tileHMM (version 1.0-7)

logSum: Calculate log(x + y) from log(x) and log(y)

Description

Given $log(x)$ and $log(y)$ this function calculates $log(x + y)$ using the identity $$\log(x+y) = \log(x) + \log\left(1 + e^{\log(y) - \log(x)}\right)$$

Usage

logSum(x, y = NULL, base = 0)

Arguments

x

Numeric vector or matrix.

y

Numeric vector or matrix of same dimensions as x or missing.

base

Base of the logarithm to be used. If base is 0 the natural logarithm is used.

Value

If only x is given a scalar is returned, representing the sum of all elements of x. Otherwise a vector or matrix of the same dimensions as x and y.

Details

If y is missing the function is applied recuresively to all elements of x, i.e., all elements of x are added up. If both x and y are given they are added element wise.

Examples

    x <- 1:4
    y <- 4:1
    ## calculate sum of x an y directly
    xy.s <- x + y
    ## and after log transformation
    xy.ls <- logSum(log(x),log(y))
    ## errors are small:
    err <- xy.ls - log(xy.s)