Commit f4555573 authored by Marco Ratto's avatar Marco Ratto
Browse files

compact all sylvester routines, with generic dimension of d argument

parent 76093094
function x=sylvester3(a,b,c,d)
% solves a*x+b*x*c=d
function x=sylvester3mr(a,b,c,d)
% solves a*x+b*x*c=d where d is [n x m x p]
% Copyright (C) 2005-2009 Dynare Team
%
......@@ -20,53 +20,72 @@ function x=sylvester3(a,b,c,d)
n = size(a,1);
m = size(c,1);
p = size(d,3);
if n == 1
x=d./(a*ones(1,m)+b*c);
for j=1:p,
x(:,:,j)=d(:,:,j)./(a*ones(1,m)+b*c);
end
return
end
if m == 1
x = (a+c*b)\d;
for j=1:p,
x(:,:,j) = (a+c*b)\d(:,:,j);
end
return;
end
x=zeros(n,m);
x=zeros(n,m,p);
[u,t]=schur(c);
if exist('OCTAVE_VERSION')
[aa,bb,qq,zz]=qz(full(a),full(b));
d=qq'*d*u;
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
d=qq*d*u;
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);
c = zeros(n,1,p);
else
c = bb*(x(:,1:i-1)*t(1:i-1,i));
for j=1:p,
c(:,:,j) = bb*(x(:,1:i-1,j)*t(1:i-1,i));
end
end
x(:,i)=(aa+bb*t(i,i))\(d(:,i)-c);
x(:,i,:)=(aa+bb*t(i,i))\squeeze(d(:,i,:)-c);
i = i+1;
else
if i == n
c = zeros(n,1);
c1 = zeros(n,1);
c = zeros(n,1,p);
c1 = zeros(n,1,p);
else
c = bb*(x(:,1:i-1)*t(1:i-1,i));
c1 = bb*(x(:,1:i-1)*t(1:i-1,i+1));
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
z = [aa+bb*t(i,i) bb*t(i+1,i); bb*t(i,i+1) aa+bb*t(i+1,i+1)]...
\[d(:,i)-c;d(:,i+1)-c1];
x(:,i) = z(1:n);
x(:,i+1) = z(n+1:end);
bigmat = ([aa+bb*t(i,i) bb*t(i+1,i); bb*t(i,i+1) aa+bb*t(i+1,i+1)]);
z = bigmat\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
c = bb*(x(:,1:m-1)*t(1:m-1,m));
x(:,m)=(aa+bb*t(m,m))\(d(:,m)-c);
for j=1:p,
c(:,:,j) = bb*(x(:,1:m-1,j)*t(1:m-1,m));
end
aabbt = (aa+bb*t(m,m));
x(:,m,:)=aabbt\squeeze(d(:,m,:)-c);
end
for j=1:p,
x(:,:,j)=zz*x(:,:,j)*u';
end
x=zz*x*u';
% 01/25/03 MJ corrected bug for i==m (sign of c in x determination)
% 01/31/03 MJ added 'real' to qz call
function x=sylvester3a(x0,a,b,c,d)
function [x0, flag]=sylvester3a(x0,a,b,c,dd)
% solves iteratively ax+bxc=d
% Copyright (C) 2005-2009 Dynare Team
% Copyright (C) 2005-2012 Dynare Team
%
% This file is part of Dynare.
%
......@@ -20,15 +20,19 @@ function x=sylvester3a(x0,a,b,c,d)
a_1 = inv(a);
b = a_1*b;
d = a_1*d;
e = 1;
iter = 1;
while e > 1e-8 & iter < 500
x = d-b*x0*c;
e = max(max(abs(x-x0)));
x0 = x;
iter = iter + 1;
end
if iter == 500
warning('sylvester3a : Only accuracy of %10.8f is achieved after 500 iterations')
flag=0;
for j=1:size(dd,3),
d = a_1*dd(:,:,j);
e = 1;
iter = 1;
while e > 1e-8 && iter < 500
x = d-b*x0(:,:,j)*c;
e = max(max(abs(x-x0(:,:,j))));
x0(:,:,j) = x;
iter = iter + 1;
end
if iter == 500
sprintf('sylvester3amr : Only accuracy of %10.8f is achieved after 500 iterations',e);
flag=1;
end
end
\ No newline at end of file
function [x0, flag]=sylvester3amr(x0,a,b,c,dd)
% solves iteratively ax+bxc=d
% Copyright (C) 2012 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/>.
a_1 = inv(a);
b = a_1*b;
flag=0;
for j=1:size(dd,3),
d = a_1*dd(:,:,j);
e = 1;
iter = 1;
while e > 1e-8 && iter < 500
x = d-b*x0(:,:,j)*c;
e = max(max(abs(x-x0(:,:,j))));
x0(:,:,j) = x;
iter = iter + 1;
end
if iter == 500
sprintf('sylvester3amr : Only accuracy of %10.8f is achieved after 500 iterations',e);
flag=1;
end
end
\ No newline at end of file
function x=sylvester3mr(a,b,c,d)
% solves a*x+b*x*c=d where d is [n x m x p]
% Copyright (C) 2005-2009 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);
x(:,i,:)=(aa+bb*t(i,i))\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]);
bigmat = ([aa+bb*t(i,i) bb*t(i+1,i); bb*t(i,i+1) aa+bb*t(i+1,i+1)]);
z = bigmat\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);
aabbt = (aa+bb*t(m,m));
x(:,m,:)=aabbt\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
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