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function [x, errorflag, errorcode] = solve1(func, x, j1, j2, jacobian_flag, gstep, tolf, tolx, maxit, fake, 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
% fake unused argument (compatibity with trust_region).
% debug debug flag
% varargin: list of extra arguments to the function
%
% OUTPUTS
% x: results
% errorflag=1: the model can not be solved
%
% SPECIAL REQUIREMENTS
% none
% Copyright © 2001-2022 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 <https://www.gnu.org/licenses/>.
nn = length(j1);
g = zeros(nn,1) ;
tolmin = tolx ;
stpmx = 100 ;
errorflag = false ;
fvec = feval(func,x,varargin{:});
fvec = fvec(j1);
idInf = isinf(fvec);
idNan = isnan(fvec);
idCpx = ~isreal(fvec);
if any(idInf)
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(idInf)')
errorcode = 0;
errorflag = true;
return
end
if any(idNan)
disp('SOLVE1: during the resolution of the non-linear system, the evaluation of the following equation(s) resulted in a nan:')
disp(j1(idNan)')
errorcode = 0;
errorflag = true;
return
end
if any(idNan)
disp('SOLVE1: during the resolution of the non-linear system, the evaluation of the following equation(s) resulted in a complex number:')
disp(j1(idCpx)')
errorcode = 0;
errorflag = true;
return
end
f = 0.5*(fvec'*fvec);
if max(abs(fvec))<tolf*tolf
% Initial guess is a solution
errorcode = -1;
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);
g = (fvec'*fjac)';
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
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;
temp=max(sum(abs(fjac2)));
if temp>0
p=-(fjac2+sqrt(nn*eps)*temp*eye(nn))\(fjac'*fvec);
else
errorflag = true;
errorcode = 5;
if nargout<3
skipline()
dprintf('SOLVE: Iteration %s', num2str(its))
disp('Zero Jacobian.')
skipline()
end
return
end
else
p = -fjac\fvec ;
end
xold = x ;
fold = f ;
[x, f, fvec, lnsearchflag] = lnsrch1(xold, fold, g, p, stpmax, func, j1, j2, tolx, varargin{:});
if debug
disp([its f])
disp([xold x])
end
if lnsearchflag
errorflag = true;
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
errorcode = 3;
if nargout<3
skipline()
dprintf('SOLVE: Iteration %s', num2str(its))
disp('Convergence on dX.')
skipline()
end
return
end
else
errorcode = 4;
if nargout<3
skipline()
dprintf('SOLVE: Iteration %s', num2str(its))
disp('Spurious convergence.')
disp(x)
end
return
end
elseif max(abs(fvec)) < tolf
errorcode = 1;
return
end
end
errorflag = true;
errorcode = 2;
if nargout<3
skipline()
disp('SOLVE: maxit has been reached')
end
% 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
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