Solves multiple generalized Sylvester equations where only d is changing.

Useful to speed up analytic derivatives in identification analysis. 

git-svn-id: https://www.dynare.org/svn/dynare/trunk@2962 ac1d8469-bf42-47a9-8791-bf33cf982152

matlab/gensylv/sylvester3mr.m

@@ -0,0 +1,95 @@
+function x=sylvester3mr(a,b,c,d)
+% solves a*x+b*x*c=d where d is [n x m x p]
+
+% Copyright (C) 2005-2008 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/>.
+
+  n = size(a,1);
+  m = size(c,1);
+  if length(size(d))==2,
+    x=sylvester3(a,b,c,d);
+    return
+  end
+  p = size(d,3);
+  if n == 1
+    for j=1:p,
+      x(:,:,j)=d(:,:,j)./(a*ones(1,m)+b*c);
+    end
+    return
+  end
+  if m == 1
+    invacb = inv(a+c*b);
+    x = invacb*d;
+    return;
+  end
+  x=zeros(n,m,p);
+  [u,t]=schur(c);
+  if exist('OCTAVE_VERSION')
+    [aa,bb,qq,zz]=qz(full(a),full(b));
+    for j=1:p,
+      d(:,:,j)=qq'*d(:,:,j)*u;
+    end
+  else
+    [aa,bb,qq,zz]=qz(full(a),full(b),'real'); % available in Matlab version 6.0
+    for j=1:p,
+      d(:,:,j)=qq*d(:,:,j)*u;
+    end
+  end
+  i = 1;
+	c = zeros(n,1,p);
+  while i < m
+    if t(i+1,i) == 0
+      if i == 1
+	c = zeros(n,1,p);
+      else
+        for j=1:p,
+	c(:,:,j) = bb*(x(:,1:i-1,j)*t(1:i-1,i));
+        end
+      end
+      aabbtinv = inv(aa+bb*t(i,i));
+      x(:,i,:)=aabbtinv*squeeze(d(:,i,:)-c);
+      i = i+1;
+    else
+      if i == n
+	c = zeros(n,1,p);
+	c1 = zeros(n,1,p);
+      else
+        for j=1:p,
+	c(:,:,j) = bb*(x(:,1:i-1,j)*t(1:i-1,i));
+	c1(:,:,j) = bb*(x(:,1:i-1,j)*t(1:i-1,i+1));
+        end
+      end
+      bigmatinv = inv([aa+bb*t(i,i) bb*t(i+1,i); bb*t(i,i+1) aa+bb*t(i+1,i+1)]);
+      z = bigmatinv * squeeze([d(:,i,:)-c;d(:,i+1,:)-c1]);
+      x(:,i,:) = z(1:n,:);
+      x(:,i+1,:) = z(n+1:end,:);
+      i = i + 2;
+    end
+  end
+  if i == m
+        for j=1:p,
+    c(:,:,j) = bb*(x(:,1:m-1,j)*t(1:m-1,m));
+        end
+      aabbtinv = inv(aa+bb*t(m,m));
+    x(:,m,:)=aabbtinv*squeeze(d(:,m,:)-c);
+  end
+  for j=1:p,
+    x(:,:,j)=zz*x(:,:,j)*u';
+  end
+  
+% 01/25/03 MJ corrected bug for i==m (sign of c in x determination)
+% 01/31/03 MJ added 'real' to qz call