73 lines
2.3 KiB
Matlab
73 lines
2.3 KiB
Matlab
function k = commutation(n, m, sparseflag)
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% k = commutation(n, m, sparseflag)
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% -------------------------------------------------------------------------
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% Returns Magnus and Neudecker's commutation matrix of dimensions n by m,
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% that solves k*vec(X)=vec(X')
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% =========================================================================
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% INPUTS
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% n: [integer] row number of original matrix
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% m: [integer] column number of original matrix
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% sparseflag: [integer] whether to use sparse matrices (=1) or not (else)
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% -------------------------------------------------------------------------
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% OUTPUTS
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% k: [n by m] commutation matrix
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% -------------------------------------------------------------------------
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% This function is called by
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% * get_first_order_solution_params_deriv.m (previously getH.m)
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% * get_identification_jacobians.m (previously getJJ.m)
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% -------------------------------------------------------------------------
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% This function calls
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% * vec (embedded)
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% =========================================================================
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% Copyright (C) 1997 Tom Minka <minka@microsoft.com>
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% Copyright (C) 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 <http://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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if nargin < 2
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m = n(2);
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n = n(1);
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end
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if nargin < 3
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sparseflag = 0;
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end
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if 0
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% first method
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i = 1:(n*m);
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a = reshape(i, n, m);
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j = vec(transpose(a));
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k = zeros(n*m,n*m);
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for r = i
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k(r, j(r)) = 1;
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end
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else
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% second method
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k = reshape(kron(vec(eye(n)), eye(m)), n*m, n*m);
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end
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if sparseflag ~= 0
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k = sparse(k);
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end
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function V = vec(A)
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V = A(:);
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end
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end
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