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package-ecosystem: "pip" # See documentation for possible values directory: "/" # Location of package manifests schedule: interval: "weekly" SALib-SALib-d6e51b1/.github/workflows/000077500000000000000000000000001525347100600174055ustar00rootroot00000000000000SALib-SALib-d6e51b1/.github/workflows/lint.yml000066400000000000000000000005741525347100600211040ustar00rootroot00000000000000name: Linting on: pull_request: push: branches: [main] concurrency: group: ${{ github.workflow }}-${{ github.head_ref || github.run_id }} cancel-in-progress: true jobs: linter: runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - uses: actions/setup-python@v5 with: python-version: "3.12" - uses: pre-commit/action@v3.0.1 SALib-SALib-d6e51b1/.github/workflows/release.yaml000066400000000000000000000011041525347100600217050ustar00rootroot00000000000000name: Release on: push: tags: - 'v*.*.*' jobs: release: runs-on: ubuntu-latest steps: - uses: actions/checkout@v3 - name: Setup Python 3.10 uses: actions/setup-python@v4 with: python-version: '3.10' architecture: 'x64' - name: Install hatch run: pip install hatch - name: Build run: hatch build - name: Publish to PyPI env: HATCH_INDEX_USER: __token__ HATCH_INDEX_AUTH: ${{ secrets.PYPI_API_TOKEN }} run: | hatch publish -y SALib-SALib-d6e51b1/.github/workflows/test.yml000066400000000000000000000022261525347100600211110ustar00rootroot00000000000000name: Test on: push: branches: [ main ] pull_request: branches: [ main ] concurrency: group: ${{ github.workflow }}-${{ github.head_ref || github.run_id }} cancel-in-progress: true jobs: pytest: runs-on: ubuntu-latest strategy: matrix: python-version: ['3.10', '3.12', '3.14'] defaults: run: shell: bash -l {0} steps: - uses: actions/checkout@v3 - name: Set up micromamba uses: mamba-org/setup-micromamba@v2 with: environment-name: SALib python-version: ${{ matrix.python-version }} channels: conda-forge cache-environment: true - name: Update Conda Environment run: | micromamba env update -n SALib -f environment.yml - name: Install package run: | pip install .[test] - name: Test if: matrix.python-version != '3.12' run: | pytest - name: Test with coverage and uploads if: matrix.python-version == '3.12' run: | python -m pip install coveralls pytest --cov SALib --cov-report html --verbose coveralls SALib-SALib-d6e51b1/.gitignore000066400000000000000000000010701525347100600157760ustar00rootroot00000000000000# Temporary and binary files *~ *.py[cod] *.so *.cfg !setup.cfg *.orig *.log *.pot __pycache__/* __pycache__ .cache/* .*.swp */.ipynb_checkpoints/* .DS_Store # Project files .ropeproject .project .pydevproject .settings .idea .vscode *.code-workspace # Package files *.egg *.eggs/ .installed.cfg *.egg-info # Unittest and coverage htmlcov/* .coverage .tox junit.xml coverage.xml .mypy_cache .pytest_cache # Build and docs folder/files build/* dist/* sdist/* docs/api/* docs/_build/* cover/* MANIFEST playground/ docs/html/ tests/data/model_output.txt uv.lock SALib-SALib-d6e51b1/.pre-commit-config.yaml000066400000000000000000000012301525347100600202650ustar00rootroot00000000000000repos: - repo: https://github.com/pre-commit/pre-commit-hooks rev: v4.5.0 hooks: - id: trailing-whitespace - id: check-added-large-files - id: check-ast - id: fix-byte-order-marker - id: check-case-conflict - id: check-docstring-first - id: check-merge-conflict - id: detect-private-key - id: end-of-file-fixer - repo: https://github.com/psf/black rev: 24.2.0 hooks: - id: black exclude: "src/SALib/sample/directions.py" - repo: https://github.com/astral-sh/ruff-pre-commit # Ruff version. rev: v0.3.0 hooks: # Run the linter. - id: ruff args: [ --fix ] SALib-SALib-d6e51b1/.readthedocs.yml000066400000000000000000000010371525347100600170770ustar00rootroot00000000000000# Read the Docs configuration file # See https://docs.readthedocs.io/en/stable/config-file/v2.html for details # Required version: 2 # Build documentation in the docs/ directory with Sphinx sphinx: configuration: docs/conf.py # Build documentation with MkDocs #mkdocs: # configuration: mkdocs.yml # Optionally build your docs in additional formats such as PDF formats: - pdf build: os: "ubuntu-22.04" tools: python: "mambaforge-4.10" python: install: - method: pip path: . conda: environment: environment.yml SALib-SALib-d6e51b1/.zenodo.json000066400000000000000000000042741525347100600162660ustar00rootroot00000000000000{ "license": "MIT", "upload_type": "software", "creators": [ { "affiliation": "UC Davis", "name": "Jon Herman", "orcid": "0000-0002-4081-3175" }, { "affiliation": "KTH Royal Institute of Technology", "name": "Will Usher", "orcid": "0000-0001-9367-1791" }, { "name": "Takuya Iwanaga", "orcid": "0000-0001-8173-0870" }, { "affiliation": "Universit\u00e9 d'Orl\u00e9ans", "name": "Lucas Teixeira" }, { "affiliation": "Universit\u00e9 Savoie Mont-Blanc", "name": "Nicolas CELLIER", "orcid": "0000-0002-3759-3546" }, { "name": "Calvin Whealton", "orcid": "0000-0001-9900-0542" }, { "affiliation": "", "name": "David Hadka" }, { "name": "xantares" }, { "name": "bernardoct" }, { "name": "Fernando Rios" }, { "affiliation": "Paul Scherrer Institute", "name": "Chris Mutel", "orcid": "0000-0002-7898-9862" }, { "affiliation": "Cederstrand IT ApS", "name": "Erik Cederstrand", "orcid": "0000-0002-4512-0933" }, { "name": "Tobias Andersen", "affiliation": "Aarhus University", "orcid": "0000-0003-1257-2201" }, { "affiliation": "Deltares", "name": "Joeri van Engelen", "orcid": "0000-0002-7628-2548" }, { "name": "ANtlord" }, { "name": "Hania Kranas" }, { "affiliation": "@PumasAI", "name": "Vaibhav Kumar Dixit" }, { "name": "Bernhard Steubing", "orcid": "0000-0002-1307-6376" } ], "access_right": "open", "related_identifiers": [ { "scheme": "doi", "identifier": "10.5281/zenodo.598306", "relation": "isVersionOf" } ] } SALib-SALib-d6e51b1/AUTHORS.rst000066400000000000000000000003471525347100600156730ustar00rootroot00000000000000========== Developers ========== * Jon Herman * Will Usher * Chris Mutel * Bernardo Trindade * Dave Hadka * Matt Woodruff * Fernando Rios * Dan Hyams * xantares * Abdullah Sahin * Takuya Iwanaga * Pamphile T. Roy SALib-SALib-d6e51b1/CHANGELOG.md000066400000000000000000000147211525347100600156260ustar00rootroot00000000000000# Changelog This changelog follows the format defined at: https://keepachangelog.com/en/1.0.0/ ## [1.4.5] - Adjusted Saltelli sampling to follow recommendation of Owen (2020) (http://arxiv.org/abs/2008.08051; https://github.com/scipy/scipy/pull/10844#issuecomment-672186615) - Initial support for parallel analysis - Updated Sobol' G-function analytic results (PR #464, Issues #335 #461) - Sobol' analysis: Optional storage of intermediate resample results to allow analysis of variation (PR #462) ### Documentation - Updated Salteli sampling examples to use powers of 2 following recommendations - Added `citations.cff` file ### Development - Upgrade PyScaffold to v4 - Replaced recommonmark with MyST (PR #466) ## [1.4.0] Shortlist of changes since v1.3.x ### Added - High Dimensional Model Representation (HDMR) method (PR #275) - PAWN method (PR #415) - Support for sampling/analysis method chaining (PR #339) - Support for truncated normal distribution (PR #383) - Confidence Interval estimation for FAST-based methods (PR #375) - Initial support for parallel model evaluation ### Documentation - Defining non-uniform sampling now explicitly documented - Many general documentation improvements - Added FAQ ### Development - Generalized support for non-uniform sampling methods (PR #346) ## [1.3.13] ### Added - Many documentation improvements - Explicitly mention extended FAST in documentation - Saltelli sampling: Warnings displayed when selected samples do not meet requirements (PR #416). - Group sampling and analysis enabled for Sobol' and morris - Enhanced DataFrame support for groups ### Bug Fixes: - Conversion to DataFrame when groups are defined with Sobol' results (PR #413 and Issue #387) ## [1.3.0] ### Added - Various minor performance enhancements (PR #253 #264) - Added some visualisation methods (PR #259) - Tidying up of the Command Line Interfance, and num samples (PR #260 #291) - Improved efficiency of summing distances in local optimization (PR #246) - Revamped fast method for consistency (PR #239) - Updated Sobol-G function to modified G-function (#269) ### Bug Fixes: - Method of morris didn't adjust with levels above 4 (PR #252) - Add missing seed option for morris sampling - Handle singular value matrix cases (PR #251) - Fixed typo (#205) - Updated import of scipy comb function (PR #243) ### Documentation: - Update documentation for Morris and DSGM methods (#261 #266) ### Development Features: - Updated PyScaffold to version 3.2.2 (#267) - Updated Travis and package config (#285) ## [1.1.0] ### New Features: - Refactored Method of Morris so the Ruano et al. local approach is default ### Bug Fixes: - Inputs to morris.analyze are provided as floats - Removed calls to standard random library as inconsistent between Python 2 & 3 - First row in Sobol sequences should be zero, not empty ### Documentation: - Added a Code of Conduct - Added DAETools, BCMD and others to citations - thanks for using SALib! - Removed misleading keyword arguments in docs and readme examples - Updated documentation for Method of Morris following refactor - Improved existing documentation where lacking e.g. for fractional factorial method ### Development Features: - Implemented automatic deployment to PyPi - Fixed a bug preventing automatic deployment to PyPi upon tagging a branch - Removed postgres from travis config ## [1.0.0] Release of our stable version of SALIB to coincide with an submission to JOSS: - Added a paper for submission to the Journal of Open-source Software - Updated back-end for documentation on read-the-docs - Updated the back-end for version introspection using PyScaffold, rather than versioneer - Updated the Travis-CI scripts - Moved the tests out of the SALib package and migrated to using pytest ## [0.7.1] Improvements to Morris sampling and Sobol groups/distributions - Adds improved sampling for the Morris method (thanks to @JoerivanEngelen) and group sampling/analysis for the Sobol method (thanks to @calvinwhealton). - @calvinwhealton has also added non-uniform distributions to the Sobol sampling. This will be a baseline for adding this to the other methods in the future. - Also includes several minor bug fixes. ## [0.7.0] New documentation, doc strings and installation requirements - @dhadka has kindly contributed a wealth of documentation to the project, including doc strings in every module - no longer test for numpy <1.8.0 and matplotlib < 1.4.3, and these requirements are implemented in a new setup script. ## [0.6.3] Parallel option for Sobol method - New option to run analyze.sobol function in parallel using multiprocessing ## [0.6.2] This release does not contain any new functionality, but SALib now is citable using a Digital Object Identifier (DOI), which can be found in the readme. Some minor updates are included: - morris: sigma has been removed from the grouped-morris results and plots, replaced by mu_star_conf - a bootstrapped confidence interval. Mu_star_conf is not equivalent to sigma when used in the non-grouped method of morris, but its all we have when using groups. - some minor updates to the tests in the plotting module ## [0.6.0] - Set up to include and test plotting functions - Specific plotting functions for Morris - Fractional Factorial SA from Saltelli et al. - Repo transferred to SALib organization, update setup and URLs - Small bugfixes ## [0.5.0] - Vectorized bootstrap calculations for Morris and Sobol - Optional trajectory optimization with Gurobi, and tests for it - Several minor bugfixes - Starting with v0.5, SALib is released under the MIT license. ## [0.4.0] - Better Python API without requiring file read/write to the OS. Consistent functional API to sampling methods so that they return numpy matrices. Analysis methods now accept numpy matrices instead of data file names. This does not change the CLI at all, but makes it much easier to use from native Python. - Also expanded tests for regression and the Sobol method. ## [0.3.0] Improvements to Morris sampling and analysis methods, some bugfixes to make consistent with previous versions of the methods. ## [0.2.0] Improvements to Morris sampling methods (support for group sampling, and optimized trajectories). Much better test coverage, and fixed Python 3 compatibility. ## [0.1.0] First numbered release. Contains reasonably well-tested versions of the Sobol, Morris, and FAST methods. Also contains newer additions of DGSM and delta methods which are not as well-tested yet. Contains setup.py for installation. SALib-SALib-d6e51b1/CITATION.cff000066400000000000000000000021131525347100600156770ustar00rootroot00000000000000cff-version: 1.2.0 message: "If you use this software, please cite it as below." authors: - family-names: "Iwanaga" given-names: "Takuya" orcid: "0000-0001-8173-0870" - family-names: "Usher" given-names: "Will" orcid: "0000-0001-9367-1791" - family-names: "Herman" given-names: "Jon" orcid: "0000-0002-4081-3175" title: "SALib: An open-source Python library for sensitivity analysis" version: 1.4.6.1 doi: 10.21105/joss.00097 date-released: 2022-05-01 url: "https://github.com/SALib/SALib" preferred-citation: type: article authors: - family-names: "Iwanaga" given-names: "Takuya" orcid: "0000-0001-8173-0870" - family-names: "Usher" given-names: "Will" orcid: "0000-0001-9367-1791" - family-names: "Herman" given-names: "Jon" orcid: "0000-0002-4081-3175" doi: "10.18174/sesmo.18155" journal: "Socio-Environmental Systems Modelling" month: 5 start: 1 # First page number end: 15 # Last page number title: "Toward SALib 2.0: Advancing the accessibility and interpretability of global sensitivity analyses" issue: 1 volume: 4 year: 2022 SALib-SALib-d6e51b1/CITATIONS.rst000066400000000000000000000057711525347100600161110ustar00rootroot00000000000000How to cite SAlib ----------------- If you would like to use our software, please cite it using the following: Iwanaga, T., Usher, W., & Herman, J. (2022). Toward SALib 2.0: Advancing the accessibility and interpretability of global sensitivity analyses. Socio-Environmental Systems Modelling, 4, 18155. doi:10.18174/sesmo.18155 Herman, J. and Usher, W. (2017) SALib: An open-source Python library for sensitivity analysis. Journal of Open Source Software, 2(9). doi:10.21105/joss.00097 If you use BibTeX, cite using the following entries:: @article{Iwanaga2022, title = {Toward {SALib} 2.0: {Advancing} the accessibility and interpretability of global sensitivity analyses}, volume = {4}, url = {https://sesmo.org/article/view/18155}, doi = {10.18174/sesmo.18155}, journal = {Socio-Environmental Systems Modelling}, author = {Iwanaga, Takuya and Usher, William and Herman, Jonathan}, month = may, year = {2022}, pages = {18155}, } @article{Herman2017, doi = {10.21105/joss.00097}, url = {https://doi.org/10.21105/joss.00097}, year = {2017}, month = {jan}, publisher = {The Open Journal}, volume = {2}, number = {9}, author = {Jon Herman and Will Usher}, title = {{SALib}: An open-source Python library for Sensitivity Analysis}, journal = {The Journal of Open Source Software} } Projects that use SALib ----------------------- Many projects now use the Global Sensitivity Analysis features provided by SALib. Here is a selection: Software ~~~~~~~~ * `The City Energy Analyst `_ * `pynoddy `_ * `savvy `_ * `rhodium `_ * `pySur `_ * `EMA workbench `_ * `Brain/Circulation Model Developer `_ * `DAE Tools `_ * `agentpy `_ * `uncertainpy `_ * `CLIMADA `_ * `parsac `_ Blogs ~~~~~ * `Sensitivity Analysis in Python `_ * `Sensitivity Analysis with SALib `_ * `Running Sobol using SALib `_ * `Extensions of SALib for more complex sensitivity analyses `_ Videos ~~~~~~ * `PyData Presentation on SALib `_ If you would like to be added to this list, please submit a pull request, or create an issue. Many thanks for using SALib. SALib-SALib-d6e51b1/CODE_OF_CONDUCT.md000066400000000000000000000062361525347100600166160ustar00rootroot00000000000000# Contributor Covenant Code of Conduct ## Our Pledge In the interest of fostering an open and welcoming environment, we as contributors and maintainers pledge to making participation in our project and our community a harassment-free experience for everyone, regardless of age, body size, disability, ethnicity, gender identity and expression, level of experience, nationality, personal appearance, race, religion, or sexual identity and orientation. ## Our Standards Examples of behavior that contributes to creating a positive environment include: * Using welcoming and inclusive language * Being respectful of differing viewpoints and experiences * Gracefully accepting constructive criticism * Focusing on what is best for the community * Showing empathy towards other community members Examples of unacceptable behavior by participants include: * The use of sexualized language or imagery and unwelcome sexual attention or advances * Trolling, insulting/derogatory comments, and personal or political attacks * Public or private harassment * Publishing others' private information, such as a physical or electronic address, without explicit permission * Other conduct which could reasonably be considered inappropriate in a professional setting ## Our Responsibilities Project maintainers are responsible for clarifying the standards of acceptable behavior and are expected to take appropriate and fair corrective action in response to any instances of unacceptable behavior. Project maintainers have the right and responsibility to remove, edit, or reject comments, commits, code, wiki edits, issues, and other contributions that are not aligned to this Code of Conduct, or to ban temporarily or permanently any contributor for other behaviors that they deem inappropriate, threatening, offensive, or harmful. ## Scope This Code of Conduct applies both within project spaces and in public spaces when an individual is representing the project or its community. Examples of representing a project or community include using an official project e-mail address, posting via an official social media account, or acting as an appointed representative at an online or offline event. Representation of a project may be further defined and clarified by project maintainers. ## Enforcement Instances of abusive, harassing, or otherwise unacceptable behavior may be reported by contacting the project team at wusher{THATSIGN}kth.se. All complaints will be reviewed and investigated and will result in a response that is deemed necessary and appropriate to the circumstances. The project team is obligated to maintain confidentiality with regard to the reporter of an incident. Further details of specific enforcement policies may be posted separately. Project maintainers who do not follow or enforce the Code of Conduct in good faith may face temporary or permanent repercussions as determined by other members of the project's leadership. ## Attribution This Code of Conduct is adapted from the [Contributor Covenant][homepage], version 1.4, available at [http://contributor-covenant.org/version/1/4][version] [homepage]: http://contributor-covenant.org [version]: http://contributor-covenant.org/version/1/4/ SALib-SALib-d6e51b1/CONTRIBUTING.md000066400000000000000000000214051525347100600162430ustar00rootroot00000000000000# Contributing Admins: [Will Usher](https://github.com/willu47) and [Jon Herman](https://github.com/jdherman) Thanks to all those who have [contributed so far](https://github.com/SALib/SALib/graphs/contributors)! ## Asking Questions, Reporting Bugs We use GitHub issues to keep track of bugs and to answer questions about the use of the library. For bugs, [create a new issue](https://github.com/SALib/SALib/issues/new) on GitHub. Use this to describe the nature of the bug and the conditions needed to recreate it, including operating system and Python version. If you have a question on interpretation of results, then we may be able to help. We cannot answer specific implementation questions (such as 'how do I run my model with SALib?') You can format your questions using GitHub Markdown, which makes it easy to [paste in short snippets of code](https://help.github.com/articles/creating-and-highlighting-code-blocks/). If including a very long Python error traceback, please use a GitHub [gist](https://gist.github.com/). ## Contributing Code To contribute new code, submit a pull request. There are two instances in which you may want to contribute code: to fix a bug, or to add a new feature, such as a new sensitivity analysis method. ### Making a development environment Note: We **strongly** recommend using a virtual environment setup, such as `venv` or `conda`. First, fork a copy of the main SALib repository in GitHub onto your own account and then create your local repository via: ```sh git clone git@github.com:YOURUSERNAME/SALib.git cd SALib ``` Next, set up your development environment. With `conda` installed (through [Miniforge or Mambaforge](https://github.com/conda-forge/miniforge), [Miniconda](https://docs.conda.io/en/latest/miniconda.html) or [Anaconda](https://www.anaconda.com/products/individual)), execute the following commands at the terminal from the base directory of your [SALib](https://github.com/SALib/SALib) clone: ```sh # Create an environment with all development dependencies conda env create -f environment.yml # works with `mamba` too # Activate the environment conda activate SALib ``` Finally, you can install SALib in editable mode in your environment: ```sh pip install -e . ``` ### Fixing a Bug First, create a new issue on GitHub with the label `bug`. Use this to describe the nature of the bug and the conditions needed to recreate it. Then, please create a new branch with the name `bug_xxx` where xxx is the number of the issue. If possible, write a test which reproduces the bug. The tests are stored in the `SALib/tests/` folder, and are run using `pytest` from the root folder of the library. You can run the tests with the command `pytest` from the root project directory. Individual tests can be run with by specifying a file, or file and test function. For example: ```bash $ pytest # run all tests $ pytest tests/test_file.py # run tests within a specific file $ pytest tests/test_file.py::specific_function # run a specific test ``` Then, fix the bug in the code so that the test passes. Submit a pull request with a descriptive title and reference the issue in the text. Once a pull request is submitted, the tests will run on Travis CI. If these tests pass, we will review and merge in your changes. ### Adding a new method Methods in SALib follow a decoupled sample/analysis workflow. In other words, the generation of parameter samples and the calculation of sensitivity indices can be performed in two separate steps. This is because many users have models in languages other than Python, so sending data to/from the model is left to the user. All methods should support a command-line interface on top of the Python functions. To add a new method, create an issue on GitHub with the label `add_method`, if one does not already exist. Please describe the method, and link to the peer reviewed article in which the method is described. The master branch should only contain published methods. First check the current [open issues with this label](https://github.com/SALib/SALib/labels/add_method) for inspiration or to see if someone is already working on a certain method. We use GitHub issues to track ideas for and [enhancements](https://github.com/SALib/SALib/labels/enhancement). If you are looking to contribute new methods to the library, check the labels for inspiration or to ensure you are not duplicating another's work. Then, create a new branch with a useful name, such as `new_method_method_name`. Methods should consist of: * A sampling module (a `method_name.py` file in `SALib.sample`). This will contain, among other things, a function `sample(problem, ...)` that accepts a problem dictionary and returns a numpy array of samples, one column for each parameter. See [SALib.sample.saltelli](https://github.com/SALib/SALib/blob/main/SALib/sample/saltelli.py) for an example. * An analysis module (a `method_name.py` file in `SALib.analyze`). This will contain a function analyze(problem, ...) that returns a dictionary of sensitivity indices. See [SALib.analyze.sobol](https://github.com/SALib/SALib/blob/main/SALib/analyze/sobol.py) for an example. * An example shell script and python file in the `examples` folder, ideally using a test function included in SALib such as the Ishigami or Sobol-G functions. * Docstrings for the `sample` and `analyze` functions that include citations. Please add an entry to `docs/index.rst` to add your method documentation to the concise API reference. * All contributed methods should also provide functions to support their use through the command line interface (CLI). These are `cli_parse()` and `cli_action()` to parse command line options and to run the sampling and analysis respectively. See the implementations in [SALib.analyze.delta](https://github.com/SALib/SALib/blob/consolidate-cli/SALib/analyze/delta.py) for an example. * Tests in the `tests` folder. We're using Travis CI and Coveralls. Ideally, every new function will have one or more corresponding tests to check that errors are raised for invalid inputs, and that functions return matrices of the proper sizes. (For example [see here](https://github.com/SALib/SALib/blob/main/tests/test_sobol.py). But at a minimum, please include a regression test for the Ishigami function, in the same format as all of the other methods [see here](https://github.com/SALib/SALib/blob/main/tests/test_regression.py). This will at least ensure that future updates don't break your code! Finally, submit a pull request. Either @willu47 or @jdherman will review the pull request and merge in your changes. ### Other Enhancements Contributions not related to new methods are also welcome. These might include new test functions (see [SALib.test_functions](https://github.com/SALib/SALib/tree/main/SALib/test_functions) for how these are set up), or other code that is general across some or all of the methods. This general code is currently included in [SALib.util.\_\_init\_\_.py](https://github.com/SALib/SALib/blob/main/SALib/util/__init__.py). ### Other Development Comments Most of the sampling techniques make heavy use of pseudo-random number generators. We use primarily `numpy.random` as the python standard library `random` library is inconsistent across Python 2 and 3. When writing tests for methods which use these random number generators, set the seeds using `numpy.random.seed(SEED)` where `SEED` is a fixed integer. This will ensure that your tests are repeatable. ### Notes about scope * SALib contains a few basic types of plots, especially for the Morris method. Indicative results can be made by calling the [`.plot()` method](https://salib.readthedocs.io/en/main/basics.html#basic-plotting) * However, we generally assume that plot types and styles are left to the user, as these are often application-specific. Users interested in more complex plot types should check out the [savvy](https://github.com/houghb/savvy) library, which is built on top of SALib. Thanks again! ## Making a release Following is the process that the development team follows in order to make a release: 1. Document overview of changes since last release in `CHANGELOG.md` 2. Build locally using `hatch build`, and verify the content of the artifacts 3. Tag release with version number and push to SALib repo 4. Check that release has been deployed to PyPI 5. Check documentation is built and deployed to readthedocs (http://salib.readthedocs.org) 6. Check that auto-generated PR is auto-merged on the conda-forge feedstock repo (conda-forge/salib-feedstock) 7. Update development roadmap on GitHub ## Building a local copy of the documentation Assuming the current location is the project root (the `SALib` directory): ```bash $ conda install pydata-sphinx-theme myst-parser -c conda-forge $ sphinx-build -b html docs docs/html ``` A copy of the documentation will be in the `docs/html` directory. Open `index.html` to view it. SALib-SALib-d6e51b1/FAQ.md000066400000000000000000000023511525347100600147420ustar00rootroot00000000000000# Frequently Asked Questions ## Installation ### I get this error when installing SALib 1.3 with Python 2.7 SALib 1.3 onwards does not support Python 2.7 ## Usage ### I've already got results from my Monte Carlo simulation - which technique can I use? DMIM, RBD-FAST, PAWN and HDMR methods are sampling scheme independent. ### Can you help me with implementing my sensitivity analysis? Check out [the examples here](https://github.com/SALib/SALib/tree/develop/examples) ### The example(s) use the Ishigami function. How do I use SALib with my own model? Two options: 1. Use SALib to generate the samples, run the model yourself, then use the results with SALib. 2. Wrap the model with a Python function. The only requirement is that the function should accept a numpy array of sample values. This is the approach most users will take. ### How do I get the sensitivity results? Call the `.to_df()` method if you would like Pandas DataFrames. If using the method chaining approach, see [the example here](https://github.com/SALib/SALib/tree/develop/examples/Problem) ### How can I plot my results? SALib provides some basic plotting functionality. See [the example here](https://github.com/SALib/SALib/tree/develop/examples/plotting). SALib-SALib-d6e51b1/LICENSE.md000066400000000000000000000021231525347100600154120ustar00rootroot00000000000000The MIT License (MIT) Copyright (c) 2013-2017 Jon Herman, Will Usher, and others. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. SALib-SALib-d6e51b1/README-advanced.md000066400000000000000000000107031525347100600170330ustar00rootroot00000000000000## SALib: Advanced options ### Parameter files In the parameter file, lines beginning with `#` will be treated as comments and ignored. ``` # name lower_bound upper_bound P1 0.0 1.0 P2 0.0 5.0 P3 0.0 5.0 ...etc. ``` Parameter files can also be comma-delimited if your parameter names or group names contain spaces. This should be detected automatically. ### Command-line interface **Generate samples** (the `-p` flag is the parameter file) ``` salib sample saltelli \ -n 1024 \ -p ./src/SALib/test_functions/params/Ishigami.txt \ -o model_input.txt ``` **Run the model** this will usually be a user-defined model, maybe even in another language. Just save the outputs. **Run the analysis** ``` salib analyze sobol \ -p ./src/SALib/test_functions/params/Ishigami.txt \ -Y model_output.txt \ -c 0 ``` This will print indices and confidence intervals to the command line. You can redirect to a file using the `>` operator. ### Parallel indices calculation (Sobol method only) ```python Si = sobol.analyze(problem, Y, calc_second_order=True, conf_level=0.95, print_to_console=False, parallel=True, n_processors=4) ``` Other methods include Morris, FAST, Delta-MIM, and DGSM. For an explanation of all command line options for each method, [see the examples here](https://github.com/SALib/SALib/tree/main/examples). ### Groups of variables (Sobol and Morris methods only) It is sometimes useful to perform sensitivity analysis on groups of input variables to reduce the number of model runs required, when variables belong to the same component of a model, or there is some reason to believe that they should behave similarly. Groups can be specified in two ways for the Sobol and Morris methods. First, as a fourth column in the parameter file: ``` # name lower_bound upper_bound group_name P1 0.0 1.0 Group_1 P2 0.0 5.0 Group_2 P3 0.0 5.0 Group_2 ...etc. ``` Or in the `problem` dictionary: ```python problem = { 'groups': ['Group_1', 'Group_2', 'Group_2'], 'names': ['x1', 'x2', 'x3'], 'num_vars': 3, 'bounds': [[-3.14, 3.14], [-3.14, 3.14], [-3.14, 3.14]] } ``` `groups` is a list of strings specifying the group name to which each variable belongs. The rest of the code stays the same: ```python param_values = saltelli.sample(problem, 1024) Y = Ishigami.evaluate(param_values) Si = sobol.analyze(problem, Y, print_to_console=True) ``` But the output is printed by group: ``` Group S1 S1_conf ST ST_conf Group_1 0.307834 0.066424 0.559577 0.082978 Group_2 0.444052 0.080255 0.667258 0.060871 Group_1 Group_2 S2 S2_conf Group_1 Group_2 0.242964 0.124229 ``` The output can then be converted to a Pandas DataFrame for further analysis. ```python total_Si, first_Si, second_Si = Si.to_df() ``` ### Generating alternate distributions In the [Quick Start](https://github.com/SALib/SALib/tree/main/README.rst) we generate a uniform sample of parameter space. ```python from SALib.sample import saltelli from SALib.analyze import sobol from SALib.test_functions import Ishigami import numpy as np problem = { 'num_vars': 3, 'names': ['x1', 'x2', 'x3'], 'bounds': [[-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359]] } param_values = saltelli.sample(problem, 1024) ``` SALib is also capable of generating alternate sampling distributions by specifying a `dist` entry in the `problem` specification. As implied in the basic example, a uniform distribution is the default. When an entry for `dist` is not 'unif', the `bounds` entry does not indicate parameter bounds but sample-specific metadata. `bounds` definitions for available distributions: * unif: uniform distribution e.g. :code:`[-np.pi, np.pi]` defines the lower and upper bounds * triang: triangular with lower and upper bounds, as well as location of peak The location of peak is in percentage of width e.g. :code:`[1.0, 3.0, 0.5]` indicates 1.0 to 3.0 with a peak at 2.0 A soon-to-be deprecated two-value format assumes the lower bound to be 0 e.g. :code:`[3, 0.5]` assumes 0 to 3, with a peak at 1.5 * norm: normal distribution with mean and standard deviation * lognorm: lognormal with ln-space mean and standard deviation An example specification is shown below: ```python problem = { 'names': ['x1', 'x2', 'x3'], 'num_vars': 3, 'bounds': [[-np.pi, np.pi], [1.0, 0.2], [3, 0.5]], 'groups': ['G1', 'G2', 'G1'], 'dists': ['unif', 'lognorm', 'triang'] } ``` SALib-SALib-d6e51b1/README.rst000066400000000000000000000233101525347100600154760ustar00rootroot00000000000000.. image:: https://raw.githubusercontent.com/SALib/SALib/main/docs/assets/logo.png :width: 232px :align: center Sensitivity Analysis Library (SALib) ==================================== Python implementations of commonly used sensitivity analysis methods. Useful in systems modeling to calculate the effects of model inputs or exogenous factors on outputs of interest. **Documentation:** `ReadTheDocs `__ **Requirements:** `NumPy `__, `SciPy `__, `matplotlib `__, `pandas `__, Python 3 (from SALib v1.2 onwards SALib does not officially support Python 2) **Installation:** ``pip install SALib`` or ``pip install .`` or ``conda install SALib`` **Build Status:** |Build Status| **Test Coverage:** |Coverage Status| Included methods ---------------- * Sobol Sensitivity Analysis (`Sobol 2001 `__, `Saltelli 2002 `__, `Saltelli et al. 2010 `__) * Method of Morris, including groups and optimal trajectories (`Morris 1991 `__, `Ruano et al. 2012 `__) * Radial OAT (`Campolongo et al. 2007 `__, `Campolongo et al. 2011 `__) * extended Fourier Amplitude Sensitivity Test (eFAST) (`Cukier et al. 1973 `__, `Saltelli et al. 1999 `__, `Pujol (2006) in Iooss et al., (2021) `__) * Random Balance Designs - Fourier Amplitude Sensitivity Test (RBD-FAST) (`Tarantola et al. 2006 `__, `Plischke 2010 `__, `Tissot et al. 2012 `__) * Delta Moment-Independent Measure (`Borgonovo 2007 `__, `Plischke et al. 2013 `__) * Derivative-based Global Sensitivity Measure (DGSM) (`Sobol and Kucherenko 2009 `__) * Shapley Effects (`Goda 2021 `__) * Fractional Factorial Sensitivity Analysis (`Saltelli et al. 2008 `__) * High-Dimensional Model Representation (HDMR) (`Rabitz et al. 1999 `__, `Li et al. 2010 `__) * PAWN (`Pianosi and Wagener 2018 `__, `Pianosi and Wagener 2015 `__) * Regional Sensitivity Analysis (based on `Hornberger and Spear, 1981 `__, `Saltelli et al. 2008 `__, `Pianosi et al., 2016 `__) **Contributing:** see `here `__ Quick Start ----------- Procedural approach ~~~~~~~~~~~~~~~~~~~ .. code:: python from SALib.sample import saltelli from SALib.analyze import sobol from SALib.test_functions import Ishigami import numpy as np problem = { 'num_vars': 3, 'names': ['x1', 'x2', 'x3'], 'bounds': [[-np.pi, np.pi]]*3 } # Generate samples param_values = saltelli.sample(problem, 1024) # Run model (example) Y = Ishigami.evaluate(param_values) # Perform analysis Si = sobol.analyze(problem, Y, print_to_console=True) # Returns a dictionary with keys 'S1', 'S1_conf', 'ST', and 'ST_conf' # (first and total-order indices with bootstrap confidence intervals) It's also possible to specify the parameter bounds in a file with 3 columns: :: # name lower_bound upper_bound P1 0.0 1.0 P2 0.0 5.0 ...etc. Then the ``problem`` dictionary above can be created from the ``read_param_file`` function: .. code:: python from SALib.util import read_param_file problem = read_param_file('/path/to/file.txt') # ... same as above Lots of other options are included for parameter files, as well as a command-line interface. See the `advanced section in the documentation `__. Method chaining approach ~~~~~~~~~~~~~~~~~~~~~~~~ Chaining calls is supported from SALib v1.4 .. code:: python from SALib import ProblemSpec from SALib.test_functions import Ishigami import numpy as np # By convention, we assign to "sp" (for "SALib Problem") sp = ProblemSpec({ 'names': ['x1', 'x2', 'x3'], # Name of each parameter 'bounds': [[-np.pi, np.pi]]*3, # bounds of each parameter 'outputs': ['Y'] # name of outputs in expected order }) (sp.sample_saltelli(1024, calc_second_order=True) .evaluate(Ishigami.evaluate) .analyze_sobol(print_to_console=True)) print(sp) # Samples, model results and analyses can be extracted: print(sp.samples) print(sp.results) print(sp.analysis) # Basic plotting functionality is also provided sp.plot() The above is equivalent to the procedural approach shown previously. Also check out the `FAQ `__ and `examples `__ for a full description of options for each method. How to cite SALib ----------------- If you would like to use our software, please cite it using the following: Iwanaga, T., Usher, W., & Herman, J. (2022). Toward SALib 2.0: Advancing the accessibility and interpretability of global sensitivity analyses. Socio-Environmental Systems Modelling, 4, 18155. doi:10.18174/sesmo.18155 Herman, J. and Usher, W. (2017) SALib: An open-source Python library for sensitivity analysis. Journal of Open Source Software, 2(9). doi:10.21105/joss.00097 |paper status| If you use BibTeX, cite using the following entries:: @article{Iwanaga2022, title = {Toward {SALib} 2.0: {Advancing} the accessibility and interpretability of global sensitivity analyses}, volume = {4}, url = {https://sesmo.org/article/view/18155}, doi = {10.18174/sesmo.18155}, journal = {Socio-Environmental Systems Modelling}, author = {Iwanaga, Takuya and Usher, William and Herman, Jonathan}, month = may, year = {2022}, pages = {18155}, } @article{Herman2017, doi = {10.21105/joss.00097}, url = {https://doi.org/10.21105/joss.00097}, year = {2017}, month = {jan}, publisher = {The Open Journal}, volume = {2}, number = {9}, author = {Jon Herman and Will Usher}, title = {{SALib}: An open-source Python library for Sensitivity Analysis}, journal = {The Journal of Open Source Software} } Projects that use SALib ----------------------- Many projects now use the Global Sensitivity Analysis features provided by SALib. Here is a selection: Software ~~~~~~~~ * `The City Energy Analyst `_ * `pynoddy `_ * `savvy `_ * `rhodium `_ * `pySur `_ * `EMA workbench `_ * `Brain/Circulation Model Developer `_ * `DAE Tools `_ * `agentpy `_ * `uncertainpy `_ * `CLIMADA `_ Blogs ~~~~~ * `Sensitivity Analysis in Python `_ * `Sensitivity Analysis with SALib `_ * `Running Sobol using SALib `_ * `Extensions of SALib for more complex sensitivity analyses `_ Videos ~~~~~~ * `PyData Presentation on SALib `_ If you would like to be added to this list, please submit a pull request, or create an issue. Many thanks for using SALib. How to contribute ----------------- See `here `__ for how to contribute to SALib. License ------- Copyright (C) 2012-2019 Jon Herman, Will Usher, and others. Versions v0.5 and later are released under the `MIT license `__. .. |Build Status| image:: https://travis-ci.com/SALib/SALib.svg?branch=master :target: https://travis-ci.com/SALib/SALib .. |Coverage Status| image:: https://img.shields.io/coveralls/SALib/SALib.svg :target: https://coveralls.io/r/SALib/SALib .. |Code Issues| image:: https://www.quantifiedcode.com/api/v1/project/ed62e70f899e4ec8af4ea6b2212d4b30/badge.svg :target: https://www.quantifiedcode.com/app/project/ed62e70f899e4ec8af4ea6b2212d4b30 .. |paper status| image:: http://joss.theoj.org/papers/431262803744581c1d4b6a95892d3343/status.svg :target: http://joss.theoj.org/papers/431262803744581c1d4b6a95892d3343 SALib-SALib-d6e51b1/docs/000077500000000000000000000000001525347100600147405ustar00rootroot00000000000000SALib-SALib-d6e51b1/docs/Makefile000066400000000000000000000022011525347100600163730ustar00rootroot00000000000000# Makefile for Sphinx documentation # # You can set these variables from the command line, and also # from the environment for the first two. SPHINXOPTS ?= SPHINXBUILD ?= sphinx-build SOURCEDIR = . BUILDDIR = _build AUTODOCDIR = api # User-friendly check for sphinx-build ifeq ($(shell which $(SPHINXBUILD) >/dev/null 2>&1; echo $?), 1) $(error "The '$(SPHINXBUILD)' command was not found. Make sure you have Sphinx installed, then set the SPHINXBUILD environment variable to point to the full path of the '$(SPHINXBUILD)' executable. Alternatively you can add the directory with the executable to your PATH. If you don't have Sphinx installed, grab it from http://sphinx-doc.org/") endif .PHONY: help clean Makefile # Put it first so that "make" without argument is like "make help". help: @$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) clean: rm -rf $(BUILDDIR)/* $(AUTODOCDIR) # Catch-all target: route all unknown targets to Sphinx using the new # "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS). %: Makefile @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) SALib-SALib-d6e51b1/docs/_static/000077500000000000000000000000001525347100600163665ustar00rootroot00000000000000SALib-SALib-d6e51b1/docs/_static/.gitignore000066400000000000000000000000221525347100600203500ustar00rootroot00000000000000# Empty directory SALib-SALib-d6e51b1/docs/_static/version_switcher.json000066400000000000000000000003751525347100600226630ustar00rootroot00000000000000[ { "name": "dev", "version": "dev", "url": "https://salib.readthedocs.io/en/latest/" }, { "name": "1.4.7 (stable)", "version":"1.4.7", "url": "https://salib.readthedocs.io/en/stable/" } ] SALib-SALib-d6e51b1/docs/api.rst000066400000000000000000000040611525347100600162440ustar00rootroot00000000000000===================== Concise API Reference ===================== This page documents the sensitivity analysis methods supported by SALib. FAST - Fourier Amplitude Sensitivity Test ----------------------------------------- .. autofunction:: SALib.sample.fast_sampler.sample :noindex: .. autofunction:: SALib.analyze.fast.analyze :noindex: RBD-FAST - Random Balance Designs Fourier Amplitude Sensitivity Test -------------------------------------------------------------------- .. autofunction:: SALib.sample.latin.sample :noindex: .. autofunction:: SALib.analyze.rbd_fast.analyze :noindex: Method of Morris ---------------- .. autofunction:: SALib.sample.morris.sample :noindex: .. autofunction:: SALib.analyze.morris.analyze :noindex: Sobol' Sensitivity Analysis --------------------------- .. autofunction:: SALib.sample.saltelli.sample :noindex: .. autofunction:: SALib.sample.sobol.sample :noindex: .. autofunction:: SALib.analyze.sobol.analyze :noindex: Delta Moment-Independent Measure -------------------------------- .. autofunction:: SALib.analyze.delta.analyze :noindex: Derivative-based Global Sensitivity Measure (DGSM) -------------------------------------------------- .. autofunction:: SALib.analyze.dgsm.analyze :noindex: Shapley Effects --------------- .. autofunction:: SALib.sample.shapley.sample :noindex: .. autofunction:: SALib.analyze.shapley.analyze :noindex: Fractional Factorial -------------------- .. autofunction:: SALib.sample.ff.sample :noindex: .. autofunction:: SALib.analyze.ff.analyze :noindex: PAWN Sensitivity Analysis ------------------------- .. autofunction:: SALib.analyze.pawn.analyze :noindex: High-Dimensional Model Representation ------------------------------------- .. autofunction:: SALib.analyze.hdmr.analyze :noindex: Regional Sensitivity Analysis ----------------------------- .. autofunction:: SALib.analyze.rsa.analyze :noindex: Discrepancy Sensitivity Indices ------------------------------- .. autofunction:: SALib.analyze.discrepancy.analyze :noindex: 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For a full # list see the documentation: # https://www.sphinx-doc.org/en/master/usage/configuration.html # # All configuration values have a default; values that are commented out # serve to show the default. from datetime import date import importlib.metadata import inspect import os import shutil import sys # -- Path setup -------------------------------------------------------------- __location__ = os.path.join( os.getcwd(), os.path.dirname(inspect.getfile(inspect.currentframe())) ) # If extensions (or modules to document with autodoc) are in another directory, # add these directories to sys.path here. If the directory is relative to the # documentation root, use os.path.abspath to make it absolute, like shown here. sys.path.insert(0, os.path.join(__location__, "../src")) # -- Run sphinx-apidoc ------------------------------------------------------- # This hack is necessary since RTD does not issue `sphinx-apidoc` before running # `sphinx-build -b html . _build/html`. See Issue: # https://github.com/rtfd/readthedocs.org/issues/1139 # DON'T FORGET: Check the box "Install your project inside a virtualenv using # setup.py install" in the RTD Advanced Settings. # Additionally it helps us to avoid running apidoc manually from sphinx.ext import apidoc output_dir = os.path.join(__location__, "api") module_dir = os.path.join(__location__, "../src/SALib") try: shutil.rmtree(output_dir) except FileNotFoundError: pass try: import sphinx cmd_line_template = ( "sphinx-apidoc --implicit-namespaces -f -o {outputdir} {moduledir}" ) cmd_line = cmd_line_template.format(outputdir=output_dir, moduledir=module_dir) args = cmd_line.split(" ") if tuple(sphinx.__version__.split(".")) >= ("1", "7"): # This is a rudimentary parse_version to avoid external dependencies args = args[1:] apidoc.main(args) except Exception as e: print("Running `sphinx-apidoc` failed!\n{}".format(e)) # -- General configuration --------------------------------------------------- # If your documentation needs a minimal Sphinx version, state it here. # needs_sphinx = '1.0' # Add any Sphinx extension module names here, as strings. They can be extensions # coming with Sphinx (named 'sphinx.ext.*') or your custom ones. extensions = [ "sphinx.ext.napoleon", "sphinx.ext.autodoc", "sphinx.ext.intersphinx", "sphinx.ext.todo", # "sphinx.ext.autosummary", "sphinx.ext.viewcode", "sphinx.ext.coverage", "sphinx.ext.doctest", "sphinx.ext.ifconfig", "sphinx.ext.mathjax", # "sphinx.ext.autosectionlabel", "myst_parser", "numpydoc", ] # Add any paths that contain templates here, relative to this directory. templates_path = ["_templates"] # The suffix of source filenames. source_suffix = { ".rst": "restructuredtext", ".md": "markdown", } # ignore autosummary autosummary_generate = False autosummary_imported_members = False numpydoc_class_members_toctree = False # The encoding of source files. # source_encoding = 'utf-8-sig' # The master toctree document. master_doc = "index" # General information about the project. project = "SALib" copyright = f"{date.today().year}, Jon Herman, Will Usher and others" version = importlib.metadata.version("SALib") release = version # The language for content autogenerated by Sphinx. Refer to documentation # for a list of supported languages. # language = None # There are two options for replacing |today|: either, you set today to some # non-false value, then it is used: # today = '' # Else, today_fmt is used as the format for a strftime call. # today_fmt = '%B %d, %Y' # List of patterns, relative to source directory, that match files and # directories to ignore when looking for source files. exclude_patterns = ["_build", "Thumbs.db", ".DS_Store", ".venv"] # The reST default role (used for this markup: `text`) to use for all documents. # default_role = None # If true, '()' will be appended to :func: etc. cross-reference text. # add_function_parentheses = True # If true, the current module name will be prepended to all description # unit titles (such as .. function::). # add_module_names = True # If true, sectionauthor and moduleauthor directives will be shown in the # output. They are ignored by default. # show_authors = False # The name of the Pygments (syntax highlighting) style to use. # pygments_style = "sphinx" # A list of ignored prefixes for module index sorting. # modindex_common_prefix = [] # If true, keep warnings as "system message" paragraphs in the built documents. # keep_warnings = False # -- Options for HTML output ------------------------------------------------- # The theme to use for HTML and HTML Help pages. See the documentation for # a list of builtin themes. html_theme = "pydata_sphinx_theme" # Theme options are theme-specific and customize the look and feel of a theme # further. For a list of options available for each theme, see the # documentation. html_theme_options = { "github_url": "https://github.com/salib/salib", "navbar_end": ["theme-switcher", "version-switcher", "navbar-icon-links"], "switcher": { "json_url": "https://salib.readthedocs.io/en/latest/_static/version_switcher.json", # noqa "version_match": version, }, } html_title = "SALib's documentation" # Add any paths that contain custom themes here, relative to this directory. # html_theme_path = [] # A shorter title for the navigation bar. Default is the same as html_title. # html_short_title = None # The name of an image file (relative to this directory) to place at the top # of the sidebar. html_logo = "assets/logo.png" # The name of an image file (within the static path) to use as favicon of the # docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 # pixels large. html_favicon = "assets/favicon.ico" # Add any paths that contain custom static files (such as style sheets) here, # relative to this directory. They are copied after the builtin static files, # so a file named "default.css" will overwrite the builtin "default.css". html_static_path = ["_static"] # If not '', a 'Last updated on:' timestamp is inserted at every page bottom, # using the given strftime format. # html_last_updated_fmt = '%b %d, %Y' # If true, SmartyPants will be used to convert quotes and dashes to # typographically correct entities. # html_use_smartypants = True # Custom sidebar templates, maps document names to template names. # html_sidebars = {} # Additional templates that should be rendered to pages, maps page names to # template names. # html_additional_pages = {} # If false, no module index is generated. # html_domain_indices = True # If false, no index is generated. # html_use_index = True # If true, the index is split into individual pages for each letter. # html_split_index = False # If true, links to the reST sources are added to the pages. # html_show_sourcelink = True # If true, "Created using Sphinx" is shown in the HTML footer. Default is True. # html_show_sphinx = True # If true, "(C) Copyright ..." is shown in the HTML footer. Default is True. # html_show_copyright = True # If true, an OpenSearch description file will be output, and all pages will # contain a tag referring to it. The value of this option must be the # base URL from which the finished HTML is served. # html_use_opensearch = '' # This is the file name suffix for HTML files (e.g. ".xhtml"). # html_file_suffix = None # Output file base name for HTML help builder. htmlhelp_basename = "SALib-doc" # -- Options for LaTeX output ------------------------------------------------ latex_elements = { # The paper size ("letterpaper" or "a4paper"). # "papersize": "letterpaper", # The font size ("10pt", "11pt" or "12pt"). # "pointsize": "10pt", # Additional stuff for the LaTeX preamble. # "preamble": "", } # Grouping the document tree into LaTeX files. List of tuples # (source start file, target name, title, author, documentclass [howto/manual]). latex_documents = [ ( "index", "user_guide.tex", "SALib Documentation", "Jon Herman, Will Usher and others", "manual", ) ] # The name of an image file (relative to this directory) to place at the top of # the title page. # latex_logo = "" # For "manual" documents, if this is true, then toplevel headings are parts, # not chapters. # latex_use_parts = False # If true, show page references after internal links. # latex_show_pagerefs = False # If true, show URL addresses after external links. # latex_show_urls = False # Documents to append as an appendix to all manuals. # latex_appendices = [] # If false, no module index is generated. # latex_domain_indices = True # -- External mapping -------------------------------------------------------- python_version = ".".join(map(str, sys.version_info[0:2])) intersphinx_mapping = { "sphinx": ("https://www.sphinx-doc.org/en/master", None), "python": ("https://docs.python.org/" + python_version, None), "matplotlib": ("https://matplotlib.org/stable", None), "numpy": ("https://numpy.org/doc/stable", None), "sklearn": ("https://scikit-learn.org/stable", None), "pandas": ("https://pandas.pydata.org/pandas-docs/stable", None), "scipy": ("https://docs.scipy.org/doc/scipy", None), "pyscaffold": ("https://pyscaffold.org/en/stable", None), } SALib-SALib-d6e51b1/docs/developers_guide.md000066400000000000000000000041021525347100600206040ustar00rootroot00000000000000# Developers Guide ## Project setup For new developers: `git` must be installed. The project and its dependencies are managed via `hatch` and `uv`. While it is possible to maintain a local version of this project using venv/pip/mamba/conda, to simplify this guide, `uv` and `hatch` is the focus. Install `uv` following instructions from [here](https://docs.astral.sh/uv/getting-started/installation/). ```bash $ uv venv # equivalent: python -m venv .venv $ .venv/Scripts/activate ``` On Windows, the commands above should work for those using PowerShell. Otherwise, run the below for classic command prompt: ```bash > uv venv > .venv/Scripts/activate.bat ``` Then install `hatch` as a tool: ```bash $ uv tool install hatch # equivalent: pip install --user hatch (but isolated) ``` Verify installation after restarting terminal with: ```bash $ hatch --version ``` Build SALib with: ```bash $ hatch build ``` ## Setup (with existing Python installation) Activate the project environment with: ```bash $ source .venv\Scripts\activate ``` Or on Windows: ```bash > .venv\Scripts\activate.bat ``` Then install SALib and its dependencies. Here, additional development dependencies are also installed. ```bash $ uv sync # equivalent: pip install -e . $ uv sync --extra dev # equivalent: pip install -e ".[dev]" # Install pre-commit as a tool and set up the hook $ uv tool install pre-commit # equivalent: pip install --user pre-commit (but isolated) $ pre-commit install # To run tests: $ uv run pytest # equivalent: pytest (but runs within the uv-managed environment) ``` ## Prior to submitting a PR Run the below to catch any formatting issues. ```bash pre-commit run --all-files ``` ## Building documentation locally Notes here assume you are at the root of the project directory. Install dependencies for documentation: ```bash $ uv sync --extra doc # equivalent: pip install -e ".[doc]" ``` ### On *nix ```bash $ cd docs $ make html ``` ### On Windows In a command prompt: ```bash > cd docs > sphinx-build . ./html ``` SALib-SALib-d6e51b1/docs/index.rst000066400000000000000000000071631525347100600166100ustar00rootroot00000000000000============================================== SALib - Sensitivity Analysis Library in Python ============================================== .. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.160164.svg :target: https://doi.org/10.5281/zenodo.160164 .. image:: https://img.shields.io/badge/DOI-10.18174%2Fsesmo.18155-blue :target: https://sesmo.org/article/view/18155 .. image:: https://joss.theoj.org/papers/10.21105/joss.00097/status.svg :target: https://doi.org/10.21105/joss.00097 Python implementations of commonly used sensitivity analysis methods, including Sobol, Morris, and FAST methods. Useful in systems modeling to calculate the effects of model inputs or exogenous factors on outputs of interest. Supported Methods ----------------- * Sobol Sensitivity Analysis (`Sobol 2001 `_, `Saltelli 2002 `_, `Saltelli et al. 2010 `_) * Method of Morris, including groups and optimal trajectories (`Morris 1991 `_, `Campolongo et al. 2007 `_) * Fourier Amplitude Sensitivity Test (FAST) (`Cukier et al. 1973 `_, `Saltelli et al. 1999 `_) * Random Balance Designs - Fourier Amplitude Sensitivity Test (RBD-FAST) (`Tarantola et al. 2006 `_, `Elmar Plischke 2010 `_, `Tissot et al. 2012 `_) * Delta Moment-Independent Measure (`Borgonovo 2007 `_, `Plischke et al. 2013 `_) * Derivative-based Global Sensitivity Measure (DGSM) (`Sobol and Kucherenko 2009 `_) * Shapley Effects (`Goda 2021 `_) * Fractional Factorial Sensitivity Analysis (`Saltelli et al. 2008 `_) * High Dimensional Model Representation (`Li et al. 2010 `_) * PAWN (`Pianosi and Wagener 2018 `__, `Pianosi and Wagener 2015 `__) * Regional Sensitivity Analysis (based on `Hornberger and Spear, 1981 `__, `Saltelli et al. 2008 `__, `Pianosi et al., 2016 `__) Getting Started --------------- .. toctree:: :maxdepth: 2 Getting started Basics SALib Interface Advanced Wrappers FAQ For Developers -------------- .. toctree:: :maxdepth: 2 API Developers Guide Release Guide Changes Complete Module Reference Other Info ---------- .. toctree:: :maxdepth: 2 License Authors Projects that use SALib SALib-SALib-d6e51b1/docs/license.rst000066400000000000000000000001021525347100600171050ustar00rootroot00000000000000.. _license: ======= License ======= .. include:: ../LICENSE.md SALib-SALib-d6e51b1/docs/release_guide.md000066400000000000000000000144551525347100600200700ustar00rootroot00000000000000# Release Guide This document outlines the process for publishing a new release of SALib to PyPI. **Prerequisites:** - Maintainer-level access to the SALib GitHub repository - PyPI and TestPyPI accounts with permissions to publish to the `SALib` project - A configured API token for both PyPI and TestPyPI (see [PyPI docs](https://pypi.org/help/#apitoken)) - A complete local development environment (see the [Developers Guide](./developers_guide.md)) The general steps are: 1. Verify the main branch is release-ready 2. Bump the version number by making an annotated git tag and push to origin (see Step 2 below) 3. Check that the new release is deployed to [PyPI](https://pypi.org/project/SALib/) 4. Create a GitHub release (must be done manually; see Step 6 below) Version numbers should follow [Semantic Versioning](https://semver.org/) and PyPI rules (e.g., v1.3-alpha). In the rare case that the deployment fails, follow the manual release process outlined below. ## Manual release process ### Overview Releases follow this sequence: 1. Verify the main branch is release-ready 2. Bump the version with an annotated git tag 3. Build and verify the distribution 4. Publish to TestPyPI 5. Publish to PyPI 6. Create a GitHub Release --- ## Step 1: Verify the main branch is release-ready Ensure all intended changes are merged into `main` and that CI passes. Run the full test suite locally to confirm: ```bash $ uv run pytest # equivalent: pytest (but runs within the uv-managed environment) ``` Also run pre-commit checks to confirm there are no outstanding formatting issues: ```bash $ pre-commit run --all-files ``` Do not proceed until all tests and checks pass. --- ## Step 2: Bump the version SALib follows [Semantic Versioning](https://semver.org/), which follows a `MAJOR.MINOR.PATCH` number format. | Change type | Example: 1.4.2 → | | --------------------------------- | ---------------- | | Bug fixes / patches | `1.4.3` | | New backwards-compatible features | `1.5.0` | | Breaking changes | `2.0.0` | Create an annotated tag with git: ```bash $ git tag -a -m "" # Example: git tag -a v1.0.0 -m "Release version 1.0.0" # Tagging an existing commit is also possible $ git tag -a -m "" # Example: git tag -a v1.2 9fceb02 -m "Release version 1.2" # Push the tag to origin $ git push origin # Sometimes it is handy to know how to push all created tags $ git push origin --tags ``` Once the tag is pushed to origin, the GitHub Action `release` will build and deploy the package to [PyPI](https://pypi.org/project/SALib/#history). View the action in progress [here](https://github.com/SALib/SALib/actions/workflows/release.yaml). You can then proceed to Step 6 below. To inspect the current version without changing it: ```bash $ hatch version ``` --- ## Step 3: Build the distribution Build the source distribution (sdist) and binary wheel: ```bash $ hatch build ``` Hatch places the build artefacts in the `dist/` directory. Verify that both a `.tar.gz` and a `.whl` file are present: ```bash $ ls dist/ SALib-X.Y.Z.tar.gz SALib-X.Y.Z-py3-none-any.whl ``` --- ## Step 4: Publish to TestPyPI Publishing to [TestPyPI](https://test.pypi.org) first allows verification that the package installs correctly before pushing to the main index. ```bash $ hatch publish -r test ``` Hatch will prompt for TestPyPI credentials. When complete, verify the release looks correct at `https://test.pypi.org/project/SALib/`. Optionally, test the install from TestPyPI in a temporary environment: ```bash $ uv venv .venv-test $ .venv-test/Scripts/activate # or: source .venv-test/bin/activate on *nix $ uv pip install --index-url https://test.pypi.org/simple/ SALib==X.Y.Z ``` --- ## Step 5: Publish to PyPI Once satisfied with the TestPyPI release, publish to the main index: ```bash $ hatch publish ``` Hatch will prompt for PyPI credentials. Verify the release at `https://pypi.org/project/SALib/`. --- ## Step 6: Create a GitHub Release GitHub Releases serve as the canonical record of each release and are the recommended way to notify users of new versions. First, push the release commit to `main`: ```bash $ git push origin main ``` Then navigate to the SALib repository on GitHub and open **Releases → Draft a new release**. 1. In the **Choose a tag** field, type `vX.Y.Z` and select **Create new tag: vX.Y.Z on publish**. This creates the Git tag automatically when the release is published, so there is no need to create it manually. 2. Set the **Target** branch to `main`. 3. Set the **Release title** to `vX.Y.Z`. 4. Click **Generate release notes**. GitHub will automatically populate the release body with a categorised list of merged pull requests and contributors since the previous tag. Review and edit the generated notes as needed — for example, to highlight breaking changes or call out particularly significant additions. 5. If this is a pre-release or release candidate, check **Set as a pre-release** to avoid it being presented to users as the latest stable version. 6. Click **Publish release**. --- ## Troubleshooting **Build artefacts from a previous release are present in `dist/`** Remove the `dist/` directory before building to avoid uploading stale files: ```bash $ rm -rf dist/ $ hatch build ``` **`hatch publish` fails with a 403 error** This typically indicates an authentication issue. Confirm that the API token is correctly configured, and that it has upload permissions for the `SALib` project on the target index. **Version already exists on PyPI** PyPI does not allow re-uploading a release under an existing version number. If a release needs to be corrected after publishing, a new patch version must be issued. --- ## conda-forge No manual action is required to release on conda-forge. After the PyPI release is published, the `regro-cf-autotick-bot` will automatically open a pull request on the [salib-feedstock](https://github.com/conda-forge/salib-feedstock) repository with the updated version. A maintainer should review and merge that PR, after which conda-forge will build and publish the package automatically. If the new release changes any dependencies, the feedstock recipe may need manual adjustment before the bot PR can be merged. SALib-SALib-d6e51b1/docs/user_guide/000077500000000000000000000000001525347100600170735ustar00rootroot00000000000000SALib-SALib-d6e51b1/docs/user_guide/advanced.rst000066400000000000000000000105321525347100600213730ustar00rootroot00000000000000================== Advanced Examples ================== Group sampling (Sobol and Morris methods only) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It is sometimes useful to perform sensitivity analysis on groups of input variables to reduce the number of model runs required, when variables belong to the same component of a model, or there is some reason to believe that they should behave similarly. Groups can be specified in two ways for the Sobol and Morris methods. First, as a fourth column in the parameter file: .. code:: python # name lower_bound upper_bound group_name P1 0.0 1.0 Group_1 P2 0.0 5.0 Group_2 P3 0.0 5.0 Group_2 ...etc. Or, as an additional key in the :code:`problem` dictionary: .. code:: python problem = { 'groups': ['Group_1', 'Group_2', 'Group_2'], 'names': ['x1', 'x2', 'x3'], 'num_vars': 3, 'bounds': [[-3.14, 3.14], [-3.14, 3.14], [-3.14, 3.14]] } :code:`groups` is a list of strings specifying the group name of each variable. The rest of the code stays the same: .. code:: python param_values = saltelli.sample(problem, 1024) Y = Ishigami.evaluate(param_values) Si = sobol.analyze(problem, Y, print_to_console=True) But the output is printed by group: :: ST ST_conf Group_1 0.555309 0.084058 Group_2 0.684332 0.057449 S1 S1_conf Group_1 0.316696 0.056797 Group_2 0.456497 0.079049 S2 S2_conf (Group_1, Group_2) 0.238909 0.127195 | ST ST_conf | Group_1 0.555309 0.084058 | Group_2 0.684332 0.057449 | S1 S1_conf | Group_1 0.316696 0.056797 | Group_2 0.456497 0.079049 | S2 S2_conf | (Group_1, Group_2) 0.238909 0.127195 The output can then be converted to a Pandas DataFrame for further analysis. .. code:: python total_Si, first_Si, second_Si = Si.to_df() Generating alternate distributions ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In :ref:`basics`, we generated a uniform sample of parameter space. .. code:: python from SALib.sample import saltelli from SALib.analyze import sobol from SALib.test_functions import Ishigami import numpy as np problem = { 'num_vars': 3, 'names': ['x1', 'x2', 'x3'], 'bounds': [[-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359]] } param_values = saltelli.sample(problem, 1024) SALib is also capable of generating alternate sampling distributions by specifying a :code:`dists` entry in the :code:`problem` specification. As implied in the basic example, a uniform distribution is the default. When an entry for :code:`dists` is not 'unif', the :code:`bounds` entry does not indicate parameter bounds but sample-specific metadata. :code:`bounds` definitions for available distributions: * unif: uniform distribution e.g. :code:`[-np.pi, np.pi]` defines the lower and upper bounds * logunif: logarithmic uniform with lower and upper bounds * triang: triangular with lower and upper bounds, as well as location of peak The location of peak is in percentage of width e.g. :code:`[1.0, 3.0, 0.5]` indicates 1.0 to 3.0 with a peak at 2.0 A soon-to-be deprecated two-value format assumes the lower bound to be 0 e.g. :code:`[3, 0.5]` assumes 0 to 3, with a peak at 1.5 * norm: normal distribution with mean and standard deviation * truncnorm: truncated normal distribution with lower and upper bounds, mean and standard deviation e.g. :code:`[-3, 3, 0, 1]` indicates a lower bound of -3, upper bound of 3, mean 0 and standard deviation of 1. * lognorm: lognormal with ln-space mean and standard deviation * weibull: weibull distribution with shape, scale, and optional location parameters. e.g. :code:`[1.5, 1.0, 5.0]` indicates a shape (k) of 1.5, scale (lambda) of 1.0, and a location of 5.0. If only two values are provided, the location is assumed to be 0. e.g. :code:`[1.5, 1.0]` assumes a location of 0. An example specification is shown below: .. code:: python problem = { 'names': ['x1', 'x2', 'x3'], 'num_vars': 3, 'bounds': [[-np.pi, np.pi], [1.0, 0.2], [3, 0.5]], 'groups': ['G1', 'G2', 'G1'], 'dists': ['unif', 'lognorm', 'triang'] } SALib-SALib-d6e51b1/docs/user_guide/basics.rst000066400000000000000000000253671525347100600211060ustar00rootroot00000000000000====== Basics ====== What is Sensitivity Analysis? ----------------------------- According to `Wikipedia `_, sensitivity analysis is "the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be apportioned to different sources of uncertainty in its inputs." The sensitivity of each input is often represented by a numeric value, called the *sensitivity index*. Sensitivity indices come in several forms: 1. First-order indices: measures the contribution to the output variance by a single model input alone. 2. Second-order indices: measures the contribution to the output variance caused by the interaction of two model inputs. 3. Total-order index: measures the contribution to the output variance caused by a model input, including both its first-order effects (the input varying alone) and all higher-order interactions. What is SALib? -------------- SALib is an open source library written in Python for performing sensitivity analyses. SALib provides a decoupled workflow, meaning it does not directly interface with the mathematical or computational model. Instead, SALib is responsible for generating the model inputs, using one of the :code:`sample` functions, and computing the sensitivity indices from the model outputs, using one of the :code:`analyze` functions. A typical sensitivity analysis using SALib follows four steps: 1. Determine the model inputs (parameters) and their sample range. 2. Run the :code:`sample` function to generate the model inputs. 3. Evaluate the model using the generated inputs, saving the model outputs. 4. Run the :code:`analyze` function on the outputs to compute the sensitivity indices. SALib provides several sensitivity analysis methods, such as Sobol, Morris, and FAST. There are many factors that determine which method is appropriate for a specific application, which we will discuss later. However, for now, just remember that regardless of which method you choose, you need to use only two functions: :code:`sample` and :code:`analyze`. To demonstrate the use of SALib, we will walk through a simple example. An Example ---------- In this example, we will perform a Sobol' sensitivity analysis of the Ishigami function (shown below) using the core SALib functions. The example is repeated in the next tutorial using an object-oriented interface which some may find easier to use. The Ishigami function is commonly used to test uncertainty and sensitivity analysis methods because it exhibits strong nonlinearity and nonmonotonicity. .. math:: f(x) = \sin(x_1) + a \sin^2(x_2) + b x_3^4 \sin(x_1) Importing SALib ~~~~~~~~~~~~~~~ The first step is the import the necessary libraries. In SALib, the :code:`sample` and :code:`analyze` functions are stored in separate Python modules. For example, below we import the :code:`saltelli` sample function and the :code:`sobol` analyze function. We also import the Ishigami function, which is provided as a test function within SALib. Lastly, we import :code:`numpy`, as it is used by SALib to store the model inputs and outputs in a matrix. .. code:: python from SALib.sample import saltelli from SALib.analyze import sobol from SALib.test_functions import Ishigami import numpy as np Defining the Model Inputs ~~~~~~~~~~~~~~~~~~~~~~~~~ Next, we must define the model inputs. The Ishigami function has three inputs, :math:`x_1, x_2, x_3` where :math:`x_i \in [-\pi, \pi]`. In SALib, we define a :code:`dict` defining the number of inputs, the names of the inputs, and the bounds on each input, as shown below. .. code:: python problem = { 'num_vars': 3, 'names': ['x1', 'x2', 'x3'], 'bounds': [[-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359]] } Generate Samples ~~~~~~~~~~~~~~~~ Next, we generate the samples. Since we are performing a Sobol' sensitivity analysis, we need to generate samples using the Saltelli sampler, as shown below. .. code:: python param_values = saltelli.sample(problem, 1024) Here, :code:`param_values` is a NumPy matrix. If we run :code:`param_values.shape`, we see that the matrix has shape 8192 by 3. The Saltelli sampler generated 8192 samples. The Saltelli sampler generates :math:`N*(2D+2)` samples, where in this example N is 1024 (the argument we supplied) and D is 3 (the number of model inputs). Had we supplied the keyword argument :code:`calc_second_order=False`, second-order indices would have been excluded, resulting in a smaller sample matrix with :math:`N*(D+2)` rows instead. Run Model ~~~~~~~~~ As mentioned above, SALib is not involved in the evaluation of the mathematical or computational model. If the model is written in Python, then generally you will loop over each sample input and evaluate the model: .. code:: python Y = np.zeros([param_values.shape[0]]) for i, X in enumerate(param_values): Y[i] = evaluate_model(X) If the model is not written in Python, then the samples can be saved to a text file: .. code:: python np.savetxt("param_values.txt", param_values) Each line in :code:`param_values.txt` is one input to the model. The output from the model should be saved to another file with a similar format: one output on each line. The outputs can then be loaded with: .. code:: python Y = np.loadtxt("outputs.txt", float) In this example, we are using the Ishigami function provided by SALib. We can evaluate these test functions as shown below: .. code:: python Y = Ishigami.evaluate(param_values) Perform Analysis ~~~~~~~~~~~~~~~~ With the model outputs loaded into Python, we can finally compute the sensitivity indices. In this example, we use :code:`sobol.analyze`, which will compute first, second, and total-order indices. .. code:: python Si = sobol.analyze(problem, Y) :code:`Si` is a Python :code:`dict`-like with the keys :code:`"S1"`, :code:`"S2"`, :code:`"ST"`, :code:`"S1_conf"`, :code:`"S2_conf"`, and :code:`"ST_conf"`. The :code:`_conf` keys store the corresponding confidence intervals, typically with a confidence level of 95%. Use the keyword argument :code:`print_to_console=True` to print all indices. Alternatively, we can print the individual values from :code:`Si` as shown below. .. code:: python print(Si['S1']) [ 0.316832 0.443763 0.012203 ] Here, we see that x1 and x2 exhibit first-order sensitivities but x3 appears to have no first-order effects. .. code:: python print(Si['ST']) [ 0.555860 0.441898 0.244675] If the total-order indices are substantially larger than the first-order indices, then there is likely higher-order interactions occurring. We can look at the second-order indices to see these higher-order interactions: .. code:: python print("x1-x2:", Si['S2'][0,1]) print("x1-x3:", Si['S2'][0,2]) print("x2-x3:", Si['S2'][1,2]) x1-x2: 0.0092542 x1-x3: 0.2381721 x2-x3: -0.0048877 We can see there are strong interactions between x1 and x3. Some computing error will appear in the sensitivity indices. For example, we observe a negative value for the x2-x3 index. Typically, these computing errors shrink as the number of samples increases. The output can then be converted to a Pandas DataFrame for further analysis. .. code:: python total_Si, first_Si, second_Si = Si.to_df() # Note that if the sample was created with `calc_second_order=False` # Then the second order sensitivities will not be returned # total_Si, first_Si = Si.to_df() Basic Plotting ~~~~~~~~~~~~~~~~ Basic plotting facilities are provided for convenience. .. code:: python Si.plot() The :code:`plot()` method returns matplotlib axes for later adjustment. Another Example --------------- When the model you want to analyse depends on parameters that are not part of the sensitivity analysis, like position or time, the analysis can be performed for each time/position "bin" separately. Consider the example of a parabola: .. math:: f(x) = a + b x^2 The parameters :math:`a` and :math:`b` will be subject to the sensitivity analysis, but :math:`x` will be not. We start with a set of imports: .. code:: python import numpy as np import matplotlib.pyplot as plt from SALib.sample import saltelli from SALib.analyze import sobol and define the parabola: .. code:: python def parabola(x, a, b): """Return y = a + b*x**2.""" return a + b*x**2 The :code:`dict` describing the problem contains therefore only :math:`a` and :math:`b`: .. code:: python problem = { 'num_vars': 2, 'names': ['a', 'b'], 'bounds': [[0, 1]]*2 } The triad of sampling, evaluating and analysing becomes: .. code:: python # sample param_values = saltelli.sample(problem, 2**6) # evaluate x = np.linspace(-1, 1, 100) y = np.array([parabola(x, *params) for params in param_values]) # analyse sobol_indices = [sobol.analyze(problem, Y) for Y in y.T] Note how we analysed for each :math:`x` separately. Now we can extract the first-order Sobol indices for each bin of :math:`x` and plot: .. code:: python S1s = np.array([s['S1'] for s in sobol_indices]) fig = plt.figure(figsize=(10, 6), constrained_layout=True) gs = fig.add_gridspec(2, 2) ax0 = fig.add_subplot(gs[:, 0]) ax1 = fig.add_subplot(gs[0, 1]) ax2 = fig.add_subplot(gs[1, 1]) for i, ax in enumerate([ax1, ax2]): ax.plot(x, S1s[:, i], label=r'S1$_\mathregular{{{}}}$'.format(problem["names"][i]), color='black') ax.set_xlabel("x") ax.set_ylabel("First-order Sobol index") ax.set_ylim(0, 1.04) ax.yaxis.set_label_position("right") ax.yaxis.tick_right() ax.legend(loc='upper right') ax0.plot(x, np.mean(y, axis=0), label="Mean", color='black') # in percent prediction_interval = 95 ax0.fill_between(x, np.percentile(y, 50 - prediction_interval/2., axis=0), np.percentile(y, 50 + prediction_interval/2., axis=0), alpha=0.5, color='black', label=f"{prediction_interval} % prediction interval") ax0.set_xlabel("x") ax0.set_ylabel("y") ax0.legend(title=r"$y=a+b\cdot x^2$", loc='upper center')._legend_box.align = "left" plt.show() .. figure:: ../assets/example_parabola.svg :width: 800 :align: center With the help of the plots, we interpret the Sobol indices. At :math:`x=0`, the variation in :math:`y` can be explained to 100 % by parameter :math:`a` as the contribution to :math:`y` from :math:`b x^2` vanishes. With larger :math:`|x|`, the contribution to the variation from parameter :math:`b` increases and the contribution from parameter :math:`a` decreases. SALib-SALib-d6e51b1/docs/user_guide/basics_with_interface.rst000066400000000000000000000346271525347100600241600ustar00rootroot00000000000000====== SALib Interface Basics ====== The earlier example is repeated on this page with the SALib `ProblemSpec` interface. The interface provides an object-oriented approach to using SALib which some may find easier to use. Note that the interface does add computational overhead (thereby increasing runtimes) as it provides additional checks for users. Developers who wish to integrate SALib into their own work may wish to use the core API as detailed in the first example instead. The Ishigami function --------------------- As a reminder, we will perform a Sobol' sensitivity analysis of the Ishigami function, shown below. .. math:: f(x) = \sin(x_1) + a \sin^2(x_2) + b x_3^4 \sin(x_1) The ProblemSpec Interface ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SALib provides a single interface from which all methods can be accessed. The interface is called the :code:`ProblemSpec` (the Problem Specification). One advantage to the interface is the method chaining approach which offers a concise workflow. The sampling, evaluation and analysis trifecta can be run with: .. code:: python import numpy as np from SALib.test_functions import Ishigami from SALib import ProblemSpec sp = ProblemSpec({ "names": ["x1", "x2", "x3"], "groups": None, "bounds": [[-np.pi, np.pi]] * 3, "outputs": ["Y"], }) ( sp.sample_sobol(1024) .evaluate(Ishigami.evaluate) .analyze_sobol() ) total_Si, first_Si, second_Si = sp.to_df() sp.plot() sp.heatmap() Each step in the above is outlined in the sections below. Importing SALib ~~~~~~~~~~~~~~~ First, the necessary packages are imported. Here, we import numpy as well as the Ishigami test function (to use for this example) and the :code:`ProblemSpec` interface. .. code:: python import numpy as np from SALib.test_functions import Ishigami from SALib import ProblemSpec Defining the Model Inputs ~~~~~~~~~~~~~~~~~~~~~~~~~ Next, we must define the model inputs. The Ishigami function has three inputs, :math:`x_1, x_2, x_3` where :math:`x_i \in [-\pi, \pi]`. In SALib, we define a :code:`dict` which holds the names of the inputs, and the bounds on each input. Optionally, the expected output(s) can also be named. .. code:: python sp = ProblemSpec({ 'names': ['x1', 'x2', 'x3'], 'bounds': [ [-np.pi, np.pi], # bounds for x1 [-np.pi, np.pi], # ... x2 [-np.pi, np.pi] # ... x3 ], 'outputs': ['Y'] }) As seen above, the :code:`ProblemSpec` simply wraps around a :code:`dict`. Here, the default is to assume all inputs are uniformly distributed. See :doc:`advanced` on how to provide further details, including alternate distributions. .. note:: If :code:`outputs` is not provided, then SALib will automatically create generic names. :code:`Y` for a single output :code:`Y1, Y2, ... Yn` for multiple outputs Method Chaining ~~~~~~~~~~~~~~~ Since we are performing a Sobol' sensitivity analysis, we need to generate samples using the Sobol' sampler, run the model, then analyze the outputs. In the example above, all the steps are expressed as a `method chain `_ .. code:: python ( sp.sample_sobol(1024) .evaluate(Ishigami.evaluate) .analyze_sobol() ) That said, each step can be run individually. Note that the :code:`sample_` and :code:`analyze_` methods are shown with default arguments. .. code:: python sp.sample_sobol(1024, calc_second_order=True) sp.evaluate(Ishigami.evaluate) sp.analyze_sobol(print_to_console=False, calc_second_order=True) The :code:`samples`, :code:`results`, and results of :code:`analysis` are all held inside the :code:`sp` object. If needed, these may be extracted via their respective attributes. .. code:: python X = sp.samples y = sp.results S = sp.analysis Internally, all data is handled as a numpy array/matrix. .. tip:: All sampling, evaluation and analysis methods may be accessed through the ProblemSpec interface and follow a standard pattern. - Sampling methods can be accessed with :code:`sp.sample_[name of method]` - Likewise, for analysis methods use :code:`sp.analyze_[name of method]` See the documentation of each method for further information. Generating Samples ~~~~~~~~~~~~~~~~~~ In this example we are using the Sobol' sampling method (shown below with the default value for :code:`calc_second_order`). .. code:: python sp.sample_sobol(1024, calc_second_order=True) If we run :code:`sp.samples.shape`, we will see the matrix is 8192 by 3. In other words, the Sobol' sampler generated :math:`N*(2D+2)` samples, where in this example N is 1024 (the argument we supplied) and D is 3 (the number of model inputs). The keyword argument :code:`calc_second_order=False` will exclude second-order indices, resulting in a smaller sample matrix with :math:`N*(D+2)` rows instead. .. note:: Specific sampling methods have their own requirements and behaviours. The documentation for each method lists a brief overview and includes references to provide further details. A generic :code:`sp.sample` method is also available, allowing use of your own sampling function. .. code:: python sp.sample(my_sampler, *args, **kwargs) The provided function must follow two requirements. 1. A :code:`ProblemSpec` must be accepted as its first argument. This can simply be defined as a dictionary following the same format as outlined above. 2. The function must return a numpy array. If a sample has already been defined, this can be provided to the interface like so: .. code:: python sp.set_samples(X) where :code:`X` is a numpy array. .. note:: :code:`sp.set_results(Y)` can be used to set existing results. .. warning:: Care must be taken to avoid inappropriately mix-and-matching sampling and analysis methods. For example, Sobol' analysis must be conducted with a Sobol' sample. Running a Model ~~~~~~~~~~~~~~~ If the model is written in Python, and is written such that it can accept a numpy array as an input in its first position, then it may be called directly with the interface. Here, we use the Ishigami function as an example. .. code:: python sp.evaluate(Ishigami.evaluate) .. note:: SALib also supports parallel model evaluation with `sp.evaluate_parallel()`. It is assumed that all results can be held in memory. The Ishigami module provides an :code:`evaluate` function that looks something like: .. code:: python def evaluate(X: np.ndarray, A: float = 7.0, B: float = 0.1): The actual implementation can be seen `here `_. Note that the inputs (:code:`X`) is the first argument. .. tip:: For user-provided models, a wrapper can be written. A wrapper is a function that accepts parameters in the expected order, then runs the model itself. See also: :ref:`Another Example` , `functools.partial `_ Note that SALib does not require direct interaction with the model. If the model is written in Python, then it may be run manually without SALib. Generally, you will loop over each sample input and evaluate the model: .. code:: python Y = np.zeros([param_values.shape[0]]) for i, X in enumerate(param_values): Y[i] = evaluate_model(X) # Provide the results to the interface sp.set_results(Y) If the model is not written in Python, then the samples can be saved to a text file: .. code:: python np.savetxt("param_values.txt", sp.samples) Each line in :code:`param_values.txt` is one input to the model. The output from the model should be saved to another file with a similar format: one output on each line. The outputs can then be loaded with: .. code:: python Y = np.loadtxt("outputs.txt", float) # Provide the results to the interface sp.set_results(Y) Perform Analysis ~~~~~~~~~~~~~~~~ With the model outputs loaded, we can finally compute the sensitivity indices. In this example, we use Sobol' analysis, which will compute first, second, and total-order indices. .. code:: python sp.analyze_sobol() We see an overview of the results once we print out the interface: .. code:: python print(sp) Samples: 3 parameters: ['x1', 'x2', 'x3'] 8192 evaluations Outputs: 1 outputs: ['Y'] 8192 evaluations Analysis: ST ST_conf x1 0.557271 0.078640 x2 0.442311 0.040564 x3 0.247103 0.025728 S1 S1_conf x1 0.317728 0.060368 x2 0.442253 0.056459 x3 0.002556 0.054109 S2 S2_conf (x1, x2) -0.000604 0.071442 (x1, x3) 0.247521 0.096797 (x2, x3) -0.002954 0.072420 Here :code:`ST`, :code:`S1`, and :code:`S2` relate to the total, first-order, and second-order sensitivity indices respectively. Those ending with `_conf` indicate the corresponding confidence intervals, typically with a confidence level of 95%. We see that x1 and x2 exhibit first-order sensitivities but x3 appears to have no first-order effects. If the total-order indices are substantially larger than the first-order indices, then there is likely higher-order interactions occurring. We can look at the second-order indices to see these higher-order interactions: .. code:: python y_S2 = sp.analysis['S2'] print("x1-x2:", y_S2[0,1]) print("x1-x3:", y_S2[0,2]) print("x2-x3:", y_S2[1,2]) x1-x2: 0.0092542 x1-x3: 0.2381721 x2-x3: -0.0048877 Results can also be extracted as Pandas DataFrames for further analysis. .. code:: python total_Si, first_Si, second_Si = Si.to_df() If the sample was created with :code:`calc_second_order=False` then the second order sensitivities will not be returned .. code:: python total_Si, first_Si = Si.to_df() For multi-output models, sensitivity results for individual outputs can be extracted: .. code:: python sp.analysis['Y1']['S1'] # First order for Y1 sp.analysis['Y2']['S2'] # Second order for Y2 Basic Plotting ~~~~~~~~~~~~~~~~ Basic plotting facilities are provided for convenience. .. code:: python Si.plot() All plotting methods will return matplotlib axes objects to allow later adjustment. In the example below, the figure is created, the y-axis for the first subplot is set to use log scale, and the figure size is adjusted with :code:`matplotlib`. .. code:: python import matplotlib.pyplot as plt axes = sp.plot() axes[0].set_yscale('log') fig = plt.gcf() # get current figure fig.set_size_inches(10, 4) plt.tight_layout() .. figure:: ../assets/example_mod_plot.svg :width: 800 :align: center In addition to the basic :code:`plot()` command, SALib can also produce a basic heatmap. .. code:: python sp.heatmap() .. figure:: ../assets/example_heatmap_plot.svg :width: 800 :align: center .. _Another example: Another Example --------------- When the model you want to analyse depends on parameters that are not part of the sensitivity analysis, like position or time, the analysis can be performed for each time/position "bin" separately. This can be useful for the purpose of factor mapping, to identify where in parameter space the model is sensitive to. Consider the example of a parabola: .. math:: f(x) = a + b x^2 The parameters :math:`a` and :math:`b` will be subject to the sensitivity analysis, but :math:`x` will be not. We start with a set of imports: .. code:: python import numpy as np import matplotlib.pyplot as plt from SALib import ProblemSpec and define the parabola: .. code:: python def parabola(x, a, b): """Return y = a + b*x**2.""" return a + b*x**2 The :code:`dict` describing the problem contains therefore only :math:`a` and :math:`b`: .. code:: python sp = ProblemSpec({ 'names': ['a', 'b'], 'bounds': [[0, 1]]*2, }) The triad of sampling, evaluating and analysing becomes: .. code:: python # Create "bins" of x x = np.linspace(-1, 1, 100) # Create wrapper (runs each a, b combination separately) def wrapped_parabola(ab, x=x): y = np.zeros((ab.shape[0], x.shape[0])) for i, (a, b) in enumerate(ab): y[i,:] = parabola(x, a, b) return y ( sp.sample_sobol(2**6) .evaluate(wrapped_parabola) .analyze_sobol() ) Note how we analyzed for each :math:`x` separately. Now we can extract the first-order Sobol indices for each bin of :math:`x` and plot: .. code:: python # Get first order sensitivities for all outputs S1s = np.array([sp.analysis[_y]['S1'] for _y in sp['outputs']]) # Get model outputs y = sp.results # Set up figure fig = plt.figure(figsize=(10, 6), constrained_layout=True) gs = fig.add_gridspec(2, 2) ax0 = fig.add_subplot(gs[:, 0]) ax1 = fig.add_subplot(gs[0, 1]) ax2 = fig.add_subplot(gs[1, 1]) # Populate figure subplots for i, ax in enumerate([ax1, ax2]): ax.plot(x, S1s[:, i], label=r'S1$_\mathregular{{{}}}$'.format(problem["names"][i]), color='black') ax.set_xlabel("x") ax.set_ylabel("First-order Sobol index") ax.set_ylim(0, 1.04) ax.yaxis.set_label_position("right") ax.yaxis.tick_right() ax.legend(loc='upper right') ax0.plot(x, np.mean(y, axis=0), label="Mean", color='black') # in percent prediction_interval = 95 ax0.fill_between(x, np.percentile(y, 50 - prediction_interval/2., axis=0), np.percentile(y, 50 + prediction_interval/2., axis=0), alpha=0.5, color='black', label=f"{prediction_interval} % prediction interval") ax0.set_xlabel("x") ax0.set_ylabel("y") ax0.legend(title=r"$y=a+b\cdot x^2$", loc='upper center')._legend_box.align = "left" plt.show() .. figure:: ../assets/example_parabola.svg :width: 800 :align: center With the help of the plots, we interpret the Sobol indices. At :math:`x=0`, the variation in :math:`y` can be explained to 100 % by parameter :math:`a` as the contribution to :math:`y` from :math:`b x^2` vanishes. With larger :math:`|x|`, the contribution to the variation from parameter :math:`b` increases and the contribution from parameter :math:`a` decreases. SALib-SALib-d6e51b1/docs/user_guide/faq.rst000066400000000000000000000027151525347100600204010ustar00rootroot00000000000000========================== Frequently Asked Questions ========================== Q. How do I wrap my model? --------------- See this guide on :doc:`wrapping models `. Q. Which technique can I use for pre-existing results? ------------------------------------------------------ DMIM, RBD-FAST, PAWN and HDMR methods are "given-data" approaches and can be independently applied. Q. How do I get the sensitivity results? ---------------------------------------- Call the :code:`.to_df()` method if you would like Pandas DataFrames. If using the SALib Interface, see :doc:`SALib Interface Basics `. Q. How can I plot my results? ----------------------------- SALib provides some basic plotting functionality. See the subsection "Basic Plotting" in :doc:`SALib Interface Basics ` See also, `these examples `_. Q. Why does the Sobol' method implemented in SALib normalize outputs? --------------------------------------------------------------------- Estimates of Sobol' indices can be biased in cases where model outputs are non-centered. We have opted to normalize outputs with the standard deviation. See the discussion `here `_. In practice, non-normalized model outputs are still usable but requires larger sample sizes for the indices to converge. SALib-SALib-d6e51b1/docs/user_guide/getting-started.rst000066400000000000000000000042131525347100600227320ustar00rootroot00000000000000=============== Getting Started =============== Installing SALib ---------------- To install the latest stable version of SALib via pip from `PyPI `__, together with all the dependencies, run the following command: :: pip install SALib To install the latest development version of SALib, run the following commands. Note that the development version may be unstable and include bugs. We encourage users use the latest stable version. :: git clone https://github.com/SALib/SALib.git cd SALib pip install . Installing Prerequisite Software -------------------------------- Core dependencies include: - `NumPy `_ - `SciPy `_ - `pandas `_ - `matplotlib `_ These should be installed automatically alongside SALib but otherwise they can be installed with the following command: :: pip install numpy scipy pandas matplotlib The packages are normally included with most Python bundles, such as Anaconda and Canopy. Testing Installation -------------------- To test your installation of SALib, run the following command :: pytest Alternatively, if you’d also like a taste of what SALib provides, start a new interactive Python session and copy/paste the code below. .. code:: python from SALib.analyze.sobol import analyze from SALib.sample.sobol import sample from SALib.test_functions import Ishigami import numpy as np # Define the model inputs problem = { 'num_vars': 3, 'names': ['x1', 'x2', 'x3'], 'bounds': [[-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359]] } # Generate samples param_values = sample(problem, 1024) # Run model (example) Y = Ishigami.evaluate(param_values) # Perform analysis Si = analyze(problem, Y, print_to_console=True) # Print the first-order sensitivity indices print(Si['S1']) If installed correctly, the last line above will print three values, similar to :code:`[ 0.31683154 0.44376306 0.01220312]`. SALib-SALib-d6e51b1/docs/user_guide/wrappers.rst000066400000000000000000000201621525347100600214710ustar00rootroot00000000000000========================== Wrapping an existing model ========================== SALib performs sensitivity analysis for any model that can be expressed in the form of :math:`f(X) = Y`, where :math:`X` is a matrix of inputs (often referred to as the model's factors). The analysis methods are independent of the model and can be applied non-intrusively such that it does not matter what :math:`f` is. Typical model implementations take the form of :math:`f(a, b, c, ...) = Y`. In other words, each model factor is supplied as a separate argument to the function. In such cases it is necessary to write a wrapper to allow use with SALib. This is illustrated here with a simple linear function: .. code:: python def linear(a, b, x): """Return y = a + b + x""" return a + b + x As SALib expects a (numpy) matrix of factors, we simply "wrap" the function above like so: .. code:: python def wrapped_linear(X, func=linear): """g(X) = Y, where X := [a b x] and g(X) := f(X)""" # We transpose to obtain each column (the model factors) as separate variables a, b, x = X.T # Then call the original model return func(a, b, x) .. note:: **Wrapped function is an argument** Note here that the model being "wrapped" is also passed in as an argument. This will be revisited further down below. .. tip:: **Interfacing with external models/programs** Here we showcase interacting with models written in Python. If the model is an external program, this is where interfacing code would be written. A pragmatic approach could be to use `subprocess `_ to start the external program, then read in the results. Constants, which SALib should not consider, can be expressed by defining default keyword arguments (for flexibility) or otherwise defined within the wrapper function itself. .. code:: python def wrapped_linear_w_constant(X, a=10, func=linear): """f(X, a) = Y, where X := [b x] and a = 10""" # We transpose to obtain each column as separate variables b, x = X.T # Then call the original model return func(a, b, x) Note that the first argument to any function provided to SALib is assumed to be a numpy array of shape :math:`N*D`, where :math:`D` is the number of model factors (dimensions) and :math:`N` is the number of their combinations. The argument name is, by convention, denoted as :code:`X`. This is to maximize compatibility with all methods provided in SALib as they expect the first argument to hold the model factor values. Using :py:func:`functools.partial` from the `functools` package to create wrappers can be useful. In this example, the model (:code:`linear()`) can be used with both scalar inputs or `numpy` arrays. In cases where `a`, `b` or `x` are a vector of inputs, `numpy` will automatically vectorize the calculation. There are many cases where the model is not (or cannot be easily) expressed in a vectorizable form. In such cases, simply apply a :code:`for` loop as in the example below. .. code:: python import numpy as np from SALib import ProblemSpec def linear(a: float, b: float, x: float) -> float: return a + b * x def wrapped_linear(X: np.ndarray, func=linear) -> np.ndarray: N, D = X.shape results = np.empty(N) for i in range(N): a, b, x = X[i, :] results[i] = func(a, b, x) return results sp = ProblemSpec({ 'names': ['a', 'b', 'x'], 'bounds': [ [-1, 0], [-1, 0], [-1, 1], ], }) ( sp.sample_sobol(2**6) .evaluate(wrapped_linear) .analyze_sobol() ) sp.to_df() # [ ST ST_conf # a 0.173636 0.072142 # b 0.167933 0.059599 # x 0.654566 0.208328, # S1 S1_conf # a 0.182788 0.111548 # b 0.179003 0.145714 # x 0.664727 0.241977, # S2 S2_conf # (a, b) -0.022070 0.185510 # (a, x) -0.010781 0.186743 # (b, x) -0.014616 0.279925] Use of the core SALib functions equivalent to the previous example are shown below: .. code:: python problem = { 'names': ['a', 'b', 'x'], 'bounds': [ [-1, 0], [-1, 0], [-1, 1], ], 'num_vars': 3 } X = saltelli.sample(problem, 64) Y = np.empty(params.shape[0]) for i in range(params.shape[0]): Y[i] = wrapped_linear(params[i, :]) res = sobol.analyze(problem, Y) res.to_df() # [ ST ST_conf # a 0.165854 0.054096 # b 0.165854 0.053200 # x 0.665366 0.192756, # S1 S1_conf # a 0.167805 0.121550 # b 0.167805 0.125178 # x 0.665366 0.230872, # S2 S2_conf # (a, b) -2.775558e-17 0.180493 # (a, x) -3.902439e-03 0.202343 # (b, x) -3.902439e-03 0.232957] Parallel evaluation and analysis -------------------------------- Here we expand on some technical details that enable parallel evaluation and analysis. We noted earlier that the model being "wrapped" is also passed in as an argument. This is to facilitate parallel evaluation, as the arguments to the wrapper are passed on to workers. The approach works be using Python's `mutable default argument `_ behavior. A further consideration is that imported modules/packages are not made available to workers in cases where functions are defined in the same file SALib is used in. Running the previous example with :code:`.evaluate(wrapped_linear, nprocs=2)` will fail with :code:`NameError: name 'np' is not defined`. The quick fix is to re-import the required packages within the model function itself: .. code:: python def wrapped_linear(X: np.ndarray, func=linear) -> np.ndarray: import numpy as np # re-import necessary packages N, D = X.shape results = np.empty(N) for i in range(N): a, b, x = X[i, :] results[i] = func(a, b, x) return results This can, however, get unwieldy for complicated models. The recommended best practice is to separate implementation (i.e., model definitions) from its use. Simply moving the model functions into a separate file is enough for this example, such that the project structure is something like: :: project_directory |-- model_definition.py └── analysis.py .. tip:: **Project structure** The project structure shown above is for example purposes only. It is highly recommended that a standardized directory structure, such as https://github.com/drivendata/cookiecutter-data-science, be adopted to improve usability and reproducibility. Here, :code:`model_definitions.py` holds the model definitions: .. code:: python import numpy as np def linear(a: float, b: float, x: float) -> float: return a + b * x def wrapped_linear(X: np.ndarray, func=linear) -> np.ndarray: N, D = X.shape results = np.empty(N) for i in range(N): a, b, x = X[i, :] results[i] = func(a, b, x) return results and :code:`analysis.py` contains use of SALib: .. code:: python from model_definition import wrapped_linear sp = ProblemSpec({ 'names': ['a', 'b', 'x'], 'bounds': [ [-1, 0], [-1, 0], [-1, 1], ], }) ( sp.sample_sobol(2**6) .evaluate(wrapped_linear, nprocs=2) .analyze_sobol(nprocs=2) ) .. note:: **Multi-processing** Some interactive Python consoles, including earlier versions of IPython, may appear to hang on Windows when utilizing parallel evaluation and analysis. In such cases, the recommended workaround is to wrap use of SALib with a :code:`__main__` check to ensure it is only run in the top-level environment. .. code:: python if __name__ == "__main__": ( sp.sample_sobol(2**6) .evaluate(wrapped_linear, nprocs=2) .analyze_sobol(nprocs=2) ) SALib-SALib-d6e51b1/environment.yml000066400000000000000000000004771525347100600171070ustar00rootroot00000000000000name: SALib channels: - conda-forge dependencies: # required - numpy>=2.0 - pandas>=2.0 - matplotlib>=3.5 - scipy>=1.9.3 - pathos>=0.3.2 # tests - pytest - pytest-cov # dev - pre-commit - hatch # doc - sphinx - numpydoc - pydata-sphinx-theme>=0.15.2 - pip - pip: - myst_parser SALib-SALib-d6e51b1/examples/000077500000000000000000000000001525347100600156265ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/Problem/000077500000000000000000000000001525347100600172265ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/Problem/multi_output.py000066400000000000000000000021521525347100600223520ustar00rootroot00000000000000"""Multi-output analysis and plotting example.""" import matplotlib.pyplot as plt import numpy as np from SALib.test_functions import lake_problem from SALib.test_functions import Ishigami from SALib import ProblemSpec if __name__ == "__main__": seed_val = 101 sp = ProblemSpec( { "names": ["a", "q", "b", "mean", "stdev", "delta", "alpha"], "bounds": [ [0.0, 0.1], [2.0, 4.5], [0.1, 0.45], [0.01, 0.05], [0.001, 0.005], [0.93, 0.99], [0.2, 0.5], ], "outputs": ["max_P", "Utility", "Inertia", "Reliability"], } ) (sp.sample_saltelli(1024).evaluate(lake_problem.evaluate).analyze_sobol(nprocs=2)) print(sp) sp.plot() plt.show() sp.analyze_delta(num_resamples=5) sp.plot() plt.show() sp = ProblemSpec( {"names": ["x1", "x2", "x3"], "bounds": [[-np.pi, np.pi]] * 3, "outputs": ["Y"]} ) (sp.sample_saltelli(512).evaluate(Ishigami.evaluate).analyze_sobol()) sp.plot() plt.show() SALib-SALib-d6e51b1/examples/Problem/problem_spec.py000066400000000000000000000063471525347100600222640ustar00rootroot00000000000000"""Example showing how to use the ProblemSpec approach. Showcases method chaining, and parallel model runs using 2 processors. The following caveats apply: 1. Functions passed into `sample`, `analyze` and `evaluate` must accept a numpy array of `X` values as the first parameter, and return a numpy array of results. 2. Parallel evaluation/analysis is only beneficial for long-running models or large datasets 3. Currently, results must fit in memory - no on-disk caching is provided. """ from SALib.analyze import sobol from SALib.sample import saltelli from SALib.test_functions import Ishigami from SALib import ProblemSpec import numpy as np import time if __name__ == "__main__": # Create the SALib Problem specification sp = ProblemSpec( { "names": ["x1", "x2", "x3"], "groups": None, "bounds": [[-np.pi, np.pi]] * 3, "outputs": ["Y"], } ) # Single core example start = time.perf_counter() ( sp.sample_saltelli(2**15) .evaluate(Ishigami.evaluate) .analyze_sobol(calc_second_order=True, conf_level=0.95) ) print("Time taken with 1 core:", time.perf_counter() - start, "\n") # Same above example, but passing in specific functions # (sp.sample(saltelli.sample, 25000, calc_second_order=True) # .evaluate(Ishigami.evaluate) # .analyze(sobol.analyze, calc_second_order=True, conf_level=0.95)) # Samples, model results and analyses can be extracted: # print(sp.samples) # print(sp.results) # print(sp.analysis) # print(sp.to_df()) # Can set pre-existing samples/results as needed # sp.samples = some_numpy_array # sp.set_samples(some_numpy_array) # # Using method chaining... # (sp.set_samples(some_numpy_array) # .set_results(some_result_array) # .analyze_sobol(calc_second_order=True, conf_level=0.95)) # Parallel example start = time.perf_counter() ( sp.sample(saltelli.sample, 2**15) # can specify number of processors to use with `nprocs` # this will be capped to the number of detected processors # or, in the case of analysis, the number of outputs. .evaluate(Ishigami.evaluate, nprocs=2).analyze_sobol( calc_second_order=True, conf_level=0.95, nprocs=2 ) ) print("Time taken with 2 cores:", time.perf_counter() - start, "\n") print(sp) # Distributed example # This example requires an additional dependency (Pathos) to be installed # `pip install pathos` or `conda install pathos -c conda-forge` # Specify itself as servers as an example servers = ("localhost:55774", "localhost:55775", "localhost:55776") start = time.perf_counter() ( sp.sample(saltelli.sample, 2**15) .evaluate_distributed( Ishigami.evaluate, nprocs=2, servers=servers, verbose=True ) .analyze(sobol.analyze, calc_second_order=True, conf_level=0.95) ) print("Time taken with distributed cores:", time.perf_counter() - start, "\n") print(sp) # To display plots: # import matplotlib.pyplot as plt # sp.plot() # plt.show() # First-order indices expected with Saltelli sampling: # x1: 0.3139 # x2: 0.4424 # x3: 0.0 SALib-SALib-d6e51b1/examples/data/000077500000000000000000000000001525347100600165375ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/data/model_input.txt000066400000000000000000000442501525347100600216240ustar00rootroot00000000000000-3.49065850e-01 -3.14159265e+00 -3.14159265e+00 -3.49065850e-01 -3.14159265e+00 3.49065850e-01 3.14159265e+00 -3.14159265e+00 3.49065850e-01 3.14159265e+00 3.49065850e-01 3.49065850e-01 3.49065850e-01 -3.14159265e+00 3.49065850e-01 3.49065850e-01 3.49065850e-01 3.49065850e-01 -3.14159265e+00 3.49065850e-01 3.49065850e-01 -3.14159265e+00 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-3.595122591737719160e-09 8.188444436937516446e-01 1.161372376721790500e+00 -3.673607251739542612e+00 -2.854762804450668767e+00 8.188444858465147025e-01 8.188444508839969327e-01 4.492451699028417345e+00 8.188444087312338748e-01 8.188444436937516446e-01 -3.595122591737719160e-09 4.492451699028417345e+00 1.161372376721790500e+00 3.425279294329164337e-01 -3.595122591737719160e-09 -3.673607251739542612e+00 -3.425279294329162116e-01 4.763165178559579660e-01 8.188444508839969327e-01 8.188444087312338748e-01 8.188444436937516446e-01 -3.595122591737719160e-09 3.425279294329164337e-01 4.763165178559579660e-01 8.188444508839969327e-01 8.188444858465147025e-01 3.855764056392843505e-08 -3.673607251739542612e+00 -3.425279294329162116e-01 3.595122772150314756e-09 8.188444508839969327e-01 -2.854762804450668767e+00 8.188444858465147025e-01 8.188444508839969327e-01 3.595122772150314756e-09 -3.595122591737719160e-09 8.188444436937516446e-01 8.188444087312338748e-01 4.492451699028417345e+00 -3.595122591737719160e-09 -3.855764038351584359e-08 8.188444087312338748e-01 4.492451699028417345e+00 8.188444858465147025e-01 3.855764056392843505e-08 -3.673607251739542612e+00 -3.425279294329162116e-01 8.188444858465147025e-01 3.855764056392843505e-08 3.595122772150314756e-09 -3.425279294329162116e-01 -3.855764038351584359e-08 -3.595122591737719160e-09 3.425279294329164337e-01 1.161372376721790500e+00 -3.595122591737719160e-09 8.188444436937516446e-01 8.188444087312338748e-01 4.492451699028417345e+00 8.188444087312338748e-01 8.188444436937516446e-01 -3.595122591737719160e-09 3.425279294329164337e-01 8.188444858465147025e-01 8.188444508839969327e-01 4.763165178559579660e-01 -3.425279294329162116e-01 -2.854762804450668767e+00 4.763165178559579660e-01 8.188444508839969327e-01 3.595122772150314756e-09 -2.854762804450668767e+00 4.763165178559579660e-01 8.188444508839969327e-01 3.595122772150314756e-09 -3.425279294329162116e-01 4.763165178559579660e-01 8.188444508839969327e-01 8.188444858465147025e-01 3.855764056392843505e-08 3.595122772150314756e-09 8.188444508839969327e-01 4.763165178559579660e-01 -3.595122591737719160e-09 -3.855764038351584359e-08 8.188444087312338748e-01 4.492451699028417345e+00 -3.855764038351584359e-08 8.188444087312338748e-01 8.188444436937516446e-01 1.161372376721790500e+00 8.188444436937516446e-01 -3.595122591737719160e-09 3.425279294329164337e-01 3.673607251739543056e+00 -3.855764038351584359e-08 -3.595122591737719160e-09 3.425279294329164337e-01 1.161372376721790500e+00 8.188444087312338748e-01 -3.855764038351584359e-08 3.673607251739543056e+00 3.425279294329164337e-01 8.188444087312338748e-01 8.188444436937516446e-01 1.161372376721790500e+00 3.425279294329164337e-01 -3.673607251739542612e+00 3.855764056392843505e-08 3.595122772150314756e-09 8.188444508839969327e-01 4.492451699028417345e+00 1.161372376721790500e+00 8.188444436937516446e-01 -3.595122591737719160e-09 8.188444087312338748e-01 4.492451699028417345e+00 1.161372376721790500e+00 3.425279294329164337e-01 8.188444508839969327e-01 4.763165178559579660e-01 -3.425279294329162116e-01 -3.673607251739542612e+00 3.595122772150314756e-09 8.188444508839969327e-01 4.763165178559579660e-01 -2.854762804450668767e+00 8.188444508839969327e-01 3.595122772150314756e-09 3.855764056392843505e-08 -3.673607251739542612e+00 3.425279294329164337e-01 -3.595122591737719160e-09 8.188444436937516446e-01 8.188444087312338748e-01 -3.425279294329162116e-01 3.595122772150314756e-09 3.855764056392843505e-08 8.188444858465147025e-01 8.188444858465147025e-01 -2.854762804450668767e+00 4.763165178559579660e-01 -3.425279294329162116e-01 -3.425279294329162116e-01 4.763165178559579660e-01 -2.854762804450668767e+00 8.188444858465147025e-01 4.492451699028417345e+00 3.673607251739543056e+00 3.425279294329164337e-01 -3.595122591737719160e-09 1.161372376721790500e+00 8.188444436937516446e-01 -3.595122591737719160e-09 -3.855764038351584359e-08 3.855764056392843505e-08 -3.673607251739542612e+00 -3.425279294329162116e-01 4.763165178559579660e-01 8.188444087312338748e-01 4.492451699028417345e+00 3.673607251739543056e+00 3.425279294329164337e-01 3.425279294329164337e-01 1.161372376721790500e+00 4.492451699028417345e+00 8.188444087312338748e-01 8.188444436937516446e-01 1.161372376721790500e+00 3.425279294329164337e-01 3.673607251739543056e+00 -3.595122591737719160e-09 -3.855764038351584359e-08 8.188444087312338748e-01 4.492451699028417345e+00 -3.855764038351584359e-08 8.188444087312338748e-01 4.492451699028417345e+00 1.161372376721790500e+00 -3.855764038351584359e-08 8.188444087312338748e-01 4.492451699028417345e+00 1.161372376721790500e+00 8.188444858465147025e-01 8.188444508839969327e-01 3.595122772150314756e-09 -3.425279294329162116e-01 SALib-SALib-d6e51b1/examples/delta/000077500000000000000000000000001525347100600167175ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/delta/delta.bat000066400000000000000000000024041525347100600205000ustar00rootroot00000000000000@echo off REM Sensitivity indices will print to command line. Use ">" to write to file. salib analyze delta ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -X ../data/model_input.txt ^ -Y ../data/model_output.txt ^ -c 0 ^ -r 10 ^ --seed=100 REM Then use the output to run the analysis. REM You can also use the module directly through Python REM python -m SALib.analyze.delta ^ REM -p ../../src/SALib/test_functions/params/Ishigami.txt ^ REM -X ../data/model_input.txt ^ REM -Y ../data/model_output.txt ^ REM -c 0 ^ REM -r 10 ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) REM REM -Y, --model-output-file: File of model output values to analyze REM REM -X, --model-input-file: File of model input values (parameter samples). REM REM -c, --column (optional): Column of model output file to analyze. REM If the file only has one column, this argument will be ignored. REM REM --delimiter (optional): Model output file delimiter. REM REM -r, --resamples (optional): Number of bootstrap resamples used to calculate confidence intervals on indices. Default 1000. REM REM -s, --seed (optional): Seed value for random number generation SALib-SALib-d6e51b1/examples/delta/delta.py000066400000000000000000000013731525347100600203660ustar00rootroot00000000000000import sys from SALib.analyze import delta from SALib.util import read_param_file import numpy as np sys.path.append("../..") # Read the parameter range file and generate samples # Since this is "given data", the bounds in the parameter file will not be used # but the columns are still expected problem = read_param_file("../../src/SALib/test_functions/params/Ishigami.txt") X = np.loadtxt("../data/model_input.txt") Y = np.loadtxt("../data/model_output.txt") # Perform the sensitivity analysis using the model output # Specify which column of the output file to analyze (zero-indexed) # Returns a dictionary with keys 'delta', 'delta_conf', 'S1', 'S1_conf' Si = delta.analyze( problem, X, Y, num_resamples=10, conf_level=0.95, print_to_console=True ) SALib-SALib-d6e51b1/examples/delta/delta.sh000066400000000000000000000023241525347100600203450ustar00rootroot00000000000000#!/bin/bash # Sensitivity indices will print to command line. Use ">" to write to file. salib analyze delta \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -X ../data/model_input.txt \ -Y ../data/model_output.txt \ -c 0 \ -r 10 \ --seed=100 # Then use the output to run the analysis. # You can also use the module directly through Python # python -m SALib.analyze.delta \ # -p ../../src/SALib/test_functions/params/Ishigami.txt \ # -X ../data/model_input.txt \ # -Y ../data/model_output.txt \ # -c 0 \ # -r 10 \ # --seed=100 # Options: # -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) # # -Y, --model-output-file: File of model output values to analyze # # -X, --model-input-file: File of model input values (parameter samples). # # -c, --column (optional): Column of model output file to analyze. # If the file only has one column, this argument will be ignored. # # --delimiter (optional): Model output file delimiter. # # -r, --resamples (optional): Number of bootstrap resamples used to calculate confidence intervals on indices. Default 1000. # # -s, --seed (optional): Seed value for random number generation SALib-SALib-d6e51b1/examples/delta_mwe/000077500000000000000000000000001525347100600175675ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/delta_mwe/delta_mwe.py000066400000000000000000000012151525347100600221010ustar00rootroot00000000000000from SALib.analyze import delta import numpy as np import pandas as pd df = pd.DataFrame() # read in dataframe here col_output = "title_outcol" # column name in df which is output Y bootstrap_fn = ( "fn_bootstrap_inspect.parquet" # parquet file to inspect bootstrap subset ) Y = np.asarray(df[col_output].values) cols_input = [col for col in df.columns if col != col_output] X = df[cols_input].values problem = { "num_vars": len(cols_input), "names": cols_input, "bounds": [[X[:, i].min(), X[:, i].max()] for i in range(len(cols_input))], } Si = delta.analyze(problem, X, Y, print_to_console=True, bootstrap_savedf=bootstrap_fn) SALib-SALib-d6e51b1/examples/dgsm/000077500000000000000000000000001525347100600165605ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/dgsm/dgsm.bat000066400000000000000000000051141525347100600202030ustar00rootroot00000000000000@echo off REM Example: generating samples from the command line salib sample finite_diff ^ -n 1000 ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -o ../data/model_input.txt ^ -d 0.001 ^ --delimiter=" " ^ --precision=8 ^ --seed=100 REM You can also use the module directly through Python REM python -m SALib.sample.finite_diff ^ REM -n 1000 ^ REM -p ../../src/SALib/test_functions/params/Ishigami.txt ^ REM -o ../data/model_input.txt ^ REM -d 0.001 ^ REM --delimiter=' ' ^ REM --precision=8 ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) REM REM -n, --samples: Sample size. REM Number of model runs is N(2D + 2) if calculating second-order indices (default) REM or N(D + 2) otherwise. REM REM -o, --output: File to output your samples into. REM REM -d, --delta (optional): Finite difference step size (percent). Default is 0.01. REM REM --delimiter (optional): Output file delimiter. REM REM --precision (optional): Digits of precision in the output file. Default is 8. REM REM -s, --seed (optional): Seed value for random number generation REM Run the model using the inputs sampled above, and save outputs python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" REM Then use the output to run the analysis. REM Sensitivity indices will print to command line. Use ">" to write to file. salib analyze dgsm ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -X ../data/model_input.txt ^ -Y ../data/model_output.txt ^ -c 0 ^ -r 1000 ^ --seed=100 REM python -m SALib.analyze.dgsm ^ REM -p ../../src/SALib/test_functions/params/Ishigami.txt ^ REM -X ../data/model_input.txt ^ REM -Y ../data/model_output.txt ^ REM -c 0 ^ REM -r 1000 ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) REM REM -Y, --model-output-file: File of model output values to analyze REM REM -X, --model-input-file: File of model input values REM REM -c, --column (optional): Column of model output file to analyze. REM If the file only has one column, this argument will be ignored. REM REM --delimiter (optional): Model output file delimiter. REM REM -r, --resamples (optional): Number of bootstrap resamples used to calculate confidence intervals on indices. Default 1000. REM REM -s, --seed (optional): Seed value for random number generation SALib-SALib-d6e51b1/examples/dgsm/dgsm.py000066400000000000000000000017701525347100600200710ustar00rootroot00000000000000import sys from SALib.analyze import dgsm from SALib.sample import finite_diff from SALib.test_functions import Ishigami from SALib.util import read_param_file sys.path.append("../..") # Read the parameter range file and generate samples problem = read_param_file("../../src/SALib/test_functions/params/Ishigami.txt") # Generate samples param_values = finite_diff.sample(problem, 1000, delta=0.001) # Run the "model" -- this will happen offline for external models Y = Ishigami.evaluate(param_values) # Perform the sensitivity analysis using the model output # Specify which column of the output file to analyze (zero-indexed) Si = dgsm.analyze(problem, param_values, Y, conf_level=0.95, print_to_console=True) # Returns a dictionary with keys 'vi', 'vi_std', 'dgsm', and 'dgsm_conf' # e.g. Si['vi'] contains the sensitivity measure for each parameter, in # the same order as the parameter file # For comparison, Morris mu* < sqrt(v_i) # and total order S_tot <= dgsm, following Sobol and Kucherenko (2009) SALib-SALib-d6e51b1/examples/dgsm/dgsm.sh000066400000000000000000000047501525347100600200540ustar00rootroot00000000000000#!/bin/bash # Example: generating samples from the command line salib sample finite_diff \ -n 1000 \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -o ../data/model_input.txt \ -d 0.001 \ --delimiter=' ' \ --precision=8 \ --seed=100 # You can also use the module directly through Python # python -m SALib.sample.finite_diff \ # -n 1000 \ # -p ../../src/SALib/test_functions/params/Ishigami.txt \ # -o ../data/model_input.txt \ # -d 0.001 \ # --delimiter=' ' \ # --precision=8 \ # --seed=100 # Options: # -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) # # -n, --samples: Sample size. # Number of model runs is N(2D + 2) if calculating second-order indices (default) # or N(D + 2) otherwise. # # -o, --output: File to output your samples into. # # -d, --delta (optional): Finite difference step size (percent). Default is 0.01. # # --delimiter (optional): Output file delimiter. # # --precision (optional): Digits of precision in the output file. Default is 8. # # -s, --seed (optional): Seed value for random number generation # Run the model using the inputs sampled above, and save outputs python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" # Then use the output to run the analysis. # Sensitivity indices will print to command line. Use ">" to write to file. salib analyze dgsm \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -X ../data/model_input.txt \ -Y ../data/model_output.txt \ -c 0 \ -r 1000 \ --seed=100 # python -m SALib.analyze.dgsm \ # -p ../../src/SALib/test_functions/params/Ishigami.txt \ # -X ../data/model_input.txt \ # -Y ../data/model_output.txt \ # -c 0 \ # -r 1000 \ # --seed=100 # Options: # -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) # # -Y, --model-output-file: File of model output values to analyze # # -X, --model-input-file: File of model input values # # -c, --column (optional): Column of model output file to analyze. # If the file only has one column, this argument will be ignored. # # --delimiter (optional): Model output file delimiter. # # -r, --resamples (optional): Number of bootstrap resamples used to calculate confidence intervals on indices. Default 1000. # # -s, --seed (optional): Seed value for random number generation SALib-SALib-d6e51b1/examples/enhanced_hdmr/000077500000000000000000000000001525347100600204055ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/enhanced_hdmr/enhanced_hdmr.bat000066400000000000000000000040621525347100600236560ustar00rootroot00000000000000@echo off REM Example: generating samples from the command line salib sample latin ^ -n 1000 ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -o ../data/model_input.txt ^ --delimiter=" " ^ --precision=8 ^ --seed=100 REM Run model and save output python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" REM Perform hdmr analysis salib analyze enhanced_hdmr ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -X ../data/model_input.txt ^ -Y ../data/model_output.txt ^ -c 0 ^ -mor 2 ^ -por 7 ^ -K 20 ^ -R 500 ^ -mit 100 ^ -l2 0.01 ^ -a 0.95 ^ -ext True ^ -print True ^ -emul True PAUSE REM Options: REM -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) REM REM -Y, --model-output-file: File of model output values to analyze REM REM -X, --model-input-file: File of model input values (parameter samples). REM REM -c, --column (optional): Column of model output file to analyze. REM If the file only has one column, this argument will be ignored. REM REM -mor, --max-order (optional): Maximum order of HDMR expansion (1,2,3). Default is 2. REM REM -por, --poly-order (optional): Maximum polynomial order (1-10). Default is 3. REM REM -K, --bootstrap (optional): Number of bootstrap (1-100). Default is 20. REM REM -R, --subset (optional): Subsample size (300-N). Default is N/2. REM REM -mit, --max-iter (optional): Maximum iteration number for backfitting algorithm (1-1000). Default is 100. REM REM -l2, --l2-penalty (optional): Regularization term. Default is 0.01. REM REM -a, --alpha (optional): Confidence interval for F-Test. Default is 0.95. REM REM -ext, --extended-base (optional): Whether to use extended base matrix. Default is True. REM REM -print, --print-to-console (optional): Whether to print out result to the console. Default is False REM REM -emul, --return-emulator (optional): Whether to attach emulate() method to the ResultDic. Default is False SALib-SALib-d6e51b1/examples/enhanced_hdmr/enhanced_hdmr.py000066400000000000000000000024711525347100600235420ustar00rootroot00000000000000import sys sys.path.append("../../src") import numpy as np from SALib.analyze import enhanced_hdmr from SALib.sample import latin from SALib.test_functions import Ishigami # Define SALib problem specification. problem = {"num_vars": 3, "names": ["x1", "x2", "x3"], "bounds": [[-np.pi, np.pi]] * 3} # Generate samples X = latin.sample(problem, 1000, seed=101) # Run the "model" and save the output in a text file Y = Ishigami.evaluate(X) # Add random error Y += np.var(Y) / 100 # SALib-HDMR options options = { "max_order": 2, "poly_order": 6, "bootstrap": 50, "subset": 500, "max_iter": 100, "l2_penalty": 0.01, "alpha": 0.95, "extended_base": True, "print_to_console": True, "return_emulator": True, "seed": 101, } # Run SALib-HDMR Si = enhanced_hdmr.analyze(problem, X, Y, **options) # Displays sensitivity results and HDMR training results Si.plot() # Generate samples int(np.random.random() * 100) X_new = latin.sample(problem, 1000, seed=int(np.random.random() * 100)) # Run the "model" Y_new = Ishigami.evaluate(X_new) # Test emulator with new Y values. # Can call `emulate()` without Y values, which will run the emulator # Emulation results will be in Si["emulated"] Y_em = Si.emulate(X_new) + np.mean(Y_new) print(f"\nSum of squared residual is: {sum((Y_em - Y_new)**2)}") SALib-SALib-d6e51b1/examples/enhanced_hdmr/enhanced_hdmr.sh000066400000000000000000000037551525347100600235320ustar00rootroot00000000000000#!/bin/bash # Example: generating samples from the command line salib sample latin \ -n 1000 \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -o ../data/model_input.txt \ --delimiter=" " \ --precision=8 \ --seed=100 # Run model and save output python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" # Perform hdmr analysis salib analyze enhanced_hdmr \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -X ../data/model_input.txt \ -Y ../data/model_output.txt \ -c 0 \ -mor 2 \ -por 7 \ -K 20 \ -R 500 \ -mit 100 \ -l2 0.01 \ -a 0.95 \ -ext True \ -print True \ -emul True # Options: # -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) # # -Y, --model-output-file: File of model output values to analyze # # -X, --model-input-file: File of model input values (parameter samples). # # -c, --column (optional): Column of model output file to analyze. # If the file only has one column, this argument will be ignored. # # -mor, --max-order (optional): Maximum order of HDMR expansion (1,2,3). Default is 2. # # -por, --poly-order (optional): Maximum polynomial order (1-10). Default is 3. # # -K, --bootstrap (optional): Number of bootstrap (1-100). Default is 20. # # -R, --subset (optional): Subsample size (300-N). Default is N/2. # # -mit, --max-iter (optional): Maximum iteration number for backfitting algorithm (1-1000). Default is 100. # # -l2, --l2-penalty (optional): Regularization term. Default is 0.01. # # -a, --alpha (optional): Confidence interval for F-Test. Default is 0.95. # # -ext, --extended-base (optional): Whether to use extended base matrix. Default is True. # # -print, --print-to-console (optional): Whether to print out result to the console. Default is False # # -emul, --return-emulator (optional): Whether to attach emulate() method to the ResultDic. Default is False SALib-SALib-d6e51b1/examples/fast/000077500000000000000000000000001525347100600165635ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/fast/fast.bat000066400000000000000000000042651525347100600202170ustar00rootroot00000000000000@echo off REM Example: generating samples from the command line salib sample fast_sampler ^ -n 1000 ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -o ../data/model_input.txt ^ --delimiter=" " ^ --precision=8 ^ -M 4 ^ --seed=100 REM You can also use the module directly through Python REM python -m SALib.sample.fast_sampler ^ REM -n 1000 ^ REM -p ../../src/SALib/test_functions/params/Ishigami.txt ^ REM -o ../data/model_input.txt ^ REM --delimiter=' ' ^ REM --precision=8 ^ REM -M 4 ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) REM REM -n, --samples: Sample size. REM Number of model runs is ND ; must choose N > 4M^2 (N > 64 under default settings) REM REM -o, --output: File to output your samples into. REM REM --delimiter (optional): Output file delimiter. REM REM --precision (optional): Digits of precision in the output file. Default is 8. REM REM -M: FAST M coefficient, default 4 REM REM -s, --seed (optional): Seed value for random number generation REM Run the model using the inputs sampled above, and save outputs python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" REM Then use the output to run the analysis. REM Sensitivity indices will print to command line. Use ">" to write to file. salib analyze fast ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -Y ../data/model_output.txt ^ -c 0 ^ --seed=100 REM python -m SALib.analyze.fast ^ REM -p ../../src/SALib/test_functions/params/Ishigami.txt ^ REM -Y ../data/model_output.txt ^ REM -c 0 ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) REM REM -Y, --model-output-file: File of model output values to analyze REM REM -c, --column (optional): Column of model output file to analyze. REM If the file only has one column, this argument will be ignored. REM REM --delimiter (optional): Model output file delimiter. REM REM -s, --seed (optional): Seed value for random number generation SALib-SALib-d6e51b1/examples/fast/fast.py000066400000000000000000000015651525347100600201010ustar00rootroot00000000000000import sys sys.path.append("../..") from SALib.analyze import fast from SALib.sample import fast_sampler from SALib.test_functions import Ishigami from SALib.util import read_param_file # Read the parameter range file and generate samples problem = read_param_file("../../src/SALib/test_functions/params/Ishigami.txt") # Generate samples param_values = fast_sampler.sample(problem, 1000, seed=100) # Run the "model" and save the output in a text file # This will happen offline for external models Y = Ishigami.evaluate(param_values) # Perform the sensitivity analysis using the model output # Specify which column of the output file to analyze (zero-indexed) Si = fast.analyze(problem, Y, print_to_console=True, seed=100) # Returns a dictionary with keys 'S1' and 'ST' # e.g. Si['S1'] contains the first-order index for each parameter, in the # same order as the parameter file SALib-SALib-d6e51b1/examples/fast/fast.sh000066400000000000000000000041371525347100600200610ustar00rootroot00000000000000#!/bin/bash # Example: generating samples from the command line salib sample fast_sampler \ -n 1000 \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -o ../data/model_input.txt \ --delimiter=' ' \ --precision=8 \ -M 4 \ --seed=100 # You can also use the module directly through Python # python -m SALib.sample.fast_sampler \ # -n 1000 \ # -p ../../src/SALib/test_functions/params/Ishigami.txt \ # -o ../data/model_input.txt \ # --delimiter=' ' \ # --precision=8 \ # -M 4 \ # --seed=100 # Options: # -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) # # -n, --samples: Sample size. # Number of model runs is ND ; must choose N > 4M^2 (N > 64 under default settings) # # -o, --output: File to output your samples into. # # --delimiter (optional): Output file delimiter. # # --precision (optional): Digits of precision in the output file. Default is 8. # # -M: FAST M coefficient, default 4 # # -s, --seed (optional): Seed value for random number generation # Run the model using the inputs sampled above, and save outputs python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" # Then use the output to run the analysis. # Sensitivity indices will print to command line. Use ">" to write to file. salib analyze fast \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -Y ../data/model_output.txt \ -c 0 \ --seed=100 # python -m SALib.analyze.fast \ # -p ../../src/SALib/test_functions/params/Ishigami.txt \ # -Y ../data/model_output.txt \ # -c 0 \ # --seed=100 # Options: # -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) # # -Y, --model-output-file: File of model output values to analyze # # -c, --column (optional): Column of model output file to analyze. # If the file only has one column, this argument will be ignored. # # --delimiter (optional): Model output file delimiter. # # -s, --seed (optional): Seed value for random number generation SALib-SALib-d6e51b1/examples/ff/000077500000000000000000000000001525347100600162215ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/ff/ff.bat000066400000000000000000000045601525347100600173110ustar00rootroot00000000000000@echo off REM Example: generating samples from the command line salib sample ff ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -o ../data/model_input.txt ^ -n 100 ^ --delimiter=" " ^ --precision=8 ^ --seed=100 REM You can also use the module directly through Python REM python -m SALib.sample.ff ^ REM -p ../../src/SALib/test_functions/params/Ishigami.txt ^ REM -o ../data/model_input.txt ^ REM -n 100 ^ REM --delimiter=" " ^ REM --precision=8 ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file REM (3 columns: parameter name, REM lower bound, REM upper bound) with an optional 4th "group" column for Morris only REM REM -o, --output: File to output your samples into. REM REM --delimiter (optional): Output file delimiter. REM REM --precision (optional): Digits of precision in the output file. Default is 8. REM REM -s, --seed (optional): Seed value for random number generation REM Run the model using the inputs sampled above, and save outputs python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" REM Then use the output to run the analysis. REM Sensitivity indices will print to command line. Use ">" to write to file. salib analyze ff ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -Y ../data/model_output.txt ^ -c 0 ^ -X ../data/model_input.txt ^ --seed=100 REM python -m SALib.analyze.ff ^ REM -p ../../src/SALib/test_functions/params/Ishigami.txt ^ REM -Y ../data/model_output.txt ^ REM -c 0 ^ REM -X ../data/model_input.txt ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file REM (3 columns: parameter name, REM lower bound, REM upper bound) REM REM -Y, --model-output-file: File of model output values to analyze REM REM -c, --column (optional): Column of model output file to analyze. REM If the file only has one column, this argument will be ignored. REM REM --delimiter (optional): Model output file delimiter. REM REM -X, --model-input-file: File of model input values (parameter samples). REM REM -s, --seed (optional): Seed value for random number generation SALib-SALib-d6e51b1/examples/ff/ff.py000066400000000000000000000021361525347100600171700ustar00rootroot00000000000000import sys from SALib.analyze.ff import analyze from SALib.sample.ff import sample from SALib.util import read_param_file sys.path.append("../..") # Read the parameter range file and generate samples problem = read_param_file("../../src/SALib/test_functions/params/Ishigami.txt") # or define manually without a parameter file: # problem = { # 'num_vars': 3, # 'names': ['x1', 'x2', 'x3'], # 'groups': None, # 'bounds': [[-3.14159265359, 3.14159265359], # [-3.14159265359, 3.14159265359], # [-3.14159265359, 3.14159265359]] # } # Generate samples X = sample(problem) # Run the "model" -- this will happen offline for external models Y = X[:, 0] + (0.1 * X[:, 1]) + ((1.2 * X[:, 2]) * (0.2 + X[:, 0])) # Perform the sensitivity analysis using the model output analyze(problem, X, Y, second_order=True, print_to_console=True) # Returns a dictionary with keys 'ME' (main effect) and 'IE' (interaction effect) # The techniques bulks out the number of parameters with dummy parameters to the # nearest 2**n. Any results involving dummy parameters should be treated with # a sceptical eye. SALib-SALib-d6e51b1/examples/ff/ff.sh000066400000000000000000000044241525347100600171540ustar00rootroot00000000000000#!/bin/bash # Example: generating samples from the command line salib sample ff \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -o ../data/model_input.txt \ -n 100 \ --delimiter=' ' \ --precision=8 \ --seed=100 # You can also use the module directly through Python # python -m SALib.sample.ff \ # -p ../../src/SALib/test_functions/params/Ishigami.txt \ # -o ../data/model_input.txt \ # -n 100 \ # --delimiter=' ' \ # --precision=8 \ # --seed=100 # Options: # -p, --paramfile: Your parameter range file # (3 columns: parameter name, # lower bound, # upper bound) with an optional 4th "group" column for Morris only # # -o, --output: File to output your samples into. # # --delimiter (optional): Output file delimiter. # # --precision (optional): Digits of precision in the output file. Default is 8. # # -s, --seed (optional): Seed value for random number generation # Run the model using the inputs sampled above, and save outputs python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" # Then use the output to run the analysis. # Sensitivity indices will print to command line. Use ">" to write to file. salib analyze ff \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -Y ../data/model_output.txt \ -c 0 \ -X ../data/model_input.txt \ --seed=100 # python -m SALib.analyze.ff \ # -p ../../src/SALib/test_functions/params/Ishigami.txt \ # -Y ../data/model_output.txt \ # -c 0 \ # -X ../data/model_input.txt \ # --seed=100 # Options: # -p, --paramfile: Your parameter range file # (3 columns: parameter name, # lower bound, # upper bound) # # -Y, --model-output-file: File of model output values to analyze # # -c, --column (optional): Column of model output file to analyze. # If the file only has one column, this argument will be ignored. # # --delimiter (optional): Model output file delimiter. # # -X, --model-input-file: File of model input values (parameter samples). # # -s, --seed (optional): Seed value for random number generation SALib-SALib-d6e51b1/examples/hdmr/000077500000000000000000000000001525347100600165605ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/hdmr/hdmr.bat000066400000000000000000000032511525347100600202030ustar00rootroot00000000000000@echo off REM Example: generating samples from the command line salib sample latin ^ -n 1000 ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -o ../data/model_input.txt ^ --delimiter=" " ^ --precision=8 ^ --seed=100 REM Run model and save output python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" REM Perform hdmr analysis salib analyze hdmr ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -X ../data/model_input.txt ^ -Y ../data/model_output.txt ^ -c 0 ^ -mor 2 ^ -mit 100 ^ -m 4 ^ -K 20 ^ -R 500 ^ -a 0.95 ^ -lambda 0.01 PAUSE REM Options: REM -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) REM REM -Y, --model-output-file: File of model output values to analyze REM REM -X, --model-input-file: File of model input values (parameter samples). REM REM -c, --column (optional): Column of model output file to analyze. REM If the file only has one column, this argument will be ignored. REM REM -mor, --maxorder (optional): Maximum order of HDMR expansion (1,2,3). Default is 2. REM REM -mit, --maxiter (optional): Maximum iteration number for backfitting algorithm (1-1000). Default is 100. REM REM -m, --m-int (optional): Number of B-spline intervals. Default is 2. REM REM -K, --K-bootstrap (optional): Number of bootstrap (1,2,3). Default is 20. REM REM -R, --R-subsample (optional): Subsample size. Default is N/2. REM REM -a, --alfa (optional): Confidence interval. Default is 0.95 REM REM -lambda, --lambdax (optional): Regularization constant. Default is 0.01 SALib-SALib-d6e51b1/examples/hdmr/hdmr.py000066400000000000000000000024611525347100600200670ustar00rootroot00000000000000import sys sys.path.append("../../src") import numpy as np from SALib.analyze import hdmr from SALib.sample import latin from SALib.test_functions import Ishigami # This is the test case taken from Li's paper # Genyuan Li et al., Journal of Physical Chemistry A., V. 114 (19), # pp. 6022-6032, 2010. # Define SALib problem specification. problem = {"num_vars": 3, "names": ["x1", "x2", "x3"], "bounds": [[-np.pi, np.pi]] * 3} # Generate samples X = latin.sample(problem, 1000, seed=101) # Run the "model" and save the output in a text file Y = Ishigami.evaluate(X) # Add random error sigma = np.var(Y) / 100 # SALib-HDMR options options = { "maxorder": 2, "maxiter": 100, "m": 4, "K": 30, "R": 500, "alpha": 0.95, "lambdax": 0.01, "print_to_console": True, "seed": 101, } # Run SALib-HDMR Si = hdmr.analyze(problem, X, Y, **options) # Displays sensitivity results and HDMR training results Si.plot() # Generate samples X = latin.sample(problem, 5000, seed=int(np.random.random() * 100)) # Run the "model" Y = Ishigami.evaluate(X) # Test emulator with new Y values. # Can call `emulate()` without Y values, which will run the emulator # Emulation results will be in Si["emulated"] Si.emulate(X, Y) # Displays results for both training and testing after emulator is tested. Si.plot() SALib-SALib-d6e51b1/examples/hdmr/hdmr.sh000066400000000000000000000031611525347100600200470ustar00rootroot00000000000000#!/bin/bash # Example: generating samples from the command line salib sample latin \ -n 1000 \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -o ../data/model_input.txt \ --delimiter=" " \ --precision=8 \ --seed=100 # Run model and save output python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" # Perform hdmr analysis salib analyze hdmr \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -X ../data/model_input.txt \ -Y ../data/model_output.txt \ -c 0 \ -mor 2 \ -mit 100 \ -m 4 \ -K 20 \ -R 500 \ -a 0.95 \ -lambda 0.01 # Options: # -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) # # -Y, --model-output-file: File of model output values to analyze # # -X, --model-input-file: File of model input values (parameter samples). # # -c, --column (optional): Column of model output file to analyze. # If the file only has one column, this argument will be ignored. # # -mor, --maxorder (optional): Maximum order of HDMR expansion (1,2,3). Default is 2. # # -mit, --maxiter (optional): Maximum iteration number for backfitting algorithm (1-1000). Default is 100. # # -m, --m-int (optional): Number of B-spline intervals. Default is 2. # # -K, --K-bootstrap (optional): Number of bootstrap (1,2,3). Default is 20. # # -R, --R-subsample (optional): Subsample size. Default is N/2. # # -a, --alpha (optional): Confidence interval. Default is 0.95 # # -lambda, --lambdax (optional): Regularization constant. Default is 0.01 SALib-SALib-d6e51b1/examples/morris/000077500000000000000000000000001525347100600171415ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/morris/morris.bat000066400000000000000000000065361525347100600211560ustar00rootroot00000000000000@echo off REM Example: generating samples from the command line salib sample morris ^ -n 100 ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -o ../data/model_input.txt ^ -lo True ^ --delimiter=" " ^ --precision=8 ^ --levels=10 ^ --seed=100 REM You can also use the module directly through Python REM python -m SALib.sample.morris ^ REM -n 100 ^ REM -p ../../src/SALib/test_functions/params/Ishigami.txt ^ REM -o ../data/model_input.txt ^ REM -lo True ^ REM --delimiter=" " ^ REM --precision=8 ^ REM --levels=10 ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file REM (3 columns: parameter name, REM lower bound, REM upper bound) with an optional 4th "group" column for Morris only REM REM -n, --samples: Sample size. REM Number of model runs is N(D + 1) REM REM -o, --output: File to output your samples into. REM REM -lo --local: Use local optimization REM REM --delimiter (optional): Output file delimiter. REM REM --precision (optional): Digits of precision in the output file. Default is 8. REM REM -l, --levels (optional): Number of levels in the OAT sampling. REM The range of each variable will be discretized into this many levels. REM Default is 4. REM REM --grid-jump (optional): Grid jump size in the OAT sampling. REM Each variable will be perturbed by this number of levels REM during each trajectory. Default is 2. REM REM -k, --k-optimal (optional): Number of optimal trajectories. REM Default behavior uses vanilla OAT if --k-optimal is not specified REM REM -s, --seed (optional): Seed value for random number generation REM Run the model using the inputs sampled above, and save outputs python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" REM Then use the output to run the analysis. REM Sensitivity indices will print to command line. Use ">" to write to file. salib analyze morris ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -Y ../data/model_output.txt ^ -c 0 ^ -X ../data/model_input.txt ^ -r 1000 ^ -l=10 ^ --seed=100 REM python -m SALib.analyze.morris ^ REM -p ../../src/SALib/test_functions/params/Ishigami.txt ^ REM -Y ../data/model_output.txt ^ REM -c 0 ^ REM -X ../data/model_input.txt ^ REM -r 1000 ^ REM -l=10 ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file REM (3 columns: parameter name, REM lower bound, REM upper bound) REM REM -Y, --model-output-file: File of model output values to analyze REM REM -c, --column (optional): Column of model output file to analyze. REM If the file only has one column, this argument will be ignored. REM REM --delimiter (optional): Model output file delimiter. REM REM -X, --model-input-file: File of model input values (parameter samples). REM REM -r, --resamples (optional): Number of bootstrap resamples used to calculate confidence REM intervals on indices. Default 1000. REM REM -s, --seed (optional): Seed value for random number generation SALib-SALib-d6e51b1/examples/morris/morris.py000066400000000000000000000037351525347100600210360ustar00rootroot00000000000000import sys from SALib.analyze import morris from SALib.sample.morris import sample from SALib.test_functions import Sobol_G from SALib.util import read_param_file from SALib.plotting.morris import ( horizontal_bar_plot, covariance_plot, sample_histograms, ) import matplotlib.pyplot as plt sys.path.append("../..") # Read the parameter range file and generate samples problem = read_param_file("../../src/SALib/test_functions/params/Sobol_G.txt") # or define manually without a parameter file: # problem = { # 'num_vars': 8, # 'names': ['x1', 'x2', 'x3', 'x4', 'x5', 'x6', 'x7', 'x8'], # 'groups': None, # 'bounds': [[0.0, 1.0], # [0.0, 1.0], # [0.0, 1.0], # [0.0, 1.0], # [0.0, 1.0], # [0.0, 1.0], # [0.0, 1.0], # [0.0, 1.0]] # } # Files with a 4th column for "group name" will be detected automatically, e.g. # param_file = '../../src/SALib/test_functions/params/Ishigami_groups.txt' # Generate samples param_values = sample(problem, N=1000, num_levels=4, optimal_trajectories=None) # To use optimized trajectories (brute force method), # give an integer value for optimal_trajectories # Run the "model" -- this will happen offline for external models Y = Sobol_G.evaluate(param_values) # Perform the sensitivity analysis using the model output # Specify which column of the output file to analyze (zero-indexed) Si = morris.analyze( problem, param_values, Y, conf_level=0.95, print_to_console=True, num_levels=4, num_resamples=100, ) # Returns a dictionary with keys 'mu', 'mu_star', 'sigma', and 'mu_star_conf' # e.g. Si['mu_star'] contains the mu* value for each parameter, in the # same order as the parameter file fig, (ax1, ax2) = plt.subplots(1, 2) horizontal_bar_plot(ax1, Si, {}, sortby="mu_star", unit=r"tCO$_2$/year") covariance_plot(ax2, Si, {}, unit=r"tCO$_2$/year") fig2 = plt.figure() sample_histograms(fig2, param_values, problem, {"color": "y"}) plt.show() SALib-SALib-d6e51b1/examples/morris/morris.sh000066400000000000000000000063241525347100600210150ustar00rootroot00000000000000#!/bin/bash # Example: generating samples from the command line salib sample morris \ -n 100 \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -o ../data/model_input.txt \ -lo True \ --delimiter=' ' \ --precision=8 \ --levels=10 \ --seed=100 # You can also use the module directly through Python # python -m SALib.sample.morris \ # -n 100 \ # -p ../../src/SALib/test_functions/params/Ishigami.txt \ # -o ../data/model_input.txt \ # -lo True \ # --delimiter=' ' \ # --precision=8 \ # --levels=10 \ # --seed=100 # Options: # -p, --paramfile: Your parameter range file # (3 columns: parameter name, # lower bound, # upper bound) with an optional 4th "group" column for Morris only # # -n, --samples: Sample size. # Number of model runs is N(D + 1) # # -o, --output: File to output your samples into. # # -lo --local: Use local optimization # # --delimiter (optional): Output file delimiter. # # --precision (optional): Digits of precision in the output file. Default is 8. # # -l, --levels (optional): Number of levels in the OAT sampling. # The range of each variable will be discretized into this many levels. # Default is 4. # # --grid-jump (optional): Grid jump size in the OAT sampling. # Each variable will be perturbed by this number of levels # during each trajectory. Default is 2. # # -k, --k-optimal (optional): Number of optimal trajectories. # Default behavior uses vanilla OAT if --k-optimal is not specified # # -s, --seed (optional): Seed value for random number generation # Run the model using the inputs sampled above, and save outputs python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" # Then use the output to run the analysis. # Sensitivity indices will print to command line. Use ">" to write to file. salib analyze morris \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -Y ../data/model_output.txt \ -c 0 \ -X ../data/model_input.txt \ -r 1000 \ -l=10 \ --seed=100 # python -m SALib.analyze.morris \ # -p ../../src/SALib/test_functions/params/Ishigami.txt \ # -Y ../data/model_output.txt \ # -c 0 \ # -X ../data/model_input.txt \ # -r 1000 \ # -l=10 \ # --seed=100 # Options: # -p, --paramfile: Your parameter range file # (3 columns: parameter name, # lower bound, # upper bound) # # -Y, --model-output-file: File of model output values to analyze # # -c, --column (optional): Column of model output file to analyze. # If the file only has one column, this argument will be ignored. # # --delimiter (optional): Model output file delimiter. # # -X, --model-input-file: File of model input values (parameter samples). # # -r, --resamples (optional): Number of bootstrap resamples used to calculate confidence # intervals on indices. Default 1000. # # -s, --seed (optional): Seed value for random number generation SALib-SALib-d6e51b1/examples/pawn/000077500000000000000000000000001525347100600165735ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/pawn/pawn.bat000066400000000000000000000040471525347100600202350ustar00rootroot00000000000000@echo off REM Example: generating samples from the command line salib sample latin ^ -n 1000 ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -o ../data/model_input.txt ^ --delimiter=" " ^ --precision=8 ^ --seed=100 REM You can also use the module directly through Python REM python -m SALib.sample.latin ^ REM -n 1000 ^ REM -p ./src/SALib/test_functions/params/Ishigami.txt ^ REM -o model_input.txt ^ REM --delimiter=" " ^ REM --precision=8 ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) REM REM -n, --samples: Sample size. REM Number of model runs is N REM REM -o, --output: File to output your samples into. REM REM --delimiter (optional): Output file delimiter. REM REM --precision (optional): Digits of precision in the output file. Default is 8. REM REM -M: RBD-FAST M coefficient, default 4 REM REM -s, --seed (optional): Seed value for random number generation REM Run the model using the inputs sampled above, and save outputs python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" REM Then use the output to run the analysis. REM Sensitivity indices will print to command line. Use ">" to write to file. salib analyze pawn ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -X ../data/model_input.txt ^ -Y ../data/model_output.txt ^ --seed=100 REM python -m SALib.analyze.rbd_fast ^ REM -p ../../src/SALib/test_functions/params/Ishigami.txt ^ REM -X ../data/model_input.txt ^ REM -Y ../data/model_output.txt ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) REM REM -X, --model-input-file: File of model input values to analyze REM -Y, --model-output-file: File of model output values to analyze REM REM --delimiter (optional): Model output file delimiter. REM REM -s, --seed (optional): Seed value for random number generation SALib-SALib-d6e51b1/examples/pawn/pawn.py000066400000000000000000000015411525347100600201130ustar00rootroot00000000000000import sys sys.path.append("../..") from SALib.analyze import pawn from SALib.sample import latin from SALib.test_functions import Ishigami from SALib.util import read_param_file # Read the parameter range file and generate samples problem = read_param_file("../../src/SALib/test_functions/params/Ishigami.txt") # Generate samples param_values = latin.sample(problem, 1000) # Run the "model" and save the output in a text file # This will happen offline for external models Y = Ishigami.evaluate(param_values) # Perform the sensitivity analysis using the model output # Specify which column of the output file to analyze (zero-indexed) Si = pawn.analyze(problem, param_values, Y, S=10, print_to_console=True) # Returns a dictionary with key 'PAWN' # e.g. Si['PAWN'] contains the total-order index for each parameter, in the # same order as the parameter file SALib-SALib-d6e51b1/examples/pawn/pawn.sh000066400000000000000000000025711525347100600201010ustar00rootroot00000000000000#!/bin/bash # Example: generating samples from the command line salib sample latin \ -n 1000 \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -o ../data/model_input.txt \ --delimiter=' ' \ --precision=8 \ --seed=100 # You can also use the module directly through Python # python -m SALib.sample.latin \ # -n 1000 \ # -p ./src/SALib/test_functions/params/Ishigami.txt \ # -o model_input.txt \ # --delimiter=' ' \ # --precision=8 \ # --seed=100 # Run the model using the inputs sampled above, and save outputs python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" # Then use the output to run the analysis. # Sensitivity indices will print to command line. Use ">" to write to file. salib analyze pawn \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -X ../data/model_input.txt \ -Y ../data/model_output.txt \ --seed=100 # Options: # -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) # # -Y, --model-output-file: File of model output values to analyze # -X, --model-input-file: File of model input values to analyze # -S, --slices: Number of slices to take # # --delimiter (optional): Model output file delimiter. # # -s, --seed (optional): Seed value for random number generation SALib-SALib-d6e51b1/examples/plotting/000077500000000000000000000000001525347100600174665ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/plotting/plotting.py000066400000000000000000000047211525347100600217040ustar00rootroot00000000000000import sys sys.path.append("../..") from SALib import ProblemSpec from SALib.test_functions import Ishigami from SALib.plotting.bar import plot as barplot import matplotlib.pyplot as plt import numpy as np # By convention, we assign to "sp" (for "SALib Problem") sp = ProblemSpec( { "names": ["x1", "x2", "x3"], # Name of each parameter "bounds": [[-np.pi, np.pi]] * 3, # bounds of each parameter "outputs": ["Y"], # name of outputs in expected order } ) ( sp.sample_saltelli(512, calc_second_order=True) .evaluate(Ishigami.evaluate) .analyze_sobol() ) # Display results in table format print(sp) # First-order indices expected with Saltelli sampling: # x1: 0.3139 # x2: 0.4424 # x3: 0.0 # Basic plotting of results sp.plot() plt.title("Basic example plot") # More advanced plotting # Plot functions actually return matplotlib axes objects # In the case of the Sobol' method if `calc_second_order=True`, there will be # 3 axes (one each for Total, First, and Second order indices) axes = sp.plot() # These can be modified as desired. # Here, for example, we set the Y-axis to log scale for ax in axes: ax.set_yscale("log") axes[0].set_title("Example custom plot with log scale") # Other custom layouts can be created in the usual matplotlib style # with the basic bar plotter. # Example: Direct control of plot elements fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(6, 16)) # Get result DataFrames total, first, second = sp.to_df() ax1 = barplot(total, ax=ax1) ax2 = barplot(first, ax=ax2) ax3 = barplot(second, ax=ax3) ax1.set_yscale("log") ax2.set_yscale("log") ax1.set_title("Customized matplotlib plot") plt.show() # Plot sensitivity indices as a heatmap # Note that plotting methods return a matplotlib axes object ax = sp.heatmap("Y") ax.set_title("Basic heatmap") plt.show() # Another heatmap plot with more fine-grain control # Displays Total and First-Order sensitivities in separate subplots fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6)) sp.heatmap("Y", "ST", "Total Order Sensitivity", ax1) sp.heatmap("Y", "S1", "First Order Sensitivity", ax2) plt.show() # Yet another heatmap example fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots( 2, 2, figsize=(10, 6), sharex=True, constrained_layout=True ) sp.heatmap("Y", "ST", "Total Order", ax=ax1) sp.heatmap("Y", "ST_conf", "Total Order Conf.", ax=ax2) sp.heatmap("Y", "S1", "First Order", ax=ax3) sp.heatmap("Y", "S1_conf", "First Order Conf.", ax=ax4) plt.show() SALib-SALib-d6e51b1/examples/radial/000077500000000000000000000000001525347100600170625ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/radial/radial_example.py000066400000000000000000000033131525347100600224030ustar00rootroot00000000000000from SALib.sample.radial import radial_sobol, radial_mc from SALib.sample import saltelli from SALib.sample.morris import sample as m_sample from SALib.analyze import sobol, morris, radial_ee, sobol_jansen from SALib.test_functions import Ishigami from SALib.util import read_param_file problem = read_param_file("../../src/SALib/test_functions/params/Ishigami.txt") sample_sets = 5000 mc_sample_sets = 5000 sobol_sample = 1000 # Radial Sobol radial_sobol_param = radial_sobol.sample(problem, sample_sets) radial_sobol_Y = Ishigami.evaluate(radial_sobol_param) radial_sobol_result = radial_ee.analyze( problem, radial_sobol_param, radial_sobol_Y, sample_sets ) # Radial MC radial_mc_param = radial_mc.sample(problem, mc_sample_sets) radial_mc_Y = Ishigami.evaluate(radial_mc_param) radial_mc_result = radial_ee.analyze( problem, radial_mc_param, radial_mc_Y, mc_sample_sets ) # Sobol Jansen sobol_jansen_result = sobol_jansen.analyze(problem, radial_sobol_Y, sample_sets) # Morris morris_param = m_sample(problem, sample_sets) morris_Y = Ishigami.evaluate(morris_param) morris_result = morris.analyze(problem, morris_param, morris_Y) # Sobol sobol_param = saltelli.sample(problem, sobol_sample) sobol_Y = Ishigami.evaluate(sobol_param) Si = sobol.analyze( problem, sobol_Y, calc_second_order=True, conf_level=0.95, print_to_console=False ) print("EE results for Radial Sobol") print(radial_sobol_result.to_df()) print("EE results for Radial MC") print(radial_mc_result.to_df()) print("Jansen results for Radial Sobol") print(sobol_jansen_result.to_df()) print("Morris results") print(morris_result.to_df()) print("Sobol/Saltelli result") total_si, first_si, second_si = Si.to_df() print(total_si) print(first_si) SALib-SALib-d6e51b1/examples/rbd_fast/000077500000000000000000000000001525347100600174125ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/rbd_fast/rbd_fast.bat000066400000000000000000000040531525347100600216700ustar00rootroot00000000000000@echo off REM Example: generating samples from the command line salib sample latin ^ -n 1000 ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -o ../data/model_input.txt ^ --delimiter=" " ^ --precision=8 ^ --seed=100 REM You can also use the module directly through Python REM python -m SALib.sample.latin ^ REM -n 1000 ^ REM -p ./src/SALib/test_functions/params/Ishigami.txt ^ REM -o model_input.txt ^ REM --delimiter=" " ^ REM --precision=8 ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) REM REM -n, --samples: Sample size. REM Number of model runs is N REM REM -o, --output: File to output your samples into. REM REM --delimiter (optional): Output file delimiter. REM REM --precision (optional): Digits of precision in the output file. Default is 8. REM REM -M: RBD-FAST M coefficient, default 4 REM REM -s, --seed (optional): Seed value for random number generation REM Run the model using the inputs sampled above, and save outputs python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" REM Then use the output to run the analysis. REM Sensitivity indices will print to command line. Use ">" to write to file. salib analyze rbd_fast ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -X ../data/model_input.txt ^ -Y ../data/model_output.txt ^ --seed=100 REM python -m SALib.analyze.rbd_fast ^ REM -p ../../src/SALib/test_functions/params/Ishigami.txt ^ REM -X ../data/model_input.txt ^ REM -Y ../data/model_output.txt ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) REM REM -X, --model-input-file: File of model input values to analyze REM -Y, --model-output-file: File of model output values to analyze REM REM --delimiter (optional): Model output file delimiter. REM REM -s, --seed (optional): Seed value for random number generation SALib-SALib-d6e51b1/examples/rbd_fast/rbd_fast.py000066400000000000000000000015371525347100600215560ustar00rootroot00000000000000import sys sys.path.append("../..") from SALib.analyze import rbd_fast from SALib.sample import latin from SALib.test_functions import Ishigami from SALib.util import read_param_file # Read the parameter range file and generate samples problem = read_param_file("../../src/SALib/test_functions/params/Ishigami.txt") # Generate samples param_values = latin.sample(problem, 1000) # Run the "model" and save the output in a text file # This will happen offline for external models Y = Ishigami.evaluate(param_values) # Perform the sensitivity analysis using the model output # Specify which column of the output file to analyze (zero-indexed) Si = rbd_fast.analyze(problem, param_values, Y, print_to_console=True) # Returns a dictionary with key 'S1' # e.g. Si['S1'] contains the first-order index for each parameter, in the # same order as the parameter file SALib-SALib-d6e51b1/examples/rbd_fast/rbd_fast.sh000066400000000000000000000037331525347100600215400ustar00rootroot00000000000000#!/bin/bash # Example: generating samples from the command line salib sample latin \ -n 1000 \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -o ../data/model_input.txt \ --delimiter=' ' \ --precision=8 \ --seed=100 # You can also use the module directly through Python # python -m SALib.sample.latin \ # -n 1000 \ # -p ./src/SALib/test_functions/params/Ishigami.txt \ # -o model_input.txt \ # --delimiter=' ' \ # --precision=8 \ # --seed=100 # Options: # -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) # # -n, --samples: Sample size. # Number of model runs is N # # -o, --output: File to output your samples into. # # --delimiter (optional): Output file delimiter. # # --precision (optional): Digits of precision in the output file. Default is 8. # # -M: RBD-FAST M coefficient, default 4 # # -s, --seed (optional): Seed value for random number generation # Run the model using the inputs sampled above, and save outputs python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" # Then use the output to run the analysis. # Sensitivity indices will print to command line. Use ">" to write to file. salib analyze rbd_fast \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -X ../data/model_input.txt \ -Y ../data/model_output.txt \ --seed=100 # python -m SALib.analyze.rbd_fast \ # -p ../../src/SALib/test_functions/params/Ishigami.txt \ # -X ../data/model_input.txt \ # -Y ../data/model_output.txt \ # --seed=100 # Options: # -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) # # -Y, --model-output-file: File of model output values to analyze # -X, --model-input-file: File of model input values to analyze # # --delimiter (optional): Model output file delimiter. # # -s, --seed (optional): Seed value for random number generation SALib-SALib-d6e51b1/examples/shapley/000077500000000000000000000000001525347100600172735ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/shapley/shapley.bat000066400000000000000000000013021525347100600214240ustar00rootroot00000000000000@echo off REM Generate N Shapley trajectories. The model requires N * (D + 1) runs. salib sample shapley ^ -n 10000 ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -o ../data/model_input.txt ^ --delimiter=" " ^ --precision=8 ^ --seed=100 REM Run the example model and store one output per sampled row. python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" REM Analyze the model inputs and outputs. salib analyze shapley ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -X ../data/model_input.txt ^ -Y ../data/model_output.txt ^ --conf-level=0.95 SALib-SALib-d6e51b1/examples/shapley/shapley.py000066400000000000000000000015431525347100600213150ustar00rootroot00000000000000import sys from SALib.analyze import shapley from SALib.sample import shapley as shapley_sampler from SALib.test_functions import Ishigami from SALib.util import read_param_file sys.path.append("../..") # Goda's estimator assumes independent input variables. It requires # N * (D + 1) model evaluations for N trajectories and D variables. problem = read_param_file("../../src/SALib/test_functions/params/Ishigami.txt") param_values = shapley_sampler.sample(problem, 10_000, seed=100) # Run the model. External models can evaluate and store these rows offline. Y = Ishigami.evaluate(param_values) # Effects are in output-variance units and their sum estimates Var[Y]. Si = shapley.analyze(problem, param_values, Y, print_to_console=True) print( "\nNormalized effects (+/- CI):\n", Si["shapley_normalized"], "\n", Si["shapley_normalized_conf"], ) SALib-SALib-d6e51b1/examples/shapley/shapley.sh000066400000000000000000000014361525347100600213000ustar00rootroot00000000000000#!/bin/bash # Generate N Shapley trajectories. The model requires N * (D + 1) runs. salib sample shapley \ -n 10000 \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -o ../data/model_input.txt \ --delimiter=' ' \ --precision=8 \ --seed=100 # Run the example model and store one output per sampled row. python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" # Analyze the model inputs and outputs. The printed effects are in # output-variance units and their sum estimates the output variance. salib analyze shapley \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -X ../data/model_input.txt \ -Y ../data/model_output.txt \ --conf-level=0.95 SALib-SALib-d6e51b1/examples/sobol/000077500000000000000000000000001525347100600167445ustar00rootroot00000000000000SALib-SALib-d6e51b1/examples/sobol/sobol.bat000066400000000000000000000061071525347100600205560ustar00rootroot00000000000000@echo off REM Example: generating samples from the command line salib sample saltelli ^ -n 1000 ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -o ../data/model_input.txt ^ --delimiter=" " ^ --precision=8 ^ --max-order=2 ^ --seed=100 REM You can also use the module directly through Python REM python -m SALib.sample.saltelli ^ REM -n 1000 ^ REM -p ../../src/SALib/test_functions/params/Ishigami.txt ^ REM -o ../data/model_input.txt ^ REM --delimiter=" " ^ REM --precision=8 ^ REM --max-order=2 ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) REM REM -n, --samples: Sample size. REM Number of model runs is N(2D + 2) if calculating second-order indices (default) REM or N(D + 2) otherwise. REM REM -o, --output: File to output your samples into. REM REM --delimiter (optional): Output file delimiter. REM REM --precision (optional): Digits of precision in the output file. Default is 8. REM REM --max-order (optional): Maximum order of indices to calculate. Choose 1 or 2, default is 2. REM Choosing 1 will reduce total model runs from N(2D + 2) to N(D + 2) REM Must use the same value (either 1 or 2) for both sampling and analysis. REM REM -s, --seed (optional): Seed value for random number generation REM Run the model using the inputs sampled above, and save outputs python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" REM Then use the output to run the analysis. REM Sensitivity indices will print to command line. Use ">" to write to file. salib analyze sobol ^ -p ../../src/SALib/test_functions/params/Ishigami.txt ^ -Y ../data/model_output.txt ^ -c 0 ^ --max-order=2 ^ -r 1000 ^ --seed=100 REM python -m SALib.analyze.sobol ^ REM -p ../../src/SALib/test_functions/params/Ishigami.txt ^ REM -Y ../data/model_output.txt ^ REM -c 0 ^ REM --max-order=2 ^ REM -r 1000 ^ REM --seed=100 REM Options: REM -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) REM REM -Y, --model-output-file: File of model output values to analyze REM REM -c, --column (optional): Column of model output file to analyze. REM If the file only has one column, this argument will be ignored. REM REM --delimiter (optional): Model output file delimiter. REM REM --max-order (optional): Maximum order of indices to calculate. REM This must match the value chosen during sampling. REM REM -r, --resamples (optional): Number of bootstrap resamples used to calculate confidence intervals on indices. Default 1000. REM REM REM -s, --seed (optional): Seed value for random number generation REM REM --parallel (optional): Flag to enable parallel execution with multiprocessing REM REM --processors (optional, int): Number of processors to be used with the parallel option REM First-order indices expected with Saltelli sampling: REM x1: 0.3139 REM x2: 0.4424 REM x3: 0.0 SALib-SALib-d6e51b1/examples/sobol/sobol.py000066400000000000000000000024741525347100600204430ustar00rootroot00000000000000import sys sys.path.append("../..") from SALib.analyze import sobol from SALib.sample import saltelli from SALib.test_functions import Ishigami from SALib.util import read_param_file # Read the parameter range file and generate samples problem = read_param_file("../../src/SALib/test_functions/params/Ishigami.txt") # Generate samples param_values = saltelli.sample(problem, 1024, calc_second_order=True, skip_values=2048) # Run the "model" and save the output in a text file # This will happen offline for external models Y = Ishigami.evaluate(param_values) # Perform the sensitivity analysis using the model output # Specify which column of the output file to analyze (zero-indexed) Si = sobol.analyze( problem, Y, calc_second_order=True, conf_level=0.95, print_to_console=True ) # Returns a dictionary with keys 'S1', 'S1_conf', 'ST', and 'ST_conf' # e.g. Si['S1'] contains the first-order index for each parameter, # in the same order as the parameter file # The optional second-order indices are now returned in keys 'S2', 'S2_conf' # These are both upper triangular DxD matrices with nan's in the duplicate # entries. # Optional keyword arguments parallel=True and n_processors=(int) for parallel execution # using multiprocessing # First-order indices expected with Saltelli sampling: # x1: 0.3139 # x2: 0.4424 # x3: 0.0 SALib-SALib-d6e51b1/examples/sobol/sobol.sh000066400000000000000000000057131525347100600204240ustar00rootroot00000000000000#!/bin/bash # Example: generating samples from the command line salib sample saltelli \ -n 1000 \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -o ../data/model_input.txt \ --delimiter=' ' \ --precision=8 \ --max-order=2 \ --seed=100 # You can also use the module directly through Python # python -m SALib.sample.saltelli \ # -n 1000 \ # -p ../../src/SALib/test_functions/params/Ishigami.txt \ # -o ../data/model_input.txt \ # --delimiter=' ' \ # --precision=8 \ # --max-order=2 \ # --seed=100 # Options: # -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) # # -n, --samples: Sample size. # Number of model runs is N(2D + 2) if calculating second-order indices (default) # or N(D + 2) otherwise. # # -o, --output: File to output your samples into. # # --delimiter (optional): Output file delimiter. # # --precision (optional): Digits of precision in the output file. Default is 8. # # --max-order (optional): Maximum order of indices to calculate. Choose 1 or 2, default is 2. # Choosing 1 will reduce total model runs from N(2D + 2) to N(D + 2) # Must use the same value (either 1 or 2) for both sampling and analysis. # # -s, --seed (optional): Seed value for random number generation # Run the model using the inputs sampled above, and save outputs python -c "from SALib.test_functions import Ishigami; import numpy as np; np.savetxt('../data/model_output.txt', Ishigami.evaluate(np.loadtxt('../data/model_input.txt')))" # Then use the output to run the analysis. # Sensitivity indices will print to command line. Use ">" to write to file. salib analyze sobol \ -p ../../src/SALib/test_functions/params/Ishigami.txt \ -Y ../data/model_output.txt \ -c 0 \ --max-order=2 \ -r 1000 \ --seed=100 # python -m SALib.analyze.sobol \ # -p ../../src/SALib/test_functions/params/Ishigami.txt \ # -Y ../data/model_output.txt \ # -c 0 \ # --max-order=2 \ # -r 1000 \ # --seed=100 # Options: # -p, --paramfile: Your parameter range file (3 columns: parameter name, lower bound, upper bound) # # -Y, --model-output-file: File of model output values to analyze # # -c, --column (optional): Column of model output file to analyze. # If the file only has one column, this argument will be ignored. # # --delimiter (optional): Model output file delimiter. # # --max-order (optional): Maximum order of indices to calculate. # This must match the value chosen during sampling. # # -r, --resamples (optional): Number of bootstrap resamples used to calculate confidence intervals on indices. Default 1000. # # # -s, --seed (optional): Seed value for random number generation # # --parallel (optional): Flag to enable parallel execution with multiprocessing # # --processors (optional, int): Number of processors to be used with the parallel option # First-order indices expected with Saltelli sampling: # x1: 0.3139 # x2: 0.4424 # x3: 0.0 SALib-SALib-d6e51b1/paper/000077500000000000000000000000001525347100600151175ustar00rootroot00000000000000SALib-SALib-d6e51b1/paper/codemeta.json000066400000000000000000000021341525347100600175730ustar00rootroot00000000000000{ "@context": "https://raw.githubusercontent.com/mbjones/codemeta/master/codemeta.jsonld", "@type": "Code", "author": [ { "@id": "http://orcid.org/0000-0001-9367-1791", "@type": "Person", "email": "william.usher@ouce.ox.ac.uk", "name": "Will Usher", "affiliation": "University of Oxford" }, { "@id": "http://orcid.org/0000-0002-4081-3175", "@type": "Person", "email": "jdherman@ucdavis.edu", "name": "jdherman", "affiliation": "University of California, Davis" } ], "identifier": "https://doi.org/10.5281/zenodo.160164", "codeRepository": "https://github.com/SALib/SALib", "datePublished": "2016-10-18", "dateModified": "2016-10-18", "dateCreated": "2016-10-18", "description": "Sensitivity Analysis Library in Python (Numpy). Contains Sobol, Morris, Fractional Factorial and FAST methods.", "keywords": "sensitivity analysis, Python, uncertainty, variance-based, global sensitivity analysis, fractional factorial, Method of Morris, elementary effects", "license": "MIT", "title": "SALib", "version": "v1.0.1" } SALib-SALib-d6e51b1/paper/paper.bib000066400000000000000000001164471525347100600167210ustar00rootroot00000000000000@article{Archer1997, author = {Archer, G. E. B. and Saltelli, Andrea and Sobol', I. M.}, doi = {10.1080/00949659708811825}, isbn = {0094965970881}, issn = {0094-9655}, journal = {Journal of Statistical Computation and Simulation}, month = {may}, number = {2}, pages = {99--120}, title = {{Sensitivity measures,anova-like Techniques and the use of bootstrap}}, url = {http://www.tandfonline.com/doi/abs/10.1080/00949659708811825}, volume = {58}, year = {1997} } @article{Borgonovo2007, abstract = {Uncertainty in parameters is present in many risk assessment problems and leads to uncertainty in model predictions. In this work, we introduce a global sensitivity indicator which looks at the influence of input uncertainty on the entire output distribution without reference to a specific moment of the output (moment independence) and which can be defined also in the presence of correlations among the parameters. We discuss its mathematical properties and highlight the differences between the present indicator, variance-based uncertainty importance measures and a moment independent sensitivity indicator previously introduced in the literature. Numerical results are discussed with application to the probabilistic risk assessment model on which Iman [A matrix-based approach to uncertainty and sensitivity analysis for fault trees. Risk Anal 1987;7(1):22-33] first introduced uncertainty importance measures. {\textcopyright} 2006 Elsevier Ltd. All rights reserved.}, author = {Borgonovo, E.}, doi = {10.1016/j.ress.2006.04.015}, isbn = {0951-8320}, issn = {09518320}, journal = {Reliability Engineering and System Safety}, keywords = {Global sensitivity analysis,Importance measures,Probabilistic risk assessment,Uncertainty analysis,Uncertainty importance measures}, number = {6}, pages = {771--784}, title = {{A new uncertainty importance measure}}, volume = {92}, year = {2007} } @article{Butler2010, author = {Butler, Martha P and Reed, Patrick M and Wagener, Thorsten and Keller, Klaus}, doi = {10.1016/j.gloenvcha.2009.12.003.Sobol}, pages = {16802}, title = {{Sobol ' Variance Decomposition of an Integrated Assessment Model ' s Global Sensitivities}}, year = {2010} } @article{Campolongo2007, abstract = {In 1991 Morris proposed an effective screening sensitivity measure to identify the few important factors in models with many factors. The method is based on computing for each input a number of incremental ratios, namely elementary effects, which are then averaged to assess the overall importance of the input. Despite its value, the method is still rarely used and instead local analyses varying one factor at a time around a baseline point are usually employed. In this piece of work we propose a revised version of the elementary effects method, improved in terms of both the definition of the measure and the sampling strategy. In the present form the method shares many of the positive qualities of the variance-based techniques, having the advantage of a lower computational cost, as demonstrated by the analytical examples. The method is employed to assess the sensitivity of a chemical reaction model for dimethylsulphide (DMS), a gas involved in climate change. Results of the sensitivity analysis open up the ground for model reconsideration: some model components may need a more thorough modelling effort while some others may need to be simplified. ?? 2006 Elsevier Ltd. All rights reserved.}, author = {Campolongo, F and Cariboni, Jessica and Saltelli, Andrea}, doi = {10.1016/j.envsoft.2006.10.004}, isbn = {13648152 (ISSN)}, issn = {13648152}, journal = {Environmental Modelling {\&} Software}, keywords = {Dimethylsulphide (DMS),Effective sampling strategy,Model-free methods,Screening problem,Sensitivity analysis,elementary effects,morrismethod}, month = {oct}, number = {10}, pages = {1509--1518}, title = {{An effective screening design for sensitivity analysis of large models}}, url = {http://linkinghub.elsevier.com/retrieve/pii/S1364815206002805}, volume = {22}, year = {2007} } @article{Campolongo2011, author = {Campolongo, F and Saltelli, Andrea and Cariboni, Jessica}, doi = {10.1016/j.cpc.2010.12.039}, issn = {00104655}, journal = {Computer Physics Communications}, keywords = {sensitivity analysis}, month = {apr}, number = {4}, pages = {978--988}, publisher = {Elsevier B.V.}, title = {{From screening to quantitative sensitivity analysis. A unified approach}}, url = {http://linkinghub.elsevier.com/retrieve/pii/S0010465510005321}, volume = {182}, year = {2011} } @article{Claxton2005, abstract = {Recently the National Institute for Clinical Excellence (NICE) updated its methods guidance for technology assessment. One aspect of the new guidance is to require the use of probabilistic sensitivity analysis with all cost-effectiveness models submitted to the Institute. The purpose of this paper is to place the NICE guidance on dealing with uncertainty into a broader context of the requirements for decision making; to explain the general approach that was taken in its development; and to address each of the issues which have been raised in the debate about the role of probabilistic sensitivity analysis in general. The most appropriate starting point for developing guidance is to establish what is required for decision making. On the basis of these requirements, the methods and framework of analysis which can best meet these needs can then be identified. It will be argued that the guidance on dealing with uncertainty and, in particular, the requirement for probabilistic sensitivity analysis, is justified by the requirements of the type of decisions that NICE is asked to make. Given this foundation, the main issues and criticisms raised during and after the consultation process are reviewed. Finally, some of the methodological challenges posed by the need fully to characterise decision uncertainty and to inform the research agenda will be identified and discussed.}, author = {Claxton, Karl and Sculpher, Mark and McCabe, Chris and Briggs, Andrew and Akehurst, Ron and Buxton, Martin and Brazier, John and O'Hagan, Anthony}, doi = {10.1002/hec.985}, issn = {1057-9230}, journal = {Health economics}, keywords = {Cost-Benefit Analysis,Decision Support Techniques,Guidelines as Topic,Models, Statistical,Technology Assessment, Biomedical,Technology Assessment, Biomedical: economics,Technology Assessment, Biomedical: standards,Technology Assessment, Biomedical: statistics {\&} nu}, month = {apr}, number = {4}, pages = {339--47}, pmid = {15736142}, title = {{Probabilistic sensitivity analysis for NICE technology assessment: not an optional extra.}}, url = {http://www.ncbi.nlm.nih.gov/pubmed/15736142}, volume = {14}, year = {2005} } @article{Cukier1973, abstract = {A method has been developed to investigate the sensitivity of the solutions of large sets of coupled nonlinear rate equations to uncertainties in the rate coefficients. This method is based on varying all the rate coefficients simultaneously through the introduction of a parameter in such a way that the output concentrations become periodic functions of this parameter at any given time t. The concentrations of the chemical species are then Fourier analyzed at time t. We show via an application of Weyl's ergodic theorem that a subset of the Fourier coefficients is related to {\textless}∂ci/∂kl{\textgreater} , the rate of change of the concentration of species i with respect to the rate constant for reaction I averaged over the uncertainties of all the other rate coefficients. Thus a large Fourier coefficient corresponds to a large sensitivity, and a small Fourier coefficient corresponds to a small sensitivity. The amount of numerical integration required to calculate these Fourier coefficients is considerably less than that required in tests of sensitivity where one varies one rate coefficient at a time, while holding all others fixed. The Fourier method developed in this paper is not limited to chemical rate equations, but can be applied to the study of the sensitivity of any large system of coupled, nonlinear differential equations with respect to the uncertainties in the modeling parameters.}, author = {Cukier, R. I. and Fortuin, C. M. and Shuler, K. E. and Petschek, A. G. and Schaibly, J. H.}, doi = {10.1063/1.1680571}, isbn = {0021-9606}, issn = {10897690}, journal = {Journal of Chemical Physics}, number = {8}, pages = {3873--3878}, title = {{Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I Theory}}, volume = {59}, year = {1973} } @article{Cukier1978, author = {Cukier, R.I and Levine, H.B and Shuler, K.E}, doi = {10.1016/0021-9991(78)90097-9}, issn = {00219991}, journal = {Journal of Computational Physics}, month = {jan}, number = {1}, pages = {1--42}, title = {{Nonlinear sensitivity analysis of multiparameter model systems}}, url = {http://linkinghub.elsevier.com/retrieve/pii/0021999178900979}, volume = {26}, year = {1978} } @article{DaVeiga2009, author = {{Da Veiga}, Sebastien and Wahl, Francois and Gamboa, Fabrice}, doi = {10.1198/TECH.2009.08124}, issn = {0040-1706}, journal = {Technometrics}, keywords = {achieving better knowledge of,calls for a kinetic,components introduced in the,conditional moments estimation,description of both the,global sensitivity index,inputs are the detailed,model in which the,nonparametric regression,refining processes usually,unit and}, month = {nov}, number = {4}, pages = {452--463}, title = {{Local Polynomial Estimation for Sensitivity Analysis on Models With Correlated Inputs}}, url = {http://www.tandfonline.com/doi/abs/10.1198/TECH.2009.08124}, volume = {51}, year = {2009} } @article{Hamby1994, abstract = {Mathematical models are utilized to approximate various highly complex engineering, physical, environmental, social, and economic phenomena. Model parameters exerting the most influence on model results are identified through a 'sensitivity analysis'. A comprehensive review is presented of more than a dozen sensitivity analysis methods. This review is intended for those not intimately familiar with statistics or the techniques utilized for sensitivity analysis of computer models. The most fundamental of sensitivity techniques utilizes partial differentiation whereas the simplest approach requires varying parameter values one-at-a-time. Correlation analysis is used to determine relationships between independent and dependent variables. Regression analysis provides the most comprehensive sensitivity measure and is commonly utilized to build response surfaces that approximate complex models.}, author = {Hamby, D M}, doi = {10.1007/BF00547132}, isbn = {http://hdl.handle.net/2027.42/42691}, issn = {0167-6369}, journal = {Environmental Monitoring and Assessment}, keywords = {Atmospheric Protection/Air Quality Control/Air Pol,Ecology,Environment,Environmental Management,Health Sciences,Monitoring/Environmental Analysis/Environmental Ec,Public Health}, month = {sep}, number = {2}, pages = {135--154}, pmid = {24214086}, title = {{A review of techniques for parameter sensitivity analysis of environmental models}}, url = {http://deepblue.lib.umich.edu/handle/2027.42/42691 http://link.springer.com/10.1007/BF00547132}, volume = {32}, year = {1994} } @article{Helton2005, author = {Helton, J.C. and Davis, F.J. and Johnson, J.D.}, doi = {10.1016/j.ress.2004.09.006}, isbn = {5052844808}, issn = {09518320}, journal = {Reliability Engineering {\&} System Safety}, keywords = {concordance,epistemic uncertainty,kendall,latin hypercube sampling,monte carlo analysis,random sampling,replicated,s coefficient of concordance,sampling,sensitivity analysis,stability,subjective uncertainty,top down coefficient of,two-phase fluid flow,uncertainty analysis}, month = {sep}, number = {3}, pages = {305--330}, title = {{A comparison of uncertainty and sensitivity analysis results obtained with random and Latin hypercube sampling}}, url = {http://linkinghub.elsevier.com/retrieve/pii/S0951832004002340}, volume = {89}, year = {2005} } @article{Homma1996, abstract = {The present paper deals with a new method of global sensitivity analysis of nonlinear models. This is based on a measure of importance to calculate the fractional contribution of the input parameters to the variance of the model prediction. Measures of importance in sensitivity analysis have been suggested by several authors, whose work is reviewed in this article. More emphasis is given to the developments of sensitivity indices by the Russian mathematician I.M. Sobol'. Given that Sobol' treatment of the measure of importance is the most general, his formalism is employed throughout this paper where conceptual and computational improvements of the method are presented. The computational novelty of this study is the introduction of the 'total effect' parameter index. This index provides a measure of the total effect of a given parameter, including all the possible synergetic terms between that parameter and all the others. Rank transformation of the data is also introduced in order to increase the reproducibility of the method. These methods are tested on a few analytical and computer models. The main conclusion of this work is the identification of a sensitivity analysis methodology which is both flexible, accurate and informative, and which can be achieved at reasonable computational cost. (C) 1996 Elsevier Science Limited.}, author = {Homma, T and Saltelli, Andrea}, doi = {10.1016/0951-8320(96)00002-6}, isbn = {0951-8320}, issn = {09518320}, journal = {Reliability Engineering {\&} System Safety}, pages = {1--17}, title = {{Importance measures in global sensitivity analysis of nonlinear models}}, url = {http://www.sciencedirect.com/science/article/pii/0951832096000026}, volume = {52}, year = {1996} } @article{Imam1988, abstract = {"Risk Analysis; {\#}sns; N1; V8; p71"}, author = {Imam, Ronald L and Helton, Jon C}, keywords = {43f,4l,4q,A19,rsk}, number = {1}, title = {{An Investigation of Uncertainty and Sensitivity Analysis Techniques for Computer Models}}, volume = {8}, year = {1988} } @book{Kruger2012, address = {Chichester, UK}, author = {Kruger, Uwe and Xie, Lei}, doi = {10.1002/9780470517253}, isbn = {9780470517253}, month = {sep}, publisher = {John Wiley {\&} Sons, Ltd}, title = {{Statistical Monitoring of Complex Multivariate Processes}}, url = {http://doi.wiley.com/10.1002/9780470517253}, year = {2012} } @article{Kucherenko2012, author = {Kucherenko, S. and Tarantola, S. and Annoni, P.}, doi = {10.1016/j.cpc.2011.12.020}, issn = {00104655}, journal = {Computer Physics Communications}, keywords = {global sensitivity analysis}, month = {apr}, number = {4}, pages = {937--946}, publisher = {Elsevier B.V.}, title = {{Estimation of global sensitivity indices for models with dependent variables}}, url = {http://linkinghub.elsevier.com/retrieve/pii/S0010465511004085}, volume = {183}, year = {2012} } @book{Kuo2012, address = {Chichester, UK}, author = {Kuo, Way and Zhu, Xiaoyan}, doi = {10.1002/9781118314593.ch18}, isbn = {9781118314593}, month = {may}, publisher = {John Wiley {\&} Sons, Ltd}, title = {{Importance Measures in Reliability, Risk, and Optimization}}, year = {2012} } @article{Morris1991, abstract = {A computational model is a representation of some physical or other system of interest, first expressed mathematically and then implemented in the form of a computer program; it may be viewed as a function of inputs that, when evaluated, produces outputs. Motivation for this article comes from computational models that are deterministic, complicated enough to make classical mathematical analysis impractical and that have a moderate-to-large number of inputs. The problem of designing computational experiments to determine which inputs have important effects on an output is considered. The proposed experimental plans are composed of individually randomized one-factor-at-a-time designs, and data analysis is based on the resulting random sample of observed elementary effects, those changes in an output due solely to changes in a particular input. Advantages of this approach include a lack of reliance on assumptions of relative sparsity of important inputs, monotonicity of outputs with respect to inputs, or adequacy of a low-order polynomial as an approximation to the computational model.}, annote = {Contains useful justifaction of distinction of Morris method from LHS and similar methods.}, author = {Morris, Max D}, doi = {10.2307/1269043}, isbn = {00401706}, issn = {0040-1706}, journal = {Technometrics}, keywords = {elementary effects,morrismethod}, mendeley-tags = {elementary effects,morrismethod}, pages = {161--174}, pmid = {20541559}, title = {{Factorial Sampling Plans for Preliminary Computational Experiments}}, url = {http://www.jstor.org/stable/1269043}, volume = {33}, year = {1991} } @article{Nossent2011, abstract = {Complex environmental models are controlled by a high number of parameters. Accurately estimating the values of all these parameters is almost impossible. Sensitivity analysis (SA) results enable the selection of the parameters to include in a calibration procedure, but can also assist in the identification of the model processes. Additionally, a sensitivity analysis can yield crucial information on the use and meaning of the model parameters. This paper presents a Sobol' sensitivity analysis for flow simulations by a SWAT model of the river Kleine Nete, with the objective to assess the first order, second order and total sensitivity effects. Confidence intervals for the resulting sensitivity indices are inferred by applying bootstrapping. The results indicate that the curve number value (CN2) is the most important parameter of the model and that no more than 9 parameters (out of 26) are needed to have an adequate representation of the model variability. The convergence of the parameter ranking for total sensitivity effects is relatively fast, which is promising for factor fixing purposes. It is also shown that the Sobol' sensitivity analysis enhances the understanding of the model, by e.g. pointing out 3 significant pairwise interactions. In general, it can be concluded that the Sobol' sensitivity analysis can be successfully applied for factor fixing and factor prioritization with respect to the input parameters of a SWAT model, even with a limited number of model evaluations. The analysis also supports the identification of model processes, parameter values and parameter interaction effects}, author = {Nossent, Jiri and Elsen, Pieter and Bauwens, Willy}, doi = {10.1016/j.envsoft.2011.08.010}, issn = {13648152}, journal = {Environmental Modelling {\&} Software}, keywords = {process identi fi cation,sensitivity analysis}, month = {dec}, number = {12}, pages = {1515--1525}, publisher = {Elsevier Ltd}, title = {{Sobol' sensitivity analysis of a complex environmental model}}, url = {http://linkinghub.elsevier.com/retrieve/pii/S1364815211001939}, volume = {26}, year = {2011} } @article{O'Hagan2007, abstract = {Probabilistic sensitivity analysis (PSA) is required to account for uncertainty in cost-effectiveness calculations arising from health economic models. The simplest way to perform PSA in practice is by Monte Carlo methods, which involves running the model many times using randomly sampled values of the model inputs. However, this can be impractical when the economic model takes appreciable amounts of time to run. This situation arises, in particular, for patient-level simulation models (also known as micro-simulation or individual-level simulation models), where a single run of the model simulates the health care of many thousands of individual patients. The large number of patients required in each run to achieve accurate estimation of cost-effectiveness means that only a relatively small number of runs is possible. For this reason, it is often said that PSA is not practical for patient-level models. We develop a way to reduce the computational burden of Monte Carlo PSA for patient-level models, based on the algebra of analysis of variance. Methods are presented to estimate the mean and variance of the model output, with formulae for determining optimal sample sizes. The methods are simple to apply and will typically reduce the computational demand very substantially.}, author = {O'Hagan, Anthony and Stevenson, Matt and Madan, Jason}, doi = {10.1002/hec.1199}, issn = {1057-9230}, journal = {Health economics}, keywords = {Analysis of Variance,Computer Simulation,Cost-Benefit Analysis,Economic,Humans,Models,Monte Carlo Method,Statistical}, month = {oct}, number = {10}, pages = {1009--23}, pmid = {17173339}, title = {{Monte Carlo probabilistic sensitivity analysis for patient level simulation models: efficient estimation of mean and variance using ANOVA.}}, url = {http://www.ncbi.nlm.nih.gov/pubmed/17173339}, volume = {16}, year = {2007} } @article{Oakley2004a, author = {Oakley, Jeremy E. and O'Hagan, Anthony}, doi = {10.1111/j.1467-9868.2004.05304.x}, issn = {1369-7412}, journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)}, keywords = {bayesian inference,computer model,gaussian process,sensitivity analysis,uncertainty analysis}, month = {aug}, number = {3}, pages = {751--769}, title = {{Probabilistic sensitivity analysis of complex models: a Bayesian approach}}, url = {http://doi.wiley.com/10.1111/j.1467-9868.2004.05304.x}, volume = {66}, year = {2004} } @article{Painter2007, abstract = {The method chosen to incorporate uncertainty into remediation design can have a significant effect on the feasibility and potential success of a remediation project. Three methods for analyzing uncertainty are explored to better allow their application to optimization of remediation designs: scenario analysis combined with one-way sensitivity analysis, factorial analysis, and fractional factorial analysis. The three methods are analyzed using a deterministic optimization model for design of a permeable reactive barrier (PRB) to remediate nitrate contamination. Although the combined scenario/one-way sensitivity approach is simpler than the factorial approaches, it has the comparative disadvantage of missing potentially important interactions between design inputs. Fractional factorial analysis is shown to have the added advantage of being useful in screening the importance of a number of model inputs without a large number of computer experiments. Hypothetical examples highlight the likely importance of uncertainty in hydraulic conductivity when choosing the optimal PRB design specification and the potential interaction of this input and the incoming pollutant concentration.}, annote = {Useful comparison between fractional factorial and scenario analysis approaches}, author = {Painter, Brett D.M. and Milke, Mark W.}, doi = {10.1111/j.1745-6592.2007.00152.x}, issn = {1069-3629}, journal = {Ground Water Monitoring {\&} Remediation}, keywords = {fractional factorial,full factorial,scenario analysis}, mendeley-tags = {fractional factorial,full factorial,scenario analysis}, month = {jun}, number = {3}, pages = {102--110}, title = {{Comparison of Factorial and Scenario Analysis Methods for Assessing Uncertainty in the Design of Permeable Reactive Barriers}}, url = {http://doi.wiley.com/10.1111/j.1745-6592.2007.00152.x}, volume = {27}, year = {2007} } @article{Pianosi2016, author = {Pianosi, Francesca and Beven, Keith and Freer, Jim and Hall, Jim W and Rougier, Jonathan and Stephenson, David B and Wagener, Thorsten}, doi = {10.1016/j.envsoft.2016.02.008}, issn = {13648152}, journal = {Environmental Modelling {\&} Software}, keywords = {sensitivity analysis,uncertainty analysis}, month = {may}, pages = {214--232}, publisher = {Elsevier Ltd}, title = {{Sensitivity analysis of environmental models: A systematic review with practical workflow}}, url = {http://dx.doi.org/10.1016/j.envsoft.2016.02.008 http://linkinghub.elsevier.com/retrieve/pii/S1364815216300287}, volume = {79}, year = {2016} } @article{Plischke2013, author = {Plischke, Elmar and Borgonovo, Emanuele and Smith, Curtis L.}, doi = {10.1016/j.ejor.2012.11.047}, issn = {03772217}, journal = {European Journal of Operational Research}, keywords = {global sensitivity analysis,uncertainty analysis}, month = {may}, number = {3}, pages = {536--550}, publisher = {Elsevier B.V.}, title = {{Global sensitivity measures from given data}}, url = {http://linkinghub.elsevier.com/retrieve/pii/S0377221712008995}, volume = {226}, year = {2013} } @article{Ricotti1999, author = {Ricotti, M E and Zio, E}, doi = {0951-8320/99/$}, keywords = {error backpropagation,feedforward neural networks,multi-layered,sensitivity and uncertainty analysis,steam generator,superposition,transient simulation}, number = {July 1998}, pages = {59--71}, title = {{Neural network approach to sensitivity and uncertainty analysis}}, volume = {64}, year = {1999} } @article{Saltelli2002a, abstract = {This paper deals with computations of sensitivity indices in sensitivity analysis. Given a mathematical or computational model y =f(x1,x2,...,xk), where the input factors xi 's are uncorrelated with one another, one can see y as the realization of a stochastic process obtained by sampling each of the xi from its marginal distribution. The sensitivity indices are related to the decomposition of the variance of y into terms either due to each xi taken singularly (first order indices), as well as into terms due to the cooperative effects of more than one xi . In this paper we assume that one has computed the full set of first order sensitivity indices as well as the full set of total-order sensitivity indices (a fairly common strategy in sensitivity analysis), and show that in this case the same set of model evaluations can be used to compute double estimates of: • the total effect of two factors taken together, for all such (k,2) couples, where k is the dimentionality of the model; • the total effect of k−2 factors taken together, for all (k,2) such (k−2) couples. We further introduce a new strategy for the computation of the full sets of first plus total order sensitivity indices that is about 50{\%} cheaper in terms of model evaluations with respect to previously published works. We discuss separately the case where the input factors xi's are not independent from each other.}, author = {Saltelli, Andrea}, doi = {10.1016/S0010-4655(02)00280-1}, issn = {00104655}, journal = {Computer Physics Communications}, keywords = {importance measures,sensitivity analysis,sensitivity indices,sensitivity measures}, mendeley-tags = {sensitivity analysis}, month = {may}, number = {2}, pages = {280--297}, title = {{Making best use of model evaluations to compute sensitivity indices}}, url = {http://linkinghub.elsevier.com/retrieve/pii/S0010465502002801}, volume = {145}, year = {2002} } @article{Saltelli1995, abstract = {The present article is a sequel to an earlier study in this journal (Saltelli et al., 1993) where two new sensitivity analysis techniques were presented. Those techniques, the modified Hora and Iman importance measure (HIM*) (Hora and Iman, 1986; Iman and Hora 1990; Ishigami and Homma, 1989, 1990) and the iterated fractional factorial design (IFFD) (Andres, 1987; Andres and Hajas, 1993) were proposed in order to overcome limitations in existing methods (Saltelli and Homma, 1992). Sensitivity analysis (SA) of model output investigates how the predictions of a model are related to its input parameters. In particular, Monte Carlo-based SA attempts to explain the uncertainly in model output by apportioning the total output uncertainty to the uncertainties of individual input parameters. It was pointed out in Saltelli and Homma (1992) that techniques employed in the existing literature were affected by severe limitations in the presence of nonmonotonic relationships between input and output. The search for better SA methods was pursued with reference to their “reproducibilityâ€� and “accuracyâ€�. The former is a measure of how well SA predictions are replicated when repeating the analysis on independent samples taken from the same input parameter space. The latter deals with the correctness of the SA results. The present note continues and completes the analysis of the performance of IFFD with respect to the two requirements. IFFD was found to generate highly reproducible results for sufficiently large sample sizes. It exceeded the capability of linear methods by detecting quadratic effects in the relationship between input parameters and model predictions, but had difficulty in dealing with higher order effects.}, author = {Saltelli, Andrea and Andres, T.H. and Homma, T.}, doi = {10.1016/0167-9473(95)92843-M}, issn = {01679473}, journal = {Computational Statistics {\&} Data Analysis}, number = {4}, pages = {387--407}, title = {{Sensitivity analysis of model output. Performance of the iterated fractional factorial design method}}, volume = {20}, year = {1995} } @article{Saltelli1999, author = {Saltelli, A. and Tarantola, S. and Chan, K. P.-S.}, doi = {10.1080/00401706.1999.10485594}, issn = {0040-1706}, journal = {Technometrics}, keywords = {computational model,fast,fourier amplitude sensitivity test,nonlinear and,nonmonotonic models,total sensitivity indices}, mendeley-groups = {PhD/Techniques/SA/methods}, month = {feb}, number = {1}, pages = {39--56}, title = {{A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output}}, url = {http://www.tandfonline.com/doi/abs/10.1080/00401706.1999.10485594}, volume = {41}, year = {1999} } @article{Saltelli2010, author = {Saltelli, Andrea and Annoni, Paola}, doi = {10.1016/j.envsoft.2010.04.012}, issn = {13648152}, journal = {Environmental Modelling {\&} Software}, keywords = {mathematical modeling,sensitivity analysis,uncertainty analysis}, month = {dec}, number = {12}, pages = {1508--1517}, publisher = {Elsevier Ltd}, title = {{How to avoid a perfunctory sensitivity analysis}}, url = {http://linkinghub.elsevier.com/retrieve/pii/S1364815210001180}, volume = {25}, year = {2010} } @article{Saltelli2010a, author = {Saltelli, Andrea and Annoni, Paola and Azzini, Ivano and Campolongo, F and Ratto, Marco and Tarantola, S.}, doi = {10.1016/j.cpc.2009.09.018}, issn = {00104655}, journal = {Computer Physics Communications}, month = {feb}, number = {2}, pages = {259--270}, publisher = {Elsevier B.V.}, title = {{Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index}}, url = {http://linkinghub.elsevier.com/retrieve/pii/S0010465509003087}, volume = {181}, year = {2010} } @article{Saltelli1998, abstract = {In this article we investigate the relationship between two coefficients used in sensitivity analysis of model output. One is the Fourier amplitude sensitivity test's coefficient, developed in the 1970s, and the other the Sobol' sensitivity indices, developed in the 1990s. Supposedly both methods are capable of computing the “main effectâ€� contribution of model's input parameters to model's output variance. We discuss the equivalence of the two methods, and prove the identity of their prediction on two test cases. Relative advantage and disadvantages of the methods are also illustrated.}, author = {Saltelli, Andrea and Bolado, Ricardo}, doi = {10.1016/S0167-9473(97)00043-1}, isbn = {0167-9473}, issn = {01679473}, journal = {Computational Statistics {\&} Data Analysis}, number = {4}, pages = {445--460}, title = {{An alternative way to compute Fourier amplitude sensitivity test (FAST)}}, volume = {26}, year = {1998} } @book{Saltelli2000c, author = {Saltelli, Andrea and Chan, K and Scott, E M}, isbn = {9780471998921}, publisher = {Wiley}, series = {Wiley Series in Probability and Statistics}, title = {{Sensitivity Analysis: Gauging the Worth of Scientific Models}}, url = {http://books.google.co.uk/books?id=v3zNQwAACAAJ}, year = {2000} } @book{Saltelli2008b, author = {Saltelli, Andrea and Ratto, M and Andres, T and Campolongo, F and Cariboni, J and Gatelli, D and Saisana, M and Tarantola, S.}, isbn = {9780470725177}, publisher = {Wiley}, title = {{Global Sensitivity Analysis: The Primer}}, url = {http://books.google.co.uk/books?id=wAssmt2vumgC}, year = {2008} } @article{Saltelli2005, author = {Saltelli, Andrea and Ratto, M and Tarantola, S. and Campolongo, F}, doi = {10.1021/cr040659d}, isbn = {0009-2665 (Print)}, issn = {0009-2665}, journal = {Chemical Reviews}, number = {7}, pages = {2811}, pmid = {16011325}, title = {{Sensitivity analysis for chemical models.}}, url = {papers2://publication/uuid/C649A15C-DDC4-4705-A66D-C42B34D88729}, volume = {105}, year = {2005} } @incollection{Saltelli2008a, author = {Saltelli, Andrea and Ratto, M. and Andres, T. and Campolongo, F and Cariboni, J. and Gatelli, D. and Saisana, M. and Tarantola, S.}, booktitle = {Global Sensitivity Analysis. The Primer}, chapter = {4}, doi = {10.1002/9780470725184.ch4}, isbn = {9780470059975}, pages = {155--174}, title = {{Varianceâ€�Based Methods}}, url = {http://onlinelibrary.wiley.com/doi/10.1002/9780470725184.ch4/summary}, year = {2008} } @article{Saltelli2002, author = {Saltelli, Andrea and Tarantola, S.}, doi = {10.1198/016214502388618447}, issn = {0162-1459}, journal = {Journal of the American Statistical Association}, keywords = {analysis of variance,correlated input,nonadditive model,sensitivity analysis}, month = {sep}, number = {459}, pages = {702--709}, title = {{On the Relative Importance of Input Factors in Mathematical Models}}, url = {http://www.tandfonline.com/doi/abs/10.1198/016214502388618447}, volume = {97}, year = {2002} } @book{Saltelli2004, author = {Saltelli, Andrea and Tarantola, S. and Campolongo, F and Ratto, M}, isbn = {9780470870945}, publisher = {Wiley}, title = {{Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models}}, url = {http://books.google.co.uk/books?id=NsAVmohPNpQC}, year = {2004} } @article{Santiago2012, abstract = {This paper presents a new sensitivity analysis method called ISTHME based on the principles of Morris's method without the construction of randomized one-at-time (OAT) design. The presented method can be applied on any experimental design and more particularly on space filling designs. This specificity is very interesting in terms of time and calculation economy. Indeed, we can use a universal design, which is adapted to sensitivity analysis as well as optimization without any supplementary simulation. ?? 2011 Elsevier B.V.}, author = {Santiago, J. and Corre, B. and Claeys-Bruno, M. and Sergent, M.}, doi = {10.1016/j.chemolab.2011.10.006}, issn = {01697439}, journal = {Chemometrics and Intelligent Laboratory Systems}, keywords = {Computer experiment,Morris's screening method,Sensitivity study,Space-filling design,elementary effects,morrismethod}, mendeley-tags = {elementary effects,morrismethod}, pages = {52--57}, publisher = {Elsevier B.V.}, title = {{Improved sensitivity through Morris extension}}, url = {http://dx.doi.org/10.1016/j.chemolab.2011.10.006}, volume = {113}, year = {2012} } @article{Sobol2009, abstract = {A model function f(x1,...,xn) defined in the unit hypercube Hn with Lebesque measure dx = dx1...dxn is considered. If the function is square integrable, global sensitivity indices provide adequate estimates for the influence of individual factors xi or groups of such factors. Alternative estimators that require less computer time can also be used. If the function f is differentiable, functionals depending on ???f/???xi have been suggested as estimators for the influence of xi. The Morris importance measure modified by Campolongo, Cariboni and Saltelli ??* is an approximation of the functional ??i = ???Hn fenced(??? f / ??? xi) d x. In this paper a similar functional is studied??i = ???Hn fenced(frac(??? f, ??? xi))2 d xEvidently, ??i ??? sqrt(??i), and ??i ??? C ??i if fenced(??? f / ??? xi) ??? C. A link between ??i and the sensitivity index Sit o t is established:Sit o t ??? frac(??i, ??2 D)where D is the total variance of f(x1,...,xn). Thus small ??i imply small Sit o t, and unessential factors xi (that is xi corresponding to a very small Sit o t) can be detected analyzing computed values ??1,...,??n. However, ranking influential factors xi using these values can give false conclusions. Generalized Sit o t and ??i can be applied in situations where the factors x1,...,xn are independent random variables. If xi is a normal random variable with variance ??i2, then Sit o t ??? ??i ??i2 / D. ?? 2009 IMACS.}, author = {Sobol', I. M. and Kucherenko, S.}, doi = {10.1016/j.matcom.2009.01.023}, issn = {03784754}, journal = {Mathematics and Computers in Simulation}, keywords = {Derivative based global sensitivity measure,Global sensitivity index,Morris method,Quasi Monte Carlo method}, number = {10}, pages = {3009--3017}, title = {{Derivative based global sensitivity measures and their link with global sensitivity indices}}, volume = {79}, year = {2009} } @article{Sobol2001, author = {Sobol', I. M.}, doi = {10.1016/S0378-4754(00)00270-6}, issn = {03784754}, journal = {Mathematics and Computers in Simulation}, keywords = {mathematical modelling,monte carlo method,quasi-monte carlo method,sensitivity analysis}, month = {feb}, number = {1-3}, pages = {271--280}, title = {{Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates}}, url = {http://linkinghub.elsevier.com/retrieve/pii/S0378475400002706}, volume = {55}, year = {2001} } @article{Sobol1990, abstract = {A theorem about decomposition of an integrable function into summands of different dimensions is proved. A Monte Carlo algorithm is proposed for estimating the sensitivity of a function with respect to arbitrary groups of variables.}, author = {Sobol', Il'ya Meerovich}, issn = {0234-0879}, journal = {Matematicheskoe Modelirovanie}, number = {1}, pages = {112--118}, title = {{On sensitivity estimation for nonlinear mathematical models}}, volume = {2}, year = {1990} } @article{Tarantola2006, author = {Tarantola, S. and Gatelli, D. and Mara, T.a.}, doi = {10.1016/j.ress.2005.06.003}, issn = {09518320}, journal = {Reliability Engineering {\&} System Safety}, keywords = {computational models,global sensitivity analysis,uncertainty analysis}, month = {jun}, number = {6}, pages = {717--727}, title = {{Random balance designs for the estimation of first order global sensitivity indices}}, url = {http://linkinghub.elsevier.com/retrieve/pii/S0951832005001444}, volume = {91}, year = {2006} } @article{Wainwright2014, abstract = {This study presents improved understanding of sensitivity analysis methods through a comparison of the local sensitivity and two global sensitivity analysis methods: the Morris and Sobol′/Saltelli methods.We re-interpret the variance-based sensitivity indices from the Sobol′/Saltelli method as difference-based measures. It suggests that the difference-based local and Morris methods provide the effect of each parameter including its interaction with others, similar to the total sensitivity index from the Sobol ′/Saltelli method.We also develop an alternative approximation method to efficiently compute the Sobol′ index, using one-dimensional fitting of system responses from a Monte-Carlo simulation. For illustration, we conduct a sensitivity analysis of pressure propagation induced by fluid injection and leakage in a reservoir–aquitard–aquifer system. The results show that the three methods provide consistent para- meter importance rankings in this system. Our study also reveals that the three methods can provide additional information to improve system understanding.}, author = {Wainwright, Haruko M. and Finsterle, Stefan and Jung, Yoojin and Zhou, Quanlin and Birkholzer, Jens T.}, doi = {10.1016/j.cageo.2013.06.006}, issn = {00983004}, journal = {Computers {\&} Geosciences}, keywords = {Global sensitivity analysis,Morris OAT method,Sobol index,Variance-based sensitivity indices,global sensitivity analysis}, pages = {84--94}, publisher = {Elsevier}, title = {{Making sense of global sensitivity analyses}}, url = {http://linkinghub.elsevier.com/retrieve/pii/S0098300413001702}, volume = {65}, year = {2014} } SALib-SALib-d6e51b1/paper/paper.md000066400000000000000000000030511525347100600165470ustar00rootroot00000000000000--- title: 'SALib: An open-source Python library for Sensitivity Analysis' tags: - sensitivity analysis - Python - uncertainty - variance-based - global sensitivity analysis - fractional factorial - Method of Morris authors: - name: Jon Herman orcid: 0000-0002-4081-3175 affiliation: 1 - name: Will Usher orcid: 0000-0001-9367-1791 affiliation: 2 affiliations: - name: University of California, Davis index: 1 - name: University of Oxford index: 2 date: 11th October 2016 bibliography: paper.bib --- # Summary SALib contains Python implementations of commonly used global sensitivity analysis methods, including Sobol [@Sobol2001,@Saltelli2002a,@Saltelli2010a], Morris [@Morris1991,@Campolongo2007], FAST [@Cukier1973,@Saltelli1999], Delta Moment-Independent Measure [@Borgonovo2007,@Plischke2013] Derivative-based Global Sensitivity Measure (DGSM) [@Sobol2009] , and Fractional Factorial Sensitivity Analysis [@Saltelli2008b] methods. SALib is useful in simulation, optimisation and systems modelling to calculate the influence of model inputs or exogenous factors on outputs of interest. SALib exposes a range of global sensitivity analysis techniques to the scientist, researcher and modeller, making it very easy to easily implement the range of techniques into typical modelling workflows. The library facilitates the generation of samples associated with a model's inputs, and then provides functions to analyse the outputs from a model and visualise those results. # References SALib-SALib-d6e51b1/pyproject.toml000066400000000000000000000035571525347100600167360ustar00rootroot00000000000000[build-system] requires = ["hatchling", "hatch-vcs"] build-backend = "hatchling.build" [project] name = "SALib" dynamic = ["version"] description = "Tools for global sensitivity analysis. Contains Sobol', Morris, FAST, DGSM, PAWN, HDMR, Moment Independent and fractional factorial methods" readme = "README.rst" requires-python = ">=3.10" license = "MIT" authors = [ { name = "Jon Herman" }, { name = "Will Usher" }, { name = "Takuya Iwanaga" }, ] maintainers = [ { name = "SALib contributors" }, ] classifiers = [ "Development Status :: 5 - Production/Stable", "Programming Language :: Python :: 3", "Programming Language :: Python :: 3.10", "Programming Language :: Python :: 3.11", "Programming Language :: Python :: 3.12", "Programming Language :: Python :: 3.14", "License :: OSI Approved :: MIT License", "Intended Audience :: End Users/Desktop", "Intended Audience :: Developers", "Intended Audience :: Science/Research", "Operating System :: OS Independent", ] dependencies = [ "numpy>=2.0", "scipy>=1.9.3", "matplotlib>=3.5", "pandas>=2.0", "multiprocess", ] [project.optional-dependencies] distributed = [ "pathos>=0.3.2", ] test = [ "SALib[distributed]", "pytest", "pytest-cov", ] doc = [ "sphinx", "myst_parser", "numpydoc", "pydata-sphinx-theme>=0.15.2" ] dev = [ "SALib[distributed]", "SALib[test]", "SALib[doc]", "pre-commit>=4.3.0", "ipython", "hatch", ] [project.scripts] salib = "SALib.scripts.salib:main" [project.urls] Documentation = "https://salib.readthedocs.io" "Source code" = "https://github.com/SALib/SALib" [tool.hatch] version.source = "vcs" build.targets.sdist.exclude = [ ".github", "docs", "examples", "paper", "tests", "*.md", "*.rst", "*.yml", "*.cff", ".*", ] [tool.pytest.ini_options] addopts = "--durations 10" testpaths = [ "tests", ] SALib-SALib-d6e51b1/src/000077500000000000000000000000001525347100600145775ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/000077500000000000000000000000001525347100600155315ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/__init__.py000066400000000000000000000000761525347100600176450ustar00rootroot00000000000000from SALib.util import ProblemSpec __all__ = ["ProblemSpec"] SALib-SALib-d6e51b1/src/SALib/analyze/000077500000000000000000000000001525347100600171745ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/analyze/__init__.py000066400000000000000000000000001525347100600212730ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/analyze/common_args.py000066400000000000000000000023431525347100600220540ustar00rootroot00000000000000import argparse def setup(parser): parser = argparse.ArgumentParser( description="Perform sensitivity analysis on model output" ) parser.add_argument( "-p", "--paramfile", type=str, required=True, help="Parameter range file" ) parser.add_argument( "-Y", "--model-output-file", type=str, required=True, help="Model output file" ) parser.add_argument( "-c", "--column", type=int, required=False, default=0, help="Column of output to analyze", ) parser.add_argument( "--delimiter", type=str, required=False, default=" ", help="Column delimiter in model output file", ) parser.add_argument( "-s", "--seed", type=int, required=False, default=None, help="Random Seed" ) return parser def create(cli_parser=None): parser = argparse.ArgumentParser( description="Perform sensitivity analysis on model output" ) parser = setup(parser) if cli_parser: parser = cli_parser(parser) return parser def run_cli(cli_parser, run_analysis, known_args=None): parser = create(cli_parser) args = parser.parse_args(known_args) run_analysis(args) SALib-SALib-d6e51b1/src/SALib/analyze/delta.py000066400000000000000000000552771525347100600206570ustar00rootroot00000000000000from typing import Optional, Dict from scipy.stats import norm, gaussian_kde, rankdata import numpy as np import pandas as pd from . import common_args from ..util import read_param_file, ResultDict import warnings import json class AnalysisError(Exception): def __init__(self, cmd, note=None): self.cmd = cmd self.note = note or cmd super().__init__(self.note) warnings.warn(self.cmd) def exception_handler(e, name, Ysize): if isinstance(e, AnalysisError): return e.note elif isinstance(e, np.linalg.LinAlgError): raise ValueError( f"ERROR [{name}]: Singular matrix - likely due to degenerate input or small sample size (N={Ysize})" ) from e else: warnings.warn(f"Unhandled exception: {type(e).__name__} - {e}") return str(e) def custom_warning_formatter(message, category, filename, lineno, line=None): return f"{message}\n" def analyze( problem: Dict, X: np.ndarray, Y: np.ndarray, num_resamples: int = 100, conf_level: float = 0.95, print_to_console: bool = False, seed: Optional[int] = None, y_resamples: Optional[int] = None, method: str = "all", bootstrap_savedf: Optional[str] = None, bins_specs: Dict = {}, ) -> Dict: """Perform Delta Moment-Independent Analysis on model outputs. Returns a dictionary with keys: - 'delta_balanced' - 'delta_balanced_conf' - 'delta_raw' - 'delta_raw_conf' - 'delta_step' - 'delta_step_conf' - 'S1' - 'S1_conf' - 'names' where each entry is a list of size D (the number of parameters) containing the indices in the same order as the input file and 'names'. The different delta configurations/methods 'balanced', 'step', 'raw', their corresponding confidence scores (*_conf), and other keys in returned dictionary: - 'names' input column/feature names in X - 'notes' Notes and insights on analysis, warnings, errors, etc. - 'balanced' Divides the input into bins during bootstrapping (default 10) and divides bootstrap subset equally among those bins - 'step' Generates all entries in the input into 1 (X>0) or 0 (X<=0) and bootstrap subset is approximately 50% - 'raw' Bootstraps the input column as is, with random bootstrap sampling with replacement - 'S1' Sobol' first indices, on raw dataset with no bootstrap manipulations (random, with replacement) Notes ----- Compatible with: all samplers Interpretaion: 'balanced' tells us how important variation in that input feature is on the output feature. - Answers the question: "How important is input feature X on output Y?" 'step' tells us how important that input feature as active (versus inactive) is on the output feature. - Answers the question: "What is the impact of input feature X when it is greater than zero/active, versus inactive, regardless of its actual value?" 'raw' tells us how much the input feature affects variation in the output feature, specifically in this dataset and its composition. This score may be skewed or biased toward frequently occurring values in the dataset. (eg. if most values of the input feature lie between 15-20 in your dataset, then the delta score will likely primarily be biased toward influence within that range, rather than its total influence over its entire input range) - Answers the question: "How important is input feature X, and how prominent is its influence specifically in my dataset?" - Is a valid interpretation for real-world scenario, if the input data is representative of the real-world sample and variability without inconsistent or incomplete sampling (rare for real-world data capture) 'notes' contains flags, warnings, or error messages. - Will raise a flag if 'balanced' and 'raw' delta scores differ by >0.1. This suggests that the input dataset is likely skewed or biased with frequently occuring values in a specific range. - Raises errors if binning cannot be executed, if there aren't enough/any zeroes/>0s present to do step analysis, etc. - Guides user with results interpretation Examples -------- >>> X = latin.sample(problem, 1000) >>> Y = Ishigami.evaluate(X) >>> Si = delta.analyze(problem, X, Y, print_to_console=True) Parameters ---------- problem : dict The problem definition X: numpy.matrix A NumPy matrix containing the model inputs Y : numpy.array A NumPy array containing the model outputs num_resamples : int The number of resamples when computing confidence intervals (default 100) conf_level : float The confidence interval level (default 0.95) print_to_console : bool Print results directly to console (default False) y_resamples : int, optional Number of samples to use when resampling (bootstrap) (default None) method : {"all", "delta", "sobol"}, optional Whether to compute "delta", "sobol" or both ("all") indices (default "all") bootstrap_savedf : str, optional User inputs path or filename if they want to save a bootstrap sample to inspect subset composition bins_specs : dict, optional Dict with parameter title as key and bin_input as entry. If bin_input is an int, number of bins. If bin_input is a list, it specifies bin boundaries ( number of bins = len(list)+1 ) Default is 10 bins equally distributed across input feature range References ---------- 1. Borgonovo, E. (2007). "A new uncertainty importance measure." Reliability Engineering & System Safety, 92(6):771-784, doi:10.1016/j.ress.2006.04.015. 2. Plischke, E., E. Borgonovo, and C. L. Smith (2013). "Global sensitivity measures from given data." European Journal of Operational Research, 226(3):536-550, doi:10.1016/j.ejor.2012.11.047. """ if seed: np.random.seed(seed) valid_methods = {"delta", "sobol", "all"} warnings.formatwarning = custom_warning_formatter warnings.simplefilter("once") if X.shape[0] != Y.shape[0]: raise RuntimeError("Input X and output Y must have the same number of rows") if not 0 < conf_level < 1: raise RuntimeError("Confidence level must be between 0-1.") if method not in valid_methods: raise ValueError(f"Method must be one of {valid_methods}") delta_warn_threshold = 0.1 D = problem["num_vars"] if y_resamples is None: y_resamples = Y.size methods = ["delta", "sobol"] if method == "all" else [method] if bootstrap_savedf is not None: if not bootstrap_savedf.endswith(".parquet"): bootstrap_savedf = bootstrap_savedf + ".parquet" if not y_resamples <= Y.size: raise RuntimeError( "y_resamples must be less than or equal to the total number of samples" ) # equal frequency partition exp = 2.0 / (7.0 + np.tanh((1500.0 - y_resamples) / 500.0)) M = int(np.round(min(int(np.ceil(y_resamples**exp)), 48))) m = np.linspace(0, y_resamples, M + 1) Ygrid = np.linspace(np.min(Y), np.max(Y), 100) # S keys = [] if "delta" in methods: keys += [ "delta_balanced", "delta_balanced_conf", "delta_raw", "delta_raw_conf", "delta_step", "delta_step_conf", ] if "sobol" in methods: keys += ["S1", "S1_conf"] S = ResultDict((k, np.full(D, np.nan)) for k in keys) nameslist = problem["names"] if any( any(col.endswith(s) for s in ["_raw", "_balanced", "_step", "_conf"]) for col in nameslist ): raise ValueError( "Forbidden column name suffix: columns may not end with ['_raw', '_balanced', '_step', '_conf'] " ) keys += ["notes"] S["names"] = problem["names"] notes = [] bootstrap_matrix = {} for i in range(D): name = problem["names"][i] X_i = X[:, i] min_class_size = max(int(len(X_i) * 0.005), 10) bininfo = bins_specs.get(name, None) bin_edges, note = check_specified_bininfo( bininfo=bininfo, Xmin=X_i.min(), Xmax=X_i.max(), paramname=name ) try: if "delta" in methods: for mode in ["balanced", "raw", "step"]: if mode == "step": zeroes = np.sum(X_i <= 0) nonzeroes = np.sum(X_i > 0) if zeroes < min_class_size or nonzeroes < min_class_size: S["delta_step"][i] = np.nan S["delta_step_conf"][i] = np.nan note += f"Step: too few samples. {zeroes} (<=0), {nonzeroes} (>0); " continue S[f"delta_{mode}"][i], S[f"delta_{mode}_conf"][i], boot_idx = ( bias_reduced_delta( Y, Ygrid, X_i, m, num_resamples, conf_level, y_resamples, mode, bin_edges, name, min_class_size, ) ) if bootstrap_savedf is not None: bootstrap_matrix[f"{name}_{mode}"] = ( X_i[boot_idx] if len(boot_idx) == y_resamples else np.full(y_resamples, np.nan) ) diff = abs(S["delta_balanced"][i] - S["delta_raw"][i]) if diff > delta_warn_threshold: note += f"Raw delta differs from balanced by {diff:.2f}; " warnings.warn( f"[{name}] Potential Bias Notice: Raw delta score differs from balanced delta by {diff:.2f}. Potential dataset bias, take care in interpretation." ) if "sobol" in methods: ind = np.random.randint(Y.size, size=y_resamples) S["S1"][i] = sobol_first(Y[ind], X_i[ind], m) S["S1_conf"][i] = sobol_first_conf( Y, X_i, m, num_resamples, conf_level, y_resamples ) notes.append(note.strip() if note else "") except Exception as e: note = exception_handler(e, name, Y.size) notes.append(note) continue S["notes"] = notes if print_to_console: # Merge dictionaries summary_dict = {"names": problem["names"]} | S df_summary = pd.DataFrame(summary_dict) print(df_summary.to_string(index=False)) if bootstrap_savedf is not None: df_boot = pd.DataFrame(bootstrap_matrix) try: df_boot.to_parquet(bootstrap_savedf, engine="pyarrow", compression="snappy") except Exception as e: warnings.warn( f"WARNING: Failed to write bootstrap file to {bootstrap_savedf}. Reason: {e}" ) return S def check_specified_bininfo(bininfo, Xmin, Xmax, paramname): """Validate user-specified bin edges or number of bins; fallback to default if invalid.""" defaultbins = 10 if bininfo is None: return np.linspace(Xmin, Xmax, defaultbins + 1), "" elif isinstance(bininfo, int): return np.linspace(Xmin, Xmax, bininfo + 1), "" elif isinstance(bininfo, (list, np.ndarray)): bin_edges = np.array(bininfo) if not np.issubdtype(bin_edges.dtype, np.number): warnings.warn( f"[{paramname}] Input Error: Bin value error - Custom bin list only contain numeric values. Resorting to default binning ({defaultbins} bins)." ) return ( np.linspace(Xmin, Xmax, defaultbins + 1), f"Custom bin list had non-numeric values. Used default {defaultbins} bins; ", ) elif np.any(bin_edges < Xmin) or np.any(bin_edges > Xmax): warnings.warn( f"[{paramname}] Input Error: Bin boundary error - Custom bin boundaries must be within the X range. Resorting to default binning ({defaultbins} bins)." ) return ( np.linspace(Xmin, Xmax, defaultbins + 1), f"Custom bin bounds out of X range. Used default {defaultbins} bins; ", ) elif not np.all(np.diff(bin_edges) > 0): warnings.warn( f"[{paramname}] Input Error: Bin edge error - Custom bin edges must be ascending. Resorting to default binning ({defaultbins} bins)." ) return ( np.linspace(Xmin, Xmax, defaultbins + 1), f"Custom bin edges not ascending. Used default {defaultbins} bins; ", ) return np.concatenate(([Xmin - 1e-9], bin_edges, [Xmax + 1e-9])), "" else: warnings.warn( f"[{paramname}] Input Error: Invalid custom bin dtype - Must be int, list or None. Resorting to default binning ({defaultbins} bins)." ) return ( np.linspace(Xmin, Xmax, defaultbins + 1), f"Custom bin invalid dtype. Used default {defaultbins} bins; ", ) def calc_delta(Y, Ygrid, X, m): """Plischke et al. (2013) delta index estimator (eqn 26) for d_hat.""" N = len(Y) fy = gaussian_kde(Y, bw_method="silverman")(Ygrid) xr = rankdata(X, method="ordinal") d_hat = 0.0 total_bins = len(m) - 1 num_skipped = 0 for j in range(total_bins): ix = np.where((xr > m[j]) & (xr <= m[j + 1]))[0] nm = len(ix) if nm == 0: # Skip empty bins. Even if it doesn't throw an error, # can't estimate local distribution for gaussian_kde from empty data continue Y_ix = Y[ix] if np.ptp(Y_ix) != 0.0: fyc = gaussian_kde(Y_ix, bw_method="silverman")(Ygrid) fy_ = np.abs(fy - fyc) else: num_skipped += 1 continue d_hat += (nm / (2 * N)) * np.trapezoid(fy_, Ygrid) if num_skipped / total_bins > 0.35: warnings.warn( f"{num_skipped}/{total_bins} bins skipped (>35%)" "This may indicate under-sampling or poor binning." "Try increasing sample size (y_resamples) or decreasing the number of bins (M)." ) return d_hat def bias_reduced_delta( Y, Ygrid, X, m, num_resamples, conf_level, y_resamples, mode, bin_edges, paramname, min_class_size, ): """Plischke et al. 2013 bias reduction technique (eqn 30)""" d = np.empty(num_resamples) ind = obtain_resampled_subset( X, y_resamples, mode, bin_edges, paramname, min_class_size, warn_print=True ) d_hat = calc_delta(Y[ind], Ygrid, X[ind], m) try: r = [ obtain_resampled_subset( X, y_resamples, mode, bin_edges, paramname, min_class_size, warn_print=False, ) for _ in range(num_resamples) ] except ValueError as e: raise RuntimeError(f"Bootstrap error: [{paramname}][{mode}]: {e}") from e for i, r_i in enumerate(r): d[i] = calc_delta(Y[r_i], Ygrid, X[r_i], m) d = 2.0 * d_hat - d return (d.mean(), norm.ppf(0.5 + conf_level / 2) * d.std(ddof=1), ind) def obtain_bins_indices(bin_edges, X, min_class_size): """ Returns indices for all specified bins, ensuring that all bins are at least minimum_class_size """ init_indices = [] for i in range(len(bin_edges) - 1): if i == 0: idx = np.where((X >= bin_edges[i]) & (X <= bin_edges[i + 1]))[0] else: idx = np.where((X > bin_edges[i]) & (X <= bin_edges[i + 1]))[0] init_indices.append(idx) final_indices = [] # for the case where some bins are underpopulated i = 0 while i < len(init_indices): current_bin = init_indices[i] while len(current_bin) < min_class_size and i + 1 < len(init_indices): current_bin = np.concatenate((current_bin, init_indices[i + 1])) i += 1 final_indices.append(current_bin) i += 1 return init_indices, final_indices def obtain_resampled_subset( X, y_resamples, mode, bin_edges, paramname, min_class_size, warn_print=False ): """Returns subset indices for X""" N = len(X) X = np.asarray(X) if X.max() == X.min(): raise ValueError( f"[{paramname}] has constant values, cannot bin or calculate delta.", "Cannot bin or calc delta from constants; ", ) if mode == "raw": return np.random.randint(N, size=y_resamples) elif mode in ["balanced", "step"]: indices = [] X_select = X binselectionsize = y_resamples if mode == "step": zeroes = np.where(X <= 0)[0] nonzeroes = np.where(X > 0)[0] n_zeroes = int(0.5 * y_resamples) binselectionsize = y_resamples - n_zeroes min_class_size = min_class_size // 2 chosen_zeroes = np.random.choice(zeroes, size=n_zeroes, replace=True) indices.append(chosen_zeroes) X_select = X[nonzeroes] bin_edges, _ = check_specified_bininfo( bininfo=5, Xmin=X_select.min(), Xmax=X_select.max(), paramname=paramname ) init_indices, final_indices = obtain_bins_indices( bin_edges, X_select, min_class_size ) n_bins = len(final_indices) n_per_bin = binselectionsize // n_bins remaining = binselectionsize - (n_per_bin * n_bins) if n_bins < 2: raise AnalysisError( f"[{paramname}][{mode}] Only one bin remains. Revisit whether processing method is suitable for this parameter, or increase dataset size or spread. Highly biased input.", f"[{mode}] Single valid bin. Insufficient spread in feature, highly biased input; ", ) if n_bins != len(init_indices): if warn_print: warnings.warn( f"[{paramname}][{mode}] Bin Merge Notice: Final no. bins is {len(final_indices)}. Min samples per bin: {min_class_size}" ) if n_per_bin < min_class_size: raise ValueError( f"[{paramname}][{mode}] Dataset size error: Dataset is not large enough for number of bins.", f"[{mode}]: Dataset too small for no. bins; ", ) for i, bin_idx in enumerate(final_indices): if len(bin_idx) == 0: continue binsize = n_per_bin + (1 if i < remaining else 0) sampled = np.random.choice(bin_idx, size=binsize, replace=True) if mode == "step": sampled = nonzeroes[sampled] # type: ignore indices.append(sampled) return np.concatenate(indices) else: raise ValueError( f"{paramname} Issue with mode {mode} suffix. \ This line should never execute." ) def sobol_first(Y, X, m): # Pre-process to catch constant array # see: https://github.com/numpy/numpy/issues/9631 if np.ptp(Y) == 0.0: # Catch constant results # If Y does not change then it is not sensitive to anything... return 0.0 xr = rankdata(X, method="ordinal") Vi = 0 N = len(Y) Y_mean = Y.mean() for j in range(len(m) - 1): ix = np.where((xr > m[j]) & (xr <= m[j + 1]))[0] nm = len(ix) Vi += (nm / N) * ((Y[ix].mean() - Y_mean) ** 2) return Vi / np.var(Y) def sobol_first_conf(Y, X, m, num_resamples, conf_level, y_resamples): s = np.zeros(num_resamples) N = len(Y) r = np.random.choice( N, size=(num_resamples, y_resamples), replace=True ) # bootstrap-like behaviour, on raw vals without removing input bias for i in range(num_resamples): r_i = r[i, :] s[i] = sobol_first(Y[r_i], X[r_i], m) return norm.ppf(0.5 + conf_level / 2) * s.std(ddof=1) def cli_parse(parser): parser.add_argument( "-X", "--model-input-file", type=str, required=True, default=None, help="Model input file", ) parser.add_argument( "-r", "--resamples", type=int, required=False, default=10, help="Number of bootstrap resamples for \ Sobol confidence intervals", ) parser.add_argument( "-m", "--method", type=str, required=False, default="all", help="Method to compute sensitivities \ 'delta', 'sobol' or 'all'", ) parser.add_argument( "--y_resamples", type=int, required=False, default=None, help="Number of samples to use when \ resampling (bootstrap)", ) parser.add_argument( "--bootstrap_savedf", type=str, help="Optional path to save bootstrap \ feature values", ) parser.add_argument( "--bins_specs", type=str, default=None, help="Optional: JSON string or path to a \ JSON file specifying bin info per \ input feature", ) return parser def cli_action(args): problem = read_param_file(args.paramfile) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,) ) X = np.loadtxt(args.model_input_file, delimiter=args.delimiter, ndmin=2) if len(X.shape) == 1: X = X.reshape((len(X), 1)) try: if args.bins_specs is None: bins_specs = {} elif args.bins_specs.strip().startswith("{"): bins_specs = json.loads(args.bins_specs) else: with open(args.bins_specs) as f: bins_specs = json.load(f) except (json.JSONDecodeError, FileNotFoundError) as e: raise ValueError( f"Failed to parse bins_specs. Must be a JSON string or \ file path. Error: {e}" ) analyze( problem, X, Y, num_resamples=args.resamples, print_to_console=True, seed=args.seed, method=args.method, y_resamples=args.y_resamples, bootstrap_savedf=args.bootstrap_savedf, bins_specs=bins_specs, ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/analyze/dgsm.py000066400000000000000000000120571525347100600205050ustar00rootroot00000000000000from scipy.stats import norm import numpy as np from . import common_args from ..util import read_param_file, ResultDict def analyze( problem, X, Y, num_resamples=100, conf_level=0.95, print_to_console=False, seed=None ): """Calculates Derivative-based Global Sensitivity Measure on model outputs. Returns a dictionary with keys 'vi', 'vi_std', 'dgsm', and 'dgsm_conf', where each entry is a list of size D (the number of parameters) containing the indices in the same order as the parameter file. Notes ----- Compatible with: `finite_diff` : :func:`SALib.sample.finite_diff.sample` Examples -------- >>> X = finite_diff.sample(problem, 1000) >>> Y = Ishigami.evaluate(X) >>> Si = dgsm.analyze(problem, X, Y, print_to_console=False) Parameters ---------- problem : dict The problem definition X : numpy.matrix The NumPy matrix containing the model inputs Y : numpy.array The NumPy array containing the model outputs num_resamples : int The number of resamples used to compute the confidence intervals (default 1000) conf_level : float The confidence interval level (default 0.95) print_to_console : bool Print results directly to console (default False) seed : int Seed to generate a random number References ---------- 1. Sobol, I. M. and S. Kucherenko (2009). "Derivative based global sensitivity measures and their link with global sensitivity indices." Mathematics and Computers in Simulation, 79(10):3009-3017, doi:10.1016/j.matcom.2009.01.023. """ if seed: np.random.seed(seed) D = problem["num_vars"] Y_size = Y.size if Y_size % (D + 1) == 0: N = int(Y_size / (D + 1)) else: raise RuntimeError("Incorrect number of samples in model output file.") if not 0 < conf_level < 1: raise RuntimeError("Confidence level must be between 0-1.") dims = (N, D) base = np.empty(N) X_base = np.empty(dims) perturbed = np.empty(dims) X_perturbed = np.empty(dims) step = D + 1 base = Y[0:Y_size:step] X_base = X[0:Y_size:step, :] # First order (+conf.) and Total order (+conf.) keys = ("vi", "vi_std", "dgsm", "dgsm_conf") S = ResultDict((k, np.empty(D)) for k in keys) S["names"] = problem["names"] bounds = problem["bounds"] for j in range(D): perturbed[:, j] = Y[(j + 1) : Y_size : step] X_perturbed[:, j] = X[(j + 1) : Y_size : step, j] diff = X_perturbed[:, j] - X_base[:, j] perturbed_j = perturbed[:, j] S["vi"][j], S["vi_std"][j] = calc_vi_stats(base, perturbed_j, diff) S["dgsm"][j], S["dgsm_conf"][j] = calc_dgsm( base, perturbed_j, diff, bounds[j], num_resamples, conf_level ) if print_to_console: print(S.to_df()) return S def calc_vi_stats(base, perturbed, x_delta): """Calculate v_i mean and std. v_i sensitivity measure following Sobol and Kucherenko (2009) For comparison, Morris mu* < sqrt(v_i) Same as calc_vi_mean but returns standard deviation as well. """ dfdx = ((perturbed - base) / x_delta) ** 2 return np.mean(dfdx), np.std(dfdx) def calc_vi_mean(base, perturbed, x_delta): """Calculate v_i mean. Same as calc_vi_stats but only returns the mean. """ dfdx = ((perturbed - base) / x_delta) ** 2 return dfdx.mean() def calc_dgsm(base, perturbed, x_delta, bounds, num_resamples, conf_level): """v_i sensitivity measure following Sobol and Kucherenko (2009). For comparison, total order S_tot <= dgsm """ D = np.var(base) vi = calc_vi_mean(base, perturbed, x_delta) dgsm = vi * (bounds[1] - bounds[0]) ** 2 / (D * np.pi**2) len_base = len(base) s = np.empty(num_resamples) r = np.random.randint(len_base, size=(num_resamples, len_base)) for i in range(num_resamples): r_i = r[i] s[i] = calc_vi_mean(base[r_i], perturbed[r_i], x_delta[r_i]) return dgsm, norm.ppf(0.5 + conf_level / 2.0) * s.std(ddof=1) def cli_parse(parser): parser.add_argument( "-X", "--model-input-file", type=str, required=True, default=None, help="Model input file", ) parser.add_argument( "-r", "--resamples", type=int, required=False, default=1000, help="Number of bootstrap resamples for Sobol \ confidence intervals", ) return parser def cli_action(args): problem = read_param_file(args.paramfile) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,) ) X = np.loadtxt(args.model_input_file, delimiter=args.delimiter, ndmin=2) if len(X.shape) == 1: X = X.reshape((len(X), 1)) analyze( problem, X, Y, num_resamples=args.resamples, print_to_console=True, seed=args.seed, ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/analyze/discrepancy.py000066400000000000000000000107531525347100600220600ustar00rootroot00000000000000from typing import Dict import numpy as np from scipy.stats import qmc from SALib.analyze import common_args from SALib.util import read_param_file, ResultDict, _check_groups def analyze( problem: Dict, X: np.ndarray, Y: np.ndarray, method: str = "WD", print_to_console: bool = False, seed: int = None, ): """Discrepancy indices. Parameters ---------- problem : dict The problem definition X, Y : numpy.ndarray An array of model inputs and outputs. method : {"WD", "CD", "MD", "L2-star"} Type of discrepancy. Refer to `scipy.stats.qmc.discrepancy` for more details. Default is "WD". print_to_console : bool, optional Print results directly to console (default False) seed : int, optional Seed value to ensure deterministic results Unused, but defined to maintain compatibility with other functions. Notes ----- Compatible with: all samplers Based on 2D sub projections of ``[Xi,Y]``, the discrepancy of each sample is calculated which gives a value for all ``Xi``. This information is used as a measure of sensitivity. Discrepancy analysis is very fast and is visually explainable. Considering two variables ``X1`` and ``X2``, ``X1`` is more influential than ``X2`` when the scatterplot of ``X1`` against ``Y`` displays a more discernible shape than the scatterplot of ``X2`` against ``Y``. For the method to work properly, the input parameter space need to be uniformly covered as the quality of the measure depends on the value of the discrepancy. Taking a 2D sub projection, if the distribution of sample along ``Xi`` is not uniform, it will have an impact on the discrepancy, the value will increase, i.e. the importance of this parameter would be inflated. References ---------- 1. A. Puy, P.T. Roy and A. Saltelli. 2023. Discrepancy measures for sensitivity analysis. https://arxiv.org/abs/2206.13470 2. A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, and S. Tarantola. 2008. Global Sensitivity Analysis: The Primer. Wiley, West Sussex, U.K. https://dx.doi.org/10.1002/9780470725184 Accessible at: http://www.andreasaltelli.eu/file/repository/Primer_Corrected_2022.pdf Examples -------- >>> import numpy as np >>> from SALib.sample import latin >>> from SALib.analyze import discrepancy >>> from SALib.test_functions import Ishigami >>> problem = { ... 'num_vars': 3, ... 'names': ['x1', 'x2', 'x3'], ... 'bounds': [[-np.pi, np.pi]]*3 ... } >>> X = latin.sample(problem, 1000) >>> Y = Ishigami.evaluate(X) >>> Si = discrepancy.analyze(problem, X, Y, print_to_console=True) """ D = problem["num_vars"] groups = _check_groups(problem) Y = Y.reshape(-1, 1) bounds = np.asarray(problem["bounds"]).T X = qmc.scale(sample=X, l_bounds=bounds[0], u_bounds=bounds[1], reverse=True) Y = qmc.scale(sample=Y, l_bounds=np.min(Y), u_bounds=np.max(Y), reverse=True) s_discrepancy = [ qmc.discrepancy(np.concatenate([X[:, i, None], Y], axis=1), method=method) for i in range(D) ] s_discrepancy = s_discrepancy / np.sum(s_discrepancy) if groups: groups = np.array(groups) unique_grps = [*dict.fromkeys(groups)] tmp = np.full((len(unique_grps), 1), np.nan) # Take the mean of effects from parameters that are grouped together for grp_id, grp in enumerate(unique_grps): tmp[grp_id, :] = np.mean(s_discrepancy[groups == grp], axis=0) s_discrepancy = tmp.flatten() keys = ("s_discrepancy",) Si = ResultDict((k, np.zeros(D)) for k in keys) Si["names"] = problem["names"] Si["s_discrepancy"] = s_discrepancy if print_to_console: print(Si.to_df()) return Si def cli_parse(parser): parser.add_argument( "-X", "--model-input-file", type=str, required=True, help="Model input file" ) return parser def cli_action(args): problem = read_param_file(args.paramfile) X = np.loadtxt(args.model_input_file, delimiter=args.delimiter) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,) ) analyze( problem, X, Y, print_to_console=True, seed=args.seed, ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/analyze/enhanced_hdmr.py000066400000000000000000001506411525347100600223340ustar00rootroot00000000000000import math import warnings from typing import Dict, Tuple from types import MethodType from itertools import combinations as comb, product from collections import defaultdict, namedtuple import numpy as np from pandas import DataFrame as df from numpy.linalg import det, pinv, matrix_rank from scipy.linalg import svd, LinAlgError, solve from scipy import stats, special from . import common_args from ..util import read_param_file, ResultDict __all__ = ["analyze", "cli_parse", "cli_action"] def analyze( problem: Dict, X: np.ndarray, Y: np.ndarray, max_order: int = 2, poly_order: int = 3, bootstrap: int = 20, subset: int = None, max_iter: int = 100, l2_penalty: float = 0.01, alpha: float = 0.95, extended_base: bool = True, print_to_console: bool = False, return_emulator: bool = False, seed: int = None, ) -> Dict: """Compute global sensitivity indices using the meta-modeling technique known as High-Dimensional Model Representation (HDMR). Introduction ------------ HDMR itself is not a sensitivity analysis method but a surrogate modeling approach. It constructs a map of relationship between sets of high dimensional inputs and output system variables [1]. This I/O relation can be constructed using different basis functions (orthonormal polynomials, splines, etc.). The model decomposition can be expressed as .. math:: \\tilde{y} \\approx \\widehat{y} &= f_0 + \\sum_{i=1}^{d} f_i(x_i) + \\sum_{i=1}^{d-1} \\sum_{j=i+1}^{d} f_{ij} (x_{ij}) + \\sum_{i=1}^{d-2} \\sum_{j=i+1}^{d-1} \\sum_{j+1}^{d} f_{ijk} (x_{ijk}) + \\epsilon \\ \\widehat{y} &= f_0 + \\sum_{u \\subseteq \\{1, 2, ..., d \\}}^{2^n - 1} f_u + \\epsilon where :math:`u` represents any subset including an empty set. There is a unique decomposition regardless of correlation among the input variables under the following condition. .. math:: \\forall v \\subseteq u, \\forall g_v: \\int f_u (x_u) g_v (x_v) w(\\bm(x)) d\\bm(x) = 0 This condition implies that a component function is only required to be orthogonal to all nested lower order component functions whose variables are a subset of its variables. For example, :math:`f_{ijk} (x_i, x_j, x_k )` is only required to be orthogonal to :math:`f_i(x_i), f_j(x_j), f_k (x_k), f_{ij}(x_i, x_j), f_{ik}(x_i, x_k),` and :math:`f_{jk} (x_j, x_k)`. Please keep in mind that this condition is only satisfied when `extended_base` is set to `True`. HDMR becomes extremely useful when the computational cost of obtaining sufficient Monte Carlo samples are prohibitive, as may be the case with Sobol's method. It uses least-square regression to reduce the required number of samples and thus the number of function (model) evaluations. Another advantage of this method is that it can account for correlation among the model input. Unlike other variance-based methods, the main effects are the combination of structural (uncorrelated) and correlated contributions. Covariance Decomposition ------------------------ Variance-based sensitivity analysis methods employ a decomposition approach to assess the contributions of input sets towards the variance observed in the model's output. This method uses the same technique while also considering the influence of correlation in the decomposition of output variance.The following equation ilustrates how correlation plays a role in variance decomposition. .. math:: Var[y] = \\sum_{u=1}^{2^n - 1} Var[f_u] + \\sum_{u=1}^{2^n - 1} Cov \\left[f_u, \\sum_{v \\neq u} f_v \\right] The first component on the right hand side of the equation depicts the uncorrelated contribution to the overall variance, while the subsequent component signifies the associated contribution of a specific component function in correlation with other component functions. In this method, we used `Sa` and `Sb` to represent uncorrelated contribution and correlated contribution. This method uses as input - a N x d matrix of N different d-vectors of model inputs (factors/parameters) - a N x 1 vector of corresponding model outputs Notes ----- Compatible with: all samplers Sets an `emulate` method allowing re-use of the emulator. Examples -------- .. code-block:: python :linenos: sp = ProblemSpec({ 'names': ['X1', 'X2', 'X3'], 'bounds': [[-np.pi, np.pi]] * 3, 'outputs': ['Y'] }) (sp.sample_saltelli(2048) .evaluate(Ishigami.evaluate) .analyze_enhanced_hdmr() ) sp.emulate() Parameters ---------- problem : dict The problem definition X : numpy.matrix The NumPy matrix containing the model inputs, N rows by d columns Y : numpy.array The NumPy array containing the model outputs for each row of X max_order : int (1-3, default: 2) Maximum HDMR expansion order poly_order : int (1-10, default: 3) Maximum polynomial order bootstrap : int (1-100, default: 20) Number of bootstrap iterations subset : int (300-N, default: N/2) Number of bootstrap samples. Will be set to length of `Y` if `K` is set to 1. max_iter : int (1-1000, default: 100) Max iterations backfitting. Not used if extended_base is `True` l2_penalty : float (0-10, default: 0.01) Regularization term alpha : float (0.5-1, default: 0.95) Confidence interval for F-test extended_base : bool (default: True) Extends base matrix if `True`. This guarantees the hierarchical orthogonality print_to_console : bool (default: False) Prints results directly to console (default: False) return_emulator: bool (default: False) Attaches emulate method to the Si if `True` seed : int (default: None) Seed to generate a random number Returns ------- Si : ResultDict, -"Sa" : Sensitivity index (uncorrelated contribution) -"Sa_conf" : Statistical confidence interval of `Sa` -"Sb" : Sensitivity index (correlated contribution) -"Sb_conf" : Statistical confidence interval of `Sb` -"S" : Sensitivity index (total contribution) -"S_conf" : Statistical confidence interval of `S` -"ST" : Total Sensitivity indexes of features/inputs -"ST_conf" : Statistical confidence interval of `ST` -"Signf" : Signigicancy for each bootstrap iteration -"Term" : Component name -emulate() : Emulator method when return_emulator is set to `True` References ---------- 1. Rabitz, H. and AliÅŸ, Ö.F., General foundations of high dimensional model representations, Journal of Mathematical Chemistry 25, 197-233 (1999) https://doi.org/10.1023/A:1019188517934 2. Genyuan Li, H. Rabitz, P.E. Yelvington, O.O. Oluwole, F. Bacon, C.E. Kolb, and J. Schoendorf, "Global Sensitivity Analysis for Systems with Independent and/or Correlated Inputs", Journal of Physical Chemistry A, Vol. 114 (19), pp. 6022 - 6032, 2010, https://doi.org/10.1021/jp9096919 3. Gao, Y., Sahin, A., & Vrugt, J. A. (2023) Probabilistic sensitivity analysis with dependent variables: Covariance-based decomposition of hydrologic models. Water Resources Research, 59, e2022WR032834. https://doi.org/10.1029/2022WR032834 """ # Random Seed if seed: np.random.seed(seed) # Check arguments Y, problem, subset, max_iter = _check_args( problem, X, Y, max_order, poly_order, bootstrap, subset, max_iter, l2_penalty, alpha, extended_base, ) # Instantiate Core Parameters hdmr, Si = _core_params( problem, *X.shape, np.mean(Y), poly_order, max_order, bootstrap, subset, extended_base, ) # Calculate HDMR Basis Matrix b_m = _basis_matrix(X, hdmr) # Functional ANOVA decomposition Si, hdmr = _fanova(b_m, hdmr, Si, Y, bootstrap, max_iter, l2_penalty, alpha) # HDMR finalize Si = _finalize(hdmr, Si, alpha, return_emulator) # Print results to console if print_to_console: _print(Si) return Si def _check_args( problem, X, Y, max_order, poly_order, bootstrap, subset, max_iter, l2_penalty, alpha, extended_base, ): """Validates all parameters to ensure that they are within the limits""" # Make sure Y, output array, is a matrix Y = Y.reshape(-1, 1) # Get dimensions of input-output N, d = X.shape y_row = Y.shape[0] # If parameter names are not defined if "names" not in problem: problem["names"] = [f"x_{i}" for i in range(d)] # If parameter bounds are not defined if "bounds" not in problem: problem["bounds"] = [[X[:, i].min(), X[:, i].max()] for i in range(d)] # If parameter num_vars are not defined if "num_vars" not in problem: problem["num_vars"] = d # If the length of 'num_vars' in ProblemSpec != Columns in X matrix msg = "Problem definition must be consistent with the number of dimension in `X`" if "num_vars" in problem and problem["num_vars"] != d: raise ValueError(msg) # If the length of 'names' in ProblemSpec != Columns in X matrix if "names" in problem and len(problem["names"]) != d: raise ValueError(msg) # If the length of 'bounds' in ProblemSpec != Columns in X matrix if "bounds" in problem and len(problem["bounds"]) != d: raise ValueError(msg) # Now check input-output mismatch if d == 1: raise RuntimeError( "Matrix X contains only a single column: No point to do" " sensitivity analysis when d = 1." ) if N < 300: raise RuntimeError( f"Number of samples in the input matrix X, {N}, is insufficient." "Need at least 300." ) if N != y_row: raise ValueError( f"Dimension mismatch. The number of outputs ({y_row}) should match" f" number of samples ({N})" ) if max_order not in (1, 2, 3): raise ValueError( f"'max_order' key of options should be an integer with values of" f" 1, 2 or 3, got {max_order}" ) # Important next check for max_order - as max_order relates to d if (d == 2) and (max_order > 2): max_order = 2 warnings.warn("max_order is set to 2 due to lack of third input factor") if poly_order not in np.arange(1, 11): raise ValueError( "'poly_order' key of options should be an integer between 1 to 10." ) if bootstrap not in np.arange(1, 101): raise ValueError("'bootstrap' should be an integer between 1 to 100.") if (bootstrap == 1) and (subset != y_row): subset = y_row warnings.warn(f"subset is set to {y_row} due to no bootstrap") if subset is None: subset = y_row // 2 elif subset not in np.arange(300, N + 1): raise ValueError( f"'subset' should be an integer between 300 and {N}, " f"the number of rows matrix X." ) if alpha < 0.5 or alpha > 1.0: raise ValueError("'alpha' should be a float between 0.5 to 1.0") if extended_base: max_iter = None else: if max_iter not in np.arange(100, 1000): raise ValueError("'max_iter' should be between 100 and 1000") if l2_penalty < 0.0 or l2_penalty > 10: raise ValueError("'l2_penalty' should be in between 0 and 10") return Y, problem, subset, max_iter def _core_params( problem: Dict, N: int, d: int, f0: float, poly_order: int, max_order: int, bootstrap: int, subset: int, extended_base: bool, ) -> Tuple[namedtuple, ResultDict]: """This function establishes the core parameters of an HDMR (High Dimensional Model Representation) expansion and returns them in a namedtuple an ResultDict datatype. These parameters are used across all functions and procedures related to HDMR. Parameters ---------- problem : Dict Problem definition N : int Number of samples in input matrix `X`. d : int Dimensionality of the problem. f0 : float Zero-th component function poly_order : int Polynomial order to be used to calculate orthonormal polynomial. max_order : int Maximum functional ANOVA expansion order. bootstrap : int Number of iteration to be used in bootstrap. subset : int Number of samples to be used in bootstrap. extended_base : bool Whether to use extended basis matrix or not. Returns ------- hdmr : namedtuple Core parameters of hdmr expansion Si : ResultDict Sensitivity Indices HDMR Attributes --------------- N : int Number of samples in input matrix `X`. d : int Dimensionality of the problem. max_order : int Maximum functional ANOVA expansion order. ext_base : bool Whether to use extended basis matrix or not. subset : int Number of samples to be used in bootstrap. p_o : int Polynomial order to be used to calculated orthonormal polynomial. nc1 : int Number of component functions in 1st order. nc2 : int Number of component functions in 2nd order. nc3 int Number of component functions in 3rd order. nc_t : int Total number of component functions. nt1 : int Total number of terms(columns) for a given 1st order component function nt2 : int Total number of terms(columns) for a given 2nd order component function nt3 : int Total number of terms(columns) for a given 3rd order component function tnt1 : int Total number of terms(columns) for all 1st order component functions tnt2 : int Total number of terms(columns) for all 2nd order component functions tnt3 : int Total number of terms(columns) for all 3rd order component functions a_tnt : int All terms (columns) in a hdmr expansion x : numpy.array Solution of hdmr expansion idx : numpy.array Indexes of subsamples to be used for bootstrap beta : numpy.array Arrangement of second-order component functions gamma : numpy.array Arrangement of third-order component functions f0 : float Zero-th component function Si Keys ------- - "S" : numpy.array Sensitivity index (total contribution) - "S_conf" : numpy.array Statistical confidence interval of `S` - "S_sum" : numpy.array Sum of sensitivity indexes (total contribution) - "S_sum_conf" : numpy.array Statistical confidence interval of sum of `S` - "Sa" : numpy.array Sensitivity index (uncorrelated contribution) - "Sa_conf" : numpy.array Statistical confidence interval of `Sa` - "Sa_sum" : numpy.array Sum of sensitivity indexes (uncorrelated contribution) - "Sa_sum_conf" : numpy.array Statistical confidence interval of sum of `Sa` - "Sb" : numpy.array Sensitivity index (correlated contribution) - "Sb_conf" : numpy.array Statistical confidence interval of `Sb` - "Sb_sum" : numpy.array Sum of sensitivity indexes (correlated contribution) - "Sb_sum_conf" : numpy.array Statistical confidence interval of sum of `Sb` - "ST" : numpy.array Total Sensitivity indexes of features/inputs - "ST_conf" : numpy.array Statistical confidence interval of `ST` - "Signf" : numpy.array Signigicancy for each bootstrap iteration - "Term" : numpy.array Component name """ cp = defaultdict(int) cp["n_comp_func"], cp["n_coeff"] = [0] * 3, [0] * 3 cp["n_comp_func"][0] = d cp["n_coeff"][0] = poly_order if max_order > 1: cp["n_comp_func"][1] = math.comb(d, 2) cp["n_coeff"][1] = poly_order**2 if extended_base: cp["n_coeff"][1] += 2 * poly_order if max_order == 3: cp["n_comp_func"][2] = math.comb(d, 3) cp["n_coeff"][2] = poly_order**3 if extended_base: cp["n_coeff"][2] += 3 * poly_order + 3 * poly_order**2 # Setup Bootstrap (if bootstrap > 1) idx = ( np.arange(0, N).reshape(-1, 1) if bootstrap == 1 else np.argsort(np.random.rand(N, bootstrap), axis=0)[:subset] ) CoreParams = namedtuple( "CoreParams", [ "N", "d", "max_order", "ext_base", "subset", "p_o", "nc1", "nc2", "nc3", "nc_t", "nt1", "nt2", "nt3", "tnt1", "tnt2", "tnt3", "a_tnt", "x", "idx", "beta", "gamma", "f0", ], ) n_comp_func = cp["n_comp_func"] n_coeff = cp["n_coeff"] hdmr = CoreParams( N, d, max_order, extended_base, subset, poly_order, n_comp_func[0], n_comp_func[1], n_comp_func[2], sum(n_comp_func), n_coeff[0], n_coeff[1], n_coeff[2], n_coeff[0] * n_comp_func[0], n_coeff[1] * n_comp_func[1], n_coeff[2] * n_comp_func[2], n_coeff[0] * n_comp_func[0] + n_coeff[1] * n_comp_func[1] + n_coeff[2] * n_comp_func[2], np.zeros( ( n_coeff[0] * n_comp_func[0] + n_coeff[1] * n_comp_func[1] + n_coeff[2] * n_comp_func[2], bootstrap, ) ), idx, np.array(list(comb(range(d), 2))), np.array(list(comb(range(d), 3))), # Returns empty list when d < 3 f0, ) # Create Sensitivity Indices Result Dictionary keys = ( "Sa", "Sa_conf", "Sb", "Sb_conf", "S", "S_conf", "Signf", "Sa_sum", "Sa_sum_conf", "Sb_sum", "Sb_sum_conf", "S_sum", "S_sum_conf", ) Si = ResultDict( ( (k, np.zeros((hdmr.nc_t, bootstrap))) if k in ("S", "Sa", "Sb", "Signf") else (k, np.zeros(hdmr.nc_t)) ) for k in keys ) Si["Term"] = problem["names"] Si["ST"] = np.full(hdmr.nc_t, np.nan) Si["ST_conf"] = np.full(hdmr.nc_t, np.nan) # Generate index column for printing results if max_order > 1: for i in range(hdmr.nc2): Si["Term"].extend( [ "/".join( [ problem["names"][hdmr.beta[i, 0]], problem["names"][hdmr.beta[i, 1]], ] ) ] ) if max_order == 3: for i in range(hdmr.nc3): Si["Term"].extend( [ "/".join( [ problem["names"][hdmr.gamma[i, 0]], problem["names"][hdmr.gamma[i, 1]], problem["names"][hdmr.gamma[i, 2]], ] ) ] ) return (hdmr, Si) def _basis_matrix(X, hdmr): """The basis matrix represents the foundation of the component functions. It is constructed using orthonormal polynomials for each input variable, ensuring that it captures the data optimally. The component functions are formed by linearly combining the columns of this matrix. Parameters ---------- X : numpy.array Model input matrix hdmr : namedtuple Core parameters of hdmr expansion Returns ------- b_m : numpy.array Basis matrix """ # Compute normalized X-values X_n = (X - np.tile(X.min(0), (X.shape[0], 1))) / np.tile( (X.max(0)) - X.min(0), (X.shape[0], 1) ) # Compute Orthonormal Polynomial Coefficients coeff = _orth_poly_coeff(X_n, hdmr) # Initialize Basis Matrix b_m = np.zeros((X.shape[0], hdmr.a_tnt)) # First order columns of basis matrix col = 0 for i, j in product(range(hdmr.d), range(hdmr.p_o)): b_m[:, col] = np.polyval(coeff[j, : j + 2, i], X_n[:, i]) col += 1 # Second order columns of basis matrix if hdmr.max_order > 1: for i, j in _prod(range(0, hdmr.d - 1), range(1, hdmr.d)): if hdmr.ext_base: b_m[:, col : col + hdmr.p_o] = b_m[:, i * hdmr.p_o : (i + 1) * hdmr.p_o] col += hdmr.p_o b_m[:, col : col + hdmr.p_o] = b_m[:, j * hdmr.p_o : (j + 1) * hdmr.p_o] col += hdmr.p_o for k1, k2 in _prod( range(i * hdmr.p_o, (i + 1) * hdmr.p_o), range(j * hdmr.p_o, (j + 1) * hdmr.p_o), ): b_m[:, col] = np.multiply(b_m[:, k1], b_m[:, k2]) col += 1 # Third order columns of basis matrix if hdmr.max_order == 3: for i, j, k in _prod( range(0, hdmr.d - 2), range(1, hdmr.d - 1), range(2, hdmr.d) ): if hdmr.ext_base: b_m[:, col : col + hdmr.p_o] = b_m[:, i * hdmr.p_o : (i + 1) * hdmr.p_o] col += hdmr.p_o b_m[:, col : col + hdmr.p_o] = b_m[:, j * hdmr.p_o : (j + 1) * hdmr.p_o] col += hdmr.p_o b_m[:, col : col + hdmr.p_o] = b_m[:, k * hdmr.p_o : (k + 1) * hdmr.p_o] col += hdmr.p_o p_o_2 = hdmr.p_o**2 b_m[:, col : col + p_o_2] = b_m[ :, hdmr.tnt1 + (2 * hdmr.nt1) * (i + 1) + i * p_o_2 : hdmr.tnt1 + (i + 1) * (p_o_2 + 2 * hdmr.nt1), ] col += p_o_2 b_m[:, col : col + p_o_2] = b_m[ :, hdmr.tnt1 + (2 * hdmr.nt1) * (j + 1) + j * p_o_2 : hdmr.tnt1 + (j + 1) * (p_o_2 + 2 * hdmr.nt1), ] col += p_o_2 b_m[:, col : col + p_o_2] = b_m[ :, hdmr.tnt1 + (2 * hdmr.nt1) * (k + 1) + k * p_o_2 : hdmr.tnt1 + (k + 1) * (p_o_2 + 2 * hdmr.nt1), ] col += p_o_2 for l1, l2, l3 in _prod( range(i * hdmr.p_o, (i + 1) * hdmr.p_o), range(j * hdmr.p_o, (j + 1) * hdmr.p_o), range(k * hdmr.p_o, (k + 1) * hdmr.p_o), ): b_m[:, col] = np.multiply( np.multiply(b_m[:, l1], b_m[:, l2]), b_m[:, l3] ) col += 1 return b_m def _orth_poly_coeff(X, hdmr): """Calculates the coefficients of orthonormal polynomials based on a given input matrix `X` Parameters ---------- X : numpy.array Normalized Input matrix `X` hdmr : namedtuple Core parameters of hdmr expansion Returns ------- coeff : numpy.array Orthonormal polynomial coefficients from highes degree to constant term with trailing zeros Notes ---------- Please see the reference below .. [1] SzegÅ‘, G. 1975. . Orthogonal Polynomials. American Mathematical Society. """ p_o_1 = hdmr.p_o + 1 M = np.zeros((p_o_1, p_o_1, hdmr.d)) for i in range(hdmr.d): k = 0 for j in range(p_o_1): for z in range(p_o_1): M[j, z, i] = sum(X[:, i] ** k) / X.shape[0] k += 1 k = j + 1 coeff = np.zeros((hdmr.p_o, p_o_1, hdmr.d)) for i, j in product(range(hdmr.d), range(hdmr.p_o)): z = range(j + 2) for k in z: z__k = list(z) z__k.pop(k) det_ij = det(M[: j + 1, : j + 1, i]) * det(M[: j + 2, : j + 2, i]) coeff[j, j + 1 - k, i] = ( (-1) ** (j + k + 1) * det(M[: j + 1, z__k, i]) / np.sqrt(det_ij) ) return coeff def _prod(*args): """Generator that returns unique cartesian product of given tuple arguments Parameters ---------- *args : List[Tuple] Variable length argument list. Yields ------ Tuple A non-duplicate numbers in a tuple. """ seen = set() for prod in product(*args): prod_set = frozenset(prod) if len(prod_set) != len(prod): continue if prod_set not in seen: seen.add(prod_set) yield prod def _fanova(b_m, hdmr, Si, Y, bootstrap, max_iter, l2_penalty, alpha): """The functional ANOVA decomposition offers two main approaches: the extended base approach and the non-extended base approach. These approaches follow the guidelines presented in [1] and [2]. The extended base approach provides additional information to ensure hierarchical orthogonality. Parameters ---------- b_m : numpy.array Basis matrix hdmr : namedtuple Core parameters of hdmr expansion Si : ResultDict Sensitivity Indices Y : numpy.array Model output bootstrap : int Number of iteration to be used in bootstrap max_iter : int Maximum number of iteration used in backfitting algorithm l2_penalty : float Penalty term for ridge regression alpha : float Significant level Returns ------- Si : ResultDict Sensitivity Indices hdmr : namedtuple Core parameters of hdmr expansion Notes ----- .. [1] Li, G., Rabitz, H., Yelvington, P., Oluwole, O., Bacon, F., Kolb, C., and Schoendorf, J. 2010. Global Sensitivity Analysis for Systems with Independent and/or Correlated Inputs. The Journal of Physical Chemistry A, 114(19), p.6022-6032. .. [2] Li, G., Rabitz, H. General formulation of HDMR component functions with independent and correlated variables. J Math Chem 50, 99–130 (2012). https://doi.org/10.1007/s10910-011-9898-0 """ for t in range(bootstrap): # Extract model output for a corresponding bootstrap iteration Y_idx = Y[hdmr.idx[:, t], 0] # Subtract mean from it Y_idx -= np.mean(Y_idx) if hdmr.ext_base: cost = _cost_matrix(b_m[hdmr.idx[:, t], :], hdmr) hdmr.x[:, t] = _d_morph( b_m[hdmr.idx[:, t], :], cost, Y_idx, bootstrap, hdmr ) else: Y_res = _first_order( b_m[hdmr.idx[:, t], : hdmr.tnt1], Y_idx, max_iter, l2_penalty, hdmr, t ) if hdmr.max_order > 1: Y_res = _second_order( b_m[hdmr.idx[:, t], hdmr.tnt1 : hdmr.tnt1 + hdmr.tnt2], Y_res, max_iter, l2_penalty, hdmr, t, ) if hdmr.max_order == 3: _third_order( b_m[hdmr.idx[:, t], hdmr.tnt1 + hdmr.tnt2 :], Y_res, l2_penalty, hdmr, ) # Calculate component functions Y_e = _comp_func(b_m[hdmr.idx[:, t], :], hdmr, t) # Test significancy Si["Signf"][:, t] = _f_test(Y_idx, Y_e, alpha, hdmr) # Sensitivity Analysis Si["S"][:, t], Si["Sa"][:, t], Si["Sb"][:, t] = _ancova(Y_idx, Y_e, hdmr) return Si, hdmr def _cost_matrix(b_m, hdmr): """The cost matrix stores information about hierarchical orthogonality. It is structured in a way that ensures orthogonality between component functions that are hierarchically related. Parameters ---------- b_m : numpy.array Basis matrix hdmr : namedtuple Core parameters of hdmr expansion Returns ------- cost : numpy.array Cost matrix """ cost = np.zeros((hdmr.a_tnt, hdmr.a_tnt)) range_2nd_1 = lambda x: range( # noqa: E731 hdmr.tnt1 + (x) * hdmr.nt2, hdmr.tnt1 + (x + 1) * hdmr.nt2 ) range_2nd_2 = lambda x: range( # noqa: E731 hdmr.tnt1 + (x) * hdmr.nt2, hdmr.tnt1 + (x) * hdmr.nt2 + hdmr.p_o * 2 ) range_3rd_1 = lambda x: range( # noqa: E731 hdmr.tnt1 + hdmr.tnt2 + (x) * hdmr.nt3, hdmr.tnt1 + hdmr.tnt2 + (x + 1) * hdmr.nt3, ) range_3rd_2 = lambda x: range( # noqa: E731 hdmr.tnt1 + hdmr.tnt2 + (x) * hdmr.nt3, hdmr.tnt1 + hdmr.tnt2 + (x) * hdmr.nt3 + 3 * hdmr.p_o + 3 * hdmr.p_o**2, ) if hdmr.max_order > 1: sr_i = np.mean(b_m, axis=0, keepdims=True) sr_ij = np.zeros((2 * hdmr.p_o + 1, hdmr.nt2)) ct = 0 for _ in _prod(range(0, hdmr.d - 1), range(1, hdmr.d)): sr_ij[0, :] = sr_i[0, range_2nd_1(ct)] sr_ij[1:, :] = ( b_m[:, range_2nd_2(ct)].T @ b_m[:, range_2nd_1(ct)] ) / hdmr.subset cost[np.ix_(range_2nd_1(ct), range_2nd_1(ct))] = sr_ij.T @ sr_ij ct += 1 if hdmr.max_order == 3: sr_ijk = np.zeros((3 * hdmr.p_o + 3 * hdmr.p_o**2 + 1, hdmr.nt3)) ct = 0 for _ in _prod(range(0, hdmr.d - 2), range(1, hdmr.d - 1), range(2, hdmr.d)): sr_ijk[0, :] = sr_i[0, range_3rd_1(ct)] sr_ijk[1:, :] = ( b_m[:, range_3rd_2(ct)].T @ b_m[:, range_3rd_1(ct)] / hdmr.subset ) cost[np.ix_(range_3rd_1(ct), range_3rd_1(ct))] = sr_ijk.T @ sr_ijk ct += 1 return cost def _d_morph(b_m, cost, Y_idx, subset, hdmr): """D-Morph Regression finds the best solution that aligns with the cost matrix. Cost matrix in this case represents the hierarchical orthogonality between component functions. Parameters ---------- b_m : numpy.array Basis matrix for all component functions cost : numpy.array Cost matrix that satisfies hierarchical orthogonality Y_idx : numpy.array Model output for a single bootstrap iteration subset : int Number of subsamples hdmr : namedtuple Core parameters of hdmr expansion Returns ------- soltn : numpy.array D-MORPH solution Notes ----- Detailed information about D-Morph Regression can be found at .. [1] Li, G., Rey-de-Castro, R. & Rabitz, H. D-MORPH regression for modeling with fewer unknown parameters than observation data. J Math Chem 50, 1747–1764 (2012). https://doi.org/10.1007/s10910-012-0004-z """ # Left Matrix Multiplication with the transpose of cost matrix a = (b_m.T @ b_m) / subset # LHS b = (b_m.T @ Y_idx) / subset # RHS try: # Pseudo-Inverse of LHS a_pinv = pinv(a, hermitian=True) rank = matrix_rank(a) # Least-Square Solution x = a_pinv @ b # Projection Matrix pr = np.eye(hdmr.a_tnt) - (a_pinv @ a) pb = pr @ cost U, _, Vh = svd(pb) except LinAlgError: raise LinAlgError("D-Morph: Pseudo-Inverse did not converge") nullity = min(b_m.shape) - rank V = Vh.T U = np.delete(U, range(0, nullity), axis=1) V = np.delete(V, range(0, nullity), axis=1) # D-Morph Regression Solution soltn = V @ pinv(U.T @ V) @ U.T @ x return soltn def _first_order(b_m1, Y_idx, max_iter, l2_penalty, hdmr, t): """Sequential determination of first order component functions. First, it computes component functions via ridge regression, i.e. fitting model inputs/features to the model output. Later, it takes advantage of backfitting algorithm to satisfy hierarchical orthogonality. Backfitting algorithm does not guarantee the hierarchical orthogonality. We suggest to set extended base option to `True` for those who want to guaranteed functional ANOVA expansion. Parameters ---------- b_m1 : numpy.array Basis matrix for first-order component functions Y_idx : numpy.array Model output for a single bootstrap iteration max_iter : int Maximum number of iteration used in backfitting algorithm l2_penalty : float Penalty term for ridge regression hdmr : namedtuple Core parameters of hdmr expansion t : int bootstrap iteration Returns ------- Y_res : numpy.array Residual model output """ # Temporary first order component matrix Y_i = np.empty((hdmr.subset, hdmr.nc1)) # Initialize iter iter = 0 # To increase readibility n1 = hdmr.nt1 # L2 Penalty lambda_eye = l2_penalty * np.identity(n1) for i in range(hdmr.nc1): try: # Left hand side a = ( b_m1[:, i * n1 : n1 * (i + 1)].T @ b_m1[:, i * n1 : n1 * (i + 1)] ) / hdmr.subset # Adding L2 Penalty (Ridge Regression) a += lambda_eye # Right hand side b = (b_m1[:, i * n1 : n1 * (i + 1)].T @ Y_idx) / hdmr.subset # Solution hdmr.x[i * n1 : n1 * (i + 1), t] = solve(a, b) # Component functions Y_i[:, i] = ( b_m1[:, i * n1 : n1 * (i + 1)] @ hdmr.x[i * n1 : n1 * (i + 1), t] ) except LinAlgError: raise LinAlgError( "First Order: Least-square regression did not converge." "Try increasing L2 penalty term" ) # Backfitting method var_old = np.square(hdmr.x[: hdmr.tnt1, t]) z_t = list(range(hdmr.d)) while True: for i in range(hdmr.d): z = z_t[:] z.remove(i) Y_res = Y_idx - np.sum(Y_i[:, z], axis=1) # Left hand side a = ( b_m1[:, i * n1 : n1 * (i + 1)].T @ b_m1[:, i * n1 : n1 * (i + 1)] ) / hdmr.subset # Right hand side b = (b_m1[:, i * n1 : n1 * (i + 1)].T @ Y_res) / hdmr.subset # Solution hdmr.x[i * n1 : n1 * (i + 1), t] = solve(a, b) # Component functions Y_i[:, i] = ( b_m1[:, i * n1 : n1 * (i + 1)] @ hdmr.x[i * n1 : n1 * (i + 1), t] ) var_max = np.absolute(var_old - np.square(hdmr.x[: hdmr.tnt1, t])).max() iter += 1 if (var_max < 1e-4) or (iter > max_iter): break var_old = np.square(hdmr.x[: hdmr.tnt1, t]) return Y_idx - np.sum(Y_i, axis=1) def _second_order(b_m2, Y_res, max_iter, l2_penalty, hdmr, t): """Sequential determination of second-order component functions. First, it computes component functions via ridge regression, i.e. fitting model inputs/features to the model output. Later, it takes advantage of backfitting algorithm to satisfy hierarchical orthogonality. Backfitting algorithm does not guarantee the hierarchical orthogonality. We suggest to set extended base option to `True` for those who want to guaranteed functional ANOVA expansion. Parameters ---------- b_m2 : numpy.array Basis matrix for second-order component functions Y_res : numpy.array Residual model output max_iter : int Maximum number of iteration used in backfitting algorithm l2_penalty : float Penalty term for ridge regression hdmr : namedtuple Core parameters of hdmr expansion t : int bootstrap iteration Returns ------- Y_res : numpy.array Residual model output """ # Temporary second order component matrix Y_ij = np.empty((hdmr.subset, hdmr.nc2)) # To increase readibility n2 = hdmr.nt2 # Initialize iteration counter iter = 0 # L2 Penalty lambda_eye = l2_penalty * np.identity(n2) for i in range(hdmr.nc2): try: # Left hand side a = ( b_m2[:, i * n2 : n2 * (i + 1)].T @ b_m2[:, i * n2 : n2 * (i + 1)] ) / hdmr.subset # Adding L2 Penalty (Ridge Regression) a += lambda_eye # Right hand side b = (b_m2[:, i * n2 : n2 * (i + 1)].T @ Y_res) / hdmr.subset # Solution hdmr.x[hdmr.tnt1 + i * n2 : hdmr.tnt1 + n2 * (i + 1), t] = solve(a, b) # Component functions Y_ij[:, i] = ( b_m2[:, i * n2 : n2 * (i + 1)] @ hdmr.x[hdmr.tnt1 + i * n2 : hdmr.tnt1 + n2 * (i + 1), t] ) except LinAlgError: raise LinAlgError( "Second Order: Least-square regression did not converge." "Try increasing L2 penalty term" ) var_old = np.square(hdmr.x[hdmr.tnt1 : hdmr.tnt1 + hdmr.tnt2, t]) # Backfitting method while True: for i in range(hdmr.nc2): z = list(range(hdmr.nc2)) z.remove(i) Y_r = Y_res - np.sum(Y_ij[:, z], axis=1) # Left hand side a = ( b_m2[:, i * n2 : n2 * (i + 1)].T @ b_m2[:, i * n2 : n2 * (i + 1)] ) / hdmr.subset # Right hand side b = (b_m2[:, i * n2 : n2 * (i + 1)].T @ Y_r) / hdmr.subset # Solution hdmr.x[hdmr.tnt1 + i * n2 : hdmr.tnt1 + n2 * (i + 1), t] = solve(a, b) # Component functions Y_ij[:, i] = ( b_m2[:, i * n2 : n2 * (i + 1)] @ hdmr.x[hdmr.tnt1 + i * n2 : hdmr.tnt1 + n2 * (i + 1), t] ) var_max = np.absolute( var_old - np.square(hdmr.x[hdmr.tnt1 : hdmr.tnt1 + hdmr.tnt2, t]) ).max() iter += 1 if (var_max < 1e-4) or (iter > max_iter): break var_old = np.square(hdmr.x[hdmr.tnt1 : hdmr.tnt1 + hdmr.tnt2, t]) return Y_res - np.sum(Y_ij, axis=1) def _third_order(b_m3, Y_res, l2_penalty, hdmr, t): """Sequential determination of third-order component functions. it computes component functions via ridge regression, i.e. fitting model inputs/features to the model output. Parameters ---------- b_m3 : numpy.array Basis matrix for third-order component functions Y_res : numpy.array Residual model output l2_penalty : float Penalty term for ridge regression hdmr : namedtuple Core parameters of hdmr expansion t : int bootstrap iteration Notes ----- Backfitting algorithm is not used here because it may be unstable when residual model, Y_res, is close to arrays of zero. """ # To increase readibility n3 = hdmr.nt3 # L2 Penalty lambda_eye = l2_penalty * np.identity(n3) for i in range(hdmr.nc3): try: # Left hand side a = ( b_m3[:, i * n3 : n3 * (i + 1)].T @ b_m3[:, i * n3 : n3 * (i + 1)] ) / hdmr.subset # Adding L2 Penalty (Ridge Regression) a += lambda_eye # Right hand side b = (b_m3[:, i * n3 : n3 * (i + 1)].T @ Y_res) / hdmr.subset # Solution hdmr.x[ hdmr.tnt1 + hdmr.tnt2 + i * n3 : hdmr.tnt1 + hdmr.tnt2 + n3 * (i + 1), t ] = solve(a, b) except LinAlgError: raise LinAlgError( "Third Order: Least-square regression did not converge." "Try increasing L2 penalty term" ) def _comp_func(b_m, hdmr, t=None, emulator=None): """Computes the component function based on basis matrix and the solution Parameters ---------- b_m : numpy.array Basis matrix hdmr : namedtuple Core parameters of hdmr expansion t : int Bootstrap iteration emulator : bool Whether it is called by emulator or not Returns ------- Y_e : numpy.array Emualated model output for each components """ Y_t = np.zeros((b_m.shape[0], hdmr.a_tnt)) Y_e = np.zeros((b_m.shape[0], hdmr.nc_t)) # Temporary matrix if emulator: # Use average of solutions if it is called by emulator Y_t = np.multiply(b_m, np.tile(hdmr.x.mean(axis=1), [b_m.shape[0], 1])) else: # Use the t-th solution if it is called by fanova Y_t = np.multiply(b_m, np.tile(hdmr.x[:, t], [b_m.shape[0], 1])) # First order component functions for i in range(hdmr.nc1): Y_e[:, i] = np.sum(Y_t[:, i * hdmr.p_o : (i + 1) * hdmr.p_o], axis=1) # Second order component functions if hdmr.max_order > 1: for i in range(hdmr.nc2): Y_e[:, hdmr.nc1 + i] = np.sum( Y_t[:, hdmr.tnt1 + (i) * hdmr.nt2 : hdmr.tnt1 + (i + 1) * hdmr.nt2], axis=1, ) # Third order component functions if hdmr.max_order == 3: for i in range(hdmr.nc3): Y_e[:, hdmr.nc1 + hdmr.nc2 + i] = np.sum( Y_t[ :, hdmr.tnt1 + hdmr.tnt2 + (i) * hdmr.nt3 : hdmr.tnt1 + hdmr.tnt2 + (i + 1) * hdmr.nt3, ], axis=1, ) return Y_e def _ancova(Y_idx, Y_e, hdmr): """Analysis of Covariance. It calculates uncorrelated and correlated contribution to the model output variance Parameters ---------- Y_idx : numpy.array Model output for a single bootstrap iteration Y_e : numpy.array Emulated output hdmr : namedtuple Core parameters of hdmr expansion Returns ------- S : numpy.array Sensitivity index (total contribution) Sa : numpy.array Sensitivity index (uncorrelated contribution) Sb : numpy.array Sensitivity index (correlated contribution) Notes ----- Please see the reference below .. [1] Li, G., Rabitz, H., Yelvington, P., Oluwole, O., Bacon, F., Kolb, C., and Schoendorf, J. 2010. Global Sensitivity Analysis for Systems with Independent and/or Correlated Inputs. The Journal of Physical Chemistry A, 114(19), p.6022-6032. """ # Initialize sensitivity indices S = np.zeros(hdmr.nc_t) Sa = np.zeros(hdmr.nc_t) Sb = np.zeros(hdmr.nc_t) # Compute the sum of all Y_em terms Y_sum = np.sum(Y_e, axis=1) # Total Variance tot_v = np.var(Y_idx) # Analysis of covariance for j in range(hdmr.nc_t): # Covariance matrix of jth term of Y_em and actual Y c = np.cov(np.stack((Y_e[:, j], Y_idx), axis=0)) # Total sensitivity of jth term S[j] = c[0, 1] / tot_v # Eq. 19 # Covariance matrix of jth term with emulator Y without jth term c = np.cov(np.stack((Y_e[:, j], Y_sum - Y_e[:, j]), axis=0)) # Structural contribution of jth term Sa[j] = c[0, 0] / tot_v # Eq. 20 # Correlative contribution of jth term Sb[j] = c[0, 1] / tot_v # Eq. 21 return S, Sa, Sb def _f_test(Y_idx, Y_e, alpha, hdmr): """Finds component functions that make significant contribution to the model output. This statistical analysis is done by F-test which uses F-distribution. Parameters ---------- Y_idx : numpy.array Model output for a single bootstrap iteration Y_e : numpy.array Emulated output alpha : float Significance level hdmr : namedtuple Core parameters of hdmr expansion Returns ------- result : numpy.array Binary array that shows significant components """ # Initialize result array result = np.zeros(hdmr.nc_t) # Sum of squared residuals of smaller model SSR0 = (Y_idx**2).sum() # Now adding each term to the model for i in range(hdmr.nc_t): # Model with ith term excluded Y_res = Y_idx - Y_e[:, i] # Number of parameters of proposed model (order dependent) if i < hdmr.nc1: p1 = hdmr.nt1 # 1st order elif hdmr.nc1 <= i < (hdmr.nc1 + hdmr.nc2): p1 = hdmr.nt2 # 2nd order else: p1 = hdmr.nt3 # 3rd order # Sum of squared residuals of bigger model SSR1 = (Y_res**2).sum() # Now calculate the F_stat (F_stat > 0 -> SSR1 < SSR0 ) F_stat = ((SSR0 - SSR1) / p1) / (SSR1 / (hdmr.subset - p1)) # Now calculate critical F value F_crit = stats.f.ppf(q=alpha, dfn=p1, dfd=hdmr.subset - p1) # Now determine whether to accept ith component into model if F_stat > F_crit: # ith term is significant and should be included in model result[i] = 1 return result def _finalize(hdmr, Si, alpha, return_emulator): """Final processing of sensivity analysis. Calculates confidence interval using statistical analysis. Parameters ---------- hdmr : namedtuple Core parameters of hdmr expansion Si : ResultDict Sensitivity Indices alpha : float Significance level return_emulator : bool Whether to attach emulator to the Si ResultDict Returns ------- Si : ResultDict Sensitivity Indices """ # Z score def z(p): return (-1) * np.sqrt(2) * special.erfcinv(p * 2) # Multiplier for confidence interval mult = z(alpha + (1 - alpha) / 2) # Compute the total sensitivity of each parameter/coefficient for r in range(hdmr.d): if hdmr.max_order == 1: TS = hdmr.S[r, :] elif hdmr.max_order == 2: ij = hdmr.d + np.where(np.sum(hdmr.beta == r, axis=1) == 1)[0] TS = np.sum(Si["S"][np.append(r, ij), :], axis=0) elif hdmr.max_order == 3: ij = hdmr.d + np.where(np.sum(hdmr.beta == r, axis=1) == 1)[0] ijk = hdmr.d + hdmr.nc2 + np.where(np.sum(hdmr.nc3 == r, axis=1) == 1)[0] TS = np.sum(Si["S"][np.append(r, np.append(ij, ijk)), :], axis=0) Si["ST"][r] = np.mean(TS) Si["ST_conf"][r] = mult * np.std(TS) # Compute Confidence Interval Si["Sa_conf"] = mult * np.std(Si["Sa"], axis=1) Si["Sb_conf"] = mult * np.std(Si["Sb"], axis=1) Si["S_conf"] = mult * np.std(Si["S"], axis=1) Si["Sa_sum_conf"] = mult * np.std(np.sum(Si["Sa"])) Si["Sb_sum_conf"] = mult * np.std(np.sum(Si["Sb"])) Si["S_sum_conf"] = mult * np.std(np.sum(Si["S"])) # Assign Bootstrap Results to Si Dict Si["Sa"] = np.mean(Si["Sa"], axis=1) Si["Sb"] = np.mean(Si["Sb"], axis=1) Si["S"] = np.mean(Si["S"], axis=1) Si["Sa_sum"] = np.mean(np.sum(Si["Sa"], axis=0)) Si["Sb_sum"] = np.mean(np.sum(Si["Sb"], axis=0)) Si["S_sum"] = np.mean(np.sum(Si["S"], axis=0)) # F-test number of selection to print out Si["Signf"] = 100 * Si["Signf"].mean(axis=1) # Bind emulator method to the ResultDict if return_emulator: Si["hdmr"] = hdmr Si.emulate = MethodType(emulate, Si) # Bind Pandas Dataframe conversion to the ResultDict Si.to_df = MethodType(to_df, Si) return Si def to_df(self): """Conversion method to Pandas DataFrame. To be attached to ResultDict. Returns ------- Pandas DataFrame """ names = self["Term"] # Only convert these elements in dict to DF include_list = ["Sa", "Sb", "S", "ST"] include_list += [f"{name}_conf" for name in include_list] new_spec = {k: v for k, v in self.items() if k in include_list} return df(new_spec, index=names) def emulate(self, X): """Emulates model output with new input data. Constructs orthonormal polynomials with new input matrix, X, and multiplies it with solution array, hdmr.x Compares emulated results with observed vector, Y. Returns ======== Y_em : numpy.array Emulated output """ # Calculate HDMR Basis Matrix b_m = _basis_matrix(X, self["hdmr"]) # Get component functions Y_em = _comp_func(b_m, self["hdmr"], emulator=True) return np.sum(Y_em, axis=1) def _print(Si): nc_t = len(Si["Sa"]) d = np.isnan(Si["ST"]).sum() print("\n") cols = "Term \t Sa Sb S ST Significancy " # noqa: E501 print(cols) print("-" * 88) # Header break format1 = "%-11s \t %5.2f (\261%.2f) %5.2f (\261%.2f) %5.2f (\261%.2f) %5.2f (\261%.2f) %-3.2f%%" # noqa: E501 format2 = "%-11s \t %5.2f (\261%.2f) %5.2f (\261%.2f) %5.2f (\261%.2f) %-3.2f%%" # noqa: E501 for i in range(nc_t): if i < d: print( format1 % ( Si["Term"][i], Si["Sa"][i], Si["Sa_conf"][i], Si["Sb"][i], Si["Sb_conf"][i], Si["S"][i], Si["S_conf"][i], Si["ST"][i], Si["ST_conf"][i], Si["Signf"][i], ) ) else: print( format2 % ( Si["Term"][i], Si["Sa"][i], Si["Sa_conf"][i], Si["Sb"][i], Si["Sb_conf"][i], Si["S"][i], Si["S_conf"][i], Si["Signf"][i], ) ) print("-" * 88) # Header break format3 = "%-11s \t %5.2f (\261%.2f) %5.2f (\261%.2f) %5.2f (\261%.2f)" print( format3 % ( "Sum", Si["Sa_sum"], Si["Sa_sum_conf"], Si["Sb_sum"], Si["Sb_sum_conf"], Si["S_sum"], Si["S_sum_conf"], ) ) keys = ("Sa_sum", "Sb_sum", "S_sum", "Sa_sum_conf", "Sb_sum_conf", "S_sum_conf") for k in keys: Si.pop(k, None) def cli_parse(parser): parser.add_argument( "-X", "--model-input-file", type=str, required=True, default=None, help="Model input file", ) parser.add_argument( "-mor", "--max-order", type=int, required=True, default=2, help="Order of HDMR expansion 1-3", ) parser.add_argument( "-por", "--poly-order", type=int, required=True, default=2, help="Maximum polynomial order 1-10", ) parser.add_argument( "-K", "--bootstrap", type=int, required=False, default=20, help="Number of bootstrap iteration 1-100", ) parser.add_argument( "-R", "--subset", type=int, required=False, default=None, help="Number of bootstrap samples 300-N", ) parser.add_argument( "-mit", "--max-iter", type=int, required=False, default=100, help="Maximum iteration for backfitting method 1-1000", ) parser.add_argument( "-l2", "--l2-penalty", type=float, required=False, default=0.01, help="Regularization term", ) parser.add_argument( "-a", "--alpha", type=float, required=False, default=0.95, help="Confidence interval for F-Test", ) parser.add_argument( "-ext", "--extended-base", type=lambda x: (str(x).lower() == "true"), required=True, default=True, help="Whether to use extended base matrix", ) parser.add_argument( "-print", "--print-to-console", type=lambda x: (str(x).lower() == "true"), required=False, default=False, help="Whether to print out result to the console", ) parser.add_argument( "-emul", "--return-emulator", type=lambda x: (str(x).lower() == "true"), required=False, default=False, help="Whether to attach emulate() method to the ResultDict", ) return parser def cli_action(args): problem = read_param_file(args.paramfile) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,) ) X = np.loadtxt(args.model_input_file, delimiter=args.delimiter, ndmin=2) options = { "max_order": args.max_order, "poly_order": args.poly_order, "bootstrap": args.bootstrap, "subset": args.subset, "max_iter": args.max_iter, "l2_penalty": args.l2_penalty, "alpha": args.alpha, "extended_base": args.extended_base, "print_to_console": args.print_to_console, "return_emulator": args.return_emulator, } if len(X.shape) == 1: X = X.reshape((len(X), 1)) analyze(problem, X, Y, **options) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/analyze/fast.py000066400000000000000000000140651525347100600205110ustar00rootroot00000000000000import math import warnings import numpy as np from scipy.stats import norm from . import common_args from ..util import read_param_file, ResultDict def analyze( problem, Y, M=4, num_resamples=100, conf_level=0.95, print_to_console=False, seed=None, ): """Perform extended Fourier Amplitude Sensitivity Test on model outputs. Returns a dictionary with keys 'S1' and 'ST', where each entry is a list of size D (the number of parameters) containing the indices in the same order as the parameter file. Notes ----- Compatible with: `fast_sampler` : :func:`SALib.sample.fast_sampler.sample` Examples -------- >>> X = fast_sampler.sample(problem, 1000) >>> Y = Ishigami.evaluate(X) >>> Si = fast.analyze(problem, Y, print_to_console=False) Parameters ---------- problem : dict The problem definition Y : numpy.array A NumPy array containing the model outputs M : int The interference parameter, i.e., the number of harmonics to sum in the Fourier series decomposition (default 4) print_to_console : bool Print results directly to console (default False) seed : int Seed to generate a random number References ---------- 1. Cukier, R. I., C. M. Fortuin, K. E. Shuler, A. G. Petschek, and J. H. Schaibly (1973). Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. J. Chem. Phys., 59(8):3873-3878 doi:10.1063/1.1680571 2. Saltelli, A., S. Tarantola, and K. P.-S. Chan (1999). A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output. Technometrics, 41(1):39-56, doi:10.1080/00401706.1999.10485594. 3. Pujol, G. (2006) fast99 - R `sensitivity` package https://github.com/cran/sensitivity/blob/master/R/fast99.R Warnings -------- The confidence intervals (``S1_conf``/``ST_conf``) are estimated by bootstrap resampling of the search-curve output. This is known to be statistically unreliable for (e)FAST - see discussion at https://github.com/SALib/SALib/issues/649 - and the CI estimates should be treated as indicative only. This feature may be reworked or removed in a future release. """ warnings.warn( "FAST confidence intervals are estimated via bootstrap resampling, " "which is known to be unreliable for this method (see " "https://github.com/SALib/SALib/issues/649). Treat S1_conf/ST_conf " "as indicative only. This feature may be reworked or removed in a " "future release.", stacklevel=2, ) if seed: np.random.seed(seed) D = problem["num_vars"] if Y.size % (D) == 0: N = int(Y.size / D) else: msg = """ Error: Number of samples in model output file must be a multiple of D, where D is the number of parameters. """ raise ValueError(msg) # Recreate the vector omega used in the sampling omega_0 = math.floor((N - 1) / (2 * M)) # Calculate and Output the First and Total Order Values Si = ResultDict((k, [None] * D) for k in ["S1", "ST", "S1_conf", "ST_conf"]) Si["names"] = problem["names"] for i in range(D): z = np.arange(i * N, (i + 1) * N) Y_l = Y[z] S1, ST = compute_orders(Y_l, N, M, omega_0) Si["S1"][i] = S1 Si["ST"][i] = ST S1_d_conf, ST_d_conf = bootstrap(Y_l, M, num_resamples, conf_level) Si["S1_conf"][i] = S1_d_conf Si["ST_conf"][i] = ST_d_conf if print_to_console: print(Si.to_df()) return Si def compute_orders(outputs: np.ndarray, N: int, M: int, omega: int): f = np.fft.fft(outputs) Sp = np.power(np.absolute(f[np.arange(1, math.ceil(N / 2))]) / N, 2) V = 2.0 * np.sum(Sp) # Calculate first and total order D1 = 2.0 * np.sum(Sp[np.arange(1, M + 1) * omega - 1]) Dt = 2.0 * np.sum(Sp[np.arange(math.floor(omega / 2.0))]) return (D1 / V), (1.0 - Dt / V) def bootstrap(Y: np.ndarray, M: int, resamples: int, conf_level: float): """Compute CIs. Infers ``N`` from results of sub-sample ``Y`` and re-estimates omega (ω) for the above ``N``. """ # Use half of available data each time T_data = Y.shape[0] n_size = math.ceil(T_data * 0.5) res_S1 = np.zeros(resamples) res_ST = np.zeros(resamples) for i in range(resamples): begin_id = np.random.randint(0, T_data) if begin_id + n_size <= T_data: sample_idx = np.arange(begin_id, begin_id + n_size) else: sample_idx = np.concatenate( (np.arange(begin_id, T_data), np.arange(0, begin_id + n_size - T_data)) ) Y_rs = Y[sample_idx] N = len(Y_rs) omega = math.floor((N - 1) / (2 * M)) S1, ST = compute_orders(Y_rs, N, M, omega) res_S1[i] = S1 res_ST[i] = ST bnd = norm.ppf(0.5 + conf_level / 2.0) S1_conf = bnd * res_S1.std(ddof=1) ST_conf = bnd * res_ST.std(ddof=1) return S1_conf, ST_conf # No additional arguments required for FAST def cli_parse(parser): """Add method specific options to CLI parser. Parameters ---------- parser : argparse object Returns ------- Updated argparse object """ parser.add_argument( "-M", "--M", type=int, required=False, default=4, help="Inference parameter" ) parser.add_argument( "-r", "--resamples", type=int, required=False, default=100, help="Number of bootstrap resamples for Sobol " "confidence intervals", ) return parser def cli_action(args): problem = read_param_file(args.paramfile) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,) ) analyze( problem, Y, M=args.M, num_resamples=args.resamples, print_to_console=True, seed=args.seed, ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/analyze/ff.py000066400000000000000000000121061525347100600201410ustar00rootroot00000000000000""" Created on 30 Jun 2015 @author: will2 """ import numpy as np from . import common_args import pandas as pd from types import MethodType from SALib.util import read_param_file, ResultDict from SALib.sample.ff import generate_contrast, extend_bounds def analyze(problem, X, Y, second_order=False, print_to_console=False, seed=None): """Perform a fractional factorial analysis Returns a dictionary with keys 'ME' (main effect) and 'IE' (interaction effect). The techniques bulks out the number of parameters with dummy parameters to the nearest 2**n. Any results involving dummy parameters could indicate a problem with the model runs. Notes ----- Compatible with: `ff` : :func:`SALib.sample.ff.sample` Examples -------- >>> X = sample(problem) >>> Y = X[:, 0] + (0.1 * X[:, 1]) + ((1.2 * X[:, 2]) * (0.2 + X[:, 0])) >>> analyze(problem, X, Y, second_order=True, print_to_console=True) Parameters ---------- problem: dict The problem definition X: numpy.matrix The NumPy matrix containing the model inputs Y: numpy.array The NumPy array containing the model outputs second_order: bool, default=False Include interaction effects print_to_console: bool, default=False Print results directly to console seed : int Seed to generate a random number Returns ------- Si: dict A dictionary of sensitivity indices, including main effects ``ME``, and interaction effects ``IE`` (if ``second_order`` is True) References ---------- 1. Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S., 2008. Global Sensitivity Analysis: The Primer. Wiley, West Sussex, U.K. http://doi.org/10.1002/9780470725184 """ if seed: np.random.seed(seed) problem = extend_bounds(problem) num_vars = problem["num_vars"] X = generate_contrast(problem) main_effect = (1.0 / (2 * num_vars)) * np.dot(Y, X) Si = ResultDict((k, [None] * num_vars) for k in ["names", "ME"]) Si["ME"] = main_effect Si["names"] = problem["names"] if second_order: interaction_names, interaction_effects = interactions(problem, Y) Si["interaction_names"] = interaction_names Si["IE"] = interaction_effects Si.to_df = MethodType(to_df, Si) if print_to_console: for S in Si.to_df(): print(S) return Si def to_df(self): """Conversion method to Pandas DataFrame. To be attached to ResultDict. Returns ------- main_effect, inter_effect: tuple A tuple of DataFrames for main effects and interaction effects. The second element (for interactions) will be `None` if not available. """ names = self["names"] main_effect = self["ME"] interactions = self.get("IE", None) inter_effect = None if interactions: interaction_names = self.get("interaction_names") names = [name for name in names if not isinstance(name, list)] inter_effect = pd.DataFrame({"IE": interactions}, index=interaction_names) main_effect = pd.DataFrame({"ME": main_effect}, index=names) return main_effect, inter_effect def interactions(problem, Y): """Computes the second order effects Computes the second order effects (interactions) between all combinations of pairs of input factors Parameters ---------- problem: dict The problem definition Y: numpy.array The NumPy array containing the model outputs Returns ------- ie_names: list The names of the interaction pairs IE: list The sensitivity indices for the pairwise interactions """ names = problem["names"] num_vars = problem["num_vars"] X = generate_contrast(problem) ie_names = [] IE = [] for col in range(X.shape[1]): for col_2 in range(col): x = X[:, col] * X[:, col_2] var_names = (names[col_2], names[col]) ie_names.append(var_names) IE.append((1.0 / (2 * num_vars)) * np.dot(Y, x)) return ie_names, IE def cli_parse(parser): parser.add_argument( "-X", "--model-input-file", type=str, required=True, default=None, help="Model input file", ) parser.add_argument( "--max-order", type=int, required=False, default=2, choices=[1, 2], help="Maximum order of sensitivity \ indices to calculate", ) return parser def cli_action(args): problem = read_param_file(args.paramfile) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,) ) X = np.loadtxt(args.model_input_file, delimiter=args.delimiter, ndmin=2) if len(X.shape) == 1: X = X.reshape((len(X), 1)) analyze(problem, X, Y, (args.max_order == 2), print_to_console=True, seed=args.seed) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/analyze/hdmr.py000066400000000000000000000756751525347100600205240ustar00rootroot00000000000000from typing import Dict, Union from types import MethodType import itertools import time import warnings import numpy as np from numpy.linalg import solve as lin_solve from numpy.linalg import svd from numpy import identity import pandas as pd from scipy import stats, special, interpolate from . import common_args from ..util import read_param_file, ResultDict, handle_seed from SALib.plotting.hdmr import plot as hdmr_plot from SALib.util.problem import ProblemSpec __all__ = ["analyze", "cli_parse", "cli_action"] def analyze( problem: Dict, X: np.ndarray, Y: np.ndarray, maxorder: int = 2, maxiter: int = 100, m: int = 2, K: int = 20, R: int = None, alpha: float = 0.95, lambdax: float = 0.01, print_to_console: bool = False, seed: Union[int, bool, None] = None, ) -> Dict: """Compute global sensitivity indices using the meta-modeling technique known as High-Dimensional Model Representation (HDMR). HDMR itself is not a sensitivity analysis method but a surrogate modeling approach. It constructs a map of relationship between sets of high dimensional inputs and output system variables [1]. This I/O relation can be constructed using different basis functions (orthonormal polynomials, splines, etc.). The model decomposition can be expressed as .. math:: \\widehat{y} = \\sum_{u \\subseteq \\{1, 2, ..., d \\}} f_u where :math:`u` represents any subset including an empty set. HDMR becomes extremely useful when the computational cost of obtaining sufficient Monte Carlo samples are prohibitive, as may be the case with Sobol's method. It uses least-square regression to reduce the required number of samples and thus the number of function (model) evaluations. Another advantage of this method is that it can account for correlation among the model input. Unlike other variance-based methods, the main effects are the combination of structural (uncorrelated) and correlated contributions. This method uses as input - a N x d matrix of N different d-vectors of model inputs (factors/parameters) - a N x 1 vector of corresponding model outputs Notes ----- Compatible with: all samplers Sets an `emulate` method allowing re-use of the emulator. Examples -------- .. code-block:: python :linenos: sp = ProblemSpec({ 'names': ['X1', 'X2', 'X3'], 'bounds': [[-np.pi, np.pi]] * 3, # 'groups': ['A', 'B', 'A'], 'outputs': ['Y'] }) (sp.sample_saltelli(2048) .evaluate(Ishigami.evaluate) .analyze_hdmr() ) sp.emulate() Parameters ---------- problem : dict The problem definition X : numpy.matrix The NumPy matrix containing the model inputs, N rows by d columns Y : numpy.array The NumPy array containing the model outputs for each row of X maxorder : int (1-3, default: 2) Maximum HDMR expansion order maxiter : int (1-1000, default: 100) Max iterations backfitting m : int (2-10, default: 2) Number of B-spline intervals K : int (1-100, default: 20) Number of bootstrap iterations R : int (100-N/2, default: N/2) Number of bootstrap samples. Will be set to length of `Y` if `K` is set to 1. alpha : float (0.5-1) Confidence interval F-test lambdax : float (0-10, default: 0.01) Regularization term print_to_console : bool Print results directly to console (default: False) seed : {int, bool, None} Seed to generate a random number Returns ------- Si : ResultDict, Sa : Uncorrelated contribution of a term Sa_conf : Confidence interval of Sa Sb : Correlated contribution of a term Sb_conf : Confidence interval of Sb S : Total contribution of a particular term Sum of Sa and Sb, representing first/second/third order sensitivity indices S_conf : Confidence interval of S ST : Total contribution of a particular dimension/parameter ST_conf : Confidence interval of ST select : Number of selection (F-Test) Em : Emulator result set C1: First order coefficient C2: Second order coefficient C3: Third Order coefficient References ---------- 1. Rabitz, H. and AliÅŸ, Ö.F., "General foundations of high dimensional model representations", Journal of Mathematical Chemistry 25, 197-233 (1999) https://doi.org/10.1023/A:1019188517934 2. Genyuan Li, H. Rabitz, P.E. Yelvington, O.O. Oluwole, F. Bacon, C.E. Kolb, and J. Schoendorf, "Global Sensitivity Analysis for Systems with Independent and/or Correlated Inputs", Journal of Physical Chemistry A, Vol. 114 (19), pp. 6022 - 6032, 2010, https://doi.org/10.1021/jp9096919 """ warnings.warn( "This method will be retired in future, please use enhanced_hdmr instead.", DeprecationWarning, stacklevel=2, ) # Random Seed if seed: rng = handle_seed(seed) # noqa # Initial part: Check input arguments and define HDMR variables settings = _check_settings(X, Y, maxorder, maxiter, m, K, R, alpha, lambdax) init_vars = _init(X, Y, settings) # Sensitivity Analysis Computation with/without bootstrapping SA, Em, RT, Y_em, idx = _compute(X, Y, settings, init_vars) # Finalize results Si = _finalize( problem, SA, Em, problem["num_vars"], alpha, maxorder, RT, Y_em, idx, X, Y ) # Print results to console if print_to_console: _print(Si, problem["num_vars"]) return Si def _check_settings(X, Y, maxorder, maxiter, m, K, R, alpha, lambdax): """Perform checks to ensure all parameters are within usable/expected ranges.""" # Get dimensionality of numpy arrays N, d = X.shape y_row = Y.shape[0] # Now check input-output mismatch if d == 1: raise RuntimeError( "Matrix X contains only a single column: No point to do" " sensitivity analysis when d = 1." ) if N < 300: raise RuntimeError( f"Number of samples in matrix X, {N}, is insufficient. Need at least 300." ) if N != y_row: raise RuntimeError( f"Dimension mismatch. The number of outputs ({y_row}) should match" f" number of samples ({N})" ) if Y.size != N: raise RuntimeError( "Y should be a N x 1 vector with one simulated output for each" " N parameter vectors." ) if maxorder not in (1, 2, 3): raise RuntimeError( f'Field "maxorder" of options should be an integer with values of' f" 1, 2 or 3, got {maxorder}" ) # Important next check for maxorder - as maxorder relates to d if (d == 2) and (maxorder > 2): raise RuntimeError( 'SALib-HDMR ERROR: Field "maxorder" of options has to be 2 as' " d = 2 (X has two columns)" ) if maxiter not in np.arange(1, 1001): raise RuntimeError( 'Field "maxiter" of options should be an integer between 1 to 1000.' ) if m not in np.arange(1, 11): raise RuntimeError('Field "m" of options should be an integer between 1 to 10.') if K not in np.arange(1, 101): raise RuntimeError( 'Field "K" of options should be an integer between 1 to 100.' ) if R is None: R = y_row // 2 elif R not in np.arange(300, N + 1): raise RuntimeError( f'Field "R" of options should be an integer between 300 and {N},' f" the number of rows matrix X." ) if (K == 1) and (R != y_row): R = y_row if alpha < 0.5 or alpha > 1.0: raise RuntimeError( 'Field "alpha" of options should be an integer between 0.5 to 1.0' ) if lambdax > 10.0: raise RuntimeError( 'SALib-HDMR WARNING: Field "lambdax" of options set rather large.' " Default: lambdax = 0.01" ) elif lambdax < 0.0: raise RuntimeError( 'Field "lambdax" (regularization term) of options cannot be' " smaller than zero. Default: 0.01" ) return [N, d, maxorder, maxiter, m, K, R, alpha, lambdax] def _compute(X, Y, settings, init_vars): """Compute HDMR""" N, d, maxorder, maxiter, m, K, R, alpha, lambdax = settings Em, idx, SA, RT, Y_em, Y_id, m1, m2, m3, j1, j2, j3 = init_vars # DYNAMIC PART: Bootstrap for confidence intervals for k in range(K): tic = time.time() # Start timer # Extract the "right" Y values Y_id[:] = Y[idx[:, k]] # Compute the variance of the model output SA["V_Y"][k, 0] = np.var(Y_id) # Mean of the output Em["f0"][k] = np.sum(Y_id) / R # Compute residuals Y_res = Y_id - Em["f0"][k] # 1st order component functions: ind/backfitting Y_em[:, j1], Y_res, Em["C1"][:, :, k] = _first_order( Em["B1"][idx[:, k], :, :], Y_res, Em["C1"][:, :, k], R, Em["n1"], m1, maxiter, lambdax, ) # 2nd order component functions: individual if maxorder > 1: Y_em[:, j2], Y_res, Em["C2"][:, :, k] = _second_order( Em["B2"][idx[:, k], :, :], Y_res, Em["C2"][:, :, k], R, Em["n2"], m2, lambdax, ) # 3rd order component functions: individual if maxorder == 3: Y_em[:, j3], Em["C3"][:, :, k] = _third_order( Em["B3"][idx[:, k], :, :], Y_res, Em["C3"][:, :, k], R, Em["n3"], m3, lambdax, ) # Identify significant and insignificant terms Em["select"][:, k] = f_test( Y_id, Em["f0"][k], Y_em, R, alpha, m1, m2, m3, Em["n1"], Em["n2"], Em["n3"], Em["n"], ) # Store the emulated output Em["Y_e"][:, k] = Em["f0"][k] + np.sum(Y_em, axis=1) # RMSE of emulator Em["RMSE"][k] = np.sqrt(np.sum(np.square(Y_id - Em["Y_e"][:, k])) / R) # Compute sensitivity indices SA["S"][:, k], SA["Sa"][:, k], SA["Sb"][:, k] = ancova( Y_id, Y_em, SA["V_Y"][k], R, Em["n"] ) RT[k] = time.time() - tic # Compute CPU time kth emulator return (SA, Em, RT, Y_em, idx) def _init(X, Y, settings): """Initialize HDMR variables.""" N, d, maxorder, maxiter, m, K, R, alpha, lambdax = settings # Setup Bootstrap (if K > 1) if K == 1: # No Bootstrap idx = np.arange(0, N).reshape(N, 1) else: # Now setup the bootstrap matrix with selection matrix, idx, for samples idx = np.argsort(np.random.rand(N, K), axis=0)[:R] # Compute normalized X-values X_n = (X - np.tile(X.min(0), (N, 1))) / np.tile((X.max(0)) - X.min(0), (N, 1)) # DICT Em: Important variables n2 = 0 n3 = 0 c2 = np.empty c3 = np.empty # determine all combinations of parameters (coefficients) for each order c1 = np.arange(0, d) n1 = d # now return based on maxorder used if maxorder > 1: c2 = np.asarray(list(itertools.combinations(np.arange(0, d), 2))) n2 = c2.shape[0] if maxorder == 3: c3 = np.asarray(list(itertools.combinations(np.arange(0, d), 3))) n3 = c3.shape[0] # calculate total number of coefficients n = n1 + n2 + n3 # Initialize m1, m2 and m3 - number of coefficients first, second, third # order m1 = m + 3 m2 = m1**2 m3 = m1**3 # STRUCTURE Em: Initialization Em = { "nterms": np.zeros(K), "RMSE": np.zeros(K), "m": m, "Y_e": np.zeros((R, K)), "f0": np.zeros(K), "c1": c1, "C1": np.zeros((m1, n1, K)), "C2": np.zeros((1, 1, K)), "C3": np.zeros((1, 1, K)), "n": n, "n1": n1, "n2": n2, "n3": n3, "maxorder": maxorder, "select": np.zeros((n, K)), "B1": np.zeros((N, m1, n1)), } if maxorder >= 2: Em.update({"c2": c2, "B2": np.zeros((N, m2, n2)), "C2": np.zeros((m2, n2, K))}) if maxorder >= 3: Em.update({"c3": c3, "B3": np.zeros((N, m3, n3)), "C3": np.zeros((m3, n3, K))}) # Compute cubic B-spline Em["B1"] = B_spline(X_n, m, d) # Now compute B values for second order if maxorder > 1: beta = np.array(list(itertools.product(range(m1), repeat=2))) for k, j in itertools.product(range(n2), range(m2)): Em["B2"][:, j, k] = np.multiply( Em["B1"][:, beta[j, 0], Em["c2"][k, 0]], Em["B1"][:, beta[j, 1], Em["c2"][k, 1]], ) # Compute B values for third order if maxorder == 3: # Now compute B values for third order beta = np.array(list(itertools.product(range(m1), repeat=3))) EmB1 = Em["B1"] for k, j in itertools.product(range(n3), range(m3)): Emc3_k = Em["c3"][k] beta_j = beta[j] Em["B3"][:, j, k] = np.multiply( np.multiply( EmB1[:, beta_j[0], Emc3_k[0]], EmB1[:, beta_j[1], Emc3_k[1]] ), EmB1[:, beta_j[2], Emc3_k[2]], ) # DICT SA: Sensitivity analysis and analysis of variance decomposition em_k = np.zeros((Em["n"], K)) SA = { "S": em_k, "Sa": em_k.copy(), "Sb": em_k.copy(), "ST": np.zeros((d, K)), "V_Y": np.zeros((K, 1)), } # Return runtime RT = np.zeros(K) # Initialize emulator matrix Y_em = np.zeros((R, Em["n"])) # Initialize index of first, second and third order terms (columns of Y_em) j1 = range(n1) j2 = range(n1, n1 + n2) j3 = range(n1 + n2, n1 + n2 + n3) # Initialize temporary Y_id for bootstrap Y_id = np.zeros(R) return [Em, idx, SA, RT, Y_em, Y_id, m1, m2, m3, j1, j2, j3] def B_spline(X, m, d): """Generate cubic B-splines using scipy basis_element method. Knot points (`t`) are automatically determined. References ---------- .. [1] https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.BSpline.basis_element.html # noqa: E501 """ # Initialize B matrix B = np.zeros((X.shape[0], m + 3, d)) # Cubic basis-spline settings k = np.arange(-1, m + 2) # Compute B-Splines for j, i in itertools.product(range(d), range(m + 3)): k_i = k[i] t = np.arange(k_i - 2, k_i + 3) / m temp = interpolate.BSpline.basis_element(t)(X[:, j]) * np.power(m, 3) B[:, i, j] = np.where(temp < 0, 0, temp) return B def _first_order(B1, Y_res, C1, R, n1, m1, maxiter, lambdax): """Compute first order sensitivities.""" Y_i = np.empty((R, n1)) # Initialize 1st order contributions T1 = np.empty((m1, R, n1)) # Initialize T(emporary) matrix - 1st it = 0 # Initialize iteration counter lam_eye_m1 = lambdax * identity(m1) # Avoid memory allocations by using temporary store B1_j = np.empty(B1[:, :, 0].shape) B11 = np.empty((m1, m1)) # First order individual estimation for j in range(n1): # Regularized least squares inversion ( minimize || C1 ||_2 ) B1_j[:, :] = B1[:, :, j] B11[:, :] = B1_j.T @ B1_j # if it is ill-conditioned matrix, the default value is zero if np.all(svd(B11)[1]): # sigma, diagonal matrix, from svd T1[:, :, j] = lin_solve(B11 + lam_eye_m1, B1_j.T) C1[:, j] = T1[:, :, j] @ Y_res Y_i[:, j] = B1_j @ C1[:, j] # Backfitting Method var1b_old = np.sum(np.square(C1), axis=0) varmax = 1 while (varmax > 1e-3) and (it < maxiter): for j in range(n1): Y_r = Y_res for z in range(n1): if j != z: Y_r = Y_r - B1[:, :, z] @ C1[:, z] C1[:, j] = T1[:, :, j] @ Y_r var1b_new = np.sum(np.square(C1), axis=0) varmax = np.max(np.absolute(var1b_new - var1b_old)) var1b_old = var1b_new it += 1 # Now compute first-order terms for j in range(n1): Y_i[:, j] = B1[:, :, j] @ C1[:, j] # Subtract each first order term from residuals Y_res = Y_res - Y_i[:, j] return (Y_i, Y_res, C1) def _second_order(B2, Y_res, C2, R, n2, m2, lambdax): """Compute second order sensitivities.""" Y_ij = np.empty((R, n2)) # Initialize 2nd order contributions T2 = np.empty((m2, R)) # Initialize T(emporary) matrix - 1st lam_eye_m2 = lambdax * identity(m2) # Avoid memory allocations by using temporary store B2_j = np.empty(B2[:, :, 0].shape) B22 = np.empty((m2, m2)) # First order individual estimation for j in range(n2): # Regularized least squares inversion ( minimize || C1 ||_2 ) B2_j[:, :] = B2[:, :, j] B22[:, :] = B2_j.T @ B2_j # if it is ill-conditioned matrix, the default value is zero if np.all(svd(B22)[1]): # sigma, diagonal matrix, from svd T2[:, :] = lin_solve(B22 + lam_eye_m2, B2_j.T) else: T2[:, :] = 0.0 C2[:, j] = T2 @ Y_res Y_ij[:, j] = B2_j @ C2[:, j] # Now compute second-order terms for j in range(n2): # Subtract each first order term from residuals Y_res = Y_res - Y_ij[:, j] return (Y_ij, Y_res, C2) def _third_order(B3, Y_res, C3, R, n3, m3, lambdax): """Compute third order sensitivities.""" Y_ijk = np.empty((R, n3)) # Initialize 3rd order contributions T3 = np.empty((m3, R)) # Initialize T(emporary) matrix - 1st lam_eye_m3 = lambdax * identity(m3) # Avoid memory allocations by using temporary store B3_j = np.empty(B3[:, :, 0].shape) B33 = np.empty((m3, m3)) # First order individual estimation for j in range(n3): # Regularized least squares inversion ( minimize || C1 ||_2 ) B3_j[:, :] = B3[:, :, j] B33[:, :] = B3_j.T @ B3_j # if it is ill-conditioned matrix, the default value is zero if np.all(svd(B33)[1]): # sigma, diagonal matrix, from svd T3[:, :] = lin_solve(B33 + lam_eye_m3, B3_j.T) else: T3[:, :] = 0.0 C3[:, j] = T3 @ Y_res Y_ijk[:, j] = B3_j @ C3[:, j] return (Y_ijk, C3) def f_test(Y, f0, Y_em, R, alpha, m1, m2, m3, n1, n2, n3, n): """Use F-test for model selection.""" # Initialize ind with zeros (all terms insignificant) select = np.zeros(n) # Determine the significant components of the HDMR model via the F-test Y_res0 = Y - f0 SSR0 = np.sum(np.square(Y_res0)) p0 = 0 for i in range(n): # model with ith term included Y_res1 = Y_res0 - Y_em[:, i] # Number of parameters of proposed model (order dependent) if i <= n1: p1 = m1 # 1st order elif n1 < i <= (n1 + n2): p1 = m2 # 2nd order else: p1 = m3 # 3rd order # Calculate SSR of Y1 SSR1 = np.sum(np.square(Y_res1)) # Now calculate the F_stat (F_stat > 0 -> SSR1 < SSR0 ) F_stat = ((SSR0 - SSR1) / (p1 - p0)) / (SSR1 / (R - p1)) # Now calculate critical F value F_crit = stats.f.ppf(q=alpha, dfn=p1 - p0, dfd=R - p1) # Now determine whether to accept ith component into model if F_stat > F_crit: # ith term is significant and should be included in model select[i] = 1 return select def ancova(Y, Y_em, V_Y, n, R): """ Perform Analysis of Covariance (ANCOVA) on model and emulator outputs. Returns -------- tuple : A tuple containing sensitivity indices (S), of structural contributions (S_a) and of correlative contributions (S_b). """ # R is currently unused # Compute the sum of all Y_em terms m = Y_em.shape[1] Y0 = np.sum(Y_em, axis=1) Y0_minus_Y_em = Y0[:, None] - Y_em # Covariance matrix of Y_em terms with actual Y C_all = np.cov(Y_em, Y, rowvar=False)[:m, m] # Total sensitivity of each term (vectorized computation) S = C_all / V_Y # For each term, compute covariance with the emulator Y without the current term # See Li et al. (2010) for more details # Structural contribution of jth term ( = Eq. 20 of Li et al ) S_a = np.var(Y_em, axis=0) / V_Y # Correlative contribution of jth term ( = Eq. 21 of Li et al ) cov_matrix = np.empty((m, m)) for i in range(m): cov_matrix[i] = np.cov(Y_em[:, i], Y0_minus_Y_em[:, i])[0, 1] S_b = cov_matrix.diagonal() / V_Y return (S, S_a, S_b) def _finalize(problem, SA, Em, d, alpha, maxorder, RT, Y_em, bootstrap_idx, X, Y): """Creates ResultDict to be returned.""" # Create Sensitivity Indices Result Dictionary keys = ( "Sa", "Sa_conf", "Sb", "Sb_conf", "S", "S_conf", "select", "Sa_sum", "Sa_sum_conf", "Sb_sum", "Sb_sum_conf", "S_sum", "S_sum_conf", ) Si = ResultDict((k, np.zeros(Em["n"])) for k in keys) Si["Term"] = [None] * Em["n"] Si["ST"] = [ np.nan, ] * Em["n"] Si["ST_conf"] = [ np.nan, ] * Em["n"] # Z score def z(p): return (-1) * np.sqrt(2) * special.erfcinv(p * 2) # Multiplier for confidence interval mult = z(alpha + (1 - alpha) / 2) # Compute the total sensitivity of each parameter/coefficient for r in range(Em["n1"]): if maxorder == 1: TS = SA["S"][r, :] elif maxorder == 2: ij = Em["n1"] + np.where(np.sum(Em["c2"] == r, axis=1) == 1)[0] TS = np.sum(SA["S"][np.append(r, ij), :], axis=0) elif maxorder == 3: ij = Em["n1"] + np.where(np.sum(Em["c2"] == r, axis=1) == 1)[0] ijk = Em["n1"] + Em["n2"] + np.where(np.sum(Em["c3"] == r, axis=1) == 1)[0] TS = np.sum(SA["S"][np.append(r, np.append(ij, ijk)), :], axis=0) Si["ST"][r] = np.mean(TS) Si["ST_conf"][r] = mult * np.std(TS) # Fill Expansion Terms ct = 0 p_names = problem["names"] if maxorder > 1: p_c2 = Em["c2"] if maxorder == 3: p_c3 = Em["c3"] for i in range(Em["n1"]): Si["Term"][ct] = p_names[i] ct += 1 for i in range(Em["n2"]): Si["Term"][ct] = "/".join([p_names[p_c2[i, 0]], p_names[p_c2[i, 1]]]) ct += 1 for i in range(Em["n3"]): Si["Term"][ct] = "/".join( [p_names[p_c3[i, 0]], p_names[p_c3[i, 1]], p_names[p_c3[i, 2]]] ) ct += 1 # Assign Bootstrap Results to Si Dict Si["Sa"] = np.mean(SA["Sa"], axis=1) Si["Sb"] = np.mean(SA["Sb"], axis=1) Si["S"] = np.mean(SA["S"], axis=1) Si["Sa_sum"] = np.mean(np.sum(SA["Sa"], axis=0)) Si["Sb_sum"] = np.mean(np.sum(SA["Sb"], axis=0)) Si["S_sum"] = np.mean(np.sum(SA["S"], axis=0)) # Compute Confidence Interval Si["Sa_conf"] = mult * np.std(SA["Sa"], axis=1) Si["Sb_conf"] = mult * np.std(SA["Sb"], axis=1) Si["S_conf"] = mult * np.std(SA["S"], axis=1) Si["Sa_sum_conf"] = mult * np.std(np.sum(SA["Sa"])) Si["Sb_sum_conf"] = mult * np.std(np.sum(SA["Sb"])) Si["S_sum_conf"] = mult * np.std(np.sum(SA["S"])) # F-test # of selection to print out Si["select"] = Em["select"].flatten() Si["names"] = Si["Term"] # Additional data for plotting. Si["Em"] = Em Si["RT"] = RT Si["Y_em"] = Y_em Si["idx"] = bootstrap_idx Si["X"] = X Si["Y"] = Y Si.emulate = MethodType(emulate, Si) Si.to_df = MethodType(to_df, Si) Si._plot = Si.plot Si.plot = MethodType(plot, Si) if not isinstance(problem, ProblemSpec): Si.problem = problem else: problem.update(Si) problem.emulate = MethodType(emulate, problem) return Si def emulate(self, X, Y=None): """Emulates model output with new input data. Generates B-Splines with new input matrix, X, and multiplies it with coefficient matrix, C. Compares emulated results with observed vector, Y. Returns ======== Si : ResultDict, Updated """ # Dimensionality N, d = X.shape # Expand C Em = self["Em"] C1, C2, C3 = Em["C1"], Em["C2"], Em["C3"] # Take average coefficient C1 = np.mean(C1, axis=2) C2 = np.mean(C2, axis=2) C3 = np.mean(C3, axis=2) # Get maxorder and other information from C matrix m = C1.shape[0] - 3 m1 = m + 3 n1, n2, n3 = d, 0, 0 maxorder = 1 if C2.shape[0] != 1: maxorder = 2 m2 = C2.shape[0] c2 = np.asarray(list(itertools.combinations(np.arange(0, d), 2))) n2 = c2.shape[0] if C3.shape[0] != 1: maxorder = 3 m3 = C3.shape[0] c3 = np.asarray(list(itertools.combinations(np.arange(0, d), 3))) n3 = c3.shape[0] # Initialize emulated Y's Y_em = np.zeros((N, n1 + n2 + n3)) # Compute normalized X-values X_n = (X - np.tile(X.min(0), (N, 1))) / np.tile((X.max(0)) - X.min(0), (N, 1)) # Now compute B values B1 = B_spline(X_n, m, d) if maxorder > 1: B2 = np.zeros((N, m2, n2)) beta = np.array(list(itertools.product(range(m1), repeat=2))) for k, j in itertools.product(range(n2), range(m2)): B2[:, j, k] = np.multiply( B1[:, beta[j, 0], c2[k, 0]], B1[:, beta[j, 1], c2[k, 1]] ) if maxorder == 3: B3 = np.zeros((N, m3, n3)) beta = np.array(list(itertools.product(range(m1), repeat=3))) for k, j in itertools.product(range(n3), range(m3)): Emc3_k = c3[k] beta_j = beta[j] B3[:, j, k] = np.multiply( np.multiply(B1[:, beta_j[0], Emc3_k[0]], B1[:, beta_j[1], Emc3_k[1]]), B1[:, beta_j[2], Emc3_k[2]], ) # Calculate emulated output: First Order for j in range(0, n1): Y_em[:, j] = B1[:, :, j] @ C1[:, j] # Second Order if maxorder > 1: for j in range(n1, n1 + n2): Y_em[:, j] = B2[:, :, j - n1] @ C2[:, j - n1] # Third Order if maxorder == 3: for j in range(n1 + n2, n1 + n2 + n3): Y_em[:, j] = B3[:, :, j - n1 - n2] @ C3[:, j - n1 - n2] Y_mean = 0 if Y is not None: Y_mean = np.mean(Y) self["Y_test"] = Y self["emulated"] = np.sum(Y_em, axis=1) + Y_mean def to_df(self): """Conversion method to Pandas DataFrame. To be attached to ResultDict. Returns ------- Pandas DataFrame """ names = self["names"] # Only convert these elements in dict to DF include_list = ["Sa", "Sb", "S", "ST"] include_list += [f"{name}_conf" for name in include_list] new_spec = {k: v for k, v in self.items() if k in include_list} return pd.DataFrame(new_spec, index=names) def plot(self): """HDMR specific plotting. Gets attached to the SALib problem spec. """ return hdmr_plot(self) def _print(Si, d): print("\n") print( "Term \t Sa Sb S ST #select " ) print("-" * 84) # Header break format1 = "%-11s \t %5.2f (\261%.2f) %5.2f (\261%.2f) %5.2f (\261%.2f) %5.2f (\261%.2f) %-3.0f" # noqa: E501 format2 = "%-11s \t %5.2f (\261%.2f) %5.2f (\261%.2f) %5.2f (\261%.2f) %-3.0f" # noqa: E501 for i in range(len(Si["Sa"])): if i < d: print( format1 % ( Si["Term"][i], Si["Sa"][i], Si["Sa_conf"][i], Si["Sb"][i], Si["Sb_conf"][i], Si["S"][i], Si["S_conf"][i], Si["ST"][i], Si["ST_conf"][i], np.sum(Si["select"][i]), ) ) else: print( format2 % ( Si["Term"][i], Si["Sa"][i], Si["Sa_conf"][i], Si["Sb"][i], Si["Sb_conf"][i], Si["S"][i], Si["S_conf"][i], np.sum(Si["select"][i]), ) ) print("-" * 84) # Header break format3 = "%-11s \t %5.2f (\261%.2f) %5.2f (\261%.2f) %5.2f (\261%.2f)" print( format3 % ( "Sum", Si["Sa_sum"], Si["Sa_sum_conf"], Si["Sb_sum"], Si["Sb_sum_conf"], Si["S_sum"], Si["S_sum_conf"], ) ) keys = ("Sa_sum", "Sb_sum", "S_sum", "Sa_sum_conf", "Sb_sum_conf", "S_sum_conf") for k in keys: Si.pop(k, None) return Si def cli_parse(parser): parser.add_argument( "-X", "--model-input-file", type=str, required=True, default=None, help="Model input file", ) parser.add_argument( "-mor", "--maxorder", type=int, required=False, default=2, help="Maximum order of expansion 1-3", ) parser.add_argument( "-mit", "--maxiter", type=int, required=False, default=100, help="Maximum iteration number", ) parser.add_argument( "-m", "--m-int", type=int, required=False, default=2, help="B-spline interval" ) parser.add_argument( "-K", "--K-bootstrap", type=int, required=False, default=20, help="Number of bootstrap", ) parser.add_argument( "-R", "--R-subsample", type=int, required=False, default=None, help="Subsample size", ) parser.add_argument( "-a", "--alpha", type=float, required=False, default=0.95, help="Confidence interval", ) parser.add_argument( "-lambda", "--lambdax", type=float, required=False, default=0.01, help="Regularization constant", ) return parser def cli_action(args): problem = read_param_file(args.paramfile) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,) ) X = np.loadtxt(args.model_input_file, delimiter=args.delimiter, ndmin=2) mor = args.maxorder mit = args.maxiter m = args.m_int K = args.K_bootstrap R = args.R_subsample alpha = args.alpha lambdax = args.lambdax options = options = { "maxorder": mor, "maxiter": mit, "m": m, "K": K, "R": R, "alpha": alpha, "lambdax": lambdax, "print_to_console": True, } if len(X.shape) == 1: X = X.reshape((len(X), 1)) analyze(problem, X, Y, **options) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/analyze/morris.py000066400000000000000000000461261525347100600210720ustar00rootroot00000000000000from typing import Dict, List import numpy as np from scipy.stats import norm from . import common_args from ..util import ( read_param_file, compute_groups_matrix, ResultDict, _define_problem_with_groups, _compute_delta, handle_seed, ) def analyze( problem: Dict, X: np.ndarray, Y: np.ndarray, num_resamples: int = 100, conf_level: float = 0.95, scaled: bool = False, print_to_console: bool = False, num_levels: int = 4, seed=None, ) -> Dict: """Perform Morris Analysis on model outputs. Returns a result set with keys ``mu``, ``mu_star``, ``sigma``, and ``mu_star_conf``, where each entry corresponds to the parameters defined in the problem spec or parameter file. - ``mu`` metric indicates the mean of the distribution - ``mu_star`` metric indicates the mean of the distribution of absolute values - ``sigma`` is the standard deviation of the distribution When ``scaled`` is True, the elementary effects are scaled by the ratio of standard deviation of ``X`` and ``Y`` according to [3]. When using this option it is important to ensure that ``X`` contains the actual values passed into the model, as the elementary effects are divided by the step calculated from ``X`` rather than using `delta` which is calculated from the number of levels used in the sample. This could be the case if you perform post-processing on the values before passing them to the model. Scaled elementary effects are useful when comparing different model outputs with each other when the input and output parameters have different scales. The ranking between the ordinary elementary effects and the scaled should be the same. Notes ----- When applied with groups, the ``mu`` metric is less reliable as the effect from parameters within a group become averaged out. The ``mu_star`` metric avoids this issue as it indicates the mean of the absolute values. If the direction of effects is important, Campolongo et al., [2] suggest comparing ``mu_star`` with ``mu``. If ``mu`` is low and ``mu_star`` is high, then the effects are of different signs. ``sigma`` is used as an indicator of interactions between parameters, or groups of parameters. Compatible with: `morris` : :func:`SALib.sample.morris.sample` Examples -------- >>> X = morris.sample(problem, 1000, num_levels=4) >>> Y = Ishigami.evaluate(X) >>> Si = morris.analyze(problem, X, Y, conf_level=0.95, >>> print_to_console=True, num_levels=4) Parameters ---------- problem : dict The problem definition X : numpy.array The NumPy matrix containing the model inputs of dtype=float Y : numpy.array The NumPy array containing the model outputs of dtype=float scaled : bool, default=False If True, the elementary effects are scaled by the ratio of standard deviation of X and Y according to [3] num_resamples : int The number of resamples used to compute the confidence intervals (default 100) conf_level : float The confidence interval level (default 0.95) print_to_console : bool Print results directly to console (default False) num_levels : int The number of grid levels, must be identical to the value passed to SALib.sample.morris (default 4) seed : {int, None, np.random.Generator} Seed to generate a random number Returns ------- Si : dict A dictionary of sensitivity indices containing the following entries. - `mu` - the mean elementary effect - `mu_star` - the absolute of the mean elementary effect - `sigma` - the standard deviation of the elementary effect - `mu_star_conf` - the bootstrapped confidence interval - `names` - the names of the parameters References ---------- 1. Morris, M. (1991). Factorial Sampling Plans for Preliminary Computational Experiments. Technometrics, 33(2):161-174, doi:10.1080/00401706.1991.10484804. 2. Campolongo, F., J. Cariboni, and A. Saltelli (2007). An effective screening design for sensitivity analysis of large models. Environmental Modelling & Software, 22(10):1509-1518, doi:10.1016/j.envsoft.2006.10.004. 3. Sin and Gearney (2009) Improving the Morris Method for Sensitivity Analysis by Scaling the Elementary Effects. 19th European Symposium on Computer Aided Process Engineering ESCAPE19:925-930 4. Moret et al. (2017) Characterization of input uncertainties in strategic energy planning models. Applied Energy, Volume 202, 15 September 2017, Pages 597-617 https://doi.org/10.1016/j.apenergy.2017.05.106 """ rng = handle_seed(seed) _define_problem_with_groups(problem) _check_if_array_of_floats(X) _check_if_array_of_floats(Y) delta = _compute_delta(num_levels) num_vars = problem["num_vars"] groups, unique_group_names = compute_groups_matrix(problem["groups"]) number_of_groups = len(unique_group_names) num_trajectories = int(Y.size / (number_of_groups + 1)) trajectory_size = int(Y.size / num_trajectories) elementary_effects = _compute_elementary_effects( X, Y, trajectory_size, delta, scaling=scaled ) Si = _compute_statistical_outputs( elementary_effects, num_vars, num_resamples, conf_level, groups, unique_group_names, rng, ) if print_to_console: print(Si.to_df()) return Si def _compute_statistical_outputs( elementary_effects: np.ndarray, num_vars: int, num_resamples: int, conf_level: float, groups: np.ndarray, unique_group_names: List, rng: np.random.Generator, ) -> ResultDict: """Computes the statistical parameters related to Morris method. Parameters ---------- elementary_effects: np.ndarray Morris elementary effects. num_vars: int Number of problem's variables num_resamples: int Number of resamples conf_level: float Confidence level groups: np.ndarray Array defining the distribution of groups unique_group_names: List Names of the groups rng: np.random.Generator Returns ------- Si: ResultDict Morris statistical parameters. """ Si = ResultDict( (k, [None] * num_vars) for k in ["names", "mu", "mu_star", "sigma", "mu_star_conf"] ) Si["names"] = unique_group_names mu = np.average(elementary_effects, 1) mu_star = np.average(np.abs(elementary_effects), 1) sigma = np.std(elementary_effects, axis=1, ddof=1) mu_star_conf = _compute_mu_star_confidence( elementary_effects, num_vars, num_resamples, conf_level, rng ) Si["mu"] = _compute_grouped_metric(mu, groups) Si["mu_star"] = _compute_grouped_metric(mu_star, groups) Si["sigma"] = _compute_grouped_sigma(sigma, groups) Si["mu_star_conf"] = _compute_grouped_metric(mu_star_conf, groups) return Si def _compute_grouped_sigma( ungrouped_sigma: np.ndarray, groups: np.ndarray ) -> np.ndarray: """Sigma values for the groups. Returns sigma for the groups of parameter values in the argument ungrouped_metric where the group consists of no more than one parameter Parameters ---------- ungrouped_sigma: np.ndarray Sigma values calculated without considering the groups groups: np.ndarray Array defining the distribution of groups Returns ------- sigma: np.ndarray Sigma values for the groups. """ sigma_agg = _compute_grouped_metric(ungrouped_sigma, groups) sigma = np.zeros(groups.shape[1], dtype=float) np.copyto(sigma, sigma_agg, where=groups.sum(axis=0) == 1) np.copyto(sigma, np.nan, where=groups.sum(axis=0) != 1) return sigma def _compute_grouped_metric( ungrouped_metric: np.ndarray, groups: np.ndarray ) -> np.ndarray: """Computes the mean value for the groups of parameter values. Parameters ---------- ungrouped_metric: np.ndarray Metric calculated without considering the groups groups: np.ndarray Array defining the distribution of groups Returns ------- mean_of_mu_star: np.ndarray Mean value for the groups of parameter values """ groups = np.array(groups, dtype=bool) mu_star_masked = np.ma.masked_array( ungrouped_metric * groups.T, mask=(groups ^ 1).T ) mean_of_mu_star = np.ma.mean(mu_star_masked, axis=1) return mean_of_mu_star def _reorganize_output_matrix( output_array: np.ndarray, value_increased: np.ndarray, value_decreased: np.ndarray, increase: bool = True, ) -> np.ndarray: """Reorganize the output matrix. This method reorganizes the output matrix in a way that allows the elementary effects to be computed as a simple subtraction between two arrays. It repositions the outputs in the output matrix according to the order they changed during the formation of the trajectories. Parameters ---------- output_array: np.ndarray Matrix of model output values value_increased: np.ndarray Input variables that had their values increased when forming the trajectories matrix value_decreased: np.ndarray Input variables that had their values decreased when forming the trajectories matrix increase: bool Direction to consider (values that increased or decreased). "Increase" is the default value. Returns ------- np.ndarray """ if increase: pad_up = (1, 0) pad_lo = (0, 1) else: pad_up = (0, 1) pad_lo = (1, 0) value_increased = np.pad(value_increased, ((0, 0), pad_up, (0, 0)), "constant") value_decreased = np.pad(value_decreased, ((0, 0), pad_lo, (0, 0)), "constant") res = np.einsum("ik,ikj->ij", output_array, value_increased + value_decreased) return res.T def _compute_elementary_effects( model_inputs: np.ndarray, model_outputs: np.ndarray, trajectory_size: int, delta: float, scaling: bool = False, ) -> np.ndarray: """Computes the Morris elementary effects. Parameters ---------- model_inputs: np.ndarray matrix of inputs to the model under analysis. x-by-r where x is the number of variables and r is the number of rows (a function of x and num_trajectories) model_outputs: np.ndarray r-length vector of model outputs trajectory_size: int Number of points in a trajectory delta: float Scaling factor computed from `num_levels` scaling: bool True if the elementary effects should be in scaled as in [1] Returns --------- elementary_effects : np.array Elementary effects for each parameter References ---------- 1. Sin and Gearney (2009) Improving the Morris Method for Sensitivity Analysis by Scaling the Elementary Effects. 19th European Symposium on Computer Aided Process Engineering ESCAPE19:925-930 2. Moret et al. (2017) Characterization of input uncertainties in strategic energy planning models. Applied Energy, Volume 202, 15 September 2017, Pages 597-617 https://doi.org/10.1016/j.apenergy.2017.05.106 """ num_trajectories = _calculate_number_trajectories(model_inputs, trajectory_size) output_matrix = _reshape_model_outputs( model_outputs, num_trajectories, trajectory_size ) input_matrix = _reshape_model_inputs( model_inputs, num_trajectories, trajectory_size ) delta_variables = _calculate_delta_input_variables(input_matrix) value_increased = delta_variables > 0 value_decreased = delta_variables < 0 result_increased = _reorganize_output_matrix( output_matrix, value_increased, value_decreased ) result_decreased = _reorganize_output_matrix( output_matrix, value_increased, value_decreased, increase=False ) difference = _calc_results_difference(result_increased, result_decreased) if scaling: # calculate the scaled value of delta (step size) dx_trajectory = _calculate_step_size_x(input_matrix) see_dy_dx = np.divide(difference, dx_trajectory.T) sigma_x_per_trajectory = np.std(input_matrix, axis=1) sigma_y_per_trajectory = np.std(output_matrix, axis=1) # Create a mask to avoid division by zero mask = sigma_y_per_trajectory[:, np.newaxis] != 0 adjustment_trajectory = np.divide( sigma_x_per_trajectory, sigma_y_per_trajectory[:, np.newaxis], out=np.zeros_like(sigma_x_per_trajectory), where=mask, ) elementary_effects = see_dy_dx * adjustment_trajectory.T else: elementary_effects = difference / delta return elementary_effects def _calc_results_difference( result_up: np.ndarray, result_lo: np.ndarray ) -> np.ndarray: """Computes the difference between the output points. Parameters ---------- result_up: np.ndarray result_lo: np.ndarray Returns ------- results_difference: np.ndarray Difference between the output points """ results_difference = np.subtract(result_up, result_lo) return results_difference def _calculate_delta_input_variables(input_matrix: np.ndarray) -> np.ndarray: """Computes the delta values of the problem variables. For each point of the trajectory, computes how much each variable increased or decreased in respect to the previous point. Parameters ---------- input_matrix: np.ndarray Matrix with the values of the problem's variables for all input points. Returns ------- delta_variables: np.ndarray Variation of each variable, for each point in the trajectory. """ delta_variables = np.subtract(input_matrix[:, 1:, :], input_matrix[:, 0:-1, :]) return delta_variables def _calculate_number_trajectories( model_inputs: np.ndarray, trajectory_size: int ) -> int: """Calculate the number of trajectories. Parameters ---------- model_inputs: np.ndarray Matrix of model inputs trajectory_size: int Number of input points in each trajectory Returns ------- num_trajectories: int Number of trajectories """ num_input_points = model_inputs.shape[0] num_trajectories = int(num_input_points / trajectory_size) return num_trajectories def _reshape_model_inputs( model_inputs: np.ndarray, num_trajectories: int, trajectory_size: int ) -> np.ndarray: """Reshapes the model inputs' matrix. Parameters ---------- model_inputs: np.ndarray Matrix of model inputs num_trajectories: int Number of trajectories trajectory_size: int Number of points in a trajectory Returns ------- input_matrix: np.ndarray Reshaped input matrix. """ num_vars = model_inputs.shape[1] input_matrix = model_inputs.reshape(num_trajectories, trajectory_size, num_vars) return input_matrix def _reshape_model_outputs( model_outputs: np.ndarray, num_trajectories: int, trajectory_size: int ): """Reshapes the model outputs' matrix. Parameters ---------- model_outputs: np.ndarray Matrix of model outputs num_trajectories: int Number of trajectories trajectory_size: int Number of points in a trajectory Returns ------- output_matrix: np.ndarray Reshaped output matrix. """ output_matrix = model_outputs.reshape(num_trajectories, trajectory_size) return output_matrix def _compute_mu_star_confidence( elementary_effects: np.ndarray, num_vars: int, num_resamples: int, conf_level: float, rng: np.random.Generator, ) -> np.ndarray: """Computes the confidence intervals for the mu_star variable. Uses bootstrapping where the elementary effects are resampled with replacement to produce a histogram of resampled mu_star metrics. This resample is used to produce a confidence interval. Parameters ---------- elementary_effects : np.array Elementary effects for each parameter num_vars: int Number of problem's variables num_resamples: int Number of resamples conf_level: float Confidence level rng: np.random.Generator Returns ------- mu_star_conf: np.ndarray Confidence intervals for the mu_star variable """ if not 0 < conf_level < 1: raise ValueError("Confidence level must be between 0-1.") mu_star_conf = [] for j in range(num_vars): ee = elementary_effects[j, :] resample_index = rng.integers(len(ee), size=(num_resamples, len(ee))) ee_resampled = ee[resample_index] # Compute average of the absolute values over each of the resamples mu_star_resampled = np.average(np.abs(ee_resampled), axis=1) mu_star_conf.append( norm.ppf(0.5 + conf_level / 2) * mu_star_resampled.std(ddof=1) ) mu_star_conf = np.asarray(mu_star_conf) return mu_star_conf def _calculate_step_size_x(input_matrix): """This function calculates the step of dx for scaled elementary effects""" max_y = np.max(input_matrix, axis=1) min_y = np.min(input_matrix, axis=1) delta = max_y - min_y return delta def _check_if_array_of_floats(array_x: np.ndarray): """Checks if an arrays is made of floats. If not, raises an error. Parameters ---------- array_x: Array to be checked """ msg = "dtype of {} array must be 'float', float32 or float64" if array_x.dtype not in ["float", "float32", "float64"]: raise ValueError(msg.format(array_x)) def cli_parse(parser): parser.add_argument( "-X", "--model-input-file", type=str, required=True, default=None, help="Model input file", ) parser.add_argument( "-r", "--resamples", type=int, required=False, default=1000, help="Number of bootstrap resamples for Morris \ confidence intervals", ) parser.add_argument( "-l", "--levels", type=int, required=False, default=4, help="Number of grid levels \ (Morris only)", ) parser.add_argument( "--scaled", type=bool, required=False, default=False, help="Scale the results by ratio of stddev of X and Y (Morris)", ) return parser def cli_action(args): problem = read_param_file(args.paramfile) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,) ) X = np.loadtxt(args.model_input_file, delimiter=args.delimiter, ndmin=2) if len(X.shape) == 1: X = X.reshape((len(X), 1)) analyze( problem, X, Y, num_resamples=args.resamples, scaled=args.scaled, print_to_console=True, num_levels=args.levels, seed=args.seed, ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/analyze/pawn.py000066400000000000000000000151131525347100600205140ustar00rootroot00000000000000from typing import Dict import numpy as np from scipy.stats import ks_2samp from . import common_args from ..util import read_param_file, ResultDict, extract_group_names, _check_groups def analyze( problem: Dict, X: np.ndarray, Y: np.ndarray, S: int = 10, print_to_console: bool = False, seed: int = None, ): """Performs PAWN sensitivity analysis. The PAWN method [1] is a moment-independent approach to Global Sensitivity Analysis (GSA). It is described as producing robust results at relatively low sample sizes (see [2]) for the purpose of factor ranking and screening. The distribution of model outputs is examined rather than their variation as is typical in other common GSA approaches. The PAWN method further distinguishes itself from other moment-independent approaches by characterizing outputs by their cumulative distribution function (CDF) as opposed to their probability distribution function. As the CDF for a given random variable is typically normally distributed, PAWN can be more appropriately applied when outputs are highly-skewed or multi-modal, for which variance-based methods may produce unreliable results. PAWN characterizes the relationship between inputs and outputs by quantifying the variation in the output distributions after conditioning an input. A factor is deemed non-influential if distributions coincide at all ``S`` conditioning intervals. The Kolmogorov-Smirnov statistic is used as a measure of distance between the distributions. This implementation reports the PAWN index at the min, mean, median, and max across the slides/conditioning intervals as well as the coefficient of variation (``CV``) and standard deviation (``stdev``). The median value is the typically reported value. As the ``CV`` is (standard deviation / mean), it indicates the level of variability across the slides, with values closer to zero indicating lower variation. Notes ----- Compatible with: all samplers This implementation ignores all NaNs. When applied to grouped factors, the analysis is conducted on each factor individually, and the mean of their results are reported. Examples -------- >>> X = latin.sample(problem, 1000) >>> Y = Ishigami.evaluate(X) >>> Si = pawn.analyze(problem, X, Y, S=10, print_to_console=False) Parameters ---------- problem : dict The problem definition X : numpy.array A NumPy array containing the model inputs Y : numpy.array A NumPy array containing the model outputs S : int Number of slides; the conditioning intervals (default 10) print_to_console : bool Print results directly to console (default False) seed : int Seed value to ensure deterministic results References ---------- 1. Pianosi, F., Wagener, T., 2015. A simple and efficient method for global sensitivity analysis based on cumulative distribution functions. Environmental Modelling & Software 67, 1-11. https://doi.org/10.1016/j.envsoft.2015.01.004 2. Pianosi, F., Wagener, T., 2018. Distribution-based sensitivity analysis from a generic input-output sample. Environmental Modelling & Software 108, 197-207. https://doi.org/10.1016/j.envsoft.2018.07.019 3. Baroni, G., Francke, T., 2020. An effective strategy for combining variance- and distribution-based global sensitivity analysis. Environmental Modelling & Software, 134, 104851. https://doi.org/10.1016/j.envsoft.2020.104851 4. Baroni, G., Francke, T., 2020. GSA-cvd Combining variance- and distribution-based global sensitivity analysis https://github.com/baronig/GSA-cvd """ if seed: np.random.seed(seed) D = problem["num_vars"] var_names, _ = extract_group_names(problem) results = np.full((D, 6), np.nan) temp_pawn = np.full((S, D), np.nan) step = 1 / S for d_i in range(D): seq = np.arange(0, 1 + step, step) X_di = X[:, d_i] X_q = np.nanquantile(X_di, seq) for s in range(S): Y_sel = Y[(X_di >= X_q[s]) & (X_di < X_q[s + 1])] if len(Y_sel) == 0: # no available samples continue # KD value # Function returns a KS object which holds the KS statistic # and p-value # Note from scipy documentation: # if the K-S statistic is small or the p-value is high, then # we cannot reject the hypothesis that the distributions of # the two samples are the same. ks = ks_2samp(Y_sel, Y) temp_pawn[s, d_i] = ks.statistic p_ind = temp_pawn[:, d_i] mins = np.nanmin(p_ind) mean = np.nanmean(p_ind) med = np.nanmedian(p_ind) maxs = np.nanmax(p_ind) stdev = np.nanstd(p_ind) cv = np.nanstd(p_ind) / mean results[d_i, :] = [mins, mean, med, maxs, cv, stdev] groups = _check_groups(problem) if groups: unique_grps, n_groups = extract_group_names(problem) tmp = np.full((n_groups, results.shape[1]), np.nan) # Take the mean of effects from parameters that are grouped together unique_grps = np.array(unique_grps) grps = np.array(groups) for grp_id, grp in enumerate(unique_grps): tmp[grp_id, :] = np.mean(results[grps == grp, :], axis=0) results = tmp tmp = None Si = ResultDict( [ ("minimum", results[:, 0]), ("mean", results[:, 1]), ("median", results[:, 2]), ("maximum", results[:, 3]), ("CV", results[:, 4]), ("stdev", results[:, 5]), ] ) Si["names"] = var_names if print_to_console: print(Si.to_df()) return Si def cli_parse(parser): parser.add_argument( "-X", "--model-input-file", type=str, required=True, help="Model input file" ) parser.add_argument( "-S", "--slices", type=int, required=False, help="Number of slices to take" ) return parser def cli_action(args): problem = read_param_file(args.paramfile) X = np.loadtxt(args.model_input_file, delimiter=args.delimiter) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,) ) analyze(problem, X, Y, S=args.slices, print_to_console=True, seed=args.seed) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/analyze/radial_ee.py000066400000000000000000000143221525347100600214550ustar00rootroot00000000000000from typing import Dict, Optional import numpy as np from scipy.stats import norm from . import common_args from ..util import read_param_file, ResultDict __all__ = ["analyze"] def analyze( problem: Dict, X: np.array, Y: np.array, sample_sets: int, num_resamples: int = 100, conf_level: float = 0.95, print_to_console: bool = False, seed: Optional[int] = None, ) -> Dict: """Radial Elementary Effects Analysis. Calculates `mu`, `mu_star`, `sigma` and `mu_star_conf` as with Morris OAT. - ``mu`` metric indicates the mean of the distribution - ``mu_star`` metric indicates the mean of the distribution of absolute values - ``sigma`` is the standard deviation of the distribution Notes ----- Compatible with: - :func:`SALib.sample.radial.radial_sobol.sample` - :func:`SALib.sample.radial.radial_mc.sample` References ---------- .. [1] Campolongo, F., Saltelli, A., Cariboni, J., 2011. From screening to quantitative sensitivity analysis: A unified approach. Computer Physics Communications 182, 978–988. https://www.sciencedirect.com/science/article/pii/S0010465510005321 DOI: 10.1016/j.cpc.2010.12.039 .. [2] Campolongo, F., Cariboni, J., Saltelli, A., 2007. An effective screening design for sensitivity analysis of large models. Environmental Modelling & Software 22, 1509–1518. https://doi.org/10.1016/j.envsoft.2006.10.004 Parameters ---------- problem : dict The SALib problem specification X : np.array An array containing the model inputs of dtype=float Y : np.array An array containing the model outputs of dtype=float sample_sets : int The number of sample sets used to create result set `Y` num_resamples : int The number of resamples to calculate `mu_star_conf` (default 100) conf_level : float The confidence interval level (default 0.95) print_to_console : bool Print results directly to console (default False) seed : int Seed value to use for np.random.seed Returns -------- Si : dict """ num_vars = problem["num_vars"] # Each `n`th item from 0-position is the baseline for # that N group. nth = num_vars + 1 assert ( X.shape[0] == Y.shape[0] ), "X and Y must be of corresponding size (number of X values must match number of Y values)" assert ( X.shape[0] / sample_sets ) == nth, "Number of parameter set groups must match number of parameters + 1" assert ( Y.shape[0] / sample_sets ) == nth, "Number of result set groups must match number of parameters + 1" if seed: np.random.seed(seed) ee = np.zeros((sample_sets, num_vars)) X_base = X[0::nth] Y_base = Y[0::nth] for i in range(num_vars): pos = i + 1 # Collect every `n`th element # which is the perturbation point x_tmp = X_base[:, i] - X[pos::nth, i] # Convert zero division nan to 0 try: ee[:, i] = np.nan_to_num((Y_base - Y[pos::nth]) / x_tmp) except ZeroDivisionError: ee[:, i] = 0.0 # End for Si = ResultDict((k, [None] * num_vars) for k in ["names", "mu", "mu_star", "sigma"]) Si["mu"] = np.average(ee, axis=0) Si["mu_star"] = np.average(np.abs(ee), axis=0) Si["mu_star_conf"] = compute_radial_ee_confidence( ee, sample_sets, num_resamples, conf_level ) Si["sigma"] = np.std(ee, ddof=1, axis=0) Si["names"] = problem["names"] if print_to_console: print(Si.to_df()) return Si def compute_radial_ee_confidence( ee: np.array, N: int, num_resamples: int, conf_level: float = 0.95 ) -> np.array: """Uses bootstrapping where the elementary effects are resampled with replacement to produce a histogram of resampled mu_star metrics. This resample is used to produce a confidence interval. Based on, and largely identical to, `morris.compute_mu_star_confidence`. Arguments --------- si : np.array The sensitivity effect for each parameter N : int The number of sample sets used num_resamples : int The number of resamples to calculate `mu_star_conf` (default 1000) conf_level : float The confidence interval level (default 0.95) Returns --------- conf : np.array Confidence bounds for mu_star for each parameter """ if not 0 < conf_level < 1: raise ValueError("Confidence level must be between 0-1.") resample_index = np.random.randint(ee.shape[0], size=(num_resamples, N)) ee_resampled = ee[resample_index] # Compute average of the absolute values over each of the resamples mu_star_resampled = np.average(np.abs(ee_resampled), axis=1) return norm.ppf(0.5 + conf_level / 2.0) * mu_star_resampled.std(ddof=1, axis=0) def cli_parse(parser): parser.add_argument( "-X", "--model-input-file", type=str, required=True, default=None, help="Model input file", ) parser.add_argument( "-n", "--sample_sets", type=int, required=True, help="Number of sample sets used", ) parser.add_argument( "-r", "--resamples", type=int, required=False, default=1000, help="Number of bootstrap resamples for \ confidence intervals", ) parser.add_argument( "-L", "--conf_level", type=float, required=False, default=0.95, help="The confidence interval level (default: 0.95)", ) return parser def cli_action(args): problem = read_param_file(args.paramfile) X = np.loadtxt(args.model_input_file, delimiter=args.delimiter) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,) ) num_samples = args.sample_sets analyze( problem, X, Y, num_samples, num_resamples=args.num_resamples, conf_level=args.conf_level, print_to_console=True, seed=args.seed, ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/analyze/rbd_fast.py000066400000000000000000000130501525347100600213310ustar00rootroot00000000000000# coding=utf8 import numpy as np from scipy.signal import periodogram from scipy.stats import norm from typing import Optional, Union from . import common_args from ..util import read_param_file, ResultDict, handle_seed def analyze( problem, X, Y, M=10, num_resamples=100, conf_level=0.95, print_to_console=False, seed: Optional[Union[int, np.random.Generator]] = None, ): """Performs the Random Balanced Design - Fourier Amplitude Sensitivity Test (RBD-FAST) on model outputs. Returns a dictionary with keys 'S1', where each entry is a list of size D (the number of parameters) containing the indices in the same order as the parameter file. Notes ----- Compatible with: all samplers Examples -------- >>> X = latin.sample(problem, 1000) >>> Y = Ishigami.evaluate(X) >>> Si = rbd_fast.analyze(problem, X, Y, print_to_console=False) Parameters ---------- problem : dict The problem definition X : numpy.array A NumPy array containing the model inputs Y : numpy.array A NumPy array containing the model outputs M : int The interference parameter, i.e., the number of harmonics to sum in the Fourier series decomposition (default 10) print_to_console : bool Print results directly to console (default False) seed : int Seed to generate a random number References ---------- 1. S. Tarantola, D. Gatelli and T. Mara (2006) Random Balance Designs for the Estimation of First Order Global Sensitivity Indices, Reliability Engineering and System Safety, 91:6, 717-727 https://doi.org/10.1016/j.ress.2005.06.003 2. Elmar Plischke (2010) An effective algorithm for computing global sensitivity indices (EASI), Reliability Engineering & System Safety, 95:4, 354-360. doi:10.1016/j.ress.2009.11.005 3. Jean-Yves Tissot, Clémentine Prieur (2012) Bias correction for the estimation of sensitivity indices based on random balance designs, Reliability Engineering and System Safety, Elsevier, 107, 205-213. doi:10.1016/j.ress.2012.06.010 4. Jeanne Goffart, Mickael Rabouille & Nathan Mendes (2015) Uncertainty and sensitivity analysis applied to hygrothermal simulation of a brick building in a hot and humid climate, Journal of Building Performance Simulation. doi:10.1080/19401493.2015.1112430 """ rng = handle_seed(seed) D = problem["num_vars"] N = Y.size # Calculate and Output the First Order Value Si = ResultDict((k, [None] * D) for k in ["S1", "S1_conf"]) Si["names"] = problem["names"] for i in range(D): S1 = compute_first_order(permute_outputs(X[:, i], Y), M) S1 = unskew_S1(S1, M, N) Si["S1"][i] = S1 Si["S1_conf"][i] = bootstrap(X[:, i], Y, M, num_resamples, conf_level, rng) if print_to_console: print(Si.to_df()) return Si def permute_outputs(X, Y): """ Permute the output according to one of the inputs as in [_2] References ---------- .. [2] Elmar Plischke (2010) "An effective algorithm for computing global sensitivity indices (EASI) Reliability Engineering & System Safety", 95:4, 354-360. doi:10.1016/j.ress.2009.11.005 """ permutation_index = np.argsort(X) permutation_index = np.concatenate( [permutation_index[::2], permutation_index[1::2][::-1]] ) return Y[permutation_index] def compute_first_order(permuted_outputs, M): _, Pxx = periodogram(permuted_outputs) V = np.sum(Pxx[1:]) D1 = np.sum(Pxx[1 : M + 1]) return D1 / V def unskew_S1(S1, M, N): """ Unskew the sensitivity indices (Jean-Yves Tissot, Clémentine Prieur (2012) "Bias correction for the estimation of sensitivity indices based on random balance designs.", Reliability Engineering and System Safety, Elsevier, 107, 205-213. doi:10.1016/j.ress.2012.06.010) """ lamb = (2 * M) / N return S1 - lamb / (1 - lamb) * (1 - S1) def bootstrap(X_d, Y, M, resamples, conf_level, rng): # Use half of available data each time T_data = X_d.shape[0] n_size = int(T_data * 0.5) res = np.zeros(resamples) for i in range(resamples): sample_idx = rng.choice(T_data, replace=True, size=n_size) X_rs, Y_rs = X_d[sample_idx], Y[sample_idx] S1 = compute_first_order(permute_outputs(X_rs, Y_rs), M) S1 = unskew_S1(S1, M, Y_rs.size) res[i] = S1 return norm.ppf(0.5 + conf_level / 2.0) * res.std(ddof=1) def cli_parse(parser): parser.add_argument( "-X", "--model-input-file", type=str, required=True, help="Model input file" ) parser.add_argument( "-M", "--M", type=int, required=False, default=10, help="Inference parameter" ) parser.add_argument( "-r", "--resamples", type=int, required=False, default=100, help="Number of bootstrap resamples for Sobol " "confidence intervals", ) return parser def cli_action(args): problem = read_param_file(args.paramfile) X = np.loadtxt(args.model_input_file, delimiter=args.delimiter) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,) ) analyze( problem, X, Y, M=args.M, num_resamples=args.resamples, print_to_console=True, seed=args.seed, ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/analyze/rsa.py000066400000000000000000000223251525347100600203370ustar00rootroot00000000000000from typing import Dict from types import MethodType import warnings import numpy as np import pandas as pd from scipy.stats import cramervonmises_2samp from . import common_args from ..util import read_param_file, ResultDict, extract_group_names, _check_groups def analyze( problem: Dict, X: np.ndarray, Y: np.ndarray, bins: int = 20, target: str = "Y", print_to_console: bool = False, seed: int = None, ): """ Perform Regional Sensitivity Analysis (RSA), also known as Monte Carlo Filtering. In a usual RSA, a desirable region of output space is defined. Outputs which fall within this region is categorized as being "behavioral" (:math:`B`), and those outside are described as being "non-behavioral" (:math:`\\bar{B}`). The input factors are also partitioned into behavioral and non-behavioral subsets, such that :math:`f(X_{i}|B) \\rightarrow (Y|B)` and :math:`f(X_{i}|\\bar{B}) \\rightarrow (Y|\\bar{B})`. The distribution between the two sub-samples are compared for each factor. The greater the difference between the two distributions, the more important the given factor is in driving model outputs. The approach implemented in SALib partitions factor or output space into :math:`b` bins (default: 20) according to their percentile values. Output space is targeted for analysis by default (:code:`target="Y"`), such that :math:`(Y|b_{i})` is mapped back to :math:`(X_{i}|b_{i})`. In other words, we treat outputs falling within a given bin (:math:`b_{i}`) corresponding to their inputs as behavioral, and those outside the bin as non-behavioral. This aids in answering the question "Which :math:`X_{i}` contributes most toward a given range of outputs?". Factor space can also be assessed (:code:`target="X"`), such that :math:`f(X_{i}|b_{i}) \\rightarrow (Y|b_{i})` and :math:`f(X_{i}|b_{\\sim i}) \\rightarrow (Y|b_{\\sim i})`. This aids in answering the question "where in factor space are outputs most sensitive to?" The two-sample Cramér-von Mises (CvM) test is used to compare distributions. Results of the analysis indicate sensitivity across factor/output space. As the Cramér-von Mises criterion ranges from 0 to :math:`\\infty`, a value of zero will indicates the two distributions being compared are identical, with larger values indicating greater differences. Notes ----- Compatible with: all samplers When applied to grouped factors, the analysis is conducted on each factor individually, and the mean of the results for a group are reported. Increasing the value of :code:`bins` increases the granularity of the analysis (across factor space), but necessitates larger sample sizes. This analysis will produce NaNs, indicating areas of factor space that did not have any samples, or for which the outputs were constant. Analysis results are normalized against the maximum value such that 1.0 indicates the greatest sensitivity. Parameters ---------- problem : dict The problem definition X : numpy.array A NumPy array containing the model inputs Y : numpy.array A NumPy array containing the model outputs bins : int The number of bins to use (default: 20) target : str Assess factor space ("X") or output space ("Y") (default: "Y") print_to_console : bool Print results directly to console (default False) seed : int Seed value to ensure deterministic results Unused, but defined to maintain compatibility. References ---------- 1. Hornberger, G. M., and R. C. Spear. 1981. Approach to the preliminary analysis of environmental systems. Journal of Environmental Management 12:1. https://www.osti.gov/biblio/6396608-approach-preliminary-analysis-environmental-systems 2. Pianosi, F., K. Beven, J. Freer, J. W. Hall, J. Rougier, D. B. Stephenson, and T. Wagener. 2016. Sensitivity analysis of environmental models: A systematic review with practical workflow. Environmental Modelling & Software 79:214-232. https://dx.doi.org/10.1016/j.envsoft.2016.02.008 3. Saltelli, A., M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, and S. Tarantola. 2008. Global Sensitivity Analysis: The Primer. Wiley, West Sussex, U.K. https://dx.doi.org/10.1002/9780470725184 Accessible at: http://www.andreasaltelli.eu/file/repository/Primer_Corrected_2022.pdf """ results = rsa(X, Y, bins, target) groups = _check_groups(problem) var_names, n_groups = extract_group_names(problem) if groups: groups = np.array(var_names) tmp = np.full((bins, n_groups), np.nan) # Take the mean of effects from parameters that are grouped together for grp_id, grp in enumerate(groups): tmp[:, grp_id] = np.nanmean(results[:, groups == grp], axis=1) results = tmp tmp = None Si = ResultDict([(g, results[:, i]) for i, g in enumerate(var_names)]) Si["names"] = var_names Si["bins"] = np.arange(0.0, 1.0, (1.0 / bins)) Si["target"] = target # Attach object methods specific to this sensitivity method to ResultDict. Si.to_df = MethodType(to_df, Si) Si._plot = Si.plot Si.plot = MethodType(plot, Si) if print_to_console: print(Si.to_df()) return Si def rsa(X: np.ndarray, y: np.ndarray, bins: int = 10, target="X") -> np.ndarray: N, D = X.shape # Pre-allocated arrays to store data/results seq = np.append(np.arange(0.0, 1.0, (1 / bins)), 1.0) X_di = np.empty(N) # store of factor values r_s = np.full((bins, D), np.nan) # results if target == "X": t_arr = X_di # target factor space for analysis m_arr = y # map behavioral region of factor space to output space elif target == "Y": t_arr = y # target output space for analysis m_arr = X_di # map outputs back to factor space with warnings.catch_warnings(): warnings.simplefilter("ignore") for d_i in range(D): X_di[:] = X[:, d_i] # Assess first bin separately, making sure that the # bin edges are inclusive of the lower bound quants = np.quantile(t_arr, seq) b = (quants[0] <= t_arr) & (t_arr <= quants[1]) if _has_samples(y, b): r_s[0, d_i] = cramervonmises_2samp(m_arr[b], m_arr[~b]).statistic # Then assess the other bins for s in range(1, bins): b = (quants[s] < t_arr) & (t_arr <= quants[s + 1]) if _has_samples(y, b): r_s[s, d_i] = cramervonmises_2samp(m_arr[b], m_arr[~b]).statistic return r_s def _has_samples(y, sel): """Check if the given region of factor space has > 0 samples. Returns ------- bool, true if > 0 non-unique samples are found, false otherwise. """ return ( (np.count_nonzero(sel) != 0) and (len(y[~sel]) != 0) and np.unique(y[sel]).size > 1 ) def to_df(self): """Conversion to Pandas DataFrame specific to Regional Sensitivity Analysis results. Overrides the conversion method attached to the SALib problem spec. Returns ------- Pandas DataFrame """ names = self["names"] # Only convert these elements in dict to DF new_spec = {k: v for k, v in self.items() if k not in ["names", "bins", "target"]} return pd.DataFrame(new_spec, columns=names, index=self["bins"]) def plot(self, factors=None): """Plotting for Regional Sensitivity Analysis. Overrides the plot method attached to the SALib problem spec. """ import matplotlib.pyplot as plt Si_df = self.to_df() fig, ax = plt.subplots() xlabel = f"${self['target']}$ (Percentile)" ylabel = "$CvM_{i}$" if factors is None: factors = slice(None) with warnings.catch_warnings(): warnings.simplefilter("ignore") ax = Si_df.loc[:, factors].plot( ax=ax, xlabel=xlabel, ylabel=ylabel, subplots=True, legend=False, sharey=True, sharex=True, ) fig.legend(bbox_to_anchor=(1.1, 1.0)) fig.tight_layout() return ax def cli_parse(parser): parser.add_argument( "-X", "--model-input-file", type=str, required=True, help="Model input file" ) parser.add_argument( "-b", "--bins", type=int, required=False, help="Number of bins to partition target space into", ) parser.add_argument( "-t", "--target", type=str, required=False, help="Target input space (X) or output space (Y)", ) return parser def cli_action(args): problem = read_param_file(args.paramfile) X = np.loadtxt(args.model_input_file, delimiter=args.delimiter) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,) ) analyze( problem, X, Y, bins=args.bins, target=args.target, print_to_console=True, seed=args.seed, ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/analyze/shapley.py000066400000000000000000000200171525347100600212130ustar00rootroot00000000000000from types import MethodType import numpy as np from scipy.stats import norm from . import common_args from ..util import ResultDict, read_param_file from ..plotting.shapley import plot as shapley_plot def analyze( problem: dict, X: np.ndarray, Y: np.ndarray, conf_level: float = 0.95, print_to_console: bool = False, ) -> ResultDict: """Estimate Shapley effects with Goda's Monte Carlo algorithm. Returns Shapley effects in output-variance units (``shapley``, summing to the overall output variance) alongside normalized shares that sum to one (``shapley_normalized``), each with a normal-approximation confidence interval half-width (``shapley_conf``, ``shapley_normalized_conf``). Notes ----- Compatible with: Compatible with :func:`SALib.sample.shapley.sample`. The estimator assumes mutually independent inputs and does not support grouped parameters. Parameters ---------- problem : dict The problem definition. X : numpy.ndarray Model inputs generated by :func:`SALib.sample.shapley.sample`. Y : numpy.ndarray One-dimensional array of model outputs. conf_level : float, default=0.95 Confidence level used for normal-approximation interval half-widths. print_to_console : bool, default=False Print results directly to the console. Returns ------- ResultDict Raw and normalized Shapley effect estimates, their confidence interval half-widths, and factor names. References ---------- 1. Goda, T. (2021). A simple algorithm for global sensitivity analysis with Shapley effects. Reliability Engineering & System Safety, 213, 107702. https://doi.org/10.1016/j.ress.2021.107702 """ _validate_ungrouped(problem) X, Y, num_trajectories = _validate_inputs(problem, X, Y, conf_level) num_vars = problem["num_vars"] trajectory_size = num_vars + 1 trajectories = X.reshape(num_trajectories, trajectory_size, num_vars) outputs = Y.reshape(num_trajectories, trajectory_size) # Each trajectory step changes exactly one factor; recover which one by # diffing consecutive rows, then scatter the step-ordered contributions # into factor-ordered columns with a single vectorized reorder instead of # a per-trajectory, per-step Python loop. changed = trajectories[:, 1:, :] != trajectories[:, :-1, :] change_counts = changed.sum(axis=2) mismatched_steps = change_counts != 1 if np.any(mismatched_steps): # Identify location of mismatch trajectory_index, step = ( int(i) for i in np.unravel_index(np.argmax(mismatched_steps), change_counts.shape) ) raise ValueError( "Each Shapley trajectory step must change exactly one factor; " f"trajectory {trajectory_index}, step {step + 1} changed " f"{int(change_counts[trajectory_index, step])}." ) factors = changed.argmax(axis=2) incomplete = np.any(np.sort(factors, axis=1) != np.arange(num_vars), axis=1) if np.any(incomplete): trajectory_index = int(np.argmax(incomplete)) raise ValueError( "Each Shapley trajectory must change every factor exactly once; " f"trajectory {trajectory_index} does not." ) base_output = outputs[:, :1] before = outputs[:, :-1] after = outputs[:, 1:] step_contributions = (base_output - (before + after) / 2.0) * (before - after) contributions = np.empty_like(step_contributions) np.put_along_axis(contributions, factors, step_contributions, axis=1) effects = contributions.mean(axis=0) estimator_variance = contributions.var(axis=0, ddof=1) / num_trajectories z_score = norm.ppf(0.5 + conf_level / 2.0) confidence = z_score * np.sqrt(estimator_variance) normalized, normalized_confidence = _normalize_with_confidence( contributions, effects, z_score ) result = ResultDict( shapley_normalized=normalized, shapley_normalized_conf=normalized_confidence, shapley=effects, shapley_conf=confidence, names=problem["names"], ) result.plot = MethodType(shapley_plot, result) if print_to_console: print(result.to_df()) return result def _normalize_with_confidence(contributions, effects, z_score): """Estimate normalized Shapley shares and their confidence half-widths. Each trajectory's per-factor contributions sum to that trajectory's own estimate of ``Var[Y]``, so the normalized share of a factor is a ratio of two correlated trajectory-averaged quantities: the mean contribution to that factor, and the mean row total. Its sampling variance is approximated with the standard delta-method formula for a ratio of means (e.g. Cochran, 1977, on ratio estimators), reusing the per-trajectory contributions already computed for the raw ``shapley_conf`` interval. """ num_trajectories = contributions.shape[0] row_sums = contributions.sum(axis=1) total = row_sums.mean() if total == 0.0: undefined = np.full_like(effects, np.nan) return undefined, undefined.copy() normalized = effects / total centered = contributions - effects centered_totals = row_sums - total var_contributions = np.sum(centered**2, axis=0) / (num_trajectories - 1) covar_with_total = np.sum(centered * centered_totals[:, None], axis=0) / ( num_trajectories - 1 ) var_total = np.sum(centered_totals**2) / (num_trajectories - 1) ratio_variance = ( var_contributions - 2.0 * normalized * covar_with_total + normalized**2 * var_total ) / (num_trajectories * total**2) # Guard against tiny negative values from floating-point round-off. ratio_variance = np.clip(ratio_variance, a_min=0.0, a_max=None) return normalized, z_score * np.sqrt(ratio_variance) def _validate_inputs(problem, X, Y, conf_level): if not 0 < conf_level < 1: raise ValueError("Confidence level must be between 0 and 1.") num_vars = problem["num_vars"] if num_vars <= 0: raise ValueError("The problem must contain at least one variable.") X = np.asarray(X) Y = np.asarray(Y) if X.ndim != 2 or X.shape[1] != num_vars: raise ValueError(f"X must have shape (N * (D + 1), {num_vars}).") if Y.ndim != 1: raise ValueError("Y must be a one-dimensional array.") if X.shape[0] != Y.size: raise ValueError("X and Y must contain the same number of rows.") if Y.size % (num_vars + 1): raise ValueError("The number of model outputs must be divisible by D + 1.") num_trajectories = Y.size // (num_vars + 1) if num_trajectories < 2: raise ValueError("At least two Shapley trajectories are required.") if not np.all(np.isfinite(X)) or not np.all(np.isfinite(Y)): raise ValueError("X and Y must contain only finite values.") return X, Y, num_trajectories def _validate_ungrouped(problem: dict) -> None: groups = problem.get("groups") if groups and list(groups) != list(problem.get("names", [])): raise ValueError("Goda's Shapley estimator does not support groups.") def cli_parse(parser): parser.add_argument( "-X", "--model-input-file", type=str, required=True, help="Model input file", ) parser.add_argument( "--conf-level", type=float, required=False, default=0.95, help="Confidence interval level", ) return parser def cli_action(args): """Analyze Shapley trajectories from command-line arguments.""" problem = read_param_file(args.paramfile) X = np.loadtxt(args.model_input_file, delimiter=args.delimiter, ndmin=2) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,), ndmin=1, ) analyze( problem, X, Y, conf_level=args.conf_level, print_to_console=True, ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/analyze/sobol.py000066400000000000000000000360271525347100600206740ustar00rootroot00000000000000from types import MethodType from warnings import warn from scipy.stats import norm import numpy as np import pandas as pd from . import common_args from ..util import read_param_file, ResultDict, extract_group_names from multiprocess import Pool, cpu_count from functools import partial from itertools import combinations, zip_longest CONST_RESULT_MSG = ( "Constant values encountered, indicating model evaluations " "(or subset of evaluations) produced identical values." ) def analyze( problem, Y, calc_second_order=True, num_resamples=100, conf_level=0.95, print_to_console=False, parallel=False, n_processors=None, keep_resamples=False, seed=None, ): """Perform Sobol Analysis on model outputs. Returns a dictionary with keys 'S1', 'S1_conf', 'ST', and 'ST_conf', where each entry is a list of size D (the number of parameters) containing the indices in the same order as the parameter file. If calc_second_order is True, the dictionary also contains keys 'S2' and 'S2_conf'. There are several approaches to estimating sensitivity indices. The general approach is described in [1]. The implementation offered here follows [2] for first and total order indices, whereas estimation of second order sensitivities follows [3]. A noteworthy point is the improvement to reduce error rates in sensitivity estimation is introduced in [4]. Notes ----- Compatible with: `saltelli` : :func:`SALib.sample.saltelli.sample` `sobol` : :func:`SALib.sample.sobol.sample` Examples -------- >>> X = saltelli.sample(problem, 512) >>> Y = Ishigami.evaluate(X) >>> Si = sobol.analyze(problem, Y, print_to_console=True) Parameters ---------- problem : dict The problem definition Y : numpy.array A NumPy array containing the model outputs calc_second_order : bool Calculate second-order sensitivities (default True) num_resamples : int The number of resamples (default 100) conf_level : float The confidence interval level (default 0.95) print_to_console : bool Print results directly to console (default False) parallel : bool Perform analysis in parallel if True n_processors : int Number of parallel processes (only used if parallel is True) keep_resamples : bool Whether or not to store intermediate resampling results (default False) seed : int Seed to generate a random number References ---------- 1. Sobol, I. M. (2001). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, 55(1-3):271-280, doi:10.1016/S0378-4754(00)00270-6. 2. Saltelli, A., P. Annoni, I. Azzini, F. Campolongo, M. Ratto, and S. Tarantola (2010). Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Computer Physics Communications, 181(2):259-270, doi:10.1016/j.cpc.2009.09.018. 3. Saltelli, A. (2002). Making best use of model evaluations to compute sensitivity indices. Computer Physics Communications, 145(2):280-297 doi:10.1016/S0010-4655(02)00280-1. 4. Sobol', I. M., Tarantola, S., Gatelli, D., Kucherenko, S. S., & Mauntz, W. (2007). Estimating the approximation error when fixing unessential factors in global sensitivity analysis. Reliability Engineering & System Safety, 92(7), 957-960. https://doi.org/10.1016/j.ress.2006.07.001 """ if seed: # Set seed to ensure CIs are the same rng = np.random.default_rng(seed).integers else: rng = np.random.randint # Determine if groups are defined and adjusting the number # of rows in the cross-sampled matrix accordingly _, D = extract_group_names(problem) if calc_second_order and Y.size % (2 * D + 2) == 0: N = int(Y.size / (2 * D + 2)) elif not calc_second_order and Y.size % (D + 2) == 0: N = int(Y.size / (D + 2)) else: raise RuntimeError( """ Incorrect number of samples in model output file. Confirm that calc_second_order matches option used during sampling.""" ) if not 0 < conf_level < 1: raise RuntimeError("Confidence level must be between 0-1.") # Normalize the model output. # Estimates of the Sobol' indices can be biased for non-centered outputs # so we center here by normalizing with the standard deviation. # Other approaches opt to subtract the mean. Y = (Y - Y.mean()) / Y.std() A, B, AB, BA = separate_output_values(Y, D, N, calc_second_order) r = rng(N, size=(N, num_resamples)) Z = norm.ppf(0.5 + conf_level / 2) if not parallel: S = create_Si_dict(D, num_resamples, keep_resamples, calc_second_order) for j in range(D): S["S1"][j] = first_order(A, AB[:, j], B) S1_conf_j = first_order(A[r], AB[r, j], B[r]) if keep_resamples: S["S1_conf_all"][:, j] = S1_conf_j var_diff = np.ptp(np.r_[A[r], B[r]]) if var_diff != 0.0: S["S1_conf"][j] = Z * S1_conf_j.std(ddof=1) else: S["S1_conf"][j] = 0.0 S["ST"][j] = total_order(A, AB[:, j], B) ST_conf_j = total_order(A[r], AB[r, j], B[r]) if keep_resamples: S["ST_conf_all"][:, j] = ST_conf_j if var_diff != 0.0: S["ST_conf"][j] = Z * ST_conf_j.std(ddof=1) else: S["ST_conf"][j] = 0.0 # Second order (+conf.) if calc_second_order: for j in range(D): for k in range(j + 1, D): S["S2"][j, k] = second_order(A, AB[:, j], AB[:, k], BA[:, j], B) S["S2_conf"][j, k] = Z * second_order( A[r], AB[r, j], AB[r, k], BA[r, j], B[r] ).std(ddof=1) else: tasks, n_processors = create_task_list(D, calc_second_order, n_processors) func = partial(sobol_parallel, Z, A, AB, BA, B, r) pool = Pool(n_processors) S_list = pool.map_async(func, tasks) pool.close() pool.join() S = Si_list_to_dict( S_list.get(), D, num_resamples, keep_resamples, calc_second_order ) # Add problem context and override conversion method for special case S.problem = problem S.to_df = MethodType(to_df, S) # Print results to console if print_to_console: res = S.to_df() for df in res: print(df) return S def first_order(A, AB, B): """ First order estimator following Saltelli et al. 2010 CPC, normalized by sample variance """ y = np.r_[A, B] if np.ptp(y) <= np.finfo(float).eps: warn(CONST_RESULT_MSG) return np.zeros(y.shape[1:], dtype=np.float64) y_var = np.var(y, axis=0) return np.divide( np.mean(B * (AB - A), axis=0), y_var, out=np.zeros_like(y_var, dtype=np.float64), where=y_var > np.finfo(float).eps, ) def total_order(A, AB, B): """ Total order estimator following Saltelli et al. 2010 CPC, normalized by sample variance """ y = np.r_[A, B] if np.ptp(y) <= np.finfo(float).eps: warn(CONST_RESULT_MSG) return np.zeros(y.shape[1:], dtype=np.float64) y_var = np.var(y, axis=0) return np.divide( 0.5 * np.mean((A - AB) ** 2, axis=0), y_var, out=np.zeros_like(y_var, dtype=np.float64), where=y_var > np.finfo(float).eps, ) def second_order(A, ABj, ABk, BAj, B): """Second order estimator following Saltelli 2002""" y = np.r_[A, B] if np.ptp(y) <= np.finfo(float).eps: warn(CONST_RESULT_MSG) return np.zeros(y.shape[1:], dtype=np.float64) y_var = np.var(y, axis=0) Vjk = np.divide( np.mean(BAj * ABk - A * B, axis=0), y_var, out=np.zeros_like(y_var, dtype=np.float64), where=y_var > np.finfo(float).eps, ) Sj = first_order(A, ABj, B) Sk = first_order(A, ABk, B) return Vjk - Sj - Sk def create_Si_dict( D: int, num_resamples: int, keep_resamples: bool, calc_second_order: bool ): """initialize empty dict to store sensitivity indices""" S = ResultDict((k, np.zeros(D)) for k in ("S1", "S1_conf", "ST", "ST_conf")) if keep_resamples: # Create entries to store intermediate resampling results S["S1_conf_all"] = np.zeros((num_resamples, D)) S["ST_conf_all"] = np.zeros((num_resamples, D)) if calc_second_order: S["S2"] = np.full((D, D), np.nan) S["S2_conf"] = np.full((D, D), np.nan) return S def separate_output_values(Y, D, N, calc_second_order): AB = np.zeros((N, D)) BA = np.zeros((N, D)) if calc_second_order else None step = 2 * D + 2 if calc_second_order else D + 2 A = Y[0 : Y.size : step] B = Y[(step - 1) : Y.size : step] for j in range(D): AB[:, j] = Y[(j + 1) : Y.size : step] if calc_second_order: BA[:, j] = Y[(j + 1 + D) : Y.size : step] return A, B, AB, BA def sobol_parallel(Z, A, AB, BA, B, r, tasks): sobol_indices = [] for d, j, k in tasks: if d == "S1": s = first_order(A, AB[:, j], B) elif d == "S1_conf": s = Z * first_order(A[r], AB[r, j], B[r]).std(ddof=1) elif d == "ST": s = total_order(A, AB[:, j], B) elif d == "ST_conf": s = Z * total_order(A[r], AB[r, j], B[r]).std(ddof=1) elif d == "S2": s = second_order(A, AB[:, j], AB[:, k], BA[:, j], B) elif d == "S2_conf": s = Z * second_order(A[r], AB[r, j], AB[r, k], BA[r, j], B[r]).std(ddof=1) sobol_indices.append([d, j, k, s]) return sobol_indices def create_task_list(D, calc_second_order, n_processors): """ Create list with one entry (key, parameter 1, parameter 2) per sobol index (+conf.). This is used to supply parallel tasks to multiprocessing.Pool """ tasks_first_order = [ [d, j, None] for j in range(D) for d in ("S1", "S1_conf", "ST", "ST_conf") ] # Add second order (+conf.) to tasks tasks_second_order = [] if calc_second_order: tasks_second_order = [ [d, j, k] for j in range(D) for k in range(j + 1, D) for d in ("S2", "S2_conf") ] if n_processors is None: n_processors = min( cpu_count(), len(tasks_first_order) + len(tasks_second_order) ) if not calc_second_order: tasks = np.array_split(tasks_first_order, n_processors) else: # merges both lists alternating its elements and splits the # resulting lists into n_processors sublists tasks = np.array_split( [ v for v in sum( zip_longest(tasks_first_order[::-1], tasks_second_order), () ) if v is not None ], n_processors, ) return tasks, n_processors def Si_list_to_dict( S_list, D: int, num_resamples: int, keep_resamples: bool, calc_second_order: bool ): """Convert the parallel output into the regular dict format for printing/returning""" S = create_Si_dict(D, num_resamples, keep_resamples, calc_second_order) L = [] for list in S_list: # first reformat to flatten L += list for s in L: # First order (+conf.) if s[2] is None: S[s[0]][s[1]] = s[3] else: S[s[0]][s[1], s[2]] = s[3] return S def Si_to_pandas_dict(S_dict): """Convert Si information into Pandas DataFrame compatible dict. Examples -------- >>> X = saltelli.sample(problem, 512) >>> Y = Ishigami.evaluate(X) >>> Si = sobol.analyze(problem, Y, print_to_console=True) >>> T_Si, first_Si, (idx, second_Si) = sobol.Si_to_pandas_dict(Si, problem) Parameters ---------- S_dict : ResultDict Sobol sensitivity indices See Also -------- Si_list_to_dict Returns ------- tuple : of total, first, and second order sensitivities. Total and first order are dicts. Second order sensitivities contain a tuple of parameter name combinations for use as the DataFrame index and second order sensitivities. If no second order indices found, then returns tuple of (None, None) """ total_order = {"ST": S_dict["ST"], "ST_conf": S_dict["ST_conf"]} first_order = {"S1": S_dict["S1"], "S1_conf": S_dict["S1_conf"]} idx = None second_order = None if "S2" in S_dict: names, _ = extract_group_names(S_dict.problem) if len(names) > 2: idx = list(combinations(names, 2)) else: idx = (names,) second_order = { "S2": [S_dict["S2"][names.index(i[0]), names.index(i[1])] for i in idx], "S2_conf": [ S_dict["S2_conf"][names.index(i[0]), names.index(i[1])] for i in idx ], } return total_order, first_order, (idx, second_order) def to_df(self): """Conversion method to Pandas DataFrame. To be attached to ResultDict. Returns ------- List : of Pandas DataFrames in order of Total, First, Second Examples -------- >>> Si = sobol.analyze(problem, Y, print_to_console=True) >>> total_Si, first_Si, second_Si = Si.to_df() """ total, first, (idx, second) = Si_to_pandas_dict(self) names, _ = extract_group_names(self.problem) ret = [pd.DataFrame(total, index=names), pd.DataFrame(first, index=names)] if second: ret += [pd.DataFrame(second, index=idx)] return ret def cli_parse(parser): parser.add_argument( "--max-order", type=int, required=False, default=2, choices=[1, 2], help="Maximum order of sensitivity indices to " "calculate", ) parser.add_argument( "-r", "--resamples", type=int, required=False, default=100, help="Number of bootstrap resamples for Sobol " "confidence intervals", ) parser.add_argument( "--parallel", action="store_true", help="Makes " "use of parallelization.", dest="parallel", ) parser.add_argument( "--processors", type=int, required=False, default=None, help="Number of processors to be used with the " + "parallel option.", dest="n_processors", ) return parser def cli_action(args): problem = read_param_file(args.paramfile) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,) ) analyze( problem, Y, (args.max_order == 2), num_resamples=args.resamples, print_to_console=True, parallel=args.parallel, n_processors=args.n_processors, seed=args.seed, ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/analyze/sobol_jansen.py000066400000000000000000000136051525347100600222270ustar00rootroot00000000000000import numpy as np from scipy.stats import norm from typing import Dict, Optional from SALib.sample import common_args from ..util import read_param_file, ResultDict __all__ = ["analyze"] def analyze( problem: Dict, Y: np.array, sample_sets: int, num_resamples: int = 1000, conf_level: float = 0.95, seed: Optional[int] = None, ) -> ResultDict: """Estimation of Total Sensitivity Index using the Jansen Sensitivity Estimator. Notes ----- Compatible with: - :func:`SALib.sample.radial.radial_sobol.sample` - :func:`SALib.sample.radial.radial_mc.sample` Arguments --------- problem : dict The SALib problem specification Y : np.array An array containing the model outputs of dtype=float sample_sets : int The number of sample sets used to create `X` num_resamples : int The number of resamples to calculate `mu_star_conf` (default 1000) conf_level : float The confidence interval level (default 0.95) seed : int Seed value to use for np.random.seed Returns -------- Si : ResultDict Usage Example ------------- ```python >>> from SALib.sample.radial.radial_sobol import sample >>> X = sample(problem, N, seed) >>> r_Y = Sobol_G.evaluate(X) >>> sobol_jansen.analyze(problem, Y, N, num_resamples=1000) ``` References ---------- .. [1] Campolongo, F., Saltelli, A., Cariboni, J., 2011. From screening to quantitative sensitivity analysis: A unified approach. Computer Physics Communications 182, 978–988. https://www.sciencedirect.com/science/article/pii/S0010465510005321 DOI: 10.1016/j.cpc.2010.12.039 .. [2] M.J.W. Jansen, Analysis of variance designs for model output, Computer Physics Communication 117 (1999) 35–43. https://www.sciencedirect.com/science/article/pii/S0010465598001544 DOI: 10.1016/S0010-4655(98)00154-4 .. [3] M.J.W. Jansen, W.A.H. Rossing, R.A. Daamen, Monte Carlo estimation of uncertainty contributions from several independent multivariate sources, in: J. Gasmanand, G. van Straten (Eds.), Predictability and Nonlinear Modelling in Natural Sciences and Economics, Kluwer Academic Publishers, Dordrecht, 1994, pp. 334–343 DOI: 10.1007/978-94-011-0962-8_28 """ num_vars = problem["num_vars"] assert ( Y.shape[0] / sample_sets ) == num_vars + 1, "Number of result set groups must match number of parameters + 1" if seed: np.random.seed(seed) st = np.zeros((sample_sets, num_vars)) # Each `n`th item from 0-position is the baseline for that N group. nth = num_vars + 1 Y_base = Y[0::nth] base_variance = np.var(Y_base) for i in range(num_vars): pos = i + 1 # Collect change for every `n`th element st[:, i] = Y_base - Y[pos::nth] Si = ResultDict((k, [None] * num_vars) for k in ["names", "ST", "ST_conf"]) Si["ST"] = jansen_estimator(sample_sets, st) / base_variance Si["ST_conf"] = compute_radial_si_confidence( st, sample_sets, base_variance, num_resamples, conf_level ) Si["names"] = problem["names"] return Si def compute_radial_si_confidence( si: np.array, N: int, base_variance: np.array, num_resamples: int = 1000, conf_level: float = 0.95, ) -> np.array: """Uses bootstrapping where the sensitivity are resampled with replacement to produce a histogram of resampled metrics. This resample is used to produce a confidence interval. Largely identical to `morris.compute_mu_star_confidence`. Modified calculate conf for all parameters in one step. Arguments --------- si : np.array The sensitivity effect for each parameter N : int The number of sample sets used to create `si` num_resamples : int The number of bootstrap resamples of `ST` (default 1000) conf_level : float The confidence interval level (default 0.95) Returns --------- conf : np.array Confidence bounds for mu_star for each parameter """ if not 0 < conf_level < 1: raise ValueError("Confidence level must be between 0 and 1.") if len(si.shape) > 1: num_params = si.shape[1] else: num_params = 1 idx = np.random.randint(len(si), size=(num_resamples, num_params)) resampled = jansen_estimator(N, si[idx]) / base_variance return norm.ppf(0.5 + conf_level / 2.0) * resampled.std(ddof=1, axis=0) def jansen_estimator(N: int, si: np.array) -> np.array: """ Jansen sensitivity estimator. Arguments --------- N : int Number of sample sets. si : np.array Values of (Y_base - Y_perturbed) Returns ------- jansen estimates : np.array """ return (1.0 / (2.0 * N)) * np.sum((si**2), axis=0) def cli_parse(parser): parser.add_argument( "-n", "--sample_sets", type=int, required=True, help="Number of sample sets used", ) parser.add_argument( "-r", "--num_resamples", type=int, required=False, default=1000, help="Number of bootstrap resamples for confidence intervals", ) parser.add_argument( "-L", "--conf_level", type=float, required=False, default=0.95, help="The confidence interval level (default: 0.95)", ) return parser def cli_action(args): problem = read_param_file(args.paramfile) Y = np.loadtxt( args.model_output_file, delimiter=args.delimiter, usecols=(args.column,) ) analyze( problem, Y, args.sample_sets, conf_level=args.conf_level, num_resamples=args.num_resamples, seed=args.seed, ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/plotting/000077500000000000000000000000001525347100600173715ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/plotting/__init__.py000066400000000000000000000000001525347100600214700ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/plotting/bar.py000066400000000000000000000020061525347100600205050ustar00rootroot00000000000000__all__ = ["plot"] # magic string indicating DF columns holding conf bound values CONF_COLUMN = "_conf" def plot(Si_df, ax=None): """Create bar chart of results. Examples -------- >>> from SALib.plotting.bar import plot as barplot >>> from SALib.test_functions import Ishigami >>> >>> # See README for example problem specification >>> >>> X = saltelli.sample(problem, 512) >>> Y = Ishigami.evaluate(X) >>> Si = sobol.analyze(problem, Y, print_to_console=False) >>> total, first, second = Si.to_df() >>> barplot(total) Parameters ---------- * Si_df: pd.DataFrame, of sensitivity results Returns ------- * ax : matplotlib axes object """ conf_cols = Si_df.columns.str.contains(CONF_COLUMN) confs = Si_df.loc[:, conf_cols] confs.columns = [c.replace(CONF_COLUMN, "") for c in confs.columns] Sis = Si_df.loc[:, ~conf_cols] ax = Sis.plot(kind="bar", yerr=confs, ax=ax) return ax SALib-SALib-d6e51b1/src/SALib/plotting/hdmr.py000066400000000000000000000063411525347100600207010ustar00rootroot00000000000000""" Created on Dec 20, 2019 @author: @sahin-abdullah This submodule produces two different figures: (1) emulator vs simulator, (2) regression lines of first order component functions """ import matplotlib.pyplot as plt import numpy as np def plot(Si): # Close all figures plt.close("all") # Extract necessary data from Si try: problem = Si.problem except AttributeError: problem = Si Em = Si["Em"] RT = Si["RT"] Y_em = Si["Y_em"] idx = Si["idx"] X = Si["X"] Y = Si["Y"] # Get number of bootstrap from Runtime and sample size N K = RT.shape[0] N = Y.shape[0] row = 2 col = 5 try: ax = Si._plot() except AttributeError: # basic bar plot not found or is not available pass # Plot emulator performance Y_p = np.linspace(np.min(Y), np.max(Y), N, endpoint=True) start = max(0, K - 10) for i in range(start, K): # Only showing the last 10 if (i % (row * col) == 0) or (i == 0): fig = plt.figure(frameon=False) fig.suptitle("Showing last 10 Bootstrap Trials") it = 1 title_str = f"Trial {K - i}" ax = fig.add_subplot(row, col, it, frameon=True, title=title_str) ax.plot(Em["Y_e"][:, i], Y[idx[:, i]], "r+", label="Emulator") ax.plot(Y_p, Y_p, "darkgray", label="1:1 Line") ax.axis("square") ax.set_xlim(np.min(Y), np.max(Y)) ax.set_ylim(np.min(Y), np.max(Y)) it += 1 if i == (K - 1): handles, labels = ax.get_legend_handles_labels() fig.legend(handles, labels, loc="center right", bbox_to_anchor=(1.0, 0.5)) fig.tight_layout() # Now plot regression lines of component functions row = 3 col = 1 last_bootstrap = idx[:, -1] for i in range(X.shape[1]): if (i % (row * col) == 0) or (i == 0): fig = plt.figure(frameon=False) it = 1 title_str = ( "Regression of parameter " + problem["names"][i] + r"$^{(Last Trial)}$" ) ax = fig.add_subplot(row, col, it, frameon=True, title=title_str) ax.plot(X[last_bootstrap, i], Y[last_bootstrap], "r.") ax.plot(X[last_bootstrap, i], np.mean(Em["f0"]) + Y_em[:, i], "k.") ax.legend( [r"$\widetilde{Y}$", "$f_{" + str(i + 1) + "}$"], loc="upper left", bbox_to_anchor=(1.04, 1.0), ) it += 1 fig.tight_layout() plt.show() if "emulated" in Si: emulated = Si["emulated"] # Sum of squared residuals Y_test = Si["Y_test"] ssr = np.sum((emulated - Y_test) ** 2) # Plot testing results fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(6, 6)) ax.plot(emulated, Y_test, "r+", label="Emulator") ax.plot(Y_test, Y_test, "darkgray", label="1:1 Line") ax.axis("square") ax.set_xlabel("Emulator") ax.set_ylabel("New Observation") ax.set_xlim(np.min(Y_test), np.max(Y_test)) ax.set_ylim(np.min(Y_test), np.max(Y_test)) ax.legend(loc="lower right") plt.title(f"Testing results\nSSR = {ssr:.2f}") fig.tight_layout() plt.show() return ax if __name__ == "__main__": pass SALib-SALib-d6e51b1/src/SALib/plotting/heatmap.py000066400000000000000000000044051525347100600213650ustar00rootroot00000000000000from typing import Dict import numpy as np import matplotlib.pyplot as plt from ..util import extract_group_names __all__ = ["heatmap"] # magic string indicating DF columns holding conf bound values CONF_COLUMN = "_conf" def heatmap(sp: Dict, metric: str, index: str, title: str = None, ax=None): """Plot a heatmap of the target metric. Parameters ---------- sp : object, SALib ProblemSpec metric : str, metric to plot. Defaults to first metric/result output if `None`. index : str, sensitivity indices to plot ('S1', 'ST', etc). Displays all if `None`. title : str, plot title to use ax : axes object, matplotlib axes object to assign figure to. Returns ------- ax : matplotlib axes object """ if ax is None: fig, ax = plt.subplots(1, 1, figsize=(10, 6)) else: fig = plt.gcf() if metric is None: metric = sp["outputs"][0] if isinstance(metric, str): assert metric in sp["outputs"], f"Specified model output '{metric}' not found" is_multi_output = len(sp["outputs"]) > 1 if not index: if is_multi_output: index = list(sp.analysis[metric].keys()) else: index = list(sp.analysis.keys()) multi_index = isinstance(index, (list, tuple)) if multi_index: index = [k for k in index if not k.endswith(CONF_COLUMN) and k != "names"] if isinstance(index, str): index = [index] if is_multi_output: met_data = sp.analysis[metric] else: met_data = sp.analysis si_shape = met_data[index[0]].shape s_data = np.vstack([met_data[k] for k in index if met_data[k].shape == si_shape]) ax.imshow(s_data) fig.colorbar(ax.images[0], ax=ax, shrink=0.9) if title is None: title = metric ax.set_title(title) if isinstance(metric, str): metric = [metric] disp_names, _ = extract_group_names(sp) ax.xaxis.set_ticks(range(0, len(disp_names))) ax.xaxis.set_ticklabels(disp_names, rotation=90) # Account for indices that may have been filtered out # e.g., cannot easily show second-order values at the moment disp_idx = s_data.shape[0] ax.yaxis.set_ticks(range(0, len(index[0:disp_idx]))) ax.yaxis.set_ticklabels(index[0:disp_idx]) return ax SALib-SALib-d6e51b1/src/SALib/plotting/morris.py000066400000000000000000000104431525347100600212600ustar00rootroot00000000000000""" Created on 29 Jun 2015 @author: @willu47 This module provides the basic infrastructure for plotting charts for the Method of Morris results The procedures should build upon and return an axes instance:: import matplotlib.pyplot as plt Si = morris.analyze(problem, param_values, Y, conf_level=0.95, print_to_console=False, num_levels=10) # set plot style etc. fig, ax = plt.subplots(1) p = SALib.plotting.morris.horizontal_bar_plot(ax, Si, {'marker':'x'}) p.show() """ import numpy as np def _sort_Si(Si, key, sortby="mu_star"): return np.array([Si[key][x] for x in np.argsort(Si[sortby])]) def _sort_Si_by_index(Si, key, index): return np.array([Si[key][x] for x in index]) def horizontal_bar_plot(ax, Si, opts=None, sortby="mu_star", unit=""): """Updates a matplotlib axes instance with a horizontal bar plot of mu_star, with error bars representing mu_star_conf. """ assert sortby in ["mu_star", "mu_star_conf", "sigma", "mu"] if opts is None: opts = {} # Sort all the plotted elements by mu_star (or optionally another # metric) names_sorted = _sort_Si(Si, "names", sortby) mu_star_sorted = _sort_Si(Si, "mu_star", sortby) mu_star_conf_sorted = _sort_Si(Si, "mu_star_conf", sortby) # Plot horizontal barchart y_pos = np.arange(len(mu_star_sorted)) plot_names = names_sorted out = ax.barh( y_pos, mu_star_sorted, xerr=mu_star_conf_sorted, align="center", ecolor="black", **opts, ) ax.set_yticks(y_pos) ax.set_yticklabels(plot_names) ax.set_xlabel(r"$\mu^\star$" + unit) ax.set_ylim(min(y_pos) - 1, max(y_pos) + 1) return out def covariance_plot(ax, Si, opts=None, unit=""): """Plots mu* against sigma or the 95% confidence interval""" if opts is None: opts = {} if Si["sigma"] is not None: # sigma is not present if using morris groups y = Si["sigma"] out = ax.scatter(Si["mu_star"], y, c="k", marker="o", **opts) ax.set_ylabel(r"$\sigma$") ax.set_xlim( 0, ) ax.set_ylim( 0, ) x_axis_bounds = np.array(ax.get_xlim()) (line1,) = ax.plot(x_axis_bounds, x_axis_bounds, "k-") (line2,) = ax.plot(x_axis_bounds, 0.5 * x_axis_bounds, "k--") (line3,) = ax.plot(x_axis_bounds, 0.1 * x_axis_bounds, "k-.") ax.legend( (line1, line2, line3), ( r"$\sigma / \mu^{\star} = 1.0$", r"$\sigma / \mu^{\star} = 0.5$", r"$\sigma / \mu^{\star} = 0.1$", ), loc="best", ) else: y = Si["mu_star_conf"] out = ax.scatter(Si["mu_star"], y, c="k", marker="o", **opts) ax.set_ylabel(r"$95\% CI$") ax.set_xlabel(r"$\mu^\star$ " + unit) ax.set_ylim( 0 - (0.01 * np.array(ax.get_ylim()[1])), ) return out def sample_histograms(fig, input_sample, problem, opts=None): """Plots a set of subplots of histograms of the input sample""" if opts is None: opts = {} num_vars = problem["num_vars"] names = problem["names"] framing = 101 + (num_vars * 10) # Find number of levels num_levels = len(set(input_sample[:, 1])) out = [] for variable in range(num_vars): ax = fig.add_subplot(framing + variable) out.append( ax.hist( input_sample[:, variable], bins=num_levels, density=False, label=None, **opts, ) ) ax.set_title("%s" % (names[variable])) ax.tick_params( axis="x", # changes apply to the x-axis which="both", # both major and minor ticks are affected bottom="off", # ticks along the bottom edge are off top="off", # ticks along the top edge are off labelbottom="off", ) # labels along the bottom edge off) if variable > 0: ax.tick_params( axis="y", # changes apply to the y-axis which="both", # both major and minor ticks affected labelleft="off", ) # labels along the left edge off) return out if __name__ == "__main__": pass SALib-SALib-d6e51b1/src/SALib/plotting/shapley.py000066400000000000000000000027541525347100600214200ustar00rootroot00000000000000"""Bar chart for Shapley effects. Raw Shapley effects (output-variance units) and their normalized shares (unit interval, summing to one) sit on incompatible scales, so plotting all four ``shapley``/``shapley_conf``/``shapley_normalized``/ ``shapley_normalized_conf`` columns together in a single bar chart (the default behavior inherited from ``ResultDict.plot``) makes the smaller series unreadable. This module plots one pair at a time instead, defaulting to the normalized shares since those are what's usually of interest. """ import matplotlib.pyplot as plt from .bar import plot as barplot __all__ = ["plot"] def plot(Si, ax=None, normalized=True): """Plot Shapley effects as a bar chart. Parameters ---------- Si : ResultDict Analysis results, as returned by :func:`SALib.analyze.shapley.analyze`. ax : matplotlib axes object, optional Axes to plot onto. Creates a new figure if not provided. normalized : bool, default=True Plot the normalized shares (summing to one) rather than the raw effects in output-variance units. Returns ------- ax : matplotlib axes object """ df = Si.to_df() if normalized: cols = ["shapley_normalized", "shapley_normalized_conf"] title = "Normalized Shapley effects" else: cols = ["shapley", "shapley_conf"] title = "Shapley effects" if ax is None: _, ax = plt.subplots() barplot(df[cols], ax=ax) ax.set_title(title) return ax SALib-SALib-d6e51b1/src/SALib/sample/000077500000000000000000000000001525347100600170125ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/sample/__init__.py000066400000000000000000000000001525347100600211110ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/sample/common_args.py000066400000000000000000000035601525347100600216740ustar00rootroot00000000000000import argparse def setup(parser): """Add common sampling options to CLI parser. Parameters ---------- parser : argparse object Returns ------- Updated argparse object """ parser.add_argument( "-n", "--samples", type=int, required=True, help="Number of Samples" ) parser.add_argument( "-p", "--paramfile", type=str, required=True, help="Parameter Range File" ) parser.add_argument("-o", "--output", type=str, required=True, help="Output File") parser.add_argument( "-s", "--seed", type=int, required=False, default=None, help="Random Seed" ) parser.add_argument( "--delimiter", type=str, required=False, default=" ", help="Column delimiter" ) parser.add_argument( "--precision", type=int, required=False, default=8, help="Output floating-point precision", ) return parser def create(cli_parser=None): """Create CLI parser object. Parameters ---------- cli_parser : function [optional] Function to add method specific arguments to parser Returns ------- argparse object """ parser = argparse.ArgumentParser( description="Create parameter samples for sensitivity analysis" ) parser = setup(parser) if cli_parser: parser = cli_parser(parser) return parser def run_cli(cli_parser, run_sample, known_args=None): """Run sampling with CLI arguments. Parameters ---------- cli_parser : function Function to add method specific arguments to parser run_sample: function Method specific function that runs the sampling known_args: list [optional] Additional arguments to parse Returns ------- argparse object """ parser = create(cli_parser) args = parser.parse_args(known_args) run_sample(args) SALib-SALib-d6e51b1/src/SALib/sample/directions.py000066400000000000000000074412141525347100600215440ustar00rootroot00000000000000directions = ( (0, 1), (1, 1, 3), (1, 1, 3, 1), (2, 1, 1, 1), (1, 1, 1, 3, 3), (4, 1, 3, 5, 13), (2, 1, 1, 5, 5, 17), (4, 1, 1, 5, 5, 5), (7, 1, 1, 7, 11, 19), (11, 1, 1, 5, 1, 1), (13, 1, 1, 1, 3, 11), (14, 1, 3, 5, 5, 31), (1, 1, 3, 3, 9, 7, 49), (13, 1, 1, 1, 15, 21, 21), (16, 1, 3, 1, 13, 27, 49), (19, 1, 1, 1, 15, 7, 5), (22, 1, 3, 1, 15, 13, 25), (25, 1, 1, 5, 5, 19, 61), (1, 1, 3, 7, 11, 23, 15, 103), (4, 1, 3, 7, 13, 13, 15, 69), (7, 1, 1, 3, 13, 7, 35, 63), (8, 1, 3, 5, 9, 1, 25, 53), (14, 1, 3, 1, 13, 9, 35, 107), (19, 1, 3, 1, 5, 27, 61, 31), (21, 1, 1, 5, 11, 19, 41, 61), (28, 1, 3, 5, 3, 3, 13, 69), (31, 1, 1, 7, 13, 1, 19, 1), (32, 1, 3, 7, 5, 13, 19, 59), (37, 1, 1, 3, 9, 25, 29, 41), (41, 1, 3, 5, 13, 23, 1, 55), (42, 1, 3, 7, 3, 13, 59, 17), (50, 1, 3, 1, 3, 5, 53, 69), (55, 1, 1, 5, 5, 23, 33, 13), (56, 1, 1, 7, 7, 1, 61, 123), (59, 1, 1, 7, 9, 13, 61, 49), (62, 1, 3, 3, 5, 3, 55, 33), (14, 1, 3, 1, 15, 31, 13, 49, 245), (21, 1, 3, 5, 15, 31, 59, 63, 97), (22, 1, 3, 1, 11, 11, 11, 77, 249), (38, 1, 3, 1, 11, 27, 43, 71, 9), (47, 1, 1, 7, 15, 21, 11, 81, 45), (49, 1, 3, 7, 3, 25, 31, 65, 79), (50, 1, 3, 1, 1, 19, 11, 3, 205), (52, 1, 1, 5, 9, 19, 21, 29, 157), (56, 1, 3, 7, 11, 1, 33, 89, 185), (67, 1, 3, 3, 3, 15, 9, 79, 71), (70, 1, 3, 7, 11, 15, 39, 119, 27), (84, 1, 1, 3, 1, 11, 31, 97, 225), (97, 1, 1, 1, 3, 23, 43, 57, 177), (103, 1, 3, 7, 7, 17, 17, 37, 71), (115, 1, 3, 1, 5, 27, 63, 123, 213), (122, 1, 1, 3, 5, 11, 43, 53, 133), (8, 1, 3, 5, 5, 29, 17, 47, 173, 479), (13, 1, 3, 3, 11, 3, 1, 109, 9, 69), (16, 1, 1, 1, 5, 17, 39, 23, 5, 343), (22, 1, 3, 1, 5, 25, 15, 31, 103, 499), (25, 1, 1, 1, 11, 11, 17, 63, 105, 183), (44, 1, 1, 5, 11, 9, 29, 97, 231, 363), (47, 1, 1, 5, 15, 19, 45, 41, 7, 383), (52, 1, 3, 7, 7, 31, 19, 83, 137, 221), (55, 1, 1, 1, 3, 23, 15, 111, 223, 83), (59, 1, 1, 5, 13, 31, 15, 55, 25, 161), (62, 1, 1, 3, 13, 25, 47, 39, 87, 257), (67, 1, 1, 1, 11, 21, 53, 125, 249, 293), (74, 1, 1, 7, 11, 11, 7, 57, 79, 323), (81, 1, 1, 5, 5, 17, 13, 81, 3, 131), (82, 1, 1, 7, 13, 23, 7, 65, 251, 475), (87, 1, 3, 5, 1, 9, 43, 3, 149, 11), (91, 1, 1, 3, 13, 31, 13, 13, 255, 487), (94, 1, 3, 3, 1, 5, 63, 89, 91, 127), (103, 1, 1, 3, 3, 1, 19, 123, 127, 237), (104, 1, 1, 5, 7, 23, 31, 37, 243, 289), (109, 1, 1, 5, 11, 17, 53, 117, 183, 491), (122, 1, 1, 1, 5, 1, 13, 13, 209, 345), (124, 1, 1, 3, 15, 1, 57, 115, 7, 33), (137, 1, 3, 1, 11, 7, 43, 81, 207, 175), (138, 1, 3, 1, 1, 15, 27, 63, 255, 49), (143, 1, 3, 5, 3, 27, 61, 105, 171, 305), (145, 1, 1, 5, 3, 1, 3, 57, 249, 149), (152, 1, 1, 3, 5, 5, 57, 15, 13, 159), (157, 1, 1, 1, 11, 7, 11, 105, 141, 225), (167, 1, 3, 3, 5, 27, 59, 121, 101, 271), (173, 1, 3, 5, 9, 11, 49, 51, 59, 115), (176, 1, 1, 7, 1, 23, 45, 125, 71, 419), (181, 1, 1, 3, 5, 23, 5, 105, 109, 75), (182, 1, 1, 7, 15, 7, 11, 67, 121, 453), (185, 1, 3, 7, 3, 9, 13, 31, 27, 449), (191, 1, 3, 1, 15, 19, 39, 39, 89, 15), (194, 1, 1, 1, 1, 1, 33, 73, 145, 379), (199, 1, 3, 1, 15, 15, 43, 29, 13, 483), (218, 1, 1, 7, 3, 19, 27, 85, 131, 431), (220, 1, 3, 3, 3, 5, 35, 23, 195, 349), (227, 1, 3, 3, 7, 9, 27, 39, 59, 297), (229, 1, 1, 3, 9, 11, 17, 13, 241, 157), (230, 1, 3, 7, 15, 25, 57, 33, 189, 213), (234, 1, 1, 7, 1, 9, 55, 73, 83, 217), (236, 1, 3, 3, 13, 19, 27, 23, 113, 249), (241, 1, 3, 5, 3, 23, 43, 3, 253, 479), (244, 1, 1, 5, 5, 11, 5, 45, 117, 217), (253, 1, 3, 3, 7, 29, 37, 33, 123, 147), (4, 1, 3, 1, 15, 5, 5, 37, 227, 223, 459), (13, 1, 1, 7, 5, 5, 39, 63, 255, 135, 487), (19, 1, 3, 1, 7, 9, 7, 87, 249, 217, 599), (22, 1, 1, 3, 13, 9, 47, 7, 225, 363, 247), (50, 1, 3, 7, 13, 19, 13, 9, 67, 9, 737), (55, 1, 3, 5, 5, 19, 59, 7, 41, 319, 677), (64, 1, 1, 5, 3, 31, 63, 15, 43, 207, 789), (69, 1, 1, 7, 9, 13, 39, 3, 47, 497, 169), (98, 1, 3, 1, 7, 21, 17, 97, 19, 415, 905), (107, 1, 3, 7, 1, 3, 31, 71, 111, 165, 127), (115, 1, 1, 5, 11, 1, 61, 83, 119, 203, 847), (121, 1, 3, 3, 13, 9, 61, 19, 97, 47, 35), (127, 1, 1, 7, 7, 15, 29, 63, 95, 417, 469), (134, 1, 3, 1, 9, 25, 9, 71, 57, 213, 385), (140, 1, 3, 5, 13, 31, 47, 101, 57, 39, 341), (145, 1, 1, 3, 3, 31, 57, 125, 173, 365, 551), (152, 1, 3, 7, 1, 13, 57, 67, 157, 451, 707), (158, 1, 1, 1, 7, 21, 13, 105, 89, 429, 965), (161, 1, 1, 5, 9, 17, 51, 45, 119, 157, 141), (171, 1, 3, 7, 7, 13, 45, 91, 9, 129, 741), (181, 1, 3, 7, 1, 23, 57, 67, 141, 151, 571), (194, 1, 1, 3, 11, 17, 47, 93, 107, 375, 157), (199, 1, 3, 3, 5, 11, 21, 43, 51, 169, 915), (203, 1, 1, 5, 3, 15, 55, 101, 67, 455, 625), (208, 1, 3, 5, 9, 1, 23, 29, 47, 345, 595), (227, 1, 3, 7, 7, 5, 49, 29, 155, 323, 589), (242, 1, 3, 3, 7, 5, 41, 127, 61, 261, 717), (251, 1, 3, 7, 7, 17, 23, 117, 67, 129, 1009), (253, 1, 1, 3, 13, 11, 39, 21, 207, 123, 305), (265, 1, 1, 3, 9, 29, 3, 95, 47, 231, 73), (266, 1, 3, 1, 9, 1, 29, 117, 21, 441, 259), (274, 1, 3, 1, 13, 21, 39, 125, 211, 439, 723), (283, 1, 1, 7, 3, 17, 63, 115, 89, 49, 773), (289, 1, 3, 7, 13, 11, 33, 101, 107, 63, 73), (295, 1, 1, 5, 5, 13, 57, 63, 135, 437, 177), (301, 1, 1, 3, 7, 27, 63, 93, 47, 417, 483), (316, 1, 1, 3, 1, 23, 29, 1, 191, 49, 23), (319, 1, 1, 3, 15, 25, 55, 9, 101, 219, 607), (324, 1, 3, 1, 7, 7, 19, 51, 251, 393, 307), (346, 1, 3, 3, 3, 25, 55, 17, 75, 337, 3), (352, 1, 1, 1, 13, 25, 17, 65, 45, 479, 413), (361, 1, 1, 7, 7, 27, 49, 99, 161, 213, 727), (367, 1, 3, 5, 1, 23, 5, 43, 41, 251, 857), (382, 1, 3, 3, 7, 11, 61, 39, 87, 383, 835), (395, 1, 1, 3, 15, 13, 7, 29, 7, 505, 923), (398, 1, 3, 7, 1, 5, 31, 47, 157, 445, 501), (400, 1, 1, 3, 7, 1, 43, 9, 147, 115, 605), (412, 1, 3, 3, 13, 5, 1, 119, 211, 455, 1001), (419, 1, 1, 3, 5, 13, 19, 3, 243, 75, 843), (422, 1, 3, 7, 7, 1, 19, 91, 249, 357, 589), (426, 1, 1, 1, 9, 1, 25, 109, 197, 279, 411), (428, 1, 3, 1, 15, 23, 57, 59, 135, 191, 75), (433, 1, 1, 5, 15, 29, 21, 39, 253, 383, 349), (446, 1, 3, 3, 5, 19, 45, 61, 151, 199, 981), (454, 1, 3, 5, 13, 9, 61, 107, 141, 141, 1), (457, 1, 3, 1, 11, 27, 25, 85, 105, 309, 979), (472, 1, 3, 3, 11, 19, 7, 115, 223, 349, 43), (493, 1, 1, 7, 9, 21, 39, 123, 21, 275, 927), (505, 1, 1, 7, 13, 15, 41, 47, 243, 303, 437), (508, 1, 1, 1, 7, 7, 3, 15, 99, 409, 719), (2, 1, 3, 3, 15, 27, 49, 113, 123, 113, 67, 469), (11, 1, 3, 7, 11, 3, 23, 87, 169, 119, 483, 199), (21, 1, 1, 5, 15, 7, 17, 109, 229, 179, 213, 741), (22, 1, 1, 5, 13, 11, 17, 25, 135, 403, 557, 1433), (35, 1, 3, 1, 1, 1, 61, 67, 215, 189, 945, 1243), (49, 1, 1, 7, 13, 17, 33, 9, 221, 429, 217, 1679), (50, 1, 1, 3, 11, 27, 3, 15, 93, 93, 865, 1049), (56, 1, 3, 7, 7, 25, 41, 121, 35, 373, 379, 1547), (61, 1, 3, 3, 9, 11, 35, 45, 205, 241, 9, 59), (70, 1, 3, 1, 7, 3, 51, 7, 177, 53, 975, 89), (74, 1, 1, 3, 5, 27, 1, 113, 231, 299, 759, 861), (79, 1, 3, 3, 15, 25, 29, 5, 255, 139, 891, 2031), (84, 1, 3, 1, 1, 13, 9, 109, 193, 419, 95, 17), (88, 1, 1, 7, 9, 3, 7, 29, 41, 135, 839, 867), (103, 1, 1, 7, 9, 25, 49, 123, 217, 113, 909, 215), (104, 1, 1, 7, 3, 23, 15, 43, 133, 217, 327, 901), (112, 1, 1, 3, 3, 13, 53, 63, 123, 477, 711, 1387), (115, 1, 1, 3, 15, 7, 29, 75, 119, 181, 957, 247), (117, 1, 1, 1, 11, 27, 25, 109, 151, 267, 99, 1461), (122, 1, 3, 7, 15, 5, 5, 53, 145, 11, 725, 1501), (134, 1, 3, 7, 1, 9, 43, 71, 229, 157, 607, 1835), (137, 1, 3, 3, 13, 25, 1, 5, 27, 471, 349, 127), (146, 1, 1, 1, 1, 23, 37, 9, 221, 269, 897, 1685), (148, 1, 1, 3, 3, 31, 29, 51, 19, 311, 553, 1969), (157, 1, 3, 7, 5, 5, 55, 17, 39, 475, 671, 1529), (158, 1, 1, 7, 1, 1, 35, 47, 27, 437, 395, 1635), (162, 1, 1, 7, 3, 13, 23, 43, 135, 327, 139, 389), (164, 1, 3, 7, 3, 9, 25, 91, 25, 429, 219, 513), (168, 1, 1, 3, 5, 13, 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8031, 15391, 31263, 52657, 102721, 212195), (130748, 1, 3, 1, 7, 13, 41, 21, 103, 237, 649, 55, 1565, 6327, 8743, 15457, 29975, 34165, 80839), (130774, 1, 3, 5, 11, 15, 31, 121, 219, 375, 159, 731, 59, 3205, 15039, 10023, 46209, 34619, 110253), (130783, 1, 3, 3, 11, 31, 19, 79, 185, 363, 635, 463, 987, 2681, 6405, 30077, 21173, 14213, 58095), (130802, 1, 1, 5, 13, 23, 37, 57, 111, 293, 553, 269, 3393, 345, 1983, 1097, 47217, 22281, 212607), (130811, 1, 3, 5, 7, 7, 33, 65, 61, 185, 411, 187, 641, 6437, 4625, 17547, 38941, 81119, 48651), (130836, 1, 1, 7, 3, 19, 25, 39, 243, 139, 465, 691, 713, 7879, 14539, 31669, 35871, 130681, 255929), (130840, 1, 3, 1, 1, 3, 43, 87, 13, 179, 835, 719, 1189, 7207, 5863, 6077, 20669, 35469, 211155), (130856, 1, 3, 7, 13, 25, 59, 97, 129, 151, 985, 739, 1919, 7729, 14057, 21721, 17603, 82797, 181319), (130864, 1, 1, 7, 7, 5, 3, 21, 141, 379, 257, 207, 597, 4051, 7563, 25481, 59427, 45449, 61159), (130873, 1, 3, 3, 9, 11, 25, 5, 29, 131, 603, 637, 189, 4033, 13099, 15219, 4447, 73501, 135795), (130918, 1, 3, 1, 9, 1, 49, 57, 227, 141, 543, 1499, 3525, 3127, 11191, 4071, 47003, 7431, 155137), (130927, 1, 3, 1, 11, 27, 31, 15, 31, 113, 135, 1251, 245, 6965, 14263, 5679, 55201, 121453, 132503), (130929, 1, 1, 5, 15, 7, 23, 67, 163, 57, 513, 1809, 1343, 6165, 199, 31169, 30803, 86705, 71103), (130958, 1, 1, 3, 1, 15, 9, 75, 143, 273, 797, 819, 4037, 2305, 4841, 15697, 41191, 38187, 174131), (130966, 1, 3, 7, 7, 3, 55, 65, 135, 423, 185, 299, 2221, 7987, 4223, 28183, 32273, 95941, 260297), (130970, 1, 1, 7, 7, 7, 11, 67, 109, 507, 673, 1555, 2537, 7553, 4659, 3945, 20839, 32539, 43053), (130976, 1, 1, 7, 15, 1, 47, 61, 73, 211, 397, 1785, 4063, 6461, 13725, 11299, 17565, 80063, 118271), (131006, 1, 1, 7, 5, 29, 27, 97, 105, 379, 153, 915, 2795, 4933, 6729, 21207, 9995, 70241, 85641), (131008, 1, 3, 5, 5, 23, 13, 41, 67, 127, 649, 1351, 3597, 7077, 4989, 14649, 17401, 70883, 239841), (131020, 1, 1, 5, 1, 19, 1, 83, 3, 425, 873, 1943, 3935, 4257, 14587, 11829, 55217, 21963, 39683), (131059, 1, 1, 7, 11, 15, 7, 37, 239, 337, 245, 1557, 3681, 7357, 9639, 27367, 26869, 114603, 86317) ) SALib-SALib-d6e51b1/src/SALib/sample/fast_sampler.py000066400000000000000000000073531525347100600220540ustar00rootroot00000000000000import math from typing import Optional, Union import numpy as np from . import common_args from ..util import scale_samples, read_param_file, handle_seed def sample(problem, N, M=4, seed: Optional[Union[int, np.random.Generator]] = None): """Generate model inputs for extended Fourier Amplitude Sensitivity Test. Returns a NumPy matrix containing the model inputs required by the extended Fourier Amplitude sensitivity test. The resulting matrix contains N * D rows and D columns, where D is the number of parameters. The samples generated are intended to be used by :func:`SALib.analyze.fast.analyze`. Parameters ---------- problem : dict The problem definition N : int The number of samples to generate M : int The interference parameter, i.e., the number of harmonics to sum in the Fourier series decomposition (default 4) seed : {None, int, `numpy.random.Generator`}, optional If `seed` is None the `numpy.random.Generator` generator is used. If `seed` is an int, a new ``Generator`` instance is used, seeded with `seed`. If `seed` is already a ``Generator`` instance then that instance is used. Default is None. References ---------- 1. Cukier, R.I., Fortuin, C.M., Shuler, K.E., Petschek, A.G., Schaibly, J.H., 1973. Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I theory. Journal of Chemical Physics 59, 3873-3878. https://doi.org/10.1063/1.1680571 2. Saltelli, A., S. Tarantola, and K. P.-S. Chan (1999). A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output. Technometrics, 41(1):39-56, doi:10.1080/00401706.1999.10485594. """ rng = handle_seed(seed) if N <= 4 * M**2: raise ValueError( """ Sample size N > 4M^2 is required. M=4 by default.""" ) D = problem["num_vars"] omega = np.zeros([D]) omega[0] = math.floor((N - 1) / (2 * M)) m = math.floor(omega[0] / (2 * M)) if m >= (D - 1): omega[1:] = np.floor(np.linspace(1, m, D - 1)) else: omega[1:] = np.arange(D - 1) % m + 1 # Discretization of the frequency space, s s = (2 * math.pi / N) * np.arange(N) # Transformation to get points in the X space X = np.zeros([N * D, D]) omega2 = np.zeros([D]) for i in range(D): omega2[i] = omega[0] idx = list(range(i)) + list(range(i + 1, D)) omega2[idx] = omega[1:] z = range(i * N, (i + 1) * N) # random phase shift on [0, 2pi) following Saltelli et al. # Technometrics 1999 phi = 2 * math.pi * rng.random() for j in range(D): g = 0.5 + (1 / math.pi) * np.arcsin(np.sin(omega2[j] * s + phi)) X[z, j] = g X = scale_samples(X, problem) return X def cli_parse(parser): """Add method specific options to CLI parser. Parameters ---------- parser : argparse object Returns ------- Updated argparse object """ parser.add_argument( "-M", "--m-coef", type=int, required=False, default=4, help="M coefficient, default 4", dest="M", ) return parser def cli_action(args): """Run sampling method Parameters ---------- args : argparse namespace """ problem = read_param_file(args.paramfile) param_values = sample(problem, N=args.samples, M=args.M, seed=args.seed) np.savetxt( args.output, param_values, delimiter=args.delimiter, fmt="%." + str(args.precision) + "e", ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/sample/ff.py000066400000000000000000000101451525347100600177600ustar00rootroot00000000000000"""The sampling implementation of fractional factorial method This implementation is based on the formulation put forward in [`Saltelli et al. 2008 `_] """ from scipy.linalg import hadamard from typing import Optional, Union import numpy as np from . import common_args from ..util import scale_samples, read_param_file, handle_seed def find_smallest(num_vars): """Find the smallest exponent of two that is greater than the number of variables. Parameters ---------- num_vars : int Number of variables Returns ------- x : int Smallest exponent of two greater than `num_vars` """ for x in range(10): if num_vars <= 2**x: return x def extend_bounds(problem): """Extends the problem bounds to the nearest power of two. Parameters ---------- problem : dict The problem definition """ num_vars = problem["num_vars"] num_ff_vars = 2 ** find_smallest(num_vars) num_dummy_variables = num_ff_vars - num_vars bounds = list(problem["bounds"]) names = problem["names"] if num_dummy_variables > 0: bounds.extend([[0, 1] for x in range(num_dummy_variables)]) names.extend(["dummy_" + str(var) for var in range(num_dummy_variables)]) problem["bounds"] = bounds problem["names"] = names problem["num_vars"] = num_ff_vars return problem def generate_contrast(problem): """Generates the raw sample from the problem file. Parameters ---------- problem : dict The problem definition """ num_vars = problem["num_vars"] # Find the smallest n, such that num_vars < k k_chosen = 2 ** find_smallest(num_vars) # Generate the fractional factorial contrast contrast = np.vstack([hadamard(k_chosen), -hadamard(k_chosen)]) return contrast def sample(problem, seed: Optional[Union[int, np.random.Generator, None]] = None): """Generates model inputs using a fractional factorial sample. Returns a NumPy matrix containing the model inputs required for a fractional factorial analysis. The resulting matrix has D columns, where D is smallest power of 2 that is greater than the number of parameters. These model inputs are intended to be used with :func:`SALib.analyze.ff.analyze`. The problem file is padded with a number of dummy variables called ``dummy_0`` required for this procedure. These dummy variables can be used as a check for errors in the analyze procedure. This algorithm is an implementation of that contained in Saltelli et al [`Saltelli et al. 2008 `_] Parameters ---------- problem : dict The problem definition seed : {None, int, `numpy.random.Generator`}, optional If `seed` is None the `numpy.random.Generator` generator is used. If `seed` is an int, a new ``Generator`` instance is used, seeded with `seed`. If `seed` is already a ``Generator`` instance then that instance is used. Default is None. Returns ------- sample : :class:`numpy.array` References ---------- 1. Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S., 2008. Global Sensitivity Analysis: The Primer. Wiley, West Sussex, U.K. http://doi.org/10.1002/9780470725184 """ rng = handle_seed(seed) # noqa contrast = generate_contrast(problem) sample = np.array((contrast + 1.0) / 2, dtype=float) problem = extend_bounds(problem) sample = scale_samples(sample, problem) return sample # No additional CLI options cli_parse = None def cli_action(args): """Run sampling method Parameters ---------- args : argparse namespace """ problem = read_param_file(args.paramfile) param_values = sample(problem, seed=args.seed) np.savetxt( args.output, param_values, delimiter=args.delimiter, fmt="%." + str(args.precision) + "e", ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/sample/finite_diff.py000066400000000000000000000066571525347100600216500ustar00rootroot00000000000000from typing import Dict, Optional, Union import numpy as np from . import common_args from . import sobol_sequence from ..util import scale_samples, read_param_file, handle_seed def sample( problem: Dict, N: int, delta: float = 0.01, seed: Optional[Union[int, np.random.Generator]] = None, skip_values: int = 1024, ) -> np.ndarray: """ Generate matrix of samples for Derivative-based Global Sensitivity Measure (DGSM). Start from a QMC (Sobol') sequence and finite difference with delta % steps Parameters ---------- problem : dict SALib problem specification N : int Number of samples delta : float Finite difference step size (percent) seed : {None, int, `numpy.random.Generator`}, optional If `seed` is None the `numpy.random.Generator` generator is used. If `seed` is an int, a new ``Generator`` instance is used, seeded with `seed`. If `seed` is already a ``Generator`` instance then that instance is used. Default is None. skip_values : int How many values of the Sobol sequence to skip Returns ------- np.array : DGSM sequence References ---------- 1. Sobol', I.M., Kucherenko, S., 2009. Derivative based global sensitivity measures and their link with global sensitivity indices. Mathematics and Computers in Simulation 79, 3009-3017. https://doi.org/10.1016/j.matcom.2009.01.023 2. Sobol', I.M., Kucherenko, S., 2010. Derivative based global sensitivity measures. Procedia - Social and Behavioral Sciences 2, 7745-7746. https://doi.org/10.1016/j.sbspro.2010.05.208 """ rng = handle_seed(seed) # noqa D = problem["num_vars"] bounds = problem["bounds"] # Create base sequence - could be any type of sampling base_sequence = sobol_sequence.sample(N + skip_values, D) # scale before finite differencing base_sequence = scale_samples(base_sequence, problem) dgsm_sequence = np.empty([N * (D + 1), D]) index = 0 for i in range(skip_values, N + skip_values): # Copy the initial point dgsm_sequence[index, :] = base_sequence[i, :] index += 1 for j in range(D): temp = np.zeros(D) bnd_j = bounds[j] temp[j] = base_sequence[i, j] * delta dgsm_sequence[index, :] = base_sequence[i, :] + temp dgsm_sequence[index, j] = min(dgsm_sequence[index, j], bnd_j[1]) dgsm_sequence[index, j] = max(dgsm_sequence[index, j], bnd_j[0]) index += 1 return dgsm_sequence def cli_parse(parser): """Add method specific options to CLI parser. Parameters ---------- parser : argparse object Returns ------- Updated argparse object """ parser.add_argument( "-d", "--delta", type=float, required=False, default=0.01, help="Finite difference step size (percent)", ) return parser def cli_action(args): """Run sampling method Parameters ---------- args : argparse namespace """ problem = read_param_file(args.paramfile) param_values = sample(problem, args.samples, args.delta, seed=args.seed) np.savetxt( args.output, param_values, delimiter=args.delimiter, fmt="%." + str(args.precision) + "e", ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/sample/latin.py000066400000000000000000000060351525347100600204770ustar00rootroot00000000000000from typing import Optional, Union import numpy as np from . import common_args from ..util import read_param_file, scale_samples, compute_groups_matrix, handle_seed def sample(problem, N, seed: Optional[Union[int, np.random.Generator, None]] = None): """Generate model inputs using Latin hypercube sampling (LHS). Returns a NumPy matrix containing the model inputs generated by Latin hypercube sampling. The resulting matrix contains N rows and D columns, where D is the number of parameters. Parameters ---------- problem : dict The problem definition N : int The number of samples to generate seed : {None, int, `numpy.random.Generator`}, optional If `seed` is None the `numpy.random.Generator` generator is used. If `seed` is an int, a new ``Generator`` instance is used, seeded with `seed`. If `seed` is already a ``Generator`` instance then that instance is used. Default is None. References ---------- 1. McKay, M.D., Beckman, R.J., Conover, W.J., 1979. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21, 239-245. https://doi.org/10.2307/1268522 2. Iman, R.L., Helton, J.C., Campbell, J.E., 1981. An Approach to Sensitivity Analysis of Computer Models: Part I—Introduction, Input Variable Selection and Preliminary Variable Assessment. Journal of Quality Technology 13, 174-183. https://doi.org/10.1080/00224065.1981.11978748 """ rng = handle_seed(seed) num_samples = N groups = problem.get("groups") if groups: num_groups = len(set(groups)) G, group_names = compute_groups_matrix(groups) else: num_groups = problem["num_vars"] result = np.empty([num_samples, problem["num_vars"]]) temp = np.empty([num_samples]) d = 1.0 / num_samples temp = np.array( [ rng.uniform(low=sample * d, high=(sample + 1) * d, size=num_groups) for sample in range(num_samples) ] ) for group in range(num_groups): rng.shuffle(temp[:, group]) for sample in range(num_samples): if groups: grouped_variables = np.where(G[:, group] == 1) result[sample, grouped_variables[0]] = temp[sample, group] else: result[sample, group] = temp[sample, group] result = scale_samples(result, problem) return result # No additional CLI options cli_parse = None def cli_action(args): """Run sampling method Parameters ---------- args : argparse namespace """ problem = read_param_file(args.paramfile) param_values = sample(problem, args.samples, seed=args.seed) np.savetxt( args.output, param_values, delimiter=args.delimiter, fmt="%." + str(args.precision) + "e", ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/sample/morris/000077500000000000000000000000001525347100600203255ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/sample/morris/__init__.py000066400000000000000000000003411525347100600224340ustar00rootroot00000000000000from .local import LocalOptimisation # noqa: F401 from .brute import BruteForce # noqa: F401 from .strategy import SampleMorris # noqa: F401 from .morris import sample, _compute_delta, cli_parse, cli_action # noqa: F401 SALib-SALib-d6e51b1/src/SALib/sample/morris/brute.py000066400000000000000000000125761525347100600220330ustar00rootroot00000000000000""" """ from SALib.sample.morris.strategy import Strategy from scipy.special import comb as nchoosek # type: ignore from itertools import combinations, islice import sys import numpy as np # type: ignore from typing import List class BruteForce(Strategy): """Implements the brute force optimisation strategy""" def _sample( self, input_sample, num_samples, num_params, k_choices, num_groups=None ): return self.brute_force_most_distant( input_sample, num_samples, num_params, k_choices, num_groups ) def brute_force_most_distant( self, input_sample: np.ndarray, num_samples: int, num_params: int, k_choices: int, num_groups: int = None, ) -> List: """Use brute force method to find most distant trajectories Parameters ---------- input_sample : numpy.ndarray num_samples : int The number of samples to generate num_params : int The number of parameters k_choices : int The number of optimal trajectories num_groups : int, default=None The number of groups Returns ------- list """ scores = self.find_most_distant( input_sample, num_samples, num_params, k_choices, num_groups ) maximum_combo = self.find_maximum(scores, num_samples, k_choices) return maximum_combo def find_most_distant( self, input_sample: np.ndarray, num_samples: int, num_params: int, k_choices: int, num_groups: int = None, ) -> np.ndarray: """ Finds the 'k_choices' most distant choices from the 'num_samples' trajectories contained in 'input_sample' Parameters ---------- input_sample : numpy.ndarray num_samples : int The number of samples to generate num_params : int The number of parameters k_choices : int The number of optimal trajectories num_groups : int, default=None The number of groups Returns ------- numpy.ndarray """ # Now evaluate the (N choose k_choices) possible combinations if nchoosek(num_samples, k_choices) >= sys.maxsize: raise ValueError("Number of combinations is too large") number_of_combinations = int(nchoosek(num_samples, k_choices)) # First compute the distance matrix for each possible pairing # of trajectories and store in a shared-memory array distance_matrix = self.compute_distance_matrix( input_sample, num_samples, num_params, num_groups ) # Initialise the output array chunk = int(1e6) if chunk > number_of_combinations: chunk = number_of_combinations counter = 0 # Generate a list of all the possible combinations combo_gen = combinations(range(num_samples), k_choices) scores = np.zeros(number_of_combinations, dtype=np.float32) # Generate the pairwise indices once pairwise = np.array([y for y in combinations(range(k_choices), 2)]) mappable = self.mappable for combos in self.grouper(chunk, combo_gen): scores[(counter * chunk) : ((counter + 1) * chunk)] = mappable( combos, pairwise, distance_matrix ) counter += 1 return scores @staticmethod def grouper(n, iterable): it = iter(iterable) while True: chunk = tuple(islice(it, n)) if not chunk: return yield chunk @staticmethod def mappable(combos, pairwise, distance_matrix): """ Obtains scores from the distance_matrix for each pairwise combination held in the combos array Parameters ---------- combos : numpy.ndarray pairwise : numpy.ndarray distance_matrix : numpy.ndarray """ combos = np.array(combos) # Create a list of all pairwise combination for each combo in combos combo_list = combos[ :, pairwise[:,], ] addresses = (combo_list[:, :, 1], combo_list[:, :, 0]) all_distances = distance_matrix[addresses] new_scores = np.sqrt(np.einsum("ij,ij->i", all_distances, all_distances)) return new_scores def find_maximum(self, scores, N, k_choices): """Finds the `k_choices` maximum scores from `scores` Parameters ---------- scores : numpy.ndarray N : int k_choices : int Returns ------- list """ if not isinstance(scores, np.ndarray): raise TypeError("Scores input is not a numpy array") index_of_maximum = int(scores.argmax()) maximum_combo = self.nth( combinations(range(N), k_choices), index_of_maximum, None ) return sorted(maximum_combo) @staticmethod def nth(iterable, n, default=None): """Returns the nth item or a default value Parameters ---------- iterable : iterable n : int default : default=None The default value to return """ if not isinstance(n, int): raise TypeError("n is not an integer") return next(islice(iterable, n, None), default) SALib-SALib-d6e51b1/src/SALib/sample/morris/local.py000066400000000000000000000127111525347100600217730ustar00rootroot00000000000000""" """ from itertools import combinations import numpy as np # type: ignore from typing import List, Tuple, Union from .strategy import Strategy class LocalOptimisation(Strategy): """Implements the local optimisation algorithm using the Strategy interface""" def _sample( self, input_sample, num_samples, num_params, k_choices, num_groups=None ): return self.find_local_maximum( input_sample, num_samples, num_params, k_choices, num_groups ) def find_local_maximum( self, input_sample: np.ndarray, N: int, num_params: int, k_choices: int, num_groups: int = None, ) -> List: """Find the most different trajectories in the input sample using a local approach An alternative by Ruano et al. (2012) for the brute force approach as originally proposed by Campolongo et al. (2007). The method should improve the speed with which an optimal set of trajectories is found tremendously for larger sample sizes. Parameters ---------- input_sample : np.ndarray N : int The number of trajectories num_params : int The number of factors k_choices : int The number of optimal trajectories to return num_groups : int, default=None The number of groups Returns ------- list """ distance_matrix = self.compute_distance_matrix( input_sample, N, num_params, num_groups, local_optimization=True ) tot_indices_list = [] tot_max_array = np.zeros(k_choices - 1) maxima_template = np.zeros(len(distance_matrix)) # Loop over `k_choices`, i starts at 1 for i in range(1, k_choices): indices_list = [] row_maxima_i = maxima_template.copy() for row_nr, row in enumerate(distance_matrix): indices = tuple(row.argsort()[-i:][::-1]) + (row_nr,) row_maxima_i[row_nr] = self.sum_distances(indices, distance_matrix) indices_list.append(indices) # Find the indices belonging to the maximum distance i_max_ind = self.get_max_sum_ind(indices_list, row_maxima_i, i, 0) # Loop 'm' (called loop 'k' in Ruano) m_max_ind = i_max_ind # m starts at 1 m = 1 while m <= k_choices - i - 1: m_ind = self.add_indices(m_max_ind, distance_matrix) len_m_ind = len(m_ind) m_maxima = np.zeros(len_m_ind) for n in range(len_m_ind): m_maxima[n] = self.sum_distances(m_ind[n], distance_matrix) m_max_ind = self.get_max_sum_ind(m_ind, m_maxima, i, m) m += 1 tot_indices_list.append(m_max_ind) tot_max_array[i - 1] = self.sum_distances(m_max_ind, distance_matrix) tot_max = self.get_max_sum_ind(tot_indices_list, tot_max_array, "tot", "tot") return sorted(tot_max) def sum_distances(self, indices: Tuple, distance_matrix: np.ndarray) -> np.ndarray: """Calculate combinatorial distance between a select group of trajectories, indicated by indices Parameters ---------- indices : tuple distance_matrix : numpy.ndarray (M,M) Returns ------- numpy.ndarray Notes ----- This function can perhaps be quickened by calculating the sum of the distances. The calculated distances, as they are right now, are only used in a relative way. Purely summing distances would lead to the same result, at a perhaps quicker rate. """ combs_tup = combinations(indices, 2) combs = np.array(tuple(zip(*combs_tup))) # Calculate distance (vectorized) dist = np.sqrt(np.sum(np.square(distance_matrix[combs[0], combs[1]]), axis=0)) return dist def get_max_sum_ind( self, indices_list: List[Tuple], distances: np.ndarray, i: Union[str, int], m: Union[str, int], ) -> Tuple: """Get the indices that belong to the maximum distance in `distances` Parameters ---------- indices_list : list list of tuples distances : numpy.ndarray size M i : int m : int Returns ------- list """ if len(indices_list) != len(distances): msg = ( "Indices and distances are lists of different length." + "Length indices_list = {} and length distances = {}." + "In loop i = {} and m = {}" ) raise ValueError(msg.format(len(indices_list), len(distances), i, m)) max_index = distances.argsort()[-1:][::-1] return tuple(indices_list[max_index[0]]) def add_indices(self, indices: Tuple, distance_matrix: np.ndarray) -> List: """Adds extra indices for the combinatorial problem. Parameters ---------- indices : tuple distance_matrix : numpy.ndarray (M,M) Examples -------- >>> add_indices((1,2), numpy.array((5,5))) [(1, 2, 3), (1, 2, 4), (1, 2, 5)] """ list_new_indices = [] for i in range(len(distance_matrix)): if i not in indices: list_new_indices.append(indices + (i,)) return list_new_indices SALib-SALib-d6e51b1/src/SALib/sample/morris/morris.py000066400000000000000000000341721525347100600222210ustar00rootroot00000000000000import numpy as np from typing import Dict, Optional, Union import warnings from .local import LocalOptimisation from .brute import BruteForce from .strategy import SampleMorris from SALib.sample import common_args from SALib.util import ( scale_samples, read_param_file, compute_groups_matrix, _define_problem_with_groups, _compute_delta, handle_seed, ) __all__ = ["sample"] def sample( problem: Dict, N: int, num_levels: int = 4, optimal_trajectories: Optional[Union[int, None]] = None, local_optimization: bool = True, seed: Optional[Union[int, np.random.Generator]] = None, ) -> np.ndarray: """Generate model inputs using the Method of Morris. Three variants of Morris' sampling for elementary effects is supported: - Vanilla Morris (see [1]) when ``optimal_trajectories`` is ``None``/``False`` and ``local_optimization`` is ``False`` - Optimised trajectories when ``optimal_trajectories=True`` using Campolongo's enhancements (see [2]) and optionally Ruano's enhancement (see [3]) when ``local_optimization=True`` - Morris with groups when the problem definition specifies groups of parameters Results from these model inputs are intended to be used with :func:`SALib.analyze.morris.analyze`. Notes ----- Campolongo et al., [2] introduces an optimal trajectories approach which attempts to maximize the parameter space scanned for a given number of trajectories (where `optimal_trajectories` :math:`\\in {2, ..., N}`). The approach accomplishes this aim by randomly generating a high number of possible trajectories (500 to 1000 in [2]) and selecting a subset of ``r`` trajectories which have the highest spread in parameter space. The ``r`` variable in [2] corresponds to the ``optimal_trajectories`` parameter here. Calculating all possible combinations of trajectories can be computationally expensive. The number of factors makes little difference, but the ratio between number of optimal trajectories and the sample size results in an exponentially increasing number of scores that must be computed to find the optimal combination of trajectories. We suggest going no higher than 4 levels from a pool of 100 samples with this "brute force" approach. Ruano et al., [3] proposed an alternative approach with an iterative process that maximizes the distance between subgroups of generated trajectories, from which the final set of trajectories are selected, again maximizing the distance between each. The approach is not guaranteed to produce the most optimal spread of trajectories, but are at least locally maximized and significantly reduce the time taken to select trajectories. With ``local_optimization = True`` (which is default), it is possible to go higher than the previously suggested 4 levels from a pool of 100 samples. Parameters ---------- problem : dict The problem definition N : int The number of trajectories to generate num_levels : int, default=4 The number of grid levels (should be even) optimal_trajectories : int The number of optimal trajectories to sample (between 2 and N) local_optimization : bool, default=True Flag whether to use local optimization according to Ruano et al. (2012) Speeds up the process tremendously for bigger N and num_levels. If set to ``False`` brute force method is used, unless ``gurobipy`` is available seed : {None, int, `numpy.random.Generator`}, optional If `seed` is None the `numpy.random.Generator` generator is used. If `seed` is an int, a new ``Generator`` instance is used, seeded with `seed`. If `seed` is already a ``Generator`` instance then that instance is used. Default is None. Returns ------- sample_morris : np.ndarray Array containing the model inputs required for Method of Morris. The resulting matrix has :math:`(G/D+1)*N/T` rows and :math:`D` columns, where :math:`D` is the number of parameters, :math:`G` is the number of groups (if no groups are selected, the number of parameters). :math:`T` is the number of trajectories :math:`N`, or `optimal_trajectories` if selected. References ---------- 1. Morris, M.D., 1991. Factorial Sampling Plans for Preliminary Computational Experiments. Technometrics 33, 161-174. https://doi.org/10.1080/00401706.1991.10484804 2. Campolongo, F., Cariboni, J., & Saltelli, A. 2007. An effective screening design for sensitivity analysis of large models. Environmental Modelling & Software, 22(10), 1509-1518. https://doi.org/10.1016/j.envsoft.2006.10.004 3. Ruano, M.V., Ribes, J., Seco, A., Ferrer, J., 2012. An improved sampling strategy based on trajectory design for application of the Morris method to systems with many input factors. Environmental Modelling & Software 37, 103-109. https://doi.org/10.1016/j.envsoft.2012.03.008 """ rng = handle_seed(seed) _check_if_num_levels_is_even(num_levels) problem = _define_problem_with_groups(problem) sample_morris = _sample_morris(problem, N, rng, num_levels=num_levels) if optimal_trajectories: if local_optimization and ( not isinstance(optimal_trajectories, int) or optimal_trajectories > N ): msg = "optimal_trajectories should be an " f"integer between 2 and {N}" raise ValueError(msg) sample_morris = _compute_optimised_trajectories( problem, sample_morris, N, optimal_trajectories, local_optimization ) sample_morris = scale_samples(sample_morris, problem) return sample_morris def _sample_morris( problem: Dict, number_trajectories: int, rng: np.random.Generator, num_levels: int = 4, ) -> np.ndarray: """Generate trajectories for groups Returns an :math:`N(g+1)`-by-:math:`k` array of `N` trajectories, where :math:`g` is the number of groups and :math:`k` is the number of factors Parameters --------- problem : dict The problem definition number_trajectories : int The number of trajectories to generate rng : np.random.Generator num_levels : int, default=4 The number of grid levels Returns ------- numpy.ndarray """ group_membership, _ = compute_groups_matrix(problem["groups"]) _check_group_membership(group_membership) num_params = group_membership.shape[0] num_groups = group_membership.shape[1] sample_morris = [ _generate_trajectory(group_membership, rng, num_levels=num_levels) for _ in range(number_trajectories) ] sample_morris = np.array(sample_morris) return sample_morris.reshape((number_trajectories * (num_groups + 1), num_params)) def _generate_trajectory( group_membership: np.ndarray, rng: np.random.Generator, num_levels: int = 4 ) -> np.ndarray: """Return a single trajectory Return a single trajectory of size :math:`(g+1)`-by-:math:`k` where :math:`g` is the number of groups, and :math:`k` is the number of factors, both implied by the dimensions of `group_membership` Parameters --------- group_membership : np.ndarray a k-by-g matrix which notes factor membership of groups rng : numpy.random.Generator num_levels : int, default=4 The number of levels in the grid Returns ------- np.ndarray """ delta = _compute_delta(num_levels) # Infer number of groups `g` and number of params `k` from # `group_membership` matrix num_params = group_membership.shape[0] num_groups = group_membership.shape[1] # Matrix B - size (g + 1) * g - lower triangular matrix B = np.tril(np.ones([num_groups + 1, num_groups], dtype=int), -1) P_star = _generate_p_star(num_groups, rng) # Matrix J - a (g+1)-by-num_params matrix of ones J = np.ones((num_groups + 1, num_params)) # Matrix D* - num_params-by-num_params matrix which describes whether # factors move up or down D_star = np.diag(rng.choice([-1, 1], num_params)) x_star = _generate_x_star(num_params, num_levels, rng) # Matrix B* - size (num_groups + 1) * num_params B_star = _compute_b_star(J, x_star, delta, B, group_membership, P_star, D_star) return B_star def _compute_b_star( J: np.ndarray, x_star: np.ndarray, delta: float, B: np.ndarray, G: np.ndarray, P_star: np.ndarray, D_star: np.ndarray, ) -> np.ndarray: """ Compute the random sampling matrix B*. Parameters ---------- J: matrix of 1's x_star: randomly chosen "base value" of x delta: parameters variation B: sampling matrix (not random) G: groups matrix P_star: random permutation matrix D_star: diagonal matrix with each element being +1 or -1, with equal probability Returns ------- Random sampling matrix B* """ element_a = J[0, :] * x_star element_b = np.matmul(G, P_star).T element_c = np.matmul(2.0 * B, element_b) element_d = np.matmul((element_c - J), D_star) b_star = element_a + (delta / 2.0) * (element_d + J) return b_star def _generate_p_star(num_groups: int, rng: np.random.Generator) -> np.ndarray: """Describe the order in which groups move Parameters --------- num_groups : int rng : numpy.random.Generator Returns ------- np.ndarray Matrix P* - size (g-by-g) """ p_star = np.eye(num_groups, num_groups) rng.shuffle(p_star) return p_star def _generate_x_star( num_params: int, num_levels: int, rng: np.random.Generator ) -> np.ndarray: """Generate an 1-by-num_params array to represent initial position for EE This should be a randomly generated array in the p level grid :math:`\\omega` Parameters --------- num_params : int The number of parameters (factors) num_levels : int The number of levels rng : numpy.random.Generator Returns ------- numpy.ndarray The initial starting positions of the trajectory """ x_star = np.zeros((1, num_params)) delta = _compute_delta(num_levels) bound = 1 - delta grid = np.linspace(0, bound, int(num_levels / 2)) x_star[0, :] = rng.choice(grid, num_params) return x_star def _compute_optimised_trajectories( problem: Dict, input_sample: int, N: int, k_choices: int, local_optimization: bool = False, ) -> np.ndarray: """ Calls the procedure to compute the optimum k_choices of trajectories from the input_sample. If there are groups, then this procedure allocates the groups to the correct call here. Parameters --------- problem : dict The problem definition input_sample : N : int The number of samples to generate k_choices : int The number of optimal trajectories local_optimization : bool, default=False If true, uses local optimisation heuristic """ if local_optimization is False and k_choices > 10: msg = "Running optimal trajectories greater than values of 10 \ will take a long time." raise ValueError(msg) if np.any((input_sample < 0) | (input_sample > 1)): raise ValueError("Input sample must be scaled between 0 and 1") num_groups = len(set(problem["groups"])) num_params = problem["num_vars"] strategy = _choose_optimization_strategy(local_optimization) context = SampleMorris(strategy) output = context.sample(input_sample, N, num_params, k_choices, num_groups) return output def _check_if_num_levels_is_even(num_levels: int): """ Checks if the number of levels is even. If not, raises a warn. Parameters ---------- num_levels: int Number of levels """ if not num_levels % 2 == 0: warnings.warn("num_levels should be an even number, " "sample may be biased") def _check_group_membership(group_membership: np.ndarray): """ Checks if the group_membership matrix was correctly defined Parameters ---------- group_membership: np.array Group membership matrix """ if group_membership is None: raise ValueError("Please define the 'group_membership' matrix") if not isinstance(group_membership, np.ndarray): raise TypeError( "Argument 'group_membership' should be formatted \ as a numpy np.ndarray" ) def _choose_optimization_strategy(local_optimization: bool): """ Choose the strategy to optimize the trajectories. Parameters ---------- local_optimization: boolean to indicate if a local optimization should be used. Returns ------- """ if local_optimization: # Use local method strategy = LocalOptimisation() else: # Use brute force approach strategy = BruteForce() return strategy def cli_parse(parser): parser.add_argument( "-l", "--levels", type=int, required=False, default=4, help="Number of grid levels \ (Morris only)", ) parser.add_argument( "-k", "--k-optimal", type=int, required=False, default=None, help="Number of optimal trajectories \ (Morris only)", ) parser.add_argument( "-lo", "--local", type=bool, required=True, default=False, help="Use the local optimisation method \ (Morris with optimization only)", ) return parser def cli_action(args): problem = read_param_file(args.paramfile) param_values = sample( problem, args.samples, num_levels=args.levels, optimal_trajectories=args.k_optimal, local_optimization=args.local, seed=args.seed, ) np.savetxt( args.output, param_values, delimiter=args.delimiter, fmt="%." + str(args.precision) + "e", ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/sample/morris/strategy.py000066400000000000000000000214751525347100600225520ustar00rootroot00000000000000""" Defines a family of algorithms for generating samples The sample a for use with :class:`SALib.analyze.morris.analyze`, encapsulate each one, and makes them interchangeable. Example ------- >>> localoptimisation = LocalOptimisation() >>> context = SampleMorris(localoptimisation) >>> context.sample(input_sample, num_samples, num_params, k_choices, groups) """ import abc import numpy as np # type: ignore from scipy.spatial.distance import cdist # type: ignore class SampleMorris(object): """Computes the optimum `k_choices` of trajectories from the input_sample. Parameters ---------- strategy : :class:`Strategy` """ def __init__(self, strategy): self._strategy = strategy def sample(self, input_sample, num_samples, num_params, k_choices, num_groups): """Computes the optimum k_choices of trajectories from the input_sample. Parameters ---------- input_sample : numpy.ndarray num_samples : int The number of samples to generate num_params : int The number of parameters k_choices : int The number of optimal trajectories num_groups : int The number of groups Returns ------- numpy.ndarray An array of optimal trajectories """ return self._strategy.sample( input_sample, num_samples, num_params, k_choices, num_groups ) class Strategy: """ Declare an interface common to all supported algorithms. :class:`SampleMorris` uses this interface to call the algorithm defined by a ConcreteStrategy. """ __metaclass__ = abc.ABCMeta @abc.abstractmethod def _sample(self, input_sample, num_samples, num_params, k_choices, num_groups): """Implement this in your class Parameters ---------- input_sample : numpy.ndarray num_samples : int The number of samples to generate num_params : int The number of parameters k_choices : int The number of optimal trajectories num_groups : int The number of groups Returns ------- list A list of trajectory indices """ pass def sample(self, input_sample, num_samples, num_params, k_choices, num_groups=None): """Computes the optimum k_choices of trajectories from the input_sample. Parameters ---------- input_sample : numpy.ndarray num_samples : int The number of samples to generate num_params : int The number of parameters k_choices : int The number of optimal trajectories num_groups : int, default=None The number of groups Returns ------- numpy.ndarray """ self.run_checks(num_samples, k_choices) maximum_combo = self._sample( input_sample, num_samples, num_params, k_choices, num_groups ) assert isinstance(maximum_combo, list) output = self.compile_output( input_sample, num_samples, num_params, maximum_combo, num_groups ) return output @staticmethod def run_checks(number_samples, k_choices): """Runs checks on `k_choices`""" assert isinstance( k_choices, int ), "Number of optimal trajectories should be an integer" if k_choices < 2: raise ValueError( "The number of optimal trajectories must be set to 2 or more." ) if k_choices >= number_samples: msg = "The number of optimal trajectories should be less than the \ number of samples" raise ValueError(msg) @staticmethod def _make_index_list(num_samples, num_params, num_groups=None): """Identify indices of input sample associated with each trajectory For each trajectory, identifies the indexes of the input sample which is a function of the number of factors/groups and the number of samples Parameters ---------- num_samples : int The number of trajectories num_params : int The number of parameters num_groups : int The number of groups Returns ------- list of numpy.ndarray Example ------- >>> BruteForce()._make_index_list(num_samples=4, num_params=3, num_groups=2) [np.array([0, 1, 2]), np.array([3, 4, 5]), np.array([6, 7, 8]), np.array([9, 10, 11])] """ if num_groups is None: num_groups = num_params index_list = [] for j in range(num_samples): index_list.append(np.arange(num_groups + 1) + j * (num_groups + 1)) return index_list def compile_output( self, input_sample, num_samples, num_params, maximum_combo, num_groups=None ): """Picks the trajectories from the input Parameters ---------- input_sample : numpy.ndarray num_samples : int num_params : int maximum_combo : list num_groups : int """ if num_groups is None: num_groups = num_params self.check_input_sample(input_sample, num_groups, num_samples) index_list = self._make_index_list(num_samples, num_params, num_groups) output = np.zeros((np.size(maximum_combo) * (num_groups + 1), num_params)) for counter, combo in enumerate(maximum_combo): output[index_list[counter]] = np.array(input_sample[index_list[combo]]) return output @staticmethod def check_input_sample(input_sample, num_params, num_samples): """Check the `input_sample` is valid Checks input sample is: - the correct size - values between 0 and 1 Parameters ---------- input_sample : numpy.ndarray num_params : int num_samples : int """ assert type(input_sample) == np.ndarray, "Input sample is not an numpy array" assert ( input_sample.shape[0] == (num_params + 1) * num_samples ), "Input sample does not match number of parameters or groups" assert np.any( (input_sample >= 0) | (input_sample <= 1) ), "Input sample must be scaled between 0 and 1" @staticmethod def compute_distance(m, l): # noqa: E741 """Compute distance between two trajectories Parameters ---------- m : np.ndarray l : np.ndarray Returns ------- numpy.ndarray """ if np.shape(m) != np.shape(l): raise ValueError("Input matrices are different sizes") if np.array_equal(m, l): # print("Trajectory %s and %s are equal" % (m, l)) distance = 0 else: distance = np.array(np.sum(cdist(m, l)), dtype=np.float32) return distance def compute_distance_matrix( self, input_sample, num_samples, num_params, num_groups=None, local_optimization=False, ): """Computes the distance between each and every trajectory Each entry in the matrix represents the sum of the geometric distances between all the pairs of points of the two trajectories If the `groups` argument is filled, then the distances are still calculated for each trajectory, Parameters ---------- input_sample : numpy.ndarray The input sample of trajectories for which to compute the distance matrix num_samples : int The number of trajectories num_params : int The number of factors num_groups : int, default=None The number of groups local_optimization : bool, default=False If True, fills the lower triangle of the distance matrix Returns ------- distance_matrix : numpy.ndarray """ if num_groups: self.check_input_sample(input_sample, num_groups, num_samples) else: self.check_input_sample(input_sample, num_params, num_samples) index_list = self._make_index_list(num_samples, num_params, num_groups) distance_matrix = np.zeros((num_samples, num_samples), dtype=np.float32) for j in range(num_samples): input_1 = input_sample[index_list[j]] for k in range(j + 1, num_samples): input_2 = input_sample[index_list[k]] # Fills the lower triangle of the matrix if local_optimization is True: distance_matrix[j, k] = self.compute_distance(input_1, input_2) distance_matrix[k, j] = self.compute_distance(input_1, input_2) return distance_matrix SALib-SALib-d6e51b1/src/SALib/sample/radial/000077500000000000000000000000001525347100600202465ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/sample/radial/__init__.py000066400000000000000000000001661525347100600223620ustar00rootroot00000000000000# By default - forward `radial_sobol` interface from .radial_sobol import sample, cli_parse, cli_action # noqa: F401 SALib-SALib-d6e51b1/src/SALib/sample/radial/radial_funcs.py000066400000000000000000000030441525347100600232530ustar00rootroot00000000000000import numpy as np def combine_samples(baseline, perturb): """Combine baseline and perturbation samples in order. The number of parameters will be inferred from the shape of `baseline`. Arguments --------- baseline : np.array baseline sample for one of `N` samples perturb : np.array perturbation value for a parameter Example ------- >>> X = combine_samples(baseline, perturb) `X` will now hold: [[x_{1,1}, x_{1,2}, ..., x_{1,p}] [b_{1,1}, x_{1,2}, ..., x_{1,p}] [x_{1,1}, b_{1,2}, ..., x_{1,p}] [x_{1,1}, x_{1,2}, ..., b_{1,p}] ... [x_{N,1}, x_{N,2}, ..., x_{N,p}] [b_{N,1}, x_{N,2}, ..., x_{N,p}] [x_{N,1}, b_{N,2}, ..., x_{N,p}] [x_{N,1}, x_{N,2}, ..., b_{N,p}]] where `p` denotes the number of parameters as specified in `problem` and `N` is the number of samples. We can now run the model using the values in `X`. The total number of model evaluations will be `N(p+1)`. Returns ------- np.array """ assert ( baseline.shape == perturb.shape ), "Baseline and perturbation data should be of same size" nrows, num_vars = baseline.shape group = num_vars + 1 sample_set = np.repeat(baseline, repeats=group, axis=0) grp_start = 0 for i in range(nrows): mod = np.diag(perturb[i]) first_ = grp_start + 1 np.copyto(sample_set[first_ : first_ + num_vars], mod, where=mod != 0.0) grp_start += group # End for return sample_set SALib-SALib-d6e51b1/src/SALib/sample/radial/radial_mc.py000066400000000000000000000061351525347100600225400ustar00rootroot00000000000000import numpy as np from SALib.util import read_param_file from typing import Dict, Optional from .. import common_args from .radial_funcs import combine_samples __all__ = ["sample"] def sample(problem: Dict, N: int, seed: Optional[int] = None): """Generates `N` monte carlo samples for a Radial OAT approach using a uniform distribution. Notes ----- Compatible with: - :func:`SALib.analyze.radial_ee.analyze` - :func:`SALib.analyze.sobol_jansen.analyze` Parameters ---------- problem : dict SALib problem specification N : int The number of sample sets to generate seed : int Seed value to use for np.random.seed Returns --------- numpy.ndarray : An array of samples Usage Example ------------- ```python >>> X = sample(problem, N, seed) ``` `X` will now hold: [ [x_{1,1}, x_{1,2}, ..., x_{1,p}] [b_{1,1}, x_{1,2}, ..., x_{1,p}] [x_{1,1}, b_{1,2}, ..., x_{1,p}] [x_{1,1}, x_{1,2}, ..., b_{1,p}] ... [x_{N,1}, x_{N,2}, ..., x_{N,p}] [b_{N,1}, x_{N,2}, ..., x_{N,p}] [x_{N,1}, b_{N,2}, ..., x_{N,p}] [x_{N,1}, x_{N,2}, ..., b_{N,p}] ] where `p` denotes the number of parameters as specified in `problem` and `b` represents perturbed values. The first parameter set in each sample set acts as the baseline. We can now run the model using the values in `X`. The total number of model evaluations will be `N(p+1)`. References ---------- .. [1] Campolongo, F., Saltelli, A., Cariboni, J., 2011. From screening to quantitative sensitivity analysis: A unified approach. Computer Physics Communications 182, 978–988. https://www.sciencedirect.com/science/article/pii/S0010465510005321 DOI: 10.1016/j.cpc.2010.12.039 .. [2] Campolongo, F., Cariboni, J., Saltelli, A., 2007. An effective screening design for sensitivity analysis of large models. Environmental Modelling & Software 22, 1509–1518. https://doi.org/10.1016/j.envsoft.2006.10.004 """ if seed: np.random.seed(seed) num_vars = problem["num_vars"] bounds = problem["bounds"] # Generate the 'nominal' parameter positions # Total number of parameter sets = N*(p+1) min_bnds = [lb[0] for lb in bounds] max_bnds = [lb[1] for lb in bounds] baselines = np.random.uniform(min_bnds, max_bnds, size=(N * 2, num_vars)) perturb = baselines[N:] baseline = baselines[:N] sample_set = combine_samples(baseline, perturb) return sample_set # No additional CLI options cli_parse = None def cli_action(args): """Run sampling method Parameters ---------- args : argparse namespace """ problem = read_param_file(args.paramfile) param_values = sample(problem, args.samples, seed=args.seed) np.savetxt( args.output, param_values, delimiter=args.delimiter, fmt="%." + str(args.precision) + "e", ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/sample/radial/radial_sobol.py000066400000000000000000000073101525347100600232530ustar00rootroot00000000000000from typing import Dict, Optional import numpy as np from SALib.util import scale_samples, read_param_file from .. import sobol_sequence from SALib.sample import common_args from .radial_funcs import combine_samples __all__ = ["sample"] def sample(problem: Dict, N: int, R=4, skip_num: int = 0, seed: Optional[int] = None): """Generates `N` sobol samples for a Radial OAT approach. Notes ----- Compatible with: - :func:`SALib.analyze.sobol_jansen.analyze` (the Jansen sensitivity estimator) - :func:`SALib.analyze.radial_ee.analyze` (Elementary Effects) References ---------- .. [1] Campolongo, F., Saltelli, A., Cariboni, J., 2011. From screening to quantitative sensitivity analysis: A unified approach. Computer Physics Communications 182, 978–988. https://www.sciencedirect.com/science/article/pii/S0010465510005321 DOI: 10.1016/j.cpc.2010.12.039 Arguments --------- problem : dict SALib problem specification N : int The number of sample sets to generate. It is assumed here that `N = r`, where `r` is the number of points/trajectories. R : int Number of rows in Sobol random matrix to shift downwards. Defaults to 4 (as given in [1]) skip_num : int Number of sobol sequence values to skip When conducting a sequential sensitivity analysis, this is the previous number of samples used seed : int Seed value to use for np.random.seed Usage Example ------------- ```python >>> X = sample(problem, N, seed) ``` `X` will now hold: [ [x_{1,1}, x_{1,2}, ..., x_{1,p}] [b_{1,1}, x_{1,2}, ..., x_{1,p}] [x_{1,1}, b_{1,2}, ..., x_{1,p}] [x_{1,1}, x_{1,2}, ..., b_{1,p}] ... [x_{N,1}, x_{N,2}, ..., x_{N,p}] [b_{N,1}, x_{N,2}, ..., x_{N,p}] [x_{N,1}, b_{N,2}, ..., x_{N,p}] [x_{N,1}, x_{N,2}, ..., b_{N,p}] ] where `p` denotes the number of parameters as specified in `problem` and `b` represents perturbed values. The first parameter set in each sample set acts as the baseline. We can now run the model using the values in `X`. The total number of model evaluations will be `N(p+1)`. Returns --------- numpy.ndarray : An array of samples """ if seed: np.random.seed(seed) num_vars = problem["num_vars"] sequence = sobol_sequence.sample(skip_num + N + R, (num_vars * 2)) sequence = sequence[skip_num:, :] # Use first N rows and `num_vars` cols as baseline points # and next `num_vars` cols and N rows as perturbation points baseline = sequence[:N, :num_vars] scale_samples(baseline, problem) # Use right-most columns for perturbation points, # starting from row `R`. perturb = sequence[R:, num_vars:] scale_samples(perturb, problem) # Total number of parameter sets = `N*(num_vars+1)` sample_set = combine_samples(baseline, perturb) return sample_set def cli_parse(parser): parser.add_argument( "-k", "--skip_num", type=int, required=False, default=0, help="Number of Sobol values to skip (default 0)", ) return parser def cli_action(args): """Run sampling method Parameters ---------- args : argparse namespace """ problem = read_param_file(args.paramfile) param_values = sample(problem, args.samples, skip_num=args.skip_num, seed=args.seed) np.savetxt( args.output, param_values, delimiter=args.delimiter, fmt="%." + str(args.precision) + "e", ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/sample/saltelli.py000066400000000000000000000213241525347100600211770ustar00rootroot00000000000000from typing import Dict import math import warnings import numpy as np from . import common_args from . import sobol_sequence from ..util import scale_samples, read_param_file, compute_groups_matrix, _check_groups def sample( problem: Dict, N: int, calc_second_order: bool = True, skip_values: int = None ): """Generates model inputs using Saltelli's extension of the Sobol' sequence The Sobol' sequence is a popular quasi-random low-discrepancy sequence used to generate uniform samples of parameter space. Returns a NumPy matrix containing the model inputs using Saltelli's sampling scheme. Saltelli's scheme extends the Sobol' sequence in a way to reduce the error rates in the resulting sensitivity index calculations. If `calc_second_order` is False, the resulting matrix has ``N * (D + 2)`` rows, where ``D`` is the number of parameters. If `calc_second_order` is `True`, the resulting matrix has ``N * (2D + 2)`` rows. These model inputs are intended to be used with :func:`SALib.analyze.sobol.analyze`. .. deprecated:: 1.4.6 Notes ----- The initial points of the Sobol' sequence has some repetition (see Table 2 in Campolongo [1]), which can be avoided by setting the `skip_values` parameter. Skipping values reportedly improves the uniformity of samples. It has been shown that naively skipping values may reduce accuracy, increasing the number of samples needed to achieve convergence (see Owen [2]). A recommendation adopted here is that both `skip_values` and `N` be a power of 2, where `N` is the desired number of samples (see [2] and discussion in [5] for further context). It is also suggested therein that ``skip_values >= N``. The method now defaults to setting `skip_values` to a power of two that is ``>= N``. If `skip_values` is provided, the method now raises a UserWarning in cases where sample sizes may be sub-optimal according to the recommendation above. Parameters ---------- problem : dict The problem definition N : int The number of samples to generate. Ideally a power of 2 and <= `skip_values`. calc_second_order : bool Calculate second-order sensitivities (default True) skip_values : int or None Number of points in Sobol' sequence to skip, ideally a value of base 2 (default: a power of 2 >= N, or 16; whichever is greater) References ---------- 1. Campolongo, F., Saltelli, A., Cariboni, J., 2011. From screening to quantitative sensitivity analysis. A unified approach. Computer Physics Communications 182, 978-988. https://doi.org/10.1016/j.cpc.2010.12.039 2. Owen, A. B., 2020. On dropping the first Sobol' point. arXiv:2008.08051 [cs, math, stat]. Available at: http://arxiv.org/abs/2008.08051 (Accessed: 20 April 2021). 3. Saltelli, A., 2002. Making best use of model evaluations to compute sensitivity indices. Computer Physics Communications 145, 280-297. https://doi.org/10.1016/S0010-4655(02)00280-1 4. Sobol', I.M., 2001. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, The Second IMACS Seminar on Monte Carlo Methods 55, 271-280. https://doi.org/10.1016/S0378-4754(00)00270-6 5. Discussion: https://github.com/scipy/scipy/pull/10844 https://github.com/scipy/scipy/pull/10844#issuecomment-672186615 https://github.com/scipy/scipy/pull/10844#issuecomment-673029539 """ warnings.warn( "`salib.sample.saltelli` will be removed in SALib 1.5.1 Please use" " `salib.sample.sobol`", category=DeprecationWarning, stacklevel=2, ) # bit-shift test to check if `N` == 2**n if not ((N & (N - 1) == 0) and (N != 0 and N - 1 != 0)): msg = f""" Convergence properties of the Sobol' sequence is only valid if `N` ({N}) is equal to `2^n`. """ warnings.warn(msg) if skip_values is None: # If not specified, set skip_values to next largest power of 2 skip_values = int(2 ** math.ceil(math.log(N) / math.log(2))) # 16 is arbitrarily selected here to avoid initial points # for very low sample sizes skip_values = max(skip_values, 16) elif skip_values > 0: M = skip_values if not ((M & (M - 1) == 0) and (M != 0 and M - 1 != 0)): msg = f""" Convergence properties of the Sobol' sequence is only valid if `skip_values` ({M}) is a power of 2. """ warnings.warn(msg) # warning when N > skip_values # see https://github.com/scipy/scipy/pull/10844#issuecomment-673029539 n_exp = int(math.log(N, 2)) m_exp = int(math.log(M, 2)) if n_exp > m_exp: msg = ( "Convergence may not be valid as the number of " "requested samples is" f" > `skip_values` ({N} > {M})." ) warnings.warn(msg) elif skip_values == 0: warnings.warn("Duplicate samples will be taken as no points are skipped.") else: assert ( isinstance(skip_values, int) and skip_values >= 0 ), "`skip_values` must be a positive integer." D = problem["num_vars"] groups = _check_groups(problem) if not groups: Dg = problem["num_vars"] else: G, group_names = compute_groups_matrix(groups) Dg = len(set(group_names)) # Create base sequence - could be any type of sampling base_sequence = sobol_sequence.sample(N + skip_values, 2 * D) if calc_second_order: saltelli_sequence = np.zeros([(2 * Dg + 2) * N, D]) else: saltelli_sequence = np.zeros([(Dg + 2) * N, D]) index = 0 for i in range(skip_values, N + skip_values): # Copy matrix "A" for j in range(D): saltelli_sequence[index, j] = base_sequence[i, j] index += 1 # Cross-sample elements of "B" into "A" for k in range(Dg): for j in range(D): if (not groups and j == k) or (groups and group_names[k] == groups[j]): saltelli_sequence[index, j] = base_sequence[i, j + D] else: saltelli_sequence[index, j] = base_sequence[i, j] index += 1 # Cross-sample elements of "A" into "B" # Only needed if you're doing second-order indices (true by default) if calc_second_order: for k in range(Dg): for j in range(D): if (not groups and j == k) or ( groups and group_names[k] == groups[j] ): saltelli_sequence[index, j] = base_sequence[i, j] else: saltelli_sequence[index, j] = base_sequence[i, j + D] index += 1 # Copy matrix "B" for j in range(D): saltelli_sequence[index, j] = base_sequence[i, j + D] index += 1 saltelli_sequence = scale_samples(saltelli_sequence, problem) return saltelli_sequence def cli_parse(parser): """Add method specific options to CLI parser. Parameters ---------- parser : argparse object Returns ------- Updated argparse object """ parser.add_argument( "--max-order", type=int, required=False, default=2, choices=[1, 2], help="Maximum order of sensitivity indices \ to calculate", ) parser.add_argument( "--skip-values", type=int, required=False, default=None, help="Number of sample points to skip \ (default: next largest power of 2 from `samples`)", ) # hacky way to remove an argument (seed option not relevant for Saltelli) remove_opts = [x for x in parser._actions if x.dest == "seed"] [ parser._handle_conflict_resolve(None, [("--seed", x), ("-s", x)]) for x in remove_opts ] return parser def cli_action(args): """Run sampling method Parameters ---------- args : argparse namespace """ problem = read_param_file(args.paramfile) param_values = sample( problem, args.samples, calc_second_order=(args.max_order == 2), skip_values=args.skip_values, ) np.savetxt( args.output, param_values, delimiter=args.delimiter, fmt="%." + str(args.precision) + "e", ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/sample/shapley.py000066400000000000000000000064671525347100600210460ustar00rootroot00000000000000from numbers import Integral from typing import Optional, Union import numpy as np from . import common_args from ..util import handle_seed, read_param_file, scale_samples def sample( problem: dict, N: int, seed: Optional[Union[int, np.random.Generator]] = None, ) -> np.ndarray: """Generate inputs for Goda's Shapley effects estimator. The method draws two independent input vectors for each Monte Carlo replication. A random permutation then defines a trajectory that replaces one coordinate at a time from the first vector with the corresponding coordinate from the second. The resulting matrix contains ``N * (D + 1)`` rows and ``D`` columns. Results from these model inputs are intended to be used with :func:`SALib.analyze.shapley.analyze`. Notes ----- Goda's estimator assumes mutually independent input variables. SALib problem definitions specify marginal distributions, so this sampler draws every input independently. Grouped parameters are not supported. Parameters ---------- problem : dict The problem definition. N : int Number of independent Monte Carlo trajectories. The model is evaluated ``N * (D + 1)`` times. seed : {None, int, `numpy.random.Generator`}, optional Seed or random generator used to draw the sample and permutations. Returns ------- numpy.ndarray Model inputs arranged as ``N`` consecutive trajectories. References ---------- 1. Goda, T. (2021). A simple algorithm for global sensitivity analysis with Shapley effects. Reliability Engineering & System Safety, 213, 107702. https://doi.org/10.1016/j.ress.2021.107702 """ if isinstance(N, bool) or not isinstance(N, Integral) or N <= 0: raise ValueError("N must be a positive integer.") _validate_ungrouped(problem) num_vars = problem["num_vars"] if num_vars <= 0: raise ValueError("The problem must contain at least one variable.") rng = handle_seed(seed) independent_pairs = scale_samples(rng.random((2 * N, num_vars)), problem) first, second = np.split(independent_pairs, 2) samples = np.empty((N * (num_vars + 1), num_vars), dtype=float) for trajectory, permutation in enumerate( (rng.permutation(num_vars) for _ in range(N)) ): start = trajectory * (num_vars + 1) samples[start] = first[trajectory] current = first[trajectory].copy() for step, factor in enumerate(permutation, start=1): current[factor] = second[trajectory, factor] samples[start + step] = current return samples def _validate_ungrouped(problem: dict) -> None: groups = problem.get("groups") if groups and list(groups) != list(problem.get("names", [])): raise ValueError("Goda's Shapley estimator does not support groups.") # No additional CLI options cli_parse = None def cli_action(args): """Generate a Shapley trajectory design from command-line arguments.""" problem = read_param_file(args.paramfile) param_values = sample(problem, args.samples, seed=args.seed) np.savetxt( args.output, param_values, delimiter=args.delimiter, fmt="%." + str(args.precision) + "e", ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/sample/sobol.py000066400000000000000000000175701525347100600205140ustar00rootroot00000000000000import warnings from typing import Dict, Optional, Union import numpy as np from scipy.stats import qmc from . import common_args from ..util import scale_samples, read_param_file, compute_groups_matrix, _check_groups def sample( problem: Dict, N: int, *, calc_second_order: bool = True, scramble: bool = True, skip_values: int = 0, seed: Optional[Union[int, np.random.Generator]] = None, ): """Generates model inputs using Saltelli's extension of the Sobol' sequence. The Sobol' sequence is a popular quasi-random low-discrepancy sequence used to generate uniform samples of parameter space. The general approach is described in [1]. Returns a NumPy matrix containing the model inputs using Saltelli's sampling scheme. Saltelli's scheme reduces the number of required model runs from ``N(2D+1)`` to ``N(D+1)`` (see [2]). If `calc_second_order` is False, the resulting matrix has ``N * (D + 2)`` rows, where ``D`` is the number of parameters. If `calc_second_order` is `True`, the resulting matrix has ``N * (2D + 2)`` rows. These model inputs are intended to be used with :func:`SALib.analyze.sobol.analyze`. Notes ----- The initial points of the Sobol' sequence has some repetition (see Table 2 in Campolongo [3]__), which can be avoided by scrambling the sequence. Another option, not recommended and available for educational purposes, is to use the `skip_values` parameter. Skipping values reportedly improves the uniformity of samples. But, it has been shown that naively skipping values may reduce accuracy, increasing the number of samples needed to achieve convergence (see Owen [4]__). Parameters ---------- problem : dict, The problem definition. N : int The number of samples to generate. Ideally a power of 2 and <= `skip_values`. calc_second_order : bool, optional Calculate second-order sensitivities. Default is True. scramble : bool, optional If True, use LMS+shift scrambling. Otherwise, no scrambling is done. Default is True. skip_values : int, optional Number of points in Sobol' sequence to skip, ideally a value of base 2. It's recommended not to change this value and use `scramble` instead. `scramble` and `skip_values` can be used together. Default is 0. seed : {None, int, `numpy.random.Generator`}, optional If `seed` is None the `numpy.random.Generator` generator is used. If `seed` is an int, a new ``Generator`` instance is used, seeded with `seed`. If `seed` is already a ``Generator`` instance then that instance is used. Default is None. References ---------- 1. Sobol', I.M., 2001. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, The Second IMACS Seminar on Monte Carlo Methods 55, 271-280. https://doi.org/10.1016/S0378-4754(00)00270-6 2. Saltelli, A. (2002). Making best use of model evaluations to compute sensitivity indices. Computer Physics Communications, 145(2), 280-297. https://doi.org/10.1016/S0010-4655(02)00280-1 3. Campolongo, F., Saltelli, A., Cariboni, J., 2011. From screening to quantitative sensitivity analysis. A unified approach. Computer Physics Communications 182, 978-988. https://doi.org/10.1016/j.cpc.2010.12.039 4. Owen, A. B., 2020. On dropping the first Sobol' point. arXiv:2008.08051 [cs, math, stat]. Available at: http://arxiv.org/abs/2008.08051 (Accessed: 20 April 2021). """ D = problem["num_vars"] groups = _check_groups(problem) # Create base sequence - could be any type of sampling qrng = qmc.Sobol(d=2 * D, scramble=scramble, seed=seed) # fast-forward logic if skip_values > 0 and isinstance(skip_values, int): M = skip_values if not ((M & (M - 1) == 0) and (M != 0 and M - 1 != 0)): msg = f""" Convergence properties of the Sobol' sequence is only valid if `skip_values` ({M}) is a power of 2. """ warnings.warn(msg, stacklevel=2) # warning when N > skip_values # see https://github.com/scipy/scipy/pull/10844#issuecomment-673029539 n_exp = int(np.log2(N)) m_exp = int(np.log2(M)) if n_exp > m_exp: msg = ( "Convergence may not be valid as the number of " "requested samples is" f" > `skip_values` ({N} > {M})." ) warnings.warn(msg, stacklevel=2) qrng.fast_forward(M) elif skip_values < 0 or not isinstance(skip_values, int): raise ValueError("`skip_values` must be a positive integer.") # sample Sobol' sequence base_sequence = qrng.random(N) if not groups: Dg = problem["num_vars"] else: G, group_names = compute_groups_matrix(groups) Dg = len(set(group_names)) if calc_second_order: saltelli_sequence = np.zeros([(2 * Dg + 2) * N, D]) else: saltelli_sequence = np.zeros([(Dg + 2) * N, D]) index = 0 for i in range(N): # Copy matrix "A" for j in range(D): saltelli_sequence[index, j] = base_sequence[i, j] index += 1 # Cross-sample elements of "B" into "A" for k in range(Dg): for j in range(D): if (not groups and j == k) or (groups and group_names[k] == groups[j]): saltelli_sequence[index, j] = base_sequence[i, j + D] else: saltelli_sequence[index, j] = base_sequence[i, j] index += 1 # Cross-sample elements of "A" into "B" # Only needed if you're doing second-order indices (true by default) if calc_second_order: for k in range(Dg): for j in range(D): if (not groups and j == k) or ( groups and group_names[k] == groups[j] ): saltelli_sequence[index, j] = base_sequence[i, j] else: saltelli_sequence[index, j] = base_sequence[i, j + D] index += 1 # Copy matrix "B" for j in range(D): saltelli_sequence[index, j] = base_sequence[i, j + D] index += 1 saltelli_sequence = scale_samples(saltelli_sequence, problem) return saltelli_sequence def cli_parse(parser): """Add method specific options to CLI parser. Parameters ---------- parser : argparse object Returns ------- Updated argparse object """ parser.add_argument( "--max-order", type=int, required=False, default=2, choices=[1, 2], help="Maximum order of sensitivity indices to calculate", ) parser.add_argument( "--scramble", type=int, required=False, default=True, help="Use scrambled sequence", ) parser.add_argument( "--skip-values", type=int, required=False, default=None, help="Number of sample points to skip (default: next largest power of" " 2 from `samples`). Not recommended (use `scramble` instead).", ) return parser def cli_action(args): """Run sampling method Parameters ---------- args : argparse namespace """ problem = read_param_file(args.paramfile) param_values = sample( problem, args.samples, calc_second_order=(args.max_order == 2), scramble=args.scramble, ) np.savetxt( args.output, param_values, delimiter=args.delimiter, fmt="%." + str(args.precision) + "e", ) if __name__ == "__main__": common_args.run_cli(cli_parse, cli_action) SALib-SALib-d6e51b1/src/SALib/sample/sobol_sequence.py000066400000000000000000000070251525347100600223760ustar00rootroot00000000000000import math import sys import numpy as np from .directions import directions if sys.version_info[0] > 2: long = int # ============================================================================== # The following code is based on the Sobol sequence generator by Frances # Y. Kuo and Stephen Joe. The license terms are provided below. # # Copyright (c) 2008, Frances Y. Kuo and Stephen Joe # All rights reserved. # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions are # met: # # Redistributions of source code must retain the above copyright # notice, this list of conditions and the following disclaimer. # # Redistributions in binary form must reproduce the above copyright # notice, this list of conditions and the following disclaimer in the # documentation and/or other materials provided with the distribution. # # Neither the names of the copyright holders nor the names of the # University of New South Wales and the University of Waikato # and its contributors may be used to endorse or promote products derived # from this software without specific prior written permission. # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY # EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED # WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE # DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY # DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL # DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS # OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) # HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, # STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN # ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE # POSSIBILITY OF SUCH DAMAGE. # ============================================================================== def sample(N, D): """Generate (N x D) numpy array of Sobol sequence samples""" scale = 31 result = np.zeros([N, D]) if D > len(directions) + 1: raise ValueError("Error in Sobol sequence: not enough dimensions") L = int(math.ceil(math.log(N) / math.log(2))) if L > scale: raise ValueError("Error in Sobol sequence: not enough bits") for i in range(D): V = np.zeros(L + 1, dtype=long) if i == 0: for j in range(1, L + 1): V[j] = 1 << (scale - j) # all m's = 1 else: m = np.array(directions[i - 1], dtype=int) a = m[0] s = len(m) - 1 # The following code discards the first row of the ``m`` array # Because it has floating point errors, e.g. values of 2.24e-314 if L <= s: for j in range(1, L + 1): V[j] = m[j] << (scale - j) else: for j in range(1, s + 1): V[j] = m[j] << (scale - j) for j in range(s + 1, L + 1): V[j] = V[j - s] ^ (V[j - s] >> s) for k in range(1, s): V[j] ^= ((a >> (s - 1 - k)) & 1) * V[j - k] X = long(0) for j in range(1, N): X ^= V[index_of_least_significant_zero_bit(j - 1)] result[j][i] = float(X / math.pow(2, scale)) return result def index_of_least_significant_zero_bit(value): index = 1 while (value & 1) != 0: value >>= 1 index += 1 return index SALib-SALib-d6e51b1/src/SALib/scripts/000077500000000000000000000000001525347100600172205ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/scripts/__init__.py000066400000000000000000000000001525347100600213170ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/scripts/salib.bat000066400000000000000000000002161525347100600210010ustar00rootroot00000000000000@echo off setlocal if exist "%~dp0\python.exe" ( "%~dp0\python" "%~dp0salib" %* ) else ( "%~dp0..\python" "%~dp0salib" %* ) endlocal SALib-SALib-d6e51b1/src/SALib/scripts/salib.py000066400000000000000000000036501525347100600206700ustar00rootroot00000000000000"""Command-line utility for SALib""" import importlib import argparse from SALib import analyze, sample from SALib.util import avail_approaches def parse_subargs(module, parser, method, opts): """Attach argument parser for action specific options. Parameters ---------- module : module name of module to extract action from parser : argparser argparser object to attach additional arguments to method : str name of method (morris, sobol, etc). Must match one of the available submodules opts : list A list of argument options to parse Returns ------- subargs : argparser namespace object """ module.cli_args(parser) subargs = parser.parse_args(opts) return subargs def main(): parser = argparse.ArgumentParser(description="SALib - Sensitivity Analysis Library") subparsers = parser.add_subparsers(help="Sample or Analysis method", dest="action") sample_parser = subparsers.add_parser( "sample", description="Select one of the sample methods" ) analyze_parser = subparsers.add_parser("analyze") # Get list of available samplers and analyzers samplers = avail_approaches(sample) analyzers = avail_approaches(analyze) sample_parser.add_argument("method", choices=samplers) analyze_parser.add_argument("method", choices=analyzers) known_args, opts = parser.parse_known_args() action = known_args.action if not action: parser.print_help() exit() method_name = known_args.method common_args = importlib.import_module(".".join(["SALib", action, "common_args"])) module = importlib.import_module(".".join(["SALib", action, method_name])) if len(opts) == 0: cmd_parse = common_args.create(module.cli_parse) cmd_parse.print_help() exit() common_args.run_cli(module.cli_parse, module.cli_action, opts) if __name__ == "__main__": main() SALib-SALib-d6e51b1/src/SALib/test_functions/000077500000000000000000000000001525347100600206005ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/test_functions/Ishigami.py000066400000000000000000000034161525347100600227100ustar00rootroot00000000000000import numpy as np def evaluate(X: np.ndarray, A: float = 7.0, B: float = 0.1) -> np.ndarray: r"""Non-monotonic Ishigami-Homma three parameter test function: `f(x) = \sin(x_{1}) + A \sin(x_{2})^2 + Bx^{4}_{3}\sin(x_{1})` This test function is commonly used to benchmark global sensitivity methods as variance-based sensitivities of this function can be analytically determined. See listed references below. In [2], the expected first-order indices are: x1: 0.3139 x2: 0.4424 x3: 0.0 when A = 7, B = 0.1 when conducting Sobol' analysis with the Saltelli sampling method with a sample size of 1000. Parameters ---------- X : np.ndarray An `N*D` array holding values for each parameter, where `N` is the number of samples and `D` is the number of parameters (in this case, three). A : float Constant `A` parameter B : float Constant `B` parameter Returns ------- Y : np.ndarray References ---------- .. [1] Ishigami, T., Homma, T., 1990. An importance quantification technique in uncertainty analysis for computer models. Proceedings. First International Symposium on Uncertainty Modeling and Analysis. https://doi.org/10.1109/ISUMA.1990.151285 .. [2] Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S., 2008. Global Sensitivity Analysis: The Primer. Wiley, West Sussex, U.K. https://dx.doi.org/10.1002/9780470725184 """ Y = np.zeros(X.shape[0]) Y = ( np.sin(X[:, 0]) + A * np.power(np.sin(X[:, 1]), 2) + B * np.power(X[:, 2], 4) * np.sin(X[:, 0]) ) return Y SALib-SALib-d6e51b1/src/SALib/test_functions/Sobol_G.py000066400000000000000000000076701525347100600225100ustar00rootroot00000000000000import numpy as np # Non-monotonic Sobol G Function (8 parameters) # First-order indices: # x1: 0.7165 # x2: 0.1791 # x3: 0.0237 # x4: 0.0072 # x5-x8: 0.0001 def evaluate(values, a=None, delta=None, alpha=None): """Modified Sobol G-function. Reverts to original Sobol G-function if delta and alpha are not given. .. [1] Saltelli, A., Annoni, P., Azzini, I., Campolongo, F., Ratto, M., Tarantola, S., 2010. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Computer Physics Communications 181, 259–270. https://doi.org/10.1016/j.cpc.2009.09.018 Parameters ---------- values : numpy.ndarray input variables a : numpy.ndarray parameter values delta : numpy.ndarray shift parameters alpha : numpy.ndarray curvature parameters Returns ------- Y : Result of G-function """ if type(values) != np.ndarray: raise TypeError("The argument `values` must be a numpy ndarray") if a is None: a = np.array([0, 1, 4.5, 9, 99, 99, 99, 99]) if delta is None: delta = np.zeros_like(a) else: if not isinstance(delta, np.ndarray): raise TypeError("The argument `delta` must be given as a numpy ndarray") delta_inbetween = delta[(delta < 0) | (delta > 1)] if delta_inbetween.any(): raise ValueError( "Sobol G function called with delta values less than zero or" " greater than one" ) if alpha is None: alpha = np.ones_like(a) else: if not isinstance(alpha, np.ndarray): raise TypeError("The argument `alpha` must be given as a numpy ndarray") alpha_gto = alpha <= 0.0 if alpha_gto.any(): raise ValueError( "Sobol G function called with alpha values less than or equal to zero" ) ltz = values < 0 gto = values > 1 if ltz.any(): raise ValueError("Sobol G function called with values less than zero") elif gto.any(): raise ValueError("Sobol G function called with values greater than one") Y = np.ones([values.shape[0]]) for i, row in enumerate(values): shift_of_x = row + delta integral = np.modf(shift_of_x)[1] mod_x = shift_of_x - integral temp_y = np.abs(2 * mod_x - 1) ** alpha y_elements = ((1 + alpha) * temp_y + a) / (1 + a) Y[i] = y_elements.prod() return Y def _partial_first_order_variance(a=None, alpha=None): if a is None: a = [0, 1, 4.5, 9, 99, 99, 99, 99] if alpha is None: alpha = np.ones_like(a) a = np.array(a) return np.divide((alpha**2), np.multiply((1 + 2 * alpha), np.square(1 + a))) def _total_variance(a=None, alpha=None): if a is None: a = [0, 1, 4.5, 9, 99, 99, 99, 99] if alpha is None: alpha = np.ones_like(a) a = np.array(a) return np.add(-1, np.prod(1 + _partial_first_order_variance(a, alpha), axis=0)) def sensitivity_index(a, alpha=None): a = np.array(a) return np.divide(_partial_first_order_variance(a, alpha), _total_variance(a, alpha)) def total_sensitivity_index(a, alpha=None): a = np.array(a) pv = _partial_first_order_variance(a, alpha) tv = _total_variance(a, alpha) product_pv = np.prod(1 + pv, axis=0) return np.divide(pv * np.divide(product_pv, 1 + pv.T), tv) def V_Ti_regular(V, i): result = 1.0 for j in range(len(V)): if j != i: result = result * (1.0 + V[j]) return result * V[i] def _calc_analytic(a, alpha, num_params): """Calculate analytic values for modified Sobol_G function""" V_total = _total_variance(a, alpha) V_partial = _partial_first_order_variance(a, alpha) return np.array( [ np.round(V_Ti_regular(V_partial, i) / V_total, decimals=4) for i in range(num_params) ] ) SALib-SALib-d6e51b1/src/SALib/test_functions/__init__.py000066400000000000000000000000261525347100600227070ustar00rootroot00000000000000__all__ = ["Sobol_G"] SALib-SALib-d6e51b1/src/SALib/test_functions/lake_problem.py000066400000000000000000000133021525347100600236050ustar00rootroot00000000000000from typing import Union import numpy as np from numpy import log, sqrt from scipy.optimize import brentq FLOAT_OR_ARRAY = Union[float, np.array] def lake_problem( X: FLOAT_OR_ARRAY, a: FLOAT_OR_ARRAY = 0.1, q: FLOAT_OR_ARRAY = 2.0, b: FLOAT_OR_ARRAY = 0.42, eps: FLOAT_OR_ARRAY = 0.02, ) -> float: """Lake Problem as given in Hadka et al., (2015) and Kwakkel (2017) modified for use as a test function. The `mean` and `stdev` parameters control the log normal distribution of natural inflows (`epsilon` in [1] and [2]). References ---------- .. [1] Hadka, D., Herman, J., Reed, P., Keller, K., (2015). "An open source framework for many-objective robust decision making." Environmental Modelling & Software 74, 114-129. doi:10.1016/j.envsoft.2015.07.014 .. [2] Kwakkel, J.H, (2017). "The Exploratory Modeling Workbench: An open source toolkit for exploratory modeling, scenario discovery, and (multi-objective) robust decision making." Environmental Modelling & Software 96, 239-250. doi:10.1016/j.envsoft.2017.06.054 .. [3] Singh, R., Reed, P., Keller, K., (2015). "Many-objective robust decision making for managing an ecosystem with a deeply uncertain threshold response." Ecology and Society 20. doi:10.5751/ES-07687-200312 Parameters ---------- X : float or np.ndarray normalized concentration of Phosphorus at point in time a : float or np.ndarray rate of anthropogenic pollution (0.0 to 0.1) q : float or np.ndarray exponent controlling recycling rate (2.0 to 4.5). b : float or np.ndarray decay rate for phosphorus (0.1 to 0.45, where default 0.42 is irreversible, as described in [1]) eps : float or np.ndarray natural inflows of phosphorus (pollution), see [3] Returns ------- float, phosphorus pollution for a point in time """ Xq = X**q X_t1 = X + a + (Xq / (1.0 + Xq)) - (b * X) + eps return X_t1 def evaluate_lake(values: np.ndarray, seed=101) -> np.ndarray: """Evaluate the Lake Problem with an array of parameter values. References ---------- .. [1] Hadka, D., Herman, J., Reed, P., Keller, K., (2015). "An open source framework for many-objective robust decision making." Environmental Modelling & Software 74, 114–129. doi:10.1016/j.envsoft.2015.07.014 .. [2] Singh, R., Reed, P., Keller, K., (2015). "Many-objective robust decision making for managing an ecosystem with a deeply uncertain threshold response." Ecology and Society 20. doi:10.5751/ES-07687-200312 Parameters ---------- values : np.ndarray, model inputs in the (column) order of a, q, b, mean, stdev where * `a` is rate of anthropogenic pollution * `q` is exponent controlling recycling rate * `b` is decay rate for phosphorus * `mean` and * `stdev` set the log normal distribution of `eps`, see [2] Returns ------- np.ndarray, of Phosphorus pollution over time `t` """ rng = np.random.default_rng(seed) nvars = values.shape[0] a, q, b, mean, stdev = values.T sq_mean = mean**2 sq_std = stdev**2 eps = rng.lognormal( log(sq_mean / sqrt(sq_std + sq_mean)), sqrt(log(1.0 + sq_std / sq_mean)), size=nvars, ) Y = np.zeros((nvars, nvars)) for t in range(nvars): # First X value will be last Y value (should be 0 as we are filling # an array of zeros) Y[t] = lake_problem(Y[t - 1], a, q, b, eps) return Y def evaluate(values: np.ndarray, nvars: int = 100, seed=101): """Evaluate the Lake Problem with an array of parameter values. Parameters ---------- values : np.ndarray, model inputs in the (column) order of a, q, b, mean, stdev, delta, alpha nvars : int, number of decision variables to simulate (default: 100) Returns ------- np.ndarray : max_P, utility, inertia, reliability """ a, q, b, _, __, delta, alpha = values.T nsamples = len(a) Y = np.empty((nsamples, 4)) for i in range(nsamples): tmp = evaluate_lake(values[i, :5], seed=seed) a_i = a[i] q_i = q[i] Pcrit = brentq(lambda x: x**q_i / (1.0 + x**q_i) - b[i] * x, 0.01, 1.5) reliability = len(tmp[tmp < Pcrit]) / nvars max_P = np.max(tmp) utility = np.sum(alpha[i] * a_i * np.power(delta[i], np.arange(nvars))) # In practice, `a` will be set by a separate decision model # See [2] in docstring for `lake_problem()` # Here, it is a constant for a given scenario. # The value for `tau` (0.02) is taken from [2]. inertia = len(a_i[a_i < 0.02]) / nvars Y[i, :] = max_P, utility, inertia, reliability return Y if __name__ == "__main__": from SALib.sample import latin from SALib.analyze import delta SEED_VAL = 101 LAKE_SPEC = { "num_vars": 7, "names": ["a", "q", "b", "mean", "stdev", "delta", "alpha"], "bounds": [ [0.0, 0.1], [2.0, 4.5], [0.1, 0.45], [0.01, 0.05], [0.001, 0.005], [0.93, 0.99], [0.2, 0.5], ], "outputs": ["max_P", "Utility", "Inertia", "Reliability"], } latin_samples = latin.sample(LAKE_SPEC, 1000, seed=SEED_VAL) Y = evaluate(latin_samples) for i, name in enumerate(LAKE_SPEC["outputs"]): Si = delta.analyze(LAKE_SPEC, latin_samples, Y[:, i]) print(name) print(Si.to_df()) SALib-SALib-d6e51b1/src/SALib/test_functions/linear_model_1.py000066400000000000000000000012111525347100600240170ustar00rootroot00000000000000import numpy as np def evaluate(values): """Linear model (#1) used in Li et al., (2010). y = x1 + x2 + x3 + x4 + x5 Parameters ---------- values : np.array References ---------- .. [1] Genyuan Li, H. Rabitz, P.E. Yelvington, O.O. Oluwole, F. Bacon, C.E. Kolb, and J. Schoendorf, "Global Sensitivity Analysis for Systems with Independent and/or Correlated Inputs", Journal of Physical Chemistry A, Vol. 114 (19), pp. 6022 - 6032, 2010, https://doi.org/10.1021/jp9096919 """ Y = np.zeros([values.shape[0]]) Y = np.sum(values, axis=1) return Y SALib-SALib-d6e51b1/src/SALib/test_functions/linear_model_2.py000066400000000000000000000013761525347100600240340ustar00rootroot00000000000000import numpy as np def evaluate(values): """Linear model (#2) used in Li et al., (2010). y = 5x1 + 4x2 + 3x3 + 2x4 + x5 Parameters ---------- values : np.array References ---------- .. [1] Genyuan Li, H. Rabitz, P.E. Yelvington, O.O. Oluwole, F. Bacon, C.E. Kolb, and J. Schoendorf, "Global Sensitivity Analysis for Systems with Independent and/or Correlated Inputs", Journal of Physical Chemistry A, Vol. 114 (19), pp. 6022 - 6032, 2010, https://doi.org/10.1021/jp9096919 """ Y = np.zeros([values.shape[0]]) Y = ( 5 * values[:, 0] + 4 * values[:, 1] + 3 * values[:, 2] + 2 * values[:, 3] + values[:, 4] ) return Y SALib-SALib-d6e51b1/src/SALib/test_functions/oakley2004.py000066400000000000000000000201361525347100600227460ustar00rootroot00000000000000import numpy as np from SALib import ProblemSpec def evaluate(X: np.ndarray, A: np.ndarray, M: np.ndarray) -> np.ndarray: """Test function taken from Oakley and O'Hagan (2004) (see Eqn. 21 in [1]) References ---------- .. [1] Oakley, J.E., O’Hagan, A., 2004. Probabilistic sensitivity analysis of complex models: a Bayesian approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 66, 751–769. https://doi.org/10.1111/j.1467-9868.2004.05304.x """ a1, a2, a3 = A num_ins = X.shape[0] Y = np.zeros(num_ins) for i in range(num_ins): x_i = X[i] Y[i] = a1 @ x_i + a2 @ np.sin(x_i) + a3 @ np.cos(x_i) + x_i.T @ (M @ x_i) return Y if __name__ == "__main__": # Raw values taken from: http://www.jeremy-oakley.staff.shef.ac.uk/psa_example.txt M = np.array( [ -2.25e-02, -1.85e-01, 1.34e-01, 3.69e-01, 1.72e-01, 1.37e-01, -4.40e-01, -8.14e-02, 7.13e-01, -4.44e-01, 5.04e-01, -2.41e-02, -4.59e-02, 2.17e-01, 5.59e-02, 2.57e-01, 5.38e-02, 2.58e-01, 2.38e-01, -5.91e-01, -8.16e-02, -2.87e-01, 4.16e-01, 4.98e-01, 8.39e-02, -1.11e-01, 3.32e-02, -1.40e-01, -3.10e-02, -2.23e-01, -5.60e-02, 1.95e-01, 9.55e-02, -2.86e-01, -1.44e-01, 2.24e-01, 1.45e-01, 2.90e-01, 2.31e-01, -3.19e-01, -2.90e-01, -2.10e-01, 4.31e-01, 2.44e-02, 4.49e-02, 6.64e-01, 4.31e-01, 2.99e-01, -1.62e-01, -3.15e-01, -3.90e-01, 1.77e-01, 5.80e-02, 1.72e-01, 1.35e-01, -3.53e-01, 2.51e-01, -1.88e-02, 3.65e-01, -3.25e-01, -1.21e-01, 1.25e-01, 1.07e-01, 4.66e-02, -2.17e-01, 1.95e-01, -6.55e-02, 2.44e-02, -9.68e-02, 1.94e-01, 3.34e-01, 3.13e-01, -8.36e-02, -2.53e-01, 3.73e-01, -2.84e-01, -3.28e-01, -1.05e-01, -2.21e-01, -1.37e-01, -1.44e-01, -1.15e-01, 2.24e-01, -3.04e-02, -5.15e-01, 1.73e-02, 3.90e-02, 3.61e-01, 3.09e-01, 5.00e-02, -7.79e-02, 3.75e-03, 8.87e-01, -2.66e-01, -7.93e-02, -4.27e-02, -1.87e-01, -3.56e-01, -1.75e-01, 8.87e-02, 4.00e-01, -5.60e-02, 1.37e-01, 2.15e-01, -1.13e-02, -9.23e-02, 5.92e-01, 3.13e-02, -3.31e-02, -2.43e-01, -9.98e-02, 3.45e-02, 9.51e-02, -3.38e-01, 6.39e-03, -6.12e-01, 8.13e-02, 8.87e-01, 1.43e-01, 1.48e-01, -1.32e-01, 5.29e-01, 1.27e-01, 4.51e-02, 5.84e-01, 3.73e-01, 1.14e-01, -2.95e-01, -5.70e-01, 4.63e-01, -9.41e-02, 1.40e-01, -3.86e-01, -4.49e-01, -1.46e-01, 5.81e-02, -3.23e-01, 9.31e-02, 7.24e-02, -5.69e-01, 5.26e-01, 2.37e-01, -1.18e-02, 7.18e-02, 7.83e-02, -1.34e-01, 2.27e-01, 1.44e-01, -4.52e-01, -5.56e-01, 6.61e-01, 3.46e-01, 1.41e-01, 5.19e-01, -2.80e-01, -1.60e-01, -6.84e-02, -2.04e-01, 6.97e-02, 2.31e-01, -4.44e-02, -1.65e-01, 2.16e-01, 4.27e-03, -8.74e-02, 3.16e-01, -2.76e-02, 1.34e-01, 1.35e-01, 5.40e-02, -1.74e-01, 1.75e-01, 6.03e-02, -1.79e-01, -3.11e-01, -2.54e-01, 2.58e-02, -4.30e-01, -6.23e-01, -3.40e-02, -2.90e-01, 3.41e-02, 3.49e-02, -1.21e-01, 2.60e-02, -3.35e-01, -4.14e-01, 5.32e-02, -2.71e-01, -2.63e-02, 4.10e-01, 2.66e-01, 1.56e-01, -1.87e-01, 1.99e-02, -2.44e-01, -4.41e-01, 1.26e-02, 2.49e-01, 7.11e-02, 2.46e-01, 1.75e-01, 8.53e-03, 2.51e-01, -1.47e-01, -8.46e-02, 3.69e-01, -3.00e-01, 1.10e-01, -7.57e-01, 4.15e-02, -2.60e-01, 4.64e-01, -3.61e-01, -9.50e-01, -1.65e-01, 3.09e-03, 5.28e-02, 2.25e-01, 3.84e-01, 4.56e-01, -1.86e-01, 8.23e-03, 1.67e-01, 1.60e-01, ] ).reshape(15, 15) A = np.array( [ [ 0.0118, 0.0456, 0.2297, 0.0393, 0.1177, 0.3865, 0.3897, 0.6061, 0.6159, 0.4005, 1.0741, 1.1474, 0.7880, 1.1242, 1.1982, ], [ 0.4341, 0.0887, 0.0512, 0.3233, 0.1489, 1.0360, 0.9892, 0.9672, 0.8977, 0.8083, 1.8426, 2.4712, 2.3946, 2.0045, 2.2621, ], [ 0.1044, 0.2057, 0.0774, 0.2730, 0.1253, 0.7526, 0.8570, 1.0331, 0.8388, 0.7970, 2.2145, 2.0382, 2.4004, 2.0541, 1.9845, ], ] ) sp = ProblemSpec( { "names": ["x{}".format(i) for i in range(1, 16)], "bounds": [ [0.0, 0.835], ] * 15, "dists": ["norm"] * 15, } ) ( sp.sample_latin(2048, seed=101) .evaluate(evaluate, A, M) .analyze_rbd_fast(seed=101, num_resamples=100) ) print(sp) # analytic S1 values analytic = np.array( [ 0.00156, 0.000186, 0.001307, 0.003045, 0.002905, 0.023035, 0.024151, 0.026517, 0.046036, 0.014945, 0.101823, 0.135708, 0.101989, 0.105169, 0.122818, ] ) S1 = sp.analysis.to_df() S1["lower"] = S1["S1"] - S1["S1_conf"] S1["analytic"] = analytic S1["upper"] = S1["S1"] + S1["S1_conf"] print(np.all((analytic >= S1["lower"]) & (analytic <= S1["upper"]))) print((analytic >= S1["lower"]) & (analytic <= S1["upper"])) SALib-SALib-d6e51b1/src/SALib/test_functions/params/000077500000000000000000000000001525347100600220635ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/test_functions/params/Ishigami.txt000066400000000000000000000001401525347100600243510ustar00rootroot00000000000000x1 -3.14159265359 3.14159265359 x2 -3.14159265359 3.14159265359 x3 -3.14159265359 3.14159265359 SALib-SALib-d6e51b1/src/SALib/test_functions/params/Ishigami_groups.txt000066400000000000000000000001701525347100600257530ustar00rootroot00000000000000x1 -3.14159265359 3.14159265359 Group_1 x2 -3.14159265359 3.14159265359 Group_2 x3 -3.14159265359 3.14159265359 Group_2 SALib-SALib-d6e51b1/src/SALib/test_functions/params/Sobol_G.txt000066400000000000000000000001301525347100600241420ustar00rootroot00000000000000x1 0.0 1.0 x2 0.0 1.0 x3 0.0 1.0 x4 0.0 1.0 x5 0.0 1.0 x6 0.0 1.0 x7 0.0 1.0 x8 0.0 1.0 SALib-SALib-d6e51b1/src/SALib/util/000077500000000000000000000000001525347100600165065ustar00rootroot00000000000000SALib-SALib-d6e51b1/src/SALib/util/__init__.py000066400000000000000000000320551525347100600206240ustar00rootroot00000000000000"""A set of utility functions""" from typing import Dict, Tuple import warnings import numpy as np # type: ignore import pandas as pd # type: ignore import scipy as sp # type: ignore from typing import List from .util_funcs import ( # noqa: F401, E402 avail_approaches, read_param_file, _check_bounds, _check_groups, handle_seed, ) # noqa: F401, E402 from .problem import ProblemSpec # noqa: F401, E402 from .results import ResultDict # noqa: F401, E402 __all__ = ["scale_samples", "read_param_file", "avail_approaches", "handle_seed"] def _scale_samples(params: np.ndarray, bounds: List): """Rescale samples in 0-to-1 range to arbitrary bounds Parameters ---------- params : numpy.ndarray numpy array of dimensions `num_params`-by-:math:`N`, where :math:`N` is the number of samples bounds : list list of lists of dimensions `num_params`-by-2 """ # Check bounds are legal (upper bound is greater than lower bound) lower_bounds, upper_bounds = _check_bounds(bounds) if np.any(lower_bounds >= upper_bounds): raise ValueError( "Bounds are not legal (upper bound must be greater than lower bound)" ) # This scales the samples in-place, by using the optional output # argument for the numpy ufunctions # The calculation is equivalent to: # sample * (upper_bound - lower_bound) + lower_bound np.add( np.multiply(params, (upper_bounds - lower_bounds), out=params), lower_bounds, out=params, ) def scale_samples(params: np.ndarray, problem: Dict): """Scale samples based on specified distribution (defaulting to uniform). Adds an entry to the problem specification to indicate samples have been scaled to maintain backwards compatibility (`sample_scaled`). Parameters ---------- params : np.ndarray, numpy array of dimensions `num_params`-by-:math:`N`, where :math:`N` is the number of samples problem : dictionary, SALib problem specification Returns ------- np.ndarray, scaled samples """ bounds = problem["bounds"] dists = problem.get("dists") if dists is None: _scale_samples(params, bounds) else: if params.shape[1] != len(dists): msg = "Mismatch in number of parameters and distributions.\n" msg += "Num parameters: {}".format(params.shape[1]) msg += "Num distributions: {}".format(len(dists)) raise ValueError(msg) params = _nonuniform_scale_samples(params, bounds, dists) problem["sample_scaled"] = True return params # limited_params = limit_samples(params, upper_bound, lower_bound, dists) def _unscale_samples(params, bounds): """Rescale samples from arbitrary bounds back to [0,1] range Parameters ---------- bounds : list list of lists of dimensions num_params-by-2 params : numpy.ndarray numpy array of dimensions num_params-by-N, where N is the number of samples """ # Check bounds are legal (upper bound is greater than lower bound) b = np.array(bounds) lower_bounds = b[:, 0] upper_bounds = b[:, 1] if np.any(lower_bounds >= upper_bounds): raise ValueError( "Bounds are not legal (upper bound must be greater than lower bound)" ) # This scales the samples in-place, by using the optional output # argument for the numpy ufunctions # The calculation is equivalent to: # (sample - lower_bound) / (upper_bound - lower_bound) np.divide( np.subtract(params, lower_bounds, out=params), np.subtract(upper_bounds, lower_bounds), out=params, ) def _nonuniform_scale_samples(params, bounds, dists): """Rescale samples in 0-to-1 range to other distributions Parameters ---------- params : numpy.ndarray numpy array of dimensions num_params-by-N, where N is the number of samples dists : list list of distributions, one for each parameter unif: uniform with lower and upper bounds logunif: logarithmic uniform with lower and upper bounds triang: triangular with lower and upper bounds, as well as location of peak The location of peak is in percentage of width e.g. :code:`[1.0, 3.0, 0.5]` indicates 1.0 to 3.0 with a peak at 2.0 A soon-to-be deprecated two-value format assumes the lower bound to be 0 e.g. :code:`[3, 0.5]` assumes 0 to 3, with a peak at 1.5 norm: normal distribution with mean and standard deviation truncnorm: truncated normal distribution with lower and upper bounds, mean and standard deviation lognorm: lognormal with ln-space mean and standard deviation weibull: weibull distribution with shape, scale and optional location """ b = np.array(bounds, dtype=object) # initializing matrix for converted values conv_params = np.empty_like(params) # loop over the parameters for i in range(conv_params.shape[1]): # setting first and second arguments for distributions b1 = b[i][0] # ending b2 = b[i][1] # 0-1 if dists[i] == "triang": if len(b[i]) == 3: loc_start = b[i][0] # loc start b1 = b[i][1] # triangular distribution end b2 = b[i][2] # 0-1 aka c (the peak) elif len(b[i]) == 2: msg = ( "Two-value format for triangular distributions detected.\n" "To remove this message, specify the distribution start, " "end, and peak (three values) " "instead of the current two-value format " "(distribution end and peak, with start assumed to be 0)\n" "The two-value format will be deprecated in SALib v1.5.1" ) warnings.warn(msg, DeprecationWarning, stacklevel=2) loc_start = 0 b1 = b[i][0] b2 = b[i][1] else: raise ValueError( "Unknown triangular distribution specification. Check" " problem specification." ) # checking for correct parameters if b1 < 0 or b2 < 0 or b2 >= 1 or loc_start > b1: raise ValueError( """Triangular distribution bound error: Scale must be greater than zero; peak on interval [0,1], triangular start value must be smaller than end value""" ) else: conv_params[:, i] = sp.stats.triang.ppf( params[:, i], c=b2, scale=b1 - loc_start, loc=loc_start ) elif dists[i] == "unif": if b1 >= b2: raise ValueError( """Uniform distribution: lower bound must be less than upper bound""" ) else: conv_params[:, i] = params[:, i] * (b2 - b1) + b1 elif dists[i] == "logunif": if b1 <= 0 or b2 <= 0: raise ValueError("Log-uniform distribution: both bounds must be > 0") if b1 >= b2: raise ValueError( "Log-uniform distribution: lower bound must be less than upper bound" ) conv_params[:, i] = sp.stats.loguniform.ppf(params[:, i], a=b1, b=b2) elif dists[i] == "norm": if b2 <= 0: raise ValueError("""Normal distribution: stdev must be > 0""") else: conv_params[:, i] = sp.stats.norm.ppf(params[:, i], loc=b1, scale=b2) # Truncated normal distribution # parameters are lower bound and upper bound, mean and stdev elif dists[i] == "truncnorm": b3 = b[i][2] b4 = b[i][3] if b4 <= 0: raise ValueError( """Truncated normal distribution: stdev must be > 0""" ) if b1 >= b2: raise ValueError( """Truncated normal distribution: lower bound must be less than upper bound""" ) else: conv_params[:, i] = sp.stats.truncnorm.ppf( params[:, i], (b1 - b3) / b4, (b2 - b3) / b4, loc=b3, scale=b4 ) # lognormal distribution (ln-space, not base-10) # parameters are ln-space mean and standard deviation elif dists[i] == "lognorm": # checking for valid parameters if b2 <= 0: raise ValueError("""Lognormal distribution: stdev must be > 0""") else: conv_params[:, i] = np.exp( sp.stats.norm.ppf(params[:, i], loc=b1, scale=b2) ) # Weibull distribution # parameters are shape (k), scale (lambda) and optional location elif dists[i] == "weibull": # checking for location parameter if len(b[i]) == 3: b1 = b[i][0] # shape (k) b2 = b[i][1] # scale (lambda) loc_start = b[i][2] # location elif len(b[i]) == 2: b1 = b[i][0] b2 = b[i][1] loc_start = 0 else: raise ValueError( "Unknown Weibull distribution specification. Check" " problem specification." ) if b1 <= 0 or b2 <= 0: raise ValueError( """Weibull distribution: shape and scale must be > 0""" ) else: conv_params[:, i] = sp.stats.weibull_min.ppf( params[:, i], c=b1, scale=b2, loc=loc_start ) else: valid_dists = [ "unif", "triang", "norm", "truncnorm", "lognorm", "logunif", "weibull", ] raise ValueError("Distributions: choose one of %s" % ", ".join(valid_dists)) return conv_params def extract_group_names(p: Dict) -> Tuple: """Get a unique set of the group names. Maintains specified order of group names. `groups` should be a list of parameter names if groups are not defined. Parameters ---------- p : ProblemSpec or Dict Returns ------- tuple : names, number of groups """ if "groups" not in p or not p["groups"]: groups = p["names"] else: groups = p["groups"] names = list(pd.unique(np.array(groups))) number = len(names) return names, number def compute_groups_matrix(groups: List): """Generate matrix which notes factor membership of groups Computes a k-by-g matrix which notes factor membership of groups where: k is the number of variables (factors) g is the number of groups Also returns a g-length list of unique group_names whose positions correspond to the order of groups in the k-by-g matrix Parameters ---------- groups : List Group names corresponding to each variable Returns ------- tuple containing group matrix assigning parameters to groups and a list of unique group names """ num_vars = len(groups) unique_group_names = pd.unique(np.array(groups)) number_of_groups = len(unique_group_names) indices = dict([(x, i) for (i, x) in enumerate(unique_group_names)]) output = np.zeros((num_vars, number_of_groups), dtype=int) for parameter_row, group_membership in enumerate(groups): group_index = indices[group_membership] output[parameter_row, group_index] = 1 return output, unique_group_names def _define_problem_with_groups(problem: Dict) -> Dict: """ Checks if the user defined the 'groups' key in the problem dictionary. If not, makes the 'groups' key equal to the variables names. In other words, the number of groups will be equal to the number of variables, which is equivalent to no groups. Parameters ---------- problem : dict The problem definition Returns ------- problem : dict The problem definition with the 'groups' key, even if the user doesn't define it """ # Checks if there isn't a key 'groups' or if it exists and is set to 'None' if "groups" not in problem or not problem["groups"]: problem["groups"] = problem["names"] elif len(problem["groups"]) != problem["num_vars"]: raise ValueError( "Number of entries in 'groups' should be the same " "as in 'names'" ) return problem def _compute_delta(num_levels: int) -> float: """Computes the delta value from number of levels Parameters --------- num_levels : int The number of levels Returns ------- float """ return num_levels / (2.0 * (num_levels - 1)) SALib-SALib-d6e51b1/src/SALib/util/problem.py000066400000000000000000000500341525347100600205220ustar00rootroot00000000000000import warnings import importlib from types import MethodType from functools import partial, wraps from multiprocess import Pool, cpu_count import numpy as np import SALib.sample as samplers import SALib.analyze as analyzers from .util_funcs import ( # noqa: F401, E402 avail_approaches, _define_problem_with_groups, ) # noqa: F401, E402 from .results import ResultDict ptqdm_available = True try: from p_tqdm import p_imap except ImportError: ptqdm_available = False try: from pathos.pp import ParallelPythonPool as pp_Pool pathos_available = True except ImportError: pathos_available = False __all__ = ["ProblemSpec"] class ProblemSpec(dict): """Dictionary-like object representing an SALib Problem specification. Attributes ---------- samples : np.array, of generated samples results : np.array, of evaluations (i.e., model outputs) analysis : np.array or dict, of sensitivity indices """ def __init__(self, *args, **kwargs): super(ProblemSpec, self).__init__(*args, **kwargs) _check_spec_attributes(self) self._samples = None self._results = None self._analysis = None self["num_vars"] = len(self["names"]) self = _define_problem_with_groups(self) self._add_samplers() self._add_analyzers() @property def samples(self): return self._samples @samples.setter def samples(self, vals): cols = vals.shape[1] if cols != self["num_vars"]: msg = "Mismatched sample size: Expected " msg += "{} cols, got {}".format(self["num_vars"], cols) raise ValueError(msg) self._samples = vals # Clear results to avoid confusion self._results = None @property def results(self): return self._results @results.setter def results(self, vals): val_shape = vals.shape if len(val_shape) == 1: cols = 1 else: cols = vals.shape[1] out_cols = self.get("outputs", None) if out_cols is None: if cols == 1: self["outputs"] = ["Y"] else: self["outputs"] = [f"Y{i}" for i in range(1, cols + 1)] else: if cols != len(self["outputs"]): msg = "Mismatched sample size: Expected " msg += "{} cols, got {}".format(self["outputs"], cols) raise ValueError(msg) self._results = vals @property def analysis(self): return self._analysis def sample(self, func, *args, **kwargs): """Create sample using given function. Parameters ---------- func : function, Sampling method to use. The given function must accept the SALib problem specification as the first parameter and return a numpy array. *args : list, Additional arguments to be passed to `func` **kwargs : dict, Additional keyword arguments passed to `func` Returns ------- self : ProblemSpec object """ # Clear model output and analysis results to avoid confusion # especially if samples are forcibly changed... self._analysis = None self._results = None self._samples = func(self, *args, **kwargs) return self def set_samples(self, samples: np.ndarray): """Set previous samples used.""" self.samples = samples return self def set_results(self, results: np.ndarray): """Set previously available model results.""" if self.samples is not None: assert self.samples.shape[0] == results.shape[0], ( "Provided result array does not match existing number of" " existing samples!" ) self.results = results return self def evaluate(self, func, *args, **kwargs): """Evaluate a given model. Parameters ---------- func : function, Model, or function that wraps a model, to be run/evaluated. The provided function is required to accept a numpy array of inputs as its first parameter and must return a numpy array of results. *args : list, Additional arguments to be passed to `func` nprocs : int, If specified, attempts to parallelize model evaluations **kwargs : dict, Additional keyword arguments passed to `func` Returns ------- self : ProblemSpec object """ nprocs = kwargs.pop("nprocs", 1) if nprocs > 1: return self.evaluate_parallel(func, *args, nprocs=nprocs, **kwargs) self.results = func(self._samples, *args, **kwargs) return self def evaluate_parallel(self, func, *args, nprocs=None, **kwargs): """Evaluate model locally in parallel. All detected processors will be used if `nprocs` is not specified. Parameters ---------- func : function, Model, or function that wraps a model, to be run in parallel. The provided function needs to accept a numpy array of inputs as its first parameter and must return a numpy array of results. nprocs : int, Number of processors to use. Capped to the number of available processors. *args : list, Additional arguments to be passed to `func` **kwargs : dict, Additional keyword arguments passed to `func` Returns ------- self : ProblemSpec object """ warnings.warn( "Parallel evaluation is an experimental feature and may not work." ) if self._samples is None: raise RuntimeError("Sampling not yet conducted") max_procs = cpu_count() if nprocs is None: nprocs = max_procs else: if nprocs > max_procs: warnings.warn( f"{nprocs} processors requested but only {max_procs} found." ) nprocs = min(max_procs, nprocs) # Create wrapped partial function to allow passing of additional args tmp_f = self._wrap_func(func, *args, **kwargs) # Split into even chunks chunks = np.array_split(self._samples, int(nprocs), axis=0) if ptqdm_available: # Display progress bar if available res = list(p_imap(tmp_f, chunks, num_cpus=nprocs)) else: with Pool(nprocs) as pool: res = list(pool.imap(tmp_f, chunks)) self.results = self._collect_results(res) return self def evaluate_distributed( self, func, *args, nprocs=1, servers=None, verbose=False, **kwargs ): """Distribute model evaluation across a cluster. Usage Conditions: * The provided function needs to accept a numpy array of inputs as its first parameter * The provided function must return a numpy array of results Parameters ---------- func : function, Model, or function that wraps a model, to be run in parallel nprocs : int, Number of processors to use for each node. Defaults to 1. servers : list[str] or None, IP addresses or alias for each server/node to use. verbose : bool, Display job execution statistics. Defaults to False. *args : list, Additional arguments to be passed to `func` **kwargs : dict, Additional keyword arguments passed to `func` Returns ------- self : ProblemSpec object """ if not pathos_available: raise RuntimeError( "Pathos is required to run in distributed mode. Please install" " with `pip install pathos` or" " `conda install pathos -c conda-forge`" ) if verbose: from pathos.parallel import stats warnings.warn( "Distributed evaluation is an untested experimental feature and" " may not work." ) workers = pp_Pool(nprocs, servers=servers) # Split into even chunks chunks = np.array_split(self._samples, int(nprocs) * len(servers), axis=0) tmp_f = self._wrap_func(func) res = list(workers.map(tmp_f, chunks)) self.results = self._collect_results(res) if verbose: print(stats(), "\n") workers.clear() return self def analyze(self, func, *args, **kwargs): """Analyze sampled results using given function. Parameters ---------- func : function, Analysis method to use. The provided function must accept the problem specification as the first parameter, X values if needed, Y values, and return a numpy array. *args : list, Additional arguments to be passed to `func` nprocs : int, If specified, attempts to parallelize model evaluations **kwargs : dict, Additional keyword arguments passed to `func` Returns ------- self : ProblemSpec object """ if self["num_vars"] == 1 or (self["groups"] and len("groups") == 1): msg = ( "There is only a single parameter or group defined. There is " "no point in conducting sensitivity analysis as any and all" "effect(s) will be mapped to the single parameter/group." ) raise ValueError(msg) if "nprocs" in kwargs: # Call parallel method instead return self.analyze_parallel(func, *args, **kwargs) if self._results is None: raise RuntimeError("Model not yet evaluated") if "X" in func.__code__.co_varnames: # enforce passing of X if expected func = partial(func, *args, X=self._samples, **kwargs) else: func = partial(func, *args, **kwargs) out_cols = self.get("outputs", None) if out_cols is None: if len(self._results.shape) == 1: self["outputs"] = ["Y"] else: num_cols = self._results.shape[1] self["outputs"] = [f"Y{i}" for i in range(1, num_cols + 1)] if len(self["outputs"]) > 1: self._analysis = {} for i, out in enumerate(self["outputs"]): self._analysis[out] = func(self, Y=self._results[:, i]) else: self._analysis = func(self, Y=self._results) return self def analyze_parallel(self, func, *args, nprocs=None, **kwargs): """Analyze sampled results using the given function in parallel. Parameters ---------- func : function, Analysis method to use. The provided function must accept the problem specification as the first parameter, X values if needed, Y values, and return a numpy array. *args : list, Additional arguments to be passed to `func` nprocs : int, Number of processors to use. Capped to the number of outputs or available processors. **kwargs : dict, Additional keyword arguments passed to `func` Returns ------- self : ProblemSpec object """ warnings.warn("Parallel analysis is an experimental feature and may not work.") if self._results is None: raise RuntimeError("Model not yet evaluated") if "X" in func.__code__.co_varnames: # enforce passing of X if expected func = partial(func, *args, X=self._samples, **kwargs) else: func = partial(func, *args, **kwargs) out_cols = self.get("outputs", None) if out_cols is None: if len(self._results.shape) == 1: self["outputs"] = ["Y"] else: num_cols = self._results.shape[1] self["outputs"] = [f"Y{i}" for i in range(1, num_cols + 1)] # Cap number of processors used Yn = len(self["outputs"]) if Yn == 1: # Only single output, cannot parallelize warnings.warn( f"Analysis was not parallelized: {nprocs} processors requested" f" for 1 output." ) res = func(self, Y=self._results) else: max_procs = cpu_count() if nprocs is None: nprocs = max_procs else: nprocs = min(Yn, nprocs, max_procs) if ptqdm_available: # Display progress bar if available res = p_imap( lambda y: func(self, Y=y), [self._results[:, i] for i in range(Yn)], num_cpus=nprocs, ) else: with Pool(nprocs) as pool: res = list( pool.imap( lambda y: func(self, Y=y), [self._results[:, i] for i in range(Yn)], ) ) # Assign by output name if more than 1 output, otherwise # attach directly if Yn > 1: self._analysis = {} for out, Si in zip(self["outputs"], list(res)): self._analysis[out] = Si else: self._analysis = res return self def to_df(self): """Convert results to Pandas DataFrame.""" an_res = self._analysis if isinstance(an_res, ResultDict): return an_res.to_df() elif isinstance(an_res, dict): # case where analysis result is a dict of ResultDicts return [an.to_df() for an in list(an_res.values())] raise RuntimeError("Analysis not yet conducted") def plot(self, **kwargs): """Plot results as a bar chart. Returns ------- axes : matplotlib axes object """ if self._analysis is None: raise RuntimeError("Analysis not yet conducted") num_rows = len(self["outputs"]) if num_rows == 1: return self._analysis.plot(**kwargs) try: plt except NameError: import matplotlib.pyplot as plt num_cols = 1 fk = list(self._analysis.keys())[0] if isinstance(self._analysis[fk].to_df(), (list, tuple)): # have to divide by 2 to account for CI columns num_cols = len(self._analysis[fk]) // 2 p_width = max(num_cols * 3, 5) p_height = max(num_rows * 3, 6) _, axes = plt.subplots( num_rows, num_cols, sharey=True, figsize=(p_width, p_height) ) for res, ax in zip(self._analysis, axes): self._analysis[res].plot(ax=ax, **kwargs) try: ax[0].set_title(res) except TypeError: ax.set_title(res) plt.tight_layout() return axes def heatmap( self, metric: str = None, index: str = None, title: str = None, ax=None ): """Plot results as a heatmap. Parameters ---------- metric : str or None, name of output to analyze (display all if `None`) index : str or None, name of index to plot, dependent on what analysis was conducted (ST, S1, etc; displays all if `None`) title : str, title of plot to use (defaults to the same as `metric`) ax : axes object, matplotlib axes object to use for plot. Creates a new figure if not provided. Returns ------- ax : matplotlib axes object """ from SALib.plotting.heatmap import heatmap # type: ignore return heatmap(self, metric, index, title, ax) def _wrap_func(self, func, *args, **kwargs): # Create wrapped partial function to allow passing of additional args tmp_f = func if (len(args) > 0) or (len(kwargs) > 0): tmp_f = lambda x: func(x, *args, **kwargs) # noqa return tmp_f def _collect_results(self, res): res_shape = res[0].shape if len(res_shape) > 1: res_shape = (len(self._samples), *res_shape[1:]) else: res_shape = len(self._samples) final_res = np.empty(res_shape) # Collect results # Cannot enumerate over this as the length # of individual results may vary i = 0 for r in res: r_len = len(r) final_res[i : i + r_len] = r i += r_len return final_res def _method_creator(self, func, method): """Generate convenience methods for specified `method`.""" @wraps(func) def modfunc(self, *args, **kwargs): return getattr(self, method)(func, *args, **kwargs) return modfunc def _add_samplers(self): """Dynamically add available SALib samplers as ProblemSpec methods.""" for sampler in avail_approaches(samplers): func = getattr( importlib.import_module("SALib.sample.{}".format(sampler)), "sample" ) method_name = "sample_{}".format(sampler.replace("_sampler", "")) self.__setattr__( method_name, MethodType(self._method_creator(func, "sample"), self) ) def _add_analyzers(self): """Dynamically add available SALib analyzers as ProblemSpec methods.""" for analyzer in avail_approaches(analyzers): func = getattr( importlib.import_module("SALib.analyze.{}".format(analyzer)), "analyze" ) method_name = "analyze_{}".format(analyzer.replace("_analyzer", "")) self.__setattr__( method_name, MethodType(self._method_creator(func, "analyze"), self) ) def _repr_pretty_(self, p, cycle): p.text(str(self) if not cycle else "...") def __str__(self): rep = "" if self._samples is not None: arr_shape = self._samples.shape if len(arr_shape) == 1: arr_shape = (arr_shape[0], 1) nr, nx = arr_shape rep += ( "Samples:\n" f"\t{nx} parameters: {self['names']}\n" f"\t{nr} samples\n" ) if self._results is not None: arr_shape = self._results.shape if len(arr_shape) == 1: arr_shape = (arr_shape[0], 1) nr, ny = arr_shape rep += ( "Outputs:\n" f"\t{ny} outputs: {self['outputs']}\n" f"\t{nr} evaluations\n" ) if self._analysis is not None: rep += "Analysis:\n" an_res = self._analysis allowed_types = (list, tuple) if isinstance(an_res, ResultDict): an_res = an_res.to_df() if not isinstance(an_res, allowed_types): rep += f"{an_res}\n" else: for df in an_res: rep += f"{df}\n" elif isinstance(an_res, dict): for res_name in an_res: rep += "{}:\n".format(res_name) dfs = an_res[res_name].to_df() if isinstance(dfs, allowed_types): for df in dfs: rep += f"{df}:\n" else: rep += f"{dfs}:\n" if len(rep) == 0: rep = ( "ProblemSpec does not currently contain any samples, " "evaluations or results." ) return rep def _check_spec_attributes(spec: ProblemSpec): assert "names" in spec, "Names not defined" assert "bounds" in spec, "Bounds not defined" assert len(spec["bounds"]) == len( spec["names"] ), f"""Number of bounds do not match number of names Number of names: {len(spec['names'])} | {spec['names']} ---------------- Number of bounds: {len(spec['bounds'])} """ SALib-SALib-d6e51b1/src/SALib/util/results.py000066400000000000000000000020271525347100600205620ustar00rootroot00000000000000import pandas as pd # type: ignore from SALib.plotting.bar import plot as barplot class ResultDict(dict): """Dictionary holding analysis results. Conversion methods (e.g. to Pandas DataFrames) to be attached as necessary by each implementing method """ def __init__(self, *args, **kwargs): super(ResultDict, self).__init__(*args, **kwargs) def to_df(self): """Convert dict structure into Pandas DataFrame.""" return pd.DataFrame( {k: v for k, v in self.items() if k != "names"}, index=self["names"] ) def plot(self, ax=None): """Create bar chart of results""" Si_df = self.to_df() if isinstance(Si_df, (list, tuple)): import matplotlib.pyplot as plt # type: ignore if ax is None: fig, ax = plt.subplots(1, len(Si_df)) for idx, f in enumerate(Si_df): barplot(f, ax=ax[idx]) axes = ax else: axes = barplot(Si_df, ax=ax) return axes SALib-SALib-d6e51b1/src/SALib/util/util_funcs.py000066400000000000000000000130671525347100600212420ustar00rootroot00000000000000from typing import Dict, Union, Sequence import pkgutil import csv import numpy as np from numpy.random import Generator, BitGenerator, SeedSequence def avail_approaches(pkg): """Create list of available modules. Parameters ---------- pkg : module module to inspect Returns ------- method : list A list of available submodules """ methods = [ modname for importer, modname, ispkg in pkgutil.walk_packages(path=pkg.__path__) if modname not in ["common_args", "directions", "sobol_sequence"] and "test" not in modname ] return methods def read_param_file(filename, delimiter=None): """Unpacks a parameter file into a dictionary Reads a parameter file of format:: Param1,0,1,Group1,dist1 Param2,0,1,Group2,dist2 Param3,0,1,Group3,dist3 (Group and Dist columns are optional) Returns a dictionary containing: - names - the names of the parameters - bounds - a list of lists of lower and upper bounds - num_vars - a scalar indicating the number of variables (the length of names) - groups - a list of group names (strings) for each variable - dists - a list of distributions for the problem, None if not specified or all uniform Parameters ---------- filename : str The path to the parameter file delimiter : str, default=None The delimiter used in the file to distinguish between columns """ names = [] bounds = [] groups = [] dists = [] num_vars = 0 fieldnames = ["name", "lower_bound", "upper_bound", "group", "dist"] with open(filename, "r") as csvfile: dialect = csv.Sniffer().sniff(csvfile.read(1024), delimiters=delimiter) csvfile.seek(0) reader = csv.DictReader(csvfile, fieldnames=fieldnames, dialect=dialect) for row in reader: if row["name"].strip().startswith("#"): pass else: num_vars += 1 names.append(row["name"]) bounds.append([float(row["lower_bound"]), float(row["upper_bound"])]) # If the fourth column does not contain a group name, use # the parameter name if row["group"] is None: groups.append(row["name"]) elif row["group"] == "NA": groups.append(row["name"]) else: groups.append(row["group"]) # If the fifth column does not contain a distribution # use uniform if row["dist"] is None: dists.append("unif") else: dists.append(row["dist"]) if groups == names: groups = None elif len(set(groups)) == 1: raise ValueError( """Only one group defined, results will not be meaningful""" ) # setting dists to none if all are uniform # because non-uniform scaling is not needed if all([d == "unif" for d in dists]): dists = None return { "names": names, "bounds": bounds, "num_vars": num_vars, "groups": groups, "dists": dists, } def _check_groups(problem): """Check if there is more than 1 group.""" groups = problem.get("groups") if not groups: return False if groups == problem["names"]: return False if len(set(groups)) == 1: return False return groups def _check_bounds(bounds): """Check user supplied distribution bounds for validity. Parameters ---------- problem : dict The problem definition Returns ------- tuple : containing upper and lower bounds """ b = np.array(bounds) lower_bounds = b[:, 0] upper_bounds = b[:, 1] if np.any(lower_bounds >= upper_bounds): raise ValueError("Bounds are not legal") return lower_bounds, upper_bounds def _define_problem_with_groups(problem: Dict) -> Dict: """ Checks if the user defined the 'groups' key in the problem dictionary. If not, makes the 'groups' key equal to the variables names. In other words, the number of groups will be equal to the number of variables, which is equivalent to no groups. Parameters ---------- problem : dict The problem definition Returns ------- problem : dict The problem definition with the 'groups' key, even if the user doesn't define it """ # Checks if there isn't a key 'groups' or if it exists and is set to 'None' if "groups" not in problem or not problem["groups"]: problem["groups"] = problem["names"] elif len(problem["groups"]) != problem["num_vars"]: raise ValueError( "Number of entries in 'groups' should be the same " "as in 'names'" ) return problem def handle_seed( seed: Union[Generator, BitGenerator, SeedSequence, int, Sequence[int], None] ) -> np.random.Generator: """Set (or create) a random number generator.""" if isinstance(seed, np.random.Generator): # Spawn a Generator that we can own and reset. rng = seed.spawn(1)[0] elif isinstance( seed, (np.random.BitGenerator, np.random.SeedSequence, int, type(None)) ): rng = np.random.default_rng(seed) elif isinstance(seed, (list, tuple, np.ndarray)): # Handle sequences of integers rng = np.random.default_rng(seed) else: raise ValueError(f"Unsupported seed type: {type(seed)}") return rng SALib-SALib-d6e51b1/tests/000077500000000000000000000000001525347100600151525ustar00rootroot00000000000000SALib-SALib-d6e51b1/tests/conftest.py000066400000000000000000000032431525347100600173530ustar00rootroot00000000000000#!/usr/bin/env python # -*- coding: utf-8 -*- import pytest import tempfile @pytest.fixture def make_temporary_file(): """Returns a temporary file name Returns ========= openfile.name : str Name of the temporary file """ with tempfile.NamedTemporaryFile() as openfile: return openfile.name @pytest.fixture(scope="function") def setup_function(make_temporary_file): filename = make_temporary_file with open(filename, "w+") as ofile: ofile.write("Test1 0.0 100.0\n") ofile.write("Test2 5.0 51.0\n") return filename @pytest.fixture(scope="function") def setup_param_file(make_temporary_file): filename = make_temporary_file with open(filename, "w") as ofile: ofile.write("Test 1,0,1.0\n") ofile.write("Test 2,0,1.0\n") ofile.write("Test 3,0,1.0\n") return filename @pytest.fixture(scope="function") def setup_param_file_with_groups(make_temporary_file): filename = make_temporary_file with open(filename, "w") as ofile: ofile.write("Test 1,0,1.0,Group 1\n") ofile.write("Test 2,0,1.0,Group 1\n") ofile.write("Test 3,0,1.0,Group 2\n") return filename @pytest.fixture(scope="function") def setup_param_groups_prime(make_temporary_file): filename = make_temporary_file with open(filename, "w") as ofile: ofile.write("Test 1,0,1.0,Group 1\n") ofile.write("Test 2,0,1.0,Group 2\n") ofile.write("Test 3,0,1.0,Group 2\n") ofile.write("Test 4,0,1.0,Group 3\n") ofile.write("Test 5,0,1.0,Group 3\n") ofile.write("Test 6,0,1.0,Group 3\n") ofile.write("Test 7,0,1.0,Group 3\n") return filename 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3.09403925e+00 9.61805954e-01 -2.49271878e+00 3.09403925e+00 -1.27473803e+00 -3.13085479e+00 4.06504909e-01 -2.17978670e+00 6.48873873e-01 4.06504909e-01 -2.17978670e+00 -3.13085479e+00 -4.75534044e-02 -2.17978670e+00 -3.13085479e+00 4.06504909e-01 1.86685462e+00 -3.13085479e+00 -4.75534044e-02 1.86685462e+00 6.48873873e-01 4.06504909e-01 1.86685462e+00 6.48873873e-01 -4.75534044e-02 -2.17978670e+00 6.48873873e-01 -4.75534044e-02 1.86685462e+00 SALib-SALib-d6e51b1/tests/sample/000077500000000000000000000000001525347100600164335ustar00rootroot00000000000000SALib-SALib-d6e51b1/tests/sample/morris/000077500000000000000000000000001525347100600177465ustar00rootroot00000000000000SALib-SALib-d6e51b1/tests/sample/morris/test_morris.py000066400000000000000000000253431525347100600227010ustar00rootroot00000000000000from numpy.testing import assert_equal, assert_allclose from pytest import raises, fixture, warns, mark import numpy as np import warnings from SALib.sample.morris.morris import ( sample, _check_group_membership, _check_if_num_levels_is_even, _compute_optimised_trajectories, _generate_p_star, _compute_b_star, _generate_trajectory, _generate_x_star, ) from SALib.util import ( read_param_file, compute_groups_matrix, _define_problem_with_groups, _compute_delta, handle_seed, ) @fixture(scope="function") def setup_input(): input_1 = [[0, 1 / 3.0], [0, 1.0], [2 / 3.0, 1.0]] input_2 = [[0, 1 / 3.0], [2 / 3.0, 1 / 3.0], [2 / 3.0, 1.0]] input_3 = [[2 / 3.0, 0], [2 / 3.0, 2 / 3.0], [0, 2 / 3.0]] input_4 = [[1 / 3.0, 1.0], [1.0, 1.0], [1, 1 / 3.0]] input_5 = [[1 / 3.0, 1.0], [1 / 3.0, 1 / 3.0], [1, 1 / 3.0]] input_6 = [[1 / 3.0, 2 / 3.0], [1 / 3.0, 0], [1.0, 0]] input_sample = np.concatenate( [input_1, input_2, input_3, input_4, input_5, input_6] ) return input_sample @fixture(scope="function") def expected_sample(): input_1 = [[0, 1 / 3.0], [0, 1.0], [2 / 3.0, 1.0]] input_3 = [[2 / 3.0, 0], [2 / 3.0, 2 / 3.0], [0, 2 / 3.0]] input_4 = [[1 / 3.0, 1.0], [1.0, 1.0], [1, 1 / 3.0]] input_6 = [[1 / 3.0, 2 / 3.0], [1 / 3.0, 0], [1.0, 0]] return np.concatenate([input_1, input_3, input_4, input_6]) def test_odd_num_levels_raises_warning(setup_param_file_with_groups): parameter_file = setup_param_file_with_groups problem = read_param_file(parameter_file) with warnings.catch_warnings(record=True) as w: # Cause all warnings to always be triggered. warnings.simplefilter("always") # Trigger a UserWarning as num_levels should be an even number sample(problem, 10, num_levels=3) categories = [issubclass(m.category, UserWarning) for m in w] assert any(categories), "Expected warning not raised" needle = "num_levels should be an even number, sample may be biased" messages = [str(m.message) for m in w] msg_check = [needle in hay for hay in messages] assert any(msg_check), "Inappropriate num_levels warning not found" def test_even_num_levels_no_warning(setup_param_file_with_groups): parameter_file = setup_param_file_with_groups problem = read_param_file(parameter_file) with warnings.catch_warnings(record=True) as w: # Cause all warnings to always be triggered. warnings.simplefilter("always") # Check that num_levels warning is not raised sample(problem, 10, num_levels=4) if len(w) > 0: needle = "num_levels should be an even number, sample may be biased" messages = [str(m.message) for m in w] msg_check = [needle in hay for hay in messages] assert not any( msg_check ), "Inappropriate num_levels warning raised when all okay" def test_group_in_param_file_read(setup_param_file_with_groups): """ Tests that groups in a parameter file are read correctly """ parameter_file = setup_param_file_with_groups problem = read_param_file(parameter_file) groups, group_names = compute_groups_matrix(problem.get("groups")) assert_equal(problem["names"], ["Test 1", "Test 2", "Test 3"]) assert_equal(groups, np.array([[1, 0], [1, 0], [0, 1]], dtype=int)) assert_equal(group_names, ["Group 1", "Group 2"]) def test_optimal_trajectories_lt_samples(setup_param_file): parameter_file = setup_param_file problem = read_param_file(parameter_file) samples = 10 num_levels = 4 with raises(ValueError): sample(problem, samples, num_levels, optimal_trajectories=samples) def test_optimal_trajectories_lt_10(setup_param_file): parameter_file = setup_param_file problem = read_param_file(parameter_file) samples = 10 num_levels = 4 optimal_trajectories = 11 with raises(ValueError): sample(problem, samples, num_levels, optimal_trajectories=optimal_trajectories) def test_optimal_trajectories_gte_one(setup_param_file): parameter_file = setup_param_file problem = read_param_file(parameter_file) samples = 10 num_levels = 4 optimal_trajectories = 1 with raises(ValueError): sample(problem, samples, num_levels, optimal_trajectories) def test_find_optimum_trajectories(setup_input, expected_sample): N = 6 problem = {"num_vars": 2, "names": ["x1", "x2"], "groups": None} k_choices = 4 problem = _define_problem_with_groups(problem) output = _compute_optimised_trajectories(problem, setup_input, N, k_choices) expected = expected_sample np.testing.assert_equal(output, expected) def test_catch_inputs_not_in_zero_one_range(setup_input): problem = {"num_vars": 2, "groups": None} k_choices = 4 N = 10 with raises(ValueError): _compute_optimised_trajectories(problem, setup_input * 10, N, k_choices) def test_group_sample_fails_with_wrong_G_matrix(): N = 6 num_levels = 4 problem = { "bounds": [[0.0, 1.0], [0.0, 1.0], [0.0, 1.0], [0.0, 1.0]], "num_vars": 4, "groups": list([1, 2, 3]), } with raises(ValueError) as err: sample(problem, N, num_levels) assert "Number of entries in 'groups' should be the same as in " "'names'" in str( err.value ) class TestGroupSampleGeneration: def test_generate_p_star(self): """ Matrix P* - size (g * g) - describes order in which groups move each row contains one element equal to 1, all others are 0 no two columns have 1s in the same position """ rng = handle_seed(101) for i in range(1, 100): output = _generate_p_star(i, rng) if np.any(np.sum(output, 0) != np.ones(i)): raise AssertionError("Not legal P along axis 0") elif np.any(np.sum(output, 1) != np.ones(i)): raise AssertionError("Not legal P along axis 1") def test_compute_delta(self): fixture = np.arange(2, 10) output = [_compute_delta(f) for f in fixture] desired = np.array( [1.0, 0.75, 0.666667, 0.625, 0.6, 0.583333, 0.571429, 0.5625] ) assert_allclose(output, desired, rtol=1e-2) def test_generate_trajectory(self): rng = handle_seed(101) # Two groups of three factors G = np.array([[1, 0], [0, 1], [0, 1]]) # Four levels rng = handle_seed(101) num_levels = 4 output = _generate_trajectory(G, rng, num_levels=num_levels) if np.any((output > 1) | (output < 0)): raise AssertionError("Bound not working: %s", output) assert_equal(output.shape[0], 3) assert_equal(output.shape[1], 3) def test_compute_B_star(self): """ Tests for expected output Taken from example 3.2 in Saltelli et al. (2008) pg 122 """ k = 3 g = 2 x_star = np.array([[1.0 / 3, 1.0 / 3, 0.0]]) J = np.ones((g + 1, k)) G = np.array([[1, 0], [0, 1], [0, 1]]) D_star = np.array([[1, 0, 0], [0, -1, 0], [0, 0, 1]]) P_star = np.array([[1, 0], [0, 1]]) delta = 2.0 / 3 B = np.tril(np.ones([g + 1, g], dtype=int), -1) desired = np.array([[1.0 / 3, 1, 0], [1, 1, 0], [1, 1.0 / 3, 2.0 / 3]]) output = _compute_b_star(J, x_star, delta, B, G, P_star, D_star) assert_allclose(output, desired) def test_generate_x_star(self): """Test against previously generated x_star values.""" num_params = 4 num_levels = 4 rng = handle_seed(101) actual = _generate_x_star(num_params, num_levels, rng) expected = np.array([[0.0, 0.33333333, 0.33333333, 0.0]]) assert_allclose(actual, expected, rtol=1e-05) def test_define_problem_with_groups_all_ok(self): """ Checks if the function works when the user defines different groups for each variable. """ problem = { "num_vars": 8, "names": ["x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8"], "groups": ["G1", "G1", "G1", "G2", "G2", "G2", "G3", "G3"], } expected = problem result = _define_problem_with_groups(problem) assert expected == result def test_define_problem_with_groups_no_group_definition(self): """ Checks if the function works when the user doesn't define groups at all. """ problem = { "num_vars": 8, "names": ["x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8"], } expected = { "num_vars": 8, "names": ["x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8"], "groups": ["x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8"], } result = _define_problem_with_groups(problem) assert expected == result def test_define_problem_with_groups_exception(self): """ Checks if the function raises an exception when the user makes an inconsistent definition of groups, i.e, only define groups for some variables. """ problem = { "num_vars": 8, "names": ["x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8"], "groups": ["G1", "G1", "G1", "G2", "G2", "G2"], } with raises(ValueError): _define_problem_with_groups(problem) def test_check_if_num_levels_is_even_check_odd(self): """ Checks if a warn is raised when the number of tests is odd """ with warns(UserWarning): _check_if_num_levels_is_even(5) def test_check_if_num_levels_is_even_check_even(self): """ Checks if a warn is not raised when the number of tests is even. """ with warnings.catch_warnings(): warnings.simplefilter("error") _check_if_num_levels_is_even(4) @mark.xfail() def test_check_group_membership_all_ok(self): """ Checks if no errors are raised when group_membership is defined correctly. This test is expected to fail. """ # Creates a dummy variable group_membership = np.empty((3, 3), dtype=int) with raises(ValueError): _check_group_membership(group_membership) with raises(TypeError): _check_group_membership(group_membership) def test_check_group_membership_error(self): """ Checks if an error is raised if group_membership has a wrong type. """ # Creates a dummy variable group_membership = 1.0 with raises(TypeError): _check_group_membership(group_membership) group_membership = None with raises(ValueError): _check_group_membership(group_membership) SALib-SALib-d6e51b1/tests/sample/morris/test_morris_strategies.py000066400000000000000000000340361525347100600251320ustar00rootroot00000000000000""" """ from SALib.sample.morris import SampleMorris, LocalOptimisation, BruteForce from SALib.sample.morris.morris import _sample_morris from SALib.util import read_param_file, handle_seed import numpy as np from numpy.testing import assert_equal, assert_allclose import numpy.random as rd import pytest from pytest import fixture, raises @fixture(scope="function") def setup_input(): input_1 = [[0, 1 / 3.0], [0, 1.0], [2 / 3.0, 1.0]] input_2 = [[0, 1 / 3.0], [2 / 3.0, 1 / 3.0], [2 / 3.0, 1.0]] input_3 = [[2 / 3.0, 0], [2 / 3.0, 2 / 3.0], [0, 2 / 3.0]] input_4 = [[1 / 3.0, 1.0], [1.0, 1.0], [1, 1 / 3.0]] input_5 = [[1 / 3.0, 1.0], [1 / 3.0, 1 / 3.0], [1, 1 / 3.0]] input_6 = [[1 / 3.0, 2 / 3.0], [1 / 3.0, 0], [1.0, 0]] return np.concatenate([input_1, input_2, input_3, input_4, input_5, input_6]) @fixture(scope="function") def setup_problem(setup_input): input_sample = setup_input num_samples = 6 problem = {"num_vars": 2, "groups": None} k_choices = 4 groups = None num_params = problem.get("num_vars") input_1 = [[0, 1 / 3.0], [0, 1.0], [2 / 3.0, 1.0]] input_3 = [[2 / 3.0, 0], [2 / 3.0, 2 / 3.0], [0, 2 / 3.0]] input_4 = [[1 / 3.0, 1.0], [1.0, 1.0], [1, 1 / 3.0]] input_6 = [[1 / 3.0, 2 / 3.0], [1 / 3.0, 0], [1.0, 0]] expected = np.concatenate([input_1, input_3, input_4, input_6]) return (input_sample, num_samples, problem, k_choices, groups, num_params, expected) @fixture(scope="function") def strategy(): return BruteForce() class TestSharedMethods: def test_check_input_sample_N(self, strategy, setup_input): input_sample = setup_input num_params = 4 N = 5 with raises(AssertionError): strategy.check_input_sample(input_sample, num_params, N) def test_check_input_sample_num_vars(self, strategy, setup_input): input_sample = setup_input num_params = 3 N = 6 with raises(AssertionError): strategy.check_input_sample(input_sample, num_params, N) def test_check_input_sample_range(self, strategy, setup_input): input_sample = setup_input input_sample *= 100 num_params = 4 N = 6 with raises(AssertionError): strategy.check_input_sample(input_sample, num_params, N) def test_find_maximum(self, strategy): scores = np.array(range(15)) k_choices = 4 N = 6 output = strategy.find_maximum(scores, N, k_choices) expected = [2, 3, 4, 5] assert_equal(output, expected) def test_distance(self, strategy): """ Tests the computation of the distance of two trajectories """ input_1 = np.array([[0, 1 / 3.0], [0, 1.0], [2 / 3.0, 1.0]], dtype=np.float32) input_3 = np.array( [[2 / 3.0, 0], [2 / 3.0, 2 / 3.0], [0, 2 / 3.0]], dtype=np.float32 ) output = strategy.compute_distance(input_1, input_3) assert_allclose(output, 6.18, atol=1e-2) def test_distance_of_identical_matrices_is_min(self, strategy): input_1 = np.array([[1.0, 1.0], [1.0, 0.33333333], [0.33333333, 0.33333333]]) input_2 = input_1.copy() actual = strategy.compute_distance(input_1, input_2) desired = 0 assert_allclose(actual, desired, atol=1e-2) def test_distance_fail_with_difference_size_ip(self, strategy): input_1 = np.array([[0, 1 / 3.0], [0, 1.0]], dtype=np.float32) input_3 = np.array( [[2 / 3.0, 0], [2 / 3.0, 2 / 3.0], [0, 2 / 3.0]], dtype=np.float32 ) expected_err = ".*Input matrices are different sizes.*" with raises(ValueError, match=expected_err): strategy.compute_distance(input_1, input_3) def test_compute_distance_matrix(self, strategy, setup_input): """ Tests that a distance matrix is computed correctly for an input of six trajectories and two parameters """ sample_inputs = setup_input output = strategy.compute_distance_matrix(sample_inputs, 6, 2) expected = np.zeros((6, 6), dtype=np.float32) expected[1, :] = [5.50, 0, 0, 0, 0, 0] expected[2, :] = [6.18, 5.31, 0, 0, 0, 0] expected[3, :] = [6.89, 6.18, 6.57, 0, 0, 0] expected[4, :] = [6.18, 5.31, 5.41, 5.5, 0, 0] expected[5, :] = [7.52, 5.99, 5.52, 7.31, 5.77, 0] assert_allclose(output, expected, rtol=1e-2) def test_compute_distance_matrix_local(self, strategy, setup_input): """ Tests that a distance matrix is computed correctly for the local distance optimization. The only change is that the local method needs the upper triangle of the distance matrix instead of the lower one. This is for an input of six trajectories and two parameters """ sample_inputs = setup_input output = strategy.compute_distance_matrix( sample_inputs, 6, 2, local_optimization=True ) expected = np.zeros((6, 6), dtype=np.float32) expected[0, :] = [0, 5.50, 6.18, 6.89, 6.18, 7.52] expected[1, :] = [5.50, 0, 5.31, 6.18, 5.31, 5.99] expected[2, :] = [6.18, 5.31, 0, 6.57, 5.41, 5.52] expected[3, :] = [6.89, 6.18, 6.57, 0, 5.50, 7.31] expected[4, :] = [6.18, 5.31, 5.41, 5.5, 0, 5.77] expected[5, :] = [7.52, 5.99, 5.52, 7.31, 5.77, 0] assert_allclose(output, expected, rtol=1e-2) class TestLocallyOptimalStrategy: def test_local(self, setup_problem): rd.seed(12345) ( input_sample, num_samples, _, k_choices, groups, num_params, expected, ) = setup_problem local_strategy = LocalOptimisation() context = SampleMorris(local_strategy) actual = context.sample( input_sample, num_samples, num_params, k_choices, groups ) np.testing.assert_equal(actual, expected) def test_find_local_maximum_distance(self, setup_input): """ Test whether finding the local maximum distance equals the global maximum distance in a simple case for a defined random seed. From Saltelli et al. 2008, in the solution to exercise 3a, Chapter 3, page 134. Note that local and brute force methods are not guaranteed to produce the same results, even for simple problems, hence forcing the seed here. """ rd.seed(12345) local_strategy = LocalOptimisation() brute_strategy = BruteForce() sample_inputs = setup_input N = 6 num_params = 2 k_choices = 4 output_global = brute_strategy.brute_force_most_distant( sample_inputs, N, num_params, k_choices ) output_local = local_strategy.find_local_maximum( sample_inputs, N, num_params, k_choices ) assert_equal(output_global, output_local) def test_random_seed(self, setup_param_groups_prime): """Setting the seed before generating a sample results in two identical samples """ N = 8 param_file = setup_param_groups_prime problem = read_param_file(param_file) num_levels = 4 rng = handle_seed(12345) expected = _sample_morris(problem, N, rng, num_levels=num_levels) rng = handle_seed(12345) actual = _sample_morris(problem, N, rng, num_levels=num_levels) assert_equal(actual, expected) @pytest.mark.parametrize("execution_number", range(1)) def test_local_optimised_groups(self, setup_param_groups_prime, execution_number): """ Tests that the local optimisation problem gives the same answer as the brute force problem (for small values of `k_choices` and `N`) with groups for a defined random seed. Note that local and brute force methods are not guaranteed to produce exact answers, even for small problems. """ rng = handle_seed(12345) N = 8 param_file = setup_param_groups_prime problem = read_param_file(param_file) num_levels = 4 k_choices = 4 num_params = problem["num_vars"] num_groups = len(set(problem["groups"])) input_sample = _sample_morris(problem, N, rng, num_levels=num_levels) local = LocalOptimisation() # From local optimal trajectories actual = local.find_local_maximum( input_sample, N, num_params, k_choices, num_groups ) brute = BruteForce() desired = brute.brute_force_most_distant( input_sample, N, num_params, k_choices, num_groups ) print("Actual: {}\nDesired: {}\n".format(actual, desired)) print(input_sample) assert_equal(actual, desired) class TestLocalMethods: def test_sum_distances(self, setup_input): """ Tests whether the combinations are summed correctly. """ strategy = LocalOptimisation() dist_matr = strategy.compute_distance_matrix( setup_input, 6, 2, num_groups=None, local_optimization=True ) indices = (1, 3, 2) distance = strategy.sum_distances(indices, dist_matr) expected = 10.47 assert_allclose(distance, expected, rtol=1e-2) def test_get_max_sum_ind(self): """ Tests whether the right maximum indices are returned. """ strategy = LocalOptimisation() indices = np.array([(1, 2, 4), (3, 2, 1), (4, 2, 1)]) distances = np.array([20, 40, 50]) output = strategy.get_max_sum_ind(indices, distances, 0, 0) expected = (4, 2, 1) assert_equal(output, expected) def test_add_indices(self): """ Tests whether the right indices are added. """ strategy = LocalOptimisation() indices = (1, 3, 4) matr = np.zeros((6, 6), dtype=np.int16) ind_extra = strategy.add_indices(indices, matr) expected = [(1, 3, 4, 0), (1, 3, 4, 2), (1, 3, 4, 5)] assert_equal(ind_extra, expected) def test_get_max_sum_index_raises_error(self): strategy = LocalOptimisation() indices = [(1, 2, 4), (3, 2, 1), (4, 2, 1)] distances_wrong = [20, 40] with raises(ValueError): strategy.get_max_sum_ind(indices, distances_wrong, 0, 0) def test_combo_from_locally_optimal_method(self, setup_input): """ Tests whether the correct combination is picked from the fixture drawn from Saltelli et al. 2008, in the solution to exercise 3a, Chapter 3, page 134. """ sample_inputs = setup_input N = 6 num_params = 2 k_choices = 4 strategy = LocalOptimisation() output = strategy.find_local_maximum(sample_inputs, N, num_params, k_choices) expected = [0, 2, 3, 5] # trajectories 1, 3, 4, 6 assert_equal(output, expected) class TestBruteForceStrategy: def test_brute_force(self, setup_problem): ( input_sample, num_samples, _, k_choices, groups, num_params, expected, ) = setup_problem strategy = BruteForce() context = SampleMorris(strategy) actual = context.sample( input_sample, num_samples, num_params, k_choices, groups ) np.testing.assert_equal(actual, expected) class TestBruteForceMethods: def test_combo_from_find_most_distant(self, setup_input): """ Tests whether the correct combination is picked from the fixture drawn from Saltelli et al. 2008, in the solution to exercise 3a, Chapter 3, page 134. """ sample_inputs = setup_input N = 6 num_params = 2 k_choices = 4 strategy = BruteForce() scores = strategy.find_most_distant(sample_inputs, N, num_params, k_choices) output = strategy.find_maximum(scores, N, k_choices) expected = [0, 2, 3, 5] # trajectories 1, 3, 4, 6 assert_equal(output, expected) def test_scores_from_find_most_distant(self, setup_input): """ Checks whether array of scores from (6 4) is correct. Data is derived from Saltelli et al. 2008, in the solution to exercise 3a, Chapter 3, page 134. """ sample_inputs = setup_input N = 6 num_params = 2 k_choices = 4 strategy = BruteForce() output = strategy.find_most_distant(sample_inputs, N, num_params, k_choices) expected = np.array( [ 15.022, 13.871, 14.815, 14.582, 16.178, 14.912, 15.055, 16.410, 15.685, 16.098, 14.049, 15.146, 14.333, 14.807, 14.825, ], dtype=np.float32, ) assert_allclose(output, expected, rtol=1e-1, atol=1e-2) def test_catch_combos_too_large(self): N = int(1e6) k_choices = 4 num_params = 2 input_sample = np.random.random_sample((N, num_params)) strategy = BruteForce() with raises(ValueError): strategy.find_most_distant(input_sample, N, num_params, k_choices) def test_make_index_list(self): N = 4 num_params = 2 groups = None strategy = BruteForce() actual = strategy._make_index_list(N, num_params, groups) desired = [ np.array([0, 1, 2]), np.array([3, 4, 5]), np.array([6, 7, 8]), np.array([9, 10, 11]), ] assert_equal(desired, actual) def test_make_index_list_with_groups(self): N = 4 num_params = 3 groups = 2 strategy = BruteForce() actual = strategy._make_index_list(N, num_params, groups) desired = [ np.array([0, 1, 2]), np.array([3, 4, 5]), np.array([6, 7, 8]), np.array([9, 10, 11]), ] assert_equal(actual, desired) SALib-SALib-d6e51b1/tests/sample/radial/000077500000000000000000000000001525347100600176675ustar00rootroot00000000000000SALib-SALib-d6e51b1/tests/sample/radial/test_radial_oat.py000066400000000000000000000051361525347100600234040ustar00rootroot00000000000000import numpy as np from SALib.sample.radial.radial_sobol import sample as r_sample from SALib.sample.radial.radial_mc import sample as rmc_sample from SALib.analyze.radial_ee import analyze as ree_analyze from SALib.test_functions import Sobol_G from test_setup import setup_G4 def test_mc_oat_sample(): """Radial OAT with a sample size of 1 should be equivalent to OAT""" num_sample_sets = 1 problem, _, _, _ = setup_G4() r_X = rmc_sample(problem, num_sample_sets, seed=101) assert len(r_X) == 21, "Number of parameter sets should equal `N*(p+1)`" num_sample_sets = 5 problem, _, _, _ = setup_G4() r_X = rmc_sample(problem, num_sample_sets, seed=101) assert len(r_X) == ( num_sample_sets * 21 ), "Number of parameter sets should equal `N*(p+1)`" def test_sobol_oat(): """Radial OAT with a sample size of 1 should be equivalent to OAT""" num_sample_sets = 1 problem, _, _, _ = setup_G4() r_X = r_sample(problem, num_sample_sets, seed=101) assert len(r_X) == 21, "Number of parameter sets should equal `N*(p+1)`" # Also ensure same size array is returned when skipping rows. r_X = r_sample(problem, num_sample_sets, skip_num=1) assert len(r_X) == 21, "Number of parameter sets should equal `N*(p+1)`" def test_mc_oat(): """Radial OAT with a sample size of 1 should be equivalent to OAT. Generated sample size should be `p+1`, where `p` is number of parameters. References ---------- .. [1] Herman, J.D., Kollat, J.B., Reed, P.M., Wagener, T., 2013. Technical Note: Method of Morris effectively reduces the computational demands of global sensitivity analysis for distributed watershed models. Hydrology and Earth System Sciences 17, 2893–2903. https://doi.org/10.5194/hess-17-2893-2013 """ num_sample_sets = 5000 problem, alpha, a, analytic_vals = setup_G4() r_X = rmc_sample(problem, num_sample_sets, seed=42) delta = np.random.rand(20) r_Y = Sobol_G.evaluate(r_X, a, alpha=alpha, delta=delta) res = ree_analyze(problem, r_X, r_Y, num_sample_sets, seed=42) # Mu* does not give a quantitative interpretation of percent variance (Herman et al. 2013) # See Ref [1] # Here, we normalize to values between 0 - 1 scaled = (res["mu_star"] / (res["mu_star"].max() - res["mu_star"].min())).round(2) assert np.array_equal( np.where(analytic_vals > 0.05), np.where(scaled > 0.15) ), "Mismatch in identified vs expected sensitive parameters." if __name__ == "__main__": test_sobol_oat() test_mc_oat_sample() test_mc_oat() SALib-SALib-d6e51b1/tests/sample/radial/test_radial_sobol.py000066400000000000000000000061171525347100600237370ustar00rootroot00000000000000"""Tests for Radial OAT using Sobol sampling""" from numpy.testing import assert_allclose import numpy as np from SALib.sample.radial.radial_sobol import sample as r_sample from SALib.analyze.sobol_jansen import analyze as j_analyze from SALib.test_functions import Sobol_G from test_setup import setup_G10, setup_G4 def test_radial_jansen_G4(): """Calculate and compare analytic values against reported ST values for G*4. We use the values for `a` and `alpha` from [1], but note that the analytic values provided in the paper are incorrect. References ---------- .. [1] Campolongo, F., Saltelli, A., Cariboni, J., 2011. From screening to quantitative sensitivity analysis: A unified approach. Computer Physics Communications 182, 978–988. https://www.sciencedirect.com/science/article/pii/S0010465510005321 DOI: 10.1016/j.cpc.2010.12.039 """ num_sample_sets = 12500 problem, alpha, a, analytic_vals = setup_G4() delta = np.random.RandomState(101).rand(20) r_X = r_sample(problem, num_sample_sets, seed=101) r_Y = Sobol_G.evaluate(r_X, a, alpha=alpha, delta=delta) g4_result = j_analyze(problem, r_Y, num_sample_sets, num_resamples=1000, seed=101) ST_res = g4_result["ST"].round(4) assert_allclose(analytic_vals, ST_res, atol=0.04, rtol=0.04) num_analytic = len(np.where(analytic_vals > 0.05)[0]) assert num_analytic == 4, "Expected 4 analytic values, but only found {}".format( num_analytic ) assert np.array_equal( np.where(analytic_vals > 0.05), np.where(ST_res > 0.05) ), "Mismatch in identified vs expected sensitive parameters." def test_radial_jansen_G10(): """Calculate and compare analytic values against reported ST values for G*10. We use the values for `a` and `alpha` from [1], but note that the analytic values provided in the paper are incorrect. References ---------- .. [1] Campolongo, F., Saltelli, A., Cariboni, J., 2011. From screening to quantitative sensitivity analysis: A unified approach. Computer Physics Communications 182, 978–988. https://www.sciencedirect.com/science/article/pii/S0010465510005321 DOI: 10.1016/j.cpc.2010.12.039 """ num_sample_sets = 17500 problem, alpha, a, analytic_vals = setup_G10() delta = np.random.RandomState(101).rand(20) r_X = r_sample(problem, num_sample_sets, seed=101) r_Y = Sobol_G.evaluate(r_X, a, alpha=alpha, delta=delta) g10_result = j_analyze(problem, r_Y, num_sample_sets, num_resamples=1000, seed=101) ST_res = g10_result["ST"].round(4) assert_allclose(analytic_vals, ST_res, atol=0.04, rtol=0.04) num_analytic = len(np.where(analytic_vals > 0.05)[0]) assert num_analytic == 10, "Expected 10 analytic values, but only found {}".format( num_analytic ) assert np.array_equal( np.where(analytic_vals > 0.05), np.where(ST_res > 0.05) ), "Mismatch in identified vs expected sensitive parameters." if __name__ == "__main__": test_radial_jansen_G4() test_radial_jansen_G10() SALib-SALib-d6e51b1/tests/sample/radial/test_setup.py000066400000000000000000000024001525347100600224340ustar00rootroot00000000000000import numpy as np from SALib.test_functions import Sobol_G def setup_G4(): problem = { "num_vars": 20, "names": ["x{}".format(i) for i in range(1, 21)], "bounds": [[0, 1] * 20], } a = np.array( [ 100, 0, 100, 100, 100, 100, 1, 0, 100, 100, 0, 100, 100, 100, 1, 100, 100, 0, 100, 1, ] ) alpha = np.array( [1, 4, 1, 1, 1, 1, 0.5, 3, 1, 1, 2, 1, 1, 1, 0.5, 1, 1, 1.5, 1, 0.5] ) analytic_vals = Sobol_G._calc_analytic(a, alpha, 20) return problem, alpha, a, analytic_vals def setup_G10(): problem = { "num_vars": 20, "names": ["x{}".format(i) for i in range(1, 21)], "bounds": [[0, 1] * 20], } a = np.array( [100, 0, 100, 100, 100, 100, 0, 1, 0, 0, 1, 0, 100, 100, 0, 100, 100, 3, 100, 0] ) alpha = np.array( [1, 4, 1, 1, 1, 1, 0.4, 3, 0.8, 0.7, 2, 1.3, 1, 1, 0.5, 1, 1, 2.5, 1, 0.6] ) analytic_vals = Sobol_G._calc_analytic(a, alpha, 20) return problem, alpha, a, analytic_vals SALib-SALib-d6e51b1/tests/sample/test_latin.py000066400000000000000000000106411525347100600211550ustar00rootroot00000000000000from SALib.sample.latin import sample from pytest import approx import numpy as np class TestLatinSample: def test_latin_sample_trivial(self): problem = {"num_vars": 1, "bounds": [[0, 1]], "names": ["var1"]} actual = sample(problem, 10, seed=42) expected = np.array( [ [0.77860643], [0.0773956], [0.40941773], [0.28585979], [0.3697368], [0.59756224], [0.14388784], [0.81281136], [0.67611397], [0.94503859], ] ) np.testing.assert_allclose(actual, expected) def test_latin_sample_trivial_group(self): problem = { "num_vars": 1, "bounds": [[0, 1]], "names": ["var1"], "groups": ["group1"], } actual = sample(problem, 10, seed=42) expected = np.array( [ [0.77860643], [0.0773956], [0.40941773], [0.28585979], [0.3697368], [0.59756224], [0.14388784], [0.81281136], [0.67611397], [0.94503859], ] ) np.testing.assert_allclose(actual, expected) def test_latin_sample_one_group(self): problem = { "num_vars": 2, "bounds": [[0, 1], [0, 1]], "names": ["var1", "var2"], "groups": ["group1", "group1"], } actual = sample(problem, 10, seed=42) expected = np.array( [ [0.77860643, 0.77860643], [0.0773956, 0.0773956], [0.40941773, 0.40941773], [0.28585979, 0.28585979], [0.3697368, 0.3697368], [0.59756224, 0.59756224], [0.14388784, 0.14388784], [0.81281136, 0.81281136], [0.67611397, 0.67611397], [0.94503859, 0.94503859], ] ) np.testing.assert_allclose(actual, expected) def test_latin_sample_no_groups(self): problem = { "num_vars": 2, "bounds": [[0, 1], [0, 1]], "names": ["var1", "var2"], "groups": None, } actual = sample(problem, 10, seed=42) expected = np.array( [ [0.86011150, 0.15247564], [0.27319939, 0.84560700], [0.03745401, 0.73663618], [0.60580836, 0.51394939], [0.78661761, 0.46118529], [0.97080726, 0.97851760], [0.35986585, 0.03042422], [0.19507143, 0.32912291], [0.41560186, 0.62921446], [0.51559945, 0.24319450], ] ) approx(actual, expected) def test_latin_sample_two_groups(self): problem = { "num_vars": 2, "bounds": [[0, 1], [0, 1]], "names": ["var1", "var2"], "groups": ["group1", "group2"], } actual = sample(problem, 10, seed=42) expected = np.array( [ [0.20941773, 0.68227616], [0.98276312, 0.37860643], [0.0773956, 0.80638173], [0.85545848, 0.29756224], [0.41281136, 0.96316644], [0.18585979, 0.5926765], [0.66438651, 0.1697368], [0.74434142, 0.72272387], [0.37611397, 0.44503859], [0.5370798, 0.04388784], ] ) np.testing.assert_allclose(actual, expected) def test_latin_group_constant(self): """Ensure grouped parameters have identical values.""" problem = { "num_vars": 6, "names": ["P1", "P2", "P3", "P4", "P5", "P6"], "bounds": [[-100.0, 100.0] * 6], "groups": ["A", "B"] * 3, } samples = sample(problem, 10, seed=42) # Group samples should have the same values # Get (max - min) with the `ptp()` method, the result of which should be # an array of zeros diff = np.ptp(samples[:, ::2], axis=1) assert np.all(diff == 0), "Grouped samples do not have the same values" diff = np.ptp(samples[:, 1::2], axis=1) assert np.all(diff == 0), "Grouped samples do not have the same values" SALib-SALib-d6e51b1/tests/sample/test_shapley.py000066400000000000000000000025131525347100600215120ustar00rootroot00000000000000import numpy as np import pytest from SALib.sample import shapley @pytest.fixture def problem(): return { "num_vars": 3, "names": ["x1", "x2", "x3"], "bounds": [[-1.0, 1.0], [0.0, 2.0], [10.0, 20.0]], } def test_sample_shape_and_trajectory_structure(problem): samples = shapley.sample(problem, 8, seed=42) assert samples.shape == (32, 3) trajectories = samples.reshape(8, 4, 3) for trajectory in trajectories: changed = [ np.flatnonzero(trajectory[step + 1] != trajectory[step]) for step in range(3) ] assert all(factors.size == 1 for factors in changed) assert sorted(int(factors[0]) for factors in changed) == [0, 1, 2] def test_sample_seed_is_reproducible(problem): first = shapley.sample(problem.copy(), 4, seed=101) second = shapley.sample(problem.copy(), 4, seed=101) np.testing.assert_array_equal(first, second) @pytest.mark.parametrize("N", [0, -1, 1.5, True]) def test_sample_rejects_invalid_sample_count(problem, N): with pytest.raises(ValueError, match="positive integer"): shapley.sample(problem, N, seed=1) def test_sample_rejects_groups(problem): problem["groups"] = ["A", "A", "B"] with pytest.raises(ValueError, match="does not support groups"): shapley.sample(problem, 4, seed=1) SALib-SALib-d6e51b1/tests/test_analyze_delta.py000066400000000000000000000237741525347100600214140ustar00rootroot00000000000000from SALib.analyze import delta from SALib.util import handle_seed import numpy as np import pandas as pd import pytest def create_base_dataframe(seed=42): rng = handle_seed(seed) n = 15000 col_a = np.linspace(10, 80, n, endpoint=False) + rng.uniform(0, 70 / n, size=n) col_b = np.linspace(-20, 50, n, endpoint=False) + rng.uniform(0, 70 / n, size=n) rng.shuffle(col_a) rng.shuffle(col_b) df = pd.DataFrame( data={ "output_col": np.clip( rng.normal(loc=22, scale=1.3, size=n), 17, 32 ), # Normal distribution centered at 22 with small std dev "column_a": col_a, "column_b": col_b, } ) return df def create_problemspec(df): Y = np.asarray(df["output_col"].values) cols_input = [col for col in df.columns if col != "output_col"] X = df[cols_input].values problem = { "num_vars": len(cols_input), "names": cols_input, "bounds": [[X[:, i].min(), X[:, i].max()] for i in range(len(cols_input))], } return problem, X, Y def test_constant_input_column(): """Show how delta handles constant values in an input feature column.""" df = create_base_dataframe() df["column_consts"] = 7.77 problem, X, Y = create_problemspec(df) with pytest.warns(UserWarning, match=r"has constant values"): _ = delta.analyze(problem=problem, X=X, Y=Y, num_resamples=3) def test_binary_unbalanced(): """If dataset too small for binning minimum""" df = create_base_dataframe() rng = handle_seed(42) n = len(df) n_zeroes = max(1, int(n * 0.001)) zeroes_and_ones = np.array([0] * n_zeroes + [1] * (len(df) - n_zeroes)) rng.shuffle(zeroes_and_ones) df["binary_small_zeroes"] = zeroes_and_ones problem, X, Y = create_problemspec(df) with pytest.warns(UserWarning, match=r"Only one bin remains"): _ = delta.analyze(problem=problem, X=X, Y=Y, num_resamples=3) def test_binning_adaptation(): """Data bin modification and adaptation.""" df = create_base_dataframe() rng = handle_seed(42) n = len(df) counts = { 0: int(0.0004 * n), 1: int(0.0005 * n), 2: int(0.0010 * n), 3: int(0.0100 * n), 4: int(0.0200 * n), 5: int(0.2500 * n), 6: int(0.2500 * n), 7: int(0.3700 * n), 8: int(0.0020 * n), 9: int(0.0009 * n), } total_assigned = sum(counts.values()) counts[10] = n - total_assigned value_col = np.array([val for val, count in counts.items() for _ in range(count)]) rng.shuffle(value_col) df["binning_combination"] = value_col problem, X, Y = create_problemspec(df) with pytest.warns(UserWarning, match=r"Bin Merge Notice: Final no. bins is 6."): _ = delta.analyze(problem=problem, X=X, Y=Y, num_resamples=3) def test_usererror_binspecs_datatype(): """ Show how delta handles when bininfo is specified as invalid datatype. If bin is specified incorrectly, it defaults to the default number of bins, equally distributed across X range. (default 10) """ df = create_base_dataframe() rng = handle_seed(42) n = len(df) df["invalid_dtype"] = rng.integers(35, 500, n) bins_specs = { "invalid_dtype": "25", } problem, X, Y = create_problemspec(df) with pytest.warns(UserWarning, match=r"Input Error: Invalid custom bin dtype"): _ = delta.analyze( problem=problem, X=X, Y=Y, bins_specs=bins_specs, num_resamples=3 ) def test_usererror_binspecs_notascending(): """ Show how delta handles when bininfo is specified as not ascending list. If bin specified is incorrect, then it defaults to the default number of bins equally distributed across X range. (default 10) """ df = create_base_dataframe() rng = handle_seed(42) n = len(df) df["order_notascending"] = rng.integers(35, 500, n) bins_specs = { "order_notascending": [100, 300, 200, 450], } problem, X, Y = create_problemspec(df) with pytest.warns(UserWarning, match=r"Input Error: Bin edge error"): _ = delta.analyze( problem=problem, X=X, Y=Y, bins_specs=bins_specs, num_resamples=3 ) def test_usererror_binspecs_outofrange(): """ Show how delta handles when bininfo is specified as list with boundaries out of X range. If bin specified is incorrect, then it defaults to the default number of bins equally distributed across X range. (default 10) """ df = create_base_dataframe() rng = handle_seed(42) n = len(df) df["boundaries_outofXrange"] = rng.integers(35, 500, n) bins_specs = { "boundaries_outofXrange": [25, 100, 200, 300, 450], } problem, X, Y = create_problemspec(df) with pytest.warns(UserWarning, match=r"Input Error: Bin boundary error"): _ = delta.analyze( problem=problem, X=X, Y=Y, bins_specs=bins_specs, num_resamples=3 ) def test_usererror_binspecs_nonnumeric(): """ Show how delta handles when bininfo is specified as list including non-numeric values. If bin specified is incorrect, then it defaults to the default number of bins equally distributed across X range. (default 10) """ df = create_base_dataframe() rng = handle_seed(42) n = len(df) df["binvals_nonnumeric"] = rng.integers(35, 500, n) bins_specs = { "binvals_nonnumeric": [100, "200", 300, 450], } problem, X, Y = create_problemspec(df) with pytest.warns(UserWarning, match=r"Input Error: Bin value error"): _ = delta.analyze( problem=problem, X=X, Y=Y, bins_specs=bins_specs, num_resamples=3 ) def test_binspecs_correct_use(): """ Show how delta handles when bininfo is specified correctly. Int, list (numeric, ascending), None, or unspecified. """ df = create_base_dataframe() rng = handle_seed(42) n = len(df) # Examples of correct cases: integer, list of boundaries, None, or not specified in dict bins_specs df["correct_numbins"] = rng.integers(1, 550, n) df["correct_listbins"] = rng.integers(1, 550, n) df["correct_none"] = rng.integers(1, 550, n) df["correct_unspecified"] = rng.integers(1, 550, n) bins_specs = { "correct_numbins": 15, "correct_listbins": [100, 200, 300, 450], "correct_none": None, } problem, X, Y = create_problemspec(df) _ = delta.analyze(problem=problem, X=X, Y=Y, bins_specs=bins_specs, num_resamples=3) def test_samplesize_mismatch(): """If input X and output Y are not same number of rows.""" df = create_base_dataframe() problem, X, Y = create_problemspec(df) Y = Y[::2] with pytest.raises(RuntimeError, match=r"Input X and output Y"): _ = delta.analyze(problem=problem, X=X, Y=Y, num_resamples=3) def test_conf_level_too_low(): """If conf level specified less than 0""" df = create_base_dataframe() problem, X, Y = create_problemspec(df) conf = -0.1 with pytest.raises(RuntimeError, match=r"Confidence level"): _ = delta.analyze(problem=problem, X=X, Y=Y, conf_level=conf, num_resamples=3) def test_conf_level_too_high(): """If conf level specified greater than 1""" df = create_base_dataframe() problem, X, Y = create_problemspec(df) conf = 1.1 with pytest.raises(RuntimeError, match=r"Confidence level"): _ = delta.analyze(problem=problem, X=X, Y=Y, conf_level=conf, num_resamples=3) def test_invalid_userspec_method(): """If user specified method is invalid (not delta, sobol, all)""" df = create_base_dataframe() problem, X, Y = create_problemspec(df) method = "something_else" with pytest.raises(ValueError, match=r"Method must be"): _ = delta.analyze(problem=problem, X=X, Y=Y, method=method, num_resamples=3) def test_y_resamples_error(): """If user specified y_resamples as greater than Y.size""" df = create_base_dataframe() rng = handle_seed(42) problem, X, Y = create_problemspec(df) y_resamples = rng.integers(len(Y) + 1, len(Y) + 500) with pytest.raises(RuntimeError, match=r"y_resamples must be"): _ = delta.analyze( problem=problem, X=X, Y=Y, y_resamples=y_resamples, num_resamples=3 ) def test_invalid_columnnames_user(): """ If user provides any column name which has a forbidden suffix (raw, balanced, step, conf) """ df = create_base_dataframe() rng = handle_seed(42) n = len(df) suffixes = ["_raw", "_balanced", "_step", "_conf"] suffix = suffixes[rng.integers(0, 4)] df[f"column{suffix}"] = rng.integers(35, 500, n) problem, X, Y = create_problemspec(df) with pytest.raises(ValueError, match=r"Forbidden column name"): _ = delta.analyze(problem=problem, X=X, Y=Y, num_resamples=3) def test_data_bias_warning(): """ Warns user of potential data input bias, if raw and balanced deltas differ by > 0.1 """ df = create_base_dataframe() rng = handle_seed(42) n = len(df) output_col = df["output_col"].to_numpy() col_biased = np.zeros(n) col_biased[output_col < 20] = rng.uniform(0, 0.2, size=(output_col < 20).sum()) col_biased[(output_col >= 20) & (output_col < 23)] = rng.uniform( 0.8, 1.0, size=((output_col >= 20) & (output_col < 23)).sum() ) col_biased[output_col >= 23] = rng.uniform(0.3, 0.5, size=(output_col >= 23).sum()) df["col_biased"] = col_biased problem, X, Y = create_problemspec(df) with pytest.warns(UserWarning, match=r"Potential Bias Notice:"): _ = delta.analyze( problem=problem, X=X, Y=Y, num_resamples=3, bins_specs={"col_biased": 2} ) def test_dataset_small_size(): """Warns user if dataset size too small for number of bins""" df = create_base_dataframe() n = len(df) problem, X, Y = create_problemspec(df) with pytest.warns(UserWarning, match=r"Dataset size error:"): _ = delta.analyze( problem=problem, X=X, Y=Y, num_resamples=3, y_resamples=max(1, int(0.01 * n)), ) SALib-SALib-d6e51b1/tests/test_analyze_fast.py000066400000000000000000000035261525347100600212510ustar00rootroot00000000000000from SALib import ProblemSpec from SALib.test_functions import lake_problem import random def test_odd_sample_size(): """Specific regression test to ensure odd number of samples are handled.""" sp = ProblemSpec( { "names": ["a", "q", "b", "mean", "stdev", "delta", "alpha"], "bounds": [ [0.0, 0.1], [2.0, 4.5], [0.1, 0.45], [0.01, 0.05], [0.001, 0.005], [0.93, 0.99], [0.2, 0.5], ], "outputs": ["max_P", "Utility", "Inertia", "Reliability"], } ) # eFAST analysis with a series of odd sample sizes # These should all pass and not raise IndexError. (sp.sample_fast(511).evaluate(lake_problem.evaluate).analyze_fast()) (sp.sample_fast(1313).evaluate(lake_problem.evaluate).analyze_fast()) odds = [random.randrange(5099, 6500, 2) for _ in range(0, 3)] for No in odds: (sp.sample_fast(No).evaluate(lake_problem.evaluate).analyze_fast()) def test_even_sample_size(): """Specific regression test to ensure odd number of samples are handled.""" sp = ProblemSpec( { "names": ["a", "q", "b", "mean", "stdev", "delta", "alpha"], "bounds": [ [0.0, 0.1], [2.0, 4.5], [0.1, 0.45], [0.01, 0.05], [0.001, 0.005], [0.93, 0.99], [0.2, 0.5], ], "outputs": ["max_P", "Utility", "Inertia", "Reliability"], } ) # Test specific even number (sp.sample_fast(1024).evaluate(lake_problem.evaluate).analyze_fast()) evens = [random.randrange(5026, 6500, 2) for _ in range(0, 3)] for Ne in evens: (sp.sample_fast(Ne).evaluate(lake_problem.evaluate).analyze_fast()) SALib-SALib-d6e51b1/tests/test_analyze_morris.py000066400000000000000000000563371525347100600216370ustar00rootroot00000000000000# -*- coding: utf-8 -*- from pytest import raises, fixture import numpy as np from numpy.testing import assert_allclose, assert_equal from SALib.analyze.morris import ( analyze, _compute_mu_star_confidence, _compute_elementary_effects, _reorganize_output_matrix, _compute_grouped_metric, _compute_grouped_sigma, _check_if_array_of_floats, ) from SALib.util import handle_seed def test_compute_mu_star_confidence(): """ Tests that compute mu_star_confidence is computed correctly """ rng = handle_seed(42) ee = np.array([[2.52, 2.01, 2.30, 0.66, 0.93, 1.3]], dtype=float) num_resamples = 1000 conf_level = 0.95 num_vars = 1 actual = _compute_mu_star_confidence(ee, num_vars, num_resamples, conf_level, rng) expected = 0.5 assert_allclose(actual, expected, atol=1e-01) def test_analysis_of_morris_results(): """ Tests a one-dimensional vector of results Taken from the solution to Exercise 4 (p.138) in Saltelli (2008). """ model_input = np.array( [ [0, 1.0 / 3], [0, 1], [2.0 / 3, 1], [0, 1.0 / 3], [2.0 / 3, 1.0 / 3], [2.0 / 3, 1], [2.0 / 3, 0], [2.0 / 3, 2.0 / 3], [0, 2.0 / 3], [1.0 / 3, 1], [1, 1], [1, 1.0 / 3], [1.0 / 3, 1], [1.0 / 3, 1.0 / 3], [1, 1.0 / 3], [1.0 / 3, 2.0 / 3], [1.0 / 3, 0], [1, 0], ], dtype=float, ) model_output = np.array( [ 0.97, 0.71, 2.39, 0.97, 2.30, 2.39, 1.87, 2.40, 0.87, 2.15, 1.71, 1.54, 2.15, 2.17, 1.54, 2.20, 1.87, 1.0, ], dtype=float, ) problem = { "num_vars": 2, "names": ["Test 1", "Test 2"], "groups": None, "bounds": [[0.0, 1.0], [0.0, 1.0]], } Si = analyze( problem, model_input, model_output, num_resamples=1000, conf_level=0.95, print_to_console=False, ) desired_mu = np.array([0.66, 0.21]) assert_allclose( Si["mu"], desired_mu, rtol=1e-1, err_msg="The values for mu are incorrect" ) desired_mu_star = np.array([1.62, 0.35]) assert_allclose( Si["mu_star"], desired_mu_star, rtol=1e-2, err_msg="The values for mu star are incorrect", ) desired_sigma = np.array([1.79, 0.41]) assert_allclose( Si["sigma"], desired_sigma, rtol=1e-2, err_msg="The values for sigma are incorrect", ) desired_names = ["Test 1", "Test 2"] assert_equal( Si["names"], desired_names, err_msg="The values for names are incorrect" ) def test_analysis_of_morris_results_scaled(): """ Tests a one-dimensional vector of results Taken from the solution to Exercise 4 (p.138) in Saltelli (2008). """ model_input = np.array( [ [0, 1.0 / 3], [0, 1], [2.0 / 3, 1], [0, 1.0 / 3], [2.0 / 3, 1.0 / 3], [2.0 / 3, 1], [2.0 / 3, 0], [2.0 / 3, 2.0 / 3], [0, 2.0 / 3], [1.0 / 3, 1], [1, 1], [1, 1.0 / 3], [1.0 / 3, 1], [1.0 / 3, 1.0 / 3], [1, 1.0 / 3], [1.0 / 3, 2.0 / 3], [1.0 / 3, 0], [1, 0], ], dtype=float, ) model_output = np.array( [ 0.97, 0.71, 2.39, 0.97, 2.30, 2.39, 1.87, 2.40, 0.87, 2.15, 1.71, 1.54, 2.15, 2.17, 1.54, 2.20, 1.87, 1.0, ], dtype=float, ) problem = { "num_vars": 2, "names": ["Test 1", "Test 2"], "groups": None, "bounds": [[0.0, 1.0], [0.0, 1.0]], } Si = analyze( problem, model_input, model_output, num_resamples=1000, conf_level=0.95, scaled=True, print_to_console=False, ) desired_mu = np.array([0.090389, 0.146679]) assert_allclose( Si["mu"], desired_mu, rtol=1e-3, err_msg="The values for mu are incorrect" ) desired_mu_star = np.array([0.968042, 0.212761]) assert_allclose( Si["mu_star"], desired_mu_star, rtol=1e-3, err_msg="The values for mu star are incorrect", ) desired_sigma = np.array([1.064536844, 0.223856942]) assert_allclose( Si["sigma"], desired_sigma, rtol=1e-3, err_msg="The values for sigma are incorrect", ) desired_names = ["Test 1", "Test 2"] assert_equal( Si["names"], desired_names, err_msg="The values for names are incorrect" ) def test_conf_level_within_zero_one_bounds(): rng = handle_seed(42) ee = [0, 0, 0] num_resamples = 2 conf_level_too_low = -1 num_vars = 1 with raises(ValueError): _compute_mu_star_confidence( ee, num_vars, num_resamples, conf_level_too_low, rng ) conf_level_too_high = 2 with raises(ValueError): _compute_mu_star_confidence( ee, num_vars, num_resamples, conf_level_too_high, rng ) @fixture() def morris_data() -> tuple: """Model inputs and outputs for calculating elementary effects""" model_inputs = np.array( [ [ 1.64, -1.64, -1.64, 0.39, -0.39, 0.39, -1.64, -1.64, -0.39, -0.39, 1.64, 1.64, -0.39, 0.39, 1.64, ], [ 1.64, -1.64, -1.64, 0.39, -0.39, -1.64, -1.64, -1.64, -0.39, -0.39, 1.64, 1.64, -0.39, 0.39, 1.64, ], [ 1.64, -1.64, -1.64, 0.39, -0.39, -1.64, -1.64, -1.64, 1.64, -0.39, 1.64, 1.64, -0.39, 0.39, 1.64, ], [ 1.64, -1.64, -1.64, 0.39, -0.39, -1.64, -1.64, 0.39, 1.64, -0.39, 1.64, 1.64, -0.39, 0.39, 1.64, ], [ 1.64, -1.64, -1.64, -1.64, -0.39, -1.64, -1.64, 0.39, 1.64, -0.39, 1.64, 1.64, -0.39, 0.39, 1.64, ], [ 1.64, -1.64, -1.64, -1.64, -0.39, -1.64, -1.64, 0.39, 1.64, -0.39, 1.64, -0.39, -0.39, 0.39, 1.64, ], [ 1.64, -1.64, -1.64, -1.64, -0.39, -1.64, -1.64, 0.39, 1.64, -0.39, 1.64, -0.39, -0.39, -1.64, 1.64, ], [ 1.64, 0.39, -1.64, -1.64, -0.39, -1.64, -1.64, 0.39, 1.64, -0.39, 1.64, -0.39, -0.39, -1.64, 1.64, ], [ 1.64, 0.39, -1.64, -1.64, -0.39, -1.64, -1.64, 0.39, 1.64, -0.39, 1.64, -0.39, -0.39, -1.64, -0.39, ], [ 1.64, 0.39, -1.64, -1.64, -0.39, -1.64, -1.64, 0.39, 1.64, 1.64, 1.64, -0.39, -0.39, -1.64, -0.39, ], [ 1.64, 0.39, -1.64, -1.64, 1.64, -1.64, -1.64, 0.39, 1.64, 1.64, 1.64, -0.39, -0.39, -1.64, -0.39, ], [ 1.64, 0.39, -1.64, -1.64, 1.64, -1.64, -1.64, 0.39, 1.64, 1.64, -0.39, -0.39, -0.39, -1.64, -0.39, ], [ 1.64, 0.39, -1.64, -1.64, 1.64, -1.64, 0.39, 0.39, 1.64, 1.64, -0.39, -0.39, -0.39, -1.64, -0.39, ], [ 1.64, 0.39, 0.39, -1.64, 1.64, -1.64, 0.39, 0.39, 1.64, 1.64, -0.39, -0.39, -0.39, -1.64, -0.39, ], [ -0.39, 0.39, 0.39, -1.64, 1.64, -1.64, 0.39, 0.39, 1.64, 1.64, -0.39, -0.39, -0.39, -1.64, -0.39, ], [ -0.39, 0.39, 0.39, -1.64, 1.64, -1.64, 0.39, 0.39, 1.64, 1.64, -0.39, -0.39, 1.64, -1.64, -0.39, ], ], dtype=float, ) model_outputs = np.array( [ 24.9, 22.72, 21.04, 16.01, 10.4, 10.04, 8.6, 13.39, 4.69, 8.02, 9.98, 3.75, 1.33, 2.59, 6.37, 9.99, ], dtype=float, ) return model_inputs, model_outputs def test_compute_elementary_effects(morris_data): """ Inputs for elementary effects taken from Exercise 5 from Saltelli (2008). See page 140-145. `model_inputs` are from trajectory t_1 from table 3.10 on page 141. `desired` is equivalent to column t_1 in table 3.12 on page 145. """ model_inputs, model_outputs = morris_data delta = 2.0 / 3 actual = _compute_elementary_effects(model_inputs, model_outputs, 16, delta) desired = np.array( [ [-5.67], [7.18], [1.89], [8.42], [2.93], [3.28], [-3.62], [-7.55], [-2.51], [5.00], [9.34], [0.54], [5.43], [2.15], [13.05], ], dtype=float, ) assert_allclose(actual, desired, atol=1e-1) def test_compute_elementary_effects_scaled(morris_data): """ Inputs for elementary effects taken from Exercise 5 from Saltelli (2008). See page 140-145. `model_inputs` are from trajectory t_1 from table 3.10 on page 141. `desired` was manual calculated in an Excel spreadsheet after confirming the results from the original paper. """ model_inputs, model_outputs = morris_data delta = 2.0 / 3 actual = _compute_elementary_effects( model_inputs, model_outputs, 16, delta, scaling=True ) desired = np.array( [ [-0.181634813], [0.345250299], [0.071454753], [0.352948837], [0.137866888], [0.076670871], [-0.152252439], [-0.285251912], [-0.080726583], [0.240017431], [0.419563468], [0.024244438], [0.12731585], [0.101289958], [0.63202974], ], dtype=float, ) assert_allclose(actual, desired, atol=1e-2) def test_compute_grouped_elementary_effects(): model_inputs = np.array( [ [ 0.39, -0.39, -1.64, 0.39, -0.39, -0.39, 0.39, 0.39, -1.64, -0.39, 0.39, -1.64, 1.64, 1.64, 1.64, ], [ -1.64, 1.64, 0.39, -1.64, 1.64, 1.64, -1.64, -1.64, -1.64, 1.64, 0.39, -1.64, 1.64, 1.64, 1.64, ], [ -1.64, 1.64, 0.39, -1.64, 1.64, 1.64, -1.64, -1.64, 0.39, 1.64, -1.64, 0.39, -0.39, -0.39, -0.39, ], ] ) model_results = np.array([13.85, -10.11, 1.12]) problem = { "names": [ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", ], "bounds": [[]], "groups": ( np.array( [ [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0], ] ), ["gp1", "gp2"], ), "num_vars": 15, } ee = _compute_elementary_effects(model_inputs, model_results, 3, 2.0 / 3) mu_star = np.average(np.abs(ee), axis=1) actual = _compute_grouped_metric(mu_star, problem["groups"][0].T) desired = np.array([16.86, 35.95]) assert_allclose(actual, desired, atol=1e-1) def test_compute_elementary_effects_small(): """ Computes elementary effects for two variables, over six trajectories with four levels. """ model_inputs = np.array( [ [0, 1.0 / 3], [0, 1], [2.0 / 3, 1], [0, 1.0 / 3], [2.0 / 3, 1.0 / 3], [2.0 / 3, 1], [2.0 / 3, 0], [2.0 / 3, 2.0 / 3], [0, 2.0 / 3], [1.0 / 3, 1], [1, 1], [1, 1.0 / 3], [1.0 / 3, 1], [1.0 / 3, 1.0 / 3], [1, 1.0 / 3], [1.0 / 3, 2.0 / 3], [1.0 / 3, 0], [1, 0], ], dtype=float, ) model_outputs = np.array( [ 0.97, 0.71, 2.39, 0.97, 2.3, 2.39, 1.87, 2.40, 0.87, 2.15, 1.71, 1.54, 2.15, 2.17, 1.54, 2.2, 1.87, 1.0, ], dtype=float, ) delta = 2.0 / 3 actual = _compute_elementary_effects(model_inputs, model_outputs, 3, delta) desired = np.array( [ [2.52, 2.01, 2.30, -0.66, -0.93, -1.30], [-0.39, 0.13, 0.80, 0.25, -0.02, 0.51], ] ) assert_allclose(actual, desired, atol=1e-0) def test_reorganize_output_matrix_increased(): up = np.array( [ [[False, True], [True, False]], [[True, False], [False, True]], [[False, True], [False, False]], [[True, False], [False, False]], [[False, False], [True, False]], [[False, False], [True, False]], ], dtype=bool, ) lo = np.array( [ [[False, False], [False, False]], [[False, False], [False, False]], [[False, False], [True, False]], [[False, False], [False, True]], [[False, True], [False, False]], [[False, True], [False, False]], ], dtype=bool, ) model_outputs = np.array( [ 0.97, 0.71, 2.39, 0.97, 2.3, 2.39, 1.87, 2.40, 0.87, 2.15, 1.71, 1.54, 2.15, 2.17, 1.54, 2.2, 1.87, 1.0, ], dtype=float, ) op_vec = model_outputs.reshape(6, 3) actual = _reorganize_output_matrix(op_vec, up, lo) desired = np.array( [[2.39, 2.3, 2.4, 1.71, 1.54, 1.0], [0.71, 2.39, 2.40, 1.71, 2.15, 2.20]], dtype=float, ) assert_allclose(actual, desired, atol=1e-1) def test_reorganize_output_matrix_decreased(): up = np.array( [ [[False, True], [True, False]], [[True, False], [False, True]], [[False, True], [False, False]], [[True, False], [False, False]], [[False, False], [True, False]], [[False, False], [True, False]], ], dtype=bool, ) lo = np.array( [ [[False, False], [False, False]], [[False, False], [False, False]], [[False, False], [True, False]], [[False, False], [False, True]], [[False, True], [False, False]], [[False, True], [False, False]], ], dtype=bool, ) model_outputs = np.array( [ 0.97, 0.71, 2.39, 0.97, 2.3, 2.39, 1.87, 2.40, 0.87, 2.15, 1.71, 1.54, 2.15, 2.17, 1.54, 2.2, 1.87, 1.0, ], dtype=float, ) op_vec = model_outputs.reshape(6, 3) actual = _reorganize_output_matrix(op_vec, up, lo, increase=False) desired = np.array( [[0.71, 0.97, 0.87, 2.15, 2.17, 1.87], [0.97, 2.30, 1.87, 1.54, 2.17, 1.87]], dtype=float, ) assert_allclose(actual, desired, atol=1e-1) def test_compute_grouped_metric(): """ Computes mu_star for 3 variables grouped into 2 groups There are six trajectories. """ group_matrix = np.array([[1, 0], [0, 1], [0, 1]], dtype=int) ee = np.array( [ [2.52, 2.01, 2.30, -0.66, -0.93, -1.30], [-2.00, 0.13, -0.80, 0.25, -0.02, 0.51], [2.00, -0.13, 0.80, -0.25, 0.02, -0.51], ] ) mu_star = np.average(np.abs(ee), 1) actual = _compute_grouped_metric(mu_star, group_matrix) desired = np.array([1.62, 0.62], dtype=float) assert_allclose(actual, desired, rtol=1e-1) def test_compute_grouped_sigma(): """ Tests that a value for sigma is returned when the group contains 1 param Morris groups do not allow a value for sigma to be computed because it requires the use of mu (as opposed to mu_star). However, if the group consists of just one parameter, then the sampling will be identical to the situation in which no groups are used, but only for that parameter. An NA should be returned for all other groups (as opposed to 0, which could confuse plotting.morris) """ group_matrix = np.array([[1, 0], [0, 1], [0, 1]], dtype=int) ee = np.array( [ [2.52, 2.01, 2.30, -0.66, -0.93, -1.30], [-2.00, 0.13, -0.80, 0.25, -0.02, 0.51], [2.00, -0.13, 0.80, -0.25, 0.02, -0.51], ] ) sigma = np.std(ee, axis=1, ddof=1) actual = _compute_grouped_sigma(sigma, group_matrix) desired = np.array([1.79352911, np.nan], dtype=float) assert_allclose(actual, desired, rtol=1e-1) def test_check_if_array_of_floats(): outputs = np.array( [ 0.97, 0.71, 2.39, 0.97, 2.30, 2.39, 1.87, 2.40, 0.87, 2.15, 1.71, 1.54, 2.15, 2.17, 1.54, 2.20, 1.87, 1.0, ], dtype=int, ) with raises(ValueError): _check_if_array_of_floats(outputs) def test_doesnot_raise_error_if_floats(): inputs = np.array( [ [0, 1.0 / 3], [0, 1], [2.0 / 3, 1], [0, 1.0 / 3], [2.0 / 3, 1.0 / 3], [2.0 / 3, 1], [2.0 / 3, 0], [2.0 / 3, 2.0 / 3], [0, 2.0 / 3], [1.0 / 3, 1], [1, 1], [1, 1.0 / 3], [1.0 / 3, 1], [1.0 / 3, 1.0 / 3], [1, 1.0 / 3], [1.0 / 3, 2.0 / 3], [1.0 / 3, 0], [1, 0], ], dtype=np.float32, ) outputs = np.array( [ 0.97, 0.71, 2.39, 0.97, 2.30, 2.39, 1.87, 2.40, 0.87, 2.15, 1.71, 1.54, 2.15, 2.17, 1.54, 2.20, 1.87, 1.0, ], dtype=np.float32, ) problem = { "num_vars": 2, "names": ["Test 1", "Test 2"], "groups": None, "bounds": [[0.0, 1.0], [0.0, 1.0]], } analyze(problem, inputs, outputs) SALib-SALib-d6e51b1/tests/test_analyze_pawn.py000066400000000000000000000005351525347100600212560ustar00rootroot00000000000000from SALib.util import read_param_file from SALib import ProblemSpec from SALib.test_functions import Ishigami def test_analyze_pawn(): param_file = "src/SALib/test_functions/params/Ishigami_groups.txt" problem = read_param_file(param_file) sp = ProblemSpec(problem) sp.sample_sobol(512).evaluate(Ishigami.evaluate).analyze_pawn() SALib-SALib-d6e51b1/tests/test_analyze_shapley.py000066400000000000000000000145341525347100600217620ustar00rootroot00000000000000import numpy as np import pytest from numpy.testing import assert_allclose from scipy.stats import norm from SALib import ProblemSpec from SALib.analyze import shapley from SALib.sample import shapley as shapley_sampler from SALib.test_functions import Ishigami @pytest.fixture def two_factor_problem(): return { "num_vars": 2, "names": ["x1", "x2"], "bounds": [[0.0, 1.0], [0.0, 1.0]], } def test_analyze_matches_goda_update_and_variance_formula(two_factor_problem): X = np.array( [ [1.0, 2.0], [3.0, 2.0], [3.0, 4.0], [2.0, 1.0], [2.0, 5.0], [4.0, 5.0], ] ) Y = X[:, 0] * X[:, 1] result = shapley.analyze(two_factor_problem, X, Y) assert_allclose(result["shapley"], [69.0, 37.0]) assert_allclose( result["shapley_conf"], norm.ppf(0.975) * np.array([61.0, 5.0]), ) assert_allclose(result["shapley_normalized"], [69.0 / 106.0, 37.0 / 106.0]) assert_allclose(result["shapley_normalized"].sum(), 1.0) assert result["names"] == ["x1", "x2"] # Delta-method half-width for a ratio of correlated trajectory means; # both factors land on the same value here since there are only two # trajectories, so their contributions are mirror images about the mean. expected_half_width = norm.ppf(0.975) * (1301.0 / 5618.0) assert_allclose( result["shapley_normalized_conf"], [expected_half_width, expected_half_width] ) def test_plot_defaults_to_normalized(two_factor_problem): X = np.array( [ [1.0, 2.0], [3.0, 2.0], [3.0, 4.0], [2.0, 1.0], [2.0, 5.0], [4.0, 5.0], ] ) Y = X[:, 0] * X[:, 1] result = shapley.analyze(two_factor_problem, X, Y) # Raw (variance-unit) and normalized (unit-interval) effects sit on # incompatible scales, so plot() shouldn't mix them in one chart (the # behavior ResultDict.plot() would otherwise give); default to the # normalized shares, since those are what's usually of interest. ax = result.plot() assert ax.get_title() == "Normalized Shapley effects" ax = result.plot(normalized=False) assert ax.get_title() == "Shapley effects" def test_normalized_effects_reject_zero_total(two_factor_problem): X = np.array( [ [0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [2.0, 2.0], [3.0, 2.0], [3.0, 3.0], ] ) result = shapley.analyze(two_factor_problem, X, np.ones(6)) # Normalization is undefined when the estimated total is zero; degrades # to NaN rather than raising, consistent with SALib's degenerate-case # handling elsewhere (e.g. Sobol's zero-variance guard). assert np.all(np.isnan(result["shapley_normalized"])) assert np.all(np.isnan(result["shapley_normalized_conf"])) def test_ishigami_regression(): problem = { "num_vars": 3, "names": ["x1", "x2", "x3"], "bounds": [[-np.pi, np.pi]] * 3, } X = shapley_sampler.sample(problem, 20_000, seed=1234) Y = Ishigami.evaluate(X) result = shapley.analyze(problem, X, Y) a, b = 7.0, 0.1 interaction_share = 4 * np.pi**8 * b**2 / 225 expected = np.array( [ 0.5 + b * np.pi**4 / 5 + b**2 * np.pi**8 / 50 + interaction_share, a**2 / 8, interaction_share, ] ) assert_allclose(result["shapley"], expected, atol=0.18) trajectory_outputs = Y.reshape(20_000, 4) variance_estimate = np.mean( (trajectory_outputs[:, 0] - trajectory_outputs[:, -1]) ** 2 / 2 ) assert_allclose(np.sum(result["shapley"]), variance_estimate) def test_problem_spec_interface(): specification = ProblemSpec( { "names": ["x1", "x2", "x3"], "bounds": [[-np.pi, np.pi]] * 3, "outputs": ["Y"], } ) ( specification.sample_shapley(256, seed=123) .evaluate(Ishigami.evaluate) .analyze_shapley() ) assert specification.analysis["names"] == ["x1", "x2", "x3"] # Normalized shares and their confidence bounds are plain result keys, so # they surface through ProblemSpec.to_df() with no special-cased access. df = specification.to_df() assert "shapley_normalized" in df.columns assert "shapley_normalized_conf" in df.columns assert_allclose(df["shapley_normalized"].sum(), 1.0) @pytest.mark.parametrize("conf_level", [0.0, 1.0, -0.1, 1.1]) def test_analyze_rejects_invalid_confidence(two_factor_problem, conf_level): X = np.zeros((6, 2)) Y = np.zeros(6) with pytest.raises(ValueError, match="between 0 and 1"): shapley.analyze(two_factor_problem, X, Y, conf_level=conf_level) def test_analyze_rejects_malformed_trajectory(two_factor_problem): X = np.array( [ [0.0, 0.0], [1.0, 1.0], [1.0, 2.0], [2.0, 2.0], [3.0, 2.0], [3.0, 4.0], ] ) Y = X.sum(axis=1) with pytest.raises(ValueError, match="exactly one factor"): shapley.analyze(two_factor_problem, X, Y) def test_analyze_rejects_groups(two_factor_problem): two_factor_problem["groups"] = ["A", "B"] X = np.zeros((6, 2)) Y = np.zeros(6) with pytest.raises(ValueError, match="does not support groups"): shapley.analyze(two_factor_problem, X, Y) @pytest.mark.parametrize( ("X", "Y", "message"), [ (np.zeros(6), np.zeros(6), "X must have shape"), (np.zeros((6, 3)), np.zeros(6), "X must have shape"), (np.zeros((6, 2)), np.zeros((6, 1)), "one-dimensional"), (np.zeros((6, 2)), np.zeros(5), "same number of rows"), (np.zeros((5, 2)), np.zeros(5), "divisible"), (np.zeros((3, 2)), np.zeros(3), "At least two"), ], ) def test_analyze_rejects_invalid_shapes(two_factor_problem, X, Y, message): with pytest.raises(ValueError, match=message): shapley.analyze(two_factor_problem, X, Y) def test_analyze_rejects_non_finite_values(two_factor_problem): X = np.array( [ [0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [2.0, 2.0], [3.0, 2.0], [3.0, np.nan], ] ) with pytest.raises(ValueError, match="finite"): shapley.analyze(two_factor_problem, X, np.zeros(6)) SALib-SALib-d6e51b1/tests/test_cli.py000066400000000000000000000020511525347100600173300ustar00rootroot00000000000000import subprocess import importlib from SALib.util import avail_approaches def test_cli_usage(): cmd = ["salib"] try: out = subprocess.check_output( cmd, stderr=subprocess.STDOUT, shell=True, universal_newlines=True ) except subprocess.CalledProcessError as e: raise RuntimeError(f"Call failed:\n{e}") else: # if no error raised, check the returned string assert ( len(out) > 0 and "usage" in out.lower() ), "Incorrect message returned from utility" def test_cli_avail_methods(): method_types = ["sample", "analyze"] for method in method_types: module = importlib.import_module(f"SALib.{method}") actions = avail_approaches(module) for act in actions: approach = importlib.import_module(f"SALib.{method}.{act}") # Just try to access the functions - raises error on failure approach.cli_parse approach.cli_action if __name__ == "__main__": test_cli_usage() test_cli_avail_methods() SALib-SALib-d6e51b1/tests/test_cli_analyze.py000066400000000000000000000226011525347100600210560ustar00rootroot00000000000000"""Test CLI usage. These tests only ensure input/outputs from the CLI. Results are compared against previously obtained results. """ import subprocess from SALib.test_functions import Ishigami import numpy as np import pandas as pd from io import StringIO import re import os from os.path import join as pth_join ishigami_fp = "./src/SALib/test_functions/params/Ishigami.txt" test_dir = "tests/data" input_file = "model_input.txt" output_file = "model_output.txt" input_file = pth_join(test_dir, input_file) output_file = pth_join(test_dir, output_file) def teardown_function(func): # Removes the test file if it was created. files = os.listdir(test_dir) if input_file in files: os.remove(input_file) if output_file in files: os.remove(output_file) def test_delta(): cmd = f"salib sample saltelli -p {ishigami_fp} -o {input_file} -n 1024 \ --precision 8 --max-order 2 --skip-values 2048" subprocess.run(cmd.split()) # Run model and save output np.savetxt(output_file, Ishigami.evaluate(np.loadtxt(input_file))) analyze_cmd = f"salib analyze delta -p {ishigami_fp} -X {input_file} \ -Y {output_file} -c 0 -r 10 --seed=100".split() result = subprocess.check_output(analyze_cmd, universal_newlines=True) delta_expected = [0.228979, 0.347744, 0.163172] sobol_expected = [0.313794, 0.433776, 0.005120] test = pd.read_csv(StringIO(result), index_col=0, sep=r"\s+") test["expected"] = delta_expected lower = test["delta_raw"] - (test["delta_raw_conf"] * 4) upper = test["delta_raw"] + (test["delta_raw_conf"] * 4) comparison = test["expected"].between(lower, upper) assert comparison.all(), ( "Expected Delta results not within confidence bounds (x4)\n" f"+\\-: \n{test['delta_raw_conf']}\n" f"Expected: {delta_expected}\n" f"Got: {test['delta_raw']}\n" ) test["expected"] = sobol_expected lower = test["S1"] - test["S1_conf"] upper = test["S1"] + test["S1_conf"] comparison = test["expected"].between(lower, upper) assert comparison.all(), ( "Expected Sobol results not within confidence bounds\n" f"+\\-: \n{test['S1_conf']}\n" f"Expected: {sobol_expected}\n" f"Got: {test['S1']}\n" ) def test_dgsm(): # Generate inputs cmd = f"salib sample finite_diff -p {ishigami_fp} -o {input_file} -d 0.001\ --precision=8 -n 1000 --seed=100".split() subprocess.run(cmd) # Run model and save output np.savetxt(output_file, Ishigami.evaluate(np.loadtxt(input_file))) analyze_cmd = f"salib analyze dgsm -p {ishigami_fp} -X {input_file}\ -Y {output_file} -c 0 -r 1000 --seed=100".split() # run analysis and use regex to strip all whitespace from result result = subprocess.check_output(analyze_cmd, universal_newlines=True) dgsm_expected = [2.207554, 7.092019, 3.238259] test = pd.read_csv(StringIO(result), index_col=0, sep=r"\s+") test["calc"] = dgsm_expected lower = test["dgsm"] - test["dgsm_conf"] upper = test["dgsm"] + test["dgsm_conf"] comparison = test["calc"].between(lower, upper) assert comparison.all(), ( "Expected DGSM results not within confidence bounds\n" f"Expected +/-: {dgsm_expected}\n" f"Got +/-: {test['dgsm_conf']}\n" ) def test_fast(): # Generate inputs cmd = f"salib sample fast_sampler -p {ishigami_fp} -o {input_file} \ --precision=8 -n 1000 -M 4 --seed=100".split() subprocess.run(cmd) # Run model and save output np.savetxt(output_file, Ishigami.evaluate(np.loadtxt(input_file))) analyze_cmd = f"salib analyze fast -p {ishigami_fp} \ -Y {output_file} -c 0 --seed=100".split() # run analysis and use regex to strip all whitespace from result result = subprocess.check_output(analyze_cmd, universal_newlines=True) expected = """ S1 ST S1_conf ST_conf x1 2.933824e-01 0.525013 1.321257e-16 1.312176e-16 x2 4.425383e-01 0.469429 1.098395e-01 1.174880e-01 x3 2.636727e-34 0.239202 1.820670e-01 5.944182e-02""" col_names = ["Name", "S1", "ST", "S1_conf", "ST_conf"] data = StringIO(expected) df1 = pd.read_csv(data, sep="\t") df1 = df1.iloc[:, 0].str.split(expand=True) df1.columns = col_names df1 = df1.iloc[:, 1:].values.astype("float64") data = StringIO(result) df2 = pd.read_csv(data, sep="\t") df2 = df2.iloc[:, 0].str.split(expand=True) df2.columns = col_names df2 = df2.iloc[:, 1:].values.astype("float64") assert np.allclose( df1, df2, rtol=2e-02 ), "Unexpected FAST results.\n\nExpected:\n{}\n\nGot:{}".format(expected, result) def test_ff(): # Generate inputs cmd = f"salib sample ff -p {ishigami_fp} -o {input_file} \ --precision=8 -n 1000 --seed=100".split() subprocess.run(cmd) # Run model and save output np.savetxt(output_file, Ishigami.evaluate(np.loadtxt(input_file))) analyze_cmd = f"salib analyze ff -p {ishigami_fp} -X {input_file} \ -Y {output_file} -c 0 --seed=100".split() # run analysis and use regex to strip all whitespace from result result = subprocess.check_output(analyze_cmd, universal_newlines=True) result = re.sub(r"[\n\t\s]*", "", result) expected = "MEx13.855764e-08x20.000000e+00x30.000000e+00dummy_00.000000e+00IE(x1,x2)0.0(x1,x3)0.0(x2,x3)0.0(x1,dummy_0)0.0(x2,dummy_0)0.0(x3,dummy_0)0.0" # noqa: E501 assert ( len(result) > 0 and result == expected ), f"Unexpected FF results.\n\nExpected:\n{expected}\n\nGot:{result}" def test_morris(): # Generate inputs cmd = f"salib sample morris -p {ishigami_fp} -o {input_file} -n 100\ --precision=8 --levels=10 --seed=100 -lo False".split() subprocess.run(cmd) # Run model and save output np.savetxt(output_file, Ishigami.evaluate(np.loadtxt(input_file))) # run analysis analyze_cmd = f"salib analyze morris -p {ishigami_fp} -X {input_file}\ -Y {output_file} -c 0 -r 1000 -l 10 --seed=100".split() result = subprocess.check_output(analyze_cmd, universal_newlines=True) result = re.sub(r"[\n\t\s]*", "", result) expected_output = "mumu_starsigmamu_star_confx18.0965478.09654710.3184292.008941x2-0.0589572.6231253.1367570.335290x30.3530395.9095588.4108171.173146" # noqa: E501 assert len(result) > 0 and result == expected_output, ( f"Results did not match expected values:\n\n Expected:" f" \n{expected_output} \n\n Got: \n{result}" ) def test_morris_scaled(): # Generate inputs cmd = f"salib sample morris -p {ishigami_fp} -o {input_file} -n 100\ --precision=8 --levels=10 --seed=100 -lo False".split() subprocess.run(cmd) # Run model and save output np.savetxt(output_file, Ishigami.evaluate(np.loadtxt(input_file))) # run analysis analyze_cmd = f"salib analyze morris -p {ishigami_fp} -X {input_file}\ -Y {output_file} -c 0 -r 1000 --scaled=True -l 10 --seed=100".split() result = subprocess.check_output(analyze_cmd, universal_newlines=True) result = re.sub(r"[\n\t\s]*", "", result) expected_output = "mumu_starsigmamu_star_confx10.6357750.6357750.4077460.074370x2-0.0339410.4038920.5486050.071716x30.0398500.4381760.5601640.068822" # noqa: E501 assert len(result) > 0 and result == expected_output, ( f"Results did not match expected values:\n\n Expected:" f" \n{expected_output} \n\n Got: \n{result}" ) def test_rbd_fast(): # Generate inputs cmd = f"salib sample latin -p {ishigami_fp} -o {input_file} \ --precision=8 -n 1000 --seed=100".split() subprocess.run(cmd) # Run model and save output np.savetxt(output_file, Ishigami.evaluate(np.loadtxt(input_file))) analyze_cmd = f"salib analyze rbd_fast -p {ishigami_fp} -X {input_file}\ -Y {output_file} --seed=100".split() # run analysis and use regex to strip all whitespace from result result = subprocess.check_output(analyze_cmd, universal_newlines=True) expected = [0.351277, 0.468170, -0.005864] test = pd.read_csv(StringIO(result), index_col=0, sep=r"\s+") test["expected"] = expected lower = test["S1"] - test["S1_conf"] upper = test["S1"] + test["S1_conf"] comparison = test["expected"].between(lower, upper) assert ( comparison.all() ), "RBD-FAST results +/- CI not in line with expected results." def test_sobol(): # Generate inputs cmd = f"salib sample saltelli -p {ishigami_fp} -o {input_file} -n 1024\ --precision 8 --max-order 2 --skip-values 2048" cmd = cmd.split() result = subprocess.check_output(cmd, universal_newlines=True) np.savetxt(output_file, Ishigami.evaluate(np.loadtxt(input_file))) analyze_cmd = f"salib analyze sobol -p {ishigami_fp}\ -Y {output_file} -c 0 --max-order 2\ -r 1000 --seed=100".split() result = subprocess.check_output(analyze_cmd, universal_newlines=True) result = re.sub(r"[\n\t\s]*", "", result) expected_output = "STST_confx10.5579470.085851x20.4421890.041396x30.2414020.028607S1S1_confx10.3105760.059615x20.4436530.053436x3-0.0129620.053891S2S2_conf(x1,x2)-0.0143970.083679(x1,x3)0.2462310.103117(x2,x3)0.0005390.064169" # noqa: E501 assert len(result) > 0 and result == expected_output, ( f"Results did not match expected values:\n\n" f" Expected: \n{expected_output} \n\n Got: \n{result}" ) if __name__ == "__main__": test_delta() test_dgsm() test_fast() test_ff() test_morris() test_rbd_fast() test_sobol() SALib-SALib-d6e51b1/tests/test_cli_sample.py000066400000000000000000000062401525347100600206750ustar00rootroot00000000000000import os from os.path import join as pth_join import subprocess salib_cli = "salib" ishigami_fp = "./src/SALib/test_functions/params/Ishigami.txt" test_file = "test.txt" test_data = pth_join("./tests", "data", test_file) def teardown_function(func): # Removes the test file if it was created. files = os.listdir("./tests/data") if test_file in files: os.remove(test_data) def test_cli_entry(): cmd = "{cli} -h".format(cli=salib_cli).split() result = subprocess.check_output(cmd) assert "Errno" not in str(result), "Error occurred when trying to use CLI!" def test_ff(): cmd = "{cli} sample ff -p {fn} -o {test_data} -n 100".format( cli=salib_cli, fn=ishigami_fp, test_data=test_data ).split() result = subprocess.check_output(cmd) assert len(result) == 0, "Error occurred!" def test_fast(): cmd = "{cli} sample fast_sampler -p {fn} -o {test_data} -n 100".format( cli=salib_cli, fn=ishigami_fp, test_data=test_data ).split() result = subprocess.check_output(cmd) assert len(result) == 0, "Error occurred!" def test_finite_diff(): cmd = "{cli} sample finite_diff -p {fn} -o {test_data} -n 100".format( cli=salib_cli, fn=ishigami_fp, test_data=test_data ).split() result = subprocess.check_output(cmd) assert len(result) == 0, "Error occurred!" def test_latin(): cmd = "{cli} sample latin -p {fn} -o {test_data} -n 100".format( cli=salib_cli, fn=ishigami_fp, test_data=test_data ).split() result = subprocess.check_output(cmd) assert len(result) == 0, "Error occurred!" def test_saltelli(): cmd = "{cli} sample saltelli -p {fn} -o {test_data} -n 512".format( cli=salib_cli, fn=ishigami_fp, test_data=test_data ).split() result = subprocess.check_output(cmd) assert len(result) == 0, "Error occurred!" def test_radial_sobol(): """Only Sobol-based radial sample is offered from the CLI for now.""" cmd = "{cli} sample radial -p {fn} -o {test_data} -n 100".format( cli=salib_cli, fn=ishigami_fp, test_data=test_data ).split() result = subprocess.check_output(cmd) assert len(result) == 0, "Error occurred!" def test_saltelli_warning(): # Ensure error is raised when n_samples not a power of 2 cmd = f"salib sample saltelli -p {ishigami_fp} -o {test_data} -n 511".split() result = subprocess.check_output(cmd, stderr=subprocess.STDOUT) assert "Warning" in str(result) # Ensure warning is raised when skip_values < n_samples cmd = ( f"salib sample saltelli -p {ishigami_fp} -o {test_data}" " -n 2048 --skip-values 1024" ).split() result = subprocess.check_output(cmd, stderr=subprocess.STDOUT) assert "Warning" in str(result) # Ensure error is raised when skip_values not a power of 2 cmd = ( f"salib sample saltelli -p {ishigami_fp} -o {test_data}" " -n 512 --skip-values 1025" ).split() result = subprocess.check_output(cmd, stderr=subprocess.STDOUT) assert "Warning" in str(result) if __name__ == "__main__": test_cli_entry() test_ff() test_fast() test_finite_diff() test_latin() test_saltelli() test_radial_sobol() SALib-SALib-d6e51b1/tests/test_cli_shapley.py000066400000000000000000000021461525347100600210620ustar00rootroot00000000000000import subprocess import numpy as np from SALib.test_functions import Ishigami def test_shapley_cli_round_trip(tmp_path): param_file = "src/SALib/test_functions/params/Ishigami.txt" input_file = tmp_path / "model_input.txt" output_file = tmp_path / "model_output.txt" subprocess.run( [ "salib", "sample", "shapley", "-n", "256", "-p", param_file, "-o", str(input_file), "--seed", "123", ], check=True, ) inputs = np.loadtxt(input_file) assert inputs.shape == (1_024, 3) np.savetxt(output_file, Ishigami.evaluate(inputs)) result = subprocess.run( [ "salib", "analyze", "shapley", "-p", param_file, "-X", str(input_file), "-Y", str(output_file), ], check=True, capture_output=True, text=True, ) assert "shapley" in result.stdout assert "shapley_conf" in result.stdout SALib-SALib-d6e51b1/tests/test_discrepancy.py000066400000000000000000000010021525347100600210600ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_allclose from SALib.sample import latin from SALib.analyze import discrepancy from SALib.test_functions import Ishigami def test_discrepancy(): problem = { "num_vars": 3, "names": ["x1", "x2", "x3"], "bounds": [[-np.pi, np.pi]] * 3, } X = latin.sample(problem, 1_000, seed=42) Y = Ishigami.evaluate(X) Si = discrepancy.analyze(problem, X, Y) assert_allclose(Si["s_discrepancy"], [0.33, 0.33, 0.33], atol=5e-3) SALib-SALib-d6e51b1/tests/test_ff.py000066400000000000000000000170311525347100600171600ustar00rootroot00000000000000""" Created on 30 Jun 2015 @author: @willu47 """ import numpy as np from numpy.testing import assert_equal, assert_allclose from SALib.sample.ff import sample, find_smallest, extend_bounds from SALib.analyze.ff import analyze, interactions def test_find_smallest(): """ """ num_vars = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 16, 17, 31, 32, 33] expected = [0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6] for x, y in zip(num_vars, expected): actual = find_smallest(x) assert_equal(actual, y) def test_extend_bounds(): problem = { "bounds": np.repeat([-1, 1], 12).reshape(2, 12).T, "num_vars": 12, "names": ["x" + str(x + 1) for x in range(12)], } actual = extend_bounds(problem) expected = { "names": [ "x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8", "x9", "x10", "x11", "x12", "dummy_0", "dummy_1", "dummy_2", "dummy_3", ], "bounds": [ np.array([-1, 1]), np.array([-1, 1]), np.array([-1, 1]), np.array([-1, 1]), np.array([-1, 1]), np.array([-1, 1]), np.array([-1, 1]), np.array([-1, 1]), np.array([-1, 1]), np.array([-1, 1]), np.array([-1, 1]), np.array([-1, 1]), np.array([0, 1]), np.array([0, 1]), np.array([0, 1]), np.array([0, 1]), ], "num_vars": 16, } assert_equal(actual, expected) def test_ff_sample(): problem = { "bounds": [[0.0, 1.0], [0.0, 1.0], [0.0, 1.0], [0.0, 1.0]], "num_vars": 4, "names": ["x1", "x2", "x3", "x4"], } actual = sample(problem) expected = np.array( [ [1, 1, 1, 1], [1, 0, 1, 0], [1, 1, 0, 0], [1, 0, 0, 1], [0, 0, 0, 0], [0, 1, 0, 1], [0, 0, 1, 1], [0, 1, 1, 0], ], dtype=float, ) assert_equal(actual, expected) def test_ff_sample_scaled(): """ """ problem = { "bounds": [[0.0, 2.5], [0.0, 1.0], [0.0, 1.0], [0.0, 1.0]], "num_vars": 4, "names": ["x1", "x2", "x3", "x4"], } actual = sample(problem) expected = np.array( [ [2.5, 1, 1, 1], [2.5, 0, 1, 0], [2.5, 1, 0, 0], [2.5, 0, 0, 1], [0, 0, 0, 0], [0, 1, 0, 1], [0, 0, 1, 1], [0, 1, 1, 0], ], dtype=float, ) assert_equal(actual, expected) def test_ff_analyze(): """ """ problem = { "bounds": [[0.0, 2.5], [0.0, 1.0], [0.0, 1.0], [0.0, 1.0]], "num_vars": 4, "names": ["x1", "x2", "x3", "x4"], } X = np.array( [ [1, 1, 1, 1], [1, 0, 1, 0], [1, 1, 0, 0], [1, 0, 0, 1], [0, 0, 0, 0], [0, 1, 0, 1], [0, 0, 1, 1], [0, 1, 1, 0], ], dtype=float, ) Y = np.array([1.5, 1, 1.5, 1, 2, 2.5, 2, 2.5], dtype=float) actual = analyze(problem, X, Y) expected = { "ME": np.array([-0.5, 0.25, 0.0, 0.0]), "names": ["x1", "x2", "x3", "x4"], } assert_equal(actual, expected) def test_ff_example(): """ """ problem = { "bounds": np.repeat([-1, 1], 12).reshape(2, 12).T, "num_vars": 12, "names": ["x" + str(x + 1) for x in range(12)], } X = sample(problem) Y = X[:, 0] + 2 * X[:, 1] + 3 * X[:, 2] + 4 * X[:, 6] * X[:, 11] expected = np.array( [ 10, -2, 4, -8, 2, 6, -4, 0, 2, 6, -4, 0, 10, -2, 4, -8, -2, -6, 4, 0, -10, 2, -4, 8, -10, 2, -4, 8, -2, -6, 4, 0, ] ) assert_equal(Y, expected) Si = analyze(problem, X, Y) expected = np.array([1, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], dtype=float) assert_equal(expected, Si["ME"]) def test_interactions_from_saltelli(): """ """ problem = { "bounds": np.repeat([-1, 1], 12).reshape(2, 12).T, "num_vars": 12, "names": ["x" + str(x + 1) for x in range(12)], } X = sample(problem) Y = np.array( [ 10, -2, 4, -8, 2, 6, -4, 0, 2, 6, -4, 0, 10, -2, 4, -8, -2, -6, 4, 0, -10, 2, -4, 8, -10, 2, -4, 8, -2, -6, 4, 0, ] ) Si = analyze(problem, X, Y, second_order=True) actual = Si["IE"] expected = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ] assert_equal(actual, expected) def test_interactions(): """ """ problem = { "bounds": [[0.0, 2.5], [0.0, 1.0], [0.0, 1.0], [0.0, 1.0]], "num_vars": 4, "names": ["x1", "x2", "x3", "x4"], } X = np.array( [ [2.5, 1.0, 1.0, 1.0], [2.5, 0, 1.0, 0], [2.5, 1.0, 0, 0], [2.5, 0, 0, 1.0], [0, 0, 0, 0], [0, 1.0, 0, 1.0], [0, 0, 1.0, 1.0], [0, 1.0, 1.0, 0], ], dtype=float, ) Y = X[:, 0] + (0.1 * X[:, 1]) + ((1.2 * X[:, 2]) * (1.3 + X[:, 3])) ie_names, ie = interactions(problem, Y) actual = ie assert_allclose(actual, [0.3, 0, 0, 0, 0, 0.3], rtol=1e-4, atol=1e-4) SALib-SALib-d6e51b1/tests/test_groups.py000066400000000000000000000046541525347100600201130ustar00rootroot00000000000000"""High-level tests to ensure grouped analyses convert to Pandas DataFrame.""" import pytest import numpy as np from SALib import ProblemSpec def example_func(x): """Example linear test function.""" return np.sum(x, axis=1) @pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_sobol_group_analysis(): """Ensure valid groupings are returned from the Sobol analysis method.""" group_spec = ProblemSpec( { "names": ["P1", "P2", "P3", "P4", "P5", "P6"], "bounds": [ [0.0, 1.0], [0.0, 1.0, 0.75], [0.0, 0.2], [0.0, 0.2], [-1.0, 1.0], [0.0, 1.0, 0.25], ], "dists": ["unif", "triang", "norm", "lognorm", "unif", "triang"], "groups": ["A", "B"] * 3, } ) # fmt: off (group_spec .sample_saltelli(128) .evaluate(example_func) .analyze_sobol() ) # noqa: E124 # fmt: on ST, S1, S2 = group_spec.to_df() assert len(ST.index) == 2, "Unexpected number of groups" assert len(ST[ST.index == "A"]) == 1, "Could not find Group A" assert len(ST[ST.index == "B"]) == 1, "Could not find Group B" def test_morris_group_analysis(): r"""Ensure valid groupings are returned from the Morris analysis method. Note: $\mu$ and $\sigma$ values will be NaN. See [1]. References ---------- .. [1] Campolongo, F., Cariboni, J., Saltelli, A., 2007. An effective screening design for sensitivity analysis of large models. Environmental Modelling & Software, 22, 1509–1518. https://dx.doi.org/10.1016/j.envsoft.2006.10.004 """ group_spec = ProblemSpec( { "names": ["P1", "P2", "P3", "P4", "P5", "P6"], "bounds": [[-100.0, 100.0]] * 6, "groups": ["A", "B", "C"] * 2, } ) # fmt: off (group_spec .sample_morris(100) .evaluate(example_func) .analyze_morris() ) # noqa: E124 # fmt: on res = group_spec.to_df() assert len(res.index) == 3, "Unexpected number of groups" assert len(res[res.index == "A"]) == 1, "Could not find Group A" assert len(res[res.index == "B"]) == 1, "Could not find Group B" assert len(res[res.index == "C"]) == 1, "Could not find Group C" if __name__ == "__main__": test_sobol_group_analysis() test_morris_group_analysis() SALib-SALib-d6e51b1/tests/test_hdmr.py000066400000000000000000000047541525347100600175270ustar00rootroot00000000000000from __future__ import division import pytest from pytest import raises from SALib.analyze import hdmr from SALib.sample import latin from SALib.test_functions import Ishigami, linear_model_1 from SALib.util import read_param_file @pytest.mark.filterwarnings("ignore::DeprecationWarning") def setup_samples(N=10000): param_file = "src/SALib/test_functions/params/Ishigami.txt" problem = read_param_file(param_file) param_values = latin.sample(problem, 10000) return problem, param_values @pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_insufficient_sample_size(): problem, X = setup_samples() Y = Ishigami.evaluate(X) with raises(RuntimeError): hdmr.analyze(problem, X[:200], Y[:200]) @pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_bad_conf_level(): problem, X = setup_samples() Y = Ishigami.evaluate(X) with raises(RuntimeError): hdmr.analyze(problem, X, Y, alpha=1.02) @pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_incorrect_maxorder(): problem, X = setup_samples() Y = Ishigami.evaluate(X) with raises(RuntimeError): hdmr.analyze(problem, X, Y, maxorder=4) @pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_incorrect_maxiter(): problem, X = setup_samples() Y = Ishigami.evaluate(X) with raises(RuntimeError): hdmr.analyze(problem, X, Y, maxiter=1005) @pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_over_bootstrap_sample_size(): problem, X = setup_samples() Y = Ishigami.evaluate(X) with raises(RuntimeError): hdmr.analyze(problem, X, Y, R=10001) @pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_incorrect_maxorder_setting(): problem = {"num_vars": 2, "names": ["x1", "x2"], "bounds": [[0, 1] * 2]} X = latin.sample(problem, 10000) Y = linear_model_1.evaluate(X) with raises(RuntimeError): hdmr.analyze(problem, X, Y, maxorder=5) @pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_incorrect_lambdax(): problem, X = setup_samples() Y = Ishigami.evaluate(X) with raises(RuntimeError): hdmr.analyze(problem, X, Y, lambdax=11) @pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_dim_mismatch(): problem = {"num_vars": 2, "names": ["x1", "x2"], "bounds": [[0, 1] * 2]} X = latin.sample(problem, 10000) Y = linear_model_1.evaluate(X) with raises(RuntimeError): hdmr.analyze(problem, X, Y[:-2]) SALib-SALib-d6e51b1/tests/test_problem_spec.py000066400000000000000000000141231525347100600212360ustar00rootroot00000000000000import pytest import copy import numpy as np import pandas as pd from SALib import ProblemSpec from SALib.test_functions import Ishigami def test_sp_bounds(): """Ensure incorrect user-defined bounds raises AssertionErrors.""" with pytest.raises(AssertionError): ProblemSpec() with pytest.raises(AssertionError): ProblemSpec({"names": ["x1", "x2", "x3"], "groups": None, "outputs": ["Y"]}) with pytest.raises(AssertionError): ProblemSpec( { "names": ["x1", "x2", "x3"], "groups": None, "bounds": [[-np.pi, np.pi] * 3], "outputs": ["Y"], } ) def test_sp(): """Ensure basic usage works without raising any errors.""" sp = ProblemSpec( { "names": ["x1", "x2", "x3"], "groups": None, "bounds": [[-np.pi, np.pi]] * 3, "outputs": ["Y"], } ) ( sp.sample_sobol(128, calc_second_order=True) .evaluate(Ishigami.evaluate) .analyze_sobol(calc_second_order=True, conf_level=0.95) ) @pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_sp_setters(): """Test sample and result setters.""" sp = ProblemSpec( { "names": ["x1", "x2", "x3"], "groups": None, "bounds": [[-np.pi, np.pi]] * 3, "outputs": ["Y"], } ) nvars = sp["num_vars"] N = 128 X1 = sp.sample_sobol(N, calc_second_order=True).samples # Saltelli produces `N*(2p+2)` samples when producing samples for 2nd order analysis expected_samples = 128 * (2 * nvars + 2) assert X1.shape[0] == expected_samples, "Number of samples is not as expected" # Get another 100 samples X2 = sp.sample_sobol(128, calc_second_order=True).samples assert np.all( sp.samples == X2 ), "Stored sample and extracted samples are not identical!" # Test property setter # this approach actually overrides the underlying sp._samples attribute sp.samples = X1 assert np.all(sp.samples == X1), "Reverting samples to original set did not work!" # Setting samples should clear results attribute sp.set_samples(X2) Y2 = sp.evaluate(Ishigami.evaluate).results sp.set_samples(X1) assert ( sp.results is None ), "Results were not cleared after new sample values were set!" # Entire process should not raise errors ( sp.sample_saltelli(128, calc_second_order=True) .set_samples(X2) .set_results(Y2) .analyze_sobol(calc_second_order=True, conf_level=0.95) ) @pytest.mark.filterwarnings("ignore::UserWarning") @pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_parallel_single_output(): # Create the SALib Problem specification sp = ProblemSpec( { "names": ["x1", "x2", "x3"], "groups": None, "bounds": [[-np.pi, np.pi]] * 3, "outputs": ["Y"], } ) # Single core example ( sp.sample_saltelli(2**8) .evaluate(Ishigami.evaluate) .analyze_sobol(calc_second_order=True, conf_level=0.95, seed=101) ) # Parallel example psp = copy.deepcopy(sp) ( psp.sample_saltelli(2**8) .evaluate_parallel(Ishigami.evaluate, nprocs=2) .analyze_sobol(calc_second_order=True, conf_level=0.95, nprocs=2, seed=101) ) assert ( np.testing.assert_allclose(sp.results, psp.results, rtol=1e-3, atol=1e-3) is None ), "Model results not equal!" for col, x in sp.analysis.items(): assert ( np.testing.assert_allclose(x, psp.analysis[col]) is None ), "Analysis results not equal!" @pytest.mark.filterwarnings("ignore::UserWarning") @pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_parallel_multi_output(): from SALib.test_functions import lake_problem # Create the SALib Problem specification sp = ProblemSpec( { "names": ["a", "q", "b", "mean", "stdev", "delta", "alpha"], "bounds": [ [0.0, 0.1], [2.0, 4.5], [0.1, 0.45], [0.01, 0.05], [0.001, 0.005], [0.93, 0.99], [0.2, 0.5], ], "outputs": ["max_P", "Utility", "Inertia", "Reliability"], } ) # Single core example ( sp.sample_saltelli(2**8) .evaluate(lake_problem.evaluate) .analyze_sobol(calc_second_order=True, conf_level=0.95, seed=101) ) # Parallel example psp = copy.deepcopy(sp) ( psp.sample_saltelli(2**8) .evaluate_parallel(lake_problem.evaluate, nprocs=2) .analyze_sobol(calc_second_order=True, conf_level=0.95, nprocs=2, seed=101) ) x_df = pd.DataFrame(sp.results) y_df = pd.DataFrame(psp.results) for col in pd.DataFrame(sp.results): z = [ np.testing.assert_allclose(x, y) for x, y in zip(x_df.loc[:, col], y_df.loc[:, col]) ] assert not any(z), "Model results are not equal!" x_df = pd.DataFrame(sp.analysis) y_df = pd.DataFrame(psp.analysis) for col in pd.DataFrame(sp.analysis): z = [ np.testing.assert_allclose(x, y) for x, y in zip(x_df.loc[:, col], y_df.loc[:, col]) ] assert not any(z), "Analysis results are not equal!" def test_single_parameter(): """Ensures error is raised when attempting to conduct SA on a single parameter.""" sp = ProblemSpec({"names": ["x1"], "bounds": [[-1, 1]], "outputs": ["Y"]}) def func(X): return X[1] * X[0] sp.sample_latin(50) sp.evaluate(func) with pytest.raises(ValueError): sp.analyze_hdmr() def test_single_group(): """Ensures error is raised when attempting to conduct SA on a single group.""" sp = ProblemSpec( {"names": ["x1"], "bounds": [[-1, 1]], "groups": ["G1"], "outputs": ["Y"]} ) def func(X): return X[1] * X[0] sp.sample_latin(50) sp.evaluate(func) with pytest.raises(ValueError): sp.analyze_hdmr() SALib-SALib-d6e51b1/tests/test_ptqdm.py000066400000000000000000000045671525347100600177240ustar00rootroot00000000000000"""Test that evaluate() returns consumable results when p_tqdm is available. Regression test for https://github.com/SALib/SALib/issues/676 Without the fix, p_imap returns a generator instead of a list, causing TypeError when _collect_results() tries to consume it. """ import numpy as np from unittest import mock from SALib import ProblemSpec from SALib.test_functions import Ishigami def _make_spec(): """Create a basic ProblemSpec with samples.""" sp = ProblemSpec( { "names": ["x1", "x2", "x3"], "bounds": [[-np.pi, np.pi], [-np.pi, np.pi], [-np.pi, np.pi]], "outputs": ["Y"], } ) sp.sample_saltelli(16, calc_second_order=False) return sp def test_evaluate_with_ptqdm_returns_consumable_results(): """p_imap result should be list-wrapped for consistent consumption. Before the fix, p_imap returned a generator that couldn't be properly consumed by _collect_results(), causing TypeError. """ sp = _make_spec() def fake_p_imap(func, chunks, num_cpus=1): """ Mimic p_imap: apply func to each chunk, yield results. Note: Unused `num_cpus` is required to match `p_imap` interface. """ for chunk in chunks: yield func(chunk) # Inject p_imap into the module namespace (it may not exist if p_tqdm is not installed) import SALib.util.problem as problem_mod problem_mod.p_imap = fake_p_imap problem_mod.ptqdm_available = True try: result = sp.evaluate(Ishigami.evaluate, nprocs=2) assert result.results is not None finally: # Restore original state problem_mod.ptqdm_available = False if hasattr(problem_mod, "p_imap"): delattr(problem_mod, "p_imap") def test_evaluate_without_ptqdm_still_works(): """Verify evaluate() still works when p_tqdm is not available.""" sp = _make_spec() with mock.patch("SALib.util.problem.ptqdm_available", False): result = sp.evaluate(Ishigami.evaluate, nprocs=2) assert result.results is not None assert result.results.size > 0 def test_evaluate_single_core_no_ptqdm(): """Single-core evaluate should always work regardless of p_tqdm.""" sp = _make_spec() with mock.patch("SALib.util.problem.ptqdm_available", False): result = sp.evaluate(Ishigami.evaluate, nprocs=1) assert result.results is not None SALib-SALib-d6e51b1/tests/test_regression.py000066400000000000000000000431641525347100600207530ustar00rootroot00000000000000from pytest import fixture, mark import numpy as np from numpy.testing import assert_allclose from SALib.analyze import delta, dgsm, fast, rbd_fast, sobol, morris, hdmr from SALib.sample import ( fast_sampler, finite_diff, latin, saltelli, sobol as sobol_sampler, ) from SALib.sample.morris import sample as morris_sampler from SALib.test_functions import Ishigami from SALib.test_functions import linear_model_1 from SALib.test_functions import linear_model_2 from SALib.util import read_param_file, handle_seed @fixture(scope="function") def set_seed(): """Sets seeds for random generators so that tests can be repeated It is necessary to set seeds for both the numpy.random, and the stdlib.random libraries. """ rng = handle_seed(12345) # ensure we also keep the old stuff for the analyze functions that have not shifted over to rng yet seed = 123456 np.random.seed(seed) return rng class TestMorris: def test_regression_morris_vanilla(self, set_seed): """Note that this is a poor estimate of the Ishigami function. """ rng = set_seed param_file = "src/SALib/test_functions/params/Ishigami.txt" problem = read_param_file(param_file) param_values = morris_sampler( problem, 10000, num_levels=4, optimal_trajectories=None, seed=rng ) Y = Ishigami.evaluate(param_values) Si = morris.analyze( problem, param_values, Y, conf_level=0.95, print_to_console=False, num_levels=4, seed=rng, ) assert_allclose(Si["mu_star"], [7.682808, 7.875, 6.256295], atol=0, rtol=1e-5) def test_regression_morris_scaled(self, set_seed): """Note that this is a poor estimate of the Ishigami function. """ rng = set_seed param_file = "src/SALib/test_functions/params/Ishigami.txt" problem = read_param_file(param_file) param_values = morris_sampler( problem, 10000, 4, optimal_trajectories=None, seed=rng ) Y = Ishigami.evaluate(param_values) Si = morris.analyze( problem, param_values, Y, conf_level=0.95, scaled=True, print_to_console=False, num_levels=4, seed=rng, ) assert_allclose( Si["mu_star"], [0.540244, 0.657467, 0.433446], atol=0, rtol=1e-5 ) def test_regression_morris_groups(self, set_seed): rng = set_seed param_file = "src/SALib/test_functions/params/Ishigami_groups.txt" problem = read_param_file(param_file) param_values = morris_sampler( problem=problem, N=10000, num_levels=4, optimal_trajectories=None, seed=rng ) Y = Ishigami.evaluate(param_values) Si = morris.analyze( problem, param_values, Y, conf_level=0.95, print_to_console=False, num_levels=4, seed=rng, ) assert_allclose(Si["mu_star"], [7.771541, 10.188284], atol=0, rtol=1e-5) def test_regression_morris_groups_brute_optim(self, set_seed): rng = set_seed param_file = "src/SALib/test_functions/params/Ishigami_groups.txt" problem = read_param_file(param_file) param_values = morris_sampler( problem=problem, N=50, num_levels=4, optimal_trajectories=6, local_optimization=False, seed=rng, ) Y = Ishigami.evaluate(param_values) Si = morris.analyze( problem, param_values, Y, conf_level=0.95, print_to_console=False, num_levels=4, seed=rng, ) assert_allclose(Si["mu"], [9.786986e00, 1.776357e-15], atol=0, rtol=1e-5) assert_allclose(Si["sigma"], [6.453729, np.nan], atol=0, rtol=1e-5) assert_allclose(Si["mu_star"], [9.786986, 7.875], atol=0, rtol=1e-5) def test_regression_morris_groups_local_optim(self, set_seed): rng = set_seed param_file = "src/SALib/test_functions/params/Ishigami_groups.txt" problem = read_param_file(param_file) param_values = morris_sampler( problem=problem, N=500, num_levels=4, optimal_trajectories=20, local_optimization=True, seed=rng, ) Y = Ishigami.evaluate(param_values) Si = morris.analyze( problem, param_values, Y, conf_level=0.95, print_to_console=False, num_levels=4, seed=rng, ) assert_allclose(Si["mu_star"], [13.95285, 7.875], rtol=1e-5) def test_regression_morris_optimal(self, set_seed): """ Tests the use of optimal trajectories with Morris. Uses brute force approach Note that the relative tolerance is set to a very high value (default is 1e-05) due to the coarse nature of the num_levels. """ rng = set_seed param_file = "src/SALib/test_functions/params/Ishigami.txt" problem = read_param_file(param_file) param_values = morris_sampler( problem=problem, N=20, num_levels=4, optimal_trajectories=9, local_optimization=True, seed=rng, ) Y = Ishigami.evaluate(param_values) Si = morris.analyze( problem, param_values, Y, conf_level=0.95, print_to_console=False, num_levels=4, seed=rng, ) assert_allclose(Si["mu_star"], [11.175608, 7.875, 4.165864], atol=0, rtol=1e-5) @mark.filterwarnings("ignore::UserWarning") @mark.filterwarnings("ignore::DeprecationWarning") def test_regression_sobol(): param_file = "src/SALib/test_functions/params/Ishigami.txt" problem = read_param_file(param_file) param_values = saltelli.sample(problem, 10000, calc_second_order=True) Y = Ishigami.evaluate(param_values) Si = sobol.analyze( problem, Y, calc_second_order=True, conf_level=0.95, print_to_console=False ) assert_allclose(Si["S1"], [0.31, 0.44, 0.00], atol=5e-2, rtol=1e-1) assert_allclose(Si["ST"], [0.55, 0.44, 0.24], atol=5e-2, rtol=1e-1) assert_allclose( [Si["S2"][0][1], Si["S2"][0][2], Si["S2"][1][2]], [0.00, 0.25, 0.00], atol=5e-2, rtol=1e-1, ) @mark.filterwarnings("ignore::UserWarning") def test_regression_sobol_parallel(): param_file = "src/SALib/test_functions/params/Ishigami.txt" problem = read_param_file(param_file) param_values = sobol_sampler.sample(problem, 10000, calc_second_order=True) Y = Ishigami.evaluate(param_values) Si = sobol.analyze( problem, Y, calc_second_order=True, parallel=True, conf_level=0.95, print_to_console=False, ) assert_allclose(Si["S1"], [0.31, 0.44, 0.00], atol=5e-2, rtol=1e-1) assert_allclose(Si["ST"], [0.55, 0.44, 0.24], atol=5e-2, rtol=1e-1) assert_allclose( [Si["S2"][0][1], Si["S2"][0][2], Si["S2"][1][2]], [0.00, 0.25, 0.00], atol=5e-2, rtol=1e-1, ) @mark.filterwarnings("ignore::UserWarning") def test_regression_sobol_groups(): problem = { "num_vars": 3, "names": ["x1", "x2", "x3"], "bounds": [[-np.pi, np.pi]] * 3, "groups": ["G1", "G2", "G1"], } param_values = sobol_sampler.sample(problem, 10000, calc_second_order=True) Y = Ishigami.evaluate(param_values) Si = sobol.analyze( problem, Y, calc_second_order=True, parallel=True, conf_level=0.95, print_to_console=False, ) assert_allclose(Si["S1"], [0.55, 0.44], atol=5e-2, rtol=1e-1) assert_allclose(Si["ST"], [0.55, 0.44], atol=5e-2, rtol=1e-1) assert_allclose(Si["S2"][0][1], [0.00], atol=5e-2, rtol=1e-1) @mark.filterwarnings("ignore::UserWarning") def test_regression_sobol_groups_dists(): problem = { "num_vars": 3, "names": ["x1", "x2", "x3"], "bounds": [[-np.pi, np.pi], [1.0, 0.2], [0.0, 3, 0.5]], "groups": ["G1", "G2", "G1"], "dists": ["unif", "lognorm", "triang"], } param_values = sobol_sampler.sample(problem, 10000, calc_second_order=True) Y = Ishigami.evaluate(param_values) Si = sobol.analyze( problem, Y, calc_second_order=True, parallel=True, conf_level=0.95, print_to_console=False, ) assert_allclose(Si["S1"], [0.427, 0.573], atol=5e-2, rtol=1e-1) assert_allclose(Si["ST"], [0.428, 0.573], atol=5e-2, rtol=1e-1) assert_allclose(Si["S2"][0][1], [0.001], atol=5e-2, rtol=1e-1) def test_regression_fast(): param_file = "src/SALib/test_functions/params/Ishigami.txt" problem = read_param_file(param_file) param_values = fast_sampler.sample(problem, 10000) Y = Ishigami.evaluate(param_values) Si = fast.analyze(problem, Y, print_to_console=False) assert_allclose(Si["S1"], [0.31, 0.44, 0.00], atol=5e-2, rtol=1e-1) assert_allclose(Si["ST"], [0.55, 0.44, 0.24], atol=5e-2, rtol=1e-1) @mark.filterwarnings("ignore::DeprecationWarning") def test_regression_hdmr_ishigami(): param_file = "src/SALib/test_functions/params/Ishigami.txt" problem = read_param_file(param_file) X = latin.sample(problem, 10000) Y = Ishigami.evaluate(X) options = { "maxorder": 2, "maxiter": 100, "m": 4, "K": 1, "R": 10000, "alpha": 0.95, "lambdax": 0.01, "print_to_console": False, } Si = hdmr.analyze(problem, X, Y, **options) assert_allclose( Si["Sa"][0 : problem["num_vars"]], [0.31, 0.44, 0.00], atol=5e-2, rtol=1e-1 ) assert_allclose( Si["ST"][0 : problem["num_vars"]], [0.55, 0.44, 0.24], atol=5e-2, rtol=1e-1 ) @mark.filterwarnings("ignore::DeprecationWarning") def test_regression_hdmr_case1(): problem = { "num_vars": 5, "names": ["x1", "x2", "x3", "x4", "x5"], "bounds": [[0, 1] * 5], } X = latin.sample(problem, 10000) Y = linear_model_1.evaluate(X) options = { "maxorder": 2, "maxiter": 100, "m": 2, "K": 1, "R": 10000, "alpha": 0.95, "lambdax": 0.01, "print_to_console": False, } Si = hdmr.analyze(problem, X, Y, **options) assert_allclose(Si["Sa"][0 : problem["num_vars"]], [0.20] * 5, atol=5e-2, rtol=1e-1) assert_allclose(Si["ST"][0 : problem["num_vars"]], [0.20] * 5, atol=5e-2, rtol=1e-1) @mark.filterwarnings("ignore::DeprecationWarning") def test_regression_hdmr_case2(): problem = { "num_vars": 5, "names": ["x1", "x2", "x3", "x4", "x5"], "bounds": [[0, 1] * 5], } # Generate correlated samples mean = np.zeros((problem["num_vars"])) cov = [ [1, 0.6, 0.2, 0, 0], [0.6, 1, 0.2, 0, 0], [0.2, 0.2, 1, 0, 0], [0, 0, 0, 1, 0.2], [0, 0, 0, 0.2, 1], ] X = np.random.multivariate_normal(mean, cov, 10000) Y = linear_model_1.evaluate(X) options = { "maxorder": 2, "maxiter": 100, "m": 2, "K": 1, "R": 10000, "alpha": 0.95, "lambdax": 0.01, "print_to_console": False, } Si = hdmr.analyze(problem, X, Y, **options) assert_allclose(Si["Sa"][0 : problem["num_vars"]], [0.13] * 5, atol=5e-2, rtol=1e-1) assert_allclose( Si["Sb"][0 : problem["num_vars"]], [0.11, 0.11, 0.06, 0.03, 0.03], atol=5e-2, rtol=1e-1, ) @mark.filterwarnings("ignore::DeprecationWarning") def test_regression_hdmr_case3(): problem = { "num_vars": 5, "names": ["x1", "x2", "x3", "x4", "x5"], "bounds": [[0, 1] * 5], } # Generate correlated samples mean = np.zeros((problem["num_vars"])) cov = [ [1, 0.6, 0.2, 0, 0], [0.6, 1, 0.2, 0, 0], [0.2, 0.2, 1, 0, 0], [0, 0, 0, 1, 0.2], [0, 0, 0, 0.2, 1], ] X = np.random.multivariate_normal(mean, cov, 10000) Y = linear_model_2.evaluate(X) options = { "maxorder": 2, "maxiter": 100, "m": 2, "K": 1, "R": 10000, "alpha": 0.95, "lambdax": 0.01, "print_to_console": False, } Si = hdmr.analyze(problem, X, Y, **options) assert_allclose( Si["Sa"][0 : problem["num_vars"]], [0.28, 0.17, 0.10, 0.04, 0.02], atol=5e-2, rtol=1e-1, ) assert_allclose( Si["Sb"][0 : problem["num_vars"]], [0.16, 0.16, 0.06, 0.00, 0.00], atol=5e-2, rtol=1e-1, ) def test_regression_rbd_fast(): param_file = "src/SALib/test_functions/params/Ishigami.txt" problem = read_param_file(param_file) param_values = latin.sample(problem, 10000) Y = Ishigami.evaluate(param_values) Si = rbd_fast.analyze(problem, param_values, Y, print_to_console=False) assert_allclose(Si["S1"], [0.31, 0.44, 0.00], atol=5e-2, rtol=1e-1) def test_regression_dgsm(): param_file = "src/SALib/test_functions/params/Ishigami.txt" problem = read_param_file(param_file) param_values = finite_diff.sample(problem, 10000, delta=0.001) Y = Ishigami.evaluate(param_values) Si = dgsm.analyze(problem, param_values, Y, conf_level=0.95, print_to_console=False) assert_allclose(Si["dgsm"], [2.229, 7.066, 3.180], atol=5e-2, rtol=1e-1) def test_regression_delta(): param_file = "src/SALib/test_functions/params/Ishigami.txt" problem = read_param_file(param_file) param_values = latin.sample(problem, 10000) Y = Ishigami.evaluate(param_values) Si = delta.analyze( problem, param_values, Y, num_resamples=10, conf_level=0.95, print_to_console=True, ) assert_allclose(Si["delta_raw"], [0.210, 0.358, 0.155], atol=5e-2, rtol=1e-1) assert_allclose(Si["S1"], [0.31, 0.44, 0.00], atol=5e-2, rtol=1e-1) def test_regression_delta_svm(set_seed): # bias_reduced_delta bootstraps using NumPy's legacy global RNG. xy_input_fn = "tests/data/delta_svm_regression_data.csv" inputs = np.loadtxt(xy_input_fn, delimiter=",", skiprows=1) X = inputs[:, 0] Y = inputs[:, 1] Ygrid = [ 0.0, 0.3030303, 0.60606061, 0.90909091, 1.21212121, 1.51515152, 1.81818182, 2.12121212, 2.42424242, 2.72727273, 3.03030303, 3.33333333, 3.63636364, 3.93939394, 4.24242424, 4.54545455, 4.84848485, 5.15151515, 5.45454545, 5.75757576, 6.06060606, 6.36363636, 6.66666667, 6.96969697, 7.27272727, 7.57575758, 7.87878788, 8.18181818, 8.48484848, 8.78787879, 9.09090909, 9.39393939, 9.6969697, 10.0, 10.3030303, 10.60606061, 10.90909091, 11.21212121, 11.51515152, 11.81818182, 12.12121212, 12.42424242, 12.72727273, 13.03030303, 13.33333333, 13.63636364, 13.93939394, 14.24242424, 14.54545455, 14.84848485, 15.15151515, 15.45454545, 15.75757576, 16.06060606, 16.36363636, 16.66666667, 16.96969697, 17.27272727, 17.57575758, 17.87878788, 18.18181818, 18.48484848, 18.78787879, 19.09090909, 19.39393939, 19.6969697, 20.0, 20.3030303, 20.60606061, 20.90909091, 21.21212121, 21.51515152, 21.81818182, 22.12121212, 22.42424242, 22.72727273, 23.03030303, 23.33333333, 23.63636364, 23.93939394, 24.24242424, 24.54545455, 24.84848485, 25.15151515, 25.45454545, 25.75757576, 26.06060606, 26.36363636, 26.66666667, 26.96969697, 27.27272727, 27.57575758, 27.87878788, 28.18181818, 28.48484848, 28.78787879, 29.09090909, 29.39393939, 29.6969697, 30.0, ] m = [ 0.0, 717.82142857, 1435.64285714, 2153.46428571, 2871.28571429, 3589.10714286, 4306.92857143, 5024.75, 5742.57142857, 6460.39285714, 7178.21428571, 7896.03571429, 8613.85714286, 9331.67857143, 10049.5, 10767.32142857, 11485.14285714, 12202.96428571, 12920.78571429, 13638.60714286, 14356.42857143, 15074.25, 15792.07142857, 16509.89285714, 17227.71428571, 17945.53571429, 18663.35714286, 19381.17857143, 20099.0, ] num_resamples = 200 conf_level = 0.95 # `bias_reduced_delta` draws from the global `numpy.random` state (it does # not accept a seed/rng), so it must be seeded here to keep this # regression test deterministic (see issue #681 for the same failure mode # in `test_discrepancy`). np.random.seed(42) test_res = delta.bias_reduced_delta( Y, Ygrid, X, m, num_resamples, conf_level, Y.size, "raw", None, "testparam", int(0.005 * (Y.size)), ) test_res = test_res[:2] np.testing.assert_allclose( test_res, (0.6335098491949687, 0.026640611898969522), atol=0.05 ) SALib-SALib-d6e51b1/tests/test_sample_seed.py000066400000000000000000000033621525347100600210500ustar00rootroot00000000000000import pytest import numpy as np from SALib.sample import fast_sampler, finite_diff, latin, saltelli from SALib.sample.morris import sample as morris_sampler def problem_setup(): N = 1 problem = { "num_vars": 3, "names": ["x1", "x2", "x3"], "bounds": [[0, 1], [0, 1], [0, 1]], } return N, problem def test_morris_sample_seed(): N, problem = problem_setup() sample1 = morris_sampler(problem, N, seed=None) sample2 = morris_sampler(problem, N, seed=123) np.testing.assert_equal(np.any(np.not_equal(sample1, sample2)), True) @pytest.mark.filterwarnings("ignore::UserWarning") @pytest.mark.filterwarnings("ignore::DeprecationWarning") def test_saltelli_sample_seed(): N, problem = problem_setup() sample1 = saltelli.sample(problem, N, calc_second_order=False, skip_values=1024) sample2 = saltelli.sample(problem, N, calc_second_order=False, skip_values=1025) np.testing.assert_equal(np.any(np.not_equal(sample1, sample2)), True) def test_fast_sample_seed(): _, problem = problem_setup() sample1 = fast_sampler.sample(problem, 65, seed=None) sample2 = fast_sampler.sample(problem, 65, seed=123) np.testing.assert_equal(np.any(np.not_equal(sample1, sample2)), True) def test_finite_diff_sample_seed(): N, problem = problem_setup() sample1 = finite_diff.sample(problem, N, skip_values=1001) sample2 = finite_diff.sample(problem, N, skip_values=1002) np.testing.assert_equal(np.any(np.not_equal(sample1, sample2)), True) def test_latin_sample_seed(): N, problem = problem_setup() sample1 = latin.sample(problem, N, seed=None) sample2 = latin.sample(problem, N, seed=123) np.testing.assert_equal(np.any(np.not_equal(sample1, sample2)), True) SALib-SALib-d6e51b1/tests/test_sobol.py000066400000000000000000000220471525347100600177060ustar00rootroot00000000000000from pytest import raises, mark from numpy.testing import assert_equal, assert_allclose import numpy as np from scipy.stats import norm from SALib.analyze import sobol from SALib.sample import sobol_sequence, sobol as sobol_sampler from SALib.test_functions import Ishigami, Sobol_G from SALib.util import read_param_file def setup_samples(N=512, calc_second_order=True): param_file = "src/SALib/test_functions/params/Ishigami.txt" problem = read_param_file(param_file) param_values = sobol_sampler.sample( problem, N=N, calc_second_order=calc_second_order ) return problem, param_values def test_sobol_sequence(): # example from Joe & Kuo: http://web.maths.unsw.edu.au/~fkuo/sobol/ S = sobol_sequence.sample(10, 3) expected = [ [0, 0, 0], [0.5, 0.5, 0.5], [0.75, 0.25, 0.25], [0.25, 0.75, 0.75], [0.375, 0.375, 0.625], [0.875, 0.875, 0.125], [0.625, 0.125, 0.875], [0.125, 0.625, 0.375], [0.1875, 0.3125, 0.9375], [0.6875, 0.8125, 0.4375], ] assert_allclose(S, expected, atol=5e-2, rtol=1e-1) def test_sample_size_second_order(): N = 512 D = 3 problem, param_values = setup_samples(N=N) assert_equal(param_values.shape, [N * (2 * D + 2), D]) def test_sample_size_first_order(): N = 512 D = 3 problem, param_values = setup_samples(N=N, calc_second_order=False) assert_equal(param_values.shape, [N * (D + 2), D]) def test_incorrect_sample_size(): problem, param_values = setup_samples() Y = Ishigami.evaluate(param_values) with raises(RuntimeError): sobol.analyze(problem, Y[:-10], calc_second_order=True) def test_bad_conf_level(): problem, param_values = setup_samples() Y = Ishigami.evaluate(param_values) with raises(RuntimeError): sobol.analyze( problem, Y, calc_second_order=True, conf_level=1.01, print_to_console=False ) with raises(RuntimeError): sobol.analyze( problem, Y, calc_second_order=True, conf_level=1.0, print_to_console=False ) with raises(RuntimeError): sobol.analyze( problem, Y, calc_second_order=True, conf_level=0.0, print_to_console=False ) @mark.filterwarnings("ignore::UserWarning") def test_incorrect_second_order_setting(): # note this will still be a problem if N(2D+2) also divides by (D+2) problem, param_values = setup_samples(N=511, calc_second_order=False) Y = Ishigami.evaluate(param_values) with raises(RuntimeError): sobol.analyze(problem, Y, calc_second_order=True) def test_include_print(): problem, param_values = setup_samples() Y = Ishigami.evaluate(param_values) sobol.analyze( problem, Y, calc_second_order=True, conf_level=0.95, print_to_console=True ) def test_parallel_first_order(): c2o = False N = 8192 problem, param_values = setup_samples(N=N, calc_second_order=c2o) Y = Ishigami.evaluate(param_values) A, B, AB, BA = sobol.separate_output_values(Y, D=3, N=N, calc_second_order=c2o) r = np.random.randint(N, size=(N, 100)) Z = norm.ppf(0.5 + 0.95 / 2) tasks, n_processors = sobol.create_task_list( D=3, calc_second_order=c2o, n_processors=None ) Si_list = [] for t in tasks: Si_list.append(sobol.sobol_parallel(Z, A, AB, BA, B, r, t)) Si = sobol.Si_list_to_dict( Si_list, D=3, num_resamples=100, keep_resamples=False, calc_second_order=c2o ) assert_allclose(Si["S1"], [0.31, 0.44, 0.00], atol=5e-2, rtol=1e-1) assert_allclose(Si["ST"], [0.55, 0.44, 0.24], atol=5e-2, rtol=1e-1) def test_parallel_second_order(): c2o = True N = 8192 problem, param_values = setup_samples(N=N, calc_second_order=c2o) Y = Ishigami.evaluate(param_values) A, B, AB, BA = sobol.separate_output_values(Y, D=3, N=N, calc_second_order=c2o) r = np.random.randint(N, size=(N, 100)) Z = norm.ppf(0.5 + 0.95 / 2) tasks, n_processors = sobol.create_task_list( D=3, calc_second_order=c2o, n_processors=None ) Si_list = [] for t in tasks: Si_list.append(sobol.sobol_parallel(Z, A, AB, BA, B, r, t)) Si = sobol.Si_list_to_dict( Si_list, D=3, num_resamples=100, keep_resamples=False, calc_second_order=c2o ) assert_allclose(Si["S1"], [0.31, 0.44, 0.00], atol=5e-2, rtol=1e-1) assert_allclose(Si["ST"], [0.55, 0.44, 0.24], atol=5e-2, rtol=1e-1) assert_allclose( [Si["S2"][0][1], Si["S2"][0][2], Si["S2"][1][2]], [0.00, 0.25, 0.00], atol=5e-2, rtol=1e-1, ) def test_Sobol_G_using_sobol(): """ Tests the accuracy of the Sobol/Saltelli procedure using the Sobol_G test function, comparing the results from the Sobol/Saltelli analysis against the analytically computed sensitivity index from the Sobol_G function. """ problem = { "num_vars": 6, "names": ["x1", "x2", "x3", "x4", "x5", "x6"], "bounds": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]], } N = 4096 a = np.array([78, 12, 0.5, 2, 97, 33]) param_values = sobol_sampler.sample(problem, N, calc_second_order=False) model_results = Sobol_G.evaluate(param_values, a) Si = sobol.analyze(problem, model_results, calc_second_order=False) expected = Sobol_G.sensitivity_index(a) assert_allclose(Si["S1"], expected, atol=1e-2, rtol=1e-6) def test_constant_output(): """ No variance in model outputs, which should produce 0 sensitivity. """ def mock_model(X): r, _ = X.shape return np.array([0.4] * r) problem = { "num_vars": 3, "names": ["x1", "x2", "x3"], "bounds": [[0, 1], [0, 1], [0, 1]], } N = 256 param_values = sobol_sampler.sample(problem, N, calc_second_order=False) model_results = mock_model(param_values) Si = sobol.analyze(problem, model_results, calc_second_order=False) assert np.all( Si["S1"] == 0.0 ), "Constant outputs should produce 0 first order sensitivity" assert np.all( Si["ST"] == 0.0 ), "Constant outputs should produce 0 total order sensitivity" assert np.all(Si["S1_conf"] == 0.0), "Constant outputs should produce 0 CI" assert np.all(Si["ST_conf"] == 0.0), "Constant outputs should produce 0 CI" def test_grouped_constant_output(): """Test case where there is no variance in model outputs for grouped factors.""" def mock_model(X): r, _ = X.shape return np.array([0.4] * r) problem = { "num_vars": 3, "names": ["x1", "x2", "x3"], "groups": ["A", "B", "A"], "bounds": [[0, 1], [0, 1], [0, 1]], } N = 256 param_values = sobol_sampler.sample(problem, N, calc_second_order=False) model_results = mock_model(param_values) Si = sobol.analyze(problem, model_results, calc_second_order=False) assert np.all( Si["S1"] == 0.0 ), "Constant outputs should produce 0 first order sensitivity" assert np.all( Si["ST"] == 0.0 ), "Constant outputs should produce 0 total order sensitivity" assert np.all(Si["S1_conf"] == 0.0), "Constant outputs should produce 0 CI" assert np.all(Si["ST_conf"] == 0.0), "Constant outputs should produce 0 CI" def test_partial_constant_output(): """Sobol inner functions with some output columns constant, others varying.""" from SALib.analyze.sobol import first_order, total_order rng = np.random.default_rng(42) N = 10 D = 3 A = rng.random((N, D)) B = rng.random((N, D)) AB = rng.random((N, D)) # column 0: strictly constant A[:, 0] = 0.5 B[:, 0] = 0.5 AB[:, 0] = 0.5 s1 = first_order(A, AB, B) st = total_order(A, AB, B) # No NaN or inf for name, arr in [("S1", s1), ("ST", st)]: assert not np.any(np.isnan(arr)), f"{name} contains NaN: {arr}" assert not np.any(np.isinf(arr)), f"{name} contains inf: {arr}" # Constant column returns zero assert s1[0] == 0.0, f"S1 constant col should be 0, got {s1[0]}" assert st[0] == 0.0, f"ST constant col should be 0, got {st[0]}" # Non-constant columns should have finite, non-trivial values assert np.all(np.isfinite(s1[1:])), f"S1 non-constant cols not finite: {s1}" assert np.all(np.isfinite(st[1:])), f"ST non-constant cols not finite: {st}" def test_partial_constant_output_second_order(): """second_order with some output columns constant, others varying.""" from SALib.analyze.sobol import second_order rng = np.random.default_rng(42) N = 10 D = 3 A = rng.random((N, D)) B = rng.random((N, D)) ABj = rng.random((N, D)) ABk = rng.random((N, D)) BAj = rng.random((N, D)) # column 0: strictly constant across all inputs A[:, 0] = 0.5 B[:, 0] = 0.5 ABj[:, 0] = 0.5 ABk[:, 0] = 0.5 BAj[:, 0] = 0.5 s2 = second_order(A, ABj, ABk, BAj, B) assert not np.any(np.isnan(s2)), f"S2 contains NaN: {s2}" assert not np.any(np.isinf(s2)), f"S2 contains inf: {s2}" assert s2[0] == 0.0, f"S2 constant col should be 0, got {s2[0]}" assert np.all(np.isfinite(s2[1:])), f"S2 non-constant cols not finite: {s2}" SALib-SALib-d6e51b1/tests/test_sp_sobol.py000066400000000000000000000163231525347100600204100ustar00rootroot00000000000000"""Copy of `test_sobol.py` modified to cover SciPy sobol interface.""" from pytest import raises, mark from numpy.testing import assert_equal, assert_allclose import numpy as np from scipy.stats import norm from SALib.analyze import sobol from SALib.sample.sobol import sample as sobol_sample from SALib.sample import sobol_sequence from SALib.test_functions import Ishigami, Sobol_G from SALib.util import read_param_file def setup_samples(N=512, calc_second_order=True): param_file = "src/SALib/test_functions/params/Ishigami.txt" problem = read_param_file(param_file) param_values = sobol_sample(problem, N=N, calc_second_order=calc_second_order) return problem, param_values def test_sobol_sequence(): # example from Joe & Kuo: http://web.maths.unsw.edu.au/~fkuo/sobol/ S = sobol_sequence.sample(10, 3) expected = [ [0, 0, 0], [0.5, 0.5, 0.5], [0.75, 0.25, 0.25], [0.25, 0.75, 0.75], [0.375, 0.375, 0.625], [0.875, 0.875, 0.125], [0.625, 0.125, 0.875], [0.125, 0.625, 0.375], [0.1875, 0.3125, 0.9375], [0.6875, 0.8125, 0.4375], ] assert_allclose(S, expected, atol=5e-2, rtol=1e-1) def test_sample_size_second_order(): N = 512 D = 3 problem, param_values = setup_samples(N=N) assert_equal(param_values.shape, [N * (2 * D + 2), D]) def test_sample_size_first_order(): N = 512 D = 3 problem, param_values = setup_samples(N=N, calc_second_order=False) assert_equal(param_values.shape, [N * (D + 2), D]) def test_incorrect_sample_size(): problem, param_values = setup_samples() Y = Ishigami.evaluate(param_values) with raises(RuntimeError): sobol.analyze(problem, Y[:-10], calc_second_order=True) def test_bad_conf_level(): problem, param_values = setup_samples() Y = Ishigami.evaluate(param_values) with raises(RuntimeError): sobol.analyze( problem, Y, calc_second_order=True, conf_level=1.01, print_to_console=False ) with raises(RuntimeError): sobol.analyze( problem, Y, calc_second_order=True, conf_level=1.0, print_to_console=False ) with raises(RuntimeError): sobol.analyze( problem, Y, calc_second_order=True, conf_level=0.0, print_to_console=False ) @mark.filterwarnings("ignore::UserWarning") def test_incorrect_second_order_setting(): # note this will still be a problem if N(2D+2) also divides by (D+2) problem, param_values = setup_samples(N=511, calc_second_order=False) Y = Ishigami.evaluate(param_values) with raises(RuntimeError): sobol.analyze(problem, Y, calc_second_order=True) def test_include_print(): problem, param_values = setup_samples() Y = Ishigami.evaluate(param_values) sobol.analyze( problem, Y, calc_second_order=True, conf_level=0.95, print_to_console=True ) def test_parallel_first_order(): c2o = False N = 8192 problem, param_values = setup_samples(N=N, calc_second_order=c2o) Y = Ishigami.evaluate(param_values) A, B, AB, BA = sobol.separate_output_values(Y, D=3, N=N, calc_second_order=c2o) r = np.random.randint(N, size=(N, 100)) Z = norm.ppf(0.5 + 0.95 / 2) tasks, n_processors = sobol.create_task_list( D=3, calc_second_order=c2o, n_processors=None ) Si_list = [] for t in tasks: Si_list.append(sobol.sobol_parallel(Z, A, AB, BA, B, r, t)) Si = sobol.Si_list_to_dict( Si_list, D=3, num_resamples=100, keep_resamples=False, calc_second_order=c2o ) assert_allclose(Si["S1"], [0.31, 0.44, 0.00], atol=5e-2, rtol=1e-1) assert_allclose(Si["ST"], [0.55, 0.44, 0.24], atol=5e-2, rtol=1e-1) def test_parallel_second_order(): c2o = True N = 8192 problem, param_values = setup_samples(N=N, calc_second_order=c2o) Y = Ishigami.evaluate(param_values) A, B, AB, BA = sobol.separate_output_values(Y, D=3, N=N, calc_second_order=c2o) r = np.random.randint(N, size=(N, 100)) Z = norm.ppf(0.5 + 0.95 / 2) tasks, n_processors = sobol.create_task_list( D=3, calc_second_order=c2o, n_processors=None ) Si_list = [] for t in tasks: Si_list.append(sobol.sobol_parallel(Z, A, AB, BA, B, r, t)) Si = sobol.Si_list_to_dict( Si_list, D=3, num_resamples=100, keep_resamples=False, calc_second_order=c2o ) assert_allclose(Si["S1"], [0.31, 0.44, 0.00], atol=5e-2, rtol=1e-1) assert_allclose(Si["ST"], [0.55, 0.44, 0.24], atol=5e-2, rtol=1e-1) assert_allclose( [Si["S2"][0][1], Si["S2"][0][2], Si["S2"][1][2]], [0.00, 0.25, 0.00], atol=5e-2, rtol=1e-1, ) def test_Sobol_G_using_sobol(): """ Tests the accuracy of the Sobol/Saltelli procedure using the Sobol_G test function, comparing the results from the Sobol/Saltelli analysis against the analytically computed sensitivity index from the Sobol_G function. """ problem = { "num_vars": 6, "names": ["x1", "x2", "x3", "x4", "x5", "x6"], "bounds": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]], } N = 4096 a = np.array([78, 12, 0.5, 2, 97, 33]) param_values = sobol_sample(problem, N, calc_second_order=False) model_results = Sobol_G.evaluate(param_values, a) Si = sobol.analyze(problem, model_results, calc_second_order=False) expected = Sobol_G.sensitivity_index(a) assert_allclose(Si["S1"], expected, atol=1e-2, rtol=1e-6) def test_constant_output(): """ No variance in model outputs, which should produce 0 sensitivity. """ def mock_model(X): r, _ = X.shape return np.array([0.4] * r) problem = { "num_vars": 3, "names": ["x1", "x2", "x3"], "bounds": [[0, 1], [0, 1], [0, 1]], } N = 256 param_values = sobol_sample(problem, N, calc_second_order=False) model_results = mock_model(param_values) Si = sobol.analyze(problem, model_results, calc_second_order=False) assert np.all( Si["S1"] == 0.0 ), "Constant outputs should produce 0 first order sensitivity" assert np.all( Si["ST"] == 0.0 ), "Constant outputs should produce 0 total order sensitivity" assert np.all(Si["S1_conf"] == 0.0), "Constant outputs should produce 0 CI" assert np.all(Si["ST_conf"] == 0.0), "Constant outputs should produce 0 CI" def test_grouped_constant_output(): """Test case where there is no variance in model outputs for grouped factors.""" def mock_model(X): r, _ = X.shape return np.array([0.4] * r) problem = { "num_vars": 3, "names": ["x1", "x2", "x3"], "groups": ["A", "B", "A"], "bounds": [[0, 1], [0, 1], [0, 1]], } N = 256 param_values = sobol_sample(problem, N, calc_second_order=False) model_results = mock_model(param_values) Si = sobol.analyze(problem, model_results, calc_second_order=False) assert np.all( Si["S1"] == 0.0 ), "Constant outputs should produce 0 first order sensitivity" assert np.all( Si["ST"] == 0.0 ), "Constant outputs should produce 0 total order sensitivity" assert np.all(Si["S1_conf"] == 0.0), "Constant outputs should produce 0 CI" assert np.all(Si["ST_conf"] == 0.0), "Constant outputs should produce 0 CI" SALib-SALib-d6e51b1/tests/test_test_functions.py000066400000000000000000000311751525347100600216410ustar00rootroot00000000000000from pytest import raises from numpy.testing import assert_allclose import numpy as np from SALib.test_functions.Sobol_G import ( evaluate, _total_variance, _partial_first_order_variance, sensitivity_index, total_sensitivity_index, ) from SALib import ProblemSpec def test_Sobol_G(): """ """ parameter_values = np.zeros((1, 8)) actual = evaluate(parameter_values) expected = np.array([4.0583]) assert_allclose(actual, expected, atol=1e-4, rtol=1e-4) def test_Sobol_G_raises_error_if_values_wrong_size(): """ Tests that a value error is raised if the Sobol G function is called with the wrong number of variables """ a = [1, 2, 3, 4, 5, 6, 7, 8] with raises(ValueError): evaluate(np.array([1, 2, 3, 4, 5, 6, 7]), a) def test_Sobol_G_raises_error_if_values_gt_one(): """ Tests that a value error is raised if the Sobol G function is called with values greater than one """ with raises(ValueError): evaluate(np.array([0, 1, 0.02, 0.23, 1.234, 0.02848848, 0, 0.78])) def test_Sobol_G_raises_error_if_values_lt_zero(): """ Tests that a value error is raised if the Sobol G function is called with values less than zero. """ with raises(ValueError): evaluate(np.array([0, -1, -0.02, 1, 1, -0.1, -0, -12])) def test_Sobol_G_raises_error_if_values_not_numpy_array(): """ Tests that a type error is raised if the Sobol G function is called with values argument not as a numpy array. """ fixture = [list(range(8)), str(12345678)] for x in fixture: with raises(TypeError): evaluate(x) def test_total_variance(): a = np.array([78, 12, 0.5, 2, 97, 33]) actual = _total_variance(a) expected = 0.19347 assert_allclose(actual, expected, rtol=1e-4) def test_partial_first_order_variance(): a = np.array([78, 12, 0.5, 2, 97, 33]) actual = _partial_first_order_variance(a) expected = (len(a),) assert a.shape == expected expected = np.array([0.000053, 0.001972, 0.148148, 0.037037, 0.000035, 0.000288]) assert_allclose(actual, expected, atol=1e-4, rtol=1e-4) def test_sensitivity_index(): a = np.array([78, 12, 0.5, 2, 97, 33]) actual = sensitivity_index(a) expected = np.array([0.000276, 0.010195, 0.765743, 0.191436, 0.000179, 0.001490]) assert_allclose(actual, expected, atol=1e-2, rtol=1e-6) def test_total_sensitivity_index(): a = np.array([78, 12, 0.5, 2, 97, 33]) actual = total_sensitivity_index(a) expected = np.array( [ 3.294577e-04, 1.214324e-02, 7.959698e-01, 2.203131e-01, 2.140966e-04, 1.778255e-03, ] ) assert_allclose(actual, expected, atol=1e-2, rtol=1e-6) def test_modified_Sobol_G(): parameter_values = np.zeros((1, 8)) delta_values = np.ones_like(parameter_values) alpha_values = np.array([2] * 8) actual = evaluate(parameter_values, delta=delta_values, alpha=alpha_values) expected = np.array([10.6275]) assert_allclose(actual, expected, atol=1e-4, rtol=1e-4) def test_modified_Sobol_G_error_if_type_wrong(): parameter_values = np.zeros((1, 8)) delta_values = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8] expected_err = "The argument `delta` must be given as a numpy ndarray" with raises(TypeError, match=expected_err): evaluate(parameter_values, delta=delta_values) alpha_values = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8] expected_err = "The argument `alpha` must be given as a numpy ndarray" with raises(TypeError, match=expected_err): evaluate(parameter_values, alpha=alpha_values) def test_modified_Sobol_G_error_if_value_beyond_range(): parameter_values = np.zeros((1, 8)) delta_values = np.array([-0.5, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 1.8]) expected_err = ( "Sobol G function called with delta values less than zero or greater than one" ) with raises(ValueError, match=expected_err): evaluate(parameter_values, delta=delta_values) alpha_values = np.array([0, -0.2, -0.3, 0.4, 0.5, 0.6, 0.7, 0.8]) expected_err = ( "Sobol G function called with alpha values less than or equal to zero" ) with raises(ValueError, match=expected_err): evaluate(parameter_values, alpha=alpha_values) def test_modified_partial_first_order_variance(): a = np.array([78, 12, 0.5, 2, 97, 33]) alpha = np.array([1, 2, 15, 0.6, 8, 48]) actual = _partial_first_order_variance(a, alpha) expected = (len(a),) assert a.shape == expected expected = np.array( [ 5.34102441e-05, 4.73372781e-03, 3.22580645e00, 1.81818182e-02, 3.91993532e-04, 2.05472122e-02, ] ) assert_allclose(actual, expected, atol=1e-4, rtol=1e-4) def test_oakley_results(): """Test Oakley test function results against analytic values for first-order sensitivities provided in [1] (see Table 1). Ensure analytic results are within estimated CI. References ---------- .. [1] Oakley, J.E., O’Hagan, A., 2004. Probabilistic sensitivity analysis of complex models: a Bayesian approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 66, 751–769. https://doi.org/10.1111/j.1467-9868.2004.05304.x """ from SALib.test_functions import oakley2004 analytic = np.array( [ 0.00156, 0.000186, 0.001307, 0.003045, 0.002905, 0.023035, 0.024151, 0.026517, 0.046036, 0.014945, 0.101823, 0.135708, 0.101989, 0.105169, 0.122818, ] ) # Raw values taken from: http://www.jeremy-oakley.staff.shef.ac.uk/psa_example.txt M = np.array( [ -2.25e-02, -1.85e-01, 1.34e-01, 3.69e-01, 1.72e-01, 1.37e-01, -4.40e-01, -8.14e-02, 7.13e-01, -4.44e-01, 5.04e-01, -2.41e-02, -4.59e-02, 2.17e-01, 5.59e-02, 2.57e-01, 5.38e-02, 2.58e-01, 2.38e-01, -5.91e-01, -8.16e-02, -2.87e-01, 4.16e-01, 4.98e-01, 8.39e-02, -1.11e-01, 3.32e-02, -1.40e-01, -3.10e-02, -2.23e-01, -5.60e-02, 1.95e-01, 9.55e-02, -2.86e-01, -1.44e-01, 2.24e-01, 1.45e-01, 2.90e-01, 2.31e-01, -3.19e-01, -2.90e-01, -2.10e-01, 4.31e-01, 2.44e-02, 4.49e-02, 6.64e-01, 4.31e-01, 2.99e-01, -1.62e-01, -3.15e-01, -3.90e-01, 1.77e-01, 5.80e-02, 1.72e-01, 1.35e-01, -3.53e-01, 2.51e-01, -1.88e-02, 3.65e-01, -3.25e-01, -1.21e-01, 1.25e-01, 1.07e-01, 4.66e-02, -2.17e-01, 1.95e-01, -6.55e-02, 2.44e-02, -9.68e-02, 1.94e-01, 3.34e-01, 3.13e-01, -8.36e-02, -2.53e-01, 3.73e-01, -2.84e-01, -3.28e-01, -1.05e-01, -2.21e-01, -1.37e-01, -1.44e-01, -1.15e-01, 2.24e-01, -3.04e-02, -5.15e-01, 1.73e-02, 3.90e-02, 3.61e-01, 3.09e-01, 5.00e-02, -7.79e-02, 3.75e-03, 8.87e-01, -2.66e-01, -7.93e-02, -4.27e-02, -1.87e-01, -3.56e-01, -1.75e-01, 8.87e-02, 4.00e-01, -5.60e-02, 1.37e-01, 2.15e-01, -1.13e-02, -9.23e-02, 5.92e-01, 3.13e-02, -3.31e-02, -2.43e-01, -9.98e-02, 3.45e-02, 9.51e-02, -3.38e-01, 6.39e-03, -6.12e-01, 8.13e-02, 8.87e-01, 1.43e-01, 1.48e-01, -1.32e-01, 5.29e-01, 1.27e-01, 4.51e-02, 5.84e-01, 3.73e-01, 1.14e-01, -2.95e-01, -5.70e-01, 4.63e-01, -9.41e-02, 1.40e-01, -3.86e-01, -4.49e-01, -1.46e-01, 5.81e-02, -3.23e-01, 9.31e-02, 7.24e-02, -5.69e-01, 5.26e-01, 2.37e-01, -1.18e-02, 7.18e-02, 7.83e-02, -1.34e-01, 2.27e-01, 1.44e-01, -4.52e-01, -5.56e-01, 6.61e-01, 3.46e-01, 1.41e-01, 5.19e-01, -2.80e-01, -1.60e-01, -6.84e-02, -2.04e-01, 6.97e-02, 2.31e-01, -4.44e-02, -1.65e-01, 2.16e-01, 4.27e-03, -8.74e-02, 3.16e-01, -2.76e-02, 1.34e-01, 1.35e-01, 5.40e-02, -1.74e-01, 1.75e-01, 6.03e-02, -1.79e-01, -3.11e-01, -2.54e-01, 2.58e-02, -4.30e-01, -6.23e-01, -3.40e-02, -2.90e-01, 3.41e-02, 3.49e-02, -1.21e-01, 2.60e-02, -3.35e-01, -4.14e-01, 5.32e-02, -2.71e-01, -2.63e-02, 4.10e-01, 2.66e-01, 1.56e-01, -1.87e-01, 1.99e-02, -2.44e-01, -4.41e-01, 1.26e-02, 2.49e-01, 7.11e-02, 2.46e-01, 1.75e-01, 8.53e-03, 2.51e-01, -1.47e-01, -8.46e-02, 3.69e-01, -3.00e-01, 1.10e-01, -7.57e-01, 4.15e-02, -2.60e-01, 4.64e-01, -3.61e-01, -9.50e-01, -1.65e-01, 3.09e-03, 5.28e-02, 2.25e-01, 3.84e-01, 4.56e-01, -1.86e-01, 8.23e-03, 1.67e-01, 1.60e-01, ] ).reshape(15, 15) A = np.array( [ [ 0.0118, 0.0456, 0.2297, 0.0393, 0.1177, 0.3865, 0.3897, 0.6061, 0.6159, 0.4005, 1.0741, 1.1474, 0.7880, 1.1242, 1.1982, ], [ 0.4341, 0.0887, 0.0512, 0.3233, 0.1489, 1.0360, 0.9892, 0.9672, 0.8977, 0.8083, 1.8426, 2.4712, 2.3946, 2.0045, 2.2621, ], [ 0.1044, 0.2057, 0.0774, 0.2730, 0.1253, 0.7526, 0.8570, 1.0331, 0.8388, 0.7970, 2.2145, 2.0382, 2.4004, 2.0541, 1.9845, ], ] ) sp = ProblemSpec( { "names": ["x{}".format(i) for i in range(1, 16)], "bounds": [ [0.0, 0.835], ] * 15, "dists": ["norm"] * 15, } ) ( sp.sample_latin(2048, seed=101) .evaluate(oakley2004.evaluate, A, M) .analyze_rbd_fast(seed=101, num_resamples=100) ) S1 = sp.analysis.to_df() S1["lower"] = S1["S1"] - S1["S1_conf"] S1["analytic"] = analytic S1["upper"] = S1["S1"] + S1["S1_conf"] assert np.all((analytic >= S1["lower"]) & (analytic <= S1["upper"])) SALib-SALib-d6e51b1/tests/test_to_df.py000066400000000000000000000146231525347100600176640ustar00rootroot00000000000000import numpy as np import pandas as pd from SALib.sample import ( sobol as sobol_sample, morris as morris_sample, finite_diff, fast_sampler, ff as ff_sample, latin, ) from SALib.analyze import sobol, morris, dgsm, fast, ff, rbd_fast from SALib.test_functions import Ishigami, Sobol_G def test_morris_to_df(): params = ["x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8"] problem = { "num_vars": 8, "names": params, "groups": None, "bounds": [ [0.0, 1.0], [0.0, 1.0], [0.0, 1.0], [0.0, 1.0], [0.0, 1.0], [0.0, 1.0], [0.0, 1.0], [0.0, 1.0], ], } param_values = morris_sample.sample( problem, N=1000, num_levels=4, optimal_trajectories=None ) Y = Sobol_G.evaluate(param_values) Si = morris.analyze(problem, param_values, Y) Si_df = Si.to_df() assert isinstance( Si_df, pd.DataFrame ), "Morris Si: Expected DataFrame, got {}".format(type(Si_df)) expected_index = set(params) assert set(Si_df.index) == expected_index, "Incorrect index in DataFrame" col_names = ["mu", "mu_star", "sigma", "mu_star_conf"] assert set(Si_df.columns) == set( col_names ), "Unexpected column names in DataFrame. Expected {}, got {}".format( col_names, Si_df.columns ) # End test_morris_to_df() def test_sobol_to_df(): params = ["x1", "x2", "x3"] problem = {"num_vars": 3, "names": params, "bounds": [[-np.pi, np.pi]] * 3} X = sobol_sample.sample(problem, 512) Y = Ishigami.evaluate(X) Si = sobol.analyze(problem, Y, print_to_console=False) total, first, second = Si.to_df() assert isinstance( total, pd.DataFrame ), "Total Si: Expected DataFrame, got {}".format(type(total)) assert isinstance( first, pd.DataFrame ), "First Si: Expected DataFrame, got {}".format(type(first)) assert isinstance( second, pd.DataFrame ), "Second Si: Expected DataFrame, got {}".format(type(second)) expected_index = set(params) assert set(total.index) == expected_index, "Index for Total Si are incorrect" assert set(first.index) == expected_index, "Index for first order Si are incorrect" assert set(second.index) == set( [("x1", "x2"), ("x1", "x3"), ("x2", "x3")] ), "Index for second order Si are incorrect" # End test_sobol_to_df() def test_dgsm_to_df(): params = ["x1", "x2", "x3"] problem = { "num_vars": 3, "names": params, "groups": None, "bounds": [ [-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359], ], } param_values = finite_diff.sample(problem, 1000, delta=0.001) Y = Ishigami.evaluate(param_values) Si = dgsm.analyze(problem, param_values, Y, print_to_console=False) Si_df = Si.to_df() assert isinstance( Si_df, pd.DataFrame ), "DGSM Si: Expected DataFrame, got {}".format(type(Si_df)) assert set(Si_df.index) == set(params), "Incorrect index in DataFrame" col_names = ["vi", "vi_std", "dgsm", "dgsm_conf"] assert set(Si_df.columns) == set(col_names), "Unexpected column names in DataFrame" # End test_dgsm_to_df() def test_fast_to_df(): params = ["x1", "x2", "x3"] problem = { "num_vars": 3, "names": params, "groups": None, "bounds": [ [-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359], ], } param_values = fast_sampler.sample(problem, 1000) Y = Ishigami.evaluate(param_values) Si = fast.analyze(problem, Y, print_to_console=False) Si_df = Si.to_df() expected_index = set(params) assert isinstance( Si_df, pd.DataFrame ), "FAST Si: Expected DataFrame, got {}".format(type(Si_df)) assert set(Si_df.index) == expected_index, "Incorrect index in DataFrame" col_names = set(["S1", "ST", "S1_conf", "ST_conf"]) assert ( set(Si_df.columns) == col_names ), "Unexpected column names in DataFrame. Expected {}, got {}".format( col_names, Si_df.columns ) # End test_fast_to_df() def test_ff_to_df(): params = ["x1", "x2", "x3"] main_index = params + ["dummy_0"] problem = { "num_vars": 3, "names": params, "groups": None, "bounds": [ [-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359], ], } X = ff_sample.sample(problem) Y = X[:, 0] + (0.1 * X[:, 1]) + ((1.2 * X[:, 2]) * (0.2 + X[:, 0])) Si = ff.analyze(problem, X, Y, second_order=True, print_to_console=False) main_effect, inter_effect = Si.to_df() assert isinstance( main_effect, pd.DataFrame ), "FF ME: Expected DataFrame, got {}".format(type(main_effect)) assert isinstance( main_effect, pd.DataFrame ), "FF IE: Expected DataFrame, got {}".format(type(inter_effect)) assert set(main_effect.index) == set( main_index ), "Incorrect index in Main Effect DataFrame" inter_index = set( [ ("x1", "x2"), ("x1", "x3"), ("x2", "x3"), ("x1", "dummy_0"), ("x2", "dummy_0"), ("x3", "dummy_0"), ] ) assert ( set(inter_effect.index) == inter_index ), "Incorrect index in Interaction Effect DataFrame" # End test_ff_to_df() def test_rbd_to_df(): params = ["x1", "x2", "x3"] problem = { "num_vars": 3, "names": params, "groups": None, "bounds": [ [-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359], [-3.14159265359, 3.14159265359], ], } param_values = latin.sample(problem, 1000) Y = Ishigami.evaluate(param_values) Si = rbd_fast.analyze(problem, param_values, Y, print_to_console=False) Si_df = Si.to_df() assert isinstance(Si_df, pd.DataFrame), "RBD Si: Expected DataFrame, got {}".format( type(Si_df) ) assert set(Si_df.index) == set(params), "Incorrect index in DataFrame" col_names = set(["S1", "S1_conf"]) assert ( set(Si_df.columns) == col_names ), "Unexpected column names in DataFrame. Expected {}, got {}".format( col_names, Si_df.columns ) # End test_rbd_to_df() SALib-SALib-d6e51b1/tests/test_util.py000066400000000000000000000144631525347100600175500ustar00rootroot00000000000000from pytest import raises from numpy.testing import assert_equal, assert_allclose import numpy as np from scipy import stats import pytest from SALib.util import ( read_param_file, _scale_samples, _unscale_samples, compute_groups_matrix, ) from SALib.sample import latin @pytest.fixture(scope="function") def setup_param_file_group_dist(make_temporary_file): filename = make_temporary_file with open(filename, "w") as ofile: ofile.write("Test1 0.0 100.0 Group1 unif\n") ofile.write("Test2 5.0 51.0 Group1 triang\n") ofile.write("Test3 10.0 1.0 Group2 norm\n") return filename @pytest.fixture(scope="function") def setup_csv_param_file_space(make_temporary_file): filename = make_temporary_file with open(filename, "w") as ofile: ofile.write("Test 1,0.0,100.0\n") ofile.write("Test 2,5.0,51.0\n") return filename @pytest.fixture(scope="function") def setup_tab_param_file_espace_names(make_temporary_file): filename = make_temporary_file with open(filename, "w") as ofile: ofile.write("Test 1\t0.0\t100.0\n") ofile.write("Test 2\t5.0\t51.0\n") return filename @pytest.fixture(scope="function") def setup_csv_param_file_space_comments(make_temporary_file): filename = make_temporary_file with open(filename, "w") as ofile: ofile.write("# Here is a comment\n") ofile.write("'Test 1',0.0,100.0\n") ofile.write("'Test 2',5.0,51.0\n") return filename def test_readfile(setup_function): """ Tests a standard parameter file is read correctly """ filename = setup_function pf = read_param_file(filename) assert_equal(pf["bounds"], [[0, 100], [5, 51]]) assert_equal(pf["num_vars"], 2) assert_equal(pf["names"], ["Test1", "Test2"]) def test_readfile_group_dist(setup_param_file_group_dist): """ Tests a parameter file with groups and distributions is read correctly """ filename = setup_param_file_group_dist pf = read_param_file(filename) assert_equal(pf["bounds"], [[0, 100], [5, 51], [10, 1]]) assert_equal(pf["num_vars"], 3) assert_equal(pf["names"], ["Test1", "Test2", "Test3"]) assert_equal(pf["groups"], ["Group1", "Group1", "Group2"]) assert_equal(pf["dists"], ["unif", "triang", "norm"]) def test_csv_readfile_with_whitespace(setup_csv_param_file_space): """ A comma delimited parameter file with whitespace in the names """ filename = setup_csv_param_file_space pf = read_param_file(filename) assert_equal(pf["bounds"], [[0, 100], [5, 51]]) assert_equal(pf["num_vars"], 2) assert_equal(pf["names"], ["Test 1", "Test 2"]) def test_tab_readfile_whitespace(setup_tab_param_file_espace_names): """ A tab delimited parameter file with whitespace in the names """ filename = setup_tab_param_file_espace_names pf = read_param_file(filename) assert_equal(pf["bounds"], [[0, 100], [5, 51]]) assert_equal(pf["num_vars"], 2) assert_equal(pf["names"], ["Test 1", "Test 2"]) def test_csv_readfile_comments(setup_csv_param_file_space_comments): """ """ filename = setup_csv_param_file_space_comments pf = read_param_file(filename) print(pf["bounds"], pf["num_vars"], pf["names"]) assert_equal(pf["bounds"], [[0, 100], [5, 51]]) assert_equal(pf["num_vars"], 2) assert_equal(pf["names"], ["Test 1", "Test 2"]) # Test scale samples def test_scale_samples(): """ Simple test to ensure that samples are correctly scaled """ params = np.arange(0, 1.1, 0.1).repeat(2).reshape((11, 2)) bounds = [[10, 20], [-10, 10]] desired = np.array([np.arange(10, 21, 1), np.arange(-10, 12, 2)], dtype=float).T _scale_samples(params, bounds) assert_allclose(params, desired, atol=1e-03, rtol=1e-03) def test_unscale_samples(): """ Simple test to unscale samples back to [0,1] range """ params = np.array([np.arange(10, 21, 1), np.arange(-10, 12, 2)], dtype=float).T bounds = [[10, 20], [-10, 10]] desired = np.arange(0, 1.1, 0.1).repeat(2).reshape((11, 2)) _unscale_samples(params, bounds) assert_allclose(params, desired, atol=1e-03, rtol=1e-03) def test_scale_samples_upper_lt_lower(): """ Raise ValueError if upper bound lower than lower bound """ params = np.array([[0, 0], [0.1, 0.1], [0.2, 0.2]]) bounds = [[10, 9], [-10, 10]] with raises(ValueError): _scale_samples(params, bounds) def test_scale_samples_upper_eq_lower(): """ Raise ValueError if upper bound lower equal to lower bound """ params = np.array([[0, 0], [0.1, 0.1], [0.2, 0.2]]) bounds = [[10, 10], [-10, 10]] with raises(ValueError): _scale_samples(params, bounds) def test_compute_groups_from_parameter_file(): """ Tests that a group file is read correctly """ actual_matrix, actual_unique_names = compute_groups_matrix( ["Group 1", "Group 2", "Group 2"] ) assert_equal(actual_matrix, np.array([[1, 0], [0, 1], [0, 1]], dtype=int)) assert_equal(actual_unique_names, ["Group 1", "Group 2"]) def test_nonuniform_scale_samples_truncnorm(): """ Test the rescaling of samples for truncated normal distribution """ problem = { "num_vars": 1, "dists": ["truncnorm"], "bounds": [[0, 3.14, 2, 1]], "names": ["x1"], } actual = latin.sample(problem, 10, seed=42) expected = np.array( [ [2.48073814], [0.65022857], [1.67026181], [1.37431706], [1.57951576], [2.07713469], [0.94218613], [2.56430448], [2.24693093], [2.93899673], ] ) np.testing.assert_allclose(actual, expected) def test_nonuniform_scale_samples_logunif(): """ Test the rescaling of samples for logarithmic uniform distribution """ problem = { "num_vars": 1, "dists": ["logunif"], "bounds": [[1e-22, 1e-18]], "names": ["x1"], } actual = latin.sample(problem, 10000) rng = np.random.default_rng() x = stats.loguniform.rvs(size=100000, a=1e-22, b=1e-18, random_state=rng) res = stats.cramervonmises_2samp(actual[:, 0], x) zero_hypothesis_rejected = True if res.pvalue > 0.05: zero_hypothesis_rejected = False assert zero_hypothesis_rejected is False