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Chaospy is a numerical tool for performing uncertainty quantification using
polynomial chaos expansions and advanced Monte Carlo methods implemented in
Python.
If you are using this software in work that will be published, please cite the
journal article: Chaospy: An open source tool for designing methods of uncertainty quantification <http://dx.doi.org/10.1016/j.jocs.2015.08.008>_
.. contents:: Table of Contents:
Installation
Installation should be straight forward::
pip install chaospy
And you should be ready to go.
Alternatively, to get the most current experimental version, the code can be
installed from Github as follows::
git clone git@github.com:jonathf/chaospy.git # first time only
cd chaospy/
git pull # after the first time
pip install .
Example Usage
chaospy is created to be simple and modular. A simple script to implement
point collocation method will look as follows:
.. code-block:: python
import chaospy
import numpy
# your code wrapper goes here
def foo(coord, prm):
"""Function to do uncertainty quantification on."""
return prm[0] * numpy.e ** (-prm[1] * numpy.linspace(0, 10, 100))
# bi-variate probability distribution
distribution = chaospy.J(chaospy.Uniform(1, 2), chaospy.Uniform(0.1, 0.2))
# polynomial chaos expansion
polynomial_expansion = chaospy.orth_ttr(8, distribution)
# samples:
samples = distribution.sample(1000)
# evaluations:
evals = [foo(sample) for sample in samples.T]
# polynomial approximation
foo_approx = chaospy.fit_regression(
polynomial_expansion, samples, evals)
# statistical metrics
expected = chaospy.E(foo_approx, distribution)
deviation = chaospy.Std(foo_approx, distribution)
For a more extensive description of what going on, see the tutorial <https://chaospy.readthedocs.io/en/master/tutorial.html>_.
For a collection of recipes, see the cookbook <https://chaospy.readthedocs.io/en/master/cookbook.html>_.
Related Projects
Chaospy is being used in other related projects that requires uncertainty
quantification components chaospy provides.
+-----------------+-----------------------------------------------------------+, easyVVUQ, Library designed to facilitate verification, validation, and uncertainty quantification., +-----------------+-----------------------------------------------------------+, STARFiSh, Shell-based, scientific simulation program, for blood flow in mammals., +-----------------+-----------------------------------------------------------+, Profit, Probabilistic response model fitting via interactive, tools., +-----------------+-----------------------------------------------------------+, UncertainPy, Uncertainty quantification and sensitivity analysis,, tailored towards computational neuroscience., +-----------------+-----------------------------------------------------------+, SparseSpACE_, Spatially adaptive combination technique targeted to, solve high dimensional numerical integration., +-----------------+-----------------------------------------------------------+
.. _easyVVUQ: https://github.com/UCL-CCS/EasyVVUQ
.. _STARFiSh: https://www.ntnu.no/starfish
.. _Profit: https://github.com/redmod-team/profit
.. _UncertainPy: https://github.com/simetenn/uncertainpy
.. _SparseSpACE: https://github.com/obersteiner/sparseSpACE
Also a few shout-outs:
+--------------+--------------------------------------------------------------+, OpenTURNS, Thanks to Régis Lebrun for both proposing a collaboration, and creating an initial implementation of both, Chaospy Compatibility_ in OpenTURNS_ and, OpenTURNS Compatibility_ in chaospy., +--------------+--------------------------------------------------------------+, orthopy, Thanks to Nico Schlömer for providing the implementation, quadpy, for several of the quadrature integration methods., +--------------+--------------------------------------------------------------+, UQRF, Thanks to Florian Künzner for providing the, implementation for sample distribution_., +--------------+--------------------------------------------------------------+
.. _OpenTURNS: http://openturns.github.io/openturns/latest
.. _Régis Lebrun: https://github.com/regislebrun
.. _Chaospy Compatibility: http://openturns.github.io/openturns/latest/user_manual/_generated/openturns.ChaospyDistribution.html
.. OpenTURNS Compatibility: https://chaospy.readthedocs.io/en/master/recipes/external.html#module-chaospy.external.openturns
.. _orthopy: https://github.com/nschloe/orthopy
.. _quadpy: https://github.com/nschloe/quadpy
.. _Nico Schlömer: https://github.com/nschloe
.. _Florian Künzner: https://github.com/flo2k
.. _sample distribution: https://chaospy.readthedocs.io/en/master/recipes/external.html#module-chaospy.external.samples
Questions & Troubleshooting
For any problems and questions you might have related to chaospy, please
feel free to file an issue <https://github.com/jonathf/chaospy/issues>_.