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UQTestFuns is an open-source Python3 library of test functions commonly used within the applied uncertainty quantification (UQ) community. Specifically, the package provides:
In short, UQTestFuns is an homage to the Virtual Library of Simulation Experiments (VLSE).
UQTestFuns includes several commonly used test functions in the UQ community. To list the available functions:
>>> import uqtestfuns as uqtf
>>> uqtf.list_functions()
No. Constructor Dimension Application Description
----- ----------------------------- ----------- -------------------------------------- ----------------------------------------------------------------------------
1 Ackley() M optimization, metamodeling Optimization test function from Ackley (1987)
2 Alemazkoor2D() 2 metamodeling Two-dimensional high-degree polynomial from Alemazkoor & Meidani (2018)
3 Borehole() 8 metamodeling, sensitivity Borehole function from Harper and Gupta (1983)
4 Bratley1992a() M integration, sensitivity Integration test function #1 from Bratley et al. (1992)
5 Bratley1992b() M integration, sensitivity Integration test function #2 from Bratley et al. (1992)
6 Bratley1992c() M integration, sensitivity Integration test function #3 from Bratley et al. (1992)
7 Bratley1992d() M integration, sensitivity Integration test function #4 from Bratley et al. (1992)
8 CantileverBeam2D() 2 reliability Cantilever beam reliability problem from Rajashekhar and Ellington (1993)
9 CircularPipeCrack() 2 reliability Circular pipe under bending moment from Verma et al. (2015)
...
Consider the Borehole function, a test function commonly used for metamodeling and sensitivity analysis purposes; to create an instance of this test function:
>>> my_testfun = uqtf.Borehole()
>>> print(my_testfun)
Name : Borehole
Spatial dimension : 8
Description : Borehole function from Harper and Gupta (1983)
The probabilistic input specification of this test function is built-in:
>>> print(my_testfun.prob_input)
Name : Borehole-Harper-1983
Spatial Dim. : 8
Description : Probabilistic input model of the Borehole model from Harper and Gupta (1983).
Marginals :
No. Name Distribution Parameters Description
----- ------ -------------- --------------------- -----------------------------------------------
1 rw normal [0.1 0.0161812] radius of the borehole [m]
2 r lognormal [7.71 1.0056] radius of influence [m]
3 Tu uniform [ 63070. 115600.] transmissivity of upper aquifer [m^2/year]
4 Hu uniform [ 990. 1100.] potentiometric head of upper aquifer [m]
5 Tl uniform [ 63.1 116. ] transmissivity of lower aquifer [m^2/year]
6 Hl uniform [700. 820.] potentiometric head of lower aquifer [m]
7 L uniform [1120. 1680.] length of the borehole [m]
8 Kw uniform [ 9985. 12045.] hydraulic conductivity of the borehole [m/year]
Copulas : None
A sample of input values can be generated from the input model:
>>> xx = my_testfun.prob_input.get_sample(10)
array([[8.40623544e-02, 2.43926544e+03, 8.12290909e+04, 1.06612711e+03,
7.24216436e+01, 7.78916695e+02, 1.13125867e+03, 1.02170796e+04],
[1.27235295e-01, 3.28026293e+03, 6.36463631e+04, 1.05132831e+03,
6.81653728e+01, 8.17868370e+02, 1.16603931e+03, 1.09370944e+04],
[8.72711602e-02, 7.22496512e+02, 9.18506063e+04, 1.06436843e+03,
6.44306474e+01, 7.74700231e+02, 1.46266808e+03, 1.12531788e+04],
[1.22301709e-01, 2.29922122e+02, 8.00390345e+04, 1.05290108e+03,
1.10852262e+02, 7.94709283e+02, 1.28026313e+03, 1.01879077e+04],
...
...and used to evaluate the test function:
>>> yy = my_testfun(xx)
array([ 57.32635774, 110.12229548, 53.10585812, 96.15822154,
58.51714875, 89.40068404, 52.61710076, 61.47419171,
64.18005235, 79.00454634])
You can obtain UQTestFuns directly from PyPI using pip
:
$ pip install uqtestfuns
Alternatively, you can also install the latest version from the source:
pip install git+https://github.com/damar-wicaksono/uqtestfuns.git
NOTE: UQTestFuns is currently work in progress, therefore interfaces are subject to change.
It's a good idea to install the package in an isolated virtual environment.
For a getting-started guide on UQTestFuns, please refer to the Documentation. The documentation also includes details on each of the available test functions.
For any other questions related to the package, post your questions on the GitHub Issue page.
UQTestFuns is under ongoing development; any contribution to the code (for example, a new test function) and the documentation (including new reference results) are welcomed!
Please consider the Contribution Guidelines first, before making a pull request.
This work was partly funded by the Center for Advanced Systems Understanding (CASUS) which is financed by Germany's Federal Ministry of Education and Research (BMBF) and by the Saxony Ministry for Science, Culture and Tourism (SMWK) with tax funds on the basis of the budget approved by the Saxony State Parliament.
UQTestFuns is currently maintained by:
under the Mathematical Foundations of Complex System Science Group led by Michael Hecht (HZDR/CASUS) at CASUS.
UQTestFuns is released under the MIT License.