114 lines
2.9 KiB
Matlab
114 lines
2.9 KiB
Matlab
function X = fastgensylv(A, B, C, D, tol,maxit,X0)
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%@info:
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%! @deftypefn {Function File} {[@var{X1}, @var{info}] =} fastgensylv (@var{A},@var{B},@var{C},@var{tol},@var{maxit},@var{X0})
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%! @anchor{fastgensylv}
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%! @sp 1
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%! Solves the Sylvester equation A * X + B * X * C + D = 0 for X.
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%! @sp 2
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%! @strong{Inputs}
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%! @sp 1
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%! @table @ @var
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%! @item A
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%! Square matrix of doubles, n*n.
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%! @item B
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%! Square matrix of doubles, n*n.
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%! @item C
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%! Square matrix of doubles, n*n.
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%! @item tol
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%! Scalar double, tolerance parameter.
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%! @item maxit
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%! Integer scalar, maximum number of iterations.
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%! @item X0
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%! Square matrix of doubles, n*n, initial condition.
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%! @end table
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%! @sp 1
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%! @strong{Outputs}
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%! @sp 1
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%! @table @ @var
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%! @item X
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%! Square matrix of doubles, n*n, solution of the matrix equation.
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%! @item info
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%! Scalar integer, if nonzero the algorithm failed in finding the solution of the matrix equation.
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%! @end table
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%! @sp 2
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%! @strong{This function is called by:}
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%! @sp 2
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%! @strong{This function calls:}
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%! @sp 2
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%! @end deftypefn
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%@eod:
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% Copyright © 2012-2017 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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if size(A,1)~=size(D,1) || size(A,1)~=size(B,1) || size(C,2)~=size(D,2)
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error('fastgensylv:: Dimension error!')
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end
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if nargin<7 || isempty(X0)
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X = zeros(size(A,2),size(C,1));
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elseif nargin==7 && ~isempty(X0)
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X = X0;
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end
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kk = 0;
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cc = 1+tol;
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iA = inv(A);
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Z = - (B * X * C + D);
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while kk<=maxit && cc>tol
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X = iA * Z;
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Z_old = Z;
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Z = - (B * X * C + D);
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cc = max(sum(abs(Z-Z_old)));
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kk = kk + 1;
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end
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if kk==maxit && cc>tol
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error(['fastgensylv:: Convergence not achieved in fixed point solution of Sylvester equation after ' int2str(maxit) ' iterations']);
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end
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% function X = fastgensylv(A, B, C, D)
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% Solve the Sylvester equation:
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% A * X + B * X * C + D = 0
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% INPUTS
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% A
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% B
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% C
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% D
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% block : block number (for storage purpose)
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% tol : convergence criteria
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% OUTPUTS
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% X solution
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%
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% ALGORITHM
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% fixed point method
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% MARLLINY MONSALVE (2008): "Block linear method for large scale
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% Sylvester equations", Computational & Applied Mathematics, Vol 27, n°1,
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% p47-59
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% ||A^-1||.||B||.||C|| < 1 is a suffisant condition:
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% - to get a unique solution for the Sylvester equation
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% - to get a convergent fixed-point algorithm
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%
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% SPECIAL REQUIREMENTS
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% none.
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