93 lines
2.3 KiB
Matlab
93 lines
2.3 KiB
Matlab
function x=sylvester3(a,b,c,d)
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% solves a*x+b*x*c=d where d is [n x m x p]
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% Copyright © 2005-2023 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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n = size(a,1);
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m = size(c,1);
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p = size(d,3);
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x=zeros(n,m,p);
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if n == 1
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for j=1:p
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x(:,:,j)=d(:,:,j)./(a*ones(1,m)+b*c);
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end
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return
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end
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if m == 1
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for j=1:p
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x(:,:,j) = (a+c*b)\d(:,:,j);
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end
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return
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end
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[u,t]=schur(c);
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if isoctave && octave_ver_less_than('9')
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[aa,bb,qq,zz]=qz(full(a),full(b));
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for j=1:p
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d(:,:,j)=qq*d(:,:,j)*u;
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end
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else
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[aa,bb,qq,zz]=qz(full(a),full(b),'real');
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for j=1:p
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d(:,:,j)=qq*d(:,:,j)*u;
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end
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end
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i = 1;
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c = zeros(n,1,p);
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c1 = zeros(n,1,p);
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while i < m
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if t(i+1,i) == 0
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if i == 1
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c = zeros(n,1,p);
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else
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for j=1:p
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c(:,:,j) = bb*(x(:,1:i-1,j)*t(1:i-1,i));
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end
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end
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x(:,i,:)=(aa+bb*t(i,i))\squeeze(d(:,i,:)-c);
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i = i+1;
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else
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if i == n
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c = zeros(n,1,p);
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c1 = zeros(n,1,p);
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else
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for j=1:p
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c(:,:,j) = bb*(x(:,1:i-1,j)*t(1:i-1,i));
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c1(:,:,j) = bb*(x(:,1:i-1,j)*t(1:i-1,i+1));
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end
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end
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bigmat = ([aa+bb*t(i,i) bb*t(i+1,i); bb*t(i,i+1) aa+bb*t(i+1,i+1)]);
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z = bigmat\squeeze([d(:,i,:)-c;d(:,i+1,:)-c1]);
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x(:,i,:) = z(1:n,:);
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x(:,i+1,:) = z(n+1:end,:);
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i = i + 2;
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end
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end
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if i == m
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for j=1:p
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c(:,:,j) = bb*(x(:,1:m-1,j)*t(1:m-1,m));
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end
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aabbt = (aa+bb*t(m,m));
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x(:,m,:)=aabbt\squeeze(d(:,m,:)-c);
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end
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for j=1:p
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x(:,:,j)=zz*x(:,:,j)*u';
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end
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% 01/25/03 MJ corrected bug for i==m (sign of c in x determination)
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% 01/31/03 MJ added 'real' to qz call
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