dupl.prod: Matrix multiplication envolving the duplication matrix
In fastmatrix: Fast Computation of some Matrices Useful in Statistics

dupl.prod

R Documentation

Matrix multiplication envolving the duplication matrix

Description

Given the order of a duplication and a conformable matrix \bold{X}, performs one of the matrix-matrix operations:

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

where \bold{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

`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.

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!

fastmatrix documentation built on Oct. 12, 2023, 5:14 p.m.