rand_matrix_normal

 function B = rand_matrix_normal(n, p, M, Omega_lower_chol, Sigma_lower_chol)
 Pseudo random matrices drawn from a matrix-normal distribution
 B ~ MN_n*p(M, Omega, Sigma) 
 Equivalent to vec(B) ~ N(vec(Mu), kron(Omega, Sigma))

 INPUTS
    n:                 row
    p:                 column
    M:                 (n*p) matrix, mean
    Omega_lower_chol:  (p*p), lower Cholesky decomposition of Omega,
                       (Omega_lower_chol = chol(Omega, 'lower'))
    Sigma_lower_chol:  (n*n), lower Cholesky decomposition of Sigma,
                       (Sigma_lower_chol = chol(Sigma, 'lower'))
    
 OUTPUTS
    B:                 (n*p) matrix drawn from a Matrix-normal distribution
        
 SPECIAL REQUIREMENTS
    Same notations than: http://en.wikipedia.org/wiki/Matrix_normal_distribution

0001 function B = rand_matrix_normal(n, p, M, Omega_lower_chol, Sigma_lower_chol)
0002 
0003 % function B = rand_matrix_normal(n, p, M, Omega_lower_chol, Sigma_lower_chol)
0004 % Pseudo random matrices drawn from a matrix-normal distribution
0005 % B ~ MN_n*p(M, Omega, Sigma)
0006 % Equivalent to vec(B) ~ N(vec(Mu), kron(Omega, Sigma))
0007 %
0008 % INPUTS
0009 %    n:                 row
0010 %    p:                 column
0011 %    M:                 (n*p) matrix, mean
0012 %    Omega_lower_chol:  (p*p), lower Cholesky decomposition of Omega,
0013 %                       (Omega_lower_chol = chol(Omega, 'lower'))
0014 %    Sigma_lower_chol:  (n*n), lower Cholesky decomposition of Sigma,
0015 %                       (Sigma_lower_chol = chol(Sigma, 'lower'))
0016 %
0017 % OUTPUTS
0018 %    B:                 (n*p) matrix drawn from a Matrix-normal distribution
0019 %
0020 % SPECIAL REQUIREMENTS
0021 %    Same notations than: http://en.wikipedia.org/wiki/Matrix_normal_distribution
0022 
0023 % Copyright (C) 2003-2009 Dynare Team
0024 %
0025 % This file is part of Dynare.
0026 %
0027 % Dynare is free software: you can redistribute it and/or modify
0028 % it under the terms of the GNU General Public License as published by
0029 % the Free Software Foundation, either version 3 of the License, or
0030 % (at your option) any later version.
0031 %
0032 % Dynare is distributed in the hope that it will be useful,
0033 % but WITHOUT ANY WARRANTY; without even the implied warranty of
0034 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0035 % GNU General Public License for more details.
0036 %
0037 % You should have received a copy of the GNU General Public License
0038 % along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
0039 
0040 B1 = randn(n * p, 1);
0041 B2 = kron(Omega_lower_chol, Sigma_lower_chol) * B1;
0042 B3 = reshape(B2, n, p);
0043 B = B3 + M;