R: Lambert's W Function

LambertW {spatstat.core} | R Documentation

## Lambert's W Function

### Description

Computes Lambert's W-function.

### Usage

    LambertW(x)

### Arguments

`x` | Vector of nonnegative numbers.

### Details

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`.

### Value

Numeric vector.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### 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))

[Package spatstat.core version 2.0-0 Index]