Name: testsuite::test_lambertw - check if lambertw function work

Synopsis:

(test_lambertw) run -&gt; 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., &amp; 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., 
&amp; 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:

LambertW
LambertW0
LambertWm1
testsuite::test_iaf_psp_peak
testsuite::test_iaf_psp_normalized

Source:

/var/www/debian/nest/nest-simulator-2.20.0/testsuite/unittests/test_lambertw.sli
