73 lines
2.1 KiB
Matlab
73 lines
2.1 KiB
Matlab
function X = gensylv_fp(A, B, C, D, block, tol)
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% function X = gensylv_fp(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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% Copyright © 1996-2017 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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%tol = 1e-12;
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evol = 100;
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A1 = inv(A);
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eval(['persistent hxo_' int2str(block) ';']);
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hxo = eval(['hxo_' int2str(block) ';']);
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if isempty(hxo)
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X = zeros(size(B, 2), size(C, 1));
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else
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X = hxo;
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end
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it_fp = 0;
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maxit_fp = 1000;
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Z = - (B * X * C + D);
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while it_fp < maxit_fp && evol > tol
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%X_old = X;
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%X = - A1 * ( B * X * C + D);
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%evol = max(max(abs(X - X_old)));
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X = A1 * Z;
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Z_old = Z;
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Z = - (B * X * C + D);
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evol = max(sum(abs(Z - Z_old))); %norm_1
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%evol = max(sum(abs(Z - Z_old)')); %norm_inf
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it_fp = it_fp + 1;
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end
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%fprintf('sylvester it_fp=%d evol=%g | ',it_fp,evol);
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if evol < tol
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eval(['hxo_' int2str(block) ' = X;']);
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else
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error(['convergence not achieved in fixed point solution of Sylvester equation after ' int2str(it_fp) ' iterations']);
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end |