LambertW
Lambert's W Function
Computes Lambert's W-function.
- Keywords
- math
Usage
LambertW(x)Arguments
- x
Vector of nonnegative numbers.
Details
Lambert's W-function is the inverse function of \(f(y) = y e^y\). That is, \(W\) is the function such that $$ W(x) e^{W(x)} = x $$
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.
Value
Numeric vector.
References
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.
Examples
# NOT RUN {
LambertW(exp(1))
# }