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Change to option solve_algo=4 of steady: 

Even when the Jacobian is very badly conditioned, continue to use a Newton step


git-svn-id: https://www.dynare.org/svn/dynare/trunk@2862 ac1d8469-bf42-47a9-8791-bf33cf982152
time-shift
sebastien 2009-08-21 12:05:34 +00:00
parent 64361938bb
commit fec9486fb9
3 changed files with 13 additions and 188 deletions
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17
matlab/dynare_solve.m
View File

@ -61,7 +61,7 @@ function [x,info] = dynare_solve(func,x,jacobian_flag,varargin)
end
elseif options_.solve_algo == 1
nn = size(x,1);
[x,info]=solve1(func,x,1:nn,1:nn,jacobian_flag,varargin{:});
[x,info]=solve1(func,x,1:nn,1:nn,jacobian_flag,1,varargin{:});
elseif options_.solve_algo == 2 || options_.solve_algo == 4
nn = size(x,1) ;
tolf = options_.solve_tolf ;
@ -101,27 +101,22 @@ function [x,info] = dynare_solve(func,x,jacobian_flag,varargin)
if options_.debug
disp(['DYNARE_SOLVE (solve_algo=2|4): number of blocks = ' num2str(length(r))]);
end
% Activate bad conditioning flag for solve_algo = 2, but not for solve_algo = 4
bad_cond_flag = (options_.solve_algo == 2);
for i=length(r)-1:-1:1
if options_.debug
disp(['DYNARE_SOLVE (solve_algo=2|4): solving block ' num2str(i) ', of size ' num2str(r(i+1)-r(i)) ]);
end
if options_.solve_algo == 2
[x,info]=solve1(func,x,j1(r(i):r(i+1)-1),j2(r(i):r(i+1)-1),jacobian_flag,varargin{:});
else % solve_algo=4
[x,info]=solve2(func,x,j1(r(i):r(i+1)-1),j2(r(i):r(i+1)-1),jacobian_flag,varargin{:});
end
[x,info]=solve1(func,x,j1(r(i):r(i+1)-1),j2(r(i):r(i+1)-1),jacobian_flag, bad_cond_flag, varargin{:});
if info
return
end
end
fvec = feval(func,x,varargin{:});
if max(abs(fvec)) > tolf
if options_.solve_algo == 2
[x,info]=solve1(func,x,1:nn,1:nn,jacobian_flag,varargin{:});
else % solve_algo=4
[x,info]=solve2(func,x,1:nn,1:nn,jacobian_flag,varargin{:});
end
[x,info]=solve1(func,x,1:nn,1:nn,jacobian_flag, bad_cond_flag, varargin{:});
end
elseif options_.solve_algo == 3
if jacobian_flag

13
matlab/solve1.m
View File

@ -1,5 +1,5 @@
function [x,check] = solve1(func,x,j1,j2,jacobian_flag,varargin)
% function [x,check] = solve1(func,x,j1,j2,jacobian_flag,varargin)
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
@ -9,7 +9,9 @@ function [x,check] = solve1(func,x,j1,j2,jacobian_flag,varargin)
% j2: unknown variables index
% jacobian_flag=1: jacobian given by the 'func' function
% jacobian_flag=0: jacobian obtained numerically
% varargin: list of arguments following jacobian_flag
% 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
@ -18,7 +20,7 @@ function [x,check] = solve1(func,x,j1,j2,jacobian_flag,varargin)
% SPECIAL REQUIREMENTS
% none
% Copyright (C) 2001-2008 Dynare Team
% Copyright (C) 2001-2009 Dynare Team
%
% This file is part of Dynare.
%
@ -113,8 +115,7 @@ function [x,check] = solve1(func,x,j1,j2,jacobian_flag,varargin)
fvec = q'*fvec;
p = e*[-r(1:end-n,1:end-n)\fvec(1:end-n);zeros(n,1)];
end
% elseif cond(fjac) > 10*sqrt(eps)
elseif cond(fjac) > 1/sqrt(eps)
elseif bad_cond_flag && cond(fjac) > 1/sqrt(eps)
fjac2=fjac'*fjac;
p=-(fjac2+sqrt(nn*eps)*max(sum(abs(fjac2)))*eye(nn))\(fjac'*fvec);
else

171
matlab/solve2.m
View File

@ -1,171 +0,0 @@
function [x,check] = solve2(func,x,j1,j2,jacobian_flag,varargin)
% function [x,check] = solve1(func,x,j1,j2,jacobian_flag,varargin)
% Solves systems of non linear equations of several variables
%
% This solver is used for solve_algo = ...
%
% This is a modified version of solve1:
% In solve1, before proceeding to the Newton step, we first check
% that the condition number is reasonable, and we use an alternate
% step formula if it is not the case.
% Here, we first do the Newton step, then we check if the left
% matrix division returned a warning (in case of badly scale or
% nearly singular jacobian) in which case we use the alternate
% step formula.
%
% 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
% varargin: list of arguments following jacobian_flag
%
% OUTPUTS
% x: results
% check=1: the model can not be solved
%
% SPECIAL REQUIREMENTS
% none
% Copyright (C) 2001-2008 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*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
else
lastwarn('');
p = -fjac\fvec;
if ~isempty(lastwarn)
fjac2=fjac'*fjac;
p=-(fjac2+sqrt(nn*eps)*max(sum(abs(fjac2)))*eye(nn))\(fjac'*fvec);
end
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')