symm.prod

Matrix multiplication envolving the symmetrizer matrix

Description

Given the order of a symmetrizer and matrix x , performs one of the matrix-matrix operations:

• \(\mathbf{Y} = \mathbf{NX}\) , if side = "left" , or
• \(\mathbf{Y} = \mathbf{XN}\) , if side = "right" ,

where \(\mathbf{N}\) is the symmetrizer matrix of order \(n\) . The main aim of symm.prod is to do this matrix multiplication without forming the symmetrizer matrix.

Usage

symm.prod(n = 1, x = NULL, side = "left")

Arguments

Argument	Description
n	order of the symmetrizer matrix.
x	numeric matrix (or vector).
side	a string selecting if symmetrizer matrix is pre-multiplying x , that is side = "left" or post-multiplying x , by using side = "right" .

Details

Underlying C code only uses information provided by symm.info to performs the matrix multiplication. The symmetrizer matrix is never created.

Seealso

symmetrizer

Examples

N4 <- symmetrizer(n = 4, matrix = TRUE)
x <- matrix(1:32, ncol = 2)
y <- N4 %*% x

z <- symm.prod(n = 4, x) # N4 is not stored
all(z == y) # matrices y and z are equal!