130 lines
3.6 KiB
Matlab
130 lines
3.6 KiB
Matlab
function X = fastgensylv(A, B, C, D, tol,maxit,X0)
|
||
|
||
%@info:
|
||
%! @deftypefn {Function File} {[@var{X1}, @var{info}] =} fastgensylv (@var{A},@var{B},@var{C},@var{tol},@var{maxit},@var{X0})
|
||
%! @anchor{fastgensylv}
|
||
%! @sp 1
|
||
%! Solves the Sylvester equation A * X + B * X * C + D = 0 for X.
|
||
%! @sp 2
|
||
%! @strong{Inputs}
|
||
%! @sp 1
|
||
%! @table @ @var
|
||
%! @item A
|
||
%! Square matrix of doubles, n*n.
|
||
%! @item B
|
||
%! Square matrix of doubles, n*n.
|
||
%! @item C
|
||
%! Square matrix of doubles, n*n.
|
||
%! @item tol
|
||
%! Scalar double, tolerance parameter.
|
||
%! @item maxit
|
||
%! Integer scalar, maximum number of iterations.
|
||
%! @item X0
|
||
%! Square matrix of doubles, n*n, initial condition.
|
||
%! @end table
|
||
%! @sp 1
|
||
%! @strong{Outputs}
|
||
%! @sp 1
|
||
%! @table @ @var
|
||
%! @item X
|
||
%! Square matrix of doubles, n*n, solution of the matrix equation.
|
||
%! @item info
|
||
%! Scalar integer, if nonzero the algorithm failed in finding the solution of the matrix equation.
|
||
%! @end table
|
||
%! @sp 2
|
||
%! @strong{This function is called by:}
|
||
%! @sp 2
|
||
%! @strong{This function calls:}
|
||
%! @sp 2
|
||
%! @end deftypefn
|
||
%@eod:
|
||
|
||
% 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/>.
|
||
|
||
if size(A,1)~=size(D,1) || size(A,1)~=size(B,1) || size(C,2)~=size(D,2)
|
||
error('fastgensylv:: Dimension error!')
|
||
end
|
||
|
||
if nargin<7 || isempty(X0)
|
||
X = zeros(size(A,2),size(C,1));
|
||
elseif nargin==7 && ~isempty(X0)
|
||
X = X0;
|
||
end
|
||
|
||
kk = 0;
|
||
cc = 1+tol;
|
||
|
||
iA = inv(A);
|
||
Z = - (B * X * C + D);
|
||
|
||
while kk<=maxit && cc>tol
|
||
X = iA * Z;
|
||
Z_old = Z;
|
||
Z = - (B * X * C + D);
|
||
cc = max(sum(abs(Z-Z_old)));
|
||
kk = kk + 1;
|
||
end
|
||
|
||
if kk==maxit && cc>tol
|
||
error(['fastgensylv:: Convergence not achieved in fixed point solution of Sylvester equation after ' int2str(maxit) ' iterations']);
|
||
end
|
||
|
||
|
||
|
||
|
||
% function X = fastgensylv(A, B, C, D)
|
||
% Solve the Sylvester equation:
|
||
% A * X + B * X * C + D = 0
|
||
% INPUTS
|
||
% A
|
||
% B
|
||
% C
|
||
% D
|
||
% block : block number (for storage purpose)
|
||
% tol : convergence criteria
|
||
% OUTPUTS
|
||
% X solution
|
||
%
|
||
% ALGORITHM
|
||
% fixed point method
|
||
% MARLLINY MONSALVE (2008): "Block linear method for large scale
|
||
% Sylvester equations", Computational & Applied Mathematics, Vol 27, n<>1,
|
||
% p47-59
|
||
% ||A^-1||.||B||.||C|| < 1 is a suffisant condition:
|
||
% - to get a unique solution for the Sylvester equation
|
||
% - to get a convergent fixed-point algorithm
|
||
%
|
||
% SPECIAL REQUIREMENTS
|
||
% none.
|
||
% Copyright (C) 1996-2012 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/>.
|