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
|
function [x,check] = solve1(func,x,j1,j2,jacobian_flag,gstep,tolf,tolx,maxit,debug,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=true: jacobian given by the 'func' function
% jacobian_flag=false: jacobian obtained numerically
% gstep increment multiplier in numercial derivative
% computation
% tolf tolerance for residuals
% tolx tolerance for solution variation
% maxit maximum number of iterations
% debug debug flag
% varargin: list of extra arguments to the function
%
% OUTPUTS
% x: results
% check=1: the model can not be solved
%
% SPECIAL REQUIREMENTS
% none
% Copyright (C) 2001-2017 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/>.
nn = length(j1);
g = zeros(nn,1) ;
tolmin = tolx ;
stpmx = 100 ;
check = 0 ;
fvec = feval(func,x,varargin{:});
fvec = fvec(j1);
i = find(~isfinite(fvec));
if ~isempty(i)
disp(['SOLVE1: during the resolution of the non-linear system, the evaluation of the following ' ...
'equation(s) resulted in a non-finite number:'])
disp(j1(i)')
check = 1;
return
end
f = 0.5*(fvec'*fvec) ;
if max(abs(fvec)) < tolf*tolf
return ;
end
stpmax = stpmx*max([sqrt(x'*x);nn]) ;
first_time = 1;
if ~jacobian_flag
fjac = zeros(nn,nn) ;
end
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)),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 debug
disp(['cond(fjac) ' num2str(condest(fjac))])
end
if issparse(fjac)
rcond_fjac = 1/condest(fjac);
else
rcond_fjac = rcond(fjac);
end
if rcond_fjac < sqrt(eps)
fjac2=fjac'*fjac;
p=-(fjac2+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, tolx, varargin{:});
if 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
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
else
disp (' ')
disp (['SOLVE: Iteration ' num2str(its)])
disp (['Spurious convergence.'])
disp (x)
return
end
elseif max(abs(fvec)) < tolf
return
end
end
check = 1;
skipline()
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
|
