Command: testsuite::test_lambertw

(test_lambertw) run -> some known relations


[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.


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.