Virtual Library of Simulation Experiments:

Test Functions and Datasets

Discontinuous Integrand Family


Description:

Dimensions: d

The Discontinuous family of functions is quickly integrated analytically, to high precision. In its two-dimensional form, as shown in the plot above, the function rises up into a peak near the centre, from one portion of the integration region. The rest of the surface is flat at 0.

The d uneffective u-parameters are chosen randomly from [0, 1], and their values don't significantly affect the difficulty of integration.

Larger values of the d affective a-parameters result in a sharper peak, thus resulting in more difficult integration.

The above two-dimensional plot is created using u = (0.5, 0.5) and a = (5, 5).

Input Domain:

The function is integrated over xi ∈ [0, 1], for all i = 1, …, d.

Code:


Reference:

Genz, A. (1984, September). Testing multidimensional integration routines. In Proc. of international conference on Tools, methods and languages for scientific and engineering computation (pp. 81-94). Elsevier North-Holland, Inc..



For questions or comments, please email Derek Bingham at: dbingham@stat.sfu.ca.



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