trunk: added new solve_algo=4 in dynare_solve.m; this mode is the same than solve_algo=2, except that the solver behaves differently when the Jacobian is badly scaled or nearly singular (see header of solve2.m)
git-svn-id: https://www.dynare.org/svn/dynare/dynare_v4@2089 ac1d8469-bf42-47a9-8791-bf33cf982152time-shift
parent
082e7e3292
commit
ae68da82ff
|
@ -64,7 +64,7 @@ function [x,info] = dynare_solve(func,x,jacobian_flag,varargin)
|
|||
if options_.solve_algo == 1
|
||||
nn = size(x,1);
|
||||
[x,info]=solve1(func,x,1:nn,1:nn,jacobian_flag,varargin{:});
|
||||
elseif options_.solve_algo == 2
|
||||
elseif options_.solve_algo == 2 || options_.solve_algo == 4
|
||||
nn = size(x,1) ;
|
||||
tolf = options_.solve_tolf ;
|
||||
|
||||
|
@ -103,21 +103,29 @@ function [x,info] = dynare_solve(func,x,jacobian_flag,varargin)
|
|||
[j1,j2,r,s] = dmperm(fjac);
|
||||
|
||||
if options_.debug
|
||||
disp(['DYNARE_SOLVE (solve_algo=2): number of blocks = ' num2str(length(r))]);
|
||||
disp(['DYNARE_SOLVE (solve_algo=2|4): number of blocks = ' num2str(length(r))]);
|
||||
end
|
||||
|
||||
for i=length(r)-1:-1:1
|
||||
if options_.debug
|
||||
disp(['DYNARE_SOLVE (solve_algo=2): solving block ' num2str(i) ', of size ' num2str(r(i+1)-r(i)) ]);
|
||||
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,varargin{:});
|
||||
if info
|
||||
return
|
||||
end
|
||||
end
|
||||
fvec = feval(func,x,varargin{:});
|
||||
if max(abs(fvec)) > tolf
|
||||
[x,info]=solve1(func,x,1:nn,1:nn,jacobian_flag,varargin{:});
|
||||
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
|
||||
end
|
||||
elseif options_.solve_algo == 3
|
||||
if jacobian_flag
|
||||
|
|
|
@ -0,0 +1,171 @@
|
|||
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')
|
Loading…
Reference in New Issue