├── .coveragerc ├── .coveragerc_cpu ├── .github ├── ISSUE_TEMPLATE │ └── bug_report.md └── workflows │ ├── paper-pdf.yml │ ├── python-package.yml │ └── python-publish.yml ├── .gitignore ├── .readthedocs.yaml ├── CONTRIBUTING.md ├── LICENSE ├── MANIFEST.in ├── README.md ├── coverage_command.txt ├── docs ├── benchmark.rst ├── conf.py ├── detailed_description.rst ├── example.inc ├── figs │ ├── benchmark_cpu.jpg │ ├── benchmark_gpu.jpg │ ├── benchmark_gpu_setup.jpg │ ├── update_fig.jpg │ └── usage_example.jpg ├── index.rst ├── installation.rst ├── interface.rst └── requirements_docs.txt ├── fimpy ├── __init__.py ├── cupy_kernels.py ├── fim_base.py ├── fim_cupy.py ├── fim_cutils │ ├── __init__.py │ └── fim_cutils.pyx ├── fim_np.py ├── perm_kernel_test.cu ├── solver.py └── utils │ ├── __init__.py │ ├── comp.py │ ├── cython │ ├── __init__.py │ └── comp.pyx │ └── tsitsiklis.py ├── paper.bib ├── paper.md ├── pyproject.toml ├── setup.py └── tests ├── benchmark_data └── .gitignore ├── data └── .gitignore ├── generate_benchmark_data.py ├── generate_doc_figs.py ├── generate_test_data.py ├── run_benchmark.py ├── test_custom_kernels.py ├── test_cython_methods.py └── test_fim_solvers.py /.coveragerc: -------------------------------------------------------------------------------- 1 | # https://coverage.readthedocs.io/en/latest/config.html 2 | # .coveragerc to control coverage.py 3 | [run] 4 | branch = True 5 | #omit = fim_cupy.py 6 | 7 | [report] 8 | # Regexes for lines to exclude from consideration 9 | exclude_lines = 10 | # Have to re-enable the standard pragma 11 | pragma: no cover 12 | 13 | # Don't complain about missing debug-only code: 14 | def __repr__ 15 | if self\.debug 16 | 17 | # Don't complain if tests don't hit defensive assertion code: 18 | #raise AssertionError 19 | #raise NotImplementedError 20 | 21 | # Don't complain if non-runnable code isn't run: 22 | if 0: 23 | if __name__ == .__main__.: 24 | 25 | ignore_errors = True 26 | 27 | [html] 28 | directory = coverage_html 29 | -------------------------------------------------------------------------------- /.coveragerc_cpu: -------------------------------------------------------------------------------- 1 | # https://coverage.readthedocs.io/en/latest/config.html 2 | # .coveragerc to control coverage.py 3 | [run] 4 | branch = True 5 | omit = fimpy/fim_cupy.py 6 | 7 | [report] 8 | # Regexes for lines to exclude from consideration 9 | exclude_lines = 10 | # Have to re-enable the standard pragma 11 | pragma: no cover 12 | 13 | # Don't complain about missing debug-only code: 14 | def __repr__ 15 | if self\.debug 16 | 17 | # Don't complain if tests don't hit defensive assertion code: 18 | #raise AssertionError 19 | #raise NotImplementedError 20 | 21 | # Don't complain if non-runnable code isn't run: 22 | if 0: 23 | if __name__ == .__main__.: 24 | if cupy_enabled: 25 | if not cupy_available: 26 | 27 | ignore_errors = True 28 | 29 | [html] 30 | directory = coverage_html 31 | -------------------------------------------------------------------------------- /.github/ISSUE_TEMPLATE/bug_report.md: -------------------------------------------------------------------------------- 1 | --- 2 | name: Bug report 3 | about: Template for bug reports 4 | title: '' 5 | labels: '' 6 | assignees: '' 7 | 8 | --- 9 | 10 | **Describe the bug** 11 | A clear and concise description of what the bug is. 12 | 13 | **To Reproduce** 14 | Steps to reproduce the unexpected behavior 15 | 16 | **Please provide the following information:** 17 | - Operating system 18 | - Version numbers of 19 | - Python 20 | - Numpy 21 | - Cupy 22 | 23 | See [Contributing.md](https://github.com/thomgrand/fim-python/blob/master/CONTRIBUTING.md) for a script to automatically output the variables 24 | 25 | **Additional information [Optional]** 26 | Add any other information about the problem here. 27 | -------------------------------------------------------------------------------- /.github/workflows/paper-pdf.yml: -------------------------------------------------------------------------------- 1 | #https://github.com/marketplace/actions/open-journals-pdf-generator 2 | on: [push] 3 | 4 | jobs: 5 | paper: 6 | runs-on: ubuntu-latest 7 | name: Paper Draft 8 | steps: 9 | - name: Checkout 10 | uses: actions/checkout@v2 11 | - name: Build draft PDF 12 | uses: openjournals/openjournals-draft-action@master 13 | with: 14 | journal: joss 15 | # This should be the path to the paper within your repo. 16 | paper-path: paper.md 17 | - name: Upload 18 | uses: actions/upload-artifact@v1 19 | with: 20 | name: paper 21 | # This is the output path where Pandoc will write the compiled 22 | # PDF. Note, this should be the same directory as the input 23 | # paper.md 24 | path: paper.pdf 25 | -------------------------------------------------------------------------------- /.github/workflows/python-package.yml: -------------------------------------------------------------------------------- 1 | # This workflow will install Python dependencies, run tests and lint with a variety of Python versions 2 | # For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions 3 | 4 | name: CI Tests (CPU) 5 | 6 | on: 7 | push: 8 | branches: [ master ] 9 | pull_request: 10 | branches: [ master ] 11 | 12 | jobs: 13 | 14 | test_lib_pip_ubuntu: 15 | 16 | runs-on: ubuntu-latest 17 | strategy: 18 | fail-fast: false 19 | matrix: 20 | python-version: [3.7] 21 | 22 | steps: 23 | - uses: actions/checkout@v2 24 | - name: Set up Python ${{ matrix.python-version }} 25 | uses: actions/setup-python@v2 26 | with: 27 | python-version: ${{ matrix.python-version }} 28 | - name: Install with pip 29 | run: | 30 | python -m pip install --upgrade pip 31 | pip install -e .[tests] 32 | python tests/generate_test_data.py 33 | - name: Test with pytest 34 | run: | 35 | python -m pytest --cov-config=.coveragerc_cpu --cov=fimpy tests/ 36 | bash <(curl -s https://codecov.io/bash) -t ${{ secrets.CODECOV_TOKEN }} 37 | 38 | test_lib_pip_windows: 39 | 40 | runs-on: windows-latest 41 | strategy: 42 | fail-fast: false 43 | matrix: 44 | python-version: [3.7] 45 | 46 | steps: 47 | - uses: actions/checkout@v2 48 | - name: Set up Python ${{ matrix.python-version }} 49 | uses: actions/setup-python@v2 50 | with: 51 | python-version: ${{ matrix.python-version }} 52 | - name: Install with pip 53 | run: | 54 | python -m pip install --upgrade pip 55 | pip install -e .[tests] 56 | python tests/generate_test_data.py 57 | - name: Test with pytest 58 | run: | 59 | python -m pytest --cov-config=.coveragerc_cpu --cov=fimpy tests/ 60 | 61 | test_lib_pip_macos: 62 | 63 | runs-on: macos-latest 64 | strategy: 65 | fail-fast: false 66 | matrix: 67 | python-version: [3.7] 68 | 69 | steps: 70 | - uses: actions/checkout@v2 71 | - name: Set up Python ${{ matrix.python-version }} 72 | uses: actions/setup-python@v2 73 | with: 74 | python-version: ${{ matrix.python-version }} 75 | - name: Install with pip 76 | run: | 77 | python -m pip install --upgrade pip 78 | pip install -e .[tests] 79 | python tests/generate_test_data.py 80 | - name: Test with pytest 81 | run: | 82 | python -m pytest --cov-config=.coveragerc_cpu --cov=fimpy tests/ 83 | -------------------------------------------------------------------------------- /.github/workflows/python-publish.yml: -------------------------------------------------------------------------------- 1 | # This workflow will upload a Python Package using Twine when a release is created 2 | # For more information see: https://help.github.com/en/actions/language-and-framework-guides/using-python-with-github-actions#publishing-to-package-registries 3 | 4 | # This workflow uses actions that are not certified by GitHub. 5 | # They are provided by a third-party and are governed by 6 | # separate terms of service, privacy policy, and support 7 | # documentation. 8 | 9 | name: Upload Python Package 10 | 11 | on: 12 | release: 13 | types: [published] 14 | 15 | jobs: 16 | deploy: 17 | 18 | runs-on: ubuntu-latest 19 | 20 | steps: 21 | - uses: actions/checkout@v2 22 | - name: Set up Python 23 | uses: actions/setup-python@v2 24 | with: 25 | python-version: '3.x' 26 | - name: Install dependencies 27 | run: | 28 | python -m pip install --upgrade pip 29 | pip install build 30 | - name: Build package 31 | run: python -m build -s 32 | - name: Publish package 33 | uses: pypa/gh-action-pypi-publish@27b31702a0e7fc50959f5ad993c78deac1bdfc29 34 | with: 35 | user: __token__ 36 | password: ${{ secrets.PYPI_API_TOKEN }} 37 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | #Pip install files 2 | *.egg-info* 3 | *.pyc 4 | *__pycache__* 5 | 6 | #Cython temporaries 7 | *.cpp 8 | *.c 9 | *.cc 10 | *.pyd 11 | 12 | #Documentation build folder 13 | docs/_build/* 14 | docs/build/* 15 | docs/_autosummary* 16 | coverage_html/* 17 | 18 | #General build folders 19 | build/* -------------------------------------------------------------------------------- /.readthedocs.yaml: -------------------------------------------------------------------------------- 1 | # .readthedocs.yaml 2 | # Read the Docs configuration file 3 | # See https://docs.readthedocs.io/en/stable/config-file/v2.html for details 4 | 5 | # Required 6 | version: 2 7 | 8 | # Build documentation in the docs/ directory with Sphinx 9 | sphinx: 10 | configuration: docs/conf.py 11 | 12 | # Optionally build your docs in additional formats such as PDF 13 | #formats: 14 | # - pdf 15 | 16 | # Optionally set the version of Python and requirements required to build your docs 17 | python: 18 | version: 3.7 19 | install: 20 | - requirements: docs/requirements_docs.txt 21 | - method: pip 22 | path: . 23 | extra_requirements: 24 | - docs 25 | -------------------------------------------------------------------------------- /CONTRIBUTING.md: -------------------------------------------------------------------------------- 1 | # Contributing to FIM-Python 2 | 3 | Thank you for your interest in FIM-Python. Any help and contributions are appreciated. 4 | 5 | 6 | Reporting Bugs 7 | --------------------- 8 | 9 | Please submit bug reports to the [issue page](https://github.com/thomgrand/fim-python/issues). Make sure that you include all of the following: 10 | - Description of the bug 11 | - Steps to reconstruct the error 12 | - Operating system 13 | - Version numbers of 14 | - Python 15 | - Numpy 16 | - Cupy 17 | 18 | Fetching the version numbers and the operating system info can be automatically achieved by executing the following script in your python environment: 19 | 20 | ```python 21 | import platform 22 | import os 23 | print("OS Info: %s, %s, v%s" % (os.name, platform.system(), platform.release())) 24 | 25 | import numpy 26 | print("Numpy version: %s" % (numpy.__version__)) 27 | 28 | try: 29 | import cupy 30 | print("GPU version, version of cupy: %s" % (cupy.__version__)) 31 | except ImportError: 32 | print("CPU version only") 33 | ``` 34 | 35 | Submitting Code 36 | -------------------- 37 | FIM-Python uses the [pytest](https://docs.pytest.org) framework. Pip can take care of installing all necessary packages by listing the extra ``tests``: 38 | ```bash 39 | pip install fim-python[gpu,tests] 40 | ``` 41 | The tests can be run by executing 42 | ```bash 43 | python tests/generate_test_data.py #First time only to generate the test examples 44 | python -m pytest tests 45 | ``` 46 | 47 | Before opening a pull request for newly written code, please make sure that all tests are passing. 48 | In case you only have the CPU version, all tests for the GPU will be skipped. 49 | If you submit new features, please also write tests to ensure functionality of these features. 50 | The github-runner will also test pull-requests and committed versions of the library, but only on the CPU for the lack of a GPU on the runner. 51 | 52 | > **_Note:_** If you do **not** have a Cupy compatible GPU to test on, please clearly state this in your pull request, so somebody else from the community can test your code with all features enabled. 53 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU AFFERO GENERAL PUBLIC LICENSE 2 | Version 3, 19 November 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU Affero General Public License is a free, copyleft license for 11 | software and other kinds of works, specifically designed to ensure 12 | cooperation with the community in the case of network server software. 13 | 14 | The licenses for most software and other practical works are designed 15 | to take away your freedom to share and change the works. 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The main focus is however on the GPU implementation, since it can be better exploited for very large domains. 3 | 4 | [![codecov](https://codecov.io/gh/thomgrand/fim-python/branch/master/graph/badge.svg?token=DG05WR5030)](https://codecov.io/gh/thomgrand/fim-python) 5 | [![CI Tests](https://github.com/thomgrand/fim-python/actions/workflows/python-package.yml/badge.svg)](https://github.com/thomgrand/fim-python/actions/workflows/python-package.yml) 6 | [![DOI](https://joss.theoj.org/papers/10.21105/joss.03641/status.svg)](https://doi.org/10.21105/joss.03641) 7 | 8 | # Details 9 | The anisotropic eikonal equation is given by 10 | 11 | ![$$\left = 1$$](https://latex.codecogs.com/svg.latex?\Large&space;\left%3CD%20\nabla%20\phi,%20\nabla%20\phi\right%3E%20=%201) 12 | 13 | 14 | for given boundary conditions 15 | 16 | ![$$\phi(\mathbf{x}_0) = g(\mathbf{x}_0)$$](https://latex.codecogs.com/svg.latex?\Large\phi(\mathbf{x}_0)%20=%20g(\mathbf{x}_0)) 17 | 18 | For a given anisotropic velocity, this can calculate the geodesic distance between a set of ![$\mathbf{x}_0$](https://latex.codecogs.com/svg.latex?\Large\mathbf{x}_0) and all points on the domain like shown in the figure. 19 | 20 | ![Preview Image](docs/figs/usage_example.jpg) 21 | 22 | Note that when using multiple ![$\mathbf{x}_0$](https://latex.codecogs.com/svg.latex?\Large\mathbf{x}_0), they are not guaranteed to be in the final solution if they are not a valid viscosity solution. A recommended read for more details on the subject is: 23 | Evans, Lawrence C. "Partial differential equations." *Graduate studies in mathematics* 19.2 (1998). 24 | 25 | # Installation 26 | 27 | The easiest way to install the library is using pip 28 | ```bash 29 | pip install fim-python[gpu] #GPU version 30 | ``` 31 | 32 | If you don't have a compatible CUDA GPU, you can install the CPU only version to test the library, but the performance won't be comparable to the GPU version (see [Benchmark](#benchmark)). 33 | 34 | ```bash 35 | pip install fim-python #CPU version 36 | ``` 37 | 38 | # Usage 39 | 40 | The main interface to create a solver object to use is [`create_fim_solver`](https://fim-python.readthedocs.io/en/latest/interface.html#fimpy.solver.create_fim_solver) 41 | 42 | ```python 43 | from fimpy.solver import create_fim_solver 44 | 45 | #Create a FIM solver, by default the GPU solver will be called with the active list 46 | #Set device='cpu' to run on cpu and use_active_list=False to use Jacobi method 47 | fim = create_fim_solver(points, elems, D) 48 | ``` 49 | 50 | Example 51 | ------- 52 | 53 | The following code reproduces the [above example](#details) 54 | 55 | ```python 56 | import numpy as np 57 | import cupy as cp 58 | from fimpy.solver import create_fim_solver 59 | from scipy.spatial import Delaunay 60 | import matplotlib.pyplot as plt 61 | 62 | #Create triangulated points in 2D 63 | x = np.linspace(-1, 1, num=50) 64 | X, Y = np.meshgrid(x, x) 65 | points = np.stack([X, Y], axis=-1).reshape([-1, 2]).astype(np.float32) 66 | elems = Delaunay(points).simplices 67 | elem_centers = np.mean(points[elems], axis=1) 68 | 69 | #The domain will have a small spot where movement will be slow 70 | velocity_f = lambda x: (1 / (1 + np.exp(3.5 - 25*np.linalg.norm(x - np.array([[0.33, 0.33]]), axis=-1)**2))) 71 | velocity_p = velocity_f(points) #For plotting 72 | velocity_e = velocity_f(elem_centers) #For computing 73 | D = np.eye(2, dtype=np.float32)[np.newaxis] * velocity_e[..., np.newaxis, np.newaxis] #Isotropic propagation 74 | 75 | x0 = np.array([np.argmin(np.linalg.norm(points, axis=-1), axis=0)]) 76 | x0_vals = np.array([0.]) 77 | 78 | #Create a FIM solver, by default the GPU solver will be called with the active list 79 | fim = create_fim_solver(points, elems, D) 80 | phi = fim.comp_fim(x0, x0_vals) 81 | 82 | #Plot the data of all points to the given x0 at the center of the domain 83 | fig, axes = plt.subplots(nrows=1, ncols=2, sharey=True) 84 | cont_f1 = axes[0].contourf(X, Y, phi.get().reshape(X.shape)) 85 | axes[0].set_title("Distance from center") 86 | 87 | cont_f2 = axes[1].contourf(X, Y, velocity_p.reshape(X.shape)) 88 | axes[1].set_title("Assumed isotropic velocity") 89 | plt.show() 90 | ``` 91 | 92 | A general rule of thumb: If you only need to evaluate the eikonal equation once for a mesh, the Jacobi version (`use_active_list=False`) will probably be quicker since its initial overhead is low. 93 | Repeated evaluations with different ![$\mathbf{x}_0$](https://latex.codecogs.com/svg.latex?\Large\mathbf{x}_0) or ![$D$](https://latex.codecogs.com/svg.latex?\Large%20D) favor the active list method for larger meshes. 94 | On the CPU, `use_active_list=True` outperforms the Jacobi approach for almost all cases. 95 | 96 | # Documentation 97 | 98 | [https://fim-python.readthedocs.io/en/latest](https://fim-python.readthedocs.io/en/latest) 99 | 100 | # Citation 101 | 102 | If you find this work useful in your research, please consider citing the [paper](https://doi.org/10.21105/joss.03641) in the [Journal of Open Source Software](https://joss.theoj.org/) 103 | ```bibtex 104 | @article{grandits_fast_2021, 105 | doi = {10.21105/joss.03641}, 106 | url = {https://doi.org/10.21105/joss.03641}, 107 | year = {2021}, 108 | publisher = {The Open Journal}, 109 | volume = {6}, 110 | number = {66}, 111 | pages = {3641}, 112 | author = {Thomas Grandits}, 113 | title = {A Fast Iterative Method Python package}, 114 | journal = {Journal of Open Source Software} 115 | } 116 | ``` 117 | 118 | # Benchmark 119 | 120 | Below you can see a performance benchmark of the library for tetrahedral domains (cube in ND), triangular surfaces (plane in ND), and line networks (randomly sampled point cloud in the ND cube with successive minimum spanning tree) from left to right. 121 | In all cases, ![$\mathbf{x}_0$](https://latex.codecogs.com/svg.latex?\Large\mathbf{x}_0) was placed in the middle of the domain. 122 | The dashed lines show the performance of the implementation using active lists, the solid lines use the Jacobi method (computing all updates in each iteration). 123 | 124 | ![Preview](docs/figs/benchmark_gpu.jpg) 125 | 126 | ![Preview](docs/figs/benchmark_cpu.jpg) 127 | 128 | The library works for an arbitrary number of dimensions (manifolds in N-D), but the versions for 2 and 3D received a few optimized kernels that speed up the computations. 129 | 130 | The steps to reproduce the benchmarks can be found in the documentation at [https://fim-python.readthedocs.io/en/latest/benchmark.html](https://fim-python.readthedocs.io/en/latest/benchmark.html) 131 | 132 | # Contributing 133 | 134 | See [Contributing](CONTRIBUTING.md) for more information on how to contribute. 135 | 136 | # License 137 | 138 | This library is licensed under the [GNU Affero General Public License](LICENSE). 139 | If you need the library issued under another license for commercial use, you can contact me via e-mail [tomdev (at) gmx.net](mailto:tomdev@gmx.net). 140 | -------------------------------------------------------------------------------- /coverage_command.txt: -------------------------------------------------------------------------------- 1 | python -m pytest --cov-config=.coveragerc --cov=fimpy tests/ --cov-report html:coverage_html 2 | -------------------------------------------------------------------------------- /docs/benchmark.rst: -------------------------------------------------------------------------------- 1 | Benchmark 2 | ============ 3 | 4 | Both the *Jacobi* and *active list* methods have been tested on heterogeneous ND cubes. 5 | Here you can see the comparison of both their run- and setup-time. 6 | The dashed lines show the performance of the implementation using active lists, the solid lines use the Jacobi method (see :doc:`Detailed Description ` for more info). 7 | 8 | Runtime 9 | -------- 10 | 11 | Below you can see a performance benchmark of the library for tetrahedral domains (cube in ND), triangular surfaces (plane in ND), and line networks (randomly sampled point cloud in the ND cube with successive minimum spanning tree) from left to right. 12 | In all cases, :math:`\mathbf{x}_0` was placed in the middle of the domain. 13 | 14 | .. image:: figs/benchmark_gpu.jpg 15 | :alt: Benchmark GPU 16 | :align: center 17 | 18 | .. image:: figs/benchmark_cpu.jpg 19 | :alt: Benchmark CPU 20 | :align: center 21 | 22 | The library works for an arbitrary number of dimensions (manifolds in N-D), but the versions for 2 and 3D received a few optimized kernels that speed up the computations. 23 | 24 | Setup Time 25 | ---------- 26 | 27 | The active list method additionally needs to create a few mesh specific fields before computation to efficiently update the active list. 28 | This makes it best suited for repeated queries of the same mesh with different :math:`D, g, \mathbf{x}_0`. 29 | The figure below shows the setup time for both methods. 30 | 31 | .. image:: figs/benchmark_gpu_setup.jpg 32 | :alt: Setup Time GPU 33 | :align: center 34 | 35 | Run the Benchmark 36 | ------------- 37 | 38 | Before running the benchmark, make sure the library was installed to run the tests and the documentation: 39 | 40 | .. code-block:: bash 41 | 42 | pip install fim-python[gpu,tests,docs] 43 | 44 | The benchmark can then be initiated by first generating the data and then running the actual benchmark 45 | 46 | .. code-block:: bash 47 | 48 | python tests/generate_benchmark_data.py 49 | python tests/run_benchmark.py 50 | 51 | The routine ``generate_benchmark_plot`` in ``tests/generate_docs_figs.py`` can be called to regenerate the documentation figures, including the above benchmark plot 52 | 53 | .. code-block:: bash 54 | 55 | python tests/generate_docs_figs.py 56 | 57 | .. note:: 58 | 59 | The benchmark exhaustively tests the library for many different meshes and can therefore take one hour or more to finish. -------------------------------------------------------------------------------- /docs/conf.py: -------------------------------------------------------------------------------- 1 | # Configuration file for the Sphinx documentation builder. 2 | # 3 | # This file only contains a selection of the most common options. For a full 4 | # list see the documentation: 5 | # https://www.sphinx-doc.org/en/master/usage/configuration.html 6 | 7 | # -- Path setup -------------------------------------------------------------- 8 | 9 | # If extensions (or modules to document with autodoc) are in another directory, 10 | # add these directories to sys.path here. If the directory is relative to the 11 | # documentation root, use os.path.abspath to make it absolute, like shown here. 12 | # 13 | import os 14 | import sys 15 | #sys.path.insert(0, os.path.abspath('../')) #Only for local usage. Incompatible with readthedocs 16 | import fimpy 17 | 18 | 19 | # -- Project information ----------------------------------------------------- 20 | 21 | project = 'FIM Python' 22 | copyright = '2021, Thomas Grandits' 23 | author = 'Thomas Grandits' 24 | 25 | # The full version, including alpha/beta/rc tags 26 | release = fimpy.__version__ 27 | 28 | 29 | # -- General configuration --------------------------------------------------- 30 | 31 | # Add any Sphinx extension module names here, as strings. They can be 32 | # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom 33 | # ones. 34 | extensions = ['sphinx.ext.autodoc', 'sphinx.ext.autosummary', 'sphinx.ext.coverage', 'sphinx.ext.napoleon' 35 | ] 36 | 37 | autosummary_generate = True 38 | 39 | # Add any paths that contain templates here, relative to this directory. 40 | templates_path = ['_templates'] 41 | 42 | # List of patterns, relative to source directory, that match files and 43 | # directories to ignore when looking for source files. 44 | # This pattern also affects html_static_path and html_extra_path. 45 | exclude_patterns = ['_build', 'Thumbs.db', '.DS_Store'] 46 | 47 | 48 | # -- Options for HTML output ------------------------------------------------- 49 | 50 | # The theme to use for HTML and HTML Help pages. See the documentation for 51 | # a list of builtin themes. 52 | # 53 | #html_theme = 'alabaster' 54 | #html_theme = 'sphinx_rtd_theme' 55 | html_theme = 'pydata_sphinx_theme' 56 | 57 | # Add any paths that contain custom static files (such as style sheets) here, 58 | # relative to this directory. They are copied after the builtin static files, 59 | # so a file named "default.css" will overwrite the builtin "default.css". 60 | html_static_path = ['_static'] 61 | 62 | 63 | #https://stackoverflow.com/questions/5599254/how-to-use-sphinxs-autodoc-to-document-a-classs-init-self-method 64 | #def skip(app, what, name, obj, would_skip, options): 65 | # if name == "__init__": 66 | # return False 67 | # return would_skip 68 | # 69 | #def setup(app): 70 | # app.connect("autodoc-skip-member", skip) 71 | -------------------------------------------------------------------------------- /docs/detailed_description.rst: -------------------------------------------------------------------------------- 1 | Detailed Description 2 | ==================== 3 | 4 | The Fast Iterative Method locally computes an update rule, rooted in the Hamilton-Jacobi formalism of the eikonal problem, computing the path the front-wave will take through the current element. 5 | Since the algorithm is restricted to linear Lagrangian :math:`\mathcal{P}^1` elements, the path through an element will also be a line. 6 | To demonstrate the algorithm, consider a tetrahedron spanned by the four corners :math:`\mathbf{v}_1` through :math:`\mathbf{v}_4`. 7 | For the earliest arrival times associated to each corner, we will use the notation :math:`\phi_i = \phi(\mathbf{v}_i)`. 8 | The origin of a linear update from a face spanned by three vertices :math:`\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3` to the fourth :math:`\mathbf{v}_4` is required to be inside said face. 9 | Mathematically this is described by the following set: 10 | 11 | .. math:: 12 | \Delta_k = \left\{ \left( \lambda_1, \ldots, \lambda_k \right)^\top \middle\vert \sum_{i=1}^k \lambda_i = 1 \land \lambda_i \ge 0 \right\} 13 | 14 | The earliest arrival time :math:`\phi_4` can be found by solving the minimization problem which constitutes the local update rule 15 | 16 | .. math:: 17 | \phi_4 = \min_{\lambda_1, \lambda_2} \, \sum_{i=1}^3\lambda_i \phi_i + \sqrt{\mathbf{e}_{\Delta}^\top D^{-1} \mathbf{e}_{\Delta}} \quad \text{s.t.: } \, \left( \lambda_1, \lambda_2, \lambda_3 \right)^\top \in \Delta_3 18 | 19 | for :math:`\lambda_3 = 1 - \lambda_1 - \lambda_2` and :math:`\mathbf{e}_{\Delta} = \mathbf{v}_4 - \sum_{i=1}^3 \lambda_i \mathbf{v}_i`. 20 | The picture below visualizes the update. 21 | 22 | .. image:: figs/update_fig.jpg 23 | :width: 300 24 | :alt: Update inside a single tetrahedron 25 | :align: center 26 | 27 | When updating a tetrahedron, we compute the update of each of the faces to the opposite vertex. 28 | The newly calculated value :math:`\phi_4` will only become the new value if it is strictly smaller than the old value. 29 | 30 | For triangles and lines, the algorithm behaves similarly but the update origin is limited to a side or vertex respectively. 31 | The internally implemented updates in the algorithm to solve the minimization problem are similar to the ones reported in `An inverse Eikonal method for identifying ventricular activation sequences from epicardial activation maps `_. 32 | 33 | 34 | Jacobi vs. Active List Method 35 | ----------------------------- 36 | Two different methods are implemented in the repository: 37 | In the *Jacobi* method, the above local update rule is computed for all elements in each iteration until the change between two subsequent iterations is smaller than ``convergence_eps`` (:math:`10^{-9}` by default). 38 | This version of the algorithm is bested suited for the GPU, since it is optimal for a SIMD (single instruction multiple data) architecture. 39 | 40 | The *active list* method is more closely related to the method presented in the `paper `_: 41 | We keep track of all vertices that will be updated in the current iteration. 42 | Initially, we start off with the neighbor nodes to the initial points :math:`\mathbf{x}_0`. 43 | Once convergence has been reached for a vertex on the active list (according to ``convergence_eps``), its neighboring nodes will be recomputed and if the new value is smaller than the old, they will be added onto the active list. 44 | Convergence is achieved once the active list is empty. 45 | 46 | The active list method computes much fewer updates, but has the additional overhead of keeping track of its active list, ill-suited for the GPU. 47 | For larger meshes, the active list is still a better choice, but comes at the additional cost of a setup time (see :doc:`Benchmark `), making it best suited for repeated queries of the same mesh with different :math:`D, g, \mathbf{x}_0`. 48 | -------------------------------------------------------------------------------- /docs/example.inc: -------------------------------------------------------------------------------- 1 | .. code-block:: python 2 | 3 | import numpy as np 4 | import cupy as cp 5 | from fimpy.solver import FIMPY 6 | from scipy.spatial import Delaunay 7 | import matplotlib.pyplot as plt 8 | 9 | #Create triangulated points in 2D 10 | x = np.linspace(-1, 1, num=50) 11 | X, Y = np.meshgrid(x, x) 12 | points = np.stack([X, Y], axis=-1).reshape([-1, 2]).astype(np.float32) 13 | elems = Delaunay(points).simplices 14 | elem_centers = np.mean(points[elems], axis=1) 15 | 16 | #The domain will have a small spot where movement will be slow 17 | velocity_f = lambda x: (1 / (1 + np.exp(3.5 - 25*np.linalg.norm(x - np.array([[0.33, 0.33]]), axis=-1)**2))) 18 | velocity_p = velocity_f(points) #For plotting 19 | velocity_e = velocity_f(elem_centers) #For computing 20 | D = np.eye(2, dtype=np.float32)[np.newaxis] * velocity_e[..., np.newaxis, np.newaxis] #Isotropic propagation 21 | 22 | x0 = np.array([np.argmin(np.linalg.norm(points, axis=-1), axis=0)]) 23 | x0_vals = np.array([0.]) 24 | 25 | #Create a FIM solver, by default the GPU solver will be called with the active list 26 | #Set device='cpu' to run on cpu and use_active_list=false to use Jacobi method 27 | fim = FIMPY.create_fim_solver(points, elems, D) 28 | phi = fim.comp_fim(x0, x0_vals) 29 | 30 | #Plot the data of all points to the given x0 at the center of the domain 31 | fig, axes = plt.subplots(nrows=1, ncols=2, sharey=True) 32 | cont_f1 = axes[0].contourf(X, Y, phi.get().reshape(X.shape)) 33 | axes[0].set_title("Distance from center") 34 | 35 | cont_f2 = axes[1].contourf(X, Y, velocity_p.reshape(X.shape)) 36 | axes[1].set_title("Assumed isotropic velocity") 37 | plt.show() 38 | -------------------------------------------------------------------------------- /docs/figs/benchmark_cpu.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/thomgrand/fim-python/1840fee9870341c37f43f2fcf45c273ab339f0cd/docs/figs/benchmark_cpu.jpg -------------------------------------------------------------------------------- /docs/figs/benchmark_gpu.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/thomgrand/fim-python/1840fee9870341c37f43f2fcf45c273ab339f0cd/docs/figs/benchmark_gpu.jpg -------------------------------------------------------------------------------- /docs/figs/benchmark_gpu_setup.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/thomgrand/fim-python/1840fee9870341c37f43f2fcf45c273ab339f0cd/docs/figs/benchmark_gpu_setup.jpg -------------------------------------------------------------------------------- /docs/figs/update_fig.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/thomgrand/fim-python/1840fee9870341c37f43f2fcf45c273ab339f0cd/docs/figs/update_fig.jpg -------------------------------------------------------------------------------- /docs/figs/usage_example.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/thomgrand/fim-python/1840fee9870341c37f43f2fcf45c273ab339f0cd/docs/figs/usage_example.jpg -------------------------------------------------------------------------------- /docs/index.rst: -------------------------------------------------------------------------------- 1 | .. FIM Python documentation master file, created by 2 | sphinx-quickstart on Mon May 17 21:13:20 2021. 3 | You can adapt this file completely to your liking, but it should at least 4 | contain the root `toctree` directive. 5 | 6 | FIM-Python documentation 7 | ====================================== 8 | 9 | .. contents:: Quick Start 10 | :depth: 3 11 | 12 | Introduction 13 | ------------ 14 | 15 | This library implements the Fast Iterative method that solves the anisotropic eikonal equation on 16 | `triangulated surfaces `_, 17 | `tetrahedral meshes `_ and line networks 18 | (equivalent to the `Dijkstra's algorithm `_ in this case), 19 | for arbitrary dimensions. 20 | 21 | The anisotropic eikonal equation that is solved, is given by the partial differential equation 22 | 23 | .. math:: 24 | \left\{ 25 | \begin{array}{rll} 26 | \left<\nabla \phi, D \nabla \phi \right> &= 1 \quad &\text{on} \; \Omega \\ 27 | \phi(\mathbf{x}_0) &= g(\mathbf{x}_0) \quad &\text{on} \; \Gamma 28 | \end{array} 29 | \right. . 30 | 31 | The library computes :math:`\phi` for a given :math:`D`, :math:`\mathbf{x}_0` and :math:`g`. 32 | In practice, this problem is often associated to computing the earliest arrival times :math:`\phi` from a set of given starting points :math:`\mathbf{x}_0` through a heterogeneous medium (i.e. different velocities are assigned throughout the medium). 33 | 34 | Usage 35 | --------------------- 36 | The following shorthand notations are important to know: 37 | 38 | - :math:`n`: Number of points 39 | - :math:`m`: Number of elements 40 | - :math:`d`: Dimensionality of the points and metrics (:math:`D \in \mathbb{R}^{d \times d}`) 41 | - :math:`d_e`: Number of vertices per elements (2, 3 and 4 for lines, triangles and tetrahedra respectively) 42 | - :math:`k`: Number of discrete points :math:`\mathbf{x}_0 \in \Gamma` and respective values in :math:`g(\mathbf{x}_0)` 43 | - :math:`M := D^{-1}`: The actual metric used in all computations. This is is computed internally and automatically by the library (no need for you to invert :math:`D`) 44 | - precision: The chosen precision for the solver at the initialization 45 | 46 | This example computes the solution to the anisotropic eikonal equation for a simple square domain 47 | :math:`\Omega = [-1, 1]^2`, with :math:`n = 50^2, d = 2, d_e = 3` and a given isotropic :math:`D`. 48 | This example requires additionally matplotlib and scipy. 49 | 50 | 51 | .. include:: example.inc 52 | 53 | You should see the following figure with the computed :math:`\phi` for the given :math:`D = c I`. 54 | 55 | 56 | .. image:: figs/usage_example.jpg 57 | :alt: Usage example 58 | 59 | .. include:: installation.rst 60 | 61 | 62 | 63 | 64 | 65 | Detailed Contents 66 | -------------- 67 | .. toctree:: 68 | :maxdepth: 2 69 | 70 | interface.rst 71 | detailed_description.rst 72 | benchmark.rst 73 | 74 | 75 | Module API 76 | -------------- 77 | 78 | .. autosummary:: 79 | :toctree: _autosummary 80 | :recursive: 81 | :caption: Module 82 | 83 | fimpy 84 | 85 | 86 | Indices and tables 87 | ------------------ 88 | 89 | * :ref:`genindex` 90 | * :ref:`modindex` 91 | * :ref:`search` 92 | -------------------------------------------------------------------------------- /docs/installation.rst: -------------------------------------------------------------------------------- 1 | Installation 2 | -------------- 3 | 4 | To install, either clone the repository and install it: 5 | 6 | .. code-block:: bash 7 | 8 | git clone https://github.com/thomgrand/fim-python . 9 | pip install -e .[gpu] 10 | 11 | 12 | or simply install the library over `PyPI `_. 13 | 14 | .. code-block:: bash 15 | 16 | pip install fim-python[gpu] 17 | 18 | .. note:: 19 | 20 | Installing the GPU version might take a while since many ``cupy`` modules are compiled using your system's ``nvcc`` compiler. 21 | You can install the ``cupy`` binaries first as mentioned `here `_, before installing ``fimpy``. -------------------------------------------------------------------------------- /docs/interface.rst: -------------------------------------------------------------------------------- 1 | 2 | Interface Methods 3 | ================= 4 | All different solvers can be generated using the interface class. 5 | Note that if you specify the gpu interface, but your system does not support it (or you did not install it), you will only get a cpu solver. 6 | 7 | .. automethod:: fimpy.solver.FIMPY.create_fim_solver 8 | 9 | Computing the anisotropic eikonal equation can be easily achieved by calling :meth:`fimpy.fim_base.FIMBase.comp_fim` on the returned solver. 10 | 11 | .. automethod:: fimpy.fim_base.FIMBase.comp_fim 12 | 13 | .. toctree:: 14 | :maxdepth: 2 15 | :caption: Contents: 16 | -------------------------------------------------------------------------------- /docs/requirements_docs.txt: -------------------------------------------------------------------------------- 1 | numpy 2 | cython 3 | sphinx 4 | pydata_sphinx_theme 5 | -------------------------------------------------------------------------------- /fimpy/__init__.py: -------------------------------------------------------------------------------- 1 | #TODO: Import all symbols and methods here 2 | from .solver import create_fim_solver 3 | 4 | __version__ = "1.2.2" 5 | __author__ = "Thomas Grandits" -------------------------------------------------------------------------------- /fimpy/cupy_kernels.py: -------------------------------------------------------------------------------- 1 | """This file contains some custom CUDA kernels, used in the CUDA implementation of FIMPY 2 | """ 3 | 4 | compute_perm_kernel_str = (r''' 5 | extern "C" __global__ 6 | void perm_kernel(const int* active_elems_perm, const int* active_inds, 7 | bool* perm_mask, 8 | const unsigned int active_elems_size, 9 | const unsigned int active_inds_size) { 10 | const int nr_perms = {active_perms}; 11 | const int bidx = blockIdx.x; 12 | const int block_size = blockDim.x; 13 | const int tidx = block_size * bidx + threadIdx.x; 14 | 15 | for(int offset = tidx; offset < active_elems_size*nr_perms; offset+=block_size*{parallel_blocks}) 16 | { 17 | const int point_i = active_elems_perm[offset]; 18 | bool match = false; 19 | for(int active_i = 0; !match && (active_i < active_inds_size); active_i++) 20 | { 21 | if(active_inds[active_i] == point_i) 22 | { 23 | perm_mask[offset] = true; 24 | match = true; 25 | } 26 | } 27 | } 28 | } 29 | ''') #: CUDA kernel to compute a mask of all element permutations containing at least one active index. Old, less inefficient version not using shared memory. 30 | 31 | compute_perm_kernel_shared = (r''' 32 | extern "C"{ 33 | 34 | //https://en.cppreference.com/w/cpp/algorithm/upper_bound 35 | /** 36 | * @brief Similar to https://en.cppreference.com/w/cpp/algorithm/upper_bound , but also works on 37 | * the CUDA device. Assumes the range to be sorted, but has O(log n) runtime in return. 38 | * 39 | * @param first Beginning of the range where to find the upper bound 40 | * @param last End (exlusive) of the range where to find the upper bound 41 | * @param value The value for which we want to find the upper bound 42 | * @return int* The upper bound location. =End if outside 43 | */ 44 | __device__ int* upper_bound(int* first, int* last, const int& value) 45 | { 46 | int* it; 47 | int count, step; 48 | count = last - first; 49 | 50 | while (count > 0) { 51 | it = first; 52 | step = count / 2; 53 | it += step; 54 | if (value >= *it) { 55 | first = ++it; 56 | count -= step + 1; 57 | } 58 | else 59 | count = step; 60 | } 61 | return first; 62 | } 63 | 64 | __global__ 65 | void perm_kernel(const int* active_elems_perm, const int* active_inds, 66 | bool* perm_mask, 67 | const unsigned int active_elems_size, 68 | const unsigned int active_inds_size) { 69 | const int nr_perms = {active_perms}; 70 | const int bidx = blockIdx.x; 71 | const int block_size = blockDim.x; 72 | const int tidx_global = block_size * bidx + threadIdx.x; 73 | const int tidx_local = threadIdx.x; 74 | __shared__ int active_inds_buf[{shared_buf_size}]; 75 | const int nr_shared_bufs_needed = static_cast(ceil(static_cast(active_inds_size) / {shared_buf_size})); 76 | 77 | for(int shared_buf_run = 0; shared_buf_run < nr_shared_bufs_needed; shared_buf_run++) 78 | { 79 | const int shared_buf_offset = {shared_buf_size} * shared_buf_run; 80 | const int current_active_inds_size = min({shared_buf_size}, active_inds_size - {shared_buf_size}*shared_buf_run); 81 | if(shared_buf_run > 0) 82 | __syncthreads(); 83 | 84 | //Fill shared memory 85 | for(int active_i = tidx_local; active_i < current_active_inds_size; active_i += block_size) 86 | active_inds_buf[active_i] = active_inds[shared_buf_offset + active_i]; 87 | 88 | __syncthreads(); 89 | 90 | for(int elem_offset = tidx_global; elem_offset < active_elems_size*nr_perms; elem_offset+=block_size*{parallel_blocks}) 91 | { 92 | const int point_i = active_elems_perm[elem_offset]; 93 | bool match = perm_mask[elem_offset]; //Maybe already set in the last shared buffer run 94 | if(!match) 95 | { 96 | const int* bound = upper_bound(active_inds_buf, active_inds_buf + current_active_inds_size, point_i); 97 | const int idx = max(0, (int)((bound-1) - active_inds_buf)); 98 | if(active_inds_buf[idx] == point_i) 99 | perm_mask[elem_offset] = true; 100 | } 101 | } 102 | } 103 | } 104 | }''') #: CUDA kernel to compute a mask of all element permutations containing at least one active index. New, more efficient version using shared memory. 105 | -------------------------------------------------------------------------------- /fimpy/fim_base.py: -------------------------------------------------------------------------------- 1 | """This file contains the base implementation of the Fast Iterative Method, common to all solvers. 2 | """ 3 | 4 | from typing import Type 5 | import numpy as np 6 | from itertools import permutations 7 | from abc import abstractmethod 8 | from .utils.tsitsiklis import norm_map 9 | from .fim_cutils import compute_point_elem_map_c, compute_neighborhood_map_c 10 | 11 | class FIMBase(): 12 | """This abstract base class combines common functionality of Cupy and Numpy solvers 13 | 14 | Parameters 15 | ---------- 16 | points : Union[np.ndarray (float), cp.ndarray (float)] 17 | Array of points, :math:`n \\times d` 18 | elems : Union[np.ndarray (int), cp.ndarray (int)] 19 | Array of elements, :math:`m \\times d_e` 20 | metrics : Union[np.ndarray (float), cp.ndarray (float)], optional 21 | Specifies the initial :math:`D \\in \\mathbb{R}^{d \\times d}` tensors. 22 | If not specified, you later need to provide them in :meth:`comp_fim`, by default None 23 | precision : np.dtype, optional 24 | precision of all calculations and the final result, by default np.float32 25 | comp_connectivities : bool, optional 26 | If set to true, both a neighborhood and point to element mapping will be computed. 27 | These are used to efficiently compute the active list. 28 | By default False 29 | """ 30 | 31 | undef_val = 1e10 #: The value for points that have not been computed yet 32 | convergence_eps = 1e-9 #: The value of epsilon to check if a point has converged 33 | 34 | def __init__(self, points, elems, metrics=None, precision=np.float32, comp_connectivities=False): 35 | """ 36 | """ 37 | assert(np.issubdtype(points.dtype, np.floating)) 38 | assert(np.issubdtype(elems.dtype, np.integer)) 39 | 40 | assert(points.ndim == 2) 41 | #assert(points.shape[-1] in [1, 2, 3]) #TODO: Necessary? 42 | assert(elems.ndim == 2) 43 | assert(elems.shape[-1] in [2, 3, 4]) 44 | elems = elems.astype(np.int32) 45 | 46 | self.nr_points = points.shape[0] 47 | self.nr_elems = elems.shape[0] 48 | assert(np.unique(elems).size == self.nr_points) #All points are part of at least one element 49 | assert(np.all(np.unique(elems) == np.arange(self.nr_points))) #All points are part of at least one element 50 | 51 | self.points = points.astype(precision) 52 | self.elems = np.ascontiguousarray(elems) 53 | 54 | 55 | if metrics is not None: 56 | self.check_metrics_argument(metrics) 57 | metrics = np.linalg.inv(metrics).astype(precision) #The inverse metric is used in the FIM algorithm 58 | 59 | self.metrics = metrics 60 | 61 | #General allocations 62 | self.active_list = np.zeros(shape=[self.nr_points], dtype=bool) 63 | self.elems_perm = self.compute_unique_elem_permutations() 64 | self.points_perm = self.points[self.elems_perm] 65 | self.phi_sol = np.ones_like(self.points[..., 0]) * self.undef_val 66 | 67 | self.elem_dims = self.elems.shape[-1] 68 | if comp_connectivities: 69 | self.nh_map = self.compute_neighborhood_map() 70 | self.point_elem_map = self.compute_point_elem_map() 71 | 72 | self.precision = precision 73 | self.dims = self.points.shape[-1] 74 | self.choose_update_alg() 75 | 76 | def choose_update_alg(self): 77 | """Selects the update step of the algorithm according to the provided element type. 78 | 79 | Raises 80 | ------ 81 | TypeError 82 | If self.elem_dims is not in [2, 3, 4] (lines, triangles, tetrahedra) 83 | """ 84 | if self.elem_dims == 2: 85 | self.update_all_points = self.calculate_all_line_updates 86 | self.update_specific_points = self.calculate_specific_line_updates 87 | elif self.elem_dims == 3: 88 | self.update_all_points = self.calculate_all_triang_updates 89 | self.update_specific_points = self.calculate_specific_triang_updates 90 | elif self.elem_dims == 4: 91 | self.update_all_points = self.calculate_all_tetra_updates 92 | self.update_specific_points = self.calculate_specific_tetra_updates 93 | else: 94 | raise TypeError("Unsupported number of points per element: %d. Supported are lines, triangles and tetrahedra (2, 3, 4)" % (self.elem_dims)) 95 | 96 | def check_metrics_argument(self, metrics): 97 | """Checks the validity of the metric tensors (:math:`D \\in \\mathbb{R}^{d \\times d}`) 98 | 99 | Parameters 100 | ---------- 101 | metrics : Union[np.ndarray (float), cp.ndarray (float)], optional 102 | The :math:`D \\in \\mathbb{R}^{d \\times d}` tensors. 103 | """ 104 | assert(np.issubdtype(metrics.dtype, np.floating)) 105 | assert(metrics.shape[0] == self.nr_elems) #One constant metric for each element 106 | assert(metrics.ndim == 3) 107 | assert(metrics.shape[-1] == metrics.shape[-2] and metrics.shape[-1] == self.points.shape[-1]) 108 | assert(np.allclose(metrics - np.transpose(metrics, axes=(0, 2, 1)), 0., atol=1e-4)) #Symmetric 109 | assert(np.all(np.linalg.eigh(metrics)[0] > 1e-4)) #Positive definite 110 | 111 | 112 | def compute_unique_elem_permutations(self): 113 | """Returns all point permutations of each element (i.e. :math:`[M, d_e] \to [M, d_e, d_e]`). 114 | 115 | Returns 116 | ------- 117 | ndarray (int) 118 | An [M, d_e, d_e] array containing all permutations. 119 | """ 120 | if self.elems.shape[1] == 2: #Lines 121 | perms = np.array([[0, 1], [1, 0]]) 122 | elif self.elems.shape[1] == 3: #Triangles 123 | perms = np.array([[0, 1, 2], [0, 2, 1], [1, 2, 0]]) 124 | elif self.elems.shape[1] == 4: #Tetrahedra 125 | perms = np.array([[0, 1, 2, 3], [0, 1, 3, 2], [0, 2, 3, 1], [1, 2, 3, 0]]) 126 | 127 | elems_perm = np.stack([self.elems[np.arange(self.nr_elems)[..., np.newaxis], perm[np.newaxis]] for perm in perms], axis=1) 128 | return elems_perm 129 | 130 | def compute_neighborhood_map(self): 131 | """Computes the neighborhood map for the given mesh. 132 | 133 | Returns 134 | ------- 135 | ndarray (int) 136 | The [N, ?] array holding all neighbors for each point. 137 | shape[1] of the return value will be equal to the maximum neighbor connectivity. 138 | """ 139 | max_point_elem_ratio = np.max(np.unique(self.elems, return_counts=True)[1]) 140 | nh_map = np.zeros(shape=[self.nr_points, max_point_elem_ratio * self.elem_dims], dtype=np.int32) 141 | 142 | nh_map = np.array(compute_neighborhood_map_c(self.elems, nh_map)) 143 | 144 | nh_map = np.sort(nh_map, axis=-1) 145 | 146 | # There may be cases where the ratio was an overestimate 147 | while nh_map.shape[1] > 1 and np.all(nh_map[..., -1] == nh_map[..., -2]): 148 | nh_map = nh_map[..., :-1] 149 | 150 | return nh_map 151 | 152 | def compute_point_elem_map(self): 153 | """Computes the point element mapping for each point. 154 | 155 | Returns 156 | ------- 157 | ndarray (int) 158 | The [N, ?] array holding for each point all elements that it is contained in. 159 | shape[1] of the return value will be equal to the maximum point to element ratio. 160 | """ 161 | max_point_elem_ratio = np.max(np.unique(self.elems, return_counts=True)[1]) 162 | point_elem_map = np.zeros(shape=[self.nr_points, max_point_elem_ratio], dtype=np.int32) 163 | point_elem_map = np.sort(compute_point_elem_map_c(self.elems, point_elem_map), axis=-1) 164 | return point_elem_map 165 | 166 | def tsitsiklis_update_line(self, x1, x2, D, u1, lib=np): 167 | """Computes :math:`||\\mathbf{x}_2 - \\mathbf{x}_1||_M` in a broadcasted way. 168 | 169 | Parameters 170 | ---------- 171 | x1 : ndarray (precision) 172 | An [..., N, d] array holding :math:`\\mathbf{x}_1` 173 | x2 : ndarray (precision) 174 | An [..., N, d] array holding :math:`\\mathbf{x}_2` 175 | D : ndarray (precision) 176 | An [..., N, d, d] array holding :math:`D` 177 | u1 : ndarray (precision) 178 | An [..., N] array holding :math:`u_1` 179 | lib : Union([np, cp]), optional 180 | Module that will be used to compute the norm, by default np 181 | 182 | Returns 183 | ------- 184 | ndarray (precision) 185 | An [..., N] array that holds :math:`||\\mathbf{x}_2 - \\mathbf{x}_1||_M` 186 | """ 187 | norm_f = norm_map[lib][D.shape[-1]][0] 188 | a1 = x2 - x1 189 | return u1 + norm_f(D, a1, a1) 190 | 191 | def tsitsiklis_update_point_sol(self, x1, x2, x3, D, u1, u2, lib=np): 192 | """Computes 193 | 194 | .. math:: 195 | \\min\\{u_1 + ||\\mathbf{x}_3 - \\mathbf{x}_1||_M, u_2 + ||\\mathbf{x}_3 - \\mathbf{x}_2||_M\\} 196 | 197 | in a broadcasted way. 198 | For more information on the type and shape of the parameters and return value, see :meth:`tsitsiklis_update_line`. 199 | """ 200 | norm_f = norm_map[lib][D.shape[-1]][0] 201 | 202 | a1 = x3 - x1 203 | a2 = x3 - x2 204 | u3_1 = u1 + norm_f(D, a1, a1) 205 | u3_2 = u2 + norm_f(D, a2, a2) 206 | 207 | return lib.minimum(u3_1, u3_2) 208 | 209 | def tsitsiklis_update_triang(self, x1, x2, x3, D, u1, u2, lib=np): 210 | """Computes the update inside a single triangle as 211 | 212 | .. math:: 213 | \\min_{\\lambda} \\lambda u_1 + (1 - \\lambda) u_2 + ||\\mathbf{x}_3 - (\\lambda \\mathbf{x}_1 + (1 - \\lambda) \\mathbf{x}_2)||_M 214 | 215 | For more information on the type and shape of the parameters and return value, see :meth:`tsitsiklis_update_line`. 216 | """ 217 | k = u1 - u2 218 | z2 = x2 - x3 219 | z1 = x1 - x2 220 | 221 | norm_f, norm_sqr_f = norm_map[lib][D.shape[-1]] 222 | 223 | p11 = norm_sqr_f(D, x1=z1, x2=z1) 224 | p12 = norm_sqr_f(D, x1=z1, x2=z2) 225 | p22 = norm_sqr_f(D, x1=z2, x2=z2) 226 | denominator = p11 - k**2 227 | sqrt_val = (p11 * p22 - p12**2) / denominator 228 | sqrt_invalid_mask = sqrt_val < 0. 229 | sqrt_op = lib.sqrt(sqrt_val) 230 | rhs = k * sqrt_op 231 | alpha1 = -(p12 + rhs) / p11 232 | alpha2 = -(p12 - rhs) / p11 233 | alpha1 = lib.minimum(lib.maximum(alpha1, 0.), 1.) 234 | alpha2 = lib.minimum(lib.maximum(alpha2, 0.), 1.) 235 | 236 | u3 = [] 237 | for alpha in [alpha1, alpha2]: 238 | x = x3 - (alpha[..., lib.newaxis] * x1 + (1 - alpha[..., lib.newaxis]) * x2) 239 | u3.append(alpha * u1 + (1 - alpha) * u2 240 | + norm_f(D, x, x)) 241 | 242 | u3 = lib.minimum(*u3) 243 | u3_point = self.tsitsiklis_update_point_sol(x1, x2, x3, D, u1, u2, lib=lib) 244 | u3_computed = lib.where(sqrt_invalid_mask, u3_point, u3) 245 | u3_final = u3_computed 246 | 247 | return u3_final 248 | 249 | def tsitsiklis_update_tetra_quadr(self, D, k, z1, z2, lib=np): 250 | """Computes the quadratic equation for the tetrahedra update in :meth:`calculate_tet_update`. 251 | """ 252 | norm_f, norm_sqr_f = norm_map[lib][D.shape[-1]] 253 | p11 = norm_sqr_f(D, z1, z1) 254 | p12 = norm_sqr_f(D, z1, z2) 255 | p22 = norm_sqr_f(D, z2, z2) 256 | denominator = p11 - k*k 257 | sqrt_val = (p11 * p22 - (p12 * p12)) / denominator 258 | rhs = k * lib.sqrt(sqrt_val) 259 | alpha1 = -(p12 + rhs) / p11 260 | #alpha2 = -(p12 - rhs) / p11 261 | 262 | return alpha1 #, alpha2 263 | 264 | def tsitsiklis_update_tetra(self, x1, x2, x3, x4, D, u1, u2, u3, lib=np): 265 | """Computes the update inside a single tetrahedron by computing 266 | 267 | - the update inside the tetrahedron (:meth:`calculate_tet_update`) 268 | - the update on each face (:meth:`tsitsiklis_update_triang`) 269 | 270 | and taking the minimum across all possible values. 271 | For more information on the type and shape of the parameters and return value, see :meth:`tsitsiklis_update_line`. 272 | """ 273 | u_tet = self.calculate_tet_update(x1, x2, x3, x4, D, u1, u2, u3, lib) 274 | u_tet = lib.where(lib.isnan(u_tet), lib.inf, u_tet) 275 | 276 | #Face calculations (Includes possible line calculations) 277 | u_triang = lib.minimum(self.tsitsiklis_update_triang(x1, x2, x4, D, u1, u2, lib), 278 | self.tsitsiklis_update_triang(x1, x3, x4, D, u1, u3, lib)) 279 | u_triang = lib.minimum(u_triang, 280 | self.tsitsiklis_update_triang(x2, x3, x4, D, u2, u3, lib)) 281 | 282 | return lib.minimum(u_triang, u_tet) 283 | 284 | def calculate_tet_update(self, x1, x2, x3, x4, D, u1, u2, u3, lib=np): 285 | """Computes the update inside a single tetrahedron as 286 | 287 | .. math:: 288 | \\min_{\\lambda_1, \\lambda_2} \\lambda_1 u_1 + \\lambda_2 u_2 + \\lambda_3 u_3 + ||\\mathbf{x}_4 - \\mathbf{x}_{1, 2, 3}||_M 289 | 290 | for :math:`\\lambda_3 = 1 - \\lambda_1 - \\lambda_2` and :math:`\\mathbf{x}_{1, 2, 3} = \\lambda_1 \\mathbf{x}_1 + \\lambda_2 \\mathbf{x}_2 + \\lambda_3 \\mathbf{x}_3`. 291 | For more information on the type and shape of the parameters and return value, see :meth:`tsitsiklis_update_line`. 292 | """ 293 | xs = lib.stack([x1, x2, x3, x4], axis=-1) 294 | us = lib.stack([u1, u2, u3], axis=-1) 295 | norm_f, norm_sqr_f = norm_map[lib][D.shape[-1]] 296 | 297 | y3 = x4 - x3 298 | y1 = x3 - x1 299 | y2 = x3 - x2 300 | 301 | k1 = u1 - u3 302 | k2 = u2 - u3 303 | #k3 = u3 304 | 305 | r11 = norm_sqr_f(D, y1, y1) 306 | r12 = norm_sqr_f(D, y1, y2) 307 | r13 = norm_sqr_f(D, y1, y3) 308 | r21 = r12 309 | r22 = norm_sqr_f(D, y2, y2) 310 | r23 = norm_sqr_f(D, y2, y3) 311 | r31 = r13 312 | r32 = r23 313 | #r33 = norm_sqr_f(D, y3, y3) 314 | 315 | A1 = k2 * r11 - k1 * r12 316 | A2 = k2 * r21 - k1 * r22 317 | B = k2 * r31 - k1 * r32 318 | k = k1 - A1 / A2 * k2 319 | #u = k3 - B / A2 * k2 320 | z1 = y1 - (A1 /A2)[..., lib.newaxis] * y2 321 | z2 = y3 - (B / A2)[..., lib.newaxis] * y2 322 | 323 | alpha1 = self.tsitsiklis_update_tetra_quadr(D, k, z1, z2, lib) 324 | alpha2 = -(B + alpha1 * A1) / A2 325 | 326 | special_case1 = ((A1 == 0) & (A2 == 0)) 327 | alpha1 = lib.where(special_case1, (r12 * r23 - r13 * r22) / (r11 * r22 - (r12 * r12)), alpha1) 328 | alpha2 = lib.where(special_case1, (r12 * r13 - r11 * r23) / (r11 * r22 - (r12 * r12)), alpha2) 329 | 330 | special_case2 = ((A1 == 0) & ~special_case1) 331 | alpha1 = lib.where(special_case2, 0, alpha1) 332 | alpha2 = lib.where(special_case2, -B / A2, alpha2) 333 | 334 | special_case3 = ((A2 == 0) & ~special_case1 & ~special_case2) 335 | alpha1 = lib.where(special_case3, -B / A1, alpha1) 336 | alpha2 = lib.where(special_case3, 0, alpha2) 337 | 338 | alphas = lib.stack([alpha1, alpha2, 1 - alpha1 - alpha2], axis=-1) 339 | if alphas.ndim == xs.ndim - 1: 340 | alphas = alphas[..., lib.newaxis, :] 341 | 342 | dist = x4 - lib.sum(xs[..., :-1] * alphas, axis=-1) #dist = x4 - (alpha1 * x1 + alpha2 * x2 + alpha3 * x3) 343 | alphas = lib.squeeze(alphas) 344 | return lib.where(lib.any((alphas < 0) | (alphas > 1), axis=-1), lib.inf, norm_f(D, dist, dist) + lib.sum(alphas * us, axis=-1)) #(alpha1 * u1 + alpha2 * u2 + alpha3 * u3) 345 | 346 | 347 | 348 | def calculate_specific_triang_updates(self, elems_perm, xs_perm, D, us, lib=np): 349 | us_new = us.copy() 350 | 351 | #perms = np.array([[0, 1, 2], [0, 2, 1], [1, 2, 0]]) 352 | us_perm = us[elems_perm] 353 | 354 | us_result = self.tsitsiklis_update_triang(xs_perm[..., 0, :], xs_perm[..., 1, :], xs_perm[..., 2, :], 355 | D, us_perm[..., 0], us_perm[..., 1], lib=lib) 356 | 357 | #Now we need to take the minimum result of old and all new 358 | lib.minimum.at(us_new, elems_perm[..., -1], us_result) 359 | 360 | return us_new 361 | 362 | def calculate_specific_line_updates(self, elems_perm, xs_perm, D, us, lib=np): 363 | us_new = us.copy() 364 | us_perm = us[elems_perm] 365 | us_result = self.tsitsiklis_update_line(xs_perm[..., 0, :], xs_perm[..., 1, :], 366 | D, us_perm[..., 0], lib=lib) 367 | lib.minimum.at(us_new, elems_perm[..., -1], us_result) 368 | 369 | return us_new 370 | 371 | def calculate_all_line_updates(self, elems_perm, xs_perm, D, us, lib=np): 372 | """Calculates all lines updates for all element permutations and computes their minimum as the new solution of :math:`\\phi`. 373 | 374 | Parameters 375 | ---------- 376 | elems_perm : ndarray (int) 377 | All point permutations obtained using :meth:`compute_unique_elem_permutations` 378 | xs_perm : ndarray (float) 379 | All point coordinate permutations as an :math:`[M, d_e, d_e, d]` array. 380 | D : ndarray (float) 381 | An [M, d, d] array containing :math:`D`. 382 | us : ndarray (float) 383 | An [N] array containing the current solution of :math:`\\phi_k`. 384 | lib : library, optional 385 | Library to use for the computations, by default np 386 | 387 | Returns 388 | ------- 389 | ndarray (float) 390 | An [N] array holding the new solution :math:`\\phi_{k+1}`. 391 | """ 392 | us_new = us.copy() 393 | us_perm = us[elems_perm] 394 | D_broadcasted = D[..., lib.newaxis, :, :] #Add permutation dimension 395 | 396 | us_result = self.tsitsiklis_update_line(xs_perm[..., 0, :], xs_perm[..., 1, :], 397 | D_broadcasted, us_perm[..., 0], lib=lib) 398 | lib.minimum.at(us_new, elems_perm[..., -1], us_result) 399 | 400 | return us_new 401 | 402 | def calculate_all_triang_updates(self, elems_perm, xs_perm, D, us, lib=np): 403 | """Calculates all triangle updates for all element permutations and computes their minimum as the new solution of :math:`\\phi`. 404 | For more details on the parameters and return values, see :meth:`calculate_all_line_updates`. 405 | """ 406 | us_new = us.copy() 407 | 408 | us_perm = us[elems_perm] 409 | D_broadcasted = D[..., lib.newaxis, :, :] #Add permutation dimension 410 | 411 | us_result = self.tsitsiklis_update_triang(xs_perm[..., 0, :], xs_perm[..., 1, :], xs_perm[..., 2, :], 412 | D_broadcasted, us_perm[..., 0], us_perm[..., 1], lib=lib) 413 | 414 | #Now we need to take the minimum result of old and all new 415 | lib.minimum.at(us_new, elems_perm[..., -1], us_result) 416 | 417 | return us_new 418 | 419 | def calculate_all_tetra_updates(self, elems_perm, xs_perm, D, us, lib=np): 420 | """Calculates all tetrahedral updates for all element permutations and computes their minimum as the new solution of :math:`\\phi`. 421 | For more details on the parameters and return values, see :meth:`calculate_all_line_updates`. 422 | """ 423 | us_new = us.copy() 424 | us_perm = us[elems_perm] 425 | D_broadcasted = D[..., lib.newaxis, :, :] #Add permutation dimension 426 | 427 | us_result = self.tsitsiklis_update_tetra(xs_perm[..., 0, :], xs_perm[..., 1, :], xs_perm[..., 2, :], xs_perm[..., 3, :], 428 | D_broadcasted, us_perm[..., 0], us_perm[..., 1], us_perm[..., 2], lib=lib) 429 | lib.minimum.at(us_new, elems_perm[..., -1], us_result) 430 | 431 | return us_new 432 | 433 | def calculate_specific_tetra_updates(self, elems_perm, xs_perm, D, us, lib=np): 434 | us_new = us.copy() 435 | us_perm = us[elems_perm] 436 | us_result = self.tsitsiklis_update_tetra(xs_perm[..., 0, :], xs_perm[..., 1, :], xs_perm[..., 2, :], xs_perm[..., 3, :], 437 | D, us_perm[..., 0], us_perm[..., 1], us_perm[..., 2], lib=lib) 438 | lib.minimum.at(us_new, elems_perm[..., -1], us_result) 439 | 440 | return us_new 441 | 442 | 443 | @abstractmethod 444 | def _comp_fim(self, x0, x0_vals, metrics=None, max_iterations=int(1e10)): 445 | """Internal call to the concrete implementation of the FIM (see :meth:`comp_fim` for the parameter description). 446 | """ 447 | ... # pragma: no cover 448 | 449 | def comp_fim(self, x0, x0_vals, metrics=None, max_iterations=int(1e10)): 450 | """Computes the solution :math:`\\phi` to the anisotropic eikonal equation 451 | 452 | .. math:: 453 | \\left\\{ 454 | \\begin{array}{rll} 455 | \\left<\\nabla \\phi, D \\nabla \\phi \\right> &= 1 \\quad &\\text{on} \\; \\Omega \\\\ 456 | \\phi(\\mathbf{x}_0) &= g(\\mathbf{x}_0) \\quad &\\text{on} \\; \\Gamma 457 | \\end{array} 458 | \\right. . 459 | 460 | Parameters 461 | ---------- 462 | x0 : ndarray (int) 463 | Array of [k] discrete point indices of the mesh where we prescribe initial values :math:`\\mathbf{x}_0`. 464 | x0_vals : ndarray (float) 465 | Array of [k] discrete prescribed initial values that prescribe :math:`g(\\mathbf{x}_0)`. 466 | metrics : np.ndarray(float), optional 467 | Specifies the tensor :math:`D` of the anisotropic eikonal equation as a discrete [m, d, d] array. 468 | This is optional **only** if you specified the metrics already at construction time (:class:`FIMBase`), by default None 469 | max_iterations : int, optional 470 | Maximum number of iterations before aborting the algorithm. 471 | If the algorithm stops before reaching convergence, some vertices might still be set to :attr:`undef_val`. 472 | By default int(1e10) 473 | 474 | Returns 475 | ------- 476 | ndarray (float, cupy or numpy) 477 | The solution to the anisotropic eikonal equation, :math:`\\phi` as a [n] array. 478 | """ 479 | #Suppress warnings of the computations, since they should be handled internally 480 | with np.errstate(divide='ignore', invalid='ignore', over='ignore'): 481 | #TODO: Maybe use identity in this case? 482 | assert metrics is not None or self.metrics is not None, f"Metrics (D) need to be provided in comp_fim, or at construction in __init__" 483 | if metrics is not None: 484 | self.check_metrics_argument(metrics) 485 | metrics = np.linalg.inv(metrics).astype(self.precision) #The inverse metric is used in the FIM algorithm 486 | 487 | return self._comp_fim(x0, x0_vals, metrics, max_iterations=max_iterations) 488 | -------------------------------------------------------------------------------- /fimpy/fim_cupy.py: -------------------------------------------------------------------------------- 1 | """This file contains the GPU implementation of the Fast Iterative Method, based on cupy. 2 | """ 3 | 4 | import numpy as np 5 | 6 | #Workaround for readthedocs 7 | try: 8 | import cupy as cp 9 | import cupyx as cpx 10 | from .utils.comp import metric_norm_matrix_2D_cupy, metric_norm_matrix_3D_cupy, metric_norm_matrix, metric_sqr_norm_matrix_2D_cupy, metric_sqr_norm_matrix_3D_cupy, metric_sqr_norm_matrix 11 | cupy_enabled = True 12 | except ImportError as err: 13 | cupy_enabled = False 14 | 15 | from .fim_base import FIMBase 16 | from .cupy_kernels import compute_perm_kernel_str, compute_perm_kernel_shared 17 | 18 | if cupy_enabled: 19 | @cp.fuse() 20 | def u3_comp_cupy_2D(x1, x2, x3, u1, u2, D): 21 | """Custom cupy implementation of :meth:`fimpy.fim_base.FIMBase.tsitsiklis_update_triang` to speed up computations for :math:`d = 2`. 22 | """ 23 | k = u1 - u2 24 | z2 = x2 - x3 25 | z1 = x1 - x2 26 | p11 = metric_sqr_norm_matrix_2D_cupy(D, z1, z1) 27 | p12 = metric_sqr_norm_matrix_2D_cupy(D, z1, z2) 28 | p22 = metric_sqr_norm_matrix_2D_cupy(D, z2, z2) 29 | denominator = p11 - k**2 30 | sqrt_val = (p11 * p22 - p12**2) / denominator 31 | sqrt_invalid_mask = sqrt_val < 0. 32 | sqrt_op = cp.sqrt(sqrt_val) 33 | rhs = k * sqrt_op 34 | alpha1 = -(p12 + rhs) / p11 35 | alpha2 = -(p12 - rhs) / p11 36 | alpha1 = cp.minimum(cp.maximum(alpha1, 0.), 1.) 37 | alpha2 = cp.minimum(cp.maximum(alpha2, 0.), 1.) 38 | 39 | u3 = [] 40 | for alpha in [alpha1, alpha2]: 41 | x = x3 - (alpha[..., cp.newaxis] * x1 + (1 - alpha[..., cp.newaxis]) * x2) 42 | u3.append(alpha * u1 + (1 - alpha) * u2 43 | + metric_norm_matrix_2D_cupy(D, x, x)) 44 | 45 | return cp.minimum(*u3), sqrt_invalid_mask 46 | 47 | #@cp.fuse() 48 | def u3_comp_cupy_3D(x1, x2, x3, u1, u2, D): 49 | """Custom cupy implementation of :meth:`fimpy.fim_base.FIMBase.tsitsiklis_update_triang` to speed up computations for :math:`d = 3`. 50 | """ 51 | k = u1 - u2 52 | z2 = x2 - x3 53 | z1 = x1 - x2 54 | p11 = metric_sqr_norm_matrix_3D_cupy(D, z1, z1) 55 | p12 = metric_sqr_norm_matrix_3D_cupy(D, z1, z2) 56 | p22 = metric_sqr_norm_matrix_3D_cupy(D, z2, z2) 57 | denominator = p11 - k**2 58 | sqrt_val = (p11 * p22 - p12**2) / denominator 59 | sqrt_invalid_mask = sqrt_val < 0. 60 | sqrt_op = cp.sqrt(sqrt_val) 61 | rhs = k * sqrt_op 62 | alpha1 = -(p12 + rhs) / p11 63 | alpha2 = -(p12 - rhs) / p11 64 | alpha1 = cp.minimum(cp.maximum(alpha1, 0.), 1.) 65 | alpha2 = cp.minimum(cp.maximum(alpha2, 0.), 1.) 66 | 67 | u3 = [] 68 | for alpha in [alpha1, alpha2]: 69 | x = x3 - (alpha[..., cp.newaxis] * x1 + (1 - alpha[..., cp.newaxis]) * x2) 70 | u3.append(alpha * u1 + (1 - alpha) * u2 71 | + metric_norm_matrix_3D_cupy(D, x, x)) 72 | 73 | return cp.minimum(*u3), sqrt_invalid_mask 74 | 75 | 76 | #@cp.fuse() #TODO: formal parameter space overflow 77 | def u3_comp_cupy_ND(x1, x2, x3, u1, u2, D): 78 | """Custom cupy implementation of :meth:`fimpy.fim_base.FIMBase.tsitsiklis_update_triang` to speed up computations for :math:`d \notin \{2, 3\}`. 79 | """ 80 | #p11, p12, sqrt_invalid_mask, rhs = u3_comp_cupy_ND_part1(x1, x2, x3, u1, u2, D) 81 | #return u3_comp_cupy_ND_part2(p11, p12, rhs, x1, x2, x3, u1, u2, D), sqrt_invalid_mask 82 | k = u1 - u2 83 | z2 = x2 - x3 84 | z1 = x1 - x2 85 | p11 = metric_sqr_norm_matrix(D, z1, z1, cp) 86 | p12 = metric_sqr_norm_matrix(D, z1, z2, cp) 87 | p22 = metric_sqr_norm_matrix(D, z2, z2, cp) 88 | denominator = p11 - k**2 89 | sqrt_val = (p11 * p22 - p12**2) / denominator 90 | sqrt_invalid_mask = sqrt_val < 0. 91 | sqrt_op = cp.sqrt(sqrt_val) 92 | rhs = k * sqrt_op 93 | alpha1 = -(p12 + rhs) / p11 94 | alpha2 = -(p12 - rhs) / p11 95 | alpha1 = cp.minimum(cp.maximum(alpha1, 0.), 1.) 96 | alpha2 = cp.minimum(cp.maximum(alpha2, 0.), 1.) 97 | 98 | u3 = [] 99 | for alpha in [alpha1, alpha2]: 100 | x = x3 - (alpha[..., cp.newaxis] * x1 + (1 - alpha[..., cp.newaxis]) * x2) 101 | u3.append(alpha * u1 + (1 - alpha) * u2 102 | + metric_norm_matrix(D, x, x, cp)) 103 | 104 | return cp.minimum(*u3), sqrt_invalid_mask 105 | 106 | @cp.fuse() 107 | def tsitsiklis_update_tetra_quadr_cupy_3D(D, k, z1, z2): 108 | """Custom cupy implementation of :meth:`fimpy.fim_base.FIMBase.tsitsiklis_update_tetra_quadr` to speed up computations for :math:`d = 3`. 109 | """ 110 | norm_sqr_f = metric_sqr_norm_matrix_3D_cupy 111 | p11 = norm_sqr_f(D, z1, z1) 112 | p12 = norm_sqr_f(D, z1, z2) 113 | p22 = norm_sqr_f(D, z2, z2) 114 | denominator = p11 - k*k 115 | sqrt_val = (p11 * p22 - (p12 * p12)) / denominator 116 | rhs = k * cp.sqrt(sqrt_val) 117 | alpha1 = -(p12 + rhs) / p11 118 | #alpha2 = -(p12 - rhs) / p11 119 | 120 | return alpha1 #, alpha2 121 | 122 | class FIMCupy(FIMBase): 123 | """This class implements the Fast Iterative Method on the GPU using cupy. 124 | The employed algorithm is the Jacobi algorithm, updating all nodes in each iteration. 125 | For details on the parameters, see :class:`fimpy.fim_base.FIMBase`. 126 | """ 127 | def __init__(self, points, elems, metrics=None, precision=np.float32): 128 | super(FIMCupy, self).__init__(points, elems, metrics, precision, comp_connectivities=False) 129 | #Convert 130 | #self.nh_map = cp.array(self.nh_map) 131 | #self.point_elem_map = cp.array(self.point_elem_map) 132 | self.phi_sol = cp.array(self.phi_sol) 133 | self.points_perm = cp.array(self.points_perm) 134 | self.elems_perm = cp.array(self.elems_perm) 135 | 136 | if self.metrics is not None: 137 | self.metrics = cp.array(self.metrics) 138 | 139 | self.streams = [cp.cuda.Stream(non_blocking=False) for i in range(4)] 140 | self.mempool = cp.get_default_memory_pool() 141 | 142 | def free_gpu_mem(self): 143 | self.mempool.free_all_blocks() 144 | 145 | def calculate_all_line_updates(self, elems_perm, xs_perm, D, us, lib=np): 146 | us_new = us.copy() 147 | us_perm = us[elems_perm] 148 | D_broadcasted = D[..., cp.newaxis, :, :] #Add permutation dimension 149 | 150 | us_result = self.tsitsiklis_update_line(xs_perm[..., 0, :], xs_perm[..., 1, :], 151 | D_broadcasted, us_perm[..., 0], lib=cp) 152 | cp.minimum.at(us_new, elems_perm[..., -1], us_result) 153 | 154 | return us_new 155 | 156 | def calculate_all_triang_updates(self, elems_perm, xs_perm, D, us, lib=np): 157 | us_new = us.copy() 158 | us_perm = us[elems_perm] 159 | D_broadcasted = D[..., lib.newaxis, :, :] 160 | 161 | us_result = self.tsitsiklis_update_triang(xs_perm[..., 0, :], xs_perm[..., 1, :], xs_perm[..., 2, :], 162 | D_broadcasted, us_perm[..., 0], us_perm[..., 1], lib=lib) 163 | 164 | cp.minimum.at(us_new, elems_perm[..., -1], us_result) 165 | return us_new 166 | 167 | def tsitsiklis_update_tetra(self, x1, x2, x3, x4, D, u1, u2, u3, lib=np): 168 | 169 | with self.streams[0]: 170 | u_tet = self.calculate_tet_update(x1, x2, x3, x4, D, u1, u2, u3, cp) 171 | u_tet = lib.where(cp.isnan(u_tet), lib.inf, u_tet) 172 | 173 | #Face calculations (Includes possible line calculations) 174 | with self.streams[1]: 175 | triang1 = self.tsitsiklis_update_triang(x1, x2, x4, D, u1, u2, cp) 176 | with self.streams[2]: 177 | triang2 = self.tsitsiklis_update_triang(x1, x3, x4, D, u1, u3, cp) 178 | with self.streams[3]: 179 | triang3 = self.tsitsiklis_update_triang(x2, x3, x4, D, u2, u3, cp) 180 | 181 | u_triang = lib.minimum(triang1, triang2) 182 | u_triang = lib.minimum(u_triang, triang3) 183 | 184 | return lib.minimum(u_triang, u_tet) 185 | 186 | def calculate_all_tetra_updates(self, elems_perm, xs_perm, D, us, lib=np): 187 | us_new = us.copy() 188 | us_perm = us[elems_perm] 189 | D_broadcasted = D[..., cp.newaxis, :, :] #Add permutation dimension 190 | 191 | us_result = self.tsitsiklis_update_tetra(xs_perm[..., 0, :], xs_perm[..., 1, :], xs_perm[..., 2, :], xs_perm[..., 3, :], 192 | D_broadcasted, us_perm[..., 0], us_perm[..., 1], us_perm[..., 2], lib=cp) 193 | cp.minimum.at(us_new, elems_perm[..., -1], us_result) 194 | 195 | return us_new 196 | 197 | 198 | def _comp_fim(self, x0, x0_vals, metrics=None, max_iterations=int(1e10)): 199 | if metrics is None: 200 | metrics = self.metrics 201 | 202 | D = metrics 203 | self.phi_sol[:] = self.undef_val 204 | self.phi_sol[x0] = x0_vals 205 | 206 | if type(D) != cp.ndarray: 207 | D = cp.array(D) 208 | 209 | if D.dtype != self.precision: 210 | D = D.astype(self.precision) 211 | 212 | for i in range(max_iterations): 213 | u_new = self.update_all_points(self.elems_perm, self.points_perm, D, self.phi_sol, 214 | lib=cp) 215 | 216 | if cp.allclose(u_new, self.phi_sol): 217 | break 218 | 219 | self.phi_sol = u_new 220 | 221 | self.phi_sol = u_new 222 | 223 | return self.phi_sol.copy() 224 | 225 | 226 | def tsitsiklis_update_tetra_quadr(self, D, k, z1, z2, lib=np): 227 | if self.dims == 3: 228 | return tsitsiklis_update_tetra_quadr_cupy_3D(D, k, z1, z2) 229 | else: 230 | return super().tsitsiklis_update_tetra_quadr(D, k, z1, z2, cp) 231 | 232 | 233 | class FIMCupyAL(FIMBase): 234 | """This class implements the Fast Iterative Method on the GPU using cupy. 235 | The employed algorithm is the active list algorithm (as proposed in the original paper), updating only a current estimation of the wavefront. 236 | For details on the parameters, see :class:`fimpy.fim_base.FIMBase`. 237 | """ 238 | 239 | def __init__(self, points, elems, metrics=None, precision=np.float32): 240 | super(FIMCupyAL, self).__init__(points, elems, metrics, precision, comp_connectivities=True) 241 | #Convert 242 | #self.build_linear_nh_elem_map() 243 | self.nh_map = cp.array(self.nh_map) 244 | self.point_elem_map = cp.array(self.point_elem_map) 245 | self.phi_sol = cp.array(self.phi_sol) 246 | self.points_perm = cp.array(self.points_perm) 247 | self.elems_perm = cp.array(self.elems_perm) 248 | 249 | if self.metrics is not None: 250 | self.metrics = cp.array(self.metrics) 251 | 252 | self.active_list = cp.array(self.active_list) 253 | self.mempool = cp.get_default_memory_pool() 254 | 255 | if self.dims == 2: 256 | self.u3_comp_cupy = u3_comp_cupy_2D 257 | elif self.dims == 3: 258 | self.u3_comp_cupy = u3_comp_cupy_3D 259 | else: 260 | self.u3_comp_cupy = u3_comp_cupy_ND 261 | 262 | self.parallel_blocks_perm_kernel = 128 263 | #self.block_dims = (1024,) 264 | #self.perm_kernel = cp.RawKernel(compute_perm_kernel_str.replace("{active_perms}", str(self.elem_dims)).replace("{parallel_blocks}", str(self.parallel_blocks_perm_kernel)), 265 | # 'perm_kernel') #, backend='nvcc') #, options=("--device-c",)) 266 | 267 | #self.block_dims = (64, 16,1) #Old 268 | self.block_dims = (1024, 1,1) 269 | self.perm_kernel = cp.RawKernel(compute_perm_kernel_shared.replace("{active_perms}", str(self.elem_dims)).replace("{parallel_blocks}", str(self.parallel_blocks_perm_kernel)).replace("{shared_buf_size}", str(4096)), 270 | 'perm_kernel', options=('-std=c++11',)) #, backend='nvcc') #, options=("--device-c",)) 271 | self.streams = [cp.cuda.Stream(non_blocking=False) for i in range(7)] 272 | 273 | #To replace cp.unique 274 | self.elem_unique_map = cp.zeros(shape=[self.nr_elems], dtype=cp.int32) 275 | self.elem_ones = cp.ones(shape=[self.nr_elems], dtype=cp.int32) 276 | self.points_unique_map = cp.zeros(shape=[self.nr_points], dtype=cp.int32) 277 | self.points_ones = cp.ones(shape=[self.nr_points], dtype=cp.int32) 278 | 279 | def comp_unique_map(self, inds, elem_map=True): 280 | """Efficient implementation to compute an unique list of indices of active elements/points 281 | 282 | Parameters 283 | ---------- 284 | inds : ndarray (int) 285 | An [?] array containing the non-unique active element/point indices 286 | elem_map : bool, optional 287 | Marks if the unique indices you want to compute are point or element indices, by default True 288 | 289 | Returns 290 | ------- 291 | ndarray (int) 292 | An [?] array holding the indices of the unique element/point indices. 293 | """ 294 | if elem_map: 295 | cp.add.at(self.elem_unique_map, inds, self.elem_ones[inds]) 296 | unique_inds = self.elem_unique_map.nonzero()[0] 297 | self.elem_unique_map[:] = 0 #Reset for next run 298 | else: 299 | cp.add.at(self.points_unique_map, inds, self.points_ones[inds]) 300 | unique_inds = self.points_unique_map.nonzero()[0] 301 | self.points_unique_map[:] = 0 #Reset for next run 302 | 303 | return unique_inds 304 | 305 | def free_gpu_mem(self): 306 | self.mempool.free_all_blocks() 307 | 308 | def tsitsiklis_update_triang(self, x1, x2, x3, D, u1, u2, lib=np, use_streams=None): 309 | 310 | #Called for non tetra meshes -> Streams are available 311 | if self.elem_dims == 3: 312 | assert(use_streams is None) 313 | with self.streams[0]: 314 | u3, sqrt_invalid_mask = self.u3_comp_cupy(x1, x2, x3, u1, u2, D) 315 | 316 | with self.streams[1]: 317 | u3_point = self.tsitsiklis_update_point_sol(x1, x2, x3, D, u1, u2, lib=lib) 318 | 319 | #Use specific streams given by the calling function 320 | else: 321 | assert(use_streams is not None and len(use_streams) == 2) 322 | with use_streams[0]: 323 | u3, sqrt_invalid_mask = self.u3_comp_cupy(x1, x2, x3, u1, u2, D) 324 | with use_streams[1]: 325 | u3_point = self.tsitsiklis_update_point_sol(x1, x2, x3, D, u1, u2, lib=lib) 326 | 327 | #u3_point = u3_point_sol_cupy_2D(x1, x2, x3, D, u1, u2) 328 | u3_computed = lib.where(sqrt_invalid_mask, u3_point, u3) 329 | u3_final = u3_computed 330 | 331 | return u3_final 332 | 333 | def calculate_specific_triang_updates(self, elems_perm, xs_perm, D, us, lib=np): 334 | us_new = us.copy() 335 | 336 | us_perm = us[elems_perm] 337 | 338 | us_result = self.tsitsiklis_update_triang(xs_perm[..., 0, :], xs_perm[..., 1, :], xs_perm[..., 2, :], 339 | D, us_perm[..., 0], us_perm[..., 1], lib=lib) 340 | 341 | #Now we need to take the minimum result of old and all new 342 | cp.minimum.at(us_new, elems_perm[..., -1], us_result) 343 | 344 | return us_new 345 | 346 | def calculate_specific_line_updates(self, elems_perm, xs_perm, D, us, lib=np): 347 | us_new = us.copy() 348 | us_perm = us[elems_perm] 349 | us_result = self.tsitsiklis_update_line(xs_perm[..., 0, :], xs_perm[..., 1, :], 350 | D, us_perm[..., 0], lib=lib) 351 | cp.minimum.at(us_new, elems_perm[..., -1], us_result) 352 | 353 | return us_new 354 | 355 | def tsitsiklis_update_tetra(self, x1, x2, x3, x4, D, u1, u2, u3, lib=np): 356 | 357 | with self.streams[0]: 358 | u_tet = self.calculate_tet_update(x1, x2, x3, x4, D, u1, u2, u3, cp) 359 | u_tet = lib.where(cp.isnan(u_tet), lib.inf, u_tet) 360 | 361 | #Face calculations (Includes possible line calculations) 362 | triang1 = self.tsitsiklis_update_triang(x1, x2, x4, D, u1, u2, cp, (self.streams[1], self.streams[2])) 363 | triang2 = self.tsitsiklis_update_triang(x1, x3, x4, D, u1, u3, cp, (self.streams[3], self.streams[4])) 364 | triang3 = self.tsitsiklis_update_triang(x2, x3, x4, D, u2, u3, cp, (self.streams[5], self.streams[6])) 365 | 366 | u_triang = lib.minimum(triang1, triang2) 367 | u_triang = lib.minimum(u_triang, triang3) 368 | 369 | return lib.minimum(u_triang, u_tet) 370 | 371 | def tsitsiklis_update_tetra_quadr(self, D, k, z1, z2, lib=np): 372 | if self.dims == 3: 373 | return tsitsiklis_update_tetra_quadr_cupy_3D(D, k, z1, z2) 374 | else: 375 | return super().tsitsiklis_update_tetra_quadr(D, k, z1, z2, cp) 376 | 377 | def calculate_specific_tetra_updates(self, elems_perm, xs_perm, D, us, lib=np): 378 | us_new = us.copy() 379 | us_perm = us[elems_perm] 380 | us_result = self.tsitsiklis_update_tetra(xs_perm[..., 0, :], xs_perm[..., 1, :], xs_perm[..., 2, :], xs_perm[..., 3, :], 381 | D, us_perm[..., 0], us_perm[..., 1], us_perm[..., 2], lib=cp) 382 | cp.minimum.at(us_new, elems_perm[..., -1], us_result) 383 | 384 | return us_new 385 | 386 | def comp_marked_points(self, phi, D, active_inds, use_buffered_vals=False): 387 | """Computes the update of only the desired points. 388 | 389 | Parameters 390 | ---------- 391 | phi : np.ndarray (precision) 392 | [N] array of the values for :math:`\\phi_i` to be used for the update. 393 | D : np.ndarray (precision) 394 | [M, d, d] array of :math:`M` to be used for the updates. 395 | active_inds : np.ndarray (int) 396 | [?] array of indices that will be updated 397 | 398 | Returns 399 | ------- 400 | np.ndarray (precision) 401 | [N] array holding the updated values :math:`\\phi_{i+1}` where only indices found in ``active_inds`` were updated. 402 | """ 403 | if active_inds.size == 0: 404 | return phi 405 | 406 | if not use_buffered_vals: 407 | #""" 408 | #active_elem_mask = np.any(self.elems[:, np.newaxis, :] == active_inds[np.newaxis, :, np.newaxis], axis=(-1, -2)) 409 | #active_elem_inds = active_elem_mask.nonzero()[0] 410 | #tmp = cp.sort(self.point_elem_map[active_inds].reshape([-1])) #Performance test -> Future possible implementation 411 | #active_elem_inds = cp.unique(self.point_elem_map[active_inds]) #Compute only what's necessary #cp.unique(self.point_elem_map[active_inds].reshape([-1])) 412 | active_elem_inds = self.comp_unique_map(self.point_elem_map[active_inds].reshape([-1]), elem_map=True) 413 | #active_elem_inds = self.point_elem_map[active_inds].reshape([-1]) #Redundant computations 414 | active_elems_perm = self.elems_perm[active_elem_inds] 415 | 416 | #Custom kernel to avoid the huge memory overhead for comparisons 417 | perm_mask_output = cp.zeros(shape=active_elems_perm.shape[0:2], dtype=bool) 418 | #self.perm_kernel((1,), (1,), (cp.ascontiguousarray(active_elems_perm[..., -1].T), active_inds.astype(cp.int32), perm_mask_output, active_elems_perm.shape[0], active_inds.size)) 419 | self.perm_kernel((self.parallel_blocks_perm_kernel,), self.block_dims, (cp.ascontiguousarray(active_elems_perm[..., -1]), active_inds.astype(cp.int32), perm_mask_output, active_elems_perm.shape[0], active_inds.size)) 420 | #perm_mask_output = perm_mask_output.T 421 | 422 | #For testing 423 | #perm_mask = cp.any(active_elems_perm[..., -1, np.newaxis] == active_inds[np.newaxis, np.newaxis], axis=-1) 424 | #assert(cp.all(perm_mask == perm_mask_output)) 425 | 426 | perm_inds = perm_mask_output.nonzero() 427 | #perm_cnts = np.sum(perm_mask, axis=-1) 428 | #perm_cumsum = np.concatenate([[0], np.cumsum(perm_cnts)]) 429 | #assert (cp.all(cp.sum(perm_mask, axis=-1) > 0)) 430 | 431 | self.active_elems_perm = active_elems_perm[perm_inds] # = self.elems_perm[active_elem_inds][perm_mask] 432 | self.active_points_perm = self.points_perm[active_elem_inds][perm_inds] 433 | #active_D = D[active_elem_inds] 434 | #active_D = D[active_elems_perm] 435 | self.active_D = D[active_elem_inds][perm_inds[0]] #cp.tile(D[active_elem_inds, np.newaxis], [1, active_elems_perm.shape[1], 1, 1])[perm_inds] 436 | #""" 437 | #active_elem_inds = cp.unique(self.point_elem_map[active_inds]) 438 | #self.active_elems_perm, self.active_points_perm, self.active_D = tmp(self.elems_perm, self.point_elem_map, self.points_perm, D, active_inds, active_elem_inds) 439 | #active_elem_inds, active_elems_perm, active_points_perm, perm_inds, active_D = comp_marked_points_fuse(active_inds, self.point_elem_map, self.elems_perm) 440 | #active_elem_inds, active_elems_perm, perm_inds = comp_marked_points_njit(active_inds, self.point_elem_map, self.elems_perm) 441 | #active_elems_perm = active_elems_perm[perm_inds] 442 | #active_points_perm = self.points_perm[active_elem_inds][perm_inds] 443 | #active_D = np.tile(D[active_elem_inds, np.newaxis], [1, active_elems_perm.shape[1], 1, 1])[perm_inds] 444 | 445 | u_new = self.update_specific_points(self.active_elems_perm, # self.elems_perm, 446 | self.active_points_perm, #self.points_perm, 447 | self.active_D, 448 | phi, 449 | lib=cp) 450 | 451 | return u_new 452 | 453 | 454 | def _comp_fim(self, x0, x0_vals, metrics=None, max_iterations=int(1e10)): 455 | if metrics is None: 456 | metrics = self.metrics 457 | 458 | D = metrics 459 | self.phi_sol[:] = self.undef_val 460 | self.phi_sol[x0] = x0_vals 461 | 462 | if type(D) != cp.ndarray: 463 | D = cp.array(D) 464 | 465 | if D.dtype != self.precision: 466 | D = D.astype(self.precision) 467 | 468 | self.active_list[:] = False 469 | self.active_list[cp.unique(self.nh_map[x0])] = True 470 | update_al_interval = 1 471 | active_inds = self.active_list.nonzero()[0] 472 | for i in range(max_iterations): 473 | #active_points = self.points[self.active_list] 474 | 475 | u_new = self.comp_marked_points(self.phi_sol, D, active_inds, use_buffered_vals=(i != 0)) 476 | 477 | if i % update_al_interval == 0: 478 | converged = ((cp.abs(u_new - self.phi_sol) < self.convergence_eps) & (self.active_list)) 479 | converged_inds = converged.nonzero()[0] 480 | if converged_inds.size > 0: 481 | #converged_neighbors = cp.unique(self.nh_map[converged_inds]) 482 | converged_neighbors = self.comp_unique_map(self.nh_map[converged_inds].reshape([-1]), elem_map=False) 483 | u_neighs = self.comp_marked_points(u_new, D, converged_neighbors) 484 | neighbors_needing_updates = converged_neighbors[((cp.abs(u_new[converged_neighbors] - u_neighs[converged_neighbors]) >= self.convergence_eps))] 485 | #Check if the neighbors converged 486 | self.active_list[converged_inds] = False #Remove converged points from the active list 487 | self.active_list[neighbors_needing_updates] = True #Add neighbors to the active list 488 | active_inds = self.active_list.nonzero()[0] 489 | 490 | #Use the newly computed values in the next iteration, since they are strictly smaller 491 | u_new = u_neighs 492 | 493 | if active_inds.size == 0: #cp.all(~self.active_list): #np.allclose(u_new, self.phi_sol, atol=self.convergence_eps): 494 | break 495 | 496 | self.phi_sol = u_new 497 | 498 | self.phi_sol = u_new 499 | 500 | return self.phi_sol.copy() 501 | -------------------------------------------------------------------------------- /fimpy/fim_cutils/__init__.py: -------------------------------------------------------------------------------- 1 | """This subpackage contains the Cython implementations for multiple functions: 2 | * Generating the point to element maps 3 | * Generating the point to neighborhood maps 4 | * Computation of the permutation/active indices mask 5 | 6 | All of these are only used in solvers using the active list. 7 | """ 8 | 9 | from .fim_cutils import compute_point_elem_map_c, compute_neighborhood_map_c, compute_perm_mask 10 | -------------------------------------------------------------------------------- /fimpy/fim_cutils/fim_cutils.pyx: -------------------------------------------------------------------------------- 1 | # cython: infer_types=True 2 | # distutils: language=c++ 3 | import numpy as np 4 | cimport cython 5 | from cython.parallel import prange 6 | from libcpp cimport bool as bool_t 7 | 8 | @cython.boundscheck(False) 9 | @cython.wraparound(False) 10 | def compute_point_elem_map_c(int[:, :] elems, int[:, :] point_elem_map): 11 | """Computes the point to element map, i.e. for each point the elements it is contained in. 12 | This function assumes all points are contained in at least one element. 13 | 14 | Parameters 15 | ---------- 16 | elems : ndarray (int) 17 | An [M, d_e] array holding the mesh connectivity 18 | point_elem_map : ndarray (int) 19 | An [N, ?] array that will hold the result. 20 | Note that the last shape has to be at least long enough to hold the map for the point with the maximum number of contained elements. 21 | All points that are not contained in that many elements, will fill the array with the last occuring element index. 22 | """ 23 | nr_elems = elems.shape[0] 24 | nr_points = point_elem_map.shape[0] 25 | max_point_elem_ratio = point_elem_map.shape[1] 26 | current_offsets_arr = np.zeros_like(point_elem_map[..., 0]) 27 | 28 | cdef int[::1] current_offsets = current_offsets_arr 29 | cdef int offset, point 30 | for elem_i in range(nr_elems): 31 | for elem_j in range(elems.shape[1]): 32 | point = elems[elem_i, elem_j] 33 | offset = current_offsets[point] 34 | point_elem_map[point, offset] = elem_i 35 | current_offsets[point] += 1 36 | 37 | point_elem_map = point_elem_map[:, :np.max(current_offsets)] 38 | for point_i in range(nr_points): 39 | point_elem_map[point_i, current_offsets[point_i]:] = point_elem_map[point_i, current_offsets[point_i]-1] 40 | 41 | return point_elem_map 42 | 43 | @cython.boundscheck(False) 44 | @cython.wraparound(False) 45 | def compute_neighborhood_map_c(int[:, ::1] elems, int[:, ::1] nh_map): 46 | """Computes the point to neighborhood map, i.e. for each point the indices of its neighboring points. 47 | This function assumes all points are contained in at least one element. 48 | 49 | Parameters 50 | ---------- 51 | elems : ndarray (int) 52 | An [M, d_e] array holding the mesh connectivity 53 | nh_map : ndarray (int) 54 | An [N, ?] array that will hold the result. 55 | Note that the last shape has to be at least long enough to hold the map for the point with the maximum number of neighbors. 56 | All points that do not have that many neighbors, will fill the array with the last occuring element index. 57 | """ 58 | nh_map[:] = -1 59 | nr_points = nh_map.shape[0] 60 | nr_elems = elems.shape[0] 61 | current_offsets_arr = np.zeros_like(nh_map[..., 0]) 62 | elem_range = np.arange(elems.shape[1], dtype=np.int32) 63 | cdef int[::1] inds, points, current_offsets 64 | cdef int point, offset, elem_i, single_ind, i, inds_size, elem_j, elem_dims 65 | elem_dims = elems.shape[1] 66 | current_offsets = current_offsets_arr 67 | inds = elem_range 68 | inds_size = elem_range.size 69 | for elem_i in range(nr_elems): 70 | points = elems[elem_i] 71 | for elem_j in prange(elem_dims, nogil=True): 72 | point = points[elem_j] 73 | #inds_arr = np.delete(elem_range, elem_j) 74 | #inds = inds_arr 75 | offset = current_offsets[point] 76 | #inds_size = inds.size 77 | for i in range(inds_size): 78 | if i != elem_j: 79 | single_ind = inds[i] 80 | nh_map[point, offset+i] = elems[elem_i, single_ind] 81 | current_offsets[point] += inds_size 82 | 83 | cdef int point_i, neigh_i, unique_neighs_size 84 | cdef int[::1] unique_neighs_view 85 | for point_i in range(nr_points): 86 | unique_neighs = np.unique(nh_map[point_i]) 87 | unique_neighs = unique_neighs[unique_neighs != -1] 88 | unique_neighs_size = unique_neighs.size 89 | unique_neighs_view = unique_neighs 90 | for neigh_i in prange(nh_map.shape[1], nogil=True): 91 | if neigh_i < unique_neighs_size: 92 | nh_map[point_i, neigh_i] = unique_neighs_view[neigh_i] 93 | else: 94 | nh_map[point_i, neigh_i] = unique_neighs_view[unique_neighs_size-1] 95 | 96 | 97 | return nh_map 98 | 99 | @cython.boundscheck(False) 100 | @cython.wraparound(False) 101 | def compute_perm_mask(int[:, ::1] active_elems_perm, int[::1] active_inds): 102 | """Returns a mask with all active_elems_perm that have at least one active_inds in them. 103 | Equivalent to np.any(active_elems[..., np.newaxis] == active_inds[np.newaxis, np.newaxis], axis=-1), but does not require the full memory. 104 | 105 | Parameters 106 | ---------- 107 | active_elems_perm : ndarray (int) 108 | An [a, b] array holding all the permuted element connectivities 109 | active_inds : ndarray (int) 110 | An [c] array with all active indices (points). 111 | 112 | Returns 113 | ------- 114 | np.ndarray (bool) 115 | [a, b] array holding the computed mask. 116 | """ 117 | cdef int nr_elems, nr_perms, nr_active_inds, elem_i, perm_i, active_i, active_ind 118 | nr_elems = active_elems_perm.shape[0] 119 | nr_perms = active_elems_perm.shape[1] 120 | nr_active_inds = active_inds.size 121 | perm_mask_arr = np.zeros(shape=[nr_elems, nr_perms], dtype=bool) 122 | cdef bool_t[:, ::1] perm_mask = perm_mask_arr 123 | 124 | for elem_i in prange(nr_elems, nogil=True): 125 | for perm_i in range(nr_perms): 126 | for active_i in range(nr_active_inds): 127 | if active_inds[active_i] == active_elems_perm[elem_i, perm_i]: 128 | perm_mask[elem_i, perm_i] = True 129 | break 130 | 131 | return perm_mask_arr 132 | -------------------------------------------------------------------------------- /fimpy/fim_np.py: -------------------------------------------------------------------------------- 1 | """This file contains the CPU implementation of the Fast Iterative Method, based on numpy and cython. 2 | """ 3 | 4 | from fimpy.utils.comp import metric_norm_matrix_3D_cython 5 | import numpy as np 6 | from .fim_base import FIMBase 7 | #from utils.nh_manager import calculate_all_triang_updates, calculate_specific_triang_updates 8 | from .fim_cutils import compute_perm_mask 9 | 10 | def tsitsiklis_update_triang_3D(x1, x2, x3, D, u1, u2, p11, p12, p22): 11 | """Custom numpy implementation of :meth:`fimpy.fim_base.FIMBase.tsitsiklis_update_triang` to speed up computations for :math:`d = 3`. 12 | """ 13 | k = u1 - u2 14 | denominator = p11 - k**2 15 | sqrt_val = (p11 * p22 - p12**2) / denominator 16 | sqrt_invalid_mask = sqrt_val < 0. 17 | sqrt_op = np.sqrt(sqrt_val) 18 | rhs = k * sqrt_op 19 | alpha1 = -(p12 + rhs) / p11 20 | alpha2 = -(p12 - rhs) / p11 21 | alpha1 = np.minimum(np.maximum(alpha1, 0.), 1.) 22 | alpha2 = np.minimum(np.maximum(alpha2, 0.), 1.) 23 | 24 | u3 = [] 25 | for alpha in [alpha1, alpha2]: 26 | x = x3 - (np.expand_dims(alpha, axis=-1) * x1 + (1 - np.expand_dims(alpha, axis=-1)) * x2) 27 | u3.append(alpha * u1 + (1 - alpha) * u2 28 | + metric_norm_matrix_3D_cython(D, x, x, ret_sqrt=True)) 29 | 30 | return np.minimum(u3[0], u3[1]), sqrt_invalid_mask 31 | 32 | 33 | class FIMNP(FIMBase): 34 | """This class implements the Fast Iterative Method on the CPU using a combination of numpy and cython. 35 | The employed algorithm is the Jacobi algorithm, updating all nodes in each iteration. 36 | For details on the parameters, see :class:`fimpy.fim_base.FIMBase`. 37 | """ 38 | 39 | def __init__(self, points, elems, metrics=None, precision=np.float32): 40 | super(FIMNP, self).__init__(points, elems, metrics, precision) 41 | 42 | def _comp_fim(self, x0, x0_vals, metrics=None, max_iterations=int(1e10)): 43 | if metrics is None: 44 | metrics = self.metrics 45 | 46 | D = metrics 47 | self.phi_sol = np.ones(shape=[self.nr_points], dtype=self.precision) * self.undef_val 48 | self.phi_sol[x0] = x0_vals 49 | 50 | if D.dtype != self.precision: 51 | D = D.astype(self.precision) 52 | 53 | for i in range(max_iterations): 54 | u_new = self.update_all_points(self.elems_perm, self.points_perm, D, self.phi_sol, 55 | lib=np) 56 | 57 | if np.allclose(u_new, self.phi_sol): 58 | break 59 | 60 | self.phi_sol = u_new 61 | 62 | self.phi_sol = u_new 63 | 64 | return self.phi_sol 65 | 66 | class FIMNPAL(FIMBase): 67 | """This class implements the Fast Iterative Method on the CPU using a combination of numpy and cython. 68 | The employed algorithm is the active list algorithm (as proposed in the original paper), updating only a current estimation of the wavefront. 69 | For details on the parameters, see :class:`fimpy.fim_base.FIMBase`. 70 | """ 71 | 72 | def __init__(self, points, elems, metrics=None, precision=np.float32): 73 | super(FIMNPAL, self).__init__(points, elems, metrics, precision, comp_connectivities=True) 74 | 75 | 76 | def tsitsiklis_update_triang(self, x1, x2, x3, D, u1, u2, lib=np): 77 | """Custom numpy implementation of :meth:`fimpy.fim_base.FIMBase.tsitsiklis_update_triang` to speed up computations for :math:`d = 3`. 78 | """ 79 | 80 | if self.dims == 3: 81 | z2 = x2 - x3 82 | z1 = x1 - x2 83 | 84 | p11 = metric_norm_matrix_3D_cython(D, x1=z1, x2=z1, ret_sqrt=False) 85 | p12 = metric_norm_matrix_3D_cython(D, x1=z1, x2=z2, ret_sqrt=False) 86 | p22 = metric_norm_matrix_3D_cython(D, x1=z2, x2=z2, ret_sqrt=False) 87 | 88 | u3, sqrt_invalid_mask = tsitsiklis_update_triang_3D(x1, x2, x3, D, u1, u2, p11, p12, p22) 89 | u3_point = self.tsitsiklis_update_point_sol(x1, x2, x3, D, u1, u2, lib=lib) 90 | u3_computed = lib.where(sqrt_invalid_mask, u3_point, u3) 91 | u3_final = u3_computed 92 | 93 | return u3_final 94 | else: 95 | return super(FIMNPAL, self).tsitsiklis_update_triang(x1, x2, x3, D, u1, u2) 96 | 97 | def comp_marked_points(self, phi, D, active_inds): 98 | """Computes the update of only the desired points. 99 | 100 | Parameters 101 | ---------- 102 | phi : np.ndarray (precision) 103 | [N] array of the values for :math:`\\phi_i` to be used for the update. 104 | D : np.ndarray (precision) 105 | [M, d, d] array of :math:`M` to be used for the updates. 106 | active_inds : np.ndarray (int) 107 | [?] array of indices that will be updated 108 | 109 | Returns 110 | ------- 111 | np.ndarray (precision) 112 | [N] array holding the updated values :math:`\\phi_{i+1}` where only indices found in ``active_inds`` were updated. 113 | """ 114 | 115 | if active_inds.size == 0: 116 | return phi 117 | 118 | #active_elem_mask = np.any(self.elems[:, np.newaxis, :] == active_inds[np.newaxis, :, np.newaxis], axis=(-1, -2)) 119 | #active_elem_inds = active_elem_mask.nonzero()[0] 120 | active_elem_inds = np.unique(self.point_elem_map[active_inds].reshape([-1])) 121 | active_elems_perm = self.elems_perm[active_elem_inds] 122 | #perm_mask = np.any(active_elems_perm[..., -1, np.newaxis] == active_inds[np.newaxis, np.newaxis], axis=-1) 123 | perm_mask = compute_perm_mask(np.ascontiguousarray(active_elems_perm[..., -1]), active_inds) 124 | #TODO: Testing 125 | #assert(np.all(perm_mask == np.any(active_elems_perm[..., -1, np.newaxis] == active_inds[np.newaxis, np.newaxis], axis=-1))) 126 | perm_inds = perm_mask.nonzero() 127 | #perm_cnts = np.sum(perm_mask, axis=-1) 128 | #perm_cumsum = np.concatenate([[0], np.cumsum(perm_cnts)]) 129 | #assert (np.all(np.sum(perm_mask, axis=-1) > 0)) 130 | 131 | active_elems_perm = active_elems_perm[perm_inds] # = self.elems_perm[active_elem_inds][perm_mask] 132 | active_points_perm = self.points_perm[active_elem_inds][perm_inds] 133 | #active_D = D[active_elem_inds] 134 | #active_D = D[active_elems_perm] 135 | active_D = D[active_elem_inds][perm_inds[0]] 136 | #active_D = np.tile(D[active_elem_inds, np.newaxis], [1, active_elems_perm.shape[1], 1, 1])[perm_inds] 137 | 138 | #active_elem_inds, active_elems_perm, perm_inds = comp_marked_points_njit(active_inds, self.point_elem_map, self.elems_perm) 139 | #active_elems_perm = active_elems_perm[perm_inds] 140 | #active_points_perm = self.points_perm[active_elem_inds][perm_inds] 141 | #active_D = np.tile(D[active_elem_inds, np.newaxis], [1, active_elems_perm.shape[1], 1, 1])[perm_inds] 142 | u_new = self.update_specific_points(active_elems_perm, # self.elems_perm, 143 | active_points_perm, #self.points_perm, 144 | active_D, 145 | phi, 146 | lib=np) 147 | 148 | return u_new 149 | 150 | 151 | def _comp_fim(self, x0, x0_vals, metrics=None, max_iterations=int(1e10)): 152 | if metrics is None: 153 | metrics = self.metrics 154 | 155 | D = metrics 156 | self.phi_sol = np.ones(shape=[self.nr_points], dtype=self.precision) * self.undef_val 157 | self.phi_sol[x0] = x0_vals 158 | self.active_list[:] = False 159 | self.active_list[np.unique(self.nh_map[x0])] = True 160 | 161 | if D.dtype != self.precision: 162 | D = D.astype(self.precision) 163 | 164 | for i in range(max_iterations): 165 | #active_points = self.points[self.active_list] 166 | active_inds = self.active_list.nonzero()[0].astype(np.int32) 167 | 168 | u_new = self.comp_marked_points(self.phi_sol, D, active_inds) 169 | converged = ((np.abs(u_new - self.phi_sol) < self.convergence_eps) & (self.active_list)) 170 | converged_inds = converged.nonzero()[0] 171 | converged_neighbors = np.unique(self.nh_map[converged_inds]) 172 | u_neighs = self.comp_marked_points(u_new, D, converged_neighbors) 173 | neighbors_needing_updates = converged_neighbors[((np.abs(u_new[converged_neighbors] - u_neighs[converged_neighbors]) >= self.convergence_eps))] 174 | #Check if the neighbors converged 175 | self.active_list[converged_inds] = False #Remove converged points from the active list 176 | self.active_list[neighbors_needing_updates] = True #Add neighbors to the active list 177 | 178 | 179 | if np.all(~self.active_list): #np.allclose(u_new, self.phi_sol, atol=self.convergence_eps): 180 | break 181 | 182 | self.phi_sol = u_new 183 | 184 | self.phi_sol = u_new 185 | 186 | return self.phi_sol 187 | -------------------------------------------------------------------------------- /fimpy/perm_kernel_test.cu: -------------------------------------------------------------------------------- 1 | extern "C"{ 2 | 3 | __device__ int* upperBound(int* first, int* last, const int& value) 4 | { 5 | int* it; 6 | int count, step; 7 | count = last - first; 8 | 9 | while (count > 0) { 10 | it = first; 11 | step = count / 2; 12 | it += step; 13 | if (value >= *it) { 14 | first = ++it; 15 | count -= step + 1; 16 | } 17 | else 18 | count = step; 19 | } 20 | return first; 21 | } 22 | 23 | __global__ 24 | void perm_kernel(const int* active_elems_perm, const int* active_inds, 25 | bool* perm_mask, 26 | const unsigned int active_elems_size, 27 | const unsigned int active_inds_size) { 28 | const int nr_perms = {active_perms}; 29 | const int bidx = blockIdx.x; 30 | const int block_size = blockDim.x; 31 | const int block_size_y = blockDim.y; 32 | const int tidx_global = block_size * bidx + threadIdx.x; 33 | const int tidx_local = threadIdx.x; 34 | //const int tidx_y = threadIdx.y; 35 | //const auto grid_size = gridDim.x * gridDim.y; 36 | //const auto blockidx = blockIdx.x + blockIdx.y*gridDim.x; 37 | //const auto block_size = blockDim.x * blockDim.y; // * blockDim.z; 38 | //const auto tidx = threadIdx.y * blockDim.x + threadIdx.x; 39 | __shared__ int active_inds_buf[{shared_buf_size}]; 40 | const int nr_shared_bufs_needed = static_cast(ceil(static_cast(active_inds_size) / {shared_buf_size})); 41 | 42 | //printf("Test\n"); 43 | for(int shared_buf_run = 0; shared_buf_run < nr_shared_bufs_needed; shared_buf_run++) 44 | { 45 | //printf("%d\n", shared_buf_run); 46 | const int shared_buf_offset = {shared_buf_size} * shared_buf_run; 47 | const int current_active_inds_size = min({shared_buf_size}, active_inds_size - {shared_buf_size}*shared_buf_run); 48 | printf("%d\n", current_active_inds_size); 49 | if(shared_buf_run > 0) 50 | __syncthreads(); 51 | 52 | //Fill shared memory 53 | for(int active_i = tidx_local; active_i < current_active_inds_size; active_i += block_size) 54 | active_inds_buf[active_i] = active_inds[shared_buf_offset + active_i]; 55 | 56 | __syncthreads(); 57 | 58 | for(int elem_offset = tidx_global; elem_offset < active_elems_size*nr_perms; elem_offset+=block_size*{parallel_blocks}) 59 | { 60 | const int point_i = active_elems_perm[elem_offset]; 61 | bool match = perm_mask[elem_offset]; //Maybe already set in the last shared buffer run 62 | printf("elem_offset %d, %d\n", elem_offset, point_i); 63 | if(!match) 64 | { 65 | printf("Bounds: %x, %x\n", active_inds_buf, active_inds_buf + current_active_inds_size); 66 | printf("Range: %d\n", (active_inds_buf + current_active_inds_size) - active_inds_buf); 67 | const int* bound = upperBound(active_inds_buf, active_inds_buf + current_active_inds_size, point_i); 68 | const int* possible_equal_elem = ((active_inds_buf > (bound - 1)) ? active_inds_buf : (bound - 1)); 69 | printf("Found: %x, %x, %d\n", bound, possible_equal_elem, *possible_equal_elem); 70 | if(*possible_equal_elem == point_i) 71 | perm_mask[elem_offset] = true; 72 | } 73 | 74 | //__syncthreads(); 75 | } 76 | } 77 | } 78 | } -------------------------------------------------------------------------------- /fimpy/solver.py: -------------------------------------------------------------------------------- 1 | """This file contains the interface to create the Fast Iterative Method solvers. 2 | """ 3 | 4 | try: 5 | import cupy as cp 6 | from .fim_cupy import FIMCupyAL, FIMCupy 7 | cupy_available = True 8 | except ImportError as err: 9 | cupy_available = False 10 | print("Import of Cupy failed. The GPU version of fimpy will be unavailable. Message: %s" % (err)) 11 | 12 | from .fim_base import FIMBase 13 | from .fim_np import FIMNP, FIMNPAL 14 | import numpy as np 15 | from typing import Union 16 | 17 | available_arr_t = (Union[np.ndarray, cp.ndarray] if cupy_available else np.ndarray) 18 | 19 | """Function responsible for creating the correct Fast Iterative Method solver 20 | """ 21 | def create_fim_solver(points : available_arr_t, elems : available_arr_t, metrics : available_arr_t =None, 22 | precision=np.float32, device='cpu', use_active_list=True) -> FIMBase: 23 | """Creates a Fast Iterative Method solver for solving the anisotropic eikonal equation 24 | 25 | .. math:: 26 | \\left\\{ 27 | \\begin{array}{rll} 28 | \\left<\\nabla \\phi, D \\nabla \\phi \\right> &= 1 \\quad &\\text{on} \\; \\Omega \\\\ 29 | \\phi(\\mathbf{x}_0) &= g(\\mathbf{x}_0) \\quad &\\text{on} \\; \\Gamma 30 | \\end{array} 31 | \\right. . 32 | 33 | Parameters 34 | ---------- 35 | points : Union[np.ndarray (float), cp.ndarray (float)] 36 | Array of points, :math:`n \\times d` 37 | elems : Union[np.ndarray (int), cp.ndarray (int)] 38 | Array of elements, :math:`m \\times d_e` 39 | metrics : Union[np.ndarray (float), cp.ndarray (float)], optional 40 | Specifies the initial :math:`D \\in \\mathbb{R}^{d \\times d}` tensors. 41 | If not specified, you later need to provide them in :meth:`comp_fim `, by default None 42 | precision : np.dtype, optional 43 | precision of all calculations and the final result, by default np.float32 44 | device : str, optional 45 | Specifies the target device for the computations. One of [cpu, gpu], by default 'gpu' 46 | use_active_list : bool, optional 47 | If set to true, you will get an active list solver that only computes the necessary subset of points in each iteration. 48 | If set to false, a Jacobi solver will be returned that updates all points of the mesh in each iteration. By default True 49 | 50 | Returns 51 | ------- 52 | FIMBase 53 | Returns a Fast Iterative Method solver 54 | """ 55 | assert not device == 'gpu' or cupy_available, "Requested GPU which is not available" 56 | 57 | if device == 'cpu': 58 | return (FIMNPAL(points, elems, metrics, precision) if use_active_list else FIMNP(points, elems, metrics, precision)) 59 | elif device == 'gpu': 60 | return (FIMCupyAL(points, elems, metrics, precision) if use_active_list else FIMCupy(points, elems, metrics, precision)) 61 | else: 62 | assert False, f"Unknown device {device}, should be one of [cpu, gpu]" 63 | 64 | #Class for backwards compatibility 65 | from warnings import warn 66 | class FIMPY(): 67 | def create_fim_solver(*args, **kwargs): 68 | warn("Using the FIMPY interface is deprecated and will be removed in future releases. Use the module function create_fim_solver directly.", DeprecationWarning, stacklevel=2) 69 | return create_fim_solver(*args, **kwargs) 70 | -------------------------------------------------------------------------------- /fimpy/utils/__init__.py: -------------------------------------------------------------------------------- 1 | """This subpackage contains small custom functions to efficiently compute :math:`\\left` on the CPU and GPU for different dimensions :math:`d`. 2 | """ -------------------------------------------------------------------------------- /fimpy/utils/comp.py: -------------------------------------------------------------------------------- 1 | """This file contains small custom functions to compute :math:`\\left` for general and special dimensions :math:`d`. 2 | Note that all custom, efficient implementations assume that :math:`A` is a symmetric matrix. 3 | """ 4 | import numpy as np 5 | from .cython.comp import metric_sqr_norm_matrix_2D_vec, metric_sqr_norm_matrix_3D_vec 6 | try: 7 | import cupy as cp 8 | cupy_enabled = True 9 | except ImportError as err: 10 | cupy_enabled = False 11 | 12 | 13 | def _broadcast_metric_params(A, x1, x2): 14 | """Broadcast the metric parameters as a preperation for the Cython functions. 15 | See :func:`metric_sqr_norm_matrix`. 16 | """ 17 | if A.ndim == 4: #Broadcasting 18 | A = np.broadcast_to(A, [A.shape[0], max(A.shape[1], x1.shape[1]), x1.shape[-1], x1.shape[-1]]) 19 | x1 = np.broadcast_to(x1, A.shape[:-1]) 20 | x2 = np.broadcast_to(x2, A.shape[:-1]) 21 | 22 | return A, x1, x2 23 | 24 | 25 | def metric_norm_matrix_2D_cython(A, x1, x2, ret_sqrt=True): 26 | """Custom implementation of :func:`metric_sqr_norm_matrix` for ``lib = np`` and :math:`d = 2`. 27 | """ 28 | A, x1, x2 = _broadcast_metric_params(A, x1, x2) 29 | A_flat, x1_flat, x2_flat = A.reshape([-1, 2, 2]), x1.reshape([-1, 2]), x2.reshape([-1, 2]) 30 | norm = np.empty(shape=A_flat.shape[0], dtype=A_flat.dtype) 31 | norm = np.array(metric_sqr_norm_matrix_2D_vec(A_flat, x1_flat, x2_flat, norm)) 32 | 33 | if ret_sqrt: 34 | norm = np.sqrt(norm) 35 | 36 | return norm.reshape(A.shape[:-2]) 37 | 38 | def metric_norm_matrix_3D_cython(A, x1, x2, ret_sqrt=True): 39 | """Custom implementation of :func:`metric_sqr_norm_matrix` for ``lib = np`` and :math:`d = 3`. 40 | """ 41 | A, x1, x2 = _broadcast_metric_params(A, x1, x2) 42 | A_flat, x1_flat, x2_flat = A.reshape([-1, 3, 3]), x1.reshape([-1, 3]), x2.reshape([-1, 3]) 43 | norm = np.empty(shape=A_flat.shape[0], dtype=A_flat.dtype) 44 | norm = np.array(metric_sqr_norm_matrix_3D_vec(A_flat, x1_flat, x2_flat, norm)) 45 | 46 | if ret_sqrt: 47 | norm = np.sqrt(norm) 48 | 49 | return norm.reshape(A.shape[:-2]) 50 | 51 | 52 | if cupy_enabled: 53 | @cp.fuse() 54 | def metric_sqr_norm_matrix_2D_cupy(A, x1, x2): 55 | """Custom implementation of :func:`metric_sqr_norm_matrix` for ``lib = cp`` and :math:`d = 3`. 56 | """ 57 | a, b, c = A[..., 0, 0], A[..., 1, 1], A[..., 0, 1] 58 | return (x1[..., 0] * (a * x2[..., 0] + c * x2[..., 1]) + x1[..., 1] * (c * x2[..., 0] + b * x2[..., 1])) 59 | 60 | @cp.fuse() 61 | def metric_norm_matrix_2D_cupy(A, x1, x2): 62 | """Custom implementation of :func:`metric_norm_matrix` for ``lib = cp`` and :math:`d = 3`. 63 | """ 64 | norm = metric_sqr_norm_matrix_2D_cupy(A, x1, x2) 65 | norm = cp.sqrt(norm) 66 | 67 | return norm 68 | 69 | @cp.fuse() 70 | def metric_sqr_norm_matrix_3D_cupy(A, x1, x2): 71 | """Custom implementation of :func:`metric_sqr_norm_matrix` for ``lib = cp`` and :math:`d = 3`. 72 | """ 73 | a, b, c, d, e, f = A[..., 0, 0], A[..., 1, 1], A[..., 2, 2], A[..., 0, 1], A[..., 0, 2], A[..., 1, 2] 74 | norm = (x1[..., 0] * (a * x2[..., 0] + d * x2[..., 1] + e * x2[..., 2]) 75 | + x1[..., 1] * (d * x2[..., 0] + b * x2[..., 1] + f * x2[..., 2]) 76 | + x1[..., 2] * (e * x2[..., 0] + f * x2[..., 1] + c * x2[..., 2])) 77 | 78 | return norm 79 | 80 | @cp.fuse() 81 | def metric_norm_matrix_3D_cupy(A, x1, x2): 82 | """Custom implementation of :func:`metric_norm_matrix` for ``lib = cp`` and :math:`d = 3`. 83 | """ 84 | norm = metric_sqr_norm_matrix_3D_cupy(A, x1, x2) 85 | norm = cp.sqrt(norm) 86 | 87 | return norm 88 | 89 | 90 | def metric_sqr_norm_matrix(A, x1, x2, lib=np): 91 | """Computes :math:`\\left` in a broadcasted fashion for arbitrary :math:`d`. 92 | Details on the parameters and the return value can be found in :func:`metric_norm_matrix`. 93 | """ 94 | #assert(A.shape[-1] == x1.shape[-1] and A.shape[-2] == A.shape[-1]) 95 | 96 | #assert(np.all(np.equal(x2.shape[-1], x1.shape[-1]))) 97 | 98 | sqr_norm = lib.sum(lib.sum(A * x1[..., lib.newaxis], axis=-2) * x2, axis=-1) 99 | return sqr_norm 100 | 101 | def metric_norm_matrix(A, x1, x2, lib=np): 102 | """Computes :math:`\\sqrt{\\left}` in a broadcasted fashion for arbitrary :math:`d` 103 | 104 | Parameters 105 | ---------- 106 | A : ndarray (float) 107 | An [..., d, d] array with the stack of matrices :math:`A` 108 | x1 : ndarray (float) 109 | An [..., d] array with the stack of vectors :math:`\\mathbf{x}_1` 110 | x2 : ndarray (float) 111 | An [..., d] array with the stack of vectors :math:`\\mathbf{x}_2` 112 | lib : library, optional 113 | Library used for the computations of the norm. Needs to implement a ``sum`` method. 114 | By default np 115 | 116 | Returns 117 | ------- 118 | ndarray (float) 119 | An [...] array holding the computed norms :math:`\\sqrt{\\left}`. 120 | """ 121 | 122 | 123 | #assert(A.shape[-1] == x1.shape[-1] and A.shape[-2] == A.shape[-1]) 124 | 125 | #assert(np.all(np.equal(x2.shape[-1], x1.shape[-1]))) 126 | 127 | sqr_norm = metric_sqr_norm_matrix(A, x1, x2, lib) 128 | return lib.sqrt(sqr_norm) 129 | -------------------------------------------------------------------------------- /fimpy/utils/cython/__init__.py: -------------------------------------------------------------------------------- 1 | """This subpackage contains the Cython implementations for fast 2D and 3D metric norm computations. 2 | """ 3 | 4 | from .comp import metric_sqr_norm_matrix_2D_vec, metric_sqr_norm_matrix_3D_vec #, sqrt_cython -------------------------------------------------------------------------------- /fimpy/utils/cython/comp.pyx: -------------------------------------------------------------------------------- 1 | # cython: infer_types=True 2 | # distutils: language=c++ 3 | cimport cython 4 | from cython.parallel cimport prange 5 | from libcpp.vector cimport vector 6 | from typing import Callable 7 | from libcpp cimport bool as bool_t 8 | from libc.math cimport sqrt 9 | 10 | import numpy as np 11 | 12 | ctypedef fused mat_t: 13 | float 14 | double 15 | 16 | 17 | ctypedef fused const_mat_t: 18 | const float 19 | const double 20 | 21 | 22 | 23 | @cython.boundscheck(False) 24 | @cython.wraparound(False) 25 | def metric_sqr_norm_matrix_2D_vec(const_mat_t[:, :, :] A, const_mat_t[:, :] x1, const_mat_t[:, :] x2, mat_t[::1] result): 26 | a, b, c = A[..., 0, 0], A[..., 1, 1], A[..., 0, 1] 27 | 28 | cdef const_mat_t[:] a_ = a 29 | cdef const_mat_t[:] b_ = b 30 | cdef const_mat_t[:] c_ = c 31 | cdef int rows, row_i 32 | 33 | rows = A.shape[0] 34 | for row_i in prange(rows, nogil=True): 35 | result[row_i] = (x1[row_i, 0] * (a_[row_i] * x2[row_i, 0] + c_[row_i] * x2[row_i, 1]) 36 | + x1[row_i, 1] * (c_[row_i] * x2[row_i, 0] + b_[row_i] * x2[row_i, 1])) 37 | 38 | 39 | return result 40 | 41 | @cython.boundscheck(False) 42 | @cython.wraparound(False) 43 | def metric_sqr_norm_matrix_3D_vec(const_mat_t[:, :, :] A, const_mat_t[:, :] x1, const_mat_t[:, :] x2, mat_t[::1] result): 44 | a, b, c, d, e, f = A[..., 0, 0], A[..., 1, 1], A[..., 2, 2], A[..., 0, 1], A[..., 0, 2], A[..., 1, 2] 45 | 46 | cdef int rows, row_i 47 | cdef const_mat_t[:] a_ = a 48 | cdef const_mat_t[:] b_ = b 49 | cdef const_mat_t[:] c_ = c 50 | cdef const_mat_t[:] d_ = d 51 | cdef const_mat_t[:] e_ = e 52 | cdef const_mat_t[:] f_ = f 53 | 54 | cdef const_mat_t[:] x11_ = x1[..., 0] 55 | cdef const_mat_t[:] x12_ = x1[..., 1] 56 | cdef const_mat_t[:] x13_ = x1[..., 2] 57 | cdef const_mat_t[:] x21_ = x2[..., 0] 58 | cdef const_mat_t[:] x22_ = x2[..., 1] 59 | cdef const_mat_t[:] x23_ = x2[..., 2] 60 | 61 | rows = A.shape[0] 62 | for row_i in prange(rows, nogil=True): 63 | result[row_i] = (x11_[row_i] * (a_[row_i] * x21_[row_i] + d_[row_i] * x22_[row_i] + e_[row_i] * x23_[row_i]) 64 | + x12_[row_i] * (d_[row_i] * x21_[row_i] + b_[row_i] * x22_[row_i] + f_[row_i] * x23_[row_i]) 65 | + x13_[row_i] * (e_[row_i] * x21_[row_i] + f_[row_i] * x22_[row_i] + c_[row_i] * x23_[row_i])) 66 | 67 | 68 | return result 69 | -------------------------------------------------------------------------------- /fimpy/utils/tsitsiklis.py: -------------------------------------------------------------------------------- 1 | """This file contains the norm_map, that is in general used to efficiently select the best and fastest function to compute norms of the type :math:`\\left`. 2 | """ 3 | #import utility 4 | import numpy as np 5 | from .comp import metric_norm_matrix_2D_cython, metric_norm_matrix_3D_cython 6 | from .comp import metric_sqr_norm_matrix, metric_norm_matrix 7 | from collections import defaultdict 8 | 9 | norm_map = {np: defaultdict(lambda: (metric_norm_matrix, metric_sqr_norm_matrix))} 10 | norm_map[np][2] = (lambda A, x1, x2: metric_norm_matrix_2D_cython(A, x1, x2, True), lambda A, x1, x2: metric_norm_matrix_2D_cython(A, x1, x2, False)) 11 | norm_map[np][3] = (lambda A, x1, x2: metric_norm_matrix_3D_cython(A, x1, x2, True), lambda A, x1, x2: metric_norm_matrix_3D_cython(A, x1, x2, False)) 12 | 13 | try: 14 | import cupy as cp 15 | from .comp import metric_norm_matrix_2D_cupy, metric_norm_matrix_3D_cupy, metric_sqr_norm_matrix_2D_cupy, metric_sqr_norm_matrix_3D_cupy 16 | norm_map[cp] = defaultdict(lambda: (lambda A, x1, x2: metric_norm_matrix(A, x1, x2, cp), lambda A, x1, x2: metric_sqr_norm_matrix(A, x1, x2, cp))) 17 | norm_map[cp][2] = (lambda A, x1, x2: metric_norm_matrix_2D_cupy(A, x1, x2), lambda A, x1, x2: metric_sqr_norm_matrix_2D_cupy(A, x1, x2)) 18 | norm_map[cp][3] = (lambda A, x1, x2: metric_norm_matrix_3D_cupy(A, x1, x2), lambda A, x1, x2: metric_sqr_norm_matrix_3D_cupy(A, x1, x2)) 19 | except ImportError as err: 20 | ... 21 | -------------------------------------------------------------------------------- /paper.bib: -------------------------------------------------------------------------------- 1 | @article{fu_fast_2011, 2 | title = {A {Fast} {Iterative} {Method} for {Solving} the {Eikonal} {Equation} on {Triangulated} {Surfaces}}, 3 | volume = {33}, 4 | issn = {1064-8275}, 5 | url = {https://epubs.siam.org/doi/abs/10.1137/100788951}, 6 | doi = {10.1137/100788951}, 7 | number = {5}, 8 | urldate = {2018-07-26}, 9 | journal = {SIAM Journal on Scientific Computing}, 10 | author = {Fu, Z. and Jeong, W. and Pan, Y. and Kirby, R. and Whitaker, R.}, 11 | month = jan, 12 | year = {2011}, 13 | pages = {2468--2488} 14 | } 15 | 16 | @book{evans_partial_2010, 17 | author = {Evans, Lawrence C.}, 18 | title = {Partial differential equations}, 19 | series = {Graduate Studies in Mathematics}, 20 | volume = {19}, 21 | edition = {Second}, 22 | publisher = {American Mathematical Society, Providence, RI}, 23 | year = {2010}, 24 | pages = {xxii+749}, 25 | ISBN = {978-0-8218-4974-3}, 26 | doi = {10.1090/gsm/019}, 27 | url = {https://doi.org/10.1090/gsm/019}, 28 | } 29 | 30 | @article{fu_fast_2013, 31 | title = {A {Fast} {Iterative} {Method} for {Solving} the {Eikonal} {Equation} on {Tetrahedral} {Domains}}, 32 | volume = {35}, 33 | issn = {1064-8275}, 34 | url = {https://epubs.siam.org/doi/abs/10.1137/120881956}, 35 | doi = {10.1137/120881956}, 36 | number = {5}, 37 | urldate = {2018-07-26}, 38 | journal = {SIAM Journal on Scientific Computing}, 39 | author = {Fu, Z. and Kirby, R. and Whitaker, R.}, 40 | month = jan, 41 | year = {2013}, 42 | pages = {C473--C494} 43 | } 44 | 45 | @article{sethian_fast_1996, 46 | title={A fast marching level set method for monotonically advancing fronts}, 47 | author={Sethian, James A}, 48 | journal={Proceedings of the National Academy of Sciences}, 49 | volume={93}, 50 | number={4}, 51 | pages={1591--1595}, 52 | year={1996}, 53 | publisher={National Acad. Sciences}, 54 | doi = {10.1073/pnas.93.4.1591}, 55 | } 56 | 57 | @book{franzone2014mathematical, 58 | title={Mathematical cardiac electrophysiology}, 59 | author={Franzone, Piero Colli and Pavarino, Luca Franco and Scacchi, Simone}, 60 | volume={13}, 61 | year={2014}, 62 | publisher={Springer}, 63 | doi={10.1007/978-3-319-04801-7} 64 | } 65 | 66 | @article{grandits_inverse_2020, 67 | title = {An inverse {Eikonal} method for identifying ventricular activation sequences from epicardial activation maps}, 68 | volume = {419}, 69 | issn = {0021-9991}, 70 | url = {http://www.sciencedirect.com/science/article/pii/S0021999120304745}, 71 | doi = {10.1016/j.jcp.2020.109700}, 72 | language = {en}, 73 | urldate = {2020-07-21}, 74 | journal = {Journal of Computational Physics}, 75 | author = {Grandits, Thomas and Gillette, Karli and Neic, Aurel and Bayer, Jason and Vigmond, Edward and Pock, Thomas and Plank, Gernot}, 76 | month = oct, 77 | year = {2020}, 78 | keywords = {Fast iterative method, Fast marching, His-Purkinje system, Inverse Eikonal, Minimization}, 79 | pages = {109700} 80 | } 81 | 82 | -------------------------------------------------------------------------------- /paper.md: -------------------------------------------------------------------------------- 1 | --- 2 | title: 'A Fast Iterative Method Python package' 3 | tags: 4 | - Python 5 | - eikonal 6 | - partial differential equations 7 | - cuda 8 | authors: 9 | - name: Thomas Grandits 10 | affiliation: 1 11 | affiliations: 12 | - name: Institute of Computer Graphics and Vision, TU Graz 13 | index: 1 14 | date: July 2021 15 | bibliography: paper.bib 16 | --- 17 | 18 | # Summary 19 | 20 | 21 | The anisotropic eikonal equation is a non-linear partial differential equation, given by 22 | \begin{equation*} 23 | \left\{ 24 | \begin{array}{rll} 25 | \left<\nabla \phi, D \nabla \phi \right> &= 1 \quad &\text{on} \; \Omega \\ 26 | \phi(\mathbf{x}_0) &= g(\mathbf{x}_0) \quad &\text{on} \; \Gamma \subset \Omega 27 | \end{array} 28 | \right. . 29 | \end{equation*} 30 | In practice, this problem is often associated with computing the earliest arrival times $\phi$ of a wave from a set of given starting points $\mathbf{x}_0$ through a heterogeneous medium (i.e. different velocities are assigned throughout the medium). 31 | This equation yields infinitely many weak solutions [@evans_partial_2010] and can thus not be straight-forwardly solved using standard Finite Element approaches. 32 | 33 | ``fim-python`` implements the Fast Iterative Method (FIM), proposed in [@fu_fast_2013], purely in Python to solve the anisotropic eikonal equation by finding its unique viscosity solution. 34 | In this scenario, we compute $\phi$ on tetrahedral/triangular meshes or line networks for a given $D$, $\mathbf{x}_0$ and $g$. 35 | The method is implemented both on the CPU using [``numba``](https://numba.pydata.org/) and [``numpy``](https://numpy.org/), as well as the GPU with the help of [``cupy``](https://cupy.dev/) (depends on [CUDA](https://developer.nvidia.com/cuda-toolkit)). 36 | The library is meant to be easily and rapidly used for repeated evaluations on a mesh. 37 | 38 | The FIM locally computes an update rule to find the path the wavefront will take through a single element. 39 | Since the algorithm is restricted to linear elements, the path through an element will also be a straight line. 40 | In the case of tetrahedral domains, the FIM thus tries to find the path of the linear update from a face spanned by three vertices $\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3$ to the opposite vertex $\mathbf{v}_4$. 41 | \autoref{fig:update} visualizes the update. 42 | For triangles and lines, the algorithm behaves similarly but the update origin is limited to a side or vertex respectively. 43 | The exact equations used to solve this problem in this repository were previously described (among others) in [@grandits_inverse_2020]. 44 | 45 | ![Update inside a single tetrahedron\label{fig:update}](docs/figs/update_fig.jpg "Update inside a single tetrahedron"){ width=33% } 46 | 47 | 48 | Two different methods are implemented in ``fim-python``: 49 | In the *Jacobi* method, the above local update rule is computed for all elements in each iteration until the change between two subsequent iterations is smaller than a chosen $\varepsilon$. 50 | This version of the algorithm is bested suited for the GPU, since it is optimal for a SIMD (single instruction multiple data) architecture. 51 | The *active list* method is more closely related to the method presented in [@fu_fast_2013]: 52 | We keep track of all vertices that require a recomputation in the current iteration on a so-called active list which we keep up-to-date. 53 | 54 | # Comparison to other tools 55 | 56 | There are other tools available to solve variants of the eikonal equation, but they differ in functionality to ``fim-python``. 57 | 58 | [``scikit-fmm``](https://pypi.org/project/scikit-fmm/) implements the Fast Marching Method (FMM) [@sethian_fast_1996], which was designed to solve the isotropic eikonal equation ($D = c I$ for $c \in \mathbb{R}$ and $I$ being the identity matrix). The library works on uniform grids, rather than meshes. 59 | 60 | [``GPUTUM: Unstructured Eikonal``](https://github.com/SCIInstitute/SCI-Solver_Eikonal) implements the FIM in CUDA for triangulated surfaces and tetrahedral meshes, but has no Python bindings and is designed as a command line tool for single evaluations. 61 | 62 | # Statement of need 63 | 64 | The eikonal equation has many practical applications, including cardiac electrophysiology, image processing and geoscience, to approximate wave propagation through a medium. 65 | In the example of cardiac electrophysiology [@franzone2014mathematical], the electrical activation times $\phi$ are computed throughout the anisotropic heart muscle with varying conduction velocities $D$. 66 | 67 | ``fim-python`` tries to wrap the FIM for CPU and GPU into an easy-to-use Python package for multiple evaluations with a straight-forward installation over [PyPI](https://pypi.org/). 68 | This should provide engineers and researchers alike with an accessible tool that allows evaluations of the eikonal equation for general scenarios. 69 | 70 | # References 71 | -------------------------------------------------------------------------------- /pyproject.toml: -------------------------------------------------------------------------------- 1 | [build-system] 2 | requires = ["setuptools", "wheel", "Cython>=0.29.22"] 3 | build-backend = "setuptools.build_meta" 4 | -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | from setuptools import setup 2 | from distutils.core import setup, Extension 3 | from setuptools.command.build_ext import build_ext 4 | from Cython.Build import cythonize 5 | import sys 6 | import os 7 | 8 | class build_ext_check_openmp(build_ext): 9 | def build_extensions(self): 10 | try: 11 | build_ext.build_extensions(self) 12 | except: 13 | # remove openmp flags 14 | for ext in self.extensions: 15 | ext.extra_compile_args = [f for f in ext.extra_compile_args if not f.endswith("openmp")] 16 | ext.extra_link_args = [f for f in ext.extra_link_args if not f.endswith("openmp")] 17 | print(ext.extra_compile_args) 18 | print(ext.extra_link_args) 19 | build_ext.build_extensions(self) 20 | 21 | if sys.platform.startswith("win32"): 22 | extra_compile_args = ["/O2", "/openmp"] 23 | extra_link_args = [] #["/openmp"] 24 | else: 25 | extra_compile_args = ["-O3", "-fopenmp"] 26 | extra_link_args = ["-fopenmp"] 27 | 28 | fim_cutils_extension = Extension( 29 | name="fimpy.fim_cutils.fim_cutils", 30 | sources=["fimpy/fim_cutils/fim_cutils.pyx"], # our Cython source 31 | language="c++", # generate C++ code 32 | extra_compile_args=extra_compile_args, 33 | extra_link_args=extra_link_args, 34 | ) 35 | 36 | comp_cutils_extension = Extension( 37 | name="fimpy.utils.cython.comp", 38 | sources=["fimpy/utils/cython/comp.pyx"], # our Cython source 39 | language="c++", # generate C++ code 40 | extra_compile_args=extra_compile_args, 41 | extra_link_args=extra_link_args, 42 | ) 43 | 44 | lib_requires_cpu = ["numpy", "Cython>=0.29.22"] 45 | lib_requires_gpu = ["cupy>=9.0"] 46 | test_requires_cpu = ["scipy", "pytest", "pytest-cov", "matplotlib", "pandas", "ipython"] 47 | 48 | with open(os.path.join(os.path.dirname(__file__), 'README.md'), 'r') as readme: 49 | long_description = readme.read() 50 | 51 | setup(name="fim-python", 52 | version="1.2.2", 53 | description="This repository implements the Fast Iterative Method on tetrahedral domains and triangulated surfaces purely in python both for CPU (numpy) and GPU (cupy).", 54 | long_description=long_description, 55 | long_description_content_type="text/markdown", 56 | url="https://github.com/thomgrand/fim-python", 57 | packages=["fimpy", "fimpy.utils", "fimpy.fim_cutils", "fimpy.utils.cython"], 58 | install_requires=lib_requires_cpu, 59 | classifiers=[ 60 | "Programming Language :: Python :: 3", 61 | "Programming Language :: Cython", 62 | "Topic :: Scientific/Engineering :: Mathematics", 63 | "Operating System :: POSIX :: Linux", 64 | "Operating System :: Microsoft :: Windows", 65 | "Environment :: GPU :: NVIDIA CUDA", 66 | "License :: OSI Approved :: GNU Affero General Public License v3", 67 | ], 68 | python_requires='>=3.6', 69 | author="Thomas Grandits", 70 | author_email="tomdev@gmx.net", 71 | license="AGPL", 72 | ext_modules = cythonize([fim_cutils_extension, comp_cutils_extension], 73 | compiler_directives={'language_level' : "3"}), 74 | cmdclass={ 'build_ext': build_ext_check_openmp }, 75 | extras_require = { 76 | 'gpu': lib_requires_gpu, 77 | 'tests': test_requires_cpu, 78 | 'docs': ["sphinx", "pydata_sphinx_theme", "pandas", "ipython"] 79 | } 80 | ) 81 | 82 | -------------------------------------------------------------------------------- /tests/benchmark_data/.gitignore: -------------------------------------------------------------------------------- 1 | # Ignore everything in this directory 2 | * 3 | # Except this file 4 | !.gitignore 5 | -------------------------------------------------------------------------------- /tests/data/.gitignore: -------------------------------------------------------------------------------- 1 | # Ignore everything in this directory 2 | * 3 | # Except this file 4 | !.gitignore 5 | -------------------------------------------------------------------------------- /tests/generate_benchmark_data.py: -------------------------------------------------------------------------------- 1 | from generate_test_data import generate_test_data 2 | 3 | if __name__ == "__main__": 4 | generate_test_data(True) -------------------------------------------------------------------------------- /tests/generate_doc_figs.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | import os 4 | import numpy as np 5 | import cupy as cp 6 | import sys 7 | sys.path.append(".") 8 | from fimpy import create_fim_solver 9 | from scipy.spatial import Delaunay 10 | import matplotlib.pyplot as plt 11 | import matplotlib.colors 12 | import scipy.io as sio 13 | import pandas 14 | import json 15 | 16 | #TODO 17 | def generate_usage_example(save_fig=True): 18 | out_fname = os.path.join(os.path.dirname(__file__), *["..", "docs", "figs", "usage_example.jpg"]) 19 | #Create triangulated points in 2D 20 | x = np.linspace(-1, 1, num=50) 21 | X, Y = np.meshgrid(x, x) 22 | points = np.stack([X, Y], axis=-1).reshape([-1, 2]).astype(np.float32) 23 | elems = Delaunay(points).simplices 24 | elem_centers = np.mean(points[elems], axis=1) 25 | 26 | #The domain will have a small spot where movement will be slow 27 | velocity_p = (1 / (1 + np.exp(3.5 - 25*np.linalg.norm(points - np.array([[0.33, 0.33]]), axis=-1)**2))) 28 | velocity_e = (1 / (1 + np.exp(3.5 - 25*np.linalg.norm(elem_centers - np.array([[0.33, 0.33]]), axis=-1)**2))) 29 | D = np.eye(2, dtype=np.float32)[np.newaxis] * velocity_e[..., np.newaxis, np.newaxis] #Isotropic propagation 30 | 31 | x0 = np.array([np.argmin(np.linalg.norm(points, axis=-1), axis=0)]) 32 | x0_vals = np.array([0.]) 33 | 34 | #Create a FIM solver, by default the GPU solver will be called with the active list 35 | fim = create_fim_solver(points, elems, D) 36 | phi = fim.comp_fim(x0, x0_vals) 37 | 38 | #Plot the data of all points to the given x0 at the center of the domain 39 | fig, axes = plt.subplots(nrows=1, ncols=2, sharey=True) 40 | cont_f1 = axes[0].contourf(X, Y, phi.get().reshape(X.shape)) 41 | axes[0].set_title("Distance from center $\\phi(\\mathbf{x})$") 42 | scatter_h = axes[0].scatter(points[x0, 0], points[x0, 1], marker='x', color='r') 43 | #cbar = plt.colorbar(cont_f1) 44 | #cbar.set_label("$\\phi$") 45 | axes[0].legend([scatter_h], ["$\\mathbf{x}_0$"]) 46 | 47 | cont_f2 = axes[1].contourf(X, Y, velocity_p.reshape(X.shape)) 48 | axes[1].set_title("Assumed isotropic velocity $D(\\mathbf{x}) = c(\\mathbf{x}) I$") 49 | #cbar = plt.colorbar(cont_f2) 50 | #cbar.set_label("Velocity") 51 | 52 | fig.set_size_inches((10, 6)) 53 | plt.tight_layout() 54 | if save_fig: 55 | fig.savefig(out_fname) 56 | else: 57 | plt.show() 58 | 59 | plt.close(fig) 60 | 61 | def generate_benchmark_plot(benchmark_data_fname, data_field, save_fig=True, fname_postfix="", title=None): 62 | with open(benchmark_data_fname, "r") as bench_f: 63 | benchmark_data = json.load(bench_f) 64 | out_fname = os.path.join(os.path.dirname(__file__), *["..", "docs", "figs", "benchmark"]) 65 | all_pd_data = pandas.DataFrame(benchmark_data) 66 | 67 | all_dims = np.unique(all_pd_data["dims"]) 68 | colors = plt.cm.brg(np.linspace(0, 1, num=all_dims.size)) 69 | 70 | figs = [] 71 | #GPU 72 | for device in ["gpu", "cpu"]: 73 | plt.gca().set_prop_cycle(None) #Reset color cycle 74 | pd_data = all_pd_data[all_pd_data["device"] == device] 75 | #colors = plt.cm.get_cmap('jet', all_dims.size) 76 | fig, axes = plt.subplots(nrows=1, ncols=3) 77 | lines_hs = {2: [], 3: [], 4: []} 78 | for elem_dim_i, elem_dims in enumerate([4, 3, 2]): #np.unique(pd_data["elem_dims"])): 79 | for dim_i, dims in enumerate([1, 2, 3, 5]): #enumerate(all_dims): #[1, 2, 3, 5] 80 | for use_active_list in [False, True]: 81 | plt.sca(axes[elem_dim_i]) 82 | data = pd_data[(pd_data["active_list"] == use_active_list) & (pd_data["dims"] == dims) & (pd_data["elem_dims"] == elem_dims)] 83 | 84 | if data.size == 0: 85 | continue 86 | 87 | data = data.sort_values("resolution", ascending=False) 88 | h = 2 / data["resolution"] 89 | nr_elems = data["nr_elems"] 90 | 91 | label=("%d" % (dims) if not use_active_list else None) #('w. AL' if use_active_list else 'w/o AL') 92 | lines_h = axes[elem_dim_i].plot(nr_elems.values, data[data_field].values, linestyle=('--' if use_active_list else '-'), color=colors[dim_i], label=label) #color='b' if use_active_list else 'r') 93 | 94 | if not use_active_list: 95 | lines_hs[elem_dims].append((lines_h[0], dims)) 96 | 97 | 98 | if elem_dim_i != 0: 99 | #axes[elem_dim_i].set_yticklabels([]) 100 | pass 101 | else: 102 | plt.ylabel("Runtime [s]") 103 | 104 | #Make a nice title from the data 105 | plotted_data = pd_data[pd_data["elem_dims"] == elem_dims]["elem_fname"] 106 | if plotted_data.size > 0: 107 | axes[elem_dim_i].set_title(plotted_data.iat[0].capitalize().replace("_d", " D")) 108 | #axes[elem_dim_i].invert_xaxis() 109 | #plt.xlabel("$h$") 110 | plt.xlabel("#Elements") 111 | plt.xscale("log") 112 | plt.yscale("log") 113 | plt.grid(True, which='both', axis='both') 114 | 115 | #Search for valid handles 116 | used_elem_dims = list(lines_hs.keys()) 117 | len_handles = np.array([len(lines_hs[written_dim]) for written_dim in used_elem_dims]) 118 | 119 | if np.any(len_handles > 0): 120 | handles, plot_dims = zip(*lines_hs[used_elem_dims[int(np.where(len_handles > 0)[0][0])]]) 121 | axes[1].legend(handles, plot_dims, title="$d=$", loc='center', bbox_to_anchor=(0.15, -0.3, 0.75, 0.25), borderpad=0.8, ncol=2) 122 | 123 | if title is None: 124 | fig.suptitle("Fimpy %s Benchmark" % (device.upper())) 125 | else: 126 | fig.suptitle(title % (device.upper())) 127 | fig.set_size_inches((14, 8)) 128 | fig.tight_layout() 129 | figs.append(fig) 130 | 131 | if save_fig: 132 | fig.savefig(out_fname + "_%s%s" % (device, fname_postfix) + ".jpg") 133 | fig.savefig(out_fname + "_%s%s" % (device, fname_postfix) + ".pdf") 134 | plt.show() 135 | [plt.close(fig) for fig in figs] 136 | #plt.show() 137 | #pd_data. 138 | 139 | if __name__ == "__main__": 140 | #generate_usage_example(False) 141 | generate_benchmark_plot(os.path.join(os.path.dirname(__file__), "benchmark_results_w_cpu.json"), save_fig=True, data_field="runtime") 142 | generate_benchmark_plot(os.path.join(os.path.dirname(__file__), "benchmark_results_w_cpu.json"), save_fig=True, data_field="setup_time", fname_postfix="_setup", title="%s Setup Time") 143 | -------------------------------------------------------------------------------- /tests/generate_test_data.py: -------------------------------------------------------------------------------- 1 | """ 2 | Testcases: 3 | - Tube 4 | - Sphere 5 | - Cube 6 | - Simplified Heart 7 | - Network 8 | - Use vtkCutter to get 2D data 9 | - With and without anisotropy 10 | 11 | """ 12 | import os 13 | from scipy.sparse import coo_matrix 14 | from scipy.sparse.csgraph import minimum_spanning_tree 15 | from scipy.spatial import Delaunay 16 | import numpy as np 17 | #import pyvista as pv 18 | #import vtk 19 | import scipy.io as sio 20 | 21 | test_dims = [1, 2, 3, 5] 22 | bench_dims = test_dims + [10, 20] #, 50] #, 100] 23 | 24 | test_elem_dims = [2, 3, 4] 25 | 26 | test_resolutions = {1: [10, 25, 50], 27 | 2: [5, 10], 28 | 3: [5, 10]} 29 | 30 | bench_resolutions = {1: test_resolutions[1] + [100, 200, 400, 800, 1500], 31 | 2: test_resolutions[2] + [25, 50, 100, 200, 300, 500], #1000], 32 | 3: test_resolutions[3] + [25, 50]} #, 75, 100]} 33 | 34 | elem_fnames = {2: "network", 3: "surface", 4: "tetra_domain"} 35 | 36 | isotropic_het_vel_f = lambda x, dims, scales=1: np.eye(dims)[np.newaxis] * (dims + 0.5 + np.sum(np.sin(x * 2*np.pi / scales), axis=-1))[:, np.newaxis, np.newaxis] 37 | 38 | sanity_size_check = lambda dims, elem_dims, resolution: dims >= 5 and ((elem_dims == 4 and resolution > 50) or (elem_dims == 4 and dims > 10 and resolution > 25) 39 | or (elem_dims == 3 and resolution > 300) or (elem_dims == 2 and resolution > 400)) 40 | 41 | def generate_test_data(gen_bench_data=False): 42 | 43 | if gen_bench_data: 44 | data_dir = os.path.join(os.path.dirname(__file__), "benchmark_data") 45 | else: 46 | data_dir = os.path.join(os.path.dirname(__file__), "data") 47 | 48 | if not os.path.isdir(data_dir): 49 | os.mkdir(data_dir) 50 | 51 | for elem_dims in test_elem_dims: 52 | valid_dims = np.array(bench_dims if gen_bench_data else test_dims) 53 | valid_dims = valid_dims[valid_dims >= (elem_dims - 1)] #Request a proper manifold 54 | resolutions = (bench_resolutions if gen_bench_data else test_resolutions) 55 | 56 | for resolution in resolutions[elem_dims-1]: 57 | x = np.linspace(-1, 1, num=resolution) 58 | 59 | #Create the mesh 60 | #Line network 61 | if elem_dims == 2: 62 | pass #Will be calculated as a point cloud for each dimensional case 63 | 64 | #Triangular square surface 65 | elif elem_dims == 3: 66 | X, Y = np.meshgrid(x, x) #, indexing='ij') 67 | points = np.stack([X, Y], axis=-1).reshape([-1, 2]) 68 | elems = Delaunay(points[..., :2]).simplices 69 | 70 | #Tetrahedral cube domain 71 | elif elem_dims == 4: 72 | points = np.stack(np.meshgrid(x, x, x, indexing='ij'), axis=-1).reshape([-1, 3]) 73 | elems = Delaunay(points).simplices 74 | 75 | for dims in valid_dims: 76 | assert(elem_dims <= (dims+1)) 77 | 78 | #Skip very large examples 79 | if sanity_size_check(dims, elem_dims, resolution): 80 | continue 81 | 82 | if elem_dims == 2: 83 | points = np.random.uniform(size=[x.size**2, dims]) 84 | repetitions = np.minimum(points.shape[0]*15, points.shape[0]**2) // points.shape[0] 85 | rows = np.concatenate((np.arange(points.shape[0]),)*repetitions, axis=-1) 86 | cols = np.random.choice(points.shape[0], size=points.shape[0]*repetitions) 87 | while np.unique(cols).size != points.shape[0]: 88 | cols = np.random.choice(points.shape[0], size=points.shape[0]*repetitions) 89 | data = np.ones(rows.size) 90 | connectivity_mat = coo_matrix((data, (rows, cols))) 91 | connectivity_mat = 0.5 * (connectivity_mat + connectivity_mat.T).tocsc() 92 | span_tree = minimum_spanning_tree(connectivity_mat) 93 | span_tree.eliminate_zeros() 94 | elems = np.stack(span_tree.nonzero(), axis=-1) 95 | 96 | 97 | elem_fname = elem_fnames[elem_dims] 98 | #Fill the zero dimensions 99 | if points.shape[-1] < dims: 100 | points = np.concatenate([points, np.zeros(shape=[points.shape[0], dims - points.shape[1]])], axis=-1) 101 | 102 | elem_centers = np.mean(points[elems], axis=1) 103 | D = isotropic_het_vel_f(elem_centers, dims) 104 | 105 | fname = "elem_dims_%d_dims_%d_resolution_%d_%s.mat" % (elem_dims, dims, resolution, elem_fname) 106 | if gen_bench_data: 107 | data = {"elems": elems.astype(np.int32), "points": points.astype(np.float32), "D": D.astype(np.float32)} 108 | else: 109 | data = {"elems": elems, "points": points, "D": D} 110 | sio.savemat(os.path.join(data_dir, fname), data, do_compression=True) 111 | print("Created %s" % (fname)) 112 | #ug = pv.UnstructuredGrid({vtk_elem_type: elems}, points) 113 | #ug.cell_arrays["D"] = D 114 | #ug.save(fname) 115 | 116 | 117 | 118 | if __name__ == "__main__": 119 | generate_test_data() -------------------------------------------------------------------------------- /tests/run_benchmark.py: -------------------------------------------------------------------------------- 1 | import os 2 | import sys 3 | import numpy as np 4 | import cupy as cp 5 | #from cupy.cuda.memory import OutOfMemoryError 6 | from cupy.cuda.runtime import CUDARuntimeError 7 | import scipy.io as sio 8 | from fimpy.solver import create_fim_solver 9 | import time 10 | import timeit 11 | from IPython import get_ipython 12 | import json 13 | 14 | from generate_test_data import bench_dims, test_elem_dims, bench_resolutions, elem_fnames, sanity_size_check 15 | 16 | def run_single_test(device, use_active_list, dims, elem_dims, resolution, bench_dict=None): 17 | data_dir = os.path.join(os.path.dirname(__file__), "benchmark_data") 18 | ipython = get_ipython() 19 | 20 | elem_fname = elem_fnames[elem_dims] 21 | fname = "elem_dims_%d_dims_%d_resolution_%d_%s.mat" % (elem_dims, dims, resolution, elem_fname) 22 | fname = os.path.join(data_dir, fname) 23 | assert(os.path.isfile(fname)) #If you fail here, the generation of test data using generate_test_data.py failed or was not performed 24 | 25 | data = sio.loadmat(fname) 26 | points, elems, D = data["points"], data["elems"], data["D"] 27 | nr_points = points.shape[0] 28 | 29 | center_x0 = np.array([np.argmin(np.sum((points - np.mean(points, axis=0, keepdims=True))**2, 30 | axis=-1))]) 31 | #x0_vals = np.array([0.]) 32 | 33 | #Setup the solver 34 | bt = time.time() 35 | solver = create_fim_solver(points, elems, D, precision=np.float32, device=device, use_active_list=use_active_list) 36 | at = time.time() 37 | setup_time = at - bt 38 | 39 | x0 = center_x0 40 | x0_vals = np.array([0.]) 41 | 42 | #Dry run for compilation 43 | bt = time.time() 44 | phi1 = solver.comp_fim(x0, x0_vals) 45 | at = time.time() 46 | init_run_time = at - bt 47 | #return #For profiling 48 | 49 | # 50 | def eval_fim(): 51 | result = solver.comp_fim(x0, x0_vals) 52 | if device == 'gpu': 53 | cp.cuda.runtime.deviceSynchronize() 54 | return result 55 | 56 | if ipython is None: 57 | timing_avg = timeit.timeit(lambda: eval_fim(), number=5) / 5 58 | print("Setup time: %f, Avg. compute time: %f, First run time: %f" % (setup_time, timing_avg, init_run_time)) 59 | else: 60 | timing = ipython.run_line_magic("timeit", "-o eval_fim()") 61 | timing_avg = timing.average 62 | 63 | if bench_dict is not None: 64 | bench_dict["device"].append(device) 65 | bench_dict["active_list"].append(use_active_list) 66 | bench_dict["dims"].append(dims) 67 | bench_dict["elem_dims"].append(elem_dims) 68 | bench_dict["runtime"].append(timing_avg) 69 | bench_dict["setup_time"].append(setup_time) 70 | bench_dict["elem_fname"].append(elem_fname) 71 | bench_dict["nr_points"].append(points.shape[0]) 72 | bench_dict["nr_elems"].append(elems.shape[0]) 73 | bench_dict["resolution"].append(resolution) 74 | 75 | print("Finished %s on %s, active list: %s" % (fname, device, use_active_list)) 76 | 77 | return setup_time, timing_avg, solver, fname #, points.shape[0], elems.shape[0] 78 | 79 | if __name__ == "__main__": 80 | bench_dict = {"device": [], "active_list": [], "dims": [], "elem_dims": [], "runtime": [], "setup_time": [], "elem_fname": [], "nr_points": [], "nr_elems": [], 81 | "resolution": []} 82 | 83 | bt = time.time() 84 | for device in ['cpu', 'gpu']: 85 | for use_active_list in [True, False]: 86 | 87 | for dims in bench_dims: 88 | if device == 'cpu' and dims not in [1, 2, 3]: #if device == 'cpu' and not use_active_list and dims not in [1, 2, 3]: 89 | continue #TODO: Too slow currently (not using any multithreading) 90 | 91 | if device == 'cpu' and dims > 5: 92 | continue 93 | 94 | for elem_dims in test_elem_dims: 95 | if (dims < elem_dims - 1): 96 | continue 97 | 98 | #if dims > 5 and elem_dims > 2 and use_active_list: #elem_dims == 4 and use_active_list and dims > 3 and resolution > 10 and device == 'gpu': 99 | # continue #Very slow 100 | 101 | for resolution in bench_resolutions[elem_dims-1]: 102 | #Skip very large examples 103 | if sanity_size_check(dims, elem_dims, resolution): 104 | continue 105 | 106 | if elem_dims == 4 and resolution == 100: 107 | continue 108 | 109 | if device == 'cpu' and ((elem_dims == 2 and resolution > 500) or (elem_dims == 4 and resolution > 25) or (elem_dims == 3 and resolution > 250)): 110 | continue 111 | 112 | if device == 'cpu' and dims > 3 and elem_dims == 4 and resolution > 10: 113 | continue 114 | 115 | try: 116 | solver, fname = run_single_test(device, use_active_list, dims, elem_dims, resolution, bench_dict)[-2:] 117 | 118 | if hasattr(solver, 'mempool'): 119 | solver.mempool.free_all_blocks() 120 | except CUDARuntimeError as ex: 121 | print("A single benchmark failed with an exception (probably out of memory).", file=sys.stderr) 122 | print("Parameters: %d, %d, %d, %s" % (dims, elem_dims, resolution, use_active_list) , file=sys.stderr) 123 | 124 | 125 | with open(os.path.join(os.path.dirname(__file__), "benchmark_results_w_cpu.json"), "w") as bench_f: 126 | json.dump(bench_dict, bench_f, indent=2, sort_keys=True) 127 | #sio.savemat(os.path.join(os.path.dirname(__file__), "benchmark_results.mat"), bench_dict, do_compression=True) 128 | 129 | at = time.time() 130 | print("Benchmarking took %f seconds" % (at - bt)) -------------------------------------------------------------------------------- /tests/test_custom_kernels.py: -------------------------------------------------------------------------------- 1 | #import unittest 2 | import pytest 3 | #from . 4 | import numpy as np 5 | import os 6 | from fimpy.fim_cutils import compute_perm_mask, compute_point_elem_map_c, compute_neighborhood_map_c 7 | from scipy.spatial import Delaunay 8 | from itertools import combinations 9 | 10 | try: 11 | import cupy as cp 12 | from fimpy.cupy_kernels import compute_perm_kernel_str, compute_perm_kernel_shared 13 | cupy_enabled = True 14 | #raise ImportError("Test") #For testing the CPU only version 15 | except ImportError as err: 16 | print("Cupy import failed. The tests will skip the cupy tests") 17 | cupy_enabled = False 18 | 19 | class TestCustomKernels(): 20 | 21 | def create_mesh(self, elem_dims, resolution): 22 | x = np.linspace(-1, 1, num=resolution) 23 | pts = np.stack(np.meshgrid(*((x,) * elem_dims), indexing='ij'), axis=-1).reshape([-1, elem_dims]) 24 | elems = Delaunay(pts).simplices 25 | inds = np.arange(elem_dims+1) 26 | assert(elem_dims in [2, 3]) 27 | 28 | if elem_dims == 2: 29 | perms = np.array([[0, 1, 2], 30 | [0, 2, 1], 31 | [2, 1, 0]]) 32 | else: 33 | perms = np.array([[0, 1, 2, 3], 34 | [0, 1, 3, 2], 35 | [0, 3, 2, 1], 36 | [3, 1, 2, 0]]) 37 | elems_perm = elems[np.arange(elems.shape[0])[:, np.newaxis, np.newaxis], perms[np.newaxis]] 38 | 39 | return pts, elems, elems_perm 40 | 41 | def comp_point_elem_map(self, elems, nr_points): 42 | #TODO: Export into function? 43 | max_point_elem_ratio = np.max(np.unique(elems, return_counts=True)[1]) 44 | point_elem_map = np.zeros([nr_points, max_point_elem_ratio], dtype=np.int32) 45 | compute_point_elem_map_c(elems, point_elem_map) 46 | return point_elem_map 47 | 48 | def comp_neighborhood_map(self, elems, nr_points, elem_dims): 49 | max_point_elem_ratio = np.max(np.unique(elems, return_counts=True)[1]) 50 | nh_map = np.zeros(shape=[nr_points, max_point_elem_ratio * elem_dims], dtype=np.int32) 51 | 52 | nh_map = np.array(compute_neighborhood_map_c(elems, nh_map)) 53 | 54 | nh_map = np.sort(nh_map, axis=-1) 55 | 56 | # There may be cases where the ratio was an overestimate 57 | while nh_map.shape[1] > 1 and np.all(nh_map[..., -1] == nh_map[..., -2]): 58 | nh_map = nh_map[..., :-1] 59 | 60 | return nh_map 61 | 62 | @pytest.mark.skipif(not cupy_enabled, reason='Cupy could not be imported. GPU tests unavailable') 63 | @pytest.mark.parametrize('elem_dims', [3, 4]) 64 | @pytest.mark.parametrize('resolution', [5, 10, 15]) 65 | @pytest.mark.parametrize('nr_active_inds', [1, 20, 100]) 66 | @pytest.mark.parametrize('parallel_blocks', [1, 4, 16]) 67 | @pytest.mark.parametrize('threads_x', [1, 16, 32]) 68 | @pytest.mark.parametrize('threads_y', [1]) #, 16, 32]) #New kernel with binary search does not use this 69 | @pytest.mark.parametrize('shared_buf_size', [1, 128, 2048]) 70 | def test_perm_kernel_gpu2(self, elem_dims, resolution, nr_active_inds, parallel_blocks, threads_x, threads_y, shared_buf_size): 71 | pts, elems, elems_perm = self.create_mesh(elem_dims-1, resolution) 72 | nr_pts = pts.shape[0] 73 | 74 | elems_perm = cp.array(elems_perm) 75 | point_elem_map = cp.array(self.comp_point_elem_map(elems, nr_pts)) 76 | active_inds = cp.sort(cp.array(np.random.choice(nr_pts, np.minimum(nr_active_inds, nr_pts), replace=False))) 77 | active_elem_inds = cp.unique(point_elem_map[active_inds].reshape([-1])) 78 | active_elems_perm = elems_perm[active_elem_inds] 79 | 80 | perm_kernel = cp.RawKernel(compute_perm_kernel_shared.replace("{active_perms}", str(elem_dims)).replace("{parallel_blocks}", str(parallel_blocks)).replace("{shared_buf_size}", str(shared_buf_size)), 81 | 'perm_kernel', options=('-std=c++11',), backend='nvcc') 82 | perm_kernel.compile() 83 | perm_mask_output = cp.zeros(shape=active_elems_perm.shape[0:2], dtype=bool) 84 | perm_kernel((parallel_blocks,), (threads_x,threads_y, 1), (cp.ascontiguousarray(active_elems_perm[..., -1]), active_inds.astype(cp.int32), perm_mask_output, active_elems_perm.shape[0], active_inds.size)) 85 | #Broadcasted version is the ground truth 86 | perm_mask_gt = np.any(active_elems_perm[..., -1, np.newaxis] == active_inds[np.newaxis, np.newaxis], axis=-1) 87 | assert(np.all(perm_mask_output == perm_mask_gt)) 88 | 89 | if __name__ == "__main__": 90 | self = TestCustomKernels() 91 | parallel_blocks = 4 92 | threads_x = 32 93 | threads_y = 1 94 | shared_buf_size = 1024 95 | nr_active_inds = 5 96 | elem_dims = 3 97 | resolution = 15 98 | pts, elems, elems_perm = self.create_mesh(elem_dims-1, resolution) 99 | nr_pts = pts.shape[0] 100 | 101 | elems_perm = cp.array(elems_perm) 102 | point_elem_map = cp.array(self.comp_point_elem_map(elems, nr_pts)) 103 | active_inds = cp.sort(cp.array(np.random.choice(nr_pts, np.minimum(nr_active_inds, nr_pts), replace=False))) 104 | active_elem_inds = cp.unique(point_elem_map[active_inds].reshape([-1])) 105 | active_elems_perm = elems_perm[active_elem_inds] 106 | 107 | perm_kernel = cp.RawKernel(compute_perm_kernel_shared.replace("{active_perms}", str(elem_dims)).replace("{parallel_blocks}", str(parallel_blocks)).replace("{shared_buf_size}", str(shared_buf_size)), 108 | 'perm_kernel') 109 | perm_kernel.compile() 110 | perm_mask_output = cp.zeros(shape=active_elems_perm.shape[0:2], dtype=bool) 111 | perm_kernel((parallel_blocks,), (threads_x,threads_y, 1), (cp.ascontiguousarray(active_elems_perm[..., -1]), active_inds.astype(cp.int32), perm_mask_output, active_elems_perm.shape[0], active_inds.size)) 112 | #Broadcasted version is the ground truth 113 | perm_mask_gt = np.any(active_elems_perm[..., -1, np.newaxis] == active_inds[np.newaxis, np.newaxis], axis=-1) 114 | assert(np.all(perm_mask_output == perm_mask_gt)) -------------------------------------------------------------------------------- /tests/test_cython_methods.py: -------------------------------------------------------------------------------- 1 | from fimpy.utils.comp import metric_norm_matrix_2D_cython, metric_norm_matrix_3D_cython 2 | import numpy as np 3 | import pytest 4 | 5 | class TestCythonMethods(): 6 | 7 | @pytest.mark.parametrize("prec", [np.float32, np.float64]) 8 | def test_2D_vec(self, prec): 9 | rtol = (1e-3 if prec == np.float32 else 1e-4) 10 | A = np.random.normal(size=(100, 2, 2)).astype(prec) 11 | A[..., 1, 0] = A[..., 0, 1] #Symmetrize 12 | 13 | z1 = np.random.normal(size=(100, 2)).astype(prec) 14 | z2 = np.random.normal(size=(100, 2)).astype(prec) 15 | 16 | expected_result = np.einsum('...x,...xy,...y->...', z1, A, z2) 17 | comp_result = metric_norm_matrix_2D_cython(A, z1, z2, ret_sqrt=False) 18 | assert np.allclose(expected_result, comp_result, rtol=rtol) 19 | 20 | #Broadcasted 21 | A = np.random.normal(size=(100, 1, 2, 2)) 22 | A[..., 1, 0] = A[..., 0, 1] #Symmetrize 23 | 24 | z1 = np.random.normal(size=(100, 3, 2)) 25 | z2 = np.random.normal(size=(100, 3, 2)) 26 | 27 | expected_result = np.einsum('...x,...xy,...y->...', z1, A, z2) 28 | comp_result = metric_norm_matrix_2D_cython(A, z1, z2, ret_sqrt=False) 29 | assert np.allclose(expected_result, comp_result, rtol=rtol) #Broadcasted 30 | 31 | @pytest.mark.parametrize("prec", [np.float32, np.float64]) 32 | def test_3D_vec(self, prec): 33 | rtol = (1e-3 if prec == np.float32 else 1e-4) 34 | A = np.random.normal(size=(100, 3, 3)).astype(prec) 35 | A[..., 1, 0] = A[..., 0, 1] #Symmetrize 36 | A[..., 2, 0] = A[..., 0, 2] 37 | A[..., 2, 1] = A[..., 1, 2] 38 | 39 | z1 = np.random.normal(size=(100, 3)).astype(prec) 40 | z2 = np.random.normal(size=(100, 3)).astype(prec) 41 | 42 | expected_result = np.einsum('...x,...xy,...y->...', z1, A, z2) 43 | comp_result = metric_norm_matrix_3D_cython(A, z1, z2, ret_sqrt=False) 44 | assert np.allclose(expected_result, comp_result, rtol=rtol) #Single vectorized 45 | 46 | #Broadcasted 47 | A = np.random.normal(size=(100, 1, 3, 3)) 48 | A[..., 1, 0] = A[..., 0, 1] #Symmetrize 49 | A[..., 2, 0] = A[..., 0, 2] 50 | A[..., 2, 1] = A[..., 1, 2] 51 | 52 | z1 = np.random.normal(size=(100, 4, 3)) 53 | z2 = np.random.normal(size=(100, 4, 3)) 54 | 55 | expected_result = np.einsum('...x,...xy,...y->...', z1, A, z2) 56 | comp_result = metric_norm_matrix_3D_cython(A, z1, z2, ret_sqrt=False) 57 | assert np.allclose(expected_result, comp_result, rtol=rtol) 58 | 59 | 60 | -------------------------------------------------------------------------------- /tests/test_fim_solvers.py: -------------------------------------------------------------------------------- 1 | #import unittest 2 | import pytest 3 | #from . 4 | from fimpy.solver import create_fim_solver 5 | from fimpy.solver import FIMPY #Deprecated interface 6 | import numpy as np 7 | import os 8 | import scipy.io as sio 9 | import pickle 10 | 11 | try: 12 | import cupy as cp 13 | cupy_enabled = True 14 | #raise ImportError("Test") #For testing the CPU only version 15 | except ImportError as err: 16 | print("Cupy import failed. The tests will skip the cupy tests") 17 | cupy_enabled = False 18 | 19 | class TestFIMSolversInit(): 20 | 21 | @pytest.mark.parametrize('init_D', [True, False]) 22 | @pytest.mark.parametrize('dims', [1, 2, 3]) 23 | @pytest.mark.parametrize('precision', [np.float32, np.float64]) 24 | @pytest.mark.parametrize('use_active_list', [True, False]) 25 | @pytest.mark.parametrize('device', ['cpu', 'gpu']) 26 | def test_init(self, dims, init_D, precision, use_active_list, device): 27 | if device == 'gpu' and not cupy_enabled: 28 | pytest.skip(reason='Cupy could not be imported. GPU tests unavailable') 29 | 30 | points, elems = self.dummy_mesh(dims) 31 | D = None 32 | if init_D: 33 | D = np.eye(dims)[np.newaxis] 34 | 35 | fim_solver = create_fim_solver(points, elems, D, device=device, precision=precision, use_active_list=use_active_list) 36 | return fim_solver 37 | 38 | def dummy_mesh(self, dims): 39 | points = np.tile(np.linspace(0, 1, num=4)[:(dims+1)][:, np.newaxis], [1, dims]) 40 | elems = np.arange(points.shape[0])[np.newaxis] 41 | return points, elems 42 | 43 | @pytest.mark.parametrize('precision', [np.float32, np.float64]) 44 | def test_error_init(self, precision, device='cpu'): 45 | points = np.array([0.]) 46 | elems = np.array([0]) 47 | 48 | #Wrong dimensions 49 | with pytest.raises(Exception): 50 | create_fim_solver(points, elems) 51 | 52 | #Points not numeric 53 | points = np.array([[0, 0], [1, 0]]).astype(np.int32) 54 | elems = np.array([[0, 1]]) 55 | with pytest.raises(Exception): 56 | create_fim_solver(points, elems) 57 | 58 | #D and elems not matching 59 | points = np.array([[0., 0], [1, 0]]) 60 | elems = np.array([[0, 1]]) 61 | D = np.tile(np.eye(2)[np.newaxis], [2, 1]) 62 | with pytest.raises(Exception): 63 | create_fim_solver(points, elems, D) 64 | 65 | #elems references non-existant points 66 | points = np.array([[0., 0.], [1., 0.]]) 67 | elems = np.array([[0, 1, 2]]) 68 | with pytest.raises(Exception): 69 | create_fim_solver(points, elems, precision=precision, device=device) 70 | 71 | 72 | #points not contained in any element 73 | points = np.array([[0., 0.], [1., 0.], [0., 1.]]) 74 | elems = np.array([[0, 1]]) 75 | with pytest.raises(Exception): 76 | create_fim_solver(points, elems, precision=precision, device=device) 77 | 78 | #Unsupported element dimensions (Polygons and other elements) 79 | points = np.array([[0., 0.], [1., 0.], [0., 1.], [1., 1.], [-1., 0.]]) 80 | elems = np.array([[0, 1, 2, 3, 4]]) 81 | with pytest.raises(Exception): 82 | create_fim_solver(points, elems, precision=precision, device=device) 83 | 84 | 85 | @pytest.mark.skipif(not cupy_enabled, reason='Cupy could not be imported. GPU tests unavailable') 86 | @pytest.mark.parametrize('precision', [np.float32, np.float64]) 87 | def test_error_init_gpu(self, precision): 88 | self.test_error_init(precision, 'gpu') 89 | 90 | def test_error_init_wrong_device(self): 91 | with pytest.raises(AssertionError): 92 | self.test_init(3, True, np.float32, use_active_list=False, device='undefined_device') 93 | 94 | def test_error_deprecated(self): 95 | solver2 = FIMPY.create_fim_solver(*self.dummy_mesh(2)) 96 | solver = create_fim_solver(*self.dummy_mesh(2)) 97 | assert pickle.dumps(solver) == pickle.dumps(solver2) #Serialized objects should be exactly the same 98 | 99 | @pytest.mark.parametrize('init_D', [True, False]) 100 | @pytest.mark.parametrize('dims', [1, 2, 3]) 101 | @pytest.mark.parametrize('precision', [np.float32, np.float64]) 102 | @pytest.mark.parametrize('use_active_list', [True, False]) 103 | @pytest.mark.parametrize('device', ['cpu', 'gpu']) 104 | def test_solver_serializable(self, dims, init_D, precision, use_active_list, device): 105 | solver = self.test_init(dims, init_D, precision, use_active_list, device) 106 | solver_ser = pickle.dumps(solver) 107 | solver_unser = pickle.loads(solver_ser) 108 | assert np.all(solver.points_perm == solver_unser.points_perm) 109 | 110 | from generate_test_data import test_dims, test_elem_dims, test_resolutions, elem_fnames 111 | 112 | class TestFIMSolversComputations(): 113 | 114 | test_dir = os.path.join(__file__, "data") 115 | 116 | @pytest.mark.parametrize('precision', [np.float32, np.float64]) 117 | @pytest.mark.parametrize('dims', test_dims) 118 | @pytest.mark.parametrize('elem_dims', test_elem_dims) 119 | @pytest.mark.parametrize('use_active_list', [True, False]) 120 | def test_comp(self, dims, elem_dims, precision, use_active_list, device='cpu'): 121 | if (dims < elem_dims - 1): 122 | return 123 | 124 | np.random.seed(0) 125 | test_data_dir = os.path.join(os.path.dirname(__file__), "data") 126 | for resolution in test_resolutions[elem_dims-1]: 127 | fname = "elem_dims_%d_dims_%d_resolution_%d_%s.mat" % (elem_dims, dims, resolution, elem_fnames[elem_dims]) 128 | fname = os.path.join(test_data_dir, fname) 129 | assert(os.path.isfile(fname)) #If you fail here, the generation of test data using generate_test_data.py failed or was not performed 130 | 131 | data = sio.loadmat(fname) 132 | points, elems, D = data["points"], data["elems"], data["D"] 133 | nr_points = points.shape[0] 134 | 135 | #D specified at initialization 136 | solver = create_fim_solver(points, elems, D, precision=precision, device=device, use_active_list=use_active_list) 137 | x0 = np.array([np.random.choice(nr_points)]) 138 | x0_vals = np.array([0.]) 139 | phi1 = solver.comp_fim(x0, x0_vals) 140 | assert(phi1.dtype == precision) 141 | assert(phi1.ndim == 1) 142 | assert(phi1.size == nr_points) 143 | assert(np.all(~np.isnan(phi1))) 144 | 145 | #D specified at computation 146 | solver = create_fim_solver(points, elems, precision=precision, device=device, use_active_list=use_active_list) 147 | #Fails without specifying D 148 | with pytest.raises(Exception): 149 | solver.comp_fim(x0, x0_vals) 150 | 151 | phi2 = solver.comp_fim(x0, x0_vals, D) 152 | assert(phi2.dtype == precision) 153 | assert(phi2.ndim == 1) 154 | assert(phi2.size == nr_points) 155 | assert(np.all(~np.isnan(phi2))) 156 | 157 | #Results should be the same 158 | assert(np.allclose(phi1, phi2)) 159 | 160 | 161 | 162 | 163 | @pytest.mark.skipif(not cupy_enabled, reason='Cupy could not be imported. GPU tests unavailable') 164 | @pytest.mark.parametrize('precision', [np.float32, np.float64]) 165 | @pytest.mark.parametrize('dims', test_dims) 166 | @pytest.mark.parametrize('elem_dims', test_elem_dims) 167 | @pytest.mark.parametrize('use_active_list', [True, False]) 168 | def test_comp_gpu(self, dims, elem_dims, precision, use_active_list): 169 | self.test_comp(dims, elem_dims, precision, use_active_list=use_active_list, device='gpu') 170 | --------------------------------------------------------------------------------