dynare/matlab/dynare_solve.m

function [x,info] = dynare_solve(func,x,jacobian_flag,varargin)
% function [x,info] = dynare_solve(func,x,jacobian_flag,varargin)
% proposes different solvers
%
% INPUTS
%    func:             name of the function to be solved
%    x:                guess values
%    jacobian_flag=1:  jacobian given by the 'func' function
%    jacobian_flag=0:  jacobian obtained numerically
%    varargin:         list of arguments following jacobian_flag
%    
% OUTPUTS
%    x:                solution
%    info=1:           the model can not be solved
%
% SPECIAL REQUIREMENTS
%    none

% Copyright (C) 2001-2012 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 options_

tolf = options_.solve_tolf ;
info = 0;
nn = size(x,1);

% checking initial values
if jacobian_flag
    [fvec,fjac] = feval(func,x,varargin{:});
    if any(any(isinf(fjac) | isnan(fjac)))
        [infrow,infcol]=find(isinf(fjac) | isnan(fjac));
        M=evalin('base','M_'); %get variable names from workspace
        fprintf('\nSTEADY:  The Jacobian contains Inf or NaN. The problem arises from: \n\n')
        for ii=1:length(infrow)
            if infcol(ii)<=M.orig_endo_nbr
                fprintf('STEADY:  Derivative of Equation %d with respect to Variable %s  (initial value of %s: %g) \n',infrow(ii),deblank(M.endo_names(infcol(ii),:)),deblank(M.endo_names(infcol(ii),:)),x(infcol(ii)))
            else %auxiliary vars
                orig_var_index=M.aux_vars(1,infcol(ii)-M.orig_endo_nbr).orig_index;
                fprintf('STEADY:  Derivative of Equation %d with respect to Variable %s  (initial value of %s: %g) \n',infrow(ii),deblank(M.endo_names(orig_var_index,:)),deblank(M.endo_names(orig_var_index,:)),x(infcol(ii)))            
            end
        end
        fprintf('\nSTEADY:  The problem most often occurs, because a variable with\n')
        fprintf('STEADY:  exponent smaller than 1 has been initialized to 0. Taking the derivative\n')
        fprintf('STEADY:  and evaluating it at the steady state then results in a division by 0.\n')
        error('An element of the Jacobian is not finite or NaN') 
    end

else
    fvec = feval(func,x,varargin{:});
    fjac = zeros(nn,nn) ;
end

i = find(~isfinite(fvec));

if ~isempty(i)
    disp(['STEADY:  numerical initial values or parameters incompatible with the following' ...
          ' equations'])
    disp(i')
    disp('Please check for example')
    disp('   i) if all parameters occurring in these equations are defined')
    disp('  ii) that no division by an endogenous variable initialized to 0 occurs') 
    info = 1;
    x = NaN;
    return;
end

if max(abs(fvec)) < tolf
    return ;
end

if options_.solve_algo == 0
    if ~isoctave
        if ~user_has_matlab_license('optimization_toolbox')
            error('You can''t use solve_algo=0 since you don''t have MATLAB''s Optimization Toolbox')
        end
    end
    options=optimset('fsolve');
    options.MaxFunEvals = 50000;
    options.MaxIter = 2000;
    options.TolFun=1e-8;
    options.Display = 'iter';
    if jacobian_flag
        options.Jacobian = 'on';
    else
        options.Jacobian = 'off';
    end
    if ~isoctave
        [x,fval,exitval,output] = fsolve(func,x,options,varargin{:});
    else
        % Under Octave, use a wrapper, since fsolve() does not have a 4th arg
        func2 = str2func(func);
        func = @(x) func2(x, varargin{:});
        % The Octave version of fsolve does not converge when it starts from the solution
        fvec = feval(func,x);
        if max(abs(fvec)) >= tolf
            [x,fval,exitval,output] = fsolve(func,x,options);
        else
            exitval = 3;
        end;
    end
    
    if exitval > 0
        info = 0;
    else
        info = 1;
    end
elseif options_.solve_algo == 1
    [x,info]=solve1(func,x,1:nn,1:nn,jacobian_flag,options_.gstep, ...
                    tolf,options_.solve_tolx, ...
                    options_.steady.maxit,options_.debug,varargin{:});
elseif options_.solve_algo == 2 || options_.solve_algo == 4

    if options_.solve_algo == 2
        solver = @solve1;
    else
        solver = @trust_region;
    end

    if ~jacobian_flag
        fjac = zeros(nn,nn) ;
        dh = max(abs(x),options_.gstep(1)*ones(nn,1))*eps^(1/3);
        for j = 1:nn
            xdh = x ;
            xdh(j) = xdh(j)+dh(j) ;
            fjac(:,j) = (feval(func,xdh,varargin{:}) - fvec)./dh(j) ;
        end
    end

    [j1,j2,r,s] = dmperm(fjac);
    
    if options_.debug
        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|4): solving block ' num2str(i) ', of size ' num2str(r(i+1)-r(i)) ]);
        end
        [x,info]=solver(func,x,j1(r(i):r(i+1)-1),j2(r(i):r(i+1)-1),jacobian_flag, ...
                        options_.gstep, ...
                        tolf,options_.solve_tolx, ...
                        options_.steady.maxit,options_.debug,varargin{:});
        if info
            return
        end
    end
    fvec = feval(func,x,varargin{:});
    if max(abs(fvec)) > tolf
        [x,info]=solver(func,x,1:nn,1:nn,jacobian_flag, ...
                        options_.gstep, tolf,options_.solve_tolx, ...
                        options_.steady.maxit,options_.debug,varargin{:});
    end
elseif options_.solve_algo == 3
    if jacobian_flag
        [x,info] = csolve(func,x,func,1e-6,500,varargin{:});
    else
        [x,info] = csolve(func,x,[],1e-6,500,varargin{:});
    end
else
    error('DYNARE_SOLVE: option solve_algo must be one of [0,1,2,3,4]')
end