lambertW: Lambert W function

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Lambert W function

Description

Computes the Lambert W function, giving efficient solutions to the equation x*exp(x)==x lambertW(z, b = 0, maxiter = 10, eps = .Machine$double.eps, min.imag = 1e-09)

Usage

lambertW(z, b = 0, maxiter = 10, eps = .Machine$double.eps, min.imag = 1e-09)

Arguments

z	(complex) vector of values for which to compute the function
b	integer, defaults to 0. vector of branches: b=0 specifies the principal branch, 0 and -1 are the ones that can take non-complex values
maxiter	maximum numbers of iterations for convergence
eps	convergence tolerance
min.imag	maximum magnitude of imaginary part to chop when returning solutions

Details

Compute the Lambert W function of z. This function satisfies W(z)*exp(W(z)) = z, and can thus be used to express solutions of transcendental equations involving exponentials or logarithms. The Lambert W function is also available in Mathematica (as the ProductLog function), and in Maple and Wolfram.

Author(s)

Nici Schraudolph <schraudo at inf.ethz.ch> (original version (c) 1998), Ben Bolker (R translation) See <https://stat.ethz.ch/pipermail/r-help/2003-November/042793.html>

References

Corless, Gonnet, Hare, Jeffrey, and Knuth (1996), "On the Lambert W Function", Advances in Computational Mathematics 5(4):329-359

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