matrix.fun: Evaluate a matrix function
In fastmatrix: Fast Computation of some Matrices Useful in Statistics

matrix.fun

R Documentation

Evaluate a matrix function

Description

This function computes the matrix function \bold{F} =f(\bold{A}) where \bold{A} is upper triangular by applying a Parlett recurrence.

Usage

matrix.fun(a, FUN = "log")

Arguments

`a`	an upper triangular matrix.
`FUN`	the function to be applied, by default `"log"`.

Details

The used-defined function FUN is evaluated at the triangular matrix argument. This function can be used in conjunction with Schur decomposition to evaluate the function of a matrix.

References

Higham, N.J. (1986). Functions of Matrices: Theory and Computation. Society for Industrial and Applied Mathematics, Philadelphia.

Examples

a <- matrix(c(1,2,3,0,3,4,0,0,5), ncol = 3, byrow = TRUE)
fnc <- function(x) (1 + x) / x
f <- matrix.fun(a, FUN = fnc)
f

a <- matrix(c(-49,24,-64,31), ncol = 2, byrow = TRUE)
z <- schur(a)
m <- z$m
u <- z$vectors
m <- matrix.fun(m, FUN = exp)
u %*% m %*% t(u) # exp(a)

fastmatrix documentation built on Nov. 5, 2025, 6:21 p.m.