testsuite::test_lambertw - check if lambertw function works
(test_lambertw) run -> some known relations  

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.

[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
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