Generate Matrix Normal Random Matrix

This function samples one matrix gaussian matrix.

Usage

sim_matgaussian(mat_mean, mat_scale_u, mat_scale_v, u_prec)

Arguments

mat_mean

Mean matrix

mat_scale_u

First scale matrix

mat_scale_v

Second scale matrix

u_prec

If TRUE, use mat_scale_u as its inverse.

Value

One n x k matrix following MN distribution.

Details

Consider n x k matrix \(Y_1, \ldots, Y_n \sim MN(M, U, V)\) where M is n x k, U is n x n, and V is k x k.

1. Lower triangular Cholesky decomposition: \(U = P P^T\) and \(V = L L^T\)

2. Standard normal generation: s x m matrix \(Z_i = [z_{ij} \sim N(0, 1)]\) in row-wise direction.

3. \(Y_i = M + P Z_i L^T\)

This function only generates one matrix, i.e. \(Y_1\).