Test Functions for Numerical Integration#

The table below listed the available test functions typically used in the testing and comparison of numerical integration method.

Name

Spatial Dimension

Constructor

Bratley et al. (1992) A

M

Bratley1992a()

Bratley et al. (1992) B

M

Bratley1992b()

Bratley et al. (1992) C

M

Bratley1992c()

Bratley et al. (1992) D

M

Bratley1992d()

Sobol’-G

M

SobolG()

Welch et al. (1992)

20

Welch1992()

In a Python terminal, you can list all the available functions relevant for metamodeling applications using list_functions() and filter the results using the tag parameter:

import uqtestfuns as uqtf

uqtf.list_functions(tag="integration")

 No.    Constructor     Dimension   Description
-----  --------------  -----------  -------------------------------------------------------
  1    Bratley1992a()       M       Integration test function #1 from Bratley et al. (1992)
  2    Bratley1992b()       M       Integration test function #2 from Bratley et al. (1992)
  3    Bratley1992c()       M       Integration test function #3 from Bratley et al. (1992)
  4    Bratley1992d()       M       Integration test function #4 from Bratley et al. (1992)
  5       SobolG()          M       Sobol'-G function from Saltelli and Sobol' (1995)
  6     Welch1992()        20       20-Dimensional function from Welch et al. (1992)