VGAM (version 1.1-9)

log1mexp: Logarithms with an Unit Offset and Exponential Term

Description

Computes log(1 + exp(x)) and log(1 - exp(-x)) accurately.

Usage

log1mexp(x)
log1pexp(x)

Value

log1mexp(x) gives the value of \(\log(1-\exp(-x))\).

log1pexp(x) gives the value of \(\log(1+\exp(x))\).

Arguments

x

A vector of reals (numeric). Complex numbers not allowed since expm1 and log1p do not handle these.

Author

This is a direct translation of the function in Martin Maechler's (2012) paper by Xiangjie Xue and T. W. Yee.

Details

Computes log(1 + exp(x)) and log(1 - exp(-x)) accurately. An adjustment is made when \(x\) is away from 0 in value.

References

Maechler, Martin (2012). Accurately Computing log(1-exp(-|a|)). Assessed from the Rmpfr package.

See Also

log1p, expm1, exp, log

Examples

x <-  c(10, 50, 100, 200, 400, 500, 800, 1000, 1e4, 1e5, 1e20, Inf, NA)
log1pexp(x)
log(1 + exp(x))  # Naive; suffers from overflow
log1mexp(x)
log(1 - exp(-x))
y <- -x
log1pexp(y)
log(1 + exp(y))  # Naive; suffers from inaccuracy