# Command: testsuite::test_lambertw

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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:

- LambertW
- LambertW0
- LambertWm1
- testsuite::test_iaf_psp_peak
- testsuite::test_iaf_psp_normalized

Source:

    /opt/conda/conda-bld/nest_1512418852064/work/nest-2.12.0/testsuite/unittests/test_lambertw.sli

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