Discontinuous Integrand Family
Description:
Dimensions: dThe 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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