function [X,exitflag]=disclyap_fast(G,V,tol,ch)
% function X=disclyap_fast(G,V,ch)
% Inputs:
%   - G     [double]    first input matrix
%   - V     [double]    second input matrix
%   - tol   [scalar]    tolerance criterion 
%   - ch    empty of non-empty             if non-empty: check positive-definiteness
% 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 ch 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) 2010-2015 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( ch ) == 1 
    flag_ch = 0; 
else 
    flag_ch = 1; 
end 
s=size(G,1); 
exitflag=0;

%tol = 1e-16; 

P0=V; 
A0=G; 

matd=1; 
iter=1;
while matd > tol && iter< 2000 
    P1=P0+A0*P0*A0'; 
    A1=A0*A0;  
    matd=max( max( abs( P1 - P0 ) ) ); 
    P0=P1; 
    A0=A1; 
    iter=iter+1;
end 
if iter==5000
    X=NaN(P0);
    exitflag=1;
    return
end
clear A0 A1 P1; 

X=(P0+P0')/2; 

% Check that X is positive definite 
if flag_ch==1 
    [C,p]=chol(X); 
    if p ~= 0 
        exitflag=1;
        error('X is not positive definite')
    end 
end 