Command: testsuite::test_lambertw

Synopsis

(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.

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.

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.

File

testsuite/unittests/test_lambertw.sli

Author

July 2009
Diesmann