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function [Dp,DpMPinv] = duplication(p)
% [Dp,DpMPinv] = duplication(p)
% -------------------------------------------------------------------------
% Duplication Matrix as defined by Magnus and Neudecker (2002), p.49
% =========================================================================
% INPUTS
% p: [integer] length of vector
% -------------------------------------------------------------------------
% OUTPUTS
% Dp: Duplication matrix
% DpMPinv: Moore-Penroze inverse of Dp
% -------------------------------------------------------------------------
% This function is called by
% * get_identification_jacobians.m (previously getJJ.m)
% =========================================================================
% Copyright (C) 1997 Tom Minka <minka@microsoft.com>
% Copyright (C) 2019 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
% =========================================================================
% Original author: Thomas P Minka (tpminka@media.mit.edu), April 22, 2013
a = tril(ones(p));
i = find(a);
a(i) = 1:length(i);
a = a + transpose(tril(a,-1));
j = a(:);
m = p*(p+1)/2;
Dp = spalloc(p*p,m,p^2);
for r = 1:size(Dp,1)
Dp(r, j(r)) = 1;
end
if nargout > 1
DpMPinv = (transpose(Dp)*Dp)\transpose(Dp);
end
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