Virtual Library of Simulation Experiments:

Test Functions and Datasets

Gaussian Peak Integrand Family


Dimensions: d

The Gaussian Peak family of functions is quickly integrated analytically, to high precision. In its two-dimensional form, as shown in the plot above, the function shows a distinct two-dimensional Gaussian peak in the centre of the integration region.

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 Gaussian 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.



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: