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function [X,exitflag]=disclyap_fast(G,V,tol,check_flag,max_iter)
% [X,exitflag]=disclyap_fast(G,V,tol,check_flag)
% Inputs:
% - G [double] first input matrix
% - V [double] second input matrix
% - tol [scalar] tolerance criterion
% - check_flag [boolean] if true: check positive-definiteness
% - max_iter [scalar] maximum number of iterations
% Outputs:
% - X [double] solution matrix
% - exitflag [scalar] 0 if solution is found, 1 otherwise
%
% Solve the discrete Lyapunov Equation
% X=G*X*G'+V
% Using the Doubling Algorithm
%
% If check_flag is defined then the code will check if the resulting X
% is positive definite and generate an error message if it is not
%
% Joe Pearlman and Alejandro Justiniano
% 3/5/2005
% Copyright (C) 2010-2020 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 nargin <= 3 || isempty(check_flag)
check_flag = 0;
end
if nargin <=4
max_iter=2000;
end
exitflag=0;
P0=V;
A0=G;
matd=1;
iter=1;
while matd > tol && iter< max_iter
P1=P0+A0*P0*A0';
A1=A0*A0;
matd=max( max( abs( P1 - P0 ) ) );
P0=P1;
A0=A1;
iter=iter+1;
end
if iter==max_iter
X=NaN(size(P0));
exitflag=1;
return
end
X=(P0+P0')/2;
% Check that X is positive definite
if check_flag==1
[~,p]=chol(X);
if p ~= 0
exitflag=1;
end
end
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