1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
|
function Z=disc_riccati_fast(F,D,R,H,ch)
% function Z=disc_riccati_fast(F,D,R,H,ch)
%
% Solves discrete Riccati Equation:
% Z=FZF' - FZD'inv(DZD'+R)DZF' + H
% Using the Doubling Algorithm
%
% George Perendia: based on the doubling algorithm for Riccati
% and the disclyap_fast function provided by Prof. Joe Pearlman
% V.1 19/5/2006
% V.2 22/10/06
% =================================================================
% Copyright (C) 2006-2017 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 == 4 || isempty( ch ) == 1
flag_ch = 0;
else
flag_ch = 1;
end
% intialisation
tol = 1e-10; % iteration convergence threshold
P0=H;
X0=F;
if ~any(R) % i.e. ==0
warning('Dangerously evading inversion of zero matrix!');
Y0=zeros(size(R));
else
Y0=D'*inv(R)*D;
end
POYO=P0*Y0;
I=eye(size(POYO));
clear POYO;
% iterate Riccati equation solution
matd=1;
count=0;
while matd > tol && count < 100
INVPY=inv(I+P0*Y0);
P1=X0*INVPY*P0*X0'+ P0;
Y1=X0'*Y0*INVPY*X0+ Y0;
X1=X0*INVPY*X0;
matd=sum( sum(abs( P1 - P0 )));
% P0=(P1+P1')/2
P0=P1;
X0=X1;
Y0=Y1;
count=count+1;
% matd;
end
Z=(P0+P0')/2;
%Z=P0
% check if the convergence took place
if count==100
matd
error('Riccati not converged fast enough!');
% error.identifier='Riccati not converged!'
% error
end
%if count >5
% disp('Riccati count= ');
% count
%end
clear X0 X1 Y0 Y1 P1 I INVPY;
% Check that X is positive definite
if flag_ch==1
[C,p]=chol(Z);
if p ~= 0
error('Z is not positive definite')
end
end
|
