92 lines
2.2 KiB
Matlab
92 lines
2.2 KiB
Matlab
function Z=disc_riccati_fast(F,D,R,H,ch)
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% function Z=disc_riccati_fast(F,D,R,H,ch)
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%
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% Solves discrete Riccati Equation:
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% Z=FZF' - FZD'inv(DZD'+R)DZF' + H
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% Using the Doubling Algorithm
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%
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% George Perendia: based on the doubling algorithm for Riccati
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% and the disclyap_fast function provided by Prof. Joe Pearlman
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% V.1 19/5/2006
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% V.2 22/10/06
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% =================================================================
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% Copyright (C) 1996-2010 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 <http://www.gnu.org/licenses/>.
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if nargin == 4 | isempty( ch ) == 1
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flag_ch = 0;
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else
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flag_ch = 1;
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end
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% intialisation
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tol = 1e-10; % iteration convergence threshold
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P0=H;
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X0=F;
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if ~any(R) % i.e. ==0
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warning('Dangerously evading inversion of zero matrix!');
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Y0=zeros(size(R));
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else
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Y0=D'*inv(R)*D;
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end
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POYO=P0*Y0;
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I=eye(size(POYO));
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clear POYO;
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% iterate Riccati equation solution
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matd=1;
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count=0;
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while matd > tol && count < 100
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INVPY=inv(I+P0*Y0);
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P1=X0*INVPY*P0*X0'+ P0;
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Y1=X0'*Y0*INVPY*X0+ Y0;
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X1=X0*INVPY*X0;
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matd=sum( sum(abs( P1 - P0 )));
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% P0=(P1+P1')/2
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P0=P1;
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X0=X1;
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Y0=Y1;
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count=count+1;
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% matd;
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end
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Z=(P0+P0')/2;
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%Z=P0
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% check if the convergence took place
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if count==100
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matd
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error('Riccati not converged fast enough!');
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% error.identifier='Riccati not converged!'
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% error
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end
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%if count >5
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% disp('Riccati count= ');
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% count
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%end
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clear X0 X1 Y0 Y1 P1 I INVPY;
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% Check that X is positive definite
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if flag_ch==1
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[C,p]=chol(Z);
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if p ~= 0
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error('Z is not positive definite')
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end
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end
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