VGAM (version 1.0-2)

lambertW: 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.

Value

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

Details

The Lambert $W$ function is the root of the equation $W(z) * exp(W(z)) = z$ for complex $z$. It is multi-valued if $z$ is real and $z < -1/e$. For real $-1/e <= z="" <="" 0$="" it="" has="" two="" possible="" real="" values,="" and="" currently="" only="" the="" upper="" branch="" is="" computed.<="" p="">

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.

Examples

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