spatstat (version 1.37-0)

LambertW: Lambert's W Function

Description

Computes Lambert's W-function.

Usage

LambertW(x)

Arguments

x

Vector of nonnegative numbers.

Value

• Numeric vector.

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.

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

LambertW(exp(1))