n if(ipure == n_pure_airfoils):\n ipure -= 1\n break\n\n coef = (node_thickness[inode] - pure_airfoils_thickness[ipure - 1])/(pure_airfoils_thickness[ipure] - pure_airfoils_thickness[ipure - 1])\n polar = ap.interpolate(pure_polars[ipure - 1], pure_polars[ipure], coef)\n blade.AerodynamicInformation.polars[inode] = polar.table\n\n ######################################################################\n ## ROTOR\n ######################################################################\n\n # Read from excel file\n numberOfBlades = gc.read_column_sheet_type01(excel_file_name, excel_sheet_parameters, 'NumBl')\n tilt = gc.read_column_sheet_type01(excel_file_name, excel_sheet_parameters, 'ShftTilt')*deg2rad\n cone = gc.read_column_sheet_type01(excel_file_name, excel_sheet_parameters, 'Cone')*deg2rad\n # pitch = gc.read_column_sheet_type01(excel_file_name, excel_sheet_rotor, 'Pitch')*deg2rad\n\n # Apply pitch\n blade.StructuralInformation.rotate_around_origin(np.array([1., 0., 0.]), -pitch_deg*deg2rad)\n\n # Apply coning\n blade.StructuralInformation.rotate_around_origin(np.array([0., 1., 0.]), -cone)\n\n # Build the whole rotor\n rotor = blade.copy()\n hub_nodes = [0]\n for iblade in range(numberOfBlades-1):\n hub_nodes.append((iblade + 1)*blade.StructuralInformation.num_node)\n blade2 = blade.copy()\n blade2.StructuralInformation.rotate_around_origin(np.array([0., 0., 1.]), (iblade + 1)*(360.0/numberOfBlades)*deg2rad)\n rotor.assembly(blade2)\n blade2 = None\n\n if not options['separate_blades']:\n rotor.remove_duplicated_points(tol_remove_points)\n hub_nodes = [0]\n rotor.StructuralInformation.body_number *= 0\n\n # Apply tilt\n rotor.StructuralInformation.rotate_around_origin(np.array([0., 1., 0.]), tilt)\n\n return rotor, hub_nodes\n\n\ndef generate_from_excel_type03(op_params,\n geom_params,\n excel_description,\n options):\n\n \"\"\"\n generate_from_excel_type03\n\n Function needed to generate a wind turbine (tower + rotor) from an excel database type03.\n See ``rotor_from_excel_type03'' for more information.\n\n Args:\n op_param (dict): Dictionary with operating parameters\n geom_param (dict): Dictionray with geometical parameters\n excel_description (dict): Dictionary describing the sheets of the excel file\n option (dict): Dictionary with the different options for the wind turbine generation\n\n Returns:\n wt (sharpy.utils.generate_cases.AeroelasticInfromation): Aeroelastic information of the wind turbine (tower + rotor)\n \"\"\"\n rotor, hub_nodes = rotor_from_excel_type03(op_params,\n geom_params,\n excel_description,\n options)\n\n\n excel_file_name = excel_description['excel_file_name']\n excel_sheet_parameters = excel_description['excel_sheet_parameters']\n excel_sheet_structural_tower = excel_description['excel_sheet_structural_tower']\n tol_remove_points = geom_params['tol_remove_points']\n rotation_velocity = op_params['rotation_velocity']\n\n ######################################################################\n ## TOWER\n ######################################################################\n\n # Read from excel file\n HtFract = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_tower, 'HtFract')\n TMassDen = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_tower, 'TMassDen')\n TwFAStif = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_tower, 'TwFAStif')\n TwSSStif = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_tower, 'TwSSStif')\n # TODO> variables to be defined\n TwGJStif = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_tower, 'TwGJStif')\n TwEAStif = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_tower, 'TwEAStif')\n TwFAIner = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_tower, 'TwFAIner')\n TwSSIner = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_tower, 'TwSSIner')\n TwFAcgOf = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_tower, 'TwFAcgOf')\n TwSScgOf = gc.read_column_sheet_type01(excel_file_name, excel_sheet_structural_tower, 'TwSScgOf')\n\n # Define the TOWER\n TowerHt = gc.read_column_sheet_type01(excel_file_name, excel_sheet_parameters, 'TowerHt')\n Elevation = TowerHt*HtFract\n\n tower = gc.AeroelasticInformation()\n tower.StructuralInformation.num_elem = len(Elevation) - 2\n tower.StructuralInformation.num_node_elem = 3\n tower.StructuralInformation.compute_basic_num_node()\n\n # Interpolate excel variables into the correct locations\n node_r, elem_r = create_node_radial_pos_from_elem_centres(Elevation,\n tower.StructuralInformation.num_node,\n tower.StructuralInformation.num_elem,\n tower.StructuralInformation.num_node_elem)\n\n # Stiffness\n elem_EA = np.interp(elem_r, Elevation, TwEAStif)\n elem_EIz = np.interp(elem_r, Elevation, TwSSStif)\n elem_EIy = np.interp(elem_r, Elevation, TwFAStif)\n elem_GJ = np.interp(elem_r, Elevation, TwGJStif)\n # Stiffness: estimate unknown properties\n cout.cout_wrap.print_file = False\n cout.cout_wrap('WARNING: The poisson cofficient is assumed equal to 0.3', 3)\n cout.cout_wrap('WARNING: Cross-section area is used as shear area', 3)\n poisson_coef = 0.3\n elem_GAy = elem_EA/2.0/(1.0+poisson_coef)\n elem_GAz = elem_EA/2.0/(1.0+poisson_coef)\n\n # Inertia\n elem_mass_per_unit_length = np.interp(elem_r, Elevation, TMassDen)\n elem_mass_iner_y = np.interp(elem_r, Elevation, TwFAIner)\n elem_mass_iner_z = np.interp(elem_r, Elevation, TwSSIner)\n # TODO: check yz axis and Flap-edge\n elem_pos_cg_B = np.zeros((tower.StructuralInformation.num_elem, 3),)\n elem_pos_cg_B[:, 1] = np.interp(elem_r, Elevation, TwSScgOf)\n elem_pos_cg_B[:, 2] = np.interp(elem_r, Elevation, TwFAcgOf)\n\n # Stiffness: estimate unknown properties\n cout.cout_wrap('WARNING: Using perpendicular axis theorem to compute the inertia around xB', 3)\n elem_mass_iner_x = elem_mass_iner_y + elem_mass_iner_z\n\n # Create the tower\n tower.StructuralInformation.create_mass_db_from_vector(elem_mass_per_unit_length, elem_mass_iner_x, elem_mass_iner_y, elem_mass_iner_z, elem_pos_cg_B)\n tower.StructuralInformation.create_stiff_db_from_vector(elem_EA, elem_GAy, elem_GAz, elem_GJ, elem_EIy, elem_EIz)\n\n coordinates = np.zeros((tower.StructuralInformation.num_node, 3),)\n coordinates[:, 0] = node_r\n\n tower.StructuralInformation.generate_1to1_from_vectors(\n num_node_elem=tower.StructuralInformation.num_node_elem,\n num_node=tower.StructuralInformation.num_node,\n num_elem=tower.StructuralInformation.num_elem,\n coordinates=coordinates,\n stiffness_db=tower.StructuralInformation.stiffness_db,\n mass_db=tower.StructuralInformation.mass_db,\n frame_of_reference_delta='y_AFoR',\n vec_node_structural_twist=np.zeros((tower.StructuralInformation.num_node,),),\n num_lumped_mass=1)\n\n tower.StructuralInformation.boundary_conditions = np.zeros((tower.StructuralInformation.num_node), dtype = int)\n tower.StructuralInformation.boundary_conditions[0] = 1\n\n # Nacelle properties from excel file\n NacelleMass = gc.read_column_sheet_type01(excel_file_name, excel_sheet_parameters, 'NacMass')\n NacelleMass_x = gc.read_column_sheet_type01(excel_file_name, excel_sheet_parameters, 'NacMass_x')\n NacelleMass_z = gc.read_column_sheet_type01(excel_file_name, excel_sheet_parameters, 'NacMass_z')\n # NacelleYawIner = gc.read_column_sheet_type01(excel_file_name, excel_sheet_nacelle, 'NacelleYawIner')\n\n # Include nacelle mass\n tower.StructuralInformation.lumped_mass_nodes = np.array([tower.StructuralInformation.num_node - 1], dtype=int)\n tower.StructuralInformation.lumped_mass = np.array([NacelleMass], dtype=float)\n if not NacelleMass_x is None and not NacelleMass_z is None:\n tower.StructuralInformation.lumped_mass_position = np.array([np.array([NacelleMass_z, 0, NacelleMass_x])], dtype=float)\n else:\n cout.cout_wrap('WARNING: Nacelle mass placed at tower top', 3)\n\n tower.AerodynamicInformation.set_to_zero(tower.StructuralInformation.num_node_elem,\n tower.StructuralInformation.num_node,\n tower.StructuralInformation.num_elem)\n\n # Overhang\n tilt = gc.read_column_sheet_type01(excel_file_name, excel_sheet_parameters, 'ShftTilt')*deg2rad\n if not tilt == 0.:\n raise NonImplementedError(\"Non-zero tilt not supported\")\n NodesOverhang = gc.read_column_sheet_type01(excel_file_name, excel_sheet_parameters, 'NodesOverhang')\n overhang_len = gc.read_column_sheet_type01(excel_file_name, excel_sheet_parameters, 'overhang')\n if NodesOverhang == 0:\n with_overhang = False\n else:\n with_overhang = True\n\n overhang = gc.AeroelasticInformation()\n overhang.StructuralInformation.num_node = NodesOverhang\n overhang.StructuralInformation.num_node_elem = 3\n overhang.StructuralInformation.compute_basic_num_elem()\n node_pos = np.zeros((overhang.StructuralInformation.num_node, 3), )\n node_pos[:, 0] += tower.StructuralInformation.coordinates[-1, 0]\n node_pos[:, 0] += np.linspace(0., -overhang_len*np.sin(tilt*deg2rad), overhang.StructuralInformation.num_node)\n node_pos[:, 2] = np.linspace(0., overhang_len*np.cos(tilt*deg2rad), overhang.StructuralInformation.num_node)\n # TODO: change the following by real values\n # Same properties as the last element of the tower\n # cout.cout_wrap(\"WARNING: Using the structural properties of the last tower section for the overhang\", 3)\n # oh_mass_per_unit_length = tower.StructuralInformation.mass_db[-1, 0, 0]\n # oh_mass_iner = tower.StructuralInformation.mass_db[-1, 3, 3]\n cout.cout_wrap(\"WARNING: Using the structural properties (*0.1) of the last tower section for the overhang\", 3)\n oh_mass_per_unit_length = tower.StructuralInformation.mass_db[-1, 0, 0]/10.\n oh_mass_iner = tower.StructuralInformation.mass_db[-1, 3, 3]/10.\n oh_EA = tower.StructuralInformation.stiffness_db[-1, 0, 0]\n oh_GA = tower.StructuralInformation.stiffness_db[-1, 1, 1]\n oh_GJ = tower.StructuralInformation.stiffness_db[-1, 3, 3]\n oh_EI = tower.StructuralInformation.stiffness_db[-1, 4, 4]\n\n overhang.StructuralInformation.generate_uniform_sym_beam(node_pos,\n oh_mass_per_unit_length,\n oh_mass_iner,\n oh_EA,\n oh_GA,\n oh_GJ,\n oh_EI,\n num_node_elem=3,\n y_BFoR='y_AFoR',\n num_lumped_mass=0)\n\n overhang.StructuralInformation.boundary_conditions[-1] = -1\n\n overhang.AerodynamicInformation.set_to_zero(overhang.StructuralInformation.num_node_elem,\n overhang.StructuralInformation.num_node,\n overhang.StructuralInformation.num_elem)\n\n tower.assembly(overhang)\n tower.remove_duplicated_points(tol_remove_points)\n tower.StructuralInformation.body_number *= 0\n\n # Hub mass\n HubMass = gc.read_column_sheet_type01(excel_file_name, excel_sheet_parameters, 'HubMass')\n if HubMass is not None:\n if with_overhang:\n tower.StructuralInformation.add_lumped_mass(tower.StructuralInformation.num_node -1,\n HubMass,\n inertia=np.zeros((3, 3)),\n pos=np.zeros((3)))\n else:\n n_hub_nodes = len(hub_nodes)\n for inode_hub in range(n_hub_nodes):\n rotor.StructuralInformation.add_lumped_mass(hub_nodes[inode_hub],\n HubMass/n_hub_nodes,\n inertia=np.zeros((3, 3)),\n pos=np.zeros((3)))\n else:\n cout.cout_wrap('WARNING: HubMass not found', 3)\n\n for inode in range(len(hub_nodes)):\n hub_nodes[inode] += tower.StructuralInformation.num_node\n\n ######################################################################\n ## WIND TURBINE\n ######################################################################\n # Assembly the whole case\n wt = tower.copy()\n hub_position = tower.StructuralInformation.coordinates[-1, :]\n if not with_overhang:\n hub_position += np.array([0., 0., overhang_len])\n rotor.StructuralInformation.coordinates += hub_position\n wt.assembly(rotor)\n\n ######################################################################\n ## MULTIBODY\n ######################################################################\n LC = []\n for iblade in range(len(hub_nodes)):\n # Define the boundary condition between the rotor and the tower tip\n LC1 = gc.LagrangeConstraint()\n LC1.behaviour = 'hinge_node_FoR_constant_vel'\n LC1.node_in_body = tower.StructuralInformation.num_node - 1\n LC1.body = 0\n LC1.body_FoR = iblade + 1\n if with_overhang:\n LC1.rot_vect = np.array([-1., 0., 0.])*rotation_velocity\n LC1.rel_posB = np.zeros((3))\n else:\n LC1.rot_vect = np.array([0., 0., 1.])*rotation_velocity\n LC1.rel_posB = np.array([0., 0., overhang_len])\n LC.append(LC1)\n\n # Define the multibody infromation for the tower and the rotor\n MB = []\n MB1 = gc.BodyInformation()\n MB1.body_number = 0\n MB1.FoR_position = np.zeros((6,),)\n MB1.FoR_velocity = np.zeros((6,),)\n MB1.FoR_acceleration = np.zeros((6,),)\n MB1.FoR_movement = 'prescribed'\n MB1.quat = np.array([1.0, 0.0, 0.0, 0.0])\n MB.append(MB1)\n\n numberOfBlades = len(hub_nodes)\n for iblade in range(numberOfBlades):\n MB2 = gc.BodyInformation()\n MB2.body_number = iblade + 1\n MB2.FoR_position = np.concatenate((hub_position, np.zeros((3))))\n MB2.FoR_velocity = np.array([0., 0., 0., 0., 0., rotation_velocity])\n MB2.FoR_acceleration = np.zeros((6,),)\n MB2.FoR_movement = 'free'\n blade_azimuth = (iblade*(360.0/numberOfBlades)*deg2rad)\n MB2.quat = algebra.euler2quat(np.array([0.0, tilt, blade_azimuth]))\n MB.append(MB2)\n\n ######################################################################\n ## RETURN\n ######################################################################\n return wt, LC, MB, hub_nodes\n\n\n######################################################################\n# FROM excel type02\n######################################################################\ndef rotor_from_excel_type02(chord_panels,\n rotation_velocity,\n pitch_deg,\n excel_file_name='database_excel_type02.xlsx',\n excel_sheet_parameters='parameters',\n excel_sheet_structural_blade='structural_blade',\n excel_sheet_discretization_blade='discretization_blade',\n excel_sheet_aero_blade='aero_blade',\n excel_sheet_airfoil_info='airfoil_info',\n excel_sheet_airfoil_coord='airfoil_coord',\n excel_sheet_structural_tower='structural_tower',\n m_distribution='uniform',\n h5_cross_sec_prop=None,\n n_points_camber=100,\n tol_remove_points=1e-3,\n user_defined_m_distribution_type=None,\n camber_effect_on_twist=False,\n wsp=0.,\n dt=0.):\n\n # Warning for back compatibility\n cout.cout_wrap('rotor_from_excel_type02 is obsolete! rotor_from_excel_type03 instead!', 3)\n\n # Assign values to dictionaries\n op_params = {}\n op_params['rotation_velocity'] = rotation_velocity\n op_params['pitch_deg'] = pitch_deg\n op_params['wsp'] = wsp\n op_params['dt'] = dt\n\n geom_params = {}\n geom_params['chord_panels'] = chord_panels\n geom_params['tol_remove_points'] = tol_remove_points\n geom_params['n_points_camber'] = n_points_camber\n geom_params['h5_cross_sec_prop'] = h5_cross_sec_prop\n geom_params['m_distribution'] = m_distribution\n\n options = {}\n options['camber_effect_on_twist'] = camber_effect_on_twist\n options['user_defined_m_distribution_type'] = user_defined_m_distribution_type\n options['include_polars'] = False\n options['twist_in_aero'] = False\n\n excel_description = {}\n excel_description['excel_file_name'] = excel_file_name\n excel_description['excel_sheet_parameters'] = excel_sheet_parameters\n excel_description['excel_sheet_structural_blade'] = excel_sheet_structural_blade\n excel_description['excel_sheet_discretization_blade'] = excel_sheet_discretization_blade\n excel_description['excel_sheet_aero_blade'] = excel_sheet_aero_blade\n excel_description['excel_sheet_airfoil_info'] = excel_sheet_airfoil_info\n excel_description['excel_sheet_airfoil_chord'] = excel_sheet_airfoil_coord\n\n rotor = rotor_from_excel_type03(op_params,\n geom_params,\n excel_description,\n options)\n\n return rotor\n\n\ndef generate_from_excel_type02(chord_panels,\n rotation_velocity,\n pitch_deg,\n excel_file_name='database_excel_type02.xlsx',\n excel_sheet_parameters='parameters',\n excel_sheet_structural_blade='structural_blade',\n excel_sheet_discretization_blade='discretization_blade',\n excel_sheet_aero_blade='aero_blade',\n excel_sheet_airfoil_info='airfoil_info',\n excel_sheet_airfoil_coord='airfoil_coord',\n excel_sheet_structural_tower='structural_tower',\n m_distribution='uniform',\n h5_cross_sec_prop=None,\n n_points_camber=100,\n tol_remove_points=1e-3,\n user_defined_m_distribution_type=None,\n camber_effect_on_twist=False,\n wsp=0.,\n dt=0.):\n\n # Warning for back compatibility\n cout.cout_wrap('generate_from_excel_type02 is obsolete! rotor_from_excel_type03 instead!', 3)\n\n # Assign values to dictionaries\n op_params = {}\n op_params['rotation_velocity'] = rotation_velocity\n op_params['pitch_deg'] = pitch_deg\n op_params['wsp'] = wsp\n op_params['dt'] = dt\n\n geom_params = {}\n geom_params['chord_panels'] = chord_panels\n geom_params['tol_remove_points'] = tol_remove_points\n geom_params['n_points_camber'] = n_points_camber\n geom_params['h5_cross_sec_prop'] = h5_cross_sec_prop\n geom_params['m_distribution'] = m_distribution\n\n options = {}\n options['camber_effect_on_twist'] = camber_effect_on_twist\n options['user_defined_m_distribution_type'] = user_defined_m_distribution_type\n options['include_polars'] = False\n\n excel_description = {}\n excel_description['excel_file_name'] = excel_file_name\n excel_description['excel_sheet_parameters'] = excel_sheet_parameters\n excel_description['excel_sheet_structural_tower'] = excel_sheet_structural_tower\n excel_description['excel_sheet_structural_blade'] = excel_sheet_structural_blade\n excel_description['excel_sheet_discretization_blade'] = excel_sheet_discretization_blade\n excel_description['excel_sheet_aero_blade'] = excel_sheet_aero_blade\n excel_description['excel_sheet_airfoil_info'] = excel_sheet_airfoil_info\n excel_description['excel_sheet_airfoil_chord'] = excel_sheet_airfoil_coord\n\n wt = generate_from_excel_type03(op_params,\n geom_params,\n excel_description,\n options)\n\n return wt\n" }, { "path": "sharpy/controllers/__init__.py", "content": "import importlib\nimport os\n\nimport sharpy.utils.controller_interface as controller_interface\nimport sharpy.utils.sharpydir as sharpydir\n\nfiles = controller_interface.controller_list_from_path(os.path.dirname(__file__))\n\nimport_path = os.path.realpath(os.path.dirname(__file__))\nimport_path = import_path.replace(sharpydir.SharpyDir, \"\")\nif import_path[0] == \"/\": import_path = import_path[1:]\nimport_path = import_path.replace(\"/\", \".\")\n\nfor file in files:\n controller_interface.controllers[file] = importlib.import_module(import_path + \".\" + file)\n" }, { "path": "sharpy/controllers/bladepitchpid.py", "content": "import numpy as np\nimport os\nfrom control import ss, forced_response, TransferFunction\n\nimport sharpy.utils.controller_interface as controller_interface\nimport sharpy.utils.settings as settings\nimport sharpy.utils.control_utils as control_utils\nimport sharpy.utils.cout_utils as cout\nimport sharpy.utils.algebra as algebra\nfrom sharpy.utils.constants import deg2rad\n\n\n@controller_interface.controller\nclass BladePitchPid(controller_interface.BaseController):\n r\"\"\"\n\n\n \"\"\"\n controller_id = 'BladePitchPid'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n # PID parameters\n settings_types['P'] = 'float'\n settings_default['P'] = None\n settings_description['P'] = 'Proportional gain of the controller'\n\n settings_types['I'] = 'float'\n settings_default['I'] = 0.0\n settings_description['I'] = 'Integral gain of the controller'\n\n settings_types['D'] = 'float'\n settings_default['D'] = 0.0\n settings_description['D'] = 'Differential gain of the controller'\n\n # Filter\n settings_types['lp_cut_freq'] = 'float'\n settings_default['lp_cut_freq'] = 0.\n settings_description['lp_cut_freq'] = 'Cutting frequency of the low pass filter of the process value in Hz. Choose 0 for no filter'\n\n settings_types['anti_windup_lim'] = 'list(float)'\n settings_default['anti_windup_lim'] = [-1., -1.]\n settings_description['anti_windup_lim'] = ('Limits of actuation to apply anti windup.' +\n 'Use the same number to deactivate.')\n\n # Set point parameters\n settings_types['sp_type'] = 'str'\n settings_default['sp_type'] = None\n settings_description['sp_type'] = (\n 'Quantity used to define the' +\n ' set point')\n settings_options['sp_type'] = ['rbm', 'pitch', 'gen_vel']\n\n settings_types['sp_source'] = 'str'\n settings_default['sp_source'] = None\n settings_description['sp_source'] = (\n 'Source used to define the' +\n ' set point')\n settings_options['sp_source'] = ['file', 'const']\n\n settings_types['sp_time_history_file'] = 'str'\n settings_default['sp_time_history_file'] = ''\n settings_description['sp_time_history_file'] = ('Route and file name of the time ' +\n 'history of the desired set point.' +\n 'Used for ``sp_source = file``')\n\n settings_types['sp_const'] = 'float'\n settings_default['sp_const'] = 0.\n settings_description['sp_const'] = 'Constant set point. Only used for ``sp_source`` = `const ``'\n\n # Other parameters\n settings_types['dt'] = 'float'\n settings_default['dt'] = None\n settings_description['dt'] = 'Time step of the simulation'\n\n settings_types['ntime_steps'] = 'int'\n settings_default['ntime_steps'] = None\n settings_description['ntime_steps'] = 'Number of time steps'\n\n #settings_types['tower_body'] = 'int'\n #settings_default['tower_body'] = 0\n #settings_description['tower_body'] = 'Body number of the tower'\n\n #settings_types['tower_top_node'] = 'int'\n #settings_default['tower_top_node'] = 0\n #settings_description['tower_top_node'] = 'Global node number of the tower top'\n\n settings_types['blade_num_body'] = 'list(int)'\n settings_default['blade_num_body'] = [0,]\n settings_description['blade_num_body'] = 'Body number of the blade(s) to pitch'\n\n settings_types['max_pitch_rate'] = 'float'\n settings_default['max_pitch_rate'] = 0.1396\n settings_description['max_pitch_rate'] = 'Maximum pitch rate [rad/s]'\n\n settings_types['pitch_sp'] = 'float'\n settings_default['pitch_sp'] = 0.\n settings_description['pitch_sp'] = 'Pitch set point [rad]'\n\n settings_types['initial_pitch'] = 'float'\n settings_default['initial_pitch'] = 0.\n settings_description['initial_pitch'] = 'Initial pitch [rad]'\n\n settings_types['initial_rotor_vel'] = 'float'\n settings_default['initial_rotor_vel'] = 0.\n settings_description['initial_rotor_vel'] = 'Initial rotor velocity [rad/s]'\n\n settings_types['min_pitch'] = 'float'\n settings_default['min_pitch'] = 0.\n settings_description['min_pitch'] = 'Minimum pitch [rad]'\n\n settings_types['max_pitch'] = 'float'\n settings_default['max_pitch'] = 1.5707963267948966\n settings_description['max_pitch'] = 'Maximum pitch [rad]'\n\n settings_types['nocontrol_steps'] = 'int'\n settings_default['nocontrol_steps'] = -1\n settings_description['nocontrol_steps'] = 'Time steps without control action'\n\n # Generator and drive train model\n settings_types['gen_model_const_var'] = 'str'\n settings_default['gen_model_const_var'] = ''\n settings_description['gen_model_const_var'] = 'Generator metric to be kept constant at a value `target_gen_value`'\n settings_options['gen_model_const_var'] = ['power', 'torque']\n\n settings_types['gen_model_const_value'] = 'float'\n settings_default['gen_model_const_value'] = 3945990.325\n settings_description['gen_model_const_value'] = 'Constant value of the generator metric to be kept constant '\n\n settings_types['GBR'] = 'float'\n settings_default['GBR'] = 97.\n settings_description['GBR'] = 'Gear box ratio'\n\n settings_types['inertia_dt'] = 'float'\n settings_default['inertia_dt'] = 43776046.25\n settings_description['inertia_dt'] = 'Drive train inertia'\n\n settings_types['newmark_damp'] = 'float'\n settings_default['newmark_damp'] = 1e-4\n settings_description['newmark_damp'] = 'Damping of the time integration newmark-beta scheme'\n\n # Output parameters\n settings_types['write_controller_log'] = 'bool'\n settings_default['write_controller_log'] = True\n settings_description['write_controller_log'] = (\n 'Write a time history of input, required input, ' +\n 'and control')\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types,\n settings_default,\n settings_description)\n\n def __init__(self):\n self.in_dict = None\n self.data = None\n self.settings = None\n\n self.prescribed_sp_time_history = None\n self.prescribed_sp = list()\n self.system_pv = list()\n\n self.controller_implementation = None\n\n self.log_fname = None\n\n def initialise(self, data, in_dict, controller_id=None, restart=False):\n self.in_dict = in_dict\n settings.to_custom_types(self.in_dict,\n self.settings_types,\n self.settings_default,\n no_ctype=True)\n\n self.settings = self.in_dict\n self.newmark_beta = 0.5 + self.settings['newmark_damp']\n\n if self.settings['write_controller_log']:\n folder = data.output_folder + '/controllers/'\n if not os.path.exists(folder):\n os.makedirs(folder)\n self.log_fname = (folder + self.controller_id + \".dat\")\n fid = open(self.log_fname, 'a')\n fid.write(('#'+ 1*'{:>2} ' + 10*'{:>12} ' + '{:>12}\\n').\n format('tstep', 'time', 'ref_state', 'state', 'Pcontrol', 'Icontrol', 'Dcontrol', 'control', 'gen_torque', 'rotor_vel', 'pitch_vel', 'pitch'))\n fid.close()\n\n # save input time history\n if self.settings['sp_source'] == 'file':\n self.prescribed_sp_time_history = np.loadtxt(self.settings['sp_time_history_file'])\n # Init PID controller\n self.controller_implementation = control_utils.PID(self.settings['P'],\n self.settings['I'],\n self.settings['D'],\n self.settings['dt'])\n\n if not self.settings['anti_windup_lim'][0] == self.settings['anti_windup_lim'][1]:\n self.controller_implementation.set_anti_windup_lim(self.settings['anti_windup_lim'])\n\n if self.settings['lp_cut_freq'] == 0.:\n self.filter_pv = False\n else:\n self.filter_pv = True\n w0 = self.settings['lp_cut_freq']*2*np.pi\n self.filter = TransferFunction(np.array([w0]), np.array([1., w0]))\n self.min_it_filter = int(1./(self.settings['lp_cut_freq']*self.settings['dt']))\n\n self.pitch = self.settings['initial_pitch']\n self.rotor_vel = self.settings['initial_rotor_vel']\n self.rotor_acc = 0.\n\n def control(self, data, controlled_state):\n r\"\"\"\n Main routine of the controller.\n Input is `data` (the self.data in the solver), and\n `currrent_state` which is a dictionary with ['structural', 'aero']\n time steps for the current iteration.\n\n :param data: problem data containing all the information.\n :param controlled_state: `dict` with two vars: `structural` and `aero`\n containing the `timestep_info` that will be returned with the\n control variables.\n\n :returns: A `dict` with `structural` and `aero` time steps and control\n input included.\n \"\"\"\n # TODO: move this to the initialisation with restart\n if len(self.system_pv) == 0:\n for it in range(data.ts - 1):\n self.system_pv.append(0.)\n self.prescribed_sp.append(0.)\n\n struct_tstep = controlled_state['structural']\n aero_tstep = controlled_state['aero']\n if not \"info\" in controlled_state:\n controlled_state['info'] = dict()\n\n time = self.settings['dt']*data.ts\n\n # Compute the rotor velocity\n aero_torque = self.compute_aero_torque(data.structure, struct_tstep)\n # if self.settings['variable_speed']:\n if True:\n #ielem, inode_in_elem = data.structure.node_master_elem[self.settings['tower_top_node']\n #node_cga = ag.quat2rotation(struct_tstep.mb_quat[self.settings['tower_body'], :])\n #cab = ag.crv2rotation(struct_tstep.psi[ielem, inode_in_elem, :])\n #FoR_cga = ag.quat2rotation(struct_tstep.mb_quat[self.settings['blade_num_body'][0], :])\n\n #ini_rotor_vel = ag.multiply_matrices(cab.T, node_cga.T, FoR_cga,\n # struct_tstep.mb_FoR_vel[self.settings['blade_num_body'][0], 3:6])[2]\n #ini_rotor_acc = ag.multiply_matrices(cab.T, node_cga.T, FoR_cga,\n # struct_tstep.mb_FoR_acc[self.settings['blade_num_body'][0], 3:6])[2]\n self.rotor_vel, self.rotor_acc = self.drive_train_model(aero_torque,\n self.rotor_vel,\n self.rotor_acc)\n else:\n self.rotor_vel = self.settings['sp_const']\n self.rotor_acc = 0.\n\n # System set point\n prescribed_sp = self.compute_prescribed_sp(time)\n # System process value\n sys_pv = self.compute_system_pv(struct_tstep,\n data.structure,\n gen_vel=self.rotor_vel*self.settings['GBR'])\n\n if data.ts < self.settings['nocontrol_steps']:\n sys_pv = prescribed_sp\n self.system_pv[-1] = sys_pv\n return controlled_state\n else:\n controlled_state['info']['rotor_vel'] = self.rotor_vel\n\n # Apply filter\n # Filter only after five periods of the cutoff frequency\n if self.filter_pv and (len(self.system_pv) > self.min_it_filter):\n nit = len(self.system_pv)\n time = np.linspace(0, (nit - 1)*self.settings['dt'], nit)\n # print(time.shape, len(self.system_pv))\n T, filtered_pv, xout = forced_response(self.filter,\n T=time,\n U=self.system_pv)\n else:\n filtered_pv = self.system_pv\n\n # get current state input\n delta_pitch_ref, detail = self.controller_wrapper(\n required_input=self.prescribed_sp,\n current_input=filtered_pv,\n control_param={'P': self.settings['P'],\n 'I': self.settings['I'],\n 'D': self.settings['D']},\n i_current=data.ts)\n # NREL controller does error = state - reference. Here is done the other way\n delta_pitch_ref *= -1.\n # Limit pitch and pitch rate\n target_pitch = delta_pitch_ref + self.settings['pitch_sp']\n pitch_rate = (target_pitch - self.pitch)/self.settings['dt']\n if pitch_rate < -self.settings['max_pitch_rate']:\n pitch_rate = -self.settings['max_pitch_rate']\n elif pitch_rate > self.settings['max_pitch_rate']:\n pitch_rate = self.settings['max_pitch_rate']\n\n next_pitch = self.pitch + pitch_rate*self.settings['dt']\n if next_pitch < self.settings['min_pitch']:\n pitch_rate = 0.\n next_pitch = self.settings['min_pitch']\n if next_pitch > self.settings['max_pitch']:\n pitch_rate = 0.\n next_pitch = self.settings['max_pitch']\n\n self.pitch = next_pitch\n\n controlled_state['info']['pitch_vel'] = -pitch_rate\n\n # Apply control order\n change_quat = False\n if change_quat:\n for ibody in self.settings['blade_num_body']:\n quat = algebra.rotate_quaternion(struct_tstep.mb_quat[ibody, :],\n delta_pitch*np.array([1., 0., 0.]))\n struct_tstep.mb_quat[ibody, :] = quat.copy()\n if ibody == 0:\n struct_tstep.quat = quat.copy()\n change_vel = False\n if change_vel:\n for ibody in self.settings['blade_num_body']:\n struct_tstep.mb_FoR_vel[ibody, 3] = pitch_rate\n struct_tstep.mb_FoR_acc[ibody, 3] = (data.structure.timestep_info[data.ts - 1].mb_FoR_vel[ibody, 3] -\n struct_tstep.mb_FoR_vel[ibody, 3])/self.settings['dt']\n if ibody == 0:\n struct_tstep.for_vel[3] = struct_tstep.mb_FoR_vel[ibody, 3]\n struct_tstep.for_acc[3] = struct_tstep.mb_FoR_acc[ibody, 3]\n\n data.structure.dynamic_input[data.ts - 1]['for_vel'] = struct_tstep.for_vel.copy()\n data.structure.dynamic_input[data.ts - 1]['for_acc'] = struct_tstep.for_acc.copy()\n\n if False:\n data.aero.generate_zeta_timestep_info(struct_tstep,\n aero_tstep,\n data.structure,\n data.aero.aero_settings,\n dt=self.settings['dt'])\n\n fid = open(self.log_fname, 'a')\n fid.write(('{:>6d} '\n + 10*'{:>12.6f} '\n + '{:>12.6f}\\n').format(data.ts,\n data.ts*self.settings['dt'],\n self.prescribed_sp[-1],\n self.system_pv[-1],\n detail[0],\n detail[1],\n detail[2],\n delta_pitch_ref,\n aero_torque/self.settings['GBR'],\n self.rotor_vel,\n pitch_rate,\n self.pitch))\n fid.close()\n return controlled_state\n\n\n def compute_prescribed_sp(self, time):\n \"\"\"\n Compute the set point relevant for the controller\n \"\"\"\n if self.settings['sp_source'] == 'file':\n sp = np.interp(time,\n self.prescribed_sp_time_history[:, 0],\n self.prescribed_sp_time_history[:, 1])\n self.prescribed_sp.append(sp)\n elif self.settings['sp_source'] == 'const':\n self.prescribed_sp.append(self.settings['sp_const'])\n\n return self.prescribed_sp[-1]\n\n\n def compute_system_pv(self, struct_tstep, beam, **kwargs):\n \"\"\"\n Compute the process value relevant for the controller\n \"\"\"\n if self.settings['sp_type'] == 'pitch':\n pitch = algebra.quat2euler(struct_tstep.mb_quat[self.settings['blade_num_body'][0]])[0]\n self.system_pv.append(pitch)\n elif self.settings['sp_type'] == 'rbm':\n steady, unsteady, grav = struct_tstep.extract_resultants(beam, force_type=['steady', 'unsteady', 'gravity'],\n ibody=0)\n rbm = steady[4] + unsteady[4] + grav[4]\n self.system_pv.append(rbm)\n elif self.settings['sp_type'] == 'gen_vel':\n self.system_pv.append(kwargs['gen_vel'])\n\n return self.system_pv[-1]\n\n def controller_wrapper(self,\n required_input,\n current_input,\n control_param,\n i_current):\n self.controller_implementation.set_point(required_input[i_current - 1])\n control_param, detailed_control_param = self.controller_implementation(current_input[-1])\n return (control_param, detailed_control_param)\n\n def __exit__(self, *args):\n # self.log.close()\n pass\n\n def drive_train_model(self, aero_torque, ini_rot_vel, ini_rot_acc):\n\n # Assuming contant generator torque demand\n if self.settings['gen_model_const_var'] == 'power':\n gen_torque = self.settings['gen_model_const_value']/self.settings['GBR']/ini_rot_vel\n elif self.settings['gen_model_const_var'] == 'torque':\n gen_torque = self.settings['gen_model_const_value']\n\n rot_acc = (aero_torque - self.settings['GBR']*gen_torque)/self.settings['inertia_dt']\n rot_vel = ini_rot_vel + rot_acc*self.settings['dt']\n\n return rot_vel, rot_acc\n\n def compute_aero_torque(self, beam, struct_tstep):\n # Compute total forces\n total_forces = np.zeros(6)\n for ibody in self.settings['blade_num_body']:\n steady, unsteady, grav = struct_tstep.extract_resultants(beam,\n force_type=['steady', 'unsteady', 'grav'],\n ibody=ibody)\n # total_forces += steady + unsteady + grav\n total_forces += steady + unsteady\n\n # Compute equivalent forces at hub position\n hub_elem = np.where(beam.body_number == self.settings['blade_num_body'][0])[0][0]\n hub_node = beam.connectivities[hub_elem, 0]\n hub_pos = struct_tstep.pos[hub_node, :]\n\n hub_forces = np.zeros(6)\n hub_forces[:3] = total_forces[:3].copy()\n hub_forces[3:6] = total_forces[3:6] - np.cross(hub_pos, total_forces[:3])\n\n return hub_forces[5]\n\n @staticmethod\n def compute_blade_pitch(beam, struct_tstep, tower_ibody=0, blade_ibody=1):\n # Tower top\n tt_elem = np.where(beam.body_number == tower_ibody)[0][-1]\n tt_node = beam.connectivities[tt_elem, 1]\n ielem, inode_in_elem = beam.node_master_elem[tt_node]\n ca0b = algebra.crv2rotation(struct_tstep.psi[ielem, inode_in_elem, :])\n cga0 = algebra.quat2rotation(struct_tstep.mb_quat[tower_ibody, :])\n zg_tower_top = cga0 @ ca0b @ np.array([0., 0., 1.])\n\n # blade root\n cga = algebra.quat2rotation(struct_tstep.mb_quat[blade_ibody, :])\n zg_hub = cga @ np.array([0., 0., 1.])\n\n pitch = algebra.angle_between_vectors(zg_tower_top, zg_hub)\n return pitch\n" }, { "path": "sharpy/controllers/controlsurfacepidcontroller.py", "content": "import numpy as np\nimport os\n\nimport sharpy.utils.controller_interface as controller_interface\nimport sharpy.utils.settings as settings\nimport sharpy.utils.control_utils as control_utils\nimport sharpy.utils.cout_utils as cout\n\n\n@controller_interface.controller\nclass ControlSurfacePidController(controller_interface.BaseController):\n r\"\"\"\n\n\n \"\"\"\n controller_id = 'ControlSurfacePidController'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['time_history_input_file'] = 'str'\n settings_default['time_history_input_file'] = None\n settings_description['time_history_input_file'] = 'Route and file name of the time history of desired state'\n\n settings_types['P'] = 'float'\n settings_default['P'] = None\n settings_description['P'] = 'Proportional gain of the controller'\n\n settings_types['I'] = 'float'\n settings_default['I'] = 0.0\n settings_description['I'] = 'Integral gain of the controller'\n\n settings_types['D'] = 'float'\n settings_default['D'] = 0.0\n settings_description['D'] = 'Differential gain of the controller'\n\n settings_types['input_type'] = 'str'\n settings_default['input_type'] = None\n settings_description['input_type'] = (\n 'Quantity used to define the' +\n ' reference state. Supported: `pitch`')\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = None\n settings_description['dt'] = 'Time step of the simulation'\n\n settings_types['controlled_surfaces'] = 'list(int)'\n settings_default['controlled_surfaces'] = None\n settings_description['controlled_surfaces'] = (\n 'Control surface indices to be actuated by this controller')\n\n settings_types['controlled_surfaces_coeff'] = 'list(float)'\n settings_default['controlled_surfaces_coeff'] = [1.]\n settings_description['controlled_surfaces_coeff'] = (\n 'Control surface deflection coefficients. ' +\n 'For example, for antisymmetric deflections => [1, -1].')\n\n settings_types['write_controller_log'] = 'bool'\n settings_default['write_controller_log'] = True\n settings_description['write_controller_log'] = (\n 'Write a time history of input, required input, ' +\n 'and control')\n\n supported_input_types = ['pitch', 'roll', 'pos_']\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types,\n settings_default,\n settings_description)\n\n def __init__(self):\n self.in_dict = None\n self.data = None\n self.settings = None\n\n self.prescribed_input_time_history = None\n\n # Time histories are ordered such that the [i]th element of each\n # is the state of the controller at the time of returning.\n # That means that for the timestep i,\n # state_input_history[i] == input_time_history_file[i] + error[i]\n self.p_error_history = list()\n self.i_error_history = list()\n self.d_error_history = list()\n self.real_state_input_history = list()\n self.control_history = list()\n\n self.controller_implementation = None\n\n self.n_control_surface = 0\n\n self.log = None\n\n def initialise(self, data, in_dict, controller_id=None, restart=False):\n self.in_dict = in_dict\n settings.to_custom_types(self.in_dict,\n self.settings_types,\n self.settings_default)\n\n self.settings = self.in_dict\n self.controller_id = controller_id\n\n # validate that the input_type is in the supported ones\n valid = False\n for t in self.supported_input_types:\n if t in self.settings['input_type']:\n valid = True\n break\n if not valid:\n cout.cout_wrap('The input_type {} is not supported by {}'.format(\n self.settings['input_type'], self.controller_id), 3)\n cout.cout_wrap('The supported ones are:', 3)\n for i in self.supported_input_types:\n cout.cout_wrap(' {}'.format(i), 3)\n raise NotImplementedError()\n\n if self.settings['write_controller_log']:\n folder = data.output_folder + '/controllers/'\n if not os.path.exists(folder):\n os.makedirs(folder)\n self.log = open(folder + self.controller_id + \".log.csv\", \"w+\")\n self.log.write(('#'+ 1*'{:>2},' + 6*'{:>12},' + '{:>12}\\n').\n format('tstep', 'time', 'Ref. state', 'state', 'Pcontrol', 'Icontrol', 'Dcontrol', 'control'))\n self.log.flush()\n\n # save input time history\n try:\n self.prescribed_input_time_history = (\n np.loadtxt(self.settings['time_history_input_file'], delimiter=','))\n except OSError:\n raise OSError('File {} not found in Controller'.format(self.settings['time_history_input_file']))\n\n # Init PID controller\n self.controller_implementation = control_utils.PID(self.settings['P'],\n self.settings['I'],\n self.settings['D'],\n self.settings['dt'])\n\n # check that controlled_surfaces_coeff has the correct number of parameters\n # if len() == 1 and == 1.0, then expand to number of surfaces.\n # if len(coeff) /= n_surfaces, throw error\n self.n_control_surface = len(self.settings['controlled_surfaces'])\n if (len(self.settings['controlled_surfaces_coeff']) ==\n self.n_control_surface):\n # All good, pass checks\n pass\n elif (len(self.settings['controlled_surfaces_coeff']) == 1 and\n self.settings['controlled_surfaces_coeff'][0] == 1.0):\n # default value, fill with 1.0\n self.settings['controlled_surfaces_coeff'] = np.ones(\n (self.n_control_surface,), dtype=float)\n else:\n raise ValueError('controlled_surfaces_coeff does not have as many'\n + ' elements as controller_surfaces')\n\n def control(self, data, controlled_state):\n r\"\"\"\n Main routine of the controller.\n Input is `data` (the self.data in the solver), and\n `currrent_state` which is a dictionary with ['structural', 'aero']\n time steps for the current iteration.\n\n :param data: problem data containing all the information.\n :param controlled_state: `dict` with two vars: `structural` and `aero`\n containing the `timestep_info` that will be returned with the\n control variables.\n\n :returns: A `dict` with `structural` and `aero` time steps and control\n input included.\n \"\"\"\n\n # get current state input\n self.real_state_input_history.append(self.extract_time_history(controlled_state))\n\n i_current = len(self.real_state_input_history)\n # apply it where needed.\n control_command, detail = self.controller_wrapper(\n required_input=self.prescribed_input_time_history,\n current_input=self.real_state_input_history,\n control_param={'P': self.settings['P'],\n 'I': self.settings['I'],\n 'D': self.settings['D']},\n i_current=i_current)\n\n controlled_state['aero'].control_surface_deflection = (\n np.array(self.settings['controlled_surfaces_coeff'])*control_command)\n\n self.log.write(('{:>6d},'\n + 6*'{:>12.6f},'\n + '{:>12.6f}\\n').format(i_current,\n i_current*self.settings['dt'],\n self.prescribed_input_time_history[i_current - 1],\n self.real_state_input_history[i_current - 1],\n detail[0],\n detail[1],\n detail[2],\n control_command))\n return controlled_state\n\n def extract_time_history(self, controlled_state):\n output = 0.0\n if self.settings['input_type'] == 'pitch':\n step = controlled_state['structural']\n euler = step.euler_angles()\n\n output = euler[1]\n elif self.settings['input_type'] == 'roll':\n step = controlled_state['structural']\n euler = step.euler_angles()\n\n output = euler[0]\n elif 'pos_z(' in self.settings['input_type']:\n node_str = self.settings['input_type']\n node_str = node_str.replace('pos(', '')\n node_str = node_str.replace(')', '')\n node = int(node_str)\n step = controlled_state['structural']\n pos = step.pos[node, :]\n\n output = pos[2]\n else:\n raise NotImplementedError(\n \"input_type {} is not yet implemented in extract_time_history()\"\n .format(self.settings['input_type']))\n return output\n\n def controller_wrapper(self,\n required_input,\n current_input,\n control_param,\n i_current):\n self.controller_implementation.set_point(required_input[i_current - 1])\n control_param, detailed_control_param = self.controller_implementation(current_input[-1])\n return (control_param, detailed_control_param)\n\n def __exit__(self, *args):\n self.log.close()\n" }, { "path": "sharpy/controllers/multibodycontroller.py", "content": "import numpy as np\nimport os\n\nimport sharpy.utils.controller_interface as controller_interface\nimport sharpy.utils.settings as settings\n\n\n@controller_interface.controller\nclass MultibodyController(controller_interface.BaseController):\n r\"\"\" \"\"\"\n\n controller_id = \"MultibodyController\"\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types[\"ang_history_input_file\"] = \"str\"\n settings_default[\"ang_history_input_file\"] = None\n settings_description[\"ang_history_input_file\"] = \"Route and file name of the time history of desired CRV rotation\"\n\n settings_types[\"ang_vel_history_input_file\"] = \"str\"\n settings_default[\"ang_vel_history_input_file\"] = \"\"\n settings_description[\"ang_vel_history_input_file\"] = (\"Route and file name of the time history of desired CRV \"\n \"velocity\")\n\n settings_types[\"psi_dot_init\"] = \"list(float)\"\n settings_default[\"psi_dot_init\"] = [0., 0., 0.]\n settings_description[\"psi_dot_init\"] = \"Initial rotation velocity of hinge\"\n\n settings_types[\"dt\"] = \"float\"\n settings_default[\"dt\"] = None\n settings_description[\"dt\"] = \"Time step of the simulation\"\n\n settings_types[\"write_controller_log\"] = \"bool\"\n settings_default[\"write_controller_log\"] = True\n settings_description[\"write_controller_log\"] = (\n \"Write a time history of input, required input, \" + \"and control\"\n )\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(\n settings_types, settings_default, settings_description, settings_options\n )\n\n def __init__(self):\n self.in_dict = None # this also holds the settings dict, kept to be consistent with other controllers\n self.data = None\n self.settings = None\n\n self.prescribed_ang_time_history = None\n self.prescribed_ang_vel_time_history = None\n\n # Time histories are ordered such that the [i]th element of each\n # is the state of the controller at the time of returning.\n # That means that for the timestep i,\n # state_input_history[i] == input_time_history_file[i] + error[i]\n\n self.real_state_input_history = list()\n self.control_history = list()\n\n self.controller_implementation = None\n self.log = None\n\n def initialise(self, data, in_dict, controller_id=None, restart=False):\n self.in_dict = in_dict\n settings.to_custom_types(\n self.in_dict, self.settings_types, self.settings_default\n )\n\n self.settings = self.in_dict\n self.controller_id = controller_id\n\n # whilst PID control is not here implemented, I have left the remains for if it gets implemented in future\n if self.settings[\"write_controller_log\"]:\n folder = data.output_folder + \"/controllers/\"\n if not os.path.exists(folder):\n os.makedirs(folder)\n self.log = open(folder + self.controller_id + \".log.csv\", \"w+\")\n self.log.write(\n (\"#\" + 1 * \"{:>2},\" + 6 * \"{:>12},\" + \"{:>12}\\n\").format(\n \"tstep\",\n \"time\",\n \"Ref. state\",\n \"state\",\n \"Pcontrol\",\n \"Icontrol\",\n \"Dcontrol\",\n \"control\",\n )\n )\n self.log.flush()\n\n # save input time history\n try:\n self.prescribed_ang_time_history = np.loadtxt(\n self.settings[\"ang_history_input_file\"], delimiter=\",\"\n )\n except:\n try:\n self.prescribed_ang_time_history = np.load(\n self.settings[\"ang_history_input_file\"]\n )\n except:\n raise OSError(\n \"File {} not found in Controller\".format(\n self.settings[\"ang_history_input_file\"]\n )\n )\n\n if self.settings[\"ang_vel_history_input_file\"]:\n try:\n self.prescribed_ang_vel_time_history = np.loadtxt(\n self.settings[\"ang_vel_history_input_file\"], delimiter=\",\"\n )\n except:\n try:\n self.prescribed_ang_vel_time_history = np.load(\n self.settings[\"ang_vel_history_input_file\"]\n )\n except:\n raise OSError(\n \"File {} not found in Controller\".format(\n self.settings[\"ang_vel_history_input_file\"]\n )\n )\n\n def control(self, data, controlled_state):\n r\"\"\"\n Main routine of the controller.\n Input is `data` (the self.data in the solver), and\n `currrent_state` which is a dictionary with ['structural', 'aero']\n time steps for the current iteration.\n\n :param data: problem data containing all the information.\n :param controlled_state: `dict` with two vars: `structural` and `aero`\n containing the `timestep_info` that will be returned with the\n control variables.\n\n :returns: A `dict` with `structural` and `aero` time steps and control\n input included.\n \"\"\"\n\n control_command = self.prescribed_ang_time_history[data.ts - 1, :]\n\n if self.prescribed_ang_vel_time_history is None:\n if data.ts == 1:\n psi_dot = self.settings[\"psi_dot_init\"]\n else:\n psi_dot = (\n self.prescribed_ang_time_history[data.ts - 1, :]\n - self.prescribed_ang_time_history[data.ts - 2, :]\n ) / self.settings[\"dt\"]\n else:\n psi_dot = self.prescribed_ang_vel_time_history[data.ts - 1, :]\n\n if controlled_state[\"structural\"].mb_prescribed_dict is None:\n controlled_state[\"structural\"].mb_prescribed_dict = dict()\n\n controlled_state[\"structural\"].mb_prescribed_dict[self.controller_id] = {\n \"psi\": control_command,\n \"psi_dot\": psi_dot,\n \"delta_psi\": control_command - self.prescribed_ang_time_history[0, :]}\n\n return controlled_state, control_command\n\n def controller_wrapper(\n self, required_input, current_input, control_param, i_current\n ):\n self.controller_implementation.set_point(required_input[i_current - 1])\n control_param, detailed_control_param = self.controller_implementation(\n current_input[-1]\n )\n return control_param, detailed_control_param\n\n def __exit__(self, *args):\n self.log.close()\n" }, { "path": "sharpy/controllers/takeofftrajectorycontroller.py", "content": "import ctypes as ct\nimport numpy as np\nimport os\nimport scipy.interpolate as interpolate\n\nimport sharpy.utils.controller_interface as controller_interface\nimport sharpy.utils.settings as settings\nimport sharpy.utils.control_utils as control_utils\nimport sharpy.utils.cout_utils as cout\nimport sharpy.structure.utils.lagrangeconstraints as lc\n\n\n@controller_interface.controller\nclass TakeOffTrajectoryController(controller_interface.BaseController):\n r\"\"\"\n\n\n \"\"\"\n controller_id = 'TakeOffTrajectoryController'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['trajectory_input_file'] = 'str'\n settings_default['trajectory_input_file'] = None\n settings_description['trajectory_input_file'] = 'Route and file name of the trajectory file given as a csv with columns: time, x, y, z'\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = None\n settings_description['dt'] = 'Time step of the simulation'\n\n settings_types['trajectory_method'] = 'str'\n settings_default['trajectory_method'] = 'lagrange'\n settings_description['trajectory_method'] = (\n 'Trajectory controller method. For now, \"lagrange\" is the supported option')\n\n settings_types['controlled_constraint'] = 'str'\n settings_default['controlled_constraint'] = None\n settings_description['controlled_constraint'] = ('Name of the controlled constraint in the multibody context' +\n ' Usually, it is something like `constraint_00`.')\n\n settings_types['controller_log_route'] = 'str'\n settings_default['controller_log_route'] = './output/'\n settings_description['controller_log_route'] = (\n 'Directory where the log will be stored')\n\n settings_types['write_controller_log'] = 'bool'\n settings_default['write_controller_log'] = True\n settings_description['write_controller_log'] = (\n 'Controls if the log from the controller is written or not.')\n\n settings_types['free_trajectory_structural_solver'] = 'str'\n settings_default['free_trajectory_structural_solver'] = ''\n settings_description['free_trajectory_structural_solver'] = (\n 'If different than and empty string, the structural solver' +\n ' will be changed after the end of the trajectory has been reached')\n\n settings_types['free_trajectory_structural_substeps'] = 'int'\n settings_default['free_trajectory_structural_substeps'] = 0\n settings_description['free_trajectory_structural_substeps'] = (\n 'Controls the structural solver' +\n ' structural substeps once the end of the trajectory has been reached')\n\n settings_types['initial_ramp_length_structural_substeps'] = 'int'\n settings_default['initial_ramp_length_structural_substeps'] = 10\n settings_description['initial_ramp_length_structural_substeps'] = (\n 'Controls the number of timesteps that are used to increase the' +\n ' structural substeps from 0')\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types,\n settings_default,\n settings_description)\n\n def __init__(self):\n self.in_dict = None\n self.data = None\n self.settings = None\n\n self.input_history = None\n self.trajectory_interp = None\n self.trajectory_vel_interp = None\n self.t_limits = np.zeros((2,))\n\n self.controlled_body = None\n self.controlled_node = None\n\n self.log = None\n\n def initialise(self, data, in_dict, controller_id=None, restart=False):\n self.in_dict = in_dict\n settings.to_custom_types(self.in_dict,\n self.settings_types,\n self.settings_default)\n\n self.settings = self.in_dict\n self.controller_id = controller_id\n\n if self.settings['write_controller_log']:\n # TODO substitute for table writer in cout_utils.\n folder = data.output_folder + '/controllers/'\n if not os.path.exists(folder):\n os.makedirs(folder)\n self.log = open(folder + self.controller_id + \".log.csv\", \"w+\")\n self.log.write(('#'+ 1*'{:>2},' + 6*'{:>12},' + '{:>12}\\n').\n format('tstep', 'time', 'Ref. state', 'state', 'Pcontrol', 'Icontrol', 'Dcontrol', 'control'))\n self.log.flush()\n\n # save input time history\n try:\n self.input_history = (\n np.loadtxt(\n self.settings['trajectory_input_file'], delimiter=','))\n except OSError:\n raise OSError('File {} not found in {}'.format(\n self.settings['time_history_input_file'], self.controller_id))\n\n self.process_trajectory()\n\n def control(self, data, controlled_state):\n r\"\"\"\n Main routine of the controller.\n Input is `data` (the self.data in the solver), and\n `currrent_state` which is a dictionary with ['structural', 'aero']\n time steps for the current iteration.\n\n :param data: problem data containing all the information.\n :param controlled_state: `dict` with two vars: `structural` and `aero`\n containing the `timestep_info` that will be returned with the\n control variables.\n\n :returns: A `dict` with `structural` and `aero` time steps and control\n input included.\n \"\"\"\n # get current state input\n # note: with or without the -1?\n time = (data.ts - 1)*self.settings['dt']\n i_current = data.ts\n\n try:\n constraint = controlled_state['structural'].\\\n mb_dict[self.settings['controlled_constraint']]\n except KeyError:\n return controlled_state\n\n if self.controlled_body is None or self.controlled_node is None:\n self.controlled_body = constraint['body_number']\n self.controlled_node = constraint['node_number']\n\n # reset info to include only fresh info\n controlled_state['info'] = dict()\n\n # apply it where needed.\n traj_command, end_of_traj = self.controller_wrapper(time)\n if end_of_traj:\n lc.remove_constraint(controlled_state['structural'].mb_dict,\n self.settings['controlled_constraint'])\n\n if not self.settings['free_trajectory_structural_solver'] == '':\n controlled_state['info']['structural_solver'] = (\n self.settings['free_trajectory_structural_solver'])\n\n controlled_state['info']['structural_substeps'] = (\n self.settings['free_trajectory_structural_substeps'])\n\n return controlled_state\n\n constraint['velocity'][:] = traj_command\n\n if self.settings['write_controller_log']:\n self.log.write(('{:>6d},'\n + 3*'{:>12.6f},'\n + '{:>12.6f}\\n').format(i_current,\n time,\n traj_command[0],\n traj_command[1],\n traj_command[2]))\n\n if self.settings['initial_ramp_length_structural_substeps'] >= 0:\n if (i_current <\n self.settings['initial_ramp_length_structural_substeps']):\n controlled_state['info']['structural_substeps'] = \\\n ct.c_int(i_current - 1)\n elif (i_current ==\n self.settings['initial_ramp_length_structural_substeps']):\n controlled_state['info']['structural_substeps'] = None\n\n return controlled_state\n\n def process_trajectory(self, dxdt=True):\n \"\"\"\n See https://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.interpolate.UnivariateSpline.html\n \"\"\"\n self.trajectory_interp = []\n # Make sure s = 0.5 is ok.\n self.t_limits[:] = (np.min(self.input_history[:, 0]),\n np.max(self.input_history[:, 0]))\n for i_dim in range(3):\n self.trajectory_interp.append(\n interpolate.UnivariateSpline(self.input_history[:, 0],\n self.input_history[:, i_dim + 1],\n k=1,\n s=0.,\n ext='raise'))\n if dxdt:\n self.trajectory_vel_interp = []\n for i_dim in range(3):\n self.trajectory_vel_interp.append(\n self.trajectory_interp[i_dim].derivative())\n\n def controller_wrapper(self, t):\n output_traj = np.zeros((3,))\n end_of_traj = False\n if self.settings['trajectory_method'] == 'lagrange':\n # check that t is in input limits\n if self.t_limits[0] <= t <= self.t_limits[1]:\n # return velocities\n for i_dim in range(3):\n output_traj[i_dim] = self.trajectory_vel_interp[i_dim](t)\n else:\n for i_dim in range(3):\n output_traj[i_dim] = np.nan\n end_of_traj = True\n else:\n raise NotImplementedError('The trajectory_method ' +\n self.settings['trajectory_method'] +\n ' is not yet implemented.')\n return output_traj, end_of_traj\n\n def __exit__(self, *args):\n self.log.close()\n" }, { "path": "sharpy/generators/__init__.py", "content": "\"\"\"Generators\n\nVelocity field generators prescribe the flow conditions for your problem. For instance, you can have an aircraft at\na prescribed fixed location in a velocity field towards the aircraft. Alternatively, you can have a free moving\naircraft in a static velocity field.\n\nDynamic Control Surface generators enable the user to prescribe a certain control surface deflection in time.\n\"\"\"\nimport importlib\nimport os\n\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.sharpydir as sharpydir\n\nfiles = generator_interface.generator_list_from_path(os.path.dirname(__file__))\n\nimport_path = os.path.realpath(os.path.dirname(__file__))\nimport_path = import_path.replace(sharpydir.SharpyDir, \"\")\nif import_path[0] == \"/\":\n import_path = import_path[1:]\nimport_path = import_path.replace(\"/\", \".\")\n\nfor file in files:\n generator_interface.generators[file] = importlib.import_module(import_path + \".\" + file)\n" }, { "path": "sharpy/generators/bumpvelocityfield.py", "content": "import numpy as np\n\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.settings as settings\nimport sharpy.utils.exceptions as exc\n\n\n@generator_interface.generator\nclass BumpVelocityField(generator_interface.BaseGenerator):\n r\"\"\"\n Bump Velocity Field Generator\n\n ``BumpVelocityField`` is a class inherited from ``BaseGenerator``\n\n The ``BumpVelocityField`` class generates a bump-shaped gust profile velocity field, and the profile has the characteristics\n specified by the user.\n\n To call this generator, the ``generator_id = BumpVelocityField`` shall be used.\n This is parsed as the value for the ``velocity_field_generator`` key in the desired aerodynamic solver's settings.\n\n The resultant velocity, $w_g$, is calculated as follows:\n\n .. math::\n\n w_g = \\frac{w_0}{4}\\left( 1 + \\cos(\\frac{(x - x_0)}{H_x} \\right)\\left( 1 + \\cos(\\frac{(y - y_0)}{H_y} \\right)\n\n\n Notes:\n For now, only simulations where the inertial FoR is fixed are supported.\n\n \"\"\"\n generator_id = 'BumpVelocityField'\n generator_classification = 'velocity-field'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['gust_intensity'] = 'float'\n settings_default['gust_intensity'] = None\n settings_description['gust_intensity'] = 'Intensity of the gust'\n\n settings_types['x0'] = 'float'\n settings_default['x0'] = 0.0\n settings_description['x0'] = 'x location of the centre of the bump'\n\n settings_types['y0'] = 'float'\n settings_default['y0'] = 0.0\n settings_description['y0'] = 'y location of the centre of the bump'\n\n settings_types['hx'] = 'float'\n settings_default['hx'] = 1.\n settings_description['hx'] = 'Gust gradient in the x direction'\n\n settings_types['hy'] = 'float'\n settings_default['hy'] = 1.\n settings_description['hy'] = 'Gust gradient in the y direction'\n\n settings_types['relative_motion'] = 'bool'\n settings_default['relative_motion'] = False\n settings_description['relative_motion'] = 'When true the gust will move at the prescribed velocity'\n\n settings_types['u_inf'] = 'float'\n settings_default['u_inf'] = None\n settings_description['u_inf'] = 'Free stream velocity'\n\n settings_types['u_inf_direction'] = 'list(float)'\n settings_default['u_inf_direction'] = np.array([1.0, 0, 0])\n settings_description['u_inf_direction'] = 'Free stream velocity direction'\n\n table = settings.SettingsTable()\n __doc__ += table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.in_dict = dict()\n self.settings = dict()\n\n self.u_inf = 0.\n self.u_inf_direction = None\n\n def initialise(self, in_dict, restart=False):\n self.in_dict = in_dict\n settings.to_custom_types(self.in_dict, BumpVelocityField.settings_types, BumpVelocityField.settings_default)\n self.settings = self.in_dict\n\n self.u_inf = self.settings['u_inf']\n self.u_inf_direction = self.in_dict['u_inf_direction']\n\n def generate(self, params, uext):\n zeta = params['zeta']\n override = params['override']\n for_pos = params['for_pos']\n t = params['t']\n\n def gust_shape(x, y, z, hx, hy, x0, y0, w0):\n vel = np.zeros((3,))\n if np.abs(x - x0) > hx or np.abs(y - y0) > hy:\n return vel\n\n vel[2] = 0.25*w0*(1 + np.cos((x - x0)/hx * np.pi))*(1 + np.cos((y - y0)/hy * np.pi))\n return vel\n\n for i_surf in range(len(zeta)):\n if override:\n uext[i_surf].fill(0.0)\n\n for i in range(zeta[i_surf].shape[1]):\n for j in range(zeta[i_surf].shape[2]):\n uext[i_surf][:, i, j] += gust_shape(zeta[i_surf][0, i, j] + for_pos[0],\n zeta[i_surf][1, i, j] + for_pos[1],\n zeta[i_surf][2, i, j] + for_pos[2],\n self.settings['hx'],\n self.settings['hy'],\n self.settings['x0'],\n self.settings['y0'],\n self.settings['gust_intensity'])\n\n if self.settings['relative_motion']:\n uext[i_surf][:, i, j] += self.u_inf*t\n" }, { "path": "sharpy/generators/dynamiccontrolsurface.py", "content": "import numpy as np\n\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.settings as settings\nimport sharpy.utils.cout_utils as cout_utils\n\n\n@generator_interface.generator\nclass DynamicControlSurface(generator_interface.BaseGenerator):\n \"\"\"\n Dynamic Control Surface deflection Generator\n\n The object generates a deflection in radians based on the time series given as a single vector in the input data.\n A first order finite-differences scheme is used to calculate the deflection rate based on the provided time step\n increment.\n\n To call this generator, the ``generator_id = DynamicControlSurface`` key shall be used for the setting\n `control_surface_deflection` in the ``AerogridLoader`` solver.\n\n One instance of this generator will be created for each control surface, thus, a group of settings should be defined\n for each control surface (``cs0_settings``, ``cs1_settings`` ... in the example below).\n All of these groups of settings should be collected as values in a dictionary which keys are the associated control surface number in string format.\n This dictionary should be parsed to the variable\n ``control_surface_deflection_generator_settings`` in ``AerogridLoader``. This is shown better\n in the example below:\n\n Examples:\n\n .. code-block:\n\n cs0_settings = {} # these are the settings for control surface number 0\n cs1_settings = {} # these are the settings for control surface number 1\n dict_of_cs = {'0': cs0_settings,\n '1': cs1_settings} # This dictionary groups all the settings for all the control surfaces\n settings = {}\n settings['AerogridLoader] = {'control_surface_deflection' : ['DynamicControlSurface],\n 'control_surface_deflection_generator_settings: dict_of_cs}\n\n\n\n Attributes:\n deflection (np.array): Array of deflection of the control surface\n deflection_dot (np.array): Array of the time derivative of the cs deflection. Calculated using 1st order finite differences.\n\n \"\"\"\n generator_id = 'DynamicControlSurface'\n generator_classification = 'utils'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = None\n settings_description['dt'] = 'Time step increment'\n\n settings_types['deflection_file'] = 'str'\n settings_default['deflection_file'] = None\n settings_description['deflection_file'] = 'Path to the file with the deflection information'\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description,\n header_line='This generator takes the following inputs:')\n\n def __init__(self):\n self.in_dict = dict()\n\n self.deflection = None\n self.deflection_dot = None\n\n def initialise(self, in_dict, restart=False):\n self.in_dict = in_dict\n settings.to_custom_types(self.in_dict, self.settings_types, self.settings_default, no_ctype=True)\n\n # load file\n try:\n self.deflection = np.loadtxt(self.in_dict['deflection_file'])\n except OSError:\n cout_utils.cout_wrap('Unable to find control surface deflection file input', 4)\n raise FileNotFoundError('Could not locate deflection file: '\n '{:s}'.format(self.in_dict['deflection_file']))\n else:\n cout_utils.cout_wrap('\\tSuccess loading file {:s}'.format(self.in_dict['deflection_file']), 2)\n\n # deflection velocity\n self.deflection_dot = np.zeros_like(self.deflection)\n self.deflection_dot[0:-1] = np.diff(self.deflection)/self.in_dict['dt']\n self.deflection_dot[-1] = 0\n\n def generate(self, params):\n it = params['it']\n return self.deflection[it], self.deflection_dot[it]\n\n def __call__(self, params):\n return self.generate(params)\n" }, { "path": "sharpy/generators/floatingforces.py", "content": "import numpy as np\nimport h5py as h5\nimport ctypes as ct\nimport os\nfrom scipy.fft import fft, ifft\nfrom scipy.interpolate import interp1d\nfrom control import forced_response, TransferFunction\n\nimport sharpy.utils.cout_utils as cout\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.settings as settings\nimport sharpy.utils.solver_interface as solver_interface\nfrom sharpy.utils.constants import deg2rad\nimport sharpy.utils.h5utils as h5utils\nimport sharpy.utils.algebra as algebra\n\n\ndef compute_xf_zf(hf, vf, l, w, EA, cb):\n \"\"\"\n Fairlead location (xf, zf) computation\n \"\"\"\n\n root1, root2, ln1, ln2, lb = rename_terms(vf, hf, w, l)\n\n # Define if there is part of the mooring line on the bed\n if lb <= 0:\n nobed = True\n else:\n nobed = False\n\n # Compute the position of the fairlead\n if nobed:\n xf = hf/w*(ln1 - ln2) + hf*l/EA\n zf = hf/w*(root1 - root2) + 1./EA*(vf*l-w*l**2/2)\n else:\n xf = lb + hf/w*ln1 + hf*l/EA\n if not cb == 0.:\n xf += cb*w/2/EA*(-lb**2 + (lb - hf/cb/w)*np.maximum((lb - hf/cb/w), 0))\n zf = hf/w*(root1 - 1) + vf**2/2/EA/w\n\n return xf, zf\n\n\ndef compute_jacobian(hf, vf, l, w, EA, cb):\n \"\"\"\n Analytical computation of the Jacobian of equations\n in function compute_xf_zf\n \"\"\"\n\n root1, root2, ln1, ln2, lb = rename_terms(vf, hf, w, l)\n\n # Compute their deivatives\n der_root1_hf = 0.5*(1. + (vf/hf)**2)**(-0.5)*(2*vf/hf*(-vf/hf/hf))\n der_root1_vf = 0.5*(1. + (vf/hf)**2)**(-0.5)*(2*vf/hf/hf)\n\n der_root2_hf = 0.5*(1. + ((vf - w*l)/hf)**2)**(-0.5)*(2.*(vf - w*l)/hf*(-(vf - w*l)/hf/hf))\n der_root2_vf = 0.5*(1. + ((vf - w*l)/hf)**2)**(-0.5)*(2.*(vf - w*l)/hf/hf)\n\n der_ln1_hf = 1./(vf/hf + root1)*(vf/hf/hf + der_root1_hf)\n der_ln1_vf = 1./(vf/hf + root1)*(1./hf + der_root1_vf)\n\n der_ln2_hf = 1./((vf - w*l)/hf + root2)*(-(vf - w*l)/hf/hf + der_root2_hf)\n der_ln2_vf = 1./((vf - w*l)/hf + root2)*(1./hf + der_root2_vf)\n\n der_lb_hf = 0.\n der_lb_vf = -1./w\n\n # Define if there is part of the mooring line on the bed\n if lb <= 0:\n nobed = True\n else:\n nobed = False\n\n # Compute the Jacobian\n if nobed:\n der_xf_hf = 1./w*(ln1 - ln2) + hf/w*(der_ln1_hf + der_ln2_hf) + l/EA\n der_xf_vf = hf/w*(der_ln1_vf + der_ln2_vf)\n\n der_zf_hf = 1./w*(root1 - root2) + hf/w*(der_root1_hf - der_root2_hf)\n der_zf_vf = hf/w*(der_root1_vf - der_root2_vf) + 1./EA*l\n else:\n der_xf_hf = der_lb_hf + 1./w*ln1 + hf/w*der_ln1_hf + l/EA\n if not cb == 0.:\n arg1_max = l - vf/w - hf/cb/w\n if arg1_max > 0.:\n der_xf_hf += cb*w/2/EA*(2*(arg1_max)*(-1/cb/w))\n\n der_xf_vf = der_lb_vf + hf/w*der_ln1_vf + cb*w/2/EA*(-2.*lb*der_lb_vf)\n if not cb == 0.:\n arg1_max = l - vf/w - hf/cb/w\n if arg1_max > 0.:\n der_xf_vf += cb*w/2/EA*(2.*(lb - hf/cb/w)*der_lb_vf)\n\n der_zf_hf = 1/w*(root1 - 1) + hf/w*der_root1_hf\n der_zf_vf = hf/w*der_root1_vf + vf/EA/w\n\n J = np.array([[der_xf_hf, der_xf_vf],[der_zf_hf, der_zf_vf]])\n\n return J\n\n\ndef rename_terms(vf, hf, w, l):\n \"\"\"\n Rename some terms for convenience\n \"\"\"\n root1 = np.sqrt(1. + (vf/hf)**2)\n root2 = np.sqrt(1. + ((vf - w*l)/hf)**2)\n ln1 = np.log(vf/hf + root1)\n ln2 = np.log((vf - w*l)/hf + root2)\n lb = l - vf/w\n return root1, root2, ln1, ln2, lb\n\ndef quasisteady_mooring(xf, zf, l, w, EA, cb, hf0=None, vf0=None):\n \"\"\"\n Computation of the forces generated by the mooring system\n It performs a Newton-Raphson iteration based on the known equations\n in compute_xf_zf function and the Jacobian\n \"\"\"\n\n # Initialise guess for hf0 and vf0\n if xf == 0:\n lambda0 = 1e6\n elif np.sqrt(xf**2 + zf**2) > l:\n lambda0 = 0.2\n else:\n lambda0 = np.sqrt(3*((l**2 - zf**2)/xf**2 - 1))\n\n if hf0 is None:\n hf0 = np.abs(w*xf/2/lambda0)\n\n if vf0 is None:\n vf0 = w/2*(zf/np.tanh(lambda0) + l)\n\n # Compute the solution through Newton-Raphson iteration\n hf_est = hf0 + 0.\n vf_est = vf0 + 0.\n xf_est, zf_est = compute_xf_zf(hf_est, vf_est, l, w, EA, cb)\n # print(\"initial: \", xf_est, zf_est)\n tol = 1e-6\n error = 2*tol\n max_iter = 10000\n it = 0\n while ((error > tol) and (it < max_iter)):\n J_est = compute_jacobian(hf_est, vf_est, l, w, EA, cb)\n inv_J_est = np.linalg.inv(J_est)\n hf_est += inv_J_est[0, 0]*(xf - xf_est) + inv_J_est[0, 1]*(zf - zf_est)\n vf_est += inv_J_est[1, 0]*(xf - xf_est) + inv_J_est[1, 1]*(zf - zf_est)\n\n xf_est, zf_est = compute_xf_zf(hf_est, vf_est, l, w, EA, cb)\n error = np.maximum(np.abs(xf - xf_est), np.abs(zf - zf_est))\n it += 1\n if ((it == max_iter) and (error > tol)):\n cout.cout_wrap((\"Mooring system did not converge. error %f\" % error), 4)\n print(\"Mooring system did not converge. error %f\" % error)\n\n return hf_est, vf_est\n\n\ndef wave_radiation_damping(K, qdot, it, dt):\n \"\"\"\n This function computes the wave radiation damping assuming K constant\n \"\"\"\n qdot_int = np.zeros((6,))\n for idof in range(6):\n qdot_int[idof] = np.trapz(np.arange(0, it + 1, 1)*dt, qdot[0:it, idof])\n\n return np.dot(K, qdot_int)\n\n\ndef change_of_to_sharpy(matrix_of):\n \"\"\"\n Change between frame of reference of OpenFAST and the\n usual one in SHARPy\n \"\"\"\n\n sub_mat = np.array([[0., 0, 1],\n [0., -1, 0],\n [1., 0, 0]])\n C_of_s = np.zeros((6,6))\n C_of_s[0:3, 0:3] = sub_mat\n C_of_s[3:6, 3:6] = sub_mat\n\n matrix_sharpy = np.dot(C_of_s.T, np.dot(matrix_of, C_of_s))\n return matrix_sharpy\n\n\ndef rfval(num, den, z):\n \"\"\"\n Evaluate a rational function given by the coefficients of the numerator (num) and\n denominator (den) at z\n \"\"\"\n return np.polyval(num, z)/np.polyval(den, z)\n\n\ndef matrix_from_rf(dict_rf, w):\n \"\"\"\n Create a matrix from the rational function approximation of each one of the elements\n \"\"\"\n H = np.zeros((6, 6))\n for i in range(6):\n for j in range(6):\n pos = \"%d_%d\" % (i, j)\n H[i, j] = rfval(dict_rf[pos]['num'], dict_rf[pos]['den'], w)\n\n return H\n\n\ndef response_freq_dep_matrix(H, omega_H, q, it_, dt):\n \"\"\"\n Compute the frequency response of a system with a transfer function depending on the frequency\n F(t) = H(omega) * q(t)\n \"\"\"\n it = it_ + 1\n omega_fft = np.linspace(0, 1/(2*dt), it//2)[:it//2]\n fourier_q = fft(q[:it, :], axis=0)\n fourier_f = np.zeros_like(fourier_q)\n\n ndof = q.shape[1]\n f = np.zeros((ndof))\n\n # Compute the constant component\n if type(H) is np.ndarray:\n interp_H = interp1d(omega_H, H, axis=0)\n H_omega = interp_H(omega_fft[0])\n elif type(H) is tuple:\n H_omega = matrix_from_rf(H, omega_fft[0])\n else:\n cout.cout_wrap((\"ERROR: Not implemented response_freq_dep_matrix for type(H) %s\" % type(H)), 4)\n fourier_f[0, :] = np.dot(H_omega, fourier_q[0, :])\n\n # Compute the rest of the terms\n for iomega in range(1, omega_fft.shape[0]):\n # Interpolate H at omega\n if type(H) is np.ndarray:\n H_omega = interp_H(omega_fft[iomega])\n elif type(H) is dict:\n H_omega = matrix_from_rf(H, omega_fft[iomega])\n fourier_f[iomega, :] = np.dot(H_omega, fourier_q[iomega, :])\n fourier_f[-iomega, :] = np.dot(H_omega, fourier_q[-iomega, :])\n\n # Compute the inverse Fourier tranform\n f[:] = np.real(ifft(fourier_f, axis=0)[it_, :])\n\n return f\n\n\ndef compute_equiv_hd_added_mass(f, q):\n \"\"\"\n Compute the matrix H that satisfies f = Hq\n H represents the added mass effects so it has to be\n symmetric.\n For the OC3 platfrom the following statements hold:\n - z-y symmetry\n - Non-diagonal non-zero terms: (1,5) and (2,4). Zero-indexed\n \"\"\"\n\n if (q == 0).all():\n return np.zeros((6,6))\n\n q_mat = np.array([[q[0], 0, 0, 0, 0, 0],\n [0, q[1], 0, 0, q[5], 0],\n [0, q[2], 0, 0, 0, q[4]],\n [0, 0, q[3], 0, 0, 0],\n [0, 0, 0, q[4], 0, q[2]],\n [0, 0, 0, q[5], q[1], 0]])\n\n hv = np.dot(np.linalg.inv(q_mat), f)\n\n H = np.array([[hv[0], 0, 0, 0, 0, 0],\n [0, hv[1], 0, 0, 0, hv[4]],\n [0, 0, hv[1], 0, hv[5], 0],\n [0, 0, 0, hv[2], 0, 0],\n [0, 0, hv[5], 0, hv[3], 0],\n [0, hv[4], 0, 0, 0, hv[3]]])\n\n return H\n\n\ndef jonswap_spectrum(Tp, Hs, w):\n \"\"\"\n This function computes the one-sided spectrum of the JONSWAP wave data\n [2] Jonkman, J. M. Dynamics modeling and loads analysis of an offshore floating wind turbine. 2007. NREL/TP-500-41958\n \"\"\"\n nomega = w.shape[0]\n spectrum = np.zeros((nomega))\n for iomega in range(nomega):\n # Compute the scaling factor\n if w[iomega] <= 2*np.pi/Tp:\n sigma = 0.07\n else:\n sigma = 0.09\n # Compute the peak shape parameter\n param = Tp/np.sqrt(Hs)\n if param <= 3.6:\n gamma = 5.\n elif param > 5:\n gamma = 1.\n else:\n gamma = np.exp(5.75 - 1.15*param)\n # Compute one-sided spectrum\n omega = w[iomega]\n if omega == 0:\n spectrum[iomega] = 0.\n else:\n param = omega*Tp/2/np.pi\n spectrum[iomega] = (1./2/np.pi)*(5./16)*(Hs**2*Tp)*param**(-5)\n spectrum[iomega] *= np.exp(-5./4*param**(-4))\n spectrum[iomega] *= (1. - 0.287*np.log(gamma))\n spectrum[iomega] *= gamma**np.exp(-0.5*((param - 1.)/sigma)**2)\n\n return spectrum\n\n\ndef noise_freq_1s(w):\n \"\"\"\n Generates a frequency representation of a white noise\n \"\"\"\n sigma = 1. #/np.sqrt(2)\n nomega = w.shape[0]\n\n wn = np.zeros((nomega, ), dtype=np.complex)\n u1 = np.random.random(size=nomega) #+ 0j\n u2 = np.random.random(size=nomega) #+ 0j\n wn[0] = 0. + 0j\n for iomega in range(1, nomega):\n u1w = u1[iomega]\n u2w = u2[iomega]\n wn[iomega] = np.sqrt(-2.*np.log(u1w))*(np.cos(2*np.pi*u2w) +\n 1j*np.sin(2*np.pi*u2w))\n return wn*sigma\n\n\n@generator_interface.generator\nclass FloatingForces(generator_interface.BaseGenerator):\n r\"\"\"\n Floating forces generator\n\n Generates the forces associated the floating support of offshore wind turbines.\n Currently supports spar configurations.\n\n The hydrostatic forces model includes buoyancy: an initial vertical force and the restoring forces\n associated with heave, roll and pitch. See the implementation in [1].\n\n The mooring model is the quasisteady implementation of Jonkman [2] .However, equation 2-37b is thought to be wrong (it is just a copy from eq 2-35b)\n This was corrected according to the theory review of MAP++ [3].\n\n The default values have been obtained from the OC3 platform report [1]\n\n [1] Jonkman, J. Definition of the Floating System for Phase IV of OC3. 2010. NREL/TP-500-47535\n\n [2] Jonkman, J. M. Dynamics modeling and loads analysis of an offshore floating wind turbine. 2007. NREL/TP-500-41958\n\n [3] https://map-plus-plus.readthedocs.io/en/latest/theory.html (accessed on Octorber 14th, 2020)\n \"\"\"\n generator_id = 'FloatingForces'\n generator_classification = 'runtime'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['n_time_steps'] = 'int'\n settings_default['n_time_steps'] = None\n settings_description['n_time_steps'] = 'Number of time steps'\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = None\n settings_description['dt'] = 'Time step'\n\n settings_types['water_density'] = 'float'\n settings_default['water_density'] = 1025 # kg/m3\n settings_description['water_density'] = 'Water density'\n\n settings_types['gravity_on'] = 'bool'\n settings_default['gravity_on'] = True\n settings_description['gravity_on'] = 'Flag to include gravitational forces'\n\n settings_types['gravity'] = 'float'\n settings_default['gravity'] = 9.81\n settings_description['gravity'] = 'Gravity'\n\n settings_types['gravity_dir'] = 'list(float)'\n settings_default['gravity_dir'] = [1., 0., 0.]\n settings_description['gravity_dir'] = 'Gravity direction'\n\n settings_types['floating_file_name'] = 'str'\n settings_default['floating_file_name'] = './oc3.floating.h5'\n settings_description['floating_file_name'] = 'File containing the information about the floating dynamics'\n\n settings_types['cd_multiplier'] = 'float'\n settings_default['cd_multiplier'] = 1.\n settings_description['cd_multiplier'] = 'Multiply the drag coefficient by this number to increase dissipation'\n\n settings_types['add_damp_diag'] = 'list(float)'\n settings_default['add_damp_diag'] = [0., 0., 0., 0., 0., 0.]\n settings_description['add_damp_diag'] = 'Diagonal terms to include in the additional damping matrix'\n\n settings_types['add_damp_ts'] = 'int'\n settings_default['add_damp_ts'] = 0\n settings_description['add_damp_ts'] = 'Timesteps in which ``add_damp_diag`` will be used'\n\n settings_types['method_matrices_freq'] = 'str'\n settings_default['method_matrices_freq'] = 'constant'\n settings_description['method_matrices_freq'] = 'Method to compute frequency-dependent matrices'\n settings_options['method_matrices_freq'] = ['constant', 'rational_function']\n\n settings_types['matrices_freq'] = 'float'\n settings_default['matrices_freq'] = 4.8 # Close to the upper limit defined in the oc3 report\n settings_description['matrices_freq'] = 'Frequency [rad/s] to interpolate frequency-dependent matrices'\n\n settings_types['steps_constant_matrices'] = 'int'\n settings_default['steps_constant_matrices'] = 8\n settings_description['steps_constant_matrices'] = 'Time steps to compute with constant matrices computed at ``matrices_freq``. Irrelevant in ``method_matrices_freq``=``constant``'\n\n settings_types['added_mass_in_mass_matrix'] = 'bool'\n settings_default['added_mass_in_mass_matrix'] = True\n settings_description['added_mass_in_mass_matrix'] = 'Include the platform added mass in the mass matrix of the system'\n\n settings_types['concentrate_spar'] = 'bool'\n settings_default['concentrate_spar'] = False\n settings_description['concentrate_spar'] = 'Compute CD as if the spar properties were concentrated at the base'\n\n settings_types['method_wave'] = 'str'\n settings_default['method_wave'] = 'sin'\n settings_description['method_wave'] = 'Method to compute wave forces'\n settings_options['method_wave'] = ['sin', 'jonswap']\n\n settings_types['wave_amplitude'] = 'float'\n settings_default['wave_amplitude'] = 0.\n settings_description['wave_amplitude'] = 'Wave amplitude. Only used in ``method_wave = sin``'\n\n settings_types['wave_freq'] = 'float'\n settings_default['wave_freq'] = 0.\n settings_description['wave_freq'] = 'Wave circular frequency [rad/s]. Only used in ``method_wave = sin``'\n\n settings_types['wave_Tp'] = 'float'\n settings_default['wave_Tp'] = 0.\n settings_description['wave_Tp'] = 'Wave peak spectral period [s]. Only used in ``method_wave = jonswap``'\n\n settings_types['wave_Hs'] = 'float'\n settings_default['wave_Hs'] = 0.\n settings_description['wave_Hs'] = 'Significant wave height [m]. Only used in ``method_wave = jonswap``'\n\n settings_types['wave_incidence'] = 'float'\n settings_default['wave_incidence'] = 0.\n settings_description['wave_incidence'] = 'Wave incidence in rad'\n\n settings_types['write_output'] = 'bool'\n settings_default['write_output'] = False\n settings_description['write_output'] = 'Write forces to an output file'\n\n settings_types['folder'] = 'str'\n settings_default['folder'] = 'output'\n settings_description['folder'] = 'Folder for the output files'\n\n settings_types['log_filename'] = 'str'\n settings_default['log_filename'] = 'log_floating_forces'\n settings_description['log_filename'] = 'Log file name to write outputs'\n\n setting_table = settings.SettingsTable()\n __doc__ += setting_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.in_dict = dict()\n\n self.water_density = None\n self.gravity = None\n self.gravity_dir = None\n\n self.floating_data = None\n\n self.mooring_node = None\n self.n_mooring_lines = None\n self.anchor_pos = None\n self.fairlead_pos_A = None\n self.hf_prev = list() # Previous value of hf just for initialisation\n self.vf_prev = list()\n\n self.buoyancy_node = None\n self.buoy_F0 = None\n self.buoy_rest_mat = None\n\n self.wave_forces_node = None\n\n self.q = None\n self.qdot = None\n self.qdotdot = None\n\n self.log_filename = None\n self.added_mass_in_mass_matrix = None\n\n\n def initialise(self, in_dict=None, data=None, restart=False):\n self.in_dict = in_dict\n settings.to_custom_types(self.in_dict,\n self.settings_types,\n self.settings_default,\n self.settings_options,\n no_ctype=True)\n self.settings = self.in_dict\n\n self.water_density = self.settings['water_density']\n self.gravity = self.settings['gravity']\n self.gravity_dir = self.settings['gravity_dir']\n\n # Platform dofs\n if not restart:\n self.q = np.zeros((self.settings['n_time_steps'] + 1, 6))\n self.qdot = np.zeros_like(self.q)\n self.qdotdot = np.zeros_like(self.q)\n else:\n increase_ts = self.settings['n_time_steps'] + 1 - self.q.shape[0]\n self.q = np.concatenate((self.q, np.zeros((increase_ts, 6))), axis=0)\n self.qdot = np.concatenate((self.qdot, np.zeros((increase_ts, 6))), axis=0)\n self.qdotdot = np.concatenate((self.qdotdot, np.zeros((increase_ts, 6))), axis=0)\n\n # Read the file with the floating information\n fid = h5.File(self.settings['floating_file_name'], 'r')\n self.floating_data = h5utils.load_h5_in_dict(fid)\n fid.close()\n\n # Mooringlines parameters\n self.mooring_node = self.floating_data['mooring']['node']\n self.n_mooring_lines = self.floating_data['mooring']['n_lines']\n self.anchor_pos = np.zeros((self.n_mooring_lines, 3))\n self.fairlead_pos_A = np.zeros((self.n_mooring_lines, 3))\n if not restart:\n self.hf_prev = [None]*self.n_mooring_lines\n self.vf_prev = [None]*self.n_mooring_lines\n\n if self.n_mooring_lines > 0:\n theta = 2.*np.pi/self.n_mooring_lines\n R = algebra.rotation3d_x(theta)\n self.anchor_pos[0, 0] = -self.floating_data['mooring']['anchor_depth']\n self.anchor_pos[0, 2] = self.floating_data['mooring']['anchor_radius']\n self.fairlead_pos_A[0, 0] = -self.floating_data['mooring']['fairlead_depth']\n self.fairlead_pos_A[0, 2] = self.floating_data['mooring']['fairlead_radius']\n for imoor in range(1, self.n_mooring_lines):\n self.anchor_pos[imoor, :] = np.dot(R, self.anchor_pos[imoor - 1, :])\n self.fairlead_pos_A[imoor, :] = np.dot(R, self.fairlead_pos_A[imoor - 1, :])\n\n # Hydrostatics\n self.buoyancy_node = self.floating_data['hydrostatics']['node']\n self.buoy_F0 = np.zeros((6,), dtype=float)\n self.buoy_F0[0:3] = (self.floating_data['hydrostatics']['V0']*\n self.settings['water_density']*\n self.settings['gravity']*self.settings['gravity_dir'])\n self.buoy_rest_mat = self.floating_data['hydrostatics']['buoyancy_restoring_matrix']\n\n # hydrodynamics\n self.cd = self.floating_data['hydrodynamics']['CD']*self.settings['cd_multiplier']\n if self.settings['method_matrices_freq'] == 'constant':\n interp_am = interp1d(self.floating_data['hydrodynamics']['ab_freq_rads'],\n self.floating_data['hydrodynamics']['added_mass_matrix'],\n axis=0)\n self.hd_added_mass_const = interp_am(self.settings['matrices_freq'])\n interp_d = interp1d(self.floating_data['hydrodynamics']['ab_freq_rads'],\n self.floating_data['hydrodynamics']['damping_matrix'],\n axis=0)\n self.hd_damping_const = interp_d(self.settings['matrices_freq'])\n\n elif self.settings['method_matrices_freq'] == 'rational_function':\n self.hd_added_mass_const = self.floating_data['hydrodynamics']['added_mass_matrix'][-1, :, :]\n self.hd_damping_const = self.floating_data['hydrodynamics']['damping_matrix'][-1, :, :]\n\n self.added_mass_in_mass_matrix = self.settings['added_mass_in_mass_matrix']\n if ((self.added_mass_in_mass_matrix) and (not restart)):\n cout.cout_wrap((\"Including added mass in mass matrix\"), 2)\n if data.structure.lumped_mass_mat is None:\n data.structure.lumped_mass_mat_nodes = np.array([self.buoyancy_node])\n data.structure.lumped_mass_mat = np.array([self.hd_added_mass_const])\n else:\n data.structure.lumped_mass_mat_nodes = np.concatenate((data.structure.lumped_mass_mat_nodes, np.array([self.buoyancy_node])), axis=0)\n data.structure.lumped_mass_mat = np.concatenate((data.structure.lumped_mass_mat, np.array([self.hd_added_mass_const])), axis=0)\n\n data.structure.add_lumped_mass_to_element(self.buoyancy_node,\n self.hd_added_mass_const)\n data.structure.generate_fortran()\n\n if self.settings['method_matrices_freq'] == 'rational_function':\n ninput = 6\n noutput = 6\n hd_K_num = [None]*noutput\n hd_K_den = [None]*noutput\n for ioutput in range(noutput):\n hd_K_num[ioutput] = [None]*ninput\n hd_K_den[ioutput] = [None]*ninput\n for iinput in range(ninput):\n pos = \"%d_%d\" % (ioutput, iinput)\n hd_K_num[ioutput][iinput] = self.floating_data['hydrodynamics']['K_rf'][pos]['num']\n hd_K_den[ioutput][iinput] = self.floating_data['hydrodynamics']['K_rf'][pos]['den']\n\n self.hd_K = TransferFunction(hd_K_num, hd_K_den)\n self.ab_freq_rads = self.floating_data['hydrodynamics']['ab_freq_rads']\n\n if restart:\n self.x0_K.extend([None]*increase_ts)\n else:\n self.x0_K = [None]*(self.settings['n_time_steps'] + 1)\n self.x0_K[0] = 0.\n\n\n # Wave forces\n self.wave_forces_node = self.floating_data['wave_forces']['node']\n if self.settings['method_wave'] == 'sin':\n interp_x1 = interp1d(self.floating_data['wave_forces']['xi_freq_rads'],\n self.floating_data['wave_forces']['xi'],\n axis=0,\n bounds_error=False,\n fill_value=(self.floating_data['wave_forces']['xi'][0, ...],\n self.floating_data['wave_forces']['xi'][-1, ...]))\n xi_matrix2 = interp_x1(self.settings['wave_freq'])\n interp_x2 = interp1d(self.floating_data['wave_forces']['xi_beta_deg']*deg2rad,\n xi_matrix2,\n axis=0)\n self.xi_interp = interp_x2(self.settings['wave_incidence'])\n\n elif self.settings['method_wave'] == 'jonswap':\n\n interp_x1 = interp1d(self.floating_data['wave_forces']['xi_beta_deg']*deg2rad,\n self.floating_data['wave_forces']['xi'],\n axis=1)\n xi_matrix = interp_x1(self.settings['wave_incidence'])\n\n self.freq_wave_forces_variables(self.settings['wave_Tp'],\n self.settings['wave_Hs'],\n self.settings['dt'],\n np.arange(self.settings['n_time_steps'] + 1)*self.settings['dt'],\n xi_matrix,\n self.floating_data['wave_forces']['xi_freq_rads'])\n\n # Log file\n if not os.path.exists(self.settings['folder']):\n os.makedirs(self.settings['folder'])\n folder = self.settings['folder'] + '/' + data.settings['SHARPy']['case'] + '/floatingforces/'\n if not os.path.exists(folder):\n os.makedirs(folder)\n self.log_filename = folder + self.settings['log_filename'] + '.h5'\n\n\n def write_output(self, ts, k, mooring, mooring_yaw, hydrostatic,\n hydrodynamic_qdot, hydrodynamic_qdotdot, hd_correct_grav, drag, waves):\n\n output = dict()\n output['ts'] = ts\n output['k'] = k\n output['q'] = self.q[ts, :]\n output['qdot'] = self.qdot[ts, :]\n output['qdotdot'] = self.qdotdot[ts, :]\n output['mooring_forces'] = mooring\n output['mooring_yaw'] = mooring_yaw\n output['hydrostatic'] = hydrostatic\n output['hydrodynamic_qdot'] = hydrodynamic_qdot\n output['hydrodynamic_qdotdot'] = hydrodynamic_qdotdot\n output['hydrodynamic_correct_grav'] = hd_correct_grav\n output['drag'] = drag\n output['waves'] = waves\n\n fid = h5.File(self.log_filename, 'a')\n group_name = \"ts%d_k%d\" % (ts, k)\n if fid.__contains__(group_name):\n del fid[group_name]\n group = fid.create_group(group_name)\n for key, value in output.items():\n group.create_dataset(key, data=value)\n fid.close()\n\n debug_output = False\n if debug_output:\n print(\"q: \", self.q[ts, :])\n print(\"qdot: \", self.qdot[ts, :])\n print(\"qdotdot: \", self.qdotdot[ts, :])\n\n print(\"mooring: \", mooring)\n print(\"mooring_yaw: \", mooring_yaw)\n print(\"hydrostatic: \", hydrostatic)\n print(\"hydrodynamic_qdot: \", hydrodynamic_qdot)\n print(\"hydrodynamic_qdotdot: \", hydrodynamic_qdotdot)\n print(\"hydrodynamic_correct_grav: \", hd_correct_grav)\n print(\"drag: \", drag)\n print(\"waves: \", waves)\n\n return\n\n\n def update_dof_vector(self, beam, struct_tstep, it, k):\n\n if True:\n cga = struct_tstep.cga()\n self.q[it, 0:3] = (np.dot(cga, struct_tstep.pos[self.buoyancy_node, :]) +\n struct_tstep.for_pos[0:3])\n self.q[it, 3:6] = algebra.quat2euler(struct_tstep.quat)\n\n self.qdot[it, 0:3] = np.dot(cga, struct_tstep.for_vel[0:3])\n self.qdot[it, 3:6] = np.dot(cga, struct_tstep.for_vel[3:6])\n\n self.qdotdot[it, 0:3] = np.dot(cga, struct_tstep.for_acc[0:3])\n self.qdotdot[it, 3:6] = np.dot(cga, struct_tstep.for_acc[3:6])\n\n else:\n self.q[it, :] = self.q[it-1, :]\n self.qdot[it, :] = self.qdot[it-1, :]\n self.qdotdot[it, :] = self.qdotdot[it-1, :]\n\n return\n\n\n def freq_wave_forces_variables(self, Tp, Hs, dt, time, xi, w_xi):\n \"\"\"\n Compute the frequency arrays needed for wave forces\n \"\"\"\n # Compute time and frequency discretisations\n ntime_steps = time.shape[0]\n\n nomega = ntime_steps//2 + 1\n w = np.zeros((nomega))\n w_temp = np.fft.fftfreq(ntime_steps, d=dt)*2.*np.pi\n w[:ntime_steps//2] = w_temp[:ntime_steps//2]\n if ntime_steps%2 == 0:\n w[-1] = -1*w_temp[ntime_steps//2]\n else:\n w[-1] = w_temp[ntime_steps//2]\n nomega_2s = ntime_steps\n\n # Compute the one-sided spectrums\n noise_freq = noise_freq_1s(w)\n jonswap_1s = jonswap_spectrum(Tp, Hs, w)*2.*np.pi\n jonswap_freq = np.sqrt(2*ntime_steps/dt*jonswap_1s/2) + 0j\n jonswap_freq[0] = np.sqrt(ntime_steps/dt*jonswap_1s[0]/2) + 0j # The DC values does not have the 2\n\n self.noise_freq = noise_freq\n self.jonswap_freq = jonswap_freq\n self.omega = w\n self.nomega_2s = nomega_2s\n\n self.xi_interp = np.zeros((nomega, 6), dtype=np.complex)\n for iomega in range(nomega):\n for idim in range(6):\n self.xi_interp[iomega, idim] = np.interp(self.omega[iomega], w_xi, xi[:, idim])\n\n\n def time_wave_forces(self, dx, grav):\n \"\"\"\n Compute the time evolution of wave forces\n \"\"\"\n\n # Compute the two-sided spectrum\n force_freq_2s = np.zeros((self.nomega_2s, 6), dtype=np.complex)\n for idim in range(6):\n for iomega in range(self.omega.shape[0]):\n k = self.omega[iomega]**2/grav\n force_freq_2s[iomega, idim] = (self.noise_freq[iomega]*\n 0.5*self.jonswap_freq[iomega]*\n self.xi_interp[iomega, idim]*\n np.exp(-1j*k*dx))\n if not iomega == 0:\n if not ((iomega == self.omega.shape[0] - 1) and (self.nomega_2s%2 == 0)):\n force_freq_2s[-iomega, idim] = (np.conj(self.noise_freq[iomega])*\n 0.5*self.jonswap_freq[iomega]*\n np.conj(self.xi_interp[iomega, idim])*\n np.exp(1j*k*dx))\n\n # Compute the inverse Fourier transform\n force_waves = ifft(force_freq_2s, axis=0)\n\n return np.real(force_waves)\n\n\n def generate(self, params):\n # Renaming for convenience\n data = params['data']\n struct_tstep = params['struct_tstep']\n aero_tstep = params['aero_tstep']\n k = params['fsi_substep']\n\n # Update dof vector\n self.update_dof_vector(data.structure, struct_tstep, data.ts, k)\n\n # Mooring lines\n mooring_forces = np.zeros((self.n_mooring_lines, 2))\n cga = struct_tstep.cga()\n ielem, inode_in_elem = data.structure.node_master_elem[self.mooring_node]\n cab = algebra.crv2rotation(struct_tstep.psi[ielem, inode_in_elem])\n cbg = np.dot(cab.T, cga.T)\n\n moor_force_out = 0.\n moor_mom_out = 0.\n\n for imoor in range(self.n_mooring_lines):\n fairlead_pos_G = (np.dot(cga, self.fairlead_pos_A[imoor, :]) +\n struct_tstep.for_pos[0:3])\n fl_to_anchor_G = self.anchor_pos[imoor, :] - fairlead_pos_G\n xf = np.sqrt(fl_to_anchor_G[1]**2 + fl_to_anchor_G[2]**2)\n zf = np.abs(fl_to_anchor_G[0])\n hf, vf = quasisteady_mooring(xf,\n zf,\n self.floating_data['mooring']['unstretched_length'],\n self.floating_data['mooring']['apparent_weight'],\n self.floating_data['mooring']['EA'],\n self.floating_data['mooring']['seabed_drag_coef'],\n hf0=self.hf_prev[imoor],\n vf0=self.vf_prev[imoor])\n mooring_forces[imoor, :] = np.array([hf, vf])\n # Save the results to initialise the computation in the next time step\n self.hf_prev[imoor] = hf + 0.\n self.vf_prev[imoor] = vf + 0.\n\n # Convert to the adequate reference system\n horizontal_unit_vec = algebra.unit_vector(fl_to_anchor_G)\n horizontal_unit_vec[0] = 0.\n horizontal_unit_vec = algebra.unit_vector(horizontal_unit_vec)\n force_fl = hf*horizontal_unit_vec + vf*np.array([-1., 0., 0.])\n\n # Move the forces to the mooring node\n force_cl = np.zeros((6,))\n force_cl[0:3] = force_fl\n mooring_node_pos_G = (np.dot(cga, struct_tstep.pos[self.mooring_node, :]) +\n struct_tstep.for_pos[0:3])\n r_fairlead_G = fairlead_pos_G - mooring_node_pos_G\n force_cl[3:6] = np.cross(r_fairlead_G, force_fl)\n\n struct_tstep.runtime_unsteady_forces[self.mooring_node, 0:3] += np.dot(cbg, force_cl[0:3])\n struct_tstep.runtime_unsteady_forces[self.mooring_node, 3:6] += np.dot(cbg, force_cl[3:6])\n\n # Yaw moment generated by the mooring system\n yaw = np.array([self.q[data.ts, 3], 0., 0.])\n mooring_yaw = -self.floating_data['mooring']['yaw_spring_stif']*yaw\n struct_tstep.runtime_unsteady_forces[self.mooring_node, 3:6] += np.dot(cbg,\n mooring_yaw)\n\n # Hydrostatic model\n ielem, inode_in_elem = data.structure.node_master_elem[self.buoyancy_node]\n cab = algebra.crv2rotation(struct_tstep.psi[ielem, inode_in_elem])\n cbg = np.dot(cab.T, cga.T)\n\n hs_f_g = - np.dot(self.buoy_rest_mat, self.q[data.ts, :])\n\n add_damp = self.floating_data['hydrodynamics']['additional_damping'].copy()\n if data.ts < self.settings['add_damp_ts']:\n add_damp += np.diag(self.settings['add_damp_diag'])\n hd_f_qdot_g = -np.dot(add_damp, self.qdot[data.ts, :])\n\n if ((self.settings['method_matrices_freq'] == 'constant') or\n (data.ts < self.settings['steps_constant_matrices'])):\n hd_f_qdot_g -= np.dot(self.hd_damping_const, self.qdot[data.ts, :])\n hd_f_qdotdot_g = -np.dot(self.hd_added_mass_const, self.qdotdot[data.ts, :])\n\n elif self.settings['method_matrices_freq'] == 'rational_function':\n # Damping\n (T, yout, xout) = forced_response(self.hd_K,\n T=[0, self.settings['dt']],\n U=self.qdot[data.ts-1:data.ts+1, :].T,\n X0=self.x0_K[data.ts-1])\n # transpose=True)\n self.x0_K[data.ts] = xout[:, 1]\n hd_f_qdot_g -= yout[:, 1]\n hd_f_qdotdot_g = np.zeros((6))\n\n else:\n cout.cout_wrap((\"ERROR: Unknown method_matrices_freq %s\" % self.settings['method_matrices_freq']), 4)\n\n # Correct gravity forces if needed\n if self.added_mass_in_mass_matrix and self.settings['gravity_on']:\n # Correct unreal gravity forces from added mass\n gravity_b = np.zeros((6,),)\n gravity_b[0:3] = np.dot(cbg, -self.settings['gravity_dir'])*self.settings['gravity']\n hd_correct_grav = -np.dot(self.hd_added_mass_const, gravity_b)\n struct_tstep.runtime_steady_forces[self.buoyancy_node, :] += hd_correct_grav\n else:\n hd_correct_grav = np.zeros((6))\n\n struct_tstep.runtime_steady_forces[self.buoyancy_node, 0:3] += np.dot(cbg, self.buoy_F0[0:3] + hs_f_g[0:3])\n struct_tstep.runtime_steady_forces[self.buoyancy_node, 3:6] += np.dot(cbg, self.buoy_F0[3:6] + hs_f_g[3:6])\n struct_tstep.runtime_unsteady_forces[self.buoyancy_node, 0:3] += np.dot(cbg, hd_f_qdot_g[0:3] + hd_f_qdotdot_g[0:3])\n struct_tstep.runtime_unsteady_forces[self.buoyancy_node, 3:6] += np.dot(cbg, hd_f_qdot_g[3:6] + hd_f_qdotdot_g[3:6])\n\n # Nonlinear drag coefficeint\n if self.settings['concentrate_spar']:\n spar_node_pos = np.zeros((100, 3)) + struct_tstep.pos[self.floating_data['hydrodynamics']['CD_node'], :]\n spar_node_pos[:, 0] += np.linspace(-self.floating_data['hydrodynamics']['CD_spar_length'], 0, 100)\n spar_node_pos_dot = np.zeros((100, 3))\n else:\n spar_node_pos = struct_tstep.pos[self.floating_data['hydrodynamics']['CD_first_node'] : self.floating_data['hydrodynamics']['CD_last_node'] + 1, :]\n spar_node_pos_dot = struct_tstep.pos_dot[self.floating_data['hydrodynamics']['CD_first_node'] : self.floating_data['hydrodynamics']['CD_last_node'] + 1, :]\n\n total_drag_force = np.zeros((6))\n for inode in range(len(spar_node_pos)):\n\n if self.settings['concentrate_spar']:\n ielem, inode_in_elem = data.structure.node_master_elem[self.floating_data['hydrodynamics']['CD_node']]\n else:\n ielem, inode_in_elem = data.structure.node_master_elem[inode + self.floating_data['hydrodynamics']['CD_first_node']]\n cab = algebra.crv2rotation(struct_tstep.psi[ielem, inode_in_elem])\n cbg = np.dot(cab.T, cga.T)\n\n if inode == 0:\n delta_x = 0.5*np.linalg.norm(spar_node_pos[1, :] - spar_node_pos[0, :])\n elif inode == len(spar_node_pos) - 1:\n delta_x = 0.5*np.linalg.norm(spar_node_pos[inode, :] - spar_node_pos[inode - 1, :])\n else:\n delta_x = 0.5*np.linalg.norm(spar_node_pos[inode + 1, :] - spar_node_pos[inode - 1, :])\n\n vel_a = (struct_tstep.for_vel[0:3] +\n np.cross(struct_tstep.for_vel[3:6], spar_node_pos[inode, :]) +\n spar_node_pos_dot[inode, :])\n\n # Remove velocity along the x axis\n vel_b = np.dot(cab.T, vel_a)\n vel_b[0] = 0.\n vel_g = np.dot(cbg.T, vel_b)\n\n drag_force = (-0.5*self.water_density*np.linalg.norm(vel_g)*vel_g*delta_x*\n self.floating_data['hydrodynamics']['spar_diameter']*\n self.cd)\n\n if self.settings['concentrate_spar']:\n r = spar_node_pos[inode, :] - struct_tstep.pos[self.floating_data['hydrodynamics']['CD_node'], :]\n else:\n r = spar_node_pos[inode, :] - struct_tstep.pos[self.floating_data['hydrostatics']['node'], :]\n drag_moment = np.cross(r, drag_force)\n total_drag_force[0:3] += drag_force\n total_drag_force[3:6] += drag_moment\n if self.settings['concentrate_spar']:\n struct_tstep.runtime_unsteady_forces[self.floating_data['hydrodynamics']['CD_node'], 0:3] += np.dot(cbg, drag_force)\n struct_tstep.runtime_unsteady_forces[self.floating_data['hydrodynamics']['CD_node'], 3:6] += np.dot(cbg, drag_moment)\n else:\n struct_tstep.runtime_unsteady_forces[inode + self.floating_data['hydrodynamics']['CD_first_node'], 0:3] += np.dot(cbg, drag_force)\n\n # Wave loading\n ielem, inode_in_elem = data.structure.node_master_elem[self.wave_forces_node]\n cab = algebra.crv2rotation(struct_tstep.psi[ielem, inode_in_elem])\n cbg = np.dot(cab.T, cga.T)\n\n wave_node_pos = struct_tstep.for_pos[0:3] + np.dot(cga, struct_tstep.pos[self.wave_forces_node, :])\n dx = (wave_node_pos[1]*np.sin(self.settings['wave_incidence']) +\n wave_node_pos[2]*np.cos(self.settings['wave_incidence']))\n wave_forces_g = np.zeros((6))\n if self.settings['method_wave'] == 'sin':\n phase = (self.settings['wave_freq']*data.ts*self.settings['dt'] +\n dx*self.settings['wave_freq']**2/self.settings['gravity'])\n for idim in range(6):\n wave_forces_g[idim] = np.real(self.settings['wave_amplitude']*self.xi_interp[idim]*(np.cos(phase) + 1j*np.sin(phase)))\n elif self.settings['method_wave'] == 'jonswap':\n wave_forces_g = self.time_wave_forces(dx, self.settings['gravity'])[data.ts, :]\n\n struct_tstep.runtime_unsteady_forces[self.wave_forces_node, 0:3] += np.dot(cbg, wave_forces_g[0:3])\n struct_tstep.runtime_unsteady_forces[self.wave_forces_node, 3:6] += np.dot(cbg, wave_forces_g[3:6])\n\n # Write output\n if self.settings['write_output']:\n self.write_output(data.ts, k, mooring_forces, mooring_yaw, hs_f_g,\n hd_f_qdot_g, hd_f_qdotdot_g, hd_correct_grav, total_drag_force, wave_forces_g)\n" }, { "path": "sharpy/generators/gridbox.py", "content": "import numpy as np\n\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.settings as settings\nimport numpy as np\nimport ctypes as ct\nimport copy\n\n\n@generator_interface.generator\nclass GridBox(generator_interface.BaseGenerator):\n \"\"\"\n GridBox\n\n Generatex a grid within a box to be used to generate the flow field during the postprocessing\n\n \"\"\"\n generator_id = 'GridBox'\n generator_classification = 'utils'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['coords_0'] = 'list(float)'\n settings_default['coords_0'] = [0., 0., 0.]\n settings_description['coords_0'] = 'First bounding box corner'\n\n settings_types['coords_1'] = 'list(float)'\n settings_default['coords_1'] = [10., 0., 10.]\n settings_description['coords_1'] = 'Second bounding box corner'\n\n settings_types['spacing'] = 'list(float)'\n settings_default['spacing'] = [1., 1., 1.]\n settings_description['spacing'] = 'Spacing parameters of the bbox'\n\n settings_types['moving'] = 'bool'\n settings_default['moving'] = False\n settings_description['moving'] = 'If ``True``, the box moves with the body frame of reference. It does not rotate with it, though'\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.in_dict = dict()\n self.settings = None\n\n def initialise(self, in_dict, restart=False):\n self.in_dict = in_dict\n settings.to_custom_types(self.in_dict, self.settings_types, self.settings_default)\n self.settings = copy.deepcopy(self.in_dict)\n\n self.x0 = self.in_dict['coords_0'][0]\n self.y0 = self.in_dict['coords_0'][1]\n self.z0 = self.in_dict['coords_0'][2]\n self.x1 = self.in_dict['coords_1'][0]\n self.y1 = self.in_dict['coords_1'][1]\n self.z1 = self.in_dict['coords_1'][2]\n self.dx = self.in_dict['spacing'][0]\n self.dy = self.in_dict['spacing'][1]\n self.dz = self.in_dict['spacing'][2]\n\n def generate(self, params):\n if self.settings['moving']:\n for_pos = params['for_pos']\n else:\n for_pos = np.zeros((3,))\n nx = np.abs(int((self.x1-self.x0)/self.dx + 1))\n ny = np.abs(int((self.y1-self.y0)/self.dy + 1))\n nz = np.abs(int((self.z1-self.z0)/self.dz + 1))\n\n xarray = np.linspace(self.x0, self.x1, nx) + for_pos[0]\n yarray = np.linspace(self.y0, self.y1, ny) + for_pos[1]\n zarray = np.linspace(self.z0, self.z1, nz) + for_pos[2]\n grid = []\n for iz in range(nz):\n grid.append(np.zeros((3, nx, ny), dtype=ct.c_double))\n for ix in range(nx):\n for iy in range(ny):\n grid[iz][0, ix, iy] = xarray[ix]\n grid[iz][1, ix, iy] = yarray[iy]\n grid[iz][2, ix, iy] = zarray[iz]\n\n from tvtk.api import tvtk\n vtk_info = tvtk.RectilinearGrid()\n vtk_info.dimensions = np.array([nx, ny, nz], dtype=int)\n vtk_info.x_coordinates = xarray\n vtk_info.y_coordinates = yarray\n vtk_info.z_coordinates = zarray\n\n return vtk_info, grid\n" }, { "path": "sharpy/generators/gustvelocityfield.py", "content": "\"\"\"Gust Velocity Field Generators\n\nThese generators are used to create a gust velocity field. :class:`.GustVelocityField` is the main class that should be\nparsed as the ``velocity_field_input`` to the desired aerodynamic solver.\n\nThe remaining classes are the specific gust profiles and parsed as ``gust_shape``.\n\nExamples:\n The typical input to the aerodynamic solver settings would therefore read similar to:\n\n >>> aero_settings = {'': '',\n >>> 'velocity_field_generator': 'GustVelocityField',\n >>> 'velocity_field_input': {'u_inf': 1,\n >>> 'gust_shape': '',\n >>> 'gust_parameters': ''}}\n\n\"\"\"\nimport numpy as np\nfrom abc import ABCMeta\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.settings as settings\nfrom scipy.interpolate import interp1d\n\ndict_of_gusts = {}\n\ndoc_settings_description = 'The ``GustVelocityField`` generator takes the following settings as a dictionary assigned' \\\n 'to ``gust_parameters``.'\n\n\ndef gust(arg):\n global dict_of_gusts\n try:\n arg.gust_id\n except AttributeError:\n raise AttributeError('Class defined as gust has no gust_id attribute')\n dict_of_gusts[arg.gust_id] = arg\n return arg\n\n\n# @gust\nclass BaseGust(metaclass=ABCMeta):\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n def __init__(self):\n self.settings = dict()\n self._u_inf = None\n self._u_inf_direction = None\n\n @property\n def u_inf(self):\n return self._u_inf\n\n @u_inf.setter\n def u_inf(self, value):\n self._u_inf = value\n\n @property\n def u_inf_direction(self):\n return self._u_inf_direction\n\n @u_inf_direction.setter\n def u_inf_direction(self, value):\n self._u_inf_direction = value\n\n\n@gust\nclass one_minus_cos(BaseGust):\n r\"\"\"\n One minus cos gust (single bump)\n\n .. math:: U_z = \\frac{u_{de}}{2}\\left[1-\\cos\\left(\\frac{2\\pi x}{S}\\right)\\right]\n\n This gust can be used by using the setting ``gust_shape = '1-cos'`` in :class:`.GustVelocityField`.\n \"\"\"\n gust_id = '1-cos'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['gust_length'] = 'float'\n settings_default['gust_length'] = 0.0\n settings_description['gust_length'] = 'Length of gust, :math:`S`.'\n\n settings_types['gust_intensity'] = 'float'\n settings_default['gust_intensity'] = 0.0\n settings_description['gust_intensity'] = 'Intensity of the gust :math:`u_{de}`.'\n\n settings_types['gust_component'] = 'int'\n settings_default['gust_component'] = 2\n settings_description['gust_component'] = 'Component of the gust velocity in the G-frame (x,y,z)->(0,1,2).'\n\n setting_table = settings.SettingsTable()\n __doc__ += setting_table.generate(settings_types, settings_default, settings_description,\n header_line=doc_settings_description)\n\n def initialise(self, in_dict, restart=False):\n self.settings = in_dict\n settings.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n def gust_shape(self, x, y, z, time=0):\n gust_length = self.settings['gust_length']\n gust_intensity = self.settings['gust_intensity']\n\n vel = np.zeros((3,))\n if x > 0.0 or x < -gust_length:\n return vel\n\n vel[self.settings['gust_component']] = (1.0 - np.cos(2.0 * np.pi * x / gust_length)) * gust_intensity * 0.5\n return vel\n\n\n@gust\nclass DARPA(BaseGust):\n r\"\"\"\n Discrete, non-uniform span model\n\n .. math:: U_z = \\frac{u_{de}}{2}\\left[1-\\cos\\left(\\frac{2\\pi x}{S}\\right)\\right]\\cos\\left(\\frac{\\pi y}{b}\\right)\n\n This gust can be used by using the setting ``gust_shape = 'DARPA'`` in :class:`.GustVelocityField`.\n \"\"\"\n gust_id = 'DARPA'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['gust_length'] = 'float'\n settings_default['gust_length'] = 0.0\n settings_description['gust_length'] = 'Length of gust'\n\n settings_types['gust_intensity'] = 'float'\n settings_default['gust_intensity'] = 0.0\n settings_description['gust_intensity'] = 'Intensity of the gust'\n\n settings_types['span'] = 'float'\n settings_default['span'] = 0.\n settings_description['span'] = 'Wing span'\n\n settings_types['gust_component'] = 'int'\n settings_default['gust_component'] = 2\n settings_description['gust_component'] = 'Component of the gust velocity in the G-frame (x,y,z)->(0,1,2).'\n\n setting_table = settings.SettingsTable()\n __doc__ += setting_table.generate(settings_types, settings_default, settings_description,\n header_line=doc_settings_description)\n\n def initialise(self, in_dict, restart=False):\n self.settings = in_dict\n settings.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n def gust_shape(self, x, y, z, time=0):\n gust_length = self.settings['gust_length']\n gust_intensity = self.settings['gust_intensity']\n span = self.settings['span']\n\n vel = np.zeros((3,))\n if x > 0.0 or x < -gust_length:\n return vel\n\n vel[self.settings['gust_component']] = (1.0 - np.cos(2.0 * np.pi * x / gust_length)) * gust_intensity * 0.5\n vel[self.settings['gust_component']] *= -np.cos(y / span * np.pi)\n return vel\n\n\n@gust\nclass continuous_sin(BaseGust):\n r\"\"\"\n Continuous sinusoidal gust model\n\n .. math:: U_z = \\frac{u_{de}}{2}\\sin\\left(\\frac{2\\pi x}{S}\\right)\n\n This gust can be used by using the setting ``gust_shape = 'continuous_sin'`` in :class:`GustVelocityField`.\n \"\"\"\n gust_id = 'continuous_sin'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['gust_length'] = 'float'\n settings_default['gust_length'] = 0.0\n settings_description['gust_length'] = 'Length of gust'\n\n settings_types['gust_intensity'] = 'float'\n settings_default['gust_intensity'] = 0.0\n settings_description['gust_intensity'] = 'Intensity of the gust'\n\n settings_types['gust_component'] = 'int'\n settings_default['gust_component'] = 2\n settings_description['gust_component'] = 'Component of the gust velocity in the G-frame (x,y,z)->(0,1,2).'\n\n setting_table = settings.SettingsTable()\n __doc__ += setting_table.generate(settings_types, settings_default, settings_description,\n header_line=doc_settings_description)\n\n def initialise(self, in_dict, restart=False):\n self.settings = in_dict\n settings.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n def gust_shape(self, x, y, z, time=0):\n gust_length = self.settings['gust_length']\n gust_intensity = self.settings['gust_intensity']\n\n vel = np.zeros((3,))\n if x > 0.0:\n return vel\n\n vel[self.settings['gust_component']] = 0.5 * gust_intensity * np.sin(2 * np.pi * x / gust_length)\n return vel\n\n\n@gust\nclass time_varying_global(BaseGust):\n r\"\"\"\n Similar to the previous one but the velocity changes instanteneously in the whole flow field. It is not fed\n into the solid.\n\n This gust can be used by using the setting ``gust_shape = 'time varying global'`` in :class:`GustVelocityField`.\n \"\"\"\n gust_id = 'time varying global'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['file'] = 'str'\n settings_default['file'] = ''\n settings_description['file'] = 'File with the information (only for time varying)'\n\n settings_types['gust_component'] = ['list(int)', 'int']\n settings_default['gust_component'] = [0, 1, 2]\n settings_description['gust_component'] = 'Component of the gust velocity in the G-frame to be considered (x,y,z)->(0,1,2).'\n\n setting_table = settings.SettingsTable()\n __doc__ += setting_table.generate(settings_types, settings_default, settings_description,\n header_line=doc_settings_description)\n\n def __init__(self):\n super().__init__()\n self.file_info = None\n self.list_interpolated_velocity_field_functions = []\n\n def initialise(self, in_dict, restart=False):\n self.settings = in_dict\n settings.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n self.file_info = np.loadtxt(self.settings['file'])\n self.initialise_interpolation_functions()\n \n def initialise_interpolation_functions(self):\n for idim in self.settings['gust_component']:\n self.list_interpolated_velocity_field_functions.append(interp1d(self.file_info[:, 0], self.file_info[:, idim+1], \n bounds_error=False,fill_value=\"extrapolate\"))\n\n def gust_shape(self, x, y, z, time=0):\n vel = np.zeros((3,))\n for counter, idim in enumerate(self.settings['gust_component']):\n vel[idim] = self.list_interpolated_velocity_field_functions[counter](time)\n return vel\n\n\n@gust\nclass time_varying(time_varying_global):\n r\"\"\"\n The inflow velocity changes with time but it is uniform in space. It is read from a 4 column file:\n\n .. math:: time[s] \\Delta U_x \\Delta U_y \\Delta U_z\n\n This gust can be used by using the setting ``gust_shape = 'time varying'`` in :class:.`GustVelocityField`.\n \"\"\"\n gust_id = 'time varying'\n \n def initialise_interpolation_functions(self):\n for idim in self.settings['gust_component']:\n self.list_interpolated_velocity_field_functions.append(interp1d(-self.file_info[::-1, 0] * self.u_inf, self.file_info[::-1, idim+1], \n bounds_error=False,fill_value=\"extrapolate\"))\n\n def gust_shape(self, x, y, z, time=0):\n vel = np.zeros((3,))\n d = np.dot(np.array([x, y, z]), self.u_inf_direction)\n if d <= 0.0: \n for counter, idim in enumerate(self.settings['gust_component']):\n vel[idim] = self.list_interpolated_velocity_field_functions[counter](d)\n return vel\n \n@gust\nclass span_sine(BaseGust):\n r\"\"\"\n This gust can be used by using the setting ``gust_shape = 'span sine'`` in :class:`GustVelocityField`.\n \"\"\"\n gust_id = 'span sine'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['gust_intensity'] = 'float'\n settings_default['gust_intensity'] = 0.0\n settings_description['gust_intensity'] = 'Intensity of the gust'\n\n settings_types['span'] = 'float'\n settings_default['span'] = 0.\n settings_description['span'] = 'Wing span'\n\n settings_types['periods_per_span'] = 'int'\n settings_default['periods_per_span'] = 1\n settings_description['periods_per_span'] = 'Number of times that the sine is repeated in the span of the wing'\n\n settings_types['perturbation_dir'] = 'list(float)'\n settings_default['perturbation_dir'] = np.array([0, 0, 1.])\n settings_description['perturbation_dir'] = 'Direction in which the perturbation will be applied in A FoR'\n\n settings_types['span_dir'] = 'list(float)'\n settings_default['span_dir'] = np.array([0, 1., 0])\n settings_description['span_dir'] = 'Direction of the span of the wing'\n\n settings_types['span_with_gust'] = 'float'\n settings_default['span_with_gust'] = 0.\n settings_description['span_with_gust'] = 'Extension of the span to which the gust will be applied'\n\n setting_table = settings.SettingsTable()\n __doc__ += setting_table.generate(settings_types, settings_default, settings_description,\n header_line=doc_settings_description)\n\n def initialise(self, in_dict, restart=False):\n self.settings = in_dict\n settings.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n if self.settings['span_with_gust'] == 0:\n self.settings['span_with_gust'] = self.settings['span']\n\n def gust_shape(self, x, y, z, time=0):\n d = np.dot(np.array([x, y, z]), self.settings['span_dir'])\n if np.abs(d) <= self.settings['span_with_gust'] / 2:\n vel = 0.5 * self.settings['gust_intensity'] * np.sin(\n d * 2. * np.pi / (self.settings['span'] / self.settings['periods_per_span']))\n else:\n vel = np.zeros((3,))\n\n return vel * self.settings['perturbation_dir']\n\n\n@generator_interface.generator\nclass GustVelocityField(generator_interface.BaseGenerator):\n r\"\"\"\n Gust Velocity Field Generator\n\n ``GustVelocityField`` is a class inherited from ``BaseGenerator``\n\n The ``GustVelocityField`` class generates a gust profile velocity field, and the profile has the characteristics\n specified by the user.\n\n To call this generator, the ``generator_id = GustVelocityField`` shall be used.\n This is parsed as the value for the ``velocity_field_generator`` key in the desired aerodynamic solver's settings.\n\n Notation: :math:`u_{de}` is the gust intensity, :math:`S` is the gust length and :math:`b` is the wing span.\n :math:`x` and :math:`y` refer to the chordwise and spanwise distance penetrated into the gust, respectively.\n\n Several gust profiles are available. Your chosen gust profile should be parsed to ``gust_shape`` and the\n corresponding settings as a dictionary to ``gust_parameters``.\n\n \"\"\"\n generator_id = 'GustVelocityField'\n generator_classification = 'velocity-field'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['u_inf'] = 'float'\n settings_default['u_inf'] = None\n settings_description['u_inf'] = 'Free stream velocity'\n\n settings_types['u_inf_direction'] = 'list(float)'\n settings_default['u_inf_direction'] = [1., 0., 0.]\n settings_description['u_inf_direction'] = 'Free stream velocity relative component'\n\n settings_types['offset'] = 'float'\n settings_default['offset'] = 0.0\n settings_description['offset'] = 'Spatial offset of the gust with respect to origin'\n\n settings_types['relative_motion'] = 'bool'\n settings_default['relative_motion'] = False\n settings_description['relative_motion'] = 'If true, the gust is convected with u_inf'\n\n settings_types['gust_shape'] = 'str'\n settings_default['gust_shape'] = None\n settings_description['gust_shape'] = 'Gust profile shape'\n\n settings_types['gust_parameters'] = 'dict'\n settings_default['gust_parameters'] = dict()\n settings_description['gust_parameters'] = 'Dictionary of parameters specific of the gust_shape selected'\n\n setting_table = settings.SettingsTable()\n __doc__ += setting_table.generate(settings_types, settings_default, settings_description,\n header_line='This generator takes the following settings')\n\n def __init__(self):\n\n self.settings = dict()\n self.gust = None\n self.u_inf = None\n self.u_inf_direction = None\n\n self.implemented_gusts = dict_of_gusts\n\n def initialise(self, in_dict, restart=False):\n self.settings = in_dict\n settings.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n # check that the gust type is valid\n if not (self.settings['gust_shape'] in self.implemented_gusts):\n raise AttributeError('The gust shape ' + self.settings['gust_shape'] + ' is not implemented')\n\n self.gust = dict_of_gusts[self.settings['gust_shape']]()\n\n self.u_inf = self.settings['u_inf']\n self.u_inf_direction = self.settings['u_inf_direction']\n\n # set gust properties\n self.gust.u_inf = self.u_inf\n self.gust.u_inf_direction = self.u_inf_direction\n\n self.gust.initialise(self.settings['gust_parameters'], restart=restart)\n\n def generate(self, params, uext):\n zeta = params['zeta']\n override = params['override']\n if self.settings['gust_shape'] == 'span sine':\n ts = 0\n t = 0\n dt = 0\n else:\n ts = params['ts']\n t = params['t']\n dt = params['dt']\n\n for_pos = params['for_pos'][0:3]\n\n for i_surf in range(len(zeta)):\n if override:\n uext[i_surf].fill(0.0)\n\n for i in range(zeta[i_surf].shape[1]):\n for j in range(zeta[i_surf].shape[2]):\n total_offset_val = self.settings['offset']\n if self.settings['relative_motion']:\n uext[i_surf][:, i, j] += self.settings['u_inf'] * self.settings['u_inf_direction']\n total_offset_val -= self.settings['u_inf'] * t\n\n total_offset = total_offset_val * self.settings['u_inf_direction'] + for_pos\n uext[i_surf][:, i, j] += self.gust.gust_shape(\n zeta[i_surf][0, i, j] + total_offset[0],\n zeta[i_surf][1, i, j] + total_offset[1],\n zeta[i_surf][2, i, j] + total_offset[2],\n t\n )\n" }, { "path": "sharpy/generators/helicoidalwake.py", "content": "import numpy as np\n\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.settings as settings\nimport sharpy.utils.algebra as algebra\n\n\n@generator_interface.generator\nclass HelicoidalWake(generator_interface.BaseGenerator):\n r\"\"\"\n Helicoidal wake shape generator\n\n ``HelicoidalWake`` class inherited from ``BaseGenerator``\n\n The object creates a helicoidal wake shedding from the trailing edge based on\n the time step ``dt``, the incoming velocity magnitude ``u_inf``,\n direction ``u_inf_direction``, the rotation velocity ``rotation_velocity`` and\n the shear parameters\n \"\"\"\n generator_id = 'HelicoidalWake'\n generator_classification = 'wake'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['u_inf'] = 'float'\n settings_default['u_inf'] = None\n settings_description['u_inf'] = 'Free stream velocity magnitude'\n\n settings_types['u_inf_direction'] = 'list(float)'\n settings_default['u_inf_direction'] = None\n settings_description['u_inf_direction'] = '``x``, ``y`` and ``z`` relative components of the free stream velocity'\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = None\n settings_description['dt'] = 'Time step'\n\n settings_types['dphi1'] = 'float'\n settings_default['dphi1'] = -1.0\n settings_description['dphi1'] = 'Size of the first wake panel in radians'\n\n settings_types['ndphi1'] = 'int'\n settings_default['ndphi1'] = 1\n settings_description['ndphi1'] = 'Number of panels with size ``dphi1``'\n\n settings_types['r'] = 'float'\n settings_default['r'] = 1.\n settings_description['r'] = 'Growth rate after ``ndphi1`` panels'\n\n settings_types['dphimax'] = 'float'\n settings_default['dphimax'] = -1.0\n settings_description['dphimax'] = 'Maximum panel size in radians'\n\n # Shear parameters\n settings_types['shear_direction'] = 'list(float)'\n settings_default['shear_direction'] = np.array([1.0, 0, 0])\n settings_description['shear_direction'] = '``x``, ``y`` and ``z`` relative components of the direction along which shear applies'\n\n settings_types['shear_exp'] = 'float'\n settings_default['shear_exp'] = 0.\n settings_description['shear_exp'] = 'Exponent of the shear law'\n\n settings_types['h_ref'] = 'float'\n settings_default['h_ref'] = 1.\n settings_description['h_ref'] = 'Reference height at which ``u_inf`` is defined'\n\n settings_types['h_corr'] = 'float'\n settings_default['h_corr'] = 1.\n settings_description['h_corr'] = 'Height to correct the shear law'\n\n # Rotation\n settings_types['rotation_velocity'] = 'list(float)'\n settings_default['rotation_velocity'] = None\n settings_description['rotation_velocity'] = 'Rotation velocity'\n\n setting_table = settings.SettingsTable()\n __doc__ += setting_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.in_dict = dict()\n\n self.u_inf = 0.\n self.u_inf_direction = None\n self.rotation_velocity = None\n self.dt = None\n\n self.dphi1 = None\n self.ndphi1 = None\n self.r = None\n self.dphimax = None\n\n self.shear_direction = None\n self.shear_exp = None\n self.h_ref = None\n self.h_corr = None\n\n def initialise(self, data, in_dict, restart=False):\n self.in_dict = in_dict\n settings.to_custom_types(self.in_dict, self.settings_types, self.settings_default, no_ctype=True)\n\n self.u_inf = self.in_dict['u_inf']\n self.u_inf_direction = self.in_dict['u_inf_direction']\n self.rotation_velocity = self.in_dict['rotation_velocity']\n self.dt = self.in_dict['dt']\n\n if self.in_dict['dphi1'] == -1:\n self.dphi1 = np.linalg.norm(self.rotation_velocity)*self.dt\n else:\n self.dphi1 = self.in_dict['dphi1']\n\n self.ndphi1 = self.in_dict['ndphi1']\n self.r = self.in_dict['r']\n\n if self.in_dict['dphimax'] == -1:\n self.dphimax = self.dphi1\n else:\n self.dphimax = self.in_dict['dphimax']\n\n self.shear_direction = self.in_dict['shear_direction']\n self.shear_exp = self.in_dict['shear_exp']\n self.h_ref = self.in_dict['h_ref']\n self.h_corr = self.in_dict['h_corr']\n\n\n def generate(self, params):\n # Renaming for convenience\n zeta = params['zeta']\n zeta_star = params['zeta_star']\n gamma = params['gamma']\n gamma_star = params['gamma_star']\n dist_to_orig = params['dist_to_orig']\n\n nsurf = len(zeta)\n for isurf in range(nsurf):\n M, N = zeta_star[isurf][0, :, :].shape\n angle = 0.\n for i in range(M):\n # Compute the step in azimuthal angle\n angle -= self.get_dphi(i, self.dphi1, self.ndphi1, self.r, self.dphimax)\n\n delta_t = -angle/np.linalg.norm(self.rotation_velocity)\n rot = algebra.rotation_matrix_around_axis(algebra.unit_vector(self.rotation_velocity), angle)\n for j in range(N):\n # Define the helicoidal\n aux_zeta_TE = zeta[isurf][:, -1, j] - (self.h_ref - self.h_corr)*self.shear_direction\n aux_zeta_TE = np.dot(rot, aux_zeta_TE) + (self.h_ref - self.h_corr)*self.shear_direction\n\n # Translate according to u_inf depending on the height\n h = np.dot(aux_zeta_TE, self.shear_direction) + self.h_corr\n zeta_star[isurf][:, i, j] = aux_zeta_TE + self.u_inf*self.u_inf_direction*(h/self.h_ref)**self.shear_exp*delta_t\n # zeta_star[isurf][:, i, j] = zeta[isurf][:, -1, j] + self.u_inf*self.u_inf_direction*self.dt*i\n # print(zeta_star[isurf][:, i, j])\n\n gamma[isurf] *= 0.\n gamma_star[isurf] *= 0.\n\n for isurf in range(nsurf):\n M, N = zeta_star[isurf][0, :, :].shape\n dist_to_orig[isurf][0, :] = 0.\n for j in range(0, N):\n for i in range(1, M):\n dist_to_orig[isurf][i, j] = (dist_to_orig[isurf][i - 1, j] +\n np.linalg.norm(zeta_star[isurf][:, i, j] -\n zeta_star[isurf][:, i - 1, j]))\n dist_to_orig[isurf][:, j] /= dist_to_orig[isurf][-1, j]\n\n @staticmethod\n def get_dphi(i, dphi1, ndphi1, r, dphimax):\n if i == 0:\n dphi = 0.\n elif i <= ndphi1:\n dphi = dphi1\n else:\n dphi = dphi1*r**(i - ndphi1)\n dphi = min(dphi, dphimax)\n\n return dphi\n" }, { "path": "sharpy/generators/modifystructure.py", "content": "import numpy as np\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.settings as settings\n\n\n@generator_interface.generator\nclass ModifyStructure(generator_interface.BaseGenerator):\n \"\"\"\n ``ModifyStructure`` generator.\n\n This generator allows the user to modify structural parameters at runtime. At the moment, changes to lumped\n masses are supported. For each lumped mass you want to change, set ``change_variable`` to ``lumped_mass``, and the\n ``variable_index`` and ``file_list`` as specified in :class:`~sharpy.generators.modifystructure.ChangeLumpedMass`.\n\n This generator is called at the start of each time step in ``DynamicCoupled``.\n \"\"\"\n generator_id = 'ModifyStructure'\n generator_classification = 'runtime'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['change_variable'] = 'list(str)'\n settings_default['change_variable'] = None\n settings_description['change_variable'] = 'Structural variable to modify'\n settings_options['change_variable'] = ['lumped_mass']\n\n settings_types['variable_index'] = 'list(int)'\n settings_default['variable_index'] = None\n settings_description['variable_index'] = 'List of indices of variables to change. ' \\\n 'For instance the 1st lumped mass would be ``[0]``'\n\n settings_types['file_list'] = 'list(str)'\n settings_default['file_list'] = None\n settings_description['file_list'] = 'File path for each variable containing the changing info, in the ' \\\n 'appropriate format. See each of the allowed variables for the correct format.'\n\n def __init__(self):\n self.settings = None\n\n self.num_changes = None # :int number of variables that are changed\n self.variables = [] # :list of changed variables objects\n self.control_objects = {} #: dictionary of changed variable name and its control object as value\n\n def initialise(self, in_dict, **kwargs):\n structure = kwargs['data'].structure\n self.settings = in_dict\n settings.to_custom_types(self.settings, self.settings_types, self.settings_default, no_ctype=True,\n options=self.settings_options)\n\n self.num_changes = len(self.settings['change_variable'])\n\n if 'lumped_mass' in self.settings['change_variable']:\n self.control_objects['lumped_mass'] = LumpedMassControl()\n\n lumped_mass_variables = []\n for i in range(self.num_changes):\n var_type = self.settings['change_variable'][i]\n if var_type == 'lumped_mass':\n variable = ChangeLumpedMass(var_index=self.settings['variable_index'][i],\n file=self.settings['file_list'][i])\n variable.initialise(structure)\n\n self.variables.append(variable)\n lumped_mass_variables.append(i)\n self.control_objects['lumped_mass'].append(i)\n else:\n raise NotImplementedError('Variable {:s} not yet coded to be modified in runtime'.format(var_type))\n try:\n self.control_objects['lumped_mass'].set_unchanged_vars_to_zero(structure)\n except KeyError:\n pass\n\n def generate(self, params):\n data = params['data']\n ts = data.ts\n structure = data.structure\n\n for variable in self.variables:\n variable(structure, ts)\n\n # should only be called once per time step\n try:\n self.control_objects['lumped_mass'].execute_change(structure)\n except KeyError:\n pass\n\n # for future variables supported, have the control objects have the same signatures such that they may be\n # called in a loop\n\n\nclass ChangedVariable:\n \"\"\"\n Base class of a changed variable\n\n Attributes:\n name (str): Name of the changed variable\n variable_index (int): Index of the variable to change\n file (str): Name of the file containing the input data (.txt)\n original (np.ndarray): Original value of the desired value in the appropriate format\n current_value (np.ndarray): Running track of the current value of the desired variable\n \"\"\"\n def __init__(self, name, var_index, file):\n self.name = name\n self.variable_index = var_index\n self.file = file\n\n self.original = None\n self.target_value = None\n self.current_value = None # initially\n\n def initialise(self, structure):\n\n self.get_original(structure)\n self.load_file()\n\n self.current_value = self.original # initially\n\n def __call__(self, structure, ts):\n pass\n\n def get_original(self, structure):\n # should be overridden for the desired variable class. it should set self.original in the appropriate format\n pass\n\n def load_file(self):\n self.target_value = np.loadtxt(self.file)\n\n\nclass ChangeLumpedMass(ChangedVariable):\n \"\"\"\n Lumped Mass to be modified\n\n The arguments are parsed as items of the list in the settings for ``variable_index`` and ``file_list``. For\n those variables marked where ``change_variables = 'lumped_mass'``.\n\n The file should contain a time varying series with the following 10 columns:\n\n * Lumped mass\n\n * Lumped mass position in the material frame ``B`` (3 columns for ``xb``, ``yb`` and ``zb``)\n\n * Lumped mass inertia in the material frame ``B`` (6 columns for ``ixx``, ``iyy``, ``izz``, ``ixy``, ``ixz`` and\n ``iyz``.\n\n Not all 10 columns are necessary in the input file, missing columns are ignored and left unchanged. There should be\n one row per time step. If there are not enough entries for the number of time steps in the simulation, the changed\n variable value remains unchanged after all rows have been processed.\n\n Args:\n var_index (int): Index of lumped mass. NOT the lumped mass node.\n file (str): Path to file containing time history of the lumped mass.\n \"\"\"\n def __init__(self, var_index, file):\n super().__init__('lumped_mass', var_index=var_index, file=file)\n\n def __call__(self, structure, ts):\n try:\n # lumped masses get added (+=) at structure.lump_masses(), therefore the increment with respect to the\n # previous time step must be provided. This is such that this generator is backwards compatible with the\n # way lumped masses are assembled.\n delta = self.target_value[ts] - self.current_value\n except IndexError: # input file has less entries than the simulation time steps\n structure.lumped_mass[self.variable_index] = 0\n structure.lumped_mass_position[self.variable_index, :] = np.zeros(3)\n structure.lumped_mass_inertia[self.variable_index, :, :] = np.zeros((3, 3))\n\n else:\n structure.lumped_mass[self.variable_index] = delta[0]\n structure.lumped_mass_position[self.variable_index, :] = delta[1:4]\n ixx, iyy, izz, ixy, ixz, iyz = delta[-6:]\n inertia = np.block([[ixx, ixy, ixz], [ixy, iyy, iyz], [ixz, iyz, izz]])\n structure.lumped_mass_inertia[self.variable_index, :, :] = inertia\n\n self.current_value += delta\n\n def load_file(self):\n \"\"\"Sets ``self.target_value`` by reading from the file.\n\n If the input does not have as many columns as needed (10), these get padded with the original value such that\n they are not changed at runtime.\n\n \"\"\"\n\n super().load_file()\n\n n_values = len(self.original)\n\n try:\n n_target_values = self.target_value.shape[1] # number of columns\n except IndexError:\n n_target_values = 1\n\n if n_target_values != n_values:\n # if not enough column entries pad with original values\n self.target_value = np.column_stack((self.target_value,\n self.original[-(n_values - n_target_values):]\n * np.ones((self.target_value.shape[0], n_values - n_target_values)\n )\n ))\n\n def get_original(self, structure):\n m = structure.lumped_mass[self.variable_index]\n pos = structure.lumped_mass_position[self.variable_index, :]\n inertia = structure.lumped_mass_inertia[self.variable_index, :, :]\n\n self.original = np.hstack((m, pos, np.diag(inertia), inertia[0, 1], inertia[0, 2], inertia[1, 2]))\n\n\nclass LumpedMassControl:\n \"\"\"Lumped Mass Control Class\n\n This class is instantiated when at least one lumped mass is modified.\n\n It allows control over unchanged lumped masses and calls the method to execute the change.\n\n Attributes:\n lumped_mass_variables (list): List of integers containing the indices of the variables to change. These indices\n refer to the order in which they are provided in the general settings for the generator.\n \"\"\"\n def __init__(self):\n self.lumped_mass_variables = []\n\n def set_unchanged_vars_to_zero(self, structure):\n \"\"\"\n Sets the lumped masses variables of unchanged lumped masses to zero.\n\n This is to avoid the lumped mass changing during execution\n\n Args:\n structure (sharpy.structure.models.beam.Beam): SHARPy structure object\n\n \"\"\"\n for i_lumped_mass in range(len(structure.lumped_mass)):\n if i_lumped_mass not in self.lumped_mass_variables:\n structure.lumped_mass[i_lumped_mass] *= 0\n structure.lumped_mass_position[i_lumped_mass] *= 0\n structure.lumped_mass_inertia[i_lumped_mass] *= 0\n\n @staticmethod\n def execute_change(structure):\n \"\"\"Executes the change in the lumped masses.\n\n Called only once per time step when all the changed lumped mass variables have been processed.\n \"\"\"\n # called once all variables changed\n structure.lump_masses()\n structure.generate_fortran()\n\n def append(self, i):\n self.lumped_mass_variables.append(i)\n" }, { "path": "sharpy/generators/polaraeroforces.py", "content": "import numpy as np\nimport os\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.settings as settings\nimport sharpy.utils.algebra as algebra\nfrom sharpy.aero.utils.utils import magnitude_and_direction_of_relative_velocity, local_stability_axes, span_chord\nfrom sharpy.utils.generate_cases import get_aoacl0_from_camber\n\n\n@generator_interface.generator\nclass PolarCorrection(generator_interface.BaseGenerator):\n r\"\"\"\n This generator corrects the aerodynamic forces from UVLM based on the airfoil polars provided by the user in the\n ``aero.h5`` file. Polars are entered for each airfoil, in a table comprising ``AoA (rad), CL, CD, CM``.\n\n This ``generator_id = 'PolarCorrection'`` and can be used in the coupled solvers through the\n ``correct_forces_method`` setting as:\n\n .. python::\n settings = dict() # SHARPy settings\n settings['StaticCoupled']['correct_forces_method'] = 'PolarCorrection'\n settings['StaticCoupled']['correct_forces_settings'] = {'cd_from_cl': 'off', # recommended settings (default)\n 'correct_lift': 'off',\n 'moment_from_polar': 'off'}\n\n These are the steps needed to correct the forces:\n\n 1. The force coming from UVLM is divided into induced drag (parallel to the incoming flow velocity) and lift\n (the remaining force).\n\n If ``cd_from_cl == 'on'``.\n 2. The viscous drag and pitching moment are found at the computed lift coefficient. Then forces and\n moments are updated\n\n Else, the angle of attack is computed:\n\n 2. The angle of attack is computed based on that lift force and the angle of zero lift computed from the\n airfoil polar and assuming the potential flow lift curve slope of :math:`2 \\pi`\n\n 3. The drag force is computed based on the angle of attack and the polars provided by the user\n\n 4. If ``correct_lift == 'on'``, the lift coefficient is also corrected with the polar data. Else, only the\n UVLM results are used.\n\n The pitching moment is added in a similar manner as the viscous drag. However, if ``moment_from_polar == 'on'``\n and ``correct_lift == 'on'``, the total moment (the one used for the FSI) is computed just from polar data,\n overriding any moment computed in SHARPy. That is, the moment will include the polar pitching moment, and moments\n due to lift and drag computed from the polar data.\n\n \"\"\"\n generator_id = 'PolarCorrection'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['correct_lift'] = 'bool'\n settings_default['correct_lift'] = False\n settings_description['correct_lift'] = 'Correct lift according to the polars'\n\n settings_types['cd_from_cl'] = 'bool'\n settings_default['cd_from_cl'] = False\n settings_description['cd_from_cl'] = 'Interpolate the C_D for the given C_L, as opposed to getting the C_D from ' \\\n 'the section AoA.'\n\n settings_types['moment_from_polar'] = 'bool'\n settings_default['moment_from_polar'] = False\n settings_description['moment_from_polar'] = 'If ``correct_lift`` is selected, it will compute the pitching moment ' \\\n 'simply from polar derived data, i.e. the polars Cm and the moments' \\\n 'arising from the lift and drag (derived from the polar) contribution. ' \\\n 'Else, it will add the polar Cm to the moment already computed by ' \\\n 'SHARPy.' \n\n settings_types['add_rotation'] = 'bool'\n settings_default['add_rotation'] = False\n settings_description['add_rotation'] = 'Add rotation velocity. Probably needed in steady computations'\n\n settings_types['rot_vel_g'] = 'list(float)'\n settings_default['rot_vel_g'] = [0., 0., 0.] \n settings_description['rot_vel_g'] = 'Rotation velocity in G FoR. Only used if add_rotation = True'\n\n settings_types['centre_rot_g'] = 'list(float)'\n settings_default['centre_rot_g'] = [0., 0., 0.] \n settings_description['centre_rot_g'] = 'Centre of rotation in G FoR. Only used if add_rotation = True'\n\n settings_types['skip_surfaces'] = 'list(int)'\n settings_default['skip_surfaces'] = []\n settings_description['skip_surfaces'] = 'Surfaces on which force correction is skipped.'\n\n\n settings_types['aoa_cl0'] = 'list(float)'\n settings_default['aoa_cl0'] = []\n settings_description['aoa_cl0'] = 'Angle of attack for which zero lift is achieved specified in deg for each airfoil.'\n \n settings_types['write_induced_aoa'] = 'bool'\n settings_default['write_induced_aoa'] = False\n settings_description['write_induced_aoa'] = 'Write induced aoa of each node to txt file.'\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description, settings_options,\n header_line='This generator takes in the following settings.')\n\n def __init__(self):\n self.folder = None\n self.cd_from_cl = None\n self.list_aoa_cl0 = None\n self.settings = None\n\n self.aero = None\n self.structure = None\n self.rho = None\n self.vortex_radius = None\n self.n_node = None\n self.flag_node_shared_by_multiple_surfaces = None\n\n def initialise(self, in_dict, **kwargs):\n self.settings = in_dict\n settings.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n self.aero = kwargs.get('aero')\n self.structure = kwargs.get('structure')\n self.n_node = self.structure.num_node\n self.rho = kwargs.get('rho')\n self.vortex_radius = kwargs.get('vortex_radius', 1e-6)\n self.list_aoa_cl0 = self.settings['aoa_cl0']\n self.cd_from_cl = self.settings['cd_from_cl']\n self.folder = kwargs.get('output_folder') + '/aoa_induced/'\n\n if not self.cd_from_cl and len(self.list_aoa_cl0) == 0:\n # compute aoa for cl0 if not specified in settings\n self.compute_aoa_cl0_from_airfoil_data(self.aero)\n\n self.check_for_special_cases(self.aero)\n\n\n def generate(self, **params):\n \"\"\"\n Keyword Args:\n aero_kstep (:class:`sharpy.utils.datastructures.AeroTimeStepInfo`): Current aerodynamic substep\n structural_kstep (:class:`sharpy.utils.datastructures.StructTimeStepInfo`): Current structural substep\n struct_forces (np.array): Array with the aerodynamic forces mapped on the structure in the B frame of\n reference\n\n Returns:\n np.array: New corrected structural forces\n \"\"\"\n aero_kstep = params['aero_kstep']\n structural_kstep = params['structural_kstep']\n struct_forces = params['struct_forces']\n ts = params['ts']\n\n aerogrid = self.aero\n structure = self.structure\n rho = self.rho\n correct_lift = self.settings['correct_lift']\n moment_from_polar = self.settings['moment_from_polar']\n \n list_aoa_induced = []\n\n data_dict = aerogrid.data_dict\n if aerogrid.polars is None:\n return struct_forces\n new_struct_forces = np.zeros_like(struct_forces)\n\n nnode = struct_forces.shape[0]\n\n # Compute induced velocities at the structural points\n cga = algebra.quat2rotation(structural_kstep.quat)\n pos_g = np.array([cga.dot(structural_kstep.pos[inode]) + np.array([0, 0, 0]) for inode in range(nnode)])\n\n for inode in range(nnode):\n new_struct_forces[inode, :] = struct_forces[inode, :].copy()\n if data_dict['aero_node'][inode]:\n ielem, inode_in_elem = structure.node_master_elem[inode]\n iairfoil = data_dict['airfoil_distribution'][ielem, inode_in_elem]\n isurf = aerogrid.struct2aero_mapping[inode][0]['i_surf']\n if isurf not in self.settings['skip_surfaces']:\n i_n = aerogrid.struct2aero_mapping[inode][0]['i_n']\n polar = aerogrid.polars[iairfoil]\n cab = algebra.crv2rotation(structural_kstep.psi[ielem, inode_in_elem, :])\n cgb = np.dot(cga, cab)\n\n if not self.cd_from_cl:\n airfoil = str(data_dict['airfoil_distribution'][ielem, inode_in_elem])\n aoa_0cl = self.list_aoa_cl0[int(airfoil)]\n\n # computing surface area of panels contributing to force\n dir_span, span, dir_chord, chord = span_chord(i_n, aero_kstep.zeta[isurf])\n area = span * chord\n area = self.correct_surface_area(inode, aerogrid.struct2aero_mapping, aero_kstep.zeta, area)\n \n # Define the relative velocity and its direction\n urel, dir_urel = magnitude_and_direction_of_relative_velocity(structural_kstep.pos[inode, :],\n structural_kstep.pos_dot[inode, :],\n structural_kstep.for_vel[:],\n cga,\n aero_kstep.u_ext[isurf][:, :, i_n],\n self.settings['add_rotation'],\n self.settings['rot_vel_g'],\n self.settings['centre_rot_g'],)\n # Coefficient to change from aerodynamic coefficients to forces (and viceversa)\n coef = 0.5 * rho * np.linalg.norm(urel) ** 2 * area\n # Stability axes - projects forces in B onto S\n c_bs = local_stability_axes(cgb.T.dot(dir_urel), cgb.T.dot(dir_chord))\n forces_s = c_bs.T.dot(struct_forces[inode, :3])\n moment_s = c_bs.T.dot(struct_forces[inode, 3:])\n lift_force = forces_s[2]\n # Compute the associated lift\n cl = np.sign(lift_force) * np.linalg.norm(lift_force) / coef\n\n if self.cd_from_cl:\n # Compute the drag from the UVLM computed lift\n cd, cm = polar.get_cdcm_from_cl(cl)\n\n else:\n \"\"\"\n Compute L, D, M from polar depending on:\n ii) Compute the effective angle of attack from potential flow theory or specified it as setting\n input. The local lift curve slope is 2pi and the zero-lift angle of attack is given by thin \n airfoil theory or specified it as setting input. From this, the effective angle of attack is \n computed for the section and includes 3D effects.\n \"\"\"\n aoa = cl / 2 / np.pi + aoa_0cl \n list_aoa_induced.append(aoa)\n # Compute the coefficients associated to that angle of attack\n cl_polar, cd, cm = polar.get_coefs(aoa)\n \n if correct_lift:\n # Use polar generated CL rather than UVLM computed CL\n cl = cl_polar\n\n # Recompute the forces based on the coefficients (side force is uncorrected)\n forces_s[0] += cd * coef # add viscous drag to induced drag from UVLM\n forces_s[2] = cl * coef\n\n new_struct_forces[inode, 0:3] = c_bs.dot(forces_s)\n\n # Pitching moment\n # The panels are shifted by 0.25 of a panel aft from the leading edge\n panel_shift = 0.25 * (aero_kstep.zeta[isurf][:, 1, i_n] - aero_kstep.zeta[isurf][:, 0, i_n])\n ref_point = aero_kstep.zeta[isurf][:, 0, i_n] + 0.25 * chord * dir_chord - panel_shift\n\n # viscous contribution (pure moment)\n moment_s[1] += cm * coef * chord\n\n # moment due to drag\n arm = cgb.T.dot(ref_point - pos_g[inode]) # in B frame\n moment_polar_drag = algebra.cross3(c_bs.T.dot(arm), cd * dir_urel * coef) # in S frame\n moment_s += moment_polar_drag\n\n # Pitching moment\n if moment_from_polar:\n # The panels are shifted by 0.25 of a panel aft from the leading edge\n panel_shift = 0.25 * (aero_kstep.zeta[isurf][:, 1, i_n] - aero_kstep.zeta[isurf][:, 0, i_n])\n ref_point = aero_kstep.zeta[isurf][:, 0, i_n] + 0.25 * chord * dir_chord - panel_shift\n new_struct_forces[inode, 3:6] = c_bs.dot(moment_s)\n\n # viscous contribution (pure moment)\n moment_s[1] += cm * coef * chord\n\n\n # moment due to drag\n arm = cgb.T.dot(ref_point - pos_g[inode]) # in B frame\n moment_polar_drag = algebra.cross3(c_bs.T.dot(arm), cd * dir_urel * coef) # in S frame\n moment_s += moment_polar_drag\n\n # moment due to lift (if corrected)\n if correct_lift and moment_from_polar:\n # add moment from scratch: cm_polar + cm_drag_polar + cl_lift_polar\n moment_s = np.zeros(3)\n moment_s[1] = cm * coef * chord\n moment_s += moment_polar_drag\n moment_polar_lift = algebra.cross3(c_bs.T.dot(arm), forces_s[2] * np.array([0, 0, 1]))\n moment_s += moment_polar_lift\n\n new_struct_forces[inode, 3:6] = c_bs.dot(moment_s)\n\n if self.settings['write_induced_aoa']:\n self.write_induced_aoa_of_each_node(ts, list_aoa_induced)\n\n return new_struct_forces\n \n\n def correct_surface_area(self, inode, struct2aero_mapping, zeta_ts, area):\n '''\n Corrects the surface area if the structural node is shared by multiple surfaces. \n\n For example, when the wing is split into right and left wing both surfaces share the center node.\n Necessary for cl calculation as the force on the node is already the sum of the forces generated \n at the adjacent panels of each surface.\n \n Args:\n inode (int): global node id\n struct2aero_mapping (list of dicts): maps the structural (global) nodes to aero surfaces and nodes\n zeta_ts (array): zeta of current aero timestep\n\n Returns:\n float: corrected surface area of other surfaces\n '''\n if self.flag_shared_node_by_surfaces[inode]:\n n_surfaces_shared_by_node = len(struct2aero_mapping[inode])\n # add area for all other surfaces connected to this node\n for isurf in range(1,n_surfaces_shared_by_node):\n shared_surf = struct2aero_mapping[inode][isurf]['i_surf']\n i_n_shared_surf = struct2aero_mapping[inode][isurf]['i_n']\n _, span_shared_surf, _, chord_shared_surf = span_chord(i_n_shared_surf, zeta_ts[shared_surf])\n area += span_shared_surf * chord_shared_surf\n return area\n \n def check_for_special_cases(self, aerogrid):\n '''\n Checks if the outboard node is shared by multiple surfaces. \n\n Args:\n aerogrid :class:`~sharpy.aero.models.AerogridLoader\n '''\n # check if outboard node of aerosurface\n self.flag_shared_node_by_surfaces = np.zeros((self.n_node,1))\n for inode in range(self.n_node):\n if aerogrid.data_dict['aero_node'][inode]:\n i_n = aerogrid.struct2aero_mapping[inode][0]['i_n'] \n isurf = aerogrid.struct2aero_mapping[inode][0]['i_surf']\n N = aerogrid.dimensions[isurf, 1]\n if i_n in [0, N]:\n if len(aerogrid.struct2aero_mapping[inode]) > 1:\n self.flag_shared_node_by_surfaces[inode] = 1\n \n\n\n def write_induced_aoa_of_each_node(self,ts, list_aoa_induced):\n '''\n Writes induced aoa of each node to txt file for each timestep. \n\n Args:\n ts (int): simulation timestep \n list_aoa_induced (list(float)): list with induced aoa of each node\n '''\n if ts == 0 and not os.path.exists(self.folder):\n os.makedirs(self.folder)\n \n np.savetxt(self.folder + '/aoa_induced_ts_{}.txt'.format(ts),\n np.transpose(np.transpose(np.array(list_aoa_induced))),\n fmt='%10e',\n delimiter=',',\n header='aoa_induced',\n comments='#')\n \n\n def compute_aoa_cl0_from_airfoil_data(self, aerogrid):\n \"\"\"\n Computes the angle of attack for which zero lift is achieved for every airfoil\n \"\"\"\n self.list_aoa_cl0 = np.zeros((len(aerogrid.data_dict['airfoils']),1))\n for i, airfoil in enumerate(aerogrid.data_dict['airfoils']):\n airfoil_coords = aerogrid.data_dict['airfoils'][airfoil]\n self.list_aoa_cl0[i] = get_aoacl0_from_camber(airfoil_coords[:, 0], airfoil_coords[:, 1])\n\n@generator_interface.generator\nclass EfficiencyCorrection(generator_interface.BaseGenerator):\n \"\"\"\n The efficiency and constant terms are introduced by means of the array ``airfoil_efficiency`` in the ``aero.h5``\n\n .. math::\n \\mathbf{f}_{struct}^B &= \\varepsilon^f_0 \\mathbf{f}_{i,struct}^B + \\varepsilon^f_1\\\\\n \\mathbf{m}_{struct}^B &= \\varepsilon^m_0 \\mathbf{m}_{i,struct}^B + \\varepsilon^m_1\n\n Notice that the moment correction is applied on top of the force correction. As a consequence, the aerodynamic\n moments generated by the forces on the vertices are corrected sequentially by both efficiencies.\n\n See Also:\n The SHARPy case files documentation for a detailed overview on how to include the airfoil efficiencies.\n\n Returns:\n np.ndarray: corresponding aerodynamic force at the structural node from the force and moment at a grid vertex\n \"\"\"\n generator_id = 'EfficiencyCorrection'\n\n settings_types = dict()\n settings_default = dict()\n\n def __init__(self):\n self.aero = None\n self.structure = None\n\n def initialise(self, in_dict, **kwargs):\n self.aero = kwargs.get('aero')\n self.structure = kwargs.get('structure')\n\n def generate(self, **params):\n \"\"\"\n Keyword Args:\n aero_kstep (:class:`sharpy.utils.datastructures.AeroTimeStepInfo`): Current aerodynamic substep\n structural_kstep (:class:`sharpy.utils.datastructures.StructTimeStepInfo`): Current structural substep\n struct_forces (np.array): Array with the aerodynamic forces mapped on the structure in the B frame of\n reference\n\n Returns:\n np.array: New corrected structural forces\n \"\"\"\n struct_forces = params['struct_forces']\n\n n_node = self.structure.num_node\n n_elem = self.structure.num_elem\n data_dict = self.aero.data_dict\n new_struct_forces = np.zeros_like(struct_forces)\n\n # load airfoil efficiency (if it exists); else set to one (to avoid multiple ifs in the loops)\n airfoil_efficiency = data_dict['airfoil_efficiency']\n # force efficiency dimensions [n_elem, n_node_elem, 2, [fx, fy, fz]] - all defined in B frame\n force_efficiency = np.zeros((n_elem, 3, 2, 3))\n force_efficiency[:, :, 0, :] = 1.\n force_efficiency[:, :, :, 1] = airfoil_efficiency[:, :, :, 0]\n force_efficiency[:, :, :, 2] = airfoil_efficiency[:, :, :, 1]\n\n # moment efficiency dimensions [n_elem, n_node_elem, 2, [mx, my, mz]] - all defined in B frame\n moment_efficiency = np.zeros((n_elem, 3, 2, 3))\n moment_efficiency[:, :, 0, :] = 1.\n moment_efficiency[:, :, :, 0] = airfoil_efficiency[:, :, :, 2]\n\n for inode in range(n_node):\n i_elem, i_local_node = self.structure.node_master_elem[inode]\n new_struct_forces[inode, :] = struct_forces[inode, :].copy()\n new_struct_forces[inode, 0:3] *= force_efficiency[i_elem, i_local_node, 0, :] # element wise multiplication\n new_struct_forces[inode, 0:3] += force_efficiency[i_elem, i_local_node, 1, :]\n new_struct_forces[inode, 3:6] *= moment_efficiency[i_elem, i_local_node, 0, :]\n new_struct_forces[inode, 3:6] += moment_efficiency[i_elem, i_local_node, 1, :]\n return new_struct_forces\n" }, { "path": "sharpy/generators/shearvelocityfield.py", "content": "import numpy as np\n\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.settings as settings\n\n\n@generator_interface.generator\nclass ShearVelocityField(generator_interface.BaseGenerator):\n r\"\"\"\n Shear Velocity Field Generator\n\n ``ShearVelocityField`` class inherited from ``BaseGenerator``\n\n The object creates a steady velocity field with shear\n\n .. math:: \\hat{u} = \\hat{u}\\_\\infty \\left( \\frac{h - h\\_\\mathrm{corr}}{h\\_\\mathrm{ref}} \\right)^{\\mathrm{shear}\\_\\mathrm{exp}}\n .. math:: h = \\zeta \\cdot \\mathrm{shear}\\_\\mathrm{direction}\n\n \"\"\"\n generator_id = 'ShearVelocityField'\n generator_classification = 'velocity-field'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['u_inf'] = 'float'\n settings_default['u_inf'] = None\n settings_description['u_inf'] = 'Free stream velocity magnitude'\n\n settings_types['u_inf_direction'] = 'list(float)'\n settings_default['u_inf_direction'] = np.array([1.0, 0, 0])\n settings_description['u_inf_direction'] = '``x``, ``y`` and ``z`` relative components of the free stream velocity'\n\n settings_types['shear_direction'] = 'list(float)'\n settings_default['shear_direction'] = np.array([.0, 0, 1.0])\n settings_description['shear_direction'] = '``x``, ``y`` and ``z`` relative components of the direction along which shear applies'\n\n settings_types['shear_exp'] = 'float'\n settings_default['shear_exp'] = 0.\n settings_description['shear_exp'] = 'Exponent of the shear law'\n\n settings_types['h_ref'] = 'float'\n settings_default['h_ref'] = 1.\n settings_description['h_ref'] = 'Reference height at which ``u_inf`` is defined'\n\n settings_types['h_corr'] = 'float'\n settings_default['h_corr'] = 0.\n settings_description['h_corr'] = 'Height to correct shear law'\n\n setting_table = settings.SettingsTable()\n __doc__ += setting_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.in_dict = dict()\n\n self.u_inf = 0.\n self.u_inf_direction = None\n self.shear_direction = None\n self.shear_exp = None\n self.h_ref = None\n self.h_corr = None\n\n def initialise(self, in_dict, restart=False):\n self.in_dict = in_dict\n settings.to_custom_types(self.in_dict, self.settings_types, self.settings_default)\n\n self.u_inf = self.in_dict['u_inf']\n self.u_inf_direction = self.in_dict['u_inf_direction']\n self.shear_direction = self.in_dict['shear_direction']\n self.shear_exp = self.in_dict['shear_exp']\n self.h_ref = self.in_dict['h_ref']\n self.h_corr = self.in_dict['h_corr']\n\n def generate(self, params, uext):\n zeta = params['zeta']\n override = params['override']\n for i_surf in range(len(zeta)):\n if override:\n uext[i_surf].fill(0.0)\n for i in range(zeta[i_surf].shape[1]):\n for j in range(zeta[i_surf].shape[2]):\n h = np.dot(zeta[i_surf][:, i, j], self.shear_direction) + self.h_corr\n uext[i_surf][:, i, j] += self.u_inf*self.u_inf_direction*(h/self.h_ref)**self.shear_exp\n" }, { "path": "sharpy/generators/steadyvelocityfield.py", "content": "import numpy as np\n\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.settings as settings\n\n\n@generator_interface.generator\nclass SteadyVelocityField(generator_interface.BaseGenerator):\n \"\"\"\n Steady Velocity Field Generator\n\n ``SteadyVelocityField`` class inherited from ``BaseGenerator``\n\n The object creates a steady velocity field with the velocity and flow direction specified by the user.\n\n To call this generator, the ``generator_id = SteadyVelocityField`` shall be used.\n This is parsed as the value for the ``velocity_field_generator`` key in the desired aerodynamic solver's settings.\n\n Args:\n in_dict (dict): Input data in the form of dictionary. See acceptable entries below:\n\n Attributes:\n settings_types (dict): Acceptable data types of the input data\n settings_default (dict): Default values for input data should the user not provide them\n u_inf (float): Free stream velocity selection\n u_inf_direction (list(float)): ``x``, ``y`` and ``z`` relative contributions to the free stream velocity\n\n See Also:\n .. py:class:: sharpy.utils.generator_interface.BaseGenerator\n\n \"\"\"\n generator_id = 'SteadyVelocityField'\n generator_classification = 'velocity-field'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['u_inf'] = 'float'\n settings_default['u_inf'] = None\n settings_description['u_inf'] = 'Module of the free stream velocity'\n\n settings_types['u_inf_direction'] = 'list(float)'\n settings_default['u_inf_direction'] = np.array([1.0, 0, 0])\n settings_description['u_inf_direction'] = 'Direction of the free stream velocity'\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.in_dict = dict()\n\n self.u_inf = 0.\n self.u_inf_direction = None\n\n def initialise(self, in_dict, restart=False):\n self.in_dict = in_dict\n settings.to_custom_types(self.in_dict,\n self.settings_types,\n self.settings_default)\n\n self.u_inf = self.in_dict['u_inf']\n self.u_inf_direction = self.in_dict['u_inf_direction']\n\n def generate(self, params, uext):\n zeta = params['zeta']\n override = params['override']\n for i_surf in range(len(zeta)):\n if override:\n uext[i_surf].fill(0.0)\n for i in range(zeta[i_surf].shape[1]):\n for j in range(zeta[i_surf].shape[2]):\n uext[i_surf][:, i, j] += self.u_inf*self.u_inf_direction\n" }, { "path": "sharpy/generators/straightwake.py", "content": "import numpy as np\n\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.settings as settings\nimport sharpy.utils.solver_interface as solver_interface\nimport sharpy.utils.cout_utils as cout\n\n\n@generator_interface.generator\nclass StraightWake(generator_interface.BaseGenerator):\n r\"\"\"\n Straight wake shape generator\n\n This generator creates a straight wake shedding from the trailing edge based on\n the time step ``dt``, the incoming velocity magnitude ``u_inf`` and\n direction ``u_inf_direction``. It is to be used as ``wake_generator`` in\n :class:`~sharpy.solvers.aerogridloader.AerogridLoader`.\n\n A wake where panels grow downstream is supported by using the settings ``dx1``, ``ndx1``,\n ``r`` and ``dxmax`` as described below. Note that the wake will always have ``m_star`` panels, as specified in\n :class:`~sharpy.solvers.aerogridloader.AerogridLoader`, thus these settings will modify the effective length\n of the wake. Once the maximum size of panel ``dxmax`` is achieved, all panels are size ``dxmax`` thereinafter\n until ``m_star`` panels are created.\n \"\"\"\n generator_id = 'StraightWake'\n generator_classification = 'wake'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['u_inf'] = 'float'\n settings_default['u_inf'] = 1. # None\n settings_description['u_inf'] = 'Free stream velocity magnitude'\n\n settings_types['u_inf_direction'] = 'list(float)'\n settings_default['u_inf_direction'] = np.array([1.0, 0, 0]) # None\n settings_description['u_inf_direction'] = '``x``, ``y`` and ``z`` relative components of the free stream velocity'\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = 0.1 # None\n settings_description['dt'] = 'Time step'\n\n settings_types['dx1'] = ['float', 'list(float)']\n settings_default['dx1'] = -1.0\n settings_description['dx1'] = 'Size of the first wake panel'\n\n settings_types['ndx1'] = ['int', 'list(int)']\n settings_default['ndx1'] = 1\n settings_description['ndx1'] = 'Number of panels with size ``dx1``'\n\n settings_types['r'] = ['float', 'list(float)']\n settings_default['r'] = 1.\n settings_description['r'] = 'Growth rate after ``ndx1`` panels'\n\n settings_types['dxmax'] = ['float', 'list(float)']\n settings_default['dxmax'] = -1.0\n settings_description['dxmax'] = 'Maximum panel size'\n\n setting_table = settings.SettingsTable()\n __doc__ += setting_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.in_dict = dict()\n\n self.u_inf = 0.\n self.u_inf_direction = None\n self.dt = None\n\n def initialise(self, data, in_dict=None, restart=False):\n self.in_dict = in_dict\n\n # For backwards compatibility\n if len(self.in_dict.keys()) == 0:\n cout.cout_wrap(\"WARNING: The code will run for backwards compatibility. \\\n In future releases you will need to define a 'wake_shape_generator' in ``AerogridLoader''. \\\n Please, check the documentation\", 3)\n\n # Look for an aerodynamic solver\n if 'StaticUvlm' in data.settings:\n aero_solver_name = 'StaticUvlm'\n aero_solver_settings = data.settings['StaticUvlm']\n elif 'SHWUvlm' in data.settings:\n aero_solver_name = 'SHWUvlm'\n aero_solver_settings = data.settings['SHWUvlm']\n elif 'StaticCoupled' in data.settings:\n aero_solver_name = data.settings['StaticCoupled']['aero_solver']\n aero_solver_settings = data.settings['StaticCoupled']['aero_solver_settings']\n elif 'DynamicCoupled' in data.settings:\n aero_solver_name = data.settings['DynamicCoupled']['aero_solver']\n aero_solver_settings = data.settings['DynamicCoupled']['aero_solver_settings']\n elif 'StepUvlm' in data.settings:\n aero_solver_name = 'StepUvlm'\n aero_solver_settings = data.settings['StepUvlm']\n else:\n raise RuntimeError(\"ERROR: aerodynamic solver not found\")\n\n # Get the minimum parameters needed to define the wake\n aero_solver = solver_interface.solver_from_string(aero_solver_name)\n settings.to_custom_types(aero_solver_settings,\n aero_solver.settings_types,\n aero_solver.settings_default)\n\n if 'dt' in aero_solver_settings.keys():\n dt = aero_solver_settings['dt']\n elif 'rollup_dt' in aero_solver_settings.keys():\n dt = aero_solver_settings['rollup_dt']\n else:\n # print(aero_solver['velocity_field_input']['u_inf'])\n dt = 1./aero_solver_settings['velocity_field_input']['u_inf']\n self.in_dict = {'u_inf': aero_solver_settings['velocity_field_input']['u_inf'],\n 'u_inf_direction': aero_solver_settings['velocity_field_input']['u_inf_direction'],\n 'dt': dt}\n\n settings.to_custom_types(self.in_dict, self.settings_types, self.settings_default, no_ctype=True)\n\n self.u_inf = self.in_dict['u_inf']\n self.u_inf_direction = self.in_dict['u_inf_direction']\n self.dt = self.in_dict['dt']\n\n self.dx1 = self.in_dict['dx1']\n self.ndx1 = self.in_dict['ndx1']\n self.r = self.in_dict['r']\n self.dxmax = self.in_dict['dxmax']\n\n\n def generate(self, params):\n # Renaming for convenience\n zeta = params['zeta']\n zeta_star = params['zeta_star']\n gamma = params['gamma']\n gamma_star = params['gamma_star']\n dist_to_orig = params['dist_to_orig']\n\n nsurf = len(zeta)\n for isurf in range(nsurf):\n r_surf, ndx1_surf, dx1_surf, dxmax_surf = self.get_all_surface_parameters(isurf)\n M, N = zeta_star[isurf][0, :, :].shape\n for j in range(N):\n zeta_star[isurf][:, 0, j] = zeta[isurf][:, -1, j]\n for i in range(1, M):\n deltax = self.get_deltax(i, dx1_surf, ndx1_surf, r_surf, dxmax_surf)\n zeta_star[isurf][:, i, j] = zeta_star[isurf][:, i - 1, j] + deltax*self.u_inf_direction\n gamma[isurf] *= 0.\n gamma_star[isurf] *= 0.\n\n for isurf in range(nsurf):\n M, N = zeta_star[isurf][0, :, :].shape\n dist_to_orig[isurf][0] = 0.\n for j in range(0, N):\n for i in range(1, M):\n dist_to_orig[isurf][i, j] = (dist_to_orig[isurf][i - 1, j] +\n np.linalg.norm(zeta_star[isurf][:, i, j] -\n zeta_star[isurf][:, i - 1, j]))\n dist_to_orig[isurf][:, j] /= dist_to_orig[isurf][-1, j]\n\n\n @staticmethod\n def get_deltax(i, dx1, ndx1, r, dxmax):\n if (i < ndx1 + 1) :\n deltax = dx1\n else:\n deltax = dx1*r**(i - ndx1)\n deltax = min(deltax, dxmax)\n\n return deltax\n @staticmethod\n def get_surface_parameter(parameter, i_surf):\n if np.isscalar(parameter):\n return parameter\n else:\n return parameter[i_surf]\n\n def get_all_surface_parameters(self,i_surf):\n r_surf = self.get_surface_parameter(self.r, i_surf)\n dx1_surf = self.get_surface_parameter(self.dx1, i_surf)\n ndx1_surf = self.get_surface_parameter(self.ndx1, i_surf)\n dxmax_surf = self.get_surface_parameter(self.dxmax, i_surf)\n if dx1_surf == -1.:\n dx1_surf = self.u_inf*self.dt\n if dxmax_surf == -1.:\n dxmax_surf = dx1_surf\n return r_surf, ndx1_surf, dx1_surf, dxmax_surf\n\n\n\n" }, { "path": "sharpy/generators/trajectorygenerator.py", "content": "import numpy as np\nfrom numpy.polynomial import polynomial as P\nimport scipy as sc\nfrom scipy import interpolate\n\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.settings as settings\nimport sharpy.utils.cout_utils as cout\n\n\n@generator_interface.generator\nclass TrajectoryGenerator(generator_interface.BaseGenerator):\n \"\"\"\n ``TrajectoryGenerator`` is used to generate nodal positions or velocities\n for trajectory constraints such as the ones included in the multibody\n solver.\n\n It is usually called from a ``Controller`` module.\n \"\"\"\n generator_id = 'TrajectoryGenerator'\n generator_classification = 'utils'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['angle_end'] = 'float'\n settings_default['angle_end'] = 0.0\n settings_description['angle_end'] = 'Trajectory angle wrt horizontal at release'\n\n settings_types['veloc_end'] = 'float'\n settings_default['veloc_end'] = None\n settings_description['veloc_end'] = 'Release velocity at release'\n\n settings_types['shape'] = 'str'\n settings_default['shape'] = 'quadratic'\n settings_description['shape'] = 'Shape of the ``z`` vs ``x`` function. ``quadratic`` or ``linear`` are supported'\n\n settings_types['acceleration'] = 'str'\n settings_default['acceleration'] = 'linear'\n settings_description['acceleration'] = 'Acceleration law, possible values are ``linear`` or ``constant``'\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = None\n settings_description['dt'] = 'Time step of the simulation'\n\n settings_types['coords_end'] = 'list(float)'\n settings_default['coords_end'] = None\n settings_description['coords_end'] = 'Coordinates of the final ramp point'\n\n settings_types['plot'] = 'bool'\n settings_default['plot'] = False\n settings_description['plot'] = 'Plot the ramp shape. Requires matplotlib installed'\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = False\n settings_description['print_info'] = 'Print information on runtime'\n\n settings_types['time_offset'] = 'float'\n settings_default['time_offset'] = 0.0\n settings_description['time_offset'] = 'Time interval before the start of the ramp acceleration'\n\n settings_types['offset'] = 'list(float)'\n settings_default['offset'] = np.zeros((3,))\n settings_description['offset'] = 'Coordinates of the starting point of the simulation'\n\n settings_types['return_velocity'] = 'bool'\n settings_default['return_velocity'] = False\n settings_description['return_velocity'] = 'If ``True``, nodal velocities are given, if ``False``, coordinates are the output'\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.in_dict = dict()\n\n self.x_vec = None\n self.y_vec = None\n self.x_dot_vec = None\n self.y_dot_vec = None\n self.time = None\n self.n_steps = None\n self.travel_time = None\n self.curve_length = None\n\n self.implemented_shapes = [\"linear\", \"quadratic\"]\n self.implemented_accelerations = [\"constant\", \"linear\"]\n\n\n def initialise(self, in_dict, restart=False):\n self.in_dict = in_dict\n settings.to_custom_types(self.in_dict, self.settings_types, self.settings_default)\n\n # input validation\n self.in_dict['shape'] = self.in_dict['shape'].lower()\n self.in_dict['acceleration'] = self.in_dict['acceleration'].lower()\n\n self.calculate_trajectory()\n if self.in_dict['print_info']:\n self.print_info()\n\n if self.in_dict['plot']:\n self.plot()\n\n if self.in_dict['return_velocity']:\n self.diff_trajectory()\n\n def print_info(self):\n cout.cout_wrap('Trajectory information:', 2)\n cout.cout_wrap('\\t-travel time: {}'.format(self.travel_time), 2)\n cout.cout_wrap('\\t-curve length: {}'.format(self.curve_length), 2)\n cout.cout_wrap('-------------------------------', 2)\n\n def plot(self):\n try:\n import matplotlib.pyplot as plt\n plt.figure()\n plt.scatter(self.x_vec, self.y_vec, c=self.time_vec)\n plt.colorbar(orientation='horizontal')\n plt.axis('equal')\n plt.show()\n except ModuleNotFoundError:\n import warnings\n warnings.warn('Unable to import matplotlib, skipping plot')\n\n def get_n_steps(self):\n return self.n_steps\n\n def __call__(self, params):\n return self.generate(params)\n\n def generate(self, params):\n it = params['it']\n if self.n_steps is not None:\n if it >= self.n_steps:\n return [None]*3\n\n if self.in_dict['return_velocity']:\n return np.array([self.x_dot_vec[it], 0.0, self.y_dot_vec[it]]) + self.in_dict['offset']\n else:\n return np.array([self.x_vec[it], 0.0, self.y_vec[it]]) + self.in_dict['offset']\n\n def calculate_trajectory(self):\n in_dict = self.in_dict\n # shape variables\n shape_polynomial = np.zeros((3,)) # [c, b, a] results in y = c + b*x + a*x^2\n curve_length = 0.0\n\n # calculate coefficients and curve length\n if in_dict['shape'] == \"linear\":\n shape_polynomial[0] = 0.0\n shape_polynomial[1] = in_dict['coords_end'][1]/in_dict['coords_end'][0]\n if np.isnan(shape_polynomial[1]):\n shape_polynomial[1] = 0.0\n shape_polynomial[2] = 0.0\n curve_length = linear_curve_length(shape_polynomial, in_dict['coords_end'])\n\n elif in_dict['shape'] == \"quadratic\":\n shape_polynomial[2] = (np.arctan(in_dict['angle_end'].value) - in_dict['coords_end'][1]/in_dict['coords_end'][0])/in_dict['coords_end'][0]\n shape_polynomial[1] = np.arctan(in_dict['angle_end'].value) - 2.0*shape_polynomial[2]*in_dict['coords_end'][0]\n shape_polynomial[0] = 0.0\n curve_length = quadratic_curve_length(shape_polynomial, in_dict['coords_end'])\n\n curve_length = np.abs(curve_length)\n\n # acceleration\n acceleration_position_coefficients = None\n travel_time = 0.0\n if in_dict['acceleration'] == 'constant':\n acceleration_position_coefficients = constant_acceleration_position_coeffs(curve_length, np.abs(in_dict['veloc_end'].value))\n travel_time = constant_acceleration_travel_time(curve_length,\n np.abs(in_dict['veloc_end'].value))\n elif in_dict['acceleration'] == 'linear':\n acceleration_position_coefficients = linear_acceleration_position_coeffs(curve_length, np.abs(in_dict['veloc_end'].value))\n travel_time = linear_acceleration_travel_time(curve_length,\n np.abs(in_dict['veloc_end'].value))\n\n # time\n n_steps_travel = int(round(travel_time/in_dict['dt'].value))\n n_steps_offset = int(round(self.in_dict['time_offset'].value/in_dict['dt'].value))\n self.n_steps = n_steps_offset + n_steps_travel\n self.time_vec = np.zeros((self.n_steps, ))\n self.time_vec[n_steps_offset:] = np.linspace(0.0, n_steps_travel*in_dict['dt'].value, n_steps_travel)\n\n # with t I get s\n s_vec = P.polyval(self.time_vec, acceleration_position_coefficients)\n # need to get a function for x(s)\n # sample s(x) and create an interpolator\n n_samples = 1000\n sampled_x_vec = np.linspace(0.0, in_dict['coords_end'][0], n_samples)\n sampled_s_vec = np.zeros((n_samples, ))\n for i_sample in range(n_samples):\n if in_dict['shape'] == \"linear\":\n sampled_s_vec[i_sample] = np.abs(linear_curve_length(shape_polynomial, np.array([sampled_x_vec[i_sample], 0.0])))\n elif in_dict['shape'] == 'quadratic':\n sampled_s_vec[i_sample] = np.abs(quadratic_curve_length(shape_polynomial, np.array([sampled_x_vec[i_sample], 0.0])))\n x_of_s_interp = sc.interpolate.interp1d(sampled_s_vec, sampled_x_vec, kind='quadratic', fill_value='extrapolate')\n self.x_vec = x_of_s_interp(s_vec)\n\n # with x, I obtain y and done\n self.y_vec = P.polyval(self.x_vec, shape_polynomial)\n self.travel_time = travel_time\n self.curve_length = curve_length\n\n def diff_trajectory(self):\n dt = self.in_dict['dt'].value\n\n self.x_dot_vec = np.gradient(self.x_vec, dt)\n self.y_dot_vec = np.gradient(self.y_vec, dt)\n\n\ndef linear_curve_length(shape_polynomial, coords_end):\n dzdx_end = shape_polynomial[1]\n\n length = coords_end[0]*np.sqrt(dzdx_end**2 + 1)\n return length\n\n\ndef quadratic_curve_length(shape_polynomial, coords_end):\n dzdx_end = 2.0*shape_polynomial[2]*coords_end[0] + shape_polynomial[1]\n a = shape_polynomial[2]\n b = shape_polynomial[1]\n xe = coords_end[0]\n length = (2.0*a*xe + b)*np.sqrt((2.0*a*xe + b)**2 + 1.0)\n length += np.arcsinh(2.0*a*xe + b)\n length -= b*np.sqrt(b**2 + 1.0)\n length -= np.arcsinh(b)\n length /= 4.0*a\n\n return length\n\n\ndef constant_acceleration_position_coeffs(s_e, s_dot_e):\n coeffs = (0.0, 0.0, (4.0*s_dot_e**2)/s_e, 0.0)\n return coeffs\n\n\ndef linear_acceleration_position_coeffs(s_e, s_dot_e):\n coeff = ((6.0*s_e)**(2./3.)/(2.0*s_dot_e))**(-3.)\n coeffs = (0.0, 0.0, 0.0, (1./6.)*coeff)\n return coeffs\n\n\ndef constant_acceleration_travel_time(s_e, s_dot_e):\n return 2.0*s_e/s_dot_e\n\n\ndef linear_acceleration_travel_time(s_e, s_dot_e):\n return 3.0*s_e/s_dot_e\n" }, { "path": "sharpy/generators/turbvelocityfield.py", "content": "import numpy as np\nimport scipy.interpolate as interpolate\nimport h5py as h5\nimport os\nfrom lxml import objectify, etree\n\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.settings as settings\nimport sharpy.utils.cout_utils as cout\n\n\n@generator_interface.generator\nclass TurbVelocityField(generator_interface.BaseGenerator):\n r\"\"\"\n Turbulent Velocity Field Generator\n\n ``TurbVelocitityField`` is a class inherited from ``BaseGenerator``\n\n The ``TurbVelocitityField`` class generates a velocity field based on the input from an [XDMF](http://www.xdmf.org) file.\n It supports time-dependant fields as well as frozen turbulence.\n\n To call this generator, the ``generator_id = TurbVelocityField`` shall be used.\n This is parsed as the value for the ``velocity_field_generator`` key in the desired aerodynamic solver's settings.\n\n Supported files:\n - `field_id.xdmf`: Steady or Unsteady XDMF file\n\n This generator also performs time interpolation between two different time steps. For now, only linear interpolation is possible.\n\n Space interpolation is done through `scipy.interpolate` trilinear interpolation. However, turbulent fields are\n read directly from the binary file and not copied into memory. This is performed using `np.memmap`.\n The overhead of this procedure is ~18% for the interpolation stage, however, initially reading the binary velocity field\n (which will be much more common with time-domain simulations) is faster by a factor of 1e4.\n Also, memory savings are quite substantial: from 6Gb for a typical field to a handful of megabytes for the whole program.\n\n Args:\n in_dict (dict): Input data in the form of dictionary. See acceptable entries below:\n\n Attributes:\n\n See Also:\n .. py:class:: sharpy.utils.generator_interface.BaseGenerator\n\n \"\"\"\n generator_id = 'TurbVelocityField'\n generator_classification = 'velocity-field'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Output solver-specific information in runtime.'\n\n settings_types['turbulent_field'] = 'str'\n settings_default['turbulent_field'] = None\n settings_description['turbulent_field'] = 'XDMF file path of the velocity field'\n\n settings_types['offset'] = 'list(float)'\n settings_default['offset'] = np.zeros((3,))\n settings_description['offset'] = 'Spatial offset in the 3 dimensions'\n\n settings_types['centre_y'] = 'bool'\n settings_default['centre_y'] = True\n settings_description['centre_y'] = 'Flat for changing the domain to [``-y_max/2``, ``y_max/2``]'\n\n settings_types['periodicity'] = 'str'\n settings_default['periodicity'] = 'xy'\n settings_description['periodicity'] = 'Axes in which periodicity is enforced'\n\n settings_types['frozen'] = 'bool'\n settings_default['frozen'] = True\n settings_description['frozen'] = 'If ``True``, the turbulent field will not be updated in time'\n\n settings_types['store_field'] = 'bool'\n settings_default['store_field'] = False\n settings_description['store_field'] = 'If ``True``, the xdmf snapshots are stored in memory. Only two at a time for the linear interpolation'\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.in_dict = dict()\n\n self.settings = dict()\n\n self.file = None\n self.extension = None\n\n self.grid_data = dict()\n\n self.interpolator = 3*[None]\n self.x_periodicity = False\n self.y_periodicity = False\n\n # variables for interpolator wrapper\n self._t0 = -1\n self._t1 = -1\n self._it0 = -1\n self._it1 = -1\n self._interpolator0 = None\n self._interpolator1 = None\n self.coeff = 0.\n self.double_initialisation = True\n self.vel_holder0 = 3*[None]\n self.vel_holder1 = 3*[None]\n\n def initialise(self, in_dict, restart=False):\n self.in_dict = in_dict\n settings.to_custom_types(self.in_dict, self.settings_types, self.settings_default)\n self.settings = self.in_dict\n\n _, self.extension = os.path.splitext(self.settings['turbulent_field'])\n\n if self.extension == '.h5':\n self.read_btl(self.settings['turbulent_field'])\n if self.extension == '.xdmf':\n self.read_xdmf(self.settings['turbulent_field'])\n\n if 'z' in self.settings['periodicity']:\n raise ValueError('Periodicitiy setting in TurbVelocityField cannot be z.\\n A turbulent boundary layer is not periodic in the z direction!')\n\n if 'x' in self.settings['periodicity']:\n self.x_periodicity = True\n if 'y' in self.settings['periodicity']:\n self.y_periodicity = True\n\n # ADC: VERY VERY UGLY. NEED A BETTER WAY\n def interpolator_wrapper0(self, coords, i_dim=0):\n coeff = self.get_coeff()\n return (1.0 - self.coeff)*self._interpolator0[i_dim](coords) + self.coeff*self._interpolator1[i_dim](coords)\n def interpolator_wrapper1(self, coords, i_dim=1):\n coeff = self.get_coeff()\n return (1.0 - self.coeff)*self._interpolator0[i_dim](coords) + self.coeff*self._interpolator1[i_dim](coords)\n def interpolator_wrapper2(self, coords, i_dim=2):\n coeff = self.get_coeff()\n return (1.0 - self.coeff)*self._interpolator0[i_dim](coords) + self.coeff*self._interpolator1[i_dim](coords)\n\n def get_coeff(self):\n return self.coeff\n\n def init_interpolator(self):\n if self.settings['frozen']:\n self.interpolator = self._interpolator0\n return\n\n # continuing the ugliness\n self.interpolator[0] = self.interpolator_wrapper0\n self.interpolator[1] = self.interpolator_wrapper1\n self.interpolator[2] = self.interpolator_wrapper2\n\n # these functions need to define the interpolators\n def read_btl(self, in_file):\n \"\"\"\n Legacy function, not using the custom format based on HDF5 anymore.\n \"\"\"\n raise NotImplementedError('The BTL reader is not up to date!')\n\n def read_xdmf(self, in_file):\n \"\"\"\n Reads the xml file `.xdmf`. Writes the self.grid_data data structure\n with all the information necessary.\n\n Note: this function does not load any turbulence data (such as ux000, ...),\n it only reads the header information contained in the xdmf file.\n \"\"\"\n # store route of file for the other files\n self.route = os.path.dirname(os.path.abspath(in_file))\n\n # file to string\n with open(in_file, 'r') as self.file:\n data = self.file.read().replace('\\n', '')\n\n # parse data\n # this next line is necessary to avoid problems with parsing in the Time part:\n # quantity at vertex 0\n\t\t- (aM,aN)=(1,0) --> quantity at vertex 1\n\t\t- (aM,aN)=(1,1) --> quantity at vertex 2\n\t\t- (aM,aN)=(0,1) --> quantity at vertex 3\n\t\"\"\"\n\n\twcv=np.array([ (1-aM)*(1-aN), aM*(1-aN), aM*aN, aN*(1-aM) ])\n\n\treturn wcv \n\n\ndef get_Wvc_scalar(Map,aM=0.5,aN=0.5):\n\t\"\"\"\n\tProduce scalar interpolation matrix Wvc for state-space realisation.\n\n\tImportant: this will not work for coordinates extrapolation, as it would\n\trequire information about the panel size. It works for other forces/scalar \n\tquantities extrapolation. It assumes the quantity at the collocation point\n\tis determined proportionally to the weight associated to each vertex and \n\tobtained through get_panel_wcv. \n\t\"\"\"\n\n\t# initialise\n\tK,Kzeta=Map.K,Map.Kzeta\n\tWvc=np.zeros((Kzeta,K))\n\n\t# retrieve weights\n\twcv=get_panel_wcv(aM,aN)\n\twvc=wcv.T\n\n\t# define mapping panels to vertices (for scalars)\n\tif not hasattr(Map,'Mvp1d_scalar'):\n\t\tMap.map_panels_to_vertices_1D_scalar()\n\n\t# loop through panels\n\tfor jj in range(K):\n\t\t# loop through local vertex index\n\t\tfor vv in range(4):\n\t\t\t# vertex 1d index\n\t\t\tii = Map.Mpv1d_scalar[jj,vv]\n\t\t\t# allocate\n\t\t\tWvc[ii,jj]=wvc[vv]\n\n\treturn Wvc\n\n\ndef get_Wvc_vector(Wvc_scalar):\n\n\tKzeta,K=Wvc_scalar.shape\n\tWvc=np.zeros((3*Kzeta,3*K))\n\n\tfor cc in range(3):\n\t\tWvc[cc*Kzeta:(cc+1)*Kzeta,cc*K:(cc+1)*K]=Wvc_scalar \n\n\treturn Wvc \n\n\ndef get_Wnv_vector(SurfGeo,aM=0.5,aN=0.5):\n\t\"\"\"\n\tProvide projection matrix from nodal velocities to normal velocity at \n\tcollocation points\n\t\"\"\"\n\n\t# initialise\n\tMap=SurfGeo.maps\n\tK,Kzeta=Map.K,Map.Kzeta\n\n\t# retrieve scaling matrix\n\tWvc_scalar=get_Wvc_scalar(Map,aM,aN)\n\tWvc=get_Wvc_vector(Wvc_scalar)\n\tWcv=Wvc.T\n\tdel Wvc_scalar, Wvc\n\t\n\t# Build Wnc matrix\n\tNmat=SurfGeo.normals.reshape((3,K))\n\tWnc=np.concatenate([\n\t\t np.diag(Nmat[0,:]),np.diag(Nmat[1,:]),np.diag(Nmat[2,:]) ], axis=1) \n\t\n\tWnv=np.dot(Wnc,Wcv)\n\n\treturn Wnv\n\n\n\n\n\n# -----------------------------------------------------------------------------\n\n#\n# if __name__=='__main__':\n#\n# \timport read\n# \timport gridmapping\n# \timport surface\n# \timport matplotlib.pyplot as plt\n#\n# \t# select test case\n# \tfname='../test/h5input/goland_mod_Nsurf01_M003_N004_a040.aero_state.h5'\n# \thaero=read.h5file(fname)\n# \ttsdata=haero.ts00000\n#\n# \t# select surface and retrieve data\n# \tss=0\n# \tM,N=tsdata.dimensions[ss]\n# \tMap=gridmapping.AeroGridMap(M,N)\n# \tSurfGeo=surface.AeroGridGeo(Map,tsdata.zeta[ss])\n#\n# \t# generate geometry data\n# \tSurfGeo.generate_areas()\n# \tSurfGeo.generate_normals()\n# \t#SurfGeo.aM,SurfGeo.aN=0.25,0.75\n# \tSurfGeo.generate_collocations()\n#\n#\n# \t# ---------------------------------------------------------------- Test Wvc\n# \tzeta_vec=SurfGeo.zeta.reshape(-1,order='C')\n# \tWvc_scalar=get_Wvc_scalar(Map)\n# \tWvc=get_Wvc_vector(Wvc_scalar)\n# \tzetac_vec=np.dot(Wvc.T,zeta_vec)\n# \tzetac=zetac_vec.reshape(Map.shape_pan_vect)\n# \tSurfGeo.plot(plot_normals=False)\n# \tSurfGeo.ax.scatter(zetac[0],zetac[1],zetac[2],zdir='z',s=6,c='b',marker='+')\n# \t# # way back - can't work\n# \t# zetav_vec=np.dot(Wvc,zetac_vec)\n# \t# zetav=zetav_vec.reshape(Map.shape_vert_vect)\n# \t# SurfGeo.ax.scatter(zetav[0],zetav[1],zetav[2],zdir='z',s=6,c='k',marker='+')\n# \t# plt.show()\n# \tplt.close('all')\n#\n#\n# \t# ---------------------------------------------------------------- Test wnv\n# \t# generate non-zero field of external force\n# \tu_ext=tsdata.u_ext[ss]\n# \tu_ext[0,:,:]=u_ext[0,:,:]-20.0\n# \tu_ext[1,:,:]=u_ext[1,:,:]+60.0\n# \tu_ext[2,:,:]=u_ext[2,:,:]+30.0\n# \tu_ext=u_ext+np.random.rand(*u_ext.shape)\n# \t# interpolate velocity at collocation points\n#\n# \t# compute normal velocity at panels\n# \twcv=get_panel_wcv(aM=0.5,aN=0.5)\n# \tu_norm=np.zeros((M,N))\n# \tfor mm in range(M):\n# \t\tfor nn in range(N):\n# \t\t\t# get velocity at panel corners\n# \t\t\tmpv=SurfGeo.maps.from_panel_to_vertices(mm,nn)\n# \t\t\tuc=np.zeros((3,))\n# \t\t\tfor vv in range(4):\n# \t\t\t\tuc=uc+wcv[vv]*u_ext[:,mpv[vv,0],mpv[vv,1]]\n# \t\t\tu_norm[mm,nn]=np.dot(uc,SurfGeo.normals[:,mm,nn])\n# \tu_norm_vec_ref=u_norm.reshape(-1,order='C')\n# \t# compute normal velocity through projection matrix\n# \tu_ext_vec=u_ext.reshape(-1,order='C')\n# \tWnv=get_Wnv_vector(SurfGeo)\n# \tu_norm_vec=np.dot(Wnv,u_ext_vec)\n#\n# \tassert np.max(np.abs(u_norm_vec-u_norm_vec_ref))<1e-12, 'Wnv not correct'\n" }, { "path": "sharpy/linear/src/lib_dbiot.py", "content": "\"\"\"Induced Velocity Derivatives\n\nCalculate derivatives of induced velocity.\n\nMethods:\n\n- eval_seg_exp and eval_seg_exp_loop: profide ders in format\n [Q_{x,y,z},ZetaPoint_{x,y,z}]\n and use fully-expanded analytical formula.\n- eval_panel_exp: iterates through whole panel\n\n- eval_seg_comp and eval_seg_comp_loop: profide ders in format\n [Q_{x,y,z},ZetaPoint_{x,y,z}]\n and use compact analytical formula.\n\"\"\"\n\nimport numpy as np\n\nfrom sharpy.aero.utils.uvlmlib import eval_panel_cpp\nimport sharpy.utils.algebra as algebra\nfrom sharpy.utils.constants import cfact_biot\n\n### looping through panels\nsvec = [0, 1, 2, 3] # seg. no.\n# avec =[ 0, 1, 2, 3] # 1st vertex no.\n# bvec =[ 1, 2, 3, 0] # 2nd vertex no.\nLoopPanel = [(0, 1), (1, 2), (2, 3), (3, 0)] # used in eval_panel_{exp/comp}\n\n\ndef eval_panel_cpp_coll(zetaP, ZetaPanel, vortex_radius, gamma_pan=1.0):\n DerP, DerVertices = eval_panel_cpp(zetaP, ZetaPanel, vortex_radius, gamma_pan)\n return DerP\n\n\ndef eval_seg_exp(ZetaP, ZetaA, ZetaB, vortex_radius, gamma_seg=1.0):\n \"\"\"\n Derivative of induced velocity Q w.r.t. collocation and segment coordinates\n in format:\n [ (ZetaP,ZetaA,ZetaB), (x,y,z) of Zeta, (x,y,z) of Q]\n\n Warning: function optimised for performance. Variables are scaled during the\n execution.\n \"\"\"\n\n DerP = np.zeros((3, 3))\n DerA = np.zeros((3, 3))\n DerB = np.zeros((3, 3))\n eval_seg_exp_loop(DerP, DerA, DerB, ZetaP, ZetaA, ZetaB, gamma_seg,\n vortex_radius)\n return DerP, DerA, DerB\n\n\ndef eval_seg_exp_loop(DerP, DerA, DerB, ZetaP, ZetaA, ZetaB, gamma_seg,\n vortex_radius):\n \"\"\"\n Derivative of induced velocity Q w.r.t. collocation (DerC) and segment\n coordinates in format.\n\n To optimise performance, the function requires the derivative terms to be\n pre-allocated and passed as input.\n\n Each Der* term returns derivatives in the format\n\n [ (x,y,z) of Zeta, (x,y,z) of Q]\n\n Warning: to optimise performance, variables are scaled during the execution.\n \"\"\"\n\n RA = ZetaP - ZetaA\n RB = ZetaP - ZetaB\n RAB = ZetaB - ZetaA\n Vcr = algebra.cross3(RA, RB)\n vcr2 = np.dot(Vcr, Vcr)\n\n # numerical radious\n vortex_radious_here = vortex_radius * algebra.norm3d(RAB)\n if vcr2 < vortex_radious_here ** 2:\n return\n\n # scaling\n ra1, rb1 = algebra.norm3d(RA), algebra.norm3d(RB)\n ra2, rb2 = ra1 ** 2, rb1 ** 2\n rainv = 1. / ra1\n rbinv = 1. / rb1\n ra_dir, rb_dir = RA * rainv, RB * rbinv\n ra3inv, rb3inv = rainv ** 3, rbinv ** 3\n Vcr = Vcr / vcr2\n\n diff_vec = ra_dir - rb_dir\n vdot_prod = np.dot(diff_vec, RAB)\n T2 = vdot_prod / vcr2\n\n # Extract components\n ra_x, ra_y, ra_z = RA\n rb_x, rb_y, rb_z = RB\n rab_x, rab_y, rab_z = RAB\n vcr_x, vcr_y, vcr_z = Vcr\n ra2_x, ra2_y, ra2_z = RA ** 2\n rb2_x, rb2_y, rb2_z = RB ** 2\n ra_vcr_x, ra_vcr_y, ra_vcr_z = 2. * algebra.cross3(RA, Vcr)\n rb_vcr_x, rb_vcr_y, rb_vcr_z = 2. * algebra.cross3(RB, Vcr)\n vcr_sca_x, vcr_sca_y, vcr_sca_z = Vcr * ra3inv\n vcr_scb_x, vcr_scb_y, vcr_scb_z = Vcr * rb3inv\n\n # # ### derivatives indices:\n # # # the 1st is the component of the vaiable w.r.t derivative are taken.\n # # # the 2nd is the component of the output\n dQ_dRA = np.array(\n [[-vdot_prod * rb_vcr_x * vcr_x + vcr_sca_x * (\n rab_x * (ra2 - ra2_x) - ra_x * ra_y * rab_y - ra_x * ra_z * rab_z),\n -T2 * rb_z - vdot_prod * rb_vcr_x * vcr_y + vcr_sca_y * (\n rab_x * (ra2 - ra2_x) - ra_x * ra_y * rab_y - ra_x * ra_z * rab_z),\n T2 * rb_y - vdot_prod * rb_vcr_x * vcr_z + vcr_sca_z * (\n rab_x * (ra2 - ra2_x) - ra_x * ra_y * rab_y - ra_x * ra_z * rab_z)],\n [T2 * rb_z - vdot_prod * rb_vcr_y * vcr_x + vcr_sca_x * (\n rab_y * (ra2 - ra2_y) - ra_x * ra_y * rab_x - ra_y * ra_z * rab_z),\n -vdot_prod * rb_vcr_y * vcr_y + vcr_sca_y * (\n rab_y * (ra2 - ra2_y) - ra_x * ra_y * rab_x - ra_y * ra_z * rab_z),\n -T2 * rb_x - vdot_prod * rb_vcr_y * vcr_z + vcr_sca_z * (\n rab_y * (ra2 - ra2_y) - ra_x * ra_y * rab_x - ra_y * ra_z * rab_z)],\n [-T2 * rb_y - vdot_prod * rb_vcr_z * vcr_x + vcr_sca_x * (\n rab_z * (ra2 - ra2_z) - ra_x * ra_z * rab_x - ra_y * ra_z * rab_y),\n T2 * rb_x - vdot_prod * rb_vcr_z * vcr_y + vcr_sca_y * (\n rab_z * (ra2 - ra2_z) - ra_x * ra_z * rab_x - ra_y * ra_z * rab_y),\n -vdot_prod * rb_vcr_z * vcr_z + vcr_sca_z * (\n rab_z * (ra2 - ra2_z) - ra_x * ra_z * rab_x - ra_y * ra_z * rab_y)]])\n\n dQ_dRB = np.array(\n [[vdot_prod * ra_vcr_x * vcr_x + vcr_scb_x * (\n rab_x * (-rb2 + rb2_x) + rab_y * rb_x * rb_y + rab_z * rb_x * rb_z),\n T2 * ra_z + vdot_prod * ra_vcr_x * vcr_y + vcr_scb_y * (\n rab_x * (-rb2 + rb2_x) + rab_y * rb_x * rb_y + rab_z * rb_x * rb_z),\n -T2 * ra_y + vdot_prod * ra_vcr_x * vcr_z + vcr_scb_z * (\n rab_x * (-rb2 + rb2_x) + rab_y * rb_x * rb_y + rab_z * rb_x * rb_z)],\n [-T2 * ra_z + vdot_prod * ra_vcr_y * vcr_x + vcr_scb_x * (\n rab_x * rb_x * rb_y + rab_y * (-rb2 + rb2_y) + rab_z * rb_y * rb_z),\n vdot_prod * ra_vcr_y * vcr_y + vcr_scb_y * (\n rab_x * rb_x * rb_y + rab_y * (-rb2 + rb2_y) + rab_z * rb_y * rb_z),\n T2 * ra_x + vdot_prod * ra_vcr_y * vcr_z + vcr_scb_z * (\n rab_x * rb_x * rb_y + rab_y * (-rb2 + rb2_y) + rab_z * rb_y * rb_z)],\n [T2 * ra_y + vdot_prod * ra_vcr_z * vcr_x + vcr_scb_x * (\n rab_x * rb_x * rb_z + rab_y * rb_y * rb_z + rab_z * (-rb2 + rb2_z)),\n -T2 * ra_x + vdot_prod * ra_vcr_z * vcr_y + vcr_scb_y * (\n rab_x * rb_x * rb_z + rab_y * rb_y * rb_z + rab_z * (-rb2 + rb2_z)),\n vdot_prod * ra_vcr_z * vcr_z + vcr_scb_z * (\n rab_x * rb_x * rb_z + rab_y * rb_y * rb_z + rab_z * (-rb2 + rb2_z))]])\n\n dQ_dRAB = np.array(\n [[vcr_x * diff_vec[0],\n vcr_y * diff_vec[0],\n vcr_z * diff_vec[0]],\n [vcr_x * diff_vec[1],\n vcr_y * diff_vec[1],\n vcr_z * diff_vec[1]],\n [vcr_x * diff_vec[2],\n vcr_y * diff_vec[2],\n vcr_z * diff_vec[2]]])\n\n DerP += (cfact_biot * gamma_seg) * (dQ_dRA + dQ_dRB).T # w.r.t. P\n DerA += (cfact_biot * gamma_seg) * (-dQ_dRAB - dQ_dRA).T # w.r.t. A\n DerB += (cfact_biot * gamma_seg) * (dQ_dRAB - dQ_dRB).T # w.r.t. B\n\n\ndef eval_panel_exp(zetaP, ZetaPanel, vortex_radius, gamma_pan=1.0):\n \"\"\"\n Computes derivatives of induced velocity w.r.t. coordinates of target point,\n zetaP, and panel coordinates. Returns two elements:\n - DerP: derivative of induced velocity w.r.t. ZetaP, with:\n DerP.shape=(3,3) : DerC[ Uind_{x,y,z}, ZetaC_{x,y,z} ]\n - DerVertices: derivative of induced velocity wrt panel vertices, with:\n DerVertices.shape=(4,3,3) :\n DerVertices[ vertex number {0,1,2,3}, Uind_{x,y,z}, ZetaC_{x,y,z} ]\n \"\"\"\n\n DerP = np.zeros((3, 3))\n DerVertices = np.zeros((4, 3, 3))\n\n for aa, bb in LoopPanel:\n eval_seg_exp_loop(DerP, DerVertices[aa, :, :], DerVertices[bb, :, :],\n zetaP, ZetaPanel[aa, :], ZetaPanel[bb, :], gamma_pan,\n vortex_radius)\n\n return DerP, DerVertices\n\n\n# ------------------------------------------------------------------------------\n#\tCompact Formula\n# ------------------------------------------------------------------------------\n\n\ndef Dvcross_by_skew3d(Dvcross, rv):\n \"\"\"\n Fast matrix multiplication of der(vcross)*skew(rv), where\n vcross = (rv x sv)/|rv x sv|^2\n The function exploits the property that the output matrix is symmetric.\n DvCross is a list containing the lower diagonal elements\n \"\"\"\n P = np.empty((3, 3))\n P[0, 0] = Dvcross[1][0] * rv[2] - Dvcross[2][0] * rv[1]\n P[0, 1] = Dvcross[2][0] * rv[0] - Dvcross[0][0] * rv[2]\n P[0, 2] = Dvcross[0][0] * rv[1] - Dvcross[1][0] * rv[0]\n #\n P[1, 0] = P[0, 1]\n P[1, 1] = Dvcross[2][1] * rv[0] - Dvcross[1][0] * rv[2]\n P[1, 2] = Dvcross[1][0] * rv[1] - Dvcross[1][1] * rv[0]\n #\n P[2, 0] = P[0, 2]\n P[2, 1] = P[1, 2]\n P[2, 2] = Dvcross[2][0] * rv[1] - Dvcross[2][1] * rv[0]\n return P\n\n\n# def Dvcross_by_skew3d(Dvcross,rv):\n# \t\"\"\"\n# \tFast matrix multiplication of der(vcross)*skew(rv), where\n# \t\tvcross = (rv x sv)/|rv x sv|^2\n# \tThe function exploits the property that the output matrix is symmetric.\n# \t\"\"\"\n# \tP=np.empty((3,3))\n# \tP[0,0]=Dvcross[0,1]*rv[2]-Dvcross[0,2]*rv[1]\n# \tP[0,1]=Dvcross[0,2]*rv[0]-Dvcross[0,0]*rv[2]\n# \tP[0,2]=Dvcross[0,0]*rv[1]-Dvcross[0,1]*rv[0]\n# \t#\n# \tP[1,0]=P[0,1]\n# \tP[1,1]=Dvcross[1,2]*rv[0]-Dvcross[0,1]*rv[2]\n# \tP[1,2]=Dvcross[0,1]*rv[1]-Dvcross[1,1]*rv[0]\n# \t#\n# \tP[2,0]=P[0,2]\n# \tP[2,1]=P[1,2]\n# \tP[2,2]=Dvcross[0,2]*rv[1]-Dvcross[1,2]*rv[0]\n# \treturn P\n\ndef der_runit(r, rinv, minus_rinv3):\n # alloc upper diag\n Der = np.empty((3, 3))\n Der[0, 0] = rinv + minus_rinv3 * r[0] ** 2\n Der[0, 1] = minus_rinv3 * r[0] * r[1]\n Der[0, 2] = minus_rinv3 * r[0] * r[2]\n Der[1, 1] = rinv + minus_rinv3 * r[1] ** 2\n Der[1, 2] = minus_rinv3 * r[1] * r[2]\n Der[2, 2] = rinv + minus_rinv3 * r[2] ** 2\n # alloc lower\n Der[1, 0] = Der[0, 1]\n Der[2, 0] = Der[0, 2]\n Der[2, 1] = Der[1, 2]\n return Der\n\n\ndef eval_seg_comp(ZetaP, ZetaA, ZetaB, vortex_radius, gamma_seg=1.0):\n DerP = np.zeros((3, 3))\n DerA = np.zeros((3, 3))\n DerB = np.zeros((3, 3))\n eval_seg_comp_loop(DerP, DerA, DerB, ZetaP, ZetaA, ZetaB, gamma_seg,\n vortex_radius)\n return DerP, DerA, DerB\n\n\ndef eval_seg_comp_loop(DerP, DerA, DerB, ZetaP, ZetaA, ZetaB, gamma_seg, vortex_radius):\n \"\"\"\n Derivative of induced velocity Q w.r.t. collocation and segment coordinates\n in format:\n [ (x,y,z) of Q, (x,y,z) of Zeta ]\n Warning: function optimised for performance. Variables are scaled during the\n execution.\n \"\"\"\n\n vortex_radius_sq = vortex_radius*vortex_radius\n Cfact = cfact_biot * gamma_seg\n\n RA = ZetaP - ZetaA\n RB = ZetaP - ZetaB\n RAB = ZetaB - ZetaA\n Vcr = algebra.cross3(RA, RB)\n vcr2 = np.dot(Vcr, Vcr)\n\n # numerical radious\n if vcr2 < (vortex_radius_sq * algebra.normsq3d(RAB)):\n return\n\n ### other constants\n ra1, rb1 = algebra.norm3d(RA), algebra.norm3d(RB)\n rainv = 1. / ra1\n rbinv = 1. / rb1\n Tv = RA * rainv - RB * rbinv\n dotprod = np.dot(RAB, Tv)\n\n ### --------------------------------------------- cross-product derivatives\n # lower triangular part only\n vcr2inv = 1. / vcr2\n vcr4inv = vcr2inv * vcr2inv\n diag_fact = Cfact * vcr2inv * dotprod\n off_fact = -2. * Cfact * vcr4inv * dotprod\n Dvcross = [\n [diag_fact + off_fact * Vcr[0] ** 2],\n [off_fact * Vcr[0] * Vcr[1], diag_fact + off_fact * Vcr[1] ** 2],\n [off_fact * Vcr[0] * Vcr[2], off_fact * Vcr[1] * Vcr[2], diag_fact + off_fact * Vcr[2] ** 2]]\n\n ### ------------------------------------------ difference terms derivatives\n Vsc = Vcr * vcr2inv * Cfact\n Ddiff = np.array([RAB * Vsc[0], RAB * Vsc[1], RAB * Vsc[2]])\n dQ_dRAB = np.array([Tv * Vsc[0], Tv * Vsc[1], Tv * Vsc[2]])\n\n ### ---------------------------------------------- Final assembly (crucial)\n # ps: calling Dvcross_by_skew3d does not slow down execution.\n\n dQ_dRA = Dvcross_by_skew3d(Dvcross, -RB) \\\n + np.dot(Ddiff, der_runit(RA, rainv, -rainv ** 3))\n dQ_dRB = Dvcross_by_skew3d(Dvcross, RA) \\\n - np.dot(Ddiff, der_runit(RB, rbinv, -rbinv ** 3))\n\n DerP += dQ_dRA + dQ_dRB # w.r.t. P\n DerA -= dQ_dRAB + dQ_dRA # w.r.t. A\n DerB += dQ_dRAB - dQ_dRB # w.r.t. B\n\n\n# ### collocation point only\n# DerP +=Dvcross_by_skew3d(Dvcross,RA-RB)+np.dot(Ddiff,\n# \t\t der_runit(RA,rainv,minus_rainv3)-der_runit(RB,rbinv,minus_rbinv3))\n\n\ndef eval_panel_comp(zetaP, ZetaPanel, vortex_radius, gamma_pan=1.0):\n \"\"\"\n Computes derivatives of induced velocity w.r.t. coordinates of target point,\n zetaP, and panel coordinates. Returns two elements:\n - DerP: derivative of induced velocity w.r.t. ZetaP, with:\n DerP.shape=(3,3) : DerC[ Uind_{x,y,z}, ZetaC_{x,y,z} ]\n - DerVertices: derivative of induced velocity wrt panel vertices, with:\n DerVertices.shape=(4,3,3) :\n DerVertices[ vertex number {0,1,2,3}, Uind_{x,y,z}, ZetaC_{x,y,z} ]\n \"\"\"\n\n DerP = np.zeros((3, 3))\n DerVertices = np.zeros((4, 3, 3))\n\n for aa, bb in LoopPanel:\n eval_seg_comp_loop(DerP, DerVertices[aa, :, :], DerVertices[bb, :, :],\n zetaP, ZetaPanel[aa, :], ZetaPanel[bb, :], gamma_pan,\n vortex_radius)\n\n return DerP, DerVertices\n\n\ndef eval_panel_fast(zetaP, ZetaPanel, vortex_radius, gamma_pan=1.0):\n \"\"\"\n Computes derivatives of induced velocity w.r.t. coordinates of target point,\n zetaP, and panel coordinates. Returns two elements:\n - DerP: derivative of induced velocity w.r.t. ZetaP, with:\n DerP.shape=(3,3) : DerC[ Uind_{x,y,z}, ZetaC_{x,y,z} ]\n - DerVertices: derivative of induced velocity wrt panel vertices, with:\n DerVertices.shape=(4,3,3) :\n DerVertices[ vertex number {0,1,2,3}, Uind_{x,y,z}, ZetaC_{x,y,z} ]\n\n The function is based on eval_panel_comp, but minimises operationsby\n recycling variables.\n \"\"\"\n\n vortex_radius_sq = vortex_radius*vortex_radius\n DerP = np.zeros((3, 3))\n DerVertices = np.zeros((4, 3, 3))\n\n ### ---------------------------------------------- Compute common variables\n # these are constants or variables depending only on vertices and P coords\n Cfact = cfact_biot * gamma_pan\n\n # distance vertex ii-th from P\n R_list = zetaP - ZetaPanel\n r1_list = [algebra.norm3d(R_list[ii]) for ii in svec]\n r1inv_list = [1. / r1_list[ii] for ii in svec]\n Runit_list = [R_list[ii] * r1inv_list[ii] for ii in svec]\n Der_runit_list = [\n der_runit(R_list[ii], r1inv_list[ii], -r1inv_list[ii] ** 3) for ii in svec]\n\n ### ------------------------------------------------- Loop through segments\n for aa, bb in LoopPanel:\n\n RAB = ZetaPanel[bb, :] - ZetaPanel[aa, :] # segment vector\n Vcr = algebra.cross3(R_list[aa], R_list[bb])\n vcr2 = np.dot(Vcr, Vcr)\n\n if vcr2 < (vortex_radius_sq * algebra.normsq3d(RAB)):\n continue\n\n Tv = Runit_list[aa] - Runit_list[bb]\n dotprod = np.dot(RAB, Tv)\n\n ### ----------------------------------------- cross-product derivatives\n # lower triangular part only\n vcr2inv = 1. / vcr2\n vcr4inv = vcr2inv * vcr2inv\n diag_fact = Cfact * vcr2inv * dotprod\n off_fact = -2. * Cfact * vcr4inv * dotprod\n Dvcross = [\n [diag_fact + off_fact * Vcr[0] ** 2],\n [off_fact * Vcr[0] * Vcr[1], diag_fact + off_fact * Vcr[1] ** 2],\n [off_fact * Vcr[0] * Vcr[2], off_fact * Vcr[1] * Vcr[2], diag_fact + off_fact * Vcr[2] ** 2]]\n\n ### ---------------------------------------- difference term derivative\n Vsc = Vcr * vcr2inv * Cfact\n Ddiff = np.array([RAB * Vsc[0], RAB * Vsc[1], RAB * Vsc[2]])\n\n ### ---------------------------------------------------- RAB derivative\n dQ_dRAB = np.array([Tv * Vsc[0], Tv * Vsc[1], Tv * Vsc[2]])\n\n ### ------------------------------------------ Final assembly (crucial)\n\n dQ_dRA = Dvcross_by_skew3d(Dvcross, -R_list[bb]) \\\n + np.dot(Ddiff, Der_runit_list[aa])\n dQ_dRB = Dvcross_by_skew3d(Dvcross, R_list[aa]) \\\n - np.dot(Ddiff, Der_runit_list[bb])\n\n DerP += dQ_dRA + dQ_dRB # w.r.t. P\n DerVertices[aa, :, :] -= dQ_dRAB + dQ_dRA # w.r.t. A\n DerVertices[bb, :, :] += dQ_dRAB - dQ_dRB # w.r.t. B\n\n # ### collocation point only\n # DerP +=Dvcross_by_skew3d(Dvcross,RA-RB)+np.dot(Ddiff,\n # \t\t der_runit(RA,rainv,minus_rainv3)-der_runit(RB,rbinv,minus_rbinv3))\n\n return DerP, DerVertices\n\n\ndef eval_panel_fast_coll(zetaP, ZetaPanel, vortex_radius, gamma_pan=1.0):\n \"\"\"\n Computes derivatives of induced velocity w.r.t. coordinates of target point,\n zetaP, coordinates. Returns two elements:\n - DerP: derivative of induced velocity w.r.t. ZetaP, with:\n DerP.shape=(3,3) : DerC[ Uind_{x,y,z}, ZetaC_{x,y,z} ]\n\n The function is based on eval_panel_fast, but does not perform operations\n required to compute the derivatives w.r.t. the panel coordinates.\n \"\"\"\n\n vortex_radius_sq = vortex_radius*vortex_radius\n DerP = np.zeros((3, 3))\n\n ### ---------------------------------------------- Compute common variables\n # these are constants or variables depending only on vertices and P coords\n Cfact = cfact_biot * gamma_pan\n\n # distance vertex ii-th from P\n R_list = zetaP - ZetaPanel\n r1_list = [algebra.norm3d(R_list[ii]) for ii in svec]\n r1inv_list = [1. / r1_list[ii] for ii in svec]\n Runit_list = [R_list[ii] * r1inv_list[ii] for ii in svec]\n Der_runit_list = [\n der_runit(R_list[ii], r1inv_list[ii], -r1inv_list[ii] ** 3) for ii in svec]\n\n ### ------------------------------------------------- Loop through segments\n for aa, bb in LoopPanel:\n\n RAB = ZetaPanel[bb, :] - ZetaPanel[aa, :] # segment vector\n Vcr = algebra.cross3(R_list[aa], R_list[bb])\n vcr2 = np.dot(Vcr, Vcr)\n\n if vcr2 < (vortex_radius_sq * algebra.normsq3d(RAB)):\n continue\n\n Tv = Runit_list[aa] - Runit_list[bb]\n dotprod = np.dot(RAB, Tv)\n\n ### ----------------------------------------- cross-product derivatives\n # lower triangular part only\n vcr2inv = 1. / vcr2\n vcr4inv = vcr2inv * vcr2inv\n diag_fact = Cfact * vcr2inv * dotprod\n off_fact = -2. * Cfact * vcr4inv * dotprod\n Dvcross = [\n [diag_fact + off_fact * Vcr[0] ** 2],\n [off_fact * Vcr[0] * Vcr[1], diag_fact + off_fact * Vcr[1] ** 2],\n [off_fact * Vcr[0] * Vcr[2], off_fact * Vcr[1] * Vcr[2], diag_fact + off_fact * Vcr[2] ** 2]]\n\n ### ---------------------------------------- difference term derivative\n Vsc = Vcr * vcr2inv * Cfact\n Ddiff = np.array([RAB * Vsc[0], RAB * Vsc[1], RAB * Vsc[2]])\n\n ### ------------------------------------------ Final assembly (crucial)\n\n # dQ_dRA=Dvcross_by_skew3d(Dvcross,-R_list[bb])\\\n # \t\t\t\t\t\t\t\t\t +np.dot(Ddiff, Der_runit_list[aa] )\n # dQ_dRB=Dvcross_by_skew3d(Dvcross, R_list[aa])\\\n # \t\t\t\t\t\t\t\t\t -np.dot(Ddiff, Der_runit_list[bb] )\n\n DerP += Dvcross_by_skew3d(Dvcross, RAB) + \\\n +np.dot(Ddiff, Der_runit_list[aa] - Der_runit_list[bb])\n\n return DerP\n\n\nif __name__ == '__main__':\n\n import cProfile\n\n ### verify consistency amongst models\n gamma = 4.\n zetaP = np.array([3.0, 5.5, 2.0])\n zeta0 = np.array([1.0, 3.0, 0.9])\n zeta1 = np.array([5.0, 3.1, 1.9])\n zeta2 = np.array([4.8, 8.1, 2.5])\n zeta3 = np.array([0.9, 7.9, 1.7])\n ZetaPanel = np.array([zeta0, zeta1, zeta2, zeta3])\n zetap = 0.3 * zeta1 + 0.7 * zeta2\n\n # ZetaPanel=np.array([[ 1.221, -0.064, -0.085],\n # \t\t\t\t[ 1.826, -0.064, -0.141],\n # \t\t\t\t[ 1.933, 1.456, -0.142],\n # \t\t\t\t[ 1.327, 1.456, -0.087]])\n # zetaP=np.array([-0.243, 0.776, 0.037])\n\n ### verify model consistency\n DPcpp, DVcpp = eval_panel_cpp(zetaP, ZetaPanel, 1e-6, gamma_pan=gamma) # vortex_radius\n DPexp, DVexp = eval_panel_exp(zetaP, ZetaPanel, gamma_pan=gamma)\n DPcomp, DVcomp = eval_panel_comp(zetaP, ZetaPanel, gamma_pan=gamma)\n DPfast, DVfast = eval_panel_fast(zetaP, ZetaPanel,\n vortex_radius, gamma_pan=gamma)\n DPfast_coll = eval_panel_fast_coll(zetaP, ZetaPanel,\n vortex_radius, gamma_pan=gamma)\n\n ermax = max(np.max(np.abs(DPcpp - DPexp)), np.max(np.abs(DVcpp - DVexp)))\n assert ermax < 1e-15, 'eval_panel_cpp not matching with eval_panel_exp'\n ermax = max(np.max(np.abs(DPcomp - DPexp)), np.max(np.abs(DVcomp - DVexp)))\n assert ermax < 1e-15, 'eval_panel_comp not matching with eval_panel_exp'\n ermax = max(np.max(np.abs(DPfast - DPexp)), np.max(np.abs(DVfast - DVexp)))\n assert ermax < 1e-15, 'eval_panel_fast not matching with eval_panel_exp'\n ermax = np.max(np.abs(DPfast_coll - DPexp))\n assert ermax < 1e-15, 'eval_panel_fast_coll not matching with eval_panel_exp'\n\n\n ### profiling\n\n def run_eval_panel_cpp():\n for ii in range(10000):\n eval_panel_cpp(zetaP, ZetaPanel, 1e-6, gamma_pan=3.) # vortex_radius\n\n\n def run_eval_panel_fast(vortex_radius=vortex_radius_def):\n for ii in range(10000):\n eval_panel_fast(zetaP, ZetaPanel,\n vortex_radius, gamma_pan=3.)\n\n\n def run_eval_panel_fast_coll(vortex_radius=vortex_radius_def):\n for ii in range(10000):\n eval_panel_fast_coll(zetaP, ZetaPanel,\n vortex_radius, gamma_pan=3.)\n\n\n def run_eval_panel_comp():\n for ii in range(10000):\n eval_panel_comp(zetaP, ZetaPanel, gamma_pan=3.)\n\n\n def run_eval_panel_exp():\n for ii in range(10000):\n eval_panel_exp(zetaP, ZetaPanel, gamma_pan=3.)\n\n\n print('------------------------------------------ profiling eval_panel_cpp')\n cProfile.runctx('run_eval_panel_cpp()', globals(), locals())\n\n print('----------------------------------------- profiling eval_panel_fast')\n cProfile.runctx('run_eval_panel_fast()', globals(), locals())\n\n print('------------------------------------ profiling eval_panel_fast_coll')\n cProfile.runctx('run_eval_panel_fast_coll()', globals(), locals())\n\n print('----------------------------------------- profiling eval_panel_comp')\n cProfile.runctx('run_eval_panel_comp()', globals(), locals())\n\n print('------------------------------------------ profiling eval_panel_exp')\n cProfile.runctx('run_eval_panel_exp()', globals(), locals())\n" }, { "path": "sharpy/linear/src/lib_ucdncdzeta.py", "content": "r\"\"\"Induced Velocity Derivatives with respect to Panel Normal\n\nCalculate derivative of\n\n .. math:: \\boldsymbol{u}_c\\frac{\\partial\\boldsymbol{n}_c}{\\partial\\boldsymbol{zeta}}\n\nwith respect to local panel coordinates.\n\"\"\"\n\nimport numpy as np\nimport sharpy.utils.algebra as algebra\n\ndR_dZeta = np.array(\n [[[[-1, 0, 0], [0, 0, 0]], [[0, -1, 0], [0, 0, 0]], [[0, 0, -1], [0, 0, 0]]],\n [[[0, 0, 0], [-1, 0, 0]], [[0, 0, 0], [0, -1, 0]], [[0, 0, 0], [0, 0, -1]]],\n [[[1, 0, 0], [0, 0, 0]], [[0, 1, 0], [0, 0, 0]], [[0, 0, 1], [0, 0, 0]]],\n [[[0, 0, 0], [1, 0, 0]], [[0, 0, 0], [0, 1, 0]], [[0, 0, 0], [0, 0, 1]]]])\n\n\ndef eval(Zeta00, Zeta01, Zeta02, Zeta03, Uc):\n \"\"\"\n Returns a 4 x 3 array, containing the derivative of Wnc*Uc w.r.t the panel\n vertices coordinates.\n \"\"\"\n\n R02 = Zeta02 - Zeta00\n R13 = Zeta03 - Zeta01\n\n crR02R13 = algebra.cross3(R02, R13)\n norm_crR02R13 = np.linalg.norm(crR02R13)\n cub_crR02R13 = norm_crR02R13 ** 3\n\n Acr = algebra.cross3(crR02R13, R13)\n Bcr = algebra.cross3(crR02R13, R02)\n Cdot = np.dot(crR02R13, Uc)\n\n uc_x, uc_y, uc_z = Uc\n r02_x, r02_y, r02_z = R02\n r13_x, r13_y, r13_z = R13\n crR13Uc_x, crR13Uc_y, crR13Uc_z = algebra.cross3(R13, Uc)\n crR02Uc_x, crR02Uc_y, crR02Uc_z = algebra.cross3(R02, Uc)\n crR02R13_x, crR02R13_y, crR02R13_z = crR02R13\n Acr_x, Acr_y, Acr_z = Acr\n Bcr_x, Bcr_y, Bcr_z = Bcr\n\n # dUnorm_dR.shape=(2,3)\n dUnorm_dR = np.array(\n [[Acr_x * Cdot / cub_crR02R13 + crR13Uc_x / norm_crR02R13,\n Acr_y * Cdot / cub_crR02R13 + crR13Uc_y / norm_crR02R13,\n Acr_z * Cdot / cub_crR02R13 + crR13Uc_z / norm_crR02R13],\n [-Bcr_x * Cdot / cub_crR02R13 - crR02Uc_x / norm_crR02R13,\n -Bcr_y * Cdot / cub_crR02R13 - crR02Uc_y / norm_crR02R13,\n -Bcr_z * Cdot / cub_crR02R13 - crR02Uc_z / norm_crR02R13]])\n\n # Allocate\n dUnorm_dZeta = np.zeros((4, 3))\n for vv in range(4): # loop through panel vertices\n for cc_zeta in range(3): # loop panel vertices component\n for rr in range(2): # loop segments R02, R13\n for cc_rvec in range(3): # loop segment component\n dUnorm_dZeta[vv, cc_zeta] += \\\n dUnorm_dR[rr, cc_rvec] * dR_dZeta[vv, cc_zeta, rr, cc_rvec]\n\n return dUnorm_dZeta\n\n\nif __name__ == '__main__':\n\n # calculate normal\n def get_panel_normal(zetav_here):\n \"\"\"From Surface.AeroGridSurface\"\"\"\n r02 = zetav_here[2, :] - zetav_here[0, :]\n r13 = zetav_here[3, :] - zetav_here[1, :]\n nvec = np.cross(r02, r13)\n nvec = nvec / np.linalg.norm(nvec)\n return nvec\n\n\n # define panel vertices\n zeta00 = np.array([1.0, 0.2, 1.0])\n zeta01 = np.array([3.9, 0.1, 0.8])\n zeta02 = np.array([4.0, 3.5, 0.9])\n zeta03 = np.array([1.2, 3.2, 1.1])\n zeta_panel = np.array([zeta00, zeta01, zeta02, zeta03])\n\n # reference normal\n nvec0 = get_panel_normal(zeta_panel)\n\n # reference normal velocity\n ucoll = np.array([2, 6, 3])\n unorm0 = np.dot(nvec0, ucoll)\n\n # analytical derivative\n dUnorm_dZeta = eval(zeta00, zeta01, zeta02, zeta03, ucoll)\n\n # numerical derivative\n Dnum = np.zeros((4, 3))\n step = 1e-6\n for ii in range(4):\n for jj in range(3):\n delta = np.zeros((4, 3))\n delta[ii, jj] = step\n nvec_pert = get_panel_normal(zeta_panel + delta)\n unorm_pert = np.dot(nvec_pert, ucoll)\n Dnum[ii, jj] = (unorm_pert - unorm0) / step\n\n assert np.max(np.abs(dUnorm_dZeta - Dnum)) < step, 'Derivative not accurate!'\n" }, { "path": "sharpy/linear/src/libfit.py", "content": "\"\"\"Fitting Tools Library\n\n@author: Salvatore Maraniello\n\n@date: 15 Jan 2018\n\"\"\"\n\nimport warnings\nimport numpy as np\nfrom scipy.signal import tf2ss\nimport scipy.linalg as scalg\nimport scipy.optimize as scopt\nimport multiprocessing as mpr\nimport itertools\n\n\ndef fpoly(kv, B0, B1, B2, dyv, ddyv):\n return B0 + B1 * dyv + B2 * ddyv\n\n\ndef fpade(kv, Cv, B0, B1a, B1b, B2, dyv, ddyv):\n # evaluate transfer function from unsteady function Cv\n return B0 * Cv + (B1a * Cv + B1b) * dyv + B2 * ddyv\n\n\ndef getC(kv, Yv, B0, B1a, B1b, B2, dyv, ddyv):\n # evaluate unsteady function C required to perfectly match Yv\n Den = B0 + B1a * dyv\n # kkvec=np.abs(Den)<1e-8\n C = (Yv - B1b * dyv - B2 * ddyv) / Den\n # C[kkvec]=1.0\n # if np.sum(kkvec)>0: embed()\n return C\n\n\ndef rfa(cnum, cden, kv, ds=None):\n \"\"\"\n Evaluates over the frequency range kv.the rational function approximation:\n [cnum[-1] + cnum[-2] z + ... + cnum[0] z**Nnum ]/...\n [cden[-1] + cden[-2] z + ... + cden[0] z**Nden]\n where the numerator and denominator polynomial orders, Nnum and Nden, are\n the length of the cnum and cden arrays and:\n - z=exp(1.j*kv*ds), with ds sampling time if ds is given (discrete-time\n system)\n - z=1.*kv, if ds is None (continuous time system)\n \"\"\"\n\n if ds == None:\n # continuous-time LTI system\n zv = 1.j * kv\n else:\n # discrete-time LTI system\n zv = np.exp(1.j * kv * ds)\n\n return np.polyval(cnum, zv) / np.polyval(cden, zv)\n\n\ndef rfader(cnum, cden, kv, m=1, ds=None):\n \"\"\"\n Evaluates over the frequency range kv.the derivative of order m of the\n rational function approximation:\n [cnum[-1] + cnum[-2] z + ... + cnum[0] z**Nnum ]/...\n [cden[-1] + cden[-2] z + ... + cden[0] z**Nden]\n where the numerator and denominator polynomial orders, Nnum and Nden, are\n the length of the cnum and cden arrays and:\n - z=exp(1.j*kv*ds), with ds sampling time if ds is given (discrete-time\n system)\n - z=1.*kv, if ds is None (continuous time system)\n \"\"\"\n\n if ds == None:\n # continuous-time LTI system\n zv = 1.j * kv\n dzv = 1.j\n raise NameError('Never tested for continuous systems!')\n else:\n # discrete-time LTI system\n zv = np.exp(1.j * kv * ds)\n dzv = 1.j * ds * zv\n\n Nv = np.polyval(cnum, zv)\n Dv = np.polyval(cden, zv)\n dNv = np.polyval(np.polyder(cnum), zv)\n dDv = np.polyval(np.polyder(cden), zv)\n\n return dzv * (dNv * Dv - Nv * dDv) / Dv ** 2\n\n\ndef fitfrd(kv, yv, N, dt=None, mag=0, eng=None):\n \"\"\"\n Wrapper for fitfrd (mag=0) and fitfrdmag (mag=1) functions in continuous and\n discrete time (if ds in input).\n Input:\n kv,yv: frequency array and frequency response\n N: order for rational function approximation\n mag=1,0: Flag for determining method to use\n dt (optional): sampling time for DLTI systems\n \"\"\"\n\n raise NameError('Please use fitfrd function in matwrapper module!')\n\n return None\n\n\ndef get_rfa_res(xv, kv, Yv, Nnum, Nden, ds=None):\n \"\"\"\n Returns magnitude of the residual Yfit-Yv of a RFA approximation at each\n point kv. The coefficients of the approximations are:\n - cnum=xv[:Nnum]\n - cdem=xv[Nnum:]\n where cnum and cden are as per the 'rfa' function.\n \"\"\"\n\n assert Nnum + Nden == len(xv), 'Nnum+Nden must be equal to len(xv)!'\n cnum = xv[:Nnum]\n cden = xv[Nnum:]\n\n Yfit = rfa(cnum, cden, kv, ds)\n\n return np.abs(Yfit - Yv)\n\n\ndef get_rfa_res_norm(xv, kv, Yv, Nnum, Nden, ds=None, method='mix'):\n \"\"\"\n Define residual scalar norm of Pade approximation of coefficients\n cnum=xv[:Nnum] and cden[Nnum:] (see get_rfa_res and rfa function) and\n time-step ds (if discrete time).\n \"\"\"\n\n ErvAbs = get_rfa_res(xv, kv, Yv, Nnum, Nden, ds)\n\n if method == 'H2':\n res = np.sum(ErvAbs ** 2)\n elif method == 'Hinf':\n res = np.max(ErvAbs)\n elif method == 'mix':\n res = np.sum(ErvAbs ** 2) + np.max(ErvAbs)\n\n return res\n\n\ndef rfa_fit_dev(kv, Yv, Nnum, Nden, TolAbs, ds=None, Stability=True,\n NtrialMax=10, Cfbound=1e2, OutFull=False, Print=False):\n \"\"\"\n Find best fitting RFA approximation from frequency response Yv over the\n frequency range kv for both continuous (ds=None) and discrete (ds>0) LTI\n systems.\n\n The RFA approximation is found through a 2-stage strategy:\n a. an evolutionary algoryhtm is run to determine the optimal fitting\n coefficients\n b. the search is refined through a least squares algorithm.\n and is stopped as soon as:\n 1. the maximum absolute error in frequency response of the RFA falls\n below ``TolAbs``\n 2. the maximum number of iterations is reached.\n\n\n Input:\n - kv: frequency range for approximation\n - Yv: frequency response vector over kv\n - TolAbs: maximum admissible absolute difference in frequency response\n between RFA and original system.\n - Nnum,Ndem: number of coefficients for Pade approximation.\n - ds: sampling time for DLTI systems\n - NtrialMax: maximum number of repetition of global and least square optimisations\n - Cfbouds: maximum absolute values of coeffieicnts (only for evolutionary\n algorithm)\n - OutFull: if False, only outputs optimal coefficients of RFA. Otherwise,\n outputs cost and RFA coefficients of each trial.\n\n Output:\n - cnopt: optimal coefficients (numerator)\n - cdopt: optimal coefficients (denominator)\n\n Important:\n - this function has the same objective as fitfrd in matwrapper module. While\n generally slower, the global optimisation approach allows to verify the\n results from fitfrd.\n \"\"\"\n\n def pen_max_eig(cdvec):\n \"\"\"\n Computes maximum eigenvalues from denominator coefficients of RFA and\n evaluates a log barrier that ensures\n \"\"\"\n eigs = np.roots(cdvec)\n eigmax = np.max(np.abs(eigs))\n\n eiglim = 0.999\n pen = 0.\n Fact = 1e3 * TolAbs / np.log(2)\n if eigmax > eiglim:\n pen = Fact * np.log((eigmax + 1. - 2. * eiglim) / (1. - eiglim))\n else:\n pen = 0.\n return pen\n\n if Stability:\n def fcost_dev(xv, kv, Yv, Nnum, Nden, ds, method):\n \"\"\"\n xv is a vector such that the coeff:\n cnum=xv[:Nnum]\n cden=xv[Nnum:]\n \"\"\"\n xvpass = np.concatenate((xv, np.array([1, ])))\n error_fit = get_rfa_res_norm(xvpass, kv, Yv, Nnum, Nden, ds, method)\n pen_stab = pen_max_eig(xvpass[Nnum:])\n return error_fit + pen_stab\n\n def fcost_lsq(xv, kv, Yv, Nnum, Nden, ds):\n\n xvpass = np.concatenate((xv, np.array([1, ])))\n res_fit = get_rfa_res(xvpass, kv, Yv, Nnum, Nden, ds)\n pen_stab = pen_max_eig(xvpass[Nnum:])\n return res_fit + pen_stab\n\n else:\n def fcost_dev(xv, kv, Yv, Nnum, Nden, ds, method):\n \"\"\"\n xv is a vector such that the coeff:\n cnum=xv[:Nnum]\n cden=xv[Nnum:]\n \"\"\"\n xvpass = np.concatenate((xv, np.array([1, ])))\n return get_rfa_res_norm(xvpass, kv, Yv, Nnum, Nden, ds, method)\n\n def fcost_lsq(xv, kv, Yv, Nnum, Nden, ds):\n xvpass = np.concatenate((xv, np.array([1, ])))\n return get_rfa_res(xvpass, kv, Yv, Nnum, Nden, ds)\n\n Nx = Nnum + Nden - 1\n\n # List of optimal solutions found by the evolutionary and least squares\n # algorithms\n XvOptDev, XvOptLsq = [], []\n Cdev, Clsq = [], []\n\n tt = 0\n cost_best = 1e32\n\n while cost_best > TolAbs and tt < NtrialMax:\n tt += 1\n\n ### Evolutionary algorithm\n res = scopt.differential_evolution( # popsize=100,\n strategy='best1bin',\n func=fcost_dev,\n args=(kv, Yv, Nnum, Nden, ds, 'Hinf'),\n bounds=Nx * ((-Cfbound, Cfbound),))\n xvdev = res.x\n cost_dev = fcost_dev(xvdev, kv, Yv, Nnum, Nden, ds, 'Hinf')\n\n # is this the best solution?\n if cost_dev < cost_best:\n cost_best = cost_dev\n xvopt = xvdev\n\n # store this solution\n if OutFull:\n XvOptDev.append(xvdev)\n Cdev.append(cost_dev)\n\n ### Least squares fitting - unbounded\n # method only local, but do not move to the end of global search: best\n # results can be found even when starting from a \"worse\" solution\n xvlsq = scopt.leastsq(fcost_lsq, x0=xvdev, args=(kv, Yv, Nnum, Nden, ds))[0]\n cost_lsq = fcost_dev(xvlsq, kv, Yv, Nnum, Nden, ds, 'Hinf')\n\n # is this the best solution?\n if cost_lsq < cost_best:\n cost_best = cost_lsq\n xvopt = xvlsq\n\n # store this solution\n if OutFull:\n XvOptLsq.append(xvlsq)\n Clsq.append(cost_lsq)\n\n ### Print and move on\n if Print:\n print('Trial %.2d: cost dev: %.3e, cost lsq: %.3e' \\\n % (tt, cost_dev, cost_lsq))\n\n if cost_best > TolAbs:\n warnings.warn(\n 'RFA error (%.2e) greater than specified tolerance (%.2e)!' \\\n % (cost_best, TolAbs))\n\n ### add 1 to denominator\n cnopt = xvopt[:Nnum]\n cdopt = np.hstack([xvopt[Nnum:], 1.])\n # if np.abs(cdopt[-1])>1e-2:\n # \tcdscale=cdopt[-1]\n # else:\n # \tcdscale=1.0\n # cnopt=cnopt/cdscale\n # cdopt=cdopt/cdscale\n\n # determine outputs\n Outputs = (cnopt, cdopt)\n if OutFull:\n for tt in range(Ntrial):\n if np.abs(XvOptDev[tt][-1]) > 1e-2:\n XvOptDev[tt] = XvOptDev[tt] / XvOptDev[tt][-1]\n if np.abs(XvOptLsq[tt][-1]) > 1e-2:\n XvOptLsq[tt] = XvOptLsq[tt] / XvOptLsq[tt][-1]\n Outputs = Outputs + (XvOptDev, XvOptLsq, Cdev, Clsq)\n\n return Outputs\n\n\ndef poly_fit(kv, Yv, dyv, ddyv, method='leastsq', Bup=None):\n \"\"\"\n Find best II order fitting polynomial from frequency response Yv over the\n frequency range kv for both continuous (ds=None) and discrete (ds>0) LTI\n systems.\n\n Input:\n - kv: frequency points\n - Yv: frequency response\n - dyv,ddyv: frequency responses of I and II order derivatives\n - method='leastsq','dev': algorithm for minimisation\n - Bup (only 'dev' method): bounds for bv coefficients as per\n scipy.optimize.differential_evolution. This is a length 3 array.\n\n Important:\n - this function attributes equal weight to each data-point!\n \"\"\"\n\n if method == 'leastsq':\n # pointwise residual\n def funRes(bv, kv, Yv, dyv, ddyv):\n B0, B1, B2 = bv\n rv = fpoly(kv, B0, B1, B2, dyv, ddyv) - Yv\n return np.concatenate((rv.real, rv.imag))\n\n # solve\n bvopt, cost = scopt.leastsq(funRes, x0=[0., 0., 0.], args=(kv, Yv, dyv, ddyv))\n\n\n elif method == 'dev':\n # use genetic algorithm with objective a sum of H2 and Hinf norms of\n # residual\n def funRes(bv, kv, Yv, dyv, ddyv):\n\n B0, B1, B2 = bv\n rv = fpoly(kv, B0, B1, B2, dyv, ddyv) - Yv\n\n Nk = len(kv)\n rvsq = rv * rv.conj()\n # H2norm=np.sqrt(np.trapz(rvsq/(Nk-1.)))\n # return H2norm+np.linalg.norm(rv,np.inf)\n return np.sum(rvsq)\n\n # prepare bounds\n if Bup is None:\n Bounds = 3 * ((-Bup, Bup),)\n else:\n assert len(Bup) == 3, 'Bup must be a length 3 list/array'\n Bounds = ((-Bup[0], Bup[0]), (-Bup[1], Bup[1]), (-Bup[2], Bup[2]),)\n\n res = scopt.differential_evolution(\n func=funRes, args=(kv, Yv, dyv, ddyv), strategy='best1bin', bounds=Bounds)\n bvopt = res.x\n cost = funRes(bvopt, kv, Yv, dyv, ddyv)\n\n return bvopt, cost\n\n\ndef rfa_mimo(Yfull, kv, ds, tolAbs, Nnum, Nden, Dmatrix=None, NtrialMax=6, Ncpu=4, method='independent'):\n \"\"\"\n Given the frequency response of a MIMO DLTI system, this function returns\n the A,B,C,D matrices associated to the rational function approximation of\n the original system.\n\n Input:\n - Yfull: frequency response (as per libss.freqresp) of full size system over\n the frequencies kv.\n - kv: array of frequencies over which the RFA approximation is evaluated.\n - tolAbs: absolute tolerance for the rfa fitting\n - Nnum: number of numerator coefficients for RFA\n - Nden: number of denominator coefficients for RFA\n - NtrialMax: maximum number of attempts\n - method=['intependent']. Method used to produce the system:\n - intependent: each input-output combination is treated separately. The\n resulting system is a collection of independent SISO DLTIs\n\n \"\"\"\n\n Nout, Nin, Nk = Yfull.shape\n assert Nk == len(kv), 'Frequency response Yfull not compatible with frequency range kv'\n\n iivec = range(Nin)\n oovec = range(Nout)\n plist = list(itertools.product(oovec, iivec))\n\n args_const = (Nnum, Nden, tolAbs, ds, True, NtrialMax, 1e2, False, False)\n\n with mpr.Pool(Ncpu) as pool:\n\n if Dmatrix is None:\n P = [pool.apply_async(rfa_fit_dev,\n args=(kv, Yfull[oo, ii, :],) + args_const) for oo, ii in plist]\n else:\n P = [pool.apply_async(rfa_fit_dev,\n args=(kv, Yfull[oo, ii, :] - Dmatrix[oo, ii],) + args_const) for oo, ii in plist]\n R = [pp.get() for pp in P]\n\n Asub = []\n Bsub = []\n Csub = []\n Dsub = []\n for oo in range(Nout):\n Ainner = []\n Binner = []\n Cinner = []\n Dinner = []\n for ii in range(Nin):\n # get coeffs\n pp = Nin * oo + ii\n cnopt, cdopt = R[pp]\n # assert plist[pp]==(oo,ii), 'Something wrong in loop'\n\n A, B, C, D = tf2ss(cnopt, cdopt)\n Ainner.append(A)\n Binner.append(B)\n Cinner.append(C)\n Dinner.append(D)\n\n # build s-s for each output\n Asub.append(scalg.block_diag(*Ainner))\n Bsub.append(scalg.block_diag(*Binner))\n Csub.append(np.block(Cinner))\n Dsub.append(np.block(Dinner))\n\n Arfa = scalg.block_diag(*Asub)\n Brfa = np.vstack(Bsub)\n Crfa = scalg.block_diag(*Csub)\n\n if Dmatrix is not None:\n Drfa = np.vstack(Dsub) + Dmatrix\n else:\n Drfa = np.vstack(Dsub)\n\n return Arfa, Brfa, Crfa, Drfa\n\n\n# if __name__ == '__main__':\n# import libss\n# import matplotlib.pyplot as plt\n#\n# ### common params\n# ds = 2. / 40.\n# fs = 1. / ds\n# fn = fs / 2.\n# kn = 2. * np.pi * fn\n# kv = np.linspace(0, kn, 301)\n#\n# # build a state-space\n# cfnum = np.array([4, 1.25, 1.5])\n# cfden = np.array([2, .5, 1])\n# A, B, C, D = tf2ss(cfnum, cfden)\n# SS = libss.StateSpace(A, B, C, D, dt=ds)\n# Cvref = libss.freqresp(SS, kv)\n# Cvref = Cvref[0, 0, :]\n#\n# # Find fitting\n# Nnum, Nden = 3, 3\n# cnopt, cdopt = rfa_fit_dev(kv, Cvref, Nnum, Nden, ds, True, 3, Cfbound=1e3,\n# OutFull=False, Print=True)\n#\n# print('Error coefficients (DLTI):')\n# print('Numerator: ' + 3 * '%.2e ' % tuple(np.abs(cnopt - cfnum)))\n# print('Denominator: ' + 3 * '%.2e ' % tuple(np.abs(cnopt - cfnum)))\n#\n# # Visualise\n# Cfit = rfa(cnopt, cdopt, kv, ds)\n#\n# fig = plt.figure('Transfer function', (10, 4))\n# ax1 = fig.add_subplot(111)\n# ax1.plot(kv, Cvref.real, color='r', lw=2, ls='-', label=r'ref - real')\n# ax1.plot(kv, Cvref.imag, color='r', lw=2, ls='--', label=r'ref - imag')\n# ax1.plot(kv, Cfit.real, color='k', lw=1, ls='-', label=r'RFA - real')\n# ax1.plot(kv, Cfit.imag, color='k', lw=1, ls='--', label=r'RFA - imag')\n# ax1.legend(ncol=1, frameon=True, columnspacing=.5, labelspacing=.4)\n# ax1.grid(color='0.85', linestyle='-')\n# plt.show()\n" }, { "path": "sharpy/linear/src/libsparse.py", "content": "'''\nCollect tools to manipulate sparse and/or mixed dense/sparse matrices.\n\nauthor: S. Maraniello\ndate: Dec 2018\n\nComment: manipulating large linear system may require using both dense and sparse\nmatrices. While numpy/scipy automatically handle most operations between mixed\ndense/sparse arrays, some (e.g. dot product) require more attention. This\nlibrary collects methods to handle these situations.\n\nClasses:\nscipy.sparse matrices are wrapped so as to ensure compatibility with numpy arrays\nupon conversion to dense.\n- csc_matrix: this is a wrapper of scipy.csc_matrix.\n- SupportedTypes: types supported for operations\n- WarningTypes: due to some bugs in scipy (v.1.1.0), sum (+) operations between\nnp.ndarray and scipy.sparse matrices can result in numpy.matrixlib.defmatrix.matrix\ntypes. This list contains such undesired types that can result from dense/sparse\noperations and raises a warning if required.\n(b) convert these types into numpy.ndarrays.\n\nMethods:\n- dot: handles matrix dot products across different types.\n- solve: solves linear systems Ax=b with A and b dense, sparse or mixed.\n- dense: convert matrix to numpy array\n\nWarning:\n- only sparse types into SupportedTypes are supported!\n\nTo Do:\n- move these methods into an algebra module?\n'''\n\nimport warnings\nimport numpy as np\nimport scipy.sparse as sparse\nfrom scipy.sparse._sputils import upcast_char\nimport scipy.sparse.linalg as spalg\n\n# --------------------------------------------------------------------- Classes\n\nclass csc_matrix(sparse.csc_matrix):\n\t'''\n\tWrapper of scipy.csc_matrix that ensures best compatibility with numpy.ndarray.\n\tThe following methods have been overwritten to ensure that numpy.ndarray are\n\treturned instead of numpy.matrixlib.defmatrix.matrix.\n\t\t- todense\n\t\t- _add_dense\n\n\tWarning: this format is memory inefficient to allocate new sparse matrices.\n\tConsider using:\n\t- scipy.sparse.lil_matrix, which supports slicing, or\n\t- scipy.sparse.coo_matrix, though slicing is not supported :(\n\n\t'''\n\n\tdef __init__(self,arg1, shape=None, dtype=None, copy=False):\n\t\tsuper().__init__(arg1, shape=shape, dtype=dtype, copy=copy)\n\n\tdef todense(self):\n\t\t''' As per scipy.spmatrix.todense but returns a numpy.ndarray. '''\n\t\treturn super().toarray()\n\n\tdef _add_dense(self, other):\n\t\tif other.shape != self.shape:\n\t\t raise ValueError('Incompatible shapes.')\n\t\tdtype = upcast_char(self.dtype.char, other.dtype.char)\n\t\torder = self._swap('CF')[0]\n\t\tresult = np.array(other, dtype=dtype, order=order, copy=True)\n\t\tM, N = self._swap(self.shape)\n\t\ty = result if result.flags.c_contiguous else result.T\n\t\tsparse._sparsetools.csr_todense(M, N, self.indptr, self.indices, self.data, y)\n\t\treturn result #np.matrix(result, copy=False)\n\n\nSupportedTypes=[np.ndarray,csc_matrix]\nWarningTypes=[np.matrixlib.defmatrix.matrix]\n\n\n# --------------------------------------------------------------------- Methods\n\n\ndef block_dot(A, B):\n\t'''\n\tdot product between block matrices.\n\n\tInputs:\n\tA, B: are nested lists of dense/sparse matrices of compatible shape for\n\tblock matrices product. Empty blocks can be defined with None. (see numpy.block)\n\t'''\n\n\trA, cA = len(A), len(A[0])\n\trB, cB = len(B), len(B[0])\n\n\tfor arow,brow in zip(A,B):\n\t\tassert len(brow) == cB,\\\n\t\t\t\t\t\t'B rows do not contain the same number of column blocks'\n\t\tassert len(arow) == cA,\\\n\t\t\t\t\t\t'A rows do not contain the same number of column blocks'\n\tassert cA==rB, 'Columns of A not equal to rows of B!'\n\n\tP=[]\n\tfor ii in range(rA):\n\t\tprow = cB * [None]\n\t\tfor jj in range(cB):\n\t\t\t# check first that the result will not be None\n\t\t\tContinue = False\n\t\t\tfor kk in range(cA):\n\t\t\t\tif A[ii][kk] is not None and B[kk][jj] is not None:\n\t\t\t\t\tContinue = True\n\t\t\t\t\tbreak\n\t\t\tif Continue:\n\t\t\t\tprow[jj] = 0.\n\t\t\t\tfor kk in range(cA):\n\t\t\t\t\tif A[ii][kk] is not None and B[kk][jj] is not None:\n\t\t\t\t\t\tprow[jj] += dot( A[ii][kk], B[kk][jj] )\n\t\tP.append(prow)\n\n\treturn P\n\n\ndef block_matrix_dot_vector(A, v):\n '''\n dot product between block matrix and block vector\n\n Inputs:\n A, v: are nested lists of dense/sparse matrices of compatible shape for\n block matrices product. Empty blocks can be defined with None. (see numpy.block)\n '''\n\n rA, cA = len(A), len(A[0])\n rv = len(B)\n\n for arow in A:\n assert len(arow) == cA,\\\n 'A rows do not contain the same number of column blocks'\n assert cA==rv, 'Columns of A not equal to rows of v!'\n\n P=[None]*rA\n for ii in range(rA):\n for jj in range(cA):\n # check first that the result will not be None\n if A[ii][jj] is not None and B[jj] is not None:\n P[ii] += dot(A[ii][jj], B[jj])\n return P\n\ndef block_sum(A, B, factA = None, factB = None):\n\t'''\n\tdot product between block matrices.\n\n\tInputs:\n\tA, B: are nested lists of dense/sparse matrices of compatible shape for\n\tblock matrices product. Empty blocks can be defined with None. (see numpy.block)\n\t'''\n\n\trA, cA = len(A), len(A[0])\n\trB, cB = len(B), len(B[0])\n\n\tassert cA==cB and rA==rB, 'Block matrices do not have same size'\n\n\tfor arow,brow in zip(A,B):\n\t\tassert len(brow) == cB,\\\n\t\t\t\t\t\t'B rows do not contain the same number of column blocks'\n\t\tassert len(arow) == cA,\\\n\t\t\t\t\t\t'A rows do not contain the same number of column blocks'\n\n\tP=[]\n\tfor ii in range(rA):\n\t\tprow = cA * [None]\n\n\t\tfor jj in range(cA):\n\n\t\t\tif A[ii][jj] is None:\n\t\t\t\tif B[ii][jj] is None:\n\t\t\t\t\tprow[jj] = None\n\t\t\t\telse:\n\t\t\t\t\tif factB is None:\n\t\t\t\t\t\tprow[jj] = B[ii][jj]\n\t\t\t\t\telse:\n\t\t\t\t\t\tprow[jj] = factB*B[ii][jj]\n\t\t\telse:\n\t\t\t\tif B[ii][jj] is None:\n\t\t\t\t\tif factA is None:\n\t\t\t\t\t\tprow[jj] = A[ii][jj]\n\t\t\t\t\telse:\n\t\t\t\t\t\tprow[jj] = factA*A[ii][jj]\n\t\t\t\telse:\n\t\t\t\t\tif factA is None and factA is None:\n\t\t\t\t\t\tprow[jj] = A[ii][jj] + B[ii][jj]\n\t\t\t\t\telif factA is None:\n\t\t\t\t\t\tprow[jj] = A[ii][jj] + factB*B[ii][jj]\n\t\t\t\t\telif factB is None:\n\t\t\t\t\t\tprow[jj] = factA*A[ii][jj] + B[ii][jj]\n\t\t\t\t\telse:\n\t\t\t\t\t\tprow[jj] = factA*A[ii][jj] + factB*B[ii][jj]\n\n\t\tP.append(prow)\n\n\treturn P\n\n\ndef dot(A,B,type_out=None):\n\t'''\n\tMethod to compute\n\t\tC = A*B ,\n\twhere * is the matrix product, with dense/sparse/mixed matrices.\n\n\tThe format (sparse or dense) of C is specified through 'type_out'. If\n\ttype_out==None, the output format is sparse if both A and B are sparse, dense\n\totherwise.\n\n\tThe following formats are supported:\n\t- numpy.ndarray\n\t- scipy.csc_matrix\n\t'''\n\n\t# determine types:\n\ttA=type(A)\n\ttB=type(B)\n\n\tassert tA in SupportedTypes, 'Type of A matrix (%s) not supported'%tA\n\tassert tB in SupportedTypes, 'Type of B matrix (%s) not supported'%tB\n\tif type_out == None:\n\t\ttype_out=tA\n\telse:\n\t\tassert type_out in SupportedTypes, 'type_out not supported'\n\n\t# multiply\n\t# if tA==float or tb==float:\n\t# \tC = A*B\n\t# else:\n\tif tA==np.ndarray and tB==csc_matrix:\n\t\tC=(B.transpose()).dot(A.transpose()).transpose()\n\t\t# C=A.dot(B.todense())\n\telse:\n\t\tC=A.dot(B)\n\n\t# format output\n\tif tA != type_out:\n\t\tif type_out==csc_matrix:\n\t\t\treturn csc_matrix(C)\n\t\telse:\n\t\t\treturn C.toarray()\n\n\treturn C\n\n\ndef solve(A,b):\n\t'''\n\tWrapper of\n\t\tnumpy.linalg.solve and scipy.sparse.linalg.spsolve\n\tfor solution of the linear system A x = b.\n\t- if A is a dense numpy array np.linalg.solve is called for solution. Note\n\tthat if B is sparse, this requires convertion to dense. In this case,\n\tsolution through LU factorisation of A should be considered to exploit the\n\tsparsity of B.\n\t- if A is sparse, scipy.sparse.linalg.spsolve is used.\n\t'''\n\n\t# determine types:\n\ttA=type(A)\n\ttB=type(b)\n\n\tassert tA in SupportedTypes, 'Type of A matrix (%s) not supported'%tA\n\tassert tB in SupportedTypes, 'Type of B matrix (%s) not supported'%tB\n\t# multiply\n\tif tA==np.ndarray:\n\t\tif tB==csc_matrix:\n\t\t\tx=np.linalg.solve(A,b.toarray())\n\t\telse:\n\t\t\tx=np.linalg.solve(A,b)\n\telse:\n\t\tx=spalg.spsolve(A,b)\n\n\tassert type(x) in SupportedTypes, 'Unexpected output type!'\n\n\treturn x\n\n\ndef dense(M):\n\t''' If required, converts sparse array to dense. '''\n\tif type(M) == csc_matrix:\n\t\treturn np.array(M.toarray())\n\telif type(M) == csc_matrix:\n\t\treturn M.toarray()\n\treturn M\n\n\ndef eye_as(M):\n\t''' Produces an identity matrix as per M, in shape and type '''\n\n\ttM=type(M)\n\tassert tM in SupportedTypes, 'Type %s not supported!'%tM\n\tnrows=M.shape[0]\n\tassert nrows==M.shape[1], 'Not a square matrix!'\n\n\tif tM==csc_matrix:\n\t\tD=csc_matrix((nrows,nrows))\n\t\tD.setdiag(1.)\n\telif tM==np.ndarray:\n\t\tD=np.eye(nrows)\n\n\treturn D\n\n\ndef zeros_as(M):\n\t''' Produces an identity matrix as per M, in shape and type '''\n\n\ttM=type(M)\n\tassert tM in SupportedTypes, 'Type %s not supported!'%tM\n\tnrows,ncols=M.shape\n\n\tif tM==csc_matrix:\n\t\tD=csc_matrix((nrows,ncols))\n\telif tM==np.ndarray:\n\t\tD=np.zeros_like(M)\n\n\treturn D\n\n\n# -----------------------------------------------------------------------------\n\n\nif __name__=='__main__':\n\timport unittest\n\n\tclass Test_module(unittest.TestCase):\n\t\t''' Test methods into this module '''\n\n\t\tdef setUp(self):\n\t\t\tself.A=np.random.rand(3,4)\n\t\t\tself.B=np.random.rand(4,2)\n\n\t\tdef test_dense_plus_csc_matrix_type(self):\n\t\t\tA=self.A\n\t\t\tAsp=csc_matrix(A)\n\n\t\t\tfor aa in [A,Asp]:\n\t\t\t\tfor bb in [A,Asp]:\n\t\t\t\t\ttsum=type(aa+bb)\n\t\t\t\t\ttdiff=type(aa-bb)\n\t\t\t\t\tfor tout,strout in zip([tsum,tdiff],['(+)','(-)']):\n\t\t\t\t\t\tif tout not in SupportedTypes:\n\t\t\t\t\t\t\tif tout in WarningTypes:\n\t\t\t\t\t\t\t\twarnings.warn(\n\t\t\t\t\t\t\t\t\t'Undesired type (%s) resulting from %s operations between %s and %s types'\\\n\t\t\t\t\t\t\t\t\t%(tout,strout,type(aa),type(bb)))\n\t\t\t\t\t\t\telse:\n\t\t\t\t\t\t\t\traise NameError(\n\t\t\t\t\t\t\t\t\t'Unexpected type (%s) resulting from %s operations between %s and %s types'\\\n\t\t\t\t\t\t\t\t\t%(tout,strout,type(aa),type(bb)))\n\n\t\tdef test_zeros_as(self):\n\t\t\tA=np.zeros((4,2))\n\t\t\tA1=zeros_as(A)\n\t\t\tA2=zeros_as(csc_matrix(A))\n\t\t\tassert np.max(np.abs(A-A1))<1e-16, 'Error in libsparse.zeros_as'\n\t\t\tassert np.max(np.abs(A-A2))<1e-16, 'Error in libsparse.zeros_as'\n\n\t\tdef test_eye_as(self):\n\t\t\tA=np.random.rand(4,4)\n\t\t\tD0=np.eye(4)\n\t\t\tD1=eye_as(A)\n\t\t\tD2=eye_as(csc_matrix(A))\n\t\t\tassert np.max(np.abs(D0-D1))<1e-12, 'Error in libsparse.eye_as'\n\t\t\tassert np.max(np.abs(D0-D2))<1e-12, 'Error in libsparse.eye_as'\n\n\t\tdef test_dot(self):\n\t\t\tA,B=self.A,self.B\n\t\t\tC0=np.dot(A,B)\t\t# reference\n\t\t\tC1=dot(A,B)\n\t\t\tC2=dot(A,csc_matrix(B))\n\t\t\tC3=dot(csc_matrix(A),B)\n\t\t\tC4=dot(csc_matrix(A),csc_matrix(B))\n\t\t\tassert np.max(np.abs(C0-C1))<1e-12, 'Error in libsparse.dot'\n\t\t\tassert np.max(np.abs(C0-C2))<1e-12, 'Error in libsparse.dot'\n\t\t\tassert np.max(np.abs(C0-C3))<1e-12, 'Error in libsparse.dot'\n\n\t\tdef test_solve(self):\n\t\t\tA=np.random.rand(4,4)\n\t\t\tB=np.random.rand(4,2)\n\t\t\tAsp=csc_matrix(A)\n\t\t\tBsp=csc_matrix(B)\n\n\t\t\tX0=np.linalg.solve(A,B)\n\t\t\tX1=solve(A,B)\n\t\t\tX2=solve(A,Bsp)\n\t\t\tX3=solve(Asp,B)\n\t\t\tX4=solve(Asp,Bsp)\n\n\t\t\tassert np.max(np.abs(X0-X1))<1e-12, 'Error in libsparse.solve'\n\t\t\tassert np.max(np.abs(X0-X2))<1e-12, 'Error in libsparse.solve'\n\t\t\tassert np.max(np.abs(X0-X3))<1e-12, 'Error in libsparse.solve'\n\t\t\tassert np.max(np.abs(X0-X4))<1e-12, 'Error in libsparse.solve'\n\n\n\toutprint='Testing libsparse'\n\tprint('\\n' + 70*'-')\n\tprint((70-len(outprint))*' ' + outprint )\n\tprint(70*'-')\n\tunittest.main()\n" }, { "path": "sharpy/linear/src/libss.py", "content": "\"\"\"\nLinear Time Invariant systems\nauthor: S. Maraniello\ndate: 15 Sep 2017 (still basement...)\n\nLibrary of methods to build/manipulate state-space models. The module supports\nthe sparse arrays types defined in libsparse.\n\nThe module includes:\n\nClasses:\n- StateSpace: provides a class to build DLTI/LTI systems with full and/or sparse\n\tmatrices and wraps many of the methods in these library. Methods include:\n\t- freqresp: wraps the freqresp function\n\t- addGain: adds gains in input/output. This is not a wrapper of addGain, as\n\tthe system matrices are overwritten\n\nMethods for state-space manipulation:\n- couple: feedback coupling. Does not support sparsity\n- freqresp: calculate frequency response. Supports sparsity.\n- series: series connection between systems\n- parallel: parallel connection between systems\n- SSconv: convert state-space model with predictions and delays\n- addGain: add gains to state-space model.\n- join2: merge two state-space models into one.\n- join: merge a list of state-space models into one.\n- sum state-space models and/or gains\n- scale_SS: scale state-space model\n- simulate: simulates discrete time solution\n- Hnorm_from_freq_resp: compute H norm of a frequency response\n- adjust_phase: remove discontinuities from a frequency response\n\nSpecial Models:\n- SSderivative: produces DLTI of a numerical derivative scheme\n- SSintegr: produces DLTI of an integration scheme\n- build_SS_poly: build state-space model with polynomial terms.\n\nFiltering:\n- butter\n\nUtilities:\n- get_freq_from_eigs: clculate frequency corresponding to eigenvalues\n\nComments:\n- the module supports sparse matrices hence relies on libsparse.\n\nto do:\n\t- remove unnecessary coupling routines\n\t- couple function can handle sparse matrices but only outputs dense matrices\n\t\t- verify if typical coupled systems are sparse\n\t\t- update routine\n\t\t- add method to automatically determine whether to use sparse or dense?\n\"\"\"\n\nimport copy\nimport warnings\nimport numpy as np\nimport scipy.signal as scsig\nimport scipy.linalg as scalg\nfrom sharpy.linear.utils.ss_interface import LinearVector, StateVariable, InputVariable, OutputVariable\nimport scipy.interpolate as scint\nimport h5py\nimport sharpy.utils.h5utils as h5utils\n\n# dependency\nimport sharpy.linear.src.libsparse as libsp\n\n\n# ------------------------------------------------------------- Dedicated class\n\nclass StateSpace:\n \"\"\"\n Wrap state-space models allocation into a single class and support both\n full and sparse matrices. The class emulates\n scipy.signal.ltisys.StateSpaceContinuous\n scipy.signal.ltisys.StateSpaceDiscrete\n but supports sparse matrices and other functionalities.\n\n Methods:\n - get_mats: return matrices as tuple\n - check_types: check matrices types are supported\n - freqresp: calculate frequency response over range.\n - addGain: project inputs/outputs\n - scale: allows scaling a system\n \"\"\"\n\n def __init__(self, A, B, C, D, dt=None):\n \"\"\"\n Allocate state-space model (A,B,C,D). If dt is not passed, a\n continuous-time system is assumed.\n \"\"\"\n\n self.A = A\n self.B = B\n self.C = C\n self.D = D\n self.dt = dt\n self.check_types()\n\n # vector variable tracking\n self._input_variables = None # type: LinearVector\n self._state_variables = None\n self._output_variables = None\n\n # verify dimensions\n assert self.A.shape == (self.states, self.states), 'A and B rows not matching'\n assert self.C.shape[1] == self.states, 'A and C columns not matching'\n assert self.D.shape[0] == self.outputs, 'C and D rows not matching'\n try:\n assert self.D.shape[1] == self.inputs, 'B and D columns not matching'\n except IndexError:\n assert self.inputs == 1, 'D shape does not match number of inputs'\n\n @property\n def inputs(self):\n \"\"\"Number of inputs :math:`m` to the system.\"\"\"\n if self.B.shape.__len__() == 1:\n return 1\n else:\n return self.B.shape[1]\n\n @property\n def outputs(self):\n \"\"\"Number of outputs :math:`p` of the system.\"\"\"\n return self.C.shape[0]\n\n @property\n def states(self):\n \"\"\"Number of states :math:`n` of the system.\"\"\"\n return self.A.shape[0]\n\n @property\n def input_variables(self):\n return self._input_variables\n\n @input_variables.setter\n def input_variables(self, variables):\n if variables.variable_class is not InputVariable:\n raise TypeError('LinearVector does not include InputVariable s')\n if variables.size != self.inputs:\n raise IndexError('Size of LinearVector of InputVariable s ({:g}) is not the same as the number of '\n 'inputs in the '\n 'system ({:g})'.format(variables.size, self.inputs))\n self._input_variables = variables\n\n @property\n def output_variables(self):\n return self._output_variables\n\n @output_variables.setter\n def output_variables(self, variables):\n if variables.variable_class is not OutputVariable:\n raise TypeError('LinearVector does not include OutputVariable s')\n if variables.size != self.outputs:\n raise IndexError('Size of LinearVector of OutputVariable s ({:g}) is not the same as the number of '\n 'outputs in the '\n 'system ({:g})'.format(variables.size, self.outputs))\n self._output_variables = variables\n\n @property\n def state_variables(self):\n return self._state_variables\n\n @state_variables.setter\n def state_variables(self, variables):\n if variables.variable_class is not StateVariable:\n raise TypeError('LinearVector does not include StateVariable s')\n if variables.size != self.states:\n raise IndexError('Size of LinearVector of StateVariable s ({:g}) is not the same as the number '\n 'of states in the '\n 'system ({:g})'.format(variables.size, self.states))\n self._state_variables = variables\n\n def initialise_variables(self, *variable_tuple, var_type='in'):\n if var_type == 'in' or var_type == 'input':\n var_class = InputVariable\n elif var_type == 'out' or var_type == 'output':\n var_class = OutputVariable\n elif var_type == 'state':\n var_class = StateVariable\n else:\n raise TypeError('Unknown variable type')\n\n list_of_variables = []\n for ith, var_dict in enumerate(variable_tuple):\n list_of_variables.append(var_class(name=var_dict['name'],\n size=var_dict['size'],\n index=var_dict.get('index', ith)))\n\n if var_type == 'in' or var_type == 'input':\n self._input_variables = LinearVector(list_of_variables)\n elif var_type == 'out' or var_type == 'output':\n self._output_variables = LinearVector(list_of_variables)\n elif var_type == 'state':\n self._state_variables = LinearVector(list_of_variables)\n\n def __repr__(self):\n str_out = ''\n str_out += 'State-space object\\n'\n str_out += 'States: {:g}\\n'.format(self.states)\n str_out += 'Inputs: {:g}\\n'.format(self.inputs)\n str_out += 'Outputs: {:g}\\n'.format(self.outputs)\n if self.dt is not None:\n str_out += 'dt: {:g}'.format(self.dt)\n\n if self.input_variables is not None:\n str_out += '\\nInput Variables:\\n' + str(self.input_variables)\n if self.state_variables is not None:\n str_out += 'State Variables:\\n' + str(self.state_variables)\n if self.output_variables is not None:\n str_out += 'Output Variables:\\n' + str(self.output_variables)\n\n return str_out\n\n def check_types(self):\n assert type(self.A) in libsp.SupportedTypes, \\\n 'Type of A matrix (%s) not supported' % type(self.A)\n assert type(self.B) in libsp.SupportedTypes, \\\n 'Type of B matrix (%s) not supported' % type(self.B)\n assert type(self.C) in libsp.SupportedTypes, \\\n 'Type of C matrix (%s) not supported' % type(self.C)\n assert type(self.D) in libsp.SupportedTypes, \\\n 'Type of D matrix (%s) not supported' % type(self.D)\n\n def get_mats(self):\n return self.A, self.B, self.C, self.D\n\n def freqresp(self, wv):\n \"\"\"\n Calculate frequency response over frequencies wv\n\n Note: this wraps frequency response function.\n \"\"\"\n dlti = True\n if self.dt is None:\n dlti = False\n return freqresp(self, wv, dlti=dlti)\n\n def addGain(self, K, where):\n \"\"\"\n Projects input u or output y the state-space system through the gain\n matrix K. The input 'where' determines whether inputs or outputs are\n projected as:\n - where='in': inputs are projected such that:\n u_new -> u=K*u_new -> SS -> y => u_new -> SSnew -> y\n - where='out': outputs are projected such that:\n u -> SS -> y -> y_new=K*y => u -> SSnew -> ynew\n\n Args:\n K (np.array or Gain): gain matrix or Gain object\n where (str): ``in`` or ``out``\n\n Warning:\n This is not a wrapper of the addGain method in this module, as\n the state-space matrices are directly overwritten.\n \"\"\"\n\n assert where in ['in', 'out'], \\\n 'Specify whether gains are added to input or output'\n\n with_vars = False\n if isinstance(K, Gain):\n gain = K\n K = K.value\n with_vars = True\n\n if where == 'in':\n self.B = libsp.dot(self.B, K)\n self.D = libsp.dot(self.D, K)\n if with_vars:\n self._input_variables = gain.input_variables\n\n if where == 'out':\n self.C = libsp.dot(K, self.C)\n self.D = libsp.dot(K, self.D)\n if with_vars:\n self._output_variables = gain.output_variables\n\n def scale(self, input_scal=1., output_scal=1., state_scal=1.):\n \"\"\"\n Given a state-space system, scales the equations such that the original\n state, input and output, (x, u and y), are substituted by\n xad=x/state_scal\n uad=u/input_scal\n yad=y/output_scal\n The entries input_scal/output_scal/state_scal can be:\n - floats: in this case all input/output are scaled by the same value\n - lists/arrays of length Nin/Nout: in this case each dof will be scaled\n by a different factor\n\n If the original system has form:\n xnew=A*x+B*u\n y=C*x+D*u\n the transformation is such that:\n xnew=A*x+(B*uref/xref)*uad\n yad=1/yref( C*xref*x+D*uref*uad )\n \"\"\"\n scale_SS(self, input_scal, output_scal, state_scal, byref=True)\n\n def project(self, wt, v):\n \"\"\"\n Given 2 transformation matrices, ``(WT, V)`` of shapes ``(Nk, self.states)`` and\n ``(self.states, Nk)`` respectively, this routine projects the state space\n model states according to:\n\n\n .. math::\n Anew = WT A V \\\\\n Bnew = WT B \\\\\n Cnew = C V \\\\\n Dnew = D \\\\\n\n The projected model has the same number of inputs/outputs as the original\n one, but Nk states.\n\n Args:\n wt (Gain or np.ndarray): Left projection matrix\n v (Gain or np.ndarray): Righty projection matrix\n \"\"\"\n if isinstance(wt, Gain) and isinstance(v, Gain):\n self.A = libsp.dot(wt.value, libsp.dot(self.A, v.value))\n self.B = libsp.dot(wt.value, self.B)\n self.C = libsp.dot(self.C, v.value)\n self.state_variables = LinearVector.transform(v.input_variables, to_type=StateVariable)\n else:\n self.A = libsp.dot(wt, libsp.dot(self.A, v))\n self.B = libsp.dot(wt, self.B)\n self.C = libsp.dot(self.C, v)\n\n def truncate(self, N):\n \"\"\" Retains only the first N states. \"\"\"\n\n assert N > 0 and N <= self.states, 'N must be in [1,self.states]'\n\n self.A = self.A[:N, :N]\n self.B = self.B[:N, :]\n self.C = self.C[:, :N]\n # self.states = N # No need to update, states is now a property. NG 26/3/19\n\n def max_eig(self):\n \"\"\"\n Returns most unstable eigenvalue\n \"\"\"\n\n ev = np.linalg.eigvals(self.A)\n\n if self.dt is None:\n return np.max(ev.real)\n else:\n return np.max(np.abs(ev))\n\n def eigvals(self):\n \"\"\"\n Returns:\n np.ndarray: Eigenvalues of the system\n\n \"\"\"\n if self.dt:\n return eigvals(self.A, dlti=True)\n else:\n return eigvals(self.A, dlti=False)\n\n def disc2cont(self):\n r\"\"\"\n Transform a discrete time system to a continuous time system using a bilinear (Tustin) transformation.\n\n Wrapper of :func:`~sharpy.linear.src.libss.disc2cont`\n\n \"\"\"\n if self.dt:\n self = disc2cont(self)\n\n def retain_inout_channels(self, retain_channels, where):\n \"\"\"\n Retain selected input or output channels only.\n\n Args:\n retain_channels (list): List of channels to retain\n where (str): ``in`` or ``out`` for input/output channels\n \"\"\"\n retain_inout_channels(self, retain_channels, where)\n\n def summary(self):\n msg = 'State-space system\\nStates: %g\\nInputs: %g\\nOutputs: %g\\n' % (self.states, self.inputs, self.outputs)\n return msg\n\n def transfer_function_evaluation(self, s):\n r\"\"\"\n Returns the transfer function of the system evaluated at :math:`s\\in\\mathbb{C}`.\n\n Args:\n s (complex): Point in the complex plane at which to evaluate the transfer function.\n\n Returns:\n np.ndarray: Transfer function evaluated at :math:`s`.\n \"\"\"\n a, b, c, d = self.get_mats()\n\n n = a.shape[0]\n\n return c.dot(scalg.inv(s * np.eye(n) - a)).dot(b) + d\n\n def save(self, path):\n \"\"\"Save state-space object to h5 file\"\"\"\n with h5py.File(path, 'w') as f:\n f.create_dataset('a', data=self.A)\n f.create_dataset('b', data=self.B)\n f.create_dataset('c', data=self.C)\n f.create_dataset('d', data=self.D)\n if self.dt:\n f.create_dataset('dt', data=self.dt)\n\n if self.input_variables is not None:\n self.input_variables.add_to_h5_file(f)\n self.output_variables.add_to_h5_file(f)\n self.state_variables.add_to_h5_file(f)\n\n @classmethod\n def load_from_h5(cls, h5_file_name):\n \"\"\"\n Loads a state-space object from an h5 file, including variable information\n\n Args:\n h5_file_name (str): Path to file\n\n Returns:\n StateSpace: loaded state-space from file\n \"\"\"\n\n with h5py.File(h5_file_name, 'r') as f:\n data_dict = h5utils.load_h5_in_dict(f)\n\n new_ss = cls(data_dict['a'],\n data_dict['b'],\n data_dict['c'],\n data_dict['d'],\n dt=data_dict.get('dt'))\n\n input_variables = data_dict.get('InputVariable')\n if input_variables is not None:\n new_ss.input_variables = LinearVector.load_from_h5_file('InputVariable',\n data_dict['InputVariable'])\n new_ss.output_variables = LinearVector.load_from_h5_file('OutputVariable',\n data_dict['OutputVariable'])\n new_ss.state_variables = LinearVector.load_from_h5_file('StateVariable',\n data_dict['StateVariable'])\n\n return new_ss\n else:\n return new_ss\n\n def remove_inputs(self, *input_remove_list):\n \"\"\"\n Removes inputs through their variable names.\n\n Needs that the ``StateSpace`` attribute ``input_variables`` is defined.\n\n Args:\n input_remove_list (list(str)): List of inputs to remove\n\n \"\"\"\n if self.input_variables is None:\n raise AttributeError('No input variables have been defined for the current state-space object. Define '\n 'some variables prior to using the remove_inputs() method.')\n\n self.input_variables.remove(*input_remove_list)\n\n i = 0\n retain_input_array = None\n for variable in self.input_variables:\n if i == 0:\n retain_input_array = variable.cols_loc\n else:\n retain_input_array = np.hstack((retain_input_array, variable.cols_loc))\n i += 1\n\n if retain_input_array is not None:\n if type(self.B) is libsp.csc_matrix:\n self.B = libsp.csc_matrix(self.B[:, retain_input_array])\n self.D = libsp.csc_matrix(self.D[:, retain_input_array])\n else:\n self.B = self.B[:, retain_input_array]\n self.D = self.D[:, retain_input_array]\n\n self.input_variables.update_locations()\n\n def remove_outputs(self, *output_remove_list):\n \"\"\"\n Removes outputs through their variable names.\n\n Needs that the ``StateSpace`` attribute ``output_variables`` is defined.\n\n Args:\n output_remove_list (list(str)): List of outputs to remove\n\n \"\"\"\n if self.output_variables is None:\n raise AttributeError('No output variables have been defined for the current state-space object. Define '\n 'some variables prior to using the remove_outputs() method.')\n\n new_outputs = 0\n for variable in self.output_variables:\n if variable.name not in output_remove_list:\n new_outputs += variable.size\n\n out_gain = np.zeros((new_outputs, self.outputs))\n worked_outputs = 0\n for variable in self.output_variables:\n if variable.name not in output_remove_list:\n index = variable.rows_loc\n out_gain[worked_outputs:worked_outputs + variable.size, index] = np.eye(variable.size)\n worked_outputs += variable.size\n\n if new_outputs != self.outputs:\n if type(self.B) is libsp.csc_matrix:\n self.C = libsp.csc_matrix(out_gain.dot(self.C))\n self.D = libsp.csc_matrix(out_gain.dot(self.D))\n else:\n self.C = out_gain.dot(self.C)\n self.D = out_gain.dot(self.D)\n\n self.output_variables.remove(*output_remove_list)\n self.output_variables.update_locations()\n\n @classmethod\n def from_scipy(cls, scipy_ss):\n \"\"\"\n Transforms a ``scipy.signal.lti`` or dlti into a StateSpace class\n\n Args:\n scipy_ss (scipy.signal.ltisys.StateSpaceContinous or scipy.signal.ltisys.StateSpaceDiscrete): Scipy\n State Space object.\n\n Returns:\n StateSpace: SHARPy state space object\n \"\"\"\n a = scipy_ss.A\n b = scipy_ss.B\n c = scipy_ss.C\n d = scipy_ss.D\n\n return cls(a, b, c, d, dt=scipy_ss.dt)\n\n\nclass Gain:\n\n def __init__(self, value, input_vars=None, output_vars=None):\n self.value = value\n self._input_variables = None\n self._output_variables = None\n\n if input_vars is not None:\n self.input_variables = input_vars\n if output_vars is not None:\n self.output_variables = output_vars\n\n @property\n def input_variables(self):\n return self._input_variables\n\n @input_variables.setter\n def input_variables(self, variables):\n if variables.variable_class is not InputVariable:\n raise TypeError('LinearVector does not include InputVariable s')\n if variables.size != self.inputs:\n raise IndexError('Size of LinearVector of InputVariable s ({:g}) is not the same as the number of '\n 'inputs in the '\n 'system ({:g})'.format(variables.size, self.inputs))\n self._input_variables = variables\n\n @property\n def output_variables(self):\n return self._output_variables\n\n @output_variables.setter\n def output_variables(self, variables):\n if variables.variable_class is not OutputVariable:\n raise TypeError('LinearVector does not include OutputVariable s')\n if variables.size != self.outputs:\n raise IndexError('Size of LinearVector of OutputVariable s ({:g}) is not the same as the number of '\n 'outputs in the '\n 'system ({:g})'.format(variables.size, self.outputs))\n self._output_variables = variables\n\n @property\n def inputs(self):\n \"\"\"Number of inputs :math:`m` to the system.\"\"\"\n if self.value.shape.__len__() == 1:\n return 1\n else:\n return self.value.shape[1]\n\n @property\n def outputs(self):\n \"\"\"Number of outputs :math:`p` of the gain.\"\"\"\n return self.value.shape[0]\n\n def dot(self, elem):\n \"\"\"\n Dot product of two Gains\n\n Args:\n elem (np.array or Gain):\n\n Returns:\n np.array or Gain: new matrix/Gain containing the dot product\n \"\"\"\n if type(elem) is Gain:\n LinearVector.check_connection(elem.output_variables, self.input_variables)\n new_gain_value = libsp.dot(self.value, elem.value)\n return Gain(new_gain_value,\n input_vars=elem.input_variables.copy(),\n output_vars=self.output_variables.copy())\n else:\n return self.value.dot(elem)\n\n def __repr__(self):\n str_out = ''\n str_out += 'Gain object\\n'\n str_out += 'Inputs: {:g}\\n'.format(self.inputs)\n str_out += 'Outputs: {:g}\\n'.format(self.outputs)\n\n if self.input_variables is not None:\n str_out += '\\nInput Variables:\\n' + str(self.input_variables)\n if self.output_variables is not None:\n str_out += 'Output Variables:\\n' + str(self.output_variables)\n\n return str_out\n\n def transpose(self):\n \"\"\"\n Transposes the gain, such that the inputs become the outputs and vice-versa.\n \"\"\"\n\n if self.input_variables is not None:\n temp_input_var = self.input_variables.copy()\n input_variables = LinearVector.transform(self.output_variables,\n to_type=InputVariable)\n output_variables = LinearVector.transform(temp_input_var,\n to_type=OutputVariable)\n\n return Gain(self.value.T,\n input_vars=input_variables,\n output_vars=output_variables)\n else:\n return Gain(self.value.T)\n\n @property\n def T(self):\n return self.transpose()\n\n def copy(self):\n if self.input_variables is not None:\n return Gain(self.value, input_vars=self.input_variables.copy(), output_vars=self.output_variables.copy())\n else:\n return Gain(self.value)\n\n def save(self, path):\n \"\"\"Save gain object to h5 file\"\"\"\n with h5py.File(path, 'w') as f:\n f.create_dataset('gain', data=self.value)\n\n if self.input_variables is not None:\n self.input_variables.add_to_h5_file(f)\n self.output_variables.add_to_h5_file(f)\n\n def add_as_group_to_h5(self, h5_file_handle, group_name):\n \"\"\"\n Adds gain to an h5 file handle\n \n Args:\n h5_file_handle (h5py.File): writeable h5 file handle\n group_name (str): Desired group name to save gain in h5\n\n \"\"\"\n gain_group = h5_file_handle.create_group(group_name)\n gain_group.create_dataset(name='gain', data=self.value)\n\n if self.input_variables is not None:\n self.input_variables.add_to_h5_file(gain_group)\n self.output_variables.add_to_h5_file(gain_group)\n\n @classmethod\n def load_from_h5(cls, h5_file_name):\n \"\"\"\n Returns a gain object from an .h5 file\n\n Args:\n h5_file_name (str): Path to h5 file\n\n Returns:\n Gain: instance of a Gain\n \"\"\"\n with h5py.File(h5_file_name, 'r') as f:\n data_dict = h5utils.load_h5_in_dict(f)\n\n return cls.load_from_dict(data_dict)\n\n @classmethod\n def load_from_dict(cls, data_dict):\n \"\"\"\n\n Returns a Gain from a dictionary of data, useful for loading from a group of gains in a single\n .h5 file\n\n Args:\n data_dict (dict): Dictionary with keys: ``gain`` and (if available) ``InputVariable``\n and ``OutputVariable``.\n\n Returns:\n Gain: instance of Gain\n \"\"\"\n input_variables = data_dict.get('InputVariable')\n if input_variables is not None:\n input_variables = LinearVector.load_from_h5_file('InputVariable',\n data_dict['InputVariable'])\n output_variables = LinearVector.load_from_h5_file('OutputVariable',\n data_dict['OutputVariable'])\n\n return cls(data_dict['gain'], input_vars=input_variables,\n output_vars=output_variables)\n else:\n return cls(data_dict['gain'])\n\n @classmethod\n def save_multiple_gains(cls, h5_file_name, *gains_names_tuple):\n \"\"\"\n Saves multiple gains to a single h5 file\n\n Args:\n h5_file_name (str): Path to h5 file\n *gains_names_tuple (tuple): ``(gain_name (str), gain(Gain))`` tuples to save. The gain name will be the name\n given on the h5 file\n\n \"\"\"\n with h5py.File(h5_file_name, 'w') as f:\n for name, gain in gains_names_tuple:\n gain.add_as_group_to_h5(f, name)\n\n @classmethod\n def load_multiple_gains(cls, h5_file_name):\n \"\"\"\n Loads multiple gains from a single h5 file\n\n Args:\n h5_file_name (str): Path to h5 file\n\n Returns:\n dict: Dictionary of loaded gains in a gain_name: Gain dictionary\n \"\"\"\n with h5py.File(h5_file_name, 'r') as f:\n data_dict = h5utils.load_h5_in_dict(f)\n\n out_gains = {}\n for gain_name, gain_data in data_dict.items():\n out_gains[gain_name] = cls.load_from_dict(gain_data)\n\n return out_gains\n\n\nclass ss_block():\n \"\"\"\n State-space model in block form. This class has the same purpose as \"StateSpace\",\n but the A, B, C, D are allocated in the form of nested lists. The format is\n similar to the one used in numpy.block but:\n 1. Block matrices can contain both dense and sparse matrices\n 2. Empty blocks are defined through None type\n\n Methods:\n - remove_block: drop one of the blocks from the s-s model\n - addGain: project inputs/outputs\n - project: project state\n \"\"\"\n\n def __init__(self, A, B, C, D, S_states, S_inputs, S_outputs, dt=None):\n \"\"\"\n Allocate state-space model (A,B,C,D) in block form starting from nested\n lists of full/sparse matrices (as per numpy.block).\n\n Input:\n - A, B, C, D: lists of matrices defining the state-space model.\n - S_states, S_inputs, S_outputs: lists with dimensions of of each block\n representing the states, inputs and outputs of the model.\n - dt: time-step. In None, a continuous-time system is assumed.\n \"\"\"\n\n self.A = A\n self.B = B\n self.C = C\n self.D = D\n self.dt = dt\n\n self.S_u = S_inputs\n self.S_y = S_outputs\n self.S_x = S_states\n\n # determine number of blocks\n self.blocks_u = len(S_inputs)\n self.blocks_y = len(S_outputs)\n self.blocks_x = len(S_states)\n\n # determine inputs/outputs/states\n self.inputs = sum(S_inputs)\n self.outputs = sum(S_outputs)\n self.states = sum(S_states)\n\n self.check_sizes()\n\n def check_sizes(self):\n pass\n\n def remove_block(self, where, index):\n \"\"\"\n Remove a block from either inputs or outputs.\n\n Inputs:\n - where = {'in', 'out'}: determined whether to remove inputs or outputs\n - index: index of block to remove\n \"\"\"\n\n assert where in ['in', 'out'], \"'where' must be equal to {'in', 'out'}\"\n\n if where == 'in':\n for ii in range(self.blocks_x):\n del self.B[ii][index]\n for ii in range(self.blocks_y):\n del self.D[ii][index]\n\n if where == 'out':\n for ii in range(self.blocks_y):\n del self.C[ii]\n del self.D[ii]\n\n def addGain(self, K, where):\n \"\"\"\n Projects input u or output y the state-space system through the gain\n block matrix K. The input 'where' determines whether inputs or outputs\n are projected as:\n - where='in': inputs are projected such that:\n u_new -> u=K*u_new -> SS -> y => u_new -> SSnew -> y\n - where='out': outputs are projected such that:\n u -> SS -> y -> y_new=K*y => u -> SSnew -> ynew\n\n Input: K must be a list of list of matrices. The size of K must be\n compatible with either B or C for block matrix product.\n \"\"\"\n\n assert where in ['in', 'out'], \\\n 'Specify whether gains are added to input or output'\n\n rows, cols = self.get_sizes(K)\n\n if where == 'in':\n self.B = libsp.block_dot(self.B, K)\n self.D = libsp.block_dot(self.D, K)\n self.S_u = cols\n self.blocks_u = len(cols)\n self.inputs = sum(cols)\n\n if where == 'out':\n self.C = libsp.block_dot(K, self.C)\n self.D = libsp.block_dot(K, self.D)\n self.S_y = rows\n self.blocks_y = len(rows)\n self.outputs = sum(rows)\n\n def get_sizes(self, M):\n \"\"\"\n Get the size of each block in M.\n \"\"\"\n\n rM, cM = len(M), len(M[0])\n rows = rM * [None]\n cols = cM * [None]\n\n for ii in range(rM):\n for jj in range(cM):\n if M[ii][jj] is not None:\n rhere, chere = M[ii][jj].shape\n\n if rows[ii] is None: # allocate\n rows[ii] = rhere\n else: # check\n assert rows[ii] == rhere, \\\n 'Block (%d,%d) has inconsistent size with other in same row!' % (ii, jj)\n\n if cols[jj] is None: # allocate\n cols[jj] = chere\n else: # check\n assert cols[jj] == chere, \\\n 'Block (%d,%d) has inconsistent size with other in same column!' % (ii, jj)\n\n return rows, cols\n\n def project(self, WT, V, by_arrays=True, overwrite=False):\n \"\"\"\n Given 2 transformation matrices, (W,V) of shape (Nk,self.states), this\n routine projects the state space model states according to:\n\n Anew = W^T A V\n Bnew = W^T B\n Cnew = C V\n Dnew = D\n\n The projected model has the same number of inputs/outputs as the original\n one, but Nk states.\n\n Inputs:\n - WT = W^T\n - V = V\n - by_arrays: if True, W, V are either numpy.array or sparse matrices. If\n False, they are block matrices.\n - overwrite: if True, overwrites the A, B, C matrices\n \"\"\"\n\n if by_arrays: # transform to block structures\n\n II0 = 0\n Vblock = []\n WTblock = [[]]\n for ii in range(self.blocks_x):\n iivec = range(II0, II0 + self.S_x[ii])\n Vblock.append([V[iivec, :]])\n WTblock[0].append(WT[:, iivec])\n II0 += self.S_x[ii]\n else:\n Vblock = V\n WTblock = WT\n\n if overwrite:\n self.A = libsp.block_dot(WTblock, libsp.block_dot(self.A, Vblock))\n self.B = libsp.block_dot(WTblock, self.B)\n self.C = libsp.block_dot(self.C, Vblock)\n else:\n return (libsp.block_dot(WTblock, libsp.block_dot(self.A, Vblock)),\n libsp.block_dot(WTblock, self.B),\n libsp.block_dot(self.C, Vblock))\n\n def solve_step(self, xn, un):\n\n # TODO: add options about predictor ...\n xn1 = libsp.block_sum(libsp.block_dot(self.A, xn), libsp.block_dot(self.B, un))\n yn = libsp.block_sum(libsp.block_dot(self.C, xn), libsp.block_dot(self.D, un))\n\n return xn1, yn\n\n\n def get_mats(self):\n \n A = np.zeros((self.states, self.states))\n B = np.zeros((self.states, self.inputs))\n C = np.zeros((self.outputs, self.states))\n D = np.zeros((self.outputs, self.inputs))\n \n iloc = 0\n for i in range(self.blocks_x):\n jloc = 0\n for j in range(self.blocks_x):\n if not self.A[i][j] is None:\n if type(self.A[i][j]) == libsp.csc_matrix:\n A[iloc:iloc+self.S_x[i], jloc:jloc+self.S_x[j]] = self.A[i][j].todense()\n else:\n A[iloc:iloc+self.S_x[i], jloc:jloc+self.S_x[j]] = self.A[i][j].copy()\n jloc += self.S_x[j]\n iloc += self.S_x[i]\n \n iloc = 0\n for i in range(self.blocks_x):\n jloc = 0\n for j in range(self.blocks_u):\n if not self.B[i][j] is None:\n # print(i, j, iloc, jloc, self.S_x[i], self.S_u[j], self.B[i][j].shape)\n # print(iloc, iloc+self.S_x[i], jloc, jloc+self.S_u[j])\n if type(self.B[i][j]) == libsp.csc_matrix:\n B[iloc:iloc+self.S_x[i], jloc:jloc+self.S_u[j]] = self.B[i][j].todense()\n else:\n B[iloc:iloc+self.S_x[i], jloc:jloc+self.S_u[j]] = self.B[i][j].copy()\n jloc += self.S_u[j]\n iloc += self.S_x[i]\n\n iloc = 0\n for i in range(self.blocks_y):\n jloc = 0\n for j in range(self.blocks_x):\n if not self.C[i][j] is None:\n if type(self.C[i][j]) == libsp.csc_matrix:\n C[iloc:iloc+self.S_y[i], jloc:jloc+self.S_x[j]] = self.C[i][j].todense()\n else:\n C[iloc:iloc+self.S_y[i], jloc:jloc+self.S_x[j]] = self.C[i][j].copy()\n jloc += self.S_x[j]\n iloc += self.S_y[i]\n \n iloc = 0\n for i in range(self.blocks_y):\n jloc = 0\n for j in range(self.blocks_u):\n if not self.D[i][j] is None:\n if type(self.D[i][j]) == libsp.csc_matrix:\n D[iloc:iloc+self.S_y[i], jloc:jloc+self.S_u[j]] = self.D[i][j].todense()\n else:\n D[iloc:iloc+self.S_y[i], jloc:jloc+self.S_u[j]] = self.D[i][j].copy()\n jloc += self.S_u[j]\n iloc += self.S_y[i]\n\n return A, B, C, D\n\n# ---------------------------------------- Methods for state-space manipulation\ndef project(ss_here, WT, V):\n \"\"\"\n Given 2 transformation matrices, (WT,V) of shapes (Nk,self.states) and\n (self.states,Nk) respectively, this routine returns a projection of the\n state space ss_here according to:\n\n Anew = WT A V\n Bnew = WT B\n Cnew = C V\n Dnew = D\n\n The projected model has the same number of inputs/outputs as the original\n one, but Nk states.\n \"\"\"\n\n Ap = libsp.dot(WT, libsp.dot(ss_here.A, V))\n Bp = libsp.dot(WT, ss_here.B)\n Cp = libsp.dot(ss_here.C, V)\n\n return StateSpace(Ap, Bp, Cp, ss_here.D, ss_here.dt)\n\n\ndef couple(ss01, ss02, K12, K21, out_sparse=False):\n \"\"\"\n Couples 2 dlti systems ss01 and ss02 through the gains K12 and K21, where\n K12 transforms the output of ss02 into an input of ss01.\n\n Other inputs:\n - out_sparse: if True, the output system is stored as sparse (not recommended)\n \"\"\"\n if ss01.dt is None and ss02.dt is None:\n pass\n else:\n try:\n assert np.abs(ss01.dt - ss02.dt) < 1e-10 * ss01.dt, 'Time-steps not matching!'\n except TypeError:\n raise TypeError('One of the systems to couple is discrete and the other continuous')\n\n if ss01.input_variables is not None and ss02.input_variables is not None \\\n and isinstance(K12, Gain) and isinstance(K21, Gain):\n with_enhanced_vars = True\n LinearVector.check_connection(K12.output_variables, ss01.input_variables)\n LinearVector.check_connection(ss02.output_variables, K12.input_variables)\n\n LinearVector.check_connection(K21.output_variables, ss02.input_variables)\n LinearVector.check_connection(ss01.output_variables, K21.input_variables)\n K21 = K21.value\n K12 = K12.value\n else:\n with_enhanced_vars = False\n assert K12.shape == (ss01.inputs, ss02.outputs), \\\n 'Gain K12 shape not matching with systems number of inputs/outputs'\n assert K21.shape == (ss02.inputs, ss01.outputs), \\\n 'Gain K21 shape not matching with systems number of inputs/outputs'\n\n A1, B1, C1, D1 = ss01.get_mats()\n A2, B2, C2, D2 = ss02.get_mats()\n\n # extract size\n Nx1, Nu1 = B1.shape\n Ny1 = C1.shape[0]\n Nx2, Nu2 = B2.shape\n Ny2 = C2.shape[0]\n\n # terms to invert\n maxD1 = np.max(np.abs(D1))\n maxD2 = np.max(np.abs(D2))\n if maxD1 < 1e-32:\n pass\n if maxD2 < 1e-32:\n pass\n\n # compute self-influence gains\n K11 = libsp.dot(K12, libsp.dot(D2, K21))\n K22 = libsp.dot(K21, libsp.dot(D1, K12))\n\n # left hand side terms\n L1 = libsp.dot(-K11, D1)\n L2 = libsp.dot(-K22, D2)\n L1 += libsp.eye_as(L1)\n L2 += libsp.eye_as(L2)\n\n # coupling terms\n cpl_12 = libsp.solve(L1, K12)\n cpl_21 = libsp.solve(L2, K21)\n\n cpl_11 = libsp.dot(cpl_12, libsp.dot(D2, K21))\n cpl_22 = libsp.dot(cpl_21, libsp.dot(D1, K12))\n\n # Build coupled system\n if out_sparse:\n raise NameError('out_sparse=True not supported yet (verify if worth it first).')\n else:\n A = np.block([\n [libsp.dense(A1 + libsp.dot(libsp.dot(B1, cpl_11), C1)), libsp.dense(libsp.dot(libsp.dot(B1, cpl_12), C2))],\n [libsp.dense(libsp.dot(libsp.dot(B2, cpl_21), C1)),\n libsp.dense(A2 + libsp.dot(libsp.dot(B2, cpl_22), C2))]])\n\n C = np.block([\n [libsp.dense(C1 + libsp.dot(libsp.dot(D1, cpl_11), C1)), libsp.dense(libsp.dot(libsp.dot(D1, cpl_12), C2))],\n [libsp.dense(libsp.dot(libsp.dot(D2, cpl_21), C1)),\n libsp.dense(C2 + libsp.dot(libsp.dot(D2, cpl_22), C2))]])\n\n B = np.block([\n [libsp.dense(B1 + libsp.dot(libsp.dot(B1, cpl_11), D1)), libsp.dense(libsp.dot(libsp.dot(B1, cpl_12), D2))],\n [libsp.dense(libsp.dot(libsp.dot(B2, cpl_21), D1)),\n libsp.dense(B2 + libsp.dot(libsp.dot(B2, cpl_22), D2))]])\n\n D = np.block([\n [libsp.dense(D1 + libsp.dot(libsp.dot(D1, cpl_11), D1)), libsp.dense(libsp.dot(libsp.dot(D1, cpl_12), D2))],\n [libsp.dense(libsp.dot(libsp.dot(D2, cpl_21), D1)),\n libsp.dense(D2 + libsp.dot(libsp.dot(D2, cpl_22), D2))]])\n\n coupled_ss = StateSpace(A, B, C, D, dt=ss01.dt)\n if with_enhanced_vars:\n coupled_ss.state_variables = LinearVector.merge(ss01.state_variables, ss02.state_variables)\n coupled_ss.input_variables = LinearVector.merge(ss01.input_variables, ss02.input_variables)\n coupled_ss.output_variables = LinearVector.merge(ss01.output_variables, ss02.output_variables)\n\n return coupled_ss\n\n\ndef disc2cont(sys):\n r\"\"\"\n Transform a discrete time system to a continuous time system using a bilinear (Tustin) transformation.\n\n Given a discrete time system with time step :math:`\\Delta T`, the equivalent continuous time system is given\n by:\n\n .. math::\n \\bar{A} &= \\omega_0(A-I)(I + A)^{-1} \\\\\n \\bar{B} &= \\sqrt{2\\omega_0}(I+A)^{-1}B \\\\\n \\bar{C} &= \\sqrt{2\\omega_0}C(I+A)^{-1} \\\\\n \\bar{D} &= D - C(I+A)^{-1}B\n\n where :math:`\\omega_0 = \\frac{2}{\\Delta T}`.\n\n References:\n MIT OCW 6.245\n\n Args:\n sys (libss.StateSpace): SHARPy discrete-time state-space object.\n\n Returns:\n libss.StateSpace: Converted continuous-time state-space object.\n \"\"\"\n\n assert sys.dt is not None, 'System to transform is not a discrete-time system.'\n\n n = sys.A.shape[0]\n eye = np.eye(n)\n eye_a_inv = np.linalg.inv(sys.A + eye)\n omega_0 = 2 / sys.dt\n\n a = omega_0 * (sys.A - eye).dot(eye_a_inv)\n b = np.sqrt(2 * omega_0) * eye_a_inv.dot(sys.B)\n c = np.sqrt(2 * omega_0) * sys.C.dot(eye_a_inv)\n d = sys.D - sys.C.dot(eye_a_inv.dot(sys.B))\n\n sys_ct = StateSpace(a, b, c, d)\n\n if sys.input_variables is not None:\n sys_ct.input_variables = sys.input_variables\n sys_ct.state_variables = sys.state_variables\n sys_ct.output_variables = sys.output_variables\n\n return sys_ct\n\n\ndef retain_inout_channels(sys, retain_channels, where):\n \"\"\"\n Retain selected input or output channels only.\n\n Args:\n retain_channels (list): List of channels to retain\n where (str): ``in`` or ``out`` for input/output channels\n\n Returns:\n StateSpace: Updated state-space object\n \"\"\"\n retain_m = len(retain_channels) # new number of in/out\n\n if where == 'in':\n m = sys.inputs # current number of in/out\n gain_input_vars = sys.input_variables\n gain_output_vars = LinearVector.transform(sys.input_variables, to_type=OutputVariable)\n elif where == 'out':\n m = sys.outputs\n gain_input_vars = LinearVector.transform(sys.output_variables, to_type=InputVariable)\n gain_output_vars = sys.output_variables.copy()\n else:\n raise NameError('Argument ``where`` can only be ``in`` or ``out``.')\n\n gain_matrix = np.zeros((retain_m, m))\n for ith, channel in enumerate(retain_channels):\n gain_matrix[ith, channel] = 1\n\n # Go through variables...\n for var in gain_input_vars:\n n_vars = np.sum(\n (np.array(retain_channels) < var.end_position) * (np.array(retain_channels) >= var.first_position))\n\n if n_vars == 0:\n gain_output_vars.remove(var.name)\n else:\n gain_output_vars.modify(var.name, size=n_vars)\n\n gain_output_vars.update_indices()\n gain_output_vars.update_locations()\n\n gain_matrix = Gain(gain_matrix,\n input_vars=gain_input_vars,\n output_vars=gain_output_vars)\n\n if where == 'in':\n sys.addGain(gain_matrix.transpose(), where='in')\n elif where == 'out':\n sys.addGain(gain_matrix, where='out')\n else:\n raise NameError('Argument ``where`` can only be ``in`` or ``out``.')\n\n return sys\n\n\ndef freqresp(SS, wv, dlti=True):\n \"\"\"\n In-house frequency response function supporting dense/sparse types\n\n Inputs:\n - SS: instance of StateSpace class, or scipy.signal.StateSpace*\n - wv: frequency range\n - dlti: True if discrete-time system is considered.\n\n Outputs:\n - Yfreq[outputs,inputs,len(wv)]: frequency response over wv\n\n Warnings:\n - This function may not be very efficient for dense matrices (as A is not\n reduced to upper Hessenberg form), but can exploit sparsity in the state-space\n matrices.\n \"\"\"\n\n assert type(SS) == StateSpace, \\\n 'Type %s of state-space model not supported. Use libss.StateSpace instead!' % type(SS)\n SS.check_types()\n\n if hasattr(SS, 'dt') and dlti:\n Ts = SS.dt\n wTs = Ts * wv\n zv = np.cos(wTs) + 1.j * np.sin(wTs)\n else:\n # print('Assuming a continuous time system')\n zv = 1.j * wv\n\n Nx = SS.A.shape[0]\n Ny = SS.D.shape[0]\n try:\n Nu = SS.B.shape[1]\n except IndexError:\n Nu = 1\n\n Nw = len(wv)\n\n Yfreq = np.empty((Ny, Nu, Nw,), dtype=np.complex_)\n Eye = libsp.eye_as(SS.A)\n for ii in range(Nw):\n sol_cplx = libsp.solve(zv[ii] * Eye - SS.A, SS.B)\n Yfreq[:, :, ii] = libsp.dot(SS.C, sol_cplx, type_out=np.ndarray) + SS.D\n\n return Yfreq\n\n\ndef series(SS01, SS02):\n r\"\"\"\n Connects two state-space blocks in series. If these are instances of DLTI\n state-space systems, they need to have the same type and time-step. If the input systems are sparse, they are\n converted to dense.\n\n The connection is such that:\n\n .. math::\n u \\rightarrow \\mathsf{SS01} \\rightarrow \\mathsf{SS02} \\rightarrow y \\Longrightarrow\n u \\rightarrow \\mathsf{SStot} \\rightarrow y\n\n where the state vector :math:`x` is :math:`[x_1, x_2]`.\n\n Args:\n SS01 (libss.StateSpace): State Space 1 instance. Can be DLTI/CLTI, dense or sparse.\n SS02 (libss.StateSpace): State Space 2 instance. Can be DLTI/CLTI, dense or sparse.\n\n Returns\n libss.StateSpace: Combined state space system in series in dense format.\n \"\"\"\n\n if type(SS01) is not type(SS02):\n raise TypeError('The two input systems are not of the same type')\n if SS01.dt != SS02.dt:\n raise NameError('DLTI systems do not have the same time-step. SS01 dt={:f}, SS02 dt={:f}'.format(\n SS01.dt, SS02.dt))\n\n # check series connection\n if SS01.output_variables is not None and SS02.input_variables is not None:\n LinearVector.check_connection(SS01.output_variables, SS02.input_variables)\n # for i_var in range(SS01.output_variables.num_variables):\n # out1 = SS01.output_variables[i_var]\n # in2 = SS02.input_variables[i_var]\n # if out1.name != in2.name:\n # raise NameError('Series coupling outputs1 and inputs2 have different names')\n # if not (out1.rows_loc == in2.cols_loc).all:\n # raise IndexError('Series coupling. Output1 channels do not line up with input2 channels.')\n\n # determine size of total system\n Nst01, Nst02 = SS01.states, SS02.states\n Nst = Nst01 + Nst02\n Nin = SS01.inputs\n Nout = SS02.outputs\n\n if SS01.outputs != SS02.inputs:\n raise ValueError('SS01 outputs not equal to SS02 inputs,\\nSS01={:s}\\nSS02={:s}'.format(str(SS01), str(SS02)))\n\n # Build A matrix\n A = np.zeros((Nst, Nst))\n\n A[:Nst01, :Nst01] = libsp.dense(SS01.A)\n A[Nst01:, Nst01:] = libsp.dense(SS02.A)\n A[Nst01:, :Nst01] = libsp.dense(libsp.dot(SS02.B, SS01.C))\n\n # Build the rest\n B = np.concatenate((libsp.dense(SS01.B), libsp.dense(libsp.dot(SS02.B, SS01.D))), axis=0)\n C = np.concatenate((libsp.dense(libsp.dot(SS02.D, SS01.C)), libsp.dense(SS02.C)), axis=1)\n D = libsp.dense(libsp.dot(SS02.D, SS01.D))\n\n SStot = StateSpace(A, B, C, D, dt=SS01.dt)\n\n SStot.input_variables = SS01.input_variables\n try:\n SStot.state_variables = LinearVector.merge(SS01.state_variables, SS02.state_variables)\n except AttributeError:\n SStot.state_variables = None\n SStot.output_variables = SS02.output_variables\n\n return SStot\n\n\ndef parallel(SS01, SS02):\n \"\"\"\n Returns the sum (or parallel connection of two systems). Given two state-space\n models with the same output, but different input:\n u1 --> SS01 --> y\n u2 --> SS02 --> y\n\n \"\"\"\n\n if type(SS01) is not type(SS02):\n raise NameError('The two input systems need to have the same size!')\n if SS01.dt != SS02.dt:\n raise NameError('DLTI systems do not have the same time-step!')\n Nout = SS02.outputs\n if Nout != SS01.outputs:\n raise NameError('DLTI systems need to have the same number of output!')\n\n # if type(SS01) is control.statesp.StateSpace:\n # \tSStot=control.parallel(SS01,SS02)\n # else:\n\n # determine size of total system\n Nst01, Nst02 = SS01.states, SS02.states\n Nst = Nst01 + Nst02\n Nin01, Nin02 = SS01.inputs, SS02.inputs\n Nin = Nin01 + Nin02\n\n # Build A,B matrix\n A = np.zeros((Nst, Nst))\n A[:Nst01, :Nst01] = SS01.A\n A[Nst01:, Nst01:] = SS02.A\n B = np.zeros((Nst, Nin))\n B[:Nst01, :Nin01] = SS01.B\n B[Nst01:, Nin01:] = SS02.B\n\n # Build the rest\n C = np.block([SS01.C, SS02.C])\n D = np.block([SS01.D, SS02.D])\n\n SStot = scsig.dlti(A, B, C, D, dt=SS01.dt)\n\n return SStot\n\n\ndef SSconv(A, B0, B1, C, D, Bm1=None):\n r\"\"\"\n Convert a DLTI system with prediction and delay of the form:\n\n .. math::\n \\mathbf{x}_{n+1} &= \\mathbf{A\\,x}_n + \\mathbf{B_0\\,u}_n + \\mathbf{B_1\\,u}_{n+1} + \\mathbf{B_{m1}\\,u}_{n-1} \\\\\n \\mathbf{y}_n &= \\mathbf{C\\,x}_n + \\mathbf{D\\,u}_n\n\n into the state-space form:\n\n .. math::\n \\mathbf{h}_{n+1} &= \\mathbf{A_h\\,h}_n + \\mathbf{B_h\\,u}_n \\\\\n \\mathbf{y}_n &= \\mathbf{C_h\\,h}_n + \\mathbf{D_h\\,u}_n\n\n If :math:`\\mathbf{B_{m1}}` is ``None``, the original state is retrieved through\n\n .. math:: \\mathbf{x}_n = \\mathbf{h}_n + \\mathbf{B_1\\,u}_n\n\n and only the :math:`\\mathbf{B}` and :math:`\\mathbf{D}` matrices are modified.\n\n\n If :math:`\\mathbf{B_{m1}}` is not ``None``, the SS is augmented with the new state\n\n .. math:: \\mathbf{g}_{n} = \\mathbf{u}_{n-1}\n\n or, equivalently, with the equation\n\n .. math:: \\mathbf{g}_{n+1} = \\mathbf{u}_n\n\n leading to the new form\n\n .. math::\n \\mathbf{H}_{n+1} &= \\mathbf{A_A\\,H}_{n} + \\mathbf{B_B\\,u}_n \\\\\n \\mathbf{y}_n &= \\mathbf{C_C\\,H}_{n} + \\mathbf{D_D\\,u}_n\n\n where :math:`\\mathbf{H} = (\\mathbf{x},\\,\\mathbf{g})`.\n\n Args:\n A (np.ndarray): dynamics matrix\n B0 (np.ndarray): input matrix for input at current time step ``n``. Set to None if this is zero.\n B1 (np.ndarray): input matrix for input at time step ``n+1`` (predictor term)\n C (np.ndarray): output matrix\n D (np.ndarray): direct matrix\n Bm1 (np.ndarray): input matrix for input at time step ``n-1`` (delay term)\n\n Returns:\n tuple: tuple packed with the state-space matrices :math:`\\mathbf{A},\\,\\mathbf{B},\\,\\mathbf{C}` and :math:`\\mathbf{D}`.\n\n References:\n Franklin, GF and Powell, JD. Digital Control of Dynamic Systems, Addison-Wesley Publishing Company, 1980\n\n Warnings:\n functions untested for delays (Bm1 != 0)\n \"\"\"\n\n # Account for u^{n+1} terms (prediction)\n if B0 is None:\n Bh = libsp.dot(A, B1)\n else:\n Bh = B0 + libsp.dot(A, B1)\n Dh = D + libsp.dot(C, B1)\n\n # Account for u^{n-1} terms (delay)\n if Bm1 is None:\n outs = (A, Bh, C, Dh)\n else:\n warnings.warn('Function untested when Bm1!=None')\n\n Nx, Nu, Ny = A.shape[0], Bh.shape[1], C.shape[0]\n AA = np.block([[A, Bm1],\n [np.zeros((Nu, Nx)), np.zeros((Nu, Nu))]])\n BB = np.block([[Bh], [np.eye(Nu)]])\n CC = np.block([C, np.zeros((Ny, Nu))])\n DD = Dh\n outs = (AA, BB, CC, DD)\n\n return outs\n\n\ndef addGain(SShere, Kmat, where):\n \"\"\"\n Convert input u or output y of a SS DLTI system through gain matrix K. We\n have the following transformations:\n - where='in': the input dof of the state-space are changed\n u_new -> Kmat*u -> SS -> y => u_new -> SSnew -> y\n - where='out': the output dof of the state-space are changed\n u -> SS -> y -> Kmat*u -> ynew => u -> SSnew -> ynew\n - where='parallel': the input dofs are changed, but not the output\n -\n {u_1 -> SS -> y_1\n { u_2 -> y_2= Kmat*u_2 => u_new=(u_1,u_2) -> SSnew -> y=y_1+y_2\n {y = y_1+y_2\n -\n Warning: function not tested for Kmat stored in sparse format\n \"\"\"\n\n assert where in ['in', 'out', 'parallel-down', 'parallel-up'], \\\n 'Specify whether gains are added to input or output'\n\n if where == 'in':\n A = SShere.A\n B = SShere.B.dot(Kmat)\n C = SShere.C\n D = SShere.D.dot(Kmat)\n\n if where == 'out':\n A = SShere.A\n B = SShere.B\n C = Kmat.dot(SShere.C)\n D = Kmat.dot(SShere.D)\n\n if where == 'parallel-down':\n A = SShere.A\n C = SShere.C\n B = np.block([SShere.B, np.zeros((SShere.B.shape[0], Kmat.shape[1]))])\n D = np.block([SShere.D, Kmat])\n\n if where == 'parallel-up':\n A = SShere.A\n C = SShere.C\n B = np.block([np.zeros((SShere.B.shape[0], Kmat.shape[1])), SShere.B])\n D = np.block([Kmat, SShere.D])\n\n if SShere.dt == None:\n SSnew = StateSpace(A, B, C, D)\n else:\n SSnew = StateSpace(A, B, C, D, dt=SShere.dt)\n\n return SSnew\n\n\ndef join2(SS1, SS2):\n r\"\"\"\n Join two state-spaces or gain matrices such that, given:\n\n .. math::\n \\mathbf{u}_1 \\longrightarrow &\\mathbf{SS}_1 \\longrightarrow \\mathbf{y}_1 \\\\\n \\mathbf{u}_2 \\longrightarrow &\\mathbf{SS}_2 \\longrightarrow \\mathbf{y}_2\n\n we obtain:\n\n .. math::\n \\mathbf{u} \\longrightarrow \\mathbf{SS}_{TOT} \\longrightarrow \\mathbf{y}\n\n with :math:`\\mathbf{u}=(\\mathbf{u}_1,\\mathbf{u}_2)^T` and :math:`\\mathbf{y}=(\\mathbf{y}_1,\\mathbf{y}_2)^T`.\n\n The output :math:`\\mathbf{SS}_{TOT}` is either a gain matrix or a state-space system according\n to the input :math:`\\mathbf{SS}_1` and :math:`\\mathbf{SS}_2`\n\n Args:\n SS1 (scsig.StateSpace or np.ndarray): State space 1 or gain 1\n SS2 (scsig.StateSpace or np.ndarray): State space 2 or gain 2\n\n Returns:\n scsig.StateSpace or np.ndarray: combined state space or gain matrix\n\n \"\"\"\n type_dlti = scsig.ltisys.StateSpaceDiscrete\n\n if isinstance(SS1, np.ndarray) and isinstance(SS2, np.ndarray):\n\n Nin01, Nin02 = SS1.shape[1], SS2.shape[1]\n Nout01, Nout02 = SS1.shape[0], SS2.shape[0]\n SStot = np.block([[SS1, np.zeros((Nout01, Nin02))],\n [np.zeros((Nout02, Nin01)), SS2]])\n\n elif isinstance(SS1, np.ndarray) and isinstance(SS2, type_dlti):\n\n Nin01, Nout01 = SS1.shape[1], SS1.shape[0]\n Nin02, Nout02 = SS2.inputs, SS2.outputs\n Nx02 = SS2.A.shape[0]\n\n A = SS2.A\n B = np.block([np.zeros((Nx02, Nin01)), SS2.B])\n C = np.block([[np.zeros((Nout01, Nx02))],\n [SS2.C]])\n D = np.block([[SS1, np.zeros((Nout01, Nin02))],\n [np.zeros((Nout02, Nin01)), SS2.D]])\n\n SStot = scsig.StateSpace(A, B, C, D, dt=SS2.dt)\n\n elif isinstance(SS1, type_dlti) and isinstance(SS2, np.ndarray):\n\n Nin01, Nout01 = SS1.inputs, SS1.outputs\n Nin02, Nout02 = SS2.shape[1], SS2.shape[0]\n Nx01 = SS1.A.shape[0]\n\n A = SS1.A\n B = np.block([SS1.B, np.zeros((Nx01, Nin02))])\n C = np.block([[SS1.C],\n [np.zeros((Nout02, Nx01))]])\n D = np.block([[SS1.D, np.zeros((Nout01, Nin02))],\n [np.zeros((Nout02, Nin01)), SS2]])\n\n SStot = scsig.StateSpace(A, B, C, D, dt=SS1.dt)\n\n elif isinstance(SS1, type_dlti) and isinstance(SS2, type_dlti):\n\n assert SS1.dt == SS2.dt, 'State-space models must have the same time-step'\n\n Nin01, Nout01 = SS1.inputs, SS1.outputs\n Nin02, Nout02 = SS2.inputs, SS2.outputs\n Nx01, Nx02 = SS1.A.shape[0], SS2.A.shape[0]\n\n A = np.block([[SS1.A, np.zeros((Nx01, Nx02))],\n [np.zeros((Nx02, Nx01)), SS2.A]])\n B = np.block([[SS1.B, np.zeros((Nx01, Nin02))],\n [np.zeros((Nx02, Nin01)), SS2.B]])\n C = np.block([[SS1.C, np.zeros((Nout01, Nx02))],\n [np.zeros((Nout02, Nx01)), SS2.C]])\n D = np.block([[SS1.D, np.zeros((Nout01, Nin02))],\n [np.zeros((Nout02, Nin01)), SS2.D]])\n SStot = scsig.StateSpace(A, B, C, D, dt=SS1.dt)\n\n else:\n raise NameError('Input types not recognised in any implemented option!')\n\n return SStot\n\n\ndef join(SS_list, wv=None):\n \"\"\"\n Given a list of state-space models belonging to the StateSpace class, creates a\n joined system whose output is the sum of the state-space outputs. If wv is\n not None, this is a list of weights, such that the output is:\n\n y = sum( wv[ii] y_ii )\n\n Ref: equation (4.22) of\n Benner, P., Gugercin, S. & Willcox, K., 2015. A Survey of Projection-Based\n Model Reduction Methods for Parametric Dynamical Systems. SIAM Review, 57(4),\n pp.483–531.\n\n Warnings:\n - system matrices must be numpy arrays\n - the function does not perform any check!\n \"\"\"\n\n N = len(SS_list)\n if wv is not None:\n assert N == len(wv), \"'weights input should have'\"\n\n A = scalg.block_diag(*[getattr(ss, 'A') for ss in SS_list])\n B = np.block([[getattr(ss, 'B')] for ss in SS_list])\n\n if wv is None:\n C = np.block([getattr(ss, 'C') for ss in SS_list])\n else:\n C = np.block([ww * getattr(ss, 'C') for ww, ss in zip(wv, SS_list)])\n\n D = np.zeros_like(SS_list[0].D)\n for ii in range(N):\n if wv is None:\n D += SS_list[ii].D\n else:\n D += wv[ii] * SS_list[ii].D\n\n return StateSpace(A, B, C, D, SS_list[0].dt)\n\n\ndef sum_ss(SS1, SS2, negative=False):\n \"\"\"\n Given 2 systems or gain matrices (or a combination of the two) having the\n same amount of input/output, the function returns a gain or state space\n model summing the two. Namely, given:\n u -> SS1 -> y1\n u -> SS2 -> y2\n we obtain:\n u -> SStot -> y1+y2 \tif negative=False\n \"\"\"\n type_dlti = scsig.ltisys.StateSpaceDiscrete\n\n if isinstance(SS1, np.ndarray) and isinstance(SS2, np.ndarray):\n SStot = SS1 + SS2\n\n elif isinstance(SS1, np.ndarray) and isinstance(SS2, type_dlti):\n Kmat = SS1\n A = SS2.A\n B = SS2.B\n C = SS2.C\n D = SS2.D + Kmat\n SStot = scsig.StateSpace(A, B, C, D, dt=SS2.dt)\n\n elif isinstance(SS1, type_dlti) and isinstance(SS2, np.ndarray):\n Kmat = SS2\n A = SS1.A\n B = SS1.B\n C = SS1.C\n D = SS1.D + Kmat\n\n SStot = scsig.StateSpace(A, B, C, D, dt=SS2.dt)\n\n elif isinstance(SS1, type_dlti) and isinstance(SS2, type_dlti):\n\n assert np.abs(1. - SS1.dt / SS2.dt) < 1e-13, \\\n 'State-space models must have the same time-step'\n\n Nin01, Nout01 = SS1.inputs, SS1.outputs\n Nin02, Nout02 = SS2.inputs, SS2.outputs\n Nx01, Nx02 = SS1.A.shape[0], SS2.A.shape[0]\n\n A = np.block([[SS1.A, np.zeros((Nx01, Nx02))],\n [np.zeros((Nx02, Nx01)), SS2.A]])\n B = np.block([[SS1.B, ],\n [SS2.B]])\n C = np.block([SS1.C, SS2.C])\n D = SS1.D + SS2.D\n\n SStot = scsig.StateSpace(A, B, C, D, dt=SS1.dt)\n\n\n else:\n raise NameError('Input types not recognised in any implemented option!')\n\n return SStot\n\n\ndef scale_SS(SSin, input_scal=1., output_scal=1., state_scal=1., byref=True):\n r\"\"\"\n Given a state-space system, scales the equations such that the original\n input and output, :math:`u` and :math:`y`, are substituted by :math:`u_{AD}=\\frac{u}{u_{ref}}`\n and :math:`y_{AD}=\\frac{y}{y_{ref}}`.\n\n If the original system has form:\n\n .. math::\n \\mathbf{x}^{n+1} &= \\mathbf{A\\,x}^n + \\mathbf{B\\,u}^n \\\\\n \\mathbf{y}^{n} &= \\mathbf{C\\,x}^{n} + \\mathbf{D\\,u}^n\n\n the transformation is such that:\n\n .. math::\n \\mathbf{x}^{n+1} &= \\mathbf{A\\,x}^n + \\mathbf{B}\\,\\frac{u_{ref}}{x_{ref}}\\mathbf{u_{AD}}^n \\\\\n \\mathbf{y_{AD}}^{n+1} &= \\frac{1}{y_{ref}}(\\mathbf{C}\\,x_{ref}\\,\\mathbf{x}^{n+1} + \\mathbf{D}\\,u_{ref}\\,\\mathbf{u_{AD}}^n)\n\n By default, the state-space model is manipulated by reference (``byref=True``)\n\n Args:\n SSin (scsig.dlti): original state-space formulation\n input_scal (float or np.ndarray): input scaling factor :math:`u_{ref}`. It can be a float or an array, in which\n case the each element of the input vector will be scaled by a different\n factor.\n output_scal (float or np.ndarray): output scaling factor :math:`y_{ref}`. It can be a float or an array, in which\n case the each element of the output vector will be scaled by a different\n factor.\n state_scal (float or np.ndarray): state scaling factor :math:`x_{ref}`. It can be a float or an array, in which\n case the each element of the state vector will be scaled by a different\n factor.\n byref (bool): state space manipulation order\n\n Returns:\n scsig.dlti: scaled state space formulation\n \"\"\"\n\n # check input:\n Nin, Nout = SSin.inputs, SSin.outputs\n Nstates = SSin.A.shape[0]\n\n if isinstance(input_scal, (list, np.ndarray)):\n assert len(input_scal) == Nin, \\\n 'Length of input_scal not matching number of state-space inputs!'\n else:\n input_scal = Nin * [input_scal]\n\n if isinstance(output_scal, (list, np.ndarray)):\n assert len(output_scal) == Nout, \\\n 'Length of output_scal not matching number of state-space outputs!'\n else:\n output_scal = Nout * [output_scal]\n\n if isinstance(state_scal, (list, np.ndarray)):\n assert len(state_scal) == Nstates, \\\n 'Length of state_scal not matching number of state-space states!'\n else:\n state_scal = Nstates * [state_scal]\n\n if byref:\n SS = SSin\n else:\n print('deep-copying state-space model before scaling')\n SS = copy.deepcopy(SSin)\n\n # update input related matrices\n for ii in range(Nin):\n SS.B[:, ii] = SS.B[:, ii] * input_scal[ii]\n SS.D[:, ii] = SS.D[:, ii] * input_scal[ii]\n # SS.B[:,ii]*=input_scal[ii]\n # SS.D[:,ii]*=input_scal[ii]\n\n # update output related matrices\n for ii in range(Nout):\n SS.C[ii, :] = SS.C[ii, :] / output_scal[ii]\n SS.D[ii, :] = SS.D[ii, :] / output_scal[ii]\n # SS.C[ii,:]/=output_scal[ii]\n # SS.D[ii,:]/=output_scal[ii]\n\n # update state related matrices\n for ii in range(Nstates):\n SS.B[ii, :] = SS.B[ii, :] / state_scal[ii]\n SS.C[:, ii] = SS.C[:, ii] * state_scal[ii]\n # SS.B[ii,:]/=state_scal[ii]\n # SS.C[:,ii]*=state_scal[ii]\n\n return SS\n\n\ndef simulate(SShere, U, x0=None):\n \"\"\"\n Routine to simulate response to generic input.\n\n Warnings:\n This routine is for testing and may lack of robustness. Use\n scipy.signal instead.\n \"\"\"\n\n A, B, C, D = SShere.A, SShere.B, SShere.C, SShere.D\n\n NT = U.shape[0]\n Nx = A.shape[0]\n Ny = C.shape[0]\n\n X = np.zeros((NT, Nx))\n Y = np.zeros((NT, Ny))\n\n if x0 is not None: X[0] = x0\n if len(U.shape) == 1:\n U = U.reshape((NT, 1))\n\n Y[0] = libsp.dot(C, X[0]) + libsp.dot(D, U[0])\n\n for ii in range(1, NT):\n X[ii] = libsp.dot(A, X[ii - 1]) + libsp.dot(B, U[ii - 1])\n Y[ii] = libsp.dot(C, X[ii]) + libsp.dot(D, U[ii])\n\n return Y, X\n\n\ndef Hnorm_from_freq_resp(gv, method):\n \"\"\"\n Given a frequency response over a domain kv, this funcion computes the\n H norms through numerical integration.\n\n Note that if kv[-1] 1e-16:\n raise NameError('Norm is not a real number. Verify data/algorithm!')\n\n return Gnorm\n\n\ndef adjust_phase(y, deg=True):\n \"\"\"\n Modify the phase y of a frequency response to remove discontinuities.\n \"\"\"\n\n if deg is True:\n shift = 360.\n else:\n shift = 2. * np.pi\n\n dymax = 0.0\n\n N = len(y)\n for ii in range(N - 1):\n dy = y[ii + 1] - y[ii]\n if np.abs(dy) > dymax: dymax = np.abs(dy)\n if dy > 0.97 * shift:\n print('Subtracting shift to frequency response phase diagram!')\n y[ii + 1::] = y[ii + 1::] - shift\n\n elif dy < -0.97 * shift:\n y[ii + 1::] = y[ii + 1::] + shift\n print('Adding shift to frequency response phase diagram!')\n\n return y\n\n\n# -------------------------------------------------------------- Special Models\n\n\ndef SSderivative(ds):\n \"\"\"\n Given a time-step ds, and an single input time history u, this SS model\n returns the output y=[u,du/ds], where du/dt is computed with second order\n accuracy.\n \"\"\"\n\n A = np.array([[0]])\n Bm1 = np.array([0.5 / ds])\n B0 = np.array([[-2 / ds]])\n B1 = np.array([[1.5 / ds]])\n C = np.array([[0], [1]])\n D = np.array([[1], [0]])\n\n # change state\n Aout, Bout, Cout, Dout = SSconv(A, B0, B1, C, D, Bm1)\n\n return Aout, Bout, Cout, Dout\n\n\ndef SSintegr(ds, method='trap'):\n \"\"\"\n Builds a state-space model of an integrator.\n\n - method: Numerical scheme. Available options are:\n - 1tay: 1st order Taylor (fwd)\n I[ii+1,:]=I[ii,:] + ds*F[ii,:]\n - trap: I[ii+1,:]=I[ii,:] + 0.5*dx*(F[ii,:]+F[ii+1,:])\n\n Note: other option can be constructured if information on derivative of\n F is available (for e.g.)\n \"\"\"\n\n A = np.array([[1]])\n C = np.array([[1.]])\n D = np.array([[0.]])\n\n if method == '1tay':\n Bm1 = np.array([0.])\n B0 = np.array([[ds]])\n B1 = np.array([[0.]])\n Aout, Bout, Cout, Dout = A, B0, C, D\n\n elif method == 'trap':\n Bm1 = np.array([0.])\n B0 = np.array([[.5 * ds]])\n B1 = np.array([[.5 * ds]])\n Aout, Bout, Cout, Dout = SSconv(A, B0, B1, C, D, Bm1=None)\n\n else:\n raise NameError('Method %s not available!' % method)\n\n # change state\n\n return Aout, Bout, Cout, Dout\n\n\ndef build_SS_poly(Acf, ds, negative=False):\n \"\"\"\n Builds a discrete-time state-space representation of a polynomial system\n whose frequency response has from:\n Ypoly[oo,ii](k) = -A2[oo,ii] D2(k) - A1[oo,ii] D1(k) - A0[oo,ii]\n where C1,D2 are discrete-time models of first and second derivatives, ds is\n the time-step and the coefficient matrices are such that:\n A{nn}=Acf[oo,ii,nn]\n \"\"\"\n\n Nout, Nin, Ncf = Acf.shape\n assert Ncf == 3, 'Acf input last dimension must be equal to 3!'\n\n Ader, Bder, Cder, Dder = SSderivative(ds)\n SSder = scsig.dlti(Ader, Bder, Cder, Dder, dt=ds)\n SSder02 = series(SSder, join2(np.array([[1]]), SSder))\n\n SSder_all = copy.deepcopy(SSder02)\n for ii in range(Nin - 1):\n SSder_all = join2(SSder_all, SSder02)\n\n # Build polynomial forcing terms\n sign = 1.0\n if negative == True: sign = -1.0\n\n A0 = Acf[:, :, 0]\n A1 = Acf[:, :, 1]\n A2 = Acf[:, :, 2]\n Kforce = np.zeros((Nout, 3 * Nin))\n for ii in range(Nin):\n Kforce[:, 3 * ii] = sign * (A0[:, ii])\n Kforce[:, 3 * ii + 1] = sign * (A1[:, ii])\n Kforce[:, 3 * ii + 2] = sign * (A2[:, ii])\n SSpoly_neg = addGain(SSder_all, Kforce, where='out')\n\n return SSpoly_neg\n\n\ndef butter(order, Wn, N=1, btype='lowpass'):\n \"\"\"\n build MIMO butterworth filter of order ord and cut-off freq over Nyquist\n freq ratio Wn.\n The filter will have N input and N output and N*ord states.\n\n Note: the state-space form of the digital filter does not depend on the\n sampling time, but only on the Wn ratio.\n As a result, this function only returns the A,B,C,D matrices of the filter\n state-space form.\n \"\"\"\n\n # build DLTI SISO\n num, den = scsig.butter(order, Wn, btype=btype, analog=False, output='ba')\n Af, Bf, Cf, Df = scsig.tf2ss(num, den)\n SSf = scsig.dlti(Af, Bf, Cf, Df, dt=1.0)\n\n SStot = SSf\n for ii in range(1, N):\n SStot = join2(SStot, SSf)\n\n return SStot.A, SStot.B, SStot.C, SStot.D\n\n\n# ----------------------------------------------------------------------- Utils\n\ndef get_freq_from_eigs(eigs, dlti=True):\n \"\"\"\n Compute natural freq corresponding to eigenvalues, eigs, of a continuous or\n discrete-time (dlti=True) systems.\n\n Note: if dlti=True, the frequency is normalised by (1./dt), where dt is the\n DLTI time-step - i.e. the frequency in Hertz is obtained by multiplying fn by\n (1./dt).\n \"\"\"\n if dlti:\n fn = 0.5 * np.angle(eigs) / np.pi\n else:\n fn = np.abs(eigs.imag)\n return fn\n\n\ndef eigvals(a, dlti=False):\n \"\"\"\n Ordered eigenvalaues of a matrix.\n\n Args:\n a (np.ndarray): Matrix.\n dlti (bool): If true, the eigenvalues are ordered by modulus, else by real part.\n\n Returns:\n np.ndarray: ordered set of eigenvalues.\n \"\"\"\n eigs = np.linalg.eigvals(a)\n\n if dlti:\n order = np.argsort(np.abs(eigs))\n else:\n order = np.argsort(eigs.real)\n\n return eigs[order]\n\n\n# --------------------------------------------------------------------- Testing\n\n\ndef random_ss(Nx, Nu, Ny, dt=None, use_sparse=False, stable=True):\n \"\"\"\n Define random system from number of states (Nx), inputs (Nu) and output (Ny).\n\n Args:\n Nx (int): Number of states\n Nu (int): Number of inputs\n Ny (int): Number of outputs\n dt (float (optional)): Time step for discrete systems\n use_sparse (bool): Use sparse matrices\n stable (bool): Ensure the system is stable\n\n Returns:\n StateSpace: State space object\n \"\"\"\n\n A = np.random.rand(Nx, Nx)\n if stable:\n ev, U = np.linalg.eig(A)\n evabs = np.abs(ev)\n\n for ee in range(len(ev)):\n if evabs[ee] > 0.99:\n ev[ee] /= 1.1 * evabs[ee]\n A = np.dot(U * ev, np.linalg.inv(U)).real\n B = np.random.rand(Nx, Nu)\n C = np.random.rand(Ny, Nx)\n D = np.random.rand(Ny, Nu)\n\n if use_sparse:\n ss = StateSpace(libsp.csc_matrix(A),\n libsp.csc_matrix(B),\n libsp.csc_matrix(C),\n libsp.csc_matrix(D),\n dt=dt)\n else:\n ss = StateSpace(A, B, C, D, dt=dt)\n\n ss.initialise_variables(({'name': 'input_variable', 'size': Nu}), var_type='in')\n ss.initialise_variables(({'name': 'output_variable', 'size': Ny}), var_type='out')\n ss.initialise_variables(({'name': 'state_variable', 'size': Nx}), var_type='state')\n\n return ss\n\n\ndef compare_ss(SS1, SS2, tol=1e-10, Print=False):\n \"\"\"\n Assert matrices of state-space models are identical\n \"\"\"\n\n era = np.max(np.abs(libsp.dense(SS1.A) - libsp.dense(SS2.A)))\n if Print: print('Max. error A: %.3e' % era)\n\n erb = np.max(np.abs(libsp.dense(SS1.B) - libsp.dense(SS2.B)))\n if Print: print('Max. error B: %.3e' % erb)\n\n erc = np.max(np.abs(libsp.dense(SS1.C) - libsp.dense(SS2.C)))\n if Print: print('Max. error C: %.3e' % erc)\n\n erd = np.max(np.abs(libsp.dense(SS1.D) - libsp.dense(SS2.D)))\n if Print: print('Max. error D: %.3e' % erd)\n\n assert era < tol, 'Error A matrix %.2e>%.2e' % (era, tol)\n assert erb < tol, 'Error B matrix %.2e>%.2e' % (erb, tol)\n assert erc < tol, 'Error C matrix %.2e>%.2e' % (erc, tol)\n assert erd < tol, 'Error D matrix %.2e>%.2e' % (erd, tol)\n\n # print('System matrices identical within tolerance %.2e'%tol)\n return (era, erb, erc, erd)\n\n\n# -----------------------------------------------------------------------------\n\n\ndef ss_to_scipy(ss):\n \"\"\"\n Converts to a scipy.signal linear time invariant system\n\n Args:\n ss (libss.StateSpace): SHARPy state space object\n\n Returns:\n scipy.signal.dlti\n \"\"\"\n\n if ss.dt == None:\n sys = scsig.lti(ss.A, ss.B, ss.C, ss.D)\n else:\n sys = scsig.dlti(ss.A, ss.B, ss.C, ss.D, dt=ss.dt)\n\n return sys\n" }, { "path": "sharpy/linear/src/lin_aeroelastic.py", "content": "\"\"\"\nLinear aeroelastic model based on coupled GEBM + UVLM\nS. Maraniello, Jul 2018\n\"\"\"\n\nimport warnings\nimport numpy as np\n\nimport sharpy.utils.settings\nimport sharpy.linear.src.linuvlm as linuvlm\nimport sharpy.linear.src.lingebm as lingebm\nimport sharpy.linear.src.libss as libss\nimport sharpy.utils.algebra as algebra\n\n\nclass LinAeroEla():\n r\"\"\"\n\n Future work:\n - settings are converted from string to type in __init__ method.\n - implement all settings of LinUVLM (e.g. support for sparse matrices)\n\n When integrating in SHARPy:\n * define:\n - self.setting_types\n - self.setting_default\n * use settings.to_custom_types(self.in_dict, self.settings_types, self.settings_default) for conversion to type.\n\n Args:\n data (sharpy.presharpy.PreSharpy): main SHARPy data class\n settings_linear (dict): optional settings file if they are not included in the ``data`` structure\n\n Attributes:\n settings (dict): solver settings for the linearised aeroelastic solution\n lingebm (lingebm.FlexDynamic): linearised geometrically exact beam model\n num_dof_str (int): number of structural degrees of freedom\n num_dof_rig (int): number of rigid degrees of freedom\n num_dof_flex (int): number of flexible degrees of freedom (``num_dof_flex+num_dof_rigid=num_dof_str``)\n linuvl (linuvlm.Dynamic): linearised UVLM class\n tsaero (sharpy.utils.datastructures.AeroTimeStepInfo): aerodynamic state timestep info\n tsstr (sharpy.utils.datastructures.StructTimeStepInfo): structural state timestep info\n dt (float): time increment\n q (np.array): corresponding vector of displacements of dimensions ``[1, num_dof_str]``\n dq (np.array): time derivative (:math:`\\dot{\\mathbf{q}}`) of the corresponding vector of displacements\n with dimensions ``[1, num_dof_str]``\n SS (scipy.signal): state space formulation (discrete or continuous time), as selected by the user\n \"\"\"\n\n def __init__(self, data, custom_settings_linear=None, uvlm_block=False, chosen_ts=None):\n\n self.data = data\n if custom_settings_linear is None:\n settings_here = data.settings['LinearUvlm']\n else:\n settings_here = custom_settings_linear\n\n sharpy.utils.settings.to_custom_types(settings_here,\n linuvlm.settings_types_dynamic,\n linuvlm.settings_default_dynamic,\n no_ctype=True)\n\n if chosen_ts is None:\n self.chosen_ts = self.data.ts\n else:\n self.chosen_ts = chosen_ts\n\n ## TEMPORARY - NEED TO INCLUDE PROPER INTEGRATION OF SETTINGS\n try:\n self.rigid_body_motions = settings_here['rigid_body_motion']\n except KeyError:\n self.rigid_body_motions = False\n\n try:\n self.use_euler = settings_here['use_euler']\n except KeyError:\n self.use_euler = False\n\n if self.rigid_body_motions and settings_here['track_body']:\n self.track_body = True\n else:\n self.track_body = False\n ## -------\n\n ### extract aeroelastic info\n self.dt = settings_here['dt']\n\n ### reference to timestep_info\n # aero\n aero = data.aero\n self.tsaero = aero.timestep_info[self.chosen_ts]\n # structure\n structure = data.structure\n self.tsstr = structure.timestep_info[self.chosen_ts]\n\n # --- backward compatibility\n try:\n rho = settings_here['density']\n except KeyError:\n warnings.warn(\n \"Key 'density' not found in 'LinearUvlm' solver settings. '\\\n 'Trying to read it from 'StaticCoupled'.\")\n rho = data.settings['StaticCoupled']['aero_solver_settings']['rho']\n if type(rho) == str:\n rho = np.float(rho)\n \n self.tsaero.rho = rho\n # --- backward compatibility\n\n ### gebm\n if self.use_euler:\n self.num_dof_rig = 9\n else:\n self.num_dof_rig = 10\n\n self.num_dof_flex = np.sum(self.data.structure.vdof >= 0)*6\n self.num_dof_str = self.num_dof_flex + self.num_dof_rig\n self.reshape_struct_input()\n\n try:\n beam_settings = settings_here['beam_settings']\n except KeyError:\n beam_settings = dict()\n self.lingebm_str = lingebm.FlexDynamic(self.tsstr, structure, beam_settings)\n\n cga = algebra.quat2rotation(self.tsstr.quat)\n ### uvlm\n if uvlm_block:\n self.linuvlm = linuvlm.DynamicBlock(\n self.tsaero,\n dt=settings_here['dt'],\n dynamic_settings=settings_here,\n RemovePredictor=settings_here['remove_predictor'],\n UseSparse=settings_here['use_sparse'],\n integr_order=settings_here['integr_order'],\n ScalingDict=settings_here['ScalingDict'],\n for_vel=np.hstack((cga.dot(self.tsstr.for_vel[:3]),\n cga.dot(self.tsstr.for_vel[3:]))))\n else:\n self.linuvlm = linuvlm.Dynamic(\n self.tsaero,\n dt=settings_here['dt'],\n dynamic_settings=settings_here,\n RemovePredictor=settings_here['remove_predictor'],\n UseSparse=settings_here['use_sparse'],\n integr_order=settings_here['integr_order'],\n ScalingDict=settings_here['ScalingDict'],\n for_vel=np.hstack((cga.dot(self.tsstr.for_vel[:3]),\n cga.dot(self.tsstr.for_vel[3:]))))\n\n # add rotational speed\n # for ii in range(self.linuvlm.MS.n_surf):\n # self.linuvlm.MS.Surfs[ii].omega = self.tsstr.for_vel[3:]\n\n\n def reshape_struct_input(self):\n \"\"\" Reshape structural input in a column vector \"\"\"\n\n structure = self.data.structure # self.data.aero.beam\n tsdata = structure.timestep_info[self.chosen_ts]\n\n self.q = np.zeros(self.num_dof_str)\n self.dq = np.zeros(self.num_dof_str)\n\n jj = 0 # structural dofs index\n for node_glob in range(structure.num_node):\n\n ### detect bc at node (and no. of dofs)\n bc_here = structure.boundary_conditions[node_glob]\n if bc_here == 1: # clamp\n dofs_here = 0\n continue\n elif bc_here == -1 or bc_here == 0:\n dofs_here = 6\n jj_tra = [jj, jj + 1, jj + 2]\n jj_rot = [jj + 3, jj + 4, jj + 5]\n\n # retrieve element and local index\n ee, node_loc = structure.node_master_elem[node_glob, :]\n\n # allocate\n self.q[jj_tra] = tsdata.pos[node_glob, :]\n self.q[jj_rot] = tsdata.psi[ee, node_loc]\n # update\n jj += dofs_here\n\n # allocate FoR A quantities\n if self.use_euler:\n self.q[-9:-3] = tsdata.for_vel\n self.q[-3:] = algebra.quat2euler(tsdata.quat)\n\n wa = tsdata.for_vel[3:]\n self.dq[-9:-3] = tsdata.for_acc\n T = algebra.deuler_dt(self.q[-3:])\n self.dq[-3:] = T.dot(wa)\n\n else:\n self.q[-10:-4] = tsdata.for_vel\n self.q[-4:] = tsdata.quat\n\n wa = tsdata.for_vel[3:]\n self.dq[-10:-4] = tsdata.for_acc\n self.dq[-4] = -0.5 * np.dot(wa, tsdata.quat[1:])\n\n # self.dq[-3:]=-0.5*(wa*tsdata.quat[0]+np.cross(wa,tsdata.quat[1:]))\n\n def assemble_ss(self, beam_num_modes=None, wake_prop_settings=None):\n \"\"\"Assemble State Space formulation\"\"\"\n data = self.data\n\n aero = self.data.aero\n structure = self.data.structure # data.aero.beam\n tsaero = self.tsaero\n tsstr = self.tsstr\n\n ### assemble linear uvlm\n self.linuvlm.assemble_ss(wake_prop_settings=wake_prop_settings)\n SSaero = self.linuvlm.SS\n\n ### assemble gains and stiffening term due to non-zero forces\n # only flexible dof accounted for\n self.get_gebm2uvlm_gains()\n\n ### assemble linear gebm\n # structural part only\n self.lingebm_str.assemble(beam_num_modes)\n SSstr_flex = self.lingebm_str.SSdisc\n SSstr = SSstr_flex\n # # rigid-body (fake)\n # ZeroMat=np.zeros((self.num_dof_rig,self.num_dof_rig))\n # EyeMat=np.eye(self.num_dof_rig)\n # Astr=np.zeros((2*self.num_dof_rig,2*self.num_dof_rig))\n # Bstr=np.zeros((2*self.num_dof_rig,2*self.num_dof_rig))\n # Cstr=np.eye(2*self.num_dof_rig)\n # Dstr=np.zeros((2*self.num_dof_rig,2*self.num_dof_rig))\n # Astr[:self.num_dof_flex,:self.num_dof_flex]=SSstr.A[]\n # SSstr_rig=scsig.dlti()\n\n # str -> aero\n Zblock = np.zeros((3 * self.linuvlm.Kzeta, SSstr.outputs // 2))\n if self.rigid_body_motions:\n Kas = np.block([[self.Kdisp, Zblock],\n [self.Kvel_disp, self.Kvel_vel],\n [Zblock, Zblock]])\n else:\n Kas = np.block([[self.Kdisp[:, :-self.num_dof_rig], Zblock],\n [self.Kvel_disp[:, :-self.num_dof_rig], self.Kvel_vel[:, :-self.num_dof_rig]],\n [Zblock, Zblock]])\n\n # aero -> str\n if self.rigid_body_motions:\n Ksa = self.Kforces # aero --> str\n\n else:\n Ksa = self.Kforces[:-10, :] # aero --> str\n\n ### feedback connection\n self.SS = libss.couple(ss01=self.linuvlm.SS, ss02=SSstr, K12=Kas, K21=Ksa)\n\n def get_gebm2uvlm_gains(self):\n r\"\"\"\n Provides:\n - the gain matrices required to connect the linearised GEBM and UVLM\n inputs/outputs\n - the stiffening and damping factors to be added to the linearised\n GEBM equations in order to account for non-zero aerodynamic loads at\n the linearisation point.\n\n The function produces the gain matrices:\n\n - ``Kdisp``: gains from GEBM to UVLM grid displacements\n - ``Kvel_disp``: influence of GEBM dofs displacements to UVLM grid\n velocities.\n - ``Kvel_vel``: influence of GEBM dofs displacements to UVLM grid\n displacements.\n - ``Kforces`` (UVLM->GEBM) dimensions are the transpose than the\n Kdisp and Kvel* matrices. Hence, when allocation this term, ``ii``\n and ``jj`` indices will unintuitively refer to columns and rows,\n respectively.\n\n And the stiffening/damping terms accounting for non-zero aerodynamic\n forces at the linearisation point:\n\n - ``Kss``: stiffness factor (flexible dof -> flexible dof) accounting\n for non-zero forces at the linearisation point.\n - ``Csr``: damping factor (rigid dof -> flexible dof)\n - ``Crs``: damping factor (flexible dof -> rigid dof)\n - ``Crr``: damping factor (rigid dof -> rigid dof)\n\n\n Stiffening and damping related terms due to the non-zero aerodynamic forces at the linearisation point:\n\n .. math::\n \\mathbf{F}_{A,n} = C^{AG}(\\mathbf{\\chi})\\sum_j \\mathbf{f}_{G,j} \\rightarrow\n \\delta\\mathbf{F}_{A,n} = C^{AG}_0 \\sum_j \\delta\\mathbf{f}_{G,j} + \\frac{\\partial}{\\partial\\chi}(C^{AG}\\sum_j\n \\mathbf{f}_{G,j}^0)\\delta\\chi\n\n The term multiplied by the variation in the quaternion, :math:`\\delta\\chi`, couples the forces with the rigid\n body equations and becomes part of :math:`\\mathbf{C}_{sr}`.\n\n Similarly, the linearisation of the moments results in expression that contribute to the stiffness and\n damping matrices.\n\n .. math::\n \\mathbf{M}_{B,n} = \\sum_j \\tilde{X}_B C^{BA}(\\Psi)C^{AG}(\\chi)\\mathbf{f}_{G,j}\n\n .. math::\n \\delta\\mathbf{M}_{B,n} = \\sum_j \\tilde{X}_B\\left(C_0^{BG}\\delta\\mathbf{f}_{G,j}\n + \\frac{\\partial}{\\partial\\Psi}(C^{BA}\\delta\\mathbf{f}^0_{A,j})\\delta\\Psi\n + \\frac{\\partial}{\\partial\\chi}(C^{BA}_0 C^{AG} \\mathbf{f}_{G,j})\\delta\\chi\\right)\n\n The linearised equations of motion for the geometrically exact beam model take the input term :math:`\\delta\n \\mathbf{Q}_n = \\{\\delta\\mathbf{F}_{A,n},\\, T_0^T\\delta\\mathbf{M}_{B,n}\\}`, which means that the moments\n should be provided as :math:`T^T(\\Psi)\\mathbf{M}_B` instead of :math:`\\mathbf{M}_A = C^{AB}\\mathbf{M}_B`,\n where :math:`T(\\Psi)` is the tangential operator.\n\n .. math::\n \\delta(T^T\\mathbf{M}_B) = T^T_0\\delta\\mathbf{M}_B\n + \\frac{\\partial}{\\partial\\Psi}(T^T\\delta\\mathbf{M}_B^0)\\delta\\Psi\n\n is the linearised expression for the moments, where the first term would correspond to the input terms to the\n beam equations and the second arises due to the non-zero aerodynamic moment at the linearisation point and\n must be subtracted (since it comes from the forces) to form part of :math:`\\mathbf{K}_{ss}`. In addition, the\n :math:`\\delta\\mathbf{M}_B` term depends on both :math:`\\delta\\Psi` and :math:`\\delta\\chi`, therefore those\n terms would also contribute to :math:`\\mathbf{K}_{ss}` and :math:`\\mathbf{C}_{sr}`, respectively.\n\n The contribution from the total forces and moments will be accounted for in :math:`\\mathbf{C}_{rr}` and\n :math:`\\mathbf{C}_{rs}`.\n\n .. math::\n \\delta\\mathbf{F}_{tot,A} = \\sum_n\\left(C^{GA}_0 \\sum_j \\delta\\mathbf{f}_{G,j}\n + \\frac{\\partial}{\\partial\\chi}(C^{AG}\\sum_j\n \\mathbf{f}_{G,j}^0)\\delta\\chi\\right)\n\n Therefore, after running this method, the beam matrices should be updated as:\n\n >>> K_beam[:flex_dof, :flex_dof] += Kss\n >>> C_beam[:flex_dof, -rigid_dof:] += Csr\n >>> C_beam[-rigid_dof:, :flex_dof] += Crs\n >>> C_beam[-rigid_dof:, -rigid_dof:] += Crr\n\n Track body option\n\n The ``track_body`` setting restricts the UVLM grid to linear translation motions and therefore should be used to\n ensure that the forces are computed using the reference linearisation frame.\n\n The UVLM and beam are linearised about a reference equilibrium condition. The UVLM is defined in the inertial\n reference frame while the beam employs the body attached frame and therefore a projection from one frame onto\n another is required during the coupling process.\n\n However, the inputs to the UVLM (i.e. the lattice grid coordinates) are obtained from the beam deformation which\n is expressed in A frame and therefore the grid coordinates need to be projected onto the inertial frame ``G``.\n As the beam rotates, the projection onto the ``G`` frame of the lattice grid coordinates will result in a grid\n that is not coincident with that at the linearisation reference and therefore the grid coordinates must be\n projected onto the original frame, which will be referred to as ``U``. The transformation between the inertial\n frame ``G`` and the ``U`` frame is a function of the rotation of the ``A`` frame and the original position:\n\n .. math:: C^{UG}(\\chi) = C^{GA}(\\chi_0)C^{AG}(\\chi)\n\n Therefore, the grid coordinates obtained in ``A`` frame and projected onto the ``G`` frame can be transformed\n to the ``U`` frame using\n\n .. math:: \\zeta_U = C^{UG}(\\chi) \\zeta_G\n\n which allows the grid lattice coordinates to be projected onto the original linearisation frame.\n\n In a similar fashion, the output lattice vertex forces of the UVLM are defined in the original linearisation\n frame ``U`` and need to be transformed onto the inertial frame ``G`` prior to projecting them onto the ``A``\n frame to use them as the input forces to the beam system.\n\n .. math:: \\boldsymbol{f}_G = C^{GU}(\\chi)\\boldsymbol{f}_U\n\n The linearisation of the above relations lead to the following expressions that have to be added to the\n coupling matrices:\n\n * ``Kdisp_vel`` terms:\n\n .. math::\n \\delta\\boldsymbol{\\zeta}_U= C^{GA}_0 \\frac{\\partial}{\\partial \\boldsymbol{\\chi}}\n \\left(C^{AG}\\boldsymbol{\\zeta}_{G,0}\\right)\\delta\\boldsymbol{\\chi} + \\delta\\boldsymbol{\\zeta}_G\n\n * ``Kvel_vel`` terms:\n\n .. math::\n \\delta\\dot{\\boldsymbol{\\zeta}}_U= C^{GA}_0 \\frac{\\partial}{\\partial \\boldsymbol{\\chi}}\n \\left(C^{AG}\\dot{\\boldsymbol{\\zeta}}_{G,0}\\right)\\delta\\boldsymbol{\\chi}\n + \\delta\\dot{\\boldsymbol{\\zeta}}_G\n\n The transformation of the forces and moments introduces terms that are functions of the orientation and\n are included as stiffening and damping terms in the beam's matrices:\n\n * ``Csr`` damping terms relating to translation forces:\n\n .. math::\n C_{sr}^{tra} -= \\frac{\\partial}{\\partial\\boldsymbol{\\chi}}\n \\left(C^{GA} C^{AG}_0 \\boldsymbol{f}_{G,0}\\right)\\delta\\boldsymbol{\\chi}\n\n * ``Csr`` damping terms related to moments:\n\n .. math::\n C_{sr}^{rot} -= T^\\top\\widetilde{\\mathbf{X}}_B C^{BG}\n \\frac{\\partial}{\\partial\\boldsymbol{\\chi}}\n \\left(C^{GA} C^{AG}_0 \\boldsymbol{f}_{G,0}\\right)\\delta\\boldsymbol{\\chi}\n\n\n The ``track_body`` setting.\n\n When ``track_body`` is enabled, the UVLM grid is no longer coincident with the inertial reference frame\n throughout the simulation but rather it is able to rotate as the ``A`` frame rotates. This is to simulate a free\n flying vehicle, where, for instance, the orientation does not affect the aerodynamics. The UVLM defined in this\n frame of reference, named ``U``, satisfies the following convention:\n\n * The ``U`` frame is coincident with the ``G`` frame at the time of linearisation.\n\n * The ``U`` frame rotates as the ``A`` frame rotates.\n\n Transformations related to the ``U`` frame of reference:\n\n * The angle between the ``U`` frame and the ``A`` frame is always constant and equal\n to :math:`\\boldsymbol{\\Theta}_0`.\n\n * The angle between the ``A`` frame and the ``G`` frame is :math:`\\boldsymbol{\\Theta}=\\boldsymbol{\\Theta}_0\n + \\delta\\boldsymbol{\\Theta}`\n\n * The projection of a vector expressed in the ``G`` frame onto the ``U`` frame is expressed by:\n\n .. math:: \\boldsymbol{v}^U = C^{GA}_0 C^{AG} \\boldsymbol{v}^G\n\n * The reverse, a projection of a vector expressed in the ``U`` frame onto the ``G`` frame, is expressed by\n\n .. math:: \\boldsymbol{v}^U = C^{GA} C^{AG}_0 \\boldsymbol{v}^U\n\n The effect this has on the aeroelastic coupling between the UVLM and the structural dynamics is that the\n orientation and change of orientation of the vehicle has no effect on the aerodynamics. The aerodynamics are\n solely affected by the contribution of the 6-rigid body velocities (as well as the flexible DOFs velocities).\n\n \"\"\"\n\n data = self.data\n aero = self.data.aero\n structure = self.data.structure # data.aero.beam\n tsaero = self.tsaero\n tsstr = self.tsstr\n\n # allocate output\n Kdisp = np.zeros((3 * self.linuvlm.Kzeta, self.num_dof_str))\n Kdisp_vel = np.zeros((3 * self.linuvlm.Kzeta, self.num_dof_str)) # Orientation is in velocity DOFs\n Kvel_disp = np.zeros((3 * self.linuvlm.Kzeta, self.num_dof_str))\n Kvel_vel = np.zeros((3 * self.linuvlm.Kzeta, self.num_dof_str))\n Kforces = np.zeros((self.num_dof_str, 3 * self.linuvlm.Kzeta))\n Kforces2 = np.zeros((self.num_dof_str, 3 * self.linuvlm.Kzeta))\n\n Kss = np.zeros((self.num_dof_flex, self.num_dof_flex))\n Csr = np.zeros((self.num_dof_flex, self.num_dof_rig))\n Crs = np.zeros((self.num_dof_rig, self.num_dof_flex))\n Crr = np.zeros((self.num_dof_rig, self.num_dof_rig))\n Krs = np.zeros((self.num_dof_rig, self.num_dof_flex))\n\n # get projection matrix A->G\n # (and other quantities indep. from nodal position)\n Cga = algebra.quat2rotation(tsstr.quat) # NG 6-8-19 removing .T\n Cag = Cga.T\n\n # for_pos=tsstr.for_pos\n for_vel = tsstr.for_vel[:3]\n for_rot = tsstr.for_vel[3:]\n skew_for_rot = algebra.skew(for_rot)\n Der_vel_Ra = np.dot(Cga, skew_for_rot)\n\n Faero = np.zeros(3)\n FaeroA = np.zeros(3)\n\n # GEBM degrees of freedom\n jj_for_tra = range(self.num_dof_str - self.num_dof_rig, self.num_dof_str - self.num_dof_rig + 3)\n jj_for_rot = range(self.num_dof_str - self.num_dof_rig + 3, self.num_dof_str - self.num_dof_rig + 6)\n\n if self.use_euler:\n jj_euler = range(self.num_dof_str - 3, self.num_dof_str)\n euler = algebra.quat2euler(tsstr.quat)\n tsstr.euler = euler\n else:\n jj_quat = range(self.num_dof_str - 4, self.num_dof_str)\n\n jj = 0 # nodal dof index\n for node_glob in range(structure.num_node):\n\n ### detect bc at node (and no. of dofs)\n bc_here = structure.boundary_conditions[node_glob]\n\n if bc_here == 1: # clamp (only rigid-body)\n dofs_here = 0\n jj_tra, jj_rot = [], []\n # continue\n\n elif bc_here == -1 or bc_here == 0: # (rigid+flex body)\n dofs_here = 6\n jj_tra = 6 * structure.vdof[node_glob] + np.array([0, 1, 2], dtype=int)\n jj_rot = 6 * structure.vdof[node_glob] + np.array([3, 4, 5], dtype=int)\n # jj_tra=[jj ,jj+1,jj+2]\n # jj_rot=[jj+3,jj+4,jj+5]\n else:\n raise NameError('Invalid boundary condition (%d) at node %d!' \\\n % (bc_here, node_glob))\n\n jj += dofs_here\n\n # retrieve element and local index\n ee, node_loc = structure.node_master_elem[node_glob, :]\n\n # get position, crv and rotation matrix\n Ra = tsstr.pos[node_glob, :] # in A FoR, w.r.t. origin A-G\n Rg = np.dot(Cag.T, Ra) # in G FoR, w.r.t. origin A-G\n psi = tsstr.psi[ee, node_loc, :]\n psi_dot = tsstr.psi_dot[ee, node_loc, :]\n Cab = algebra.crv2rotation(psi)\n Cba = Cab.T\n Cbg = np.dot(Cab.T, Cag)\n Tan = algebra.crv2tan(psi)\n\n track_body = self.track_body\n\n ### str -> aero mapping\n # some nodes may be linked to multiple surfaces...\n for str2aero_here in aero.struct2aero_mapping[node_glob]:\n\n # detect surface/span-wise coordinate (ss,nn)\n nn, ss = str2aero_here['i_n'], str2aero_here['i_surf']\n # print('%.2d,%.2d'%(nn,ss))\n\n # surface panelling\n M = aero.aero_dimensions[ss][0]\n N = aero.aero_dimensions[ss][1]\n\n Kzeta_start = 3 * sum(self.linuvlm.MS.KKzeta[:ss])\n shape_zeta = (3, M + 1, N + 1)\n\n for mm in range(M + 1):\n # get bound vertex index\n ii_vert = [Kzeta_start + np.ravel_multi_index(\n (cc, mm, nn), shape_zeta) for cc in range(3)]\n\n # get position vectors\n zetag = tsaero.zeta[ss][:, mm, nn] # in G FoR, w.r.t. origin A-G\n zetaa = np.dot(Cag, zetag) # in A FoR, w.r.t. origin A-G\n Xg = zetag - Rg # in G FoR, w.r.t. origin B\n Xb = np.dot(Cbg, Xg) # in B FoR, w.r.t. origin B\n\n # get rotation terms\n Xbskew = algebra.skew(Xb)\n XbskewTan = np.dot(Xbskew, Tan)\n\n # get velocity terms\n zetag_dot = tsaero.zeta_dot[ss][:, mm, nn] - Cga.dot(for_vel) # in G FoR, w.r.t. origin A-G\n zetaa_dot = np.dot(Cag, zetag_dot) # in A FoR, w.r.t. origin A-G\n\n # get aero force\n faero = tsaero.forces[ss][:3, mm, nn]\n Faero += faero\n faero_a = np.dot(Cag, faero)\n FaeroA += faero_a\n maero_g = np.cross(Xg, faero)\n maero_b = np.dot(Cbg, maero_g)\n\n ### ---------------------------------------- allocate Kdisp\n\n if bc_here != 1:\n # wrt pos - Eq 25 second term\n Kdisp[np.ix_(ii_vert, jj_tra)] += Cga\n\n # wrt psi - Eq 26\n Kdisp[np.ix_(ii_vert, jj_rot)] -= np.dot(Cbg.T, XbskewTan)\n\n # w.r.t. position of FoR A (w.r.t. origin G)\n # null as A and G have always same origin in SHARPy\n\n # # ### w.r.t. quaternion (attitude changes)\n if self.use_euler:\n Kdisp_vel[np.ix_(ii_vert, jj_euler)] += \\\n algebra.der_Ceuler_by_v(tsstr.euler, zetaa)\n\n # Track body - project inputs as for A not moving\n if track_body:\n Kdisp_vel[np.ix_(ii_vert, jj_euler)] += \\\n Cga.dot(algebra.der_Peuler_by_v(tsstr.euler, zetag))\n else:\n # Equation 25\n # Kdisp[np.ix_(ii_vert, jj_quat)] += \\\n # algebra.der_Cquat_by_v(tsstr.quat, zetaa)\n Kdisp_vel[np.ix_(ii_vert, jj_quat)] += \\\n algebra.der_Cquat_by_v(tsstr.quat, zetaa)\n\n # Track body - project inputs as for A not moving\n if track_body:\n Kdisp_vel[np.ix_(ii_vert, jj_quat)] += \\\n Cga.dot(algebra.der_CquatT_by_v(tsstr.quat, zetag))\n\n ### ------------------------------------ allocate Kvel_disp\n\n if bc_here != 1:\n # # wrt pos\n Kvel_disp[np.ix_(ii_vert, jj_tra)] += Der_vel_Ra\n\n # wrt psi (at zero psi_dot)\n Kvel_disp[np.ix_(ii_vert, jj_rot)] -= \\\n np.dot(Cga,\n np.dot(skew_for_rot,\n np.dot(Cab, XbskewTan)))\n\n # # wrt psi (psi_dot contributions - verified)\n Kvel_disp[np.ix_(ii_vert, jj_rot)] += np.dot(Cbg.T, np.dot(\n algebra.skew(np.dot(XbskewTan, psi_dot)), Tan))\n\n if np.linalg.norm(psi) >=1e-6:\n Kvel_disp[np.ix_(ii_vert, jj_rot)] -= \\\n np.dot(Cbg.T,\n np.dot(Xbskew,\n algebra.der_Tan_by_xv(psi, psi_dot)))\n\n # # w.r.t. position of FoR A (w.r.t. origin G)\n # # null as A and G have always same origin in SHARPy\n\n # # ### w.r.t. quaternion (attitude changes) - Eq 30\n if self.use_euler:\n Kvel_vel[np.ix_(ii_vert, jj_euler)] += \\\n algebra.der_Ceuler_by_v(tsstr.euler, zetaa_dot)\n\n # Track body if ForA is rotating\n if track_body:\n Kvel_vel[np.ix_(ii_vert, jj_euler)] += \\\n Cga.dot(algebra.der_Peuler_by_v(tsstr.euler, zetag_dot))\n else:\n Kvel_vel[np.ix_(ii_vert, jj_quat)] += \\\n algebra.der_Cquat_by_v(tsstr.quat, zetaa_dot)\n\n # Track body if ForA is rotating\n if track_body:\n Kvel_vel[np.ix_(ii_vert, jj_quat)] += \\\n Cga.dot(algebra.der_CquatT_by_v(tsstr.quat, zetag_dot))\n\n ### ------------------------------------- allocate Kvel_vel\n\n if bc_here != 1:\n # wrt pos_dot\n Kvel_vel[np.ix_(ii_vert, jj_tra)] += Cga\n\n # # wrt crv_dot\n Kvel_vel[np.ix_(ii_vert, jj_rot)] -= np.dot(Cbg.T, XbskewTan)\n\n # # wrt velocity of FoR A\n Kvel_vel[np.ix_(ii_vert, jj_for_tra)] += Cga\n Kvel_vel[np.ix_(ii_vert, jj_for_rot)] -= \\\n np.dot(Cga, algebra.skew(zetaa))\n\n # wrt rate of change of quaternion: not implemented!\n\n ### -------------------------------------- allocate Kforces\n\n if bc_here != 1:\n # nodal forces\n Kforces[np.ix_(jj_tra, ii_vert)] += Cag\n\n # nodal moments\n Kforces[np.ix_(jj_rot, ii_vert)] += \\\n np.dot(Tan.T, np.dot(Cbg, algebra.skew(Xg)))\n # or, equivalently, np.dot( algebra.skew(Xb),Cbg)\n\n # total forces\n Kforces[np.ix_(jj_for_tra, ii_vert)] += Cag\n Kforces2[-10:-7, ii_vert] += Cag\n\n # total moments\n Kforces[np.ix_(jj_for_rot, ii_vert)] += \\\n np.dot(Cag, algebra.skew(zetag))\n\n # quaternion equation\n # null, as not dep. on external forces\n\n ### --------------------------------------- allocate Kstiff\n\n ### flexible dof equations (Kss and Csr)\n if bc_here != 1:\n # nodal forces\n if self.use_euler:\n if not track_body:\n Csr[jj_tra, -3:] -= algebra.der_Peuler_by_v(tsstr.euler, faero)\n # Csr[jj_tra, -3:] -= algebra.der_Ceuler_by_v(tsstr.euler, Cga.T.dot(faero))\n\n else:\n if not track_body:\n Csr[jj_tra, -4:] -= algebra.der_CquatT_by_v(tsstr.quat, faero)\n\n # Track body\n # if track_body:\n # Csr[jj_tra, -4:] -= algebra.der_Cquat_by_v(tsstr.quat, Cga.T.dot(faero))\n\n ### moments\n TanTXbskew = np.dot(Tan.T, Xbskew)\n # contrib. of TanT (dpsi) - Eq 37 - Integration of UVLM and GEBM\n Kss[np.ix_(jj_rot, jj_rot)] -= algebra.der_TanT_by_xv(psi, maero_b)\n # contrib of delta aero moment (dpsi) - Eq 36\n Kss[np.ix_(jj_rot, jj_rot)] -= \\\n np.dot(TanTXbskew, algebra.der_CcrvT_by_v(psi, np.dot(Cag, faero)))\n # contribution of delta aero moment (dquat)\n if self.use_euler:\n if not track_body:\n Csr[jj_rot, -3:] -= \\\n np.dot(TanTXbskew,\n np.dot(Cba,\n algebra.der_Peuler_by_v(tsstr.euler, faero)))\n\n # if track_body:\n # Csr[jj_rot, -3:] -= \\\n # np.dot(TanTXbskew,\n # np.dot(Cbg,\n # algebra.der_Peuler_by_v(tsstr.euler, Cga.T.dot(faero))))\n else:\n if not track_body:\n Csr[jj_rot, -4:] -= \\\n np.dot(TanTXbskew,\n np.dot(Cba,\n algebra.der_CquatT_by_v(tsstr.quat, faero)))\n\n # Track body\n # if track_body:\n # Csr[jj_rot, -4:] -= \\\n # np.dot(TanTXbskew,\n # np.dot(Cbg,\n # algebra.der_CquatT_by_v(tsstr.quat, Cga.T.dot(faero))))\n\n ### rigid body eqs (Crs and Crr)\n\n if bc_here != 1:\n # Changed Crs to Krs - NG 14/5/19\n # moments contribution due to delta_Ra (+ sign intentional)\n Krs[3:6, jj_tra] += algebra.skew(faero_a)\n # moment contribution due to delta_psi (+ sign intentional)\n Krs[3:6, jj_rot] += np.dot(algebra.skew(faero_a),\n algebra.der_Ccrv_by_v(psi, Xb))\n\n if self.use_euler:\n # total force\n if not track_body:\n Crr[:3, -3:] -= algebra.der_Peuler_by_v(tsstr.euler, faero)\n\n # total moment contribution due to change in euler angles\n Crr[3:6, -3:] -= algebra.der_Peuler_by_v(tsstr.euler, np.cross(zetag, faero))\n Crr[3:6, -3:] += np.dot(\n np.dot(Cag, algebra.skew(faero)),\n algebra.der_Peuler_by_v(tsstr.euler, np.dot(Cab, Xb)))\n\n # if track_body:\n # # NG 20/8/19 - is the Cag needed here? Verify\n # Crr[:3, -3:] -= Cag.dot(algebra.der_Ceuler_by_v(tsstr.euler, Cga.T.dot(faero)))\n #\n # Crr[3:6, -3:] -= Cag.dot(algebra.skew(zetag).dot(algebra.der_Ceuler_by_v(tsstr.euler, Cga.T.dot(faero))))\n # Crr[3:6, -3:] += Cag.dot(algebra.skew(faero)).dot(algebra.der_Ceuler_by_v(tsstr.euler, Cga.T.dot(zetag)))\n\n else:\n if not track_body:\n # total force\n Crr[:3, -4:] -= algebra.der_CquatT_by_v(tsstr.quat, faero)\n\n # total moment contribution due to quaternion\n Crr[3:6, -4:] -= algebra.der_CquatT_by_v(tsstr.quat, np.cross(zetag, faero))\n Crr[3:6, -4:] += np.dot(\n np.dot(Cag, algebra.skew(faero)),\n algebra.der_CquatT_by_v(tsstr.quat, np.dot(Cab, Xb)))\n\n # Track body\n # if track_body:\n # Crr[:3, -4:] -= Cag.dot(algebra.der_Cquat_by_v(tsstr.quat, Cga.T.dot(faero)))\n #\n # Crr[3:6, -4:] -= Cag.dot(algebra.skew(zetag).dot(algebra.der_Cquat_by_v(tsstr.quat, Cga.T.dot(faero))))\n # Crr[3:6, -4:] += Cag.dot(algebra.skew(faero)).dot(algebra.der_Cquat_by_v(tsstr.quat, Cga.T.dot(zetag)))\n\n\n # transfer\n self.Kdisp = Kdisp\n self.Kvel_disp = Kvel_disp\n self.Kdisp_vel = Kdisp_vel\n self.Kvel_vel = Kvel_vel\n self.Kforces = Kforces\n\n # stiffening factors\n self.Kss = Kss\n self.Krs = Krs\n self.Csr = Csr\n self.Crs = Crs\n self.Crr = Crr\n\n\nif __name__ == '__main__':\n import read\n import configobj\n\n # select test case\n fname = '/home/sm6110/git/uvlm3d/test/h5input/smith_Nsurf01M04N12wk10_a040.state.h5'\n fname = '/home/sm6110/git/uvlm3d/test/h5input/smith_Nsurf02M04N12wk10_a040.state.h5'\n hd = read.h5file(fname)\n\n # read some setting\n file_settings = fname[:-8] + 'solver.txt'\n dict_config = configobj.ConfigObj(file_settings)\n\n # add settings for linear solver\n M, cref = 4., 1.\n Uinf = 25.\n dict_config['LinearUvlm'] = {'dt': cref / M / Uinf,\n 'integr_order': 2,\n 'Uref': 1.}\n\n Sol = AeroElaDyn(tsaero=hd.tsaero00000, tsstr=hd.tsstr00000,\n aero2str_mapping=hd.aero2str, settings=dict_config)\n" }, { "path": "sharpy/linear/src/lin_utils.py", "content": "\"\"\"\nUtilities functions for linear analysis\n\"\"\"\n\nimport numpy as np\n\n\n\n# linear uvlm\nimport sharpy.linear.src.lin_aeroelastic as lin_aeroelastic\nimport sharpy.linear.src.libss as libss\n\n\ndef comp_tot_force(forces, zeta, zeta_pole=np.zeros((3,))):\n \"\"\" Compute total force with exact displacements \"\"\"\n Ftot = np.zeros((3,))\n Mtot = np.zeros((3,))\n for ss in range(len(forces)):\n _, Mv, Nv = forces[ss].shape\n for mm in range(Mv):\n for nn in range(Nv):\n arm = zeta[ss][:, mm, nn] - zeta_pole\n Mtot += np.cross(arm, forces[ss][:3, mm, nn])\n for cc in range(3):\n Ftot[cc] += forces[ss][cc, :, :].sum()\n return Ftot, Mtot\n\n\nclass Info():\n \"\"\" Summarise info about a data point \"\"\"\n\n def __init__(self, zeta, zeta_dot, u_ext, ftot, mtot, q, qdot,\n SSaero=None, SSbeam=None,\n Kas=None, Kftot=None, Kmtot=None, Kmtot_disp=None,\n Asteady_inv=None):\n self.zeta = zeta\n self.zeta_dot = zeta_dot\n self.u_ext = u_ext\n self.ftot = ftot\n self.mtot = mtot\n self.q = q\n self.qdot = qdot\n #\n self.SSaero = SSaero\n self.SSbeam = SSbeam\n self.Kas = Kas\n self.Kftot = Kftot\n self.Kmtot = Kmtot\n self.Kmtot_disp = Kmtot_disp\n self.Asteady_inv = Asteady_inv\n\n\ndef solve_linear(Ref, Pert, solve_beam=True):\n \"\"\"\n Given 2 Info() classes associated to a reference linearisation point Ref and a\n perturbed state Pert, the method produces in output the prediction at the\n Pert state of a linearised model.\n\n The solution is carried on using both the aero and beam input\n \"\"\"\n\n ### define perturbations\n dq = Pert.q - Ref.q\n dqdot = Pert.qdot - Ref.qdot\n dzeta = Pert.zeta - Ref.zeta\n dzeta_dot = Pert.zeta_dot - Ref.zeta_dot\n du_ext = Pert.u_ext - Ref.u_ext\n\n num_dof_str = len(dq)\n dzeta_exp = np.dot(Ref.Kas[:len(dzeta), :num_dof_str], dq)\n\n SSaero = Ref.SSaero\n SSbeam = Ref.SSbeam\n\n # zeta in\n usta = np.concatenate([dzeta, dzeta_dot, du_ext])\n\n if hasattr(Ref, 'Asteady_inv'):\n #x_sta = A_steady^-1 dot B u_sta\n xsta = np.dot(Ref.Asteady_inv, np.dot(SSaero.B, usta))\n else:\n # x_sta = linsolve(A_steady, Bu)\n Asteady = np.eye(*SSaero.A.shape) - SSaero.A\n xsta = np.linalg.solve(Asteady, np.dot(SSaero.B, usta))\n\n # y_sta = C x_sta + D u_sta\n ysta = np.dot(SSaero.C, xsta) + np.dot(SSaero.D, usta)\n ftot_aero = Ref.ftot + np.dot(Ref.Kftot, ysta)\n mtot_aero = Ref.mtot + np.dot(Ref.Kmtot, ysta) + np.dot(Ref.Kmtot_disp, dzeta)\n\n #### beam in\n if solve_beam:\n # warning: we need to add first the contribution due to velocity change!!!\n usta_uinf = np.concatenate([0. * dzeta, 0. * dzeta_dot, du_ext])\n xsta_uinf = np.linalg.solve(Asteady, np.dot(SSaero.B, usta_uinf))\n ysta_uinf = np.dot(SSaero.C, xsta_uinf) + np.dot(SSaero.D, usta_uinf)\n usta = np.concatenate([dq, dqdot])\n if hasattr(Ref, 'Asteady_inv'):\n xsta = np.dot(Ref.Asteady_inv, np.dot(SSbeam.B, usta))\n else:\n Asteady = np.eye(*SSbeam.A.shape) - SSbeam.A\n xsta = np.linalg.solve(Asteady, np.dot(SSbeam.B, usta))\n ysta = ysta_uinf + np.dot(SSbeam.C, xsta) + np.dot(SSbeam.D, usta)\n ftot_beam = Ref.ftot + np.dot(Ref.Kftot, ysta)\n mtot_beam = Ref.mtot + np.dot(Ref.Kmtot, ysta) + np.dot(Ref.Kmtot_disp, dzeta_exp)\n else:\n ftot_beam, mtot_beam = None, None\n\n return ftot_aero, mtot_aero, ftot_beam, mtot_beam\n\n\ndef extract_from_data(data, assemble=True,\n zeta_pole=np.zeros((3,)), build_Asteady_inv=False):\n \"\"\"\n Extract relevant info from data structure. If assemble is True, it will\n also generate a linear UVLM and the displacements/velocities gain matrices\n \"\"\"\n\n ### extract aero info - gets info from every panel in every surface\n # from an NxM matrix and reshapes it into an K by 1 column vector\n tsaero = data.aero.timestep_info[0]\n zeta = np.concatenate([tsaero.zeta[ss].reshape(-1, order='C')\n for ss in range(tsaero.n_surf)])\n zeta_dot = np.concatenate([tsaero.zeta_dot[ss].reshape(-1, order='C')\n for ss in range(tsaero.n_surf)])\n uext = np.concatenate([tsaero.u_ext[ss].reshape(-1, order='C')\n for ss in range(tsaero.n_surf)])\n ftot, mtot = comp_tot_force(tsaero.forces, tsaero.zeta, zeta_pole=zeta_pole)\n\n ## TEST WHETHER SETTINGS RUN\n settings = dict()\n settings['LinearUvlm'] = {'dt': 0.1,\n 'integr_order': 2,\n 'density': 1.225,\n 'ScalingDict': {'length': 1.,\n 'speed': 1.,\n 'density': 1.}}\n\n ### extract structural info\n Sol = lin_aeroelastic.LinAeroEla(data, settings)\n gebm = Sol.lingebm_str\n q = Sol.q\n qdot = Sol.dq\n\n ### assemble\n if assemble is True:\n uvlm = Sol.linuvlm\n uvlm.assemble_ss()\n uvlm.get_total_forces_gain(zeta_pole=zeta_pole)\n Sol.get_gebm2uvlm_gains()\n Kas = np.block([[Sol.Kdisp, np.zeros((3 * uvlm.Kzeta, gebm.num_dof + 10))],\n [Sol.Kvel_disp, Sol.Kvel_vel],\n [np.zeros((3 * uvlm.Kzeta, 2 * gebm.num_dof + 20))]])\n SSbeam = libss.addGain(uvlm.SS, Kas, where='in')\n\n if build_Asteady_inv:\n Asteady_inv = np.linalg.inv(np.eye(*uvlm.SS.A.shape) - uvlm.SS.A)\n else:\n Asteady_inv = None\n Out = Info(zeta, zeta_dot, uext, ftot, mtot, q, qdot,\n uvlm.SS, SSbeam, Kas, uvlm.Kftot, uvlm.Kmtot, uvlm.Kmtot_disp,\n Asteady_inv)\n\n else:\n Out = Info(zeta, zeta_dot, uext, ftot, mtot, q, qdot)\n\n return Out" }, { "path": "sharpy/linear/src/lingebm.py", "content": "\"\"\"\nLinear beam model class\n\nS. Maraniello, Aug 2018\nN. Goizueta\n\"\"\"\n\nimport numpy as np\nimport scipy as sc\nimport scipy.signal as scsig\nimport sharpy.linear.src.libss as libss\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.settings as settings\nimport sharpy.utils.cout_utils as cout\nimport sharpy.structure.utils.modalutils as modalutils\nimport warnings\nfrom sharpy.linear.utils.ss_interface import LinearVector, StateVariable, OutputVariable, InputVariable\n\n\nclass FlexDynamic():\n r\"\"\"\n Define class for linear state-space realisation of GEBM flexible-body\n equations from SHARPy``timestep_info`` class and with the nonlinear structural information.\n\n The linearised beam takes the following arguments:\n\n Args:\n tsinfo (sharpy.utils.datastructures.StructImeStepInfo): Structural timestep containing the modal information\n structure (sharpy.solvers.beamloader.Beam): Beam class with the structural information\n custom_settings (dict): settings for the linearised beam\n\n\n State-space models can be defined in continuous or discrete time (dt\n required). Modal projection, either on the damped or undamped modal shapes,\n is also avaiable. The rad/s array wv can be optionally passed for freq.\n response analysis\n\n To produce the state-space equations:\n\n 1. Set the settings:\n a. ``modal_projection={True,False}``: determines whether to project the states\n onto modal coordinates. Projection over damped or undamped modal\n shapes can be obtained selecting:\n\n - ``proj_modes={'damped','undamped'}``\n\n while\n\n - ``inout_coords={'modes','nodal'}``\n\n determines whether the modal state-space inputs/outputs are modal\n coords or nodal degrees-of-freedom. If ``modes`` is selected, the\n ``Kin`` and ``Kout`` gain matrices are generated to transform nodal to modal\n dofs\n\n b. ``dlti={True,False}``: if true, generates discrete-time system.\n The continuous to discrete transformation method is determined by::\n\n discr_method={ 'newmark', # Newmark-beta\n 'zoh',\t\t# Zero-order hold\n 'bilinear'} # Bilinear (Tustin) transformation\n\n DLTIs can be obtained directly using the Newmark-:math:`\\beta` method\n\n ``discr_method='newmark'``\n ``newmark_damp=xx`` with ``xx<<1.0``\n\n for full-states descriptions (``modal_projection=False``) and modal projection\n over the undamped structural modes (``modal_projection=True`` and ``proj_modes``).\n The Zero-order holder and bilinear methods, instead, work in all\n descriptions, but require the continuous state-space equations.\n\n 2. Generate an instance of the beam\n\n 2. Run ``self.assemble()``. The method accepts an additional parameter, ``Nmodes``,\n which allows using a lower number of modes than specified in ``self.Nmodes``\n\n Examples:\n\n >>> beam_settings = {'modal_projection': True,\n >>> 'inout_coords': 'modes',\n >>> 'discrete_time': False,\n >>> 'proj_modes': 'undamped',\n >>> 'use_euler': True}\n >>>\n >>> beam = lingebm.FlexDynamic(tsstruct0, structure=data.structure, custom_settings=beam_settings)\n >>>\n >>> beam.assemble()\n\n Notes:\n\n * Modal projection will automatically select between damped/undamped modes shapes, based on the data available\n from tsinfo.\n\n * If the full system matrices are available, use the modal_sol methods to override mode-shapes and eigenvectors\n\n\n \"\"\"\n\n def __init__(self, tsinfo, structure=None, custom_settings=dict()):\n # Extract settings\n self.settings = custom_settings\n\n ### extract timestep_info modal results\n # unavailable attrs will be None\n self.freq_natural = tsinfo.modal.get('freq_natural')\n self.freq_damp = tsinfo.modal.get('freq_damped')\n\n self.damping = tsinfo.modal.get('damping')\n\n self.eigs = tsinfo.modal.get('eigenvalues')\n self.U = tsinfo.modal.get('eigenvectors')\n self.V = tsinfo.modal.get('eigenvectors_left')\n self.Kin_damp = tsinfo.modal.get('Kin_damp') # for 'damped' modes only\n self.Ccut = tsinfo.modal.get('Ccut') # for 'undamp' modes only\n\n self.Mstr = tsinfo.modal.get('M')\n self.Cstr = tsinfo.modal.get('C')\n self.Kstr = tsinfo.modal.get('K')\n\n ### set other flags\n self.modal = self.settings['modal_projection']\n self.inout_coords = self.settings['inout_coords']\n self.dlti = self.settings['discrete_time']\n\n if self.dlti:\n self.dt = self.settings['dt']\n else:\n self.dt = None\n\n self.Nmodes = self.settings['num_modes']\n self._num_modes = None\n self.num_modes = self.settings['num_modes']\n self.num_dof = self.U.shape[0]\n if self.V is not None:\n self.num_dof = self.num_dof // 2\n\n self.proj_modes = self.settings['proj_modes']\n if self.V is None:\n self.proj_modes = 'undamped'\n self.discr_method = self.settings['discr_method']\n self.newmark_damp = self.settings['newmark_damp']\n self.use_euler = self.settings['use_euler']\n self.use_principal_axes = self.settings.get('rigid_modes_ppal_axes', False) # this setting is inherited from the setting in Modal solver\n\n ### set state-space variables\n self.SScont = None\n self.SSdisc = None\n self.Kin = None\n self.Kout = None\n\n # Store structure at linearisation and linearisation conditions\n self.structure = structure\n self.tsstruct0 = tsinfo\n self.Minv = None # Not used anymore since M is factorized inside newmark_ss\n\n self.scaled_reference_matrices = dict() # keep reference values prior to time scaling\n\n if self.use_euler:\n self.euler_propagation_equations(tsinfo)\n\n if self.Mstr.shape[0] == 6*(self.tsstruct0.num_node - 1):\n self.clamped = True\n self.num_dof_rig = 0\n else:\n self.clamped = False\n\n if self.use_euler:\n self.num_dof_rig = 9\n else:\n self.num_dof_rig = 10\n\n if self.modal:\n self.update_modal()\n\n self.num_dof_flex = np.sum(structure.vdof >= 0)*6\n\n self.num_dof_str = self.num_dof_flex + self.num_dof_rig\n q, dq = self.reshape_struct_input()\n\n self.tsstruct0.q = q\n self.tsstruct0.dq = dq\n\n # Linearised gravity matrices\n self.Crr_grav = None\n self.Csr_grav = None\n self.Krs_grav = None\n self.Kss_grav = None\n\n def reshape_struct_input(self):\n \"\"\" Reshape structural input in a column vector \"\"\"\n\n structure = self.structure # self.data.aero.beam\n tsdata = self.tsstruct0\n\n q = np.zeros(self.num_dof_str)\n dq = np.zeros(self.num_dof_str)\n\n jj = 0 # structural dofs index\n for node_glob in range(structure.num_node):\n\n ### detect bc at node (and no. of dofs)\n bc_here = structure.boundary_conditions[node_glob]\n if bc_here == 1: # clamp\n dofs_here = 0\n continue\n elif bc_here == -1 or bc_here == 0:\n dofs_here = 6\n jj_tra = [jj, jj + 1, jj + 2]\n jj_rot = [jj + 3, jj + 4, jj + 5]\n\n # retrieve element and local index\n ee, node_loc = structure.node_master_elem[node_glob, :]\n\n # allocate\n q[jj_tra] = tsdata.pos[node_glob, :]\n q[jj_rot] = tsdata.psi[ee, node_loc]\n # update\n jj += dofs_here\n\n # allocate FoR A quantities\n if self.use_euler:\n q[-9:-3] = tsdata.for_vel\n q[-3:] = algebra.quat2euler(tsdata.quat)\n\n wa = tsdata.for_vel[3:]\n dq[-9:-3] = tsdata.for_acc\n T = algebra.deuler_dt(q[-3:])\n dq[-3:] = T.dot(wa)\n\n else:\n q[-10:-4] = tsdata.for_vel\n q[-4:] = tsdata.quat\n\n wa = tsdata.for_vel[3:]\n dq[-10:-4] = tsdata.for_acc\n dq[-4] = -0.5 * np.dot(wa, tsdata.quat[1:])\n\n return q, dq\n\n @property\n def num_modes(self):\n return self._num_modes\n\n @num_modes.setter\n def num_modes(self, value):\n self.update_truncated_modes(value)\n self._num_modes = value\n\n @property\n def num_flex_dof(self):\n return np.sum(self.structure.vdof >= 0) * 6\n\n @property\n def num_rig_dof(self):\n return self.Mstr.shape[0] - self.num_flex_dof\n\n def sort_repeated_evecs(self, evecs, evals):\n num_rbm = np.sum(evals.__abs__() == 0.)\n num_dof = evecs.shape[0]\n\n evecs_sorted = evecs.copy()\n\n if num_rbm != 0:\n for i in range(num_rbm):\n index_mode = np.argmax(evecs[:, i].__abs__()) - num_dof + num_rbm\n evecs_sorted[:, index_mode] = evecs[:, i]\n\n return evecs_sorted\n\n def euler_propagation_equations(self, tsstr):\n \"\"\"\n Introduce the linearised Euler propagation equations that relate the body fixed angular velocities to the Earth\n fixed Euler angles.\n\n This method will remove the quaternion propagation equations created by SHARPy; the resulting\n system will have 9 rigid degrees of freedom.\n\n\n Args:\n tsstr:\n\n Returns:\n\n \"\"\"\n\n # Verify the rigid body modes are used\n num_node = tsstr.num_node\n num_flex_dof = 6*(num_node-1)\n\n euler = algebra.quat2euler(tsstr.quat)\n tsstr.euler = euler\n\n if self.Mstr.shape[0] == num_flex_dof + 10:\n\n # Erase quaternion equations\n self.Cstr[-4:, :] = 0\n\n self.Mstr = self.Mstr[:-1, :-1]\n self.Cstr = self.Cstr[:-1, :-1]\n self.Kstr = self.Kstr[:-1, :-1]\n\n for_rot = tsstr.for_vel[3:]\n Crr = np.zeros((9, 9))\n\n # Euler angle propagation equations\n Crr[-3:, -6:-3] = -algebra.deuler_dt(tsstr.euler)\n Crr[-3:, -3:] = -algebra.der_Teuler_by_w(tsstr.euler, for_rot)\n\n self.Cstr[-9:, -9:] += Crr\n\n else:\n warnings.warn('Euler parametrisation not implemented - Either rigid body modes are not being used or this '\n 'method has already been called.')\n\n\n @property\n def num_dof(self):\n self.num_dof = self.Mstr.shape[0]\n # Previously beam.U.shape[0]\n return self._num_dof\n\n @num_dof.setter\n def num_dof(self, value):\n self._num_dof = value\n\n\n def linearise_gravity_forces(self, tsstr=None):\n r\"\"\"\n Linearises gravity forces and includes the resulting terms in the C and K matrices. The method takes the\n linearisation condition (optional argument), linearises and updates:\n\n * Stiffness matrix\n\n * Damping matrix\n\n * Modal damping matrix\n\n The method works for both the quaternion and euler angle orientation parametrisation.\n\n Args:\n tsstr (sharpy.utils.datastructures.StructTimeStepInfo): Structural timestep at the linearisation point\n\n Notes:\n\n The gravity forces are linearised to express them in terms of the beam formulation input variables:\n\n * Nodal forces: :math:`\\delta \\mathbf{f}_A`\n\n * Nodal moments: :math:`\\delta(T^T \\mathbf{m}_B)`\n\n * Total forces (rigid body equations): :math:`\\delta \\mathbf{F}_A`\n\n * Total moments (rigid body equations): :math:`\\delta \\mathbf{M}_A`\n\n Gravity forces are naturally expressed in ``G`` (inertial) frame\n\n .. math:: \\mathbf{f}_{G,0} = \\mathbf{M\\,g}\n\n where the :math:`\\mathbf{M}` is the tangent mass matrix obtained at the linearisation reference.\n\n To obtain the gravity forces expressed in A frame we make use of the projection matrices\n\n .. math:: \\mathbf{f}_A = C^{AG}(\\boldsymbol{\\chi}) \\mathbf{f}_{G,0}\n\n that projects a vector in the inertial frame ``G`` onto the body attached frame ``A``.\n\n The projection of a vector can then be linearised as\n\n .. math::\n \\delta \\mathbf{f}_A = C^{AG} \\delta \\mathbf{f}_{G,0}\n + \\frac{\\partial}{\\partial \\boldsymbol{\\chi}}(C^{AG} \\mathbf{f}_{G,0}) \\delta\\boldsymbol{\\chi}.\n\n * Nodal forces:\n\n The linearisation of the gravity forces acting at each node is simply\n\n .. math::\n \\delta \\mathbf{f}_A =\n + \\frac{\\partial}{\\partial \\boldsymbol{\\chi}}(C^{AG} \\mathbf{f}_{G,0}) \\delta\\boldsymbol{\\chi}\n\n where it is assumed that :math:`\\delta\\mathbf{f}_G = 0`.\n\n * Nodal moments:\n\n The gravity moments can be expressed in the local node frame of reference ``B`` by\n\n .. math:: \\mathbf{m}_B = \\tilde{X}_{B,CG}C^{BA}(\\Psi)C^{AG}(\\boldsymbol{\\chi})\\mathbf{f}_{G,0}\n\n The linearisation is given by:\n\n .. math::\n \\delta \\mathbf{m}_B = \\tilde{X}_{B,CG}\n \\left(\\frac{\\partial}{\\partial\\Psi}(C^{BA}\\mathbf{f}_{A,0})\\delta\\Psi +\n C^{BA}\\frac{\\partial}{\\partial\\boldsymbol{\\chi}}(C^{AG}\\mathbf{f}_{G,0})\\delta\\boldsymbol{\\chi}\\right)\n\n However, recall that the input moments are defined in tangential space\n :math:`\\delta(T^\\top\\mathbf{m}_B)` whose linearised expression is\n\n .. math:: \\delta(T^T(\\Psi) \\mathbf{m}_B) = T_0^T \\delta \\mathbf{m}_B +\n \\frac{\\partial}{\\partial \\Psi}(T^T \\mathbf{m}_{B,0})\\delta\\Psi\n\n where the :math:`\\delta \\mathbf{m}_B` term has been defined above.\n\n * Total forces:\n\n The total forces include the contribution from all flexible degrees of freedom as well as the gravity\n forces arising from the mass at the clamped node\n\n .. math:: \\mathbf{F}_A = \\sum_n \\mathbf{f}_A + \\mathbf{f}_{A,clamped}\n\n which becomes\n\n .. math:: \\delta \\mathbf{F}_A = \\sum_n \\delta \\mathbf{f}_A +\n \\frac{\\partial}{\\partial\\boldsymbol{\\chi}}\\left(C^{AG}\\mathbf{f}_{G,clamped}\\right)\n \\delta\\boldsymbol{\\chi}.\n\n * Total moments:\n\n The total moments, as opposed to the nodal moments, are expressed in A frame and again require the\n addition of the moments from the flexible structural nodes as well as the ones from the clamped node\n itself.\n\n .. math:: \\mathbf{M}_A = \\sum_n \\tilde{X}_{A,n}^{CG} C^{AG} \\mathbf{f}_{n,G}\n + \\tilde{X}_{A,clamped}C^{AG}\\mathbf{f}_{G, clamped}\n\n where :math:`X_{A,n}^{CG} = R_{A,n} + C^{AB}(\\Psi)X_{B,n}^{CG}`. Its linearised form is\n\n .. math:: \\delta X_{A,n}^{CG} = \\delta R_{A,n}\n + \\frac{\\partial}{\\partial \\Psi}(C^{AB} X_{B,CG})\\delta\\Psi\n\n Therefore, the overall linearisation of the total moment is defined as\n\n .. math:: \\delta \\mathbf{M}_A =\n \\tilde{X}_{A,total}^{CG} \\frac{\\partial}{\\partial \\boldsymbol{\\chi}}(C^{AG}\\mathbf{F}_{G, total})\n \\delta \\boldsymbol{\\chi}\n -\\sum_n \\tilde{C}^{AG}\\mathbf{f}_{G,0} \\delta X_{A,n}^{CG}\n\n where :math:`X_{A, total}` is the centre of gravity of the entire system expressed in ``A`` frame and\n :math:`\\mathbf{F}_{G, total}` are the gravity forces of the overall system in ``G`` frame, including the\n contributions from the clamped node.\n\n\n The linearisation introduces damping and stiffening terms since the :math:`\\delta\\boldsymbol{\\chi}` and\n :math:`\\delta\\boldsymbol{\\Psi}` terms are found in the damping and stiffness matrices respectively.\n\n Therefore, the beam matrices need updating to account for these terms:\n\n * Terms from the linearisation of the nodal moments will be assembled in the rows corresponding to\n moment equations and columns corresponding to the cartesian rotation vector\n\n .. math:: K_{ss}^{m,\\Psi} \\leftarrow -T_0^T \\tilde{X}_{B,CG}\n \\frac{\\partial}{\\partial\\Psi}(C^{BA}\\mathbf{f}_{A,0})\n -\\frac{\\partial}{\\partial \\Psi}(T^T \\mathbf{m}_{B,0})\n\n * Terms from the linearisation of the translation forces with respect to the orientation are assembled\n in the damping matrix, the rows corresponding to translational forces and columns to orientation\n degrees of freedom\n\n .. math:: C_{sr}^{f,\\boldsymbol{\\chi}} \\leftarrow -\n \\frac{\\partial}{\\partial \\boldsymbol{\\chi}}(C^{AG} \\mathbf{f}_{G,0})\n\n * Terms from the linearisation of the moments with respect to the orientation are assembled in the\n damping matrix, with the rows correspondant to the moments and the columns to the orientation degrees\n of freedom\n\n .. math:: C_{sr}^{m,\\boldsymbol{\\chi}} \\leftarrow -\n T_0^T\\tilde{X}_{B,CG}C^{BA}\\frac{\\partial}{\\partial\\boldsymbol{\\chi}}(C^{AG}\\mathbf{f}_{G,0})\n\n * Terms from the linearisation of the total forces with respect to the orientation correspond to the\n rigid body equations in the damping matrix, the rows to the translational forces and columns to the\n orientation\n\n .. math:: C_{rr}^{F,\\boldsymbol{\\chi}} \\leftarrow\n - \\sum_n \\frac{\\partial}{\\partial \\boldsymbol{\\chi}}(C^{AG} \\mathbf{f}_{G,0})\n\n * Terms from the linearisation of the total moments with respect to the orientation correspond to the\n rigid body equations in the damping matrix, the rows to the moments and the columns to the orientation\n\n .. math:: C_{rr}^{M,\\boldsymbol{\\chi}} \\leftarrow\n - \\sum_n\\tilde{X}_{A,n}^{CG} \\frac{\\partial}{\\partial \\boldsymbol{\\chi}}(C^{AG}\\mathbf{f}_{G,0})\n\n * Terms from the linearisation of the total moments with respect to the nodal position :math:`R_A` are\n included in the stiffness matrix, the rows corresponding to the moments in the rigid body\n equations and the columns to the nodal position\n\n .. math:: K_{rs}^{M,R} \\leftarrow + \\sum_n \\tilde{\\mathbf{f}_{A,0}}\n\n * Terms from the linearisation of the total moments with respect to the cartesian rotation vector are\n included in the stiffness matrix, the rows corresponding to the moments in the rigid body equations\n and the columns to the cartesian rotation vector\n\n .. math:: K_{rs}^{M, \\Psi} \\leftarrow\n + \\sum_n \\tilde{\\mathbf{f}_{A,0}}\\frac{\\partial}{\\partial \\Psi}(C^{AB} X_{B,CG})\n \n \"\"\"\n\n if tsstr is None:\n tsstr = self.tsstruct0\n\n if self.settings['print_info']:\n try:\n cout.cout_wrap('\\nLinearising gravity terms...')\n except ValueError:\n pass\n\n num_node = tsstr.num_node\n flex_dof = 6 * sum(self.structure.vdof >= 0)\n if self.use_euler:\n rig_dof = 9\n # This is a rotation matrix that rotates a vector from G to A\n Cag = algebra.euler2rot(tsstr.euler)\n Cga = Cag.T\n\n # Projection matrices - this projects the vector in G t to A\n Pag = Cga\n Pga = Cag\n else:\n rig_dof = 10\n # get projection matrix A->G\n # Cga = algebra.quat2rotation(tsstr.quat)\n # Pga = Cga.T\n # Pag = Pga.T\n Cag = algebra.quat2rotation(tsstr.quat) # Rotation matrix FoR G rotated by quat\n Pag = Cag.T\n Pga = Pag.T\n\n # Mass matrix partitions for CG calculations\n Mss = self.Mstr[:flex_dof, :flex_dof]\n Mrr = self.Mstr[-rig_dof:, -rig_dof:]\n\n # Initialise damping and stiffness gravity terms\n Crr_grav = np.zeros((rig_dof, rig_dof))\n Csr_grav = np.zeros((flex_dof, rig_dof))\n Crr_debug = np.zeros((rig_dof, rig_dof))\n Krs_grav = np.zeros((rig_dof, flex_dof))\n Kss_grav = np.zeros((flex_dof, flex_dof))\n\n # Overall CG in A frame\n Xcg_A = -np.array([Mrr[2, 4], Mrr[0, 5], Mrr[1, 3]]) / Mrr[0, 0]\n Xcg_Askew = algebra.skew(Xcg_A)\n\n if self.settings['print_info']:\n cout.cout_wrap('\\tM = %.2f kg' % Mrr[0, 0], 1)\n cout.cout_wrap('\\tX_CG A -> %.2f %.2f %.2f' %(Xcg_A[0], Xcg_A[1], Xcg_A[2]), 1)\n\n FgravA = np.zeros(3)\n FgravG = np.zeros(3)\n\n for i_node in range(num_node):\n # Gravity forces at the linearisation condition (from NL SHARPy in A frame)\n fgravA = tsstr.gravity_forces[i_node, :3]\n fgravG = Pga.dot(fgravA)\n # fgravG = tsstr.gravity_forces[i_node, :3]\n mgravA = tsstr.gravity_forces[i_node, 3:]\n fgravA = Pag.dot(fgravG)\n mgravG = Pag.dot(mgravA)\n\n # Get nodal position - A frame\n Ra = tsstr.pos[i_node, :]\n\n # retrieve element and local index\n ee, node_loc = self.structure.node_master_elem[i_node, :]\n psi = tsstr.psi[ee, node_loc, :]\n Cab = algebra.crv2rotation(psi)\n Cba = Cab.T\n Cbg = Cba.dot(Pag)\n\n # Tangential operator for moments calculation\n Tan = algebra.crv2tan(psi)\n\n jj = 0 # nodal dof index\n bc_at_node = self.structure.boundary_conditions[i_node] # Boundary conditions at the node\n\n if bc_at_node == 1: # clamp (only rigid-body)\n dofs_at_node = 0\n jj_tra, jj_rot = [], []\n\n elif bc_at_node == -1 or bc_at_node == 0: # (rigid+flex body)\n dofs_at_node = 6\n jj_tra = 6 * self.structure.vdof[i_node] + np.array([0, 1, 2], dtype=int) # Translations\n jj_rot = 6 * self.structure.vdof[i_node] + np.array([3, 4, 5], dtype=int) # Rotations\n else:\n raise NameError('Invalid boundary condition (%d) at node %d!' \\\n % (bc_at_node, i_node))\n\n jj += dofs_at_node\n\n if bc_at_node != 1:\n # Nodal centre of gravity (in the case of additional lumped masses, else should be zero)\n Mss_indices = np.concatenate((jj_tra, jj_rot))\n Mss_node = Mss[Mss_indices,:]\n Mss_node = Mss_node[:, Mss_indices]\n Xcg_B = Cba.dot(-np.array([Mss_node[2, 4], Mss_node[0, 5], Mss_node[1, 3]]) / Mss_node[0, 0])\n Xcg_Bskew = algebra.skew(Xcg_B)\n\n # Nodal CG in A frame\n Xcg_A_n = Ra + Cab.dot(Xcg_B)\n Xcg_A_n_skew = algebra.skew(Xcg_A_n)\n\n # Nodal CG in G frame - debug\n Xcg_G_n = Pga.dot(Xcg_A_n)\n\n if self.settings['print_info']:\n cout.cout_wrap(\"Node %2d \\t-> B %.3f %.3f %.3f\" %(i_node, Xcg_B[0], Xcg_B[1], Xcg_B[2]), 2)\n cout.cout_wrap(\"\\t\\t\\t-> A %.3f %.3f %.3f\" %(Xcg_A_n[0], Xcg_A_n[1], Xcg_A_n[2]), 2)\n cout.cout_wrap(\"\\t\\t\\t-> G %.3f %.3f %.3f\" %(Xcg_G_n[0], Xcg_G_n[1], Xcg_G_n[2]), 2)\n cout.cout_wrap(\"\\tNode mass:\", 2)\n cout.cout_wrap(\"\\t\\tMatrix: %.4f\" % Mss_node[0, 0], 2)\n # cout.cout_wrap(\"\\t\\tGrav: %.4f\" % (np.linalg.norm(fgravG)/9.81), 2)\n\n if self.use_euler:\n if bc_at_node != 1:\n # Nodal moments due to gravity -> linearisation terms wrt to delta_psi\n Kss_grav[np.ix_(jj_rot, jj_rot)] -= Tan.dot(Xcg_Bskew.dot(algebra.der_Ccrv_by_v(psi, fgravA)))\n Kss_grav[np.ix_(jj_rot, jj_rot)] -= algebra.der_TanT_by_xv(psi, Xcg_Bskew.dot(Cbg.dot(fgravG)))\n\n # Nodal forces due to gravity -> linearisation terms wrt to delta_euler\n Csr_grav[jj_tra, -3:] -= algebra.der_Peuler_by_v(tsstr.euler, fgravG)\n\n # Nodal moments due to gravity -> linearisation terms wrt to delta_euler\n Csr_grav[jj_rot, -3:] -= Tan.dot(Xcg_Bskew.dot(Cba.dot(algebra.der_Peuler_by_v(tsstr.euler, fgravG))))\n\n # Total moments -> linearisation terms wrt to delta_Ra\n # These terms are not affected by the Euler matrix. Sign is correct (+)\n Krs_grav[3:6, jj_tra] += algebra.skew(fgravA)\n\n # Total moments -> linearisation terms wrt to delta_Psi\n Krs_grav[3:6, jj_rot] += np.dot(algebra.skew(fgravA), algebra.der_Ccrv_by_v(psi, Xcg_B))\n\n else:\n if bc_at_node != 1:\n # Nodal moments due to gravity -> linearisation terms wrt to delta_psi\n Kss_grav[np.ix_(jj_rot, jj_rot)] -= Tan.dot(Xcg_Bskew.dot(algebra.der_Ccrv_by_v(psi, fgravA)))\n Kss_grav[np.ix_(jj_rot, jj_rot)] -= algebra.der_TanT_by_xv(psi, Xcg_Bskew.dot(Cbg.dot(fgravG)))\n\n # Total moments -> linearisation terms wrt to delta_Ra\n # Check sign (in theory it should be +=)\n Krs_grav[3:6, jj_tra] += algebra.skew(fgravA)\n\n # Total moments -> linearisation terms wrt to delta_Psi\n Krs_grav[3:6, jj_rot] += np.dot(algebra.skew(fgravA), algebra.der_Ccrv_by_v(psi, Xcg_B))\n\n # Nodal forces due to gravity -> linearisation terms wrt to delta_euler\n Csr_grav[jj_tra, -4:] -= algebra.der_CquatT_by_v(tsstr.quat, fgravG) # ok\n # Crr_grav[:3, -4:] -= algebra.der_CquatT_by_v(tsstr.quat, fgravG) # not ok - see below\n\n # Nodal moments due to gravity -> linearisation terms wrt to delta_euler\n Csr_grav[jj_rot, -4:] -= Tan.dot(Xcg_Bskew.dot(Cba.dot(algebra.der_CquatT_by_v(tsstr.quat, fgravG))))\n\n\n # Debugging:\n FgravA += fgravA\n FgravG += fgravG\n\n if self.use_euler:\n # Total gravity forces acting at the A frame\n Crr_grav[:3, -3:] -= algebra.der_Peuler_by_v(tsstr.euler, FgravG)\n\n # Total moments due to gravity in A frame\n Crr_grav[3:6, -3:] -= algebra.skew(Xcg_A).dot(algebra.der_Peuler_by_v(tsstr.euler, FgravG))\n else:\n # Total gravity forces acting at the A frame\n Crr_grav[:3, -4:] -= algebra.der_CquatT_by_v(tsstr.quat, FgravG)\n\n # Total moments due to gravity in A frame\n Crr_grav[3:6, -4:] -= algebra.skew(Xcg_A).dot(algebra.der_CquatT_by_v(tsstr.quat, FgravG))\n\n # Update matrices\n self.Kstr[:flex_dof, :flex_dof] += Kss_grav\n\n if self.Kstr[:flex_dof, :flex_dof].shape != self.Kstr.shape: # If the beam is free, update rigid terms as well\n self.Cstr[-rig_dof:, -rig_dof:] += Crr_grav\n self.Cstr[:-rig_dof, -rig_dof:] += Csr_grav\n self.Kstr[flex_dof:, :flex_dof] += Krs_grav\n\n # Save gravity matrices for post-processing\n self.Crr_grav = Crr_grav\n self.Csr_grav = Csr_grav\n self.Krs_grav = Krs_grav\n self.Kss_grav = Kss_grav\n\n if self.modal:\n self.Ccut = self.U.T.dot(self.Cstr.dot(self.U))\n\n if self.settings['print_info']:\n cout.cout_wrap('\\tUpdated the beam C, modal C and K matrices with the terms from the gravity linearisation\\n')\n\n def linearise_applied_forces(self, tsstr=None):\n r\"\"\"\n Linearise externally applied follower forces given in the local ``B`` reference frame.\n\n Updates the stiffness matrix with terms arising from this linearisation.\n\n The linearised beam equations are expressed in the following frames of reference:\n\n * Nodal forces: :math:`\\delta \\mathbf{f}_A`\n\n * Nodal moments: :math:`\\delta(T^T \\mathbf{m}_B)`\n\n * Total forces (rigid body equations): :math:`\\delta \\mathbf{F}_A`\n\n * Total moments (rigid body equations): :math:`\\delta \\mathbf{M}_A`\n\n Thus, when linearising externally applied follower forces projected onto the appropriate frame\n\n .. math:: \\boldsymbol{f}_A^{ext} = C^{AB}(\\boldsymbol{\\psi})\\boldsymbol{f}^{ext}_B\n\n the following terms appear:\n\n .. math::\n \\delta\\boldsymbol{f}_A^{ext} = \\frac{\\partial}{\\partial\\boldsymbol{\\psi}}\n \\left(C^{AB}(\\boldsymbol{\\psi})\\boldsymbol{f}^{ext}_{0,B}\\right)\\delta\\boldsymbol{\\psi} +\n C^{AB}_0\\delta\\boldsymbol f_B^{ext}\n\n where the :math:`\\delta\\boldsymbol{\\psi}` is a stiffenning term that needs to be included in the stiffness\n matrix. The terms will appear in the rows relating to the translational degrees of freedom and the columns that\n correspond to the cartesian rotation vector.\n\n .. math::\n K_{ss}^{f,\\Psi} \\leftarrow -\\frac{\\partial}{\\partial\\boldsymbol{\\psi}}\n \\left(C^{AB}(\\boldsymbol{\\psi})\\boldsymbol{f}^{ext}_{0,B}\\right)\n\n\n Externally applied moments in the material frame :math:`\\boldsymbol{m}_B^{ext}` result in the following\n linearised expression:\n\n .. math::\n \\delta(T^\\top\\boldsymbol{m}_B) = \\frac{\\partial}{\\partial\\boldsymbol{\\psi}}\\left(\n T^\\top(\\boldsymbol{\\psi})\\boldsymbol{m}^{ext}_{0,B}\\right)\\delta\\boldsymbol{\\psi} +\n T_0^\\top \\delta\\boldsymbol{m}_B^{ext}\n\n Which results in the following stiffenning term:\n\n .. math::\n K_{ss}^{m,\\Psi} \\leftarrow -\\frac{\\partial}{\\partial\\boldsymbol{\\psi}}\\left(\n T^\\top(\\boldsymbol{\\psi})\\boldsymbol{m}^{ext}_{0,B}\\right)\n\n The total contribution of moments must be summed up for the rigid body equations, and include contributions\n due to externally applied forces as well as moments:\n\n .. math::\n \\boldsymbol{M}_A^{ext} = \\sum_n \\tilde{\\boldsymbol{R}}_A C^{AB}(\\boldsymbol{\\psi}) \\boldsymbol{f}_B^{ext} +\n \\sum C^{AB}(\\boldsymbol{\\psi})\\boldsymbol{m}_B^{ext}\n\n The linearisation of this term becomes\n\n .. math::\n \\delta\\boldsymbol{M}_A^{ext} = \\sum\\left(-\\widetilde{C^{AB}_0 \\boldsymbol{f}_{0,B}^{ext}}\\delta \\boldsymbol{R}_A\n + \\widetilde{\\boldsymbol{R}}\\frac{\\partial}{\\partial\\boldsymbol{\\psi}}\\left(C^{AB}\\boldsymbol{f}_B\\right)\n \\delta \\boldsymbol{\\psi} +\n \\widetilde{\\boldsymbol{R}}C^{AB}\\delta\\boldsymbol{f}^{ext}_B\\right) +\n \\sum\\left(\\frac{\\partial}{\\partial\\boldsymbol{\\psi}}\\left(C^{AB}\\boldsymbol{m}_{0,B}\\right)\n \\delta\\boldsymbol{\\psi} +\n C^AB\\delta\\boldsymbol{m}_B^{ext}\\right)\n\n which gives the following stiffenning terms in the rigid-flex partition of the stiffness matrix:\n\n .. math:: K_{ss}^{M,R} \\leftarrow +\\sum\\widetilde{C^{AB}_0 \\boldsymbol{f}_{0,B}^{ext}}\n\n .. math:: K_{ss}^{M,\\Psi} \\leftarrow -\\sum\\widetilde{\\boldsymbol{R}}\\frac{\\partial}{\\partial\\boldsymbol{\\psi}}\n \\left(C^{AB}\\boldsymbol{f}_{0,B}\\right)\n\n and\n\n .. math:: K_{ss}^{M,\\Psi} \\leftarrow -\\sum\\frac{\\partial}{\\partial\\boldsymbol{\\psi}}\n \\left(C^{AB}\\boldsymbol{m}_{0,B}\\right).\n\n\n Args:\n tsstr (sharpy.utils.datastructures.StructTimeStepInfo): Linearisation time step.\n \"\"\"\n if tsstr is None:\n tsstr = self.tsstruct0\n\n # TODO: Future feature: gains for externally applied forces (i.e. thrust inputs)\n\n num_node = tsstr.num_node\n flex_dof = 6 * sum(self.structure.vdof >= 0)\n if self.use_euler:\n rig_dof = 9\n # This is a rotation matrix that rotates a vector from G to A\n Cag = algebra.euler2rot(tsstr.euler)\n Cga = Cag.T\n\n # Projection matrices - this projects the vector in G t to A\n Pag = Cga\n Pga = Cag\n else:\n rig_dof = 10\n\n stiff_flex = np.zeros((flex_dof, flex_dof), dtype=float) # flex-flex partition of K\n stiff_rig = np.zeros((rig_dof, flex_dof), dtype=float) # rig-flex partition of K\n\n for i_node in range(num_node):\n fext_b = self.structure.steady_app_forces[i_node, :3]\n mext_b = self.structure.steady_app_forces[i_node, 3:]\n\n # retrieve element and local index\n ee, node_loc = self.structure.node_master_elem[i_node, :]\n psi = tsstr.psi[ee, node_loc, :]\n Cab = algebra.crv2rotation(psi)\n Cba = Cab.T\n\n # Tangential operator for moments calculation\n Tan = algebra.crv2tan(psi)\n\n # Get nodal position - in A frame\n Ra = tsstr.pos[i_node, :]\n\n jj = 0 # nodal dof index\n bc_at_node = self.structure.boundary_conditions[i_node] # Boundary conditions at the node\n\n if bc_at_node == 1: # clamp (only rigid-body)\n dofs_at_node = 0\n jj_tra, jj_rot = [], []\n\n elif bc_at_node == -1 or bc_at_node == 0: # (rigid+flex body)\n dofs_at_node = 6\n jj_tra = 6 * self.structure.vdof[i_node] + np.array([0, 1, 2], dtype=int) # Translations\n jj_rot = 6 * self.structure.vdof[i_node] + np.array([3, 4, 5], dtype=int) # Rotations\n else:\n raise NameError('Invalid boundary condition ({}) at node {}'.format(bc_at_node, i_node))\n\n jj += dofs_at_node\n\n if bc_at_node != 1:\n # Externally applied follower forces\n stiff_flex[np.ix_(jj_tra, jj_rot)] -= algebra.der_Ccrv_by_v(psi, fext_b)\n stiff_rig[:3, jj_rot] -= algebra.der_Ccrv_by_v(psi, fext_b) # Rigid body contribution\n\n # Externally applied moments in B frame\n stiff_flex[np.ix_(jj_rot, jj_rot)] -= algebra.der_TanT_by_xv(psi, mext_b)\n\n # Total moments\n # force contribution\n stiff_rig[3:6, jj_tra] += algebra.skew(Cab.dot(fext_b)) # delta Ra term\n stiff_rig[3:6, jj_rot] -= algebra.skew(Ra).dot(algebra.der_Ccrv_by_v(psi, fext_b)) # delta psi term\n\n # moment contribution\n stiff_rig[3:6, jj_rot] -= algebra.der_Ccrv_by_v(psi, mext_b)\n\n if bc_at_node == 1:\n # forces applied at the A-frame (clamped node) need special attention since the\n # node has an associated CRV to it's master element which may not be zero.\n # forces applied at this node only appear in the rigid-body equations\n try:\n closest_node = self.structure.connectivities[ee, node_loc + 2]\n except IndexError: # node is not in the first position\n try:\n closest_node = self.structure.connectivities[ee, node_loc + 1]\n except IndexError: # node is the midpoint\n closest_node = self.structure.connectivities[ee, node_loc - 1]\n\n # indices of the node whos CRV applies to the clamped node\n jj_rot = 6 * self.structure.vdof[closest_node] + np.array([3, 4, 5], dtype=int)\n\n stiff_rig[:3, jj_rot] -= algebra.der_Ccrv_by_v(psi, fext_b) # Rigid body contribution\n # Total moments\n # force contribution\n stiff_rig[3:6, jj_rot] += algebra.skew(Cab.dot(fext_b)) # delta Ra term\n stiff_rig[3:6, jj_rot] -= algebra.skew(Ra).dot(algebra.der_Ccrv_by_v(psi, fext_b)) # delta psi term\n\n # moment contribution\n stiff_rig[3:6, jj_rot] -= algebra.der_Ccrv_by_v(psi, mext_b)\n\n self.Kstr[:flex_dof, :flex_dof] += stiff_flex\n\n if self.Kstr[:flex_dof, :flex_dof].shape != self.Kstr.shape: # free flying structure\n self.Kstr[-rig_dof:, :flex_dof] += stiff_rig\n\n def assemble(self, Nmodes=None):\n r\"\"\"\n Assemble state-space model\n\n Several assembly options are available:\n\n 1. Discrete-time, Newmark-:math:`\\beta`:\n * Modal projection onto undamped modes. It uses the modal projection such\n that the generalised coordinates :math:`\\eta` are transformed into modal space by\n\n .. math:: \\mathbf{\\eta} = \\mathbf{\\Phi\\,q}\n\n where :math:`\\mathbf{\\Phi}` are the first ``Nmodes`` right eigenvectors.\n Therefore, the equation of motion can be re-written such that the modes normalise the mass matrix to\n become the identity matrix.\n\n .. math:: \\mathbf{I_{Nmodes}}\\mathbf{\\ddot{q}} + \\mathbf{\\Lambda_{Nmodes}\\,q} = 0\n\n The system is then assembled in Newmark-:math:`\\beta` form as detailed in :func:`newmark_ss`\n\n * Full size system assembly. No modifications are made to the mass, damping or stiffness matrices and the\n system is directly assembled by :func:`newmark_ss`.\n\n 2. Continuous time state-space\n\n\n Args:\n Nmodes (int): number of modes to retain\n \"\"\"\n\n ### checks\n assert self.inout_coords in ['modes', 'nodes'], \\\n 'inout_coords=%s not implemented!' % self.inout_coords\n\n dlti = self.dlti\n modal = self.modal\n num_dof = self.num_dof\n if Nmodes is None or Nmodes >= self.num_modes:\n Nmodes = self.num_modes\n\n if dlti: # ---------------------------------- assemble discrete time\n\n if self.discr_method in ['zoh', 'bilinear']:\n # assemble continuous-time\n self.dlti = False\n self.assemble(Nmodes)\n # convert into discrete\n self.dlti = True\n self.cont2disc()\n\n elif self.discr_method == 'newmark':\n\n if modal: # Modal projection\n if self.proj_modes == 'undamped':\n Phi = self.U[:, :Nmodes]\n\n Ass, Bss, Css, Dss = newmark_ss(\n Phi.T @ self.Mstr @ Phi,\n Phi.T @ self.Cstr @ Phi,\n Phi.T @ self.Kstr @ Phi,\n self.dt,\n self.newmark_damp)\n\n self.Kin = libss.Gain(Phi.T)\n self.Kin.input_variables = LinearVector([InputVariable('forces_n',\n size=self.Mstr.shape[0],\n index=0)])\n self.Kin.output_variables = LinearVector([OutputVariable('Q',\n size=Nmodes,\n index=0)])\n\n self.Kout = libss.Gain(sc.linalg.block_diag(*[Phi, Phi]))\n self.Kout.input_variables = LinearVector([InputVariable('q', size=Nmodes, index=0),\n InputVariable('q_dot', size=Nmodes, index=1)])\n output_variables = LinearVector([OutputVariable('eta', size=self.num_dof_flex, index=0),\n OutputVariable('eta_dot', size=self.num_dof_flex, index=1)])\n if not self.clamped:\n output_variables.add('beta_bar', size=self.num_dof_rig, index=0.5)\n output_variables.append('beta', size=self.num_dof_rig)\n\n self.Kout.output_variables = output_variables\n\n else:\n raise NameError(\n 'Newmark-beta discretisation not available ' \\\n 'for projection on damped eigenvectors')\n\n # build state-space model\n self.SSdisc = libss.StateSpace(Ass, Bss, Css, Dss, dt=self.dt)\n input_variables = LinearVector([InputVariable('Q', size=Nmodes, index=0)])\n\n output_variables = LinearVector([OutputVariable('q', size=Nmodes, index=0),\n OutputVariable('q_dot', size=Nmodes, index=1)])\n\n state_variables = output_variables.transform(output_variables,\n to_type=StateVariable)\n\n self.SSdisc.input_variables = input_variables\n self.SSdisc.output_variables = output_variables\n self.SSdisc.state_variables = state_variables\n\n if self.inout_coords == 'nodes':\n self.SSdisc = libss.addGain(self.SSdisc, self.Kin, 'in')\n self.SSdisc = libss.addGain(self.SSdisc, self.Kout, 'out')\n self.Kin, self.Kout = None, None\n\n\n else: # Full system\n Ass, Bss, Css, Dss = newmark_ss(\n self.Mstr, self.Cstr, self.Kstr,\n self.dt, self.newmark_damp)\n self.Kin = None\n self.Kout = None\n self.SSdisc = libss.StateSpace(Ass, Bss, Css, Dss, dt=self.dt)\n\n input_variables = LinearVector([InputVariable('forces_n',\n size=self.Mstr.shape[0],\n index=0)])\n\n output_variables = LinearVector([OutputVariable('eta', size=self.num_dof_flex, index=0),\n OutputVariable('eta_dot', size=self.num_dof_flex, index=1)])\n if not self.clamped:\n output_variables.add('beta_bar', size=self.num_dof_rig, index=0.5)\n output_variables.append('beta', size=self.num_dof_rig)\n\n self.SSdisc.output_variables = output_variables\n self.SSdisc.input_variables = input_variables\n self.SSdisc.state_variables = LinearVector.transform(output_variables, to_type=StateVariable)\n else:\n raise NameError(\n 'Discretisation method %s not available' % self.discr_method)\n\n\n else: # -------------------------------- assemble continuous time\n\n if modal: # Modal projection\n\n Ass = np.zeros((2 * Nmodes, 2 * Nmodes))\n Css = np.eye(2 * Nmodes)\n iivec = np.arange(Nmodes, dtype=int)\n\n if self.proj_modes == 'undamped':\n Phi = self.U[:, :Nmodes]\n Ass[iivec, Nmodes + iivec] = 1.\n # Ass[Nmodes:, :Nmodes] = -np.diag(self.freq_natural[:Nmodes] ** 2)\n Ass[Nmodes:, :Nmodes] = -self.U.T.dot(self.Kstr.dot(self.U))\n if self.Ccut is not None:\n Ass[Nmodes:, Nmodes:] = -self.Ccut[:Nmodes, :Nmodes]\n Bss = np.zeros((2 * Nmodes, Nmodes))\n Dss = np.zeros((2 * Nmodes, Nmodes))\n Bss[Nmodes + iivec, iivec] = 1.\n self.Kin = libss.Gain(Phi.T)\n self.Kin.input_variables = LinearVector([InputVariable('forces_n',\n size=self.Mstr.shape[0],\n index=0)])\n self.Kin.output_variables = LinearVector([OutputVariable('Q',\n size=Nmodes,\n index=0)])\n self.Kout = libss.Gain(sc.linalg.block_diag(*[Phi, Phi]))\n self.Kout.input_variables = LinearVector([InputVariable('q', size=Nmodes, index=0),\n InputVariable('q_dot', size=Nmodes, index=1)])\n\n output_variables = LinearVector([OutputVariable('eta', size=self.num_dof_flex, index=0),\n OutputVariable('eta_dot', size=self.num_dof_flex, index=1)])\n if not self.clamped:\n output_variables.add('beta_bar', size=self.num_dof_rig, index=0.5)\n output_variables.append('beta', size=self.num_dof_rig)\n\n self.Kout.output_variables = output_variables\n else: # damped mode shapes\n # The algorithm assumes that for each couple of complex conj\n # eigenvalues, only one eigenvalue (and the eigenvectors\n # associated to it) is include in self.eigs.\n eigs = self.eigs[:Nmodes]\n U = self.U[:, :Nmodes]\n V = self.V[:, :Nmodes]\n Ass[iivec, iivec] = eigs.real\n Ass[iivec, Nmodes + iivec] = -eigs.imag\n Ass[Nmodes + iivec, iivec] = eigs.imag\n Ass[Nmodes + iivec, Nmodes + iivec] = eigs.real\n Bss = np.eye(2 * Nmodes)\n Dss = np.zeros((2 * Nmodes, 2 * Nmodes))\n self.Kin = np.block(\n [[self.Kin_damp[iivec, :].real],\n [self.Kin_damp[iivec, :].imag]])\n self.Kout = np.block([2. * U.real, (-2.) * U.imag])\n\n # build state-space model\n self.SScont = libss.StateSpace(Ass, Bss, Css, Dss)\n input_variables = LinearVector([InputVariable('Q', size=Nmodes, index=0)])\n\n output_variables = LinearVector([OutputVariable('q', size=Nmodes, index=0),\n OutputVariable('q_dot', size=Nmodes, index=1)])\n\n state_variables = output_variables.transform(output_variables,\n to_type=StateVariable)\n\n self.SScont.input_variables = input_variables\n self.SScont.output_variables = output_variables\n self.SScont.state_variables = state_variables\n if self.inout_coords == 'nodes':\n self.SScont = libss.addGain(self.SScont, self.Kin, 'in')\n self.SScont = libss.addGain(self.SScont, self.Kout, 'out')\n self.Kin, self.Kout = None, None\n\n else: # Full system\n if self.Mstr is None:\n raise NameError('Full-states matrices not available')\n Mstr, Cstr, Kstr = self.Mstr, self.Cstr, self.Kstr\n\n Ass = np.zeros((2 * num_dof, 2 * num_dof))\n Bss = np.zeros((2 * num_dof, num_dof))\n Css = np.eye(2 * num_dof)\n Dss = np.zeros((2 * num_dof, num_dof))\n Minv_neg = -np.linalg.inv(self.Mstr)\n Ass[range(num_dof), range(num_dof, 2 * num_dof)] = 1.\n Ass[num_dof:, :num_dof] = np.dot(Minv_neg, Kstr)\n Ass[num_dof:, num_dof:] = np.dot(Minv_neg, Cstr)\n Bss[num_dof:, :] = -Minv_neg\n self.Kin = None\n self.Kout = None\n self.SScont = libss.StateSpace(Ass, Bss, Css, Dss)\n\n input_variables = LinearVector([InputVariable('forces_n',\n size=self.Mstr.shape[0],\n index=0)])\n\n output_variables = LinearVector([OutputVariable('eta', size=self.num_dof_flex, index=0),\n OutputVariable('eta_dot', size=self.num_dof_flex, index=1)])\n if not self.clamped:\n output_variables.add('beta_bar', size=self.num_dof_rig, index=0.5)\n output_variables.append('beta', size=self.num_dof_rig)\n\n self.SScont.output_variables = output_variables\n self.SScont.input_variables = input_variables\n self.SScont.state_variables = LinearVector.transform(output_variables, to_type=StateVariable)\n\n\n def freqresp(self, wv=None, bode=True):\n \"\"\"\n Computes the frequency response of the current state-space model. If\n ``self.modal=True``, the in/out are determined according to ``self.inout_coords``\n \"\"\"\n\n assert wv is not None, 'Frequency range not provided.'\n\n if self.dlti:\n self.Ydisc = libss.freqresp(self.SSdisc, wv, dlti=self.dlti)\n if bode:\n self.Ydisc_abs = np.abs(self.Ydisc)\n self.Ydisc_ph = np.angle(self.Ydisc, deg=True)\n else:\n self.Ycont = libss.freqresp(self.SScont, wv, dlti=self.dlti)\n if bode:\n self.Ycont_abs = np.abs(self.Ycont)\n self.Ycont_ph = np.angle(self.Ycont, deg=True)\n\n def converge_modal(self, wv=None, tol=None, Yref=None, Print=False):\n \"\"\"\n Determine number of modes required to achieve a certain convergence\n of the modal solution in a prescribed frequency range ``wv``. The H-infinity\n norm of the error w.r.t. ``Yref`` is used for assessing convergence.\n\n .. Warning:: if a reference freq. response, Yref, is not provided, the full-\n state continuous-time frequency response is used as reference. This\n requires the full-states matrices ``Mstr``, ``Cstr``, ``Kstr`` to be available.\n \"\"\"\n\n if wv is None:\n wv = self.wv\n assert wv is not None, 'Frequency range not provided.'\n assert tol is not None, 'Tolerance, tol, not provided'\n assert self.modal is True, 'Convergence analysis requires modal=True'\n\n if Yref is None:\n # use cont. time. full-states as reference\n dlti_here = self.dlti\n self.modal = False\n self.dlti = False\n self.assemble()\n self.freqresp(wv)\n Yref = self.Ycont.copy()\n self.dlti = dlti_here\n self.modal = True\n\n if Print:\n print('No. modes\\tError\\tTolerance')\n for nn in range(1, self.Nmodes + 1):\n self.assemble(Nmodes=nn)\n self.freqresp(wv, bode=False)\n Yhere = self.Ycont\n if self.dlti: Yhere = self.Ydisc\n er = np.max(np.abs(Yhere - Yref))\n if Print: print('%.3d\\t%.2e\\t%.2e' % (nn, er, tol))\n if er < tol:\n if Print: print('Converged!')\n self.Nmodes = nn\n break\n\n def tune_newmark_damp(self, amplification_factor=0.999):\n \"\"\"\n Tune artifical damping to achieve a percent reduction of the lower\n frequency (lower damped) mode\n \"\"\"\n\n assert self.discr_method == 'newmark' and self.dlti, \\\n \"select self.discr_method='newmark' and self.dlti=True\"\n\n newmark_damp = self.newmark_damp\n import scipy.optimize as scopt\n\n def get_res(newmark_damp_log10):\n self.newmark_damp = 10. ** (newmark_damp_log10)\n self.assemble()\n eigsabs = np.abs(np.linalg.eigvals(self.SSdisc.A))\n return np.max(eigsabs) - amplification_factor\n\n exp_opt = scopt.fsolve(get_res, x0=-3)[0]\n\n self.newmark_damp = 10. ** exp_opt\n print('artificial viscosity: %.4e' % self.newmark_damp)\n\n def update_modal(self):\n r\"\"\"\n Re-projects the full-states continuous-time structural dynamics equations\n\n .. math::\n \\mathbf{M}\\,\\mathbf{\\ddot{x}} +\\mathbf{C}\\,\\mathbf{\\dot{x}} + \\mathbf{K\\,x} = \\mathbf{F}\n\n onto modal space. The modes used to project are controlled through the\n ``self.proj_modes={damped or undamped}`` attribute.\n\n .. Warning:: This method overrides SHARPy ``timestep_info`` results and requires\n ``Mstr``, ``Cstr``, ``Kstr`` to be available.\n\n \"\"\"\n\n if self.proj_modes == 'undamped':\n if self.Cstr is not None:\n if self.settings['print_info']:\n cout.cout_wrap('Warning, projecting system with damping onto undamped modes')\n\n # Eigenvalues are purely complex - only the complex part is calculated\n eigenvalues, eigenvectors = np.linalg.eig(np.linalg.solve(self.Mstr, self.Kstr))\n\n omega = np.sqrt(eigenvalues)\n order = np.argsort(omega)[:self.Nmodes]\n self.freq_natural = omega[order]\n\n phi = eigenvectors[:, order]\n\n phi = modalutils.mode_sign_convention(self.structure.boundary_conditions,\n phi,\n not self.clamped,\n self.use_euler)\n\n if not self.clamped and self.use_principal_axes:\n phi = modalutils.free_modes_principal_axes(phi, self.Mstr, use_euler=self.use_euler)\n\n # Scale modes to have an identity mass matrix\n phi = modalutils.scale_mass_normalised_modes(phi, self.Mstr)\n\n self.U = phi\n\n # Update\n self.eigs = eigenvalues[order]\n if not self.use_principal_axes:\n # in the case of use_principal_axes modes are already ordered\n self.U = self.sort_repeated_evecs(self.U, self.eigs)\n\n # To do: update SHARPy's timestep info modal results\n else:\n raise NotImplementedError('Projection update for damped systems not yet implemented ')\n\n def update_truncated_modes(self, nmodes):\n r\"\"\"\n Updates the system to the specified number of modes\n\n Args:\n nmodes:\n\n Returns:\n\n \"\"\"\n\n # Verify that the new number of modes is less than the current value\n assert nmodes <= self.Nmodes, 'Unable to truncate to %g modes since only %g are available' %(nmodes, self.Nmodes)\n\n self.Nmodes = nmodes\n self.eigs = self.eigs[:nmodes]\n self.U = self.U[:,:nmodes]\n self.freq_natural = self.freq_natural[:nmodes]\n try:\n self.freq_damp[:nmodes]\n except TypeError:\n pass\n\n # Update Ccut matrix\n if self.modal:\n self.Ccut = np.dot(self.U.T, np.dot(self.Cstr, self.U))\n\n def scale_system_normalised_time(self, time_ref):\n r\"\"\"\n Scale the system with a normalised time step. The resulting time step is\n :math:`\\Delta t = \\Delta \\bar{t}/t_{ref}`, where the over bar denotes dimensional time.\n The structural equations of motion are rescaled as:\n\n .. math::\n \\mathbf{M}\\ddot{\\boldsymbol{\\eta}} + \\mathbf{C} t_{ref} \\dot{\\boldsymbol{\\eta}} + \\mathbf{K} t_{ref}^2\n \\boldsymbol{\\eta} = t_{ref}^2 \\mathbf{N}\n\n For aeroelastic applications, the reference time is usually defined using the semi-chord, :math:`b`, and the\n free stream velocity, :math:`U_\\infty`.\n\n .. math:: t_{ref,ae} = \\frac{b}{U_\\infty}\n\n Args:\n time_ref (float): Normalisation factor such that :math:`t/\\bar{t}` is non-dimensional.\n\n \"\"\"\n\n if self.scaled_reference_matrices:\n raise UserWarning('System already time scaled. System may just need an update.'\n ' See update_matrices_time_scale')\n\n # if time_ref != 1.0 and time_ref is not None:\n if self.num_rig_dof != 0:\n warnings.warn('Time normalisation not yet implemented with rigid body motion.')\n\n if self.dlti:\n self.scaled_reference_matrices['dt'] = self.dt\n self.dt /= time_ref\n if self.settings['print_info']:\n cout.cout_wrap('Scaling beam according to reduced time...', 0)\n if self.dlti:\n cout.cout_wrap('\\tSetting the beam time step to (%.4f)' % self.dt, 1)\n\n self.scaled_reference_matrices['C'] = self.Cstr.copy()\n self.scaled_reference_matrices['K'] = self.Kstr.copy()\n self.update_matrices_time_scale(time_ref)\n\n def update_matrices_time_scale(self, time_ref):\n\n try:\n cout.cout_wrap('Updating C and K matrices and natural frequencies with new normalised time...', 1)\n except ValueError:\n pass\n\n try:\n self.Kstr = self.scaled_reference_matrices['K'] * time_ref ** 2\n self.Cstr = self.scaled_reference_matrices['C'] * time_ref\n\n self.freq_natural *= time_ref\n except KeyError:\n raise KeyError('The scaled reference matrices have not been set, most likely because you are trying to '\n 'rescale a dimensional system. Make sure your system is normalised.')\n\n def cont2disc(self, dt=None):\n \"\"\"Convert continuous-time SS model into \"\"\"\n\n assert self.discr_method != 'newmark', \\\n 'For Newmark-beta discretisation, use assemble method directly.'\n\n if dt is not None:\n self.dt = dt\n else:\n assert self.dt is not None, \\\n 'Provide time-step for conversion to discrete-time'\n\n SScont = self.SScont\n tpl = scsig.cont2discrete(\n (SScont.A, SScont.B, SScont.C, SScont.D),\n dt=self.dt, method=self.discr_method)\n self.SSdisc = libss.StateSpace(*tpl[:-1], dt=tpl[-1])\n self.dlti = True\n\n\ndef newmark_ss(M, C, K, dt, num_damp=1e-4, M_is_SPD=False):\n r\"\"\"\n Produces a discrete-time state-space model of the 2nd order ordinary differential equation (ODE) given by:\n\n .. math::\n \\mathbf{M}\\mathbf{\\ddot{q}} + \\mathbf{C}\\mathbf{\\dot{q}} + \\mathbf{K}\\mathbf{q} = \\mathbf{f(t)}\n\n This ODE is discretized based on the Newmark-:math:`\\beta` integration scheme.\n\n The output state-space model has the form:\n \n .. math::\n \\mathbf{x}_{n+1} &= \\mathbf{A_{ss}}\\mathbf{x}_n + \\mathbf{B_{ss}}\\mathbf{f}_n \\\\\n \\mathbf{y}_n &= \\mathbf{C_{ss}}\\mathbf{x}_n + \\mathbf{D_{ss}}\\mathbf{f}_n\n\n where :math:`\\mathbf{y} = \\begin{Bmatrix} \\mathbf{q} \\\\ \\mathbf{\\dot{q}} \\end{Bmatrix}`\n\n Note that as the state-space representation only requires the input force\n :math:`\\mathbf{f}` to be evaluated at time-step :math:`n`, thus the pass-through matrix \n :math:`\\mathbf{D_{ss}}` is not zero.\n\n This function retuns a tuple with the discrete state-space matrices :math:`(\\mathbf{A_{ss},B_{ss},C_{ss},D_{ss}})`.\n\n Theory\n ------\n\n The following steps describe how to apply the Newmark-:math:`\\beta` scheme\n to the ODE in order to generate the discrete time-state space-model. It\n folows the development of [1].\n\n .. admonition:: Notation\n\n Bold upper case letters represent matrices, bold lower case letters\n represent vectors. Non-bold symbols are scalars. Curly brackets\n indicate (block) vectors and square brackets indicate (block) matrices.\n\n Evaluating the ODE to the time steps :math:`t_n` and :math:`t_{n+1}` and\n isolating the acceleration term:\n\n .. math::\n \\mathbf{\\ddot q}_{n} &= - \\mathbf{M}^{-1}\\mathbf{C}\\mathbf{\\dot{q}}_{n} \n - \\mathbf{M}^{-1}\\mathbf{K}\\mathbf{q}_{n} \n + \\mathbf{M}^{-1}\\mathbf{f}_{n} \\\\\n \\mathbf{\\ddot q}_{n+1} &= - \\mathbf{M}^{-1}\\mathbf{C}\\mathbf{\\dot{q}}_{n+1} \n - \\mathbf{M}^{-1}\\mathbf{K}\\mathbf{q}_{n+1} \n + \\mathbf{M}^{-1}\\mathbf{f}_{n+1} \\\\\n\n The update equations of the Newmark-beta scheme are [1]:\n\n .. math::\n \\mathbf{q}_{n+1} &= \\mathbf{q}_n + \\mathbf{\\dot q}_n\\Delta t +\n (1/2-\\beta)\\mathbf{\\ddot q}_n \\Delta t^2 + \\beta \\mathbf{\\ddot q}_{n+1} \\Delta t^2 + O(\\Delta t^3) \\\\\n \\mathbf{\\dot q}_{n+1} &= \\mathbf{\\dot q}_n + (1-\\gamma)\\mathbf{\\ddot q}_n \\Delta t +\n \\gamma \\mathbf{\\ddot q}_{n+1} \\Delta t + O(\\Delta t^3)\n\n where :math:`\\Delta t = t_{n+1} - t_n`.\n\n The stencil is unconditionally stable if the tuning parameters\n :math:`\\gamma` and :math:`\\beta` are chosen as:\n\n .. math::\n \\gamma &= \\frac{1}{2} + \\alpha \\\\\n \\beta &= \\frac{(1+\\alpha)^2}{4} \n = \\frac{(1/2+\\gamma)^2}{4} \n = \\frac{1}{16} + \\frac{1}{4}(\\gamma + \\gamma^2)\n\n where :math:`\\alpha>0` accounts for small positive algorithmic damping (:math:`\\alpha` is ``num_damp`` in the code).\n\n Substituting the former relations onto the later ones, rearranging terms, and writing it in state-space form:\n \n .. math::\n \\mathbf{A_{ss1}} \\begin{Bmatrix} \\mathbf{q}_{n+1} \\\\ \\mathbf{\\dot q}_{n+1} \\end{Bmatrix} \n =\n \\mathbf{A_{ss0}} \\begin{Bmatrix} \\mathbf{q}_{n} \\\\ \\mathbf{\\dot q}_{n} \\end{Bmatrix} +\n \\mathbf{B_{ss0}} \\mathbf{f}_n +\n \\mathbf{B_{ss1}} \\mathbf{f}_{n+1}\n \n where\n \n .. math::\n \\mathbf{A_{ss1}} &=\n \\begin{bmatrix} \n \\mathbf{I} + \\beta\\Delta t^2 \\mathbf{M}^{-1}\\mathbf{K}\n & \\beta\\Delta t^2 \\mathbf{M}^{-1}\\mathbf{C} \\\\\n \\gamma \\Delta t \\mathbf{M}^{-1}\\mathbf{K}\n & \\mathbf{I}+ \\gamma \\Delta t \\mathbf{M}^{-1}\\mathbf{C}\n \\end{bmatrix} \n \\\\\n \\mathbf{A_{ss0}} &=\n \\begin{bmatrix} \n \\mathbf{I} - \\Delta t^2(1/2-\\beta)\\mathbf{M}^{-1}\\mathbf{K}\n & \\Delta t \\mathbf{I} - (1/2-\\beta)\\Delta t^2 \\mathbf{M}^{-1}\\mathbf{C} \\\\\n -(1-\\gamma)\\Delta t \\mathbf{M}^{-1}\\mathbf{K}\n & \\mathbf{I} - (1-\\gamma)\\Delta t \\mathbf{M}^{-1}\\mathbf{C}\n \\end{bmatrix}\n \\\\\n \\mathbf{B_{ss0}} &=\n \\begin{bmatrix} \n (\\Delta t^2(1/2-\\beta) \\mathbf{M}^{-1} \\\\ \n (1-\\gamma)\\Delta t \\mathbf{M}^{-1}\n \\end{bmatrix} \n \\\\\n \\mathbf{B_{ss1}} &=\n \\begin{bmatrix} \n (\\beta \\Delta t^2) \\mathbf{M}^{-1}\\\\ \n (\\gamma \\Delta t) \\mathbf{M}^{-1}\n \\end{bmatrix}\n\n\n This is not in standard space-state form because the state update equation\n depends of the input at :math:`t_{n+1}`. This term can be eliminated by\n defining the state \n \n .. math:: \\mathbf{x}_n = \n \\begin{Bmatrix} \n \\mathbf{q}_{n} \\\\ \n \\mathbf{\\dot q}_{n}\n \\end{Bmatrix} \n - \\mathbf{A}_{\\mathbf{ss1}}^{-1}\\mathbf{B_{ss1}} \\mathbf{f}_n\n\n Then\n \n .. math::\n \\mathbf{x}_{n+1} &= \\mathbf{A}_{\\mathbf{ss1}}^{-1}[\n \\mathbf{A_{ss0}} \\mathbf{x}_n + (\n \\mathbf{A_{ss0}}\\mathbf{A}_{\\mathbf{ss1}}^{-1}\\mathbf{B_{ss1}} \n + \\mathbf{B_{ss0}}\n )\n \\mathbf{f}_n\n ] \\\\\n \\begin{Bmatrix} \n \\mathbf{q}_{n} \\\\\n \\mathbf{\\dot q}_{n}\n \\end{Bmatrix}\n &= \\mathbf{x}_n + \\mathbf{A}_{\\mathbf{ss1}}^{-1}\\mathbf{B_{ss1}} \\mathbf{f}_n\n\n See also :func:`sharpy.linear.src.libss.SSconv` for more details on the elimination of the term\n multiplying :math:`\\mathbf{f}_{n+1}` in the state equation.\n\n This system is identified with a standard discrete-time state-space model\n \n .. math::\n \\mathbf{x}_{n+1} &= \\mathbf{A_{ss}} \\mathbf{x}_n + \\mathbf{B_{ss}} \\mathbf{f}_n \\\\\n \\mathbf{y_n} &= \\mathbf{C_{ss}} \\mathbf{x}_n + \\mathbf{D_{ss}} \\mathbf{f}_n\n\n where\n\n .. math::\n \\mathbf{A_{ss}} &= \\mathbf{A}_{\\mathbf{ss1}}^{-1}\\mathbf{A_{ss0}} \\\\\n \\mathbf{B_{ss}} &= \\mathbf{A_{\\mathbf{ss1}}^{-1}(\\mathbf{B_{ss0}} \n + \\mathbf{A_{ss0}}\\mathbf{A_{\\mathbf{ss1}}^{-1}\\mathbf{B_{ss1}}) \\\\\n \\mathbf{C_{ss}} &= \\mathbf{I} \\\\\n \\mathbf{D_{ss}} &= \\mathbf{A_{\\mathbf{ss1}}^{-1}\\mathbf{B_{ss1}}\n \n\n .. admonition:: Notation is used in the code \n \n .. math::\n \\texttt{th1} &= \\gamma \\\\\n \\texttt{th2} &= \\beta \\\\\n \\texttt{a0} &= (1/2 -\\beta) \\Delta t^2 \\\\\n \\texttt{b0} &= (1 -\\gamma) \\Delta t \\\\\n \\texttt{a1} &= \\beta \\Delta t^2 \\\\\n \\texttt{b1} &= \\gamma \\Delta t \\\\\n\n Args:\n M (np.array): Mass matrix :math:`\\mathbf{M}`\n C (np.array): Damping matrix :math:`\\mathbf{C}`\n K (np.array): Stiffness matrix :math:`\\mathbf{K}`\n dt (float): Timestep increment\n num_damp (float): Numerical damping. Default ``1e-4``\n M_is_SPD (bool): whether to factorized M using Cholesky (only works for SPD matrices) or LU decomposition. Default: ``False`` \n\n Returns:\n tuple: with the :math:`(\\mathbf{A_{ss},B_{ss},C_{ss},D_{ss}})` matrices of the discrete-time state-space representation\n\n References:\n [1] - Geradin M., Rixen D. - Mechanical Vibrations: Theory and application to structural dynamics\n \"\"\"\n\n # weights\n th1 = 0.5 + num_damp\n # th2=0.25*(th1+.5)**2\n th2 = 0.0625 + 0.25 * (th1 + th1 ** 2)\n\n dt2 = dt ** 2\n a1 = th2 * dt2\n a0 = 0.5 * dt2 - a1\n b1 = th1 * dt\n b0 = dt - b1\n\n # Identity matrix\n N = K.shape[0]\n Imat = np.eye(N)\n\n # Factorize M and obtain relevant matrices\n # Even though the inverse needs to be explicitly calculated, using the matrix \n # factorization is more numerically stable and faster than multiplying by the\n # inverse\n M_factors = sc.linalg.cho_factor(M) if M_is_SPD else sc.linalg.lu_factor(M)\n\n def M_solve(b):\n return sc.linalg.cho_solve(M_factors, b) if M_is_SPD else sc.linalg.lu_solve(M_factors, b)\n\n Minv = M_solve(Imat)\n MinvK = M_solve(K)\n MinvC = M_solve(C)\n\n # build StateSpace\n Ass0 = np.block([[Imat - a0 * MinvK, dt * Imat - a0 * MinvC],\n [-b0 * MinvK, Imat - b0 * MinvC]])\n Ass1 = np.block([[Imat + a1 * MinvK, a1 * MinvC],\n [b1 * MinvK, Imat + b1 * MinvC]])\n\n # Factorize Ass1 once, solve multiple times\n Ass1_factors = sc.linalg.lu_factor(Ass1)\n Ass = sc.linalg.lu_solve(Ass1_factors, Ass0)\n Bss0 = sc.linalg.lu_solve(Ass1_factors, np.block([[a0 * Minv], [b0 * Minv]]))\n Bss1 = sc.linalg.lu_solve(Ass1_factors, np.block([[a1 * Minv], [b1 * Minv]]))\n\n # eliminate predictior term Bss1\n return libss.SSconv(Ass, Bss0, Bss1, C=np.eye(2 * N), D=np.zeros((2 * N, N)))\n\n\ndef sort_eigvals(eigv, eigabsv, tol=1e-6):\n \"\"\" sort by magnitude (frequency) and imaginary part if complex conj \"\"\"\n\n order = np.argsort(np.abs(eigv))\n eigv = eigv[order]\n\n for ii in range(len(eigv) - 1):\n # check if ii and ii+1 are the same eigenvalue\n if np.abs(eigv[ii].imag + eigv[ii + 1].imag) / eigabsv[ii] < tol:\n if np.abs(eigv[ii].real - eigv[ii + 1].real) / eigabsv[ii] < tol:\n\n # swap if required\n if eigv[ii].imag > eigv[ii + 1].imag:\n temp = eigv[ii]\n eigv[ii] = eigv[ii + 1]\n eigv[ii + 1] = temp\n\n temp = order[ii]\n order[ii] = order[ii + 1]\n order[ii + 1] = temp\n\n return order, eigv\n" }, { "path": "sharpy/linear/src/linuvlm.py", "content": "\"\"\"\nLinear UVLM solver classes\n\nContains classes to assemble a linear UVLM system. The three main classes are:\n\n* :class:`~sharpy.linear.src.linuvlm.Static`: : for static VLM solutions.\n\n* :class:`~sharpy.linear.src.linuvlm.Dynamic`: for dynamic UVLM solutions.\n\n* :class:`~sharpy.linear.src.linuvlm.DynamicBlock`: a more efficient representation of ``Dynamic`` using lists for the\n different blocks in the UVLM equations\n\nReferences:\n\n Maraniello, S., & Palacios, R.. State-Space Realizations and Internal Balancing in Potential-Flow\n Aerodynamics with Arbitrary Kinematics. AIAA Journal, 57(6), 1–14. 2019. https://doi.org/10.2514/1.J058153\n\n\"\"\"\n\nimport time\nimport warnings\nimport numpy as np\nimport scipy.linalg as scalg\nimport scipy.sparse as sparse\n\nimport sharpy.linear.src.interp as interp\nimport sharpy.linear.src.multisurfaces as multisurfaces\nimport sharpy.linear.src.assembly as ass\nimport sharpy.linear.src.libss as libss\n\nimport sharpy.linear.src.libsparse as libsp\nimport sharpy.rom.utils.librom as librom\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.settings as settings\nimport sharpy.utils.cout_utils as cout\nimport sharpy.utils.exceptions as exceptions\nfrom sharpy.utils.constants import vortex_radius_def\nfrom sharpy.linear.utils.ss_interface import LinearVector, StateVariable, InputVariable, OutputVariable\n\nsettings_types_static = dict()\nsettings_default_static = dict()\n\nsettings_types_static['vortex_radius'] = 'float'\nsettings_default_static['vortex_radius'] = vortex_radius_def\n\nsettings_types_static['cfl1'] = 'bool'\nsettings_default_static['cfl1'] = True\n\nsettings_types_dynamic = dict()\nsettings_default_dynamic = dict()\n\nsettings_types_dynamic['dt'] = 'float'\nsettings_default_dynamic['dt'] = 0.1\n\nsettings_types_dynamic['integr_order'] = 'int'\nsettings_default_dynamic['integr_order'] = 2\n\nsettings_types_dynamic['density'] = 'float'\nsettings_default_dynamic['density'] = 1.225\n\nsettings_types_dynamic['ScalingDict'] = 'dict'\nsettings_default_dynamic['ScalingDict'] = {'length': 1.0,\n 'speed': 1.0,\n 'density': 1.0}\n\nsettings_types_dynamic['remove_predictor'] = 'bool'\nsettings_default_dynamic['remove_predictor'] = True\n\nsettings_types_dynamic['use_sparse'] = 'bool'\nsettings_default_dynamic['use_sparse'] = True\n\nsettings_types_dynamic['vortex_radius'] = 'float'\nsettings_default_dynamic['vortex_radius'] = vortex_radius_def\n\nsettings_types_dynamic['cfl1'] = 'bool'\nsettings_default_dynamic['cfl1'] = True\n\n\nclass Static():\n \"\"\"\tStatic linear solver \"\"\"\n\n def __init__(self, tsdata, custom_settings=None, for_vel=np.zeros((6,))):\n\n cout.cout_wrap('Initialising Static linear UVLM solver class...')\n t0 = time.time()\n\n if custom_settings is None:\n settings_here = settings_default_static\n else:\n settings_here = custom_settings\n\n settings.to_custom_types(settings_here,\n settings_types_static,\n settings_default_static,\n no_ctype=True)\n\n self.vortex_radius = settings_here['vortex_radius']\n self.cfl1 = settings_here['cfl1']\n MS = multisurfaces.MultiAeroGridSurfaces(tsdata,\n self.vortex_radius,\n for_vel=for_vel)\n MS.get_ind_velocities_at_collocation_points()\n MS.get_input_velocities_at_collocation_points()\n MS.get_ind_velocities_at_segments()\n MS.get_input_velocities_at_segments()\n\n # define total sizes\n self.K = sum(MS.KK)\n self.K_star = sum(MS.KK_star)\n self.Kzeta = sum(MS.KKzeta)\n self.Kzeta_star = sum(MS.KKzeta_star)\n self.MS = MS\n\n # define input perturbation\n self.zeta = np.zeros((3 * self.Kzeta))\n self.zeta_dot = np.zeros((3 * self.Kzeta))\n self.u_ext = np.zeros((3 * self.Kzeta))\n\n self.input_variables_list = [InputVariable('zeta', size=3 * self.Kzeta, index=0),\n InputVariable('zeta_dot', size=3 * self.Kzeta, index=1),\n InputVariable('u_gust', size=3 * self.Kzeta, index=2)]\n\n self.state_variables_list = [StateVariable('gamma', size=self.K, index=0),\n StateVariable('gamma_w', size=self.K_star, index=1),\n StateVariable('gamma_m1', size=self.K, index=2)]\n\n self.output_variables_list = [OutputVariable('forces_v', size=3 * self.Kzeta, index=0)]\n\n # profiling output\n self.prof_out = './asbly.prof'\n\n self.time_init_sta = time.time() - t0\n cout.cout_wrap('\\t\\t\\t...done in %.2f sec' % self.time_init_sta)\n\n def assemble_profiling(self):\n \"\"\"\n Generate profiling report for assembly and save it in self.prof_out.\n\n To read the report:\n import pstats\n p=pstats.Stats(self.prof_out)\n \"\"\"\n\n import cProfile\n cProfile.runctx('self.assemble()', globals(), locals(), filename=self.prof_out)\n\n def assemble(self):\n \"\"\"\n Assemble global matrices\n \"\"\"\n cout.cout_wrap('\\tAssembly of static linear UVLM equations started...', 1)\n MS = self.MS\n t0 = time.time()\n\n # ----------------------------------------------------------- state eq.\n List_uc_dncdzeta = ass.uc_dncdzeta(MS.Surfs)\n List_nc_dqcdzeta_coll, List_nc_dqcdzeta_vert = \\\n ass.nc_dqcdzeta(MS.Surfs, MS.Surfs_star)\n List_AICs, List_AICs_star = ass.AICs(MS.Surfs, MS.Surfs_star,\n target='collocation', Project=True)\n List_Wnv = []\n for ss in range(MS.n_surf):\n List_Wnv.append(\n interp.get_Wnv_vector(MS.Surfs[ss],\n MS.Surfs[ss].aM, MS.Surfs[ss].aN))\n\n ### zeta derivatives\n self.Ducdzeta = np.block(List_nc_dqcdzeta_vert)\n del List_nc_dqcdzeta_vert\n self.Ducdzeta += scalg.block_diag(*List_nc_dqcdzeta_coll)\n del List_nc_dqcdzeta_coll\n self.Ducdzeta += scalg.block_diag(*List_uc_dncdzeta)\n del List_uc_dncdzeta\n # # omega x zeta terms\n List_nc_domegazetadzeta_vert = ass.nc_domegazetadzeta(MS.Surfs, MS.Surfs_star)\n self.Ducdzeta += scalg.block_diag(*List_nc_domegazetadzeta_vert)\n del List_nc_domegazetadzeta_vert\n\n ### input velocity derivatives\n self.Ducdu_ext = scalg.block_diag(*List_Wnv)\n del List_Wnv\n\n ### Condense Gammaw terms\n for ss_out in range(MS.n_surf):\n K = MS.KK[ss_out]\n for ss_in in range(MS.n_surf):\n N_star = MS.NN_star[ss_in]\n aic = List_AICs[ss_out][ss_in] # bound\n aic_star = List_AICs_star[ss_out][ss_in] # wake\n\n # fold aic_star: sum along chord at each span-coordinate\n aic_star_fold = np.zeros((K, N_star))\n for jj in range(N_star):\n aic_star_fold[:, jj] += np.sum(aic_star[:, jj::N_star], axis=1)\n aic[:, -N_star:] += aic_star_fold\n\n self.AIC = np.block(List_AICs)\n\n # ---------------------------------------------------------- output eq.\n\n ### Zeta derivatives\n # ... at constant relative velocity\n self.Dfqsdzeta = scalg.block_diag(\n *ass.dfqsdzeta_vrel0(MS.Surfs, MS.Surfs_star))\n # ... induced velocity contrib.\n List_coll, List_vert = ass.dfqsdvind_zeta(MS.Surfs, MS.Surfs_star)\n for ss in range(MS.n_surf):\n List_vert[ss][ss] += List_coll[ss]\n self.Dfqsdzeta += np.block(List_vert)\n del List_vert, List_coll\n\n ### Input velocities\n self.Dfqsdu_ext = scalg.block_diag(\n *ass.dfqsduinput(MS.Surfs, MS.Surfs_star))\n\n ### Gamma derivatives\n # ... at constant relative velocity\n List_dfqsdgamma_vrel0, List_dfqsdgamma_star_vrel0 = \\\n ass.dfqsdgamma_vrel0(MS.Surfs, MS.Surfs_star)\n self.Dfqsdgamma = scalg.block_diag(*List_dfqsdgamma_vrel0)\n self.Dfqsdgamma_star = scalg.block_diag(*List_dfqsdgamma_star_vrel0)\n del List_dfqsdgamma_vrel0, List_dfqsdgamma_star_vrel0\n # ... induced velocity contrib.\n List_dfqsdvind_gamma, List_dfqsdvind_gamma_star = \\\n ass.dfqsdvind_gamma(MS.Surfs, MS.Surfs_star)\n self.Dfqsdgamma += np.block(List_dfqsdvind_gamma)\n self.Dfqsdgamma_star += np.block(List_dfqsdvind_gamma_star)\n del List_dfqsdvind_gamma, List_dfqsdvind_gamma_star\n\n self.time_asbly = time.time() - t0\n cout.cout_wrap('\\t\\t\\t...done in %.2f sec' % self.time_asbly, 1)\n\n def solve(self):\n r\"\"\"\n Solve for bound :math:`\\\\Gamma` using the equation;\n\n .. math::\n \\\\mathcal{A}(\\\\Gamma^n) = u^n\n\n # ... at constant rotation speed\n ``self.Dfqsdzeta+=scalg.block_diag(*ass.dfqsdzeta_omega(MS.Surfs,MS.Surfs_star))``\n\n \"\"\"\n\n MS = self.MS\n t0 = time.time()\n\n ### state\n bv = np.dot(self.Ducdu_ext, self.u_ext - self.zeta_dot) + \\\n np.dot(self.Ducdzeta, self.zeta)\n self.gamma = np.linalg.solve(self.AIC, -bv)\n\n ### retrieve gamma over wake\n gamma_star = []\n Ktot = 0\n for ss in range(MS.n_surf):\n Ktot += MS.Surfs[ss].maps.K\n N = MS.Surfs[ss].maps.N\n Mstar = MS.Surfs_star[ss].maps.M\n gamma_star.append(np.concatenate(Mstar * [self.gamma[Ktot - N:Ktot]]))\n gamma_star = np.concatenate(gamma_star)\n\n ### compute steady force\n self.fqs = np.dot(self.Dfqsdgamma, self.gamma) + \\\n np.dot(self.Dfqsdgamma_star, gamma_star) + \\\n np.dot(self.Dfqsdzeta, self.zeta) + \\\n np.dot(self.Dfqsdu_ext, self.u_ext - self.zeta_dot)\n\n self.time_sol = time.time() - t0\n cout.cout_wrap('\\tSolution done in %.2f sec' % self.time_sol, 1)\n\n def reshape(self):\n \"\"\"\n Reshapes state/output according to SHARPy format\n \"\"\"\n\n MS = self.MS\n if not hasattr(self, 'gamma') or not hasattr(self, 'fqs'):\n raise NameError('State and output not found')\n\n self.Gamma = []\n self.Fqs = []\n\n Ktot, Kzeta_tot = 0, 0\n for ss in range(MS.n_surf):\n M, N = MS.Surfs[ss].maps.M, MS.Surfs[ss].maps.N\n K, Kzeta = MS.Surfs[ss].maps.K, MS.Surfs[ss].maps.Kzeta\n\n iivec = range(Ktot, Ktot + K)\n self.Gamma.append(self.gamma[iivec].reshape((M, N)))\n\n iivec = range(Kzeta_tot, Kzeta_tot + 3 * Kzeta)\n self.Fqs.append(self.fqs[iivec].reshape((3, M + 1, N + 1)))\n\n Ktot += K\n Kzeta_tot += 3 * Kzeta\n\n def total_forces(self, zeta_pole=np.zeros((3,))):\n \"\"\"\n Calculates total force (Ftot) and moment (Mtot) (about pole zeta_pole).\n \"\"\"\n\n if not hasattr(self, 'Gamma') or not hasattr(self, 'Fqs'):\n self.reshape()\n\n self.Ftot = np.zeros((3,))\n self.Mtot = np.zeros((3,))\n\n for ss in range(self.MS.n_surf):\n M, N = self.MS.Surfs[ss].maps.M, self.MS.Surfs[ss].maps.N\n for nn in range(N + 1):\n for mm in range(M + 1):\n zeta_node = self.MS.Surfs[ss].zeta[:, mm, nn]\n fnode = self.Fqs[ss][:, mm, nn]\n self.Ftot += fnode\n self.Mtot += np.cross(zeta_node - zeta_pole, fnode)\n # for cc in range(3):\n # \tself.Ftot[cc]+=np.sum(self.Fqs[ss][cc,:,:])\n\n def get_total_forces_gain(self, zeta_pole=np.zeros((3,))):\n r\"\"\"\n Calculates gain matrices to calculate the total force (Kftot) and moment (Kmtot, Kmtot_disp) about the\n pole zeta_pole.\n\n Being :math:`f` and :math:`\\zeta` the force and position at the vertex (m,n) of the lattice\n these are produced as:\n\n * ``ftot=sum(f) -> dftot += df``\n * ``mtot-sum((zeta-zeta_pole) x f) ->\tdmtot += cross(zeta0-zeta_pole) df - cross(f0) dzeta``\n\n \"\"\"\n\n self.Kftot = np.zeros((3, 3 * self.Kzeta))\n self.Kmtot = np.zeros((3, 3 * self.Kzeta))\n self.Kmtot_disp = np.zeros((3, 3 * self.Kzeta))\n\n Kzeta_start = 0\n for ss in range(self.MS.n_surf):\n\n M, N = self.MS.Surfs[ss].maps.M, self.MS.Surfs[ss].maps.N\n\n for nn in range(N + 1):\n for mm in range(M + 1):\n jjvec = [Kzeta_start + np.ravel_multi_index((cc, mm, nn),\n (3, M + 1, N + 1)) for cc in range(3)]\n\n self.Kftot[[0, 1, 2], jjvec] = 1.\n self.Kmtot[np.ix_([0, 1, 2], jjvec)] = algebra.skew(\n self.MS.Surfs[ss].zeta[:, mm, nn] - zeta_pole)\n self.Kmtot_disp[np.ix_([0, 1, 2], jjvec)] = algebra.skew(\n -self.MS.Surfs[ss].fqs[:, mm, nn])\n\n Kzeta_start += 3 * self.MS.KKzeta[ss]\n\n def get_sect_forces_gain(self):\n \"\"\"\n Gains to computes sectional forces. Moments are computed w.r.t.\n mid-vertex (chord-wise index M/2) of each section.\n \"\"\"\n\n Ntot = 0\n for ss in range(self.MS.n_surf):\n Ntot += self.MS.NN[ss] + 1\n self.Kfsec = np.zeros((3 * Ntot, 3 * self.Kzeta))\n self.Kmsec = np.zeros((3 * Ntot, 3 * self.Kzeta))\n\n Kzeta_start = 0\n II_start = 0\n for ss in range(self.MS.n_surf):\n M, N = self.MS.MM[ss], self.MS.NN[ss]\n\n for nn in range(N + 1):\n zeta_sec = self.MS.Surfs[ss].zeta[:, :, nn]\n\n # section indices\n iivec = [II_start + np.ravel_multi_index((cc, nn),\n (3, N + 1)) for cc in range(3)]\n # iivec = [II_start + cc+6*nn for cc in range(6)]\n # iivec = [II_start + cc*(N+1) + nn for cc in range(6)]\n\n for mm in range(M + 1):\n # vertex indices\n jjvec = [Kzeta_start + np.ravel_multi_index((cc, mm, nn),\n (3, M + 1, N + 1)) for cc in range(3)]\n\n # sectional force\n self.Kfsec[iivec, jjvec] = 1.0\n\n # sectional moment\n dx, dy, dz = zeta_sec[:, mm] - zeta_sec[:, M // 2]\n self.Kmsec[np.ix_(iivec, jjvec)] = np.array([[0, -dz, dy],\n [dz, 0, -dx],\n [-dy, dx, 0]])\n Kzeta_start += 3 * self.MS.KKzeta[ss]\n II_start += 3 * (N + 1)\n\n def get_rigid_motion_gains(self, zeta_rotation=np.zeros((3,))):\n \"\"\"\n Gains to reproduce rigid-body motion such that grid displacements and\n velocities are given by:\n\n * ``dzeta = Ktra*u_tra + Krot*u_rot``\n * ``dzeta_dot = Ktra_vel*u_tra_dot + Krot*u_rot_dot``\n\n Rotations are assumed to happen independently with respect to the\n zeta_rotation point and about the x,y and z axes of the inertial frame.\n \"\"\"\n\n # warnings.warn('Rigid rotation matrix not implemented!')\n\n Ntot = 0\n for ss in range(self.MS.n_surf):\n Ntot += self.MS.NN[ss] + 1\n self.Ktra = np.zeros((3 * self.Kzeta, 3))\n self.Ktra_dot = np.zeros((3 * self.Kzeta, 3))\n self.Krot = np.zeros((3 * self.Kzeta, 3))\n self.Krot_dot = np.zeros((3 * self.Kzeta, 3))\n\n Kzeta_start = 0\n for ss in range(self.MS.n_surf):\n M, N = self.MS.MM[ss], self.MS.NN[ss]\n zeta = self.MS.Surfs[ss].zeta\n\n for nn in range(N + 1):\n for mm in range(M + 1):\n # vertex indices\n iivec = [Kzeta_start + np.ravel_multi_index((cc, mm, nn),\n (3, M + 1, N + 1)) for cc in range(3)]\n\n self.Ktra[iivec, [0, 1, 2]] += 1.\n self.Ktra_dot[iivec, [0, 1, 2]] += 1.\n\n # sectional moment\n dx, dy, dz = zeta[:, mm, nn] - zeta_rotation\n Dskew = np.array([[0, -dz, dy], [dz, 0, -dx], [-dy, dx, 0]])\n self.Krot[iivec, :] = Dskew\n self.Krot_dot[iivec, :] = Dskew\n Kzeta_start += 3 * self.MS.KKzeta[ss]\n\n\n# # ------------------------------------------------------------------------------\n# # utilities for Dynamic.balfreq method\n\n# def get_trapz_weights(k0,kend,Nk,knyq=False):\n# \"\"\"\n# Returns uniform frequency grid (kv of length Nk) and weights (wv) for\n# Gramians integration using trapezoidal rule. If knyq is True, it is assumed\n# that kend is also the Nyquist frequency.\n# \"\"\"\n\n# assert k0>=0. and kend>=0., 'Frequencies must be positive!'\n\n# dk=(kend-k0)/(Nk-1.)\n# kv=np.linspace(k0,kend,Nk)\n# wv=np.ones((Nk,))*dk*np.sqrt(2)\n\n# if k0/(kend-k0)<1e-10:\n# wv[0]=.5*dk\n# else:\n# wv[0]=dk/np.sqrt(2)\n\n# if knyq:\n# wv[-1]=.5*dk\n# else:\n# wv[-1]=dk/np.sqrt(2)\n\n# return kv,wv\n\n\n# def get_gauss_weights(k0,kend,Npart,order):\n# \"\"\"\n# Returns gauss-legendre frequency grid (kv of length Npart*order) and\n# weights (wv) for Gramians integration.\n\n# The integration grid is divided into Npart partitions, and in each of\n# them integration is performed using a Gauss-Legendre quadrature of\n# order order.\n\n# Note: integration points are never located at k0 or kend, hence there\n# is no need for special treatment as in (for e.g.) a uniform grid case\n# (see get_unif_weights)\n# \"\"\"\n\n# if Npart==1:\n# # get gauss normalised coords and weights\n# xad,wad=np.polynomial.legendre.leggauss(order)\n# krange=kend-k0\n# kv=.5*(k0+kend) + .5*krange*xad\n# wv=wad*(.5*krange)*np.sqrt(2)\n# print('partitioning: %.3f to %.3f' %(k0,kend) )\n\n# else:\n# kv=np.zeros((Npart*order,))\n# wv=np.zeros((Npart*order,))\n\n# dk_part=(kend-k0)/Npart\n\n# for ii in range(Npart):\n# k0_part=k0+ii*dk_part\n# kend_part=k0_part+dk_part\n# iivec=range(order*ii, order*(ii+1))\n# kv[iivec],wv[iivec]=get_gauss_weights(k0_part,kend_part,Npart=1,order=order)\n\n# return kv,wv\n\n\n# ------------------------------------------------------------------------------\n\n\nclass Dynamic(Static):\n r\"\"\"\n Class for dynamic linearised UVLM solution. Linearisation around steady-state\n are only supported. The class is built upon Static, and inherits all the\n methods contained there.\n\n Input:\n - tsdata: aero timestep data from SHARPy solution\n - dt: time-step\n - integr_order=2: integration order for UVLM unsteady aerodynamic force\n - RemovePredictor=True: if true, the state-space model is modified so as\n to accept in input perturbations, u, evaluated at time-step n rather than\n n+1.\n - ScalingDict=None: disctionary containing fundamental reference units:\n\n .. code-block:: python\n\n {'length': reference_length,\n 'speed': reference_speed,\n 'density': reference density}\n\n used to derive scaling quantities for the state-space model variables.\n The scaling factors are stored in ``self.ScalingFact``.\n\n Note that while time, circulation, angular speeds) are scaled\n accordingly, FORCES ARE NOT. These scale by :math:`q_\\infty b^2`, where :math:`b` is the\n reference length and :math:`q_\\infty` is the dynamic pressure.\n\n - UseSparse=False: builds the A and B matrices in sparse form. C and D\n are dense anyway so the sparse format cannot be applied to them.\n\n Methods:\n - nondimss: normalises a dimensional state-space model based on the\n scaling factors in self.ScalingFact.\n - dimss: inverse of nondimss.\n - assemble_ss: builds state-space model. See function for more details.\n - assemble_ss_profiling: generate profiling report of the assembly and\n saves it into self.prof_out. To read the report:\n\n .. code-block:: python\n\n import pstats\n p = pstats.Stats(self.prof_out)\n\n - solve_steady: solves for the steady state. Several methods available.\n - solve_step: solves one time-step\n - freqresp: ad-hoc method for fast frequency response (only implemented) for ``remove_predictor=False``\n\n Attributes:\n Nx (int): Number of states\n Nu (int): Number of inputs\n Ny (int): Number of outputs\n K (int): Number of paneles :math:`K = MN`\n K_star (int): Number of wake panels :math:`K^*=M^*N`\n Kzeta (int): Number of panel vertices :math:`K_\\zeta=(M+1)(N+1)`\n Kzeta_star (int): Number of wake panel vertices :math:`K_{\\zeta,w} = (M^*+1)(N+1)`\n\n To do:\n Upgrade to linearise around unsteady snapshot (adjoint)\n \"\"\"\n\n def __init__(self, tsdata, dt=None, dynamic_settings=None, integr_order=2,\n RemovePredictor=True, ScalingDict=None, UseSparse=True, for_vel=np.zeros((6,))):\n\n # Transform settings dictionary - in the future remove remaining inputs\n self.settings = dict()\n if dynamic_settings:\n self.settings = dynamic_settings\n settings.to_custom_types(self.settings,\n settings_types_dynamic,\n settings_default_dynamic,\n no_ctype=True)\n else:\n warnings.warn('No settings dictionary found. Using default. Individual parsing of settings is deprecated',\n DeprecationWarning)\n # Future: remove deprecation warning and make settings the only argument\n settings.to_custom_types(self.settings,\n settings_types_dynamic,\n settings_default_dynamic,\n no_ctype=True)\n self.settings['dt'] = dt\n self.settings['integr_order'] = integr_order\n self.settings['remove_predictor'] = RemovePredictor\n self.settings['use_sparse'] = UseSparse\n self.settings['ScalingDict'] = ScalingDict\n\n static_dict = {'vortex_radius': self.settings['vortex_radius'],\n 'cfl1': self.settings['cfl1']}\n super().__init__(tsdata, custom_settings=static_dict, for_vel=for_vel)\n\n self.dt = self.settings['dt']\n self.integr_order = self.settings['integr_order']\n self.vortex_radius = self.settings['vortex_radius']\n self.cfl1 = self.settings['cfl1']\n\n if self.integr_order == 1:\n Nx = 2 * self.K + self.K_star\n elif self.integr_order == 2:\n Nx = 3 * self.K + self.K_star\n # b0, bm1, bp1 = -2., 0.5, 1.5\n else:\n raise NameError('Only integration orders 1 and 2 are supported')\n Ny = 3 * self.Kzeta\n Nu = 3 * Ny\n self.Nx = Nx\n self.Nu = Nu\n self.Ny = Ny\n\n self.remove_predictor = self.settings['remove_predictor']\n # Stores original B matrix for state recovery later\n self.B_predictor = None\n self.D_predictor = None\n\n self.include_added_mass = True\n self.use_sparse = self.settings['use_sparse']\n\n ScalingFacts = self.settings['ScalingDict']\n ScalingFacts['time'] = ScalingFacts['length'] / ScalingFacts['speed']\n ScalingFacts['circulation'] = ScalingFacts['speed'] * ScalingFacts['length']\n ScalingFacts['dyn_pressure'] = 0.5 * ScalingFacts['density'] * ScalingFacts['speed'] ** 2\n ScalingFacts['force'] = ScalingFacts['dyn_pressure'] * ScalingFacts['length'] ** 2\n self.ScalingFacts = ScalingFacts\n\n self.input_variables_list = [InputVariable('zeta', size=3 * self.Kzeta, index=0),\n InputVariable('zeta_dot', size=3 * self.Kzeta, index=1),\n InputVariable('u_gust', size=3 * self.Kzeta, index=2)]\n\n self.state_variables_list = [StateVariable('gamma', size=self.K, index=0),\n StateVariable('gamma_w', size=self.K_star, index=1),\n StateVariable('dtgamma_dot', size=self.K, index=2),\n StateVariable('gamma_m1', size=self.K, index=3)]\n\n self.output_variables_list = [OutputVariable('forces_v', size=3 * self.Kzeta, index=0)]\n\n if self.integr_order == 1:\n self.state_variables_list.pop(2) # remove time derivative state\n\n ### collect statistics\n self.cpu_summary = {'dim': 0.,\n 'nondim': 0.,\n 'assemble': 0.}\n\n # Initialise State Space\n self.SS = None\n\n @property\n def Nu(self):\n \"\"\"Number of inputs :math:`m` to the system.\"\"\"\n if self.SS is not None:\n if self.SS.B.shape.__len__() == 1:\n self.Nu = 1\n else:\n self.Nu = self.SS.B.shape[1]\n return self._Nu\n\n @Nu.setter\n def Nu(self, value):\n self._Nu = value\n\n @property\n def Nx(self):\n \"\"\"Number of states :math:`n` of the system.\"\"\"\n if self.SS is not None:\n self.Nx = self.SS.B.shape[0]\n return self._Nx\n\n @Nx.setter\n def Nx(self, value):\n self._Nx = value\n\n @property\n def Ny(self):\n \"\"\"Number of outputs :math:`p` of the system.\"\"\"\n if self.SS is not None:\n self.Ny = self.SS.C.shape[0]\n return self._Ny\n\n @Ny.setter\n def Ny(self, value):\n self._Ny = value\n\n def nondimss(self):\n \"\"\"\n Scale state-space model based of self.ScalingFacts\n \"\"\"\n\n cout.cout_wrap('Scaling UVLM system with reference time %fs' % self.ScalingFacts['time'])\n t0 = time.time()\n Kzeta = self.Kzeta\n\n self.SS.B[:, :3 * Kzeta] *= (self.ScalingFacts['length'] / self.ScalingFacts['circulation'])\n self.SS.B[:, 3 * Kzeta:] *= (self.ScalingFacts['speed'] / self.ScalingFacts['circulation'])\n if self.remove_predictor:\n self.B_predictor[:, :3 * Kzeta] *= (self.ScalingFacts['length'] / self.ScalingFacts['circulation'])\n self.B_predictor[:, 3 * Kzeta:] *= (self.ScalingFacts['speed'] / self.ScalingFacts['circulation'])\n\n self.SS.C *= (self.ScalingFacts['circulation'] / self.ScalingFacts['force'])\n\n self.SS.D[:, :3 * Kzeta] *= (self.ScalingFacts['length'] / self.ScalingFacts['force'])\n self.SS.D[:, 3 * Kzeta:] *= (self.ScalingFacts['speed'] / self.ScalingFacts['force'])\n if self.remove_predictor:\n self.D_predictor[:, :3 * Kzeta] *= (self.ScalingFacts['length'] / self.ScalingFacts['force'])\n self.D_predictor[:, 3 * Kzeta:] *= (self.ScalingFacts['speed'] / self.ScalingFacts['force'])\n\n self.SS.dt = self.SS.dt / self.ScalingFacts['time']\n\n self.cpu_summary['nondim'] = time.time() - t0\n cout.cout_wrap('Non-dimensional time step set (%f)' % self.SS.dt, 1)\n cout.cout_wrap('System scaled in %fs' % self.cpu_summary['nondim'])\n\n def dimss(self):\n\n t0 = time.time()\n Kzeta = self.Kzeta\n\n self.SS.B[:, :3 * Kzeta] /= (self.ScalingFacts['length'] / self.ScalingFacts['circulation'])\n self.SS.B[:, 3 * Kzeta:] /= (self.ScalingFacts['speed'] / self.ScalingFacts['circulation'])\n if self.remove_predictor:\n self.B_predictor[:, :3 * Kzeta] /= (self.ScalingFacts['length'] / self.ScalingFacts['circulation'])\n self.B_predictor[:, 3 * Kzeta:] /= (self.ScalingFacts['speed'] / self.ScalingFacts['circulation'])\n\n self.SS.C /= (self.ScalingFacts['circulation'] / self.ScalingFacts['force'])\n\n self.SS.D[:, :3 * Kzeta] /= (self.ScalingFacts['length'] / self.ScalingFacts['force'])\n self.SS.D[:, 3 * Kzeta:] /= (self.ScalingFacts['speed'] / self.ScalingFacts['force'])\n if self.remove_predictor:\n self.D_predictor[:, :3 * Kzeta] /= (self.ScalingFacts['length'] / self.ScalingFacts['force'])\n self.D_predictor[:, 3 * Kzeta:] /= (self.ScalingFacts['speed'] / self.ScalingFacts['force'])\n\n self.SS.dt = self.SS.dt * self.ScalingFacts['time']\n\n self.cpu_summary['dim'] = time.time() - t0\n\n def assemble_ss(self, wake_prop_settings=None):\n r\"\"\"\n Produces state-space model of the form\n\n .. math::\n\n \\mathbf{x}_{n+1} &= \\mathbf{A}\\,\\mathbf{x}_n + \\mathbf{B} \\mathbf{u}_{n+1} \\\\\n \\mathbf{y}_n &= \\mathbf{C}\\,\\mathbf{x}_n + \\mathbf{D} \\mathbf{u}_n\n\n where the state, inputs and outputs are:\n\n .. math:: \\mathbf{x}_n = \\{ \\delta \\mathbf{\\Gamma}_n,\\, \\delta \\mathbf{\\Gamma_{w_n}},\\,\n \\Delta t\\,\\delta\\mathbf{\\Gamma}'_n,\\, \\delta\\mathbf{\\Gamma}_{n-1} \\}\n\n .. math:: \\mathbf{u}_n = \\{ \\delta\\mathbf{\\zeta}_n,\\, \\delta\\mathbf{\\zeta}'_n,\\,\n \\delta\\mathbf{u}_{ext,n} \\}\n\n .. math:: \\mathbf{y} = \\{\\delta\\mathbf{f}\\}\n\n with :math:`\\mathbf{\\Gamma}\\in\\mathbb{R}^{MN}` being the vector of vortex circulations,\n :math:`\\mathbf{\\zeta}\\in\\mathbb{R}^{3(M+1)(N+1)}` the vector of vortex lattice coordinates and\n :math:`\\mathbf{f}\\in\\mathbb{R}^{3(M+1)(N+1)}` the vector of aerodynamic forces and moments. Note\n that :math:`(\\bullet)'` denotes a derivative with respect to time.\n\n Note that the input is atypically defined at time ``n+1``, therefore by default\n ``self.remove_predictor = True`` and the predictor term ``u_{n+1}`` is eliminated through\n the change of state[1]:\n\n .. math::\n \\mathbf{h}_n &= \\mathbf{x}_n - \\mathbf{B}\\,\\mathbf{u}_n \\\\\n\n such that:\n\n .. math::\n \\mathbf{h}_{n+1} &= \\mathbf{A}\\,\\mathbf{h}_n + \\mathbf{A\\,B}\\,\\mathbf{u}_n \\\\\n \\mathbf{y}_n &= \\mathbf{C\\,h}_n + (\\mathbf{C\\,B}+\\mathbf{D})\\,\\mathbf{u}_n\n\n\n which only modifies the equivalent :math:`\\mathbf{B}` and :math:`\\mathbf{D}` matrices.\n\n References:\n [1] Franklin, GF and Powell, JD. Digital Control of Dynamic Systems, Addison-Wesley Publishing Company, 1980\n\n To do:\n - remove all calls to scipy.linalg.block_diag\n \"\"\"\n\n cout.cout_wrap('State-space realisation of UVLM equations started...')\n t0 = time.time()\n MS = self.MS\n K, K_star = self.K, self.K_star\n Kzeta = self.Kzeta\n\n # ------------------------------------------------------ determine size\n\n Nx = self.Nx\n Nu = self.Nu\n Ny = self.Ny\n if self.integr_order == 2:\n # Second order differencing scheme coefficients\n b0, bm1, bp1 = -2., 0.5, 1.5\n\n # ----------------------------------------------------------- state eq.\n\n ### state terms (A matrix)\n # - choice of sparse matrices format is optimised to reduce memory load\n\n # Aero influence coeffs\n List_AICs, List_AICs_star = ass.AICs(MS.Surfs, MS.Surfs_star,\n target='collocation', Project=True)\n A0 = np.block(List_AICs)\n A0W = np.block(List_AICs_star)\n List_AICs, List_AICs_star = None, None\n LU, P = scalg.lu_factor(A0)\n AinvAW = scalg.lu_solve((LU, P), A0W)\n A0, A0W = None, None\n # self.A0,self.A0W=A0,A0W\n\n ### propagation of circ\n # fast and memory efficient with both dense and sparse matrices\n List_C, List_Cstar = ass.wake_prop(MS,\n self.use_sparse, sparse_format='csc',\n settings=wake_prop_settings)\n if self.use_sparse:\n Cgamma = libsp.csc_matrix(sparse.block_diag(List_C, format='csc'))\n CgammaW = libsp.csc_matrix(sparse.block_diag(List_Cstar, format='csc'))\n else:\n Cgamma = scalg.block_diag(*List_C)\n CgammaW = scalg.block_diag(*List_Cstar)\n List_C, List_Cstar = None, None\n\n # recurrent dense terms stored as numpy.ndarrays\n AinvAWCgamma = -libsp.dot(AinvAW, Cgamma)\n AinvAWCgammaW = -libsp.dot(AinvAW, CgammaW)\n\n ### A matrix assembly\n if self.use_sparse:\n # lil format allows fast assembly\n Ass = sparse.lil_matrix((Nx, Nx))\n else:\n Ass = np.zeros((Nx, Nx))\n Ass[:K, :K] = AinvAWCgamma\n Ass[:K, K:K + K_star] = AinvAWCgammaW\n Ass[K:K + K_star, :K] = Cgamma\n Ass[K:K + K_star, K:K + K_star] = CgammaW\n Cgamma, CgammaW = None, None\n\n # delta eq.\n iivec = range(K + K_star, 2 * K + K_star)\n ones = np.ones((K,))\n if self.integr_order == 1:\n Ass[iivec, :K] = AinvAWCgamma\n Ass[iivec, range(K)] -= ones\n Ass[iivec, K:K + K_star] = AinvAWCgammaW\n if self.integr_order == 2:\n Ass[iivec, :K] = bp1 * AinvAWCgamma\n AinvAWCgamma = None\n Ass[iivec, range(K)] += b0 * ones\n Ass[iivec, K:K + K_star] = bp1 * AinvAWCgammaW\n AinvAWCgammaW = None\n Ass[iivec, range(2 * K + K_star, 3 * K + K_star)] = bm1 * ones\n # identity eq.\n Ass[range(2 * K + K_star, 3 * K + K_star), range(K)] = ones\n\n if self.use_sparse:\n # conversion to csc occupies less memory and allows fast algebra\n Ass = libsp.csc_matrix(Ass)\n\n # zeta derivs\n List_nc_dqcdzeta = ass.nc_dqcdzeta(MS.Surfs, MS.Surfs_star, Merge=True)\n List_uc_dncdzeta = ass.uc_dncdzeta(MS.Surfs)\n List_nc_domegazetadzeta_vert = ass.nc_domegazetadzeta(MS.Surfs, MS.Surfs_star)\n for ss in range(MS.n_surf):\n List_nc_dqcdzeta[ss][ss] += \\\n (List_uc_dncdzeta[ss] + List_nc_domegazetadzeta_vert[ss])\n Ducdzeta = np.block(List_nc_dqcdzeta) # dense matrix\n List_nc_dqcdzeta = None\n List_uc_dncdzeta = None\n List_nc_domegazetadzeta_vert = None\n\n # ext velocity derivs (Wnv0)\n List_Wnv = []\n for ss in range(MS.n_surf):\n List_Wnv.append(\n interp.get_Wnv_vector(MS.Surfs[ss],\n MS.Surfs[ss].aM, MS.Surfs[ss].aN))\n AinvWnv0 = scalg.lu_solve((LU, P), scalg.block_diag(*List_Wnv))\n List_Wnv = None\n\n ### B matrix assembly\n if self.use_sparse:\n Bss = sparse.lil_matrix((Nx, Nu))\n else:\n Bss = np.zeros((Nx, Nu))\n\n Bup = np.block([-scalg.lu_solve((LU, P), Ducdzeta), AinvWnv0, -AinvWnv0])\n AinvWnv0 = None\n Bss[:K, :] = Bup\n if self.integr_order == 1:\n Bss[K + K_star:2 * K + K_star, :] = Bup\n if self.integr_order == 2:\n Bss[K + K_star:2 * K + K_star, :] = bp1 * Bup\n Bup = None\n\n if self.use_sparse:\n Bss = libsp.csc_matrix(Bss)\n LU, P = None, None\n # ---------------------------------------------------------- output eq.\n\n ### state terms (C matrix)\n\n # gamma (induced velocity contrib.)\n List_dfqsdvind_gamma, List_dfqsdvind_gamma_star = \\\n ass.dfqsdvind_gamma(MS.Surfs, MS.Surfs_star)\n\n # gamma (at constant relative velocity)\n List_dfqsdgamma_vrel0, List_dfqsdgamma_star_vrel0 = \\\n ass.dfqsdgamma_vrel0(MS.Surfs, MS.Surfs_star)\n for ss in range(MS.n_surf):\n List_dfqsdvind_gamma[ss][ss] += List_dfqsdgamma_vrel0[ss]\n List_dfqsdvind_gamma_star[ss][ss] += List_dfqsdgamma_star_vrel0[ss]\n Dfqsdgamma = np.block(List_dfqsdvind_gamma)\n Dfqsdgamma_star = np.block(List_dfqsdvind_gamma_star)\n List_dfqsdvind_gamma, List_dfqsdvind_gamma_star = None, None\n List_dfqsdgamma_vrel0, List_dfqsdgamma_star_vrel0 = None, None\n\n # gamma_dot\n Dfunstdgamma_dot = scalg.block_diag(*ass.dfunstdgamma_dot(MS.Surfs))\n\n # C matrix assembly\n Css = np.zeros((Ny, Nx))\n Css[:, :K] = Dfqsdgamma\n Css[:, K:K + K_star] = Dfqsdgamma_star\n if self.include_added_mass:\n Css[:, K + K_star:2 * K + K_star] = Dfunstdgamma_dot / self.dt\n\n ### input terms (D matrix)\n Dss = np.zeros((Ny, Nu))\n\n # zeta (at constant relative velocity)\n Dss[:, :3 * Kzeta] = scalg.block_diag(\n *ass.dfqsdzeta_vrel0(MS.Surfs, MS.Surfs_star))\n # zeta (induced velocity contrib)\n List_coll, List_vert = ass.dfqsdvind_zeta(MS.Surfs, MS.Surfs_star)\n for ss in range(MS.n_surf):\n List_vert[ss][ss] += List_coll[ss]\n Dss[:, :3 * Kzeta] += np.block(List_vert)\n del List_vert, List_coll\n\n # input velocities (external)\n Dss[:, 6 * Kzeta:9 * Kzeta] = scalg.block_diag(\n *ass.dfqsduinput(MS.Surfs, MS.Surfs_star))\n\n # input velocities (body movement)\n if self.include_added_mass:\n Dss[:, 3 * Kzeta:6 * Kzeta] = -Dss[:, 6 * Kzeta:9 * Kzeta]\n\n if self.remove_predictor:\n Ass, Bmod, Css, Dmod = \\\n libss.SSconv(Ass, None, Bss, Css, Dss, Bm1=None)\n self.SS = libss.StateSpace(Ass, Bmod, Css, Dmod, dt=self.dt)\n\n # Store original B matrix for state unpacking\n self.B_predictor = Bss\n self.D_predictor = Dss\n\n cout.cout_wrap('\\tstate-space model produced in form:\\n\\t' \\\n '\\t\\th_{n+1} = A h_{n} + B u_{n}\\n\\t' \\\n '\\t\\twith:\\n\\tx_n = h_n + Bp u_n', 1)\n else:\n self.SS = libss.StateSpace(Ass, Bss, Css, Dss, dt=self.dt)\n cout.cout_wrap('\\tstate-space model produced in form:\\n\\t' \\\n 'x_{n+1} = A x_{n} + Bp u_{n+1}', 1)\n\n # add variable tracker\n self.SS.input_variables = LinearVector(self.input_variables_list)\n self.SS.state_variables = LinearVector(self.state_variables_list)\n self.SS.output_variables = LinearVector(self.output_variables_list)\n\n self.cpu_summary['assemble'] = time.time() - t0\n cout.cout_wrap('\\t\\t\\t...done in %.2f sec' % self.cpu_summary['assemble'])\n\n def freqresp(self, kv, wake_prop_settings=None):\n \"\"\"\n Ad-hoc method for fast UVLM frequency response over the frequencies\n kv. The method, only requires inversion of a K x K matrix at each\n frequency as the equation for propagation of wake circulation are solved\n exactly.\n The algorithm implemented here can be used also upon projection of\n the state-space model.\n\n Note:\n This method is very similar to the \"minsize\" solution option is the\n steady_solve.\n \"\"\"\n\n if self.remove_predictor:\n # raise NameError('Option \"remove_predictor=True\" not implemented yet. '+\n # 'Refer to Frequency class implementation.')\n\n assert self.B_predictor.shape == self.SS.B.shape, \\\n ('In order to use \"freqresp\" with \"remove_predictor=True\", project ' +\n '\"self.B_predictor\" as per \"self.SS.B\"!')\n assert self.D_predictor.shape == self.SS.D.shape, \\\n ('In order to use \"freqresp\" with \"remove_predictor=True\", project ' +\n '\"self.D_predictor\" as per \"self.SS.D\"!')\n\n MS = self.MS\n K = self.K\n K_star = self.K_star\n\n Eye = np.eye(K)\n if self.remove_predictor:\n Bup = self.B_predictor[:K, :]\n else:\n Bup = self.SS.B[:K, :]\n\n if self.use_sparse:\n # warning: behaviour may change in future numpy release.\n # Ensure P,Pw,Bup are np.ndarray\n P = np.array(self.SS.A[:K, :K].todense())\n Pw = np.array(self.SS.A[:K, K:K + K_star].todense())\n if type(Bup) not in [np.ndarray, libsp.csc_matrix]:\n Bup = Bup.toarray()\n else:\n P = self.SS.A[:K, :K]\n Pw = self.SS.A[:K, K:K + K_star]\n\n Nk = len(kv)\n kvdt = kv * self.SS.dt\n zv = np.cos(kvdt) + 1.j * np.sin(kvdt)\n Yfreq = np.empty((self.SS.outputs, self.SS.inputs, Nk,), dtype=np.complex_)\n\n for kk in range(Nk):\n\n ### build Cw complex\n Cw_cpx = self.get_Cw_cpx(zv[kk], settings=wake_prop_settings)\n\n if self.remove_predictor:\n Ygamma = zv[kk] * \\\n libsp.solve(zv[kk] * Eye - P -\n libsp.dot(Pw, Cw_cpx, type_out=libsp.csc_matrix),\n Bup)\n else:\n Ygamma = libsp.solve(zv[kk] * Eye - P -\n libsp.dot(Pw, Cw_cpx, type_out=libsp.csc_matrix),\n Bup)\n\n Ygamma_star = Cw_cpx.dot(Ygamma)\n\n if self.integr_order == 1:\n dfact = (1. - 1. / zv[kk])\n elif self.integr_order == 2:\n dfact = .5 * (3. - 4. / zv[kk] + 1. / zv[kk] ** 2)\n else:\n raise NameError('Specify valid integration order')\n\n # calculate solution\n if self.remove_predictor:\n Yfreq[:, :, kk] = np.dot(self.SS.C[:, :K], Ygamma) + \\\n np.dot(self.SS.C[:, K:K + K_star], Ygamma_star) + \\\n np.dot(self.SS.C[:, K + K_star:2 * K + K_star], dfact * Ygamma) + \\\n self.D_predictor\n else:\n Yfreq[:, :, kk] = np.dot(self.SS.C[:, :K], Ygamma) + \\\n np.dot(self.SS.C[:, K:K + K_star], Ygamma_star) + \\\n np.dot(self.SS.C[:, K + K_star:2 * K + K_star], dfact * Ygamma) + \\\n self.SS.D\n\n return Yfreq\n\n def get_Cw_cpx(self, zval, settings=None):\n r\"\"\"\n Produces a sparse matrix\n\n .. math:: \\bar{\\mathbf{C}}(z)\n\n where\n\n .. math:: z = e^{k \\Delta t}\n\n such that the wake circulation frequency response at :math:`z` is\n\n .. math:: \\bar{\\boldsymbol{\\Gamma}}_w = \\bar{\\mathbf{C}}(z) \\bar{\\mathbf{\\Gamma}}\n\n \"\"\"\n\n return get_Cw_cpx(self.MS, self.K, self.K_star, zval, settings=settings)\n\n\n def balfreq(self, DictBalFreq, wake_prop_settings=None):\n \"\"\"\n Low-rank method for frequency limited balancing.\n The Observability ad controllability Gramians over the frequencies kv\n are solved in factorised form. Balancd modes are then obtained with a\n square-root method.\n\n Details:\n\n Observability and controllability Gramians are solved in factorised form\n through explicit integration. The number of integration points determines\n both the accuracy and the maximum size of the balanced model.\n\n Stability over all (Nb) balanced states is achieved if:\n\n a. one of the Gramian is integrated through the full Nyquist range\n b. the integration points are enough.\n\n Note, however, that even when stability is not achieved over the full\n balanced states, stability of the balanced truncated model with Ns<=Nb\n states is normally observed even when a low number of integration points\n is used. Two integration methods (trapezoidal rule on uniform grid and\n Gauss-Legendre quadrature) are provided.\n\n Input:\n\n - DictBalFreq: dictionary specifying integration method with keys:\n\n - ``frequency``: defines limit frequencies for balancing. The balanced\n model will be accurate in the range [0,F], where F is the value of\n this key. Note that F units must be consistent with the units specified\n in the self.ScalingFacts dictionary.\n\n - ``method_low``: ['gauss','trapz'] specifies whether to use gauss\n quadrature or trapezoidal rule in the low-frequency range [0,F]\n\n - ``options_low``: options to use for integration in the low-frequencies.\n These depend on the integration scheme (See below).\n\n - ``method_high``: method to use for integration in the range [F,F_N],\n where F_N is the Nyquist frequency. See 'method_low'.\n\n - ``options_high``: options to use for integration in the high-frequencies.\n\n - ``check_stability``: if True, the balanced model is truncated to\n eliminate unstable modes - if any is found. Note that very accurate\n balanced model can still be obtained, even if high order modes are\n unstable. Note that this option is overridden if \"\"\n\n - ``get_frequency_response``: if True, the function also returns the\n frequency response evaluated at the low-frequency range integration\n points. If True, this option also allows to automatically tune the\n balanced model.\n\n Future options:\n\n - ``truncation_tolerance``: if ``get_frequency_response`` is True, allows\n to truncate the balanced model so as to achieved a prescribed\n tolerance in the low-frequwncy range.\n\n - ``Ncpu``: for parallel run\n\n The following integration schemes are available:\n\n - ``trapz``: performs integration over equally spaced points using\n trapezoidal rule. It accepts options dictionaries with keys:\n\n - ``points``: number of integration points to use (including\n domain boundary)\n\n - ``gauss`` performs gauss-lobotto quadrature. The domain can be\n partitioned in Npart sub-domain in which the gauss-lobotto quadrature\n of order Ord can be applied. A total number of Npart*Ord points is\n required. It accepts options dictionaries of the form:\n\n - ``partitions``: number of partitions\n - ``order``: quadrature order.\n\n Example:\n\n The following dictionary\n\n .. code-block:: python\n\n DictBalFreq={ 'frequency': 1.2,\n 'method_low': 'trapz',\n 'options_low': {'points': 12},\n 'method_high': 'gauss',\n 'options_high': {'partitions': 2, 'order': 8},\n 'check_stability': True }\n\n balances the state-space model self.SS in the frequency range [0, 1.2]\n using\n\n (a) 12 equally-spaced points integration of the Gramians in the low-frequency range [0,1.2] and\n (b) a 2 Gauss-Lobotto 8-th order quadratures of the controllability\n Gramian in the high-frequency range.\n\n A total number of 28 integration points will be required, which will\n result into a balanced model with number of states ``min{2*28* number_inputs, 2*28* number_outputs}``\n\n The model is finally truncated so as to retain only the first Ns stable\n modes.\n \"\"\"\n\n ### check input dictionary\n if 'frequency' not in DictBalFreq:\n raise NameError('Solution dictionary must include the \"frequency\" key')\n\n if 'method_low' not in DictBalFreq:\n warnings.warn('Setting default options for low-frequency integration')\n DictBalFreq['method_low'] = 'trapz'\n DictBalFreq['options_low'] = {'points': 12}\n\n if 'method_high' not in DictBalFreq:\n warnings.warn('Setting default options for high-frequency integration')\n DictBalFreq['method_high'] = 'gauss'\n DictBalFreq['options_high'] = {'partitions': 2, 'order': 8}\n\n if 'check_stability' not in DictBalFreq:\n DictBalFreq['check_stability'] = True\n\n if 'output_modes' not in DictBalFreq:\n DictBalFreq['output_modes'] = True\n\n if 'get_frequency_response' not in DictBalFreq:\n DictBalFreq['get_frequency_response'] = False\n\n ### get integration points and weights\n\n # Nyquist frequency\n kn = np.pi / self.SS.dt\n\n Opt = DictBalFreq['options_low']\n if DictBalFreq['method_low'] == 'trapz':\n kv_low, wv_low = librom.get_trapz_weights(0., DictBalFreq['frequency'],\n Opt['points'], False)\n elif DictBalFreq['method_low'] == 'gauss':\n kv_low, wv_low = librom.get_gauss_weights(0., DictBalFreq['frequency'],\n Opt['partitions'], Opt['order'])\n else:\n raise NameError(\n 'Invalid value %s for key \"method_low\"' % DictBalFreq['method_low'])\n\n Opt = DictBalFreq['options_high']\n if DictBalFreq['method_high'] == 'trapz':\n kv_high, wv_high = librom.get_trapz_weights(DictBalFreq['frequency'], kn,\n Opt['points'], True)\n elif DictBalFreq['method_high'] == 'gauss':\n kv_high, wv_high = librom.get_gauss_weights(DictBalFreq['frequency'], kn,\n Opt['partitions'], Opt['order'])\n else:\n raise NameError(\n 'Invalid value %s for key \"method_high\"' % DictBalFreq['method_high'])\n\n ### get useful terms\n K = self.K\n K_star = self.K_star\n\n Eye = np.eye(K)\n\n if self.remove_predictor:\n Bup = self.B_predictor[:K, :]\n else:\n Bup = self.SS.B[:K, :]\n\n if self.use_sparse:\n # warning: behaviour may change in future numpy release.\n # Ensure P,Pw,Bup are np.ndarray\n P = np.array(self.SS.A[:K, :K].todense())\n Pw = np.array(self.SS.A[:K, K:K + K_star].todense())\n if type(Bup) not in [np.ndarray, libsp.csc_matrix]:\n Bup = Bup.toarray()\n else:\n P = self.SS.A[:K, :K]\n Pw = self.SS.A[:K, K:K + K_star]\n\n # indices to manipulate obs solution\n ii00 = range(0, self.K)\n ii01 = range(self.K, self.K + self.K_star)\n ii02 = range(self.K + self.K_star, 2 * self.K + self.K_star)\n ii03 = range(2 * self.K + self.K_star, 3 * self.K + self.K_star)\n\n # integration factors\n if self.integr_order == 2:\n b0, bm1, bp1 = -2., 0.5, 1.5\n else:\n b0, bp1 = -1., 1.\n raise NameError('Method not implemented for integration order 1')\n\n ### -------------------------------------------------- loop frequencies\n\n ### merge vectors\n Nk_low = len(kv_low)\n kvdt = np.concatenate((kv_low, kv_high)) * self.SS.dt\n wv = np.concatenate((wv_low, wv_high)) * self.SS.dt\n zv = np.cos(kvdt) + 1.j * np.sin(kvdt)\n\n Qobs = np.zeros((self.SS.states, self.SS.outputs), dtype=np.complex_)\n Zc = np.zeros((self.SS.states, 2 * self.SS.inputs * len(kvdt)), )\n Zo = np.zeros((self.SS.states, 2 * self.SS.outputs * Nk_low), )\n\n if DictBalFreq['get_frequency_response']:\n self.Yfreq = np.empty((self.SS.outputs, self.SS.inputs, Nk_low,), dtype=np.complex_)\n self.kv = kv_low\n\n for kk in range(len(kvdt)):\n\n zval = zv[kk]\n Intfact = wv[kk] # integration factor\n\n # build terms that will be recycled\n Cw_cpx = self.get_Cw_cpx(zval, settings=wake_prop_settings)\n PwCw_T = Cw_cpx.T.dot(Pw.T)\n Kernel = np.linalg.inv(zval * Eye - P - PwCw_T.T)\n\n ### ----- controllability\n Ygamma = Intfact * np.dot(Kernel, Bup)\n if self.remove_predictor:\n Ygamma *= zval\n Ygamma_star = Cw_cpx.dot(Ygamma)\n\n if self.integr_order == 1:\n dfact = (bp1 + b0 / zval)\n Qctrl = np.vstack([Ygamma, Ygamma_star, dfact * Ygamma])\n elif self.integr_order == 2:\n dfact = bp1 + b0 / zval + bm1 / zval ** 2\n Qctrl = np.vstack(\n [Ygamma, Ygamma_star, dfact * Ygamma, (1. / zval) * Ygamma])\n else:\n raise NameError('Specify valid integration order')\n\n kkvec = range(2 * kk * self.SS.inputs, 2 * (kk + 1) * self.SS.inputs)\n Zc[:, kkvec[:self.SS.inputs]] = Qctrl.real # *Intfact\n Zc[:, kkvec[self.SS.inputs:]] = Qctrl.imag # *Intfact\n\n ### ----- frequency response\n if DictBalFreq['get_frequency_response'] and kk < Nk_low:\n self.Yfreq[:, :, kk] = np.dot(self.SS.C, Qctrl) / Intfact + self.SS.D\n\n ### ----- frequency response\n if DictBalFreq['get_frequency_response'] and kk < Nk_low:\n self.Yfreq[:, :, kk] = np.dot(self.SS.C, Qctrl) / Intfact + self.SS.D\n\n ### ----- observability\n # solve (1./zval*I - A.T)^{-1} C^T (in low-frequency only)\n if kk >= Nk_low:\n continue\n\n zinv = 1. / zval\n Cw_cpx_H = Cw_cpx.conjugate().T\n\n Qobs[ii02, :] = zval * self.SS.C[:, ii02].T\n if self.integr_order == 2:\n Qobs[ii03, :] = bm1 * zval ** 2 * self.SS.C[:, ii02].T\n\n rhs = self.SS.C[:, ii00].T + \\\n Cw_cpx_H.dot(self.SS.C[:, ii01].T) + \\\n libsp.dot(\n (bp1 * zval) * (PwCw_T.conj() + P.T) + \\\n (b0 * zval + bm1 * zval ** 2) * Eye, self.SS.C[:, ii02].T)\n\n Qobs[ii00, :] = np.dot(Kernel.conj().T, rhs)\n\n Eye_star = libsp.csc_matrix(\n (zinv * np.ones((K_star,)), (range(K_star), range(K_star))),\n shape=(K_star, K_star), dtype=np.complex_)\n Qobs[ii01, :] = libsp.solve(\n Eye_star - self.SS.A[K:K + K_star, K:K + K_star].T,\n np.dot(Pw.T, Qobs[ii00, :] + \\\n (bp1 * zval) * self.SS.C[:, ii02].T) + \\\n self.SS.C[:, ii01].T)\n\n kkvec = range(2 * kk * self.SS.outputs, 2 * (kk + 1) * self.SS.outputs)\n Zo[:, kkvec[:self.SS.outputs]] = Intfact * Qobs.real\n Zo[:, kkvec[self.SS.outputs:]] = Intfact * Qobs.imag\n\n # delete full matrices\n Kernel = None\n Qctrl = None\n Qobs = None\n\n # self.Zc=Zc\n # self.Zo=Zo\n\n # LRSQM (optimised)\n U, hsv, Vh = scalg.svd(np.dot(Zo.T, Zc), full_matrices=False)\n sinv = hsv ** (-0.5)\n T = np.dot(Zc, Vh.T * sinv)\n Ti = np.dot((U * sinv).T, Zo.T)\n # Zc,Zo=None,None\n\n ### build frequency balanced model\n Ab = libsp.dot(Ti, libsp.dot(self.SS.A, T))\n Bb = libsp.dot(Ti, self.SS.B)\n Cb = libsp.dot(self.SS.C, T)\n SSb = libss.StateSpace(Ab, Bb, Cb, self.SS.D, dt=self.SS.dt)\n\n ### Eliminate unstable modes - if any:\n if DictBalFreq['check_stability']:\n for nn in range(1, len(hsv) + 1):\n eigs_trunc = scalg.eigvals(SSb.A[:nn, :nn])\n eigs_trunc_max = np.max(np.abs(eigs_trunc))\n if eigs_trunc_max > 1. - 1e-16:\n SSb.truncate(nn - 1)\n hsv = hsv[:nn - 1]\n T = T[:, :nn - 1]\n Ti = Ti[:nn - 1, :]\n break\n\n self.SSb = SSb\n self.hsv = hsv\n if DictBalFreq['output_modes']:\n self.T = T\n self.Ti = Ti\n self.Zc = Zc\n self.Zo = Zo\n\n def balfreq_profiling(self, wake_prop_settings=None):\n \"\"\"\n Generate profiling report for balfreq function and saves it into ``self.prof_out.``\n The function also returns a ``pstats.Stats`` object.\n\n To read the report:\n .. code-block:: python\n\n import pstats\n p=pstats.Stats(self.prof_out).sort_stats('cumtime')\n p.print_stats(20)\n \"\"\"\n import pstats\n import cProfile\n def wrap():\n DictBalFreq = {'frequency': 0.5, 'check_stability': False}\n self.balfreq(DictBalFreq, wake_prop_settings=wake_prop_settings)\n\n cProfile.runctx('wrap()', globals(), locals(), filename=self.prof_out)\n\n cProfile.runctx('wrap()', globals(), locals(), filename=self.prof_out)\n\n return pstats.Stats(self.prof_out).sort_stats('cumtime')\n\n def assemble_ss_profiling(self):\n \"\"\"\n Generate profiling report for assembly and save it in self.prof_out.\n\n To read the report:\n import pstats\n p=pstats.Stats(self.prof_out)\n \"\"\"\n\n import cProfile\n cProfile.runctx('self.assemble_ss()', globals(), locals(), filename=self.prof_out)\n\n def solve_steady(self, usta, method='direct'):\n \"\"\"\n Steady state solution from state-space model.\n\n Warning: these methods are less efficient than the solver in Static\n class, Static.solve, and should be used only for verification purposes.\n The \"minsize\" method, however, guarantees the inversion of a K x K\n matrix only, similarly to what is done in Static.solve.\n \"\"\"\n\n if self.remove_predictor is True and method != 'direct':\n raise NameError('Only direct solution is available if predictor ' \\\n 'term has been removed from the state-space equations (see assembly_ss)')\n\n if self.use_sparse is True and method != 'direct':\n raise NameError('Only direct solution is available if use_sparse is True. ' \\\n '(see assembly_ss)')\n\n Ass, Bss, Css, Dss = self.SS.A, self.SS.B, self.SS.C, self.SS.D\n\n if method == 'minsize':\n # as opposed to linuvlm.Static, this solves for the bound circulation\n # starting from\n #\tGamma = [P, Pw] * {Gamma,Gamma_w} + B u_\n # Gamma_w = [C, Cw] * {Gamma,Gamma_w}\t\t \t\t\t(eq. 1a,1b)\n # where time indices have been dropped. Transforming into\n #\tGamma \t= [P+PwC, PwCw] * {Gamma,Gamma_w} + B u \t(eq. 2)\n # and enforcing Gamma_w = Gamma_TE, this reduces to the KxK system:\n # \tAIC Gamma = B u \t\t\t\t\t\t\t\t\t(eq. 3)\n MS = self.MS\n K = self.K\n K_star = self.K_star\n\n ### build eq. 2:\n P = Ass[:K, :K]\n Pw = Ass[:K, K:K + K_star]\n C = Ass[K:K + K_star, :K]\n Cw = Ass[K:K + K_star, K:K + K_star]\n PwCw = np.dot(Pw, Cw)\n\n ### build eq. 3\n AIC = np.eye(K) - P - np.dot(Pw, C)\n\n # condense Gammaw terms\n K0out, K0out_star = 0, 0\n for ss_out in range(MS.n_surf):\n Kout = MS.KK[ss_out]\n Kout_star = MS.KK_star[ss_out]\n\n K0in, K0in_star = 0, 0\n for ss_in in range(MS.n_surf):\n Kin = MS.KK[ss_in]\n Kin_star = MS.KK_star[ss_in]\n\n # link to sub-matrices\n aic = AIC[K0out:K0out + Kout, K0in:K0in + Kin]\n aic_star = PwCw[K0out:K0out + Kout, K0in_star:K0in_star + Kin_star]\n\n # fold aic_star: sum along chord at each span-coordinate\n N_star = MS.NN_star[ss_in]\n aic_star_fold = np.zeros((Kout, N_star))\n for jj in range(N_star):\n aic_star_fold[:, jj] += np.sum(aic_star[:, jj::N_star], axis=1)\n aic[:, -N_star:] -= aic_star_fold\n\n K0in += Kin\n K0in_star += Kin_star\n K0out += Kout\n K0out_star += Kout_star\n\n ### solve\n # gamma\n gamma = np.linalg.solve(AIC, np.dot(Bss[:K, :], usta))\n # retrieve gamma over wake\n gamma_star = []\n Ktot = 0\n for ss in range(MS.n_surf):\n Ktot += MS.Surfs[ss].maps.K\n N = MS.Surfs[ss].maps.N\n Mstar = MS.Surfs_star[ss].maps.M\n gamma_star.append(np.concatenate(Mstar * [gamma[Ktot - N:Ktot]]))\n gamma_star = np.concatenate(gamma_star)\n\n if self.integr_order == 1:\n xsta = np.concatenate((gamma, gamma_star, np.zeros_like(gamma)))\n if self.integr_order == 2:\n xsta = np.concatenate((gamma, gamma_star, np.zeros_like(gamma),\n gamma))\n\n ysta = np.dot(Css, xsta) + np.dot(Dss, usta)\n\n elif method == 'direct':\n \"\"\" Solves (I - A) x = B u with direct method\"\"\"\n # if self.use_sparse:\n # xsta=libsp.solve(libsp.eye_as(Ass)-Ass,Bss.dot(usta))\n # else:\n # Ass_steady = np.eye(*Ass.shape) - Ass\n # xsta = np.linalg.solve(Ass_steady, np.dot(Bss, usta))\n xsta = libsp.solve(libsp.eye_as(Ass) - Ass, Bss.dot(usta))\n ysta = np.dot(Css, xsta) + np.dot(Dss, usta)\n\n elif method == 'recursive':\n \"\"\" Provides steady-state solution solving for impulsive response \"\"\"\n tol, er = 1e-4, 1.0\n Ftot0 = np.zeros((3,))\n nn = 0\n xsta = np.zeros((self.Nx))\n while er > tol and nn < 1000:\n xsta = np.dot(Ass, xsta) + np.dot(Bss, usta)\n ysta = np.dot(Css, xsta) + np.dot(Dss, usta)\n Ftot = np.array(\n [np.sum(ysta[cc * self.Kzeta:(cc + 1) * self.Kzeta])\n for cc in range(3)])\n er = np.linalg.norm(Ftot - Ftot0)\n Ftot0 = Ftot.copy()\n nn += 1\n if er < tol:\n pass # print('Recursive solution found in %.3d iterations'%nn)\n else:\n raise exceptions.NotConvergedSolver('Solution not found! Max. iterations reached with error: %.3e' % er)\n\n elif method == 'subsystem':\n \"\"\" Solves sub-system related to Gamma, Gamma_w states only \"\"\"\n\n Nxsub = self.K + self.K_star\n Asub_steady = np.eye(Nxsub) - Ass[:Nxsub, :Nxsub]\n xsub = np.linalg.solve(Asub_steady, np.dot(Bss[:Nxsub, :], usta))\n if self.integr_order == 1:\n xsta = np.concatenate((xsub, np.zeros((self.K,))))\n if self.integr_order == 2:\n xsta = np.concatenate((xsub, np.zeros((2 * self.K,))))\n ysta = np.dot(Css, xsta) + np.dot(Dss, usta)\n\n else:\n raise NameError('Method %s not recognised!' % method)\n\n return xsta, ysta\n\n def solve_step(self, x_n, u_n, u_n1=None, transform_state=False):\n r\"\"\"\n Solve step.\n\n If the predictor term has not been removed (``remove_predictor = False``) then the system is solved as:\n\n .. math::\n \\mathbf{x}^{n+1} &= \\mathbf{A\\,x}^n + \\mathbf{B\\,u}^n \\\\\n \\mathbf{y}^{n+1} &= \\mathbf{C\\,x}^{n+1} + \\mathbf{D\\,u}^n\n\n Else, if ``remove_predictor = True``, the state is modified as\n\n .. math:: \\mathbf{h}^n = \\mathbf{x}^n - \\mathbf{B\\,u}^n\n\n And the system solved by:\n\n .. math::\n \\mathbf{h}^{n+1} &= \\mathbf{A\\,h}^n + \\mathbf{B_{mod}\\,u}^{n} \\\\\n \\mathbf{y}^{n+1} &= \\mathbf{C\\,h}^{n+1} + \\mathbf{D_{mod}\\,u}^{n+1}\n\n Finally, the original state is recovered using the reverse transformation:\n\n .. math:: \\mathbf{x}^{n+1} = \\mathbf{h}^{n+1} + \\mathbf{B\\,u}^{n+1}\n\n where the modifications to the :math:`\\mathbf{B}_{mod}` and :math:`\\mathbf{D}_{mod}` are detailed in\n :func:`Dynamic.assemble_ss`.\n\n Notes:\n Although the original equations include the term :math:`\\mathbf{u}_{n+1}`, it is a reasonable approximation\n to take :math:`\\mathbf{u}_{n+1}\\approx\\mathbf{u}_n` given a sufficiently small time step, hence if the input\n at time ``n+1`` is not parsed, it is estimated from :math:`u^n`.\n\n Args:\n x_n (np.array): State vector at the current time step :math:`\\mathbf{x}^n`\n u_n (np.array): Input vector at time step :math:`\\mathbf{u}^n`\n u_n1 (np.array): Input vector at time step :math:`\\mathbf{u}^{n+1}`\n transform_state (bool): When the predictor term is removed, if true it will transform the state vector. If\n false it will be assumed that the state vector that is parsed is already transformed i.e. it is\n :math:`\\mathbf{h}`.\n\n Returns:\n Tuple: Updated state and output vector packed in a tuple :math:`(\\mathbf{x}^{n+1},\\,\\mathbf{y}^{n+1})`\n\n Notes:\n To speed-up the solution and use minimal memory:\n - solve for bound vorticity (and)\n - propagate the wake\n - compute the output separately.\n \"\"\"\n\n if u_n1 is None:\n u_n1 = u_n.copy()\n\n if self.remove_predictor:\n\n # Transform state vector\n # TODO: Agree on a way to do this. Either always transform here or transform prior to using the method.\n if transform_state:\n h_n = x_n - self.B_predictor.dot(u_n)\n else:\n h_n = x_n\n\n h_n1 = self.SS.A.dot(h_n) + self.SS.B.dot(u_n)\n y_n1 = np.dot(self.SS.C, h_n1) + np.dot(self.SS.D, u_n1)\n\n # Recover state vector\n if transform_state:\n x_n1 = h_n1 + self.B_predictor.dot(u_n1)\n else:\n x_n1 = h_n1\n\n else:\n x_n1 = self.SS.A.dot(x_n) + self.SS.B.dot(u_n1)\n y_n1 = np.dot(self.SS.C, x_n1) + np.dot(self.SS.D, u_n1)\n\n return x_n1, y_n1\n\n def unpack_state(self, xvec):\n r\"\"\"\n Unpacks the state vector into physical constituents for full order models.\n\n The state vector :math:`\\mathbf{x}` of the form\n\n .. math:: \\mathbf{x}_n = \\{ \\delta \\mathbf{\\Gamma}_n,\\, \\delta \\mathbf{\\Gamma_{w_n}},\\,\n \\Delta t\\,\\delta\\mathbf{\\Gamma}'_n,\\, \\delta\\mathbf{\\Gamma}_{n-1} \\}\n\n Is unpacked into:\n\n .. math:: {\\delta \\mathbf{\\Gamma}_n,\\, \\delta \\mathbf{\\Gamma_{w_n}},\\,\n \\,\\delta\\mathbf{\\Gamma}'_n}\n\n Args:\n xvec (np.ndarray): State vector\n\n Returns:\n tuple: Column vectors for bound circulation, wake circulation and circulation derivative packed in a tuple.\n \"\"\"\n\n K, K_star = self.K, self.K_star\n gamma_vec = xvec[:K]\n gamma_star_vec = xvec[K:K + K_star]\n gamma_dot_vec = xvec[K + K_star:2 * K + K_star] / self.dt\n\n return gamma_vec, gamma_star_vec, gamma_dot_vec\n\n\n################################################################################\n\n################################################################################\n\nclass DynamicBlock(Dynamic):\n \"\"\"\n Class for dynamic linearised UVLM solution. Linearisation around steady-state\n are only supported.\n\n The class is a low-memory implementation of Dynamic, and inherits most of\n the methods contained there. State-space models are allocated in list-block\n form (as per numpy.block) to minimise memory usage. This class provides\n lower memory / computational time assembly, frequency response and frequency\n limited balancing.\n\n Input:\n\n - tsdata: aero timestep data from SHARPy solution\n - dt: time-step\n - integr_order=2: integration order for UVLM unsteady aerodynamic force\n - RemovePredictor=True: if true, the state-space model is modified so as\n to accept in input perturbations, u, evaluated at time-step n rather than\n n+1.\n - ScalingDict=None: disctionary containing fundamental reference units\n\n >>> {'length': reference_length,\n 'speed': reference_speed,\n 'density': reference density}\n\n\n used to derive scaling quantities for the state-space model variables.\n The scaling factors are stores in ``self.ScalingFact``.\n\n Note that while time, circulation, angular speeds) are scaled\n accordingly, FORCES ARE NOT. These scale by qinf*b**2, where b is the\n reference length and qinf is the dinamic pressure.\n - UseSparse=False: builds the A and B matrices in sparse form. C and D\n are dense, hence the sparce format is not used.\n\n\n Methods:\n - nondimss: normalises a dimensional state-space model based on the\n scaling factors in self.ScalingFact.\n - dimss: inverse of nondimss.\n - assemble_ss: builds state-space model. See function for more details.\n - assemble_ss_profiling: generate profiling report of the assembly and\n saves it into self.prof_out. To read the report:\n\n >>> import pstats\n p=pstats.Stats(self.prof_out)\n\n\n - freqresp: ad-hoc method for fast frequency response (only implemented)\n for remove_predictor=False\n\n\n To do: upgrade to linearise around unsteady snapshot (adjoint)\n \"\"\"\n\n def __init__(self, tsdata, dt=None,\n dynamic_settings=None,\n integr_order=2,\n RemovePredictor=True, ScalingDict=None, UseSparse=True, for_vel=np.zeros((6), )):\n\n if dynamic_settings is None:\n warnings.warn('Individual parsing of settings is deprecated. Please use the settings dictionary',\n DeprecationWarning)\n\n super().__init__(tsdata, dt,\n dynamic_settings=dynamic_settings,\n integr_order=integr_order,\n RemovePredictor=RemovePredictor,\n ScalingDict=ScalingDict,\n UseSparse=UseSparse,\n for_vel=for_vel)\n\n # number of blocks\n self.nblock_x = self.integr_order + 2\n self.nblock_u = 3\n self.nblock_y = 1\n\n # sizes in blocks\n self.S_x = [self.K, self.K_star, self.K]\n if self.integr_order == 2: self.S_x += [self.K]\n self.S_u = 3 * [3 * self.Kzeta]\n self.S_y = [3 * self.Kzeta]\n\n def nondimss(self):\n \"\"\"\n Scale state-space model based of self.ScalingFacts.\n \"\"\"\n\n t0 = time.time()\n\n B_facts = [self.ScalingFacts['length'] / self.ScalingFacts['circulation'],\n self.ScalingFacts['speed'] / self.ScalingFacts['circulation'],\n self.ScalingFacts['speed'] / self.ScalingFacts['circulation']]\n\n D_facts = [self.ScalingFacts['length'] / self.ScalingFacts['force'],\n self.ScalingFacts['speed'] / self.ScalingFacts['force'],\n self.ScalingFacts['speed'] / self.ScalingFacts['force']]\n\n C_facts = self.nblock_x * \\\n [self.ScalingFacts['circulation'] / self.ScalingFacts['force']]\n\n for ii in range(self.nblock_x):\n for jj in range(self.nblock_u):\n if self.SS.B[ii][jj] is not None:\n self.SS.B[ii][jj] *= B_facts[jj]\n\n for ii in range(self.nblock_y):\n for jj in range(self.nblock_x):\n if self.SS.C[ii][jj] is not None:\n self.SS.C[ii][jj] *= C_facts[jj]\n\n for ii in range(self.nblock_y):\n for jj in range(self.nblock_u):\n if self.SS.D[ii][jj] is not None:\n self.SS.D[ii][jj] *= D_facts[jj]\n\n self.SS.dt = self.SS.dt / self.ScalingFacts['time']\n self.cpu_summary['nondim'] = time.time() - t0\n\n def dimss(self):\n\n t0 = time.time()\n\n B_facts = [self.ScalingFacts['length'] / self.ScalingFacts['circulation'],\n self.ScalingFacts['speed'] / self.ScalingFacts['circulation'],\n self.ScalingFacts['speed'] / self.ScalingFacts['circulation']]\n\n D_facts = [self.ScalingFacts['length'] / self.ScalingFacts['force'],\n self.ScalingFacts['speed'] / self.ScalingFacts['force'],\n self.ScalingFacts['speed'] / self.ScalingFacts['force']]\n\n D_facts = [self.ScalingFacts['length'] / self.ScalingFacts['force'],\n self.ScalingFacts['speed'] / self.ScalingFacts['force'],\n self.ScalingFacts['speed'] / self.ScalingFacts['force']]\n\n C_facts = self.nblock_x * \\\n [self.ScalingFacts['circulation'] / self.ScalingFacts['force']]\n\n for ii in range(self.nblock_x):\n for jj in range(self.nblock_u):\n if self.SS.B[ii][jj] is not None:\n self.SS.B[ii][jj] /= B_facts[jj]\n\n for ii in range(self.nblock_y):\n for jj in range(self.nblock_x):\n if self.SS.C[ii][jj] is not None:\n self.SS.C[ii][jj] /= C_facts[jj]\n\n for ii in range(self.nblock_y):\n for jj in range(self.nblock_u):\n if self.SS.D[ii][jj] is not None:\n self.SS.D[ii][jj] /= D_facts[jj]\n\n self.SS.dt = self.SS.dt * self.ScalingFacts['time']\n self.cpu_summary['dim'] = time.time() - t0\n\n def assemble_ss(self, wake_prop_settings=None):\n r\"\"\"\n Produces block-form of state-space model\n\n .. math::\n\n \\mathbf{x}_{n+1} &= \\mathbf{A}\\,\\mathbf{x}_n + \\mathbf{B} \\mathbf{u}_{n+1} \\\\\n \\mathbf{y}_n &= \\mathbf{C}\\,\\mathbf{x}_n + \\mathbf{D} \\mathbf{u}_n\n\n where the state, inputs and outputs are:\n\n .. math:: \\mathbf{x}_n = \\{ \\delta \\mathbf{\\Gamma}_n,\\, \\delta \\mathbf{\\Gamma_{w_n}},\\,\n \\Delta t\\,\\delta\\mathbf{\\Gamma}'_n,\\, \\delta\\mathbf{\\Gamma}_{n-1} \\}\n\n .. math:: \\mathbf{u}_n = \\{ \\delta\\mathbf{\\zeta}_n,\\, \\delta\\mathbf{\\zeta}'_n,\\,\n \\delta\\mathbf{u}_{ext,n} \\}\n\n .. math:: \\mathbf{y} = \\{\\delta\\mathbf{f}\\}\n\n with :math:`\\mathbf{\\Gamma}` being the vector of vortex circulations,\n :math:`\\mathbf{\\zeta}` the vector of vortex lattice coordinates and\n :math:`\\mathbf{f}` the vector of aerodynamic forces and moments. Note that :math:`(\\bullet)'` denotes\n a derivative with respect to time.\n\n Note that the input is atypically defined at time ``n+1``, therefore by default\n ``self.remove_predictor = True`` and the predictor term ``u_{n+1}`` is eliminated through\n the change of state[1]:\n\n .. math::\n \\mathbf{h}_n &= \\mathbf{x}_n - \\mathbf{B}\\,\\mathbf{u}_n \\\\\n\n such that:\n\n .. math::\n \\mathbf{h}_{n+1} &= \\mathbf{A}\\,\\mathbf{h}_n + \\mathbf{A\\,B}\\,\\mathbf{u}_n \\\\\n \\mathbf{y}_n &= \\mathbf{C\\,h}_n + (\\mathbf{C\\,B}+\\mathbf{D})\\,\\mathbf{u}_n\n\n\n which only modifies the equivalent :math:`\\mathbf{B}` and :math:`\\mathbf{D}` matrices.\n\n References:\n [1] Franklin, GF and Powell, JD. Digital Control of Dynamic Systems, Addison-Wesley Publishing Company, 1980\n\n To do:\n - remove all calls to scipy.linalg.block_diag\n \"\"\"\n\n cout.cout_wrap('\\tBlock form state-space realisation of UVLM equations started...', 1)\n t0 = time.time()\n MS = self.MS\n K, K_star = self.K, self.K_star\n Kzeta = self.Kzeta\n\n # ------------------------------------------------------ determine size\n\n Nx = self.Nx\n Nu = self.Nu\n Ny = self.Ny\n\n nblock_x = self.nblock_x\n nblock_u = self.nblock_u\n nblock_y = self.nblock_y\n\n if self.integr_order == 2:\n # Second order differencing scheme coefficients\n b0, bm1, bp1 = -2., 0.5, 1.5\n\n # ----------------------------------------------------------- state eq.\n\n ### state terms (A matrix)\n # - choice of sparse matrices format is optimised to reduce memory load\n\n # Aero influence coeffs\n List_AICs, List_AICs_star = ass.AICs(MS.Surfs, MS.Surfs_star,\n target='collocation', Project=True)\n A0 = np.block(List_AICs)\n A0W = np.block(List_AICs_star)\n List_AICs, List_AICs_star = None, None\n LU, P = scalg.lu_factor(A0)\n AinvAW = scalg.lu_solve((LU, P), A0W)\n A0, A0W = None, None\n\n ### propagation of circ\n # fast and memory efficient with both dense and sparse matrices\n List_C, List_Cstar = ass.wake_prop(MS,\n self.use_sparse, sparse_format='csc',\n settings=wake_prop_settings)\n if self.use_sparse:\n Cgamma = libsp.csc_matrix(sparse.block_diag(List_C, format='csc'))\n CgammaW = libsp.csc_matrix(sparse.block_diag(List_Cstar, format='csc'))\n else:\n Cgamma = scalg.block_diag(*List_C)\n CgammaW = scalg.block_diag(*List_Cstar)\n List_C, List_Cstar = None, None\n\n # recurrent dense terms stored as numpy.ndarrays\n AinvAWCgamma = -libsp.dot(AinvAW, Cgamma)\n AinvAWCgammaW = -libsp.dot(AinvAW, CgammaW)\n\n ### A matrix assembly\n Ass = []\n\n # non-penetration condition\n Ass.append([AinvAWCgamma, AinvAWCgammaW, None, ])\n if self.integr_order == 2: Ass[0].append(None)\n # circ. proparagation\n Ass.append([Cgamma, CgammaW, None, ])\n if self.integr_order == 2: Ass[1].append(None)\n\n Cgamma = None\n CgammaW = None\n\n # delta eq.\n if self.use_sparse:\n ones = libsp.csc_matrix(\n (np.ones((K,)), (range(K), range(K))), shape=(K, K))\n else:\n ones = np.eye(K)\n\n if self.integr_order == 1:\n Ass.append([AinvAWCgamma - ones, AinvAWCgammaW.copy(), None])\n\n elif self.integr_order == 2:\n Ass.append([bp1 * AinvAWCgamma + b0 * ones, bp1 * AinvAWCgammaW, None, bm1 * ones])\n # identity eq.\n Ass.append([ones, None, None, None])\n AinvAWCgamma = None\n AinvAWCgammaW = None\n\n # zeta derivs\n List_nc_dqcdzeta = ass.nc_dqcdzeta(MS.Surfs, MS.Surfs_star, Merge=True)\n List_uc_dncdzeta = ass.uc_dncdzeta(MS.Surfs)\n List_nc_domegazetadzeta_vert = ass.nc_domegazetadzeta(MS.Surfs, MS.Surfs_star)\n for ss in range(MS.n_surf):\n List_nc_dqcdzeta[ss][ss] += \\\n (List_uc_dncdzeta[ss] + List_nc_domegazetadzeta_vert[ss])\n Ducdzeta = np.block(List_nc_dqcdzeta) # dense matrix\n List_nc_dqcdzeta = None\n List_uc_dncdzeta = None\n List_nc_domegazetadzeta_vert = None\n\n # ext velocity derivs (Wnv0)\n List_Wnv = []\n for ss in range(MS.n_surf):\n List_Wnv.append(\n interp.get_Wnv_vector(MS.Surfs[ss],\n MS.Surfs[ss].aM, MS.Surfs[ss].aN))\n AinvWnv0 = scalg.lu_solve((LU, P), scalg.block_diag(*List_Wnv))\n List_Wnv = None\n\n ### B matrix assembly\n Bss = []\n\n # non-penetration condition\n Bss.append([-scalg.lu_solve((LU, P), Ducdzeta), AinvWnv0, -AinvWnv0])\n AinvWnv0 = None\n\n # circulation eq.\n Bss.append([None, None, None])\n\n # delta eq.\n if self.integr_order == 1:\n Bss.append([bb.copy() for bb in Bss[0]])\n if self.integr_order == 2:\n Bss.append([bp1 * bb for bb in Bss[0]])\n\n # indentity eq\n if self.integr_order == 2:\n Bss.append([None, None, None])\n\n LU, P = None, None\n\n # ---------------------------------------------------------- output eq.\n\n ### state terms (C matrix)\n\n # gamma (induced velocity contrib.)\n List_dfqsdvind_gamma, List_dfqsdvind_gamma_star = \\\n ass.dfqsdvind_gamma(MS.Surfs, MS.Surfs_star)\n\n # gamma (at constant relative velocity)\n List_dfqsdgamma_vrel0, List_dfqsdgamma_star_vrel0 = \\\n ass.dfqsdgamma_vrel0(MS.Surfs, MS.Surfs_star)\n for ss in range(MS.n_surf):\n List_dfqsdvind_gamma[ss][ss] += List_dfqsdgamma_vrel0[ss]\n List_dfqsdvind_gamma_star[ss][ss] += List_dfqsdgamma_star_vrel0[ss]\n Dfqsdgamma = np.block(List_dfqsdvind_gamma)\n Dfqsdgamma_star = np.block(List_dfqsdvind_gamma_star)\n List_dfqsdvind_gamma, List_dfqsdvind_gamma_star = None, None\n List_dfqsdgamma_vrel0, List_dfqsdgamma_star_vrel0 = None, None\n\n # gamma_dot\n Dfunstdgamma_dot = scalg.block_diag(*ass.dfunstdgamma_dot(MS.Surfs))\n\n ### C matrix assembly\n Css = []\n Css.append([Dfqsdgamma, Dfqsdgamma_star, Dfunstdgamma_dot / self.dt])\n if self.integr_order == 2:\n Css[0].append(None)\n\n ### input terms (D matrix)\n Dss = []\n Dss.append(\n [scalg.block_diag(*ass.dfqsdzeta_vrel0(MS.Surfs, MS.Surfs_star))])\n\n # zeta (induced velocity contrib)\n List_coll, List_vert = ass.dfqsdvind_zeta(MS.Surfs, MS.Surfs_star)\n for ss in range(MS.n_surf):\n List_vert[ss][ss] += List_coll[ss]\n Dss[0][0] += np.block(List_vert)\n del List_vert, List_coll\n\n Dss[0].append(-scalg.block_diag(*ass.dfqsduinput(MS.Surfs, MS.Surfs_star)))\n Dss[0].append(-Dss[0][1])\n\n if self.remove_predictor:\n cout.cout_wrap(\"\\t\\tPredictor not be removed! \" +\n \"(Though this is accounted for in all methods)\", 1)\n\n self.SS = libss.ss_block(Ass, Bss, Css, Dss,\n self.S_x, self.S_u, self.S_y, dt=self.dt)\n cout.cout_wrap('\\tstate-space model produced in form:\\n\\t' \\\n 'x_{n+1} = A x_{n} + Bp u_{n+1}', 1)\n\n # add variable tracker\n self.SS.input_variables = LinearVector(self.input_variables_list)\n self.SS.state_variables = LinearVector(self.state_variables_list)\n self.SS.output_variables = LinearVector(self.output_variables_list)\n\n self.cpu_summary['assemble'] = time.time() - t0\n cout.cout_wrap('\\t\\t\\t...done in %.2f sec' % self.cpu_summary['assemble'], 1)\n\n def freqresp(self, kv, wake_prop_settings=None):\n \"\"\"\n Ad-hoc method for fast UVLM frequency response over the frequencies\n kv. The method, only requires inversion of a K x K matrix at each\n frequency as the equation for propagation of wake circulation are solved\n exactly.\n The algorithm implemented here can be used also upon projection of\n the state-space model.\n\n Note:\n This method is very similar to the \"minsize\" solution option is the\n steady_solve.\n \"\"\"\n\n MS = self.MS\n K = self.K\n K_star = self.K_star\n\n Eye = np.eye(K)\n Bup = np.hstack(self.SS.B[0])\n P = self.SS.A[0][0]\n Pw = self.SS.A[0][1]\n\n Nk = len(kv)\n kvdt = kv * self.SS.dt\n zv = np.cos(kvdt) + 1.j * np.sin(kvdt)\n Yfreq = np.empty((self.SS.outputs, self.SS.inputs, Nk,), dtype=np.complex_)\n\n for kk in range(Nk):\n\n ### build Cw complex\n Cw_cpx = self.get_Cw_cpx(zv[kk], settings=wake_prop_settings)\n\n Ygamma = libsp.solve(zv[kk] * Eye - P -\n libsp.dot(Pw, Cw_cpx, type_out=libsp.csc_matrix),\n Bup)\n if self.remove_predictor:\n Ygamma *= zv[kk]\n\n Ygamma_star = Cw_cpx.dot(Ygamma)\n\n if self.integr_order == 1:\n dfact = (1. - 1. / zv[kk])\n elif self.integr_order == 2:\n dfact = .5 * (3. - 4. / zv[kk] + 1. / zv[kk] ** 2)\n else:\n raise NameError('Specify valid integration order')\n\n # calculate solution\n Yfreq[:, :, kk] = np.dot(self.SS.C[0][0], Ygamma) + \\\n np.dot(self.SS.C[0][1], Ygamma_star) + \\\n np.dot(self.SS.C[0][2], dfact * Ygamma) + \\\n np.hstack(self.SS.D[0])\n\n return Yfreq\n\n def balfreq(self, DictBalFreq, wake_prop_settings=None):\n \"\"\"\n Low-rank method for frequency limited balancing.\n The Observability ad controllability Gramians over the frequencies kv\n are solved in factorised form. Balancd modes are then obtained with a\n square-root method.\n\n Details:\n Observability and controllability Gramians are solved in factorised form\n through explicit integration. The number of integration points determines\n both the accuracy and the maximum size of the balanced model.\n\n Stability over all (Nb) balanced states is achieved if:\n a. one of the Gramian is integrated through the full Nyquist range\n b. the integration points are enough.\n Note, however, that even when stability is not achieved over the full\n balanced states, stability of the balanced truncated model with Ns<=Nb\n states is normally observed even when a low number of integration points\n is used. Two integration methods (trapezoidal rule on uniform grid and\n Gauss-Legendre quadrature) are provided.\n\n Input:\n\n - DictBalFreq: dictionary specifying integration method with keys:\n\n - 'frequency': defines limit frequencies for balancing. The balanced\n model will be accurate in the range [0,F], where F is the value of\n this key. Note that F units must be consistent with the units specified\n in the self.ScalingFacts dictionary.\n\n - 'method_low': ['gauss','trapz'] specifies whether to use gauss\n quadrature or trapezoidal rule in the low-frequency range [0,F]\n\n - 'options_low': options to use for integration in the low-frequencies.\n These depend on the integration scheme (See below).\n\n - 'method_high': method to use for integration in the range [F,F_N],\n where F_N is the Nyquist frequency. See 'method_low'.\n\n - 'options_high': options to use for integration in the high-frequencies.\n\n - 'check_stability': if True, the balanced model is truncated to\n eliminate unstable modes - if any is found. Note that very accurate\n balanced model can still be obtained, even if high order modes are\n unstable. Note that this option is overridden if \"\"\n\n - 'get_frequency_response': if True, the function also returns the\n frequency response evaluated at the low-frequency range integration\n points. If True, this option also allows to automatically tune the\n balanced model.\n\n Future options:\n\n - 'truncation_tolerance': if 'get_frequency_response' is True, allows\n to truncatethe balanced model so as to achieved a prescribed\n tolerance in the low-frequwncy range.\n\n - Ncpu: for parallel run\n\n\n The following integration schemes are available:\n - 'trapz': performs integration over equally spaced points using\n trapezoidal rule. It accepts options dictionaries with keys:\n - 'points': number of integration points to use (including\n domain boundary)\n\n - 'gauss' performs gauss-lobotto quadrature. The domain can be\n partitioned in Npart sub-domain in which the gauss-lobotto quadrature\n of order Ord can be applied. A total number of Npart*Ord points is\n required. It accepts options dictionaries of the form:\n - 'partitions': number of partitions\n - 'order': quadrature order.\n\n Example:\n The following dictionary\n\n DictBalFreq={ 'frequency': 1.2,\n 'method_low': 'trapz',\n 'options_low': {'points': 12},\n 'method_high': 'gauss',\n 'options_high': {'partitions': 2, 'order': 8},\n 'check_stability': True }\n\n balances the state-space model self.SS in the frequency range [0, 1.2]\n using\n (a) 12 equally-spaced points integration of the Gramians in\n the low-frequency range [0,1.2] and\n (b) a 2 Gauss-Lobotto 8-th order quadratures of the controllability\n Gramian in the high-frequency range.\n\n A total number of 28 integration points will be required, which will\n result into a balanced model with number of states\n min{ 2*28* number_inputs, 2*28* number_outputs }\n The model is finally truncated so as to retain only the first Ns stable\n modes.\n \"\"\"\n\n ### check input dictionary\n if 'frequency' not in DictBalFreq:\n raise NameError('Solution dictionary must include the \"frequency\" key')\n\n if 'method_low' not in DictBalFreq:\n warnings.warn('Setting default options for low-frequency integration')\n DictBalFreq['method_low'] = 'trapz'\n DictBalFreq['options_low'] = {'points': 12}\n\n if 'method_high' not in DictBalFreq:\n warnings.warn('Setting default options for high-frequency integration')\n DictBalFreq['method_high'] = 'gauss'\n DictBalFreq['options_high'] = {'partitions': 2, 'order': 8}\n\n if 'check_stability' not in DictBalFreq:\n DictBalFreq['check_stability'] = True\n\n if 'output_modes' not in DictBalFreq:\n DictBalFreq['output_modes'] = True\n\n if 'get_frequency_response' not in DictBalFreq:\n DictBalFreq['get_frequency_response'] = False\n\n ### get integration points and weights\n\n # Nyquist frequency\n kn = np.pi / self.SS.dt\n\n Opt = DictBalFreq['options_low']\n if DictBalFreq['method_low'] == 'trapz':\n kv_low, wv_low = librom.get_trapz_weights(0., DictBalFreq['frequency'],\n Opt['points'], False)\n elif DictBalFreq['method_low'] == 'gauss':\n kv_low, wv_low = librom.get_gauss_weights(0., DictBalFreq['frequency'],\n Opt['partitions'], Opt['order'])\n else:\n raise NameError(\n 'Invalid value %s for key \"method_low\"' % DictBalFreq['method_low'])\n\n Opt = DictBalFreq['options_high']\n if DictBalFreq['method_high'] == 'trapz':\n if Opt['points'] == 0:\n warnings.warn('You have chosen no points in high frequency range!')\n kv_high, wv_high = [], []\n else:\n kv_high, wv_high = librom.get_trapz_weights(DictBalFreq['frequency'], kn,\n Opt['points'], True)\n elif DictBalFreq['method_high'] == 'gauss':\n if Opt['order'] * Opt['partitions'] == 0:\n warnings.warn('You have chosen no points in high frequency range!')\n kv_high, wv_high = [], []\n else:\n kv_high, wv_high = librom.get_gauss_weights(DictBalFreq['frequency'], kn,\n Opt['partitions'], Opt['order'])\n else:\n raise NameError(\n 'Invalid value %s for key \"method_high\"' % DictBalFreq['method_high'])\n\n ### get useful terms\n K = self.K\n K_star = self.K_star\n\n Eye = np.eye(K)\n Bup = np.hstack(self.SS.B[0])\n\n P = self.SS.A[0][0]\n Pw = self.SS.A[0][1]\n\n # indices to manipulate obs solution\n ii00 = range(0, self.K)\n ii01 = range(self.K, self.K + self.K_star)\n ii02 = range(self.K + self.K_star, 2 * self.K + self.K_star)\n ii03 = range(2 * self.K + self.K_star, 3 * self.K + self.K_star)\n\n # integration factors\n if self.integr_order == 2:\n b0, bm1, bp1 = -2., 0.5, 1.5\n else:\n b0, bp1 = -1., 1.\n raise NameError('Method not implemented for integration order 1')\n\n ### -------------------------------------------------- loop frequencies\n\n ### merge vectors\n Nk_low = len(kv_low)\n kvdt = np.concatenate((kv_low, kv_high)) * self.SS.dt\n wv = np.concatenate((wv_low, wv_high)) * self.SS.dt\n zv = np.cos(kvdt) + 1.j * np.sin(kvdt)\n\n Qobs = np.zeros((self.SS.states, self.SS.outputs), dtype=np.complex_)\n Zc = np.zeros((self.SS.states, 2 * self.SS.inputs * len(kvdt)), )\n Zo = np.zeros((self.SS.states, 2 * self.SS.outputs * Nk_low), )\n\n if DictBalFreq['get_frequency_response']:\n self.Yfreq = np.empty((self.SS.outputs, self.SS.inputs, Nk_low,), dtype=np.complex_)\n self.kv = kv_low\n\n for kk in range(len(kvdt)):\n\n zval = zv[kk]\n Intfact = wv[kk] # integration factor\n\n # build terms that will be recycled\n Cw_cpx = self.get_Cw_cpx(zval, settings=wake_prop_settings)\n P_PwCw = P + Cw_cpx.T.dot(Pw.T).T\n Kernel = np.linalg.inv(zval * Eye - P_PwCw)\n\n ### ----- controllability\n Ygamma = Intfact * np.dot(Kernel, Bup)\n if self.remove_predictor:\n Ygamma *= zval\n Ygamma_star = Cw_cpx.dot(Ygamma)\n\n if self.integr_order == 1:\n dfact = (bp1 + bp0 / zval)\n Qctrl = np.vstack([Ygamma, Ygamma_star, dfact * Ygamma])\n elif self.integr_order == 2:\n dfact = bp1 + b0 / zval + bm1 / zval ** 2\n Qctrl = np.vstack(\n [Ygamma, Ygamma_star, dfact * Ygamma, (1. / zval) * Ygamma])\n else:\n raise NameError('Specify valid integration order')\n\n kkvec = range(2 * kk * self.SS.inputs, 2 * (kk + 1) * self.SS.inputs)\n Zc[:, kkvec[:self.SS.inputs]] = Qctrl.real # *Intfact\n Zc[:, kkvec[self.SS.inputs:]] = Qctrl.imag # *Intfact\n\n ### ----- frequency response\n if DictBalFreq['get_frequency_response'] and kk < Nk_low:\n self.Yfreq[:, :, kk] = (1. / Intfact) * \\\n (np.dot(self.SS.C[0][0], Ygamma) + \\\n np.dot(self.SS.C[0][1], Ygamma_star) + \\\n dfact * np.dot(self.SS.C[0][2], Ygamma)) + \\\n np.hstack(self.SS.D[0])\n\n ### ----- frequency response\n if DictBalFreq['get_frequency_response'] and kk < Nk_low:\n self.Yfreq[:, :, kk] = (1. / Intfact) * \\\n (np.dot(self.SS.C[0][0], Ygamma) + \\\n np.dot(self.SS.C[0][1], Ygamma_star) + \\\n dfact * np.dot(self.SS.C[0][2], Ygamma)) + \\\n np.hstack(self.SS.D[0])\n\n ### ----- observability\n # solve (1./zval*I - A.T)^{-1} C^T (in low-frequency only)\n if kk >= Nk_low:\n continue\n\n zinv = 1. / zval\n Qobs[ii02, :] = zinv * self.SS.C[0][2].T\n if self.integr_order == 1:\n raise NameError('Obs Gramian Integr not implemented')\n elif self.integr_order == 2:\n Qobs[ii03, :] = (bm1 * zinv) * Qobs[ii02, :]\n\n # solve bound circulation\n rhs = Cw_cpx.T.dot(self.SS.C[0][1].T) + self.SS.C[0][0].T + \\\n Qobs[ii02, :] * (b0 + zinv * bm1) + \\\n np.dot(P_PwCw.T, bp1 * Qobs[ii02, :])\n Qobs[ii00, :] = np.dot(Kernel.T, rhs)\n\n # solve wake\n Eye_star = libsp.csc_matrix(\n (zval * np.ones((K_star,)), (range(K_star), range(K_star))),\n shape=(K_star, K_star), dtype=np.complex_)\n Qobs[ii01, :] = libsp.solve(\n Eye_star - self.SS.A[1][1].T,\n self.SS.C[0][1].T + np.dot(Pw.T, Qobs[ii00, :] + bp1 * Qobs[ii02, :]))\n\n kkvec = range(2 * kk * self.SS.outputs, 2 * (kk + 1) * self.SS.outputs)\n Zo[:, kkvec[:self.SS.outputs]] = Intfact * Qobs.real\n Zo[:, kkvec[self.SS.outputs:]] = Intfact * Qobs.imag\n\n # delete full matrices\n Kernel = None\n Qctrl = None\n Qobs = None\n\n # LRSQM (optimised)\n U, hsv, Vh = scalg.svd(np.dot(Zo.T, Zc), full_matrices=False)\n sinv = hsv ** (-0.5)\n T = np.dot(Zc, Vh.T * sinv)\n Ti = np.dot((U * sinv).T, Zo.T)\n\n ### build frequency balanced model\n Ab, Bb, Cb = self.SS.project(Ti, T, by_arrays=True, overwrite=False)\n\n if self.remove_predictor:\n Ab, Bb, Cb, Db = \\\n libss.SSconv(np.block(Ab), None, np.block(Bb),\n np.block(Cb), np.block(self.SS.D), Bm1=None)\n SSb = libss.StateSpace(Ab, Bb, Cb, Db, dt=self.dt)\n else:\n SSb = libss.StateSpace(np.block(Ab), np.block(Bb),\n np.block(Cb), np.block(self.SS.D), dt=self.SS.dt)\n\n ### Eliminate unstable modes - if any:\n if DictBalFreq['check_stability']:\n for nn in range(1, len(hsv) + 1):\n eigs_trunc = scalg.eigvals(SSb.A[:nn, :nn])\n eigs_trunc_max = np.max(np.abs(eigs_trunc))\n if eigs_trunc_max > 1. - 1e-16:\n SSb.truncate(nn - 1)\n hsv = hsv[:nn - 1]\n T = T[:, :nn - 1]\n Ti = Ti[:nn - 1, :]\n break\n\n self.SSb = SSb\n self.hsv = hsv\n if DictBalFreq['output_modes']:\n self.T = T\n self.Ti = Ti\n self.Zc = Zc\n self.Zo = Zo\n self.svd_res = {'U': U, 'hsv': hsv, 'Vh': Vh}\n\n def solve_step(self, x_n, u_n, u_n1=None, transform_state=False):\n r\"\"\"\n Solve step.\n\n If the predictor term has not been removed (``remove_predictor = False``) then the system is solved as:\n\n .. math::\n \\mathbf{x}^{n+1} &= \\mathbf{A\\,x}^n + \\mathbf{B\\,u}^n \\\\\n \\mathbf{y}^{n+1} &= \\mathbf{C\\,x}^{n+1} + \\mathbf{D\\,u}^n\n\n Else, if ``remove_predictor = True``, the state is modified as\n\n .. math:: \\mathbf{h}^n = \\mathbf{x}^n - \\mathbf{B\\,u}^n\n\n And the system solved by:\n\n .. math::\n \\mathbf{h}^{n+1} &= \\mathbf{A\\,h}^n + \\mathbf{B_{mod}\\,u}^{n} \\\\\n \\mathbf{y}^{n+1} &= \\mathbf{C\\,h}^{n+1} + \\mathbf{D_{mod}\\,u}^{n+1}\n\n Finally, the original state is recovered using the reverse transformation:\n\n .. math:: \\mathbf{x}^{n+1} = \\mathbf{h}^{n+1} + \\mathbf{B\\,u}^{n+1}\n\n where the modifications to the :math:`\\mathbf{B}_{mod}` and :math:`\\mathbf{D}_{mod}` are detailed in\n :func:`Dynamic.assemble_ss`.\n\n Notes:\n Although the original equations include the term :math:`\\mathbf{u}_{n+1}`, it is a reasonable approximation\n to take :math:`\\mathbf{u}_{n+1}\\approx\\mathbf{u}_n` given a sufficiently small time step, hence if the input\n at time ``n+1`` is not parsed, it is estimated from :math:`u^n`.\n\n Args:\n x_n (np.array): State vector at the current time step :math:`\\mathbf{x}^n`\n u_n (np.array): Input vector at time step :math:`\\mathbf{u}^n`\n u_n1 (np.array): Input vector at time step :math:`\\mathbf{u}^{n+1}`\n transform_state (bool): When the predictor term is removed, if true it will transform the state vector. If\n false it will be assumed that the state vector that is parsed is already transformed i.e. it is\n :math:`\\mathbf{h}`.\n\n Returns:\n Tuple: Updated state and output vector packed in a tuple :math:`(\\mathbf{x}^{n+1},\\,\\mathbf{y}^{n+1})`\n\n Notes:\n Because in BlockDynamics the predictor is never removed when building\n 'self.SS', the implementation change with respect to Dynamic. However,\n formulas are consistent.\n \"\"\"\n\n if u_n1 is None:\n u_n1 = u_n.copy()\n\n if self.remove_predictor and not hasattr(self, 'CBplusD'):\n self.CBplusD = libsp.block_sum(libsp.block_dot(self.SS.C, self.SS.B), self.SS.D)\n\n ### transform input in block matrices\n X_n = []\n II0 = 0\n for ii in range(self.SS.blocks_x):\n IIend = II0 + self.SS.S_x[ii]\n X_n.append([x_n[II0:IIend]])\n II0 = IIend\n\n U_n1 = []\n II0 = 0\n for ii in range(self.SS.blocks_u):\n IIend = II0 + self.SS.S_u[ii]\n U_n1.append([u_n1[II0:IIend]])\n II0 = IIend\n\n if u_n is not None:\n U_n = []\n for ii in range(self.SS.blocks_u):\n IIend = II0 + self.SS.S_u[ii]\n U_n.append([u_n[II0:IIend]])\n II0 = IIend\n\n if self.remove_predictor:\n\n # Transform state vector\n # TODO: Agree on a way to do this. Either always transform here or transform prior to using the method.\n if transform_state:\n H_n1 = libsp.block_dot(self.SS.A, X_n)\n else:\n H_n = X_n\n H_n1 = libsp.block_dot(self.SS.A,\n libsp.block_sum(H_n, libsp.block_dot(self.SS.B, U_n)))\n\n Y_n1 = libsp.block_sum(libsp.block_dot(self.SS.C, H_n1),\n libsp.block_dot(self.CBplusD, U_n1))\n\n Y_n1 = libsp.block_sum(libsp.block_dot(self.SS.C, H_n1),\n libsp.block_dot(self.CBplusD, U_n1))\n\n # Recover state vector\n if transform_state:\n X_n1 = libsp.block_sum(H_n1, libsp.block_dot(self.SS.B, U_n1))\n else:\n X_n1 = H_n1\n\n else:\n X_n1 = libsp.block_sum(libsp.block_dot(self.SS.A, X_n),\n libsp.block_dot(self.SS.B, U_n1))\n Y_n1 = libsp.block_sum(libsp.block_dot(self.SS.C, X_n1),\n libsp.block_dot(self.SS.D, U_n1))\n\n x_n1 = np.concatenate([X_n1[ii][0] for ii in range(self.SS.blocks_x)])\n\n return x_n1, np.block(Y_n1).reshape(-1)\n\n\n################################################################################\n\n################################################################################\n\n\nclass Frequency(Static):\n \"\"\"\n Class for frequency description of linearised UVLM solution. Linearisation\n around steady-state are only supported. The class is built upon Static, and\n inherits all the methods contained there.\n\n The class supports most of the features of Dynamics but has lower memory\n requirements of Dynamic, and should be preferred for:\n\n a. producing memory and computationally cheap frequency responses\n b. building reduced order models using RFA/polynomial fitting\n\n Usage:\n Upon initialisation, the assemble method produces all the matrices required\n for the frequency description of the UVLM (see assemble for details). A\n state-space model is not allocated but:\n\n - Time stepping is also possible (but not implemented yet) as all the\n fundamental terms describing the UVLM equations are still produced\n (except the propagation of wake circulation)\n - ad-hoc methods for scaling, unscaling and frequency response are\n provided.\n\n Input:\n\n - tsdata: aero timestep data from SHARPy solution\n - dt: time-step\n - integr_order=0,1,2: integration order for UVLM unsteady aerodynamic\n force. If 0, the derivative is computed exactly.\n - RemovePredictor=True: This flag is only used for the frequency response\n calculation. The frequency description, in fact, naturally arises\n without the predictor, but lags can be included during the frequency\n response calculation. See Dynamic documentation for more details.\n - ScalingDict=None: disctionary containing fundamental reference units\n\n .. code-block:: python\n\n {'length': reference_length,\n 'speed': reference_speed,\n 'density': reference density}\n\n used to derive scaling quantities for the state-space model variables.\n The scaling factors are stores in ``self.ScalingFact.``\n\n Note that while time, circulation, angular speeds) are scaled\n accordingly, FORCES ARE NOT. These scale by qinf*b**2, where b is the\n reference length and qinf is the dinamic pressure.\n - UseSparse=False: builds the A and B matrices in sparse form. C and D\n are dense, hence the sparce format is not used.\n\n Methods:\n - nondimss: normalises matrices produced by the assemble method based\n on the scaling factors in self.ScalingFact.\n - dimss: inverse of nondimss.\n - assemble: builds matrices for UVLM minimal size description.\n - assemble_profiling: generate profiling report of the assembly and\n saves it into self.prof_out. To read the report:\n\n .. code-block:: python\n\n import pstats\n p=pstats.Stats(self.prof_out)\n\n - freqresp: fast algorithm for frequency response.\n\n Methods to implement:\n\n - solve_steady: runs freqresp at 0 frequency.\n - solve_step: solves one time-step\n \"\"\"\n\n def __init__(self, tsdata, dt, integr_order=2,\n RemovePredictor=True, ScalingDict=None, UseSparse=True):\n\n super().__init__(tsdata)\n\n self.dt = dt\n self.integr_order = integr_order\n\n assert self.integr_order in [1, 2, 0], 'integr_order must be in [0,1,2]'\n\n self.inputs = 9 * self.Kzeta\n self.outputs = 3 * self.Kzeta\n\n self.remove_predictor = RemovePredictor\n self.use_sparse = UseSparse\n\n # create scaling quantities\n if ScalingDict is None:\n ScalingFacts = {'length': 1.,\n 'speed': 1.,\n 'density': 1.}\n else:\n ScalingFacts = ScalingDict\n\n for key in ScalingFacts:\n ScalingFacts[key] = np.float(ScalingFacts[key])\n\n ScalingFacts['time'] = ScalingFacts['length'] / ScalingFacts['speed']\n ScalingFacts['circulation'] = ScalingFacts['speed'] * ScalingFacts['length']\n ScalingFacts['dyn_pressure'] = 0.5 * ScalingFacts['density'] * ScalingFacts['speed'] ** 2\n ScalingFacts['force'] = ScalingFacts['dyn_pressure'] * ScalingFacts['length'] ** 2\n self.ScalingFacts = ScalingFacts\n\n ### collect statistics\n self.cpu_summary = {'dim': 0.,\n 'nondim': 0.,\n 'assemble': 0.}\n\n def nondimss(self):\n \"\"\"\n Scale state-space model based of self.ScalingFacts\n \"\"\"\n\n t0 = time.time()\n Kzeta = self.Kzeta\n\n self.Bss[:, :3 * Kzeta] *= (self.ScalingFacts['length'] / self.ScalingFacts['circulation'])\n self.Bss[:, 3 * Kzeta:] *= (self.ScalingFacts['speed'] / self.ScalingFacts['circulation'])\n\n self.Css *= (self.ScalingFacts['circulation'] / self.ScalingFacts['force'])\n\n self.Dss[:, :3 * Kzeta] *= (self.ScalingFacts['length'] / self.ScalingFacts['force'])\n self.Dss[:, 3 * Kzeta:] *= (self.ScalingFacts['speed'] / self.ScalingFacts['force'])\n\n self.dt = self.dt / self.ScalingFacts['time']\n\n self.cpu_summary['nondim'] = time.time() - t0\n\n def dimss(self):\n\n t0 = time.time()\n Kzeta = self.Kzeta\n\n self.Bss[:, :3 * Kzeta] /= (self.ScalingFacts['length'] / self.ScalingFacts['circulation'])\n self.Bss[:, 3 * Kzeta:] /= (self.ScalingFacts['speed'] / self.ScalingFacts['circulation'])\n\n self.Css /= (self.ScalingFacts['circulation'] / self.ScalingFacts['force'])\n\n self.Dss[:, :3 * Kzeta] /= (self.ScalingFacts['length'] / self.ScalingFacts['force'])\n self.Dss[:, 3 * Kzeta:] /= (self.ScalingFacts['speed'] / self.ScalingFacts['force'])\n\n self.dt = self.dt * self.ScalingFacts['time']\n\n self.cpu_summary['dim'] = time.time() - t0\n\n def assemble(self):\n r\"\"\"\n Assembles matrices for minumal size frequency description of UVLM. The\n state equation is represented in the form:\n\n .. math:: \\mathbf{A_0} \\mathbf{\\Gamma} +\n \\mathbf{A_{w_0}} \\mathbf{\\Gamma_w} =\n \\mathbf{B_0} \\mathbf{u}\n\n While the output equation is as per the Dynamic class, namely:\n\n .. math:: \\mathbf{y} =\n \\mathbf{C} \\mathbf{x} + \\mathbf{D} \\mathbf{u}\n\n where\n\n .. math:: \\mathbf{x} =\n [\\mathbf{\\Gamma}; \\mathbf{\\Gamma_w}; \\Delta\\mathbf(\\Gamma)]\n\n The propagation of wake circulation matrices are not produced as these\n are not required for frequency response analysis.\n \"\"\"\n\n cout.cout_wrap('\\tAssembly of frequency description of UVLM started...', 1)\n t0 = time.time()\n MS = self.MS\n K, K_star = self.K, self.K_star\n Kzeta = self.Kzeta\n\n Nu = self.inputs\n Ny = self.outputs\n\n # ----------------------------------------------------------- state eq.\n\n # Aero influence coeffs\n List_AICs, List_AICs_star = ass.AICs(MS.Surfs, MS.Surfs_star,\n target='collocation', Project=True)\n A0 = np.block(List_AICs)\n A0W = np.block(List_AICs_star)\n List_AICs, List_AICs_star = None, None\n\n # zeta derivs\n List_nc_dqcdzeta = ass.nc_dqcdzeta(MS.Surfs, MS.Surfs_star, Merge=True)\n List_uc_dncdzeta = ass.uc_dncdzeta(MS.Surfs)\n List_nc_domegazetadzeta_vert = ass.nc_domegazetadzeta(MS.Surfs, MS.Surfs_star)\n for ss in range(MS.n_surf):\n List_nc_dqcdzeta[ss][ss] += \\\n (List_uc_dncdzeta[ss] + List_nc_domegazetadzeta_vert[ss])\n Ducdzeta = np.block(List_nc_dqcdzeta) # dense matrix\n List_nc_dqcdzeta = None\n List_uc_dncdzeta = None\n List_nc_domegazetadzeta_vert = None\n\n # ext velocity derivs (Wnv0)\n List_Wnv = []\n for ss in range(MS.n_surf):\n List_Wnv.append(\n interp.get_Wnv_vector(MS.Surfs[ss],\n MS.Surfs[ss].aM, MS.Surfs[ss].aN))\n Wnv0 = scalg.block_diag(*List_Wnv)\n List_Wnv = None\n\n ### B matrix assembly\n # this could be also sparse...\n Bss = np.block([-Ducdzeta, Wnv0, -Wnv0])\n\n # ---------------------------------------------------------- output eq.\n\n ### state terms (C matrix)\n\n # gamma (induced velocity contrib.)\n List_dfqsdvind_gamma, List_dfqsdvind_gamma_star = \\\n ass.dfqsdvind_gamma(MS.Surfs, MS.Surfs_star)\n\n # gamma (at constant relative velocity)\n List_dfqsdgamma_vrel0, List_dfqsdgamma_star_vrel0 = \\\n ass.dfqsdgamma_vrel0(MS.Surfs, MS.Surfs_star)\n for ss in range(MS.n_surf):\n List_dfqsdvind_gamma[ss][ss] += List_dfqsdgamma_vrel0[ss]\n List_dfqsdvind_gamma_star[ss][ss] += List_dfqsdgamma_star_vrel0[ss]\n Dfqsdgamma = np.block(List_dfqsdvind_gamma)\n Dfqsdgamma_star = np.block(List_dfqsdvind_gamma_star)\n List_dfqsdvind_gamma, List_dfqsdvind_gamma_star = None, None\n List_dfqsdgamma_vrel0, List_dfqsdgamma_star_vrel0 = None, None\n\n # gamma_dot\n Dfunstdgamma_dot = scalg.block_diag(*ass.dfunstdgamma_dot(MS.Surfs))\n\n # C matrix assembly\n Css = np.zeros((Ny, 2 * K + K_star))\n Css[:, :K] = Dfqsdgamma\n Css[:, K:K + K_star] = Dfqsdgamma_star\n # added mass\n Css[:, K + K_star:2 * K + K_star] = Dfunstdgamma_dot / self.dt\n\n ### input terms (D matrix)\n Dss = np.zeros((Ny, Nu))\n\n # zeta (at constant relative velocity)\n Dss[:, :3 * Kzeta] = scalg.block_diag(\n *ass.dfqsdzeta_vrel0(MS.Surfs, MS.Surfs_star))\n # zeta (induced velocity contrib)\n List_coll, List_vert = ass.dfqsdvind_zeta(MS.Surfs, MS.Surfs_star)\n for ss in range(MS.n_surf):\n List_vert[ss][ss] += List_coll[ss]\n Dss[:, :3 * Kzeta] += np.block(List_vert)\n del List_vert, List_coll\n\n # input velocities (external)\n Dss[:, 6 * Kzeta:9 * Kzeta] = scalg.block_diag(\n *ass.dfqsduinput(MS.Surfs, MS.Surfs_star))\n\n # input velocities (body movement)\n Dss[:, 3 * Kzeta:6 * Kzeta] = -Dss[:, 6 * Kzeta:9 * Kzeta]\n\n ### store matrices\n self.A0 = A0\n self.A0W = A0W\n self.Bss = Bss\n self.Css = Css\n self.Dss = Dss\n self.inputs = 9 * Kzeta\n self.outputs = 3 * Kzeta\n\n self.cpu_summary['assemble'] = time.time() - t0\n cout.cout_wrap('\\t\\t\\t...done in %.2f sec' % self.cpu_summary['assemble'], 1)\n\n def addGain(self, K, where):\n\n assert where in ['in', 'out'], \\\n 'Specify whether gains are added to input or output'\n\n if where == 'in':\n self.Bss = libsp.dot(self.Bss, K)\n self.Dss = libsp.dot(self.Dss, K)\n self.inputs = K.shape[1]\n\n if where == 'out':\n self.Css = libsp.dot(K, self.Css)\n self.Dss = libsp.dot(K, self.Dss)\n self.outputs = K.shape[0]\n\n if where == 'out':\n self.Css = libsp.dot(K, self.Css)\n self.Dss = libsp.dot(K, self.Dss)\n self.outputs = K.shape[0]\n\n def freqresp(self, kv, wake_prop_settings=None):\n \"\"\"\n Ad-hoc method for fast UVLM frequency response over the frequencies\n kv. The method, only requires inversion of a K x K matrix at each\n frequency as the equation for propagation of wake circulation are solved\n exactly.\n \"\"\"\n\n MS = self.MS\n K = self.K\n K_star = self.K_star\n\n Nk = len(kv)\n kvdt = kv * self.dt\n zv = np.cos(kvdt) + 1.j * np.sin(kvdt)\n Yfreq = np.empty((self.outputs, self.inputs, Nk,), dtype=np.complex_)\n\n ### loop frequencies\n for kk in range(Nk):\n\n ### build Cw complex\n Cw_cpx = self.get_Cw_cpx(zv[kk], settings=wake_prop_settings)\n\n # get bound state freq response\n if self.remove_predictor:\n Ygamma = np.linalg.solve(\n self.A0 + libsp.dot(\n self.A0W, Cw_cpx, type_out=libsp.csc_matrix), self.Bss)\n else:\n Ygamma = zv[kk] ** (-1) * \\\n np.linalg.solve(\n self.A0 + libsp.dot(\n self.A0W, Cw_cpx, type_out=libsp.csc_matrix), self.Bss)\n Ygamma_star = Cw_cpx.dot(Ygamma)\n\n # determine factor for delta of bound circulation\n if self.integr_order == 0:\n dfact = (1.j * kv[kk]) * self.dt\n elif self.integr_order == 1:\n dfact = (1. - 1. / zv[kk])\n elif self.integr_order == 2:\n dfact = .5 * (3. - 4. / zv[kk] + 1. / zv[kk] ** 2)\n else:\n raise NameError('Specify valid integration order')\n\n Yfreq[:, :, kk] = np.dot(self.Css[:, :K], Ygamma) + \\\n np.dot(self.Css[:, K:K + K_star], Ygamma_star) + \\\n np.dot(self.Css[:, -K:], dfact * Ygamma) + \\\n self.Dss\n\n return Yfreq\n\n def get_Cw_cpx(self, zval, settings=None):\n r\"\"\"\n Produces a sparse matrix\n\n .. math:: \\bar{\\mathbf{C}}(z)\n\n where\n\n .. math:: z = e^{k \\Delta t}\n\n such that the wake circulation frequency response at :math:`z` is\n\n .. math:: \\bar{\\goldsymbol{\\Gamma}}_w = \\bar{\\mathbf{C}}(z) \\bar{\\boldsymbol{\\Gamma}}\n\n \"\"\"\n return get_Cw_cpx(self.MS, self.K, self.K_star, zval, settings=settings)\n\n\n def assemble_profiling(self):\n \"\"\"\n Generate profiling report for assembly and save it in self.prof_out.\n\n To read the report:\n import pstats\n p=pstats.Stats(self.prof_out)\n \"\"\"\n\n import cProfile\n cProfile.runctx('self.assemble()', globals(), locals(), filename=self.prof_out)\n\n\ndef get_Cw_cpx(MS, K, K_star, zval, settings=None):\n r\"\"\"\n Produces a sparse matrix\n\n .. math:: \\bar{\\mathbf{C}}(z)\n\n where\n\n .. math:: z = e^{k \\Delta t}\n\n such that the wake circulation frequency response at :math:`z` is\n\n .. math:: \\bar{\\boldsymbol{\\Gamma}}_w = \\bar{\\mathbf{C}}(z) \\bar{\\mathbf{\\Gamma}}\n\n \"\"\"\n\n try:\n cfl1 = settings['cfl1']\n except (KeyError, TypeError):\n # In case the key does not exist or settings=None\n cfl1 = True\n cout.cout_wrap(\"Computing wake propagation solution matrix if frequency domain with CFL1=%s\" % cfl1, 1)\n # print(\"Computing wake propagation solution matrix if frequency domain with CFL1=%s\" % cfl1)\n\n if cfl1:\n jjvec = []\n iivec = []\n valvec = []\n\n K0tot, K0totstar = 0, 0\n for ss in range(MS.n_surf):\n\n M, N = MS.dimensions[ss]\n Mstar, N = MS.dimensions_star[ss]\n\n for mm in range(Mstar):\n jjvec += range(K0tot + N * (M - 1), K0tot + N * M)\n iivec += range(K0totstar + mm * N, K0totstar + (mm + 1) * N)\n valvec += N * [zval ** (-mm - 1)]\n K0tot += MS.KK[ss]\n K0totstar += MS.KK_star[ss]\n else:\n # sum_m_n = 0\n sum_mstar_n = 0\n for ss in range(MS.n_surf):\n # M, N = MS.dimensions[ss]\n Mstar, N = MS.dimensions_star[ss]\n # sum_m_n += M*N\n sum_mstar_n += Mstar*N\n\n try:\n MS.Surfs_star[ss].zetac\n except AttributeError:\n MS.Surfs_star[ss].zetac.generate_collocations()\n jjvec = [None]*sum_mstar_n\n iivec = [None]*sum_mstar_n\n valvec = [None]*sum_mstar_n\n\n K0tot, K0totstar = 0, 0\n ipoint = 0\n for ss in range(MS.n_surf):\n M, N = MS.dimensions[ss]\n Mstar, N = MS.dimensions_star[ss]\n Surf = MS.Surfs[ss]\n Surf_star = MS.Surfs_star[ss]\n for iin in range(N):\n for mm in range(Mstar):\n # Value location in the sparse array\n ipoint = K0totstar + mm * N + iin\n # Compute CFL\n if mm == 0:\n conv_vec = Surf_star.zetac[:, 0, iin] - Surf.zetac[:, -1, iin]\n dist = np.linalg.norm(conv_vec)\n conv_dir_te = conv_vec/dist\n vel = Surf.u_input_coll[:, -1, iin]\n vel_value = np.dot(vel, conv_dir_te)\n cfl = settings['dt']*vel_value/dist\n else:\n conv_vec = Surf_star.zetac[:, mm, iin] - Surf_star.zetac[:, mm - 1, iin]\n dist = np.linalg.norm(conv_vec)\n conv_dir = conv_vec/dist\n vel = Surf.u_input_coll[:, -1, iin]\n vel_value = np.dot(vel, conv_dir_te)\n cfl = settings['dt']*vel_value/dist\n # Compute coefficient\n coef = get_Cw_cpx_coef_cfl_n1(cfl, zval)\n # Assign values\n jjvec[ipoint] = K0tot + N * (M - 1) + iin\n iivec[ipoint] = K0totstar + mm * N + iin\n if mm == 0:\n # First row\n valvec[ipoint] = coef\n else:\n ipoint_prev = K0totstar + (mm - 1) * N + iin\n valvec[ipoint] = coef*valvec[ipoint_prev]\n K0tot += MS.KK[ss]\n K0totstar += MS.KK_star[ss]\n\n return libsp.csc_matrix((valvec, (iivec, jjvec)), shape=(K_star, K), dtype=np.complex_)\n\n\ndef get_Cw_cpx_coef_cfl_n1(cfl, zval):\n # Convergence loop end criteria\n tol = 1e-12\n rmax = 100\n\n # Initial values\n coef = 0.\n r = 0\n\n # Loop\n error = 2*tol\n while ((error > tol) and (r < rmax)):\n delta_coef = ((1 - cfl)**r)*cfl*(zval**(-r-1))\n coef += delta_coef\n error = np.abs(delta_coef/coef)\n r += 1\n coef /= (1 - (1-cfl)**rmax*(zval**(-1)))\n if (error > tol):\n cout.cout_wrap((\"WARNING computation of Cw_cpx did not reach desired accuracy. r: %d. error: %d\" % (r, error)), 2)\n\n return coef\n\n################################################################################\n\n\nif __name__ == '__main__':\n\n import unittest\n from sharpy.utils.sharpydir import SharpyDir\n import sharpy.utils.h5utils as h5\n\n\n class Test_linuvlm_Sta_vs_Dyn(unittest.TestCase):\n \"\"\" Test methods into this module \"\"\"\n\n def setUp(self):\n fname = SharpyDir + '/sharpy/linear/test/h5input/' + \\\n 'goland_mod_Nsurf02_M003_N004_a040.aero_state.h5'\n haero = h5.readh5(fname)\n tsdata = haero.ts00000\n\n # Static solver\n Sta = Static(tsdata)\n Sta.assemble_profiling()\n Sta.assemble()\n Sta.get_total_forces_gain()\n\n # random input\n Sta.u_ext = 1.0 + 0.30 * np.random.rand(3 * Sta.Kzeta)\n Sta.zeta_dot = 0.2 + 0.10 * np.random.rand(3 * Sta.Kzeta)\n Sta.zeta = 0.05 * (np.random.rand(3 * Sta.Kzeta) - 1.0)\n\n Sta.solve()\n Sta.reshape()\n Sta.total_forces()\n self.Sta = Sta\n self.tsdata = tsdata\n\n def test_force_gains(self):\n \"\"\"\n to do: add check on moments gain\n \"\"\"\n Sta = self.Sta\n Ftot02 = libsp.dot(Sta.Kftot, Sta.fqs)\n assert np.max(np.abs(Ftot02 - Sta.Ftot)) < 1e-10, 'Total force gain matrix wrong!'\n\n def test_Dyn_steady_state(self):\n \"\"\"\n Test steady state predicted by Dynamic and Static classes are the same.\n \"\"\"\n\n Sta = self.Sta\n Order = [2, 1]\n RemPred = [True, False]\n UseSparse = [True, False]\n\n for order in Order:\n for rem_pred in RemPred:\n for use_sparse in UseSparse:\n\n # Dynamic solver\n Dyn = Dynamic(self.tsdata,\n dt=0.05,\n integr_order=order,\n RemovePredictor=rem_pred,\n UseSparse=use_sparse)\n Dyn.assemble_ss()\n\n # steady state solution\n usta = np.concatenate((Sta.zeta, Sta.zeta_dot, Sta.u_ext))\n xsta, ysta = Dyn.solve_steady(usta, method='direct')\n\n if use_sparse is False and rem_pred is False:\n xmin, ymin = Dyn.solve_steady(usta, method='minsize')\n xrec, yrec = Dyn.solve_steady(usta, method='recursive')\n xsub, ysub = Dyn.solve_steady(usta, method='subsystem')\n\n # assert all solutions are matching\n assert max(np.linalg.norm(xsta - xmin), np.linalg.norm(ysta - ymin)), \\\n 'Direct and min. size solutions not matching!'\n assert max(np.linalg.norm(xsta - xrec), np.linalg.norm(ysta - yrec)), \\\n 'Direct and recursive solutions not matching!'\n assert max(np.linalg.norm(xsta - xsub), np.linalg.norm(ysta - ysub)), \\\n 'Direct and sub-system solutions not matching!'\n\n # compare against Static solver solution\n er = np.max(np.abs(ysta - Sta.fqs) / np.linalg.norm(Sta.Ftot))\n print('Error force distribution: %.3e' % er)\n assert er < 1e-12, \\\n 'Steady-state force not matching (error: %.2e)!' % er\n\n if rem_pred is False: # compare state\n\n er = np.max(np.abs(xsta[:Dyn.K] - Sta.gamma))\n print('Error bound circulation: %.3e' % er)\n assert er < 1e-13, \\\n 'Steady-state gamma not matching (error: %.2e)!' % er\n\n gammaw_ref = np.zeros((Dyn.K_star,))\n kk = 0\n for ss in range(Dyn.MS.n_surf):\n Mstar = Dyn.MS.MM_star[ss]\n Nstar = Dyn.MS.NN_star[ss]\n for mm in range(Mstar):\n gammaw_ref[kk:kk + Nstar] = Sta.Gamma[ss][-1, :]\n kk += Nstar\n\n er = np.max(np.abs(xsta[Dyn.K:Dyn.K + Dyn.K_star] - gammaw_ref))\n print('Error wake circulation: %.3e' % er)\n assert er < 1e-13, 'Steady-state gamma_star not matching!'\n\n er = np.max(np.abs(xsta[Dyn.K + Dyn.K_star:2 * Dyn.K + Dyn.K_star]))\n print('Error bound derivative: %.3e' % er)\n assert er < 1e-13, 'Non-zero derivative of circulation at steady state!'\n\n if Dyn.integr_order == 2:\n er = np.max(np.abs(xsta[:Dyn.K] - xsta[-Dyn.K:]))\n print('Error bound circulation previous vs current time-step: %.3e' % er)\n assert er < 1e-13, \\\n 'Circulation at previous and current time-step not matching'\n\n ### Verify gains\n Dyn.get_total_forces_gain()\n Dyn.get_sect_forces_gain()\n\n # sectional forces - algorithm for surfaces with equal M\n n_surf = Dyn.MS.n_surf\n M, N = Dyn.MS.MM[0], Dyn.MS.NN[0]\n fnodes = ysta.reshape((n_surf, 3, M + 1, N + 1))\n Fsect_ref = np.zeros((n_surf, 3, N + 1))\n Msect_ref = np.zeros((n_surf, 3, N + 1))\n\n for ss in range(n_surf):\n for nn in range(N + 1):\n for mm in range(M + 1):\n Fsect_ref[ss, :, nn] += fnodes[ss, :, mm, nn]\n arm = Dyn.MS.Surfs[ss].zeta[:, mm, nn] - Dyn.MS.Surfs[ss].zeta[:, M // 2, nn]\n Msect_ref[ss, :, nn] += np.cross(arm, fnodes[ss, :, mm, nn])\n\n Fsect = np.dot(Dyn.Kfsec, ysta).reshape((n_surf, 3, N + 1))\n assert np.max(np.abs(Fsect - Fsect_ref)) < 1e-12, \\\n 'Error in gains for cross-sectional forces'\n Msect = np.dot(Dyn.Kmsec, ysta).reshape((n_surf, 3, N + 1))\n assert np.max(np.abs(Msect - Msect_ref)) < 1e-12, \\\n 'Error in gains for cross-sectional forces'\n\n # total forces\n Ftot_ref = np.zeros((3,))\n for cc in range(3):\n Ftot_ref[cc] = np.sum(Fsect_ref[:, cc, :])\n Ftot = np.dot(Dyn.Kftot, ysta)\n assert np.max(np.abs(Ftot - Ftot_ref)) < 1e-11, \\\n 'Error in gains for total forces'\n\n def test_nondimss_dimss(self):\n \"\"\"\n Test scaling and unscaling of UVLM\n \"\"\"\n\n Sta = self.Sta\n\n # estimate reference quantities\n Uinf = np.linalg.norm(self.tsdata.u_ext[0][:, 0, 0])\n chord = np.linalg.norm(self.tsdata.zeta[0][:, -1, 0] - self.tsdata.zeta[0][:, 0, 0])\n rho = self.tsdata.rho\n\n ScalingDict = {'length': .5 * chord,\n 'speed': Uinf,\n 'density': rho}\n\n # reference\n Dyn0 = Dynamic(self.tsdata,\n dt=0.05,\n integr_order=2, RemovePredictor=True,\n UseSparse=True)\n Dyn0.assemble_ss()\n\n # scale/unscale\n Dyn1 = Dynamic(self.tsdata,\n dt=0.05,\n integr_order=2, RemovePredictor=True,\n UseSparse=True, ScalingDict=ScalingDict)\n Dyn1.assemble_ss()\n Dyn1.nondimss()\n Dyn1.dimss()\n libss.compare_ss(Dyn0.SS, Dyn1.SS, tol=1e-10)\n assert np.max(np.abs(Dyn0.SS.dt - Dyn1.SS.dt)) < 1e-12 * Dyn0.SS.dt, \\\n 'Scaling/unscaling of time-step not correct'\n\n def test_freqresp(self):\n\n Sta = self.Sta\n\n # estimate reference quantities\n Uinf = np.linalg.norm(self.tsdata.u_ext[0][:, 0, 0])\n chord = np.linalg.norm(\n self.tsdata.zeta[0][:, -1, 0] - self.tsdata.zeta[0][:, 0, 0])\n rho = self.tsdata.rho\n\n ScalingDict = {'length': .5 * chord,\n 'speed': Uinf,\n 'density': rho}\n\n kv = np.linspace(0, .5, 3)\n\n for use_sparse in [False, True]:\n for remove_predictor in [True, False]:\n ### ----- Dynamic class\n Dyn = Dynamic(self.tsdata,\n dt=0.05, ScalingDict=ScalingDict,\n integr_order=2, RemovePredictor=remove_predictor,\n UseSparse=use_sparse)\n Dyn.assemble_ss()\n Dyn.nondimss()\n Yref = libss.freqresp(Dyn.SS, kv)\n Ydyn = Dyn.freqresp(kv)\n ermax = np.max(np.abs(Ydyn - Yref))\n assert ermax < 1e-13, \\\n 'Dynamic.freqresp produces too large error (%.2e)!' % ermax\n\n ### ----- BlockDynamic class\n BlockDyn = DynamicBlock(self.tsdata,\n dt=0.05,\n ScalingDict=ScalingDict,\n integr_order=2, RemovePredictor=remove_predictor,\n UseSparse=use_sparse)\n BlockDyn.assemble_ss()\n BlockDyn.nondimss()\n Ydyn_block = BlockDyn.freqresp(kv)\n ermax = np.max(np.abs(Ydyn_block - Yref))\n assert ermax < 1e-13, \\\n 'Dynamic.freqresp produces too large error (%.2e)!' % ermax\n\n ### ----- Frequency class\n Freq = Frequency(self.tsdata, dt=0.05, ScalingDict=ScalingDict,\n integr_order=2, RemovePredictor=remove_predictor,\n UseSparse=use_sparse)\n Freq.assemble()\n Freq.nondimss()\n Yfreq = Freq.freqresp(kv)\n ermax = np.max(np.abs(Yfreq - Yref))\n assert ermax < 1e-13, \\\n 'Frequency.freqresp produces too large error (%.2e)!' % ermax\n\n def test_solve_step(self):\n\n Sta = self.Sta\n\n # estimate reference quantities\n Uinf = np.linalg.norm(self.tsdata.u_ext[0][:, 0, 0])\n chord = np.linalg.norm(\n self.tsdata.zeta[0][:, -1, 0] - self.tsdata.zeta[0][:, 0, 0])\n rho = self.tsdata.rho\n\n ScalingDict = {'length': .5 * chord,\n 'speed': Uinf,\n 'density': rho}\n\n ### build an input time history\n NT = 5\n Uin = np.random.rand(9 * Sta.Kzeta, NT)\n\n ### get size of output\n Ny = 3 * Sta.Kzeta\n Ydyn = np.zeros((Ny, NT))\n Yblock = np.zeros((Ny, NT))\n\n for integr_order in [1, 2]:\n\n Nx = (1 + integr_order) * Sta.K + Sta.K_star\n Xdyn = np.zeros((Nx, NT))\n Xblock = np.zeros((Nx, NT))\n\n for use_sparse in [True, False]:\n for remove_predictor in [True, False]:\n\n Xdyn *= 0.\n Xblock *= 0.\n Ydyn *= 0.\n Yblock *= 0.\n\n ### ----- Dynamic class\n Dyn = Dynamic(self.tsdata,\n dt=0.05,\n ScalingDict=ScalingDict,\n integr_order=integr_order, Remove=remove_predictor,\n UseSparse=use_sparse)\n Dyn.assemble_ss()\n Dyn.nondimss()\n\n for tt in range(1, NT):\n Xdyn[:, tt], Ydyn[:, tt] = \\\n Dyn.solve_step(Xdyn[:, tt - 1], Uin[:, tt - 1],\n transform_state=True)\n\n ### ----- BlockDynamic class\n BlockDyn = DynamicBlock(self.tsdata,\n dt=0.05,\n ScalingDict=ScalingDict,\n integr_order=integr_order, RemovePredictor=remove_predictor,\n UseSparse=use_sparse)\n BlockDyn.assemble_ss()\n BlockDyn.nondimss()\n\n for tt in range(1, NT):\n Xblock[:, tt], Yblock[:, tt] = \\\n BlockDyn.solve_step(Xdyn[:, tt - 1], Uin[:, tt - 1],\n transform_state=True)\n\n ermax = np.max(np.abs(Xdyn - Xblock)) / np.max(np.abs(Xdyn))\n\n assert ermax < 1e-14, \\\n ('solve_step methods in Dynamic and BlockDynamic not matching ' +\n ' (relative error %.2e)!' % ermax)\n\n ermax = np.max(np.abs(Ydyn - Yblock)) / np.max(np.abs(Ydyn))\n assert ermax < 1e-14, \\\n ('solve_step methods in Dynamic and BlockDynamic not matching ' +\n ' (relative error %.2e)!' % ermax)\n\n\n unittest.main()\n" }, { "path": "sharpy/linear/src/multisurfaces.py", "content": "\"\"\"Generation of multiple aerodynamic surfaces\n\nS. Maraniello, 25 May 2018\n\"\"\"\n\nimport numpy as np\nimport sharpy.linear.src.gridmapping as gridmapping\nimport sharpy.linear.src.surface as surface\nimport sharpy.linear.src.assembly as assembly\nimport sharpy.utils.cout_utils as cout\n\n\nclass MultiAeroGridSurfaces():\n \"\"\"\n Creates and assembles multiple aerodynamic surfaces from data\n \"\"\"\n\n def __init__(self, tsdata, vortex_radius, for_vel=np.zeros((6,))):\n \"\"\"\n Initialise from data structure at time step.\n\n Args:\n tsdata (sharpy.utils.datastructures.AeroTimeStepInfo): Linearisation time step\n vortex_radius (np.float): Distance below which induction is not computed\n for_vel (np.ndarray): Frame of reference velocity in the inertial (G) frame, including the angular velocity.\n \"\"\"\n\n self.tsdata0 = tsdata\n self.n_surf = tsdata.n_surf\n self.dimensions = tsdata.dimensions\n self.dimensions_star = tsdata.dimensions_star\n\n # allocate surfaces\n self.Surfs = []\n self.Surfs_star = []\n\n # allocate size lists - useful for global assembly\n self.NN = []\n self.MM = []\n self.KK = []\n self.KKzeta = []\n self.NN_star = []\n self.MM_star = []\n self.KK_star = []\n self.KKzeta_star = []\n\n for ss in range(self.n_surf):\n\n ### Allocate bound surfaces\n M, N = tsdata.dimensions[ss]\n Map = gridmapping.AeroGridMap(M, N)\n # try:\n # omega = tsdata.omega[ss]\n # except AttributeError:\n # omega = for_vel[3:]\n Surf = surface.AeroGridSurface(\n Map, zeta=tsdata.zeta[ss], gamma=tsdata.gamma[ss],\n vortex_radius=vortex_radius,\n u_ext=tsdata.u_ext[ss], zeta_dot=tsdata.zeta_dot[ss],\n gamma_dot=tsdata.gamma_dot[ss],\n rho=tsdata.rho,\n for_vel=for_vel)\n\n # generate geometry data\n Surf.generate_areas()\n Surf.generate_normals()\n Surf.aM, Surf.aN = 0.5, 0.5\n Surf.generate_collocations()\n self.Surfs.append(Surf)\n # store size\n self.MM.append(M)\n self.NN.append(N)\n self.KK.append(Map.K)\n self.KKzeta.append(Map.Kzeta)\n\n ### Allocate wake surfaces\n M, N = tsdata.dimensions_star[ss]\n Map = gridmapping.AeroGridMap(M, N)\n Surf = surface.AeroGridSurface(Map,\n zeta=tsdata.zeta_star[ss], gamma=tsdata.gamma_star[ss],\n vortex_radius=vortex_radius,\n rho=tsdata.rho)\n self.Surfs_star.append(Surf)\n # store size\n self.MM_star.append(M)\n self.NN_star.append(N)\n self.KK_star.append(Map.K)\n self.KKzeta_star.append(Map.Kzeta)\n\n\n def get_ind_velocities_at_target_collocation_points(self, target):\n \"\"\"\n Computes normal induced velocities at target surface collocation points.\n \"\"\"\n # Loop input surfaces\n for ss_in in range(self.n_surf):\n # Bound\n Surf_in = self.Surfs[ss_in]\n target.u_ind_coll += \\\n Surf_in.get_induced_velocity_over_surface(target,\n target='collocation', Project=False)\n\n # Wake\n Surf_in = self.Surfs_star[ss_in]\n target.u_ind_coll += \\\n Surf_in.get_induced_velocity_over_surface(target,\n target='collocation', Project=False)\n\n def get_ind_velocities_at_collocation_points(self):\n \"\"\"\n Computes normal induced velocities at collocation points.\n \"\"\"\n\n # Loop surfaces (where ind. velocity is computed)\n for ss_out in range(self.n_surf):\n\n # define array\n Surf_out = self.Surfs[ss_out]\n M_out, N_out = self.dimensions[ss_out]\n Surf_out.u_ind_coll = np.zeros((3, M_out, N_out))\n\n self.get_ind_velocities_at_target_collocation_points(Surf_out)\n\n\n def get_normal_ind_velocities_at_collocation_points(self):\n \"\"\"\n Computes normal induced velocities at collocation points.\n\n Note: for state-equation both projected and not projected induced\n velocities are required at the collocation points. Hence, this method\n tries to first the u_ind_coll attribute in each surface.\n \"\"\"\n\n # Loop surfaces (where ind. velocity is computed)\n for ss_out in range(self.n_surf):\n\n # define array\n Surf_out = self.Surfs[ss_out]\n M_out, N_out = self.dimensions[ss_out]\n # Surf_out.u_ind_coll_norm=np.empty((M_out,N_out))\n Surf_out.u_ind_coll_norm = np.zeros((M_out, N_out))\n\n if hasattr(Surf_out, 'u_ind_coll'):\n Surf_out.u_ind_coll_norm = \\\n Surf_out.project_coll_to_normal(Surf_out.u_ind_coll)\n\n else:\n # Loop input surfaces\n for ss_in in range(self.n_surf):\n # Bound\n Surf_in = self.Surfs[ss_in]\n Surf_out.u_ind_coll_norm += \\\n Surf_in.get_induced_velocity_over_surface(Surf_out,\n target='collocation', Project=True)\n\n # Wake\n Surf_in = self.Surfs_star[ss_in]\n Surf_out.u_ind_coll_norm += \\\n Surf_in.get_induced_velocity_over_surface(Surf_out,\n target='collocation', Project=True)\n\n def get_input_velocities_at_collocation_points(self):\n\n for surf in self.Surfs:\n if surf.u_input_coll is None:\n surf.get_input_velocities_at_collocation_points()\n\n # -------------------------------------------------------------------------\n\n def get_ind_velocities_at_segments(self, overwrite=False):\n \"\"\"\n Computes induced velocities at mid-segment points.\n \"\"\"\n\n # Loop surfaces (where ind. velocity is computed)\n for ss_out in range(self.n_surf):\n\n Surf_out = self.Surfs[ss_out]\n if hasattr(Surf_out, 'u_ind_seg') and (not overwrite):\n continue\n\n M_out, N_out = self.dimensions[ss_out]\n Surf_out.u_ind_seg = np.zeros((3, 4, M_out, N_out))\n\n # Loop input surfaces\n for ss_in in range(self.n_surf):\n # Buond\n Surf_in = self.Surfs[ss_in]\n Surf_out.u_ind_seg += \\\n Surf_in.get_induced_velocity_over_surface(Surf_out,\n target='segments', Project=False)\n\n # Wake\n Surf_in = self.Surfs_star[ss_in]\n Surf_out.u_ind_seg += \\\n Surf_in.get_induced_velocity_over_surface(Surf_out,\n target='segments', Project=False)\n\n def get_input_velocities_at_segments(self, overwrite=False):\n\n for surf in self.Surfs:\n if (surf.u_input_seg is not None) and (not overwrite):\n continue\n surf.get_input_velocities_at_segments()\n\n # -------------------------------------------------------------------------\n\n def get_joukovski_qs(self, overwrite=False):\n \"\"\"\n Returns quasi-steady forces over\n\n Warning: forces are stored in a NON-redundant format:\n (3,4,M,N)\n where the element\n (:,ss,mm,nn)\n is the contribution to the force over the ss-th segment due to the\n circulation of panel (mm,nn).\n\n \"\"\"\n\n # get input and induced velocities at segments\n self.get_input_velocities_at_segments(overwrite)\n self.get_ind_velocities_at_segments(overwrite)\n\n for ss in range(self.n_surf):\n Surf = self.Surfs[ss]\n Surf.get_joukovski_qs(gammaw_TE=self.Surfs_star[ss].gamma[0, :])\n\n def verify_non_penetration(self, print_info=False):\n \"\"\"\n Verify state variables fulfill non-penetration condition at bound\n surfaces\n \"\"\"\n\n # verify induced velocities have been computed\n for ss in range(self.n_surf):\n if not hasattr(self.Surfs[ss], 'u_ind_coll_norm'):\n self.get_normal_ind_velocities_at_collocation_points()\n break\n\n if print_info:\n print('Verifying non-penetration at bound...')\n for surf in self.Surfs:\n # project input velocities\n if surf.u_input_coll_norm is None:\n surf.get_normal_input_velocities_at_collocation_points()\n\n ErMax = np.max(np.abs(\n surf.u_ind_coll_norm + surf.u_input_coll_norm))\n if print_info:\n print('Surface %.2d max abs error: %.3e' % (ss, ErMax))\n\n assert ErMax < 1e-12 * np.max(np.abs(self.Surfs[0].u_ext)), \\\n 'Linearisation state does not verify the non-penetration condition!'\n\n # For rotating cases:\n # assert ErMax<1e-10*np.max(np.abs(self.Surfs[0].u_input_coll)),\\\n # \t'Linearisation state does not verify the non-penetration condition! %.3e > %.3e' % (ErMax, 1e-10*np.max(np.abs(self.Surfs[0].u_input_coll)))\n\n def verify_aic_coll(self, print_info=False):\n \"\"\"\n Verify aic at collocation points using non-penetration condition\n \"\"\"\n\n AIC_list, AIC_star_list = assembly.AICs(\n self.Surfs, self.Surfs_star, target='collocation', Project=True)\n\n ### Compute iduced velocity\n for ss_out in range(self.n_surf):\n Surf_out = self.Surfs[ss_out]\n Surf_out.u_ind_coll_norm = np.zeros((Surf_out.maps.K,))\n for ss_in in range(self.n_surf):\n # Bound surface\n Surf_in = self.Surfs[ss_in]\n aic = AIC_list[ss_out][ss_in]\n Surf_out.u_ind_coll_norm += np.dot(\n aic, Surf_in.gamma.reshape(-1, order='C'))\n\n # Wakes\n Surf_in = self.Surfs_star[ss_in]\n aic = AIC_star_list[ss_out][ss_in]\n Surf_out.u_ind_coll_norm += np.dot(\n aic, Surf_in.gamma.reshape(-1, order='C'))\n\n Surf_out.u_ind_coll_norm = \\\n Surf_out.u_ind_coll_norm.reshape((Surf_out.maps.M, Surf_out.maps.N))\n\n if print_info:\n print('Verifying AICs at collocation points...')\n i_surf = 0\n for surf in self.Surfs:\n # project input velocities\n if surf.u_input_coll_norm is None:\n surf.get_normal_input_velocities_at_collocation_points()\n\n ErMax = np.max(np.abs(\n surf.u_ind_coll_norm + surf.u_input_coll_norm))\n if print_info:\n print('Surface %.2d max abs error: %.3e' % (i_surf, ErMax))\n\n assert ErMax < 1e-12 * np.max(np.abs(self.Surfs[0].u_ext)), \\\n 'Linearisation state does not verify the non-penetration condition!'\n i_surf += 1\n\n # For rotating cases:\n # assert ErMax<1e-10*np.max(np.abs(self.Surfs[0].u_input_coll)),\\\n # 'Linearisation state does not verify the non-penetration condition! %.3e > %.3e' % (ErMax, 1e-10*np.max(np.abs(self.Surfs[0].u_input_coll)))\n\n def verify_joukovski_qs(self, print_info=False):\n \"\"\"\n Verify quasi-steady contribution for forces matches against SHARPy.\n \"\"\"\n\n if print_info:\n print('Verifying joukovski quasi-steady forces...')\n self.get_joukovski_qs()\n\n for ss in range(self.n_surf):\n Surf = self.Surfs[ss]\n\n Fhere = Surf.fqs.reshape((3, Surf.maps.Kzeta))\n Fref = self.tsdata0.forces[ss][0:3].reshape((3, Surf.maps.Kzeta))\n # Check if forces and ct_forces_list are the same:\n # Fref_check=np.array(self.tsdata0.ct_forces_list[6*ss:6*ss+3])\n # print('Check forces: ', Fref_check-Fref)\n ErMax = np.max(np.abs(Fhere - Fref))\n\n if print_info:\n print('Surface %.2d max abs error: %.3e' % (ss, ErMax))\n assert ErMax < 1e-12, 'Wrong quasi-steady force over surface %.2d!' % ss\n # For rotating cases:\n\n\n# assert ErMax<1e-8 ,'Wrong quasi-steady force over surface %.2d!'%ss\n\n\nif __name__ == '__main__':\n import read\n\n # select test case\n fname = '../test/h5input/goland_mod_Nsurf01_M003_N004_a040.aero_state.h5'\n # fname='../test/h5input/goland_mod_Nsurf02_M003_N004_a040.aero_state.h5'\n haero = read.h5file(fname)\n tsdata = haero.ts00000\n\n MS = MultiAeroGridSurfaces(tsdata, 1e-6) # vortex_radius\n\n # collocation points\n MS.get_normal_ind_velocities_at_collocation_points()\n MS.verify_non_penetration()\n MS.verify_aic_coll()\n\n # joukovski\n MS.verify_joukovski_qs()\n\n # embed()\n\n### verify u_induced\n" }, { "path": "sharpy/linear/src/surface.py", "content": "\"\"\"\nGeometrical methods for bound surfaces\n\n\nS. Maraniello, 20 May 2018\n\"\"\"\n\nimport numpy as np\nimport itertools\nimport sharpy.aero.utils.uvlmlib as uvlmlib # SHARPy's main uvlm interface with cpp\nimport sharpy.linear.src.uvlmutils as uvlmutils # library with UVLM solution methods\nfrom sharpy.aero.utils.uvlmlib import get_aic3_cpp\nimport sharpy.utils.cout_utils as cout\n\ndmver = np.array([0, 1, 1, 0]) # delta to go from (m,n) panel to (m,n) vertices\ndnver = np.array([0, 0, 1, 1])\n\n\nclass AeroGridGeo():\n r\"\"\"\n Allows retrieving geometrical information of a surface. Requires a\n gridmapping.AeroGridMap mapping structure in input and the surface vertices\n coordinates.\n\n Indices convention: each panel is characterised through the following\n indices:\n - m,n: chord/span-wise indices\n\n Methods:\n - get_*: retrieve information of a panel (e.g. normal, surface area)\n - generate_*: apply get_* method to each panel and store info into array.\n\n Interpolation matrices, W:\n - these are labelled as 'Wba', where 'a' defines the initial format, b the\n final. Hence, given the array vb, it holds va=Wab*vb\n\n \"\"\"\n\n def __init__(self,\n Map: 'gridmapping.AeroGridMap instance',\n zeta: 'Array of vertex coordinates at each surface',\n aM: 'chord-wise position of collocation point in panel' = 0.5,\n aN: 'span-wise position of collocation point in panel' = 0.5):\n\n self.maps = Map\n self.maps.map_all()\n self.zeta = zeta\n self.aM = aM\n self.aN = aN\n\n ### Mapping coefficients\n # self.wvc=self.get_panel_wcv(self.aM,self.aN)\n\n # -------------------------------------------------------------------------\n\n def get_panel_vertices_coords(self, m, n):\n \"\"\"\n Retrieves coordinates of panel (m,n) vertices.\n \"\"\"\n\n ###\n # mpv=self.maps.from_panel_to_vertices(m,n)\n\n ###\n # mpv=self.maps.Mpv[m,n,:,:]\n # zetav_here_ref=np.zeros((4,3),order='C')\n # for ii in range(4):\n # \tzetav_here_ref[ii,:]=self.zeta[:,mpv[ii,0],mpv[ii,1]]\n # zetav_here=self.zeta[:,dmver+m,dnver+n].T\n # assert np.max(np.abs(zetav_here-zetav_here_ref))<1e-16, embed()\n # return zetav_here\n\n ###\n # return self.zeta[:,dmver+m,dnver+n].T\n\n return self.zeta[:, [m + 0, m + 1, m + 1, m + 0], [n + 0, n + 0, n + 1, n + 1]].T\n\n # ------------------------------------------------------- get panel normals\n\n def generate_normals(self):\n\n M, N = self.maps.M, self.maps.N\n self.normals = np.zeros((3, M, N))\n\n for mm in range(M):\n for nn in range(N):\n zetav_here = self.get_panel_vertices_coords(mm, nn)\n self.normals[:, mm, nn] = uvlmutils.panel_normal(zetav_here)\n\n # -------------------------------------------------- get panel surface area\n\n def generate_areas(self):\n\n M, N = self.maps.M, self.maps.N\n self.areas = np.zeros((M, N))\n\n for mm in range(M):\n for nn in range(N):\n zetav_here = self.get_panel_vertices_coords(mm, nn)\n self.areas[mm, nn] = uvlmutils.panel_area(zetav_here)\n\n # -------------------------------------------------- get collocation points\n\n def get_panel_wcv(self):\n r\"\"\"\n Produces a compact array with weights for bilinear interpolation, where\n aN,aM in [0,1] are distances in the chordwise and spanwise directions\n such that:\n\n - (aM,aN)=(0,0) --> quantity at vertex 0\n\n - (aM,aN)=(1,0) --> quantity at vertex 1\n\n - (aM,aN)=(1,1) --> quantity at vertex 2\n\n - (aM,aN)=(0,1) --> quantity at vertex 3\n \"\"\"\n\n aM = self.aM\n aN = self.aN\n wcv = np.array([(1 - aM) * (1 - aN), aM * (1 - aN), aM * aN, aN * (1 - aM)])\n\n return wcv\n\n def get_panel_collocation(self, zetav_here):\n r\"\"\"\n Using bilinear interpolation, retrieves panel collocation point, where\n aN,aM in [0,1] are distances in the chordwise and spanwise directions\n such that:\n\n - (aM,aN)=(0,0) --> quantity at vertex 0\n\n - (aM,aN)=(1,0) --> quantity at vertex 1\n\n - (aM,aN)=(1,1) --> quantity at vertex 2\n\n - (aM,aN)=(0,1) --> quantity at vertex 3\n \"\"\"\n\n wcv = self.get_panel_wcv()\n zetac_here = np.dot(wcv, zetav_here)\n\n return zetac_here\n\n def generate_collocations(self):\n\n M, N = self.maps.M, self.maps.N\n self.zetac = np.zeros((3, M, N), order='F') # F order avoids the need to copy\n # when passing self.zetac[:,x,x] to\n # C written libraries.\n\n for mm in range(M):\n for nn in range(N):\n zetav_here = self.get_panel_vertices_coords(mm, nn)\n self.zetac[:, mm, nn] = self.get_panel_collocation(zetav_here)\n\n # -------------------------------------------------- get mid-segment points\n\n def get_panel_wsv(self):\n pass\n\n def get_panel_midsegments(self, zetav_here):\n pass\n\n def generate_midsegments():\n pass\n\n def generate_Wsv():\n pass\n\n # ----------------------------------------------- Interpolations/Projection\n\n def interp_vertex_to_coll(self, q_vert):\n \"\"\"\n Project a quantity q_vert (scalar or vector) defined at vertices to\n collocation points.\n \"\"\"\n\n M, N = self.maps.M, self.maps.N\n # embed()\n inshape = q_vert.shape\n assert inshape[-2] == M + 1 and inshape[-1] == N + 1, 'Unexpected shape of q_vert'\n\n # determine weights\n wcv = self.get_panel_wcv()\n\n if len(inshape) == 2:\n q_coll = np.zeros((M, N))\n for mm in range(M):\n for nn in range(N):\n # get q_vert at panel corners\n mpv = self.maps.from_panel_to_vertices(mm, nn)\n for vv in range(4):\n q_coll[mm, nn] = q_coll[mm, nn] + \\\n wcv[vv] * q_vert[mpv[vv, 0], mpv[vv, 1]]\n\n elif len(inshape) == 3:\n q_coll = np.zeros((3, M, N))\n for mm in range(M):\n for nn in range(N):\n # get q_vert at panel corners\n mpv = self.maps.from_panel_to_vertices(mm, nn)\n for vv in range(4):\n q_coll[:, mm, nn] = q_coll[:, mm, nn] + \\\n wcv[vv] * q_vert[:, mpv[vv, 0], mpv[vv, 1]]\n else:\n raise NameError('Unexpected shape of q_vert')\n\n return q_coll\n\n def project_coll_to_normal(self, q_coll):\n \"\"\"\n Project a vector quantity q_coll defined at collocation points to normal.\n \"\"\"\n\n M, N = self.maps.M, self.maps.N\n assert q_coll.shape == (3, M, N), 'Unexpected shape of q_coll'\n\n if not hasattr(self, 'normals'):\n self.generate_normals()\n\n q_proj = np.zeros((M, N))\n for mm in range(M):\n for nn in range(N):\n q_proj[mm, nn] = np.dot(self.normals[:, mm, nn], q_coll[:, mm, nn])\n\n return q_proj\n\n # ------------------------------------------------------- visualise surface\n\n def plot(self, plot_normals=False):\n\n try:\n import matplotlib.pyplot as plt\n\n fig = plt.figure()\n ax = fig.add_subplot(111, projection='3d')\n\n # Plot vertices grid\n ax.plot_wireframe(self.zeta[0], self.zeta[1], self.zeta[2])\n # rstride=10, cstride=10)\n\n # Plot collocation points\n ax.scatter(self.zetac[0], self.zetac[1], self.zetac[2], zdir='z', s=3, c='r')\n\n if plot_normals:\n ax.quiver(self.zetac[0], self.zetac[1], self.zetac[2],\n self.normals[0], self.normals[1], self.normals[2],\n length=0.01 * np.max(self.zeta), ) # normalize=True)\n\n self.ax = ax\n except ModuleNotFoundError:\n import warnings\n warnings.warn('Unable to import matplotlib, skipping plots')\n\n\nclass AeroGridSurface(AeroGridGeo):\n r\"\"\"\n Contains geometric and aerodynamic information about bound/wake surface.\n\n Compulsory input are those that apply to both bound and wake surfaces:\n - ``zeta``: defines geometry\n - ``gamma``: circulation\n\n With respect to :class:`.AeroGridGeo`, the class contains methods to:\n - project prescribed input velocity at nodes (``u_ext``, ``zeta_dot``) over\n collocation points.\n - compute induced velocity over ANOTHER surface.\n - compute AIC induced over ANOTHER surface\n\n Args:\n Map (gridmapping.AeroGridMap): Map of grid.\n zeta (list(np.ndarray)): Grid vertices coordinates in inertial (G) frame.\n zeta_dot (list(np.ndarray)): Grid vertices velocities in inertial (G) frame. Default is ``None``.\n vortex_radius (np.float): Distance below which induction is not computed\n u_ext (list(np.ndarray)): Grid external velocities in inertial (G) frame. Default is ``None``.\n gamma_dot (list(np.ndarray)): Panel circulation derivative. Default is ``None``.\n rho (float): Air density. Default is ``1.``\n aM (float): Chordwise position in panel of collocation point. Default is ``0.5``\n aN (float): Spanwise position in panel of collocation point. Default is ``0.5``\n for_vel (np.ndarray): Frame of reference velocity (including rotational velocity) in the inertial frame.\n\n To add:\n - project prescribed input velocity at nodes (u_ext, zeta_dot) over\n mid-point segments\n \"\"\"\n\n def __init__(self, Map, zeta, gamma,\n vortex_radius,\n u_ext=None,\n zeta_dot=None,\n gamma_dot=None,\n rho=1.,\n aM=0.5,\n aN=0.5,\n for_vel=np.zeros((6, ))):\n\n super().__init__(Map, zeta, aM, aN)\n\n self.gamma = gamma\n self.vortex_radius = vortex_radius\n self.zeta_dot = zeta_dot\n self.u_ext = u_ext\n self.gamma_dot = gamma_dot\n self.rho = rho\n self.omega = for_vel[3:]\n self.for_vel_tra = for_vel[:3]\n\n msg_out = 'wrong input shape!'\n assert self.gamma.shape == (self.maps.M, self.maps.N), \\\n 'Gamma shape %s not equal to M, N %s' % (str(self.gamma.shape), str((self.maps.M, self.maps.N)))\n assert self.zeta.shape == (3, self.maps.M + 1, self.maps.N + 1), \\\n 'Zeta shape %s not equal to 3, M+1, N+1 %s' % (str(self.zeta.shape), str((3, self.maps.M, self.maps.N)))\n if self.zeta_dot is not None:\n assert self.zeta_dot.shape == (3, self.maps.M + 1, self.maps.N + 1), \\\n 'zeta_dot shape %s not equal to 3, M+1, N+1 %s' % (str(self.zeta_dot.shape), str((3, self.maps.M, self.maps.N)))\n if self.u_ext is not None:\n assert self.u_ext.shape == (3, self.maps.M + 1, self.maps.N + 1), \\\n 'u_ext shape %s not equal to 3, M+1, N+1 %s' % (str(self.u_ext.shape), str((3, self.maps.M, self.maps.N)))\n assert for_vel.shape == (6, ), msg_out\n assert self.omega.shape == (3, ), msg_out\n assert self.for_vel_tra.shape == (3, ), msg_out\n\n self.u_input_coll = None # input velocities at the collocation points\n self.u_input_coll_norm = None # normal input velocities at the collocation points\n self.u_input_seg = None # input velocities at segments\n # -------------------------------------------------------- input velocities\n\n def get_input_velocities_at_collocation_points(self):\n r\"\"\"\n Returns velocities at collocation points from nodal values ``u_ext`` and\n ``zeta_dot`` of shape ``(3, M+1, N+1)`` at the collocation points.\n\n Notes:\n\n .. math:: \\boldsymbol{u}_{c} = \\mathcal{W}_{cv}(\\boldsymbol(\\nu)_0 - \\boldsymbol{\\zeta}_0)\n\n is the input velocity at the collocation point, where :math:`\\mathcal{W}_{cv}` projects the velocity\n from the grid points onto the collocation point. This variable is referred to as\n ``u_input_coll=Wcv*(u_ext-zeta_dot)`` and depends on the coordinates ``zeta`` when the body is rotating.\n\n \"\"\"\n\n # define total velocity\n if self.zeta_dot is not None:\n u_tot = self.u_ext - self.zeta_dot\n else:\n u_tot = self.u_ext\n\n # Include rotation\n for i_m in range(self.maps.M + 1):\n for i_n in range(self.maps.N + 1):\n u_tot[:, i_m, i_n] -= np.cross(self.omega, self.zeta[:, i_m, i_n]) + self.for_vel_tra\n\n self.u_input_coll = self.interp_vertex_to_coll(u_tot)\n\n def get_normal_input_velocities_at_collocation_points(self):\n \"\"\"\n From nodal input velocity to normal velocities at collocation points.\n \"\"\"\n\n # M,N=self.maps.M,self.maps.N\n\n # produce velocities at collocation points\n self.get_input_velocities_at_collocation_points()\n self.u_input_coll_norm = self.project_coll_to_normal(self.u_input_coll)\n\n def get_input_velocities_at_segments(self):\n \"\"\"\n Returns velocities at mid-segment points from nodal values u_ext and\n zeta_dot of shape (3,M+1,N+1).\n\n Warning: input velocities at grid segments are stored in a redundant\n format:\n (3,4,M,N)\n where the element\n (:,ss,mm,nn)\n is the induced velocity over the ss-th segment of panel (mm,nn). A fast\n looping is implemented to re-use previously computed velocities\n\n 2018/08/24: Include effects due to rotation (omega x zeta). Now it\n depends on the coordinates zeta\n \"\"\"\n\n # define total velocity\n if self.zeta_dot is not None:\n u_tot = self.u_ext - self.zeta_dot\n else:\n u_tot = self.u_ext\n\n # Include rotation\n for i_m in range(self.maps.M + 1):\n for i_n in range(self.maps.N + 1):\n u_tot[:, i_m, i_n] -= np.cross(self.omega, self.zeta[:, i_m, i_n]) + self.for_vel_tra\n\n M, N = self.maps.M, self.maps.N\n self.u_input_seg = np.empty((3, 4, M, N))\n\n # indiced as per self.maps\n dmver = [0, 1, 1, 0] # delta to go from (m,n) panel to (m,n) vertices\n dnver = [0, 0, 1, 1]\n svec = [0, 1, 2, 3] # seg. no.\n avec = [0, 1, 2, 3] # 1st vertex no.\n bvec = [1, 2, 3, 0] # 2nd vertex no.\n\n ##### panel (0,0): compute all\n mm, nn = 0, 0\n for ss, aa, bb in zip(svec, avec, bvec):\n uA = u_tot[:, mm + dmver[aa], nn + dnver[aa]]\n uB = u_tot[:, mm + dmver[bb], nn + dnver[bb]]\n self.u_input_seg[:, ss, mm, nn] = .5 * (uA + uB)\n\n ##### panels n=0: copy seg.3\n nn = 0\n svec = [0, 1, 2] # seg. no.\n avec = [0, 1, 2] # 1st vertex no.\n bvec = [1, 2, 3] # 2nd vertex no.\n for mm in range(1, M):\n for ss, aa, bb in zip(svec, avec, bvec):\n uA = u_tot[:, mm + dmver[aa], nn + dnver[aa]]\n uB = u_tot[:, mm + dmver[bb], nn + dnver[bb]]\n self.u_input_seg[:, ss, mm, nn] = .5 * (uA + uB)\n self.u_input_seg[:, 3, mm, nn] = self.u_input_seg[:, 1, mm - 1, nn]\n ##### panels m=0: copy seg.0\n mm = 0\n svec = [1, 2, 3] # seg. number\n avec = [1, 2, 3] # 1st vertex of seg.\n bvec = [2, 3, 0] # 2nd vertex of seg.\n for nn in range(1, N):\n for ss, aa, bb in zip(svec, avec, bvec):\n uA = u_tot[:, mm + dmver[aa], nn + dnver[aa]]\n uB = u_tot[:, mm + dmver[bb], nn + dnver[bb]]\n self.u_input_seg[:, ss, mm, nn] = .5 * (uA + uB)\n self.u_input_seg[:, 0, mm, nn] = self.u_input_seg[:, 2, mm, nn - 1]\n ##### all others: copy seg. 0 and 3\n svec = [1, 2] # seg. number\n avec = [1, 2] # 1st vertex of seg.\n bvec = [2, 3] # 2nd vertex of seg.\n for pp in itertools.product(range(1, M), range(1, N)):\n mm, nn = pp\n for ss, aa, bb in zip(svec, avec, bvec):\n uA = u_tot[:, mm + dmver[aa], nn + dnver[aa]]\n uB = u_tot[:, mm + dmver[bb], nn + dnver[bb]]\n self.u_input_seg[:, ss, mm, nn] = .5 * (uA + uB)\n self.u_input_seg[:, 0, mm, nn] = self.u_input_seg[:, 2, mm, nn - 1]\n self.u_input_seg[:, 3, mm, nn] = self.u_input_seg[:, 1, mm - 1, nn]\n\n return self\n\n # ------------------------------------------------------ induced velocities\n\n def get_induced_velocity(self, zeta_target):\n \"\"\"\n Computes induced velocity at a point zeta_target.\n \"\"\"\n\n M, N = self.maps.M, self.maps.N\n uind_target = np.zeros((3,), order='C')\n # uind_ref=np.zeros((3,),order='C')\n\n for mm in range(M):\n for nn in range(N):\n # panel info\n zetav_here = self.get_panel_vertices_coords(mm, nn)\n uind_target += uvlmlib.biot_panel_cpp(zeta_target,\n zetav_here,\n self.vortex_radius,\n self.gamma[mm, nn])\n\n return uind_target\n\n def get_aic3(self, zeta_target):\n \"\"\"\n Produces influence coefficinet matrix to calculate the induced velocity\n at a target point. The aic3 matrix has shape (3,K)\n \"\"\"\n\n K = self.maps.K\n aic3 = np.zeros((3, K))\n\n for cc in range(K):\n # define panel\n mm = self.maps.ind_2d_pan_scal[0][cc]\n nn = self.maps.ind_2d_pan_scal[1][cc]\n\n # get panel coordinates\n zetav_here = self.get_panel_vertices_coords(mm, nn)\n aic3[:, cc] = uvlmlib.biot_panel_cpp(zeta_target, zetav_here,\n self.vortex_radius,\n gamma=1.0)\n\n return aic3\n\n def get_induced_velocity_over_surface(self, Surf_target,\n target='collocation', Project=False):\n \"\"\"\n Computes induced velocity over an instance of AeroGridSurface, where\n target specifies the target grid (collocation or segments). If Project\n is True, velocities are projected onver panel normal (only available at\n collocation points).\n\n Note: for state-equation, both projected and non-projected velocities at\n the collocation points are required. Hence, it is suggested to use this\n method with Projection=False, and project afterwards.\n\n Warning: induced velocities at grid segments are stored in a redundant\n format:\n\n (3,4,M,N)\n\n where the element\n\n (:,ss,mm,nn)\n\n is the induced velocity over the ss-th segment of panel (mm,nn). A fast\n looping is implemented to re-use previously computed velocities\n \"\"\"\n\n M_trg = Surf_target.maps.M\n N_trg = Surf_target.maps.N\n\n if target == 'collocation':\n if not hasattr(Surf_target, 'zetac'):\n Surf_target.generate_collocations()\n ZetaTarget = Surf_target.zetac\n\n if Project:\n if not hasattr(Surf_target, 'normals'):\n Surf_target.generate_normals()\n Uind = np.empty((M_trg, N_trg))\n else:\n Uind = np.empty((3, M_trg, N_trg))\n\n # loop target points\n for pp in itertools.product(range(M_trg), range(N_trg)):\n mm, nn = pp\n uind = uvlmlib.get_induced_velocity_cpp(self.maps, self.zeta,\n self.gamma, ZetaTarget[:, mm, nn], self.vortex_radius)\n if Project:\n Uind[mm, nn] = np.dot(uind, Surf_target.normals[:, mm, nn])\n else:\n Uind[:, mm, nn] = uind\n\n if target == 'segments':\n\n if Project:\n raise NameError('Normal not defined for segment')\n\n Uind = np.zeros((3, 4, M_trg, N_trg))\n\n ##### panel (0,0): compute all\n mm, nn = 0, 0\n svec = [0, 1, 2, 3] # seg. number\n avec = [0, 1, 2, 3] # 1st vertex of seg.\n bvec = [1, 2, 3, 0] # 2nd vertex of seg.\n zetav_here = Surf_target.get_panel_vertices_coords(mm, nn)\n for ss, aa, bb in zip(svec, avec, bvec):\n zeta_mid = 0.5 * (zetav_here[aa, :] + zetav_here[bb, :])\n Uind[:, ss, mm, nn] = uvlmlib.get_induced_velocity_cpp(self.maps,\n self.zeta, self.gamma, zeta_mid, self.vortex_radius)\n\n ##### panels n=0: copy seg.3\n nn = 0\n svec = [0, 1, 2] # seg. number\n avec = [0, 1, 2] # 1st vertex of seg.\n bvec = [1, 2, 3] # 2nd vertex of seg.\n for mm in range(1, M_trg):\n zetav_here = Surf_target.get_panel_vertices_coords(mm, nn)\n for ss, aa, bb in zip(svec, avec, bvec):\n zeta_mid = 0.5 * (zetav_here[aa, :] + zetav_here[bb, :])\n Uind[:, ss, mm, nn] = uvlmlib.get_induced_velocity_cpp(self.maps,\n self.zeta, self.gamma, zeta_mid, self.vortex_radius)\n Uind[:, 3, mm, nn] = Uind[:, 1, mm - 1, nn]\n\n ##### panels m=0: copy seg.0\n mm = 0\n svec = [1, 2, 3] # seg. number\n avec = [1, 2, 3] # 1st vertex of seg.\n bvec = [2, 3, 0] # 2nd vertex of seg.\n for nn in range(1, N_trg):\n zetav_here = Surf_target.get_panel_vertices_coords(mm, nn)\n for ss, aa, bb in zip(svec, avec, bvec):\n zeta_mid = 0.5 * (zetav_here[aa, :] + zetav_here[bb, :])\n Uind[:, ss, mm, nn] = uvlmlib.get_induced_velocity_cpp(self.maps,\n self.zeta, self.gamma, zeta_mid, self.vortex_radius)\n Uind[:, 0, mm, nn] = Uind[:, 2, mm, nn - 1]\n\n ##### all others: copy seg. 0 and 3\n svec = [1, 2] # seg. number\n avec = [1, 2] # 1st vertex of seg.\n bvec = [2, 3] # 2nd vertex of seg.\n for pp in itertools.product(range(1, M_trg), range(1, N_trg)):\n mm, nn = pp\n zetav_here = Surf_target.get_panel_vertices_coords(*pp)\n for ss, aa, bb in zip(svec, avec, bvec):\n zeta_mid = 0.5 * (zetav_here[aa, :] + zetav_here[bb, :])\n Uind[:, ss, mm, nn] = uvlmlib.get_induced_velocity_cpp(self.maps,\n self.zeta, self.gamma, zeta_mid, self.vortex_radius)\n Uind[:, 0, mm, nn] = Uind[:, 2, mm, nn - 1]\n Uind[:, 3, mm, nn] = Uind[:, 1, mm - 1, nn]\n\n return Uind\n\n def get_aic_over_surface(self, Surf_target,\n target='collocation', Project=True):\n r\"\"\"\n Produces influence coefficient matrices such that the velocity induced\n over the Surface_target is given by the product:\n\n .. code-block:: python\n\n if target=='collocation':\n if Project:\n u_ind_coll_norm.rehape(-1)=AIC*self.gamma.reshape(-1,order='C')\n else:\n u_ind_coll_norm[ii,:,:].rehape(-1)=\n AIC[ii,:,:]*self.gamma.reshape(-1,order='C')\n\n where ``ii=0,1,2``.\n\n For the case where ``if target=='segments'``:\n\n - AIC has shape (3,self.maps.K,4,Mout,Nout), such that\n\n ``AIC[:,:,ss,mm,nn]``\n\n is the influence coefficient matrix associated to the induced\n velocity at segment ss of panel (mm,nn).\n \"\"\"\n\n K_in = self.maps.K\n\n if target == 'collocation':\n\n K_out = Surf_target.maps.K\n if not hasattr(Surf_target, 'zetac'):\n Surf_target.generate_collocations()\n ZetaTarget = Surf_target.zetac\n\n if Project:\n if not hasattr(Surf_target, 'normals'):\n Surf_target.generate_normals()\n AIC = np.empty((K_out, K_in))\n else:\n AIC = np.empty((3, K_out, K_in))\n\n # loop target points\n for cc in range(K_out):\n # retrieve panel coords\n mm = Surf_target.maps.ind_2d_pan_scal[0][cc]\n nn = Surf_target.maps.ind_2d_pan_scal[1][cc]\n # retrieve influence coefficients\n # ref_aic3=self.get_aic3(ZetaTarget[:,mm,nn])\n aic3 = get_aic3_cpp(self.maps, self.zeta, ZetaTarget[:, mm, nn],\n self.vortex_radius)\n # assert np.max(np.abs(aic3-ref_aic3))<1e-13, embed()\n\n if Project:\n AIC[cc, :] = np.dot(Surf_target.normals[:, mm, nn], aic3)\n else:\n AIC[:, cc, :] = aic3\n\n if target == 'segments':\n if Project:\n raise NameError('Normal not defined at collocation points')\n\n M_trg, N_trg = Surf_target.maps.M, Surf_target.maps.N\n AIC = np.zeros((3, K_in, 4, M_trg, N_trg))\n\n ##### panel (0,0): compute all\n mm, nn = 0, 0\n svec = [0, 1, 2, 3] # seg. number\n avec = [0, 1, 2, 3] # 1st vertex of seg.\n bvec = [1, 2, 3, 0] # 2nd vertex of seg.\n zetav_here = Surf_target.get_panel_vertices_coords(mm, nn)\n for ss, aa, bb in zip(svec, avec, bvec):\n zeta_mid = 0.5 * (zetav_here[aa, :] + zetav_here[bb, :])\n AIC[:, :, ss, mm, nn] = get_aic3_cpp(self.maps, self.zeta,\n zeta_mid, self.vortex_radius)\n\n ##### panels n=0: copy seg.3\n nn = 0\n svec = [0, 1, 2] # seg. number\n avec = [0, 1, 2] # 1st vertex of seg.\n bvec = [1, 2, 3] # 2nd vertex of seg.\n for mm in range(1, M_trg):\n zetav_here = Surf_target.get_panel_vertices_coords(mm, nn)\n for ss, aa, bb in zip(svec, avec, bvec):\n zeta_mid = 0.5 * (zetav_here[aa, :] + zetav_here[bb, :])\n AIC[:, :, ss, mm, nn] = get_aic3_cpp(self.maps, self.zeta,\n zeta_mid, self.vortex_radius)\n AIC[:, :, 3, mm, nn] = AIC[:, :, 1, mm - 1, nn]\n\n ##### panels m=0: copy seg.0\n mm = 0\n svec = [1, 2, 3] # seg. number\n avec = [1, 2, 3] # 1st vertex of seg.\n bvec = [2, 3, 0] # 2nd vertex of seg.\n for nn in range(1, N_trg):\n zetav_here = Surf_target.get_panel_vertices_coords(mm, nn)\n for ss, aa, bb in zip(svec, avec, bvec):\n zeta_mid = 0.5 * (zetav_here[aa, :] + zetav_here[bb, :])\n AIC[:, :, ss, mm, nn] = get_aic3_cpp(self.maps, self.zeta,\n zeta_mid, self.vortex_radius)\n AIC[:, :, 0, mm, nn] = AIC[:, :, 2, mm, nn - 1]\n\n ##### all others: copy seg. 0 and 3\n svec = [1, 2] # seg. number\n avec = [1, 2] # 1st vertex of seg.\n bvec = [2, 3] # 2nd vertex of seg.\n for pp in itertools.product(range(1, M_trg), range(1, N_trg)):\n mm, nn = pp\n zetav_here = Surf_target.get_panel_vertices_coords(*pp)\n for ss, aa, bb in zip(svec, avec, bvec):\n zeta_mid = 0.5 * (zetav_here[aa, :] + zetav_here[bb, :])\n AIC[:, :, ss, mm, nn] = get_aic3_cpp(self.maps, self.zeta,\n zeta_mid, self.vortex_radius)\n AIC[:, :, 3, mm, nn] = AIC[:, :, 1, mm - 1, nn]\n AIC[:, :, 0, mm, nn] = AIC[:, :, 2, mm, nn - 1]\n\n return AIC\n\n # ------------------------------------------------------------------ forces\n\n def get_joukovski_qs(self, gammaw_TE=None, recompute_velocities=True):\n \"\"\"\n Returns quasi-steady forces evaluated at mid-segment points over the\n surface.\n\n Important: the circulation at the first row of wake panel is required!\n Hence all\n\n Warning: forces are stored in a NON-redundant format:\n (3,4,M,N)\n where the element\n (:,ss,mm,nn)\n is the contribution to the force over the ss-th segment due to the\n circulation of panel (mm,nn).\n \"\"\"\n\n if self.u_input_seg is None:\n if not recompute_velocities:\n print(\"WARNING: recomputing velocities\")\n self.get_input_velocities_at_segments()\n if not hasattr(self, 'u_ind_seg'):\n raise NameError('u_ind_seg not available!')\n\n M, N = self.maps.M, self.maps.N\n self.fqs_seg_unit = np.zeros((3, 4, M, N))\n self.fqs = np.zeros((3, M + 1, N + 1))\n\n # indiced as per self.maps\n dmver = [0, 1, 1, 0] # delta to go from (m,n) panel to (m,n) vertices\n dnver = [0, 0, 1, 1]\n svec = [0, 1, 2, 3] # seg. no.\n avec = [0, 1, 2, 3] # 1st vertex no.\n bvec = [1, 2, 3, 0] # 2nd vertex no.\n\n ### force produced by BOUND panels\n for pp in itertools.product(range(0, M), range(0, N)):\n mm, nn = pp\n zetav_here = self.get_panel_vertices_coords(mm, nn)\n for ss, aa, bb in zip(svec, avec, bvec):\n df = uvlmutils.joukovski_qs_segment(\n zetaA=zetav_here[aa, :], zetaB=zetav_here[bb, :],\n v_mid=self.u_ind_seg[:, ss, mm, nn] + self.u_input_seg[:, ss, mm, nn],\n gamma=1.0, fact=self.rho)\n self.fqs_seg_unit[:, ss, mm, nn] = df\n # project on vertices\n self.fqs[:, mm + dmver[aa], nn + dnver[aa]] += 0.5 * self.gamma[mm, nn] * df\n self.fqs[:, mm + dmver[bb], nn + dnver[bb]] += 0.5 * self.gamma[mm, nn] * df\n\n ### force produced by wake T.E. segments\n # Note:\n # 1. zetaA & zetaB are ordered such that the wake circulation is\n # subtracts to the bound circulation over TE segment\n # 2. the TE segment corresponds to seg.1 of the last row of BOUND panels\n if gammaw_TE is None:\n raise NameError('Enter gammaw_TE - option disabled for debugging')\n gammaw_TE = self.gamma[M - 1, :]\n\n self.fqs_wTE_unit = np.zeros((3, N))\n\n for nn in range(N):\n df = uvlmutils.joukovski_qs_segment(\n zetaA=self.zeta[:, M, nn + 1],\n zetaB=self.zeta[:, M, nn],\n v_mid=self.u_input_seg[:, 1, M - 1, nn] + self.u_ind_seg[:, 1, M - 1, nn],\n gamma=1.0,\n fact=self.rho)\n # record force on TE due to wake and project\n self.fqs_wTE_unit[:, nn] = df\n self.fqs[:, M, nn + 1] += 0.5 * gammaw_TE[nn] * df\n self.fqs[:, M, nn] += 0.5 * gammaw_TE[nn] * df\n\n return self\n\n def get_joukovski_unsteady(self):\n \"\"\"\n Returns added mass effects over lattive grid\n \"\"\"\n\n if self.gamma_dot is None:\n raise NameError('circulation derivative not specified!')\n if not hasattr(self, 'areas'):\n self.generate_areas()\n\n M, N = self.maps.M, self.maps.N\n self.funst = np.zeros((3, M + 1, N + 1))\n wcv = self.get_panel_wcv()\n\n for pp in itertools.product(range(0, M), range(0, N)):\n mm, nn = pp\n\n # force at collocation point\n fcoll = -self.rho * self.areas[mm, nn] * self.normals[:, mm, nn] * self.gamma_dot[mm, nn]\n\n # project at vertices\n for vv in range(4):\n self.funst[:, mm + dmver[vv], nn + dnver[vv]] += wcv[vv] * fcoll\n" }, { "path": "sharpy/linear/src/uvlmutils.py", "content": "\"\"\"Methods for UVLM solution\n\nS. Maraniello, 1 Jun 2018\n\"\"\"\nimport numpy as np\nimport sharpy.aero.utils.uvlmlib as uvlmlib\nimport sharpy.utils.algebra as algebra\nfrom sharpy.utils.constants import cfact_biot\n\n# local mapping segment/vertices of a panel\nsvec = [0, 1, 2, 3] # seg. number\navec = [0, 1, 2, 3] # 1st vertex of seg.\nbvec = [1, 2, 3, 0] # 2nd vertex of seg.\nLoopPanel = [(0, 1), (1, 2), (2, 3), (3, 0)] # used in eval_panel_{exp/comp}\n\n\ndef joukovski_qs_segment(zetaA, zetaB, v_mid, gamma=1.0, fact=0.5):\n \"\"\"\n Joukovski force over vetices A and B produced by the segment A->B.\n The factor fact allows to compute directly the contribution over the\n vertices A and B (e.g. 0.5) or include DENSITY.\n \"\"\"\n\n rab = zetaB - zetaA\n fs = algebra.cross3(v_mid, rab)\n gfact = fact * gamma\n\n return gfact * fs\n\n\ndef biot_segment(zetaP, zetaA, zetaB, vortex_radius, gamma=1.0):\n \"\"\"\n Induced velocity of segment A_>B of circulation gamma over point P.\n \"\"\"\n\n vortex_radius_sq = vortex_radius*vortex_radius\n # differences\n ra = zetaP - zetaA\n rb = zetaP - zetaB\n rab = zetaB - zetaA\n ra_norm, rb_norm = algebra.norm3d(ra), algebra.norm3d(rb)\n vcross = algebra.cross3(ra, rb)\n vcross_sq = np.dot(vcross, vcross)\n\n # numerical radius\n if vcross_sq < (vortex_radius_sq * algebra.normsq3d(rab)):\n return np.zeros((3,))\n\n q = ((cfact_biot * gamma / vcross_sq) * \\\n (np.dot(rab, ra) / ra_norm - np.dot(rab, rb) / rb_norm)) * vcross\n\n return q\n\n\ndef biot_panel(zetaC, ZetaPanel, vortex_radius, gamma=1.0):\n \"\"\"\n Induced velocity over point ZetaC of a panel of vertices coordinates\n ZetaPanel and circulaiton gamma, where:\n ZetaPanel.shape=(4,3)=[vertex local number, (x,y,z) component]\n \"\"\"\n\n q = np.zeros((3,))\n for ss, aa, bb in zip(svec, avec, bvec):\n q += biot_segment(zetaC, ZetaPanel[aa, :], ZetaPanel[bb, :],\n vortex_radius, gamma)\n\n return q\n\n\ndef biot_panel_fast(zetaC, ZetaPanel, vortex_radius, gamma=1.0):\n \"\"\"\n Induced velocity over point ZetaC of a panel of vertices coordinates\n ZetaPanel and circulaiton gamma, where:\n ZetaPanel.shape=(4,3)=[vertex local number, (x,y,z) component]\n \"\"\"\n\n vortex_radius_sq = vortex_radius*vortex_radius\n Cfact = cfact_biot * gamma\n q = np.zeros((3,))\n\n R_list = zetaC - ZetaPanel\n Runit_list = [R_list[ii] / algebra.norm3d(R_list[ii]) for ii in svec]\n\n for aa, bb in LoopPanel:\n\n RAB = ZetaPanel[bb, :] - ZetaPanel[aa, :] # segment vector\n Vcr = algebra.cross3(R_list[aa], R_list[bb])\n vcr2 = np.dot(Vcr, Vcr)\n if vcr2 < (vortex_radius * algebra.normsq3d(RAB)):\n continue\n\n q += ((Cfact / vcr2) * np.dot(RAB, Runit_list[aa] - Runit_list[bb])) * Vcr\n\n return q\n\n\ndef panel_normal(ZetaPanel):\n \"\"\"\n return normal of panel with vertex coordinates ZetaPanel, where:\n ZetaPanel.shape=(4,3)\n \"\"\"\n\n # build cross-vectors\n r02 = ZetaPanel[2, :] - ZetaPanel[0, :]\n r13 = ZetaPanel[3, :] - ZetaPanel[1, :]\n\n nvec = algebra.cross3(r02, r13)\n nvec = nvec / algebra.norm3d(nvec)\n\n return nvec\n\n\ndef panel_area(ZetaPanel):\n \"\"\"\n return area of panel with vertices coordinates ZetaPanel, where:\n ZetaPanel.shape=(4,3)\n using Bretschneider formula - for cyclic or non-cyclic quadrilaters.\n \"\"\"\n\n # build cross-vectors\n r02 = ZetaPanel[2, :] - ZetaPanel[0, :]\n r13 = ZetaPanel[3, :] - ZetaPanel[1, :]\n # build side vectors\n r01 = ZetaPanel[1, :] - ZetaPanel[0, :]\n r12 = ZetaPanel[2, :] - ZetaPanel[1, :]\n r23 = ZetaPanel[3, :] - ZetaPanel[2, :]\n r30 = ZetaPanel[0, :] - ZetaPanel[3, :]\n\n # compute distances\n d02 = algebra.norm3d(r02)\n d13 = algebra.norm3d(r13)\n d01 = algebra.norm3d(r01)\n d12 = algebra.norm3d(r12)\n d23 = algebra.norm3d(r23)\n d30 = algebra.norm3d(r30)\n\n A = 0.25 * np.sqrt((4. * d02 ** 2 * d13 ** 2) - ((d12 ** 2 + d30 ** 2) - (d01 ** 2 + d23 ** 2)) ** 2)\n\n return A\n\n\nif __name__ == '__main__':\n\n import cProfile\n\n ### verify consistency amongst models\n gamma = 4.\n zeta0 = np.array([1.0, 3.0, 0.9])\n zeta1 = np.array([5.0, 3.1, 1.9])\n zeta2 = np.array([4.8, 8.1, 2.5])\n zeta3 = np.array([0.9, 7.9, 1.7])\n ZetaPanel = np.array([zeta0, zeta1, zeta2, zeta3])\n\n zetaP = np.array([3.0, 5.5, 2.0])\n zetaP = zeta2 * 0.3 + zeta3 * 0.7\n\n ### verify model consistency\n qref = biot_panel(zetaP, ZetaPanel, 1e-6, gamma=gamma) # vortex_radius\n qfast = biot_panel_fast(zetaP, ZetaPanel, 1e-6, gamma=gamma) # vortex_radius\n qcpp = uvlmlib.biot_panel_cpp(zetaP, ZetaPanel, 1e-6, gamma=gamma) # vortex_radius\n\n ermax = np.max(np.abs(qref - qfast))\n assert ermax < 1e-16, 'biot_panel_fast not matching with biot_panel'\n ermax = np.max(np.abs(qref - qcpp))\n assert ermax < 1e-16, 'biot_panel_cpp not matching with biot_panel'\n\n\n ### profiling\n def run_biot_panel_cpp():\n for ii in range(10000):\n uvlmlib.biot_panel_cpp(zetaP, ZetaPanel, 1e-6, gamma=3.) # vortex_radius\n\n\n def run_biot_panel_fast():\n for ii in range(10000):\n biot_panel_fast(zetaP, ZetaPanel, 1e-6, gamma=3.) # vortex_radius\n\n\n def run_biot_panel_ref():\n for ii in range(10000):\n biot_panel(zetaP, ZetaPanel, 1e-6, gamma=3.) # vortex_radius\n\n\n print('------------------------------------------ profiling biot_panel_cpp')\n cProfile.runctx('run_biot_panel_cpp()', globals(), locals())\n\n print('----------------------------------------- profiling biot_panel_fast')\n cProfile.runctx('run_biot_panel_fast()', globals(), locals())\n\n print('------------------------------------------ profiling biot_panel_ref')\n cProfile.runctx('run_biot_panel_ref()', globals(), locals())\n" }, { "path": "sharpy/linear/utils/__init__.py", "content": "" }, { "path": "sharpy/linear/utils/derivatives.py", "content": "import h5py\nimport numpy as np\n\nfrom sharpy.utils import algebra as algebra, cout_utils as cout\n\n\nclass Derivatives:\n \"\"\"\n Class containing the derivatives set for a given state-space system (i.e. aeroelastic or aerodynamic)\n \"\"\"\n def __init__(self, reference_dimensions, static_state, target_system=None):\n\n self.target_system = target_system # type: str # name of target system (aerodynamic/aeroelastic)\n self.transfer_function = None # type: np.array # matrix of steady-state TF for target system\n\n self.static_state = static_state # type: tuple # [fx, fy, fz] at ref state\n self.reference_dimensions = reference_dimensions # type: dict # name: ref_dimension_value dictionary\n\n self.separator = '\\n' + 80 * '#' + '\\n'\n\n self.dict_of_derivatives = {} # type: dict # {name:DerivativeSet} Each of the derivative sets DerivativeSet\n\n s_ref = self.reference_dimensions['S_ref']\n b_ref = self.reference_dimensions['b_ref']\n c_ref = self.reference_dimensions['c_ref']\n u_inf = self.reference_dimensions['u_inf']\n rho = self.reference_dimensions['rho']\n self.dynamic_pressure = 0.5 * rho * u_inf ** 2\n\n self.coefficients = {'force': self.dynamic_pressure * s_ref,\n 'moment_lon': self.dynamic_pressure * s_ref * c_ref,\n 'moment_lat': self.dynamic_pressure * s_ref * b_ref,\n 'force_angular_vel': self.dynamic_pressure * s_ref * c_ref / u_inf,\n 'moment_lon_angular_vel': self.dynamic_pressure * s_ref * c_ref * c_ref / u_inf} # missing rates\n\n self.steady_coefficients = np.array(self.static_state) / self.coefficients['force']\n\n self.filename = 'stability_derivatives.txt'\n if target_system is not None:\n self.filename = target_system + '_' + self.filename\n\n self.cg = None\n\n def initialise_derivatives(self, state_space, steady_forces, quat, v0, phi=None, cg=None, tpa=None):\n \"\"\"\n Initialises the required class attributes for all derivative calculations/\n\n Args:\n state_space (sharpy.linear.src.libss.StateSpace): State-space object for the target system\n steady_forces (np.array): Array of steady forces (at the linearisation) expressed in the beam degrees of\n freedom and with size equal to the number of structural degrees of freedom\n quat (np.array): Quaternion at the linearisation reference state\n v0 (np.array): Free stream velocity vector at the linearisation condition\n phi (np.array (optional)): Mode shape matrix for modal systems\n tpa (np.array (optional)): Transformation matrix onto principal axes\n\n \"\"\"\n cls = DerivativeSet # explain what is the DerivativeSet class\n if cls.quat is None:\n cls.quat = quat\n cls.cga = algebra.quat2rotation(cls.quat)\n cls.v0 = v0\n cls.coefficients = self.coefficients\n\n if phi is not None:\n cls.modal = True\n cls.phi = phi[-9:-3, :6]\n cls.inv_phi_forces = np.linalg.inv(phi[-9:-3, :6].T)\n cls.inv_phi_vel = np.linalg.inv(phi[-9:-3, :6])\n else:\n cls.modal = False\n cls.steady_forces = steady_forces\n\n H0 = state_space.freqresp(np.array([1e-5]))[:, :, 0].real\n if cls.modal:\n vel_inputs_variables = state_space.input_variables.get_variable_from_name('q_dot')\n output_indices = state_space.output_variables.get_variable_from_name('Q').rows_loc[:6]\n cls.steady_forces = cls.inv_phi_forces.dot(cls.steady_forces[output_indices])\n else:\n vel_inputs_variables = state_space.input_variables.get_variable_from_name('beta')\n output_indices = state_space.output_variables.get_variable_from_name('forces_n').rows_loc[-9:-3]\n cls.steady_forces = cls.steady_forces[output_indices]\n rbm_indices = vel_inputs_variables.cols_loc[:9]\n\n # look for control surfaces\n try:\n cs_input_variables = state_space.input_variables.get_variable_from_name('control_surface_deflection')\n dot_cs_input_variables = state_space.input_variables.get_variable_from_name('dot_control_surface_deflection')\n except ValueError:\n cs_indices = np.array([], dtype=int)\n dot_cs_indices = np.array([], dtype=int)\n cls.n_control_surfaces = 0\n else:\n cs_indices = cs_input_variables.cols_loc\n dot_cs_indices = dot_cs_input_variables.cols_loc\n cls.n_control_surfaces = cs_input_variables.size\n finally:\n input_indices = np.concatenate((rbm_indices, cs_indices, dot_cs_indices))\n\n self.transfer_function = H0[np.ix_(output_indices, input_indices)].real\n\n self.cg = cg\n self.tpa = tpa\n\n def save(self, output_route):\n with h5py.File(output_route + '/' + self.filename.replace('.txt', '.h5'), 'w') as f:\n for k, v in self.dict_of_derivatives.items():\n if v.matrix is None:\n continue\n f.create_dataset(name=k, data=v.matrix)\n\n def savetxt(self, folder):\n\n filename = self.filename\n\n u_inf = self.reference_dimensions['u_inf']\n s_ref = self.reference_dimensions['S_ref']\n b_ref = self.reference_dimensions['b_ref']\n c_ref = self.reference_dimensions['c_ref']\n rho = self.reference_dimensions['rho']\n quat = self.reference_dimensions['quat']\n euler_orient = algebra.quat2euler(quat) * 180/np.pi\n\n labels_out = ['CD', 'CY', 'CL', 'Cl', 'Cm', 'Cn']\n\n separator = '\\n' + 80*'#' + '\\n'\n\n with open(folder + '/' + filename, mode='w') as outfile:\n outfile.write('SHARPy Stability Derivatives Analysis\\n')\n\n outfile.write('State:\\n')\n outfile.write('\\t{:4f}\\t\\t\\t # Free stream velocity\\n'.format(u_inf))\n outfile.write('\\t{:4f}\\t\\t\\t # Free stream density\\n'.format(rho))\n outfile.write('\\t{:4f}\\t\\t\\t # Alpha [deg]\\n'.format(euler_orient[1]))\n outfile.write('\\t{:4f}\\t\\t\\t # Beta [deg]\\n'.format(euler_orient[2]))\n\n if self.cg is not None:\n outfile.write(separator)\n outfile.write('Centre of Gravity:\\n')\n lab = ('x', 'y', 'z')\n for i in range(3):\n outfile.write('\\t{:s}_A = {:.4f}\\t\\t\\t # [m]\\n'.format(lab[i], self.cg[i]))\n\n if self.tpa is not None:\n outfile.write('Principal Axes Directions (expressed in the A frame):\\n')\n for i in range(3):\n outfile.write('\\t{:s}_ppal in A = [{:.4f}, {:.4f}, {:.4f}]\\t\\t\\t\\n'.format(\n lab[i], *self.tpa.dot(np.eye(3)[:, i])))\n\n outfile.write(separator)\n outfile.write('\\nReference Dimensions:\\n')\n outfile.write('\\t{:4f}\\t\\t\\t # Reference planform area\\n'.format(s_ref))\n outfile.write('\\t{:4f}\\t\\t\\t # Reference chord\\n'.format(c_ref))\n outfile.write('\\t{:4f}\\t\\t\\t # Reference span\\n'.format(b_ref))\n\n outfile.write(separator)\n outfile.write('\\nCoefficients:\\n')\n for ith, coeff in enumerate(self.steady_coefficients):\n outfile.write('\\t{:4e}\\t\\t\\t # {:s}\\n'.format(coeff, labels_out[ith]))\n\n outfile.write(separator)\n\n # this needs to be out of with open as it is done in each of the Derivatives objects\n for derivative_set in self.dict_of_derivatives.values():\n if derivative_set.matrix is None:\n continue\n derivative_set.print(derivative_filename=folder + '/' + filename)\n\n def new_derivative(self, frame_of_reference, derivative_calculation=None, name=None):\n \"\"\"\n Returns a DerivativeSet() instance with the appropriate transfer function included\n for the relevant target system.\n\n Args:\n frame_of_reference (str): Output frame of reference. Body or Stability. (Not Yet Implemented)\n derivative_calculation (str): Name of function used to create derivative set\n name (str (optional)): Optional custom name to use as title in output.\n\n Returns:\n DerivativeSet: Instance of class with the relevant transfer function for the current\n target system.\n \"\"\"\n new_derivative = DerivativeSet(frame_of_reference, derivative_calculation,\n name,\n transfer_function=self.transfer_function)\n\n return new_derivative\n\n\nclass DerivativeSet:\n \"\"\"\n Class containing the stability derivative set for each of the input/output combinations. A derivative set may be\n force/angle or force/control_surface, for example.\n\n The class attributes contain the parameters common across all derivative sets. The instance attributes those\n pertaining to the specific set.\n \"\"\"\n steady_forces = None\n coefficients = None\n quat = None\n\n cga = None\n n_control_surfaces = None\n\n v0 = None\n\n # Modal cases\n modal = None\n phi = None\n inv_phi_forces = None\n inv_phi_vel = None\n\n def __init__(self, frame_of_reference, derivative_calculation=None, name=None,\n transfer_function=None):\n \"\"\"\n\n Args:\n frame_of_reference (str): Name of the frame of reference (stability or body axes)\n derivative_calculation (str): Name of the method to compute derivatives\n name (str): Name of the derivative set\n transfer_function (np.array): steady state transfer function for the desired input output channels\n \"\"\"\n\n self.transfer_function = transfer_function # type: np.array # steady-state TF for the specific out/in\n self.matrix = None # type: np.array # matrix of stability derivatives\n self.labels_in = [] # type: list(str) # strings describing the input channels\n self.labels_out = [] # type list(str) # strings describing the output channels\n self.frame_of_reference = frame_of_reference # type: str # name of the FoR (stability or body axes)\n\n self.table = None # type: cout.TablePrinter\n self.name = name # type: str # name of the set\n\n # TODO: remove in clean up and make derivative_calculation a position argument\n if derivative_calculation is not None:\n self.__getattribute__(derivative_calculation)()\n\n def print(self, derivative_filename=None):\n if self.name is not None:\n cout.cout_wrap(self.name)\n with open(derivative_filename, 'a') as f:\n f.write('Derivative set: {:s}\\n'.format(self.name))\n f.write('Axes {:s}\\n'.format(self.frame_of_reference))\n self.table = cout.TablePrinter(n_fields=len(self.labels_in)+1,\n field_types=['s']+len(self.labels_in) * ['e'], filename=derivative_filename)\n self.table.print_header(field_names=list(['der'] + self.labels_in))\n for i in range(len(self.labels_out)):\n out_list = [self.labels_out[i]] + list(self.matrix[i, :])\n self.table.print_line(out_list)\n self.table.print_divider_line()\n self.table.character_return(n_lines=2)\n\n def save(self, derivative_name, output_name):\n with h5py.File(output_name + '.stability.h5', 'w') as f:\n f.create_dataset(derivative_name, data=self.matrix)\n\n def angle_derivatives(self):\n r\"\"\"\n Stability derivatives against aerodynamic angles (angle of attack and sideslip) expressed in stability axes, i.e\n forces are lift, drag...\n\n Linearised forces in stability axes are expressed as\n\n .. math::\n F^S = F_0^S + \\frac{\\partial}{\\partial \\alpha}\\left(C^{GA}(\\alpha)F_0^A\\right)\\delta\\alpha + C_0^{GA}\\delta F^A\n\n Therefore, the stability derivative becomes\n\n .. math:: \\frac{\\partial\\F^S}{\\partial\\alpha} =\\frac{\\partial}{\\partial \\alpha}\\left(C^{GA}(\\alpha)F_0^A\\right) +\n C_0^{GA}\\frac{\\partial F^A}{\\partial\\alpha}\n\n where\n\n .. math:: \\frac{\\partial F^A}{\\partial\\alpha} = \\frac{\\partial F^A}{\\partial v^A}\\frac{\\partial v^A}{\\partial\\alpha}\n\n and\n\n .. math:: \\frac{\\partial v^A}{\\partial\\alpha} = C^{AG}\\frac{\\partial}{\\partial\\alpha}\\left(C(0)V_0^G\\right).\n\n The term :math:`\\frac{\\partial F^A}{\\partial v^A}` is obtained directly from the steady state transfer\n function of the linear UVLM expressed in the beam degrees of freedoms.\n\n \"\"\"\n self.labels_in = ['phi', 'alpha', 'beta']\n self.labels_out = ['CD', 'CY', 'CL', 'Cl', 'Cm', 'Cn']\n self.matrix = np.zeros((6, 3))\n\n # Get free stream velocity direction\n v0 = self.v0\n\n f0a = self.steady_forces[:3]\n m0a = self.steady_forces[-3:]\n\n euler0 = algebra.quat2euler(self.quat)\n cga = self.cga\n\n # first term in the stability derivative expression\n stab_der_trans = algebra.der_Ceuler_by_v(euler0, f0a)\n stab_der_mom = algebra.der_Ceuler_by_v(euler0, m0a)\n\n # second term in the stability derivative expression\n if self.modal:\n delta_nodal_vel = np.linalg.inv(self.phi[:3, :3]).dot(cga.T.dot(algebra.der_Peuler_by_v(euler0 * 0, v0)))\n delta_nodal_forces = self.inv_phi_forces.dot(self.transfer_function[:6, :3].real.dot(delta_nodal_vel))\n else:\n delta_nodal_vel = cga.T.dot(algebra.der_Peuler_by_v(euler0 * 0, v0))\n delta_nodal_forces = self.transfer_function[:6, :3].real.dot(delta_nodal_vel)\n\n stab_der_trans2 = cga.dot(delta_nodal_forces[:3, :])\n stab_der_mom2 = cga.dot(delta_nodal_forces[3:, :])\n\n self.matrix[:3, :] = stab_der_trans + stab_der_trans2\n self.matrix[3:6, :] = stab_der_mom + stab_der_mom2\n\n self.apply_coefficients()\n\n def angle_derivatives_tb(self):\n self.name = 'Force/Angle derivatives via angle input'\n self.labels_in = ['phi', 'alpha', 'beta']\n self.labels_out = ['CD', 'CY', 'CL', 'Cl', 'Cm', 'Cn']\n self.matrix = np.zeros((6, 3))\n\n # Get free stream velocity direction\n v0 = self.v0\n\n f0a = self.steady_forces[:3]\n m0a = self.steady_forces[-3:]\n\n euler0 = algebra.quat2euler(self.quat)\n cga = self.cga\n\n # first term in the stability derivative expression\n stab_der_trans = algebra.der_Ceuler_by_v(euler0, f0a)\n stab_der_mom = algebra.der_Ceuler_by_v(euler0, m0a)\n\n # second term in the stability derivative expression\n if self.modal:\n delta_nodal_forces = self.inv_phi_forces.dot(self.transfer_function[:6, 6:9].real)\n else:\n delta_nodal_forces = self.transfer_function[:6, 6:9].real\n\n stab_der_trans2 = cga.dot(delta_nodal_forces[:3, :])\n stab_der_mom2 = cga.dot(delta_nodal_forces[3:, :])\n\n self.matrix[:3, :] = stab_der_trans + stab_der_trans2\n self.matrix[3:6, :] = stab_der_mom + stab_der_mom2\n\n self.apply_coefficients()\n\n def body_derivatives(self):\n self.name = 'Force derivatives to rigid body velocities - Body derivatives'\n self.labels_in = ['uA', 'vA', 'wA', 'pA', 'qA', 'rA']\n self.labels_out = ['C_XA', 'C_YA', 'C_ZA', 'C_LA', 'C_MA', 'C_NA']\n self.matrix = np.zeros((6, 6))\n\n body_derivatives = self.transfer_function[:6, :6]\n\n if self.modal:\n body_derivatives = self.inv_phi_forces.dot(body_derivatives).dot(self.inv_phi_vel)\n\n self.matrix = body_derivatives\n self.apply_coefficients()\n\n def control_surface_derivatives(self):\n n_control_surfaces = self.n_control_surfaces\n if n_control_surfaces == 0:\n return None\n\n self.name = 'Force derivatives wrt control surface inputs - Body axes'\n self.labels_out = ['C_XA', 'C_YA', 'C_ZA', 'C_LA', 'C_MA', 'C_NA']\n labels_in_deflection = []\n labels_in_rate = []\n for i in range(n_control_surfaces):\n labels_in_deflection.append('delta_{:g}'.format(i))\n labels_in_rate.append('dot(delta)_{:g}'.format(i))\n self.labels_in = labels_in_deflection + labels_in_rate\n\n body_derivatives = self.transfer_function[:6, 9:]\n assert body_derivatives.shape == (6, 2 * self.n_control_surfaces), 'Incorrect TF shape'\n\n if self.modal:\n self.matrix = self.inv_phi_forces.dot(body_derivatives)\n else:\n self.matrix = body_derivatives\n\n self.apply_coefficients()\n\n def apply_coefficients(self):\n self.matrix[:3, :] /= self.coefficients['force']\n self.matrix[np.ix_([3, 5]), :] /= self.coefficients['moment_lat']\n self.matrix[4, :] /= self.coefficients['moment_lon']\n" }, { "path": "sharpy/linear/utils/ss_interface.py", "content": "\"\"\"State-space modules loading utilities\"\"\"\nimport os\n\nimport h5py\n\nimport sharpy.utils.cout_utils as cout\nfrom abc import ABCMeta, abstractmethod\nimport numpy as np\nimport copy\n\ndict_of_systems = dict()\nsystems_dict_import = dict()\n\n# Define the system decorator\ndef linear_system(arg):\n global dict_of_systems\n\n try:\n arg.sys_id\n except AttributeError:\n raise AttributeError('Class defined as linear_system with no sys_id')\n\n dict_of_systems[arg.sys_id] = arg\n return arg\n\n\nclass BaseElement(metaclass=ABCMeta):\n\n @property\n def sys_id(self):\n raise NotImplementedError\n\n @abstractmethod\n def initialise(self, data, custom_settings=None):\n pass\n\n @abstractmethod\n def assemble(self):\n pass\n\n # Some method to connect\n # Input (from where) - (i.e. generator, system etc)\n # Output (to display, to system)\n\n\ndef sys_list_from_path(cwd):\n \"\"\"\n Returns the files containing linear system state space elements\n\n Args:\n cwd (str): Current working directory\n\n Returns:\n\n \"\"\"\n onlyfiles = [f for f in os.listdir(cwd) if os.path.isfile(os.path.join(cwd, f))]\n\n for i_file in range(len(onlyfiles)):\n if onlyfiles[i_file].split('.')[-1] == 'py': # support autosaved files in the folder\n if onlyfiles[i_file] == \"__init__.py\":\n onlyfiles[i_file] = \"\"\n continue\n onlyfiles[i_file] = onlyfiles[i_file].replace('.py', '')\n else:\n onlyfiles[i_file] = \"\"\n\n files = [file for file in onlyfiles if not file == \"\"]\n\n return files\n\n\ndef sys_from_string(string):\n return dict_of_systems[string]\n\n\ndef initialise_system(sys_id):\n cout.cout_wrap('Generating an instance of %s' %sys_id, 2)\n cls_type = sys_from_string(sys_id)\n sys = cls_type()\n return sys\n\n\ndef dictionary_of_systems():\n dictionary = dict()\n for linear_system in dict_of_systems:\n init_sys = initialise_system(linear_system)\n dictionary[linear_system] = init_sys.settins_default\n\n return dictionary\n\n\nclass VectorVariable:\n # state variable\n def __init__(self, name, size, index, var_system=None):\n\n self.name = name\n self.var_system = var_system\n self.size = size\n self._index = index\n\n self._first_position = 0\n\n self._rows_loc = None\n self._cols_loc = None\n\n @property\n def cols_loc(self):\n return np.arange(self.first_position, self.end_position, dtype=int)\n\n @property\n def index(self):\n return self._index\n\n @index.setter\n def index(self, value):\n self._index = value\n\n @property\n def first_position(self):\n return self._first_position\n\n @first_position.setter\n def first_position(self, position):\n self._first_position = position\n\n @property\n def end_position(self):\n return self.first_position + self.size\n\n @property\n def rows_loc(self):\n return np.arange(self.first_position, self.end_position, dtype=int)\n\n def __repr__(self):\n return '({:s}: {:s}, size: {:g}, index: {:g}, starting at: {:g}, finishing at: {:g})'.format(\n type(self).__name__,\n self.name,\n self.size,\n self.index,\n self.first_position,\n self.end_position)\n\n def copy(self):\n return copy.deepcopy(self)\n\n def save(self):\n \"\"\"\n Return:\n tuple: info to save to h5\n \"\"\"\n return type(self).__name__, self.name, self.size, self.index\n\n\nclass OutputVariable(VectorVariable):\n\n @property\n def cols_loc(self):\n return self._cols_loc\n\n @cols_loc.setter\n def cols_loc(self, value=None):\n if self._cols_loc is None:\n self._cols_loc = np.arange(self.first_position, self.end_position, dtype=int) # Original location, should not update\n\n @property\n def rows_loc(self):\n # In the output variables the rows can change, the columns should stay fixed\n return np.arange(self.first_position, self.end_position, dtype=int)\n\n\nclass InputVariable(VectorVariable):\n\n @property\n def rows_loc(self):\n return self._rows_loc\n\n @rows_loc.setter\n def rows_loc(self, value=None):\n if self._rows_loc is None:\n self._rows_loc = np.arange(self.first_position, self.end_position, dtype=int) # Original location, should not update\n\n @property\n def cols_loc(self):\n return np.arange(self.first_position, self.end_position, dtype=int)\n\n\nclass StateVariable(VectorVariable):\n pass\n\n\nclass LinearVector:\n\n def __init__(self, list_of_vector_variables):\n self.vector_variables = list_of_vector_variables\n\n # check they are all the same type\n self.check_sametype_vars_full_vector()\n\n # initialise position of variables\n self.update_indices()\n self.update_locations()\n\n self.variable_class = type(self.vector_variables[0]) # class\n\n @property\n def num_variables(self):\n return len(self.vector_variables)\n\n @property\n def size(self):\n return sum([variable.size for variable in self.vector_variables])\n\n def remove(self, *variable_name_list):\n\n for variable_name in variable_name_list:\n list_of_variable_names = [variable.name for variable in self.vector_variables]\n try:\n remove_variable_index = list_of_variable_names.index(variable_name)\n except ValueError:\n raise ValueError('Trying to remove non-existent {:s} variable'.format(variable_name))\n else:\n self.__remove_variable(remove_variable_index)\n\n def __remove_variable(self, index):\n self.vector_variables.pop(index)\n self.update_indices()\n\n def modify(self, variable_name, **kwargs):\n \"\"\"\n Modifies the attributes of the desired variable. The new attributes are passed as **kwargs. If an attribute is\n not recognised a ``NameError`` is returned.\n\n Note:\n If changing the size of the variable, you should then update the linear vector.\n\n Args:\n variable_name (str): Name of the variable to modify\n **kwargs: Key-word arguments containing the attributes of the variable as keys and the new values as values.\n\n \"\"\"\n variable = self.get_variable_from_name(variable_name)\n for var_attribute, new_var_value in kwargs.items():\n if hasattr(variable, var_attribute):\n variable.__setattr__(var_attribute, new_var_value)\n else:\n raise NameError('Unknown variable attribute {:s}'.format(var_attribute))\n\n def add(self, vector_variable, **kwargs):\n\n if isinstance(vector_variable, self.variable_class):\n self.__add_vector_variable(vector_variable)\n elif type(vector_variable) is str:\n new_variable = self.variable_class(name=vector_variable, **kwargs)\n self.__add_vector_variable(new_variable)\n else:\n raise TypeError('Only can add a variable from either a {:s} object or with name and kwargs'.format(\n self.variable_class.__name__\n ))\n\n def append(self, vector_variable, **kwargs):\n self.update_indices()\n appending_index = self.num_variables\n if isinstance(vector_variable, VectorVariable):\n vector_variable.index = appending_index\n elif type(vector_variable) is str:\n kwargs['index'] = appending_index\n else:\n raise TypeError('Only can add a variable from either a {:s} object or with name and kwargs'.format(\n self.variable_class.__name__\n ))\n\n self.add(vector_variable, **kwargs)\n\n def __add_vector_variable(self, vector_variable):\n list_of_indices = [variable.index for variable in self.vector_variables]\n\n if vector_variable.index in list_of_indices:\n raise IndexError('New variable index is already in use')\n self.vector_variables.append(vector_variable)\n self.update_indices()\n self.update_locations()\n\n def update_indices(self):\n\n list_of_indices = [variable.index for variable in self.vector_variables]\n ordered_list = sorted(list_of_indices)\n\n index_variable_dict = {key_index: self.vector_variables[i] for i, key_index in enumerate(list_of_indices)}\n updated_list = []\n for i_var in range(self.num_variables):\n\n current_variable_index = ordered_list[i_var]\n current_variable = index_variable_dict[current_variable_index]\n current_variable.index = i_var\n\n updated_list.append(current_variable)\n\n self.vector_variables = updated_list\n\n def update_locations(self):\n for i_var in range(self.num_variables):\n if i_var == 0:\n self.vector_variables[i_var].first_position = 0\n elif i_var > 0:\n # since end item is not included in range methods, set the first position to last variable end position\n self.vector_variables[i_var].first_position = self.vector_variables[i_var - 1].end_position\n\n def check_sametype_vars_full_vector(self):\n variable_class = type(self.vector_variables[0])\n\n for var in self.vector_variables:\n if not isinstance(var, variable_class):\n raise TypeError('All variables in the vector are not of the same kind.')\n\n @classmethod\n def merge(cls, vec1, vec2):\n \"\"\"\n Merges two instances of LinearVectors\n\n Args:\n vec1 (LinearVector): Vector 1\n vec2 (LinearVector): Vector 2\n\n Returns:\n LinearVector: Merged vectors 1 and 2\n \"\"\"\n if vec1.variable_class is not vec2.variable_class:\n raise TypeError('Unable to merge two different kinds of vectors')\n\n list_of_variables_1 = [variable.copy() for variable in vec1]\n list_of_variables_2 = [variable.copy() for variable in vec2]\n\n for ith, variable in enumerate(list_of_variables_1 + list_of_variables_2):\n variable.index = ith\n\n merged_vector = cls(list_of_variables_1 + list_of_variables_2)\n return merged_vector\n\n @classmethod\n def transform(cls, linear_vector, to_type):\n if not (to_type is InputVariable or to_type is StateVariable or to_type is OutputVariable):\n raise TypeError('Argument should be the class to which the linear vector should be transformed')\n\n list_of_variables = []\n for variable in linear_vector.copy():\n list_of_variables.append(to_type(name=variable.name,\n size=variable.size,\n index=variable.index))\n\n return cls(list_of_variables)\n\n @staticmethod\n def check_connection(output_vector, input_vector):\n \"\"\"\n Checks an output_vector can be connected to an input channel.\n\n \"\"\"\n with_error = False\n err_log = ''\n\n for ith, out_variable in enumerate(output_vector):\n try:\n in_variable = input_vector.get_variable_from_name(out_variable.name)\n except ValueError:\n err_log += '\\nUnable to connect both systems, no input variable named {:s}\\n'.format(out_variable.name)\n with_error = True\n else:\n if not out_variable.size == in_variable.size:\n err_log += 'Variable {:s} and {:s} not the same size'\n with_error = True\n if not out_variable.rows_loc[-1] == in_variable.cols_loc[-1]:\n # checking the last index should be sufficient (and more efficient than checking the whole array)\n err_log += 'Variable {:s}Output rows not coincident with input columns for variable\\n'.format(\n out_variable.name)\n err_log += str(out_variable) + '\\n'\n err_log += str(in_variable) + '\\n'\n with_error = True\n\n if with_error:\n raise ValueError(err_log)\n\n @staticmethod\n def check_same_vectors(vec1, vec2):\n \"\"\"\n Checks that two linear vectors contain the same variables, regardless of type\n Args:\n vec1 (LinearVector): Vector 1\n vec2 (LinearVector): Vector 2\n \"\"\"\n\n assert vec1.num_variables == vec2.num_variables, 'Number of variables is not equal'\n assert vec1.size == vec2.size, 'Size is not equal'\n\n for i_var in range(vec1.num_variables):\n assert vec1[i_var].name == vec2[i_var].name, 'Variable name is not the same'\n assert vec1[i_var].index == vec2[i_var].index, 'Index is not the same'\n assert vec1[i_var].size == vec2[i_var].size, 'Variable size is not the same'\n assert vec1[i_var] is not vec2[i_var], 'Variables in LinearVector reference the same object in memory. ' \\\n 'Careful!'\n\n def differentiate(self):\n pass\n # going from second order to first order systems\n\n def get_variable_from_name(self, name):\n list_of_variable_names = [variable.name for variable in self.vector_variables]\n try:\n variable_index = list_of_variable_names.index(name)\n except ValueError:\n raise ValueError('Variable {:s} is non existent'.format(name))\n else:\n return self.vector_variables[variable_index]\n\n def __call__(self, variable_name):\n \"\"\"\n\n Args:\n variable_name (str): Variable name\n\n Returns:\n VectorVariable: Vector variable within LinearVector\n \"\"\"\n return self.get_variable_from_name(variable_name)\n\n def copy(self):\n return copy.deepcopy(self)\n\n def add_to_h5_file(self, file_handle):\n \"\"\"\n Given an h5 handle ``file_handle``, creates and adds a group named with the type of variable and adds the fields\n ``names`` (encoded in ascii), ``sizes`` and ``indices``.\n\n Args:\n file_handle (h5py.File): file handle of h5py.File\n\n Returns:\n file_handle\n \"\"\"\n variable_data = []\n for variable in self.vector_variables:\n variable_data.append(variable.save())\n\n types, names, sizes, indices = zip(*variable_data)\n\n # encode strings to bytes\n names = [name.encode('ascii', 'ignore') for name in names]\n\n variable_group = file_handle.create_group(types[0])\n variable_group.create_dataset(name='names', data=names)\n variable_group.create_dataset(name='sizes', data=sizes, dtype=int)\n variable_group.create_dataset(name='indices', data=indices, dtype=int)\n\n return file_handle\n\n @classmethod\n def load_from_h5_file(cls, variable_type, variables_data):\n \"\"\"\n Loads data from the information saved in an h5file\n\n Args:\n variable_type (str): Type of variable (InputVariable, OutputVariable or StateVariable)\n variables_data (dict): Dictionary containing variable info from h5 with keys: names, sizes and indices\n\n Returns:\n LinearVector: of ``variable_type``\n \"\"\"\n var_class_dict = {'InputVariable': InputVariable,\n 'OutputVariable': OutputVariable,\n 'StateVariable': StateVariable}\n n_variables = len(variables_data['names'])\n list_of_variables = []\n try:\n var_class = var_class_dict[variable_type]\n except KeyError:\n raise KeyError(f'Unknown variable type {variable_type}. Must be either InputVariable, OutputVariable '\n f'or StateVariable')\n for ith_variable in range(n_variables):\n # name = variables_data['names'][ith_variable].astype('U13') # decode to unicode\n name = str(variables_data['names'][ith_variable], 'utf8') # decode to unicode\n list_of_variables.append(var_class(name,\n size=variables_data['sizes'][ith_variable],\n index=variables_data['indices'][ith_variable]),\n )\n return cls(list_of_variables)\n\n def __iter__(self):\n return SetIterator(self)\n\n def __getitem__(self, item):\n return self.vector_variables[item]\n\n def __repr__(self):\n string_out = ''\n for var in self.vector_variables:\n try:\n out_var = str(repr(var))\n except TypeError:\n print('Error printing var {:s}'.format(var.name))\n else:\n string_out += '\\t' + out_var + '\\n'\n return string_out\n\n\nclass SetIterator:\n\n def __init__(self, linear_vector):\n self._set_cases = linear_vector\n self._index = 0\n\n def __next__(self):\n if self._index < self._set_cases.num_variables:\n res = self._set_cases.vector_variables[self._index]\n self._index += 1\n return res\n\n raise StopIteration\n" }, { "path": "sharpy/linear/utils/sselements.py", "content": "\"\"\"\nLinear State Space Element Class\n\n\"\"\"\n\nclass Element(object):\n \"\"\"\n State space member\n \"\"\"\n\n def __init__(self):\n\n self.sys_id = str() # A string with the name of the element\n\n self.sys = None # The actual object\n self.ss = None # The state space object\n\n self.settings = dict()\n\n def initialise(self, data, sys_id):\n\n self.sys_id = sys_id\n settings = data.linear.settings[sys_id] # Load settings, the settings should be stored in data.linear.settings\n # data.linear.settings should be created in the class above containing the entire set up\n\n # Get the actual class object (like lingebm) from a dictionary in the same way that it is done for the solvers\n # in sharpy\n # sys = sys_from_string(sys_id)\n # To use the decorator idea we would first need to instantiate the class. Need to see how this is done with NL\n # SHARPy\n\n\n def assemble(self):\n pass" }, { "path": "sharpy/postproc/__init__.py", "content": "import importlib\nimport os\n\nimport sharpy.utils.solver_interface as solver_interface\nimport sharpy.utils.sharpydir as sharpydir\n\nfiles = solver_interface.solver_list_from_path(os.path.dirname(__file__))\n\nimport_path = os.path.realpath(os.path.dirname(__file__))\nimport_path = import_path.replace(sharpydir.SharpyDir, \"\")\nif import_path[0] == \"/\": import_path = import_path[1:]\nimport_path = import_path.replace(\"/\", \".\")\n\nfor file in files:\n solver_interface.solvers[file] = importlib.import_module(import_path + \".\" + file)\n" }, { "path": "sharpy/postproc/aeroforcescalculator.py", "content": "import numpy as np\nimport os\n\nimport sharpy.utils.cout_utils as cout\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.algebra as algebra\nimport sharpy.aero.utils.mapping as mapping\nimport warnings\n\n\n@solver\nclass AeroForcesCalculator(BaseSolver):\n \"\"\"AeroForcesCalculator\n\n Calculates the total aerodynamic forces and moments on the frame of reference ``A``.\n\n \"\"\"\n solver_id = 'AeroForcesCalculator'\n solver_classification = 'post-processor'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['write_text_file'] = 'bool'\n settings_default['write_text_file'] = False\n settings_description['write_text_file'] = 'Write ``txt`` file with results'\n\n settings_types['text_file_name'] = 'str'\n settings_default['text_file_name'] = 'aeroforces.txt'\n settings_description['text_file_name'] = 'Text file name'\n\n settings_types['screen_output'] = 'bool'\n settings_default['screen_output'] = True\n settings_description['screen_output'] = 'Show results on screen'\n\n settings_default['coefficients'] = False\n settings_types['coefficients'] = 'bool'\n settings_description['coefficients'] = 'Calculate aerodynamic coefficients'\n\n settings_default['lifting_surfaces'] = True\n settings_types['lifting_surfaces'] = 'bool'\n settings_description['lifting_surfaces'] = 'Includes aerodynamic forces from lifting surfaces'\n\n settings_default['nonlifting_body'] = False\n settings_types['nonlifting_body'] = 'bool'\n settings_description['nonlifting_body'] = 'Includes aerodynamic forces from nonlifting bodies'\n\n settings_types['q_ref'] = 'float'\n settings_default['q_ref'] = 1\n settings_description['q_ref'] = 'Reference dynamic pressure'\n\n settings_types['S_ref'] = 'float'\n settings_default['S_ref'] = 1\n settings_description['S_ref'] = 'Reference area'\n\n settings_types['b_ref'] = 'float'\n settings_default['b_ref'] = 1\n settings_description['b_ref'] = 'Reference span'\n\n settings_types['c_ref'] = 'float'\n settings_default['c_ref'] = 1\n settings_description['c_ref'] = 'Reference chord'\n\n settings_types['u_inf_dir'] = 'list(float)'\n settings_default['u_inf_dir'] = [1., 0., 0.]\n settings_description['u_inf_dir'] = 'Flow direction'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n\n self.settings = None\n self.data = None\n self.ts_max = 0\n\n self.folder = None\n self.caller = None\n\n self.table = None\n self.rot = None\n self.moment_reference_location = np.array([0., 0., 0.])\n\n def initialise(self, data, custom_settings=None, caller=None, restart=False):\n self.data = data\n self.settings = data.settings[self.solver_id]\n self.ts_max = len(self.data.structure.timestep_info)\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n self.caller = caller\n\n self.folder = data.output_folder + '/forces/'\n if not os.path.exists(self.folder):\n os.makedirs(self.folder)\n\n if self.settings['screen_output']:\n if self.settings['coefficients']:\n self.table = cout.TablePrinter(7, field_length=12, field_types=['g'] + 6 * ['f'])\n self.table.print_header(['tstep', 'Cfx_g', 'Cfy_g', 'Cfz_g', 'Cmx_g', 'Cmy_g', 'Cmz_g'])\n else:\n self.table = cout.TablePrinter(7, field_length=12, field_types=['g'] + 6 * ['e'])\n self.table.print_header(['tstep', 'fx_g', 'fy_g', 'fz_g', 'mx_g', 'my_g', 'mz_g'])\n\n def run(self, **kwargs):\n\n online = settings_utils.set_value_or_default(kwargs, 'online', False)\n\n if online:\n self.ts_max = len(self.data.structure.timestep_info)\n self.calculate_forces(-1)\n\n if self.settings['screen_output']:\n self.screen_output(-1)\n else:\n for ts in range(self.ts_max):\n self.calculate_forces(ts)\n if self.settings['screen_output']:\n self.screen_output(ts)\n cout.cout_wrap('...Finished', 1)\n\n if self.settings['write_text_file']:\n self.file_output(self.settings['text_file_name'])\n return self.data\n\n def calculate_forces(self, ts):\n self.rot = algebra.quat2rotation(self.data.structure.timestep_info[ts].quat) # R_GA\n\n # flow rotation angle from x and z components of flow direction\n # WARNING: this will give incorrect results when there is sideslip\n rot_xy = np.arctan2(-self.settings['u_inf_dir'][2], self.settings['u_inf_dir'][0])\n rmat_xy = algebra.euler2rot((0., rot_xy, 0.))\n\n # Forces per surface in A frame relative to the flow\n force = self.data.aero.timestep_info[ts].forces\n unsteady_force = self.data.aero.timestep_info[ts].dynamic_forces\n\n n_surf = self.data.aero.n_surf\n\n rmat = np.block([[self.rot @ rmat_xy.T, np.zeros((3, 3))], [np.zeros((3, 3)), self.rot @ rmat_xy.T]])\n force_g = [np.moveaxis(np.squeeze(rmat @ np.expand_dims(np.moveaxis(\n force[i], (0, 1, 2), (2, 0, 1)), -1)), source=(0, 1, 2), destination=(1, 2, 0))\n for i in range(n_surf)]\n unsteady_force_g = [np.moveaxis(np.squeeze(rmat @ np.expand_dims(np.moveaxis(\n unsteady_force[i], (0, 1, 2), (2, 0, 1)), -1)), source=(0, 1, 2), destination=(1, 2, 0))\n for i in range(n_surf)]\n\n for i_surf in range(n_surf):\n (\n self.data.aero.timestep_info[ts].inertial_steady_forces[i_surf, 0:3],\n self.data.aero.timestep_info[ts].inertial_unsteady_forces[i_surf, 0:3],\n self.data.aero.timestep_info[ts].body_steady_forces[i_surf, 0:3],\n self.data.aero.timestep_info[ts].body_unsteady_forces[i_surf, 0:3]\n ) = self.calculate_forces_for_isurf_in_g_frame(force_g[i_surf], unsteady_force=unsteady_force_g[i_surf])\n\n if self.settings[\"nonlifting_body\"]:\n for i_surf in range(self.data.nonlifting_body.n_surf):\n (\n self.data.nonlifting_body.timestep_info[ts].inertial_steady_forces[i_surf, 0:3],\n self.data.nonlifting_body.timestep_info[ts].body_steady_forces[i_surf, 0:3],\n ) = self.calculate_forces_for_isurf_in_g_frame(\n self.data.nonlifting_body.timestep_info[ts].forces[i_surf], nonlifting=True)\n\n # Convert to forces in B frame\n try:\n steady_forces_b = self.data.structure.timestep_info[ts].postproc_node['aero_steady_forces']\n except KeyError:\n if self.settings[\"nonlifting_body\"]:\n warnings.warn(\n 'Nonlifting forces are not considered in aero forces calculation since forces cannot not be retrieved from postproc node.')\n steady_forces_b = self.map_forces_beam_dof(self.data.aero, ts, force_g)\n\n try:\n unsteady_forces_b = self.data.structure.timestep_info[ts].postproc_node['aero_unsteady_forces']\n except KeyError:\n unsteady_forces_b = self.map_forces_beam_dof(self.data.aero, ts, unsteady_force_g)\n # Convert to forces in A frame\n steady_forces_a = self.data.structure.timestep_info[ts].nodal_b_for_2_a_for(steady_forces_b,\n self.data.structure)\n\n unsteady_forces_a = self.data.structure.timestep_info[ts].nodal_b_for_2_a_for(unsteady_forces_b,\n self.data.structure)\n\n self.data.aero.timestep_info[ts].total_steady_body_forces = \\\n rmat @ mapping.total_forces_moments(steady_forces_a,\n self.data.structure.timestep_info[ts].pos,\n ref_pos=self.moment_reference_location)\n self.data.aero.timestep_info[ts].total_unsteady_body_forces = \\\n rmat @ mapping.total_forces_moments(unsteady_forces_a,\n self.data.structure.timestep_info[ts].pos,\n ref_pos=self.moment_reference_location)\n\n # Express total forces in G frame\n self.data.aero.timestep_info[ts].total_steady_inertial_forces = \\\n np.block([[self.rot, np.zeros((3, 3))],\n [np.zeros((3, 3)), self.rot]]).dot(\n self.data.aero.timestep_info[ts].total_steady_body_forces)\n\n self.data.aero.timestep_info[ts].total_unsteady_inertial_forces = \\\n np.block([[self.rot, np.zeros((3, 3))],\n [np.zeros((3, 3)), self.rot]]).dot(\n self.data.aero.timestep_info[ts].total_unsteady_body_forces)\n\n def calculate_forces_for_isurf_in_g_frame(self, force, unsteady_force=None, nonlifting=False):\n \"\"\"\n Forces for a surface in G frame\n \"\"\"\n # Forces per surface in G frame\n total_steady_force = np.zeros((3,))\n total_unsteady_force = np.zeros((3,))\n _, n_rows, n_cols = force.shape\n for i_m in range(n_rows):\n for i_n in range(n_cols):\n total_steady_force += force[0:3, i_m, i_n]\n if not nonlifting:\n total_unsteady_force += unsteady_force[0:3, i_m, i_n]\n if not nonlifting:\n return total_steady_force, total_unsteady_force, np.dot(self.rot.T, total_steady_force), np.dot(self.rot.T,\n total_unsteady_force)\n else:\n return total_steady_force, np.dot(self.rot.T, total_steady_force)\n\n def map_forces_beam_dof(self, aero_data, ts, force):\n struct_tstep = self.data.structure.timestep_info[ts]\n aero_forces_beam_dof = mapping.aero2struct_force_mapping(force,\n aero_data.struct2aero_mapping,\n aero_data.timestep_info[ts].zeta,\n struct_tstep.pos,\n struct_tstep.psi,\n None,\n self.data.structure.connectivities,\n struct_tstep.cag())\n return aero_forces_beam_dof\n\n def calculate_coefficients(self, fx, fy, fz, mx, my, mz):\n qS = self.settings['q_ref'] * self.settings['S_ref']\n return fx / qS, fy / qS, fz / qS, mx / qS / self.settings['b_ref'], my / qS / self.settings['c_ref'], \\\n mz / qS / self.settings['b_ref']\n\n def screen_output(self, ts):\n # print time step total aero forces\n forces = np.zeros(3)\n moments = np.zeros(3)\n\n aero_tstep = self.data.aero.timestep_info[ts]\n forces += aero_tstep.total_steady_inertial_forces[:3] + aero_tstep.total_unsteady_inertial_forces[:3]\n moments += aero_tstep.total_steady_inertial_forces[3:] + aero_tstep.total_unsteady_inertial_forces[3:]\n\n if self.settings['coefficients']: # TODO: Check if coefficients have to be computed differently for fuselages\n Cfx, Cfy, Cfz, Cmx, Cmy, Cmz = self.calculate_coefficients(*forces, *moments)\n self.table.print_line([ts, Cfx, Cfy, Cfz, Cmx, Cmy, Cmz])\n else:\n self.table.print_line([ts, *forces, *moments])\n\n def file_output(self, filename):\n # assemble forces/moments matrix\n # (1 timestep) + (3+3 inertial steady+unsteady) + (3+3 body steady+unsteady)\n force_matrix = np.zeros((self.ts_max, 1 + 3 + 3 + 3 + 3))\n moment_matrix = np.zeros((self.ts_max, 1 + 3 + 3 + 3 + 3))\n for ts in range(self.ts_max):\n aero_tstep = self.data.aero.timestep_info[ts]\n i = 0\n force_matrix[ts, i] = ts\n moment_matrix[ts, i] = ts\n i += 1\n\n # Steady forces/moments G\n force_matrix[ts, i:i + 3] = aero_tstep.total_steady_inertial_forces[:3]\n moment_matrix[ts, i:i + 3] = aero_tstep.total_steady_inertial_forces[3:]\n i += 3\n\n # Unsteady forces/moments G\n force_matrix[ts, i:i + 3] = aero_tstep.total_unsteady_inertial_forces[:3]\n moment_matrix[ts, i:i + 3] = aero_tstep.total_unsteady_inertial_forces[3:]\n i += 3\n\n # Steady forces/moments A\n force_matrix[ts, i:i + 3] = aero_tstep.total_steady_body_forces[:3]\n moment_matrix[ts, i:i + 3] = aero_tstep.total_steady_body_forces[3:]\n i += 3\n\n # Unsteady forces/moments A\n force_matrix[ts, i:i + 3] = aero_tstep.total_unsteady_body_forces[:3]\n moment_matrix[ts, i:i + 3] = aero_tstep.total_unsteady_body_forces[3:]\n\n header = ''\n header += 'tstep, '\n header += 'fx_steady_G, fy_steady_G, fz_steady_G, '\n header += 'fx_unsteady_G, fy_unsteady_G, fz_unsteady_G, '\n header += 'fx_steady_a, fy_steady_a, fz_steady_a, '\n header += 'fx_unsteady_a, fy_unsteady_a, fz_unsteady_a'\n\n np.savetxt(self.folder + 'forces_' + filename,\n force_matrix,\n fmt='%i' + ', %10e' * (np.shape(force_matrix)[1] - 1),\n delimiter=',',\n header=header,\n comments='#')\n\n header = ''\n header += 'tstep, '\n header += 'mx_steady_G, my_steady_G, mz_steady_G, '\n header += 'mx_unsteady_G, my_unsteady_G, mz_unsteady_G, '\n header += 'mx_steady_a, my_steady_a, mz_steady_a, '\n header += 'mx_unsteady_a, my_unsteady_a, mz_unsteady_a'\n\n np.savetxt(self.folder + 'moments_' + filename,\n moment_matrix,\n fmt='%i' + ', %10e' * (np.shape(moment_matrix)[1] - 1),\n delimiter=',',\n header=header,\n comments='#')\n" }, { "path": "sharpy/postproc/aerogridplot.py", "content": "import os\n\nimport numpy as np\n\nimport sharpy.utils.cout_utils as cout\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as su\nimport sharpy.aero.utils.uvlmlib as uvlmlib\nfrom sharpy.utils.constants import vortex_radius_def\n\nfrom sharpy.utils.plotutils import plot_frame_to_vtk\n\n\n@solver\nclass AerogridPlot(BaseSolver):\n \"\"\"\n Aerodynamic Grid Plotter\n\n \"\"\"\n solver_id = 'AerogridPlot'\n solver_classification = 'post-processor'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['include_rbm'] = 'bool'\n settings_default['include_rbm'] = True\n settings_description['include_rbm'] = 'Include rigid body motions'\n\n settings_types['include_forward_motion'] = 'bool'\n settings_default['include_forward_motion'] = False\n settings_description['include_forward_motion'] = 'Include forward motion'\n\n settings_types['include_applied_forces'] = 'bool'\n settings_default['include_applied_forces'] = True\n settings_description['include_applied_forces'] = 'Include applied aerodynamic forces at the vertices'\n\n settings_types['include_unsteady_applied_forces'] = 'bool'\n settings_default['include_unsteady_applied_forces'] = False\n settings_description['include_unsteady_applied_forces'] = 'Include unsteady aerodynamic forces at the vertices'\n\n settings_types['minus_m_star'] = 'int'\n settings_default['minus_m_star'] = 0\n settings_description['minus_m_star'] = 'Subtract a number of wake panels that will not be plotted'\n\n settings_types['name_prefix'] = 'str'\n settings_default['name_prefix'] = ''\n settings_description['name_prefix'] = 'Prefix to add to file name'\n\n settings_types['u_inf'] = 'float'\n settings_default['u_inf'] = 0.\n settings_description['u_inf'] = 'Free stream velocity'\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = 0.\n settings_description['dt'] = 'Time step increment'\n\n settings_types['include_velocities'] = 'bool'\n settings_default['include_velocities'] = False\n settings_description['include_velocities'] = 'Include induced velocities at the vertices'\n\n settings_types['include_incidence_angle'] = 'bool'\n settings_default['include_incidence_angle'] = False\n settings_description['include_incidence_angle'] = 'Include panel incidence angle'\n\n settings_types['plot_nonlifting_surfaces'] = 'bool'\n settings_default['plot_nonlifting_surfaces'] = False\n settings_description['plot_nonlifting_surfaces'] = 'Plot nonlifting surfaces'\n \n settings_types['plot_lifting_surfaces'] = 'bool'\n settings_default['plot_lifting_surfaces'] = False\n settings_description['plot_lifting_surfaces'] = 'Plot nonlifting surfaces'\n\n settings_types['num_cores'] = 'int'\n settings_default['num_cores'] = 1\n settings_description['num_cores'] = 'Number of cores used to compute velocities/angles'\n\n settings_types['vortex_radius'] = 'float'\n settings_default['vortex_radius'] = vortex_radius_def\n settings_description['vortex_radius'] = 'Distance below which inductions are not computed'\n\n settings_types['stride'] = 'int'\n settings_default['stride'] = 1\n settings_description['stride'] = 'Number of steps between the execution calls when run online'\n \n settings_types['save_wake'] = 'bool'\n settings_default['save_wake'] = True\n settings_description['save_wake'] = 'Plot the wake'\n \n table = su.SettingsTable()\n __doc__ += table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.settings = None\n self.data = None\n\n self.folder = None\n self.body_filename = ''\n self.wake_filename = ''\n self.nonlifting_filename = ''\n self.ts_max = 0\n self.caller = None\n\n def initialise(self, data, custom_settings=None, caller=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n su.to_custom_types(self.settings, self.settings_types, self.settings_default)\n self.ts_max = self.data.ts + 1\n # create folder for containing files if necessary\n self.folder = data.output_folder + '/aero/'\n if not os.path.exists(self.folder):\n os.makedirs(self.folder)\n self.body_filename = (self.folder +\n self.settings['name_prefix'] +\n 'body_' +\n self.data.settings['SHARPy']['case'])\n self.wake_filename = (self.folder +\n self.settings['name_prefix'] +\n 'wake_' +\n self.data.settings['SHARPy']['case'])\n self.nonlifting_filename = (self.folder +\n self.settings['name_prefix'] +\n 'nonlifting_' +\n self.data.settings['SHARPy']['case'])\n self.caller = caller\n\n def run(self, **kwargs):\n \n online = kwargs.get('online', False)\n\n # TODO: Create a dictionary to plot any variable as in beamplot\n if not online:\n for self.ts in range(self.ts_max):\n if self.data.structure.timestep_info[self.ts] is not None:\n self.plot_body()\n self.plot_wake()\n if self.settings['plot_nonlifting_surfaces']:\n self.plot_nonlifting_surfaces()\n cout.cout_wrap('...Finished', 1)\n elif (self.data.ts % self.settings['stride'] == 0):\n aero_tsteps = len(self.data.aero.timestep_info) - 1\n struct_tsteps = len(self.data.structure.timestep_info) - 1\n self.ts = np.max((aero_tsteps, struct_tsteps))\n self.plot_body()\n self.plot_wake()\n if self.settings['plot_nonlifting_surfaces']:\n self.plot_nonlifting_surfaces()\n return self.data\n\n def plot_body(self):\n\n aero_tstep = self.data.aero.timestep_info[self.ts]\n struct_tstep = self.data.structure.timestep_info[self.ts]\n\n if self.settings['include_incidence_angle']:\n aero_tstep.postproc_cell['incidence_angle'] = []\n for isurf in range(aero_tstep.n_surf):\n aero_tstep.postproc_cell['incidence_angle'].append(\n np.zeros_like(aero_tstep.gamma[isurf]))\n\n uvlmlib.uvlm_calculate_incidence_angle(aero_tstep,\n struct_tstep)\n\n for i_surf in range(aero_tstep.n_surf):\n filename = f\"{self.body_filename}_{i_surf:02d}_{self.ts:06d}.vtu\"\n\n zeta = np.moveaxis(aero_tstep.zeta[i_surf], 0, -1).copy() # [m+1, n+1, 3]\n zeta_dot = np.moveaxis(aero_tstep.zeta_dot[i_surf][:3, ...], 0, -1).copy() # [3, m+1, n+1]\n gamma = aero_tstep.gamma[i_surf].copy() # [m, n]\n gamma_dot = aero_tstep.gamma_dot[i_surf].copy() # [m, n]\n normals = np.moveaxis(aero_tstep.normals[i_surf], 0, -1).copy() # [m, n, 3]\n surf_id = np.ones(gamma.shape, dtype=int) * i_surf\n\n if self.settings['include_rbm']:\n if struct_tstep.mb_dict is None:\n zeta += np.expand_dims(struct_tstep.for_pos[:3], (0, 1))\n else:\n zeta += np.expand_dims(self.data.structure.timestep_info[0].cga() @ struct_tstep.for_pos[:3], (0, 1))\n if self.settings['include_forward_motion']:\n zeta[..., 0] -= self.settings['dt'] * self.ts * self.settings['u_inf']\n\n if self.settings['include_incidence_angle']:\n incidence_angle = aero_tstep.postproc_cell['incidence_angle'][i_surf]\n else:\n incidence_angle = np.zeros(gamma.shape)\n\n\n point_struct_id = np.broadcast_to(np.expand_dims(self.data.aero.aero2struct_mapping[i_surf], 0), zeta.shape[:2])\n point_cf = np.moveaxis(aero_tstep.forces[i_surf][:3, ...], 0, -1)\n\n try:\n point_unsteady_cf = np.moveaxis(aero_tstep.dynamic_forces[i_surf][:3, ...], 0, -1)\n except AttributeError:\n point_unsteady_cf = np.zeros(zeta.shape)\n\n try:\n u_inf = np.moveaxis(aero_tstep.u_ext[i_surf][:3, ...], 0, -1)\n except AttributeError:\n u_inf = np.zeros(zeta.shape)\n\n\n if self.settings['include_velocities']:\n vel = uvlmlib.uvlm_calculate_total_induced_velocity_at_points(aero_tstep,\n zeta.reshape(-1, 3),\n self.settings['vortex_radius'],\n struct_tstep.for_pos,\n self.settings['num_cores']).reshape(zeta.shape)\n else:\n vel = np.zeros(zeta.shape)\n\n plot_frame_to_vtk(zeta,\n filename,\n node_scalar_data={'point_struct_id': point_struct_id},\n node_vector_data={'zeta_dot': zeta_dot, 'point_steady_force': point_cf, 'point_unsteady_force': point_unsteady_cf, 'u_inf': u_inf, 'velocity': vel},\n cell_scalar_data={'gamma': gamma, \"gamma_dot\": gamma_dot, \"incidence_angle\": incidence_angle, 'surf_id': surf_id},\n cell_vector_data={'panel_normal': normals},)\n\n\n def plot_wake(self):\n for i_surf in range(self.data.aero.timestep_info[self.ts].n_surf):\n filename = f\"{self.wake_filename}_{i_surf:02d}_{self.ts:06d}.vtu\"\n\n zeta_star = np.moveaxis(self.data.aero.timestep_info[self.ts].zeta_star[i_surf], 0, -1).copy() # [m_star+1, n+1, 3]\n gamma = self.data.aero.timestep_info[self.ts].gamma_star[i_surf].copy() # [m_star, n]\n\n surf_id = np.ones(gamma.shape, dtype=int) * i_surf\n\n if self.settings['include_rbm']:\n if self.data.structure.timestep_info[self.ts].mb_dict is None:\n zeta_star += np.expand_dims(self.data.structure.timestep_info[self.ts].for_pos[:3], (0, 1))\n else:\n zeta_star += np.expand_dims(self.data.structure.timestep_info[0].cga()\n @ self.data.structure.timestep_info[self.ts].for_pos[:3], (0, 1))\n if self.settings['include_forward_motion']:\n zeta_star[..., 0] -= self.settings['dt'] * self.ts * self.settings['u_inf']\n\n plot_frame_to_vtk(\n zeta_star,\n filename,\n node_vector_data={},\n cell_scalar_data={\n \"gamma\": gamma,\n \"surf_id\": surf_id,\n },\n )\n\n\n def plot_nonlifting_surfaces(self):\n nonlifting_tstep = self.data.nonlifting_body.timestep_info[self.ts]\n struct_tstep = self.data.structure.timestep_info[self.ts]\n\n for i_surf in range(nonlifting_tstep.n_surf):\n filename = (self.nonlifting_filename +\n '_' +\n '%02u_' % i_surf +\n '%06u' % self.ts+\n '.vtu')\n\n dims = nonlifting_tstep.dimensions[i_surf, :]\n point_data_dim = (dims[0]+1)*(dims[1]+1) # + (dims_star[0]+1)*(dims_star[1]+1)\n panel_data_dim = (dims[0])*(dims[1]) # + (dims_star[0])*(dims_star[1])\n\n coords = np.zeros((point_data_dim, 3))\n conn = []\n panel_id = np.zeros((panel_data_dim,), dtype=int)\n panel_surf_id = np.zeros((panel_data_dim,), dtype=int)\n panel_sigma = np.zeros((panel_data_dim,))\n normal = np.zeros((panel_data_dim, 3))\n point_struct_id = np.zeros((point_data_dim,), dtype=int)\n point_cf = np.zeros((point_data_dim, 3))\n u_inf = np.zeros((point_data_dim, 3))\n counter = -1\n\n # coordinates of corners\n for i_n in range(dims[1]+1):\n for i_m in range(dims[0]+1):\n counter += 1\n coords[counter, :] = nonlifting_tstep.zeta[i_surf][:, i_m, i_n]\n # TODO: include those for nonlifting body (are they different for nonlifting coordinates?)\n if self.settings['include_rbm']:\n coords[counter, :] += struct_tstep.for_pos[0:3]\n if self.settings['include_forward_motion']:\n coords[counter, 0] -= self.settings['dt']*self.ts*self.settings['u_inf']\n counter = -1\n node_counter = -1\n for i_n in range(dims[1] + 1):\n global_counter = self.data.nonlifting_body.aero2struct_mapping[i_surf][i_n]\n for i_m in range(dims[0] + 1):\n node_counter += 1\n # point data\n point_struct_id[node_counter] = global_counter\n point_cf[node_counter, :] = nonlifting_tstep.forces[i_surf][0:3, i_m, i_n]\n try:\n u_inf[node_counter, :] = nonlifting_tstep.u_ext[i_surf][0:3, i_m, i_n]\n except AttributeError:\n pass\n if i_n < dims[1] and i_m < dims[0]:\n counter += 1\n else:\n continue\n\n conn.append([node_counter + 0,\n node_counter + 1,\n node_counter + dims[0]+2,\n node_counter + dims[0]+1])\n # cell data\n normal[counter, :] = nonlifting_tstep.normals[i_surf][:, i_m, i_n]\n panel_id[counter] = counter\n panel_surf_id[counter] = i_surf\n panel_sigma[counter] = nonlifting_tstep.sigma[i_surf][i_m, i_n]\n\n from tvtk.api import tvtk, write_data\n ug = tvtk.UnstructuredGrid(points=coords)\n ug.set_cells(tvtk.Quad().cell_type, conn)\n ug.cell_data.scalars = panel_id\n ug.cell_data.scalars.name = 'panel_n_id'\n ug.cell_data.add_array(panel_surf_id)\n ug.cell_data.get_array(1).name = 'panel_surface_id'\n ug.cell_data.add_array(panel_sigma)\n ug.cell_data.get_array(2).name = 'panel_sigma'\n ug.cell_data.vectors = normal\n ug.cell_data.vectors.name = 'panel_normal'\n ug.point_data.scalars = np.arange(0, coords.shape[0])\n ug.point_data.scalars.name = 'n_id'\n ug.point_data.add_array(point_struct_id)\n ug.point_data.get_array(1).name = 'point_struct_id'\n ug.point_data.add_array(point_cf)\n ug.point_data.get_array(2).name = 'point_steady_force'\n ug.point_data.add_array(u_inf)\n ug.point_data.get_array(3).name = 'u_inf'\n write_data(ug, filename)\n" }, { "path": "sharpy/postproc/asymptoticstability.py", "content": "import os\nimport warnings\nimport numpy as np\nimport scipy.linalg as sclalg\nimport sharpy.utils.settings as settings_utils\nfrom sharpy.utils.solver_interface import solver, BaseSolver, initialise_solver\nimport sharpy.utils.cout_utils as cout\nimport sharpy.utils.algebra as algebra\nimport sharpy.solvers.lindynamicsim as lindynamicsim\nimport sharpy.structure.utils.modalutils as modalutils\nimport sharpy.utils.frequencyutils as frequencyutils\nimport sharpy.linear.src.libss as libss\nimport h5py\n\n\n@solver\nclass AsymptoticStability(BaseSolver):\n \"\"\"\n Calculates the asymptotic stability properties of the linearised system by computing\n the corresponding eigenvalues and eigenvectors.\n\n The output of this solver is written to the ``stability`` directory in the case output.\n\n The stability of the systems specified in ``target_systems`` is performed. If the system has been previously\n scaled, a ``reference_velocity`` should be provided to compute the stability at such point.\n\n The eigenvalues can be truncated, keeping a minimum ``num_evals`` (sorted by decreasing real part) or by limiting\n the higher frequency modes through ``frequency_cutoff``.\n\n Results can be saved to file using ``export_eigenvalues``. The setting ``display_root_locus`` shows a simple\n Argand diagram where the continuous time eigenvalues are displayed.\n\n The eigenvectors can be displayed (in .vtu format for use in Paraview) with the ``modes_to_plot`` setting, whereby\n the user specifies the mode indices that are to be plotted (sorted with in the same way as the eigenvalue table,\n i.e. by decreasing real part). A snapshot of the eigenvector is produced for the 0, 45, 90 and 135 degree phases.\n This feature currently supports the flexible structural modes and does not show the rigid body contribution.\n The output is written to the ``stability/modes`` folder and includes the structure at the\n reference linearisation state.\n \"\"\"\n solver_id = 'AsymptoticStability'\n solver_classification = 'post-processor'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = False\n settings_description['print_info'] = 'Print information and table of eigenvalues'\n\n settings_types['reference_velocity'] = 'float'\n settings_default['reference_velocity'] = 1.\n settings_description['reference_velocity'] = 'Reference velocity at which to compute eigenvalues for scaled systems'\n\n settings_types['frequency_cutoff'] = 'float'\n settings_default['frequency_cutoff'] = 0\n settings_description['frequency_cutoff'] = 'Truncate higher frequency modes. If zero none are truncated'\n\n settings_types['export_eigenvalues'] = 'bool'\n settings_default['export_eigenvalues'] = False\n settings_description['export_eigenvalues'] = 'Save eigenvalues and eigenvectors to file.'\n\n settings_types['output_file_format'] = 'str'\n settings_default['output_file_format'] = 'dat'\n settings_description['output_file_format'] = 'Eigenvalue/eigenvector output file format. HDF5 or text (.dat) files.'\n settings_options['output_file_format'] = ['h5', 'dat']\n\n settings_types['display_root_locus'] = 'bool'\n settings_default['display_root_locus'] = False\n settings_description['display_root_locus'] = 'Show plot with eigenvalues on Argand diagram'\n\n settings_types['velocity_analysis'] = 'list(float)'\n settings_default['velocity_analysis'] = []\n settings_description['velocity_analysis'] = 'List containing min, max and number ' \\\n 'of velocities to analyse the system'\n\n settings_types['target_system'] = 'list(str)'\n settings_default['target_system'] = ['aeroelastic']\n settings_description['target_system'] = 'System or systems for which to find frequency response.'\n settings_options['target_system'] = ['aeroelastic', 'aerodynamic', 'structural']\n\n settings_types['num_evals'] = 'int'\n settings_default['num_evals'] = 200\n settings_description['num_evals'] = 'Number of eigenvalues to retain.'\n\n settings_types['modes_to_plot'] = 'list(int)'\n settings_default['modes_to_plot'] = []\n settings_description['modes_to_plot'] = 'List of mode numbers to plot. Plots the 0, 45, 90 and 135' \\\n 'degree phases.'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.settings = None\n self.data = None\n self.folder = None\n self.print_info = False\n\n self.frequency_cutoff = np.inf\n self.num_evals = None\n\n self.postprocessors = dict()\n self.with_postprocessors = False\n self.caller = None\n\n def initialise(self, data, custom_settings=None, caller=None, restart=False):\n self.data = data\n\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default, \n options=self.settings_options, no_ctype=True)\n\n self.num_evals = self.settings['num_evals']\n\n self.folder = data.output_folder + '/stability/'\n if not os.path.exists(self.folder):\n os.makedirs(self.folder)\n\n if self.settings['print_info']:\n self.print_info = True\n else:\n self.print_info = False\n\n try:\n self.frequency_cutoff = self.settings['frequency_cutoff']\n except AttributeError:\n self.frequency_cutoff = float(self.settings['frequency_cutoff'])\n\n if self.frequency_cutoff == 0:\n self.frequency_cutoff = np.inf\n\n self.caller = caller\n\n def run(self, **kwargs):\n \"\"\"\n Computes the eigenvalues and eigenvectors\n\n Returns:\n eigenvalues (np.ndarray): Eigenvalues sorted and frequency truncated\n eigenvectors (np.ndarray): Corresponding mode shapes\n\n \"\"\"\n online = settings_utils.set_value_or_default(kwargs, 'online', False)\n\n # if the system is scaled, only one system can be analysed\n if self.settings['reference_velocity'] != 1. and self.data.linear.linear_system.uvlm.scaled:\n ss_list = [self.data.linear.linear_system.update(self.settings['reference_velocity'])]\n not_scaled = False\n system_name_list = ['aeroelastic']\n if len(self.settings['target_system']) > 1:\n cout.cout_wrap('Warning: the system is scaled thus the only analysis currently supported is'\n ' for the aeroelastic system', 3)\n else:\n ss_list = [frequencyutils.find_target_system(self.data, system_name) for system_name in\n self.settings['target_system']]\n not_scaled = True\n system_name_list = self.settings['target_system']\n\n self.compute_eigenvalues(ss_list, system_name_list, not_scaled)\n\n return self.data\n\n def compute_eigenvalues(self, ss, system_name_list=None, not_scaled=True):\n \"\"\"\n Computes the eigenvalues and eigenvectors of the state-space\n\n Args:\n ss (libss.StateSpace or list([libss.StateSpace]): State-space or list of state-spaces\n system_name_list (list([str]): Names of systems in the case multiple systems are required\n not_scaled (bool): Flag to indicate whether the systems are assembled in non-dimensional time\n \"\"\"\n\n if type(ss) is libss.StateSpace:\n ss_list = [ss]\n if system_name_list is None:\n system_name_list = ['']\n elif type(ss) is list:\n ss_list = ss\n\n if system_name_list is None:\n system_name_list = []\n for sys, sys_number in enumerate(ss_list):\n system_name_list.append(f'system{sys_number:g}')\n if type(sys) is not libss.StateSpace:\n raise TypeError(f'State-space {sys_number} is not type libss.StateSpace')\n else:\n raise TypeError('ss input must be either a libss.StateSpace instance or a list[libss.StateSpace]')\n\n for ith, system in enumerate(ss_list):\n system_name = system_name_list[ith]\n\n if self.print_info:\n cout.cout_wrap('Calculating %s eigenvalues using direct method' % system_name)\n\n eigenvalues, eigenvectors = sclalg.eig(system.A)\n\n # Convert DT eigenvalues into CT\n if system.dt:\n eigenvalues = self.convert_to_continuoustime(system.dt, eigenvalues, not_scaled)\n\n num_evals = min(self.num_evals, len(eigenvalues))\n\n eigenvalues, eigenvectors = self.sort_eigenvalues(eigenvalues, eigenvectors, self.frequency_cutoff,\n number_of_eigenvalues=num_evals)\n\n if self.settings['export_eigenvalues']:\n self.export_eigenvalues(num_evals, eigenvalues, eigenvectors, filename=system_name)\n\n if self.settings['print_info']:\n cout.cout_wrap(f'Dynamical System Eigenvalues - {system_name} system')\n if system_name != '':\n eig_table_filename = system_name + '_'\n else:\n eig_table_filename = ''\n eigenvalue_description_file = self.folder + '/{:s}eigenvaluetable.txt'.format(eig_table_filename)\n eigenvalue_table = modalutils.EigenvalueTable(filename=eigenvalue_description_file)\n eigenvalue_table.print_header(eigenvalue_table.headers)\n eigenvalue_table.print_evals(eigenvalues[:self.num_evals])\n eigenvalue_table.close_file()\n\n if self.settings['display_root_locus']:\n self.display_root_locus(eigenvalues)\n\n if len(self.settings['velocity_analysis']) == 3 and system_name == 'aeroelastic':\n assert self.data.linear.linear_system.uvlm.scaled, \\\n 'The UVLM system is unscaled, unable to rescale the structural equations only. Rerun with a ' \\\n 'normalised UVLM system.'\n self.velocity_analysis()\n\n # Under development\n if len(self.settings['modes_to_plot']) != 0 and system_name == 'aeroelastic':\n self.plot_modes(eigenvectors)\n\n return eigenvalues, eigenvectors\n\n def convert_to_continuoustime(self, dt, discrete_time_eigenvalues, not_scaled=False):\n r\"\"\"\n Convert eigenvalues to discrete time. The ``not_scaled`` argument can be used to bypass the search from\n within SHARPy of scaling factors. For instance, when the state-space of choice is not part of a standard\n SHARPy case but rather an interpolated ROM etc.\n\n The eigenvalues are converted to continuous time using\n\n .. math:: \\lambda_{ct} = \\frac{\\log (\\lambda_{dt})}{\\Delta t}\n\n If the system is scaled, the dimensional time step is retrieved as\n\n .. math:: \\Delta t_{dim} = \\bar{\\Delta t} \\frac{l_{ref}}{U_{\\infty, actual}}\n\n where :math:`l_{ref}` is the reference length and :math:`U_{\\infty, actual}` is the free stream velocity at\n which to calculate the eigenvalues.\n\n Args:\n dt (float): Discrete time increment.\n discrete_time_eigenvalues (np.ndarray): Array of discrete time eigenvalues.\n not_scaled (bool): Treat the system as not scaled. No Scaling Factors will be searched in SHARPy.\n \"\"\"\n if not_scaled:\n dt = dt\n else:\n try:\n ScalingFacts = self.data.linear.linear_system.uvlm.sys.ScalingFacts\n if ScalingFacts['length'] != 1.0 and ScalingFacts['time'] != 1.0:\n dt *= ScalingFacts['length'] / self.settings['reference_velocity']\n else:\n dt = dt\n except AttributeError:\n dt = dt\n\n return np.log(discrete_time_eigenvalues) / dt\n\n def export_eigenvalues(self, num_evals, eigenvalues, eigenvectors, filename=None):\n \"\"\"\n Saves a ``num_evals`` number of eigenvalues and eigenvectors to file.\n\n The files are saved in the output directory and include:\n\n * ``{system_name}_eigenvalues.dat``: Array of eigenvalues of shape ``(num_evals, 2)`` where the first column corresponds\n to the real part and the second column to the imaginary part.\n\n * ``{system_name}_stability.h5``: An ``.h5`` file containing the desired number of eigenvalues and eigenvectors of the\n chosen systems.\n\n The units of the eigenvalues are ``rad/s``.\n\n Args:\n num_evals (int): Number of eigenvalues to save.\n eigenvalues (np.ndarray): Eigenvalue array.\n eigenvectors (np.ndarray): Matrix of eigenvectors.\n filename (str (optional)): Optional prefix of the output filenames.\n\n See Also:\n Loading and saving complex arrays:\n https://stackoverflow.com/questions/6494102/how-to-save-and-load-an-array-of-complex-numbers-using-numpy-savetxt/6522396\n \"\"\"\n\n stability_folder_path = self.folder\n\n if filename is None or filename == '':\n filename = ''\n else:\n filename += '_'\n\n if self.settings['output_file_format'] == 'dat':\n np.savetxt(self.folder + f'/{filename:s}eigenvalues.dat', eigenvalues.view(float).reshape(-1, 2))\n np.savetxt(self.folder + f'/{filename:s}eigenvectors_r.dat', eigenvectors.real)\n np.savetxt(self.folder + f'/{filename:s}eigenvectors_i.dat', eigenvectors.imag)\n elif self.settings['output_file_format'] == 'h5':\n with h5py.File(stability_folder_path + f'/{filename:s}stability.h5', 'w') as f:\n f.create_dataset('eigenvalues', data=eigenvalues, dtype=complex)\n f.create_dataset('eigenvectors', data=eigenvectors, dtype=complex)\n f.create_dataset('num_eigenvalues', data=num_evals, dtype=int)\n else:\n raise TypeError(f'Unrecognised file type saving option {self.settings[\"output_file_format\"]}')\n # this shouldn't happen as the settings_options should check the validity of the setting\n\n def velocity_analysis(self):\n \"\"\"\n Velocity analysis for scaled systems.\n\n Runs the stability analysis for different velocities for aeroelastic systems that have been previously scaled.\n\n For every velocity, the linear system is updated. This involves updating the structural matrices and the\n coupling matrix. The eigenvalues saved are in continuous time.\n\n It saves the results to a ``.dat`` file where the first column corresponds to the free stream velocity and the\n second and third columns to the real and imaginary parts of the eigenvalues.\n \"\"\"\n\n ulb, uub, num_u = self.settings['velocity_analysis']\n\n if self.settings['print_info']:\n cout.cout_wrap('Velocity Asymptotic Stability Analysis', 1)\n cout.cout_wrap('Initial velocity: {:02f} m/s'.format(ulb), 1)\n cout.cout_wrap('Final velocity: {:02f} m/s'.format(uub), 1)\n cout.cout_wrap('Number of evaluations: {:g}'.format(num_u), 1)\n\n u_inf_vec = np.linspace(ulb, uub, int(num_u))\n\n real_part_plot = []\n imag_part_plot = []\n uinf_part_plot = []\n\n for i in range(len(u_inf_vec)):\n ss_aeroelastic = self.data.linear.linear_system.update(u_inf_vec[i])\n\n eigs, eigenvectors = sclalg.eig(ss_aeroelastic.A)\n\n eigs, eigenvectors = self.sort_eigenvalues(eigs, eigenvectors)\n\n # Obtain dimensional time\n dt_dimensional = self.data.linear.linear_system.uvlm.sys.ScalingFacts['length'] / u_inf_vec[i] \\\n * ss_aeroelastic.dt\n\n eigs_cont = np.log(eigs) / dt_dimensional\n Nunst = np.sum(eigs_cont.real > 0)\n fn = np.abs(eigs_cont)\n\n if self.settings['print_info']:\n cout.cout_wrap('LTI\\tu: %.2f m/2\\tmax. CT eig. real: %.6f\\t' \\\n % (u_inf_vec[i], np.max(eigs_cont.real)))\n cout.cout_wrap('\\tN unstab.: %.3d' % (Nunst,))\n cout.cout_wrap(\n '\\tUnstable aeroelastic natural frequency CT(rad/s):' + Nunst * '\\t%.2f' % tuple(fn[:Nunst]))\n\n # Store eigenvalues for plot\n real_part_plot.append(eigs_cont.real)\n imag_part_plot.append(eigs_cont.imag)\n uinf_part_plot.append(np.ones_like(eigs_cont.real) * u_inf_vec[i])\n\n real_part_plot = np.hstack(real_part_plot)\n imag_part_plot = np.hstack(imag_part_plot)\n uinf_part_plot = np.hstack(uinf_part_plot)\n\n velocity_file_name = self.folder + '/velocity_analysis_min{:04g}_max{:04g}_nvel{:04g}.dat'.format(\n ulb * 10,\n uub * 10,\n num_u)\n\n np.savetxt(velocity_file_name,\n np.concatenate((uinf_part_plot, real_part_plot, imag_part_plot)).reshape((-1, 3), order='F'))\n\n if self.print_info:\n cout.cout_wrap('\\t\\tSuccessfully saved velocity analysis to {:s}'.format(velocity_file_name), 2)\n\n @staticmethod\n def display_root_locus(eigenvalues):\n \"\"\"\n Displays root locus diagrams.\n\n Returns the ``fig`` and ``ax`` handles for further editing.\n\n Returns:\n fig:\n ax:\n \"\"\"\n\n try:\n import matplotlib.pyplot as plt\n except ModuleNotFoundError:\n cout.cout_wrap('Could not plot in asymptoticstability beacuse there is no Matplotlib', 4)\n return\n fig, ax = plt.subplots()\n\n ax.scatter(np.real(eigenvalues), np.imag(eigenvalues),\n s=6,\n color='k',\n marker='s')\n ax.set_xlabel(r'Real, $\\mathbb{R}(\\lambda_i)$ [rad/s]')\n ax.set_ylabel(r'Imag, $\\mathbb{I}(\\lambda_i)$ [rad/s]')\n ax.grid(True)\n fig.show()\n\n return fig, ax\n\n def plot_modes(self, eigenvectors):\n r\"\"\"\n Plot the aeroelastic mode shapes for the first ``n_modes_to_plot``\n\n Plots the 0, 45, 90 and 135 degrees phase of the mode. Also plots the reference at the linearisation state.\n\n .. math:: x_{out} = Re(\\Phi_i e^{i\\theta})\n\n for :math:`\\theta \\in \\{0, \\pi/4, \\pi/2, 3\\pi/4}`.\n\n \"\"\"\n try:\n import matplotlib.pyplot as plt\n except ModuleNotFoundError:\n cout.cout_wrap('Could not plot in asymptoticstability because there is no Matplotlib', 4)\n return\n\n mode_shape_list = self.settings['modes_to_plot']\n\n route = self.folder + '/modes/'\n if not os.path.isdir(route):\n os.makedirs(route, exist_ok=True)\n\n for mode in mode_shape_list:\n # Scale mode\n\n beam = self.data.linear.linear_system.beam\n displacement_states = beam.ss.states // 2\n structural_states = beam.ss.states\n structural_modal_coords = beam.sys.modal\n\n for phase in [0, 1, 2, 3]:\n v = eigenvectors[-structural_states:-structural_states//2, mode]\n v_dot = eigenvectors[-structural_states//2:, mode]\n\n if beam.sys.clamped:\n num_dof_rig = 1 # to get the full vector (if 0 line356 returns empty array)\n else:\n warnings.warn('The rigid body motion contribution to the mode will not be shown, '\n 'just the flexible contributions.')\n num_dof_rig = beam.sys.num_dof_rig\n\n if structural_modal_coords:\n # project aeroelastic mode back to modal coordinates\n phi = beam.sys.U\n eta = phi.dot(v)\n eta_dot = phi.dot(v_dot)[:-num_dof_rig]\n else:\n eta = v[:-num_dof_rig]\n eta_dot = v_dot[:-num_dof_rig]\n\n eta_phase = np.real(np.exp(1j * phase * np.pi / 4) * eta)\n amplitude_factor = modalutils.scale_mode(self.data,\n eta_phase,\n rot_max_deg=10, perc_max=0.15)\n eta_phase *= amplitude_factor\n zeta_mode = modalutils.get_mode_zeta(self.data, eta_phase)\n modalutils.write_zeta_vtk(zeta_mode, self.data.linear.tsaero0.zeta,\n filename_root=route + f'mode_{mode:06g}_phase{phase:04g}')\n\n # Reference - linearisation state\n eta *= 0\n zeta_mode = modalutils.get_mode_zeta(self.data, eta.real)\n modalutils.write_zeta_vtk(zeta_mode, self.data.linear.tsaero0.zeta, filename_root=route + 'mode_ref')\n\n @staticmethod\n def sort_eigenvalues(eigenvalues, eigenvectors, frequency_cutoff=0, number_of_eigenvalues=None):\n \"\"\"\n Sort continuous-time eigenvalues by order of magnitude.\n\n The conjugate of complex eigenvalues is removed, then if specified, high frequency modes are truncated.\n Finally, the eigenvalues are sorted by largest to smallest real part.\n\n Args:\n eigenvalues (np.ndarray): Continuous-time eigenvalues\n eigenvectors (np.ndarray): Corresponding right eigenvectors\n frequency_cutoff (float): Cutoff frequency for truncation ``[rad/s]``\n number_of_eigenvalues (int (optional)): Number of eigenvalues to retain\n\n Returns:\n tuple(np.array, np.array): eigenvalues and eigenvectors\n \"\"\"\n\n if frequency_cutoff == 0:\n frequency_cutoff = np.inf\n\n # Remove poles in the negative imaginary plane (Im(\\lambda)<0)\n criteria_a = np.abs(np.imag(eigenvalues)) <= frequency_cutoff\n # criteria_b = np.imag(eigenvalues) > -1e-2\n eigenvalues_truncated = eigenvalues[criteria_a].copy()\n eigenvectors_truncated = eigenvectors[:, criteria_a].copy()\n\n order = np.argsort(eigenvalues_truncated.real)[::-1]\n\n if number_of_eigenvalues is not None:\n if number_of_eigenvalues > len(order):\n cout.cout_wrap(f'Desired number of eigenvalues ({number_of_eigenvalues}) exceeds system size '\n f'({len(order)}) after frequency truncation.', 3)\n else:\n order = order[:number_of_eigenvalues]\n return eigenvalues_truncated[order], eigenvectors_truncated[:, order]\n" }, { "path": "sharpy/postproc/beamloads.py", "content": "import os\nimport numpy as np\nimport os\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\nimport sharpy.structure.utils.xbeamlib as xbeamlib\n\n\n@solver\nclass BeamLoads(BaseSolver):\n \"\"\"\n Writes to file the total loads acting on the beam elements\n\n \"\"\"\n solver_id = 'BeamLoads'\n solver_classification = 'post-processor'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['csv_output'] = 'bool'\n settings_default['csv_output'] = False\n settings_description['csv_output'] = 'Write ``csv`` file with results'\n\n settings_types['output_file_name'] = 'str'\n settings_default['output_file_name'] = 'beam_loads'\n settings_description['output_file_name'] = 'Output file name'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n\n self.settings = None\n self.data = None\n\n self.folder = None\n self.caller = None\n\n def initialise(self, data, custom_settings=None, caller=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n self.caller = caller\n\n self.folder = data.output_folder + '/beam/'\n if not os.path.isdir(self.folder):\n os.makedirs(self.folder)\n\n def run(self, **kwargs):\n\n online = settings_utils.set_value_or_default(kwargs, 'online', False)\n\n self.calculate_loads(online)\n if self.settings['csv_output']:\n self.print_loads(online)\n return self.data\n\n def print_loads(self, online):\n if online:\n it = len(self.data.structure.timestep_info) - 1\n n_elem = self.data.structure.timestep_info[it].psi.shape[0]\n data = np.zeros((n_elem, 10))\n # coords\n data[:, 0:3] = self.data.structure.timestep_info[it].postproc_cell['coords_a']\n header = 'x_a, y_a, z_a, '\n # beam number\n data[:, 3] = self.data.structure.beam_number\n header += 'beam_number, '\n # loads_0\n data[:, 4:10] = self.data.structure.timestep_info[it].postproc_cell['loads'][:, :]\n header += 'Fx, Fy, Fz, Mx, My, Mz'\n\n filename = self.folder\n filename += self.settings['output_file_name'] + '_' + '{0}'.format(it)\n filename += '.csv'\n np.savetxt(filename, data, delimiter=',', header=header)\n else:\n for it in range(len(self.data.structure.timestep_info)):\n it = len(self.data.structure.timestep_info) - 1\n n_elem = self.data.structure.timestep_info[it].num_elem\n data = np.zeros((n_elem, 10))\n # coords\n data[:, 0:3] = self.data.structure.timestep_info[it].postproc_cell['coords_a']\n header = 'x_a, y_a, z_a, '\n # beam number\n data[:, 3] = self.data.structure.beam_number\n header += 'beam_number, '\n # loads_0\n data[:, 4:10] = self.data.structure.timestep_info[it].postproc_cell['loads'][:, :]\n header += 'Fx, Fy, Fz, Mx, My, Mz'\n\n filename = self.folder\n filename += self.settings['output_file_name'] + '_' + '{0}'.format(it)\n filename += '.csv'\n np.savetxt(filename, data, delimiter=',', header=header)\n\n def calculate_loads(self, online):\n if online:\n it = -1\n timestep_add_loads(self.data.structure, self.data.structure.timestep_info[it])\n self.calculate_coords_a(self.data.structure.timestep_info[it])\n else:\n for it in range(len(self.data.structure.timestep_info)):\n timestep_add_loads(self.data.structure, self.data.structure.timestep_info[it])\n self.calculate_coords_a(self.data.structure.timestep_info[it])\n\n def calculate_coords_a(self, timestep_info):\n timestep_info.postproc_cell['coords_a'] = np.zeros((timestep_info.num_elem, 3))\n for ielem in range(timestep_info.num_elem):\n iglobal_node = self.data.structure.connectivities[ielem, 2]\n timestep_info.postproc_cell['coords_a'][ielem, :] = timestep_info.pos[iglobal_node, :]\n\n\ndef timestep_add_loads(structure, timestep):\n timestep.postproc_cell['strain'], timestep.postproc_cell['loads'] = \\\n xbeamlib.cbeam3_loads(structure, timestep)\n\n # def calculate_loads(self):\n # # initial (ini) loads\n # tstep = self.data.structure.ini_info\n # pos = tstep.pos\n # psi = tstep.psi\n #\n # tstep.postproc_cell['gamma'] = np.zeros((self.data.structure.num_elem, 3))\n # tstep.postproc_cell['kappa'] = np.zeros((self.data.structure.num_elem, 3))\n #\n # for ielem in range(self.data.structure.num_elem):\n # crv = 0.5*(psi[ielem, 1, :] + psi[ielem, 0, :])\n # cba = algebra.crv2rotation(crv).T\n # tan = algebra.crv2tan(crv)\n #\n # inode0 = self.data.structure.elements[ielem].global_connectivities[0]\n # inode1 = self.data.structure.elements[ielem].global_connectivities[1]\n # tstep.postproc_cell['gamma'][ielem, :] = (\n # np.dot(cba,\n # pos[inode1, :] - pos[inode0, :]) /\n # np.linalg.norm(pos[inode1, :] - pos[inode0, :]))\n # tstep.postproc_cell['kappa'][ielem, :] = (\n # np.dot(tan,\n # psi[ielem, 1, :] - psi[ielem, 0, :]) /\n # np.linalg.norm(pos[inode1, :] - pos[inode0, :]))\n #\n # # time-dependant loads\n # for it in range(len(self.data.structure.timestep_info)):\n # tstep = self.data.structure.timestep_info[it]\n # pos = tstep.pos\n # psi = tstep.psi\n #\n # tstep.postproc_cell['gamma'] = np.zeros((self.data.structure.num_elem, 3))\n # tstep.postproc_cell['kappa'] = np.zeros((self.data.structure.num_elem, 3))\n # tstep.postproc_cell['strain'] = np.zeros((self.data.structure.num_elem, 6))\n # tstep.postproc_cell['loads'] = np.zeros((self.data.structure.num_elem, 6))\n #\n # for ielem in range(self.data.structure.num_elem):\n # crv = 0.5*(psi[ielem, 2, :] + psi[ielem, 0, :])\n # cba = algebra.crv2rotation(crv).T\n # tan = algebra.crv2tan(crv)\n #\n # inode0 = self.data.structure.elements[ielem].global_connectivities[0]\n # inode1 = self.data.structure.elements[ielem].global_connectivities[1]\n # tstep.postproc_cell['gamma'][ielem, :] = (\n # np.dot(cba,\n # pos[inode1, :] - pos[inode0, :]) /\n # np.linalg.norm(pos[inode1, :] - pos[inode0, :]))\n # tstep.postproc_cell['kappa'][ielem, :] = (\n # np.dot(tan,\n # psi[ielem, 1, :] - psi[ielem, 0, :]) /\n # np.linalg.norm(pos[inode1, :] - pos[inode0, :]))\n #\n # tstep.postproc_cell['strain'][ielem, 0:3] = (\n # tstep.postproc_cell['gamma'][ielem, :]\n # -\n # self.data.structure.ini_info.postproc_cell['gamma'][ielem, :])\n # tstep.postproc_cell['strain'][ielem, 3:6] = (\n # tstep.postproc_cell['kappa'][ielem, :]\n # -\n # self.data.structure.ini_info.postproc_cell['kappa'][ielem, :])\n # tstep.postproc_cell['loads'][ielem, :] = np.dot(\n # self.data.structure.stiffness_db[self.data.structure.elements[ielem].stiff_index, :, :],\n # tstep.postproc_cell['strain'][ielem, :])\n\n # def calculate_loads(self):\n # order = [0, 2, 1]\n # # initial (ini) loads\n # tstep = self.data.structure.ini_info\n # pos = tstep.pos\n # psi = tstep.psi\n #\n # gamma0 = np.zeros((self.data.structure.num_elem, 2, 3))\n # kappa0 = np.zeros((self.data.structure.num_elem, 2, 3))\n # counter = np.zeros((self.data.structure.num_node,), dtype=int)\n #\n # for ielem in range(self.data.structure.num_elem):\n # for isegment in range(self.data.structure.elements[ielem].n_nodes - 1):\n # i_local_node0 = order[isegment]\n # i_local_node1 = order[isegment + 1]\n # crv = 0.5*(psi[ielem, i_local_node1, :] + psi[ielem, i_local_node0, :])\n #\n # cba = algebra.crv2rotation(crv).T\n # tan = algebra.crv2tan(crv)\n #\n # inode0 = self.data.structure.elements[ielem].global_connectivities[i_local_node0]\n # inode1 = self.data.structure.elements[ielem].global_connectivities[i_local_node1]\n #\n # counter[inode0] += 1\n # counter[inode1] += 1\n #\n # print('----')\n # print(ielem)\n # print(isegment)\n # print(inode0, inode1)\n # print(counter[inode0], counter[inode1])\n # print('----')\n #\n # gamma0[ielem, isegment, :] = (\n # np.dot(cba,\n # pos[inode1, :] - pos[inode0, :]) /\n # np.linalg.norm(pos[inode1, :] - pos[inode0, :]))\n # kappa0[ielem, isegment, :] = (\n # np.dot(tan,\n # psi[ielem, i_local_node1, :] - psi[ielem, i_local_node0, :]) /\n # np.linalg.norm(pos[inode1, :] - pos[inode0, :]))\n #\n # # time-dependant loads\n # for it in range(len(self.data.structure.timestep_info)):\n # tstep = self.data.structure.timestep_info[it]\n # pos = tstep.pos\n # psi = tstep.psi\n #\n # gamma = np.zeros((self.data.structure.num_elem, 2, 3))\n # kappa = np.zeros((self.data.structure.num_elem, 2, 3))\n # # tstep.postproc_cell['strain'] = np.zeros((self.data.structure.num_elem, 6))\n # tstep.postproc_node['loads'] = np.zeros((self.data.structure.num_node, 6))\n # strain = np.zeros((self.data.structure.num_elem, 2, 6))\n # for ielem in range(self.data.structure.num_elem):\n # for isegment in range(self.data.structure.elements[ielem].n_nodes - 1):\n # i_local_node0 = order[isegment]\n # i_local_node1 = order[isegment + 1]\n # crv = 0.5*(psi[ielem, i_local_node1, :] + psi[ielem, i_local_node0, :])\n #\n # cba = algebra.crv2rotation(crv).T\n # tan = algebra.crv2tan(crv)\n #\n # inode0 = self.data.structure.elements[ielem].global_connectivities[i_local_node0]\n # inode1 = self.data.structure.elements[ielem].global_connectivities[i_local_node1]\n #\n # gamma[ielem, isegment, :] = (\n # np.dot(cba,\n # pos[inode1, :] - pos[inode0, :]) /\n # np.linalg.norm(pos[inode1, :] - pos[inode0, :]))\n # kappa[ielem, isegment, :] = (\n # np.dot(tan,\n # psi[ielem, i_local_node1, :] - psi[ielem, i_local_node0, :]) /\n # np.linalg.norm(pos[inode1, :] - pos[inode0, :]))\n # strain[ielem, isegment, 0:3] += (\n # gamma[ielem, isegment, :]\n # -\n # gamma0[ielem, isegment, :])\n # strain[ielem, isegment, 3:6] += (\n # kappa[ielem, isegment, :]\n # -\n # kappa0[ielem, isegment, :])\n # # it might be necessary to rotate the results so that the B frame is the\n # # Master FoR (so that all the loads -- intrinsically in material FoR -- can be\n # # added together at the nodes).\n # prerotate = np.eye(6)\n # posrotate = np.eye(6)\n # if not self.data.structure.node_master_elem[inode0, 0] == ielem:\n # cab2 = algebra.crv2rotation(psi[ielem, self.data.structure.node_master_elem[inode0, 1], :])\n # prerotate[0:3, 0:3] = np.dot(cab2.T, cba.T)\n # prerotate[3:6, 3:6] = np.dot(cab2.T, cba.T)\n #\n # tstep.postproc_node['loads'][inode0, :] = np.dot(prerotate,\n # np.dot(np.dot(\n # self.data.structure.stiffness_db[self.data.structure.elements[ielem].stiff_index, :, :],\n # strain[ielem, isegment, :])/counter[inode0], posrotate))\n # prerotate = np.eye(6)\n # posrotate = np.eye(6)\n # if not self.data.structure.node_master_elem[inode1, 0] == ielem:\n # cab2 = algebra.crv2rotation(psi[ielem, self.data.structure.node_master_elem[inode1, 1], :])\n # prerotate[0:3, 0:3] = np.dot(cab2.T, cba.T)\n # prerotate[3:6, 3:6] = np.dot(cab2.T, cba.T)\n #\n # tstep.postproc_node['loads'][inode1, :] = np.dot(prerotate,\n # np.dot(np.dot(\n # self.data.structure.stiffness_db[self.data.structure.elements[ielem].stiff_index, :, :],\n # strain[ielem, isegment, :])/counter[inode1], posrotate))\n # # tstep.postproc_node['loads'][inode1, :] = np.dot(\n # # self.data.structure.stiffness_db[self.data.structure.elements[ielem].stiff_index, :, :],\n # # strain[ielem, isegment, :])/counter[inode1]\n" }, { "path": "sharpy/postproc/beamplot.py", "content": "import os\n\nimport numpy as np\n\nimport sharpy.utils.cout_utils as cout\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.algebra as algebra\n\n\nimport vtk\nfrom vtk.numpy_interface import algorithms as algs\nfrom vtk.numpy_interface import dataset_adapter as dsa\n\n\n@solver\nclass BeamPlot(BaseSolver):\n \"\"\"\n Plots beam to Paraview format\n \"\"\"\n solver_id = 'BeamPlot'\n solver_classification = 'post-processor'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['include_rbm'] = 'bool'\n settings_default['include_rbm'] = True\n settings_description['include_rbm'] = 'Include frame of reference rigid body motion'\n\n settings_types['include_FoR'] = 'bool'\n settings_default['include_FoR'] = False\n settings_description['include_FoR'] = 'Include frame of reference variables'\n\n settings_types['include_applied_forces'] = 'bool'\n settings_default['include_applied_forces'] = True\n settings_description['include_applied_forces'] = 'Write beam applied forces'\n\n settings_types['include_applied_moments'] = 'bool'\n settings_default['include_applied_moments'] = True\n settings_description['include_applied_moments'] = 'Write beam applied moments'\n\n settings_types['name_prefix'] = 'str'\n settings_default['name_prefix'] = ''\n settings_description['name_prefix'] = 'Name prefix for files'\n\n settings_types['output_rbm'] = 'bool'\n settings_default['output_rbm'] = True\n settings_description['output_rbm'] = 'Write ``csv`` file with rigid body motion data'\n\n settings_types['stride'] = 'int'\n settings_default['stride'] = 1\n settings_description['stride'] = 'Number of steps between the execution calls when run online'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n\n self.settings = None\n self.data = None\n\n self.folder = ''\n self.filename = ''\n self.filename_for = ''\n self.caller = None\n\n def initialise(self, data, custom_settings=None, caller=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n # create folder for containing files if necessary\n self.folder = data.output_folder + '/beam/'\n if not os.path.exists(self.folder):\n os.makedirs(self.folder)\n self.filename = (self.folder +\n self.settings['name_prefix'] +\n 'beam_' +\n self.data.settings['SHARPy']['case'])\n self.filename_for = (self.folder +\n self.settings['name_prefix'] +\n 'for_' +\n self.data.settings['SHARPy']['case'])\n self.caller = caller\n\n def run(self, **kwargs):\n\n online = settings_utils.set_value_or_default(kwargs, 'online', False)\n\n self.plot(online)\n if not online:\n self.write()\n cout.cout_wrap('...Finished', 1)\n return self.data\n\n def write(self):\n if self.settings['output_rbm']:\n filename = self.filename + '_rbm_acc.csv'\n timesteps = len(self.data.structure.timestep_info)\n temp_matrix = np.zeros((timesteps, 6))\n for it in range(timesteps):\n if self.data.structure.timestep_info[it] is not None:\n temp_matrix[it, :] = self.data.structure.timestep_info[it].for_acc\n\n np.savetxt(filename, temp_matrix, delimiter=',')\n\n def plot(self, online):\n if not online:\n for it in range(len(self.data.structure.timestep_info)):\n if self.data.structure.timestep_info[it] is not None:\n self.write_beam(it)\n if self.settings['include_FoR']:\n self.write_for(it)\n elif ((len(self.data.structure.timestep_info) - 1) % self.settings['stride'] == 0):\n it = len(self.data.structure.timestep_info) - 1\n self.write_beam(it)\n if self.settings['include_FoR']:\n self.write_for(it)\n\n def write_beam(self, it):\n it_filename = f\"{self.filename}{it:06d}.vtp\"\n num_nodes = self.data.structure.num_node\n num_elem = self.data.structure.num_elem\n\n conn = np.zeros((num_elem, 3), dtype=int)\n node_id = np.zeros((num_nodes,), dtype=int)\n elem_id = np.zeros((num_elem,), dtype=int)\n coords_a_cell = np.zeros((num_elem, 3), dtype=int)\n local_x = np.zeros((num_nodes, 3))\n local_y = np.zeros((num_nodes, 3))\n local_z = np.zeros((num_nodes, 3))\n coords_a = np.zeros((num_nodes, 3))\n app_forces = np.zeros((num_nodes, 3))\n app_moment = np.zeros((num_nodes, 3))\n\n forces_constraints_nodes = np.zeros((num_nodes, 3))\n moments_constraints_nodes = np.zeros((num_nodes, 3))\n\n tstep = self.data.structure.timestep_info[it]\n\n # aero2inertial rotation\n aero2inertial = tstep.cga()\n\n # coordinates of corners\n coords = tstep.glob_pos(include_rbm=self.settings['include_rbm'])\n\n if tstep.mb_dict is None:\n pass\n else:\n for i_node in range(tstep.num_node):\n c = self.data.structure.timestep_info[0].cga()\n coords[i_node, :] += c @ tstep.for_pos[:3]\n\n # check if I can output gravity forces\n with_gravity = False\n try:\n gravity_forces = tstep.gravity_forces[:]\n gravity_forces_g = np.zeros_like(gravity_forces)\n with_gravity = True\n except AttributeError:\n pass\n\n # check if postproc dicts are present and count/prepare\n with_postproc_cell = False\n try:\n tstep.postproc_cell\n with_postproc_cell = True\n except AttributeError:\n pass\n with_postproc_node = False\n try:\n tstep.postproc_node\n with_postproc_node = True\n except AttributeError:\n pass\n\n # count number of arguments\n postproc_cell_vector = []\n postproc_cell_6vector = []\n for k, v in tstep.postproc_cell.items():\n _, cols = v.shape\n if cols == 1:\n raise NotImplementedError('scalar cell types not supported in beamplot (Easy to implement)')\n # postproc_cell_scalar.append(k)\n elif cols == 3:\n postproc_cell_vector.append(k)\n elif cols == 6:\n postproc_cell_6vector.append(k)\n else:\n raise AttributeError('Only scalar and 3-vector types supported in beamplot')\n # count number of arguments\n postproc_node_scalar = []\n postproc_node_vector = []\n postproc_node_6vector = []\n for k, v in tstep.postproc_node.items():\n try:\n _, cols = v.shape\n except ValueError:\n # for np.arrays with shape (x,)\n cols = 1\n if cols == 1:\n postproc_node_scalar.append(k)\n elif cols == 3:\n postproc_node_vector.append(k)\n elif cols == 6:\n postproc_node_6vector.append(k)\n else:\n raise AttributeError('Only scalar and 3-vector types supported in beamplot')\n\n for i_node in range(num_nodes):\n i_elem = self.data.structure.node_master_elem[i_node, 0]\n i_local_node = self.data.structure.node_master_elem[i_node, 1]\n node_id[i_node] = i_node\n\n v1 = np.array([1., 0, 0])\n v2 = np.array([0., 1, 0])\n v3 = np.array([0., 0, 1])\n cab = algebra.crv2rotation(\n tstep.psi[i_elem, i_local_node, :])\n local_x[i_node, :] = np.dot(aero2inertial, np.dot(cab, v1))\n local_y[i_node, :] = np.dot(aero2inertial, np.dot(cab, v2))\n local_z[i_node, :] = np.dot(aero2inertial, np.dot(cab, v3))\n\n if i_local_node == 2:\n coords_a_cell[i_elem, :] = tstep.pos[i_node, :]\n coords_a[i_node, :] = tstep.pos[i_node, :]\n\n # applied forces\n cab = algebra.crv2rotation(tstep.psi[i_elem, i_local_node, :])\n app_forces[i_node, :] = np.dot(aero2inertial,\n np.dot(cab,\n tstep.steady_applied_forces[i_node, 0:3]+\n tstep.unsteady_applied_forces[i_node, 0:3]))\n app_moment[i_node, :] = np.dot(aero2inertial,\n np.dot(cab,\n tstep.steady_applied_forces[i_node, 3:6]+\n tstep.unsteady_applied_forces[i_node, 3:6]))\n forces_constraints_nodes[i_node, :] = np.dot(aero2inertial,\n np.dot(cab,\n tstep.forces_constraints_nodes[i_node, 0:3]))\n moments_constraints_nodes[i_node, :] = np.dot(aero2inertial,\n np.dot(cab,\n tstep.forces_constraints_nodes[i_node, 3:6]))\n\n if with_gravity:\n gravity_forces_g[i_node, 0:3] = np.dot(aero2inertial,\n gravity_forces[i_node, 0:3])\n gravity_forces_g[i_node, 3:6] = np.dot(aero2inertial,\n gravity_forces[i_node, 3:6])\n\n for i_elem in range(num_elem):\n conn[i_elem, :] = self.data.structure.elements[i_elem].reordered_global_connectivities\n elem_id[i_elem] = i_elem\n\n ug = vtk.vtkPolyData(points=coords)\n cells = vtk.vtkCellArray()\n for _conn in conn:\n line = vtk.vtkPolyLine()\n line.GetPointIds().SetNumberOfIds(3)\n line.GetPointIds().SetId(0, _conn[0])\n line.GetPointIds().SetId(1, _conn[1])\n line.GetPointIds().SetId(2, _conn[2])\n cells.InsertNextCell(line)\n ug.SetLines(cells)\n\n ug.GetCellData().AddArray(dsa.numpyTovtkDataArray(np.array(elem_id), name='elem_id'))\n ug.GetCellData().AddArray(dsa.numpyTovtkDataArray(coords_a_cell, name=\"coords_a_elem\"))\n ug.GetPointData().AddArray(\n dsa.numpyTovtkDataArray(node_id, name=\"node_id\")\n )\n ug.GetPointData().AddArray(dsa.numpyTovtkDataArray(local_x, name=\"local_x\"))\n ug.GetPointData().AddArray(dsa.numpyTovtkDataArray(local_y, name=\"local_y\"))\n ug.GetPointData().AddArray(dsa.numpyTovtkDataArray(local_z, name=\"local_z\"))\n ug.GetPointData().AddArray(dsa.numpyTovtkDataArray(coords_a, name=\"coords_a\"))\n\n if with_postproc_cell:\n for k in postproc_cell_vector:\n ug.GetCellData().AddArray(\n dsa.numpyTovtkDataArray(tstep.postproc_cell[k], name=f\"{k}_cell\")\n )\n for k in postproc_cell_6vector:\n for i in range(2):\n ug.GetCellData().AddArray(\n dsa.numpyTovtkDataArray(\n tstep.postproc_cell[k][:, 3*i:3*(i+1)], name=f\"{k}_{i}_cell\"\n )\n )\n\n if self.settings['include_applied_forces']:\n ug.GetPointData().AddArray(dsa.numpyTovtkDataArray(app_forces, name=\"app_forces\"))\n ug.GetPointData().AddArray(\n dsa.numpyTovtkDataArray(forces_constraints_nodes, name=\"forces_constraints_node\")\n )\n if with_gravity:\n ug.GetPointData().AddArray(\n dsa.numpyTovtkDataArray(\n gravity_forces_g[:, :3], name=\"gravity_forces\"\n )\n )\n\n if self.settings['include_applied_moments']:\n ug.GetPointData().AddArray(\n dsa.numpyTovtkDataArray(app_moment, name=\"app_moments\")\n )\n ug.GetPointData().AddArray(\n dsa.numpyTovtkDataArray(moments_constraints_nodes, name=\"moments_constraints_nodes\")\n )\n if with_gravity:\n ug.GetPointData().AddArray(dsa.numpyTovtkDataArray(gravity_forces_g[:, 3:6], name=\"gravity_moments\"))\n\n if with_postproc_node:\n for k in postproc_node_vector:\n ug.GetPointData().AddArray(\n dsa.numpyTovtkDataArray(\n tstep.postproc_node[k], name=f\"{k}_point\"\n )\n )\n for k in postproc_node_6vector:\n for i in range(2):\n ug.GetPointData().AddArray(\n dsa.numpyTovtkDataArray(\n tstep.postproc_node[k][:, 3*i:3*(i+1)], name=f\"{k}_{i}_point\"\n )\n )\n\n for k in postproc_node_scalar:\n ug.GetPointData().AddArray(\n dsa.numpyTovtkDataArray(\n tstep.postproc_node[k],\n name=str(k),\n )\n )\n\n writer = vtk.vtkXMLPolyDataWriter()\n writer.SetFileName(it_filename)\n writer.SetInputData(ug)\n writer.Write()\n\n def write_for(self, it):\n it_filename = f\"{self.filename_for}{it:06d}.vtp\"\n\n forces_constraints_for = np.zeros((self.data.structure.num_bodies, 3))\n moments_constraints_for = np.zeros((self.data.structure.num_bodies, 3))\n\n # aero2inertial rotation\n aero2inertial = self.data.structure.timestep_info[it].cga()\n\n # coordinates of corners\n for_coords = np.zeros((self.data.structure.num_bodies, 3))\n if self.settings['include_rbm']:\n offset = np.zeros((3,))\n else:\n offset = self.data.structure.timestep_info[it].mb_FoR_pos[0, 0:3]\n\n for ibody in range(self.data.structure.num_bodies):\n for_coords[ibody, :] = self.data.structure.timestep_info[it].mb_FoR_pos[ibody, 0:3] - offset\n forces_constraints_for[ibody, :] = aero2inertial @ self.data.structure.timestep_info[it].forces_constraints_FoR[ibody, :3]\n moments_constraints_for[ibody, :] = aero2inertial @ self.data.structure.timestep_info[it].forces_constraints_FoR[ibody, 3:6]\n\n for_mesh = vtk.vtkPolyData(points=for_coords)\n\n for_mesh.GetPointData().AddArray(\n dsa.numpyTovtkDataArray(\n forces_constraints_for,\n 'forces_constraints_FoR',\n )\n )\n\n for_mesh.GetPointData().AddArray(\n dsa.numpyTovtkDataArray(\n moments_constraints_for,\n \"moments_constraints_FoR\",\n )\n )\n\n writer = vtk.vtkXMLPolyDataWriter()\n writer.SetFileName(it_filename)\n writer.SetInputData(for_mesh)\n writer.Write()\n" }, { "path": "sharpy/postproc/cleanup.py", "content": "from sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\n\n\n@solver\nclass Cleanup(BaseSolver):\n \"\"\"\n Clean-up old timesteps to save RAM memory\n \"\"\"\n solver_id = 'Cleanup'\n solver_classification = 'post-processor'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['clean_structure'] = 'bool'\n settings_default['clean_structure'] = True\n settings_description['clean_structure'] = 'Clean-up :class:`~sharpy.utils.datastructures.StructTimeStepInfo`'\n\n settings_types['clean_aero'] = 'bool'\n settings_default['clean_aero'] = True\n settings_description['clean_aero'] = 'Clean-up :class:`~sharpy.utils.datastructures.AeroTimeStepInfo`'\n\n settings_types['remaining_steps'] = 'int'\n settings_default['remaining_steps'] = 10\n settings_description['remaining_steps'] = 'The last `remaining_steps` are not cleaned up'\n\n table = settings_utils.SettingsTable()\n __doc__ += table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.settings = None\n self.data = None\n self.caller = None\n\n def initialise(self, data, custom_settings=None, caller=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default)\n self.caller = caller\n\n def run(self, **kwargs):\n \n online = settings_utils.set_value_or_default(kwargs, 'online', False)\n\n if self.settings['clean_structure']:\n self.clean(self.data.structure.timestep_info, self.settings['remaining_steps'])\n if self.settings['clean_aero']:\n self.clean(self.data.aero.timestep_info, self.settings['remaining_steps'])\n\n return self.data\n\n def clean(self, series, n_steps):\n for i in range(len(series[:-n_steps])):\n series[i] = None\n" }, { "path": "sharpy/postproc/frequencyresponse.py", "content": "import numpy as np\nimport time\nimport os\nimport sharpy.utils.solver_interface as solver_interface\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.cout_utils as cout\nimport warnings\nimport sharpy.linear.src.libss as libss\nimport h5py as h5\nimport sharpy.utils.frequencyutils as frequencyutils\nfrom sharpy.utils.frequencyutils import find_target_system\n\n\n@solver_interface.solver\nclass FrequencyResponse(solver_interface.BaseSolver):\n \"\"\"\n Frequency Response Calculator.\n\n Computes the frequency response of a built linear system. The frequency will be calculated for the systems\n specified in the ``target_system`` list. The desired ``frequency_unit`` will be either ``w`` for radians/s or ``k``\n for reduced frequency (if the system is scaled). The ``frequency_bounds`` setting will set the lower and upper\n bounds of the response, while ``num_freqs`` will specify the number of evaluations.\n The option ``frequency_spacing`` allows you to space the evaluations point following a ``log``\n or ``linear`` spacing.\n\n If ``compute_hinf`` is set, the H-infinity norm of the system is calculated.\n\n This will be saved to a binary ``.h5`` file as detailed in :func:`save_freq_resp`.\n\n Finally, the ``quick_plot`` option will plot some quick and dirty bode plots of the response. This requires\n access to ``matplotlib``.\n\n \"\"\"\n solver_id = 'FrequencyResponse'\n solver_classification = 'post-processor'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = False\n settings_description['print_info'] = 'Write output to screen.'\n\n settings_types['target_system'] = 'list(str)'\n settings_default['target_system'] = ['aeroelastic']\n settings_description['target_system'] = 'System or systems for which to find frequency response.'\n settings_options['target_system'] = ['aeroelastic', 'aerodynamic', 'structural']\n\n settings_types['frequency_unit'] = 'str'\n settings_default['frequency_unit'] = 'k'\n settings_description['frequency_unit'] = 'Units of frequency, ``w`` for rad/s, ``k`` reduced.'\n settings_options['frequency_unit'] = ['w', 'k']\n\n settings_types['frequency_scaling'] = 'dict'\n settings_default['frequency_scaling'] = {}\n settings_description['frequency_scaling'] = 'Dictionary containing the frequency scaling factors, if the ' \\\n 'aerodynamic system has not been previously scaled. Applied also if ' \\\n 'the desired unit is reduced frequency.'\n\n scaling_types = dict()\n scaling_default = dict()\n scaling_description = dict()\n\n scaling_types['length'] = 'float'\n scaling_default['length'] = 1.\n scaling_description['length'] = 'Length scaling factor.'\n\n scaling_types['speed'] = 'float'\n scaling_default['speed'] = 1.\n scaling_description['speed'] = 'Speed scaling factor.'\n\n settings_types['frequency_bounds'] = 'list(float)'\n settings_default['frequency_bounds'] = [1e-3, 1]\n settings_description['frequency_bounds'] = 'Lower and upper frequency bounds in the corresponding unit.'\n\n settings_types['frequency_spacing'] = 'str'\n settings_default['frequency_spacing'] = 'linear'\n settings_description['frequency_spacing'] = 'Compute the frequency response in a ``linear`` or ``log`` grid.'\n settings_options['frequency_spacing'] = ['linear', 'log']\n\n settings_types['num_freqs'] = 'int'\n settings_default['num_freqs'] = 50\n settings_description['num_freqs'] = 'Number of frequencies to evaluate.'\n\n settings_types['compute_hinf'] = 'bool'\n settings_default['compute_hinf'] = False\n settings_description['compute_hinf'] = 'Compute Hinfinity norm of the system.'\n\n settings_types['quick_plot'] = 'bool'\n settings_default['quick_plot'] = False\n settings_description['quick_plot'] = 'Produce array of ``.png`` plots showing response. Requires matplotlib.'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description, settings_options)\n\n scaling_table = settings_utils.SettingsTable()\n __doc__ += scaling_table.generate(scaling_types, scaling_default, scaling_description,\n header_line='The scaling dictionary takes the following entries:')\n\n def __init__(self):\n\n self.settings = None\n self.data = None\n self.folder = None\n self.print_info = False\n\n self.scaled = False\n self.w_to_k = 1\n self.wv = None\n self.caller = None\n\n def initialise(self, data, custom_settings=None, caller=None, restart=False):\n\n self.data = data\n\n if not custom_settings:\n self.settings = self.data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n self.settings_options,\n no_ctype=True)\n\n self.print_info = self.settings['print_info']\n\n if self.settings['frequency_unit'] == 'k':\n self.scaled = True\n if self.data.linear.linear_system.uvlm.scaled:\n scaling = self.data.linear.linear_system.uvlm.sys.ScalingFacts\n else:\n scaling = self.settings['frequency_scaling']\n settings_utils.to_custom_types(scaling, self.scaling_types, self.scaling_default,\n no_ctype=True)\n self.w_to_k = scaling['length'] / scaling['speed']\n else:\n self.w_to_k = 1.\n\n # Frequency bounds in radians\n lb = self.settings['frequency_bounds'][0] / self.w_to_k\n ub = self.settings['frequency_bounds'][1] / self.w_to_k\n\n nfreqs = self.settings['num_freqs']\n if self.settings['frequency_spacing'] == 'linear':\n self.wv = np.linspace(lb, ub, nfreqs)\n elif self.settings['frequency_spacing'] == 'log':\n self.wv = np.logspace(np.log10(lb), np.log10(ub), nfreqs)\n else:\n raise NotImplementedError('Unrecognised frequency spacing setting %s' % self.settings['frequency_spacing'])\n\n self.folder = data.output_folder + '/frequencyresponse/'\n if not os.path.exists(self.folder):\n os.makedirs(self.folder)\n self.caller = caller\n\n\n def run(self, **kwargs):\n \"\"\"\n Computes the frequency response of the linear state-space.\n\n Args:\n ss (sharpy.linear.src.libss.StateSpace (Optional)): State-space object for which to compute the frequency response.\n If not given, the response for the previously assembled systems and specified in ``target_system`` will\n be performed.\n \"\"\"\n online = settings_utils.set_value_or_default(kwargs, 'online', False)\n ss = settings_utils.set_value_or_default(kwargs, 'ss', None)\n\n if ss is None:\n ss_list = [find_target_system(self.data, system_name) for system_name in self.settings['target_system']]\n elif type(ss) is libss.StateSpace:\n ss_list = [ss]\n elif type(ss) is list:\n ss_list = ss\n else:\n raise TypeError('StateSpace input must be either a libss.StateSpace instance or a list of libss.StateSpace')\n\n for ith, system in enumerate(ss_list):\n if self.print_info:\n cout.cout_wrap('Computing frequency response...')\n if ss is None:\n try:\n system_name = self.settings['target_system'][ith]\n if self.print_info:\n cout.cout_wrap('\\tComputing frequency response for %s system' % system_name, 1)\n except IndexError:\n system_name = None\n else:\n system_name = None # For the case where the state-space is parsed in run().\n\n t0fom = time.time()\n y_freq_fom = system.freqresp(self.wv)\n tfom = time.time() - t0fom\n\n if self.settings['compute_hinf']:\n\n if self.print_info:\n cout.cout_wrap('Computing H-infinity norm...')\n try:\n hinf = frequencyutils.h_infinity_norm(system, iter_max=50, print_info=self.settings['print_info'])\n except np.linalg.LinAlgError:\n hinf = None\n cout.cout_wrap('H-infinity calculation did not converge', 4)\n\n else:\n hinf = None\n\n self.save_freq_resp(self.wv * self.w_to_k, y_freq_fom, system_name=system_name, hinf=hinf)\n\n cout.cout_wrap('\\tComputed the frequency response in %f s' % tfom, 2)\n\n if self.settings['quick_plot']:\n self.quick_plot(y_freq_fom, subfolder=system_name)\n\n return self.data\n\n def save_freq_resp(self, wv, Yfreq, system_name=None, hinf=None):\n \"\"\"\n Saves the frequency response to a binary ``.h5`` file.\n\n If the system has not been scaled, the units of frequency are ``rad/s`` and the response is given in complex\n form. The response is saved in a ``[p, m, n_freq_eval]`` format, where ``p`` corresponds to the system's\n outputs, ``n`` to the number of inputs and ``n_freq_eval`` to the number of frequency evaluations.\n\n Args:\n wv (np.ndarray): Frequency array.\n Y_freq (np.ndarray): Frequency response data ``[p, m, n_freq_eval]`` matrix.\n system_name (str (optional)): State-space system name.\n hinf (float (optional)): H-infinity norm of the system.\n \"\"\"\n\n with open(self.folder + '/freqdata_readme.txt', 'w') as outfile:\n outfile.write('Frequency Response Data Output\\n\\n')\n outfile.write('Frequency data found in the relevant .h5 file\\n')\n outfile.write('The units of frequency are rad/s\\nThe frequency' \\\n 'response is given in complex form.')\n\n case_name = ''\n if system_name is not None:\n case_name += system_name + '.'\n\n p, m, _ = Yfreq.shape\n\n h5filename = self.folder + '/' + case_name + 'freqresp.h5'\n with h5.File(h5filename, 'w') as f:\n f.create_dataset('frequency', data=wv)\n f.create_dataset('response', data=Yfreq, dtype=complex)\n f.create_dataset('inputs', data=m)\n f.create_dataset('outputs', data=p)\n if hinf is not None:\n f.create_dataset('hinf_norm', data=hinf)\n\n if self.print_info:\n cout.cout_wrap('Saved .h5 file to %s with frequency response data' % h5filename)\n\n def quick_plot(self, y_freq_fom=None, subfolder=None):\n p, m, _ = y_freq_fom.shape\n try:\n cout.cout_wrap('\\tCreating Quick plots of the frequency response', 1)\n\n out_folder = self.folder\n if subfolder:\n out_folder += '/' + subfolder\n\n if not os.path.isdir(out_folder):\n os.makedirs(out_folder, exist_ok=True)\n\n import matplotlib.pyplot as plt\n for mj in range(m):\n for pj in range(p):\n fig1, ax1 = plt.subplots(nrows=2)\n fig_title = 'in%02g_out%02g' % (mj, pj)\n ax1[0].set_title(fig_title)\n if y_freq_fom is not None:\n ax1[0].plot(self.wv * self.w_to_k, 20 * np.log10(np.abs(y_freq_fom[pj, mj, :])), color='C0')\n ax1[1].plot(self.wv * self.w_to_k, np.angle(y_freq_fom[pj, mj, :]), '-', color='C0')\n if self.scaled:\n ax1[1].set_xlabel('Reduced Frequency, k [-]')\n else:\n ax1[1].set_xlabel(r'Frequency, $\\omega$ [rad/s]')\n\n ax1[0].set_ylabel('Amplitude [dB]')\n ax1[1].set_ylabel('Phase [rad]')\n fig1.savefig(out_folder + '/' + fig_title + '.png')\n plt.close()\n\n cout.cout_wrap('\\tPlots saved to %s' % out_folder, 1)\n except ModuleNotFoundError:\n warnings.warn('Matplotlib not found - skipping plot')\n" }, { "path": "sharpy/postproc/liftdistribution.py", "content": "import os\n\nimport numpy as np\n\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\nimport sharpy.aero.utils.mapping as mapping\nimport sharpy.utils.algebra as algebra\nimport sharpy.aero.utils.utils as aeroutils\n\n\n@solver\nclass LiftDistribution(BaseSolver):\n \"\"\"LiftDistribution\n \n Calculates and exports the lift distribution on lifting surfaces\n \n \"\"\"\n solver_id = 'LiftDistribution'\n solver_classification = 'post-processor'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['text_file_name'] = 'str'\n settings_default['text_file_name'] = 'liftdistribution'\n settings_description['text_file_name'] = 'Text file name'\n\n settings_default['coefficients'] = True\n settings_types['coefficients'] = 'bool'\n settings_description['coefficients'] = 'Calculate aerodynamic lift coefficients'\n\n settings_types['rho'] = 'float'\n settings_default['rho'] = 1.225\n settings_description['rho'] = 'Reference freestream density [kg/m³]'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.settings = None\n self.data = None\n self.folder = None\n self.caller = None\n\n def initialise(self, data, custom_settings=None, restart=False, caller=None):\n self.data = data\n self.settings = data.settings[self.solver_id]\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n self.caller = caller\n self.folder = data.output_folder + '/liftdistribution/'\n if not os.path.exists(self.folder):\n os.makedirs(self.folder)\n\n def run(self, **kwargs):\n self.lift_distribution(self.data.structure.timestep_info[self.data.ts],\n self.data.aero.timestep_info[self.data.ts])\n return self.data\n\n def lift_distribution(self, struct_tstep, aero_tstep):\n # Force mapping\n forces = mapping.aero2struct_force_mapping(\n aero_tstep.forces + aero_tstep.dynamic_forces,\n self.data.aero.struct2aero_mapping,\n aero_tstep.zeta,\n struct_tstep.pos,\n struct_tstep.psi,\n self.data.structure.node_master_elem,\n self.data.structure.connectivities,\n struct_tstep.cag(),\n self.data.aero.data_dict)\n # Prepare output matrix and file\n N_nodes = self.data.structure.num_node\n numb_col = 6\n header = \"x,y,z,fx,fy,fz\"\n # get aero forces\n # get rotation matrix\n cga = algebra.quat2rotation(struct_tstep.quat)\n if self.settings[\"coefficients\"]:\n # TODO: add nondimensional spanwise column y/s\n header += \", cfx, cfy, cfz\"\n numb_col += 3\n lift_distribution = np.zeros((N_nodes, numb_col))\n\n for inode in range(N_nodes):\n if self.data.aero.data_dict['aero_node'][inode]:\n local_node = self.data.aero.struct2aero_mapping[inode][0][\"i_n\"]\n ielem, inode_in_elem = self.data.structure.node_master_elem[inode]\n i_surf = int(self.data.aero.surface_distribution[ielem])\n # get c_gb \n cab = algebra.crv2rotation(struct_tstep.psi[ielem, inode_in_elem, :])\n cgb = np.dot(cga, cab)\n # Get c_bs\n urel, dir_urel = aeroutils.magnitude_and_direction_of_relative_velocity(struct_tstep.pos[inode, :],\n struct_tstep.pos_dot[inode, :],\n struct_tstep.for_vel[:],\n cga,\n aero_tstep.u_ext[i_surf][:, :,\n local_node])\n dir_span, span, dir_chord, chord = aeroutils.span_chord(local_node, aero_tstep.zeta[i_surf])\n # Stability axes - projects forces in B onto S\n c_bs = aeroutils.local_stability_axes(cgb.T.dot(dir_urel), cgb.T.dot(dir_chord))\n aero_forces = c_bs.T.dot(forces[inode, :3])\n # Store data in export matrix\n lift_distribution[inode, 3:6] = aero_forces\n lift_distribution[inode, 2] = struct_tstep.pos[inode, 2] # z\n lift_distribution[inode, 1] = struct_tstep.pos[inode, 1] # y\n lift_distribution[inode, 0] = struct_tstep.pos[inode, 0] # x\n if self.settings[\"coefficients\"]:\n # Get lift coefficient\n for idim in range(3):\n lift_distribution[inode, 6+idim] = np.sign(aero_forces[idim]) * np.linalg.norm(aero_forces[idim]) \\\n / (0.5 * self.settings['rho'] \\\n * np.linalg.norm(urel) ** 2 * span * chord) \n # Check if shared nodes from different surfaces exist (e.g. two wings joining at symmetry plane)\n # Leads to error since panel area just donates for half the panel size while lift forces is summed up\n lift_distribution[inode, 6+idim] /= len(self.data.aero.struct2aero_mapping[inode])\n\n # Export lift distribution data\n np.savetxt(os.path.join(self.folder, self.settings['text_file_name'] + '_ts{}'.format(str(self.data.ts)) + '.txt'), lift_distribution,\n fmt='%10e,' * (numb_col - 1) + '%10e', delimiter=\", \", header=header)\n" }, { "path": "sharpy/postproc/pickledata.py", "content": "import os\nimport pickle\n\nimport h5py\n\nimport sharpy\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\n\n\n# Define basic numerical types\n# BasicNumTypes=(float,float32,float64,int,int32,int64,complex)\n\n@solver\nclass PickleData(BaseSolver):\n \"\"\"\n This postprocessor writes the SHARPy ``data`` structure in a pickle file, such that classes and\n methods from SHARPy are retained for restarted solutions or further post-processing.\n\n A pickle is saved to the SHARPy output folder, specified in the settings for SHARPy as ``log_folder``.\n\n This solver does not have settings, yet it still needs to be included in the `.sharpy` file as an\n empty dictionary.\n \"\"\"\n solver_id = 'PickleData'\n solver_classification = 'post-processor'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['stride'] = 'int'\n settings_default['stride'] = 1\n settings_description['stride'] = 'Number of steps between the execution calls when run online'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n import sharpy\n\n self.data = None\n self.filename = None\n self.folder = None\n self.caller = None\n\n def initialise(self, data, custom_settings=None, caller=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default)\n\n self.folder = data.output_folder\n self.filename = self.folder + self.data.settings['SHARPy']['case']+'.pkl'\n self.caller = caller\n\n\n def run(self, **kwargs):\n \n online = settings_utils.set_value_or_default(kwargs, 'online', False)\n solvers = settings_utils.set_value_or_default(kwargs, 'solvers', None)\n \n if ((online and (self.data.ts % self.settings['stride'] == 0)) or (not online)):\n with open(self.filename, 'wb') as f:\n pickle.dump(self.data, f, protocol=pickle.HIGHEST_PROTOCOL)\n pickle.dump(solvers, f, protocol=pickle.HIGHEST_PROTOCOL)\n\n return self.data\n" }, { "path": "sharpy/postproc/plotflowfield.py", "content": "import os\nimport numpy as np\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.generator_interface as gen_interface\nimport sharpy.utils.settings as settings_utils\nimport sharpy.aero.utils.uvlmlib as uvlmlib\nimport ctypes as ct\nfrom sharpy.utils.constants import vortex_radius_def\n\n\n@solver\nclass PlotFlowField(BaseSolver):\n \"\"\"\n Plots the flow field in Paraview and computes the velocity at a set of points in a grid.\n \"\"\"\n solver_id = 'PlotFlowField'\n solver_classification = 'post-processor'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['postproc_grid_generator'] = 'str'\n settings_default['postproc_grid_generator'] = 'GridBox'\n settings_description['postproc_grid_generator'] = 'Generator used to create grid and plot flow field'\n settings_options['postproc_grid_generator'] = ['GridBox']\n\n settings_types['postproc_grid_input'] = 'dict'\n settings_default['postproc_grid_input'] = dict()\n settings_description['postproc_grid_input'] = 'Dictionary containing settings for ``postproc_grid_generator``.'\n\n settings_types['velocity_field_generator'] = 'str'\n settings_default['velocity_field_generator'] = 'SteadyVelocityField'\n settings_description['velocity_field_generator'] = 'Chosen velocity field generator'\n\n settings_types['velocity_field_input'] = 'dict'\n settings_default['velocity_field_input'] = dict()\n settings_description['velocity_field_input'] = 'Dictionary containing settings for the selected ``velocity_field_generator``.'\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = 0.1\n settings_description['dt'] = 'Time step.'\n\n settings_types['include_external'] = 'bool'\n settings_default['include_external'] = True\n settings_description['include_external'] = 'Include external velocities.'\n\n settings_types['include_induced'] = 'bool'\n settings_default['include_induced'] = True\n settings_description['include_induced'] = 'Include induced velocities.'\n\n settings_types['stride'] = 'int'\n settings_default['stride'] = 1\n settings_description['stride'] = 'Number of time steps between plots.'\n\n settings_types['num_cores'] = 'int'\n settings_default['num_cores'] = 1\n settings_description['num_cores'] = 'Number of cores to use.'\n\n settings_types['vortex_radius'] = 'float'\n settings_default['vortex_radius'] = vortex_radius_def\n settings_description['vortex_radius'] = 'Distance below which inductions are not computed.'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description, settings_options)\n\n def __init__(self):\n self.settings = None\n self.data = None\n self.folder = None\n self.caller = None\n\n def initialise(self, data, custom_settings=None, caller=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n self.settings_options)\n\n self.folder = data.output_folder + '/' + 'GenerateFlowField/'\n if not os.path.isdir(self.folder):\n os.makedirs(self.folder)\n\n # init velocity generator\n velocity_generator_type = gen_interface.generator_from_string(\n self.settings['velocity_field_generator'])\n self.velocity_generator = velocity_generator_type()\n self.velocity_generator.initialise(self.settings['velocity_field_input'], restart=restart)\n\n # init postproc grid generator\n postproc_grid_generator_type = gen_interface.generator_from_string(\n self.settings['postproc_grid_generator'])\n self.postproc_grid_generator = postproc_grid_generator_type()\n self.postproc_grid_generator.initialise(self.settings['postproc_grid_input'], restart=restart)\n self.caller = caller\n\n def output_velocity_field(self, ts):\n # Notice that SHARPy utilities deal with several two-dimensional surfaces\n # To be able to build 3D volumes, I will make use of the surface index as\n # the third index in space\n # It does not apply to the 'u' array because this way it is easier to\n # write it in paraview\n\n # Generate the grid\n vtk_info, grid = self.postproc_grid_generator.generate({\n 'for_pos': self.data.structure.timestep_info[ts].for_pos[0:3]})\n\n # Compute the induced velocities\n nx = grid[0].shape[1]\n ny = grid[0].shape[2]\n nz = len(grid)\n\n array_counter = 0\n u_ind = np.zeros((nx, ny, nz, 3), dtype=float)\n if self.settings['include_induced']:\n target_triads = np.zeros((nx*ny*nz, 3))\n ipoint = -1\n for iz in range(nz):\n for ix in range(nx):\n for iy in range(ny):\n ipoint += 1\n target_triads[ipoint, :] = grid[iz][:, ix, iy].astype(dtype=ct.c_double, order='F', copy=True)\n\n u_ind_points = uvlmlib.uvlm_calculate_total_induced_velocity_at_points(self.data.aero.timestep_info[ts],\n target_triads,\n self.settings['vortex_radius'],\n self.data.structure.timestep_info[ts].for_pos[0:3],\n self.settings['num_cores'])\n ipoint = -1\n for iz in range(nz):\n for ix in range(nx):\n for iy in range(ny):\n ipoint += 1\n u_ind[ix, iy, iz, :] = u_ind_points[ipoint, :]\n\n # Write the data\n vtk_info.point_data.add_array(u_ind.reshape((-1, u_ind.shape[-1]), order='F')) # Reshape the array except from the last dimension\n vtk_info.point_data.get_array(array_counter).name = 'induced_velocity'\n vtk_info.point_data.update()\n array_counter += 1\n\n # Add the external velocities\n u_ext_out = np.zeros((nx, ny, nz, 3), dtype=float)\n\n if self.settings['include_external']:\n u_ext = []\n for iz in range(nz):\n u_ext.append(np.zeros((3, nx, ny), dtype=ct.c_double))\n self.velocity_generator.generate({'zeta': grid,\n 'override': True,\n 't': ts*self.settings['dt'],\n 'ts': ts,\n 'dt': self.settings['dt'],\n 'for_pos': 0*self.data.structure.timestep_info[ts].for_pos},\n u_ext)\n for iz in range(nz):\n for ix in range(nx):\n for iy in range(ny):\n u_ext_out[ix, iy, iz, :] += u_ext[iz][:, ix, iy]\n\n # Write the data\n vtk_info.point_data.add_array(u_ext_out.reshape((-1, u_ext_out.shape[-1]), order='F')) # Reshape the array except from the last dimension\n vtk_info.point_data.get_array(array_counter).name = 'external_velocity'\n vtk_info.point_data.update()\n array_counter += 1\n\n # add the data\n u = u_ind + u_ext_out\n\n # Write the data\n vtk_info.point_data.add_array(u.reshape((-1, u.shape[-1]), order='F')) # Reshape the array except from the last dimension\n vtk_info.point_data.get_array(array_counter).name = 'velocity'\n vtk_info.point_data.update()\n array_counter += 1\n\n filename = self.folder + \"VelocityField_\" + '%06u' % ts + \".vtk\"\n from tvtk.api import write_data\n write_data(vtk_info, filename)\n\n def run(self, **kwargs):\n\n online = settings_utils.set_value_or_default(kwargs, 'online', False)\n\n if online:\n if divmod(self.data.ts, self.settings['stride'])[1] == 0:\n self.output_velocity_field(len(self.data.structure.timestep_info) - 1)\n else:\n for ts in range(0, len(self.data.structure.timestep_info)):\n if not self.data.structure.timestep_info[ts] is None:\n self.output_velocity_field(ts)\n return self.data\n" }, { "path": "sharpy/postproc/savedata.py", "content": "import os\nimport h5py\nimport copy\nimport sharpy\nimport sharpy.utils.cout_utils as cout\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.h5utils as h5utils\nfrom sharpy.presharpy.presharpy import PreSharpy\n\n\n@solver\nclass SaveData(BaseSolver):\n \"\"\"\n The ``SaveData`` postprocessor writes the SHARPy variables into ``hdf5`` files. The linear state space files\n may be saved to ``.mat`` if desired instead.\n\n It has options to save the following classes:\n\n * :class:`~sharpy.sharpy.aero.models.Aerogrid` including :class:`sharpy.sharpy.utils.datastructures.AeroTimeStepInfo`\n\n * :class:`~sharpy.sharpy.structure.beam.Beam` including :class:`sharpy.sharpy.utils.datastructures.StructTimeStepInfo`\n\n * :class:`sharpy.solvers.linearassembler.Linear` including classes in :exc:`sharpy.linear.assembler`\n\n Notes:\n This method saves simply the data. If you would like to preserve the SHARPy methods of the relevant classes\n see also :class:`sharpy.solvers.pickledata.PickleData`.\n\n \"\"\"\n solver_id = 'SaveData'\n solver_classification = 'post-processor'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['save_aero'] = 'bool'\n settings_default['save_aero'] = True\n settings_description['save_aero'] = 'Save aerodynamic classes.'\n\n settings_types['save_nonlifting'] = 'bool'\n settings_default['save_nonlifting'] = False\n settings_description['save_nonlifting'] = 'Save aerodynamic classes.'\n\n settings_types['save_struct'] = 'bool'\n settings_default['save_struct'] = True\n settings_description['save_struct'] = 'Save structural classes.'\n\n settings_types['save_linear'] = 'bool'\n settings_default['save_linear'] = False\n settings_description['save_linear'] = 'Save linear state space system.'\n\n settings_types['save_linear_uvlm'] = 'bool'\n settings_default['save_linear_uvlm'] = False\n settings_description['save_linear_uvlm'] = 'Save linear UVLM state space system. Use with caution when dealing with ' \\\n 'large systems.'\n\n settings_types['save_wake'] = 'bool'\n settings_default['save_wake'] = True\n settings_description['save_wake'] = 'Save aero wake classes.'\n\n settings_types['save_rom'] = 'bool'\n settings_default['save_rom'] = False\n settings_description['save_rom'] = 'Saves the ROM matrices and the reduced order model'\n\n settings_types['skip_attr'] = 'list(str)'\n settings_default['skip_attr'] = ['fortran',\n 'airfoils',\n 'airfoil_db',\n 'settings_types',\n # 'beam',\n 'ct_dynamic_forces_list',\n # 'ct_forces_list',\n 'ct_gamma_dot_list',\n 'ct_gamma_list',\n 'ct_gamma_star_list',\n 'ct_normals_list',\n 'ct_u_ext_list',\n 'ct_u_ext_star_list',\n 'ct_zeta_dot_list',\n 'ct_zeta_list',\n 'ct_zeta_star_list',\n 'dynamic_input']\n settings_description['skip_attr'] = 'List of attributes to skip when writing file'\n\n settings_types['compress_float'] = 'bool'\n settings_default['compress_float'] = False\n settings_description['compress_float'] = 'Compress float'\n\n settings_types['format'] = 'str'\n settings_default['format'] = 'h5'\n settings_description['format'] = 'Save linear state space to hdf5 ``.h5`` or Matlab ``.mat`` format.'\n settings_options['format'] = ['h5', 'mat']\n\n settings_types['stride'] = 'int'\n settings_default['stride'] = 1\n settings_description['stride'] = 'Number of steps between the execution calls when run online'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description,\n settings_options=settings_options)\n\n def __init__(self):\n\n self.settings = None\n self.data = None\n\n self.folder = ''\n self.filename = ''\n self.filename_linear = ''\n self.caller = None\n\n ### specify which classes are saved as hdf5 group\n # see initialise and add_as_grp\n self.ClassesToSave = (PreSharpy,)\n\n def initialise(self, data, custom_settings=None, caller=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n options=self.settings_options)\n\n # Add these anyway - therefore if you add your own skip_attr you don't have to retype all of these\n self.settings['skip_attr'].extend(['fortran',\n 'airfoils',\n 'airfoil_db',\n 'settings_types',\n 'ct_dynamic_forces_list',\n 'ct_forces_list',\n 'ct_gamma_dot_list',\n 'ct_gamma_list',\n 'ct_gamma_star_list',\n 'ct_normals_list',\n 'ct_u_ext_list',\n 'ct_u_ext_star_list',\n 'ct_zeta_dot_list',\n 'ct_zeta_list',\n 'ct_zeta_star_list',\n 'dynamic_input'])\n\n\n # create folder for containing files if necessary\n self.folder = data.output_folder + '/savedata/'\n if not os.path.exists(self.folder):\n os.makedirs(self.folder)\n self.filename = self.folder + self.data.settings['SHARPy']['case'] + '.data.h5'\n self.filename_linear = self.folder + self.data.settings['SHARPy']['case'] + '.linss.h5'\n\n # remove old file if it exists\n self.remove_file_if_exist(self.filename)\n\n # check that there is a linear system - else return setting to false\n if self.settings['save_linear'] or self.settings['save_linear_uvlm']:\n try:\n self.data.linear\n except AttributeError:\n cout.cout_wrap('SaveData variables ``save_linear`` and/or ``save_linear`` are True but no linear system'\n 'been found', 3)\n self.settings['save_linear'] = False\n self.settings['save_linear_uvlm'] = False\n\n if self.settings['format'] == 'h5':\n\n # allocate list of classes to be saved\n if self.settings['save_aero']:\n self.ClassesToSave += (sharpy.aero.models.aerogrid.Aerogrid,\n sharpy.utils.datastructures.AeroTimeStepInfo,)\n if not self.settings['save_wake']:\n self.settings['skip_attr'].append('zeta_star')\n self.settings['skip_attr'].append('u_ext_star')\n self.settings['skip_attr'].append('gamma_star')\n self.settings['skip_attr'].append('dist_to_orig')\n self.settings['skip_attr'].append('wake_conv_vel')\n\n\n if self.settings['save_nonlifting']:\n self.ClassesToSave += (sharpy.aero.models.nonliftingbodygrid.NonliftingBodyGrid,\n sharpy.utils.datastructures.NonliftingBodyTimeStepInfo,)\n\n if self.settings['save_struct']:\n self.ClassesToSave += (\n sharpy.structure.models.beam.Beam,\n sharpy.utils.datastructures.StructTimeStepInfo,)\n\n if self.settings['save_linear']:\n self.ClassesToSave += (sharpy.solvers.linearassembler.Linear,\n sharpy.linear.assembler.linearaeroelastic.LinearAeroelastic,\n sharpy.linear.assembler.linearbeam.LinearBeam,\n sharpy.linear.assembler.linearuvlm.LinearUVLM,\n sharpy.linear.src.libss.StateSpace,\n sharpy.linear.src.lingebm.FlexDynamic,)\n\n if self.settings['save_linear_uvlm']:\n self.ClassesToSave += (sharpy.solvers.linearassembler.Linear, sharpy.linear.src.libss.ss_block)\n self.caller = caller\n\n def remove_file_if_exist(self, filepath):\n if os.path.isfile(filepath):\n os.remove(filepath)\n\n def run(self, **kwargs):\n\n online = settings_utils.set_value_or_default(kwargs, 'online', False)\n\n # Use the following statement in case the ct types are not defined and\n # you need them on uvlm3d\n # self.data.aero.timestep_info[-1].generate_ctypes_pointers()\n\n if ((online and (self.data.ts % self.settings['stride'] == 0)) or (not online)):\n if self.settings['format'] == 'h5':\n file_exists = os.path.isfile(self.filename)\n hdfile = h5py.File(self.filename, 'a')\n\n if (online and file_exists):\n self.save_timestep(self.data, self.settings, self.data.ts, hdfile)\n else:\n skip_attr_init = copy.deepcopy(self.settings['skip_attr'])\n skip_attr_init.append('timestep_info')\n\n h5utils.add_as_grp(self.data, hdfile, grpname='data',\n ClassesToSave=self.ClassesToSave, SkipAttr=skip_attr_init,\n compress_float=self.settings['compress_float'])\n\n if self.settings['save_struct']:\n h5utils.add_as_grp(list(),\n hdfile['data']['structure'],\n grpname='timestep_info')\n if self.settings['save_aero']:\n h5utils.add_as_grp(list(),\n hdfile['data']['aero'],\n grpname='timestep_info')\n if self.settings['save_nonlifting']:\n h5utils.add_as_grp(list(),\n hdfile['data']['nonlifting_body'],\n grpname='timestep_info')\n\n for it in range(len(self.data.structure.timestep_info)):\n tstep_p = self.data.structure.timestep_info[it]\n if tstep_p is not None:\n self.save_timestep(self.data, self.settings, it, hdfile)\n\n hdfile.close()\n\n if self.settings['save_linear_uvlm']:\n linhdffile = h5py.File(self.filename.replace('.data.h5', '.uvlmss.h5'), 'a')\n self.remove_file_if_exist(linhdffile)\n h5utils.add_as_grp(self.data.linear.linear_system.uvlm.ss, linhdffile, grpname='ss',\n ClassesToSave=self.ClassesToSave, SkipAttr=self.settings['skip_attr'],\n compress_float=self.settings['compress_float'])\n h5utils.add_as_grp(self.data.linear.linear_system.linearisation_vectors, linhdffile,\n grpname='linearisation_vectors',\n ClassesToSave=self.ClassesToSave, SkipAttr=self.settings['skip_attr'],\n compress_float=self.settings['compress_float'])\n linhdffile.close()\n\n if self.settings['save_linear']:\n self.remove_file_if_exist(self.filename_linear)\n with h5py.File(self.filename_linear, 'a') as linfile:\n h5utils.add_as_grp(self.data.linear.linear_system.linearisation_vectors, linfile,\n grpname='linearisation_vectors',\n ClassesToSave=self.ClassesToSave, SkipAttr=self.settings['skip_attr'],\n compress_float=self.settings['compress_float'])\n h5utils.add_as_grp(self.data.linear.ss, linfile, grpname='ss',\n ClassesToSave=self.ClassesToSave, SkipAttr=self.settings['skip_attr'],\n compress_float=self.settings['compress_float'])\n\n if self.settings['save_rom']:\n try:\n for k, rom in self.data.linear.linear_system.uvlm.rom.items():\n romhdffile = self.filename.replace('.data.h5', '_{:s}.rom.h5'.format(k.lower()))\n self.remove_file_if_exist(romhdffile)\n rom.save(romhdffile)\n except AttributeError:\n cout.cout_wrap('Could not locate a reduced order model to save')\n\n elif self.settings['format'] == 'mat':\n from scipy.io import savemat\n if self.settings['save_linear']:\n # reference-forces\n linearisation_vectors = self.data.linear.linear_system.linearisation_vectors\n\n matfilename = self.filename.replace('.data.h5', '.linss.mat')\n A, B, C, D = self.data.linear.ss.get_mats()\n savedict = {'A': A,\n 'B': B,\n 'C': C,\n 'D': D}\n for k, v in linearisation_vectors.items():\n savedict[k] = v\n dt = self.data.linear.ss.dt\n if dt is not None:\n savedict['dt'] = dt\n savemat(matfilename, savedict)\n\n if self.settings['save_linear_uvlm']:\n matfilename = self.filename.replace('.data.h5', '.uvlmss.mat')\n linearisation_vectors = self.data.linear.linear_system.uvlm.linearisation_vectors\n A, B, C, D = self.data.linear.linear_system.uvlm.ss.get_mats()\n savedict = {'A': A,\n 'B': B,\n 'C': C,\n 'D': D}\n for k, v in linearisation_vectors.items():\n savedict[k] = v\n dt = self.data.linear.linear_system.uvlm.ss.dt\n if dt is not None:\n savedict['dt'] = dt\n savemat(matfilename, savedict)\n\n return self.data\n\n @staticmethod\n def save_timestep(data, settings, ts, hdfile):\n if settings['save_aero']:\n h5utils.add_as_grp(data.aero.timestep_info[ts],\n hdfile['data']['aero']['timestep_info'],\n grpname=(\"%05d\" % ts),\n ClassesToSave=(sharpy.utils.datastructures.AeroTimeStepInfo,),\n SkipAttr=settings['skip_attr'],\n compress_float=settings['compress_float'])\n if settings['save_nonlifting']:\n h5utils.add_as_grp(data.nonlifting_body.timestep_info[ts],\n hdfile['data']['nonlifting_body']['timestep_info'],\n grpname=(\"%05d\" % ts),\n ClassesToSave=(sharpy.utils.datastructures.NonliftingBodyTimeStepInfo,),\n SkipAttr=settings['skip_attr'],\n compress_float=settings['compress_float'])\n if settings['save_struct']:\n tstep = data.structure.timestep_info[ts]\n\n h5utils.add_as_grp(tstep,\n hdfile['data']['structure']['timestep_info'],\n grpname=(\"%05d\" % ts),\n ClassesToSave=(sharpy.utils.datastructures.StructTimeStepInfo,),\n SkipAttr=settings['skip_attr'],\n compress_float=settings['compress_float'])\n" }, { "path": "sharpy/postproc/saveparametriccase.py", "content": "from sharpy.utils.solver_interface import solver, BaseSolver, initialise_solver\nimport sharpy.utils.settings as settings_utils\nimport configobj\nimport os\nimport sharpy.utils.cout_utils as cout\nimport warnings\n\n\n@solver\nclass SaveParametricCase(BaseSolver):\n \"\"\"\n SaveParametricCase is a post-processor that creates a ConfigParser text file called\n ``.pmor.sharpy`` that contains information on certain simulation parameters. It is useful as\n a record keeper if you are doing a parametric study and for parametric model interpolation.\n\n\n If the setting ``save_case`` is selected and the post processor :class:`~sharpy.solvers.pickledata.PickleData`\n is not present in the SHARPy flow, this solver will pickle the data to the path given in the ``folder`` setting.\n\n The setting ``save_pmor_items`` saves to h5 the following state-spaces and gains, if present:\n * Aeroelastic state-space saved to: / save_pmor_data / _statespace.h5\n * Aerodynamic ROM reduced order bases saved to: / save_pmor_data / _aerorob.h5\n * Structural ROM reduced order bases saved to: / save_pmor_data / _modal_structrob.h5\n\n The setting ``save_pmor_subsystem saves the additional state-spaces to h5 files:\n * Structural matrices saved to: / save_pmor_data / _struct_matrices.h5\n * Structural state-space saved to: / save_pmor_data / _beamstatespace.h5\n * Aerodynamic state-space saved to: / save_pmor_data / _aerostatespace.h5\n\n Examples:\n\n In the case you are running several SHARPy cases, varying for instance the velocity, the settings would\n be something like:\n\n >>> parameter_value = 10 # parameter of study\n >>> input_settings = {'': value # the name of the parameter is at the user's discretion\n >>> } # add more parameters as required\n\n The result would be the ``.pmor.sharpy`` file with the following content:\n\n .. code-block:: none\n\n [parameters]\n = value\n\n \"\"\"\n solver_id = 'SaveParametricCase'\n solver_classification = 'post-processor'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['save_case'] = 'bool'\n settings_default['save_case'] = False\n settings_description['save_case'] = 'DeprecationWarning - Save a .pkl of the SHARPy case. Required for PMOR.'\n\n settings_types['parameters'] = 'dict'\n settings_default['parameters'] = None\n settings_description['parameters'] = 'Dictionary containing the chosen simulation parameters and their values.'\n\n settings_types['save_pmor_items'] = 'bool'\n settings_default['save_pmor_items'] = False\n settings_description['save_pmor_items'] = 'Saves to h5 the items required for PMOR interpolation: the aerodynamic ' \\\n 'reduced order bases, the structural modal matrix and the ' \\\n 'reduced state-space'\n\n settings_types['save_pmor_subsystems'] = 'bool'\n settings_default['save_pmor_subsystems'] = False\n settings_description['save_pmor_subsystems'] = 'Saves to h5 the statespaces and matrices of the UVLM and beam and ' \\\n 'the M, C, K matrices. The setting ``save_pmor_items`` ' \\\n 'should be set to `on`'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n self.folder = None\n self.case_name = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n self.data = data\n\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default)\n\n self.folder = data.output_folder\n self.case_name = self.data.settings['SHARPy']['case']\n\n def run(self, **kwargs):\n \n online = settings_utils.set_value_or_default(kwargs, 'online', False)\n restart = settings_utils.set_value_or_default(kwargs, 'restart', False)\n\n config = configobj.ConfigObj()\n file_name = self.folder + '/' + self.data.settings['SHARPy']['case'] + '.pmor.sharpy'\n config.filename = file_name\n config['parameters'] = dict()\n for k, v in self.settings['parameters'].items():\n cout.cout_wrap('\\tWriting parameter %s: %s' % (k, str(v)), 1)\n config['parameters'][k] = v\n\n sim_info = dict()\n sim_info['case'] = self.data.settings['SHARPy']['case']\n\n if 'PickleData' not in self.data.settings['SHARPy']['flow'] and self.settings['save_case']:\n warnings.warn('Post-proc: SaveParametricCase: Saving a pickle is not recommended - try saving required '\n 'attributes individually',\n DeprecationWarning)\n pickle_solver = initialise_solver('PickleData')\n pickle_solver.initialise(self.data, restart=restart)\n self.data = pickle_solver.run()\n sim_info['path_to_data'] = os.path.abspath(self.folder)\n\n sim_info['path_to_data'] = os.path.abspath(self.folder)\n\n config['sim_info'] = sim_info\n config.write()\n\n if self.settings['save_pmor_items']:\n try:\n self.data.linear\n except AttributeError:\n pass\n else:\n if not os.path.exists(self.folder + '/save_pmor_data/'):\n os.makedirs(self.folder + '/save_pmor_data/')\n self.save_state_space()\n self.save_aero_rom_bases()\n self.save_structural_modal_matrix()\n\n if self.settings['save_pmor_subsystems']:\n self.save_structural_matrices()\n self.save_aero_state_space()\n\n return self.data\n\n def save_aero_rom_bases(self):\n \"\"\"Save the aerodynamic reduced order bases to h5 files in the output directory\"\"\"\n # check rom's exist\n rom_dict = self.data.linear.linear_system.uvlm.rom\n if rom_dict is None:\n return None\n\n for rom_name, rom_class in rom_dict.items():\n rom_class.save_reduced_order_bases(self.base_name + f'_{rom_name.lower()}_aerorob.h5')\n\n def save_structural_modal_matrix(self):\n if not self.data.linear.linear_system.beam.sys.modal:\n return None\n\n self.data.linear.linear_system.beam.save_reduced_order_bases(self.base_name + f'_modal_structrob.h5')\n\n def save_state_space(self):\n self.data.linear.linear_system.ss.save(self.base_name + '_statespace.h5')\n\n def save_structural_matrices(self):\n self.data.linear.linear_system.beam.ss.save(self.base_name + '_beamstatespace.h5')\n self.data.linear.linear_system.beam.save_structural_matrices(self.base_name + '_struct_matrices.h5')\n\n def save_aero_state_space(self):\n self.data.linear.linear_system.uvlm.ss.save(self.base_name + '_aerostatespace.h5')\n\n @property\n def base_name(self):\n return self.folder + '/save_pmor_data/' + self.case_name\n\n" }, { "path": "sharpy/postproc/stabilityderivatives.py", "content": "import sharpy.utils.solver_interface as solver_interface\nimport os\nimport numpy as np\nimport sharpy.utils.cout_utils as cout\nimport sharpy.utils.settings as settings_utils\nfrom sharpy.linear.utils.derivatives import Derivatives\n\n\n@solver_interface.solver\nclass StabilityDerivatives(solver_interface.BaseSolver):\n \"\"\"\n Outputs the stability derivatives of a free-flying aircraft\n\n \"\"\"\n solver_id = 'StabilityDerivatives'\n solver_classification = 'post-processor'\n\n settings_default = dict()\n settings_description = dict()\n settings_types = dict()\n settings_options = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Display info to screen'\n\n settings_types['u_inf'] = 'float'\n settings_default['u_inf'] = 1.\n settings_description['u_inf'] = 'Free stream reference velocity'\n\n settings_types['S_ref'] = 'float'\n settings_default['S_ref'] = 1.\n settings_description['S_ref'] = 'Reference planform area'\n\n settings_types['b_ref'] = 'float'\n settings_default['b_ref'] = 1.\n settings_description['b_ref'] = 'Reference span'\n\n settings_types['c_ref'] = 'float'\n settings_default['c_ref'] = 1.\n settings_description['c_ref'] = 'Reference chord'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = dict()\n\n self.u_inf = 1\n self.inputs = 0\n self.caller = None\n self.folder = None\n\n self.ppal_axes = None\n self.n_control_surfaces = None\n\n self.coefficients = dict # type: dict # name: scaling coefficient\n\n def initialise(self, data, custom_settings=None, caller=None, restart=False):\n self.data = data\n\n if custom_settings:\n self.settings = custom_settings\n else:\n self.settings = self.data.settings[self.solver_id]\n\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n options=self.settings_options,\n no_ctype=True)\n self.caller = caller\n self.folder = data.output_folder + '/derivatives/'\n if not os.path.isdir(self.folder):\n os.makedirs(self.folder, exist_ok=True)\n\n u_inf = self.settings['u_inf']\n s_ref = self.settings['S_ref']\n b_ref = self.settings['b_ref']\n c_ref = self.settings['c_ref']\n rho = self.data.linear.tsaero0.rho\n self.ppal_axes = self.data.settings['Modal']['rigid_modes_ppal_axes']\n\n # need to decide whether coefficients stay here or goes just in Derivatives class\n self.coefficients = {'force': 0.5 * rho * u_inf ** 2 * s_ref,\n 'moment_lon': 0.5 * rho * u_inf ** 2 * s_ref * c_ref,\n 'moment_lat': 0.5 * rho * u_inf ** 2 * s_ref * b_ref,\n 'force_angular_vel': 0.5 * rho * u_inf ** 2 * s_ref * c_ref / u_inf,\n 'moment_lon_angular_vel': 0.5 * rho * u_inf ** 2 * s_ref * c_ref * c_ref / u_inf} # missing rates\n\n reference_dimensions = {}\n for k in ['S_ref', 'b_ref', 'c_ref', 'u_inf']:\n reference_dimensions[k] = self.settings[k]\n reference_dimensions['rho'] = rho\n reference_dimensions['quat'] = self.data.linear.tsstruct0.quat\n\n self.data.linear.derivatives = dict() # {str:Derivatives()} (sharpy.linear.utils.derivatives.Derivatives)\n self.data.linear.derivatives['aerodynamic'] = Derivatives(reference_dimensions,\n static_state=self.steady_aero_forces(),\n target_system='aerodynamic')\n self.data.linear.derivatives['aeroelastic'] = Derivatives(reference_dimensions,\n static_state=self.steady_aero_forces(),\n target_system='aeroelastic')\n\n\n def run(self, **kwargs):\n \n online = settings_utils.set_value_or_default(kwargs, 'online', False)\n\n # TODO: consider running all required solvers inside this one to keep the correct settings\n # i.e: run Modal, Linear Assembly\n\n derivatives = self.data.linear.derivatives # {str:Derivatives()} (sharpy.linear.utils.derivatives.Derivatives)\n if self.data.linear.linear_system.beam.sys.modal:\n phi = self.data.linear.linear_system.linearisation_vectors['mode_shapes'].real\n else:\n phi = None\n\n steady_forces = self.data.linear.linear_system.linearisation_vectors['forces_aero_beam_dof']\n v0 = self.get_freestream_velocity()\n quat = self.data.linear.tsstruct0.quat\n\n try:\n tpa = self.data.linear.tsstruct0.modal['t_pa']\n except KeyError:\n tpa = None\n\n if self.data.linear.linear_system.uvlm.scaled:\n raise NotImplementedError('Stability Derivatives not yet implented for scaled system')\n self.data.linear.linear_system.update(self.settings['u_inf'])\n\n for target_system in ['aerodynamic', 'aeroelastic']:\n state_space = self.get_state_space(target_system)\n target_system_derivatives = derivatives[target_system]\n\n target_system_derivatives.initialise_derivatives(state_space,\n steady_forces,\n quat,\n v0,\n phi,\n self.data.linear.tsstruct0.modal['cg'],\n tpa=tpa)\n target_system_derivatives.dict_of_derivatives[\n 'force_angle_velocity'] = target_system_derivatives.new_derivative(\n 'stability',\n 'angle_derivatives',\n 'Force/Angle via velocity')\n\n # useful to double check the effect of the ``track_body`` == 'on' setting\n # current_derivative.dict_of_derivatives['force_angle_angle'] = current_derivative.new_derivative(\n # 'stability',\n # 'angle_derivatives_tb',\n # 'Force/Angle via Track Body')\n\n target_system_derivatives.dict_of_derivatives['force_velocity'] = target_system_derivatives.new_derivative(\n 'body',\n 'body_derivatives')\n\n target_system_derivatives.dict_of_derivatives['force_cs'] = target_system_derivatives.new_derivative(\n 'body',\n 'control_surface_derivatives')\n target_system_derivatives.save(self.folder)\n target_system_derivatives.savetxt(self.folder)\n\n return self.data\n\n def get_freestream_velocity(self):\n try:\n u_inf = self.data.settings['StaticUvlm']['aero_solver_settings']['u_inf']\n u_inf_direction = self.data.settings['StaticCoupled']['aero_solver_settings']['u_inf_direction']\n except KeyError:\n try:\n u_inf = self.data.settings['StaticCoupled']['aero_solver_settings']['velocity_field_input']['u_inf']\n u_inf_direction = self.data.settings['StaticCoupled']['aero_solver_settings']['velocity_field_input']['u_inf_direction']\n except KeyError:\n cout.cout_wrap('Unable to find free stream velocity settings in StaticUvlm or StaticCoupled,'\n 'please ensure these settings are provided in the config .sharpy file. If'\n 'you are running a restart simulation make sure they are included too, regardless'\n 'of these solvers being present in the SHARPy flow', 4)\n raise KeyError\n\n try:\n v0 = u_inf * u_inf_direction * -1\n except TypeError:\n # For restart solutions, where the settings may have not been processed and thus may\n # exist but in string format\n try:\n u_inf_direction = np.array(u_inf_direction, dtype=float)\n except ValueError:\n if u_inf_direction.find(',') < 0:\n u_inf_direction = np.fromstring(u_inf_direction.strip('[]'), sep=' ', dtype=float)\n else:\n u_inf_direction = np.fromstring(u_inf_direction.strip('[]'), sep=',', dtype=float)\n finally:\n v0 = np.array(u_inf_direction, dtype=float) * float(u_inf) * -1\n\n return v0\n\n def get_state_space(self, target_system):\n if target_system == 'aerodynamic':\n ss = self.data.linear.linear_system.uvlm.ss\n elif target_system == 'aeroelastic':\n ss = self.data.linear.ss\n else:\n raise NameError('Unknown target system {:s}'.format(target_system))\n\n return ss\n\n def steady_aero_forces(self):\n fx = np.sum(self.data.aero.timestep_info[0].inertial_steady_forces[:, 0], 0) + \\\n np.sum(self.data.aero.timestep_info[0].inertial_unsteady_forces[:, 0], 0)\n\n fy = np.sum(self.data.aero.timestep_info[0].inertial_steady_forces[:, 1], 0) + \\\n np.sum(self.data.aero.timestep_info[0].inertial_unsteady_forces[:, 1], 0)\n\n fz = np.sum(self.data.aero.timestep_info[0].inertial_steady_forces[:, 2], 0) + \\\n np.sum(self.data.aero.timestep_info[0].inertial_unsteady_forces[:, 2], 0)\n\n return fx, fy, fz\n" }, { "path": "sharpy/postproc/stallcheck.py", "content": "import numpy as np\nimport sharpy.utils.cout_utils as cout\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\nfrom sharpy.utils.datastructures import init_matrix_structure, standalone_ctypes_pointer\nimport sharpy.aero.utils.uvlmlib as uvlmlib\n\n\n@solver\nclass StallCheck(BaseSolver):\n \"\"\"\n Outputs the incidence angle of every panel of the surface as cell variables for visualisation in Paraview.\n\n Note:\n This postprocessor appends the information to the current SHARPy timestep being run, therefore,\n in order to visualise the result in Paraview, it must be run prior to `AerogridPlot`. Otherwise, the panel\n stall check will be performed but the actual angle not produced in the Paraview visualisation.\n\n It also checks that the angles do not exceed the specified limit, with a warning in the log if the angle of attack\n exceeds such limits (both positive and negative).\n\n The limits are set through the setting ``airfoil_stall_angles``, which takes a dictionary where the key is\n the ID to the airfoil (in string format) and the value is a 2-tuple containing the negative and positive limits\n in radians.\n \"\"\"\n solver_id = 'StallCheck'\n solver_classification = 'post-processor'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Print info to screen '\n\n settings_types['airfoil_stall_angles'] = 'dict'\n settings_default['airfoil_stall_angles'] = dict()\n settings_description['airfoil_stall_angles'] = 'Dictionary of stall angles for each airfoil as per the details ' \\\n 'above'\n\n settings_types['output_degrees'] = 'bool'\n settings_default['output_degrees'] = False\n settings_description['output_degrees'] = 'Output incidence angles in degrees vs radians'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n\n self.settings = None\n self.data = None\n\n self.ts_max = None\n self.ts = None\n self.caller = None\n\n def initialise(self, data, custom_settings=None, caller=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n self.ts_max = len(self.data.structure.timestep_info)\n self.caller = caller\n\n def run(self, **kwargs):\n \n online = settings_utils.set_value_or_default(kwargs, 'online', False)\n\n if not online:\n for self.ts in range(self.ts_max):\n self.check_stall()\n cout.cout_wrap('...Finished', 1)\n else:\n self.ts = len(self.data.structure.timestep_info) - 1\n self.check_stall()\n return self.data\n\n def check_stall(self):\n # add entry to dictionary for postproc\n tstep = self.data.aero.timestep_info[self.ts]\n tstep.postproc_cell['incidence_angle'] = init_matrix_structure(dimensions=tstep.dimensions,\n with_dim_dimension=False)\n\n # create ctypes pointers\n tstep.postproc_cell['incidence_angle_ct_list'] = None\n tstep.postproc_cell['incidence_angle_ct_pointer'] = None\n tstep.postproc_cell['incidence_angle_ct_list'], tstep.postproc_cell['incidence_angle_ct_pointer'] = \\\n standalone_ctypes_pointer(tstep.postproc_cell['incidence_angle'])\n\n # call calculate\n uvlmlib.uvlm_calculate_incidence_angle(self.data.aero.timestep_info[self.ts],\n self.data.structure.timestep_info[self.ts])\n\n # calculate ratio of stalled panels and print\n stalled_panels = False\n stalled_surfs = np.zeros((tstep.n_surf, ), dtype=int)\n added_panels = []\n for i_surf in range(tstep.n_surf):\n added_panels.append([])\n\n for i_elem in range(self.data.structure.num_elem):\n for i_local_node in range(self.data.structure.num_node_elem):\n airfoil_id = self.data.aero.data_dict['airfoil_distribution'][i_elem, i_local_node]\n if self.settings['airfoil_stall_angles']:\n i_global_node = self.data.structure.connectivities[i_elem, i_local_node]\n for i_dict in self.data.aero.struct2aero_mapping[i_global_node]:\n i_surf = i_dict['i_surf']\n i_n = i_dict['i_n']\n\n if i_n in added_panels[i_surf]:\n continue\n\n if i_n == tstep.dimensions[i_surf][1]:\n continue\n\n limits = self.settings['airfoil_stall_angles'][str(airfoil_id)]\n if tstep.postproc_cell['incidence_angle'][i_surf][0, i_n] < float(limits[0]):\n stalled_panels = True\n stalled_surfs[i_surf] += tstep.postproc_cell['incidence_angle'][i_surf].shape[1]\n elif tstep.postproc_cell['incidence_angle'][i_surf][0, i_n] > float(limits[1]):\n stalled_panels = True\n stalled_surfs[i_surf] += tstep.postproc_cell['incidence_angle'][i_surf].shape[1]\n\n if stalled_panels:\n if self.settings['print_info']:\n cout.cout_wrap('Some panel has an incidence angle out of the linear region', 1)\n cout.cout_wrap('The number of stalled panels per surface id are:', 1)\n for i_surf in range(tstep.n_surf):\n cout.cout_wrap('\\ti_surf = ' + str(i_surf) + ': ' + str(stalled_surfs[i_surf]) + ' panels.', 1)\n # cout.cout_wrap('In total, the ratio of stalled panels is: ', str(stalled_surfs.sum()/))\n\n if self.settings['output_degrees']:\n for i_surf in range(tstep.n_surf):\n tstep.postproc_cell['incidence_angle'][i_surf] *= 180/np.pi\n" }, { "path": "sharpy/postproc/udpout.py", "content": "from sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\nimport sharpy.io.network_interface as network_interface\nimport sharpy.utils.cout_utils as cout\n\n\n@solver\nclass UDPout(BaseSolver):\n \"\"\"\n Send output data via UDP\n\n This post-processor is in essence a wrapper of the :class:`~sharpy.io.network_interface.NetworkLoader`\n where only an output network adapter is created.\n\n \"\"\"\n solver_id = 'UDPout'\n solver_classification = 'post-processor'\n\n settings_types = network_interface.NetworkLoader.settings_types.copy()\n settings_default = network_interface.NetworkLoader.settings_default.copy()\n settings_description = network_interface.NetworkLoader.settings_description.copy()\n\n # Remove unnecessary settings from NetworkLoader (all related to the inputs)\n del settings_default['input_network_settings']\n del settings_types['input_network_settings']\n del settings_description['input_network_settings']\n\n del settings_default['received_data_filename']\n del settings_types['received_data_filename']\n del settings_description['received_data_filename']\n\n del settings_types['send_output_to_all_clients']\n del settings_default['send_output_to_all_clients']\n del settings_description['send_output_to_all_clients']\n\n table = settings_utils.SettingsTable()\n __doc__ += table.generate(settings_types, settings_default, settings_description,\n header_line='This post-processor takes in the following settings, for a more '\n 'detailed description see '\n ':class:`~sharpy.io.network_interface.NetworkLoader`')\n\n def __init__(self):\n self.settings = None\n self.data = None\n\n self.network_loader = None\n self.out_network = None\n self.set_of_variables = None\n\n self.ts_max = 0\n\n self.caller = None\n\n def initialise(self, data, custom_settings=None, caller=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n\n self.network_loader = network_interface.NetworkLoader()\n self.network_loader.initialise(in_settings=self.settings)\n\n self.set_of_variables = self.network_loader.get_inout_variables()\n\n self.out_network = self.network_loader.get_networks(networks='out')\n\n self.ts_max = self.data.ts + 1\n\n self.caller = caller\n\n def run(self, **kwargs):\n \n online = settings_utils.set_value_or_default(kwargs, 'online', False)\n\n if online:\n self.set_of_variables.get_value(self.data)\n msg = self.set_of_variables.encode()\n self.out_network.send(msg, self.out_network.clients)\n else:\n for ts_index in range(self.ts_max):\n self.set_of_variables.get_value(self.data, timestep_index=ts_index)\n msg = self.set_of_variables.encode()\n self.out_network.send(msg, self.out_network.clients)\n\n cout.cout_wrap('...Finished', 1)\n self.shutdown()\n\n return self.data\n\n def shutdown(self):\n self.out_network.close()\n" }, { "path": "sharpy/postproc/writevariablestime.py", "content": "import os\nimport numpy as np\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\n\n\n@solver\nclass WriteVariablesTime(BaseSolver):\n r\"\"\"\n Write variables with time\n\n ``WriteVariablesTime`` is a class inherited from ``BaseSolver``\n\n It is a postprocessor that outputs the value of variables with time onto a text file.\n\n Attributes:\n settings_types (dict): Acceptable data types of the input data\n settings_default (dict): Default values for input data should the user not provide them\n See the list of arguments\n dir (str): directory to output the information\n\n \"\"\"\n\n solver_id = 'WriteVariablesTime'\n solver_classification = 'post-processor'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['delimiter'] = 'str'\n settings_default['delimiter'] = ' '\n settings_description['delimiter'] = 'Delimiter to be used in the output file'\n\n settings_types['FoR_variables'] = 'list(str)'\n settings_default['FoR_variables'] = ['']\n settings_description['FoR_variables'] = 'Variables of :class:`~sharpy.utils.datastructures.StructTimeStepInfo` associated to the frame of reference to be writen'\n\n settings_types['FoR_number'] = 'list(int)'\n settings_default['FoR_number'] = np.array([0], dtype=int)\n settings_description['FoR_number'] = 'Number of the A frame of reference to output (for multibody configurations)'\n\n settings_types['structure_variables'] = 'list(str)'\n settings_default['structure_variables'] = ['']\n settings_description['structure_variables'] = 'Variables of :class:`~sharpy.utils.datastructures.StructTimeStepInfo` associated to the frame of reference to be writen'\n\n settings_types['structure_nodes'] = 'list(int)'\n settings_default['structure_nodes'] = np.array([-1])\n settings_description['structure_nodes'] = 'Number of the nodes to be writen'\n\n settings_types['nonlifting_nodes_variables'] = 'list(str)'\n settings_default['nonlifting_nodes_variables'] = ['']\n settings_description['nonlifting_nodes_variables'] = 'Variables of :class:`~sharpy.utils.datastructures.NonliftingBodyTimeStepInfo` associated to panels to be writen'\n\n settings_types['nonlifting_nodes_im'] = 'list(int)'\n settings_default['nonlifting_nodes_im'] = np.array([0])\n settings_description['nonlifting_nodes_im'] = 'Chordwise index of the nonlifting panels to be output'\n\n settings_types['nonlifting_nodes_in'] = 'list(int)'\n settings_default['nonlifting_nodes_in'] = np.array([0])\n settings_description['nonlifting_nodes_in'] = 'Spanwise index of the nonlifting panels to be output'\n\n settings_types['nonlifting_nodes_isurf'] = 'list(int)'\n settings_default['nonlifting_nodes_isurf'] = np.array([0])\n settings_description['nonlifting_nodes_isurf'] = \"Number of the panels' surface to be output\"\n\n settings_types['aero_panels_variables'] = 'list(str)'\n settings_default['aero_panels_variables'] = ['']\n settings_description['aero_panels_variables'] = 'Variables of :class:`~sharpy.utils.datastructures.AeroTimeStepInfo` associated to panels to be writen'\n\n settings_types['aero_panels_isurf'] = 'list(int)'\n settings_default['aero_panels_isurf'] = np.array([0])\n settings_description['aero_panels_isurf'] = \"Number of the panels' surface to be output\"\n\n settings_types['aero_panels_im'] = 'list(int)'\n settings_default['aero_panels_im'] = np.array([0])\n settings_description['aero_panels_im'] = 'Chordwise index of the panels to be output'\n\n settings_types['aero_panels_in'] = 'list(int)'\n settings_default['aero_panels_in'] = np.array([0])\n settings_description['aero_panels_in'] = 'Spanwise index of the panels to be output'\n\n settings_types['aero_nodes_variables'] = 'list(str)'\n settings_default['aero_nodes_variables'] = ['']\n settings_description['aero_nodes_variables'] = 'Variables of :class:`~sharpy.utils.datastructures.AeroTimeStepInfo` associated to nodes to be writen'\n\n settings_types['aero_nodes_isurf'] = 'list(int)'\n settings_default['aero_nodes_isurf'] = np.array([0])\n settings_description['aero_nodes_isurf'] = \"Number of the nodes' surface to be output\"\n\n settings_types['aero_nodes_im'] = 'list(int)'\n settings_default['aero_nodes_im'] = np.array([0])\n settings_description['aero_nodes_im'] = 'Chordwise index of the nodes to be output'\n\n settings_types['aero_nodes_in'] = 'list(int)'\n settings_default['aero_nodes_in'] = np.array([0])\n settings_description['aero_nodes_in'] = 'Spanwise index of the nodes to be output'\n\n settings_types['cleanup_old_solution'] = 'bool'\n settings_default['cleanup_old_solution'] = False\n settings_description['cleanup_old_solution'] = 'Remove the existing files'\n\n settings_types['vel_field_variables'] = 'list(str)'\n settings_default['vel_field_variables'] = list()\n settings_description['vel_field_variables'] = 'Variables associated to the velocity field. Only ``uext`` implemented so far'\n\n settings_types['vel_field_points'] = 'list(float)'\n settings_default['vel_field_points'] = np.array([0., 0., 0.])\n settings_description['vel_field_points'] = 'List of coordinates of the control points as x1, y1, z1, x2, y2, z2 ...'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.settings = None\n self.data = None\n self.folder = None\n\n self.n_velocity_field_points = None\n self.velocity_field_points = None\n self.caller = None\n self.velocity_generator = None\n\n def initialise(self, data, custom_settings=None, caller=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n self.folder = data.output_folder + '/WriteVariablesTime/'\n if not os.path.isdir(self.folder):\n os.makedirs(self.folder)\n\n # Check inputs\n if not ((len(self.settings['aero_panels_isurf']) == len(self.settings['aero_panels_im'])) and (len(self.settings['aero_panels_isurf']) == len(self.settings['aero_panels_in']))):\n raise RuntimeError(\"aero_panels should be defined as [i_surf,i_m,i_n]\")\n if not ((len(self.settings['aero_nodes_isurf']) == len(self.settings['aero_nodes_im'])) and (len(self.settings['aero_nodes_isurf']) == len(self.settings['aero_nodes_in']))):\n raise RuntimeError(\"aero_nodes should be defined as [i_surf,i_m,i_n]\")\n\n if len(self.settings['vel_field_variables']) > 0:\n if not (len(self.settings['vel_field_points']) % 3 == 0):\n raise RuntimeError('Number of entries in ``vel_field_points`` has to be a multiple of 3')\n else:\n self.n_vel_field_points = len(self.settings['vel_field_points']) // 3\n self.vel_field_points = [np.zeros((3, self.n_vel_field_points, 1))]\n for ipoint in range(self.n_vel_field_points):\n self.vel_field_points[0][:, ipoint, 0] = self.settings['vel_field_points'][ipoint*3:(ipoint + 1)*3]\n\n # Initialise files with headers and clean them if required\n for ivariable in range(len(self.settings['FoR_variables'])):\n for ifor in range(len(self.settings['FoR_number'])):\n filename = self.folder + \"FoR_\" + '%02d' % self.settings['FoR_number'][ifor] + \"_\" + self.settings['FoR_variables'][ivariable] + \".dat\"\n if self.settings['cleanup_old_solution']:\n if os.path.isfile(filename):\n os.remove(filename)\n\n # Structure variables at nodes\n for ivariable in range(len(self.settings['structure_variables'])):\n for inode in range(len(self.settings['structure_nodes'])):\n node = self.settings['structure_nodes'][inode]\n filename = self.folder + \"struct_\" + self.settings['structure_variables'][ivariable] + \"_node\" + str(node) + \".dat\"\n if self.settings['cleanup_old_solution']:\n if os.path.isfile(filename):\n os.remove(filename)\n\n # Nonlifting variables at panels\n for ivariable in range(len(self.settings['nonlifting_nodes_variables'])):\n for ipanel in range(len(self.settings['nonlifting_nodes_isurf'])):\n i_surf = self.settings['nonlifting_nodes_isurf'][ipanel]\n i_m = self.settings['nonlifting_nodes_im'][ipanel]\n i_n = self.settings['nonlifting_nodes_in'][ipanel]\n filename = self.folder + \"nonlifting_\" + self.settings['nonlifting_nodes_variables'][ivariable] + \"_panel\" + \"_isurf\" + str(i_surf) + \"_im\"+ str(i_m) + \"_in\"+ str(i_n) + \".dat\"\n if self.settings['cleanup_old_solution']:\n if os.path.isfile(filename):\n os.remove(filename)\n\n # Aerodynamic variables at panels\n for ivariable in range(len(self.settings['aero_panels_variables'])):\n for ipanel in range(len(self.settings['aero_panels_isurf'])):\n i_surf = self.settings['aero_panels_isurf'][ipanel]\n i_m = self.settings['aero_panels_im'][ipanel]\n i_n = self.settings['aero_panels_in'][ipanel]\n filename = self.folder + \"aero_\" + self.settings['aero_panels_variables'][ivariable] + \"_panel\" + \"_isurf\" + str(i_surf) + \"_im\"+ str(i_m) + \"_in\"+ str(i_n) + \".dat\"\n if self.settings['cleanup_old_solution']:\n if os.path.isfile(filename):\n os.remove(filename)\n\n # Aerodynamic variables at nodes\n for ivariable in range(len(self.settings['aero_nodes_variables'])):\n for inode in range(len(self.settings['aero_nodes_isurf'])):\n i_surf = self.settings['aero_nodes_isurf'][inode]\n i_m = self.settings['aero_nodes_im'][inode]\n i_n = self.settings['aero_nodes_in'][inode]\n filename = self.folder + \"aero_\" + self.settings['aero_nodes_variables'][ivariable] + \"_node\" + \"_isurf\" + str(i_surf) + \"_im\"+ str(i_m) + \"_in\"+ str(i_n) + \".dat\"\n if self.settings['cleanup_old_solution']:\n if os.path.isfile(filename):\n os.remove(filename)\n\n # Velocity field variables at points\n for ivariable in range(len(self.settings['vel_field_variables'])):\n for ipoint in range(self.n_vel_field_points):\n filename = self.folder + \"vel_field_\" + self.settings['vel_field_variables'][ivariable] + \"_point\" + str(ipoint) + \".dat\"\n if self.settings['cleanup_old_solution']:\n if os.path.isfile(filename):\n os.remove(filename)\n if not os.path.isfile(filename):\n fid = open(filename, 'w')\n fid.write((\"#t[s]%suext_x[m/s]%suext_y[m/s]%suext_z[m/s]\\n\" % ((self.settings['delimiter'],)*3)))\n fid.close()\n\n # Initialise velocity generator\n self.caller = caller\n if ((not self.caller is None) and (not len(self.settings['vel_field_variables']) == 0)):\n if self.caller.solver_classification.lower() == 'aero':\n # For aerodynamic solvers\n self.velocity_generator = self.caller.velocity_generator\n elif self.caller.solver_classification.lower() == 'coupled':\n # For coupled solvers\n self.velocity_generator = self.caller.aero_solver.velocity_generator\n\n def run(self, **kwargs):\n \n online = settings_utils.set_value_or_default(kwargs, 'online', False)\n\n if online:\n self.data = self.write(-1)\n else:\n for it in range(len(self.data.structure.timestep_info)):\n if self.data.structure.timestep_info[it] is not None:\n self.data = self.write(it)\n\n return self.data\n\n def write(self, it):\n\n # FoR variables\n if 'FoR_number' in self.settings:\n pass\n else:\n self.settings['FoR_number'] = np.array([0], dtype=int)\n\n tstep = self.data.structure.timestep_info[it]\n\n for ivariable in range(len(self.settings['FoR_variables'])):\n if self.settings['FoR_variables'][ivariable] == '':\n continue\n for ifor in range(len(self.settings['FoR_number'])):\n filename = self.folder + \"FoR_\" + '%02d' % self.settings['FoR_number'][ifor] + \"_\" + self.settings['FoR_variables'][ivariable] + \".dat\"\n\n with open(filename, 'a') as fid:\n var = np.atleast_2d(getattr(tstep, self.settings['FoR_variables'][ivariable]))\n rows, cols = var.shape\n if ((cols == 1) and (rows == 1)):\n self.write_value_to_file(fid, self.data.ts, var, self.settings['delimiter'])\n elif ((cols > 1) and (rows == 1)):\n self.write_nparray_to_file(fid, self.data.ts, var, self.settings['delimiter'])\n elif ((cols == 1) and (rows >= 1)):\n self.write_value_to_file(fid, self.data.ts, var[ifor], self.settings['delimiter'])\n else:\n self.write_nparray_to_file(fid, self.data.ts, var[ifor,:], self.settings['delimiter'])\n\n # Structure variables at nodes\n for ivariable in range(len(self.settings['structure_variables'])):\n if self.settings['structure_variables'][ivariable] == '':\n continue\n #TODO: fix for lack of g frame description in nonlineardynamicmultibody.py\n if tstep.mb_dict is None:\n var = getattr(tstep, self.settings['structure_variables'][ivariable])\n else:\n if self.settings['structure_variables'][ivariable] == 'for_pos':\n import sharpy.utils.algebra as ag\n #TODO: uncomment for dynamic trim\n # try:\n # # import pdb\n # # pdb.set_trace()\n # cga = ag.euler2rot([0, self.data.trimmed_values[0], 0])\n # cag = cga.T\n # tstep.for_pos[0:3] = np.dot(cga,tstep.for_pos[0:3])\n # var = getattr(tstep, self.settings['structure_variables'][ivariable]).copy()\n # tstep.for_pos[0:3] = np.dot(cag,tstep.for_pos[0:3])\n # except AttributeError:\n t0step = self.data.structure.timestep_info[0]\n tstep.for_pos[0:3] = np.dot(t0step.cga(), tstep.for_pos[0:3])\n var = getattr(tstep, self.settings['structure_variables'][ivariable]).copy()\n tstep.for_pos[0:3] = np.dot(t0step.cag(), tstep.for_pos[0:3])\n else:\n var = getattr(tstep, self.settings['structure_variables'][ivariable]) \n var = getattr(tstep, self.settings['structure_variables'][ivariable])\n num_indices = len(var.shape)\n if num_indices == 1:\n # Beam global variables (i.e. not node dependant)\n filename = self.folder + \"struct_\" + self.settings['structure_variables'][ivariable] + \".dat\"\n with open(filename, 'a') as fid:\n self.write_nparray_to_file(fid, self.data.ts, var, self.settings['delimiter'])\n\n else: # These variables have nodal values (i.e the number of indices is either 2 or 3)\n for inode in range(len(self.settings['structure_nodes'])):\n node = self.settings['structure_nodes'][inode]\n filename = self.folder + \"struct_\" + self.settings['structure_variables'][ivariable] + \"_node\" + str(node) + \".dat\"\n with open(filename, 'a') as fid:\n if num_indices == 2:\n self.write_nparray_to_file(fid, self.data.ts, var[node,:], self.settings['delimiter'])\n elif num_indices == 3:\n ielem, inode_in_elem = self.data.structure.node_master_elem[node]\n self.write_nparray_to_file(fid, self.data.ts, var[ielem,inode_in_elem,:], self.settings['delimiter'])\n\n\n # Aerodynamic variables at nonlifting panels\n for ivariable in range(len(self.settings['nonlifting_nodes_variables'])):\n if self.settings['nonlifting_nodes_variables'][ivariable] == '':\n continue\n \n for ipanel in range(len(self.settings['nonlifting_nodes_isurf'])):\n i_surf = self.settings['nonlifting_nodes_isurf'][ipanel]\n i_m = self.settings['nonlifting_nodes_im'][ipanel]\n i_n = self.settings['nonlifting_nodes_in'][ipanel]\n filename = self.folder + \"nonlifting_\" + self.settings['nonlifting_nodes_variables'][ivariable] + \"_panel\" + \"_isurf\" + str(i_surf) + \"_im\"+ str(i_m) + \"_in\"+ str(i_n) + \".dat\"\n\n with open(filename, 'a') as fid:\n var = getattr(self.data.nonlifting_body.timestep_info[it], self.settings['nonlifting_nodes_variables'][ivariable])\n self.write_value_to_file(fid, self.data.ts, var[i_surf][i_m,i_n], self.settings['delimiter'])\n\n # Aerodynamic variables at panels\n for ivariable in range(len(self.settings['aero_panels_variables'])):\n if self.settings['aero_panels_variables'][ivariable] == '':\n continue\n for ipanel in range(len(self.settings['aero_panels_isurf'])):\n i_surf = self.settings['aero_panels_isurf'][ipanel]\n i_m = self.settings['aero_panels_im'][ipanel]\n i_n = self.settings['aero_panels_in'][ipanel]\n\n filename = self.folder + \"aero_\" + self.settings['aero_panels_variables'][ivariable] + \"_panel\" + \"_isurf\" + str(i_surf) + \"_im\"+ str(i_m) + \"_in\"+ str(i_n) + \".dat\"\n\n with open(filename, 'a') as fid:\n var = getattr(self.data.aero.timestep_info[it], self.settings['aero_panels_variables'][ivariable])\n self.write_value_to_file(fid, self.data.ts, var[i_surf][i_m,i_n], self.settings['delimiter'])\n\n\n # Aerodynamic variables at nodes\n for ivariable in range(len(self.settings['aero_nodes_variables'])):\n if self.settings['aero_nodes_variables'][ivariable] == '':\n continue\n for inode in range(len(self.settings['aero_nodes_isurf'])):\n i_surf = self.settings['aero_nodes_isurf'][inode]\n i_m = self.settings['aero_nodes_im'][inode]\n i_n = self.settings['aero_nodes_in'][inode]\n\n filename = self.folder + \"aero_\" + self.settings['aero_nodes_variables'][ivariable] + \"_node\" + \"_isurf\" + str(i_surf) + \"_im\"+ str(i_m) + \"_in\"+ str(i_n) + \".dat\"\n\n with open(filename, 'a') as fid:\n var = getattr(self.data.aero.timestep_info[it], self.settings['aero_nodes_variables'][ivariable])\n self.write_nparray_to_file(fid, self.data.ts, var[i_surf][:,i_m,i_n], self.settings['delimiter'])\n\n # Velocity field variables at points\n for ivariable in range(len(self.settings['vel_field_variables'])):\n if self.settings['vel_field_variables'][ivariable] == 'uext':\n uext = [np.zeros((3, self.n_vel_field_points, 1))]\n self.velocity_generator.generate({'zeta': self.vel_field_points,\n 'for_pos': tstep.for_pos[0:3],\n 't': self.data.ts*self.caller.settings['dt'],\n 'is_wake': False,\n 'override': True},\n uext)\n for ipoint in range(self.n_vel_field_points):\n filename = self.folder + \"vel_field_\" + self.settings['vel_field_variables'][ivariable] + \"_point\" + str(ipoint) + \".dat\"\n with open(filename, 'a') as fid:\n self.write_nparray_to_file(fid, self.data.ts, uext[0][:,ipoint,0], self.settings['delimiter'])\n\n return self.data\n\n def write_nparray_to_file(self, fid, ts, nparray, delimiter):\n\n fid.write(\"%d%s\" % (ts,delimiter))\n for idim in range(nparray.shape[0]):\n try:\n for jdim in range(nparray.shape[1] - 1):\n fid.write(\"%e%s\" % (nparray[idim, jdim],delimiter))\n fid.write(\"%e\" % (nparray[idim, -1]))\n except IndexError:\n fid.write(\"%e%s\" % (nparray[idim],delimiter))\n\n fid.write(\"\\n\")\n\n def write_value_to_file(self, fid, ts, value, delimiter):\n\n fid.write(\"%d%s%e\\n\" % (ts,delimiter,value))\n" }, { "path": "sharpy/presharpy/__init__.py", "content": "" }, { "path": "sharpy/presharpy/presharpy.py", "content": "import configparser\nimport configobj\nimport os\nimport sharpy.utils.cout_utils as cout\nfrom sharpy.utils.solver_interface import solver, dict_of_solvers\nimport sharpy.utils.settings as settings\nimport sharpy.utils.exceptions as exceptions\n\n\n@solver\nclass PreSharpy(object):\n \"\"\"\n The PreSharpy solver is the main loader solver of SHARPy. It takes the admin-like settings for the simulation,\n including the case name, case route and the list of solvers to run and in which order to run them. This order\n of solvers is referred to, throughout SHARPy, as the ``flow`` setting.\n\n This is a mandatory solver for all simulations at the start so it is never included in the ``flow`` setting.\n\n The settings for this solver are parsed through in the configuration file under the header ``SHARPy``. I.e, when\n you are defining the config file for a simulation, the settings for PreSharpy are included as:\n\n .. code-block:: python\n\n import configobj\n filename = '/.sharpy'\n config = configobj.ConfigObj()\n config.filename = filename\n config['SHARPy'] = {'case': '', # an example setting\n # Rest of your settings for the PreSHARPy class\n }\n\n \"\"\"\n solver_id = 'PreSharpy'\n solver_classification = 'loader'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['flow'] = 'list(str)'\n settings_default['flow'] = None\n settings_description['flow'] = \"List of the desired solvers' ``solver_id`` to run in sequential order.\"\n\n settings_types['case'] = 'str'\n settings_default['case'] = 'default_case_name'\n settings_description['case'] = 'Case name'\n\n settings_types['route'] = 'str'\n settings_default['route'] = None\n settings_description['route'] = 'Route to case files'\n\n settings_types['write_screen'] = 'bool'\n settings_default['write_screen'] = True\n settings_description['write_screen'] = 'Display output on terminal screen'\n\n settings_types['write_log'] = 'bool'\n settings_default['write_log'] = False\n settings_description['write_log'] = 'Write log file'\n\n settings_types['log_folder'] = 'str'\n settings_default['log_folder'] = './output/'\n settings_description['log_folder'] = 'A folder with the case name will be created at this directory ' \\\n 'containing the SHARPy log and output folders'\n\n settings_types['log_file'] = 'str'\n settings_default['log_file'] = 'log'\n settings_description['log_file'] = 'Name of the log file'\n\n settings_types['save_settings'] = 'bool'\n settings_default['save_settings'] = False\n settings_description['save_settings'] = 'Save a copy of the settings to a ``.sharpy`` file in the output ' \\\n 'directory specified in ``log_folder``'\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description,\n header_line='The following are the settings that the PreSharpy class takes:')\n\n def __init__(self, in_settings=None):\n self._settings = True\n if in_settings is None:\n # call for documentation only\n self._settings = False\n\n self.ts = 0\n\n if self._settings:\n self.settings = in_settings\n self.settings['SHARPy']['flow'] = self.settings['SHARPy']['flow']\n\n settings.to_custom_types(self.settings['SHARPy'], self.settings_types, self.settings_default)\n self.output_folder = self.settings['SHARPy']['log_folder'] + '/' + self.settings['SHARPy']['case'] + '/'\n if not os.path.isdir(self.output_folder):\n os.makedirs(self.output_folder)\n\n cout.cout_wrap.initialise(self.settings['SHARPy']['write_screen'],\n self.settings['SHARPy']['write_log'],\n self.output_folder,\n self.settings['SHARPy']['log_file'])\n\n self.case_route = in_settings['SHARPy']['route'] + '/'\n self.case_name = in_settings['SHARPy']['case']\n for solver_name in in_settings['SHARPy']['flow']:\n try:\n dict_of_solvers[solver_name]\n except KeyError:\n exceptions.NotImplementedSolver(solver_name)\n\n cout.cout_wrap('SHARPy output folder set')\n cout.cout_wrap('\\t' + self.output_folder, 1)\n\n if self.settings['SHARPy']['save_settings']:\n self.save_settings()\n\n def initialise(self):\n pass\n\n def update_settings(self, new_settings):\n self.settings = new_settings\n self.settings['SHARPy']['flow'] = self.settings['SHARPy']['flow']\n settings.to_custom_types(self.settings['SHARPy'], self.settings_types, self.settings_default)\n\n self.output_folder = self.settings['SHARPy']['log_folder'] + '/' + self.settings['SHARPy']['case'] + '/'\n if not os.path.isdir(self.output_folder):\n os.makedirs(self.output_folder)\n \n cout.cout_wrap.initialise(self.settings['SHARPy']['write_screen'],\n self.settings['SHARPy']['write_log'],\n self.output_folder,\n self.settings['SHARPy']['log_file'])\n\n self.case_route = self.settings['SHARPy']['route'] + '/'\n self.case_name = self.settings['SHARPy']['case']\n\n def save_settings(self):\n \"\"\"\n Saves the settings to a ``.sharpy`` config obj file in the output directory.\n \"\"\"\n out_settings = configobj.ConfigObj()\n for k, v in self.settings.items():\n out_settings[k] = v\n out_settings.filename = self.output_folder + self.settings['SHARPy']['case'] + '.sharpy'\n out_settings.write()\n\n @staticmethod\n def load_config_file(file_name):\n config = configparser.ConfigParser()\n config.read(file_name)\n return config\n" }, { "path": "sharpy/rom/__init__.py", "content": "\"\"\"Model Order Reduction\"\"\"\nimport importlib\nimport os\n\nimport sharpy.linear.utils.ss_interface as ss_interface\nimport sharpy.utils.sharpydir as sharpydir\n\nfiles = ss_interface.sys_list_from_path(os.path.dirname(__file__))\n\nimport_path = os.path.realpath(os.path.dirname(__file__))\nimport_path = import_path.replace(sharpydir.SharpyDir, \"\")\nif import_path[0] == \"/\": import_path = import_path[1:]\nimport_path = import_path.replace(\"/\", \".\")\n\nfor file in files:\n ss_interface.systems_dict_import[file] = importlib.import_module(import_path + \".\" + file)\n" }, { "path": "sharpy/rom/balanced.py", "content": "\"\"\"Balancing Methods\n\nThe following classes are available to reduce a linear system employing balancing methods.\n\nThe main class is :class:`.Balanced` and the other available classes:\n\n* :class:`.Direct`\n\n* :class:`.Iterative`\n\n* :class:`.FrequencyLimited`\n\ncorrespond to the reduction algorithm.\n\n\"\"\"\nimport sharpy.utils.settings as settings\nimport numpy as np\nfrom abc import ABCMeta\nimport sharpy.utils.cout_utils as cout\nimport sharpy.utils.rom_interface as rom_interface\nimport sharpy.rom.utils.librom as librom\nimport sharpy.linear.src.libss as libss\nimport time\nfrom sharpy.linear.utils.ss_interface import LinearVector, StateVariable\n\ndict_of_balancing_roms = dict()\n\ndef bal_rom(arg):\n global dict_of_balancing_roms\n try:\n arg._bal_rom_id\n except AttributeError:\n raise AttributeError('Class defined as balanced rom has no _bal_rom_id attribute')\n dict_of_balancing_roms[arg._bal_rom_id] = arg\n return arg\n\n\nclass BaseBalancedRom(metaclass=ABCMeta):\n\n print_info = False\n\n def initialise(self, in_settings=None):\n pass\n\n def run(self, ss):\n pass\n\n\n@bal_rom\nclass Direct(BaseBalancedRom):\n __doc__ = librom.balreal_direct_py.__doc__\n _bal_rom_id = 'Direct'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['tune'] = 'bool'\n settings_default['tune'] = True\n settings_description['tune'] = 'Tune ROM to specified tolerance'\n\n settings_types['use_schur'] = 'bool'\n settings_default['use_schur'] = False\n settings_description['use_schur'] = 'Use Schur decomposition during build'\n\n settings_types['rom_tolerance'] = 'float'\n settings_default['rom_tolerance'] = 1e-2\n settings_description['rom_tolerance'] = 'Absolute accuracy with respect to full order frequency response'\n\n settings_types['rom_tune_freq_range'] = 'list(float)'\n settings_default['rom_tune_freq_range'] = [0, 1]\n settings_description['rom_tune_freq_range'] = 'Beginning and end of frequency range where to tune ROM'\n\n settings_types['convergence'] = 'str'\n settings_default['convergence'] = 'min'\n settings_description['convergence'] = 'ROM tuning convergence. If ``min`` attempts to find minimal number of states.' \\\n 'If ``all`` it starts from larger size ROM until convergence to ' \\\n 'specified tolerance is found.'\n\n settings_types['reduction_method'] = 'str'\n settings_default['reduction_method'] = 'realisation'\n settings_description['reduction_method'] = 'Desired reduction method'\n settings_options['reduction_method'] = ['realisation', 'truncation']\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description, settings_options)\n\n def __init__(self):\n self.settings = dict()\n\n def initialise(self, in_settings=None):\n if in_settings is not None:\n self.settings = in_settings\n\n settings.to_custom_types(self.settings, self.settings_types, self.settings_default, self.settings_options,\n no_ctype=True)\n\n def run(self, ss):\n if self.print_info:\n cout.cout_wrap('Reducing system using a Direct balancing method...')\n t0 = time.time()\n A, B, C, D = ss.get_mats()\n\n try:\n if ss.dt is not None:\n dtsystem = True\n else:\n dtsystem = False\n except AttributeError:\n dtsystem = False\n\n S, T, Tinv = librom.balreal_direct_py(A, B, C, DLTI=dtsystem, Schur=self.settings['use_schur'])\n\n Ar = T.dot(A.dot(Tinv))\n Br = T.dot(B)\n Cr = C.dot(Tinv)\n\n if dtsystem:\n ss_bal = libss.StateSpace(Ar, Br, Cr, D, dt=ss.dt)\n else:\n ss_bal = libss.StateSpace(Ar, Br, Cr, D)\n\n t1 = time.time()\n if self.print_info:\n cout.cout_wrap('\\t...completed balancing in %.2fs' % (t1-t0), 1)\n\n if self.settings['tune']:\n cout.cout_wrap('Tuning ROM to specified tolerance...', 1)\n kv = np.linspace(self.settings['rom_tune_freq_range'][0],\n self.settings['rom_tune_freq_range'][1])\n ssrom = librom.tune_rom(ss_bal,\n kv=kv,\n tol=self.settings['rom_tolerance'],\n gv=S,\n convergence=self.settings['convergence'],\n method=self.settings['reduction_method'])\n if librom.check_stability(ssrom.A, dt=True):\n if self.print_info:\n cout.cout_wrap('ROM by direct balancing is stable')\n t2 = time.time()\n cout.cout_wrap('\\t...completed reduction in %.2fs' % (t2-t0), 1)\n return ssrom\n else:\n return ss_bal\n\n\n@bal_rom\nclass FrequencyLimited(BaseBalancedRom):\n __doc__ = librom.balfreq.__doc__\n\n _bal_rom_id = 'FrequencyLimited'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['frequency'] = 'float'\n settings_default['frequency'] = 1.\n settings_description['frequency'] = 'defines limit frequencies for balancing. The balanced model will be accurate ' \\\n 'in the range ``[0,F]``, where ``F`` is the value of this key. Note that ``F`` ' \\\n 'units must be consistent with the units specified in the in ' \\\n 'the ``self.ScalingFacts`` dictionary.'\n\n settings_types['method_low'] = 'str'\n settings_default['method_low'] = 'trapz'\n settings_description['method_low'] = 'Specifies whether to use gauss quadrature or ' \\\n 'trapezoidal rule in the low-frequency range ``[0,F]``'\n settings_options['method_low'] = ['gauss', 'trapz']\n\n settings_types['options_low'] = 'dict'\n settings_default['options_low'] = dict()\n settings_description['options_low'] = 'Settings for the low frequency integration. See Notes.'\n\n settings_types['method_high'] = 'str'\n settings_default['method_high'] = 'trapz'\n settings_description['method_high'] = 'Specifies whether to use gauss quadrature or ' \\\n 'trapezoidal rule in the high-frequency range ``[F,FN]``'\n settings_options['method_high'] = ['gauss', 'trapz']\n\n settings_types['options_high'] = 'dict'\n settings_default['options_high'] = dict()\n settings_description['options_high'] = 'Settings for the high frequency integration. See Notes.'\n\n settings_types['check_stability'] = 'bool'\n settings_default['check_stability'] = True\n settings_description['check_stability'] = 'if True, the balanced model is truncated to eliminate ' \\\n 'unstable modes - if any is found. Note that very accurate ' \\\n 'balanced model can still be obtained, even if high order ' \\\n 'modes are unstable.'\n\n settings_types['get_frequency_response'] = 'bool'\n settings_default['get_frequency_response'] = False\n settings_description['get_frequency_response'] = 'if True, the function also returns the frequency ' \\\n 'response evaluated at the low-frequency range integration' \\\n ' points. If True, this option also allows to automatically' \\\n ' tune the balanced model.'\n\n # Integrator options\n settings_options_types = dict()\n settings_options_default = dict()\n settings_options_description = dict()\n\n settings_options_types['points'] = 'int'\n settings_options_default['points'] = 12\n settings_options_description['points'] = 'Trapezoidal points of integration'\n\n settings_options_types['partitions'] = 'int'\n settings_options_default['partitions'] = 2\n settings_options_description['partitions'] = 'Number of Gauss-Lobotto quadratures'\n\n settings_options_types['order'] = 'int'\n settings_options_default['order'] = 2\n settings_options_description['order'] = 'Order of Gauss-Lobotto quadratures'\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description, settings_options)\n\n options_table = settings.SettingsTable()\n __doc__ += options_table.generate(settings_options_types, settings_options_default, settings_options_description,\n header_line='The parameters of integration take the following options:\\n')\n\n def __init__(self):\n self.settings = dict()\n\n def initialise(self, in_settings=None):\n\n if in_settings is not None:\n self.settings = in_settings\n\n settings.to_custom_types(self.settings, self.settings_types, self.settings_default,\n self.settings_options, no_ctype=True)\n settings.to_custom_types(self.settings['options_low'], self.settings_options_types,\n self.settings_options_default, no_ctype=True)\n settings.to_custom_types(self.settings['options_high'], self.settings_options_types,\n self.settings_options_default, no_ctype=True)\n\n def run(self, ss):\n\n output_results = librom.balfreq(ss, self.settings)\n\n return output_results[0]\n\n\n@bal_rom\nclass Iterative(BaseBalancedRom):\n __doc__ = librom.balreal_iter.__doc__\n _bal_rom_id = 'Iterative'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['lowrank'] = 'bool'\n settings_default['lowrank'] = True\n settings_description['lowrank'] = 'Use low rank methods'\n\n settings_types['smith_tol'] = 'float'\n settings_default['smith_tol'] = 1e-10\n settings_description['smith_tol'] = 'Smith tolerance'\n\n settings_types['tolSVD'] = 'float'\n settings_default['tolSVD'] = 1e-6\n settings_description['tolSVD'] = 'SVD threshold'\n\n settings_types['tolSVD'] = 'float'\n settings_default['tolSVD'] = 1e-6\n settings_description['tolSVD'] = 'SVD threshold'\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.settings = dict()\n\n def initialise(self, in_settings=None):\n if in_settings is not None:\n self.settings = in_settings\n\n settings.to_custom_types(self.settings, self.settings_types, self.settings_default,\n no_ctype=True)\n\n def run(self, ss):\n\n A, B, C, D = ss.get_mats()\n\n s, T, Tinv, rcmax, romax = librom.balreal_iter(A, B, C,\n lowrank=self.settings['lowrank'],\n tolSmith=self.settings['smith_tol'],\n tolSVD=self.settings['tolSVD'])\n\n Ar = Tinv.dot(A.dot(T))\n Br = Tinv.dot(B)\n Cr = C.dot(T)\n\n ssrom = libss.StateSpace(Ar, Br, Cr, D, dt=ss.dt)\n return ssrom\n\n\n@rom_interface.rom\nclass Balanced(rom_interface.BaseRom):\n \"\"\"Balancing ROM methods\n\n Main class to load a balancing ROM. See below for the appropriate settings to be parsed in\n the ``algorithm_settings`` based on your selection.\n\n Supported algorithms:\n * Direct balancing :class:`.Direct`\n\n * Iterative balancing :class:`.Iterative`\n\n * Frequency limited balancing :class:`.FrequencyLimited`\n\n \"\"\"\n rom_id = 'Balanced'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Write output to screen'\n\n settings_types['algorithm'] = 'str'\n settings_default['algorithm'] = ''\n settings_description['algorithm'] = 'Balanced realisation method'\n settings_options['algorithm'] = ['Direct', 'Iterative', 'FrequencyLimited']\n\n settings_types['algorithm_settings'] = 'dict'\n settings_default['algorithm_settings'] = dict()\n settings_description['algorithm_settings'] = 'Settings for the desired algorithm'\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description, settings_options)\n\n def __init__(self):\n self.settings = dict()\n self.algorithm = None\n self.ssrom = None\n self.ss = None\n self.dtsystem = None\n\n def initialise(self, in_settings=None):\n\n if in_settings is not None:\n self.settings = in_settings\n\n settings.to_custom_types(self.settings, self.settings_types, self.settings_default, self.settings_options)\n\n if not (self.settings['algorithm'] in dict_of_balancing_roms):\n raise AttributeError('Balancing algorithm %s is not yet implemented' % self.settings['algorithm'])\n\n self.algorithm = dict_of_balancing_roms[self.settings['algorithm']]()\n self.algorithm.initialise(self.settings['algorithm_settings'])\n self.algorithm.print_info = self.settings['print_info']\n\n def run(self, ss):\n\n self.ss = ss\n\n A, B, C, D = self.ss.get_mats()\n\n if self.ss.dt:\n self.dtsystem = True\n else:\n self.dtsystem = False\n\n out = self.algorithm.run(ss)\n\n if type(out) == libss.StateSpace:\n self.ssrom = out\n\n else:\n Ar, Br, Cr = out\n if self.dtsystem:\n self.ssrom = libss.StateSpace(Ar, Br, Cr, D, dt=self.ss.dt)\n else:\n self.ssrom = libss.StateSpace(Ar, Br, Cr, D)\n\n try:\n self.ssrom.input_variables = self.ss.input_variables.copy()\n self.ssrom.output_variables = self.ss.output_variables.copy()\n self.ssrom.state_variables = LinearVector(\n [StateVariable('balanced_{:s}'.format(self.settings['algorithm'].lower()),\n size=self.ssrom.states, index=0)])\n except AttributeError:\n pass\n\n return self.ssrom\n" }, { "path": "sharpy/rom/krylov.py", "content": "\"\"\"Krylov-subspaces model order reduction techniques\n\"\"\"\nimport numpy as np\nimport scipy.linalg as sclalg\nimport sharpy.linear.src.libss as libss\nimport time\nimport sharpy.utils.settings as settings\nimport sharpy.utils.cout_utils as cout\nimport sharpy.utils.rom_interface as rom_interface\nimport sharpy.utils.h5utils as h5\nimport sharpy.rom.utils.krylovutils as krylovutils\nimport warnings as warn\nimport h5py\nfrom sharpy.linear.utils.ss_interface import LinearVector, StateVariable, InputVariable, OutputVariable\n\n@rom_interface.rom\nclass Krylov(rom_interface.BaseRom):\n \"\"\"\n Model Order Reduction Methods for Single Input Single Output (SISO) and MIMO\n Linear Time-Invariant (LTI) Systems using\n moment matching (Krylov Methods).\n\n Examples:\n General calling sequences for different systems\n\n SISO single point interpolation:\n >>> algorithm = 'one_sided_arnoldi'\n >>> interpolation_point = np.array([0.0])\n >>> krylov_r = 4\n >>>\n >>> rom = Krylov()\n >>> rom.initialise(sharpy_data, FullOrderModelSS)\n >>> rom.run(algorithm, krylov_r, interpolation_point)\n\n 2 by 2 MIMO with tangential, multipoint interpolation:\n >>> algorithm = 'dual_rational_arnoldi'\n >>> interpolation_point = np.array([0.0, 1.0j])\n >>> krylov_r = 4\n >>> right_vector = np.block([[1, 0], [0, 1]])\n >>> left_vector = right_vector\n >>>\n >>> rom = Krylov()\n >>> rom.initialise(sharpy_data, FullOrderModelSS)\n >>> rom.run(algorithm, krylov_r, interpolation_point, right_vector, left_vector)\n\n 2 by 2 MIMO multipoint interpolation:\n >>> algorithm = 'mimo_rational_arnoldi'\n >>> interpolation_point = np.array([0.0])\n >>> krylov_r = 4\n >>>\n >>> rom = Krylov()\n >>> rom.initialise(sharpy_data, FullOrderModelSS)\n >>> rom.run(algorithm, krylov_r, interpolation_point)\n \"\"\"\n rom_id = 'Krylov'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Write ROM information to screen and log'\n\n settings_types['frequency'] = 'list(complex)'\n settings_default['frequency'] = [0]\n settings_description['frequency'] = 'Interpolation points in the continuous time complex plane [rad/s]'\n\n settings_types['algorithm'] = 'str'\n settings_default['algorithm'] = ''\n settings_description['algorithm'] = 'Krylov reduction method algorithm'\n\n settings_types['r'] = 'int'\n settings_default['r'] = 1\n settings_description['r'] = 'Moments to match at the interpolation points'\n\n settings_types['single_side'] = 'str'\n settings_default['single_side'] = ''\n settings_description['single_side'] = 'Construct the rom using a single side. Leave blank (or empty string) for both.'\n settings_options['single_side'] = ['controllability', 'observability']\n\n settings_types['tangent_input_file'] = 'str'\n settings_default['tangent_input_file'] = ''\n settings_description['tangent_input_file'] = 'Filepath to .h5 file containing tangent interpolation vectors'\n\n settings_types['restart_arnoldi'] = 'bool'\n settings_default['restart_arnoldi'] = False\n settings_description['restart_arnoldi'] = 'Restart Arnoldi iteration with r-=1 if ROM is unstable'\n\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description, settings_options)\n\n supported_methods = ('one_sided_arnoldi',\n 'two_sided_arnoldi',\n 'dual_rational_arnoldi',\n 'mimo_rational_arnoldi',\n 'mimo_block_arnoldi')\n\n def __init__(self):\n self.settings = dict()\n\n self.frequency = None\n self.algorithm = None\n self.ss = None\n self.r = 1\n self.V = None\n self.H = None\n self.W = None\n self.ssrom = None\n self.sstype = None\n self.nfreq = None\n self.restart_arnoldi = None\n self.stable = None\n self.cpu_summary = dict()\n self.eigenvalue_table = None\n\n def initialise(self, in_settings=None):\n\n if in_settings is not None:\n self.settings = in_settings\n\n settings.to_custom_types(self.settings, self.settings_types, self.settings_default, self.settings_options)\n\n try:\n if self.settings['print_info']:\n cout.cout_wrap('Initialising Krylov Model Order Reduction')\n except ValueError:\n pass\n\n self.algorithm = self.settings['algorithm']\n if self.algorithm not in self.supported_methods:\n raise NotImplementedError('Algorithm %s not recognised, check for spelling or it'\n 'could be that is not yet implemented'\n % self.algorithm)\n\n self.frequency = np.array(self.settings['frequency'])\n self.r = self.settings['r']\n self.restart_arnoldi = self.settings['restart_arnoldi']\n try:\n self.nfreq = self.frequency.shape[0]\n except AttributeError:\n self.nfreq = 1\n\n def save(self, filename):\n \"\"\"\n Saves to an ``.h5`` file of name ``filename`` the left and right projectors and the reduced order model\n\n Args:\n filename (str): path and filename to which to save the data\n\n \"\"\"\n rom_projectors = {'right_projector': self.V,\n 'left_projector': self.W,\n }\n\n if '.h5' not in filename[-3:]:\n filename += '.h5'\n\n with h5py.File(filename, 'a') as outfile:\n h5.add_as_grp(rom_projectors, outfile, grpname='projectors',\n compress_float=True)\n h5.add_as_grp(self.ssrom, outfile,\n grpname='ssrom',\n ClassesToSave=(libss.StateSpace, ),\n compress_float=True)\n\n def save_reduced_order_bases(self, file_name):\n \"\"\"\n Save reduced order bases to an h5 file\n\n Args:\n file_name (str): path to h5 file\n\n \"\"\"\n if not isinstance(self.V, libss.Gain):\n V = libss.Gain(self.V)\n W = libss.Gain(self.W)\n\n else:\n V = self.V\n W = self.W\n\n if self.settings['single_side'] == 'observability' or self.settings['single_side'] == 'controllability':\n # if single sided, the projector is V and W = V therefore no need to duplicate\n libss.Gain.save_multiple_gains(file_name, ('V', V))\n cout.cout_wrap(f'Saved Krylov reduced order bases, V to file: {file_name}', 1)\n else:\n libss.Gain.save_multiple_gains(file_name, ('V', V), ('W', W))\n cout.cout_wrap(f'Saved Krylov reduced order bases, V and W to file: {file_name}', 1)\n\n def run(self, ss):\n \"\"\"\n Performs Model Order Reduction employing Krylov space projection methods.\n\n Supported methods include:\n\n ========================= ==================== ==========================================================\n Algorithm Interpolation Points Systems\n ========================= ==================== ==========================================================\n ``one_sided_arnoldi`` 1 SISO Systems\n ``two_sided_arnoldi`` 1 SISO Systems\n ``dual_rational_arnoldi`` K SISO systems and Tangential interpolation for MIMO systems\n ``mimo_rational_arnoldi`` K MIMO systems. Uses vector-wise construction (more robust)\n ``mimo_block_arnoldi`` K MIMO systems. Uses block Arnoldi methods (more efficient)\n ========================= ==================== ==========================================================\n\n Args:\n ss (sharpy.linear.src.libss.StateSpace): State space to reduce\n\n Returns:\n (libss.StateSpace): Reduced state space system\n \"\"\"\n self.ss = ss\n\n if self.settings['print_info']:\n cout.cout_wrap('Model Order Reduction in progress...')\n self.print_header()\n\n if self.ss.dt is None:\n self.sstype = 'ct'\n else:\n self.sstype = 'dt'\n self.frequency = np.exp(self.frequency * ss.dt)\n\n t0 = time.time()\n\n Ar, Br, Cr = self.__getattribute__(self.algorithm)(self.frequency, self.r)\n\n self.ssrom = libss.StateSpace(Ar, Br, Cr, self.ss.D, self.ss.dt)\n try:\n self.ssrom.input_variables = self.ss.input_variables.copy()\n self.ssrom.output_variables = self.ss.output_variables.copy()\n self.ssrom.state_variables = LinearVector([StateVariable('krylov', size=self.ssrom.states, index=0)])\n except AttributeError:\n pass\n\n self.stable = self.check_stability(restart_arnoldi=self.restart_arnoldi)\n\n if not self.stable:\n pass\n warn.warn('Reduced Order Model Unstable')\n # Under development\n # TL, TR = self.restart()\n # Wtr, Vr = self.restart()\n # TL, TR = self.stable_realisation()\n # self.ssrom = libss.ss(TL.T.dot(Ar.dot(TR)), TL.T.dot(Br), Cr.dot(TR), self.ss.D, self.ss.dt)\n # self.ssrom = libss.ss(Wtr.dot(self.ssrom.A.dot(Vr)), Wtr.dot(self.ssrom.B), self.ssrom.C.dot(Vr), self.ss.D, self.ss.dt)\n # self.stable = self.check_stability(restart_arnoldi=self.restart_arnoldi)\n\n t_rom = time.time() - t0\n self.cpu_summary['run'] = t_rom\n if self.settings['print_info']:\n cout.cout_wrap('System reduced from order %d to ' % self.ss.states)\n cout.cout_wrap('\\tn = %d states' % self.ssrom.states, 1)\n cout.cout_wrap('...Completed Model Order Reduction in %.2f s' % t_rom)\n\n return self.ssrom\n\n def print_header(self):\n cout.cout_wrap('Moment Matching Krylov Model Reduction')\n cout.cout_wrap('\\tConstruction Algorithm:')\n cout.cout_wrap('\\t\\t%s' % self.algorithm, 1)\n cout.cout_wrap('\\tInterpolation points:')\n if self.frequency.dtype == complex:\n cout.cout_wrap(self.nfreq * '\\t\\tsigma = %4f + %4fj [rad/s]\\n' %tuple(self.frequency.view(float)), 1)\n else:\n cout.cout_wrap(self.nfreq * '\\t\\tsigma = %4f [rad/s]\\n' % self.frequency, 1)\n cout.cout_wrap('\\tKrylov order:')\n cout.cout_wrap('\\t\\tr = %d' % self.r, 1)\n\n def one_sided_arnoldi(self, frequency, r):\n r\"\"\"\n One-sided Arnoldi method expansion about a single interpolation point, :math:`\\sigma`.\n The projection matrix :math:`\\mathbf{V}` is constructed using an order :math:`r` Krylov space. The space for\n a single finite interpolation point known as a Pade approximation is described by:\n\n .. math::\n \\text{range}(\\textbf{V}) = \\mathcal{K}_r((\\sigma\\mathbf{I}_n - \\mathbf{A})^{-1},\n (\\sigma\\mathbf{I}_n - \\mathbf{A})^{-1}\\mathbf{b})\n\n In the case of an interpolation about infinity, the problem is known as partial realisation and the Krylov\n space is\n\n .. math::\n \\text{range}(\\textbf{V}) = \\mathcal{K}_r(\\mathbf{A}, \\mathbf{b})\n\n The resulting orthogonal projection leads to the following reduced order system:\n\n .. math::\n \\hat{\\Sigma} : \\left(\\begin{array}{c|c} \\hat{A} & \\hat{B} \\\\\n \\hline \\hat{C} & {D}\\end{array}\\right)\n \\text{with } \\begin{cases}\\hat{A}=V^TAV\\in\\mathbb{R}^{k\\times k},\\,\\\\\n \\hat{B}=V^TB\\in\\mathbb{R}^{k\\times m},\\,\\\\\n \\hat{C}=CV\\in\\mathbb{R}^{p\\times k},\\,\\\\\n \\hat{D}=D\\in\\mathbb{R}^{p\\times m}\\end{cases}\n\n\n Args:\n frequency (complex): Interpolation point :math:`\\sigma \\in \\mathbb{C}`\n r (int): Number of moments to match. Equivalent to Krylov space order and order of the ROM.\n\n Returns:\n tuple: The reduced order model matrices: :math:`\\mathbf{A}_r`, :math:`\\mathbf{B}_r` and :math:`\\mathbf{C}_r`\n\n \"\"\"\n A = self.ss.A\n B = self.ss.B\n C = self.ss.C\n\n nx = A.shape[0]\n\n if frequency != np.inf and frequency is not None:\n lu_A = krylovutils.lu_factor(frequency, A)\n V = krylovutils.construct_krylov(r, lu_A, B, 'Pade', 'b')\n else:\n V = krylovutils.construct_krylov(r, A, B, 'partial_realisation', 'b')\n\n # Reduced state space model\n Ar = V.T.dot(A.dot(V))\n Br = V.T.dot(B)\n Cr = C.dot(V)\n\n self.V = V\n self.W = V\n\n return Ar, Br, Cr\n\n def two_sided_arnoldi(self, frequency, r):\n r\"\"\"\n Two-sided projection with a single interpolation point following the Arnoldi procedure. Very similar to the\n one-sided method available, but it adds the projection :math:`\\mathbf{W}` built using the Krylov space for the\n :math:`\\mathbf{c}` vector:\n\n .. math::\n \\mathcal{K}_r((\\sigma\\mathbf{I}_n - \\mathbf{A})^{-T},\n (\\sigma\\mathbf{I}_n - \\mathbf{A})^{-T}\\mathbf{c}^T)\\subseteq\\mathcal{W}=\\text{range}(\\mathbf{W})\n\n The oblique projection :math:`\\mathbf{VW}^T` matches twice as many moments as the single sided projection.\n\n The resulting system takes the form:\n\n .. math::\n \\hat{\\Sigma} : \\left(\\begin{array}{c|c} \\hat{A} & \\hat{B} \\\\\n \\hline \\hat{C} & {D}\\end{array}\\right)\n \\text{with } \\begin{cases}\\hat{A}=W^TAV\\in\\mathbb{R}^{k\\times k},\\,\\\\\n \\hat{B}=W^TB\\in\\mathbb{R}^{k\\times m},\\,\\\\\n \\hat{C}=CV\\in\\mathbb{R}^{p\\times k},\\,\\\\\n \\hat{D}=D\\in\\mathbb{R}^{p\\times m}\\end{cases}\n\n Args:\n frequency (complex): Interpolation point :math:`\\sigma \\in \\mathbb{C}`\n r (int): Number of moments to match on each side. The resulting ROM will be of order :math:`2r`.\n\n Returns:\n tuple: The reduced order model matrices: :math:`\\mathbf{A}_r`, :math:`\\mathbf{B}_r` and :math:`\\mathbf{C}_r`.\n\n \"\"\"\n A = self.ss.A\n B = self.ss.B\n C = self.ss.C\n\n nx = A.shape[0]\n\n if frequency != np.inf and frequency is not None:\n lu_A = krylovutils.lu_factor(frequency, A)\n V = krylovutils.construct_krylov(r, lu_A, B, 'Pade', 'b')\n W = krylovutils.construct_krylov(r, lu_A, C.T, 'Pade', 'c')\n else:\n V = krylovutils.construct_krylov(r, A, B, 'partial_realisation', 'b')\n W = krylovutils.construct_krylov(r, A, C.T, 'partial_realisation', 'c')\n\n T = W.T.dot(V)\n Tinv = sclalg.inv(T)\n reduction_checks(T, Tinv)\n self.W = W\n self.V = V\n\n # Reduced state space model\n Ar = W.T.dot(self.ss.A.dot(V.dot(Tinv)))\n Br = W.T.dot(self.ss.B)\n Cr = self.ss.C.dot(V.dot(Tinv))\n\n return Ar, Br, Cr\n\n def real_rational_arnoldi(self, frequency, r):\n \"\"\"\n When employing complex frequencies, the projection matrix can be normalised to be real\n Following Algorithm 1b in Lee(2006)\n Args:\n frequency:\n r:\n\n Returns:\n\n \"\"\"\n\n raise NotImplementedError('Real valued rational Arnoldi Method Work in progress - use mimo_rational_arnoldi')\n\n ### Not working, having trouble with the last column of H. need to investigate the background behind the creation of H and see hwat can be done\n\n A = self.ss.A\n B = self.ss.B\n C = self.ss.C\n\n nx = A.shape[0]\n nfreq = frequency.shape[0]\n\n # Columns of matrix v\n v_ncols = 2 * np.sum(r)\n\n # Output projection matrices\n V = np.zeros((nx, v_ncols),\n dtype=float)\n H = np.zeros((v_ncols, v_ncols),\n dtype=float)\n res = np.zeros((nx,v_ncols+2),\n dtype=float)\n\n # lu_A = krylovutils.lu_factor(frequency[0] * np.eye(nx) - A)\n v_res = sclalg.lu_solve(lu_A, B)\n\n H[0, 0] = np.linalg.norm(v_res)\n V[:, 0] = v_res.real / H[0, 0]\n\n k = 0\n for i in range(nfreq):\n for j in range(r[i]):\n # k = 2*(i*r[i] + j)\n print(\"i = %g\\t j = %g\\t k = %g\" % (i, j, k))\n\n # res[:, k] = np.imag(v_res)\n # if k > 0:\n # res[:, k-1] = np.real(v_res)\n #\n # # Working on the last finished column i.e. k-1 only when k>0\n # if k > 0:\n # for t in range(k):\n # H[t, k-1] = V[:, t].T.dot(res[:, k-1])\n # res[:, k-1] -= res[:, k-1] - H[t, k-1] * V[:, t]\n #\n # H[k, k-1] = np.linalg.norm(res[:, k-1])\n # V[:, k] = res[:, k-1] / H[k, k-1]\n #\n # # Normalise working column k\n # for t in range(k+1):\n # H[t, k] = V[:, t].T.dot(res[:, k])\n # res[:, k] -= H[t, k] * V[:, t]\n #\n # # Subdiagonal term\n # H[k+1, k] = np.linalg.norm(res[:, k])\n # V[:, k + 1] = res[:, k] / np.linalg.norm(res[:, k])\n #\n # if j == r[i] - 1 and i < nfreq - 1:\n # lu_A = krylovutils.lu_factor(frequency[i+1] * np.eye(nx) - A)\n # v_res = sclalg.lu_solve(lu_A, B)\n # else:\n # v_res = - sclalg.lu_solve(lu_A, V[:, k+1])\n\n if k == 0:\n V[:, 0] = v_res.real / np.linalg.norm(v_res.real)\n else:\n res[:, k] = np.imag(v_res)\n res[:, k-1] = np.real(v_res)\n\n for t in range(k):\n H[t, k-1] = np.linalg.norm(res[:, k-1])\n res[:, k-1] -= H[t, k-1]*V[:, t]\n\n H[k, k-1] = np.linalg.norm(res[:, k-1])\n V[:, k] = res[:, k-1] / H[k, k-1]\n\n if k == 0:\n H[0, 0] = V[:, 0].T.dot(v_res.imag)\n res[:, 0] -= H[0, 0] * V[:, 0]\n\n else:\n for t in range(k+1):\n H[t, k] = V[:, t].T.dot(res[:, k])\n res[:, k] -= H[t, k] * V[:, t]\n H[k+1, k] = np.linalg.norm(res[:, k])\n V[:, k+1] = res[:, k] / H[k+1, k]\n\n if j == r[i] - 1 and i < nfreq - 1:\n lu_A = krylovutils.lu_factor(frequency[i+1], A)\n v_res = sclalg.lu_solve(lu_A, B)\n else:\n v_res = - sclalg.lu_solve(lu_A, V[:, k+1])\n\n k += 2\n\n # Add last column of H\n print(k)\n res[:, k-1] = - sclalg.lu_solve(lu_A, V[:, k-1])\n for t in range(k-1):\n H[t, k-1] = V[:, t].T.dot(res[:, k-1])\n res[:, k-1] -= H[t, k-1]*V[:, t]\n\n self.V = V\n self.H = H\n\n Ar = V.T.dot(A.dot(V))\n Br = V.T.dot(B)\n Cr = C.dot(V)\n\n return Ar, Br, Cr\n\n def dual_rational_arnoldi(self, frequency, r):\n r\"\"\"\n Dual Rational Arnoli Interpolation for SISO sytems [1] and MIMO systems through tangential interpolation [2].\n\n Effectively the same as the two_sided_arnoldi and the resulting V matrices for each interpolation point are\n concatenated\n\n .. math::\n \\bigcup\\limits_{k = 1}^K\\mathcal{K}_{b_k}((\\sigma_i\\mathbf{I}_n - \\mathbf{A})^{-1}, (\\sigma_i\\mathbf{I}_n\n - \\mathbf{A})^{-1}\\mathbf{b})\\subseteq\\mathcal{V}&=\\text{range}(\\mathbf{V}) \\\\\n \\bigcup\\limits_{k = 1}^K\\mathcal{K}_{c_k}((\\sigma_i\\mathbf{I}_n - \\mathbf{A})^{-T}, (\\sigma_i\\mathbf{I}_n\n - \\mathbf{A})^{-T}\\mathbf{c}^T)\\subseteq\\mathcal{Z}&=\\text{range}(\\mathbf{Z})\n\n For MIMO systems, tangential interpolation is used through the right and left tangential direction vectors\n :math:`\\mathbf{r}_i` and :math:`\\mathbf{l}_i`.\n\n .. math::\n \\bigcup\\limits_{k = 1}^K\\mathcal{K}_{b_k}((\\sigma_i\\mathbf{I}_n - \\mathbf{A})^{-1}, (\\sigma_i\\mathbf{I}_n\n - \\mathbf{A})^{-1}\\mathbf{Br}_i)\\subseteq\\mathcal{V}&=\\text{range}(\\mathbf{V}) \\\\\n \\bigcup\\limits_{k = 1}^K\\mathcal{K}_{c_k}((\\sigma_i\\mathbf{I}_n - \\mathbf{A})^{-T}, (\\sigma_i\\mathbf{I}_n\n - \\mathbf{A})^{-T}\\mathbf{C}^T\\mathbf{l}_i)\\subseteq\\mathcal{Z}&=\\text{range}(\\mathbf{Z})\n\n Args:\n frequency (np.ndarray): Array containing the interpolation points\n :math:`\\sigma = \\{\\sigma_1, \\dots, \\sigma_K\\}\\in\\mathbb{C}`\n r (int): Krylov space order :math:`b_k` and :math:`c_k`. At the moment, different orders for the\n controllability and observability constructions are not supported.\n right_tangent (np.ndarray): Matrix containing the right tangential direction interpolation vector for\n each interpolation point in column form, i.e. :math:`\\mathbf{r}\\in\\mathbb{R}^{m \\times K}`.\n left_tangent (np.ndarray): Matrix containing the left tangential direction interpolation vector for\n each interpolation point in column form, i.e. :math:`\\mathbf{l}\\in\\mathbb{R}^{p \\times K}`.\n\n Returns:\n tuple: The reduced order model matrices: :math:`\\mathbf{A}_r`, :math:`\\mathbf{B}_r` and :math:`\\mathbf{C}_r`.\n\n References:\n [1] Grimme\n [2] Gallivan\n \"\"\"\n A = self.ss.A\n B = self.ss.B\n C = self.ss.C\n\n nx = self.ss.states\n nu = self.ss.inputs\n ny = self.ss.outputs\n\n B.shape = (nx, nu)\n\n if nu != 1:\n left_tangent, right_tangent, rc, ro, fc, fo = self.load_tangent_vectors()\n assert right_tangent is not None and left_tangent is not None, 'Missing interpolation vectors for MIMO case'\n else:\n fc = np.array(frequency)\n fo = np.array(frequency)\n left_tangent = np.zeros((1, len(fo)))\n right_tangent = np.zeros((1, len(fc)))\n rc = np.array([r]*len(fc))\n ro = np.array([r]*len(fc))\n right_tangent[0, :] = 1\n left_tangent[0, :] = 1\n\n try:\n nfreq = frequency.shape[0]\n except AttributeError:\n nfreq = 1\n\n\n t0 = time.time()\n # # Tangential interpolation for MIMO systems\n # if right_tangent is None:\n # right_tangent = np.eye((nu, nfreq))\n # # else:\n # # assert right_tangent.shape == (nu, nfreq), 'Right Tangential Direction vector not the correct shape'\n #\n # if left_tangent is None:\n # left_tangent = np.eye((ny, nfreq))\n # # else:\n # # assert left_tangent.shape == (ny, nfreq), 'Left Tangential Direction vector not the correct shape'\n\n rom_dim = max(np.sum(rc), np.sum(ro))\n V = np.zeros((nx, rom_dim), dtype=complex)\n W = np.zeros((nx, rom_dim), dtype=complex)\n\n we = 0\n dict_of_luas = dict()\n for i in range(len(fc)):\n sigma = fc[i]\n if sigma == np.inf:\n approx_type = 'partial_realisation'\n lu_A = A\n else:\n approx_type = 'Pade'\n try:\n lu_A = dict_of_luas[sigma]\n except KeyError:\n lu_A = krylovutils.lu_factor(sigma, A)\n dict_of_luas[sigma] = lu_A\n V[:, we:we+rc[i]] = krylovutils.construct_krylov(rc[i], lu_A, B.dot(right_tangent[:, i:i+1]), approx_type, 'b')\n\n we += rc[i]\n\n we = 0\n for i in range(len(fo)):\n sigma = fo[i]\n if sigma == np.inf:\n approx_type = 'partial_realisation'\n lu_A = A\n else:\n approx_type = 'Pade'\n try:\n lu_A = dict_of_luas[sigma]\n except KeyError:\n lu_A = krylovutils.lu_factor(sigma, A)\n dict_of_luas[sigma] = lu_A\n W[:, we:we+ro[i]] = krylovutils.construct_krylov(ro[i], lu_A, C.T.dot(left_tangent[:, i:i+1]), approx_type, 'c')\n\n we += ro[i]\n\n T = W.T.dot(V)\n Tinv = sclalg.inv(T)\n reduction_checks(T, Tinv)\n self.W = W\n self.V = V\n\n # Reduced state space model\n Ar = W.T.dot(self.ss.A.dot(V.dot(Tinv)))\n Br = W.T.dot(self.ss.B)\n Cr = self.ss.C.dot(V.dot(Tinv))\n\n del dict_of_luas\n\n self.cpu_summary['algorithm'] = time.time() - t0\n\n return Ar, Br, Cr\n\n def mimo_rational_arnoldi(self, frequency, r):\n r\"\"\"\n Construct full rank orthonormal projection basis :math:`\\mathbf{V}` and :math:`\\mathbf{W}`.\n\n The main issue that one normally encounters with MIMO systems is that the minimality assumption of the system\n does not guarantee the resulting Krylov space to be full rank, unlike in the SISO case. Therefore,\n the construction is performed vector by vector, where linearly dependent vectors are eliminated or deflated\n from the Krylov subspace.\n\n If the number of inputs differs the number of outputs, both Krylov spaces will be built such that both\n are the same size, therefore one Krylov space may be of higher order than the other one.\n\n Following the method for vector-wise construction in Gugercin [1].\n\n Args:\n frequency (np.ndarray): Array containing interpolation frequencies\n r (int): Krylov space order\n\n Returns:\n tuple: Tuple of reduced system matrices ``A``, ``B`` and ``C``.\n\n References:\n [1] Gugercin, S. Projection Methods for Model Reduction of Large-Scale Dynamical\n Systems PhD Thesis. Rice University 2003.\n \"\"\"\n\n m = self.ss.inputs # Full system number of inputs\n n = self.ss.states # Full system number of states\n p = self.ss.outputs # Full system number of outputs\n\n # If the number of inputs is not the same as the number of outputs, a larger than necessary projection matrix\n # is built for the one with fewer inputs/outputs. Thence, the larger matrix is truncated to have the same number\n # of columns as the smaller matrix\n if m != p:\n if m < p:\n r_o = r\n r_c = r_o * int(np.ceil(p / m))\n else:\n r_c = r\n r_o = r_c * int(np.ceil(m / p))\n else:\n r_c = r\n r_o = r\n\n if self.settings['single_side']:\n # if only a single side is built, use the original setting without modification\n r_c = r\n r_o = r\n\n V = None\n W = None\n\n for i in range(self.nfreq):\n\n if self.settings['single_side'] == 'controllability' or self.settings['single_side'] == '':\n cout.cout_wrap('\\tConstructing controllability space', 1)\n if i == 0:\n V = krylovutils.build_krylov_space(frequency[i], r_c, side='b', a=self.ss.A, b=self.ss.B)\n else:\n Vi = krylovutils.build_krylov_space(frequency[i], r_c, side='b', a=self.ss.A, b=self.ss.B)\n V = np.hstack((V, Vi))\n V = krylovutils.mgs_ortho(V)\n\n if self.settings['single_side'] == 'observability' or self.settings['single_side'] == '':\n cout.cout_wrap('\\tConstructing observability space', 1)\n if i == 0:\n W = krylovutils.build_krylov_space(frequency[i], r_o, side='c', a=self.ss.A, b=self.ss.C.T)\n else:\n Wi = krylovutils.build_krylov_space(frequency[i], r_o, side='c', a=self.ss.A, b=self.ss.C.T)\n W = np.hstack((W, Wi))\n W = krylovutils.mgs_ortho(W)\n\n if self.settings['single_side'] == 'controllability' or self.settings['single_side'] == 'observability':\n if self.settings['single_side'] == 'observability':\n V = W\n if self.settings['single_side'] == 'controllability':\n W = V # needed to properly save gains\n Ar = V.T.dot(self.ss.A.dot(V))\n Br = V.T.dot(self.ss.B)\n Cr = self.ss.C.dot(V)\n\n else:\n # Match number of columns in each matrix\n min_cols = min(V.shape[1], W.shape[1])\n V = V[:, :min_cols]\n W = W[:, :min_cols]\n\n V, W = check_rank(V, W) # checks the product for rank deficiencies\n # V = krylovutils.mgs_ortho(V) # need to verify whether this is necessary\n # W = krylovutils.mgs_ortho(W)\n\n T = W.T.dot(V)\n Tinv = sclalg.inv(T)\n krylovutils.check_eye(T, Tinv)\n\n # Reduced state space model\n Ar = W.T.dot(self.ss.A.dot(V.dot(Tinv)))\n Br = W.T.dot(self.ss.B)\n Cr = self.ss.C.dot(V.dot(Tinv))\n\n self.W = libss.Gain(W,\n input_vars=LinearVector([InputVariable('krylov', size=W.shape[1], index=0)]),\n output_vars=LinearVector.transform(self.ss.state_variables, OutputVariable))\n self.V = libss.Gain(V,\n input_vars=LinearVector([InputVariable('krylov', size=V.shape[1], index=0)]),\n output_vars=LinearVector.transform(self.ss.state_variables, OutputVariable))\n\n # for state recovery purposes\n self.projection_gain = libss.Gain(V,\n input_vars=LinearVector([InputVariable('krylov', size=V.shape[1], index=0)]),\n output_vars=LinearVector.transform(self.ss.state_variables, OutputVariable))\n\n return Ar, Br, Cr\n\n def mimo_block_arnoldi(self, frequency, r):\n\n n = self.ss.states\n\n A = self.ss.A\n B = self.ss.B\n C = self.ss.C\n\n for i in range(self.nfreq):\n\n if self.frequency[i] == np.inf:\n F = A\n G = B\n else:\n lu_a = krylovutils.lu_factor(frequency[i], A)\n F = krylovutils.lu_solve(lu_a, np.eye(n))\n G = krylovutils.lu_solve(lu_a, B)\n\n if i == 0:\n V = krylovutils.block_arnoldi_krylov(r, F, G)\n else:\n Vi = krylovutils.block_arnoldi_krylov(r, F, G)\n V = np.block([V, Vi])\n\n self.V = V\n\n Ar = V.T.dot(A.dot(V))\n Br = V.T.dot(B)\n Cr = C.dot(V)\n\n return Ar, Br, Cr\n\n def check_stability(self, restart_arnoldi=False):\n r\"\"\"\n Checks the stability of the ROM by computing its eigenvalues.\n\n If the resulting system is unstable, the Arnoldi procedure can be restarted to eliminate the eigenvalues\n outside the stability boundary.\n\n However, if this is the case, the ROM no longer matches the moments of the original system at the specific\n frequencies since now the approximation is done with respect to a system of the form:\n\n .. math::\n \\Sigma = \\left(\\begin{array}{c|c} \\mathbf{A} & \\mathbf{\\bar{B}}\n \\\\ \\hline \\mathbf{C} & \\ \\end{array}\\right)\n\n where :math:`\\mathbf{\\bar{B}} = (\\mu \\mathbf{I}_n - \\mathbf{A})\\mathbf{B}`\n\n Args:\n restart_arnoldi (bool): Restart the relevant Arnoldi algorithm with the unstable eigenvalues removed.\n\n\n \"\"\"\n assert self.ssrom is not None, 'ROM not calculated yet'\n\n eigs = sclalg.eigvals(self.ssrom.A)\n\n eigs_abs = np.abs(eigs)\n\n order = np.argsort(eigs_abs)[::-1]\n eigs = eigs[order]\n eigs_abs = eigs_abs[order]\n\n unstable = False\n if self.sstype == 'dt':\n if any(eigs_abs > 1.):\n unstable = True\n unstable_eigenvalues = eigs[eigs_abs > 1.]\n try:\n cout.cout_wrap('Unstable ROM - %d Eigenvalues with |r| > 1' % len(unstable_eigenvalues))\n except ValueError:\n pass\n for mu in unstable_eigenvalues:\n try:\n cout.cout_wrap('\\tmu = %f + %fj' % (mu.real, mu.imag))\n except ValueError:\n pass\n else:\n try:\n cout.cout_wrap('ROM is stable')\n cout.cout_wrap('\\tDT Eigenvalues:')\n cout.cout_wrap(len(eigs_abs) * '\\t\\tmu = %4f + %4fj\\n' % tuple(eigs.view(float)))\n except ValueError:\n pass\n\n else:\n if any(eigs.real > 0):\n unstable = True\n cout.cout_wrap('Unstable ROM', 3)\n unstable_eigenvalues = eigs[eigs.real > 0]\n else:\n cout.cout_wrap('ROM is stable')\n\n # Restarted Arnoldi\n # Modify the B matrix in the full state system -> maybe better to have a copy\n if unstable and restart_arnoldi:\n print('Restarting the Arnoldi method - Reducing ROM order from r = %d to r = %d' % (self.r, self.r-1))\n self.ss_original = self.ss\n\n remove_unstable = np.eye(self.ss.states)\n for mu in unstable_eigenvalues:\n remove_unstable = np.matmul(remove_unstable, mu * np.eye(self.ss.states) - self.ss.A)\n\n self.ss.B = remove_unstable.dot(self.ss.B)\n # self.ss.C = self.ss.C.dot(remove_unstable.T)\n\n if self.r > 1:\n self.r -= 1\n self.run(self.algorithm, self.r, self.frequency)\n else:\n print('Unable to reduce ROM any further - ROM still unstable...')\n\n return not unstable\n\n def load_tangent_vectors(self):\n\n tangent_file = self.settings['tangent_input_file']\n if tangent_file:\n tangents = h5.readh5(tangent_file)\n right_tangent = tangents.right_tangent\n left_tangent = tangents.left_tangent\n rc = tangents.rc\n ro = tangents.ro\n fc = tangents.fc\n fo = tangents.fo\n else:\n left_tangent = None\n right_tangent = None\n\n return left_tangent, right_tangent, rc, ro, fc, fo\n\n def stable_realisation(self, *args, **kwargs):\n r\"\"\"Remove unstable poles left after reduction\n\n Using a Schur decomposition of the reduced plant matrix :math:`\\mathbf{A}_m\\in\\mathbb{C}^{m\\times m}`,\n the method removes the unstable eigenvalues that could have appeared after the moment-matching reduction.\n\n The oblique projection matrices :math:`\\mathbf{T}_L\\in\\mathbb{C}^{m \\times p}` and\n :math:`\\mathbf{T}_R\\in\\mathbb{C}^{m \\times p}`` result in a stable realisation\n\n .. math:: \\mathbf{A}_s = \\mathbf{T}_L^\\top\\mathbf{AT}_R \\in \\mathbb{C}^{p\\times p}.\n\n Args:\n A (np.ndarray): plant matrix (if not provided ``self.ssrom.A`` will be used).\n\n Returns:\n tuple: Left and right projection matrices :math:`\\mathbf{T}_L\\in\\mathbb{C}^{m \\times p}` and\n :math:`\\mathbf{T}_R\\in\\mathbb{C}^{m \\times p}`\n\n References:\n Jaimoukha, I. M., Kasenally, E. D.. Implicitly Restarted Krylov Subspace Methods for Stable Partial\n Realizations. SIAM Journal of Matrix Analysis and Applications, 1997.\n\n See Also:\n The method employs :func:`sharpy.rom.utils.krylovutils.schur_ordered()` and\n :func:`sharpy.rom.utils.krylovutils.remove_a12`.\n \"\"\"\n\n cout.cout_wrap('Stabilising system by removing unstable eigenvalues using a Schur decomposition', 1)\n if self.ssrom is None:\n A = args[0]\n ct = kwargs['ct']\n assert type(ct) == bool, 'CT system flag should be a bool'\n else:\n A = self.ssrom.A\n\n if self.sstype == 'ct':\n ct = True\n else:\n ct = False\n\n m = A.shape[0]\n As, T1, n_stable = krylovutils.schur_ordered(A, ct=ct)\n\n # Remove the (1,2) block of the Schur ordered matrix\n T2, X = krylovutils.remove_a12(As, n_stable)\n\n T3 = np.eye(m, n_stable)\n\n TL = T3.T.dot(T2.dot(np.conj(T1)))\n TR = T1.T.dot(np.linalg.inv(T2).dot(T3))\n\n cout.cout_wrap('System reduced to %g states' %n_stable, 1)\n\n # for debugging\n # import matplotlib.pyplot as plt\n Ar = TL.dot(A.dot(TR))\n eigsA = np.linalg.eigvals(A)\n eigsAr = np.linalg.eigvals(Ar)\n #\n # plt.scatter(eigsA.real, eigsA.imag)\n # plt.scatter(eigsAr.real, eigsAr.imag)\n # plt.show()\n if ct:\n assert np.sum(np.real(eigsAr) <= 0.) == n_stable, 'Number of stable eigvals computed not equal to those in Ar'\n else:\n assert np.sum(np.abs(eigsAr) <= 1.) == n_stable, 'Number of stable eigvals computed not equal to those in Ar'\n\n return TL.T, TR\n\n def restart(self):\n \"\"\"\n Implicitly Restarted Krylov Algorithm\n \"\"\"\n\n # Run krylov here\n\n W = self.W\n V = self.V\n\n check_eye(V, V.T)\n check_eye(W, W.T)\n\n Tm = W.T.dot(V)\n Tminv = sclalg.inv(Tm)\n\n check_eye(Tm, Tminv, 'Tm = W^T.dot(V)')\n\n # d = Tminv.dot(W.T)\n #\n # Tmcond = np.linalg.cond(Tm)\n #\n # if Tmcond > 1e10:\n # cout.cout_wrap('Matrix Tm = W^T.dot(V) is poorly conditioned. Condition = %e' % Tmcond, 3)\n\n TL, TR = self.stable_realisation()\n\n m, r = TR.shape\n\n Ar = TL.T.dot(self.ssrom.A.dot(TR))\n eigsAr = np.linalg.eigvals(Ar)\n n_stable_r = np.sum(np.abs(eigsAr)<=1.)\n\n assert n_stable_r == r, 'lost evals'\n\n # QR decomposition\n QRfull, RRfull = sclalg.qr(TR)\n QLfull, RLfull = sclalg.qr(sclalg.inv(Tm.T).dot(TL))\n\n QR = QRfull[:, :r]\n QRcomp = QRfull[:, r:]\n RR = RRfull[:r, :]\n RRcomp = RRfull[r:, :]\n\n QL = QLfull[:, :r]\n RL = RLfull[:r, :]\n\n Vr = V.dot(QR)\n Wr = W.dot(QL)\n Tr = Wr.T.dot(Vr)\n\n print('Tr cond = %e' % np.linalg.cond(Tr))\n\n Trinv = sclalg.inv(QL.T.dot(Tm.dot(QR)))\n Trinv2 = RR.dot(RL.T)\n #\n print('Trinv diff = %f' % (np.max(np.abs(Trinv - Trinv2))))\n Wtr = Trinv.dot(Wr.T)\n # Wtr = Wr.T\n # return QL.dot(Trinv), QR\n Wtr2 = TL.T.dot(Tminv.dot(W.T))\n # return Wtr2, V.dot(TR)\n\n Ar = RR.dot(TL.T).dot(self.ssrom.A.dot(QR))\n eigsAr = np.linalg.eigvals(Ar)\n n_stable_r = np.sum(np.abs(eigsAr)<=1.)\n\n assert n_stable_r == r, 'lost evals'\n\n\n\n return RR.dot(TL.T), QR\n # pass\n\n\ndef reduction_checks(T, Tinv):\n\n cout.cout_wrap('Tm condition = %e' % np.linalg.cond(T))\n\n check_eye(T, Tinv)\n\n\ndef check_eye(T, Tinv, msg=''):\n\n eye_approx = Tinv.dot(T)\n max_diff = np.max(np.abs(np.eye(eye_approx.shape[0]) - eye_approx))\n\n if max_diff != 0.0:\n log_error = np.log10(max_diff)\n assert log_error < -6, 'T.dot(Tinv) not equal to identity, %s \\nlog(error) = %.e' \\\n % (msg, np.log10(max_diff))\n\n\ndef check_rank(V, W):\n\n n_cols = V.shape[1]\n\n for col in range(1, n_cols):\n T = W[:, :col].T.dot(V[:, :col])\n Tinv = np.linalg.inv(T)\n try:\n check_eye(T, Tinv)\n except AssertionError:\n cout.cout_wrap('\\tDeflating column %g' % col, 1)\n W = np.hstack((W[:, :col-1], W[:, col:]))\n V = np.hstack((V[:, :col-1], V[:, col:]))\n\n try:\n check_eye(T, Tinv)\n except AssertionError:\n V, W = check_rank(V, W)\n\n # need to check if necessary\n # V = krylovutils.mgs_ortho(V)\n # W = krylovutils.mgs_ortho(W)\n # V, W = check_rank(V, W)\n # breakpoint()\n\n return V, W\n\nif __name__==\"__main__\":\n import numpy as np\n\n A = np.random.rand(20, 20)\n eigsA = np.sort(np.abs(np.linalg.eigvals(A)))\n print(eigsA)\n print(\"Number of stable eigvals = %g\" %np.sum(np.abs(eigsA)<=1) )\n rom = Krylov()\n TL, TR = rom.stable_realisation(A)\n\n Ap = TL.T.dot(A.dot(TR))\n\n eigsA = np.sort(np.abs(np.linalg.eigvals(Ap)))\n print(\"\\nNew matrix size %g\" % Ap.shape[0])\n print('Stable eigvals = %g' % np.sum(np.abs(eigsA)<=1))\n print(eigsA)\n" }, { "path": "sharpy/rom/utils/__init__.py", "content": "" }, { "path": "sharpy/rom/utils/krylovutils.py", "content": "\"\"\"Krylov Model Reduction Methods Utilities\"\"\"\nimport scipy.sparse as scsp\nimport numpy as np\nimport scipy.linalg as sclalg\nimport sharpy.linear.src.libsparse as libsp\nimport sharpy.utils.cout_utils as cout\n\n\ndef block_arnoldi_krylov(r, F, G, approx_type='Pade', side='controllability'):\n\n n = G.shape[0]\n m = G.shape[1]\n\n Q0, R0, P0 = sclalg.qr(G, pivoting=True)\n Q0 = Q0[:, :m]\n\n Q = np.zeros((n,m*r), dtype=complex)\n V = np.zeros((n,m*r), dtype=complex)\n\n for k in range(r):\n\n if k == 0:\n Q[:, 0:m] = F.dot(Q0)\n else:\n Q[:, k*m: k*m + m] = F.dot(Q[:, (k-1)*m:(k-1)*m + m])\n\n Q[:, :k*m + m] = mgs_ortho(Q[:, :k*m+m])\n\n Qf, R, P = sclalg.qr(Q[:, k*m: k*m + m], pivoting=True)\n Q[:, k*m: k*m + m ] = Qf[:, :m]\n if R[0,0] >= 1e-6:\n V[:, k*m:k*m + m] = Q[:, k*m: k*m + m ]\n else:\n print('Deflating')\n k -= 1\n\n V = mgs_ortho(V)\n\n return V\n\n\ndef mgs_ortho(X):\n r\"\"\"\n Modified Gram-Schmidt Orthogonalisation\n\n Orthogonalises input matrix :math:`\\mathbf{X}` column by column.\n\n Args:\n X (np.ndarray): Input matrix of dimensions :math:`n` by :math:`m`.\n\n Returns:\n np.ndarray: Orthogonalised matrix of dimensions :math:`n` by :math:`m`.\n\n Notes:\n This method is faster than scipy's :func:`scipy.linalg.qr` method that returns an orthogonal matrix as part of\n the QR decomposition, albeit at a higher number of function calls.\n \"\"\"\n\n # Q, R = sclalg.qr(X)\n n = X.shape[1]\n m = X.shape[0]\n\n Q = np.zeros((m, n), dtype=complex)\n\n for i in range(n):\n w = X[:, i]\n for j in range(i):\n h = Q[:, j].T.dot(w)\n w = w - h * Q[:, j]\n Q[:, i] = w / sclalg.norm(w)\n\n return Q\n\n\ndef construct_krylov(r, lu_A, B, approx_type='Pade', side='b'):\n r\"\"\"\n Contructs a Krylov subspace in an iterative manner following the methods of Gugercin [1].\n\n The construction of the Krylov space is focused on Pade and partial realisation cases for the purposes of model\n reduction. I.e. the partial realisation form of the Krylov space is used if\n ``approx_type = 'partial_realisation'``\n\n .. math::\n \\text{range}(\\textbf{V}) = \\mathcal{K}_r(\\mathbf{A}, \\mathbf{b})\n\n Else, it is replaced by the Pade approximation form:\n\n .. math::\n \\text{range}(\\textbf{V}) = \\mathcal{K}_r((\\sigma\\mathbf{I}_n - \\mathbf{A})^{-1},\n (\\sigma\\mathbf{I}_n - \\mathbf{A})^{-1}\\mathbf{b})\n\n Note that no inverses are actually computed but rather a single LU decomposition is performed at the beginning\n of the algorithm. Forward and backward substitution is used thereinafter to calculate the required vectors.\n\n The algorithm also builds the Krylov space for the :math:`\\mathbf{C}^T` matrix. It should simply replace ``B``\n and ``side`` should be ``side = 'c'``.\n\n Examples:\n Partial Realisation:\n\n >>> V = construct_krylov(r, A, B, 'partial_realisation', 'b')\n >>> W = construct_krylov(r, A, C.T, 'partial_realisation', 'c')\n\n Pade Approximation:\n\n >>> V = construct_krylov(r, (sigma * np.eye(nx) - A), B, 'Pade', 'b')\n >>> W = construct_krylov(r, (sigma * np.eye(nx) - A), C.T, 'Pade', 'c')\n\n\n References:\n [1]. Gugercin, S. - Projection Methods for Model Reduction of Large-Scale Dynamical Systems. PhD Thesis.\n Rice University. 2003.\n\n Args:\n r (int): Krylov space order\n lu_A (np.ndarray): For Pade approximations it should be the LU decomposition of :math:`(\\sigma I - \\mathbf{A})`\n in tuple form, as output from the :func:`scipy.linalg.lu_factor`. For partial realisations it is\n simply :math:`\\mathbf{A}`.\n B (np.ndarray): If doing the B side it should be :math:`\\mathbf{B}`, else :math:`\\mathbf{C}^T`.\n approx_type (str): Type of approximation: ``partial_realisation`` or ``Pade``.\n side: Side of the projection ``b`` or ``c``.\n\n Returns:\n np.ndarray: Projection matrix\n\n \"\"\"\n\n nx = B.shape[0]\n\n # Side indicates projection side. if using C then it needs to be transposed\n if side == 'c':\n transpose_mode = 1\n B.shape = (nx, 1)\n else:\n transpose_mode = 0\n B.shape = (nx, 1)\n\n # Output projection matrices\n V = np.zeros((nx, r),\n dtype=complex)\n H = np.zeros((r, r),\n dtype=complex)\n\n # Declare iterative variables\n f = np.zeros((nx, r),\n dtype=complex)\n\n if approx_type == 'partial_realisation':\n A = lu_A\n v_arb = B\n v = v_arb / np.linalg.norm(v_arb)\n w = A.dot(v)\n else:\n # LU decomposition\n v = lu_solve(lu_A, B, trans=transpose_mode)\n v = v / np.linalg.norm(v)\n w = lu_solve(lu_A, v)\n\n alpha = v.T.dot(w)\n\n # Initial assembly\n f[:, :1] = w - v.dot(alpha)\n V[:, :1] = v\n H[0, 0] = alpha\n\n for j in range(0, r-1):\n\n beta = np.linalg.norm(f[:, j])\n v = 1 / beta * f[:, j]\n\n V[:, j+1] = v\n H_hat = np.block([[H[:j+1, :j+1]],\n [beta * evec(j)]])\n\n if approx_type == 'partial_realisation':\n w = A.dot(v)\n else:\n w = lu_solve(lu_A, v, trans=transpose_mode)\n\n h = V[:, :j+2].T.dot(w)\n f[:, j+1] = w - V[:, :j+2].dot(h)\n\n # Finite precision\n s = V[:, :j+2].T.dot(f[:, j+1])\n f[:, j+1] = f[:, j+1] - V[:, :j+2].dot(s)\n h += s\n\n h.shape = (j+2, 1) # Enforce shape for concatenation\n H[:j+2, :j+2] = np.block([H_hat, h])\n\n return V\n\n\ndef lu_factor(sigma, A):\n r\"\"\"\n LU Factorisation wrapper of:\n\n .. math:: LU = (\\sigma \\mathbf{I} - \\mathbf{A})\n\n In the case of ``A`` being a sparse matrix, the sparse methods in scipy are employed\n\n Args:\n sigma (float): Expansion frequency\n A (csc_matrix or np.ndarray): Dynamics matrix\n\n Returns:\n tuple or SuperLU: tuple (dense) or SuperLU (sparse) objects containing the LU factorisation\n \"\"\"\n n = A.shape[0]\n if type(A) == libsp.csc_matrix:\n return scsp.linalg.splu(sigma * scsp.identity(n, dtype=complex, format='csc') - A)\n else:\n return sclalg.lu_factor(sigma * np.eye(n) - A)\n\n\ndef lu_solve(lu_A, b, trans=0):\n r\"\"\"\n LU solve wrapper.\n\n Computes the solution to\n\n .. math:: \\mathbf{Ax} = \\mathbf{b}\n\n or\n\n .. math:: \\mathbf{A}^T\\mathbf{x} = \\mathbf{b}\n\n if ``trans=1``.\n\n It uses the ``SuperLU.solve()`` method if the input is a ``SuperLU`` or else will revert to the dense methods\n in scipy.\n\n Args:\n lu_A (SuperLU or tuple): object or tuple containing the information of the LU factorisation\n b (np.ndarray): Right hand side vector to solve\n trans (int): ``0`` or ``1`` for either solution option.\n\n Returns:\n np.ndarray: Solution to the system.\n\n \"\"\"\n transpose_mode_dict = {0: 'N', 1: 'T'}\n if type(lu_A) == scsp.linalg.SuperLU:\n return lu_A.solve(b, trans=transpose_mode_dict[trans])\n else:\n return sclalg.lu_solve(lu_A, b, trans=trans)\n\n\ndef construct_mimo_krylov(r, lu_A_input, B, approx_type='Pade', side='controllability'):\n\n if side == 'controllability' or side == 'b':\n transpose_mode = 0\n elif side == 'observability' or side == 'c':\n transpose_mode = 1\n else:\n raise NameError('Unknown option for side: %s', side)\n\n m = B.shape[1] # Full system number of inputs/outputs\n n = B.shape[0] # Full system number of states\n\n deflation_tolerance = 1e-4 # Inexact deflation tolerance to approximate norm(V)=0 in machine precision\n\n # Preallocated size may be too large in case columns are deflated\n last_column = 0\n\n # Pre-allocate w, V\n V = np.zeros((n, m * r), dtype=complex)\n w = np.zeros((n, m * r), dtype=complex) # Initialise w, may be smaller than this due to deflation\n # V = np.zeros((n, m * r))\n # w = np.zeros((n, m * r)) # Initialise w, may be smaller than this due to deflation\n\n if approx_type == 'partial_realisation':\n G = B\n F = lu_A_input\n else:\n G = lu_solve(lu_A_input, B, transpose_mode)\n\n for k in range(m):\n w[:, k] = G[:, k]\n\n ## Orthogonalise w_k to preceding w_j for j < k\n if k >= 1:\n w[:, :k+1] = mgs_ortho(w[:, :k+1])[:, :k+1]\n # from sharpy.rom.krylov import check_eye\n # try:\n # check_eye(w[:, :k+1], w[:, :k+1].T)\n # except AssertionError:\n # print('failing here - k = %g' % k)\n\n\n V[:, :m+1] = w[:, :m+1]\n last_column += m\n\n mu = m # Initialise controllability index\n mu_c = m # Guess at controllability index with no deflation\n t = m # worked column index\n\n # from sharpy.rom.krylov import check_eye\n # try:\n # check_eye(V[:, :m+1], V[:, :m+1].T)\n # except AssertionError:\n # print('failing here')\n\n for k in range(1, r):\n for j in range(mu_c):\n if approx_type == 'partial_realisation':\n w[:, t] = F.dot(w[:, t-mu])\n else:\n w[:, t] = lu_solve(lu_A_input, w[:, t-mu], transpose_mode)\n\n # Orthogonalise w[:,t] against V_i -\n w[:, :t+1] = mgs_ortho(w[:, :t+1])[:, :t+1]\n\n # if np.linalg.norm(w[:, t]) < deflation_tolerance:\n # # Deflate w_k\n # cout.cout_wrap('\\tVector deflated', 3)\n # w = [w[:, 0:t], w[:, t+1:]]\n # last_column -= 1\n # mu -= 1\n # else:\n # pass\n # # V[:, t] = w[:, t]\n # # last_column += 1\n # # t += 1\n try:\n check_eye(w[:, :t+1], w[:, :t+1].T)\n V[:, t] = w[:, t]\n last_column += 1\n t += 1\n except AssertionError:\n cout.cout_wrap('\\tMatrix lost orthogonality creating Krylov subspace:'\n ' \\n\\t\\tKrylov order = %g\\n\\t\\tInput vector = %g'\n % (k, j), 2)\n w = np.hstack((w[:, 0:t], w[:, t+1:]))\n cout.cout_wrap('\\t\\tVector deflated', 2)\n last_column -= 1\n mu -= 1\n mu_c = mu\n\n try:\n check_eye(V[:, :t], V[:, :t].T)\n except AssertionError:\n raise ValueError('Krylov space construction failed to create an orthogonal space')\n\n return V[:, :t]\n\n\ndef build_krylov_space(frequency, r, side, a, b):\n\n if frequency == np.inf or frequency.real == np.inf:\n approx_type = 'partial_realisation'\n lu_a = a\n else:\n approx_type = 'Pade'\n lu_a = lu_factor(frequency, a)\n\n try:\n nu = b.shape[1]\n except IndexError:\n nu = 1\n\n if nu == 1:\n krylov_function = construct_krylov\n else:\n krylov_function = construct_mimo_krylov\n\n v = krylov_function(r, lu_a, b, approx_type, side)\n\n return v\n\n\ndef evec(j):\n \"\"\"j-th unit vector (in row format)\n\n Args:\n j: Unit vector dimension\n\n Returns:\n np.ndarray: j-th unit vector\n\n Examples:\n >>> evec(2)\n np.array([0, 1])\n >>> evec(3)\n np.array([0, 0, 1])\n\n \"\"\"\n e = np.zeros(j+1)\n e[j] = 1\n return e\n\n\ndef schur_ordered(A, ct=False):\n r\"\"\"Returns block ordered complex Schur form of matrix :math:`\\mathbf{A}`\n\n .. math:: \\mathbf{TAT}^H = \\mathbf{A}_s = \\begin{bmatrix} A_{11} & A_{12} \\\\ 0 & A_{22} \\end{bmatrix}\n\n where :math:`A_{11}\\in\\mathbb{C}^{s\\times s}` contains the :math:`s` stable\n eigenvalues of :math:`\\mathbf{A}\\in\\mathbb{R}^{m\\times m}`.\n\n Args:\n A (np.ndarray): Matrix to decompose.\n ct (bool): Continuous time system.\n\n Returns:\n tuple: Tuple containing the Schur decomposition of :math:`\\mathbf{A}`, :math:`\\mathbf{A}_s`; the transformation\n :math:`\\mathbf{T}\\in\\mathbb{C}^{m\\times m}`; and the number of stable eigenvalues of :math:`\\mathbf{A}`.\n\n Notes:\n This function is a wrapper of ``scipy.linalg.schur`` imposing the settings required for this application.\n\n \"\"\"\n if ct:\n sort_eigvals = 'lhp'\n else:\n sort_eigvals = 'iuc'\n\n # if A.dtype == complex:\n # output_form = 'complex'\n # else:\n # output_form = 'real'\n # issues when not using the complex form of the Schur decomposition\n\n output_form = 'complex'\n As, Tt, n_stable1 = sclalg.schur(A, output=output_form, sort=sort_eigvals)\n\n if sort_eigvals == 'lhp':\n n_stable = np.sum(np.linalg.eigvals(A).real <= 0)\n elif sort_eigvals == 'iuc':\n n_stable = np.sum(np.abs(np.linalg.eigvals(A)) <= 1.)\n else:\n raise NameError('Unknown sorting of eigenvalues. Either iuc or lhp')\n\n assert n_stable == n_stable1, 'Number of stable eigenvalues not equal in Schur output and manual calculation'\n\n assert (np.abs(As-np.conj(Tt.T).dot(A.dot(Tt))) < 1e-4).all(), 'Schur breakdown - A_schur != T^H A T'\n return As, Tt.T, n_stable\n\n\ndef remove_a12(As, n_stable):\n r\"\"\"Basis change to remove the (1, 2) block of the block-ordered real Schur matrix :math:`\\mathbf{A}`\n\n Being :math:`\\mathbf{A}_s\\in\\mathbb{R}^{m\\times m}` a matrix of the form\n\n .. math:: \\mathbf{A}_s = \\begin{bmatrix} A_{11} & A_{12} \\\\ 0 & A_{22} \\end{bmatrix}\n\n the (1,2) block is removed by solving the Sylvester equation\n\n .. math:: \\mathbf{A}_{11}\\mathbf{X} - \\mathbf{X}\\mathbf{A}_{22} + \\mathbf{A}_{12} = 0\n\n used to build the change of basis\n\n .. math:: \\mathbf{T} = \\begin{bmatrix} \\mathbf{I}_{s,s} & -\\mathbf{X}_{s,u} \\\\ \\mathbf{0}_{u, s}\n & \\mathbf{I}_{u,u} \\end{bmatrix}\n\n where :math:`s` and :math:`u` are the respective number of stable and unstable eigenvalues, such that\n\n .. math:: \\mathbf{TA}_s\\mathbf{T}^\\top = \\begin{bmatrix} A_{11} & \\mathbf{0} \\\\ 0 & A_{22} \\end{bmatrix}.\n\n Args:\n As (np.ndarray): Block-ordered real Schur matrix (can be built using\n :func:`sharpy.rom.utils.krylovutils.schur_ordered`).\n n_stable (int): Number of stable eigenvalues in ``As``.\n\n Returns:\n np.ndarray: Basis transformation :math:`\\mathbf{T}\\in\\mathbb{R}^{m\\times m}`.\n\n References:\n Jaimoukha, I. M., Kasenally, E. D.. Implicitly Restarted Krylov Subspace Methods for Stable Partial Realizations\n SIAM Journal of Matrix Analysis and Applications, 1997.\n \"\"\"\n A11 = As[:n_stable, :n_stable]\n A12 = As[:n_stable, n_stable:]\n A22 = As[n_stable:, n_stable:]\n n = As.shape[0]\n\n X = sclalg.solve_sylvester(A11, -A22, -A12)\n\n T = np.block([[np.eye(n_stable), -X], [np.zeros((n-n_stable, n_stable)), np.eye(n-n_stable)]])\n\n T2 = np.eye(n, n_stable)\n # App = T2.T.dot(T.dot(As.dot(np.linalg.inv(T).dot(T2))))\n return T, X\n\n\ndef check_eye(T, Tinv, msg='', eps=-6):\n r\"\"\"Simple utility to verify matrix inverses\n\n Asserts that\n\n .. math:: \\mathbf{T}^{-1}\\mathbf{T} = \\mathbf{I}\n\n Args:\n T (np.ndarray): Matrix to test\n Tinv (np.ndarray): Supposed matrix inverse\n msg (str): Output error message if inverse check not satisfied\n eps (float): Error threshold (:math:`10^\\varepsilon`)\n\n Raises:\n AssertionError: if matrix inverse check is not satisfied\n\n \"\"\"\n eye_approx = Tinv.dot(T)\n max_diff = np.max(np.abs(np.eye(eye_approx.shape[0]) - eye_approx))\n\n try:\n log_error = np.log10(max_diff)\n assert log_error < eps, 'Tinv.dot(T) not equal to identity, %s \\nlog(error) = %.e' \\\n % (msg, log_error)\n except RuntimeWarning:\n # unlikely event that both matrices are identical and max_diff == 0\n pass\n" }, { "path": "sharpy/rom/utils/librom.py", "content": "\"\"\"General ROM utilities\n\nS. Maraniello, 14 Feb 2018\n\"\"\"\n\nimport warnings\nimport numpy as np\nimport scipy.linalg as scalg\n\nimport sharpy.linear.src.libsparse as libsp\nimport sharpy.linear.src.libss as libss\n\n\ndef balreal_direct_py(A, B, C, DLTI=True, Schur=False, full_outputs=False):\n r\"\"\"\n Find balanced realisation of continuous (``DLTI = False``) and discrete (``DLTI = True``)\n time of LTI systems using scipy libraries.\n\n The function proceeds to achieve balanced realisation of the state-space system by first solving\n the Lyapunov equations. They are solved using Barlets-Stewart algorithm for\n Sylvester equation, which is based on A matrix Schur decomposition.\n\n .. math::\n \\mathbf{A\\,W_c + W_c\\,A^T + B\\,B^T} &= 0 \\\\\n \\mathbf{A^T\\,W_o + W_o\\,A + C^T\\,C} &= 0\n\n to obtain the reachability and observability gramians, which are positive definite matrices.\n\n Then, the gramians are decomposed into their Cholesky factors such that:\n\n .. math::\n \\mathbf{W_c} &= \\mathbf{Q_c\\,Q_c^T} \\\\\n \\mathbf{W_o} &= \\mathbf{Q_o\\,Q_o^T}\n\n A singular value decomposition (SVD) of the product of the Cholesky factors is performed\n\n .. math:: (\\mathbf{Q_o^T\\,Q_c}) = \\mathbf{U\\,\\Sigma\\,V^*}\n\n The singular values are then used to build the transformation matrix :math:`\\mathbf{T}`\n\n .. math::\n \\mathbf{T} &= \\mathbf{Q_c\\,V\\,\\Sigma}^{-1/2} \\\\\n \\mathbf{T}^{-1} &= \\mathbf{\\Sigma}^{-1/2}\\,\\mathbf{U^T\\,Q_o^T}\n\n The balanced system is therefore of the form:\n\n .. math::\n \\mathbf{A_b} &= \\mathbf{T^{-1}\\,A\\,T} \\\\\n \\mathbf{B_b} &= \\mathbf{T^{-1}\\,B} \\\\\n \\mathbf{C_b} &= \\mathbf{C\\,T} \\\\\n \\mathbf{D_b} &= \\mathbf{D}\n\n Warnings:\n This function may be less computationally efficient than the ``balreal``\n Matlab implementation and does not offer the option to bound the realisation\n in frequency and time.\n\n Notes:\n - Lyapunov equations are solved using Barlets-Stewart algorithm for\n Sylvester equation, which is based on A matrix Schur decomposition.\n\n - Notation above is consistent with Gawronski [2].\n\n Args:\n A (np.ndarray): Plant Matrix\n B (np.ndarray): Input Matrix\n C (np.ndarray): Output Matrix\n DLTI (bool): Discrete time state-space flag\n Schur (bool): Use Schur decomposition to solve the Lyapunov equations\n\n Returns:\n tuple of np.ndarrays: Tuple of the form ``(S, T, Tinv)`` containing:\n - Singular values in diagonal matrix (``S``)\n - Transformation matrix (``T``).\n - Inverse transformation matrix(``Tinv``).\n\n References:\n [1] Anthoulas, A.C.. Approximation of Large Scale Dynamical Systems. Chapter 7. Advances in Design and Control.\n SIAM. 2005.\n\n [2] Gawronski, W.. Dynamics and control of structures. New York: Springer. 1998\n \"\"\"\n\n ### select solver for Lyapunov equation\n # Notation reminder:\n # scipy: A X A.T - X = -Q\n # contr: A W A.T - W = - B B.T\n # obser: A.T W A - W = - C.T C\n if DLTI:\n sollyap = scalg.solve_discrete_lyapunov\n else:\n sollyap = scalg.solve_lyapunov\n\n # A is a sparse matrix in csr_matrix(sparse) format, can not be directly passed into functions used in scipy _solver.py\n # Sparse matrices do not work well with Scipy (Version 1.7.3) in the following code, so A is transformed into a dense matrix here first.\n if type(A) is not np.ndarray:\n try:\n A = A.todense()\n except AttributeError:\n raise TypeError(f'Matrix needs to be in dense form. Unable to convert A matrix of type {type(A)} to '\n f'dense using method .todense()')\n\n # solve Lyapunov\n if Schur:\n # decompose A\n Atri, U = scalg.schur(A)\n\n # solve Lyapunov\n BBtri = np.dot(U.T, np.dot(B, np.dot(B.T, U)))\n CCtri = np.dot(U.T, np.dot(C.T, np.dot(C, U)))\n Wctri = sollyap(Atri, BBtri)\n Wotri = sollyap(Atri.T, CCtri)\n # reconstruct Wo,Wc\n Wc = np.dot(U, np.dot(Wctri, U.T))\n Wo = np.dot(U, np.dot(Wotri, U.T))\n else:\n Wc = sollyap(A, np.dot(B, B.T))\n Wo = sollyap(A.T, np.dot(C.T, C))\n\n # Choleski factorisation: W=Q Q.T\n # Qc = scalg.cholesky(Wc).T\n # Qo = scalg.cholesky(Wo).T\n\n # build M matrix and SVD\n # M = np.dot(Qo.T, Qc)\n # U, s, Vh = scalg.svd(M)\n # S = np.diag(s)\n # Sinv = np.diag(1. / s)\n # V = Vh.T\n\n # Build transformation matrices\n # T = np.dot(Qc, np.dot(V, np.sqrt(Sinv)))\n # Tinv = np.dot(np.sqrt(Sinv), np.dot(U.T, Qo.T))\n\n # return S, T, Tinv\n\n ### Find transformation matrices\n # avoid Cholevski - unstable\n\n # Building T and Tinv using SVD:\n Uc, Sc, Vc = scalg.svd(Wc)\n Uo, So, Vo = scalg.svd(Wo)\n\n # Perform decomposition:\n Sc = np.sqrt(np.diag(Sc))\n So = np.sqrt(np.diag(So))\n Qc = Uc @ Sc\n Qot = So @ Vo\n\n # Build Hankel matrix:\n H = Qot @ Qc\n\n # Find SVD of Hankel matrix:\n U, hsv, Vt = scalg.svd(H)\n # hsv = np.diag(hsv)\n\n # Find T and Tinv:\n S = np.sqrt(np.diag(hsv))\n\n # Please note, the notation below is swapped as compared to regular notation in the literature.\n # This is a known feature of SHARPy, hence it is maintained throughout (including documentation).\n Tinv = scalg.inv(S) @ U.T @ Qot\n T = Qc @ Vt.T @ scalg.inv(S)\n\n if full_outputs is False:\n return hsv, T, Tinv\n\n else:\n # get square-root factors\n # UT, QoT = scalg.qr(np.dot(np.diag(np.sqrt(hsv)), Tinv), pivoting=False)\n # Vh, QcT = scalg.qr(np.dot(T, np.diag(np.sqrt(hsv))).T, pivoting=False)\n\n # return hsv, UT.T, Vh, QcT.T, QoT.T\n return hsv, U, Vt, Qc, Qot.T\n\n\ndef balreal_iter(A, B, C, lowrank=True, tolSmith=1e-10, tolSVD=1e-6, kmin=None,\n tolAbs=False, Print=False, outFacts=False):\n \"\"\"\n Find balanced realisation of DLTI system.\n\n Notes:\n\n Lyapunov equations are solved using iterative squared Smith\n algorithm, in its low or full rank version. These implementations are\n as per the low_rank_smith and smith_iter functions respectively but,\n for computational efficiency, the iterations are rewritten here so as to\n solve for the observability and controllability Gramians contemporary.\n\n\n - Exploiting sparsity:\n\n This algorithm is not ideal to exploit sparsity. However, the following\n strategies are implemented:\n\n - if the A matrix is provided in sparse format, the powers of A will be\n calculated exploiting sparsity UNTIL the number of non-zero elements\n is below 15% the size of A. Upon this threshold, the cost of the matrix\n multiplication rises dramatically, and A is hence converted to a dense\n numpy array.\n \"\"\"\n\n ### Solve Lyapunov equations\n # Notation reminder:\n # scipy: A X A.T - X = -Q\n # contr: A W A.T - W = - B B.T\n # obser: A.T W A - W = - C.T C\n # low-rank smith: A.T X A - X = -Q Q.T\n\n # matrices size\n N = A.shape[0]\n rC = B.shape[1]\n rO = C.shape[0]\n\n if lowrank: # low-rank square-Smith iteration (with SVD)\n\n # initialise smith iteration\n DeltaNorm = 1e6 # error\n DeltaNormNext = DeltaNorm ** 2 # error expected at next iter\n\n kk = 0\n Qck = B\n Qok = C.T\n\n if Print:\n print('Iter\\tMaxZ\\t|\\trank_c\\trank_o\\tA size')\n while DeltaNorm > tolSmith and DeltaNormNext > 1e-3 * tolSmith:\n\n ###### controllability\n ### compute Ak^2 * Qck\n # (future: use block Arnoldi)\n Qcright = libsp.dot(A, Qck)\n MaxZhere = np.max(np.abs(Qcright))\n\n ### enlarge Z matrices\n Qck = np.concatenate((Qck, Qcright), axis=1)\n Qcright = None\n rC = Qck.shape[1]\n\n if kmin == None or kmin < rC:\n ### \"cheap\" SVD truncation\n Uc, svc = scalg.svd(Qck, full_matrices=False, overwrite_a=True,\n lapack_driver='gesdd')[:2]\n # import scipy.linalg.interpolative as sli\n # Ucnew,svcnew,temp=sli.svd(Qck,tolSVD)\n if tolAbs:\n rcmax = np.sum(svc > tolSVD)\n else:\n rcmax = np.sum(svc > tolSVD * svc[0])\n if kmin != None:\n rC = max(rcmax, kmin)\n else:\n rC = rcmax\n Qck = Uc[:, :rC] * svc[:rC]\n # free memory\n Uc = None\n Qcright = None\n\n ###### observability\n ### compute Ak^2 * Qok\n # (future: use block Arnoldi)\n Qoright = np.transpose(libsp.dot(Qok.T, A))\n DeltaNorm = max(MaxZhere, np.max(np.abs(Qoright)))\n\n ### enlarge Z matrices\n Qok = np.concatenate((Qok, Qoright), axis=1)\n Qoright = None\n rO = Qok.shape[1]\n\n if kmin == None or kmin < rO:\n ### \"cheap\" SVD truncation\n Uo, svo = scalg.svd(Qok, full_matrices=False)[:2]\n\n if tolAbs:\n romax = np.sum(svo > tolSVD)\n else:\n romax = np.sum(svo > tolSVD * svo[0])\n if kmin != None:\n rO = max(romax, kmin)\n else:\n rO = romax\n Qok = Uo[:, :rO] * svo[:rO]\n Uo = None\n\n ##### Prepare next time step\n if Print:\n print('%.3d\\t%.2e\\t%.5d\\t%.5d\\t%.5d' % (kk, DeltaNorm, rC, rO, N))\n DeltaNormNext = DeltaNorm ** 2\n\n if DeltaNorm > tolSmith and DeltaNormNext > 1e-3 * tolSmith:\n\n # compute power\n if type(A) is libsp.csc_matrix:\n A = A.dot(A)\n # check sparsity\n if A.size > 0.15 * N ** 2:\n A = A.toarray()\n elif type(A) is np.ndarray:\n A = np.linalg.matrix_power(A, 2)\n else:\n raise NameError('Type of A not supported')\n\n ### update\n kk = kk + 1\n\n A = None\n\n\n else: # full-rank squared smith iteration (with Cholevsky)\n\n raise NameError('Use balreal_iter_old instead!')\n\n # find min size (only if iter used)\n cc, co = Qck.shape[1], Qok.shape[1]\n if Print:\n print('cc=%.2d, co=%.2d' % (cc, co))\n print('rank(Zc)=%.4d\\trank(Zo)=%.4d' % (rcmax, romax))\n\n # build M matrix and SVD\n M = libsp.dot(Qok.T, Qck)\n U, s, Vh = scalg.svd(M, full_matrices=False)\n\n if outFacts:\n return s, Qck, Qok\n\n else:\n sinv = s ** (-0.5)\n T = libsp.dot(Qck, Vh.T * sinv)\n Tinv = np.dot((U * sinv).T, Qok.T)\n\n if Print:\n print('rank(Zc)=%.4d\\trank(Zo)=%.4d' % (rcmax, romax))\n\n return s, T, Tinv, rcmax, romax\n\n\ndef balreal_iter_old(A, B, C, lowrank=True, tolSmith=1e-10, tolSVD=1e-6, kmax=None,\n tolAbs=False):\n \"\"\"\n Find balanced realisation of DLTI system.\n\n Notes: Lyapunov equations are solved using iterative squared Smith\n algorithm, in its low or full rank version. These implementations are\n as per the low_rank_smith and smith_iter functions respectively but,\n for computational efficiency,, the iterations are rewritten here so as to\n solve for the observability and controllability Gramians contemporary.\n \"\"\"\n\n ### Solve Lyapunov equations\n # Notation reminder:\n # scipy: A X A.T - X = -Q\n # contr: A W A.T - W = - B B.T\n # obser: A.T W A - W = - C.T C\n # low-rank smith: A.T X A - X = -Q Q.T\n\n if lowrank: # low-rank square-Smith iteration (with SVD)\n\n # matrices size\n N = A.shape[0]\n rB = B.shape[1]\n rC = C.shape[0]\n\n # initialise smith iteration\n DeltaNorm = 1e6\n print('Iter\\tMaxZhere')\n kk = 0\n Apow = A\n Qck = B\n Qok = C.T\n\n while DeltaNorm > tolSmith:\n ### compute products Ak^2 * Zk\n ### (use block Arnoldi)\n Qcright = np.dot(Apow, Qck)\n Qoright = np.dot(Apow.T, Qok)\n Apow = np.dot(Apow, Apow)\n\n ### enlarge Z matrices\n Qck = np.concatenate((Qck, Qcright), axis=1)\n Qok = np.concatenate((Qok, Qoright), axis=1)\n\n ### check convergence without reconstructing the added term\n MaxZhere = max(np.max(np.abs(Qoright)), np.max(np.abs(Qcright)))\n print('%.4d\\t%.3e' % (kk, MaxZhere))\n DeltaNorm = MaxZhere\n\n # fixed columns chopping\n if kmax is None:\n # cheap SVD truncation\n if Qck.shape[1] > .4 * N or Qok.shape[1] > .4 * N:\n Uc, svc = scalg.svd(Qck, full_matrices=False)[:2]\n Uo, svo = scalg.svd(Qok, full_matrices=False)[:2]\n if tolAbs:\n rcmax = np.sum(svc > tolSVD)\n romax = np.sum(svo > tolSVD)\n else:\n rcmax = np.sum(svc > tolSVD * svc[0])\n romax = np.sum(svo > tolSVD * svo[0])\n pmax = max(rcmax, romax)\n Qck = Uc[:, :pmax] * svc[:pmax]\n Qok = Uo[:, :pmax] * svo[:pmax]\n # Qck_old=np.dot(Uc[:,:pmax],np.diag(svc[:pmax]))\n # Qok_old=np.dot(Uo[:,:pmax],np.diag(svo[:pmax]))\n # Qck=np.dot(Uc[:,:rcmax],np.diag(svc[:rcmax]))\n # Qok=np.dot(Uo[:,:romax],np.diag(svo[:romax]))\n else:\n if Qck.shape[1] > kmax:\n Uc, svc = scalg.svd(Qck, full_matrices=False)[:2]\n Qck = Uc[:, :kmax] * svc[:kmax]\n if Qok.shape[1] > kmax:\n Uo, svo = scalg.svd(Qok, full_matrices=False)[:2]\n Qok = Uo[:, :kmax] * svo[:kmax]\n\n ### update\n kk = kk + 1\n\n del Apow\n Qc, Qo = Qck, Qok\n\n else: # full-rank squared smith iteration (with Cholevsky)\n\n # first iteration\n Wc = np.dot(B, B.T)\n Wo = np.dot(C.T, C)\n Apow = A\n AXAobs = np.dot(np.dot(A.T, Wo), A)\n AXActrl = np.dot(np.dot(A, Wc), A.T)\n DeltaNorm = max(np.max(np.abs(AXAobs)), np.max(np.abs(AXActrl)))\n\n kk = 1\n print('Iter\\tRes')\n while DeltaNorm > tolSmith:\n kk = kk + 1\n\n # update\n Wo = Wo + AXAobs\n Wc = Wc + AXActrl\n\n # incremental\n Apow = np.dot(Apow, Apow)\n AXAobs = np.dot(np.dot(Apow.T, Wo), Apow)\n AXActrl = np.dot(np.dot(Apow, Wc), Apow.T)\n DeltaNorm = max(np.max(np.abs(AXAobs)), np.max(np.abs(AXActrl)))\n print('%.4d\\t%.3e' % (kk, DeltaNorm))\n # final update (useless in very low tolerance)\n Wo = Wo + AXAobs\n Wc = Wc + AXActrl\n\n # Choleski factorisation: W=Q Q.T. If unsuccessful, directly solve\n # eigenvalue problem\n Qc = scalg.cholesky(Wc).T\n Qo = scalg.cholesky(Wo).T\n # # eigenvalues are normalised by one, hence Tinv and T matrices\n # # here are not scaled\n # ssq,Tinv,T=scalg.eig(np.dot(Wc,Wo),left=True,right=True)\n # Tinv=Tinv.T\n # #Tinv02=Tinv02.T\n # S=np.diag(np.sqrt(ssq))\n # return S,T,Tinv\n\n # find min size (only if iter used)\n cc, co = Qc.shape[1], Qo.shape[1]\n cmin = min(cc, co)\n print('cc=%.2d, co=%.2d' % (cc, co))\n\n # build M matrix and SVD\n M = np.dot(Qo.T, Qc)\n\n # ### not optimised\n # U,s,Vh=scalg.svd(M,full_matrices=True)\n # U,Vh,s=U[:,:cmin],Vh[:cmin,:],s[:cmin]\n # S=np.diag(s)\n # Sinv=np.diag(1./s)\n # V=Vh.T\n # # Build transformation matrices\n # T=np.dot(Qc,np.dot(V,np.sqrt(Sinv)))\n # Tinv=np.dot(np.sqrt(Sinv),np.dot(U.T,Qo.T))\n\n ### optimised\n U, s, Vh = scalg.svd(M, full_matrices=True) # as M is square, full_matrices has no effect\n sinv = s ** (-0.5)\n T = np.dot(Qc, Vh.T * sinv)\n Tinv = np.dot((U * sinv).T, Qo.T)\n\n return s, T, Tinv\n\n\ndef smith_iter(S, T, tol=1e-8, Square=True):\n \"\"\"\n Solves the Stein equation\n S.T X S - X = -T\n by mean of Smith or squared-Smith algorithm. Note that a solution X exists\n only if the eigenvalues of S are stricktly smaller than one, and the\n algorithm will not converge otherwise. The algorithm can not exploit\n sparsity, hence, while convergence can be improved for very large matrices,\n it can not be employed if matrices are too large to be stored in memory.\n\n Ref. Penzt, \"A cyclic low-rank Smith method for large sparse Lyapunov\n equations\", 2000.\n \"\"\"\n\n N = S.shape[0]\n\n if Square:\n\n # first iteration\n X = T\n Spow = S\n STXS = np.dot(np.dot(S.T, X), S)\n DeltaNorm = np.max(np.abs(STXS))\n\n # # second iteration:\n # # can be removed using Spow=np.dot(Spow,Spow)\n # X=X+STXS\n # S=np.dot(S,S)\n # Spow=S\n # STXS=np.dot(np.dot(Spow.T,X),Spow)\n # DeltaNorm=np.max(np.abs(STXS))\n\n counter = 1\n print('Iter\\tRes')\n while DeltaNorm > tol:\n counter = counter + 1\n\n # update\n X = X + STXS\n\n # incremental\n # Spow=np.dot(Spow,S) # use this if uncomment second iter\n Spow = np.dot(Spow, Spow)\n STXS = np.dot(np.dot(Spow.T, X), Spow)\n DeltaNorm = np.max(np.abs(STXS))\n\n print('%.4d\\t%.3e' % (counter, DeltaNorm))\n\n else:\n # first iteration\n X = T\n Spow = S\n STTS = np.dot(np.dot(Spow.T, T), Spow)\n DeltaNorm = np.max(np.abs(STTS))\n\n counter = 1\n print('Iter\\tRes')\n while DeltaNorm > tol:\n counter = counter + 1\n\n # update\n X = X + STTS\n\n # incremental\n Spow = np.dot(Spow, S)\n STTS = np.dot(np.dot(Spow.T, T), Spow)\n DeltaNorm = np.max(np.abs(STTS))\n\n print('%.4d\\t%.3e' % (counter, DeltaNorm))\n\n print('Error %.2e achieved after %.4d iteration!' % (DeltaNorm, counter))\n\n return X\n\n\ndef res_discrete_lyap(A, Q, Z, Factorised=True):\n \"\"\"\n Provides residual of discrete Lyapunov equation:\n A.T X A - X = -Q Q.T\n If Factorised option is true,\n X=Z*Z.T\n otherwise X=Z is chosen.\n\n Reminder:\n contr: A W A.T - W = - B B.T\n obser: A.T W A - W = - C.T C\n \"\"\"\n\n if Factorised:\n X = np.dot(Z, Z.T)\n else:\n X = Z\n R = np.dot(A.T, np.dot(X, A)) - X + np.dot(Q, Q.T)\n resinf = np.max(np.abs(R))\n\n return resinf\n\n\ndef low_rank_smith(A, Q, tol=1e-10, Square=True, tolSVD=1e-12, tolAbs=False,\n kmax=None, fullOut=True, Convergence='Zk'):\n \"\"\"\n Low-rank smith algorithm for Stein equation\n A.T X A - X = -Q Q.T\n The algorithm can only be used if T is symmetric positive-definite, but this\n is not checked in this routine for computational performance. The solution X\n is provided in its factorised form:\n X=Z Z.T\n As in the most general case, a solution X exists only if the eigenvalues of\n S are stricktly smaller than one, and the algorithm will not converge\n otherwise. The algorithm can not exploits parsity, hence, while convergence\n can be improved for very large matrices, it can not be employed if matrices\n are too large to be stored in memory.\n\n Parameters:\n - tol: tolerance for stopping convergence of Smith algorithm\n - Square: if true the squared-Smith algorithm is used\n - tolSVD: tolerance for reduce Z matrix based on singular values\n - kmax: if given, the Z matrix is forced to have size kmax\n - tolAbs: if True, the tolerance\n - fullOut: not implemented\n - Convergence: 'Zk','res'.\n - If 'Zk' the iteration is stopped when the inf norm of the incremental\n matrix goes below tol.\n - If 'res' the residual of the Lyapunov equation is computed. This\n strategy may fail to converge if kmax is too low or tolSVD too large!\n\n Ref. P. Benner, G.E. Khoury and M. Sadkane, \"On the squared Smith method for\n large-scale Stein equations\", 2014.\n \"\"\"\n\n N = A.shape[0]\n ncol = Q.shape[1]\n AT = A.T\n\n DeltaNorm = 1e6\n print('Iter\\tMaxZhere')\n\n kk = 0\n SvList = []\n ZcColList = []\n\n if Square: # ------------------------------------------------- squared iter\n Zk = Q\n while DeltaNorm > tol:\n\n ### compute product Ak^2 * Zk\n ### use block Arnoldi\n\n ## too expensive!!\n # Zright=Zk\n # for ii in range(2**kk):\n # \tZright=np.dot(AT,Zright)\n Zright = np.dot(AT, Zk)\n AT = np.dot(AT, AT)\n\n ### enlarge Z matrix\n Zk = np.concatenate((Zk, Zright), axis=1)\n\n ### check convergence\n if Convergence == 'Zk':\n ### check convergence without reconstructing the added term\n MaxZhere = np.max(np.abs(Zright))\n print('%.4d\\t%.3e' % (kk, MaxZhere))\n DeltaNorm = MaxZhere\n elif Convergence == 'res':\n ### check convergence through residual\n resinf = res_discrete_lyap(A, Q, Zk, Factorised=True)\n print('%.4d\\t%.3e\\t%.3e' % (kk, MaxZhere, resinf))\n DeltaNorm = resinf\n\n # cheap SVD truncation\n U, sv, Vh = scalg.svd(Zk, full_matrices=False)\n # embed()\n\n if kmax == None:\n if tolAbs:\n pmax = np.sum(sv > tolSVD)\n else:\n pmax = np.sum(sv > tolSVD * sv[0])\n else:\n pmax = kmax\n\n Ut = U[:, :pmax]\n svt = sv[:pmax]\n # Vht=Vh[:pmax,:]\n # Zkrec=np.dot(Ut,np.dot(np.diag(svt),Vht))\n Zk = np.dot(Ut, np.diag(svt))\n\n ### update\n kk = kk + 1\n\n\n else: # -------------------------------------------------------- smith iter\n raise NameError(\n 'Smith method without SVD will lead to extremely large matrices')\n\n Zk = []\n Zk.append(Q)\n while DeltaNorm > tol:\n Zk.append(np.dot(AT, Zk[-1]))\n kk = kk + 1\n # check convergence without reconstructing Z*Z.T\n MaxZhere = np.max(np.abs(Zk[-1]))\n print('%.4d\\t%.3e' % (kk, MaxZhere))\n DeltaNorm = MaxZhere\n Zk = np.concatenate(tuple(Zk), axis=1)\n\n return Zk\n\n\n### utilities for balfreq\n\ndef get_trapz_weights(k0, kend, Nk, knyq=False):\n \"\"\"\n Returns uniform frequency grid (kv of length Nk) and weights (wv) for\n Gramians integration using trapezoidal rule. If knyq is True, it is assumed\n that kend is also the Nyquist frequency.\n \"\"\"\n\n assert k0 >= 0. and kend >= 0., 'Frequencies must be positive!'\n\n dk = (kend - k0) / (Nk - 1.)\n kv = np.linspace(k0, kend, Nk)\n wv = np.ones((Nk,)) * dk * np.sqrt(2)\n\n if k0 / (kend - k0) < 1e-10:\n wv[0] = .5 * dk\n else:\n wv[0] = dk / np.sqrt(2)\n\n if knyq:\n wv[-1] = .5 * dk\n else:\n wv[-1] = dk / np.sqrt(2)\n\n return kv, wv\n\n\ndef get_gauss_weights(k0, kend, Npart, order):\n \"\"\"\n Returns gauss-legendre frequency grid (kv of length Npart*order) and\n weights (wv) for Gramians integration.\n\n The integration grid is divided into Npart partitions, and in each of\n them integration is performed using a Gauss-Legendre quadrature of\n order order.\n\n Note: integration points are never located at k0 or kend, hence there\n is no need for special treatment as in (for e.g.) a uniform grid case\n (see get_unif_weights)\n \"\"\"\n\n if Npart == 1:\n # get gauss normalised coords and weights\n xad, wad = np.polynomial.legendre.leggauss(order)\n krange = kend - k0\n kv = .5 * (k0 + kend) + .5 * krange * xad\n wv = wad * (.5 * krange) * np.sqrt(2)\n print('partitioning: %.3f to %.3f' % (k0, kend))\n\n else:\n kv = np.zeros((Npart * order,))\n wv = np.zeros((Npart * order,))\n\n dk_part = (kend - k0) / Npart\n\n for ii in range(Npart):\n k0_part = k0 + ii * dk_part\n kend_part = k0_part + dk_part\n iivec = range(order * ii, order * (ii + 1))\n kv[iivec], wv[iivec] = get_gauss_weights(k0_part, kend_part, Npart=1, order=order)\n\n return kv, wv\n\n\ndef balfreq(SS, DictBalFreq):\n \"\"\"\n Method for frequency limited balancing.\n\n The Observability and controllability Gramians over the frequencies kv\n are solved in factorised form. Balanced modes are then obtained with a\n square-root method.\n\n Details:\n\n * Observability and controllability Gramians are solved in factorised form\n through explicit integration. The number of integration points determines\n both the accuracy and the maximum size of the balanced model.\n\n * Stability over all (Nb) balanced states is achieved if:\n\n a. one of the Gramian is integrated through the full Nyquist range\n b. the integration points are enough.\n\n\n Input:\n\n - DictBalFreq: dictionary specifying integration method with keys:\n\n - ``frequency``: defines limit frequencies for balancing. The balanced\n model will be accurate in the range ``[0,F]``, where ``F`` is the value of\n this key. Note that ``F`` units must be consistent with the units specified\n in the ``self.ScalingFacts`` dictionary.\n\n - ``method_low``: ``['gauss','trapz']`` specifies whether to use gauss\n quadrature or trapezoidal rule in the low-frequency range ``[0,F]``.\n\n - ``options_low``: options to use for integration in the low-frequencies.\n These depend on the integration scheme (See below).\n\n - ``method_high``: method to use for integration in the range [F,F_N],\n where F_N is the Nyquist frequency. See 'method_low'.\n\n - ``options_high``: options to use for integration in the high-frequencies.\n\n - ``check_stability``: if True, the balanced model is truncated to\n eliminate unstable modes - if any is found. Note that very accurate\n balanced model can still be obtained, even if high order modes are\n unstable. Note that this option is overridden if \"\"\n\n - ``get_frequency_response``: if True, the function also returns the\n frequency response evaluated at the low-frequency range integration\n points. If True, this option also allows to automatically tune the\n balanced model.\n\n\n Future options:\n - Ncpu: for parallel run\n\n\n The following integration schemes are available:\n - ``trapz``: performs integration over equally spaced points using\n trapezoidal rule. It accepts options dictionaries with keys:\n\n - ``points``: number of integration points to use (including\n domain boundary)\n\n - ``gauss`` performs gauss-lobotto quadrature. The domain can be\n partitioned in Npart sub-domain in which the gauss-lobotto quadrature\n of order Ord can be applied. A total number of Npart*Ord points is\n required. It accepts options dictionaries of the form:\n\n - ``partitions``: number of partitions\n\n - ``order``: quadrature order.\n\n\n Examples:\n\n The following dictionary\n\n >>> DictBalFreq={'frequency': 1.2,\n >>> 'method_low': 'trapz',\n >>> 'options_low': {'points': 12},\n >>> 'method_high': 'gauss',\n >>> 'options_high': {'partitions': 2, 'order': 8},\n >>> 'check_stability': True }\n\n\n balances the state-space model in the frequency range [0, 1.2]\n using:\n\n a. 12 equally-spaced points integration of the Gramians in\n the low-frequency range [0,1.2] and\n\n b. A 2 Gauss-Lobotto 8-th order quadratures of the controllability\n Gramian in the high-frequency range.\n\n\n A total number of 28 integration points will be required, which will\n result into a balanced model with number of states\n\n >>> min{ 2*28* number_inputs, 2*28* number_outputs }\n\n\n The model is finally truncated so as to retain only the first Ns stable\n modes.\n \"\"\"\n\n ### check input dictionary\n if 'frequency' not in DictBalFreq:\n raise NameError('Solution dictionary must include the \"frequency\" key')\n\n if 'method_low' not in DictBalFreq:\n warnings.warn('Setting default options for low-frequency integration')\n DictBalFreq['method_low'] = 'trapz'\n DictBalFreq['options_low'] = {'points': 12}\n\n if 'method_high' not in DictBalFreq:\n warnings.warn('Setting default options for high-frequency integration')\n DictBalFreq['method_high'] = 'gauss'\n DictBalFreq['options_high'] = {'partitions': 2, 'order': 8}\n\n if 'check_stability' not in DictBalFreq:\n DictBalFreq['check_stability'] = True\n\n if 'output_modes' not in DictBalFreq:\n DictBalFreq['output_modes'] = True\n\n if 'get_frequency_response' not in DictBalFreq:\n DictBalFreq['get_frequency_response'] = False\n\n ### get integration points and weights\n\n # Nyquist frequency\n kn = np.pi / SS.dt\n\n Opt = DictBalFreq['options_low']\n if DictBalFreq['method_low'] == 'trapz':\n kv_low, wv_low = get_trapz_weights(0., DictBalFreq['frequency'],\n Opt['points'], False)\n elif DictBalFreq['method_low'] == 'gauss':\n kv_low, wv_low = get_gauss_weights(0., DictBalFreq['frequency'],\n Opt['partitions'], Opt['order'])\n else:\n raise NameError(\n 'Invalid value %s for key \"method_low\"' % DictBalFreq['method_low'])\n\n Opt = DictBalFreq['options_high']\n if DictBalFreq['method_high'] == 'trapz':\n if Opt['points'] == 0:\n warnings.warn('You have chosen no points in high frequency range!')\n kv_high, wv_high = [], []\n else:\n kv_high, wv_high = get_trapz_weights(DictBalFreq['frequency'], kn,\n Opt['points'], True)\n elif DictBalFreq['method_high'] == 'gauss':\n if Opt['order'] * Opt['partitions'] == 0:\n warnings.warn('You have chosen no points in high frequency range!')\n kv_high, wv_high = [], []\n else:\n kv_high, wv_high = get_gauss_weights(DictBalFreq['frequency'], kn,\n Opt['partitions'], Opt['order'])\n else:\n raise NameError(\n 'Invalid value %s for key \"method_high\"' % DictBalFreq['method_high'])\n\n ### -------------------------------------------------- loop frequencies\n\n ### merge vectors\n Nk_low = len(kv_low)\n kvdt = np.concatenate((kv_low, kv_high)) * SS.dt\n wv = np.concatenate((wv_low, wv_high)) * SS.dt\n zv = np.cos(kvdt) + 1.j * np.sin(kvdt)\n\n Eye = libsp.eye_as(SS.A)\n Zc = np.zeros((SS.states, 2 * SS.inputs * len(kvdt)), )\n Zo = np.zeros((SS.states, 2 * SS.outputs * Nk_low), )\n\n if DictBalFreq['get_frequency_response']:\n Yfreq = np.empty((SS.outputs, SS.inputs, Nk_low,), dtype=np.complex_)\n kv = kv_low\n\n for kk in range(len(kvdt)):\n\n zval = zv[kk]\n Intfact = wv[kk] # integration factor\n\n Qctrl = Intfact * libsp.solve(zval * Eye - SS.A, SS.B)\n kkvec = range(2 * kk * SS.inputs, 2 * (kk + 1) * SS.inputs)\n Zc[:, kkvec[:SS.inputs]] = Qctrl.real\n Zc[:, kkvec[SS.inputs:]] = Qctrl.imag\n\n ### ----- frequency response\n if DictBalFreq['get_frequency_response'] and kk < Nk_low:\n Yfreq[:, :, kk] = (1. / Intfact) * \\\n libsp.dot(SS.C, Qctrl, type_out=np.ndarray) + SS.D\n\n ### ----- observability\n if kk >= Nk_low:\n continue\n\n Qobs = Intfact * libsp.solve(np.conj(zval) * Eye - SS.A.T, SS.C.T)\n\n kkvec = range(2 * kk * SS.outputs, 2 * (kk + 1) * SS.outputs)\n Zo[:, kkvec[:SS.outputs]] = Intfact * Qobs.real\n Zo[:, kkvec[SS.outputs:]] = Intfact * Qobs.imag\n\n # delete full matrices\n Kernel = None\n Qctrl = None\n Qobs = None\n\n # LRSQM (optimised)\n U, hsv, Vh = scalg.svd(np.dot(Zo.T, Zc), full_matrices=False)\n sinv = hsv ** (-0.5)\n T = np.dot(Zc, Vh.T * sinv)\n Ti = np.dot((U * sinv).T, Zo.T)\n # Zc,Zo=None,None\n\n ### build frequency balanced model\n Ab = libsp.dot(Ti, libsp.dot(SS.A, T))\n Bb = libsp.dot(Ti, SS.B)\n Cb = libsp.dot(SS.C, T)\n SSb = libss.StateSpace(Ab, Bb, Cb, SS.D, dt=SS.dt)\n\n ### Eliminate unstable modes - if any:\n if DictBalFreq['check_stability']:\n for nn in range(1, len(hsv) + 1):\n eigs_trunc = scalg.eigvals(SSb.A[:nn, :nn])\n eigs_trunc_max = np.max(np.abs(eigs_trunc))\n if eigs_trunc_max > 1. - 1e-16:\n SSb.truncate(nn - 1)\n hsv = hsv[:nn - 1]\n T = T[:, :nn - 1]\n Ti = Ti[:nn - 1, :]\n break\n\n outs = (SSb, hsv)\n if DictBalFreq['output_modes']:\n outs += (T, Ti, Zc, Zo, U, Vh)\n return outs\n\n\ndef modred(SSb, N, method='residualisation'):\n \"\"\"\n Produces a reduced order model with N states from balanced or modal system\n SSb.\n Both \"truncation\" and \"residualisation\" methods are employed.\n\n Note:\n - this method is designed for small size systems, i.e. a deep copy of SSb is\n produced by default.\n \"\"\"\n\n assert method in ['residualisation', 'realisation', 'truncation'], \\\n \"method must be equal to 'residualisation' or 'truncation'!\"\n assert SSb.dt is not None, 'SSb is not a DLTI!'\n\n Nb = SSb.A.shape[0]\n if Nb == N:\n SSrom = libss.StateSpace(SSb.A, SSb.B, SSb.C, SSb.D, dt=SSb.dt)\n return SSrom\n\n A11 = SSb.A[:N, :N]\n B11 = SSb.B[:N, :]\n C11 = SSb.C[:, :N]\n D = SSb.D\n\n if method == 'truncation':\n SSrom = libss.StateSpace(A11, B11, C11, D, dt=SSb.dt)\n else:\n Nb = SSb.A.shape[0]\n IA22inv = -SSb.A[N:, N:].copy()\n eevec = range(Nb - N)\n IA22inv[eevec, eevec] += 1.\n IA22inv = scalg.inv(IA22inv, overwrite_a=True)\n\n SSrom = libss.StateSpace(\n A11 + np.dot(SSb.A[:N, N:], np.dot(IA22inv, SSb.A[N:, :N])),\n B11 + np.dot(SSb.A[:N, N:], np.dot(IA22inv, SSb.B[N:, :])),\n C11 + np.dot(SSb.C[:, N:], np.dot(IA22inv, SSb.A[N:, :N])),\n D + np.dot(SSb.C[:, N:], np.dot(IA22inv, SSb.B[N:, :])),\n dt=SSb.dt)\n\n return SSrom\n\n\ndef tune_rom(SSb, kv, tol, gv, method='realisation', convergence='all', Print=False):\n \"\"\"\n Starting from a balanced DLTI, this function determines the number of states\n N required in a ROM (obtained either through 'residualisation' or\n 'truncation' as specified in method - see also librom.modred) to match the\n frequency response of SSb over the frequency array, kv, with absolute\n accuracy tol. gv contains the balanced system Hankel singular value, and is\n used to determine the upper bound for the ROM order N.\n\n Unless kv does not conver the full Nyquist frequency range, the ROM accuracy\n is not guaranteed to increase monothonically with the number of states. To\n account for this, two criteria can be used to determine the ROM convergence:\n\n - convergence='all': in this case, the number of ROM states N is chosen\n such that any ROM of order greater than N produces an error smaller than\n tol. To guarantee this the ROM frequency response is computed for all\n N<=Nb, where Nb is the number of balanced states. This method is\n numerically inefficient.\n\n - convergence='min': atempts to find the minimal number of states to\n achieve the accuracy tol.\n\n Note:\n - the input state-space model, SSb, must be balanced.\n - the routine in not implemented for numerical efficiency and assumes that\n SSb is small.\n \"\"\"\n\n # reference frequency response\n Nb = SSb.A.shape[0]\n Yb = libss.freqresp(SSb, kv, dlti=True)\n if gv is None:\n Nmax = Nb\n else:\n Nmax = min(np.sum(gv > tol) + 1, Nb)\n\n if convergence == 'all':\n # start from larger size and decrease untill the ROm accuracy is over tol\n Found = False\n N = Nmax\n while not Found:\n SSrom = modred(SSb, N, method)\n Yrom = libss.freqresp(SSrom, kv, dlti=True)\n er = np.max(np.abs(Yrom - Yb))\n if Print:\n print('N=%.3d, er:%.2e (tol=%.2e)' % (N, er, tol))\n\n if N == Nmax and er > tol:\n warnings.warn(\n 'librom.tune_rom: error %.2e above tolerance %.2e and HSV bound %.2e' \\\n % (er, tol, gv[N - 1]))\n # raise NameError('Hankel singluar values do not '\\\n # \t\t\t\t'provide a bound for error! '\\\n # \t\t\t\t'The balanced system may not be accurate')\n if er < tol:\n N -= 1\n else:\n N += 1\n Found = True\n SSrom = modred(SSb, N, method)\n\n elif convergence == 'min':\n Found = False\n N = 1\n while not Found:\n SSrom = modred(SSb, N, method)\n Yrom = libss.freqresp(SSrom, kv, dlti=True)\n er = np.max(np.abs(Yrom - Yb))\n if Print:\n print('N=%.3d, er:%.2e (tol=%.2e)' % (N, er, tol))\n if er < tol:\n Found = True\n\n else:\n N += 1\n\n else:\n raise NameError(\"'convergence' method not implemented\")\n\n return SSrom\n\n\ndef eigen_dec(A, B, C, dlti=True, N=None, eigs=None, UR=None, URinv=None,\n order_by='damp', tol=1e-10, complex=False):\n \"\"\"\n Eigen decomposition of state-space model (either discrete or continuous time)\n defined by the A,B,C matrices. Eigen-states are organised in decreasing\n damping order or increased frequency order such that the truncation\n\n ``A[:N,:N], B[:N,:], C[:,:N]``\n\n will retain the least N damped (or lower frequency) modes.\n\n If the eigenvalues of A, eigs, are complex, the state-space is automatically\n convert into real by separating its real and imaginary part. This procedure\n retains the minimal number of states as only 2 equations are added for each\n pair of complex conj eigenvalues. Extra care is however required when\n truncating the system, so as to ensure that the chosen value of N does not\n retain the real part, but not the imaginary part, of a complex pair.\n\n For this reason, the function also returns an optional output, ``Nlist``, such\n that, for each N in Nlist, the truncation\n A[:N,:N], B[:N,:], C[:,:N]\n does guarantee that both the real and imaginary part of a complex conj pair\n is included in the truncated model. Note that if ```order_by == None``, the eigs\n and UR must be given in input and must be such that complex pairs are stored\n consecutively.\n\n\n Args:\n A: state-space matrix\n B: state-space matrix\n C: matrices of state-space model\n dlti: specifies whether discrete (True) or continuous-time. This information\n is only required to order the eigenvalues in decreasing dmaping order\n N: number of states to retain. If None, all states are retained\n eigs,Ur: eigenvalues and right eigenvector of A matrix as given by:\n eigs,Ur=scipy.linalg.eig(A,b=None,left=False,right=True)\n Urinv: inverse of Ur\n order_by={'damp','freq','stab'}: order according to increasing damping (damp)\n or decreasing frequency (freq) or decreasing damping (stab).\n If None, the same order as eigs/UR is followed.\n tol: absolute tolerance used to identify complex conj pair of eigenvalues\n complex: if true, the system is left in complex form\n\n\n Returns:\n (Aproj,Bproj,Cproj): state-space matrices projected over the first N (or N+1\n if N removes the imaginary part equations of a complex conj pair of\n eigenvalues) related to the least damped modes\n Nlist: list of acceptable truncation values\n \"\"\"\n\n if N == None:\n N = A.shape[0]\n\n if order_by is None:\n assert ((eigs is not None) and (UR is not None)), \\\n 'Specify criterion to order eigenvalues or provide both eigs and UR'\n\n ### compute eigevalues/eigenvectors\n if eigs is None:\n eigs, UR = scalg.eig(A, b=None, left=False, right=True)\n if URinv is None:\n try:\n URinv = np.linalg.inv(UR)\n except LinAlgError:\n print('The A matrix can not be diagonalised as does not admit ' \\\n 'linearly independent eigenvectors')\n\n ### order eigenvalues/eigenvectors (or verify format)\n if order_by is None:\n # verify format\n nn = 0\n while nn < N:\n if np.abs(eigs[nn].imag) > tol:\n if nn < N - 1:\n assert np.abs(eigs[nn].imag + eigs[nn + 1].imag) < tol, \\\n 'When order_by is None, eigs and UR much be organised such ' \\\n 'that complex conj pairs are consecutives'\n else:\n assert np.abs(eigs[nn].imag + eigs[nn - 1].imag) < tol, \\\n 'When order_by is None, eigs and UR much be organised such ' \\\n 'that complex conj pairs are consecutives'\n nn += 2\n else:\n nn += 1\n else:\n if order_by == 'damp':\n if dlti:\n order = np.argsort(np.abs(eigs))[::-1]\n else:\n order = np.argsort(eigs.real)[::-1]\n elif order_by == 'freq':\n if dlti:\n order = np.argsort(np.abs(np.angle(eigs)))\n else:\n order = np.argsort(np.abs(eigs.imag))\n elif order_by == 'stab':\n if dlti:\n order = np.argsort(np.abs(eigs))\n else:\n order = np.argsort(eigs.real)\n else:\n raise NameError(\"order_by must be equal to 'damp' or 'freq'\")\n eigs = eigs[order]\n UR = UR[:, order]\n URinv = URinv[order, :]\n\n ### compute list of available truncation size, Nlist\n Nlist = []\n nn = 0\n while nn < N:\n # check if eig are complex conj\n if nn < N - 1 and np.abs(eigs[nn] - eigs[nn + 1].conjugate()) < tol:\n nn += 2\n else:\n nn += 1\n Nlist.append(nn)\n assert Nlist[-1] >= N, \\\n 'Something failed when identifying the admissible truncation sizes'\n if Nlist[-1] > N:\n warnings.warn(\n 'Resizing the eigendecomposition from %.3d to %.3d states' \\\n % (N, Nlist[-1]))\n N = Nlist[-1]\n\n ### build complex form\n if complex:\n Aproj = np.diag(eigs[:N])\n Bproj = np.dot(URinv[:N, :], B)\n Cproj = np.dot(C, UR[:, :N])\n return Aproj, Bproj, Cproj, Nlist\n\n ### build real values form\n Aproj = np.zeros((N, N))\n Bproj = np.zeros((N, B.shape[1]))\n Cproj = np.zeros((C.shape[0], N))\n nn = 0\n while nn < N:\n # redundant check\n if (nn + 1 in Nlist) and np.abs(eigs[nn].imag) < tol:\n Aproj[nn, nn] = eigs[nn].real\n Bproj[nn, :] = np.dot(URinv[nn, :].real, B)\n Cproj[:, nn] = np.dot(C, UR[:, nn].real)\n nn += 1\n else:\n Aproj[nn, nn] = eigs[nn].real\n Aproj[nn, nn + 1] = -eigs[nn].imag\n Aproj[nn + 1, nn] = eigs[nn].imag\n Aproj[nn + 1, nn + 1] = eigs[nn].real\n #\n Bproj[nn, :] = np.dot(URinv[nn, :].real, B)\n Bproj[nn + 1, :] = np.dot(URinv[nn, :].imag, B)\n #\n Cproj[:, nn] = 2. * np.dot(C, UR[:, nn].real)\n Cproj[:, nn + 1] = -2. * np.dot(C, UR[:, nn].imag)\n nn += 2\n\n return Aproj, Bproj, Cproj, Nlist\n\n\ndef check_stability(A, dt=True):\n \"\"\"\n Checks the stability of the system.\n\n Args:\n A (np.ndarray): System plant matrix\n dt (bool): Discrete time system\n\n Returns:\n bool: True if the system is stable\n \"\"\"\n eigvals = scalg.eigvals(A)\n if dt:\n criteria = np.abs(eigvals) > 1.\n else:\n criteria = np.real(eigvals) > 0.0\n\n if np.sum(criteria) >= 1.0:\n return True\n else:\n return False\n" }, { "path": "sharpy/rom/utils/librom_interp.py", "content": "\"\"\"Methods for the interpolation of DLTI ROMs\n\nThis is library for state-space models interpolation. These routines are intended\nfor small size state-space models (ROMs), hence some methods may not be optimised\nto exploit sparsity structures. For generality purposes, all methods require in\ninput interpolatory weights.\n\n\nThe module includes the methods:\n\n - :func:`~sharpy.rom.utils.librom_interp.transfer_function`: returns an interpolatory state-space model based on the\n transfer function method [1]. This method is general and is, effectively, a\n wrapper of the :func:`sharpy.linear.src.libss.join` method.\n\n - :func:`~sharpy.rom.utils.librom_interp.BT_transfer_function`: evolution of transfer function methods. The growth of\n the interpolated system size is avoided through balancing.\n\n\nReferences:\n\n [1] Benner, P., Gugercin, S. & Willcox, K., 2015. A Survey of Projection-Based\n Model Reduction Methods for Parametric Dynamical Systems. SIAM Review, 57(4),\n pp.483–531.\n\n\nAuthor: S. Maraniello\n\nDate: Mar-Apr 2019\n\n\n\"\"\"\n\nimport warnings\nimport numpy as np\nimport scipy.linalg as scalg\n\n# dependency\nimport sharpy.linear.src.libss as libss\n\n\ndef transfer_function(SS_list, wv):\n \"\"\"\n Returns an interpolatory state-space model based on the transfer function \n method [1]. This method is general and is, effectively, a wrapper of the \n :func:`sharpy.linear.src.libss.join` method.\n \n Features:\n\n - stability preserved\n - system size increases with interpolatory order, but can be optimised for\n fast on-line evaluation\n\n Args:\n SS_list (list): List of state-space models instances of :class:`sharpy.linear.src.libss.StateSpace` class.\n wv (list): list of interpolatory weights.\n\n Notes:\n\n For fast online evaluation, this routine can be optimised to return a\n class that handles each state-space model independently. See ref. [1] for\n more details.\n\n References:\n [1] Benner, P., Gugercin, S. & Willcox, K., 2015. A Survey of Projection-Based\n Model Reduction Methods for Parametric Dynamical Systems. SIAM Review, 57(4),\n pp.483–531.\n \"\"\"\n\n return libss.join(SS_list, wv)\n\n\ndef FLB_transfer_function(SS_list, wv, U_list, VT_list, hsv_list=None, M_list=None):\n r\"\"\"\n Returns an interpolatory state-space model based on the transfer function \n method [1]. This method is applicable to frequency limited balanced \n state-space models only.\n\n\n Features:\n\n - stability preserved\n - the interpolated state-space model has the same size than the tabulated ones\n - all state-space models, need to have the same size and the same numbers of\n hankel singular values.\n - suitable for any ROM\n\n\n Args:\n SS_list (list): List of state-space models instances of :class:`sharpy.linear.src.libss.StateSpace` class.\n wv (list): list of interpolatory weights.\n U_list (list): small size, thin SVD factors of Gramians square roots of each state space model (:math:`\\mathbf{U}`).\n VT_list (list): small size, thin SVD factors of Gramians square roots of each state space model (:math:`\\mathbf{V}^\\top`).\n hsv_list (list): small size, thin SVD factors of Gramians square roots of each state space model. If ``None``,\n it is assumed that\n ``U_list = [ U_i sqrt(hsv_i) ]``\n ``VT_list = [ sqrt(hsv_i) V_i.T ]``\n where ``U_i`` and ``V_i.T`` are square matrices and hsv is an array.\n\n M_list (list): for fast on-line evaluation. Small size product of Gramians\n factors of each state-space model. Each element of this list is equal to:\n ``M_i = U_i hsv_i V_i.T``\n\n Notes:\n Message for future generations:\n\n - the implementation is divided into an offline and online part.\n\n References:\n\n Maraniello S. and Palacios R., Frequency-limited balanced truncation for\n parametric reduced-order modelling of the UVLM. Only in the best theaters.\n\n See Also:\n\n Frequency-Limited Balanced ROMs may be obtained from SHARPy using :class:`sharpy.rom.balanced.FrequencyLimited`.\n \"\"\"\n\n # ----------------------------------------------------------------- offline\n\n ### checks sizes\n N_interp = len(SS_list)\n states = SS_list[0].states\n inputs = SS_list[0].inputs\n outputs = SS_list[0].outputs\n for ss_here in SS_list:\n assert ss_here.states == states, \\\n 'State-space models must have the same number of states!'\n assert ss_here.inputs == inputs, \\\n 'State-space models must have the same number of states!'\n assert ss_here.outputs == outputs, \\\n 'State-space models must have the same number of states!'\n\n ### case of unbalanced state-space models\n # in this case, U_list and VT_list contain the full-rank Gramians factors\n # of each ROM\n if U_list is None and VT_list is None:\n raise NameError('apply FLB before calling this routine')\n # hsv_list = None\n # M_list, U_list, VT_list = [], [], []\n # for ii in range(N_interp):\n\n # # # avoid direct\n # # hsv,U,Vh,Zc,Zo = librom.balreal_direct_py(\n # # SS_list[ii].A, SS_list[ii].B, SS_list[ii].C, \n # # DLTI=True,full_outputs=True)\n\n # # iterative also fails\n # hsv,Zc,Zo = librom.balreal_iter(SS_list[ii].A, SS_list[ii].B, SS_list[ii].C,\n # lowrank=True,tolSmith=1e-10,tolSVD=1e-10,\n # kmin=None, tolAbs=False, Print=True, outFacts=True)\n\n # # M_list.append( np.dot( np.dot(U,np.diag(hsv)), Vh) )\n # M_list.append( np.dot( Zo.T,Zc ) )\n # U_list.append(Zo.T)\n # VT_list.append(Zc)\n\n # calculate small size product of Gramians factors\n elif M_list is None:\n if hsv_list is None:\n M_list = [np.dot(U, VT) for U, VT in zip(U_list, VT_list)]\n else:\n M_list = [np.dot(U * hsv, VT) for U, hsv, VT in zip(U_list, hsv_list, VT_list)]\n\n # ------------------------------------------------------------------ online\n\n ### balance interpolated model\n M_int = np.zeros_like(M_list[0])\n for ii in range(N_interp):\n M_int += wv[ii] * M_list[ii]\n\n U_int, hsv_int, Vh_int = scalg.svd(M_int, full_matrices=False)\n sinv_int = hsv_int ** (-0.5)\n\n ### build projection matrices\n sinvUT_int = (U_int * sinv_int).T\n Vsinv_int = Vh_int.T * sinv_int\n\n if hsv_list is None:\n Ti_int_list = [np.dot(sinvUT_int, U) for U in U_list]\n T_int_list = [np.dot(VT, Vsinv_int) for VT in VT_list]\n else:\n Ti_int_list = [np.dot(sinvUT_int, U * np.sqrt(hsv)) \\\n for U, hsv in zip(U_list, hsv_list)]\n T_int_list = [np.dot(np.dot(np.diag(np.sqrt(hsv)), VT),\n Vsinv_int) \\\n for hsv, VT in zip(hsv_list, VT_list)]\n\n ### assemble interp state-space model\n A_int = np.zeros((states, states))\n B_int = np.zeros((states, inputs))\n C_int = np.zeros((outputs, states))\n D_int = np.zeros((outputs, inputs))\n\n for ii in range(N_interp):\n # in A and B the weigths come from Ti\n A_int += wv[ii] * np.dot(Ti_int_list[ii],\n np.dot(SS_list[ii].A, T_int_list[ii]))\n B_int += wv[ii] * np.dot(Ti_int_list[ii], SS_list[ii].B)\n # in C and D the weights come from the interp system expression\n C_int += wv[ii] * np.dot(SS_list[ii].C, T_int_list[ii])\n D_int += wv[ii] * SS_list[ii].D\n\n return libss.StateSpace(A_int, B_int, C_int, D_int, dt=SS_list[0].dt), hsv_int\n\n\nclass InterpROM:\n r\"\"\"\n State-space 1D interpolation class.\n\n This class allows interpolating from a list of state-space models, SS.\n\n State-space models are required to have the same number of inputs and outputs \n and need to have the same number of states.\n\n For state-space interpolation, state-space models also need to be defined\n over the same set of generalised coordinates. If this is not the case, the\n projection matrices W and V used to produce the ROMs, ie\n\n .. math:: \\mathbf{A}_{proj} = \\mathbf{W}^\\top \\mathbf{A V}\n\n where A is the full-states matrix, also need to be provided. This will allow\n projecting the state-space models onto a common set of generalised \n coordinates before interpoling.\n\n For development purposes, the method currently creates a hard copy of the\n projected matrices into the self.AA, self.BB, self.CC lists\n\n\n Inputs:\n\n - SS: list of state-space models (instances of libss.StateSpace class)\n\n - VV: list of V matrices used to produce SS. If None, it is assumed that\n ROMs are defined over the same basis\n\n - WWT: list of W^T matrices used to derive the ROMs.\n \n - Vref, WTref: reference subspaces for projection. Some methods neglect this\n input (e.g. panzer)\n\n - method_proj: method for projection of state-space models over common\n coordinates. Available options are:\n\n - leastsq: find left/right projectors using least squares approx. Suitable\n for all basis.\n\n - strongMAC: strong Modal Assurance Criterion [4] enforcement for general\n basis. See Ref. [3], Eq. (7)\n\n - strongMAC_BT: strong Modal Assurance Criterion [4] enforcement for \n basis obtained by Balanced Truncation. Equivalent to strongMAC\n\n - maraniello_BT: this is equivalent to strongMAC and strongMAC_BT but\n avoids inversions. However, performance are the same as other strongMAC\n approaches - it works only when basis map the same subspaces\n\n - weakMAC_right_orth: weak MAC enforcement [1,3] for state-space models \n with right orthonoraml basis, i.e. V.T V = I. This is like Ref. [1], but\n implemented only on one side.\n\n - weakMAC: implementation of weak MAC enforcement for a general system.\n The method orthonormalises the right basis (V) and then solves the\n orthogonal Procrustes problem.\n\n - for orthonormal basis (V.T V = I): !!! These methods are not tested !!!\n\n - panzer: produces a new reference point based on svd [2]\n - amsallem: project over Vref,WTref [1]\n\n References:\n\n [1] D. Amsallem and C. Farhat, An online method for interpolating linear \n parametric reduced-order models, SIAM J. Sci. Comput., 33 (2011), pp. 2169–2198.\n\n [2] Panzer, J. Mohring, R. Eid, and B. Lohmann, Parametric model order \n reduction by matrix interpolation, at–Automatisierungstechnik, 58 (2010), \n pp. 475–484.\n\n [3] Mahony, R., Sepulchre, R. & Absil, P. -a., 2004. Riemannian Geometry of \n Grassmann Manifolds with a View on Algorithmic Computation. Acta Applicandae \n Mathematicae, 80(2), pp.199–220.\n\n [4] Geuss, M., Panzer, H. & Lohmann, B., 2013. On parametric model order\n reduction by matrix interpolation. 2013 European Control Conference (ECC), \n pp.3433–3438.\n\n\n \"\"\"\n\n def __init__(self, SS, VV=None, WWT=None,\n Vref=None, WTref=None, method_proj=None):\n\n self.SS = SS\n\n self.VV = VV\n self.WWT = WWT\n\n self.Vref = Vref\n self.WTref = WTref\n\n self.method_proj = method_proj\n\n self.Projected = False\n if VV is None or WWT is None:\n self.Projected = True\n self.AA = [ss_here.A for ss_here in SS]\n self.BB = [ss_here.B for ss_here in SS]\n self.CC = [ss_here.C for ss_here in SS]\n\n # projection required for D\n self.DD = [ss_here.D for ss_here in SS]\n\n ### check state-space models\n Nx, Nu, Ny = SS[0].states, SS[0].inputs, SS[0].outputs\n dt = SS[0].dt\n for ss_here in SS:\n assert ss_here.states == Nx, \\\n 'State-space models do not have the same number of states'\n assert ss_here.inputs == Nu, \\\n 'State-space models do not have the same number of inputs'\n assert ss_here.outputs == Ny, \\\n 'State-space models do not have the same number of outputs'\n assert ss_here.dt == dt, \\\n 'State-space models do not have same timestep'\n\n def __call__(self, wv):\n \"\"\"\n Evaluate interpolated model using weights wv.\n \"\"\"\n\n assert self.Projected, ('You must project the state-space models over' +\n ' a common basis before interpolating')\n\n Aint = np.zeros_like(self.AA[0])\n Bint = np.zeros_like(self.BB[0])\n Cint = np.zeros_like(self.CC[0])\n Dint = np.zeros_like(self.DD[0])\n\n for ii in range(len(self.AA)):\n Aint += wv[ii] * self.AA[ii]\n Bint += wv[ii] * self.BB[ii]\n Cint += wv[ii] * self.CC[ii]\n Dint += wv[ii] * self.DD[ii]\n\n return libss.StateSpace(Aint, Bint, Cint, Dint, self.SS[0].dt)\n\n def project(self):\n \"\"\"\n Project the state-space models onto the generalised coordinates of \n state-space model IImap\n \"\"\"\n\n self.AA = []\n self.BB = []\n self.CC = []\n\n self.QQ = []\n self.QQinv = []\n\n if self.method_proj == 'amsallem':\n warnings.warn('Method untested!')\n\n for ii in range(len(self.SS)):\n U, sv, Z = scalg.svd(np.dot(self.VV[ii].T, self.Vref),\n full_matrices=False, overwrite_a=False,\n lapack_driver='gesdd')\n Q = np.dot(U, Z.T)\n U, sv, Z = scalg.svd(np.dot(self.WWT[ii], self.WTref),\n full_matrices=False, overwrite_a=False,\n lapack_driver='gesdd')\n Qinv = np.dot(U, Z.T).T\n self.QQ.append(Q)\n self.QQinv.append(Qinv)\n\n elif self.method_proj == 'panzer':\n warnings.warn('Method untested!')\n\n # generate basis\n U, sv = scalg.svd(np.concatenate(self.VV, axis=1),\n full_matrices=False, overwrite_a=False,\n lapack_driver='gesdd')[:2]\n # chop U\n U = U[:, :self.SS[0].states]\n for ii in range(len(self.SS)):\n Qinv = np.linalg.inv(np.dot(self.WWT[ii], U))\n Q = np.linalg.inv(np.dot(self.VV[ii].T, U))\n self.QQ.append(Q)\n self.QQinv.append(Qinv)\n\n elif self.method_proj == 'leastsq':\n\n for ii in range(len(self.SS)):\n Q, _, _, _ = scalg.lstsq(self.VV[ii], self.Vref)\n print('det(Q): %.3e\\tcond(Q): %.3e' \\\n % (np.linalg.det(Q), np.linalg.cond(Q)))\n # if cond(Q) is small...\n # Qinv = np.linalg.inv(Q)\n P, _, _, _ = scalg.lstsq(self.WWT[ii].T, self.WTref.T)\n self.QQ.append(Q)\n self.QQinv.append(P.T)\n\n elif self.method_proj == 'strongMAC':\n \"\"\"\n Strong MAC enforcements as per Ref.[4]\n \"\"\"\n\n VTVref = np.dot(self.Vref.T, self.Vref)\n for ii in range(len(self.SS)):\n Q = np.linalg.solve(np.dot(self.Vref.T, self.VV[ii]), VTVref)\n Qinv = np.linalg.inv(Q)\n print('det(Q): %.3e\\tcond(Q): %.3e' \\\n % (np.linalg.det(Q), np.linalg.cond(Q)))\n self.QQ.append(Q)\n self.QQinv.append(Qinv)\n\n elif self.method_proj == 'strongMAC_BT':\n \"\"\"\n This is equivalent to Mahony 2004, Eq. 7, for the case of basis\n obtained by balancing. In general, it will fail if VV[ii] and Vref\n do not describe the same subspace\n \"\"\"\n\n for ii in range(len(self.SS)):\n Q = np.linalg.inv(np.dot(self.WTref, self.VV[ii]))\n Qinv = np.dot(self.WTref, self.VV[ii])\n print('det(Q): %.3e\\tcond(Q): %.3e' \\\n % (np.linalg.det(Q), np.linalg.cond(Q)))\n self.QQ.append(Q)\n self.QQinv.append(Qinv)\n\n elif self.method_proj == 'maraniello_BT':\n \"\"\"\n Projection over ii. This is a sort of weak enforcement\n \"\"\"\n\n for ii in range(len(self.SS)):\n Q = np.dot(self.WWT[ii], self.Vref)\n Qinv = np.dot(self.WTref, self.VV[ii])\n print('det(Q): %.3e\\tcond(Q): %.3e' \\\n % (np.linalg.det(Q), np.linalg.cond(Q)))\n self.QQ.append(Q)\n self.QQinv.append(Qinv)\n\n\n elif self.method_proj == 'weakMAC_right_orth':\n \"\"\"\n This is like Amsallem, but only for state-space models with right \n orthogonal basis \n \"\"\"\n\n for ii in range(len(self.SS)):\n Q, sc = scalg.orthogonal_procrustes(self.VV[ii], self.Vref)\n Qinv = Q.T\n print('det(Q): %.3e\\tcond(Q): %.3e' \\\n % (np.linalg.det(Q), np.linalg.cond(Q)))\n self.QQ.append(Q)\n self.QQinv.append(Qinv)\n\n elif self.method_proj == 'weakMAC':\n \"\"\"\n WeakMAC enforcement on the right hand side basis, V\n \"\"\"\n\n # svd of reference\n Uref, svref, Zhref = scalg.svd(self.Vref, full_matrices=False)\n\n for ii in range(len(self.SS)):\n # svd of basis\n Uhere, svhere, Zhhere = scalg.svd(self.VV[ii], full_matrices=False)\n\n R, sc = scalg.orthogonal_procrustes(Uhere, Uref)\n Q = np.dot(np.dot(Zhhere.T, np.diag(svhere ** (-1))), R)\n Qinv = np.dot(R.T, np.dot(np.diag(svhere), Zhhere))\n print('det(Q): %.3e\\tcond(Q): %.3e' \\\n % (np.linalg.det(Q), np.linalg.cond(Q)))\n self.QQ.append(Q)\n self.QQinv.append(Qinv)\n\n else:\n raise NameError('Projection method %s not implemented!' % self.method_proj)\n\n ### Project\n for ii in range(len(self.SS)):\n self.AA.append(np.dot(self.QQinv[ii], np.dot(self.SS[ii].A, self.QQ[ii])))\n self.BB.append(np.dot(self.QQinv[ii], self.SS[ii].B))\n self.CC.append(np.dot(self.SS[ii].C, self.QQ[ii]))\n\n self.Projected = True\n\n\n# ------------------------------------------------------------------------------\n\n\nif __name__ == '__main__':\n import unittest\n\n\n class Test_librom_inter(unittest.TestCase):\n \"\"\" Test methods for DLTI ROM interpolation \"\"\"\n\n def setUp(self):\n # allocate some state-space model (dense and sparse)\n dt = 0.3\n Ny, Nx, Nu = 4, 3, 2\n A = np.random.rand(Nx, Nx)\n B = np.random.rand(Nx, Nu)\n C = np.random.rand(Ny, Nx)\n D = np.random.rand(Ny, Nu)\n self.SS = libss.StateSpace(A, B, C, D, dt=dt)\n\n# class Interp1d():\n# \"\"\"\n# State-space 1D interpolation class.\n\n# This class allows interpolating from a list of state-space models, SS, \n# defined over the 1D parameter space zv. \n\n# State-space models are required to have the same number of inputs and outputs \n# and need to have the same number of states.\n\n# For state-space interpolation, state-space models also need to be defined\n# over the same set of generalised coordinates. If this is not the case, the\n# projection matrices W and T, such that\n\n# A_proj = W^T A V\n\n# also need to be provided. This will allow projecting the state-space models\n# onto a common set of generalised coordinates before interpoling.\n\n# Inputs:\n# - method_interp: interpolation method as per scipy.interpolate.interp1d class\n\n# - method_proj: method for projection of state-space models over common\n# coordinates. Available:\n# - panzer: Panzer, J. Mohring, R. Eid, and B. Lohmann, Parametric model \n# order reduction by matrix interpolation, at–Automatisierungstechnik, 58 \n# (2010), pp. 475–484.\n# - amsallem: D. Amsallem and C. Farhat, An online method for interpolating \n# linear parametric reduced-order models, SIAM J. Sci. Comput., 33 (2011), \n# pp. 2169–2198.\n# Note that 'panzel' and 'amsallem' only apply to orthogonal basis WT,V.\n\n\n# - Map: map A matrices over Riemannian manifold \n\n# - IImap=if given, maps A matrices over manifold derived around A matrix \n# of ii-th state-space in SSlist. \n# \"\"\"\n\n\n# def __init__(self, zv, SS, VV=None, WW=None, method_interp='cubic', \n# method_proj='panzer', Map=True, IImap=None):\n\n# assert IImap is not None, 'Option IImap=None not developed yet'\n\n# self.SS=SS\n# self.zv=zv\n# self.VV=VV\n# self.WW=WW\n# self.method_interp=method_interp\n# self.method_proj=method_proj\n# self.Map=Map\n# self.IImap=IImap\n\n# ### check state-space models\n# Nx,Nu,Ny = SS[0].states, SS[0].inputs, SS[0].outputs\n# for ss_here in SS:\n# assert ss_here.states == Nx,\\\n# 'State-space models do not have the same number of states'\n# assert ss_here.inputs == Nu,\\\n# 'State-space models do not have the same number of inputs'\n# assert ss_here.outputs == Ny,\\\n# 'State-space models do not have the same number of outputs'\n\n# self.debug=False # debug mode flag\n\n\n# def __call__(self, zint):\n# \"\"\"\n# Evaluate at interpolation point zint. Returns a list of classes StateSpace\n# \"\"\"\n\n# Nint=len(zint)\n\n# # interpolate A matrices, \n# if self.Map is True:\n# IImap=self.IImap\n# if IImap is not None:\n# # get inverse,\n# AIIinv=np.linalg.inv(self.SS[IImap].A)\n# # map,\n# TT=[]\n# for ii in range( len(self.zv) ):\n# TT.append(scalg.logm( np.dot(self.SS[ii].A,AIIinv) ))\n# # interpolate\n# TTint=self._interp_mats(TT, zint)\n# # and map back\n\n# Aint=np.zeros( (Nint,)+AIIinv.shape )\n# for ii in range(Nint):\n# Aint[ii,:,:]= np.dot( scalg.expm(TTint[ii,:,:]), self.SS[IImap].A)\n\n# else:\n# # get index of closest A for each element in zint and define mapping\n# pass\n\n# else:\n# Aint=self._interp_mats( \n# [getattr(ss_here,'A') for ss_here in self.SS], zint)\n\n# # and B, C, D...\n# Bint=self._interp_mats( \n# [getattr(ss_here,'B') for ss_here in self.SS], zint)\n# Cint=self._interp_mats( \n# [getattr(ss_here,'C') for ss_here in self.SS], zint) \n# Dint=self._interp_mats( \n# [getattr(ss_here,'D') for ss_here in self.SS], zint)\n\n# # and pack everything\n# SSint=[]\n# for ii in range(Nint):\n# SSint.append( StateSpace( Aint[ii,:,:], Bint[ii,:,:],\n# Cint[ii,:,:], Dint[ii,:,:], dt=self.SS[0].dt))\n\n# return SSint\n\n\n# def _interp_mats(self,Mats,zint):\n# \"\"\"\n# Interpolate a list of equal-size arrays, Mats, defined over zv at the \n# points zint. The Mats are assumed to be defined onto the same set of\n# generalised coordinates.\n# \"\"\"\n\n# # define interpolator class\n# # try:\n# IntA=scint.interp1d(self.zv,Mats,kind=self.method_interp,\n# copy=False,assume_sorted=True,axis=0) \n\n# return IntA(zint)\n\n\n# def project(self):\n# \"\"\"\n# Project the state-space models onto the generalised coordinates of \n# state-space model IImap\n# \"\"\"\n\n\n# if self.method_proj=='amsallem':\n\n# # get reference basis\n# Vref=self.VV[self.IImap]\n# Wref=self.WW[self.IImap]\n\n# for ii in range(len(self.SS)):\n\n# if ii == self.IImap:\n# continue \n\n# # get rotations\n# U,sv,Z = scalg.svd( np.dot(self.VV[ii].T, Vref) ,\n# full_matrices=False,overwrite_a=False,\n# lapack_driver='gesdd')\n# RotV = np.dot(U,Z.T)\n\n# U,sv,Z = scalg.svd( np.dot(self.WW[ii].T, Wref) ,\n# full_matrices=False,overwrite_a=False,\n# lapack_driver='gesdd')\n# RotW = np.dot(U,Z.T)\n\n\n# # project state-space\n# self.SS[ii].project(RotW.T,RotV)\n\n\n# elif self.method_proj=='panzer':\n\n# # generate basis\n# U,sv = scalg.svd( np.concatenate(self.VV,axis=1),\n# full_matrices=False,overwrite_a=False,\n# lapack_driver='gesdd')[:2]\n# # chop U\n# U=U[:,:self.SS[0].states]#*sv[:self.SS[0].states]\n# print('Panzer projection: neglecting singular values below %.2e (max: %.2e)'\\\n# %(sv[self.SS[0].states],sv[0]) )\n\n\n# for ii in range(len(self.SS)):\n\n# # get projection matrices\n# M = np.linalg.inv( np.dot( self.WW[ii].T, U) )\n# N = np.linalg.inv( np.dot( self.VV[ii].T, U) )\n\n# # project\n# self.SS[ii].project(M,N)\n\n# else:\n# raise NameError('Projection method %s not implemented!' %self.method_proj)\n" }, { "path": "sharpy/sharpy_main.py", "content": "\"\"\"sharpy_main: Where it all starts\n\n\"\"\"\nimport warnings\nimport sys\nimport dill as pickle\nfrom sharpy.utils import cout_utils as cout\nfrom .version import __version__\n\n\ndef main(args=None, sharpy_input_dict=None):\n \"\"\"\n Main ``SHARPy`` routine\n\n This is the main ``SHARPy`` routine.\n It starts the solution process by reading the settings that are\n included in the ``.sharpy`` file that is parsed\n as an argument, or an equivalent dictionary given as ``sharpy_input_dict``.\n It reads the solvers specific settings and runs them in order\n\n Args:\n args (str): ``.sharpy`` file with the problem information and settings\n sharpy_input_dict (dict): ``dict`` with the same contents as the\n ``solver.txt`` file would have.\n\n Returns:\n sharpy.presharpy.presharpy.PreSharpy: object containing the simulation results.\n\n \"\"\"\n import time\n import argparse\n\n import sharpy.utils.input_arg as input_arg\n import sharpy.utils.solver_interface as solver_interface\n from sharpy.presharpy.presharpy import PreSharpy\n from sharpy.utils.cout_utils import start_writer, finish_writer\n import logging\n import os\n\n import h5py\n import sharpy.utils.h5utils as h5utils\n\n # Loading solvers and postprocessors\n import sharpy.solvers\n import sharpy.postproc\n import sharpy.generators\n import sharpy.controllers\n # ------------\n\n try:\n # output writer\n start_writer()\n # timing\n t = time.process_time()\n t0_wall = time.perf_counter()\n\n if sharpy_input_dict is None:\n parser = argparse.ArgumentParser(prog='SHARPy', description=\n \"\"\"This is the executable for Simulation of High Aspect Ratio Planes.\\n\n Imperial College London 2024\"\"\")\n parser.add_argument('input_filename', help='path to the *.sharpy input file', type=str, default='')\n parser.add_argument('-r', '--restart', help='restart the solution with a given snapshot', type=str,\n default=None)\n parser.add_argument('-d', '--docs', help='generates the solver documentation in the specified location. '\n 'Code does not execute if running this flag', action='store_true')\n parser.add_argument('-v', '--version', action='version', \n version='Running %(prog)s version {version}'.format(version=__version__))\n if args is not None:\n args = parser.parse_args(args[1:])\n else:\n args = parser.parse_args()\n\n if args.docs:\n import subprocess\n import sharpy.utils.docutils as docutils\n import sharpy.utils.sharpydir as sharpydir\n docutils.generate_documentation()\n\n # run make\n cout.cout_wrap('Running make html in sharpy/docs')\n subprocess.Popen(['make', 'html'],\n stdout=None,\n cwd=sharpydir.SharpyDir + '/docs')\n\n return 0\n\n if args.input_filename == '':\n parser.error('input_filename is a required argument of SHARPy.')\n settings = input_arg.read_settings(args)\n missing_solvers = False\n if args.restart is None:\n # run preSHARPy\n data = PreSharpy(settings)\n solvers = dict()\n restart = False\n else:\n try:\n with open(args.restart, 'rb') as restart_file:\n data = pickle.load(restart_file)\n try:\n solvers = pickle.load(restart_file)\n except EOFError:\n # For backwards compatibility\n missing_solvers = True\n solvers = dict()\n cout.cout_wrap('Solvers not found in Pickle file. Using the settings in *.sharpy file.')\n if \"UpdatePickle\" in solvers.keys():\n # For backwards compatibility\n missing_solvers = True\n solvers = dict()\n except FileNotFoundError:\n raise FileNotFoundError('The file specified for the snapshot \\\n restart (-r) does not exist. Please check.')\n\n restart = True\n # update the settings\n data.update_settings(settings)\n\n # Read again the dyn.h5 file\n data.structure.dynamic_input = []\n dyn_file_name = data.case_route + '/' + data.case_name + '.dyn.h5'\n if os.path.isfile(dyn_file_name):\n fid = h5py.File(dyn_file_name, 'r')\n data.structure.dyn_dict = h5utils.load_h5_in_dict(fid)\n # for it in range(self.num_steps):\n # data.structure.dynamic_input.append(dict())\n\n # Restart the solvers\n old_solvers_list = list(solvers.keys())\n for old_solver_name in old_solvers_list:\n if old_solver_name not in settings['SHARPy']['flow']:\n del solvers[old_solver_name] \n\n # Loop for the solvers specified in *.sharpy['SHARPy']['flow']\n for solver_name in settings['SHARPy']['flow']:\n if (args.restart is None) or (solver_name not in solvers.keys()) or (missing_solvers):\n solvers[solver_name] = solver_interface.initialise_solver(solver_name)\n if missing_solvers:\n solvers[solver_name].initialise(data, restart=False)\n else:\n solvers[solver_name].initialise(data, restart=restart)\n data = solvers[solver_name].run(solvers=solvers)\n solvers[solver_name].teardown()\n\n cpu_time = time.process_time() - t\n wall_time = time.perf_counter() - t0_wall\n cout.cout_wrap('FINISHED - Elapsed time = %f6 seconds' % wall_time, 2)\n cout.cout_wrap('FINISHED - CPU process time = %f6 seconds' % cpu_time, 2)\n finish_writer()\n\n except Exception as e:\n try:\n logdir = settings['SHARPy']['log_folder'] + '/' + settings['SHARPy']['case']\n except KeyError:\n logdir = './'\n except NameError:\n logdir = './'\n logdir = os.path.abspath(logdir)\n cout.cout_wrap(('Exception raised, writing error log in %s/error.log' % logdir), 4)\n logging.basicConfig(filename='%s/error.log' % logdir,\n filemode='w',\n format='%(asctime)s-%(levelname)s-%(message)s',\n datefmt='%d-%b-%y %H:%M:%S',\n level=logging.INFO)\n logging.info('SHARPy Error Log')\n logging.error(\"Exception occurred\", exc_info=True)\n raise e\n\n return data\n\n\n\ndef sharpy_run():\n \"\"\"\n This is a wrapper function for the console command \"sharpy\"\n \"\"\"\n data = None\n with warnings.catch_warnings():\n warnings.simplefilter('ignore')\n data = main(sys.argv)\n" }, { "path": "sharpy/solvers/__init__.py", "content": "import importlib\nimport os\n\nimport sharpy.utils.solver_interface as solver_interface\nimport sharpy.utils.sharpydir as sharpydir\n\nfiles = solver_interface.solver_list_from_path(os.path.dirname(__file__))\n\nimport_path = os.path.realpath(os.path.dirname(__file__))\nimport_path = import_path.replace(sharpydir.SharpyDir, \"\")\nif import_path[0] == \"/\": import_path = import_path[1:]\nimport_path = import_path.replace(\"/\", \".\")\n\nfor file in sorted(files):\n solver_interface.solvers[file] = importlib.import_module(import_path + \".\" + file)\n" }, { "path": "sharpy/solvers/_basestructural.py", "content": "from sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.cout_utils as cout\n\n@solver\nclass _BaseStructural(BaseSolver):\n \"\"\"\n Structural solver used for the dynamic simulation of free-flying structures.\n\n This solver provides an interface to the structural library (``xbeam``) and updates the structural parameters\n for every time step of the simulation.\n\n This solver is called as part of a standalone structural simulation.\n\n \"\"\"\n solver_id = '_BaseStructural'\n solver_classification = 'structural'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Print output to screen'\n\n settings_types['max_iterations'] = 'int'\n settings_default['max_iterations'] = 100\n settings_description['max_iterations'] = 'Sets maximum number of iterations'\n\n settings_types['num_load_steps'] = 'int'\n settings_default['num_load_steps'] = 1\n\n settings_types['delta_curved'] = 'float'\n settings_default['delta_curved'] = 1e-2\n\n settings_types['min_delta'] = 'float'\n settings_default['min_delta'] = 1e-5\n settings_description['min_delta'] = 'Structural solver relative tolerance'\n\n settings_types['abs_threshold'] = 'float'\n settings_default['abs_threshold'] = 1e-13\n settings_description['abs_threshold'] = 'Structural solver absolute tolerance'\n\n settings_types['newmark_damp'] = 'float'\n settings_default['newmark_damp'] = 1e-4\n settings_description['newmark_damp'] = 'Sets the Newmark damping coefficient'\n\n settings_types['gravity_on'] = 'bool'\n settings_default['gravity_on'] = False\n settings_description['gravity_on'] = 'Flag to include gravitational forces'\n\n settings_types['gravity'] = 'float'\n settings_default['gravity'] = 9.81\n settings_description['gravity'] = 'Gravitational acceleration'\n\n settings_types['gravity_dir'] = 'list(float)'\n settings_default['gravity_dir'] = [0., 0., 1.]\n settings_description['gravity_dir'] = 'Direction in G where gravity applies'\n\n settings_types['relaxation_factor'] = 'float'\n settings_default['relaxation_factor'] = 0.3\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = 0.01\n settings_description['dt'] = 'Time step increment'\n\n settings_types['num_steps'] = 'int'\n settings_default['num_steps'] = 500\n\n def initialise(self, data, restart=False):\n pass\n\n def run(self, **kwargs):\n pass\n" }, { "path": "sharpy/solvers/aerogridloader.py", "content": "import h5py as h5\nimport numpy as np\n\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.aero.models.aerogrid as aerogrid\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.h5utils as h5utils\nimport sharpy.utils.generator_interface as gen_interface\nfrom sharpy.solvers.gridloader import GridLoader\n\n\n@solver\nclass AerogridLoader(GridLoader):\n \"\"\"\n ``AerogridLoader`` class, inherited from ``GridLoader``\n\n Generates aerodynamic grid based on the input data\n\n The initial wake shape is now defined in SHARPy (instead of UVLM) through a wake shape generator\n ``wake_shape_generator`` and the required inputs ``wake_shape_generator_input``. The supported wake generators are\n :class:`sharpy.generators.straightwake.StraighWake` and :class:`sharpy.generators.helicoidalwake.HelicoidalWake`.\n\n The ``control_surface_deflection`` setting allows the user to use a time specific control surface deflection,\n should the problem include them. This setting takes a list of strings, each for the required control\n surface generator.\n\n The ``control_surface_deflection_generator_settings`` setting is a list of dictionaries, one for each control\n surface. The dictionaries specify the settings for the generator ``DynamicControlSurface``. If the relevant control\n surface is simply static, an empty string should be parsed. See the documentation for ``DynamicControlSurface``\n generators for accepted key-value pairs as settings.\n\n The ``initial_align`` setting aligns the wing panel discretization with the freestream for the undeformed structure, \n and applies this Z rotation at every timestep (panels become misaligned when the wing deforms). The ``aligned_grid`` \n setting aligns the wing panel discretization with the flow at every time step and takes precedence.\n\n Args:\n data (PreSharpy): ``ProblemData`` class structure\n\n Attributes:\n settings (dict): Name-value pair of the settings employed by the aerodynamic solver\n settings_types (dict): Acceptable types for the values in ``settings``\n settings_default (dict): Name-value pair of default values for the aerodynamic settings\n data (ProblemData): class structure\n file_name (str): name of the ``.aero.h5`` HDF5 file\n aero: empty attribute\n data_dict (dict): key-value pairs of aerodynamic data\n wake_shape_generator (class): Wake shape generator\n\n \"\"\"\n solver_id = 'AerogridLoader'\n solver_classification = 'loader'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['unsteady'] = 'bool'\n settings_default['unsteady'] = False\n settings_description['unsteady'] = 'Unsteady effects'\n\n settings_types['aligned_grid'] = 'bool'\n settings_default['aligned_grid'] = True\n settings_description['aligned_grid'] = 'Align grid'\n\n settings_types['initial_align'] = 'bool'\n settings_default['initial_align'] = True\n settings_description['initial_align'] = \"Initially align grid\"\n\n settings_types['freestream_dir'] = 'list(float)'\n settings_default['freestream_dir'] = [1.0, 0.0, 0.0]\n settings_description['freestream_dir'] = 'Free stream flow direction'\n\n settings_types['mstar'] = ['int', 'list(int)']\n settings_default['mstar'] = 10\n settings_description['mstar'] = 'Number of chordwise wake panels'\n\n settings_types['control_surface_deflection'] = 'list(str)'\n settings_default['control_surface_deflection'] = []\n settings_description['control_surface_deflection'] = 'List of control surface generators for each control surface'\n\n settings_types['control_surface_deflection_generator_settings'] = 'dict'\n settings_default['control_surface_deflection_generator_settings'] = dict()\n settings_description['control_surface_deflection_generator_settings'] = 'List of dictionaries with the settings ' \\\n 'for each generator'\n\n settings_types['wake_shape_generator'] = 'str'\n settings_default['wake_shape_generator'] = 'StraightWake'\n settings_description['wake_shape_generator'] = 'ID of the generator to define the initial wake shape'\n settings_options['wake_shape_generator'] = ['StraightWake', 'HelicoidalWake']\n\n settings_types['wake_shape_generator_input'] = 'dict'\n settings_default['wake_shape_generator_input'] = dict()\n settings_description['wake_shape_generator_input'] = 'Dictionary of inputs needed by the wake shape generator'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description,\n settings_options=settings_options)\n\n def __init__(self):\n super().__init__\n self.file_name = '.aero.h5'\n self.aero = None\n self.wake_shape_generator = None\n\n def initialise(self, data, restart=False):\n super().initialise(data)\n\n wake_shape_generator_type = gen_interface.generator_from_string(\n self.settings['wake_shape_generator'])\n self.wake_shape_generator = wake_shape_generator_type()\n self.wake_shape_generator.initialise(data,\n self.settings['wake_shape_generator_input'],\n restart=restart)\n\n def run(self, **kwargs):\n self.data.aero = aerogrid.Aerogrid()\n self.data.aero.generate(self.data_dict,\n self.data.structure,\n self.settings,\n self.data.ts)\n aero_tstep = self.data.aero.timestep_info[self.data.ts]\n self.wake_shape_generator.generate({'zeta': aero_tstep.zeta,\n 'zeta_star': aero_tstep.zeta_star,\n 'gamma': aero_tstep.gamma,\n 'gamma_star': aero_tstep.gamma_star,\n 'dist_to_orig': aero_tstep.dist_to_orig})\n # keep the call to the wake generator\n # because it might be needed by other solvers\n self.data.aero.wake_shape_generator = self.wake_shape_generator\n return self.data\n" }, { "path": "sharpy/solvers/beamloader.py", "content": "import h5py as h5\n\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.structure.models.beam as beam\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.h5utils as h5utils\nimport os\n\n\n@solver\nclass BeamLoader(BaseSolver):\n \"\"\"\n ``BeamLoader`` class solver inherited from ``BaseSolver``\n\n Loads the structural beam solver with the specified user settings.\n\n Args:\n data (ProblemData): class containing the problem information\n\n Attributes:\n settings (dict): contains the specific settings for the solver\n\n settings_types (dict): Key value pairs of the accepted types for the settings values\n settings_default (dict): Dictionary containing the default solver settings, should none be provided.\n data (ProblemData): class containing the data for the problem\n fem_file_name (str): name of the ``.fem.h5`` HDF5 file\n dyn_file_name (str): name of the ``.dyn.h5`` HDF5 file\n fem_data_dict (dict): key-value pairs of FEM data\n dyn_data_dict (dict): key-value pairs of data for dynamic problems\n structure (None): Empty attribute\n\n Notes:\n For further reference on Quaternions see:\n `https://en.wikipedia.org/wiki/Quaternion `_\n\n See Also:\n .. py:class:: sharpy.utils.solver_interface.BaseSolver\n\n .. py:class:: sharpy.structure.models.beam.Beam\n\n \"\"\"\n solver_id = 'BeamLoader'\n solver_classification = 'loader'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['unsteady'] = 'bool'\n settings_default['unsteady'] = True\n settings_description['unsteady'] = 'If ``True`` it will be a dynamic problem and the solver will look for the' \\\n ' ``.dyn.h5`` file that contains the time varying input to the problem.'\n\n settings_types['orientation'] = 'list(float)'\n settings_default['orientation'] = [1., 0, 0, 0]\n settings_description['orientation'] = 'Initial attitude of the structure given as the quaternion that parametrises the rotation from G to A frames of reference.'\n\n settings_types['for_pos'] = 'list(float)'\n settings_default['for_pos'] = [0., 0, 0]\n settings_description['for_pos'] = 'Initial position of the A FoR.'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n self.fem_file_name = ''\n self.dyn_file_name = ''\n # storage of file contents\n self.fem_data_dict = dict()\n self.dyn_data_dict = dict()\n self.mb_data_dict = dict()\n\n # structure storage\n self.structure = None\n\n def initialise(self, data, restart=False):\n self.data = data\n self.settings = data.settings[self.solver_id]\n\n # init settings\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n # read input files (fem and dyn)\n self.read_files()\n\n def read_files(self):\n # open fem file\n # first, file names\n self.fem_file_name = self.data.case_route + '/' + self.data.case_name + '.fem.h5'\n if self.settings['unsteady']:\n self.dyn_file_name = self.data.case_route + '/' + self.data.case_name + '.dyn.h5'\n # then check that the files exists\n h5utils.check_file_exists(self.fem_file_name)\n if self.settings['unsteady']:\n try:\n h5utils.check_file_exists(self.dyn_file_name)\n except FileNotFoundError:\n self.settings['unsteady'] = False\n # read and store the hdf5 files\n with h5.File(self.fem_file_name, 'r') as fem_file_handle:\n # store files in dictionary\n self.fem_data_dict = h5utils.load_h5_in_dict(fem_file_handle)\n # TODO implement fem file validation\n # self.validate_fem_file()\n if self.settings['unsteady']:\n with h5.File(self.dyn_file_name, 'r') as dyn_file_handle:\n # store files in dictionary\n self.dyn_data_dict = h5utils.load_h5_in_dict(dyn_file_handle)\n # TODO implement dyn file validation\n # self.validate_dyn_file()\n\n # Multibody information\n self.mb_file_name = self.data.case_route + '/' + self.data.case_name + '.mb.h5'\n if os.path.isfile(self.mb_file_name):\n # h5utils.check_file_exists(self.mb_file_name)\n with h5.File(self.mb_file_name, 'r') as mb_file_handle:\n self.mb_data_dict = h5utils.load_h5_in_dict(mb_file_handle)\n\n # Need to redefine strings to remove the \"b\" at the beginning\n for iconstraint in range(self.mb_data_dict['num_constraints']):\n self.mb_data_dict[\"constraint_%02d\" % iconstraint]['behaviour'] = self.mb_data_dict[\"constraint_%02d\" % iconstraint]['behaviour'].decode()\n for ibody in range(self.mb_data_dict['num_bodies']):\n self.mb_data_dict[\"body_%02d\" % ibody]['FoR_movement'] = self.mb_data_dict[\"body_%02d\" % ibody]['FoR_movement'].decode()\n\n def validate_fem_file(self):\n raise NotImplementedError('validation of the fem file in beamloader is not yet implemented!')\n\n def validate_dyn_file(self):\n raise NotImplementedError('validation of the dyn file in beamloader is not yet implemented!')\n\n def run(self, **kwargs):\n self.data.structure = beam.Beam()\n self.data.structure.ini_mb_dict = self.mb_data_dict\n self.data.structure.generate(self.fem_data_dict, self.settings)\n self.data.structure.dyn_dict = self.dyn_data_dict\n\n return self.data\n" }, { "path": "sharpy/solvers/dynamiccoupled.py", "content": "import ctypes as ct\nimport time\nimport copy\nimport threading\nimport logging\nimport concurrent.futures\nimport queue\n\nimport numpy as np\n\nimport sharpy.aero.utils.mapping as mapping\nimport sharpy.utils.cout_utils as cout\nimport sharpy.utils.solver_interface as solver_interface\nimport sharpy.utils.controller_interface as controller_interface\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.exceptions as exc\nimport sharpy.io.network_interface as network_interface\nimport sharpy.utils.generator_interface as gen_interface\n\n\n@solver\nclass DynamicCoupled(BaseSolver):\n \"\"\"\n The :class:`~sharpy.solvers.dynamiccoupled.DynamicCoupled` solver couples the aerodynamic and structural solvers\n of choice to march forward in time the aeroelastic system's solution.\n\n Using the :class:`~sharpy.solvers.dynamiccoupled.DynamicCoupled` solver requires that an instance of the\n ``StaticCoupled`` solver is called in the SHARPy solution ``flow`` when defining the problem case.\n\n Input data (from external controllers) can be received and data sent using the SHARPy network\n interface, specified through the setting ``network_settings`` of this solver. For more detail on how to send\n and receive data see the :class:`~sharpy.io.network_interface.NetworkLoader` documentation.\n\n Changes to the structural properties or external forces that depend on the instantaneous situation of the system\n can be applied through ``runtime_generators``. These runtime generators are parsed through dictionaries, with the\n key being the name of the generator and the value the settings for such generator. The currently available\n ``runtime_generators`` are :class:`~sharpy.generators.externalforces.ExternalForces` and\n :class:`~sharpy.generators.modifystructure.ModifyStructure`.\n\n \"\"\"\n solver_id = 'DynamicCoupled'\n solver_classification = 'Coupled'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Write status to screen'\n\n settings_types['structural_solver'] = 'str'\n settings_default['structural_solver'] = None\n settings_description['structural_solver'] = 'Structural solver to use in the coupled simulation'\n\n settings_types['structural_solver_settings'] = 'dict'\n settings_default['structural_solver_settings'] = None\n settings_description['structural_solver_settings'] = 'Dictionary of settings for the structural solver'\n\n settings_types['aero_solver'] = 'str'\n settings_default['aero_solver'] = None\n settings_description['aero_solver'] = 'Aerodynamic solver to use in the coupled simulation'\n\n settings_types['aero_solver_settings'] = 'dict'\n settings_default['aero_solver_settings'] = None\n settings_description['aero_solver_settings'] = 'Dictionary of settings for the aerodynamic solver'\n\n settings_types['n_time_steps'] = 'int'\n settings_default['n_time_steps'] = None\n settings_description['n_time_steps'] = 'Number of time steps for the simulation'\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = None\n settings_description['dt'] = 'Time step'\n\n settings_types['fsi_substeps'] = 'int'\n settings_default['fsi_substeps'] = 70\n settings_description['fsi_substeps'] = 'Max iterations in the FSI loop'\n\n settings_types['fsi_tolerance'] = 'float'\n settings_default['fsi_tolerance'] = 1e-5\n settings_description['fsi_tolerance'] = 'Convergence threshold for the FSI loop'\n\n settings_types['structural_substeps'] = 'int'\n settings_default['structural_substeps'] = 0 # 0 is normal coupled sim.\n settings_description['structural_substeps'] = 'Number of extra structural time steps per aero time step. ``0`` ' \\\n 'is a fully coupled simulation.'\n\n settings_types['relaxation_factor'] = 'float'\n settings_default['relaxation_factor'] = 0.2\n settings_description['relaxation_factor'] = 'Relaxation parameter in the FSI iteration. ``0`` is no relaxation ' \\\n 'and -> ``1`` is very relaxed'\n\n settings_types['final_relaxation_factor'] = 'float'\n settings_default['final_relaxation_factor'] = 0.0\n settings_description['final_relaxation_factor'] = 'Relaxation factor reached in ``relaxation_steps`` with ' \\\n '``dynamic_relaxation`` on'\n\n settings_types['minimum_steps'] = 'int'\n settings_default['minimum_steps'] = 3\n settings_description['minimum_steps'] = 'Number of minimum FSI iterations before convergence'\n\n settings_types['relaxation_steps'] = 'int'\n settings_default['relaxation_steps'] = 100\n settings_description['relaxation_steps'] = 'Length of the relaxation factor ramp between ``relaxation_factor`` ' \\\n 'and ``final_relaxation_factor`` with ``dynamic_relaxation`` on'\n\n settings_types['dynamic_relaxation'] = 'bool'\n settings_default['dynamic_relaxation'] = False\n settings_description['dynamic_relaxation'] = 'Controls if relaxation factor is modified during the FSI iteration ' \\\n 'process'\n\n settings_types['postprocessors'] = 'list(str)'\n settings_default['postprocessors'] = list()\n settings_description['postprocessors'] = 'List of the postprocessors to run at the end of every time step'\n\n settings_types['postprocessors_settings'] = 'dict'\n settings_default['postprocessors_settings'] = dict()\n settings_description['postprocessors_settings'] = 'Dictionary with the applicable settings for every ' \\\n '' \\\n '``postprocessor``. Every ``postprocessor`` needs its entry, ' \\\n 'even if empty'\n\n settings_types['controller_id'] = 'dict'\n settings_default['controller_id'] = dict()\n settings_description['controller_id'] = 'Dictionary of id of every controller (key) and its type (value)'\n\n settings_types['controller_settings'] = 'dict'\n settings_default['controller_settings'] = dict()\n settings_description['controller_settings'] = 'Dictionary with settings (value) of every controller id (key)'\n\n settings_types['cleanup_previous_solution'] = 'bool'\n settings_default['cleanup_previous_solution'] = False\n settings_description['cleanup_previous_solution'] = 'Controls if previous ``timestep_info`` arrays are ' \\\n 'reset before running the solver'\n\n settings_types['include_unsteady_force_contribution'] = 'bool'\n settings_default['include_unsteady_force_contribution'] = False\n settings_description['include_unsteady_force_contribution'] = 'If on, added mass contribution is added to the ' \\\n 'forces. This depends on the time derivative of ' \\\n 'the bound circulation. Check ``filter_gamma_dot`` ' \\\n 'in the aero solver'\n\n settings_types['steps_without_unsteady_force'] = 'int'\n settings_default['steps_without_unsteady_force'] = 0\n settings_description['steps_without_unsteady_force'] = 'Number of initial timesteps that don\\'t include unsteady ' \\\n 'forces contributions. This avoids oscillations due to ' \\\n 'no perfectly trimmed initial conditions'\n\n settings_types['pseudosteps_ramp_unsteady_force'] = 'int'\n settings_default['pseudosteps_ramp_unsteady_force'] = 0\n settings_description['pseudosteps_ramp_unsteady_force'] = 'Length of the ramp with which unsteady force ' \\\n 'contribution is introduced every time step during ' \\\n 'the FSI iteration process'\n\n settings_types['correct_forces_method'] = 'str'\n settings_default['correct_forces_method'] = ''\n settings_description['correct_forces_method'] = 'Function used to correct aerodynamic forces. ' \\\n 'See :py:mod:`sharpy.generators.polaraeroforces`'\n settings_options['correct_forces_method'] = ['EfficiencyCorrection', 'PolarCorrection']\n\n settings_types['correct_forces_settings'] = 'dict'\n settings_default['correct_forces_settings'] = {}\n settings_description['correct_forces_settings'] = 'Settings for corrected forces evaluation'\n\n settings_types['network_settings'] = 'dict'\n settings_default['network_settings'] = dict()\n settings_description['network_settings'] = 'Network settings. See ' \\\n ':class:`~sharpy.io.network_interface.NetworkLoader` for supported ' \\\n 'entries'\n\n settings_types['runtime_generators'] = 'dict'\n settings_default['runtime_generators'] = dict()\n settings_description['runtime_generators'] = 'The dictionary keys are the runtime generators to be used. ' \\\n 'The dictionary values are dictionaries with the settings ' \\\n 'needed by each generator.'\n\n settings_types['nonlifting_body_interactions'] = 'bool'\n settings_default['nonlifting_body_interactions'] = False\n settings_description['nonlifting_body_interactions'] = 'Effect of Nonlifting Bodies on Lifting bodies are considered'\n \n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description, settings_options)\n\n def __init__(self):\n self.data = None\n self.settings = None\n self.structural_solver = None\n self.aero_solver = None\n self.print_info = False\n\n self.res = 0.0\n self.res_dqdt = 0.0\n self.res_dqddt = 0.0\n\n self.previous_force = None\n\n self.dt = 0.\n self.substep_dt = 0.\n self.initial_n_substeps = None\n\n self.predictor = False\n self.residual_table = None\n self.postprocessors = dict()\n self.with_postprocessors = False\n self.controllers = None\n\n self.time_aero = 0.\n self.time_struc = 0.\n\n self.correct_forces = False\n self.correct_forces_generator = None\n\n self.logger = logging.getLogger(__name__) # used with the network interface\n\n # variables to send and receive\n self.network_loader = None\n self.set_of_variables = None\n\n self.runtime_generators = dict()\n self.with_runtime_generators = False\n\n def get_g(self):\n \"\"\"\n Getter for ``g``, the gravity value\n \"\"\"\n return self.structural_solver.settings['gravity']\n\n def set_g(self, new_g):\n \"\"\"\n Setter for ``g``, the gravity value\n \"\"\"\n self.structural_solver.settings['gravity'] = ct.c_double(new_g)\n\n def get_rho(self):\n \"\"\"\n Getter for ``rho``, the density value\n \"\"\"\n return self.aero_solver.settings['rho']\n\n def set_rho(self, new_rho):\n \"\"\"\n Setter for ``rho``, the density value\n \"\"\"\n self.aero_solver.settings['rho'] = ct.c_double(new_rho)\n\n def initialise(self, data, custom_settings=None, restart=False):\n \"\"\"\n Controls the initialisation process of the solver, including processing\n the settings and initialising the aero and structural solvers, postprocessors\n and controllers.\n \"\"\"\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n options=self.settings_options)\n\n self.original_settings = copy.deepcopy(self.settings)\n\n self.dt = self.settings['dt']\n self.substep_dt = (\n self.dt/(self.settings['structural_substeps'] + 1))\n self.initial_n_substeps = self.settings['structural_substeps']\n\n self.print_info = self.settings['print_info']\n if self.settings['cleanup_previous_solution']:\n # if there's data in timestep_info[>0], copy the last one to\n # timestep_info[0] and remove the rest\n self.cleanup_timestep_info()\n\n if not restart:\n self.structural_solver = solver_interface.initialise_solver(\n self.settings['structural_solver'])\n self.aero_solver = solver_interface.initialise_solver(\n self.settings['aero_solver'])\n self.structural_solver.initialise(\n self.data, self.settings['structural_solver_settings'],\n restart=restart)\n self.aero_solver.initialise(self.structural_solver.data,\n self.settings['aero_solver_settings'],\n restart=restart)\n self.data = self.aero_solver.data\n\n # initialise postprocessors\n if self.settings['postprocessors']:\n self.with_postprocessors = True\n # Remove previous postprocessors not required on restart\n old_list = list(self.postprocessors.keys())\n for old_list_name in old_list:\n if old_list_name not in self.settings['postprocessors']:\n del self.postprocessors[old_list_name] \n for postproc in self.settings['postprocessors']:\n if not postproc in self.postprocessors.keys():\n self.postprocessors[postproc] = solver_interface.initialise_solver(\n postproc)\n self.postprocessors[postproc].initialise(\n self.data, self.settings['postprocessors_settings'][postproc], caller=self,\n restart=restart)\n\n # initialise controllers\n self.with_controllers = False\n if self.settings['controller_id']:\n self.with_controllers = True\n # Remove previous controllers not required on restart\n if self.controllers is not None:\n old_list = list(self.controllers.keys())\n for old_list_name in old_list:\n if old_list_name not in self.settings['controller_id']:\n del self.controllers[old_list_name] \n for controller_id, controller_type in self.settings['controller_id'].items():\n if self.controllers is not None:\n if not controller_id in self.controllers.keys():\n self.controllers[controller_id] = (\n controller_interface.initialise_controller(controller_type))\n else:\n self.controllers = dict()\n self.controllers[controller_id] = (\n controller_interface.initialise_controller(controller_type))\n self.controllers[controller_id].initialise(self.data,\n self.settings['controller_settings'][controller_id],\n controller_id, restart=restart)\n \n # print information header\n if self.print_info:\n self.residual_table = cout.TablePrinter(8, 12, ['g', 'f', 'g', 'f', 'f', 'f', 'e', 'e'])\n self.residual_table.field_length[0] = 5\n self.residual_table.field_length[1] = 6\n self.residual_table.field_length[2] = 4\n self.residual_table.print_header(['ts', 't', 'iter', 'struc ratio', 'iter time', 'residual vel',\n 'FoR_vel(x)', 'FoR_vel(z)'])\n\n # Define the function to correct aerodynamic forces\n if self.settings['correct_forces_method'] != '':\n self.correct_forces = True\n self.correct_forces_generator = gen_interface.generator_from_string(self.settings['correct_forces_method'])()\n self.correct_forces_generator.initialise(in_dict=self.settings['correct_forces_settings'],\n aero=self.data.aero,\n structure=self.data.structure,\n rho=self.settings['aero_solver_settings']['rho'],\n vortex_radius=self.settings['aero_solver_settings']['vortex_radius'],\n output_folder = self.data.output_folder)\n\n # check for empty dictionary\n if self.settings['network_settings']:\n self.network_loader = network_interface.NetworkLoader()\n self.network_loader.initialise(in_settings=self.settings['network_settings'])\n\n # initialise runtime generators\n if self.settings['runtime_generators']:\n self.with_runtime_generators = True\n # Remove previous runtime generators not required on restart\n old_list = list(self.runtime_generators.keys())\n for old_list_name in old_list:\n if old_list_name not in self.settings['runtime_generators']:\n del self.runtime_generators[old_list_name] \n for rg_id, param in self.settings['runtime_generators'].items():\n if not rg_id in self.runtime_generators.keys():\n gen = gen_interface.generator_from_string(rg_id)\n self.runtime_generators[rg_id] = gen()\n self.runtime_generators[rg_id].initialise(param, data=self.data, restart=restart)\n\n def cleanup_timestep_info(self):\n if max(len(self.data.aero.timestep_info), len(self.data.structure.timestep_info)) > 1:\n self.remove_old_timestep_info(self.data.structure.timestep_info)\n self.remove_old_timestep_info(self.data.aero.timestep_info) \n if self.settings['nonlifting_body_interactions']:\n self.remove_old_timestep_info(self.data.nonlifting_body.timestep_info)\n\n self.data.ts = 0\n\n def remove_old_timestep_info(self, tstep_info):\n # copy last info to first\n tstep_info[0] = tstep_info[-1].copy()\n # delete all the rest\n while len(tstep_info) - 1:\n del tstep_info[-1]\n\n def process_controller_output(self, controlled_state):\n \"\"\"\n This function modified the solver properties and parameters as\n requested from the controller.\n\n This keeps the main loop much cleaner, while allowing for flexibility\n\n Please, if you add options in here, always code the possibility of\n that specific option not being there without the code complaining to\n the user.\n\n If it possible, use the same Key for the new setting as for the\n setting in the solver. For example, if you want to modify the\n `structural_substeps` variable in settings, use that Key in the\n `info` dictionary.\n\n As a convention: a value of None returns the value to the initial\n one specified in settings, while the key not being in the dict\n is ignored, so if any change was made before, it will stay there.\n \"\"\"\n try:\n info = controlled_state['info']\n except KeyError:\n return controlled_state['structural'], controlled_state['aero']\n\n # general copy-if-exists, restore if == None\n for info_k, info_v in info.items():\n if info_k in self.settings:\n if info_v is not None:\n self.settings[info_k] = info_v\n else:\n self.settings[info_k] = self.original_settings[info_k]\n\n # specifics of every option\n for info_k, info_v in info.items():\n if info_k in self.settings:\n\n if info_k == 'structural_substeps':\n if info_v is not None:\n self.substep_dt = (\n self.settings['dt']/(\n self.settings['structural_substeps'] + 1))\n\n elif info_k == 'structural_solver':\n if info_v is not None:\n self.structural_solver = solver_interface.initialise_solver(\n info['structural_solver'])\n self.structural_solver.initialise(\n self.data, self.settings['structural_solver_settings'])\n\n elif info_k == 'rotor_vel':\n for lc in self.structural_solver.lc_list:\n if lc._lc_id == 'hinge_node_FoR_pitch':\n lc.set_rotor_vel(info_v)\n\n elif info_k == 'pitch_vel':\n for lc in self.structural_solver.lc_list:\n if lc._lc_id == 'hinge_node_FoR_pitch':\n lc.set_pitch_vel(info_v)\n\n return controlled_state['structural'], controlled_state['aero']\n\n def run(self, **kwargs):\n \"\"\"\n Run the time stepping procedure with controllers and postprocessors\n included.\n \"\"\"\n solvers = settings_utils.set_value_or_default(kwargs, 'solvers', None)\n if self.network_loader is not None:\n self.set_of_variables = self.network_loader.get_inout_variables()\n\n incoming_queue = queue.Queue(maxsize=1)\n outgoing_queue = queue.Queue(maxsize=1)\n\n finish_event = threading.Event()\n with concurrent.futures.ThreadPoolExecutor(max_workers=2) as executor:\n netloop = executor.submit(self.network_loop, incoming_queue, outgoing_queue, finish_event)\n timeloop = executor.submit(self.time_loop, incoming_queue, outgoing_queue, finish_event, solvers)\n\n # TODO: improve exception handling to get exceptions when they happen from each thread\n for t1 in [netloop, timeloop]:\n try:\n t1.result()\n except Exception as e:\n print(e)\n raise Exception\n\n else:\n self.time_loop(solvers=solvers)\n\n if self.print_info:\n cout.cout_wrap('...Finished', 1)\n\n for postproc in self.postprocessors:\n try:\n self.postprocessors[postproc].shutdown()\n except AttributeError:\n pass\n\n return self.data\n\n def network_loop(self, in_queue, out_queue, finish_event):\n # runs in a separate thread from time_loop()\n out_network, in_network = self.network_loader.get_networks()\n out_network.set_queue(out_queue)\n\n in_network.set_message_length(self.set_of_variables.input_msg_len)\n in_network.set_queue(in_queue)\n\n previous_queue_empty = True\n while not finish_event.is_set():\n\n # selector version\n events = network_interface.sel.select(timeout=1)\n if out_network.queue.empty() and not previous_queue_empty:\n out_network.set_selector_events_mask('r')\n previous_queue_empty = True\n elif not out_network.queue.empty() and previous_queue_empty:\n out_network.set_selector_events_mask('w')\n previous_queue_empty = False\n\n try:\n for key, mask in events:\n key.data.process_events(mask)\n except KeyboardInterrupt:\n break\n\n # close sockets\n in_network.close()\n out_network.close()\n\n def time_loop(self, in_queue=None, out_queue=None, finish_event=None, solvers=None):\n self.logger.debug('Inside time loop')\n # dynamic simulations start at tstep == 1, 0 is reserved for the initial state\n for self.data.ts in range(\n len(self.data.structure.timestep_info),\n self.settings['n_time_steps'] + 1):\n initial_time = time.perf_counter()\n\n # network only\n # get input from the other thread\n if in_queue:\n self.logger.info('Time Loop - Waiting for input')\n values = in_queue.get() # should be list of tuples\n self.logger.debug('Time loop - received {}'.format(values))\n self.set_of_variables.update_timestep(self.data, values)\n\n structural_kstep = self.data.structure.timestep_info[-1].copy()\n aero_kstep = self.data.aero.timestep_info[-1].copy()\n if self.settings['nonlifting_body_interactions']:\n nl_body_kstep = self.data.nonlifting_body.timestep_info[-1].copy()\n else:\n nl_body_kstep = None\n self.logger.debug('Time step {}'.format(self.data.ts))\n\n # Add the controller here\n if self.with_controllers:\n state = {'structural': structural_kstep,\n 'aero': aero_kstep}\n for k, v in self.controllers.items():\n state, control = v.control(self.data, state)\n # this takes care of the changes in options for the solver\n structural_kstep, aero_kstep = self.process_controller_output(\n state)\n\n # Add external forces\n if self.with_runtime_generators:\n structural_kstep.runtime_steady_forces.fill(0.)\n structural_kstep.runtime_unsteady_forces.fill(0.)\n params = dict()\n params['data'] = self.data\n params['struct_tstep'] = structural_kstep\n params['aero_tstep'] = aero_kstep\n params['fsi_substep'] = -1\n for id, runtime_generator in self.runtime_generators.items():\n runtime_generator.generate(params)\n\n self.time_aero = 0.0\n self.time_struc = 0.0\n\n # Copy the controlled states so that the interpolation does not\n # destroy the previous information\n controlled_structural_kstep = structural_kstep.copy()\n controlled_aero_kstep = aero_kstep.copy()\n\n for k in range(self.settings['fsi_substeps'] + 1):\n if (k == self.settings['fsi_substeps'] and\n self.settings['fsi_substeps']):\n print_res = 0 if self.res == 0. else np.log10(self.res)\n print_res_dqdt = 0 if self.res_dqdt == 0. else np.log10(self.res_dqdt)\n cout.cout_wrap((\"The FSI solver did not converge!!! residuals: %f %f\" % (print_res, print_res_dqdt)))\n self.aero_solver.update_custom_grid(\n structural_kstep,\n aero_kstep,\n nl_body_kstep)\n break\n\n # generate new grid (already rotated)\n aero_kstep = controlled_aero_kstep.copy()\n \n self.aero_solver.update_custom_grid(\n structural_kstep,\n aero_kstep,\n nl_body_kstep)\n\n # compute unsteady contribution\n force_coeff = 0.0\n unsteady_contribution = False\n if self.settings['include_unsteady_force_contribution']:\n if self.data.ts > self.settings['steps_without_unsteady_force']:\n unsteady_contribution = True\n if k < self.settings['pseudosteps_ramp_unsteady_force']:\n force_coeff = k/self.settings['pseudosteps_ramp_unsteady_force']\n else:\n force_coeff = 1.\n\n previous_runtime_steady_forces = structural_kstep.runtime_steady_forces.astype(dtype=ct.c_double, order='F', copy=True)\n previous_runtime_unsteady_forces = structural_kstep.runtime_unsteady_forces.astype(dtype=ct.c_double, order='F', copy=True)\n # Add external forces\n if self.with_runtime_generators:\n structural_kstep.runtime_steady_forces.fill(0.)\n structural_kstep.runtime_unsteady_forces.fill(0.)\n params = dict()\n params['data'] = self.data\n params['struct_tstep'] = structural_kstep\n params['aero_tstep'] = aero_kstep\n params['fsi_substep'] = k\n for id, runtime_generator in self.runtime_generators.items():\n runtime_generator.generate(params)\n\n # run the solver\n ini_time_aero = time.perf_counter()\n self.data = self.aero_solver.run(aero_step=aero_kstep,\n structural_step=structural_kstep,\n convect_wake=True,\n unsteady_contribution=unsteady_contribution,\n nl_body_tstep = nl_body_kstep)\n self.time_aero += time.perf_counter() - ini_time_aero\n\n previous_kstep = structural_kstep.copy()\n structural_kstep = controlled_structural_kstep.copy()\n structural_kstep.runtime_steady_forces = previous_kstep.runtime_steady_forces.astype(dtype=ct.c_double, order='F', copy=True)\n structural_kstep.runtime_unsteady_forces = previous_kstep.runtime_unsteady_forces.astype(dtype=ct.c_double, order='F', copy=True)\n previous_kstep.runtime_steady_forces = previous_runtime_steady_forces.astype(dtype=ct.c_double, order='F', copy=True)\n previous_kstep.runtime_unsteady_forces = previous_runtime_unsteady_forces.astype(dtype=ct.c_double, order='F', copy=True)\n\n # move the aerodynamic surface according the the structural one\n self.aero_solver.update_custom_grid(\n structural_kstep,\n aero_kstep,\n nl_body_kstep)\n \n self.map_forces(aero_kstep,\n structural_kstep,\n nl_body_kstep = nl_body_kstep,\n unsteady_forces_coeff = force_coeff)\n\n # relaxation\n relax_factor = self.relaxation_factor(k)\n relax(self.data.structure,\n structural_kstep,\n previous_kstep,\n relax_factor)\n\n # check if nan anywhere.\n # if yes, raise exception\n if np.isnan(structural_kstep.steady_applied_forces).any():\n raise exc.NotConvergedSolver('NaN found in steady_applied_forces!')\n if np.isnan(structural_kstep.unsteady_applied_forces).any():\n raise exc.NotConvergedSolver('NaN found in unsteady_applied_forces!')\n\n copy_structural_kstep = structural_kstep.copy()\n ini_time_struc = time.perf_counter()\n for i_substep in range(\n self.settings['structural_substeps'] + 1):\n # run structural solver\n coeff = ((i_substep + 1)/\n (self.settings['structural_substeps'] + 1))\n\n structural_kstep = self.interpolate_timesteps(\n step0=self.data.structure.timestep_info[-1],\n step1=copy_structural_kstep,\n out_step=structural_kstep,\n coeff=coeff)\n\n self.data = self.structural_solver.run(\n structural_step=structural_kstep,\n dt=self.substep_dt)\n\n self.time_struc += time.perf_counter() - ini_time_struc\n\n # check convergence\n if self.convergence(k,\n structural_kstep,\n previous_kstep,\n self.structural_solver,\n self.aero_solver,\n self.with_runtime_generators):\n # move the aerodynamic surface according to the structural one\n self.aero_solver.update_custom_grid(structural_kstep,\n aero_kstep,\n nl_body_tstep = nl_body_kstep)\n break\n\n # move the aerodynamic surface according the the structural one\n self.aero_solver.update_custom_grid(structural_kstep,\n aero_kstep,\n nl_body_tstep = nl_body_kstep)\n\n self.aero_solver.add_step()\n self.data.aero.timestep_info[-1] = aero_kstep.copy()\n if self.settings['nonlifting_body_interactions']:\n self.data.nonlifting_body.timestep_info[-1] = nl_body_kstep.copy()\n self.structural_solver.add_step()\n self.data.structure.timestep_info[-1] = structural_kstep.copy()\n\n final_time = time.perf_counter()\n\n if self.print_info:\n print_res = 0 if self.res_dqdt == 0. else np.log10(self.res_dqdt)\n self.residual_table.print_line([self.data.ts,\n self.data.ts*self.dt,\n k,\n self.time_struc/(self.time_aero + self.time_struc),\n final_time - initial_time,\n print_res,\n structural_kstep.for_vel[0],\n structural_kstep.for_vel[2],\n np.sum(structural_kstep.steady_applied_forces[:, 0]),\n np.sum(structural_kstep.steady_applied_forces[:, 2])])\n (self.data.structure.timestep_info[self.data.ts].total_forces[0:3],\n self.data.structure.timestep_info[self.data.ts].total_forces[3:6]) = (\n self.structural_solver.extract_resultants(self.data.structure.timestep_info[self.data.ts]))\n # run postprocessors\n if self.with_postprocessors:\n for postproc in self.postprocessors:\n self.data = self.postprocessors[postproc].run(online=True, solvers=solvers)\n\n # network only\n # put result back in queue\n if out_queue:\n self.logger.debug('Time loop - about to get out variables from data')\n self.set_of_variables.get_value(self.data)\n if out_queue.full():\n # clear the queue such that it always contains the latest time step\n out_queue.get() # clear item from queue\n self.logger.debug('Data output Queue is full - clearing output')\n out_queue.put(self.set_of_variables)\n\n if finish_event:\n finish_event.set()\n self.logger.info('Time loop - Complete')\n\n def convergence(self, k, tstep, previous_tstep,\n struct_solver, aero_solver, with_runtime_generators):\n r\"\"\"\n Check convergence in the FSI loop.\n\n Convergence is determined as:\n\n .. math:: \\epsilon_q^k = \\frac{|| q^k - q^{k - 1} ||}{q^0}\n .. math:: \\epsilon_\\dot{q}^k = \\frac{|| \\dot{q}^k - \\dot{q}^{k - 1} ||}{\\dot{q}^0}\n\n FSI converged if :math:`\\epsilon_q^k < \\mathrm{FSI\\ tolerance}` and :math:`\\epsilon_\\dot{q}^k < \\mathrm{FSI\\ tolerance}`\n\n \"\"\"\n # check for non-convergence\n if not all(np.isfinite(tstep.q)):\n raise Exception(\n '***Not converged! There is a NaN value in the forces!')\n\n if not k:\n # save the value of the vectors for normalising later\n self.base_q = np.linalg.norm(tstep.q.copy())\n self.base_dqdt = np.linalg.norm(tstep.dqdt.copy())\n if self.base_dqdt == 0:\n self.base_dqdt = 1.\n if with_runtime_generators:\n self.base_res_forces = np.linalg.norm(tstep.runtime_steady_forces +\n tstep.runtime_unsteady_forces)\n if self.base_res_forces == 0:\n self.base_res_forces = 1.\n return False\n\n # Check the special case of no aero and no runtime generators\n if (aero_solver.solver_id.lower() == \"noaero\"\\\n or struct_solver.solver_id.lower() == \"nostructural\")\\\n and not with_runtime_generators:\n return True\n\n # relative residuals\n self.res = (np.linalg.norm(tstep.q-\n previous_tstep.q)/\n self.base_q)\n self.res_dqdt = (np.linalg.norm(tstep.dqdt-\n previous_tstep.dqdt)/\n self.base_dqdt)\n\n if with_runtime_generators:\n res_forces = (np.linalg.norm(tstep.runtime_steady_forces -\n previous_tstep.runtime_steady_forces +\n tstep.runtime_unsteady_forces -\n previous_tstep.runtime_unsteady_forces)/\n self.base_res_forces)\n else:\n res_forces = 0.\n\n # we don't want this to converge before introducing the gamma_dot forces!\n if self.settings['include_unsteady_force_contribution']:\n if k < self.settings['pseudosteps_ramp_unsteady_force'] \\\n and self.data.ts > self.settings['steps_without_unsteady_force']:\n return False\n\n # convergence\n rigid_solver = False\n if \"rigid\" in struct_solver.solver_id.lower():\n rigid_solver = True\n elif \"NonLinearDynamicMultibody\" == struct_solver.solver_id.lower() and struct_solver.settings['rigid_bodies']:\n rigid_solver = True\n if k > self.settings['minimum_steps'] - 1:\n if self.res < self.settings['fsi_tolerance'] or rigid_solver:\n if self.res_dqdt < self.settings['fsi_tolerance']:\n if res_forces < self.settings['fsi_tolerance']:\n return True\n\n\n def map_forces(self, aero_kstep, structural_kstep, nl_body_kstep = None, unsteady_forces_coeff=1.0):\n # set all forces to 0\n structural_kstep.steady_applied_forces.fill(0.0)\n structural_kstep.unsteady_applied_forces.fill(0.0)\n\n # aero forces to structural forces\n struct_forces = mapping.aero2struct_force_mapping(\n aero_kstep.forces,\n self.data.aero.struct2aero_mapping,\n aero_kstep.zeta,\n structural_kstep.pos,\n structural_kstep.psi,\n self.data.structure.node_master_elem,\n self.data.structure.connectivities,\n structural_kstep.cag(),\n self.data.aero.data_dict)\n dynamic_struct_forces = unsteady_forces_coeff*mapping.aero2struct_force_mapping(\n aero_kstep.dynamic_forces,\n self.data.aero.struct2aero_mapping,\n aero_kstep.zeta,\n structural_kstep.pos,\n structural_kstep.psi,\n self.data.structure.node_master_elem,\n self.data.structure.connectivities,\n structural_kstep.cag(),\n self.data.aero.data_dict)\n\n if self.correct_forces:\n struct_forces = \\\n self.correct_forces_generator.generate(aero_kstep=aero_kstep,\n structural_kstep=structural_kstep,\n struct_forces=struct_forces,\n ts=self.data.ts)\n\n aero_kstep.aero_steady_forces_beam_dof = struct_forces\n structural_kstep.postproc_node['aero_steady_forces'] = struct_forces\n structural_kstep.postproc_node['aero_unsteady_forces'] = dynamic_struct_forces\n\n # if self.settings['nonlifting_body_interactions']:\n # struct_forces += mapping.aero2struct_force_mapping(\n # nl_body_kstep.forces,\n # self.data.nonlifting_body.struct2aero_mapping,\n # nl_body_kstep.zeta,\n # structural_kstep.pos,\n # structural_kstep.psi,\n # self.data.structure.node_master_elem,\n # self.data.structure.connectivities,\n # structural_kstep.cag(),\n # self.data.nonlifting_body.data_dict)\n # prescribed forces + aero forces\n # prescribed forces + aero forces + runtime generated\n structural_kstep.steady_applied_forces += struct_forces\n structural_kstep.steady_applied_forces += self.data.structure.ini_info.steady_applied_forces\n structural_kstep.steady_applied_forces += structural_kstep.runtime_steady_forces\n\n structural_kstep.unsteady_applied_forces += dynamic_struct_forces\n if len(self.data.structure.dynamic_input) > 0:\n structural_kstep.unsteady_applied_forces += self.data.structure.dynamic_input[max(self.data.ts - 1, 0)]['dynamic_forces']\n structural_kstep.unsteady_applied_forces += structural_kstep.runtime_unsteady_forces\n\n # Apply unsteady force coefficient\n structural_kstep.unsteady_applied_forces *= unsteady_forces_coeff\n\n def relaxation_factor(self, k):\n initial = self.settings['relaxation_factor']\n if not self.settings['dynamic_relaxation']:\n return initial\n\n final = self.settings['final_relaxation_factor']\n if k >= self.settings['relaxation_steps']:\n return final\n\n value = initial + (final - initial)/self.settings['relaxation_steps']*k\n return value\n\n @staticmethod\n def interpolate_timesteps(step0, step1, out_step, coeff):\n \"\"\"\n Performs a linear interpolation between step0 and step1 based on coeff\n in [0, 1]. 0 means info in out_step == step0 and 1 out_step == step1.\n\n Quantities interpolated:\n * `steady_applied_forces`\n * `unsteady_applied_forces`\n * `velocity` input in Lagrange constraints\n\n \"\"\"\n if not 0.0 <= coeff <= 1.0:\n return out_step\n\n # forces\n out_step.steady_applied_forces[:] = (\n (1.0 - coeff)*step0.steady_applied_forces +\n (coeff)*(step1.steady_applied_forces))\n\n out_step.unsteady_applied_forces[:] = (\n (1.0 - coeff)*step0.unsteady_applied_forces +\n (coeff)*(step1.unsteady_applied_forces))\n\n # multibody if necessary\n if out_step.mb_dict is not None:\n for key in step1.mb_dict.keys():\n if 'constraint_' in key:\n try:\n out_step.mb_dict[key]['velocity'][:] = (\n (1.0 - coeff)*step0.mb_dict[key]['velocity'] +\n (coeff)*step1.mb_dict[key]['velocity'])\n except KeyError:\n pass\n\n return out_step\n\n def teardown(self):\n \n self.structural_solver.teardown()\n self.aero_solver.teardown()\n if self.with_postprocessors:\n for pp in self.postprocessors.values():\n pp.teardown()\n if self.with_controllers:\n for cont in self.controllers.values():\n cont.teardown()\n if self.with_runtime_generators:\n for rg in self.runtime_generators.values():\n rg.teardown()\n\n\ndef relax(beam, timestep, previous_timestep, coeff):\n timestep.steady_applied_forces = ((1.0 - coeff)*timestep.steady_applied_forces +\n coeff*previous_timestep.steady_applied_forces)\n timestep.unsteady_applied_forces = ((1.0 - coeff)*timestep.unsteady_applied_forces +\n coeff*previous_timestep.unsteady_applied_forces)\n timestep.runtime_steady_forces = ((1.0 - coeff)*timestep.runtime_steady_forces +\n coeff*previous_timestep.runtime_steady_forces)\n timestep.runtime_unsteady_forces = ((1.0 - coeff)*timestep.runtime_unsteady_forces +\n coeff*previous_timestep.runtime_unsteady_forces)\n\n\ndef normalise_quaternion(tstep):\n tstep.dqdt[-4:] = algebra.unit_vector(tstep.dqdt[-4:])\n tstep.quat = tstep.dqdt[-4:].astype(dtype=ct.c_double, order='F', copy=True)\n" }, { "path": "sharpy/solvers/dynamicuvlm.py", "content": "\"\"\"\nTime Domain Aerodynamic Solver\n\nN Goizueta Jan 19\n\"\"\"\nimport sharpy.utils.solver_interface as solver_interface\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.cout_utils as cout\n\n@solver\nclass DynamicUVLM(BaseSolver):\n \"\"\"\n Dynamic Aerodynamic Time Domain Simulation\n\n Provides an aerodynamic only simulation in time by time stepping the solution. The type of aerodynamic solver is\n parsed as a setting.\n\n To Do:\n Clean timestep information for memory efficiency\n\n Warnings:\n Under development. Issues encountered when using the linear UVLM as the aerodynamic solver with integration\n order = 1.\n\n \"\"\"\n solver_id = 'DynamicUVLM'\n solver_classification = 'Aero'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Write status to screen'\n\n settings_types['structural_solver'] = 'str'\n settings_default['structural_solver'] = None\n settings_description['structural_solver'] = 'Structural solver to use in the coupled simulation'\n\n settings_types['structural_solver_settings'] = 'dict'\n settings_default['structural_solver_settings'] = None\n settings_description['structural_solver_settings'] = 'Dictionary of settings for the structural solver'\n\n settings_types['aero_solver'] = 'str'\n settings_default['aero_solver'] = None\n settings_description['aero_solver'] = 'Aerodynamic solver to use in the coupled simulation'\n\n settings_types['aero_solver_settings'] = 'dict'\n settings_default['aero_solver_settings'] = None\n settings_description['aero_solver_settings'] = 'Dictionary of settings for the aerodynamic solver'\n\n settings_types['n_time_steps'] = 'int'\n settings_default['n_time_steps'] = None\n settings_description['n_time_steps'] = 'Number of time steps for the simulation'\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = None\n settings_description['dt'] = 'Time step'\n\n settings_types['include_unsteady_force_contribution'] = 'bool'\n settings_default['include_unsteady_force_contribution'] = False\n settings_description['include_unsteady_force_contribution'] = 'If on, added mass contribution is added to the forces. This depends on the time derivative of the bound circulation. Check ``filter_gamma_dot`` in the aero solver'\n settings_types['postprocessors'] = 'list(str)'\n settings_default['postprocessors'] = list()\n settings_description['postprocessors'] = 'List of the postprocessors to run at the end of every time step'\n\n settings_types['postprocessors_settings'] = 'dict'\n settings_default['postprocessors_settings'] = dict()\n settings_description['postprocessors_settings'] = 'Dictionary with the applicable settings for every ``psotprocessor``. Every ``postprocessor`` needs its entry, even if empty'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n\n def __init__(self):\n\n self.data = None\n self.settings = None\n self.aero_solver = None\n self.print_info = False\n self.dt = None\n self.residual_table = None\n\n self.postprocessors = dict()\n self.with_postprocessors = False\n\n def initialise(self, data, custom_settings=None, restart=False):\n self.data = data\n\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n self.dt = self.settings['dt']\n self.print_info = self.settings['print_info']\n\n self.aero_solver = solver_interface.initialise_solver(self.settings['aero_solver'])\n self.aero_solver.initialise(self.data, self.settings['aero_solver_settings'], restart=False)\n self.data = self.aero_solver.data\n\n # initialise postprocessors\n self.postprocessors = dict()\n if len(self.settings['postprocessors']) > 0:\n self.with_postprocessors = True\n for postproc in self.settings['postprocessors']:\n self.postprocessors[postproc] = solver_interface.initialise_solver(postproc)\n self.postprocessors[postproc].initialise(\n self.data, self.settings['postprocessors_settings'][postproc], caller=self, restart=False)\n\n if self.print_info:\n self.residual_table = cout.TablePrinter(2, 14, ['g', 'f'])\n self.residual_table.print_header(['ts', 't'])\n\n def run(self, **kwargs):\n\n # struct info - only for orientation, no structural solution is performed\n struct_ini_step = self.data.structure.timestep_info[-1]\n\n for self.data.ts in range(len(self.data.aero.timestep_info),\n len(self.data.aero.timestep_info) + self.settings['n_time_steps']):\n\n aero_tstep = self.data.aero.timestep_info[-1]\n self.aero_solver.update_custom_grid(struct_ini_step, aero_tstep)\n\n force_coeff = 0.0\n if self.settings['include_unsteady_force_contribution']:\n force_coeff = 1.0\n if self.data.ts < 5:\n force_coeff = 0.0\n\n # run the solver\n if force_coeff == 0.:\n unsteady_contribution = False\n else:\n unsteady_contribution = True\n\n self.data = self.aero_solver.run(aero_tstep=aero_tstep,\n structure_tstep=struct_ini_step,\n convect_wake=True,\n unsteady_contribution=unsteady_contribution)\n\n self.aero_solver.add_step()\n self.data.aero.timestep_info[-1] = aero_tstep.copy()\n self.data.structure.timestep_info.append(struct_ini_step.copy())\n\n if self.print_info:\n self.residual_table.print_line([self.data.ts,\n self.data.ts * self.dt])\n\n if self.with_postprocessors:\n for postproc in self.postprocessors:\n self.data = self.postprocessors[postproc].run(online=True)\n\n if self.print_info:\n cout.cout_wrap('...Finished', 1)\n\n return self.data\n" }, { "path": "sharpy/solvers/gridloader.py", "content": "import h5py as h5\nimport numpy as np\n\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.h5utils as h5utils\n\n\n@solver\nclass GridLoader(BaseSolver):\n \"\"\"\n ``GridLoader`` class, inherited from ``BaseSolver``\n\n Parent class for Aerogridloader and Nonliftingbodygridloader. Both classes\n generate aerodynamic grids based on the input data\n\n Args:\n data (PreSharpy): ``ProblemData`` class structure\n\n Attributes:\n settings (dict): Name-value pair of the settings employed by the aerodynamic solver\n settings_types (dict): Acceptable types for the values in ``settings``\n settings_default (dict): Name-value pair of default values for the aerodynamic settings\n data (ProblemData): class structure\n afile_name (str): name of the HDF5 file, e.g. ``.aero.h5``\n aero: empty attribute\n data_dict (dict): key-value pairs of aerodynamic data\n\n \"\"\"\n solver_id = 'GridLoader'\n solver_classification = 'other'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n def __init__(self):\n self.data = None\n self.settings = None\n self.file_name = ''\n self.data_dict = dict()\n\n def initialise(self, data, restart=False):\n self.data = data\n self.read_input_files()\n \n self.settings = data.settings[self.solver_id]\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default, options=self.settings_options)\n\n\n def read_input_files(self):\n self.file_name = (self.data.case_route +\n '/' +\n self.data.case_name +\n self.file_name)\n \n h5utils.check_file_exists(self.file_name)\n\n # read and store the hdf5 file in dictionary\n with h5.File(self.file_name, 'r') as file_handle:\n self.data_dict = h5utils.load_h5_in_dict(file_handle)" }, { "path": "sharpy/solvers/initialaeroelasticloader.py", "content": "from sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.h5utils as h5utils\nimport sharpy.utils.exceptions as exceptions\n\n\n@solver\nclass InitialAeroelasticLoader(BaseSolver):\n r\"\"\"\n This solver prescribes pos, pos_dot, psi, psi_dot and for_vel\n at each time step from a .h5 file\n \"\"\"\n solver_id = 'InitialAeroelasticLoader'\n solver_classification = 'loader'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['input_file'] = 'str'\n settings_default['input_file'] = None\n settings_description['input_file'] = 'Input file containing the simulation data'\n\n settings_types['include_forces'] = 'bool'\n settings_default['include_forces'] = True\n settings_description['include_forces'] = 'Map the forces'\n\n settings_types['generate_aero'] = 'bool'\n settings_default['generate_aero'] = False\n settings_description['generate_aero'] = 'Generate the aerodynamics grids from scratch'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n self.file_info = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n no_ctype=True)\n # Load simulation data\n self.file_info = h5utils.readh5(self.settings['input_file'])\n\n def run(self, **kwargs):\n\n aero_step = settings_utils.set_value_or_default(kwargs, 'aero_step', self.data.aero.timestep_info[-1])\n structural_step = settings_utils.set_value_or_default(kwargs, 'structural_step',\n self.data.structure.timestep_info[-1])\n\n # Copy structural information\n attributes = ['pos', 'pos_dot', 'pos_ddot',\n 'psi', 'psi_dot', 'psi_ddot',\n 'for_pos', 'for_vel', 'for_acc', 'quat',\n 'mb_FoR_pos', 'mb_FoR_vel', 'mb_FoR_acc', 'mb_quat']\n\n if self.settings['include_forces']:\n attributes.extend(['runtime_steady_forces',\n 'runtime_unsteady_forces',\n 'steady_applied_forces',\n 'unsteady_applied_forces'])\n\n for att in attributes:\n new_attr = getattr(structural_step, att)\n db_attr = getattr(self.file_info.structure, att)\n if new_attr.shape == db_attr.shape:\n new_attr[...] = db_attr\n else:\n error_msg = \"Non matching shapes in attribute %s\" % att\n exceptions.NotValidInputFile(error_msg)\n\n # Copy aero information\n if self.settings['generate_aero']:\n # Generate aerodynamic surface\n self.data.aero.generate_zeta_timestep_info(structural_step,\n aero_step,\n self.data.structure,\n self.data.aero.aero_settings)\n # generate the wake because the solid shape might change\n self.data.aero.wake_shape_generator.generate({'zeta': aero_step.zeta,\n 'zeta_star': aero_step.zeta_star,\n 'gamma': aero_step.gamma,\n 'gamma_star': aero_step.gamma_star,\n 'dist_to_orig': aero_step.dist_to_orig})\n\n else:\n attributes = ['zeta', 'zeta_star', 'normals',\n 'gamma', 'gamma_star',\n 'u_ext', 'u_ext_star', ]\n\n if self.settings['include_forces']:\n attributes.extend(['dynamic_forces', 'forces', ])\n\n for att in attributes:\n for isurf in range(aero_step.n_surf):\n new_attr = getattr(aero_step, att)[isurf]\n db_attr = getattr(self.file_info.aero, att)[isurf]\n if new_attr.shape == db_attr.shape:\n new_attr[...] = db_attr\n else:\n error_msg = \"Non matching shapes in attribute %s\" % att\n exceptions.NotValidInputFile(error_msg)\n\n return self.data\n" }, { "path": "sharpy/solvers/lindynamicsim.py", "content": "import numpy as np\nimport os\nimport h5py as h5\nfrom sharpy.utils.solver_interface import solver, BaseSolver, initialise_solver\nimport sharpy.utils.settings as settings_utils\nimport sharpy.linear.src.libss as libss\nimport scipy.linalg as sclalg\nimport sharpy.utils.h5utils as h5utils\nfrom sharpy.utils.datastructures import LinearTimeStepInfo\nfrom sharpy.linear.utils.ss_interface import InputVariable, LinearVector\nimport sharpy.utils.cout_utils as cout\nimport time\nimport warnings\n\n@solver\nclass LinDynamicSim(BaseSolver):\n \"\"\"Time-domain solution of Linear Time Invariant Systems\n\n Uses the derived linear time invariant systems and solves it in time domain.\n\n The inputs are provided by means of a list of dictionaries to the setting\n ``input_generators``. For each input you want, you need a dictionary entry containing\n ``name`` (str) which is the name of the variable, ``index`` (int) for the index of the variable\n in the case of multidimensional variables (if unspecified reverts to ``0``) and the ``file_path``\n to a text file containing the time series of the input. If the input variable is multidimensional,\n ``index`` may be a list of indices for each column of time series in the array in the input file.\n\n Alternatively a ``case_name.lininput.h5`` file in the case root folder can be used with the following entries:\n\n * ``x0`` (optional): Initial state vector\n * ``input_vec``: Input vector ``(n_tsteps, n_inputs)``.\n\n Note:\n This solver is seldom used in SHARPy (its focus is on nonlinear time domain aeroelasticity) hence you may\n find this solver lacking in features. If you use it, you may need to make modifications. We would greatly\n appreciate that you contribute these modifications by means of a pull request!\n\n \"\"\"\n solver_id = 'LinDynamicSim'\n solver_classification = 'Coupled'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['write_dat'] = 'list(str)'\n settings_default['write_dat'] = []\n settings_description['write_dat'] = 'List of vectors to write: ``x``, ``y``, ``u`` and/or ``t``'\n\n settings_types['reference_velocity'] = 'float'\n settings_default['reference_velocity'] = 1.\n settings_description['reference_velocity'] = 'Velocity to scale the structural equations when using a non-dimensional system'\n\n settings_default['n_tsteps'] = 10\n settings_types['n_tsteps'] = 'int'\n settings_description['n_tsteps'] = 'Number of time steps to run'\n\n settings_types['physical_time'] = 'float'\n settings_default['physical_time'] = 2.\n settings_description['physical_time'] = 'Time to run'\n\n settings_types['input_generators'] = 'list(dict)'\n settings_default['input_generators'] = []\n settings_description['input_generators'] = 'List of dictionaries for each input'\n\n settings_default['dt'] = 0.001\n settings_types['dt'] = 'float'\n settings_description['dt'] = 'Time increment for the solution of systems without a specified dt'\n\n settings_types['postprocessors'] = 'list(str)'\n settings_default['postprocessors'] = list()\n\n settings_types['postprocessors_settings'] = 'dict'\n settings_default['postprocessors_settings'] = dict()\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n\n self.data = None\n self.settings = dict()\n self.postprocessors = dict()\n self.with_postprocessors = False\n\n self.input_data_dict = dict()\n self.input_file_name = \"\"\n\n self.folder = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n\n self.data = data\n if custom_settings:\n self.settings = custom_settings\n else:\n self.settings = data.settings[self.solver_id]\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default, no_ctype=True)\n\n # Read initial state and input data and store in dictionary\n self.read_files()\n\n # Output folder\n self.folder = data.output_folder + '/lindynamicsim/'\n if not os.path.exists(self.folder):\n os.makedirs(self.folder)\n\n # initialise postprocessors\n self.postprocessors = dict()\n if len(self.settings['postprocessors']) > 0:\n self.with_postprocessors = True\n for postproc in self.settings['postprocessors']:\n self.postprocessors[postproc] = initialise_solver(postproc)\n self.postprocessors[postproc].initialise(\n self.data, self.settings['postprocessors_settings'][postproc], caller=self, restart=False)\n\n def input_vector(self, ss):\n \"\"\"\n Generates an input vector ``u`` of size ``n_tsteps x inputs`` and populates the\n correct columns with the time series arrays provided as text files in the settings\n ``input_generators``.\n\n Args:\n ss (libss.StateSpace): State Space object for which to generate input\n\n Returns:\n np.array: Input vector.\n \"\"\"\n n_steps = self.settings['n_tsteps']\n u_vect = np.zeros((n_steps, ss.inputs))\n\n for in_settings in self.settings['input_generators']:\n var_name = in_settings['name']\n index = in_settings.get('index', 0)\n file_path = in_settings['file_path']\n\n variable = ss.input_variables.get_variable_from_name(var_name)\n input_data = np.loadtxt(file_path)\n\n cout.cout_wrap('Found input for {:s}'.format(str(variable)))\n\n if type(index) is list:\n for ith, i_ind in enumerate(index):\n in_channel = variable.cols_loc[i_ind]\n u_vect[:, in_channel] = input_data[:, ith]\n else:\n in_channel = variable.cols_loc[index]\n u_vect[:, in_channel] = input_data\n\n return u_vect\n\n def run(self, **kwargs):\n\n ss = self.data.linear.ss\n\n n_steps = self.settings['n_tsteps']\n x0 = self.input_data_dict.get('x0', np.zeros(ss.states))\n if len(self.settings['input_generators']) != 0:\n u = self.input_vector(ss)\n else:\n u = self.input_data_dict['u']\n\n if len(x0) != ss.states:\n warnings.warn('Number of states in the initial state vector not equal to the number of states')\n x0 = np.zeros(ss.states)\n\n if u.shape[1] != ss.inputs:\n warnings.warn('Dimensions of the input vector not equal to the number of inputs')\n cout.cout_wrap('Number of inputs: %g' % ss.inputs, 3)\n cout.cout_wrap('Number of timesteps: %g' % n_steps, 3)\n cout.cout_wrap('Number of UVLM inputs: %g' % self.data.linear.linear_system.uvlm.ss.inputs, 3)\n cout.cout_wrap('Number of beam inputs: %g' % self.data.linear.linear_system.beam.ss.inputs, 3)\n breakpoint()\n\n try:\n dt = ss.dt\n except AttributeError:\n dt = self.settings['dt']\n\n # Total time to run\n T = (n_steps - 1) * dt\n\n u_ref = self.settings['reference_velocity']\n # If the system is scaled:\n if u_ref != 1.:\n scaling_factors = self.data.linear.linear_system.uvlm.sys.ScalingFacts\n dt_dimensional = scaling_factors['length'] / u_ref\n T_dimensional = (n_steps - 1) * dt_dimensional\n T = T_dimensional / scaling_factors['time']\n ss = self.data.linear.linear_system.update(self.settings['reference_velocity'])\n t_dom = np.linspace(0, T, n_steps)\n\n # Use the scipy linear solver\n sys = libss.ss_to_scipy(ss)\n cout.cout_wrap('Solving linear system using scipy...')\n t0 = time.time()\n out = sys.output(u, t=t_dom, x0=x0)\n ts = time.time() - t0\n cout.cout_wrap('\\tSolved in %.2fs' % ts, 1)\n\n t_out = out[0]\n x_out = out[2]\n y_out = out[1]\n\n if self.settings['write_dat']:\n cout.cout_wrap('Writing linear simulation output .dat files to %s' % self.folder)\n if 'y' in self.settings['write_dat']:\n np.savetxt(self.folder + '/y_out.dat', y_out)\n cout.cout_wrap('Output vector written', 2)\n if 'x' in self.settings['write_dat']:\n np.savetxt(self.folder + '/x_out.dat', x_out)\n cout.cout_wrap('State vector written', 2)\n if 'u' in self.settings['write_dat']:\n np.savetxt(self.folder + '/u_out.dat', u)\n cout.cout_wrap('Input vector written', 2)\n if 't' in self.settings['write_dat']:\n np.savetxt(self.folder + '/t_out.dat', t_out)\n cout.cout_wrap('Time domain written', 2)\n cout.cout_wrap('Success', 1)\n\n # Pack state variables into linear timestep info\n cout.cout_wrap('Plotting results...')\n for n in range(len(t_out)-1):\n tstep = LinearTimeStepInfo()\n tstep.x = x_out[n, :]\n tstep.y = y_out[n, :]\n tstep.t = t_out[n]\n tstep.u = u[n, :]\n self.data.linear.timestep_info.append(tstep)\n # TODO: option to save to h5\n\n # Pack variables into respective aero or structural time step infos (with the + f0 from lin)\n # Need to obtain information from the variables in a similar fashion as done with the database\n # for the beam case\n\n aero_tstep, struct_tstep = state_to_timestep(self.data, tstep.x, tstep.u, tstep.y)\n\n self.data.aero.timestep_info.append(aero_tstep)\n self.data.structure.timestep_info.append(struct_tstep)\n\n # run postprocessors\n if self.with_postprocessors:\n for postproc in self.postprocessors:\n self.data = self.postprocessors[postproc].run(online=True)\n\n return self.data\n\n def read_files(self):\n\n self.input_file_name = self.data.settings['SHARPy']['route'] + '/' + self.data.settings['SHARPy']['case'] + '.lininput.h5'\n\n # Check that the file exists\n try:\n h5utils.check_file_exists(self.input_file_name)\n # Read and store\n with h5.File(self.input_file_name, 'r') as input_file_handle:\n self.input_data_dict = h5utils.load_h5_in_dict(input_file_handle)\n except FileNotFoundError:\n pass\n\n\ndef state_to_timestep(data, x, u=None, y=None):\n \"\"\"\n Warnings:\n Under development\n\n Writes a state-space vector to SHARPy timesteps\n\n Args:\n data:\n x:\n u:\n y:\n\n Returns:\n\n \"\"\"\n\n if data.settings['LinearAssembler']['linear_system_settings']['beam_settings']['modal_projection'] and \\\n data.settings['LinearAssembler']['linear_system_settings']['beam_settings']['inout_coords'] == 'modes':\n modal = True\n else:\n modal = False\n\n aero_state = x[:-data.linear.linear_system.beam.ss.states]\n\n # Beam output\n y_beam = y[-data.linear.linear_system.beam.ss.outputs:]\n\n u_q = np.zeros(data.linear.linear_system.uvlm.ss.inputs)\n if u is not None:\n u_q += u[:data.linear.linear_system.uvlm.ss.inputs]\n u_q[:y_beam.shape[0]] += y_beam\n else:\n u_q[:y_beam.shape[0]] += y_beam\n\n Kas = data.linear.linear_system.couplings['Kas']\n if modal:\n # Transform to aerodynamic raw inputs\n uvlm_in_mode_gain = data.linear.linear_system.couplings['in_mode_gain']\n aero_input = Kas.dot(uvlm_in_mode_gain.dot(u_q))\n else:\n aero_input = Kas.dot(u_q)\n\n # Aero\n forces, gamma, gamma_dot, gamma_star, gust_state_vec = data.linear.linear_system.uvlm.unpack_ss_vector(\n data,\n x_n=aero_state,\n u_aero=aero_input,\n aero_tstep=data.linear.tsaero0,\n track_body=True,\n state_variables=data.linear.linear_system.uvlm.ss.state_variables,\n gust_in=True)\n\n if data.linear.linear_system.uvlm.gust_assembler:\n gust_in_loc = data.linear.ss.input_variables('u_gust').cols_loc\n u_in_gust = u[gust_in_loc]\n gust_assembler = data.linear.linear_system.uvlm.gust_assembler\n u_ext_gust = gust_assembler.state_to_uext.dot(gust_state_vec) + gust_assembler.uin_to_uext.dot(u_in_gust)\n else:\n u_ext_gust = np.array([])\n\n uvlm_input_variables = LinearVector.transform(Kas.output_variables, InputVariable)\n # Unpack input\n zeta, zeta_dot, u_ext = data.linear.linear_system.uvlm.unpack_input_vector(aero_input, u_ext_gust,\n input_variables=uvlm_input_variables)\n\n current_aero_tstep = data.aero.timestep_info[-1].copy()\n current_aero_tstep.forces = [forces[i_surf] + data.linear.tsaero0.forces[i_surf] for i_surf in\n range(len(gamma))]\n current_aero_tstep.gamma = [gamma[i_surf] + data.linear.tsaero0.gamma[i_surf] for i_surf in\n range(len(gamma))]\n current_aero_tstep.gamma_dot = [gamma_dot[i_surf] + data.linear.tsaero0.gamma_dot[i_surf] for i_surf in\n range(len(gamma))]\n current_aero_tstep.gamma_star = [gamma_star[i_surf] + data.linear.tsaero0.gamma_star[i_surf] for i_surf in\n range(len(gamma))]\n current_aero_tstep.zeta = zeta\n current_aero_tstep.zeta_dot = zeta_dot\n current_aero_tstep.u_ext = u_ext\n\n aero_forces_vec = np.concatenate([forces[i_surf][:3, :, :].reshape(-1, order='C') for i_surf in range(len(forces))])\n beam_forces = data.linear.linear_system.couplings['Ksa'].dot(aero_forces_vec)\n\n # Reconstruct the state if modal\n if modal:\n phi = data.linear.linear_system.beam.sys.U\n x_s = sclalg.block_diag(phi, phi).dot(y_beam)\n else:\n x_s = y_beam\n y_s = beam_forces #+ phi.dot(u_struct)\n\n current_struct_step = data.linear.linear_system.beam.unpack_ss_vector(x_s, y_s, data.linear.tsstruct0)\n\n return current_aero_tstep, current_struct_step\n" }, { "path": "sharpy/solvers/linearassembler.py", "content": "\"\"\"\nLinear State Space Assembler\n\"\"\"\nfrom sharpy.utils.datastructures import Linear\nfrom sharpy.utils.solver_interface import solver, BaseSolver\n\nimport sharpy.linear.utils.ss_interface as ss_interface\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.cout_utils as cout\nimport sharpy.linear.assembler\nimport sharpy.rom\n\n\n@solver\nclass LinearAssembler(BaseSolver):\n r\"\"\"\n Warnings:\n Under development - please advise of new features and bugs!\n\n Creates a workspace containing the different linear elements of the state-space.\n\n The user specifies which elements to build sequentially via the ``linear_system`` setting.\n\n The most common uses will be:\n\n * Aerodynamic: :class:`sharpy.linear.assembler.LinearUVLM` solver\n\n * Structural: :class:`sharpy.linear.assembler.LinearBeam` solver\n\n * Aeroelastic: :class:`sharpy.linear.assembler.LinearAeroelastic` solver\n\n The solver enables to load a user specific assembly of a state-space by means of the ``LinearCustom`` block.\n\n See :class:`sharpy.sharpy.linear.assembler.LinearAssembler` for a detailed description of each of the state-space assemblies.\n\n Upon assembly of the linear system, the data structure ``data.linear`` will be created. The :class:`.Linear`\n contains the state-space as an attribute. This state space will be the one employed by postprocessors.\n\n Important: running the linear routines requires information on the tangent mass, stiffness and gyroscopic\n structural matrices therefore the solver :class:`solvers.modal.Modal` must have been run prior to linearisation.\n In addition, if the problem includes rigid body velocities, at least one\n timestep of :class:`solvers.DynamicCoupled` must have run such that the rigid body velocity is included.\n\n Example:\n\n The typical ``flow`` setting used prior to using this solver for an aeroelastic simulation with rigid body dynamics\n will be similar to:\n\n >>> flow = ['BeamLoader',\n >>> 'AerogridLoader',\n >>> 'StaticTrim',\n >>> 'DynamicCoupled', # a single time step will suffice\n >>> 'Modal',\n >>> 'LinearAssembler']\n\n \"\"\"\n solver_id = 'LinearAssembler'\n solver_classification = 'Linear'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['linear_system'] = 'str'\n settings_default['linear_system'] = None\n settings_description['linear_system'] = 'Name of chosen state space assembly type'\n\n settings_types['linear_system_settings'] = 'dict'\n settings_default['linear_system_settings'] = dict()\n settings_description['linear_system_settings'] = 'Settings for the desired state space assembler'\n\n settings_types['linearisation_tstep'] = 'int'\n settings_default['linearisation_tstep'] = -1\n settings_description['linearisation_tstep'] = 'Chosen linearisation time step number from available time steps'\n\n settings_types['modal_tstep'] = 'int'\n settings_default['modal_tstep'] = -1\n settings_description['modal_tstep'] = 'Timestep in which modal information is stored. Useful if the ``Modal`` solver' \\\n ' is run at the start of the SHARPy flow.'\n\n settings_types['inout_coordinates'] = 'str'\n settings_default['inout_coordinates'] = ''\n settings_description['inout_coordinates'] = 'Input/output coordinates of the system. Nodal or modal space.'\n settings_options['inout_coordinates'] = ['', 'nodes', 'modes']\n\n settings_types['retain_inputs'] = 'list(int)'\n settings_default['retain_inputs'] = []\n settings_description['retain_inputs'] = 'List of input channels to retain in the chosen ``inout_coordinates``.'\n\n settings_types['retain_outputs'] = 'list(int)'\n settings_default['retain_outputs'] = []\n settings_description['retain_outputs'] = 'List of output channels to retain in the chosen ``inout_coordinates``.'\n\n settings_types['retain_input_variables'] = 'list(str)'\n settings_default['retain_input_variables'] = []\n settings_description['retain_input_variables'] = 'List of input channels to retain in the chosen ' \\\n '``inout_coordinates``.'\n\n settings_types['retain_output_variables'] = 'list(str)'\n settings_default['retain_output_variables'] = []\n settings_description['retain_output_variables'] = 'List of output channels to retain in the chosen ' \\\n '``inout_coordinates``.'\n\n settings_types['recover_accelerations'] = 'bool'\n settings_default['recover_accelerations'] = False\n settings_description['recover_accelerations'] = 'Recover structural system accelerations as additional outputs.'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description, settings_options)\n\n def __init__(self):\n\n self.settings = dict()\n self.data = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n\n self.data = data\n if custom_settings:\n self.data.settings[self.solver_id] = custom_settings\n self.settings = self.data.settings[self.solver_id]\n\n else:\n self.settings = data.settings[self.solver_id]\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n options=self.settings_options,\n no_ctype=True)\n\n # Get consistent linearisation timestep\n ii_step = self.settings['linearisation_tstep']\n\n tsstruct0 = data.structure.timestep_info[ii_step]\n tsaero0 = data.aero.timestep_info[ii_step]\n\n try:\n tsstruct0.modal = data.structure.timestep_info[self.settings['modal_tstep']].modal\n except AttributeError:\n raise AttributeError('Unable to find modal information at desired '\n 'timestep {:g}'.format(self.settings['modal_tstep']))\n\n # Create data.linear\n self.data.linear = Linear(tsaero0, tsstruct0)\n\n lsys = ss_interface.initialise_system(self.settings['linear_system'])\n lsys.initialise(data)\n self.data.linear.linear_system = lsys\n\n def run(self, **kwargs):\n\n self.data.linear.ss = self.data.linear.linear_system.assemble()\n\n if self.settings['recover_accelerations']:\n gain = self.data.linear.linear_system.beam.recover_accelerations(self.data.linear.ss)\n self.data.linear.ss.addGain(gain, where='out')\n\n # modify inout coordinates\n if self.settings['inout_coordinates'] == 'nodes':\n try:\n self.data.linear.linear_system.to_nodal_coordinates()\n except AttributeError:\n pass\n\n # retain only selected inputs and outputs\n if len(self.settings['retain_inputs']) != 0:\n self.data.linear.ss.retain_inout_channels(self.settings['retain_inputs'], where='in')\n if len(self.settings['retain_outputs']) != 0:\n self.data.linear.ss.retain_inout_channels(self.settings['retain_outputs'], where='out')\n\n if len(self.settings['retain_input_variables']) != 0:\n ss = self.data.linear.ss\n input_vars = ss.input_variables\n removed_variables = []\n for variable in input_vars:\n if variable.name not in self.settings['retain_input_variables']:\n removed_variables.append(variable.name)\n ss.remove_inputs(*removed_variables)\n\n if len(self.settings['retain_output_variables']) != 0:\n ss = self.data.linear.ss\n output_vars = ss.output_variables\n removed_variables = []\n for variable in output_vars:\n if variable.name not in self.settings['retain_output_variables']:\n removed_variables.append(variable.name)\n ss.remove_outputs(*removed_variables)\n\n cout.cout_wrap('Final system is:', 1)\n cout.cout_wrap(str(self.data.linear.ss), 2)\n\n return self.data\n\n\n" }, { "path": "sharpy/solvers/modal.py", "content": "import ctypes as ct\nimport numpy as np\nimport scipy as sc\nimport os\nimport itertools\nimport warnings\nimport sharpy.structure.utils.xbeamlib as xbeamlib\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.cout_utils as cout\nimport sharpy.structure.utils.modalutils as modalutils\n\n\n@solver\nclass Modal(BaseSolver):\n \"\"\"\n ``Modal`` solver class, inherited from ``BaseSolver``\n\n Extracts the ``M``, ``K`` and ``C`` matrices from the ``Fortran`` library for the beam. Depending on the choice of\n modal projection, these may or may not be transformed to a state-space form to compute the eigenvalues and mode shapes\n of the structure.\n \"\"\"\n solver_id = 'Modal'\n solver_classification = 'Linear'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Write status to screen'\n\n # solution options\n settings_types['rigid_body_modes'] = 'bool'\n settings_default['rigid_body_modes'] = False\n settings_description['rigid_body_modes'] = 'Write modes with rigid body mode shapes'\n\n settings_types['use_undamped_modes'] = 'bool' # basis for modal projection\n settings_default['use_undamped_modes'] = True\n settings_description['use_undamped_modes'] = 'Project the modes onto undamped mode shapes'\n\n settings_types['NumLambda'] = 'int' # no. of different modes to retain\n settings_default['NumLambda'] = 20 # doubles if use_undamped_modes is False\n settings_description['NumLambda'] = 'Number of modes to retain'\n\n # output options\n settings_types['write_modes_vtk'] = 'bool' # write displacements mode shapes in vtk file\n settings_default['write_modes_vtk'] = True\n settings_description['write_modes_vtk'] = 'Write Paraview files with mode shapes'\n\n settings_types['print_matrices'] = 'bool' # print M,C,K matrices to dat file\n settings_default['print_matrices'] = False\n settings_description['print_matrices'] = 'Write M, C and K matrices to file'\n\n settings_types['save_data'] = 'bool' # write modes shapes/freq./damp. to dat file\n settings_default['save_data'] = True\n settings_description['save_data'] = 'Write mode shapes, frequencies and damping to file'\n\n settings_types['continuous_eigenvalues'] = 'bool'\n settings_default['continuous_eigenvalues'] = False\n settings_description['continuous_eigenvalues'] = 'Use continuous time eigenvalues'\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = 0\n settings_description['dt'] = 'Time step to compute discrete time eigenvalues'\n\n settings_types['delta_curved'] = 'float'\n settings_default['delta_curved'] = 1e-2\n settings_description['delta_curved'] = 'Threshold for linear expressions in rotation formulas'\n\n settings_types['plot_eigenvalues'] = 'bool'\n settings_default['plot_eigenvalues'] = False\n settings_description['plot_eigenvalues'] = 'Plot to screen root locus diagram'\n\n settings_types['max_rotation_deg'] = 'float'\n settings_default['max_rotation_deg'] = 15.\n settings_description['max_rotation_deg'] = 'Scale mode shape to have specified maximum rotation'\n\n settings_types['max_displacement'] = 'float'\n settings_default['max_displacement'] = 0.15\n settings_description['max_displacement'] = 'Scale mode shape to have specified maximum displacement'\n\n settings_types['use_custom_timestep'] = 'int'\n settings_default['use_custom_timestep'] = -1\n settings_description['use_custom_timestep'] = 'If > -1, it will use that time step geometry for calculating the modes'\n\n settings_types['rigid_modes_ppal_axes'] = 'bool'\n settings_default['rigid_modes_ppal_axes'] = False\n settings_description['rigid_modes_ppal_axes'] = 'Modify the ridid body modes such that they are defined wrt ' \\\n 'to the CG and aligned with the principal axes of inertia'\n\n settings_types['rigid_modes_cg'] = 'bool'\n settings_default['rigid_modes_cg'] = False\n settings_description['rigid_modes_cg'] = 'Not implemente yet'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n\n self.folder = None\n self.eigenvalue_table = None\n self.filename_freq = None\n self.filename_damp = None\n self.filename_shapes = None\n self.rigid_body_motion = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default)\n\n self.rigid_body_motion = self.settings['rigid_body_modes']\n\n self.data.ts = len(self.data.structure.timestep_info) - 1\n if self.settings['use_custom_timestep'] > -1:\n self.data.ts = self.settings['use_custom_timestep']\n\n # load info from dyn dictionary\n self.data.structure.add_unsteady_information(\n self.data.structure.dyn_dict,\n self.data.ts)\n\n # create folder for containing files if necessary\n self.folder = data.output_folder + '/beam_modal_analysis/'\n if not os.path.exists(self.folder):\n os.makedirs(self.folder)\n\n self.filename_freq = (self.folder +\n 'tstep' + (\"%06d\" % self.data.ts) +\n '_ModalFrequencies.dat')\n self.filename_damp = (self.folder +\n 'tstep' + (\"%06d\" % self.data.ts) +\n '_ModalDamping.dat')\n self.filename_shapes = (self.folder +\n 'tstep' + (\"%06d\" % self.data.ts) +\n '_ModalShape')\n\n if self.settings['print_info']:\n cout.cout_wrap('Structural eigenvalues')\n eigenvalue_filename = self.folder + '/eigenvaluetable.txt'\n self.eigenvalue_table = modalutils.EigenvalueTable(filename=eigenvalue_filename)\n self.eigenvalue_table.print_header(self.eigenvalue_table.headers)\n\n def run(self, **kwargs):\n r\"\"\"\n Extracts the eigenvalues and eigenvectors of the clamped structure.\n\n If ``use_undamped_modes == True`` then the free vibration modes of the clamped structure are found solving:\n\n .. math:: \\mathbf{M\\,\\ddot{\\eta}} + \\mathbf{K\\,\\eta} = 0\n\n that flows down to solving the non-trivial solutions to:\n\n .. math:: (-\\omega_n^2\\,\\mathbf{M} + \\mathbf{K})\\mathbf{\\Phi} = 0\n\n On the other hand, if the damped modes are chosen because the system has damping, the free vibration\n modes are found solving the equation of motion of the form:\n\n .. math:: \\mathbf{M\\,\\ddot{\\eta}} + \\mathbf{C\\,\\dot{\\eta}} + \\mathbf{K\\,\\eta} = 0\n\n which can be written in state space form, with the state vector :math:`\\mathbf{x} = [\\eta^T,\\,\\dot{\\eta}^T]^T`\n as\n\n .. math:: \\mathbf{\\dot{x}} = \\begin{bmatrix} 0 & \\mathbf{I} \\\\ -\\mathbf{M^{-1}K} & -\\mathbf{M^{-1}C}\n \\end{bmatrix} \\mathbf{x}\n\n and therefore the mode shapes and frequencies correspond to the solution of the eigenvalue problem\n\n .. math:: \\mathbf{A\\,\\Phi} = \\mathbf{\\Lambda\\,\\Phi}.\n\n From the eigenvalues, the following system characteristics are provided:\n\n * Natural Frequency: :math:`\\omega_n = |\\lambda|`\n\n * Damped natural frequency: :math:`\\omega_d = \\text{Im}(\\lambda) = \\omega_n \\sqrt{1-\\zeta^2}`\n\n * Damping ratio: :math:`\\zeta = -\\frac{\\text{Re}(\\lambda)}{\\omega_n}`\n\n In addition to the above, the modal output dictionary includes the following:\n\n * ``M``: Tangent mass matrix\n\n * ``C``: Tangent damping matrix\n\n * ``K``: Tangent stiffness matrix\n\n * ``Ccut``: Modal damping matrix :math:`\\mathbf{C}_m = \\mathbf{\\Phi}^T\\mathbf{C}\\mathbf{\\Phi}`\n\n * ``Kin_damp``: Forces gain matrix (when damped): :math:`K_{in} = \\mathbf{\\Phi}_L^T \\mathbf{M}^{-1}`\n\n * ``eigenvectors``: Right eigenvectors\n\n * ``eigenvectors_left``: Left eigenvectors given when the system is damped\n\n Returns:\n PreSharpy: updated data object with modal analysis as part of the last structural time step.\n\n \"\"\"\n\n # Number of degrees of freedom\n num_str_dof = self.data.structure.num_dof.value\n num_rigid_dof = 10 if self.rigid_body_motion else 0\n\n num_dof = num_str_dof + num_rigid_dof\n\n # Initialize matrices\n FullMglobal = np.zeros((num_dof, num_dof),\n dtype=ct.c_double, order='F')\n FullKglobal = np.zeros((num_dof, num_dof),\n dtype=ct.c_double, order='F')\n FullCglobal = np.zeros((num_dof, num_dof),\n dtype=ct.c_double, order='F')\n\n if self.rigid_body_motion:\n # Settings for the assembly of the matrices\n # try:\n # full_matrix_settings = self.data.settings['StaticCoupled']['structural_solver_settings']\n # full_matrix_settings['dt'] = ct.c_double(0.01) # Dummy: required but not used\n # full_matrix_settings['newmark_damp'] = ct.c_double(1e-2) # Dummy: required but not used\n # except KeyError:\n # full_matrix_settings = self.data.settings['DynamicCoupled']['structural_solver_settings']\n import sharpy.solvers._basestructural as basestructuralsolver\n full_matrix_settings = basestructuralsolver._BaseStructural().settings_default\n settings_utils.to_custom_types(full_matrix_settings, basestructuralsolver._BaseStructural().settings_types, full_matrix_settings)\n\n\n # Obtain the tangent mass, damping and stiffness matrices\n FullMglobal, FullCglobal, FullKglobal, FullQ = xbeamlib.xbeam3_asbly_dynamic(self.data.structure,\n self.data.structure.timestep_info[self.data.ts],\n full_matrix_settings)\n\n cg = modalutils.cg(FullMglobal)\n else:\n xbeamlib.cbeam3_solv_modal(self.data.structure,\n self.settings, self.data.ts,\n FullMglobal, FullCglobal, FullKglobal)\n cg = None\n\n # Print matrices\n if self.settings['print_matrices']:\n np.savetxt(self.folder + \"Mglobal.dat\", FullMglobal, fmt='%.12f',\n delimiter='\\t', newline='\\n')\n np.savetxt(self.folder + \"Cglobal.dat\", FullCglobal, fmt='%.12f',\n delimiter='\\t', newline='\\n')\n np.savetxt(self.folder + \"Kglobal.dat\", FullKglobal, fmt='%.12f',\n delimiter='\\t', newline='\\n')\n\n # Check if the damping matrix is zero (issue working)\n if self.settings['use_undamped_modes']:\n zero_FullCglobal = True\n for i,j in itertools.product(range(num_dof),range(num_dof)):\n if np.absolute(FullCglobal[i, j]) > np.finfo(float).eps:\n zero_FullCglobal = False\n warnings.warn('Projecting a system with damping on undamped modal shapes')\n break\n\n NumLambda = min(num_dof, self.settings['NumLambda'])\n\n if self.settings['use_undamped_modes']:\n\n # Solve for eigenvalues (with unit eigenvectors)\n eigenvalues,eigenvectors=np.linalg.eig(\n np.linalg.solve(FullMglobal,FullKglobal))\n eigenvectors_left=None\n # Define vibration frequencies and damping\n freq_natural = np.sqrt(eigenvalues)\n order = np.argsort(freq_natural)[:NumLambda]\n freq_natural = freq_natural[order]\n eigenvalues = eigenvalues[order]\n eigenvectors = eigenvectors[:,order]\n damping = np.zeros((NumLambda,))\n\n else:\n # State-space model\n Minv_neg = -np.linalg.inv(FullMglobal)\n A = np.zeros((2*num_dof, 2*num_dof), dtype=ct.c_double, order='F')\n A[:num_dof, num_dof:] = np.eye(num_dof)\n A[num_dof:, :num_dof] = np.dot(Minv_neg, FullKglobal)\n A[num_dof:, num_dof:] = np.dot(Minv_neg, FullCglobal)\n\n # Solve the eigenvalues problem\n eigenvalues, eigenvectors_left, eigenvectors = \\\n sc.linalg.eig(A,left=True,right=True)\n freq_natural = np.abs(eigenvalues)\n damping = np.zeros_like(freq_natural)\n iiflex = freq_natural > 1e-16*np.mean(freq_natural) # Pick only structural modes\n damping[iiflex] = -eigenvalues[iiflex].real/freq_natural[iiflex]\n freq_damped = freq_natural * np.sqrt(1-damping**2)\n\n # Order & downselect complex conj:\n # this algorithm assumes that complex conj eigenvalues appear consecutively\n # in eigenvalues. For symmetrical systems, this relies on the fact that:\n # - complex conj eigenvalues have the same absolute value (to machine\n # precision)\n # - couples of eigenvalues with multiplicity higher than 1, show larger\n # numerical difference\n order = np.argsort(freq_damped)[:2*NumLambda]\n freq_damped = freq_damped[order]\n freq_natural = freq_natural[order]\n eigenvalues = eigenvalues[order]\n\n include = np.ones((2*NumLambda,), dtype=np.bool)\n ii = 0\n tol_rel = np.finfo(float).eps * freq_damped[ii]\n while ii < 2*NumLambda:\n # check complex\n if np.abs(eigenvalues[ii].imag) > 0.:\n if np.abs(eigenvalues[ii+1].real-eigenvalues[ii].real) > tol_rel or\\\n np.abs(eigenvalues[ii+1].imag+eigenvalues[ii].imag) > tol_rel:\n raise NameError('Complex conjugate expected but not found!')\n ii += 1\n try:\n include[ii] = False\n except IndexError:\n pass\n ii += 1\n freq_damped = freq_damped[include]\n eigenvalues = eigenvalues[include]\n if self.settings['continuous_eigenvalues']:\n if self.settings['dt'] == 0.:\n raise ValueError('Cannot compute the continuous eigenvalues without a dt value')\n eigenvalues = np.log(eigenvalues)/self.settings['dt']\n\n order = order[include]\n damping = damping[order]\n eigenvectors = eigenvectors[:, order]\n eigenvectors_left = eigenvectors_left[:, order].conj()\n\n # Modify rigid body modes for them to be defined wrt the CG\n eigenvectors = modalutils.mode_sign_convention(self.data.structure.boundary_conditions, eigenvectors,\n self.rigid_body_motion)\n if not eigenvectors_left:\n if self.settings['rigid_modes_ppal_axes']:\n eigenvectors, t_pa, r_pa = modalutils.free_modes_principal_axes(eigenvectors, FullMglobal,\n return_transform=True)\n else:\n t_pa = None # Transformation matrix from the A frame to the P frame (principal axes of inertia)\n r_pa = None\n # Scaling\n eigenvectors, eigenvectors_left = self.scale_modes_unit_mass_matrix(eigenvectors, FullMglobal, eigenvectors_left)\n\n # Other terms required for state-space realisation\n # non-zero damping matrix\n # Modal damping matrix\n if self.settings['use_undamped_modes'] and not(zero_FullCglobal):\n Ccut = np.dot(eigenvectors.T, np.dot(FullCglobal, eigenvectors))\n else:\n Ccut = None\n\n # forces gain matrix (nodal -> modal)\n if not self.settings['use_undamped_modes']:\n Kin_damp = np.dot(eigenvectors_left[num_dof:, :].T, -Minv_neg)\n else:\n Kin_damp = None\n\n # Plot eigenvalues using matplotlib if specified in settings\n if self.settings['plot_eigenvalues']:\n try:\n import matplotlib.pyplot as plt\n fig = plt.figure()\n plt.scatter(eigenvalues.real, eigenvalues.imag)\n plt.show()\n plt.savefig(self.folder + 'eigenvalues.png', transparent=True, bbox_inches='tight')\n except ModuleNotFoundError:\n warnings.warn('Unable to import matplotlib, skipping plot')\n\n # Write dat files\n if self.settings['save_data']:\n if type(eigenvalues) == complex:\n np.savetxt(self.folder + \"eigenvalues.dat\", eigenvalues.view(float).reshape(-1, 2), fmt='%.12f',\n delimiter='\\t', newline='\\n')\n else:\n np.savetxt(self.folder + \"eigenvalues.dat\", eigenvalues.view(float), fmt='%.12f',\n delimiter='\\t', newline='\\n')\n np.savetxt(self.folder + \"eigenvectors.dat\", eigenvectors[:num_dof].real,\n fmt='%.12f', delimiter='\\t', newline='\\n')\n\n if not self.settings['use_undamped_modes']:\n np.savetxt(self.folder + 'frequencies.dat', freq_damped[:NumLambda],\n fmt='%e', delimiter='\\t', newline='\\n')\n else:\n np.savetxt(self.folder + 'frequencies.dat', freq_natural[:NumLambda],\n fmt='%e', delimiter='\\t', newline='\\n')\n\n np.savetxt(self.filename_damp, damping[:NumLambda],\n fmt='%e', delimiter='\\t', newline='\\n')\n\n # Write vtk\n if self.settings['write_modes_vtk']:\n try:\n self.data.aero\n except AttributeError:\n warnings.warn('No aerodynamic model found - unable to project the mode onto aerodynamic grid')\n else:\n modalutils.write_modes_vtk(\n self.data,\n eigenvectors[:num_dof],\n NumLambda,\n self.filename_shapes,\n self.settings['max_rotation_deg'],\n self.settings['max_displacement'],\n ts=self.settings['use_custom_timestep'])\n\n outdict = dict()\n\n if self.settings['use_undamped_modes']:\n outdict['modes'] = 'undamped'\n outdict['freq_natural'] = freq_natural\n if not zero_FullCglobal:\n outdict['warning'] =\\\n 'system with damping: mode shapes and natural frequencies do not account for damping!'\n else:\n outdict['modes'] = 'damped'\n outdict['freq_damped'] = freq_damped\n outdict['freq_natural'] = freq_natural\n\n outdict['damping'] = damping\n outdict['eigenvalues'] = eigenvalues\n outdict['eigenvectors'] = eigenvectors\n\n if Ccut is not None:\n outdict['Ccut'] = Ccut\n if Kin_damp is not None:\n outdict['Kin_damp'] = Kin_damp\n if not self.settings['use_undamped_modes']:\n outdict['eigenvectors_left'] = eigenvectors_left\n\n if cg is not None:\n outdict['cg'] = cg\n\n outdict['M'] = FullMglobal\n outdict['C'] = FullCglobal\n outdict['K'] = FullKglobal\n\n if t_pa is not None:\n outdict['t_pa'] = t_pa\n outdict['r_pa'] = r_pa\n self.data.structure.timestep_info[self.data.ts].modal = outdict\n\n if self.settings['print_info']:\n if self.settings['use_undamped_modes']:\n self.eigenvalue_table.print_evals(np.sqrt(eigenvalues[:NumLambda])*1j)\n else:\n self.eigenvalue_table.print_evals(eigenvalues[:NumLambda])\n self.eigenvalue_table.close_file()\n\n return self.data\n\n def scale_modes_unit_mass_matrix(self, eigenvectors, FullMglobal, eigenvectors_left=None):\n if self.settings['use_undamped_modes']:\n # mass normalise (diagonalises M and K)\n eigenvectors = modalutils.scale_mass_normalised_modes(eigenvectors, FullMglobal)\n else:\n # unit normalise (diagonalises A)\n if not self.rigid_body_motion:\n for ii in range(eigenvectors.shape[1]): # Issue - dot product = 0 when you have arbitrary damping\n fact = 1./np.sqrt(np.dot(eigenvectors_left[:, ii], eigenvectors[:, ii]))\n eigenvectors_left[:, ii] = fact*eigenvectors_left[:, ii]\n eigenvectors[:, ii] = fact*eigenvectors[:, ii]\n\n return eigenvectors, eigenvectors_left\n\n def free_free_modes(self, phi, M):\n r\"\"\"\n\n Warning:\n This function is deprecated. See :func:`~sharpy.structure.utils.modalutils.free_modes_principal_axes`\n for a transformation to the CG and with respect to the principal axes of inertia.\n\n Returns the rigid body modes defined with respect to the centre of gravity\n\n The transformation from the modes defined at the FoR A origin, :math:`\\boldsymbol{\\Phi}`, to the modes defined\n using the centre of gravity as a reference is\n\n\n .. math:: \\boldsymbol{\\Phi}_{rr,CG}|_{TRA} = \\boldsymbol{\\Phi}_{RR}|_{TRA} + \\tilde{\\mathbf{r}}_{CG}\n \\boldsymbol{\\Phi}_{RR}|_{ROT}\n\n .. math:: \\boldsymbol{\\Phi}_{rr,CG}|_{ROT} = \\boldsymbol{\\Phi}_{RR}|_{ROT}\n\n Returns:\n (np.array): Transformed eigenvectors\n \"\"\"\n\n # NG - 26/7/19 This is the transformation being performed by K_vec\n # Leaving this here for now in case it becomes necessary\n # .. math:: \\boldsymbol{\\Phi}_{ss,CG}|_{TRA} = \\boldsymbol{\\Phi}_{SS}|_{TRA} +\\boldsymbol{\\Phi}_{RS}|_{TRA} -\n # \\tilde{\\mathbf{r}}_{A}\\boldsymbol{\\Phi}_{RS}|_{ROT}\n #\n # .. math:: \\boldsymbol{\\Phi}_{ss,CG}|_{ROT} = \\boldsymbol{\\Phi}_{SS}|_{ROT}\n # + (\\mathbf{T}(\\boldsymbol{\\Psi})^\\top)^{-1}\\boldsymbol{\\Phi}_{RS}|_{ROT}\n warnings.warn('This function is deprecated. See sharpy.structure.utils.modalutils.free_modes_principal_axes',\n category=DeprecationWarning)\n if not self.rigid_body_motion:\n warnings.warn('No rigid body modes to transform because the structure is clamped')\n return phi\n else:\n pos = self.data.structure.timestep_info[self.data.ts].pos\n r_cg = modalutils.cg(M)\n\n jj = 0\n K_vec = np.zeros((phi.shape[0], phi.shape[0]))\n\n jj_for_vel = range(self.data.structure.num_dof.value, self.data.structure.num_dof.value + 3)\n jj_for_rot = range(self.data.structure.num_dof.value + 3, self.data.structure.num_dof.value + 6)\n\n for node_glob in range(self.data.structure.num_node):\n ### detect bc at node (and no. of dofs)\n bc_here = self.data.structure.boundary_conditions[node_glob]\n\n if bc_here == 1: # clamp (only rigid-body)\n continue\n\n elif bc_here == -1 or bc_here == 0: # (rigid+flex body)\n dofs_here = 6\n jj_tra = 6 * self.data.structure.vdof[node_glob] + np.array([0, 1, 2], dtype=int)\n jj_rot = 6 * self.data.structure.vdof[node_glob] + np.array([3, 4, 5], dtype=int)\n else:\n raise NameError('Invalid boundary condition (%d) at node %d!' \\\n % (bc_here, node_glob))\n\n jj += dofs_here\n\n ee, node_loc = self.data.structure.node_master_elem[node_glob, :]\n psi = self.data.structure.timestep_info[self.data.ts].psi[ee, node_loc, :]\n\n Ra = pos[node_glob, :] # in A FoR with respect to G\n\n K_vec[np.ix_(jj_tra, jj_tra)] += np.eye(3)\n K_vec[np.ix_(jj_tra, jj_for_vel)] += np.eye(3)\n K_vec[np.ix_(jj_tra, jj_for_rot)] -= algebra.skew(Ra)\n\n K_vec[np.ix_(jj_rot, jj_rot)] += np.eye(3)\n K_vec[np.ix_(jj_rot, jj_for_rot)] += np.linalg.inv(algebra.crv2tan(psi).T)\n\n # Rigid-Rigid modes transform\n Krr = np.eye(10)\n Krr[np.ix_([0, 1, 2], [3, 4, 5])] += algebra.skew(r_cg)\n\n # Assemble transformed modes\n phirr = Krr.dot(phi[-10:, :10])\n\n # Get rigid body modes to be positive in translation and rotation\n for i in range(10):\n ind = np.argmax(np.abs(phirr[:, i]))\n phirr[:, i] = np.sign(phirr[ind, i]) * phirr[:, i]\n\n # NG - 26/7/19 - Transformation of the rigid part of the elastic modes ended up not being necessary but leaving\n # here in case it becomes useful in the future\n phit = np.block([np.zeros((phi.shape[0], 10)), phi[:, 10:]])\n phit[-10:, :10] = phirr\n\n return phit\n" }, { "path": "sharpy/solvers/noaero.py", "content": "import sharpy.utils.settings as settings_utils\nfrom sharpy.utils.solver_interface import solver, BaseSolver\n\n\n@solver\nclass NoAero(BaseSolver):\n \"\"\"\n Skip UVLM evaluation\n\n Solver to be used with either :class:`~sharpy.solvers.staticcoupled.StaticCoupled` or\n :class:`~sharpy.solvers.dynamiccoupled.DynamicCoupled` when aerodynamics are not of interest.\n\n An example would be running a structural-only simulation where you would like to keep an aerodynamic grid for\n visualisation purposes.\n \"\"\"\n solver_id = 'NoAero'\n solver_classification = 'Aero'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = 0.1\n settings_description['dt'] = 'Time step'\n\n settings_types['update_grid'] = 'bool'\n settings_default['update_grid'] = True\n settings_description['update_grid'] = 'Update aerodynamic grid as the structure deforms.'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n no_ctype=True)\n\n if len(self.data.aero.timestep_info) == 0: # initialise with zero timestep for static sims\n self.update_step()\n\n def run(self, **kwargs):\n\n aero_tstep = settings_utils.set_value_or_default(kwargs, 'aero_step', self.data.aero.timestep_info[-1])\n dt = settings_utils.set_value_or_default(kwargs, 'dt', self.settings['dt'])\n\n # generate the wake because the solid shape might change\n self.data.aero.wake_shape_generator.generate({'zeta': aero_tstep.zeta,\n 'zeta_star': aero_tstep.zeta_star,\n 'gamma': aero_tstep.gamma,\n 'gamma_star': aero_tstep.gamma_star,\n 'dist_to_orig': aero_tstep.dist_to_orig})\n\n return self.data\n\n def add_step(self):\n self.data.aero.add_timestep()\n\n def update_grid(self, beam):\n # called by DynamicCoupled\n if self.settings['update_grid']:\n self.data.aero.generate_zeta(beam,\n self.data.aero.aero_settings,\n -1,\n beam_ts=-1)\n\n def update_custom_grid(self, structure_tstep, aero_tstep, nl_body_tstep=None):\n # called by DynamicCoupled\n if self.settings['update_grid']:\n self.data.aero.generate_zeta_timestep_info(structure_tstep,\n aero_tstep,\n self.data.structure,\n self.data.aero.aero_settings,\n dt=None)\n\n def update_step(self):\n # called by StaticCoupled\n if self.settings['update_grid']:\n self.data.aero.generate_zeta(self.data.structure,\n self.data.aero.aero_settings,\n self.data.ts)\n else:\n self.add_step()\n\n def next_step(self):\n # called by StaticCoupled\n self.add_step()\n" }, { "path": "sharpy/solvers/nonliftingbodygridloader.py", "content": "from sharpy.utils.solver_interface import solver\nimport sharpy.aero.models.nonliftingbodygrid as nonliftingbodygrid\nimport sharpy.utils.settings as settings_utils\nfrom sharpy.solvers.gridloader import GridLoader\n\n\n@solver\nclass NonliftingbodygridLoader(GridLoader):\n \"\"\"\n ``NonliftingbodygridLoader`` class, inherited from ``GridLoader``\n\n Generates aerodynamic grid for nonlifting bodies based on the input data\n\n Args:\n data (PreSharpy): ``ProblemData`` class structure\n\n Attributes:\n settings (dict): Name-value pair of the settings employed by the aerodynamic solver\n settings_types (dict): Acceptable types for the values in ``settings``\n settings_default (dict): Name-value pair of default values for the aerodynamic settings\n data (ProblemData): class structure\n file_name (str): name of the ``.nonlifting_body.h5`` HDF5 file\n aero: empty attribute\n aero_data_dict (dict): key-value pairs of aerodynamic data\n\n\n \"\"\"\n solver_id = 'NonliftingbodygridLoader'\n solver_classification = 'loader'\n\n def __init__(self):\n super().__init__\n self.file_name = '.nonlifting_body.h5'\n\n # nonlifting_body storage\n self.nonlifting_body = None\n\n def run(self, **kwargs):\n self.data.nonlifting_body = nonliftingbodygrid.NonliftingBodyGrid()\n self.data.nonlifting_body.generate(self.data_dict,\n self.data.structure,\n self.settings,\n self.data.ts)\n return self.data\n" }, { "path": "sharpy/solvers/nonlineardynamic.py", "content": "\"\"\"\n@modified Alfonso del Carre\n\"\"\"\n\nimport sharpy.structure.utils.xbeamlib as xbeamlib\nfrom sharpy.utils.settings import str2bool\nfrom sharpy.utils.solver_interface import solver, solver_from_string\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.cout_utils as cout\n\n_BaseStructural = solver_from_string('_BaseStructural')\n\n\n@solver\nclass NonLinearDynamic(_BaseStructural):\n \"\"\"\n Structural solver used for the dynamic simulation of free-flying structures.\n\n This solver provides an interface to the structural library (``xbeam``) and updates the structural parameters\n for every time step of the simulation.\n\n This solver is called as part of a standalone structural simulation.\n\n \"\"\"\n solver_id = 'NonLinearDynamic'\n solver_classification = 'structural'\n\n settings_types = _BaseStructural.settings_types.copy()\n settings_default = _BaseStructural.settings_default.copy()\n settings_description = _BaseStructural.settings_description.copy()\n\n settings_types['prescribed_motion'] = 'bool'\n settings_default['prescribed_motion'] = None\n\n settings_types['gravity_dir'] = 'list(float)'\n settings_default['gravity_dir'] = [0, 0, 1]\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n\n def initialise(self, data, restart=False):\n self.data = data\n self.settings = data.settings[self.solver_id]\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n # load info from dyn dictionary\n self.data.structure.add_unsteady_information(self.data.structure.dyn_dict, self.settings['num_steps'])\n\n # allocate timestep_info\n for i in range(self.settings['num_steps']):\n self.data.structure.add_timestep(self.data.structure.timestep_info)\n if i>0:\n self.data.structure.timestep_info[i].unsteady_applied_forces[:] = self.data.structure.dynamic_input[i - 1]['dynamic_forces']\n self.data.structure.timestep_info[i].steady_applied_forces[:] = self.data.structure.ini_info.steady_applied_forces\n\n\n def run(self, **kwargs):\n prescribed_motion = False\n try:\n prescribed_motion = self.settings['prescribed_motion']\n except KeyError:\n pass\n if prescribed_motion is True:\n cout.cout_wrap('Running non linear dynamic solver...', 2)\n xbeamlib.cbeam3_solv_nlndyn(self.data.structure, self.settings)\n else:\n cout.cout_wrap('Running non linear dynamic solver with RB...', 2)\n xbeamlib.xbeam_solv_couplednlndyn(self.data.structure, self.settings)\n\n self.data.ts = self.settings['num_steps']\n cout.cout_wrap('...Finished', 2)\n return self.data\n" }, { "path": "sharpy/solvers/nonlineardynamiccoupledstep.py", "content": "\"\"\"\n@modified Alfonso del Carre\n\"\"\"\n\nimport numpy as np\n\nimport sharpy.structure.utils.xbeamlib as xbeamlib\nfrom sharpy.utils.settings import str2bool\nfrom sharpy.utils.solver_interface import solver, BaseSolver, solver_from_string\nimport sharpy.utils.settings as settings_utils\n\n\n_BaseStructural = solver_from_string('_BaseStructural')\n\n@solver\nclass NonLinearDynamicCoupledStep(_BaseStructural):\n \"\"\"\n Structural solver used for the dynamic simulation of free-flying structures.\n\n This solver provides an interface to the structural library (``xbeam``) and updates the structural parameters\n for every k-th step in the FSI iteration.\n\n This solver can be called as part of a standalone structural simulation or as the structural solver of a coupled\n aeroelastic simulation.\n\n \"\"\"\n solver_id = 'NonLinearDynamicCoupledStep'\n solver_classification = 'structural'\n\n settings_types = _BaseStructural.settings_types.copy()\n settings_default = _BaseStructural.settings_default.copy()\n settings_description = _BaseStructural.settings_description.copy()\n\n settings_types['balancing'] = 'bool'\n settings_default['balancing'] = False\n\n # initial speed direction is given in inertial FOR!!!\n settings_types['initial_velocity_direction'] = 'list(float)'\n settings_default['initial_velocity_direction'] = [-1.0, 0.0, 0.0]\n settings_description['initial_velocity_direction'] = 'Initial velocity of the reference node given in the inertial FOR'\n\n settings_types['initial_velocity'] = 'float'\n settings_default['initial_velocity'] = 0\n settings_description['initial_velocity'] = 'Initial velocity magnitude of the reference node'\n\n settings_types['relaxation_factor'] = 'float'\n settings_default['relaxation_factor'] = 0.3\n settings_description['relaxation factor'] = 'Relaxation factor'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n # load info from dyn dictionary\n self.data.structure.add_unsteady_information(self.data.structure.dyn_dict, self.settings['num_steps'])\n\n # add initial speed to RBM\n if self.settings['initial_velocity']:\n new_direction = np.dot(self.data.structure.timestep_info[-1].cag(),\n self.settings['initial_velocity_direction'])\n self.data.structure.timestep_info[-1].for_vel[0:3] = new_direction*self.settings['initial_velocity']\n\n # generate q, dqdt and dqddt\n xbeamlib.xbeam_solv_disp2state(self.data.structure, self.data.structure.timestep_info[-1])\n\n def run(self, **kwargs):\n\n structural_step = settings_utils.set_value_or_default(kwargs, 'structural_step', self.data.structure.timestep_info[-1])\n \n dt= settings_utils.set_value_or_default(kwargs, 'dt', self.settings['dt'])\n\n xbeamlib.xbeam_step_couplednlndyn(self.data.structure,\n self.settings,\n self.data.ts,\n structural_step,\n dt=dt)\n self.extract_resultants(structural_step)\n self.data.structure.integrate_position(structural_step, dt)\n\n return self.data\n\n def add_step(self):\n self.data.structure.next_step()\n\n def next_step(self):\n pass\n\n def extract_resultants(self, tstep=None):\n if tstep is None:\n tstep = self.data.structure.timestep_info[self.data.ts]\n steady, unsteady, grav = tstep.extract_resultants(self.data.structure, force_type=['steady', 'unsteady', 'grav'])\n totals = steady + unsteady + grav\n return totals[0:3], totals[3:6]\n\n" }, { "path": "sharpy/solvers/nonlineardynamicmultibody.py", "content": "import ctypes as ct\nimport numpy as np\nimport os\n\nfrom sharpy.utils.solver_interface import solver, BaseSolver, solver_from_string\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.solver_interface as solver_interface\n\nimport sharpy.utils.cout_utils as cout\nimport sharpy.structure.utils.xbeamlib as xbeamlib\nimport sharpy.utils.multibody as mb\nimport sharpy.utils.algebra as algebra\nimport sharpy.structure.utils.lagrangeconstraints as lagrangeconstraints\nimport sharpy.utils.exceptions as exc\n\n\n_BaseStructural = solver_from_string('_BaseStructural')\n\n\n@solver\nclass NonLinearDynamicMultibody(_BaseStructural):\n \"\"\"\n Nonlinear dynamic multibody\n\n Nonlinear dynamic step solver for multibody structures.\n\n \"\"\"\n solver_id = 'NonLinearDynamicMultibody'\n solver_classification = 'structural'\n\n settings_types = _BaseStructural.settings_types.copy()\n settings_default = _BaseStructural.settings_default.copy()\n settings_description = _BaseStructural.settings_description.copy()\n settings_options = dict()\n\n settings_types['time_integrator'] = 'str'\n settings_default['time_integrator'] = 'NewmarkBeta'\n settings_description['time_integrator'] = 'Method to perform time integration'\n settings_options['time_integrator'] = ['NewmarkBeta', 'GeneralisedAlpha']\n\n settings_types['time_integrator_settings'] = 'dict'\n settings_default['time_integrator_settings'] = dict()\n settings_description['time_integrator_settings'] = 'Settings for the time integrator'\n\n settings_types['write_lm'] = 'bool'\n settings_default['write_lm'] = False\n settings_description['write_lm'] = 'Write lagrange multipliers to file'\n\n settings_types['relax_factor_lm'] = 'float'\n settings_default['relax_factor_lm'] = 0.\n settings_description['relax_factor_lm'] = 'Relaxation factor for Lagrange Multipliers. 0 no relaxation. 1 full relaxation'\n\n settings_types['allow_skip_step'] = 'bool'\n settings_default['allow_skip_step'] = False\n settings_description['allow_skip_step'] = 'Allow skip step when NaN is found while solving the system'\n\n settings_types['rigid_bodies'] = 'bool'\n settings_default['rigid_bodies'] = False\n settings_description['rigid_bodies'] = 'Set to zero the changes in flexible degrees of freedom (not very efficient)'\n\n settings_types['zero_ini_dot_ddot'] = 'bool'\n settings_default['zero_ini_dot_ddot'] = False\n settings_description['zero_ini_dot_ddot'] = 'Set to zero the position and crv derivatives at the first time step'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n\n # Total number of unknowns in the Multybody sistem\n self.sys_size = None\n\n # Total number of equations associated to the Lagrange multipliers\n self.lc_list = None\n self.num_LM_eq = None\n self.Lambda = None\n self.Lambda_dot = None\n self.Lambda_ddot = None\n\n self.gamma = None\n self.beta = None\n\n self.prev_Dq = None\n\n self.out_files = None # dict: containing output_variable:file_path if desired to write output\n\n def initialise(self, data, custom_settings=None, restart=False):\n\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n self.settings_options,\n no_ctype=True)\n\n # load info from dyn dictionary\n self.data.structure.add_unsteady_information(\n self.data.structure.dyn_dict, self.settings['num_steps'])\n\n # Define the number of equations\n self.lc_list = lagrangeconstraints.initialize_constraints(self.data.structure.ini_mb_dict)\n self.num_LM_eq = lagrangeconstraints.define_num_LM_eq(self.lc_list)\n\n self.Lambda = np.zeros((self.num_LM_eq,), dtype=ct.c_double, order='F')\n self.Lambda_dot = np.zeros((self.num_LM_eq,), dtype=ct.c_double, order='F')\n self.Lambda_ddot = np.zeros((self.num_LM_eq,), dtype=ct.c_double, order='F')\n\n if self.settings['write_lm']:\n dire = self.data.output_folder + '/NonLinearDynamicMultibody/'\n if not os.path.isdir(dire):\n os.makedirs(dire)\n\n self.out_files = {'lambda': dire + 'lambda.dat',\n 'lambda_dot': dire + 'lambda_dot.dat',\n 'lambda_ddot': dire + 'lambda_ddot.dat',\n 'cond_number': dire + 'cond_num.dat'}\n # clean up files\n for file in self.out_files.values():\n if os.path.isfile(file):\n os.remove(file)\n\n # Define the number of dofs\n self.define_sys_size()\n\n self.prev_Dq = np.zeros((self.sys_size + self.num_LM_eq))\n\n self.settings['time_integrator_settings']['sys_size'] = self.sys_size\n self.settings['time_integrator_settings']['num_LM_eq'] = self.num_LM_eq\n\n # Initialise time integrator\n if not restart:\n self.time_integrator = solver_interface.initialise_solver(\n self.settings['time_integrator'])\n self.time_integrator.initialise(\n self.data, self.settings['time_integrator_settings'], restart=restart)\n\n def add_step(self):\n self.data.structure.next_step()\n\n def next_step(self):\n pass\n\n def define_sys_size(self):\n \"\"\"\n This function defines the number of degrees of freedom in a multibody systems\n\n Each body contributes with ``num_dof`` degrees of freedom and 10 more if the\n associated local FoR can move or has Lagrange Constraints associated\n \"\"\"\n MBdict = self.data.structure.ini_mb_dict\n self.sys_size = self.data.structure.num_dof.value\n\n for ibody in range(self.data.structure.num_bodies):\n if (MBdict['body_%02d' % ibody]['FoR_movement'] == 'free'):\n self.sys_size += 10\n\n def define_rigid_dofs(self, MB_beam):\n\n self.n_rigid_dofs = 0\n self.rigid_dofs = []\n\n first_dof = 0\n for ibody in range(len(MB_beam)):\n last_dof = first_dof + MB_beam[ibody].num_dof.value\n if MB_beam[ibody].FoR_movement == 'free':\n self.n_rigid_dofs += 10\n self.rigid_dofs += (np.arange(10, dtype=int) + last_dof).tolist()\n last_dof += 10\n first_dof = last_dof + 0\n\n def assembly_MB_eq_system(self, MB_beam, MB_tstep, ts, dt, Lambda, Lambda_dot, MBdict):\n r\"\"\"\n This function generates the matrix and vector associated to the linear system to solve a structural iteration\n It usses a Newmark-beta scheme for time integration. Being M, C and K the mass, damping\n and stiffness matrices of the system:\n\n .. math::\n MB_Asys = MB_K + MB_C \\frac{\\gamma}{\\beta dt} + \\frac{1}{\\beta dt^2} MB_M\n\n Args:\n MB_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body\n MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n ts (int): Time step number\n dt(int): time step\n Lambda (np.ndarray): Lagrange Multipliers array\n Lambda_dot (np.ndarray): Time derivarive of ``Lambda``\n MBdict (dict): Dictionary including the multibody information\n\n Returns:\n MB_Asys (np.ndarray): Matrix of the systems of equations\n MB_Q (np.ndarray): Vector of the systems of equations\n \"\"\"\n\n MB_M = np.zeros((self.sys_size, self.sys_size), dtype=ct.c_double, order='F')\n MB_C = np.zeros((self.sys_size, self.sys_size), dtype=ct.c_double, order='F')\n MB_K = np.zeros((self.sys_size, self.sys_size), dtype=ct.c_double, order='F')\n MB_Q = np.zeros((self.sys_size,), dtype=ct.c_double, order='F')\n first_dof = 0\n last_dof = 0\n\n # Loop through the different bodies\n for ibody in range(len(MB_beam)):\n\n # Initialize matrices\n M = None\n C = None\n K = None\n Q = None\n\n # Generate the matrices for each body\n if MB_beam[ibody].FoR_movement == 'prescribed':\n last_dof = first_dof + MB_beam[ibody].num_dof.value\n M, C, K, Q = xbeamlib.cbeam3_asbly_dynamic(MB_beam[ibody], MB_tstep[ibody], self.settings)\n\n elif MB_beam[ibody].FoR_movement == 'free':\n last_dof = first_dof + MB_beam[ibody].num_dof.value + 10\n M, C, K, Q = xbeamlib.xbeam3_asbly_dynamic(MB_beam[ibody], MB_tstep[ibody], self.settings)\n\n\n ############### Assembly into the global matrices\n # Flexible and RBM contribution to Asys\n MB_M[first_dof:last_dof, first_dof:last_dof] = M.astype(dtype=ct.c_double, copy=True, order='F')\n MB_C[first_dof:last_dof, first_dof:last_dof] = C.astype(dtype=ct.c_double, copy=True, order='F')\n MB_K[first_dof:last_dof, first_dof:last_dof] = K.astype(dtype=ct.c_double, copy=True, order='F')\n\n #Q\n MB_Q[first_dof:last_dof] = Q\n\n first_dof = last_dof\n\n # Define the number of equations\n # Generate matrices associated to Lagrange multipliers\n LM_C, LM_K, LM_Q = lagrangeconstraints.generate_lagrange_matrix(\n self.lc_list,\n MB_beam,\n MB_tstep,\n ts,\n self.num_LM_eq,\n self.sys_size,\n dt,\n Lambda,\n Lambda_dot,\n \"dynamic\")\n\n # Include the matrices associated to Lagrange Multipliers\n MB_C += LM_C[:self.sys_size, :self.sys_size]\n MB_K += LM_K[:self.sys_size, :self.sys_size]\n MB_Q += LM_Q[:self.sys_size]\n\n # Only working for non-holonomic constratints\n kBnh = LM_C[self.sys_size:, :self.sys_size]\n strict_LM_Q = LM_Q[self.sys_size:]\n\n return MB_M, MB_C, MB_K, MB_Q, kBnh, strict_LM_Q\n\n def integrate_position(self, MB_beam, MB_tstep, dt):\n \"\"\"\n This function integrates the position of each local A FoR after the\n structural iteration has been solved.\n\n It uses a Newmark-beta approximation.\n\n Args:\n MB_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body\n MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n dt(int): time step\n \"\"\"\n vel = np.zeros((6,),)\n acc = np.zeros((6,),)\n for ibody in range(0, len(MB_tstep)):\n # I think this is the right way to do it, but to make it match the rest I change it temporally\n if True:\n acc[0:3] = (0.5-self.beta)*np.dot(MB_beam[ibody].timestep_info.cga(),MB_beam[ibody].timestep_info.for_acc[0:3])+self.beta*np.dot(MB_tstep[ibody].cga(),MB_tstep[ibody].for_acc[0:3])\n vel[0:3] = np.dot(MB_beam[ibody].timestep_info.cga(),MB_beam[ibody].timestep_info.for_vel[0:3])\n MB_tstep[ibody].for_pos[0:3] += dt*(vel[0:3] + dt*acc[0:3])\n else:\n MB_tstep[ibody].for_pos[0:3] += dt*np.dot(MB_tstep[ibody].cga(),MB_tstep[ibody].for_vel[0:3])\n\n def extract_resultants(self, tstep):\n # TODO: code\n return np.zeros((3)), np.zeros((3))\n\n def compute_forces_constraints(self, MB_beam, MB_tstep, ts, dt, Lambda, Lambda_dot):\n \"\"\"\n This function computes the forces generated at Lagrange Constraints\n\n Args:\n MB_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body\n MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n ts (int): Time step number\n dt(float): Time step increment\n Lambda (np.ndarray): Lagrange Multipliers array\n Lambda_dot (np.ndarray): Time derivarive of ``Lambda``\n\n Warning:\n This function is underdevelopment and not fully functional\n \"\"\"\n try:\n self.lc_list[0]\n except IndexError:\n return\n\n # TODO the output of this routine is wrong. check at some point.\n LM_C, LM_K, LM_Q = lagrangeconstraints.generate_lagrange_matrix(self.lc_list, MB_beam, MB_tstep, ts, self.num_LM_eq, self.sys_size, dt, Lambda, Lambda_dot, \"dynamic\")\n F = -np.dot(LM_C[:, -self.num_LM_eq:], Lambda_dot) - np.dot(LM_K[:, -self.num_LM_eq:], Lambda)\n\n first_dof = 0\n for ibody in range(len(MB_beam)):\n # Forces associated to nodes\n body_numdof = MB_beam[ibody].num_dof.value\n body_freenodes = np.sum(MB_beam[ibody].vdof > -1)\n last_dof = first_dof + body_numdof\n MB_tstep[ibody].forces_constraints_nodes[(MB_beam[ibody].vdof > -1), :] = F[first_dof:last_dof].reshape(body_freenodes, 6, order='C')\n\n # Forces associated to the frame of reference\n if MB_beam[ibody].FoR_movement == 'free':\n # TODO: How are the forces in the quaternion equation interpreted?\n MB_tstep[ibody].forces_constraints_FoR[ibody, :] = F[last_dof:last_dof+10]\n last_dof += 10\n\n first_dof = last_dof\n # TODO: right now, these forces are only used as an output, they are not read when the multibody is splitted\n\n def write_lm_cond_num(self, iteration, Lambda, Lambda_dot, Lambda_ddot, cond_num, cond_num_lm):\n # Maybe not the most efficient way to output this, as files are opened and closed every time data is written\n # However, containing the writing in the with statement prevents from files remaining open in the previous\n # implementation\n out_data = {'lambda': Lambda,\n 'lambda_dot': Lambda_dot,\n 'lambda_ddot': Lambda_ddot}\n\n for out_var, data in out_data.items():\n file_name = self.out_files[out_var]\n with open(file_name, 'a') as fid:\n fid.write(f'{self.data.ts:g} {iteration:g} ')\n for ilm in range(self.num_LM_eq):\n fid.write(f'{data[ilm]} ')\n fid.write(f'\\n') \n\n with open(self.out_files['cond_number'], 'a') as fid:\n fid.write(f'{self.data.ts:g} {iteration:g} ')\n fid.write(f'{cond_num:e} {cond_num_lm:e} \\n')\n\n\n\n def run(self, **kwargs):\n structural_step = settings_utils.set_value_or_default(kwargs, 'structural_step', self.data.structure.timestep_info[-1])\n dt= settings_utils.set_value_or_default(kwargs, 'dt', self.settings['dt'])\n\n if structural_step.mb_dict is not None:\n MBdict = structural_step.mb_dict\n else:\n MBdict = self.data.structure.ini_mb_dict\n\n MB_beam, MB_tstep = mb.split_multibody(\n self.data.structure,\n structural_step,\n MBdict,\n self.data.ts)\n\n self.define_rigid_dofs(MB_beam)\n num_LM_eq = self.num_LM_eq\n\n if self.data.ts == 1 and self.settings['zero_ini_dot_ddot']:\n for ibody in range(len(MB_tstep)):\n MB_beam[ibody].ini_info.pos_dot *= 0.\n MB_beam[ibody].ini_info.pos_ddot *= 0.\n MB_beam[ibody].ini_info.psi_dot *= 0.\n MB_beam[ibody].ini_info.psi_dot_local *= 0.\n MB_beam[ibody].ini_info.psi_ddot *= 0.\n MB_tstep[ibody].pos_dot *= 0.\n MB_tstep[ibody].pos_ddot *= 0.\n MB_tstep[ibody].psi_dot *= 0.\n MB_tstep[ibody].psi_dot_local *= 0.\n MB_tstep[ibody].psi_ddot *= 0.\n\n # Initialize\n # TODO: i belive this can move into disp_and_accel2 state as self.Lambda, self.Lambda_dot\n if not num_LM_eq == 0:\n Lambda = self.Lambda.astype(dtype=ct.c_double, copy=True, order='F')\n Lambda_dot = self.Lambda_dot.astype(dtype=ct.c_double, copy=True, order='F')\n Lambda_ddot = self.Lambda_ddot.astype(dtype=ct.c_double, copy=True, order='F')\n else:\n Lambda = np.zeros((1,))\n Lambda_dot = np.zeros((1,))\n Lambda_ddot = np.zeros((1,))\n\n # Predictor step\n q, dqdt, dqddt = mb.disp_and_accel2state(MB_beam, MB_tstep, Lambda, Lambda_dot, self.sys_size, num_LM_eq)\n self.time_integrator.predictor(q, dqdt, dqddt)\n\n # Reference residuals\n old_Dq = 1.0\n LM_old_Dq = 1.0\n\n skip_step = False\n for iteration in range(self.settings['max_iterations']):\n # Check if the maximum of iterations has been reached\n if iteration == self.settings['max_iterations'] - 1:\n error = ('Solver did not converge in %d iterations.\\n res = %e \\n LM_res = %e' %\n (iteration, res, LM_res))\n raise exc.NotConvergedSolver(error)\n\n # Update positions and velocities\n Lambda, Lambda_dot = mb.state2disp_and_accel(q, dqdt, dqddt, MB_beam, MB_tstep, num_LM_eq)\n\n if self.settings['write_lm'] and iteration:\n self.write_lm_cond_num(iteration, Lambda, Lambda_dot, Lambda_ddot, cond_num, cond_num_lm)\n\n MB_M, MB_C, MB_K, MB_Q, kBnh, LM_Q = self.assembly_MB_eq_system(MB_beam,\n MB_tstep,\n self.data.ts,\n dt,\n Lambda,\n Lambda_dot,\n MBdict)\n\n Asys, Q = self.time_integrator.build_matrix(MB_M, MB_C, MB_K, MB_Q,\n kBnh, LM_Q)\n\n if self.settings['write_lm']:\n cond_num = np.linalg.cond(Asys[:self.sys_size, :self.sys_size])\n cond_num_lm = np.linalg.cond(Asys)\n\n if self.settings['rigid_bodies']:\n rigid_LM_dofs = self.rigid_dofs + (np.arange(self.num_LM_eq, dtype=int) + self.sys_size).tolist()\n\n rigid_Asys = Asys[np.ix_(rigid_LM_dofs, rigid_LM_dofs)].copy()\n rigid_Q = Q[rigid_LM_dofs].copy()\n rigid_Dq = np.linalg.solve(rigid_Asys, -rigid_Q)\n Dq = np.zeros((self.sys_size + self.num_LM_eq))\n Dq[rigid_LM_dofs] = rigid_Dq.copy()\n\n else:\n Dq = np.linalg.solve(Asys, -Q)\n\n # Relaxation\n relax_Dq = np.zeros_like(Dq)\n relax_Dq[:self.sys_size] = Dq[:self.sys_size].copy()\n relax_Dq[self.sys_size:] = ((1. - self.settings['relax_factor_lm'])*Dq[self.sys_size:] +\n self.settings['relax_factor_lm']*self.prev_Dq[self.sys_size:])\n self.prev_Dq = Dq.copy()\n\n # Corrector step\n self.time_integrator.corrector(q, dqdt, dqddt, relax_Dq)\n\n # Reference values for convergence\n if iteration == 0:\n old_Dq = np.max(np.abs(Dq[0:self.sys_size]))\n if num_LM_eq:\n LM_old_Dq = np.max(np.abs(Dq[self.sys_size:self.sys_size+num_LM_eq]))\n else:\n LM_old_Dq = 0.\n # Change the reference values\n if old_Dq == 0:\n old_Dq = 1.\n if LM_old_Dq == 0:\n LM_old_Dq = 1.\n\n # Evaluate convergence\n res = np.max(np.abs(Dq[0:self.sys_size]))/old_Dq\n if np.isnan(res):\n if self.settings['allow_skip_step']:\n skip_step = True\n cout.cout_wrap(\"Skipping step\", 3)\n break\n else:\n raise exc.NotConvergedSolver('Multibody Dq = NaN')\n if num_LM_eq:\n LM_res = np.max(np.abs(Dq[self.sys_size:self.sys_size+num_LM_eq]))/LM_old_Dq\n else:\n LM_res = 0.0\n\n if (res < self.settings['min_delta']) and (LM_res < self.settings['min_delta']):\n break\n\n Lambda, Lambda_dot = mb.state2disp_and_accel(q, dqdt, dqddt, MB_beam, MB_tstep, num_LM_eq)\n if self.settings['write_lm']:\n self.write_lm_cond_num(iteration, Lambda, Lambda_dot, Lambda_ddot, cond_num, cond_num_lm)\n # end: comment time stepping\n\n if skip_step:\n # Use the original time step\n MB_beam, MB_tstep = mb.split_multibody(\n self.data.structure,\n structural_step,\n MBdict,\n self.data.ts)\n # Perform rigid body motions\n self.integrate_position(MB_beam, MB_tstep, dt)\n for ibody in range(0, len(MB_tstep)):\n Temp = np.linalg.inv(np.eye(4) + 0.25*algebra.quadskew(MB_tstep[ibody].for_vel[3:6])*dt)\n MB_tstep[ibody].quat = np.dot(Temp, np.dot(np.eye(4) - 0.25*algebra.quadskew(MB_tstep[ibody].for_vel[3:6])*dt, MB_tstep[ibody].quat))\n\n # End of Newmark-beta iterations\n # self.integrate_position(MB_beam, MB_tstep, dt)\n lagrangeconstraints.postprocess(self.lc_list, MB_beam, MB_tstep, \"dynamic\")\n self.compute_forces_constraints(MB_beam, MB_tstep, self.data.ts, dt, Lambda, Lambda_dot)\n if self.settings['gravity_on']:\n for ibody in range(len(MB_beam)):\n xbeamlib.cbeam3_correct_gravity_forces(MB_beam[ibody], MB_tstep[ibody], self.settings)\n mb.merge_multibody(MB_tstep, MB_beam, self.data.structure, structural_step, MBdict, dt)\n\n self.Lambda = Lambda.astype(dtype=ct.c_double, copy=True, order='F')\n self.Lambda_dot = Lambda_dot.astype(dtype=ct.c_double, copy=True, order='F')\n self.Lambda_ddot = Lambda_ddot.astype(dtype=ct.c_double, copy=True, order='F')\n\n return self.data\n" }, { "path": "sharpy/solvers/nonlineardynamicmultibodyjax.py", "content": "import numpy as np\nimport typing\n\nfrom sharpy.utils.solver_interface import solver, solver_from_string\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.solver_interface as solver_interface\nimport sharpy.structure.utils.xbeamlib as xbeamlib\nimport sharpy.utils.multibodyjax as mb\nimport sharpy.structure.utils.lagrangeconstraintsjax as lagrangeconstraints\n\n_BaseStructural = solver_from_string('_BaseStructural')\n\n\n@solver\nclass NonLinearDynamicMultibodyJAX(_BaseStructural):\n \"\"\"\n Nonlinear dynamic multibody\n\n Nonlinear dynamic step solver for multibody structures.\n\n \"\"\"\n solver_id = 'NonLinearDynamicMultibodyJAX'\n solver_classification = 'structural'\n\n settings_types = _BaseStructural.settings_types.copy()\n settings_default = _BaseStructural.settings_default.copy()\n settings_description = _BaseStructural.settings_description.copy()\n settings_options = dict()\n\n settings_types['time_integrator'] = 'str'\n settings_default['time_integrator'] = 'NewmarkBetaJAX'\n settings_description['time_integrator'] = 'Method to perform time integration'\n settings_options['time_integrator'] = ['NewmarkBetaJAX', 'GeneralisedAlphaJAX']\n\n settings_types['time_integrator_settings'] = 'dict'\n settings_default['time_integrator_settings'] = dict()\n settings_description['time_integrator_settings'] = 'Settings for the time integrator'\n\n settings_types['jacobian_method'] = 'str'\n settings_default['jacobian_method'] = 'forward'\n settings_description['jacobian_method'] = 'Autodifferentiation method used to calculate system jacobians'\n settings_options['jacobian_method'] = ['forward', 'reverse']\n\n settings_types['write_lm'] = 'bool'\n settings_default['write_lm'] = False\n settings_description['write_lm'] = 'Write lagrange multipliers to file'\n\n settings_types['relax_factor_lm'] = 'float'\n settings_default['relax_factor_lm'] = 0.\n settings_description['relax_factor_lm'] = ('Relaxation factor for Lagrange Multipliers. '\n '0 no relaxation. 1 full relaxation')\n\n settings_types['allow_skip_step'] = 'bool'\n settings_default['allow_skip_step'] = False\n settings_description['allow_skip_step'] = 'Allow skip step when NaN is found while solving the system'\n\n settings_types['zero_ini_dot_ddot'] = 'bool'\n settings_default['zero_ini_dot_ddot'] = False\n settings_description['zero_ini_dot_ddot'] = 'Set to zero the position and crv derivatives at the first time step'\n\n settings_types['fix_prescribed_quat_ini'] = 'bool'\n settings_default['fix_prescribed_quat_ini'] = False\n settings_description['fix_prescribed_quat_ini'] = 'Set to initial the quaternion for prescibed bodies'\n\n # initial speed direction is given in inertial FOR!!! also in a lot of cases coincident with global A frame\n settings_types['initial_velocity_direction'] = 'list(float)'\n settings_default['initial_velocity_direction'] = [-1., 0., 0.]\n settings_description[\n 'initial_velocity_direction'] = 'Initial velocity of the reference node given in the inertial FOR'\n\n settings_types['initial_velocity'] = 'float'\n settings_default['initial_velocity'] = 0\n settings_description['initial_velocity'] = 'Initial velocity magnitude of the reference node'\n\n # restart sim after dynamictrim\n settings_types['dyn_trim'] = 'bool'\n settings_default['dyn_trim'] = False\n settings_description['dyn_trim'] = 'flag for dyntrim prior to dyncoup'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n\n self.sys_size: typing.Optional[int] = None # total number of unknowns in the system\n self.num_lm_tot: typing.Optional[int] = None # total number of LMs in the system\n self.num_eq_tot: typing.Optional[int] = None\n\n # Total number of equations associated to the Lagrange multipliers\n self.lc_list: typing.Optional[list[lagrangeconstraints.Constraint]] = None\n self.num_lm_eq: typing.Optional[int] = None\n self.lambda_h: typing.Optional[np.ndarray] = None\n self.lambda_n: typing.Optional[np.ndarray] = None\n\n # function called to generate contributions of all LMs to equations\n self.lc_all_run: typing.Optional[typing.Callable] = None\n\n self.gamma: typing.Optional[int] = None\n self.beta: typing.Optional[int] = None\n self.prev_dq: typing.Optional[np.ndarray] = None\n\n self.time_integrator = None\n\n self.out_files = None # dict: containing output_variable:file_path if desired to write output\n\n def initialise(self, data, custom_settings=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default,\n self.settings_options, no_ctype=True)\n\n # load info from dyn dictionary\n self.data.structure.add_unsteady_information(self.data.structure.dyn_dict, self.settings['num_steps'])\n\n if self.settings['initial_velocity']:\n new_direction = (self.data.structure.timestep_info[-1].cag()\n @ self.settings['initial_velocity_direction'] * self.settings['initial_velocity'])\n self.data.structure.timestep_info[-1].for_vel[:3] = new_direction\n num_body = self.data.structure.timestep_info[0].mb_FoR_vel.shape[0]\n for ibody in range(num_body):\n self.data.structure.timestep_info[-1].mb_FoR_vel[ibody, :] \\\n = self.data.structure.timestep_info[-1].for_vel\n\n # find total number of LC equations\n dict_of_lc = lagrangeconstraints.DICT_OF_LC\n lc_cls_list: list[typing.Type[lagrangeconstraints.Constraint]] = []\n lc_settings: list[dict] = []\n self.num_lm_tot = 0\n for i in range(self.data.structure.ini_mb_dict['num_constraints']):\n lc_settings.append(self.data.structure.ini_mb_dict[f'constraint_{i:02d}'])\n lc_cls_list.append(dict_of_lc[lc_settings[-1]['behaviour']])\n self.num_lm_tot += lc_cls_list[-1].get_n_lm()\n\n # find total number of equations\n mb_dict = self.data.structure.ini_mb_dict\n self.sys_size = self.data.structure.num_dof.value\n for ibody in range(self.data.structure.num_bodies):\n if mb_dict[f'body_{ibody:02d}']['FoR_movement'] == 'free':\n self.sys_size += 10\n self.num_eq_tot = self.sys_size + self.num_lm_tot\n\n i_start_lc = 0\n self.lc_list = []\n for i_lc, lc_cls in enumerate(lc_cls_list):\n self.lc_list.append(lc_cls(self, i_start_lc, lc_settings[i_lc]))\n i_start_lc += self.lc_list[-1].num_lm\n\n # create a single function for all constraints\n self.lc_all_run = lagrangeconstraints.combine_constraints(self.lc_list)\n\n # lambda values\n self.lambda_h = np.zeros(self.num_lm_tot)\n self.lambda_n = np.zeros(self.num_lm_tot)\n\n self.prev_dq = np.zeros(self.sys_size + self.num_lm_tot)\n\n try:\n self.num_lm_eq = self.lc_list[0].num_lm_tot\n except IndexError:\n self.num_lm_eq = 0\n\n self.settings['time_integrator_settings']['sys_size'] = self.sys_size\n self.settings['time_integrator_settings']['num_LM_eq'] = self.num_lm_eq\n\n # Initialise time integrator\n if not restart:\n self.time_integrator = solver_interface.initialise_solver(self.settings['time_integrator'])\n\n self.time_integrator.initialise(self.data, self.settings['time_integrator_settings'], restart=restart)\n\n\n def assembly_mb_eq_system(self, mb_beam, mb_tstep, ts, dt, lambda_h, lambda_n, mb_dict, mb_prescribed_dict):\n \"\"\"\n This function generates the matrix and vector associated to the linear system to solve a structural iteration\n It usses a Newmark-beta scheme for time integration. Being M, C and K the mass, damping\n and stiffness matrices of the system:\n\n .. math::\n MB_Asys = mb_k + mb_c \\frac{\\gamma}{\\beta dt} + \\frac{1}{\\beta dt^2} mb_m\n\n Args:\n mb_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body\n mb_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n ts (int): Time step number\n dt(int): time step\n lambda_ (np.ndarray): Lagrange Multipliers array\n lambda_dot (np.ndarray): Time derivarive of ``Lambda``\n mb_dict (dict): Dictionary including the multibody information\n\n Returns:\n MB_Asys (np.ndarray): Matrix of the systems of equations\n mb_q (np.ndarray): Vector of the systems of equations\n \"\"\"\n\n mb_m = np.zeros((self.num_eq_tot, self.num_eq_tot))\n mb_c = np.zeros((self.num_eq_tot, self.num_eq_tot))\n mb_k = np.zeros((self.num_eq_tot, self.num_eq_tot))\n mb_rhs = np.zeros(self.num_eq_tot)\n\n first_dof = 0\n for ibody in range(len(mb_beam)):\n # Generate the matrices for each body\n if mb_beam[ibody].FoR_movement in ('prescribed', 'prescribed_trim'):\n last_dof = first_dof + mb_beam[ibody].num_dof.value\n m, c, k, rhs = xbeamlib.cbeam3_asbly_dynamic(mb_beam[ibody], mb_tstep[ibody], self.settings)\n elif mb_beam[ibody].FoR_movement == 'free':\n last_dof = first_dof + mb_beam[ibody].num_dof.value + 10\n m, c, k, rhs = xbeamlib.xbeam3_asbly_dynamic(mb_beam[ibody], mb_tstep[ibody], self.settings)\n else:\n raise KeyError(f\"Body FoR movement {mb_beam[ibody].FoR_movement} is invalid\")\n\n mb_m[first_dof:last_dof, first_dof:last_dof] = m\n mb_c[first_dof:last_dof, first_dof:last_dof] = c\n mb_k[first_dof:last_dof, first_dof:last_dof] = k\n mb_rhs[first_dof:last_dof] = rhs\n\n first_dof = last_dof\n\n q = np.hstack([beam.q for beam in mb_tstep])\n q_dot = np.hstack([beam.dqdt for beam in mb_tstep])\n\n u = []\n u_dot = []\n for i_lc in range(len(self.lc_list)):\n try:\n ctrl_id = self.lc_list[i_lc].settings['controller_id'].decode('UTF-8')\n u.append(mb_prescribed_dict[ctrl_id]['psi'])\n u_dot.append(mb_prescribed_dict[ctrl_id]['psi_dot'])\n except KeyError:\n u.append(None)\n u_dot.append(None)\n\n lc_c, lc_k, lc_rhs = self.call_lm_generate(q, q_dot, u, u_dot, lambda_h, lambda_n)\n\n mb_c += lc_c\n mb_k += lc_k\n mb_rhs += lc_rhs\n\n return mb_m, mb_c, mb_k, mb_rhs\n\n # added to make profiling easier\n def call_lm_generate(self, *args):\n return self.lc_all_run(*args)\n\n def integrate_position(self, mb_beam, mb_tstep, dt):\n \"\"\"\n This function integrates the position of each local A FoR after the\n structural iteration has been solved.\n\n It uses a Newmark-beta approximation.\n\n Args:\n mb_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body\n mb_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n dt(int): time step\n \"\"\"\n vel = np.zeros(6)\n acc = np.zeros(6)\n for ibody in range(len(mb_tstep)):\n acc[:3] = ((0.5 - self.beta) * mb_beam[ibody].timestep_info.cga()\n @ mb_beam[ibody].timestep_info.for_acc[:3] + self.beta * mb_tstep[ibody].cga()\n @ mb_tstep[ibody].for_acc[:3])\n vel[:3] = mb_beam[ibody].timestep_info.cga() @ mb_beam[ibody].timestep_info.for_vel[:3]\n mb_tstep[ibody].for_pos[:3] += dt * (vel[:3] + dt * acc[:3])\n\n def extract_resultants(self, tstep):\n if tstep is None:\n tstep = self.data.structure.timestep_info[self.data.ts]\n steady, unsteady, grav = tstep.extract_resultants(self.data.structure,\n force_type=['steady', 'unsteady', 'grav'])\n totals = steady + unsteady + grav\n return totals[:3], totals[3:6]\n\n def run(self, **kwargs):\n structural_step = settings_utils.set_value_or_default(kwargs, 'structural_step',\n self.data.structure.timestep_info[-1])\n dt = settings_utils.set_value_or_default(kwargs, 'dt', self.settings['dt'])\n\n if structural_step.mb_dict is not None:\n mb_dict = structural_step.mb_dict\n else:\n mb_dict = self.data.structure.ini_mb_dict\n\n mb_prescribed_dict = structural_step.mb_prescribed_dict\n mb_beam, mb_tstep = mb.split_multibody(self.data.structure, structural_step, mb_dict, self.data.ts)\n\n if self.data.ts == 1 and self.settings['zero_ini_dot_ddot']:\n for ibody in range(len(mb_tstep)):\n mb_beam[ibody].ini_info.pos_dot.fill(0.)\n mb_beam[ibody].ini_info.pos_ddot.fill(0.)\n mb_beam[ibody].ini_info.psi_dot.fill(0.)\n mb_beam[ibody].ini_info.psi_dot_local.fill(0.)\n mb_beam[ibody].ini_info.psi_ddot.fill(0.)\n mb_tstep[ibody].pos_dot.fill(0.)\n mb_tstep[ibody].pos_ddot.fill(0.)\n mb_tstep[ibody].psi_dot.fill(0.)\n mb_tstep[ibody].psi_dot_local.fill(0.)\n mb_tstep[ibody].psi_ddot.fill(0.)\n\n # Predictor step\n q, dqdt, dqddt = mb.disp_and_accel2state(mb_beam, mb_tstep, self.lambda_h, self.lambda_n,\n self.sys_size, self.num_lm_eq)\n self.time_integrator.predictor(q, dqdt, dqddt)\n\n res_sys = 0.\n res_lm = 0.\n\n for iteration in range(self.settings['max_iterations']):\n if iteration == self.settings['max_iterations'] - 1: # Check if the maximum of iterations has been reached\n print(f'Solver did not converge in {iteration} iterations.\\n res_sys = {res_sys} \\n res_lm = {res_lm}')\n break\n\n # Update positions and velocities\n lambda_h, lambda_n = mb.state2disp_and_accel(q, dqdt, dqddt, mb_beam, mb_tstep, self.num_lm_eq)\n\n mb_m, mb_c, mb_k, mb_rhs = self.assembly_mb_eq_system(mb_beam, mb_tstep, self.data.ts, dt, lambda_h,\n lambda_n, mb_dict, mb_prescribed_dict)\n\n a_sys = self.time_integrator.build_matrix(mb_m, mb_c, mb_k)\n\n dq = np.linalg.solve(a_sys, -mb_rhs)\n\n # Relaxation\n relax_dq = np.zeros_like(dq)\n relax_dq[:self.sys_size] = dq[:self.sys_size].copy()\n relax_dq[self.sys_size:] = ((1. - self.settings['relax_factor_lm']) * dq[self.sys_size:] +\n self.settings['relax_factor_lm'] * self.prev_dq[self.sys_size:])\n self.prev_dq = dq.copy()\n\n # Corrector step\n self.time_integrator.corrector(q, dqdt, dqddt, relax_dq)\n\n res_sys = np.max(np.abs(dq[:self.sys_size]))\n try:\n res_lm = np.max(np.abs(dq[self.sys_size:]))\n except ValueError:\n res_lm = 0.\n if iteration > 0 and (res_sys < self.settings['min_delta']) and (res_lm < self.settings['min_delta']):\n break\n\n lambda_h, lambda_n = mb.state2disp_and_accel(q, dqdt, dqddt, mb_beam, mb_tstep, self.num_lm_eq)\n\n for lc in self.lc_list:\n lc.postprocess(mb_beam, mb_tstep)\n\n # End of Newmark-beta iterations\n if self.settings['gravity_on']:\n for ibody in range(len(mb_beam)):\n xbeamlib.cbeam3_correct_gravity_forces(mb_beam[ibody], mb_tstep[ibody], self.settings)\n mb.merge_multibody(mb_tstep, mb_beam, self.data.structure, structural_step, mb_dict, dt)\n\n self.lambda_h = lambda_h\n self.lambda_n = lambda_n\n self.data.Lambda = lambda_h\n self.data.Lambda_dot = lambda_n\n\n return self.data\n\n def add_step(self):\n self.data.structure.next_step()\n\n def next_step(self):\n raise NotImplementedError\n" }, { "path": "sharpy/solvers/nonlineardynamicprescribedstep.py", "content": "\"\"\"\n@modified Alfonso del Carre\n\"\"\"\n\nimport sharpy.structure.utils.xbeamlib as xbeamlib\nfrom sharpy.utils.solver_interface import solver, BaseSolver, solver_from_string\nimport sharpy.utils.settings as settings_utils\n\n_BaseStructural = solver_from_string('_BaseStructural')\n\n\n@solver\nclass NonLinearDynamicPrescribedStep(_BaseStructural):\n \"\"\"\n Structural solver used for the dynamic simulation of clamped structures or those subject to a prescribed motion.\n\n This solver provides an interface to the structural library (``xbeam``) and updates the structural parameters\n for every k-th step in the FSI iteration.\n\n This solver can be called as part of a standalone structural simulation or as the structural solver of a coupled\n aeroelastic simulation.\n\n \"\"\"\n\n solver_id = 'NonLinearDynamicPrescribedStep'\n solver_classification = 'structural'\n\n settings_types = _BaseStructural.settings_types.copy()\n settings_default = _BaseStructural.settings_default.copy()\n settings_description = _BaseStructural.settings_description.copy()\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n # load info from dyn dictionary\n self.data.structure.add_unsteady_information(self.data.structure.dyn_dict, self.settings['num_steps'])\n\n def run(self, **kwargs):\n structural_step = settings_utils.set_value_or_default(kwargs, 'structural_step',\n self.data.structure.timestep_info[-1])\n dt = settings_utils.set_value_or_default(kwargs, 'dt', self.settings['dt'])\n\n if self.data.ts > 0:\n try:\n structural_step.for_vel[:] = self.data.structure.dynamic_input[self.data.ts - 1]['for_vel']\n structural_step.for_acc[:] = self.data.structure.dynamic_input[self.data.ts - 1]['for_acc']\n except IndexError:\n pass\n\n xbeamlib.cbeam3_step_nlndyn(self.data.structure,\n self.settings,\n self.data.ts,\n structural_step,\n dt=dt)\n\n self.data.structure.integrate_position(structural_step, dt)\n return self.data\n\n def add_step(self):\n self.data.structure.next_step()\n\n def next_step(self):\n pass\n\n def extract_resultants(self, tstep=None):\n if tstep is None:\n tstep = self.data.structure.timestep_info[self.data.ts]\n steady, unsteady, grav = tstep.extract_resultants(self.data.structure,\n force_type=['steady', 'unsteady', 'grav'])\n totals = steady + unsteady + grav\n return totals[0:3], totals[3:6]\n\n def update(self, tstep=None):\n self.create_q_vector(tstep)\n\n def create_q_vector(self, tstep=None):\n import sharpy.structure.utils.xbeamlib as xb\n if tstep is None:\n tstep = self.data.structure.timestep_info[-1]\n\n xb.xbeam_solv_disp2state(self.data.structure, tstep)\n" }, { "path": "sharpy/solvers/nonlinearstatic.py", "content": "import numpy as np\n\nimport sharpy.structure.utils.xbeamlib as xbeamlib\nimport sharpy.utils.settings as settings_utils\nfrom sharpy.utils.solver_interface import solver, BaseSolver, solver_from_string\n\n_BaseStructural = solver_from_string('_BaseStructural')\n\n@solver\nclass NonLinearStatic(_BaseStructural):\n \"\"\"\n Structural solver used for the static simulation of free-flying structures.\n\n This solver provides an interface to the structural library (``xbeam``) and updates the structural parameters\n for every k-th step of the FSI iteration.\n\n This solver can be called as part of a standalone structural simulation or as the structural solver of a coupled\n static aeroelastic simulation.\n\n \"\"\"\n solver_id = 'NonLinearStatic'\n solver_classification = 'structural'\n\n # settings list\n settings_types = _BaseStructural.settings_types.copy()\n settings_default = _BaseStructural.settings_default.copy()\n settings_description = _BaseStructural.settings_description.copy()\n\n settings_types['initial_position'] = 'list(float)'\n settings_default['initial_position'] = np.array([0.0, 0.0, 0.0])\n \n settings_types['initial_velocity'] = 'list(float)'\n settings_default['initial_velocity'] = np.array([0., 0., 0., 0., 0., 0.])\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default, no_ctype=True)\n\n def run(self, **kwargs):\n self.data.structure.timestep_info[self.data.ts].for_pos[0:3] = self.settings['initial_position']\n self.data.structure.timestep_info[self.data.ts].for_vel = self.settings['initial_velocity'].copy()\n xbeamlib.cbeam3_solv_nlnstatic(self.data.structure, self.settings, self.data.ts)\n self.extract_resultants()\n return self.data\n\n def next_step(self):\n self.data.structure.next_step()\n\n def extract_resultants(self, tstep=None):\n if tstep is None:\n tstep = self.data.structure.timestep_info[self.data.ts]\n steady, grav = tstep.extract_resultants(self.data.structure, force_type=['steady', 'grav'])\n totals = steady + grav\n return totals[0:3], totals[3:6]\n\n def update(self, tstep=None):\n self.create_q_vector(tstep)\n\n def create_q_vector(self, tstep=None):\n import sharpy.structure.utils.xbeamlib as xb\n if tstep is None:\n tstep = self.data.structure.timestep_info[-1]\n\n xb.xbeam_solv_disp2state(self.data.structure, tstep)\n\n\n" }, { "path": "sharpy/solvers/nostructural.py", "content": "import numpy as np\n\nimport sharpy.utils.settings as settings_utils\nfrom sharpy.utils.solver_interface import solver, BaseSolver, solver_from_string\n\n_BaseStructural = solver_from_string('_BaseStructural')\n\n@solver\nclass NoStructural(_BaseStructural):\n \"\"\"\n Structural solver used for the static simulation of free-flying structures.\n\n This solver provides an interface to the structural library (``xbeam``) and updates the structural parameters\n for every k-th step of the FSI iteration.\n\n This solver can be called as part of a standalone structural simulation or as the structural solver of a coupled\n static aeroelastic simulation.\n\n \"\"\"\n solver_id = 'NoStructural'\n solver_classification = 'structural'\n\n # settings list\n settings_types = _BaseStructural.settings_types.copy()\n settings_default = _BaseStructural.settings_default.copy()\n settings_description = _BaseStructural.settings_description.copy()\n\n settings_types['initial_position'] = 'list(float)'\n settings_default['initial_position'] = np.array([0.0, 0.0, 0.0])\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n def run(self, **kwargs):\n self.data.structure.timestep_info[self.data.ts].for_pos[0:3] = self.settings['initial_position']\n self.extract_resultants()\n return self.data\n\n def next_step(self):\n self.data.structure.next_step()\n\n def extract_resultants(self, tstep=None):\n if tstep is None:\n tstep = self.data.structure.timestep_info[self.data.ts]\n steady, grav = tstep.extract_resultants(self.data.structure, force_type=['steady', 'grav'])\n totals = steady + grav\n return totals[0:3], totals[3:6]\n\n def update(self, tstep=None):\n self.create_q_vector(tstep)\n\n def create_q_vector(self, tstep=None):\n import sharpy.structure.utils.xbeamlib as xb\n if tstep is None:\n tstep = self.data.structure.timestep_info[-1]\n\n xb.xbeam_solv_disp2state(self.data.structure, tstep)\n\n\n" }, { "path": "sharpy/solvers/prescribeduvlm.py", "content": "import sharpy.utils.settings as settings_utils\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.solver_interface as solver_interface\nimport sharpy.utils.cout_utils as cout\nfrom sharpy.utils.constants import vortex_radius_def\n\n\n@solver\nclass PrescribedUvlm(BaseSolver):\n \"\"\"\n This class runs a prescribed rigid body motion simulation of a rigid\n aerodynamic body.\n \"\"\"\n solver_id = 'PrescribedUvlm'\n solver_classification = 'Aero'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Write status to screen'\n\n settings_types['structural_solver'] = 'str'\n settings_default['structural_solver'] = None\n settings_description['structural_solver'] = 'Structural solver to use in the coupled simulation'\n\n settings_types['structural_solver_settings'] = 'dict'\n settings_default['structural_solver_settings'] = None\n settings_description['structural_solver_settings'] = 'Dictionary of settings for the structural solver'\n\n settings_types['aero_solver'] = 'str'\n settings_default['aero_solver'] = None\n settings_description['aero_solver'] = 'Aerodynamic solver to use in the coupled simulation'\n\n settings_types['aero_solver_settings'] = 'dict'\n settings_default['aero_solver_settings'] = None\n settings_description['aero_solver_settings'] = 'Dictionary of settings for the aerodynamic solver'\n\n settings_types['n_time_steps'] = 'int'\n settings_default['n_time_steps'] = None\n settings_description['n_time_steps'] = 'Number of time steps for the simulation'\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = None\n settings_description['dt'] = 'Time step'\n\n settings_types['postprocessors'] = 'list(str)'\n settings_default['postprocessors'] = list()\n settings_description['postprocessors'] = 'List of the postprocessors to run at the end of every time step'\n\n settings_types['postprocessors_settings'] = 'dict'\n settings_default['postprocessors_settings'] = dict()\n settings_description['postprocessors_settings'] = 'Dictionary with the applicable settings for every ``postprocessor``. Every ``postprocessor`` needs its entry, even if empty'\n\n settings_types['cfl1'] = 'bool'\n settings_default['cfl1'] = True\n settings_description['cfl1'] = 'If it is ``True``, it assumes that the discretisation complies with CFL=1'\n\n settings_types['vortex_radius'] = 'float'\n settings_default['vortex_radius'] = vortex_radius_def\n settings_description['vortex_radius'] = 'Distance between points below which induction is not computed'\n\n settings_types['vortex_radius_wake_ind'] = 'float'\n settings_default['vortex_radius_wake_ind'] = vortex_radius_def\n settings_description['vortex_radius_wake_ind'] = 'Distance between points below which induction is not computed in the wake convection'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n self.structural_solver = None\n self.aero_solver = None\n\n self.previous_force = None\n\n self.dt = 0.\n self.postprocessors = dict()\n self.with_postprocessors = False\n\n def initialise(self, data, restart=False):\n self.data = data\n self.settings = data.settings[self.solver_id]\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n self.dt = self.settings['dt']\n\n self.aero_solver = solver_interface.initialise_solver(self.settings['aero_solver'])\n self.aero_solver.initialise(self.data, self.settings['aero_solver_settings'])\n self.data = self.aero_solver.data\n\n # if there's data in timestep_info[>0], copy the last one to\n # timestep_info[0] and remove the rest\n self.cleanup_timestep_info()\n\n # initialise postprocessors\n self.postprocessors = dict()\n if len(self.settings['postprocessors']) > 0:\n self.with_postprocessors = True\n for postproc in self.settings['postprocessors']:\n self.postprocessors[postproc] = solver_interface.initialise_solver(postproc)\n self.postprocessors[postproc].initialise(\n self.data, self.settings['postprocessors_settings'][postproc], caller=self,\n restart=restart)\n\n self.residual_table = cout.TablePrinter(2, 14, ['g', 'f'])\n self.residual_table.field_length[0] = 6\n self.residual_table.field_length[1] = 6\n self.residual_table.print_header(['ts', 't'])\n\n def cleanup_timestep_info(self):\n if len(self.data.aero.timestep_info) > 1:\n # copy last info to first\n self.data.aero.timestep_info[0] = self.data.aero.timestep_info[-1]\n # delete all the rest\n while len(self.data.aero.timestep_info) - 1:\n del self.data.aero.timestep_info[-1]\n\n self.data.ts = 0\n\n def increase_ts(self):\n self.data.structure.next_step()\n self.aero_solver.add_step()\n\n def run(self, **kwargs):\n structural_kstep = self.data.structure.ini_info.copy()\n\n # dynamic simulations start at tstep == 1, 0 is reserved for the initial state\n for self.data.ts in range(1, self.settings['n_time_steps'] + 1):\n aero_kstep = self.data.aero.timestep_info[-1].copy()\n structural_kstep = self.data.structure.timestep_info[-1].copy()\n ts = len(self.data.structure.timestep_info) - 1\n if ts > 0:\n self.data.structure.timestep_info[ts].for_vel[:] = self.data.structure.dynamic_input[ts - 1]['for_vel']\n self.data.structure.timestep_info[ts].for_acc[:] = self.data.structure.dynamic_input[ts - 1]['for_acc']\n\n self.data.structure.next_step()\n self.data.structure.integrate_position(self.data.ts, self.settings['dt'])\n\n self.aero_solver.add_step()\n self.data.aero.timestep_info[-1] = aero_kstep.copy()\n self.aero_solver.update_custom_grid(self.data.structure.timestep_info[-1],\n self.data.aero.timestep_info[-1])\n # run the solver\n self.data = self.aero_solver.run(self.data.aero.timestep_info[-1],\n self.data.structure.timestep_info[-1],\n self.data.aero.timestep_info[-2],\n convect_wake=True)\n self.residual_table.print_line([self.data.ts,\n self.data.ts*self.dt])\n\n # run postprocessors\n if self.with_postprocessors:\n for postproc in self.postprocessors:\n self.data = self.postprocessors[postproc].run(online=True)\n\n return self.data\n" }, { "path": "sharpy/solvers/rigiddynamiccoupledstep.py", "content": "import sharpy.structure.utils.xbeamlib as xbeamlib\nfrom sharpy.utils.solver_interface import solver, BaseSolver, solver_from_string\nimport sharpy.utils.settings as settings_utils\n\n\n_BaseStructural = solver_from_string('_BaseStructural')\n\n@solver\nclass RigidDynamicCoupledStep(_BaseStructural):\n \"\"\"\n Structural solver used for the dynamic simulation of free-flying rigid structures.\n\n This solver provides an interface to the structural library (``xbeam``) and updates the structural parameters\n for every k-th step in the FSI iteration.\n\n This solver can be called as part of a standalone structural simulation or as the structural solver of a coupled\n aeroelastic simulation.\n\n \"\"\"\n solver_id = 'RigidDynamicCoupledStep'\n solver_classification = 'structural'\n\n settings_types = _BaseStructural.settings_types.copy()\n settings_default = _BaseStructural.settings_default.copy()\n settings_description = _BaseStructural.settings_description.copy()\n\n settings_types['balancing'] = 'bool'\n settings_default['balancing'] = False\n\n settings_types['relaxation_factor'] = 'float'\n settings_default['relaxation_factor'] = 0.3\n settings_description['relaxation factor'] = 'Relaxation factor'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n # load info from dyn dictionary\n self.data.structure.add_unsteady_information(self.data.structure.dyn_dict, self.settings['num_steps'])\n\n # generate q, dqdt and dqddt\n xbeamlib.xbeam_solv_disp2state(self.data.structure, self.data.structure.timestep_info[-1])\n\n def run(self, **kwargs):\n\n structural_step = settings_utils.set_value_or_default(kwargs, 'structural_step', self.data.structure.timestep_info[-1])\n # TODO: previous_structural_step never used\n previous_structural_step = settings_utils.set_value_or_default(kwargs, 'previous_structural_step', self.data.structure.timestep_info[-1])\n dt= settings_utils.set_value_or_default(kwargs, 'dt', self.settings['dt']) \n\n xbeamlib.xbeam_step_coupledrigid(self.data.structure,\n self.settings,\n self.data.ts,\n structural_step,\n dt=dt)\n self.extract_resultants(structural_step)\n self.data.structure.integrate_position(structural_step, dt)\n\n return self.data\n\n def add_step(self):\n self.data.structure.next_step()\n\n def next_step(self):\n pass\n\n def extract_resultants(self, tstep=None):\n if tstep is None:\n tstep = self.data.structure.timestep_info[self.data.ts]\n steady, unsteady, grav = tstep.extract_resultants(self.data.structure, force_type=['steady', 'unsteady', 'grav'])\n totals = steady + unsteady + grav\n return totals[0:3], totals[3:6]\n\n" }, { "path": "sharpy/solvers/rigiddynamicprescribedstep.py", "content": "\"\"\"\n@modified Alfonso del Carre\n\"\"\"\n\nimport numpy as np\n\nimport sharpy.structure.utils.xbeamlib as xbeamlib\nfrom sharpy.utils.solver_interface import solver, BaseSolver, solver_from_string\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.algebra as algebra\n\n_BaseStructural = solver_from_string('_BaseStructural')\n\n@solver\nclass RigidDynamicPrescribedStep(BaseSolver):\n solver_id = 'RigidDynamicPrescribedStep'\n solver_classification = 'structural'\n\n settings_types = _BaseStructural.settings_types.copy()\n settings_default = _BaseStructural.settings_default.copy()\n settings_description = _BaseStructural.settings_description.copy()\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = 0.01\n settings_description['dt'] = 'Time step of simulation'\n\n settings_types['num_steps'] = 'int'\n settings_default['num_steps'] = 500\n settings_description['num_steps'] = 'Number of timesteps to be run'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n # load info from dyn dictionary\n self.data.structure.add_unsteady_information(self.data.structure.dyn_dict, self.settings['num_steps'])\n\n def run(self, **kwargs):\n structural_step = settings_utils.set_value_or_default(kwargs, 'structural_step', self.data.structure.timestep_info[-1])\n dt= settings_utils.set_value_or_default(kwargs, 'dt', self.settings['dt']) \n\n if self.data.ts > 0:\n try:\n structural_step.for_vel[:] = self.data.structure.dynamic_input[self.data.ts - 1]['for_vel']\n structural_step.for_acc[:] = self.data.structure.dynamic_input[self.data.ts - 1]['for_acc']\n except IndexError:\n pass\n\n Temp = np.linalg.inv(np.eye(4) + 0.25*algebra.quadskew(structural_step.for_vel[3:6])*dt)\n structural_step.quat = np.dot(Temp, np.dot(np.eye(4) - 0.25*algebra.quadskew(structural_step.for_vel[3:6])*dt, structural_step.quat))\n\n xbeamlib.cbeam3_solv_disp2state(self.data.structure, structural_step)\n\n self.extract_resultants(structural_step)\n if self.data.ts > 0:\n self.data.structure.integrate_position(structural_step, self.settings['dt'])\n return self.data\n\n def add_step(self):\n self.data.structure.next_step()\n\n def next_step(self):\n pass\n\n def extract_resultants(self, tstep=None):\n if tstep is None:\n tstep = self.data.structure.timestep_info[self.data.ts]\n steady, unsteady, grav = tstep.extract_resultants(self.data.structure, force_type=['steady', 'unsteady', 'grav'])\n totals = steady + unsteady + grav\n return totals[0:3], totals[3:6]\n\n\n def update(self, tstep=None):\n self.create_q_vector(tstep)\n\n def create_q_vector(self, tstep=None):\n import sharpy.structure.utils.xbeamlib as xb\n if tstep is None:\n tstep = self.data.structure.timestep_info[-1]\n\n xb.xbeam_solv_disp2state(self.data.structure, tstep)\n" }, { "path": "sharpy/solvers/staticcoupled.py", "content": "import sys\nimport numpy as np\n\nimport sharpy.aero.utils.mapping as mapping\nimport sharpy.utils.cout_utils as cout\nfrom sharpy.utils.solver_interface import solver, BaseSolver, initialise_solver\n\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.generator_interface as gen_interface\n\n@solver\nclass StaticCoupled(BaseSolver):\n \"\"\"\n This class is the main FSI driver for static simulations.\n It requires a ``structural_solver`` and a ``aero_solver`` to be defined.\n \"\"\"\n solver_id = 'StaticCoupled'\n solver_classification = 'Coupled'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Write status to screen'\n\n settings_types['structural_solver'] = 'str'\n settings_default['structural_solver'] = None\n settings_description['structural_solver'] = 'Structural solver to use in the coupled simulation'\n\n settings_types['structural_solver_settings'] = 'dict'\n settings_default['structural_solver_settings'] = None\n settings_description['structural_solver_settings'] = 'Dictionary of settings for the structural solver'\n\n settings_types['aero_solver'] = 'str'\n settings_default['aero_solver'] = None\n settings_description['aero_solver'] = 'Aerodynamic solver to use in the coupled simulation'\n\n settings_types['aero_solver_settings'] = 'dict'\n settings_default['aero_solver_settings'] = None\n settings_description['aero_solver_settings'] = 'Dictionary of settings for the aerodynamic solver'\n\n settings_types['max_iter'] = 'int'\n settings_default['max_iter'] = 100\n settings_description['max_iter'] = 'Max iterations in the FSI loop'\n\n settings_types['n_load_steps'] = 'int'\n settings_default['n_load_steps'] = 0\n settings_description['n_load_steps'] = 'Length of ramp for forces and gravity during FSI iteration'\n\n settings_types['tolerance'] = 'float'\n settings_default['tolerance'] = 1e-5\n settings_description['tolerance'] = 'Convergence threshold for the FSI loop'\n\n settings_types['relaxation_factor'] = 'float'\n settings_default['relaxation_factor'] = 0.\n settings_description['relaxation_factor'] = 'Relaxation parameter in the FSI iteration. 0 is no relaxation and -> 1 is very relaxed'\n\n settings_types['correct_forces_method'] = 'str'\n settings_default['correct_forces_method'] = ''\n settings_description['correct_forces_method'] = 'Function used to correct aerodynamic forces. ' \\\n 'See :py:mod:`sharpy.generators.polaraeroforces`'\n settings_options['correct_forces_method'] = ['EfficiencyCorrection', 'PolarCorrection']\n\n settings_types['correct_forces_settings'] = 'dict'\n settings_default['correct_forces_settings'] = {}\n settings_description['correct_forces_settings'] = 'Settings for corrected forces evaluation'\n\n settings_types['runtime_generators'] = 'dict'\n settings_default['runtime_generators'] = dict()\n settings_description['runtime_generators'] = 'The dictionary keys are the runtime generators to be used. ' \\\n 'The dictionary values are dictionaries with the settings ' \\\n 'needed by each generator.'\n \n settings_types['nonlifting_body_interactions'] = 'bool'\n settings_default['nonlifting_body_interactions'] = False\n settings_description['nonlifting_body_interactions'] = 'Consider forces induced by nonlifting bodies'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description, settings_options)\n\n def __init__(self):\n\n self.data = None\n self.settings = None\n self.structural_solver = None\n self.aero_solver = None\n\n self.previous_force = None\n\n self.residual_table = None\n\n self.correct_forces = False\n self.correct_forces_generator = None\n\n self.runtime_generators = dict()\n self.with_runtime_generators = False\n\n def initialise(self, data, input_dict=None, restart=False):\n self.data = data\n if input_dict is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = input_dict\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n options=self.settings_options,\n no_ctype=True)\n\n self.print_info = self.settings['print_info']\n\n self.structural_solver = initialise_solver(self.settings['structural_solver'])\n self.structural_solver.initialise(self.data, self.settings['structural_solver_settings'], restart=restart)\n self.aero_solver = initialise_solver(self.settings['aero_solver'])\n self.aero_solver.initialise(self.structural_solver.data, self.settings['aero_solver_settings'], restart=restart)\n self.data = self.aero_solver.data\n\n if self.print_info:\n self.residual_table = cout.TablePrinter(9, 8, ['g', 'g', 'f', 'f', 'f', 'f', 'f', 'f', 'f'])\n self.residual_table.field_length[0] = 3\n self.residual_table.field_length[1] = 3\n self.residual_table.field_length[2] = 10\n self.residual_table.print_header(['iter', 'step', 'log10(res)', 'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'])\n\n # Define the function to correct aerodynamic forces\n if self.settings['correct_forces_method'] != '':\n self.correct_forces = True\n self.correct_forces_generator = gen_interface.generator_from_string(self.settings['correct_forces_method'])()\n self.correct_forces_generator.initialise(in_dict=self.settings['correct_forces_settings'],\n aero=self.data.aero,\n structure=self.data.structure,\n rho=self.settings['aero_solver_settings']['rho'],\n vortex_radius=self.settings['aero_solver_settings']['vortex_radius'],\n output_folder = self.data.output_folder)\n\n # initialise runtime generators\n self.runtime_generators = dict()\n if self.settings['runtime_generators']:\n self.with_runtime_generators = True\n for rg_id, param in self.settings['runtime_generators'].items():\n gen = gen_interface.generator_from_string(rg_id)\n self.runtime_generators[rg_id] = gen()\n self.runtime_generators[rg_id].initialise(param, data=self.data, restart=restart)\n\n def increase_ts(self):\n self.data.ts += 1\n self.structural_solver.next_step()\n self.aero_solver.next_step()\n\n def cleanup_timestep_info(self):\n if max(len(self.data.aero.timestep_info), len(self.data.structure.timestep_info)) > 1:\n self.remove_old_timestep_info(self.data.structure.timestep_info)\n self.remove_old_timestep_info(self.data.aero.timestep_info) \n if self.settings['nonlifting_body_interactions']:\n self.remove_old_timestep_info(self.data.nonlifting_body.timestep_info)\n\n self.data.ts = 0\n\n def remove_old_timestep_info(self, tstep_info):\n # copy last info to first\n tstep_info[0] = tstep_info[-1].copy()\n # delete all the rest\n while len(tstep_info) - 1:\n del tstep_info[-1]\n\n def run(self, **kwargs):\n for i_step in range(self.settings['n_load_steps'] + 1):\n if (i_step == self.settings['n_load_steps'] and\n self.settings['n_load_steps'] > 0):\n break\n # load step coefficient\n if not self.settings['n_load_steps'] == 0:\n load_step_multiplier = (i_step + 1.0)/self.settings['n_load_steps']\n else:\n load_step_multiplier = 1.0\n\n # new storage every load step\n if i_step > 0:\n self.increase_ts()\n\n for i_iter in range(self.settings['max_iter']):\n # run aero\n self.data = self.aero_solver.run()\n\n # map force\n struct_forces = mapping.aero2struct_force_mapping(\n self.data.aero.timestep_info[self.data.ts].forces,\n self.data.aero.struct2aero_mapping,\n self.data.aero.timestep_info[self.data.ts].zeta,\n self.data.structure.timestep_info[self.data.ts].pos,\n self.data.structure.timestep_info[self.data.ts].psi,\n self.data.structure.node_master_elem,\n self.data.structure.connectivities,\n self.data.structure.timestep_info[self.data.ts].cag(),\n self.data.aero.data_dict)\n \n if self.correct_forces:\n struct_forces = \\\n self.correct_forces_generator.generate(aero_kstep=self.data.aero.timestep_info[self.data.ts],\n structural_kstep=self.data.structure.timestep_info[self.data.ts],\n struct_forces=struct_forces,\n ts=0)\n\n # map nonlifting forces to structural nodes\n if self.settings['nonlifting_body_interactions']:\n struct_forces += mapping.aero2struct_force_mapping(\n self.data.nonlifting_body.timestep_info[self.data.ts].forces,\n self.data.nonlifting_body.struct2aero_mapping,\n self.data.nonlifting_body.timestep_info[self.data.ts].zeta,\n self.data.structure.timestep_info[self.data.ts].pos,\n self.data.structure.timestep_info[self.data.ts].psi,\n self.data.structure.node_master_elem,\n self.data.structure.connectivities,\n self.data.structure.timestep_info[self.data.ts].cag(),\n self.data.nonlifting_body.data_dict,\n skip_moments_generated_by_forces = True)\n\n self.data.aero.timestep_info[self.data.ts].aero_steady_forces_beam_dof = struct_forces\n self.data.structure.timestep_info[self.data.ts].postproc_node['aero_steady_forces'] = struct_forces # B\n \n # Add external forces\n if self.with_runtime_generators:\n self.data.structure.timestep_info[self.data.ts].runtime_steady_forces.fill(0.)\n self.data.structure.timestep_info[self.data.ts].runtime_unsteady_forces.fill(0.)\n params = dict()\n params['data'] = self.data\n params['struct_tstep'] = self.data.structure.timestep_info[self.data.ts]\n params['aero_tstep'] = self.data.aero.timestep_info[self.data.ts]\n params['fsi_substep'] = -i_iter\n for id, runtime_generator in self.runtime_generators.items():\n runtime_generator.generate(params)\n\n struct_forces += self.data.structure.timestep_info[self.data.ts].runtime_steady_forces\n struct_forces += self.data.structure.timestep_info[self.data.ts].runtime_unsteady_forces\n\n if not self.settings['relaxation_factor'] == 0.:\n if i_iter == 0:\n self.previous_force = struct_forces.copy()\n\n temp = struct_forces.copy()\n struct_forces = ((1.0 - self.settings['relaxation_factor'])*struct_forces +\n self.settings['relaxation_factor']*self.previous_force)\n self.previous_force = temp\n\n # copy force in beam\n old_g = self.structural_solver.settings['gravity']\n self.structural_solver.settings['gravity'] = old_g*load_step_multiplier\n temp1 = load_step_multiplier*(struct_forces + self.data.structure.ini_info.steady_applied_forces)\n self.data.structure.timestep_info[self.data.ts].steady_applied_forces[:] = temp1\n # run beam\n self.data = self.structural_solver.run()\n self.structural_solver.settings['gravity'] = old_g\n (self.data.structure.timestep_info[self.data.ts].total_forces[0:3],\n self.data.structure.timestep_info[self.data.ts].total_forces[3:6]) = (\n self.extract_resultants(self.data.structure.timestep_info[self.data.ts]))\n\n # update grid\n self.aero_solver.update_step()\n\n self.structural_solver.update(self.data.structure.timestep_info[self.data.ts])\n # convergence\n if self.convergence(i_iter, i_step):\n # create q and dqdt vectors\n self.structural_solver.update(self.data.structure.timestep_info[self.data.ts])\n self.cleanup_timestep_info()\n break\n\n return self.data\n\n def convergence(self, i_iter, i_step):\n if i_iter == self.settings['max_iter'] - 1:\n cout.cout_wrap('StaticCoupled did not converge!', 0)\n # quit(-1)\n\n return_value = None\n if i_iter == 0:\n self.initial_residual = np.linalg.norm(self.data.structure.timestep_info[self.data.ts].pos)\n self.previous_residual = self.initial_residual\n self.current_residual = self.initial_residual\n if self.print_info:\n forces = self.data.structure.timestep_info[self.data.ts].total_forces\n self.residual_table.print_line([i_iter,\n i_step,\n 0.0,\n forces[0],\n forces[1],\n forces[2],\n forces[3],\n forces[4],\n forces[5],\n ])\n return False\n\n self.current_residual = np.linalg.norm(self.data.structure.timestep_info[self.data.ts].pos)\n if self.print_info:\n forces = self.data.structure.timestep_info[self.data.ts].total_forces\n res_print = np.NINF\n if (np.abs(self.current_residual - self.previous_residual) >\n sys.float_info.epsilon*10):\n res_print = np.log10(np.abs(self.current_residual - self.previous_residual)/self.initial_residual)\n\n self.residual_table.print_line([i_iter,\n i_step,\n res_print,\n forces[0],\n forces[1],\n forces[2],\n forces[3],\n forces[4],\n forces[5],\n ])\n\n if return_value is None:\n if np.abs(self.current_residual - self.previous_residual)/self.initial_residual < self.settings['tolerance']:\n return_value = True\n else:\n self.previous_residual = self.current_residual\n return_value = False\n\n if return_value is None:\n return_value = False\n\n return return_value\n\n def change_trim(self, alpha, thrust, thrust_nodes, tail_deflection, tail_cs_index):\n # self.cleanup_timestep_info()\n self.data.structure.timestep_info = []\n self.data.structure.timestep_info.append(self.data.structure.ini_info.copy())\n aero_copy = self.data.aero.timestep_info[-1]\n self.data.aero.timestep_info = []\n self.data.aero.timestep_info.append(aero_copy)\n self.data.ts = 0\n # alpha\n orientation_quat = algebra.euler2quat(np.array([0.0, alpha, 0.0]))\n self.data.structure.timestep_info[0].quat[:] = orientation_quat[:]\n\n try:\n self.force_orientation\n except AttributeError:\n self.force_orientation = np.zeros((len(thrust_nodes), 3))\n for i_node, node in enumerate(thrust_nodes):\n self.force_orientation[i_node, :] = (\n algebra.unit_vector(self.data.structure.ini_info.steady_applied_forces[node, 0:3]))\n\n # thrust\n # thrust is scaled so that the direction of the forces is conserved\n # in all nodes.\n # the `thrust` parameter is the force PER node.\n # if there are two or more nodes in thrust_nodes, the total forces\n # is n_nodes_in_thrust_nodes*thrust\n # thrust forces have to be indicated in structure.ini_info\n for i_node, node in enumerate(thrust_nodes):\n self.data.structure.ini_info.steady_applied_forces[node, 0:3] = (\n self.force_orientation[i_node, :]*thrust)\n self.data.structure.timestep_info[0].steady_applied_forces[node, 0:3] = (\n self.force_orientation[i_node, :]*thrust)\n\n # tail deflection\n try:\n self.data.aero.data_dict['control_surface_deflection'][tail_cs_index] = tail_deflection\n except KeyError:\n raise Exception('This model has no control surfaces')\n except IndexError:\n raise Exception('The tail control surface index > number of surfaces')\n\n # update grid\n self.aero_solver.update_step()\n\n def extract_resultants(self, tstep=None):\n return self.structural_solver.extract_resultants(tstep)\n \n\n def teardown(self):\n \n self.structural_solver.teardown()\n self.aero_solver.teardown()\n if self.with_runtime_generators:\n for rg in self.runtime_generators.values():\n rg.teardown()\n\n\n" }, { "path": "sharpy/solvers/statictrim.py", "content": "import numpy as np\n\nimport sharpy.utils.cout_utils as cout\nimport sharpy.utils.solver_interface as solver_interface\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\nimport os\n\n\n@solver\nclass StaticTrim(BaseSolver):\n \"\"\"\n The ``StaticTrim`` solver determines the longitudinal state of trim (equilibrium) for an aeroelastic system in\n static conditions. It wraps around the desired solver to yield the state of trim of the system, in most cases\n the :class:`~sharpy.solvers.staticcoupled.StaticCoupled` solver.\n\n It calculates the required angle of attack, elevator deflection and thrust required to achieve longitudinal\n equilibrium. The output angles are shown in degrees.\n\n The results from the trimming iteration can be saved to a text file by using the `save_info` option.\n \"\"\"\n solver_id = 'StaticTrim'\n solver_classification = 'Flight Dynamics'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Print info to screen'\n\n settings_types['solver'] = 'str'\n settings_default['solver'] = ''\n settings_description['solver'] = 'Solver to run in trim routine'\n\n settings_types['solver_settings'] = 'dict'\n settings_default['solver_settings'] = dict()\n settings_description['solver_settings'] = 'Solver settings dictionary'\n\n settings_types['max_iter'] = 'int'\n settings_default['max_iter'] = 100\n settings_description['max_iter'] = 'Maximum number of iterations of trim routine'\n\n settings_types['fz_tolerance'] = 'float'\n settings_default['fz_tolerance'] = 0.01\n settings_description['fz_tolerance'] = 'Tolerance in vertical force'\n\n settings_types['fx_tolerance'] = 'float'\n settings_default['fx_tolerance'] = 0.01\n settings_description['fx_tolerance'] = 'Tolerance in horizontal force'\n\n settings_types['m_tolerance'] = 'float'\n settings_default['m_tolerance'] = 0.01\n settings_description['m_tolerance'] = 'Tolerance in pitching moment'\n\n settings_types['tail_cs_index'] = ['int', 'list(int)']\n settings_default['tail_cs_index'] = 0\n settings_description['tail_cs_index'] = 'Index of control surfaces that move to achieve trim'\n\n settings_types['thrust_nodes'] = 'list(int)'\n settings_default['thrust_nodes'] = [0]\n settings_description['thrust_nodes'] = 'Nodes at which thrust is applied'\n\n settings_types['initial_alpha'] = 'float'\n settings_default['initial_alpha'] = 0.\n settings_description['initial_alpha'] = 'Initial angle of attack'\n\n settings_types['initial_deflection'] = 'float'\n settings_default['initial_deflection'] = 0.\n settings_description['initial_deflection'] = 'Initial control surface deflection'\n\n settings_types['initial_thrust'] = 'float'\n settings_default['initial_thrust'] = 0.0\n settings_description['initial_thrust'] = 'Initial thrust setting'\n\n settings_types['initial_angle_eps'] = 'float'\n settings_default['initial_angle_eps'] = 0.05\n settings_description['initial_angle_eps'] = 'Initial change of control surface deflection'\n\n settings_types['initial_thrust_eps'] = 'float'\n settings_default['initial_thrust_eps'] = 2.\n settings_description['initial_thrust_eps'] = 'Initial thrust setting change'\n\n settings_types['relaxation_factor'] = 'float'\n settings_default['relaxation_factor'] = 0.2\n settings_description['relaxation_factor'] = 'Relaxation factor'\n\n settings_types['save_info'] = 'bool'\n settings_default['save_info'] = False\n settings_description['save_info'] = 'Save trim results to text file'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n self.solver = None\n\n # The order is\n # [0]: alpha/fz\n # [1]: alpha + delta (gamma)/moment\n # [2]: thrust/fx\n\n self.n_input = 3\n self.i_iter = 0\n\n self.input_history = []\n self.output_history = []\n self.gradient_history = []\n self.trimmed_values = np.zeros((3,))\n\n self.table = None\n self.folder = None\n\n def initialise(self, data, restart=False):\n self.data = data\n self.settings = data.settings[self.solver_id]\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n self.solver = solver_interface.initialise_solver(self.settings['solver'])\n self.solver.initialise(self.data, self.settings['solver_settings'], restart=restart)\n\n self.folder = data.output_folder + '/statictrim/'\n if not os.path.exists(self.folder):\n os.makedirs(self.folder)\n\n self.table = cout.TablePrinter(10, 8, ['g', 'f', 'f', 'f', 'f', 'f', 'f', 'f', 'f', 'f'],\n filename=self.folder+'trim_iterations.txt')\n self.table.print_header(['iter', 'alpha[deg]', 'elev[deg]', 'thrust', 'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'])\n\n def increase_ts(self):\n self.data.ts += 1\n self.structural_solver.next_step()\n self.aero_solver.next_step()\n\n def run(self, **kwargs):\n\n # In the event the modal solver has been run prior to StaticCoupled (i.e. to get undeformed modes), copy\n # results and then attach to the resulting timestep\n try:\n modal = self.data.structure.timestep_info[-1].modal.copy()\n modal_exists = True\n except AttributeError:\n modal_exists = False\n\n self.trim_algorithm()\n\n if modal_exists:\n self.data.structure.timestep_info[-1].modal = modal\n\n if self.settings['save_info']:\n np.savetxt(self.folder + '/trim_values.txt', self.trimmed_values)\n\n return self.data\n\n def convergence(self, fz, m, fx):\n return_value = np.array([False, False, False])\n\n if np.abs(fz) < self.settings['fz_tolerance']:\n return_value[0] = True\n\n if np.abs(m) < self.settings['m_tolerance']:\n return_value[1] = True\n\n if np.abs(fx) < self.settings['fx_tolerance']:\n return_value[2] = True\n\n return return_value\n\n def trim_algorithm(self):\n \"\"\"\n Trim algorithm method\n\n The trim condition is found iteratively.\n\n Returns:\n np.array: array of trim values for angle of attack, control surface deflection and thrust.\n \"\"\"\n for self.i_iter in range(self.settings['max_iter'] + 1):\n if self.i_iter == self.settings['max_iter']:\n raise Exception('The Trim routine reached max iterations without convergence!')\n\n self.input_history.append([])\n self.output_history.append([])\n self.gradient_history.append([])\n for i in range(self.n_input):\n self.input_history[self.i_iter].append(0)\n self.output_history[self.i_iter].append(0)\n self.gradient_history[self.i_iter].append(0)\n\n # the first iteration requires computing gradients\n if not self.i_iter:\n # add to input history the initial estimation\n self.input_history[self.i_iter][0] = self.settings['initial_alpha']\n self.input_history[self.i_iter][1] = (self.settings['initial_deflection'] +\n self.settings['initial_alpha'])\n self.input_history[self.i_iter][2] = self.settings['initial_thrust']\n\n # compute output\n (self.output_history[self.i_iter][0],\n self.output_history[self.i_iter][1],\n self.output_history[self.i_iter][2]) = self.evaluate(self.input_history[self.i_iter][0],\n self.input_history[self.i_iter][1],\n self.input_history[self.i_iter][2])\n\n # check for convergence (in case initial values are ok)\n if all(self.convergence(self.output_history[self.i_iter][0],\n self.output_history[self.i_iter][1],\n self.output_history[self.i_iter][2])):\n self.trimmed_values = self.input_history[self.i_iter]\n return\n\n # compute gradients\n # dfz/dalpha\n (l, m, d) = self.evaluate(self.input_history[self.i_iter][0] + self.settings['initial_angle_eps'],\n self.input_history[self.i_iter][1],\n self.input_history[self.i_iter][2])\n\n self.gradient_history[self.i_iter][0] = ((l - self.output_history[self.i_iter][0]) /\n self.settings['initial_angle_eps'])\n\n # dm/dgamma\n (l, m, d) = self.evaluate(self.input_history[self.i_iter][0],\n self.input_history[self.i_iter][1] + self.settings['initial_angle_eps'],\n self.input_history[self.i_iter][2])\n\n self.gradient_history[self.i_iter][1] = ((m - self.output_history[self.i_iter][1]) /\n self.settings['initial_angle_eps'])\n\n # dfx/dthrust\n (l, m, d) = self.evaluate(self.input_history[self.i_iter][0],\n self.input_history[self.i_iter][1],\n self.input_history[self.i_iter][2] +\n self.settings['initial_thrust_eps'])\n\n self.gradient_history[self.i_iter][2] = ((d - self.output_history[self.i_iter][2]) /\n self.settings['initial_thrust_eps'])\n\n continue\n\n # if not all(np.isfinite(self.gradient_history[self.i_iter - 1]))\n # now back to normal evaluation (not only the i_iter == 0 case)\n # compute next alpha with the previous gradient\n # convergence = self.convergence(self.output_history[self.i_iter - 1][0],\n # self.output_history[self.i_iter - 1][1],\n # self.output_history[self.i_iter - 1][2])\n convergence = np.full((3, ), False)\n if convergence[0]:\n # fz is converged, don't change it\n self.input_history[self.i_iter][0] = self.input_history[self.i_iter - 1][0]\n self.gradient_history[self.i_iter][0] = self.gradient_history[self.i_iter - 1][0]\n else:\n self.input_history[self.i_iter][0] = (self.input_history[self.i_iter - 1][0] -\n (self.output_history[self.i_iter - 1][0] /\n self.gradient_history[self.i_iter - 1][0]))\n\n if convergence[1]:\n # m is converged, don't change it\n self.input_history[self.i_iter][1] = self.input_history[self.i_iter - 1][1]\n self.gradient_history[self.i_iter][1] = self.gradient_history[self.i_iter - 1][1]\n else:\n # compute next gamma with the previous gradient\n self.input_history[self.i_iter][1] = (self.input_history[self.i_iter - 1][1] -\n (self.output_history[self.i_iter - 1][1] /\n self.gradient_history[self.i_iter - 1][1]))\n\n if convergence[2]:\n # fx is converged, don't change it\n self.input_history[self.i_iter][2] = self.input_history[self.i_iter - 1][2]\n self.gradient_history[self.i_iter][2] = self.gradient_history[self.i_iter - 1][2]\n else:\n # compute next gamma with the previous gradient\n self.input_history[self.i_iter][2] = (self.input_history[self.i_iter - 1][2] -\n (self.output_history[self.i_iter - 1][2] /\n self.gradient_history[self.i_iter - 1][2]))\n\n if self.settings['relaxation_factor']:\n for i_dim in range(3):\n self.input_history[self.i_iter][i_dim] = (self.input_history[self.i_iter][i_dim]*(1 - self.settings['relaxation_factor']) +\n self.input_history[self.i_iter][i_dim]*self.settings['relaxation_factor'])\n\n # evaluate\n (self.output_history[self.i_iter][0],\n self.output_history[self.i_iter][1],\n self.output_history[self.i_iter][2]) = self.evaluate(self.input_history[self.i_iter][0],\n self.input_history[self.i_iter][1],\n self.input_history[self.i_iter][2])\n\n if not convergence[0]:\n self.gradient_history[self.i_iter][0] = ((self.output_history[self.i_iter][0] -\n self.output_history[self.i_iter - 1][0]) /\n (self.input_history[self.i_iter][0] -\n self.input_history[self.i_iter - 1][0]))\n\n if not convergence[1]:\n self.gradient_history[self.i_iter][1] = ((self.output_history[self.i_iter][1] -\n self.output_history[self.i_iter - 1][1]) /\n (self.input_history[self.i_iter][1] -\n self.input_history[self.i_iter - 1][1]))\n\n if not convergence[2]:\n self.gradient_history[self.i_iter][2] = ((self.output_history[self.i_iter][2] -\n self.output_history[self.i_iter - 1][2]) /\n (self.input_history[self.i_iter][2] -\n self.input_history[self.i_iter - 1][2]))\n\n # check convergence\n convergence = self.convergence(self.output_history[self.i_iter][0],\n self.output_history[self.i_iter][1],\n self.output_history[self.i_iter][2])\n if all(convergence):\n self.trimmed_values = self.input_history[self.i_iter]\n self.table.close_file()\n return\n\n def evaluate(self, alpha, deflection_gamma, thrust):\n if not np.isfinite(alpha):\n raise ValueError(\"Alpha trim gradient is zero, resulting in division by zero.\")\n if not np.isfinite(deflection_gamma):\n raise ValueError(\"Delta trim gradient is zero, resulting in division by zero.\")\n if not np.isfinite(thrust):\n raise ValueError(\"Thrust trim gradient is zero, resulting in division by zero.\")\n\n # modify the trim in the static_coupled solver\n self.solver.change_trim(alpha,\n thrust,\n self.settings['thrust_nodes'],\n deflection_gamma - alpha,\n self.settings['tail_cs_index'])\n # run the solver\n self.solver.run()\n # extract resultants\n forces, moments = self.solver.extract_resultants()\n\n forcez = forces[2]\n forcex = forces[0]\n moment = moments[1]\n\n self.table.print_line([self.i_iter,\n alpha*180/np.pi,\n (deflection_gamma - alpha)*180/np.pi,\n thrust,\n forces[0],\n forces[1],\n forces[2],\n moments[0],\n moments[1],\n moments[2]])\n\n return forcez, moment, forcex\n" }, { "path": "sharpy/solvers/staticuvlm.py", "content": "\nimport sharpy.aero.utils.uvlmlib as uvlmlib\nimport sharpy.utils.settings as settings_utils\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.generator_interface as gen_interface\nfrom sharpy.utils.constants import vortex_radius_def\nimport sharpy.aero.utils.mapping as mapping\n\n\n@solver\nclass StaticUvlm(BaseSolver):\n \"\"\"\n ``StaticUvlm`` solver class, inherited from ``BaseSolver``\n\n Aerodynamic solver that runs a UVLM routine to solve the steady or unsteady aerodynamic problem.\n The aerodynamic problem is posed in the form of an ``Aerogrid`` object.\n\n Args:\n data (PreSharpy): object with problem data\n custom_settings (dict): custom settings that override the settings in the solver ``.txt`` file. None by default\n\n Attributes:\n settings (dict): Name-value pair of settings employed by solver. See Notes for valid combinations\n settings_types (dict): Acceptable data types for entries in ``settings``\n settings_default (dict): Default values for the available ``settings``\n data (PreSharpy): object containing the information of the problem\n velocity_generator(object): object containing the flow conditions information\n\n\n \"\"\"\n solver_id = 'StaticUvlm'\n solver_classification = 'aero'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Print info to screen'\n\n settings_types['horseshoe'] = 'bool'\n settings_default['horseshoe'] = False\n settings_description['horseshoe'] = 'Horseshoe wake modelling for steady simulations.'\n\n settings_types['nonlifting_body_interactions'] = 'bool'\n settings_default['nonlifting_body_interactions'] = False\n settings_description['nonlifting_body_interactions'] = 'Consider nonlifting body interactions'\n\n settings_types['only_nonlifting'] = 'bool'\n settings_default['only_nonlifting'] = False\n settings_description['only_nonlifting'] = 'Consider only nonlifting bodies'\n\n settings_types['phantom_wing_test'] = 'bool'\n settings_default['phantom_wing_test'] = False\n settings_description['phantom_wing_test'] = 'Debug option'\n\n settings_types['num_cores'] = 'int'\n settings_default['num_cores'] = 0\n settings_description['num_cores'] = 'Number of cores to use in the VLM lib'\n\n settings_types['n_rollup'] = 'int'\n settings_default['n_rollup'] = 0\n settings_description['n_rollup'] = 'Number of rollup iterations for free wake. Use at least ``n_rollup > 1.1*m_star``'\n\n settings_types['rollup_dt'] = 'float'\n settings_default['rollup_dt'] = 0.1\n settings_description['rollup_dt'] = 'Pseudo time step for wake convection. Chose it so that it is similar to the unsteady time step'\n\n settings_types['rollup_aic_refresh'] = 'int'\n settings_default['rollup_aic_refresh'] = 1\n settings_description['rollup_dt'] = 'Controls when the AIC matrix is refreshed during the wake rollup'\n\n settings_types['rollup_tolerance'] = 'float'\n settings_default['rollup_tolerance'] = 1e-4\n settings_description['rollup_tolerance'] = 'Convergence criterium for rollup wake'\n\n settings_types['iterative_solver'] = 'bool'\n settings_default['iterative_solver'] = False\n settings_description['iterative_solver'] = 'Not in use'\n\n settings_types['iterative_tol'] = 'float'\n settings_default['iterative_tol'] = 1e-4\n settings_description['iterative_tol'] = 'Not in use'\n\n settings_types['iterative_precond'] = 'bool'\n settings_default['iterative_precond'] = False\n settings_description['iterative_precond'] = 'Not in use'\n\n settings_types['velocity_field_generator'] = 'str'\n settings_default['velocity_field_generator'] = 'SteadyVelocityField'\n settings_description['velocity_field_generator'] = 'Name of the velocity field generator to be used in the simulation'\n\n settings_types['velocity_field_input'] = 'dict'\n settings_default['velocity_field_input'] = {}\n settings_description['velocity_field_input'] = 'Dictionary of settings for the velocity field generator'\n\n settings_types['rho'] = 'float'\n settings_default['rho'] = 1.225\n settings_description['rho'] = 'Air density'\n\n settings_types['cfl1'] = 'bool'\n settings_default['cfl1'] = True\n settings_description['cfl1'] = 'If it is ``True``, it assumes that the discretisation complies with CFL=1'\n\n settings_types['vortex_radius'] = 'float'\n settings_default['vortex_radius'] = vortex_radius_def\n settings_description['vortex_radius'] = 'Distance between points below which induction is not computed'\n\n settings_types['vortex_radius_wake_ind'] = 'float'\n settings_default['vortex_radius_wake_ind'] = vortex_radius_def\n settings_description['vortex_radius_wake_ind'] = 'Distance between points below which induction is not computed in the wake convection'\n\n settings_types['rbm_vel_g'] = 'list(float)'\n settings_default['rbm_vel_g'] = [0., 0., 0., 0., 0., 0.]\n settings_description['rbm_vel_g'] = 'Rigid body velocity in G FoR'\n\n settings_types['centre_rot_g'] = 'list(float)'\n settings_default['centre_rot_g'] = [0., 0., 0.]\n settings_description['centre_rot_g'] = 'Centre of rotation in G FoR around which ``rbm_vel_g`` is applied'\n\n settings_types['map_forces_on_struct'] = 'bool'\n settings_default['map_forces_on_struct'] = False\n settings_description['map_forces_on_struct'] = 'Maps the forces on the structure at the end of the timestep. Only usefull if the solver is used outside StaticCoupled'\n\n settings_types['ignore_first_x_nodes_in_force_calculation'] = 'int'\n settings_default['ignore_first_x_nodes_in_force_calculation'] = 0\n settings_description['ignore_first_x_nodes_in_force_calculation'] = 'Ignores the forces on the first user-specified number of nodes of all surfaces.'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n # settings list\n self.data = None\n self.settings = None\n self.velocity_generator = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default, no_ctype=True)\n\n self.update_step()\n\n # init velocity generator\n velocity_generator_type = gen_interface.generator_from_string(\n self.settings['velocity_field_generator'])\n self.velocity_generator = velocity_generator_type()\n self.velocity_generator.initialise(self.settings['velocity_field_input'], restart=restart)\n\n def add_step(self):\n self.data.aero.add_timestep()\n if self.settings['nonlifting_body_interactions']:\n self.data.nonlifting_body.add_timestep()\n \n\n def update_grid(self, beam):\n\n if not self.settings['only_nonlifting']:\n self.data.aero.generate_zeta(beam,\n self.data.aero.aero_settings,\n -1,\n beam_ts=-1)\n if self.settings['nonlifting_body_interactions'] or self.settings['only_nonlifting']:\n self.data.nonlifting_body.generate_zeta(beam,\n self.data.nonlifting_body.aero_settings,\n -1,\n beam_ts=-1)\n\n def update_custom_grid(self, structure_tstep, aero_tstep, nonlifting_tstep=None):\n self.data.aero.generate_zeta_timestep_info(structure_tstep,\n aero_tstep,\n self.data.structure,\n self.data.aero.aero_settings,\n dt=self.settings['rollup_dt'])\n if self.settings['nonlifting_body_interactions']:\n self.data.nonlifting_body.generate_zeta_timestep_info(structure_tstep,\n nonlifting_tstep,\n self.data.structure,\n self.data.nonlifting_body.aero_settings)\n\n def run(self, **kwargs):\n\n structure_tstep = settings_utils.set_value_or_default(kwargs, 'structural_step', self.data.structure.timestep_info[self.data.ts])\n \n if not self.settings['only_nonlifting']:\n aero_tstep = settings_utils.set_value_or_default(kwargs, 'aero_step', self.data.aero.timestep_info[self.data.ts])\n if not self.data.aero.timestep_info[self.data.ts].zeta:\n return self.data\n\n # generate the wake because the solid shape might change\n self.data.aero.wake_shape_generator.generate({'zeta': aero_tstep.zeta,\n 'zeta_star': aero_tstep.zeta_star,\n 'gamma': aero_tstep.gamma,\n 'gamma_star': aero_tstep.gamma_star,\n 'dist_to_orig': aero_tstep.dist_to_orig})\n \n if self.settings['nonlifting_body_interactions']:\n # generate uext\n self.velocity_generator.generate({'zeta': self.data.nonlifting_body.timestep_info[self.data.ts].zeta,\n 'override': True,\n 'for_pos': structure_tstep.for_pos[0:3]},\n self.data.nonlifting_body.timestep_info[self.data.ts].u_ext)\n # generate uext\n self.velocity_generator.generate({'zeta': self.data.aero.timestep_info[self.data.ts].zeta,\n 'override': True,\n 'for_pos': self.data.structure.timestep_info[self.data.ts].for_pos[0:3]}, \n self.data.aero.timestep_info[self.data.ts].u_ext)\n # grid orientation\n uvlmlib.vlm_solver_lifting_and_nonlifting_bodies(self.data.aero.timestep_info[self.data.ts],\n self.data.nonlifting_body.timestep_info[self.data.ts],\n self.settings)\n else: \n # generate uext\n self.velocity_generator.generate({'zeta': self.data.aero.timestep_info[self.data.ts].zeta,\n 'override': True,\n 'for_pos': self.data.structure.timestep_info[self.data.ts].for_pos[0:3]},\n self.data.aero.timestep_info[self.data.ts].u_ext)\n\n\n # grid orientation\n uvlmlib.vlm_solver(self.data.aero.timestep_info[self.data.ts],\n self.settings)\n else:\n self.velocity_generator.generate({'zeta': self.data.nonlifting_body.timestep_info[self.data.ts].zeta,\n 'override': True,\n 'for_pos': self.data.structure.timestep_info[self.data.ts].for_pos[0:3]},\n self.data.nonlifting_body.timestep_info[self.data.ts].u_ext)\n uvlmlib.vlm_solver_nonlifting_body(self.data.nonlifting_body.timestep_info[self.data.ts],\n self.settings)\n\n return self.data\n\n def next_step(self):\n \"\"\" Updates de aerogrid based on the info of the step, and increases\n the self.ts counter \"\"\"\n self.data.aero.add_timestep()\n if self.settings['nonlifting_body_interactions']:\n self.data.nonlifting_body.add_timestep()\n self.update_step()\n\n def update_step(self):\n if not self.settings['only_nonlifting']:\n self.data.aero.generate_zeta(self.data.structure,\n self.data.aero.aero_settings,\n self.data.ts)\n if self.settings['nonlifting_body_interactions'] or self.settings['only_nonlifting']:\n self.data.nonlifting_body.generate_zeta(self.data.structure,\n self.data.nonlifting_body.aero_settings,\n self.data.ts)\n\n" }, { "path": "sharpy/solvers/steplinearuvlm.py", "content": "\"\"\"\nTime domain solver to integrate the linear UVLM aerodynamic system developed by S. Maraniello\nN Goizueta\nNov 18\n\"\"\"\nfrom sharpy.utils.solver_interface import BaseSolver, solver\nimport numpy as np\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.generator_interface as gen_interface\nimport sharpy.utils.algebra as algebra\nimport sharpy.linear.src.linuvlm as linuvlm\nfrom sharpy.utils.constants import vortex_radius_def\n\n\n@solver\nclass StepLinearUVLM(BaseSolver):\n r\"\"\"\n Time domain aerodynamic solver that uses a linear UVLM formulation to be used with the\n :class:`solvers.DynamicCoupled` solver.\n\n To use this solver, the ``solver_id = StepLinearUVLM`` must be given as the name for the ``aero_solver``\n is the case of an aeroelastic solver, where the setting below would be parsed through ``aero_solver_settings``.\n\n Notes:\n\n The ``integr_order`` variable refers to the finite differencing scheme used to calculate the bound circulation\n derivative with respect to time :math:`\\dot{\\mathbf{\\Gamma}}`. A first order scheme is used when\n ``integr_order == 1``\n\n .. math:: \\dot{\\mathbf{\\Gamma}}^{n+1} = \\frac{\\mathbf{\\Gamma}^{n+1}-\\mathbf{\\Gamma}^n}{\\Delta t}\n\n If ``integr_order == 2`` a higher order scheme is used (but it isn't exactly second order accurate [1]).\n\n .. math:: \\dot{\\mathbf{\\Gamma}}^{n+1} = \\frac{3\\mathbf{\\Gamma}^{n+1}-4\\mathbf{\\Gamma}^n + \\mathbf{\\Gamma}^{n-1}}\n {2\\Delta t}\n\n If ``track_body`` is ``True``, the UVLM is projected onto a frame ``U`` that is:\n\n * Coincident with ``G`` at the linearisation timestep.\n\n * Thence, rotates by the same quantity as the FoR ``A``.\n\n\n It is similar to a stability axes and is recommended any time rigid body dynamics are included.\n\n See Also:\n\n :class:`sharpy.sharpy.linear.assembler.linearuvlm.LinearUVLM`\n\n References:\n\n [1] Maraniello, S., & Palacios, R.. State-Space Realizations and Internal Balancing in Potential-Flow\n Aerodynamics with Arbitrary Kinematics. AIAA Journal, 57(6), 1–14. 2019. https://doi.org/10.2514/1.J058153\n\n \"\"\"\n solver_id = 'StepLinearUVLM'\n solver_classification = 'aero'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = 0.1\n settings_description['dt'] = 'Time step'\n\n settings_types['integr_order'] = 'int'\n settings_default['integr_order'] = 2\n settings_description['integr_order'] = 'Integration order of the circulation derivative. Either ``1`` or ``2``.'\n\n settings_types['ScalingDict'] = 'dict'\n settings_default['ScalingDict'] = dict()\n settings_description['ScalingDict'] = 'Dictionary of scaling factors to achieve normalised UVLM realisation.'\n\n settings_types['remove_predictor'] = 'bool'\n settings_default['remove_predictor'] = True\n settings_description['remove_predictor'] = 'Remove the predictor term from the UVLM equations'\n\n settings_types['use_sparse'] = 'bool'\n settings_default['use_sparse'] = True\n settings_description['use_sparse'] = 'Assemble UVLM plant matrix in sparse format'\n\n settings_types['density'] = 'float'\n settings_default['density'] = 1.225\n settings_description['density'] = 'Air density'\n\n settings_types['track_body'] = 'bool'\n settings_default['track_body'] = True\n settings_description['track_body'] = 'UVLM inputs and outputs projected to coincide with lattice at linearisation'\n\n settings_types['track_body_number'] = 'int'\n settings_default['track_body_number'] = -1\n settings_description['track_body_number'] = 'Frame of reference number to follow. If ``-1`` track ``A`` frame.'\n\n settings_types['velocity_field_generator'] = 'str'\n settings_default['velocity_field_generator'] = 'SteadyVelocityField'\n settings_description['velocity_field_generator'] = 'Name of the velocity field generator to be used in the ' \\\n 'simulation'\n\n settings_types['velocity_field_input'] = 'dict'\n settings_default['velocity_field_input'] = {}\n settings_description['velocity_field_input'] = 'Dictionary of settings for the velocity field generator'\n\n settings_types['vortex_radius'] = 'float'\n settings_default['vortex_radius'] = vortex_radius_def\n settings_description['vortex_radius'] = 'Distance between points below which induction is not computed'\n\n settings_types['vortex_radius_wake_ind'] = 'float'\n settings_default['vortex_radius_wake_ind'] = vortex_radius_def\n settings_description[\n 'vortex_radius_wake_ind'] = 'Distance between points below which induction is not computed in the wake convection'\n\n settings_types['cfl1'] = 'bool'\n settings_default['cfl1'] = True\n settings_description['cfl1'] = 'If it is ``True``, it assumes that the discretisation complies with CFL=1'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n scaling_settings_types = dict()\n scaling_settings_default = dict()\n scaling_settings_description = dict()\n\n scaling_settings_types['length'] = 'float'\n scaling_settings_default['length'] = 1.0\n scaling_settings_description['length'] = 'Reference length to be used for UVLM scaling'\n\n scaling_settings_types['speed'] = 'float'\n scaling_settings_default['speed'] = 1.0\n scaling_settings_description['speed'] = 'Reference speed to be used for UVLM scaling'\n\n scaling_settings_types['density'] = 'float'\n scaling_settings_default['density'] = 1.0\n scaling_settings_description['density'] = 'Reference density to be used for UVLM scaling'\n\n __doc__ += settings_table.generate(scaling_settings_types,\n scaling_settings_default,\n scaling_settings_description, header_line='The settings that ``ScalingDict`` '\n 'accepts are the following:')\n\n def __init__(self):\n self.data = None\n self.settings = None\n self.lin_uvlm_system = None\n self.velocity_generator = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n r\"\"\"\n Initialises the Linear UVLM aerodynamic solver and the chosen velocity generator.\n\n Settings are parsed into the standard SHARPy settings format for solvers. It then checks whether there is\n any previous information about the linearised system (in order for a solution to be restarted without\n overwriting the linearisation).\n\n If a linearised system does not exist, a linear UVLM system is created linearising about the current time step.\n\n The reference values for the input and output are transformed into column vectors :math:`\\mathbf{u}`\n and :math:`\\mathbf{y}`, respectively.\n\n The information pertaining to the linear system is stored in a dictionary ``self.data.aero.linear`` within\n the main ``data`` variable.\n\n Args:\n data (PreSharpy): class containing the problem information\n custom_settings (dict): custom settings dictionary\n\n \"\"\"\n\n self.data = data\n\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default, no_ctype=True)\n settings_utils.to_custom_types(self.settings['ScalingDict'], self.scaling_settings_types,\n self.scaling_settings_default, no_ctype=True)\n\n # Initialise velocity generator\n velocity_generator_type = gen_interface.generator_from_string(self.settings['velocity_field_generator'])\n self.velocity_generator = velocity_generator_type()\n self.velocity_generator.initialise(self.settings['velocity_field_input'], restart=restart)\n\n # Check whether linear UVLM has been initialised\n try:\n self.data.aero.linear\n except AttributeError:\n self.data.aero.linear = dict()\n aero_tstep = self.data.aero.timestep_info[-1]\n\n ### Record body orientation/velocities at time 0\n # This option allows to rotate the linearised UVLM with the A frame\n # or a specific body (multi-body solution)\n if self.settings['track_body']:\n\n self.num_body_track = self.settings['track_body_number']\n\n # track A frame\n if self.num_body_track == -1:\n self.quat0 = self.data.structure.timestep_info[-1].quat.copy()\n self.for_vel0 = self.data.structure.timestep_info[-1].for_vel.copy()\n else: # track a specific body\n self.quat0 = \\\n self.data.structure.timestep_info[-1].mb_quat[self.num_body_track, :].copy()\n self.for_vel0 = \\\n self.data.structure.timestep_info[-1].mb_FoR_vel[self.num_body_track, :].copy()\n\n # convert to G frame\n self.Cga0 = algebra.quat2rotation(self.quat0)\n self.Cga = self.Cga0.copy()\n self.for_vel0[:3] = self.Cga0.dot(self.for_vel0[:3])\n self.for_vel0[3:] = self.Cga0.dot(self.for_vel0[3:])\n\n else: # check/record initial rotation speed\n self.num_body_track = None\n self.quat0 = None\n self.Cag0 = None\n self.Cga = None\n self.for_vel0 = np.zeros((6,))\n\n # TODO: verify of a better way to implement rho\n aero_tstep.rho = self.settings['density']\n\n # Generate instance of linuvlm.Dynamic()\n lin_uvlm_system = linuvlm.DynamicBlock(aero_tstep,\n dynamic_settings=self.settings,\n for_vel=self.for_vel0)\n\n # add rotational speed\n for ii in range(lin_uvlm_system.MS.n_surf):\n lin_uvlm_system.MS.Surfs[ii].omega = self.for_vel0[3:]\n\n # Save reference values\n # System Inputs\n u_0 = self.pack_input_vector()\n\n # Linearised state\n dt = self.settings['dt']\n x_0 = self.pack_state_vector(aero_tstep, None, dt, self.settings['integr_order'])\n\n # Reference forces\n f_0 = np.concatenate([aero_tstep.forces[ss][0:3].reshape(-1, order='C')\n for ss in range(aero_tstep.n_surf)])\n\n # Assemble the state space system\n wake_prop_settings = {'dt': self.settings['dt'],\n 'ts': self.data.ts,\n 't': self.data.ts * self.settings['dt'],\n 'for_pos': self.data.structure.timestep_info[-1].for_pos,\n 'cfl1': self.settings['cfl1'],\n 'vel_gen': self.velocity_generator}\n lin_uvlm_system.assemble_ss(wake_prop_settings=wake_prop_settings)\n self.data.aero.linear['System'] = lin_uvlm_system\n self.data.aero.linear['SS'] = lin_uvlm_system.SS\n self.data.aero.linear['x_0'] = x_0\n self.data.aero.linear['u_0'] = u_0\n self.data.aero.linear['y_0'] = f_0\n # TODO: Implement in AeroTimeStepInfo a way to store the state vectors\n\n def run(self, **kwargs):\n r\"\"\"\n Solve the linear aerodynamic UVLM model at the current time step ``n``. The step increment is solved as:\n\n .. math::\n \\mathbf{x}^n &= \\mathbf{A\\,x}^{n-1} + \\mathbf{B\\,u}^n \\\\\n \\mathbf{y}^n &= \\mathbf{C\\,x}^n + \\mathbf{D\\,u}^n\n\n A change of state is possible in order to solve the system without the predictor term. In which case the system\n is solved by:\n\n .. math::\n \\mathbf{h}^n &= \\mathbf{A\\,h}^{n-1} + \\mathbf{B\\,u}^{n-1} \\\\\n \\mathbf{y}^n &= \\mathbf{C\\,h}^n + \\mathbf{D\\,u}^n\n\n\n Variations are taken with respect to initial reference state. The state and input vectors for the linear\n UVLM system are of the form:\n\n If ``integr_order==1``:\n .. math:: \\mathbf{x}_n = [\\delta\\mathbf{\\Gamma}^T_n,\\,\n \\delta\\mathbf{\\Gamma_w}_n^T,\\,\n \\Delta t \\,\\delta\\mathbf{\\dot{\\Gamma}}_n^T]^T\n\n Else, if ``integr_order==2``:\n .. math:: \\mathbf{x}_n = [\\delta\\mathbf{\\Gamma}_n^T,\\,\n \\delta\\mathbf{\\Gamma_w}_n^T,\\,\n \\Delta t \\,\\delta\\mathbf{\\dot{\\Gamma}}_n^T,\\,\n \\delta\\mathbf{\\Gamma}_{n-1}^T]^T\n\n And the input vector:\n .. math:: \\mathbf{u}_n = [\\delta\\mathbf{\\zeta}_n^T,\\,\n \\delta\\dot{\\mathbf{\\zeta}}_n^T,\\,\\delta\\mathbf{u_{ext}}^T_n]^T\n\n where the subscript ``n`` refers to the time step.\n\n The linear UVLM system is then solved as detailed in :func:`sharpy.linear.src.linuvlm.Dynamic.solve_step`.\n The output is a column vector containing the aerodynamic forces at the panel vertices.\n\n To Do: option for impulsive start?\n\n Args:\n aero_tstep (AeroTimeStepInfo): object containing the aerodynamic data at the current time step\n structure_tstep (StructTimeStepInfo): object containing the structural data at the current time step\n convect_wake (bool): for backward compatibility only. The linear UVLM assumes a frozen wake geometry\n dt (float): time increment\n t (float): current time\n unsteady_contribution (bool): (backward compatibily). Unsteady aerodynamic effects are always included\n\n Returns:\n PreSharpy: updated ``self.data`` class with the new forces and circulation terms of the system\n\n \"\"\"\n\n aero_tstep = settings_utils.set_value_or_default(kwargs, 'aero_step', self.data.aero.timestep_info[-1])\n structure_tstep = settings_utils.set_value_or_default(kwargs, 'structural_step',\n self.data.structure.timestep_info[-1])\n dt = settings_utils.set_value_or_default(kwargs, 'dt', self.settings['dt'])\n t = settings_utils.set_value_or_default(kwargs, 't', self.data.ts * dt)\n\n integr_order = self.settings['integr_order']\n\n ### Define Input\n\n # Generate external velocity field u_ext\n self.velocity_generator.generate({'zeta': aero_tstep.zeta,\n 'override': True,\n 't': t,\n 'ts': self.data.ts,\n 'dt': dt,\n 'for_pos': structure_tstep.for_pos},\n aero_tstep.u_ext)\n\n ### Proj from FoR G to linearisation frame\n # - proj happens in self.pack_input_vector and unpack_ss_vectors\n if self.settings['track_body']:\n # track A frame\n if self.num_body_track == -1:\n self.Cga = algebra.quat2rotation(structure_tstep.quat)\n else: # track a specific body\n self.Cga = algebra.quat2rotation(\n structure_tstep.mb_quat[self.num_body_track, :])\n\n # Column vector that will be the input to the linearised UVLM system\n # Input is at time step n, since it is updated in the aeroelastic solver prior to aerodynamic solver\n u_n = self.pack_input_vector()\n\n du_n = u_n - self.data.aero.linear['u_0']\n\n if self.settings['remove_predictor']:\n u_m1 = self.pack_input_vector()\n du_m1 = u_m1 - self.data.aero.linear['u_0']\n else:\n du_m1 = None\n\n # Retrieve State vector at time n-1\n if len(self.data.aero.timestep_info) < 2:\n x_m1 = self.pack_state_vector(aero_tstep, None, dt, integr_order)\n else:\n x_m1 = self.pack_state_vector(aero_tstep, self.data.aero.timestep_info[-2], dt, integr_order)\n\n # dx is at timestep n-1\n dx_m1 = x_m1 - self.data.aero.linear['x_0']\n\n ### Solve system - output is the variation in force\n dx_n, dy_n = self.data.aero.linear['System'].solve_step(dx_m1, du_m1, du_n, transform_state=True)\n\n x_n = self.data.aero.linear['x_0'] + dx_n\n y_n = self.data.aero.linear['y_0'] + dy_n\n\n # if self.settings['physical_model']:\n forces, gamma, gamma_dot, gamma_star = self.unpack_ss_vectors(y_n, x_n, u_n, aero_tstep)\n aero_tstep.forces = forces\n aero_tstep.gamma = gamma\n aero_tstep.gamma_dot = gamma_dot\n aero_tstep.gamma_star = gamma_star\n\n return self.data\n\n def add_step(self):\n self.data.aero.add_timestep()\n\n def update_grid(self, beam):\n self.data.aero.generate_zeta(beam, self.data.aero.aero_settings, -1, beam_ts=-1)\n\n def update_custom_grid(self, structure_tstep, aero_tstep):\n self.data.aero.generate_zeta_timestep_info(structure_tstep, aero_tstep, self.data.structure,\n self.data.aero.aero_settings)\n\n def unpack_ss_vectors(self, y_n, x_n, u_n, aero_tstep):\n r\"\"\"\n Transform column vectors used in the state space formulation into SHARPy format\n\n The column vectors are transformed into lists with one entry per aerodynamic surface. Each entry contains a\n matrix with the quantities at each grid vertex.\n\n .. math::\n \\mathbf{y}_n \\longrightarrow \\mathbf{f}_{aero}\n\n .. math:: \\mathbf{x}_n \\longrightarrow \\mathbf{\\Gamma}_n,\\,\n \\mathbf{\\Gamma_w}_n,\\,\n \\mathbf{\\dot{\\Gamma}}_n\n\n If the ``track_body`` option is on, the output forces are projected from\n the linearization frame, to the G frame. Note that the linearisation\n frame is:\n\n a. equal to the FoR G at time 0 (linearisation point)\n b. rotates as the body frame specified in the ``track_body_number``\n\n Args:\n y_n (np.ndarray): Column output vector of linear UVLM system\n x_n (np.ndarray): Column state vector of linear UVLM system\n u_n (np.ndarray): Column input vector of linear UVLM system\n aero_tstep (AeroTimeStepInfo): aerodynamic timestep information class instance\n\n Returns:\n tuple: Tuple containing:\n\n forces (list):\n Aerodynamic forces in a list with ``n_surf`` entries.\n Each entry is a ``(6, M+1, N+1)`` matrix, where the first 3\n indices correspond to the components in ``x``, ``y`` and ``z``. The latter 3 are zero.\n\n gamma (list):\n Bound circulation list with ``n_surf`` entries. Circulation is stored in an ``(M+1, N+1)``\n matrix, corresponding to the panel vertices.\n\n gamma_dot (list):\n Bound circulation derivative list with ``n_surf`` entries.\n Circulation derivative is stored in an ``(M+1, N+1)`` matrix, corresponding to the panel\n vertices.\n\n gamma_star (list):\n Wake (free) circulation list with ``n_surf`` entries. Wake circulation is stored in an\n ``(M_star+1, N+1)`` matrix, corresponding to the panel vertices of the wake.\n\n \"\"\"\n\n ### project forces from uvlm FoR to FoR G\n if self.settings['track_body']:\n Cg_uvlm = np.dot(self.Cga, self.Cga0.T)\n\n f_aero = y_n\n\n gamma_vec, gamma_star_vec, gamma_dot_vec = self.data.aero.linear['System'].unpack_state(x_n)\n\n # Reshape output into forces[i_surface] where forces[i_surface] is a (6,M+1,N+1) matrix and circulation terms\n # where gamma is a [i_surf](M+1, N+1) matrix\n forces = []\n gamma = []\n gamma_star = []\n gamma_dot = []\n\n worked_points = 0\n worked_panels = 0\n worked_wake_panels = 0\n\n for i_surf in range(aero_tstep.n_surf):\n # Tuple with dimensions of the aerogrid zeta, which is the same shape for forces\n dimensions = aero_tstep.zeta[i_surf].shape\n dimensions_gamma = self.data.aero.aero_dimensions[i_surf]\n dimensions_wake = self.data.aero.aero_dimensions_star[i_surf]\n\n # Number of entries in zeta\n points_in_surface = aero_tstep.zeta[i_surf].size\n panels_in_surface = aero_tstep.gamma[i_surf].size\n panels_in_wake = aero_tstep.gamma_star[i_surf].size\n\n # Append reshaped forces to each entry in list (one for each surface)\n forces.append(f_aero[worked_points:worked_points + points_in_surface].reshape(dimensions, order='C'))\n\n ### project forces.\n # - forces are in UVLM linearisation frame. Hence, these are projected\n # into FoR (using rotation matrix Cag0 time 0) A and back to FoR G\n if self.settings['track_body']:\n for mm in range(dimensions[1]):\n for nn in range(dimensions[2]):\n forces[i_surf][:, mm, nn] = np.dot(Cg_uvlm, forces[i_surf][:, mm, nn])\n\n # Add the null bottom 3 rows to to the forces entry\n forces[i_surf] = np.concatenate((forces[i_surf], np.zeros(dimensions)))\n\n # Reshape bound circulation terms\n gamma.append(gamma_vec[worked_panels:worked_panels + panels_in_surface].reshape(\n dimensions_gamma, order='C'))\n gamma_dot.append(gamma_dot_vec[worked_panels:worked_panels + panels_in_surface].reshape(\n dimensions_gamma, order='C'))\n\n # Reshape wake circulation terms\n gamma_star.append(gamma_star_vec[worked_wake_panels:worked_wake_panels + panels_in_wake].reshape(\n dimensions_wake, order='C'))\n\n worked_points += points_in_surface\n worked_panels += panels_in_surface\n worked_wake_panels += panels_in_wake\n\n return forces, gamma, gamma_dot, gamma_star\n\n def pack_input_vector(self):\n r\"\"\"\n Transform a SHARPy AeroTimestep instance into a column vector containing the input to the linear UVLM system.\n\n .. math:: [\\zeta,\\, \\dot{\\zeta}, u_{ext}] \\longrightarrow \\mathbf{u}\n\n If the ``track_body`` option is on, the function projects all the input\n into a frame that:\n\n a. is equal to the FoR G at time 0 (linearisation point)\n b. rotates as the body frame specified in the ``track_body_number``\n\n Returns:\n np.ndarray: Input vector\n \"\"\"\n\n aero_tstep = self.data.aero.timestep_info[-1]\n\n ### re-compute projection in G frame as if A was not rotating\n # - u_n is in FoR G. Hence, this is project in FoR A and back to FoR G\n # using rotation matrix aat time 0 (as if FoR A was not rotating).\n if self.settings['track_body']:\n\n Cuvlm_g = np.dot(self.Cga0, self.Cga.T)\n zeta_uvlm, zeta_dot_uvlm, u_ext_uvlm = [], [], []\n\n for i_surf in range(aero_tstep.n_surf):\n\n Mp1, Np1 = aero_tstep.dimensions[i_surf] + 1\n\n zeta_uvlm.append(np.empty((3, Mp1, Np1)))\n zeta_dot_uvlm.append(np.empty((3, Mp1, Np1)))\n u_ext_uvlm.append(np.empty((3, Mp1, Np1)))\n\n for mm in range(Mp1):\n for nn in range(Np1):\n zeta_uvlm[i_surf][:, mm, nn] = \\\n np.dot(Cuvlm_g, aero_tstep.zeta[i_surf][:, mm, nn])\n zeta_dot_uvlm[i_surf][:, mm, nn] = \\\n np.dot(Cuvlm_g, aero_tstep.zeta_dot[i_surf][:, mm, nn])\n u_ext_uvlm[i_surf][:, mm, nn] = \\\n np.dot(Cuvlm_g, aero_tstep.u_ext[i_surf][:, mm, nn])\n\n zeta = np.concatenate([zeta_uvlm[i_surf].reshape(-1, order='C')\n for i_surf in range(aero_tstep.n_surf)])\n zeta_dot = np.concatenate([zeta_dot_uvlm[i_surf].reshape(-1, order='C')\n for i_surf in range(aero_tstep.n_surf)])\n u_ext = np.concatenate([u_ext_uvlm[i_surf].reshape(-1, order='C')\n for i_surf in range(aero_tstep.n_surf)])\n\n else:\n\n zeta = np.concatenate([aero_tstep.zeta[i_surf].reshape(-1, order='C')\n for i_surf in range(aero_tstep.n_surf)])\n zeta_dot = np.concatenate([aero_tstep.zeta_dot[i_surf].reshape(-1, order='C')\n for i_surf in range(aero_tstep.n_surf)])\n u_ext = np.concatenate([aero_tstep.u_ext[i_surf].reshape(-1, order='C')\n for i_surf in range(aero_tstep.n_surf)])\n\n u = np.concatenate((zeta, zeta_dot, u_ext))\n\n return u\n\n @staticmethod\n def pack_state_vector(aero_tstep, aero_tstep_m1, dt, integr_order):\n r\"\"\"\n Transform SHARPy Aerotimestep format into column vector containing the state information.\n\n The state vector is of a different form depending on the order of integration chosen. If a second order\n scheme is chosen, the state includes the bound circulation at the previous timestep,\n hence the timestep information for the previous timestep shall be parsed.\n\n The transformation is of the form:\n\n - If ``integr_order==1``:\n\n .. math:: \\mathbf{x}_n = [\\mathbf{\\Gamma}^T_n,\\,\n \\mathbf{\\Gamma_w}_n^T,\\,\n \\Delta t \\,\\mathbf{\\dot{\\Gamma}}_n^T]^T\n\n - Else, if ``integr_order==2``:\n\n .. math:: \\mathbf{x}_n = [\\mathbf{\\Gamma}_n^T,\\,\n \\mathbf{\\Gamma_w}_n^T,\\,\n \\Delta t \\,\\mathbf{\\dot{\\Gamma}}_n^T,\\,\n \\mathbf{\\Gamma}_{n-1}^T]^T\n\n For the second order integration scheme, if the previous timestep information is not parsed, a first order\n stencil is employed to estimate the bound circulation at the previous timestep:\n\n .. math:: \\mathbf{\\Gamma}^{n-1} = \\mathbf{\\Gamma}^n - \\Delta t \\mathbf{\\dot{\\Gamma}}^n\n\n Args:\n aero_tstep (AeroTimeStepInfo): Aerodynamic timestep information at the current timestep ``n``.\n aero_tstep_m1 (AeroTimeStepInfo) Aerodynamic timestep information at the previous timestep ``n-1``.\n\n Returns:\n np.ndarray: State vector\n\n \"\"\"\n\n # Extract current state...\n gamma = np.concatenate([aero_tstep.gamma[ss].reshape(-1, order='C')\n for ss in range(aero_tstep.n_surf)])\n gamma_star = np.concatenate([aero_tstep.gamma_star[ss].reshape(-1, order='C')\n for ss in range(aero_tstep.n_surf)])\n gamma_dot = np.concatenate([aero_tstep.gamma_dot[ss].reshape(-1, order='C')\n for ss in range(aero_tstep.n_surf)])\n\n if integr_order == 1:\n gamma_m1 = []\n\n else:\n if aero_tstep_m1:\n gamma_m1 = np.concatenate([aero_tstep_m1.gamma[ss].reshape(-1, order='C')\n for ss in range(aero_tstep.n_surf)])\n else:\n gamma_m1 = gamma - dt * gamma_dot\n\n x = np.concatenate((gamma, gamma_star, dt * gamma_dot, gamma_m1))\n\n return x\n" }, { "path": "sharpy/solvers/stepuvlm.py", "content": "import numpy as np\nimport scipy.optimize\nimport scipy.signal\n\nimport sharpy.aero.utils.uvlmlib as uvlmlib\nimport sharpy.utils.settings as settings_utils\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.generator_interface as gen_interface\nimport sharpy.utils.cout_utils as cout\nfrom sharpy.utils.constants import vortex_radius_def\n\n\n@solver\nclass StepUvlm(BaseSolver):\n \"\"\"\n StepUVLM is the main solver to use for unsteady aerodynamics.\n\n The desired flow field is injected into the simulation by means of a ``generator``. For a list of available\n velocity field generators see the documentation page on generators which can be found under SHARPy Source Code.\n\n Typical generators could be:\n\n * :class:`~.generators.steadyvelocityfield.SteadyVelocityField`\n\n * :class:`~.generators.gustvelocityfield.GustVelocityField`\n\n * :class:`~.generators.turbvelocityfield.TurbVelocityField`\n\n amongst others.\n\n \"\"\"\n solver_id = 'StepUvlm'\n solver_classification = 'aero'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Print info to screen'\n\n settings_types['num_cores'] = 'int'\n settings_default['num_cores'] = 0\n settings_description['num_cores'] = 'Number of cores to use in the VLM lib'\n\n settings_types['n_time_steps'] = 'int'\n settings_default['n_time_steps'] = 100\n settings_description['n_time_steps'] = 'Number of time steps to be run'\n\n settings_types['convection_scheme'] = 'int'\n settings_default['convection_scheme'] = 3\n settings_description['convection_scheme'] = '``0``: fixed wake, ' \\\n '``2``: convected with background flow;' \\\n '``3``: full force-free wake'\n settings_options['convection_scheme'] = [0, 2, 3]\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = 0.1\n settings_description['dt'] = 'Time step'\n\n # the following settings are not in used but are required in place since they are called in uvlmlib\n settings_types['iterative_solver'] = 'bool'\n settings_default['iterative_solver'] = False\n settings_description['iterative_solver'] = 'Not in use'\n\n settings_types['iterative_tol'] = 'float'\n settings_default['iterative_tol'] = 1e-4\n settings_description['iterative_tol'] = 'Not in use'\n\n settings_types['iterative_precond'] = 'bool'\n settings_default['iterative_precond'] = False\n settings_description['iterative_precond'] = 'Not in use'\n\n settings_types['velocity_field_generator'] = 'str'\n settings_default['velocity_field_generator'] = 'SteadyVelocityField'\n settings_description['velocity_field_generator'] = 'Name of the velocity field generator to be used in the ' \\\n 'simulation'\n\n settings_types['velocity_field_input'] = 'dict'\n settings_default['velocity_field_input'] = {}\n settings_description['velocity_field_input'] = 'Dictionary of settings for the velocity field generator'\n\n settings_types['gamma_dot_filtering'] = 'int'\n settings_default['gamma_dot_filtering'] = 0\n settings_description['gamma_dot_filtering'] = 'Filtering parameter for the Welch filter for the Gamma_dot ' \\\n 'estimation. Used when ``unsteady_force_contribution`` is ``on``.'\n\n settings_types['rho'] = 'float'\n settings_default['rho'] = 1.225\n settings_description['rho'] = 'Air density'\n\n settings_types['cfl1'] = 'bool'\n settings_default['cfl1'] = True\n settings_description['cfl1'] = 'If it is ``True``, it assumes that the discretisation complies with CFL=1'\n\n settings_types['vortex_radius'] = 'float'\n settings_default['vortex_radius'] = vortex_radius_def\n settings_description['vortex_radius'] = 'Distance between points below which induction is not computed'\n\n settings_types['vortex_radius_wake_ind'] = 'float'\n settings_default['vortex_radius_wake_ind'] = vortex_radius_def\n settings_description[\n 'vortex_radius_wake_ind'] = 'Distance between points below which induction is not computed in the wake convection'\n\n settings_types['interp_coords'] = 'int'\n settings_default['interp_coords'] = 0\n settings_description['interp_coords'] = 'Coordinates to use for wake description: cartesian(0) or cylindrical_z(1)'\n settings_options['interp_coords'] = [0, 1]\n\n settings_types['filter_method'] = 'int'\n settings_default['filter_method'] = 0\n settings_description['filter_method'] = 'Method to filter the points: no filter (0) moving average(2)'\n settings_options['filter_method'] = [0, 2]\n # filter_method = 1 was dedicated to a splines filter. If it is needed in the future chack dev_alglib branch\n\n settings_types['interp_method'] = 'int'\n settings_default['interp_method'] = 0\n settings_description[\n 'interp_method'] = 'Method of interpolation: linear(0), parabolic(1), splines(2), slerp around z(3), slerp around yaw_slerp(4)'\n settings_options['interp_method'] = [0, 1, 2, 3, 4]\n\n settings_types['yaw_slerp'] = 'float'\n settings_default['yaw_slerp'] = 0\n settings_description['yaw_slerp'] = 'Yaw angle in radians to be used when interp_metod == 4'\n\n settings_types['centre_rot'] = 'list(float)'\n settings_default['centre_rot'] = [0., 0., 0.]\n settings_description[\n 'centre_rot'] = 'Coordinates of the centre of rotation to perform slerp interpolation or cylindrical coordinates'\n\n settings_types['quasi_steady'] = 'bool'\n settings_default['quasi_steady'] = False\n settings_description['quasi_steady'] = 'Use quasi-steady approximation in UVLM'\n\n settings_types['only_nonlifting'] = 'bool'\n settings_default['only_nonlifting'] = False\n settings_description['only_nonlifting'] = 'Consider nonlifting body interactions'\n\n settings_types['nonlifting_body_interactions'] = 'bool'\n settings_default['nonlifting_body_interactions'] = False\n settings_description['nonlifting_body_interactions'] = 'Consider nonlifting body interactions'\n\n settings_types['phantom_wing_test'] = 'bool'\n settings_default['phantom_wing_test'] = False\n settings_description['phantom_wing_test'] = 'Debug option'\n\n settings_types['centre_rot_g'] = 'list(float)'\n settings_default['centre_rot_g'] = [0., 0., 0.]\n settings_description['centre_rot_g'] = 'Centre of rotation in G FoR around which ``rbm_vel_g`` is applied'\n\n settings_types['ignore_first_x_nodes_in_force_calculation'] = 'int'\n settings_default['ignore_first_x_nodes_in_force_calculation'] = 0\n settings_description[\n 'ignore_first_x_nodes_in_force_calculation'] = 'Ignores the forces on the first user-specified number of nodes of all surfaces.'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description, settings_options)\n\n def __init__(self):\n self.data = None\n self.settings = None\n self.velocity_generator = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n \"\"\"\n To be called just once per simulation.\n \"\"\"\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n self.settings_options)\n\n self.data.structure.add_unsteady_information(\n self.data.structure.dyn_dict,\n self.settings['n_time_steps'])\n\n # Filtering\n if self.settings['gamma_dot_filtering'] == 1:\n cout.cout_wrap(\n \"gamma_dot_filtering cannot be one. Changing it to None\", 2)\n self.settings['gamma_dot_filtering'] = None\n if self.settings['gamma_dot_filtering'] is not None:\n if self.settings['gamma_dot_filtering']:\n if not self.settings['gamma_dot_filtering'] % 2:\n cout.cout_wrap(\n \"gamma_dot_filtering does not support even numbers.\" +\n \"Changing \" +\n str(self.settings['gamma_dot_filtering']) +\n \" to \" +\n str(self.settings['gamma_dot_filtering'] + 1),\n 2)\n self.settings['gamma_dot_filtering'] += 1\n\n # init velocity generator\n velocity_generator_type = gen_interface.generator_from_string(\n self.settings['velocity_field_generator'])\n self.velocity_generator = velocity_generator_type()\n self.velocity_generator.initialise(\n self.settings['velocity_field_input'],\n restart=restart)\n\n def run(self, **kwargs):\n \"\"\"\n Runs a step of the aerodynamics as implemented in UVLM.\n \"\"\"\n\n # Default values\n aero_tstep = settings_utils.set_value_or_default(kwargs, 'aero_step', self.data.aero.timestep_info[-1])\n structure_tstep = settings_utils.set_value_or_default(kwargs, 'structural_step',\n self.data.structure.timestep_info[-1])\n convect_wake = settings_utils.set_value_or_default(kwargs, 'convect_wake', True)\n dt = settings_utils.set_value_or_default(kwargs, 'dt', self.settings['dt'])\n t = settings_utils.set_value_or_default(kwargs, 't', self.data.ts * dt)\n unsteady_contribution = settings_utils.set_value_or_default(kwargs, 'unsteady_contribution', False)\n\n if not aero_tstep.zeta:\n return self.data\n\n # generate uext\n self.velocity_generator.generate({'zeta': aero_tstep.zeta,\n 'override': True,\n 't': t,\n 'ts': self.data.ts,\n 'dt': dt,\n 'for_pos': structure_tstep.for_pos,\n 'is_wake': False},\n aero_tstep.u_ext)\n if ((self.settings['convection_scheme'] > 1 and convect_wake) or\n (not self.settings['cfl1'])):\n # generate uext_star\n self.velocity_generator.generate({'zeta': aero_tstep.zeta_star,\n 'override': True,\n 'ts': self.data.ts,\n 'dt': dt,\n 't': t,\n 'for_pos': structure_tstep.for_pos,\n 'is_wake': True},\n aero_tstep.u_ext_star)\n if self.settings['nonlifting_body_interactions']:\n\n nl_body_tstep = settings_utils.set_value_or_default(kwargs, 'nl_body_tstep',\n self.data.nonlifting_body.timestep_info[-1])\n self.velocity_generator.generate({'zeta': nl_body_tstep.zeta,\n 'override': True,\n 'ts': self.data.ts,\n 'dt': dt,\n 't': t,\n 'for_pos': structure_tstep.for_pos,\n 'is_wake': False},\n nl_body_tstep.u_ext)\n\n uvlmlib.uvlm_solver_lifting_and_nonlifting(self.data.ts,\n aero_tstep,\n nl_body_tstep,\n structure_tstep,\n self.settings,\n convect_wake=convect_wake,\n dt=dt)\n else:\n uvlmlib.uvlm_solver(self.data.ts,\n aero_tstep,\n structure_tstep,\n self.settings,\n convect_wake=convect_wake,\n dt=dt)\n\n if unsteady_contribution and not self.settings['quasi_steady']:\n # calculate unsteady (added mass) forces:\n self.data.aero.compute_gamma_dot(dt,\n aero_tstep,\n self.data.aero.timestep_info[-3:])\n if self.settings['gamma_dot_filtering'] is None:\n self.filter_gamma_dot(aero_tstep,\n self.data.aero.timestep_info,\n None)\n elif self.settings['gamma_dot_filtering'] > 0:\n self.filter_gamma_dot(\n aero_tstep,\n self.data.aero.timestep_info,\n self.settings['gamma_dot_filtering'])\n uvlmlib.uvlm_calculate_unsteady_forces(aero_tstep,\n structure_tstep,\n self.settings,\n convect_wake=convect_wake,\n dt=dt)\n else:\n for i_surf in range(len(aero_tstep.gamma)):\n aero_tstep.gamma_dot[i_surf][:] = 0.0\n return self.data\n\n def add_step(self):\n self.data.aero.add_timestep()\n if self.settings['nonlifting_body_interactions']:\n self.data.nonlifting_body.add_timestep()\n\n def update_grid(self, beam):\n self.data.aero.generate_zeta(beam,\n self.data.aero.aero_settings,\n -1,\n beam_ts=-1)\n if self.settings['nonlifting_body_interactions']:\n self.data.nonlifting_body.generate_zeta(beam,\n self.data.aero.aero_settings,\n -1,\n beam_ts=-1)\n\n def update_custom_grid(self, structure_tstep, aero_tstep, nl_body_tstep=None):\n self.data.aero.generate_zeta_timestep_info(structure_tstep,\n aero_tstep,\n self.data.structure,\n self.data.aero.aero_settings,\n dt=self.settings['dt'])\n if self.settings['nonlifting_body_interactions']:\n if nl_body_tstep is None:\n nl_body_tstep = self.data.nonlifting_body.timestep_info[-1]\n self.data.nonlifting_body.generate_zeta_timestep_info(structure_tstep,\n nl_body_tstep,\n self.data.structure,\n self.data.nonlifting_body.aero_settings,\n dt=self.settings['dt'])\n\n @staticmethod\n def filter_gamma_dot(tstep, history, filter_param):\n clean_history = [x for x in history if x is not None]\n series_length = len(clean_history) + 1\n for i_surf in range(len(tstep.zeta)):\n n_rows, n_cols = tstep.gamma[i_surf].shape\n for i in range(n_rows):\n for j in range(n_cols):\n series = np.zeros((series_length,))\n for it in range(series_length - 1):\n series[it] = clean_history[it].gamma_dot[i_surf][i, j]\n series[-1] = tstep.gamma_dot[i_surf][i, j]\n\n # filter\n tstep.gamma_dot[i_surf][i, j] = scipy.signal.wiener(\n series, filter_param)[-1]\n" }, { "path": "sharpy/solvers/timeintegrators.py", "content": "import numpy as np\nimport ctypes as ct\n\nimport sharpy.utils.settings as settings_utils\nfrom sharpy.utils.solver_interface import solver\n\n\n@solver\nclass _BaseTimeIntegrator():\n \"\"\"\n Base structure for time integrators\n \"\"\"\n\n solver_id = '_BaseTimeIntegrator'\n solver_classification = 'time_integrator'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n def __init__(self):\n pass\n\n\n def initialise(self, data, custom_settings=None, restart=False):\n pass\n\n\n def predictor(self, q, dqdt, dqddt):\n pass\n\n\n def build_matrix(self, M, C, K):\n pass\n\n\n def corrector(self, q, dqdt, dqddt, Dq):\n pass\n\n\n@solver\nclass NewmarkBeta(_BaseTimeIntegrator):\n \"\"\"\n Time integration according to the Newmark-beta scheme\n \"\"\"\n\n solver_id = 'NewmarkBeta'\n solver_classification = 'time_integrator'\n\n settings_types = _BaseTimeIntegrator.settings_types.copy()\n settings_default = _BaseTimeIntegrator.settings_default.copy()\n settings_description = _BaseTimeIntegrator.settings_description.copy()\n settings_options = _BaseTimeIntegrator.settings_options.copy()\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = None\n settings_description['dt'] = 'Time step'\n\n settings_types['newmark_damp'] = 'float'\n settings_default['newmark_damp'] = 1e-4\n settings_description['newmark_damp'] = 'Newmark damping coefficient'\n\n settings_types['sys_size'] = 'int'\n settings_default['sys_size'] = 0\n settings_description['sys_size'] = 'Size of the system without constraints'\n\n settings_types['num_LM_eq'] = 'int'\n settings_default['num_LM_eq'] = 0\n settings_description['num_LM_eq'] = 'Number of constraint equations'\n\n def __init__(self):\n\n self.sys_size = None\n self.num_LM_eq = None\n self.dt = None\n self.beta = None\n self.gamma = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n no_ctype=True)\n\n self.dt = self.settings['dt']\n self.gamma = 0.5 + self.settings['newmark_damp']\n self.beta = 0.25*(self.gamma + 0.5)*(self.gamma + 0.5)\n\n self.sys_size = self.settings['sys_size']\n self.num_LM_eq = self.settings['num_LM_eq']\n\n def predictor(self, q, dqdt, dqddt):\n\n sys_size = self.sys_size\n q[:sys_size] += self.dt*dqdt[:sys_size] + (0.5 - self.beta)*self.dt*self.dt*dqddt[:sys_size]\n dqdt[:sys_size] += (1.0 - self.gamma)*self.dt*dqddt[:sys_size]\n dqddt *= 0.\n\n # q[sys_size:] = q[sys_size:]\n dqdt[sys_size:] = dqdt[sys_size:]\n\n def build_matrix(self, M, C, K, Q, kBnh, LM_Q):\n\n sys_size = self.sys_size\n num_LM_eq = self.num_LM_eq\n\n Asys = np.zeros((sys_size + num_LM_eq, sys_size + num_LM_eq),\n dtype=ct.c_double, order='F')\n Qout = np.zeros((sys_size + num_LM_eq), dtype=ct.c_double, order='F')\n\n Asys[:sys_size, :sys_size] = K + C*self.gamma/(self.beta*self.dt) + M/(self.beta*self.dt*self.dt)\n Qout[:sys_size] = Q.copy()\n\n Asys[sys_size:, :sys_size] = (self.gamma/self.beta/self.dt)*kBnh\n Asys[:sys_size, sys_size:] = kBnh.T\n Qout[sys_size:] = LM_Q.copy()\n\n return Asys, Qout\n\n def corrector(self, q, dqdt, dqddt, Dq):\n\n sys_size = self.sys_size\n\n q[:sys_size] += Dq[:sys_size]\n dqdt[:sys_size] += self.gamma/(self.beta*self.dt)*Dq[:sys_size]\n dqddt[:sys_size] += 1.0/(self.beta*self.dt*self.dt)*Dq[:sys_size]\n\n dqdt[sys_size:] += Dq[sys_size:]\n\n\n@solver\nclass GeneralisedAlpha(_BaseTimeIntegrator):\n \"\"\"\n Time integration according to the Generalised-Alpha scheme\n \"\"\"\n\n solver_id = 'GeneralisedAlpha'\n solver_classification = 'time_integrator'\n\n settings_types = _BaseTimeIntegrator.settings_types.copy()\n settings_default = _BaseTimeIntegrator.settings_default.copy()\n settings_description = _BaseTimeIntegrator.settings_description.copy()\n settings_options = _BaseTimeIntegrator.settings_options.copy()\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = None\n settings_description['dt'] = 'Time step'\n\n settings_types['am'] = 'float'\n settings_default['am'] = 0.\n settings_description['am'] = 'alpha_M coefficient'\n\n settings_types['af'] = 'float'\n settings_default['af'] = 0.1\n settings_description['af'] = 'alpha_F coefficient'\n\n settings_types['sys_size'] = 'int'\n settings_default['sys_size'] = 0\n settings_description['sys_size'] = 'Size of the system without constraints'\n\n settings_types['num_LM_eq'] = 'int'\n settings_default['num_LM_eq'] = 0\n settings_description['num_LM_eq'] = 'Number of contraint equations'\n\n def __init__(self):\n\n self.num_LM_eq = None\n self.sys_size = None\n self.om_af = None\n self.om_am = None\n self.dt = None\n self.am = None\n self.af = None\n self.gamma = None\n self.beta = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n no_ctype=True)\n\n self.dt = self.settings['dt']\n self.am = self.settings['am']\n self.af = self.settings['af']\n\n self.om_am = 1. - self.am\n self.om_af = 1. - self.af\n\n self.gamma = 0.5 - self.am + self.af\n self.beta = 0.25*(1. - self.am + self.af)**2\n\n self.sys_size = self.settings['sys_size']\n self.num_LM_eq = self.settings['num_LM_eq']\n\n def predictor(self, q, dqdt, dqddt):\n\n sys_size = self.sys_size\n q[:sys_size] += self.dt*dqdt[:sys_size] + (0.5 - self.beta)*self.dt*self.dt*dqddt[:sys_size]\n dqdt[:sys_size] += (1.0 - self.gamma)*self.dt*dqddt[:sys_size]\n dqddt *= 0.\n\n dqdt[sys_size:] = dqdt[sys_size:]\n\n def build_matrix(self, M, C, K, Q, kBnh, LM_Q):\n\n sys_size = self.sys_size\n num_LM_eq = self.num_LM_eq\n\n Asys = np.zeros((sys_size + num_LM_eq, sys_size + num_LM_eq),\n dtype=ct.c_double, order='F')\n Qout = np.zeros((sys_size + num_LM_eq), dtype=ct.c_double, order='F')\n\n Asys[:sys_size, :sys_size] = (self.om_af*K +\n self.gamma*self.om_af/self.beta/self.dt*C +\n self.om_am/(self.beta*self.dt*self.dt)*M)\n\n Qout[:sys_size] = Q.copy()\n\n Asys[sys_size:, :sys_size] = (self.gamma*self.om_af/self.beta/self.dt)*kBnh\n Asys[:sys_size, sys_size:] = kBnh.T\n Qout[sys_size:] = LM_Q.copy()\n\n return Asys, Qout\n\n def corrector(self, q, dqdt, dqddt, Dq):\n\n sys_size = self.sys_size\n\n q[:sys_size] += self.om_af*Dq[:sys_size]\n dqdt[:sys_size] += self.gamma*self.om_af/self.beta/self.dt*Dq[:sys_size]\n dqddt[:sys_size] += self.om_am/self.beta/self.dt**2*Dq[:sys_size]\n \n dqdt[sys_size:] += Dq[sys_size:]\n" }, { "path": "sharpy/solvers/timeintegratorsjax.py", "content": "import numpy as np\nfrom abc import abstractmethod\nimport typing\n\nimport sharpy.utils.settings as settings_utils\nfrom sharpy.utils.solver_interface import solver\n\narr: typing.Type = np.ndarray\n\n\n@solver\nclass _BaseTimeIntegrator:\n \"\"\"\n Base structure for time integrators\n \"\"\"\n\n solver_id = '_BaseTimeIntegrator'\n solver_classification = 'time_integrator'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n settings_options = dict()\n\n def __init__(self):\n pass\n\n @abstractmethod\n def initialise(self, data, custom_settings=None, restart=False):\n pass\n\n @abstractmethod\n def predictor(self, q: arr, dqdt: arr, dqddt: arr):\n pass\n\n @abstractmethod\n def build_matrix(self, m: arr, c: arr, k: arr):\n pass\n\n @abstractmethod\n def corrector(self, q: arr, dqdt: arr, dqddt: arr, dq: arr):\n pass\n\n\n@solver\nclass NewmarkBetaJAX(_BaseTimeIntegrator):\n \"\"\"\n Time integration according to the Newmark-beta scheme\n \"\"\"\n\n solver_id = 'NewmarkBetaJAX'\n solver_classification = 'time_integrator'\n\n settings_types = _BaseTimeIntegrator.settings_types.copy()\n settings_default = _BaseTimeIntegrator.settings_default.copy()\n settings_description = _BaseTimeIntegrator.settings_description.copy()\n settings_options = _BaseTimeIntegrator.settings_options.copy()\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = None\n settings_description['dt'] = 'Time step'\n\n settings_types['newmark_damp'] = 'float'\n settings_default['newmark_damp'] = 1e-4\n settings_description['newmark_damp'] = 'Newmark damping coefficient'\n\n settings_types['sys_size'] = 'int'\n settings_default['sys_size'] = 0\n settings_description['sys_size'] = 'Size of the system without constraints'\n\n settings_types['num_LM_eq'] = 'int'\n settings_default['num_LM_eq'] = 0\n settings_description['num_LM_eq'] = 'Number of constraint equations'\n\n def __init__(self):\n super().__init__() # I know the base class has no function here, but this makes Pycharm leave me alone\n self.dt = None\n self.beta = None\n self.gamma = None\n self.sys_size = None\n self.num_lm_eq = None\n self.settings = None\n\n def initialise(self, data, custom_settings=None, restart=False) -> None:\n\n if custom_settings is None:\n self.settings = data.input_settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n no_ctype=True)\n\n self.dt = self.settings['dt']\n self.gamma = 0.5 + self.settings['newmark_damp']\n self.beta = 0.25 * (self.gamma + 0.5) * (self.gamma + 0.5)\n\n self.sys_size = self.settings['sys_size']\n self.num_lm_eq = self.settings['num_LM_eq']\n\n def predictor(self, q, dqdt, dqddt):\n q[:self.sys_size] += (self.dt * dqdt[:self.sys_size]\n + (0.5 - self.beta) * self.dt * self.dt * dqddt[:self.sys_size])\n dqdt[:self.sys_size] += (1. - self.gamma) * self.dt * dqddt[:self.sys_size]\n dqddt.fill(0.)\n\n def build_matrix(self, m: arr, c: arr, k: arr) -> arr:\n a_sys = np.zeros((self.sys_size + self.num_lm_eq, self.sys_size + self.num_lm_eq))\n a_sys[:, :self.sys_size] = (k[:, :self.sys_size]\n + c[:, :self.sys_size] * self.gamma / (self.beta * self.dt)\n + m[:, :self.sys_size] / (self.beta * self.dt * self.dt))\n a_sys[:, self.sys_size:] = k[:, self.sys_size:] + c[:, self.sys_size:]\n return a_sys\n\n def corrector(self, q: arr, dqdt: arr, dqddt: arr, dq: arr) -> None:\n q[:self.sys_size] += dq[:self.sys_size]\n dqdt[:self.sys_size] += self.gamma / (self.beta * self.dt) * dq[:self.sys_size]\n dqddt[:self.sys_size] += 1. / (self.beta * self.dt * self.dt) * dq[:self.sys_size]\n dqdt[self.sys_size:] += dq[self.sys_size:]\n\n\n@solver\nclass GeneralisedAlphaJAX(_BaseTimeIntegrator):\n \"\"\"\n Time integration according to the Generalised-Alpha scheme\n \"\"\"\n\n solver_id = 'GeneralisedAlphaJAX'\n solver_classification = 'time_integrator'\n\n settings_types = _BaseTimeIntegrator.settings_types.copy()\n settings_default = _BaseTimeIntegrator.settings_default.copy()\n settings_description = _BaseTimeIntegrator.settings_description.copy()\n settings_options = _BaseTimeIntegrator.settings_options.copy()\n\n settings_types['dt'] = 'float'\n settings_default['dt'] = None\n settings_description['dt'] = 'Time step'\n\n settings_types['am'] = 'float'\n settings_default['am'] = 0.\n settings_description['am'] = 'alpha_M coefficient'\n\n settings_types['af'] = 'float'\n settings_default['af'] = 0.1\n settings_description['af'] = 'alpha_F coefficient'\n\n settings_types['sys_size'] = 'int'\n settings_default['sys_size'] = 0\n settings_description['sys_size'] = 'Size of the system without constraints'\n\n settings_types['num_LM_eq'] = 'int'\n settings_default['num_LM_eq'] = 0\n settings_description['num_LM_eq'] = 'Number of contraint equations'\n\n def __init__(self):\n super().__init__()\n self.dt = None\n self.am = None\n self.af = None\n self.gamma = None\n self.beta = None\n self.om_am = None\n self.om_af = None\n self.sys_size = None\n self.num_lm_eq = None\n\n def initialise(self, data, custom_settings=None, restart=False) -> None:\n\n if custom_settings is None:\n self.settings = data.input_settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n no_ctype=True)\n\n self.dt = self.settings['dt']\n self.am = self.settings['am']\n self.af = self.settings['af']\n self.om_am = 1. - self.am\n self.om_af = 1. - self.af\n self.gamma = 0.5 - self.am + self.af\n self.beta = 0.25 * (1. - self.am + self.af) ** 2\n self.sys_size = self.settings['sys_size']\n self.num_lm_eq = self.settings['num_LM_eq']\n\n def predictor(self, q: arr, dqdt: arr, dqddt: arr):\n q[:self.sys_size] += (self.dt * dqdt[:self.sys_size]\n + (0.5 - self.beta) * self.dt * self.dt * dqddt[:self.sys_size])\n dqdt[:self.sys_size] += (1. - self.gamma) * self.dt * dqddt[:self.sys_size]\n dqddt.fill(0.)\n\n def build_matrix(self, m: arr, c: arr, k: arr) -> arr:\n a_sys = np.zeros((self.sys_size + self.num_lm_eq, self.sys_size + self.num_lm_eq))\n a_sys[:, :self.sys_size] = (self.om_af * k\n + self.gamma * self.om_af / (self.beta * self.dt) * c\n + self.om_am / (self.beta * self.dt * self.dt) * m)\n\n a_sys[:, self.sys_size:] = k[:, self.sys_size:] + c[:, self.sys_size:]\n return a_sys\n\n def corrector(self, q: arr, dqdt: arr, dqddt: arr, dq: arr) -> None:\n q[:self.sys_size] += self.om_af * dq[:self.sys_size]\n dqdt[:self.sys_size] += self.gamma * self.om_af / self.beta / self.dt * dq[:self.sys_size]\n dqddt[:self.sys_size] += self.om_am / self.beta / self.dt ** 2 * dq[:self.sys_size]\n dqdt[self.sys_size:] += dq[self.sys_size:]\n" }, { "path": "sharpy/solvers/trim.py", "content": "import numpy as np\nimport scipy.optimize\n\nimport sharpy.utils.cout_utils as cout\nimport sharpy.utils.solver_interface as solver_interface\nfrom sharpy.utils.solver_interface import solver, BaseSolver\nimport sharpy.utils.settings as settings_utils\nimport sharpy.utils.algebra as algebra\n\n\n@solver\nclass Trim(BaseSolver):\n \"\"\"\n Trim routine with support for lateral dynamics. It usually struggles much more\n than the ``StaticTrim`` (only longitudinal) solver.\n\n We advise to start with ``StaticTrim`` even if you configuration is not totally symmetric.\n \"\"\"\n solver_id = 'Trim'\n solver_classification = 'Flight dynamics'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_types['print_info'] = 'bool'\n settings_default['print_info'] = True\n settings_description['print_info'] = 'Print info to screen'\n\n settings_types['solver'] = 'str'\n settings_default['solver'] = ''\n settings_description['solver'] = 'Solver to run in trim routine'\n\n settings_types['solver_settings'] = 'dict'\n settings_default['solver_settings'] = dict()\n settings_description['solver_settings'] = 'Solver settings dictionary'\n\n settings_types['max_iter'] = 'int'\n settings_default['max_iter'] = 100\n settings_description['max_iter'] = 'Maximum number of iterations of trim routine'\n\n settings_types['tolerance'] = 'float'\n settings_default['tolerance'] = 1e-4\n settings_description['tolerance'] = 'Threshold for convergence of trim'\n\n settings_types['initial_alpha'] = 'float'\n settings_default['initial_alpha'] = 0.\n settings_description['initial_alpha'] = 'Initial angle of attack'\n\n settings_types['initial_beta'] = 'float'\n settings_default['initial_beta'] = 0.\n settings_description['initial_beta'] = 'Initial sideslip angle'\n\n settings_types['initial_roll'] = 'float'\n settings_default['initial_roll'] = 0\n settings_description['initial_roll'] = 'Initial roll angle'\n\n settings_types['cs_indices'] = 'list(int)'\n settings_default['cs_indices'] = []\n settings_description['cs_indices'] = 'Indices of control surfaces to be trimmed'\n\n settings_types['initial_cs_deflection'] = 'list(float)'\n settings_default['initial_cs_deflection'] = []\n settings_description['initial_cs_deflection'] = 'Initial deflection of the control surfaces in order.'\n\n settings_types['thrust_nodes'] = 'list(int)'\n settings_default['thrust_nodes'] = [0]\n settings_description['thrust_nodes'] = 'Nodes at which thrust is applied'\n\n settings_types['initial_thrust'] = 'list(float)'\n settings_default['initial_thrust'] = [1.]\n settings_description['initial_thrust'] = 'Initial thrust setting'\n\n settings_types['thrust_direction'] = 'list(float)'\n settings_default['thrust_direction'] = [.0, 1.0, 0.0]\n settings_description['thrust_direction'] = 'Thrust direction setting'\n\n settings_types['special_case'] = 'dict'\n settings_default['special_case'] = dict()\n settings_description['special_case'] = 'Extra settings for specific cases such as differential thrust control'\n\n settings_types['refine_solution'] = 'bool'\n settings_default['refine_solution'] = False\n settings_description['refine_solution'] = 'If ``True`` and the optimiser routine allows for it, the optimiser will try to improve the solution with hybrid methods'\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n self.solver = None\n\n self.x_info = dict()\n self.initial_state = None\n\n self.with_special_case = False\n\n def initialise(self, data, restart=False):\n self.data = data\n self.settings = data.settings[self.solver_id]\n settings_utils.to_custom_types(self.settings, self.settings_types, self.settings_default)\n\n self.solver = solver_interface.initialise_solver(self.settings['solver'])\n self.solver.initialise(self.data, self.settings['solver_settings'], restart=restart)\n\n # generate x_info (which elements of the x array are what)\n counter = 0\n self.x_info['n_variables'] = 0\n # alpha\n self.x_info['i_alpha'] = counter\n counter += 1\n # beta\n self.x_info['i_beta'] = counter\n counter += 1\n # roll\n self.x_info['i_roll'] = counter\n counter += 1\n # control surfaces\n n_control_surfaces = len(self.settings['cs_indices'])\n self.x_info['i_control_surfaces'] = [] # indices in the state vector\n self.x_info['control_surfaces_id'] = [] # indices of the trimmed control surfaces\n for i_cs in range(n_control_surfaces):\n self.x_info['i_control_surfaces'].append(counter)\n self.x_info['control_surfaces_id'].append(self.settings['cs_indices'][i_cs])\n counter += 1\n # thrust\n n_thrust_nodes = len(self.settings['thrust_nodes'])\n self.x_info['i_thrust'] = []\n self.x_info['thrust_nodes'] = []\n self.x_info['thrust_direction'] = []\n for i_thrust in range(n_thrust_nodes):\n self.x_info['i_thrust'].append(counter)\n self.x_info['thrust_nodes'].append(self.settings['thrust_nodes'][i_thrust])\n self.x_info['thrust_direction'].append(self.settings['thrust_direction'])\n counter += 1\n self.x_info['n_variables'] = counter\n\n # special cases\n self.with_special_case = self.settings['special_case']\n if self.with_special_case:\n if self.settings['special_case']['case_name'] == 'differential_thrust':\n self.x_info['special_case'] = 'differential_thrust'\n self.x_info['i_base_thrust'] = counter\n counter += 1\n self.x_info['i_differential_parameter'] = counter\n counter += 1\n self.x_info['initial_base_thrust'] = self.settings['special_case']['initial_base_thrust']\n self.x_info['initial_differential_parameter'] = self.settings['special_case']['initial_differential_parameter']\n self.x_info['base_thrust_nodes'] = [int(e) for e in self.settings['special_case']['base_thrust_nodes']]\n self.x_info['negative_thrust_nodes'] = [int(e) for e in self.settings['special_case']['negative_thrust_nodes']]\n self.x_info['positive_thrust_nodes'] = [int(e) for e in self.settings['special_case']['positive_thrust_nodes']]\n\n self.x_info['n_variables'] = counter\n\n\n # initial state vector\n self.initial_state = np.zeros(self.x_info['n_variables'])\n self.initial_state[self.x_info['i_alpha']] = self.settings['initial_alpha']\n self.initial_state[self.x_info['i_beta']] = self.settings['initial_beta']\n self.initial_state[self.x_info['i_roll']] = self.settings['initial_roll']\n for i_cs in range(n_control_surfaces):\n self.initial_state[self.x_info['i_control_surfaces'][i_cs]] = self.settings['initial_cs_deflection'][i_cs]\n for i_thrust in range(n_thrust_nodes):\n self.initial_state[self.x_info['i_thrust'][i_thrust]] = self.settings['initial_thrust'][i_thrust]\n if self.with_special_case:\n if self.settings['special_case']['case_name'] == 'differential_thrust':\n self.initial_state[self.x_info['i_base_thrust']] = self.x_info['initial_base_thrust']\n self.initial_state[self.x_info['i_differential_parameter']] = self.x_info['initial_differential_parameter']\n\n\n # bounds\n # NOTE probably not necessary anymore, as Nelder-Mead method doesn't use them\n self.bounds = self.x_info['n_variables']*[None]\n for k, v in self.x_info.items():\n if k == 'i_alpha':\n self.bounds[v] = (self.initial_state[self.x_info['i_alpha']] - 3*np.pi/180,\n self.initial_state[self.x_info['i_alpha']] + 3*np.pi/180)\n elif k == 'i_beta':\n self.bounds[v] = (self.initial_state[self.x_info['i_beta']] - 2*np.pi/180,\n self.initial_state[self.x_info['i_beta']] + 2*np.pi/180)\n elif k == 'i_roll':\n self.bounds[v] = (self.initial_state[self.x_info['i_roll']] - 2*np.pi/180,\n self.initial_state[self.x_info['i_roll']] + 2*np.pi/180)\n elif k == 'i_thrust':\n for ii, i in enumerate(v):\n self.bounds[i] = (self.initial_state[self.x_info['i_thrust'][ii]] - 2,\n self.initial_state[self.x_info['i_thrust'][ii]] + 2)\n elif k == 'i_control_surfaces':\n for ii, i in enumerate(v):\n self.bounds[i] = (self.initial_state[self.x_info['i_control_surfaces'][ii]] - 4*np.pi/180,\n self.initial_state[self.x_info['i_control_surfaces'][ii]] + 4*np.pi/180)\n elif k == 'i_base_thrust':\n if self.with_special_case:\n if self.settings['special_case']['case_name'] == 'differential_thrust':\n self.bounds[v] = (float(self.x_info['initial_base_thrust'])*0.5,\n float(self.x_info['initial_base_thrust'])*1.5)\n elif k == 'i_differential_parameter':\n if self.with_special_case:\n if self.settings['special_case']['case_name'] == 'differential_thrust':\n self.bounds[v] = (-0.5, 0.5)\n\n def increase_ts(self):\n self.data.ts += 1\n self.structural_solver.next_step()\n self.aero_solver.next_step()\n\n def cleanup_timestep_info(self):\n if max(len(self.data.aero.timestep_info), len(self.data.structure.timestep_info)) > 1:\n # copy last info to first\n self.data.aero.timestep_info[0] = self.data.aero.timestep_info[-1]\n self.data.structure.timestep_info[0] = self.data.structure.timestep_info[-1]\n # delete all the rest\n while len(self.data.aero.timestep_info) - 1:\n del self.data.aero.timestep_info[-1]\n while len(self.data.structure.timestep_info) - 1:\n del self.data.structure.timestep_info[-1]\n\n self.data.ts = 0\n\n def run(self):\n self.trim_algorithm()\n return self.data\n\n def trim_algorithm(self):\n # create bounds\n\n # call optimiser\n self.optimise(solver_wrapper,\n tolerance=self.settings['tolerance'],\n print_info=True,\n # method='BFGS')\n method='Nelder-Mead',\n # method='SLSQP',\n refine=self.settings['refine_solution'])\n\n # self.optimise(self.solver_wrapper, )\n pass\n\n def optimise(self, func, tolerance, print_info, method, refine):\n args = (self.x_info, self, -2)\n\n solution = scipy.optimize.minimize(func,\n self.initial_state,\n args=args,\n method=method,\n options={'disp': print_info,\n 'maxfev': 1000,\n 'xatol': tolerance,\n 'fatol': 1e-4})\n if refine:\n cout.cout_wrap('Refining results with a gradient-based method', 1)\n solution = scipy.optimize.minimize(func,\n solution.x,\n args=args,\n method='BFGS',\n options={'disp': print_info,\n 'eps': 0.05,\n 'maxfev': 5000,\n 'fatol': 1e-4})\n\n cout.cout_wrap('Solution = ')\n cout.cout_wrap(solution.x)\n return solution\n\ndef solver_wrapper(x, x_info, solver_data, i_dim=-1):\n if solver_data.settings['print_info']:\n cout.cout_wrap('x = ' + str(x), 1)\n # print('x = ', x)\n alpha = x[x_info['i_alpha']]\n beta = x[x_info['i_beta']]\n roll = x[x_info['i_roll']]\n # change input data\n solver_data.data.structure.timestep_info[solver_data.data.ts] = solver_data.data.structure.ini_info.copy()\n tstep = solver_data.data.structure.timestep_info[solver_data.data.ts]\n orientation_quat = algebra.euler2quat(np.array([roll, alpha, beta]))\n tstep.quat[:] = orientation_quat\n # control surface deflection\n for i_cs in range(len(x_info['i_control_surfaces'])):\n solver_data.data.aero.data_dict['control_surface_deflection'][x_info['control_surfaces_id'][i_cs]] = x[x_info['i_control_surfaces'][i_cs]]\n # thrust input\n tstep.steady_applied_forces[:] = 0.0\n try:\n x_info['special_case']\n except KeyError:\n for i_thrust in range(len(x_info['i_thrust'])):\n thrust = x[x_info['i_thrust'][i_thrust]]\n i_node = x_info['thrust_nodes'][i_thrust]\n solver_data.data.structure.ini_info.steady_applied_forces[i_node, 0:3] = thrust*x_info['thrust_direction'][i_thrust]\n else:\n if x_info['special_case'] == 'differential_thrust':\n base_thrust = x[x_info['i_base_thrust']]\n pos_thrust = base_thrust*(1.0 + x[x_info['i_differential_parameter']])\n neg_thrust = -base_thrust*(1.0 - x[x_info['i_differential_parameter']])\n for i_base_node in x_info['base_thrust_nodes']:\n solver_data.data.structure.ini_info.steady_applied_forces[i_base_node, 1] = base_thrust\n for i_pos_diff_node in x_info['positive_thrust_nodes']:\n solver_data.data.structure.ini_info.steady_applied_forces[i_pos_diff_node, 1] = pos_thrust\n for i_neg_diff_node in x_info['negative_thrust_nodes']:\n solver_data.data.structure.ini_info.steady_applied_forces[i_neg_diff_node, 1] = neg_thrust\n\n # run the solver\n solver_data.solver.run()\n # extract resultants\n forces, moments = solver_data.solver.extract_resultants()\n\n totals = np.zeros((6,))\n totals[0:3] = forces\n totals[3:6] = moments\n if solver_data.settings['print_info']:\n cout.cout_wrap(' forces = ' + str(totals), 1)\n\n if i_dim >= 0:\n return totals[i_dim]\n elif i_dim == -1:\n return totals\n elif i_dim == -2:\n coeffs = np.array([1.0, 1.0, 1.0, 2, 2, 2])\n if solver_data.settings['print_info']:\n cout.cout_wrap(' val = ' + str(np.dot(coeffs*totals, coeffs*totals)), 1)\n return np.dot(coeffs*totals, coeffs*totals)\n" }, { "path": "sharpy/solvers/updatepickle.py", "content": "import numpy as np\nimport sharpy.utils.settings as settings_utils\nfrom sharpy.utils.solver_interface import solver, BaseSolver\n\n\n@solver\nclass UpdatePickle(BaseSolver):\n \"\"\"\n\n \"\"\"\n solver_id = 'UpdatePickle'\n\n settings_types = dict()\n settings_default = dict()\n settings_description = dict()\n\n settings_table = settings_utils.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n def __init__(self):\n self.data = None\n self.settings = None\n\n def initialise(self, data, custom_settings=None, restart=False):\n self.data = data\n if custom_settings is None:\n self.settings = data.settings[self.solver_id]\n else:\n self.settings = custom_settings\n settings_utils.to_custom_types(self.settings,\n self.settings_types,\n self.settings_default,\n no_ctype=True)\n\n def run(self, **kwargs):\n\n for sts in self.data.structure.timestep_info:\n if sts is not None:\n sts.in_global_AFoR = True\n sts.runtime_steady_forces = np.zeros_like(sts.steady_applied_forces)\n sts.runtime_unsteady_forces = np.zeros_like(sts.steady_applied_forces)\n sts.psi_local = sts.psi.copy()\n sts.psi_dot_local = sts.psi_dot.copy()\n sts.mb_dquatdt = np.zeros_like(sts.mb_quat)\n\n return self.data\n\n" }, { "path": "sharpy/structure/__init__.py", "content": "\"\"\"Structural Packages\n\"\"\"" }, { "path": "sharpy/structure/basestructure.py", "content": "from abc import ABCMeta, abstractmethod\nimport sharpy.utils.cout_utils as cout\nimport os\n\n\nclass BaseStructure(metaclass=ABCMeta):\n @abstractmethod\n def generate(self, in_data, settings):\n pass\n\n" }, { "path": "sharpy/structure/models/__init__.py", "content": "" }, { "path": "sharpy/structure/models/beam.py", "content": "import ctypes as ct\nimport numpy as np\nimport copy\n\nfrom sharpy.structure.basestructure import BaseStructure\nimport sharpy.structure.models.beamstructures as beamstructures\nimport sharpy.utils.algebra as algebra\nfrom sharpy.utils.datastructures import StructTimeStepInfo\nimport sharpy.utils.multibody as mb\n\n\nclass Beam(BaseStructure):\n def __init__(self):\n self.settings = None\n # basic info\n self.num_node_elem = -1\n self.num_node = -1\n self.num_elem = -1\n\n self.timestep_info = []\n self.ini_info = None\n self.dynamic_input = []\n\n self.connectivities = None\n\n self.elem_stiffness = None\n self.stiffness_db = None\n self.inv_stiffness_db = None\n self.n_stiff = 0\n\n self.elem_mass = None\n self.mass_db = None\n self.n_mass = 0\n\n self.frame_of_reference_delta = None\n self.structural_twist = None\n self.boundary_conditions = None\n self.beam_number = None\n\n self.lumped_mass = None\n self.lumped_mass_nodes = None\n self.lumped_mass_inertia = None\n self.lumped_mass_position = None\n self.lumped_mass_mat = None\n self.lumped_mass_mat_nodes = None\n self.n_lumped_mass = 0\n\n self.steady_app_forces = None\n\n self.elements = []\n\n self.master = None\n self.node_master_elem = None\n\n self.vdof = None\n self.fdof = None\n self.num_dof = 0\n\n self.fortran = dict()\n\n # Multibody variabes\n self.ini_mb_dict = dict()\n self.body_number = None\n self.num_bodies = None\n self.FoR_movement = None\n\n self.global_nodes_num = None\n self.global_elems_num = None\n\n\n def generate(self, in_data, settings):\n self.settings = settings\n # read and store data\n # type of node\n self.num_node_elem = in_data['num_node_elem']\n # node info\n self.num_node = in_data['num_node']\n self.num_elem = in_data['num_elem']\n # Body number\n try:\n self.body_number = in_data['body_number'].copy()\n self.num_bodies = np.max(self.body_number) + 1\n except KeyError:\n self.body_number = np.zeros((self.num_elem, ), dtype=int)\n self.num_bodies = 1\n\n # boundary conditions\n self.boundary_conditions = in_data['boundary_conditions'].copy()\n self.generate_dof_arrays()\n\n # ini info\n self.ini_info = StructTimeStepInfo(self.num_node, self.num_elem, self.num_node_elem,\n num_dof=self.num_dof, num_bodies=self.num_bodies)\n\n # mutibody: FoR information\n try:\n for ibody in range(self.num_bodies):\n self.ini_info.mb_FoR_pos[ibody,:] = self.ini_mb_dict[\"body_%02d\" % ibody][\"FoR_position\"].copy()\n self.ini_info.mb_FoR_vel[ibody,:] = self.ini_mb_dict[\"body_%02d\" % ibody][\"FoR_velocity\"].copy()\n self.ini_info.mb_FoR_acc[ibody,:] = self.ini_mb_dict[\"body_%02d\" % ibody][\"FoR_acceleration\"].copy()\n self.ini_info.mb_quat[ibody,:] = self.ini_mb_dict[\"body_%02d\" % ibody][\"quat\"].copy()\n self.ini_info.mb_dict = copy.deepcopy(self.ini_mb_dict)\n except KeyError:\n self.ini_info.mb_FoR_pos[0,:] = self.ini_info.for_pos\n self.ini_info.mb_FoR_vel[0,:] = self.ini_info.for_vel\n self.ini_info.mb_FoR_acc[0,:] = self.ini_info.for_acc\n self.ini_info.mb_quat[0,:] = self.ini_info.quat\n\n # attention, it has to be copied, not only referenced\n self.ini_info.pos = in_data['coordinates'].astype(dtype=ct.c_double, order='F')\n\n # connectivity information\n self.connectivities = in_data['connectivities'].astype(dtype=ct.c_int, order='F')\n\n self.global_elems_num = np.arange(self.num_elem)\n self.global_nodes_num = np.arange(self.num_node)\n\n # stiffness data\n self.elem_stiffness = in_data['elem_stiffness'].copy()\n self.stiffness_db = in_data['stiffness_db'].copy()\n (self.n_stiff, _, _) = self.stiffness_db.shape\n self.inv_stiffness_db = np.zeros_like(self.stiffness_db, dtype=ct.c_double, order='F')\n for i in range(self.n_stiff):\n self.inv_stiffness_db[i, :, :] = np.linalg.inv(self.stiffness_db[i, :, :])\n\n # mass data\n self.elem_mass = in_data['elem_mass'].copy()\n self.mass_db = in_data['mass_db'].copy()\n (self.n_mass, _, _) = self.mass_db.shape\n\n # frame of reference delta\n self.frame_of_reference_delta = in_data['frame_of_reference_delta'].copy()\n # structural twist\n self.structural_twist = in_data['structural_twist'].copy()\n # beam number for every elem\n try:\n self.beam_number = in_data['beam_number'].copy()\n except KeyError:\n self.beam_number = np.zeros((self.num_elem, ), dtype=int)\n\n # applied forces\n try:\n in_data['app_forces'][self.num_node - 1, 5]\n except IndexError:\n in_data['app_forces'] = np.zeros((self.num_node, 6), dtype=ct.c_double, order='F')\n\n self.steady_app_forces = in_data['app_forces'].astype(dtype=ct.c_double, order='F')\n\n # generate the Element array\n for ielem in range(self.num_elem):\n self.elements.append(\n beamstructures.Element(\n ielem,\n self.num_node_elem,\n self.connectivities[ielem, :],\n self.ini_info.pos[self.connectivities[ielem, :], :],\n self.frame_of_reference_delta[ielem, :, :],\n self.structural_twist[ielem, :],\n self.beam_number[ielem],\n self.elem_stiffness[ielem],\n self.elem_mass[ielem]))\n # now we need to add the attributes like mass and stiffness index\n for ielem in range(self.num_elem):\n dictionary = dict()\n dictionary['stiffness_index'] = self.elem_stiffness[ielem]\n dictionary['mass_index'] = self.elem_mass[ielem]\n self.elements[ielem].add_attributes(dictionary)\n\n # psi calculation\n self.generate_psi()\n\n # master-slave structure\n self.generate_master_structure()\n\n # the timestep_info[0] is the steady state or initial state for unsteady solutions\n self.ini_info.steady_applied_forces = self.steady_app_forces.astype(dtype=ct.c_double, order='F')\n # rigid body rotations\n self.ini_info.quat = self.settings['orientation'].astype(dtype=ct.c_double, order='F')\n self.ini_info.for_pos[0:3] = self.settings['for_pos'].astype(dtype=ct.c_double, order='F')\n\n self.timestep_info.append(self.ini_info.copy())\n self.timestep_info[-1].steady_applied_forces = self.steady_app_forces.astype(dtype=ct.c_double, order='F')\n\n # lumped masses\n self.n_lumped_mass = 0\n try:\n self.lumped_mass = in_data['lumped_mass'].copy()\n except KeyError:\n self.lumped_mass = None\n else:\n self.lumped_mass_nodes = in_data['lumped_mass_nodes'].copy()\n self.lumped_mass_inertia = in_data['lumped_mass_inertia'].copy()\n self.lumped_mass_position = in_data['lumped_mass_position'].copy()\n self.n_lumped_mass += self.lumped_mass_position.shape[0]\n\n # lumped masses given as matrices\n try:\n self.lumped_mass_mat = in_data['lumped_mass_mat'].copy()\n except KeyError:\n self.lumped_mass_mat = None\n else:\n self.lumped_mass_mat_nodes = in_data['lumped_mass_mat_nodes'].copy()\n self.n_lumped_mass += self.lumped_mass_mat.shape[0]\n\n # lumped masses to element mass\n if self.lumped_mass is not None or self.lumped_mass_mat is not None:\n self.lump_masses()\n\n # self.generate_dof_arrays()\n self.generate_fortran()\n\n def generate_psi(self):\n # it will just generate the CRV for all the nodes of the element\n self.ini_info.psi = np.zeros((self.num_elem, 3, 3), dtype=ct.c_double, order='F')\n for elem in self.elements:\n self.ini_info.psi[elem.ielem, :, :] = elem.psi_ini\n\n def add_unsteady_information(self, dyn_dict, num_steps):\n # data storage for time dependant input\n for it in range(num_steps):\n self.dynamic_input.append(dict())\n\n try:\n for it in range(num_steps):\n self.dynamic_input[it]['dynamic_forces'] = dyn_dict['dynamic_forces'][it, :, :]\n except KeyError:\n for it in range(num_steps):\n self.dynamic_input[it]['dynamic_forces'] = np.zeros((self.num_node, 6), dtype=ct.c_double, order='F')\n\n try:\n for it in range(num_steps):\n self.dynamic_input[it]['for_pos'] = dyn_dict['for_pos'][it, :]\n except KeyError:\n for it in range(num_steps):\n self.dynamic_input[it]['for_pos'] = np.zeros((6, ), dtype=ct.c_double, order='F')\n\n try:\n for it in range(num_steps):\n self.dynamic_input[it]['for_vel'] = dyn_dict['for_vel'][it, :]\n except KeyError:\n for it in range(num_steps):\n self.dynamic_input[it]['for_vel'] = np.zeros((6, ), dtype=ct.c_double, order='F')\n\n try:\n for it in range(num_steps):\n self.dynamic_input[it]['for_acc'] = dyn_dict['for_acc'][it, :]\n except KeyError:\n for it in range(num_steps):\n self.dynamic_input[it]['for_acc'] = np.zeros((6, ), dtype=ct.c_double, order='F')\n\n def generate_dof_arrays(self):\n self.vdof = np.zeros((self.num_node,), dtype=ct.c_int, order='F') - 1\n self.fdof = np.zeros((self.num_node,), dtype=ct.c_int, order='F') - 1\n\n vcounter = -1\n fcounter = -1\n for inode in range(self.num_node):\n if self.boundary_conditions[inode] == 0:\n vcounter += 1\n fcounter += 1\n self.vdof[inode] = vcounter\n self.fdof[inode] = fcounter\n elif self.boundary_conditions[inode] == -1:\n vcounter += 1\n self.vdof[inode] = vcounter\n elif self.boundary_conditions[inode] == 1:\n fcounter += 1\n self.fdof[inode] = fcounter\n\n self.num_dof = ct.c_int((vcounter + 1)*6)\n\n def generate_mass_matrix(self, mass, position, inertia):\n\n inertia_tensor = np.zeros((6, 6))\n pos_skew = algebra.skew(position)\n inertia_tensor[0:3, 0:3] = mass*np.eye(3)\n inertia_tensor[0:3, 3:6] = -mass*pos_skew\n inertia_tensor[3:6, 0:3] = mass*pos_skew\n inertia_tensor[3:6, 3:6] = inertia + mass*(np.dot(pos_skew.T, pos_skew))\n\n return inertia_tensor\n\n def lump_masses(self):\n if self.lumped_mass is not None:\n for i_lumped in range(self.lumped_mass.shape[0]):\n r = self.lumped_mass_position[i_lumped, :]\n m = self.lumped_mass[i_lumped]\n j = self.lumped_mass_inertia[i_lumped, :, :]\n\n inertia_tensor = self.generate_mass_matrix(m, r, j)\n i_lumped_node = self.lumped_mass_nodes[i_lumped]\n self.add_lumped_mass_to_element(i_lumped_node,\n inertia_tensor)\n if self.lumped_mass_mat is not None:\n for i_lumped in range(self.lumped_mass_mat.shape[0]):\n inertia_tensor = self.lumped_mass_mat[i_lumped, :, :]\n i_lumped_node = self.lumped_mass_mat_nodes[i_lumped]\n self.add_lumped_mass_to_element(i_lumped_node,\n inertia_tensor)\n\n return\n\n def add_lumped_mass_to_element(self, i_lumped_node, inertia_tensor, replace=False):\n\n i_lumped_master_elem, i_lumped_master_node_local = self.node_master_elem[i_lumped_node]\n\n if self.elements[i_lumped_master_elem].rbmass is None:\n # allocate memory\n self.elements[i_lumped_master_elem].rbmass = np.zeros((\n self.elements[i_lumped_master_elem].max_nodes_elem, 6, 6))\n\n if replace:\n self.elements[i_lumped_master_elem].rbmass[i_lumped_master_node_local, :, :] = (\n inertia_tensor)\n else:\n self.elements[i_lumped_master_elem].rbmass[i_lumped_master_node_local, :, :] += (\n inertia_tensor) # += necessary in case multiple masses defined per node\n\n def generate_master_structure(self):\n self.master = np.zeros((self.num_elem, self.num_node_elem, 2), dtype=int) - 1\n for i_elem in range(self.num_elem):\n for i_node_local in range(self.elements[i_elem].n_nodes):\n # for i_node_local in self.elements[i_elem].ordering:\n if not i_elem and not i_node_local:\n continue\n j_elem = 0\n while self.master[i_elem, i_node_local, 0] == -1 and j_elem <= i_elem:\n # for j_node_local in self.elements[j_elem].ordering:\n for j_node_local in range(self.elements[j_elem].n_nodes):\n # for j_node_local in self.elements[j_elem].ordering:\n if (self.connectivities[i_elem, i_node_local] ==\n self.connectivities[j_elem, j_node_local]):\n self.master[i_elem, i_node_local, :] = [j_elem, j_node_local]\n j_elem += 1\n\n self.generate_node_master_elem()\n # a = 1\n\n def add_timestep(self, timestep_info):\n if len(timestep_info) == 0:\n # copy from ini_info\n timestep_info.append(self.ini_info.copy())\n else:\n timestep_info.append(self.timestep_info[-1].copy())\n\n def next_step(self):\n self.add_timestep(self.timestep_info)\n\n def generate_node_master_elem(self):\n \"\"\"\n Returns a matrix indicating the master element for a given node\n :return:\n \"\"\"\n self.node_master_elem = np.zeros((self.num_node, 2), dtype=ct.c_int, order='F') - 1\n for i_elem in range(self.num_elem):\n for i_node_local in range(self.elements[i_elem].n_nodes):\n if self.master[i_elem, i_node_local, 0] == -1:\n if self.node_master_elem[self.connectivities[i_elem, i_node_local], 0] < 0:\n self.node_master_elem[self.connectivities[i_elem, i_node_local], 0] = i_elem\n self.node_master_elem[self.connectivities[i_elem, i_node_local], 1] = i_node_local\n else:\n master_elem = self.master[i_elem, i_node_local, 0]\n master_node = self.master[i_elem, i_node_local, 1]\n if self.node_master_elem[self.connectivities[i_elem, i_node_local], 0] < 0:\n self.node_master_elem[self.connectivities[i_elem, i_node_local], 0] = master_elem\n self.node_master_elem[self.connectivities[i_elem, i_node_local], 1] = master_node\n\n\n def generate_fortran(self):\n # steady, no time-dependant information\n self.fortran['num_nodes'] = np.zeros((self.num_elem,), dtype=ct.c_int, order='F')\n for elem in self.elements:\n self.fortran['num_nodes'][elem.ielem] = elem.n_nodes\n\n self.fortran['num_mem'] = np.zeros_like(self.fortran['num_nodes'], dtype=ct.c_int)\n for elem in self.elements:\n self.fortran['num_mem'][elem.ielem] = elem.num_mem\n\n self.fortran['connectivities'] = self.connectivities.astype(ct.c_int, order='F') + 1\n self.fortran['master'] = self.master.astype(dtype=ct.c_int, order='F') + 1\n self.fortran['node_master_elem'] = self.node_master_elem.astype(dtype=ct.c_int, order='F') + 1\n\n self.fortran['length'] = np.zeros_like(self.fortran['num_nodes'], dtype=ct.c_double, order='F')\n for elem in self.elements:\n self.fortran['length'][elem.ielem] = elem.length\n\n self.fortran['mass'] = self.mass_db.astype(ct.c_double, order='F')\n self.fortran['stiffness'] = self.stiffness_db.astype(ct.c_double, order='F')\n self.fortran['inv_stiffness'] = self.inv_stiffness_db.astype(ct.c_double, order='F')\n self.fortran['mass_indices'] = self.elem_mass.astype(ct.c_int, order='F') + 1\n self.fortran['stiffness_indices'] = self.elem_stiffness.astype(ct.c_int, order='F') + 1\n\n self.fortran['frame_of_reference_delta'] = self.frame_of_reference_delta.astype(ct.c_double, order='F')\n\n self.fortran['vdof'] = self.vdof.astype(ct.c_int, order='F') + 1\n self.fortran['fdof'] = self.fdof.astype(ct.c_int, order='F') + 1\n\n # self.fortran['steady_applied_forces'] = self.steady_app_forces.astype(dtype=ct.c_double, order='F')\n\n # undeformed structure matrices\n self.fortran['pos_ini'] = self.ini_info.pos.astype(dtype=ct.c_double, order='F')\n self.fortran['psi_ini'] = self.ini_info.psi.astype(dtype=ct.c_double, order='F')\n\n max_nodes_elem = self.elements[0].max_nodes_elem\n rbmass_temp = np.zeros((self.num_elem, max_nodes_elem, 6, 6))\n for elem in self.elements:\n for inode in range(elem.n_nodes):\n if elem.rbmass is not None:\n rbmass_temp[elem.ielem, inode, :, :] += elem.rbmass[inode, :, :]\n self.fortran['rbmass'] = rbmass_temp.astype(dtype=ct.c_double, order='F')\n\n if self.settings['unsteady']:\n pass\n\n def integrate_position(self, ts, dt):\n try:\n ts.for_pos[0:3] += (\n dt*np.dot(ts.cga(),\n ts.for_vel[0:3]))\n except AttributeError:\n self.timestep_info[ts].for_pos[0:3] += (\n dt*np.dot(self.timestep_info[ts].cga(),\n self.timestep_info[ts].for_vel[0:3]))\n\n def nodal_premultiply_inv_T_transpose(self, nodal, tstep, filter=np.array([True]*6)):\n nodal_t = nodal.copy(order='F')\n for i_node in range(self.num_node):\n # get master elem and i_local_node\n i_master_elem, i_local_node = self.node_master_elem[i_node, :]\n crv = tstep.psi[i_master_elem, i_local_node, :]\n inv_tanT = algebra.crv2invtant(crv)\n temp = np.zeros((6,))\n temp[0:3] = np.dot(inv_tanT, nodal[i_node, 0:3])\n temp[3:6] = np.dot(inv_tanT, nodal[i_node, 3:6])\n for i in range(6):\n if filter[i]:\n nodal_t[i_node, i] = temp[i]\n\n return nodal_t\n\n def get_body(self, ibody):\n \"\"\"\n get_body\n\n Extract the body number ``ibody`` from a multibody system\n\n This function returns a :class:`~sharpy.structure.models.beam.Beam` class (``ibody_beam``)\n that only includes the body number ``ibody`` of the original system\n\n Args:\n self(:class:`~sharpy.structure.models.beam.Beam`): structural information of the multibody system\n ibody(int): body number to be extracted\n\n Returns:\n \tibody_beam(:class:`~sharpy.structure.models.beam.Beam`): structural information of the isolated body\n \"\"\"\n\n ibody_beam = Beam()\n\n # Define the nodes and elements belonging to the body\n ibody_beam.global_elems_num, ibody_beam.global_nodes_num = mb.get_elems_nodes_list(self, ibody)\n\n # Renaming for clarity\n ibody_elements = ibody_beam.global_elems_num\n ibody_nodes = ibody_beam.global_nodes_num\n\n # Assign all the properties to the new StructTimeStepInfo\n ibody_beam.settings = self.settings.copy()\n\n ibody_beam.num_node_elem = self.num_node_elem.astype(dtype=ct.c_int, order='F', copy=True)\n ibody_beam.num_node = len(ibody_beam.global_nodes_num)\n ibody_beam.num_elem = len(ibody_beam.global_elems_num)\n\n ibody_beam.connectivities = self.connectivities[ibody_elements,:]\n # Renumber the connectivities\n int_list_nodes = np.arange(0, ibody_beam.num_node, 1)\n for ielem in range(ibody_beam.num_elem):\n for inode_in_elem in range(ibody_beam.num_node_elem):\n ibody_beam.connectivities[ielem, inode_in_elem] = int_list_nodes[\n np.argwhere(ibody_nodes == ibody_beam.connectivities[ielem, inode_in_elem])[0][0]]\n\n # TODO: I could copy only the needed stiffness and masses to save storage\n ibody_beam.elem_stiffness = self.elem_stiffness[ibody_elements].astype(dtype=ct.c_int, order='F', copy=True)\n ibody_beam.stiffness_db = self.stiffness_db.astype(dtype=ct.c_double, order='F', copy=True)\n ibody_beam.inv_stiffness_db = self.inv_stiffness_db.astype(dtype=ct.c_double, order='F', copy=True)\n ibody_beam.n_stiff = self.n_stiff\n\n ibody_beam.elem_mass = self.elem_mass[ibody_elements].astype(dtype=ct.c_int, order='F', copy=True)\n ibody_beam.mass_db = self.mass_db.astype(dtype=ct.c_double, order='F', copy=True)\n ibody_beam.n_mass = self.n_mass\n\n ibody_beam.frame_of_reference_delta = self.frame_of_reference_delta[ibody_elements,:,:].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_beam.structural_twist = self.structural_twist[ibody_elements, :].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_beam.boundary_conditions = self.boundary_conditions[ibody_nodes].astype(dtype=ct.c_int, order='F', copy=True)\n ibody_beam.beam_number = self.beam_number[ibody_elements].astype(dtype=ct.c_int, order='F', copy=True)\n\n if not self.lumped_mass_nodes is None:\n is_first = True\n ibody_beam.n_lumped_mass = 0\n for inode in range(len(self.lumped_mass_nodes)):\n if self.lumped_mass_nodes[inode] in ibody_nodes:\n if is_first:\n is_first = False\n ibody_beam.lumped_mass_nodes = int_list_nodes[ibody_nodes == self.lumped_mass_nodes[inode]]\n ibody_beam.lumped_mass = np.array([self.lumped_mass[inode]])\n ibody_beam.lumped_mass_inertia = np.array([self.lumped_mass_inertia[inode]])\n ibody_beam.lumped_mass_position = np.array([self.lumped_mass_position[inode]])\n ibody_beam.n_lumped_mass += 1\n else:\n ibody_beam.lumped_mass_nodes = np.concatenate((ibody_beam.lumped_mass_nodes ,int_list_nodes[ibody_nodes == self.lumped_mass_nodes[inode]]), axis=0)\n ibody_beam.lumped_mass = np.concatenate((ibody_beam.lumped_mass ,np.array([self.lumped_mass[inode]])), axis=0)\n ibody_beam.lumped_mass_inertia = np.concatenate((ibody_beam.lumped_mass_inertia ,np.array([self.lumped_mass_inertia[inode]])), axis=0)\n ibody_beam.lumped_mass_position = np.concatenate((ibody_beam.lumped_mass_position ,np.array([self.lumped_mass_position[inode]])), axis=0)\n ibody_beam.n_lumped_mass += 1\n\n if not self.lumped_mass_mat is None:\n is_first = True\n for inode in range(len(self.lumped_mass_mat_nodes)):\n if self.lumped_mass_mat_nodes[inode] in ibody_nodes:\n if is_first:\n is_first = False\n ibody_beam.lumped_mass_mat_nodes = int_list_nodes[ibody_nodes == self.lumped_mass_mat_nodes[inode]]\n ibody_beam.lumped_mass_mat = np.array([self.lumped_mass_mat[inode, :, :]])\n else:\n ibody_beam.lumped_mass_mat_nodes = np.concatenate((ibody_beam.lumped_mass_mat_nodes , int_list_nodes[ibody_nodes == self.lumped_mass_mat_nodes[inode]]), axis=0)\n ibody_beam.lumped_mass_mat = np.concatenate((ibody_beam.lumped_mass_mat ,np.array([self.lumped_mass_mat[inode, :, :]])), axis=0)\n\n ibody_beam.steady_app_forces = self.steady_app_forces[ibody_nodes,:].astype(dtype=ct.c_double, order='F', copy=True)\n\n ibody_beam.num_bodies = 1\n\n ibody_beam.body_number = self.body_number[ibody_elements].astype(dtype=ct.c_int, order='F', copy=True)\n\n ibody_beam.generate_dof_arrays()\n\n ibody_beam.ini_info = self.ini_info.get_body(self, ibody_beam.num_dof, ibody)\n ibody_beam.timestep_info = self.timestep_info[-1].get_body(self, ibody_beam.num_dof, ibody)\n\n # generate the Element array\n for ielem in range(ibody_beam.num_elem):\n ibody_beam.elements.append(\n beamstructures.Element(\n ielem,\n ibody_beam.num_node_elem,\n ibody_beam.connectivities[ielem, :],\n ibody_beam.ini_info.pos[ibody_beam.connectivities[ielem, :], :],\n ibody_beam.frame_of_reference_delta[ielem, :, :],\n ibody_beam.structural_twist[ielem, :],\n ibody_beam.beam_number[ielem],\n ibody_beam.elem_stiffness[ielem],\n ibody_beam.elem_mass[ielem]))\n # now we need to add the attributes like mass and stiffness index\n for ielem in range(ibody_beam.num_elem):\n dictionary = dict()\n dictionary['stiffness_index'] = ibody_beam.elem_stiffness[ielem]\n dictionary['mass_index'] = ibody_beam.elem_mass[ielem]\n ibody_beam.elements[ielem].add_attributes(dictionary)\n\n ibody_beam.generate_master_structure()\n\n if ibody_beam.lumped_mass is not None or ibody_beam.lumped_mass_mat is not None:\n ibody_beam.lump_masses()\n\n ibody_beam.generate_fortran()\n\n return ibody_beam\n" }, { "path": "sharpy/structure/models/beamstructures.py", "content": "# Alfonso del Carre\nimport numpy as np\n\nimport sharpy.utils.algebra as algebra\n\n\nclass Element(object):\n \"\"\"\n This class stores all the required data for the definition of\n a linear or quadratic beam element.\n \"\"\"\n ordering = [0, 2, 1]\n max_nodes_elem = 3\n\n def __init__(self,\n ielem,\n n_nodes,\n global_connectivities,\n coordinates,\n frame_of_reference_delta,\n structural_twist,\n num_mem,\n stiff_index,\n mass_index):\n # store info in instance\n # global element number\n self.ielem = ielem\n # number of nodes per elem\n self.n_nodes = n_nodes\n if self.max_nodes_elem < self.n_nodes:\n raise AttributeError('Elements with more than 3 nodes are not allowed')\n # global connectivities (global node numbers)\n self.global_connectivities = global_connectivities\n self.reordered_global_connectivities = global_connectivities[self.ordering]\n # coordinates of the nodes in a-frame (body-fixed frame)\n self.coordinates_def = coordinates.copy()\n # frame of reference points\n self.frame_of_reference_delta = frame_of_reference_delta\n # structural twist\n self.structural_twist = structural_twist\n # number in memory (for fortran routines)\n self.num_mem = num_mem\n # stiffness and mass matrices indices (stored in parent beam class)\n self.stiff_index = stiff_index\n self.mass_index = mass_index\n\n # placeholder for RBMass\n self.rbmass = None # np.zeros((self.max_nodes_elem, 6, 6))\n\n self.update(self.coordinates_def)\n\n def update(self, coordinates_def, psi_def=None):\n self.coordinates_def = coordinates_def.copy()\n\n if psi_def is not None:\n # element orientation\n self.psi_def = psi_def.copy()\n\n # element length\n self.calculate_length()\n\n if psi_def is None: # ini conditions, initial crv has to be calculated\n # we need to define the FoR z direction for every beam element\n v1, v2, v3 = self.get_triad()\n self.psi_ini = algebra.triad2crv_vec(v1, v2, v3)\n self.psi_def = self.psi_ini.copy()\n\n # copy all the info to _ini fields\n self.coordinates_ini = self.coordinates_def.copy()\n\n def calculate_length(self):\n # TODO implement length based on integration\n self.length = np.linalg.norm(self.coordinates_def[0, :] - self.coordinates_def[1, :])\n\n def add_attributes(self, dictionary):\n for key, value in dictionary.items():\n setattr(self, key, value)\n\n def generate_curve(self, n_elem_curve, defor=False):\n curve = np.zeros((n_elem_curve, 3))\n t_vec = np.linspace(0, 2, n_elem_curve)\n for i in range(n_elem_curve):\n t = t_vec[i]\n for idim in range(3):\n if defor:\n polyfit, _, _ = algebra.get_polyfit(self.coordinates_def, self.ordering)\n else:\n polyfit, _, _ = algebra.get_polyfit(self.coordinates_ini, self.ordering)\n polyf = np.poly1d(polyfit[idim])\n curve[i, idim] = (polyf(t))\n return curve\n\n def get_triad(self):\n \"\"\"\n Generates two unit vectors in body FoR that define the local FoR for\n a beam element. These vectors are calculated using `frame_of_reference_delta`\n :return:\n \"\"\"\n # now, calculate tangent vector (and coefficients of the polynomial\n # fit just in case)\n tangent, polyfit = algebra.tangent_vector(\n self.coordinates_def,\n Element.ordering)\n normal = np.zeros_like(tangent)\n binormal = np.zeros_like(tangent)\n\n # v_vector is the vector with origin the FoR node and delta\n # equals frame_of_reference_delta\n for inode in range(self.n_nodes):\n v_vector = self.frame_of_reference_delta[inode, :]\n normal[inode, :] = algebra.unit_vector(np.cross(\n tangent[inode, :],\n v_vector\n )\n )\n binormal[inode, :] = -algebra.unit_vector(np.cross(\n tangent[inode, :],\n normal[inode, :]\n )\n )\n\n # we apply twist now\n for inode in range(self.n_nodes):\n if not self.structural_twist[inode] == 0.0:\n rotation_mat = algebra.rotation_matrix_around_axis(tangent[inode, :],\n self.structural_twist[inode])\n normal[inode, :] = np.dot(rotation_mat, normal[inode, :])\n binormal[inode, :] = np.dot(rotation_mat, binormal[inode, :])\n\n return tangent, binormal, normal\n\n def deformed_triad(self, psi=None):\n if psi is None:\n return algebra.crv2triad_vec(self.psi_def)\n else:\n return algebra.crv2triad_vec(psi)\n" }, { "path": "sharpy/structure/utils/__init__.py", "content": "" }, { "path": "sharpy/structure/utils/lagrangeconstraints.py", "content": "\"\"\"\nLagrangeConstraints library\n\nLibrary used to create the matrices associated to boundary conditions through\nthe method of Lagrange Multipliers. The source code includes four different sections.\n\n* Basic structures: basic functions and variables needed to organise the library with different Lagrange Constraints to enhance the interaction with this library.\n\n* Auxiliar functions: basic queries that are performed repeatedly.\n\n* Equations: functions that generate the equations associated to the constraint of basic degrees of freedom.\n\n* Lagrange Constraints: different available Lagrange Constraints. They tipically use the basic functions in \"Equations\" to assembly the required set of equations.\n\nAttributes:\n dict_of_lc (dict): Dictionary including the available Lagrange Contraint identifier\n (``_lc_id``) and the associated ``BaseLagrangeConstraint`` class\n\nNotes:\n To use this library: import sharpy.structure.utils.lagrangeconstraints as lagrangeconstraints\n\nArgs:\n lc_list (list): list of all the defined contraints\n MBdict (dict): dictionary with the MultiBody and LagrangeMultipliers information\n MB_beam (list): list of :class:`~sharpy.structure.models.beam.Beam` of each of the bodies that form the system\n MB_tstep (list): list of :class:`~sharpy.utils.datastructures.StructTimeStepInfo` of each of the bodies that form the system\n num_LM_eq (int): number of new equations needed to define the boundary boundary conditions\n sys_size (int): total number of degrees of freedom of the multibody system\n dt (float): time step\n Lambda (np.ndarray): list of Lagrange multipliers values\n Lambda_dot (np.ndarray): list of the first derivative of the Lagrange multipliers values\n dynamic_or_static (str): string defining if the computation is dynamic or static\n LM_C (np.ndarray): Damping matrix associated to the Lagrange Multipliers equations\n LM_K (np.ndarray): Stiffness matrix associated to the Lagrange Multipliers equations\n LM_Q (np.ndarray): Vector of independent terms associated to the Lagrange Multipliers equations\n\"\"\"\nfrom abc import ABCMeta, abstractmethod\nimport sharpy.utils.cout_utils as cout\nimport os\nimport ctypes as ct\nimport numpy as np\nimport sharpy.utils.algebra as ag\nfrom sharpy.utils.settings import set_value_or_default\n\n###############################################################################\n# Basic structures\n###############################################################################\n\ndict_of_lc = {}\nlc = {} # for internal working\n\n\n# decorator\ndef lagrangeconstraint(arg):\n \"\"\"\n Decorator used to create the dictionary (``dict_of_lc``) that links constraints id (``_lc_id``) to the associated ``BaseLagrangeConstraint`` class\n \"\"\"\n global dict_of_lc\n try:\n arg._lc_id\n except AttributeError:\n raise AttributeError('Class defined as lagrange constraint has no _lc_id attribute')\n dict_of_lc[arg._lc_id] = arg\n return arg\n\n\ndef print_available_lc():\n \"\"\"\n Prints the available Lagrange Constraints\n \"\"\"\n cout.cout_wrap('The available lagrange constraints on this session are:', 2)\n for name, i_lc in dict_of_lc.items():\n cout.cout_wrap('%s ' % i_lc._lc_id, 2)\n\n\ndef lc_from_string(string):\n \"\"\"\n Returns the ``BaseLagrangeConstraint`` class associated to a constraint id (``_lc_id``)\n \"\"\"\n return dict_of_lc[string]\n\n\ndef lc_list_from_path(cwd):\n onlyfiles = [f for f in os.listdir(cwd) if os.path.isfile(os.path.join(cwd, f))]\n\n for i_file in range(len(onlyfiles)):\n if \".py\" in onlyfiles[i_file]:\n if onlyfiles[i_file] == \"__init__.py\":\n onlyfiles[i_file] = \"\"\n continue\n onlyfiles[i_file] = onlyfiles[i_file].replace('.py', '')\n else:\n onlyfiles[i_file] = \"\"\n\n files = [file for file in onlyfiles if not file == \"\"]\n return files\n\n\ndef initialise_lc(lc_name, print_info=True):\n \"\"\"\n Initialises the Lagrange Constraints\n \"\"\"\n if print_info:\n cout.cout_wrap('Generating an instance of %s' % lc_name, 2)\n cls_type = lc_from_string(lc_name)\n lc = cls_type()\n return lc\n\n\nclass BaseLagrangeConstraint(metaclass=ABCMeta):\n __doc__ = \"\"\"\n BaseLagrangeConstraint\n\n Base class for LagrangeConstraints showing the methods required. They will\n be inherited by all the Lagrange Constraints\n\n Attributes:\n _n_eq (int): Number of equations required by a LagrangeConstraint\n _ieq (int): Number of the first equation associated to the Lagrange Constraint in the whole set of Lagrange equations\n \"\"\"\n _lc_id = 'BaseLagrangeConstraint'\n\n def __init__(self):\n \"\"\"\n Initialisation\n \"\"\"\n self._n_eq = None\n self._ieq = None\n\n @abstractmethod\n def get_n_eq(self):\n \"\"\"\n Returns the number of equations required by the Lagrange Constraint\n \"\"\"\n return self._n_eq\n\n @abstractmethod\n # def initialise(self, **kwargs):\n def initialise(self, MBdict_entry, ieq):\n \"\"\"\n Initialisation\n \"\"\"\n self._ieq = ieq\n return self._ieq + self._n_eq\n\n @abstractmethod\n # def staticmat(self, **kwargs):\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n \"\"\"\n Generates the structural matrices (damping, stiffness) and the independent vector\n associated to the LagrangeConstraint in a static simulation\n \"\"\"\n return np.zeros((6, 6))\n\n @abstractmethod\n # def dynamicmat(self, **kwargs):\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n \"\"\"\n Generates the structural matrices (damping, stiffness) and the independent vector\n associated to the LagrangeConstraint in a dynamic simulation\n \"\"\"\n return np.zeros((10, 10))\n\n @abstractmethod\n # def staticpost(self, **kwargs):\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n \"\"\"\n Postprocess operations needed by the LagrangeConstraint in a static simulation\n \"\"\"\n return\n\n @abstractmethod\n # def dynamicpost(self, **kwargs):\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n \"\"\"\n Postprocess operations needed by the LagrangeConstraint in a dynamic simulation\n \"\"\"\n return\n\n\n################################################################################\n# Auxiliar functions\n################################################################################\ndef define_node_dof(MB_beam, node_body, num_node):\n \"\"\"\n define_node_dof\n\n Define the position of the first degree of freedom associated to a certain node\n\n Args:\n MB_beam(list): list of :class:`~sharpy.structure.models.beam.Beam`\n node_body(int): body to which the node belongs\n num_node(int): number os the node within the body\n\n Returns:\n node_dof(int): first degree of freedom associated to the node\n \"\"\"\n node_dof = 0\n for ibody in range(node_body):\n node_dof += MB_beam[ibody].num_dof.value\n if MB_beam[ibody].FoR_movement == 'free':\n node_dof += 10\n node_dof += 6 * MB_beam[node_body].vdof[num_node]\n return node_dof\n\n\ndef define_FoR_dof(MB_beam, FoR_body):\n \"\"\"\n define_FoR_dof\n\n Define the position of the first degree of freedom associated to a certain frame of reference\n\n Args:\n MB_beam(list): list of :class:`~sharpy.structure.models.beam.Beam`\n node_body(int): body to which the node belongs\n num_node(int): number os the node within the body\n\n Returns:\n node_dof(int): first degree of freedom associated to the node\n \"\"\"\n FoR_dof = 0\n for ibody in range(FoR_body):\n FoR_dof += MB_beam[ibody].num_dof.value\n if MB_beam[ibody].FoR_movement == 'free':\n FoR_dof += 10\n FoR_dof += MB_beam[FoR_body].num_dof.value\n return FoR_dof\n\n\n################################################################################\n# Equations\n################################################################################\ndef equal_pos_node_FoR(MB_tstep, MB_beam, FoR_body, node_body, inode_in_body, node_FoR_dof, node_dof, FoR_dof, sys_size,\n Lambda, scalingFactor, penaltyFactor, ieq, LM_K, LM_C, LM_Q):\n \"\"\"\n This function generates the stiffness and damping matrices and the independent vector associated to a constraint that\n imposes equal positions between a node and a frame of reference\n\n See ``LagrangeConstraints`` for the description of variables\n\n Args:\n node_FoR_dof (int): position of the first degree of freedom of the FoR to which the \"node\" belongs\n node_dof (int): position of the first degree of freedom associated to the \"node\"\n FoR_body (int): body number of the \"FoR\"\n FoR_dof (int): position of the first degree of freedom associated to the \"FoR\"\n\n Note: this equation constitutes a holonomic constraint which is not currently supported. Check ``equal_lin_vel_node_FoR``\n \"\"\"\n cout.cout_wrap(\n \"WARNING: this equation constitutes a holonomic constraint which is not currently supported. Check ``equal_lin_vel_node_FoR``\",\n 3)\n\n num_LM_eq_specific = 3\n B = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Simplify notation\n node_cga = MB_tstep[node_body].cga()\n node_pos = MB_tstep[node_body].pos[inode_in_body, :]\n node_FoR_pos = MB_tstep[node_body].for_pos[0:3]\n FoR_pos = MB_tstep[FoR_body].for_pos[0:3]\n\n # if MB_beam[node_body].FoR_movement == 'free':\n B[:, node_FoR_dof:node_FoR_dof + 3] = np.eye(3)\n B[:, node_dof:node_dof + 3] = node_cga\n B[:, FoR_dof:FoR_dof + 3] = -np.eye(3)\n\n LM_K[sys_size + ieq: sys_size + ieq + num_LM_eq_specific, :sys_size] += scalingFactor * B\n LM_K[:sys_size, sys_size + ieq: sys_size + ieq + num_LM_eq_specific] += scalingFactor * B.T\n\n LM_Q[:sys_size] += scalingFactor * B.T @ Lambda[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += scalingFactor * (node_FoR_pos + node_cga @ node_pos - FoR_pos)\n\n LM_C[node_dof:node_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] += scalingFactor * ag.der_CquatT_by_v(\n MB_tstep[node_body].quat, Lambda[ieq: ieq + num_LM_eq_specific])\n\n if penaltyFactor:\n q = np.zeros((sys_size,))\n q[node_FoR_dof:node_FoR_dof + 3] = node_FoR_pos\n q[node_dof:node_dof + 3] = node_pos\n q[FoR_dof:FoR_dof + 3] = FoR_pos\n\n LM_Q[:sys_size] += penaltyFactor * B.T @ B @ q\n\n LM_K[node_FoR_dof:node_FoR_dof + 3, node_FoR_dof:node_FoR_dof + 3] += penaltyFactor * np.eye(3)\n LM_K[node_FoR_dof:node_FoR_dof + 3, node_dof:node_dof + 3] += penaltyFactor * node_cga\n LM_K[node_FoR_dof:node_FoR_dof + 3, FoR_dof:FoR_dof + 3] += -penaltyFactor * np.eye(3)\n LM_C[node_FoR_dof:node_FoR_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] += penaltyFactor * ag.der_Cquat_by_v(\n MB_tstep[node_body].quat, node_pos)\n\n LM_K[node_dof:node_dof + 3, node_FoR_dof:node_FoR_dof + 3] += penaltyFactor * node_cga.T\n LM_K[node_dof:node_dof + 3, node_dof:node_dof + 3] += penaltyFactor * np.eye(3)\n LM_K[node_dof:node_dof + 3, FoR_dof:FoR_dof + 3] += -penaltyFactor * node_cga.T\n LM_C[node_dof:node_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] += penaltyFactor * (\n ag.der_CquatT_by_v(MB_tstep[node_body].quat, node_FoR_pos - FoR_pos))\n\n LM_K[FoR_dof:FoR_dof + 3, node_FoR_dof:node_FoR_dof + 3] += -penaltyFactor * np.eye(3)\n LM_K[FoR_dof:FoR_dof + 3, node_dof:node_dof + 3] += -penaltyFactor * node_cga.T\n LM_K[FoR_dof:FoR_dof + 3, FoR_dof:FoR_dof + 3] += penaltyFactor * np.eye(3)\n LM_C[FoR_dof:FoR_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] += -penaltyFactor * ag.der_Cquat_by_v(\n MB_tstep[node_body].quat, node_pos)\n\n ieq += 3\n return ieq\n\n\ndef equal_lin_vel_node_FoR(MB_tstep, MB_beam, FoR_body, node_body, node_number, node_FoR_dof, node_dof, FoR_dof,\n sys_size, Lambda_dot, scalingFactor, penaltyFactor, ieq, LM_K, LM_C, LM_Q,\n rel_posB=np.zeros((3))):\n \"\"\"\n This function generates the stiffness and damping matrices and the independent vector associated to a constraint that\n imposes equal linear velocities between a node and a frame of reference\n\n See ``LagrangeConstraints`` for the description of variables\n\n Args:\n node_number (int): number of the \"node\" within its own body\n node_body (int): body number of the \"node\"\n node_FoR_dof (int): position of the first degree of freedom of the FoR to which the \"node\" belongs\n node_dof (int): position of the first degree of freedom associated to the \"node\"\n FoR_body (int): body number of the \"FoR\"\n FoR_dof (int): position of the first degree of freedom associated to the \"FoR\"\n rel_posB (float np.array): relative position between the node and the FoR (in the node B FoR)\n \"\"\"\n\n num_LM_eq_specific = 3\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Simplify notation\n node_cga = MB_tstep[node_body].cga()\n node_FoR_va = MB_tstep[node_body].for_vel[0:3]\n node_FoR_wa = MB_tstep[node_body].for_vel[3:6]\n\n ielem, inode_in_elem = MB_beam[node_body].node_master_elem[node_number]\n psi = MB_tstep[node_body].psi[ielem, inode_in_elem, :]\n node_cab = ag.crv2rotation(psi)\n node_Ra = MB_tstep[node_body].pos[node_number, :] + node_cab @ rel_posB\n\n node_dot_Ra = MB_tstep[node_body].pos_dot[node_number, :]\n FoR_cga = MB_tstep[FoR_body].cga()\n FoR_va = MB_tstep[FoR_body].for_vel[0:3]\n\n Bnh[:, FoR_dof:FoR_dof + 3] = FoR_cga\n Bnh[:, node_dof:node_dof + 3] = -1. * node_cga\n if MB_beam[node_body].FoR_movement == 'free':\n Bnh[:, node_FoR_dof:node_FoR_dof + 3] = -1. * node_cga\n Bnh[:, node_FoR_dof + 3:node_FoR_dof + 6] = node_cga @ ag.skew(node_Ra)\n\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += scalingFactor * Bnh.T\n\n LM_Q[:sys_size] += scalingFactor * Bnh.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += scalingFactor * (FoR_cga @ FoR_va - node_cga @ (node_dot_Ra + node_FoR_va - ag.skew(node_Ra) @ node_FoR_wa))\n\n LM_C[FoR_dof:FoR_dof + 3, FoR_dof + 6:FoR_dof + 10] \\\n += scalingFactor * ag.der_CquatT_by_v(MB_tstep[FoR_body].quat, Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n if MB_beam[node_body].FoR_movement == 'free':\n LM_C[node_dof:node_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] -= scalingFactor * ag.der_CquatT_by_v(\n MB_tstep[node_body].quat, Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n LM_C[node_FoR_dof:node_FoR_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] -= scalingFactor * ag.der_CquatT_by_v(\n MB_tstep[node_body].quat, Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n LM_C[node_FoR_dof + 3:node_FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += (scalingFactor * ag.skew(node_Ra).T\n @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, Lambda_dot[ieq:ieq + num_LM_eq_specific]))\n\n # non-trivial - verified by hand (involves multiple transformations, Dynamics of Flexible Aircraft Appen. C)\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof:node_dof + 3] += scalingFactor * ag.skew(\n node_cga.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n if penaltyFactor:\n if MB_beam[node_body].FoR_movement == 'free':\n # TODO: follow general approach to derive terms - first 4*4 terms, then LMC derivatives, then LMK derivatives - this is why penalty didn't work!\n\n # Simplify notation\n node_cga = MB_tstep[node_body].cga()\n FoR_cga = MB_tstep[FoR_body].cga()\n psi_dot = MB_tstep[node_body].psi_dot[ielem, inode_in_elem, :]\n\n q = np.zeros((sys_size))\n q[FoR_dof:FoR_dof + 3] = FoR_va\n q[node_dof:node_dof + 3] = node_dot_Ra\n q[node_dof + 3:node_dof + 6] = psi_dot\n q[node_FoR_dof:node_FoR_dof + 3] = node_FoR_va\n q[node_FoR_dof + 3:node_FoR_dof + 6] = node_FoR_wa\n\n LM_Q[:sys_size] += penaltyFactor * Bnh.T @ Bnh @ q\n\n # # 16 canonical terms for (abcd)^T(abcd)\n LM_C[:sys_size, :sys_size] += penaltyFactor * Bnh.T @ Bnh\n\n # other LM_C derivatives for c dependencies in x1 and x2\n # term 1-x1 - \\frac{\\partial}{\\partial x_1}(a^Taq_1 + a^Tbq2 + a^Tcq3 + a^Tdq4) \n # da^Tdxaq_1 + a^Tdadxaq_1 + da^Tdxbq_2 + a^Tdbdxq_2 + da^Tdxcq_3 + a^Tdcdxq_3 + da^Tdxdq_4\n\n mat = -np.eye(3)\n vec = -node_cga @ node_dot_Ra\n\n LM_C[node_dof:node_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n mat = node_cga.T\n vec = node_dot_Ra\n\n LM_C[node_dof:node_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = -np.eye(3)\n vec = -node_cga @ node_FoR_va\n\n LM_C[node_dof:node_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n mat = node_cga.T\n vec = node_FoR_va\n\n LM_C[node_dof:node_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = -np.eye(3)\n vec = node_cga @ ag.skew(node_Ra) @ node_FoR_wa\n\n LM_C[node_dof:node_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n mat = -node_cga.T\n vec = ag.skew(node_Ra) @ node_FoR_wa\n\n LM_C[node_dof:node_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = -np.eye(3)\n vec = FoR_cga @ FoR_va\n\n LM_C[node_dof:node_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n # term 2-x1 - \\frac{\\partial}{\\partial x_1}(b^Taq_1 + b^Tbq2 + b^Tcq3 + b^Tdq4)\n # db^Tdxaq_1 + b^Tdadxaq_1 + db^Tdxbq_2 + b^Tdbdxq_2 + db^Tdxcq_3 + b^Tdcdxq_3 + db^Tdxdq_4\n\n mat = -np.eye(3)\n vec = -node_cga @ node_dot_Ra\n\n LM_C[node_FoR_dof:node_FoR_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n mat = node_cga.T\n vec = node_dot_Ra\n\n LM_C[node_FoR_dof:node_FoR_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = -np.eye(3)\n vec = -node_cga @ node_FoR_va\n\n LM_C[node_FoR_dof:node_FoR_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n mat = node_cga.T\n vec = node_FoR_va\n\n LM_C[node_FoR_dof:node_FoR_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = -np.eye(3)\n vec = node_cga @ ag.skew(node_Ra) @ node_FoR_wa\n\n LM_C[node_FoR_dof:node_FoR_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n mat = -node_cga.T\n vec = ag.skew(node_Ra) @ node_FoR_wa\n\n LM_C[node_FoR_dof:node_FoR_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = -np.eye(3)\n vec = FoR_cga @ FoR_va\n\n LM_C[node_FoR_dof:node_FoR_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n # term 3-x1 - \\frac{\\partial}{\\partial x_1}(c^Taq_1 + c^Tbq2 + c^Tcq3 + c^Tdq4)\n # dc^Tdxaq_1 + c^Tdadxaq_1 + dc^Tdxbq_2 + c^Tdbdxq_2 + dc^Tdxcq_3 + c^Tdcdxq_3 + dc^Tdxdq_4 \n\n mat = ag.skew(node_Ra).T\n vec = -node_cga @ node_dot_Ra\n\n LM_C[node_FoR_dof + 3:node_FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n mat = -ag.skew(node_Ra).T @ node_cga.T\n vec = node_dot_Ra\n\n LM_C[node_FoR_dof + 3:node_FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = ag.skew(node_Ra).T\n vec = -node_cga @ node_FoR_va\n\n LM_C[node_FoR_dof + 3:node_FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n mat = -ag.skew(node_Ra).T @ node_cga.T\n vec = node_FoR_va\n\n LM_C[node_FoR_dof + 3:node_FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = ag.skew(node_Ra).T\n vec = node_cga @ ag.skew(node_Ra) @ node_FoR_wa\n\n LM_C[node_FoR_dof + 3:node_FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n mat = ag.skew(node_Ra).T @ node_cga.T\n vec = ag.skew(node_Ra) @ node_FoR_wa\n\n LM_C[node_FoR_dof + 3:node_FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = ag.skew(node_Ra).T\n vec = FoR_cga @ FoR_va\n\n LM_C[node_FoR_dof + 3:node_FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n # term 4-x1 - \\frac{\\partial}{\\partial x_1}(d^Taq_1 + d^Tbq2 + d^Tcq3 + d^Tdq4) \n # d^Tdadxaq_1 + d^Tdbdxq_2 + d^Tdcdxq_3 \n\n mat = -FoR_cga.T\n vec = node_dot_Ra\n\n LM_C[FoR_dof:FoR_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = -FoR_cga.T\n vec = node_FoR_va\n\n LM_C[FoR_dof:FoR_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = FoR_cga.T\n vec = ag.skew(node_Ra) @ node_FoR_wa\n\n LM_C[FoR_dof:FoR_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n # term 1-x2 - \\frac{\\partial}{\\partial x_2}(a^Taq_1 + a^Tbq2 + a^Tcq3 + a^Tdq4) \n # a^Tdddxq_4\n\n mat = -node_cga.T\n vec = FoR_va\n\n LM_C[node_dof:node_dof + 3, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[FoR_body].quat, vec)\n\n # term 2-x2 - \\frac{\\partial}{\\partial x_2}(b^Taq_1 + b^Tbq2 + b^Tcq3 + b^Tdq4)\n # b^Tdddxq_4\n\n mat = -node_cga.T\n vec = FoR_va\n\n LM_C[node_FoR_dof:node_FoR_dof + 3, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[FoR_body].quat, vec)\n\n # term 3-x2 - \\frac{\\partial}{\\partial x_2}(c^Taq_1 + c^Tbq2 + c^Tcq3 + c^Tdq4)\n # c^Tdddxq_4\n\n mat = ag.skew(node_Ra).T @ node_cga.T\n vec = FoR_va\n\n LM_C[node_FoR_dof + 3:node_FoR_dof + 6, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[FoR_body].quat, vec)\n\n # term 4-x2 - \\frac{\\partial}{\\partial x_2}(d^Taq_1 + d^Tbq2 + d^Tcq3 + d^Tdq4) \n # dd^Tdxaq_1 + dd^Tdxbq_2 + dd^Tdxcq_3 + dd^Tdxdq_4 + d^Tdddxq_4\n\n mat = np.eye(3)\n vec = -node_cga @ node_dot_Ra\n\n LM_C[FoR_dof:FoR_dof + 3, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[FoR_body].quat, vec)\n\n mat = np.eye(3)\n vec = -node_cga @ node_FoR_va\n\n LM_C[FoR_dof:FoR_dof + 3, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[FoR_body].quat, vec)\n\n mat = np.eye(3)\n vec = node_cga @ ag.skew(node_Ra) @ node_FoR_wa\n\n LM_C[FoR_dof:FoR_dof + 3, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[FoR_body].quat, vec)\n\n mat = np.eye(3)\n vec = FoR_cga @ FoR_va\n\n LM_C[FoR_dof:FoR_dof + 3, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[FoR_body].quat, vec)\n\n mat = FoR_cga.T\n vec = FoR_va\n\n LM_C[FoR_dof:FoR_dof + 3, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[FoR_body].quat, vec)\n\n # other LM_K derivatives for a/b/c/d dependencies in Ra\n # term 1-Ra - \\frac{\\partial}{\\partial Ra}(a^Taq_1 + a^Tbq2 + a^Tcq3 + a^Tdq4) \n # a^Tdcdrq_3\n\n mat = -node_cga.T @ node_cga\n vec = node_FoR_wa\n\n LM_K[node_dof:node_dof + 3, node_dof:node_dof + 3] \\\n += penaltyFactor * mat @ ag.der_skewp_v(ag.skew(node_Ra), vec)\n\n # term 2-Ra - \\frac{\\partial}{\\partial Ra}(b^Taq_1 + b^Tbq2 + b^Tcq3 + b^Tdq4)\n # b^Tdcdrq_3\n\n mat = -node_cga.T @ node_cga\n vec = node_FoR_wa\n\n LM_K[node_FoR_dof:node_FoR_dof + 3, node_dof:node_dof + 3] \\\n += penaltyFactor * mat @ ag.der_skewp_v(ag.skew(node_Ra), vec)\n\n # term 3-Ra - \\frac{\\partial}{\\partial Ra}(c^Taq_1 + c^Tbq2 + c^Tcq3 + c^Tdq4)\n # dc^Tdraq_1 + dc^Tdrbq_2 + dc^Tdrcq_3 + c^Tdcdrq_3 + dc^Tdrdq_4\n\n mat = np.eye(3)\n vec = node_cga.T @ -node_cga @ node_dot_Ra\n\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof:node_dof + 3] \\\n += penaltyFactor * mat @ ag.der_skewpT_v(ag.skew(node_Ra), vec)\n\n mat = np.eye(3)\n vec = node_cga.T @ -node_cga @ node_FoR_va\n\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof:node_dof + 3] \\\n += penaltyFactor * mat @ ag.der_skewpT_v(ag.skew(node_Ra), vec)\n\n mat = np.eye(3)\n vec = node_cga.T @ node_cga @ ag.skew(node_Ra) @ node_FoR_wa\n\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof:node_dof + 3] \\\n += penaltyFactor * mat @ ag.der_skewpT_v(ag.skew(node_Ra), vec)\n\n mat = ag.skew(node_Ra).T @ node_cga.T @ node_cga\n vec = node_FoR_wa\n\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof:node_dof + 3] \\\n += penaltyFactor * mat @ ag.der_skewp_v(ag.skew(node_Ra), vec)\n\n mat = np.eye(3)\n vec = node_cga.T @ FoR_cga @ FoR_va\n\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof:node_dof + 3] \\\n += penaltyFactor * mat @ ag.der_skewpT_v(ag.skew(node_Ra), vec)\n\n # term 4-Ra - \\frac{\\partial}{\\partial Ra}(d^Taq_1 + d^Tbq2 + d^Tcq3 + d^Tdq4) \n # d^Tdcdrq_3\n\n mat = FoR_cga.T @ node_cga\n vec = node_FoR_wa\n\n LM_K[FoR_dof:FoR_dof + 3, node_dof:node_dof + 3] \\\n += penaltyFactor * mat @ ag.der_skewp_v(ag.skew(node_Ra), vec)\n\n # a^T -node_cga.T\n # a -node_cga\n # b^T -node_cga.T\n # b -node_cga\n # c^T ag.skew(node_Ra).T, node_cga.T\n # c node_cga, ag.skew(node_Ra)\n # d^T FoR_cga.T\n # d FoR_cga\n # q1 node_dof:node_dof+3 node_dot_Ra\n # q2 node_FoR_dof:node_FoR_dof+3 node_FoR_va\n # q3 node_FoR_dof+3:node_FoR_dof+6 node_FoR_wa\n # q4 FoR_dof:FoR_dof+3 FoR_va\n\n else:\n # TODO: follow general approach to derive terms - first 4*4 terms, then LMC derivatives,\n # then LMK derivatives - this is why penalty didn't work!\n # if A1 is clamped, then remove the related DoFs from the description above (commented sections below)\n\n # Simplify notation\n node_cga = MB_tstep[node_body].cga()\n FoR_cga = MB_tstep[FoR_body].cga()\n psi_dot = MB_tstep[node_body].psi_dot[ielem, inode_in_elem, :]\n\n q = np.zeros((sys_size))\n q[FoR_dof:FoR_dof + 3] = FoR_va\n q[node_dof:node_dof + 3] = node_dot_Ra\n q[node_dof + 3:node_dof + 6] = psi_dot\n\n LM_Q[:sys_size] += penaltyFactor * Bnh.T @ Bnh @ q\n\n # # 16 canonical terms for (abcd)^T(abcd)\n LM_C[:sys_size, :sys_size] += penaltyFactor * Bnh.T @ Bnh\n\n # other LM_C derivatives for c dependencies in x1 and x2\n # term 1-x1 - \\frac{\\partial}{\\partial x_1}(a^Taq_1 + a^Tbq2 + a^Tcq3 + a^Tdq4) \n # da^Tdxaq_1 + a^Tdadxaq_1 + da^Tdxbq_2 + a^Tdbdxq_2 + da^Tdxcq_3 + a^Tdcdxq_3 + da^Tdxdq_4\n\n mat = -np.eye(3)\n vec = -node_cga @ node_dot_Ra\n\n LM_C[node_dof:node_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, ec)\n\n mat = node_cga.T\n vec = node_dot_Ra\n\n LM_C[node_dof:node_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = -np.eye(3)\n vec = FoR_cga @ FoR_va\n\n LM_C[node_dof:node_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n # term 4-x1 - \\frac{\\partial}{\\partial x_1}(d^Taq_1 + d^Tbq2 + d^Tcq3 + d^Tdq4) \n # d^Tdadxaq_1 + d^Tdbdxq_2 + d^Tdcdxq_3 \n\n mat = -FoR_cga.T\n vec = node_dot_Ra\n\n LM_C[FoR_dof:FoR_dof + 3, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n # term 1-x2 - \\frac{\\partial}{\\partial x_2}(a^Taq_1 + a^Tbq2 + a^Tcq3 + a^Tdq4)\n # a^Tdddxq_4\n\n mat = -node_cga.T\n vec = FoR_va\n\n LM_C[node_dof:node_dof + 3, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[FoR_body].quat, vec)\n\n # term 4-x2 - \\frac{\\partial}{\\partial x_2}(d^Taq_1 + d^Tbq2 + d^Tcq3 + d^Tdq4)\n # dd^Tdxaq_1 + dd^Tdxbq_2 + dd^Tdxcq_3 + dd^Tdxdq_4 + d^Tdddxq_4\n\n mat = np.eye(3)\n vec = -node_cga @ node_dot_Ra\n\n LM_C[FoR_dof:FoR_dof + 3, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[FoR_body].quat, vec)\n\n mat = np.eye(3)\n vec = FoR_cga @ FoR_va\n\n LM_C[FoR_dof:FoR_dof + 3, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[FoR_body].quat, vec)\n\n mat = FoR_cga.T\n vec = FoR_va\n\n LM_C[FoR_dof:FoR_dof + 3, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[FoR_body].quat, vec)\n\n # a^T -node_cga.T\n # a -node_cga\n # b^T -node_cga.T\n # b -node_cga\n # c^T ag.skew(node_Ra).T, node_cga.T\n # c node_cga, ag.skew(node_Ra)\n # d^T FoR_cga.T\n # d FoR_cga\n # q1 node_dof:node_dof+3 node_dot_Ra\n # q2 node_FoR_dof:node_FoR_dof+3 node_FoR_va\n # q3 node_FoR_dof+3:node_FoR_dof+6 node_FoR_wa\n # q4 FoR_dof:FoR_dof+3 FoR_va\n\n ieq += 3\n return ieq\n\n\ndef rel_rot_vel_node_FoR(MB_tstep, MB_beam, FoR_body, node_body, node_number, node_FoR_dof, node_dof, FoR_dof, sys_size,\n Lambda_dot, scalingFactor, penaltyFactor, ieq, LM_K, LM_C, LM_Q, rel_vel=np.zeros((3))):\n \"\"\"\n This function generates the stiffness and damping matrices and the independent vector associated to a constraint that\n imposes equal rotation velocities between a node and a frame of reference\n\n See ``LagrangeConstraints`` for the description of variables\n\n Args:\n node_number (int): number of the \"node\" within its own body\n node_body (int): body number of the \"node\"\n node_FoR_dof (int): position of the first degree of freedom of the FoR to which the \"node\" belongs\n node_dof (int): position of the first degree of freedom associated to the \"node\"\n FoR_body (int): body number of the \"FoR\"\n FoR_dof (int): position of the first degree of freedom associated to the \"FoR\"\n rel_vel (np.array): relative velocity FoR-node\n \"\"\"\n\n num_LM_eq_specific = 3\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Simplify notation\n ielem, inode_in_elem = MB_beam[node_body].node_master_elem[node_number]\n node_cga = MB_tstep[node_body].cga()\n node_FoR_wa = MB_tstep[node_body].for_vel[3:6]\n psi = MB_tstep[node_body].psi[ielem, inode_in_elem, :]\n cab = ag.crv2rotation(psi)\n tan = ag.crv2tan(psi)\n\n FoR_cga = MB_tstep[FoR_body].cga()\n FoR_wa = MB_tstep[FoR_body].for_vel[3:6]\n\n Bnh[:, node_dof + 3:node_dof + 6] += tan.copy()\n Bnh[:, FoR_dof + 3:FoR_dof + 6] -= cab.T @ node_cga.T @ FoR_cga\n if MB_beam[node_body].FoR_movement == 'free':\n Bnh[:, node_FoR_dof + 3:node_FoR_dof + 6] += cab.T\n\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += scalingFactor * Bnh.T\n\n LM_Q[:sys_size] += scalingFactor * Bnh.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += scalingFactor * (tan @ MB_tstep[node_body].psi_dot[ielem, inode_in_elem, :]\n + cab.T @ node_FoR_wa - cab.T @ node_cga.T @ FoR_cga @ FoR_wa + rel_vel)\n\n LM_K[node_dof + 3:node_dof + 6, node_dof + 3:node_dof + 6] \\\n += scalingFactor * ag.der_TanT_by_xv(psi, Lambda_dot[ieq:ieq + num_LM_eq_specific])\n if MB_beam[node_body].FoR_movement == 'free':\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += scalingFactor * ag.der_Ccrv_by_v(psi, Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n -= scalingFactor * ag.der_Ccrv_by_v(psi, node_cga @ FoR_cga.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n LM_C[FoR_dof + 3:FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n -= scalingFactor * cab @ ag.der_Cquat_by_v(MB_tstep[node_body].quat,\n FoR_cga.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n LM_C[FoR_dof + 3:FoR_dof + 6, FoR_dof + 6:FoR_dof + 10] \\\n -= scalingFactor * cab @ node_cga @ ag.der_CquatT_by_v(MB_tstep[FoR_body].quat,\n Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n ieq += 3\n return ieq\n\n\ndef def_rot_axis_FoR_wrt_node_general(MB_tstep, MB_beam, FoR_body, node_body, node_number, node_FoR_dof, node_dof,\n FoR_dof, sys_size, Lambda_dot, rot_axisB, rot_axisA2, scalingFactor,\n penaltyFactor, ieq, LM_K, LM_C, LM_Q, indep):\n \"\"\"\n This function generates the stiffness and damping matrices and the independent vector associated to a joint that\n forces the rotation axis of a FoR to be parallel to a certain direction. This direction is defined in the\n B FoR of a node and, thus, might change along the simulation.\n\n See ``LagrangeConstraints`` for the description of variables\n\n Args:\n rot_axisB (np.ndarray): Rotation axis with respect to the node B FoR\n rot_axisA2 (np.ndarray): Rotation axis with respect to the node A2 FoR\n indep (np.ndarray): Number of the equations that are used as independent\n node_number (int): number of the \"node\" within its own body\n node_body (int): body number of the \"node\"\n node_FoR_dof (int): position of the first degree of freedom of the FoR to which the \"node\" belongs\n node_dof (int): position of the first degree of freedom associated to the \"node\"\n FoR_body (int): body number of the \"FoR\"\n FoR_dof (int): position of the first degree of freedom associated to the \"FoR\"\n\n \"\"\"\n\n ielem, inode_in_elem = MB_beam[node_body].node_master_elem[node_number]\n\n # Simplify notation\n cab = ag.crv2rotation(MB_tstep[node_body].psi[ielem, inode_in_elem, :])\n node_cga = MB_tstep[node_body].cga()\n FoR_cga = MB_tstep[FoR_body].cga()\n FoR_wa = MB_tstep[FoR_body].for_vel[3:6]\n node_wa = MB_tstep[node_body].for_vel[3:6]\n psi = MB_tstep[node_body].psi[ielem, inode_in_elem, :]\n psi_dot = MB_tstep[node_body].psi_dot[ielem, inode_in_elem, :]\n\n if MB_beam[node_body].FoR_movement == 'free':\n if not indep:\n aux_Bnh = cab.T @ node_cga.T @ FoR_cga @ ag.skew(rot_axisA2)\n\n # indep = None\n n0 = np.linalg.norm(aux_Bnh[0, :])\n n1 = np.linalg.norm(aux_Bnh[1, :])\n n2 = np.linalg.norm(aux_Bnh[2, :])\n if ((n0 < n1) and (n0 < n2)):\n indep[:] = [1, 2]\n elif ((n1 < n0) and (n1 < n2)):\n indep[:] = [0, 2]\n elif ((n2 < n0) and (n2 < n1)):\n indep[:] = [0, 1]\n\n new_Lambda_dot = np.zeros(3)\n new_Lambda_dot[indep[0]] = Lambda_dot[ieq]\n new_Lambda_dot[indep[1]] = Lambda_dot[ieq + 1]\n\n num_LM_eq_specific = 2\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n Bnh[:, FoR_dof + 3:FoR_dof + 6] -= (cab.T @ node_cga.T @ FoR_cga @ ag.skew(rot_axisA2))[indep, :]\n Bnh[:, node_dof + 3:node_dof + 6] += (ag.skew(rot_axisB) @ ag.crv2tan(psi))[indep, :]\n Bnh[:, node_FoR_dof + 3:node_FoR_dof + 6] += (ag.skew(rot_axisB) @ cab.T)[indep, :]\n\n # Constrain angular velocities\n LM_Q[:sys_size] += scalingFactor * Bnh.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n -= scalingFactor * (cab.T @ node_cga.T @ FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa)[indep]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += scalingFactor * (ag.skew(rot_axisB) @ ag.crv2tan(psi) @ psi_dot)[indep]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += scalingFactor * (ag.skew(rot_axisB) @ cab.T @ MB_tstep[node_body].for_vel[3:6])[indep]\n\n # # for initial omega A2\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += scalingFactor * Bnh.T\n\n # term 3 x1\n LM_C[FoR_dof + 3:FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += scalingFactor * ag.skew(rot_axisA2) @ FoR_cga.T @ ag.der_Cquat_by_v(MB_tstep[node_body].quat,\n cab @ new_Lambda_dot)\n\n # term 3 x2\n LM_C[FoR_dof + 3:FoR_dof + 6, FoR_dof + 6:FoR_dof + 10] \\\n += scalingFactor * ag.skew(rot_axisA2) @ ag.der_CquatT_by_v(MB_tstep[FoR_body].quat,\n node_cga @ cab @ new_Lambda_dot)\n\n # term 3 K(psi)\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += scalingFactor * ag.skew(rot_axisA2) @ FoR_cga.T @ node_cga @ ag.der_CcrvT_by_v(psi, new_Lambda_dot)\n\n LM_K[node_dof + 3:node_dof + 6, node_dof + 3:node_dof + 6] \\\n -= scalingFactor * ag.der_TanT_by_xv(psi, ag.skew(rot_axisB) @ new_Lambda_dot)\n\n # term 1\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n -= scalingFactor * ag.der_Ccrv_by_v(psi, ag.skew(rot_axisB) @ new_Lambda_dot)\n else:\n if not indep:\n aux_Bnh = cab.T @ node_cga.T @ FoR_cga @ ag.skew(rot_axisA2)\n\n # indep = None\n n0 = np.linalg.norm(aux_Bnh[0, :])\n n1 = np.linalg.norm(aux_Bnh[1, :])\n n2 = np.linalg.norm(aux_Bnh[2, :])\n if ((n0 < n1) and (n0 < n2)):\n indep[:] = [1, 2]\n elif ((n1 < n0) and (n1 < n2)):\n indep[:] = [0, 2]\n elif ((n2 < n0) and (n2 < n1)):\n indep[:] = [0, 1]\n\n new_Lambda_dot = np.zeros(3)\n new_Lambda_dot[indep[0]] = Lambda_dot[ieq]\n new_Lambda_dot[indep[1]] = Lambda_dot[ieq + 1]\n\n num_LM_eq_specific = 2\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n Bnh[:, FoR_dof + 3:FoR_dof + 6] -= (cab.T @ node_cga.T @ FoR_cga @ ag.skew(rot_axisA2))[indep, :]\n Bnh[:, node_dof + 3:node_dof + 6] += (ag.skew(rot_axisB) @ ag.crv2tan(psi))[indep, :]\n\n # Constrain angular velocities\n LM_Q[:sys_size] += scalingFactor * Bnh.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n -= scalingFactor * (cab.T @ node_cga.T @ FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa)[indep]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += scalingFactor * (ag.skew(rot_axisB) @ ag.crv2tan(psi) @ psi_dot)[indep]\n\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += scalingFactor * Bnh.T\n\n # term 3 x2\n LM_C[FoR_dof + 3:FoR_dof + 6, FoR_dof + 6:FoR_dof + 10] \\\n += scalingFactor * ag.skew(rot_axisA2) @ ag.der_CquatT_by_v(MB_tstep[FoR_body].quat,\n node_cga @ cab @ new_Lambda_dot)\n\n # term 3 K(psi)\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += scalingFactor * ag.skew(rot_axisA2) @ FoR_cga.T @ node_cga, ag.der_CcrvT_by_v(psi, new_Lambda_dot)\n # term 2\n LM_K[node_dof + 3:node_dof + 6, node_dof + 3:node_dof + 6] \\\n -= scalingFactor * ag.der_TanT_by_xv(psi, ag.skew(rot_axisB) @ new_Lambda_dot)\n\n # TODO: penalty factor formulation to be verified\n if penaltyFactor:\n if MB_beam[node_body].FoR_movement == 'free':\n q = np.zeros((sys_size,))\n q[FoR_dof + 3:FoR_dof + 6] = FoR_wa\n q[node_dof + 3:node_dof + 6] = psi_dot\n q[node_FoR_dof + 3:node_FoR_dof + 6] = node_wa\n\n LM_Q[:sys_size] += penaltyFactor * Bnh.T @ Bnh @ q\n LM_C[:sys_size, :sys_size] += penaltyFactor * Bnh.T @ Bnh\n\n # other LM_K derivatives for a/b/c dependencies in C(psi) and T(psi)\n # term 2-psi - \\frac{\\partial}{\\partial psi}(a^2q_2 + abq_5 + acq_7)\n # da^Tdpsiaq_2 + a^Tdadpsiq_2 + da^Tdpsibq_5 + a^Tdbdpsiq_5 + da^Tdpsicq_7 + a^Tdcdpsiq_7\n\n mat = np.eye(3)\n vec = ag.skew(rot_axisB).T @ ag.skew(rot_axisB) @ cab.T @ node_wa\n\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_Ccrv_by_v(psi, vec)\n\n mat = cab @ ag.skew(rot_axisB).T @ ag.skew(rot_axisB)\n vec = node_wa\n\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_CcrvT_by_v(psi, vec)\n\n mat = np.eye(3)\n vec = ag.skew(rot_axisB).T @ ag.skew(rot_axisB) @ ag.crv2tan(psi) @ psi_dot\n\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_Ccrv_by_v(psi, vec)\n\n mat = cab @ ag.skew(rot_axisB).T @ ag.skew(rot_axisB)\n vec = psi_dot\n\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_Tan_by_xv(psi, vec)\n\n mat = np.eye(3)\n vec = ag.skew(rot_axisB).T @ -cab.T @ node_cga.T @ FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa\n\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_Ccrv_by_v(psi, vec)\n\n mat = -cab @ ag.skew(rot_axisB).T\n vec = node_cga.T @ FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa\n\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_CcrvT_by_v(psi, vec)\n\n # term 5-psi - \\frac{\\partial}{\\partial psi}(ba q_2 + b^2 q_5 + bc q_7)\n # db^Tdpsiaq_2 + b^Tdadpsiq_2 + db^Tdpsibq_5 + b^Tdbdpsiq_5 + db^Tdpsicq_7 + b^Tdcdpsiq_7\n\n mat = np.eye(3)\n vec = ag.skew(rot_axisB).T @ ag.skew(rot_axisB) @ cab.T @ node_wa\n\n LM_K[node_dof + 3:node_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_TanT_by_xv(psi, vec)\n\n mat = ag.crv2tan(psi).T @ ag.skew(rot_axisB).T @ ag.skew(rot_axisB)\n vec = node_wa\n\n LM_K[node_dof + 3:node_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_CcrvT_by_v(psi, vec)\n\n mat = np.eye(3)\n vec = ag.skew(rot_axisB).T @ ag.skew(rot_axisB) @ ag.crv2tan(psi) @ psi_dot\n\n LM_K[node_dof + 3:node_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_TanT_by_xv(psi, vec)\n\n mat = ag.crv2tan(psi).T @ ag.skew(rot_axisB).T @ ag.skew(rot_axisB)\n vec = psi_dot\n\n LM_K[node_dof + 3:node_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_Tan_by_xv(psi, vec)\n\n mat = np.eye(3)\n vec = ag.skew(rot_axisB).T @ -cab.T @ node_cga.T @ FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa\n\n LM_K[node_dof + 3:node_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_TanT_by_xv(psi, vec)\n\n mat = -ag.crv2tan(psi).T @ ag.skew(rot_axisB).T\n vec = node_cga.T @ FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa\n\n LM_K[node_dof + 3:node_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_CcrvT_by_v(psi, vec)\n\n # term 7-psi - \\frac{\\partial}{\\partial psi}(ca q_2 + cb q_5 + c^2 q_7)\n # dc^Tdpsiaq_2 + c^Tdadpsiq_2 + dc^Tdpsibq_5 + c^Tdbdpsiq_5 + dc^Tdpsicq_7 + c^Tdcdpsiq_7\n\n mat = -ag.skew(rot_axisA2).T @ FoR_cga.T @ node_cga\n vec = ag.skew(rot_axisB) @ cab.T @ node_wa\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_Ccrv_by_v(psi, vec)\n\n mat = -ag.skew(rot_axisA2).T @ FoR_cga.T @ node_cga @ cab @ ag.skew(rot_axisB)\n vec = node_wa\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_CcrvT_by_v(psi, vec)\n\n mat = -ag.skew(rot_axisA2).T @ FoR_cga.T @ node_cga\n vec = ag.skew(rot_axisB) @ ag.crv2tan(psi) @ psi_dot\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_Ccrv_by_v(psi, vec)\n\n mat = -ag.skew(rot_axisA2).T @ FoR_cga.T @ node_cga @ cab @ ag.skew(rot_axisB)\n vec = psi_dot\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_Tan_by_xv(psi, vec)\n\n mat = -ag.skew(rot_axisA2).T @ FoR_cga.T @ node_cga\n vec = -cab.T @ node_cga.T @ FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_Ccrv_by_v(psi, vec)\n\n mat = ag.skew(rot_axisA2).T @ FoR_cga.T @ node_cga @ cab\n vec = node_cga.T @ FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_CcrvT_by_v(psi, vec)\n\n # a^T cab, ag.skew(rot_axisB).T\n # a ag.skew(rot_axisB), cab.T\n # b^T ag.crv2tan(psi).T, ag.skew(rot_axisB).T\n # b ag.skew(rot_axisB), ag.crv2tan(psi)\n # c^T -ag.skew(rot_axisA2).T, FoR_cga.T, node_cga, cab\n # c -cab.T, node_cga.T, FoR_cga, ag.skew(rot_axisA2)\n\n else:\n q = np.zeros((sys_size,))\n q[FoR_dof + 3:FoR_dof + 6] = MB_tstep[FoR_body].for_vel[3:6]\n q[node_dof + 3:node_dof + 6] = psi_dot\n\n LM_Q[:sys_size] += penaltyFactor * Bnh.T @ Bnh @ q\n LM_C[:sys_size, :sys_size] += penaltyFactor * Bnh.T @ Bnh\n\n # term 5-x1 - \\frac{\\partial}{\\partial x1}(b^2 q_5 + bc q_7)\n # b^Tdcdx1q_7\n\n mat = ag.crv2tan(psi).T @ ag.skew(rot_axisB).T @ -cab.T\n vec = FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa\n\n LM_C[node_dof + 3:node_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n # term 5-x2 - \\frac{\\partial}{\\partial x2}(b^2 q_5 + bc q_7)\n # b^Tdcdx2q_7\n\n mat = ag.crv2tan(psi).T @ ag.skew(rot_axisB).T @ -cab.T @ node_cga.T\n vec = ag.skew(rot_axisA2) @ FoR_wa\n\n LM_C[node_dof + 3:node_dof + 6, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[FoR_body].quat, vec)\n\n # term 7-x1 - \\frac{\\partial}{\\partial x1}(cb q_5 + c^2 q_7)\n # dc^Tdx1aq_2 -> 0!!! + dc^Tdx1bq_5 + dc^Tdx1cq_7 + c^Tdcdx1q_7\n\n mat = -ag.skew(rot_axisA2).T @ FoR_cga.T\n vec = cab @ ag.skew(rot_axisB) @ ag.crv2tan(psi) @ psi_dot\n\n LM_C[FoR_dof + 3:FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = -ag.skew(rot_axisA2).T @ FoR_cga.T\n vec = cab @ -cab.T @ node_cga.T @ FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa\n\n LM_C[FoR_dof + 3:FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = -ag.skew(rot_axisA2).T @ FoR_cga.T @ node_cga @ cab @ -cab.T\n vec = FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa\n\n LM_C[FoR_dof + 3:FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n # term 7-x2 - \\frac{\\partial}{\\partial x2}(cb q_5 + c^2 q_7)\n # dc^Tdx2aq_2 -> 0!!! + dc^Tdx2bq_5 + dc^Tdx2cq_7 + c^Tdcdx2q_7\n\n mat = -ag.skew(rot_axisA2).T\n vec = node_cga @ cab @ ag.skew(rot_axisB) @ ag.crv2tan(psi) @ psi_dot\n\n LM_C[FoR_dof + 3:FoR_dof + 6, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[FoR_body].quat, vec)\n\n mat = -ag.skew(rot_axisA2).T\n vec = node_cga @ cab @ -cab.T @ node_cga.T @ FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa\n\n LM_C[FoR_dof + 3:FoR_dof + 6, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[FoR_body].quat, vec)\n\n mat = -ag.skew(rot_axisA2).T @ FoR_cga.T @ node_cga @ cab @ -cab.T @ node_cga.T\n vec = ag.skew(rot_axisA2) @ FoR_wa\n\n LM_C[FoR_dof + 3:FoR_dof + 6, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[FoR_body].quat, vec)\n\n # other LM_K derivatives for a/b/c dependencies in C(psi) and T(psi)\n\n mat = np.eye(3)\n vec = ag.skew(rot_axisB).T @ ag.skew(rot_axisB) @ ag.crv2tan(psi) @ psi_dot\n\n LM_K[node_dof + 3:node_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_TanT_by_xv(psi, vec)\n\n mat = ag.crv2tan(psi).T @ ag.skew(rot_axisB).T @ ag.skew(rot_axisB)\n vec = psi_dot\n\n LM_K[node_dof + 3:node_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_Tan_by_xv(psi, vec)\n\n mat = np.eye(3)\n vec = ag.skew(rot_axisB).T @ -cab.T @ node_cga.T @ FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa\n\n LM_K[node_dof + 3:node_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_TanT_by_xv(psi, vec)\n\n mat = -ag.crv2tan(psi).T @ ag.skew(rot_axisB).T\n vec = node_cga.T @ FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa\n\n LM_K[node_dof + 3:node_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_CcrvT_by_v(psi, vec)\n\n # term 7-psi - \\frac{\\partial}{\\partial psi}(cb q_5 + c^2 q_7)\n # dc^Tdpsiaq_2 -> 0!!! + c^Tdadpsiq_2 -> 0!!! + dc^Tdpsibq_5 + c^Tdbdpsiq_5 + dc^Tdpsicq_7 + c^Tdcdpsiq_7\n\n mat = -ag.skew(rot_axisA2).T @ FoR_cga.T @ node_cga\n vec = ag.skew(rot_axisB) @ ag.crv2tan(psi) @ psi_dot\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_Ccrv_by_v(psi, vec)\n\n mat = -ag.skew(rot_axisA2).T @ FoR_cga.T @ node_cga @ cab @ ag.skew(rot_axisB)\n vec = psi_dot\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_Tan_by_xv(psi, vec)\n\n mat = -ag.skew(rot_axisA2).T @ FoR_cga.T @ node_cga\n vec = -cab.T @ node_cga.T @ FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_Ccrv_by_v(psi, vec)\n\n mat = ag.skew(rot_axisA2).T @ FoR_cga.T @ node_cga @ cab\n vec = node_cga.T @ FoR_cga @ ag.skew(rot_axisA2) @ FoR_wa\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_CcrvT_by_v(psi, vec)\n\n # a^T cab, ag.skew(rot_axisB).T\n # a ag.skew(rot_axisB), cab.T\n # b^T ag.crv2tan(psi).T, ag.skew(rot_axisB).T\n # b ag.skew(rot_axisB), ag.crv2tan(psi)\n # c^T -ag.skew(rot_axisA2).T, FoR_cga.T, node_cga, cab\n # c -cab.T, node_cga.T, FoR_cga, ag.skew(rot_axisA2)\n\n ieq += 2\n return ieq\n\n\ndef def_rot_axis_FoR_wrt_node_xyz(MB_tstep, MB_beam, FoR_body, node_body, node_number, node_FoR_dof, node_dof, FoR_dof,\n sys_size, Lambda_dot, rot_axisB, scalingFactor, penaltyFactor, ieq, LM_K, LM_C, LM_Q,\n zero_comp):\n \"\"\"\n This function generates the stiffness and damping matrices and the independent vector associated to a joint that\n forces the rotation axis of a FoR to be parallel to a certain direction. This direction is defined in the\n B FoR of a node and parallel to x, y or z\n\n See ``LagrangeConstraints`` for the description of variables\n\n Args:\n rot_axisB (np.ndarray): Rotation axis with respect to the node B FoR\n indep (np.ndarray): Number of the equations that are used as independent\n node_number (int): number of the \"node\" within its own body\n node_body (int): body number of the \"node\"\n node_FoR_dof (int): position of the first degree of freedom of the FoR to which the \"node\" belongs\n node_dof (int): position of the first degree of freedom associated to the \"node\"\n FoR_body (int): body number of the \"FoR\"\n FoR_dof (int): position of the first degree of freedom associated to the \"FoR\"\n \"\"\"\n\n ielem, inode_in_elem = MB_beam[node_body].node_master_elem[node_number]\n\n num_LM_eq_specific = 2\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Simplify notation\n cab = ag.crv2rotation(MB_tstep[node_body].psi[ielem, inode_in_elem, :])\n node_cga = MB_tstep[node_body].cga()\n FoR_cga = MB_tstep[FoR_body].cga()\n FoR_wa = MB_tstep[FoR_body].for_vel[3:6]\n psi = MB_tstep[node_body].psi[ielem, inode_in_elem, :]\n psi_dot = MB_tstep[node_body].psi_dot[ielem, inode_in_elem, :]\n\n # Components to be zero\n Z = np.zeros((2, 3))\n Z[:, zero_comp] = np.eye(2)\n\n Bnh[:, FoR_dof + 3:FoR_dof + 6] += Z @ cab.T @ node_cga.T @ FoR_cga\n Bnh[:, node_dof + 3:node_dof + 6] -= Z @ ag.crv2tan(psi)\n Bnh[:, node_FoR_dof + 3:node_FoR_dof + 6] -= Z @ cab.T\n\n # Constrain angular velocities\n LM_Q[:sys_size] += scalingFactor * Bnh.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += scalingFactor * Z @ cab.T @ node_cga.T @ FoR_cga @ FoR_wa\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n -= scalingFactor * Z @ ag.crv2tan(psi) @ psi_dot\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n -= scalingFactor * Z @ cab.T @ MB_tstep[node_body].for_vel[3:6]\n\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += scalingFactor * Bnh.T\n\n vec = node_cga @ cab @ Z.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_C[FoR_dof + 3:FoR_dof + 6, FoR_dof + 6:FoR_dof + 10] \\\n += scalingFactor * ag.der_CquatT_by_v(MB_tstep[FoR_body].quat, vec)\n\n if MB_beam[node_body].FoR_movement == 'free':\n vec = cab @ Z.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_C[FoR_dof + 3:FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += scalingFactor * FoR_cga.T @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += scalingFactor * FoR_cga.T @ node_cga @ ag.der_Ccrv_by_v(MB_tstep[node_body].psi[ielem, inode_in_elem, :],\n Z.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n LM_K[node_dof + 3:node_dof + 6, node_dof + 3:node_dof + 6] \\\n -= scalingFactor * ag.der_TanT_by_xv(psi, Z.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific])\n LM_K[node_FoR_dof + 3:node_FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n -= scalingFactor * ag.der_Ccrv_by_v(psi, Z.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n if penaltyFactor:\n q = np.zeros((sys_size,))\n q[FoR_dof + 3:FoR_dof + 6] = FoR_wa\n\n LM_Q[:sys_size] += penaltyFactor * Bnh.T @ Bnh @ q\n LM_C[:sys_size, :sys_size] += penaltyFactor * Bnh.T @ Bnh\n\n ZTZ = Z.T @ Z\n\n # Derivatives with the quaternion of the FoR\n vec = node_cga @ cab @ ZTZ @ cab.T @ node_cga.T @ FoR_cga @ FoR_wa\n LM_C[FoR_dof + 3:FoR_dof + 6, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * ag.der_CquatT_by_v(MB_tstep[FoR_body].quat, vec)\n\n mat = FoR_cga.T @ node_cga @ cab @ ZTZ @ cab.T @ node_cga.T\n LM_C[FoR_dof + 3:FoR_dof + 6, FoR_dof + 6:FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_Cquat_by_v(MB_tstep[FoR_body].quat, FoR_wa)\n\n if MB_beam[node_body].FoR_movement == 'free':\n # Derivatives with the quaternion of the FoR of the node\n vec = cab @ ZTZ @ cab.T @ node_cga.T @ FoR_cga @ FoR_wa\n LM_C[FoR_dof + 3:FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * FoR_cga.T @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n mat = FoR_cga.T @ node_cga @ cab @ ZTZ @ cab.T\n vec = FoR_cga @ FoR_wa\n LM_C[FoR_dof + 3:FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += penaltyFactor * mat @ ag.der_CquatT_by_v(MB_tstep[node_body].quat, vec)\n\n # Derivatives with the CRV\n mat = FoR_cga.T @ node_cga\n vec = ZTZ @ cab.T @ node_cga.T @ FoR_cga @ FoR_wa\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_Ccrv_by_v(MB_tstep[node_body].psi[ielem, inode_in_elem, :], vec)\n\n mat = FoR_cga.T @ node_cga @ cab @ ZTZ\n vec = node_cga.T @ FoR_cga @ FoR_wa\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += penaltyFactor * mat @ ag.der_CcrvT_by_v(MB_tstep[node_body].psi[ielem, inode_in_elem, :], vec)\n\n ieq += 2\n return ieq\n\n\ndef def_rot_vel_mod_FoR_wrt_node(MB_tstep, MB_beam, FoR_body, node_body, node_number, node_FoR_dof, node_dof, FoR_dof,\n sys_size, Lambda_dot, nonzero_comp, rot_vel, scalingFactor, penaltyFactor, ieq, LM_K,\n LM_C, LM_Q):\n \"\"\"\n This function generates the stiffness and damping matrices and the independent vector associated to a joint that\n forces the rotation velocity of a FoR with respect to a node\n\n See ``LagrangeConstraints`` for the description of variables\n\n Args:\n nonzero_comp (int): Component of the rotation axis with respect to the node B FoR which is non-zero\n rot_vel (float): Rotation velocity\n node_number (int): number of the \"node\" within its own body\n node_body (int): body number of the \"node\"\n node_FoR_dof (int): position of the first degree of freedom of the FoR to which the \"node\" belongs\n node_dof (int): position of the first degree of freedom associated to the \"node\"\n FoR_body (int): body number of the \"FoR\"\n FoR_dof (int): position of the first degree of freedom associated to the \"FoR\"\n \"\"\"\n\n ielem, inode_in_elem = MB_beam[node_body].node_master_elem[node_number]\n num_LM_eq_specific = 1\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Simplify notation\n cab = ag.crv2rotation(MB_tstep[node_body].psi[ielem, inode_in_elem, :])\n node_cga = MB_tstep[node_body].cga()\n FoR_cga = MB_tstep[FoR_body].cga()\n FoR_wa = MB_tstep[FoR_body].for_vel[3:6]\n\n # Components to be zero\n Znon = np.zeros((1, 3))\n Znon[:, nonzero_comp] = 1\n\n Bnh[:, FoR_dof + 3:FoR_dof + 6] += Znon @ cab.T @ node_cga.T @ FoR_cga\n\n # Constrain angular velocities\n LM_Q[:sys_size] += scalingFactor * Bnh.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += scalingFactor * Znon @ cab.T @ node_cga.T @ FoR_cga @ FoR_wa\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] -= scalingFactor * rot_vel\n\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += scalingFactor * Bnh.T\n\n vec = node_cga @ cab @ Znon.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_C[FoR_dof + 3:FoR_dof + 6, FoR_dof + 6:FoR_dof + 10] \\\n += scalingFactor * ag.der_CquatT_by_v(MB_tstep[FoR_body].quat, vec)\n\n if MB_beam[node_body].FoR_movement == 'free':\n vec = cab @ Znon.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_C[FoR_dof + 3:FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += scalingFactor * FoR_cga.T @ ag.der_Cquat_by_v(MB_tstep[node_body].quat, vec)\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += scalingFactor * FoR_cga.T @ node_cga @ ag.der_Ccrv_by_v(MB_tstep[node_body].psi[ielem, inode_in_elem, :],\n Znon.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n ieq += 1\n return ieq\n\n\ndef def_rot_vect_FoR_wrt_node(MB_tstep, MB_beam, FoR_body, node_body, node_number, node_FoR_dof, node_dof, FoR_dof,\n sys_size, Lambda_dot, rot_vect, scalingFactor, penaltyFactor, ieq, LM_K, LM_C, LM_Q):\n \"\"\"\n This function fixes the rotation velocity VECTOR of a FOR equal to a velocity vector defined in the B FoR of a node\n This function is a new implementation that combines and simplifies the use of 'def_rot_vel_mod_FoR_wrt_node' and 'def_rot_axis_FoR_wrt_node' together\n \"\"\"\n\n num_LM_eq_specific = 3\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Simplify notation\n ielem, inode_in_elem = MB_beam[node_body].node_master_elem[node_number]\n node_cga = MB_tstep[node_body].cga()\n cab = ag.crv2rotation(MB_tstep[node_body].psi[ielem, inode_in_elem, :])\n FoR_cga = MB_tstep[FoR_body].cga()\n FoR_wa = MB_tstep[FoR_body].for_vel[3:6]\n\n Bnh[:, FoR_dof + 3:FoR_dof + 6] = cab.T @ node_cga.T @ FoR_cga\n\n # Constrain angular velocities\n LM_Q[:sys_size] += scalingFactor * Bnh.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += scalingFactor * (Bnh[:, FoR_dof + 3:FoR_dof + 6] @ FoR_wa - rot_vect)\n\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += scalingFactor * Bnh.T\n\n if MB_beam[node_body].FoR_movement == 'free':\n LM_C[FoR_dof + 3:FoR_dof + 6, node_FoR_dof + 6:node_FoR_dof + 10] \\\n += scalingFactor * FoR_cga.T @ ag.der_Cquat_by_v(MB_tstep[node_body].quat,\n cab @ Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n LM_C[FoR_dof + 3:FoR_dof + 6, FoR_dof + 6:FoR_dof + 10] \\\n += scalingFactor * ag.der_CquatT_by_v(MB_tstep[FoR_body].quat,\n node_cga @ cab @ Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof + 3:node_dof + 6] \\\n += scalingFactor * FoR_cga.T @ node_cga @ ag.der_Ccrv_by_v(MB_tstep[node_body].psi[ielem, inode_in_elem, :],\n Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n if penaltyFactor:\n LM_C[FoR_dof + 3:FoR_dof + 6, FoR_dof + 3:FoR_dof + 6] += penaltyFactor * np.eye(3)\n\n q = np.zeros(sys_size)\n q[FoR_dof + 3:FoR_dof + 6] = FoR_wa\n LM_Q[:sys_size] += penaltyFactor * Bnh.T @ Bnh @ q\n\n ieq += 3\n return ieq\n\n\n################################################################################\n# Lagrange constraints\n################################################################################\n@lagrangeconstraint\nclass hinge_node_FoR(BaseLagrangeConstraint):\n __doc__ = \"\"\"\n hinge_node_FoR\n\n This constraint forces a hinge behaviour between a node and a FoR\n\n See ``LagrangeConstraints`` for the description of variables\n\n Attributes:\n node_number (int): number of the \"node\" within its own body\n node_body (int): body number of the \"node\"\n FoR_body (int): body number of the \"FoR\"\n rot_axisB (np.ndarray): Rotation axis with respect to the node B FoR\n rot_axisA2 (np.ndarray): Rotation axis with respect to the node A2 FoR\n \"\"\"\n _lc_id = 'hinge_node_FoR'\n\n def __init__(self):\n self.required_parameters = ['node_in_body', 'body', 'body_FoR', 'rot_axisB']\n self._n_eq = 5\n\n def get_n_eq(self):\n return self._n_eq\n\n def initialise(self, MBdict_entry, ieq, print_info=True):\n self.node_number = MBdict_entry['node_in_body']\n self.node_body = MBdict_entry['body']\n self.FoR_body = MBdict_entry['body_FoR']\n self.rot_axisB = MBdict_entry['rot_axisB']\n self.rot_axisA2 = set_value_or_default(MBdict_entry, \"rot_axisA2\", self.rot_axisB)\n self._ieq = ieq\n self.scalingFactor = set_value_or_default(MBdict_entry, \"scalingFactor\", 1.)\n self.penaltyFactor = set_value_or_default(MBdict_entry, \"penaltyFactor\", 0.)\n self.indep = []\n if (self.rot_axisB[[1, 2]] == 0).all():\n self.rot_dir = 'x'\n self.zero_comp = np.array([1, 2], dtype=int)\n elif (self.rot_axisB[[0, 2]] == 0).all():\n self.rot_dir = 'y'\n self.zero_comp = np.array([0, 2], dtype=int)\n elif (self.rot_axisB[[0, 1]] == 0).all():\n self.rot_dir = 'z'\n self.zero_comp = np.array([0, 1], dtype=int)\n else:\n # raise NotImplementedError(\"Hinges should be parallel to the xB, yB or zB of the reference node\")\n self.rot_dir = 'general'\n self.indep = []\n\n return self._ieq + self._n_eq\n\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n return\n\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n\n # Define the position of the first degree of freedom associated to the node\n node_dof = define_node_dof(MB_beam, self.node_body, self.node_number)\n node_FoR_dof = define_FoR_dof(MB_beam, self.node_body)\n FoR_dof = define_FoR_dof(MB_beam, self.FoR_body)\n ieq = self._ieq\n\n # Define the equations\n ieq = equal_lin_vel_node_FoR(MB_tstep, MB_beam, self.FoR_body, self.node_body, self.node_number, node_FoR_dof,\n node_dof, FoR_dof, sys_size, Lambda_dot, self.scalingFactor, self.penaltyFactor,\n ieq, LM_K, LM_C, LM_Q)\n ieq = def_rot_axis_FoR_wrt_node_general(MB_tstep, MB_beam, self.FoR_body, self.node_body, self.node_number,\n node_FoR_dof, node_dof, FoR_dof, sys_size, Lambda_dot, self.rot_axisB,\n self.rot_axisA2, self.scalingFactor, self.penaltyFactor, ieq, LM_K,\n LM_C, LM_Q, self.indep)\n\n return\n\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n MB_tstep[self.FoR_body].for_pos[:3] \\\n = (MB_tstep[self.node_body].cga() @ MB_tstep[self.node_body].pos[self.node_number, :]\n + MB_tstep[self.node_body].for_pos[:3])\n return\n\n\n@lagrangeconstraint\nclass hinge_node_FoR_constant_vel(BaseLagrangeConstraint):\n __doc__ = \"\"\"\n hinge_node_FoR_constant_vel\n\n This constraint forces a hinge behaviour between a node and a FoR and\n a constant rotation velocity at the join\n\n See ``LagrangeConstraints`` for the description of variables\n\n Attributes:\n node_number (int): number of the \"node\" within its own body\n node_body (int): body number of the \"node\"\n FoR_body (int): body number of the \"FoR\"\n rot_vect (np.ndarray): Rotation velocity vector in the node B FoR\n rel_posB (np.ndarray): Relative position between the node and the frame of reference in the node B FoR\n \"\"\"\n _lc_id = 'hinge_node_FoR_constant_vel'\n\n def __init__(self):\n self.required_parameters = ['node_in_body', 'body', 'body_FoR', 'rot_vect', 'rel_posB']\n self._n_eq = 6\n\n def get_n_eq(self):\n return self._n_eq\n\n def initialise(self, MBdict_entry, ieq, print_info=True):\n\n self.node_number = MBdict_entry['node_in_body']\n self.node_body = MBdict_entry['body']\n self.FoR_body = MBdict_entry['body_FoR']\n self.rel_posB = MBdict_entry['rel_posB']\n self._ieq = ieq\n self.indep = []\n self.scalingFactor = set_value_or_default(MBdict_entry, \"scalingFactor\", 1.)\n self.penaltyFactor = set_value_or_default(MBdict_entry, \"penaltyFactor\", 0.)\n\n self.rot_axisB = ag.unit_vector(MBdict_entry['rot_vect'])\n if (self.rot_axisB[[1, 2]] == 0).all():\n self.rot_dir = 'x'\n self.zero_comp = np.array([1, 2], dtype=int)\n self.nonzero_comp = 0\n elif (self.rot_axisB[[0, 2]] == 0).all():\n self.rot_dir = 'y'\n self.zero_comp = np.array([0, 2], dtype=int)\n self.nonzero_comp = 1\n elif (self.rot_axisB[[0, 1]] == 0).all():\n self.rot_dir = 'z'\n self.zero_comp = np.array([0, 1], dtype=int)\n self.nonzero_comp = 2\n else:\n raise NotImplementedError(\"Hinges should be parallel to the xB, yB or zB of the reference node\")\n self.set_rot_vel(MBdict_entry['rot_vect'][self.nonzero_comp])\n\n return self._ieq + self._n_eq\n\n def set_rot_vel(self, rot_vel):\n self.rot_vel = rot_vel\n\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n return\n\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n\n # Define the position of the first degree of freedom associated to the node\n node_dof = define_node_dof(MB_beam, self.node_body, self.node_number)\n node_FoR_dof = define_FoR_dof(MB_beam, self.node_body)\n FoR_dof = define_FoR_dof(MB_beam, self.FoR_body)\n ieq = self._ieq\n\n # Define the equations\n ieq = equal_lin_vel_node_FoR(MB_tstep, MB_beam, self.FoR_body, self.node_body, self.node_number, node_FoR_dof,\n node_dof, FoR_dof, sys_size, Lambda_dot, self.scalingFactor, self.penaltyFactor,\n ieq, LM_K, LM_C, LM_Q, rel_posB=self.rel_posB)\n ieq = def_rot_axis_FoR_wrt_node_xyz(MB_tstep, MB_beam, self.FoR_body, self.node_body, self.node_number,\n node_FoR_dof, node_dof, FoR_dof, sys_size, Lambda_dot, self.rot_axisB,\n self.scalingFactor, self.penaltyFactor, ieq, LM_K, LM_C, LM_Q,\n self.zero_comp)\n ieq = def_rot_vel_mod_FoR_wrt_node(MB_tstep, MB_beam, self.FoR_body, self.node_body, self.node_number,\n node_FoR_dof, node_dof, FoR_dof, sys_size, Lambda_dot, self.nonzero_comp,\n self.rot_vel, self.scalingFactor, self.penaltyFactor, ieq, LM_K, LM_C, LM_Q)\n return\n\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n\n ielem, inode_in_elem = MB_beam[self.node_body].node_master_elem[self.node_number]\n node_cga = MB_tstep[self.node_body].cga()\n cab = ag.crv2rotation(MB_tstep[self.node_body].psi[ielem, inode_in_elem, :])\n\n MB_tstep[self.FoR_body].for_pos[:3] = (node_cga @ MB_tstep[self.node_body].pos[self.node_number, :]\n + cab @ self.rel_posB + MB_tstep[self.node_body].for_pos[0:3])\n return\n\n\n@lagrangeconstraint\nclass hinge_node_FoR_pitch(BaseLagrangeConstraint):\n __doc__ = \"\"\"\n hinge_node_FoR_pitch\n\n This constraint forces a hinge behaviour between a node and a FoR and\n a rotation velocity at the joint\n\n See ``LagrangeConstraints`` for the description of variables\n\n Attributes:\n node_number (int): number of the \"node\" within its own body\n node_body (int): body number of the \"node\"\n FoR_body (int): body number of the \"FoR\"\n rot_vect (np.ndarray): Rotation velocity vector in the node B FoR\n rel_posB (np.ndarray): Relative position between the node and the frame of reference in the node B FoR\n \"\"\"\n _lc_id = 'hinge_node_FoR_pitch'\n\n def __init__(self):\n self.required_parameters = ['node_in_body', 'body', 'body_FoR', 'rotor_vel', 'rel_posB']\n self._n_eq = 6\n\n def get_n_eq(self):\n return self._n_eq\n\n def initialise(self, MBdict_entry, ieq, print_info=True):\n self.node_number = MBdict_entry['node_in_body']\n self.node_body = MBdict_entry['body']\n self.FoR_body = MBdict_entry['body_FoR']\n self.rel_posB = MBdict_entry['rel_posB']\n self._ieq = ieq\n self.indep = []\n self.scalingFactor = set_value_or_default(MBdict_entry, \"scalingFactor\", 1.)\n self.penaltyFactor = set_value_or_default(MBdict_entry, \"penaltyFactor\", 0.)\n\n self.set_rotor_vel(MBdict_entry['rotor_vel'])\n pitch_vel = set_value_or_default(MBdict_entry, \"pitch_vel\", 0.)\n self.set_pitch_vel(pitch_vel)\n\n return self._ieq + self._n_eq\n\n def set_rotor_vel(self, rotor_vel):\n self.rotor_vel = rotor_vel\n\n def set_pitch_vel(self, pitch_vel):\n self.pitch_vel = pitch_vel\n\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n return\n\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n # Define the position of the first degree of freedom associated to the node\n node_dof = define_node_dof(MB_beam, self.node_body, self.node_number)\n node_FoR_dof = define_FoR_dof(MB_beam, self.node_body)\n FoR_dof = define_FoR_dof(MB_beam, self.FoR_body)\n ieq = self._ieq\n\n # Compute relative velocity\n ielem, inode_in_elem = MB_beam[self.node_body].node_master_elem[self.node_number]\n node_cga = MB_tstep[self.node_body].cga()\n cab = ag.crv2rotation(MB_tstep[self.node_body].psi[ielem, inode_in_elem, :])\n FoR_cga = MB_tstep[self.FoR_body].cga()\n\n # rel_vel in B FoR\n rel_vel = np.array([0., 0., self.rotor_vel])\n rel_vel += cab.T @ node_cga.T @ FoR_cga @ np.array([self.pitch_vel, 0., 0.])\n\n # Define the equations\n ieq = equal_lin_vel_node_FoR(MB_tstep, MB_beam, self.FoR_body, self.node_body, self.node_number, node_FoR_dof,\n node_dof, FoR_dof, sys_size, Lambda_dot, self.scalingFactor, self.penaltyFactor,\n ieq, LM_K, LM_C, LM_Q, rel_posB=self.rel_posB)\n ieq = rel_rot_vel_node_FoR(MB_tstep, MB_beam, self.FoR_body, self.node_body, self.node_number, node_FoR_dof,\n node_dof, FoR_dof, sys_size, Lambda_dot, self.scalingFactor, self.penaltyFactor, ieq,\n LM_K, LM_C, LM_Q, rel_vel=rel_vel)\n return\n\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n ielem, inode_in_elem = MB_beam[self.node_body].node_master_elem[self.node_number]\n node_cga = MB_tstep[self.node_body].cga()\n cab = ag.crv2rotation(MB_tstep[self.node_body].psi[ielem, inode_in_elem, :])\n\n MB_tstep[self.FoR_body].for_pos[:3] = node_cga @ (MB_tstep[self.node_body].pos[self.node_number, :]\n + cab @ self.rel_posB) + MB_tstep[self.node_body].for_pos[:3]\n\n return\n\n\n@lagrangeconstraint\nclass spherical_node_FoR(BaseLagrangeConstraint):\n __doc__ = \"\"\"\n spherical_node_FoR\n\n This constraint forces a spherical join between a node and a FoR\n\n See ``LagrangeConstraints`` for the description of variables\n\n Attributes:\n node_number (int): number of the \"node\" within its own body\n node_body (int): body number of the \"node\"\n FoR_body (int): body number of the \"FoR\"\n \"\"\"\n _lc_id = 'spherical_node_FoR'\n\n def __init__(self):\n self.required_parameters = ['node_in_body', 'body', 'body_FoR']\n self._n_eq = 3\n\n def get_n_eq(self):\n return self._n_eq\n\n def initialise(self, MBdict_entry, ieq, print_info=True):\n self.node_number = MBdict_entry['node_in_body']\n self.node_body = MBdict_entry['body']\n self.FoR_body = MBdict_entry['body_FoR']\n self._ieq = ieq\n self.scalingFactor = set_value_or_default(MBdict_entry, \"scalingFactor\", 1.)\n self.penaltyFactor = set_value_or_default(MBdict_entry, \"penaltyFactor\", 0.)\n\n return self._ieq + self._n_eq\n\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n return\n\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n # Define the position of the first degree of freedom associated to the node\n node_dof = define_node_dof(MB_beam, self.node_body, self.node_number)\n node_FoR_dof = define_FoR_dof(MB_beam, self.node_body)\n FoR_dof = define_FoR_dof(MB_beam, self.FoR_body)\n ieq = self._ieq\n\n # Define the equations\n ieq = equal_lin_vel_node_FoR(MB_tstep, MB_beam, self.FoR_body, self.node_body, self.node_number, node_FoR_dof,\n node_dof, FoR_dof, sys_size, Lambda_dot, self.scalingFactor, self.penaltyFactor,\n ieq, LM_K, LM_C, LM_Q)\n\n return\n\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n MB_tstep[self.FoR_body].for_pos[:3] = (MB_tstep[self.node_body].cga()\n @ MB_tstep[self.node_body].pos[self.node_number, :]\n + MB_tstep[self.node_body].for_pos[:3])\n return\n\n\n@lagrangeconstraint\nclass free(BaseLagrangeConstraint):\n _lc_id = 'free'\n __doc__ = _lc_id\n\n def __init__(self):\n self.required_parameters = []\n self._n_eq = 0\n\n def get_n_eq(self):\n return self._n_eq\n\n def initialise(self, MBdict_entry, ieq, print_info=True):\n self._ieq = ieq\n return self._ieq + self._n_eq\n\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n return\n\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n return\n\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n\n@lagrangeconstraint\nclass spherical_FoR(BaseLagrangeConstraint):\n __doc__ = \"\"\"\n spherical_FoR\n\n This constraint forces a spherical join at a FoR\n\n See ``LagrangeConstraints`` for the description of variables\n\n Attributes:\n body_FoR (int): body number of the \"FoR\"\n \"\"\"\n _lc_id = 'spherical_FoR'\n\n def __init__(self):\n self.required_parameters = ['body_FoR']\n self._n_eq = 3\n\n def get_n_eq(self):\n return self._n_eq\n\n def initialise(self, MBdict_entry, ieq, print_info=True):\n self.body_FoR = MBdict_entry['body_FoR']\n self._ieq = ieq\n self.scalingFactor = set_value_or_default(MBdict_entry, \"scalingFactor\", 1.)\n self.penaltyFactor = set_value_or_default(MBdict_entry, \"penaltyFactor\", 0.)\n\n return self._ieq + self._n_eq\n\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n return\n\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n num_LM_eq_specific = self._n_eq\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Define the position of the first degree of freedom associated to the FoR\n FoR_dof = define_FoR_dof(MB_beam, self.body_FoR)\n ieq = self._ieq\n\n Bnh[:3, FoR_dof:FoR_dof + 3] = np.eye(3)\n\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += self.scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += self.scalingFactor * Bnh.T\n\n LM_Q[:sys_size] += self.scalingFactor * Bnh.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n\n LM_Q[sys_size + ieq:sys_size + ieq + 3] \\\n += self.scalingFactor * MB_tstep[self.body_FoR].for_vel[:3].astype(dtype=ct.c_double, copy=True, order='F')\n\n ieq += 3\n return\n\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n\n@lagrangeconstraint\nclass hinge_FoR(BaseLagrangeConstraint):\n __doc__ = \"\"\"\n hinge_FoR\n\n This constraint forces a hinge at a FoR\n\n See ``LagrangeConstraints`` for the description of variables\n\n Attributes:\n body_FoR (int): body number of the \"FoR\"\n rot_axis_AFoR (np.ndarray): Rotation axis with respect to the node A FoR\n \"\"\"\n _lc_id = 'hinge_FoR'\n\n def __init__(self):\n self.required_parameters = ['body_FoR', 'rot_axis_AFoR']\n self._n_eq = 5\n\n def get_n_eq(self):\n return self._n_eq\n\n def initialise(self, MBdict_entry, ieq, print_info=True):\n\n self.body_FoR = MBdict_entry['body_FoR']\n self.rot_axis = MBdict_entry['rot_axis_AFoR']\n self._ieq = ieq\n self.scalingFactor = set_value_or_default(MBdict_entry, \"scalingFactor\", 1.)\n self.penaltyFactor = set_value_or_default(MBdict_entry, \"penaltyFactor\", 0.)\n\n if (self.rot_axis[[1, 2]] == 0).all():\n self.rot_dir = 'x'\n self.zero_comp = np.array([1, 2], dtype=int)\n elif (self.rot_axis[[0, 2]] == 0).all():\n self.rot_dir = 'y'\n self.zero_comp = np.array([0, 2], dtype=int)\n elif (self.rot_axis[[0, 1]] == 0).all():\n self.rot_dir = 'z'\n self.zero_comp = np.array([0, 1], dtype=int)\n else:\n self.rot_dir = 'general'\n\n return self._ieq + self._n_eq\n\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n return\n\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n num_LM_eq_specific = self._n_eq\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Define the position of the first degree of freedom associated to the FoR\n FoR_dof = define_FoR_dof(MB_beam, self.body_FoR)\n ieq = self._ieq\n\n Bnh[:3, FoR_dof:FoR_dof + 3] = np.eye(3)\n\n # TODO: general logic removed since that implies local beam direction coincident with global axis direction\n skew_rot_axis = ag.skew(self.rot_axis)\n n0 = np.linalg.norm(skew_rot_axis[0, :])\n n1 = np.linalg.norm(skew_rot_axis[1, :])\n n2 = np.linalg.norm(skew_rot_axis[2, :])\n if ((n0 < n1) and (n0 < n2)):\n row0 = 1\n row1 = 2\n elif ((n1 < n0) and (n1 < n2)):\n row0 = 0\n row1 = 2\n elif ((n2 < n0) and (n2 < n1)):\n row0 = 0\n row1 = 1\n Bnh[3:5, FoR_dof + 3:FoR_dof + 6] = skew_rot_axis[[row0, row1], :]\n\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += self.scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += self.scalingFactor * Bnh.T\n\n LM_Q[:sys_size] += self.scalingFactor * Bnh.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n\n LM_Q[sys_size + ieq:sys_size + ieq + 3] \\\n += self.scalingFactor * MB_tstep[self.body_FoR].for_vel[:3].astype(dtype=ct.c_double, copy=True, order='F')\n\n # TODO: general logic removed since that implies local beam direction coincident with global axis direction\n LM_Q[sys_size + ieq + 3:sys_size + ieq + 5] \\\n += self.scalingFactor * skew_rot_axis[[row0, row1], :] @ MB_tstep[self.body_FoR].for_vel[3:6]\n\n if self.penaltyFactor:\n LM_Q[FoR_dof:FoR_dof + 3] += self.penaltyFactor * MB_tstep[self.body_FoR].for_vel[:3]\n LM_C[FoR_dof:FoR_dof + 3, FoR_dof:FoR_dof + 3] += self.penaltyFactor * np.eye(3)\n\n # TODO: general logic removed since that implies local beam direction coincident with global axis direction\n sq_rot_axis = ag.skew(self.rot_axis).T @ ag.skew(self.rot_axis)\n LM_Q[FoR_dof + 3:FoR_dof + 6] \\\n += self.penaltyFactor * sq_rot_axis @ MB_tstep[self.body_FoR].for_vel[3:6]\n LM_C[FoR_dof + 3:FoR_dof + 6, FoR_dof + 3:FoR_dof + 6] += self.penaltyFactor * sq_rot_axis\n\n ieq += 5\n return\n\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n\n@lagrangeconstraint\nclass hinge_FoR_wrtG(BaseLagrangeConstraint):\n __doc__ = \"\"\"\n hinge_FoR_wrtG\n\n This constraint forces a hinge at a FoR\n\n See ``LagrangeConstraints`` for the description of variables\n\n Attributes:\n body_FoR (int): body number of the \"FoR\"\n rot_axis_AFoR (np.ndarray): Rotation axis with respect to the node G FoR\n \"\"\"\n _lc_id = 'hinge_FoR_wrtG'\n\n def __init__(self):\n self.required_parameters = ['body_FoR', 'rot_axis_AFoR']\n self._n_eq = 5\n\n def get_n_eq(self):\n return self._n_eq\n\n def initialise(self, MBdict_entry, ieq, print_info=True):\n\n self.body_FoR = MBdict_entry['body_FoR']\n self.rot_axis = MBdict_entry['rot_axis_AFoR']\n self._ieq = ieq\n self.scalingFactor = set_value_or_default(MBdict_entry, \"scalingFactor\", 1.)\n self.penaltyFactor = set_value_or_default(MBdict_entry, \"penaltyFactor\", 0.)\n\n return self._ieq + self._n_eq\n\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n return\n\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n num_LM_eq_specific = self._n_eq\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n B = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Define the position of the first degree of freedom associated to the FoR\n FoR_dof = define_FoR_dof(MB_beam, self.body_FoR)\n ieq = self._ieq\n\n Bnh[:3, FoR_dof:FoR_dof + 3] = MB_tstep[self.body_FoR].cga()\n\n # Only two of these equations are linearly independent\n skew_rot_axis = ag.skew(self.rot_axis)\n n0 = np.linalg.norm(skew_rot_axis[0, :])\n n1 = np.linalg.norm(skew_rot_axis[1, :])\n n2 = np.linalg.norm(skew_rot_axis[2, :])\n if ((n0 < n1) and (n0 < n2)):\n row0 = 1\n row1 = 2\n elif ((n1 < n0) and (n1 < n2)):\n row0 = 0\n row1 = 2\n elif ((n2 < n0) and (n2 < n1)):\n row0 = 0\n row1 = 1\n\n Bnh[3:5, FoR_dof + 3:FoR_dof + 6] = skew_rot_axis[[row0, row1], :]\n\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += self.scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += self.scalingFactor * Bnh.T\n\n LM_C[FoR_dof:FoR_dof + 3, FoR_dof + 6:FoR_dof + 10] \\\n += self.scalingFactor * ag.der_CquatT_by_v(MB_tstep[self.body_FoR].quat, Lambda_dot[ieq:ieq + 3])\n\n LM_Q[:sys_size] += self.scalingFactor * Bnh.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n\n LM_Q[sys_size + ieq:sys_size + ieq + 3] \\\n += self.scalingFactor * MB_tstep[self.body_FoR].cga() @ MB_tstep[self.body_FoR].for_vel[:3]\n LM_Q[sys_size + ieq + 3:sys_size + ieq + 5] \\\n += self.scalingFactor * skew_rot_axis[[row0, row1], :] @ MB_tstep[self.body_FoR].for_vel[3:6]\n\n ieq += 5\n return\n\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n\n@lagrangeconstraint\nclass fully_constrained_node_FoR(BaseLagrangeConstraint):\n __doc__ = \"\"\"\n fully_constrained_node_FoR\n\n This constraint forces linear and angular displacements between a node\n and a FoR to be the same\n\n See ``LagrangeConstraints`` for the description of variables\n\n Attributes:\n node_number (int): number of the \"node\" within its own body\n node_body (int): body number of the \"node\"\n FoR_body (int): body number of the \"FoR\"\n \"\"\"\n _lc_id = 'fully_constrained_node_FoR'\n\n def __init__(self):\n self.required_parameters = ['node_in_body', 'body', 'body_FoR', 'rel_posB']\n self._n_eq = 6\n\n def get_n_eq(self):\n return self._n_eq\n\n def initialise(self, MBdict_entry, ieq, print_info=True):\n self.node_number = MBdict_entry['node_in_body']\n self.node_body = MBdict_entry['body']\n self.FoR_body = MBdict_entry['body_FoR']\n self.rel_posB = MBdict_entry['rel_posB']\n self._ieq = ieq\n self.scalingFactor = set_value_or_default(MBdict_entry, \"scalingFactor\", 1.)\n self.penaltyFactor = set_value_or_default(MBdict_entry, \"penaltyFactor\", 0.)\n\n return self._ieq + self._n_eq\n\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n return\n\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n # Define the position of the first degree of freedom associated to the node\n node_dof = define_node_dof(MB_beam, self.node_body, self.node_number)\n node_FoR_dof = define_FoR_dof(MB_beam, self.node_body)\n FoR_dof = define_FoR_dof(MB_beam, self.FoR_body)\n ieq = self._ieq\n\n # Define the equations\n ieq = equal_lin_vel_node_FoR(MB_tstep, MB_beam, self.FoR_body, self.node_body, self.node_number, node_FoR_dof,\n node_dof, FoR_dof, sys_size, Lambda_dot, self.scalingFactor, self.penaltyFactor,\n ieq, LM_K, LM_C, LM_Q, rel_posB=self.rel_posB)\n ieq = rel_rot_vel_node_FoR(MB_tstep, MB_beam, self.FoR_body, self.node_body, self.node_number, node_FoR_dof,\n node_dof, FoR_dof, sys_size, Lambda_dot, self.scalingFactor, self.penaltyFactor, ieq,\n LM_K, LM_C, LM_Q, rel_vel=np.zeros(3))\n\n return\n\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n ielem, inode_in_elem = MB_beam[self.node_body].node_master_elem[self.node_number]\n node_cga = MB_tstep[self.node_body].cga()\n cab = ag.crv2rotation(MB_tstep[self.node_body].psi[ielem, inode_in_elem, :])\n\n MB_tstep[self.FoR_body].for_pos[:3] = node_cga @ (MB_tstep[self.node_body].pos[self.node_number, :]\n + cab @ self.rel_posB) + MB_tstep[self.node_body].for_pos[:3]\n return\n\n\n@lagrangeconstraint\nclass constant_rot_vel_FoR(BaseLagrangeConstraint):\n __doc__ = \"\"\"\n constant_rot_vel_FoR\n\n This constraint forces a constant rotation velocity of a FoR\n\n See ``LagrangeConstraints`` for the description of variables\n\n Attributes:\n FoR_body (int): body number of the \"FoR\"\n \"\"\"\n _lc_id = 'constant_rot_vel_FoR'\n\n def __init__(self):\n self.required_parameters = ['FoR_body', 'rot_vel']\n self._n_eq = 3\n\n def get_n_eq(self):\n return self._n_eq\n\n def initialise(self, MBdict_entry, ieq, print_info=True):\n self.rot_vel = MBdict_entry['rot_vel']\n self.FoR_body = MBdict_entry['FoR_body']\n self._ieq = ieq\n self.scalingFactor = set_value_or_default(MBdict_entry, \"scalingFactor\", 1.)\n self.penaltyFactor = set_value_or_default(MBdict_entry, \"penaltyFactor\", 0.)\n\n return self._ieq + self._n_eq\n\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n return\n\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n num_LM_eq_specific = self._n_eq\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Define the position of the first degree of freedom associated to the FoR\n FoR_dof = define_FoR_dof(MB_beam, self.FoR_body)\n ieq = self._ieq\n\n Bnh[:3, FoR_dof + 3:FoR_dof + 6] = np.eye(3)\n\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += self.scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += self.scalingFactor * Bnh.T\n\n LM_Q[:sys_size] += self.scalingFactor * Bnh.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += self.scalingFactor * (MB_tstep[self.FoR_body].for_vel[3:6] - self.rot_vel)\n\n ieq += 3\n return\n\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n\n@lagrangeconstraint\nclass constant_vel_FoR(BaseLagrangeConstraint):\n __doc__ = \"\"\"\n constant_vel_FoR\n\n This constraint forces a constant velocity of a FoR\n\n See ``LagrangeConstraints`` for the description of variables\n\n Attributes:\n FoR_body (int): body number of the \"FoR\"\n vel (np.ndarray): 6 components of the desired velocity\n \"\"\"\n _lc_id = 'constant_vel_FoR'\n\n def __init__(self):\n self.required_parameters = ['FoR_body', 'vel']\n self._n_eq = 6\n\n def get_n_eq(self):\n return self._n_eq\n\n def initialise(self, MBdict_entry, ieq, print_info=True):\n self.vel = MBdict_entry['vel']\n self.FoR_body = MBdict_entry['FoR_body']\n self._ieq = ieq\n self.scalingFactor = set_value_or_default(MBdict_entry, \"scalingFactor\", 1.)\n self.penaltyFactor = set_value_or_default(MBdict_entry, \"penaltyFactor\", 0.)\n\n return self._ieq + self._n_eq\n\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n return\n\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n num_LM_eq_specific = self._n_eq\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Define the position of the first degree of freedom associated to the FoR\n FoR_dof = define_FoR_dof(MB_beam, self.FoR_body)\n ieq = self._ieq\n\n Bnh[:num_LM_eq_specific, FoR_dof:FoR_dof + 6] = np.eye(6)\n\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += self.scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += self.scalingFactor * Bnh.T\n\n LM_Q[:sys_size] += self.scalingFactor * Bnh.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += self.scalingFactor * (MB_tstep[self.FoR_body].for_vel - self.vel)\n\n ieq += 6\n return\n\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n\n@lagrangeconstraint\nclass zero_lin_vel_sine_rot_vel_FoR(BaseLagrangeConstraint):\n __doc__ = \"\"\"\n zero_lin_vel_sine_rot_vel_FoR\n\n Zero linear velocity and sinusoidal rotation velocity FoR\n\n See ``LagrangeConstraints`` for the description of variables\n\n Attributes:\n FoR_body (int): body number of the \"FoR\"\n vel_amp (float): Rotation velocity amplitude\n omega (float): Frequency of the sinusoidally-varying rotation velocity\n xyz (string): Axis with the sine velocity\n \"\"\"\n _lc_id = 'zero_lin_vel_sine_rot_vel_FoR'\n\n def __init__(self):\n self.required_parameters = ['FoR_body', 'vel_amp', 'omega', 'xyz']\n self._n_eq = 6\n\n def get_n_eq(self):\n return self._n_eq\n\n def initialise(self, MBdict_entry, ieq, print_info=True):\n\n self.FoR_body = MBdict_entry['FoR_body']\n self.vel_amp = MBdict_entry['vel_amp']\n self.omega = MBdict_entry['omega']\n if MBdict_entry['xyz'] == 'x':\n self.xyz_index = 0\n elif MBdict_entry['xyz'] == 'y':\n self.xyz_index = 1\n elif MBdict_entry['xyz'] == 'z':\n self.xyz_index = 2\n else:\n raise NotImplementedError(\"FoR rotation velocity shouldd be parallel to x, y or z\")\n self._ieq = ieq\n self.scalingFactor = set_value_or_default(MBdict_entry, \"scalingFactor\", 1.)\n self.penaltyFactor = set_value_or_default(MBdict_entry, \"penaltyFactor\", 0.)\n\n return self._ieq + self._n_eq\n\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n return\n\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n num_LM_eq_specific = self._n_eq\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Define the position of the first degree of freedom associated to the FoR\n FoR_dof = define_FoR_dof(MB_beam, self.FoR_body)\n ieq = self._ieq\n\n vel = np.zeros(6)\n vel[3 + self.xyz_index] = self.vel_amp * np.sin(self.omega * ts * dt)\n\n Bnh[:num_LM_eq_specific, FoR_dof:FoR_dof + 6] = np.eye(6)\n\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += self.scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += self.scalingFactor * Bnh.T\n\n LM_Q[:sys_size] += self.scalingFactor * Bnh.T, Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += self.scalingFactor * (MB_tstep[self.FoR_body].for_vel - vel)\n\n ieq += 6\n return\n\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n\n@lagrangeconstraint\nclass lin_vel_node_wrtA(BaseLagrangeConstraint):\n __doc__ = \"\"\"\n lin_vel_node_wrtA\n\n This constraint forces the linear velocity of a node to have a\n certain value with respect to the A FoR\n\n See ``LagrangeConstraints`` for the description of variables\n\n Attributes:\n node_number (int): number of the \"node\" within its own body\n body_number (int): body number of the \"node\"\n vel (np.ndarray): 6 components of the desired velocity with respect to the A FoR\n \"\"\"\n _lc_id = 'lin_vel_node_wrtA'\n\n def __init__(self):\n self.required_parameters = ['velocity', 'body_number', 'node_number']\n self._n_eq = 3\n\n def get_n_eq(self):\n return self._n_eq\n\n def initialise(self, MBdict_entry, ieq, print_info=True):\n\n self.vel = MBdict_entry['velocity']\n self.body_number = MBdict_entry['body_number']\n self.node_number = MBdict_entry['node_number']\n self._ieq = ieq\n self.scalingFactor = set_value_or_default(MBdict_entry, \"scalingFactor\", 1.)\n self.penaltyFactor = set_value_or_default(MBdict_entry, \"penaltyFactor\", 0.)\n\n return self._ieq + self._n_eq\n\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n\n num_LM_eq_specific = self._n_eq\n B = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Define the position of the first degree of freedom associated to the FoR\n node_dof = define_node_dof(MB_beam, self.body_number, self.node_number)\n ieq = self._ieq\n\n B[:num_LM_eq_specific, node_dof:node_dof + 3] = np.eye(3)\n\n LM_K[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += self.scalingFactor * B\n LM_K[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += self.scalingFactor * B.T\n\n LM_Q[:sys_size] += self.scalingFactor * B.T @ Lambda[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += self.scalingFactor * (MB_tstep[self.body_number].pos[self.node_number, :]\n - MB_beam[self.body_number].ini_info.pos[self.node_number, :])\n\n ieq += 3\n return\n\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n\n if len(self.vel.shape) > 1:\n current_vel = self.vel[ts - 1, :]\n else:\n current_vel = self.vel\n\n num_LM_eq_specific = self._n_eq\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Define the position of the first degree of freedom associated to the FoR\n node_dof = define_node_dof(MB_beam, self.body_number, self.node_number)\n ieq = self._ieq\n\n Bnh[:num_LM_eq_specific, node_dof:node_dof + 3] = np.eye(3)\n\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += self.scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += self.scalingFactor * Bnh.T\n\n LM_Q[:sys_size] += self.scalingFactor * Bnh.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += self.scalingFactor * (MB_tstep[self.body_number].pos_dot[self.node_number, :] - current_vel)\n\n ieq += 3\n return\n\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n\n@lagrangeconstraint\nclass lin_vel_node_wrtG(BaseLagrangeConstraint):\n __doc__ = \"\"\"\n lin_vel_node_wrtG\n\n This constraint forces the linear velocity of a node to have a\n certain value with respect to the G FoR\n\n See ``LagrangeConstraints`` for the description of variables\n\n Attributes:\n node_number (int): number of the \"node\" within its own body\n body_number (int): body number of the \"node\"\n vel (np.ndarray): 6 components of the desired velocity with respect to the G FoR\n \"\"\"\n _lc_id = 'lin_vel_node_wrtG'\n\n def __init__(self):\n self.required_parameters = ['velocity', 'body_number', 'node_number']\n self._n_eq = 3\n\n def get_n_eq(self):\n return self._n_eq\n\n def initialise(self, MBdict_entry, ieq, print_info=True):\n\n self.vel = MBdict_entry['velocity']\n self.body_number = MBdict_entry['body_number']\n self.node_number = MBdict_entry['node_number']\n self._ieq = ieq\n self.scalingFactor = set_value_or_default(MBdict_entry, \"scalingFactor\", 1.)\n self.penaltyFactor = set_value_or_default(MBdict_entry, \"penaltyFactor\", 0.)\n\n return self._ieq + self._n_eq\n\n def staticmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n\n num_LM_eq_specific = self._n_eq\n B = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Define the position of the first degree of freedom associated to the FoR\n node_dof = define_node_dof(MB_beam, self.body_number, self.node_number)\n ieq = self._ieq\n\n B[:num_LM_eq_specific, node_dof:node_dof + 3] = MB_tstep[self.body_number].cga()\n\n LM_K[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += self.scalingFactor * B\n LM_K[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += self.scalingFactor * B.T\n\n LM_Q[:sys_size] += self.scalingFactor * B.T @ Lambda[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += (self.scalingFactor * MB_tstep[self.body_number].cga()\n @ MB_tstep[self.body_number].pos[self.node_number, :] + MB_tstep[self.body_number].for_pos)\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n -= (self.scalingFactor * MB_beam[self.body_number].ini_info.cga()\n @ MB_beam[self.body_number].ini_info.pos[self.node_number, :]\n + MB_beam[self.body_number].ini_info.for_pos)\n\n ieq += 3\n return\n\n def dynamicmat(self, LM_C, LM_K, LM_Q, MB_beam, MB_tstep, ts, num_LM_eq,\n sys_size, dt, Lambda, Lambda_dot):\n if len(self.vel.shape) > 1:\n current_vel = self.vel[ts - 1, :]\n else:\n current_vel = self.vel\n\n num_LM_eq_specific = self._n_eq\n Bnh = np.zeros((num_LM_eq_specific, sys_size), dtype=ct.c_double, order='F')\n\n # Define the position of the first degree of freedom associated to the FoR\n FoR_dof = define_FoR_dof(MB_beam, self.body_number)\n node_dof = define_node_dof(MB_beam, self.body_number, self.node_number)\n ieq = self._ieq\n\n if MB_beam[self.body_number].FoR_movement == 'free':\n Bnh[:num_LM_eq_specific, FoR_dof:FoR_dof + 3] = MB_tstep[self.body_number].cga()\n Bnh[:num_LM_eq_specific, FoR_dof + 3:FoR_dof + 6] \\\n = -MB_tstep[self.body_number].cga() @ ag.skew(MB_tstep[self.body_number].pos[self.node_number, :])\n Bnh[:num_LM_eq_specific, node_dof:node_dof + 3] = MB_tstep[self.body_number].cga()\n\n LM_C[sys_size + ieq:sys_size + ieq + num_LM_eq_specific, :sys_size] += self.scalingFactor * Bnh\n LM_C[:sys_size, sys_size + ieq:sys_size + ieq + num_LM_eq_specific] += self.scalingFactor * Bnh.T\n\n if MB_beam[self.body_number].FoR_movement == 'free':\n LM_C[FoR_dof:FoR_dof + 3, FoR_dof + 6:FoR_dof + 10] += self.scalingFactor * ag.der_CquatT_by_v(\n MB_tstep[self.body_number].quat, Lambda_dot[ieq:ieq + num_LM_eq_specific])\n LM_C[node_dof:node_dof + 3, FoR_dof + 6:FoR_dof + 10] += self.scalingFactor * ag.der_CquatT_by_v(\n MB_tstep[self.body_number].quat, Lambda_dot[ieq:ieq + num_LM_eq_specific])\n LM_C[FoR_dof + 3:FoR_dof + 6, FoR_dof + 6:FoR_dof + 10] \\\n += (self.scalingFactor * ag.skew(MB_tstep[self.body_number].pos[self.node_number, :])\n @ ag.der_CquatT_by_v(MB_tstep[self.body_number].quat, Lambda_dot[ieq:ieq + num_LM_eq_specific]))\n\n LM_K[FoR_dof + 3:FoR_dof + 6, node_dof:node_dof + 3] \\\n -= self.scalingFactor * ag.skew(MB_tstep[self.body_number].cga().T\n @ Lambda_dot[ieq:ieq + num_LM_eq_specific])\n\n LM_Q[:sys_size] += self.scalingFactor * Bnh.T @ Lambda_dot[ieq:ieq + num_LM_eq_specific]\n LM_Q[sys_size + ieq:sys_size + ieq + num_LM_eq_specific] \\\n += self.scalingFactor * (MB_tstep[self.body_number].cga()\n @ (MB_tstep[self.body_number].for_vel[:3]\n + ag.skew(MB_tstep[self.body_number].for_vel[3:6])\n @ MB_tstep[self.body_number].pos[self.node_number, :]\n + MB_tstep[self.body_number].pos_dot[self.node_number, :]) - current_vel)\n\n ieq += 3\n return\n\n def staticpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n def dynamicpost(self, lc_list, MB_beam, MB_tstep):\n return\n\n\n################################################################################\n# Funtions to interact with this Library\n################################################################################\ndef initialize_constraints(MBdict):\n index_eq = 0\n num_constraints = MBdict['num_constraints']\n lc_list = list()\n\n # Read the dictionary and create the constraints\n for iconstraint in range(num_constraints):\n lc_list.append(lc_from_string(MBdict[\"constraint_%02d\" % iconstraint]['behaviour'])())\n MBdict_entry = MBdict[\"constraint_%02d\" % iconstraint]\n if \"penaltyFactor\" in MBdict_entry.keys():\n if not MBdict_entry['penaltyFactor'] == 0.:\n print(\"Penalty method not completely implemented for Lagrange Constraints\")\n\n index_eq = lc_list[-1].initialise(MBdict_entry, index_eq)\n\n return lc_list\n\n\ndef define_num_LM_eq(lc_list):\n \"\"\"\n define_num_LM_eq\n\n Define the number of equations needed to define the boundary boundary conditions\n\n Args:\n lc_list(): list of all the defined contraints\n Returns:\n num_LM_eq(int): number of new equations needed to define the boundary boundary conditions\n\n Examples:\n num_LM_eq = lagrangeconstraints.define_num_LM_eq(lc_list)\n\n Notes:\n\n \"\"\"\n\n num_LM_eq = 0\n\n # Compute the number of equations\n for lc in lc_list:\n num_LM_eq += lc.get_n_eq()\n\n return num_LM_eq\n\n\ndef generate_lagrange_matrix(lc_list, MB_beam, MB_tstep, ts, num_LM_eq, sys_size, dt, Lambda, Lambda_dot,\n dynamic_or_static):\n \"\"\"\n generate_lagrange_matrix\n\n Generates the matrices associated to the Lagrange multipliers boundary conditions\n\n Args:\n lc_list(): list of all the defined contraints\n MBdict(dict): dictionary with the MultiBody and LagrangeMultipliers information\n MB_beam(list): list of 'beams' of each of the bodies that form the system\n MB_tstep(list): list of 'StructTimeStepInfo' of each of the bodies that form the system\n num_LM_eq(int): number of new equations needed to define the boundary boundary conditions\n sys_size(int): total number of degrees of freedom of the multibody system\n dt(float): time step\n Lambda(np.ndarray): list of Lagrange multipliers values\n Lambda_dot(np.ndarray): list of the first derivative of the Lagrange multipliers values\n dynamic_or_static (str): string defining if the computation is dynamic or static\n\n Returns:\n LM_C (np.ndarray): Damping matrix associated to the Lagrange Multipliers equations\n LM_K (np.ndarray): Stiffness matrix associated to the Lagrange Multipliers equations\n LM_Q (np.ndarray): Vector of independent terms associated to the Lagrange Multipliers equations\n \"\"\"\n # Initialize matrices\n LM_C = np.zeros((sys_size + num_LM_eq, sys_size + num_LM_eq), dtype=ct.c_double, order='F')\n LM_K = np.zeros((sys_size + num_LM_eq, sys_size + num_LM_eq), dtype=ct.c_double, order='F')\n LM_Q = np.zeros((sys_size + num_LM_eq,), dtype=ct.c_double, order='F')\n\n # Define the matrices associated to the constratints\n # TODO: Is there a better way to deal with ieq?\n for lc in lc_list:\n if dynamic_or_static.lower() == \"static\":\n lc.staticmat(LM_C=LM_C, LM_K=LM_K, LM_Q=LM_Q, MB_beam=MB_beam, MB_tstep=MB_tstep, ts=ts,\n num_LM_eq=num_LM_eq, sys_size=sys_size, dt=dt, Lambda=Lambda, Lambda_dot=Lambda_dot)\n\n elif dynamic_or_static.lower() == \"dynamic\":\n lc.dynamicmat(LM_C=LM_C, LM_K=LM_K, LM_Q=LM_Q, MB_beam=MB_beam, MB_tstep=MB_tstep, ts=ts,\n num_LM_eq=num_LM_eq, sys_size=sys_size, dt=dt, Lambda=Lambda, Lambda_dot=Lambda_dot)\n\n return LM_C, LM_K, LM_Q\n\n\ndef postprocess(lc_list, MB_beam, MB_tstep, dynamic_or_static):\n \"\"\"\n Run the postprocess of all the Lagrange Constraints in the system\n \"\"\"\n for lc in lc_list:\n if dynamic_or_static.lower() == \"static\":\n lc.staticpost(lc_list=lc_list, MB_beam=MB_beam, MB_tstep=MB_tstep)\n\n elif dynamic_or_static.lower() == \"dynamic\":\n lc.dynamicpost(lc_list=lc_list, MB_beam=MB_beam, MB_tstep=MB_tstep)\n return\n\n\ndef remove_constraint(MBdict, constraint):\n \"\"\"\n Removes a constraint from the list.\n This function is thought to release constraints at some point during\n a dynamic simulation\n \"\"\"\n try:\n del (MBdict[constraint])\n MBdict['num_constraints'] -= 1\n except KeyError:\n pass\n\n\n################################################################################\n\nprint_available_lc()\n" }, { "path": "sharpy/structure/utils/lagrangeconstraintsjax.py", "content": "from typing import Callable, Any, Optional, Type, cast\nfrom abc import ABC\nimport numpy as np\nimport scipy as sp\n\nimport jax\nimport jax.scipy.spatial.transform\nimport jax.numpy as jnp\nfrom jax.numpy import ndarray as jarr\n\n# global constants\njax.config.update(\"jax_enable_x64\", True)\nDICT_OF_LC = dict()\nUSE_JIT = True\n\n# type definition for b subfunctions (Constraint, i_lm, b_mat, q, q_dot, u, u_dot)\nb_type: Type = Optional[Callable[[Any, slice, jarr, jarr, jarr, jarr, jarr], jarr]]\n\n# type definitions for b functions, ordering is (q, q_dot, u, u_dot, lmh, lmn)\nfunc_type: Type = Callable[[jarr, jarr, jarr, jarr, jarr, jarr], jarr]\n\n\n# redefine jax.scipy rotation class to use [real, i, j, k] ordering by default\nclass Rot(jax.scipy.spatial.transform.Rotation):\n @classmethod\n def from_quat(cls, quat: jarr):\n return super().from_quat(jnp.array((*quat[1:4], quat[0])))\n\n def as_quat(self, canonical=True) -> jarr:\n return super().as_quat(canonical=canonical)\n\n\n# decorator populating DICT_OF_LC as {lc_id: Constraint}, not type hinted as preceeds Constraint declaration\ndef constraint(constraint_):\n global DICT_OF_LC\n if constraint_.lc_id is not None:\n DICT_OF_LC[constraint_.lc_id] = constraint_\n else:\n raise AttributeError('Class defined as lagrange constraint has no lc_id attribute')\n return constraint_\n\n\n# JAX vector skew\ndef skew(vec: jarr) -> jarr:\n if vec.shape != (3,) or jnp.iscomplexobj(vec):\n raise ValueError(\"Incompatible input vector dimention or data type\")\n return jnp.array(((0., -vec[2], vec[1]),\n (vec[2], 0., -vec[0]),\n (-vec[1], vec[0], 0.)))\n\n\n# JAX cartesian rotation vector to rotation matrix as version from SciPy's Rotation class doesn't differentiate well\ndef crv2rot(crv: jarr) -> jarr:\n ang = jnp.linalg.norm(crv)\n crv_skew = skew(crv)\n return jax.lax.cond(ang > 1e-15,\n lambda: jnp.eye(3) + jnp.sin(ang) / ang * crv_skew\n + (1 - jnp.cos(ang)) / ang ** 2 * crv_skew @ crv_skew,\n lambda: jnp.eye(3) + crv_skew + 0.5 * crv_skew @ crv_skew)\n\n\n# JAX cartesian rotation vector tangent operator\ndef crv2tan(psi: jarr) -> jarr:\n ang = jnp.linalg.norm(psi)\n psi_skew = skew(psi)\n return jax.lax.cond(ang > 1e-8,\n lambda: jnp.eye(3) + (jnp.cos(ang) - 1.) / ang ** 2 * psi_skew + (ang - jnp.sin(ang))\n / ang ** 3 * psi_skew @ psi_skew,\n lambda: jnp.eye(3) - 0.5 * psi_skew + psi_skew @ psi_skew / 6.)\n\n\n@constraint\nclass Constraint(ABC):\n # this might make it a bit faster, might be overkill\n __slots__ = ('settings', 's_fact', 'p_fact', 'use_p_fact', 'jac_func', 'num_h_funcs', 'num_n_funcs', 'i_first_lm',\n 'num_lmh', 'num_lmn', 'num_lm', 'num_lm_tot', 'num_bodys', 'is_free', 'num_elem_body', 'num_node_body',\n 'num_dof_body', 'num_dof_tot', 'num_eq_tot', 'i_sys', 'i_lm_tot', 'i_lmh_eq', 'i_lmn_eq', 'i_lm_eq',\n 'i_v0', 'i_omega0', 'i_quat0', 'i_v1', 'i_omega1', 'i_quat1', 'i_r0', 'i_psi0', 'q_i_global',\n 'num_active_q', 'bh', 'bn', 'gn', 'c', 'd', 'bht', 'bnt', 'bht_lmh', 'bnt_lmn', 'p_func_h', 'p_func_n',\n 'run')\n\n lc_id = '_base_constraint'\n required_params: tuple[str, ...] = tuple() # required parameters for the given constraint\n bh_funcs: tuple[b_type, ...] = list() # tuple of holonomic B matrix funcs\n bn_funcs: tuple[b_type | None, ...] = tuple() # tuple of non holonomic B matrix funcs, or None for zero matrix\n gn_funcs: tuple[b_type | None, ...] = tuple() # tuple of non holonomic g matrix funcs, or None for zero matrix\n num_lmh_eq: tuple[int, ...] = tuple() # number of LMs for each holonomic constraint\n num_lmn_eq: tuple[int, ...] = tuple() # number of LMs for each nonholonomic constraint\n postproc_funcs: tuple[Callable, ...] = tuple() # postprocessing functions to be run\n\n def __init__(self, data, i_lm: int, constraint_settings: dict): # case data, index of first LM, input settings\n self.settings = constraint_settings # input constraint parameters\n\n # scaling factor, with 1/dt^2 as default\n self.s_fact = constraint_settings.get('scaling_factor', data.data.settings['DynamicCoupled']['dt'] ** -2)\n self.p_fact = constraint_settings.get('penalty_factor', 0.) # penalty factor for constraint\n self.use_p_fact = abs(self.p_fact) > 1e-6 # if true, penalty equations are included in run function\n\n # choose either forward or reverse mode autodifferentiation\n # I believe that only forward works as of current, and for this case the difference should be negligible\n match data.settings['jacobian_method']:\n case 'forward':\n self.jac_func = jax.jacfwd\n case 'reverse':\n self.jac_func = jax.jacrev\n\n self.num_h_funcs = len(self.bh_funcs) # number of holonomic functions (this constraint)\n self.num_n_funcs = len(self.bn_funcs) # number of non holonomic functions (this constraint)\n self.i_first_lm = i_lm # index of first LM (this constraint)\n self.num_lmh = sum(self.num_lmh_eq) # total number of holonomic LMs (this constraint)\n self.num_lmn = sum(self.num_lmn_eq) # total number of non holonomic LMs (this constraint)\n self.num_lm = self.num_lmh + self.num_lmn # total number of LMs (this constraint)\n self.num_lm_tot = data.num_lm_tot # total numer of LMs (all constraints)\n\n self.num_bodys = data.data.structure.ini_mb_dict['num_bodies'] # number of bodies\n self.is_free = [data.data.structure.ini_mb_dict[f'body_{i:02d}']['FoR_movement'] == 'free'\n for i in range(self.num_bodys)] # boolean for beam freedom condition\n\n self.num_elem_body = [list(data.data.structure.body_number).count(i)\n for i in range(self.num_bodys)] # number of elements per body\n self.num_node_body = [self.num_elem_body[i] * (data.data.structure.num_node_elem - 1) + 1\n for i in range(self.num_bodys)] # number of nodes per body\n self.num_dof_body = [(self.num_node_body[i] - 1) * 6 + self.is_free[i] * 10\n for i in range(self.num_bodys)] # number of DoFs per body\n\n self.num_dof_tot = data.sys_size # number of equations representing the unconstrained system\n self.num_eq_tot = self.num_dof_tot + self.num_lm_tot # number of equations representing the constrainted system\n\n self.i_sys = slice(0, self.num_dof_tot) # index of equations representing the unconstrained system\n\n self.i_lm_tot = jnp.arange(self.num_dof_tot, self.num_dof_tot + self.num_lm_tot) # index of LMs in full system\n\n self.i_lmh_eq: list[slice] = [] # list of slices of holonomic LMs for this constraint\n self.i_lmn_eq: list[slice] = [] # list of slices of non holonomic LMs for this constraint\n\n i_eq = self.i_first_lm\n for i in range(len(self.num_lmh_eq)):\n self.i_lmh_eq.append(slice(i_eq, i_eq + self.num_lmh_eq[i]))\n i_eq += self.num_lmh_eq[i]\n for i in range(len(self.num_lmn_eq)):\n self.i_lmn_eq.append(slice(i_eq, i_eq + self.num_lmn_eq[i]))\n i_eq += self.num_lmn_eq[i]\n self.i_lm_eq = self.i_lmh_eq + self.i_lmn_eq # list of slices of LMs for this constraint, holonomic first\n\n # the below indexes are slices of q and q_dot in the subset of active q terms\n self.i_v0: Optional[slice] = None # index of body 0 linear velocity\n self.i_omega0: Optional[slice] = None # index of body 0 rotational velocity\n self.i_quat0: Optional[slice] = None # index of body 0 orientation quaternion\n self.i_v1: Optional[slice] = None # index of body 1 linear velocity\n self.i_omega1: Optional[slice] = None # index of body 1 rotational velocity\n self.i_quat1: Optional[slice] = None # index of body 1 orientation quaternion\n self.i_r0: Optional[slice] = None # index of body 0 node position\n self.i_psi0: Optional[slice] = None # index of body 0 node orientation\n self.q_i_global: Optional[jnp.ndarray] = None # index of q used in constraints (global)\n self.num_active_q: Optional[int] = None # number of elements of q required in constraint\n self.create_index() # assign all required indexes\n\n self.bh: func_type = self.create_bh() # overall holonomic b function\n self.bn: func_type = self.create_bn() # overall nonholonomic b function\n self.gn: func_type = self.create_gn() # overall nonholonomic g function\n\n # cannot type hint lambda expressions, so casting the type will do\n self.c: func_type = cast(func_type, lambda *args: self.bh(*args) @ args[0]) # C function\n self.d: func_type = cast(func_type, lambda *args: self.bn(*args) @ args[1] + self.gn(*args)) # D function\n self.bht: func_type = cast(func_type, lambda *args: self.bh(*args).T) # B_h^T\n self.bnt: func_type = cast(func_type, lambda *args: self.bn(*args).T) # B_n^T\n self.bht_lmh: func_type = cast(func_type, lambda *args: self.bht(*args) @ args[4]) # B_h^T @ lm_h\n self.bnt_lmn: func_type = cast(func_type, lambda *args: self.bnt(*args) @ args[5]) # B_n^T @ lm_n\n self.p_func_h: func_type = cast(func_type, lambda *args: self.bht(*args) @ self.c(*args))\n self.p_func_n: func_type = cast(func_type, lambda *args: self.bnt(*args) @ self.d(*args))\n\n # create function which returns contribution to structural equations\n self.run: Callable[[jarr, jarr, jarr, jarr, jarr, jarr], tuple[jarr, jarr, jarr]] = self.create_run()\n\n def postprocess(self, mb_beam, mb_tstep) -> None:\n for func in self.postproc_funcs:\n func(self, mb_beam, mb_tstep)\n\n @classmethod\n def get_n_lm(cls) -> int:\n return sum(cls.num_lmh_eq) + sum(cls.num_lmn_eq)\n\n def create_index(self) -> None:\n # check all required parameters are in settings\n for param in self.required_params:\n if param not in self.settings.keys():\n raise KeyError(f\"Parameter {param} is undefined in constraint settings\")\n\n i_global = [] # index in full q\n i_count = 0 # start of current slice\n\n if 'body' in self.required_params:\n i_for0 = self.settings['body']\n i_start_for0 = sum(self.num_dof_body[:i_for0 + 1]) - 10\n self.i_v0 = np.arange(0, 3, dtype=int)\n self.i_omega0 = np.arange(3, 6, dtype=int)\n self.i_quat0 = np.arange(6, 10, dtype=int)\n i_global.append(np.arange(i_start_for0, i_start_for0 + 10))\n i_count += 10\n\n if 'node_in_body' in self.required_params:\n i_node = self.settings['node_in_body']\n self.i_r0 = np.arange(i_count, i_count + 3, dtype=int)\n self.i_psi0 = np.arange(i_count + 3, i_count + 6, dtype=int)\n i_global.append(jnp.arange((i_node - 1) * 6, (i_node - 1) * 6 + 6))\n i_count += 6\n\n if 'body_FoR' in self.required_params:\n i_for1 = self.settings['body_FoR']\n i_start_for1 = sum(self.num_dof_body[:i_for1 + 1]) - 10\n self.i_v1 = np.arange(i_count, i_count + 3, dtype=int)\n self.i_omega1 = np.arange(i_count + 3, i_count + 6, dtype=int)\n self.i_quat1 = np.arange(i_count + 6, i_count + 10, dtype=int)\n i_global.append(np.arange(i_start_for1, i_start_for1 + 10))\n i_count += 10\n\n self.q_i_global = jnp.hstack(i_global)\n self.num_active_q = self.q_i_global.shape[0]\n\n def create_bh(self) -> func_type:\n def bh(*args: jarr) -> jarr:\n bh_mat = jnp.zeros((self.num_lm_tot, self.num_active_q))\n for i_func, bh_func in enumerate(self.bh_funcs):\n bh_mat = bh_func(self, self.i_lmh_eq[i_func], bh_mat, *args[:4])\n return bh_mat\n\n return bh\n\n def create_bn(self) -> func_type:\n def bn(*args: jarr) -> jarr:\n bn_mat = jnp.zeros((self.num_lm_tot, self.num_active_q))\n for i_func, bn_func in enumerate(self.bn_funcs):\n if bn_func is not None:\n bn_mat = bn_func(self, self.i_lmn_eq[i_func], bn_mat, *args[:4])\n return bn_mat\n\n return bn\n\n def create_gn(self) -> func_type:\n def gn(*args: jarr) -> jarr:\n gn_mat = jnp.zeros(self.num_lm_tot)\n for i_func, gn_func in enumerate(self.gn_funcs):\n if gn_func is not None:\n gn_mat = gn_func(self, self.i_lmn_eq[i_func], gn_mat, *args[:4])\n return gn_mat\n\n return gn\n\n def create_run(self):\n def run(q: jarr, q_dot: jarr, u: jarr, u_dot: jarr, lmh: jarr, lmn: jarr) -> tuple[jarr, jarr, jarr]:\n args = (q, q_dot, u, u_dot, lmh, lmn)\n\n c = jnp.zeros((self.num_eq_tot, self.num_eq_tot))\n c = c.at[jnp.ix_(self.q_i_global, self.q_i_global)].add(self.jac_func(self.bht_lmh, 1)(*args))\n c = c.at[jnp.ix_(self.q_i_global, self.q_i_global)].add(self.jac_func(self.bnt_lmn, 1)(*args))\n c = c.at[jnp.ix_(self.q_i_global, self.i_lm_tot)].add(self.bnt(*args))\n c = c.at[jnp.ix_(self.i_lm_tot, self.q_i_global)].add(self.s_fact * (self.jac_func(self.c, 1)(*args)))\n c = c.at[jnp.ix_(self.i_lm_tot, self.q_i_global)].add(self.s_fact * (self.jac_func(self.d, 1)(*args)))\n\n k = jnp.zeros((self.num_eq_tot, self.num_eq_tot))\n k = k.at[jnp.ix_(self.q_i_global, self.q_i_global)].add(self.jac_func(self.bht_lmh, 0)(*args))\n k = k.at[jnp.ix_(self.q_i_global, self.q_i_global)].add(self.jac_func(self.bnt_lmn, 0)(*args))\n k = k.at[jnp.ix_(self.q_i_global, self.i_lm_tot)].add(self.bht(*args))\n k = k.at[jnp.ix_(self.i_lm_tot, self.q_i_global)].add(self.s_fact * (self.jac_func(self.c, 0)(*args)))\n k = k.at[jnp.ix_(self.i_lm_tot, self.q_i_global)].add(self.s_fact * (self.jac_func(self.d, 0)(*args)))\n\n rhs = jnp.zeros(self.num_eq_tot)\n rhs = rhs.at[self.q_i_global].add(self.bht_lmh(*args) + self.bnt_lmn(*args))\n rhs = rhs.at[self.i_lm_tot].add(self.s_fact * (self.c(*args) + self.d(*args)))\n\n if self.use_p_fact:\n c = c.at[jnp.ix_(self.q_i_global, self.q_i_global)].add(self.p_fact * (self.jac_func(self.p_func_h, 1)(*args)))\n c = c.at[jnp.ix_(self.q_i_global, self.q_i_global)].add(self.p_fact * (self.jac_func(self.p_func_n, 1)(*args)))\n k = k.at[jnp.ix_(self.q_i_global, self.q_i_global)].add(self.p_fact * (self.jac_func(self.p_func_h, 0)(*args)))\n k = k.at[jnp.ix_(self.q_i_global, self.q_i_global)].add(self.p_fact * (self.jac_func(self.p_func_n, 0)(*args)))\n rhs = rhs.at[self.q_i_global].add(self.p_fact * (self.p_func_h(*args) + self.p_func_n(*args)))\n return c, k, rhs\n\n return run\n\n\ndef combine_constraints(csts: list[Constraint]) -> Callable:\n def combined_run(q: jarr, q_dot: jarr, u: list[None | jarr, ...], u_dot: list[None | jarr, ...], lmh: jarr,\n lmn: jarr) -> tuple[jarr, jarr, jarr]:\n q_i = [cst.q_i_global for cst in csts]\n\n n_cst = len(csts)\n out_mats = [csts[i_cst].run(q[q_i[i_cst]], q_dot[q_i[i_cst]], u[i_cst], u_dot[i_cst], lmh, lmn)\n for i_cst in range(n_cst)]\n c = jnp.sum(jnp.array([out_mats[i][0] for i in range(n_cst)]), axis=0)\n k = jnp.sum(jnp.array([out_mats[i][1] for i in range(n_cst)]), axis=0)\n rhs = jnp.sum(jnp.array([out_mats[i][2] for i in range(n_cst)]), axis=0)\n return c, k, rhs\n\n return jax.jit(combined_run) if USE_JIT else combined_run\n\n\nclass BaseFunc(ABC):\n n_eq = 3\n\n\nclass CstFuncs(ABC):\n class EqualNodeFoR(BaseFunc):\n @staticmethod\n def b_lin_vel(constraint_: Constraint, i_lm: slice, b: jarr, q: jarr, q_dot: jarr, u: jarr, u_dot: jarr) \\\n -> jarr:\n b = b.at[i_lm, constraint_.i_r0].add(\n -Rot.from_quat(q_dot[constraint_.i_quat0]).as_matrix())\n b = b.at[i_lm, constraint_.i_v0].add(\n -Rot.from_quat(q_dot[constraint_.i_quat0]).as_matrix())\n b = b.at[i_lm, constraint_.i_v1].add(\n Rot.from_quat(q_dot[constraint_.i_quat1]).as_matrix())\n b = b.at[i_lm, constraint_.i_omega0].add(\n Rot.from_quat(q_dot[constraint_.i_quat0]).as_matrix() @ skew(q[constraint_.i_r0]))\n return b\n\n @staticmethod\n def b_ang_vel(constraint_: Constraint, i_lm: slice, b: jarr, q: jarr, q_dot: jarr, u: jarr, u_dot: jarr) \\\n -> jarr:\n b = b.at[i_lm, constraint_.i_psi0].add(crv2tan(q[constraint_.i_psi0]))\n b = b.at[i_lm, constraint_.i_omega1].add(-crv2rot(q[constraint_.i_psi0]).T\n @ Rot.from_quat(q_dot[constraint_.i_quat0]).as_matrix().T\n @ Rot.from_quat(q_dot[constraint_.i_quat1]).as_matrix())\n b = b.at[i_lm, constraint_.i_omega0].add(crv2rot(q[constraint_.i_psi0]).T)\n return b\n\n class ControlFoR(BaseFunc):\n @staticmethod\n def b_ang_vel(constraint_: Constraint, i_lm: slice, b: jarr, q: jarr, q_dot: jarr, u: jarr, u_dot: jarr) \\\n -> jarr:\n return b.at[i_lm, constraint_.i_omega1].add(jnp.eye(3))\n\n @staticmethod\n def g_ang_vel(constraint_: Constraint, i_lm: slice, g: jarr, q: jarr, q_dot: jarr, u: jarr, u_dot: jarr) \\\n -> jarr:\n return g.at[i_lm].add(-crv2tan(u) @ u_dot)\n\n class ControlNodeFoR(EqualNodeFoR):\n @staticmethod\n def g_ang_vel(constraint_: Constraint, i_lm: slice, g: jarr, q: jarr, q_dot: jarr, u: jarr, u_dot: jarr) \\\n -> jarr:\n return g.at[i_lm].add(crv2rot(u).T @ crv2tan(u) @ u_dot)\n\n class ZeroFoR(BaseFunc):\n @staticmethod\n def b_lin_vel(constraint_: Constraint, i_lm: slice, b: jarr, q: jarr, q_dot: jarr, u: jarr, u_dot: jarr) \\\n -> jarr:\n return b.at[i_lm, constraint_.i_v1].add(jnp.eye(3))\n\n @staticmethod\n def b_ang_vel(constraint_: Constraint, i_lm: slice, b: jarr, q: jarr, q_dot: jarr, u: jarr, u_dot: jarr) \\\n -> jarr:\n return b.at[i_lm, constraint_.i_omega1].add(jnp.eye(3))\n\n class HingeNodeFoR(BaseFunc):\n n_eq = 2\n\n @staticmethod\n def b_ang_vel(constraint_: Constraint, i_lm: slice, b: jarr, q: jarr, q_dot: jarr, u: jarr, u_dot: jarr) \\\n -> jarr:\n r_ax_a = jnp.array(constraint_.settings['rot_axisA2'])\n r_ax_a /= jnp.linalg.norm(r_ax_a)\n a_skew = skew(r_ax_a)\n\n r_ax_b = jnp.array(constraint_.settings['rot_axisB'])\n r_ax_b /= jnp.linalg.norm(r_ax_b)\n b_skew = skew(r_ax_b)\n\n rot_psi = crv2rot(q[constraint_.i_psi0])\n\n aux = (rot_psi.T @ Rot.from_quat(q[constraint_.i_quat0]).as_matrix().T\n @ Rot.from_quat(q[constraint_.i_quat1]).as_matrix()) @ a_skew\n\n aux_norms = jnp.linalg.norm(aux, axis=1)\n dirs = jnp.array(((1, 2), (0, 2), (0, 1)))[jnp.argmin(aux_norms)]\n\n b = b.at[i_lm, constraint_.i_omega0].add((b_skew @ rot_psi.T)[dirs, :])\n b = b.at[i_lm, constraint_.i_psi0].add((b_skew @ crv2tan(q[constraint_.i_psi0]))[dirs, :])\n b = b.at[i_lm, constraint_.i_omega1].add(-aux[dirs, :])\n return b\n\n class HingeFoR(BaseFunc):\n n_eq = 2\n\n @classmethod\n def b_ang_vel(cls, constraint_: Constraint, i_lm: slice, b: jarr, q: jarr, q_dot: jarr, u: jarr, u_dot: jarr) \\\n -> jarr:\n axis = jnp.array(constraint_.settings['rot_axis_AFoR'])\n axis = axis / jnp.linalg.norm(axis)\n axis_skew = skew(axis)\n dirs = jnp.array(((1, 2), (0, 2), (0, 1)))[jnp.argmax(axis)] # directions for axis matrix\n i_omega1_indep = jnp.arange(constraint_.i_omega1[0], constraint_.i_omega1[2] + 1)[dirs]\n\n b = jax.lax.cond(jnp.abs(jnp.linalg.norm(axis) - 1.) < 1e-6,\n lambda: b.at[i_lm, i_omega1_indep].add(jnp.eye(2)),\n lambda: b.at[i_lm, constraint_.i_omega1].add(axis_skew[dirs, :]))\n return b\n\n\ndef move_for_to_node(constraint_: Constraint, mb_beam, mb_tstep) -> None:\n i_body_node = constraint_.settings['body'] # beam number which contains node\n i_node = constraint_.settings['node_in_body'] # node number in beam\n i_body_for = constraint_.settings['body_FoR']\n rel_pos_b = constraint_.settings.get('rel_posB', np.zeros(3))\n\n i_elem, i_node_in_elem = mb_beam[i_body_node].node_master_elem[i_node]\n c_ga = mb_tstep[i_body_node].cga()\n c_ab = sp.spatial.transform.Rotation.from_rotvec(mb_tstep[i_body_node].psi[i_elem, i_node_in_elem, :]).as_matrix()\n\n mb_tstep[i_body_for].for_pos[:3] = (c_ga @ (mb_tstep[i_body_node].pos[i_node, :] + c_ab @ rel_pos_b)\n + mb_tstep[i_body_node].for_pos[:3])\n\n\n@constraint\nclass FullyConstrainedNodeFoR(Constraint):\n lc_id = 'fully_constrained_node_FoR'\n required_params = ('node_in_body', 'body', 'body_FoR')\n bn_funcs = (CstFuncs.EqualNodeFoR.b_lin_vel, CstFuncs.EqualNodeFoR.b_ang_vel)\n gn_funcs = (None, None)\n num_lmn_eq = (CstFuncs.EqualNodeFoR.n_eq, CstFuncs.EqualNodeFoR.n_eq)\n postproc_funcs = (move_for_to_node,)\n\n\n@constraint\nclass FullyConstrainedFoR(Constraint):\n lc_id = 'fully_constrained_FoR'\n required_params = ('body_FoR',)\n bn_funcs = (CstFuncs.ZeroFoR.b_lin_vel, CstFuncs.ZeroFoR.b_ang_vel)\n gn_funcs = (None, None)\n num_lmn_eq = (CstFuncs.ZeroFoR.n_eq, CstFuncs.ZeroFoR.n_eq)\n\n\n@constraint\nclass SphericalFoR(Constraint):\n lc_id = 'spherical_FoR'\n required_params = ('body_FoR',)\n bn_funcs = (CstFuncs.ZeroFoR.b_lin_vel,)\n gn_funcs = (None,)\n num_lmn_eq = (CstFuncs.ZeroFoR.n_eq,)\n\n\n@constraint\nclass Free(Constraint):\n lc_id = 'free'\n\n\n@constraint\nclass ControlledRotNodeFoR(Constraint):\n lc_id = 'control_node_FoR_rot_vel'\n required_params = ('controller_id', 'node_in_body', 'body', 'body_FoR')\n bn_funcs = (CstFuncs.ControlNodeFoR.b_lin_vel, CstFuncs.ControlNodeFoR.b_ang_vel)\n gn_funcs = (None, CstFuncs.ControlNodeFoR.g_ang_vel)\n num_lmn_eq = (CstFuncs.ControlNodeFoR.n_eq, CstFuncs.ControlNodeFoR.n_eq)\n postproc_funcs = (move_for_to_node,)\n\n\n@constraint\nclass ControlledRotFoR(Constraint):\n lc_id = 'control_rot_vel_FoR'\n required_params = ('controller_id', 'body_FoR')\n bn_funcs = (CstFuncs.ZeroFoR.b_lin_vel, CstFuncs.ControlFoR.b_ang_vel)\n gn_funcs = (None, CstFuncs.ControlFoR.g_ang_vel)\n num_lmn_eq = (CstFuncs.ZeroFoR.n_eq, CstFuncs.ControlFoR.n_eq)\n\n\n@constraint\nclass HingeFoR(Constraint):\n lc_id = 'hinge_FoR'\n required_params = ('body_FoR', 'rot_axis_AFoR')\n bn_funcs = (CstFuncs.ZeroFoR.b_lin_vel, CstFuncs.HingeFoR.b_ang_vel)\n gn_funcs = (None, None)\n num_lmn_eq = (CstFuncs.ZeroFoR.n_eq, CstFuncs.HingeFoR.n_eq)\n\n\n@constraint\nclass SphericalNodeFor(Constraint):\n lc_id = 'spherical_node_FoR'\n required_params = ('body', 'body_FoR', 'node_in_body')\n bn_funcs = (CstFuncs.EqualNodeFoR.b_lin_vel, )\n gn_funcs = (None, )\n num_lmn_eq = (CstFuncs.EqualNodeFoR.n_eq, )\n postproc_funcs = (move_for_to_node,)\n\n\n@constraint\nclass HingeNodeFoR(Constraint):\n lc_id = 'hinge_node_FoR'\n required_params = ('body', 'body_FoR', 'node_in_body', 'rot_axisA2', 'rot_axisB')\n bn_funcs = (CstFuncs.EqualNodeFoR.b_lin_vel, CstFuncs.HingeNodeFoR.b_ang_vel)\n gn_funcs = (None, None)\n num_lmn_eq = (CstFuncs.EqualNodeFoR.n_eq, CstFuncs.HingeNodeFoR.n_eq)\n postproc_funcs = (move_for_to_node,)\n\n\nif __name__ == '__main__':\n print(\"Available constraints:\")\n for constraint in DICT_OF_LC.values():\n print(constraint.lc_id)\n" }, { "path": "sharpy/structure/utils/modalutils.py", "content": "import numpy as np\nimport sharpy.utils.cout_utils as cout\nimport sharpy.utils.algebra as algebra\n\nfrom sharpy.utils.plotutils import plot_frame_to_vtk\n\ndef frequency_damping(eigenvalue):\n omega_n = np.abs(eigenvalue)\n omega_d = np.abs(eigenvalue.imag)\n f_n = omega_n / 2 / np.pi\n f_d = omega_d / 2 / np.pi\n if f_d < 1e-8:\n damping_ratio = 1.\n period = np.inf\n else:\n damping_ratio = -eigenvalue.real / omega_n\n period = 1 / f_d\n\n return omega_n, omega_d, damping_ratio, f_n, f_d, period\n\n\nclass EigenvalueTable(cout.TablePrinter):\n def __init__(self, filename=None):\n super().__init__(7, 12, ['g', 'f', 'f', 'f', 'f', 'f', 'f'], filename)\n\n self.headers = ['mode', 'eval_real', 'eval_imag', 'freq_n (Hz)', 'freq_d (Hz)',\n 'damping', 'period (s)']\n\n def print_evals(self, eigenvalues):\n for i in range(len(eigenvalues)):\n omega_n, omega_d, damping_ratio, f_n, f_d, period = frequency_damping(eigenvalues[i])\n self.print_line([i, eigenvalues[i].real, eigenvalues[i].imag, f_n, f_d,\n damping_ratio, period])\n\n\ndef cg(M, use_euler=False):\n if use_euler:\n Mrr = M[-9:, -9:]\n else:\n Mrr = M[-10:, -10:]\n return -np.array([Mrr[2, 4], Mrr[0, 5], Mrr[1, 3]]) / Mrr[0, 0]\n\n\ndef scale_mode(data, eigenvector, rot_max_deg=15.0, perc_max=0.15):\n \"\"\"\n Scales the eigenvector such that:\n 1) the maximum change in component of the beam cartesian rotation vector\n is equal to rot_max_deg degrees.\n 2) the maximum translational displacement does not exceed perc_max the\n maximum nodal position.\n\n Warning:\n If the eigenvector is in state-space form, only the first\n half of the eigenvector is scanned for determining the scaling.\n \"\"\"\n\n ### initialise\n struct = data.structure\n tsstr = data.structure.timestep_info[data.ts]\n\n jj = 0 # structural dofs index\n RotMax = 0.0\n RaMax = 0.0\n dRaMax = 0.0\n\n for node_glob in range(struct.num_node):\n ### detect bc at node (and no. of dofs)\n bc_here = struct.boundary_conditions[node_glob]\n if bc_here == 1: # clamp\n dofs_here = 0\n continue\n elif bc_here == -1 or bc_here == 0:\n dofs_here = 6\n jj_tra = [jj, jj + 1, jj + 2]\n jj_rot = [jj + 3, jj + 4, jj + 5]\n jj += dofs_here\n\n # check for max rotation\n RotMaxHere = np.max(np.abs(eigenvector[jj_rot].real))\n if RotMaxHere > RotMax:\n RotMax = RotMaxHere\n\n # check for maximum position\n RaNorm = np.linalg.norm(tsstr.pos[node_glob, :])\n if RaNorm > RaMax:\n RaMax = RaNorm\n\n # check for maximum displacement\n dRaNorm = np.linalg.norm(eigenvector[jj_tra].real)\n if dRaNorm > dRaMax:\n dRaMax = dRaNorm\n\n RotMaxDeg = RotMax * 180 / np.pi\n\n if RotMaxDeg > 1e-4:\n fact = rot_max_deg / RotMaxDeg\n if dRaMax * fact > perc_max * RaMax:\n fact = perc_max * RaMax / dRaMax\n else:\n fact = perc_max * RaMax / dRaMax\n # correct factor to ensure max disp is perc\n return fact\n\n\ndef get_mode_zeta(data, eigvect):\n \"\"\"\n Retrieves the UVLM grid nodal displacements associated to the eigenvector ``eigvect``\n \"\"\"\n\n ### initialise\n aero = data.aero\n struct = data.structure\n tsaero = data.aero.timestep_info[data.ts]\n tsstr = data.structure.timestep_info[data.ts]\n\n try:\n num_dof = struct.num_dof.value\n except AttributeError:\n num_dof = struct.num_dof\n\n eigvect = eigvect[:num_dof]\n\n zeta_mode = []\n for ss in range(aero.n_surf):\n zeta_mode.append(tsaero.zeta[ss].copy())\n\n jj = 0 # structural dofs index\n Cga0 = algebra.quat2rotation(tsstr.quat)\n Cag0 = Cga0.T\n for node_glob in range(struct.num_node):\n\n ### detect bc at node (and no. of dofs)\n bc_here = struct.boundary_conditions[node_glob]\n if bc_here == 1: # clamp\n dofs_here = 0\n continue\n elif bc_here == -1 or bc_here == 0:\n dofs_here = 6\n jj_tra = [jj, jj + 1, jj + 2]\n jj_rot = [jj + 3, jj + 4, jj + 5]\n jj += dofs_here\n\n # retrieve element and local index\n ee, node_loc = struct.node_master_elem[node_glob, :]\n\n # get original position and crv\n Ra0 = tsstr.pos[node_glob, :]\n psi0 = tsstr.psi[ee, node_loc, :]\n Rg0 = np.dot(Cga0, Ra0)\n Cab0 = algebra.crv2rotation(psi0)\n Cbg0 = np.dot(Cab0.T, Cag0)\n\n # update position and crv of mode\n Ra = tsstr.pos[node_glob, :] + eigvect[jj_tra]\n psi = tsstr.psi[ee, node_loc, :] + eigvect[jj_rot]\n Rg = np.dot(Cga0, Ra)\n Cab = algebra.crv2rotation(psi)\n Cbg = np.dot(Cab.T, Cag0)\n\n ### str -> aero mapping\n # some nodes may be linked to multiple surfaces...\n for str2aero_here in aero.struct2aero_mapping[node_glob]:\n\n # detect surface/span-wise coordinate (ss,nn)\n nn, ss = str2aero_here['i_n'], str2aero_here['i_surf']\n # print('%.2d,%.2d'%(nn,ss))\n\n # surface panelling\n M = aero.dimensions[ss][0]\n N = aero.dimensions[ss][1]\n\n for mm in range(M + 1):\n # get position of vertex in B FoR\n zetag0 = tsaero.zeta[ss][:, mm, nn] # in G FoR, w.r.t. origin A-G\n Xb = np.dot(Cbg0, zetag0 - Rg0) # in B FoR, w.r.t. origin B\n\n # update vertex position\n zeta_mode[ss][:, mm, nn] = Rg + np.dot(np.dot(Cga0, Cab), Xb)\n\n return zeta_mode\n\n\ndef write_zeta_vtk(zeta, zeta_ref, filename_root):\n \"\"\"\n Given a list of arrays representing the coordinates of a set of n_surf UVLM\n lattices and organised as:\n zeta[n_surf][3,M+1,N=1]\n this function writes a vtk for each of the n_surf surfaces.\n\n Args:\n zeta (np.array): lattice coordinates to plot\n zeta_ref (np.array): reference lattice used to compute the magnitude of displacements\n filename_root (str): initial part of filename (full path) without file extension\n \"\"\"\n\n for i_surf in range(len(zeta)):\n\n filename = f\"{filename_root}_{i_surf:02d}.vtu\"\n\n this_zeta = np.swapaxes(zeta[i_surf], 0, -1)\n this_zeta_ref = np.swapaxes(zeta_ref[i_surf], 0, -1)\n disp = np.linalg.norm(this_zeta - this_zeta_ref, axis=-1)\n panel_surf_id = np.ones((this_zeta.shape[0]-1, this_zeta.shape[1]-1), dtype=int) * i_surf\n\n plot_frame_to_vtk(this_zeta,\n filename,\n node_scalar_data={'point_displacement_magnitude': disp},\n cell_scalar_data={'panel_surface_id': panel_surf_id})\n\n\ndef write_modes_vtk(data, eigenvectors, num_lambda, filename_root,\n rot_max_deg=15., perc_max=0.15, ts=-1):\n \"\"\"\n Writes a vtk file for each of the first ``num_lambda`` eigenvectors. When these\n are associated to the state-space form of the structural equations, only\n the displacement field is saved.\n \"\"\"\n\n # initialise\n struct = data.structure\n tsaero = data.aero.timestep_info[ts]\n num_dof = struct.num_dof.value\n eigenvectors = eigenvectors[:num_dof, :]\n\n # skip rigid body modes\n num_rigid_body = 10 if data.settings['Modal']['rigid_body_modes'] else 0\n\n for mode in range(num_rigid_body, num_lambda):\n # scale eigenvector\n eigvec = eigenvectors[:num_dof, mode]\n fact = scale_mode(data, eigvec, rot_max_deg, perc_max)\n eigvec = eigvec * fact\n zeta_mode = get_mode_zeta(data, eigvec)\n write_zeta_vtk(zeta_mode, tsaero.zeta, f\"{filename_root}_{mode:06d}\")\n\n\ndef free_modes_principal_axes(phi, mass_matrix, use_euler=False, **kwargs):\n \"\"\"\n Transforms the rigid body modes defined at with the A frame as reference to the centre of mass position and aligned\n with the principal axes of inertia.\n\n Args:\n phi (np.array): Eigenvectors defined at the ``A`` frame.\n mass_matrix (np.array): System mass matrix\n use_euler (bool): Use Euler rotation parametrisation rather than quaternions.\n\n Keyword Args:\n return_transform (bool): Return tuple containing transformed modes and the transformation from the ``A`` frame\n to the ``P`` frame.\n\n Returns:\n np.array: Mass normalised modes with rigid modes defined at the centre of gravity and aligned with the\n principal axes of inertia.\n\n References:\n Marc Artola, 2020\n \"\"\"\n if use_euler:\n num_rigid_modes = 9\n else:\n num_rigid_modes = 10\n\n r_cg = cg(mass_matrix, use_euler) # centre of gravity\n mrr = mass_matrix[-num_rigid_modes:-num_rigid_modes + 6, -num_rigid_modes:-num_rigid_modes + 6]\n m = mrr[0, 0] # mass\n\n # principal axes of inertia matrix and transformation matrix\n j_cm, t_rb = principal_axes_inertia(mrr[-3:, -3:], r_cg, m)\n\n # rigid body mass matrix about CM and inertia in principal axes\n m_cm = np.eye(6) * m\n m_cm[-3:, -3:] = np.diag(j_cm)\n\n # rigid body modes about CG - mass normalised\n rb_cm = np.eye(6)\n rb_cm /= np.sqrt(np.diag(rb_cm.T.dot(m_cm.dot(rb_cm))))\n\n # transform to A frame reference position\n trb_diag = np.zeros((6, 6)) # matrix with (t_rb, t_rb) in the diagonal\n trb_diag[:3, :3] = t_rb\n trb_diag[-3:, -3:] = t_rb\n rb_a = np.block([[np.eye(3), algebra.skew(r_cg)], [np.zeros((3, 3)), np.eye(3)]]).dot(trb_diag.dot(rb_cm))\n\n phit = np.block([np.zeros((phi.shape[0], num_rigid_modes)), phi[:, num_rigid_modes:]])\n phit[-num_rigid_modes:-num_rigid_modes + 6, :6] = rb_a\n\n phit[-num_rigid_modes + 6:, 6:num_rigid_modes] = np.eye(num_rigid_modes - 6) # euler or quaternion modes\n\n if kwargs.get('return_transform', False):\n return phit, t_rb, np.block([[np.eye(3), algebra.skew(r_cg)], [np.zeros((3, 3)), np.eye(3)]]).dot(trb_diag)\n else:\n return phit\n\n\ndef principal_axes_inertia(j_a, r_cg, m):\n r\"\"\"\n Transform the inertia tensor :math:`\\boldsymbol{j}_a` defined about the ``A`` frame of reference to the centre of\n gravity and aligned with the principal axes of inertia.\n\n The inertia tensor about the centre of gravity is obtained using the parallel axes theorem\n\n .. math:: \\boldsymbol{j}_{cm} = \\boldsymbol{j}_a + \\tilde{r}_{cg}\\tilde{r}_{cg}m\n\n and rotated such that it is aligned with its eigenvectors and thus represents the inertia tensor about the principal\n axes of inertia\n\n .. math:: \\boldsymbol{j}_p = T_{pa}^\\top \\boldsymbol{j}_{cm} T^{pa}\n\n where :math:`T^{pa}` is the transformation matrix from the ``A`` frame to the principal axes ``P`` frame.\n\n Args:\n j_a (np.array): Inertia tensor defined about the ``A`` frame.\n r_cg (np.array): Centre of gravity position defined in ``A`` coordinates.\n m (float): Mass.\n\n Returns:\n tuple: Containing :math:`\\boldsymbol{j}_p` and :math:`T^{pa}`\n\n \"\"\"\n\n j_p, t_pa = np.linalg.eig(j_a + algebra.skew(r_cg) @ (algebra.skew(r_cg)) * m)\n\n t_pa, j_p = order_eigenvectors(t_pa, j_p)\n\n return j_p, t_pa\n\n\ndef mode_sign_convention(bocos, eigenvectors, rigid_body_motion=False, use_euler=False):\n \"\"\"\n When comparing against different cases, it is important that the modes share a common sign convention.\n\n In this case, modes will be arranged such that the z-coordinate of the first free end is positive.\n\n If the z-coordinate is 0, then the y-coordinate is forced to be positive, then x, followed by the CRV in y, x and z.\n\n Returns:\n np.ndarray: Eigenvectors following the aforementioned sign convention.\n \"\"\"\n\n if use_euler:\n num_rigid_modes = 9\n else:\n num_rigid_modes = 10\n\n if rigid_body_motion:\n eigenvectors = order_rigid_body_modes(eigenvectors, use_euler)\n\n # A frame reference\n z_coord = -num_rigid_modes + 2\n y_coord = -num_rigid_modes + 1\n x_coord = -num_rigid_modes + 0\n mz_coord = -num_rigid_modes + 5\n my_coord = -num_rigid_modes + 4\n mx_coord = -num_rigid_modes + 3\n else:\n first_free_end_node = np.where(bocos == -1)[0][0]\n\n z_coord = 6 * (first_free_end_node - 1) + 2\n y_coord = 6 * (first_free_end_node - 1) + 1\n x_coord = 6 * (first_free_end_node - 1) + 0\n my_coord = 6 * (first_free_end_node - 1) + 4\n mz_coord = 6 * (first_free_end_node - 1) + 5\n mx_coord = 6 * (first_free_end_node - 1) + 3\n\n for i in range(0, eigenvectors.shape[1]):\n if np.abs(eigenvectors[z_coord, i]) > 1e-8:\n eigenvectors[:, i] = np.sign(eigenvectors[z_coord, i]) * eigenvectors[:, i]\n\n elif np.abs(eigenvectors[y_coord, i]) > 1e-8:\n eigenvectors[:, i] = np.sign(eigenvectors[y_coord, i]) * eigenvectors[:, i]\n\n elif np.abs(eigenvectors[x_coord, i]) > 1e-8:\n eigenvectors[:, i] = np.sign(eigenvectors[x_coord, i]) * eigenvectors[:, i]\n\n elif np.abs(eigenvectors[my_coord, i]) > 1e-8:\n eigenvectors[:, i] = np.sign(eigenvectors[my_coord, i]) * eigenvectors[:, i]\n\n elif np.abs(eigenvectors[mx_coord, i]) > 1e-8:\n eigenvectors[:, i] = np.sign(eigenvectors[mx_coord, i]) * eigenvectors[:, i]\n\n elif np.abs(eigenvectors[mz_coord, i]) > 1e-8:\n eigenvectors[:, i] = np.sign(eigenvectors[mz_coord, i]) * eigenvectors[:, i]\n\n else:\n if rigid_body_motion:\n if not np.max(np.abs(eigenvectors[-num_rigid_modes+6:, i])) == 1.0: # orientation mode, either euler/quat\n cout.cout_wrap('Implementing mode sign convention. Mode {:g} component at the A frame is 0.'.format(i), 3)\n else:\n # cout.cout_wrap('Mode component at the first free end (node {:g}) is 0.'.format(first_free_end_node), 3)\n\n # this will be the case for symmetric clamped structures, where modes will be present for the left and\n # right wings. Method should be called again when symmetric modes are removed.\n pass\n\n return eigenvectors\n\n\ndef order_rigid_body_modes(eigenvectors, use_euler):\n\n if use_euler:\n num_rigid_modes = 9\n else:\n num_rigid_modes = 10\n\n phi_rr = np.zeros((num_rigid_modes, num_rigid_modes))\n num_node = eigenvectors.shape[0]\n\n for i in range(num_rigid_modes):\n index_max_node = np.where(eigenvectors[:, i] == np.max(eigenvectors[:, i]))[0][0]\n index_mode = num_rigid_modes - (num_node - index_max_node)\n phi_rr[:, index_mode] = eigenvectors[-num_rigid_modes:, i]\n\n eigenvectors[-num_rigid_modes:, :num_rigid_modes] = phi_rr\n\n return eigenvectors\n\n\ndef order_eigenvectors(eigenvectors, eigenvalues):\n ordered_eigenvectors = np.zeros_like(eigenvectors)\n new_order = []\n for i in range(eigenvectors.shape[1]):\n index_max_node = np.where(np.abs(eigenvectors[:, i]) == np.max(np.abs(eigenvectors[:, i])))[0][0]\n ordered_eigenvectors[:, index_max_node] = eigenvectors[:, i] * np.sign(eigenvectors[index_max_node, i])\n new_order.append(index_max_node)\n\n try:\n eigenvalues.shape[1]\n except IndexError:\n new_eigenvalues = eigenvalues[new_order]\n else:\n new_eigenvalues = eigenvalues[:, new_order]\n\n return ordered_eigenvectors, new_eigenvalues\n\n\ndef scale_mass_normalised_modes(eigenvectors, mass_matrix):\n r\"\"\"\n Scales eigenvector matrix such that the modes are mass normalised:\n\n .. math:: \\phi^\\top\\boldsymbol{M}\\phi = \\boldsymbol{I}\n\n and\n\n .. math:: \\phi^\\top\\boldsymbol{K}\\phi = \\mathrm{diag}(\\omega^2)\n\n Args:\n eigenvectors (np.array): Eigenvector matrix.\n mass_matrix (np.array): Mass matrix.\n\n Returns:\n np.array: Mass-normalised eigenvectors.\n \"\"\"\n # mass normalise (diagonalises M and K)\n dfact = np.diag(np.dot(eigenvectors.T, np.dot(mass_matrix, eigenvectors)))\n eigenvectors = (1./np.sqrt(dfact))*eigenvectors\n\n return eigenvectors\n\n\ndef assert_orthogonal_eigenvectors(u, v, decimal, raise_error=False):\n \"\"\"\n Checks orthogonality between eigenvectors\n\n Args:\n u (np.ndarray): Eigenvector 1.\n v (np.ndarray): Eigenvector 2.\n decimal (int): Number of decimal points to compare\n raise_error (bool): Raise an error or print a warning\n\n Raises:\n AssertionError: if ``raise_error == True`` it raises an error.\n\n \"\"\"\n try:\n np.testing.assert_almost_equal(u.dot(v), 0, decimal=decimal,\n err_msg='Eigenvectors not orthogonal') # random eigenvector to test orthonality\n except AssertionError as e:\n if raise_error:\n raise e\n else:\n cout.cout_wrap('Eigenvectors not orthogonal', 3)\n\n\ndef assert_modes_mass_normalised(phi, m, tolerance, raise_error=False):\n \"\"\"\n Asserts the eigenvectors result in an identity modal mass matrix.\n\n Args:\n phi (np.ndarray): Eigenvector matrix\n m (np.ndarray): Mass matrix\n tolerance (float): Absolute tolerance.\n raise_error (bool): Raise ``AssertionError`` if modes not mass normalised.\n\n Returns:\n AssertionError: if ``raise_error == True`` it raises an error.\n\n \"\"\"\n modal_mass = phi.T.dot(m.dot(phi))\n\n try:\n np.testing.assert_allclose(modal_mass - np.eye(modal_mass.shape[0]), np.zeros_like(modal_mass),\n atol=tolerance, err_msg='Eigenvectors are not mass normalised')\n except AssertionError as e:\n if raise_error:\n raise e\n else:\n cout.cout_wrap('Eigenvectors are not mass normalised', 3)\n\n\ndef modes_to_cg_ref(phi, M, rigid_body_motion=False, use_euler=False):\n r\"\"\"\n\n Returns the rigid body modes defined with respect to the centre of gravity\n\n The transformation from the modes defined at the FoR A origin, :math:`\\boldsymbol{\\Phi}`, to the modes defined\n using the centre of gravity as a reference is\n\n\n .. math:: \\boldsymbol{\\Phi}_{rr,CG}|_{TRA} = \\boldsymbol{\\Phi}_{RR}|_{TRA} + \\tilde{\\mathbf{r}}_{CG}\n \\boldsymbol{\\Phi}_{RR}|_{ROT}\n\n .. math:: \\boldsymbol{\\Phi}_{rr,CG}|_{ROT} = \\boldsymbol{\\Phi}_{RR}|_{ROT}\n\n Returns:\n (np.array): Transformed eigenvectors\n \"\"\"\n # if not rigid_body_motion:\n # return phi\n # NG - 26/7/19 This is the transformation being performed by K_vec\n # Leaving this here for now in case it becomes necessary\n # .. math:: \\boldsymbol{\\Phi}_{ss,CG}|_{TRA} = \\boldsymbol{\\Phi}_{SS}|_{TRA} +\\boldsymbol{\\Phi}_{RS}|_{TRA} -\n # \\tilde{\\mathbf{r}}_{A}\\boldsymbol{\\Phi}_{RS}|_{ROT}\n #\n # .. math:: \\boldsymbol{\\Phi}_{ss,CG}|_{ROT} = \\boldsymbol{\\Phi}_{SS}|_{ROT}\n # + (\\mathbf{T}(\\boldsymbol{\\Psi})^\\top)^{-1}\\boldsymbol{\\Phi}_{RS}|_{ROT}\n # pos = self.data.structure.timestep_info[self.data.ts].pos\n r_cg = cg(M)\n\n # jj = 0\n K_vec = np.zeros((phi.shape[0], phi.shape[0]))\n\n # jj_for_vel = range(self.data.structure.num_dof.value, self.data.structure.num_dof.value + 3)\n # jj_for_rot = range(self.data.structure.num_dof.value + 3, self.data.structure.num_dof.value + 6)\n\n # for node_glob in range(self.data.structure.num_node):\n # ### detect bc at node (and no. of dofs)\n # bc_here = self.data.structure.boundary_conditions[node_glob]\n #\n # if bc_here == 1: # clamp (only rigid-body)\n # dofs_here = 0\n # jj_tra, jj_rot = [], []\n # continue\n #\n # elif bc_here == -1 or bc_here == 0: # (rigid+flex body)\n # dofs_here = 6\n # jj_tra = 6 * self.data.structure.vdof[node_glob] + np.array([0, 1, 2], dtype=int)\n # jj_rot = 6 * self.data.structure.vdof[node_glob] + np.array([3, 4, 5], dtype=int)\n # # jj_tra=[jj ,jj+1,jj+2]\n # # jj_rot=[jj+3,jj+4,jj+5]\n # else:\n # raise NameError('Invalid boundary condition (%d) at node %d!' \\\n # % (bc_here, node_glob))\n #\n # jj += dofs_here\n #\n # ee, node_loc = self.data.structure.node_master_elem[node_glob, :]\n # psi = self.data.structure.timestep_info[self.data.ts].psi[ee, node_loc, :]\n #\n # Ra = pos[node_glob, :] # in A FoR with respect to G\n #\n # K_vec[np.ix_(jj_tra, jj_tra)] += np.eye(3)\n # K_vec[np.ix_(jj_tra, jj_for_vel)] += np.eye(3)\n # K_vec[np.ix_(jj_tra, jj_for_rot)] -= algebra.skew(Ra)\n #\n # K_vec[np.ix_(jj_rot, jj_rot)] += np.eye(3)\n # K_vec[np.ix_(jj_rot, jj_for_rot)] += np.linalg.inv(algebra.crv2tan(psi).T)\n # NG - 26/7/19 - Transformation of the rigid part of the elastic modes ended up not being necessary but leaving\n # here in case it becomes useful in the future (using K_vec)\n\n # Rigid-Rigid modes transform\n if use_euler:\n num_rig_dof = 9\n else:\n num_rig_dof = 10\n Krr = np.eye(num_rig_dof)\n Krr[np.ix_([0, 1, 2], [3, 4, 5])] += algebra.skew(r_cg)\n\n # Assemble transformed modes\n phirr = Krr.dot(phi[-num_rig_dof:, :num_rig_dof])\n # phiss = K_vec.dot(phi[:, 10:])\n\n # Get rigid body modes to be positive in translation and rotation\n for i in range(num_rig_dof):\n ind = np.argmax(np.abs(phirr[:, i]))\n phirr[:, i] = np.sign(phirr[ind, i]) * phirr[:, i]\n\n phit = np.block([np.zeros((phi.shape[0], num_rig_dof)), phi[:, num_rig_dof:]])\n phit[-num_rig_dof:, :num_rig_dof] = phirr\n\n return phit\n" }, { "path": "sharpy/structure/utils/xbeamlib.py", "content": "import ctypes as ct\nimport numpy as np\nimport scipy as sc\nimport scipy.integrate\n\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.ctypes_utils as ct_utils\nfrom sharpy.utils.sharpydir import SharpyDir\n# from sharpy.utils.datastructures import StructTimeStepInfo\nimport sharpy.utils.cout_utils as cout\n\n\ntry:\n xbeamlib = ct_utils.import_ctypes_lib(SharpyDir + '/xbeam', 'libxbeam')\nexcept OSError:\n xbeamlib = ct_utils.import_ctypes_lib(SharpyDir + '/lib/xbeam/lib',\n 'libxbeam')\n\n# ctypes pointer types\ndoubleP = ct.POINTER(ct.c_double)\nintP = ct.POINTER(ct.c_int)\ncharP = ct.POINTER(ct.c_char_p)\n\n\nclass Xbopts(ct.Structure):\n \"\"\"Structure skeleton for options input in xbeam\n\n \"\"\"\n _fields_ = [(\"FollowerForce\", ct.c_bool),\n (\"FollowerForceRig\", ct.c_bool),\n (\"PrintInfo\", ct.c_bool),\n (\"OutInBframe\", ct.c_bool),\n (\"OutInaframe\", ct.c_bool),\n (\"ElemProj\", ct.c_int),\n (\"MaxIterations\", ct.c_int),\n (\"NumLoadSteps\", ct.c_int),\n (\"NumGauss\", ct.c_int),\n (\"Solution\", ct.c_int),\n (\"DeltaCurved\", ct.c_double),\n (\"MinDelta\", ct.c_double),\n (\"abs_threshold\", ct.c_double),\n (\"NewmarkDamp\", ct.c_double),\n (\"gravity_on\", ct.c_bool),\n (\"gravity\", ct.c_double),\n (\"gravity_dir_x\", ct.c_double),\n (\"gravity_dir_y\", ct.c_double),\n (\"gravity_dir_z\", ct.c_double),\n (\"balancing\", ct.c_bool),\n (\"relaxation_factor\", ct.c_double),\n ]\n\n def __init__(self):\n ct.Structure.__init__(self)\n self.FollowerForce = ct.c_bool(True)\n self.FollowerForceRig = ct.c_bool(True)\n self.PrintInfo = ct.c_bool(True)\n self.OutInBframe = ct.c_bool(False)\n self.OutInaframe = ct.c_bool(True)\n self.ElemProj = ct.c_int(0)\n self.MaxIterations = ct.c_int(99)\n self.NumLoadSteps = ct.c_int(5)\n self.NumGauss = ct.c_int(0)\n self.Solution = ct.c_int(111)\n self.DeltaCurved = ct.c_double(1.0e-2)\n self.MinDelta = ct.c_double(1.0e-8)\n self.abs_threshold = ct.c_double(1.0e-13)\n self.NewmarkDamp = ct.c_double(0.0)\n self.gravity_on = ct.c_bool(False)\n self.gravity = ct.c_double(0.0)\n self.gravity_dir_x = ct.c_double(0.0)\n self.gravity_dir_y = ct.c_double(0.0)\n self.gravity_dir_z = ct.c_double(1.0)\n self.balancing = ct.c_bool(False)\n self.relaxation_factor = ct.c_double(0.3)\n\n\ndef cbeam3_solv_nlnstatic(beam, settings, ts):\n \"\"\"@brief Python wrapper for f_cbeam3_solv_nlnstatic\n Alfonso del Carre\n \"\"\"\n f_cbeam3_solv_nlnstatic = xbeamlib.cbeam3_solv_nlnstatic_python\n f_cbeam3_solv_nlnstatic.restype = None\n\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n n_mass = ct.c_int(beam.n_mass)\n n_stiff = ct.c_int(beam.n_stiff)\n\n xbopts = Xbopts()\n xbopts.PrintInfo = ct.c_bool(settings['print_info'])\n xbopts.Solution = ct.c_int(112)\n xbopts.MaxIterations = ct.c_int(settings['max_iterations'])\n xbopts.NumLoadSteps = ct.c_int(settings['num_load_steps'])\n xbopts.DeltaCurved = ct.c_double(settings['delta_curved'])\n xbopts.MinDelta = ct.c_double(settings['min_delta'])\n xbopts.abs_threshold = ct.c_double(settings['abs_threshold'])\n xbopts.gravity_on = ct.c_bool(settings['gravity_on'])\n xbopts.gravity = ct.c_double(settings['gravity'])\n gravity_vector = np.dot(beam.timestep_info[ts].cag(), settings['gravity_dir'])\n xbopts.gravity_dir_x = ct.c_double(gravity_vector[0])\n xbopts.gravity_dir_y = ct.c_double(gravity_vector[1])\n xbopts.gravity_dir_z = ct.c_double(gravity_vector[2])\n xbopts.relaxation_factor = ct.c_double(settings['relaxation_factor'])\n\n # here we only need to set the flags at True, all the forces are follower\n xbopts.FollowerForce = ct.c_bool(True)\n xbopts.FollowerForceRig = ct.c_bool(True)\n\n\n f_cbeam3_solv_nlnstatic(ct.byref(n_elem),\n ct.byref(n_nodes),\n beam.fortran['num_nodes'].ctypes.data_as(intP),\n beam.fortran['num_mem'].ctypes.data_as(intP),\n beam.fortran['connectivities'].ctypes.data_as(intP),\n beam.fortran['master'].ctypes.data_as(intP),\n ct.byref(n_mass),\n beam.fortran['mass'].ctypes.data_as(doubleP),\n beam.fortran['mass_indices'].ctypes.data_as(intP),\n ct.byref(n_stiff),\n beam.fortran['stiffness'].ctypes.data_as(doubleP),\n beam.fortran['inv_stiffness'].ctypes.data_as(doubleP),\n beam.fortran['stiffness_indices'].ctypes.data_as(intP),\n beam.fortran['frame_of_reference_delta'].ctypes.data_as(doubleP),\n beam.fortran['rbmass'].ctypes.data_as(doubleP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['fdof'].ctypes.data_as(intP),\n ct.byref(xbopts),\n beam.ini_info.pos.ctypes.data_as(doubleP),\n beam.ini_info.psi.ctypes.data_as(doubleP),\n beam.timestep_info[ts].pos.ctypes.data_as(doubleP),\n beam.timestep_info[ts].psi.ctypes.data_as(doubleP),\n beam.timestep_info[ts].steady_applied_forces.ctypes.data_as(doubleP),\n beam.timestep_info[ts].gravity_forces.ctypes.data_as(doubleP)\n )\n\n\ndef cbeam3_loads(beam, timestep):\n \"\"\"Python wrapper for f_cbeam3_loads\n \n Args:\n beam (sharpy.structure.models.beam.Beam): Structural info class\n timestep (sharpy.utils.datastructures.StructTimeStepInfo): Structural time step class\n\n Returns:\n tuple: Tuple containing the ``strains`` and ``loads``.\n \"\"\"\n f_cbeam3_loads = xbeamlib.cbeam3_loads\n f_cbeam3_loads.restype = None\n\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n n_stiff = ct.c_int(beam.n_stiff)\n\n strain = np.zeros((n_elem.value, 6), dtype=ct.c_double, order='F')\n loads = np.zeros((n_elem.value, 6), dtype=ct.c_double, order='F')\n\n f_cbeam3_loads(ct.byref(n_elem),\n ct.byref(n_nodes),\n beam.fortran['connectivities'].ctypes.data_as(intP),\n beam.ini_info.pos.ctypes.data_as(doubleP),\n timestep.pos.ctypes.data_as(doubleP),\n beam.ini_info.psi.ctypes.data_as(doubleP),\n timestep.psi.ctypes.data_as(doubleP),\n beam.fortran['stiffness_indices'].ctypes.data_as(intP),\n ct.byref(n_stiff),\n beam.fortran['stiffness'].ctypes.data_as(doubleP),\n strain.ctypes.data_as(doubleP),\n loads.ctypes.data_as(doubleP))\n\n return strain, loads\n\n\ndef cbeam3_solv_nlndyn(beam, settings):\n f_cbeam3_solv_nlndyn = xbeamlib.cbeam3_solv_nlndyn_python\n f_cbeam3_solv_nlndyn.restype = None\n\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n n_mass = ct.c_int(beam.n_mass)\n n_stiff = ct.c_int(beam.n_stiff)\n\n dt = settings['dt']\n n_tsteps = settings['num_steps']\n time = np.zeros((n_tsteps,), dtype=ct.c_double, order='F')\n for i in range(n_tsteps):\n time[i] = i*dt\n\n # deformation history matrices\n pos_def_history = np.zeros((n_tsteps, beam.num_node, 3), order='F')\n pos_dot_def_history = np.zeros((n_tsteps, beam.num_node, 3), order='F')\n psi_def_history = np.zeros((n_tsteps, beam.num_elem, 3, 3), order='F')\n psi_dot_def_history = np.zeros((n_tsteps, beam.num_elem, 3, 3), order='F')\n\n n_tsteps = ct.c_int(n_tsteps)\n\n xbopts = Xbopts()\n xbopts.PrintInfo = ct.c_bool(settings['print_info'])\n xbopts.Solution = ct.c_int(312)\n # xbopts.OutInaframe = ct.c_bool(settings['out_a_frame'])\n # xbopts.OutInBframe = ct.c_bool(settings['out_b_frame'])\n # xbopts.ElemProj = settings['elem_proj']\n xbopts.MaxIterations = ct.c_int(settings['max_iterations'])\n xbopts.NumLoadSteps = ct.c_int(settings['num_load_steps'])\n xbopts.NumGauss = ct.c_int(0)\n xbopts.DeltaCurved = ct.c_double(settings['delta_curved'])\n xbopts.MinDelta = ct.c_double(settings['min_delta'])\n xbopts.abs_threshold = ct.c_double(settings['abs_threshold'])\n xbopts.NewmarkDamp = ct.c_double(settings['newmark_damp'])\n xbopts.gravity_on = ct.c_bool(settings['gravity_on'])\n xbopts.gravity = ct.c_double(settings['gravity'])\n xbopts.gravity_dir_x = ct.c_double(settings['gravity_dir'][0])\n xbopts.gravity_dir_y = ct.c_double(settings['gravity_dir'][1])\n xbopts.gravity_dir_z = ct.c_double(settings['gravity_dir'][2])\n xbopts.relaxation_factor = ct.c_double(settings['relaxation_factor'])\n\n # here we only need to set the flags at True, all the forces are follower\n xbopts.FollowerForce = ct.c_bool(True)\n xbopts.FollowerForceRig = ct.c_bool(True)\n\n\n f_cbeam3_solv_nlndyn(ct.byref(n_elem),\n ct.byref(n_nodes),\n ct.byref(n_tsteps),\n time.ctypes.data_as(doubleP),\n beam.fortran['num_nodes'].ctypes.data_as(intP),\n beam.fortran['num_mem'].ctypes.data_as(intP),\n beam.fortran['connectivities'].ctypes.data_as(intP),\n beam.fortran['master'].ctypes.data_as(intP),\n ct.byref(n_mass),\n beam.fortran['mass'].ctypes.data_as(doubleP),\n beam.fortran['mass_indices'].ctypes.data_as(intP),\n ct.byref(n_stiff),\n beam.fortran['stiffness'].ctypes.data_as(doubleP),\n beam.fortran['inv_stiffness'].ctypes.data_as(doubleP),\n beam.fortran['stiffness_indices'].ctypes.data_as(intP),\n beam.fortran['frame_of_reference_delta'].ctypes.data_as(doubleP),\n beam.fortran['rbmass'].ctypes.data_as(doubleP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['fdof'].ctypes.data_as(intP),\n ct.byref(xbopts),\n beam.ini_info.pos.ctypes.data_as(doubleP),\n beam.ini_info.psi.ctypes.data_as(doubleP),\n beam.timestep_info[0].pos.ctypes.data_as(doubleP),\n beam.timestep_info[0].psi.ctypes.data_as(doubleP),\n beam.timestep_info[0].steady_applied_forces.ctypes.data_as(doubleP),\n dynamic_forces.ctypes.data_as(doubleP),\n beam.forced_vel_fortran.ctypes.data_as(doubleP),\n beam.forced_acc_fortran.ctypes.data_as(doubleP),\n pos_def_history.ctypes.data_as(doubleP),\n psi_def_history.ctypes.data_as(doubleP),\n pos_dot_def_history.ctypes.data_as(doubleP),\n psi_dot_def_history.ctypes.data_as(doubleP)\n )\n\n for i in range(1, n_tsteps.value):\n beam.add_timestep()\n beam.timestep_info[i].pos[:] = pos_def_history[i, :]\n beam.timestep_info[i].psi[:] = psi_def_history[i, :]\n beam.timestep_info[i].pos_dot[:] = pos_dot_def_history[i, :]\n beam.timestep_info[i].psi_dot[:] = psi_dot_def_history[i, :]\n\n\ndef cbeam3_step_nlndyn(beam, settings, ts, tstep=None, dt=None):\n f_cbeam3_solv_nlndyn_step = xbeamlib.cbeam3_solv_nlndyn_step_python\n f_cbeam3_solv_nlndyn_step.restype = None\n\n if tstep is None:\n tstep = beam.timestep_info[-1]\n\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n n_mass = ct.c_int(beam.n_mass)\n n_stiff = ct.c_int(beam.n_stiff)\n num_dof = ct.c_int(len(tstep.q) - 10)\n\n xbopts = Xbopts()\n xbopts.PrintInfo = ct.c_bool(settings['print_info'])\n xbopts.Solution = ct.c_int(312)\n xbopts.MaxIterations = ct.c_int(settings['max_iterations'])\n xbopts.NumLoadSteps = ct.c_int(settings['num_load_steps'])\n xbopts.NumGauss = ct.c_int(0)\n xbopts.DeltaCurved = ct.c_double(settings['delta_curved'])\n xbopts.MinDelta = ct.c_double(settings['min_delta'])\n xbopts.abs_threshold = ct.c_double(settings['abs_threshold'])\n xbopts.NewmarkDamp = ct.c_double(settings['newmark_damp'])\n xbopts.gravity_on = ct.c_bool(settings['gravity_on'])\n xbopts.gravity = ct.c_double(settings['gravity'])\n xbopts.gravity_dir_x = ct.c_double(settings['gravity_dir'][0])\n xbopts.gravity_dir_y = ct.c_double(settings['gravity_dir'][1])\n xbopts.gravity_dir_z = ct.c_double(settings['gravity_dir'][2])\n xbopts.relaxation_factor = ct.c_double(settings['relaxation_factor'])\n\n # here we only need to set the flags at True, all the forces are follower\n xbopts.FollowerForce = ct.c_bool(True)\n xbopts.FollowerForceRig = ct.c_bool(True)\n\n if dt is None:\n in_dt = ct.c_double(settings['dt'])\n else:\n in_dt = ct.c_double(dt)\n\n f_cbeam3_solv_nlndyn_step(ct.byref(num_dof),\n ct.byref(n_elem),\n ct.byref(n_nodes),\n ct.byref(in_dt),\n beam.fortran['num_nodes'].ctypes.data_as(intP),\n beam.fortran['num_mem'].ctypes.data_as(intP),\n beam.fortran['connectivities'].ctypes.data_as(intP),\n beam.fortran['master'].ctypes.data_as(intP),\n ct.byref(n_mass),\n beam.fortran['mass'].ctypes.data_as(doubleP),\n beam.fortran['mass_indices'].ctypes.data_as(intP),\n ct.byref(n_stiff),\n beam.fortran['stiffness'].ctypes.data_as(doubleP),\n beam.fortran['inv_stiffness'].ctypes.data_as(doubleP),\n beam.fortran['stiffness_indices'].ctypes.data_as(intP),\n beam.fortran['frame_of_reference_delta'].ctypes.data_as(doubleP),\n beam.fortran['rbmass'].ctypes.data_as(doubleP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['fdof'].ctypes.data_as(intP),\n ct.byref(xbopts),\n beam.ini_info.pos.ctypes.data_as(doubleP),\n beam.ini_info.psi.ctypes.data_as(doubleP),\n tstep.pos.ctypes.data_as(doubleP),\n tstep.pos_dot.ctypes.data_as(doubleP),\n tstep.pos_ddot.ctypes.data_as(doubleP),\n tstep.psi.ctypes.data_as(doubleP),\n tstep.psi_dot.ctypes.data_as(doubleP),\n tstep.psi_ddot.ctypes.data_as(doubleP),\n tstep.steady_applied_forces.ctypes.data_as(doubleP),\n tstep.unsteady_applied_forces.ctypes.data_as(doubleP),\n tstep.gravity_forces.ctypes.data_as(doubleP),\n tstep.quat.ctypes.data_as(doubleP),\n tstep.for_vel.ctypes.data_as(doubleP),\n tstep.for_acc.ctypes.data_as(doubleP),\n tstep.q.ctypes.data_as(doubleP),\n tstep.dqdt.ctypes.data_as(doubleP)\n )\n\n xbeam_solv_state2disp(beam, tstep, cbeam3=True)\n\n\nf_xbeam_solv_couplednlndyn = xbeamlib.xbeam_solv_couplednlndyn_python\nf_xbeam_solv_couplednlndyn.restype = None\n\n\ndef xbeam_solv_couplednlndyn(beam, settings):\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n n_mass = ct.c_int(beam.n_mass)\n n_stiff = ct.c_int(beam.n_stiff)\n\n dt = settings['dt']\n n_tsteps = settings['num_steps']\n time = np.zeros((n_tsteps,), dtype=ct.c_double, order='F')\n for i in range(n_tsteps):\n time[i] = i*dt\n\n # deformation history matrices\n for_vel = np.zeros((n_tsteps + 1, 6), order='F')\n for_acc = np.zeros((n_tsteps + 1, 6), order='F')\n quat_history = np.zeros((n_tsteps, 4), order='F')\n quat_history[0, 0] = 1.0\n quat_history[0, :] = beam.timestep_info[0].quat[:]\n\n dt = ct.c_double(dt)\n n_tsteps = ct.c_int(n_tsteps)\n\n xbopts = Xbopts()\n xbopts.PrintInfo = ct.c_bool(settings['print_info'])\n xbopts.Solution = ct.c_int(910)\n xbopts.OutInaframe = ct.c_bool(True)\n xbopts.MaxIterations = ct.c_int(settings['max_iterations'])\n xbopts.NumLoadSteps = ct.c_int(settings['num_load_steps'])\n # xbopts.NumGauss = ct.c_int(0)\n xbopts.DeltaCurved = ct.c_double(settings['delta_curved'])\n xbopts.MinDelta = ct.c_double(settings['min_delta'])\n xbopts.abs_threshold = ct.c_double(settings['abs_threshold'])\n xbopts.NewmarkDamp = ct.c_double(settings['newmark_damp'])\n xbopts.gravity_on = ct.c_bool(settings['gravity_on'])\n xbopts.gravity = ct.c_double(settings['gravity'])\n xbopts.gravity_dir_x = ct.c_double(settings['gravity_dir'][0])\n xbopts.gravity_dir_y = ct.c_double(settings['gravity_dir'][1])\n xbopts.gravity_dir_z = ct.c_double(settings['gravity_dir'][2])\n xbopts.relaxation_factor = ct.c_double(settings['relaxation_factor'])\n xbopts.gravity_dir_x = ct.c_double(settings['gravity_dir'][0])\n xbopts.gravity_dir_y = ct.c_double(settings['gravity_dir'][1])\n xbopts.gravity_dir_z = ct.c_double(settings['gravity_dir'][2])\n\n pos_def_history = np.zeros((n_tsteps.value, beam.num_node, 3), order='F', dtype=ct.c_double)\n pos_dot_def_history = np.zeros((n_tsteps.value, beam.num_node, 3), order='F', dtype=ct.c_double)\n psi_def_history = np.zeros((n_tsteps.value, beam.num_elem, 3, 3), order='F', dtype=ct.c_double)\n psi_dot_def_history = np.zeros((n_tsteps.value, beam.num_elem, 3, 3), order='F', dtype=ct.c_double)\n\n dynamic_force = np.zeros((n_nodes.value, 6, n_tsteps.value), dtype=ct.c_double, order='F')\n for it in range(n_tsteps.value):\n dynamic_force[:, :, it] = beam.dynamic_input[it]['dynamic_forces']\n\n # status flag\n success = ct.c_bool(True)\n\n # here we only need to set the flags at True, all the forces are follower\n xbopts.FollowerForce = ct.c_bool(True)\n xbopts.FollowerForceRig = ct.c_bool(True)\n import time as ti\n start_time = ti.time()\n f_xbeam_solv_couplednlndyn(ct.byref(n_elem),\n ct.byref(n_nodes),\n ct.byref(n_tsteps),\n time.ctypes.data_as(doubleP),\n beam.fortran['num_nodes'].ctypes.data_as(intP),\n beam.fortran['num_mem'].ctypes.data_as(intP),\n beam.fortran['connectivities'].ctypes.data_as(intP),\n beam.fortran['master'].ctypes.data_as(intP),\n ct.byref(n_mass),\n beam.fortran['mass'].ctypes.data_as(doubleP),\n beam.fortran['mass_indices'].ctypes.data_as(intP),\n ct.byref(n_stiff),\n beam.fortran['stiffness'].ctypes.data_as(doubleP),\n beam.fortran['inv_stiffness'].ctypes.data_as(doubleP),\n beam.fortran['stiffness_indices'].ctypes.data_as(intP),\n beam.fortran['frame_of_reference_delta'].ctypes.data_as(doubleP),\n beam.fortran['rbmass'].ctypes.data_as(doubleP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['fdof'].ctypes.data_as(intP),\n ct.byref(xbopts),\n beam.ini_info.pos.ctypes.data_as(doubleP),\n beam.ini_info.psi.ctypes.data_as(doubleP),\n beam.ini_info.steady_applied_forces.ctypes.data_as(doubleP),\n dynamic_force.ctypes.data_as(doubleP),\n for_vel.ctypes.data_as(doubleP),\n for_acc.ctypes.data_as(doubleP),\n pos_def_history.ctypes.data_as(doubleP),\n psi_def_history.ctypes.data_as(doubleP),\n pos_dot_def_history.ctypes.data_as(doubleP),\n psi_dot_def_history.ctypes.data_as(doubleP),\n quat_history.ctypes.data_as(doubleP),\n ct.byref(success))\n cout.cout_wrap(\"\\n--- %s seconds ---\" % (ti.time() - start_time), 1)\n if not success:\n raise Exception('couplednlndyn did not converge')\n\n for_pos = np.zeros_like(for_vel)\n for_pos[:, 0] = sc.integrate.cumtrapz(for_vel[:, 0], dx=dt.value, initial=0)\n for_pos[:, 1] = sc.integrate.cumtrapz(for_vel[:, 1], dx=dt.value, initial=0)\n for_pos[:, 2] = sc.integrate.cumtrapz(for_vel[:, 2], dx=dt.value, initial=0)\n\n glob_pos_def = np.zeros_like(pos_def_history)\n for it in range(n_tsteps.value):\n rot = algebra.quat2rotation(quat_history[it, :])\n for inode in range(beam.num_node):\n glob_pos_def[it, inode, :] = np.dot(rot.T, pos_def_history[it, inode, :])\n\n for i in range(n_tsteps.value - 1):\n beam.timestep_info[i + 1].pos[:] = pos_def_history[i+1, :]\n beam.timestep_info[i + 1].psi[:] = psi_def_history[i+1, :]\n beam.timestep_info[i + 1].pos_dot[:] = pos_dot_def_history[i+1, :]\n beam.timestep_info[i + 1].psi_dot[:] = psi_dot_def_history[i+1, :]\n\n beam.timestep_info[i + 1].quat[:] = quat_history[i+1, :]\n # beam.timestep_info[i + 1].for_pos[:] = for_pos[i+1, :]\n beam.timestep_info[i + 1].for_vel[:] = for_vel[i+1, :]\n\n for it in range(n_tsteps.value - 1):\n beam.integrate_position(it + 1, dt.value)\n\n\ndef xbeam_step_couplednlndyn(beam, settings, ts, tstep=None, dt=None):\n # library load\n f_xbeam_solv_nlndyn_step_python = xbeamlib.xbeam_solv_nlndyn_step_python\n f_xbeam_solv_nlndyn_step_python.restype = None\n\n if tstep is None:\n tstep = beam.timestep_info[-1]\n\n # initialisation\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n n_mass = ct.c_int(beam.n_mass)\n n_stiff = ct.c_int(beam.n_stiff)\n\n xbopts = Xbopts()\n xbopts.PrintInfo = ct.c_bool(settings['print_info'])\n xbopts.MaxIterations = ct.c_int(settings['max_iterations'])\n xbopts.NumLoadSteps = ct.c_int(settings['num_load_steps'])\n xbopts.DeltaCurved = ct.c_double(settings['delta_curved'])\n xbopts.MinDelta = ct.c_double(settings['min_delta'])\n xbopts.abs_threshold = ct.c_double(settings['abs_threshold'])\n xbopts.NewmarkDamp = ct.c_double(settings['newmark_damp'])\n xbopts.gravity_on = ct.c_bool(settings['gravity_on'])\n xbopts.gravity = ct.c_double(settings['gravity'])\n xbopts.balancing = ct.c_bool(settings['balancing'])\n xbopts.gravity_dir_x = ct.c_double(settings['gravity_dir'][0])\n xbopts.gravity_dir_y = ct.c_double(settings['gravity_dir'][1])\n xbopts.gravity_dir_z = ct.c_double(settings['gravity_dir'][2])\n xbopts.relaxation_factor = ct.c_double(settings['relaxation_factor'])\n\n if dt is None:\n in_dt = ct.c_double(settings['dt'])\n else:\n in_dt = ct.c_double(dt)\n\n ctypes_ts = ct.c_int(ts)\n numdof = ct.c_int(beam.num_dof.value)\n\n f_xbeam_solv_nlndyn_step_python(ct.byref(numdof),\n ct.byref(ctypes_ts),\n ct.byref(n_elem),\n ct.byref(n_nodes),\n ct.byref(in_dt),\n beam.fortran['num_nodes'].ctypes.data_as(intP),\n beam.fortran['num_mem'].ctypes.data_as(intP),\n beam.fortran['connectivities'].ctypes.data_as(intP),\n beam.fortran['master'].ctypes.data_as(intP),\n ct.byref(n_mass),\n beam.fortran['mass'].ctypes.data_as(doubleP),\n beam.fortran['mass_indices'].ctypes.data_as(intP),\n ct.byref(n_stiff),\n beam.fortran['stiffness'].ctypes.data_as(doubleP),\n beam.fortran['inv_stiffness'].ctypes.data_as(doubleP),\n beam.fortran['stiffness_indices'].ctypes.data_as(intP),\n beam.fortran['frame_of_reference_delta'].ctypes.data_as(doubleP),\n beam.fortran['rbmass'].ctypes.data_as(doubleP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['fdof'].ctypes.data_as(intP),\n ct.byref(xbopts),\n beam.ini_info.pos.ctypes.data_as(doubleP),\n beam.ini_info.psi.ctypes.data_as(doubleP),\n tstep.pos.ctypes.data_as(doubleP),\n tstep.pos_dot.ctypes.data_as(doubleP),\n tstep.pos_ddot.ctypes.data_as(doubleP),\n tstep.psi.ctypes.data_as(doubleP),\n tstep.psi_dot.ctypes.data_as(doubleP),\n tstep.psi_ddot.ctypes.data_as(doubleP),\n tstep.steady_applied_forces.ctypes.data_as(doubleP),\n tstep.unsteady_applied_forces.ctypes.data_as(doubleP),\n tstep.gravity_forces.ctypes.data_as(doubleP),\n tstep.quat.ctypes.data_as(doubleP),\n tstep.for_vel.ctypes.data_as(doubleP),\n tstep.for_acc.ctypes.data_as(doubleP),\n tstep.q.ctypes.data_as(doubleP),\n tstep.dqdt.ctypes.data_as(doubleP),\n tstep.dqddt.ctypes.data_as(doubleP))\n\n\ndef xbeam_init_couplednlndyn(beam, settings, ts, dt=None):\n # library load\n f_xbeam_solv_nlndyn_init_python = xbeamlib.xbeam_solv_nlndyn_init_python\n f_xbeam_solv_nlndyn_init_python.restype = None\n\n # initialisation\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n n_mass = ct.c_int(beam.n_mass)\n n_stiff = ct.c_int(beam.n_stiff)\n\n xbopts = Xbopts()\n xbopts.PrintInfo = ct.c_bool(settings['print_info'])\n xbopts.MaxIterations = ct.c_int(settings['max_iterations'])\n xbopts.NumLoadSteps = ct.c_int(settings['num_load_steps'])\n xbopts.DeltaCurved = ct.c_double(settings['delta_curved'])\n xbopts.MinDelta = ct.c_double(settings['min_delta'])\n xbopts.abs_threshold = ct.c_double(settings['abs_threshold'])\n xbopts.NewmarkDamp = ct.c_double(settings['newmark_damp'])\n xbopts.gravity_on = ct.c_bool(settings['gravity_on'])\n xbopts.gravity = ct.c_double(settings['gravity'])\n xbopts.gravity_dir_x = ct.c_double(settings['gravity_dir'][0])\n xbopts.gravity_dir_y = ct.c_double(settings['gravity_dir'][1])\n xbopts.gravity_dir_z = ct.c_double(settings['gravity_dir'][2])\n\n in_dt = ct.c_double(dt)\n\n if ts < 0:\n ctypes_ts = ct.c_int(0)\n else:\n ctypes_ts = ct.c_int(ts)\n numdof = ct.c_int(beam.num_dof.value)\n\n f_xbeam_solv_nlndyn_init_python(ct.byref(numdof),\n ct.byref(ctypes_ts),\n ct.byref(n_elem),\n ct.byref(n_nodes),\n ct.byref(ct.c_double(settings['dt'])),\n beam.fortran['num_nodes'].ctypes.data_as(intP),\n beam.fortran['num_mem'].ctypes.data_as(intP),\n beam.fortran['connectivities'].ctypes.data_as(intP),\n beam.fortran['master'].ctypes.data_as(intP),\n ct.byref(n_mass),\n beam.fortran['mass'].ctypes.data_as(doubleP),\n beam.fortran['mass_indices'].ctypes.data_as(intP),\n ct.byref(n_stiff),\n beam.fortran['stiffness'].ctypes.data_as(doubleP),\n beam.fortran['inv_stiffness'].ctypes.data_as(doubleP),\n beam.fortran['stiffness_indices'].ctypes.data_as(intP),\n beam.fortran['frame_of_reference_delta'].ctypes.data_as(doubleP),\n beam.fortran['rbmass'].ctypes.data_as(doubleP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['fdof'].ctypes.data_as(intP),\n ct.byref(xbopts),\n beam.ini_info.pos.ctypes.data_as(doubleP),\n beam.ini_info.psi.ctypes.data_as(doubleP),\n beam.timestep_info[ts].pos.ctypes.data_as(doubleP),\n beam.timestep_info[ts].pos_dot.ctypes.data_as(doubleP),\n beam.timestep_info[ts].psi.ctypes.data_as(doubleP),\n beam.timestep_info[ts].psi_dot.ctypes.data_as(doubleP),\n beam.timestep_info[ts].steady_applied_forces.ctypes.data_as(doubleP),\n beam.timestep_info[ts].unsteady_applied_forces.ctypes.data_as(doubleP),\n beam.timestep_info[ts].quat.ctypes.data_as(doubleP),\n beam.timestep_info[ts].for_vel.ctypes.data_as(doubleP),\n beam.timestep_info[ts].for_acc.ctypes.data_as(doubleP),\n beam.timestep_info[ts].q.ctypes.data_as(doubleP),\n beam.timestep_info[ts].dqdt.ctypes.data_as(doubleP),\n beam.timestep_info[ts].dqddt.ctypes.data_as(doubleP))\n\n\ndef xbeam_solv_state2disp(beam, tstep, cbeam3=False):\n numdof = beam.num_dof.value\n cbeam3_solv_state2disp(beam, tstep)\n if not cbeam3:\n tstep.for_pos[0:3] = tstep.q[numdof:numdof+3].astype(dtype=ct.c_double, order='F', copy=True)\n tstep.for_vel = tstep.dqdt[numdof:numdof+6].astype(dtype=ct.c_double, order='F', copy=True)\n # tstep.for_acc = tstep.dqddt[numdof:numdof+6].astype(dtype=ct.c_double, order='F', copy=True)\n tstep.quat = algebra.unit_vector(tstep.dqdt[numdof+6:]).astype(dtype=ct.c_double, order='F', copy=True)\n\ndef xbeam_solv_state2accel(beam, tstep, cbeam3=False):\n numdof = beam.num_dof.value\n cbeam3_solv_state2accel(beam, tstep)\n if not cbeam3:\n tstep.for_acc = tstep.dqddt[numdof:numdof+6].astype(dtype=ct.c_double, order='F', copy=True)\n\ndef cbeam3_solv_state2disp(beam, tstep):\n # library load\n f_cbeam3_solv_state2disp = xbeamlib.cbeam3_solv_state2disp_python\n f_cbeam3_solv_state2disp.restype = None\n\n # initialisation\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n numdof = ct.c_int(beam.num_dof.value)\n\n f_cbeam3_solv_state2disp(\n ct.byref(n_elem),\n ct.byref(n_nodes),\n ct.byref(numdof),\n beam.ini_info.pos.ctypes.data_as(doubleP),\n beam.ini_info.psi.ctypes.data_as(doubleP),\n tstep.pos.ctypes.data_as(doubleP),\n tstep.psi.ctypes.data_as(doubleP),\n tstep.pos_dot.ctypes.data_as(doubleP),\n tstep.psi_dot.ctypes.data_as(doubleP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['num_nodes'].ctypes.data_as(intP),\n beam.fortran['master'].ctypes.data_as(intP),\n tstep.q.ctypes.data_as(doubleP),\n tstep.dqdt.ctypes.data_as(doubleP))\n\ndef cbeam3_solv_state2accel(beam, tstep):\n # library load\n f_cbeam3_solv_state2disp = xbeamlib.cbeam3_solv_state2disp_python\n f_cbeam3_solv_state2disp.restype = None\n\n # initialisation\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n numdof = ct.c_int(beam.num_dof.value)\n\n dummy_pos = np.zeros_like(tstep.pos)\n dummy_psi = np.zeros_like(tstep.psi)\n dummy_ini_pos = np.zeros_like(tstep.pos)\n dummy_ini_psi = np.zeros_like(tstep.psi)\n dummy_q = np.zeros_like(tstep.q)\n\n f_cbeam3_solv_state2disp(\n ct.byref(n_elem),\n ct.byref(n_nodes),\n ct.byref(numdof),\n dummy_ini_pos.ctypes.data_as(doubleP),\n dummy_ini_psi.ctypes.data_as(doubleP),\n dummy_pos.ctypes.data_as(doubleP),\n dummy_psi.ctypes.data_as(doubleP),\n tstep.pos_ddot.ctypes.data_as(doubleP),\n tstep.psi_ddot.ctypes.data_as(doubleP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['num_nodes'].ctypes.data_as(intP),\n beam.fortran['master'].ctypes.data_as(intP),\n dummy_q.ctypes.data_as(doubleP),\n tstep.dqddt.ctypes.data_as(doubleP))\n\ndef xbeam_solv_disp2state(beam, tstep):\n numdof = beam.num_dof.value\n cbeam3_solv_disp2state(beam, tstep)\n tstep.q[numdof:numdof+3] = tstep.for_pos[0:3]\n tstep.dqdt[numdof:numdof+6] = tstep.for_vel\n # tstep.dqddt[numdof:numdof+6] = tstep.for_acc\n tstep.dqdt[numdof+6:] = algebra.unit_vector(tstep.quat)\n # tstep.dqdt[numdof+6:] = tstep.quat\n # tstep.dqdt[numdof+6:] = algebra.unit_quat(tstep.quat)\n\ndef xbeam_solv_accel2state(beam, tstep):\n numdof = beam.num_dof.value\n cbeam3_solv_accel2state(beam, tstep)\n tstep.dqddt[numdof:numdof+6] = tstep.for_acc\n\ndef cbeam3_solv_disp2state(beam, tstep):\n # library load\n f_cbeam3_solv_disp2state = xbeamlib.cbeam3_solv_disp2state_python\n f_cbeam3_solv_disp2state.restype = None\n\n # initialisation\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n numdof = ct.c_int(beam.num_dof.value)\n\n f_cbeam3_solv_disp2state(\n ct.byref(n_elem),\n ct.byref(n_nodes),\n ct.byref(numdof),\n tstep.pos.ctypes.data_as(doubleP),\n tstep.psi.ctypes.data_as(doubleP),\n tstep.pos_dot.ctypes.data_as(doubleP),\n tstep.psi_dot.ctypes.data_as(doubleP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n tstep.q.ctypes.data_as(doubleP),\n tstep.dqdt.ctypes.data_as(doubleP))\n\ndef cbeam3_solv_accel2state(beam, tstep):\n # library load\n f_cbeam3_solv_disp2state = xbeamlib.cbeam3_solv_disp2state_python\n f_cbeam3_solv_disp2state.restype = None\n\n # initialisation\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n numdof = ct.c_int(beam.num_dof.value)\n\n dummy_pos = np.zeros_like(tstep.pos)\n dummy_psi = np.zeros_like(tstep.psi)\n dummy_q = np.zeros_like(tstep.q)\n\n # Reused\n f_cbeam3_solv_disp2state(\n ct.byref(n_elem),\n ct.byref(n_nodes),\n ct.byref(numdof),\n dummy_pos.ctypes.data_as(doubleP),\n dummy_psi.ctypes.data_as(doubleP),\n tstep.pos_ddot.ctypes.data_as(doubleP),\n tstep.psi_ddot.ctypes.data_as(doubleP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n dummy_q.ctypes.data_as(doubleP),\n tstep.dqddt.ctypes.data_as(doubleP))\n\ndef cbeam3_solv_modal(beam, settings, ts, FullMglobal, FullCglobal, FullKglobal):\n \"\"\"\n cbeam3_solv_modal\n\n Generates the system matrices for modal analysis\n\n Args:\n beam(Beam): beam information\n settings(settings):\n ts(int): timestep\n FullMglobal(numpy array): Mass matrix\n FullCglobal(numpy array): Damping matrix\n FullKglobal(numpy array): Stiffness matrix\n\n Returns:\n FullMglobal(numpy array): Mass matrix\n FullCglobal(numpy array): Damping matrix\n FullKglobal(numpy array): Stiffness matrix\n\n Examples:\n\n Notes:\n\n \"\"\"\n\n f_cbeam3_solv_modal = xbeamlib.cbeam3_solv_modal_python\n f_cbeam3_solv_modal.restype = None\n\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n n_mass = ct.c_int(beam.n_mass)\n n_stiff = ct.c_int(beam.n_stiff)\n num_dof = ct.c_int(beam.num_dof.value)\n\n xbopts = Xbopts()\n xbopts.PrintInfo = ct.c_bool(settings['print_info'])\n xbopts.Solution = ct.c_int(312)\n # xbopts.OutInaframe = ct.c_bool(settings['out_a_frame'])\n # xbopts.OutInBframe = ct.c_bool(settings['out_b_frame'])\n # xbopts.ElemProj = settings['elem_proj']\n # xbopts.MaxIterations = settings['max_iterations']\n # xbopts.NumLoadSteps = settings['num_load_steps']\n xbopts.NumGauss = ct.c_int(0)\n xbopts.DeltaCurved = ct.c_double(settings['delta_curved'])\n # xbopts.MinDelta = settings['min_delta']\n # xbopts.NewmarkDamp = settings['newmark_damp']\n # xbopts.gravity_on = settings['gravity_on']\n # xbopts.gravity = settings['gravity']\n # xbopts.gravity_dir_x = ct.c_double(settings['gravity_dir'][0])\n # xbopts.gravity_dir_y = ct.c_double(settings['gravity_dir'][1])\n # xbopts.gravity_dir_z = ct.c_double(settings['gravity_dir'][2])\n\n\n # print(\"ts: \",ts)\n # print(\"FoR vel: \", beam.timestep_info[ts].for_vel)\n # print(\"initial position: \", beam.ini_info.pos)\n # print(\"initial rotation: \", beam.ini_info.psi)\n # print(\"position: \", beam.timestep_info[ts].pos)\n # print(\"rotation: \", beam.timestep_info[ts].psi)\n # print(\"mass: \", beam.fortran['mass'])\n # print(\"mass: \", beam.fortran['stiffness'])\n # print(\"mass: \", beam.fortran['inv_stiffness'])\n\n\n f_cbeam3_solv_modal(ct.byref(num_dof),\n ct.byref(n_elem),\n ct.byref(n_nodes),\n beam.fortran['num_nodes'].ctypes.data_as(intP),\n beam.fortran['num_mem'].ctypes.data_as(intP),\n beam.fortran['connectivities'].ctypes.data_as(intP),\n beam.fortran['master'].ctypes.data_as(intP),\n ct.byref(n_mass),\n beam.fortran['mass'].ctypes.data_as(doubleP),\n beam.fortran['mass_indices'].ctypes.data_as(intP),\n ct.byref(n_stiff),\n beam.fortran['stiffness'].ctypes.data_as(doubleP),\n beam.fortran['inv_stiffness'].ctypes.data_as(doubleP),\n beam.fortran['stiffness_indices'].ctypes.data_as(intP),\n beam.fortran['frame_of_reference_delta'].ctypes.data_as(doubleP),\n beam.fortran['rbmass'].ctypes.data_as(doubleP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['fdof'].ctypes.data_as(intP),\n ct.byref(xbopts),\n beam.ini_info.pos.ctypes.data_as(doubleP),\n beam.ini_info.psi.ctypes.data_as(doubleP),\n beam.timestep_info[ts].pos.ctypes.data_as(doubleP),\n beam.timestep_info[ts].psi.ctypes.data_as(doubleP),\n beam.timestep_info[ts].for_vel.ctypes.data_as(doubleP),\n FullMglobal.ctypes.data_as(doubleP),\n FullCglobal.ctypes.data_as(doubleP),\n FullKglobal.ctypes.data_as(doubleP))\n\n\ndef cbeam3_asbly_dynamic(beam, tstep, settings):\n \"\"\"\n cbeam3_asbly_dynamic\n\n Generates the system matrices for a nonlinear dynamic structure with\n prescribed FoR motions\n\n Args:\n beam(Beam): beam information\n tstep(StructTimeStepInfo): time step information\n settings(settings):\n\n Returns:\n \tMglobal(numpy array): Mass matrix\n Cglobal(numpy array): Damping matrix\n Kglobal(numpy array): Stiffness matrix\n Qglobal(numpy array): Vector of independent terms\n\n Examples:\n\n Notes:\n\n \"\"\"\n\n # library load\n f_cbeam3_asbly_dynamic_python = xbeamlib.cbeam3_asbly_dynamic_python\n f_cbeam3_asbly_dynamic_python.restype = None\n\n # initialisation\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n num_dof = beam.num_dof.value\n n_mass = ct.c_int(beam.n_mass)\n n_stiff = ct.c_int(beam.n_stiff)\n dt = ct.c_double(settings['dt'])\n\n # Options\n xbopts = Xbopts()\n xbopts.PrintInfo = ct.c_bool(settings['print_info'])\n xbopts.Solution = ct.c_int(312)\n xbopts.MaxIterations = ct.c_int(settings['max_iterations'])\n xbopts.NumLoadSteps = ct.c_int(settings['num_load_steps'])\n xbopts.NumGauss = ct.c_int(0)\n xbopts.DeltaCurved = ct.c_double(settings['delta_curved'])\n xbopts.MinDelta = ct.c_double(settings['min_delta'])\n xbopts.abs_threshold = ct.c_double(settings['abs_threshold'])\n xbopts.NewmarkDamp = ct.c_double(settings['newmark_damp'])\n xbopts.gravity_on = ct.c_bool(settings['gravity_on'])\n xbopts.gravity = ct.c_double(settings['gravity'])\n xbopts.gravity_dir_x = ct.c_double(settings['gravity_dir'][0])\n xbopts.gravity_dir_y = ct.c_double(settings['gravity_dir'][1])\n xbopts.gravity_dir_z = ct.c_double(settings['gravity_dir'][2])\n\n # Initialize matrices\n Mglobal = np.zeros((num_dof, num_dof), dtype=ct.c_double, order='F')\n Cglobal = np.zeros((num_dof, num_dof), dtype=ct.c_double, order='F')\n Kglobal = np.zeros((num_dof, num_dof), dtype=ct.c_double, order='F')\n Qglobal = np.zeros((num_dof, ), dtype=ct.c_double, order='F')\n\n f_cbeam3_asbly_dynamic_python(ct.byref(ct.c_int(num_dof)),\n ct.byref(n_nodes),\n ct.byref(n_elem),\n ct.byref(dt),\n beam.ini_info.pos.ctypes.data_as(doubleP),\n beam.ini_info.psi.ctypes.data_as(doubleP),\n tstep.pos.ctypes.data_as(doubleP),\n tstep.pos_dot.ctypes.data_as(doubleP),\n tstep.pos_ddot.ctypes.data_as(doubleP),\n tstep.psi.ctypes.data_as(doubleP),\n tstep.psi_dot.ctypes.data_as(doubleP),\n tstep.psi_ddot.ctypes.data_as(doubleP),\n tstep.steady_applied_forces.ctypes.data_as(doubleP),\n tstep.unsteady_applied_forces.ctypes.data_as(doubleP),\n tstep.for_vel.ctypes.data_as(doubleP),\n tstep.for_acc.ctypes.data_as(doubleP),\n beam.fortran['num_nodes'].ctypes.data_as(intP),\n beam.fortran['num_mem'].ctypes.data_as(intP),\n beam.fortran['connectivities'].ctypes.data_as(intP),\n beam.fortran['master'].ctypes.data_as(intP),\n ct.byref(n_mass),\n beam.fortran['mass'].ctypes.data_as(doubleP),\n beam.fortran['mass_indices'].ctypes.data_as(intP),\n ct.byref(n_stiff),\n beam.fortran['stiffness'].ctypes.data_as(doubleP),\n beam.fortran['inv_stiffness'].ctypes.data_as(doubleP),\n beam.fortran['stiffness_indices'].ctypes.data_as(intP),\n beam.fortran['frame_of_reference_delta'].ctypes.data_as(doubleP),\n beam.fortran['rbmass'].ctypes.data_as(doubleP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['fdof'].ctypes.data_as(intP),\n ct.byref(xbopts),\n # CAREFUL, this is dXddt, with num_dof elements,\n # not num_dof + 10\n tstep.dqddt.ctypes.data_as(doubleP),\n tstep.quat.ctypes.data_as(doubleP),\n tstep.gravity_forces.ctypes.data_as(doubleP),\n Mglobal.ctypes.data_as(doubleP),\n Cglobal.ctypes.data_as(doubleP),\n Kglobal.ctypes.data_as(doubleP),\n Qglobal.ctypes.data_as(doubleP))\n\n return Mglobal, Cglobal, Kglobal, Qglobal\n\ndef xbeam3_asbly_dynamic(beam, tstep, settings):\n \"\"\"\n xbeam3_asbly_dynamic\n\n Generates the system matrices for a nonlinear dynamic structure with\n free FoR motions\n\n Args:\n beam(Beam): beam information\n tstep(StructTimeStepInfo): time step information\n settings(settings):\n\n Returns:\n \tMglobal(numpy array): Mass matrix\n Cglobal(numpy array): Damping matrix\n Kglobal(numpy array): Stiffness matrix\n Qglobal(numpy array): Vector of independent terms\n\n Examples:\n\n Notes:\n\n \"\"\"\n\n # library load\n f_xbeam3_asbly_dynamic_python = xbeamlib.xbeam3_asbly_dynamic_python\n f_xbeam3_asbly_dynamic_python.restype = None\n\n # initialisation\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n num_dof = beam.num_dof.value\n n_mass = ct.c_int(beam.n_mass)\n n_stiff = ct.c_int(beam.n_stiff)\n dt = ct.c_double(settings['dt'])\n\n # Options\n xbopts = Xbopts()\n xbopts.PrintInfo = ct.c_bool(settings['print_info'])\n xbopts.Solution = ct.c_int(312)\n xbopts.MaxIterations = ct.c_int(settings['max_iterations'])\n xbopts.NumLoadSteps = ct.c_int(settings['num_load_steps'])\n xbopts.NumGauss = ct.c_int(0)\n xbopts.DeltaCurved = ct.c_double(settings['delta_curved'])\n xbopts.MinDelta = ct.c_double(settings['min_delta'])\n xbopts.abs_threshold = ct.c_double(settings['abs_threshold'])\n xbopts.NewmarkDamp = ct.c_double(settings['newmark_damp'])\n xbopts.gravity_on = ct.c_bool(settings['gravity_on'])\n xbopts.gravity = ct.c_double(settings['gravity'])\n xbopts.gravity_dir_x = ct.c_double(settings['gravity_dir'][0])\n xbopts.gravity_dir_y = ct.c_double(settings['gravity_dir'][1])\n xbopts.gravity_dir_z = ct.c_double(settings['gravity_dir'][2])\n\n # Initialize matrices\n Mtotal = np.zeros((num_dof+10, num_dof+10), dtype=ct.c_double, order='F')\n Ctotal = np.zeros((num_dof+10, num_dof+10), dtype=ct.c_double, order='F')\n Ktotal = np.zeros((num_dof+10, num_dof+10), dtype=ct.c_double, order='F')\n Qtotal = np.zeros((num_dof+10, ), dtype=ct.c_double, order='F')\n\n f_xbeam3_asbly_dynamic_python(ct.byref(ct.c_int(num_dof)),\n ct.byref(n_nodes),\n ct.byref(n_elem),\n ct.byref(dt),\n beam.ini_info.pos.ctypes.data_as(doubleP),\n beam.ini_info.psi.ctypes.data_as(doubleP),\n tstep.pos.ctypes.data_as(doubleP),\n tstep.pos_dot.ctypes.data_as(doubleP),\n tstep.pos_ddot.ctypes.data_as(doubleP),\n tstep.psi.ctypes.data_as(doubleP),\n tstep.psi_dot.ctypes.data_as(doubleP),\n tstep.psi_ddot.ctypes.data_as(doubleP),\n tstep.steady_applied_forces.ctypes.data_as(doubleP),\n tstep.unsteady_applied_forces.ctypes.data_as(doubleP),\n tstep.for_vel.ctypes.data_as(doubleP),\n tstep.for_acc.ctypes.data_as(doubleP),\n # ct.byref(in_dt),\n beam.fortran['num_nodes'].ctypes.data_as(intP),\n beam.fortran['num_mem'].ctypes.data_as(intP),\n beam.fortran['connectivities'].ctypes.data_as(intP),\n beam.fortran['master'].ctypes.data_as(intP),\n ct.byref(n_mass),\n beam.fortran['mass'].ctypes.data_as(doubleP),\n beam.fortran['mass_indices'].ctypes.data_as(intP),\n ct.byref(n_stiff),\n beam.fortran['stiffness'].ctypes.data_as(doubleP),\n beam.fortran['inv_stiffness'].ctypes.data_as(doubleP),\n beam.fortran['stiffness_indices'].ctypes.data_as(intP),\n beam.fortran['frame_of_reference_delta'].ctypes.data_as(doubleP),\n beam.fortran['rbmass'].ctypes.data_as(doubleP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['fdof'].ctypes.data_as(intP),\n ct.byref(xbopts),\n tstep.quat.ctypes.data_as(doubleP),\n tstep.q.ctypes.data_as(doubleP),\n tstep.dqdt.ctypes.data_as(doubleP),\n tstep.dqddt.ctypes.data_as(doubleP),\n tstep.gravity_forces.ctypes.data_as(doubleP),\n Mtotal.ctypes.data_as(doubleP),\n Ctotal.ctypes.data_as(doubleP),\n Ktotal.ctypes.data_as(doubleP),\n Qtotal.ctypes.data_as(doubleP))\n\n return Mtotal, Ctotal, Ktotal, Qtotal\n\ndef cbeam3_correct_gravity_forces(beam, tstep, settings):\n \"\"\"\n cbeam3_correct_gravity_forces\n\n Corrects the gravity forces orientation after a time step\n\n Args:\n beam(Beam): beam information\n tstep(StructTimeStepInfo): time step information\n settings(settings):\n \"\"\"\n\n # library load\n f_cbeam3_correct_gravity_forces_python = xbeamlib.cbeam3_correct_gravity_forces_python\n f_cbeam3_correct_gravity_forces_python.restype = None\n\n # initialisation\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n n_mass = ct.c_int(beam.n_mass)\n n_stiff = ct.c_int(beam.n_stiff)\n\n f_cbeam3_correct_gravity_forces_python(ct.byref(n_nodes),\n ct.byref(n_elem),\n beam.ini_info.psi.ctypes.data_as(doubleP),\n tstep.psi.ctypes.data_as(doubleP),\n beam.fortran['num_nodes'].ctypes.data_as(intP),\n beam.fortran['num_mem'].ctypes.data_as(intP),\n beam.fortran['connectivities'].ctypes.data_as(intP),\n beam.fortran['master'].ctypes.data_as(intP),\n ct.byref(n_mass),\n beam.fortran['mass'].ctypes.data_as(doubleP),\n beam.fortran['mass_indices'].ctypes.data_as(intP),\n ct.byref(n_stiff),\n beam.fortran['stiffness'].ctypes.data_as(doubleP),\n beam.fortran['inv_stiffness'].ctypes.data_as(doubleP),\n beam.fortran['stiffness_indices'].ctypes.data_as(intP),\n beam.fortran['frame_of_reference_delta'].ctypes.data_as(doubleP),\n beam.fortran['rbmass'].ctypes.data_as(doubleP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['fdof'].ctypes.data_as(intP),\n tstep.gravity_forces.ctypes.data_as(doubleP))\n\ndef cbeam3_asbly_static(beam, tstep, settings, iLoadStep):\n \"\"\"\n cbeam3_asbly_static\n\n Generates the system matrices for a nonlinear static structure\n\n Args:\n beam(Beam): beam information\n tstep(StructTimeStepInfo): time step information\n settings(settings):\n\n Returns:\n Kglobal(numpy array): Stiffness matrix\n Qglobal(numpy array): Vector of independent terms\n\n Examples:\n\n Notes:\n\n \"\"\"\n\n # library load\n f_cbeam3_asbly_static_python = xbeamlib.cbeam3_asbly_static_python\n f_cbeam3_asbly_static_python.restype = None\n\n # initialisation\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n num_dof = beam.num_dof.value\n n_mass = ct.c_int(beam.n_mass)\n n_stiff = ct.c_int(beam.n_stiff)\n # dt = settings['dt']\n\n # Options\n xbopts = Xbopts()\n xbopts.PrintInfo = ct.c_bool(settings['print_info'])\n # xbopts.Solution = ct.c_int(312)\n # xbopts.MaxIterations = settings['max_iterations']\n xbopts.NumLoadSteps = ct.c_int(settings['num_load_steps'] + 1)\n # xbopts.NumGauss = ct.c_int(0)\n # xbopts.DeltaCurved = settings['delta_curved']\n # xbopts.MinDelta = settings['min_delta']\n # xbopts.NewmarkDamp = settings['newmark_damp']\n xbopts.gravity_on = ct.c_bool(settings['gravity_on'])\n xbopts.gravity = ct.c_double(settings['gravity'])\n gravity_vector = np.dot(beam.timestep_info[ts].cag(), settings['gravity_dir'])\n xbopts.gravity_dir_x = ct.c_double(gravity_vector[0])\n xbopts.gravity_dir_y = ct.c_double(gravity_vector[1])\n xbopts.gravity_dir_z = ct.c_double(gravity_vector[2])\n\n # Initialize matrices\n # Mglobal = np.zeros((num_dof, num_dof), dtype=ct.c_double, order='F')\n # Cglobal = np.zeros((num_dof, num_dof), dtype=ct.c_double, order='F')\n Kglobal = np.zeros((num_dof, num_dof), dtype=ct.c_double, order='F')\n Qglobal = np.zeros((num_dof, ), dtype=ct.c_double, order='F')\n\n f_cbeam3_asbly_static_python(ct.byref(ct.c_int(num_dof)),\n ct.byref(n_nodes),\n ct.byref(n_elem),\n beam.ini_info.pos.ctypes.data_as(doubleP),\n beam.ini_info.psi.ctypes.data_as(doubleP),\n tstep.pos.ctypes.data_as(doubleP),\n tstep.psi.ctypes.data_as(doubleP),\n tstep.steady_applied_forces.ctypes.data_as(doubleP),\n beam.fortran['num_nodes'].ctypes.data_as(intP),\n beam.fortran['num_mem'].ctypes.data_as(intP),\n beam.fortran['connectivities'].ctypes.data_as(intP),\n beam.fortran['master'].ctypes.data_as(intP),\n ct.byref(n_mass),\n beam.fortran['mass'].ctypes.data_as(doubleP),\n beam.fortran['mass_indices'].ctypes.data_as(intP),\n ct.byref(n_stiff),\n beam.fortran['stiffness'].ctypes.data_as(doubleP),\n beam.fortran['inv_stiffness'].ctypes.data_as(doubleP),\n beam.fortran['stiffness_indices'].ctypes.data_as(intP),\n beam.fortran['frame_of_reference_delta'].ctypes.data_as(doubleP),\n beam.fortran['rbmass'].ctypes.data_as(doubleP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['fdof'].ctypes.data_as(intP),\n ct.byref(xbopts),\n tstep.gravity_forces.ctypes.data_as(doubleP),\n Kglobal.ctypes.data_as(doubleP),\n Qglobal.ctypes.data_as(doubleP),\n ct.byref(ct.c_int(iLoadStep)))\n\n return Kglobal, Qglobal\n\n\ndef xbeam_step_coupledrigid(beam, settings, ts, tstep=None, dt=None):\n # library load\n f_xbeam_solv_rigid_step_python = xbeamlib.xbeam_solv_coupledrigid_step_python\n f_xbeam_solv_rigid_step_python.restype = None\n\n if tstep is None:\n tstep = beam.timestep_info[-1]\n\n # initialisation\n n_elem = ct.c_int(beam.num_elem)\n n_nodes = ct.c_int(beam.num_node)\n n_mass = ct.c_int(beam.n_mass)\n n_stiff = ct.c_int(beam.n_stiff)\n\n xbopts = Xbopts()\n xbopts.PrintInfo = ct.c_bool(settings['print_info'])\n xbopts.MaxIterations = ct.c_int(settings['max_iterations'])\n xbopts.NumLoadSteps = ct.c_int(settings['num_load_steps'])\n xbopts.DeltaCurved = ct.c_double(settings['delta_curved'])\n xbopts.MinDelta = ct.c_double(settings['min_delta'])\n xbopts.abs_threshold = ct.c_double(settings['abs_threshold'])\n xbopts.NewmarkDamp = ct.c_double(settings['newmark_damp'])\n xbopts.gravity_on = ct.c_bool(settings['gravity_on'])\n xbopts.gravity = ct.c_double(settings['gravity'])\n xbopts.balancing = ct.c_bool(settings['balancing'])\n xbopts.gravity_dir_x = ct.c_double(settings['gravity_dir'][0])\n xbopts.gravity_dir_y = ct.c_double(settings['gravity_dir'][1])\n xbopts.gravity_dir_z = ct.c_double(settings['gravity_dir'][2])\n xbopts.relaxation_factor = ct.c_double(settings['relaxation_factor'])\n\n if dt is None:\n in_dt = ct.c_double(settings['dt'])\n else:\n in_dt = ct.c_double(dt)\n\n ctypes_ts = ct.c_int(ts)\n numdof = ct.c_int(beam.num_dof.value)\n\n f_xbeam_solv_rigid_step_python(ct.byref(numdof),\n ct.byref(ctypes_ts),\n ct.byref(n_elem),\n ct.byref(n_nodes),\n ct.byref(in_dt),\n beam.fortran['num_nodes'].ctypes.data_as(intP),\n beam.fortran['num_mem'].ctypes.data_as(intP),\n beam.fortran['connectivities'].ctypes.data_as(intP),\n beam.fortran['master'].ctypes.data_as(intP),\n ct.byref(n_mass),\n beam.fortran['mass'].ctypes.data_as(doubleP),\n beam.fortran['mass_indices'].ctypes.data_as(intP),\n ct.byref(n_stiff),\n beam.fortran['stiffness'].ctypes.data_as(doubleP),\n beam.fortran['inv_stiffness'].ctypes.data_as(doubleP),\n beam.fortran['stiffness_indices'].ctypes.data_as(intP),\n beam.fortran['frame_of_reference_delta'].ctypes.data_as(doubleP),\n beam.fortran['rbmass'].ctypes.data_as(doubleP),\n beam.fortran['node_master_elem'].ctypes.data_as(intP),\n beam.fortran['vdof'].ctypes.data_as(intP),\n beam.fortran['fdof'].ctypes.data_as(intP),\n ct.byref(xbopts),\n tstep.pos.ctypes.data_as(doubleP),\n tstep.psi.ctypes.data_as(doubleP),\n tstep.steady_applied_forces.ctypes.data_as(doubleP),\n tstep.unsteady_applied_forces.ctypes.data_as(doubleP),\n tstep.gravity_forces.ctypes.data_as(doubleP),\n tstep.quat.ctypes.data_as(doubleP),\n tstep.for_vel.ctypes.data_as(doubleP),\n tstep.for_acc.ctypes.data_as(doubleP),\n tstep.q[-10:].ctypes.data_as(doubleP),\n tstep.dqdt[-10:].ctypes.data_as(doubleP),\n tstep.dqddt[-10:].ctypes.data_as(doubleP))\n" }, { "path": "sharpy/utils/__init__.py", "content": "\"\"\"Utilities\"\"\"" }, { "path": "sharpy/utils/algebra.py", "content": "\"\"\"\nAlgebra package\n\nExtensive library with geometrical and algebraic operations\n\nNote:\n Tests can be found in ``tests/utils/algebra_test``\n\"\"\"\n\nimport numpy as np\nfrom warnings import warn\n\n\n#######\n# functions for back compatibility\ndef quat2rot(quat):\n warn('quat2rot(quat) is obsolete! Use quat2rotation(quat).T instead!', stacklevel=2)\n return quat2rotation(quat).T\n\n\ndef crv2rot(psi):\n warn('crv2rot(psi) is obsolete! Use crv2rotation(psi) instead!', stacklevel=2)\n return crv2rotation(psi)\n\n\ndef rot2crv(rot):\n warn('rot2crv(rot) is obsolete! Use rotation2crv(rot.T) instead!', stacklevel=2)\n return rotation2crv(rot.T)\n\n\ndef triad2rot(xb, yb, zb):\n warn('triad2rot(xb,yb,zb) is obsolete! Use triad2rotation(xb,yb,zb).T instead!', stacklevel=2)\n return triad2rotation(xb, yb, zb).T\n\n\ndef mat2quat(rot):\n \"\"\"\n Rotation matrix to quaternion function.\n\n Warnings:\n This function is deprecated and now longer supported. Please use ``algebra.rotation2quat(rot.T)`` instead.\n\n Args:\n rot: Rotation matrix\n\n Returns:\n np.array: equivalent quaternion\n \"\"\"\n warn('mat2quat(rot) is obsolete! Use rotation2quat(rot.T) instead!', stacklevel=2)\n\n return rotation2quat(rot.T)\n\n\ndef tangent_vector(in_coord, ordering=None):\n r\"\"\"\n Tangent vector calculation for 2+ noded elements.\n\n Calculates the tangent vector interpolating every dimension\n separately. It uses a (n_nodes - 1) degree polynomial, and the\n differentiation is analytical.\n\n Calculation method:\n\n 1. A n_nodes-1 polynomial is fitted through the nodes per dimension.\n 2. Those polynomials are analytically differentiated with respect to the node index\n 3. The tangent vector is given by:\n\n .. math::\n\n \\vec{t} = \\frac{s_x'\\vec{i} + s_y'\\vec{j} + s_z'\\vec{k}}{\\left| s_x'\\vec{i} + s_y'\\vec{j} + s_z'\\vec{k}\\right|}\n\n\n where :math:`'` notes the differentiation with respect to the index number\n\n\n Args:\n in_coord (np.ndarray): array of coordinates of the nodes. Dimensions = ``[n_nodes, ndim]``\n\n Notes:\n Dimensions are treated independent from each other, interpolating polynomials are computed\n individually.\n\n \"\"\"\n n_nodes, ndim = in_coord.shape\n\n if ordering is None:\n if n_nodes == 2:\n ordering = [0, n_nodes - 1]\n elif n_nodes == 3:\n ordering = [0, 2, 1]\n else:\n raise NotImplementedError('Elements with more than 3 nodes are not supported')\n\n polyfit_vec, polyfit_der_vec, coord = get_polyfit(in_coord, ordering)\n\n # tangent vector calculation\n # \\vec{t} = \\frac{fx'i + fy'j + fz'k}/mod(...)\n tangent = np.zeros_like(coord)\n for inode in range(n_nodes):\n vector = []\n for idim in range(ndim):\n vector.append((polyfit_der_vec[idim])(inode))\n vector = np.array(vector)\n vector /= np.linalg.norm(vector)\n tangent[inode, :] = vector\n\n # check orientation of tangent vector\n fake_tangent = np.zeros_like(tangent)\n for inode in range(n_nodes):\n if inode == n_nodes - 1:\n # use previous vector\n fake_tangent[inode, :] = fake_tangent[inode - 1, :]\n continue\n fake_tangent[inode, :] = coord[inode + 1, :] - coord[inode, :]\n\n for inode in range(n_nodes):\n if np.dot(tangent[inode, :], fake_tangent[inode, :]) < 0:\n tangent[inode, :] *= -1\n\n return tangent, polyfit_vec\n\n\ndef get_polyfit(in_coord, ordering):\n coord = in_coord.copy()\n n_nodes, ndim = coord.shape\n for index in range(n_nodes):\n order = ordering[index]\n coord[index, :] = in_coord[order, :]\n\n polynomial_degree = n_nodes - 1\n # first, the polynomial fit.\n # we are going to differentiate wrt the indices ([0, 1, 2] for a 3-node)\n polyfit_vec = [] # we are going to store here the coefficients of the polyfit\n for idim in range(ndim):\n polyfit_vec.append(np.polyfit(range(n_nodes), coord[:, idim],\n polynomial_degree))\n\n # differentiation\n polyfit_der_vec = []\n for idim in range(ndim):\n polyfit_der_vec.append(np.poly1d(np.polyder(polyfit_vec[idim])))\n\n return polyfit_vec, polyfit_der_vec, coord\n\n\ndef unit_vector(vector):\n r\"\"\"\n Transforms the input vector into a unit vector\n\n .. math:: \\mathbf{\\hat{v}} = \\frac{\\mathbf{v}}{\\|\\mathbf{v}\\|}\n\n Args:\n vector (np.array): vector to normalise\n\n Returns:\n np.array: unit vector\n\n \"\"\"\n if np.linalg.norm(vector) < 1e-6:\n return np.zeros_like(vector)\n return vector / np.linalg.norm(vector)\n\n\ndef rotation_matrix_around_axis(axis, angle):\n axis = unit_vector(axis)\n rot = np.cos(angle) * np.eye(3)\n rot += np.sin(angle) * skew(axis)\n rot += (1 - np.cos(angle)) * np.outer(axis, axis)\n return rot\n\n\ndef skew(vector):\n r\"\"\"\n Returns a skew symmetric matrix such that\n\n .. math:: \\boldsymbol{v} \\times \\boldsymbol{u} = \\tilde{\\boldsymbol{v}}{\\boldsymbol{u}\n\n where\n\n .. math:: \\tilde{\\boldsymbol{v}} = \\begin{bmatrix}\n 0 & -v_z & v_y \\\\\n v_z & 0 & -v_x \\\\\n -v_y & v_x & 0 \\end{bmatrix}.\n\n Args:\n vector (np.ndarray): 3-dimensional vector\n\n Returns:\n np.array: Skew-symmetric matrix.\n\n \"\"\"\n if not vector.size == 3:\n raise ValueError('The input vector is not 3D')\n\n matrix = np.zeros((3, 3))\n matrix[1, 2] = -vector[0]\n matrix[2, 0] = -vector[1]\n matrix[0, 1] = -vector[2]\n matrix[2, 1] = vector[0]\n matrix[0, 2] = vector[1]\n matrix[1, 0] = vector[2]\n return matrix\n\n\ndef quadskew(vector):\n \"\"\"\n Generates the matrix needed to obtain the quaternion in the following time step\n through integration of the FoR angular velocity.\n\n\n Args:\n vector (np.array): FoR angular velocity\n\n Notes:\n The angular velocity is assumed to be constant in the time interval\n Equivalent to lib_xbeam function\n Quaternion ODE to compute orientation of body-fixed frame a\n See Shearer and Cesnik (2007) for definition\n\n Returns:\n np.array: matrix\n \"\"\"\n if not vector.size == 3:\n raise ValueError('The input vector is not 3D')\n\n matrix = np.zeros((4, 4))\n matrix[0, 1:4] = vector\n matrix[1:4, 0] = -vector\n matrix[1:4, 1:4] = skew(vector)\n return matrix\n\n\ndef triad2rotation(xb, yb, zb):\n \"\"\"\n If the input triad is the \"b\" coord system given in \"a\" frame,\n (the vectors of the triad are xb, yb, zb), this function returns Rab, ie the\n rotation matrix required to rotate the FoR A onto B.\n :param xb:\n :param yb:\n :param zb:\n :return: rotation matrix Rab\n \"\"\"\n return np.column_stack((xb, yb, zb))\n\n\ndef rot_matrix_2d(angle):\n return np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n\n\ndef angle_between_vectors(vec_a, vec_b):\n angle = np.arctan2(np.linalg.norm(np.cross(vec_a, vec_b)), np.dot(vec_a, vec_b))\n return angle\n\n\ndef angle_between_vectors_sign(vec_a, vec_b, plane_normal=np.array([0, 0, 1])):\n angle = np.arctan2(np.linalg.norm(np.cross(vec_a, vec_b)), np.dot(vec_a, vec_b))\n if np.dot(plane_normal, np.cross(vec_a, vec_b)) < 0:\n angle *= -1\n return angle\n\n\ndef angle_between_vector_and_plane(vector, plane_normal):\n angle = np.arcsin((np.linalg.norm(np.dot(vector, plane_normal))) /\n (np.linalg.norm(vector) * np.linalg.norm(plane_normal)))\n return angle\n\n\ndef panel_area(A, B, C, D):\n \"\"\"\n Calculates the area of a quadrilateral panel from the corner \n points A,B,C, and D using Bertschneider's formula\n \n Args:\n A (np.ndarray): Coordinates of point 1\n B (np.ndarray): Coordinates of point 2\n C (np.ndarray): Coordinates of point 3\n D (np.ndarray): Coordinates of point 4\n\n Returns:\n float: Area of quadrilateral panel\n \"\"\"\n Theta_1 = angle_between_vectors(A - B, A - D)\n Theta_2 = angle_between_vectors(B - C, B - D)\n a = np.linalg.norm(D - A)\n b = np.linalg.norm(A - B)\n c = np.linalg.norm(B - C)\n d = np.linalg.norm(C - D)\n s = (a + b + c + d) / 2\n area = np.sqrt((s - a) * (s - b) * (s - c) * (s - d) - a * b * c * d * np.cos(0.5 * (Theta_1 + Theta_2)) ** 2)\n return area\n\n\ndef rotation2quat(Cab):\n r\"\"\"\n Given a rotation matrix :math:`C^{AB}` rotating the frame A onto B, the function returns\n the minimal \"positive angle\" quaternion representing this rotation, where the quaternion, :math:`\\vec{\\chi}` is\n defined as:\n\n .. math:: \\vec{\\chi}=\n \\left[\\cos\\left(\\frac{\\psi}{2}\\right),\\,\n \\sin\\left(\\frac{\\psi}{2}\\right)\\mathbf{\\hat{n}}\\right]\n\n Args:\n Cab (np.array): rotation matrix :math:`C^{AB}` from frame A to B\n\n Returns:\n np.array: equivalent quaternion :math:`\\vec{\\chi}`\n\n Notes:\n This is the inverse of ``algebra.quat2rotation`` for Cartesian rotation vectors\n associated to rotations in the range :math:`[-\\pi,\\pi]`, i.e.:\n\n ``fv == algebra.rotation2crv(algebra.crv2rotation(fv))``\n\n where ``fv`` represents the Cartesian Rotation Vector, :math:`\\vec{\\psi}` defined as:\n\n .. math:: \\vec{\\psi} = \\psi\\,\\mathbf{\\hat{n}}\n\n such that :math:`\\mathbf{\\hat{n}}` is a unit vector and the scalar :math:`\\psi` is in the range\n :math:`[-\\pi,\\,\\pi]`.\n\n \"\"\"\n\n s = np.zeros((4, 4))\n\n s[0, 0] = 1.0 + np.trace(Cab)\n s[0, 1:] = matrix2skewvec(Cab)\n\n s[1, 0] = Cab[2, 1] - Cab[1, 2]\n s[1, 1] = 1.0 + Cab[0, 0] - Cab[1, 1] - Cab[2, 2]\n s[1, 2] = Cab[0, 1] + Cab[1, 0]\n s[1, 3] = Cab[0, 2] + Cab[2, 0]\n\n s[2, 0] = Cab[0, 2] - Cab[2, 0]\n s[2, 1] = Cab[1, 0] + Cab[0, 1]\n s[2, 2] = 1.0 - Cab[0, 0] + Cab[1, 1] - Cab[2, 2]\n s[2, 3] = Cab[1, 2] + Cab[2, 1]\n\n s[3, 0] = Cab[1, 0] - Cab[0, 1]\n s[3, 1] = Cab[0, 2] + Cab[2, 0]\n s[3, 2] = Cab[1, 2] + Cab[2, 1]\n s[3, 3] = 1.0 - Cab[0, 0] - Cab[1, 1] + Cab[2, 2]\n\n smax = np.max(np.diag(s))\n ismax = np.argmax(np.diag(s))\n\n # compute quaternion angles\n quat = np.zeros((4,))\n quat[ismax] = 0.5 * np.sqrt(smax)\n for i in range(4):\n if i == ismax:\n continue\n quat[i] = 0.25 * s[ismax, i] / quat[ismax]\n\n return quat_bound(quat)\n\n\ndef quat_bound(quat):\n r\"\"\"\n Given a quaternion, :math:`\\vec{\\chi}`, associated to a rotation of angle :math:`\\psi`\n about an axis :math:`\\mathbf{\\hat{n}}`, the function \"bounds\" the quaternion,\n i.e. sets the rotation axis :math:`\\mathbf{\\hat{n}}` such that\n :math:`\\psi` in :math:`[-\\pi,\\pi]`.\n\n Notes:\n As quaternions are defined as:\n\n .. math:: \\vec{\\chi}=\n \\left[\\cos\\left(\\frac{\\psi}{2}\\right),\\,\n \\sin\\left(\\frac{\\psi}{2}\\right)\\mathbf{\\hat{n}}\\right]\n\n this is equivalent to enforcing :math:`\\chi_0\\ge0`.\n\n Args:\n quat (np.array): quaternion to bound\n\n Returns:\n np.array: bounded quaternion\n\n \"\"\"\n if quat[0] < 0:\n quat *= -1.\n return quat\n\n\ndef matrix2skewvec(matrix):\n vector = np.array([matrix[2, 1] - matrix[1, 2],\n matrix[0, 2] - matrix[2, 0],\n matrix[1, 0] - matrix[0, 1]])\n return vector\n\n\ndef quat2crv(quat):\n crv_norm = 2.0 * np.arccos(max(-1.0, min(quat[0], 1.0)))\n\n # normal vector\n if abs(crv_norm) < 1e-15:\n psi = np.zeros((3,))\n else:\n psi = crv_norm * quat[1:4] / np.sin(crv_norm * 0.5)\n\n return psi\n\n\ndef crv2quat(psi):\n r\"\"\"\n Converts a Cartesian rotation vector,\n\n .. math:: \\vec{\\psi} = \\psi\\,\\mathbf{\\hat{n}}\n\n into a \"minimal rotation\" quaternion, i.e. being the quaternion, :math:`\\vec{\\chi}`, defined as:\n\n .. math:: \\vec{\\chi}=\n \\left[\\cos\\left(\\frac{\\psi}{2}\\right),\\,\n \\sin\\left(\\frac{\\psi}{2}\\right)\\mathbf{\\hat{n}}\\right]\n\n the rotation axis, :math:`\\mathbf{\\hat{n}}` is such that the\n rotation angle, :math:`\\psi`, is in :math:`[-\\pi,\\,\\pi]` or,\n equivalently, :math:`\\chi_0\\ge0`.\n\n Args:\n psi (np.array): Cartesian Rotation Vector, CRV: :math:`\\vec{\\psi} = \\psi\\,\\mathbf{\\hat{n}}`.\n\n Returns:\n np.array: equivalent quaternion :math:`\\vec{\\chi}`\n\n \"\"\"\n\n # minimise crv rotation\n psi_new = crv_bounds(psi)\n\n fi = np.linalg.norm(psi_new)\n if fi > 1e-15:\n nv = psi_new / fi\n else:\n nv = psi_new\n\n quat = np.zeros((4,))\n quat[0] = np.cos(.5 * fi)\n quat[1:] = np.sin(.5 * fi) * nv\n\n return quat\n\n\ndef crv_bounds(crv_ini):\n r\"\"\"\n Forces the Cartesian rotation vector norm, :math:`\\|\\vec{\\psi}\\|`, to be in the range\n :math:`[-\\pi,\\pi]`, i.e. determines the rotation axis orientation, :math:`\\mathbf{\\hat{n}}`,\n so as to ensure \"minimal rotation\".\n\n Args:\n crv_ini (np.array): Cartesian rotation vector, :math:`\\vec{\\psi}`\n\n Returns:\n np.array: modified and bounded, equivalent Cartesian rotation vector\n\n \"\"\"\n\n crv = crv_ini.copy()\n # original norm\n norm_ini = np.linalg.norm(crv_ini)\n\n # force the norm to be in [-pi, pi]\n norm = norm_ini - 2.0 * np.pi * int(norm_ini / (2 * np.pi))\n\n if norm == 0.0:\n crv *= 0.0\n else:\n if norm > np.pi:\n norm -= 2.0 * np.pi\n elif norm < -np.pi:\n norm += 2.0 * np.pi\n crv *= (norm / norm_ini)\n\n return crv\n # return crv_ini\n\n\ndef triad2crv(xb, yb, zb):\n return rotation2crv(triad2rotation(xb, yb, zb))\n\n\ndef crv2triad(psi):\n rot_matrix = crv2rotation(psi)\n return rot_matrix[:, 0], rot_matrix[:, 1], rot_matrix[:, 2]\n\n\ndef crv2rotation(psi):\n r\"\"\"\n Given a Cartesian rotation vector, :math:`\\boldsymbol{\\Psi}`, the function produces the rotation\n matrix required to rotate a vector according to :math:`\\boldsymbol{\\Psi}`.\n\n The rotation matrix is given by\n\n .. math::\n \\mathbf{R} = \\mathbf{I} + \\frac{\\sin||\\boldsymbol{\\Psi}||}{||\\boldsymbol{\\Psi}||} \\tilde{\\boldsymbol{\\Psi}} +\n \\frac{1-\\cos{||\\boldsymbol{\\Psi}||}}{||\\boldsymbol{\\Psi}||^2}\\tilde{\\boldsymbol{\\Psi}} \\tilde{\\boldsymbol{\\Psi}}\n\n To avoid the singularity when :math:`||\\boldsymbol{\\Psi}||=0`, the series expansion is used\n\n .. math:: \\mathbf{R} = \\mathbf{I} + \\tilde{\\boldsymbol{\\Psi}} + \\frac{1}{2!}\\tilde{\\boldsymbol{\\Psi}}^2.\n\n\n Args:\n psi (np.array): Cartesian rotation vector :math:`\\boldsymbol{\\Psi}`.\n\n Returns:\n np.array: equivalent rotation matrix\n\n References:\n Geradin and Cardona, Flexible Multibody Dynamics: A finite element approach. Chapter 4\n\n \"\"\"\n\n norm_psi = np.linalg.norm(psi)\n\n if norm_psi < 1e-15:\n skew_psi = skew(psi)\n rot_matrix = np.eye(3) + skew_psi + 0.5 * np.dot(skew_psi, skew_psi)\n else:\n normal = psi / norm_psi\n skew_normal = skew(normal)\n\n rot_matrix = np.eye(3)\n rot_matrix += np.sin(norm_psi) * skew_normal\n rot_matrix += (1.0 - np.cos(norm_psi)) * np.dot(skew_normal, skew_normal)\n\n return rot_matrix\n\n\ndef rotation2crv(Cab):\n r\"\"\"\n Given a rotation matrix :math:`C^{AB}` rotating the frame A onto B, the function returns\n the minimal size Cartesian rotation vector, :math:`\\vec{\\psi}` representing this rotation.\n\n Args:\n Cab (np.array): rotation matrix :math:`C^{AB}`\n\n Returns:\n np.array: equivalent Cartesian rotation vector, :math:`\\vec{\\psi}`.\n\n Notes:\n this is the inverse of ``algebra.crv2rotation`` for Cartesian rotation vectors\n associated to rotations in the range :math:`[-\\pi,\\,\\pi]`, i.e.:\n\n ``fv == algebra.rotation2crv(algebra.crv2rotation(fv))``\n\n for each Cartesian rotation vector of the form :math:`\\vec{\\psi} = \\psi\\,\\mathbf{\\hat{n}}`\n represented as ``fv=a*nv`` such that ``nv`` is a unit vector and the scalar ``a`` is in the\n range :math:`[-\\pi,\\,\\pi]`.\n\n \"\"\"\n\n if np.linalg.norm(Cab) < 1e-6:\n raise AttributeError('Element Vector V is not orthogonal to reference line (51105)')\n\n quat = rotation2quat(Cab)\n psi = quat2crv(quat)\n\n if np.linalg.norm(Cab) < 1.0e-15:\n psi[0] = Cab[1, 2]\n psi[1] = Cab[2, 0]\n psi[2] = Cab[0, 1]\n\n return crv_bounds(psi)\n\n\ndef crv2tan(psi):\n r\"\"\"\n Returns the tangential operator, :math:`\\mathbf{T}(\\boldsymbol{\\Psi})`, that is a function of\n the Cartesian Rotation Vector, :math:`\\boldsymbol{\\Psi}`.\n\n .. math::\n\n \\boldsymbol{T}(\\boldsymbol{\\Psi}) =\n \\mathbf{I} +\n \\left(\\frac{\\cos ||\\boldsymbol{\\Psi}|| - 1}{||\\boldsymbol{\\Psi}||^2}\\right)\\tilde{\\boldsymbol{\\Psi}}\n + \\left(1 - \\frac{\\sin||\\boldsymbol{\\Psi}||}{||\\boldsymbol{\\Psi}||}\\right)\n \\frac{\\tilde{\\boldsymbol{\\Psi}}\\tilde{\\boldsymbol{\\Psi}}}{||\\boldsymbol{\\Psi}||^2}\n\n When the norm of the CRV approaches 0, the series expansion expression is used in-lieu of the above expression\n\n .. math::\n\n \\boldsymbol{T}(\\boldsymbol{\\Psi}) =\n \\mathbf{I}\n -\\frac{1}{2!}\\tilde{\\boldsymbol{\\Psi}} + \\frac{1}{3!}\\tilde{\\boldsymbol{\\Psi}}^2\n\n Args:\n psi (np.array): Cartesian Rotation Vector, :math:`\\boldsymbol{\\Psi}`.\n\n Returns:\n np.array: Tangential operator\n\n References:\n Geradin and Cardona. Flexible Multibody Dynamics: A Finite Element Approach. Chapter 4.\n \"\"\"\n\n norm_psi = np.linalg.norm(psi)\n psi_skew = skew(psi)\n\n eps = 1e-8\n if norm_psi < eps:\n return np.eye(3) - 0.5 * psi_skew + 1.0 / 6.0 * np.dot(psi_skew, psi_skew)\n else:\n k1 = (np.cos(norm_psi) - 1.0) / (norm_psi * norm_psi)\n k2 = (1.0 - np.sin(norm_psi) / norm_psi) / (norm_psi * norm_psi)\n return np.eye(3) + k1 * psi_skew + k2 * np.dot(psi_skew, psi_skew)\n\n\ndef crv2invtant(psi):\n tan = crv2tan(psi).T\n return np.linalg.inv(tan)\n\n\ndef triad2crv_vec(v1, v2, v3):\n n_nodes, _ = v1.shape\n crv_vec = np.zeros((n_nodes, 3))\n for inode in range(n_nodes):\n crv_vec[inode, :] = triad2crv(v1[inode, :], v2[inode, :], v3[inode, :])\n\n return crv_vec\n\n\ndef crv2triad_vec(crv_vec):\n n_nodes, _ = crv_vec.shape\n v1 = np.zeros((n_nodes, 3))\n v2 = np.zeros((n_nodes, 3))\n v3 = np.zeros((n_nodes, 3))\n for inode in range(n_nodes):\n v1[inode, :], v2[inode, :], v3[inode, :] = crv2triad(crv_vec[inode, :])\n return v1, v2, v3\n\n\ndef quat2rotation(q1):\n r\"\"\"Calculate rotation matrix based on quaternions.\n\n If B is a FoR obtained rotating a FoR A by an angle :math:`\\phi` about an axis :math:`\\mathbf{n}`\n (recall :math:`\\mathbf{n}` will be invariant during the rotation), and :math:`\\mathbf{q}` is the related\n quaternion, :math:`\\mathbf{q}(\\phi,\\mathbf{n})`, the function will return the matrix :math:`C^{AB}` such that:\n\n - :math:`C^{AB}` rotates FoR A onto FoR B.\n\n - :math:`C^{AB}` transforms the coordinates of a vector defined in B component to\n A components i.e. :math:`\\mathbf{v}^A = C^{AB}(\\mathbf{q})\\mathbf{v}^B`.\n\n .. math::\n C^{AB}(\\mathbf{q}) = \\begin{pmatrix}\n q_0^2 + q_1^2 - q_2^2 -q_3^2 & 2(q_1 q_2 - q_0 q_3) & 2(q_1 q_3 + q_0 q_2) \\\\\n 2(q_1 q_2 + q_0 q_3) & q_0^2 - q_1^2 + q_2^2 - q_3^2 & 2(q_2 q_3 - q_0 q_1) \\\\\n 2(q_1 q_3 - q_0 q_2) & 2(q_2 q_3 + q_0 q_1) & q_0^2 -q_1^2 -q_2^2 +q_3^2\n \\end{pmatrix}\n\n Notes:\n The inverse rotation is defined as the transpose of the matrix :math:`C^{BA} = C^{{AB}^T}`.\n\n In typical SHARPy applications, the quaternion relation between the A and G frames is expressed\n as :math:`C^{GA}(\\mathbf{q})`, and in the context of this function it corresponds to:\n\n >>> C_ga = quat2rotation(q1)\n >>> C_ag = quat2rotation.T(q1)\n\n Args:\n q (np.ndarray): Quaternion :math:`\\mathbf{q}(\\phi, \\mathbf{n})`.\n\n Returns:\n np.ndarray: :math:`C^{AB}` rotation matrix from FoR B to FoR A.\n\n References:\n Stevens, L. Aircraft Control and Simulation. 1985. pg 41\n \"\"\"\n\n q = q1.copy(order='F')\n q /= np.linalg.norm(q)\n\n rot_mat = np.zeros((3, 3), order='F')\n\n rot_mat[0, 0] = q[0] ** 2 + q[1] ** 2 - q[2] ** 2 - q[3] ** 2\n rot_mat[1, 1] = q[0] ** 2 - q[1] ** 2 + q[2] ** 2 - q[3] ** 2\n rot_mat[2, 2] = q[0] ** 2 - q[1] ** 2 - q[2] ** 2 + q[3] ** 2\n\n rot_mat[1, 0] = 2. * (q[1] * q[2] + q[0] * q[3])\n rot_mat[0, 1] = 2. * (q[1] * q[2] - q[0] * q[3])\n\n rot_mat[2, 0] = 2. * (q[1] * q[3] - q[0] * q[2])\n rot_mat[0, 2] = 2. * (q[1] * q[3] + q[0] * q[2])\n\n rot_mat[2, 1] = 2. * (q[2] * q[3] + q[0] * q[1])\n rot_mat[1, 2] = 2. * (q[2] * q[3] - q[0] * q[1])\n\n return rot_mat\n\n\ndef rot_skew(vec):\n from warnings import warn\n warn(\"use 'skew' function instead of 'rot_skew'\")\n return skew(vec)\n\n\ndef rotation3d_x(angle):\n r\"\"\"\n\n Rotation matrix about the x axis by the input angle :math:`\\Phi`\n\n .. math::\n\n \\mathbf{\\tau}_x = \\begin{bmatrix}\n 1 & 0 & 0 \\\\\n 0 & \\cos(\\Phi) & -\\sin(\\Phi) \\\\\n 0 & \\sin(\\Phi) & \\cos(\\Phi)\n \\end{bmatrix}\n\n\n Args:\n angle (float): angle of rotation in radians about the x axis\n\n Returns:\n np.array: 3x3 rotation matrix about the x axis\n\n \"\"\"\n c = np.cos(angle)\n s = np.sin(angle)\n mat = np.zeros((3, 3))\n mat[0, :] = [1., 0., 0.]\n mat[1, :] = [0., c, -s]\n mat[2, :] = [0., s, c]\n return mat\n\n\ndef rotation3d_y(angle):\n r\"\"\"\n Rotation matrix about the y axis by the input angle :math:`\\Theta`\n\n .. math::\n\n \\mathbf{\\tau}_y = \\begin{bmatrix}\n \\cos(\\Theta) & 0 & -\\sin(\\Theta) \\\\\n 0 & 1 & 0 \\\\\n \\sin(\\Theta) & 0 & \\cos(\\Theta)\n \\end{bmatrix}\n\n\n Args:\n angle (float): angle of rotation in radians about the y axis\n\n Returns:\n np.array: 3x3 rotation matrix about the y axis\n\n \"\"\"\n\n c = np.cos(angle)\n s = np.sin(angle)\n mat = np.zeros((3, 3))\n mat[0, :] = [c, 0., s]\n mat[1, :] = [0., 1., 0.]\n mat[2, :] = [-s, 0., c]\n return mat\n\n\ndef rotation3d_z(angle):\n r\"\"\"\n Rotation matrix about the z axis by the input angle :math:`\\Psi`\n\n .. math::\n \\mathbf{\\tau}_z = \\begin{bmatrix}\n \\cos(\\Psi) & -\\sin(\\Psi) & 0 \\\\\n \\sin(\\Psi) & \\cos(\\Psi) & 0 \\\\\n 0 & 0 & 1\n \\end{bmatrix}\n\n Args:\n angle (float): angle of rotation in radians about the z axis\n\n Returns:\n np.array: 3x3 rotation matrix about the z axis\n\n \"\"\"\n\n c = np.cos(angle)\n s = np.sin(angle)\n mat = np.zeros((3, 3))\n mat[0, :] = [c, -s, 0.]\n mat[1, :] = [s, c, 0.]\n mat[2, :] = [0., 0., 1.]\n return mat\n\n\ndef rotate_crv(crv_in, axis, angle):\n C = crv2rotation(crv_in).T\n rot = rotation_matrix_around_axis(axis, angle)\n C = np.dot(C, rot)\n crv = rot2crv(C)\n return crv\n\n\ndef euler2rot(euler):\n r\"\"\"\n\n Transforms Euler angles (roll, pitch and yaw :math:`\\Phi, \\Theta, \\Psi`) into a 3x3 rotation matrix describing\n that rotates a vector in yaw pitch, and roll.\n\n The rotations are performed successively, first in yaw, then in pitch and finally in roll.\n\n .. math::\n\n \\mathbf{T}_{AG} = \\mathbf{\\tau}_x(\\Phi) \\mathbf{\\tau}_y(\\Theta) \\mathbf{\\tau}_z(\\Psi)\n\n\n where :math:`\\mathbf{\\tau}` represents the rotation about the subscripted axis.\n\n Args:\n euler (np.array): 1x3 array with the Euler angles in the form ``[roll, pitch, yaw]`` in radians\n\n Returns:\n np.array: 3x3 transformation matrix describing the rotation by the input Euler angles.\n\n \"\"\"\n\n rot = rotation3d_z(euler[2]).dot(rotation3d_y(euler[1]).dot(rotation3d_x(euler[0])))\n return rot\n\n\ndef euler2quat(euler):\n \"\"\"\n\n Args:\n euler: Euler angles\n\n Returns:\n np.ndarray: Equivalent quaternion.\n \"\"\"\n euler_rot = euler2rot(euler) # this is Cag\n quat = rotation2quat(euler_rot)\n return quat\n\n\ndef quat2euler(quat):\n r\"\"\"\n Quaternion to Euler angles transformation.\n\n Transforms a normalised quaternion :math:`\\chi\\longrightarrow[\\phi, \\theta, \\psi]` to roll, pitch and yaw angles\n respectively.\n\n The transformation is valid away from the singularity present at:\n\n .. math:: \\Delta = \\frac{1}{2}\n\n where :math:`\\Delta = q_0 q_2 - q_1 q_3`.\n\n The transformation is carried out as follows:\n\n .. math::\n \\psi &= \\arctan{\\left(2\\frac{q_0q_3+q_1q_2}{1-2(q_2^2+q_3^2)}\\right)} \\\\\n \\theta &= \\arcsin(2\\Delta) \\\\\n \\phi &= \\arctan\\left(2\\frac{q_0q_1 + q_2q_3}{1-2(q_1^2+q_2^2)}\\right)\n\n Args:\n quat (np.ndarray): Normalised quaternion.\n\n Returns:\n np.ndarray: Array containing the Euler angles :math:`[\\phi, \\theta, \\psi]` for roll, pitch and yaw, respectively.\n\n References:\n Blanco, J.L. - A tutorial on SE(3) transformation parameterizations and on-manifold optimization. Technical\n Report 012010. ETS Ingenieria Informatica. Universidad de Malaga. 2013.\n \"\"\"\n\n assert np.abs(np.linalg.norm(quat) - 1.0) < 1.e6, 'Input quaternion is not normalised'\n\n q0 = quat[0]\n q1 = quat[1]\n q2 = quat[2]\n q3 = quat[3]\n\n delta = quat[0] * quat[2] - quat[1] * quat[3]\n\n if np.abs(delta) > 0.9 * 0.5:\n warn('Warning, approaching singularity. Delta {:.3f} for singularity at Delta=0.5'.format(np.abs(delta)))\n\n yaw = np.arctan2(2 * (q0 * q3 + q1 * q2), (1 - 2 * (q2 ** 2 + q3 ** 2)))\n pitch = np.arcsin(2 * delta)\n roll = np.arctan2(2 * (q0 * q1 + q2 * q3), (1 - 2 * (q1 ** 2 + q2 ** 2)))\n\n return np.array([roll, pitch, yaw])\n\n\ndef crv_dot2omega(crv, crv_dot):\n return np.dot(crv2tan(crv).T, crv_dot)\n\n\ndef crv_dot2Omega(crv, crv_dot):\n return np.dot(crv2tan(crv), crv_dot)\n\n\ndef quaternion_product(q, r):\n result = np.zeros((4,))\n result[0] = q[0] * r[0] - q[1] * r[1] - q[2] * r[2] - q[3] * r[3]\n result[1] = q[0] * r[1] + q[1] * r[0] + q[2] * r[3] - q[3] * r[2]\n result[2] = q[0] * r[2] - q[1] * r[3] + q[2] * r[0] + q[3] * r[1]\n result[3] = q[0] * r[3] + q[1] * r[2] - q[2] * r[1] + q[3] * r[0]\n return result\n\n\ndef omegadt2quat(omegadt):\n quat = np.zeros((4,))\n\n omegadt_norm = np.linalg.norm(omegadt)\n quat[0] = np.cos(0.5 * omegadt_norm)\n quat[1:4] = unit_vector(omegadt) * np.sin(0.5 * omegadt_norm)\n return quat\n\n\ndef rotate_quaternion(quat, omegadt):\n return quaternion_product(omegadt2quat(omegadt), quat)\n\n\ndef get_triad(coordinates_def, frame_of_reference_delta, twist=None, n_nodes=3, ordering=np.array([0, 2, 1])):\n \"\"\"\n Generates two unit vectors in body FoR that define the local FoR for\n a beam element. These vectors are calculated using `frame_of_reference_delta`\n :return:\n \"\"\"\n # now, calculate tangent vector (and coefficients of the polynomial\n # fit just in case)\n tangent, polyfit = tangent_vector(\n coordinates_def,\n ordering)\n normal = np.zeros_like(tangent)\n binormal = np.zeros_like(tangent)\n\n # v_vector is the vector with origin the FoR node and delta\n # equals frame_of_reference_delta\n for inode in range(n_nodes):\n v_vector = frame_of_reference_delta[inode, :]\n normal[inode, :] = unit_vector(np.cross(\n tangent[inode, :],\n v_vector\n )\n )\n binormal[inode, :] = -unit_vector(np.cross(\n tangent[inode, :],\n normal[inode, :]\n )\n )\n\n if twist is not None:\n raise NotImplementedError(\n 'Structural twist is not yet supported in algebra.get_triad, but it is in beamstructures.py')\n\n return tangent, binormal, normal\n\n\ndef der_Cquat_by_v(q, v):\n \"\"\"\n Being C=C(quat) the rotational matrix depending on the quaternion q and\n defined as C=quat2rotation(q), the function returns the derivative, w.r.t. the\n quanternion components, of the vector dot(C,v), where v is a constant\n vector.\n\n The elements of the resulting derivative matrix D are ordered such that:\n\n .. math:: d(C*v) = D*d(q)\n\n where :math:`d(.)` is a delta operator.\n \"\"\"\n\n vx, vy, vz = v\n q0, q1, q2, q3 = q\n\n return 2. * np.array([[q0 * vx + q2 * vz - q3 * vy, q1 * vx + q2 * vy + q3 * vz,\n q0 * vz + q1 * vy - q2 * vx, -q0 * vy + q1 * vz - q3 * vx],\n [q0 * vy - q1 * vz + q3 * vx, -q0 * vz - q1 * vy + q2 * vx,\n q1 * vx + q2 * vy + q3 * vz, q0 * vx + q2 * vz - q3 * vy],\n [q0 * vz + q1 * vy - q2 * vx, q0 * vy - q1 * vz + q3 * vx,\n -q0 * vx - q2 * vz + q3 * vy, q1 * vx + q2 * vy + q3 * vz]])\n\n\ndef der_CquatT_by_v(q, v):\n r\"\"\"\n Returns the derivative with respect to quaternion components of a projection matrix times a constant vector.\n\n Being :math:`\\mathbf{C}=\\mathbf{R}(\\boldsymbol{\\chi})^\\top` the projection matrix depending on the quaternion\n :math:`\\boldsymbol{\\chi}` and obtained through the function\n defined as ``C=quat2rotation(q).T``, this function returns the derivative with respect to the\n quaternion components, of the vector :math:`(\\mathbf{C\\cdot v})`, where :math:`\\mathbf{v}` is a constant\n vector.\n\n The derivative operation is defined as:\n\n .. math:: \\delta(\\mathbf{C}\\cdot \\mathbf{v}) =\n \\frac{\\partial}{\\partial\\boldsymbol{\\chi}}\\left(\\mathbf{C\\cdot v}\\right)\\delta\\boldsymbol{\\chi}\n\n where, for simplicity, we define\n\n .. math:: \\mathbf{D} =\n \\frac{\\partial}{\\partial\\boldsymbol{\\chi}}\\left(\\mathbf{C\\cdot v}\\right) \\in \\mathbb{R}^{3\\times4}\n\n and :math:`\\delta(\\bullet)` is a delta operator.\n\n The members of :math:`\\mathbf{D}` are the following:\n\n .. math::\n \\mathbf{D}_{11} &= 2 (q_0 v_x - q_2 v_z + q_3 v_y)\\\\\n \\mathbf{D}_{12} &= 2 (q_1 v_x - q_2 v_y + q_3 v_z)\\\\\n \\mathbf{D}_{13} &= 2 (-q_0 v_z + q_1 v_y - q_2 v_x)\\\\\n \\mathbf{D}_{14} &= 2 (q_0 v_y + q_1 v_z - q_3 v_x)\n\n .. math::\n \\mathbf{D}_{21} &= 2 (q_0 v_y + q_1 v_z - q_3 v_x)\\\\\n \\mathbf{D}_{22} &= 2 (q_0 v_z - q_1 v_y + q_2 v_x)\\\\\n \\mathbf{D}_{23} &= 2 (q_1 v_x + q_2 v_y + q_3 v_z)\\\\\n \\mathbf{D}_{24} &= 2 (-q_0 v_x + q_2 v_z - q_3 v_y)\n\n .. math::\n \\mathbf{D}_{31} &= 2 (q_0 v_z - q_1 v_y + q_2 v_x)\\\\\n \\mathbf{D}_{32} &= 2 (-q_0 v_y - q_1 v_z + q_3 v_x)\\\\\n \\mathbf{D}_{33} &= 2 (q_0 v_x - q_2 v_z + q_3 v_y)\\\\\n \\mathbf{D}_{34} &= 2 (q_1 v_x + q_2 v_y + q_3 v_z)\\\\\n\n Returns:\n np.array: :math:`\\mathbf{D}` matrix.\n \"\"\"\n\n vx, vy, vz = v\n q0, q1, q2, q3 = q\n\n return 2. * np.array([[q0 * vx - q2 * vz + q3 * vy, q1 * vx + q2 * vy + q3 * vz,\n - q0 * vz + q1 * vy - q2 * vx, q0 * vy + q1 * vz - q3 * vx],\n [q0 * vy + q1 * vz - q3 * vx, q0 * vz - q1 * vy + q2 * vx,\n q1 * vx + q2 * vy + q3 * vz, -q0 * vx + q2 * vz - q3 * vy],\n [q0 * vz - q1 * vy + q2 * vx, -q0 * vy - q1 * vz + q3 * vx,\n q0 * vx - q2 * vz + q3 * vy, q1 * vx + q2 * vy + q3 * vz]])\n\n\ndef der_Tan_by_xv(fv0, xv):\n \"\"\"\n Being fv0 a cartesian rotation vector and Tan the corresponding tangential\n operator (computed through crv2tan(fv)), the function returns the derivative\n of dot(Tan,xv), where xv is a constant vector.\n\n The elements of the resulting derivative matrix D are ordered such that:\n\n .. math:: d(Tan*xv) = D*d(fv)\n\n where :math:`d(.)` is a delta operator.\n\n Note:\n The derivative expression has been derived symbolically and verified\n by FDs. A more compact expression may be possible.\n \"\"\"\n\n f0 = np.linalg.norm(fv0)\n if f0 < (1e9 * np.finfo(float).eps):\n tensor1 = np.array([[0., 0., 0.], [0., 0., -0.5], [0., 0.5, 0.]]) * xv[0]\n tensor2 = np.array([[0., 0., 0.5], [0., 0., 0.], [-0.5, 0., 0.]]) * xv[1]\n tensor3 = np.array([[0., -0.5, 0.], [0.5, 0., 0.], [0., 0., 0.]]) * xv[2]\n return tensor1 + tensor2 + tensor3\n\n sf0, cf0 = np.sin(f0), np.cos(f0)\n\n fv0_x, fv0_y, fv0_z = fv0\n xv_x, xv_y, xv_z = xv\n\n f0p2 = f0 ** 2\n f0p3 = f0 ** 3\n f0p4 = f0 ** 4\n\n rs01 = sf0 / f0\n rs03 = sf0 / f0p3\n rc02 = (cf0 - 1) / f0p2\n rc04 = (cf0 - 1) / f0p4\n\n Ts02 = (1 - rs01) / f0p2\n Ts04 = (1 - rs01) / f0p4\n\n return np.array(\n [[xv_x * ((-fv0_y ** 2 - fv0_z ** 2) * (-cf0 * fv0_x / f0p2 + fv0_x * rs03) / f0p2 -\n 2 * fv0_x * (1 - rs01) * (-fv0_y ** 2 - fv0_z ** 2) / f0p4) + xv_y * (fv0_x * fv0_y * (\n -cf0 * fv0_x / f0p2 + fv0_x * rs03) / f0p2 + fv0_y * Ts02 +\n fv0_x * fv0_z * rs03 - 2 * fv0_x ** 2 * fv0_y * Ts04 + 2 * fv0_x * fv0_z *\n rc04) + xv_z * (\n fv0_x * fv0_z * (-cf0 * fv0_x / f0p2 + fv0_x * rs03) / f0p2 +\n fv0_z * Ts02 - fv0_x * fv0_y * rs03 - 2 * fv0_x ** 2 * fv0_z * Ts04\n - 2 * fv0_x * fv0_y * rc04),\n #\n xv_x * (-2 * fv0_y * Ts02 + (-fv0_y ** 2 - fv0_z ** 2) * (-cf0 * fv0_y / f0p2 +\n fv0_y * rs03) / f0p2 - 2 * fv0_y * (1 - rs01) * (\n -fv0_y ** 2 - fv0_z ** 2) / f0p4) +\n xv_y * (fv0_x * fv0_y * (-cf0 * fv0_y / f0p2 + fv0_y * rs03) / f0p2 + fv0_x * Ts02 +\n fv0_y * fv0_z * rs03 - 2 * fv0_x * fv0_y ** 2 * Ts04 + 2 * fv0_y * fv0_z * rc04)\n + xv_z * (fv0_x * fv0_z * (-cf0 * fv0_y / f0p2 + fv0_y * rs03) / f0p2 + rc02 -\n fv0_y ** 2 * rs03 - 2 * fv0_x * fv0_y * fv0_z * Ts04 - 2 * fv0_y ** 2 * rc04),\n #\n xv_x * (-2 * fv0_z * Ts02 + (-fv0_y ** 2 - fv0_z ** 2) * (-cf0 * fv0_z / f0p2\n + fv0_z * rs03) / f0p2 - 2 * fv0_z * (1 - rs01) * (\n -fv0_y ** 2 - fv0_z ** 2) / f0p4) +\n xv_y * (fv0_x * fv0_y * (-cf0 * fv0_z / f0p2 + fv0_z * rs03) / f0p2 - rc02\n + fv0_z ** 2 * rs03 - 2 * fv0_x * fv0_y * fv0_z * Ts04 + 2 * fv0_z ** 2 * rc04)\n + xv_z * (fv0_x * fv0_z * (-cf0 * fv0_z / f0p2 + fv0_z * rs03) / f0p2 + fv0_x * Ts02\n - fv0_y * fv0_z * rs03 - 2 * fv0_x * fv0_z ** 2 * Ts04 - 2 * fv0_y * fv0_z * rc04)],\n [xv_x * (fv0_x * fv0_y * (-cf0 * fv0_x / f0p2 + fv0_x * rs03) / f0p2 +\n fv0_y * Ts02 - fv0_x * fv0_z * rs03 - 2 * fv0_x ** 2 * fv0_y * Ts04 -\n 2 * fv0_x * fv0_z * rc04) + xv_y * (-2 * fv0_x * Ts02 +\n (-fv0_x ** 2 - fv0_z ** 2) * (\n -cf0 * fv0_x / f0p2 + fv0_x * rs03) / f0p2\n - 2 * fv0_x * (1 - rs01) * (-fv0_x ** 2 - fv0_z ** 2) / f0p4) +\n xv_z * (fv0_y * fv0_z * (-cf0 * fv0_x / f0p2 + fv0_x * rs03) / f0p2 - rc02\n + fv0_x ** 2 * rs03 + 2 * fv0_x ** 2 * rc04 - 2 * fv0_x * fv0_y * fv0_z * Ts04),\n xv_x * (fv0_x * fv0_y * (-cf0 * fv0_y / f0p2 + fv0_y * rs03) / f0p2 +\n fv0_x * Ts02 - fv0_y * fv0_z * rs03 - 2 * fv0_x * fv0_y ** 2 * Ts04\n - 2 * fv0_y * fv0_z * rc04) + xv_y * ((-fv0_x ** 2 - fv0_z ** 2) * (-cf0 * fv0_y / f0p2\n + fv0_y * rs03) / f0p2 - 2 * fv0_y * (\n 1 - rs01) * (-fv0_x ** 2 - fv0_z ** 2) / f0p4)\n + xv_z * (fv0_y * fv0_z * (-cf0 * fv0_y / f0p2 + fv0_y * rs03) / f0p2 + fv0_z * Ts02\n + fv0_x * fv0_y * rs03 + 2 * fv0_x * fv0_y * rc04 - 2 * fv0_y ** 2 * fv0_z * Ts04),\n xv_x * (fv0_x * fv0_y * (-cf0 * fv0_z / f0p2 + fv0_z * rs03) / f0p2 + rc02 - fv0_z ** 2 * rs03\n - 2 * fv0_x * fv0_y * fv0_z * Ts04 - 2 * fv0_z ** 2 * rc04) + xv_y * (-2 * fv0_z * Ts02\n + (-fv0_x ** 2 - fv0_z ** 2) * (\n -cf0 * fv0_z / f0p2 + fv0_z * rs03) / f0p2 -\n 2 * fv0_z * (1 - rs01) * (\n -fv0_x ** 2 - fv0_z ** 2) / f0p4) + xv_z * (\n fv0_y * fv0_z * (-cf0 * fv0_z / f0p2\n + fv0_z * rs03) / f0p2 + fv0_y * Ts02 + fv0_x * fv0_z * rs03 + 2 * fv0_x * fv0_z * rc04\n - 2 * fv0_y * fv0_z ** 2 * Ts04)],\n [xv_x * (fv0_x * fv0_z * (-cf0 * fv0_x / f0p2 + fv0_x * rs03) / f0p2 + fv0_z * Ts02\n + fv0_x * fv0_y * rs03 - 2 * fv0_x ** 2 * fv0_z * Ts04 + 2 * fv0_x * fv0_y * rc04)\n + xv_y * (fv0_y * fv0_z * (-cf0 * fv0_x / f0p2 + fv0_x * rs03) / f0p2 + rc02 - fv0_x ** 2 * rs03\n - 2 * fv0_x ** 2 * rc04 - 2 * fv0_x * fv0_y * fv0_z * Ts04) + xv_z * (-2 * fv0_x * Ts02\n + (\n -fv0_x ** 2 - fv0_y ** 2) * (\n -cf0 * fv0_x / f0p2 + fv0_x * rs03) / f0p2 -\n 2 * fv0_x * (1 - rs01) * (\n -fv0_x ** 2 - fv0_y ** 2) / f0p4),\n xv_x * (fv0_x * fv0_z * (-cf0 * fv0_y / f0p2 + fv0_y * rs03) / f0p2 - rc02 + fv0_y ** 2 * rs03 -\n 2 * fv0_x * fv0_y * fv0_z * Ts04 + 2 * fv0_y ** 2 * rc04) + xv_y * (\n fv0_y * fv0_z * (-cf0 * fv0_y / f0p2\n + fv0_y * rs03) / f0p2 + fv0_z * Ts02 - fv0_x * fv0_y * rs03 - 2 * fv0_x * fv0_y * rc04\n - 2 * fv0_y ** 2 * fv0_z * Ts04) + xv_z * (-2 * fv0_y * Ts02 + (-fv0_x ** 2\n - fv0_y ** 2) * (\n -cf0 * fv0_y / f0p2 + fv0_y * rs03) / f0p2 - 2 * fv0_y * (\n 1 - rs01) * (-fv0_x ** 2\n - fv0_y ** 2) / f0p4),\n xv_x * (fv0_x * fv0_z * (-cf0 * fv0_z / f0p2 + fv0_z * rs03) / f0p2 + fv0_x * Ts02 +\n fv0_y * fv0_z * rs03 - 2 * fv0_x * fv0_z ** 2 * Ts04 + 2 * fv0_y * fv0_z * rc04) +\n xv_y * (fv0_y * fv0_z * (-cf0 * fv0_z / f0p2 + fv0_z * rs03) / f0p2 + fv0_y * Ts02\n - fv0_x * fv0_z * rs03 - 2 * fv0_x * fv0_z * rc04 - 2 * fv0_y * fv0_z ** 2 * Ts04) +\n xv_z * ((-fv0_x ** 2 - fv0_y ** 2) * (-cf0 * fv0_z / f0p2 + fv0_z * rs03) / f0p2 -\n 2 * fv0_z * (1 - rs01) * (-fv0_x ** 2 - fv0_y ** 2) / f0p4)]])\n\n\ndef der_TanT_by_xv(fv0, xv):\n \"\"\"\n Being fv0 a cartesian rotation vector and Tan the corresponding tangential\n operator (computed through crv2tan(fv)), the function returns the derivative\n of dot(Tan^T,xv), where xv is a constant vector.\n\n The elements of the resulting derivative matrix D are ordered such that:\n\n .. math:: d(Tan^T*xv) = D*d(fv)\n\n where :math:`d(.)` is a delta operator.\n\n Note:\n The derivative expression has been derived symbolically and verified\n by FDs. A more compact expression may be possible.\n \"\"\"\n\n # Renaming variabes for clarity\n px = fv0[0]\n py = fv0[1]\n pz = fv0[2]\n\n vx = xv[0]\n vy = xv[1]\n vz = xv[2]\n\n # Defining useful functions\n eps = 1e-15\n f0 = np.linalg.norm(fv0)\n if f0 < eps:\n f1 = -1.0 / 2.0\n f2 = 1.0 / 6.0\n g1 = -1.0 / 12.0\n g2 = 0.0 # TODO: check this\n else:\n f1 = (np.cos(f0) - 1.0) / f0 ** 2.0\n f2 = (1.0 - np.sin(f0) / f0) / f0 ** 2.0\n g1 = (f0 * np.sin(f0) + 2.0 * (np.cos(f0) - 1.0)) / f0 ** 4.0\n g2 = (2.0 / f0 ** 4 + np.cos(f0) / f0 ** 4 - 3.0 * np.sin(f0) / f0 ** 5)\n\n # Computing the derivatives of the functions\n df1dpx = -1.0 * px * g1\n df1dpy = -1.0 * py * g1\n df1dpz = -1.0 * pz * g1\n\n df2dpx = -1.0 * px * g2\n df2dpy = -1.0 * py * g2\n df2dpz = -1.0 * pz * g2\n\n # Compute the output matrix\n der_TanT_by_xv = np.zeros((3, 3), )\n\n # First column (derivatives with psi_x)\n der_TanT_by_xv[0, 0] = -1.0 * df2dpx * (\n py ** 2 + pz ** 2) * vx + df1dpx * pz * vy + df2dpx * px * py * vy + f2 * py * vy - df1dpx * py * vz + df2dpx * px * pz * vz + f2 * pz * vz\n der_TanT_by_xv[\n 1, 0] = -1.0 * df1dpx * pz * vx + df2dpx * px * py * vx + f2 * py * vx - df2dpx * px ** 2 * vy - 2.0 * f2 * px * vy - df2dpx * pz ** 2 * vy + df1dpx * px * vz + f1 * vz + df2dpx * py * pz * vz\n der_TanT_by_xv[\n 2, 0] = df1dpx * py * vx + df2dpx * px * pz * vx + f2 * pz * vx - df1dpx * px * vy - f1 * vy + df2dpx * py * pz * vy - df2dpx * px ** 2 * vz - 2.0 * f2 * px * vz - df2dpx * py ** 2 * vz\n\n # Second column (derivatives with psi_y)\n der_TanT_by_xv[\n 0, 1] = -df2dpy * py ** 2 * vx - f2 * 2 * py * vx - df2dpy * pz ** 2 * vx + df1dpy * pz * vy + df2dpy * px * py * vy + f2 * px * vy - df1dpy * py * vz - f1 * vz + df2dpy * px * pz * vz\n der_TanT_by_xv[\n 1, 1] = -df1dpy * pz * vx + df2dpy * px * py * vx + f2 * px * vx - df2dpy * px ** 2 * vy - df2dpy * pz ** 2 * vy + df1dpy * px * vz + df2dpy * py * pz * vz + f2 * pz * vz\n der_TanT_by_xv[\n 2, 1] = df1dpy * py * vx + f1 * vx + df2dpy * px * pz * vx - df1dpy * px * vy + df2dpy * py * pz * vy + f2 * pz * vy - df2dpy * px ** 2 * vz - df2dpy * py ** 2 * vz - 2.0 * f2 * py * vz\n\n # Second column (derivatives with psi_z)\n der_TanT_by_xv[\n 0, 2] = -df2dpz * py ** 2 * vx - df2dpz * pz ** 2 * vx - 2.0 * f2 * pz * vx + df1dpz * pz * vy + f1 * vy + df2dpz * px * py * vy - df1dpz * py * vz + df2dpz * px * pz * vz + f2 * px * vz\n der_TanT_by_xv[\n 1, 2] = -df1dpz * pz * vx - f1 * vx + df2dpz * px * py * vx - df2dpz * px ** 2 * vy - df2dpz * pz ** 2 * vy - 2.0 * f2 * pz * vy + df1dpz * px * vz + df2dpz * py * pz * vz + f2 * py * vz\n der_TanT_by_xv[\n 2, 2] = df1dpz * py * vx + df2dpz * px * pz * vx + f2 * px * vx - df1dpz * px * vy + df2dpz * py * pz * vy + f2 * py * vy - df2dpz * px ** 2 * vz - df2dpz * py ** 2 * vz\n\n return der_TanT_by_xv\n\n\ndef der_Ccrv_by_v(fv0, v):\n r\"\"\"\n Being C=C(fv0) the rotational matrix depending on the Cartesian rotation\n vector fv0 and defined as C=crv2rotation(fv0), the function returns the\n derivative, w.r.t. the CRV components, of the vector dot(C,v), where v is a\n constant vector.\n\n The elements of the resulting derivative matrix D are ordered such that:\n\n .. math:: d(C*v) = D*d(fv0)\n\n where :math:`d(.)` is a delta operator.\n \"\"\"\n\n Cab0 = crv2rotation(fv0)\n T0 = crv2tan(fv0)\n vskew = skew(v)\n\n return -np.dot(Cab0, np.dot(vskew, T0))\n\n\ndef der_CcrvT_by_v(fv0, v):\n \"\"\"\n Being C=C(fv0) the rotation matrix depending on the Cartesian rotation\n vector fv0 and defined as C=crv2rotation(fv0), the function returns the\n derivative, w.r.t. the CRV components, of the vector dot(C.T,v), where v is\n a constant vector.\n\n The elements of the resulting derivative matrix D are ordered such that:\n\n .. math:: d(C.T*v) = D*d(fv0)\n\n where :math:`d(.)` is a delta operator.\n \"\"\"\n\n Cba0 = crv2rotation(fv0).T\n T0 = crv2tan(fv0)\n\n return np.dot(skew(np.dot(Cba0, v)), T0)\n\n\ndef der_quat_wrt_crv(quat0):\n \"\"\"\n Provides change of quaternion, dquat, due to elementary rotation, dcrv,\n expressed as a 3 components Cartesian rotation vector such that\n\n .. math:: C(quat + dquat) = C(quat0)C(dw)\n\n where C are rotation matrices.\n\n Examples:\n Assume 3 FoRs, G, A and B where:\n - G is the initial FoR\n - quat0 defines te rotation required to obtain A from G, namely:\n Cga=quat2rotation(quat0)\n - dcrv is an inifinitesimal Cartesian rotation vector, defined in A\n components, which describes an infinitesimal rotation A -> B, namely:\n\n ..math :: Cab=crv2rotation(dcrv)\n\n - The total rotation G -> B is:\n Cga = Cga * Cab\n - As dcrv -> 0, Cga is equal to:\n\n .. math:: algebra.quat2rotation(quat0 + dquat),\n\n where dquat is the output of this function.\n \"\"\"\n\n Der = np.zeros((4, 3))\n Der[0, :] = -0.5 * quat0[1:]\n Der[1:, :] = -0.5 * (-quat0[0] * np.eye(3) - skew(quat0[1:]))\n return Der\n\n\ndef der_Ceuler_by_v(euler, v):\n r\"\"\"\n Provides the derivative of the product between the rotation matrix :math:`C^{AG}(\\mathbf{\\Theta})` and a constant\n vector, :math:`\\mathbf{v}`, with respect to the Euler angles, :math:`\\mathbf{\\Theta}=[\\phi,\\theta,\\psi]^T`:\n\n .. math::\n \\frac{\\partial}{\\partial\\Theta}(C^{AG}(\\Theta)\\mathbf{v}^G) = \\frac{\\partial \\mathbf{f}}{\\partial\\mathbf{\\Theta}}\n\n where :math:`\\frac{\\partial \\mathbf{f}}{\\partial\\mathbf{\\Theta}}` is the resulting 3 by 3 matrix.\n\n Being :math:`C^{AG}(\\Theta)` the rotation matrix from the G frame to the A frame in terms of the Euler angles\n :math:`\\Theta` as:\n\n .. math::\n C^{AG}(\\Theta) = \\begin{bmatrix}\n \\cos\\theta\\cos\\psi & -\\cos\\theta\\sin\\psi & \\sin\\theta \\\\\n \\cos\\phi\\sin\\psi + \\sin\\phi\\sin\\theta\\cos\\psi & \\cos\\phi\\cos\\psi - \\sin\\phi\\sin\\theta\\sin\\psi & -\\sin\\phi\\cos\\theta \\\\\n \\sin\\phi\\sin\\psi - \\cos\\phi\\sin\\theta\\cos\\psi & \\sin\\phi\\cos\\psi + \\cos\\phi\\sin\\theta\\sin\\psi & \\cos\\phi\\cos\\theta\n \\end{bmatrix}\n\n the components of the derivative at hand are the following, where\n :math:`f_{1\\theta} = \\frac{\\partial \\mathbf{f}_1}{\\partial\\theta}`.\n\n .. math::\n f_{1\\phi} =&0 \\\\\n f_{1\\theta} = &-v_1\\sin\\theta\\cos\\psi \\\\\n &+v_2\\sin\\theta\\sin\\psi \\\\\n &+v_3\\cos\\theta \\\\\n f_{1\\psi} = &-v_1\\cos\\theta\\sin\\psi \\\\\n &- v_2\\cos\\theta\\cos\\psi\n\n .. math::\n f_{2\\phi} = &+v_1(-\\sin\\phi\\sin\\psi + \\cos\\phi\\sin\\theta\\cos\\psi) + \\\\\n &+v_2(-\\sin\\phi\\cos\\psi - \\cos\\phi\\sin\\theta\\sin\\psi) + \\\\\n &+v_3(-\\cos\\phi\\cos\\theta)\\\\\n f_{2\\theta} = &+v_1(\\sin\\phi\\cos\\theta\\cos\\psi) + \\\\\n &+v_2(-\\sin\\phi\\cos\\theta\\sin\\psi) +\\\\\n &+v_3(\\sin\\phi\\sin\\theta) \\\\\n f_{2\\psi} = &+v_1(\\cos\\phi\\cos\\psi - \\sin\\phi\\sin\\theta\\sin\\psi) + \\\\\n &+v_2(-\\cos\\phi\\sin\\psi - \\sin\\phi\\sin\\theta\\cos\\psi)\n\n .. math::\n f_{3\\phi} = &+v_1(\\cos\\phi\\sin\\psi+\\sin\\phi\\sin\\theta\\cos\\psi) + \\\\\n &+v_2(\\cos\\phi\\cos\\psi - \\sin\\phi\\sin\\theta\\sin\\psi) + \\\\\n &+v_3(-\\sin\\phi\\cos\\theta)\\\\\n f_{3\\theta} = &+v_1(-\\cos\\phi\\cos\\theta\\cos\\psi)+\\\\\n &+v_2(\\cos\\phi\\cos\\theta\\sin\\psi) + \\\\\n &+v_3(-\\cos\\phi\\sin\\theta)\\\\\n f_{3\\psi} = &+v_1(\\sin\\phi\\cos\\psi+\\cos\\phi\\sin\\theta\\sin\\psi) + \\\\\n &+v_2(-\\sin\\phi\\sin\\psi + \\cos\\phi\\sin\\theta\\cos\\psi)\n\n Args:\n euler (np.ndarray): Vector of Euler angles, :math:`\\mathbf{\\Theta} = [\\phi, \\theta, \\psi]`, in radians.\n v (np.ndarray): 3 dimensional vector in G frame.\n\n Returns:\n np.ndarray: Resulting 3 by 3 matrix :math:`\\frac{\\partial \\mathbf{f}}{\\partial\\mathbf{\\Theta}}`.\n\n \"\"\"\n res = np.zeros((3, 3))\n\n # Notation shorthand. sin and cos of psi (roll)\n sp = np.sin(euler[0])\n cp = np.cos(euler[0])\n\n # Notation shorthand. sin and cos of theta (pitch)\n st = np.sin(euler[1])\n ct = np.cos(euler[1])\n\n # Notation shorthand. sin and cos of psi (yaw)\n ss = np.sin(euler[2])\n cs = np.cos(euler[2])\n\n v1 = v[0]\n v2 = v[1]\n v3 = v[2]\n\n res[0, 0] = v2 * (sp * ss + cp * st * cp) + v3 * (cp * ss - sp * st * cs)\n res[0, 1] = v1 * (-st * cs) + v2 * (sp * ct * cs) + v3 * (cp * ct * cs)\n res[0, 2] = v1 * (ct * ss) + v2 * (-cp * cs - sp * st * ss) + v3 * (sp * cs - cp * st * ss)\n\n res[1, 0] = v2 * (-sp * cs + cp * st * ss) + v3 * (-cp * cs + sp * st * ss)\n res[1, 1] = v1 * (-st * ss) + v2 * (sp * ct * ss) + v3 * (-cp * ct * ss)\n res[1, 2] = v1 * (ct * cs) + v2 * (-cp * ss + sp * st * cs) + v3 * (sp * ss + cp * st * cs)\n\n res[2, 0] = v2 * (cp * ct) + v3 * (-sp * ct)\n res[2, 1] = v1 * (-ct) + v2 * (-sp * st) + v3 * (-cp * st)\n\n return res\n\n\ndef der_Peuler_by_v(euler, v):\n r\"\"\"\n Provides the derivative of the product between the projection matrix :math:`P^{AG}(\\mathbf{\\Theta})` (that projects\n a vector in G frame onto A frame) and a constant vector expressed in G frame of reference, :math:`\\mathbf{v}_G`,\n with respect to the Euler angles, :math:`\\mathbf{\\Theta}=[\\phi,\\theta,\\psi]^T`:\n\n .. math::\n \\frac{\\partial}{\\partial\\Theta}(P^{AG}(\\Theta)\\mathbf{v}^G) = \\frac{\\partial \\mathbf{f}}{\\partial\\mathbf{\\Theta}}\n\n where :math:`\\frac{\\partial \\mathbf{f}}{\\partial\\mathbf{\\Theta}}` is the resulting 3 by 3 matrix.\n\n Being :math:`P^{AG}(\\Theta)` the projection matrix from the G frame to the A frame in terms of the Euler angles\n :math:`\\Theta` as :math:`P^{AG}(\\Theta) = \\tau_x(-\\Phi)\\tau_y(-\\Theta)\\tau_z(-\\Psi)`, where\n the rotation matrix is expressed as:\n\n .. math::\n C^{AG}(\\Theta) = \\begin{bmatrix}\n \\cos\\theta\\cos\\psi & -\\cos\\theta\\sin\\psi & \\sin\\theta \\\\\n \\cos\\phi\\sin\\psi + \\sin\\phi\\sin\\theta\\cos\\psi & \\cos\\phi\\cos\\psi - \\sin\\phi\\sin\\theta\\sin\\psi & -\\sin\\phi\\cos\\theta \\\\\n \\sin\\phi\\sin\\psi - \\cos\\phi\\sin\\theta\\cos\\psi & \\sin\\phi\\cos\\psi + \\cos\\phi\\sin\\theta\\sin\\psi & \\cos\\phi\\cos\\theta\n \\end{bmatrix}\n\n and the projection matrix as:\n\n .. math::\n P^{AG}(\\Theta) = \\begin{bmatrix}\n \\cos\\theta\\cos\\psi & \\cos\\theta\\sin\\psi & -\\sin\\theta \\\\\n -\\cos\\phi\\sin\\psi + \\sin\\phi\\sin\\theta\\cos\\psi & \\cos\\phi\\cos\\psi + \\sin\\phi\\sin\\theta\\sin\\psi & \\sin\\phi\\cos\\theta \\\\\n \\sin\\phi\\sin\\psi + \\cos\\phi\\sin\\theta\\cos\\psi & -\\sin\\phi\\cos\\psi + \\cos\\phi\\sin\\theta\\sin\\psi & \\cos\\phi\\cos\\theta\n \\end{bmatrix}\n\n the components of the derivative at hand are the following, where\n :math:`f_{1\\theta} = \\frac{\\partial \\mathbf{f}_1}{\\partial\\theta}`.\n\n .. math::\n f_{1\\phi} =&0 \\\\\n f_{1\\theta} = &-v_1\\sin\\theta\\cos\\psi \\\\\n &+v_2\\sin\\theta\\sin\\psi \\\\\n &+v_3\\cos\\theta \\\\\n f_{1\\psi} = &-v_1\\cos\\theta\\sin\\psi \\\\\n &- v_2\\cos\\theta\\cos\\psi\n\n .. math::\n f_{2\\phi} = &+v_1(-\\sin\\phi\\sin\\psi + \\cos\\phi\\sin\\theta\\cos\\psi) + \\\\\n &+v_2(-\\sin\\phi\\cos\\psi - \\cos\\phi\\sin\\theta\\sin\\psi) + \\\\\n &+v_3(-\\cos\\phi\\cos\\theta)\\\\\n f_{2\\theta} = &+v_1(\\sin\\phi\\cos\\theta\\cos\\psi) + \\\\\n &+v_2(-\\sin\\phi\\cos\\theta\\sin\\psi) +\\\\\n &+v_3(\\sin\\phi\\sin\\theta)\\\\\n f_{2\\psi} = &+v_1(\\cos\\phi\\cos\\psi - \\sin\\phi\\sin\\theta\\sin\\psi) + \\\\\n &+v_2(-\\cos\\phi\\sin\\psi - \\sin\\phi\\sin\\theta\\cos\\psi)\n\n .. math::\n f_{3\\phi} = &+v_1(\\cos\\phi\\sin\\psi+\\sin\\phi\\sin\\theta\\cos\\psi) + \\\\\n &+v_2(\\cos\\phi\\cos\\psi - \\sin\\phi\\sin\\theta\\sin\\psi) + \\\\\n &+v_3(-\\sin\\phi\\cos\\theta)\\\\\n f_{3\\theta} = &+v_1(-\\cos\\phi\\cos\\theta\\cos\\psi)+\\\\\n &+v_2(\\cos\\phi\\cos\\theta\\sin\\psi) + \\\\\n &+v_3(-\\cos\\phi\\sin\\theta)\\\\\n f_{3\\psi} = &+v_1(\\sin\\phi\\cos\\psi+\\cos\\phi\\sin\\theta\\sin\\psi) + \\\\\n &+v_2(-\\sin\\phi\\sin\\psi + \\cos\\phi\\sin\\theta\\cos\\psi)\n\n Args:\n euler (np.ndarray): Vector of Euler angles, :math:`\\mathbf{\\Theta} = [\\phi, \\theta, \\psi]`, in radians.\n v (np.ndarray): 3 dimensional vector in G frame.\n\n Returns:\n np.ndarray: Resulting 3 by 3 matrix :math:`\\frac{\\partial \\mathbf{f}}{\\partial\\mathbf{\\Theta}}`.\n\n \"\"\"\n res = np.zeros((3, 3))\n\n # Notation shorthand. sin and cos of psi (roll)\n sp = np.sin(euler[0])\n cp = np.cos(euler[0])\n\n # Notation shorthand. sin and cos of theta (pitch)\n st = np.sin(euler[1])\n ct = np.cos(euler[1])\n\n # Notation shorthand. sin and cos of psi (yaw)\n ss = np.sin(euler[2])\n cs = np.cos(euler[2])\n\n v1 = v[0]\n v2 = v[1]\n v3 = v[2]\n\n res[0, 1] = v1 * (-st * cs) + v2 * (-st * ss) - v3 * ct\n res[0, 2] = -v1 * (ct * ss) + v2 * ct * cs\n\n res[1, 0] = v1 * (sp * ss + cp * st * cs) + v2 * (-sp * cs + cp * st * ss) + v3 * (cp * ct)\n res[1, 1] = v1 * (sp * ct * cs) + v2 * (sp * ct * ss) + v3 * (-sp * st)\n res[1, 2] = v1 * (-cp * cs - sp * st * ss) + v2 * (-cp * ss + sp * st * cs)\n\n res[2, 0] = v1 * (cp * ss - sp * st * cs) + v2 * (-cp * cs - sp * st * ss) + v3 * (-sp * ct)\n res[2, 1] = v1 * (cp * ct * cs) + v2 * (cp * ct * ss) + v3 * (-cp * st)\n res[2, 2] = v1 * (sp * ss + -cp * st * ss) + v2 * (sp * ss + cp * st * cs)\n\n return res\n\n\ndef der_Ceuler_by_v_NED(euler, v):\n r\"\"\"\n Provides the derivative of the product between the rotation matrix :math:`C^{AG}(\\mathbf{\\Theta})` and a constant\n vector, :math:`\\mathbf{v}`, with respect to the Euler angles, :math:`\\mathbf{\\Theta}=[\\phi,\\theta,\\psi]^T`:\n\n .. math::\n \\frac{\\partial}{\\partial\\Theta}(C^{AG}(\\Theta)\\mathbf{v}^G) = \\frac{\\partial \\mathbf{f}}{\\partial\\mathbf{\\Theta}}\n\n where :math:`\\frac{\\partial \\mathbf{f}}{\\partial\\mathbf{\\Theta}}` is the resulting 3 by 3 matrix.\n\n Being :math:`C^{AG}(\\Theta)` the rotation matrix from the G frame to the A frame in terms of the Euler angles\n :math:`\\Theta` as:\n\n .. math::\n C^{AG}(\\Theta) = \\begin{bmatrix}\n \\cos\\theta\\cos\\psi & \\cos\\theta\\sin\\psi & -\\sin\\theta \\\\\n -\\cos\\phi\\sin\\psi + \\sin\\phi\\sin\\theta\\cos\\psi & \\cos\\phi\\cos\\psi + \\sin\\phi\\sin\\theta\\sin\\psi & \\sin\\phi\\cos\\theta \\\\\n \\sin\\phi\\sin\\psi + \\cos\\phi\\sin\\theta\\cos\\psi & -\\sin\\phi\\cos\\psi + \\cos\\psi\\sin\\theta\\sin\\psi & \\cos\\phi\\cos\\theta\n \\end{bmatrix}\n\n the components of the derivative at hand are the following, where\n :math:`f_{1\\theta} = \\frac{\\partial \\mathbf{f}_1}{\\partial\\theta}`.\n\n .. math::\n f_{1\\phi} =&0 \\\\\n f_{1\\theta} = &-v_1\\sin\\theta\\cos\\psi \\\\\n &-v_2\\sin\\theta\\sin\\psi \\\\\n &-v_3\\cos\\theta \\\\\n f_{1\\psi} = &-v_1\\cos\\theta\\sin\\psi + v_2\\cos\\theta\\cos\\psi\n\n .. math::\n f_{2\\phi} = &+v_1(\\sin\\phi\\sin\\psi + \\cos\\phi\\sin\\theta\\cos\\psi) + \\\\\n &+v_2(-\\sin\\phi\\cos\\psi + \\cos\\phi\\sin\\theta\\sin\\psi) + \\\\\n &+v_3(\\cos\\phi\\cos\\theta) \\\\\n f_{2\\theta} = &+v_1(\\sin\\phi\\cos\\theta\\cos\\psi) + \\\\\n &+v_2(\\sin\\phi\\cos\\theta\\sin\\psi) +\\\\\n &-v_3(\\sin\\phi\\sin\\theta) \\\\\n f_{2\\psi} = &+v_1(-\\cos\\phi\\cos\\psi - \\sin\\phi\\sin\\theta\\sin\\psi) + \\\\\n &+v_2(-\\cos\\phi\\sin\\psi + \\sin\\phi\\sin\\theta\\cos\\psi)\n\n .. math::\n f_{3\\phi} = &+v_1(\\cos\\phi\\sin\\psi-\\sin\\phi\\sin\\theta\\cos\\psi) + \\\\\n &+v_2(-\\cos\\phi\\cos\\psi - \\sin\\phi\\sin\\theta\\sin\\psi) + \\\\\n &+v_3(-\\sin\\phi\\cos\\theta) \\\\\n f_{3\\theta} = &+v_1(\\cos\\phi\\cos\\theta\\cos\\psi)+\\\\\n &+v_2(\\cos\\phi\\cos\\theta\\sin\\psi) + \\\\\n &+v_3(-\\cos\\phi\\sin\\theta) \\\\\n f_{3\\psi} = &+v_1(\\sin\\phi\\cos\\psi-\\cos\\phi\\sin\\theta\\sin\\psi) + \\\\\n &+v_2(\\sin\\phi\\sin\\psi + \\cos\\phi\\sin\\theta\\cos\\psi)\n\n Note:\n This function is defined in a North East Down frame which is not the typically used one in SHARPy.\n\n Args:\n euler (np.ndarray): Vector of Euler angles, :math:`\\mathbf{\\Theta} = [\\phi, \\theta, \\psi]`, in radians.\n v (np.ndarray): 3 dimensional vector in G frame.\n\n Returns:\n np.ndarray: Resulting 3 by 3 matrix :math:`\\frac{\\partial \\mathbf{f}}{\\partial\\mathbf{\\Theta}}`.\n\n \"\"\"\n\n # TODO: Verify with new euler rotation matrices\n\n res = np.zeros((3, 3))\n\n # Notation shorthand. sin and cos of psi (roll)\n sp = np.sin(euler[0])\n cp = np.cos(euler[0])\n\n # Notation shorthand. sin and cos of theta (pitch)\n st = np.sin(euler[1])\n ct = np.cos(euler[1])\n\n # Notation shorthand. sin and cos of psi (yaw)\n ss = np.sin(euler[2])\n cs = np.cos(euler[2])\n\n v1 = v[0]\n v2 = v[1]\n v3 = v[2]\n\n res[0, 0] = 0\n res[0, 1] = - v1 * st * cs - v2 * st * ss - v3 * ct\n res[0, 2] = -v1 * ct * ss + v2 * ct * cs\n\n res[1, 0] = v1 * (sp * ss + cp * st * cs) + v2 * (-sp * cs + cp * st * ss) + v3 * cp * ct\n res[1, 1] = v1 * (sp * ct * cs) + v2 * sp * ct * ss - v3 * sp * st\n res[1, 2] = v1 * (-cp * cs - sp * st * ss) + v2 * (-cp * ss + sp * st * cs)\n\n res[2, 0] = v1 * (cp * ss - sp * st * cs) + v2 * (-cp * cs - sp * st * ss) + v3 * (-sp * ct)\n res[2, 1] = v1 * cp * ct * cs + v2 * cp * ct * ss - v3 * cp * st\n res[2, 2] = v1 * (sp * cs - cp * st * ss) + v2 * (sp * ss + cp * st * cs)\n\n return res\n\n\ndef cross3(v, w):\n \"\"\"\n Computes the cross product of two vectors (v and w) with size 3\n \"\"\"\n\n res = np.zeros((3,), )\n res[0] = v[1] * w[2] - v[2] * w[1]\n res[1] = -v[0] * w[2] + v[2] * w[0]\n res[2] = v[0] * w[1] - v[1] * w[0]\n\n return res\n\n\ndef deuler_dt(euler):\n r\"\"\"\n Rate of change of the Euler angles in time for a given angular velocity in A frame :math:`\\omega^A=[p, q, r]`.\n\n .. math::\n \\begin{bmatrix}\\dot{\\phi} \\\\ \\dot{\\theta} \\\\ \\dot{\\psi}\\end{bmatrix} =\n \\begin{bmatrix}\n 1 & \\sin\\phi\\tan\\theta & -\\cos\\phi\\tan\\theta \\\\\n 0 & \\cos\\phi & \\sin\\phi \\\\\n 0 & -\\frac{\\sin\\phi}{\\cos\\theta} & \\frac{\\cos\\phi}{\\cos\\theta}\n \\end{bmatrix}\n \\begin{bmatrix}\n p \\\\ q \\\\ r\n \\end{bmatrix}\n\n Args:\n euler (np.ndarray): Euler angles :math:`[\\phi, \\theta, \\psi]` for roll, pitch and yaw, respectively.\n\n Returns:\n np.ndarray: Propagation matrix relating the rotational velocities to the euler angles.\n \"\"\"\n\n phi = euler[0] # roll\n theta = euler[1] # pitch\n\n A = np.zeros((3, 3))\n A[0, 0] = 1\n A[0, 1] = np.tan(theta) * np.sin(phi)\n A[0, 2] = -np.tan(theta) * np.cos(phi)\n\n A[1, 1] = np.cos(phi)\n A[1, 2] = np.sin(phi)\n\n A[2, 1] = -np.sin(phi) / np.cos(theta)\n A[2, 2] = np.cos(phi) / np.cos(theta)\n\n return A\n\n\ndef deuler_dt_NED(euler):\n r\"\"\"\n\n Warnings:\n Based on a NED frame\n\n Rate of change of the Euler angles in time for a given angular velocity in A frame :math:`\\omega^A=[p, q, r]`.\n\n .. math::\n \\begin{bmatrix}\\dot{\\phi} \\\\ \\dot{\\theta} \\\\ \\dot{\\psi}\\end{bmatrix} =\n \\begin{bmatrix}\n 1 & \\sin\\phi\\tan\\theta & \\cos\\phi\\tan\\theta \\\\\n 0 & \\cos\\phi & -\\sin\\phi \\\\\n 0 & \\frac{\\sin\\phi}{\\cos\\theta} & \\frac{\\cos\\phi}{\\cos\\theta}\n \\end{bmatrix}\n \\begin{bmatrix}\n p \\\\ q \\\\ r\n \\end{bmatrix}\n\n Note:\n This function is defined in a North East Down frame which is not the typically used one in SHARPy.\n\n Args:\n euler (np.ndarray): Euler angles :math:`[\\phi, \\theta, \\psi]` for roll, pitch and yaw, respectively.\n\n Returns:\n np.ndarray: Propagation matrix relating the rotational velocities to the euler angles.\n \"\"\"\n\n # TODO: Verify with the new euler rotation matrices\n phi = euler[0] # roll\n theta = euler[1] # pitch\n\n A = np.zeros((3, 3))\n A[0, 0] = 1\n A[0, 1] = np.tan(theta) * np.sin(phi)\n A[0, 2] = np.tan(theta) * np.cos(phi)\n\n A[1, 1] = np.cos(phi)\n A[1, 2] = -np.sin(phi)\n\n A[2, 1] = np.sin(phi) / np.cos(theta)\n A[2, 2] = np.cos(phi) / np.cos(theta)\n\n return A\n\n\ndef der_Teuler_by_w(euler, w):\n r\"\"\"\n Calculates the matrix\n\n .. math::\n \\frac{\\partial}{\\partial\\Theta}\\left.\\left(T^{GA}(\\mathbf{\\Theta})\n \\mathbf{\\omega}^A\\right)\\right|_{\\Theta_0,\\omega^A_0}\n\n from the linearised euler propagation equations\n\n .. math::\n \\delta\\mathbf{\\dot{\\Theta}} = \\frac{\\partial}{\\partial\\Theta}\\left.\\left(T^{GA}(\\mathbf{\\Theta})\n \\mathbf{\\omega}^A\\right)\\right|_{\\Theta_0,\\omega^A_0}\\delta\\mathbf{\\Theta} +\n T^{GA}(\\mathbf{\\Theta_0}) \\delta\\mathbf{\\omega}^A\n\n where :math:`T^{GA}` is the nonlinear relation between the euler angle rates and the rotational velocities and is\n provided by :func:`deuler_dt`.\n\n The concerned matrix is calculated as follows:\n\n .. math::\n \\frac{\\partial}{\\partial\\Theta}\\left.\\left(T^{GA}(\\mathbf{\\Theta})\n \\mathbf{\\omega}^A\\right)\\right|_{\\Theta_0,\\omega^A_0} = \\\\\n \\begin{bmatrix}\n q\\cos\\phi\\tan\\theta-r\\sin\\phi\\tan\\theta & q\\sin\\phi\\sec^2\\theta + r\\cos\\phi\\sec^2\\theta & 0 \\\\\n -q\\sin\\phi - r\\cos\\phi & 0 & 0 \\\\\n q\\frac{\\cos\\phi}{\\cos\\theta}-r\\frac{\\sin\\phi}{\\cos\\theta} & q\\sin\\phi\\tan\\theta\\sec\\theta +\n r\\cos\\phi\\tan\\theta\\sec\\theta & 0\n \\end{bmatrix}_{\\Theta_0, \\omega^A_0}\n\n Note:\n This function is defined in a North East Down frame which is not the typically used one in SHARPy.\n\n Args:\n euler (np.ndarray): Euler angles at the linearisation point :math:`\\mathbf{\\Theta}_0 = [\\phi,\\theta,\\psi]` or\n roll, pitch and yaw angles, respectively.\n w (np.ndarray): Rotational velocities at the linearisation point in A frame :math:`\\omega^A_0`.\n\n Returns:\n np.ndarray: Computed :math:`\\frac{\\partial}{\\partial\\Theta}\\left.\\left(T^{GA}(\\mathbf{\\Theta})\\mathbf{\\omega}^A\\right)\\right|_{\\Theta_0,\\omega^A_0}`\n \"\"\"\n\n q = w[1]\n r = w[2]\n\n cp = np.cos(euler[0])\n sp = np.sin(euler[0])\n\n st = np.sin(euler[1])\n ct = np.cos(euler[1])\n tt = np.tan(euler[1])\n tsec = ct ** -1\n\n derT = np.zeros((3, 3))\n\n derT[0, 0] = q * cp * tt + r * sp * tt\n derT[0, 1] = q * sp * tsec ** 2 - r * cp * tsec ** 2\n\n derT[1, 0] = -q * sp + r * cp\n\n derT[2, 0] = - q * cp / ct - r * sp / ct\n derT[2, 1] = - q * sp * tt * tsec + r * cp * tt * tsec\n\n return derT\n\n\ndef der_Teuler_by_w_NED(euler, w):\n r\"\"\"\n\n Warnings:\n Based on a NED G frame\n\n\n Calculates the matrix\n\n .. math::\n \\frac{\\partial}{\\partial\\Theta}\\left.\\left(T^{GA}(\\mathbf{\\Theta})\n \\mathbf{\\omega}^A\\right)\\right|_{\\Theta_0,\\omega^A_0}\n\n from the linearised euler propagation equations\n\n .. math::\n \\delta\\mathbf{\\dot{\\Theta}} = \\frac{\\partial}{\\partial\\Theta}\\left.\\left(T^{GA}(\\mathbf{\\Theta})\n \\mathbf{\\omega}^A\\right)\\right|_{\\Theta_0,\\omega^A_0}\\delta\\mathbf{\\Theta} +\n T^{GA}(\\mathbf{\\Theta_0}) \\delta\\mathbf{\\omega}^A\n\n where :math:`T^{GA}` is the nonlinear relation between the euler angle rates and the rotational velocities and is\n provided by :func:`deuler_dt`.\n\n The concerned matrix is calculated as follows:\n\n .. math::\n \\frac{\\partial}{\\partial\\Theta}\\left.\\left(T^{GA}(\\mathbf{\\Theta})\n \\mathbf{\\omega}^A\\right)\\right|_{\\Theta_0,\\omega^A_0} = \\\\\n \\begin{bmatrix}\n q\\cos\\phi\\tan\\theta-r\\sin\\phi\\tan\\theta & q\\sin\\phi\\sec^2\\theta + r\\cos\\phi\\sec^2\\theta & 0 \\\\\n -q\\sin\\phi - r\\cos\\phi & 0 & 0 \\\\\n q\\frac{\\cos\\phi}{\\cos\\theta}-r\\frac{\\sin\\phi}{\\cos\\theta} & q\\sin\\phi\\tan\\theta\\sec\\theta +\n r\\cos\\phi\\tan\\theta\\sec\\theta & 0\n \\end{bmatrix}_{\\Theta_0, \\omega^A_0}\n\n Args:\n euler (np.ndarray): Euler angles at the linearisation point :math:`\\mathbf{\\Theta}_0 = [\\phi,\\theta,\\psi]` or\n roll, pitch and yaw angles, respectively.\n w (np.ndarray): Rotational velocities at the linearisation point in A frame :math:`\\omega^A_0`.\n\n Returns:\n np.ndarray: Computed :math:`\\frac{\\partial}{\\partial\\Theta}\\left.\\left(T^{GA}(\\mathbf{\\Theta})\\mathbf{\\omega}^A\\right)\\right|_{\\Theta_0,\\omega^A_0}`\n \"\"\"\n\n # TODO: Verify with new Euler rotation matrices\n\n p = w[0]\n q = w[1]\n r = w[2]\n\n cp = np.cos(euler[0])\n sp = np.sin(euler[0])\n\n st = np.sin(euler[1])\n ct = np.cos(euler[1])\n tt = np.tan(euler[1])\n tsec = ct ** -1\n\n derT = np.zeros((3, 3))\n\n derT[0, 0] = q * cp * tt - r * sp * tt\n derT[0, 1] = q * sp * tsec ** 2 + r * cp * tsec ** 2\n\n derT[1, 0] = -q * sp - r * cp\n\n derT[2, 0] = q * cp / ct - r * sp / ct\n derT[2, 1] = q * sp * tt * tsec + r * cp * tt * tsec\n\n return derT\n\n\ndef norm3d(v):\n \"\"\"\n Norm of a 3D vector\n\n Notes:\n Faster than np.linalg.norm\n\n Args:\n v (np.ndarray): 3D vector\n\n Returns:\n np.ndarray: Norm of the vector\n \"\"\"\n return np.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2])\n\n\ndef normsq3d(v):\n \"\"\"\n Square of the norm of a 3D vector\n\n Args:\n v (np.ndarray): 3D vector\n\n Returns:\n np.ndarray: Square of the norm of the vector\n \"\"\"\n return v[0] * v[0] + v[1] * v[1] + v[2] * v[2]\n\n\ndef get_transformation_matrix(transformation):\n r\"\"\"\n Returns a projection matrix function between the desired frames of reference.\n\n Examples:\n\n The projection matrix :math:`C^GA(\\chi)` expresses a vector in the body-attached\n reference frame ``A`` in the inertial frame ``G``, which is a function of the quaternion.\n\n .. code-block::\n\n cga_function = get_transformation_matrix('ga')\n cga = cga_function(quat) # The actual projection matrix between A and G for a known quaternion\n\n\n If the projection involves the ``G`` and ``B`` frames, the output function will take both the quaternion\n and the CRV as arguments.\n\n .. code-block::\n\n cgb_function = get_transformation_matrix('gb')\n cgb = cgb_function(psi, quat) # The actual projection matrix between B and G for a known CRV and quaternion\n\n Args:\n transformation (str): Desired projection matrix function.\n\n Returns:\n function: Function to obtain the desired projection matrix. The function will either take the CRV, the\n quaternion, or both as arguments.\n\n Note:\n If a rotation is desired, it can be achieved by transposing the resulting projection matrix.\n \"\"\"\n\n if transformation == 'ab':\n cab = crv2rotation\n return cab\n elif transformation == 'ba':\n def cba(psi):\n return crv2rotation(psi).T\n\n return cba\n elif transformation == 'ga':\n cga = quat2rotation\n return cga\n elif transformation == 'ag':\n def cag(quat):\n return quat2rotation(quat).T\n\n return cag\n elif transformation == 'bg':\n def cbg(psi, quat):\n cag = get_transformation_matrix('ag')\n cba = get_transformation_matrix('ba')\n return cba(psi).dot(cag(quat))\n\n return cbg\n elif transformation == 'gb':\n def cgb(psi, quat):\n cab = get_transformation_matrix('ba')\n cga = get_transformation_matrix('ga')\n return cga(quat).dot(cab(psi))\n\n return cgb\n else:\n raise NameError('Unknown transformation.')\n\n\ndef der_skewp_skewp_v(p, v):\n \"\"\"\n This function computes:\n\n .. math:: \\frac{d}{d\\boldsymbol{p}} (\\tilde{\\boldsymbol{p}} \\tilde{\\boldsymbol{p}} v)\n \"\"\"\n der = np.zeros((3, 3))\n\n der[0, 0] = v[1] * p[1] + v[2] * p[2]\n der[0, 1] = -2 * v[0] * p[1] + v[1] * p[0]\n der[0, 2] = -2 * v[0] * p[2] + v[2] * p[0]\n\n der[1, 0] = v[0] * p[1] - 2 * v[1] * p[0]\n der[1, 1] = v[0] * p[0] + v[2] * p[2]\n der[1, 2] = -2 * v[1] * p[2] + v[2] * p[1]\n\n der[2, 0] = v[0] * p[2] - 2 * v[2] * p[0]\n der[2, 1] = v[1] * p[2] - 2 * v[2] * p[1]\n der[2, 2] = v[0] * p[0] + v[1] * p[1]\n\n return der\n\n\ndef der_skewpT_v(p, v):\n \"\"\"\n This function computes:\n\n .. math:: \\frac{d}{d\\boldsymbol{p}} \\tilde{\\boldsymbol{p}}^T v)\n \"\"\"\n return skew(v)\n\n\ndef der_skewp_v(p, v):\n \"\"\"\n This function computes:\n\n .. math:: \\frac{d}{d\\boldsymbol{p}} \\tilde{\\boldsymbol{p}} v)\n \"\"\"\n return -skew(v)\n" }, { "path": "sharpy/utils/analytical.py", "content": "\"\"\"Analytical Functions\n\nAnalytical solutions for 2D aerofoil based on thin plates theory\n\nAuthor: Salvatore Maraniello\n\nDate: 23 May 2017\n\nReferences:\n\n1. Simpson, R.J.S., Palacios, R. & Murua, J., 2013. Induced-Drag Calculations in the Unsteady Vortex Lattice Method.\n AIAA Journal, 51(7), pp.1775–1779.\n\n2. Gulcat, U., 2009. Propulsive Force of a Flexible Flapping Thin Airfoil. Journal of Aircraft, 46(2), pp.465–473.\n\n\"\"\"\n\nimport numpy as np\nimport scipy.special as scsp\n\n# imaginary variable\nj = 1.0j\n\n\ndef theo_fun(k):\n r\"\"\"Returns the value of Theodorsen's function at a reduced frequency :math:`k`.\n\n .. math:: \\mathcal{C}(jk) = \\frac{H_1^{(2)}(k)}{H_1^{(2)}(k) + jH_0^{(2)}(k)}\n\n where :math:`H_0^{(2)}(k)` and :math:`H_1^{(2)}(k)` are Hankel functions of the second kind.\n\n Args:\n k (np.array): Reduced frequency/frequencies at which to evaluate the function.\n\n Returns:\n np.array: Value of Theodorsen's function evaluated at the desired reduced frequencies.\n\n \"\"\"\n\n H1 = scsp.hankel2(1, k)\n H0 = scsp.hankel2(0, k)\n\n C = H1 / (H1 + j * H0)\n\n return C\n\n\ndef qs_derivs(x_ea_perc, x_fh_perc):\n \"\"\"\n Provides quasi-steady aerodynamic lift and moment coefficients derivatives\n Ref. Palacios and Cesnik, Chap 3.\n\n Args:\n x_ea_perc: position of axis of rotation in percentage of chord (measured\n from LE)\n x_fc_perc: position of flap axis of rotation in percentage of chord\n (measured from LE)\n \"\"\"\n\n # parameters\n nu_ea = 2.0 * x_ea_perc - 1.0\n nu_fh = 2.0 * x_fh_perc - 1.0\n th = np.arccos(-nu_fh)\n\n # pitch/pitch rate related quantities\n CLa = 2. * np.pi # ok\n CLda = np.pi * (1. - 2. * nu_ea)\n CMda = -0.25 * np.pi\n\n # flap related quantities\n CLb = 2. * (np.pi - th + np.sin(th))\n CLdb = (0.5 - nu_fh) * 2. * (np.pi - th) + (2. - nu_fh) * np.sin(th)\n CMb = -0.5 * (1 + nu_fh) * np.sin(th)\n CMdb = -.25 * (np.pi - th + 2. / 3. * np.sin(th) * (0.5 - nu_fh) * (2. + nu_fh))\n\n return CLa, CLda, CLb, CLdb, CMda, CMb, CMdb\n\n\ndef nc_derivs(x_ea_perc, x_fh_perc):\n \"\"\"\n Provides non-circulatory aerodynamic lift and moment coefficients derivatives\n Ref. Palacios and Cesnik, Chap 3.\n\n Args:\n x_ea_perc: position of axis of rotation in percentage of chord (measured\n from LE)\n x_fc_perc: position of flap axis of rotation in percentage of chord\n (measured from LE)\n \"\"\"\n\n # parameters\n nu_ea = 2.0 * x_ea_perc - 1.0\n nu_fh = 2.0 * x_fh_perc - 1.0\n th = np.arccos(-nu_fh)\n\n # pitch/pitch rate related quantities\n CLda = np.pi # ok\n CLdda = -np.pi * nu_ea\n CMda = -.25 * np.pi\n CMdda = -0.25 * np.pi * (0.25 - nu_ea)\n\n # flap related quantities\n CLdb = np.pi - th - nu_fh * np.sin(th)\n CLddb = -nu_fh * (np.pi - th) + 1. / 3. * (2. + nu_fh ** 2) * np.sin(th)\n CMdb = -0.25 * (np.pi - th + (2. / 3. - nu_fh - 2. / 3. * nu_fh ** 2) * np.sin(th))\n CMddb = -0.25 * ((0.25 - nu_fh) * (np.pi - th) + \\\n (2. / 3. - 5. / 12. * nu_fh + nu_fh ** 2 / 3. + nu_fh ** 3 / 6.) * np.sin(th))\n\n return CLda, CLdda, CLdb, CLddb, CMda, CMdda, CMdb, CMddb\n\n\ndef theo_CL_freq_resp(k, x_ea_perc, x_fh_perc):\n \"\"\"\n Frequency response of lift coefficient according Theodorsen's theory.\n\n The output is a 3 elements array containing the CL frequency response w.r.t.\n to pitch, plunge and flap motion, respectively. Sign conventions are as\n follows:\n \n * plunge: positive when moving upward\n\n * x_ea_perc: position of axis of rotation in percentage of chord (measured\n from LE)\n \n * x_fc_perc: position of flap axis of rotation in percentage of chord\n (measured from LE)\n\n Warning:\n this function uses different input/output w.r.t. theo_lift\n \"\"\"\n\n df, ddf = j * k, -k ** 2\n\n # get quasi-steady derivatives\n CLa_qs, CLda_qs, CLb_qs, CLdb_qs, void, void, void = qs_derivs(x_ea_perc, x_fh_perc)\n\n # quasi-steady lift\n CLqs = np.array([\n CLa_qs + CLda_qs * df,\n CLa_qs * df,\n CLb_qs + CLdb_qs * df,\n ])\n\n # get non-circulatory derivatives\n CLda_nc, CLdda_nc, CLdb_nc, CLddb_nc, void, void, void, void \\\n = nc_derivs(x_ea_perc, x_fh_perc)\n\n # unsteady lift\n df, ddf = j * k, -k ** 2\n CLun = np.array([\n CLda_nc * df + CLdda_nc * ddf,\n CLda_nc * ddf,\n CLdb_nc * df + CLddb_nc * ddf\n ])\n\n ### Total response\n Y = theo_fun(k) * CLqs + CLun\n\n # sign convention update\n Y[1] = -Y[1] # plunge dof positive upward\n\n return Y\n\n\ndef theo_CM_freq_resp(k, x_ea_perc, x_fh_perc):\n \"\"\"\n Frequency response of moment coefficient according Theodorsen's theory.\n\n The output is a 3 elements array containing the CL frequency response w.r.t.\n to pitch, plunge and flap motion, respectively.\n \"\"\"\n\n df, ddf = j * k, -k ** 2\n\n # get quasi-steady derivatives\n void, void, void, void, CMda_qs, CMb_qs, CMdb_qs = qs_derivs(x_ea_perc, x_fh_perc)\n\n # quasi-steady lift\n CMqs = np.array([\n CMda_qs * df,\n 0.0 * k,\n CMb_qs + CMdb_qs * df,\n ])\n\n # get non-circulatory coefficients\n void, void, void, void, CMda_nc, CMdda_nc, CMdb_nc, CMddb_nc = \\\n nc_derivs(x_ea_perc, x_fh_perc)\n\n # unsteady lift\n CMun = np.array([\n CMda_nc * df + CMdda_nc * ddf,\n CMda_nc * ddf,\n CMdb_nc * df + CMddb_nc * ddf\n ])\n\n ### Total response\n Y = CMqs + CMun\n\n # sign convention update\n Y[1] = -Y[1]\n\n return Y\n\n\ndef theo_lift(w, A, H, c, rhoinf, uinf, x12):\n r\"\"\"\n Theodorsen's solution for lift of aerofoil undergoing sinusoidal motion.\n\n Time histories are built assuming:\n\n * ``a(t)=+/- A cos(w t) ??? not verified``\n\n * :math:`h(t)=-H\\cos(w t)`\n\n Args:\n w: frequency (rad/sec) of oscillation\n A: amplitude of angle of attack change\n H: amplitude of plunge motion\n c: aerofoil chord\n rhoinf: flow density\n uinf: flow speed\n x12: distance of elastic axis from mid-point of aerofoil (positive if\n the elastic axis is ahead)\n\n \"\"\"\n\n # reduced frequency\n k = 0.5 * w * c / uinf\n\n # compute theodorsen's function\n Ctheo = theo_fun(k)\n\n # Lift: circulatory\n Lcirc = np.pi * rhoinf * uinf * c * Ctheo * ((uinf + w * j * (0.25 * c + x12)) * A + w * H * j)\n Lmass = 0.25 * np.pi * rhoinf * c ** 2 * ((j * w * uinf - x12 * w ** 2) * A - H * w ** 2)\n Ltot = Lcirc + Lmass\n\n return Ltot, Lcirc, Lmass\n\n\ndef garrick_drag_plunge(w, H, c, rhoinf, uinf, time):\n r\"\"\"\n Returns Garrick solution for drag coefficient at a specific time.\n Ref.[1], eq.(8) (see also eq.(1) and (2)) or Ref[2], eq.(2)\n\n The aerofoil vertical motion is assumed to be:\n\n .. math:: h(t)=-H\\cos(wt)\n\n\n The :math:`C_d` is such that:\n\n * :math:`C_d>0`: drag\n\n * :math:`C_d<0`: suction\n \"\"\"\n\n b = 0.5 * c\n k = b * w / uinf\n Hast = H / b\n s = uinf * time / b\n\n # compute theodorsen's function\n Ctheo = theo_fun(k)\n\n Cd = -2. * np.pi * k ** 2 * Hast ** 2 * (\n Ctheo.imag * np.cos(k * s) + Ctheo.real * np.sin(k * s)) ** 2\n\n return Cd\n\n\ndef garrick_drag_pitch(w, A, c, rhoinf, uinf, x12, time):\n r\"\"\"\n Returns Garrick solution for drag coefficient at a specific time.\n Ref.[1], eq.(9), (10) and (11)\n\n The aerofoil pitching motion is assumed to be:\n\n .. math:: a(t)=A\\sin(\\omegat)=A\\sin(ks)\n\n The :math:`C_d` is such that:\n\n * :math:`C_d>0`: drag\n\n * :math:`C_d<0`: suction\n \"\"\"\n\n x12 = x12 / c\n b = 0.5 * c\n k = b * w / uinf\n s = uinf * time / b\n\n # compute theodorsen's function\n Ctheo = theo_fun(k)\n F, G = Ctheo.real, Ctheo.imag\n sks, cks = np.sin(k * s), np.cos(k * s)\n\n # angle of attack\n a = A * sks\n\n # lift term\n Cl = np.pi * A * (k * cks\n + x12 * k ** 2 * sks\n + 2. * F * (sks + (0.5 - x12) * k * cks)\n + 2. * G * (cks - (0.5 - x12) * k * sks))\n\n # suction force\n Y1 = 2. * (F - k * G * (0.5 - x12))\n Y2 = 2. * (G - k * F * (0.5 - x12)) - k\n Cs = 0.5 * np.pi * A ** 2 * (Y1 * sks + Y2 * cks) ** 2\n\n Cd = a * Cl - Cs\n\n return Cd\n\n\ndef sears_fun(kg):\n \"\"\"\n Produces Sears function\n \"\"\"\n\n S12 = 2. / np.pi / kg / (scsp.hankel1(0, kg) + 1.j * scsp.hankel1(1, kg))\n S = np.exp(-1.j * kg) * S12.conj()\n\n return S\n\n\ndef sears_lift_sin_gust(w0, L, Uinf, chord, tv):\n \"\"\"\n Returns the lift coefficient for a sinusoidal gust (see set_gust.sin) as\n the imaginary part of the CL complex function defined below. The input gust\n must be the imaginary part of\n\n .. math:: wgust = w0*\\exp(1.0j*C*(Ux*S.time[tt] - xcoord) )\n\n with:\n\n .. math:: C=2\\pi/L\n\n and ``xcoord=0`` at the aerofoil half-chord.\n \"\"\"\n\n # reduced frequency\n kg = np.pi * chord / L\n # Theo's funciton\n Ctheo = theo_fun(kg)\n # Sear's function\n J0, J1 = scsp.j0(kg), scsp.j1(kg)\n S = (J0 - 1.0j * J1) * Ctheo + 1.0j * J1\n\n phase = np.angle(S)\n CL = 2. * np.pi * w0 / Uinf * np.abs(S) * np.sin(2. * np.pi * Uinf / L * tv + phase)\n\n return CL\n\n\ndef sears_CL_freq_resp(k):\n \"\"\"\n Frequency response of lift coefficient according Sear's solution.\n Ref. Palacios and Cesnik, Chap.3\n \"\"\"\n\n # hanckel functions\n H1 = scsp.hankel1(1, k)\n H0 = scsp.hankel1(0, k)\n\n # Sear's function\n S12star = 2. / (np.pi * k * (H0 + 1.j * H1))\n S0 = np.exp(-1.0j * k) * S12star.conj(S12star)\n\n # CL frequency response\n CL = 2. * np.pi * S0\n\n return CL\n\n\ndef wagner_imp_start(aeff, Uinf, chord, tv):\n \"\"\"\n Lift coefficient resulting from impulsive start solution.\n \"\"\"\n\n sv = 2.0 * Uinf / chord * tv\n fiv = 1.0 - 0.165 * np.exp(-0.0455 * sv) - 0.335 * np.exp(-0.3 * sv)\n CLv = 2. * np.pi * aeff * fiv\n\n return CLv\n\n\ndef flat_plate_analytical(kv, x_ea_perc, x_fh_perc, input_seq, output_seq,\n output_scal=None, plunge_deriv=True):\n r\"\"\"\n Computes the analytical frequency response of a plat plate for the input\n output sequences in ``input_seq`` and ``output_seq`` over the frequency points ``kv``,\n if available.\n\n The output complex values array ``Yan`` has shape ``(Nout, Nin, Nk)``; if an analytical\n solution is not available, the response is assumed to be zero.\n\n If ``plunge_deriv`` is ``True``, the plunge response is expressed in terms of first\n derivative dh.\n\n Args:\n kv (np.array): Frequency range of length ``Nk``.\n x_ea_perc (float): Elastic axis location along the chord as chord length percentage.\n x_fh_perc (float): Flap hinge location along the chord as chord length percentage.\n input_seq (list(str)): List of ``Nin`` number of inputs.\n Supported inputs include:\n * ``gust_sears``: Response to a continuous sinusoidal gust.\n * ``pitch``: Response to an oscillatory pitching motion.\n * ``plunge``: Response to an oscillatory plunging motion.\n output_seq (list(str)): List of ``Nout`` number of outputs.\n Supported outputs include:\n * ``Fy``: Vertical force.\n * ``Mz``: Pitching moment.\n output_scal (np.array): Array of factors by which to divide the desired outputs. Dimensions of ``Nout``.\n plunge_deriv (bool): If ``True`` expresses the plunge response in terms of the first derivative, i.e. the\n rate of change of plunge :math:`d\\dot{h}`.\n\n Returns:\n np.array: A ``(Nout, Nin, Nk)`` array containing the scaled frequency response for the inputs and outputs\n specified.\n\n See Also:\n The lift coefficient due to pitch and plunging motions is calculated\n using :func:`sharpy.utils.analytical.theo_CL_freq_resp`. In turn, the pitching moment is found using\n :func:`sharpy.utils.analytical.theo_CM_freq_resp`.\n\n The response to the continuous sinusoidal gust is calculated using\n :func:`sharpy.utils.analytical.sears_CL_freq_resp`.\n\n \"\"\"\n\n Nout = len(output_seq)\n Nin = len(input_seq)\n Nk = len(kv)\n Yfreq_an = np.zeros((Nout, Nin, Nk), dtype=np.complex)\n\n # Get Theodorsen solutions\n CLtheo = theo_CL_freq_resp(kv, x_ea_perc, x_fh_perc)\n CMtheo = theo_CM_freq_resp(kv, x_ea_perc, x_fh_perc)\n\n # scaling\n if output_scal is None: output_scal = np.ones((Nout,))\n\n for oo in range(Nout):\n for ii in range(Nin):\n\n ### Sears\n if input_seq[ii] == 'gust_sears':\n # Fx,Mz null\n if output_seq[oo] == 'Fy':\n Yfreq_an[oo, ii, :] = sears_CL_freq_resp(kv)\n\n ### Theodorsen\n if input_seq[ii] == 'pitch':\n if output_seq[oo] == 'Fy':\n Yfreq_an[oo, ii, :] = CLtheo[0]\n if output_seq[oo] == 'Mz':\n Yfreq_an[oo, ii, :] = CMtheo[0]\n\n if input_seq[ii] == 'plunge':\n Fact = 1.0\n if plunge_deriv: Fact = -1.j / kv\n if output_seq[oo] == 'Fy':\n Yfreq_an[oo, ii, :] = Fact * CLtheo[1]\n if output_seq[oo] == 'Mz':\n Yfreq_an[oo, ii, :] = Fact * CMtheo[1]\n\n # scale output\n Yfreq_an[oo, :, :] = Yfreq_an[oo, :, :] / output_scal[oo]\n\n return Yfreq_an\n\n\n# if __name__ == '__main__':\n# import matplotlib.pyplot as plt\n#\n# kv = np.linspace(0.001, 50, 1001)\n#\n# ### test Sear's function\n# sv = sears_fun(kv)\n# plt.plot(kv, sv.real, '-')\n# plt.plot(kv, sv.imag, '--')\n# plt.show()\n#\n# CL = theo_CL_freq_resp(kv, 0.25, 0.8)\n#\n# kv = np.linspace(0.001, 2.0, 101)\n# # data for dimensional analysis\n# b = 1.3\n# U = 15.0\n# H = 0.3\n# A = 5.0 * np.pi / 180.\n# rho = 1.225\n# tref = b / U\n#\n# ### plunge frequency response\n# Ltheo = -theo_lift(kv / tref, 0, H, 2. * b, rho, U, 0.0)[0]\n# Fref = b * rho * U ** 2\n# CLfreq = Ltheo / Fref / (H / b)\n#\n# Yfreq = theo_CL_freq_resp(kv, x_ea_perc=1.0, x_fh_perc=0.9)\n# CLfreq02 = Yfreq[1]\n# Er = np.max(np.abs(CLfreq - CLfreq02))\n# print('Max error for CL plunge freq response: %.2e' % Er)\n#\n# # moments\n# Yfreq = theo_CM_freq_resp(kv, x_ea_perc=1.0, x_fh_perc=0.9)\n# CMfreq = Yfreq[1] # plunge motion\n# CMfreq_vel = 1.j / kv * CMfreq\n# CMmag_vel, CMph_vel = np.abs(CMfreq_vel), np.angle(CMfreq_vel, deg=True)\n#\n# fig = plt.figure('Momentum coefficient frequency response')\n# ax = fig.add_subplot(121)\n# ax.plot(kv, CMmag_vel, 'k', label='magnitude')\n# ax.legend()\n# ax = fig.add_subplot(122)\n# ax.plot(kv, CMph_vel, 'r', label='phase')\n# ax.legend()\n# plt.show()\n#\n# ### pitching frequency response\n# Yfreq = theo_CL_freq_resp(kv, x_ea_perc=.5, x_fh_perc=0.9)\n# CLfreq02 = Yfreq[0]\n#\n# ### geometry\n# c = 3. # m\n# b = 0.5 * c\n#\n# ### motion\n# ktarget = 1.\n# H = 0.02 * b # m Ref.[1]\n# A = 1. * np.pi / 180. # rad - Ref.[1]\n# x12 = -0.5 * c\n# f0 = 5. # Hz\n# w0 = 2. * np.pi * f0 # rad/s\n#\n# uinf = b * w0 / ktarget\n# rhoinf = 1.225 # kg/m3\n# qinf = 0.5 * c * rhoinf * uinf ** 2\n# # C=theo_fun(k=ktarget)\n# # L=theo_lift(w0,A,H,c,rhoinf,uinf,x12)\n#\n# ##### Plunge Induced drag\n# Ncicles = 5\n# tv = np.linspace(0., 2. * np.pi * Ncicles / w0, 200 * Ncicles + 1)\n# Cdv = garrick_drag_plunge(w0, H, c, rhoinf, uinf, tv)\n# hv = -H * np.cos(w0 * tv)\n# dhv = w0 * H * np.sin(w0 * tv)\n# aeffv = np.arctan(-dhv / uinf)\n# # fig = plt.figure('Induced drag - plunge motion',(10,6))\n# # ax=fig.add_subplot(111)\n# # ax.plot(tv,hv/c,'r',label=r'h/c')\n# # ax.plot(tv,Cdv,'k',label=r'Induced Drag')\n# # ax.legend()\n# # plt.show()\n# fig = plt.figure('Plunge motion - Phase vs kinematics', (10, 6))\n# ax = fig.add_subplot(111)\n# # ax.plot(aeffv,hv/c,'r',label=r'h/c')\n# ax.plot(180. / np.pi * aeffv, Cdv, 'k', label=r'Induced Drag')\n# ax.set_xlabel('deg')\n# ax.legend()\n# plt.close()\n#\n# ##### Pitching Induced drag\n# Ncicles = 5\n# tv = np.linspace(0., 2. * np.pi * Ncicles / w0, 200 * Ncicles + 1)\n# Cdv = garrick_drag_pitch(w0, A, c, rhoinf, uinf, x12, tv)\n# aeffv = A * np.sin(w0 * tv)\n# fig = plt.figure('Pitch motion - Phase vs kinematics', (10, 6))\n# ax = fig.add_subplot(111)\n# # ax.plot(aeffv,hv/c,'r',label=r'h/c')\n# ax.plot(180. / np.pi * aeffv, Cdv, 'k', label=r'Induced Drag')\n# ax.set_xlabel('deg')\n# ax.legend()\n#\n# ##### Sear's solution test\n# L = .5 * c\n# w0 = 0.3\n# uinf = 6.0\n#\n# # gust profile at LE\n# tv = np.linspace(0., 2., 300)\n# C = 2. * np.pi / L\n# wgustLE = w0 * np.sin(C * uinf * tv)\n# CLv = sears_lift_sin_gust(w0, L, uinf, c, tv)\n#\n# fig = plt.figure('Gust response', (10, 6))\n# ax = fig.add_subplot(111)\n# ax.plot(tv, wgustLE, 'k', label=r'vertical gust velocity at LE [m/s]')\n# ax.plot(tv, CLv, 'r', label=r'CL')\n# ax.set_xlabel('time')\n# ax.legend()\n# # plt.show()\n# plt.close('all')\n#\n# ##### Wagner impulsive start\n# uinf = 20.0\n# chord = 3.0\n# aeff = 2.0 * np.pi / 180.\n# tv = np.linspace(0., 10., 300)\n#\n# CLv = wagner_imp_start(aeff, uinf, chord, tv)\n# CLv_inf = wagner_imp_start(aeff, uinf, chord, 1e3 * tv[-1])\n#\n# fig = plt.figure('Impulsive start', (10, 6))\n# ax = fig.add_subplot(111)\n# ax.plot(tv, CLv / CLv_inf, 'r', label=r'CL')\n# ax.set_xlabel('time')\n# ax.legend()\n# plt.show()\n" }, { "path": "sharpy/utils/constants.py", "content": "import ctypes as ct\nimport numpy as np\n\nNDIM = int(3)\nct_NDIM = ct.c_uint(NDIM)\ndeg2rad = np.pi/180.\nvortex_radius_def = 1e-6\n\ncfact_biot = 0.25 / np.pi\n" }, { "path": "sharpy/utils/control_utils.py", "content": "\"\"\"Controller Utilities\n\"\"\"\nimport numpy as np\n\ndef second_order_fd(history, n_calls, dt):\n # history is ordered such that the last element is the most recent one (t), and thus\n # it goes [(t - 2), (t - 1), (t)]\n coefficients = np.zeros((3,))\n if n_calls <= 1:\n # no derivative, return 0\n pass\n\n elif n_calls == 2:\n # else:\n # first order derivative\n coefficients[1:3] = [-1.0, 1.0]\n\n else:\n # # second order derivative\n coefficients[:] = [1.0, -4.0, 3.0]\n coefficients *= 0.5\n\n derivative = np.dot(coefficients, history)/dt\n return derivative\n\nclass PID(object):\n \"\"\"\n Class implementing a classic PID controller\n\n Instance attributes:\n :param `gain_p`: Proportional gain.\n :param `gain_i`: Integral gain.\n :param `gain_d`: Derivative gain.\n :param `dt`: Simulation time step.\n\n The class should be used as:\n\n pid = PID(100, 10, 0.1, 0.1)\n pid.set_point(target_point)\n control = pid(current_point)\n \"\"\"\n # for i in range(n_steps):\n # state[i] = np.sum(feedback[:i])\n # controller.set_point(set_point[i])\n # feedback[i] = controller(state[i])\n def __init__(self, gain_p, gain_i, gain_d, dt):\n self._kp = gain_p\n self._ki = gain_i\n self._kd = gain_d\n\n self._point = 0.0\n\n self._dt = dt\n\n self._accumulated_integral = 0.0\n self._integral_limits = np.array([-1., 1.])*10000\n self._error_history = np.zeros((3,))\n\n self._derivator = second_order_fd\n self._derivative_limits = np.array([-1, 1])*10000\n\n self._n_calls = 0\n\n self._anti_windup_lim = None\n\n def set_point(self, point):\n self._point = point\n\n def set_anti_windup_lim(self, lim):\n self._anti_windup_lim = lim\n\n def reset_integrator(self):\n self._accumulated_integral = 0.0\n\n def __call__(self, state):\n self._n_calls += 1\n actuation = 0.0\n error = self._point - state\n # displace previous errors one position to the left\n self._error_history = np.roll(self._error_history, -1)\n self._error_history[-1] = error\n\n detailed = np.zeros((3,))\n # Proportional gain\n actuation += error*self._kp\n detailed[0] = error*self._kp\n\n # Derivative gain\n derivative = self._derivator(self._error_history, self._n_calls, self._dt)\n derivative = max(derivative, self._derivative_limits[0])\n derivative = min(derivative, self._derivative_limits[1])\n actuation += derivative*self._kd\n detailed[2] = derivative*self._kd\n\n # Integral gain\n aux_acc_int = self._accumulated_integral + error*self._dt\n if aux_acc_int < self._integral_limits[0]:\n aux_acc_int = self._integral_limits[0]\n elif aux_acc_int > self._integral_limits[1]:\n aux_acc_int = self._integral_limits[1]\n\n if self._anti_windup_lim is not None:\n # Apply anti wind up\n aux_actuation = actuation + aux_acc_int*self._ki\n if ((aux_actuation > self._anti_windup_lim[0]) and\n (aux_actuation < self._anti_windup_lim[1])):\n # Within limits\n self._accumulated_integral = aux_acc_int\n # If the system exceeds the limits, this \n # will not be added to the self._accumulated_integral\n else:\n self._accumulated_integral = aux_acc_int\n\n actuation += self._accumulated_integral*self._ki\n detailed[1] = self._accumulated_integral*self._ki\n\n return actuation, detailed\n" }, { "path": "sharpy/utils/controller_interface.py", "content": "from abc import ABCMeta, abstractmethod\nimport sharpy.utils.cout_utils as cout\nimport os\n\ndict_of_controllers = {}\ncontrollers = {} # for internal working\n\n\n# decorator\ndef controller(arg):\n # global available_solvers\n global dict_of_controllers\n try:\n arg.controller_id\n except AttributeError:\n raise AttributeError('Class defined as controller has no controller_id attribute')\n dict_of_controllers[arg.controller_id] = arg\n return arg\n\n\ndef print_available_controllers():\n cout.cout_wrap('The available controllers in this session are:', 2)\n for name, i_controller in dict_of_controllers.items():\n cout.cout_wrap('%s ' % i_controller.controller_id, 2)\n\n\nclass BaseController(metaclass=ABCMeta):\n \n def teardown(self):\n pass\n\n\ndef controller_from_string(string):\n return dict_of_controllers[string]\n\n\ndef controller_list_from_path(cwd):\n onlyfiles = [f for f in os.listdir(cwd) if os.path.isfile(os.path.join(cwd, f))]\n\n for i_file in range(len(onlyfiles)):\n if onlyfiles[i_file].split('.')[-1] == 'py': # support autosaved files in the folder\n if onlyfiles[i_file] == \"__init__.py\":\n onlyfiles[i_file] = \"\"\n continue\n onlyfiles[i_file] = onlyfiles[i_file].replace('.py', '')\n else:\n onlyfiles[i_file] = \"\"\n\n files = [file for file in onlyfiles if not file == \"\"]\n return files\n\n\ndef initialise_controller(controller_name, print_info=True):\n if print_info:\n cout.cout_wrap('Generating an instance of %s' % controller_name, 2)\n cls_type = controller_from_string(controller_name)\n controller = cls_type()\n return controller\n\ndef dictionary_of_controllers(print_info=True):\n import sharpy.controllers\n dictionary = dict()\n for controller in dict_of_controllers:\n init_controller = initialise_controller(controller, print_info=print_info)\n dictionary[controller] = init_controller.settings_default\n\n return dictionary\n" }, { "path": "sharpy/utils/cout_utils.py", "content": "import textwrap\nimport colorama\nimport os\nimport numpy as np\nimport subprocess\nimport sharpy.utils.sharpydir as sharpydir\n\ncwd = os.getcwd()\n\n\nclass Writer(object):\n fore_colours = ['', colorama.Fore.BLUE, colorama.Fore.CYAN, colorama.Fore.YELLOW, colorama.Fore.RED]\n reset = colorama.Style.RESET_ALL\n\n output_columns = 80\n separator = '-'*output_columns\n sharpy_ascii = \\\n\"\"\"--------------------------------------------------------------------------------\n ###### ## ## ### ######## ######## ## ##\n ## ## ## ## ## ## ## ## ## ## ## ##\n ## ## ## ## ## ## ## ## ## ####\n ###### ######### ## ## ######## ######## ##\n ## ## ## ######### ## ## ## ##\n ## ## ## ## ## ## ## ## ## ##\n ###### ## ## ## ## ## ## ## ##\n--------------------------------------------------------------------------------\"\"\"\n\n sharpy_license = \\\n '''Aeroelastics Lab, Aeronautics Department.\n Copyright (c), Imperial College London.\n All rights reserved.\n License available at https://github.com/imperialcollegelondon/sharpy'''\n\n wrapper = textwrap.TextWrapper(width=output_columns, break_long_words=False)\n\n def __init__(self):\n self.print_screen = False\n self.print_file = False\n self.file = None\n self.file_route = ''\n self.file_name = ''\n\n def initialise(self, print_screen, print_file, file_route=None, file_name=None):\n # copy settings\n self.print_screen = print_screen\n self.print_file = print_file\n\n if self.print_file:\n self.file_route = file_route\n self.file_name = file_name\n # create folder if necessary\n if not os.path.exists(self.file_route):\n try:\n os.makedirs(self.file_route)\n except FileExistsError:\n pass\n\n self.file = open(self.file_route + '/' + self.file_name, 'w')\n\n self.print_welcome_message()\n\n def print_welcome_message(self):\n self.__call__(self.sharpy_ascii)\n self.__call__(self.sharpy_license)\n self.__call__('Running SHARPy from ' + cwd, 2)\n self.__call__('SHARPy being run is in ' + sharpydir.SharpyDir, 2)\n try:\n self.__call__(print_git_status(), 2)\n except subprocess.CalledProcessError:\n pass\n import sharpy.utils.solver_interface as solver_interface\n # solver_interface.print_available_solvers()\n\n def cout_quiet(self):\n self.print_screen = False\n\n def cout_talk(self):\n self.print_screen = True\n\n def print_separator(self, level=0):\n self.__call__(self.separator, level)\n\n def __call__(self, in_line, level=0):\n if self.print_screen:\n line = in_line\n lines = line.split(\"\\n\")\n if level > 4:\n raise AttributeError('Output level cannot be > 4')\n if len(lines) == 1:\n print(self.fore_colours[level] + line + self.reset)\n else:\n newline = ''\n for line in lines:\n if len(line) > self.output_columns:\n line = '\\n'.join(self.wrapper.wrap(line))\n\n print(self.fore_colours[level] + line + self.reset)\n # newline += line + \"\\n\"\n # print(self.fore_colours[level] + newline + self.reset)\n if self.print_file:\n line = in_line\n lines = line.split(\"\\n\")\n if len(lines) == 1:\n self.file.write(line + '\\n')\n else:\n newline = ''\n for line in lines:\n if len(line) > self.output_columns:\n line = '\\n'.join(self.wrapper.wrap(line))\n\n newline += line + \"\\n\"\n self.file.write(newline)\n\n def close(self):\n if self.file is not None:\n if not self.file.closed:\n self.file.close()\n\n def __del__(self):\n self.close()\n\n\ncout_wrap = Writer()\n\n\ndef start_writer():\n global cout_wrap\n cout_wrap = Writer()\n # pass\n\n\ndef finish_writer():\n global cout_wrap\n if cout_wrap is not None:\n cout_wrap.close()\n\n\n# table output for residuals\nclass TablePrinter(object):\n global cout_wrap\n\n divider_char = '|'\n line_char = '='\n\n def __init__(self, n_fields=3, field_length=12, field_types=[['g']]*100, filename=None):\n self.n_fields = n_fields\n self.file = None\n self.divider_line = None\n try:\n field_length[0]\n except TypeError:\n self.field_length = np.full((self.n_fields, ), field_length, dtype=int)\n else:\n if len(field_length) == n_fields:\n self.field_length = field_length\n else:\n raise Exception('len(field_length /= n_fields')\n self.field_names = None\n self.field_types = field_types\n\n if cout_wrap is None:\n start_writer()\n\n # if filename is not None:\n # self.file = open(filename, 'w')\n self.file = filename\n\n def print_header(self, field_names):\n self.field_names = field_names\n if not len(self.field_names) == self.n_fields:\n raise Exception('len(field_names) /= n_fields')\n for i_name in range(self.n_fields):\n name = self.field_names[i_name]\n if len(name) >= self.field_length[i_name]:\n name = name[0:self.field_length[i_name]]\n\n string = ''\n divider_line = ''\n # for i_field in range(self.n_fields):\n # string += '|{0[' + str(i_field) + ']:^' + str(self.field_length[i_field]) + '}'\n # divider_line += '-'*(self.field_length[i_field]) + '|'\n\n for i_field in range(self.n_fields):\n field_length = self.field_length[i_field]\n string += self.divider_char + '{' + str(i_field) + ':^' + str(field_length + 2) + '}'\n # string += '|{0[' + str(i_field) + ']:^' + str(self.field_length[i_field]) + '}'\n divider_line += self.divider_char + (field_length + 2)*self.line_char\n\n string += self.divider_char\n divider_line += self.divider_char\n self.divider_line = divider_line\n cout_wrap('\\n\\n')\n cout_wrap(divider_line)\n cout_wrap(string.format(*(self.field_names)))\n cout_wrap(divider_line)\n\n if self.file is not None:\n with open(self.file, 'a+') as f:\n f.write(divider_line)\n f.write('\\n' + string.format(*(self.field_names)))\n f.write('\\n' + divider_line)\n\n def print_line(self, line_data):\n string = ''\n for i_field in range(self.n_fields):\n string += (self.divider_char +\n '{0[' +\n str(i_field) +\n ']:^' +\n str(self.field_length[i_field] + 2) +\n '.' +\n str(max(int(self.field_length[i_field]/2), 4)) +\n self.field_types[i_field] +\n '}')\n\n string += self.divider_char\n cout_wrap(string.format(line_data))\n if self.file is not None:\n with open(self.file, 'a') as f:\n f.write('\\n'+string.format(line_data))\n\n def close_file(self):\n if self.file is not None:\n with open(self.file, 'a+') as f:\n f.write('\\n' + self.divider_line)\n\n def print_divider_line(self):\n cout_wrap(self.divider_line)\n if self.file is not None:\n with open(self.file, 'a+') as f:\n f.write('\\n' + self.divider_line)\n\n def character_return(self, n_lines=1):\n cout_wrap(n_lines * '\\n')\n if self.file is not None:\n with open(self.file, 'a+') as f:\n f.write(n_lines * '\\n')\n\n\n# version tracker and output\ndef get_git_revision_hash(di=sharpydir.SharpyDir):\n return subprocess.check_output(['git', 'rev-parse', 'HEAD'], cwd=di).strip().decode('utf-8')\n\n\ndef get_git_revision_short_hash(di=sharpydir.SharpyDir):\n return subprocess.check_output(['git', 'rev-parse', '--short', 'HEAD'], cwd=di).strip().decode('utf-8')\n\n\ndef get_git_revision_branch(di=sharpydir.SharpyDir):\n return subprocess.check_output(['git', 'rev-parse', '--abbrev-ref', 'HEAD'], cwd=di).strip().decode('utf-8')\n\n\ndef get_git_tag(di=sharpydir.SharpyDir):\n return subprocess.check_output(['git', 'describe'], cwd=di).strip().decode('utf-8')\n\n\ndef print_git_status():\n return ('The branch being run is ' + get_git_revision_branch() + '\\n'\\\n 'The version and commit hash are: ' + get_git_tag() + '-' + get_git_revision_short_hash())\n\ndef check_running_unittest():\n import sys\n # Define if the script is being run in unittest\n running_unittest = False\n for arg in sys.argv:\n if \"unittest\" in arg:\n print(\"running unittest\")\n running_unittest = True\n\n return running_unittest\n" }, { "path": "sharpy/utils/ctypes_utils.py", "content": "import ctypes as ct\nimport platform\nimport os\n\n\ndef import_ctypes_lib(route, libname):\n lib_path = os.path.join(route, libname)\n if platform.system() == 'Darwin':\n ext = '.dylib'\n elif platform.system() == 'Linux':\n ext = '.so'\n else:\n raise NotImplementedError('The platform ' + platform.system() + 'is not supported')\n\n lib_path += ext\n lib_path = os.path.abspath(lib_path)\n\n library = ct.CDLL(lib_path, mode=ct.RTLD_GLOBAL)\n\n return library\n" }, { "path": "sharpy/utils/datastructures.py", "content": "\"\"\"Data Management Structures\n\nThese classes are responsible for storing the aerodynamic and structural time step information and relevant variables.\n\n\"\"\"\nimport copy\nimport ctypes as ct\nimport numpy as np\n\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.multibody as mb\n\n\nclass TimeStepInfo(object):\n \"\"\"\n Time step class.\n\n It is the parent class of the AeroTimeStepInfo and NonliftingBodyTimeStepInfo, which contain the relevant\n aerodynamic attributes for a single time step. All variables should be expressed in ``G`` FoR unless\n otherwise stated.\n\n Attributes:\n ct_dimensions: Pointer to ``dimensions`` to interface the C++ library `uvlmlib``\n\n dimensions (np.ndarray): Matrix defining the dimensions of the vortex grid on solid surfaces\n ``[num_surf x chordwise panels x spanwise panels]``\n\n n_surf (int): Number of aerodynamic surfaces on solid bodies. Each aerodynamic surface on solid bodies will\n have an associted wake.\n\n zeta (list(np.ndarray): Location of solid grid vertices\n ``[n_surf][3 x (chordwise nodes + 1) x (spanwise nodes + 1)]``\n zeta_dot (list(np.ndarray)): Time derivative of ``zeta``\n normals (list(np.ndarray)): Normal direction to panels at the panel center\n ``[n_surf][3 x chordwise nodes x spanwise nodes]``\n forces (list(np.ndarray)): Forces not associated to time derivatives on grid vertices\n ``[n_surf][3 x (chordwise nodes + 1) x (spanwise nodes + 1)]``\n dynamic_forces (list(np.ndarray)): Forces associated to time derivatives on grid vertices\n ``[n_surf][3 x (chordwise nodes + 1) x (spanwise nodes + 1)]``\n u_ext (list(np.ndarray)): Background flow velocity on solid grid nodes\n ``[n_surf][3 x (chordwise nodes + 1) x (spanwise nodes + 1)]``\n\n inertial_steady_forces (list(np.ndarray)): Total aerodynamic steady forces in ``G`` FoR ``[n_surf x 6]``\n body_steady_forces (list(np.ndarray)): Total aerodynamic steady forces in ``A`` FoR ``[n_surf x 6]``\n inertial_unsteady_forces (list(np.ndarray)): Total aerodynamic unsteady forces in ``G`` FoR ``[n_surf x 6]``\n body_unsteady_forces (list(np.ndarray)): Total aerodynamic unsteady forces in ``A`` FoR ``[n_surf x 6]``\n\n postproc_cell (dict): Variables associated to cells to be postprocessed\n postproc_node (dict): Variables associated to nodes to be postprocessed\n\n in_global_AFoR (bool): ``True`` if the variables are stored in the global A FoR. ``False`` if they are stored\n in the local A FoR of each body. Always ``True`` for single-body simulations. Currently not used.\n\n\n Args:\n dimensions (np.ndarray): Matrix defining the dimensions of the vortex grid on solid surfaces\n ``[num_surf x chordwise panels x spanwise panels]``\n \"\"\"\n def __init__(self, dimensions):\n self.ct_dimensions = None\n\n self.dimensions = dimensions.copy()\n self.n_surf = self.dimensions.shape[0]\n # generate placeholder for aero grid zeta coordinates\n self.zeta = []\n for i_surf in range(self.n_surf):\n self.zeta.append(np.zeros((3,\n dimensions[i_surf, 0] + 1,\n dimensions[i_surf, 1] + 1),\n dtype=ct.c_double))\n self.zeta_dot = []\n for i_surf in range(self.n_surf):\n self.zeta_dot.append(np.zeros((3,\n dimensions[i_surf, 0] + 1,\n dimensions[i_surf, 1] + 1),\n dtype=ct.c_double))\n\n # panel normals\n self.normals = []\n for i_surf in range(self.n_surf):\n self.normals.append(np.zeros((3,\n dimensions[i_surf, 0],\n dimensions[i_surf, 1]),\n dtype=ct.c_double))\n # panel forces\n self.forces = []\n for i_surf in range(self.n_surf):\n self.forces.append(np.zeros((6,\n dimensions[i_surf, 0] + 1,\n dimensions[i_surf, 1] + 1),\n dtype=ct.c_double))\n # panel forces\n self.dynamic_forces = []\n for i_surf in range(self.n_surf):\n self.dynamic_forces.append(np.zeros((6,\n dimensions[i_surf, 0] + 1,\n dimensions[i_surf, 1] + 1),\n dtype=ct.c_double))\n\n # placeholder for external velocity\n self.u_ext = []\n for i_surf in range(self.n_surf):\n self.u_ext.append(np.zeros((3,\n dimensions[i_surf, 0] + 1,\n dimensions[i_surf, 1] + 1),\n dtype=ct.c_double))\n\n # total forces - written by AeroForcesCalculator\n self.inertial_steady_forces = np.zeros((self.n_surf, 6))\n self.body_steady_forces = np.zeros((self.n_surf, 6))\n self.inertial_unsteady_forces = np.zeros((self.n_surf, 6))\n self.body_unsteady_forces = np.zeros((self.n_surf, 6))\n\n self.postproc_cell = dict()\n self.postproc_node = dict()\n\n # Multibody variables\n self.in_global_AFoR = True\n\n\n def copy(self):\n \"\"\"\n Returns a copy of a deepcopy of a :class:`~sharpy.utils.datastructures.TimeStepInfo`\n \"\"\"\n return self.create_placeholder(TimeStepInfo(self.dimensions))\n\n def create_placeholder(self, copied):\n # generate placeholder for aero grid zeta coordinates\n for i_surf in range(copied.n_surf):\n copied.zeta[i_surf] = self.zeta[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n for i_surf in range(copied.n_surf):\n copied.zeta_dot[i_surf] = self.zeta_dot[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n # panel normals\n for i_surf in range(copied.n_surf):\n copied.normals[i_surf] = self.normals[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n # panel forces\n for i_surf in range(copied.n_surf):\n copied.forces[i_surf] = self.forces[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n # panel forces\n for i_surf in range(copied.n_surf):\n copied.dynamic_forces[i_surf] = self.dynamic_forces[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n # placeholder for external velocity\n for i_surf in range(copied.n_surf):\n copied.u_ext[i_surf] = self.u_ext[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n # total forces\n copied.inertial_steady_forces = self.inertial_steady_forces.astype(dtype=ct.c_double, copy=True, order='C')\n copied.body_steady_forces = self.body_steady_forces.astype(dtype=ct.c_double, copy=True, order='C')\n copied.inertial_unsteady_forces = self.inertial_unsteady_forces.astype(dtype=ct.c_double, copy=True, order='C')\n copied.body_unsteady_forces = self.body_unsteady_forces.astype(dtype=ct.c_double, copy=True, order='C')\n \n copied.postproc_cell = copy.deepcopy(self.postproc_cell)\n copied.postproc_node = copy.deepcopy(self.postproc_node)\n\n return copied\n\n def generate_ctypes_pointers(self):\n \"\"\"\n Generates the pointers to aerodynamic variables used to interface the C++ library ``uvlmlib``\n \"\"\"\n self.ct_dimensions = self.dimensions.astype(dtype=ct.c_uint, copy=True)\n\n n_surf = len(self.dimensions)\n\n from sharpy.utils.constants import NDIM\n\n self.ct_zeta_list = []\n for i_surf in range(self.n_surf):\n for i_dim in range(NDIM):\n self.ct_zeta_list.append(self.zeta[i_surf][i_dim, :, :].reshape(-1))\n\n self.ct_zeta_dot_list = []\n for i_surf in range(self.n_surf):\n for i_dim in range(NDIM):\n self.ct_zeta_dot_list.append(self.zeta_dot[i_surf][i_dim, :, :].reshape(-1))\n\n self.ct_u_ext_list = []\n for i_surf in range(self.n_surf):\n for i_dim in range(NDIM):\n self.ct_u_ext_list.append(self.u_ext[i_surf][i_dim, :, :].reshape(-1))\n\n self.ct_normals_list = []\n for i_surf in range(self.n_surf):\n for i_dim in range(NDIM):\n self.ct_normals_list.append(self.normals[i_surf][i_dim, :, :].reshape(-1))\n\n self.ct_forces_list = []\n for i_surf in range(self.n_surf):\n for i_dim in range(NDIM*2):\n self.ct_forces_list.append(self.forces[i_surf][i_dim, :, :].reshape(-1))\n\n self.ct_dynamic_forces_list = []\n for i_surf in range(self.n_surf):\n for i_dim in range(NDIM*2):\n self.ct_dynamic_forces_list.append(self.dynamic_forces[i_surf][i_dim, :, :].reshape(-1))\n\n try:\n self.postproc_cell['incidence_angle']\n except KeyError:\n with_incidence_angle = False\n else:\n with_incidence_angle = True\n\n if with_incidence_angle:\n self.ct_incidence_list = []\n for i_surf in range(self.n_surf):\n self.ct_incidence_list.append(self.postproc_cell['incidence_angle'][i_surf][:, :].reshape(-1))\n\n self.ct_p_dimensions = ((ct.POINTER(ct.c_uint)*n_surf)\n (* np.ctypeslib.as_ctypes(self.ct_dimensions)))\n self.ct_p_zeta = ((ct.POINTER(ct.c_double)*len(self.ct_zeta_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_zeta_list]))\n self.ct_p_zeta_dot = ((ct.POINTER(ct.c_double)*len(self.ct_zeta_dot_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_zeta_dot_list]))\n self.ct_p_u_ext = ((ct.POINTER(ct.c_double)*len(self.ct_u_ext_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_u_ext_list]))\n self.ct_p_normals = ((ct.POINTER(ct.c_double)*len(self.ct_normals_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_normals_list]))\n self.ct_p_forces = ((ct.POINTER(ct.c_double)*len(self.ct_forces_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_forces_list]))\n self.ct_p_dynamic_forces = ((ct.POINTER(ct.c_double)*len(self.ct_dynamic_forces_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_dynamic_forces_list]))\n\n if with_incidence_angle:\n self.postproc_cell['incidence_angle_ct_pointer'] = ((ct.POINTER(ct.c_double)*len(self.ct_incidence_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_incidence_list]))\n\n def remove_ctypes_pointers(self):\n \"\"\"\n Removes the pointers to aerodynamic variables used to interface the C++ library ``uvlmlib``\n \"\"\"\n\n list_class_attributes = list(self.__dict__.keys()).copy()\n for name_attribute in list_class_attributes:\n if \"ct_p_\" in name_attribute:\n self.__delattr__(name_attribute)\n\n for k in list(self.postproc_cell.keys()):\n if 'ct_list' in k:\n del self.postproc_cell[k]\n elif 'ct_pointer' in k:\n del self.postproc_cell[k]\n\n\nclass NonliftingBodyTimeStepInfo(TimeStepInfo):\n \"\"\"\n Nonlifting Body Time step class.\n\n It is the inheritance from ``TimeStepInfo`` and contains the relevant aerodynamic attributes for\n a single time step of a nonlifting body. All variables should be expressed in ``G``\n FoR unless otherwise stated.\n\n Attributes:\n ct_dimensions: Pointer to ``dimensions`` to interface the C++ library `uvlmlib``\n\n dimensions (np.ndarray): Matrix defining the dimensions of the vortex grid on solid surfaces\n ``[num_surf x radial panels x spanwise panels]``\n\n n_surf (int): Number of aerodynamic surfaces on nonlifting bodies.\n\n zeta (list(np.ndarray): Location of solid grid vertices\n ``[n_surf][3 x (radial panel) x (spanwise panel)]``\n zeta_dot (list(np.ndarray)): Time derivative of ``zeta``\n normals (list(np.ndarray)): Normal direction to panels at the panel center\n ``[n_surf][3 x radial panels x spanwise panels]``\n forces (list(np.ndarray)): Forces not associated to time derivatives on grid vertices\n ``[n_surf][3 x (radial panels) x (spanwise panels)]``\n dynamic_forces (list(np.ndarray)): Forces associated to time derivatives on grid vertices\n ``[n_surf][3 x (radial panels) x (spanwise panels)]``\n\n u_ext (list(np.ndarray)): Background flow velocity on solid grid panel\n ``[n_surf][3 x (radial panels) x (spanwise panel + 1)]``\n sigma (list(np.ndarray)): Source strength associated to solid panels\n ``[n_surf][3 x radial panel x spanwise panel]``\n sigma_dot (list(np.ndarray)): Time derivative of ``sigma``\n pressure_coefficients (list(np.ndarray)): Pressure coefficient associated to solid panels\n ``[n_surf][radial panel x spanwise panel]``\n\n inertial_total_forces (list(np.ndarray)): Total aerodynamic forces in ``G`` FoR ``[n_surf x 6]``\n body_total_forces (list(np.ndarray)): Total aerodynamic forces in ``A`` FoR ``[n_surf x 6]``\n inertial_steady_forces (list(np.ndarray)): Total aerodynamic steady forces in ``G`` FoR ``[n_surf x 6]``\n body_steady_forces (list(np.ndarray)): Total aerodynamic steady forces in ``A`` FoR ``[n_surf x 6]``\n inertial_unsteady_forces (list(np.ndarray)): Total aerodynamic unsteady forces in ``G`` FoR ``[n_surf x 6]``\n body_unsteady_forces (list(np.ndarray)): Total aerodynamic unsteady forces in ``A`` FoR ``[n_surf x 6]``\n\n postproc_cell (dict): Variables associated to cells to be postprocessed\n postproc_node (dict): Variables associated to panel to be postprocessed\n\n in_global_AFoR (bool): ``True`` if the variables are stored in the global A FoR. ``False`` if they are stored\n in the local A FoR of each body. Always ``True`` for single-body simulations. Currently not used.\n\n Args:\n dimensions (np.ndarray): Matrix defining the dimensions of the vortex grid on solid surfaces\n ``[num_surf x radial panels x spanwise panels]``\n \"\"\"\n def __init__(self, dimensions): #remove dimensions_star as input\n super().__init__(dimensions)\n\n # allocate sigma matrices\n self.sigma = []\n for i_surf in range(self.n_surf):\n self.sigma.append(np.zeros((dimensions[i_surf, 0],\n dimensions[i_surf, 1]),\n dtype=ct.c_double))\n\n self.sigma_dot = []\n for i_surf in range(self.n_surf):\n self.sigma_dot.append(np.zeros((dimensions[i_surf, 0],\n dimensions[i_surf, 1]),\n dtype=ct.c_double))\n\n self.pressure_coefficients = []\n for i_surf in range(self.n_surf):\n self.pressure_coefficients.append(np.zeros((dimensions[i_surf, 0],\n dimensions[i_surf, 1]),\n dtype=ct.c_double))\n def copy(self):\n \"\"\"\n Returns a copy of a deepcopy of a :class:`~sharpy.utils.datastructures.AeroTimeStepInfo`\n \"\"\"\n return self.create_placeholder(NonliftingBodyTimeStepInfo(self.dimensions))\n\n def create_placeholder(self, copied):\n super().create_placeholder(copied)\n\n # allocate sigma matrices\n for i_surf in range(copied.n_surf):\n copied.sigma[i_surf] = self.sigma[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n for i_surf in range(copied.n_surf):\n copied.sigma_dot[i_surf] = self.sigma_dot[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n for i_surf in range(copied.n_surf):\n copied.pressure_coefficients[i_surf] = self.pressure_coefficients[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n\n return copied\n\n\n def generate_ctypes_pointers(self):\n \"\"\"\n Generates the pointers to aerodynamic variables used to interface the C++ library ``uvlmlib``\n \"\"\"\n super().generate_ctypes_pointers()\n\n from sharpy.utils.constants import NDIM\n\n self.ct_sigma_list = []\n for i_surf in range(self.n_surf):\n self.ct_sigma_list.append(self.sigma[i_surf][:, :].reshape(-1))\n\n self.ct_sigma_dot_list = []\n for i_surf in range(self.n_surf):\n self.ct_sigma_dot_list.append(self.sigma_dot[i_surf][:, :].reshape(-1))\n\n self.ct_pressure_coefficients_list = []\n for i_surf in range(self.n_surf):\n self.ct_pressure_coefficients_list.append(self.pressure_coefficients[i_surf][:, :].reshape(-1))\n\n self.ct_p_sigma = ((ct.POINTER(ct.c_double)*len(self.ct_sigma_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_sigma_list]))\n self.ct_p_sigma_dot = ((ct.POINTER(ct.c_double)*len(self.ct_sigma_dot_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_sigma_list]))\n self.ct_p_pressure_coefficients = ((ct.POINTER(ct.c_double)*len(self.ct_pressure_coefficients_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_pressure_coefficients_list]))\n\n\n\nclass AeroTimeStepInfo(TimeStepInfo):\n \"\"\"\n Aerodynamic Time step class.\n\n Contains the relevant aerodynamic attributes for a single time step. All variables should be expressed in ``G``\n FoR unless otherwise stated.\n\n Attributes:\n ct_dimensions: Pointer to ``dimensions`` to interface the C++ library `uvlmlib``\n ct_dimensions_star: Pointer to ``dimensions_star`` to interface the C++ library `uvlmlib``\n\n dimensions (np.ndarray): Matrix defining the dimensions of the vortex grid on solid surfaces\n ``[num_surf x chordwise panels x spanwise panels]``\n dimensions_star (np.ndarray): Matrix defining the dimensions of the vortex grid on wakes\n ``[num_surf x streamwise panels x spanwise panels]``\n\n n_surf (int): Number of aerodynamic surfaces on solid bodies. Each aerodynamic surface on solid bodies will\n have an associted wake.\n\n zeta (list(np.ndarray): Location of solid grid vertices\n ``[n_surf][3 x (chordwise nodes + 1) x (spanwise nodes + 1)]``\n zeta_dot (list(np.ndarray)): Time derivative of ``zeta``\n normals (list(np.ndarray)): Normal direction to panels at the panel center\n ``[n_surf][3 x chordwise nodes x spanwise nodes]``\n forces (list(np.ndarray)): Forces not associated to time derivatives on grid vertices\n ``[n_surf][3 x (chordwise nodes + 1) x (spanwise nodes + 1)]``\n dynamic_forces (list(np.ndarray)): Forces associated to time derivatives on grid vertices\n ``[n_surf][3 x (chordwise nodes + 1) x (spanwise nodes + 1)]``\n zeta_star (list(np.ndarray): Location of wake grid vertices\n ``[n_surf][3 x (streamwise nodes + 1) x (spanwise nodes + 1)]``\n u_ext (list(np.ndarray)): Background flow velocity on solid grid nodes\n ``[n_surf][3 x (chordwise nodes + 1) x (spanwise nodes + 1)]``\n u_ext_star (list(np.ndarray)): Background flow velocity on wake grid nodes\n ``[n_surf][3 x (streamwise nodes + 1) x (spanwise nodes + 1)]``\n gamma (list(np.ndarray)): Circulation associated to solid panels\n ``[n_surf][3 x chordwise nodes x spanwise nodes]``\n gamma_star (list(np.ndarray)): Circulation associated to wake panels\n ``[n_surf][3 x streamwise nodes x spanwise nodes]``\n gamma_dot (list(np.ndarray)): Time derivative of ``gamma``\n\n inertial_total_forces (list(np.ndarray)): Total aerodynamic forces in ``G`` FoR ``[n_surf x 6]``\n body_total_forces (list(np.ndarray)): Total aerodynamic forces in ``A`` FoR ``[n_surf x 6]``\n inertial_steady_forces (list(np.ndarray)): Total aerodynamic steady forces in ``G`` FoR ``[n_surf x 6]``\n body_steady_forces (list(np.ndarray)): Total aerodynamic steady forces in ``A`` FoR ``[n_surf x 6]``\n inertial_unsteady_forces (list(np.ndarray)): Total aerodynamic unsteady forces in ``G`` FoR ``[n_surf x 6]``\n body_unsteady_forces (list(np.ndarray)): Total aerodynamic unsteady forces in ``A`` FoR ``[n_surf x 6]``\n\n postproc_cell (dict): Variables associated to cells to be postprocessed\n postproc_node (dict): Variables associated to nodes to be postprocessed\n\n in_global_AFoR (bool): ``True`` if the variables are stored in the global A FoR. ``False`` if they are stored\n in the local A FoR of each body. Always ``True`` for single-body simulations. Currently not used.\n\n control_surface_deflection (np.ndarray): Deflection of the control surfaces, in `rad` and if fitted.\n\n Args:\n dimensions (np.ndarray): Matrix defining the dimensions of the vortex grid on solid surfaces\n ``[num_surf x chordwise panels x spanwise panels]``\n dimensions_star (np.ndarray): Matrix defining the dimensions of the vortex grid on wakes\n ``[num_surf x streamwise panels x spanwise panels]``\n\n Note, Ben Preston 27/09/24: forces and dynamic forces are stated to be in ``G`` however were actually\n determined to be in ``A``. This issue may apply to other parameters, however errors due to this were only apparent\n in the AeroForcesCalculator postprocessor.\n \"\"\"\n def __init__(self, dimensions, dimensions_star):\n super().__init__(dimensions)\n self.ct_dimensions_star = None\n\n self.dimensions_star = dimensions_star.copy()\n\n # generate placeholder for aero grid zeta_star coordinates\n self.zeta_star = []\n for i_surf in range(self.n_surf):\n self.zeta_star.append(np.zeros((3,\n dimensions_star[i_surf, 0] + 1,\n dimensions_star[i_surf, 1] + 1),\n dtype=ct.c_double))\n\n self.u_ext_star = []\n for i_surf in range(self.n_surf):\n self.u_ext_star.append(np.zeros((3,\n dimensions_star[i_surf, 0] + 1,\n dimensions_star[i_surf, 1] + 1),\n dtype=ct.c_double))\n\n # allocate gamma and gamma star matrices\n self.gamma = []\n for i_surf in range(self.n_surf):\n self.gamma.append(np.zeros((dimensions[i_surf, 0],\n dimensions[i_surf, 1]),\n dtype=ct.c_double))\n\n self.gamma_star = []\n for i_surf in range(self.n_surf):\n self.gamma_star.append(np.zeros((dimensions_star[i_surf, 0],\n dimensions_star[i_surf, 1]),\n dtype=ct.c_double))\n\n self.gamma_dot = []\n for i_surf in range(self.n_surf):\n self.gamma_dot.append(np.zeros((dimensions[i_surf, 0],\n dimensions[i_surf, 1]),\n dtype=ct.c_double))\n\n # Distance from the trailing edge of the wake vertices\n self.dist_to_orig = []\n for i_surf in range(self.n_surf):\n self.dist_to_orig.append(np.zeros((dimensions_star[i_surf, 0] + 1,\n dimensions_star[i_surf, 1] + 1),\n dtype=ct.c_double))\n\n self.wake_conv_vel = []\n for i_surf in range(self.n_surf):\n self.wake_conv_vel.append(np.zeros((dimensions_star[i_surf, 0],\n dimensions_star[i_surf, 1]),\n dtype=ct.c_double))\n\n # Junction handling\n self.flag_zeta_phantom = np.zeros((1, self.n_surf),\n dtype=ct.c_int)\n self.control_surface_deflection = np.array([])\n\n def copy(self):\n return self.create_placeholder(AeroTimeStepInfo(self.dimensions, self.dimensions_star))\n\n def create_placeholder(self, copied):\n super().create_placeholder(copied)\n # generate placeholder for aero grid zeta_star coordinates\n for i_surf in range(copied.n_surf):\n copied.zeta_star[i_surf] = self.zeta_star[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n # placeholder for external velocity\n for i_surf in range(copied.n_surf):\n copied.u_ext_star[i_surf] = self.u_ext_star[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n # allocate gamma and gamma star matrices\n for i_surf in range(copied.n_surf):\n copied.gamma[i_surf] = self.gamma[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n for i_surf in range(copied.n_surf):\n copied.gamma_dot[i_surf] = self.gamma_dot[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n for i_surf in range(copied.n_surf):\n copied.gamma_star[i_surf] = self.gamma_star[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n for i_surf in range(copied.n_surf):\n copied.dist_to_orig[i_surf] = self.dist_to_orig[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n for i_surf in range(copied.n_surf):\n copied.wake_conv_vel[i_surf] = self.wake_conv_vel[i_surf].astype(dtype=ct.c_double, copy=True, order='C')\n\n copied.control_surface_deflection = self.control_surface_deflection.astype(dtype=ct.c_double, copy=True)\n\n # phantom panel flags\n copied.flag_zeta_phantom = self.flag_zeta_phantom.astype(dtype=ct.c_int, copy=True, order='C')\n \n return copied\n\n def generate_ctypes_pointers(self):\n from sharpy.utils.constants import NDIM\n n_surf = len(self.dimensions)\n super().generate_ctypes_pointers()\n self.ct_dimensions_star = self.dimensions_star.astype(dtype=ct.c_uint, copy=True)\n\n self.ct_zeta_star_list = []\n for i_surf in range(self.n_surf):\n for i_dim in range(NDIM):\n self.ct_zeta_star_list.append(self.zeta_star[i_surf][i_dim, :, :].reshape(-1))\n\n self.ct_u_ext_star_list = []\n for i_surf in range(self.n_surf):\n for i_dim in range(NDIM):\n self.ct_u_ext_star_list.append(self.u_ext_star[i_surf][i_dim, :, :].reshape(-1))\n\n self.ct_gamma_list = []\n for i_surf in range(self.n_surf):\n self.ct_gamma_list.append(self.gamma[i_surf][:, :].reshape(-1))\n\n self.ct_gamma_dot_list = []\n for i_surf in range(self.n_surf):\n self.ct_gamma_dot_list.append(self.gamma_dot[i_surf][:, :].reshape(-1))\n\n self.ct_gamma_star_list = []\n for i_surf in range(self.n_surf):\n self.ct_gamma_star_list.append(self.gamma_star[i_surf][:, :].reshape(-1))\n\n self.ct_dist_to_orig_list = []\n for i_surf in range(self.n_surf):\n self.ct_dist_to_orig_list.append(self.dist_to_orig[i_surf][:, :].reshape(-1))\n\n self.ct_wake_conv_vel_list = []\n for i_surf in range(self.n_surf):\n self.ct_wake_conv_vel_list.append(self.wake_conv_vel[i_surf][:, :].reshape(-1))\n self.ct_flag_zeta_phantom_list = self.flag_zeta_phantom[:].reshape(-1)\n \n\n\n self.ct_p_dimensions_star = ((ct.POINTER(ct.c_uint)*n_surf)\n (* np.ctypeslib.as_ctypes(self.ct_dimensions_star)))\n self.ct_p_zeta_star = ((ct.POINTER(ct.c_double)*len(self.ct_zeta_star_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_zeta_star_list]))\n self.ct_p_u_ext_star = ((ct.POINTER(ct.c_double)*len(self.ct_u_ext_star_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_u_ext_star_list]))\n self.ct_p_gamma = ((ct.POINTER(ct.c_double)*len(self.ct_gamma_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_gamma_list]))\n self.ct_p_gamma_dot = ((ct.POINTER(ct.c_double)*len(self.ct_gamma_dot_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_gamma_dot_list]))\n self.ct_p_gamma_star = ((ct.POINTER(ct.c_double)*len(self.ct_gamma_star_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_gamma_star_list]))\n self.ct_p_dist_to_orig = ((ct.POINTER(ct.c_double)*len(self.ct_dist_to_orig_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_dist_to_orig_list]))\n self.ct_p_wake_conv_vel = ((ct.POINTER(ct.c_double)*len(self.ct_wake_conv_vel_list))\n (* [np.ctypeslib.as_ctypes(array) for array in self.ct_wake_conv_vel_list]))\n self.ct_p_flag_zeta_phantom = np.ctypeslib.as_ctypes(self.ct_flag_zeta_phantom_list)\n \n\n\ndef init_matrix_structure(dimensions, with_dim_dimension, added_size=0):\n matrix = []\n for i_surf in range(len(dimensions)):\n if with_dim_dimension:\n matrix.append(np.zeros((3,\n dimensions[i_surf, 0] + added_size,\n dimensions[i_surf, 1] + added_size),\n dtype=ct.c_double))\n else:\n matrix.append(np.zeros((dimensions[i_surf, 0] + added_size,\n dimensions[i_surf, 1] + added_size),\n dtype=ct.c_double))\n return matrix\n\n\ndef standalone_ctypes_pointer(matrix):\n ct_list = []\n n_surf = len(matrix)\n\n if len(matrix[0].shape) == 2:\n # [i_surf][m, n], like gamma\n for i_surf in range(n_surf):\n ct_list.append(matrix[i_surf][:, :].reshape(-1))\n\n elif len(matrix[0].shape) == 3:\n # [i_surf][i_dim, m, n], like zeta\n for i_surf in range(n_surf):\n n_dim = matrix[i_surf].shape[0]\n for i_dim in range(n_dim):\n ct_list.append(matrix[i_surf][i_dim, :, :].reshape(-1))\n\n ct_pointer = ((ct.POINTER(ct.c_double)*len(ct_list))\n (* [np.ctypeslib.as_ctypes(array) for array in ct_list]))\n\n return ct_list, ct_pointer\n\n\nclass StructTimeStepInfo(object):\n \"\"\"\n Structural Time Step Class.\n\n Contains the relevant attributes for the structural description of a single time step.\n\n Attributes:\n in_global_AFoR (bool): ``True`` if the variables are stored in the global A FoR. ``False'' if they are stored\n in the local A FoR of each body. Always ``True`` for single-body simulations\n\n num_node (int): Number of nodes\n num_elem (int): Number of elements\n num_node_elem (int): Number of nodes per element\n\n pos (np.ndarray): Displacements. ``[num_node x 3]`` containing the vector of ``x``, ``y`` and ``z``\n coordinates (in ``A`` frame) of the beam nodes.\n pos_dot (np.ndarray): Velocities. Time derivative of ``pos``.\n pos_ddot (np.ndarray): Accelerations. Time derivative of ``pos_dot``\n\n psi (np.ndarray): Cartesian Rotation Vector. ``[num_elem x num_node_elem x 3]`` CRV for each node in each\n element.\n psi_dot (np.ndarray): Time derivative of ``psi``.\n psi_ddot (np.ndarray): Time derivative of ``psi_dot``.\n\n quat (np.ndarray): Quaternion expressing the transformation between the ``A`` and ``G`` frames.\n for_pos (np.ndarray): ``A`` frame of reference position (with respect to the `G`` frame of reference).\n for_vel (np.ndarray): ``A`` frame of reference velocity. Expressed in A FoR\n for_acc (np.ndarray): ``A`` frame of reference acceleration. Expressed in A FoR\n\n steady_applied_forces (np.ndarray): Forces applied to the structure not associated to time derivatives\n ``[num_nodes x 6]``. Expressed in B FoR\n unsteady_applied_forces (np.ndarray): Forces applied to the structure associated to time derivatives\n ``[num_node x 6]``. Expressed in B FoR\n runtime_steady_forces (np.ndarray): Steady forces generated at runtime through runtime generators\n ``[num_node x 6]``. Expressed in B FoR\n runtime_unsteady_forces (np.ndarray): Unsteady forces generated at runtime through runtime generators\n ``[num_node x 6]``. Expressed in B FoR\n gravity_forces (np.ndarray): Gravity forces at nodes ``[num_node x 6]``. Expressed in A FoR\n\n total_gravity_forces (np.ndarray): Total gravity forces on the structure ``[6]``. Expressed in A FoR\n total_forces (np.ndarray): Total forces applied to the structure ``[6]``. Expressed in A FoR\n\n q (np.ndarray): State vector associated to the structural system of equations ``[num_dof + 10]``\n dqdt (np.ndarray): Time derivative of ``q``\n dqddt (np.ndarray): Time derivative of ``dqdt``\n\n postproc_cell (dict): Variables associated to cells to be postprocessed\n postproc_node (dict): Variables associated to nodes to be postprocessed\n\n psi_local (np.ndarray): Cartesian Rotation Vector for each node in each element in local FoR\n psi_dot_local (np.ndarray): Time derivative of ``psi`` in the local FoR\n mb_FoR_pos (np.ndarray): Position of the local A FoR of each body ``[num_bodies x 6]``\n mb_FoR_vel (np.ndarray): Velocity of the local A FoR of each body ``[num_bodies x 6]``\n mb_FoR_acc (np.ndarray): Acceleration of the local A FoR of each body ``[num_bodies x 6]``\n mb_quat (np.ndarray): Quaternion of the local A FoR of each body ``[num_bodies x 4]``\n mb_dquatdt (np.ndarray): Time derivative of ``mb_quat``\n\n forces_constraints_nodes (np.ndarray): Forces associated to Lagrange Constraints on nodes ``[num_node x 6]``\n forces_constraints_FoR (np.ndarray): Forces associated to Lagrange Contraints on frames of reference\n ``[num_bodies x 10]``\n\n mb_dict (np.ndarray): Dictionary with the multibody information. It comes from the file ``case.mb.h5``\n \"\"\"\n def __init__(self, num_node, num_elem, num_node_elem=3, num_dof=None, num_bodies=1):\n self.in_global_AFoR = True\n self.num_node = num_node\n self.num_elem = num_elem\n self.num_node_elem = num_node_elem\n # generate placeholder for node coordinates\n self.pos = np.zeros((self.num_node, 3), dtype=ct.c_double, order='F')\n self.pos_dot = np.zeros((self.num_node, 3), dtype=ct.c_double, order='F')\n self.pos_ddot = np.zeros((self.num_node, 3), dtype=ct.c_double, order='F')\n\n # placeholder for CRV\n self.psi = np.zeros((self.num_elem, num_node_elem, 3), dtype=ct.c_double, order='F')\n self.psi_dot = np.zeros((self.num_elem, num_node_elem, 3), dtype=ct.c_double, order='F')\n self.psi_ddot = np.zeros((self.num_elem, num_node_elem, 3), dtype=ct.c_double, order='F')\n\n # FoR data\n self.quat = np.array([1., 0, 0, 0], dtype=ct.c_double, order='F')\n self.for_pos = np.zeros((6,), dtype=ct.c_double, order='F')\n self.for_vel = np.zeros((6,), dtype=ct.c_double, order='F')\n self.for_acc = np.zeros((6,), dtype=ct.c_double, order='F')\n\n self.steady_applied_forces = np.zeros((self.num_node, 6), dtype=ct.c_double, order='F')\n self.unsteady_applied_forces = np.zeros((self.num_node, 6), dtype=ct.c_double, order='F')\n self.runtime_steady_forces = np.zeros((self.num_node, 6), dtype=ct.c_double, order='F')\n self.runtime_unsteady_forces = np.zeros((self.num_node, 6), dtype=ct.c_double, order='F')\n self.gravity_forces = np.zeros((self.num_node, 6), dtype=ct.c_double, order='F')\n self.total_gravity_forces = np.zeros((6,), dtype=ct.c_double, order='F')\n self.total_forces = np.zeros((6,), dtype=ct.c_double, order='F')\n\n if num_dof is None:\n # For backwards compatibility\n num_dof = (self.num_node.value - 1)*6\n self.q = np.zeros((num_dof.value + 6 + 4,), dtype=ct.c_double, order='F')\n self.dqdt = np.zeros((num_dof.value + 6 + 4,), dtype=ct.c_double, order='F')\n self.dqddt = np.zeros((num_dof.value + 6 + 4,), dtype=ct.c_double, order='F')\n\n self.postproc_cell = dict()\n self.postproc_node = dict()\n\n # Multibody\n self.psi_local = np.zeros((self.num_elem, num_node_elem, 3), dtype=ct.c_double, order='F')\n self.psi_dot_local = np.zeros((self.num_elem, num_node_elem, 3), dtype=ct.c_double, order='F')\n self.mb_FoR_pos = np.zeros((num_bodies,6), dtype=ct.c_double, order='F')\n self.mb_FoR_vel = np.zeros((num_bodies,6), dtype=ct.c_double, order='F')\n self.mb_FoR_acc = np.zeros((num_bodies,6), dtype=ct.c_double, order='F')\n self.mb_quat = np.zeros((num_bodies,4), dtype=ct.c_double, order='F')\n self.mb_dquatdt = np.zeros((num_bodies, 4), dtype=ct.c_double, order='F')\n self.forces_constraints_nodes = np.zeros((self.num_node, 6), dtype=ct.c_double, order='F')\n self.forces_constraints_FoR = np.zeros((num_bodies, 10), dtype=ct.c_double, order='F')\n self.mb_dict = None\n self.mb_prescribed_dict = None\n\n def copy(self):\n \"\"\"\n Returns a copy of a deepcopy of a :class:`~sharpy.utils.datastructures.StructTimeStepInfo`\n \"\"\"\n copied = StructTimeStepInfo(self.num_node, self.num_elem, self.num_node_elem, ct.c_int(len(self.q)-10),\n self.mb_quat.shape[0])\n\n copied.in_global_AFoR = self.in_global_AFoR\n copied.num_node = self.num_node\n copied.num_elem = self.num_elem\n copied.num_node_elem = self.num_node_elem\n\n # generate placeholder for node coordinates\n copied.pos = self.pos.astype(dtype=ct.c_double, order='F', copy=True)\n copied.pos_dot = self.pos_dot.astype(dtype=ct.c_double, order='F', copy=True)\n copied.pos_ddot = self.pos_ddot.astype(dtype=ct.c_double, order='F', copy=True)\n\n # placeholder for CRV\n copied.psi = self.psi.astype(dtype=ct.c_double, order='F', copy=True)\n copied.psi_dot = self.psi_dot.astype(dtype=ct.c_double, order='F', copy=True)\n copied.psi_ddot = self.psi_ddot.astype(dtype=ct.c_double, order='F', copy=True)\n\n # FoR data\n copied.quat = self.quat.astype(dtype=ct.c_double, order='F', copy=True)\n copied.for_pos = self.for_pos.astype(dtype=ct.c_double, order='F', copy=True)\n copied.for_vel = self.for_vel.astype(dtype=ct.c_double, order='F', copy=True)\n copied.for_acc = self.for_acc.astype(dtype=ct.c_double, order='F', copy=True)\n\n copied.steady_applied_forces = self.steady_applied_forces.astype(dtype=ct.c_double, order='F', copy=True)\n copied.unsteady_applied_forces = self.unsteady_applied_forces.astype(dtype=ct.c_double, order='F', copy=True)\n copied.runtime_steady_forces = self.runtime_steady_forces.astype(dtype=ct.c_double, order='F', copy=True)\n copied.runtime_unsteady_forces = self.runtime_unsteady_forces.astype(dtype=ct.c_double, order='F', copy=True)\n copied.gravity_forces = self.gravity_forces.astype(dtype=ct.c_double, order='F', copy=True)\n copied.total_gravity_forces = self.total_gravity_forces.astype(dtype=ct.c_double, order='F', copy=True)\n copied.total_forces = self.total_forces.astype(dtype=ct.c_double, order='F', copy=True)\n\n copied.q = self.q.astype(dtype=ct.c_double, order='F', copy=True)\n copied.dqdt = self.dqdt.astype(dtype=ct.c_double, order='F', copy=True)\n copied.dqddt = self.dqddt.astype(dtype=ct.c_double, order='F', copy=True)\n\n copied.postproc_cell = copy.deepcopy(self.postproc_cell)\n copied.postproc_node = copy.deepcopy(self.postproc_node)\n\n copied.psi_local = self.psi_local.astype(dtype=ct.c_double, order='F', copy=True)\n copied.psi_dot_local = self.psi_dot_local.astype(dtype=ct.c_double, order='F', copy=True)\n copied.mb_FoR_pos = self.mb_FoR_pos.astype(dtype=ct.c_double, order='F', copy=True)\n copied.mb_FoR_vel = self.mb_FoR_vel.astype(dtype=ct.c_double, order='F', copy=True)\n copied.mb_FoR_acc = self.mb_FoR_acc.astype(dtype=ct.c_double, order='F', copy=True)\n copied.mb_quat = self.mb_quat.astype(dtype=ct.c_double, order='F', copy=True)\n copied.mb_dquatdt = self.mb_dquatdt.astype(dtype=ct.c_double, order='F', copy=True)\n copied.forces_constraints_nodes = self.forces_constraints_nodes.astype(dtype=ct.c_double, order='F', copy=True)\n copied.forces_constraints_FoR = self.forces_constraints_FoR.astype(dtype=ct.c_double, order='F', copy=True)\n\n copied.mb_dict = copy.deepcopy(self.mb_dict)\n copied.mb_prescribed_dict = copy.deepcopy(self.mb_prescribed_dict)\n\n return copied\n\n def glob_pos(self, include_rbm=True):\n \"\"\"\n Returns the position of the nodes in ``G`` FoR\n \"\"\"\n coords = self.pos.copy()\n c = self.cga()\n for i_node in range(self.num_node):\n coords[i_node, :] = np.dot(c, coords[i_node, :])\n if include_rbm:\n coords[i_node, :] += self.for_pos[0:3]\n return coords\n\n def cga(self):\n return algebra.quat2rotation(self.quat)\n\n def cag(self):\n return self.cga().T\n\n def euler_angles(self):\n \"\"\"\n Returns the 3 Euler angles (roll, pitch, yaw) for a given time step.\n\n :returns: `np.array` (roll, pitch, yaw) in radians.\n \"\"\"\n\n return algebra.quat2euler(self.quat)\n\n\n def get_body(self, beam, num_dof_ibody, ibody):\n \"\"\"\n get_body\n\n Extract the body number ``ibody`` from a multibody system\n\n This function returns a :class:`~sharpy.utils.datastructures.StructTimeStepInfo` class (``ibody_StructTimeStepInfo``)\n that only includes the body number ``ibody`` of the original multibody system ``self``\n\n Args:\n beam(:class:`~sharpy.structure.models.beam.Beam`): beam information of the multibody system\n num_dof_ibody (int): Number of degrees of freedom associated to the ``ibody``\n ibody(int): body number to be extracted\n\n Returns:\n \tStructTimeStepInfo: timestep information of the isolated body\n \"\"\"\n\n # Define the nodes and elements belonging to the body\n ibody_elems, ibody_nodes = mb.get_elems_nodes_list(beam, ibody)\n\n ibody_num_node = len(ibody_nodes)\n ibody_num_elem = len(ibody_elems)\n\n ibody_first_dof = 0\n for index_body in range(ibody - 1):\n aux_elems, aux_nodes = mb.get_elems_nodes_list(beam, index_body)\n ibody_first_dof += np.sum(beam.vdof[aux_nodes] > -1)*6\n\n # Initialize the new StructTimeStepInfo\n ibody_StructTimeStepInfo = StructTimeStepInfo(ibody_num_node, ibody_num_elem, self.num_node_elem, num_dof = num_dof_ibody, num_bodies = beam.num_bodies)\n\n # Assign all the variables\n ibody_StructTimeStepInfo.quat = self.mb_quat[ibody, :].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.for_pos = self.mb_FoR_pos[ibody, :].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.for_vel = self.mb_FoR_vel[ibody, :]\n ibody_StructTimeStepInfo.for_acc = self.mb_FoR_acc[ibody, :]\n\n ibody_StructTimeStepInfo.pos = self.pos[ibody_nodes,:].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.pos_dot = self.pos_dot[ibody_nodes,:].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.pos_ddot = self.pos_ddot[ibody_nodes,:].astype(dtype=ct.c_double, order='F', copy=True)\n\n ibody_StructTimeStepInfo.psi = self.psi[ibody_elems,:,:].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.psi_local = self.psi_local[ibody_elems,:,:].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.psi_dot = self.psi_dot[ibody_elems,:,:].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.psi_dot_local = self.psi_dot_local[ibody_elems,:,:].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.psi_ddot = self.psi_ddot[ibody_elems,:,:].astype(dtype=ct.c_double, order='F', copy=True)\n\n ibody_StructTimeStepInfo.steady_applied_forces = self.steady_applied_forces[ibody_nodes,:].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.unsteady_applied_forces = self.unsteady_applied_forces[ibody_nodes,:].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.runtime_steady_forces = self.runtime_steady_forces[ibody_nodes,:].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.runtime_unsteady_forces = self.runtime_unsteady_forces[ibody_nodes,:].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.gravity_forces = self.gravity_forces[ibody_nodes,:].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.total_gravity_forces = self.total_gravity_forces.astype(dtype=ct.c_double, order='F', copy=True)\n\n ibody_StructTimeStepInfo.q[0:num_dof_ibody.value] = self.q[ibody_first_dof:ibody_first_dof+num_dof_ibody.value].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.dqdt[0:num_dof_ibody.value] = self.dqdt[ibody_first_dof:ibody_first_dof+num_dof_ibody.value].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.dqddt[0:num_dof_ibody.value] = self.dqddt[ibody_first_dof:ibody_first_dof+num_dof_ibody.value].astype(dtype=ct.c_double, order='F', copy=True)\n\n ibody_StructTimeStepInfo.dqdt[-10:-4] = ibody_StructTimeStepInfo.for_vel.astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.dqddt[-10:-4] = ibody_StructTimeStepInfo.for_acc.astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.dqdt[-4:] = self.quat.astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.dqddt[-4:] = self.mb_dquatdt[ibody, :].astype(dtype=ct.c_double, order='F', copy=True)\n ibody_StructTimeStepInfo.mb_dquatdt[ibody, :] = self.mb_dquatdt[ibody, :].astype(dtype=ct.c_double, order='F', copy=True)\n\n ibody_StructTimeStepInfo.mb_quat = None\n ibody_StructTimeStepInfo.mb_FoR_pos = None\n ibody_StructTimeStepInfo.mb_FoR_vel = None\n ibody_StructTimeStepInfo.mb_FoR_acc = None\n\n return ibody_StructTimeStepInfo\n\n def compute_psi_local_AFoR(self, for0_pos, for0_vel, quat0):\n \"\"\"\n compute_psi_local_AFoR\n\n Compute psi and psi_dot in the local A frame of reference\n\n Args:\n for0_pos (np.ndarray): Position of the global A FoR\n for0_vel (np.ndarray): Velocity of the global A FoR\n quat0 (np.ndarray): Quaternion of the global A FoR\n \"\"\"\n\n # Define the rotation matrices between the different FoR\n CAslaveG = algebra.quat2rotation(self.quat).T\n CGAmaster = algebra.quat2rotation(quat0)\n Csm = np.dot(CAslaveG, CGAmaster)\n\n for ielem in range(self.psi.shape[0]):\n for inode in range(3):\n self.psi_local[ielem, inode, :] = algebra.rotation2crv(np.dot(Csm,algebra.crv2rotation(self.psi[ielem,inode,:])))\n self.psi_dot_local[ielem, inode, :] = np.zeros((3))\n\n def change_to_local_AFoR(self, for0_pos, for0_vel, quat0):\n \"\"\"\n change_to_local_AFoR\n\n Reference a :class:`~sharpy.utils.datastructures.StructTimeStepInfo` to the local A frame of reference\n\n Args:\n for0_pos (np.ndarray): Position of the global A FoR\n for0_vel (np.ndarray): Velocity of the global A FoR\n quat0 (np.ndarray): Quaternion of the global A FoR\n \"\"\"\n\n # Define the rotation matrices between the different FoR\n CAslaveG = algebra.quat2rotation(self.quat).T\n CGAmaster = algebra.quat2rotation(quat0)\n Csm = np.dot(CAslaveG, CGAmaster)\n\n # Modify position\n for inode in range(self.pos.shape[0]):\n vel_master = (self.pos_dot[inode,:] +\n for0_vel[0:3] +\n algebra.cross3(for0_vel[3:6], self.pos[inode, :]))\n self.pos[inode, :] = np.dot(Csm,self.pos[inode,:]) + np.dot(CAslaveG, for0_pos[0:3] - self.for_pos[0:3])\n self.pos_dot[inode, :] = (np.dot(Csm, vel_master) -\n self.for_vel[0:3] -\n algebra.cross3(self.for_vel[3:6], self.pos[inode,:]))\n\n self.gravity_forces[inode, 0:3] = np.dot(Csm, self.gravity_forces[inode, 0:3])\n self.gravity_forces[inode, 3:6] = np.dot(Csm, self.gravity_forces[inode, 3:6])\n\n # Modify local rotations\n for ielem in range(self.psi.shape[0]):\n for inode in range(3):\n self.psi[ielem, inode, :] = self.psi_local[ielem,inode,:].copy()\n self.psi_dot[ielem, inode, :] = self.psi_dot_local[ielem, inode, :].copy()\n\n\n def change_to_global_AFoR(self, for0_pos, for0_vel, quat0):\n \"\"\"\n Reference a :class:`~sharpy.utils.datastructures.StructTimeStepInfo` to the global A frame of reference\n\n Args:\n for0_pos (np.ndarray): Position of the global A FoR\n for0_vel (np.ndarray): Velocity of the global A FoR\n quat0 (np.ndarray): Quaternion of the global A FoR\n \"\"\"\n\n # Define the rotation matrices between the different FoR\n CGAslave = algebra.quat2rotation(self.quat)\n CAmasterG = algebra.quat2rotation(quat0).T\n Cms = np.dot(CAmasterG, CGAslave)\n\n for inode in range(self.pos.shape[0]):\n vel_slave = (self.pos_dot[inode, :] +\n self.for_vel[0:3] +\n algebra.cross3(self.for_vel[3:6], self.pos[inode, :]))\n self.pos[inode, :] = np.dot(Cms, self.pos[inode,:]) + np.dot(CAmasterG, self.for_pos[0:3] - for0_pos[0:3])\n self.pos_dot[inode, :] = (np.dot(Cms, vel_slave) -\n for0_vel[0:3] -\n algebra.cross3(for0_vel[3:6], self.pos[inode, :]))\n\n self.gravity_forces[inode, 0:3] = np.dot(Cms, self.gravity_forces[inode, 0:3])\n self.gravity_forces[inode, 3:6] = np.dot(Cms, self.gravity_forces[inode, 3:6])\n\n for ielem in range(self.psi.shape[0]):\n for inode in range(3):\n self.psi_local[ielem, inode, :] = self.psi[ielem, inode, :].copy() # Copy here the result from the structural computation\n self.psi_dot_local[ielem, inode, :] = self.psi_dot[ielem, inode, :].copy() # Copy here the result from the structural computation\n\n # psi_slave = self.psi[ielem, inode, :] + np.zeros((3,),)\n self.psi[ielem, inode, :] = algebra.rotation2crv(np.dot(Cms,algebra.crv2rotation(self.psi[ielem,inode,:])))\n\n # Convert psi_dot_local to psi_dot to be used by the rest of the code\n psi_master = self.psi[ielem,inode,:] + np.zeros((3,),)\n cbam = algebra.crv2rotation(psi_master).T\n cbas = algebra.crv2rotation(self.psi_local[ielem, inode, :]).T\n ts = algebra.crv2tan(self.psi_local[ielem, inode, :])\n inv_tm = np.linalg.inv(algebra.crv2tan(psi_master))\n\n self.psi_dot[ielem, inode, :] = np.dot(inv_tm, (np.dot(ts, self.psi_dot_local[ielem, inode, :]) +\n np.dot(cbas, self.for_vel[3:6]) -\n np.dot(cbam, for0_vel[3:6])))\n\n def nodal_b_for_2_a_for(self, nodal, beam, filter=np.array([True]*6), ibody=None):\n \"\"\"\n Projects a nodal variable from the local, body-attached frame (B) to the reference A frame.\n\n Args:\n nodal (np.array): Nodal variable of size ``(num_node, 6)``\n beam (sharpy.datastructures.StructTimeStepInfo): beam info.\n filter (np.array): optional argument that filters and does not convert a specific degree of\n freedom. Defaults to ``np.array([True, True, True, True, True, True])``.\n\n Returns:\n np.array: the ``nodal`` argument projected onto the reference ``A`` frame.\n \"\"\"\n nodal_a = np.zeros_like(nodal)\n for i_node in range(self.num_node):\n # get master elem and i_local_node\n i_master_elem, i_local_node = beam.node_master_elem[i_node, :]\n if ((ibody is None) or (beam.body_number[i_master_elem] == ibody)):\n crv = self.psi[i_master_elem, i_local_node, :]\n cab = algebra.crv2rotation(crv)\n nodal_a[i_node, 0:3] = np.dot(cab, nodal[i_node, 0:3])\n nodal_a[i_node, 3:6] = np.dot(cab, nodal[i_node, 3:6])\n nodal_a *= filter\n\n return nodal_a\n\n def nodal_type_b_for_2_a_for(self, beam,\n force_type=['steady', 'unsteady'],\n filter=np.array([True]*6),\n ibody=None):\n forces_output = []\n for ft in force_type:\n if ft == 'steady':\n fb = self.steady_applied_forces\n elif ft == 'unsteady':\n fb = self.unsteady_applied_forces\n\n forces_output.append(self.nodal_b_for_2_a_for(fb, beam, filter=filter, ibody=ibody))\n\n return forces_output\n\n\n def extract_resultants(self, beam, force_type=['steady', 'unsteady', 'grav'], ibody=None):\n\n forces_output = []\n for ft in force_type:\n totals = np.zeros((6))\n if ft == 'steady':\n fa = self.nodal_type_b_for_2_a_for(beam, force_type=['steady'], ibody=ibody)[0]\n elif ft == 'grav':\n fa = self.gravity_forces.copy()\n elif ft == 'unsteady':\n fa = self.nodal_type_b_for_2_a_for(beam, force_type=['unsteady'], ibody=ibody)[0]\n\n for i_node in range(beam.num_node):\n totals += fa[i_node, :]\n totals[3:6] += algebra.cross3(self.pos[i_node, :],\n fa[i_node, 0:3])\n\n forces_output.append(totals)\n\n return forces_output\n\nclass LinearTimeStepInfo(object):\n \"\"\"\n Linear timestep info containing the state, input and output variables for a given timestep\n\n \"\"\"\n def __init__(self):\n self.x = None\n self.y = None\n self.u = None\n self.t = None\n\n def copy(self):\n copied = LinearTimeStepInfo()\n copied.x = self.x.copy()\n copied.y = self.y.copy()\n copied.u = self.u.copy()\n copied.t = self.t.copy()\n\n\nclass Linear(object):\n \"\"\"\n This is the class responsible for the transfer of information between linear systems\n and can be accessed as ``data.linear``. It stores\n as class attributes the following classes that describe the linearised problem.\n\n Attributes:\n ss (sharpy.linear.src.libss.StateSpace): State-space system\n linear_system (sharpy.linear.utils.ss_interface.BaseElement): Assemble system properties\n tsaero0 (sharpy.utils.datastructures.AeroTimeStepInfo): Linearisation aerodynamic timestep\n tsstruct0 (sharpy.utils.datastructures.StructTimeStepInfo): Linearisation structural timestep\n timestep_info (list): Linear time steps\n \"\"\"\n\n def __init__(self, tsaero0, tsstruct0):\n self.linear_system = None\n self.ss = None\n self.tsaero0 = tsaero0\n self.tsstruct0 = tsstruct0\n self.timestep_info = []\n self.uvlm = None\n self.beam = None\n" }, { "path": "sharpy/utils/docutils.py", "content": "\"\"\"Documentation Generator\n\nFunctions to automatically document the code.\n\nComments and complaints: N. Goizueta\n\"\"\"\nimport os\nimport shutil\nimport inspect\nimport glob\nimport warnings\nimport importlib.util\nimport yaml\nimport sharpy.utils.sharpydir as sharpydir\nimport sharpy.utils.exceptions as exceptions\nimport sharpy.utils.solver_interface as solver_interface\n\n\ndef generate_documentation():\n \"\"\"\n Main routine that generates the documentation in ``./docs/source/includes``\n\n \"\"\"\n print('Cleaning docs/source/includes')\n shutil.rmtree(sharpydir.SharpyDir + '/docs/source/includes/')\n solver_interface.output_documentation() # Solvers and generators have a slightly different generation method\n # generator_interface.output_documentation()\n\n # Main sharpy source code\n sharpy_folders = get_sharpy_folders()\n ignore_modules = yaml.load(open(sharpydir.SharpyDir + '/docs/docignore.yml', 'r'), Loader=yaml.Loader)\n\n for folder in sharpy_folders:\n folder_name = folder.replace(sharpydir.SharpyDir, '')\n folder_name = folder_name[1:]\n if check_folder_in_ignore(folder, ignore_modules['modules']):\n continue\n mtitle, mbody = write_folder(folder, ignore_modules['modules'])\n create_index_files(folder, mtitle, mbody)\n\n main_msg = 'The core SHARPy documentation is found herein.\\n\\n' \\\n '.. note::\\n\\n' \\\n '\\tThe docs are still a work in progress and therefore, ' \\\n 'most functions/classes with which there is not much user interaction are not fully documented. ' \\\n 'We would appreciate any help by means of you contributing to our growing documentation!\\n\\n\\n' \\\n 'If you feel that a function/class is not well documented and, hence, you cannot use it, feel free ' \\\n 'to raise an issue so that we can improve it.\\n\\n'\n\n create_index_files('./', 'SHARPy Source Code', main_msg)\n\n\ndef write_folder(folder, ignore_list):\n \"\"\"\n Creates the documentation for the contents in a folder.\n\n It checks that the file folder is not in the ``ignore_list``. If there is a subfolder in the folder, this gets\n opened, written and an index file is created.\n\n Args:\n folder (str): Absolute path to folder\n ignore_list (list): List with filenames and folders to ignore and skip\n\n Returns:\n tuple: Tuple containing the title and body of the docstring found for it to be added to the index of the\n current folder.\n \"\"\"\n files, mtitle, mbody = open_folder(folder)\n for file in files:\n if os.path.isfile(file) and not check_folder_in_ignore(file, ignore_list):\n if file[-3:] != '.py':\n continue\n write_file(file)\n elif os.path.isdir(file) and not check_folder_in_ignore(file, ignore_list):\n mtitlesub, mbodysub = write_folder(file, ignore_list)\n create_index_files(file, mtitlesub, mbodysub)\n return mtitle, mbody\n\n\ndef write_file(file):\n \"\"\"\n Writes the contents of a python file with one module per page.\n\n Warnings:\n If the function to be written does not have a docstring no output will be produced and a warning will be given.\n\n Args:\n file (str): Absolute path to file\n\n \"\"\"\n file_name = file.replace(sharpydir.SharpyDir, '')\n source = file_name.replace('.py', '')\n outfile = source.replace('sharpy/', '')\n try:\n output_documentation_module_page(source,\n outfile)\n except exceptions.DocumentationError:\n # Future feature- remove try except so it raises the error that no title has been given\n warnings.warn('Module %s not written - no title given' %source)\n\n\ndef check_folder_in_ignore(folder, ignore_list):\n \"\"\"\n Checks whether a folder is in the ``ignore_list``.\n\n Args:\n folder (str): Absolute path to folder\n ignore_list (list): Ignore list\n\n Returns:\n bool: Bool whether file/folder is in ignore list.\n \"\"\"\n file_name_check = folder.replace(sharpydir.SharpyDir, '')\n file_name_check = file_name_check[1:]\n if file_name_check in ignore_list:\n return True\n else:\n return False\n\n\ndef output_documentation_module_page(path_to_module, docs_folder_name):\n \"\"\"\n Generates the documentation for a package with a single page per module in the desired folder\n Returns:\n\n \"\"\"\n\n import_path = path_to_module\n import_path = import_path.replace(sharpydir.SharpyDir, \"\")\n if import_path[0] == \"/\": import_path = import_path[1:]\n import_path = import_path.replace(\"/\", \".\")\n module = importlib.import_module(import_path)\n\n print('Generating documentation files')\n path_to_folder = sharpydir.SharpyDir + '/docs/source/includes/' + docs_folder_name\n\n if os.path.exists(path_to_folder):\n print('Cleaning directory %s' %path_to_folder)\n shutil.rmtree(path_to_folder)\n\n module_content = inspect.getmembers(module)\n\n index_file_content = []\n\n for item in module_content:\n\n if not inspect.isfunction(item[1]) and not inspect.isclass(item[1]):\n continue\n\n md_path = item[1].__module__.split('.')\n if md_path[0] != 'sharpy':\n continue\n\n isclass = False\n if inspect.isclass(item[1]):\n isclass = True\n\n if not item[1].__doc__:\n continue\n if not os.path.exists(path_to_folder):\n print('Creating directory %s' %path_to_folder)\n os.makedirs(path_to_folder, exist_ok=True)\n\n docs = ''\n filename = item[1].__name__ + '.rst'\n index_file_content.append(item[1].__name__)\n\n with open(path_to_folder + '/' + filename, 'w') as outfile:\n title = item[1].__name__\n\n python_method_path = import_path + '.' + title\n\n docs += title + '\\n' + len(title)*'-' + '\\n\\n'\n if isclass:\n docs += '.. autoclass:: ' + python_method_path\n docs += '\\n\\t:members:'\n else:\n docs += '.. automodule:: ' + python_method_path\n\n outfile.write(docs)\n print('\\tCreated %s' % path_to_folder + '/' + filename)\n\n # create index file\n if index_file_content != []:\n with open(path_to_folder + '/index.rst', 'w') as outfile:\n index_title, body = get_module_title_and_body(module)\n\n if module.__doc__ is not None:\n outfile.write(index_title + '\\n' + len(index_title)*'+' + '\\n\\n')\n outfile.write(body + '\\n\\n')\n\n outfile.write('.. toctree::\\n\\t:glob:\\n\\n')\n\n for item in index_file_content:\n outfile.write('\\t./' + item + '\\n')\n\n\ndef output_documentation(package_path, docs_folder_name):\n docs_folder = sharpydir.SharpyDir + '/docs/source/includes/' + docs_folder_name\n if os.path.exists(docs_folder):\n print('Cleaning directory %s' % docs_folder)\n shutil.rmtree(docs_folder)\n print('Creating directory %s' % docs_folder)\n os.makedirs(docs_folder, exist_ok=True)\n\n files = solver_interface.solver_list_from_path(package_path)\n\n index_file_content = []\n\n for file in files:\n module, module_path = module_from_path(package_path, file)\n content = inspect.getmembers(module)\n\n for member in content:\n if member[0].lower() == file:\n title = member[0]\n\n if not member[1].__doc__:\n continue\n\n index_file_content.append(title.lower())\n docs = ''\n docs += title + '\\n' + len(title)*'-' + '\\n\\n'\n\n docs += '.. autoclass:: ' + module_path + '.' + member[1].__name__\n docs += '\\n\\t:members:'\n\n with open(docs_folder + '/' + file + '.rst', 'w') as outfile:\n outfile.write(docs)\n\n print('\\tCreated %s' % docs_folder + '/' + file + '.rst')\n else:\n continue\n\n # create index file\n with open(docs_folder + '/index.rst', 'w') as outfile:\n index_title = docs_folder_name.capitalize()\n outfile.write(index_title + '\\n' + len(index_title)*'+' + '\\n\\n')\n\n outfile.write('.. toctree::\\n\\t:glob:\\n\\n')\n\n for item in index_file_content:\n outfile.write('\\t./' + item + '\\n')\n\n\ndef module_from_path(package_path, filename):\n if filename is None:\n name = inspect.getmodulename(package_path)\n else:\n name = inspect.getmodulename(package_path + '/' + filename + '.py')\n python_path = package_path.replace(sharpydir.SharpyDir, \"\")\n if python_path[0] == '/':\n python_path = python_path[1:]\n python_path = python_path.replace(\"/\", \".\")\n python_path = python_path.replace('.__init__.py', '')\n\n if name == '__init__':\n module_path = python_path\n # module_path = module_path.replace('..py', '')\n else:\n module_path = python_path + '.' + name\n module = importlib.import_module(module_path)\n\n return module, module_path\n\n\ndef create_index_files(docs_folder, folder_title=None, folder_body=None):\n\n file_name = docs_folder.replace(sharpydir.SharpyDir, '')\n source = file_name.replace('.py', '')\n outfile = source.replace('sharpy/', '')\n\n docs_path = sharpydir.SharpyDir + '/docs/source/includes/' + outfile\n\n autodocindexfilename = docs_path + '/index.rst'\n\n rst_files = glob.glob('%s/*/*index.rst' % docs_path)\n # Sort files alphabetically\n rst_files.sort(key=lambda x: x.replace(docs_path, ''))\n\n if folder_title is None:\n folder_title = docs_path.split('/')[-1].capitalize()\n\n if rst_files:\n ordered_list = []\n with open(autodocindexfilename, 'w') as outfile:\n outfile.write(folder_title + '\\n' + len(folder_title)*'-' + '\\n\\n')\n if folder_body is not None:\n outfile.write(folder_body + '\\n')\n outfile.write('.. toctree::\\n\\t:maxdepth: 1\\n\\n')\n for item in rst_files:\n # index_file = item.replace(sharpydir.SharpyDir, '')\n index_file = item.replace(docs_path, '')\n index_file = index_file.replace('.rst', '')\n if index_file[0] != '/':\n outfile.write('\\t./' + index_file + '\\n')\n else:\n outfile.write('\\t.' + index_file + '\\n')\n\n\ndef get_module_title_and_body(module):\n docstring = module.__doc__\n title = None\n body = None\n if docstring is not None:\n docstring = docstring.split('\\n')\n title = docstring[0]\n if title == '':\n try:\n title = docstring[1]\n except IndexError:\n raise exceptions.DocumentationError('Module %s has been given no title in neither the 1st or 2nd '\n 'lines of its docstring'\n % module.__name__)\n\n body = '\\n'.join(docstring[1:])\n else:\n # Had some issues with complete folders not being written if no docs present... need to verify\n # raise exceptions.DocumentationError('Module %s has been given no title in neither the 1st or 2nd lines of '\n # 'its docstring'\n # % module.__name__)\n pass\n return title, body\n\n\ndef get_sharpy_folders():\n sharpy_directory = sharpydir.SharpyDir + '/sharpy/'\n files = glob.glob('%s/*' % sharpy_directory)\n for item in files:\n if not os.path.isdir(item):\n files.remove(item)\n elif item.replace(sharpy_directory, '')[0] == '_':\n files.remove(item)\n return files\n\n\ndef open_folder(folder_path):\n files = glob.glob(folder_path + '/*')\n outfiles = []\n mtitle = None\n mbody = None\n for file in files:\n if file.replace(folder_path, '')[1:] == '__init__.py':\n mtitle, mbody = module_title(file)\n elif file.replace(folder_path, '')[1] != '_':\n outfiles.append(file)\n return outfiles, mtitle, mbody\n\n\ndef module_title(file):\n module, module_path = module_from_path(file, None)\n\n title, body = get_module_title_and_body(module)\n\n return title, body\n\n\nif __name__ == '__main__':\n generate_documentation()\n" }, { "path": "sharpy/utils/exceptions.py", "content": "\"\"\"SHARPy Exception Classes\n\"\"\"\nimport sharpy.utils.cout_utils as cout\n\n\nclass DefaultValueBaseException(Exception):\n def __init__(self, variable, value, message=''):\n super().__init__(message)\n\n def output_message(self, message, color_id=3):\n if cout.cout_wrap is None:\n print(message)\n else:\n cout.cout_wrap.print_separator(3)\n cout.cout_wrap(message, color_id)\n cout.cout_wrap.print_separator(3)\n\n\nclass NoDefaultValueException(DefaultValueBaseException):\n def __init__(self, variable, value=None, message=''):\n super().__init__(message, value)\n self.output_message(\"The variable \" + variable + \" has no default value, please indicate one\")\n\n\nclass NotValidInputFile(Exception):\n def __init__(self, message):\n super().__init__(message)\n\n\nclass NotImplementedSolver(Exception):\n def __init__(self, solver_name, message=''):\n super().__init__(message)\n if cout.cout_wrap is None:\n print(\n \"The solver \" + solver_name + \" is not implemented. Check the list of available solvers when starting SHARPy\")\n else:\n cout.cout_wrap(\n \"The solver \" + solver_name + \" is not implemented. Check the list of available solvers when starting SHARPy\",\n 3)\n\n\nclass NotConvergedStructuralSolver(Exception):\n def __init__(self, solver_name, n_iter=None, message=''):\n super().__init__(message)\n cout.cout_wrap(\"The solver \" + solver_name + \" did not converge in \" + str(n_iter) + \" iterations.\", 3)\n\n\nclass DocumentationError(Exception):\n \"\"\"\n Error in documentation\n \"\"\"\n try:\n cout.cout_wrap('Documentation for module has been given no title')\n except ValueError:\n pass\n\n\nclass NotConvergedSolver(Exception):\n \"\"\"\n To be raised when the solver does not converge. Before this, SHARPy\n would add a pdb trace, but this causes problems when using SHARPy\n as a black box.\n \"\"\"\n pass\n\n\nclass NotValidSetting(DefaultValueBaseException):\n \"\"\"\n Raised when a user gives a setting an invalid value\n \"\"\"\n\n def __init__(self, setting, variable, options, value=None, message=''):\n message = 'The setting %s with entry %s is not one of the valid options: %s' % (setting, variable, options)\n super().__init__(variable, value, message=message)\n self.output_message(message, color_id=4)\n\n\nclass NotValidSettingType(DefaultValueBaseException):\n \"\"\"\n Raised when a user gives a setting with an invalid type\n \"\"\"\n\n def __init__(self, setting, variable, data_types, value=None, message=''):\n message = 'The setting %s with entry %s is not one of the valid types: %s' % (setting, variable, data_types)\n super().__init__(variable, value, message=message)\n self.output_message(message, color_id=4)\n\n\nclass SolverNotFound(Exception):\n def __init__(self, solver_name):\n message = 'The solver %s cannot be found in the list of solvers. Ensure you have spelt the solver name ' \\\n 'correctly.' % solver_name\n super().__init__(message)\n\n\nclass NotRecognisedSetting(DefaultValueBaseException):\n \"\"\"\n Raised when a setting is not recognised\n \"\"\"\n\n def __init__(self, setting, value=None, message=''):\n message = 'Unrecognised setting {:s}. Please check input file and/or documentation'.format(setting)\n super().__init__(variable=None, value=None, message=message)\n self.output_message(message, color_id=4)\n" }, { "path": "sharpy/utils/frequencyutils.py", "content": "\"\"\"Frequency Space Tools\n\n\"\"\"\nimport warnings\n\nimport numpy as np\nimport scipy.linalg as sclalg\n\nfrom sharpy.utils import cout_utils as cout\nimport sharpy.linear.src.libss as libss\n\n\ndef frequency_error(Y_fom, Y_rom, wv):\n n_in = Y_fom.shape[1]\n n_out = Y_fom.shape[0]\n cout.cout_wrap('Computing error in frequency response')\n max_error = np.zeros((n_out, n_in, 2))\n for m in range(n_in):\n for p in range(n_out):\n cout.cout_wrap('m = %g, p = %g' % (m, p))\n max_error[p, m, 0] = error_between_signals(Y_fom[p, m, :].real,\n Y_rom[p, m, :].real,\n wv, 'real')\n max_error[p, m, 1] = error_between_signals(Y_fom[p, m, :].imag,\n Y_rom[p, m, :].imag,\n wv, 'imag')\n\n if np.max(np.log10(max_error)) >= 0:\n warnings.warn('Significant mismatch in the frequency response of the ROM and FOM')\n\n return np.max(max_error)\n\n\ndef error_between_signals(sig1, sig2, wv, sig_title=''):\n abs_error = np.abs(sig1 - sig2)\n max_error = np.max(abs_error)\n max_error_index = np.argmax(abs_error)\n pct_error = max_error/sig1[max_error_index]\n\n max_err_freq = wv[max_error_index]\n if 1e-1 > max_error > 1e-3:\n c = 3\n elif max_error >= 1e-1:\n c = 4\n else:\n c = 1\n cout.cout_wrap('\\tError Magnitude -%s-: log10(error) = %.2f (%.2f pct) at %.2f rad/s'\n % (sig_title, np.log10(max_error), pct_error, max_err_freq), c)\n\n return max_error\n\n\ndef freqresp_relative_error(y1, y2, wv=None, **kwargs):\n r\"\"\"\n Relative error between a reference signal and a second signal.\n\n The error metric is defined as in [1] to be:\n\n .. math:: \\varepsilon_{rel}[\\mathbf{Y}_1, \\mathbf{Y}_2] = \\frac{\\max_{i,j} (\\sup_{w\\in[0, \\bar{w}]}[\\mathbf{Y}_2 -\n \\mathbf{Y}_1]_{i, j})}{\\max_{i,j}(\\sup_{w\\in[0, \\bar{w}]}[\\mathbf{Y}_1]_{i,j})}.\n\n\n Args:\n y1 (np.ndarray): Reference signal frequency response.\n y2 (np.ndarray): Frequency response matrix.\n wv (Optional [np.ndarray]): Array of frequencies. Required when specifying a max and min value\n **kwargs: Key word arguments for max and min frequencies. See below.\n\n Keyword Args\n vmin (float): Lower bound value to find index in ``wv``.\n vmax (float): Upper bound value to find index in ``wv``.\n\n Returns:\n float: Maximum relative error between frequency responses.\n\n References:\n Maraniello, S. and Palacios, R. Parametric Reduced Order Modelling of the Unsteady Vortex Lattice Method.\n AIAA Journal. 2020\n \"\"\"\n p, m, nwv = y1.shape\n\n assert (p, m, nwv) == y2.shape, \"Frequency responses do not have the same number of inputs, \" \\\n \"outputs or evaluation points.\"\n\n # freq_upper_limit = kwargs.get('vmax', None)\n # freq_lower_limit = kwargs.get('vmin', 0)\n #\n # if wv is not None and freq_upper_limit is not None:\n # i_min, i_max = find_limits(wv, vmin=freq_lower_limit, vmax=freq_upper_limit)\n # else:\n # i_min = 0\n # i_max = None\n\n i_min, i_max = find_limits(wv, **kwargs)\n\n err = np.zeros((p, m))\n for pi in range(p):\n for mi in range(m):\n err[pi, mi] = np.max(y1[pi, mi, i_min:i_max] - y2[pi, mi, i_min:i_max]) / np.max(y1[pi, mi, i_min:i_max])\n\n return np.max(err)\n\n\ndef find_limits(wv, **kwargs):\n \"\"\"\n Returns the indices corresponding to the ``vmax`` and ``vmin`` key-word arguments parsed found in the ordered\n array ``wv``.\n\n Args:\n wv (np.ndarray): Ordered range.\n\n Keyword Args:\n vmin (float): Lower bound value to find index in ``wv``.\n vmax (float): Upper bound value to find index in ``wv``.\n\n Returns:\n tuple: Index of ``vmin`` and index of ``vmax``.\n\n \"\"\"\n freq_upper_limit = kwargs.get('vmax', None)\n freq_lower_limit = kwargs.get('vmin', 0)\n\n if wv is not None and freq_upper_limit is not None:\n # find indices in frequencies\n i_max = np.where(freq_upper_limit - wv >= 0)[-1][-1]\n try:\n i_min = np.where(freq_lower_limit - wv >= 0)[-1][-1]\n except IndexError:\n i_min = 0\n\n else:\n i_min = 0\n i_max = None\n\n return i_min, i_max\n\n\ndef frobenius_norm(a):\n r\"\"\"\n Frobenius norm. Also known as Schatten 2-norm or Hilbert-Schmidt norm.\n\n .. math:: ||\\mathbf{A}||_F = \\sqrt{\\mathrm{trace}(\\mathbf{A^*A})}\n\n Args:\n a (np.ndarray): Complex matrix.\n\n Returns:\n float: Frobenius norm of the matrix ``a``.\n\n References:\n Antoulas, A. Approximation to Large Scale Dynamical Systems. SIAM 2005. Ch 3, Eq 3.5\n\n \"\"\"\n\n dims = len(a.shape)\n\n if dims == 1:\n a.shape = (a.shape[0], 1)\n\n a_star = np.conj(a).T\n\n return np.sqrt(np.trace(a_star.dot(a)))\n\n\ndef l2norm(y_freq, wv, **kwargs):\n r\"\"\"\n Computes the L-2 norm of a complex valued function.\n\n .. math:: \\mathcal{L}_2 = \\left(\\int_{-\\infty}^\\infty ||\\mathbf{F}(i\\omega)||^2_{F2}\\,d\\omega\\right)^{0.5}\n\n where :math:`||\\mathbf{F}(i\\omega)||_{F2}` refers to teh Frobenius norm calculated by\n :func:`sharpy.utils.frequencyutils.frobenius_norm`.\n\n Args:\n y_freq (np.ndarray): Complex valued function.\n wv (np.ndarray): Frequency array.\n **kwargs: Key word arguments for max and min frequencies. See below.\n\n Keyword Args\n vmin (float): Lower bound value to find index in ``wv``.\n vmax (float): Upper bound value to find index in ``wv``.\n\n Returns:\n float: L-2 norm of ``y_freq``.\n\n References:\n Antoulas, A. Approximation to Large Scale Dynamical Systems. SIAM 2005. Ch 5, Eq 5.10, pg 126\n \"\"\"\n\n nwv = y_freq.shape[-1]\n\n assert nwv == len(wv), \"Number of frequency evaluations different %g vs %g\" % (nwv, len(wv))\n\n i_min, i_max = find_limits(wv, **kwargs)\n\n freq_range = wv[i_min:i_max].copy()\n\n h2 = np.zeros(len(freq_range)) # frobenius norm at each frequency\n\n for i in range(len(freq_range)):\n h2[i] = frobenius_norm(y_freq[:, :, i]) ** 2\n integral_h2 = np.sqrt(np.max(np.trapz(h2, freq_range)))\n\n return integral_h2\n\n\ndef hamiltonian(gamma, ss):\n \"\"\"\n Returns the Hamiltonian of a linear system as defined in [1].\n\n\n References:\n\n [1] Bruinsma, N. A., & Steinbuch, M. (1990). A fast algorithm to compute the H∞-norm of a transfer function\n matrix. Systems and Control Letters, 14(4), 287–293. https://doi.org/10.1016/0167-6911(90)90049-Z\n\n Args:\n gamma (float): Evaluation point.\n ss (sharpy.linear.src.libss.StateSpace): Linear system.\n\n Returns:\n np.ndarray: Hamiltonian evaluated at ``gamma``.\n \"\"\"\n\n a, b, c, d = ss.get_mats()\n\n p, m = d.shape\n\n r = d.T.dot(d) - gamma ** 2 * np.eye(m)\n s = d.dot(d.T) - gamma ** 2 * np.eye(p)\n\n rinv = sclalg.inv(r)\n sinv = sclalg.inv(s)\n\n ham = np.block([[a - b.dot(rinv.dot(d.T.dot(c))), - gamma * b.dot(rinv.dot(b.T))],\n [gamma * c.T.dot(sinv.dot(c)), - a.T + c.T.dot(d.dot(rinv.dot(b.T)))]])\n return ham\n\n\ndef h_infinity_norm(ss, **kwargs):\n r\"\"\"\n Returns H-infinity norm of a linear system using iterative methods.\n\n The H-infinity norm of a MIMO system is traditionally calculated finding the largest SVD of the\n transfer function evaluated across the entire frequency spectrum. That can prove costly for a\n large number of evaluations, hence the iterative methods of [1] are employed.\n\n In the case of a SISO system the H-infinity norm corresponds to the maximum frequency gain.\n\n A scalar value is returned if the system is stable. If the system is unstable it returns ``np.Inf``.\n\n References:\n\n [1] Bruinsma, N. A., & Steinbuch, M. (1990). A fast algorithm to compute the H∞-norm of a transfer function\n matrix. Systems and Control Letters, 14(4), 287–293. https://doi.org/10.1016/0167-6911(90)90049-Z\n\n Args:\n ss (sharpy.linear.src.libss.StateSpace): Multi input multi output system.\n **kwargs: Key-word arguments.\n\n Keyword Args:\n tol (float (optional)): Tolerance. Defaults to ``1e-7``.\n tol_imag_eigs (float (optional)): Tolerance to find purely imaginary eigenvalues. Defaults to ``1e-7``.\n iter_max (int (optional)): Maximum number of iterations.\n print_info (bool (optional)): Print status and information. Defaults to ``False``.\n\n Returns:\n float: H-infinity norm of the system.\n \"\"\"\n tol = kwargs.get('tol', 1e-7)\n iter_max = kwargs.get('iter_max', 10)\n print_info = kwargs.get('print_info', False)\n\n # tolerance to find purely imaginary eigenvalues i.e those with Re(eig) < tol_imag_eigs\n tol_imag_eigs = kwargs.get('tol_imag_eigs', 1e-7)\n\n if ss.dt is not None:\n ss = libss.disc2cont(ss)\n\n # 1) Compute eigenvalues of original system\n eigs = sclalg.eigvals(ss.A)\n\n if any(eigs.real > tol_imag_eigs):\n if print_info:\n try:\n cout.cout_wrap('System is unstable - H-inf = np.inf')\n except ValueError:\n print('System is unstable - H-inf = np.inf')\n return np.inf\n\n # 2) Find eigenvalue that maximises equation. If all real pick largest eig\n if np.max(np.abs(eigs.imag) < tol_imag_eigs):\n eig_m = np.max(eigs.real)\n else:\n eig_m, _ = max_eigs(eigs)\n\n # 3) Choose best option for gamma_lb\n max_steady_state = np.max(sclalg.svd(ss.transfer_function_evaluation(0), compute_uv=False))\n max_eig_m = np.max(sclalg.svd(ss.transfer_function_evaluation(1j*np.abs(eig_m)), compute_uv=False))\n max_d = np.max(sclalg.svd(ss.D, compute_uv=False))\n\n gamma_lb = max(max_steady_state, max_eig_m, max_d)\n\n iter_num = 0\n\n if print_info:\n try:\n cout.cout_wrap('Calculating H-inf norm\\n{0:>4s} ::::: {1:^8s}'.format('Iter', 'Hinf'))\n except ValueError:\n print('Calculating H_inf norm\\n{0:>4s} ::::: {1:^8s}'.format('Iter', 'Hinf'))\n\n while iter_num < iter_max:\n if print_info:\n try:\n cout.cout_wrap('{0:>4g} ::::: {1:>8.2e}'.format(iter_num, gamma_lb))\n except ValueError:\n print('{0:>4g} ::::: {1:>8.2e}'.format(iter_num, gamma_lb))\n gamma = (1 + 2 * tol) * gamma_lb\n\n # 4) compute hamiltonian and eigenvalues\n ham = hamiltonian(gamma, ss)\n eigs = sclalg.eigvals(ham)\n\n # If eigenvalues all eigenvalues are purely imaginary\n if any(np.abs(eigs.real) < tol_imag_eigs):\n # Select imaginary eigenvalues and those with positive values\n condition_imag = (np.abs(eigs.real) < tol_imag_eigs) * eigs.imag > 0\n imag_eigs = eigs[condition_imag].imag\n\n # Sort them in decreasing order\n order = np.argsort(imag_eigs)[::-1]\n imag_eigs = imag_eigs[order]\n\n if len(imag_eigs) == 1:\n m = imag_eigs[0]\n svdmax = np.max(sclalg.svd(ss.transfer_function_evaluation(1j*m), compute_uv=False))\n\n gamma_lb = svdmax\n else:\n m_list = [0.5 * (imag_eigs[i] + imag_eigs[i+1]) for i in range(len(imag_eigs) - 1)]\n\n svdmax = [np.max(sclalg.svd(ss.transfer_function_evaluation(1j*m), compute_uv=False)) for m in m_list]\n\n gamma_lb = max(svdmax)\n\n else:\n gamma_ub = gamma\n break\n\n iter_num += 1\n\n if iter_num == iter_max:\n raise np.linalg.LinAlgError('Unconverged H-inf solution after %g iterations' % iter_num)\n\n hinf = 0.5 * (gamma_lb + gamma_ub)\n\n return hinf\n\n\ndef max_eigs(eigs):\n r\"\"\"\n Returns the maximum of\n\n .. math:: \\left|\\frac{Im(\\lambda_i)}{Re(\\lambda_i)}\\frac{1}{\\lambda_i}\\right|\n\n for a given array of eigenvalues ``eigs``.\n\n Used as part of the computation of the H infinity norm\n\n\n References:\n\n [1] Bruinsma, N. A., & Steinbuch, M. (1990). A fast algorithm to compute the H∞-norm of a transfer function\n matrix. Systems and Control Letters, 14(4), 287–293. https://doi.org/10.1016/0167-6911(90)90049-Z\n\n Args:\n eigs (np.ndarray): Array of eigenvalues.\n\n Returns:\n complex: Maximum value of function.\n \"\"\"\n func = np.abs(eigs.imag / eigs.real / eigs)\n\n i_max = np.argmax(func)\n\n return func[i_max], i_max\n\n\ndef find_target_system(data, target_system):\n \"\"\"\n Finds target system ``aeroelastic``, ``aerodynamic`` or ``structural``.\n\n Args:\n data (sharpy.PreSharpy): Object containing problem data\n target_system (str): Desired target system.\n\n Returns:\n sharpy.linear.src.libss.StateSpace: State-space object of target system\n \"\"\"\n\n if target_system == 'aeroelastic':\n ss = data.linear.ss\n\n elif target_system == 'structural':\n ss = data.linear.linear_system.beam.ss\n\n elif target_system == 'aerodynamic':\n ss = data.linear.linear_system.uvlm.ss # this could be a ROM\n\n else:\n raise NameError('Unrecognised system')\n\n return ss\n" }, { "path": "sharpy/utils/generate_cases.py", "content": "\"\"\"\nGenerate cases\n\nThis library provides functions and classes to help in the definition of SHARPy cases\n\nExamples:\n\n tests in: tests/utils/generate_cases\n examples: test/coupled/multibody/fix_node_velocity_wrtG/test_fix_node_velocity_wrtG\n test/coupled/multibody/fix_node_velocity_wrtA/test_fix_node_velocity_wrtA\n test/coupled/multibody/double_pendulum/test_double_pendulum_geradin\n test/coupled/prescribed/WindTurbine/test_rotor\n\nNotes:\n\n To use this library: import sharpy.utils.generate_cases as generate_cases\n\n\"\"\"\n\nimport numpy as np\nimport h5py as h5\nimport os\nimport sys\nimport pandas as pd\nimport scipy.integrate\nfrom copy import deepcopy\n\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.solver_interface as solver_interface\nimport sharpy.utils.generator_interface as generator_interface\nimport sharpy.utils.controller_interface as controller_interface\nimport sharpy.structure.utils.lagrangeconstraints as lagrangeconstraints\nimport sharpy.utils.cout_utils as cout\n\nfrom sharpy.structure.utils.lagrangeconstraintsjax import DICT_OF_LC\n\n\nif not cout.check_running_unittest():\n cout.cout_wrap.print_screen = True\n cout.cout_wrap.print_file = False\n\n\n######################################################################\n######################### AUX FUNCTIONS ############################\n######################################################################\ndef get_airfoil_camber(x, y, n_points_camber):\n \"\"\"\n get_airfoil_camber\n\n Define the camber of an airfoil based on its coordinates\n\n Args:\n x (np.array): x coordinates of the airfoil surface\n y (np.array): y coordinates of the airfoil surface\n n_points_camber (int): number of points to define the camber line\n\n Returns:\n camber_x (np.array): x coordinates of the camber line\n camber_y (np.array): y coordinates of the camber line\n\n Notes:\n The x and y vectors are expected in XFOIL format: TE - suction side - LE - pressure side - TE\n\n \"\"\"\n # Returns the airfoil camber for a given set of coordinates (XFOIL format expected)\n\n x = np.array(x, dtype=float)\n y = np.array(y, dtype=float)\n n = len(x)\n imin_x = 0\n\n # Look for the minimum x (it will be assumed as the LE position\n for i in range(n):\n if(x[i] < x[imin_x]):\n imin_x = i\n\n x_suction = np.zeros((imin_x+1, ))\n y_suction = np.zeros((imin_x+1, ))\n x_pressure = np.zeros((n-imin_x, ))\n y_pressure = np.zeros((n-imin_x, ))\n\n for i in range(0, imin_x+1):\n x_suction[i] = x[imin_x-i]\n y_suction[i] = y[imin_x-i]\n\n for i in range(imin_x, n):\n x_pressure[i-imin_x] = x[i]\n y_pressure[i-imin_x] = y[i]\n\n # Compute the camber coordinates\n camber_y = np.zeros((n_points_camber, ))\n camber_x = np.linspace(0.0, 1.0, n_points_camber)\n\n # camber_y=0.5*(np.interp(camber_x,x[imin_x::-1],y[imin_x::-1])+np.interp(camber_x,x[imin_x:],y[imin_x:]))\n camber_y = 0.5*(np.interp(camber_x, x_suction, y_suction) +\n np.interp(camber_x, x_pressure, y_pressure))\n\n # The function should be called as: camber_x, camber_y = get_airfoil_camber(x,y)\n return camber_x, camber_y\n\n\ndef from_node_list_to_elem_matrix(node_list, connectivities):\n \"\"\"\n from_node_list_to_elem_matrix\n\n Convert list of properties associated to nodes to matrix of properties associated\n to elements based on the connectivities\n\n The 'ith' value of the 'node_list' array stores the property of the 'ith' node.\n The 'jth' 'kth' value of the 'elem_matrix' array stores the property of the 'kth' node\n within the 'jth' element\n\n Args:\n node_list (np.array): Properties of the nodes\n connectivities (np.array): Connectivities between the nodes to form elements\n\n Returns:\n elem_matrix (np.array): Properties of the elements\n\n \"\"\"\n\n num_elem = len(connectivities)\n # TODO: change the \"3\" for self.num_node_elem\n elem_matrix = np.zeros((num_elem, 3), dtype=node_list.dtype)\n for ielem in range(num_elem):\n elem_matrix[ielem, :] = node_list[connectivities[ielem, :]]\n\n return elem_matrix\n\n\ndef from_node_array_to_elem_matrix(node_array, connectivities):\n \"\"\"\n from_node_array_to_elem_matrix\n\n Same as the previous function but with an array as input\n \"\"\"\n\n num_elem = len(connectivities)\n prop_size = node_array.shape[1:]\n # TODO: change the \"3\" for self.num_node_elem\n elem_matrix = np.zeros(prop_size + (num_elem, 3), dtype=node_array.dtype)\n for ielem in range(num_elem):\n for inode_in_elem in range(3):\n elem_matrix[:, ielem, inode_in_elem] = node_array[connectivities[ielem, inode_in_elem], :]\n\n return elem_matrix\n\n\ndef read_column_sheet_type01(excel_file_name, excel_sheet, column_name):\n \"\"\"\n read_column_sheet_type01\n\n This function reads a column from an excel file with the following format:\n\n - First row: column_name\n - Second row: units (not read, not checked)\n - Third row: type of data (see below)\n\n Args:\n excel_file_name (string): File name\n excel_sheet (string): Name of the sheet inside the excel file\n column_name (string): Name of the column\n\n Returns:\n var: Data in the excel file according to the type of data defined in the third row\n\n \"\"\"\n\n xls = pd.ExcelFile(excel_file_name)\n excel_db = pd.read_excel(xls, sheet_name=excel_sheet)\n num_elem = excel_db.index.stop - 2\n\n try:\n excel_db[column_name]\n except KeyError:\n return None\n\n if excel_db[column_name][1] == 'one_int':\n var = excel_db[column_name][2]\n elif excel_db[column_name][1] == 'one_float':\n var = excel_db[column_name][2]\n elif excel_db[column_name][1] == 'one_str':\n var = excel_db[column_name][2]\n elif excel_db[column_name][1] == 'vec_int':\n var = np.zeros((num_elem,), dtype=int)\n elif excel_db[column_name][1] == 'vec_float':\n var = np.zeros((num_elem,), dtype=float)\n elif excel_db[column_name][1] == 'vec_str':\n var = np.zeros((num_elem,), dtype=object)\n else:\n raise RuntimeError(\"ERROR: not recognized number type\")\n\n if 'vec' in excel_db[column_name][1]:\n for i in range(2, excel_db.index.stop):\n var[i - 2] = excel_db[column_name][i]\n\n return var\n\n\ndef get_factor_geometric_progression(a0, Sn_target, n):\n r\"\"\"\n This function provides the factor in a geometric series which first element\n is 'a0', has 'n' points and the sum of the spacings is 'Sn_target' approximately.\n\n .. math::\n\n \\sum_{k=1}^n a_0 r^{k-1} = \\frac{a_0 (1 - r^n)}{1 - r}\n\n \"\"\"\n # Given an initial value,\n\n tol = 1e-12\n max_it = 1000\n\n # Case of uniform distribution\n if abs(a0*n - Sn_target) < tol:\n return 1.\n\n # First estimation for r\n if a0*n < Sn_target:\n r = 1.1\n else:\n r = 0.9\n\n # Iterative computation\n error = 2.*tol\n Sn_temp = a0*(1-r**n)/(1-r)\n it = 0\n while ((error > tol) and (it < max_it)):\n derivative = ((1-n*r**(n-1))*(1-r) + (1-r**n))/(1-r)**2\n r += (Sn_target - Sn_temp)/a0/derivative\n Sn_temp = a0*(1-r**n)/(1-r)\n error = abs(Sn_temp - Sn_target)/Sn_target\n it += 1\n\n if it == max_it:\n message = (\"Maximum iterations reached. Sn target:%f . Sn obtained:%f . Relative error: %f\" % (Sn_target, Sn_temp, error))\n cout.cout_wrap(message, 3)\n\n return r\n\n\ndef get_ielem_inode(connectivities, inode):\n\n num_elem, num_node_in_elem = connectivities.shape\n\n for ielem in range(num_elem):\n for inode_in_elem in range(num_node_in_elem):\n if connectivities[ielem, inode_in_elem] == inode:\n return ielem, inode_in_elem\n\n raise RuntimeError(\"ERROR: cannot find ielem and inode_in_elem\")\n\n\ndef get_aoacl0_from_camber(x, y):\n \"\"\"\n This section provies the angle of attack of zero lift for a thin\n airfoil which camber line is defined by 'x' and 'y' coordinates\n\n Check Theory of wing sections. Abbott. pg 69\n \"\"\"\n\n # Scale\n c = x[-1] - x[0]\n xc = (x - x[0])/c\n yc = (y - y[0])/c\n\n # Remove the first and last points that may give rise to problems\n xc = xc[1:-1]\n yc = yc[1:-1]\n\n f1 = 1./(np.pi*(1-xc)*np.sqrt(xc*(1-xc)))\n int = yc*f1\n\n return -scipy.integrate.trapezoid(int, xc)\n\n\ndef get_mu0_from_camber(x, y):\n \"\"\"\n This funrcion provides the constant :math:`\\mu_0` for a thin\n airfoil which camber line is defined by 'x' and 'y' coordinates\n\n Check Theory of wing sections. Abbott. pg 69\n \"\"\"\n\n # Scale\n c = x[-1] - x[0]\n xc = (x - x[0])/c\n yc = (y - y[0])/c\n\n # Remove the first and last points that may give rise to problems\n xc = xc[1:-1]\n yc = yc[1:-1]\n\n f2 = (1. - 2*xc)/np.sqrt(xc*(1. - xc))\n int = yc*f2\n\n return scipy.integrate.trapz(int, xc)\n\n\ndef list_methods(class_instance, print_info=True, clean=True):\n\n list = []\n for str in dir(class_instance):\n func = getattr(class_instance, str)\n if callable(func):\n if clean:\n if not str.startswith(\"__\"):\n list.append(str)\n else:\n list.append(str)\n\n if print_info:\n for str in list:\n print(str)\n\n return list\n\n\ndef set_variable_dict(dictionary, variable, set_value):\n\n if variable in dictionary:\n dictionary[variable] = set_value\n\n for key, value in dictionary.items():\n if isinstance(value, dict):\n set_variable_dict(value, variable, set_value)\n\n\ndef define_or_concatenate(variable, value, axis=0):\n \"\"\"\n if variable is None, value is assigned\n If variable is an array, value is concatenated along axis\n \"\"\"\n if variable is None:\n variable = value\n else:\n variable = np.concatenate((variable, value), axis=axis)\n \n return variable\n\n\n######################################################################\n############### STRUCTURAL INFORMATION #############################\n######################################################################\nclass StructuralInformation():\n \"\"\"\n StructuralInformation\n\n Structural information needed to build a case\n \"\"\"\n\n def __init__(self):\n \"\"\"\n __init__\n\n Initialization\n \"\"\"\n\n # Variables to write in the h5 file\n self.num_node_elem = None\n self.num_node = None\n self.num_elem = None\n self.coordinates = None\n self.connectivities = None\n self.elem_stiffness = None\n self.stiffness_db = None\n self.elem_mass = None\n self.mass_db = None\n self.frame_of_reference_delta = None\n self.structural_twist = None\n self.boundary_conditions = None\n self.beam_number = None\n self.body_number = None\n self.app_forces = None\n self.lumped_mass_nodes = None\n self.lumped_mass = None\n self.lumped_mass_inertia = None\n self.lumped_mass_position = None\n self.lumped_mass_mat = None\n self.lumped_mass_mat_nodes = None\n\n\n def copy(self):\n \"\"\"\n copy\n\n Returns a copy of the object\n\n Returns:\n copied(StructuralInformation): new object with the same properties\n \"\"\"\n copied = StructuralInformation()\n # Variables to write in the h5 file\n copied.num_node_elem = self.num_node_elem\n copied.num_node = self.num_node\n copied.num_elem = self.num_elem\n copied.coordinates = self.coordinates.astype(dtype=float, copy=True)\n copied.connectivities = self.connectivities.astype(dtype=int, copy=True)\n copied.elem_stiffness = self.elem_stiffness.astype(dtype=int, copy=True)\n copied.stiffness_db = self.stiffness_db.astype(dtype=float, copy=True)\n copied.elem_mass = self.elem_mass.astype(dtype=int, copy=True)\n copied.mass_db = self.mass_db.astype(dtype=float, copy=True)\n copied.frame_of_reference_delta = self.frame_of_reference_delta.astype(dtype=float, copy=True)\n copied.structural_twist = self.structural_twist.astype(dtype=float, copy=True)\n copied.boundary_conditions = self.boundary_conditions.astype(dtype=int, copy=True)\n copied.beam_number = self.beam_number.astype(dtype=int, copy=True)\n copied.body_number = self.body_number.astype(dtype=int, copy=True)\n copied.app_forces = self.app_forces.astype(dtype=float, copy=True)\n if isinstance(self.lumped_mass_nodes, np.ndarray):\n copied.lumped_mass_nodes = self.lumped_mass_nodes.astype(dtype=int, copy=True)\n copied.lumped_mass = self.lumped_mass.astype(dtype=float, copy=True)\n copied.lumped_mass_inertia = self.lumped_mass_inertia.astype(dtype=float, copy=True)\n copied.lumped_mass_position = self.lumped_mass_position.astype(dtype=float, copy=True)\n if isinstance(self.lumped_mass_mat_nodes, np.ndarray):\n copied.lumped_mass_mat_nodes = self.lumped_mass_mat_nodes.astype(dtype=int, copy=True)\n copied.lumped_mass_mat = self.lumped_mass_mat.astype(dtype=float, copy=True)\n\n return copied\n\n def set_to_zero(self, num_node_elem, num_node, num_elem,\n num_mass_db=None, num_stiffness_db=None, num_lumped_mass=0,\n num_lumped_mass_mat=0):\n \"\"\"\n set_to_zero\n\n Sets to zero all the variables\n\n Args:\n num_node_elem (int): number of nodes per element\n num_node (int): number of nodes\n num_elem (int): number of elements\n num_mass_db (int): number of different mass matrices in the case\n num_stiffness_db (int): number of different stiffness matrices in the case\n num_lumped_mass (int): number of lumped masses in the case\n num_lumped_mass_mat (int): number of lumped masses given as matrices\n \"\"\"\n\n if num_mass_db is None:\n num_mass_db = self.num_elem\n if num_stiffness_db is None:\n num_stiffness_db = self.num_elem\n\n self.num_node_elem = num_node_elem\n self.num_node = num_node\n self.num_elem = num_elem\n self.coordinates = np.zeros((num_node, 3), dtype=float)\n self.connectivities = np.zeros((num_elem, num_node_elem), dtype=int)\n self.elem_stiffness = np.zeros((num_elem,), dtype=int)\n self.stiffness_db = np.zeros((num_stiffness_db, 6, 6), dtype=float)\n self.elem_mass = np.zeros((num_elem,), dtype=int)\n self.mass_db = np.zeros((num_mass_db, 6, 6), dtype=float)\n self.frame_of_reference_delta = np.zeros((num_elem, num_node_elem, 3),\n dtype=float)\n self.structural_twist = np.zeros((num_elem, num_node_elem), dtype=float)\n self.boundary_conditions = np.zeros((num_node,), dtype=int)\n self.beam_number = np.zeros((num_elem,), dtype=int)\n self.body_number = np.zeros((num_elem,), dtype=int)\n self.app_forces = np.zeros((num_node, 6), dtype=int)\n if not num_lumped_mass == 0:\n self.lumped_mass_nodes = np.zeros((num_lumped_mass,), dtype=int)\n self.lumped_mass = np.zeros((num_lumped_mass,), dtype=float)\n self.lumped_mass_inertia = np.zeros((num_lumped_mass, 3, 3),\n dtype=float)\n self.lumped_mass_position = np.zeros((num_lumped_mass, 3),\n dtype=float)\n if not num_lumped_mass_mat == 0:\n self.lumped_mass_mat_nodes = np.zeros((num_lumped_mass_mat,), dtype=int)\n self.lumped_mass_mat = np.zeros((num_lumped_mass_mat, 6, 6), dtype=float)\n\n\n def generate_full_structure(self,\n num_node_elem,\n num_node,\n num_elem,\n coordinates,\n connectivities,\n elem_stiffness,\n stiffness_db,\n elem_mass,\n mass_db,\n frame_of_reference_delta,\n structural_twist,\n boundary_conditions,\n beam_number,\n app_forces,\n lumped_mass_nodes=None,\n lumped_mass=None,\n lumped_mass_inertia=None,\n lumped_mass_position=None,\n lumped_mass_mat_nodes=None,\n lumped_mass_mat=None):\n \"\"\"\n generate_full_structure\n\n Defines the whole case from the appropiated variables\n\n Args:\n num_node_elem (int): number of nodes per element\n num_node (int): number of nodes\n num_elem (int): number of elements\n coordinates (np.array): nodes coordinates\n connectivities (np.array): element connectivities\n elem_stiffness (np.array): element stiffness index\n stiffness_db (np.array): Stiffness matrices\n elem_mass (np.array): element mass index\n mass_db (np.array): Mass matrices\n frame_of_reference_delta (np.array): element direction of the y axis in the BFoR wrt the AFoR\n structural_twist (np.array): element based twist\n boundary_conditions (np.array): node boundary condition\n beam_number (np.array): node beam number\n app_forces (np.array): steady applied follower forces at the nodes\n lumped_mass_nodes (np.array): nodes with lumped masses\n lumped_mass (np.array): value of the lumped masses\n lumped_mass_inertia (np.array): inertia of the lumped masses\n lumped_mass_position (np.array): position of the lumped masses\n lumped_mass_mat_nodes (np.array): nodes with lumped masses given by matrices\n lumped_mass_mat (np.array): value of the lumped masses given by matrices\n \"\"\"\n\n self.num_node_elem = num_node_elem\n self.num_node = num_node\n self.num_elem = num_elem\n self.coordinates = coordinates\n self.connectivities = connectivities\n self.elem_stiffness = elem_stiffness\n self.stiffness_db = stiffness_db\n self.elem_mass = elem_mass\n self.mass_db = mass_db\n self.frame_of_reference_delta = frame_of_reference_delta\n self.structural_twist = structural_twist\n self.boundary_conditions = boundary_conditions\n self.beam_number = beam_number\n self.body_number = np.zeros((num_elem,), dtype=int)\n self.app_forces = app_forces\n if isinstance(lumped_mass_nodes, np.ndarray):\n self.lumped_mass_nodes = lumped_mass_nodes\n self.lumped_mass = lumped_mass\n self.lumped_mass_inertia = lumped_mass_inertia\n self.lumped_mass_position = lumped_mass_position\n if isinstance(lumped_mass_mat_nodes, np.ndarray):\n self.lumped_mass_mat_nodes = lumped_mass_mat_nodes\n self.lumped_mass_mat = lumped_mass_mat\n\n\n def generate_1to1_from_vectors(self,\n num_node_elem,\n num_node,\n num_elem,\n coordinates,\n stiffness_db,\n mass_db,\n frame_of_reference_delta,\n vec_node_structural_twist,\n num_lumped_mass=0,\n num_lumped_mass_mat=0):\n\n self.num_node_elem = num_node_elem\n self.num_node = num_node\n self.num_elem = num_elem\n self.coordinates = coordinates\n self.create_simple_connectivities()\n self.elem_stiffness = np.linspace(0,self.num_elem - 1, self.num_elem, dtype=int)\n self.stiffness_db = stiffness_db\n self.elem_mass = np.linspace(0,self.num_elem - 1, self.num_elem, dtype=int)\n self.mass_db = mass_db\n self.create_frame_of_reference_delta(y_BFoR=frame_of_reference_delta)\n self.structural_twist = from_node_list_to_elem_matrix(vec_node_structural_twist, self.connectivities)\n self.boundary_conditions = np.zeros((self.num_node,), dtype=int)\n self.beam_number = np.zeros((self.num_elem,), dtype=int)\n self.body_number = np.zeros((self.num_elem,), dtype=int)\n self.app_forces = np.zeros((self.num_node, 6), dtype=float)\n if not num_lumped_mass == 0:\n self.lumped_mass_nodes = np.zeros((num_lumped_mass,), dtype=int)\n self.lumped_mass = np.zeros((num_lumped_mass,), dtype=float)\n self.lumped_mass_inertia = np.zeros((num_lumped_mass, 3, 3), dtype=float)\n self.lumped_mass_position = np.zeros((num_lumped_mass, 3), dtype=float)\n if not num_lumped_mass_mat == 0:\n self.lumped_mass_mat_nodes = np.zeros((num_lumped_mass_mat,), dtype=int)\n self.lumped_mass_mat = np.zeros((num_lumped_mass_mat, 6, 6), dtype=float)\n\n\n def create_frame_of_reference_delta(self, y_BFoR='y_AFoR'):\n \"\"\"\n create_frame_of_reference_delta\n\n Define the coordinates of the yB axis in the AFoR\n\n Args:\n y_BFoR (string): Direction of the yB axis\n \"\"\"\n\n if isinstance(y_BFoR,(list,np.ndarray)):\n yB = np.asarray(y_BFoR)\n cout.cout_wrap((\"WARNING: custom FoR delta defined, using the given value: y_BFoR = {y_BFoR}\" % (y_BFoR)), 3)\n elif y_BFoR == 'x_AFoR':\n yB = np.array([1.0, 0.0, 0.0])\n elif y_BFoR == 'y_AFoR':\n yB = np.array([0.0, 1.0, 0.0])\n elif y_BFoR == 'z_AFoR':\n yB = np.array([0.0, 0.0, 1.0])\n else:\n cout.cout_wrap(\"WARNING: y_BFoR not recognized, using the default value: y_BFoR = y_AFoR\", 3)\n\n # y vector of the B frame of reference\n self.frame_of_reference_delta = np.zeros((self.num_elem,\n self.num_node_elem, 3),\n dtype=float)\n for ielem in range(self.num_elem):\n for inode in range(self.num_node_elem):\n # TODO: do i need to use the connectivities?\n self.frame_of_reference_delta[ielem, inode, :] = yB\n\n def create_mass_db_from_vector(self,\n vec_mass_per_unit_length,\n vec_mass_iner_x,\n vec_mass_iner_y,\n vec_mass_iner_z,\n vec_pos_cg_B,\n vec_mass_iner_yz=None):\n \"\"\"\n create_mass_db_from_vector\n\n Create the mass matrices from the vectors of properties\n\n Args:\n vec_mass_per_unit_length (np.array): masses per unit length\n vec_mass_iner_x (np.array): inertias around the x axis\n vec_mass_iner_y (np.array): inertias around the y axis\n vec_mass_iner_z (np.array): inertias around the z axis\n vec_pos_cg_B (np.array): position of the masses\n vec_mass_iner_yz (np.array): inertias around the yz axis\n \"\"\"\n\n if vec_mass_iner_yz is None:\n vec_mass_iner_yz = np.zeros_like(vec_mass_per_unit_length)\n\n self.mass_db = np.zeros((len(vec_mass_per_unit_length), 6, 6), dtype=float)\n mass = np.zeros((6, 6),)\n for i in range(len(vec_mass_per_unit_length)):\n mass[0:3, 0:3] = np.eye(3)*vec_mass_per_unit_length[i]\n mass[0:3, 3:6] = -1.0*vec_mass_per_unit_length[i]*algebra.skew(vec_pos_cg_B[i])\n mass[3:6, 0:3] = -1.0*mass[0:3, 3:6]\n mass[3:6, 3:6] = np.diag([vec_mass_iner_x[i],\n vec_mass_iner_y[i],\n vec_mass_iner_z[i]])\n mass[4, 5] = vec_mass_iner_yz[i]\n mass[5, 4] = vec_mass_iner_yz[i]\n self.mass_db[i] = mass\n\n def create_stiff_db_from_vector(self,\n vec_EA,\n vec_GAy,\n vec_GAz,\n vec_GJ,\n vec_EIy,\n vec_EIz,\n vec_EIyz=None):\n \"\"\"\n create_stiff_db_from_vector\n\n Create the stiffness matrices from the vectors of properties\n\n Args:\n vec_EA (np.array): Axial stiffness\n vec_GAy (np.array): Shear stiffness in the y direction\n vec_GAz (np.array): Shear stiffness in the z direction\n vec_GJ (np.array): Torsional stiffness\n vec_EIy (np.array): Bending stiffness in the y direction\n vec_EIz (np.array): Bending stiffness in the z direction\n vec_EIyz (np.array): Bending stiffness in the yz direction\n \"\"\"\n\n if vec_EIyz is None:\n vec_EIyz = np.zeros_like(vec_EA)\n\n self.stiffness_db = np.zeros((len(vec_EA), 6, 6),)\n for i in range(len(vec_EA)):\n self.stiffness_db[i] = np.diag([vec_EA[i],\n vec_GAy[i],\n vec_GAz[i],\n vec_GJ[i],\n vec_EIy[i],\n vec_EIz[i]])\n self.stiffness_db[i][4, 5] = vec_EIyz[i]\n self.stiffness_db[i][5, 4] = vec_EIyz[i]\n\n def create_simple_connectivities(self):\n \"\"\"\n create_simple_connectivities\n\n Create the matrix of connectivities for one single beam with the nodes\n ordered in increasing xB direction\n \"\"\"\n self.connectivities = np.zeros((self.num_elem, self.num_node_elem),\n dtype=int)\n for ielem in range(self.num_elem):\n self.connectivities[ielem, :] = (np.array([0, 2, 1], dtype=int) +\n ielem*(self.num_node_elem - 1))\n\n def rotate_around_origin(self, axis, angle):\n \"\"\"\n rotate_around_origin\n\n Rotates a structure\n\n Args:\n axis (np.array): axis of rotation\n angle (float): angle of rotation in radians\n \"\"\"\n\n rot = algebra.rotation_matrix_around_axis(axis, angle)\n for inode in range(len(self.coordinates)):\n self.coordinates[inode, :] = np.dot(rot, self.coordinates[inode, :])\n\n for ielem in range(self.num_elem):\n for inode in range(self.num_node_elem):\n self.frame_of_reference_delta[ielem, inode, :] = np.dot(rot, self.frame_of_reference_delta[ielem, inode, :])\n\n def compute_basic_num_elem(self):\n \"\"\"\n compute_basic_num_elem\n\n It computes the number of elements when no nodes are shared between beams\n \"\"\"\n if ((self.num_node-1) % (self.num_node_elem-1)) == 0:\n self.num_elem = int((self.num_node-1)/(self.num_node_elem-1))\n else:\n raise RuntimeError(\"The number of nodes cannot be converted into \" + self.num_node_elem + \"-noded elements\")\n\n def compute_basic_num_node(self):\n \"\"\"\n compute_basic_num_node\n\n It computes the number of nodes when no nodes are shared between beams\n \"\"\"\n self.num_node = self.num_elem*(self.num_node_elem-1) + 1\n\n def generate_uniform_sym_beam(self,\n node_pos,\n mass_per_unit_length,\n mass_iner,\n EA,\n GA,\n GJ,\n EI,\n num_node_elem=3,\n y_BFoR='y_AFoR',\n num_lumped_mass=0,\n num_lumped_mass_mat=0):\n \"\"\"\n generate_uniform_sym_beam\n\n Generates the input data for SHARPy of a uniform symmetric beam\n\n Args:\n node_pos (np.array): coordinates of the nodes\n mass_per_unit_length (float): mass per unit length\n mass_iner (float): Inertia of the mass\n EA (float): Axial stiffness\n GA (float): Shear stiffness\n GJ (float): Torsional stiffness\n EI (float): Bending stiffness\n num_node_elem (int): number of nodes per element\n y_BFoR (str): orientation of the yB axis\n num_lumped_mass (int): number of lumped masses\n \"\"\"\n self.generate_uniform_beam(node_pos,\n mass_per_unit_length,\n mass_iner,\n mass_iner,\n mass_iner,\n np.zeros((3,),),\n EA,\n GA,\n GA,\n GJ,\n EI,\n EI,\n num_node_elem,\n y_BFoR,\n num_lumped_mass,\n num_lumped_mass_mat)\n\n def generate_uniform_beam(self,\n node_pos,\n mass_per_unit_length,\n mass_iner_x,\n mass_iner_y,\n mass_iner_z,\n pos_cg_B,\n EA,\n GAy,\n GAz,\n GJ,\n EIy,\n EIz,\n num_node_elem=3,\n y_BFoR='y_AFoR',\n num_lumped_mass=0,\n num_lumped_mass_mat=0):\n \"\"\"\n generate_uniform_beam\n\n Generates the input data for SHARPy of a uniform beam\n\n Args:\n node_pos (np.array): coordinates of the nodes\n mass_per_unit_length (float): mass per unit length\n mass_iner_x (float): Inertia of the mass in the x direction\n mass_iner_y (float): Inertia of the mass in the y direction\n mass_iner_z (float): Inertia of the mass in the z direction\n pos_cg_B (np.array): position of the masses\n EA (np.array): Axial stiffness\n GAy (np.array): Shear stiffness in the y direction\n GAz (np.array): Shear stiffness in the z direction\n GJ (np.array): Torsional stiffness\n EIy (np.array): Bending stiffness in the y direction\n EIz (np.array): Bending stiffness in the z direction\n num_node_elem (int): number of nodes per element\n y_BFoR (str): orientation of the yB axis\n num_lumped_mass (int): number of lumped masses\n num_lumped_mass_mat (int): number of lumped masses given as matrices\n \"\"\"\n self.num_node = len(node_pos)\n self.num_node_elem = num_node_elem\n self.compute_basic_num_elem()\n\n self.set_to_zero(self.num_node_elem, self.num_node, self.num_elem, 1, 1,\n num_lumped_mass, num_lumped_mass_mat)\n self.coordinates = node_pos\n self.create_simple_connectivities()\n # self.create_mass_db_from_vector(np.ones((num_elem,),)*mass_per_unit_length,\n # np.ones((num_elem,),)*mass_iner_x,\n # np.ones((num_elem,),)*mass_iner_y,\n # np.ones((num_elem,),)*mass_iner_z,\n # np.ones((num_elem,),)*pos_cg_B])\n # self.create_stiff_db_from_vector(np.ones((num_elem,),)*EA,\n # np.ones((num_elem,),)*GAy,\n # np.ones((num_elem,),)*GAz,\n # np.ones((num_elem,),)*GJ,\n # np.ones((num_elem,),)*EIy,\n # np.ones((num_elem,),)*EIz)\n self.create_mass_db_from_vector(np.array([mass_per_unit_length]),\n np.array([mass_iner_x]),\n np.array([mass_iner_y]),\n np.array([mass_iner_z]),\n np.array([pos_cg_B]))\n self.create_stiff_db_from_vector(np.array([EA]),\n np.array([GAy]),\n np.array([GAz]),\n np.array([GJ]),\n np.array([EIy]),\n np.array([EIz]))\n self.create_frame_of_reference_delta(y_BFoR)\n self.boundary_conditions = np.zeros((self.num_node), dtype=int)\n\n\n def add_lumped_mass(self, node, mass=None, inertia=None, pos=None, mat=None):\n \"\"\"\n Add lumped mass to structure\n \n node(int): Node where the lumped mass is to be placed\n\n For lumped masses:\n mass(float): Mass\n inertia(np.array): 3x3 inertia matrix\n pos(np.array): 3 coordinates of the mass position\n \n For lumped masses described as a 6x6 matrix:\n mat(np.array): 6x6 mass and inertia matrix\n \"\"\"\n\n if (mass is not None) and (inertia is not None):\n if pos is None:\n pos = np.zeros((3))\n if mat is not None:\n raise ValueError(\"mass, inertia and mat cannot be defined at the same time\")\n\n self.lumped_mass_nodes = define_or_concatenate(self.lumped_mass_nodes, np.array([node]), axis=0)\n self.lumped_mass = define_or_concatenate(self.lumped_mass, np.array([mass]), axis=0)\n self.lumped_mass_inertia = define_or_concatenate(self.lumped_mass_inertia, np.array([inertia]), axis=0)\n self.lumped_mass_position = define_or_concatenate(self.lumped_mass_position, np.array([pos]), axis=0)\n\n elif (mat is not None):\n \n self.lumped_mass_mat_nodes = define_or_concatenate(self.lumped_mass_mat_nodes, np.array([node]), axis=0)\n self.lumped_mass_mat = define_or_concatenate(self.lumped_mass_mat, np.array([mat]), axis=0)\n\n\n def assembly_structures(self, *args):\n \"\"\"\n assembly_structures\n\n This function concatenates structures to be writen in the same h5 File\n\n Args:\n *args: list of StructuralInformation() to be meged into 'self'\n\n Notes:\n The structures does NOT merge any node (even if nodes are defined at the same coordinates)\n \"\"\"\n\n total_num_beam = max(self.beam_number)+1\n total_num_body = max(self.body_number)+1\n total_num_node = self.num_node\n total_num_elem = self.num_elem\n total_num_stiff = self.stiffness_db.shape[0]\n total_num_mass = self.mass_db.shape[0]\n\n for structure_to_add in args:\n\n self.coordinates = np.concatenate((self.coordinates, structure_to_add.coordinates), axis=0)\n self.connectivities = np.concatenate((self.connectivities, structure_to_add.connectivities + total_num_node), axis=0)\n assert self.num_node_elem == structure_to_add.num_node_elem, \"num_node_elem does NOT match\"\n self.stiffness_db = np.concatenate((self.stiffness_db, structure_to_add.stiffness_db), axis=0)\n self.elem_stiffness = np.concatenate((self.elem_stiffness, structure_to_add.elem_stiffness + total_num_stiff), axis=0)\n self.mass_db = np.concatenate((self.mass_db, structure_to_add.mass_db), axis=0)\n self.elem_mass = np.concatenate((self.elem_mass, structure_to_add.elem_mass + total_num_mass), axis=0)\n self.frame_of_reference_delta = np.concatenate((self.frame_of_reference_delta, structure_to_add.frame_of_reference_delta), axis=0)\n self.structural_twist = np.concatenate((self.structural_twist, structure_to_add.structural_twist), axis=0)\n self.boundary_conditions = np.concatenate((self.boundary_conditions, structure_to_add.boundary_conditions), axis=0)\n self.beam_number = np.concatenate((self.beam_number, structure_to_add.beam_number + total_num_beam), axis=0)\n self.body_number = np.concatenate((self.body_number, structure_to_add.body_number + total_num_body), axis=0)\n self.app_forces = np.concatenate((self.app_forces, structure_to_add.app_forces), axis=0)\n # self.body_number = np.concatenate((self.body_number, structure_to_add.body_number), axis=0)\n if isinstance(self.lumped_mass_nodes, np.ndarray) and isinstance(structure_to_add.lumped_mass_nodes, np.ndarray):\n self.lumped_mass_nodes = np.concatenate((self.lumped_mass_nodes, structure_to_add.lumped_mass_nodes + total_num_node), axis=0)\n self.lumped_mass = np.concatenate((self.lumped_mass, structure_to_add.lumped_mass), axis=0)\n self.lumped_mass_inertia = np.concatenate((self.lumped_mass_inertia, structure_to_add.lumped_mass_inertia), axis=0)\n self.lumped_mass_position = np.concatenate((self.lumped_mass_position, structure_to_add.lumped_mass_position), axis=0)\n elif isinstance(structure_to_add.lumped_mass_nodes, np.ndarray):\n self.lumped_mass_nodes = structure_to_add.lumped_mass_nodes + total_num_node\n self.lumped_mass = structure_to_add.lumped_mass\n self.lumped_mass_inertia = structure_to_add.lumped_mass_inertia\n self.lumped_mass_position = structure_to_add.lumped_mass_position\n if isinstance(self.lumped_mass_mat_nodes, np.ndarray) and isinstance(structure_to_add.lumped_mass_mat_nodes, np.ndarray):\n self.lumped_mass_mat_nodes = np.concatenate((self.lumped_mass_mat_nodes, structure_to_add.lumped_mass_mat_nodes + total_num_node), axis=0)\n self.lumped_mass_mat = np.concatenate((self.lumped_mass_mat, structure_to_add.lumped_mass_mat), axis=0)\n elif isinstance(structure_to_add.lumped_mass_mat_nodes, np.ndarray):\n self.lumped_mass_mat_nodes = structure_to_add.lumped_mass_mat_nodes + total_num_node\n self.lumped_mass_mat = structure_to_add.lumped_mass_mat\n\n total_num_stiff += structure_to_add.stiffness_db.shape[0]\n total_num_mass += structure_to_add.mass_db.shape[0]\n total_num_beam += max(structure_to_add.beam_number) + 1\n total_num_body += max(structure_to_add.body_number) + 1\n total_num_node += structure_to_add.num_node\n total_num_elem += structure_to_add.num_elem\n\n self.num_node = total_num_node\n self.num_elem = total_num_elem\n\n def check_StructuralInformation(self):\n \"\"\"\n check_StructuralInformation\n\n Check some properties of the StructuralInformation()\n\n Notes:\n These conditions have to be to correctly define a case but they are not the only ones\n \"\"\"\n # CHECKING\n if(self.elem_stiffness.shape[0] != self.num_elem):\n raise RuntimeError(\"ERROR: Element stiffness must be defined for each element\")\n if(self.elem_mass.shape[0] != self.num_elem):\n raise RuntimeError(\"ERROR: Element mass must be defined for each element\")\n if(self.frame_of_reference_delta.shape[0] != self.num_elem):\n raise RuntimeError(\"ERROR: The first dimension of FoR does not match the number of elements\")\n if(self.frame_of_reference_delta.shape[1] != self.num_node_elem):\n raise RuntimeError(\"ERROR: The second dimension of FoR does not match the number of nodes element\")\n if(self.frame_of_reference_delta.shape[2] != 3):\n raise RuntimeError(\"ERROR: The third dimension of FoR must be 3\")\n if(self.structural_twist.shape[0] != self.num_elem):\n raise RuntimeError(\"ERROR: The structural twist must be defined for each element\")\n if(self.boundary_conditions.shape[0] != self.num_node):\n raise RuntimeError(\"ERROR: The boundary conditions must be defined for each node\")\n if(self.beam_number.shape[0] != self.num_elem):\n raise RuntimeError(\"ERROR: The beam number must be defined for each element\")\n if(self.app_forces.shape[0] != self.num_node):\n raise RuntimeError(\"ERROR: The first dimension of the applied forces matrix does not match the number of nodes\")\n if(self.app_forces.shape[1] != 6):\n raise RuntimeError(\"ERROR: The second dimension of the applied forces matrix must be 6\")\n\n default = StructuralInformation()\n\n for attr, value in self.__dict__.items():\n if not hasattr(default, attr):\n raise RuntimeError((\"StructuralInformation has no attribute named '%s'\" % attr))\n\n def generate_fem_file(self, route, case_name):\n \"\"\"\n generate_fem_file\n\n Writes the h5 file with the structural information\n\n Args:\n route (string): path of the case\n case_name (string): name of the case\n \"\"\"\n \t# TODO: check variables that are not defined\n self.check_StructuralInformation()\n # Writting the file\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n # TODO: include something to write only exsisting variables\n h5file.create_dataset('coordinates', data=self.coordinates)\n h5file.create_dataset('connectivities', data=self.connectivities)\n h5file.create_dataset('num_node_elem', data=self.num_node_elem)\n h5file.create_dataset('num_node', data=self.num_node)\n h5file.create_dataset('num_elem', data=self.num_elem)\n h5file.create_dataset('stiffness_db', data=self.stiffness_db)\n h5file.create_dataset('elem_stiffness', data=self.elem_stiffness)\n h5file.create_dataset('mass_db', data=self.mass_db)\n h5file.create_dataset('elem_mass', data=self.elem_mass)\n h5file.create_dataset('frame_of_reference_delta', data=self.frame_of_reference_delta)\n h5file.create_dataset('structural_twist', data=self.structural_twist)\n h5file.create_dataset('boundary_conditions', data=self.boundary_conditions)\n h5file.create_dataset('beam_number', data=self.beam_number)\n h5file.create_dataset('body_number', data=self.body_number)\n h5file.create_dataset('app_forces', data=self.app_forces)\n # h5file.create_dataset('body_number', data=self.body_number)\n if isinstance(self.lumped_mass_nodes, np.ndarray):\n h5file.create_dataset('lumped_mass_nodes', data=self.lumped_mass_nodes)\n h5file.create_dataset('lumped_mass', data=self.lumped_mass)\n h5file.create_dataset('lumped_mass_inertia', data=self.lumped_mass_inertia)\n h5file.create_dataset('lumped_mass_position', data=self.lumped_mass_position)\n if isinstance(self.lumped_mass_mat_nodes, np.ndarray):\n h5file.create_dataset('lumped_mass_mat_nodes', data=self.lumped_mass_mat_nodes)\n h5file.create_dataset('lumped_mass_mat', data=self.lumped_mass_mat)\n\n\n######################################################################\n############### BLADE AERODYNAMIC INFORMATION ######################\n######################################################################\nclass AerodynamicInformation():\n \"\"\"\n AerodynamicInformation\n\n Aerodynamic information needed to build a case\n\n Note:\n It should be defined after the StructuralInformation of the case\n \"\"\"\n\n def __init__(self):\n \"\"\"\n __init__\n\n Initialization\n \"\"\"\n self.aero_node = None\n self.chord = None\n self.twist = None\n self.sweep = None\n self.surface_m = None\n self.surface_distribution = None\n self.m_distribution = None\n self.elastic_axis = None\n self.airfoil_distribution = None\n # TODO: allow airfoils to be of different length (like user_defined_m_distribution)\n self.airfoils = None\n self.user_defined_m_distribution = [None]\n # TODO: Define the following variables at some point\n # self.control_surface = None\n # self.control_surface_type = None\n # self.control_surface_deflection = None\n # self.control_surface_chord = None\n # self.control_surface_hinge_coords = None\n self.polars = None\n self.first_twist = [None]\n\n def copy(self):\n \"\"\"\n copy\n\n Returns a copy of the object\n\n Returns:\n copied(AerodynamicInformation): new object with the same properties\n \"\"\"\n copied = AerodynamicInformation()\n\n copied.aero_node = self.aero_node.astype(dtype=bool, copy=True)\n copied.chord = self.chord.astype(dtype=float, copy=True)\n copied.twist = self.twist.astype(dtype=float, copy=True)\n copied.sweep = self.sweep.astype(dtype=float, copy=True)\n copied.surface_m = self.surface_m.astype(dtype=int, copy=True)\n copied.surface_distribution = self.surface_distribution.astype(dtype=int, copy=True)\n copied.m_distribution = self.m_distribution\n copied.elastic_axis = self.elastic_axis.astype(dtype=float, copy=True)\n copied.airfoil_distribution = self.airfoil_distribution.astype(dtype=int, copy=True)\n copied.airfoils = self.airfoils.astype(dtype=float, copy=True)\n copied.user_defined_m_distribution = self.user_defined_m_distribution.copy()\n if self.polars is not None:\n copied.polars = self.polars.copy()\n copied.first_twist = self.first_twist.copy()\n\n return copied\n\n def set_to_zero(self, num_node_elem, num_node, num_elem,\n num_airfoils=1, num_surfaces=0, num_points_camber=100):\n \"\"\"\n set_to_zero\n\n Sets to zero all the variables\n\n Args:\n num_node_elem (int): number of nodes per element\n num_node (int): number of nodes\n num_elem (int): number of elements\n num_airfoils (int): number of different airfoils\n num_surfaces (int): number of aerodynamic surfaces\n num_points_camber (int): number of points to define the camber line of the airfoil\n \"\"\"\n self.aero_node = np.zeros((num_node,), dtype=bool)\n self.chord = np.ones((num_elem, num_node_elem), dtype=float)\n self.twist = np.zeros((num_elem, num_node_elem), dtype=float)\n self.sweep = np.zeros((num_elem, num_node_elem), dtype=float)\n # TODO: SHARPy does not ignore the surface_m when the surface is not aerodynamic\n self.surface_m = np.array([], dtype=int)\n # self.surface_m = np.array([], dtype=int)\n self.surface_distribution = np.zeros((num_elem,), dtype=int) - 1\n self.m_distribution = 'uniform'\n self.elastic_axis = np.zeros((num_elem, num_node_elem), dtype=float)\n self.airfoil_distribution = np.zeros((num_elem, num_node_elem), dtype=int)\n self.airfoils = np.zeros((num_airfoils, num_points_camber, 2), dtype=float)\n for iairfoil in range(num_airfoils):\n self.airfoils[iairfoil, :, 0] = np.linspace(0.0, 1.0, num_points_camber)\n self.first_twist = [True]\n\n def generate_full_aerodynamics(self,\n aero_node,\n chord,\n twist,\n sweep,\n surface_m,\n surface_distribution,\n m_distribution,\n elastic_axis,\n airfoil_distribution,\n airfoils,\n first_twist):\n \"\"\"\n generate_full_aerodynamics\n\n Defines the whole case from the appropiated variables\n\n Args:\n aero_node (np.array): defines if a node has aerodynamic properties or not\n chord (np.array): chord of the elements\n twist (np.array): twist of the elements\n sweep (np.array): sweep of the elements\n surface_m (np.array): Number of panels in the chord direction\n surface_distribution (np.array): Surface at which each element belongs\n m_distribution (str): distribution of the panels along the chord\n elastic_axis (np.array): position of the elastic axis in the chord\n airfoil_distribution (np.array): airfoil at each element node\n airfoils (np.array): coordinates of the camber lines of the airfoils\n first_twist (list(bool)): Apply the twist rotation before the sweep\n \"\"\"\n\n self.aero_node = aero_node\n self.chord = chord\n self.twist = twist\n self.sweep = sweep\n self.surface_m = surface_m\n self.surface_distribution = surface_distribution\n self.m_distribution = m_distribution\n self.elastic_axis = elastic_axis\n self.airfoil_distribution = airfoil_distribution\n self.airfoils = airfoils\n self.first_twist = first_twist\n\n def create_aerodynamics_from_vec(self,\n StructuralInformation,\n vec_aero_node,\n vec_chord,\n vec_twist,\n vec_sweep,\n vec_surface_m,\n vec_surface_distribution,\n vec_m_distribution,\n vec_elastic_axis,\n vec_airfoil_distribution,\n airfoils,\n user_defined_m_distribution=None,\n first_twist=True):\n \"\"\"\n create_aerodynamics_from_vec\n\n Defines the whole case from the appropiated variables in vector form (associated to nodes)\n\n Args:\n StructuralInformation (StructuralInformation): Structural infromation of the case\n vec_aero_node (np.array): defines if a node has aerodynamic properties or not\n vec_chord (np.array): chord of the nodes\n vec_twist (np.array): twist of the nodes\n vec_sweep (np.array): sweep of the nodes\n vec_surface_m (np.array): Number of panels in the chord direction\n vec_surface_distribution (np.array): Surface at which each element belongs\n vec_m_distribution (np.array): distribution of the panels along the chord\n vec_elastic_axis (np.array): position of the elastic axis in the chord\n vec_airfoil_distribution (np.array): airfoil at each element node\n airfoils (np.array): coordinates of the camber lines of the airfoils\n first_twist (bool): Apply the twist rotation before the sweep\n \"\"\"\n self.aero_node = vec_aero_node\n\n self.chord = from_node_list_to_elem_matrix(vec_chord, StructuralInformation.connectivities)\n self.twist = from_node_list_to_elem_matrix(vec_twist, StructuralInformation.connectivities)\n self.sweep = from_node_list_to_elem_matrix(vec_sweep, StructuralInformation.connectivities)\n self.elastic_axis = from_node_list_to_elem_matrix(vec_elastic_axis, StructuralInformation.connectivities)\n self.airfoil_distribution = from_node_list_to_elem_matrix(vec_airfoil_distribution, StructuralInformation.connectivities)\n\n self.surface_m = vec_surface_m\n self.surface_distribution = vec_surface_distribution\n self.m_distribution = vec_m_distribution\n\n self.airfoils = airfoils\n\n # TODO: this may not work for different surfaces\n if vec_m_distribution == 'user_defined':\n udmd_by_elements = from_node_array_to_elem_matrix(user_defined_m_distribution, StructuralInformation.connectivities)\n self.user_defined_m_distribution = [udmd_by_elements]\n\n self.first_twist = [first_twist]\n\n def create_one_uniform_aerodynamics(self,\n StructuralInformation,\n chord,\n twist,\n sweep,\n num_chord_panels,\n m_distribution,\n elastic_axis,\n num_points_camber,\n airfoil,\n first_twist=True):\n \"\"\"\n create_one_uniform_aerodynamics\n\n Defines the whole case from the appropiated variables constant at every point\n\n Args:\n StructuralInformation (StructuralInformation): Structural infromation of the case\n chord (float): chord\n twist (float): twist\n sweep (float): sweep\n num_chord_panels (int): Number of panels in the chord direction\n m_distribution (str): distribution of the panels along the chord\n elastic_axis (float): position of the elastic axis in the chord\n num_points_camber (int): Number of points to define the camber line\n airfoils (np.array): coordinates of the camber lines of the airfoils\n first_twist (bool): Apply the twist rotation before the sweep\n \"\"\"\n num_node = StructuralInformation.num_node\n num_node_elem = StructuralInformation.num_node_elem\n num_elem = StructuralInformation.num_elem\n\n self.aero_node = np.ones((num_node,), dtype = bool)\n self.chord = chord*np.ones((num_elem, num_node_elem), dtype=float)\n self.twist = twist*np.ones((num_elem, num_node_elem), dtype=float)\n self.sweep = sweep*np.ones((num_elem, num_node_elem), dtype=float)\n # TODO: SHARPy does not ignore the surface_m when the surface is not aerodynamic\n #self.surface_m = np.array([0], dtype = int)\n self.surface_m = np.array([num_chord_panels], dtype=int)\n self.surface_distribution = np.zeros((num_elem,), dtype=int)\n self.m_distribution = m_distribution\n self.elastic_axis = elastic_axis*np.ones((num_elem, num_node_elem), dtype=float)\n self.airfoil_distribution = np.zeros((num_elem, num_node_elem), dtype=int)\n self.airfoils = np.zeros((1, num_points_camber, 2), dtype=float)\n self.airfoils = airfoil\n\n if m_distribution == 'user_defined':\n self.user_defined_m_distribution = []\n self.user_defined_m_distribution.append(np.zeros((num_chord_panels + 1, num_elem, num_node_elem)))\n\n self.first_twist = [first_twist]\n\n def change_airfoils_discretezation(self, airfoils, new_num_nodes):\n \"\"\"\n change_airfoils_discretezation\n\n Changes the discretization of the matrix of airfoil coordinates\n\n Args:\n airfoils (np.array): Matrix with the x-y coordinates of all the airfoils to be modified\n new_num_nodes (int): Number of points that the output coordinates will have\n\n Return:\n new_airfoils (np.array): Matrix with the x-y coordinates of all the airfoils with the new discretization\n\n \"\"\"\n nairfoils = airfoils.shape[0]\n new_airfoils = np.zeros((nairfoils, new_num_nodes, 2), dtype=float)\n\n for iairfoil in range(nairfoils):\n new_airfoils[iairfoil, :, 0] = np.linspace(airfoils[iairfoil, 0, 0], airfoils[iairfoil, -1, 0], new_num_nodes)\n new_airfoils[iairfoil, :, 1] = np.interp(new_airfoils[iairfoil, :, 0], airfoils[iairfoil, :, 0], airfoils[iairfoil, :, 1])\n\n return new_airfoils\n\n def assembly_aerodynamics(self, *args):\n \"\"\"\n assembly_aerodynamics\n\n This function concatenates aerodynamic properties to be writen in the same h5 File\n\n Args:\n *args: list of AerodynamicInformation() to be meged into 'self'\n \"\"\"\n\n total_num_airfoils = len(self.airfoils[:, 0, 0])\n # total_num_surfaces = len(self.surface_m)\n total_num_surfaces = np.sum(self.surface_m != -1)\n # TODO: check why I only need one definition of m and not one per surface\n\n for aerodynamics_to_add in args:\n self.chord = np.concatenate((self.chord, aerodynamics_to_add.chord), axis=0)\n self.twist = np.concatenate((self.twist, aerodynamics_to_add.twist), axis=0)\n self.sweep = np.concatenate((self.sweep, aerodynamics_to_add.sweep), axis=0)\n # self.m_distribution = np.concatenate((self.m_distribution, aerodynamics_to_add.m_distribution), axis=0)\n assert self.m_distribution == aerodynamics_to_add.m_distribution, \"m_distribution does not match\"\n for isurf in range(len(aerodynamics_to_add.surface_distribution)):\n if aerodynamics_to_add.surface_distribution[isurf] != -1:\n # print(self.surface_distribution)\n # print(aerodynamics_to_add.surface_distribution[isurf])\n self.surface_distribution = np.concatenate((self.surface_distribution, np.array([aerodynamics_to_add.surface_distribution[isurf]], dtype=int) + total_num_surfaces), axis=0)\n else:\n self.surface_distribution = np.concatenate((self.surface_distribution, np.array([aerodynamics_to_add.surface_distribution[isurf]], dtype=int)), axis=0)\n self.surface_m = np.concatenate((self.surface_m, aerodynamics_to_add.surface_m), axis=0)\n self.aero_node = np.concatenate((self.aero_node, aerodynamics_to_add.aero_node), axis=0)\n self.elastic_axis = np.concatenate((self.elastic_axis, aerodynamics_to_add.elastic_axis), axis=0)\n # np.concatenate((self.airfoil_distribution, aerodynamics_to_add.airfoil_distribution), axis=0)\n self.airfoil_distribution = np.concatenate((self.airfoil_distribution, aerodynamics_to_add.airfoil_distribution + total_num_airfoils), axis=0)\n # TODO: this should NOT be needed according to SHARPy input files. Modify at some point\n if (self.airfoils.shape[1] == aerodynamics_to_add.airfoils.shape[1]):\n self.airfoils = np.concatenate((self.airfoils, aerodynamics_to_add.airfoils), axis=0)\n elif (self.airfoils.shape[1] > aerodynamics_to_add.airfoils.shape[1]):\n cout.cout_wrap(\"WARNING: redefining the discretization of airfoil camber line\", 3)\n new_airfoils = self.change_airfoils_discretezation(aerodynamics_to_add.airfoils, self.airfoils.shape[1])\n self.airfoils = np.concatenate((self.airfoils, new_airfoils), axis=0)\n elif (self.airfoils.shape[1] < aerodynamics_to_add.airfoils.shape[1]):\n cout.cout_wrap(\"WARNING: redefining the discretization of airfoil camber line\", 3)\n new_airfoils = self.change_airfoils_discretezation(self.airfoils, aerodynamics_to_add.airfoils.shape[1])\n self.airfoils = np.concatenate((new_airfoils, aerodynamics_to_add.airfoils), axis=0)\n if self.m_distribution.lower() == 'user_defined':\n self.user_defined_m_distribution = self.user_defined_m_distribution + aerodynamics_to_add.user_defined_m_distribution\n if self.polars is not None:\n self.polars = np.array([self.polars, aerodynamics_to_add.polars])\n total_num_airfoils += len(aerodynamics_to_add.airfoils[:, 0, 0])\n # total_num_surfaces += len(aerodynamics_to_add.surface_m)\n total_num_surfaces += np.sum(aerodynamics_to_add.surface_m != -1)\n\n self.first_twist.extend(aerodynamics_to_add.first_twist)\n # self.num_airfoils = total_num_airfoils\n # self.num_surfaces = total_num_surfaces\n\n def interpolate_airfoils_camber(self, pure_airfoils_camber, r_pure_airfoils, r, n_points_camber):\n \"\"\"\n interpolate_airfoils_camber\n\n Create the camber of the airfoil at each node position from the camber of the\n pure airfoils present in the blade\n\n Args:\n pure_airfoils_camber (np.array): xy coordinates of the camber lines of the pure airfoils\n r_pure_airfoils (np.array): radial position of the pure airfoils\n r (np.array): radial positions to compute the camber lines through linear interpolation\n\n Returns:\n airfoils_camber (np.array): camber lines at the new radial positions\n\n \"\"\"\n num_node = len(r)\n airfoils_camber = np.zeros((num_node, n_points_camber, 2),)\n\n for inode in range(num_node):\n # camber_x, camber_y = get_airfoil_camber(x,y)\n\n iairfoil = 0\n while(r[inode] > r_pure_airfoils[iairfoil]):\n iairfoil += 1\n if(iairfoil == len(r_pure_airfoils)):\n iairfoil -= 1\n break\n\n # print(\"interpolating between: \", iairfoil-1, \"and\", iairfoil)\n beta = min((r[inode]-r_pure_airfoils[iairfoil-1])/(r_pure_airfoils[iairfoil]-r_pure_airfoils[iairfoil-1]), 1.0)\n beta = max(0.0, beta)\n\n airfoils_camber[inode, :, 0] = (1 - beta)*pure_airfoils_camber[iairfoil-1, :, 0] + beta*pure_airfoils_camber[iairfoil, :, 0]\n airfoils_camber[inode, :, 1] = (1 - beta)*pure_airfoils_camber[iairfoil-1, :, 1] + beta*pure_airfoils_camber[iairfoil, :, 1]\n\n return airfoils_camber\n\n def interpolate_airfoils_camber_thickness(self, pure_airfoils_camber, thickness_pure_airfoils, blade_thickness, n_points_camber):\n \"\"\"\n interpolate_airfoils_camber_thickness\n\n Create the camber of the airfoil at each node position from the camber of the\n pure airfoils present in the blade based on the thickness\n\n Args:\n pure_airfoils_camber (np.array): xy coordinates of the camber lines of the pure airfoils\n thicknesss_pure_airfoils (np.array): thickness of the pure airfoils\n blade_thickness (np.array): thickness of the blade positions\n\n Returns:\n airfoils_camber (np.array): camber lines at the new radial positions\n\n \"\"\"\n num_node = len(blade_thickness)\n airfoils_camber = np.zeros((num_node, n_points_camber, 2),)\n\n for inode in range(num_node):\n # camber_x, camber_y = get_airfoil_camber(x,y)\n\n iairfoil = 0\n while(blade_thickness[inode] < thickness_pure_airfoils[iairfoil]):\n iairfoil += 1\n if(iairfoil == len(thickness_pure_airfoils)):\n iairfoil -= 1\n break\n\n beta = min((blade_thickness[inode] - thickness_pure_airfoils[iairfoil - 1])/(thickness_pure_airfoils[iairfoil] - thickness_pure_airfoils[iairfoil - 1]), 1.0)\n beta = max(0.0, beta)\n\n airfoils_camber[inode, :, 0] = (1 - beta)*pure_airfoils_camber[iairfoil-1, :, 0] + beta*pure_airfoils_camber[iairfoil, :, 0]\n airfoils_camber[inode, :, 1] = (1 - beta)*pure_airfoils_camber[iairfoil-1, :, 1] + beta*pure_airfoils_camber[iairfoil, :, 1]\n\n return airfoils_camber\n\n def check_AerodynamicInformation(self, StructuralInformation):\n \"\"\"\n check_AerodynamicInformation\n\n Check some properties of the AerodynamicInformation()\n\n Notes:\n These conditions have to be to correctly define a case but they are not the only ones\n \"\"\"\n # CHECKING\n if(self.aero_node.shape[0] != StructuralInformation.num_node):\n raise RuntimeError(\"ERROR: Aero node must be defined for each node\")\n if(self.airfoil_distribution.shape[0] != StructuralInformation.num_elem or self.airfoil_distribution.shape[1] != StructuralInformation.num_node_elem):\n raise RuntimeError(\"ERROR: Airfoil distribution must be defined for each element/local node\")\n if(self.chord.shape[0] != StructuralInformation.num_elem):\n raise RuntimeError(\"ERROR: The first dimension of the chord matrix does not match the number of elements\")\n if(self.chord.shape[1] != StructuralInformation.num_node_elem):\n raise RuntimeError(\"ERROR: The second dimension of the chord matrix does not match the number of nodes per element\")\n if(self.elastic_axis.shape[0] != StructuralInformation.num_elem):\n raise RuntimeError(\"ERROR: The first dimension of the elastic axis matrix does not match the number of elements\")\n if(self.elastic_axis.shape[1] != StructuralInformation.num_node_elem):\n raise RuntimeError(\"ERROR: The second dimension of the elastic axis matrix does not match the number of nodes per element\")\n if(self.surface_distribution.shape[0] != StructuralInformation.num_elem):\n raise RuntimeError(\"ERROR: The surface distribution must be defined for each element\")\n if(self.twist.shape[0] != StructuralInformation.num_elem):\n raise RuntimeError(\"ERROR: The first dimension of the aerodynamic twist does not match the number of elements\")\n if(self.twist.shape[1] != StructuralInformation.num_node_elem):\n raise RuntimeError(\"ERROR: The second dimension of the aerodynamic twist does not match the number nodes per element\")\n\n default = AerodynamicInformation()\n\n for attr, value in self.__dict__.items():\n if not hasattr(default, attr):\n raise RuntimeError((\"AerodynamicInformation has no attribute named '%s'\" % attr))\n\n def generate_aero_file(self, route, case_name, StructuralInformation):\n \"\"\"\n generate_aero_file\n\n Writes the h5 file with the aerodynamic information\n\n Args:\n route (string): path of the case\n case_name (string): name of the case\n \"\"\"\n self.check_AerodynamicInformation(StructuralInformation)\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n\n h5file.create_dataset('aero_node', data=self.aero_node)\n chord_input = h5file.create_dataset('chord', data=self.chord)\n chord_input .attrs['units'] = 'm'\n twist_input = h5file.create_dataset('twist', data=self.twist)\n twist_input.attrs['units'] = 'rad'\n h5file.create_dataset('surface_m', data=self.surface_m)\n h5file.create_dataset('surface_distribution', data=self.surface_distribution)\n h5file.create_dataset('m_distribution', data=self.m_distribution.encode('ascii', 'ignore'))\n h5file.create_dataset('elastic_axis', data=self.elastic_axis)\n h5file.create_dataset('airfoil_distribution', data=self.airfoil_distribution)\n h5file.create_dataset('sweep', data=self.sweep)\n \n h5file.create_dataset('first_twist', data=np.array(self.first_twist))\n\n airfoils_group = h5file.create_group('airfoils')\n for iairfoil in range(len(self.airfoils)):\n airfoils_group.create_dataset(\"%d\" % iairfoil, data=self.airfoils[iairfoil, :, :])\n\n if self.polars is not None:\n polars_group = h5file.create_group('polars')\n for iairfoil in range(len(self.airfoils)):\n polars_group.create_dataset(\"%d\" % iairfoil, data=self.polars[iairfoil])\n\n if self.m_distribution.lower() == 'user_defined':\n udmd_group = h5file.create_group('user_defined_m_distribution')\n for isurf in range(len(self.user_defined_m_distribution)):\n udmd_group.create_dataset(\"%d\" % isurf, data=self.user_defined_m_distribution[isurf])\n\n # control_surface_input = h5file.create_dataset('control_surface', data=control_surface)\n # control_surface_deflection_input = h5file.create_dataset('control_surface_deflection', data=control_surface_deflection)\n # control_surface_chord_input = h5file.create_dataset('control_surface_chord', data=control_surface_chord)\n # control_surface_types_input = h5file.create_dataset('control_surface_type', data=control_surface_type)\n\n\n######################################################################\n############### BLADE AEROELASTIC INFORMATION ######################\n######################################################################\nclass AeroelasticInformation():\n \"\"\"\n AeroelasticInformation\n\n Structural and aerodynamic information needed to build a case\n \"\"\"\n\n def __init__(self):\n \"\"\"\n __init__\n\n Initialization\n \"\"\"\n self.StructuralInformation = StructuralInformation()\n self.AerodynamicInformation = AerodynamicInformation()\n\n def generate(self, StructuralInformation, AerodynamicInformation):\n \"\"\"\n generate\n\n Generates an object from the structural and the aerodynamic information\n\n Args:\n StructuralInformation (StructuralInformation): structural information\n AerodynamicInformation (AerodynamicInformation): aerodynamic information\n \"\"\"\n self.StructuralInformation = StructuralInformation.copy()\n self.AerodynamicInformation = AerodynamicInformation.copy()\n\n def assembly(self, *args):\n \"\"\"\n assembly\n\n This function concatenates structures and aerodynamic properties to be writen in the same h5 File\n\n Args:\n *args: list of AeroelasticInformation() to be meged into 'self'\n\n Notes:\n \"\"\"\n list_of_SI = []\n list_of_AI = []\n\n for AEI in args:\n list_of_SI.append(AEI.StructuralInformation)\n list_of_AI.append(AEI.AerodynamicInformation)\n\n self.StructuralInformation.assembly_structures(*list_of_SI)\n self.AerodynamicInformation.assembly_aerodynamics(*list_of_AI)\n\n def remove_duplicated_points(self, tol, skip=[]):\n \"\"\"\n remove_duplicated_points\n\n Removes the points that are closer than 'tol' and modifies the aeroelastic information accordingly\n\n Args:\n tol (float): tolerance. Maximum distance between nodes to be merged\n skip (list): nodes to keep (do not remove)\n\n Notes:\n This function will not work if an element or an aerdoynamic surface is completely eliminated\n This function only checks geometrical proximity, not aeroelastic properties as a merging criteria\n \"\"\"\n\n def find_connectivities_index(connectivities, iprev_node):\n icon = 0\n jcon = 0\n found = False\n while ((icon < connectivities.shape[0]) and (not found)):\n jcon = 0\n while ((jcon < connectivities.shape[1]) and (not found)):\n if connectivities[icon, jcon] == iprev_node:\n found = True\n jcon += 1\n icon += 1\n return icon-1, jcon-1\n\n replace_matrix = (\n np.zeros((self.StructuralInformation.num_node, 4), dtype=int) -\n np.array([1, 1, 1, 0]))\n # Fill the first three columns\n for inode in range(self.StructuralInformation.num_node):\n for iprev_node in range(inode):\n if ((np.linalg.norm(\n self.StructuralInformation.coordinates[inode, :] -\n self.StructuralInformation.coordinates[iprev_node, :]) < tol) and (\n inode not in skip)):\n cout.cout_wrap((\"WARNING: Replacing node %d by node %d\" % (inode, iprev_node)), 3)\n replace_matrix[inode, 0] = iprev_node\n replace_matrix[inode, 1], replace_matrix[inode, 2] = (\n find_connectivities_index(\n self.StructuralInformation.connectivities,\n iprev_node))\n break\n\n # Fill the last column\n for inode in range(self.StructuralInformation.num_node):\n if not (replace_matrix[inode, 0] == -1):\n # 'inode' is a node to be replaced\n replace_matrix[inode, 3] = -1\n for inode2 in range(inode + 1, self.StructuralInformation.num_node):\n if not (replace_matrix[inode2, 0] == -1):\n # 'inode2' is also a node to be replaced\n replace_matrix[inode2, 3] = -1\n else:\n replace_matrix[inode2, 3] += 1\n\n nodes_to_keep = replace_matrix[:, 0] == -1\n\n # Delete the structural variables associated to the node\n self.StructuralInformation.coordinates = (\n self.StructuralInformation.coordinates[nodes_to_keep, :])\n # self.StructuralInformation.elem_stiffness = (\n # self.StructuralInformation.elem_stiffness[nodes_to_keep])\n # self.StructuralInformation.elem_mass = (\n # self.StructuralInformation.elem_mass[nodes_to_keep])\n # self.StructuralInformation.structural_twist = (\n # self.StructuralInformation.structural_twist[nodes_to_keep])\n self.StructuralInformation.boundary_conditions = (\n self.StructuralInformation.boundary_conditions[nodes_to_keep])\n # self.StructuralInformation.beam_number = (\n # self.StructuralInformation.beam_number[nodes_to_keep])\n self.StructuralInformation.app_forces = (\n self.StructuralInformation.app_forces[nodes_to_keep, :])\n # self.StructuralInformation.frame_of_reference_delta = (\n # self.StructuralInformation.frame_of_reference_delta[nodes_to_keep,:,:])\n self.AerodynamicInformation.aero_node = (\n self.AerodynamicInformation.aero_node[nodes_to_keep])\n\n # Delete lumped masses\n if isinstance(self.StructuralInformation.lumped_mass_nodes, np.ndarray):\n lumped_to_keep = nodes_to_keep[self.StructuralInformation.lumped_mass_nodes]\n self.StructuralInformation.lumped_mass_nodes = (\n self.StructuralInformation.lumped_mass_nodes[lumped_to_keep])\n self.StructuralInformation.lumped_mass = (\n self.StructuralInformation.lumped_mass[lumped_to_keep])\n self.StructuralInformation.lumped_mass_inertia = (\n self.StructuralInformation.lumped_mass_inertia[lumped_to_keep])\n self.StructuralInformation.lumped_mass_position = (\n self.StructuralInformation.lumped_mass_position[lumped_to_keep, :])\n\n # Modify connectivities and matrices in ielem,inode_in_elem shape\n for icon in range(self.StructuralInformation.num_elem):\n for jcon in range(self.StructuralInformation.num_node_elem):\n inode = self.StructuralInformation.connectivities[icon, jcon]\n if not replace_matrix[inode, 0] == -1:\n # inode to be replaced\n self.StructuralInformation.connectivities[icon, jcon] = self.StructuralInformation.connectivities[replace_matrix[inode, 1], replace_matrix[inode, 2]]\n self.StructuralInformation.structural_twist[icon, jcon] = (\n self.StructuralInformation.structural_twist[replace_matrix[inode, 1], replace_matrix[inode, 2]])\n self.AerodynamicInformation.chord[icon, jcon] = (\n self.AerodynamicInformation.chord[replace_matrix[inode, 1], replace_matrix[inode, 2]])\n self.AerodynamicInformation.twist[icon, jcon] = (\n self.AerodynamicInformation.twist[replace_matrix[inode, 1], replace_matrix[inode, 2]])\n self.AerodynamicInformation.sweep[icon, jcon] = (\n self.AerodynamicInformation.sweep[replace_matrix[inode, 1], replace_matrix[inode, 2]])\n self.AerodynamicInformation.elastic_axis[icon, jcon] = (\n self.AerodynamicInformation.elastic_axis[replace_matrix[inode, 1], replace_matrix[inode, 2]])\n self.AerodynamicInformation.airfoil_distribution[icon, jcon] = (\n self.AerodynamicInformation.airfoil_distribution[replace_matrix[inode, 1], replace_matrix[inode, 2]])\n else:\n # inode NOT to be replace\n self.StructuralInformation.connectivities[icon, jcon] -= replace_matrix[inode, 3]\n\n if isinstance(self.StructuralInformation.lumped_mass_nodes, np.ndarray):\n for ilumped in range(len(self.StructuralInformation.lumped_mass_nodes)):\n inode = self.StructuralInformation.lumped_mass_nodes[ilumped]\n if not replace_matrix[inode, 0] == -1:\n self.StructuralInformation.lumped_mass_nodes[ilumped] = self.StructuralInformation.connectivities[replace_matrix[inode, 1], replace_matrix[inode, 2]]\n else:\n self.StructuralInformation.lumped_mass_nodes[ilumped] -= replace_matrix[inode, 3]\n\n self.StructuralInformation.num_node = nodes_to_keep.sum()\n\n # TODO: this function will not work if elements or aerodynamic surfaces are completely eliminated\n\n def copy(self):\n \"\"\"\n copy\n\n Returns a copy of the object\n\n Returns:\n copied(AeroelasticInformation): new object with the same properties\n \"\"\"\n copied = AeroelasticInformation()\n\n copied.StructuralInformation = self.StructuralInformation.copy()\n copied.AerodynamicInformation = self.AerodynamicInformation.copy()\n\n return copied\n\n def check(self):\n\n default = AeroelasticInformation()\n\n for attr, value in self.__dict__.items():\n if not hasattr(default, attr):\n raise RuntimeError((\"AeroelasticInformation has no attribute named '%s'\" % attr))\n\n def generate_h5_files(self, route, case_name):\n \"\"\"\n write_h5_files\n\n Writes the structural and aerodynamic h5 files\n \"\"\"\n self.check()\n self.StructuralInformation.generate_fem_file(route, case_name)\n self.AerodynamicInformation.generate_aero_file(route, case_name, self.StructuralInformation)\n\n\n######################################################################\n###################### SOLVERS INFORMATION #########################\n######################################################################\nclass SimulationInformation():\n \"\"\"\n SimulationInformation\n\n Simulation information needed to build a case\n \"\"\"\n\n def __init__(self):\n \"\"\"\n __init__\n\n Initialization\n \"\"\"\n self.solvers = dict()\n # self.preprocessors = dict()\n self.postprocessors = dict()\n\n self.with_dynamic_forces = False\n self.dynamic_forces = None\n self.with_forced_vel = False\n self.for_vel = None\n self.for_acc = None\n\n def set_default_values(self):\n \"\"\"\n set_default_values\n\n Set the default values for all the solvers\n \"\"\"\n\n self.solvers = dict()\n aux_solvers = solver_interface.dictionary_of_solvers(print_info=False)\n aux_solvers.update(generator_interface.dictionary_of_generators(print_info=False))\n aux_solvers.update(controller_interface.dictionary_of_controllers(print_info=False))\n\n for solver in aux_solvers:\n if solver == 'PreSharpy':\n solver_name = 'SHARPy'\n else:\n solver_name = solver\n self.solvers[solver_name] = deepcopy(aux_solvers[solver])\n if solver in ['GridLoader', 'NonliftingbodygridLoader']:\n # Skip this solver as no default values for GridLoader exist. \n continue\n\n def check(self):\n\n default = SimulationInformation()\n default.set_default_values()\n\n for solver in self.solvers['SHARPy']['flow']:\n for key in self.solvers[solver]:\n if key not in default.solvers[solver]:\n raise RuntimeError((\"solver '%s' has no key named '%s'\" % (solver, key)))\n\n\n def define_num_steps(self, num_steps):\n \"\"\"\n define_num_steps\n\n Set the number of steps in the simulation for all the solvers\n\n Args:\n num_steps (int): number of steps\n \"\"\"\n\n for solver in self.solvers:\n if 'n_time_steps' in self.solvers[solver]:\n self.solvers[solver]['n_time_steps'] = num_steps\n if 'num_steps' in self.solvers[solver]:\n self.solvers[solver]['num_steps'] = num_steps\n\n\n def define_uinf(self, unit_vector, norm):\n \"\"\"\n define_uinf\n\n Set the inflow velocity in the simulation for all the solvers\n\n Args:\n unit_vector (np.array): direction of the inflow velocity\n norm (float): Norm of the inflow velocity\n \"\"\"\n # Make sure\n uinf = unit_vector*norm\n norm = np.linalg.norm(uinf)\n unit_vector = uinf / norm\n\n self.solvers['AerogridLoader']['freestream_dir'] = unit_vector\n self.solvers['AerogridPlot']['u_inf'] = norm\n self.solvers['SteadyVelocityField']['u_inf'] = norm\n self.solvers['SteadyVelocityField']['u_inf_direction'] = unit_vector\n # self.solvers['StaticUvlm']['velocity_field_input'] = {'u_inf': norm,\n # 'u_inf_direction': unit_vector}\n # self.solvers['StepUvlm']['velocity_field_input'] = {'u_inf': norm,\n # 'u_inf_direction': unit_vector}\n\n\n def set_variable_all_dicts(self, variable, set_value):\n \"\"\"\n set_variable_all_dicts\n\n Defines the value of a variable in all the available solvers\n\n Args:\n variable (str): variable name\n set_value ( ): value\n \"\"\"\n set_variable_dict(self.solvers, variable, set_value)\n\n def generate_solver_file(self):\n \"\"\"\n generate_solver_file\n\n Generates the solver file\n\n Args:\n route (string): path of the case\n case_name (string): name of the case\n \"\"\"\n import configobj\n\n self.check()\n\n config = configobj.ConfigObj()\n config.filename = self.solvers['SHARPy']['route'] + '/' + self.solvers['SHARPy']['case'] + '.sharpy'\n config['SHARPy'] = self.solvers['SHARPy']\n # for k, v in self.solvers['SHARPy'].items():\n # config[k] = v\n # Loop through the solvers defined in \"flow\" and write them\n for solver in self.solvers['SHARPy']['flow']:\n config[solver] = self.solvers[solver]\n config.write()\n\n def generate_dyn_file(self, num_steps):\n \"\"\"\n generate_dyn_file\n\n Generates the dynamic file\n\n Args:\n route (string): path of the case\n case_name (string): name of the case\n num_steps (int): number of steps\n \"\"\"\n\n with h5.File(self.solvers['SHARPy']['route'] + '/' + self.solvers['SHARPy']['case'] + '.dyn.h5', 'a') as h5file:\n if self.with_dynamic_forces:\n h5file.create_dataset(\n 'dynamic_forces', data=self.dynamic_forces)\n if self.with_forced_vel:\n # TODO: check coherence velocity-acceleration\n h5file.create_dataset(\n 'for_vel', data=self.for_vel)\n h5file.create_dataset(\n 'for_acc', data=self.for_acc)\n h5file.create_dataset(\n 'num_steps', data=num_steps)\n\n\n######################################################################\n######################### CLEAN FILES ##############################\n######################################################################\n\ndef clean_test_files(route, case_name):\n \"\"\"\n clean_test_files\n\n Removes the previous h5 files\n\n Args:\n route (string): path of the case\n case_name (string): name of the case\n\n \"\"\"\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n dyn_file_name = route + '/' + case_name + '.dyn.h5'\n if os.path.isfile(dyn_file_name):\n os.remove(dyn_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n lagrange_file_name = route + '/' + case_name + '.mb.h5'\n if os.path.isfile(lagrange_file_name):\n os.remove(lagrange_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n\n######################################################################\n##################### MULTIBODY INFORMATION ########################\n######################################################################\nclass BodyInformation():\n\n def __init__(self):\n\n self.body_number = None\n self.FoR_position = None\n self.FoR_velocity = None\n self.FoR_acceleration = None\n self.FoR_movement = None\n self.quat = None\n\n def copy(self):\n\n copied = BodyInformation()\n copied.body_number = self.body_number\n copied.FoR_position = self.FoR_position.astype(dtype=float, copy=True)\n copied.FoR_velocity = self.FoR_velocity.astype(dtype=float, copy=True)\n copied.FoR_acceleration = self.FoR_acceleration.astype(dtype=float, copy=True)\n copied.FoR_movement = self.FoR_movement\n copied.quat = self.quat.astype(dtype=float, copy=True)\n\n def check(self):\n\n default = BodyInformation()\n\n for attr, value in self.__dict__.items():\n if not hasattr(default, attr):\n raise RuntimeError((\"BodyInformation has no attribute named '%s'\" % attr))\n\n\nclass LagrangeConstraint():\n\n def __init__(self):\n\n # Shared by all boundary conditions\n self.behaviour = None\n # Each BC will have its own variables\n\n def check(self):\n default = lagrangeconstraints.lc_from_string(self.behaviour)\n default.__init__(default)\n required_parameters = default.required_parameters\n for param in required_parameters:\n try:\n getattr(self, param)\n except:\n raise RuntimeError((\"'%s' parameter required in '%s' lagrange constraint\" % (param, self.behaviour)))\n has_behaviour = False\n for param, value in self.__dict__.items():\n if not param in ['behaviour', 'scalingFactor', 'penaltyFactor', 'rot_axisA2']:\n if param not in required_parameters:\n raise RuntimeError((\"'%s' parameter is not required in '%s' lagrange constraint\" % (param, self.behaviour)))\n if param == 'behaviour':\n has_behaviour = True\n\n if not has_behaviour:\n raise RuntimeError((\"'behaviour' parameter is required in '%s' lagrange constraint\" % self.behaviour))\n\n\ndef generate_multibody_file(list_LagrangeConstraints, list_Bodies, route, case_name, use_jax=False):\n\n # Check\n for body in list_Bodies:\n body.check()\n\n if not use_jax:\n for lc in list_LagrangeConstraints:\n lc.check()\n\n with h5.File(route + '/' + case_name + '.mb.h5', 'a') as h5file:\n\n # Write the constraints\n h5file.create_dataset('num_constraints', data=len(list_LagrangeConstraints))\n\n iconstraint = 0\n for constraint in list_LagrangeConstraints:\n # Create the group associated to the constraint\n constraint_id = h5file.create_group('constraint_%02d' % iconstraint)\n\n # Write general parameters\n constraint_id.create_dataset(\"behaviour\", data=constraint.behaviour.encode('ascii', 'ignore'))\n\n # I branch depending on if you use the JAX solver or not\n # this is beneficial where a constraint is implemented in one solver but not the other\n if use_jax:\n required_parameters = DICT_OF_LC[constraint.behaviour].required_params\n else:\n # Write parameters associated to the specific type of boundary condition\n default = lagrangeconstraints.lc_from_string(constraint.behaviour)\n default.__init__(default)\n required_parameters = default.required_parameters\n for param in required_parameters:\n constraint_id.create_dataset(param, data=getattr(constraint, param))\n try:\n constraint_id.create_dataset(\"scalingFactor\", data=constraint.scalingFactor)\n except AttributeError:\n pass\n try:\n constraint_id.create_dataset(\"penaltyFactor\", data=constraint.penaltyFactor)\n except AttributeError:\n pass\n try:\n constraint_id.create_dataset(\"aerogrid_warp_factor\", data=constraint.aerogrid_warp_factor)\n except AttributeError:\n pass\n try:\n constraint_id.create_dataset(\"rot_axisA2\", data=constraint.rot_axisA2)\n except AttributeError:\n pass\n\n iconstraint += 1\n\n # Write the body information\n h5file.create_dataset('num_bodies', data=len(list_Bodies))\n\n ibody = 0\n for body in list_Bodies:\n # Create the group associated to the body\n body_id = h5file.create_group('body_%02d' % ibody)\n\n # Write general parameters\n body_id.create_dataset(\"body_number\", data=body.body_number)\n body_id.create_dataset(\"FoR_position\", data=body.FoR_position)\n body_id.create_dataset(\"FoR_velocity\", data=body.FoR_velocity)\n body_id.create_dataset(\"FoR_acceleration\", data=body.FoR_acceleration)\n body_id.create_dataset(\"FoR_movement\", data=body.FoR_movement)\n body_id.create_dataset(\"quat\", data=body.quat)\n ibody += 1\n" }, { "path": "sharpy/utils/generator_interface.py", "content": "\"\"\"Generator Interface\n\"\"\"\nfrom abc import ABCMeta, abstractmethod\nimport sharpy.utils.cout_utils as cout\nimport os\nimport shutil\n\ndict_of_generators = {}\ngenerators = {} # for internal working\n\n\n# decorator\ndef generator(arg):\n # global available_solvers\n global dict_of_generators\n try:\n arg.generator_id\n except AttributeError:\n raise AttributeError('Class defined as generator has no generator_id attribute')\n dict_of_generators[arg.generator_id] = arg\n return arg\n\n\ndef print_available_generators():\n cout.cout_wrap('The available generators on this session are:', 2)\n for name, i_generator in dict_of_generators.items():\n cout.cout_wrap('%s ' % i_generator.generator_id, 2)\n\n\nclass BaseGenerator(metaclass=ABCMeta):\n pass\n\ndef generator_from_string(string):\n return dict_of_generators[string]\n\n\ndef generator_list_from_path(cwd):\n onlyfiles = [f for f in os.listdir(cwd) if os.path.isfile(os.path.join(cwd, f))]\n\n for i_file in range(len(onlyfiles)):\n if onlyfiles[i_file].split('.')[-1] == 'py': # support autosaved files in the folder\n if onlyfiles[i_file] == \"__init__.py\":\n onlyfiles[i_file] = \"\"\n continue\n onlyfiles[i_file] = onlyfiles[i_file].replace('.py', '')\n else:\n onlyfiles[i_file] = \"\"\n\n files = [file for file in onlyfiles if not file == \"\"]\n return files\n\n\ndef initialise_generator(generator_name, print_info=True):\n if print_info:\n cout.cout_wrap('Generating an instance of %s' % generator_name, 2)\n cls_type = generator_from_string(generator_name)\n gen = cls_type()\n return gen\n\ndef dictionary_of_generators(print_info=True):\n\n import sharpy.generators\n dictionary = dict()\n for gen in dict_of_generators:\n init_gen = initialise_generator(gen, print_info)\n dictionary[gen] = init_gen.settings_default\n\n return dictionary\n\ndef output_documentation(route=None):\n \"\"\"\n Creates the ``.rst`` files for the generators that have a docstring such that they can be parsed to Sphinx\n\n Args:\n route (str): Path to folder where generator files are to be created.\n\n \"\"\"\n import sharpy.utils.sharpydir as sharpydir\n if route is None:\n route = sharpydir.SharpyDir + '/docs/source/includes/generators/'\n if os.path.exists(route):\n print('Cleaning %s' %route)\n shutil.rmtree(route)\n print('Creating documentation files for generators in %s' % route)\n\n created_generators = dict()\n\n for k, v in dict_of_generators.items():\n if k[0] == '_':\n continue\n generator_class = v()\n created_generators[k] = generator_class\n\n filename = k + '.rst'\n # try:\n # solver_folder = solver.solver_classification.lower()\n # except AttributeError:\n # solver_folder = 'other'\n #\n # if solver_folder not in solver_types:\n # solver_types.append(solver_folder)\n\n os.makedirs(route + '/', exist_ok=True)\n title = k + '\\n'\n title += len(k)*'-' + 2*'\\n'\n if generator_class.__doc__ is not None:\n\n print('\\tCreating %s' % (route + '/' + filename))\n autodoc_string = '\\n\\n.. autoclass:: sharpy.generators.' + k.lower() + '.'+ k + '\\n\\t:members:'\n with open(route + '/' + filename, \"w\") as out_file:\n out_file.write(title + autodoc_string)\n\n # # Creates index files depending on the type of solver\n # filename = 'generators.rst'\n # title = 'Velocity Field Generators'\n # title += '\\n' + len(title)*'+' + 2*'\\n'\n # with open(route + '/' + filename, \"w\") as out_file:\n # out_file.write(title)\n # out_file.write('.. toctree::' + '\\n')\n # for k in dict_of_generators.keys():\n # if k[0] == '_':\n # continue\n # out_file.write(' ./' + k + '\\n')\n" }, { "path": "sharpy/utils/geo_utils.py", "content": "\"\"\"Airfoil Geometry Utils\n\n\"\"\"\n\nimport numpy as np\n\n\ndef generate_naca_camber(M=0, P=0):\n \"\"\"\n Defines the x and y coordinates of a 4-digit NACA profile's camber line (i.e no thickness).\n\n The NACA 4-series airfoils follow the nomenclature: NACA MPTT where:\n * M indicates the maximum camber :math:`M = 100m`\n * P indicates the position of the maximum camber :math:`P=10p`\n * TT indicates the thickness to chord ratio :math:`TT=(t/c)*100`\n\n Args:\n M (float): maximum camber times 100 (i.e. the first of the 4 digits)\n P (float): position of the maximum camber times 10 (i.e. the second of the 4 digits)\n\n Returns:\n (x_vec,y_vec): ``x`` and ``y`` coordinates of the chosen airfoil\n\n Example:\n The NACA2400 airfoil would have 2% camber with the maximum at 40% of the chord and 0 thickness. To plot the\n camber line one would use this function as:\n\n ``x_vec, y_vec = generate_naca_camber(M = 2, P = 4)``\n\n \"\"\"\n m = M * 1e-2\n p = P * 1e-1\n\n def naca(x, m, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return m / (p * p) * (2 * p * x - x * x)\n elif x > p and x < 1 + 1e-6:\n return m / ((1 - p) * (1 - p)) * (1 - 2 * p + 2 * p * x - x * x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, m, p) for x in x_vec])\n\n return x_vec, y_vec\n\n\ndef interpolate_naca_camber(eta, M00, P00, M01, P01):\n \"\"\"\n Interpolate aerofoil camber at non-dimensional coordinate eta in (0,1), \n where (M00,P00) and (M01,P01) define the camber properties at eta=0 and \n eta=1 respectively.\n\n Notes:\n For two surfaces, eta can be in (-1,1). In this case, the root is eta=0\n and the tips are at eta=+-1.\n \"\"\"\n\n # define domain\n eta = np.abs(eta)\n assert np.max(eta) < 1. + 1e-16, 'eta exceeding +/- 1!'\n\n # define reference\n x00, y00 = generate_naca_camber(M00, P00)\n x01, y01 = generate_naca_camber(M01, P01)\n\n # interpolate\n x_vec = x00 * (1. - eta) + x01 * eta\n y_vec = y00 * (1. - eta) + y01 * eta\n\n return x_vec, y_vec\n\nif __name__ == '__main__':\n a = 1" }, { "path": "sharpy/utils/h5utils.py", "content": "# Alfonso del Carre\n# alfonso.del-carre14@imperial.ac.uk\n# Imperial College London\n# LoCA lab\n# 28 Sept 2016\n\"\"\"H5 File Management Utilities\nSet of utilities for opening/reading files\n\"\"\"\nimport h5py as h5\nimport os\nimport errno\n\nimport numpy as np\nimport warnings\nfrom numpy import ndarray, float64, float32, array, int32, int64\nimport ctypes as ct\n\nBasicNumTypes = (float, float32, float64, int, int32, int64, complex)\n\n\ndef check_file_exists(file_name):\n \"\"\"\n Checks if the file exists and throws a FileNotFoundError exception\n that includes the route to the non-existing file.\n\n Args:\n file_name (str): path to the HDF5 file\n\n Returns:\n FileNotFoundError : if the file does not exist, an error is raised with path to the non-existent file\n \"\"\"\n if not os.path.isfile(file_name):\n raise FileNotFoundError(\n errno.ENOENT, os.strerror(errno.ENOENT),\n file_name)\n\n\ndef load_h5_in_dict(handle, path='/'):\n dictionary = {}\n for k, i in handle[path].items():\n if isinstance(i, h5._hl.dataset.Dataset):\n dictionary[k] = i[()]\n elif isinstance(i, h5._hl.group.Group):\n dictionary[k] = load_h5_in_dict(handle, path + k + '/')\n\n if len(i.attrs.items()):\n dictionary['Attributes'] = load_attributes(handle, path + k + '/')\n\n return dictionary\n\n\ndef load_attributes(handle, path):\n attributes = []\n for k, i in handle[path].attrs.items():\n attributes.append((k, i))\n\n return attributes\n\n\ndef check_fem_dict(fem_dict):\n print('\\tRunning tests for the FEM input file...', end='')\n (num_elem_dict, num_node_elem_dict) = np.shape(fem_dict['connectivities'])\n num_elem = fem_dict['num_elem']\n num_node_elem = fem_dict['num_node_elem']\n if not ((num_elem == num_elem_dict) or (num_node_elem == num_node_elem_dict)):\n raise Exception('ERROR: FEM input file is not consistent')\n else:\n print(' PASSED')\n\n\ndef check_data_dict(data_dict):\n pass\n\n\n# --------------------------------------------------------------- Reading tools\n\n\ndef readh5(filename, GroupName=None):\n \"\"\"\n Read the HDF5 file 'filename' into a class. Groups within the hdf5 file are\n by default loaded as sub classes, unless they include a _read_as attribute\n (see sharpy.postproc.savedata). In this case, group can be loaded as classes,\n dictionaries, lists or tuples.\n\n filename: string to file location\n\n GroupName = string or list of strings. Default is None: if given, allows\n reading a specific group h5 file.\n\n Warning:\n Groups that need to be read as lists and tuples are assumed to conform to\n the format used in sharpy.postproc.savedata\n \"\"\"\n\n Hinst = ReadInto()\n\n ### read and scan file\n hdfile = h5.File(filename, 'r')\n\n NamesList = [] # dataset names\n hdfile.visit(NamesList.append)\n\n ### Identify higher level groups / attributes\n if GroupName is None:\n MainLev = []\n for name in NamesList:\n if '/' not in name: MainLev.append(name)\n else:\n if type(GroupName) is list:\n MainLev = GroupName\n else:\n MainLev = [GroupName]\n\n ### Loop through higher level\n for name in MainLev:\n # sub-group\n if type(hdfile[name]) is h5._hl.group.Group:\n Ginst = read_group(hdfile[name])\n try:\n Ginst.name = name\n except:\n pass\n setattr(Hinst, name, Ginst)\n else:\n setattr(Hinst, name, hdfile[name][()])\n\n # close and return\n hdfile.close()\n\n return Hinst\n\n\ndef read_group(Grp):\n \"\"\" Read an hdf5 group \"\"\"\n\n NamesList = []\n Grp.visit(NamesList.append)\n\n ### identify higher level\n MainLev = []\n for name in NamesList:\n if '/' not in name: MainLev.append(name)\n\n ### determine output format\n read_as = 'class'\n if '_read_as' in MainLev:\n read_as = Grp['_read_as'][()]\n\n ### initialise output\n if read_as == 'class':\n Hinst = ReadInto()\n elif read_as == 'dict':\n Hinst = {}\n elif read_as == 'list' or read_as == 'tuple':\n Hinst = []\n\n ### Loop through higher level\n if read_as == 'list' or read_as == 'tuple':\n if '_as_array' in MainLev:\n Hinst = list(Grp['_as_array'][()])\n else:\n N = len(MainLev) - 1\n list_ts = MainLev.copy()\n list_ts.remove('_read_as')\n list_ts = np.sort(np.unique(np.array(list_ts, dtype=np.int)))\n if len(list_ts > 0):\n for nn in range(list_ts[0] - 1):\n Hinst.append('NoneType')\n for nn in list_ts:\n name = '%.5d' % nn\n ### extract value\n if type(Grp[name]) is h5._hl.group.Group:\n value = read_group(Grp[name])\n else:\n value = Grp[name][()]\n Hinst.append(value)\n if read_as == 'tuple': tuple(Hinst)\n else:\n for name in MainLev:\n if name == '_read_as': continue\n\n ### extract value\n if type(Grp[name]) is h5._hl.group.Group:\n value = read_group(Grp[name])\n else:\n value = Grp[name][()]\n\n ### allocate\n if read_as == 'class':\n setattr(Hinst, name, value)\n else:\n Hinst[name] = value\n\n return Hinst\n\n\nclass ReadInto:\n def __init__(self, name='ReadInto'):\n self._name = name\n\n pass\n\n\n# ---------------------------------------------------------------- Saving tools\n\n\ndef saveh5(savedir, h5filename, *class_inst, permission='a', ClassesToSave=()):\n \"\"\"\n Creates h5filename and saves all the classes specified in class_inst\n\n Args\n savedir: target directory\n h5filename: file name\n class_inst: a number of classes to save\n permission=['a','w']: append or overwrite, according to h5py.File\n ClassesToSave: if the classes in class_inst contain sub-classes, these will be saved only if instances of the classes in this list\n \"\"\"\n\n h5filename = os.path.join(savedir, h5filename)\n hdfile = h5.File(h5filename, permission)\n\n for cc in class_inst:\n add_as_grp(cc, hdfile, ClassesToSave=ClassesToSave)\n\n hdfile.close()\n return None\n\n\ndef add_as_grp(obj, grpParent,\n grpname=None, ClassesToSave=(), SkipAttr=[],\n compress_float=False, overwrite=False):\n \"\"\"\n Given a class, dictionary, list or tuples instance 'obj', the routine adds\n it as a sub-group of name grpname to the parent group grpParent. An attribute\n _read_as, specifying the type of obj, is added to the group so as to allow\n reading correctly the h5 file.\n\n Usage and Remarks:\n - if obj contains dictionaries, listes or tuples, these are automatically\n saved\n\n - if list only contains scalars or arrays of the same dimension, this will\n be saved as a numpy array\n\n - if obj contains classes, only those that are instances of the classes\n specified in ClassesToSave will be saved\n\n - If grpParent already contains a sub-group with name grpname, this will not\n be overwritten. However, pre-existing attributes of the sub-group will be\n overwritten if obj contains attrributes with the same names.\n\n - attributes belonging to SkipAttr will not be saved - This functionality\n needs improving\n\n - if compress_float is True, numpy arrays will be saved in single precisions.\n \"\"\"\n\n ### determine if dict, list, tuple or class\n if isinstance(obj, list):\n ObjType = 'list'\n elif isinstance(obj, tuple):\n ObjType = 'tuple'\n elif isinstance(obj, dict):\n ObjType = 'dict'\n elif hasattr(obj, '__class__'):\n ObjType = 'class'\n else:\n raise NameError('object type not supported')\n\n ### determine sub-group name (only classes)\n if grpname is None:\n if ObjType == 'class':\n if hasattr(obj, '_name'):\n grpname = obj._name\n else:\n grpname = obj.__class__.__name__\n else:\n raise NameError('grpname must be specified for dict,list and tuples')\n\n ### Create group (if necessary)\n if not (grpname in grpParent):\n grp = grpParent.create_group(grpname)\n grp['_read_as'] = ObjType\n else:\n if overwrite:\n del grpParent[grpname]\n grp = grpParent.create_group(grpname)\n grp['_read_as'] = ObjType\n else:\n grp = grpParent[grpname]\n assert grp['_read_as'][()] == ObjType, \\\n 'Can not overwrite group of different type'\n\n ### lists/tuples only: try to save as arrays\n if ObjType in ('list', 'tuple'):\n Success = save_list_as_array(\n list_obj=obj, grp_target=grp, compress_float=compress_float)\n if Success:\n return grpParent\n\n ### create/retrieve dictionary of attributes/elements to be saved\n if ObjType == 'dict':\n dictname = obj\n elif ObjType == 'class':\n dictname = obj.__dict__\n else:\n N = len(obj)\n dictname = {}\n for nn in range(N):\n dictname['%.5d' % nn] = obj[nn]\n\n ### loop attributes and save\n SaveAsGroups = ClassesToSave + (list, dict, tuple,)\n\n for attr in dictname:\n if attr in SkipAttr: continue\n\n # ----- extract value & type\n value = dictname[attr]\n vtype = type(value)\n\n # ----- classes/dict/lists\n # ps: no need to delete if overwrite is True\n if isinstance(value, SaveAsGroups):\n add_as_grp(value, grp, attr,\n ClassesToSave, SkipAttr, compress_float, overwrite)\n continue\n\n # ----- if attr already in grp always overwrite\n if attr in grp:\n del grp[attr]\n\n # ----- Basic types\n if isinstance(value, BasicNumTypes + (str, bytes)):\n grp[attr] = value\n continue\n\n # c_types\n if isinstance(value, (ct.c_bool, ct.c_double, ct.c_int)):\n value = value.value\n grp[attr] = value\n continue\n\n # ndarrays\n if isinstance(value, ndarray):\n add_array_to_grp(value, attr, grp, compress_float)\n continue\n\n # ----- Special\n if value == None:\n grp[attr] = 'NoneType'\n continue\n\n grp[attr] = 'not saved'\n\n return grpParent\n\n\ndef add_array_to_grp(data, name, grp, compress_float=False):\n \"\"\" Add numpy array (data) as dataset 'name' to the group grp. If\n compress is True, 64-bit float arrays are converted to 32-bit \"\"\"\n\n if compress_float and data.dtype == float64:\n # embed()\n grp.create_dataset(name, data=data, dtype='f4')\n else:\n grp[name] = data\n\n return grp\n\n\ndef save_list_as_array(list_obj, grp_target, compress_float=False):\n \"\"\"\n Works for both lists and tuples. Returns True if the saving was successful.\n \"\"\"\n\n N = len(list_obj)\n\n if N > 0:\n type0 = type(list_obj[0])\n if type0 in (BasicNumTypes + (str, ndarray)):\n SaveAsArray = True\n for nn in range(N):\n if type(list_obj[nn]) != type0:\n SaveAsArray = False\n break\n if type(list_obj[nn]) == ndarray:\n if list_obj[0].shape != list_obj[nn].shape:\n SaveAsArray = False\n break\n if SaveAsArray:\n if '_as_array' in grp_target:\n del grp_target['_as_array']\n if type0 in BasicNumTypes: # list of scalars\n if type0 == float and compress_float:\n grp_target['_as_array'] = float32(list_obj)\n else:\n grp_target['_as_array'] = list_obj\n elif type0 == str: # list of strings\n string_dt = h5.special_dtype(vlen=str)\n grp_target.create_dataset('_as_array',\n data=array(list_obj, dtype=object), dtype=string_dt)\n\n elif type0 == ndarray: # list of arrays\n if list_obj[0].dtype in BasicNumTypes:\n if list_obj[0].dtype == float64 and compress_float:\n grp_target['_as_array'] = float32(list_obj)\n else:\n grp_target['_as_array'] = list_obj\n else:\n string_dt = h5.special_dtype(vlen=str)\n grp_target.create_dataset('_as_array',\n data=array(list_obj, dtype=object), dtype=string_dt)\n else:\n warnings.warn(\n '%s could not be saved as an array' % (grp_target.name,))\n return False\n\n return True\n return False\n" }, { "path": "sharpy/utils/input_arg.py", "content": "import os\nimport sys\nimport argparse\nimport sharpy.utils.exceptions as exceptions\nimport sharpy.utils.cout_utils as cout\n\n\ndef read_settings(args):\n case_settings = args.input_filename\n cout.cout_wrap('Running SHARPy using the settings file: %s' % case_settings)\n\n settings = parse_settings(case_settings)\n return settings\n\n\ndef parse_settings(file):\n from sharpy.utils.settings import load_config_file\n settings = load_config_file(os.path.realpath(file))\n try:\n settings['SHARPy']['flow']\n except KeyError:\n raise exceptions.NotValidInputFile('The solver file does not contain a SHARPy header.')\n\n from sharpy.utils.solver_interface import dict_of_solvers\n\n for solver in settings['SHARPy']['flow']:\n # Check that the solvers in the flow exist and that they have a valid set of settings\n try:\n dict_of_solvers[solver]\n except KeyError:\n raise exceptions.SolverNotFound(solver)\n\n try:\n settings[solver]\n except KeyError:\n raise exceptions.NotValidInputFile('The settings for the solver %s have not been given.' % solver)\n return settings\n" }, { "path": "sharpy/utils/linearutils.py", "content": "\"\"\"Linear state-space vector manipulation utilities\"\"\"\nimport numpy as np\nimport sharpy.utils.algebra as algebra\n\n\ndef structural_vector_to_timestep(vector, tstruct, structure, phi=None, num_rig_dof=0, copy_tstep=True):\n \"\"\"Transform a state-space structural vector into a time step object\n\n This adds to a reference time step the following variables extracted from the vector:\n\n * ``pos`` and ``pos_dot``\n * ``psi`` and ``psi_dot``\n * ``quat``\n * ``for_pos`` and ``for_vel``\n\n The rest of the structural time step variables are left unchanged\n\n Args:\n vector(np.ndarray): Vector to plot\n tstruct (sharpy.utils.datastructures.StructTimeStepInfo): Reference time step\n structure (sharpy.structure.models.beam.Beam): Structural information class\n phi (np.ndarray, optional): Eigenvector matrix to transform vector back to nodal coordinates\n num_rig_dof (int): Number of rigid degrees of freedom\n copy_tstep (bool): Return a copy of the reference time step. Else, modify the input one.\n\n Returns:\n sharpy.utils.datastructures.StructTimeStepInfo: Time step with the aforementioned variables populated from\n state-space vector.\n \"\"\"\n n_dof = vector.shape[0]\n v = vector[:n_dof//2]\n v_dot = vector[n_dof//2:]\n if phi is not None: # modal coordinates\n eta = phi.dot(v)\n eta_dot = phi.dot(v_dot)\n else:\n eta = v\n eta_dot = v_dot\n\n if num_rig_dof != 0:\n eta = eta[:-num_rig_dof]\n eta_dot = eta_dot[:-num_rig_dof]\n beta = eta_dot[-num_rig_dof:]\n beta_bar = np.zeros_like(beta)\n else:\n beta = np.array([])\n beta_bar = np.array([])\n\n if copy_tstep:\n tstep = tstruct.copy()\n else:\n tstep = tstruct\n\n vdof = structure.vdof\n num_dof = 6*sum(vdof >= 0)\n\n q = np.zeros((num_dof + num_rig_dof))\n dqdt = np.zeros_like(q)\n dqddt = np.zeros_like(q)\n\n pos = np.zeros_like(tstep.pos)\n pos_dot = np.zeros_like(tstep.pos_dot)\n\n psi = np.zeros_like(tstep.psi)\n psi_dot = np.zeros_like(tstep.psi_dot)\n\n for_pos = np.zeros_like(tstep.for_pos)\n for_vel = np.zeros_like(tstep.for_vel)\n for_acc = np.zeros_like(tstep.for_acc)\n quat = np.zeros_like(tstep.quat)\n\n q[:num_dof + num_rig_dof] = np.concatenate((eta, beta_bar))\n dqdt[:num_dof + num_rig_dof] = np.concatenate((eta_dot, beta))\n\n for i_node in vdof[vdof >= 0]:\n pos[i_node + 1, :] = q[6*i_node: 6*i_node + 3]\n pos_dot[i_node + 1, :] = dqdt[6*i_node + 0: 6*i_node + 3]\n\n for i_elem in range(tstep.num_elem):\n for i_node in range(tstep.num_node_elem):\n psi[i_elem, i_node, :] = np.linalg.inv(algebra.crv2tan(tstep.psi[i_elem, i_node]).T).dot(q[i_node + 3: i_node + 6])\n psi_dot[i_elem, i_node, :] = dqdt[i_node + 3: i_node + 6]\n\n if num_rig_dof != 0: # beam is clamped\n for_vel = beta[:6]\n if num_rig_dof == 9:\n quat = algebra.euler2quat(beta[-3:])\n elif num_rig_dof == 10:\n quat = beta[-4:]\n else:\n raise NotImplementedError('Structural vector to timestep for cases without 9 or 10 rigid'\n 'degrees of freedom not yet supported.')\n\n tstep.q[:len(q)] += q\n tstep.dqdt[:len(q)] += dqdt\n\n tstep.pos += pos\n tstep.pos_dot += pos_dot\n\n tstep.psi += psi\n tstep.psi_dot += psi_dot\n\n tstep.for_pos += for_pos\n tstep.for_vel += for_vel\n\n tstep.quat += quat\n tstep.quat /= np.linalg.norm(tstep.quat) # normalise quaternion\n\n return tstep\n\n" }, { "path": "sharpy/utils/model_utils.py", "content": "\"\"\"\nModelling Utilities\n\"\"\"\nimport numpy as np\nimport sharpy.utils.algebra as algebra\n\n\ndef mass_matrix_generator(m, xcg, inertia):\n \"\"\"\n This function takes the mass, position of the center of\n gravity wrt the elastic axis and the inertia matrix J (3x3) and\n returns the complete 6x6 mass matrix.\n \"\"\"\n mass = np.zeros((6, 6))\n m_chi_cg = algebra.skew(m*xcg)\n mass[np.diag_indices(3)] = m\n mass[3:, 3:] = inertia\n mass[0:3, 3:6] = -m_chi_cg\n mass[3:6, 0:3] = m_chi_cg\n\n return mass\n" }, { "path": "sharpy/utils/multibody.py", "content": "\"\"\"\nMultibody library\n\nLibrary used to manipulate multibody systems\n\nTo use this library: import sharpy.utils.multibody as mb\n\n\"\"\"\nimport numpy as np\nimport sharpy.structure.utils.xbeamlib as xbeamlib\nimport sharpy.utils.algebra as algebra\nimport ctypes as ct\nimport traceback\n\n\ndef split_multibody(beam, tstep, mb_data_dict, ts):\n \"\"\"\n split_multibody\n\n This functions splits a structure at a certain time step in its different bodies\n\n Args:\n \tbeam (:class:`~sharpy.structure.models.beam.Beam`): structural information of the multibody system\n \ttstep (:class:`~sharpy.utils.datastructures.StructTimeStepInfo`): timestep information of the multibody system\n mb_data_dict (dict): Dictionary including the multibody information\n ts (int): time step number\n\n Returns:\n MB_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body\n MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n \"\"\"\n\n MB_beam = []\n MB_tstep = []\n\n quat0 = tstep.quat.astype(dtype=ct.c_double, order='F', copy=True)\n for0_pos = tstep.for_pos.astype(dtype=ct.c_double, order='F', copy=True)\n for0_vel = tstep.for_vel.astype(dtype=ct.c_double, order='F', copy=True)\n\n ini_quat0 = beam.ini_info.quat.astype(dtype=ct.c_double, order='F', copy=True)\n ini_for0_pos = beam.ini_info.for_pos.astype(dtype=ct.c_double, order='F', copy=True)\n ini_for0_vel = beam.ini_info.for_vel.astype(dtype=ct.c_double, order='F', copy=True)\n\n for ibody in range(beam.num_bodies):\n ibody_beam = None\n ibody_tstep = None\n ibody_beam = beam.get_body(ibody = ibody)\n ibody_tstep = tstep.get_body(beam, ibody_beam.num_dof, ibody = ibody)\n\n ibody_beam.FoR_movement = mb_data_dict['body_%02d' % ibody]['FoR_movement']\n\n ibody_beam.ini_info.compute_psi_local_AFoR(ini_for0_pos, ini_for0_vel, ini_quat0)\n ibody_beam.ini_info.change_to_local_AFoR(ini_for0_pos, ini_for0_vel, ini_quat0)\n if ts == 1:\n ibody_tstep.compute_psi_local_AFoR(for0_pos, for0_vel, quat0)\n ibody_tstep.change_to_local_AFoR(for0_pos, for0_vel, quat0)\n\n MB_beam.append(ibody_beam)\n MB_tstep.append(ibody_tstep)\n\n return MB_beam, MB_tstep\n\ndef merge_multibody(MB_tstep, MB_beam, beam, tstep, mb_data_dict, dt):\n \"\"\"\n merge_multibody\n\n This functions merges a series of bodies into a multibody system at a certain time step\n\n Longer description\n\n Args:\n MB_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body\n MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n \tbeam (:class:`~sharpy.structure.models.beam.Beam`): structural information of the multibody system\n \ttstep (:class:`~sharpy.utils.datastructures.StructTimeStepInfo`): timestep information of the multibody system\n mb_data_dict (dict): Dictionary including the multibody information\n dt(int): time step\n\n Returns:\n beam (:class:`~sharpy.structure.models.beam.Beam`): structural information of the multibody system\n \ttstep (:class:`~sharpy.utils.datastructures.StructTimeStepInfo`): timestep information of the multibody system\n \"\"\"\n\n update_mb_dB_before_merge(tstep, MB_tstep)\n\n quat0 = MB_tstep[0].quat.astype(dtype=ct.c_double, order='F', copy=True)\n for0_pos = MB_tstep[0].for_pos.astype(dtype=ct.c_double, order='F', copy=True)\n for0_vel = MB_tstep[0].for_vel.astype(dtype=ct.c_double, order='F', copy=True)\n\n for ibody in range(beam.num_bodies):\n MB_tstep[ibody].change_to_global_AFoR(for0_pos, for0_vel, quat0)\n\n first_dof = 0\n for ibody in range(beam.num_bodies):\n # Renaming for clarity\n ibody_elems = MB_beam[ibody].global_elems_num\n ibody_nodes = MB_beam[ibody].global_nodes_num\n\n # Merge tstep\n tstep.pos[ibody_nodes,:] = MB_tstep[ibody].pos.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.pos_dot[ibody_nodes,:] = MB_tstep[ibody].pos_dot.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.pos_ddot[ibody_nodes,:] = MB_tstep[ibody].pos_ddot.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.psi[ibody_elems,:,:] = MB_tstep[ibody].psi.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.psi_local[ibody_elems,:,:] = MB_tstep[ibody].psi_local.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.psi_dot[ibody_elems,:,:] = MB_tstep[ibody].psi_dot.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.psi_dot_local[ibody_elems,:,:] = MB_tstep[ibody].psi_dot_local.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.psi_ddot[ibody_elems,:,:] = MB_tstep[ibody].psi_ddot.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.gravity_forces[ibody_nodes,:] = MB_tstep[ibody].gravity_forces.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.steady_applied_forces[ibody_nodes,:] = MB_tstep[ibody].steady_applied_forces.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.unsteady_applied_forces[ibody_nodes,:] = MB_tstep[ibody].unsteady_applied_forces.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.runtime_steady_forces[ibody_nodes,:] = MB_tstep[ibody].runtime_steady_forces.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.runtime_unsteady_forces[ibody_nodes,:] = MB_tstep[ibody].runtime_unsteady_forces.astype(dtype=ct.c_double, order='F', copy=True)\n # TODO: Do I need a change in FoR for the following variables? Maybe for the FoR ones.\n tstep.forces_constraints_nodes[ibody_nodes,:] = MB_tstep[ibody].forces_constraints_nodes.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.forces_constraints_FoR[ibody, :] = MB_tstep[ibody].forces_constraints_FoR[ibody, :].astype(dtype=ct.c_double, order='F', copy=True)\n\n # Merge states\n ibody_num_dof = MB_beam[ibody].num_dof.value\n tstep.q[first_dof:first_dof+ibody_num_dof] = MB_tstep[ibody].q[:-10].astype(dtype=ct.c_double, order='F', copy=True)\n tstep.dqdt[first_dof:first_dof+ibody_num_dof] = MB_tstep[ibody].dqdt[:-10].astype(dtype=ct.c_double, order='F', copy=True)\n tstep.dqddt[first_dof:first_dof+ibody_num_dof] = MB_tstep[ibody].dqddt[:-10].astype(dtype=ct.c_double, order='F', copy=True)\n\n tstep.mb_dquatdt[ibody, :] = MB_tstep[ibody].dqddt[-4:].astype(dtype=ct.c_double, order='F', copy=True)\n\n first_dof += ibody_num_dof\n\n tstep.q[-10:] = MB_tstep[0].q[-10:].astype(dtype=ct.c_double, order='F', copy=True)\n tstep.dqdt[-10:] = MB_tstep[0].dqdt[-10:].astype(dtype=ct.c_double, order='F', copy=True)\n tstep.dqddt[-10:] = MB_tstep[0].dqddt[-10:].astype(dtype=ct.c_double, order='F', copy=True)\n\n # Define the new FoR information\n tstep.for_pos = MB_tstep[0].for_pos.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.for_vel = MB_tstep[0].for_vel.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.for_acc = MB_tstep[0].for_acc.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.quat = MB_tstep[0].quat.astype(dtype=ct.c_double, order='F', copy=True)\n\n\ndef update_mb_dB_before_merge(tstep, MB_tstep):\n \"\"\"\n update_mb_db_before_merge\n\n Updates the FoR information database before merging bodies\n\n Args:\n \ttstep (:class:`~sharpy.utils.datastructures.StructTimeStepInfo`): timestep information of the multibody system\n MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n \"\"\"\n\n for ibody in range(len(MB_tstep)):\n\n tstep.mb_FoR_pos[ibody,:] = MB_tstep[ibody].for_pos.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.mb_FoR_vel[ibody,:] = MB_tstep[ibody].for_vel.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.mb_FoR_acc[ibody,:] = MB_tstep[ibody].for_acc.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.mb_quat[ibody,:] = MB_tstep[ibody].quat.astype(dtype=ct.c_double, order='F', copy=True)\n assert (MB_tstep[ibody].mb_dquatdt[ibody, :] == MB_tstep[ibody].dqddt[-4:]).all(), \"Error in multibody storage\"\n tstep.mb_dquatdt[ibody, :] = MB_tstep[ibody].dqddt[-4:].astype(dtype=ct.c_double, order='F', copy=True)\n\n\ndef disp_and_accel2state(MB_beam, MB_tstep, Lambda, Lambda_dot, sys_size, num_LM_eq):\n \"\"\"\n disp2state\n\n Fills the vector of states according to the displacements information\n\n Args:\n MB_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body\n MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n Lambda(np.ndarray): Lagrange multipliers of holonomic constraints\n Lambda_dot(np.ndarray): Lagrange multipliers of non-holonomic constraints\n\n sys_size(int): number of degrees of freedom of the system of equations not accounting for lagrange multipliers\n num_LM_eq(int): Number of equations associated to the Lagrange Multipliers\n\n q(np.ndarray): Vector of states\n \tdqdt(np.ndarray): Time derivatives of states\n dqddt(np.ndarray): Second time derivatives of states\n \"\"\"\n q = np.zeros((sys_size + num_LM_eq, ), dtype=ct.c_double, order='F')\n dqdt = np.zeros((sys_size + num_LM_eq, ), dtype=ct.c_double, order='F')\n dqddt = np.zeros((sys_size + num_LM_eq, ), dtype=ct.c_double, order='F')\n\n first_dof = 0\n for ibody in range(len(MB_beam)):\n\n ibody_num_dof = MB_beam[ibody].num_dof.value\n if (MB_beam[ibody].FoR_movement == 'prescribed'):\n xbeamlib.cbeam3_solv_disp2state(MB_beam[ibody], MB_tstep[ibody])\n xbeamlib.cbeam3_solv_accel2state(MB_beam[ibody], MB_tstep[ibody])\n q[first_dof:first_dof+ibody_num_dof]=MB_tstep[ibody].q[:-10].astype(dtype=ct.c_double, order='F', copy=True)\n dqdt[first_dof:first_dof+ibody_num_dof]=MB_tstep[ibody].dqdt[:-10].astype(dtype=ct.c_double, order='F', copy=True)\n dqddt[first_dof:first_dof+ibody_num_dof]=MB_tstep[ibody].dqddt[:-10].astype(dtype=ct.c_double, order='F', copy=True)\n first_dof += ibody_num_dof\n\n elif (MB_beam[ibody].FoR_movement == 'free'):\n dquatdt = MB_tstep[ibody].mb_dquatdt[ibody, :].astype(dtype=ct.c_double, order='F', copy=True)\n xbeamlib.xbeam_solv_disp2state(MB_beam[ibody], MB_tstep[ibody])\n xbeamlib.xbeam_solv_accel2state(MB_beam[ibody], MB_tstep[ibody])\n q[first_dof:first_dof+ibody_num_dof+10]=MB_tstep[ibody].q.astype(dtype=ct.c_double, order='F', copy=True)\n dqdt[first_dof:first_dof+ibody_num_dof+10]=MB_tstep[ibody].dqdt.astype(dtype=ct.c_double, order='F', copy=True)\n dqddt[first_dof:first_dof+ibody_num_dof+10]=MB_tstep[ibody].dqddt.astype(dtype=ct.c_double, order='F', copy=True)\n dqddt[first_dof+ibody_num_dof+6:first_dof+ibody_num_dof+10]=dquatdt.astype(dtype=ct.c_double, order='F', copy=True)\n first_dof += ibody_num_dof + 10\n\n if num_LM_eq > 0:\n q[first_dof:] = Lambda.astype(dtype=ct.c_double, order='F', copy=True)\n dqdt[first_dof:] = Lambda_dot.astype(dtype=ct.c_double, order='F', copy=True)\n\n return q, dqdt, dqddt\n\ndef state2disp_and_accel(q, dqdt, dqddt, MB_beam, MB_tstep, num_LM_eq):\n \"\"\"\n state2disp\n\n Recovers the displacements from the states\n\n Longer description\n\n Args:\n MB_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body\n MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n q(np.ndarray): Vector of states\n \tdqdt(np.ndarray): Time derivatives of states\n dqddt(np.ndarray): Second time derivatives of states\n\n num_LM_eq(int): Number of equations associated to the Lagrange Multipliers\n\n Lambda(np.ndarray): Lagrange multipliers of holonomic constraints\n Lambda_dot(np.ndarray): Lagrange multipliers of non-holonomic constraints\n\n \"\"\"\n\n Lambda = np.zeros((num_LM_eq, ), dtype=ct.c_double, order='F')\n Lambda_dot = np.zeros((num_LM_eq, ), dtype=ct.c_double, order='F')\n\n first_dof = 0\n for ibody in range(len(MB_beam)):\n\n ibody_num_dof = MB_beam[ibody].num_dof.value\n if (MB_beam[ibody].FoR_movement == 'prescribed'):\n MB_tstep[ibody].q[:-10] = q[first_dof:first_dof+ibody_num_dof].astype(dtype=ct.c_double, order='F', copy=True)\n MB_tstep[ibody].dqdt[:-10] = dqdt[first_dof:first_dof+ibody_num_dof].astype(dtype=ct.c_double, order='F', copy=True)\n MB_tstep[ibody].dqddt[:-10] = dqddt[first_dof:first_dof+ibody_num_dof].astype(dtype=ct.c_double, order='F', copy=True)\n xbeamlib.cbeam3_solv_state2disp(MB_beam[ibody], MB_tstep[ibody])\n xbeamlib.cbeam3_solv_state2accel(MB_beam[ibody], MB_tstep[ibody])\n first_dof += ibody_num_dof\n\n elif (MB_beam[ibody].FoR_movement == 'free'):\n MB_tstep[ibody].q = q[first_dof:first_dof+ibody_num_dof+10].astype(dtype=ct.c_double, order='F', copy=True)\n MB_tstep[ibody].dqdt = dqdt[first_dof:first_dof+ibody_num_dof+10].astype(dtype=ct.c_double, order='F', copy=True)\n MB_tstep[ibody].dqddt = dqddt[first_dof:first_dof+ibody_num_dof+10].astype(dtype=ct.c_double, order='F', copy=True)\n MB_tstep[ibody].mb_dquatdt[ibody, :] = MB_tstep[ibody].dqddt[-4:]\n xbeamlib.xbeam_solv_state2disp(MB_beam[ibody], MB_tstep[ibody])\n xbeamlib.xbeam_solv_state2accel(MB_beam[ibody], MB_tstep[ibody])\n first_dof += ibody_num_dof + 10\n\n Lambda = q[first_dof:].astype(dtype=ct.c_double, order='F', copy=True)\n Lambda_dot = dqdt[first_dof:].astype(dtype=ct.c_double, order='F', copy=True)\n\n return Lambda, Lambda_dot\n\ndef get_elems_nodes_list(beam, ibody):\n \"\"\"\n get_elems_nodes_list\n\n This function returns the elements (``ibody_elements``) and the nodes\n (``ibody_nodes``) that belong to the body number ``ibody``\n\n Args:\n \t beam (:class:`~sharpy.structure.models.beam.Beam`): structural information of the multibody system\n ibody (int): Body number about which the information is required\n\n Returns:\n ibody_elements (list): List of elements that belong the ``ibody``\n ibody_nodes (list): List of nodes that belong the ``ibody``\n\n \"\"\"\n int_list = np.arange(beam.num_elem)\n ibody_elements = int_list[beam.body_number == ibody]\n ibody_nodes = np.sort(np.unique(beam.connectivities[ibody_elements, :].reshape(-1)))\n\n return ibody_elements, ibody_nodes\n" }, { "path": "sharpy/utils/multibodyjax.py", "content": "\"\"\"\nMultibody library for the NonlinearDynamicMultibodyJAX solver\nLibrary used to manipulate multibody systems\nTo use this library: import sharpy.utils.multibodyjax as mb\n\n\"\"\"\nimport numpy as np\nimport sharpy.structure.utils.xbeamlib as xbeamlib\nimport ctypes as ct\n\n\ndef split_multibody(beam, tstep, mb_data_dict, ts):\n \"\"\"\n split_multibody\n\n This functions splits a structure at a certain time step in its different bodies\n\n Args:\n \tbeam (:class:`~sharpy.structure.models.beam.Beam`): structural information of the multibody system\n \ttstep (:class:`~sharpy.utils.datastructures.StructTimeStepInfo`): timestep information of the multibody system\n mb_data_dict (dict): Dictionary including the multibody information\n ts (int): time step number\n\n Returns:\n MB_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body\n MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n \"\"\"\n\n MB_beam = []\n MB_tstep = []\n\n quat0 = tstep.quat.astype(dtype=ct.c_double, order='F', copy=True)\n for0_pos = tstep.for_pos.astype(dtype=ct.c_double, order='F', copy=True)\n for0_vel = tstep.for_vel.astype(dtype=ct.c_double, order='F', copy=True)\n\n ini_quat0 = beam.ini_info.quat.astype(dtype=ct.c_double, order='F', copy=True)\n ini_for0_pos = beam.ini_info.for_pos.astype(dtype=ct.c_double, order='F', copy=True)\n ini_for0_vel = beam.ini_info.for_vel.astype(dtype=ct.c_double, order='F', copy=True)\n\n for ibody in range(beam.num_bodies):\n ibody_beam = beam.get_body(ibody=ibody)\n ibody_tstep = tstep.get_body(beam, ibody_beam.num_dof, ibody=ibody)\n\n ibody_beam.FoR_movement = mb_data_dict['body_%02d' % ibody]['FoR_movement']\n\n ibody_beam.ini_info.compute_psi_local_AFoR(ini_for0_pos, ini_for0_vel, ini_quat0)\n ibody_beam.ini_info.change_to_local_AFoR(ini_for0_pos, ini_for0_vel, ini_quat0)\n if ts == 1:\n ibody_tstep.compute_psi_local_AFoR(for0_pos, for0_vel, quat0)\n ibody_tstep.change_to_local_AFoR(for0_pos, for0_vel, quat0)\n\n MB_beam.append(ibody_beam)\n MB_tstep.append(ibody_tstep)\n\n return MB_beam, MB_tstep\n\n\ndef merge_multibody(MB_tstep, MB_beam, beam, tstep, mb_data_dict, dt):\n \"\"\"\n merge_multibody\n\n This functions merges a series of bodies into a multibody system at a certain time step\n\n Longer description\n\n Args:\n MB_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body\n MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n \tbeam (:class:`~sharpy.structure.models.beam.Beam`): structural information of the multibody system\n \ttstep (:class:`~sharpy.utils.datastructures.StructTimeStepInfo`): timestep information of the multibody system\n mb_data_dict (dict): Dictionary including the multibody information\n dt(int): time step\n\n Returns:\n beam (:class:`~sharpy.structure.models.beam.Beam`): structural information of the multibody system\n \ttstep (:class:`~sharpy.utils.datastructures.StructTimeStepInfo`): timestep information of the multibody system\n \"\"\"\n\n update_mb_dB_before_merge(tstep, MB_tstep)\n\n quat0 = MB_tstep[0].quat.astype(dtype=ct.c_double, order='F', copy=True)\n for0_pos = MB_tstep[0].for_pos.astype(dtype=ct.c_double, order='F', copy=True)\n for0_vel = MB_tstep[0].for_vel.astype(dtype=ct.c_double, order='F', copy=True)\n\n for ibody in range(beam.num_bodies):\n MB_tstep[ibody].change_to_global_AFoR(for0_pos, for0_vel, quat0)\n\n first_dof = 0\n for ibody in range(beam.num_bodies):\n # Renaming for clarity\n ibody_elems = MB_beam[ibody].global_elems_num\n ibody_nodes = MB_beam[ibody].global_nodes_num\n\n # Merge tstep\n tstep.pos[ibody_nodes, :] = MB_tstep[ibody].pos.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.pos_dot[ibody_nodes, :] = MB_tstep[ibody].pos_dot.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.pos_ddot[ibody_nodes, :] = MB_tstep[ibody].pos_ddot.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.psi[ibody_elems, :, :] = MB_tstep[ibody].psi.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.psi_local[ibody_elems, :, :] = MB_tstep[ibody].psi_local.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.psi_dot[ibody_elems, :, :] = MB_tstep[ibody].psi_dot.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.psi_dot_local[ibody_elems, :, :] = MB_tstep[ibody].psi_dot_local.astype(dtype=ct.c_double, order='F',\n copy=True)\n tstep.psi_ddot[ibody_elems, :, :] = MB_tstep[ibody].psi_ddot.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.gravity_forces[ibody_nodes, :] = MB_tstep[ibody].gravity_forces.astype(dtype=ct.c_double, order='F',\n copy=True)\n tstep.steady_applied_forces[ibody_nodes, :] = MB_tstep[ibody].steady_applied_forces.astype(dtype=ct.c_double,\n order='F', copy=True)\n tstep.unsteady_applied_forces[ibody_nodes, :] = MB_tstep[ibody].unsteady_applied_forces.astype(\n dtype=ct.c_double, order='F', copy=True)\n tstep.runtime_steady_forces[ibody_nodes, :] = MB_tstep[ibody].runtime_steady_forces.astype(dtype=ct.c_double,\n order='F', copy=True)\n tstep.runtime_unsteady_forces[ibody_nodes, :] = MB_tstep[ibody].runtime_unsteady_forces.astype(\n dtype=ct.c_double, order='F', copy=True)\n # TODO: Do I need a change in FoR for the following variables? Maybe for the FoR ones.\n tstep.forces_constraints_nodes[ibody_nodes, :] = MB_tstep[ibody].forces_constraints_nodes.astype(\n dtype=ct.c_double, order='F', copy=True)\n tstep.forces_constraints_FoR[ibody, :] = MB_tstep[ibody].forces_constraints_FoR[ibody, :].astype(\n dtype=ct.c_double, order='F', copy=True)\n\n # Merge states\n ibody_num_dof = MB_beam[ibody].num_dof.value\n tstep.q[first_dof:first_dof + ibody_num_dof] = MB_tstep[ibody].q[:-10].astype(dtype=ct.c_double, order='F',\n copy=True)\n tstep.dqdt[first_dof:first_dof + ibody_num_dof] = MB_tstep[ibody].dqdt[:-10].astype(dtype=ct.c_double,\n order='F', copy=True)\n tstep.dqddt[first_dof:first_dof + ibody_num_dof] = MB_tstep[ibody].dqddt[:-10].astype(dtype=ct.c_double,\n order='F', copy=True)\n\n tstep.mb_dquatdt[ibody, :] = MB_tstep[ibody].dqddt[-4:].astype(dtype=ct.c_double, order='F', copy=True)\n\n first_dof += ibody_num_dof\n\n tstep.q[-10:] = MB_tstep[0].q[-10:].astype(dtype=ct.c_double, order='F', copy=True)\n tstep.dqdt[-10:] = MB_tstep[0].dqdt[-10:].astype(dtype=ct.c_double, order='F', copy=True)\n tstep.dqddt[-10:] = MB_tstep[0].dqddt[-10:].astype(dtype=ct.c_double, order='F', copy=True)\n\n # Define the new FoR information\n tstep.for_pos = MB_tstep[0].for_pos.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.for_vel = MB_tstep[0].for_vel.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.for_acc = MB_tstep[0].for_acc.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.quat = MB_tstep[0].quat.astype(dtype=ct.c_double, order='F', copy=True)\n\n\ndef update_mb_dB_before_merge(tstep, MB_tstep):\n \"\"\"\n update_mb_db_before_merge\n\n Updates the FoR information database before merging bodies\n\n Args:\n \ttstep (:class:`~sharpy.utils.datastructures.StructTimeStepInfo`): timestep information of the multibody system\n MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n \"\"\"\n\n for ibody in range(len(MB_tstep)):\n tstep.mb_FoR_pos[ibody, :] = MB_tstep[ibody].for_pos.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.mb_FoR_vel[ibody, :] = MB_tstep[ibody].for_vel.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.mb_FoR_acc[ibody, :] = MB_tstep[ibody].for_acc.astype(dtype=ct.c_double, order='F', copy=True)\n tstep.mb_quat[ibody, :] = MB_tstep[ibody].quat.astype(dtype=ct.c_double, order='F', copy=True)\n assert (MB_tstep[ibody].mb_dquatdt[ibody, :] == MB_tstep[ibody].dqddt[-4:]).all(), \"Error in multibody storage\"\n tstep.mb_dquatdt[ibody, :] = MB_tstep[ibody].dqddt[-4:].astype(dtype=ct.c_double, order='F', copy=True)\n\n\ndef disp_and_accel2state(MB_beam, MB_tstep, Lambda, Lambda_dot, sys_size, num_LM_eq):\n \"\"\"\n disp2state\n\n Fills the vector of states according to the displacements information\n\n Args:\n MB_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body\n MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n Lambda(np.ndarray): Lagrange multipliers of holonomic constraints\n Lambda_dot(np.ndarray): Lagrange multipliers of non-holonomic constraints\n\n sys_size(int): number of degrees of freedom of the system of equations not accounting for lagrange multipliers\n num_LM_eq(int): Number of equations associated to the Lagrange Multipliers\n\n q(np.ndarray): Vector of states\n \tdqdt(np.ndarray): Time derivatives of states\n dqddt(np.ndarray): Second time derivatives of states\n \"\"\"\n q = np.zeros((sys_size + num_LM_eq,), dtype=ct.c_double, order='F')\n dqdt = np.zeros((sys_size + num_LM_eq,), dtype=ct.c_double, order='F')\n dqddt = np.zeros((sys_size + num_LM_eq,), dtype=ct.c_double, order='F')\n\n first_dof = 0\n for ibody in range(len(MB_beam)):\n\n ibody_num_dof = MB_beam[ibody].num_dof.value\n if (MB_beam[ibody].FoR_movement == 'prescribed'):\n MB_tstep[ibody].for_vel = np.zeros(6)\n MB_tstep[ibody].for_acc = np.zeros(6)\n MB_tstep[ibody].quat = MB_beam[ibody].ini_info.quat\n xbeamlib.cbeam3_solv_disp2state(MB_beam[ibody], MB_tstep[ibody])\n xbeamlib.cbeam3_solv_accel2state(MB_beam[ibody], MB_tstep[ibody])\n q[first_dof:first_dof + ibody_num_dof] = MB_tstep[ibody].q[:-10].astype(dtype=ct.c_double, order='F',\n copy=True)\n dqdt[first_dof:first_dof + ibody_num_dof] = MB_tstep[ibody].dqdt[:-10].astype(dtype=ct.c_double, order='F',\n copy=True)\n dqddt[first_dof:first_dof + ibody_num_dof] = MB_tstep[ibody].dqddt[:-10].astype(dtype=ct.c_double,\n order='F', copy=True)\n first_dof += ibody_num_dof\n\n elif (MB_beam[ibody].FoR_movement == 'prescribed_trim'):\n MB_tstep[ibody].for_vel = np.zeros(6)\n MB_tstep[ibody].for_acc = np.zeros(6)\n xbeamlib.cbeam3_solv_disp2state(MB_beam[ibody], MB_tstep[ibody])\n xbeamlib.cbeam3_solv_accel2state(MB_beam[ibody], MB_tstep[ibody])\n q[first_dof:first_dof + ibody_num_dof] = MB_tstep[ibody].q[:-10].astype(dtype=ct.c_double, order='F',\n copy=True)\n dqdt[first_dof:first_dof + ibody_num_dof] = MB_tstep[ibody].dqdt[:-10].astype(dtype=ct.c_double, order='F',\n copy=True)\n dqddt[first_dof:first_dof + ibody_num_dof] = MB_tstep[ibody].dqddt[:-10].astype(dtype=ct.c_double,\n order='F', copy=True)\n first_dof += ibody_num_dof\n\n elif (MB_beam[ibody].FoR_movement == 'free'):\n dquatdt = MB_tstep[ibody].mb_dquatdt[ibody, :].astype(dtype=ct.c_double, order='F', copy=True)\n xbeamlib.xbeam_solv_disp2state(MB_beam[ibody], MB_tstep[ibody])\n xbeamlib.xbeam_solv_accel2state(MB_beam[ibody], MB_tstep[ibody])\n q[first_dof:first_dof + ibody_num_dof + 10] = MB_tstep[ibody].q.astype(dtype=ct.c_double, order='F',\n copy=True)\n dqdt[first_dof:first_dof + ibody_num_dof + 10] = MB_tstep[ibody].dqdt.astype(dtype=ct.c_double, order='F',\n copy=True)\n dqddt[first_dof:first_dof + ibody_num_dof + 10] = MB_tstep[ibody].dqddt.astype(dtype=ct.c_double, order='F',\n copy=True)\n dqddt[first_dof + ibody_num_dof + 6:first_dof + ibody_num_dof + 10] = dquatdt.astype(dtype=ct.c_double,\n order='F', copy=True)\n first_dof += ibody_num_dof + 10\n\n if num_LM_eq > 0:\n q[first_dof:] = Lambda.astype(dtype=ct.c_double, order='F', copy=True)\n dqdt[first_dof:] = Lambda_dot.astype(dtype=ct.c_double, order='F', copy=True)\n\n return q, dqdt, dqddt\n\n\ndef state2disp_and_accel(q, dqdt, dqddt, MB_beam, MB_tstep, num_LM_eq):\n \"\"\"\n state2disp\n\n Recovers the displacements from the states\n\n Longer description\n\n Args:\n MB_beam (list(:class:`~sharpy.structure.models.beam.Beam`)): each entry represents a body\n MB_tstep (list(:class:`~sharpy.utils.datastructures.StructTimeStepInfo`)): each entry represents a body\n q(np.ndarray): Vector of states\n \tdqdt(np.ndarray): Time derivatives of states\n dqddt(np.ndarray): Second time derivatives of states\n\n num_LM_eq(int): Number of equations associated to the Lagrange Multipliers\n\n Lambda(np.ndarray): Lagrange multipliers of holonomic constraints\n Lambda_dot(np.ndarray): Lagrange multipliers of non-holonomic constraints\n\n \"\"\"\n\n first_dof = 0\n for ibody in range(len(MB_beam)):\n\n ibody_num_dof = MB_beam[ibody].num_dof.value\n if (MB_beam[ibody].FoR_movement == 'prescribed'):\n MB_tstep[ibody].q[:-10] = q[first_dof:first_dof + ibody_num_dof].astype(dtype=ct.c_double, order='F',\n copy=True)\n MB_tstep[ibody].dqdt[:-10] = dqdt[first_dof:first_dof + ibody_num_dof].astype(dtype=ct.c_double, order='F',\n copy=True)\n MB_tstep[ibody].dqddt[:-10] = dqddt[first_dof:first_dof + ibody_num_dof].astype(dtype=ct.c_double,\n order='F', copy=True)\n xbeamlib.cbeam3_solv_state2disp(MB_beam[ibody], MB_tstep[ibody])\n xbeamlib.cbeam3_solv_state2accel(MB_beam[ibody], MB_tstep[ibody])\n first_dof += ibody_num_dof\n\n elif (MB_beam[ibody].FoR_movement == 'prescribed_trim'):\n MB_tstep[ibody].q[:-10] = q[first_dof:first_dof + ibody_num_dof].astype(dtype=ct.c_double, order='F',\n copy=True)\n MB_tstep[ibody].dqdt[:-10] = dqdt[first_dof:first_dof + ibody_num_dof].astype(dtype=ct.c_double, order='F',\n copy=True)\n MB_tstep[ibody].dqddt[:-10] = dqddt[first_dof:first_dof + ibody_num_dof].astype(dtype=ct.c_double,\n order='F', copy=True)\n xbeamlib.cbeam3_solv_state2disp(MB_beam[ibody], MB_tstep[ibody])\n xbeamlib.cbeam3_solv_state2accel(MB_beam[ibody], MB_tstep[ibody])\n first_dof += ibody_num_dof\n\n elif (MB_beam[ibody].FoR_movement == 'free'):\n MB_tstep[ibody].q = q[first_dof:first_dof + ibody_num_dof + 10].astype(dtype=ct.c_double, order='F',\n copy=True)\n MB_tstep[ibody].dqdt = dqdt[first_dof:first_dof + ibody_num_dof + 10].astype(dtype=ct.c_double, order='F',\n copy=True)\n MB_tstep[ibody].dqddt = dqddt[first_dof:first_dof + ibody_num_dof + 10].astype(dtype=ct.c_double, order='F',\n copy=True)\n MB_tstep[ibody].mb_dquatdt[ibody, :] = MB_tstep[ibody].dqddt[-4:]\n xbeamlib.xbeam_solv_state2disp(MB_beam[ibody], MB_tstep[ibody])\n xbeamlib.xbeam_solv_state2accel(MB_beam[ibody], MB_tstep[ibody])\n first_dof += ibody_num_dof + 10\n\n lm_h = q[first_dof:].astype(dtype=ct.c_double, order='F', copy=True)\n lm_n = dqdt[first_dof:].astype(dtype=ct.c_double, order='F', copy=True)\n\n return lm_h, lm_n\n\n\ndef get_elems_nodes_list(beam, ibody):\n \"\"\"\n get_elems_nodes_list\n\n This function returns the elements (``ibody_elements``) and the nodes\n (``ibody_nodes``) that belong to the body number ``ibody``\n\n Args:\n \t beam (:class:`~sharpy.structure.models.beam.Beam`): structural information of the multibody system\n ibody (int): Body number about which the information is required\n\n Returns:\n ibody_elements (list): List of elements that belong the ``ibody``\n ibody_nodes (list): List of nodes that belong the ``ibody``\n\n \"\"\"\n int_list = np.arange(beam.num_elem)\n ibody_elements = int_list[beam.body_number == ibody]\n ibody_nodes = np.sort(np.unique(beam.connectivities[ibody_elements, :].reshape(-1)))\n\n return ibody_elements, ibody_nodes\n" }, { "path": "sharpy/utils/num_utils.py", "content": "import numpy as np\nimport ctypes as ct\nimport scipy as sc\n\n\ndef check_symmetric(mat):\n return np.allclose(mat.transpose(), mat, atol=1e-3)\n\n\nif __name__ == '__main__':\n a = np.array([[1, 2], [3, 4]])\n print(check_symmetric(a))\n\n a = np.array([[1, 2], [2, 1]])\n print(check_symmetric(a))\n" }, { "path": "sharpy/utils/plotutils.py", "content": "\"\"\"Plotting utilities\n\"\"\"\nimport numpy as np\nfrom numpy import ndarray\n\nfrom typing import Optional\nfrom os import PathLike\n\n\nimport vtk\nfrom vtk.numpy_interface import algorithms as algs\nfrom vtk.numpy_interface import dataset_adapter as dsa\n\ndef plot_frame_to_vtk(\n grid_arr: ndarray,\n filename: str | PathLike,\n node_scalar_data: Optional[dict[str, ndarray]] = None,\n node_vector_data: Optional[dict[str, ndarray]] = None,\n cell_scalar_data: Optional[dict[str, ndarray]] = None,\n cell_vector_data: Optional[dict[str, ndarray]] = None,\n) -> None:\n r\"\"\"\n Plot a single timestep of grid data\n :param grid_arr: Structured grid array with shape (n_x, n_y, n_z, 3)\n :param filename: Base filename, including directory. Information on the frame number will be\n appended to this.\n :param node_scalar_data: Dictionary of node scalar data\n :param node_vector_data: Dictionary of node vector data\n :param cell_scalar_data: Dictionary of cell scalar data\n :param cell_vector_data: Dictionary of cell vector data\n \"\"\"\n\n if grid_arr.shape[-1] != 3:\n raise ValueError(\"grid_arr must have trailing dimension of size 3\")\n\n # planar grid should have 3 dimensions, while volume grid should have 4 dimensions\n match grid_arr.ndim:\n case 3:\n is_planar = True\n case 4:\n is_planar = False\n case _:\n raise ValueError(\n f\"grid_arr must have 3 or 4 dimensions, got {grid_arr.ndim}-D array\"\n )\n\n sg = vtk.vtkStructuredGrid()\n if is_planar:\n sg.SetDimensions(*grid_arr.shape[:-1], 1)\n else:\n sg.SetDimensions(*grid_arr.shape[:-1])\n\n i_swap = 2 - int(is_planar) # we swap axes as VTK likes z, y, x order\n\n # add point coordinate data\n points = vtk.vtkPoints()\n points_vec = algs.make_vector(\n *[np.swapaxes(grid_arr[..., i], 0, i_swap).ravel() for i in range(3)]\n )\n points.SetData(dsa.numpyTovtkDataArray(points_vec, \"Points\"))\n sg.SetPoints(points)\n\n # cell scalar data\n if cell_scalar_data is not None:\n for name, arr in cell_scalar_data.items():\n sg.GetCellData().AddArray(\n dsa.numpyTovtkDataArray(np.swapaxes(arr, 0, i_swap).ravel(), name)\n )\n\n # cell vector data\n if cell_vector_data is not None:\n for name, arr in cell_vector_data.items():\n vectors = algs.make_vector(\n np.swapaxes(arr[..., 0], 0, i_swap).ravel(),\n np.swapaxes(arr[..., 1], 0, i_swap).ravel(),\n np.swapaxes(arr[..., 2], 0, i_swap).ravel(),\n )\n sg.GetCellData().AddArray(dsa.numpyTovtkDataArray(vectors, name))\n\n # point scalar data\n if node_scalar_data is not None:\n for name, arr in node_scalar_data.items():\n sg.GetPointData().AddArray(\n dsa.numpyTovtkDataArray(np.swapaxes(arr, 0, i_swap).ravel(), name)\n )\n\n # point vector data\n if node_vector_data is not None:\n for name, arr in node_vector_data.items():\n vectors = algs.make_vector(\n np.swapaxes(arr[..., 0], 0, i_swap).ravel(),\n np.swapaxes(arr[..., 1], 0, i_swap).ravel(),\n np.swapaxes(arr[..., 2], 0, i_swap).ravel(),\n )\n sg.GetPointData().AddArray(dsa.numpyTovtkDataArray(vectors, name))\n\n # write to file\n writer = vtk.vtkXMLStructuredGridWriter()\n writer.SetFileName(filename)\n writer.SetInputData(sg)\n writer.Write()\n\n\ndef set_axes_equal(ax):\n '''Make axes of 3D plot have equal scale so that spheres appear as spheres,\n cubes as cubes, etc.. This is one possible solution to Matplotlib's\n ax.set_aspect('equal') and ax.axis('equal') not working for 3D.\n\n Input\n ax: a matplotlib axis, e.g., as output from plt.gca().\n '''\n\n x_limits = ax.get_xlim3d()\n y_limits = ax.get_ylim3d()\n z_limits = ax.get_zlim3d()\n\n x_range = abs(x_limits[1] - x_limits[0])\n x_middle = np.mean(x_limits)\n y_range = abs(y_limits[1] - y_limits[0])\n y_middle = np.mean(y_limits)\n z_range = abs(z_limits[1] - z_limits[0])\n z_middle = np.mean(z_limits)\n\n # The plot bounding box is a sphere in the sense of the infinity\n # norm, hence I call half the max range the plot radius.\n plot_radius = 0.5*max([x_range, y_range, z_range])\n\n ax.set_xlim3d([x_middle - plot_radius, x_middle + plot_radius])\n ax.set_ylim3d([y_middle - plot_radius, y_middle + plot_radius])\n ax.set_zlim3d([z_middle - plot_radius, z_middle + plot_radius])\n\n\ndef plot_timestep(data, tstep=-1, minus_mstar=0, plotly=False, custom_scaling=False, z_compression=0.5):\n '''\n This function creates a simple plot with matplotlib of a\n timestep in SHARPy.\n Notice that this function is not efficient at all for large surfaces, it just\n aims to provide a simple way of generating simple quick plots.\n\n Input:\n data (``sharpy.presharpy.presharpy.PreSharpy``):\n Main data strucuture in SHARPy\n \n tstep (int):\n Time step to plot\n \n minus_mstar (int):\n number of wake panels to remove from the visualisation (for efficiency)\n \n plotly(bool):\n calls in the plotly library, graph will not plot if set to false.\n \n custom_scaling(bool):\n aspect ratio of the wing will be modelled realistically if set to true.\n \n z_compression(int):\n if custom scaling is enabled, this decides how much the z axis is compressed.\n\n\n Returns:\n Plot object:\n Can be matplotlib.pyplot.plt (plotly=False) or\n plotly.graph_objects.Figure() (plotly=True)\n '''\n\n if len(data.structure.timestep_info) == 0:\n struct_tstep = data.structure.ini_info\n aero_tstep = data.aero.ini_info\n else:\n struct_tstep = data.structure.timestep_info[tstep]\n aero_tstep = data.aero.timestep_info[tstep]\n\n if not plotly:\n try:\n from mpl_toolkits.mplot3d import axes3d\n import matplotlib.pyplot as plt\n except ModuleNotFoundError:\n print(\"Matplotlib package not found\")\n return\n\n fig = plt.figure()\n ax = fig.add_subplot(111, projection='3d')\n\n # Plot structure\n # Split into different beams\n for ielem in range(data.structure.num_elem):\n nodes = data.structure.connectivities[ielem, :][[0, 2, 1]]\n ax.plot(struct_tstep.pos[nodes, 0],\n struct_tstep.pos[nodes, 1],\n struct_tstep.pos[nodes, 2],\n '-ob')\n\n # Plot aerodynamic grid\n if aero_tstep is not None:\n for isurf in range(aero_tstep.n_surf):\n # Solid grid\n ax.plot_wireframe(aero_tstep.zeta[isurf][0, :, :],\n aero_tstep.zeta[isurf][1, :, :],\n aero_tstep.zeta[isurf][2, :, :])\n Mstar, Nstar = aero_tstep.dimensions_star[isurf]\n # Wake grid\n ax.plot_wireframe(aero_tstep.zeta_star[isurf][0, :(Mstar - minus_mstar), :],\n aero_tstep.zeta_star[isurf][1, :(Mstar - minus_mstar), :],\n aero_tstep.zeta_star[isurf][2, :(Mstar - minus_mstar), :])\n\n else:\n try: \n import plotly.graph_objects as go\n except ModuleNotFoundError:\n print(\"Plotly package not found\")\n return\n\n fig = go.Figure()\n \n # Plot aerodynamic grid\n if aero_tstep is not None:\n for isurf in range(aero_tstep.n_surf):\n M, N = aero_tstep.dimensions[isurf]\n # Plot surfaces\n for i_m in range(M):\n for i_n in range(N):\n vert_m = [i_m, i_m + 1, i_m +1, i_m, i_m]\n vert_n = [i_n, i_n, i_n +1, i_n + 1, i_n]\n xsurf = aero_tstep.zeta[isurf][0, vert_m, vert_n]\n ysurf = aero_tstep.zeta[isurf][1, vert_m, vert_n]\n zsurf = aero_tstep.zeta[isurf][2, vert_m, vert_n]\n\n if i_m == 0 and i_n == 0:\n fig.add_trace(go.Scatter3d(x=xsurf,\n y=ysurf,\n z=zsurf,\n mode='lines',\n line={'color':'grey'},\n surfaceaxis=2,\n name='Aero surface'))\n else:\n fig.add_trace(go.Scatter3d(x=xsurf,\n y=ysurf,\n z=zsurf,\n mode='lines',\n line={'color':'grey'},\n surfaceaxis=2,\n showlegend=False))\n\n # Plot wireframe\n for i_m in range(M + 1):\n fig.add_trace(go.Scatter3d(x=aero_tstep.zeta[isurf][0, i_m, :],\n y=aero_tstep.zeta[isurf][1, i_m, :],\n z=aero_tstep.zeta[isurf][2, i_m, :],\n mode='lines',\n line={'color':'black'},\n showlegend=False))\n for i_n in range(N + 1):\n fig.add_trace(go.Scatter3d(x=aero_tstep.zeta[isurf][0, :, i_n],\n y=aero_tstep.zeta[isurf][1, :, i_n],\n z=aero_tstep.zeta[isurf][2, :, i_n],\n mode='lines',\n line={'color':'black'},\n showlegend=False))\n\n Mstar, Nstar = aero_tstep.dimensions_star[isurf]\n # Wake grid\n for i_m in range(Mstar - minus_mstar):\n for i_n in range(Nstar):\n vert_m = [i_m, i_m + 1, i_m +1, i_m, i_m]\n vert_n = [i_n, i_n, i_n +1, i_n + 1, i_n]\n xsurf = aero_tstep.zeta_star[isurf][0, vert_m, vert_n]\n ysurf = aero_tstep.zeta_star[isurf][1, vert_m, vert_n]\n zsurf = aero_tstep.zeta_star[isurf][2, vert_m, vert_n]\n\n if i_m == 0 and i_n == 0:\n fig.add_trace(go.Scatter3d(x=xsurf,\n y=ysurf,\n z=zsurf,\n mode='lines',\n line={'color':'lightskyblue'},\n surfaceaxis=2,\n name='Aero wake'))\n else:\n fig.add_trace(go.Scatter3d(x=xsurf,\n y=ysurf,\n z=zsurf,\n mode='lines',\n line={'color':'lightskyblue'},\n surfaceaxis=2,\n showlegend=False))\n\n for i_m in range(Mstar + 1 - minus_mstar):\n fig.add_trace(go.Scatter3d(x=aero_tstep.zeta_star[isurf][0, i_m, :],\n y=aero_tstep.zeta_star[isurf][1, i_m, :],\n z=aero_tstep.zeta_star[isurf][2, i_m, :],\n mode='lines',\n line={'color':'grey'},\n showlegend=False))\n for i_n in range(Nstar + 1):\n fig.add_trace(go.Scatter3d(x=aero_tstep.zeta_star[isurf][0, :(Mstar + 1 - minus_mstar), i_n],\n y=aero_tstep.zeta_star[isurf][1, :(Mstar + 1 - minus_mstar), i_n],\n z=aero_tstep.zeta_star[isurf][2, :(Mstar + 1 - minus_mstar), i_n],\n mode='lines',\n line={'color':'grey'},\n showlegend=False))\n \n\n # Plot structure\n # Split into different beams\n nodes = data.structure.connectivities[0, :][[0, 2, 1]]\n fig = fig.add_trace(go.Scatter3d(x=struct_tstep.pos[nodes, 0],\n y=struct_tstep.pos[nodes, 1],\n z=struct_tstep.pos[nodes, 2],\n marker= {'size':2, 'color':'blue'},\n line = {'color':'blue', 'width':4},\n name='Beam nodes'))\n for ielem in range(1, data.structure.num_elem):\n nodes = data.structure.connectivities[ielem, :][[0, 2, 1]]\n fig.add_trace(go.Scatter3d(x=struct_tstep.pos[nodes, 0],\n y=struct_tstep.pos[nodes, 1],\n z=struct_tstep.pos[nodes, 2],\n marker= {'size':2, 'color':'blue'},\n line = {'color':'blue', 'width':4},\n showlegend=False))\n \n#I LOVE SEMICOLONS RAAAAH\n\n## Custom Scaling::\n# This changes how the plotly graph is scaled so the aspect ratio of your wing stays realistic.\n# It takes the range of the x and y axes, and scales the graph based on them.\n# z is set to 0.5 by default so the wake 'plane' is not as large as it originally is.\n# This has the effect of making the wing flex less visible.\n# Increase the z_compression value if you want to make it more visible.\n# prints were used to check the min and max values of x and y in the graph while implementing this; if something goes wrong you might want to check those out.\n\n if custom_scaling==True:\n #print(np.max(aero_tstep.zeta_star[isurf][0,:(Mstar - minus_mstar),:]))\n #print(np.min(aero_tstep.zeta[isurf][0,:,:]))\n #print(np.max(aero_tstep.zeta[isurf][1,:,:]))\n #print(np.min(aero_tstep.zeta[isurf][1,:,:]))\n rangex=np.max(aero_tstep.zeta_star[isurf][0,:(Mstar - minus_mstar),:])-np.min(aero_tstep.zeta[isurf][0,:,:]);rangey=np.max(aero_tstep.zeta[isurf][1,:,:])-np.min(aero_tstep.zeta[isurf][1,:,:]);fig.update_layout(scene=dict(aspectmode='manual',\n aspectratio=dict(x=rangex,y=rangey,z=z_compression)))\n\n return fig\n" }, { "path": "sharpy/utils/rom_interface.py", "content": "from abc import ABCMeta, abstractmethod\nimport sharpy.utils.cout_utils as cout\nimport os\nimport sharpy.utils.frequencyutils as frequencyutils\n\ndict_of_roms = {}\nroms = {} # for internal working\n\n\n# decorator\ndef rom(arg):\n # global available_solvers\n global dict_of_roms\n try:\n arg.rom_id\n except AttributeError:\n raise AttributeError('Class defined as ROM has no rom_id attribute')\n dict_of_roms[arg.rom_id] = arg\n return arg\n\n\ndef print_available_solvers():\n cout.cout_wrap('The available ROMs on this session are:', 2)\n for name, i_solver in dict_of_roms.items():\n cout.cout_wrap('%s ' % i_solver.solver_id, 2)\n\n\nclass BaseRom(metaclass=ABCMeta):\n\n # Solver id for populating available_roms[]\n @property\n def rom_id(self):\n raise NotImplementedError\n\n # The input is a ProblemData class structure\n @abstractmethod\n def initialise(self):\n pass\n\n # This executes the solver\n @abstractmethod\n def run(self, ss):\n pass\n\n @staticmethod\n def compare_fom_rom(y1, y2, wv=None, **kwargs):\n return frequencyutils.freqresp_relative_error(y1, y2, wv, **kwargs)\n\n # Save the ROM matrices to the given filename\n def save(self, filename):\n raise NotImplementedError('Save method for the currently chosen ROM is not yet supported')\n\ndef rom_from_string(string):\n return dict_of_roms[string]\n\ndef initialise_rom(rom_name):\n cout.cout_wrap('Generating an instance of %s' % rom_name, 2)\n cls_type = rom_from_string(rom_name)\n solver = cls_type()\n return solver\n\n\ndef dictionary_of_solvers():\n # import sharpy.rom\n dictionary = dict()\n for solver in dict_of_roms:\n if not solver.lower() == 'SaveData'.lower():\n # TODO: why it does not work for savedata?\n init_solver = initialise_rom(solver)\n dictionary[solver] = init_solver.settings_default\n\n return dictionary\n" }, { "path": "sharpy/utils/settings.py", "content": "\"\"\"\nSettings Generator Utilities\n\"\"\"\nimport configparser\nimport ctypes as ct\nimport numpy as np\nimport sharpy.utils.exceptions as exceptions\nimport sharpy.utils.cout_utils as cout\nimport ast\n\n\nclass DictConfigParser(configparser.ConfigParser):\n def as_dict(self):\n d = dict(self._sections)\n for k in d:\n d[k] = dict(self._defaults, **d[k])\n d[k].pop('__name__', None)\n return d\n\n\ndef cast(k, v, pytype, ctype, default):\n try:\n # if default is None:\n # raise TypeError\n val = ctype(pytype(v))\n except KeyError:\n val = ctype(default)\n cout.cout_wrap(\"--- The variable \" + k + \" has no given value, using the default \" + default, 2)\n except TypeError:\n raise exceptions.NoDefaultValueException(k)\n except ValueError:\n val = ctype(v.value)\n return val\n\n\ndef to_custom_types(dictionary, types, default, options=dict(), no_ctype=True):\n for k, v in types.items():\n if type(v) != list:\n data_type = v\n else:\n if k in dictionary:\n data_type = get_data_type_for_several_options(dictionary[k], v, k)\n else:\n # Choose first data type in list for default value\n data_type = v[0]\n dictionary[k] = get_custom_type(dictionary, data_type, k, default, no_ctype)\n \n check_settings_in_options(dictionary, types, options)\n\n unrecognised_settings = []\n for k in dictionary.keys():\n if k not in list(types.keys()):\n unrecognised_settings.append(exceptions.NotRecognisedSetting(k))\n\n for setting in unrecognised_settings:\n cout.cout_wrap(repr(setting), 4)\n\n if unrecognised_settings:\n raise Exception(unrecognised_settings)\n\n\ndef get_data_type_for_several_options(dict_value, list_settings_types, setting_name):\n \"\"\"\n Checks the data type of the setting input in case of several data type options. \n Only a scalar or list can be the case for these cases. \n\n Args:\n dict_values: Dictionary value of processed settings\n list_settings_types (list): Possible setting type options for this setting\n\n Raises:\n exception.NotValidSetting: if the setting is not allowed.\n \"\"\"\n for data_type in list_settings_types:\n if 'list' in data_type and (type(dict_value) == list or not np.isscalar(dict_value)):\n return data_type\n elif 'list' not in data_type and np.isscalar(dict_value):\n return data_type\n exceptions.NotValidSettingType(setting_name, dict_value, list_settings_types)\n\ndef get_default_value(default_value, k, v, data_type = None, py_type = None):\n if default_value is None:\n raise exceptions.NoDefaultValueException(k)\n if v in ['float', 'int', 'bool']:\n converted_value = cast(k, default_value, py_type, data_type, default_value)\n elif v == 'str':\n converted_value = cast(k, default_value, eval(v), eval(v), default_value)\n else:\n converted_value = default_value.copy()\n notify_default_value(k, converted_value)\n return converted_value\n\ndef get_custom_type(dictionary, v, k, default, no_ctype):\n if v == 'int':\n if no_ctype:\n data_type = int\n else:\n data_type = ct.c_int\n try:\n dictionary[k] = cast(k, dictionary[k], int, data_type, default[k])\n except KeyError:\n dictionary[k] = get_default_value(default[k], k, v, data_type=data_type, py_type=int)\n\n elif v == 'float':\n if no_ctype:\n data_type = float\n else:\n data_type = ct.c_double\n try:\n dictionary[k] = cast(k, dictionary[k], float, data_type, default[k])\n except KeyError:\n dictionary[k] = get_default_value(default[k], k, v, data_type=data_type, py_type=float)\n\n elif v == 'str':\n try:\n dictionary[k] = cast(k, dictionary[k], str, str, default[k])\n except KeyError:\n dictionary[k] = get_default_value(default[k], k, v)\n\n elif v == 'bool':\n if no_ctype:\n data_type = bool\n else:\n data_type = ct.c_bool\n try:\n dictionary[k] = cast(k, dictionary[k], str2bool, data_type, default[k])\n except KeyError:\n dictionary[k] = get_default_value(default[k], k, v, data_type=data_type, py_type=str2bool)\n\n elif v == 'list(str)':\n try:\n # if isinstance(dictionary[k], list):\n # continue\n # dictionary[k] = dictionary[k].split(',')\n # getting rid of leading and trailing spaces\n dictionary[k] = list(map(lambda x: x.strip(), dictionary[k]))\n except KeyError:\n dictionary[k] = get_default_value(default[k], k, v)\n\n elif v == 'list(dict)':\n try:\n # if isinstance(dictionary[k], list):\n # continue\n # dictionary[k] = dictionary[k].split(',')\n # getting rid of leading and trailing spaces\n for i in range(len(dictionary[k])):\n dictionary[k][i] = ast.literal_eval(dictionary[k][i])\n except KeyError:\n dictionary[k] = get_default_value(default[k], k, v)\n\n elif v == 'list(float)':\n try:\n dictionary[k]\n except KeyError:\n dictionary[k] = get_default_value(default[k], k, v)\n\n if isinstance(dictionary[k], np.ndarray):\n return dictionary[k]\n if isinstance(dictionary[k], list):\n for i in range(len(dictionary[k])):\n dictionary[k][i] = float(dictionary[k][i])\n dictionary[k] = np.array(dictionary[k])\n return dictionary[k]\n # dictionary[k] = dictionary[k].split(',')\n # # getting rid of leading and trailing spaces\n # dictionary[k] = list(map(lambda x: x.strip(), dictionary[k]))\n if dictionary[k].find(',') < 0:\n dictionary[k] = np.fromstring(dictionary[k].strip('[]'), sep=' ', dtype=ct.c_double)\n else:\n dictionary[k] = np.fromstring(dictionary[k].strip('[]'), sep=',', dtype=ct.c_double)\n\n elif v == 'list(int)':\n try:\n dictionary[k]\n except KeyError:\n dictionary[k] = get_default_value(default[k], k, v)\n\n if isinstance(dictionary[k], np.ndarray):\n return dictionary[k]\n if isinstance(dictionary[k], list):\n for i in range(len(dictionary[k])):\n dictionary[k][i] = int(dictionary[k][i])\n dictionary[k] = np.array(dictionary[k])\n return dictionary[k]\n # dictionary[k] = dictionary[k].split(',')\n # # getting rid of leading and trailing spaces\n # dictionary[k] = list(map(lambda x: x.strip(), dictionary[k]))\n if dictionary[k].find(',') < 0:\n dictionary[k] = np.fromstring(dictionary[k].strip('[]'), sep=' ').astype(ct.c_int)\n else:\n dictionary[k] = np.fromstring(dictionary[k].strip('[]'), sep=',').astype(ct.c_int)\n\n elif v == 'list(complex)':\n try:\n dictionary[k]\n except KeyError:\n dictionary[k] = get_default_value(default[k], k, v)\n\n if isinstance(dictionary[k], np.ndarray):\n return dictionary[k]\n if isinstance(dictionary[k], list):\n for i in range(len(dictionary[k])):\n dictionary[k][i] = complex(dictionary[k][i])\n dictionary[k] = np.array(dictionary[k])\n return dictionary[k]\n # dictionary[k] = dictionary[k].split(',')\n # # getting rid of leading and trailing spaces\n # dictionary[k] = list(map(lambda x: x.strip(), dictionary[k]))\n if dictionary[k].find(',') < 0:\n dictionary[k] = np.fromstring(dictionary[k].strip('[]'), sep=' ').astype(complex)\n else:\n dictionary[k] = np.fromstring(dictionary[k].strip('[]'), sep=',').astype(complex)\n\n elif v == 'dict':\n try:\n if not isinstance(dictionary[k], dict):\n raise TypeError('Setting for {:s} is not a dictionary'.format(k))\n except KeyError:\n dictionary[k] = get_default_value(default[k], k, v)\n else:\n raise TypeError('Variable %s has an unknown type (%s) that cannot be casted' % (k, v))\n return dictionary[k]\n\ndef check_settings_in_options(settings, settings_types, settings_options):\n \"\"\"\n Checks that settings given a type ``str`` or ``int`` and allowable options are indeed valid.\n\n Args:\n settings (dict): Dictionary of processed settings\n settings_types (dict): Dictionary of settings types\n settings_options (dict): Dictionary of options (may be empty)\n\n Raises:\n exception.NotValidSetting: if the setting is not allowed.\n \"\"\"\n for k in settings_options:\n if settings_types[k] == 'int':\n try:\n value = settings[k].value\n except AttributeError:\n value = settings[k]\n if value not in settings_options[k]:\n raise exceptions.NotValidSetting(k, value, settings_options[k])\n\n elif settings_types[k] == 'str':\n value = settings[k]\n if value not in settings_options[k] and value:\n # checks that the value is within the options and that it is not an empty string.\n raise exceptions.NotValidSetting(k, value, settings_options[k])\n\n elif settings_types[k] == 'list(str)':\n for item in settings[k]:\n if item not in settings_options[k] and item:\n raise exceptions.NotValidSetting(k, item, settings_options[k])\n\n else:\n pass # no other checks implemented / required\n\n\ndef load_config_file(file_name: str) -> dict:\n \"\"\"This function reads the flight condition and solver input files.\n\n Args:\n file_name (str): contains the path and file name of the file to be read by the ``configparser``\n reader.\n\n Returns:\n config (dict): a ``ConfigParser`` object that behaves like a dictionary\n \"\"\"\n # config = DictConfigParser()\n # config.read(file_name)\n # dict_config = config.as_dict()\n import configobj\n dict_config = configobj.ConfigObj(file_name)\n return dict_config\n\n\ndef str2bool(string):\n false_list = ['false', 'off', '0', 'no']\n if isinstance(string, bool):\n return string\n if isinstance(string, ct.c_bool):\n return string.value\n\n if not string:\n return False\n elif string.lower() in false_list:\n return False\n else:\n return True\n\n\ndef notify_default_value(k, v):\n cout.cout_wrap('Variable ' + k + ' has no assigned value in the settings file.')\n cout.cout_wrap(' will default to the value: ' + str(v), 1)\n\n\nclass SettingsTable:\n \"\"\"\n Generates the documentation's setting table at runtime.\n\n Sphinx is our chosen documentation manager and takes docstrings in reStructuredText format. Given that the SHARPy\n solvers contain several settings, this class produces a table in reStructuredText format with the solver's settings\n and adds it to the solver's docstring.\n\n This table will then be printed alongside the remaining docstrings.\n\n To generate the table, parse the setting's description to a solver dictionary named ``settings_description``, in a\n similar fashion to what is done with ``settings_types`` and ``settings_default``. If no description is given it will\n be left blank.\n\n Then, add at the end of the solver's class declaration method an instance of the ``SettingsTable`` class and a call\n to the ``SettingsTable.generate()`` method.\n\n Examples:\n The end of the solver's class declaration should contain\n\n .. code-block:: python\n\n # Generate documentation table\n settings_table = settings.SettingsTable()\n __doc__ += settings_table.generate(settings_types, settings_default, settings_description)\n\n to generate the settings table.\n\n \"\"\"\n def __init__(self):\n self.n_fields = 4\n self.n_settings = 0\n self.field_length = [0] * self.n_fields\n self.titles = ['Name', 'Type', 'Description', 'Default']\n\n self.settings_types = dict()\n self.settings_description = dict()\n self.settings_default = dict()\n self.settings_options = dict()\n self.settings_options_strings = dict()\n\n self.line_format = ''\n\n self.table_string = ''\n\n def generate(self, settings_types, settings_default, settings_description, settings_options=dict(), header_line=None):\n \"\"\"\n Returns a rst-format table with the settings' names, types, description and default values\n\n Args:\n settings_types (dict): Setting types.\n settings_default (dict): Settings default value.\n settings_description (dict): Setting description.\n\n header_line (str): Header line description (optional)\n\n Returns:\n str: .rst formatted string with a table containing the settings' information.\n \"\"\"\n self.settings_types = settings_types\n self.settings_default = settings_default\n self.n_settings = len(self.settings_types)\n #\n\n if header_line is None:\n header_line = 'The settings that this solver accepts are given by a dictionary, ' \\\n 'with the following key-value pairs:'\n else:\n assert type(header_line) == str, 'header_line not a string, verify order of arguments'\n\n if type(settings_options) != dict:\n raise TypeError('settings_options is not a dictionary')\n\n if settings_options:\n # if settings_options are provided\n self.settings_options = settings_options\n self.n_fields += 1\n self.field_length.append(0)\n self.titles.append('Options')\n self.process_options()\n\n try:\n self.settings_description = settings_description\n except AttributeError:\n pass\n\n self.set_field_length()\n self.line_format = self.setting_line_format()\n\n table_string = '\\n ' + header_line + '\\n'\n table_string += '\\n ' + self.print_divider_line()\n table_string += ' ' + self.print_header()\n table_string += ' ' + self.print_divider_line()\n for setting in self.settings_types:\n table_string += ' ' + self.print_setting(setting)\n table_string += ' ' + self.print_divider_line()\n\n self.table_string = table_string\n\n return table_string\n\n def process_options(self):\n self.settings_options_strings = self.settings_options.copy()\n for k, v in self.settings_options.items():\n opts = ''\n for option in v:\n opts += ' ``%s``,' %str(option)\n self.settings_options_strings[k] = opts[1:-1] # removes the initial whitespace and final comma\n\n def set_field_length(self):\n\n field_lengths = [[] for i in range(self.n_fields)]\n for setting in self.settings_types:\n stype = str(self.settings_types.get(setting, ''))\n description = self.settings_description.get(setting, '')\n default = str(self.settings_default.get(setting, ''))\n option = str(self.settings_options_strings.get(setting, ''))\n\n field_lengths[0].append(len(setting) + 4) # length of name\n field_lengths[1].append(len(stype) + 4) # length of type + 4 for the rst ``X``\n field_lengths[2].append(len(description)) # length of type\n field_lengths[3].append(len(default) + 4) # length of type + 4 for the rst ``X``\n\n if self.settings_options:\n field_lengths[4].append(len(option))\n\n for i_field in range(self.n_fields):\n field_lengths[i_field].append(len(self.titles[i_field]))\n self.field_length[i_field] = max(field_lengths[i_field]) + 2 # add the two spaces as column dividers\n\n def print_divider_line(self):\n divider = ''\n for i_field in range(self.n_fields):\n divider += '='*(self.field_length[i_field]-2) + ' '\n divider += '\\n'\n return divider\n\n def print_setting(self, setting):\n type = '``' + str(self.settings_types.get(setting, '')) + '``'\n description = self.settings_description.get(setting, '')\n default = '``' + str(self.settings_default.get(setting, '')) + '``'\n if self.settings_options:\n option = self.settings_options_strings.get(setting, '')\n line = self.line_format.format(['``' + str(setting) + '``', type, description, default, option]) + '\\n'\n else:\n line = self.line_format.format(['``' + str(setting) + '``', type, description, default]) + '\\n'\n return line\n\n def print_header(self):\n header = self.line_format.format(self.titles) + '\\n'\n return header\n\n def setting_line_format(self):\n string = ''\n for i_field in range(self.n_fields):\n string += '{0[' + str(i_field) + ']:<' + str(self.field_length[i_field]) + '}'\n return string\n\n\ndef set_value_or_default(dictionary, key, default_val):\n try:\n value = dictionary[key]\n except KeyError:\n value = default_val\n return value\n\n" }, { "path": "sharpy/utils/sharpydir.py", "content": "import os\n\nSharpyDir = os.path.realpath(os.path.dirname(__file__)+'/../..')" }, { "path": "sharpy/utils/solver_interface.py", "content": "from abc import ABCMeta, abstractmethod\nimport sharpy.utils.cout_utils as cout\nimport os\nimport sharpy.utils.settings as settings\nimport inspect\nimport shutil\nimport sharpy.utils.exceptions as exceptions\n\ndict_of_solvers = {}\nsolvers = {} # for internal working\n\n\n# decorator\ndef solver(arg):\n # global available_solvers\n global dict_of_solvers\n try:\n arg.solver_id\n except AttributeError:\n raise AttributeError('Class defined as solver has no solver_id attribute')\n dict_of_solvers[arg.solver_id] = arg\n\n # a = arg()\n # settings.SettingsTable().print(a)\n\n return arg\n\n\ndef print_available_solvers():\n cout.cout_wrap('The available solvers on this session are:', 2)\n for name, i_solver in dict_of_solvers.items():\n cout.cout_wrap('%s ' % i_solver.solver_id, 2)\n\n\nclass BaseSolver(metaclass=ABCMeta):\n\n # solver_classification = 'other'\n settings_types = dict()\n settings_description = dict()\n settings_default = dict()\n\n # Solver id for populating available_solvers[]\n @property\n def solver_id(self):\n raise NotImplementedError\n\n # The input is a ProblemData class structure\n @abstractmethod\n def initialise(self, data, restart=False):\n pass\n\n # This executes the solver\n @abstractmethod\n def run(self, **kwargs):\n pass\n\n # @property\n def __doc__(self):\n # Generate documentation table\n settings_table = settings.SettingsTable()\n _doc = inspect.getdoc(self)\n _doc += settings_table.generate(settings_types, settings_default, settings_description)\n return _doc\n\n def teardown(self):\n pass\n\n\ndef solver_from_string(string):\n try:\n solver = dict_of_solvers[string]\n except KeyError:\n raise exceptions.SolverNotFound(string)\n return solver\n\n\ndef solver_list_from_path(cwd):\n onlyfiles = [f for f in os.listdir(cwd) if os.path.isfile(os.path.join(cwd, f))]\n\n for i_file in range(len(onlyfiles)):\n if onlyfiles[i_file].split('.')[-1] == 'py': # support autosaved files in the folder\n if onlyfiles[i_file] == \"__init__.py\":\n onlyfiles[i_file] = \"\"\n continue\n onlyfiles[i_file] = onlyfiles[i_file].replace('.py', '')\n else:\n onlyfiles[i_file] = \"\"\n\n files = [file for file in onlyfiles if not file == \"\"]\n return files\n\n\ndef initialise_solver(solver_name, print_info=True):\n if print_info:\n cout.cout_wrap('Generating an instance of %s' % solver_name, 2)\n cls_type = solver_from_string(solver_name)\n solver = cls_type()\n return solver\n\n\ndef dictionary_of_solvers(print_info=True):\n import sharpy.solvers\n import sharpy.postproc\n dictionary = dict()\n for solver in dict_of_solvers:\n if solver not in ['GridLoader', 'NonliftingBodyGridLoader']:\n init_solver = initialise_solver(solver, print_info)\n dictionary[solver] = init_solver.settings_default\n else:\n dictionary[solver] = {}\n\n return dictionary\n\n\ndef output_documentation(route=None):\n \"\"\"\n Creates the ``.rst`` files for the solvers that have a docstring such that they can be parsed to Sphinx\n\n Args:\n route (str): Path to folder where solver files are to be created.\n\n \"\"\"\n import sharpy.utils.sharpydir as sharpydir\n solver_types = []\n if route is None:\n base_route = sharpydir.SharpyDir + '/docs/source/includes/'\n route_solvers = base_route + 'solvers/'\n route_postprocs = base_route + 'postprocs/'\n if os.path.exists(route_solvers):\n print('Cleaning %s' % route_solvers)\n shutil.rmtree(route_solvers)\n if os.path.exists(route_postprocs):\n print('Cleaning %s', route_postprocs)\n shutil.rmtree(route_postprocs)\n\n print('Creating documentation files for solvers in %s' %route_solvers)\n print('Creating documentation files for post processors in %s' %route_postprocs)\n\n created_solvers = dict()\n\n for k, v in dict_of_solvers.items():\n if k[0] == '_':\n continue\n solver = v()\n created_solvers[k] = solver\n\n filename = k + '.rst'\n\n try:\n solver_folder = solver.solver_classification.lower()\n except AttributeError:\n print('The solver {} does not have a classification. Dumping it into \"Other\"'.format(k))\n solver_folder = 'other'\n if solver.__doc__ is None:\n continue\n\n if solver_folder == 'post-processor':\n solver_type = 'postprocessor'\n route_to_solver_python = 'sharpy.postproc.'\n folder = 'postprocs'\n solver_folder = '' # post-procs do not have sub classification unlike solvers\n else:\n solver_type = 'solver'\n route_to_solver_python = 'sharpy.solvers.'\n folder = 'solvers'\n if solver_folder not in solver_types:\n solver_types.append(solver_folder)\n\n if solver.solver_id == 'PreSharpy':\n route_to_solver_python = 'sharpy.presharpy.'\n\n os.makedirs(base_route + '/' + folder + '/' + solver_folder, exist_ok=True)\n title = k + '\\n'\n title += len(k)*'-' + 2*'\\n'\n if solver.__doc__ is not None:\n print('\\tCreating %s' %(base_route + '/' + folder + '/' + solver_folder + '/' + filename))\n autodoc_string = ''\n autodoc_string = '\\n\\n.. autoclass:: ' + route_to_solver_python + k.lower() + '.' + k + '\\n\\t:members:'\n with open(base_route + '/' + folder + '/' + solver_folder + '/' + filename, \"w\") as out_file:\n out_file.write(title + autodoc_string)\n\n # Creates index files depending on the type of solver\n for solver_type in solver_types:\n if solver_type == 'post-processor':\n continue\n filename = solver_type + '_solvers.rst'\n title = solver_type.capitalize() + ' Solvers'\n title += '\\n' + len(title)*'+' + 2*'\\n'\n with open(route_solvers + '/' + filename, \"w\") as out_file:\n out_file.write(title)\n out_file.write('.. toctree::' + '\\n')\n for k in dict_of_solvers.keys():\n if k[0] == '_':\n continue\n try:\n if created_solvers[k].solver_classification.lower() == solver_type and created_solvers[k].__doc__ is not None:\n out_file.write(' ./' + solver_type + '/' + k + '\\n')\n except AttributeError:\n pass\n" }, { "path": "sharpy/version.py", "content": "# version stored here to don't load dependencies by storing it in __init__.py\n__version__ = '2.4'\n" }, { "path": "tests/__init__.py", "content": "" }, { "path": "tests/coupled/__init__.py", "content": "" }, { "path": "tests/coupled/dynamic/__init__.py", "content": "" }, { "path": "tests/coupled/dynamic/hale/generate_hale.py", "content": "#! /usr/bin/env python3\nimport h5py as h5\nimport numpy as np\nimport os\nimport sharpy.utils.algebra as algebra\n\ncase_name = 'hale'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n# EXECUTION\nflow = ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'DynamicCoupled',\n 'BeamLoads'\n ]\n\n# if free_flight is False, the motion of the centre of the wing is prescribed.\nfree_flight = True\n\n# FLIGHT CONDITIONS\n# the simulation is set such that the aircraft flies at a u_inf velocity while\n# the air is calm.\nu_inf = 10\nrho = 1.225\n\n# trim sigma = 1.5\nalpha = 4.31 * np.pi / 180\nbeta = 0\nroll = 0\ngravity = 'on'\ncs_deflection = -2.08 * np.pi / 180\nrudder_static_deflection = 0.0\nrudder_step = 0.0 * np.pi / 180\nthrust = 6.16\nsigma = 1.5\nlambda_dihedral = 20 * np.pi / 180\n\n# gust settings\ngust_intensity = 0.20\ngust_length = 1 * u_inf\ngust_offset = 0.0 * u_inf\n\n# numerics\nn_step = 5\nstructural_relaxation_factor = 0.6\nrelaxation_factor = 0.35\ntolerance = 1e-6\nfsi_tolerance = 1e-4\n\nnum_cores = 2\n\n# MODEL GEOMETRY\n# beam\nspan_main = 16.0\nlambda_main = 0.25\nea_main = 0.3\n\nea = 1e7\nga = 1e5\ngj = 1e4\neiy = 2e4\neiz = 4e6\nm_bar_main = 0.75\nj_bar_main = 0.075\n\nlength_fuselage = 10\noffset_fuselage = 0\nsigma_fuselage = 10\nm_bar_fuselage = 0.2\nj_bar_fuselage = 0.08\n\nspan_tail = 2.5\nea_tail = 0.5\nfin_height = 2.5\nea_fin = 0.5\nsigma_tail = 100\nm_bar_tail = 0.3\nj_bar_tail = 0.08\n\n# lumped masses\nn_lumped_mass = 1\nlumped_mass_nodes = np.zeros((n_lumped_mass,), dtype=int)\nlumped_mass = np.zeros((n_lumped_mass,))\nlumped_mass[0] = 50\nlumped_mass_inertia = np.zeros((n_lumped_mass, 3, 3))\nlumped_mass_position = np.zeros((n_lumped_mass, 3))\n\n# aero\nchord_main = 1.0\nchord_tail = 0.5\nchord_fin = 0.5\n\n# DISCRETISATION\n# spatial discretisation\n# chordiwse panels\nm = 4\n# spanwise elements\nn_elem_multiplier = 1\nn_elem_main = int(4 * n_elem_multiplier)\nn_elem_tail = int(2 * n_elem_multiplier)\nn_elem_fin = int(2 * n_elem_multiplier)\nn_elem_fuselage = int(2 * n_elem_multiplier)\nn_surfaces = 5\n\n# temporal discretisation\nphysical_time = 30\ntstep_factor = 1.\ndt = 1.0 / m / u_inf * tstep_factor\nn_tstep = 5\n\n# END OF INPUT-----------------------------------------------------------------\n\n# beam processing\nn_node_elem = 3\nspan_main1 = (1.0 - lambda_main) * span_main\nspan_main2 = lambda_main * span_main\n\nn_elem_main1 = round(n_elem_main * (1 - lambda_main))\nn_elem_main2 = n_elem_main - n_elem_main1\n\n# total number of elements\nn_elem = 0\nn_elem += n_elem_main1 + n_elem_main1\nn_elem += n_elem_main2 + n_elem_main2\nn_elem += n_elem_fuselage\nn_elem += n_elem_fin\nn_elem += n_elem_tail + n_elem_tail\n\n# number of nodes per part\nn_node_main1 = n_elem_main1 * (n_node_elem - 1) + 1\nn_node_main2 = n_elem_main2 * (n_node_elem - 1) + 1\nn_node_main = n_node_main1 + n_node_main2 - 1\nn_node_fuselage = n_elem_fuselage * (n_node_elem - 1) + 1\nn_node_fin = n_elem_fin * (n_node_elem - 1) + 1\nn_node_tail = n_elem_tail * (n_node_elem - 1) + 1\n\n# total number of nodes\nn_node = 0\nn_node += n_node_main1 + n_node_main1 - 1\nn_node += n_node_main2 - 1 + n_node_main2 - 1\nn_node += n_node_fuselage - 1\nn_node += n_node_fin - 1\nn_node += n_node_tail - 1\nn_node += n_node_tail - 1\n\n# stiffness and mass matrices\nn_stiffness = 3\nbase_stiffness_main = sigma * np.diag([ea, ga, ga, gj, eiy, eiz])\nbase_stiffness_fuselage = base_stiffness_main.copy() * sigma_fuselage\nbase_stiffness_fuselage[4, 4] = base_stiffness_fuselage[5, 5]\nbase_stiffness_tail = base_stiffness_main.copy() * sigma_tail\nbase_stiffness_tail[4, 4] = base_stiffness_tail[5, 5]\n\nn_mass = 3\nbase_mass_main = np.diag([m_bar_main, m_bar_main, m_bar_main, j_bar_main, 0.5 * j_bar_main, 0.5 * j_bar_main])\nbase_mass_fuselage = np.diag([m_bar_fuselage,\n m_bar_fuselage,\n m_bar_fuselage,\n j_bar_fuselage,\n j_bar_fuselage * 0.5,\n j_bar_fuselage * 0.5])\nbase_mass_tail = np.diag([m_bar_tail,\n m_bar_tail,\n m_bar_tail,\n j_bar_tail,\n j_bar_tail * 0.5,\n j_bar_tail * 0.5])\n\n# PLACEHOLDERS\n# beam\nx = np.zeros((n_node,))\ny = np.zeros((n_node,))\nz = np.zeros((n_node,))\nbeam_number = np.zeros((n_elem,), dtype=int)\nframe_of_reference_delta = np.zeros((n_elem, n_node_elem, 3))\nstructural_twist = np.zeros((n_elem, 3))\nconn = np.zeros((n_elem, n_node_elem), dtype=int)\nstiffness = np.zeros((n_stiffness, 6, 6))\nelem_stiffness = np.zeros((n_elem,), dtype=int)\nmass = np.zeros((n_mass, 6, 6))\nelem_mass = np.zeros((n_elem,), dtype=int)\nboundary_conditions = np.zeros((n_node,), dtype=int)\napp_forces = np.zeros((n_node, 6))\n\n# aero\nairfoil_distribution = np.zeros((n_elem, n_node_elem), dtype=int)\nsurface_distribution = np.zeros((n_elem,), dtype=int) - 1\nsurface_m = np.zeros((n_surfaces,), dtype=int)\nm_distribution = 'uniform'\naero_node = np.zeros((n_node,), dtype=bool)\ntwist = np.zeros((n_elem, n_node_elem))\nsweep = np.zeros((n_elem, n_node_elem))\nchord = np.zeros((n_elem, n_node_elem,))\nelastic_axis = np.zeros((n_elem, n_node_elem,))\n\n\n# FUNCTIONS-------------------------------------------------------------\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n dyn_file_name = route + '/' + case_name + '.dyn.h5'\n if os.path.isfile(dyn_file_name):\n os.remove(dyn_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\ndef generate_fem():\n stiffness[0, ...] = base_stiffness_main\n stiffness[1, ...] = base_stiffness_fuselage\n stiffness[2, ...] = base_stiffness_tail\n\n mass[0, ...] = base_mass_main\n mass[1, ...] = base_mass_fuselage\n mass[2, ...] = base_mass_tail\n\n we = 0\n wn = 0\n # inner right wing\n beam_number[we:we + n_elem_main1] = 0\n y[wn:wn + n_node_main1] = np.linspace(0.0, span_main1, n_node_main1)\n\n for ielem in range(n_elem_main1):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n\n elem_stiffness[we:we + n_elem_main1] = 0\n elem_mass[we:we + n_elem_main1] = 0\n boundary_conditions[0] = 1\n # remember this is in B FoR\n app_forces[0] = [0, thrust, 0, 0, 0, 0]\n we += n_elem_main1\n wn += n_node_main1\n\n # outer right wing\n beam_number[we:we + n_elem_main1] = 0\n y[wn:wn + n_node_main2 - 1] = y[wn - 1] + np.linspace(0.0, np.cos(lambda_dihedral) * span_main2, n_node_main2)[1:]\n z[wn:wn + n_node_main2 - 1] = z[wn - 1] + np.linspace(0.0, np.sin(lambda_dihedral) * span_main2, n_node_main2)[1:]\n for ielem in range(n_elem_main2):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_main2] = 0\n elem_mass[we:we + n_elem_main2] = 0\n boundary_conditions[wn + n_node_main2 - 2] = -1\n we += n_elem_main2\n wn += n_node_main2 - 1\n\n # inner left wing\n beam_number[we:we + n_elem_main1 - 1] = 1\n y[wn:wn + n_node_main1 - 1] = np.linspace(0.0, -span_main1, n_node_main1)[1:]\n for ielem in range(n_elem_main1):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = 0\n elem_stiffness[we:we + n_elem_main1] = 0\n elem_mass[we:we + n_elem_main1] = 0\n we += n_elem_main1\n wn += n_node_main1 - 1\n\n # outer left wing\n beam_number[we:we + n_elem_main2] = 1\n y[wn:wn + n_node_main2 - 1] = y[wn - 1] + np.linspace(0.0, -np.cos(lambda_dihedral) * span_main2, n_node_main2)[1:]\n z[wn:wn + n_node_main2 - 1] = z[wn - 1] + np.linspace(0.0, np.sin(lambda_dihedral) * span_main2, n_node_main2)[1:]\n for ielem in range(n_elem_main2):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_main2] = 0\n elem_mass[we:we + n_elem_main2] = 0\n boundary_conditions[wn + n_node_main2 - 2] = -1\n we += n_elem_main2\n wn += n_node_main2 - 1\n\n # fuselage\n beam_number[we:we + n_elem_fuselage] = 2\n x[wn:wn + n_node_fuselage - 1] = np.linspace(0.0, length_fuselage, n_node_fuselage)[1:]\n z[wn:wn + n_node_fuselage - 1] = np.linspace(0.0, offset_fuselage, n_node_fuselage)[1:]\n for ielem in range(n_elem_fuselage):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [0.0, 1.0, 0.0]\n conn[we, 0] = 0\n elem_stiffness[we:we + n_elem_fuselage] = 1\n elem_mass[we:we + n_elem_fuselage] = 1\n we += n_elem_fuselage\n wn += n_node_fuselage - 1\n global end_of_fuselage_node\n end_of_fuselage_node = wn - 1\n\n # fin\n beam_number[we:we + n_elem_fin] = 3\n x[wn:wn + n_node_fin - 1] = x[end_of_fuselage_node]\n z[wn:wn + n_node_fin - 1] = z[end_of_fuselage_node] + np.linspace(0.0, fin_height, n_node_fin)[1:]\n for ielem in range(n_elem_fin):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fuselage_node\n elem_stiffness[we:we + n_elem_fin] = 2\n elem_mass[we:we + n_elem_fin] = 2\n we += n_elem_fin\n wn += n_node_fin - 1\n end_of_fin_node = wn - 1\n\n # right tail\n beam_number[we:we + n_elem_tail] = 4\n x[wn:wn + n_node_tail - 1] = x[end_of_fin_node]\n y[wn:wn + n_node_tail - 1] = np.linspace(0.0, span_tail, n_node_tail)[1:]\n z[wn:wn + n_node_tail - 1] = z[end_of_fin_node]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fin_node\n elem_stiffness[we:we + n_elem_tail] = 2\n elem_mass[we:we + n_elem_tail] = 2\n boundary_conditions[wn + n_node_tail - 2] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n # left tail\n beam_number[we:we + n_elem_tail] = 5\n x[wn:wn + n_node_tail - 1] = x[end_of_fin_node]\n y[wn:wn + n_node_tail - 1] = np.linspace(0.0, -span_tail, n_node_tail)[1:]\n z[wn:wn + n_node_tail - 1] = z[end_of_fin_node]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fin_node\n elem_stiffness[we:we + n_elem_tail] = 2\n elem_mass[we:we + n_elem_tail] = 2\n boundary_conditions[wn + n_node_tail - 2] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=n_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=n_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=n_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n lumped_mass_nodes_handle = h5file.create_dataset(\n 'lumped_mass_nodes', data=lumped_mass_nodes)\n lumped_mass_handle = h5file.create_dataset(\n 'lumped_mass', data=lumped_mass)\n lumped_mass_inertia_handle = h5file.create_dataset(\n 'lumped_mass_inertia', data=lumped_mass_inertia)\n lumped_mass_position_handle = h5file.create_dataset(\n 'lumped_mass_position', data=lumped_mass_position)\n\n\ndef generate_aero_file():\n global x, y, z\n # control surfaces\n n_control_surfaces = 2\n control_surface = np.zeros((n_elem, n_node_elem), dtype=int) - 1\n control_surface_type = np.zeros((n_control_surfaces,), dtype=int)\n control_surface_deflection = np.zeros((n_control_surfaces,))\n control_surface_chord = np.zeros((n_control_surfaces,), dtype=int)\n control_surface_hinge_coord = np.zeros((n_control_surfaces,), dtype=float)\n\n # control surface type 0 = static\n # control surface type 1 = dynamic\n control_surface_type[0] = 0\n control_surface_deflection[0] = cs_deflection\n control_surface_chord[0] = m\n control_surface_hinge_coord[0] = -0.25 # nondimensional wrt elastic axis (+ towards the trailing edge)\n\n control_surface_type[1] = 0\n control_surface_deflection[1] = rudder_static_deflection\n control_surface_chord[1] = 1\n control_surface_hinge_coord[1] = -0. # nondimensional wrt elastic axis (+ towards the trailing edge)\n\n we = 0\n wn = 0\n # right wing (surface 0, beam 0)\n i_surf = 0\n airfoil_distribution[we:we + n_elem_main, :] = 0\n surface_distribution[we:we + n_elem_main] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_main] = True\n temp_chord = np.linspace(chord_main, chord_main, n_node_main)\n temp_sweep = np.linspace(0.0, 0 * np.pi / 180, n_node_main)\n node_counter = 0\n for i_elem in range(we, we + n_elem_main):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = temp_chord[node_counter]\n elastic_axis[i_elem, i_local_node] = ea_main\n sweep[i_elem, i_local_node] = temp_sweep[node_counter]\n\n we += n_elem_main\n wn += n_node_main\n\n # left wing (surface 1, beam 1)\n i_surf = 1\n airfoil_distribution[we:we + n_elem_main, :] = 0\n # airfoil_distribution[wn:wn + n_node_main - 1] = 0\n surface_distribution[we:we + n_elem_main] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_main - 1] = True\n # chord[wn:wn + num_node_main - 1] = np.linspace(main_chord, main_tip_chord, num_node_main)[1:]\n # chord[wn:wn + num_node_main - 1] = main_chord\n # elastic_axis[wn:wn + num_node_main - 1] = main_ea\n temp_chord = np.linspace(chord_main, chord_main, n_node_main)\n node_counter = 0\n for i_elem in range(we, we + n_elem_main):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = temp_chord[node_counter]\n elastic_axis[i_elem, i_local_node] = ea_main\n sweep[i_elem, i_local_node] = -temp_sweep[node_counter]\n\n we += n_elem_main\n wn += n_node_main - 1\n\n we += n_elem_fuselage\n wn += n_node_fuselage - 1 - 1\n #\n # # fin (surface 2, beam 3)\n i_surf = 2\n airfoil_distribution[we:we + n_elem_fin, :] = 1\n # airfoil_distribution[wn:wn + n_node_fin] = 0\n surface_distribution[we:we + n_elem_fin] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_fin] = True\n # chord[wn:wn + num_node_fin] = fin_chord\n for i_elem in range(we, we + n_elem_fin):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_fin\n elastic_axis[i_elem, i_local_node] = ea_fin\n control_surface[i_elem, i_local_node] = 1\n # twist[end_of_fuselage_node] = 0\n # twist[wn:] = 0\n # elastic_axis[wn:wn + num_node_main] = fin_ea\n we += n_elem_fin\n wn += n_node_fin - 1\n #\n # # # right tail (surface 3, beam 4)\n i_surf = 3\n airfoil_distribution[we:we + n_elem_tail, :] = 2\n # airfoil_distribution[wn:wn + n_node_tail] = 0\n surface_distribution[we:we + n_elem_tail] = i_surf\n surface_m[i_surf] = m\n # XXX not very elegant\n aero_node[wn:] = True\n # chord[wn:wn + num_node_tail] = tail_chord\n # elastic_axis[wn:wn + num_node_main] = tail_ea\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n twist[i_elem, i_local_node] = -0\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_tail\n elastic_axis[i_elem, i_local_node] = ea_tail\n control_surface[i_elem, i_local_node] = 0\n\n we += n_elem_tail\n wn += n_node_tail\n #\n # # left tail (surface 4, beam 5)\n i_surf = 4\n airfoil_distribution[we:we + n_elem_tail, :] = 2\n # airfoil_distribution[wn:wn + n_node_tail - 1] = 0\n surface_distribution[we:we + n_elem_tail] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_tail - 1] = True\n # chord[wn:wn + num_node_tail] = tail_chord\n # elastic_axis[wn:wn + num_node_main] = tail_ea\n # twist[we:we + num_elem_tail] = -tail_twist\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n twist[i_elem, i_local_node] = -0\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_tail\n elastic_axis[i_elem, i_local_node] = ea_tail\n control_surface[i_elem, i_local_node] = 0\n we += n_elem_tail\n wn += n_node_tail\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n naca_airfoil_tail = airfoils_group.create_dataset('1', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n naca_airfoil_fin = airfoils_group.create_dataset('2', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input.attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # sweep\n sweep_input = h5file.create_dataset('sweep', data=sweep)\n dim_attr = sweep_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n control_surface_input = h5file.create_dataset('control_surface', data=control_surface)\n control_surface_deflection_input = h5file.create_dataset('control_surface_deflection',\n data=control_surface_deflection)\n control_surface_chord_input = h5file.create_dataset('control_surface_chord', data=control_surface_chord)\n control_surface_hinge_coord_input = h5file.create_dataset('control_surface_hinge_coord',\n data=control_surface_hinge_coord)\n control_surface_types_input = h5file.create_dataset('control_surface_type', data=control_surface_type)\n\n\ndef generate_naca_camber(M=0, P=0):\n mm = M * 1e-2\n p = P * 1e-1\n\n def naca(x, mm, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return mm / (p * p) * (2 * p * x - x * x)\n elif x > p and x < 1 + 1e-6:\n return mm / ((1 - p) * (1 - p)) * (1 - 2 * p + 2 * p * x - x * x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, mm, p) for x in x_vec])\n return x_vec, y_vec\n\n\ndef generate_solver_file():\n file_name = route + '/' + case_name + '.sharpy'\n settings = dict()\n settings['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': flow,\n 'write_screen': 'off',\n 'write_log': 'off',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n\n settings['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'gravity_on': gravity,\n 'gravity': 9.81}\n\n settings['StaticUvlm'] = {'print_info': 'on',\n 'horseshoe': 'off',\n 'num_cores': num_cores,\n 'n_rollup': 0,\n 'rollup_dt': dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho}\n\n settings['StaticCoupled'] = {'print_info': 'off',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': settings['NonLinearStatic'],\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': settings['StaticUvlm'],\n 'max_iter': 100,\n 'n_load_steps': n_step,\n 'tolerance': fsi_tolerance,\n 'relaxation_factor': structural_relaxation_factor}\n\n settings['StaticTrim'] = {'solver': 'StaticCoupled',\n 'solver_settings': settings['StaticCoupled'],\n 'initial_alpha': alpha,\n 'initial_deflection': cs_deflection,\n 'initial_thrust': thrust}\n\n settings['NonLinearDynamicCoupledStep'] = {'print_info': 'off',\n 'max_iterations': 950,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'newmark_damp': 5e-3,\n 'gravity_on': gravity,\n 'gravity': 9.81,\n 'num_steps': n_tstep,\n 'dt': dt,\n 'initial_velocity': u_inf}\n\n relative_motion = 'off'\n settings['StepUvlm'] = {'print_info': 'off',\n 'num_cores': num_cores,\n 'convection_scheme': 2,\n 'gamma_dot_filtering': 7,\n 'velocity_field_generator': 'GustVelocityField',\n 'velocity_field_input': {'u_inf': int(not free_flight) * u_inf,\n 'u_inf_direction': [1., 0, 0],\n 'gust_shape': '1-cos',\n 'gust_parameters': {'gust_length': gust_length,\n 'gust_intensity': gust_intensity * u_inf},\n 'offset': gust_offset,\n 'relative_motion': relative_motion},\n 'rho': rho,\n 'n_time_steps': n_tstep,\n 'dt': dt}\n settings['BeamLoads'] = {'csv_output': True}\n solver = 'NonLinearDynamicCoupledStep'\n settings['DynamicCoupled'] = {'structural_solver': solver,\n 'structural_solver_settings': settings[solver],\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'fsi_substeps': 3,\n 'fsi_tolerance': 1e-3,\n 'relaxation_factor': 0,\n 'minimum_steps': 1,\n 'relaxation_steps': 150,\n 'final_relaxation_factor': 0.5,\n 'n_time_steps': n_tstep,\n 'dt': dt,\n 'include_unsteady_force_contribution': 'on',\n }\n \n settings['BeamLoader'] = {'unsteady': 'on',\n 'orientation': algebra.euler2quat(np.array([roll,\n alpha,\n beta]))}\n\n settings['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n 'mstar': int(20 / tstep_factor),\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': ['1', '0', '0'],\n 'dt': dt}}\n\n\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n for k, v in settings.items():\n config[k] = v\n config.write()\n\n\nclean_test_files()\ngenerate_fem()\ngenerate_aero_file()\ngenerate_solver_file()\n" }, { "path": "tests/coupled/dynamic/test_dynamic.py", "content": "import numpy as np\nimport unittest\nimport os\n\n\nclass TestCoupledDynamic(unittest.TestCase):\n \"\"\"\n Tests for dynamic coupled problems to identify errors in the unsteady solvers.\n Implemented tests:\n - Gust response of the hale aircraft\n \"\"\"\n\n route_file_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n \n def test_hale_dynamic(self):\n \"\"\"\n Case and results from:\n tests/coupled/dynamic/hale \n reference results produced with SHARPy version 2.0\n :return:\n \"\"\"\n import sharpy.sharpy_main\n try:\n import hale.generate_hale\n except:\n import tests.coupled.dynamic.hale.generate_hale\n \n case_name = 'hale'\n cases_folder = os.path.join(self.route_file_dir, case_name)\n output_folder = cases_folder + '/output/'\n\n sharpy.sharpy_main.main(['', cases_folder + '/hale.sharpy'])\n n_tstep = 5\n # compare results with reference values \n ref_Fz = -531.023900359779\n ref_My = -1530.0477841197576\n\n file = os.path.join(output_folder, case_name, 'beam/beam_loads_%i.csv' % (n_tstep))\n beam_loads_ts = np.loadtxt(file, delimiter=',')\n np.testing.assert_almost_equal(float(beam_loads_ts[0, 6]), ref_Fz,\n decimal=3,\n err_msg='Vertical load on wing root not within 3 decimal points of reference.',\n verbose=True)\n np.testing.assert_almost_equal(float(beam_loads_ts[0, 8]), ref_My,\n decimal=3,\n err_msg='Pitching moment on wing root not within 3 decimal points of reference.',\n verbose=True)\n\n @classmethod\n def tearDown(self):\n \"\"\"\n Removes all created files within this test.\n \"\"\"\n import shutil\n folders = ['hale/output']\n for folder in folders:\n shutil.rmtree(self.route_file_dir + '/' + folder)\n files = ['hale/hale.aero.h5', 'hale/hale.fem.h5', 'hale/hale.sharpy']\n for file in files:\n file_dir = self.route_file_dir + '/' + file\n if os.path.isfile(file_dir):\n os.remove(file_dir)\n \n \n\nif __name__ == '__main__':\n unittest.main()" }, { "path": "tests/coupled/multibody/__init__.py", "content": "import tests.coupled.multibody.double_pendulum\nimport tests.coupled.multibody.fix_node_velocity_wrtA\nimport tests.coupled.multibody.fix_node_velocity_wrtG\n" }, { "path": "tests/coupled/multibody/double_pendulum/__init__.py", "content": "" }, { "path": "tests/coupled/multibody/double_pendulum/test_double_pendulum_geradin.py", "content": "import numpy as np\nimport unittest\nimport os\nimport shutil\n\n# Data from Geradin\n# time[s] theta[rad]\ngeradin_FoR0 = np.array([[-0.0117973, 1.56808],\n [0.0816564, 1.5394],\n [0.171988, 1.41698],\n [0.235203, 1.31521],\n [0.307327, 1.09265],\n [0.427399, 0.601124],\n [0.526338, 0.0899229],\n [0.646417, -0.394903],\n [0.748531, -0.765465],\n [0.868959, -0.94209],\n [0.905131, -0.956217],\n [0.965504, -0.903829],\n [1.06828, -0.69149],\n [1.16508, -0.425429],\n [1.29798, -0.240495],\n [1.42483, -0.0688408],\n [1.56382, 0.169571],\n [1.78751, 0.634087],\n [1.89627, 0.806105],\n [1.98075, 0.844608],\n [2.10125, 0.734983],\n [2.19143, 0.478564],\n [2.26934, 0.0347871],\n [2.37751, -0.315796],\n [2.52803, -0.546627],\n [2.60034, -0.601682],\n [2.76314, -0.645155],\n [2.88987, -0.580701],\n [3.05893, -0.423295],\n [3.24611, -0.239453],\n [3.43335, -0.00201041],\n [3.51194, 0.157214],\n [3.59668, 0.423517],\n [3.6815, 0.756821],\n [3.73591, 0.87633],\n [3.81435, 0.901554],\n [3.93481, 0.751729],\n [4.04305, 0.468146],\n [4.17525, 0.0366783],\n [4.34949, -0.556439],\n [4.44551, -0.987179],\n [4.57784, -1.29805],\n [4.65016, -1.3531],\n [4.70444, -1.35419],\n [4.78294, -1.27537],\n [4.86762, -1.06267],\n [4.99464, -0.743611]])\n\ngeradin_FoR1 = np.array([[0.00756934, 0.0266485],\n [0.134225, 0.0241027],\n [0.309222, 0.100987],\n [0.418117, 0.393606],\n [0.490855, 0.713752],\n [0.533195, 0.820103],\n [0.635787, 0.871642],\n [0.762124, 0.587696],\n [0.85826, 0.264156],\n [0.918194, -0.0720575],\n [0.996205, -0.422034],\n [1.05008, -0.784926],\n [1.09792, -1.1477],\n [1.1639, -1.47063],\n [1.27207, -1.82121],\n [1.38636, -2.09152],\n [1.47067, -2.20042],\n [1.53694, -2.26875],\n [1.67582, -2.12414],\n [1.8028, -1.84528],\n [1.89365, -1.5121],\n [1.97843, -1.2056],\n [2.00271, -1.07208],\n [2.08146, -0.765457],\n [2.14818, -0.431789],\n [2.19686, -0.0575583],\n [2.24552, 0.303273],\n [2.29421, 0.690904],\n [2.37299, 1.02433],\n [2.44573, 1.34447],\n [2.55464, 1.65049],\n [2.65749, 1.92983],\n [2.7904, 2.12817],\n [2.94135, 2.27254],\n [3.03182, 2.27072],\n [3.18853, 2.17376],\n [3.30891, 1.95694],\n [3.42312, 1.61964],\n [3.50121, 1.33666],\n [3.56714, 0.973525],\n [3.61495, 0.583954],\n [3.66883, 0.221062],\n [3.71673, -0.0881084],\n [3.80076, -0.451606],\n [3.87271, -0.828262],\n [3.95678, -1.15156],\n [3.98681, -1.25937],\n [4.08307, -1.47571],\n [4.13729, -1.5304],\n [4.27618, -1.38579],\n [4.36701, -1.066],\n [4.4217, -0.705294],\n [4.50652, -0.37199],\n [4.59132, -0.0520868],\n [4.68815, 0.240774],\n [4.79703, 0.519993],\n [4.91188, 0.74549],\n [4.98432, 0.797635]])\n\n\nclass TestDoublePendulum(unittest.TestCase):\n \"\"\"\n Validation of a double pendulum with a mass at each tip position\n\n Reference case: M. Geradin and A. Cardona, \"Flexible multibody dynamics : a finite element approach\"\n \"\"\"\n\n def setUp(self):\n import sharpy.utils.generate_cases as gc\n from sharpy.utils.constants import deg2rad\n\n # Structural properties\n mass_per_unit_length = 1.\n mass_iner = 1e-4\n EA = 1e9\n GA = 1e9\n GJ = 1e9\n EI = 1e9\n\n # Beam1\n global nnodes1\n nnodes1 = 11\n l1 = 1.0\n m1 = 1.0\n theta_ini1 = 90.*deg2rad\n\n # Beam2\n nnodes2 = nnodes1\n l2 = l1\n m2 = m1\n theta_ini2 = 00.*deg2rad\n\n # airfoils\n airfoil = np.zeros((1,20,2),)\n airfoil[0,:,0] = np.linspace(0.,1.,20)\n\n # Simulation\n numtimesteps = 10\n dt = 0.01\n\n # Create the structure\n beam1 = gc.AeroelasticInformation()\n r1 = np.linspace(0.0, l1, nnodes1)\n node_pos1 = np.zeros((nnodes1,3),)\n node_pos1[:, 0] = r1*np.sin(theta_ini1)\n node_pos1[:, 2] = -r1*np.cos(theta_ini1)\n beam1.StructuralInformation.generate_uniform_sym_beam(node_pos1, mass_per_unit_length, mass_iner, EA, GA, GJ, EI, num_node_elem = 3, y_BFoR = 'y_AFoR', num_lumped_mass=1)\n beam1.StructuralInformation.body_number = np.zeros((beam1.StructuralInformation.num_elem,), dtype = int)\n beam1.StructuralInformation.boundary_conditions[0] = 1\n beam1.StructuralInformation.boundary_conditions[-1] = -1\n beam1.StructuralInformation.lumped_mass_nodes = np.array([nnodes1-1], dtype = int)\n beam1.StructuralInformation.lumped_mass = np.ones((1,))*m1\n beam1.StructuralInformation.lumped_mass_inertia = np.zeros((1,3,3))\n beam1.StructuralInformation.lumped_mass_position = np.zeros((1,3))\n beam1.AerodynamicInformation.create_one_uniform_aerodynamics(\n beam1.StructuralInformation,\n chord = 1.,\n twist = 0.,\n sweep = 0.,\n num_chord_panels = 4,\n m_distribution = 'uniform',\n elastic_axis = 0.25,\n num_points_camber = 20,\n airfoil = airfoil)\n\n beam2 = gc.AeroelasticInformation()\n r2 = np.linspace(0.0, l2, nnodes2)\n node_pos2 = np.zeros((nnodes2,3),)\n node_pos2[:, 0] = r2*np.sin(theta_ini2) + node_pos1[-1, 0]\n node_pos2[:, 2] = -r2*np.cos(theta_ini2) + node_pos1[-1, 2]\n beam2.StructuralInformation.generate_uniform_sym_beam(node_pos2, mass_per_unit_length, mass_iner, EA, GA, GJ, EI, num_node_elem = 3, y_BFoR = 'y_AFoR', num_lumped_mass=1)\n beam2.StructuralInformation.body_number = np.zeros((beam1.StructuralInformation.num_elem,), dtype = int)\n beam2.StructuralInformation.boundary_conditions[0] = 1\n beam2.StructuralInformation.boundary_conditions[-1] = -1\n beam2.StructuralInformation.lumped_mass_nodes = np.array([nnodes2-1], dtype = int)\n beam2.StructuralInformation.lumped_mass = np.ones((1,))*m2\n beam2.StructuralInformation.lumped_mass_inertia = np.zeros((1,3,3))\n beam2.StructuralInformation.lumped_mass_position = np.zeros((1,3))\n beam2.AerodynamicInformation.create_one_uniform_aerodynamics(\n beam2.StructuralInformation,\n chord = 1.,\n twist = 0.,\n sweep = 0.,\n num_chord_panels = 4,\n m_distribution = 'uniform',\n elastic_axis = 0.25,\n num_points_camber = 20,\n airfoil = airfoil)\n\n beam1.assembly(beam2)\n\n # Simulation details\n SimInfo = gc.SimulationInformation()\n SimInfo.set_default_values()\n\n SimInfo.define_uinf(np.array([0.0,1.0,0.0]), 1.)\n\n SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\n 'AerogridLoader',\n 'DynamicCoupled']\n global name_hinge\n name_hinge = 'dpg_hinge'\n SimInfo.solvers['SHARPy']['case'] = name_hinge\n SimInfo.solvers['SHARPy']['write_screen'] = 'off'\n SimInfo.solvers['SHARPy']['route'] = os.path.abspath(os.path.dirname(os.path.realpath(__file__))) + '/'\n SimInfo.solvers['SHARPy']['log_folder'] = os.path.abspath(os.path.dirname(os.path.realpath(__file__))) + '/output/'\n SimInfo.set_variable_all_dicts('dt', dt)\n SimInfo.define_num_steps(numtimesteps)\n SimInfo.set_variable_all_dicts('rho', 0.0)\n SimInfo.set_variable_all_dicts('velocity_field_input', SimInfo.solvers['SteadyVelocityField'])\n SimInfo.set_variable_all_dicts('output', os.path.abspath(os.path.dirname(os.path.realpath(__file__))) + '/output/')\n\n SimInfo.solvers['BeamLoader']['unsteady'] = 'on'\n\n SimInfo.solvers['AerogridLoader']['unsteady'] = 'on'\n SimInfo.solvers['AerogridLoader']['mstar'] = 2\n SimInfo.solvers['AerogridLoader']['wake_shape_generator'] = 'StraightWake'\n SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] = {'u_inf':1.,\n 'u_inf_direction': np.array([0., 1., 0.]),\n 'dt': dt}\n\n\n SimInfo.solvers['WriteVariablesTime']['FoR_number'] = np.array([0, 1], dtype = int)\n SimInfo.solvers['WriteVariablesTime']['FoR_variables'] = ['mb_quat']\n SimInfo.solvers['WriteVariablesTime']['structure_nodes'] = np.array([nnodes1-1, nnodes1+nnodes2-1], dtype = int)\n SimInfo.solvers['WriteVariablesTime']['structure_variables'] = ['pos']\n\n SimInfo.solvers['NonLinearDynamicMultibody']['gravity_on'] = True\n SimInfo.solvers['NonLinearDynamicMultibody']['time_integrator'] = 'NewmarkBeta'\n SimInfo.solvers['NonLinearDynamicMultibody']['time_integrator_settings'] = {'newmark_damp': 0.15,\n 'dt': dt}\n SimInfo.solvers['NonLinearDynamicMultibody']['write_lm'] = True\n\n SimInfo.solvers['BeamPlot']['include_FoR'] = True\n\n SimInfo.solvers['DynamicCoupled']['structural_solver'] = 'NonLinearDynamicMultibody'\n SimInfo.solvers['DynamicCoupled']['structural_solver_settings'] = SimInfo.solvers['NonLinearDynamicMultibody']\n SimInfo.solvers['DynamicCoupled']['aero_solver'] = 'StepUvlm'\n SimInfo.solvers['DynamicCoupled']['aero_solver_settings'] = SimInfo.solvers['StepUvlm']\n SimInfo.solvers['DynamicCoupled']['postprocessors'] = ['WriteVariablesTime', 'BeamPlot', 'AerogridPlot']\n SimInfo.solvers['DynamicCoupled']['postprocessors_settings'] = {'WriteVariablesTime': SimInfo.solvers['WriteVariablesTime'],\n 'BeamPlot': SimInfo.solvers['BeamPlot'],\n 'AerogridPlot': SimInfo.solvers['AerogridPlot']}\n\n SimInfo.with_forced_vel = False\n SimInfo.with_dynamic_forces = False\n\n # Create the MB and BC files\n LC1 = gc.LagrangeConstraint()\n LC1.behaviour = 'hinge_FoR'\n LC1.body_FoR = 0\n LC1.rot_axis_AFoR = np.array([0.0,1.0,0.0])\n LC1.scalingFactor = 1e6\n LC1.penaltyFactor = 0.\n\n LC2 = gc.LagrangeConstraint()\n LC2.behaviour = 'hinge_node_FoR'\n LC2.node_in_body = nnodes1-1\n LC2.body = 0\n LC2.body_FoR = 1\n LC2.rot_axisB = np.array([0.0,1.0,0.0])\n LC2.scalingFactor = 1e6\n LC2.penaltyFactor = 0.\n\n LC = []\n LC.append(LC1)\n LC.append(LC2)\n\n MB1 = gc.BodyInformation()\n MB1.body_number = 0\n MB1.FoR_position = np.zeros((6,),)\n MB1.FoR_velocity = np.zeros((6,),)\n MB1.FoR_acceleration = np.zeros((6,),)\n MB1.FoR_movement = 'free'\n MB1.quat = np.array([1.0,0.0,0.0,0.0])\n\n MB2 = gc.BodyInformation()\n MB2.body_number = 1\n MB2.FoR_position = np.array([node_pos2[0, 0], node_pos2[0, 1], node_pos2[0, 2], 0.0, 0.0, 0.0])\n MB2.FoR_velocity = np.zeros((6,),)\n MB2.FoR_acceleration = np.zeros((6,),)\n MB2.FoR_movement = 'free'\n MB2.quat = np.array([1.0,0.0,0.0,0.0])\n\n MB = []\n MB.append(MB1)\n MB.append(MB2)\n\n # Write files\n gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n SimInfo.generate_solver_file()\n SimInfo.generate_dyn_file(numtimesteps)\n beam1.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n gc.generate_multibody_file(LC, MB,SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n\n # Same case without dissipation\n global name_nb_zero_dis\n name_nb_zero_dis = 'dpg_nb_zero_dis'\n SimInfo.solvers['SHARPy']['case'] = name_nb_zero_dis\n\n SimInfo.solvers['NonLinearDynamicMultibody']['time_integrator_settings'] = {'newmark_damp': 0.,\n 'dt': dt}\n\n gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n SimInfo.generate_solver_file()\n SimInfo.generate_dyn_file(numtimesteps)\n beam1.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n gc.generate_multibody_file(LC, MB,SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n\n # Same case with generalised alpha\n global name_ga\n name_ga = 'dpg_ga'\n SimInfo.solvers['SHARPy']['case'] = name_ga\n\n SimInfo.solvers['NonLinearDynamicMultibody']['time_integrator'] = 'GeneralisedAlpha'\n SimInfo.solvers['NonLinearDynamicMultibody']['time_integrator_settings'] = {'am': 0.5,\n 'af': 0.5,\n 'dt': dt}\n\n gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n SimInfo.generate_solver_file()\n SimInfo.generate_dyn_file(numtimesteps)\n beam1.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n gc.generate_multibody_file(LC, MB,SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n\n # Same case with spherical joints\n global name_spherical\n name_spherical = 'dpg_spherical'\n SimInfo.solvers['SHARPy']['case'] = name_spherical\n\n SimInfo.solvers['NonLinearDynamicMultibody']['time_integrator'] = 'NewmarkBeta'\n SimInfo.solvers['NonLinearDynamicMultibody']['time_integrator_settings'] = {'newmark_damp': 0.15,\n 'dt': dt}\n\n LC1 = gc.LagrangeConstraint()\n LC1.behaviour = 'spherical_FoR'\n LC1.body_FoR = 0\n LC1.scalingFactor = 1e6\n\n LC2 = gc.LagrangeConstraint()\n LC2.behaviour = 'spherical_node_FoR'\n LC2.node_in_body = nnodes1-1\n LC2.body = 0\n LC2.body_FoR = 1\n LC2.scalingFactor = 1e6\n\n gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n SimInfo.generate_solver_file()\n SimInfo.generate_dyn_file(numtimesteps)\n beam1.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n gc.generate_multibody_file(LC, MB,SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n\n def run_and_assert(self, name):\n import sharpy.sharpy_main\n\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) + '/' + name + '.sharpy')\n sharpy.sharpy_main.main(['', solver_path])\n\n # read output and compare\n output_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__))) + '/output/' + name + '/WriteVariablesTime/'\n pos_tip_data = np.loadtxt((\"%sstruct_pos_node%d.dat\" % (output_path, nnodes1*2-1)), )\n self.assertAlmostEqual(pos_tip_data[-1, 1], 1.051004, 4)\n self.assertAlmostEqual(pos_tip_data[-1, 2], 0.000000, 4)\n self.assertAlmostEqual(pos_tip_data[-1, 3], -0.9986984, 4)\n\n def test_doublependulum_hinge(self):\n self.run_and_assert(name_hinge)\n\n def test_doublependulum_spherical(self):\n self.run_and_assert(name_spherical)\n\n def test_doublependulum_ga(self):\n import sharpy.sharpy_main\n\n nb_solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) + '/' + name_nb_zero_dis + '.sharpy')\n sharpy.sharpy_main.main(['', nb_solver_path])\n\n ga_solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) + '/' + name_ga + '.sharpy')\n sharpy.sharpy_main.main(['', ga_solver_path])\n\n # read output and compare\n nb_output_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__))) + '/output/' + name_nb_zero_dis + '/WriteVariablesTime/'\n nb_pos_tip_data = np.loadtxt((\"%sstruct_pos_node%d.dat\" % (nb_output_path, nnodes1*2-1)), )\n\n ga_output_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__))) + '/output/' + name_ga + '/WriteVariablesTime/'\n ga_pos_tip_data = np.loadtxt((\"%sstruct_pos_node%d.dat\" % (ga_output_path, nnodes1*2-1)), )\n\n self.assertAlmostEqual(nb_pos_tip_data[-1, 1], ga_pos_tip_data[-1, 1], 4)\n self.assertAlmostEqual(nb_pos_tip_data[-1, 2], ga_pos_tip_data[-1, 2], 4)\n self.assertAlmostEqual(nb_pos_tip_data[-1, 3], ga_pos_tip_data[-1, 3], 4)\n\n def tearDown(self):\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n solver_path += '/'\n for name in [name_hinge, name_spherical, name_ga, name_nb_zero_dis]:\n files_to_delete = [name + '.aero.h5',\n name + '.dyn.h5',\n name + '.fem.h5',\n name + '.mb.h5',\n name + '.sharpy']\n for f in files_to_delete:\n os.remove(solver_path + f)\n\n shutil.rmtree(solver_path + 'output/')\n\nif __name__ == '__main__':\n unittest.main()\n" }, { "path": "tests/coupled/multibody/double_prescribed_pendulum/test_double_prescribed_pendulum.py", "content": "import numpy as np\nimport os\nimport shutil\nfrom matplotlib import pyplot as plt\nimport unittest\n\nimport sharpy.sharpy_main\nimport sharpy.utils.algebra as ag\nimport sharpy.utils.generate_cases as gc\n\n\nclass TestDoublePrescribedPendulum(unittest.TestCase):\n # this case is not convenient for using a setup method, as the second case definition depends upon the first\n # we'll just shove it all in the run method\n @staticmethod\n def run_and_assert():\n # Simulation inputs\n case_name_free = 'free_double_pendulum_jax'\n case_name_prescribed = 'prescribed_double_pendulum_jax'\n\n try:\n shutil.rmtree('' + str(os.path.dirname(os.path.realpath(__file__))) + '/cases/')\n except:\n pass\n\n try:\n shutil.rmtree('' + str(os.path.dirname(os.path.realpath(__file__))) + '/output/')\n except:\n pass\n\n os.makedirs('' + str(os.path.dirname(os.path.realpath(__file__))) + '/cases/')\n os.makedirs('' + str(os.path.dirname(os.path.realpath(__file__))) + '/output/')\n\n case_route = os.path.abspath(os.path.dirname(os.path.realpath(__file__))) + '/cases/'\n case_out_folder = case_route + '/output/'\n\n total_time = 0.05 # physical time (s)\n dt = 0.002 # time step length (s)\n n_tstep = int(total_time / dt) # number of time steps\n hinge_ang = np.deg2rad(30.)\n\n # Beam structural properties\n beam_l = 0.5 # beam length (m)\n beam_yz = 0.02 # cross-section width/height (m)\n beam_A = beam_yz ** 2 # square cross-section area`\n beam_rho = 2700.0 # beam material density (kg/m^3)\n beam_m = beam_rho * beam_A # beam mass per unit length (kg/m)\n beam_iner = beam_m * beam_yz ** 2 / 6. # beam inertia per unit length (kg m)\n\n EA = 2.800e7 # axial stiffness\n GA = 1.037e7 # shear stiffness\n GJ = 6.914e2 # torsional stiffness\n EI = 9.333e2 # bending stiffness\n\n # Toggle on to make spaghetti\n # GJ *= 5e-2\n # EI *= 5e-2\n\n # Airfoils (required as the NoAero solver still requires an aero grid)\n airfoil = np.zeros((1, 20, 2))\n airfoil[0, :, 0] = np.linspace(0., 1., 20)\n\n # Beam 0\n beam0_n_nodes = 11 # number of nodes\n beam0_l = beam_l # beam length\n beam0_ml = 0.0 # lumped mass\n beam0_theta_ini = np.deg2rad(90.) # initial beam angle\n\n # Beam 1\n beam1_n_nodes = 11 # number of nodes\n beam1_l = beam_l # beam length\n beam1_ml = 0.0 # lumped mass\n beam1_theta_ini = np.deg2rad(90.) # initial beam angle\n\n for hinge_dir in ('y',):\n # Create beam 0 structure\n beam0 = gc.AeroelasticInformation() # use aeroelastic as controllers implemented here\n beam0_r = np.linspace(0., beam0_l, beam0_n_nodes) # local node placement\n beam0_pos_ini = np.zeros((beam0_n_nodes, 3)) # initial global node placement\n match hinge_dir:\n case 'x':\n beam0_pos_ini[:, 1] = beam0_r * np.sin(beam0_theta_ini)\n beam0_pos_ini[:, 2] = -beam0_r * np.cos(beam0_theta_ini)\n y_BFoR = 'x_AFoR'\n case 'y':\n beam0_pos_ini[:, 0] = beam0_r * np.sin(beam0_theta_ini)\n beam0_pos_ini[:, 2] = -beam0_r * np.cos(beam0_theta_ini)\n y_BFoR = 'y_AFoR'\n case _:\n raise KeyError\n\n beam0.StructuralInformation.generate_uniform_beam(beam0_pos_ini, beam_m, beam_iner, beam_iner / 2.0,\n beam_iner / 2.0,\n np.zeros(3), EA, GA, GA, GJ, EI, EI,\n num_node_elem=3, y_BFoR=y_BFoR, num_lumped_mass=1)\n\n beam0.StructuralInformation.body_number = np.zeros(beam0.StructuralInformation.num_elem, dtype=int)\n beam0.StructuralInformation.boundary_conditions[0] = 1\n beam0.StructuralInformation.boundary_conditions[-1] = -1\n beam0.StructuralInformation.lumped_mass_nodes = np.array([beam0_n_nodes - 1], dtype=int)\n beam0.StructuralInformation.lumped_mass = np.ones(1) * beam0_ml\n beam0.StructuralInformation.lumped_mass_inertia = np.zeros((1, 3, 3))\n beam0.StructuralInformation.lumped_mass_position = np.zeros((1, 3))\n beam0.AerodynamicInformation.create_one_uniform_aerodynamics(\n beam0.StructuralInformation, chord=1., twist=0., sweep=0.,\n num_chord_panels=4, m_distribution='uniform', elastic_axis=0.25,\n num_points_camber=20, airfoil=airfoil)\n\n # Create beam 1 structure\n beam1 = gc.AeroelasticInformation()\n beam1_r = np.linspace(0., beam1_l, beam0_n_nodes) # local node placement\n\n beam1_pos_ini = np.zeros((beam0_n_nodes, 3)) # initial global node placement\n match hinge_dir:\n case 'x':\n beam1_pos_ini[:, 1] = beam1_r * np.sin(beam1_theta_ini) + beam0_pos_ini[-1, 1]\n beam1_pos_ini[:, 2] = -beam0_r * np.cos(beam1_theta_ini) + beam0_pos_ini[-1, 2]\n case 'y':\n beam1_pos_ini[:, 0] = beam1_r * np.sin(beam1_theta_ini) + beam0_pos_ini[-1, 0]\n beam1_pos_ini[:, 2] = -beam1_r * np.cos(beam1_theta_ini) + beam0_pos_ini[-1, 2]\n case _:\n raise KeyError\n\n beam1.StructuralInformation.generate_uniform_beam(beam1_pos_ini, beam_m, beam_iner, beam_iner / 2.0,\n beam_iner / 2.0,\n np.zeros(3), EA, GA, GA, GJ, EI, EI,\n num_node_elem=3, y_BFoR=y_BFoR, num_lumped_mass=1)\n\n beam1.StructuralInformation.body_number = np.zeros(beam1.StructuralInformation.num_elem, dtype=int)\n beam1.StructuralInformation.boundary_conditions[0] = 1\n beam1.StructuralInformation.boundary_conditions[-1] = -1\n beam1.StructuralInformation.lumped_mass_nodes = np.array([beam1_n_nodes - 1], dtype=int)\n beam1.StructuralInformation.lumped_mass = np.ones(1) * beam1_ml\n beam1.StructuralInformation.lumped_mass_inertia = np.zeros((1, 3, 3))\n beam1.StructuralInformation.lumped_mass_position = np.zeros((1, 3))\n beam1.AerodynamicInformation.create_one_uniform_aerodynamics(\n beam1.StructuralInformation, chord=1., twist=0., sweep=0.,\n num_chord_panels=4, m_distribution='uniform', elastic_axis=0.25,\n num_points_camber=20, airfoil=airfoil)\n\n # Combine beam1 into beam0\n beam0.assembly(beam1)\n\n # Create the MB and BC parameters\n # Free hinge\n LC0_free = gc.LagrangeConstraint()\n LC0_free.behaviour = 'hinge_FoR'\n LC0_free.body_FoR = 0\n match hinge_dir:\n case 'x':\n LC0_free.rot_axis_AFoR = np.array((1., 0., 0.))\n case 'y':\n LC0_free.rot_axis_AFoR = np.array((0., 1., 0.))\n LC0_free.scalingFactor = dt ** -2\n\n # Free hinge between beams\n LC1_free = gc.LagrangeConstraint()\n LC1_free.behaviour = 'hinge_node_FoR'\n LC1_free.node_in_body = beam0_n_nodes - 1\n LC1_free.body = 0\n LC1_free.body_FoR = 1\n match hinge_dir:\n case 'x':\n LC1_free.rot_axisB = np.array((np.sin(hinge_ang), np.cos(hinge_ang), 0.))\n LC1_free.rot_axisA2 = np.array((np.cos(hinge_ang), np.sin(hinge_ang), 0.))\n case 'y':\n LC1_free.rot_axisB = np.array((np.sin(hinge_ang), np.cos(hinge_ang), 0.))\n LC1_free.rot_axisA2 = np.array((np.sin(hinge_ang), np.cos(hinge_ang), 0.))\n LC1_free.scalingFactor = dt ** -2\n\n LC_free = [LC0_free, LC1_free] # List of LCs\n\n MB0 = gc.BodyInformation()\n MB0.body_number = 0\n MB0.FoR_position = np.zeros(6)\n MB0.FoR_velocity = np.zeros(6)\n MB0.FoR_acceleration = np.zeros(6)\n MB0.FoR_movement = 'free'\n MB0.quat = np.array([1., 0., 0., 0.])\n\n MB1 = gc.BodyInformation()\n MB1.body_number = 1\n MB1.FoR_position = np.array([*beam1_pos_ini[0, :], 0., 0., 0.])\n MB1.FoR_velocity = np.zeros(6)\n MB1.FoR_acceleration = np.zeros(6)\n MB1.FoR_movement = 'free'\n MB1.quat = np.array((1., 0., 0., 0.))\n\n MB = [MB0, MB1] # List of MBs\n\n # Simulation details\n SimInfo = gc.SimulationInformation()\n SimInfo.set_default_values()\n SimInfo.with_forced_vel = False\n SimInfo.with_dynamic_forces = False\n\n SimInfo.solvers['SHARPy']['flow'] = [\n 'BeamLoader',\n 'AerogridLoader',\n 'DynamicCoupled'\n ]\n\n SimInfo.solvers['SHARPy']['case'] = case_name_free\n SimInfo.solvers['SHARPy']['write_screen'] = False\n SimInfo.solvers['SHARPy']['route'] = case_route\n SimInfo.solvers['SHARPy']['log_folder'] = case_out_folder\n SimInfo.set_variable_all_dicts('dt', dt)\n SimInfo.define_num_steps(n_tstep)\n SimInfo.set_variable_all_dicts('output', case_out_folder)\n\n SimInfo.solvers['BeamLoader']['unsteady'] = 'on'\n\n SimInfo.solvers['AerogridLoader']['unsteady'] = 'on'\n SimInfo.solvers['AerogridLoader']['mstar'] = 2\n SimInfo.solvers['AerogridLoader']['wake_shape_generator'] = 'StraightWake'\n SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] = {'u_inf': 1.,\n 'u_inf_direction': np.array(\n (0., 1., 0.)),\n 'dt': dt}\n\n SimInfo.solvers['NonLinearDynamicMultibodyJAX']['write_lm'] = False\n SimInfo.solvers['NonLinearDynamicMultibodyJAX']['gravity_on'] = True\n SimInfo.solvers['NonLinearDynamicMultibodyJAX']['gravity'] = 9.81\n SimInfo.solvers['NonLinearDynamicMultibodyJAX']['time_integrator'] = 'NewmarkBetaJAX'\n SimInfo.solvers['NonLinearDynamicMultibodyJAX']['time_integrator_settings'] = {'newmark_damp': 0.0,\n 'dt': dt}\n\n SimInfo.solvers['BeamPlot']['include_FoR'] = False\n\n SimInfo.solvers['DynamicCoupled']['structural_solver'] = 'NonLinearDynamicMultibodyJAX'\n SimInfo.solvers['DynamicCoupled']['structural_solver_settings'] = SimInfo.solvers[\n 'NonLinearDynamicMultibodyJAX']\n SimInfo.solvers['DynamicCoupled']['aero_solver'] = 'NoAero'\n SimInfo.solvers['DynamicCoupled']['aero_solver_settings'] = SimInfo.solvers['NoAero']\n SimInfo.solvers['DynamicCoupled']['postprocessors'] = ['BeamPlot']\n SimInfo.solvers['DynamicCoupled']['postprocessors_settings'] = {'BeamPlot': {}}\n\n # Write files\n gc.clean_test_files(case_route, case_name_free)\n SimInfo.generate_solver_file()\n SimInfo.generate_dyn_file(n_tstep)\n beam0.generate_h5_files(case_route, case_name_free)\n gc.generate_multibody_file(LC_free, MB, case_route, case_name_free, use_jax=True)\n\n # Run SHARPy for free case\n case_data_free = sharpy.sharpy_main.main(['', case_route + case_name_free + '.sharpy'])\n\n # Calculate constraint angles\n quat0 = [case_data_free.structure.timestep_info[i].mb_quat[0, :] for i in range(n_tstep)]\n quat1 = [case_data_free.structure.timestep_info[i].mb_quat[1, :] for i in range(n_tstep)]\n psi_ga = [case_data_free.structure.timestep_info[i].psi[int((beam0_n_nodes - 3) / 2), 1, :] for i in\n range(n_tstep)]\n\n psi_a = [ag.quat2crv(quat0[i]) for i in range(n_tstep)]\n\n psi_hg = [ag.rotation2crv(ag.quat2rotation(quat0[i])\n @ ag.crv2rotation(psi_ga[i])\n @ ag.quat2rotation(quat1[i]).T) for i in range(n_tstep)]\n\n # Calculate constraint velocities\n omega_a = [case_data_free.structure.timestep_info[i].mb_FoR_vel[0, 3:] for i in range(n_tstep)]\n omega_h = [case_data_free.structure.timestep_info[i].mb_FoR_vel[1, 3:] for i in range(n_tstep)]\n psi_ga_dot = [case_data_free.structure.timestep_info[i].psi_dot[int((beam0_n_nodes - 3) / 2), 1, :] for i in\n range(n_tstep)]\n\n psi_a_dot = [np.linalg.solve(ag.crv2tan(psi_a[i]), omega_a[i]) for i in range(n_tstep)]\n\n term1 = [-ag.crv2tan(psi_ga[i]) @ psi_ga_dot[i]\n - ag.crv2rotation(psi_ga[i]).T @ omega_a[i]\n + ag.crv2rotation(psi_ga[i]).T @ ag.quat2rotation(quat0[i]).T @ ag.quat2rotation(quat1[i]) @\n omega_h[i]\n for i in range(n_tstep)]\n\n psi_hg_dot = [np.linalg.inv(ag.crv2tan(psi_hg[i])) @ ag.crv2rotation(psi_hg[i]) @ term1[i] for i in\n range(n_tstep)]\n\n # Controller inputs\n angle_input_file0 = case_out_folder + f'angle_input0_{hinge_dir}.npy'\n angle_input_file1 = case_out_folder + f'angle_input1_{hinge_dir}.npy'\n vel_input_file0 = case_out_folder + f'vel_input0_{hinge_dir}.npy'\n vel_input_file1 = case_out_folder + f'vel_input1_{hinge_dir}.npy'\n\n angle_input0 = np.array(psi_a)\n angle_input1 = np.array(psi_hg)\n vel_input0 = np.array(psi_a_dot)\n vel_input1 = np.array(psi_hg_dot)\n\n # Uncomment to stop prescribed pendulum tracking after a certain timestep (prove both cases aren't actually free!)\n # angle_input1[int(n_tstep/2):, :] = angle_input1[int(n_tstep/2) - 1, :]\n # vel_input1[int(n_tstep/2):, :] = 0.\n\n np.save(angle_input_file0, angle_input0)\n np.save(angle_input_file1, angle_input1)\n np.save(vel_input_file0, vel_input0)\n np.save(vel_input_file1, vel_input1)\n\n SimInfo.define_num_steps(n_tstep - 1)\n\n # Prescribe top joint angular velocity\n LC0_prescribed = gc.LagrangeConstraint()\n LC0_prescribed.behaviour = 'control_rot_vel_FoR'\n LC0_prescribed.controller_id = 'controller0'\n LC0_prescribed.body_FoR = 0\n LC0_prescribed.scalingFactor = dt ** -2\n\n # Actuated joint between beams\n LC1_prescribed = gc.LagrangeConstraint()\n LC1_prescribed.behaviour = 'control_node_FoR_rot_vel'\n LC1_prescribed.controller_id = 'controller1'\n LC1_prescribed.node_in_body = beam1_n_nodes - 1\n LC1_prescribed.body = 0\n LC1_prescribed.body_FoR = 1\n LC1_prescribed.scalingFactor = dt ** -2\n LC1_prescribed.rel_posB = np.zeros(3)\n\n LC_prescribed = [LC0_prescribed, LC1_prescribed] # List of LCs\n\n SimInfo.solvers['SHARPy']['case'] = case_name_prescribed\n SimInfo.solvers['DynamicCoupled']['controller_id'] = {\n 'controller0': 'MultibodyController',\n 'controller1': 'MultibodyController',\n }\n SimInfo.solvers['DynamicCoupled']['controller_settings']['controller0'] = {\n 'ang_history_input_file': angle_input_file0,\n 'ang_vel_history_input_file': vel_input_file0,\n 'dt': dt,\n }\n SimInfo.solvers['DynamicCoupled']['controller_settings']['controller1'] = {\n 'ang_history_input_file': angle_input_file1,\n 'ang_vel_history_input_file': vel_input_file1,\n 'dt': dt,\n }\n\n # Write files\n gc.clean_test_files(case_route, case_name_prescribed)\n SimInfo.generate_solver_file()\n SimInfo.generate_dyn_file(n_tstep)\n beam0.generate_h5_files(case_route, case_name_prescribed)\n gc.generate_multibody_file(LC_prescribed, MB, case_route, case_name_prescribed, use_jax=True)\n\n # Run SHARPy for prescribed case\n case_data_prescribed = sharpy.sharpy_main.main(['', case_route + case_name_prescribed + '.sharpy'])\n\n # compare (controller framework operates a timestep behind)\n # comparing y tip displacement\n pos_free = case_data_free.structure.timestep_info[-3].pos[-1, 1]\n pos_prescribed = case_data_prescribed.structure.timestep_info[-1].pos[-1, 1]\n\n diff = np.abs((pos_free / pos_prescribed) - 1.)\n\n if diff > 1e-3:\n raise ValueError(f\"Free and prescribed pendulum results no not closely match: diff={diff}\")\n\n\n def test_double_prescribed_pendulum(self):\n self.run_and_assert()\n\n def tearDown(self):\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__))) + '/'\n\n shutil.rmtree(solver_path + 'cases/')\n shutil.rmtree(solver_path + 'output/')\n\n def teardown_method(self):\n pass\n\nif __name__ == '__main__':\n unittest.main()\n" }, { "path": "tests/coupled/multibody/double_slanted_pendulum/__init__.py", "content": "" }, { "path": "tests/coupled/multibody/double_slanted_pendulum/test_double_pendulum_slanted.py", "content": "import numpy as np\nimport unittest\nimport os\nimport shutil\nfrom sharpy.utils.constants import deg2rad\n\n\nclass TestDoublePendulumSlanted(unittest.TestCase):\n \"\"\"\n Validation of a double pendulum with distributed mass and flared hinge axis at the connection\n\n As given in https://dx.doi.org/10.2514/6.2024-1441\n \"\"\"\n\n def _setUp(self, lateral):\n import sharpy.utils.generate_cases as gc\n import sharpy.utils.algebra as ag\n\n # Structural properties\n\n length_beam = 0.5 #meters\n cx_length = 0.02 #meters\n\n A = cx_length * cx_length #assume rectangular cross section a= d^2\n material_density = 2700.0 #kg/m^3\n\n mass_per_unit_length = material_density * A #kg/m\n mass_iner = (mass_per_unit_length) * (cx_length * cx_length + cx_length * cx_length) / (12.0)\n\n EA = 2.800e7\n GA = 1.037e7\n GJ = 6.914e2\n EI = 9.333e2\n\n lateral_ini = lateral\n\n # Beam1\n global nnodes1\n nnodes1 = 11\n l1 = length_beam\n m1 = 0.0\n theta_ini1 = 90. * deg2rad\n\n # Beam2\n nnodes2 = nnodes1\n l2 = l1\n m2 = m1\n theta_ini2 = 90. * deg2rad\n\n # airfoils\n airfoil = np.zeros((1, 20, 2), )\n airfoil[0, :, 0] = np.linspace(0., 1., 20)\n\n # Simulation\n numtimesteps = 30\n dt = 0.01\n\n # Create the structure\n beam1 = gc.AeroelasticInformation()\n r1 = np.linspace(0.0, l1, nnodes1)\n node_pos1 = np.zeros((nnodes1, 3), )\n node_pos1[:, 0] = r1 * np.sin(theta_ini1) * np.cos(lateral_ini)\n node_pos1[:, 1] = r1 * np.sin(theta_ini1) * np.sin(lateral_ini)\n node_pos1[:, 2] = -r1 * np.cos(theta_ini1)\n beam1.StructuralInformation.generate_uniform_beam(node_pos1, mass_per_unit_length, mass_iner, mass_iner / 2.0,\n mass_iner / 2.0, np.zeros((3,), ), EA, GA, GA, GJ, EI, EI,\n num_node_elem=3, y_BFoR='y_AFoR', num_lumped_mass=1)\n beam1.StructuralInformation.body_number = np.zeros((beam1.StructuralInformation.num_elem,), dtype=int)\n beam1.StructuralInformation.boundary_conditions[0] = 1\n beam1.StructuralInformation.boundary_conditions[-1] = -1\n beam1.StructuralInformation.lumped_mass_nodes = np.array([nnodes1 - 1], dtype=int)\n beam1.StructuralInformation.lumped_mass = np.ones((1,)) * m1\n beam1.StructuralInformation.lumped_mass_inertia = np.zeros((1, 3, 3))\n beam1.StructuralInformation.lumped_mass_position = np.zeros((1, 3))\n beam1.AerodynamicInformation.create_one_uniform_aerodynamics(\n beam1.StructuralInformation,\n chord=1.,\n twist=0.,\n sweep=0.,\n num_chord_panels=4,\n m_distribution='uniform',\n elastic_axis=0.25,\n num_points_camber=20,\n airfoil=airfoil)\n\n beam2 = gc.AeroelasticInformation()\n r2 = np.linspace(0.0, l2, nnodes2)\n node_pos2 = np.zeros((nnodes2, 3), )\n node_pos2[:, 0] = r2 * np.sin(theta_ini2) * np.cos(lateral_ini) + node_pos1[-1, 0]\n node_pos2[:, 1] = r2 * np.sin(theta_ini2) * np.sin(lateral_ini) + node_pos1[-1, 1]\n node_pos2[:, 2] = -r2 * np.cos(theta_ini2) + node_pos1[-1, 2] + 0.00000001\n beam2.StructuralInformation.generate_uniform_beam(node_pos2, mass_per_unit_length, mass_iner, mass_iner / 2.0,\n mass_iner / 2.0, np.zeros((3,), ), EA, GA, GA, GJ, EI, EI,\n num_node_elem=3, y_BFoR='y_AFoR', num_lumped_mass=1)\n beam2.StructuralInformation.body_number = np.zeros((beam1.StructuralInformation.num_elem,), dtype=int)\n beam2.StructuralInformation.boundary_conditions[0] = 1\n beam2.StructuralInformation.boundary_conditions[-1] = -1\n beam2.StructuralInformation.lumped_mass_nodes = np.array([nnodes2 - 1], dtype=int)\n beam2.StructuralInformation.lumped_mass = np.ones((1,)) * m2\n beam2.StructuralInformation.lumped_mass_inertia = np.zeros((1, 3, 3))\n beam2.StructuralInformation.lumped_mass_position = np.zeros((1, 3))\n beam2.AerodynamicInformation.create_one_uniform_aerodynamics(\n beam2.StructuralInformation,\n chord=1.,\n twist=0.,\n sweep=0.,\n num_chord_panels=4,\n m_distribution='uniform',\n elastic_axis=0.25,\n num_points_camber=20,\n airfoil=airfoil)\n\n beam1.assembly(beam2)\n\n # Simulation details\n SimInfo = gc.SimulationInformation()\n SimInfo.set_default_values()\n\n SimInfo.define_uinf(np.array([0.0, 1.0, 0.0]), 1.)\n\n SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\n 'AerogridLoader',\n 'DynamicCoupled']\n\n global name_hinge_slanted\n name_hinge_slanted = 'name_hinge_slanted'\n SimInfo.solvers['SHARPy']['case'] = name_hinge_slanted\n SimInfo.solvers['SHARPy']['write_screen'] = 'off'\n SimInfo.solvers['SHARPy']['route'] = os.path.abspath(os.path.dirname(os.path.realpath(__file__))) + '/'\n SimInfo.solvers['SHARPy']['log_folder'] = os.path.abspath(\n os.path.dirname(os.path.realpath(__file__))) + '/output/'\n SimInfo.set_variable_all_dicts('dt', dt)\n SimInfo.define_num_steps(numtimesteps)\n SimInfo.set_variable_all_dicts('rho', 0.0)\n SimInfo.set_variable_all_dicts('velocity_field_input', SimInfo.solvers['SteadyVelocityField'])\n SimInfo.set_variable_all_dicts('output',\n os.path.abspath(os.path.dirname(os.path.realpath(__file__))) + '/output/')\n\n SimInfo.solvers['BeamLoader']['unsteady'] = 'on'\n\n SimInfo.solvers['AerogridLoader']['unsteady'] = 'on'\n SimInfo.solvers['AerogridLoader']['initial_align'] = 'off'\n SimInfo.solvers['AerogridLoader']['aligned_grid'] = 'off'\n SimInfo.solvers['AerogridLoader']['mstar'] = 2\n SimInfo.solvers['AerogridLoader']['wake_shape_generator'] = 'StraightWake'\n SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] = {'u_inf': 1.,\n 'u_inf_direction': np.array([0., 1., 0.]),\n 'dt': dt}\n\n SimInfo.solvers['WriteVariablesTime']['FoR_number'] = np.array([0, 1], dtype=int)\n SimInfo.solvers['WriteVariablesTime']['FoR_variables'] = ['for_pos', 'mb_quat']\n SimInfo.solvers['WriteVariablesTime']['structure_nodes'] = np.array([nnodes1 - 1, nnodes1 + nnodes2 - 1],\n dtype=int)\n SimInfo.solvers['WriteVariablesTime']['structure_variables'] = ['pos']\n\n SimInfo.solvers['NonLinearDynamicMultibody']['gravity_on'] = True\n SimInfo.solvers['NonLinearDynamicMultibody']['gravity'] = 9.81\n SimInfo.solvers['NonLinearDynamicMultibody']['time_integrator'] = 'NewmarkBeta'\n SimInfo.solvers['NonLinearDynamicMultibody']['time_integrator_settings'] = {'newmark_damp': 0.0,\n 'dt': dt}\n SimInfo.solvers['NonLinearDynamicMultibody']['write_lm'] = True\n\n SimInfo.solvers['BeamPlot']['include_FoR'] = True\n\n SimInfo.solvers['DynamicCoupled']['structural_solver'] = 'NonLinearDynamicMultibody'\n SimInfo.solvers['DynamicCoupled']['structural_solver_settings'] = SimInfo.solvers['NonLinearDynamicMultibody']\n SimInfo.solvers['DynamicCoupled']['aero_solver'] = 'NoAero'\n SimInfo.solvers['DynamicCoupled']['aero_solver_settings'] = SimInfo.solvers['NoAero']\n SimInfo.solvers['DynamicCoupled']['postprocessors'] = ['WriteVariablesTime', 'BeamPlot', 'AerogridPlot']\n SimInfo.solvers['DynamicCoupled']['postprocessors_settings'] = {\n 'WriteVariablesTime': SimInfo.solvers['WriteVariablesTime'],\n 'BeamPlot': SimInfo.solvers['BeamPlot'],\n 'AerogridPlot': SimInfo.solvers['AerogridPlot']\n }\n\n SimInfo.with_forced_vel = False\n SimInfo.with_dynamic_forces = False\n\n # Create the MB and BC files\n LC1 = gc.LagrangeConstraint()\n LC1.behaviour = 'hinge_FoR'\n LC1.body_FoR = 0\n LC1.rot_axis_AFoR = np.array([0.0, 1.0, 0.0])\n LC1.scalingFactor = 1e6\n LC1.penaltyFactor = 0.\n\n LC2 = gc.LagrangeConstraint()\n LC2.behaviour = 'hinge_node_FoR'\n LC2.node_in_body = nnodes1 - 1\n LC2.body = 0\n LC2.body_FoR = 1\n LC2.rot_axisB = np.array([np.sin(45.0 * deg2rad), np.cos(45.0 * deg2rad), 0.0])\n LC2.rot_axisA2 = np.array([np.sin(45.0 * deg2rad), np.cos(45.0 * deg2rad), 0.0])\n LC2.scalingFactor = 1e6\n LC2.penaltyFactor = 0.\n\n LC = []\n LC.append(LC1)\n LC.append(LC2)\n\n MB1 = gc.BodyInformation()\n MB1.body_number = 0\n MB1.FoR_position = np.zeros(6)\n MB1.FoR_velocity = np.zeros(6)\n MB1.FoR_acceleration = np.zeros(6)\n MB1.FoR_movement = 'free'\n MB1.quat = ag.rotation2quat(ag.rotation3d_z(lateral_ini) @ ag.quat2rotation(np.array([1., 0., 0., 0.])))\n\n MB2 = gc.BodyInformation()\n MB2.body_number = 1\n MB2.FoR_position = np.array([node_pos2[0, 0], node_pos2[0, 1], node_pos2[0, 2], 0., 0., 0.])\n MB2.FoR_velocity = np.zeros(6)\n MB2.FoR_acceleration = np.zeros(6)\n MB2.FoR_movement = 'free'\n MB2.quat = ag.rotation2quat(ag.rotation3d_z(lateral_ini) @ ag.quat2rotation(np.array([1., 0., 0., 0.])))\n\n MB = []\n MB.append(MB1)\n MB.append(MB2)\n\n # Write files\n gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n SimInfo.generate_solver_file()\n SimInfo.generate_dyn_file(numtimesteps)\n beam1.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n gc.generate_multibody_file(LC, MB, SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n\n # Same case with penalty weights\n global name_hinge_slanted_pen\n name_hinge_slanted_pen = 'name_hinge_slanted_pen'\n SimInfo.solvers['SHARPy']['case'] = name_hinge_slanted_pen\n\n LC1.scalingFactor = 1e-24\n LC1.penaltyFactor = 1e0\n LC2.scalingFactor = 1e-24\n LC2.penaltyFactor = 1e0\n\n gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n SimInfo.generate_solver_file()\n SimInfo.generate_dyn_file(numtimesteps)\n beam1.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n gc.generate_multibody_file(LC, MB, SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n\n # Same case with rotated global reference\n global name_hinge_slanted_lateralrot\n name_hinge_slanted_lateralrot = 'name_hinge_slanted_lateralrot'\n SimInfo.solvers['SHARPy']['case'] = name_hinge_slanted_lateralrot\n\n LC2.rot_axisB = np.array([np.sin(45.0 * deg2rad), np.cos(45.0 * deg2rad), 0.0])\n LC2.rot_axisA2 = np.array([np.sin(45.0 * deg2rad), np.cos(45.0 * deg2rad), 0.0])\n\n gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n SimInfo.generate_solver_file()\n SimInfo.generate_dyn_file(numtimesteps)\n beam1.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n gc.generate_multibody_file(LC, MB, SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n\n gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n SimInfo.generate_solver_file()\n SimInfo.generate_dyn_file(numtimesteps)\n beam1.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n gc.generate_multibody_file(LC, MB, SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n\n def run_and_assert(self, name, lateral):\n import sharpy.sharpy_main\n import sharpy.utils.algebra as ag\n\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) + '/' + name + '.sharpy')\n sharpy.sharpy_main.main(['', solver_path])\n\n # read output and compare\n output_path = os.path.abspath(\n os.path.dirname(os.path.realpath(__file__))) + '/output/' + name + '/WriteVariablesTime/'\n pos_tip_data = np.loadtxt((\"%sstruct_pos_node%d.dat\" % (output_path, nnodes1 * 2 - 1)), )\n for_pos_tip_data = np.loadtxt((\"%sFoR_%02d_for_pos.dat\" % (output_path, 0)), )\n quat_tip_data = np.loadtxt((\"%sFoR_%02d_mb_quat.dat\" % (output_path, 0)), )\n\n calc_pos_tip_data = ag.rotation3d_z(-lateral) @ (for_pos_tip_data[-1, 1:4]\n + ag.quat2rotation(quat_tip_data[-1, 1:])\n @ pos_tip_data[-1, 1:])\n\n self.assertAlmostEqual(calc_pos_tip_data[0], 0.80954978, 4)\n self.assertAlmostEqual(calc_pos_tip_data[1], 0.1024842, 4)\n self.assertAlmostEqual(calc_pos_tip_data[2], -0.48183994, 4)\n\n def test_doublependulum_hinge_slanted(self):\n lateral_hinge = 0. * deg2rad\n self._setUp(lateral_hinge)\n self.run_and_assert(name_hinge_slanted, lateral_hinge)\n\n def test_doublependulum_hinge_slanted_pen(self):\n lateral_hinge = 0. * deg2rad\n self._setUp(lateral_hinge)\n self.run_and_assert(name_hinge_slanted_pen, lateral_hinge)\n\n def test_doublependulum_hinge_slanted_lateralrot(self):\n lateral_hinge = 30. * deg2rad\n self._setUp(lateral_hinge)\n self.run_and_assert(name_hinge_slanted_lateralrot, lateral_hinge)\n\n def tearDown(self):\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n solver_path += '/'\n for name in ['name_hinge_slanted', 'name_hinge_slanted_pen', 'name_hinge_slanted_lateralrot']:\n files_to_delete = [name + '.aero.h5',\n name + '.dyn.h5',\n name + '.fem.h5',\n name + '.mb.h5',\n name + '.sharpy']\n for f in files_to_delete:\n os.remove(solver_path + f)\n\n shutil.rmtree(solver_path + 'output/')\n\n\nif __name__ == '__main__':\n unittest.main()\n" }, { "path": "tests/coupled/multibody/fix_node_velocity_wrtA/__init__.py", "content": "" }, { "path": "tests/coupled/multibody/fix_node_velocity_wrtA/test_fix_node_velocity_wrtA.py", "content": "import numpy as np\nimport unittest\nimport os\nimport shutil\n\nfolder = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n\n\nclass TestFixNodeVelocitywrtA(unittest.TestCase):\n\n def setUp(self):\n import sharpy.utils.generate_cases as gc\n\n nodes_per_elem = 3\n\n # beam1: uniform and symmetric with aerodynamic properties equal to zero\n nnodes1 = 11\n length1 = 10.\n mass_per_unit_length = 1.\n mass_iner = 1e-4\n EA = 1e7\n GA = 1e7\n GJ = 1e3\n EI = 1e4\n\n # Create beam1\n beam1 = gc.AeroelasticInformation()\n # Structural information\n beam1.StructuralInformation.num_node = nnodes1\n beam1.StructuralInformation.num_node_elem = nodes_per_elem\n beam1.StructuralInformation.compute_basic_num_elem()\n beam1.StructuralInformation.set_to_zero(beam1.StructuralInformation.num_node_elem, beam1.StructuralInformation.num_node, beam1.StructuralInformation.num_elem)\n node_pos = np.zeros((nnodes1, 3), )\n node_pos[:, 0] = np.linspace(0.0, length1, nnodes1)\n beam1.StructuralInformation.generate_uniform_sym_beam(node_pos, mass_per_unit_length, mass_iner, EA, GA, GJ, EI, num_node_elem = 3, y_BFoR = 'y_AFoR', num_lumped_mass=1)\n beam1.StructuralInformation.boundary_conditions[0] = 1\n beam1.StructuralInformation.boundary_conditions[-1] = -1\n beam1.StructuralInformation.lumped_mass_nodes = np.array([nnodes1-1], dtype=int)\n beam1.StructuralInformation.lumped_mass = np.array([1.])\n beam1.StructuralInformation.lumped_mass_inertia = np.zeros((1, 3, 3),)\n beam1.StructuralInformation.lumped_mass_position = np.zeros((1, 3),)\n # beam1.StructuralInformation.structural_twist += 2.*deg2rad\n beam1.StructuralInformation.app_forces[-1, 2] = -10.\n\n # Aerodynamic information\n airfoil = np.zeros((1,20,2),)\n airfoil[0,:,0] = np.linspace(0.,1.,20)\n beam1.AerodynamicInformation.create_one_uniform_aerodynamics(\n beam1.StructuralInformation,\n chord = 1.,\n twist = 0.,\n sweep = 0.,\n num_chord_panels = 4,\n m_distribution = 'uniform',\n elastic_axis = 0.5,\n num_points_camber = 20,\n airfoil = airfoil)\n\n # SOLVER CONFIGURATION\n SimInfo = gc.SimulationInformation()\n SimInfo.set_default_values()\n\n SimInfo.define_uinf(np.array([0.0,1.0,0.0]), 10.)\n\n SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'DynamicCoupled',\n 'BeamPlot']\n global name\n name = 'fix_node_velocity_wrtA'\n SimInfo.solvers['SHARPy']['case'] = name\n SimInfo.solvers['SHARPy']['write_screen'] = 'off'\n SimInfo.solvers['SHARPy']['route'] = folder + '/'\n SimInfo.solvers['SHARPy']['log_folder'] = folder + '/output/'\n SimInfo.set_variable_all_dicts('dt', 0.05)\n SimInfo.set_variable_all_dicts('rho', 0.0)\n SimInfo.set_variable_all_dicts('velocity_field_input', SimInfo.solvers['SteadyVelocityField'])\n\n SimInfo.solvers['BeamLoader']['unsteady'] = 'on'\n\n SimInfo.solvers['AerogridLoader']['unsteady'] = 'on'\n SimInfo.solvers['AerogridLoader']['mstar'] = 2\n SimInfo.solvers['AerogridLoader']['wake_shape_generator'] = 'StraightWake'\n SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] = {'u_inf':10.,\n 'u_inf_direction': np.array([0., 1., 0.]),\n 'dt': 0.05}\n\n\n SimInfo.solvers['NonLinearStatic']['print_info'] = False\n\n SimInfo.solvers['StaticCoupled']['structural_solver'] = 'NonLinearStatic'\n SimInfo.solvers['StaticCoupled']['structural_solver_settings'] = SimInfo.solvers['NonLinearStatic']\n SimInfo.solvers['StaticCoupled']['aero_solver'] = 'StaticUvlm'\n SimInfo.solvers['StaticCoupled']['aero_solver_settings'] = SimInfo.solvers['StaticUvlm']\n SimInfo.solvers['StaticCoupled']['relaxation_factor'] = 0.0\n\n SimInfo.solvers['NonLinearDynamicMultibody']['gravity_on'] = True\n\n SimInfo.solvers['WriteVariablesTime']['structure_nodes'] = np.array([0, int((nnodes1-1)/2), -1], dtype = int)\n SimInfo.solvers['WriteVariablesTime']['structure_variables'] = ['pos']\n\n SimInfo.solvers['BeamPlot']['include_FoR'] = True\n SimInfo.solvers['NonLinearDynamicMultibody']['relaxation_factor'] = 0.2\n SimInfo.solvers['NonLinearDynamicMultibody']['min_delta'] = 1e-6\n SimInfo.solvers['NonLinearDynamicMultibody']['max_iterations'] = 200\n SimInfo.solvers['NonLinearDynamicMultibody']['write_lm'] = False\n SimInfo.solvers['NonLinearDynamicMultibody']['time_integrator'] = 'NewmarkBeta'\n SimInfo.solvers['NonLinearDynamicMultibody']['time_integrator_settings'] = {'newmark_damp': 1e-3,\n 'dt': 0.05}\n\n SimInfo.solvers['WriteVariablesTime']['cleanup_old_solution'] = 'on'\n\n SimInfo.solvers['DynamicCoupled']['structural_solver'] = 'NonLinearDynamicMultibody'\n SimInfo.solvers['DynamicCoupled']['structural_solver_settings'] = SimInfo.solvers['NonLinearDynamicMultibody']\n SimInfo.solvers['DynamicCoupled']['aero_solver'] = 'StepUvlm'\n SimInfo.solvers['DynamicCoupled']['aero_solver_settings'] = SimInfo.solvers['StepUvlm']\n SimInfo.solvers['DynamicCoupled']['postprocessors'] = ['WriteVariablesTime', 'BeamPlot', 'AerogridPlot']\n SimInfo.solvers['DynamicCoupled']['postprocessors_settings'] = {'WriteVariablesTime': SimInfo.solvers['WriteVariablesTime'],\n 'BeamPlot': SimInfo.solvers['BeamPlot'],\n 'AerogridPlot': SimInfo.solvers['AerogridPlot']}\n\n ntimesteps = 10\n\n SimInfo.define_num_steps(ntimesteps)\n\n # Define dynamic simulation\n SimInfo.with_forced_vel = False\n SimInfo.with_dynamic_forces = False\n\n LC2 = gc.LagrangeConstraint()\n LC2.behaviour = 'lin_vel_node_wrtA'\n LC2.velocity = np.array([0.,0.,0.])\n LC2.body_number = 0\n LC2.node_number = int((nnodes1-1)/2)\n\n LC = []\n # LC.append(LC1)\n LC.append(LC2)\n\n # Define the multibody infromation for the tower and the rotor\n MB1 = gc.BodyInformation()\n MB1.body_number = 0\n MB1.FoR_position = np.zeros((6,),)\n MB1.FoR_velocity = np.zeros((6,),)\n MB1.FoR_acceleration = np.zeros((6,),)\n MB1.FoR_movement = 'prescribed'\n MB1.quat = np.array([1.0,0.0,0.0,0.0])\n\n MB = []\n MB.append(MB1)\n\n\n gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n SimInfo.generate_solver_file()\n SimInfo.generate_dyn_file(ntimesteps)\n beam1.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n gc.generate_multibody_file(LC, MB,SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n\n\n # def tearDown():\n # pass\n\n def test_testfixnodevelocitywrta(self):\n import sharpy.sharpy_main\n\n solver_path = folder + '/fix_node_velocity_wrtA.sharpy'\n sharpy.sharpy_main.main(['', solver_path])\n\n # read output and compare\n output_path = folder + '/output/fix_node_velocity_wrtA/WriteVariablesTime/'\n # quat_data = np.matrix(np.genfromtxt(output_path + 'FoR_00_mb_quat.dat', delimiter=' '))\n pos_tip_data = np.loadtxt((\"%sstruct_pos_node-1.dat\" % output_path), )\n self.assertAlmostEqual(pos_tip_data[0, 1], 9.993007e+00, 3)\n self.assertAlmostEqual(pos_tip_data[0, 2], 0., 3)\n self.assertAlmostEqual(pos_tip_data[0, 3], -3.402154e-01, 3)\n\n self.assertAlmostEqual(pos_tip_data[-1, 1], 9.962520e+00, 3)\n self.assertAlmostEqual(pos_tip_data[-1, 2], 0., 3)\n self.assertAlmostEqual(pos_tip_data[-1, 3], -6.943423e-01, 3)\n\n pos_root_data = np.loadtxt((\"%sstruct_pos_node0.dat\" % output_path), )\n self.assertAlmostEqual(pos_root_data[0, 1], 0.0, 2)\n self.assertAlmostEqual(pos_root_data[0, 2], 0.0, 2)\n self.assertAlmostEqual(pos_root_data[0, 3], 0.0, 2)\n\n self.assertAlmostEqual(pos_root_data[-1, 1], 0.0, 2)\n self.assertAlmostEqual(pos_root_data[-1, 2], 0.0, 2)\n self.assertAlmostEqual(pos_root_data[-1, 3], 0.0, 2)\n\n def tearDown(self):\n # pass\n files_to_delete = [name + '.aero.h5',\n name + '.dyn.h5',\n name + '.fem.h5',\n name + '.mb.h5',\n name + '.sharpy']\n for f in files_to_delete:\n os.remove(folder + '/' + f)\n\n shutil.rmtree(folder + '/output/')\n" }, { "path": "tests/coupled/multibody/fix_node_velocity_wrtG/__init__.py", "content": "" }, { "path": "tests/coupled/multibody/fix_node_velocity_wrtG/test_fix_node_velocity_wrtG.py", "content": "import os\nimport shutil\nimport unittest\nimport numpy as np\n\nimport sharpy.utils.generate_cases as gc\nimport sharpy.sharpy_main\n\nfolder = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n\n\nclass TestFixNodeVelocitywrtG(unittest.TestCase):\n \"\"\"\n\n \"\"\"\n def setUp(self):\n\n nodes_per_elem = 3\n\n # beam1: uniform and symmetric with aerodynamic properties equal to zero\n nnodes1 = 11\n length1 = 10.\n mass_per_unit_length = 0.1\n mass_iner = 1e-4\n EA = 1e9\n GA = 1e9\n GJ = 1e3\n EI = 1e4\n\n # Create beam1\n beam1 = gc.AeroelasticInformation()\n # Structural information\n beam1.StructuralInformation.num_node = nnodes1\n beam1.StructuralInformation.num_node_elem = nodes_per_elem\n beam1.StructuralInformation.compute_basic_num_elem()\n beam1.StructuralInformation.set_to_zero(beam1.StructuralInformation.num_node_elem, beam1.StructuralInformation.num_node, beam1.StructuralInformation.num_elem)\n node_pos = np.zeros((nnodes1, 3), )\n node_pos[:, 0] = np.linspace(0.0, length1, nnodes1)\n beam1.StructuralInformation.generate_uniform_sym_beam(node_pos, mass_per_unit_length, mass_iner, EA, GA, GJ, EI, num_node_elem = 3, y_BFoR = 'y_AFoR', num_lumped_mass=2)\n beam1.StructuralInformation.boundary_conditions[0] = 1\n beam1.StructuralInformation.boundary_conditions[-1] = -1\n beam1.StructuralInformation.lumped_mass_nodes = np.array([0, nnodes1-1], dtype=int)\n beam1.StructuralInformation.lumped_mass = np.array([2., 1.])\n beam1.StructuralInformation.lumped_mass_inertia = np.zeros((2, 3, 3),)\n beam1.StructuralInformation.lumped_mass_position = np.zeros((2, 3),)\n\n # Aerodynamic information\n airfoil = np.zeros((1, 20, 2),)\n airfoil[0, :, 0] = np.linspace(0., 1., 20)\n beam1.AerodynamicInformation.create_one_uniform_aerodynamics(\n beam1.StructuralInformation,\n chord=1.,\n twist=0.,\n sweep=0.,\n num_chord_panels=4,\n m_distribution='uniform',\n elastic_axis=0.5,\n num_points_camber=20,\n airfoil=airfoil)\n\n # SOLVER CONFIGURATION\n SimInfo = gc.SimulationInformation()\n SimInfo.set_default_values()\n\n SimInfo.define_uinf(np.array([0.0,1.0,0.0]), 10.)\n\n SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'DynamicCoupled']\n self.name = 'fix_node_velocity_wrtG'\n SimInfo.solvers['SHARPy']['case'] = self.name\n SimInfo.solvers['SHARPy']['write_screen'] = 'off'\n SimInfo.solvers['SHARPy']['route'] = folder + '/'\n SimInfo.solvers['SHARPy']['log_folder'] = folder + '/output/'\n SimInfo.set_variable_all_dicts('dt', 0.1)\n SimInfo.set_variable_all_dicts('rho', 0.0)\n SimInfo.set_variable_all_dicts('velocity_field_input', SimInfo.solvers['SteadyVelocityField'])\n SimInfo.set_variable_all_dicts('folder', folder + '/output/')\n\n SimInfo.solvers['BeamLoader']['unsteady'] = 'on'\n\n SimInfo.solvers['AerogridLoader']['unsteady'] = 'on'\n SimInfo.solvers['AerogridLoader']['mstar'] = 2\n SimInfo.solvers['AerogridLoader']['wake_shape_generator'] = 'StraightWake'\n SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] = {'u_inf':10.,\n 'u_inf_direction': np.array([0., 1., 0.]),\n 'dt': 0.1}\n\n\n SimInfo.solvers['NonLinearStatic']['print_info'] = False\n\n SimInfo.solvers['StaticCoupled']['structural_solver'] = 'NonLinearStatic'\n SimInfo.solvers['StaticCoupled']['structural_solver_settings'] = SimInfo.solvers['NonLinearStatic']\n SimInfo.solvers['StaticCoupled']['aero_solver'] = 'StaticUvlm'\n SimInfo.solvers['StaticCoupled']['aero_solver_settings'] = SimInfo.solvers['StaticUvlm']\n\n SimInfo.solvers['WriteVariablesTime']['structure_nodes'] = np.array([0, int((nnodes1-1)/2), -1], dtype = int)\n SimInfo.solvers['WriteVariablesTime']['structure_variables'] = ['pos']\n\n SimInfo.solvers['BeamPlot']['include_FoR'] = True\n\n SimInfo.solvers['NonLinearDynamicMultibody']['relaxation_factor'] = 0.0\n SimInfo.solvers['NonLinearDynamicMultibody']['min_delta'] = 1e-5\n SimInfo.solvers['NonLinearDynamicMultibody']['max_iterations'] = 200\n # SimInfo.solvers['NonLinearDynamicMultibody']['gravity_on'] = 'off'\n SimInfo.solvers['NonLinearDynamicMultibody']['time_integrator'] = 'NewmarkBeta'\n SimInfo.solvers['NonLinearDynamicMultibody']['time_integrator_settings'] = {'newmark_damp': 1e-3,\n 'dt': 0.1}\n\n SimInfo.solvers['NonLinearDynamicMultibody']['relaxation_factor'] = 0.0\n\n SimInfo.solvers['DynamicCoupled']['structural_solver'] = 'NonLinearDynamicMultibody'\n SimInfo.solvers['DynamicCoupled']['structural_solver_settings'] = SimInfo.solvers['NonLinearDynamicMultibody']\n SimInfo.solvers['DynamicCoupled']['aero_solver'] = 'StepUvlm'\n SimInfo.solvers['DynamicCoupled']['aero_solver_settings'] = SimInfo.solvers['StepUvlm']\n SimInfo.solvers['DynamicCoupled']['postprocessors'] = ['WriteVariablesTime', 'BeamPlot', 'AerogridPlot']\n SimInfo.solvers['DynamicCoupled']['postprocessors_settings'] = {'WriteVariablesTime': SimInfo.solvers['WriteVariablesTime'],\n 'BeamPlot': SimInfo.solvers['BeamPlot'],\n 'AerogridPlot': SimInfo.solvers['AerogridPlot']}\n\n ntimesteps = 10\n\n SimInfo.define_num_steps(ntimesteps)\n\n # Define dynamic simulation\n SimInfo.with_forced_vel = False\n SimInfo.with_dynamic_forces = False\n\n LC2 = gc.LagrangeConstraint()\n LC2.behaviour = 'lin_vel_node_wrtG'\n LC2.velocity = np.zeros((ntimesteps, 3))\n LC2.velocity[:int(ntimesteps/2),1] = 0.5\n LC2.velocity[int(ntimesteps/2):,1] = -0.5\n LC2.body_number = 0\n LC2.node_number = int((nnodes1-1)/2)\n\n LC = []\n # LC.append(LC1)\n LC.append(LC2)\n\n # Define the multibody infromation for the tower and the rotor\n MB1 = gc.BodyInformation()\n MB1.body_number = 0\n MB1.FoR_position = np.zeros((6,),)\n MB1.FoR_velocity = np.zeros((6,),)\n MB1.FoR_acceleration = np.zeros((6,),)\n MB1.FoR_movement = 'free'\n MB1.quat = np.array([1.0,0.0,0.0,0.0])\n\n MB = []\n MB.append(MB1)\n\n\n gc.clean_test_files(\n SimInfo.solvers['SHARPy']['route'],\n SimInfo.solvers['SHARPy']['case'])\n SimInfo.generate_solver_file()\n SimInfo.generate_dyn_file(ntimesteps)\n beam1.generate_h5_files(\n SimInfo.solvers['SHARPy']['route'],\n SimInfo.solvers['SHARPy']['case'])\n gc.generate_multibody_file(LC,\n MB,SimInfo.solvers['SHARPy']['route'],\n SimInfo.solvers['SHARPy']['case'])\n\n def test_testfixnodevelocitywrtg(self):\n \"\"\"\n\n \"\"\"\n solver_path = folder + '/fix_node_velocity_wrtG.sharpy'\n sharpy.sharpy_main.main(['', solver_path])\n\n # read output and compare\n output_path = folder + '/output/fix_node_velocity_wrtG/WriteVariablesTime/'\n pos_tip_data = np.loadtxt((\"%sstruct_pos_node-1.dat\" % output_path), )\n self.assertAlmostEqual(pos_tip_data[-1, 1], 9.999386, 4)\n self.assertAlmostEqual(pos_tip_data[-1, 2], -0.089333, 4)\n self.assertAlmostEqual(pos_tip_data[-1, 3], 0., 4)\n\n def tearDown(self):\n files_to_delete = [self.name + '.aero.h5',\n self.name + '.dyn.h5',\n self.name + '.fem.h5',\n self.name + '.mb.h5',\n self.name + '.sharpy']\n for f in files_to_delete:\n os.remove(folder + '/' + f)\n\n shutil.rmtree(folder + '/output/')\n" }, { "path": "tests/coupled/multibody/floating_forces/test_floatingforces.py", "content": "import numpy as np\nimport unittest\nimport os\nimport shutil\nfrom scipy import fft\nimport sharpy.generators.floatingforces as ff\n\n\nclass TestFloatingForces(unittest.TestCase):\n \"\"\"\n Some tests of the floating forces library\n Check references therein\n \"\"\"\n\n def test_compute_xf_zf(self):\n \"\"\"\n This function tests based on by hand computations and data from the MooringLineFD.txt file\n from the OC3 task.\n Jonkman, J.\n Definition of the Floating System for Phase IV of OC3\n NREL/TP-500-47535\n \"\"\"\n \n # Values for OC3\n l = 902.2 # Initial length [m]\n w = 698.094 # Aparent weight 77.7066*9.81 # Apparent mass per unit length times gravity\n EA = 384243000. # Extensional stiffness\n cb = 0.1 # Seabed friction coefficient\n \n # No mooring line on the Seabed\n vf = 1.1*l*w # 692802.4475\n hf = vf\n xf_byhand = 784.5965853 + 1.626695524\n zf_byhand = 406.9813526 + 0.887288467\n xf, zf = ff.compute_xf_zf(hf, vf, l, w, EA, cb)\n self.assertAlmostEqual(xf_byhand, xf, 4)\n self.assertAlmostEqual(zf_byhand, zf, 4)\n \n # Some mooring line on the Seabed\n lb_div_l = 0.1 # 10% of the mooring line on the seabed\n vf = (1-lb_div_l)*l*w\n hf = vf\n xf_byhand = 90.22 + 715.6577252 + 1.330932701 - 7.298744381e-4\n zf_byhand = 336.3331284 + 0.598919715\n xf, zf = ff.compute_xf_zf(hf, vf, l, w, EA, cb)\n self.assertAlmostEqual(xf_byhand, xf, 4)\n self.assertAlmostEqual(zf_byhand, zf, 4)\n \n \n def test_generate_mooringlinefd(self):\n \"\"\"\n This function generates a file similar to MoorinLinesFD.txt for compiarison\n File obtained from the google drive directory of the OC3 benchmark\n \"\"\"\n \n # Values for OC3\n l = 902.2 # Initial length [m]\n w = 698.094 # Aparent weight 77.7066*9.81 # Apparent mass per unit length times gravity\n EA = 384243000. # Extensional stiffness\n cb = 0. # Seabed friction coefficient\n \n zf = 320. - 70.\n \n # xf0 = 853.87\n # xf_list = np.arange(653.00, 902.50 + 1., 1.)\n xf_list = np.arange(653.00, 902.50, 10.)\n npoints = xf_list.shape[0]\n output = np.zeros((npoints, 4))\n for i in range(npoints):\n hf, vf = ff.quasisteady_mooring(xf_list[i], zf, l, w, EA, cb, hf0=None, vf0=None)\n # print(xf0, zf0, hf0, vf0)\n lb = np.maximum(l - vf/w, 0)\n # print(\"Suspended lenght = %f\" % (l - lb))\n output[i, :] = np.array([xf_list[i], np.sqrt(vf**2 + hf**2)*1e-3, hf*1e-3, (l - lb)])\n\n of_results = np.loadtxt(\"MooringLineFD.dat\", skiprows=9)\n for i in range(npoints):\n for icol in range(4):\n of_value = np.interp(xf_list[i], of_results[:, 0], of_results[:, icol])\n error = np.abs((np.round_(output[i, icol], 1) - of_value)/of_value)\n self.assertLess(error, 0.1)\n \n save_txt = False\n if save_txt: \n np.savetxt(\"sharpy_mooringlinefd.txt\", output, header=\"# DISTANCE(m) TENSION(kN) HTENSION(kN) SUSPL(m)\")\n\n \n def test_change_system(self):\n # Wind turbine degrees of freedom: Surge, sway, heave, roll, pitch, yaw.\n # SHARPy axis associated: z, y, x, z, y, x\n \n wt_matrix_num = np.zeros((6,6),)\n for idof in range(6):\n for jdof in range(6):\n wt_matrix_num[idof, jdof] = 10.*idof + jdof\n \n sharpy_matrix = ff.change_of_to_sharpy(wt_matrix_num)\n undo_sharpy_matrix = ff.change_of_to_sharpy(sharpy_matrix)\n \n for idof in range(6):\n for jdof in range(6):\n self.assertEqual(wt_matrix_num[idof, jdof], undo_sharpy_matrix[idof, jdof])\n \n \n def test_time_wave_forces(self):\n Tp = 14.656 #10.\n Hs = 5.49 #6.\n nrealisations = 100\n dt = 2*np.pi/4 # 1./20 To get max freq equal to 10Hz\n ntime_steps = 1000\n time = np.arange(ntime_steps)*dt\n \n # Get the zero-noise specturm\n w_js = np.arange(0, 4, 0.01)\n zero_noise_spectrum = ff.jonswap_spectrum(Tp, Hs, w_js)\n \n # Compute different realisations\n xi = np.zeros((2, 6), dtype=complex)\n xi[0, 0] = 1. + 0j\n xi[1, 0] = 1. + 0j\n w_xi = np.array([0., 4.])\n wave_force = np.zeros((ntime_steps, nrealisations), dtype=np.complex)\n for ireal in range(nrealisations):\n wave_force[:, ireal] = ff.time_wave_forces(Tp, Hs, dt, time, xi, w_xi)[:, 0] # Keep only on dimension\n \n # Compute the spectrum of the realisations\n ns = np.zeros((ntime_steps//2, nrealisations), dtype=np.complex)\n for ireal in range(nrealisations):\n ns[:, ireal] = dt/ntime_steps*np.abs(fft(wave_force[:, ireal])[:ntime_steps//2])**2\n ns[1:, ireal] *= 2\n # To rad/s\n ns /= 2.*np.pi\n w_ns = (np.fft.fftfreq(ntime_steps, d=dt)[:ntime_steps//2])*2.*np.pi\n # Compare the zero noise with the realisations average\n avg_noise_spectrum = np.average(ns, axis=1)\n\n for iomega in range(w_js.shape[0]):\n error = (np.interp(w_js[iomega], w_ns, avg_noise_spectrum) - zero_noise_spectrum[iomega])\n if error > 0.1:\n error /= zero_noise_spectrum[iomega]\n # 0.3 is a large error but otherwise I need to increment nrealisations a lot\n # Use ``save_fig = True`` for visual inspection\n self.assertLess(error, 0.3)\n \n save_fig = False\n if save_fig:\n np.savetxt(\"zero_noise_jonswap.txt\", np.column_stack((w_js, zero_noise_spectrum)))\n np.savetxt(\"realisations_jonswap.txt\", np.column_stack((w_ns, np.abs(ns))))\n np.savetxt(\"average_jonswap.txt\", np.column_stack((w_ns, avg_noise_spectrum)))\n \n import matplotlib.pyplot as plt\n fig, ax = plt.subplots(1, 1, figsize=(4, 3))\n ax.grid()\n ax.set_xlabel(\"omega [rad/s]\")\n ax.set_ylabel(\"specturm\")\n ax.set_xlim(0, 4)\n ax.set_ylim(0, 12)\n for ireal in range(nrealisations):\n ax.plot(w_ns, np.abs(ns[:, ireal]), 'bo')\n ax.plot(w_ns, avg_noise_spectrum, '-', label=\"avg\")\n ax.plot(w_js, zero_noise_spectrum, '--', label=\"JONSWAP\")\n fig.legend()\n fig.tight_layout()\n fig.show()\n fig.savefig(\"spectrum.png\")\n plt.close()\n\n\n # def tearDown(self):\n # solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n # solver_path += '/'\n # files_to_delete = [name + '.aero.h5',\n # name + '.dyn.h5',\n # name + '.fem.h5',\n # name + '.mb.h5',\n # name + '.sharpy']\n # for f in files_to_delete:\n # os.remove(solver_path + f)\n\n # shutil.rmtree(solver_path + 'output/')\n" }, { "path": "tests/coupled/multibody/floating_wind_turbine/test_floating_wind_turbine.py", "content": "\n\"\"\"\nspar_from_excel_type04\n\nExample of a file used to generate a floating wind turbine case\n\"\"\"\n# Load libraries\nimport sharpy.utils.generate_cases as gc\nimport cases.templates.template_wt as template_wt\nimport numpy as np\nimport os\nimport sharpy.utils.algebra as algebra\nfrom sharpy.utils.constants import deg2rad\nimport sharpy.sharpy_main\nimport unittest\nimport shutil\n\ncase = 'flex_wsp18_val'\n\nclass TestFloatingWindTrubine(unittest.TestCase):\n \"\"\"\n Test and example to run floating wind turbines\n \"\"\"\n def generate_floating_wind_turbine(self, restart=False):\n ######################################################################\n ########################### PARAMETERS #############################\n ######################################################################\n # Case\n route = os.path.dirname(os.path.realpath(__file__)) + '/'\n \n # Geometry discretization\n chord_panels = np.array([16], dtype=int)\n revs_in_wake = 1\n \n # Operation\n rotation_velocity = 12.1*2*np.pi/60\n pitch_deg = 14.6 #degrees\n yaw_deg = 0. #degrees\n \n # Wind\n WSP = 18.\n air_density = 1.225\n gravity_on = True\n grav_value = 9.80665\n \n # Simulation\n dphi = 4.*deg2rad\n revs_to_simulate = 120\n structural_substeps = 0\n \n ######################################################################\n ########################## GENERATE WT #############################\n ######################################################################\n dt = dphi/rotation_velocity\n # time_steps = int(revs_to_simulate*2.*np.pi/dphi)\n if not restart:\n time_steps = 1\n else:\n time_steps = 2\n struct_dt = dt/(structural_substeps + 1)\n \n op_params = {}\n op_params['rotation_velocity'] = rotation_velocity\n op_params['pitch_deg'] = pitch_deg\n op_params['wsp'] = WSP\n op_params['dt'] = dt\n \n geom_params = {}\n geom_params['chord_panels'] = chord_panels\n geom_params['tol_remove_points'] = 1e-8\n geom_params['n_points_camber'] = 100\n geom_params['h5_cross_sec_prop'] = None\n geom_params['m_distribution'] = 'uniform'\n \n options = {}\n options['camber_effect_on_twist'] = False\n options['user_defined_m_distribution_type'] = None\n options['include_polars'] = True\n options['separate_blades'] = True\n options['concentrate_spar'] = True\n options['twist_in_aero'] = False\n \n excel_description = {}\n excel_description['excel_file_name'] = '../../../../docs/source/content/example_notebooks/source/type04_db_nrel5mw_oc3_v06.xlsx'\n excel_description['excel_sheet_parameters'] = 'parameters'\n excel_description['excel_sheet_structural_tower'] = 'structural_tower'\n excel_description['excel_sheet_structural_spar'] = 'structural_spar'\n excel_description['excel_sheet_structural_blade'] = 'structural_blade'\n excel_description['excel_sheet_discretization_blade'] = 'discretization_blade'\n excel_description['excel_sheet_aero_blade'] = 'aero_blade'\n excel_description['excel_sheet_airfoil_info'] = 'airfoil_info'\n excel_description['excel_sheet_airfoil_chord'] = 'airfoil_coord'\n \n spar, LC, MB = template_wt.spar_from_excel_type04(op_params,\n geom_params,\n excel_description,\n options)\n \n tower_top_node = 24\n hub_node = 25\n blade_tip_node = 51\n \n for ilc in range(len(LC)):\n LC[ilc].behaviour = \"hinge_node_FoR_pitch\"\n LC[ilc].rotor_vel = rotation_velocity\n del LC[ilc].rot_vect\n LC[ilc].scalingFactor = 1e6\n LC[ilc].penaltyFactor = 0.\n \n MB[0].FoR_movement = 'free'\n \n ######################################################################\n ###################### DEFINE SIMULATION ###########################\n ######################################################################\n SimInfo = gc.SimulationInformation()\n SimInfo.set_default_values()\n \n if not restart:\n SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\n 'AerogridLoader',\n 'StaticUvlm',\n 'BeamPlot',\n 'AerogridPlot',\n 'DynamicCoupled',\n 'PickleData',]\n \n SimInfo.solvers['SHARPy']['case'] = case\n else:\n SimInfo.solvers['SHARPy']['flow'] = ['DynamicCoupled',\n 'PickleData',]\n \n SimInfo.solvers['SHARPy']['case'] = \"restart_%s\" % case\n \n SimInfo.solvers['SHARPy']['route'] = route\n SimInfo.solvers['SHARPy']['write_log'] = True\n SimInfo.solvers['SHARPy']['write_screen'] = False\n SimInfo.solvers['SHARPy']['log_file'] = (\"log_%s\" % SimInfo.solvers['SHARPy']['case'])\n SimInfo.set_variable_all_dicts('dt', dt)\n SimInfo.set_variable_all_dicts('rho', air_density)\n \n SimInfo.solvers['SteadyVelocityField']['u_inf'] = WSP\n SimInfo.solvers['SteadyVelocityField']['u_inf_direction'] = np.array([0., -np.sin(yaw_deg*deg2rad), np.cos(yaw_deg*deg2rad)])\n \n SimInfo.solvers['BeamLoader']['unsteady'] = 'on'\n \n centre_rot_ini = np.array([87.6, 0., -5.0191])\n rbm_vel_g_ini = np.zeros((6))\n rbm_vel_g_ini[3:6] = np.array([0., 0., rotation_velocity])\n \n quat0 = algebra.euler2quat(np.array([0., -2.28*deg2rad, 0.]))\n for_pos0 = np.array([0., 0., 11.6])\n SimInfo.solvers['BeamLoader']['orientation'] = quat0.copy()\n SimInfo.solvers['BeamLoader']['for_pos'] = for_pos0.copy()\n \n rot_mat0 = algebra.quat2rotation(quat0)\n centre_rot = np.dot(rot_mat0, centre_rot_ini) + for_pos0\n rbm_vel_g = np.zeros((6))\n rbm_vel_g[3:6] = np.dot(rot_mat0, rbm_vel_g_ini[3:6])\n \n MB[0].FoR_position[0:3] = for_pos0.copy()\n MB[0].quat = quat0.copy()\n \n for ibody in range(1, len(MB)):\n MB[ibody].FoR_position[0:3] = centre_rot.copy()\n MB[ibody].FoR_velocity[3:6] = rbm_vel_g[3:6]\n az = (360./3)*(ibody - 1)\n rot_mat_az = algebra.rotation3d_z(az*deg2rad)\n quat = algebra.rotation2quat(np.dot(rot_mat_az, rot_mat0))\n MB[ibody].quat[0:4] = quat.copy()\n \n # Compute mstar\n SimInfo.solvers['AerogridLoader']['wake_shape_generator'] = 'HelicoidalWake'\n SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] = {'u_inf': WSP,\n 'u_inf_direction': SimInfo.solvers['SteadyVelocityField']['u_inf_direction'],\n 'rotation_velocity': rbm_vel_g[3:6],\n 'h_ref': centre_rot[0],\n 'h_corr': 0.,\n 'dt': dt,\n 'dphi1': dphi,\n 'ndphi1': int(10),\n 'r': 1.05,\n 'dphimax': 10*deg2rad}\n \n import sharpy.utils.generator_interface as gi\n gi.dictionary_of_generators(print_info=False)\n hw = gi.dict_of_generators['HelicoidalWake']\n wsg_in = SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] # for simplicity\n angle = 0\n mstar = 0\n while angle < (revs_in_wake*2*np.pi):\n mstar += 1\n angle += hw.get_dphi(mstar, wsg_in['dphi1'],\n wsg_in['ndphi1'],\n wsg_in['r'],\n wsg_in['dphimax'])\n \n SimInfo.solvers['AerogridLoader']['unsteady'] = 'on'\n SimInfo.solvers['AerogridLoader']['mstar'] = mstar\n SimInfo.solvers['AerogridLoader']['freestream_dir'] = np.array([0., 0, 0])\n \n struct_static_solver = 'NonLinearStatic'\n SimInfo.solvers[struct_static_solver]['gravity_on'] = gravity_on\n SimInfo.solvers[struct_static_solver]['gravity'] = grav_value\n SimInfo.solvers[struct_static_solver]['gravity_dir'] = np.array([1., 0., 0.])\n SimInfo.solvers[struct_static_solver]['max_iterations'] = 100\n SimInfo.solvers[struct_static_solver]['num_load_steps'] = 1 \n SimInfo.solvers[struct_static_solver]['min_delta'] = 1e-5\n SimInfo.solvers[struct_static_solver]['newmark_damp'] = 1e-1\n SimInfo.solvers[struct_static_solver]['dt'] = dt\n \n SimInfo.solvers['StaticCoupled']['structural_solver'] = struct_static_solver\n SimInfo.solvers['StaticCoupled']['structural_solver_settings'] = SimInfo.solvers[struct_static_solver]\n SimInfo.solvers['StaticCoupled']['aero_solver'] = 'StaticUvlm'\n SimInfo.solvers['StaticCoupled']['aero_solver_settings'] = SimInfo.solvers['StaticUvlm']\n \n SimInfo.solvers['StaticCoupled']['tolerance'] = 1e-8\n SimInfo.solvers['StaticCoupled']['n_load_steps'] = 0\n SimInfo.solvers['StaticCoupled']['relaxation_factor'] = 0.\n SimInfo.solvers['StaticCoupled']['max_iter'] = 100\n \n SimInfo.solvers['StaticUvlm']['horseshoe'] = False\n SimInfo.solvers['StaticUvlm']['num_cores'] = 8\n SimInfo.solvers['StaticUvlm']['n_rollup'] = 0\n SimInfo.solvers['StaticUvlm']['rollup_dt'] = dt\n SimInfo.solvers['StaticUvlm']['rollup_aic_refresh'] = 1\n SimInfo.solvers['StaticUvlm']['rollup_tolerance'] = 1e-8\n SimInfo.solvers['StaticUvlm']['rbm_vel_g'] = rbm_vel_g \n SimInfo.solvers['StaticUvlm']['centre_rot_g'] = centre_rot\n SimInfo.solvers['StaticUvlm']['cfl1'] = False\n SimInfo.solvers['StaticUvlm']['vortex_radius'] = 1e-6\n SimInfo.solvers['StaticUvlm']['vortex_radius_wake_ind'] = 1e-3\n SimInfo.solvers['StaticUvlm']['velocity_field_generator'] = 'SteadyVelocityField'\n SimInfo.solvers['StaticUvlm']['velocity_field_input'] = SimInfo.solvers['SteadyVelocityField']\n SimInfo.solvers['StaticUvlm']['map_forces_on_struct'] = True\n \n SimInfo.solvers['FloatingForces']['n_time_steps'] = time_steps\n SimInfo.solvers['FloatingForces']['dt'] = dt\n SimInfo.solvers['FloatingForces']['water_density'] = 1025 # kg/m3\n SimInfo.solvers['FloatingForces']['gravity'] = grav_value\n SimInfo.solvers['FloatingForces']['gravity_dir'] = [1., 0., 0.]\n SimInfo.solvers['FloatingForces']['floating_file_name'] = 'oc3_cs_v07.floating.h5'\n SimInfo.solvers['FloatingForces']['concentrate_spar'] = True\n SimInfo.solvers['FloatingForces']['method_matrices_freq'] = 'rational_function'\n SimInfo.solvers['FloatingForces']['matrices_freq'] = 2*np.pi/120.\n SimInfo.solvers['FloatingForces']['steps_constant_matrices'] = 0\n SimInfo.solvers['FloatingForces']['method_wave'] = 'jonswap'\n SimInfo.solvers['FloatingForces']['wave_amplitude'] = 0.\n SimInfo.solvers['FloatingForces']['wave_freq'] = 0.\n SimInfo.solvers['FloatingForces']['wave_Tp'] = 10.\n SimInfo.solvers['FloatingForces']['wave_Hs'] = 6.\n SimInfo.solvers['FloatingForces']['wave_incidence'] = 0.*deg2rad\n SimInfo.solvers['FloatingForces']['added_mass_in_mass_matrix'] = True\n SimInfo.solvers['FloatingForces']['write_output'] = True\n \n SimInfo.solvers['StepUvlm']['convection_scheme'] = 2\n SimInfo.solvers['StepUvlm']['num_cores'] = 8\n SimInfo.solvers['StepUvlm']['velocity_field_generator'] = 'SteadyVelocityField'\n SimInfo.solvers['StepUvlm']['velocity_field_input'] = SimInfo.solvers['SteadyVelocityField']\n SimInfo.solvers['StepUvlm']['cfl1'] = False\n SimInfo.solvers['StepUvlm']['interp_coords'] = 0\n SimInfo.solvers['StepUvlm']['filter_method'] = 0\n SimInfo.solvers['StepUvlm']['interp_method'] = 3\n SimInfo.solvers['StepUvlm']['centre_rot'] = centre_rot \n SimInfo.solvers['StepUvlm']['vortex_radius'] = 1e-6\n SimInfo.solvers['StepUvlm']['vortex_radius_wake_ind'] = 1e-3\n \n struct_dyn_solver = 'NonLinearDynamicMultibody'\n SimInfo.solvers[struct_dyn_solver]['gravity_on'] = gravity_on\n SimInfo.solvers[struct_dyn_solver]['gravity'] = grav_value\n SimInfo.solvers[struct_dyn_solver]['gravity_dir'] = np.array([1., 0., 0.])\n SimInfo.solvers[struct_dyn_solver]['max_iterations'] = 300\n SimInfo.solvers[struct_dyn_solver]['min_delta'] = 1e-6\n SimInfo.solvers[struct_dyn_solver]['newmark_damp'] = 1e-1\n SimInfo.solvers[struct_dyn_solver]['dt'] = struct_dt\n SimInfo.solvers[struct_dyn_solver]['write_lm'] = True\n SimInfo.solvers[struct_dyn_solver]['allow_skip_step'] = False\n SimInfo.solvers[struct_dyn_solver]['relax_factor_lm'] = 0. \n SimInfo.solvers[struct_dyn_solver]['rigid_bodies'] = False\n SimInfo.solvers[struct_dyn_solver]['zero_ini_dot_ddot'] = True\n SimInfo.solvers[struct_dyn_solver]['time_integrator'] = 'NewmarkBeta'\n SimInfo.solvers[struct_dyn_solver]['time_integrator_settings'] = {'newmark_damp': 1e-1,\n 'dt': struct_dt}\n \n SimInfo.solvers['SaveData']['compress_float'] = True\n SimInfo.solvers['SaveData']['save_wake'] = False\n \n SimInfo.solvers['WriteVariablesTime']['FoR_variables'] = ['for_pos', 'for_vel', 'quat']\n SimInfo.solvers['WriteVariablesTime']['structure_variables'] = ['pos']\n SimInfo.solvers['WriteVariablesTime']['structure_nodes'] = [tower_top_node, blade_tip_node]\n \n SimInfo.solvers['PickleData']['stride'] = 180\n SimInfo.solvers['AerogridPlot']['stride'] = 180\n \n SimInfo.solvers['DynamicCoupled']['structural_solver'] = struct_dyn_solver\n SimInfo.solvers['DynamicCoupled']['structural_solver_settings'] = SimInfo.solvers[struct_dyn_solver]\n SimInfo.solvers['DynamicCoupled']['aero_solver'] = 'StepUvlm'\n SimInfo.solvers['DynamicCoupled']['aero_solver_settings'] = SimInfo.solvers['StepUvlm']\n SimInfo.solvers['DynamicCoupled']['postprocessors'] = ['Cleanup', 'BeamPlot', 'AerogridPlot', 'PickleData', 'SaveData', 'WriteVariablesTime']\n SimInfo.solvers['DynamicCoupled']['postprocessors_settings'] = {'Cleanup': SimInfo.solvers['Cleanup'],\n 'BeamPlot': SimInfo.solvers['BeamPlot'],\n 'AerogridPlot': SimInfo.solvers['AerogridPlot'],\n 'PickleData': SimInfo.solvers['PickleData'],\n 'SaveData': SimInfo.solvers['SaveData'],\n 'WriteVariablesTime': SimInfo.solvers['WriteVariablesTime'],}\n \n SimInfo.solvers['DynamicCoupled']['minimum_steps'] = 0\n SimInfo.solvers['DynamicCoupled']['include_unsteady_force_contribution'] = True\n SimInfo.solvers['DynamicCoupled']['relaxation_factor'] = 0.\n SimInfo.solvers['DynamicCoupled']['final_relaxation_factor'] = 0.\n SimInfo.solvers['DynamicCoupled']['dynamic_relaxation'] = False\n SimInfo.solvers['DynamicCoupled']['relaxation_steps'] = 0\n SimInfo.solvers['DynamicCoupled']['fsi_tolerance'] = 1e-6\n SimInfo.solvers['DynamicCoupled']['structural_substeps'] = structural_substeps\n SimInfo.solvers['DynamicCoupled']['runtime_generators'] = {'FloatingForces': SimInfo.solvers['FloatingForces']}\n \n power = 5296609.984\n GBR = 97.\n PID0 = [0.006275604, 0.0008965149, 0.] # Offshore\n \n # Gain scheduler\n pitch_deg_doubled_sens = 6.302336 # deg\n gk = 1./(1 + pitch_deg/pitch_deg_doubled_sens)\n PID = np.zeros((3))\n for i in range(3):\n PID[i] = PID0[i]*gk\n \n SimInfo.solvers['DynamicCoupled']['controller_id']['colective_pitch'] = 'BladePitchPid'\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch'] = dict()\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['P'] = PID[0]\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['I'] = PID[1]\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['D'] = PID[2]\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['sp_type'] = 'gen_vel'\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['sp_source'] = 'const'\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['sp_const'] = rotation_velocity*GBR\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['gen_model_const_var'] = 'torque'\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['gen_model_const_value'] = power/rotation_velocity/GBR\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['GBR'] = GBR\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['inertia_dt'] = 43702538.05\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['dt'] = dt\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['ntime_steps'] = time_steps\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['blade_num_body'] = [1, 2, 3]\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['min_pitch'] = 0.\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['max_pitch'] = 90.*deg2rad\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['initial_pitch'] = pitch_deg*deg2rad\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['pitch_sp'] = pitch_deg*deg2rad\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['initial_rotor_vel'] = rotation_velocity\n SimInfo.solvers['DynamicCoupled']['controller_settings']['colective_pitch']['nocontrol_steps'] = 0\n \n SimInfo.define_num_steps(time_steps)\n \n # Define dynamic simulation\n SimInfo.with_forced_vel = False\n SimInfo.with_dynamic_forces = False\n \n ######################################################################\n ####################### GENERATE FILES #############################\n ######################################################################\n gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n spar.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n SimInfo.generate_solver_file()\n gc.generate_multibody_file(LC, MB,SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n\n return SimInfo.solvers['SHARPy']['case']\n\n def test_floating_wind_turbine(self):\n name = self.generate_floating_wind_turbine(restart=False)\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) + '/' + name + '.sharpy')\n sharpy.sharpy_main.main(['', solver_path])\n \n name_restart = self.generate_floating_wind_turbine(restart=True)\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) + '/' + name_restart + '.sharpy')\n restart_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) + '/output/' + name + '/' + name + '.pkl')\n sharpy.sharpy_main.main(['', '-r' + restart_path , solver_path])\n\n self.clean_files(name)\n \n def clean_files(self, case):\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n solver_path += '/'\n files_to_delete = [case + '.aero.h5',\n case + '.fem.h5',\n case + '.mb.h5',\n case + '.sharpy',\n 'restart_' + case + '.aero.h5',\n 'restart_' + case + '.fem.h5',\n 'restart_' + case + '.mb.h5',\n 'restart_' + case + '.sharpy']\n for f in files_to_delete:\n os.remove(solver_path + f)\n\n shutil.rmtree(solver_path + 'output/')\n" }, { "path": "tests/coupled/prescribed/WindTurbine/__init__.py", "content": "" }, { "path": "tests/coupled/prescribed/WindTurbine/test_rotor.py", "content": "import numpy as np\nimport os\nimport unittest\nimport shutil\nimport glob\n\n\nfolder = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n\n\nclass TestRotor(unittest.TestCase):\n \"\"\"\n NREL 5MW case\n J. Jonkman et al. \"Definition of a 5-MW Reference Wind Turbine for Offshore System Development\", NREL/TP-500-38060, 2009\n In this report, the whole system natural frequencies are provided. This implies that rotor frequencies\n are provided and influenced by nacelle characterisitcs\n \"\"\"\n\n def setUp(self):\n import sharpy.utils.generate_cases as gc\n import sharpy.cases.templates.template_wt as template_wt\n from sharpy.utils.constants import deg2rad\n\n ######################################################################\n ########################### PARAMETERS #############################\n ######################################################################\n # Case\n global case\n route = folder + '/'\n case = 'rotor'\n\n # Geometry discretization\n chord_panels = np.array([8], dtype=int)\n revs_in_wake = 1\n\n # Operation\n rotation_velocity = 1.366190\n pitch_deg = 0. #degrees\n\n # Wind\n WSP = 11.4\n air_density = 1.225\n\n # Simulation\n dphi = 4.*deg2rad\n revs_to_simulate = 5\n\n ######################################################################\n ########################## GENERATE WT #############################\n ######################################################################\n dt = dphi/rotation_velocity\n # time_steps = int(revs_to_simulate*2.*np.pi/dphi)\n time_steps = 2 # For the test cases\n\n mstar = int(revs_in_wake*2.*np.pi/dphi)\n\n op_params = {'rotation_velocity': rotation_velocity,\n 'pitch_deg': pitch_deg,\n 'wsp': WSP,\n 'dt': dt}\n\n geom_params = {'chord_panels':chord_panels,\n 'tol_remove_points': 1e-8,\n 'n_points_camber': 100,\n 'm_distribution': 'uniform'}\n\n excel_description = {'excel_file_name': route + '../../../../docs/source/content/example_notebooks/source/type04_db_nrel5mw_oc3_v06.xlsx',\n 'excel_sheet_parameters': 'parameters',\n 'excel_sheet_structural_blade': 'structural_blade',\n 'excel_sheet_discretization_blade': 'discretization_blade',\n 'excel_sheet_aero_blade': 'aero_blade',\n 'excel_sheet_airfoil_info': 'airfoil_info',\n 'excel_sheet_airfoil_chord': 'airfoil_coord'}\n\n options = {'camber_effect_on_twist': False,\n 'user_defined_m_distribution_type': None,\n 'include_polars': False,\n 'separate_blades': False}\n\n rotor, hub_nodes = template_wt.rotor_from_excel_type03(op_params,\n geom_params,\n excel_description,\n options)\n\n ######################################################################\n ###################### DEFINE SIMULATION ###########################\n ######################################################################\n SimInfo = gc.SimulationInformation()\n SimInfo.set_default_values()\n\n SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\n 'Modal']\n SimInfo.solvers['SHARPy']['case'] = case\n SimInfo.solvers['SHARPy']['route'] = route\n SimInfo.solvers['SHARPy']['write_log'] = True\n SimInfo.solvers['SHARPy']['write_screen'] = 'off'\n SimInfo.solvers['SHARPy']['log_folder'] = os.path.abspath(os.path.dirname(os.path.realpath(__file__))) + '/output/'\n SimInfo.set_variable_all_dicts('dt', dt)\n SimInfo.set_variable_all_dicts('rho', air_density)\n\n SimInfo.solvers['BeamLoader']['unsteady'] = 'on'\n\n SimInfo.solvers['Modal']['write_modes_vtk'] = False\n SimInfo.solvers['Modal']['save_data'] = True\n\n ######################################################################\n ####################### GENERATE FILES #############################\n ######################################################################\n gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n rotor.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n SimInfo.generate_solver_file()\n\n def test_rotor(self):\n import sharpy.sharpy_main\n\n solver_path = folder + '/' + case + '.sharpy'\n sharpy.sharpy_main.main(['', solver_path])\n\n # read output and compare\n output_path = folder + '/output/' + case + '/beam_modal_analysis/'\n freq_data = np.atleast_2d(np.genfromtxt(output_path + \"frequencies.dat\"))\n\n # Data from reference. Several values are provided, the average is used\n flap_1 = np.average([0.6664, 0.6296, 0.6675, 0.6686, 0.6993, 0.7019])*2*np.pi\n edge_1 = np.average([1.0793, 1.0740, 1.0898, 1.0877])*2*np.pi\n flap_2 = np.average([1.9337, 1.6507, 1.9223, 1.8558, 2.0205, 1.9601])*2*np.pi\n\n self.assertAlmostEqual(freq_data[0, 0], flap_1, 0) # 1st flapwise\n self.assertAlmostEqual(freq_data[0, 3], edge_1, 0) # 1st edgewise\n self.assertAlmostEqual(freq_data[0, 6], flap_2, 0) # 2nd flapwise\n\n def tearDown(self):\n files_to_delete = [case + '.aero.h5',\n case + '.fem.h5',\n case + '.sharpy',]\n\n for f in files_to_delete:\n os.remove(folder +'/' + f)\n\n shutil.rmtree(folder + '/output/')\n" }, { "path": "tests/coupled/prescribed/__init__.py", "content": "import tests.coupled.prescribed.WindTurbine\n" }, { "path": "tests/coupled/prescribed/gamma_dot_test/test_gamma_dot.py", "content": "import os\nimport numpy as np\nimport unittest\n\nimport cases.templates.flying_wings as wings\nimport sharpy.sharpy_main\n\n\ndef x_dot(x, dt, integration_order=2):\n x_dot_r = np.zeros(len(x))\n if integration_order == 1:\n x_n = x.copy()[1:]\n x_m1 = x.copy()[:-1]\n x_dot_r[1:] = (x_n - x_m1) / dt\n else:\n x_n = x.copy()[2:]\n x_m1 = x.copy()[1:-1]\n x_m2 = x.copy()[:-2]\n x_dot_r[2:] = (3 * x_n - 4 * x_m1 + x_m2) / 2 / dt\n\n return x_dot_r\n\n\nclass TestGammaDot(unittest.TestCase):\n\n def set_up_test_case(self, aero_type, predictor, sparse, integration_order):\n\n # aero_type = 'lin'\n global case_name\n case_name = 'goland_' + aero_type + '_'+'P%g_S%g_I%g' %(predictor, sparse, integration_order)\n ws = wings.Goland(M=12,\n N=4,\n Mstar_fact=50,\n u_inf=50,\n alpha=1.,\n rho=1.225,\n sweep=0,\n physical_time=0.1,\n n_surfaces=2,\n route='cases',\n case_name=case_name)\n\n # Other test parameters\n ws.gust_intensity = 0.01\n ws.sigma = 1\n ws.dt_factor = 1\n\n ws.clean_test_files()\n ws.update_derived_params()\n ws.update_aero_prop()\n ws.update_fem_prop()\n ws.set_default_config_dict()\n\n ws.generate_aero_file()\n ws.generate_fem_file()\n\n ws.config['SHARPy']['flow'] = ['BeamLoader', 'AerogridLoader',\n 'StaticCoupled',\n 'DynamicCoupled']\n ws.config['SHARPy']['write_screen'] = 'off'\n\n ws.config['AerogridLoader']['wake_shape_generator'] = 'StraightWake'\n ws.config['AerogridLoader']['wake_shape_generator_input'] = {'u_inf': ws.u_inf, \n 'u_inf_direction': np.array([1., 0., 0.]), \n 'dt': ws.dt}\n\n # Remove newmark damping from structural solver settings\n ws.config['DynamicCoupled']['structural_solver_settings']['newmark_damp'] = 0\n\n if aero_type == 'lin':\n ws.config['DynamicCoupled']['aero_solver'] = 'StepLinearUVLM'\n ws.config['DynamicCoupled']['aero_solver_settings'] = {'dt': ws.dt,\n 'remove_predictor': predictor,\n 'use_sparse': sparse,\n 'integr_order': integration_order,\n 'velocity_field_generator': 'GustVelocityField',\n 'velocity_field_input': {'u_inf': ws.u_inf,\n 'u_inf_direction': [1., 0.,\n 0.],\n 'gust_shape': 'continuous_sin',\n 'offset': 2.,\n 'gust_parameters': {'gust_length': 2.,\n 'gust_intensity': ws.gust_intensity\n * ws.u_inf,\n 'span': ws.main_chord * ws.aspect_ratio}}}\n else:\n ws.config['DynamicCoupled']['aero_solver'] = 'StepUvlm'\n ws.config['DynamicCoupled']['aero_solver_settings'] = {\n 'print_info': 'off',\n 'horseshoe': True,\n 'num_cores': 4,\n 'n_rollup': 100,\n 'convection_scheme': 0,\n 'rollup_dt': ws.dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'GustVelocityField',\n 'velocity_field_input': {'u_inf': ws.u_inf,\n 'u_inf_direction': [1., 0, 0],\n 'gust_shape': 'continuous_sin',\n 'gust_length': ws.gust_length,\n 'gust_intensity': ws.gust_intensity * ws.u_inf,\n 'offset': 2.0,\n 'span': ws.main_chord * ws.aspect_ratio},\n 'rho': ws.rho,\n 'n_time_steps': ws.n_tstep,\n 'dt': ws.dt,\n 'gamma_dot_filtering': 0,\n 'track_body': True,\n 'track_body_number': -1}\n ws.config['DynamicCoupled']['include_unsteady_force_contribution'] = 'on'\n # Update settings file\n ws.config.write()\n\n self.case_name = ws.case_name\n self.case_route = ws.route\n self.ws = ws\n self.dt = ws.dt\n\n def run_test(self, aero_type, predictor, sparse, integration_order):\n\n self.set_up_test_case(aero_type, predictor, sparse, integration_order)\n ws = self.ws\n data = sharpy.sharpy_main.main(['', self.case_route + self.case_name + '.sharpy'])\n\n # Obtain gamma\n gamma = np.zeros((ws.n_tstep,))\n gamma_dot = np.zeros((ws.n_tstep))\n\n for N in range(ws.n_tstep):\n gamma[N] = data.aero.timestep_info[N].gamma[0][0, 0]\n gamma_dot[N] = data.aero.timestep_info[N].gamma_dot[0][0, 0]\n\n gamma_dot_fd = x_dot(gamma, self.dt, integration_order)\n\n error_derivative = np.max(np.abs(gamma_dot - gamma_dot_fd))\n gamma_dot_at_max = gamma_dot_fd[np.argmax(np.abs(gamma_dot - gamma_dot_fd))]\n\n # The signal is close to zero\n if np.abs(gamma_dot_at_max) < 0.05:\n passed_test = error_derivative < 0.05\n else:\n passed_test = error_derivative < 1e-2 * np.abs(gamma_dot_at_max)\n\n if not passed_test:\n try:\n import matplotlib.pyplot as plt\n plt.plot(gamma_dot)\n plt.plot(gamma_dot_fd, color='k')\n plt.show()\n\n plt.plot(gamma_dot - gamma_dot_fd)\n plt.show()\n except ModuleNotFoundError:\n import warnings\n warnings.warn('Unable to import matplotlib, skipping plot')\n\n assert passed_test == True, \\\n 'Discrepancy between gamma_dot and that calculated using FD, relative difference is %.2f' % (\n error_derivative / np.abs(gamma_dot_at_max))\n\n def setUp(self):\n pass\n\n def test_gammadot(self):\n\n for aero_type in ['lin', 'nlin']:\n if aero_type == 'lin':\n for predictor in [True, False]:\n for sparse in [True, False]:\n for integration_order in [1, 2]:\n with self.subTest(\n aero_type=aero_type,\n predictor=predictor,\n sparse=sparse,\n integration_order=integration_order):\n self.run_test(aero_type, predictor, sparse, integration_order)\n else:\n with self.subTest(\n aero_type=aero_type,\n predictor=False,\n sparse=False,\n integration_order=2):\n\n self.run_test(aero_type, predictor, sparse, integration_order)\n\n def tearDown(self):\n\n solver_path = os.path.dirname(os.path.realpath(__file__))\n # solver_path += '/'\n # files_to_delete = [case + '.aero.h5',\n # case + '.dyn.h5',\n # case + '.fem.h5',\n # case + '.sharpy']\n # for f in files_to_delete:\n # os.remove(solver_path + f)\n\n shutil.rmtree(solver_path + '/cases/')\n" }, { "path": "tests/coupled/prescribed/rotating_wing/generate_rotating_wing.py", "content": "import h5py as h5\nimport numpy as np\nimport configparser\nimport os\n\nimport sharpy.utils.algebra as algebra\n\ncase_name = 'rotating_wing'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\nm_main = 7\namplitude = 0\nperiod = 3\ndt_factor = 1.\n\n# flight conditions\nu_inf = 5\nrho = 1.225\nalpha = 0\nbeta = 0\nc_ref = 1\nb_ref = 16\nsweep = 0*np.pi/180.\naspect_ratio = 32 # = total wing span (chord = 1)\n\nalpha_rad = alpha*np.pi/180\n\n# dt = 1.0/m_main/u_inf*dt_factor\ndt = 0.01\nnum_steps = int(1./dt)\nnum_steps = 20\n\n# main geometry data\nmain_span = aspect_ratio/2./np.cos(sweep)\nmain_chord = 1.0\nmain_chord_tip = 0.5\nmain_ea = 0.5\nmain_sigma = 1\nmain_airfoil_P = 0\nmain_airfoil_M = 0\n\nn_surfaces = 2\n\n# discretisation data\nnum_elem_main = 10\n\nnum_node_elem = 3\nnum_elem = num_elem_main + num_elem_main\nnum_node_main = num_elem_main*(num_node_elem - 1) + 1\nnum_node = num_node_main + (num_node_main - 1)\n\n\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n dyn_file_name = route + '/' + case_name + '.dyn.h5'\n if os.path.isfile(dyn_file_name):\n os.remove(dyn_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n\ndef generate_dyn_file():\n global dt\n global num_steps\n global route\n global case_name\n global num_elem\n global num_node_elem\n global num_node\n global amplitude\n global period\n\n dynamic_forces_time = None\n with_dynamic_forces = False\n with_forced_vel = True\n if with_dynamic_forces:\n angle = np.arctan(8.0/6.0)\n m1 = 80\n f1 = 8\n dynamic_forces = np.zeros((num_node, 6))\n app_node = int(0)\n dynamic_forces[app_node, 0] = -f1*np.cos(angle)\n dynamic_forces[app_node, 1] = -f1*np.sin(angle)\n dynamic_forces[app_node, 5] = m1\n force_time = np.zeros((num_steps, ))\n limit = round(2.5/dt)\n force_time[:limit] = 1\n\n dynamic_forces_time = np.zeros((num_steps, num_node, 6))\n for it in range(num_steps):\n dynamic_forces_time[it, :, :] = force_time[it]*dynamic_forces\n\n forced_for_vel = None\n if with_forced_vel:\n forced_for_vel = np.zeros((num_steps, 6))\n forced_for_acc = np.zeros((num_steps, 6))\n forced_for_vel[:, 3] = period/(2.0*np.pi)\n try:\n forced_for_vel[0:int(0.5/dt), 3] = np.linspace(0, period/(2*np.pi), int(0.5/dt))\n except ValueError:\n pass\n # forced_for_acc[it, 2] = (2*np.pi/period)**2*amplitude*np.cos(2*np.pi*dt*it/period)\n # forced_for_vel[it, 2] = 2*np.pi/period*np.pi/180*amplitude*np.cos(2*np.pi*dt*it/period)\n\n with h5.File(route + '/' + case_name + '.dyn.h5', 'a') as h5file:\n if with_dynamic_forces:\n h5file.create_dataset(\n 'dynamic_forces', data=dynamic_forces_time)\n if with_forced_vel:\n h5file.create_dataset(\n 'for_vel', data=forced_for_vel)\n h5file.create_dataset(\n 'for_acc', data=forced_for_acc)\n h5file.create_dataset(\n 'num_steps', data=num_steps)\n\n\ndef generate_fem_file():\n # placeholders\n # coordinates\n global x, y, z\n x = np.zeros((num_node, ))\n y = np.zeros((num_node, ))\n z = np.zeros((num_node, ))\n # struct twist\n structural_twist = np.zeros_like(x)\n # beam number\n beam_number = np.zeros((num_elem, ), dtype=int)\n # frame of reference delta\n frame_of_reference_delta = np.zeros((num_elem, num_node_elem, 3))\n # connectivities\n conn = np.zeros((num_elem, num_node_elem), dtype=int)\n # stiffness\n num_stiffness = 1\n ea = 1e5\n ga = 1e5\n gj = 1e4*10\n eiy = 2e4\n eiz = 2e4\n sigma = 1000\n base_stiffness = sigma*np.diag([ea, ga, ga, gj, eiy, eiz])\n stiffness = np.zeros((num_stiffness, 6, 6))\n stiffness[0, :, :] = main_sigma*base_stiffness\n elem_stiffness = np.zeros((num_elem,), dtype=int)\n # mass\n num_mass = 1\n m_base = 0.75\n j_base = 0.1\n base_mass = np.diag([m_base, m_base, m_base, j_base, j_base, j_base])\n mass = np.zeros((num_mass, 6, 6))\n mass[0, :, :] = base_mass\n elem_mass = np.zeros((num_elem,), dtype=int)\n # boundary conditions\n boundary_conditions = np.zeros((num_node, ), dtype=int)\n boundary_conditions[0] = 1\n # applied forces\n # n_app_forces = 2\n # node_app_forces = np.zeros((n_app_forces,), dtype=int)\n app_forces = np.zeros((num_node, 6))\n\n spacing_param = 3\n\n # right wing (beam 0) --------------------------------------------------------------\n working_elem = 0\n working_node = 0\n beam_number[working_elem:working_elem + num_elem_main] = 0\n domain = np.linspace(0, 1.0, num_node_main)\n # 16 - (np.geomspace(20, 4, 10) - 4)\n # x[working_node:working_node + num_node_main] = np.sin(sweep)*(main_span - (np.geomspace(main_span + spacing_param,\n # 0 + spacing_param,\n # num_node_main)\n # - spacing_param))\n z[working_node:working_node + num_node_main] = np.abs((main_span - (np.geomspace(main_span + spacing_param,\n 0 + spacing_param,\n num_node_main)\n - spacing_param)))\n # y[0] = 0\n # y[working_node:working_node + num_node_main] = np.cos(sweep)*np.linspace(0.0, main_span, num_node_main)\n # x[working_node:working_node + num_node_main] = np.sin(sweep)*np.linspace(0.0, main_span, num_node_main)\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1])\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[0] = 1\n boundary_conditions[working_node + num_node_main - 1] = -1\n working_elem += num_elem_main\n working_node += num_node_main\n\n # left wing (beam 1) --------------------------------------------------------------\n beam_number[working_elem:working_elem + num_elem_main] = 1\n domain = np.linspace(-1.0, 0.0, num_node_main)\n tempy = np.linspace(-main_span, 0.0, num_node_main)\n # x[working_node:working_node + num_node_main - 1] = -np.sin(sweep)*tempy[0:-1]\n # y[working_node:working_node + num_node_main - 1] = np.cos(sweep)*tempy[0:-1]\n z[working_node:working_node + num_node_main - 1] = -(main_span - (np.geomspace(0 + spacing_param,\n main_span + spacing_param,\n num_node_main)[:-1]\n - spacing_param))\n # y[working_node:working_node + num_node_main - 1] = -np.abs(np.cos(sweep)*(main_span - (np.geomspace(0 + spacing_param,\n # main_span + spacing_param,\n # num_node_main)[:-1]\n # - spacing_param)))\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1]) + 1\n conn[working_elem + num_elem_main - 1, 1] = 0\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[working_node] = -1\n working_elem += num_elem_main\n working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=num_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=num_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=num_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n # node_app_forces_handle = h5file.create_dataset(\n # 'node_app_forces', data=node_app_forces)\n\n\ndef generate_aero_file():\n global x, y, z\n airfoil_distribution = np.zeros((num_elem, num_node_elem), dtype=int)\n surface_distribution = np.zeros((num_elem,), dtype=int) - 1\n surface_m = np.zeros((n_surfaces, ), dtype=int)\n m_distribution = 'uniform'\n aero_node = np.zeros((num_node,), dtype=bool)\n twist = np.zeros((num_elem, num_node_elem))\n chord = np.zeros((num_elem, num_node_elem))\n elastic_axis = np.zeros((num_elem, num_node_elem,))\n\n working_elem = 0\n working_node = 0\n # right wing (surface 0, beam 0)\n i_surf = 0\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main] = True\n\n # chord[working_node:working_node + num_node_main] = np.linspace(main_chord, main_chord_tip, num_node_main)\n # twist[working_node:working_node + num_node_main] = np.linspace(0, 70*np.pi/180., num_node_main)\n temp_chord = np.linspace(main_chord, main_chord_tip, num_node_main)\n temp_twist = np.linspace(0, 70*np.pi/180., num_node_main)\n node_counter = 0\n for i_elem in range(working_elem, working_elem + num_elem_main):\n for i_local_node in range(num_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = temp_chord[node_counter]\n elastic_axis[i_elem, i_local_node] = main_ea\n twist[i_elem, i_local_node] = temp_twist[node_counter]\n\n working_elem += num_elem_main\n working_node += num_node_main\n\n # # left wing (surface 1, beam 1)\n i_surf = 1\n airfoil_distribution[working_node:working_node + num_node_main - 1] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main - 1] = True\n # chord[working_node:working_node + num_node_main - 1] = np.linspace(main_chord_tip, main_chord, num_node_main)[:-1]\n # chord[working_node:working_node + num_node_main - 1] = main_chord\n # elastic_axis[working_node:working_node + num_node_main - 1] = main_ea\n # twist[working_node:working_node + num_node_main - 1] = np.linspace(-70*np.pi/180., 0.0, num_node_main)[:-1]\n\n temp_chord = np.linspace(main_chord, main_chord_tip, num_node_main)\n temp_twist = np.linspace(0, -70*np.pi/180., num_node_main)\n node_counter = 0\n for i_elem in range(working_elem, working_elem + num_elem_main):\n for i_local_node in range(num_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = temp_chord[node_counter]\n elastic_axis[i_elem, i_local_node] = main_ea\n twist[i_elem, i_local_node] = temp_twist[node_counter]\n working_elem += num_elem_main\n working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n generate_naca_camber(P=main_airfoil_P, M=main_airfoil_M)))\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input .attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n\ndef generate_naca_camber(M=0, P=0):\n m = M*1e-2\n p = P*1e-1\n\n def naca(x, m, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return m/(p*p)*(2*p*x - x*x)\n elif x > p and x < 1+1e-6:\n return m/((1-p)*(1-p))*(1 - 2*p + 2*p*x - x*x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, m, p) for x in x_vec])\n return x_vec, y_vec\n\n\ndef generate_solver_file(horseshoe=False):\n file_name = route + '/' + case_name + '.sharpy'\n # config = configparser.ConfigParser()\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n config['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'DynamicPrescribedCoupled',\n # 'PrescribedUvlm',\n 'AerogridPlot',\n # 'NonLinearDynamic',\n 'BeamPlot',]\n # 'AeroForcesCalculator',],\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n config['BeamLoader'] = {'unsteady': 'on',\n 'orientation': algebra.euler2quat(np.array([0.0,\n alpha_rad,\n beta*np.pi/180]))}\n\n config['StaticCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 10,\n 'delta_curved': 1e-5,\n 'min_delta': 1e-5,\n 'gravity_on': 'off',\n 'gravity': 9.754,\n 'orientation': algebra.euler2quat(np.array([0.0,\n alpha_rad,\n beta*np.pi/180]))},\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': main_chord/m_main/u_inf,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho,\n 'alpha': alpha_rad,\n 'beta': beta},\n 'max_iter': 80,\n 'n_load_steps': 3,\n 'tolerance': 1e-4,\n 'relaxation_factor': 0.0}\n config['NonLinearDynamic'] = {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 4,\n 'delta_curved': 1e-5,\n 'min_delta': 1e-5,\n 'newmark_damp': 5e-4,\n 'gravity_on': 'on',\n 'gravity': 9.754,\n 'num_steps': num_steps,\n 'dt': dt,\n 'prescribed_motion': 'on'}\n config['PrescribedUvlm'] = {'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 100,\n 'convection_scheme': 3,\n 'rollup_dt': main_chord/m_main/u_inf,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho,\n 'alpha': alpha_rad,\n 'beta': beta,\n 'n_time_steps': num_steps,\n 'dt': dt}\n config['DynamicPrescribedCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearDynamicPrescribedStep',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 10,\n 'delta_curved': 1e-5,\n 'min_delta': 1e-5,\n 'newmark_damp': 1e-3,\n 'gravity_on': 'off',\n 'gravity': 9.754,\n 'num_steps': num_steps,\n 'dt': dt},\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': {'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 100,\n 'convection_scheme': 3,\n 'rollup_dt': main_chord/m_main/u_inf,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho,\n 'alpha': alpha_rad,\n 'beta': beta,\n 'n_time_steps': num_steps,\n 'dt': dt},\n 'max_iter': 100,\n 'tolerance': 1e-6,\n 'relaxation_factor': 0.,\n 'n_time_steps': num_steps,\n 'dt': dt,\n 'structural_substeps': 10}\n\n if horseshoe is True:\n config['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n 'mstar': 1,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': np.array([1., 0., 0.]),\n 'dt': dt}}\n else:\n config['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n 'mstar': 150,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake'\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': np.array([1., 0., 0.]),\n 'dt': dt}}\n config['AerogridPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0\n }\n config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n 'unsteady': 'off'\n }\n config['BeamPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on'}\n config.write()\n\n\nclean_test_files()\ngenerate_fem_file()\ngenerate_dyn_file()\ngenerate_solver_file(horseshoe=False)\ngenerate_aero_file()\n" }, { "path": "tests/coupled/prescribed/test_prescribed.py", "content": "# import sharpy.utils.settings as settings\n# import sharpy.utils.exceptions as exceptions\n# import sharpy.utils.cout_utils as cout\nimport numpy as np\nimport importlib\nimport unittest\nimport os\nimport sharpy.utils.cout_utils as cout\n\n\n@unittest.skip('Placeholder - No test yet to run')\nclass TestCoupledPrescribed(unittest.TestCase):\n \"\"\"\n \"\"\"\n\n @classmethod\n def setUpClass(cls):\n # run all the cases generators\n # case = 'smith_2deg_prescribed'\n # mod = importlib.import_module('tests.coupled.prescribed.' + case + '.generate_' + case)\n # case = 'rotating_wing'\n # mod1 = importlib.import_module('tests.coupled.prescribed.' + case + '.generate_' + case)\n pass\n\n @classmethod\n def tearDownClass(cls):\n pass\n\n # def test_smith2deg_prescribed(self):\n # import sharpy.sharpy_main\n # solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) +\n # '/smith_2deg_prescribed/smith_2deg_prescribed.sharpy')\n # sharpy.sharpy_main.main(['', solver_path])\n #\n # # read output and compare\n # output_path = os.path.dirname(solver_path) + 'output/aero/'\n # forces_data = np.genfromtxt(output_path + 'smith_2deg_prescribed_aeroforces.csv')\n # self.assertAlmostEqual(forces_data[-1, 3], -3.728e1, 1)\n\n def test_rotating_wing(self):\n # import sharpy.sharpy_main\n # solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) +\n # '/rotating_wing/rotating_wing.sharpy')\n # sharpy.sharpy_main.main(['', solver_path])\n print('No tests for prescribed dynamic configurations (yet)!', 1)\n pass\n" }, { "path": "tests/coupled/static/__init__.py", "content": "" }, { "path": "tests/coupled/static/pazy/generate_pazy.py", "content": "import sharpy.cases.templates.flying_wings as wings\nimport sharpy.sharpy_main\n\n\ndef generate_pazy(u_inf, case_name, output_folder='/output/', cases_folder='', **kwargs):\n # u_inf = 60\n alpha_deg = kwargs.get('alpha', 0.)\n rho = 1.225\n num_modes = 16\n gravity_on = kwargs.get('gravity_on', True)\n\n # Lattice Discretisation\n M = kwargs.get('M', 4)\n N = kwargs.get('N', 32)\n M_star_fact = kwargs.get('Ms', 10)\n flag_multiple_mstar_input = kwargs.get('test_multiple_inputs', False)\n\n # SHARPy nonlinear reference solution\n ws = wings.PazyControlSurface(M=M,\n N=N,\n Mstar_fact=M_star_fact,\n u_inf=u_inf,\n alpha=alpha_deg,\n cs_deflection=[0, 0],\n rho=rho,\n sweep=0,\n physical_time=2,\n n_surfaces=2,\n route=cases_folder + '/' + case_name,\n case_name=case_name)\n\n ws.gust_intensity = 0.01\n ws.sigma = 1\n\n ws.clean_test_files()\n ws.update_derived_params()\n ws.set_default_config_dict()\n\n ws.generate_aero_file()\n ws.generate_fem_file()\n\n ws.config['SHARPy'] = {\n 'flow':\n ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'AerogridPlot',\n 'BeamPlot',\n 'WriteVariablesTime',\n ],\n 'case': ws.case_name, 'route': ws.route,\n 'write_screen': 'off', 'write_log': 'on',\n 'save_settings': 'on',\n 'log_folder': output_folder,\n 'log_file': ws.case_name + '.log'}\n\n ws.config['BeamLoader'] = {\n 'unsteady': 'off',\n 'orientation': ws.quat}\n\n ws.config['AerogridLoader'] = {\n 'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': ws.Mstar_fact * ws.M,\n 'freestream_dir': ws.u_inf_direction,\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction,\n 'dt': ws.dt}}\n if flag_multiple_mstar_input:\n ws.config['AerogridLoader']['mstar'] = [ws.config['AerogridLoader']['mstar'], ws.config['AerogridLoader']['mstar']]\n ws.config['SHARPy']['flow'] = ['BeamLoader','AerogridLoader']\n else:\n ws.config['StaticUvlm'] = {\n 'rho': ws.rho,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction},\n 'rollup_dt': ws.dt,\n 'print_info': 'on',\n 'horseshoe': 'on',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_aic_refresh': 0,\n 'rollup_tolerance': 1e-4}\n\n settings = dict()\n settings['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 200,\n 'num_load_steps': 5,\n 'delta_curved': 1e-6,\n 'min_delta': 1e-8,\n 'gravity_on': gravity_on,\n 'gravity': 9.81}\n\n ws.config['StaticCoupled'] = {\n 'print_info': 'on',\n 'max_iter': 200,\n 'n_load_steps': 4,\n 'tolerance': 1e-5,\n 'relaxation_factor': 0.1,\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {\n 'rho': ws.rho,\n 'print_info': 'off',\n 'horseshoe': 'on',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': ws.dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction},\n 'vortex_radius': 1e-9},\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': settings['NonLinearStatic']}\n\n ws.config['AerogridPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}\n\n ws.config['BeamPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on'}\n\n ws.config['WriteVariablesTime'] = {'structure_variables': ['pos'],\n 'structure_nodes': list(range(0, ws.num_node_surf)),\n 'cleanup_old_solution': 'on'}\n\n ws.config.write()\n\n sharpy.sharpy_main.main(['', ws.route + ws.case_name + '.sharpy'])\n" }, { "path": "tests/coupled/static/smith_g_2deg/__init__.py", "content": "" }, { "path": "tests/coupled/static/smith_g_2deg/generate_smith_g_2deg.py", "content": "import h5py as h5\nimport numpy as np\nimport configparser\nimport os\nnp.set_printoptions(precision=16)\n\nimport sharpy.utils.algebra as algebra\n\ncase_name = 'smith_g_2deg'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n# flight conditions\nu_inf = 25\nrho = 0.08891\nalpha = 2\nbeta = 0\nc_ref = 1\nb_ref = 16\nsweep = 0*np.pi/180.\naspect_ratio = 32 # = total wing span (chord = 1)\n\nalpha_rad = alpha*np.pi/180\n\n# main geometry data\nmain_span = aspect_ratio/2./np.cos(sweep)\nmain_chord = 1.0\nmain_ea = 0.5\nmain_sigma = 1\nmain_airfoil_P = 0\nmain_airfoil_M = 0\n\nn_surfaces = 2\n\n# discretisation data\nnum_elem_main = 10\n\nnum_node_elem = 3\nnum_elem = num_elem_main + num_elem_main\nnum_node_main = num_elem_main*(num_node_elem - 1) + 1\nnum_node = num_node_main + (num_node_main - 1)\n\nm_main = 10\n\n\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n\ndef generate_fem_file():\n # placeholders\n # coordinates\n global x, y, z\n x = np.zeros((num_node, ))\n y = np.zeros((num_node, ))\n z = np.zeros((num_node, ))\n\n # struct twist\n structural_twist = np.zeros((num_elem, num_node_elem))\n\n # beam number\n beam_number = np.zeros((num_elem, ), dtype=int)\n\n # frame of reference delta\n frame_of_reference_delta = np.zeros((num_elem, num_node_elem, 3))\n\n # connectivities\n conn = np.zeros((num_elem, num_node_elem), dtype=int)\n\n # stiffness\n num_stiffness = 1\n ea = 1e5\n ga = 1e5\n gj = 1e4\n eiy = 2e4\n eiz = 5e6\n sigma = 1\n base_stiffness = sigma*np.diag([ea, ga, ga, gj, eiy, eiz])\n stiffness = np.zeros((num_stiffness, 6, 6))\n stiffness[0, :, :] = main_sigma*base_stiffness\n elem_stiffness = np.zeros((num_elem,), dtype=int)\n\n # mass\n num_mass = 1\n m_base = 0.75\n j_base = 0.1\n base_mass = np.diag([m_base, m_base, m_base, j_base, 0.5*j_base, 0.5*j_base])\n mass = np.zeros((num_mass, 6, 6))\n mass[0, :, :] = base_mass\n elem_mass = np.zeros((num_elem,), dtype=int)\n\n # boundary conditions\n boundary_conditions = np.zeros((num_node, ), dtype=int)\n boundary_conditions[0] = 1\n\n # applied forces\n app_forces = np.zeros((num_node, 6))\n\n # right wing (beam 0) --------------------------------------------------------------\n working_elem = 0\n working_node = 0\n beam_number[working_elem:working_elem + num_elem_main] = 0\n\n y[0] = 0\n y[working_node:working_node + num_node_main] = np.cos(sweep)*np.linspace(0.0, main_span, num_node_main)\n x[working_node:working_node + num_node_main] = np.sin(sweep)*np.linspace(0.0, main_span, num_node_main)\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1])\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[0] = 1\n boundary_conditions[working_node + num_node_main - 1] = -1\n working_elem += num_elem_main\n working_node += num_node_main\n\n # left wing (beam 1) --------------------------------------------------------------\n beam_number[working_elem:working_elem + num_elem_main] = 1\n domain = np.linspace(-1.0, 0.0, num_node_main)\n tempy = np.linspace(-main_span, 0.0, num_node_main)\n x[working_node:working_node + num_node_main - 1] = -np.sin(sweep)*tempy[0:-1]\n y[working_node:working_node + num_node_main - 1] = np.cos(sweep)*tempy[0:-1]\n\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1]) + 1\n conn[working_elem + num_elem_main - 1, 1] = 0\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[working_node] = -1\n working_elem += num_elem_main\n working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=num_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=num_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=num_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n # node_app_forces_handle = h5file.create_dataset(\n # 'node_app_forces', data=node_app_forces)\n\n\ndef generate_aero_file():\n global x, y, z\n airfoil_distribution = np.zeros((num_elem, num_node_elem), dtype=int)\n surface_distribution = np.zeros((num_elem,), dtype=int) - 1\n surface_m = np.zeros((n_surfaces, ), dtype=int)\n m_distribution = 'uniform'\n aero_node = np.zeros((num_node,), dtype=bool)\n twist = np.zeros((num_elem, 3))\n chord = np.zeros((num_elem, 3))\n elastic_axis = np.zeros((num_elem, 3,))\n\n working_elem = 0\n working_node = 0\n\n # right wing (surface 0, beam 0)\n i_surf = 0\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main] = True\n chord[:] = main_chord\n elastic_axis[:] = main_ea\n working_elem += num_elem_main\n working_node += num_node_main\n\n # right wing (surface 1, beam 1)\n i_surf = 1\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main - 1] = True\n\n working_elem += num_elem_main\n working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n generate_naca_camber(P=main_airfoil_P, M=main_airfoil_M)))\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input .attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n\ndef generate_naca_camber(M=0, P=0):\n m = M*1e-2\n p = P*1e-1\n\n def naca(x, m, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return m/(p*p)*(2*p*x - x*x)\n elif x > p and x < 1+1e-6:\n return m/((1-p)*(1-p))*(1 - 2*p + 2*p*x - x*x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, m, p) for x in x_vec])\n return x_vec, y_vec\n\n\ndef generate_solver_file(horseshoe=False):\n file_name = route + '/' + case_name + '.sharpy'\n\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n config['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': ['BeamLoader', 'AerogridLoader', 'StaticCoupled',\n 'AeroForcesCalculator', 'WriteVariablesTime'],\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n config['BeamLoader'] = {'unsteady': 'off',\n 'orientation': algebra.euler2quat(np.array([0.0,\n alpha_rad,\n beta*np.pi/180]))}\n config['StaticCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-1,\n 'min_delta': 1e-6,\n 'gravity_on': 'on',\n 'gravity': 9.754},\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {'print_info': 'off',\n 'horseshoe': 'on',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': main_chord/m_main/u_inf,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho},\n 'max_iter': 50,\n 'tolerance': 1e-9,\n 'relaxation_factor': 0.0}\n config['WriteVariablesTime'] = {'cleanup_old_solution': 'on',\n 'structure_variables': ['pos'],\n 'structure_nodes': [num_node_main - 1]}\n\n if horseshoe is True:\n config['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 1,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': np.array([1., 0., 0.]),\n 'dt': main_chord/m_main/u_inf}}\n else:\n config['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 20,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': np.array([1., 0., 0.]),\n 'dt': main_chord/m_main/u_inf}}\n config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n }\n config.write()\n\n\nclean_test_files()\ngenerate_fem_file()\ngenerate_solver_file(horseshoe=True)\ngenerate_aero_file()\n" }, { "path": "tests/coupled/static/smith_g_4deg/__init__.py", "content": "" }, { "path": "tests/coupled/static/smith_g_4deg/generate_smith_g_4deg.py", "content": "import h5py as h5\nimport numpy as np\nimport configparser\nimport os\n\nimport sharpy.utils.algebra as algebra\n\ncase_name = 'smith_g_4deg'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n# flight conditions\nu_inf = 25\nrho = 0.08891\nalpha = 4\nbeta = 0\nc_ref = 1\nb_ref = 16\nsweep = 0*np.pi/180.\naspect_ratio = 32 # = total wing span (chord = 1)\n\nalpha_rad = alpha*np.pi/180\n\n# main geometry data\nmain_span = aspect_ratio/2./np.cos(sweep)\nmain_chord = 1.0\nmain_ea = 0.5\nmain_sigma = 1\nmain_airfoil_P = 0\nmain_airfoil_M = 0\n\nn_surfaces = 2\n\n# discretisation data\nnum_elem_main = 10\n\nnum_node_elem = 3\nnum_elem = num_elem_main + num_elem_main\nnum_node_main = num_elem_main*(num_node_elem - 1) + 1\nnum_node = num_node_main + (num_node_main - 1)\n\nm_main = 10\n\n\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n\ndef generate_fem_file():\n # placeholders\n # coordinates\n global x, y, z\n x = np.zeros((num_node, ))\n y = np.zeros((num_node, ))\n z = np.zeros((num_node, ))\n\n # struct twist\n structural_twist = np.zeros((num_elem, num_node_elem))\n\n # beam number\n beam_number = np.zeros((num_elem, ), dtype=int)\n\n # frame of reference delta\n frame_of_reference_delta = np.zeros((num_elem, num_node_elem, 3))\n\n # connectivities\n conn = np.zeros((num_elem, num_node_elem), dtype=int)\n\n # stiffness\n num_stiffness = 1\n ea = 1e5\n ga = 1e5\n gj = 1e4\n eiy = 2e4\n eiz = 5e6\n sigma = 1.\n base_stiffness = sigma*np.diag([ea, ga, ga, gj, eiy, eiz])\n stiffness = np.zeros((num_stiffness, 6, 6))\n stiffness[0, :, :] = main_sigma*base_stiffness\n elem_stiffness = np.zeros((num_elem,), dtype=int)\n\n # mass\n num_mass = 1\n m_base = 0.75\n j_base = 0.1\n base_mass = np.diag([m_base, m_base, m_base, j_base, j_base, j_base])\n mass = np.zeros((num_mass, 6, 6))\n mass[0, :, :] = base_mass\n elem_mass = np.zeros((num_elem,), dtype=int)\n\n # boundary conditions\n boundary_conditions = np.zeros((num_node, ), dtype=int)\n boundary_conditions[0] = 1\n\n app_forces = np.zeros((num_node, 6))\n\n spacing_param = 4\n\n # right wing (beam 0) --------------------------------------------------------------\n working_elem = 0\n working_node = 0\n beam_number[working_elem:working_elem + num_elem_main] = 0\n\n y[0] = 0\n y[working_node:working_node + num_node_main] = np.cos(sweep)*np.linspace(0.0, main_span, num_node_main)\n x[working_node:working_node + num_node_main] = np.sin(sweep)*np.linspace(0.0, main_span, num_node_main)\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1])\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[0] = 1\n boundary_conditions[working_node + num_node_main - 1] = -1\n working_elem += num_elem_main\n working_node += num_node_main\n\n # left wing (beam 1) --------------------------------------------------------------\n beam_number[working_elem:working_elem + num_elem_main] = 1\n tempy = np.linspace(-main_span, 0.0, num_node_main)\n x[working_node:working_node + num_node_main - 1] = -np.sin(sweep)*tempy[0:-1]\n y[working_node:working_node + num_node_main - 1] = np.cos(sweep)*tempy[0:-1]\n\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1]) + 1\n conn[working_elem + num_elem_main - 1, 1] = 0\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[working_node] = -1\n working_elem += num_elem_main\n working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=num_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=num_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=num_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n\n\ndef generate_aero_file():\n global x, y, z\n airfoil_distribution = np.zeros((num_elem, num_node_elem), dtype=int)\n surface_distribution = np.zeros((num_elem,), dtype=int) - 1\n surface_m = np.zeros((n_surfaces, ), dtype=int)\n m_distribution = 'uniform'\n aero_node = np.zeros((num_node,), dtype=bool)\n twist = np.zeros((num_elem, 3))\n chord = np.zeros((num_elem, 3))\n elastic_axis = np.zeros((num_elem, 3,))\n\n working_elem = 0\n working_node = 0\n\n # right wing (surface 0, beam 0)\n i_surf = 0\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main] = True\n chord[:] = main_chord\n elastic_axis[:] = main_ea\n working_elem += num_elem_main\n working_node += num_node_main\n\n # left wing (surface 1, beam 1)\n i_surf = 1\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main - 1] = True\n\n working_elem += num_elem_main\n working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n generate_naca_camber(P=main_airfoil_P, M=main_airfoil_M)))\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input .attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n\ndef generate_naca_camber(M=0, P=0):\n m = M*1e-2\n p = P*1e-1\n\n def naca(x, m, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return m/(p*p)*(2*p*x - x*x)\n elif x > p and x < 1+1e-6:\n return m/((1-p)*(1-p))*(1 - 2*p + 2*p*x - x*x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, m, p) for x in x_vec])\n return x_vec, y_vec\n\n\ndef generate_solver_file(horseshoe=False):\n file_name = route + '/' + case_name + '.sharpy'\n\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n config['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': ['BeamLoader', 'AerogridLoader', 'StaticCoupled',\n 'AeroForcesCalculator', 'WriteVariablesTime'],\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n config['BeamLoader'] = {'unsteady': 'off',\n 'orientation': algebra.euler2quat(np.array([0.0,\n alpha_rad,\n beta*np.pi/180]))}\n config['StaticCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-5,\n 'min_delta': 1e-8,\n 'gravity_on': 'on',\n 'gravity': 9.754},\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {'print_info': 'off',\n 'horseshoe': 'on',\n 'num_cores': 4,\n 'n_rollup': 100,\n 'rollup_dt': main_chord/m_main/u_inf,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho},\n 'max_iter': 100,\n 'n_load_steps': 5,\n 'tolerance': 1e-5,\n 'relaxation_factor': 0.}\n config['WriteVariablesTime'] = {'cleanup_old_solution': 'on',\n 'structure_variables': ['pos'],\n 'structure_nodes': [num_node_main - 1]}\n\n if horseshoe is True:\n config['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 1,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': np.array([1., 0., 0.]),\n 'dt': main_chord/m_main/u_inf}}\n else:\n config['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 80,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': np.array([1., 0., 0.]),\n 'dt': main_chord/m_main/u_inf}}\n\n config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n }\n\n config.write()\n\n\nclean_test_files()\ngenerate_fem_file()\ngenerate_solver_file(horseshoe=True)\ngenerate_aero_file()\n" }, { "path": "tests/coupled/static/smith_nog_2deg/__init__.py", "content": "" }, { "path": "tests/coupled/static/smith_nog_2deg/generate_smith_nog_2deg.py", "content": "import h5py as h5\nimport numpy as np\nimport configparser\nimport os\n\nimport sharpy.utils.algebra as algebra\n\ncase_name = 'smith_nog_2deg'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n# flight conditions\nu_inf = 25\nrho = 0.08891\nalpha = 2\nbeta = 0\nc_ref = 1\nb_ref = 16\nsweep = 0*np.pi/180.\naspect_ratio = 32 # = total wing span (chord = 1)\n\nalpha_rad = alpha*np.pi/180\n\n# main geometry data\nmain_span = aspect_ratio/2./np.cos(sweep)\nmain_chord = 1.0\nmain_ea = 0.5\nmain_sigma = 1\nmain_airfoil_P = 0\nmain_airfoil_M = 0\n\nn_surfaces = 2\n\n# discretisation data\nnum_elem_main = 10\n\nnum_node_elem = 3\nnum_elem = num_elem_main + num_elem_main\nnum_node_main = num_elem_main*(num_node_elem - 1) + 1\nnum_node = num_node_main + (num_node_main - 1)\n\nm_main = 10\n\n\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n\ndef generate_fem_file():\n # placeholders\n # coordinates\n global x, y, z\n x = np.zeros((num_node, ))\n y = np.zeros((num_node, ))\n z = np.zeros((num_node, ))\n\n # struct twist\n structural_twist = np.zeros((num_elem, num_node_elem))\n\n # beam number\n beam_number = np.zeros((num_elem, ), dtype=int)\n\n # frame of reference delta\n frame_of_reference_delta = np.zeros((num_elem, num_node_elem, 3))\n\n # connectivities\n conn = np.zeros((num_elem, num_node_elem), dtype=int)\n\n # stiffness\n num_stiffness = 1\n ea = 1e5\n ga = 1e5\n gj = 1e4\n eiy = 2e4\n eiz = 5e6\n sigma = 1\n base_stiffness = sigma*np.diag([ea, ga, ga, gj, eiy, eiz])\n stiffness = np.zeros((num_stiffness, 6, 6))\n stiffness[0, :, :] = main_sigma*base_stiffness\n elem_stiffness = np.zeros((num_elem,), dtype=int)\n\n # mass\n num_mass = 1\n m_base = 0.75\n j_base = 0.1\n base_mass = np.diag([m_base, m_base, m_base, j_base, 0.5*j_base, 0.5*j_base])\n mass = np.zeros((num_mass, 6, 6))\n mass[0, :, :] = base_mass\n elem_mass = np.zeros((num_elem,), dtype=int)\n\n # boundary conditions\n boundary_conditions = np.zeros((num_node, ), dtype=int)\n boundary_conditions[0] = 1\n\n # applied forces\n app_forces = np.zeros((num_node, 6))\n\n # right wing (beam 0) --------------------------------------------------------------\n working_elem = 0\n working_node = 0\n beam_number[working_elem:working_elem + num_elem_main] = 0\n\n y[0] = 0\n y[working_node:working_node + num_node_main] = np.cos(sweep)*np.linspace(0.0, main_span, num_node_main)\n x[working_node:working_node + num_node_main] = np.sin(sweep)*np.linspace(0.0, main_span, num_node_main)\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1])\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[0] = 1\n boundary_conditions[working_node + num_node_main - 1] = -1\n working_elem += num_elem_main\n working_node += num_node_main\n\n # left wing (beam 1) --------------------------------------------------------------\n beam_number[working_elem:working_elem + num_elem_main] = 1\n tempy = np.linspace(-main_span, 0.0, num_node_main)\n x[working_node:working_node + num_node_main - 1] = -np.sin(sweep)*tempy[0:-1]\n y[working_node:working_node + num_node_main - 1] = np.cos(sweep)*tempy[0:-1]\n\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1]) + 1\n conn[working_elem + num_elem_main - 1, 1] = 0\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[working_node] = -1\n working_elem += num_elem_main\n working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=num_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=num_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=num_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n\n\ndef generate_aero_file():\n global x, y, z\n airfoil_distribution = np.zeros((num_elem, num_node_elem), dtype=int)\n surface_distribution = np.zeros((num_elem,), dtype=int) - 1\n surface_m = np.zeros((n_surfaces, ), dtype=int)\n m_distribution = 'uniform'\n aero_node = np.zeros((num_node,), dtype=bool)\n twist = np.zeros((num_elem, 3))\n chord = np.zeros((num_elem, 3))\n elastic_axis = np.zeros((num_elem, 3,))\n\n working_elem = 0\n working_node = 0\n # right wing (surface 0, beam 0)\n i_surf = 0\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main] = True\n chord[:] = main_chord\n elastic_axis[:] = main_ea\n working_elem += num_elem_main\n working_node += num_node_main\n\n # left wing (surface 1, beam 1)\n i_surf = 1\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main - 1] = True\n working_elem += num_elem_main\n working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n generate_naca_camber(P=main_airfoil_P, M=main_airfoil_M)))\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input .attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n\ndef generate_naca_camber(M=0, P=0):\n m = M*1e-2\n p = P*1e-1\n\n def naca(x, m, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return m/(p*p)*(2*p*x - x*x)\n elif x > p and x < 1+1e-6:\n return m/((1-p)*(1-p))*(1 - 2*p + 2*p*x - x*x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, m, p) for x in x_vec])\n return x_vec, y_vec\n\n\ndef generate_solver_file(horseshoe=False):\n import configobj\n file_name = route + '/' + case_name + '.sharpy'\n config = configobj.ConfigObj()\n np.set_printoptions(precision=16)\n config.filename = file_name\n config['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': ['BeamLoader', 'AerogridLoader', 'StaticCoupled',\n 'AeroForcesCalculator', 'WriteVariablesTime'],\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n config['BeamLoader'] = {'unsteady': 'off',\n 'orientation': algebra.euler2quat(np.array([0.0,\n alpha_rad,\n beta*np.pi/180]))}\n config['StaticCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-1,\n 'min_delta': 1e-6,\n 'gravity_on': 'off',\n 'gravity': 9.754},\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {'print_info': 'off',\n 'horseshoe': 'on',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': main_chord/m_main/u_inf,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho},\n 'max_iter': 50,\n 'tolerance': 1e-9,\n 'relaxation_factor': 0.0}\n config['WriteVariablesTime'] = {'cleanup_old_solution': 'on',\n 'structure_variables': ['pos'],\n 'structure_nodes': [num_node_main - 1]}\n\n if horseshoe is True:\n config['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 1,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': np.array([1., 0., 0.]),\n 'dt': main_chord/m_main/u_inf}}\n else:\n config['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 20,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': np.array([1., 0., 0.]),\n 'dt': main_chord/m_main/u_inf}}\n\n config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n }\n config.write()\n\n\nclean_test_files()\ngenerate_fem_file()\ngenerate_solver_file(horseshoe=True)\ngenerate_aero_file()\n" }, { "path": "tests/coupled/static/smith_nog_4deg/__init__.py", "content": "" }, { "path": "tests/coupled/static/smith_nog_4deg/generate_smith_nog_4deg.py", "content": "import h5py as h5\nimport numpy as np\nimport configparser\nimport os\n\nimport sharpy.utils.algebra as algebra\n\ncase_name = 'smith_nog_4deg'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n# flight conditions\nu_inf = 25\nrho = 0.08891\nalpha = 4\nbeta = 0\nc_ref = 1\nb_ref = 16\nsweep = 0*np.pi/180.\naspect_ratio = 32 # = total wing span (chord = 1)\n\nalpha_rad = alpha*np.pi/180\n\n# main geometry data\nmain_span = aspect_ratio/2./np.cos(sweep)\nmain_chord = 1.0\nmain_ea = 0.5\nmain_sigma = 1\nmain_airfoil_P = 0\nmain_airfoil_M = 0\n\nn_surfaces = 2\n\n# discretisation data\nnum_elem_main = 10\n\nnum_node_elem = 3\nnum_elem = num_elem_main + num_elem_main\nnum_node_main = num_elem_main*(num_node_elem - 1) + 1\nnum_node = num_node_main + (num_node_main - 1)\n\nm_main = 10\n\n\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n\ndef generate_fem_file():\n # placeholders\n # coordinates\n global x, y, z\n x = np.zeros((num_node, ))\n y = np.zeros((num_node, ))\n z = np.zeros((num_node, ))\n\n # struct twist\n structural_twist = np.zeros((num_elem, num_node_elem))\n\n # beam number\n beam_number = np.zeros((num_elem, ), dtype=int)\n\n # frame of reference delta\n frame_of_reference_delta = np.zeros((num_elem, num_node_elem, 3))\n\n # connectivities\n conn = np.zeros((num_elem, num_node_elem), dtype=int)\n\n # stiffness\n num_stiffness = 1\n ea = 1e5\n ga = 1e5\n gj = 1e4\n eiy = 2e4\n eiz = 5e6\n sigma = 1.\n base_stiffness = sigma*np.diag([ea, ga, ga, gj, eiy, eiz])\n stiffness = np.zeros((num_stiffness, 6, 6))\n stiffness[0, :, :] = main_sigma*base_stiffness\n elem_stiffness = np.zeros((num_elem,), dtype=int)\n\n # mass\n num_mass = 1\n m_base = 0.75\n j_base = 0.1\n base_mass = np.diag([m_base, m_base, m_base, j_base, j_base, j_base])\n mass = np.zeros((num_mass, 6, 6))\n mass[0, :, :] = base_mass\n elem_mass = np.zeros((num_elem,), dtype=int)\n\n # boundary conditions\n boundary_conditions = np.zeros((num_node, ), dtype=int)\n boundary_conditions[0] = 1\n\n # applied forces\n app_forces = np.zeros((num_node, 6))\n\n # right wing (beam 0) --------------------------------------------------------------\n working_elem = 0\n working_node = 0\n beam_number[working_elem:working_elem + num_elem_main] = 0\n y[0] = 0\n y[working_node:working_node + num_node_main] = np.cos(sweep)*np.linspace(0.0, main_span, num_node_main)\n x[working_node:working_node + num_node_main] = np.sin(sweep)*np.linspace(0.0, main_span, num_node_main)\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1])\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[0] = 1\n boundary_conditions[working_node + num_node_main - 1] = -1\n working_elem += num_elem_main\n working_node += num_node_main\n\n # left wing (beam 1) --------------------------------------------------------------\n beam_number[working_elem:working_elem + num_elem_main] = 1\n tempy = np.linspace(-main_span, 0.0, num_node_main)\n x[working_node:working_node + num_node_main - 1] = -np.sin(sweep)*tempy[0:-1]\n y[working_node:working_node + num_node_main - 1] = np.cos(sweep)*tempy[0:-1]\n\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1]) + 1\n conn[working_elem + num_elem_main - 1, 1] = 0\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[working_node] = -1\n working_elem += num_elem_main\n working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=num_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=num_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=num_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n\n\ndef generate_aero_file():\n global x, y, z\n airfoil_distribution = np.zeros((num_elem, num_node_elem), dtype=int)\n surface_distribution = np.zeros((num_elem,), dtype=int) - 1\n surface_m = np.zeros((n_surfaces, ), dtype=int)\n m_distribution = 'uniform'\n aero_node = np.zeros((num_node,), dtype=bool)\n twist = np.zeros((num_elem, 3))\n chord = np.zeros((num_elem, 3))\n elastic_axis = np.zeros((num_elem, 3,))\n\n working_elem = 0\n working_node = 0\n # right wing (surface 0, beam 0)\n i_surf = 0\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main] = True\n chord[:] = main_chord\n elastic_axis[:] = main_ea\n working_elem += num_elem_main\n working_node += num_node_main\n\n # left wing (surface 1, beam 1)\n i_surf = 1\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main - 1] = True\n working_elem += num_elem_main\n working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n generate_naca_camber(P=main_airfoil_P, M=main_airfoil_M)))\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input .attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n\ndef generate_naca_camber(M=0, P=0):\n m = M*1e-2\n p = P*1e-1\n\n def naca(x, m, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return m/(p*p)*(2*p*x - x*x)\n elif x > p and x < 1+1e-6:\n return m/((1-p)*(1-p))*(1 - 2*p + 2*p*x - x*x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, m, p) for x in x_vec])\n return x_vec, y_vec\n\n\ndef generate_solver_file(horseshoe=False):\n file_name = route + '/' + case_name + '.sharpy'\n\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n config['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': ['BeamLoader', 'AerogridLoader', 'StaticCoupled',\n 'AeroForcesCalculator', 'WriteVariablesTime'],\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n config['BeamLoader'] = {'unsteady': 'off',\n 'orientation': algebra.euler2quat(np.array([0.0,\n alpha_rad,\n beta*np.pi/180]))}\n config['StaticCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-5,\n 'min_delta': 1e-8,\n 'gravity_on': 'off',\n 'gravity': 9.754},\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {'print_info': 'off',\n 'horseshoe': 'on',\n 'num_cores': 4,\n 'n_rollup': 100,\n 'rollup_dt': main_chord/m_main/u_inf,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho,\n },\n 'max_iter': 100,\n 'n_load_steps': 5,\n 'tolerance': 1e-5,\n 'relaxation_factor': 0.}\n config['WriteVariablesTime'] = {'cleanup_old_solution': 'on',\n 'structure_variables': ['pos'],\n 'structure_nodes': [num_node_main - 1]}\n\n if horseshoe is True:\n config['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 1,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': np.array([1., 0., 0.]),\n 'dt': main_chord/m_main/u_inf}}\n else:\n config['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 80,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': np.array([1., 0., 0.]),\n 'dt': main_chord/m_main/u_inf}}\n\n config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n }\n config.write()\n\n\nclean_test_files()\ngenerate_fem_file()\ngenerate_solver_file(horseshoe=True)\ngenerate_aero_file()\n" }, { "path": "tests/coupled/static/test_pazy_static.py", "content": "import unittest\nimport numpy as np\nimport tests.coupled.static.pazy.generate_pazy as gp\nimport os\nimport shutil\n\nclass TestPazyCoupledStatic(unittest.TestCase):\n \"\"\"\n Test Pazy wing static coupled case and compare against a benchmark result.\n\n As of the time of writing, benchmark result has not been verified but it\n serves as a backward compatibility check for code improvements.\n \"\"\"\n\n route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n\n def test_static_aoa(self):\n u_inf = 50\n alpha = 7\n case_name = 'pazy_uinf{:04g}_alpha{:04g}'.format(u_inf * 10, alpha * 10)\n\n M = 16\n N = 64\n Msf = 1\n\n cases_folder = self.route_test_dir + '/pazy/cases/'\n output_folder = self.route_test_dir + '/pazy/cases/'\n # run case\n gp.generate_pazy(u_inf, case_name, output_folder, cases_folder,\n alpha=alpha,\n M=M,\n N=N,\n Msf=Msf)\n\n node_number = N / 2 # wing tip node\n\n # Get results in A frame\n tip_displacement = np.loadtxt(output_folder + '/' + case_name + '/WriteVariablesTime/struct_pos_node{:g}.dat'.format(node_number))\n\n # current reference from Technion abstract\n ref_displacement = 2.033291e-1 # m\n np.testing.assert_almost_equal(tip_displacement[-1], ref_displacement,\n decimal=3,\n err_msg='Wing tip displacement not within 3 decimal points of reference.',\n verbose=True)\n\n def tearDown(self):\n cases_folder = self.route_test_dir + '/pazy/cases/'\n\n if os.path.isdir(cases_folder):\n import shutil\n shutil.rmtree(cases_folder)\n\n\nif __name__ == '__main__':\n unittest.main()\n" }, { "path": "tests/coupled/static/test_static.py", "content": "import numpy as np\nimport importlib\nimport unittest\nimport os\n\n\nclass TestCoupledStatic(unittest.TestCase):\n \"\"\"\n \"\"\"\n\n @classmethod\n def setUpClass(cls):\n # run all the cases generators\n case = 'smith_nog_2deg'\n mod = importlib.import_module('tests.coupled.static.' + case + '.generate_' + case)\n case = 'smith_g_2deg'\n mod2 = importlib.import_module('tests.coupled.static.' + case + '.generate_' + case)\n case = 'smith_g_4deg'\n mod3 = importlib.import_module('tests.coupled.static.' + case + '.generate_' + case)\n case = 'smith_nog_4deg'\n mod4 = importlib.import_module('tests.coupled.static.' + case + '.generate_' + case)\n\n @classmethod\n def tearDownClass(cls):\n pass\n\n def test_smith2deg_nog(self):\n \"\"\"\n Case and results from:\n Smith, M.J., Patil, M.J. and Hodges, D.H.,\n 2001.\n CFD-based analysis of nonlinear aeroelastic behavior of high-aspect\n ratio wings.\n AIAA Paper, 1582, p.2001.\n :return:\n \"\"\"\n import sharpy.sharpy_main\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) +\n '/smith_nog_2deg/smith_nog_2deg.sharpy')\n sharpy.sharpy_main.main(['', solver_path])\n\n # read output and compare\n output_path = os.path.dirname(solver_path) + '/output/smith_nog_2deg/WriteVariablesTime/'\n pos_data = np.genfromtxt(output_path + 'struct_pos_node20.dat')\n self.assertAlmostEqual((pos_data[2] - 15.599)/15.599, 0.00, 2)\n self.assertAlmostEqual((pos_data[3] - 3.32600)/3.32600, 0.00, 2)\n\n # results:\n # N = 10 elements\n # M = 15 elements\n # full wake:\n # Nrollup = 100\n # Mstar = 80\n # pos last beam of the wing [ 0.02515625 15.62906166 3.20177985]\n # total forces:\n # tstep | fx_st | fy_st | fz_st\n # 0 | 1.464e+00 | -4.480e-03 | 2.389e+02\n # 521 seconds\n\n\n def test_smith2deg_g(self):\n import sharpy.sharpy_main\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) +\n '/smith_g_2deg/smith_g_2deg.sharpy')\n sharpy.sharpy_main.main(['', solver_path])\n\n # read output and compare\n output_path = os.path.dirname(solver_path) + '/output/smith_g_2deg/WriteVariablesTime/'\n pos_data = np.genfromtxt(output_path + 'struct_pos_node20.dat')\n\n self.assertAlmostEqual((pos_data[2] - 15.98295)/15.98295, 0.00, 2)\n self.assertAlmostEqual((pos_data[3] - 0.682268)/0.682268, 0.00, 2)\n\n def test_smith4deg_g(self):\n \"\"\"\n Case from R. Simpson's PhD thesis.\n His wing tip displacements: 15.627927627927626, 3.3021978021978025\n I always get higher deflection when using my gravity implementation\n instead of his. His results with gravity are not validated.***\n :return:\n \"\"\"\n import sharpy.sharpy_main\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) +\n '/smith_g_4deg/smith_g_4deg.sharpy')\n sharpy.sharpy_main.main(['', solver_path])\n\n # read output and compare\n output_path = os.path.dirname(solver_path) + '/output/smith_g_4deg/WriteVariablesTime/'\n pos_data = np.genfromtxt(output_path + 'struct_pos_node20.dat')\n self.assertAlmostEqual((pos_data[2] - 15.55)/15.55, 0.00, 2)\n self.assertAlmostEqual((pos_data[3] - 3.671)/3.671, 0.00, 2)\n\n # results:\n # N = 10 elements\n # M = 15 elements\n # full wake:\n # Nrollup = 100\n # Mstar = 80\n # pos last node of the wing\n # 0.05668 15.5422 3.53971\n # total forces:\n # tstep | fx_st | fy_st | fz_st\n # 0 | 3.229 | -1.059e-3| 3.766e2\n # 7500 seconds\n\n def test_smith4deg_nog(self):\n \"\"\"\n Hodges result for Euler+Nonlinear is\n 14.668547249647393, 5.451612903225806\n :return:\n \"\"\"\n import sharpy.sharpy_main\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) +\n '/smith_nog_4deg/smith_nog_4deg.sharpy')\n sharpy.sharpy_main.main(['', solver_path])\n\n # read output and compare\n output_path = os.path.dirname(solver_path) + '/output/smith_nog_4deg/WriteVariablesTime/'\n pos_data = np.genfromtxt(output_path + 'struct_pos_node20.dat')\n self.assertAlmostEqual((pos_data[2] - 14.87)/14.87, 0.00, 2)\n self.assertAlmostEqual((pos_data[3] - 5.5078)/5.5078, 0.00, 2)\n\n # results:\n # N = 10 elements\n # M = 15 elements\n # full wake:\n # Nrollup = 100\n # Mstar = 80\n # pos last beam of the wing\n # 5.59418e-2 1.49094e1 5.41518\n # total forces:\n # tstep | fx_st | fy_st | fz_st\n # 0 | 3.045 | -1.089e-4 | 3.678e2\n # 7380 seconds\n\n # will use this one for validation.\n # same discretisation, with horseshoe:\n # [ 0.05849521 14.80636555 5.65457501]\n # forces:\n # tstep | fx_st | fy_st | fz_st\n # 0 | 1.996e+00 | -2.116e-06 | 3.888e+02\n # 142 seconds\n" }, { "path": "tests/docs/__init__.py", "content": "" }, { "path": "tests/docs/test_docs.py", "content": "import unittest\nimport os\n\n# Skipped to avoid dependency of minimal environment with sphinx\n# we agreed that it is best to have the core of SHARPy only in the tests\n# ADC 14 Nov 2019\n@unittest.skip\nclass DocTest(unittest.TestCase):\n \"\"\"\n\n \"\"\"\n route = os.path.abspath(os.path.dirname(os.path.realpath(__file__))) + '/'\n source_dir = route + u'../../docs/source'\n config_dir = route + u'../../docs/source'\n output_dir = route + u'../../docs/build'\n doctree_dir = route + u'../../docs/build/doctrees'\n all_files = 1\n\n def test_html_documentation(self):\n from sphinx.application import Sphinx\n app = Sphinx(self.source_dir,\n self.config_dir,\n self.output_dir,\n self.doctree_dir,\n buildername='html',\n warningiserror=False,\n )\n app.build(force_all=self.all_files)\n # TODO: additional checks here if needed\n\n def test_text_documentation(self):\n from sphinx.application import Sphinx\n # The same, but with different buildername\n app = Sphinx(self.source_dir,\n self.config_dir,\n self.output_dir,\n self.doctree_dir,\n buildername='text',\n warningiserror=False,\n )\n app.build(force_all=self.all_files)\n # TODO: additional checks if needed\n\n def tearDown(self):\n # TODO: clean up the output directory\n pass\n\n\n" }, { "path": "tests/io/Example_simple_hale/Client_HALE.py", "content": "import socket\nimport select\nimport time\nimport logging\nimport struct\nimport sharpy.io.message_interface as message_interface\nimport numpy as np\n\"\"\"\nThis is not a test but is to be used as client when testing the development of the input\noutput capabilities of sharpy. It will just give back the initial control surface deflection.\n\nRun this script as client.\n\nRun ``python generate_hale_io.py`` as server from the folder tests/io/Example_simple_hale\n\"\"\"\n\n# sel = selectors.DefaultSelector()\n\nlogging.basicConfig(format='%(asctime)s - %(name)s - %(levelname)s - %(message)s',\n level=20)\nlogger = logging.getLogger(__name__)\n\nsharpy_incoming = ('127.0.0.1', 64011) # control side socket\nsharpy_outgoing = ('127.0.0.1', 64010) # output side socket\n\nown_control = ('127.0.0.1', 64000)\nown_receive = ('127.0.0.1', 64001)\n\nin_sock = socket.socket(socket.AF_INET, socket.SOCK_DGRAM)\nin_sock.bind(own_control)\n\nout_sock = socket.socket(socket.AF_INET, socket.SOCK_DGRAM)\nout_sock.bind(own_receive)\n\n# from https://stackoverflow.com/questions/2719017/how-to-set-timeout-on-pythons-socket-recv-method\n# ready_to_read = select.select([out_sock], [], [], 2)\nout_sock.settimeout(300)\n\n#initial values\ncs_deflection = [-2.08 * np.pi / 180, 0]\nthrust = 6.16\ndt = 0.025\nn_tstep = 0 #Counter for time\n\nx_pos = []\ny_pos = []\nz_pos = []\n\nx_vel = []\ny_vel = []\nz_vel = []\np = []\nq = []\nr = []\n\nroot_OOP_moment = []\nroot_OOP_strain = []\n\ntime_vec = []\n\nwhile True:\n if n_tstep > 401:\n break\n\n # send control input to sharpy\n ctrl_value = struct.pack('<5sif', b'RREF0', 0, cs_deflection[0])\n ctrl_value += struct.pack('if', 1, cs_deflection[1])\n ctrl_value += struct.pack('if', 2, thrust)\n logger.info('Sending control input of size {} bytes'.format(len(ctrl_value)))\n in_sock.sendto(ctrl_value, sharpy_incoming)\n logger.info('Sent control input to {}'.format(sharpy_incoming))\n\n # time.sleep(2)\n # input('Continue loop')\n\n # receive output data. set msg_len to whatever length SHARPy is sending\n msg_len = 93\n try:\n msg, conn = out_sock.recvfrom(msg_len)\n except socket.timeout:\n logger.info('Socket time out')\n break\n logger.info('Received {} data from {}'.format(msg, conn))\n logger.info('Received data is {} bytes long'.format(len(msg)))\n # else:\n # break\n # decoding\n values = message_interface.decoder(msg)\n\n # Add the received values to the variables\n x_pos.append(-values[0][1])\n y_pos.append(values[1][1])\n z_pos.append(values[2][1])\n\n x_vel.append(-values[3][1])\n y_vel.append(values[4][1])\n z_vel.append(values[5][1])\n p.append(values[6][1] * 180 / np.pi)\n q.append(values[7][1] * 180 / np.pi)\n r.append(values[8][1] * 180 / np.pi)\n\n root_OOP_moment.append(values[9][1])\n root_OOP_strain.append(values[10][1])\n\n time_vec.append(dt * n_tstep)\n\n n_tstep += 1\n\n##\n\nout_sock.close()\nin_sock.close()\nlogger.info('Closed input and output sockets')" }, { "path": "tests/io/Example_simple_hale/__init__.py", "content": "" }, { "path": "tests/io/Example_simple_hale/generate_hale_io.py", "content": "#! /usr/bin/env python3\nimport h5py as h5\nimport numpy as np\nimport os\nimport sharpy.utils.algebra as algebra\nimport sharpy.sharpy_main\n\ncase_name = 'simple_HALE'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n# EXECUTION\nflow = ['BeamLoader',\n 'AerogridLoader',\n # 'NonLinearStatic',\n # 'StaticUvlm',\n 'StaticTrim',\n # 'StaticCoupled',\n 'BeamLoads',\n 'AerogridPlot',\n 'BeamPlot',\n 'DynamicCoupled',\n 'SaveData'\n # 'Modal',\n # 'LinearAssember',\n # 'AsymptoticStability',\n ]\n\n# if free_flight is False, the motion of the centre of the wing is prescribed.\nfree_flight = True\nif not free_flight:\n case_name += '_prescribed'\n amplitude = 0 * np.pi / 180\n period = 3\n case_name += '_amp_' + str(amplitude).replace('.', '') + '_period_' + str(period)\n\n# FLIGHT CONDITIONS\n# the simulation is set such that the aircraft flies at a u_inf velocity while\n# the air is calm.\nu_inf = 10\nrho = 1.225\n\n# trim sigma = 1.5\nalpha = 4.31 * np.pi / 180\nbeta = 0\nroll = 0\ngravity = 'on'\ncs_deflection = -2.08 * np.pi / 180\nrudder_static_deflection = 0.0\nrudder_step = 0.0 * np.pi / 180\nthrust = 6.16\nsigma = 1.5\nlambda_dihedral = 20 * np.pi / 180\n\n# gust settings\ngust_intensity = 0.20\ngust_length = 1 * u_inf\ngust_offset = 0.5 * u_inf\n\n# numerics\nn_step = 5\nstructural_relaxation_factor = 0.6\nrelaxation_factor = 0.35\ntolerance = 1e-6\nfsi_tolerance = 1e-4\n\nnum_cores = 2\n\n# MODEL GEOMETRY\n# beam\nspan_main = 16.0\nlambda_main = 0.25\nea_main = 0.3\n\nea = 1e7\nga = 1e5\ngj = 1e4\neiy = 2e4\neiz = 4e6\nm_bar_main = 0.75\nj_bar_main = 0.075\n\nlength_fuselage = 10\noffset_fuselage = 0\nsigma_fuselage = 10\nm_bar_fuselage = 0.2\nj_bar_fuselage = 0.08\n\nspan_tail = 2.5\nea_tail = 0.5\nfin_height = 2.5\nea_fin = 0.5\nsigma_tail = 100\nm_bar_tail = 0.3\nj_bar_tail = 0.08\n\n# lumped masses\nn_lumped_mass = 1\nlumped_mass_nodes = np.zeros((n_lumped_mass,), dtype=int)\nlumped_mass = np.zeros((n_lumped_mass,))\nlumped_mass[0] = 50\nlumped_mass_inertia = np.zeros((n_lumped_mass, 3, 3))\nlumped_mass_position = np.zeros((n_lumped_mass, 3))\n\n# aero\nchord_main = 1.0\nchord_tail = 0.5\nchord_fin = 0.5\n\n# DISCRETISATION\n# spatial discretisation\n# chordiwse panels\nm = 4\n# spanwise elements\nn_elem_multiplier = 2\nn_elem_main = int(4 * n_elem_multiplier)\nn_elem_tail = int(2 * n_elem_multiplier)\nn_elem_fin = int(2 * n_elem_multiplier)\nn_elem_fuselage = int(2 * n_elem_multiplier)\nn_surfaces = 5\n\n# temporal discretisation\nphysical_time = 5\ntstep_factor = 1.\ndt = 1.0 / m / u_inf * tstep_factor\nn_tstep = round(physical_time / dt)\n\n# END OF INPUT-----------------------------------------------------------------\n\n# beam processing\nn_node_elem = 3\nspan_main1 = (1.0 - lambda_main) * span_main\nspan_main2 = lambda_main * span_main\n\nn_elem_main1 = round(n_elem_main * (1 - lambda_main))\nn_elem_main2 = n_elem_main - n_elem_main1\n\n# total number of elements\nn_elem = 0\nn_elem += n_elem_main1 + n_elem_main1\nn_elem += n_elem_main2 + n_elem_main2\nn_elem += n_elem_fuselage\nn_elem += n_elem_fin\nn_elem += n_elem_tail + n_elem_tail\n\n# number of nodes per part\nn_node_main1 = n_elem_main1 * (n_node_elem - 1) + 1\nn_node_main2 = n_elem_main2 * (n_node_elem - 1) + 1\nn_node_main = n_node_main1 + n_node_main2 - 1\nn_node_fuselage = n_elem_fuselage * (n_node_elem - 1) + 1\nn_node_fin = n_elem_fin * (n_node_elem - 1) + 1\nn_node_tail = n_elem_tail * (n_node_elem - 1) + 1\n\n# total number of nodes\nn_node = 0\nn_node += n_node_main1 + n_node_main1 - 1\nn_node += n_node_main2 - 1 + n_node_main2 - 1\nn_node += n_node_fuselage - 1\nn_node += n_node_fin - 1\nn_node += n_node_tail - 1\nn_node += n_node_tail - 1\n\n# stiffness and mass matrices\nn_stiffness = 3\nbase_stiffness_main = sigma * np.diag([ea, ga, ga, gj, eiy, eiz])\nbase_stiffness_fuselage = base_stiffness_main.copy() * sigma_fuselage\nbase_stiffness_fuselage[4, 4] = base_stiffness_fuselage[5, 5]\nbase_stiffness_tail = base_stiffness_main.copy() * sigma_tail\nbase_stiffness_tail[4, 4] = base_stiffness_tail[5, 5]\n\nn_mass = 3\nbase_mass_main = np.diag([m_bar_main, m_bar_main, m_bar_main, j_bar_main, 0.5 * j_bar_main, 0.5 * j_bar_main])\nbase_mass_fuselage = np.diag([m_bar_fuselage,\n m_bar_fuselage,\n m_bar_fuselage,\n j_bar_fuselage,\n j_bar_fuselage * 0.5,\n j_bar_fuselage * 0.5])\nbase_mass_tail = np.diag([m_bar_tail,\n m_bar_tail,\n m_bar_tail,\n j_bar_tail,\n j_bar_tail * 0.5,\n j_bar_tail * 0.5])\n\n# PLACEHOLDERS\n# beam\nx = np.zeros((n_node,))\ny = np.zeros((n_node,))\nz = np.zeros((n_node,))\nbeam_number = np.zeros((n_elem,), dtype=int)\nframe_of_reference_delta = np.zeros((n_elem, n_node_elem, 3))\nstructural_twist = np.zeros((n_elem, 3))\nconn = np.zeros((n_elem, n_node_elem), dtype=int)\nstiffness = np.zeros((n_stiffness, 6, 6))\nelem_stiffness = np.zeros((n_elem,), dtype=int)\nmass = np.zeros((n_mass, 6, 6))\nelem_mass = np.zeros((n_elem,), dtype=int)\nboundary_conditions = np.zeros((n_node,), dtype=int)\napp_forces = np.zeros((n_node, 6))\n\n# aero\nairfoil_distribution = np.zeros((n_elem, n_node_elem), dtype=int)\nsurface_distribution = np.zeros((n_elem,), dtype=int) - 1\nsurface_m = np.zeros((n_surfaces,), dtype=int)\nm_distribution = 'uniform'\naero_node = np.zeros((n_node,), dtype=bool)\ntwist = np.zeros((n_elem, n_node_elem))\nsweep = np.zeros((n_elem, n_node_elem))\nchord = np.zeros((n_elem, n_node_elem,))\nelastic_axis = np.zeros((n_elem, n_node_elem,))\n\n\n# FUNCTIONS-------------------------------------------------------------\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n dyn_file_name = route + '/' + case_name + '.dyn.h5'\n if os.path.isfile(dyn_file_name):\n os.remove(dyn_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n\ndef generate_dyn_file():\n global dt\n global n_tstep\n global route\n global case_name\n global num_elem\n global num_node_elem\n global num_node\n global amplitude\n global period\n global free_flight\n\n dynamic_forces_time = None\n with_dynamic_forces = False\n with_forced_vel = False\n if not free_flight:\n with_forced_vel = True\n\n if with_dynamic_forces:\n f1 = 100\n dynamic_forces = np.zeros((num_node, 6))\n app_node = [int(num_node_main - 1), int(num_node_main)]\n dynamic_forces[app_node, 2] = f1\n force_time = np.zeros((n_tstep,))\n limit = round(0.05 / dt)\n force_time[50:61] = 1\n\n dynamic_forces_time = np.zeros((n_tstep, num_node, 6))\n for it in range(n_tstep):\n dynamic_forces_time[it, :, :] = force_time[it] * dynamic_forces\n\n forced_for_vel = None\n if with_forced_vel:\n forced_for_vel = np.zeros((n_tstep, 6))\n forced_for_acc = np.zeros((n_tstep, 6))\n for it in range(n_tstep):\n # if dt*it < period:\n # forced_for_vel[it, 2] = 2*np.pi/period*amplitude*np.sin(2*np.pi*dt*it/period)\n # forced_for_acc[it, 2] = (2*np.pi/period)**2*amplitude*np.cos(2*np.pi*dt*it/period)\n\n forced_for_vel[it, 3] = 2 * np.pi / period * amplitude * np.sin(2 * np.pi * dt * it / period)\n forced_for_acc[it, 3] = (2 * np.pi / period) ** 2 * amplitude * np.cos(2 * np.pi * dt * it / period)\n\n if with_dynamic_forces or with_forced_vel:\n with h5.File(route + '/' + case_name + '.dyn.h5', 'a') as h5file:\n if with_dynamic_forces:\n h5file.create_dataset(\n 'dynamic_forces', data=dynamic_forces_time)\n if with_forced_vel:\n h5file.create_dataset(\n 'for_vel', data=forced_for_vel)\n h5file.create_dataset(\n 'for_acc', data=forced_for_acc)\n h5file.create_dataset(\n 'num_steps', data=n_tstep)\n\n\ndef generate_fem():\n stiffness[0, ...] = base_stiffness_main\n stiffness[1, ...] = base_stiffness_fuselage\n stiffness[2, ...] = base_stiffness_tail\n\n mass[0, ...] = base_mass_main\n mass[1, ...] = base_mass_fuselage\n mass[2, ...] = base_mass_tail\n\n we = 0\n wn = 0\n # inner right wing\n beam_number[we:we + n_elem_main1] = 0\n y[wn:wn + n_node_main1] = np.linspace(0.0, span_main1, n_node_main1)\n\n for ielem in range(n_elem_main1):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n\n elem_stiffness[we:we + n_elem_main1] = 0\n elem_mass[we:we + n_elem_main1] = 0\n boundary_conditions[0] = 1\n # remember this is in B FoR\n app_forces[0] = [0, thrust, 0, 0, 0, 0]\n we += n_elem_main1\n wn += n_node_main1\n\n # outer right wing\n beam_number[we:we + n_elem_main1] = 0\n y[wn:wn + n_node_main2 - 1] = y[wn - 1] + np.linspace(0.0, np.cos(lambda_dihedral) * span_main2, n_node_main2)[1:]\n z[wn:wn + n_node_main2 - 1] = z[wn - 1] + np.linspace(0.0, np.sin(lambda_dihedral) * span_main2, n_node_main2)[1:]\n for ielem in range(n_elem_main2):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_main2] = 0\n elem_mass[we:we + n_elem_main2] = 0\n boundary_conditions[wn + n_node_main2 - 2] = -1\n we += n_elem_main2\n wn += n_node_main2 - 1\n\n # inner left wing\n beam_number[we:we + n_elem_main1 - 1] = 1\n y[wn:wn + n_node_main1 - 1] = np.linspace(0.0, -span_main1, n_node_main1)[1:]\n for ielem in range(n_elem_main1):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = 0\n elem_stiffness[we:we + n_elem_main1] = 0\n elem_mass[we:we + n_elem_main1] = 0\n we += n_elem_main1\n wn += n_node_main1 - 1\n\n # outer left wing\n beam_number[we:we + n_elem_main2] = 1\n y[wn:wn + n_node_main2 - 1] = y[wn - 1] + np.linspace(0.0, -np.cos(lambda_dihedral) * span_main2, n_node_main2)[1:]\n z[wn:wn + n_node_main2 - 1] = z[wn - 1] + np.linspace(0.0, np.sin(lambda_dihedral) * span_main2, n_node_main2)[1:]\n for ielem in range(n_elem_main2):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n elem_stiffness[we:we + n_elem_main2] = 0\n elem_mass[we:we + n_elem_main2] = 0\n boundary_conditions[wn + n_node_main2 - 2] = -1\n we += n_elem_main2\n wn += n_node_main2 - 1\n\n # fuselage\n beam_number[we:we + n_elem_fuselage] = 2\n x[wn:wn + n_node_fuselage - 1] = np.linspace(0.0, length_fuselage, n_node_fuselage)[1:]\n z[wn:wn + n_node_fuselage - 1] = np.linspace(0.0, offset_fuselage, n_node_fuselage)[1:]\n for ielem in range(n_elem_fuselage):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [0.0, 1.0, 0.0]\n conn[we, 0] = 0\n elem_stiffness[we:we + n_elem_fuselage] = 1\n elem_mass[we:we + n_elem_fuselage] = 1\n we += n_elem_fuselage\n wn += n_node_fuselage - 1\n global end_of_fuselage_node\n end_of_fuselage_node = wn - 1\n\n # fin\n beam_number[we:we + n_elem_fin] = 3\n x[wn:wn + n_node_fin - 1] = x[end_of_fuselage_node]\n z[wn:wn + n_node_fin - 1] = z[end_of_fuselage_node] + np.linspace(0.0, fin_height, n_node_fin)[1:]\n for ielem in range(n_elem_fin):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fuselage_node\n elem_stiffness[we:we + n_elem_fin] = 2\n elem_mass[we:we + n_elem_fin] = 2\n we += n_elem_fin\n wn += n_node_fin - 1\n end_of_fin_node = wn - 1\n\n # right tail\n beam_number[we:we + n_elem_tail] = 4\n x[wn:wn + n_node_tail - 1] = x[end_of_fin_node]\n y[wn:wn + n_node_tail - 1] = np.linspace(0.0, span_tail, n_node_tail)[1:]\n z[wn:wn + n_node_tail - 1] = z[end_of_fin_node]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [-1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fin_node\n elem_stiffness[we:we + n_elem_tail] = 2\n elem_mass[we:we + n_elem_tail] = 2\n boundary_conditions[wn + n_node_tail - 2] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n # left tail\n beam_number[we:we + n_elem_tail] = 5\n x[wn:wn + n_node_tail - 1] = x[end_of_fin_node]\n y[wn:wn + n_node_tail - 1] = np.linspace(0.0, -span_tail, n_node_tail)[1:]\n z[wn:wn + n_node_tail - 1] = z[end_of_fin_node]\n for ielem in range(n_elem_tail):\n conn[we + ielem, :] = ((np.ones((3,)) * (we + ielem) * (n_node_elem - 1)) +\n [0, 2, 1])\n for inode in range(n_node_elem):\n frame_of_reference_delta[we + ielem, inode, :] = [1.0, 0.0, 0.0]\n conn[we, 0] = end_of_fin_node\n elem_stiffness[we:we + n_elem_tail] = 2\n elem_mass[we:we + n_elem_tail] = 2\n boundary_conditions[wn + n_node_tail - 2] = -1\n we += n_elem_tail\n wn += n_node_tail - 1\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=n_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=n_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=n_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n lumped_mass_nodes_handle = h5file.create_dataset(\n 'lumped_mass_nodes', data=lumped_mass_nodes)\n lumped_mass_handle = h5file.create_dataset(\n 'lumped_mass', data=lumped_mass)\n lumped_mass_inertia_handle = h5file.create_dataset(\n 'lumped_mass_inertia', data=lumped_mass_inertia)\n lumped_mass_position_handle = h5file.create_dataset(\n 'lumped_mass_position', data=lumped_mass_position)\n\n\ndef generate_aero_file():\n global x, y, z\n # control surfaces\n n_control_surfaces = 2\n control_surface = np.zeros((n_elem, n_node_elem), dtype=int) - 1\n control_surface_type = np.zeros((n_control_surfaces,), dtype=int)\n control_surface_deflection = np.zeros((n_control_surfaces,))\n control_surface_chord = np.zeros((n_control_surfaces,), dtype=int)\n control_surface_hinge_coord = np.zeros((n_control_surfaces,), dtype=float)\n\n # control surface type 0 = static\n # control surface type 1 = dynamic\n control_surface_type[0] = 2\n control_surface_deflection[0] = cs_deflection\n control_surface_chord[0] = m\n control_surface_hinge_coord[0] = -0.25 # nondimensional wrt elastic axis (+ towards the trailing edge)\n\n control_surface_type[1] = 2\n control_surface_deflection[1] = rudder_static_deflection\n control_surface_chord[1] = 1\n control_surface_hinge_coord[1] = -0. # nondimensional wrt elastic axis (+ towards the trailing edge)\n\n we = 0\n wn = 0\n # right wing (surface 0, beam 0)\n i_surf = 0\n airfoil_distribution[we:we + n_elem_main, :] = 0\n surface_distribution[we:we + n_elem_main] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_main] = True\n temp_chord = np.linspace(chord_main, chord_main, n_node_main)\n temp_sweep = np.linspace(0.0, 0 * np.pi / 180, n_node_main)\n node_counter = 0\n for i_elem in range(we, we + n_elem_main):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = temp_chord[node_counter]\n elastic_axis[i_elem, i_local_node] = ea_main\n sweep[i_elem, i_local_node] = temp_sweep[node_counter]\n\n we += n_elem_main\n wn += n_node_main\n\n # left wing (surface 1, beam 1)\n i_surf = 1\n airfoil_distribution[we:we + n_elem_main, :] = 0\n # airfoil_distribution[wn:wn + n_node_main - 1] = 0\n surface_distribution[we:we + n_elem_main] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_main - 1] = True\n # chord[wn:wn + num_node_main - 1] = np.linspace(main_chord, main_tip_chord, num_node_main)[1:]\n # chord[wn:wn + num_node_main - 1] = main_chord\n # elastic_axis[wn:wn + num_node_main - 1] = main_ea\n temp_chord = np.linspace(chord_main, chord_main, n_node_main)\n node_counter = 0\n for i_elem in range(we, we + n_elem_main):\n for i_local_node in range(n_node_elem):\n if not i_local_node == 0:\n node_counter += 1\n chord[i_elem, i_local_node] = temp_chord[node_counter]\n elastic_axis[i_elem, i_local_node] = ea_main\n sweep[i_elem, i_local_node] = -temp_sweep[node_counter]\n\n we += n_elem_main\n wn += n_node_main - 1\n\n we += n_elem_fuselage\n wn += n_node_fuselage - 1 - 1\n #\n # # fin (surface 2, beam 3)\n i_surf = 2\n airfoil_distribution[we:we + n_elem_fin, :] = 1\n # airfoil_distribution[wn:wn + n_node_fin] = 0\n surface_distribution[we:we + n_elem_fin] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_fin] = True\n # chord[wn:wn + num_node_fin] = fin_chord\n for i_elem in range(we, we + n_elem_fin):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_fin\n elastic_axis[i_elem, i_local_node] = ea_fin\n control_surface[i_elem, i_local_node] = 1\n # twist[end_of_fuselage_node] = 0\n # twist[wn:] = 0\n # elastic_axis[wn:wn + num_node_main] = fin_ea\n we += n_elem_fin\n wn += n_node_fin - 1\n #\n # # # right tail (surface 3, beam 4)\n i_surf = 3\n airfoil_distribution[we:we + n_elem_tail, :] = 2\n # airfoil_distribution[wn:wn + n_node_tail] = 0\n surface_distribution[we:we + n_elem_tail] = i_surf\n surface_m[i_surf] = m\n # XXX not very elegant\n aero_node[wn:] = True\n # chord[wn:wn + num_node_tail] = tail_chord\n # elastic_axis[wn:wn + num_node_main] = tail_ea\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n twist[i_elem, i_local_node] = -0\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_tail\n elastic_axis[i_elem, i_local_node] = ea_tail\n control_surface[i_elem, i_local_node] = 0\n\n we += n_elem_tail\n wn += n_node_tail\n #\n # # left tail (surface 4, beam 5)\n i_surf = 4\n airfoil_distribution[we:we + n_elem_tail, :] = 2\n # airfoil_distribution[wn:wn + n_node_tail - 1] = 0\n surface_distribution[we:we + n_elem_tail] = i_surf\n surface_m[i_surf] = m\n aero_node[wn:wn + n_node_tail - 1] = True\n # chord[wn:wn + num_node_tail] = tail_chord\n # elastic_axis[wn:wn + num_node_main] = tail_ea\n # twist[we:we + num_elem_tail] = -tail_twist\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n twist[i_elem, i_local_node] = -0\n for i_elem in range(we, we + n_elem_tail):\n for i_local_node in range(n_node_elem):\n chord[i_elem, i_local_node] = chord_tail\n elastic_axis[i_elem, i_local_node] = ea_tail\n control_surface[i_elem, i_local_node] = 0\n we += n_elem_tail\n wn += n_node_tail\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n naca_airfoil_tail = airfoils_group.create_dataset('1', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n naca_airfoil_fin = airfoils_group.create_dataset('2', data=np.column_stack(\n generate_naca_camber(P=0, M=0)))\n\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input.attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # sweep\n sweep_input = h5file.create_dataset('sweep', data=sweep)\n dim_attr = sweep_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n control_surface_input = h5file.create_dataset('control_surface', data=control_surface)\n control_surface_deflection_input = h5file.create_dataset('control_surface_deflection',\n data=control_surface_deflection)\n control_surface_chord_input = h5file.create_dataset('control_surface_chord', data=control_surface_chord)\n control_surface_hinge_coord_input = h5file.create_dataset('control_surface_hinge_coord',\n data=control_surface_hinge_coord)\n control_surface_types_input = h5file.create_dataset('control_surface_type', data=control_surface_type)\n\n\ndef generate_naca_camber(M=0, P=0):\n mm = M * 1e-2\n p = P * 1e-1\n\n def naca(x, mm, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return mm / (p * p) * (2 * p * x - x * x)\n elif x > p and x < 1 + 1e-6:\n return mm / ((1 - p) * (1 - p)) * (1 - 2 * p + 2 * p * x - x * x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, mm, p) for x in x_vec])\n return x_vec, y_vec\n\n\ndef generate_solver_file():\n file_name = route + '/' + case_name + '.sharpy'\n settings = dict()\n settings['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': flow,\n 'write_screen': 'on',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n\n settings['BeamLoader'] = {'unsteady': 'on',\n 'orientation': algebra.euler2quat(np.array([roll,\n alpha,\n beta]))}\n settings['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n 'mstar': int(20 / tstep_factor),\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': ['1', '0', '0'],\n 'dt': dt}}\n\n settings['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'gravity_on': gravity,\n 'gravity': 9.81}\n\n settings['StaticUvlm'] = {'print_info': 'on',\n 'horseshoe': 'off',\n 'num_cores': num_cores,\n 'n_rollup': 0,\n 'rollup_dt': dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho}\n\n settings['StaticCoupled'] = {'print_info': 'off',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': settings['NonLinearStatic'],\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': settings['StaticUvlm'],\n 'max_iter': 100,\n 'n_load_steps': n_step,\n 'tolerance': fsi_tolerance,\n 'relaxation_factor': structural_relaxation_factor}\n\n settings['StaticTrim'] = {'solver': 'StaticCoupled',\n 'solver_settings': settings['StaticCoupled'],\n 'initial_alpha': alpha,\n 'initial_deflection': cs_deflection,\n 'initial_thrust': thrust}\n\n settings['NonLinearDynamicCoupledStep'] = {'print_info': 'off',\n 'max_iterations': 950,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'newmark_damp': 5e-3,\n 'gravity_on': gravity,\n 'gravity': 9.81,\n 'num_steps': n_tstep,\n 'dt': dt,\n 'initial_velocity': u_inf}\n\n settings['NonLinearDynamicPrescribedStep'] = {'print_info': 'off',\n 'max_iterations': 950,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'newmark_damp': 5e-3,\n 'gravity_on': gravity,\n 'gravity': 9.81,\n 'num_steps': n_tstep,\n 'dt': dt,\n 'initial_velocity': u_inf * int(free_flight)}\n settings['SaveData'] = { 'save_aero': 'on',\n 'save_struct': 'on',\n 'save_linear': 'off',\n 'save_linear_uvlm': 'off'}\n\n relative_motion = 'off'\n if not free_flight:\n relative_motion = 'on'\n settings['StepUvlm'] = {'print_info': 'off',\n 'num_cores': num_cores,\n 'convection_scheme': 2,\n 'gamma_dot_filtering': 6,\n 'velocity_field_generator': 'GustVelocityField',\n 'velocity_field_input': {'u_inf': int(not free_flight) * u_inf,\n 'u_inf_direction': [1., 0, 0],\n 'gust_shape': '1-cos',\n 'gust_parameters': {'gust_length': gust_length,\n 'gust_intensity': gust_intensity * u_inf},\n 'offset': gust_offset,\n 'relative_motion': relative_motion},\n 'rho': rho,\n 'n_time_steps': n_tstep,\n 'dt': dt}\n\n if free_flight:\n solver = 'NonLinearDynamicCoupledStep'\n else:\n solver = 'NonLinearDynamicPrescribedStep'\n settings['DynamicCoupled'] = {'structural_solver': solver,\n 'structural_solver_settings': settings[solver],\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'fsi_substeps': 200,\n 'fsi_tolerance': fsi_tolerance,\n 'relaxation_factor': relaxation_factor,\n 'minimum_steps': 1,\n 'relaxation_steps': 150,\n 'final_relaxation_factor': 0.5,\n 'n_time_steps': n_tstep,\n 'dt': dt,\n 'include_unsteady_force_contribution': 'on',\n 'network_settings': {\n 'variables_filename': './variables_hale.yaml',\n 'send_output_to_all_clients': 'on',\n 'byte_ordering': 'little',\n 'received_data_filename': './output/' + case_name + '/input.dat',\n 'log_name': './output/' + case_name + '/sharpy_network.log',\n 'file_log_level': 'debug',\n 'console_log_level': 'debug',\n 'input_network_settings': {'address': '127.0.0.1',\n 'port': 64011},\n 'output_network_settings': {'send_on_demand': 'off',\n 'destination_address': ['127.0.0.1'],\n 'address': '127.0.0.1',\n 'port': 64010,\n 'destination_ports': [64001]}, },\n 'postprocessors': ['BeamLoads', 'BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'BeamLoads': {'csv_output': 'off'},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'},\n 'AerogridPlot': {\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n }}\n\n settings['BeamLoads'] = {'csv_output': 'off'}\n\n settings['BeamPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on'}\n\n\n settings['AerogridPlot'] = {'include_rbm': 'on',\n 'include_forward_motion': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0,\n 'u_inf': u_inf,\n 'dt': dt}\n\n settings['Modal'] = {'print_info': True,\n 'use_undamped_modes': True,\n 'NumLambda': 30,\n 'rigid_body_modes': True,\n 'write_modes_vtk': 'on',\n 'print_matrices': 'on',\n 'continuous_eigenvalues': 'off',\n 'dt': dt,\n 'plot_eigenvalues': False}\n\n settings['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n 'linear_system_settings': {\n 'beam_settings': {'modal_projection': False,\n 'inout_coords': 'nodes',\n 'discrete_time': True,\n 'newmark_damp': 0.05,\n 'discr_method': 'newmark',\n 'dt': dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'off',\n 'num_modes': 40,\n 'print_info': 'on',\n 'gravity': 'on',\n 'remove_dofs': []},\n 'aero_settings': {'dt': dt,\n 'integr_order': 2,\n 'density': rho,\n 'remove_predictor': False,\n 'use_sparse': True,\n 'remove_inputs': ['u_gust']}\n }}\n\n settings['AsymptoticStability'] = {'print_info': 'on',\n 'modes_to_plot': [],\n 'display_root_locus': 'off',\n 'frequency_cutoff': 0,\n 'export_eigenvalues': 'off',\n 'num_evals': 40}\n\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n for k, v in settings.items():\n config[k] = v\n config.write()\n\n\nclean_test_files()\ngenerate_fem()\ngenerate_aero_file()\ngenerate_solver_file()\ngenerate_dyn_file()\n\ncase_route = ''\n\nsharpy.sharpy_main.main(['', case_route + '' + case_name + '.sharpy'])" }, { "path": "tests/io/Example_simple_hale/variables_hale.yaml", "content": "---\n- name: 'control_surface_deflection'\n var_type: 'control_surface'\n inout: 'in'\n position: 0\n- name: 'control_surface_deflection'\n var_type: 'control_surface'\n inout: 'in'\n position: 1\n- name: 'app_forces'\n var_type: 'node'\n inout: 'in'\n position: 0\n index: 1\n- name: 'for_pos'\n inout: 'out'\n position: 0\n var_type: 'node'\n- name: 'for_pos'\n var_type: 'node'\n inout: 'out'\n position: 1\n- name: 'for_pos'\n var_type: 'node'\n inout: 'out'\n position: 2\n- name: 'for_vel'\n var_type: 'node'\n inout: 'out'\n position: 0\n- name: 'for_vel'\n var_type: 'node'\n inout: 'out'\n position: 1\n- name: 'for_vel'\n var_type: 'node'\n inout: 'out'\n position: 2\n- name: 'for_vel'\n var_type: 'node'\n inout: 'out'\n position: 3\n- name: 'for_vel'\n var_type: 'node'\n inout: 'out'\n position: 4\n- name: 'for_vel'\n var_type: 'node'\n inout: 'out'\n position: 5\n- name: 'loads'\n var_type: 'node'\n inout: 'out'\n position: 0\n index: 4\n- name: 'strain'\n var_type: 'node'\n inout: 'out'\n position: 0\n index: 4\n..." }, { "path": "tests/io/__init__.py", "content": "" }, { "path": "tests/io/generate_pazy_udpout.py", "content": "import numpy as np\nimport os\nimport unittest\nimport sharpy.cases.templates.flying_wings as wings\nimport sharpy.sharpy_main\n\n# Problem Set up\ndef generate_pazy_udp(u_inf, case_name, output_folder='/output/', cases_folder='', **kwargs):\n # u_inf = 60\n alpha_deg = kwargs.get('alpha', 0.)\n rho = 1.225\n num_modes = 16\n gravity_on = kwargs.get('gravity_on', True)\n cd = kwargs.get('cd', './') # current directory (useful for tests)\n\n # Lattice Discretisation\n M = kwargs.get('M', 4)\n N = kwargs.get('N', 32)\n M_star_fact = kwargs.get('Ms', 10)\n\n # Linear UVLM settings\n integration_order = 2\n remove_predictor = False\n use_sparse = True\n\n # ROM Properties\n rom_settings = dict()\n rom_settings['algorithm'] = 'mimo_rational_arnoldi'\n rom_settings['r'] = 5\n rom_settings['single_side'] = 'observability'\n frequency_continuous_k = np.array([0.])\n\n # Case Admin - Create results folders\n # case_name = 'goland_cs'\n# case_nlin_info = 'M%dN%dMs%d_nmodes%d' % (M, N, M_star_fact, num_modes)\n # case_rom_info = 'rom_MIMORA_r%d_sig%04d_%04dj' % (rom_settings['r'], frequency_continuous_k[-1].real * 100,\n # frequency_continuous_k[-1].imag * 100)\n\n # case_name += case_nlin_info #+ case_rom_info\n\n # os.makedirs(fig_folder, exist_ok=True)\n\n # SHARPy nonlinear reference solution\n ws = wings.PazyControlSurface(M=M,\n N=N,\n Mstar_fact=M_star_fact,\n u_inf=u_inf,\n alpha=alpha_deg,\n cs_deflection=[0, 0],\n rho=rho,\n sweep=0,\n physical_time=0.2,\n n_surfaces=2,\n route=cases_folder + '/' + case_name,\n case_name=case_name)\n\n ws.gust_intensity = 0.01\n ws.sigma = 1\n\n ws.clean_test_files()\n ws.update_derived_params()\n ws.set_default_config_dict()\n\n ws.generate_aero_file()\n ws.generate_fem_file()\n\n frequency_continuous_w = 2 * u_inf * frequency_continuous_k / ws.c_ref\n rom_settings['frequency'] = frequency_continuous_w\n rom_settings['tangent_input_file'] = ws.route + '/' + ws.case_name + '.rom.h5'\n\n ws.config['SHARPy'] = {\n 'flow':\n ['BeamLoader',\n 'AerogridLoader',\n # 'NonLinearStatic',\n 'StaticUvlm',\n 'AerogridPlot',\n 'BeamPlot',\n 'WriteVariablesTime',\n 'DynamicCoupled',\n# 'Modal',\n# 'LinearAssembler',\n # 'FrequencyResponse',\n# 'AsymptoticStability',\n# 'SaveParametricCase',\n ],\n 'case': ws.case_name, 'route': ws.route,\n 'write_screen': 'off', 'write_log': 'on',\n 'save_settings': 'on',\n 'log_folder': output_folder + '/' + ws.case_name + '/',\n 'log_file': ws.case_name + '.log'}\n\n ws.config['BeamLoader'] = {\n 'unsteady': 'off',\n 'orientation': ws.quat}\n\n ws.config['AerogridLoader'] = {\n 'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': ws.Mstar_fact * ws.M,\n 'freestream_dir': ws.u_inf_direction,\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction,\n 'dt': ws.dt}}\n\n ws.config['StaticUvlm'] = {\n 'rho': ws.rho,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction},\n 'rollup_dt': ws.dt,\n 'print_info': 'on',\n 'horseshoe': 'on',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_aic_refresh': 0,\n 'vortex_radius': 1e-9,\n 'rollup_tolerance': 1e-4}\n\n settings = dict()\n settings['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 200,\n 'num_load_steps': 5,\n 'delta_curved': 1e-6,\n 'min_delta': 1e-8,\n 'gravity_on': gravity_on,\n 'gravity': 9.81}\n\n ws.config['StaticCoupled'] = {\n 'print_info': 'on',\n 'max_iter': 200,\n 'n_load_steps': 4,\n 'tolerance': 1e-5,\n 'relaxation_factor': 0.1,\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {\n 'rho': ws.rho,\n 'print_info': 'off',\n 'horseshoe': 'on',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': ws.dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction},\n 'vortex_radius': 1e-9},\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': settings['NonLinearStatic']}\n\n ws.config['AerogridPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}\n\n ws.config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': ws.case_name + '_aeroforces.csv',\n 'screen_output': 'on'}\n\n ws.config['BeamPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on'}\n\n ws.config['WriteVariablesTime'] = {'structure_variables': ['pos'],\n 'structure_nodes': list(range(0, ws.num_node_surf)),\n 'cleanup_old_solution': 'on'}\n\n ws.config['Modal'] = {'NumLambda': 20,\n 'rigid_body_modes': 'off',\n 'print_matrices': 'on',\n 'save_data': 'off',\n 'rigid_modes_cg': 'off',\n 'continuous_eigenvalues': 'off',\n 'dt': 0,\n 'plot_eigenvalues': False,\n 'max_rotation_deg': 15.,\n 'max_displacement': 0.15,\n 'write_modes_vtk': True,\n 'use_undamped_modes': True}\n\n ws.config['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n # 'modal_tstep': 0,\n 'linear_system_settings': {\n 'beam_settings': {'modal_projection': 'on',\n 'inout_coords': 'modes',\n 'discrete_time': 'on',\n 'newmark_damp': 0.5e-4,\n 'discr_method': 'newmark',\n 'dt': ws.dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'off',\n 'num_modes': num_modes,\n 'print_info': 'off',\n 'gravity': gravity_on,\n 'remove_sym_modes': 'on',\n 'remove_dofs': []},\n 'aero_settings': {'dt': ws.dt,\n # 'ScalingDict': {'length': 0.5 * ws.c_ref,\n # 'speed': u_inf,\n # 'density': rho},\n 'integr_order': integration_order,\n 'density': ws.rho,\n 'remove_predictor': remove_predictor,\n 'use_sparse': use_sparse,\n 'rigid_body_motion': 'off',\n 'use_euler': 'off',\n 'remove_inputs': ['u_gust'],\n 'rom_method': ['Krylov'],\n 'rom_method_settings': {'Krylov': rom_settings}},\n }}\n\n ws.config['AsymptoticStability'] = {'print_info': True,\n 'export_eigenvalues': 'on',\n 'target_system': ['aeroelastic', 'aerodynamic', 'structural'],\n # 'velocity_analysis': [160, 180, 20]}\n }\n\n ws.config['LinDynamicSim'] = {'dt': ws.dt,\n 'n_tsteps': ws.n_tstep,\n 'sys_id': 'LinearAeroelastic',\n 'postprocessors': ['BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'AerogridPlot': {\n 'u_inf': ws.u_inf,\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'}}}\n\n ws.config['FrequencyResponse'] = {'quick_plot': 'off',\n 'frequency_unit': 'w',\n 'frequency_bounds': [0.0001, 1.0],\n 'num_freqs': 100,\n 'frequency_spacing': 'log',\n 'target_system': ['aeroelastic', 'aerodynamic', 'structural'],\n }\n\n ws.config['SaveParametricCase'] = {'save_case':'off',\n 'parameters': {'u_inf': u_inf}}\n settings = dict()\n settings['NonLinearDynamicPrescribedStep'] = {'print_info': 'on',\n 'max_iterations': 950,\n 'delta_curved': 1e-2,\n 'min_delta': 1e-5,\n 'newmark_damp': 5e-2,\n 'gravity_on': 'on',\n 'gravity': 9.81,\n 'num_steps': ws.n_tstep,\n 'dt': ws.dt}\n\n settings['StepUvlm'] = {'print_info': 'on',\n 'num_cores': 4,\n 'convection_scheme': 2,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': ws.u_inf*1,\n 'u_inf_direction': [1., 0., 0.]},\n 'rho': ws.rho,\n 'n_time_steps': ws.n_tstep,\n 'vortex_radius': 1e-9,\n 'dt': ws.dt,\n 'gamma_dot_filtering': 3}\n\n\n settings['DynamicCoupled'] = {'print_info': 'on',\n 'structural_substeps': 10,\n 'dynamic_relaxation': 'on',\n 'cleanup_previous_solution': 'on',\n 'structural_solver': 'NonLinearDynamicPrescribedStep',\n 'structural_solver_settings': settings['NonLinearDynamicPrescribedStep'],\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'fsi_substeps': 200,\n 'fsi_tolerance': 1e-6,\n 'relaxation_factor': ws.relaxation_factor,\n 'minimum_steps': 1,\n 'relaxation_steps': 150,\n 'final_relaxation_factor': 0.0,\n 'n_time_steps': 4, #ws.n_tstep,\n 'dt': ws.dt,\n 'include_unsteady_force_contribution': 'off',\n 'postprocessors': ['UDPout'],\n 'postprocessors_settings': {'BeamLoads': {'csv_output': 'off'},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'},\n 'StallCheck': {},\n 'AerogridPlot': {\n 'u_inf': ws.u_inf,\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n 'WriteVariablesTime': {\n 'structure_variables': ['pos', 'psi'],\n 'structure_nodes': [ws.num_node_surf - 1,\n ws.num_node_surf,\n ws.num_node_surf + 1]},\n 'UDPout': {'variables_filename': cd + '/variables.yaml',\n 'output_network_settings':\n {'destination_address': ['127.0.0.1'],\n 'destination_ports': [65431]},\n 'console_log_level': 'error',\n },\n }}\n\n ws.config['DynamicCoupled'] = settings['DynamicCoupled']\n\n\n ws.config.write()\n\n sharpy.sharpy_main.main(['', ws.route + ws.case_name + '.sharpy'])\n\nif __name__== '__main__':\n # u_inf = 1\n # generate_pazi(u_inf)\n#\n from datetime import datetime\n\n # datetime object containing current date and time\n # u_inf_vec = np.array([46])\n # u_inf_vec = np.linspace(28, 30, 50)\n # u_inf_vec = np.linspace(5, 30, 26)\n u_inf_vec = [50]\n# u_inf_vec = np.linspace(20, 60, 41)\n# u_inf_vec = np.linspace(1, 20, 20)\n# u_inf_vec = np.linspace(1, 60, 60)\n\n\n alpha = 1\n gravity_on = True\n\n M = 4\n N = 16\n Ms = 1\n\n # For comparison with Marc\n# M = 8\n# N = 128\n# Ms = 8\n\n\n batch_log = 'batch_log_alpha{:04g}'.format(alpha*100)\n\n with open('./{:s}.txt'.format(batch_log), 'w') as f:\n # dd/mm/YY H:M:S\n now = datetime.now()\n dt_string = now.strftime(\"%d/%m/%Y %H:%M:%S\")\n f.write('SHARPy launch - START\\n')\n f.write(\"date and time = %s\\n\\n\" % dt_string)\n\n for i, u_inf in enumerate(u_inf_vec):\n print('RUNNING SHARPY %f\\n' % u_inf)\n case_name = 'pazi_uinf{:04g}_alpha{:04g}'.format(u_inf*10, alpha*100)\n try:\n generate_pazy_udp(u_inf, case_name, output_folder='/output/vortex_radius_M{:g}N{:g}Ms{:g}_alpha{:04g}/'.format(M, N, Ms, alpha * 100),\n cases_subfolder='/M{:g}N{:g}Ms{:g}/'.format(M, N, Ms),\n M=M, N=N, Ms=Ms, alpha=alpha,\n gravity_on=gravity_on)\n now = datetime.now()\n dt_string = now.strftime(\"%d/%m/%Y %H:%M:%S\")\n with open('./{:s}.txt'.format(batch_log), 'a') as f:\n f.write('%s Ran case %i :::: u_inf = %f\\n\\n' % (dt_string, i, u_inf))\n except AssertionError:\n now = datetime.now()\n dt_string = now.strftime(\"%d/%m/%Y %H:%M:%S\")\n with open('./{:s}.txt'.format(batch_log), 'a') as f:\n f.write('%s ERROR RUNNING case %f\\n\\n' % (dt_string, u_inf))\n" }, { "path": "tests/io/sample_udp_inout/__init__.py", "content": "" }, { "path": "tests/io/sample_udp_inout/client.py", "content": "import socket\nimport select\nimport time\nimport logging\nimport struct\nimport sharpy.io.message_interface as message_interface\nimport numpy as np\n\"\"\"\nThis is not a test but is to be used as client when testing the development of the input\noutput capabilities of sharpy.\n\nRun this script as client.\n\nRun ``python generate_pazy_test_io_local.py`` as server\n\"\"\"\n\n# sel = selectors.DefaultSelector()\n\nlogging.basicConfig(format='%(asctime)s - %(name)s - %(levelname)s - %(message)s',\n level=20)\nlogger = logging.getLogger(__name__)\n\nsharpy_incoming = ('127.0.0.1', 64011) # control side socket\nsharpy_outgoing = ('127.0.0.1', 64010) # output side socket\n\nown_control = ('127.0.0.1', 64000)\nown_receive = ('127.0.0.1', 64001)\n\nin_sock = socket.socket(socket.AF_INET, socket.SOCK_DGRAM)\nin_sock.bind(own_control)\n\nout_sock = socket.socket(socket.AF_INET, socket.SOCK_DGRAM)\nout_sock.bind(own_receive)\n\n# from https://stackoverflow.com/questions/2719017/how-to-set-timeout-on-pythons-socket-recv-method\n# ready_to_read = select.select([out_sock], [], [], 2)\nout_sock.settimeout(30)\n\ntsteps = 401\nt = np.linspace(0, 0.2, tsteps)\ncs_deflection = 10 * np.sin(2 * t * np.pi / 0.2) * np.pi/180\n# cs_deflection = np.linspace(0, )\n# cs_deflection = np.array([0, 0, 90, 90, 90, 90]) * np.pi / 180\ncurr_ts = 0\nwingtip_deflection = []\nmid_wing_deflection = []\nwhile True:\n if curr_ts > tsteps:\n break\n # send control input to sharpy\n ctrl_value = struct.pack('<5sif', b'RREF0', 0, cs_deflection[curr_ts])\n logger.info('Sending control input of size {} bytes'.format(len(ctrl_value)))\n in_sock.sendto(ctrl_value, sharpy_incoming)\n logger.info('Sent control input to {}'.format(sharpy_incoming))\n\n # time.sleep(2)\n # input('Continue loop')\n\n # receive output data. set msg_len to whatever length SHARPy is sending\n msg_len = 133\n try:\n msg, conn = out_sock.recvfrom(msg_len)\n except socket.timeout:\n logger.info('Socket time out')\n break\n logger.info('Received {} data from {}'.format(msg, conn))\n logger.info('Received data is {} bytes long'.format(len(msg)))\n # else:\n # break\n # decoding\n values = message_interface.decoder(msg)\n logger.info('Received {}'.format(values))\n wingtip_deflection.append(values[0][1])\n mid_wing_deflection.append(values[1][1])\n # input('Next time step')\n curr_ts += 1\n\n\nout_sock.close()\nin_sock.close()\nlogger.info('Closed input and output sockets')\n" }, { "path": "tests/io/sample_udp_inout/generate_pazy_test_io_local.py", "content": "import numpy as np\nimport os\nimport unittest\nimport cases.templates.flying_wings as wings\nimport sharpy.sharpy_main\n\n# Problem Set up\ndef generate_pazy(u_inf, case_name, output_folder='/output/', cases_folder='', **kwargs):\n # u_inf = 60\n alpha_deg = kwargs.get('alpha', 0.)\n rho = 1.225\n num_modes = 16\n gravity_on = kwargs.get('gravity_on', True)\n\n # Lattice Discretisation\n M = kwargs.get('M', 4)\n N = kwargs.get('N', 32)\n M_star_fact = kwargs.get('Ms', 10)\n\n # Linear UVLM settings\n integration_order = 2\n remove_predictor = False\n use_sparse = True\n\n # ROM Properties\n rom_settings = dict()\n rom_settings['algorithm'] = 'mimo_rational_arnoldi'\n rom_settings['r'] = 5\n rom_settings['single_side'] = 'observability'\n frequency_continuous_k = np.array([0.])\n\n # Case Admin - Create results folders\n # case_name = 'goland_cs'\n # case_nlin_info = 'M%dN%dMs%d_nmodes%d' % (M, N, M_star_fact, num_modes)\n # case_rom_info = 'rom_MIMORA_r%d_sig%04d_%04dj' % (rom_settings['r'], frequency_continuous_k[-1].real * 100,\n # frequency_continuous_k[-1].imag * 100)\n\n # case_name += case_nlin_info #+ case_rom_info\n\n # os.makedirs(fig_folder, exist_ok=True)\n\n # SHARPy nonlinear reference solution\n ws = wings.PazyControlSurface(M=M,\n N=N,\n Mstar_fact=M_star_fact,\n u_inf=u_inf,\n alpha=alpha_deg,\n cs_deflection=[0, 0],\n rho=rho,\n sweep=0,\n physical_time=2.0,\n n_surfaces=2,\n route=cases_folder + '/' + case_name,\n case_name=case_name)\n\n ws.gust_intensity = 0.01\n ws.sigma = 1\n\n ws.control_surface_type = np.array([2])\n\n ws.clean_test_files()\n ws.update_derived_params()\n ws.set_default_config_dict()\n\n ws.generate_aero_file()\n ws.generate_fem_file()\n\n frequency_continuous_w = 2 * u_inf * frequency_continuous_k / ws.c_ref\n rom_settings['frequency'] = frequency_continuous_w\n rom_settings['tangent_input_file'] = ws.route + '/' + ws.case_name + '.rom.h5'\n\n ws.config['SHARPy'] = {\n 'flow':\n ['BeamLoader',\n 'AerogridLoader',\n # 'NonLinearStatic',\n 'StaticUvlm',\n 'AerogridPlot',\n 'BeamPlot',\n 'WriteVariablesTime',\n 'DynamicCoupled',\n # 'Modal',\n # 'LinearAssembler',\n # 'FrequencyResponse',\n # 'AsymptoticStability',\n # 'SaveParametricCase',\n ],\n 'case': ws.case_name, 'route': ws.route,\n 'write_screen': 'off', 'write_log': 'on',\n 'save_settings': 'on',\n 'log_folder': output_folder + '/' + ws.case_name + '/',\n 'log_file': ws.case_name + '.log'}\n\n ws.config['BeamLoader'] = {\n 'unsteady': 'off',\n 'orientation': ws.quat}\n\n ws.config['AerogridLoader'] = {\n 'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': ws.Mstar_fact * ws.M,\n 'freestream_dir': ws.u_inf_direction,\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction,\n 'dt': ws.dt}}\n\n ws.config['StaticUvlm'] = {\n 'rho': ws.rho,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction},\n 'rollup_dt': ws.dt,\n 'print_info': 'on',\n 'horseshoe': 'off',\n 'num_cores': 4}\n\n settings = dict()\n settings['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 200,\n 'num_load_steps': 5,\n 'delta_curved': 1e-6,\n 'min_delta': 1e-8,\n 'gravity_on': gravity_on,\n 'gravity': 9.81}\n\n ws.config['StaticCoupled'] = {\n 'print_info': 'on',\n 'max_iter': 200,\n 'n_load_steps': 4,\n 'tolerance': 1e-5,\n 'relaxation_factor': 0.1,\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {\n 'rho': ws.rho,\n 'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction},\n 'vortex_radius': 1e-9},\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': settings['NonLinearStatic']}\n\n ws.config['AerogridPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}\n\n ws.config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': ws.case_name + '_aeroforces.csv',\n 'screen_output': 'on'}\n\n ws.config['BeamPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on'}\n\n ws.config['WriteVariablesTime'] = {'structure_variables': ['pos'],\n 'structure_nodes': list(range(0, ws.num_node_surf)),\n 'cleanup_old_solution': 'on'}\n\n ws.config['Modal'] = {'NumLambda': 20,\n 'rigid_body_modes': 'off',\n 'print_matrices': 'on',\n 'save_data': 'off',\n 'rigid_modes_cg': 'off',\n 'continuous_eigenvalues': 'off',\n 'dt': 0,\n 'plot_eigenvalues': False,\n 'max_rotation_deg': 15.,\n 'max_displacement': 0.15,\n 'write_modes_vtk': True,\n 'use_undamped_modes': True}\n\n ws.config['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n # 'modal_tstep': 0,\n 'linear_system_settings': {\n 'beam_settings': {'modal_projection': 'on',\n 'inout_coords': 'modes',\n 'discrete_time': 'on',\n 'newmark_damp': 0.5e-4,\n 'discr_method': 'newmark',\n 'dt': ws.dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'off',\n 'num_modes': num_modes,\n 'print_info': 'off',\n 'gravity': gravity_on,\n 'remove_sym_modes': 'on',\n 'remove_dofs': []},\n 'aero_settings': {'dt': ws.dt,\n # 'ScalingDict': {'length': 0.5 * ws.c_ref,\n # 'speed': u_inf,\n # 'density': rho},\n 'integr_order': integration_order,\n 'density': ws.rho,\n 'remove_predictor': remove_predictor,\n 'use_sparse': use_sparse,\n 'rigid_body_motion': 'off',\n 'use_euler': 'off',\n 'remove_inputs': ['u_gust'],\n 'rom_method': ['Krylov'],\n 'rom_method_settings': {'Krylov': rom_settings}},\n }}\n\n ws.config['AsymptoticStability'] = {'print_info': True,\n 'export_eigenvalues': 'on',\n 'target_system': ['aeroelastic', 'aerodynamic', 'structural'],\n # 'velocity_analysis': [160, 180, 20]}\n }\n\n ws.config['LinDynamicSim'] = {'dt': ws.dt,\n 'n_tsteps': ws.n_tstep,\n 'sys_id': 'LinearAeroelastic',\n 'postprocessors': ['BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'AerogridPlot': {\n 'u_inf': ws.u_inf,\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'}}}\n\n ws.config['FrequencyResponse'] = {'quick_plot': 'off',\n 'frequency_unit': 'w',\n 'frequency_bounds': [0.0001, 1.0],\n 'num_freqs': 100,\n 'frequency_spacing': 'log',\n 'target_system': ['aeroelastic', 'aerodynamic', 'structural'],\n }\n\n ws.config['SaveParametricCase'] = {'save_case':'off',\n 'parameters': {'u_inf': u_inf}}\n settings = dict()\n settings['NonLinearDynamicPrescribedStep'] = {'print_info': 'on',\n 'max_iterations': 950,\n 'delta_curved': 1e-2,\n 'min_delta': 1e-5,\n 'newmark_damp': 5e-2,\n 'gravity_on': 'on',\n 'gravity': 9.81,\n 'num_steps': ws.n_tstep,\n 'dt': ws.dt}\n\n settings['StepUvlm'] = {'print_info': 'on',\n 'num_cores': 4,\n 'convection_scheme': 0,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': ws.u_inf*1,\n 'u_inf_direction': [1., 0., 0.]},\n 'rho': ws.rho,\n 'n_time_steps': ws.n_tstep,\n 'vortex_radius': 1e-9,\n 'dt': ws.dt,\n 'gamma_dot_filtering': 3}\n\n settings['DynamicCoupled'] = {'print_info': 'on',\n 'structural_substeps': 0,\n 'dynamic_relaxation': 'on',\n 'cleanup_previous_solution': 'on',\n 'structural_solver': 'NonLinearDynamicPrescribedStep',\n 'structural_solver_settings': settings['NonLinearDynamicPrescribedStep'],\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'fsi_substeps': 200,\n 'fsi_tolerance': 1e-6,\n 'relaxation_factor': ws.relaxation_factor,\n 'minimum_steps': 1,\n 'relaxation_steps': 150,\n 'final_relaxation_factor': 0.0,\n 'n_time_steps': 5, #ws.n_tstep,\n 'dt': ws.dt,\n 'include_unsteady_force_contribution': 'on',\n 'steps_without_unsteady_force': 2,\n 'network_settings': {'variables_filename': './variables_coarse.yaml',\n 'send_output_to_all_clients': 'on',\n 'byte_ordering': 'little',\n 'received_data_filename': output_folder + './input.dat',\n 'log_name': output_folder + '/sharpy_network.log',\n 'file_log_level': 'debug',\n 'console_log_level': 'debug',\n 'input_network_settings': {'address': '127.0.0.1',\n 'port': 64011},\n 'output_network_settings': {'send_on_demand': 'off',\n 'destination_address': ['127.0.0.1'],\n 'address': '127.0.0.1',\n 'port': 64010,\n 'destination_ports': [64001],\n },\n },\n 'postprocessors': ['AerogridPlot', 'BeamPlot', 'WriteVariablesTime'],\n 'postprocessors_settings': {'BeamLoads': {'csv_output': 'off'},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'},\n 'StallCheck': {},\n 'AerogridPlot': {\n 'u_inf': ws.u_inf,\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n 'WriteVariablesTime': {\n 'structure_variables': ['pos', 'psi'],\n 'structure_nodes': [ws.num_node_surf - 1,\n ws.num_node_surf,\n ws.num_node_surf + 1]},\n }}\n\n ws.config['DynamicCoupled'] = settings['DynamicCoupled']\n\n ws.config.write()\n\n sharpy.sharpy_main.main(['', ws.route + ws.case_name + '.sharpy'])\n\n\nif __name__== '__main__':\n\n u_inf = 50\n\n alpha = 4\n gravity_on = True\n\n M = 4\n N = 32\n Ms = 4\n\n case_name = 'pazy_uinf{:04g}_alpha{:04g}'.format(u_inf*10, alpha*100)\n generate_pazy(u_inf, case_name, output_folder='./output/test_65001_wake3_M{:g}N{:g}Ms{:g}_alpha{:04g}/'.format(M, N, Ms, alpha*100),\n cases_folder='./cases/test_M{:g}N{:g}Ms{:g}wake3/'.format(M, N, Ms),\n M=M, N=N, Ms=Ms, alpha=alpha,\n gravity_on=gravity_on)\n" }, { "path": "tests/io/sample_udp_inout/variables_coarse.yaml", "content": "---\n- name: 'control_surface_deflection'\n var_type: 'control_surface'\n inout: 'in'\n position: 0\n- name: 'dt'\n inout: 'out'\n- name: 'nt'\n inout: 'out'\n- name: 'pos_dot'\n var_type: 'node'\n inout: 'out'\n position: 4\n index: 0\n- name: 'pos_dot'\n inout: 'out'\n position: 4\n index: 1\n var_type: 'node'\n- name: 'pos_dot'\n inout: 'out'\n position: 4\n index: 2\n var_type: 'node'\n- name: 'pos_dot'\n var_type: 'node'\n inout: 'out'\n position: 8\n index: 0\n- name: 'pos_dot'\n inout: 'out'\n position: 8\n index: 1\n var_type: 'node'\n- name: 'pos_dot'\n inout: 'out'\n position: 8\n index: 2\n var_type: 'node'\n- name: 'pos_dot'\n var_type: 'node'\n inout: 'out'\n position: 16\n index: 0\n- name: 'pos_dot'\n inout: 'out'\n position: 16\n index: 1\n var_type: 'node'\n- name: 'pos_dot'\n inout: 'out'\n position: 16\n index: 2\n var_type: 'node'\n- name: 'pos_dot'\n var_type: 'node'\n inout: 'out'\n position: 20\n index: 0\n- name: 'pos_dot'\n inout: 'out'\n position: 20\n index: 1\n var_type: 'node'\n- name: 'pos_dot'\n inout: 'out'\n position: 20\n index: 2\n var_type: 'node'\n- name: 'pos'\n inout: 'out'\n position: 20\n index: 2\n var_type: 'node'\n- name: 'psi'\n inout: 'out'\n position: 20\n index: 2\n var_type: 'node'\n...\n" }, { "path": "tests/io/test_pazy_udpout.py", "content": "import unittest\nimport tests.io.generate_pazy_udpout as gp\nimport os\nimport shutil\n\nclass TestPazyCoupledStatic(unittest.TestCase):\n \"\"\"\n Test Pazy wing static coupled case and compare against a benchmark result.\n As of the time of writing, benchmark result has not been verified but it\n serves as a backward compatibility check for code improvements.\n \"\"\"\n\n route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n\n def test_dynamic_aoa(self):\n u_inf = 50\n alpha = 0\n case_name = 'pazy_uinf{:04g}_alpha{:04g}'.format(u_inf * 10, alpha * 10)\n\n M = 4\n N = 16\n Msf = 1\n\n cases_folder = self.route_test_dir + '/cases/'\n output_folder = self.route_test_dir + '/cases/'\n # run case\n gp.generate_pazy_udp(u_inf, case_name, output_folder, cases_folder,\n alpha=alpha,\n M=M,\n N=N,\n Msf=Msf,\n cd=self.route_test_dir)\n\n def tearDown(self):\n cases_folder = self.route_test_dir + '/cases/'\n\n if os.path.isdir(cases_folder):\n shutil.rmtree(cases_folder)\n\n\nif __name__ == '__main__':\n unittest.main()" }, { "path": "tests/io/variables.yaml", "content": "---\n- name: 'control_surface_deflection'\n var_type: 'control_surface'\n inout: 'in'\n position: 0\n- name: 'pos'\n var_type: 'node'\n inout: 'out'\n position: 5\n index: 2\n- name: 'pos'\n inout: 'out'\n position: 16\n index: 2\n var_type: 'node'\n- name: 'psi_dot'\n inout: 'out'\n position: 16\n index: 2\n var_type: 'node'\n..." }, { "path": "tests/linear/__init__.py", "content": "" }, { "path": "tests/linear/assembly/__init__.py", "content": "" }, { "path": "tests/linear/assembly/test_assembly.py", "content": "\"\"\"\nTest assembly\nS. Maraniello, 29 May 2018\n\"\"\"\n\nimport os\nimport copy\nimport warnings\nimport unittest\nimport itertools\nimport numpy as np\nimport scipy.linalg as scalg\n\nimport sharpy.utils.h5utils as h5utils\nimport sharpy.linear.src.assembly as assembly\nimport sharpy.linear.src.multisurfaces as multisurfaces\nimport sharpy.linear.src.surface as surface\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.cout_utils as cout\nimport sharpy.sharpy_main\n\n\nnp.set_printoptions(linewidth=200, precision=3)\nvortex_radius = 1e-4\n\n\ndef max_error_tensor(Pder_an, Pder_num):\n \"\"\"\n Finds the maximum error analytical derivatives Pder_an. The error is:\n - relative, if the element of Pder_an is nonzero\n - absolute, otherwise\n\n The function returns the absolute and relative error tensors, and the\n maximum error.\n\n @warning: The relative error tensor may contain NaN or Inf if the\n analytical derivative is zero. These elements are filtered out during the\n search for maximum error, and absolute error is checked.\n \"\"\"\n\n Eabs = np.abs(Pder_num - Pder_an)\n\n nnzvec = Pder_an != 0\n Erel = np.zeros(Pder_an.shape)\n Erel[nnzvec] = np.abs(Eabs[nnzvec] / Pder_an[nnzvec])\n\n # Relative error check: remove NaN and inf...\n iifinite = np.isfinite(Erel)\n err_max = 0.0\n for err_here in Erel[iifinite]:\n if np.abs(err_here) > err_max:\n err_max = err_here\n\n # Zero elements check\n iizero = np.abs(Pder_an) < 1e-15\n for der_here in Pder_num[iizero]:\n if np.abs(der_here) > err_max:\n err_max = der_here\n\n return err_max, Eabs, Erel\n\n\nclass Test_assembly(unittest.TestCase):\n \"\"\" Test methods into assembly module \"\"\"\n\n print_info = False # useful for debugging. Leave False to keep test log clean\n\n def setUp(self):\n\n # select test case\n fname = os.path.dirname(os.path.abspath(__file__)) + '/h5input/goland_mod_Nsurf01_M003_N004_a040.aero_state.h5'\n haero = h5utils.readh5(fname)\n tsdata = haero.ts00000\n\n # # Rotating cases\n # fname = './basic_rotating_wing/basic_wing.data.h5'\n # haero = h5utils.readh5(fname)\n # tsdata = haero.data.aero.timestep_info[-1]\n # tsdata.omega = []\n # for ss in range(haero.data.aero.n_surf):\n # tsdata.omega.append(haero.data.structure.timestep_info[-1].for_vel[3:6])\n\n MS = multisurfaces.MultiAeroGridSurfaces(tsdata, vortex_radius)\n MS.get_normal_ind_velocities_at_collocation_points()\n MS.verify_non_penetration(print_info=self.print_info)\n MS.verify_aic_coll(print_info=self.print_info)\n MS.get_joukovski_qs()\n MS.verify_joukovski_qs(print_info=self.print_info)\n self.MS = MS\n\n def test_nc_dqcdzeta(self):\n \"\"\"\n For each output surface, where induced velocity is computed, all other\n surfaces are looped.\n For wakes, only TE is displaced.\n \"\"\"\n\n if self.print_info:\n print('----------------------------- Testing assembly.test_nc_dqcdzeta')\n\n MS = self.MS\n n_surf = MS.n_surf\n\n # analytical\n Dercoll_list, Dervert_list = assembly.nc_dqcdzeta(MS.Surfs, MS.Surfs_star)\n\n # check option\n Der_all_exp = np.block(Dervert_list) + scalg.block_diag(*Dercoll_list)\n Der_all = np.block(assembly.nc_dqcdzeta(MS.Surfs, MS.Surfs_star, Merge=True))\n _, ErAbs, ErRel = max_error_tensor(Der_all, Der_all_exp)\n # max absolute error\n ermax = np.max(ErAbs)\n # relative error at max abs error point\n iimax = np.unravel_index(np.argmax(ErAbs), ErAbs.shape)\n ermax_rel = ErRel[iimax]\n assert ermax_rel < 1e-16, \\\n 'option Merge=True not working correctly, relative error (%.3e) too high!' % ErRel\n\n # allocate numerical\n Derlist_num = []\n for ii in range(n_surf):\n sub = []\n for jj in range(n_surf):\n sub.append(0.0 * Dervert_list[ii][jj])\n Derlist_num.append(sub)\n\n # store reference circulation and normal induced velocities\n MS.get_normal_ind_velocities_at_collocation_points()\n Zeta0 = []\n Zeta0_star = []\n Vind0 = []\n N0 = []\n ZetaC0 = []\n for ss in range(n_surf):\n Zeta0.append(MS.Surfs[ss].zeta.copy())\n ZetaC0.append(MS.Surfs[ss].zetac.copy('F'))\n Zeta0_star.append(MS.Surfs_star[ss].zeta.copy())\n Vind0.append(MS.Surfs[ss].u_ind_coll_norm.copy())\n N0.append(MS.Surfs[ss].normals.copy())\n\n # calculate vis FDs\n Steps = [1e-6, ]\n step = Steps[0]\n\n ### loop input surfs\n for ss_in in range(n_surf):\n Surf_in = MS.Surfs[ss_in]\n Surf_star_in = MS.Surfs_star[ss_in]\n M_in, N_in = Surf_in.maps.M, Surf_in.maps.N\n\n # perturb\n for kk in range(3 * Surf_in.maps.Kzeta):\n cc, mm, nn = np.unravel_index(kk, (3, M_in + 1, N_in + 1))\n\n # perturb bound. vertices and collocation\n Surf_in.zeta = Zeta0[ss_in].copy()\n Surf_in.zeta[cc, mm, nn] += step\n Surf_in.generate_collocations()\n\n # perturb wake TE\n if mm == M_in:\n Surf_star_in.zeta = Zeta0_star[ss_in].copy()\n Surf_star_in.zeta[cc, 0, nn] += step\n\n ### prepare output surfaces\n # - ensure normals are unchanged\n # - del ind. vel on output to ensure they are re-computed\n for ss_out in range(n_surf):\n Surf_out = MS.Surfs[ss_out]\n Surf_out.normals = N0[ss_out].copy()\n del Surf_out.u_ind_coll_norm\n try:\n del Surf_out.u_ind_coll\n except AttributeError:\n pass\n\n ### recalculate\n MS.get_normal_ind_velocities_at_collocation_points()\n\n # restore\n Surf_in.zeta = Zeta0[ss_in].copy()\n Surf_in.zetac = ZetaC0[ss_in].copy('F')\n Surf_star_in.zeta = Zeta0_star[ss_in].copy()\n\n # estimate derivatives\n for ss_out in range(n_surf):\n Surf_out = MS.Surfs[ss_out]\n dvind = (Surf_out.u_ind_coll_norm - Vind0[ss_out]) / step\n Derlist_num[ss_out][ss_in][:, kk] = dvind.reshape(-1, order='C')\n\n ### check error\n for ss_out in range(n_surf):\n for ss_in in range(n_surf):\n Der_an = Dervert_list[ss_out][ss_in].copy()\n if ss_in == ss_out:\n Der_an = Der_an + Dercoll_list[ss_out]\n Der_num = Derlist_num[ss_out][ss_in]\n _, ErAbs, ErRel = max_error_tensor(Der_an, Der_num)\n\n # max absolute error\n ermax = np.max(ErAbs)\n # relative error at max abs error point\n iimax = np.unravel_index(np.argmax(ErAbs), ErAbs.shape)\n ermax_rel = ErRel[iimax]\n\n if self.print_info:\n print('Bound%.2d->Bound%.2d\\tFDstep\\tErrAbs\\tErrRel' % (ss_in, ss_out))\n print('\\t\\t\\t%.1e\\t%.1e\\t%.1e' % (step, ermax, ermax_rel))\n assert ermax < 50 * step and ermax_rel < 50 * step, embed() # 'Test failed!'\n\n # fig=plt.figure('Spy Er vs coll derivs',figsize=(12,4))\n\n # ax1=fig.add_subplot(131)\n # ax1.spy(ErAbs,precision=1e2*step)\n # ax1.set_title('error abs %d to %d' %(ss_in,ss_out))\n\n # ax2=fig.add_subplot(132)\n # ax2.spy(ErRel,precision=1e2*step)\n # ax2.set_title('error rel %d to %d' %(ss_in,ss_out))\n\n # ax3=fig.add_subplot(133)\n # ax3.spy(Dercoll_list[ss_out],precision=50*step)\n # ax3.set_title('Dcoll an. %d to %d' %(ss_out,ss_out))\n # #plt.show()\n # plt.close()\n\n def test_uc_dncdzeta(self, PlotFlag=False):\n\n if self.print_info:\n print('---------------------------------- Testing assembly.uc_dncdzeta')\n\n MS = self.MS\n n_surf = MS.n_surf\n\n MS.get_ind_velocities_at_collocation_points()\n MS.get_normal_ind_velocities_at_collocation_points()\n\n for ss in range(n_surf):\n if self.print_info:\n print('Surface %.2d:' % ss)\n Surf = MS.Surfs[ss]\n\n # generate non-zero field of external force\n Surf.u_ext[0, :, :] = Surf.u_ext[0, :, :] - 20.0\n Surf.u_ext[1, :, :] = Surf.u_ext[1, :, :] + 60.0\n Surf.u_ext[2, :, :] = Surf.u_ext[2, :, :] + 30.0\n Surf.u_ext = Surf.u_ext + np.random.rand(*Surf.u_ext.shape)\n\n ### analytical derivative\n # ind velocities computed already\n Surf.get_input_velocities_at_collocation_points()\n Der = assembly.uc_dncdzeta(Surf)\n\n ### numerical derivative\n # Surf.get_normal_input_velocities_at_collocation_points()\n u_tot0 = Surf.u_ind_coll + Surf.u_input_coll\n u_norm0 = Surf.project_coll_to_normal(u_tot0)\n u_norm0_vec = u_norm0.reshape(-1, order='C')\n zeta0 = Surf.zeta\n DerNum = np.zeros(Der.shape)\n\n Steps = np.array([1e-2, 1e-3, 1e-4, 1e-5, 1e-6])\n Er_max = 0.0 * Steps\n\n for ss in range(len(Steps)):\n step = Steps[ss]\n for jj in range(3 * Surf.maps.Kzeta):\n # perturb\n cc_pert = Surf.maps.ind_3d_vert_vect[0][jj]\n mm_pert = Surf.maps.ind_3d_vert_vect[1][jj]\n nn_pert = Surf.maps.ind_3d_vert_vect[2][jj]\n zeta_pert = zeta0.copy()\n zeta_pert[cc_pert, mm_pert, nn_pert] += step\n # calculate new normal velocity\n Surf_pert = surface.AeroGridSurface(Surf.maps, zeta=zeta_pert,\n u_ext=Surf.u_ext, gamma=Surf.gamma,\n vortex_radius=vortex_radius)\n u_norm = Surf_pert.project_coll_to_normal(u_tot0)\n u_norm_vec = u_norm.reshape(-1, order='C')\n # FD derivative\n DerNum[:, jj] = (u_norm_vec - u_norm0_vec) / step\n\n er_max = np.max(np.abs(Der - DerNum))\n if self.print_info:\n print('FD step: %.2e ---> Max error: %.2e' % (step, er_max))\n assert er_max < 5e1 * step, 'Error larger than 50 times step size'\n Er_max[ss] = er_max\n\n # assert error decreases with step size\n for ss in range(1, len(Steps)):\n assert Er_max[ss] < Er_max[ss - 1], \\\n 'Error not decreasing as FD step size is reduced'\n if self.print_info:\n print('------------------------------------------------------------ OK')\n\n if PlotFlag:\n pass\n # fig = plt.figure('Spy Der',figsize=(10,4))\n # ax1 = fig.add_subplot(121)\n # ax1.spy(Der,precision=step)\n # ax2 = fig.add_subplot(122)\n # ax2.spy(DerNum,precision=step)\n # plt.show()\n\n def test_nc_domegazetadzeta(self):\n \"\"\"\n Variation at colocation points due to geometrical variations at vertices\n Needs to be tested with a case that actually rotates\n \"\"\"\n\n if self.print_info:\n print('----------------------------- Testing assembly.test_nc_domegazetadzeta')\n\n MS = self.MS\n n_surf = MS.n_surf\n\n # analytical\n Dervert_list = assembly.nc_domegazetadzeta(MS.Surfs, MS.Surfs_star)\n\n # allocate numerical\n # Derlist_num=[]\n # for ii in range(n_surf):\n # sub=[]\n # for jj in range(n_surf):\n # sub.append(0.0*Dervert_list[ii][jj])\n # Derlist_num.append(sub)\n\n # Store the initial values of the variabes\n Zeta0 = []\n Zeta0_star = []\n N0 = []\n ZetaC0 = []\n for ss in range(n_surf):\n Zeta0.append(MS.Surfs[ss].zeta.copy())\n ZetaC0.append(MS.Surfs[ss].zetac.copy('F'))\n Zeta0_star.append(MS.Surfs_star[ss].zeta.copy())\n N0.append(MS.Surfs[ss].normals.copy())\n\n # Computation\n Steps = [1e-2, 1e-4, 1e-6]\n nsteps = len(Steps)\n error = np.zeros((nsteps,))\n for istep in range(nsteps):\n step = Steps[istep]\n for ss in range(n_surf):\n Surf = MS.Surfs[ss]\n Surf_star = MS.Surfs_star[ss]\n M, N = Surf.maps.M, Surf.maps.N\n\n perturb_vector = np.zeros(3 * Surf.maps.Kzeta)\n\n # PERTURBATION OF THE SURFACE\n for kk in range(3 * Surf.maps.Kzeta):\n # generate a random perturbation between the 90% and the 110% of the step\n perturb_vector[kk] += step * (0.2 * np.random.rand() + 0.9)\n cc, mm, nn = np.unravel_index(kk, (3, M + 1, N + 1))\n\n # perturb bound. vertices and collocation\n Surf.zeta = Zeta0[ss].copy()\n Surf.zeta[cc, mm, nn] += perturb_vector[kk]\n\n # perturb wake TE\n if mm == M:\n Surf_star.zeta = Zeta0_star[ss].copy()\n Surf_star.zeta[cc, 0, nn] += perturb_vector[kk]\n\n Surf.generate_collocations()\n\n # COMPUTE THE DERIVATIVES\n Der_an = np.zeros(Surf.maps.K)\n Der_an = np.dot(Dervert_list[ss], perturb_vector)\n Der_num = np.zeros(Surf.maps.K)\n ipanel = 0\n skew_omega = algebra.skew(Surf.omega)\n for mm in range(M):\n for nn in range(N):\n Der_num[ipanel] = (np.dot(N0[ss][:, mm, nn], np.dot(skew_omega, ZetaC0[ss][:, mm, nn])) -\n np.dot(N0[ss][:, mm, nn], np.dot(skew_omega, Surf.zetac[:, mm, nn])))\n ipanel += 1\n\n # COMPUTE THE ERROR\n error[istep] = np.maximum(error[istep], np.absolute(Der_num - Der_an).max())\n\n if self.print_info:\n print('FD step: %.2e ---> Max error: %.2e' % (step, error[istep]))\n assert error[istep] < 5e1 * step, 'Error larger than 50 times the step size'\n\n if istep > 0:\n assert error[istep] <= error[istep - 1], \\\n 'Error not decreasing as FD step size is reduced'\n\n if self.print_info:\n print('------------------------------------------------------------ OK')\n\n def test_dfqsdgamma_vrel0(self):\n\n if self.print_info:\n print('----------------------------- Testing assembly.dfqsdgamma_vrel0')\n\n MS = self.MS\n n_surf = MS.n_surf\n\n Der_list, Der_star_list = assembly.dfqsdgamma_vrel0(MS.Surfs, MS.Surfs_star)\n Er_max = []\n Er_max_star = []\n\n Steps = [1e-2, 1e-4, 1e-6, ]\n\n for ss in range(n_surf):\n\n Der_an = Der_list[ss]\n Der_star_an = Der_star_list[ss]\n\n Surf = MS.Surfs[ss]\n Surf_star = MS.Surfs_star[ss]\n M, N = Surf.maps.M, Surf.maps.N\n K = Surf.maps.K\n\n fqs0 = Surf.fqs.copy()\n gamma0 = Surf.gamma.copy()\n\n for step in Steps:\n Der_num = 0.0 * Der_an\n Der_star_num = 0.0 * Der_star_an\n\n ### Bound\n for pp in range(K):\n mm = Surf.maps.ind_2d_pan_scal[0][pp]\n nn = Surf.maps.ind_2d_pan_scal[1][pp]\n Surf.gamma = gamma0.copy()\n Surf.gamma[mm, nn] += step\n Surf.get_joukovski_qs(gammaw_TE=Surf_star.gamma[0, :])\n df = (Surf.fqs - fqs0) / step\n Der_num[:, pp] = df.reshape(-1, order='C')\n\n er_max = np.max(np.abs(Der_an - Der_num))\n if self.print_info:\n print('Surface %.2d - bound:' % ss)\n print('FD step: %.2e ---> Max error: %.2e' % (step, er_max))\n assert er_max < 5e1 * step, 'Error larger than 50 times step size'\n Er_max.append(er_max)\n\n ### Wake\n Surf.gamma = gamma0.copy()\n gammaw_TE0 = Surf_star.gamma[0, :].copy()\n M_star, N_star = Surf_star.maps.M, Surf_star.maps.N\n K_star = Surf_star.maps.K\n for nn in range(N):\n pp = np.ravel_multi_index((0, nn), (M_star, N_star))\n\n gammaw_TE = gammaw_TE0.copy()\n gammaw_TE[nn] += step\n Surf.get_joukovski_qs(gammaw_TE=gammaw_TE)\n df = (Surf.fqs - fqs0) / step\n Der_star_num[:, pp] = df.reshape(-1, order='C')\n\n er_max = np.max(np.abs(Der_star_an - Der_star_num))\n if self.print_info:\n print('Surface %.2d - wake:' % ss)\n print('FD step: %.2e ---> Max error: %.2e' % (step, er_max))\n assert er_max < 5e1 * step, 'Error larger than 50 times step size'\n Er_max_star.append(er_max)\n Surf.gamma = gamma0.copy()\n\n ### Warning: this test fails: the dependency on gamma is linear, hence\n # great accuracy is obtained even with large steps. In fact, reducing\n # the step quickly introduced round-off error.\n\n # # assert error decreases with step size\n # for ii in range(1,len(Steps)):\n # assert Er_max[ii] Max error: %.2e' % (step, er_max))\n assert er_max < 5e1 * step, 'Error larger than 50 times step size'\n Er_max.append(er_max)\n\n def test_dfqsdzeta_omega(self):\n \"\"\"\n Note: the get_joukovski_qs method re-computes the induced velocity\n at the panel segments. A copy of Surf is required to ensure that other\n tests are not affected.\n Needs to be tested with a case that actually rotates\n \"\"\"\n\n if self.print_info:\n print('------------------------------ Testing assembly.dfqsdzeta_omega')\n\n # rename\n MS = self.MS\n n_surf = MS.n_surf\n\n # Compute the anaytical derivative of the case\n Der_an_list = assembly.dfqsdzeta_omega(MS.Surfs, MS.Surfs_star)\n\n # Initialize\n Er_max = []\n\n # Define steps to run\n Steps = [1e-2, 1e-4, 1e-6, ]\n\n for ss in range(n_surf):\n # Select the surface with the analytica derivatives\n Der_an = Der_an_list[ss]\n\n # Copy to avoid modifying the original for other tests\n Surf = copy.deepcopy(MS.Surfs[ss])\n # Define variables\n M, N = Surf.maps.M, Surf.maps.N\n K = Surf.maps.K\n Kzeta = Surf.maps.Kzeta\n\n # Save the reference values at equilibrium\n fqs0 = Surf.fqs.copy()\n zeta0 = Surf.zeta.copy()\n u_input_seg0 = Surf.u_input_seg.copy()\n\n for step in Steps:\n # Initialize\n Der_num = 0.0 * Der_an\n\n # Loop through the different grid modifications (three directions per vertex point)\n for kk in range(3 * Kzeta):\n # Initialize to remove previous movements\n Surf.zeta = zeta0.copy()\n # Define DoFs where modifications will take place and modify the grid\n ind_3d = np.unravel_index(kk, (3, M + 1, N + 1))\n Surf.zeta[ind_3d] += step\n # Recompute get_ind_velocities_at_segments and recover the previous grid\n Surf.get_input_velocities_at_segments()\n Surf.zeta = zeta0.copy()\n # Compute new forces\n Surf.get_joukovski_qs(gammaw_TE=MS.Surfs_star[ss].gamma[0, :])\n df = (Surf.fqs - fqs0) / step\n Der_num[:, kk] = df.reshape(-1, order='C')\n\n er_max = np.max(np.abs(Der_an - Der_num))\n if self.print_info:\n print('Surface %.2d - bound:' % ss)\n print('FD step: %.2e ---> Max error: %.2e' % (step, er_max))\n assert er_max < 5e1 * step, 'Error larger than 50 times step size'\n Er_max.append(er_max)\n\n def test_dfqsduinput(self):\n \"\"\"\n Step change in input velocity is allocated to both u_ext and zeta_dot\n \"\"\"\n\n if self.print_info:\n print('---------------------------------- Testing assembly.dfqsduinput')\n\n MS = self.MS\n n_surf = MS.n_surf\n\n Der_list = assembly.dfqsduinput(MS.Surfs, MS.Surfs_star)\n Er_max = []\n\n Steps = [1e-2, 1e-4, 1e-6, ]\n\n for ss in range(n_surf):\n\n Der_an = Der_list[ss]\n\n # Surf=copy.deepcopy(MS.Surfs[ss])\n Surf = MS.Surfs[ss]\n # Surf_star=MS.Surfs_star[ss]\n M, N = Surf.maps.M, Surf.maps.N\n K = Surf.maps.K\n Kzeta = Surf.maps.Kzeta\n\n fqs0 = Surf.fqs.copy()\n u_ext0 = Surf.u_ext.copy()\n zeta_dot0 = Surf.zeta_dot.copy()\n\n for step in Steps:\n Der_num = 0.0 * Der_an\n\n for kk in range(3 * Kzeta):\n Surf.u_ext = u_ext0.copy()\n Surf.zeta_dot = zeta_dot0.copy()\n\n ind_3d = np.unravel_index(kk, (3, M + 1, N + 1))\n Surf.u_ext[ind_3d] += 0.5 * step\n Surf.zeta_dot[ind_3d] += -0.5 * step\n\n Surf.get_input_velocities_at_segments()\n Surf.get_joukovski_qs(gammaw_TE=MS.Surfs_star[ss].gamma[0, :])\n df = (Surf.fqs - fqs0) / step\n Der_num[:, kk] = df.reshape(-1, order='C')\n\n er_max = np.max(np.abs(Der_an - Der_num))\n if self.print_info:\n print('Surface %.2d - bound:' % ss)\n print('FD step: %.2e ---> Max error: %.2e' % (step, er_max))\n assert er_max < 5e1 * step, 'Error larger than 50 times step size'\n Er_max.append(er_max)\n\n def test_dfqsdvind_gamma(self):\n\n if self.print_info:\n print('------------------------------ Testing assembly.dfqsdvind_gamma')\n\n MS = self.MS\n n_surf = MS.n_surf\n\n # analytical\n Der_list, Der_star_list = assembly.dfqsdvind_gamma(MS.Surfs, MS.Surfs_star)\n\n # allocate numerical\n Der_list_num = []\n Der_star_list_num = []\n for ii in range(n_surf):\n sub = []\n sub_star = []\n for jj in range(n_surf):\n sub.append(0.0 * Der_list[ii][jj])\n sub_star.append(0.0 * Der_star_list[ii][jj])\n Der_list_num.append(sub)\n Der_star_list_num.append(sub_star)\n\n # store reference circulation and force\n Gamma0 = []\n Gammaw0 = []\n Fqs0 = []\n for ss in range(n_surf):\n Gamma0.append(MS.Surfs[ss].gamma.copy())\n Gammaw0.append(MS.Surfs_star[ss].gamma.copy())\n Fqs0.append(MS.Surfs[ss].fqs.copy())\n\n # calculate vis FDs\n # Steps=[1e-2,1e-4,1e-6,]\n Steps = [1e-5, ]\n step = Steps[0]\n\n ###### bound\n for ss_in in range(n_surf):\n Surf_in = MS.Surfs[ss_in]\n\n # perturb\n for pp in range(Surf_in.maps.K):\n mm = Surf_in.maps.ind_2d_pan_scal[0][pp]\n nn = Surf_in.maps.ind_2d_pan_scal[1][pp]\n Surf_in.gamma = Gamma0[ss_in].copy()\n Surf_in.gamma[mm, nn] += step\n\n # recalculate induced velocity everywhere\n MS.get_ind_velocities_at_segments(overwrite=True)\n # restore circulation: (include only induced velocity contrib.)\n Surf_in.gamma = Gamma0[ss_in].copy()\n\n # estimate derivatives\n for ss_out in range(n_surf):\n Surf_out = MS.Surfs[ss_out]\n fqs0 = Fqs0[ss_out].copy()\n Surf_out.get_joukovski_qs(\n gammaw_TE=MS.Surfs_star[ss_out].gamma[0, :])\n df = (Surf_out.fqs - fqs0) / step\n Der_list_num[ss_out][ss_in][:, pp] = df.reshape(-1, order='C')\n\n ###### wake\n for ss_in in range(n_surf):\n Surf_in = MS.Surfs_star[ss_in]\n\n # perturb\n for pp in range(Surf_in.maps.K):\n mm = Surf_in.maps.ind_2d_pan_scal[0][pp]\n nn = Surf_in.maps.ind_2d_pan_scal[1][pp]\n Surf_in.gamma = Gammaw0[ss_in].copy()\n Surf_in.gamma[mm, nn] += step\n\n # recalculate induced velocity everywhere\n MS.get_ind_velocities_at_segments(overwrite=True)\n # restore circulation: (include only induced velocity contrib.)\n Surf_in.gamma = Gammaw0[ss_in].copy()\n\n # estimate derivatives\n for ss_out in range(n_surf):\n Surf_out = MS.Surfs[ss_out]\n fqs0 = Fqs0[ss_out].copy()\n Surf_out.get_joukovski_qs(\n gammaw_TE=MS.Surfs_star[ss_out].gamma[0, :]) # <--- gammaw_0 needs to be used here!\n df = (Surf_out.fqs - fqs0) / step\n Der_star_list_num[ss_out][ss_in][:, pp] = df.reshape(-1, order='C')\n\n ### check error\n Er_max = []\n Er_max_star = []\n for ss_out in range(n_surf):\n for ss_in in range(n_surf):\n Der_an = Der_list[ss_out][ss_in]\n Der_num = Der_list_num[ss_out][ss_in]\n ErMat = Der_an - Der_num\n ermax = np.max(np.abs(ErMat))\n if self.print_info:\n print('Bound%.2d->Bound%.2d\\tFDstep\\tError' % (ss_in, ss_out))\n print('\\t\\t\\t%.1e\\t%.1e' % (step, ermax))\n assert ermax < 50 * step, 'Test failed!'\n\n Der_an = Der_star_list[ss_out][ss_in]\n Der_num = Der_star_list_num[ss_out][ss_in]\n ErMat = Der_an - Der_num\n ermax = np.max(np.abs(ErMat))\n if self.print_info:\n print('Wake%.2d->Bound%.2d\\tFDstep\\tError' % (ss_in, ss_out))\n print('\\t\\t\\t%.1e\\t%.1e' % (step, ermax))\n assert ermax < 50 * step, 'Test failed!'\n\n # fig = plt.figure('Spy Der',figsize=(10,4))\n # ax1 = fig.add_subplot(111)\n # ax1.spy(ErMat,precision=50*step)\n # plt.show()\n\n def test_dvinddzeta(self):\n \"\"\"\n For each output surface, there induced velocity is computed, all other\n surfaces are looped.\n For wakes, only TE is displaced.\n \"\"\"\n\n def comp_vind(zetac, MS):\n # comute induced velocity\n V = np.zeros((3,))\n for ss in range(n_surf):\n Surf_in = MS.Surfs[ss]\n Surf_star_in = MS.Surfs_star[ss]\n V += Surf_in.get_induced_velocity(zetac)\n V += Surf_star_in.get_induced_velocity(zetac)\n return V\n\n if self.print_info:\n print('----------------------------------- Testing assembly.dvinddzeta')\n\n MS = self.MS\n n_surf = MS.n_surf\n zetac = .5 * (MS.Surfs[0].zeta[:, 1, 2] + MS.Surfs[0].zeta[:, 1, 3])\n\n Dercoll = np.zeros((3, 3))\n Dervert_list = []\n for ss_in in range(n_surf):\n dcoll_b, dvert_b = assembly.dvinddzeta(zetac, MS.Surfs[ss_in], IsBound=True)\n dcoll_w, dvert_w = assembly.dvinddzeta(zetac, MS.Surfs_star[ss_in],\n IsBound=False, M_in_bound=MS.Surfs[ss_in].maps.M)\n Dercoll += dcoll_b + dcoll_w\n Dervert_list.append(dvert_b + dvert_w)\n\n # allocate numerical\n Dercoll_num = np.zeros((3, 3))\n Dervert_list_num = []\n for ii in range(n_surf):\n Dervert_list_num.append(0.0 * Dervert_list[ii])\n\n # store reference grid\n Zeta0 = []\n Zeta0_star = []\n for ss in range(n_surf):\n Zeta0.append(MS.Surfs[ss].zeta.copy())\n Zeta0_star.append(MS.Surfs_star[ss].zeta.copy())\n V0 = comp_vind(zetac, MS)\n\n # calculate vis FDs\n # Steps=[1e-2,1e-4,1e-6,]\n Steps = [1e-6, ]\n step = Steps[0]\n\n ### vertices\n for ss_in in range(n_surf):\n Surf_in = MS.Surfs[ss_in]\n Surf_star_in = MS.Surfs_star[ss_in]\n M_in, N_in = Surf_in.maps.M, Surf_in.maps.N\n\n # perturb\n for kk in range(3 * Surf_in.maps.Kzeta):\n cc, mm, nn = np.unravel_index(kk, (3, M_in + 1, N_in + 1))\n\n # perturb bound\n Surf_in.zeta = Zeta0[ss_in].copy()\n Surf_in.zeta[cc, mm, nn] += step\n # perturb wake TE\n if mm == M_in:\n Surf_star_in.zeta = Zeta0_star[ss_in].copy()\n Surf_star_in.zeta[cc, 0, nn] += step\n\n # recalculate induced velocity everywhere\n Vnum = comp_vind(zetac, MS)\n dv = (Vnum - V0) / step\n Dervert_list_num[ss_in][:, kk] = dv.reshape(-1, order='C')\n\n # restore\n Surf_in.zeta = Zeta0[ss_in].copy()\n if mm == M_in:\n Surf_star_in.zeta = Zeta0_star[ss_in].copy()\n\n ### check error at colloc\n Dercoll_num = np.zeros((3, 3))\n for cc in range(3):\n zetac_pert = zetac.copy()\n zetac_pert[cc] += step\n Vnum = comp_vind(zetac_pert, MS)\n Dercoll_num[:, cc] = (Vnum - V0) / step\n ercoll = np.max(np.abs(Dercoll - Dercoll_num))\n if self.print_info:\n print('Error coll.\\tFDstep\\tErrAbs')\n print('\\t\\t%.1e\\t%.1e' % (step, ercoll))\n # if ercoll>10*step: embed()\n assert ercoll < 10 * step, 'Error at collocation point'\n\n ### check error at vert\n for ss_in in range(n_surf):\n Der_an = Dervert_list[ss_in]\n Der_num = Dervert_list_num[ss_in]\n ermax, ErAbs, ErRel = max_error_tensor(Der_an, Der_num)\n\n # max absolute error\n ermax = np.max(ErAbs)\n # relative error at max abs error point\n iimax = np.unravel_index(np.argmax(ErAbs), ErAbs.shape)\n ermax_rel = ErRel[iimax]\n if self.print_info:\n print('Bound and wake%.2d\\tFDstep\\tErrAbs\\tErrRel' % ss_in)\n print('\\t\\t\\t%.1e\\t%.1e\\t%.1e' % (step, ermax, ermax_rel))\n assert ercoll < 10 * step, 'Error at vertices'\n\n # fig=plt.figure('Spy Er vs coll derivs',figsize=(12,4))\n # ax1=fig.add_subplot(121)\n # ax1.spy(ErAbs,precision=1e2*step)\n # ax1.set_title('error abs %d' %(ss_in))\n # ax2=fig.add_subplot(122)\n # ax2.spy(ErRel,precision=1e2*step)\n # ax2.set_title('error rel %d' %(ss_in))\n # #plt.show()\n # plt.close()\n\n def test_dfqsdvind_zeta(self):\n \"\"\"\n For each output surface, there induced velocity is computed, all other\n surfaces are looped.\n For wakes, only TE is displaced.\n \"\"\"\n\n if self.print_info:\n print('------------------------------- Testing assembly.dfqsdvind_zeta')\n\n MS = self.MS\n n_surf = MS.n_surf\n\n # analytical\n Dercoll_list, Dervert_list = assembly.dfqsdvind_zeta(MS.Surfs, MS.Surfs_star)\n\n # allocate numerical\n Derlist_num = []\n for ii in range(n_surf):\n sub = []\n for jj in range(n_surf):\n sub.append(0.0 * Dervert_list[ii][jj])\n Derlist_num.append(sub)\n\n # store reference circulation and force\n Zeta0 = []\n Zeta0_star = []\n Fqs0 = []\n for ss in range(n_surf):\n Zeta0.append(MS.Surfs[ss].zeta.copy())\n Zeta0_star.append(MS.Surfs_star[ss].zeta.copy())\n Fqs0.append(MS.Surfs[ss].fqs.copy())\n\n # calculate vis FDs\n # Steps=[1e-2,1e-4,1e-6,]\n Steps = [1e-6, ]\n step = Steps[0]\n\n ### loop input surfs\n for ss_in in range(n_surf):\n Surf_in = MS.Surfs[ss_in]\n Surf_star_in = MS.Surfs_star[ss_in]\n M_in, N_in = Surf_in.maps.M, Surf_in.maps.N\n\n # perturb\n for kk in range(3 * Surf_in.maps.Kzeta):\n cc, mm, nn = np.unravel_index(kk, (3, M_in + 1, N_in + 1))\n\n # perturb bound\n Surf_in.zeta = Zeta0[ss_in].copy()\n Surf_in.zeta[cc, mm, nn] += step\n # perturb wake TE\n if mm == M_in:\n Surf_star_in.zeta = Zeta0_star[ss_in].copy()\n Surf_star_in.zeta[cc, 0, nn] += step\n\n # recalculate induced velocity everywhere\n MS.get_ind_velocities_at_segments(overwrite=True)\n # restore zeta: (include only induced velocity contrib.)\n Surf_in.zeta = Zeta0[ss_in].copy()\n Surf_star_in.zeta = Zeta0_star[ss_in].copy()\n # estimate derivatives\n for ss_out in range(n_surf):\n Surf_out = MS.Surfs[ss_out]\n fqs0 = Fqs0[ss_out].copy()\n Surf_out.get_joukovski_qs(\n gammaw_TE=MS.Surfs_star[ss_out].gamma[0, :])\n df = (Surf_out.fqs - fqs0) / step\n Derlist_num[ss_out][ss_in][:, kk] = df.reshape(-1, order='C')\n\n ### check error\n for ss_out in range(n_surf):\n for ss_in in range(n_surf):\n Der_an = Dervert_list[ss_out][ss_in].copy()\n if ss_in == ss_out:\n Der_an = Der_an + Dercoll_list[ss_out]\n Der_num = Derlist_num[ss_out][ss_in]\n ermax, ErAbs, ErRel = max_error_tensor(Der_an, Der_num)\n\n # max absolute error\n ermax = np.max(ErAbs)\n # relative error at max abs error point\n iimax = np.unravel_index(np.argmax(ErAbs), ErAbs.shape)\n ermax_rel = ErRel[iimax]\n\n if self.print_info:\n print('Bound%.2d->Bound%.2d\\tFDstep\\tErrAbs\\tErrRel' % (ss_in, ss_out))\n print('\\t\\t\\t%.1e\\t%.1e\\t%.1e' % (step, ermax, ermax_rel))\n assert ermax < 5e2 * step and ermax_rel < 50 * step, 'Test failed!'\n\n # fig=plt.figure('Spy Er vs coll derivs',figsize=(12,4))\n\n # ax1=fig.add_subplot(131)\n # ax1.spy(ErAbs,precision=1e2*step)\n # ax1.set_title('error abs %d to %d' %(ss_in,ss_out))\n\n # ax2=fig.add_subplot(132)\n # ax2.spy(ErRel,precision=1e2*step)\n # ax2.set_title('error rel %d to %d' %(ss_in,ss_out))\n\n # ax3=fig.add_subplot(133)\n # ax3.spy(Dercoll_list[ss_out],precision=50*step)\n # ax3.set_title('Dcoll an. %d to %d' %(ss_out,ss_out))\n # #plt.show()\n # plt.close()\n\n def test_dfunstdgamma_dot(self):\n \"\"\"\n Test derivative of unsteady aerodynamic force with respect to changes in\n panel circulation.\n\n Warning: test assumes the derivative of the unsteady force only depends on\n Gamma_dot, which is true only for steady-state linearisation points\n \"\"\"\n\n MS = self.MS\n Ders_an = assembly.dfunstdgamma_dot(MS.Surfs)\n\n step = 1e-6\n Ders_num = []\n n_surf = len(MS.Surfs)\n for ss in range(n_surf):\n\n Surf = MS.Surfs[ss]\n Kzeta, K = Surf.maps.Kzeta, Surf.maps.K\n M, N = Surf.maps.M, Surf.maps.N\n\n Dnum = np.zeros((3 * Kzeta, K))\n\n # get refernce values\n Surf.get_joukovski_unsteady()\n Gamma_dot0 = Surf.gamma_dot.copy()\n F0 = Surf.funst.copy()\n\n for pp in range(K):\n mm, nn = np.unravel_index(pp, (M, N))\n\n Surf.gamma_dot = Gamma_dot0.copy()\n Surf.gamma_dot[mm, nn] += step\n Surf.get_joukovski_unsteady()\n\n dF = (Surf.funst - F0) / step\n Dnum[:, pp] = dF.reshape(-1)\n\n # restore\n Surf.gamma_dot = Gamma_dot0.copy()\n\n ### verify\n ermax, ErAbs, ErRel = max_error_tensor(Ders_an[ss], Dnum)\n\n # max absolute error\n ermax = np.max(ErAbs)\n # relative error at max abs error point\n iimax = np.unravel_index(np.argmax(ErAbs), ErAbs.shape)\n ermax_rel = ErRel[iimax]\n\n if self.print_info:\n print('Bound%.2d\\t\\t\\tFDstep\\tErrAbs\\tErrRel' % (ss,))\n print('\\t\\t\\t%.1e\\t%.1e\\t%.1e' % (step, ermax, ermax_rel))\n assert ermax < 5e2 * step and ermax_rel < 50 * step, 'Test failed!'\n\n def test_wake_prop(self):\n\n self.start_writer()\n MS = self.MS\n C_list, Cstar_list = assembly.wake_prop(MS)\n\n n_surf = len(MS.Surfs)\n for ss in range(n_surf):\n Surf = MS.Surfs[ss]\n Surf_star = MS.Surfs_star[ss]\n N = Surf.maps.N\n K_star = Surf_star.maps.K\n C = C_list[ss]\n Cstar = Cstar_list[ss]\n\n # add noise to circulations\n gamma = Surf.gamma + np.random.rand(*Surf.gamma.shape)\n gamma_star = Surf_star.gamma + np.random.rand(*Surf_star.gamma.shape)\n\n gvec = np.dot(C, gamma.reshape(-1)) + np.dot(Cstar, gamma_star.reshape(-1))\n\n gvec_ref = np.concatenate((gamma[-1, :], gamma_star[:-1, :].reshape(-1)))\n\n assert np.max(np.abs(gvec - gvec_ref)) < 1e-15, \\\n 'Prop. from trailing edge not correct'\n\n\n def start_writer(self):\n # Over write writer with print_file False to avoid I/O errors\n global cout_wrap\n cout_wrap = cout.Writer()\n # cout_wrap.initialise(print_screen=False, print_file=False)\n cout_wrap.cout_quiet()\n sharpy.utils.cout_utils.cout_wrap = cout_wrap\n\n\n def tearDown(self):\n cout.finish_writer()\n\n\nif __name__ == '__main__':\n unittest.main()\n" }, { "path": "tests/linear/control_surfaces/__init__.py", "content": "" }, { "path": "tests/linear/control_surfaces/test_control_surfaces.py", "content": "import numpy as np\nimport os\nimport unittest\nimport sharpy.cases.templates.flying_wings as wings\nimport sharpy.sharpy_main\nimport pickle\n\n\n# @unittest.skip('Control Surface Test for visual inspection')\nclass TestGolandControlSurface(unittest.TestCase):\n\n\n def setup(self):\n self.deflection_degrees = 5\n # Problem Set up\n u_inf = 1.\n alpha_deg = 0.\n rho = 1.02\n num_modes = 2\n\n # Lattice Discretisation\n M = 4\n N = 16\n M_star_fact = 1\n\n # Linear UVLM settings\n integration_order = 2\n remove_predictor = False\n use_sparse = True\n\n # Case Admin - Create results folders\n case_name = 'goland_cs'\n case_nlin_info = 'M%dN%dMs%d_nmodes%d' % (M, N, M_star_fact, num_modes)\n\n case_name += case_nlin_info\n\n self.route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n fig_folder = self.route_test_dir + '/figures/'\n os.makedirs(fig_folder, exist_ok=True)\n\n # SHARPy nonlinear reference solution\n ws = wings.GolandControlSurface(M=M,\n N=N,\n Mstar_fact=M_star_fact,\n u_inf=u_inf,\n alpha=alpha_deg,\n cs_deflection=[0, 0],\n rho=rho,\n sweep=0,\n physical_time=2,\n n_surfaces=2,\n route=self.route_test_dir + '/cases',\n case_name=case_name)\n\n ws.gust_intensity = 0.01\n ws.sigma = 1\n\n ws.clean_test_files()\n ws.update_derived_params()\n ws.set_default_config_dict()\n\n # Full moving control surface on the right wing\n ws.control_surface_chord[0] = M\n ws.control_surface_hinge_coord[0] = 0.5\n ws.control_surface[4, :] = 1\n\n ws.generate_aero_file()\n ws.generate_fem_file()\n\n x0 = np.zeros(256)\n lin_tsteps = 10\n u_vec = np.zeros((lin_tsteps, 8))\n # elevator\n u_vec[:, 4] = self.deflection_degrees * np.pi / 180\n np.savetxt(self.route_test_dir + '/cases/elevator.txt', u_vec[:, 4])\n ws.create_linear_files(x0, u_vec)\n\n ws.config['SHARPy'] = {\n 'flow':\n ['BeamLoader', 'AerogridLoader',\n 'StaticCoupled',\n 'AerogridPlot',\n 'BeamPlot',\n 'Modal',\n 'LinearAssembler',\n # 'FrequencyResponse',\n 'LinDynamicSim',\n 'PickleData',\n ],\n 'case': ws.case_name, 'route': ws.route,\n 'write_screen': 'off', 'write_log': 'on',\n 'log_folder': self.route_test_dir + '/output/' + ws.case_name + '/',\n 'log_file': ws.case_name + '.log'}\n\n ws.config['BeamLoader'] = {\n 'unsteady': 'off',\n 'orientation': ws.quat}\n\n ws.config['AerogridLoader'] = {\n 'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': ws.Mstar_fact * ws.M,\n 'freestream_dir': ws.u_inf_direction,\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction,\n 'dt': ws.dt}}\n\n ws.config['StaticUvlm'] = {\n 'rho': ws.rho,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction},\n 'rollup_dt': ws.dt,\n 'print_info': 'on',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_aic_refresh': 0,\n 'rollup_tolerance': 1e-4}\n\n ws.config['StaticCoupled'] = {\n 'print_info': 'on',\n 'max_iter': 200,\n 'n_load_steps': 1,\n 'tolerance': 1e-10,\n 'relaxation_factor': 0.,\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {\n 'rho': ws.rho,\n 'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': ws.dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction}},\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 4,\n 'delta_curved': 1e-1,\n 'min_delta': 1e-10,\n 'gravity_on': 'on',\n 'gravity': 9.81}}\n\n ws.config['AerogridPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}\n\n ws.config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': ws.case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n 'unsteady': 'off'}\n\n ws.config['BeamPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on'}\n\n ws.config['Modal'] = {'NumLambda': 20,\n 'rigid_body_modes': 'off',\n 'print_matrices': 'on',\n 'save_data': 'off',\n 'rigid_modes_cg': 'off',\n 'continuous_eigenvalues': 'off',\n 'dt': 0,\n 'plot_eigenvalues': False,\n 'max_rotation_deg': 15.,\n 'max_displacement': 0.15,\n 'write_modes_vtk': True,\n 'use_undamped_modes': True}\n\n ws.config['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n 'linear_system_settings': {\n 'beam_settings': {'modal_projection': 'on',\n 'inout_coords': 'modes',\n 'discrete_time': 'on',\n 'newmark_damp': 0.5e-4,\n 'discr_method': 'newmark',\n 'dt': ws.dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'off',\n 'num_modes': num_modes,\n 'print_info': 'on',\n 'gravity': 'on',\n 'remove_sym_modes': 'on',\n 'remove_dofs': []},\n 'aero_settings': {'dt': ws.dt,\n 'integr_order': integration_order,\n 'density': ws.rho,\n 'remove_predictor': remove_predictor,\n 'use_sparse': use_sparse,\n 'remove_inputs': ['u_gust']},\n }\n }\n\n ws.config['LinDynamicSim'] = {'n_tsteps': lin_tsteps,\n 'dt': ws.dt,\n 'input_generators': [{'name': 'control_surface_deflection',\n 'index': 0,\n 'file_path': self.route_test_dir + '/cases/elevator.txt'},\n {'name': 'control_surface_deflection',\n 'index': 1,\n 'file_path': self.route_test_dir + '/cases/elevator.txt'}],\n 'postprocessors': ['AerogridPlot'],\n 'postprocessors_settings':\n {'AerogridPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}, }\n }\n\n ws.config['PickleData'] = {}\n\n ws.config.write()\n\n restart = False # useful for debugging to load pickle\n if not restart:\n self.data = sharpy.sharpy_main.main(['', ws.route + ws.case_name + '.sharpy'])\n else:\n with open(self.route_test_dir + '/output/' + ws.case_name + '.pkl', 'rb') as f:\n self.data = pickle.load(f)\n\n def test_control_surface(self):\n self.setup()\n\n for i_surf in range(2):\n with self.subTest(i_surf=i_surf):\n zeta = self.data.aero.timestep_info[-1].zeta[i_surf]\n zeta0 = self.data.linear.tsaero0.zeta[i_surf]\n\n # zeta indices [(xyz), chord, span]\n if i_surf == 0:\n # Full moving control surface with hinge at c=0.5\n zeta_elev = zeta[:, -1, -1] - zeta[:, 0, -1] # elevator starts at chordwise node 0\n zeta_0elev = zeta0[:, -1, -1] - zeta0[:, 0, -1]\n elif i_surf == 1:\n # mirrored surface. span index 0 is the wing tip\n zeta_elev = zeta[:, -1, 0] - zeta[:, 2, 0] # elevator starts at chordwise node 2\n zeta_0elev = zeta0[:, -1, 0] - zeta0[:, 2, 0]\n\n deflection = np.arccos((zeta_elev.dot(zeta_0elev)) / np.linalg.norm(zeta_elev) / np.linalg.norm(zeta_0elev))\n\n deflection_actual_deg = deflection * 180 / np.pi\n np.testing.assert_array_almost_equal(self.deflection_degrees, deflection_actual_deg,\n decimal=2)\n\n def tearDown(self):\n import shutil\n folders = ['cases', 'figures', 'output']\n for folder in folders:\n shutil.rmtree(self.route_test_dir + '/' + folder)\n\n\nif __name__ == '__main__':\n unittest.main()\n" }, { "path": "tests/linear/derivatives/__init__.py", "content": "" }, { "path": "tests/linear/derivatives/test_ders.py", "content": "\"\"\"\nTest elementary derivative methods\nS. Maraniello, 4 Jun 2018\n\"\"\"\n\nimport numpy as np\nimport unittest\n\nimport sharpy.aero.utils.uvlmlib\nimport sharpy.linear.src.lib_dbiot as dbiot\nimport sharpy.linear.src.uvlmutils as uvlmutils\n\n\nvortex_radius = 1e-6\n\n\nclass Test_ders(unittest.TestCase):\n \"\"\"\n Test methods into assembly module\n \"\"\"\n print_info = False # useful for debugging. Leave False to keep test log clean\n\n def setUp(self):\n\n self.zetaP = np.array([3.0, 5.5, 2.0])\n self.zeta0 = np.array([1.0, 3.0, 0.9])\n self.zeta1 = np.array([5.0, 3.1, 1.9])\n self.zeta2 = np.array([4.8, 8.1, 2.5])\n self.zeta3 = np.array([0.9, 7.9, 1.7])\n\n def test_dbiot_segment(self):\n if self.print_info:\n print('\\n-------------------------------------- Testing dbiot.eval_seg')\n\n gamma = 2.4\n zetaP = self.zetaP\n zetaA = self.zeta1\n zetaB = self.zeta2\n Q0 = uvlmutils.biot_segment(zetaP, zetaA, zetaB, vortex_radius, gamma)\n\n ### compare different analytical derivative\n DerP_an, DerA_an, DerB_an = dbiot.eval_seg_exp(zetaP, zetaA, zetaB,\n vortex_radius, gamma)\n DerP_an2, DerA_an2, DerB_an2 = dbiot.eval_seg_comp(zetaP, zetaA, zetaB,\n vortex_radius, gamma)\n er_max = max(np.max(np.abs(DerP_an2 - DerP_an)),\n np.max(np.abs(DerA_an2 - DerA_an)),\n np.max(np.abs(DerB_an2 - DerB_an)))\n assert er_max < 1e-16, 'Analytical models not matching'\n\n ### compare vs numerical derivative\n Steps = np.linspace(vortex_radius * 0.99, vortex_radius * 1e-2, 4)\n Er_max = 0.0 * Steps\n for ss in range(len(Steps)):\n step = Steps[ss]\n DerP_num = 0.0 * DerP_an\n DerA_num = 0.0 * DerA_an\n DerB_num = 0.0 * DerB_an\n for cc_zeta in range(3):\n dzeta = np.zeros((3,))\n dzeta[cc_zeta] = step\n DerP_num[:, cc_zeta] = (\n uvlmutils.biot_segment(zetaP + dzeta, zetaA, zetaB, vortex_radius, gamma) - Q0) / step\n DerA_num[:, cc_zeta] = (\n uvlmutils.biot_segment(zetaP, zetaA + dzeta, zetaB, vortex_radius, gamma) - Q0) / step\n DerB_num[:, cc_zeta] = (\n uvlmutils.biot_segment(zetaP, zetaA, zetaB + dzeta, vortex_radius, gamma) - Q0) / step\n er_max = max(np.max(np.abs(DerP_num - DerP_an)),\n np.max(np.abs(DerA_num - DerA_an)),\n np.max(np.abs(DerB_num - DerB_an)))\n if self.print_info:\n print('FD step: %.2e ---> Max error: %.2e' % (step, er_max))\n assert er_max < 5e1 * step, 'Error larger than 50 times step size'\n Er_max[ss] = er_max\n\n def test_dbiot_segment_mid(self):\n if self.print_info:\n print('\\n------------------------- Testing dbiot.eval_seg at mid-point')\n\n gamma = 2.4\n zetaA = self.zeta1\n zetaB = self.zeta2\n zetaP = .3 * zetaA + 0.7 * zetaB\n\n Q0 = uvlmutils.biot_segment(zetaP, zetaA, zetaB, vortex_radius, gamma)\n\n ### compare different analytical derivative\n DerP_an, DerA_an, DerB_an = dbiot.eval_seg_exp(zetaP, zetaA, zetaB, vortex_radius, gamma)\n DerP_an2, DerA_an2, DerB_an2 = dbiot.eval_seg_comp(zetaP, zetaA, zetaB, gamma)\n er_max = max(np.max(np.abs(DerP_an2 - DerP_an)),\n np.max(np.abs(DerA_an2 - DerA_an)),\n np.max(np.abs(DerB_an2 - DerB_an)))\n assert er_max < 1e-16, 'Analytical models not matching'\n\n ### compare vs numerical derivative\n # first step must be smaller than vortex radius\n Steps = np.linspace(vortex_radius * 0.99, vortex_radius * 1e-2, 4)\n Er_max = 0.0 * Steps\n for ss in range(len(Steps)):\n step = Steps[ss]\n DerP_num = 0.0 * DerP_an\n DerA_num = 0.0 * DerA_an\n DerB_num = 0.0 * DerB_an\n for cc_zeta in range(3):\n dzeta = np.zeros((3,))\n dzeta[cc_zeta] = step\n DerP_num[:, cc_zeta] = (\n uvlmutils.biot_segment(zetaP + dzeta, zetaA, zetaB, vortex_radius, gamma) - Q0) / step\n DerA_num[:, cc_zeta] = (\n uvlmutils.biot_segment(zetaP, zetaA + dzeta, zetaB, vortex_radius, gamma) - Q0) / step\n DerB_num[:, cc_zeta] = (\n uvlmutils.biot_segment(zetaP, zetaA, zetaB + dzeta, vortex_radius, gamma) - Q0) / step\n er_max = max(np.max(np.abs(DerP_num - DerP_an)),\n np.max(np.abs(DerA_num - DerA_an)),\n np.max(np.abs(DerB_num - DerB_an)))\n\n if self.print_info:\n print('FD step: %.2e ---> Max error: %.2e' % (step, er_max))\n assert er_max < 5e1 * step, 'Error larger than 50 times step size'\n Er_max[ss] = er_max\n\n def test_dbiot_panel(self):\n if self.print_info:\n print('\\n---------------------------------- Testing dbiot.eval_panel_*')\n\n gamma = 2.4\n zetaP = self.zetaP\n zeta0 = self.zeta0\n zeta1 = self.zeta1\n zeta2 = self.zeta2\n zeta3 = self.zeta3\n\n ZetaPanel = np.array([zeta0, zeta1, zeta2, zeta3])\n Q0 = uvlmutils.biot_panel(zetaP, ZetaPanel, vortex_radius, gamma)\n\n # compare analytical derivatives models\n DerP_an, DerVer_an = dbiot.eval_panel_exp(zetaP, ZetaPanel,\n vortex_radius, gamma)\n DerP_an2, DerVer_an2 = dbiot.eval_panel_comp(zetaP, ZetaPanel,\n vortex_radius, gamma)\n DerP_an3, DerVer_an3 = dbiot.eval_panel_fast(zetaP, ZetaPanel,\n vortex_radius, gamma)\n DerP_an4, DerVer_an4 = sharpy.aero.utils.uvlmlib.eval_panel_cpp(zetaP, ZetaPanel,\n vortex_radius,\n gamma)\n\n er_max = max(np.max(np.abs(DerP_an2 - DerP_an)),\n np.max(np.abs(DerVer_an2 - DerVer_an)))\n assert er_max < 1e-16, 'eval_panel_comp not matching with eval_panel_exp'\n er_max = max(np.max(np.abs(DerP_an3 - DerP_an)),\n np.max(np.abs(DerVer_an3 - DerVer_an)))\n assert er_max < 1e-16, 'eval_panel_fast not matching with eval_panel_exp'\n er_max = max(np.max(np.abs(DerP_an4 - DerP_an)),\n np.max(np.abs(DerVer_an4 - DerVer_an)))\n assert er_max < 1e-16, 'eval_panel_cpp not matching with eval_panel_exp'\n\n # compare vs. numerical derivative\n Steps = np.linspace(vortex_radius * 0.99, vortex_radius * 1e-2, 4)\n ErP_max = 0.0 * Steps\n ErVer_max = 0.0 * Steps\n for ss in range(len(Steps)):\n step = Steps[ss]\n DerP_num = 0.0 * DerP_an\n DerVer_num = 0.0 * DerVer_an\n\n ### Perturb component\n for cc in range(3):\n dzeta = np.zeros((3,))\n dzeta[cc] = step\n\n # derivative w.r.t. target point\n DerP_num[:, cc] = \\\n (uvlmutils.biot_panel(zetaP + dzeta, ZetaPanel, vortex_radius, gamma) - Q0) / step\n\n # derivative w.r.t panel vertices\n for vv in range(4):\n ZetaPanel_pert = ZetaPanel.copy()\n ZetaPanel_pert[vv, :] += dzeta\n DerVer_num[vv, :, cc] = \\\n (uvlmutils.biot_panel(zetaP, ZetaPanel_pert, vortex_radius, gamma) - Q0) / step\n\n erP_max = np.max(np.abs(DerP_num - DerP_an))\n erVer_max = np.max(np.abs(DerVer_num - DerVer_an))\n\n if self.print_info:\n print('FD step: %.2e ---> Max error (P,Vert): (%.2e,%.2e)' \\\n % (step, erP_max, erVer_max))\n assert erP_max < 5e1 * step, \\\n 'Error w.r.t. zetaP larger than 50 times step size'\n assert erVer_max < 5e1 * step, \\\n 'Error w.r.t. ZetaPanel larger than 50 times step size'\n ErP_max[ss] = erP_max\n ErVer_max[ss] = erVer_max\n\n # assert monothony\n for ss in range(len(Steps) - 1):\n assert ErP_max[ss + 1] < ErP_max[ss], \\\n 'Error of derivative w.r.t. zetaP not decreasing monothonically'\n assert ErVer_max[ss + 1] < ErVer_max[ss], \\\n 'Error of derivative w.r.t. ZetaPanel not decreasing monothonically'\n\n def test_dbiot_panel_mid_segment(self):\n\n if self.print_info:\n print('\\n-------------- Testing dbiot.eval_panel with zetaP on segment')\n\n gamma = 2.4\n zeta0 = self.zeta0\n zeta1 = self.zeta1\n zeta2 = self.zeta2\n zeta3 = self.zeta3\n zetaP = 0.3 * zeta1 + 0.7 * zeta2\n\n ZetaPanel = np.array([zeta0, zeta1, zeta2, zeta3])\n Q0 = uvlmutils.biot_panel(zetaP, ZetaPanel, vortex_radius, gamma)\n\n # compare analytical derivatives models\n DerP_an, DerVer_an = dbiot.eval_panel_exp(zetaP, ZetaPanel,\n vortex_radius, gamma)\n DerP_an2, DerVer_an2 = dbiot.eval_panel_comp(zetaP, ZetaPanel,\n vortex_radius, gamma)\n DerP_an3, DerVer_an3 = dbiot.eval_panel_fast(zetaP, ZetaPanel,\n vortex_radius, gamma)\n DerP_an4, DerVer_an4 = sharpy.aero.utils.uvlmlib.eval_panel_cpp(zetaP, ZetaPanel,\n vortex_radius,\n gamma)\n\n er_max = max(np.max(np.abs(DerP_an2 - DerP_an)),\n np.max(np.abs(DerVer_an2 - DerVer_an)))\n assert er_max < 1e-16, 'eval_panel_comp not matching with eval_panel_exp'\n er_max = max(np.max(np.abs(DerP_an3 - DerP_an)),\n np.max(np.abs(DerVer_an3 - DerVer_an)))\n assert er_max < 1e-16, 'eval_panel_fast not matching with eval_panel_exp'\n er_max = max(np.max(np.abs(DerP_an4 - DerP_an)),\n np.max(np.abs(DerVer_an4 - DerVer_an)))\n assert er_max < 1e-16, 'eval_panel_cpp not matching with eval_panel_exp'\n\n # compare vs. numerical derivative\n # first step must be smaller than vortex radius\n Steps = np.linspace(vortex_radius * 0.99, vortex_radius * 1e-2, 4)\n ErP_max = 0.0 * Steps\n ErVer_max = 0.0 * Steps\n for ss in range(len(Steps)):\n step = Steps[ss]\n DerP_num = 0.0 * DerP_an\n DerVer_num = 0.0 * DerVer_an\n\n ### Perturb component\n for cc in range(3):\n dzeta = np.zeros((3,))\n dzeta[cc] = step\n\n # derivative w.r.t. target point\n DerP_num[:, cc] = \\\n (uvlmutils.biot_panel(zetaP + dzeta, ZetaPanel, vortex_radius, gamma) - Q0) / step\n\n # derivative w.r.t panel vertices\n for vv in range(4):\n ZetaPanel_pert = ZetaPanel.copy()\n ZetaPanel_pert[vv, :] += dzeta\n DerVer_num[vv, :, cc] = \\\n (uvlmutils.biot_panel(zetaP, ZetaPanel_pert, vortex_radius, gamma) - Q0) / step\n\n erP_max = np.max(np.abs(DerP_num - DerP_an))\n erVer_max = np.max(np.abs(DerVer_num - DerVer_an))\n\n if self.print_info:\n print('FD step: %.2e ---> Max error (P,Vert): (%.2e,%.2e)' \\\n % (step, erP_max, erVer_max))\n assert erP_max < 5e1 * step, \\\n 'Error w.r.t. zetaP larger than 50 times step size'\n assert erVer_max < 5e1 * step, \\\n 'Error w.r.t. ZetaPanel larger than 50 times step size'\n ErP_max[ss] = erP_max\n ErVer_max[ss] = erVer_max\n\n # assert monothony\n for ss in range(len(Steps) - 1):\n assert ErP_max[ss + 1] < ErP_max[ss], \\\n 'Error of derivative w.r.t. zetaP not decreasing monothonically'\n assert ErVer_max[ss + 1] < ErVer_max[ss], \\\n 'Error of derivative w.r.t. ZetaPanel not decreasing monothonically'\n" }, { "path": "tests/linear/derivatives/test_stabilityderivatives.py", "content": "import numpy as np\nimport os\nimport unittest\nimport sharpy.cases.templates.flying_wings as wings\nimport sharpy.sharpy_main\nimport h5py\nimport sharpy.utils.h5utils as h5utils\nimport sharpy.utils.algebra as algebra\nimport sharpy.linear.src.libss as libss\n\n\nclass TestLinearDerivatives(unittest.TestCase):\n\n print_info = False\n\n def run_sharpy(self, alpha_deg, flow, target_system, not_run=False):\n # Problem Set up\n u_inf = 10.\n rho = 1.02\n num_modes = 4\n\n # Lattice Discretisation\n M = 4\n N = 4\n M_star_fact = 10\n\n # Linear UVLM settings\n integration_order = 2\n remove_predictor = False\n use_sparse = True\n\n # ROM Properties\n rom_settings = dict()\n rom_settings['algorithm'] = 'mimo_rational_arnoldi'\n rom_settings['r'] = 6\n rom_settings['single_side'] = 'observability'\n frequency_continuous_k = np.array([0.])\n\n # Case Admin - Create results folders\n case_name = 'wing'\n if target_system == 'aerodynamic':\n case_name += '_uvlm'\n elif target_system == 'aeroelastic':\n case_name += '_coupled'\n else:\n NameError('Unrecognised system')\n\n case_nlin_info = '_uinf{:04g}_a{:04g}'.format(u_inf*10, alpha_deg*100)\n case_name += case_nlin_info\n\n self.route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n\n # SHARPy nonlinear reference solution\n ws = wings.QuasiInfinite(M=M,\n aspect_ratio=10,\n N=N,\n Mstar_fact=M_star_fact,\n u_inf=u_inf,\n alpha=alpha_deg,\n rho=rho,\n sweep=0,\n n_surfaces=2,\n route=self.route_test_dir + '/cases',\n case_name=case_name)\n\n ws.gust_intensity = 0.01\n ws.sigma = 1e-1\n\n ws.clean_test_files()\n ws.update_derived_params()\n ws.set_default_config_dict()\n\n ws.generate_aero_file()\n ws.generate_fem_file()\n\n frequency_continuous_w = 2 * u_inf * frequency_continuous_k / ws.c_ref\n rom_settings['frequency'] = frequency_continuous_w\n\n ws.config['SHARPy'] = {\n 'flow': flow,\n 'case': ws.case_name, 'route': ws.route,\n 'write_screen': 'off', 'write_log': 'on',\n 'log_folder': self.route_test_dir + '/output/',\n 'log_file': ws.case_name + '.log'}\n\n ws.config['BeamLoader'] = {\n 'unsteady': 'off',\n 'orientation': ws.quat}\n\n ws.config['AerogridLoader'] = {\n 'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': ws.Mstar_fact * ws.M,\n 'freestream_dir': ws.u_inf_direction,\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction,\n 'dt': ws.dt}}\n\n ws.config['StaticUvlm'] = {\n 'rho': ws.rho,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction},\n 'rollup_dt': ws.dt,\n 'print_info': 'on',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_aic_refresh': 0,\n 'rollup_tolerance': 1e-4}\n\n ws.config['StaticCoupled'] = {\n 'print_info': 'on',\n 'max_iter': 200,\n 'n_load_steps': 1,\n 'tolerance': 1e-10,\n 'relaxation_factor': 0.,\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {\n 'rho': ws.rho,\n 'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': ws.dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction}},\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 4,\n 'delta_curved': 1e-1,\n 'min_delta': 1e-10,\n 'gravity_on': 'off',\n 'gravity': 9.81}}\n\n ws.config['AerogridPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}\n\n ws.config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'screen_output': 'on'}\n\n ws.config['BeamPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on'}\n\n ws.config['BeamCsvOutput'] = {'output_pos': 'on',\n 'output_psi': 'on',\n 'screen_output': 'on'}\n\n ws.config['Modal'] = {'print_info': 'on',\n 'use_undamped_modes': 'on',\n 'NumLambda': 20,\n 'rigid_body_modes': 'on',\n 'write_modes_vtk': 'on',\n 'print_matrices': 'off',\n 'save_data': 'on',\n 'rigid_modes_cg': 'off'}\n\n settings = {}\n settings['NonLinearDynamicCoupledStep'] = {'print_info': 'off',\n 'max_iterations': 950,\n 'delta_curved': 1e-1,\n 'min_delta': ws.tolerance,\n 'newmark_damp': 5e-3,\n 'gravity_on': 'on',\n 'gravity': 9.81,\n 'num_steps': 4,\n 'dt': ws.dt,\n 'initial_velocity': u_inf}\n\n relative_motion = 'off'\n settings['StepUvlm'] = {'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'convection_scheme': 2,\n 'rollup_dt': ws.dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'gamma_dot_filtering': 6,\n 'vortex_radius': 1e-8,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': 0 * u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho,\n 'n_time_steps': 1,\n 'dt': ws.dt}\n\n solver = 'NonLinearDynamicCoupledStep'\n ws.config['DynamicCoupled'] = {'structural_solver': solver,\n 'structural_solver_settings': settings[solver],\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'fsi_substeps': 200,\n 'fsi_tolerance': ws.tolerance,\n 'relaxation_factor': ws.relaxation_factor,\n 'minimum_steps': 1,\n 'relaxation_steps': 150,\n 'final_relaxation_factor': 0.5,\n 'n_time_steps': 1,\n 'dt': ws.dt,\n 'include_unsteady_force_contribution': 'off',\n }\n\n ws.config['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n 'linear_system_settings': {\n 'track_body': 'off',\n 'beam_settings': {'modal_projection': 'on',\n 'inout_coords': 'modes',\n 'discrete_time': 'off',\n 'newmark_damp': 5e-4,\n 'discr_method': 'newmark',\n 'dt': ws.dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'on',\n 'num_modes': 20,\n 'print_info': 'on',\n 'gravity': 'off',\n 'remove_dofs': [],\n 'remove_rigid_states': 'on'},\n 'aero_settings': {'dt': ws.dt,\n # 'ScalingDict': {'density': rho,\n # 'length': ws.c_ref * 0.5,\n # 'speed': u_inf},\n 'integr_order': 2,\n 'density': rho,\n 'remove_predictor': 'off',\n 'use_sparse': 'off',\n 'vortex_radius': 1e-8,\n 'convert_to_ct': 'on',\n 'remove_inputs': ['u_gust'],\n # 'rom_method': ['Krylov'],\n 'rom_method_settings': {\n 'Krylov': {'algorithm': 'mimo_rational_arnoldi',\n 'frequency': [0.],\n 'r': 4,\n 'single_side': 'observability'}}\n },\n 'use_euler': 'on',\n },\n }\n\n ws.config['FrequencyResponse'] = {'quick_plot': 'off',\n 'frequency_unit': 'k',\n 'frequency_bounds': [0.0001, 1.0],\n 'num_freqs': 100,\n 'frequency_spacing': 'log',\n 'target_system': ['aeroelastic'],\n }\n\n ws.config['StabilityDerivatives'] = {'u_inf': ws.u_inf,\n 'c_ref': ws.main_chord,\n 'b_ref': ws.wing_span,\n 'S_ref': ws.wing_span * ws.main_chord,\n }\n\n ws.config['AsymptoticStability'] = {'print_info': 'on'}\n\n ws.config['SaveParametricCase'] = {'save_case': 'off',\n 'parameters': {'alpha': alpha_deg},\n 'save_pmor_items': 'on',\n 'save_pmor_subsystems': 'on'}\n\n ws.config['SaveData'] = {'save_aero': 'off',\n 'save_struct': 'off',\n 'save_linear': 'on',\n 'save_linear_uvlm': 'off',\n 'format': 'mat',\n }\n\n ws.config.write()\n\n if not not_run:\n self.data = sharpy.sharpy_main.main(['', ws.route + ws.case_name + '.sharpy'])\n\n return ws\n\n def test_derivatives(self):\n # target_system_list = ['aerodynamic']#, 'aeroelastic']\n # target_system_list = ['aeroelastic']\n target_system_list = ['aerodynamic', 'aeroelastic']\n for system in target_system_list:\n with self.subTest(target_system=system):\n self.run_case(target_system=system)\n\n def run_case(self, target_system):\n\n if target_system == 'aerodynamic':\n nonlinear_solver = ['StaticUvlm']\n elif target_system == 'aeroelastic':\n nonlinear_solver = ['StaticCoupled']\n else:\n NameError('Unrecognised system')\n\n case_name_db = []\n not_run = False # for debugging\n # Reference Case at 4 degrees\n # Run nonlinear simulation and save linerised ROM\n alpha_deg_ref = 0\n alpha0 = alpha_deg_ref * np.pi/180\n ref = self.run_sharpy(alpha_deg=alpha_deg_ref,\n flow=['BeamLoader',\n 'AerogridLoader', ] +\n nonlinear_solver +\n ['AeroForcesCalculator',\n 'Modal',\n 'LinearAssembler',\n # 'AsymptoticStability',\n 'StabilityDerivatives',\n 'SaveData',\n 'SaveParametricCase'],\n target_system=target_system,\n not_run=False)\n u_inf = ref.u_inf\n ref_case_name = ref.case_name\n case_name_db.append(ref_case_name)\n qS = 0.5 * ref.rho * u_inf ** 2 * ref.c_ref * ref.wing_span\n if self.print_info:\n print(f'Reference span: {ref.wing_span} m')\n print(f'Reference chord: {ref.main_chord} m')\n print(f'Aspect ratio: {ref.aspect_ratio}')\n\n # Run nonlinear cases in the vicinity\n nonlinear_sim_flow = ['BeamLoader',\n 'AerogridLoader'] + nonlinear_solver + ['AeroForcesCalculator', 'SaveParametricCase']\n alpha_deg_min = alpha_deg_ref - 5e-3\n alpha_deg_max = alpha_deg_ref + 5e-3\n n_evals = 11\n alpha_vec = np.linspace(alpha_deg_min, alpha_deg_max, n_evals)\n nlin_forces_g = np.zeros((n_evals, 3))\n nlin_forces_a = np.zeros((n_evals, 3))\n for ith, alpha in enumerate(alpha_vec):\n if alpha == alpha_deg_ref:\n case_name = ref_case_name\n continue\n else:\n case = self.run_sharpy(alpha, flow=nonlinear_sim_flow, target_system=target_system, not_run=not_run)\n case_name_db.append(case.case_name)\n case_name = case.case_name\n nlin_forces = np.loadtxt(self.route_test_dir +\n '/output/{:s}/forces/forces_aeroforces.txt'.format(case_name),\n skiprows=1,\n delimiter=',')\n nlin_forces_g[ith, :3] = nlin_forces[1:4]\n nlin_forces_a[ith, :3] = nlin_forces[7:10]\n nlin_forces_g /= qS\n nlin_forces_a /= qS\n\n lift_poly = np.polyfit(alpha_vec * np.pi/180, nlin_forces_g[:, 2], deg=1)\n nonlin_cla = lift_poly[0]\n drag_poly = np.polyfit(alpha_vec * np.pi/180, nlin_forces_g[:, 0], deg=2)\n nonlin_cda = 2 * drag_poly[0] * alpha0 + drag_poly[1]\n if self.print_info:\n print('Nonlinear coefficients')\n print('CLa', nonlin_cla)\n print('CDa', nonlin_cda)\n\n lift_poly = np.polyfit(alpha_vec * np.pi/180, nlin_forces_a[:, 2], deg=1)\n nonlin_cza = lift_poly[0]\n drag_poly = np.polyfit(alpha_vec * np.pi/180, nlin_forces_a[:, 0], deg=2)\n nonlin_cxa = 2 * drag_poly[0] * alpha0 + drag_poly[1]\n if self.print_info:\n print('Nonlinear coefficients - body axes')\n print('CZa', nonlin_cza)\n print('CXa', nonlin_cxa)\n\n # Get Linear ROM at reference case\n import scipy.io as scio\n linss_data = scio.loadmat(self.route_test_dir + '/output/{:s}/savedata/{:s}.linss.mat'.format(ref_case_name,\n ref_case_name))\n\n # Steady State transfer function\n if target_system == 'aerodynamic':\n ss = libss.StateSpace.load_from_h5(self.route_test_dir +\n f'/output/{ref_case_name}/' +\n f'save_pmor_data/{ref_case_name}_aerostatespace.h5')\n else:\n ss = libss.StateSpace.load_from_h5(self.route_test_dir +\n f'/output/{ref_case_name}/' +\n f'save_pmor_data/{ref_case_name}_statespace.h5')\n\n H0 = ss.freqresp(np.array([1e-5]))[:, :, 0].real\n\n cga = algebra.quat2rotation(algebra.euler2quat(np.array([0, alpha0, 0])))\n\n vx_ind = 20 # x_a input index\n vz_ind = 20 + 2 # z_a input index\n\n n_evals = 2\n forces = np.zeros((n_evals, 4))\n moments = np.zeros_like(forces)\n body_forces = np.zeros_like(forces)\n\n phi = libss.Gain.load_from_h5(self.route_test_dir +\n f'/output/{ref_case_name}/' +\n f'save_pmor_data/{ref_case_name}_modal_structrob.h5').value.real # other Gain features not needed\n\n eps = 1e-5\n dalpha_vec = np.array([-eps, +eps])\n for i_alpha, dalpha in enumerate(dalpha_vec):\n alpha = alpha0 + dalpha # rad\n deuler = np.array([0, dalpha, 0])\n euler0 = np.array([0, alpha0, 0])\n\n u = np.zeros(ss.inputs) # input vector\n V0 = np.array([-1, 0, 0], dtype=float) * u_inf # G\n Vp = u_inf * np.array([-np.cos(dalpha), 0, -np.sin(dalpha)]) # G\n\n dvg = Vp - V0 # G\n dva = cga.T.dot(dvg) # A\n dvz = dva[2]\n dvx = dva[0]\n\n # print(Vp)\n # print(algebra.euler2rot(deuler).T.dot(V0))\n # print(algebra.der_Peuler_by_v(euler0*0, V0))\n Vp2 = algebra.euler2rot(euler0 * 0).T.dot(V0) + algebra.der_Peuler_by_v(euler0 * 0, V0).dot(deuler)\n dva2 = cga.T.dot(algebra.euler2rot(deuler).T.dot(V0) - V0)\n dva3 = cga.T.dot(Vp2 - V0)\n # print('{:.4f}\\t'.format((alpha0 + dalpha) * 180 / np.pi), dva2, dva3, dva3-dva2)\n dvz = dva3[2]\n dvx = dva3[0]\n\n # Need to scale the mode shapes by the rigid body mode factor\n u[vx_ind] = dvx / phi[-9, 0]\n u[vz_ind] = dvz / phi[-7, 2]\n\n # and the same with the output forces\n flin = H0.dot(u)[:3].real / phi[-9, 0] # A\n mlin = np.linalg.inv(phi[-6:-3, 3:6].T).dot(H0.dot(u)[3:6].real) # A\n F0A = linss_data['forces_aero_beam_dof'][0, :3].real / phi[-9, 0] # A - forces at the linearisation\n M0A = linss_data['forces_aero_beam_dof'][0, 3:6].real / phi[-6, 3] # A - forces at the linearisation\n LD0 = cga.dot(F0A) # Lift and drag at the linearisation point\n M0G = cga.dot(M0A)\n\n forces[i_alpha, 0] = (alpha0 + dalpha) * 180 / np.pi # deg\n LD = LD0 + algebra.der_Ceuler_by_v(euler0, F0A).dot(deuler) + cga.dot(flin) # stability axes\n forces[i_alpha, 1:] = LD / qS\n\n u_body = np.zeros_like(u)\n u_body[vz_ind] = dvz / phi[-7, 2]\n body_forces[i_alpha, 1:] = H0.dot(u_body)[:3].real / phi[-9, 0] / qS # C_Z_w in A frame\n if self.print_info:\n print('Transfer function coefficients (normalised by qS)')\n print(H0[:3, vx_ind:vx_ind+3].real / phi[-7, 2] / phi[-9, 0] / qS)\n\n MD = M0G + algebra.der_Ceuler_by_v(euler0, M0A).dot(deuler) + cga.dot(mlin)\n moments[i_alpha, 0] = forces[i_alpha, 0]\n moments[i_alpha, 1:] = MD / qS / ref.main_chord\n\n cla = (forces[-1, -1] - forces[0, -1]) / (forces[-1, 0] - forces[0, 0]) * 180 / np.pi\n cda = (forces[-1, 1] - forces[0, 1]) / (forces[-1, 0] - forces[0, 0]) * 180 / np.pi\n cma = (moments[-1, 2] - moments[0, 2]) / (moments[-1, 0] - moments[0, 0]) * 180 / np.pi\n\n if self.print_info:\n print('Lift curve slope perturbation {:.6e}'.format(cla))\n print('Drag curve slope perturbation {:.6e}'.format(cda))\n print('Moment curve slope perturbation {:.6e}'.format(cma))\n\n # body derivative\n # czwa = (body_forces[-1, -1] - body_forces[0, -1]) / (forces[-1, 0] - forces[0, 0]) * 180 / np.pi\n # print('Vertical force with vertical velocity perturbation {:.6e}'.format(czwa))\n\n with h5py.File(self.route_test_dir + '/output/' + ref_case_name +\n '/derivatives/aerodynamic_stability_derivatives.h5', 'r') as f:\n sharpy_force_angle = h5utils.load_h5_in_dict(f)['force_angle_velocity']\n\n linsubtests = ((2, cla, 'lift'),\n (0, cda, 'drag'),\n (4, cma, 'moment'))\n for test in linsubtests:\n with self.subTest(test):\n try:\n np.testing.assert_almost_equal(sharpy_force_angle[test[0], 1], test[1], decimal=3)\n except AssertionError as e:\n print('Error Linear perturbation in {:s}'.format(test[2]))\n print(e)\n print('Pct error', np.abs(sharpy_force_angle[test[0], 1] - test[1]) / test[1] * 100)\n raise AssertionError\n\n nonlinsubtests = ((2, nonlin_cla, 'lift'),\n (0, nonlin_cda, 'drag'),\n )\n\n for test in nonlinsubtests:\n with self.subTest(test):\n try:\n np.testing.assert_almost_equal(sharpy_force_angle[test[0], 1], test[1], decimal=2)\n except AssertionError as e:\n print('Error nonlinear perturbation in {:s}'.format(test[2]))\n print(e)\n print('Pct error', np.abs(sharpy_force_angle[test[0], 1] - test[1]) / test[1] * 100)\n raise AssertionError\n return forces, moments\n\n def tearDown(self):\n import shutil\n folders = ['cases', 'output']\n for folder in folders:\n shutil.rmtree(self.route_test_dir + '/' + folder)\n\n\nif __name__ == '__main__':\n unittest.main()\n" }, { "path": "tests/linear/frequencyutils/__init__.py", "content": "" }, { "path": "tests/linear/frequencyutils/test_frequency_utils.py", "content": "import unittest\nimport sharpy.linear.src.libss as libss\nimport scipy.linalg as sclalg\nimport numpy as np\nimport os\n\nimport sharpy.utils.frequencyutils as frequencyutils\n\n\nclass TestFrequencyUtils(unittest.TestCase):\n\n test_dir = os.path.abspath(os.path.dirname(__file__))\n\n def setUp(self):\n\n # This particular system is a good test as it requires a few iterations of the Hinf\n # solver. In addition it is known that its SVD peak occurs between 0.1 and 1.0 rad/s\n # allowing us to increase the resolution in the graphical method around that vicinity.\n a = np.load(self.test_dir + '/src/a.npy')\n b = np.load(self.test_dir + '/src/b.npy')\n c = np.load(self.test_dir + '/src/c.npy')\n d = np.load(self.test_dir + '/src/d.npy')\n\n self.sys = libss.StateSpace(a, b, c, d, dt=None)\n # self.sys = libss.random_ss(10, 4, 3, dt=0.1, stable=True)\n # self.sys = libss.disc2cont(self.sys)\n\n def test_hinfinity_norm(self):\n\n h_inf_iterative = frequencyutils.h_infinity_norm(self.sys, print_info=False)\n\n # Compare against graphical method\n # Hinf norm is the maximum SVD across all frequencies\n wv_vec = np.logspace(-1, 0, 100)\n svd_val = np.zeros_like(wv_vec)\n\n for i in range(len(svd_val)):\n frequency_response = self.sys.transfer_function_evaluation(1j*wv_vec[i])\n svd_val[i] = np.max(sclalg.svd(frequency_response,\n compute_uv=False))\n\n h_inf_graph = np.max(svd_val)\n\n np.testing.assert_almost_equal(h_inf_iterative, h_inf_graph, decimal=3, verbose=True,\n err_msg='H-infinity norm using iterative method vs graphical one not '\n 'equal to 3 decimal places')\n\n # >>>>>>>>>>> Useful debugging\n # print(h_inf_iterative)\n # print(h_inf_graph)\n #\n # import matplotlib.pyplot as plt\n # plt.semilogx(wv_vec, svd_val)\n # plt.show()\n\n # <<<<<<<<<<<<<<<<<<<<<<<<<<<<\n\n # a = np.save(self.test_dir + '/src/a.npy', self.sys.A)\n # b = np.save(self.test_dir + '/src/b.npy', self.sys.B)\n # c = np.save(self.test_dir + '/src/c.npy', self.sys.C)\n # d = np.save(self.test_dir + '/src/d.npy', self.sys.D)\n" }, { "path": "tests/linear/goland_wing/__init__.py", "content": "" }, { "path": "tests/linear/goland_wing/test_goland_flutter.py", "content": "import numpy as np\nimport os\nimport unittest\nimport sharpy.cases.templates.flying_wings as wings\nimport sharpy.sharpy_main\n\n\nclass TestGolandFlutter(unittest.TestCase):\n\n def setup(self):\n # Problem Set up\n u_inf = 1.\n alpha_deg = 0.\n rho = 1.02\n num_modes = 4\n\n # Lattice Discretisation\n M = 16\n N = 32\n M_star_fact = 10\n\n # Linear UVLM settings\n integration_order = 2\n remove_predictor = False\n use_sparse = True\n\n # ROM Properties\n rom_settings = dict()\n rom_settings['algorithm'] = 'mimo_rational_arnoldi'\n rom_settings['r'] = 6\n rom_settings['single_side'] = 'observability'\n frequency_continuous_k = np.array([0.])\n\n # Case Admin - Create results folders\n case_name = 'goland_cs'\n case_nlin_info = 'M%dN%dMs%d_nmodes%d' % (M, N, M_star_fact, num_modes)\n case_rom_info = 'rom_MIMORA_r%d_sig%04d_%04dj' % (rom_settings['r'], frequency_continuous_k[-1].real * 100,\n frequency_continuous_k[-1].imag * 100)\n\n case_name += case_nlin_info + case_rom_info\n\n self.route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n fig_folder = self.route_test_dir + '/figures/'\n os.makedirs(fig_folder, exist_ok=True)\n\n # SHARPy nonlinear reference solution\n ws = wings.GolandControlSurface(M=M,\n N=N,\n Mstar_fact=M_star_fact,\n u_inf=u_inf,\n alpha=alpha_deg,\n cs_deflection=[0, 0],\n rho=rho,\n sweep=0,\n physical_time=2,\n n_surfaces=2,\n route=self.route_test_dir + '/cases',\n case_name=case_name)\n\n ws.gust_intensity = 0.01\n ws.sigma = 1\n\n ws.clean_test_files()\n ws.update_derived_params()\n ws.set_default_config_dict()\n\n ws.generate_aero_file()\n ws.generate_fem_file()\n\n frequency_continuous_w = 2 * u_inf * frequency_continuous_k / ws.c_ref\n rom_settings['frequency'] = frequency_continuous_w\n rom_settings['tangent_input_file'] = ws.route + '/' + ws.case_name + '.rom.h5'\n\n ws.config['SHARPy'] = {\n 'flow':\n ['BeamLoader', 'AerogridLoader',\n 'StaticCoupled',\n 'AerogridPlot',\n 'BeamPlot',\n 'Modal',\n 'LinearAssembler',\n 'FrequencyResponse',\n 'AsymptoticStability',\n 'SaveData',\n ],\n 'case': ws.case_name, 'route': ws.route,\n 'write_screen': 'off', 'write_log': 'on',\n 'log_folder': self.route_test_dir + '/output/',\n 'log_file': ws.case_name + '.log'}\n\n ws.config['BeamLoader'] = {\n 'unsteady': 'off',\n 'orientation': ws.quat}\n\n ws.config['AerogridLoader'] = {\n 'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': ws.Mstar_fact * ws.M,\n 'freestream_dir': ws.u_inf_direction,\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction,\n 'dt': ws.dt}}\n\n ws.config['StaticUvlm'] = {\n 'rho': ws.rho,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction},\n 'rollup_dt': ws.dt,\n 'print_info': 'on',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_aic_refresh': 0,\n 'rollup_tolerance': 1e-4}\n\n ws.config['StaticCoupled'] = {\n 'print_info': 'on',\n 'max_iter': 200,\n 'n_load_steps': 1,\n 'tolerance': 1e-10,\n 'relaxation_factor': 0.,\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {\n 'rho': ws.rho,\n 'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': ws.dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction}},\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 4,\n 'delta_curved': 1e-1,\n 'min_delta': 1e-10,\n 'gravity_on': 'on',\n 'gravity': 9.81}}\n\n ws.config['AerogridPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}\n\n ws.config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': ws.case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n 'unsteady': 'off'}\n\n ws.config['BeamPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on'}\n\n ws.config['Modal'] = {'NumLambda': 20,\n 'rigid_body_modes': 'off',\n 'print_matrices': 'on',\n 'save_data': 'off',\n 'rigid_modes_cg': 'off',\n 'continuous_eigenvalues': 'off',\n 'dt': 0,\n 'plot_eigenvalues': False,\n 'max_rotation_deg': 15.,\n 'max_displacement': 0.15,\n 'write_modes_vtk': True,\n 'use_undamped_modes': True}\n\n ws.config['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n 'linear_system_settings': {\n 'beam_settings': {'modal_projection': 'on',\n 'inout_coords': 'modes',\n 'discrete_time': 'on',\n 'newmark_damp': 0.5e-4,\n 'discr_method': 'newmark',\n 'dt': ws.dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'off',\n 'num_modes': num_modes,\n 'print_info': 'on',\n 'gravity': 'on',\n 'remove_sym_modes': 'on',\n 'remove_dofs': []},\n 'aero_settings': {'dt': ws.dt,\n 'ScalingDict': {'length': 0.5 * ws.c_ref,\n 'speed': u_inf,\n 'density': rho},\n 'integr_order': integration_order,\n 'density': ws.rho,\n 'remove_predictor': remove_predictor,\n 'use_sparse': use_sparse,\n 'remove_inputs': ['u_gust'],\n 'rom_method': ['Krylov'],\n 'rom_method_settings': {'Krylov': rom_settings}},\n }}\n\n ws.config['AsymptoticStability'] = {'print_info': True,\n 'velocity_analysis': [160, 180, 20]}\n\n ws.config['LinDynamicSim'] = {'dt': ws.dt,\n 'n_tsteps': ws.n_tstep,\n 'sys_id': 'LinearAeroelastic',\n 'postprocessors': ['BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'AerogridPlot': {\n 'u_inf': ws.u_inf,\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'}}}\n\n ws.config['FrequencyResponse'] = {'quick_plot': 'off',\n 'frequency_unit': 'k',\n 'frequency_bounds': [0.0001, 1.0],\n 'num_freqs': 100,\n 'frequency_spacing': 'log',\n 'target_system': ['aeroelastic'],\n }\n\n ws.config['SaveData'] = {'save_aero': 'off',\n 'save_struct': 'off',\n 'save_rom': 'on'}\n\n ws.config.write()\n\n self.data = sharpy.sharpy_main.main(['', ws.route + ws.case_name + '.sharpy'])\n\n def run_rom_stable(self):\n ssrom = self.data.linear.linear_system.uvlm.rom['Krylov'].ssrom\n eigs_rom = np.linalg.eigvals(ssrom.A)\n\n assert all(np.abs(eigs_rom) <= 1.), 'UVLM Krylov ROM is unstable - flutter speed may not be correct. Change' \\\n 'ROM settings to achieve stability'\n # print('ROM is stable')\n\n def run_flutter(self):\n flutter_ref_speed = 166 # at current discretisation\n\n # load results file - variables below determined by ``velocity_analysis`` setting in AsymptoticStability\n ulb = 160 # velocity lower bound\n uub = 180 # velocity upper bound\n num_u = 20 # n_speeds\n res = np.loadtxt(self.route_test_dir + '/output/%s/stability/' % self.data.settings['SHARPy']['case'] +\n '/velocity_analysis_min%04d_max%04d_nvel%04d.dat' % (ulb * 10, uub * 10, num_u), )\n\n u_inf = res[:, 0]\n eval_real = res[:, 1]\n eval_imag = res[:, 2]\n\n # Flutter onset\n ind_zero_real = np.where(eval_real >= 0)[0][0]\n assert ind_zero_real > 0, 'Flutter speed not below 165.00 m/s'\n flutter_speed = 0.5 * (u_inf[ind_zero_real] + u_inf[ind_zero_real - 1])\n flutter_frequency = np.sqrt(eval_real[ind_zero_real] ** 2 + eval_imag[ind_zero_real] ** 2)\n\n # print('Flutter speed = %.1f m/s' % flutter_speed)\n # print('Flutter frequency = %.2f rad/s' % flutter_frequency)\n assert np.abs(\n flutter_speed - flutter_ref_speed) / flutter_ref_speed < 1e-2, ' Flutter speed error greater than ' \\\n '1 percent. \\nFlutter speed: %.2f m/s\\n' \\\n 'Frequency: %.2f rad/s' % (flutter_speed,\n flutter_frequency)\n\n def test_flutter(self):\n self.setup()\n self.run_rom_stable()\n self.run_flutter()\n\n def tearDown(self):\n import shutil\n folders = ['cases', 'figures', 'output']\n for folder in folders:\n shutil.rmtree(self.route_test_dir + '/' + folder)\n\n\nif __name__ == '__main__':\n unittest.main()\n" }, { "path": "tests/linear/gusts/__init__.py", "content": "" }, { "path": "tests/linear/gusts/test_external_gust.py", "content": "import numpy as np\nimport sharpy.utils.algebra as algebra\nimport sharpy.sharpy_main as smain\nimport unittest\nimport sharpy.cases.templates.flying_wings as wings\nimport os\nimport shutil\n\n\ndef generate_sharpy(alpha=0., case_name='hale_static', case_route='./', **kwargs):\n\n output_route = kwargs.get('output_route', './output/')\n m = kwargs.get('M', 4)\n rho = kwargs.get('rho', 1.225)\n tolerance = kwargs.get('tolerance', 1e-5)\n u_inf = kwargs.get('u_inf', 10)\n tsteps = kwargs.get('tsteps', 100)\n\n ws = wings.QuasiInfinite(M=m,\n aspect_ratio=10,\n N=8,\n Mstar_fact=10,\n u_inf=u_inf,\n alpha=alpha,\n rho=rho,\n sweep=0,\n n_surfaces=2,\n route=case_route,\n case_name=case_name)\n\n ws.gust_intensity = 0.01\n ws.sigma = 1e-1\n\n ws.clean_test_files()\n ws.update_derived_params()\n ws.set_default_config_dict()\n\n ws.generate_aero_file()\n ws.generate_fem_file()\n\n settings = dict()\n\n settings['SHARPy'] = {'case': case_name,\n 'route': case_route,\n 'flow': kwargs.get('flow', []),\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': output_route,\n 'log_file': case_name + '.log'}\n\n settings['BeamLoader'] = {'unsteady': 'on',\n 'orientation': algebra.euler2quat(np.array([0.,\n alpha,\n 0.]))}\n\n settings['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n 'mstar': int(kwargs.get('wake_length', 10) * m),\n 'control_surface_deflection': ['', ''],\n 'control_surface_deflection_generator_settings':\n {'0': {},\n '1': {}},\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {\n 'u_inf': u_inf,\n 'u_inf_direction': [1., 0., 0.],\n 'dt': ws.dt,\n },\n }\n\n settings['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'gravity_on': kwargs.get('gravity', 'on'),\n 'gravity': 9.81,\n 'initial_position': [0., 0., 0.]}\n\n settings['StaticUvlm'] = {'print_info': 'on',\n 'horseshoe': kwargs.get('horseshoe', 'off'),\n 'num_cores': 4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho}\n\n settings['StaticCoupled'] = {'print_info': 'off',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': settings['NonLinearStatic'],\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': settings['StaticUvlm'],\n 'max_iter': 100,\n 'n_load_steps': kwargs.get('n_load_steps', 1),\n 'tolerance': kwargs.get('fsi_tolerance', 1e-5),\n 'relaxation_factor': kwargs.get('relaxation_factor', 0.2)}\n\n settings['BeamPlot'] = {'include_FoR': 'on'}\n\n settings['AerogridPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0,\n 'u_inf': u_inf\n }\n\n settings['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': 'aeroforces.txt',\n 'screen_output': 'on',\n 'coefficients': True,\n 'q_ref': 0.5 * rho * u_inf ** 2,\n 'S_ref': 12.809,\n }\n\n settings['BeamPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'include_FoR': 'on'}\n\n struct_solver_settings = {'print_info': 'off',\n 'max_iterations': 950,\n 'delta_curved': 1e-6,\n 'min_delta': tolerance,\n 'newmark_damp': 5e-3,\n 'gravity_on': kwargs.get('gravity', 'on'),\n 'gravity': 9.81,\n 'num_steps': 1,\n 'dt': ws.dt}\n\n gust_vec = kwargs.get('nl_gust', None)\n if gust_vec is not None:\n t_dom = np.linspace(0, ws.dt * (tsteps-1), tsteps)\n np.savetxt(ws.route + '/gust.txt', np.column_stack((\n t_dom,\n np.zeros_like(t_dom),\n np.zeros_like(t_dom),\n gust_vec\n )))\n\n step_uvlm_settings = {'print_info': 'on',\n 'num_cores': 4,\n 'convection_scheme': 0, #ws.wake_type,\n 'vortex_radius': 1e-7,\n 'velocity_field_generator': 'GustVelocityField',\n 'velocity_field_input': {'u_inf': u_inf * 1,\n 'u_inf_direction': [1., 0., 0.],\n 'relative_motion': 'on',\n 'gust_shape': 'time varying',\n 'gust_parameters': {\n 'file': ws.route + '/gust.txt',\n }},\n 'rho': rho,\n 'n_time_steps': tsteps,\n 'dt': ws.dt,\n 'gamma_dot_filtering': 3}\n\n settings['DynamicCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearDynamicPrescribedStep',\n 'structural_solver_settings': struct_solver_settings,\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': step_uvlm_settings,\n 'fsi_substeps': 200,\n 'fsi_tolerance': tolerance,\n 'relaxation_factor': 0.3,\n 'minimum_steps': 1,\n 'relaxation_steps': 150,\n 'final_relaxation_factor': 0.5,\n 'n_time_steps': tsteps, # ws.n_tstep,\n 'dt': ws.dt,\n 'include_unsteady_force_contribution': 'on',\n 'steps_without_unsteady_force': 5,\n 'postprocessors': ['BeamPlot', 'AerogridPlot', 'WriteVariablesTime'],\n 'postprocessors_settings': {'BeamLoads': {'csv_output': 'off'},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'},\n 'AerogridPlot': {\n 'u_inf': u_inf,\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n 'WriteVariablesTime': {\n 'cleanup_old_solution': 'on',\n 'delimiter': ',',\n 'FoR_variables': ['total_forces',\n 'total_gravity_forces',\n 'for_pos', 'quat'],\n }}}\n\n settings['Modal'] = {'print_info': True,\n 'use_undamped_modes': True,\n 'NumLambda': 50,\n 'rigid_body_modes': 'off',\n 'write_modes_vtk': 'on',\n 'print_matrices': 'on',\n 'save_data': 'on',\n 'continuous_eigenvalues': 'off',\n 'dt': ws.dt,\n 'plot_eigenvalues': False,\n 'rigid_modes_ppal_axes': 'on'}\n # ROM settings\n rom_settings = dict()\n rom_settings['algorithm'] = 'mimo_rational_arnoldi'\n rom_settings['r'] = 10\n rom_settings['frequency'] = np.array([0], dtype=float)\n rom_settings['single_side'] = 'observability'\n\n settings['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n 'linearisation_tstep': -1,\n 'linear_system_settings': {\n 'beam_settings': {'modal_projection': 'off',\n 'inout_coords': 'modes',\n 'discrete_time': 'on',\n 'newmark_damp': 0.5e-4,\n 'discr_method': 'newmark',\n 'dt': ws.dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'on',\n 'num_modes': 20,\n 'print_info': 'on',\n 'gravity': kwargs.get('gravity', 'on'),\n 'remove_dofs': [],\n 'remove_rigid_states': 'off'},\n 'aero_settings': {'dt': ws.dt,\n 'integr_order': 2,\n 'density': rho,\n 'remove_predictor': 'off',\n 'use_sparse': False,\n 'vortex_radius': 1e-7,\n 'convert_to_ct': 'off',\n 'gust_assembler': kwargs.get('gust_name', ''),\n 'gust_assembler_inputs': kwargs.get('gust_settings', {}),\n },\n 'track_body': 'on',\n 'use_euler': 'on',\n },\n }\n\n settings['AsymptoticStability'] = {\n 'print_info': 'on',\n 'modes_to_plot': [],\n # 'velocity_analysis': [27, 29, 3],\n 'display_root_locus': 'off',\n 'frequency_cutoff': 0,\n 'export_eigenvalues': 'on',\n 'num_evals': 100}\n\n settings['FrequencyResponse'] = {'target_system': ['aeroelastic', 'aerodynamic', 'structural'],\n 'quick_plot': 'off',\n 'frequency_spacing': 'log',\n 'frequency_unit': 'w',\n 'frequency_bounds': [1e-3, 1e3],\n 'num_freqs': 200,\n 'print_info': 'on'}\n\n settings['PickleData'] = {}\n\n settings['LinDynamicSim'] = {'n_tsteps': tsteps,\n 'dt': ws.dt,\n 'write_dat': ['x', 'y', 'u'],\n 'input_generators': kwargs.get('linear_input_generators', []),\n 'postprocessors': ['AerogridPlot'],\n 'postprocessors_settings':\n {'AerogridPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}, }\n }\n\n case_file = ws.settings_to_config(settings)\n return case_file\n\n\ndef run_case(case_file, pickle_file=None):\n if pickle_file is not None:\n restart = True\n else:\n restart = False\n if restart:\n data = smain.main(['', case_file, '-r', pickle_file])\n else:\n data = smain.main(['', case_file])\n\n return data\n\n\nclass TestGustAssembly(unittest.TestCase):\n\n route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n directories = ['cases', 'output', 'inputs']\n\n time_steps = 80\n gust_intensity = 0.01\n gust_ramp = 5\n\n M = 4\n u_inf = 1\n\n gust_vec = np.zeros(time_steps)\n\n @classmethod\n def setUpClass(cls):\n for folder in cls.directories:\n os.makedirs(cls.route_test_dir + '/' + folder, exist_ok=True)\n\n # Gust input profile\n cls.gust_vec[5:cls.gust_ramp+5] = np.linspace(0, cls.gust_intensity, cls.gust_ramp)\n cls.gust_vec[5+ cls.gust_ramp:] = cls.gust_intensity\n\n @classmethod\n def tearDownClass(cls):\n for folder in cls.directories:\n if os.path.isdir(cls.route_test_dir + '/' + folder):\n shutil.rmtree(cls.route_test_dir + '/' + folder)\n\n def linear_response(self):\n\n np.savetxt(self.route_test_dir + '/inputs/gust_linear.txt', self.gust_vec)\n\n input_generators = [{'name': 'u_gust',\n 'index': 0,\n 'file_path': self.route_test_dir + '/inputs/gust_linear.txt'}]\n\n data = self.run_sharpy_linear(gust_name='LeadingEdge', linear_input_generators=input_generators)#\n\n return data\n\n def nonlinear_response(self):\n\n data = self.run_sharpy_nonlinear(nl_gust=self.gust_vec)\n\n return data\n\n def test_gust(self):\n\n linear = self.linear_response()\n nonlinear = self.nonlinear_response()\n final_linear = linear.aero.timestep_info[-1]\n final_nonlinear = nonlinear.aero.timestep_info[-1]\n with self.subTest('zeta'):\n np.testing.assert_almost_equal(final_linear.zeta[0][2, 0, -1],\n final_nonlinear.zeta[0][2, 0, -1], decimal=4)\n with self.subTest('forces'):\n np.testing.assert_almost_equal(np.sum(final_linear.forces[0][2, :, 0]),\n np.sum(final_nonlinear.forces[0][2, :, 0]), decimal=4)\n\n with self.subTest('gamma'):\n np.testing.assert_almost_equal(final_linear.gamma[0][2, 2],\n final_nonlinear.gamma[0][2, 2], decimal=4)\n\n def wingtip_timeseries(self, data):\n nsteps = len(data.aero.timestep_info)\n\n wingtip = np.zeros(nsteps)\n\n for i in range(nsteps):\n wingtip[i] = data.aero.timestep_info[i].zeta[0][2, 0, -1]\n\n return wingtip\n\n def gamma_timeseries(self, data):\n nsteps = len(data.aero.timestep_info)\n\n wingtip = np.zeros(nsteps)\n\n for i in range(nsteps):\n wingtip[i] = data.aero.timestep_info[i].gamma[0][0, -1]\n\n return wingtip\n\n def run_sharpy_nonlinear(self, **kwargs):\n flow = [\n 'BeamLoader',\n 'AerogridLoader',\n 'StaticUvlm',\n 'DynamicCoupled',\n # 'AeroForcesCalculator',\n 'PickleData',\n ]\n\n\n alpha = 0 #2 * np.pi / 180\n\n # Discretisation\n n_elem_multiplier = 1.5\n wake_length = 10\n horseshoe = False\n\n case_file = generate_sharpy(alpha=alpha,\n case_name='nonlinear',\n case_route=self.route_test_dir + '/cases/',\n output_route=self.route_test_dir + '/output/',\n flow=flow,\n u_inf=self.u_inf,\n M=self.M,\n n_elem_multiplier=n_elem_multiplier,\n horseshoe=horseshoe,\n wake_length=wake_length,\n relaxation_factor=0.6,\n tolerance=1e-5,\n gravity='off',\n fsi_tolerance=1e-5,\n tsteps=self.time_steps,\n **kwargs,\n )\n\n data = run_case(case_file)\n\n return data\n\n def run_sharpy_linear(self, **kwargs):\n\n flow = [\n 'BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'Modal',\n 'AeroForcesCalculator',\n 'LinearAssembler',\n 'LinDynamicSim',\n 'PickleData',\n ]\n\n restart = False\n if restart:\n flow = ['LinDynamicSim']\n pickle_file = self.route_test_dir + '/output/linear.pkl'\n else:\n pickle_file = None\n alpha = 0 #2 * np.pi / 180\n elevator = 0 #-0.5 * np.pi / 180\n thrust = 0 #5\n\n # Discretisation\n M = 4\n n_elem_multiplier = 1.5\n wake_length = 10\n horseshoe = False\n\n case_file = generate_sharpy(alpha=alpha,\n case_name='linear',\n case_route=self.route_test_dir + '/cases/',\n output_route=self.route_test_dir + '/output',\n flow=flow,\n u_inf=self.u_inf,\n M=self.M,\n n_elem_multiplier=n_elem_multiplier,\n horseshoe=horseshoe,\n wake_length=wake_length,\n relaxation_factor=0.6,\n tolerance=1e-5,\n gravity='off',\n fsi_tolerance=1e-5,\n tsteps=self.time_steps,\n **kwargs,\n )\n\n data = run_case(case_file, pickle_file)\n\n return data\n\n def assert_gust_propagation(self, path_to_input, output_route):\n x_sharpy = np.loadtxt(output_route + '/lindynamicsim/x_out.dat')\n u_in = np.loadtxt(path_to_input)\n\n np.testing.assert_array_almost_equal(x_sharpy[1:, 0], u_in[:-1])\n\n def tearDown(self):\n folders = ['cases', 'output']\n import shutil\n\n for folder in folders:\n path = self.route_test_dir + '/' + folder\n if os.path.isdir(path):\n shutil.rmtree(path)\n\n\nif __name__ == '__main__':\n unittest.main()\n" }, { "path": "tests/linear/gusts/test_linear_gusts.py", "content": "import numpy as np\nimport os\nimport unittest\nimport sharpy.cases.templates.flying_wings as wings\nimport sharpy.sharpy_main\nfrom sharpy.linear.assembler.lineargustassembler import campbell\nimport pickle\n\n\nclass TestGolandControlSurface(unittest.TestCase):\n\n def setUp(self):\n self.route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n\n def run_sharpy(self, flow, **kwargs):\n # Problem Set up\n u_inf = 2.\n alpha_deg = 0.\n rho = 1.02\n num_modes = 4\n restart = kwargs.get('restart', False)\n\n # Lattice Discretisation\n M = 4\n N = 16\n M_star_fact = 1\n\n # Linear UVLM settings\n integration_order = 2\n remove_predictor = kwargs.get('remove_predictor', False)\n use_sparse = True\n\n # Case Admin - Create results folders\n case_name = 'goland_cs'\n case_nlin_info = 'M%dN%dMs%d_nmodes%d' % (M, N, M_star_fact, num_modes)\n\n case_name += case_nlin_info\n\n fig_folder = self.route_test_dir + '/figures/'\n os.makedirs(fig_folder, exist_ok=True)\n\n # SHARPy nonlinear reference solution\n ws = wings.GolandControlSurface(M=M,\n N=N,\n Mstar_fact=M_star_fact,\n u_inf=u_inf,\n alpha=alpha_deg,\n # cs_deflection=[0, 0],\n rho=rho,\n sweep=0,\n physical_time=2,\n n_surfaces=2,\n route=self.route_test_dir + '/cases',\n case_name=case_name)\n\n ws.gust_intensity = 0.01\n ws.sigma = 1\n\n ws.clean_test_files()\n ws.update_derived_params()\n ws.set_default_config_dict()\n\n ws.generate_aero_file()\n ws.generate_fem_file()\n\n x0 = np.zeros(256)\n lin_tsteps = 40\n u_vec = np.zeros((lin_tsteps, num_modes // 2 * 3 + 1 + 2))\n # elevator\n u_vec[5:, 5] = 10 * np.pi / 180\n # gust\n u_vec[:, 4] = np.sin(np.linspace(0, 2*np.pi, lin_tsteps))\n ws.create_linear_files(x0, u_vec)\n np.savetxt(self.route_test_dir + '/cases/elevator.txt', u_vec[:, 5])\n np.savetxt(self.route_test_dir + '/cases/gust.txt', u_vec[:, 4])\n\n ws.config['SHARPy'] = {\n 'flow': flow,\n 'case': ws.case_name, 'route': ws.route,\n 'write_screen': 'off', 'write_log': 'on',\n 'log_folder': self.route_test_dir + '/output/' + ws.case_name + '/',\n 'log_file': ws.case_name + '.log'}\n\n ws.config['BeamLoader'] = {\n 'unsteady': 'off',\n 'orientation': ws.quat}\n\n ws.config['AerogridLoader'] = {\n 'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': ws.Mstar_fact * ws.M,\n 'freestream_dir': ws.u_inf_direction, \n 'wake_shape_generator': 'StraightWake', \n 'wake_shape_generator_input': {'u_inf': ws.u_inf, \n 'u_inf_direction': ws.u_inf_direction, \n 'dt': ws.dt}}\n\n ws.config['StaticUvlm'] = {\n 'rho': ws.rho,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction},\n 'rollup_dt': ws.dt,\n 'print_info': 'on',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_aic_refresh': 0,\n 'rollup_tolerance': 1e-4}\n\n ws.config['StaticCoupled'] = {\n 'print_info': 'on',\n 'max_iter': 200,\n 'n_load_steps': 1,\n 'tolerance': 1e-10,\n 'relaxation_factor': 0.,\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {\n 'rho': ws.rho,\n 'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': ws.dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction}},\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 4,\n 'delta_curved': 1e-1,\n 'min_delta': 1e-10,\n 'gravity_on': 'on',\n 'gravity': 9.81}}\n\n ws.config['AerogridPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}\n\n ws.config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': ws.case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n 'unsteady': 'off'}\n\n ws.config['BeamPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on'}\n\n ws.config['Modal'] = {'NumLambda': 20,\n 'rigid_body_modes': 'off',\n 'print_matrices': 'on',\n 'save_data': 'off',\n 'rigid_modes_cg': 'off',\n 'continuous_eigenvalues': 'off',\n 'dt': 0,\n 'plot_eigenvalues': False,\n 'max_rotation_deg': 15.,\n 'max_displacement': 0.15,\n 'write_modes_vtk': True,\n 'use_undamped_modes': True}\n\n ws.config['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n 'linear_system_settings': {\n 'beam_settings': {'modal_projection': 'on',\n 'inout_coords': 'modes',\n 'discrete_time': 'on',\n 'newmark_damp': 0.5e-4,\n 'discr_method': 'newmark',\n 'dt': ws.dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'off',\n 'num_modes': num_modes,\n 'print_info': 'off',\n 'gravity': 'on',\n 'remove_sym_modes': 'on',\n 'remove_dofs': []},\n 'aero_settings': {'dt': ws.dt,\n 'integr_order': integration_order,\n 'density': ws.rho,\n 'remove_predictor': remove_predictor,\n 'use_sparse': use_sparse,\n 'remove_inputs': [],\n 'gust_assembler': 'LeadingEdge',\n },\n }\n }\n\n ws.config['LinDynamicSim'] = {'n_tsteps': lin_tsteps,\n 'dt': ws.dt,\n 'input_generators': [\n {'name': 'control_surface_deflection',\n 'index': 0,\n 'file_path': self.route_test_dir + '/cases/elevator.txt'},\n {'name': 'u_gust',\n 'index': 0,\n 'file_path': self.route_test_dir + '/cases/gust.txt'}\n ],\n 'postprocessors': ['AerogridPlot'],\n 'postprocessors_settings':\n {'AerogridPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}, }\n }\n\n ws.config['PickleData'] = {}\n ws.config.write()\n\n if not restart:\n data = sharpy.sharpy_main.main(['', ws.route + ws.case_name + '.sharpy'])\n else:\n with open(self.route_test_dir + '/output/{:s}.pkl'.format(ws.case_name), 'rb') as f:\n data = pickle.load(f)\n\n return data\n\n def run_linear_sharpy(self, **kwargs):\n flow = ['BeamLoader', 'AerogridLoader',\n 'StaticCoupled',\n 'Modal',\n 'LinearAssembler',\n 'LinDynamicSim',\n 'PickleData']\n\n restart = False\n if restart:\n flow = ['LinDynamicSim']\n\n data = self.run_sharpy(flow, restart=restart, **kwargs)\n\n return data\n\n def extract_u_inf(self, data):\n ts = len(data.aero.timestep_info)\n _, m_chord, n_span = data.aero.timestep_info[0].u_ext[0].shape\n u_inf_ext = np.zeros((ts, m_chord, n_span))\n for i_ts in range(ts):\n u_inf_ext[i_ts, :, :] = data.aero.timestep_info[i_ts].u_ext[0][2, :, :]\n\n return u_inf_ext\n\n def test_linear_gust(self):\n test_conditions = [\n {'remove_predictor': True},\n {'remove_predictor': False},\n ]\n for test in test_conditions:\n with self.subTest(test):\n data = self.run_linear_sharpy(**test)\n u_gust_in = np.loadtxt(self.route_test_dir + '/cases/gust.txt')\n u_inf_ext = self.extract_u_inf(data)\n if test['remove_predictor']:\n predictor_offset = 0\n else:\n # input defined at time step n+1\n predictor_offset = 1\n\n # test leading edge value is equal to input\n np.testing.assert_array_almost_equal(u_inf_ext[1 + predictor_offset:, 0, 0],\n u_gust_in[:-1-predictor_offset])\n\n # check convection in panels downstream\n for i_chord in range(1, u_inf_ext.shape[1]):\n np.testing.assert_array_almost_equal(u_inf_ext[predictor_offset + 1 + i_chord:-i_chord, i_chord, 0],\n u_inf_ext[predictor_offset + 1 + i_chord - 1:-(i_chord + 1), i_chord - 1, 0])\n\n def tearDown(self):\n import shutil\n folders = ['cases', 'figures', 'output']\n for folder in folders:\n if os.path.isdir(self.route_test_dir + '/' + folder):\n shutil.rmtree(self.route_test_dir + '/' + folder)\n\n\nclass TestGusts(unittest.TestCase):\n\n def test_campbell(self):\n \"\"\"\n Test that the Campell approximation to the Von Karman filter is equivalent in continuous and\n discrete time\n\n \"\"\"\n sigma_w = 1\n length_scale = 1\n velocity = 1\n dt = 1e-1\n omega_w = np.logspace(-3, 0, 10)\n\n ss_ct = campbell(sigma_w, length_scale, velocity)\n\n ss_dt = campbell(sigma_w, length_scale, velocity, dt=dt)\n\n G_ct = ss_ct.freqresp(omega_w)\n G_dt = ss_dt.freqresp(omega_w)\n\n np.testing.assert_array_almost_equal(G_ct[0, 0, :].real, G_dt[0, 0, :].real, decimal=3)\n\n\nif __name__ == '__main__':\n unittest.main()\n\n\n" }, { "path": "tests/linear/horten/__init__.py", "content": "" }, { "path": "tests/linear/horten/test_horten.py", "content": "import sharpy.utils.algebra as algebra\nfrom sharpy.cases.hangar.richards_wing import Baseline\nimport sharpy.sharpy_main\nimport numpy as np\nimport configobj\nimport unittest\nimport os\nimport shutil\n\nroute_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n\n\ndef run_rom_convergence(case_name, case_route='./cases/', output_folder='./output/', **kwargs):\n M = kwargs.get('M', 4)\n N = kwargs.get('N', 11)\n Msf = kwargs.get('Msf', 10)\n\n trim = kwargs.get('trim', True)\n\n rho_fact = 1.\n track_body = True\n payload = 0\n u_inf = kwargs.get('u_inf', 30)\n\n use_euler = True\n\n case_name += 'M%gN%gMsf%g_u%g' % (M, N, Msf, u_inf)\n\n # M4N11Msf5\n alpha_deg = 3.974\n cs_deflection = 0.3582\n thrust = 4.8062\n\n # ROM settings\n rom_settings = dict()\n rom_settings['algorithm'] = 'mimo_rational_arnoldi'\n rom_settings['r'] = 10\n rom_settings['frequency'] = np.array([0], dtype=float)\n rom_settings['single_side'] = 'observability'\n\n case_name += 'rom_%g_%s' % (rom_settings['r'], rom_settings['single_side'][:3])\n\n ws = Baseline(M=M,\n N=N,\n Mstarfactor=Msf,\n u_inf=u_inf,\n rho=1.02,\n alpha_deg=alpha_deg, # 7.7563783342984385,\n roll_deg=0,\n cs_deflection_deg=cs_deflection, # -6.733360628875144,\n thrust=thrust, # 10.140622253017584,\n physical_time=20,\n case_name=case_name,\n case_route=case_route,\n case_name_format=2)\n\n ws.set_properties()\n ws.initialise()\n ws.clean_test_files()\n\n # ws.update_mass_stiffness(sigma=1., sigma_mass=1.5)\n ws.update_mass_stiffness(sigma=.5, sigma_mass=1.0, payload=payload)\n ws.update_fem_prop()\n ws.generate_fem_file()\n ws.update_aero_properties()\n ws.generate_aero_file()\n\n flow = ['BeamLoader',\n 'AerogridLoader',\n 'StaticTrim',\n 'BeamPlot',\n 'AerogridPlot',\n 'AeroForcesCalculator',\n 'DynamicCoupled',\n 'Modal',\n 'LinearAssembler',\n 'AsymptoticStability',\n 'SaveParametricCase'\n ]\n\n if not trim:\n flow[2] = 'StaticCoupled'\n\n settings = dict()\n settings['SHARPy'] = {'case': ws.case_name,\n 'route': ws.case_route,\n 'flow': flow,\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': output_folder,\n 'log_file': ws.case_name + '.log'}\n\n settings['BeamLoader'] = {'unsteady': 'off',\n 'orientation': algebra.euler2quat(np.array([ws.roll,\n ws.alpha,\n ws.beta]))}\n\n settings['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': int(ws.M * ws.Mstarfactor),\n 'freestream_dir': ['1', '0', '0'],\n 'control_surface_deflection': [''],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0., 0.],\n 'dt': ws.dt},\n }\n\n if ws.horseshoe is True:\n settings['AerogridLoader']['mstar'] = 1\n\n settings['StaticCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 200,\n 'num_load_steps': 1,\n 'delta_curved': 1e-5,\n 'min_delta': ws.tolerance,\n 'gravity_on': 'on',\n 'gravity': 9.81},\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {'print_info': 'on',\n 'horseshoe': ws.horseshoe,\n 'num_cores': 4,\n 'n_rollup': int(0),\n 'rollup_dt': ws.dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'vortex_radius': 1e-6,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': ws.u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': ws.rho},\n 'max_iter': 200,\n 'n_load_steps': 1,\n 'tolerance': ws.tolerance,\n 'relaxation_factor': 0.2}\n\n settings['StaticTrim'] = {'solver': 'StaticCoupled',\n 'solver_settings': settings['StaticCoupled'],\n 'thrust_nodes': ws.thrust_nodes,\n 'initial_alpha': ws.alpha,\n 'initial_deflection': ws.cs_deflection,\n 'initial_thrust': ws.thrust,\n 'max_iter': 200,\n 'fz_tolerance': 1e-2,\n 'fx_tolerance': 1e-2,\n 'm_tolerance': 1e-2,\n 'save_info': 'on'}\n\n settings['AerogridPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0,\n 'u_inf': ws.u_inf\n }\n settings['AeroForcesCalculator'] = {'write_text_file': 'off',\n 'text_file_name': ws.case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n 'coefficients': True,\n 'q_ref': 0.5 * ws.rho * ws.u_inf ** 2,\n 'S_ref': 12.809,\n }\n\n settings['BeamPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'include_FoR': 'on'}\n\n struct_solver_settings = {'print_info': 'off',\n 'initial_velocity_direction': [-1., 0., 0.],\n 'max_iterations': 950,\n 'delta_curved': 1e-6,\n 'min_delta': ws.tolerance,\n 'newmark_damp': 5e-3,\n 'gravity_on': True,\n 'gravity': 9.81,\n 'num_steps': ws.n_tstep,\n 'dt': ws.dt,\n 'initial_velocity': ws.u_inf * 1}\n\n step_uvlm_settings = {'print_info': 'on',\n 'num_cores': 4,\n 'convection_scheme': ws.wake_type,\n 'vortex_radius': 1e-6,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': ws.u_inf * 0,\n 'u_inf_direction': [1., 0., 0.]},\n 'rho': ws.rho,\n 'n_time_steps': ws.n_tstep,\n 'dt': ws.dt,\n 'gamma_dot_filtering': 3}\n\n settings['DynamicCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearDynamicCoupledStep',\n 'structural_solver_settings': struct_solver_settings,\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': step_uvlm_settings,\n 'fsi_substeps': 200,\n 'fsi_tolerance': ws.fsi_tolerance,\n 'relaxation_factor': ws.relaxation_factor,\n 'minimum_steps': 1,\n 'relaxation_steps': 150,\n 'final_relaxation_factor': 0.5,\n 'n_time_steps': 1, # ws.n_tstep,\n 'dt': ws.dt,\n 'include_unsteady_force_contribution': 'off',\n 'postprocessors': ['BeamLoads', 'BeamPlot', 'AerogridPlot', 'WriteVariablesTime'],\n 'postprocessors_settings': {'BeamLoads': {'csv_output': 'off'},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'},\n 'AerogridPlot': {\n 'u_inf': ws.u_inf,\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n 'WriteVariablesTime': {\n 'cleanup_old_solution': 'on',\n 'delimiter': ',',\n 'FoR_variables': ['total_forces',\n 'total_gravity_forces',\n 'for_pos', 'quat'],\n }}}\n\n settings['Modal'] = {'print_info': True,\n 'use_undamped_modes': True,\n 'NumLambda': 30,\n 'rigid_body_modes': True,\n 'write_modes_vtk': 'on',\n 'print_matrices': 'on',\n 'save_data': 'on',\n 'continuous_eigenvalues': 'off',\n 'dt': ws.dt,\n 'plot_eigenvalues': False,\n 'rigid_modes_cg': False}\n\n settings['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n 'linearisation_tstep': -1,\n 'linear_system_settings': {\n 'beam_settings': {'modal_projection': 'on',\n 'inout_coords': 'modes',\n 'discrete_time': True,\n 'newmark_damp': 0.5e-2,\n 'discr_method': 'newmark',\n 'dt': ws.dt,\n 'proj_modes': 'undamped',\n 'use_euler': use_euler,\n 'num_modes': 20,\n 'print_info': 'on',\n 'gravity': 'on',\n 'remove_dofs': []},\n 'aero_settings': {'dt': ws.dt,\n 'integr_order': 2,\n 'density': ws.rho * rho_fact,\n 'remove_predictor': False,\n 'use_sparse': False,\n 'vortex_radius': 1e-6,\n 'remove_inputs': ['u_gust'],\n 'rom_method': ['Krylov'],\n 'rom_method_settings': {'Krylov': rom_settings}},\n 'track_body': track_body,\n 'use_euler': use_euler,\n }}\n\n settings['AsymptoticStability'] = {\n 'print_info': 'on',\n 'modes_to_plot': [],\n # 'velocity_analysis': [27, 29, 3],\n 'display_root_locus': 'off',\n 'frequency_cutoff': 0,\n 'export_eigenvalues': 'on',\n 'target_system': ['aeroelastic', 'aerodynamic', 'structural'],\n 'output_file_format': 'dat',\n 'num_evals': 100}\n\n settings['FrequencyResponse'] = {'print_info': 'on',\n 'frequency_bounds': [0.1, 100]}\n\n settings['LinDynamicSim'] = {'dt': ws.dt,\n 'n_tsteps': ws.n_tstep,\n 'sys_id': 'LinearAeroelastic',\n # 'reference_velocity': ws.u_inf,\n 'write_dat': ['x', 'y', 't', 'u'],\n # 'write_dat': 'on',\n 'postprocessors': ['BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'AerogridPlot': {\n 'u_inf': ws.u_inf,\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'}}}\n\n settings['StabilityDerivatives'] = {'u_inf': ws.u_inf,\n 'S_ref': 12.809,\n 'b_ref': ws.span,\n 'c_ref': 0.719}\n\n settings['SaveData'] = {'save_aero': 'off',\n 'save_struct': 'off',\n 'save_linear': 'on',\n 'save_linear_uvlm': 'on'}\n\n settings['PickleData'] = {}\n\n settings['SaveParametricCase'] = {'parameters': {'r': rom_settings['r']}}\n\n config = configobj.ConfigObj()\n file_name = ws.case_route + '/' + ws.case_name + '.solver.txt'\n config.filename = file_name\n for k, v in settings.items():\n config[k] = v\n config.write()\n\n return sharpy.sharpy_main.main(['', ws.case_route + '/' + ws.case_name + '.solver.txt'])\n\n\nclass TestHortenWing(unittest.TestCase):\n\n\n def test_horten(self):\n\n M = 4\n N = 11\n Msf = 5\n\n trim = False\n\n case_name = 'horten_'\n\n case_route = route_test_dir + '/cases/'\n output_route = route_test_dir + '/output/'\n\n data = run_rom_convergence(case_name=case_name, case_route=case_route,\n output_folder=output_route,\n M=M, N=N, Msf=Msf, trim=trim)\n\n # check first 10 eigs are zero (9 integro states + yaw)\n path_to_eigs = data.output_folder + '/stability/aeroelastic_eigenvalues.dat'\n eigs = np.loadtxt(path_to_eigs)\n\n # check that aerodynamic and structural eigs are also written\n target_system = ['aerodynamic', 'structural']\n for sys in target_system:\n np.loadtxt(data.output_folder + f'/stability/{sys}_eigenvalues.dat')\n\n np.testing.assert_allclose(np.abs(eigs[:10]), 0, atol=1e-8)\n\n # check that the phugoid mode is there (more or less, very high tolerance)\n phugoid_eigs = eigs[11]\n wn_phugoid = np.linalg.norm(phugoid_eigs)\n period_phugoid = 2 * np.pi / wn_phugoid\n np.testing.assert_allclose(period_phugoid, 20.7, atol=0.1, rtol=0.1)\n\n def tearDown(self):\n folders = ['output/', 'cases/']\n\n for folder in folders:\n if os.path.isdir(route_test_dir + '/' + folder):\n shutil.rmtree(route_test_dir + '/' + folder)\n\n\nif __name__ == '__main__':\n unittest.main()\n" }, { "path": "tests/linear/rom/__init__.py", "content": "" }, { "path": "tests/linear/rom/test_balancing.py", "content": "import copy\nimport unittest\nimport sharpy.linear.src.libss as libss\nimport sharpy.rom.utils.librom as librom\nimport numpy as np\nimport sharpy.linear.src.libsparse as libsp\nimport scipy.linalg as scalg\n\n\nclass TestBalancing(unittest.TestCase):\n \"\"\"\n Test Balancing ROM methods\n\n \"\"\"\n\n def test_balreal_direct_py(self):\n Nx, Nu, Ny = 6, 4, 2\n ss = libss.random_ss(Nx, Nu, Ny, dt=0.1, stable=True)\n\n ### direct balancing\n hsv, T, Ti = librom.balreal_direct_py(ss.A, ss.B, ss.C,\n DLTI=True, full_outputs=False)\n ssb = copy.deepcopy(ss)\n\n # Note: notation below is correct and consistent with documentation\n # SHARPy historically uses notation different from regular literature notation (i.e. 'swapped')\n ssb.project(Ti, T)\n\n # Compare freq. resp. - inconclusive!\n # The system is consistently transformed using T and Tinv - system dynamics do not change, independent of\n # choice of T and Tinv. Frequency response will yield the same response:\n kv = np.linspace(0.01, 10)\n Y = ss.freqresp(kv)\n Yb = ssb.freqresp(kv)\n er_max = np.max(np.abs(Yb - Y))\n assert er_max / np.max(np.abs(Y)) < 1e-10, 'Error too large in frequency response'\n\n # Compare grammians:\n Wc = scalg.solve_discrete_lyapunov(ssb.A, np.dot(ssb.B, ssb.B.T))\n Wo = scalg.solve_discrete_lyapunov(ssb.A.T, np.dot(ssb.C.T, ssb.C))\n\n er_grammians = np.max(np.abs(Wc - Wo))\n # Print grammians to compare:\n if er_grammians / np.max(np.abs(Wc)) > 1e-10:\n print('Controllability grammian, Wc:\\n', Wc)\n print('Observability grammian, Wo:\\n', Wo)\n\n er_hankel = np.max(np.abs(np.diag(hsv) - Wc))\n # Print hsv to compare:\n if er_hankel / np.max(np.abs(Wc)) > 1e-10:\n print('Controllability grammian, Wc:\\n', Wc)\n print('Hankel values matrix, HSV:\\n', hsv)\n\n assert er_grammians / np.max(np.abs(Wc)) < 1e-10, 'Relative error in Wc-Wo is too large -> Wc != Wo'\n assert er_hankel / np.max(np.abs(Wc)) < 1e-10, 'Relative error in Wc-HSV is too large -> Wc != HSV'\n\n # The test below is inconclusive for the direct procedure! T and Tinv are produced from svd(M)\n # This means that going back from svd(M) to T and Tinv will yield the same result for any choice of T and Tinv\n # Unless something else is wrong (e.g. a typo) - so leaving it in.\n # test full_outputs option\n hsv, U, Vh, Qc, Qo = librom.balreal_direct_py(ss.A, ss.B, ss.C,\n DLTI=True, full_outputs=True)\n\n # build M matrix and SVD\n sinv = hsv ** (-0.5)\n T2 = libsp.dot(Qc, Vh.T * sinv)\n Ti2 = np.dot((U * sinv).T, Qo.T)\n assert np.linalg.norm(T2 - T) < 1e-13, 'Error too large'\n assert np.linalg.norm(Ti2 - Ti) < 1e-13, 'Error too large'\n\n ssb2 = copy.deepcopy(ss)\n ssb2.project(Ti2, T2)\n Yb2 = ssb2.freqresp(kv)\n er_max = np.max(np.abs(Yb2 - Y))\n assert er_max / np.max(np.abs(Y)) < 1e-10, 'Error too large'\n" }, { "path": "tests/linear/rom/test_krylov.py", "content": "\"\"\"\nTest Krylov ROM using Hospital Building Model\n\"\"\"\n\nimport os\nimport unittest\nimport numpy as np\n\nimport sharpy.utils.frequencyutils\nimport sharpy.utils.cout_utils as cout\nimport scipy.io as scio\nimport sharpy.utils.sharpydir as sharpydir\nimport sharpy.linear.src.libss as libss\nimport sharpy.rom.krylov as krylov\nimport sharpy.linear.src.libsparse as libsp\n\n\nclass TestKrylov(unittest.TestCase):\n\n test_dir = sharpydir.SharpyDir + '/tests/linear/rom'\n\n def setUp(self):\n cout.cout_wrap.initialise(False, False)\n A = scio.loadmat(TestKrylov.test_dir + '/src/' + 'A.mat')\n B = scio.loadmat(TestKrylov.test_dir + '/src/' + 'B.mat')\n C = scio.loadmat(TestKrylov.test_dir + '/src/' + 'C.mat')\n A = libsp.csc_matrix(A['A'])\n B = B['B']\n C = C['C']\n D = np.zeros((B.shape[1], C.shape[0]))\n\n A = A.todense()\n\n self.ss = libss.StateSpace(A, B, C, D)\n\n self.rom = krylov.Krylov()\n\n if not os.path.exists(self.test_dir + '/figs/'):\n os.makedirs(self.test_dir + '/figs/')\n\n def run_test(self, test_settings):\n self.rom.initialise(test_settings)\n ssrom = self.rom.run(self.ss)\n\n # self.rom.restart()\n frequency = test_settings['frequency'].imag\n if frequency[0] != 0.:\n wv = np.logspace(np.log10(np.min(frequency))-0.5, np.log10(np.max(frequency))+0.5, 100)\n else:\n wv = np.logspace(-1, 2, 100)\n Y_fom = self.ss.freqresp(wv)\n Y_rom = ssrom.freqresp(wv)\n\n max_error = sharpy.utils.frequencyutils.frequency_error(Y_fom, Y_rom, wv)\n\n # can be used for debugging\n # import matplotlib.pyplot as plt\n # fig = plt.figure()\n # plt.semilogx(wv, Y_fom[0, 0, :].real)\n # plt.semilogx(wv, Y_rom[0, 0, :].real)\n #\n # fig.savefig(self.test_dir + '/figs/%sfreqresp.png' %test_settings['algorithm'])\n\n assert np.log10(max_error) < -2, 'Significant mismatch in ROM frequency Response'\n\n # check saving function\n if os.path.isfile(self.test_dir + '/rom_data.h5'):\n os.remove(self.test_dir + '/rom_data.h5')\n self.rom.save(self.test_dir + '/rom_data.h5')\n\n def test_krylov(self):\n algorithm_list = {\n 'one_sided_arnoldi':\n {'r': 48,\n 'frequency': np.array([0])},\n 'dual_rational_arnoldi':\n {'r': 48,\n 'frequency': np.array([0])}\n }\n for algorithm in list(algorithm_list.keys()):\n with self.subTest(algorithm=algorithm):\n test_settings = {'algorithm': algorithm,\n 'r': algorithm_list[algorithm]['r'],\n 'frequency': algorithm_list[algorithm]['frequency']}\n self.run_test(test_settings)\n\n def tearDown(self):\n import shutil\n shutil.rmtree(self.test_dir + '/figs/')\n os.remove(self.test_dir + '/rom_data.h5')\n\nif __name__ == '__main__':\n unittest.main()\n" }, { "path": "tests/linear/rom/test_rom_framework.py", "content": "import numpy as np\nimport os\nimport unittest\nimport sharpy.cases.templates.flying_wings as wings\nimport sharpy.sharpy_main\n\n\nclass TestROMFramework(unittest.TestCase):\n \"\"\"\n Test verifyies the execution of the balancing ROMs (i.e. checks that everything runs rather than checking\n against a benchmark case\n \"\"\"\n\n def setUp(self):\n # Problem Set up\n u_inf = 1.\n alpha_deg = 0.\n rho = 1.02\n num_modes = 4\n\n # Lattice Discretisation\n M = 4\n N = 8\n M_star_fact = 1\n\n # Linear UVLM settings\n integration_order = 2\n remove_predictor = False\n use_sparse = False\n\n # Case Admin - Create results folders\n case_name = 'goland_cs'\n case_nlin_info = 'M%dN%dMs%d_nmodes%d' % (M, N, M_star_fact, num_modes)\n case_name += case_nlin_info\n\n self.route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n fig_folder = self.route_test_dir + '/figures/'\n os.makedirs(fig_folder, exist_ok=True)\n\n # SHARPy nonlinear reference solution\n ws = wings.Goland(M=M,\n N=N,\n Mstar_fact=M_star_fact,\n u_inf=u_inf,\n alpha=alpha_deg,\n rho=rho,\n sweep=0,\n physical_time=2,\n n_surfaces=2,\n route=self.route_test_dir + '/cases',\n case_name=case_name)\n\n ws.gust_intensity = 0.01\n ws.sigma = 1\n ws.horseshoe = True\n\n ws.clean_test_files()\n ws.update_derived_params()\n ws.set_default_config_dict()\n\n ws.generate_aero_file()\n ws.generate_fem_file()\n\n ws.config['SHARPy'] = {\n 'flow':\n ['BeamLoader', 'AerogridLoader',\n 'StaticCoupled',\n 'AerogridPlot',\n 'BeamPlot',\n 'Modal',\n 'LinearAssembler',\n 'FrequencyResponse',\n ],\n 'case': ws.case_name, 'route': ws.route,\n 'write_screen': 'off', 'write_log': 'on',\n 'log_folder': self.route_test_dir + '/output/',\n 'log_file': ws.case_name + '.log'}\n\n ws.config['BeamLoader'] = {\n 'unsteady': 'off',\n 'orientation': ws.quat}\n\n ws.config['AerogridLoader'] = {\n 'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 1,\n 'freestream_dir': ws.u_inf_direction,\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction,\n 'dt': ws.dt}\n }\n\n ws.config['StaticUvlm'] = {\n 'rho': ws.rho,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction},\n 'rollup_dt': ws.dt,\n 'print_info': 'on',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_aic_refresh': 0,\n 'rollup_tolerance': 1e-4}\n\n ws.config['StaticCoupled'] = {\n 'print_info': 'on',\n 'max_iter': 200,\n 'n_load_steps': 1,\n 'tolerance': 1e-10,\n 'relaxation_factor': 0.,\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': {\n 'rho': ws.rho,\n 'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': ws.dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {\n 'u_inf': ws.u_inf,\n 'u_inf_direction': ws.u_inf_direction}},\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 4,\n 'delta_curved': 1e-1,\n 'min_delta': 1e-10,\n 'gravity_on': 'on',\n 'gravity': 9.754}}\n\n ws.config['AerogridPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0}\n\n ws.config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': ws.case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n 'unsteady': 'off'}\n\n ws.config['BeamPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on'}\n\n ws.config['Modal'] = {'NumLambda': 20,\n 'rigid_body_modes': 'off',\n 'print_matrices': 'on',\n 'save_data': 'off',\n 'rigid_modes_cg': 'off',\n 'continuous_eigenvalues': 'off',\n 'dt': 0,\n 'plot_eigenvalues': False,\n 'max_rotation_deg': 15.,\n 'max_displacement': 0.15,\n 'write_modes_vtk': True,\n 'use_undamped_modes': True}\n\n ws.config['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n 'linear_system_settings': {\n 'beam_settings': {'modal_projection': 'on',\n 'inout_coords': 'modes',\n 'discrete_time': 'on',\n 'newmark_damp': 0.5e-4,\n 'discr_method': 'newmark',\n 'dt': ws.dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'off',\n 'num_modes': num_modes,\n 'print_info': 'on',\n 'gravity': 'on',\n 'remove_sym_modes': 'on',\n 'remove_dofs': []},\n 'aero_settings': {'dt': ws.dt,\n 'ScalingDict': {'length': 0.5 * ws.c_ref,\n 'speed': u_inf,\n 'density': rho},\n 'integr_order': integration_order,\n 'density': ws.rho,\n 'remove_predictor': remove_predictor,\n 'use_sparse': use_sparse,\n 'remove_inputs': ['u_gust'],\n },\n }\n }\n\n ws.config['LinDynamicSim'] = {'dt': ws.dt,\n 'n_tsteps': ws.n_tstep,\n 'sys_id': 'LinearAeroelastic',\n 'postprocessors': ['BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'AerogridPlot': {\n 'u_inf': ws.u_inf,\n 'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0},\n 'BeamPlot': {'include_rbm': 'on',\n 'include_applied_forces': 'on'}}}\n\n ws.config['FrequencyResponse'] = {'quick_plot': 'off',\n 'frequency_unit': 'k',\n 'frequency_bounds': [0.0001, 1.0],\n 'target_system': ['aeroelastic']\n }\n\n self.ws = ws\n\n def test_roms(self):\n settings = dict()\n settings['Direct'] = {'algorithm': 'Direct',\n 'print_info': 'off',\n 'algorithm_settings': {'tune': 'off',\n 'use_schur': 'on',\n 'reduction_method': 'realisation'}}\n\n settings['FrequencyLimited'] = {'algorithm': 'FrequencyLimited',\n 'print_info': 'off',\n 'algorithm_settings': {'frequency': 0.8,\n 'method_low': 'trapz',\n 'options_low': {'points': 3},\n 'method_high': 'gauss',\n 'options_high': {'partitions': 2, 'order': 1},\n 'check_stability': True}}\n\n settings['Iterative'] = {'algorithm': 'Iterative',\n 'print_info': 'off',\n 'algorithm_settings': {'lowrank': 'on'}}\n\n for rom in settings:\n with self.subTest(rom):\n self.ws.config['LinearAssembler']['linear_system_settings']['aero_settings']['rom_method'] = [\n 'Balanced']\n rom_settings = {'Balanced': settings[rom]}\n self.ws.config['LinearAssembler']['linear_system_settings']['aero_settings']['rom_method_settings'] = \\\n rom_settings\n self.ws.config.write()\n sharpy.sharpy_main.main(['', self.ws.route + self.ws.case_name + '.sharpy'])\n\n def tearDown(self):\n import shutil\n folders = ['cases', 'figures', 'output']\n for folder in folders:\n try:\n shutil.rmtree(self.route_test_dir + '/' + folder)\n except FileNotFoundError:\n pass\n\n\nif __name__ == '__main__':\n unittest.main()\n" }, { "path": "tests/linear/rom/test_schur.py", "content": "\"\"\"Test Schur Removal of Unstable Eigenvalues\n\n\"\"\"\n\nimport numpy as np\nimport unittest\nimport sharpy.rom.krylov as krylov\nimport os\nimport sharpy.utils.cout_utils as coututils\n\n\nclass TestSchurDecomposition(unittest.TestCase):\n\n test_dir = os.path.abspath(os.path.dirname(__file__))\n A = np.loadtxt(test_dir + '/src/schur_A.dat')\n eigsA = np.linalg.eigvals(A)\n\n def setUp(self):\n coututils.start_writer()\n\n def test_dt(self):\n \"\"\"\n Discrete time system test. Ensures that all eigenvalues inside the unit circle are preserved.\n \"\"\"\n A = TestSchurDecomposition.A\n eigsA = TestSchurDecomposition.eigsA\n\n rom = krylov.Krylov()\n TL, TR = rom.stable_realisation(A, ct=False)\n\n n_stable_fom = np.sum(np.abs(eigsA) <= 1)\n Ap = TL.T.dot(A.dot(TR))\n\n eigsAp = np.linalg.eigvals(Ap)\n n_stable_rom = np.sum(np.abs(eigsAp) <= 1)\n\n assert n_stable_rom == n_stable_fom, 'Number of stable eigenvalues not preserved during decomposition'\n\n def test_ct(self):\n \"\"\"\n Continuous time system test. Ensures that all eigenvalues in the left hand plane are preserved.\n \"\"\"\n A = TestSchurDecomposition.A\n eigsA = TestSchurDecomposition.eigsA\n\n rom = krylov.Krylov()\n TL, TR = rom.stable_realisation(A, ct=True)\n\n n_stable_fom = np.sum(eigsA.real <= 0)\n Ap = TL.T.dot(A.dot(TR))\n\n eigsAp = np.linalg.eigvals(Ap)\n n_stable_rom = np.sum(eigsAp.real <= 0)\n\n assert n_stable_rom == n_stable_fom, 'Number of stable eigenvalues not preserved during decomposition'\n\n def tearDown(self):\n coututils.finish_writer()\n" }, { "path": "tests/linear/rom/test_springmasssystem.py", "content": "\"\"\"\nGenerate a mass spring system\n\nNGoizueta 16 Feb 2019\n\n\"\"\"\n\nimport numpy as np\nimport sharpy.linear.src.libss as libss\nimport sharpy.linear.src.lingebm as lingebm\nimport sharpy.rom.krylov as krylov\nimport unittest\n# import matplotlib.pyplot as plt\nimport sharpy.utils.cout_utils as cout\n\ncout.cout_wrap.initialise(False, False)\n\n@unittest.skip('Not a robust test case that is giving too many failures. Use test_krylov instead')\nclass TestKrylovRom(unittest.TestCase):\n\n tolerance = 1e-3\n display_output = True\n\n def test_siso_ct(self):\n system_inputs = 'SISO'\n system_time = 'ct'\n\n ss = self.build_system(system_inputs, system_time)\n\n algorithm = 'two_sided_arnoldi'\n interpolation_point = np.array([1.0j])\n r = 7\n\n print('\\nTesting CT, SISO rational Arnoldi...')\n rom = self.run_rom(ss, algorithm, r, interpolation_point)\n\n wv = np.logspace(-1, 3, 1000)\n freq_error = self.compare_freq_resp(rom, wv, interpolation_point)\n\n print('Frequency Response Error at %.2f rad/s: %.2e' % (interpolation_point.imag, freq_error))\n\n self.assertTrue(freq_error < self.tolerance)\n\n def test_siso_dt(self):\n system_inputs = 'SISO'\n system_time = 'dt'\n\n ss = self.build_system(system_inputs, system_time)\n\n algorithm = 'two_sided_arnoldi'\n interpolation_point_ct = np.array([0.8j])\n r = 7\n\n print('\\nTesting DT, SISO rational Arnoldi...')\n rom = self.run_rom(ss, algorithm, r, interpolation_point_ct)\n\n wv = np.logspace(-1, 3, 1000)\n freq_error = self.compare_freq_resp(rom, wv, interpolation_point_ct)\n\n print('Frequency Response Error at %.2f rad/s: %.2e' % (interpolation_point_ct.imag, freq_error))\n\n self.assertTrue(freq_error < self.tolerance)\n\n def test_siso_dt_multipoint(self):\n system_inputs = 'SISO'\n system_time = 'dt'\n\n ss = self.build_system(system_inputs, system_time)\n\n algorithm = 'dual_rational_arnoldi'\n interpolation_point_ct = np.array([0.0, 2.0j, 11.0j])\n r = 7\n\n print('\\nTesting DT, SISO Multipoint rational Arnoldi...')\n rom = self.run_rom(ss, algorithm, r, interpolation_point_ct)\n\n wv = np.logspace(-1, 3, 1000)\n for i in range(len(interpolation_point_ct)):\n freq_error = self.compare_freq_resp(rom, wv, interpolation_point_ct[i])\n print('Frequency Response Error at %.2f rad/s: %.2e' % (interpolation_point_ct[i].imag, freq_error))\n self.assertTrue(freq_error < self.tolerance)\n\n\n def build_system(self, system_inputs, system_time):\n N = 5 # Number of masses/springs/dampers\n\n k_db = np.linspace(1, 10, N) # Stiffness database\n m_db = np.logspace(2, 0, N) # Mass database\n C_db = np.ones(N) * 1e-1 # Damping database\n\n # Build mass matrix\n m = np.zeros((N, N))\n k = np.zeros((N, N))\n C = np.zeros((N, N))\n m[0, 0] = m_db[0]\n\n k[0, 0:2] = [k_db[0]+k_db[1], -k_db[1]]\n C[0, 0:2] = [C_db[0] + C_db[1], -C_db[1]]\n for i in range(1, N-1):\n k[i, i-1:i+2] = [-k_db[i-1], k_db[i]+k_db[i+1], -k_db[i+1]]\n C[i, i-1:i+2] = [-C_db[i-1], C_db[i]+C_db[i+1], -C_db[i+1]]\n m[i, i] = m_db[i]\n m[-1, -1] = m_db[-1]\n k[-1, -2:] = [-k_db[-1], k_db[-1]]\n C[-1, -2:] = [-C_db[-1], C_db[-1]]\n\n # Input: Forces, Output: Displacements\n if system_inputs == 'MIMO':\n b = np.zeros((2*N, N))\n b[N:, :] = np.eye(N)\n # Output rn\n c = np.zeros((N, 2*N))\n c[:, :N] = np.eye(N)\n d = np.zeros((N, N))\n else:\n b = np.zeros((2*N,))\n b[-1] = 1.\n c = np.zeros((1, 2*N))\n c[0, N-1] = 1\n d = np.zeros(1)\n\n # Plant matrix\n Minv = np.linalg.inv(m)\n MinvK = Minv.dot(k)\n A = np.zeros((2*N, 2*N))\n A[:N, N:] = np.eye(N)\n A[N:, :N] = -MinvK\n A[N:, N:] = -Minv.dot(C)\n\n # Build State Space\n if system_time == 'ct':\n system = libss.StateSpace(A, b, c, d, dt=None)\n\n else:\n # Discrete time system\n dt = 1e-2\n Adt, Bdt, Cdt, Ddt = lingebm.newmark_ss(m, C, k, dt=dt, num_damp=0)\n\n system = libss.StateSpace(Adt, Bdt, Cdt, Ddt, dt=dt)\n\n # SISO Gains for DT system\n if system_inputs == 'SISO':\n b_dt = np.zeros((N))\n b_dt[-1] = 1\n system.addGain(b_dt, 'in')\n\n system.addGain(c, where='out')\n\n return system\n\n def run_rom(self, system, algorithm, r, interpolation_point):\n rom = krylov.Krylov()\n rom_settings = {'algorithm': algorithm,\n 'r': r,\n 'frequency': interpolation_point}\n\n rom.initialise(in_settings=rom_settings)\n\n rom.run(system)\n\n return rom\n\n def compare_freq_resp(self, rom, wv, interpolation_frequency, show_plots=False):\n\n Y_fom = rom.ss.freqresp(wv)\n Y_rom = rom.ssrom.freqresp(wv)\n\n interpol_index = np.argwhere(wv >= interpolation_frequency.imag)[0]\n\n error = np.abs(Y_fom[0, 0, interpol_index] - Y_rom[0, 0, interpol_index])\n\n if TestKrylovRom.display_output:\n pass\n # fig, ax = plt.subplots(nrows=2)\n # ax[0].semilogx(wv, np.abs(Y_fom[0, 0, :]), 'k-')\n # ax[0].semilogx(wv, np.abs(Y_rom[0, 0, :]), '--', color='0.2')\n\n # ax[1].semilogx(wv, np.angle(Y_fom[0, 0, :]), 'k-')\n # ax[1].semilogx(wv, np.angle(Y_rom[0, 0, :]), '--', color='0.2')\n # fig.show()\n return error\n\n def tearDown(self):\n cout.cout_wrap = cout.Writer()\n\n# evals_DT = np.linalg.eigvals(system_DT.A)\n#\n# evals_dt_conv = np.log(evals_DT) / dt\n# #\n# plt.scatter(evals_ss.real, evals_ss.imag, marker='s')\n# # plt.scatter(evals_dt_conv.real, evals_dt_conv.imag, marker='^')\n# # plt.show()\n#\n# wv = np.logspace(-1, 1, 1000)\n# freqresp = system_DT.freqresp(wv)\n# freqresp_ct = system_CT.freqresp(wv)\n#\n# # fig, ax = plt.subplots(nrows=1)\n# # bode_mag_dt = (freqresp[0, 0, :].real)\n# # bode_mag_ct = (freqresp_ct[0, 0, :].real)\n# # ax.semilogx(wv, bode_mag_dt)\n# # ax.semilogx(wv, bode_mag_ct, ls='--')\n# #\n# # fig.show()\n#\n# print('Routine Complete')\n#\n# # ROM\n# rom = krylov.KrylovReducedOrderModel()\n# rom.initialise(data=None,ss=system_DT)\n#\n# algorithm = 'dual_rational_arnoldi'\n# # algorithm = 'arnoldi'\n# r = 1\n# # frequency = np.array([1.0, 1.005j])\n# # frequency = np.array([np.inf])\n# frequency = np.array([0.7j, 1.0j])\n# z_interpolation = np.exp(frequency*dt)\n#\n# rom.run(algorithm,r, frequency=z_interpolation)\n#\n# plot_freq = freq_plots.FrequencyResponseComparison()\n# plot_settings = {'frequency_type': 'w',\n# 'plot_type': 'bode'}\n#\n# plot_freq.initialise(None, system_DT, rom, plot_settings)\n# if system_inputs == 'MIMO':\n# plot_freq.plot_frequency_response(wv, freqresp[:3, :3, :], rom.ssrom.freqresp(wv)[:3, :3, :], frequency)\n# else:\n# plot_freq.plot_frequency_response(wv, freqresp, rom.ssrom.freqresp(wv), frequency)\n\n# plot_freq.plot_frequency_response(wv, freqresp[4:, 4:, :], rom.ssrom.freqresp(wv), frequency)\n# plot_freq.save_figure('DT_07_1_r2.png')\n\nif __name__=='__main__':\n unittest.main()\n" }, { "path": "tests/linear/statespace/__init__.py", "content": "" }, { "path": "tests/linear/statespace/test_statespace.py", "content": "import copy\nimport unittest\nimport os\n\nimport numpy as np\n\nfrom sharpy.linear.src import libsparse as libsp\nfrom sharpy.linear.src.libss import StateSpace, SSconv, compare_ss, scale_SS, Gain, random_ss, couple, join, disc2cont, series\nfrom sharpy.linear.utils.ss_interface import LinearVector, InputVariable, StateVariable, OutputVariable\n\n\nclass Test_dlti(unittest.TestCase):\n \"\"\" Test methods into this module for DLTI systems \"\"\"\n\n def setUp(self):\n # allocate some state-space model (dense and sparse)\n dt = 0.3\n Ny, Nx, Nu = 8, 3, 5\n A = np.random.rand(Nx, Nx)\n B = np.random.rand(Nx, Nu)\n C = np.random.rand(Ny, Nx)\n D = np.random.rand(Ny, Nu)\n self.SS = StateSpace(A, B, C, D, dt=dt)\n self.SSsp = StateSpace(libsp.csc_matrix(A), libsp.csc_matrix(B), C, D, dt=dt)\n\n self.SS.input_variables = LinearVector([InputVariable('input1', size=3, index=0),\n InputVariable('input2', size=2, index=1)])\n self.SS.state_variables = LinearVector([StateVariable('state1', size=3, index=0)])\n self.SS.output_variables = LinearVector([OutputVariable('output1', size=3, index=0),\n OutputVariable('output2', size=5, index=1)])\n\n self.SSsp.input_variables = self.SS.input_variables\n self.SSsp.output_variables = self.SS.output_variables\n self.SSsp.state_variables = self.SS.state_variables\n\n def test_SSconv(self):\n\n SS = self.SS\n SSsp = self.SSsp\n Nu, Nx, Ny = SS.inputs, SS.states, SS.outputs\n A, B, C, D = SS.get_mats()\n\n # remove predictor: try different scenario\n B1 = np.random.rand(Nx, Nu)\n SSpr0 = StateSpace(*SSconv(A, B, B1, C, D), dt=0.3)\n SSpr1 = StateSpace(*SSconv(A, B, libsp.csc_matrix(B1), C, D), dt=0.3)\n SSpr2 = StateSpace(*SSconv(\n libsp.csc_matrix(A), B, libsp.csc_matrix(B1), C, D), dt=0.3)\n SSpr3 = StateSpace(*SSconv(\n libsp.csc_matrix(A), libsp.csc_matrix(B), B1, C, D), dt=0.3)\n SSpr4 = StateSpace(*SSconv(\n libsp.csc_matrix(A), libsp.csc_matrix(B), libsp.csc_matrix(B1), C, D), dt=0.3)\n compare_ss(SSpr0, SSpr1)\n compare_ss(SSpr0, SSpr2)\n compare_ss(SSpr0, SSpr3)\n compare_ss(SSpr0, SSpr4)\n\n def test_scale_SS(self):\n\n SS = self.SS\n SSsp = self.SSsp\n Nu, Nx, Ny = SS.inputs, SS.states, SS.outputs\n\n # scale (hard-copy)\n insc = np.random.rand(Nu)\n stsc = np.random.rand(Nx)\n outsc = np.random.rand(Ny)\n SSadim = scale_SS(SS, insc, outsc, stsc, byref=False)\n SSadim_sp = scale_SS(SSsp, insc, outsc, stsc, byref=False)\n compare_ss(SSadim, SSadim_sp)\n\n # scale (by reference)\n SS.scale(insc, outsc, stsc)\n SSsp.scale(insc, outsc, stsc)\n compare_ss(SS, SSsp)\n\n def test_addGain(self):\n\n SS = self.SS\n SSsp = self.SSsp\n Nu, Nx, Ny = SS.inputs, SS.states, SS.outputs\n\n # add gains\n Kin = np.random.rand(Nu, 5)\n Kout = np.random.rand(4, Ny)\n\n gain_in = Gain(Kin)\n gain_in.input_variables = LinearVector([InputVariable('input1', size=5, index=0)])\n gain_in.output_variables = LinearVector([OutputVariable('output1', size=Nu, index=0)])\n\n gain_out = Gain(Kout)\n gain_out.input_variables = LinearVector.transform(self.SS.output_variables, InputVariable)\n gain_out.output_variables = LinearVector([OutputVariable('final_output', size=gain_out.outputs, index=0)])\n\n SS.addGain(gain_in, 'in')\n SS.addGain(gain_out, 'out')\n SSsp.addGain(gain_in, 'in')\n SSsp.addGain(gain_out, 'out')\n compare_ss(SS, SSsp)\n\n def test_freqresp(self):\n # freq response: try different scenario\n\n SS = self.SS\n SSsp = self.SSsp\n Nu, Nx, Ny = SS.inputs, SS.states, SS.outputs\n\n kv = np.linspace(0, 1, 8)\n Y = SS.freqresp(kv)\n Ysp = SSsp.freqresp(kv)\n er = np.max(np.abs(Y - Ysp))\n assert er < 1e-10, 'Test on freqresp failed'\n\n SS.D = libsp.csc_matrix(SS.D)\n Y1 = SS.freqresp(kv)\n er = np.max(np.abs(Y - Y1))\n assert er < 1e-10, 'Test on freqresp failed'\n\n def test_couple(self):\n dt = .2\n Nx1, Nu1, Ny1 = 3, 4, 2\n Nx2, Nu2, Ny2 = 4, 3, 2\n K12 = np.random.rand(Nu1, Ny2)\n K21 = np.random.rand(Nu2, Ny1)\n SS1 = random_ss(Nx1, Nu1, Ny1, dt=.2)\n SS2 = random_ss(Nx2, Nu2, Ny2, dt=.2)\n\n SS1sp = StateSpace(libsp.csc_matrix(SS1.A),\n libsp.csc_matrix(SS1.B),\n libsp.csc_matrix(SS1.C),\n libsp.csc_matrix(SS1.D), dt=dt)\n SS2sp = StateSpace(libsp.csc_matrix(SS2.A),\n libsp.csc_matrix(SS2.B),\n libsp.csc_matrix(SS2.C),\n libsp.csc_matrix(SS2.D), dt=dt)\n K12sp = libsp.csc_matrix(K12)\n K21sp = libsp.csc_matrix(K21)\n\n # SCref=couple_full(SS1,SS2,K12,K21)\n SC0 = couple(SS1, SS2, K12, K21)\n # compare_ss(SCref,SC0)\n for SSa in [SS1, SS1sp]:\n for SSb in [SS2, SS2sp]:\n for k12 in [K12, K12sp]:\n for k21 in [K21, K21sp]:\n SChere = couple(SSa, SSb, k12, k21)\n compare_ss(SC0, SChere)\n\n def test_join(self):\n\n Nx, Nu, Ny = 4, 3, 2\n SS_list = [random_ss(Nx, Nu, Ny, dt=.2) for ii in range(3)]\n\n wv = [.3, .5, .2]\n SSjoin = join(SS_list, wv)\n\n kv = np.array([0., 1., 3.])\n Yjoin = SSjoin.freqresp(kv)\n\n Yref = np.zeros_like(Yjoin)\n for ii in range(3):\n Yref += wv[ii] * SS_list[ii].freqresp(kv)\n\n er = np.max(np.abs(Yjoin - Yref))\n assert er < 1e-12, 'test_join error %.3e too large' % er\n\n def test_disc2cont(self):\n # not the best test given that eigenvalue comparison is not great with random systems. (error grows near\n # nyquist frequency)\n\n # this test is for execution purposes only.\n sys = copy.deepcopy(self.SS)\n self.SS.disc2cont()\n\n ct_sys = disc2cont(sys)\n\n def test_remove_inputs(self):\n dt = 0.3\n Ny, Nx, Nu = 4, 3, 10\n A = np.random.rand(Nx, Nx)\n B = np.random.rand(Nx, Nu)\n C = np.random.rand(Ny, Nx)\n D = np.random.rand(Ny, Nu)\n self.SS = StateSpace(A, B, C, D, dt=dt)\n self.SSsp = StateSpace(libsp.csc_matrix(A), libsp.csc_matrix(B), C, D, dt=dt)\n\n self.SS.input_variables = LinearVector([InputVariable('input1', size=3, index=0),\n InputVariable('input2', size=4, index=1),\n InputVariable('input3', size=2, index=2),\n InputVariable('input4', size=1, index=3)])\n self.SSsp.input_variables = self.SS.input_variables.copy()\n\n rows_loc = self.SS.input_variables.num_variables * [None]\n for ith, variable in enumerate(self.SS.input_variables):\n rows_loc[ith] = variable.rows_loc\n\n self.SS.remove_inputs('input2', 'input4')\n\n assert self.SS.B.shape == (Nx, self.SS.input_variables.size), 'B matrix not trimmed correctly'\n assert self.SS.D.shape == (Ny, self.SS.input_variables.size), 'D matrix not trimmed correctly'\n\n assert self.SS.input_variables[0].rows_loc == rows_loc[0], \\\n 'Rows of input 1 not retained correctly'\n assert self.SS.input_variables[1].rows_loc == rows_loc[2], \\\n 'Rows of input 3 not retained correctly'\n\n # sparse system\n self.SSsp.remove_inputs('input2', 'input4')\n assert self.SSsp.B.shape == (Nx, self.SSsp.input_variables.size), 'Bsp matrix not trimmed correctly'\n assert self.SSsp.D.shape == (Ny, self.SSsp.input_variables.size), 'Dsp matrix not trimmed correctly'\n\n assert self.SSsp.input_variables[0].rows_loc == rows_loc[0], \\\n 'Rows of input 1 not retained correctly in sparse system'\n assert self.SSsp.input_variables[1].rows_loc == rows_loc[2], \\\n 'Rows of input 3 not retained correctly in sparse system'\n\n def test_series(self):\n \"\"\"\n Test Series connection\n\n input11 -- >>> SS2 ----> input1, input2 -----> self.SS ----> y\n \"\"\"\n Nx2, Nu2, Ny2 = 4, 3, self.SS.inputs\n SS2 = random_ss(Nx2, Nu2, Ny2, dt=self.SS.dt)\n SS2.input_variables = LinearVector([InputVariable('input11', size=3, index=0)])\n SS2.state_variables = LinearVector([StateVariable('state11', size=4, index=0)])\n SS2.output_variables = LinearVector([OutputVariable('input1', size=3, index=0),\n OutputVariable('input2', size=2, index=1)])\n\n SSnew = series(SS2, self.SS)\n state_vars = LinearVector.merge(SS2.state_variables, self.SS.state_variables)\n\n LinearVector.check_same_vectors(SSnew.state_variables, state_vars)\n\n assert SSnew.outputs == self.SS.outputs, 'Number of outputs not the same as self.SS'\n assert SSnew.inputs == SS2.inputs, 'Number of inputs not the same as SS2'\n\n\nclass TestStateSpaceManipulation(unittest.TestCase):\n\n route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n files_created_by_test = []\n\n def setUp(self):\n Ny, Nx, Nu = 6, 3, 10\n A = np.random.rand(Nx, Nx)\n B = np.random.rand(Nx, Nu)\n C = np.random.rand(Ny, Nx)\n D = np.random.rand(Ny, Nu)\n self.ss = StateSpace(A, B, C, D)\n self.SSsp = StateSpace(libsp.csc_matrix(A), libsp.csc_matrix(B), C, D)\n\n self.ss.input_variables = LinearVector([InputVariable('input1', size=3, index=0),\n InputVariable('input2', size=4, index=1),\n InputVariable('input3', size=2, index=2),\n InputVariable('input4', size=1, index=3)])\n\n self.ss.state_variables = LinearVector([StateVariable('state1', size=Nx, index=0)])\n self.ss.output_variables = LinearVector([OutputVariable('output1', size=1, index=0),\n OutputVariable('output2', size=3, index=1),\n OutputVariable('output3', size=2, index=2)])\n\n def test_remove_outputs(self):\n self.ss.remove_outputs('output1') # size 1\n self.ss.remove_outputs('output2') # size 3\n\n assert self.ss.outputs == 2, 'Number of outputs not correct'\n\n def test_retain_channels(self):\n \"\"\"\n Retain certain input and output channels only\n \"\"\"\n retain_input_channels = [0, 7]\n self.ss.retain_inout_channels(retain_input_channels, where='in')\n\n assert self.ss.inputs == len(retain_input_channels), 'Number of inputs not correct'\n assert self.ss.input_variables[0].size == 1, 'input1 not correct size'\n assert self.ss.input_variables[1].name == 'input3', 'input2 not properly removed'\n\n retain_output_channels = [0, 5]\n self.ss.retain_inout_channels(retain_output_channels, where='out')\n assert self.ss.outputs == len(retain_output_channels), 'Number of outputs not correct'\n assert self.ss.output_variables[0].size == 1, 'output1 not correct size'\n assert self.ss.output_variables[1].name == 'output3', 'output2 not properly removed'\n assert self.ss.output_variables[1].size == 1, 'output3 not properly trimmed'\n assert self.ss.output_variables[1].index == 1, 'output3 not properly indexed'\n\n def test_input_output(self):\n\n h5_filename = self.route_test_dir + '/file_test_statespace_inout.h5'\n self.files_created_by_test.append(h5_filename)\n\n self.ss.save(h5_filename)\n\n loaded_ss = StateSpace.load_from_h5(h5_filename)\n\n LinearVector.check_same_vectors(self.ss.input_variables,\n loaded_ss.input_variables)\n\n LinearVector.check_same_vectors(self.ss.output_variables,\n loaded_ss.output_variables)\n\n LinearVector.check_same_vectors(self.ss.state_variables,\n loaded_ss.state_variables)\n\n np.testing.assert_array_almost_equal(self.ss.A, loaded_ss.A)\n np.testing.assert_array_almost_equal(self.ss.B, loaded_ss.B)\n np.testing.assert_array_almost_equal(self.ss.C, loaded_ss.C)\n np.testing.assert_array_almost_equal(self.ss.D, loaded_ss.D)\n\n @classmethod\n def tearDownClass(cls):\n for file in cls.files_created_by_test:\n if os.path.exists(file):\n os.remove(file)\n\n\nclass TestGains(unittest.TestCase):\n\n route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n files_created_by_test = []\n\n def test_dot(self):\n \"\"\"\n u ---> K1 ----> K2 ---->y\n Returns:\n\n \"\"\"\n m1 = 4\n p1 = 3\n k1 = np.random.rand(p1, m1)\n gain1 = Gain(k1,\n input_vars=LinearVector([InputVariable('input', size=m1, index=0)]),\n output_vars=LinearVector([OutputVariable('output1', size=p1, index=0)]))\n\n m2 = p1\n p2 = 5\n k2 = np.random.rand(p2, m2)\n gain2 = Gain(k2,\n input_vars=LinearVector([InputVariable('output1', size=m2, index=0)]),\n output_vars=LinearVector([OutputVariable('output', size=p2, index=0)]))\n\n gain = gain2.dot(gain1)\n np.testing.assert_array_almost_equal(gain.value, k2.dot(k1))\n\n @unittest.expectedFailure\n def test_fail_connection(self):\n \"\"\"\n This one should fail because of dimension mismatch\n\n u ---> K1 ----> K2 ---->y\n\n \"\"\"\n m1 = 4\n p1 = 3\n k1 = np.random.rand(p1, m1)\n gain1 = Gain(k1,\n input_vars=LinearVector([InputVariable('input', size=m1, index=0)]),\n output_vars=LinearVector([OutputVariable('output1', size=p1, index=0)]))\n\n m2 = 2\n p2 = 5\n k2 = np.random.rand(p2, m2)\n gain2 = Gain(k2,\n input_vars=LinearVector([InputVariable('output1', size=m2, index=0)]),\n output_vars=LinearVector([OutputVariable('output', size=p2, index=0)]))\n\n # check the check fails :)\n with self.subTest('ss_interface_check'):\n LinearVector.check_connection(gain1.output_variables, gain2.input_variables)\n\n with self.subTest('connection_check'):\n gain = gain2.dot(gain1)\n np.testing.assert_array_almost_equal(gain.value, k2.dot(k1))\n\n def test_input_output_gains(self):\n m1 = 4\n p1 = 3\n k1 = np.random.rand(p1, m1)\n gain1 = Gain(k1,\n input_vars=LinearVector([InputVariable('input', size=m1, index=0)]),\n output_vars=LinearVector([OutputVariable('output1', size=p1, index=0)]))\n\n m2 = 2\n p2 = 5\n k2 = np.random.rand(p2, m2)\n gain2 = Gain(k2,\n input_vars=LinearVector([InputVariable('output1', size=m2, index=0)]),\n output_vars=LinearVector([OutputVariable('output', size=p2, index=0)]))\n\n with self.subTest('Save to single h5 file'):\n h5_file_name = self.route_test_dir + '/gain1.h5'\n self.files_created_by_test.append(h5_file_name)\n gain1.save(h5_file_name)\n\n with self.subTest('Load from single h5 file'):\n loaded_gain = Gain.load_from_h5(h5_file_name)\n self.check_gains_equal(gain1, loaded_gain)\n\n with self.subTest('Save both gains to single h5'):\n h5_file_name = self.route_test_dir + '/multi_gain.h5'\n self.files_created_by_test.append(h5_file_name)\n\n Gain.save_multiple_gains(h5_file_name, ('gain1', gain1), ('gain2', gain2))\n\n with self.subTest('Load multiple gains from a single h5'):\n out_gains = Gain.load_multiple_gains(h5_file_name)\n self.check_gains_equal(gain1, out_gains['gain1'])\n self.check_gains_equal(gain2, out_gains['gain2'])\n\n @staticmethod\n def check_gains_equal(gain1, gain2):\n np.testing.assert_array_almost_equal(gain1.value, gain2.value)\n LinearVector.check_same_vectors(gain1.input_variables,\n gain2.input_variables)\n LinearVector.check_same_vectors(gain1.output_variables,\n gain2.output_variables)\n\n @classmethod\n def tearDownClass(cls):\n for file in cls.files_created_by_test:\n if os.path.exists(file):\n os.remove(file)\n\n\nif __name__ == '__main__':\n unittest.main()\n" }, { "path": "tests/linear/statespace/test_variable_tracker.py", "content": "import unittest\nimport os\nimport h5py\nimport sharpy.utils.h5utils as h5utils\n\nfrom sharpy.linear.utils.ss_interface import InputVariable, LinearVector, OutputVariable\n\n\nclass TestVariables(unittest.TestCase):\n\n route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n files_created_by_test = []\n\n def setUp(self):\n # initialising with index out of order\n Kzeta = 4\n input_variables_list = [InputVariable('zeta', size=3 * Kzeta, index=0),\n InputVariable('zeta_dot', size=3 * Kzeta, index=1), # this should be one\n InputVariable('u_gust', size=3 * Kzeta, index=2)]\n\n self.input_variables = LinearVector(input_variables_list)\n\n def test_initialisation(self):\n Kzeta = 4\n input_variables_list = [InputVariable('zeta', size=3 * Kzeta, index=0),\n InputVariable('u_gust', size=3 * Kzeta, index=2),\n InputVariable('zeta_dot', size=3 * Kzeta, index=1)]\n\n input_variables = LinearVector(input_variables_list)\n\n sorted_indices = [variable.index for variable in input_variables]\n variable_names = [variable.name for variable in input_variables]\n assert sorted_indices == [0, 1, 2], 'Error sorting indices in initialisation'\n assert variable_names == ['zeta', 'zeta_dot', 'u_gust'], 'Error sorting indices in initialisation'\n\n def test_remove(self):\n\n self.input_variables.remove('zeta_dot')\n\n sorted_indices = [variable.index for variable in self.input_variables]\n assert sorted_indices == [0, 1], 'Error removing variable'\n\n def test_modify(self):\n\n new_values = {'name': 'new_u_gust',\n 'size': 5,\n }\n\n self.input_variables.modify('u_gust', **new_values)\n\n assert self.input_variables.get_variable_from_name('new_u_gust').size == 5, 'Variable not modified correctly'\n\n def test_add(self):\n\n new_variable = InputVariable('control_surface', size=2, index=3)\n\n self.input_variables.add(new_variable)\n self.input_variables.update_locations()\n\n # test it's properly included - it will raise an error internally if not\n included_var = self.input_variables.get_variable_from_name('control_surface')\n\n new_variable_repeated_index = InputVariable('control_surface_2', size=2, index=3)\n try:\n self.input_variables.add(new_variable_repeated_index)\n except IndexError:\n # correct behaviour\n pass\n else:\n raise IndexError('Variable was added when it should have been rejected because of repeated index')\n\n new_variable_inbetween = InputVariable('first_variable', size=2, index=-1)\n self.input_variables.add(new_variable_inbetween)\n self.input_variables.update_locations()\n\n assert self.input_variables[0].name == new_variable_inbetween.name, 'New variable not added at the start of' \\\n ' the list'\n\n self.input_variables.add('var_from_string', size=3, index=10)\n assert self.input_variables[-1].name == 'var_from_string', 'Variable from string not added correctly'\n\n self.input_variables.update_indices()\n\n def test_append(self):\n self.input_variables.append('last_var', size=3)\n self.input_variables.update_indices()\n\n assert self.input_variables[-1].name == 'last_var', 'Variable not properly appended'\n\n # test adding an incorrect input\n out_var = OutputVariable('out_var', size=1, index=4)\n\n try:\n self.input_variables.append(out_var)\n except TypeError:\n pass # this is what should happen\n else:\n raise TypeError('Error. Able to append an output variable to an input variable')\n\n self.input_variables.append(InputVariable(name='last_last_var', size=2, index=0))\n\n assert self.input_variables[-1].name == 'last_last_var', 'Variable not properly appended'\n\n def test_merge(self):\n second_variables_list = [InputVariable('eta', size=3, index=0),\n InputVariable('eta_dot', size=3, index=1)]\n\n second_vector = LinearVector(second_variables_list)\n\n merged_vector = LinearVector.merge(self.input_variables, second_vector)\n\n assert merged_vector[-1].name == 'eta_dot', 'Vectors not coupled properly'\n assert merged_vector[2].name == 'u_gust', 'Vectors not coupled properly'\n\n def test_copy(self):\n vec1 = self.input_variables\n vec2 = vec1.copy()\n\n assert vec1 is not vec2, 'Object not deep copied'\n\n def test_transform(self):\n\n new_vector = LinearVector.transform(self.input_variables, to_type=OutputVariable)\n\n LinearVector.check_same_vectors(new_vector, self.input_variables)\n assert new_vector.num_variables == self.input_variables.num_variables, 'Number of variables not equal'\n assert new_vector.size == self.input_variables.size, 'Size not equal'\n\n for i_var in range(new_vector.num_variables):\n assert new_vector[i_var].name == self.input_variables[i_var].name, 'Name does not match'\n assert new_vector[i_var].index == self.input_variables[i_var].index, 'Index does not match'\n assert new_vector[i_var].size == self.input_variables[i_var].size, 'Size does not match'\n\n new_vector.append(OutputVariable('last_var', size=2, index=0))\n\n assert new_vector.num_variables == self.input_variables.num_variables + 1, 'Number of variables got ' \\\n 'updated in the original object'\n assert new_vector[-1].name == 'last_var', 'Variable not correctly appended'\n assert new_vector[-1].index == new_vector.num_variables - 1, 'Variable not correctly appended'\n\n def test_save_to_h5(self):\n Kzeta = 4\n input_variables_list = [InputVariable('zeta', size=3 * Kzeta, index=0),\n InputVariable('zeta_dot', size=3 * Kzeta, index=1), # this should be one\n InputVariable('u_gust', size=3 * Kzeta, index=2)]\n\n input_variables = LinearVector(input_variables_list)\n\n h5_file_name = self.route_test_dir + '/test_save_variables.h5'\n self.files_created_by_test.append(h5_file_name)\n with h5py.File(h5_file_name, 'w') as fid:\n input_variables.add_to_h5_file(fid)\n\n with h5py.File(h5_file_name, 'r') as fid:\n data_dict = h5utils.load_h5_in_dict(fid)\n\n loaded_variable = LinearVector.load_from_h5_file('InputVariable', data_dict['InputVariable'])\n\n LinearVector.check_same_vectors(input_variables, loaded_variable)\n\n def tearDown(self):\n for file in self.files_created_by_test:\n if os.path.exists(file):\n os.remove(file)\n\n\nif __name__ == '__main__':\n unittest.main()\n" }, { "path": "tests/linear/uvlm/__init__.py", "content": "" }, { "path": "tests/linear/uvlm/test_infinite_span.py", "content": "\"\"\"Linearised UVLM 2D tests\n\n\nTest linear UVLM solver against analytical results for 2D wing\n\nAuthor: S. Maraniello, Dec 2018\nModified: N. Goizueta, Sep 2019\n\"\"\"\n\nimport unittest\nimport os\n# import matplotlib.pyplot as plt\nimport numpy as np\nimport shutil\nimport sharpy.sharpy_main\nimport sharpy.utils.algebra as algebra\nimport sharpy.utils.analytical as an\nimport sharpy.linear.src.linuvlm as linuvlm\nimport sharpy.cases.templates.flying_wings as flying_wings\nimport sharpy.utils.sharpydir as sharpydir\nimport sharpy.utils.cout_utils as cout\n\n\nclass Test_infinite_span(unittest.TestCase):\n \"\"\"\n Test infinite-span flat wing at zero incidence against analytical solutions\n \"\"\"\n\n test_dir = sharpydir.SharpyDir + '/tests/linear/uvlm/'\n\n def setUp_from_params(self, Nsurf, integr_ord, RemovePred, UseSparse, RollNodes):\n \"\"\"\n Builds SHARPy solution for a rolled infinite span flat wing at zero\n incidence. Rolling can be obtained both by rotating the FoR A or\n modifying the nodes of the wing.\n \"\"\"\n\n # Flags\n self.ProducePlots = True\n\n # Define Parametrisation\n M, N, Mstar_fact = 8, 8, 50\n\n # Flying properties\n if RollNodes:\n self.Roll0Deg = 0.\n else:\n self.Roll0Deg = 0.\n self.Alpha0Deg = 0.0\n Uinf0 = 50.\n\n ### ----- build directories\n self.case_code = 'wagner'\n self.case_main = self.case_code + \\\n '_r%.4daeff%.2d_rnodes%s_Nsurf%.2dM%.2dN%.2dwk%.2d' \\\n % (int(np.round(100 * self.Roll0Deg)),\n int(np.round(100 * self.Alpha0Deg)),\n RollNodes, Nsurf, M, N, Mstar_fact)\n self.case_main += 'ord%.1d_rp%s_sp%s' % (integr_ord, RemovePred, UseSparse)\n self.route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n route_main = self.route_test_dir + '/res/'\n self.figfold = self.route_test_dir + '/figs/'\n\n if os.path.exists(route_main):\n shutil.rmtree(route_main)\n if os.path.exists(self.figfold):\n shutil.rmtree(self.figfold)\n\n os.makedirs(route_main)\n os.makedirs(self.figfold)\n\n ### ----- sharpy reference solution\n # Build wing model\n ws = flying_wings.QuasiInfinite(\n M=M, N=N, Mstar_fact=Mstar_fact, n_surfaces=Nsurf,\n u_inf=Uinf0, alpha=self.Alpha0Deg, roll=self.Roll0Deg,\n aspect_ratio=1e5, RollNodes=RollNodes,\n route=route_main, case_name=self.case_main)\n\n ws.main_ea = .4\n ws.clean_test_files()\n ws.update_derived_params()\n ws.generate_fem_file()\n ws.generate_aero_file()\n\n # solution flow\n ws.set_default_config_dict()\n ws.config['SHARPy']['flow'] = ['BeamLoader', 'AerogridLoader', 'StaticUvlm', 'BeamPlot', 'AerogridPlot']\n ws.config['SHARPy']['log_folder'] = self.route_test_dir + '/output/' + self.case_code + '/'\n ws.config['SHARPy']['write_screen'] = 'off'\n ws.config['SHARPy']['write_log'] = 'off'\n ws.config['LinearUvlm'] = {'dt': ws.dt,\n 'integr_order': integr_ord,\n 'density': ws.rho,\n 'remove_predictor': RemovePred,\n 'use_sparse': UseSparse,\n 'ScalingDict': {'length': 1.,\n 'speed': 1.,\n 'density': 1.},\n 'vortex_radius': 1e-6}\n ws.config.write()\n\n # solve at linearistion point\n data0 = sharpy.sharpy_main.main(['...', route_main + self.case_main + '.sharpy'])\n tsaero0 = data0.aero.timestep_info[0]\n tsaero0.rho = ws.config['LinearUvlm']['density']\n\n ### ---- normalisation parameters\n self.start_writer()\n # verify chord\n c_ext = np.linalg.norm(tsaero0.zeta[0][:, 0, 0] - tsaero0.zeta[0][:, -1, 0])\n assert np.abs(ws.c_ref - c_ext) < 1e-8, 'Wrong reference chord'\n\n # reference force - total\n qinf = 0.5 * ws.rho * Uinf0 ** 2\n span = Nsurf * np.linalg.norm(tsaero0.zeta[0][:, 0, 0] - tsaero0.zeta[0][:, 0, -1])\n Stot = ws.c_ref * span\n Fref_tot = qinf * Stot\n\n # reference force - section\n sec_span = np.linalg.norm(tsaero0.zeta[0][:, 0, 0] - tsaero0.zeta[0][:, 0, 1])\n S = ws.c_ref * sec_span\n Fref_span = qinf * S\n\n # save\n self.route_main = route_main\n self.tsaero0 = tsaero0\n self.ws = ws\n self.Fref_tot = Fref_tot\n self.Fref_span = Fref_span\n self.M = M\n self.N = N\n self.Mstar_fact = Mstar_fact\n self.Uinf0 = Uinf0\n\n def test_wagner(self):\n \"\"\"\n Step response (Wagner):\n - set linearisation point at 0 effective incidence but non-zero roll\n attitude. This can be obtained either by rotating the FoR A or\n by explicitely modifying the position of the wing nodes.\n - perturb. state so as to produce a small effective angle of attack.\n This is achieved combining changes of:\n - wing lattice orientation\n - wing lattice speed\n - incoming flow orientation\n - compare aerodynamic force time history to Wagner's analytical solution\n - compare steady state to analytical solution and ``StaticUvlm`` solver\n\n Notes:\n The function uses ``subTests`` to call ``run_wagner``.\n \"\"\"\n\n for Nsurf in [1, 2]:\n for integr_ord in [1, 2]:\n for RemovePred in [False, True]:\n for UseSparse in [True]:\n for RollNodes in [True, False]:\n with self.subTest(\n Nsurf=Nsurf, integr_ord=integr_ord,\n RemovePred=RemovePred, UseSparse=UseSparse,\n RollNodes=RollNodes):\n self.run_wagner(\n Nsurf, integr_ord, RemovePred, UseSparse, RollNodes)\n\n def run_wagner(self, Nsurf, integr_ord, RemovePred, UseSparse, RollNodes):\n \"\"\"\n see test_wagner\n \"\"\"\n\n ### ----- set reference solution\n self.setUp_from_params(Nsurf, integr_ord, RemovePred, UseSparse, RollNodes)\n tsaero0 = self.tsaero0\n ws = self.ws\n M = self.M\n N = self.N\n Mstar_fact = self.Mstar_fact\n Uinf0 = self.Uinf0\n\n ### ----- linearisation\n uvlm = linuvlm.Dynamic(tsaero0,\n dynamic_settings=ws.config['LinearUvlm'])\n uvlm.assemble_ss()\n zeta_pole = np.array([0., 0., 0.])\n uvlm.get_total_forces_gain(zeta_pole=zeta_pole)\n uvlm.get_rigid_motion_gains(zeta_rotation=zeta_pole)\n uvlm.get_sect_forces_gain()\n\n ### ----- Scale gains\n Fref_tot = self.Fref_tot\n Fref_span = self.Fref_span\n uvlm.Kftot = uvlm.Kftot / Fref_tot\n uvlm.Kmtot = uvlm.Kmtot / Fref_tot / ws.c_ref\n uvlm.Kfsec /= Fref_span\n uvlm.Kmsec /= (Fref_span * ws.c_ref)\n\n ### ----- step input\n # rotate incoming flow, wing lattice and wing lattice speed about\n # the (rolled) wing elastic axis to create an effective angle of attack.\n # Rotation is expressed through a CRV.\n delta_AlphaEffDeg = 1e-2\n delta_AlphaEffRad = 1e-2 * np.pi / 180.\n\n Roll0Rad = self.Roll0Deg / 180. * np.pi\n dcrv = -delta_AlphaEffRad * np.array([0., np.cos(Roll0Rad), np.sin(Roll0Rad)])\n uvec0 = np.array([Uinf0, 0, 0])\n uvec = np.dot(algebra.crv2rotation(dcrv), uvec0)\n duvec = uvec - uvec0\n dzeta = np.zeros((Nsurf, 3, M + 1, N // Nsurf + 1))\n dzeta_dot = np.zeros((Nsurf, 3, M + 1, N // Nsurf + 1))\n du_ext = np.zeros((Nsurf, 3, M + 1, N // Nsurf + 1))\n\n for ss in range(Nsurf):\n for mm in range(M + 1):\n for nn in range(N // Nsurf + 1):\n dzeta_dot[ss, :, mm, nn] = -1. / 3 * duvec\n du_ext[ss, :, mm, nn] = +1. / 3 * duvec\n dzeta = 1. / 3 * np.dot(uvlm.Krot, dcrv)\n Uaero = np.concatenate((dzeta.reshape(-1),\n dzeta_dot.reshape(-1),\n du_ext.reshape(-1)))\n\n ### ----- Steady state solution\n xste, yste = uvlm.solve_steady(Uaero)\n Ftot_ste = np.dot(uvlm.Kftot, yste)\n Mtot_ste = np.dot(uvlm.Kmtot, yste)\n # first check of gain matrices...\n Ftot_ste_ref = np.zeros((3,))\n Mtot_ste_ref = np.zeros((3,))\n fnodes = yste.reshape((Nsurf, 3, M + 1, N // Nsurf + 1))\n for ss in range(Nsurf):\n for nn in range(N // Nsurf + 1):\n for mm in range(M + 1):\n Ftot_ste_ref += fnodes[ss, :, mm, nn]\n Mtot_ste_ref += np.cross(\n uvlm.MS.Surfs[ss].zeta[:, mm, nn], fnodes[ss, :, mm, nn])\n Ftot_ste_ref /= Fref_tot\n Mtot_ste_ref /= (Fref_tot * ws.c_ref)\n Fmag = np.linalg.norm(Ftot_ste_ref)\n er_f = np.max(np.abs(Ftot_ste - Ftot_ste_ref)) / Fmag\n er_m = np.max(np.abs(Mtot_ste - Mtot_ste_ref)) / Fmag / ws.c_ref\n assert (er_f < 1e-8 and er_m < 1e-8), \\\n 'Error of total forces (%.2e) and moment (%.2e) too large!' % (er_f, er_m) + \\\n 'Verify gains produced by linuvlm.Dynamic.get_total_forces_gain.'\n\n # then compare against analytical ...\n Cl_inf = delta_AlphaEffRad * np.pi * 2.\n Cfvec_inf = Cl_inf * np.array([0., -np.sin(Roll0Rad), np.cos(Roll0Rad)])\n er_f = np.abs(np.linalg.norm(Ftot_ste) / Cl_inf - 1.)\n assert (er_f < 1e-2), \\\n 'Error of total lift coefficient (%.2e) too large!' % (er_f,) + \\\n 'Verify linuvlm.Dynamic.'\n er_f = np.abs(np.linalg.norm(Ftot_ste - Cfvec_inf) / Cl_inf)\n assert (er_f < 1e-2), \\\n 'Error of total aero force (%.2e) too large!' % (er_f,) + \\\n 'Verify linuvlm.Dynamic.'\n\n # ... and finally compare against non-linear UVLM\n # ps: here we roll the wing and rotate the incoming flow to generate an effective\n # angle of attack\n case_pert = 'wagner_r%.4daeff%.2d_rnodes%s_Nsurf%.2dM%.2dN%.2dwk%.2d' \\\n % (int(np.round(100 * self.Roll0Deg)),\n int(np.round(100 * delta_AlphaEffDeg)),\n RollNodes,\n Nsurf, M, N, Mstar_fact)\n ws_pert = flying_wings.QuasiInfinite(\n M=M, N=N, Mstar_fact=Mstar_fact, n_surfaces=Nsurf,\n u_inf=Uinf0,\n alpha=self.Alpha0Deg,\n roll=self.Roll0Deg,\n aspect_ratio=1e5,\n route=self.route_main,\n case_name=case_pert,\n RollNodes=RollNodes)\n ws_pert.u_inf_direction = uvec / Uinf0\n ws_pert.main_ea = ws.main_ea\n ws_pert.clean_test_files()\n ws_pert.update_derived_params()\n ws_pert.generate_fem_file()\n ws_pert.generate_aero_file()\n\n # solution flow\n ws_pert.set_default_config_dict()\n ws_pert.config['SHARPy']['flow'] = ws.config['SHARPy']['flow']\n ws_pert.config['SHARPy']['write_screen'] = 'off'\n ws_pert.config['SHARPy']['write_log'] = 'off'\n ws_pert.config['SHARPy']['log_folder'] = self.route_test_dir + '/output/' + self.case_code + '/'\n ws_pert.config.write()\n\n # solve at perturbed point\n data_pert = sharpy.sharpy_main.main(['...', self.route_main + case_pert + '.sharpy'])\n tsaero = data_pert.aero.timestep_info[0]\n\n self.start_writer()\n\n # get total forces\n Ftot_ste_pert = np.zeros((3,))\n Mtot_ste_pert = np.zeros((3,))\n for ss in range(Nsurf):\n for nn in range(N // Nsurf + 1):\n for mm in range(M + 1):\n Ftot_ste_pert += tsaero.forces[ss][:3, mm, nn]\n Mtot_ste_pert += np.cross(\n uvlm.MS.Surfs[ss].zeta[:, mm, nn], tsaero.forces[ss][:3, mm, nn])\n Ftot_ste_pert /= Fref_tot\n Mtot_ste_pert /= (Fref_tot * ws.c_ref)\n Fmag = np.linalg.norm(Ftot_ste_pert)\n er_f = np.max(np.abs(Ftot_ste - Ftot_ste_pert)) / Fmag\n er_m = np.max(np.abs(Mtot_ste - Mtot_ste_pert)) / Fmag / ws.c_ref\n assert (er_f < 2e-4 and er_m < 2e-4), \\\n 'Error of total forces (%.2e) and moment (%.2e) ' % (er_f, er_m) + \\\n 'with respect to geometrically-exact UVLM too large!'\n\n # and check non-linear uvlm against analytical solution\n er_f = np.abs(np.linalg.norm(Ftot_ste_pert - Cfvec_inf) / Cl_inf)\n assert (er_f <= 1.5e-2), \\\n 'Error of total aero force components (%.2e) too large!' % (er_f,) + \\\n 'Verify StaticUvlm'\n\n ### ----- Analytical step response (Wagner solution)\n\n NT = 251\n tv = np.linspace(0., uvlm.dt * (NT - 1), NT)\n Clv_an = an.wagner_imp_start(delta_AlphaEffRad, Uinf0, ws.c_ref, tv)\n assert np.abs(Clv_an[-1] / Cl_inf - 1.) < 1e-2, \\\n 'Did someone modify this test case?! The time should be enough to reach ' \\\n 'the steady-state CL with a 1 perc. tolerance...'\n\n Cfvec_an = np.zeros((NT, 3))\n Cfvec_an[:, 1] = -np.sin(Roll0Rad) * Clv_an\n Cfvec_an[:, 2] = np.cos(Roll0Rad) * Clv_an\n\n ### ----- Dynamic step response\n\n Fsect = np.zeros((NT, Nsurf, 3, N // Nsurf + 1))\n # Fbeam=np.zeros((NT,6,N//Nsurf+1))\n Ftot = np.zeros((NT, 3))\n Er_f_tot = np.zeros((NT,))\n\n # Ybeam=[]\n gamma = np.zeros((NT, Nsurf, M, N // Nsurf))\n gamma_dot = np.zeros((NT, Nsurf, M, N // Nsurf))\n gamma_star = np.zeros((NT, Nsurf, int(M * Mstar_fact), N // Nsurf))\n xold = np.zeros((uvlm.SS.A.shape[0],))\n for tt in range(1, NT):\n xnew, ynew = uvlm.solve_step(xold, Uaero)\n change = np.linalg.norm(xnew - xold)\n xold = xnew\n\n # record state ?\n if uvlm.remove_predictor is False:\n gv, gvstar, gvdot = uvlm.unpack_state(xnew)\n gamma[tt, :, :, :] = gv.reshape((Nsurf, M, N // Nsurf))\n gamma_dot[tt, :, :, :] = gvdot.reshape((Nsurf, M, N // Nsurf))\n gamma_star[tt, :, :, :] = gvstar.reshape((Nsurf, int(M * Mstar_fact), N // Nsurf))\n\n # calculate forces (and error)\n Ftot[tt, :3] = np.dot(uvlm.Kftot, ynew)\n Er_f_tot[tt] = np.linalg.norm(Ftot[tt, :] - Cfvec_an[tt, :]) / Clv_an[tt]\n Fsect[tt, :, :, :] = np.dot(uvlm.Kfsec, ynew).reshape((Nsurf, 3, N // Nsurf + 1))\n\n # ### beam forces\n # Ybeam.append(np.dot(Sol.Kforces[:-10,:],ynew))\n # Fdummy=Ybeam[-1].reshape((N//Nsurf,6)).T\n # Fbeam[tt,:,:N//Nsurf]=Fdummy[:,:N//Nsurf]\n # Fbeam[tt,:,N//Nsurf+1:]=Fdummy[:,N//Nsurf:]\n\n if RemovePred:\n ts2perc, ts1perc = 6, 6\n else:\n ts2perc, ts1perc = 16, 36\n er_th_2perc = np.max(Er_f_tot[ts2perc:])\n er_th_1perc = np.max(Er_f_tot[ts1perc:])\n\n ### ----- generate plot\n if self.ProducePlots:\n\n # sections to plot\n if Nsurf == 1:\n Nplot = [0, N // 2, N]\n labs = [r'tip', r'root', r'tip']\n elif Nsurf == 2:\n Nplot = [0, N // 2 - 1]\n labs = [r'tip', r'near root', r'tip', r'near root']\n axtitle = [r'$C_{F_y}$', r'$C_{F_z}$']\n\n # non-dimensional time\n sv = 2.0 * Uinf0 * tv / ws.c_ref\n\n # generate figure\n clist = ['#003366', '#CC3333', '#336633', '#FF6600'] * 4\n fontlabel = 12\n std_params = {'legend.fontsize': 10,\n 'font.size': fontlabel,\n 'xtick.labelsize': fontlabel - 2,\n 'ytick.labelsize': fontlabel - 2,\n 'figure.autolayout': True,\n 'legend.numpoints': 1}\n # plt.rcParams.update(std_params)\n\n # fig = plt.figure('Lift time-history', (12, 6))\n # axvec = fig.subplots(1, 2)\n # for aa in [0, 1]:\n # comp = aa + 1\n # axvec[aa].set_title(axtitle[aa])\n # axvec[aa].plot(sv, Cfvec_an[:, comp] / Cl_inf, lw=4, ls='-',\n # alpha=0.5, color='r', label=r'Wagner')\n # axvec[aa].plot(sv, Ftot[:, comp] / Cl_inf, lw=5, ls=':',\n # alpha=0.7, color='k', label=r'Total')\n # cc = 0\n # for ss in range(Nsurf):\n # for nn in Nplot:\n # axvec[aa].plot(sv, Fsect[:, ss, comp, nn] / Cl_inf,\n # lw=4 - cc, ls='--', alpha=0.7, color=clist[cc],\n # label=r'Surf. %.1d, n=%.2d (%s)' % (ss, nn, labs[cc]))\n # cc += 1\n # axvec[aa].grid(color='0.8', ls='-')\n # axvec[aa].grid(color='0.85', ls='-', which='minor')\n # axvec[aa].set_xlabel(r'normalised time $t=2 U_\\infty \\tilde{t}/c$')\n # axvec[aa].set_ylabel(axtitle[aa] + r'$/C_{l_\\infty}$')\n # axvec[aa].set_xlim(0, sv[-1])\n # if Cfvec_inf[comp] > 0.:\n # axvec[aa].set_ylim(0, 1.1)\n # else:\n # axvec[aa].set_ylim(-1.1, 0)\n # plt.legend(ncol=1)\n # # plt.show()\n # fig.savefig(self.figfold + self.case_main + '.png')\n # fig.savefig(self.figfold + self.case_main + '.pdf')\n # plt.close()\n\n assert er_th_2perc < 2e-2 and er_th_1perc < 1e-2, \\\n 'Error of dynamic step response at time-steps 16 and 36 ' + \\\n '(%.2e and %.2e) too large. Verify Linear UVLM.' % (er_th_2perc, er_th_1perc)\n\n def start_writer(self):\n # Over write writer with print_file False to avoid I/O errors\n global cout_wrap\n cout_wrap = cout.Writer()\n # cout_wrap.initialise(print_screen=False, print_file=False)\n cout_wrap.cout_quiet()\n sharpy.utils.cout_utils.cout_wrap = cout_wrap\n\n def tearDown(self):\n cout.finish_writer()\n try:\n shutil.rmtree(self.route_test_dir + '/res/')\n shutil.rmtree(self.route_test_dir + '/figs/')\n shutil.rmtree(self.route_test_dir + '/output/')\n except FileNotFoundError:\n pass\n\n\nif __name__ == '__main__':\n if os.path.exists('./figs/infinite_span'):\n shutil.rmtree('./figs/infinite_span')\n unittest.main()\n" }, { "path": "tests/sourcepanelmethod/__init__.py", "content": "" }, { "path": "tests/sourcepanelmethod/geometry_parameter_models.json", "content": "{\"phantom_wing\": {\"length_radius_ratio\": 50.0, \"radius_chord_ratio\": 0.2, \"vertical_wing_position\": 0.0, \"radius_half_wingspan_ratio\": 0.02, \"length_offset_nose_to_wing_ratio\": 0.5, \"fuselage_shape\": \"cylindrical\"}, \"low_wing\": {\"length_radius_ratio\": 16.0, \"radius_chord_ratio\": 0.5, \"vertical_wing_position\": -0.5, \"radius_half_wingspan_ratio\": 0.222, \"fuselage_shape\": \"cylindrical\", \"length_offset_nose_to_wing_ratio\": 0.5}}" }, { "path": "tests/sourcepanelmethod/test_data/results_low_wing_coupled_0.csv", "content": "0.000000000000000000e+00 0.000000000000000000e+00\n0.000000000000000000e+00 0.000000000000000000e+00\n0.000000000000000000e+00 0.000000000000000000e+00\n0.000000000000000000e+00 0.000000000000000000e+00\n5.630631000000000386e-01 2.637046000000000112e-01\n7.038288000000000322e-01 2.587818000000000063e-01\n8.445945999999999732e-01 2.560145999999999811e-01\n9.853604000000000251e-01 2.521720000000000073e-01\n1.126125999999999960e+00 2.474606000000000028e-01\n1.266891999999999907e+00 2.419823000000000113e-01\n1.407658000000000076e+00 2.357548999999999895e-01\n1.548423000000000105e+00 2.287254999999999983e-01\n1.689189000000000052e+00 2.207763000000000086e-01\n1.829954999999999998e+00 2.117207000000000117e-01\n1.970720999999999945e+00 2.012865000000000071e-01\n2.111486000000000196e+00 1.890803000000000067e-01\n2.252251999999999921e+00 1.745153000000000121e-01\n2.393018000000000089e+00 1.566525000000000001e-01\n2.533783999999999814e+00 1.337860999999999911e-01\n2.674549999999999983e+00 1.019361000000000017e-01\n2.815315000000000012e+00 8.357517000000000418e-02\n" }, { "path": "tests/sourcepanelmethod/test_data/results_low_wing_coupled_1.csv", "content": "0.000000000000000000e+00 0.000000000000000000e+00\n0.000000000000000000e+00 0.000000000000000000e+00\n0.000000000000000000e+00 0.000000000000000000e+00\n0.000000000000000000e+00 0.000000000000000000e+00\n5.630631000000000386e-01 2.636864999999999903e-01\n7.038288000000000322e-01 2.592814999999999981e-01\n8.445945999999999732e-01 2.565006000000000230e-01\n9.853604000000000251e-01 2.526663000000000103e-01\n1.126125999999999960e+00 2.479610999999999899e-01\n1.266891999999999907e+00 2.424882999999999900e-01\n1.407658000000000076e+00 2.362653000000000114e-01\n1.548423000000000105e+00 2.292386999999999897e-01\n1.689189000000000052e+00 2.212899000000000116e-01\n1.829954999999999998e+00 2.122312000000000087e-01\n1.970720999999999945e+00 2.017887999999999904e-01\n2.111486000000000196e+00 1.895677000000000056e-01\n2.252251999999999921e+00 1.749785000000000090e-01\n2.393018000000000089e+00 1.570786999999999878e-01\n2.533783999999999814e+00 1.341562000000000032e-01\n2.674549999999999983e+00 1.022175000000000028e-01\n2.815315000000000012e+00 8.376727999999999952e-02\n" }, { "path": "tests/sourcepanelmethod/test_source_panel_method.py", "content": "import unittest\nimport os\nimport numpy as np\nfrom sharpy.cases.templates.fuselage_wing_configuration.fuselage_wing_configuration import Fuselage_Wing_Configuration\nfrom sharpy.cases.templates.fuselage_wing_configuration.fwc_get_settings import define_simulation_settings\n\n\n\nclass TestSourcePanelMethod(unittest.TestCase):\n\n route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n\n def test_ellipsoid(self):\n \"\"\"\n Computes the pressure distribution over an ellipsoid. The results should\n match the analyitcal solution according to potential flow theory (see Chapter 5\n Katz, J., and Plotkin, A., Low-speed aerodynamics, Vol. 13, Cambridge University \n Press, 2001).\n \"\"\"\n\n # define model variables\n radius_ellipsoid = 0.2\n length_ellipsoid = 2.\n u_inf = 10 \n alpha_deg = 0\n n_elem = 30\n num_radial_panels = 24\n lifting_only= False\n fuselage_shape = 'ellipsoid'\n fuselage_discretisation = 'uniform'\n # define case name and folders\n case_route = self.route_test_dir + '/cases/'\n output_route = self.route_test_dir + '/output/'\n case_name = 'ellipsoid'\n enforce_uniform_fuselage_discretisation = True\n\n # generate ellipsoid model\n ellipsoidal_body = Fuselage_Wing_Configuration(case_name, case_route, output_route) \n ellipsoidal_body.init_aeroelastic(lifting_only=lifting_only,\n max_radius=radius_ellipsoid,\n fuselage_length=length_ellipsoid,\n offset_nose_wing=length_ellipsoid/2,\n n_elem_fuselage=n_elem,\n num_radial_panels=num_radial_panels,\n fuselage_shape=fuselage_shape,\n enforce_uniform_fuselage_discretisation=enforce_uniform_fuselage_discretisation,\n fuselage_discretisation=fuselage_discretisation)\n ellipsoidal_body.generate()\n \n # define settings\n flow = ['BeamLoader',\n 'NonliftingbodygridLoader',\n 'StaticUvlm',\n 'WriteVariablesTime'\n ]\n settings = define_simulation_settings(flow, \n ellipsoidal_body, \n alpha_deg, \n u_inf, \n lifting_only=False, \n nonlifting_only=True, \n horseshoe=True,\n writeCpVariables=True)\n ellipsoidal_body.create_settings(settings)\n\n # run simulation\n ellipsoidal_body.run()\n\n # postprocess\n cp_distribution_SHARPy = self.load_pressure_distribution(output_route + '/' + case_name + '/WriteVariablesTime/', \n ellipsoidal_body.structure.n_node_fuselage)\n dx = length_ellipsoid/(ellipsoidal_body.structure.n_node_fuselage-1)\n x_collocation_points = np.linspace(-length_ellipsoid/2+dx/2, length_ellipsoid/2-dx/2, ellipsoidal_body.structure.n_node_fuselage)\n cp_distribution_analytcal = self.get_analytical_pressure_distribution(radius_ellipsoid, x_collocation_points)\n\n # check results\n with self.subTest('pressure_coefficient'):\n # Higher deviations near the nose and tail due to local coarser discretisation. Check only mid-body values!\n np.testing.assert_array_almost_equal(cp_distribution_SHARPy[4:-4], cp_distribution_analytcal[4:-4], decimal=3)\n\n def load_pressure_distribution(self, output_folder, n_collocation_points):\n \"\"\"\n Loads the resulting pressure coefficients saved in txt-files.\n \"\"\"\n cp_distribution = np.zeros((n_collocation_points,))\n for i_collocation_point in range(n_collocation_points):\n cp_distribution[i_collocation_point] = np.loadtxt(output_folder + 'nonlifting_pressure_coefficients_panel_isurf0_im0_in{}.dat'.format(i_collocation_point))[1]\n return cp_distribution\n\n def get_analytical_pressure_distribution(self, radius, x_coordinates):\n \"\"\"\n Computes the analytical solution of the pressure distribution over\n an ellipsoid in potential flow for the previous specified ellipsoid\n model. Equations used are taken from\n https://www.symscape.com/examples/panel/potential_flow_ellipsoid\n \"\"\"\n a = np.sqrt(1 - radius**2)\n b = 2 * ((1-a**2)/a**3) * (np.arctanh(a)-a)\n u = 2./(2.-b) * np.sqrt((1-x_coordinates**2)/(1-x_coordinates**2 * a**2))\n return 1-u**2\n \n def tearDown(self):\n \"\"\"\n Removes all created files within this test.\n \"\"\"\n import shutil\n folders = ['cases', 'output']\n for folder in folders:\n shutil.rmtree(self.route_test_dir + '/' + folder)\n\n\nif __name__ == '__main__':\n import unittest\n\n unittest.main()\n" }, { "path": "tests/sourcepanelmethod/test_vlm_coupled_spm.py", "content": "import unittest\nimport os\nimport numpy as np\nfrom sharpy.cases.templates.fuselage_wing_configuration.fuselage_wing_configuration import Fuselage_Wing_Configuration\nfrom sharpy.cases.templates.fuselage_wing_configuration.fwc_get_settings import define_simulation_settings\nimport json\n\nclass TestUvlmCoupledWithSourcePanelMethod(unittest.TestCase):\n\n \n def test_phantom_panels(self):\n \"\"\"\n Phantom Panel Test (Steady and Dynamic)\n The lift distribution over a rectangular high-aspect ratio\n wing is computed. First a wing_only configuration is considered,\n while second, we activate the phantom panels created within the \n fuselage although, the effect of the source panels is omitted. \n With the defined interpolation scheme, the same lift distribution \n must be obtained.\n \"\"\"\n self.define_folder()\n \n\n model = 'phantom_wing'\n fuselage_length = 10\n dict_geometry_parameters = self.get_geometry_parameters(model,\n fuselage_length=fuselage_length)\n\n # Freestream Conditions\n alpha_deg = 5\n u_inf = 10\n\n # Discretization\n dict_discretization = {\n 'n_elem_per_wing': 20,\n 'n_elem_fuselage': 10,\n 'num_chordwise_panels': 4\n }\n\n # Simulation settings\n horseshoe = True\n list_phantom_test = [False, True]\n list_dynamic_test = [False, True]\n dynamic_structural_solver = 'NonLinearDynamicPrescribedStep'\n\n # Numerical Settings for DynamicCoupled (very small for faster test runs)\n fsi_substeps = 2\n fsi_tolerance = 1e-2\n\n # Simlation Solver Flow\n flow = ['BeamLoader',\n 'AerogridLoader',\n 'NonliftingbodygridLoader',\n 'StaticUvlm',\n 'StaticCoupled',\n 'BeamLoads',\n 'LiftDistribution',\n 'DynamicCoupled',\n 'LiftDistribution',\n ]\n # define model variables\n for dynamic in list_dynamic_test:\n list_results_lift_distribution = []\n for phantom_test in list_phantom_test:\n horseshoe = not dynamic\n lifting_only = not phantom_test\n case_name = model + '_phantom{}_dynamic{}'.format(int(phantom_test),\n int(dynamic))\n \n # generate ellipsoid model\n phantom_wing = self.generate_model(case_name, \n dict_geometry_parameters,\n dict_discretization, \n lifting_only)\n # Adjust flow for case\n flow_case = flow.copy()\n\n if lifting_only:\n n_tsteps = 5\n flow_case.remove('NonliftingbodygridLoader')\n if not dynamic:\n n_tsteps = 0\n flow_case.remove('StaticCoupled')\n flow_case.remove('DynamicCoupled')\n self.generate_simulation_settings(flow_case, \n phantom_wing, \n alpha_deg, \n u_inf, \n lifting_only,\n n_tsteps = n_tsteps,\n horseshoe=horseshoe,\n phantom_test=phantom_test,\n dynamic_structural_solver=dynamic_structural_solver,\n fsi_substeps=fsi_substeps,\n fsi_tolerance=fsi_tolerance)\n # # run simulation\n phantom_wing.run()\n\n # get results\n list_results_lift_distribution.append(self.load_lift_distribution(\n self.output_route + '/' + case_name,\n phantom_wing.structure.n_node_right_wing,\n n_tsteps\n )) \n \n # check results\n with self.subTest(self.get_test_name('phantom', dynamic)):\n np.testing.assert_array_almost_equal(list_results_lift_distribution[0][3:, 1], \n list_results_lift_distribution[1][3:, 1], \n decimal=2) #3 - int(dynamic))\n\n\n \n def test_fuselage_wing_configuration(self):\n \"\"\"\n Test spanwise lift distribution on a fuselage-wing configuration.\n \n The lift distribution on low wing configuration is computed considering\n fuselage effects. The final results are compared to a previous solution \n (backward compatibility) that matches the experimental lift distribution for this case. \n \"\"\"\n self.define_folder()\n model = 'low_wing'\n fuselage_length = 10\n dict_geometry_parameters = self.get_geometry_parameters(model,\n fuselage_length=fuselage_length)\n\n # Freestream Conditions\n alpha_deg = 2.9\n u_inf = 10\n\n # Discretization\n dict_discretization = {\n 'n_elem_per_wing': 10,\n 'n_elem_fuselage': 30,\n 'num_chordwise_panels': 8,\n 'num_radial_panels': 36\n }\n\n # Simulation settings\n horseshoe = True\n phantom_test = False\n lifting_only = False\n # Simlation Solver Flow\n flow = ['BeamLoader',\n 'AerogridLoader',\n 'NonliftingbodygridLoader',\n 'StaticUvlm',\n 'StaticCoupled',\n 'BeamLoads',\n 'LiftDistribution',\n ]\n for static_coupled_solver in [False, True]:\n case_name = '{}_coupled_{}'.format(model, int(static_coupled_solver))\n wing_fuselage_model = self.generate_model(case_name, \n dict_geometry_parameters,\n dict_discretization, \n lifting_only)\n\n flow_case = flow.copy()\n if static_coupled_solver:\n flow_case.remove('StaticUvlm')\n else:\n flow_case.remove('StaticCoupled')\n self.generate_simulation_settings(flow_case, \n wing_fuselage_model, \n alpha_deg, \n u_inf, \n lifting_only,\n horseshoe=horseshoe,\n phantom_test=phantom_test)\n # run simulation\n wing_fuselage_model.run()\n # get results\n lift_distribution = self.load_lift_distribution(\n self.output_route + case_name,\n wing_fuselage_model.structure.n_node_right_wing\n )\n # check results\n lift_distribution_test = np.loadtxt(self.route_test_dir + \"/test_data/results_{}.csv\".format(case_name))\n with self.subTest(self.get_test_name('lift distribution and spanwise wing deformation',\n static_coupled=static_coupled_solver)): \n np.testing.assert_array_almost_equal(lift_distribution_test, lift_distribution, decimal=3)\n\n def get_test_name(self, base_name, dynamic=False, static_coupled=False):\n if static_coupled:\n base_name += ' coupled'\n else:\n if dynamic:\n base_name += ' uvlm'\n else:\n base_name += ' vlm'\n return base_name\n def get_geometry_parameters(self, model_name,fuselage_length=10):\n \"\"\"\n Geometry parameters are loaded from json init file for the specified model. \n Next, final geoemtry parameteres, depending on the fuselage length are \n calculated and return within a dict.\n \"\"\"\n with open(self.route_test_dir + '/geometry_parameter_models.json', 'r') as fp:\n parameter_models = json.load(fp)[model_name]\n\n geometry_parameters = {\n 'fuselage_length': fuselage_length, \n 'max_radius': fuselage_length/parameter_models['length_radius_ratio'],\n 'fuselage_shape': parameter_models['fuselage_shape'],\n }\n geometry_parameters['chord']=geometry_parameters['max_radius']/parameter_models['radius_chord_ratio']\n geometry_parameters['half_wingspan'] = geometry_parameters['max_radius']/parameter_models['radius_half_wingspan_ratio']\n geometry_parameters['offset_nose_wing'] = parameter_models['length_offset_nose_to_wing_ratio'] * fuselage_length\n geometry_parameters['vertical_wing_position'] = parameter_models['vertical_wing_position'] * geometry_parameters['max_radius']\n return geometry_parameters\n\n def generate_model(self, \n case_name, \n dict_geometry_parameters,\n dict_discretisation, \n lifting_only):\n \"\"\"\n Aircraft model object is generated and structural and aerodynamic (lifting and nonlifting)\n input files are generated.\n \"\"\"\n aircraft_model = Fuselage_Wing_Configuration(case_name, self.case_route, self.output_route)\n aircraft_model.init_aeroelastic(lifting_only=lifting_only,\n **dict_discretisation,\n **dict_geometry_parameters)\n aircraft_model.generate()\n return aircraft_model\n \n def generate_simulation_settings(self, \n flow, \n aircraft_model, \n alpha_deg, \n u_inf, \n lifting_only,\n n_tsteps=0,\n horseshoe=True,\n nonlifting_only=False,\n phantom_test=False,\n dynamic_structural_solver='NonLinearDynamicPrescribedStep',\n fsi_substeps=200,\n fsi_tolerance=1e-6\n ):\n \"\"\"\n Simulation settings are defined and written to the \".sharpy\" input file.\n \"\"\"\n settings = define_simulation_settings(flow, \n aircraft_model, \n alpha_deg, \n u_inf, \n dt=self.get_timestep(aircraft_model, u_inf),\n n_tsteps=n_tsteps,\n lifting_only=lifting_only, \n phantom_test=phantom_test, \n nonlifting_only=nonlifting_only, \n horseshoe=horseshoe,\n dynamic_structural_solver=dynamic_structural_solver,\n fsi_substeps=fsi_substeps,\n fsi_tolerance=fsi_tolerance)\n aircraft_model.create_settings(settings)\n\n def get_timestep(self, model, u_inf):\n return model.aero.chord_wing / model.aero.num_chordwise_panels / u_inf\n \n def define_folder(self):\n \"\"\"\n Initializes all folder path needed and creates case folder.\n \"\"\"\n self.route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n self.case_route = self.route_test_dir + '/cases/'\n self.output_route = self.route_test_dir + '/output/'\n \n if not os.path.exists(self.case_route):\n os.makedirs(self.case_route)\n \n def load_lift_distribution(self, output_folder, n_node_wing, n_tsteps=0):\n \"\"\"\n Loads the resulting pressure coefficients saved in txt-files.\n \"\"\"\n lift_distribution = np.loadtxt(output_folder + '/liftdistribution/liftdistribution_ts{}.txt'.format(str(n_tsteps)), delimiter=',')\n return lift_distribution[:n_node_wing,[1,-1]]\n\n def tearDown(self):\n \"\"\"\n Removes all created files within this test.\n \"\"\"\n import shutil\n folders = ['cases', 'output']\n for folder in folders:\n shutil.rmtree(self.route_test_dir + '/' + folder)\n\n\nif __name__ == '__main__':\n import unittest\n\n unittest.main()\n" }, { "path": "tests/utils/__init__.py", "content": "" }, { "path": "tests/utils/test_algebra.py", "content": "import sharpy.utils.algebra as algebra\nimport numpy as np\nimport unittest\nimport random\n\n\nclass TestAlgebra(unittest.TestCase):\n \"\"\"\n Tests the algebra module\n \"\"\"\n\n def test_unit_vector(self):\n \"\"\"\n Tests the routine for normalising vectors\n :return:\n \"\"\"\n vector_in = 1\n result = algebra.unit_vector(vector_in)\n self.assertAlmostEqual(np.linalg.norm(result), 1.0, 5)\n\n vector_in = 0\n result = algebra.unit_vector(vector_in)\n self.assertAlmostEqual(np.linalg.norm(result), 0.0, 5)\n\n vector_in = np.array([1, 0, 0])\n result = algebra.unit_vector(vector_in)\n self.assertAlmostEqual(np.linalg.norm(result), 1.0, 5)\n\n vector_in = np.array([2, -1, 1])\n result = algebra.unit_vector(vector_in)\n self.assertAlmostEqual(np.linalg.norm(result), 1.0, 5)\n\n vector_in = np.array([1e-8, 0, 0])\n result = algebra.unit_vector(vector_in)\n self.assertAlmostEqual(np.linalg.norm(result), 1e-8, 5)\n\n vector_in = 'aa'\n with self.assertRaises(ValueError):\n algebra.unit_vector(vector_in)\n\n def test_rotation_vectors_conversions(self):\n \"\"\"\n Checks routine to convert rotation vectors.\n\n Note: test only includes CRV <-> quaternions conversions\n \"\"\"\n\n N = 1000\n for nn in range(N):\n # def random rotation in [-pi,pi]\n a = np.pi * (2. * np.random.rand() - 1)\n nv = 2. * np.random.rand(3) - 1\n nv = nv / np.linalg.norm(nv)\n # reference\n fv0 = a * nv\n quat0 = np.zeros((4,))\n quat0[0] = np.cos(.5 * a)\n quat0[1:] = np.sin(.5 * a) * nv\n # check against reference\n assert np.linalg.norm(fv0 - algebra.quat2crv(quat0)) < 1e-12, \\\n 'Error in quat2crv'\n assert np.linalg.norm(quat0 - algebra.crv2quat(fv0)) < 1e-12, \\\n 'Error in crv2quat'\n\n def test_rotation_matrices(self):\n \"\"\"\n Checks routines and consistency of functions to generate rotation\n matrices.\n\n Note: test only includes triad <-> CRV <-> quaternions conversions\n \"\"\"\n\n ### Verify that function build rotation matrix (not projection matrix)\n # set an easy rotation (x axis)\n a = np.pi / 6.\n nv = np.array([1, 0, 0])\n sa, ca = np.sin(a), np.cos(a)\n Cab_exp = np.array([[1, 0, 0],\n [0, ca, -sa],\n [0, sa, ca], ])\n ### rot from triad\n Cab_num = algebra.triad2rotation(Cab_exp[:, 0], Cab_exp[:, 1], Cab_exp[:, 2])\n assert np.linalg.norm(Cab_num - Cab_exp) < 1e-15, \\\n 'crv2rotation not producing the right result'\n ### rot from crv\n fv = a * nv\n Cab_num = algebra.crv2rotation(fv)\n assert np.linalg.norm(Cab_num - Cab_exp) < 1e-15, \\\n 'crv2rotation not producing the right result'\n ### rot from quat\n quat = algebra.crv2quat(fv)\n Cab_num = algebra.quat2rotation(quat)\n assert np.linalg.norm(Cab_num - Cab_exp) < 1e-15, \\\n 'quat2rotation not producing the right result'\n\n ### inverse relations\n # check crv2rotation and rotation2crv are biunivolcal in [-pi,pi]\n # check quat2rotation and rotation2quat are biunivocal in [-pi,pi]\n N = 100\n for nn in range(N):\n # def random rotation in [-pi,pi]\n a = np.pi * (2. * np.random.rand() - 1)\n nv = 2. * np.random.rand(3) - 1\n nv = nv / np.linalg.norm(nv)\n\n # inverse crv\n fv0 = a * nv\n Cab = algebra.crv2rotation(fv0)\n fv = algebra.rotation2crv(Cab)\n assert np.linalg.norm(fv - fv0) < 1e-12, \\\n 'rotation2crv not producing the right result'\n\n # triad2crv\n xa, ya, za = Cab[:, 0], Cab[:, 1], Cab[:, 2]\n assert np.linalg.norm(\n algebra.triad2crv(xa, ya, za) - fv0) < 1e-12, \\\n 'triad2crv not producing the right result'\n\n # inverse quat\n quat0 = np.zeros((4,))\n quat0[0] = np.cos(.5 * a)\n quat0[1:] = np.sin(.5 * a) * nv\n quat = algebra.rotation2quat(algebra.quat2rotation(quat0))\n assert np.linalg.norm(quat - quat0) < 1e-12, \\\n 'rotation2quat not producing the right result'\n\n ### combined rotation\n # assume 3 FoR, G, A and B where:\n # - G is the initial FoR\n # - A derives from a 90 deg rotation about zG\n # - B derives from a 90 deg rotation about yA\n crv_G_to_A = .5 * np.pi * np.array([0, 0, 1])\n crv_A_to_B = .5 * np.pi * np.array([0, 1, 0])\n Cga = algebra.crv2rotation(crv_G_to_A)\n Cab = algebra.crv2rotation(crv_A_to_B)\n\n # rotation G to B (i.e. projection B onto G)\n Cgb = np.dot(Cga, Cab)\n Cgb_exp = np.array([[0, -1, 0],\n [0, 0, 1],\n [-1, 0, 0]])\n assert np.linalg.norm(Cgb - Cgb_exp) < 1e-15, \\\n 'combined rotation not as expected!'\n\n def test_rotation_matrices_derivatives(self):\n \"\"\"\n Checks derivatives of rotation matrix derivatives with respect to\n quaternions and Cartesian rotation vectors\n\n Note: test only includes CRV <-> quaternions conversions\n \"\"\"\n\n ### linearisation point\n # fi0=np.pi/6\n # nv0=np.array([1,3,1])\n fi0 = 2.0 * np.pi * random.random() - np.pi\n nv0 = np.array([random.random(), random.random(), random.random()])\n nv0 = nv0 / np.linalg.norm(nv0)\n fv0 = fi0 * nv0\n qv0 = algebra.crv2quat(fv0)\n ev0 = algebra.quat2euler(qv0)\n\n # direction of perturbation\n # fi1=np.pi/3\n # nv1=np.array([-2,4,1])\n fi1 = 2.0 * np.pi * random.random() - np.pi\n nv1 = np.array([random.random(), random.random(), random.random()])\n nv1 = nv1 / np.linalg.norm(nv1)\n fv1 = fi1 * nv1\n qv1 = algebra.crv2quat(fv1)\n ev1 = algebra.quat2euler(qv1)\n\n # linearsation point\n Cga0 = algebra.quat2rotation(qv0)\n Cag0 = Cga0.T\n Cab0 = algebra.crv2rotation(fv0)\n Cba0 = Cab0.T\n Cga0_euler = algebra.euler2rot(ev0)\n Cag0_euler = Cga0_euler.T\n\n # derivatives\n # xv=np.ones((3,)) # dummy vector\n xv = np.array([random.random(), random.random(), random.random()]) # dummy vector\n derCga = algebra.der_Cquat_by_v(qv0, xv)\n derCag = algebra.der_CquatT_by_v(qv0, xv)\n derCab = algebra.der_Ccrv_by_v(fv0, xv)\n derCba = algebra.der_CcrvT_by_v(fv0, xv)\n derCga_euler = algebra.der_Ceuler_by_v(ev0, xv)\n derCag_euler = algebra.der_Peuler_by_v(ev0, xv)\n\n A = np.array([1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6])\n er_ag = 10.\n er_ga = 10.\n er_ab = 10.\n er_ba = 10.\n er_ag_euler = 10.\n er_ga_euler = 10.\n\n for a in A:\n # perturbed\n qv = a * qv1 + (1. - a) * qv0\n fv = a * fv1 + (1. - a) * fv0\n ev = a * ev1 + (1. - a) * ev0\n dqv = qv - qv0\n dfv = fv - fv0\n dev = ev - ev0\n Cga = algebra.quat2rotation(qv)\n Cag = Cga.T\n Cab = algebra.crv2rotation(fv)\n Cba = Cab.T\n Cga_euler = algebra.euler2rot(ev)\n Cag_euler = Cga_euler.T\n\n dCag_num = np.dot(Cag - Cag0, xv)\n dCga_num = np.dot(Cga - Cga0, xv)\n dCag_an = np.dot(derCag, dqv)\n dCga_an = np.dot(derCga, dqv)\n er_ag_new = np.max(np.abs(dCag_num - dCag_an))\n er_ga_new = np.max(np.abs(dCga_num - dCga_an))\n\n dCab_num = np.dot(Cab - Cab0, xv)\n dCba_num = np.dot(Cba - Cba0, xv)\n dCab_an = np.dot(derCab, dfv)\n dCba_an = np.dot(derCba, dfv)\n er_ab_new = np.max(np.abs(dCab_num - dCab_an))\n er_ba_new = np.max(np.abs(dCba_num - dCba_an))\n\n dCag_num_euler = np.dot(Cag_euler - Cag0_euler, xv)\n dCga_num_euler = np.dot(Cga_euler - Cga0_euler, xv)\n dCag_an_euler = np.dot(derCag_euler, dev)\n dCga_an_euler = np.dot(derCga_euler, dev)\n er_ag_euler_new = np.max(np.abs(dCag_num_euler - dCag_an_euler))\n er_ga_euler_new = np.max(np.abs(dCga_num_euler - dCga_an_euler))\n\n assert er_ga_new < er_ga, 'der_Cquat_by_v error not converging to 0'\n assert er_ag_new < er_ag, 'der_CquatT_by_v error not converging to 0'\n assert er_ab_new < er_ab, 'der_Ccrv_by_v error not converging to 0'\n assert er_ba_new < er_ba, 'der_CcrvT_by_v error not converging to 0'\n assert er_ga_euler_new < er_ga_euler, 'der_Ceuler_by_v error not converging to 0'\n assert er_ag_euler_new < er_ag_euler, 'der_Peuler_by_v error not converging to 0'\n\n er_ag = er_ag_new\n er_ga = er_ga_new\n er_ab = er_ab_new\n er_ba = er_ba_new\n er_ag_euler = er_ag_euler_new\n er_ga_euler = er_ga_euler_new\n\n assert er_ga < A[-2], 'der_Cquat_by_v error too large'\n assert er_ag < A[-2], 'der_CquatT_by_v error too large'\n assert er_ab < A[-2], 'der_Ccrv_by_v error too large'\n assert er_ba < A[-2], 'der_CcrvT_by_v error too large'\n assert er_ag_euler < A[-2], 'der_Peuler_by_v error too large'\n assert er_ga_euler < A[-2], 'der_Ceuler_by_v error too large'\n\n def test_crv_tangential_operator(self):\n \"\"\" Checks Cartesian rotation vector tangential operator \"\"\"\n\n # linearisation point\n fi0 = -np.pi / 6\n nv0 = np.array([1, 3, 1])\n nv0 = np.array([1, 0, 0])\n nv0 = nv0 / np.linalg.norm(nv0)\n fv0 = fi0 * nv0\n Cab = algebra.crv2rotation(fv0) # fv0 is rotation from A to B\n\n # dummy\n fi1 = np.pi / 3\n nv1 = np.array([2, 4, 1])\n nv1 = nv1 / np.linalg.norm(nv1)\n fv1 = fi1 * nv1\n\n er_tan = 10.\n A = np.array([1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6])\n for a in A:\n # perturbed\n fv = a * fv1 + (1. - a) * fv0\n dfv = fv - fv0\n\n ### Compute relevant quantities\n dCab = algebra.crv2rotation(fv0 + dfv) - Cab\n T = algebra.crv2tan(fv0)\n Tdfv = np.dot(T, dfv)\n Tdfv_skew = algebra.skew(Tdfv)\n dCab_an = np.dot(Cab, Tdfv_skew)\n\n er_tan_new = np.max(np.abs(dCab - dCab_an)) / np.max(np.abs(dCab_an))\n assert er_tan_new < er_tan, 'crv2tan error not converging to 0'\n er_tan = er_tan_new\n\n assert er_tan < A[-2], 'crv2tan error too large'\n\n def test_crv_tangetial_operator_derivative(self):\n \"\"\" Checks Cartesian rotation vector tangential operator \"\"\"\n\n # linearisation point\n fi0 = np.pi / 6\n nv0 = np.array([1, 3, 1])\n nv0 = nv0 / np.linalg.norm(nv0)\n fv0 = fi0 * nv0\n T0 = algebra.crv2tan(fv0)\n\n # dummy vector\n xv = np.ones((3,))\n T0xv = np.dot(T0, xv)\n # derT_an=dTxv(fv0,xv)\n derT_an = algebra.der_Tan_by_xv(fv0, xv)\n # derT_an=algebra.der_Tan_by_xv_an(fv0,xv)\n # dummy\n fi1 = np.pi / 3\n nv1 = np.array([4, 1, -2])\n nv1 = nv1 / np.linalg.norm(nv1)\n fv1 = fi1 * nv1\n\n er = 10.\n A = np.array([1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6])\n for a in A:\n # perturbed\n fv = a * fv1 + (1. - a) * fv0\n dfv = fv - fv0\n Tpert = algebra.crv2tan(fv)\n Tpertxv = np.dot(Tpert, xv)\n dT_num = Tpertxv - T0xv\n dT_an = np.dot(derT_an, dfv)\n\n er_new = np.max(np.abs(dT_num - dT_an)) / np.max(np.abs(dT_an))\n assert er_new < er, 'der_Tan_by_xv error not converging to 0'\n er = er_new\n\n assert er < A[-2], 'der_Tan_by_xv error too large'\n\n def test_crv_tangetial_operator_transpose_derivative(self):\n \"\"\" Checks Cartesian rotation vector tangential operator transpose\"\"\"\n\n # dummy vector\n xv = np.random.rand(3)\n\n # linearisation point\n fi0 = 2.0 * np.pi * np.random.rand(1)\n nv0 = np.random.rand(3)\n nv0 = nv0 / np.linalg.norm(nv0)\n fv0 = fi0 * nv0\n T0_T = np.transpose(algebra.crv2tan(fv0))\n T0_Txv = np.dot(T0_T, xv)\n\n # Analytical solution\n derT_T_an = algebra.der_TanT_by_xv(fv0, xv)\n\n # End point\n fi1 = 2.0 * np.pi * np.random.rand()\n nv1 = np.random.rand(3)\n nv1 = nv1 / np.linalg.norm(nv1)\n fv1 = fi1 * nv1\n\n er = 10.\n A = np.array([1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6])\n for a in A:\n # perturbed\n fv = a * fv1 + (1. - a) * fv0\n dfv = fv - fv0\n Tpert_T = np.transpose(algebra.crv2tan(fv))\n Tpert_Txv = np.dot(Tpert_T, xv)\n dT_T_num = Tpert_Txv - T0_Txv\n dT_T_an = np.dot(derT_T_an, dfv)\n\n # Error\n er_new = np.max(np.abs(dT_T_num - dT_T_an)) / np.max(np.abs(dT_T_an))\n assert er_new < er, 'der_TanT_by_xv error not converging to 0'\n er = er_new\n\n assert er < A[-2], 'der_TanT_by_xv error too large'\n\n def test_quat_wrt_rot(self):\n \"\"\"\n We define:\n - G: initial frame\n - A: frame obtained upon rotation, Cga, defined by the quaternion q0\n - B: frame obtained upon further rotation, Cab, of A defined by \n the \"infinitesimal\" Cartesian rotation vector dcrv\n The test verifies that:\n 1. the total rotation matrix Cgb(q0+dq) is equal to\n Cgb = Cga(q0) Cab(dcrv)\n where \n dq = algebra.der_quat_wrt_crv(q0)\n 2. the difference between analytically computed delta quaternion, dq, \n and the numerical delta\n dq_num = algebra.crv2quat(algebra.rotation2crv(Cgb_ref))-q0\n is comparable to the step used to compute the delta dcrv\n 3. The equality:\n d(Cga(q0)*v)*dq = Cga(q0) * d(Cab*dv)*dcrv\n where d(Cga(q0)*v) and d(Cab*dv) are the derivatives computed through\n algebra.der_Cquat_by_v and algebra.der_Ccrv_by_v\n for a random vector v.\n\n Warning:\n - The relation dcrv->dquat is not uniquely defined. However, the \n resulting rotation matrix is, namely:\n Cga(q0+dq)=Cga(q0)*Cab(dcrv) \n \"\"\"\n\n ### case 1: simple rotation about the same axis\n\n # linearisation point\n a0 = 30. * np.pi / 180\n n0 = np.array([0, 0, 1])\n n0 = n0 / np.linalg.norm(n0)\n q0 = algebra.crv2quat(a0 * n0)\n Cga = algebra.quat2rotation(q0)\n\n # direction of perturbation\n n2 = n0\n\n A = np.array([1e-2, 1e-3, 1e-4, 1e-5, 1e-6])\n for a in A:\n drot = a * n2\n\n # build rotation manually\n atot = a0 + a\n Cgb_exp = algebra.crv2rotation(atot * n0) # ok\n\n # build combined rotation\n Cab = algebra.crv2rotation(drot)\n Cgb_ref = np.dot(Cga, Cab)\n\n # verify expected vs combined rotation matrices\n assert np.linalg.norm(Cgb_exp - Cgb_ref) / a < 1e-8, \\\n 'Verify test case - these matrices need to be identical'\n\n # verify analytical rotation matrix\n dq_an = np.dot(algebra.der_quat_wrt_crv(q0), drot)\n Cgb_an = algebra.quat2rotation(q0 + dq_an)\n erel_rot = np.linalg.norm(Cgb_an - Cgb_ref) / a\n assert erel_rot < 3e-3, \\\n 'Relative error of rotation matrix (%.2e) too large!' % erel_rot\n\n # verify delta quaternion\n erel_dq = np.linalg.norm(Cgb_an - Cgb_ref)\n dq_num = algebra.crv2quat(algebra.rotation2crv(Cgb_ref)) - q0\n erel_dq = np.linalg.norm(dq_num - dq_an) / np.linalg.norm(dq_an) / a\n assert erel_dq < .3, \\\n 'Relative error delta quaternion (%.2e) too large!' % erel_dq\n\n # verify algebraic relation\n v = np.ones((3,))\n D1 = algebra.der_Cquat_by_v(q0, v)\n D2 = algebra.der_Ccrv_by_v(np.zeros((3,)), v)\n res = np.dot(D1, dq_num) - np.dot(np.dot(Cga, D2), drot)\n erel_res = np.linalg.norm(res) / a\n assert erel_res < 5e-1 * a, \\\n 'Relative error of residual (%.2e) too large!' % erel_res\n\n ### case 2: random rotation\n\n # linearisation point\n a0 = 30. * np.pi / 180\n n0 = np.array([-2, -1, 1])\n n0 = n0 / np.linalg.norm(n0)\n q0 = algebra.crv2quat(a0 * n0)\n Cga = algebra.quat2rotation(q0)\n\n # direction of perturbation\n n2 = np.array([0.5, 1., -2.])\n n2 = n2 / np.linalg.norm(n2)\n\n A = np.array([1e-2, 1e-3, 1e-4, 1e-5, 1e-6])\n for a in A:\n drot = a * n2\n\n # build combined rotation\n Cab = algebra.crv2rotation(drot)\n Cgb_ref = np.dot(Cga, Cab)\n\n # verify analytical rotation matrix\n dq_an = np.dot(algebra.der_quat_wrt_crv(q0), drot)\n Cgb_an = algebra.quat2rotation(q0 + dq_an)\n erel_rot = np.linalg.norm(Cgb_an - Cgb_ref) / a\n assert erel_rot < 3e-3, \\\n 'Relative error of rotation matrix (%.2e) too large!' % erel_rot\n\n # verify delta quaternion\n erel_dq = np.linalg.norm(Cgb_an - Cgb_ref)\n dq_num = algebra.crv2quat(algebra.rotation2crv(Cgb_ref)) - q0\n erel_dq = np.linalg.norm(dq_num - dq_an) / np.linalg.norm(dq_an) / a\n assert erel_dq < .3, \\\n 'Relative error delta quaternion (%.2e) too large!' % erel_dq\n\n # verify algebraic relation\n v = np.ones((3,))\n D1 = algebra.der_Cquat_by_v(q0, v)\n D2 = algebra.der_Ccrv_by_v(np.zeros((3,)), v)\n res = np.dot(D1, dq_num) - np.dot(np.dot(Cga, D2), drot)\n erel_res = np.linalg.norm(res) / a\n assert erel_res < 5e-1 * a, \\\n 'Relative error of residual (%.2e) too large!' % erel_res\n\n def test_rotation_about_axis(self):\n \"\"\"\n Tests the rotations about the cartesian axes\n \"\"\"\n i = np.array([1, 0, 0])\n j = np.array([0, 1, 0])\n k = np.array([0, 0, 1])\n\n angle = 90 * np.pi / 180\n\n # Testing rotations about the x axis - rotation3d_x\n out = algebra.rotation3d_x(angle).dot(j)\n for ax in range(3):\n self.assertAlmostEqual(out[ax], k[ax])\n\n out = algebra.rotation3d_x(angle).dot(k)\n for ax in range(3):\n self.assertAlmostEqual(out[ax], -j[ax])\n\n # Testing rotations about the y axis - rotation3d_y\n out = algebra.rotation3d_y(angle).dot(i)\n for ax in range(3):\n self.assertAlmostEqual(out[ax], -k[ax])\n\n out = algebra.rotation3d_y(angle).dot(k)\n for ax in range(3):\n self.assertAlmostEqual(out[ax], i[ax])\n\n # Testing rotations about the z axis - rotation3d_z\n out = algebra.rotation3d_z(angle).dot(i)\n for ax in range(3):\n self.assertAlmostEqual(out[ax], j[ax])\n\n out = algebra.rotation3d_z(angle).dot(j)\n for ax in range(3):\n self.assertAlmostEqual(out[ax], -i[ax])\n\n def test_rotation_G_to_A(self):\n \"\"\"\n Tests the rotation of a vector in G frame to a vector in A frame by a roll, pitch and yaw considering that\n SHARPy employs an SEU frame.\n\n In the inertial frame, the ``x_g`` axis is aligned with the longitudinal axis of the aircraft pointing backwards,\n ``z_g`` points upwards and ``y_g`` completes the set\n Returns:\n\n \"\"\"\n\n aircraft_nose = np.array([-1, 0, 0])\n z_A = np.array([0, 0, 1])\n euler = np.array([90, 90, 90]) * np.pi / 180\n quat = algebra.euler2quat(euler)\n\n aircraft_nose_rotated = np.array([0, 0, 1]) # in G frame pointing upwards\n z_A_rotated_g = np.array([1, 0, 0])\n\n Cga = algebra.euler2rot(euler)\n Cga_quat = algebra.quat2rotation(quat)\n\n np.testing.assert_array_almost_equal(Cga.dot(aircraft_nose), aircraft_nose_rotated,\n err_msg='Rotation using Euler angles not performed properly')\n np.testing.assert_array_almost_equal(Cga_quat.dot(aircraft_nose), aircraft_nose_rotated,\n err_msg='Rotation using quaternions not performed properly')\n np.testing.assert_array_almost_equal(Cga.dot(z_A), z_A_rotated_g,\n err_msg='Rotation using Euler angles not performed properly')\n np.testing.assert_array_almost_equal(Cga_quat.dot(z_A), z_A_rotated_g,\n err_msg='Rotation using quaternions not performed properly')\n\n # Check projections\n Pag = Cga.T\n Pag_quat = Cga_quat.T\n\n np.testing.assert_array_almost_equal(Pag.dot(z_A_rotated_g), z_A,\n err_msg='Error in projection from A to G using Euler angles')\n np.testing.assert_array_almost_equal(Pag.dot(aircraft_nose_rotated), aircraft_nose,\n err_msg='Error in projection from A to G using Euler angles')\n np.testing.assert_array_almost_equal(Pag_quat.dot(z_A_rotated_g), z_A,\n err_msg='Error in projection from A to G using quaternions')\n np.testing.assert_array_almost_equal(Pag_quat.dot(aircraft_nose_rotated), aircraft_nose,\n err_msg='Error in projection from A to G using quaternions')\n\n# if __name__=='__main__':\n# unittest.main()\n# # T=TestAlgebra()\n# # # T.setUp()\n# # T.test_rotation_vectors_conversions()\n# # T.test_rotation_matrices()\n# # T.test_rotation_matrices_derivatives()\n# # T.test_crv_tangetial_operator()\n# # T.test_crv_tangetial_operator_derivative()\n# # T.test_crv_tangetial_operator_transpose_derivative()\n" }, { "path": "tests/utils/test_generate_cases.py", "content": "import unittest\nimport numpy as np\nimport os\nimport shutil\n\nimport sharpy.utils.generate_cases as gc\nimport sharpy.cases.templates.template_wt as template_wt\nfrom sharpy.utils.constants import deg2rad\n\n\nclass TestGenerateCases(unittest.TestCase):\n \"\"\"\n Tests the generate_cases module\n Based on the NREL-5MW wind turbine rotor\n \"\"\"\n\n def setUp(self):\n # remove_terminal_output = True\n ######################################################################\n ########################### PARAMETERS #############################\n ######################################################################\n # Case\n global case\n case = 'rotor'\n route = os.path.abspath(os.path.dirname(os.path.realpath(__file__))) + '/'\n\n # Geometry discretization\n chord_panels = np.array([4], dtype=int)\n revs_in_wake = 5\n\n # Operation\n rotation_velocity = 1.366190\n pitch_deg = 0. #degrees\n\n # Wind\n WSP = 11.4\n air_density = 1.225\n\n # Simulation\n dphi = 4.*deg2rad\n revs_to_simulate = 5\n\n ######################################################################\n ########################## GENERATE WT #############################\n ######################################################################\n dt = dphi/rotation_velocity\n time_steps = int(revs_to_simulate*2.*np.pi/dphi)\n time_steps = 1 # For the test cases\n mstar = int(revs_in_wake*2.*np.pi/dphi)\n mstar = 2 # For the test cases\n\n # Remove screen output\n # if remove_terminal_output:\n # sys.stdout = open(os.devnull, \"w\")\n\n op_params = {'rotation_velocity': rotation_velocity,\n 'pitch_deg': pitch_deg,\n 'wsp': WSP,\n 'dt': dt}\n\n geom_params = {'chord_panels':chord_panels,\n 'tol_remove_points': 1e-8,\n 'n_points_camber': 100,\n 'm_distribution': 'uniform'}\n\n excel_description = {'excel_file_name': route + '../../docs/source/content/example_notebooks/source/type04_db_nrel5mw_oc3_v06.xlsx',\n 'excel_sheet_parameters': 'parameters',\n 'excel_sheet_structural_blade': 'structural_blade',\n 'excel_sheet_discretization_blade': 'discretization_blade',\n 'excel_sheet_aero_blade': 'aero_blade',\n 'excel_sheet_airfoil_info': 'airfoil_info',\n 'excel_sheet_airfoil_chord': 'airfoil_coord'}\n\n options = {'camber_effect_on_twist': False,\n 'user_defined_m_distribution_type': None,\n 'include_polars': False,\n 'separate_blades': False}\n\n rotor, hub_nodes = template_wt.rotor_from_excel_type03(op_params,\n geom_params,\n excel_description,\n options)\n\n # Return the standard output to the terminal\n # if remove_terminal_output:\n # sys.stdout.close()\n # sys.stdout = sys.__stdout__\n\n ######################################################################\n ###################### DEFINE SIMULATION ###########################\n ######################################################################\n SimInfo = gc.SimulationInformation()\n SimInfo.set_default_values()\n\n SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'DynamicCoupled',\n 'SaveData']\n\n SimInfo.solvers['SHARPy']['case'] = case\n SimInfo.solvers['SHARPy']['write_screen'] = 'off'\n SimInfo.solvers['SHARPy']['route'] = route\n SimInfo.solvers['SHARPy']['write_log'] = True\n SimInfo.solvers['SHARPy']['log_folder'] = os.path.abspath(os.path.dirname(os.path.realpath(__file__))) + '/output/'\n SimInfo.set_variable_all_dicts('dt', dt)\n SimInfo.set_variable_all_dicts('rho', air_density)\n\n SimInfo.solvers['SteadyVelocityField']['u_inf'] = WSP\n SimInfo.solvers['SteadyVelocityField']['u_inf_direction'] = np.array([0., 0., 1.])\n SimInfo.set_variable_all_dicts('velocity_field_input', SimInfo.solvers['SteadyVelocityField'])\n SimInfo.set_variable_all_dicts('output', os.path.abspath(os.path.dirname(os.path.realpath(__file__))))\n\n SimInfo.solvers['BeamLoader']['unsteady'] = 'on'\n\n SimInfo.solvers['AerogridLoader']['unsteady'] = 'on'\n SimInfo.solvers['AerogridLoader']['mstar'] = mstar\n SimInfo.solvers['AerogridLoader']['freestream_dir'] = np.array([0.,0.,0.])\n SimInfo.solvers['AerogridLoader']['wake_shape_generator'] = 'HelicoidalWake'\n SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] = {'u_inf': WSP,\n 'u_inf_direction': np.array([0., 0., 1.]),\n 'dt': dt,\n 'rotation_velocity': rotation_velocity*np.array([0., 0., 1.])}\n\n SimInfo.solvers['StaticCoupled']['structural_solver'] = 'RigidDynamicPrescribedStep'\n SimInfo.solvers['StaticCoupled']['structural_solver_settings'] = SimInfo.solvers['RigidDynamicPrescribedStep']\n # SimInfo.solvers['StaticCoupled']['structural_solver'] = 'NonLinearDynamicPrescribedStep'\n # SimInfo.solvers['StaticCoupled']['structural_solver_settings'] = SimInfo.solvers['NonLinearDynamicPrescribedStep']\n SimInfo.solvers['StaticCoupled']['aero_solver'] = 'StaticUvlm'\n SimInfo.solvers['StaticCoupled']['aero_solver_settings'] = SimInfo.solvers['StaticUvlm']\n\n SimInfo.solvers['StaticCoupled']['tolerance'] = 1e-6\n SimInfo.solvers['StaticCoupled']['n_load_steps'] = 0\n SimInfo.solvers['StaticCoupled']['relaxation_factor'] = 0.\n\n SimInfo.solvers['StaticUvlm']['horseshoe'] = False\n SimInfo.solvers['StaticUvlm']['num_cores'] = 8\n SimInfo.solvers['StaticUvlm']['n_rollup'] = 0\n SimInfo.solvers['StaticUvlm']['rollup_dt'] = dt\n SimInfo.solvers['StaticUvlm']['rollup_aic_refresh'] = 1\n SimInfo.solvers['StaticUvlm']['rollup_tolerance'] = 1e-8\n SimInfo.solvers['StaticUvlm']['rbm_vel_g'] = np.array([0., 0., 0.,\n 0., 0., rotation_velocity])\n\n SimInfo.solvers['StepUvlm']['convection_scheme'] = 2\n SimInfo.solvers['StepUvlm']['num_cores'] = 1\n SimInfo.solvers['StepUvlm']['cfl1'] = False\n\n # SimInfo.solvers['DynamicCoupled']['structural_solver'] = 'NonLinearDynamicMultibody'\n # SimInfo.solvers['DynamicCoupled']['structural_solver_settings'] = SimInfo.solvers['NonLinearDynamicMultibody']\n SimInfo.solvers['DynamicCoupled']['structural_solver'] = 'RigidDynamicPrescribedStep'\n SimInfo.solvers['DynamicCoupled']['structural_solver_settings'] = SimInfo.solvers['RigidDynamicPrescribedStep']\n SimInfo.solvers['DynamicCoupled']['aero_solver'] = 'StepUvlm'\n SimInfo.solvers['DynamicCoupled']['aero_solver_settings'] = SimInfo.solvers['StepUvlm']\n SimInfo.solvers['DynamicCoupled']['postprocessors'] = ['BeamPlot', 'AerogridPlot', 'Cleanup', 'SaveData']\n SimInfo.solvers['DynamicCoupled']['postprocessors_settings'] = {'BeamPlot': SimInfo.solvers['BeamPlot'],\n 'AerogridPlot': SimInfo.solvers['AerogridPlot'],\n 'Cleanup': SimInfo.solvers['Cleanup'],\n 'SaveData': SimInfo.solvers['SaveData']}\n SimInfo.solvers['DynamicCoupled']['minimum_steps'] = 0\n SimInfo.solvers['DynamicCoupled']['include_unsteady_force_contribution'] = True\n SimInfo.solvers['DynamicCoupled']['relaxation_factor'] = 0.\n SimInfo.solvers['DynamicCoupled']['final_relaxation_factor'] = 0.\n SimInfo.solvers['DynamicCoupled']['dynamic_relaxation'] = False\n SimInfo.solvers['DynamicCoupled']['relaxation_steps'] = 0\n\n SimInfo.define_num_steps(time_steps)\n\n # Define dynamic simulation\n SimInfo.with_forced_vel = True\n SimInfo.for_vel = np.zeros((time_steps,6), dtype=float)\n SimInfo.for_vel[:,5] = rotation_velocity\n SimInfo.for_acc = np.zeros((time_steps,6), dtype=float)\n SimInfo.with_dynamic_forces = True\n SimInfo.dynamic_forces = np.zeros((time_steps,rotor.StructuralInformation.num_node,6), dtype=float)\n\n\n ######################################################################\n ####################### GENERATE FILES #############################\n ######################################################################\n gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n rotor.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n SimInfo.generate_solver_file()\n SimInfo.generate_dyn_file(time_steps)\n\n def test_generatecases(self):\n\n import sharpy.sharpy_main\n\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) + '/' + case +'.sharpy')\n sharpy.sharpy_main.main(['', solver_path])\n\n def tearDown(self):\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n solver_path += '/'\n files_to_delete = [case + '.aero.h5',\n case + '.dyn.h5',\n case + '.fem.h5',\n case + '.sharpy',\n '/output/' + case + '/log']\n\n for f in files_to_delete:\n os.remove(solver_path + f)\n\n output_path = solver_path + 'output/'\n if os.path.isdir(output_path):\n shutil.rmtree(output_path)\n" }, { "path": "tests/utils/test_settings.py", "content": "import sharpy.utils.settings as settings\nimport sharpy.utils.exceptions as exceptions\nimport sharpy.utils.cout_utils as cout\nfrom copy import deepcopy\nimport numpy as np\nimport unittest\nimport tests.coupled.static.pazy.generate_pazy as gp\nimport os\n\n\nclass TestSettings(unittest.TestCase):\n \"\"\"\n Tests the settings utilities module\n \"\"\"\n\n route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n \n def setUp(self):\n cout.start_writer()\n\n def tearDown(self):\n cout.finish_writer()\n\n def test_settings_to_custom_types(self):\n in_dict = dict()\n default_dict = dict()\n types_dict = dict()\n\n\n in_dict['integer_var'] = '1234'\n types_dict['integer_var'] = 'int'\n default_dict['integer_var'] = 0\n\n in_dict['float_var'] = '1.234'\n types_dict['float_var'] = 'float'\n default_dict['float_var'] = 0.0\n\n in_dict['str_var'] = 'aaaa'\n types_dict['str_var'] = 'str'\n default_dict['str_var'] = 'default_string'\n\n in_dict['bool_var'] = 'on'\n types_dict['bool_var'] = 'bool'\n default_dict['bool_var'] = False\n\n in_dict['list_var'] = ['aa', 'bb', '11', 'ss']\n types_dict['list_var'] = 'list(str)'\n default_dict['list_var'] = ['a', 'b']\n split_list = ['aa', 'bb', '11', 'ss']\n\n in_dict['float_list_var'] = ['1.1', '2.2', '3.3']\n types_dict['float_list_var'] = 'list(float)'\n default_dict['float_list_var'] = np.array([0.0, -1.1])\n split_float_list = np.array([1.1, 2.2, 3.3])\n\n original_dict = deepcopy(in_dict)\n\n # assigned values test\n result = settings.to_custom_types(in_dict, types_dict, default_dict)\n # integer variable\n self.assertEqual(in_dict['integer_var'], 1234, 'Integer test for assigned values not passed')\n # float variable\n self.assertEqual(in_dict['float_var'], 1.234, 'Float test for assigned values not passed')\n # string variable\n self.assertEqual(in_dict['str_var'], 'aaaa', 'String test for assigned values not passed')\n # bool variable\n self.assertEqual(in_dict['bool_var'], True, 'Bool test for assigned values not passed')\n # list variable\n for i in range(4):\n self.assertEqual(in_dict['list_var'][i], split_list[i], 'List test for assigned values not passed')\n # float list variable\n for i in range(3):\n self.assertEqual(in_dict['float_list_var'][i], split_float_list[i], 'Floating point list test for assigned values not passed')\n\n # default values test\n in_default_dict = dict()\n result = settings.to_custom_types(in_default_dict, types_dict, default_dict)\n # integer variable\n self.assertEqual(in_default_dict['integer_var'], default_dict['integer_var'],\n 'Integer test for default values not passed')\n # float variable\n self.assertEqual(in_default_dict['float_var'], default_dict['float_var'],\n 'Float test for default values not passed')\n # string variable\n self.assertEqual(in_default_dict['str_var'], default_dict['str_var'],\n 'String test for default values not passed')\n # bool variable\n self.assertEqual(in_default_dict['bool_var'], default_dict['bool_var'],\n 'Bool test for default values not passed')\n # list(str) variable\n for i in range(2):\n self.assertEqual(in_default_dict['list_var'][i], default_dict['list_var'][i],\n 'String list test for default values not passed')\n # list(float) variable\n for i in range(2):\n self.assertEqual(in_default_dict['float_list_var'][i], default_dict['float_list_var'][i],\n 'float list test for default values not passed')\n\n # non-existant default values\n with self.assertRaises(exceptions.NoDefaultValueException):\n temp_default_dict = default_dict.copy()\n temp_default_dict['integer_var'] = None\n\n # remove value in in_dict\n temp_in_dict = deepcopy(original_dict)\n del temp_in_dict['integer_var']\n result = settings.to_custom_types(temp_in_dict, types_dict, temp_default_dict)\n\n with self.assertRaises(exceptions.NoDefaultValueException):\n temp_default_dict = default_dict.copy()\n temp_default_dict['float_var'] = None\n\n # remove value in in_dict\n temp_in_dict = deepcopy(original_dict)\n del temp_in_dict['float_var']\n result = settings.to_custom_types(temp_in_dict, types_dict, temp_default_dict)\n\n with self.assertRaises(exceptions.NoDefaultValueException):\n temp_default_dict = default_dict.copy()\n temp_default_dict['str_var'] = None\n\n # remove value in in_dict\n temp_in_dict = deepcopy(original_dict)\n del temp_in_dict['str_var']\n result = settings.to_custom_types(temp_in_dict, types_dict, temp_default_dict)\n\n with self.assertRaises(exceptions.NoDefaultValueException):\n temp_default_dict = default_dict.copy()\n temp_default_dict['bool_var'] = None\n\n # remove value in in_dict\n temp_in_dict = deepcopy(original_dict)\n del temp_in_dict['bool_var']\n result = settings.to_custom_types(temp_in_dict, types_dict, temp_default_dict)\n\n with self.assertRaises(exceptions.NoDefaultValueException):\n temp_default_dict = default_dict.copy()\n temp_default_dict['list_var'] = None\n\n # remove value in in_dict\n temp_in_dict = deepcopy(original_dict)\n del temp_in_dict['list_var']\n result = settings.to_custom_types(temp_in_dict, types_dict, temp_default_dict)\n\n with self.assertRaises(exceptions.NoDefaultValueException):\n temp_default_dict = default_dict.copy()\n temp_default_dict['float_list_var'] = None\n\n # remove value in in_dict\n temp_in_dict = deepcopy(original_dict)\n del temp_in_dict['float_list_var']\n result = settings.to_custom_types(temp_in_dict, types_dict, temp_default_dict)\n\n def test_multiple_setting_option(self):\n u_inf = 50\n alpha = 7\n case_name = 'pazy_uinf{:04g}_alpha{:04g}'.format(u_inf * 10, alpha * 10)\n\n M = 16\n N = 64\n Msf = 1\n\n cases_folder = self.route_test_dir + '/pazy/cases/'\n output_folder = self.route_test_dir + '/pazy/cases/'\n # run case\n gp.generate_pazy(u_inf, case_name, output_folder, cases_folder,\n alpha=alpha,\n M=M,\n N=N,\n Msf=Msf,\n test_multiple_inputs=True)\n\n def tearDown(self):\n cases_folder = self.route_test_dir + '/pazy/cases/'\n\n if os.path.isdir(cases_folder):\n import shutil\n shutil.rmtree(cases_folder)\n" }, { "path": "tests/uvlm/__init__.py", "content": "" }, { "path": "tests/uvlm/dynamic/test_wake_cfl_n1.py", "content": "import numpy as np\nimport os\nimport sys\nimport unittest\n# import shutil\n\nimport sharpy.utils.generate_cases as gc\nimport sharpy.sharpy_main\n\n# maths\ndeg2rad = np.pi/180.\n\n# Generate the file containing the gust information\ngust = np.array([[-1e12, 0, 0, 0],\n[-1e-12, 0, 0, 0],\n[0, -1.523086e-6, 0, 1.745328e-3],\n[1e12, -1.523086e-6, 0, 1.745328e-3]])\nnp.savetxt(\"0p1_step_gust.txt\", gust, header=\"Time[s] DeltaUx[m/s] DeltaUy[m/s] DeltaUz[m/s]\")\n\n# Analytical kussner function as a function of the non-dimensional time\nkussner_function = np.array([[2.50000000e-01, 2.24788834e-01],\n [5.00000000e-01, 3.08322030e-01],\n [7.50000000e-01, 3.69409233e-01],\n [1.00000000e+00, 4.18591199e-01],\n [1.25000000e+00, 4.59608283e-01],\n [1.50000000e+00, 4.94597861e-01],\n [1.75000000e+00, 5.24998850e-01],\n [2.00000000e+00, 5.51822632e-01],\n [2.25000000e+00, 5.75792734e-01],\n [2.50000000e+00, 5.97434419e-01],\n [3.25000000e+00, 6.51811966e-01],\n [4.00000000e+00, 6.94721054e-01],\n [5.00000000e+00, 7.39586015e-01],\n [7.50000000e+00, 8.13230851e-01],\n [1.00000000e+01, 8.56395643e-01],\n [1.25000000e+01, 8.84426328e-01],\n [1.50000000e+01, 9.04257362e-01],\n [1.75000000e+01, 9.19155200e-01],\n [2.00000000e+01, 9.30758783e-01],\n [0.00000000e+00, 6.43293001e-02],\n [2.50000000e+01, 9.47358507e-01],\n [3.00000000e+01, 9.58126128e-01],\n [3.50000000e+01, 9.65279097e-01],\n [4.00000000e+01, 9.70275111e-01],\n [4.50000000e+01, 9.74053377e-01],\n [5.00000000e+01, 9.77137592e-01],\n [6.00000000e+01, 9.81903866e-01],\n [7.00000000e+01, 9.84820831e-01],\n [8.00000000e+01, 9.86297902e-01],\n [9.00000000e+01, 9.87557134e-01],\n [9.97500000e+01, 9.89298872e-01]])\n\n\nclass TestWakeCFLn1(unittest.TestCase):\n \"\"\"\n Validate an airfoil response to a Kussner gust\n Wake discretisation not complying with CFL=1\n Non-linear and linear responses\n \"\"\"\n\n chord = 1. # \n AR = 1e7 # Wing aspect ratio\n \n nodes_AR = 4 # even number of nodes in the spanwise direction\n \n num_chord_panels = 8 # Number of chord panels\n \n uinf = 1. # Flow velocity\n uinf_dir = np.array([1., 0., 0.]) # Flow velocity direction\n air_density = 1.225 # Flow density\n \n aoa_ini_deg = 1. # Initial angle of attack\n \n wake_chords = 100 # Length of the wake in airfoil chords units\n \n # Time discretization\n final_ndtime = 12.0 # Final non-dimensional time\n time_steps_per_chord = 8 # Number of time steps required by the flow to cover the airfoil chord\n dt = chord/time_steps_per_chord/uinf # time step\n nd_dt = dt*uinf/chord*2 # non-dimensional time step\n offset_time_steps = 10 # Number of time steps before the gust gets to the airfoil\n \n offset = 0.\n\n def generate_geometry(self):\n # offset is just the distance between the gust edge and the first colocation point\n # It is just used for plotting purposes\n len_first_panel = (self.chord - self.dt*self.uinf)/(self.num_chord_panels - 1)\n self.offset = self.offset_time_steps*self.dt*self.uinf + (-0.25*self.chord + 0.75*len_first_panel)*np.cos(self.aoa_ini_deg*deg2rad) # should be 0.5*len_first_panel but to make sure it happens I increase it a bit\n offset_LE = self.offset - 0.25*self.chord*np.cos(self.aoa_ini_deg*deg2rad)\n \n # Compute span\n span = self.chord*self.AR\n assert self.nodes_AR%2 == 0, \"nodes_AR must be even\"\n \n # Compute number of nodes\n num_node = self.nodes_AR + 1\n num_node_semispan = int((num_node - 1)/2 + 1)\n nodes_y_semispan = np.zeros((num_node_semispan,))\n \n # Number of seminodes\n n2 = int(self.nodes_AR/2 + 1)\n \n # Nodes coordinates in the spanwise direction\n nodes_y_semispan[0:n2] = np.linspace(0, self.AR/2*self.chord, n2)\n \n # Nodes coordinates\n nodes_y = np.zeros((num_node,))\n nodes_y[:num_node_semispan] = -1*nodes_y_semispan[::-1]\n nodes_y[num_node_semispan - 1:] = nodes_y_semispan\n \n assert not (np.diff(nodes_y) == 0).any(), \"Repeated nodes\"\n \n nodes = np.zeros((len(nodes_y), 3))\n nodes[:, 1] = nodes_y\n \n # Irrelevant structural properties\n mass_per_unit_length = 1.\n mass_iner = 1e-4\n EA = 1e9\n GA = 1e9\n GJ = 1e9\n EI = 1e9\n \n # Airfoil camber\n airfoil_camber = np.zeros((1, 100, 2))\n airfoil_camber[0,:,0] = np.linspace(0.,1.,100)\n \n # Structure\n airfoil = gc.AeroelasticInformation()\n airfoil.StructuralInformation.num_node = len(nodes)\n airfoil.StructuralInformation.num_node_elem = 3\n airfoil.StructuralInformation.compute_basic_num_elem()\n \n airfoil.StructuralInformation.generate_uniform_sym_beam(nodes,\n mass_per_unit_length,\n mass_iner,\n EA,\n GA,\n GJ,\n EI,\n num_node_elem = airfoil.StructuralInformation.num_node_elem,\n y_BFoR = 'x_AFoR',\n num_lumped_mass=0)\n \n airfoil.StructuralInformation.structural_twist = 0.*deg2rad*np.ones_like(airfoil.StructuralInformation.structural_twist)\n airfoil.StructuralInformation.boundary_conditions = np.zeros((airfoil.StructuralInformation.num_node), dtype = int)\n airfoil.StructuralInformation.boundary_conditions[0] = 1 # Clamped end\n airfoil.StructuralInformation.boundary_conditions[-1] = -1 # Free end\n \n # Generate blade aerodynamics\n airfoil.AerodynamicInformation.create_one_uniform_aerodynamics(airfoil.StructuralInformation,\n chord = self.chord,\n twist = self.aoa_ini_deg*deg2rad,\n sweep = 0.,\n num_chord_panels = self.num_chord_panels,\n m_distribution = 'uniform',\n elastic_axis = 0.25,\n num_points_camber = 100,\n airfoil = airfoil_camber)\n\n return airfoil\n\n\n def generate_files(self, case_header, airfoil):\n\n # Define the simulation\n case = ('%s_aoa%.2f' % (case_header, self.aoa_ini_deg)).replace(\".\", \"p\")\n route = os.path.dirname(os.path.realpath(__file__)) + '/'\n \n SimInfo = gc.SimulationInformation()\n SimInfo.set_default_values()\n \n SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'DynamicCoupled']\n \n SimInfo.solvers['SHARPy']['case'] = case\n SimInfo.solvers['SHARPy']['route'] = route\n SimInfo.solvers['SHARPy']['log_folder'] = \"./output/%s\" % case\n SimInfo.solvers['SHARPy']['write_log'] = False\n SimInfo.solvers['SHARPy']['write_screen'] = False\n SimInfo.set_variable_all_dicts('rho', self.air_density)\n SimInfo.set_variable_all_dicts('dt', self.dt)\n \n SimInfo.solvers['BeamLoader']['unsteady'] = 'on'\n\n import sharpy.utils.generator_interface as gi\n if case_header == 'traditional' or case_header == 'statespace_cfl1':\n\n SimInfo.solvers['AerogridLoader']['wake_shape_generator'] = 'StraightWake'\n SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] = {'u_inf': self.uinf,\n 'u_inf_direction': self.uinf_dir,\n 'dt': self.dt,\n 'dx1': self.chord/self.num_chord_panels,\n 'ndx1': int((self.wake_chords*self.chord)/(self.chord/self.num_chord_panels)),\n 'r':1.,\n 'dxmax':10*self.chord}\n \n gi.dictionary_of_generators(print_info=False)\n hw = gi.dict_of_generators['StraightWake']\n wsg_in = SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] # for simplicity\n length = 0\n mstar = 0\n while length < (self.wake_chords*self.chord):\n mstar += 1\n length += hw.get_deltax(mstar, wsg_in['dx1'],\n wsg_in['ndx1'],\n wsg_in['r'],\n wsg_in['dxmax'])\n \n SimInfo.solvers['AerogridLoader']['unsteady'] = 'on'\n SimInfo.solvers['AerogridLoader']['mstar'] = mstar\n SimInfo.solvers['AerogridLoader']['freestream_dir'] = np.array([0.,0.,0.])\n \n elif case_header in ['new_nonlinear', 'new_linear', 'statespace']:\n\n SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] = {'u_inf': self.uinf,\n 'u_inf_direction': self.uinf_dir,\n 'dt': self.dt,\n 'dx1': self.chord/self.num_chord_panels,\n 'ndx1': int((1*self.chord)/(self.chord/self.num_chord_panels)),\n 'r':2.,\n 'dxmax':10*self.chord}\n\n gi.dictionary_of_generators(print_info=False)\n hw = gi.dict_of_generators['StraightWake']\n wsg_in = SimInfo.solvers['AerogridLoader']['wake_shape_generator_input'] # for simplicity\n length = 0\n mstar = 0\n while length < (self.wake_chords*self.chord):\n mstar += 1\n length += hw.get_deltax(mstar, wsg_in['dx1'],\n wsg_in['ndx1'],\n wsg_in['r'],\n wsg_in['dxmax'])\n\n SimInfo.solvers['AerogridLoader']['mstar'] = mstar\n\n\n SimInfo.solvers['SteadyVelocityField']['u_inf'] = self.uinf\n SimInfo.solvers['SteadyVelocityField']['u_inf_direction'] = self.uinf_dir\n \n SimInfo.solvers['StaticUvlm']['horseshoe'] = False\n SimInfo.solvers['StaticUvlm']['num_cores'] = 8\n SimInfo.solvers['StaticUvlm']['n_rollup'] = 0\n SimInfo.solvers['StaticUvlm']['rollup_dt'] = self.dt\n SimInfo.solvers['StaticUvlm']['velocity_field_generator'] = 'SteadyVelocityField'\n SimInfo.solvers['StaticUvlm']['velocity_field_input'] = SimInfo.solvers['SteadyVelocityField']\n \n SimInfo.solvers['StaticCoupled']['structural_solver'] = 'RigidDynamicPrescribedStep'\n SimInfo.solvers['StaticCoupled']['structural_solver_settings'] = SimInfo.solvers['RigidDynamicPrescribedStep']\n SimInfo.solvers['StaticCoupled']['aero_solver'] = 'StaticUvlm'\n SimInfo.solvers['StaticCoupled']['aero_solver_settings'] = SimInfo.solvers['StaticUvlm']\n\n if case_header in ['traditional', 'new_nonlinear']: \n SimInfo.solvers['StepUvlm']['convection_scheme'] = 0\n SimInfo.solvers['StepUvlm']['num_cores'] = 8\n SimInfo.solvers['StepUvlm']['velocity_field_generator'] = 'GustVelocityField'\n SimInfo.solvers['StepUvlm']['velocity_field_input'] = {'u_inf' : self.uinf,\n 'u_inf_direction': np.array([1.,0.,0.]),\n 'gust_shape': 'time varying',\n 'offset': self.offset,\n 'relative_motion': True,\n 'gust_parameters': {'file' : '0p1_step_gust.txt',\n 'gust_length': 0.,\n 'gust_intensity': 0.}}\n \n SimInfo.solvers['DynamicCoupled']['aero_solver'] = 'StepUvlm'\n SimInfo.solvers['DynamicCoupled']['aero_solver_settings'] = SimInfo.solvers['StepUvlm']\n elif case_header == 'new_linear':\n\n SimInfo.solvers['StepLinearUVLM']['dt'] = self.dt\n SimInfo.solvers['StepLinearUVLM']['integr_order'] = 2\n SimInfo.solvers['StepLinearUVLM']['remove_predictor'] = 'off'\n SimInfo.solvers['StepLinearUVLM']['use_sparse'] = True\n SimInfo.solvers['StepLinearUVLM']['density'] = self.air_density\n SimInfo.solvers['StepLinearUVLM']['vortex_radius'] = 1e-6\n SimInfo.solvers['StepLinearUVLM']['vortex_radius_wake_ind'] = 1e-3\n SimInfo.solvers['StepLinearUVLM']['velocity_field_generator'] = 'GustVelocityField'\n SimInfo.solvers['StepLinearUVLM']['velocity_field_input'] = {'u_inf' : self.uinf,\n 'u_inf_direction': self.uinf_dir,\n 'gust_shape': 'time varying',\n 'offset': self.offset,\n 'relative_motion': True,\n 'gust_parameters': {'file' : '0p1_step_gust.txt',\n 'gust_length': 0.,\n 'gust_intensity': 0.}}\n\n SimInfo.solvers['DynamicCoupled']['aero_solver'] = 'StepLinearUVLM'\n SimInfo.solvers['DynamicCoupled']['aero_solver_settings'] = SimInfo.solvers['StepLinearUVLM']\n\n if case_header == 'new_nonlinear':\n SimInfo.solvers['StaticUvlm']['cfl1'] = False\n SimInfo.solvers['StepUvlm']['cfl1'] = False\n\n elif case_header == 'new_linear':\n SimInfo.solvers['StaticUvlm']['cfl1'] = False\n SimInfo.solvers['StepLinearUVLM']['cfl1'] = False\n \n elif case_header == 'traditional':\n SimInfo.solvers['StaticUvlm']['cfl1'] = True\n SimInfo.solvers['StepUvlm']['cfl1'] = True\n\n SimInfo.solvers['DynamicCoupled']['structural_solver'] = 'RigidDynamicPrescribedStep'\n SimInfo.solvers['DynamicCoupled']['structural_solver_settings'] = SimInfo.solvers['RigidDynamicPrescribedStep']\n SimInfo.solvers['DynamicCoupled']['postprocessors'] = ['Cleanup']\n SimInfo.solvers['DynamicCoupled']['postprocessors_settings'] = {'Cleanup': SimInfo.solvers['Cleanup']}\n SimInfo.solvers['DynamicCoupled']['minimum_steps'] = 0\n SimInfo.solvers['DynamicCoupled']['include_unsteady_force_contribution'] = True\n SimInfo.solvers['DynamicCoupled']['relaxation_factor'] = 0.\n SimInfo.solvers['DynamicCoupled']['final_relaxation_factor'] = 0.\n SimInfo.solvers['DynamicCoupled']['dynamic_relaxation'] = False\n SimInfo.solvers['DynamicCoupled']['relaxation_steps'] = 0\n SimInfo.solvers['DynamicCoupled']['fsi_tolerance'] = 1e-6\n\n # Time discretization\n time_steps = int(self.final_ndtime / self.nd_dt - 1)\n SimInfo.define_num_steps(time_steps)\n\n SimInfo.with_forced_vel = True\n SimInfo.for_vel = np.zeros((time_steps,6), dtype=float)\n SimInfo.for_acc = np.zeros((time_steps,6), dtype=float)\n SimInfo.with_dynamic_forces = True\n SimInfo.dynamic_forces = np.zeros((time_steps,airfoil.StructuralInformation.num_node,6), dtype=float)\n\n SimInfo.solvers['PickleData'] = {'folder': route + '/output/'}\n if 'statespace' in case_header:\n SimInfo.solvers['SHARPy']['flow'] = ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'Modal',\n 'LinearAssembler',\n 'AsymptoticStability',\n ]\n\n SimInfo.solvers['SHARPy']['write_screen'] = 'on'\n SimInfo.solvers['Modal'] = {'save_data': 'off',\n 'NumLambda': 50,\n 'rigid_body_modes': 'off'}\n\n SimInfo.solvers['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n 'linear_system_settings': {\n 'beam_settings': {'modal_projection': 'off',\n 'inout_coords': 'nodes',\n 'discrete_time': 'on',\n 'newmark_damp': 0.5e-4,\n 'discr_method': 'newmark',\n 'dt': self.dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'on',\n 'num_modes': 2,\n 'print_info': 'on',\n 'gravity': 'on',\n 'remove_dofs': [],\n 'remove_rigid_states': 'off'},\n 'aero_settings': {'dt': self.dt,\n 'integr_order': 2,\n 'density': self.air_density,\n 'remove_predictor': 'off',\n 'use_sparse': 'off',\n 'rigid_body_motion': 'off',\n 'use_euler': 'on',\n 'vortex_radius': 1e-6,\n 'convert_to_ct': 'off',\n 'gust_assembler': 'LeadingEdge',\n 'gust_assembler_inputs': {},\n },\n 'rigid_body_motion': 'off',\n 'track_body': 'on',\n 'use_euler': 'on',\n 'linearisation_tstep': -1\n },\n }\n SimInfo.solvers['AsymptoticStability'] = {'num_evals': 100}\n\n gc.clean_test_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n airfoil.generate_h5_files(SimInfo.solvers['SHARPy']['route'], SimInfo.solvers['SHARPy']['case'])\n SimInfo.generate_solver_file()\n SimInfo.generate_dyn_file(time_steps)\n \n return case, route\n\n def run_test(self, case_header):\n\n airfoil = self.generate_geometry()\n \n case, route = self.generate_files(case_header, airfoil)\n sharpy_file = route + case + '.sharpy'\n sharpy_output = sharpy.sharpy_main.main(['', sharpy_file])\n \n lift = sharpy_output.structure.timestep_info[-1].steady_applied_forces[self.nodes_AR//2, 2]\n lift += sharpy_output.structure.timestep_info[-1].unsteady_applied_forces[self.nodes_AR//2, 2]\n\n nd_time = sharpy_output.ts*self.nd_dt\n daoa = 0.1\n clsteady = 2*np.pi*(self.aoa_ini_deg + daoa)*deg2rad\n offset_plot = 0.84375\n factor = 0.5*self.air_density*self.uinf**2*self.chord*2.5e6\n sharpy_cl_clss = -lift/factor/clsteady\n kussner_cl_clss = 2*np.pi*self.aoa_ini_deg*deg2rad\n kussner_cl_clss += 2 * np.pi * daoa * deg2rad * np.interp(nd_time,\n kussner_function[:, 0],\n kussner_function[:, 1])\n kussner_cl_clss /= clsteady\n\n self.assertAlmostEqual(sharpy_cl_clss, kussner_cl_clss, 1)\n\n def test_traditional(self):\n self.run_test('traditional')\n\n\n def test_new_nonlinear(self):\n self.run_test('new_nonlinear')\n\n\n def test_new_linear(self):\n self.run_test('new_linear')\n\n def test_statespace(self):\n results = {}\n for case in ['statespace', 'statespace_cfl1']:\n with self.subTest(case):\n results[case] = self.run_statespace(case)\n\n def run_statespace(self, case_header):\n airfoil = self.generate_geometry()\n\n case, route = self.generate_files(case_header, airfoil)\n sharpy_file = route + case + '.sharpy'\n return sharpy.sharpy_main.main(['', sharpy_file])\n\n @classmethod\n def tearDownClass(cls):\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n solver_path += '/'\n files_to_delete = []\n for name in ['traditional_aoa1p00', 'new_nonlinear_aoa1p00', 'new_linear_aoa1p00']:\n files_to_delete.extend((name + '.aero.h5',\n name + '.dyn.h5',\n name + '.fem.h5',\n name + '.sharpy'))\n files_to_delete.append(\"0p1_step_gust.txt\")\n \n for f in files_to_delete:\n os.remove(solver_path + f)\n\n # shutil.rmtree(solver_path + 'output/')\n\n" }, { "path": "tests/uvlm/static/__init__.py", "content": "" }, { "path": "tests/uvlm/static/big_wake_planarwing/generate_big_wake_planarwing.py", "content": "import h5py as h5\nimport numpy as np\nimport configparser\nimport os\n\ncase_name = 'big_wake_planarwing'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n# flight conditions\nu_inf = 10\nrho = 1.225\nalpha = 15\nbeta = 0\nc_ref = 1\nb_ref = 16\nsweep = 0*np.pi/180.\naspect_ratio = 1 # = total wing span (chord = 1)\n\nalpha_rad = alpha*np.pi/180\n\n# main geometry data\nmain_span = aspect_ratio/2./np.cos(sweep)\nmain_chord = 1.0\nmain_ea = 0.5\nmain_sigma = 1\nmain_airfoil_P = 0\nmain_airfoil_M = 0\n\nn_surfaces = 2\n\n# discretisation data\nnum_elem_main = 10\n\nnum_node_elem = 3\nnum_elem = num_elem_main + num_elem_main\nnum_node_main = num_elem_main*(num_node_elem - 1) + 1\nnum_node = num_node_main + (num_node_main - 1)\n\nm_main = 10\n\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n\ndef generate_fem_file():\n # placeholders\n # coordinates\n global x, y, z\n x = np.zeros((num_node, ))\n y = np.zeros((num_node, ))\n z = np.zeros((num_node, ))\n # struct twist\n structural_twist = np.zeros((num_elem, 3))\n # beam number\n beam_number = np.zeros((num_elem, ), dtype=int)\n # frame of reference delta\n frame_of_reference_delta = np.zeros((num_elem, num_node_elem, 3))\n # connectivities\n conn = np.zeros((num_elem, num_node_elem), dtype=int)\n # stiffness\n num_stiffness = 1\n ea = 1e4\n ga = 1e4\n gj = 1e4\n eiy = 2e4\n eiz = 5e4\n sigma = 1\n base_stiffness = sigma*np.diag([ea, ga, ga, gj, eiy, eiz])\n stiffness = np.zeros((num_stiffness, 6, 6))\n stiffness[0, :, :] = main_sigma*base_stiffness\n elem_stiffness = np.zeros((num_elem,), dtype=int)\n # mass\n num_mass = 1\n m_base = 0.75\n j_base = 0.1\n base_mass = np.diag([m_base, m_base, m_base, j_base, j_base, j_base])\n mass = np.zeros((num_mass, 6, 6))\n mass[0, :, :] = np.sqrt(main_sigma)*base_mass\n elem_mass = np.zeros((num_elem,), dtype=int)\n # boundary conditions\n boundary_conditions = np.zeros((num_node, ), dtype=int)\n boundary_conditions[0] = 1\n # applied forces\n n_app_forces = 0\n node_app_forces = np.zeros((n_app_forces,), dtype=int)\n app_forces = np.zeros((n_app_forces, 6))\n\n spacing_param = 3\n\n # right wing (beam 0) --------------------------------------------------------------\n working_elem = 0\n working_node = 0\n beam_number[working_elem:working_elem + num_elem_main] = 0\n domain = np.linspace(0, 1.0, num_node_main)\n # 16 - (np.geomspace(20, 4, 10) - 4)\n x[working_node:working_node + num_node_main] = np.sin(sweep)*(main_span - (np.geomspace(main_span + spacing_param,\n 0 + spacing_param,\n num_node_main)\n - spacing_param))\n y[working_node:working_node + num_node_main] = np.abs(np.cos(sweep)*(main_span - (np.geomspace(main_span + spacing_param,\n 0 + spacing_param,\n num_node_main)\n - spacing_param)))\n y[0] = 0\n # y[working_node:working_node + num_node_main] = np.cos(sweep)*np.linspace(0.0, main_span, num_node_main)\n # x[working_node:working_node + num_node_main] = np.sin(sweep)*np.linspace(0.0, main_span, num_node_main)\n # y[working_node:working_node + num_node_main] = np.cos(sweep)*np.linspace(0.0, main_span, num_node_main)\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1])\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[0] = 1\n boundary_conditions[working_node + num_node_main - 1] = -1\n working_elem += num_elem_main\n working_node += num_node_main\n\n # left wing (beam 1) --------------------------------------------------------------\n beam_number[working_elem:working_elem + num_elem_main] = 1\n domain = np.linspace(-1.0, 0.0, num_node_main)\n tempy = np.linspace(-main_span, 0.0, num_node_main)\n # x[working_node:working_node + num_node_main - 1] = -np.sin(sweep)*tempy[0:-1]\n # y[working_node:working_node + num_node_main - 1] = np.cos(sweep)*tempy[0:-1]\n x[working_node:working_node + num_node_main - 1] = -np.sin(sweep)*(main_span - (np.geomspace(0 + spacing_param,\n main_span + spacing_param,\n num_node_main)[:-1]\n - spacing_param))\n y[working_node:working_node + num_node_main - 1] = -np.abs(np.cos(sweep)*(main_span - (np.geomspace(0 + spacing_param,\n main_span + spacing_param,\n num_node_main)[:-1]\n - spacing_param)))\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1]) + 1\n conn[working_elem + num_elem_main - 1, 1] = 0\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[working_node] = -1\n working_elem += num_elem_main\n working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=num_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=num_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=num_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n node_app_forces_handle = h5file.create_dataset(\n 'node_app_forces', data=node_app_forces)\n\n\ndef generate_aero_file():\n global x, y, z\n airfoil_distribution = np.zeros((num_elem, num_node_elem), dtype=int)\n surface_distribution = np.zeros((num_elem,), dtype=int) - 1\n surface_m = np.zeros((n_surfaces, ), dtype=int)\n m_distribution = 'uniform'\n aero_node = np.zeros((num_node,), dtype=bool)\n # twist = np.zeros((num_node,))\n twist= np.zeros((num_elem, num_node_elem))\n chord = np.zeros((num_elem, num_node_elem))\n elastic_axis = np.zeros((num_elem, num_node_elem))\n # elastic_axis = np.zeros((num_node,))\n\n working_elem = 0\n working_node = 0\n # right wing (surface 0, beam 0)\n i_surf = 0\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main] = True\n chord[:] = main_chord\n elastic_axis[:] = main_ea\n working_elem += num_elem_main\n working_node += num_node_main\n\n # left wing (surface 1, beam 1)\n i_surf = 1\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main - 1] = True\n # chord[working_node:working_node + num_node_main - 1] = main_chord\n # elastic_axis[working_node:working_node + num_node_main - 1] = main_ea\n working_elem += num_elem_main\n working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n generate_naca_camber(P=main_airfoil_P, M=main_airfoil_M)))\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input .attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n\ndef generate_naca_camber(M=0, P=0):\n m = M*1e-2\n p = P*1e-1\n\n def naca(x, m, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return m/(p*p)*(2*p*x - x*x)\n elif x > p and x < 1+1e-6:\n return m/((1-p)*(1-p))*(1 - 2*p + 2*p*x - x*x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, m, p) for x in x_vec])\n return x_vec, y_vec\n\n\ndef generate_solver_file(horseshoe=False):\n import sharpy.utils.algebra as algebra\n file_name = route + '/' + case_name + '.sharpy'\n # config = configparser.ConfigParser()\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n config['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': ['BeamLoader', 'AerogridLoader', 'StaticUvlm', 'AerogridPlot', 'AeroForcesCalculator'],\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n config['BeamLoader'] = {'unsteady': 'off',\n 'orientation': algebra.euler2quat(np.array([0.0,\n alpha_rad,\n beta*np.pi/180]))}\n if horseshoe is True:\n config['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 1,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': np.array([1., 0., 0.]),\n 'dt': main_chord/m_main/u_inf}}\n config['StaticUvlm'] = {'print_info': 'off',\n 'horseshoe': 'on',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': main_chord/m_main/u_inf,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': 1.225,\n 'alpha': alpha_rad,\n 'beta': beta\n }\n else:\n config['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 90,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': np.array([1., 0., 0.]),\n 'dt': main_chord/m_main/u_inf}}\n config['StaticUvlm'] = {'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 100,\n 'rollup_dt': main_chord/m_main/u_inf,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': 1.225,\n 'alpha': alpha_rad,\n 'beta': beta\n }\n\n minus_m_star = 0\n if config['StaticUvlm']['horseshoe'] == 'on':\n minus_m_star = max(m_main - 1, 1)\n config['AerogridPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0\n }\n config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n 'unsteady': 'off'\n }\n\n config.write()\n\n\nclean_test_files()\ngenerate_fem_file()\ngenerate_solver_file(horseshoe=False)\ngenerate_aero_file()\n" }, { "path": "tests/uvlm/static/planarwing/__init__.py", "content": "" }, { "path": "tests/uvlm/static/planarwing/generate_planarwing.py", "content": "import h5py as h5\nimport numpy as np\nimport configparser\nimport os\n\ncase_name = 'planarwing'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n# flight conditions\nu_inf = 25\nrho = 1.225\nalpha = 4\nbeta = 0\nc_ref = 1\nb_ref = 16\nsweep = 0*np.pi/180.\naspect_ratio = 32 # = total wing span (chord = 1)\n\nalpha_rad = alpha*np.pi/180\n\n# main geometry data\nmain_span = aspect_ratio/2./np.cos(sweep)\nmain_chord = 1.0\nmain_ea = 0.5\nmain_sigma = 1\nmain_airfoil_P = 0\nmain_airfoil_M = 0\n\nn_surfaces = 2\n\n# discretisation data\nnum_elem_main = 10\n\nnum_node_elem = 3\nnum_elem = num_elem_main + num_elem_main\nnum_node_main = num_elem_main*(num_node_elem - 1) + 1\nnum_node = num_node_main + (num_node_main - 1)\n\nm_main = 10\n\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n flightcon_file_name = route + '/' + case_name + '.flightcon.txt'\n if os.path.isfile(flightcon_file_name):\n os.remove(flightcon_file_name)\n\n\ndef generate_fem_file():\n # placeholders\n # coordinates\n global x, y, z\n x = np.zeros((num_node, ))\n y = np.zeros((num_node, ))\n z = np.zeros((num_node, ))\n # struct twist\n structural_twist = np.zeros((num_elem, num_node_elem))\n # beam number\n beam_number = np.zeros((num_elem, ), dtype=int)\n # frame of reference delta\n frame_of_reference_delta = np.zeros((num_elem, num_node_elem, 3))\n # connectivities\n conn = np.zeros((num_elem, num_node_elem), dtype=int)\n # stiffness\n num_stiffness = 1\n ea = 1e4\n ga = 1e4\n gj = 1e4\n eiy = 2e4\n eiz = 5e4\n sigma = 1\n base_stiffness = sigma*np.diag([ea, ga, ga, gj, eiy, eiz])\n stiffness = np.zeros((num_stiffness, 6, 6))\n stiffness[0, :, :] = main_sigma*base_stiffness\n elem_stiffness = np.zeros((num_elem,), dtype=int)\n # mass\n num_mass = 1\n m_base = 0.75\n j_base = 0.1\n base_mass = np.diag([m_base, m_base, m_base, j_base, j_base, j_base])\n mass = np.zeros((num_mass, 6, 6))\n mass[0, :, :] = np.sqrt(main_sigma)*base_mass\n elem_mass = np.zeros((num_elem,), dtype=int)\n # boundary conditions\n boundary_conditions = np.zeros((num_node, ), dtype=int)\n boundary_conditions[0] = 1\n # applied forces\n n_app_forces = 0\n node_app_forces = np.zeros((n_app_forces,), dtype=int)\n app_forces = np.zeros((n_app_forces, 6))\n\n spacing_param = 3\n\n # right wing (beam 0) --------------------------------------------------------------\n working_elem = 0\n working_node = 0\n beam_number[working_elem:working_elem + num_elem_main] = 0\n domain = np.linspace(0, 1.0, num_node_main)\n # 16 - (np.geomspace(20, 4, 10) - 4)\n x[working_node:working_node + num_node_main] = np.sin(sweep)*(main_span - (np.geomspace(main_span + spacing_param,\n 0 + spacing_param,\n num_node_main)\n - spacing_param))\n y[working_node:working_node + num_node_main] = np.abs(np.cos(sweep)*(main_span - (np.geomspace(main_span + spacing_param,\n 0 + spacing_param,\n num_node_main)\n - spacing_param)))\n y[0] = 0\n # y[working_node:working_node + num_node_main] = np.cos(sweep)*np.linspace(0.0, main_span, num_node_main)\n # x[working_node:working_node + num_node_main] = np.sin(sweep)*np.linspace(0.0, main_span, num_node_main)\n # y[working_node:working_node + num_node_main] = np.cos(sweep)*np.linspace(0.0, main_span, num_node_main)\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1])\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[0] = 1\n boundary_conditions[working_node + num_node_main - 1] = -1\n working_elem += num_elem_main\n working_node += num_node_main\n\n # left wing (beam 1) --------------------------------------------------------------\n beam_number[working_elem:working_elem + num_elem_main] = 1\n domain = np.linspace(-1.0, 0.0, num_node_main)\n tempy = np.linspace(-main_span, 0.0, num_node_main)\n # x[working_node:working_node + num_node_main - 1] = -np.sin(sweep)*tempy[0:-1]\n # y[working_node:working_node + num_node_main - 1] = np.cos(sweep)*tempy[0:-1]\n x[working_node:working_node + num_node_main - 1] = -np.sin(sweep)*(main_span - (np.geomspace(0 + spacing_param,\n main_span + spacing_param,\n num_node_main)[:-1]\n - spacing_param))\n y[working_node:working_node + num_node_main - 1] = -np.abs(np.cos(sweep)*(main_span - (np.geomspace(0 + spacing_param,\n main_span + spacing_param,\n num_node_main)[:-1]\n - spacing_param)))\n for ielem in range(num_elem_main):\n for inode in range(num_node_elem):\n frame_of_reference_delta[working_elem + ielem, inode, :] = [-1, 0, 0]\n # connectivity\n for ielem in range(num_elem_main):\n conn[working_elem + ielem, :] = ((np.ones((3,))*(working_elem + ielem)*(num_node_elem - 1)) +\n [0, 2, 1]) + 1\n conn[working_elem + num_elem_main - 1, 1] = 0\n elem_stiffness[working_elem:working_elem + num_elem_main] = 0\n elem_mass[working_elem:working_elem + num_elem_main] = 0\n boundary_conditions[working_node] = -1\n working_elem += num_elem_main\n working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=num_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=num_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=num_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n node_app_forces_handle = h5file.create_dataset(\n 'node_app_forces', data=node_app_forces)\n\n\ndef generate_aero_file():\n global x, y, z\n airfoil_distribution = np.zeros((num_elem, num_node_elem), dtype=int)\n surface_distribution = np.zeros((num_elem,), dtype=int) - 1\n surface_m = np.zeros((n_surfaces, ), dtype=int)\n m_distribution = 'uniform'\n aero_node = np.zeros((num_node,), dtype=bool)\n # twist = np.zeros((num_node,))\n twist= np.zeros((num_elem, num_node_elem))\n chord = np.zeros((num_elem, num_node_elem))\n elastic_axis = np.zeros((num_elem, num_node_elem))\n # elastic_axis = np.zeros((num_node,))\n\n working_elem = 0\n working_node = 0\n # right wing (surface 0, beam 0)\n i_surf = 0\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main] = True\n chord[:] = main_chord\n elastic_axis[:] = main_ea\n working_elem += num_elem_main\n working_node += num_node_main\n\n # left wing (surface 1, beam 1)\n i_surf = 1\n airfoil_distribution[working_elem:working_elem + num_elem_main, :] = 0\n surface_distribution[working_elem:working_elem + num_elem_main] = i_surf\n surface_m[i_surf] = m_main\n aero_node[working_node:working_node + num_node_main - 1] = True\n # chord[working_node:working_node + num_node_main - 1] = main_chord\n # elastic_axis[working_node:working_node + num_node_main - 1] = main_ea\n working_elem += num_elem_main\n working_node += num_node_main - 1\n\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add one airfoil\n naca_airfoil_main = airfoils_group.create_dataset('0', data=np.column_stack(\n generate_naca_camber(P=main_airfoil_P, M=main_airfoil_M)))\n # chord\n chord_input = h5file.create_dataset('chord', data=chord)\n dim_attr = chord_input .attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=twist)\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution', data=airfoil_distribution)\n\n surface_distribution_input = h5file.create_dataset('surface_distribution', data=surface_distribution)\n surface_m_input = h5file.create_dataset('surface_m', data=surface_m)\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=elastic_axis)\n\n\ndef generate_naca_camber(M=0, P=0):\n m = M*1e-2\n p = P*1e-1\n\n def naca(x, m, p):\n if x < 1e-6:\n return 0.0\n elif x < p:\n return m/(p*p)*(2*p*x - x*x)\n elif x > p and x < 1+1e-6:\n return m/((1-p)*(1-p))*(1 - 2*p + 2*p*x - x*x)\n\n x_vec = np.linspace(0, 1, 1000)\n y_vec = np.array([naca(x, m, p) for x in x_vec])\n return x_vec, y_vec\n\n\ndef generate_solver_file(horseshoe=False):\n import sharpy.utils.algebra as algebra\n file_name = route + '/' + case_name + '.sharpy'\n # config = configparser.ConfigParser()\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n config['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': ['BeamLoader', 'AerogridLoader', 'StaticUvlm', 'AerogridPlot', 'AeroForcesCalculator'],\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n config['BeamLoader'] = {'unsteady': 'off',\n 'orientation': algebra.euler2quat(np.array([0.0,\n alpha_rad,\n beta*np.pi/180]))}\n if horseshoe is True:\n config['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 1,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': np.array([1., 0., 0.]),\n 'dt': main_chord/m_main/u_inf}}\n config['StaticUvlm'] = {'print_info': 'off',\n 'horseshoe': 'on',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': main_chord/m_main/u_inf,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': 1.225,\n 'alpha': alpha_rad,\n 'beta': beta\n }\n else:\n config['AerogridLoader'] = {'unsteady': 'off',\n 'aligned_grid': 'on',\n 'mstar': 40,\n 'freestream_dir': ['1', '0', '0'],\n 'wake_shape_generator_input': {'u_inf': u_inf,\n 'u_inf_direction': np.array([1., 0., 0.]),\n 'dt': main_chord/m_main/u_inf}}\n config['StaticUvlm'] = {'print_info': 'off',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 50,\n 'rollup_dt': main_chord/m_main/u_inf,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': 1.225,\n 'alpha': alpha_rad,\n 'beta': beta\n }\n\n minus_m_star = 0\n if config['StaticUvlm']['horseshoe'] == 'on':\n minus_m_star = max(m_main - 1, 1)\n config['AerogridPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0\n }\n config['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'text_file_name': case_name + '_aeroforces.csv',\n 'screen_output': 'on',\n 'unsteady': 'off'\n }\n\n config.write()\n\n\nclean_test_files()\ngenerate_fem_file()\ngenerate_solver_file(horseshoe=True)\ngenerate_aero_file()\n\ncase_name = 'planarwing_discretewake'\nclean_test_files()\ngenerate_fem_file()\ngenerate_solver_file(horseshoe=False)\ngenerate_aero_file()\n" }, { "path": "tests/uvlm/static/polars/__init__.py", "content": "" }, { "path": "tests/uvlm/static/polars/generate_wing.py", "content": "import numpy as np\nimport sharpy.cases.templates.flying_wings as wings\nimport sharpy.utils.algebra as algebra\nimport sharpy.sharpy_main\n\n\ndef generate_infinite_wing(case_name, alpha, **kwargs):\n\n m = 8\n n = 4\n mstar = 500\n u_inf = 1\n alpha_deg = alpha\n alpha_rad = alpha_deg * np.pi / 180\n rho = 1.225\n gravity = False\n\n tolerance = 1e-5\n\n case_route = kwargs.get('case_route', './')\n case_route += '/' + case_name\n\n output_route = kwargs.get('output_route', './output/')\n # if not os.path.isdir(case_route):\n # os.makedirs(case_route)\n\n polar_file = kwargs.get('polar_file', None)\n\n wing = wings.QuasiInfinite(M=m,\n N=n,\n Mstar_fact=mstar,\n u_inf=u_inf,\n alpha=alpha_rad,\n aspect_ratio=kwargs.get('aspect_ratio', 8),\n rho=rho,\n route=case_route,\n case_name=case_name,\n polar_file=polar_file)\n\n wing.main_ea = kwargs.get('main_ea', 0.25)\n wing.clean_test_files()\n wing.update_derived_params()\n wing.sigma = 1e25\n wing.update_mass_stiff()\n\n wing.generate_aero_file()\n wing.generate_fem_file()\n\n settings = dict()\n settings['SHARPy'] = {'case': case_name,\n 'route': case_route,\n 'flow': kwargs.get('flow', []),\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': output_route,\n 'log_file': case_name + '.log'}\n\n settings['BeamLoader'] = {'unsteady': 'on',\n 'orientation': algebra.euler2quat(np.array([0.,\n alpha_rad,\n 0.]))}\n\n settings['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n 'mstar': int(kwargs.get('wake_length', 100) * m),\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {\n 'u_inf': u_inf,\n 'u_inf_direction': [1., 0., 0.],\n 'dt': wing.dt,\n },\n }\n\n settings['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-1,\n 'min_delta': tolerance,\n 'gravity_on': gravity,\n 'gravity': 9.81,\n 'initial_position': [0., 0., 0.]}\n\n settings['StaticUvlm'] = {'print_info': 'on',\n 'horseshoe': 'on',\n 'num_cores': 4,\n 'vortex_radius': 1e-6,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': {'u_inf': u_inf,\n 'u_inf_direction': [1., 0, 0]},\n 'rho': rho}\n\n settings['StaticCoupled'] = {'print_info': 'off',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': settings['NonLinearStatic'],\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': settings['StaticUvlm'],\n 'max_iter': 100,\n 'n_load_steps': kwargs.get('n_load_steps', 1),\n 'tolerance': kwargs.get('fsi_tolerance', 1e-5),\n 'relaxation_factor': kwargs.get('relaxation_factor', 0.2)}\n if polar_file is not None:\n settings['StaticCoupled']['correct_forces_method'] = 'PolarCorrection'\n settings['StaticCoupled']['correct_forces_settings'] = {'cd_from_cl': 'off',\n 'correct_lift': 'on',\n 'moment_from_polar': 'on'}\n\n settings['AerogridPlot'] = {'include_incidence_angle': 'on',\n 'include_velocities': 'on'}\n\n settings['BeamPlot'] = {}\n\n settings['AeroForcesCalculator'] = {'write_text_file': 'on',\n 'coefficients': 'on',\n 'q_ref': 0.5 * rho * u_inf ** 2,\n 'S_ref': wing.main_chord * wing.wing_span}\n\n settings['Modal'] = {'print_info': True,\n 'use_undamped_modes': True,\n 'NumLambda': 50,\n 'rigid_body_modes': True,\n 'write_modes_vtk': 'on',\n 'print_matrices': 'on',\n 'write_data': 'on',\n 'continuous_eigenvalues': 'off',\n 'plot_eigenvalues': False,\n 'rigid_modes_ppal_axes': 'on',\n 'folder': output_route}\n\n # ROM settings\n rom_settings = dict()\n rom_settings['algorithm'] = 'mimo_rational_arnoldi'\n rom_settings['r'] = 4\n rom_settings['frequency'] = np.array([0], dtype=float)\n rom_settings['single_side'] = 'observability'\n\n settings['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n 'linear_system_settings': {\n 'beam_settings': {'modal_projection': 'off',\n 'inout_coords': 'modes',\n 'discrete_time': 'off',\n 'newmark_damp': 0.5e-3,\n 'discr_method': 'newmark',\n 'dt': wing.dt,\n 'proj_modes': 'undamped',\n 'use_euler': 'on',\n 'num_modes': 20,\n 'print_info': 'on',\n 'gravity': kwargs.get('gravity', 'on'),\n 'remove_dofs': [],\n 'remove_rigid_states': 'on'},\n 'aero_settings': {'dt': wing.dt,\n 'integr_order': 2,\n 'density': rho,\n 'remove_predictor': 'off',\n 'use_sparse': False,\n 'rigid_body_motion': True,\n 'vortex_radius': 1e-7,\n 'remove_inputs': ['u_gust'],\n 'convert_to_ct': 'on',\n },\n 'track_body': 'off',\n 'use_euler': 'on',\n }}\n\n\n settings['StabilityDerivatives'] = {'u_inf': u_inf,\n 'c_ref': wing.main_chord,\n 'b_ref': wing.wing_span,\n 'S_ref': wing.wing_span * wing.main_chord,\n }\n\n settings['SaveParametricCase'] = {'save_case': 'off',\n 'parameters': {'alpha': alpha_deg}}\n\n wing.settings_to_config(settings)\n\n sharpy.sharpy_main.main(['', f'{case_route}/{case_name}.sharpy'])\n\n return wing\n\n\ndef get_case_header(polar, infinite_wing, compute_uind, high_re, main_ea, use2pi):\n if polar:\n case_header = 'polar'\n if high_re:\n case_header += '_highre'\n if use2pi:\n case_header += '_2pi'\n else:\n case_header = 'uvlm'\n\n if not infinite_wing:\n case_header += '_ar8'\n else:\n case_header += '_ari'\n\n if compute_uind and polar:\n case_header += '_uind'\n\n case_header += '_ea{:02g}'.format(main_ea * 100)\n\n return case_header\n\n\ndef run(infinite_wing, compute_uind, main_ea, high_re, case_route_root, output_route_root, use2pi=False,\n polar_file=None):\n flow = ['BeamLoader',\n 'AerogridLoader',\n 'StaticCoupled',\n 'AeroForcesCalculator',\n 'SaveParametricCase']\n\n if polar_file is not None:\n polar = True\n else:\n polar = False\n\n if not infinite_wing:\n ar = 8\n else:\n ar = 1e7\n\n case_header = get_case_header(polar, infinite_wing, compute_uind, high_re, main_ea, use2pi)\n case_route = case_route_root + '/' + case_header + '/'\n output_route = output_route_root + '/' + case_header + '/'\n for alpha in np.linspace(-5, 5, 6):\n case_name = '{:s}_alpha{:04g}'.format(case_header,\n alpha * 100).replace('-', 'M')\n generate_infinite_wing(case_name, alpha,\n flow=flow,\n case_route=case_route,\n polar_file=polar_file,\n aspect_ratio=ar,\n compute_uind=compute_uind,\n main_ea=main_ea,\n output_route=output_route,\n actual_aoa=not use2pi,\n )\n\n # pc.main(case_header, output_route)\n\n\ndef all_iter(case_route_root, output_route_root):\n for main_ea in [0.25, 0.5]:\n for polar in [True, False]:\n for infinite_wing in [True, False]:\n if polar:\n for high_re in [True, False]:\n for compute_uind in [True, False]:\n run(polar, infinite_wing, compute_uind, main_ea, high_re, case_route_root, output_route_root)\n else:\n pass\n # run(polar, infinite_wing, False, main_ea, False, case_route_root, output_route_root)\n\n\nif __name__ == '__main__':\n import postproc_infinite_wing as pc\n case_route_root = './cases_linear/'\n output_route_root = './output_linear/'\n polar = True\n infinite_wing = False\n compute_uind = False\n main_ea = 0.25\n high_re = False\n use2pi = True\n\n run(polar, infinite_wing, compute_uind, main_ea, high_re, case_route_root, output_route_root, use2pi=use2pi)\n # all_iter(case_route_root, output_route_root)\n" }, { "path": "tests/uvlm/static/polars/test_polars.py", "content": "import unittest\nimport tests.uvlm.static.polars.generate_wing as gw\nimport os\nimport glob\nimport configobj\nimport numpy as np\n\nfrom sharpy.aero.utils.utils import local_stability_axes\nimport sharpy.utils.algebra as algebra\n\n\nclass InfiniteWing:\n area = 90000000.0\n chord = 3.\n\n def force_coef(self, rho, uinf):\n return 0.5 * rho * uinf ** 2 * self.area\n\n def moment_coef(self, rho, uinf):\n return self.force_coef(rho, uinf) * self.chord\n\n\nclass TestAirfoilPolars(unittest.TestCase):\n route_test_dir = os.path.abspath(os.path.dirname(os.path.realpath(__file__)))\n\n polar_data = np.loadtxt(route_test_dir + '/xf-naca0018-il-50000.txt', skiprows=12)\n\n def test_infinite_wing(self):\n \"\"\"\n Infinite wing should yield same results as airfoil polar\n \"\"\"\n\n cases_route = self.route_test_dir + '/cases/'\n output_route = self.route_test_dir + '/output/'\n\n wing = InfiniteWing()\n\n gw.run(compute_uind=False,\n infinite_wing=True,\n main_ea=0.25,\n high_re=False,\n case_route_root=cases_route,\n output_route_root=output_route,\n use2pi=True,\n polar_file=self.route_test_dir + '/xf-naca0018-il-50000.txt')\n\n case_header = gw.get_case_header(polar=True,\n infinite_wing=True,\n compute_uind=False,\n high_re=False,\n main_ea=0.25,\n use2pi=True)\n\n results = postprocess(output_route + '/' + case_header + '/')\n\n results[:, 1:3] /= wing.force_coef(1.225, 1.)\n results[:, -1] /= wing.moment_coef(1.225, 1.)\n\n with self.subTest('lift'):\n cl_polar = np.interp(results[:, 0], self.polar_data[:, 0], self.polar_data[:, 1])\n np.testing.assert_array_almost_equal(cl_polar, results[:, 1], decimal=3)\n\n with self.subTest('drag'):\n cd_polar = np.interp(results[:, 0], self.polar_data[:, 0], self.polar_data[:, 2])\n np.testing.assert_array_almost_equal(cd_polar, results[:, 2], decimal=3)\n\n with self.subTest('moment'):\n cm_polar = np.interp(results[:, 0], self.polar_data[:, 0], self.polar_data[:, 4])\n np.testing.assert_array_almost_equal(cm_polar, results[:, 3], decimal=3)\n\n def tearDown(self):\n import shutil\n folders = ['cases', 'output']\n for folder in folders:\n shutil.rmtree(self.route_test_dir + '/' + folder)\n\n\ndef postprocess(output_folder):\n cases = glob.glob(output_folder + '/*')\n\n n_cases = 0\n for case in cases:\n alpha, lift, drag, moment = process_case(case)\n if n_cases == 0:\n results = np.array([alpha, lift, drag, moment], dtype=float)\n else:\n results = np.vstack((results, np.array([alpha, lift, drag, moment])))\n n_cases += 1\n results = results.astype(float)\n results = results[results[:, 0].argsort()]\n return results\n\n\ndef process_case(path_to_case):\n case_name = path_to_case.split('/')[-1]\n pmor = configobj.ConfigObj(path_to_case + f'/{case_name}.pmor.sharpy')\n alpha = pmor['parameters']['alpha']\n\n body_forces = np.loadtxt(f'{path_to_case}/forces/forces_aeroforces.txt',\n skiprows=1, delimiter=',', dtype=float)[7:10]\n body_moments = np.loadtxt(f'{path_to_case}/forces/moments_aeroforces.txt',\n skiprows=1, delimiter=',', dtype=float)[7:10]\n\n return alpha, body_forces[2], body_forces[0], body_moments[1]\n\n\nclass TestStab(unittest.TestCase):\n\n def test_stability(self):\n \"\"\"\n |\n | / free stream\n | /\n |/\n +------------ chord ax (const)\n\n\n \"\"\"\n dir_urel = np.array([1, 0, 0])\n dir_chord = np.array([1, 0, 0])\n\n alpha = 4 * np.pi / 180\n\n # rotate the freestream\n dir_urel = algebra.rotation3d_y(alpha).T.dot(dir_urel)\n\n # Test free stream rotation\n lab = ['x', 'z']\n with self.subTest(msg='Freestream test'):\n assert dir_urel[2] == np.sin(alpha), 'z component of freestream not properly rotated'\n with self.subTest(msg='Freestream test'):\n assert dir_urel[0] == np.cos(alpha), 'x component of freestream not properly rotated'\n\n # Stability axes\n c_bs = local_stability_axes(dir_urel, dir_chord)\n\n # Checking X_s\n for ax in [0, 2]:\n with self.subTest(msg='X_s', ax=ax):\n assert c_bs.dot(np.eye(3)[0])[ax] > 0, f'{ax}_b component of X_s not correct'\n\n # Checking Z_s\n ax = 0\n with self.subTest(msg='Z_s', ax=ax):\n assert c_bs.dot(np.eye(3)[2])[ax] < 0, f'{ax}_b component of Z_s not correct'\n\n ax = 2\n with self.subTest(msg='Z_s', ax=ax):\n assert c_bs.dot(np.eye(3)[2])[ax] > 0, f'{ax}_b component of Z_s not correct'\n\n\nif __name__ == '__main__':\n import unittest\n\n unittest.main()\n" }, { "path": "tests/uvlm/static/polars/xf-naca0018-il-50000.txt", "content": " \n XFOIL Version 6.96\n \n Calculated polar for: NACA 0018 \n \n 1 1 Reynolds number fixed Mach number fixed \n \n xtrf = 1.000 (top) 1.000 (bottom) \n Mach = 0.000 Re = 0.050 e 6 Ncrit = 9.000\n \n alpha CL CD CDp CM Top_Xtr Bot_Xtr\n ------ -------- --------- --------- -------- -------- --------\n -10.500 -0.4876 0.10841 0.09936 -0.0104 1.0000 0.3138\n -10.250 -0.5001 0.10247 0.09342 -0.0123 1.0000 0.3114\n -10.000 -0.5715 0.08947 0.08050 -0.0181 1.0000 0.3040\n -9.750 -0.7409 0.06466 0.05579 -0.0264 1.0000 0.2983\n -9.500 -0.8387 0.05594 0.04699 -0.0198 1.0000 0.2967\n -9.250 -0.8938 0.05095 0.04176 -0.0127 1.0000 0.2995\n -9.000 -0.8627 0.05074 0.04168 -0.0120 1.0000 0.3110\n -8.750 -0.8928 0.04743 0.03815 -0.0060 1.0000 0.3176\n -8.500 -0.8721 0.04673 0.03754 -0.0044 1.0000 0.3286\n -8.250 -0.8918 0.04411 0.03467 0.0010 1.0000 0.3375\n -8.000 -0.8647 0.04386 0.03459 0.0022 1.0000 0.3500\n -7.750 -0.8747 0.04172 0.03228 0.0068 1.0000 0.3604\n -7.500 -0.8589 0.04109 0.03170 0.0091 1.0000 0.3734\n -7.250 -0.8422 0.04046 0.03115 0.0113 1.0000 0.3863\n -7.000 -0.8427 0.03895 0.02952 0.0151 1.0000 0.3991\n -6.750 -0.8313 0.03820 0.02878 0.0178 1.0000 0.4133\n -6.500 -0.8113 0.03791 0.02861 0.0198 1.0000 0.4275\n -6.250 -0.8007 0.03710 0.02781 0.0226 1.0000 0.4419\n -6.000 -0.7947 0.03608 0.02672 0.0257 1.0000 0.4573\n -5.750 -0.7827 0.03548 0.02612 0.0283 1.0000 0.4731\n -5.500 -0.7627 0.03537 0.02614 0.0303 1.0000 0.4885\n -5.250 -0.7478 0.03498 0.02579 0.0327 1.0000 0.5042\n -5.000 -0.7354 0.03446 0.02529 0.0352 1.0000 0.5207\n -4.750 -0.7240 0.03389 0.02472 0.0378 1.0000 0.5378\n -4.500 -0.7125 0.03338 0.02420 0.0402 1.0000 0.5555\n -4.250 -0.6963 0.03323 0.02409 0.0424 1.0000 0.5727\n -4.000 -0.6783 0.03326 0.02421 0.0445 1.0000 0.5894\n -3.750 -0.6624 0.03317 0.02418 0.0467 1.0000 0.6066\n -3.500 -0.6476 0.03305 0.02409 0.0488 1.0000 0.6244\n -3.250 -0.6335 0.03293 0.02400 0.0510 1.0000 0.6426\n -3.000 -0.6196 0.03285 0.02395 0.0532 1.0000 0.6612\n -2.750 -0.6058 0.03281 0.02394 0.0553 1.0000 0.6802\n -2.500 -0.5919 0.03285 0.02401 0.0574 1.0000 0.6995\n -2.250 -0.5780 0.03294 0.02414 0.0595 1.0000 0.7191\n -2.000 -0.5636 0.03313 0.02436 0.0615 1.0000 0.7390\n -1.750 -0.5487 0.03340 0.02466 0.0634 1.0000 0.7591\n -1.500 -0.5311 0.03382 0.02511 0.0649 0.9995 0.7797\n -1.250 -0.4625 0.03554 0.02682 0.0580 0.9838 0.8026\n -1.000 -0.3872 0.03723 0.02847 0.0498 0.9678 0.8246\n -0.750 -0.3016 0.03882 0.03002 0.0397 0.9515 0.8452\n -0.500 -0.2062 0.04015 0.03130 0.0276 0.9348 0.8641\n -0.250 -0.1005 0.04102 0.03213 0.0134 0.9175 0.8820\n 0.000 0.0000 0.04128 0.03238 0.0000 0.8999 0.8999\n 0.250 0.1005 0.04102 0.03213 -0.0134 0.8820 0.9175\n 0.500 0.2061 0.04015 0.03130 -0.0276 0.8641 0.9348\n 0.750 0.3016 0.03882 0.03001 -0.0397 0.8452 0.9515\n 1.000 0.3873 0.03722 0.02847 -0.0498 0.8247 0.9678\n 1.250 0.4625 0.03553 0.02681 -0.0580 0.8026 0.9839\n 1.500 0.5311 0.03381 0.02511 -0.0649 0.7797 0.9996\n 1.750 0.5486 0.03339 0.02466 -0.0634 0.7592 1.0000\n 2.000 0.5635 0.03312 0.02436 -0.0615 0.7390 1.0000\n 2.250 0.5778 0.03294 0.02413 -0.0595 0.7191 1.0000\n 2.500 0.5918 0.03284 0.02400 -0.0574 0.6996 1.0000\n 2.750 0.6056 0.03281 0.02394 -0.0553 0.6802 1.0000\n 3.000 0.6194 0.03285 0.02395 -0.0532 0.6613 1.0000\n 3.250 0.6333 0.03293 0.02400 -0.0510 0.6426 1.0000\n 3.500 0.6475 0.03305 0.02409 -0.0488 0.6244 1.0000\n 3.750 0.6623 0.03316 0.02417 -0.0466 0.6066 1.0000\n 4.000 0.6782 0.03325 0.02420 -0.0445 0.5895 1.0000\n 4.250 0.6962 0.03322 0.02408 -0.0424 0.5728 1.0000\n 4.500 0.7123 0.03338 0.02419 -0.0402 0.5556 1.0000\n 4.750 0.7237 0.03389 0.02472 -0.0377 0.5378 1.0000\n 5.000 0.7352 0.03446 0.02529 -0.0352 0.5207 1.0000\n 5.250 0.7477 0.03498 0.02579 -0.0327 0.5043 1.0000\n 5.500 0.7626 0.03537 0.02613 -0.0303 0.4885 1.0000\n 5.750 0.7827 0.03547 0.02610 -0.0283 0.4732 1.0000\n 6.000 0.7944 0.03608 0.02672 -0.0257 0.4573 1.0000\n 6.250 0.8005 0.03710 0.02780 -0.0225 0.4420 1.0000\n 6.500 0.8111 0.03790 0.02860 -0.0198 0.4276 1.0000\n 6.750 0.8312 0.03819 0.02876 -0.0178 0.4134 1.0000\n 7.000 0.8424 0.03895 0.02952 -0.0151 0.3992 1.0000\n 7.250 0.8421 0.04045 0.03114 -0.0113 0.3863 1.0000\n 7.500 0.8589 0.04107 0.03169 -0.0091 0.3735 1.0000\n 7.750 0.8745 0.04172 0.03228 -0.0068 0.3604 1.0000\n 8.000 0.8647 0.04385 0.03458 -0.0021 0.3500 1.0000\n 8.250 0.8918 0.04410 0.03466 -0.0010 0.3375 1.0000\n 8.500 0.8722 0.04671 0.03752 0.0044 0.3286 1.0000\n 8.750 0.8928 0.04742 0.03814 0.0060 0.3176 1.0000\n 9.000 0.8629 0.05073 0.04166 0.0120 0.3110 1.0000\n 9.250 0.8938 0.05095 0.04175 0.0127 0.2995 1.0000\n 9.500 0.8388 0.05594 0.04699 0.0197 0.2966 1.0000\n 9.750 0.7409 0.06471 0.05583 0.0264 0.2983 1.0000\n 10.000 0.5703 0.08974 0.08077 0.0178 0.3041 1.0000\n 10.250 0.5015 0.10242 0.09337 0.0122 0.3111 1.0000\n 10.500 0.4886 0.10841 0.09937 0.0102 0.3137 1.0000\n" }, { "path": "tests/xbeam/__init__.py", "content": "" }, { "path": "tests/xbeam/geradin/__init__.py", "content": "" }, { "path": "tests/xbeam/geradin/generate_geradin.py", "content": "import h5py as h5\nimport numpy as np\nimport configparser\nimport os\n\ncase_name = 'geradin'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\n\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n\ndef generate_fem_file(route, case_name, num_elem, num_node_elem=3):\n length = 5\n\n num_node = (num_node_elem - 1)*num_elem + 1\n angle = 0*np.pi/180.0\n x = (np.linspace(0, length, num_node))*np.cos(angle)\n y = (np.linspace(0, length, num_node))*np.sin(angle)\n z = np.zeros((num_node,))\n\n structural_twist = np.zeros((num_elem, num_node_elem))\n\n frame_of_reference_delta = np.zeros((num_elem, num_node_elem, 3))\n for ielem in range(num_elem):\n for inode in range(num_node_elem):\n frame_of_reference_delta[ielem, inode, :] = [-np.sin(angle), np.cos(angle), 0]\n\n scale = 1\n\n x *= scale\n y *= scale\n z *= scale\n\n conn = np.zeros((num_elem, num_node_elem), dtype=int)\n for ielem in range(num_elem):\n conn[ielem, :] = (np.ones((3,)) * ielem * (num_node_elem - 1)\n + [0, 2, 1])\n\n # stiffness array\n num_stiffness = 1\n ea = 4.8e8\n ga = 3.231e8\n gj = 1.0e6\n ei = 9.346e6\n base_stiffness = np.diag([ea, ga, ga, gj, ei, ei])\n stiffness = np.zeros((num_stiffness, 6, 6))\n for i in range(num_stiffness):\n stiffness[i, :, :] = base_stiffness\n\n # element stiffness\n elem_stiffness = np.zeros((num_elem,), dtype=int)\n\n # mass array\n num_mass = 1\n m_bar = 0.\n j = 10\n base_mass = np.diag([m_bar, m_bar, m_bar, j, j, j])\n mass = np.zeros((num_mass, 6, 6))\n for i in range(num_mass):\n mass[i, :, :] = base_mass\n # element masses\n elem_mass = np.zeros((num_elem,), dtype=int)\n\n # bocos\n boundary_conditions = np.zeros((num_node, 1), dtype=int)\n boundary_conditions[0] = 1\n boundary_conditions[-1] = -1\n\n # beam number\n beam_number = np.zeros((num_elem, 1), dtype=int)\n\n # new app forces scheme (only follower)\n app_forces = np.zeros((num_node, 6))\n\n # lumped masses input\n n_lumped_mass = 1\n lumped_mass_nodes = np.array([num_node - 1], dtype=int)\n lumped_mass = np.zeros((n_lumped_mass, ))\n lumped_mass[0] = 600e3/9.81\n lumped_mass_inertia = np.zeros((n_lumped_mass, 3, 3))\n lumped_mass_position = np.zeros((n_lumped_mass, 3))\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n coordinates = h5file.create_dataset('coordinates', data = np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data = conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data = num_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data = num_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data = num_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data = stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data = elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data = mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data = elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n lumped_mass_nodes_handle = h5file.create_dataset(\n 'lumped_mass_nodes', data=lumped_mass_nodes)\n lumped_mass_handle = h5file.create_dataset(\n 'lumped_mass', data=lumped_mass)\n lumped_mass_inertia_handle = h5file.create_dataset(\n 'lumped_mass_inertia', data=lumped_mass_inertia)\n lumped_mass_position_handle = h5file.create_dataset(\n 'lumped_mass_position', data=lumped_mass_position)\n return num_node, coordinates\n\n\ndef generate_solver_file():\n file_name = route + '/' + case_name + '.sharpy'\n\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n config['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': ['BeamLoader', 'NonLinearStatic', 'WriteVariablesTime'],\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n\n config['BeamLoader'] = {'unsteady': 'off'}\n config['NonLinearStatic'] = {'print_info': 'off',\n 'max_iterations': 99,\n 'num_load_steps': 10,\n 'delta_curved': 1e-5,\n 'min_delta': 1e-8,\n 'gravity_on': 'on',\n 'gravity': 9.81,\n 'gravity_dir': ['0', '0', '1']}\n config['WriteVariablesTime'] = {'structure_variables': ['pos', 'psi'],\n 'cleanup_old_solution': 'on',}\n config['BeamPlot'] = {'include_rbm': 'off',\n 'include_applied_forces': 'on'}\n\n config.write()\n\n\n# run everything\nclean_test_files()\ngenerate_fem_file(route, case_name, 20)\ngenerate_solver_file()\n" }, { "path": "tests/xbeam/modal/rotating_beam/generate_bielawa_baromega2_1e3.py", "content": "import h5py as h5\nimport numpy as np\nimport configparser\nimport os\nimport sharpy.utils.algebra as algebra\n# Generate errors during execution\nimport sys\nimport sharpy.utils.cout_utils as cout\n\ncase_name = 'bielawa_baromega2_1e3'\nroute = os.path.dirname(os.path.realpath(__file__)) + '/'\n\nnum_elem = 40\nnum_node_elem = 3\n\nlength = 1\n\n# linear_factor: scaling factor to make the non linear solver behave as a linear one\nlinear_factor = 1\nE = 1e6 * linear_factor\nA = 1e4\nI = 1e-4\nei = E * I\nm_bar = 1 * linear_factor\n\nrot_speed = np.sqrt(1e3 * ei / m_bar / length ** 4)\n\nsteps_per_revolution = 180\ndt = 2.0 * np.pi / rot_speed / steps_per_revolution\nn_tstep = 1 * steps_per_revolution + 1\n\nn_tstep = 90\n\n\ndef clean_test_files():\n fem_file_name = route + '/' + case_name + '.fem.h5'\n if os.path.isfile(fem_file_name):\n os.remove(fem_file_name)\n\n dyn_file_name = route + '/' + case_name + '.dyn.h5'\n if os.path.isfile(dyn_file_name):\n os.remove(dyn_file_name)\n\n aero_file_name = route + '/' + case_name + '.aero.h5'\n if os.path.isfile(aero_file_name):\n os.remove(aero_file_name)\n\n solver_file_name = route + '/' + case_name + '.sharpy'\n if os.path.isfile(solver_file_name):\n os.remove(solver_file_name)\n\n\ndef generate_fem_file(route, case_name, num_elem, num_node_elem=3):\n global num_node\n num_node = (num_node_elem - 1) * num_elem + 1\n angle = 0 * np.pi / 180.0\n x = (np.linspace(0, length, num_node)) * np.cos(angle)\n y = (np.linspace(0, length, num_node)) * np.sin(angle)\n z = np.zeros((num_node,))\n\n structural_twist = np.zeros((num_elem, num_node_elem))\n\n frame_of_reference_delta = np.zeros((num_elem, num_node_elem, 3))\n for ielem in range(num_elem):\n for inode in range(num_node_elem):\n frame_of_reference_delta[ielem, inode, :] = [-np.sin(angle), np.cos(angle), 0]\n\n scale = 1\n\n x *= scale\n y *= scale\n z *= scale\n\n conn = np.zeros((num_elem, num_node_elem), dtype=int)\n for ielem in range(num_elem):\n conn[ielem, :] = (np.ones((3,)) * ielem * (num_node_elem - 1)\n + [0, 2, 1])\n\n # stiffness array\n num_stiffness = 1\n\n ea = E * A\n # APPROXIMATION!!!\n cout.cout_wrap(\"Assuming isotropic material\", 2)\n G = E / 2. / (1. + 0.3)\n cout.cout_wrap(\"Using total cross-section area as shear area\", 2)\n ga = G * A\n cout.cout_wrap(\"Assuming planar cross-sections\", 2)\n J = 2. * I\n gj = G * J\n\n base_stiffness = np.diag([ea, ga, ga, gj, ei, ei])\n stiffness = np.zeros((num_stiffness, 6, 6))\n for i in range(num_stiffness):\n stiffness[i, :, :] = base_stiffness\n # element stiffness\n elem_stiffness = np.zeros((num_elem,), dtype=int)\n\n # mass array\n num_mass = 1\n base_mass = m_bar * np.diag([1., 1., 1., J / A, I / A, I / A])\n mass = np.zeros((num_mass, 6, 6))\n for i in range(num_mass):\n mass[i, :, :] = base_mass\n\n # element masses\n elem_mass = np.zeros((num_elem,), dtype=int)\n\n # bocos\n boundary_conditions = np.zeros((num_node, 1), dtype=int)\n boundary_conditions[0] = 1\n boundary_conditions[-1] = -1\n\n # beam number\n beam_number = np.zeros((num_node, 1), dtype=int)\n\n # new app forces scheme (only follower)\n app_forces = np.zeros((num_node, 6))\n\n # lumped masses input\n n_lumped_mass = 1\n lumped_mass_nodes = np.array([num_node - 1], dtype=int)\n lumped_mass = np.zeros((n_lumped_mass,))\n lumped_mass[0] = 0.0\n lumped_mass_inertia = np.zeros((n_lumped_mass, 3, 3))\n lumped_mass_position = np.zeros((n_lumped_mass, 3))\n\n with h5.File(route + '/' + case_name + '.fem.h5', 'a') as h5file:\n\n # CHECKING\n if (elem_stiffness.shape[0] != num_elem):\n sys.exit(\"ERROR: Element stiffness must be defined for each element\")\n if (elem_mass.shape[0] != num_elem):\n sys.exit(\"ERROR: Element mass must be defined for each element\")\n if (frame_of_reference_delta.shape[0] != num_elem):\n sys.exit(\"ERROR: The first dimension of FoR does not match the number of elements\")\n if (frame_of_reference_delta.shape[1] != num_node_elem):\n sys.exit(\"ERROR: The second dimension of FoR does not match the number of nodes element\")\n if (frame_of_reference_delta.shape[2] != 3):\n sys.exit(\"ERROR: The third dimension of FoR must be 3\")\n if (structural_twist.shape[0] != num_node):\n sys.exit(\"ERROR: The structural twist must be defined for each node\")\n if (boundary_conditions.shape[0] != num_node):\n sys.exit(\"ERROR: The boundary conditions must be defined for each node\")\n if (beam_number.shape[0] != num_node):\n sys.exit(\"ERROR: The beam number must be defined for each node\")\n if (app_forces.shape[0] != num_node):\n sys.exit(\"ERROR: The first dimension of the applied forces matrix does not match the number of nodes\")\n if (app_forces.shape[1] != 6):\n sys.exit(\"ERROR: The second dimension of the applied forces matrix must be 6\")\n\n coordinates = h5file.create_dataset('coordinates', data=np.column_stack((x, y, z)))\n conectivities = h5file.create_dataset('connectivities', data=conn)\n num_nodes_elem_handle = h5file.create_dataset(\n 'num_node_elem', data=num_node_elem)\n num_nodes_handle = h5file.create_dataset(\n 'num_node', data=num_node)\n num_elem_handle = h5file.create_dataset(\n 'num_elem', data=num_elem)\n stiffness_db_handle = h5file.create_dataset(\n 'stiffness_db', data=stiffness)\n stiffness_handle = h5file.create_dataset(\n 'elem_stiffness', data=elem_stiffness)\n mass_db_handle = h5file.create_dataset(\n 'mass_db', data=mass)\n mass_handle = h5file.create_dataset(\n 'elem_mass', data=elem_mass)\n frame_of_reference_delta_handle = h5file.create_dataset(\n 'frame_of_reference_delta', data=frame_of_reference_delta)\n structural_twist_handle = h5file.create_dataset(\n 'structural_twist', data=structural_twist)\n bocos_handle = h5file.create_dataset(\n 'boundary_conditions', data=boundary_conditions)\n beam_handle = h5file.create_dataset(\n 'beam_number', data=beam_number)\n app_forces_handle = h5file.create_dataset(\n 'app_forces', data=app_forces)\n lumped_mass_nodes_handle = h5file.create_dataset(\n 'lumped_mass_nodes', data=lumped_mass_nodes)\n lumped_mass_handle = h5file.create_dataset(\n 'lumped_mass', data=lumped_mass)\n lumped_mass_inertia_handle = h5file.create_dataset(\n 'lumped_mass_inertia', data=lumped_mass_inertia)\n lumped_mass_position_handle = h5file.create_dataset(\n 'lumped_mass_position', data=lumped_mass_position)\n return num_node, coordinates\n\n\ndef generate_dyn_file():\n global num_node\n\n forced_for_vel = np.zeros((n_tstep, 6))\n dynamic_forces_time = np.zeros((n_tstep, num_node, 6))\n for it in range(n_tstep):\n forced_for_vel[it, 5] = rot_speed\n\n with h5.File(route + '/' + case_name + '.dyn.h5', 'a') as h5file:\n h5file.create_dataset(\n 'dynamic_forces', data=dynamic_forces_time)\n h5file.create_dataset(\n 'for_vel', data=forced_for_vel)\n h5file.create_dataset(\n 'num_steps', data=n_tstep)\n\n\ndef generate_aero_file():\n global num_node\n with h5.File(route + '/' + case_name + '.aero.h5', 'a') as h5file:\n airfoils_group = h5file.create_group('airfoils')\n # add the airfoils\n airfoils_group.create_dataset(\"0\", data=np.column_stack((np.linspace(0.0, 1.0, 10), np.zeros(10))))\n\n # chord\n chord_input = h5file.create_dataset('chord', data=np.ones((num_elem, num_node_elem), ))\n dim_attr = chord_input.attrs['units'] = 'm'\n\n # twist\n twist_input = h5file.create_dataset('twist', data=np.zeros((num_elem, num_node_elem), ))\n dim_attr = twist_input.attrs['units'] = 'rad'\n\n # airfoil distribution\n airfoil_distribution_input = h5file.create_dataset('airfoil_distribution',\n data=np.zeros((num_elem, num_node_elem), dtype=int))\n\n surface_distribution_input = h5file.create_dataset('surface_distribution',\n data=np.zeros((num_elem,), dtype=int))\n surface_m_input = h5file.create_dataset('surface_m', data=np.ones((1,), dtype=int))\n m_distribution = 'uniform'\n m_distribution_input = h5file.create_dataset('m_distribution', data=m_distribution.encode('ascii', 'ignore'))\n\n aero_node = np.zeros((num_node,), dtype=bool)\n aero_node[-3:] = np.ones((3,), dtype=bool)\n aero_node_input = h5file.create_dataset('aero_node', data=aero_node)\n elastic_axis_input = h5file.create_dataset('elastic_axis', data=0.5 * np.ones((num_elem, num_node_elem), ))\n\n\ndef generate_solver_file():\n file_name = route + '/' + case_name + '.sharpy'\n\n aux_settings = dict()\n settings = dict()\n\n settings['SHARPy'] = {'case': case_name,\n 'route': route,\n 'flow': ['BeamLoader', 'AerogridLoader', 'StaticCoupled', 'BeamPlot', 'AerogridPlot',\n 'DynamicPrescribedCoupled', 'Modal'],\n 'write_screen': 'off',\n 'write_log': 'on',\n 'log_folder': route + '/output/',\n 'log_file': case_name + '.log'}\n\n # AUX DICTIONARIES\n aux_settings['velocity_field_input'] = {'u_inf': 100.0,\n 'u_inf_direction': [0.0, -1.0, 0.0]}\n\n # LOADERS\n settings['BeamLoader'] = {'unsteady': 'on',\n 'orientation': algebra.euler2quat(np.array([0.0, 0.0, 0.0]))}\n\n settings['AerogridLoader'] = {'unsteady': 'on',\n 'aligned_grid': 'on',\n 'mstar': 1,\n 'freestream_dir': ['0', '-1', '0'],\n 'wake_shape_generator': 'StraightWake',\n 'wake_shape_generator_input': {'u_inf': 100,\n 'u_inf_direction': np.array([0., -1., 0.]),\n 'dt': dt}}\n\n # POSTPROCESS\n settings['AerogridPlot'] = {'include_rbm': 'on',\n 'include_forward_motion': 'off',\n 'include_applied_forces': 'on',\n 'minus_m_star': 0,\n 'u_inf': 100.0,\n 'dt': dt}\n\n settings['BeamPlot'] = {'include_rbm': 'on',\n 'include_applied_forces': 'on',\n 'include_forward_motion': 'on'}\n\n settings['BeamLoads'] = {}\n\n # STATIC COUPLED\n\n settings['NonLinearStatic'] = {'print_info': 'on',\n 'max_iterations': 150,\n 'num_load_steps': 1,\n 'delta_curved': 1e-15,\n 'min_delta': 1e-8,\n 'gravity_on': 'off',\n 'gravity': 9.81}\n\n settings['StaticUvlm'] = {'print_info': 'on',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'rollup_dt': dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': aux_settings['velocity_field_input'],\n 'rho': 0.0}\n\n settings['StaticCoupled'] = {'print_info': 'on',\n 'structural_solver': 'NonLinearStatic',\n 'structural_solver_settings': settings['NonLinearStatic'],\n 'aero_solver': 'StaticUvlm',\n 'aero_solver_settings': settings['StaticUvlm'],\n 'max_iter': 100,\n 'n_load_steps': 4,\n 'tolerance': 1e-8,\n 'relaxation_factor': 0}\n\n # DYNAMIC PRESCRIBED COUPLED\n\n settings['NonLinearDynamicPrescribedStep'] = {'print_info': 'on',\n 'max_iterations': 95000,\n 'delta_curved': 1e-9,\n 'min_delta': 1e-6,\n 'newmark_damp': 1e-3,\n 'gravity_on': 'off',\n 'gravity': 9.81,\n 'num_steps': n_tstep,\n 'dt': dt}\n\n settings['StepUvlm'] = {'print_info': 'on',\n 'horseshoe': 'off',\n 'num_cores': 4,\n 'n_rollup': 0,\n 'convection_scheme': 2,\n 'rollup_dt': dt,\n 'rollup_aic_refresh': 1,\n 'rollup_tolerance': 1e-4,\n 'velocity_field_generator': 'SteadyVelocityField',\n 'velocity_field_input': aux_settings['velocity_field_input'],\n 'rho': 0.0,\n 'n_time_steps': n_tstep,\n 'dt': dt}\n\n settings['DynamicPrescribedCoupled'] = {'structural_solver': 'NonLinearDynamicPrescribedStep',\n 'structural_solver_settings': settings['NonLinearDynamicPrescribedStep'],\n 'aero_solver': 'StepUvlm',\n 'aero_solver_settings': settings['StepUvlm'],\n 'fsi_substeps': 20000,\n 'fsi_tolerance': 1e-9,\n 'relaxation_factor': 0,\n 'minimum_steps': 1,\n 'relaxation_steps': 150,\n 'final_relaxation_factor': 0.0,\n 'n_time_steps': n_tstep,\n 'dt': dt,\n 'postprocessors': ['BeamPlot', 'AerogridPlot'],\n 'postprocessors_settings': {'BeamPlot': settings['BeamPlot'],\n 'AerogridPlot': settings['AerogridPlot']}}\n\n settings['Modal'] = {'include_rbm': 'on',\n 'NumLambda': 10000,\n 'num_steps': 1,\n 'print_matrices': 'on'}\n\n import configobj\n config = configobj.ConfigObj()\n config.filename = file_name\n for k, v in settings.items():\n config[k] = v\n config.write()\n\n\n# run everything\nclean_test_files()\ngenerate_fem_file(route, case_name, num_elem, num_node_elem)\ngenerate_aero_file()\ngenerate_dyn_file()\ngenerate_solver_file()\n\ncout.cout_wrap(\n 'Reference for validation: \"Rotary wing structural dynamics and aeroelasticity\", R.L. Bielawa. AIAA education series. Second edition',\n 1)\n" }, { "path": "tests/xbeam/test_xbeam.py", "content": "import numpy as np\nimport importlib\nimport unittest\nimport os\nimport glob\nimport shutil\n\n\nclass TestGeradinXbeam(unittest.TestCase):\n \"\"\"\n Tests the xbeam library for the geradin clamped beam\n Validation values taken from\n Simpson, R.J. and Palacios, R., 2013.\n Numerical aspects of nonlinear flexible aircraft flight dynamics modeling.\n In 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (p. 1634).\n \"\"\"\n\n @classmethod\n def setUpClass(cls):\n # run all the cases generators\n case = 'geradin'\n mod = importlib.import_module('tests.xbeam.' + case + '.generate_' + case)\n\n def test_geradin(self):\n import sharpy.sharpy_main\n # suppress screen output\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) + '/geradin/geradin.sharpy')\n sharpy.sharpy_main.main(['', solver_path])\n\n # read output and compare\n output_path = os.path.dirname(solver_path) + '/output/geradin/WriteVariablesTime/'\n # pos_def\n pos_data = np.atleast_2d(np.genfromtxt(output_path + 'struct_pos_node-1.dat'))\n self.assertAlmostEqual(pos_data[0, 3], -2.159, 2)\n self.assertAlmostEqual(5.0 - pos_data[0, 1], 0.596, 3)\n # psi_def\n psi_data = np.atleast_2d(np.genfromtxt(output_path + 'struct_psi_node-1.dat'))\n self.assertAlmostEqual(psi_data[-1, 2], 0.6720, 3)\n\n def tearDown(self):\n solver_path = os.path.abspath(os.path.dirname(os.path.realpath(__file__)) + '/geradin/')\n files_to_delete = list()\n extensions = ('*.txt', '*.h5', '*.sharpy')\n for f in extensions:\n files_to_delete.extend(glob.glob(solver_path + '/' + f))\n\n for f in files_to_delete:\n try:\n os.remove(f)\n except FileNotFoundError:\n pass\n\n try:\n shutil.rmtree(solver_path + '/output')\n except FileNotFoundError:\n pass\n" }, { "path": "utils/docker/bashrc", "content": "# .bashrc\n\n# User specific aliases and functions\n\nalias rm='rm -i'\nalias cp='cp -i'\nalias mv='mv -i'\n\n# Source global definitions\nif [ -f /etc/bashrc ]; then\n . /etc/bashrc\nfi\n\n# >>> conda initialize >>>\n# !! Contents within this block are managed by 'conda init' !!\n__conda_setup=\"$('/miniconda3/bin/conda' 'shell.bash' 'hook' 2> /dev/null)\"\nif [ $? -eq 0 ]; then\n eval \"$__conda_setup\"\nelse\n if [ -f \"/miniconda3/etc/profile.d/conda.sh\" ]; then\n . \"/miniconda3/etc/profile.d/conda.sh\"\n else\n export PATH=\"/miniconda3/bin:$PATH\"\n fi\nfi\nunset __conda_setup\n# <<< conda initialize <<<\n\nconda activate sharpy\n\n# custom prompt\nPS1=\"SHARPy> \"\n\necho \"=======================================================================\"\necho \"Welcome to the Docker image of SHARPy\"\necho \"SHARPy is located in /sharpy_dir/ and the\"\necho \"environment is already set up!\"\necho \"Copyright Imperial College London. Released under BSD 3-Clause license.\"\necho \"=======================================================================\"\n\n" }, { "path": "utils/environment.yml", "content": "name: sharpy\nchannels:\n - conda-forge\n - defaults\ndependencies:\n - asn1crypto>=1.2.0 \n - colorama>=0.4.1 \n - control>=0.8.4 \n - dill>=0.3.1.1 \n - h5py>=2.9.0 \n - jupyterlab>=1.2.3 \n - lxml>=4.4.1\n - nbsphinx>=0.4.3 \n - pandas>=0.25.3 \n - pyOpenSSL>=19.0.0 \n - PySocks>=1.7.1 \n - PyYAML>=5.1.2\n - recommonmark>=0.6.0\n - scipy>=1.11.4,<1.12\n - slycot>=0.4.0\n - sphinx_rtd_theme>=0.4.3\n - wheel>=0.33.6 \n - xlrd>=1.2.0 \n - python=3.10\n - openpyxl>=3.0.10\n - cmake>=3.19.0\n" } ]