MKmisc (version 1.9)

glog: Compute Generalized Logarithm

Description

The functions compute the generalized logarithm, which is more or less identical to the area hyperbolic sine, and their inverse; see details.

Usage

glog(x, base = exp(1))
glog10(x)
glog2(x)
inv.glog(x, base = exp(1))
inv.glog10(x)
inv.glog2(x)

Value

A vector of the same length as x containing the transformed values.

Arguments

x

a numeric or complex vector.

base

a positive or a positive or complex number: the base with respect to which logarithms are computed. Defaults to e=exp(1).

Author

Matthias Kohl

Details

The function computes $$\log(x + \sqrt{x^2 + 1}) - \log(2)$$ where the first part corresponds to the area hyperbolic sine. Subtracting log(2) makes the function asymptotically identical to the logarithm.

Examples

curve(log, from = -3, to = 5)
curve(glog, from = -3, to = 5, add = TRUE, col = "orange")
legend("topleft", fill = c("black", "orange"), legend = c("log", "glog"))

curve(log10(x), from = -3, to = 5)
curve(glog10(x), from = -3, to = 5, add = TRUE, col = "orange")
legend("topleft", fill = c("black", "orange"), legend = c("log10", "glog10"))

inv.glog(glog(10))
inv.glog(glog(10, base = 3), base = 3)
inv.glog10(glog10(10))
inv.glog2(glog2(10))