dupl.prod

Matrix multiplication envolving the duplication matrix

Description

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

• \(\mathbf{Y} = \mathbf{DX}\) , if side = "left" and transposed = FALSE , or
• \(\mathbf{Y} = \mathbf{D}^T\mathbf{X}\) , if side = "left" and transposed = TRUE , or
• \(\mathbf{Y} = \mathbf{XD}\) , if side = "right" and transposed = FALSE , or
• \(\mathbf{Y} = \mathbf{XD}^T\) , if side = "right" and transposed = TRUE ,

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

Usage

dupl.prod(n = 1, x, transposed = FALSE, side = "left")

Arguments

Argument	Description
n	order of the duplication matrix.
x	numeric matrix (or vector).
transposed	logical. Duplication matrix should be transposed?
side	a string selecting if duplication 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 dupl.info to performs the matrix multiplication. The duplication matrix is never created.

Seealso

duplication

Examples

D4 <- duplication(n = 4, matrix = TRUE)
x <- matrix(1, nrow = 16, ncol = 2)
y <- crossprod(D4, x)

z <- dupl.prod(n = 4, x, transposed = TRUE) # D4 is not stored
all(z == y) # matrices y and z are equal!