csolve.m

function [x,rc] = csolve(FUN,x,gradfun,crit,itmax,varargin)
%function [x,rc] = csolve(FUN,x,gradfun,crit,itmax,varargin)
% FUN should be written so that any parametric arguments are packed in to xp,
% and so that if presented with a matrix x, it produces a return value of
% same dimension of x.  The number of rows in x and FUN(x) are always the
% same.  The number of columns is the number of different input arguments
% at which FUN is to be evaluated.
%
% gradfun:  string naming the function called to evaluate the gradient matrix.  If this
%           is null (i.e. just "[]"), a numerical gradient is used instead.
% crit:     if the sum of absolute values that FUN returns is less than this,
%           the equation is solved.
% itmax:    the solver stops when this number of iterations is reached, with rc=4
% varargin: in this position the user can place any number of additional arguments, all
%           of which are passed on to FUN and gradfun (when it is non-empty) as a list of 
%           arguments following x.
% rc:       0 means normal solution, 1 and 3 mean no solution despite extremely fine adjustments
%           in step length (very likely a numerical problem, or a discontinuity). 4 means itmax
%           termination.

% Original file downloaded from:
% http://sims.princeton.edu/yftp/optimize/mfiles/csolve.m

% Copyright (C) 1993-2007 Christopher Sims
% Copyright (C) 2007-2011 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/>.

%---------- delta --------------------
% differencing interval for numerical gradient
delta = 1e-6;
%-------------------------------------
%------------ alpha ------------------
% tolerance on rate of descent
alpha=1e-3;
%---------------------------------------
%------------ verbose ----------------
verbose=0;% if this is set to zero, all screen output is suppressed
          %-------------------------------------
          %------------ analyticg --------------
analyticg=1-isempty(gradfun); %if the grad argument is [], numerical derivatives are used.
                              %-------------------------------------
nv=length(x);
tvec=delta*eye(nv);
done=0;
if isempty(varargin)
    f0=feval(FUN,x);
else
    f0=feval(FUN,x,varargin{:});
end   
af0=sum(abs(f0));
af00=af0;
itct=0;
while ~done
    %   disp([af00-af0 crit*max(1,af0)])
    if itct>3 && af00-af0<crit*max(1,af0) && rem(itct,2)==1
        randomize=1;
    else
        if ~analyticg
% $$$          if isempty(varargin)
% $$$             grad = (feval(FUN,x*ones(1,nv)+tvec)-f0*ones(1,nv))/delta;
% $$$          else
% $$$             grad = (feval(FUN,x*ones(1,nv)+tvec,varargin{:})-f0*ones(1,nv))/delta;
% $$$          end
            grad = zeros(nv,nv);
            for i=1:nv
                grad(:,i) = (feval(FUN,x+tvec(:,i),varargin{:})-f0)/delta;
            end
        else % use analytic gradient
             %         grad=feval(gradfun,x,varargin{:});
            [f0,grad] = feval(gradfun,x,varargin{:});
        end
        if isreal(grad)
            if rcond(grad)<1e-12
                grad=grad+tvec;
            end
            dx0=-grad\f0;
            randomize=0;
        else
            if(verbose),disp('gradient imaginary'),end
            randomize=1;
        end
    end
    if randomize
        if(verbose),fprintf(1,'\n Random Search'),end
        dx0=norm(x)./randn(size(x));
    end
    lambda=1;
    lambdamin=1;
    fmin=f0;
    xmin=x;
    afmin=af0;
    dxSize=norm(dx0);
    factor=.6;
    shrink=1;
    subDone=0;
    while ~subDone
        dx=lambda*dx0;
        f=feval(FUN,x+dx,varargin{:});
        af=sum(abs(f));
        if af<afmin
            afmin=af;
            fmin=f;
            lambdamin=lambda;
            xmin=x+dx;
        end
        if ((lambda >0) && (af0-af < alpha*lambda*af0)) || ((lambda<0) && (af0-af < 0) )
            if ~shrink
                factor=factor^.6;
                shrink=1;
            end
            if abs(lambda*(1-factor))*dxSize > .1*delta;
                lambda = factor*lambda;
            elseif (lambda > 0) && (factor==.6) %i.e., we've only been shrinking
                lambda=-.3;
            else %
                subDone=1;
                if lambda > 0
                    if factor==.6
                        rc = 2;
                    else
                        rc = 1;
                    end
                else
                    rc=3;
                end
            end
        elseif (lambda >0) && (af-af0 > (1-alpha)*lambda*af0)
            if shrink
                factor=factor^.6;
                shrink=0;
            end
            lambda=lambda/factor;
        else % good value found
            subDone=1;
            rc=0;
        end
    end % while ~subDone
    itct=itct+1;
    if(verbose)
        fprintf(1,'\nitct %d, af %g, lambda %g, rc %g',itct,afmin,lambdamin,rc)
        fprintf(1,'\n   x  %10g %10g %10g %10g',xmin);
        fprintf(1,'\n   f  %10g %10g %10g %10g',fmin);
    end
    x=xmin;
    f0=fmin;
    af00=af0;
    af0=afmin;
    if itct >= itmax
        done=1;
        rc=4;
    elseif af0<crit;
        done=1;
        rc=0;
    end
end