**Name:**

testsuite::test_lambertw - check if lambertw function works

**Synopsis:**

(test_lambertw) run -> some known relations

**Description:**

The script tests whether the Lambert W-function [1] provided by the

GNU Scientific Library (GSL) [2] fulfills some known relations [3].

In the absence of the GSL NEST uses a simple iterative scheme to

compute the Lambert-W function. In this case we apply less strict

criteria for the required accuracy.

The relationships tested are:

(1) the principal branch crosses the origin

(2) at -1/e both branches meet athe value W=-1

(3) the principal branch fulfills the "golden ratio" of exponentials

(4) the non-principal branch yields the same result as we find by

bisectioning for the problem given as an example in the documentation

of LambertWm1 with realistic parameters.

**References:**

[1] Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J., & Knuth, D. E.

(1996). On the lambert w function. Advances in Computational Mathematics

5, 329{359.

[2] Galassi, M., Davies, J., Theiler, J., Gough, B., Jungman, G., Booth, M.,

& Rossi, F. (2006). GNU Scientific Library Reference Manual (2nd Ed.).

Network Theory Limited.

[3] Weisstein, E. W. (1999). CRC Concise Encyclopedia of Mathematics.

"Lambert W-Function" Boca Raton, London, New York, Washington D.C.: CRC Press.

Author: July 2009, Diesmann

**SeeAlso:**

**Source:**

/home/graber/work-nest/nest-git/nest-simulator/testsuite/unittests/test_lambertw.sli