dupl.cross {fastmatrix}

Matrix crossproduct envolving the duplication matrix

Description

Given the order of two duplication matrices and a conformable matrix \bold{X}, this function performs the operation: \bold{Y} = \bold{D}_n^T\bold{X}\bold{D}_k, where \bold{D}_n and \bold{D}_k are duplication matrices of order n and k, respectively.

Usage

dupl.cross(n = 1, k = n, x = NULL)

Arguments

n

order of the duplication matrix used pre-multiplying x.

k

order of the duplication matrix used post-multiplying x. By default k = n is used.

x

numeric matrix, this argument is required.

Details

This function calls dupl.prod to performs the matrix multiplications required but without forming any duplication matrices.

See Also

dupl.prod

Examples

D2 <- duplication(n = 2, matrix = TRUE)
D3 <- duplication(n = 3, matrix = TRUE)
x <- matrix(1, nrow = 9, ncol = 4)
y <- t(D3) %*% x %*% D2

z <- dupl.cross(n = 3, k = 2, x) # D2 and D3 are not stored
all(z == y) # matrices y and z are equal!

x <- matrix(1, nrow = 9, ncol = 9)
z <- dupl.cross(n = 3, x = x) # same matrix is used to pre- and post-multiplying x
z # print result