W = lambertw(X) evaluates the Lambert W function at the elements of X, a numeric matrix or a symbolic matrix. The Lambert W function solves the equation

we^w = x

for w as a function of x.

W = lambertw(K,X) is the K-th branch of this multi-valued function.

Examples

Compute the Lambert W function:

lambertw([0 -exp(-1); pi 1])

The result is:

ans =
         0   -1.0000
    1.0737    0.5671

The statements

syms x y
lambertw([0 x;1 y])

return

ans =
[              0, lambertw(0, x)]
[ lambertw(0, 1), lambertw(0, y)]

References

[1] Corless, R.M, G.H. Gonnet, D.E.G. Hare, and D.J. Jeffrey, Lambert's W Function in Maple™, Technical Report, Dept. of Applied Math., Univ. of Western Ontario, London, Ontario, Canada.

[2] Corless, R.M, Gonnet, G.H. Gonnet, D.E.G. Hare, and D.J. Jeffrey, On Lambert's W Function, Technical Report, Dept. of Applied Math., Univ. of Western Ontario, London, Ontario, Canada.

Both papers are available by anonymous FTP from

cs-archive.uwaterloo.ca

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