DPQ (version 0.5-8)

log1mexp: Compute \(\mathrm{log}\)(1 - \(\mathrm{exp}\)(-a)) and \(\log(1 + \exp(x))\) Numerically Optimally

Description

Compute f(a) = log(1 - exp(-a)) quickly and numerically accurately.

log1mexp() is simple pure R code;
log1mexpC() is an interface to R C API (Mathlib / Rmath.h) function.

log1pexpC() is an interface to R's Mathlib double function log1pexp() which computes \(\log(1 + \exp(x))\), accurately, notably for large \(x\), say, \(x > 720\).

Usage

log1mexp (x)
log1mexpC(x)
log1pexpC(x)

Arguments

x

numeric vector of positive values.

Author

Martin Maechler

References

Martin Mächler (2012). Accurately Computing \(\log(1-\exp(-|a|))\); https://CRAN.R-project.org/package=Rmpfr/vignettes/log1mexp-note.pdf.

See Also

The log1mexp() function in CRAN package copula, and the corresponding vignette (in the ‘References’).

Examples

l1m.xy <- curve(log1mexp(x), -10, 10, n=1001)
stopifnot(with(l1m.xy, all.equal(y, log1mexpC(x))))

x <- seq(0, 710, length=1+710*2^4); stopifnot(diff(x) == 1/2^4)
l1pm <- cbind(log1p(exp(x)),
              log1pexpC(x))
matplot(x, l1pm, type="l", log="xy") # both look the same
iF <- is.finite(l1pm[,1])
stopifnot(all.equal(l1pm[iF,2], l1pm[iF,1], tol=1e-15))