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
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
|
function [x,check] = solve1(func,x,j1,j2,jacobian_flag,bad_cond_flag,varargin)
% function [x,check] = solve1(func,x,j1,j2,jacobian_flag,bad_cond_flag,varargin)
% Solves systems of non linear equations of several variables
%
% INPUTS
% func: name of the function to be solved
% x: guess values
% j1: equations index for which the model is solved
% j2: unknown variables index
% jacobian_flag=1: jacobian given by the 'func' function
% jacobian_flag=0: jacobian obtained numerically
% bad_cond_flag=1: when Jacobian is badly conditionned, use an
% alternative formula to Newton step
% varargin: list of arguments following bad_cond_flag
%
% OUTPUTS
% x: results
% check=1: the model can not be solved
%
% SPECIAL REQUIREMENTS
% none
% Copyright (C) 2001-2012 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/>.
global M_ options_ fjac
nn = length(j1);
fjac = zeros(nn,nn) ;
g = zeros(nn,1) ;
tolf = options_.solve_tolf ;
tolx = options_.solve_tolx;
tolmin = tolx ;
stpmx = 100 ;
maxit = options_.solve_maxit ;
check = 0 ;
fvec = feval(func,x,varargin{:});
fvec = fvec(j1);
i = find(~isfinite(fvec));
if ~isempty(i)
disp(['STEADY: numerical initial values incompatible with the following' ...
' equations'])
disp(j1(i)')
end
f = 0.5*fvec'*fvec ;
if max(abs(fvec)) < tolf
return ;
end
stpmax = stpmx*max([sqrt(x'*x);nn]) ;
first_time = 1;
for its = 1:maxit
if jacobian_flag
[fvec,fjac] = feval(func,x,varargin{:});
fvec = fvec(j1);
fjac = fjac(j1,j2);
else
dh = max(abs(x(j2)),options_.gstep(1)*ones(nn,1))*eps^(1/3);
for j = 1:nn
xdh = x ;
xdh(j2(j)) = xdh(j2(j))+dh(j) ;
t = feval(func,xdh,varargin{:});
fjac(:,j) = (t(j1) - fvec)./dh(j) ;
g(j) = fvec'*fjac(:,j) ;
end
end
g = (fvec'*fjac)';
if options_.debug
disp(['cond(fjac) ' num2str(cond(fjac))])
end
M_.unit_root = 0;
if M_.unit_root
if first_time
first_time = 0;
[q,r,e]=qr(fjac);
n = sum(abs(diag(r)) < 1e-12);
fvec = q'*fvec;
p = e*[-r(1:end-n,1:end-n)\fvec(1:end-n);zeros(n,1)];
disp(' ')
disp('STEADY with unit roots:')
disp(' ')
if n > 0
disp([' The following variable(s) kept their value given in INITVAL' ...
' or ENDVAL'])
disp(char(e(:,end-n+1:end)'*M_.endo_names))
else
disp(' STEADY can''t find any unit root!')
end
else
[q,r]=qr(fjac*e);
fvec = q'*fvec;
p = e*[-r(1:end-n,1:end-n)\fvec(1:end-n);zeros(n,1)];
end
elseif bad_cond_flag && cond(fjac) > 1/sqrt(eps)
fjac2=fjac'*fjac;
p=-(fjac2+1e6*sqrt(nn*eps)*max(sum(abs(fjac2)))*eye(nn))\(fjac'*fvec);
else
p = -fjac\fvec ;
end
xold = x ;
fold = f ;
[x,f,fvec,check]=lnsrch1(xold,fold,g,p,stpmax,func,j1,j2,varargin{:});
if options_.debug
disp([its f])
disp([xold x])
end
if check > 0
den = max([f;0.5*nn]) ;
if max(abs(g).*max([abs(x(j2)') ones(1,nn)])')/den < tolmin
return
else
disp (' ')
disp (['SOLVE: Iteration ' num2str(its)])
disp (['Spurious convergence.'])
disp (x)
return
end
if max(abs(x(j2)-xold(j2))./max([abs(x(j2)') ones(1,nn)])') < tolx
disp (' ')
disp (['SOLVE: Iteration ' num2str(its)])
disp (['Convergence on dX.'])
disp (x)
return
end
elseif max(abs(fvec)) < tolf
return
end
end
check = 1;
disp(' ')
disp('SOLVE: maxit has been reached')
% 01/14/01 MJ lnsearch is now a separate function
% 01/16/01 MJ added varargin to function evaluation
% 04/13/01 MJ added test f < tolf !!
% 05/11/01 MJ changed tests for 'check' so as to remove 'continue' which is
% an instruction which appears only in version 6
|
