R: Matrix multiplication envolving the commutation matrix

comm.prod {fastmatrix}

R Documentation

Matrix multiplication envolving the commutation matrix

Description

Given the row and column dimension of a commutation and matrix x, performs one of the matrix-matrix operations:

\bold{Y} = \bold{KX}, if side = "left" and transposed = FALSE, or
\bold{Y} = \bold{K}^T\bold{X}, if side = "left" and transposed = TRUE, or
\bold{Y} = \bold{XK}, if side = "right" and transposed = FALSE, or
\bold{Y} = \bold{XK}^T, if side = "right" and transposed = TRUE,

where \bold{K} is the commutation matrix of order mn. The main aim of comm.prod is to do this matrix multiplication without forming the commutation matrix.

Usage

comm.prod(m = 1, n = m, x = NULL, transposed = FALSE, side = "left")

Arguments

`m`	a positive integer row dimension.
`n`	a positive integer column dimension.
`x`	numeric matrix (or vector).
`transposed`	logical. Commutation matrix should be transposed?
`side`	a string selecting if commutation matrix is pre-multiplying `x`, that is `side = "left"` or post-multiplying `x`, by using `side = "right"`.

Details

Underlying Fortran code only uses information provided by comm.info to performs the matrix multiplication. The commutation matrix is never created.

Examples

K42 <- commutation(m = 4, n = 2, matrix = TRUE)
x <- matrix(1:24, ncol = 3)
y <- K42 %*% x

z <- comm.prod(m = 4, n = 2, x) # K42 is not stored
all(z == y) # matrices y and z are equal!