R: The Lambert W Function

lambertW {VGAM} | R Documentation

## The Lambert W Function

### Description

Computes the Lambert W function for real values.

### Usage

    lambertW(x, tolerance = 1e-10, maxit = 50)

### Arguments

`x` | A vector of reals.
`tolerance` | Accuracy desired.
`maxit` | Maximum number of iterations of third-order Halley's method.

### Details

The Lambert W function is the root of the equation W(z) * exp(W(z)) = z for complex z. If z is real and -1/e < z < 0 then it has two possible real values, and currently only the upper branch (often called W_0) is computed so that a value that is >= -1 is returned.

### Value

This function returns the principal branch of the W function for real z. It returns W(z) >= -1, and `NA` for z < -1/e.

### Note

If convergence does not occur then increase the value of `maxit` and/or `tolerance`.

Yet to do: add an argument `lbranch = TRUE` to return the lower branch (often called W_{-1}) for real -1/e <= z < 0; this would give W(z) <= -1.

### Author(s)

T. W. Yee

### References

Corless, R. M. and Gonnet, G. H. and Hare, D. E. G. and Jeffrey, D. J. and Knuth, D. E. (1996). On the Lambert W function. Advances in Computational Mathematics, 5(4), 329–359.

### See Also

`log`, `exp`, `bell`. There is also a package called LambertW.

### Examples

     ## Not run:
    curve(lambertW, -exp(-1), 3, xlim = c(-1, 3), ylim = c(-2, 1),
          las = 1, col = "orange", n = 1001)
    abline(v = -exp(-1), h = -1, lwd = 2, lty = "dotted", col = "gray")
    abline(h = 0, v = 0, lty = "dashed", col = "blue")
    ## End(Not run)

[Package VGAM version 1.1-3 Index]