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