1function [Dp,DpMPinv] = duplication(p) 2% [Dp,DpMPinv] = duplication(p) 3% ------------------------------------------------------------------------- 4% Duplication Matrix as defined by Magnus and Neudecker (2002), p.49 5% ========================================================================= 6% INPUTS 7% p: [integer] length of vector 8% ------------------------------------------------------------------------- 9% OUTPUTS 10% Dp: Duplication matrix 11% DpMPinv: Moore-Penroze inverse of Dp 12% ------------------------------------------------------------------------- 13% This function is called by 14% * get_identification_jacobians.m (previously getJJ.m) 15% ========================================================================= 16% Copyright (C) 1997 Tom Minka <minka@microsoft.com> 17% Copyright (C) 2019 Dynare Team 18% 19% This file is part of Dynare. 20% 21% Dynare is free software: you can redistribute it and/or modify 22% it under the terms of the GNU General Public License as published by 23% the Free Software Foundation, either version 3 of the License, or 24% (at your option) any later version. 25% 26% Dynare is distributed in the hope that it will be useful, 27% but WITHOUT ANY WARRANTY; without even the implied warranty of 28% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 29% GNU General Public License for more details. 30% 31% You should have received a copy of the GNU General Public License 32% along with Dynare. If not, see <http://www.gnu.org/licenses/>. 33% ========================================================================= 34% Original author: Thomas P Minka (tpminka@media.mit.edu), April 22, 2013 35 36a = tril(ones(p)); 37i = find(a); 38a(i) = 1:length(i); 39a = a + transpose(tril(a,-1)); 40 41j = a(:); 42 43m = p*(p+1)/2; 44Dp = spalloc(p*p,m,p^2); 45for r = 1:size(Dp,1) 46 Dp(r, j(r)) = 1; 47end 48 49if nargout > 1 50 DpMPinv = (transpose(Dp)*Dp)\transpose(Dp); 51end 52