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	Input 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()
Genz (Continuous)	M	GenzContinuous()
Genz (Corner Peak)	M	GenzCornerPeak()
Genz (Discontinuous)	M	GenzDiscontinuous()
Genz (Gaussian)	M	GenzGaussian()
Genz (Oscillatory)	M	GenzOscillatory()
Genz (Product Peak)	M	GenzProductPeak()
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", tablefmt="html")

No.	Constructor	# Input	# Output	Param.	Description
1	Bratley1992a()	M	1	False	Integration test function #1 from Bratley et al. (1992)
2	Bratley1992b()	M	1	False	Integration test function #2 from Bratley et al. (1992)
3	Bratley1992c()	M	1	False	Integration test function #3 from Bratley et al. (1992)
4	Bratley1992d()	M	1	False	Integration test function #4 from Bratley et al. (1992)
5	GenzContinuous()	M	1	True	Continuous (but non- differentiable) integrand from Genz (1984)
6	GenzCornerPeak()	M	1	True	Corner peak integrand from Genz (1984)
7	GenzDiscontinuous()	M	1	True	Discontinuous integrand from Genz (1984)
8	GenzGaussian()	M	1	True	Gaussian integrand from Genz (1984)
9	GenzOscillatory()	M	1	True	Oscillatory integrand from Genz (1984)
10	GenzProductPeak()	M	1	True	Product peak integrand from Genz (1984)
11	SobolG()	M	1	True	Sobol'-G function from Saltelli and Sobol' (1995)
12	Welch1992()	20	1	False	20-Dimensional function from Welch et al. (1992)