151 lines
4.2 KiB
Matlab
151 lines
4.2 KiB
Matlab
function [x,check] = solve1(func,x,j1,j2,jacobian_flag,gstep,tolf,tolx,maxit,fake,debug,varargin)
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% Solves systems of non linear equations of several variables
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%
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% INPUTS
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% func: name of the function to be solved
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% x: guess values
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% j1: equations index for which the model is solved
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% j2: unknown variables index
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% jacobian_flag=true: jacobian given by the 'func' function
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% jacobian_flag=false: jacobian obtained numerically
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% gstep increment multiplier in numercial derivative
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% computation
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% tolf tolerance for residuals
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% tolx tolerance for solution variation
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% maxit maximum number of iterations
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% fake unused argument (compatibity with trust_region).
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% debug debug flag
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% varargin: list of extra arguments to the function
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%
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% OUTPUTS
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% x: results
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% check=1: the model can not be solved
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%
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% SPECIAL REQUIREMENTS
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% none
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% Copyright © 2001-2021 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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nn = length(j1);
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g = zeros(nn,1) ;
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tolmin = tolx ;
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stpmx = 100 ;
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check = 0 ;
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fvec = feval(func,x,varargin{:});
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fvec = fvec(j1);
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i = find(~isfinite(fvec));
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if ~isempty(i)
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disp(['SOLVE1: during the resolution of the non-linear system, the evaluation of the following ' ...
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'equation(s) resulted in a non-finite number:'])
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disp(j1(i)')
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check = 1;
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return
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end
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f = 0.5*(fvec'*fvec) ;
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if max(abs(fvec)) < tolf*tolf
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return ;
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end
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stpmax = stpmx*max([sqrt(x'*x);nn]) ;
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first_time = 1;
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if ~jacobian_flag
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fjac = zeros(nn,nn) ;
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end
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for its = 1:maxit
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if jacobian_flag
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[fvec,fjac] = feval(func,x,varargin{:});
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fvec = fvec(j1);
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fjac = fjac(j1,j2);
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else
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dh = max(abs(x(j2)),gstep(1)*ones(nn,1))*eps^(1/3);
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for j = 1:nn
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xdh = x ;
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xdh(j2(j)) = xdh(j2(j))+dh(j) ;
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t = feval(func,xdh,varargin{:});
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fjac(:,j) = (t(j1) - fvec)./dh(j) ;
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g(j) = fvec'*fjac(:,j) ;
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end
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end
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g = (fvec'*fjac)';
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if debug
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disp(['cond(fjac) ' num2str(condest(fjac))])
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end
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if issparse(fjac)
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rcond_fjac = 1/condest(fjac);
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else
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rcond_fjac = rcond(fjac);
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end
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if rcond_fjac < sqrt(eps)
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fjac2=fjac'*fjac;
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p=-(fjac2+sqrt(nn*eps)*max(sum(abs(fjac2)))*eye(nn))\(fjac'*fvec);
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else
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p = -fjac\fvec ;
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end
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xold = x ;
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fold = f ;
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[x, f, fvec, check] = lnsrch1(xold, fold, g, p, stpmax, func, j1, j2, tolx, varargin{:});
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if debug
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disp([its f])
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disp([xold x])
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end
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if check > 0
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den = max([f;0.5*nn]) ;
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if max(abs(g).*max([abs(x(j2)') ones(1,nn)])')/den < tolmin
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if max(abs(x(j2)-xold(j2))./max([abs(x(j2)') ones(1,nn)])') < tolx
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disp (' ')
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disp (['SOLVE: Iteration ' num2str(its)])
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disp (['Convergence on dX.'])
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disp (x)
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return
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end
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else
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disp (' ')
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disp (['SOLVE: Iteration ' num2str(its)])
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disp (['Spurious convergence.'])
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disp (x)
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return
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end
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elseif max(abs(fvec)) < tolf
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return
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end
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end
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check = 1;
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skipline()
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disp('SOLVE: maxit has been reached')
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% 01/14/01 MJ lnsearch is now a separate function
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% 01/16/01 MJ added varargin to function evaluation
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% 04/13/01 MJ added test f < tolf !!
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% 05/11/01 MJ changed tests for 'check' so as to remove 'continue' which is
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% an instruction which appears only in version 6
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