2012-07-01 15:15:52 +02:00
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function [X, info] = cycle_reduction(A0, A1, A2, cvg_tol, ch)
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% function [X, info] = cycle_reduction(A0,A1,A2,A3, cvg_tolch)
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2012-07-09 16:00:04 +02:00
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%
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% Solves Polynomial Equation:
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2012-07-01 15:15:52 +02:00
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% A0 + A1 * X + A2 * X<> = 0
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% Using Cyclic Reduction algorithm
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% - D.A. Bini, G. Latouche, B. Meini (2002), "Solving matrix polynomial equations arising in
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% queueing problems", Linear Algebra and its Applications 340 (2002) 225<32>244
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% - D.A. Bini, B. Meini, On the solution of a nonlinear matrix equation arising in queueing problems,
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% SIAM J. Matrix Anal. Appl. 17 (1996) 906<30>926.
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% =================================================================
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2012-07-09 12:12:37 +02:00
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% Copyright (C) 2012 Dynare Team
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2012-07-01 15:15:52 +02:00
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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 <http://www.gnu.org/licenses/>.
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2012-07-09 16:00:04 +02:00
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max_it = 300;
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it = 0;
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info = 0;
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crit = 1+cvg_tol;
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A_0 = A1;
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A0_0 = A0;
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A1_0 = A1;
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A2_0 = A2;
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n = length(A0);
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id = 1:n;
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while crit > cvg_tol && it < max_it;
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2012-07-11 16:20:44 +02:00
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tmp = [A2_0; A0_0]/A1_0;
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2012-07-09 16:00:04 +02:00
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TMP = tmp*A0_0;
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2012-07-11 16:20:44 +02:00
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A2_1 = - tmp(id,:)* A2_0;
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2012-07-09 16:00:04 +02:00
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A_1 = A_0 - TMP(id,:);
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A1_1 = A1_0 - tmp(n+id,:) * A2_0 - TMP(id,:);
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crit = sum(sum(abs(A0_0)));
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A_0 = A_1;
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A0_0 = -TMP(n+id,:);
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A1_0 = A1_1;
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A2_0 = A2_1;
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it = it + 1;
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end
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2012-07-01 15:15:52 +02:00
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2012-07-09 16:00:04 +02:00
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if it==max_it
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disp(['convergence not achieved after ' int2str(it) ' iterations']);
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info = 1;
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end
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2012-07-01 15:15:52 +02:00
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2012-07-09 16:00:04 +02:00
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X = -A_0\A0;
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2012-07-01 15:15:52 +02:00
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2012-07-09 16:00:04 +02:00
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if (nargin == 5 && ~isempty( ch ) == 1 )
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%check the solution
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res = A0 + A1 * X + A2 * X * X;
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if (sum(sum(abs(res))) > cvg_tol)
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disp(['the norm residual of the residu ' num2str(res) ' compare to the tolerance criterion ' num2str(cvg_tol)]);
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end
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end
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