matrixweave: Combine covariance matrix and pseudo covariance matrix into a "double covariance matrix"

Description

Interleaves the elements of a \((p x p)\) matrix with those of a different \((p x p)\) matrix to form a \((2p x 2p)\) matrix. This function was originally made to combine the covariance and pseudo covariance matrices of a complex random vector into a single "double covariance matrix", as described in (van den Bos 1995). However, it will accept and operate on matrices of any storage mode.

Usage

matrixweave(cov, pcov, FUNC = Conj)

Value

A square matrix with dimension twice that of the input matrices. Each element of which is an element from one of the inputs, and its nearest non-diagonal neighbors are from the other input. Half of the elements from pcov present in the output matrix are replaced by FUNC operated on them. Thus if two 2x2 matrices, A and B are given to matrixweave(), the elements of the result are:

matrixweave(A,B)[i,j] = if(i+j is even) A[ceiling(i/2), ceiling(j/2)]

if(i+j is odd and i > j) B[ceiling(i/2), ceiling(j/2)]

if(i+j is odd and i < j) FUNC(B[ceiling(i/2),ceiling(j/2)])

Arguments

cov: A square matrix, such as one describing the covariance between two complex random vectors.
pcov: A square matrix with the same size as cov. Perhaps a pseudo covariance matrix.
FUNC: A function to operate on the elements of pcov. The results of which will be a quarter of the elements of the returned matrix. Default is Conj.

References

A. van den Bos, The Multivariate Complex Normal Distribution-a Generalization, IEEE Trans. Inform. Theory 41, 537 (1995).

Examples

Run this code

set.seed(4242)
mata <- matrix(rnorm(9), nrow = 3)
matb <- matrix(rnorm(9), nrow = 3)
matrixweave(mata, matb)