Lambert's W Function
Computes Lambert's W-function.
LambertW(x)
x |
Vector of nonnegative numbers. |
Lambert's W-function is the inverse function of f(y) = y * exp(y). That is, W is the function such that
W(x) * exp(W(x)) = x
This command LambertW computes W(x) for each entry
in the argument x.
If the library gsl has been installed, then the function
lambert_W0 in that library is invoked. Otherwise,
values of the W-function are computed by root-finding, using the
function uniroot.
Computation using gsl is about 100 times faster.
If any entries of x are infinite or NA, the corresponding
results are NA.
Numeric vector.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
Corless, R, Gonnet, G, Hare, D, Jeffrey, D and Knuth, D (1996), On the Lambert W function. Computational Mathematics, 5, 325–359.
Roy, R and Olver, F (2010), Lambert W function. In Olver, F, Lozier, D and Boisvert, R (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press.
LambertW(exp(1))
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