Skip to main content

A Python3 library of test functions from the uncertainty quantification community with a common interface for benchmarking purpose.

Project description


DOI Code style: black Python 3.8 License

Branches Status
main (stable) build codecov Docs
dev (latest) build codecov Docs

UQTestFuns is an open-source Python3 library of test functions commonly used within the uncertainty quantification (UQ) community. The package aims to provide:

  • a lightweight implementation (with minimal dependencies) of many test functions available in the UQ literature
  • a single entry point (combining models and their probabilistic input specification) to a wide range of test functions
  • an opportunity for an open-source contribution where new test functions and reference results are posted.

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       Spatial Dimension          Application          Description
-----  ------------------  -------------------  --------------------------  ----------------------------------------------------------------------------
  1         Ackley()                M           optimization, metamodeling  Ackley function from Ackley (1987)
  2        Borehole()               8           metamodeling, sensitivity   Borehole function from Harper and Gupta (1983)
  3    DampedOscillator()           8           metamodeling, sensitivity   Damped oscillator model from Igusa and Der Kiureghian (1985)
  4         Flood()                 8           metamodeling, sensitivity   Flood model from Iooss and Lemaître (2015)
  5        Ishigami()               3                  sensitivity          Ishigami function from Ishigami and Homma (1991)

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+

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.

Getting help

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.

Package development and contribution

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.

Credits and contributors

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:


UQTestFuns is released under the MIT License.

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

uqtestfuns-0.1.1.tar.gz (46.3 kB view hashes)

Uploaded source

Built Distribution

uqtestfuns-0.1.1-py3-none-any.whl (70.3 kB view hashes)

Uploaded py3

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page