dynare/matlab/dynare_solve.m

function [x, errorflag, fvec, fjac] = dynare_solve(f, x, options, varargin)

% Solves a nonlinear system of equations, f(x) = 0 with n unknowns
% and n equations.
%
% INPUTS
% - f            [char, fhandle]    function to be solved
% - x            [double]           n×1 vector, initial guess.
% - options      [struct]           Dynare options, aka options_.
% - varargin                        list of additional arguments to be passed to func.
%
% OUTPUTS
% - x            [double]           n×1 vector, solution.
% - errorflag    [logical]          scalar, true iff the model can not be solved.
% - fvec         [double]           n×1 vector, function value at x (f(x), used for debugging when errorflag is true).
% - fjac         [double]           n×n matrix, Jacobian value at x (J(x), used for debugging when errorflag is true).
%
% REMARKS
% Copyright © 2001-2020 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/>.

jacobian_flag = options.jacobian_flag; % true iff Jacobian is returned by f routine (as a second output argument).

% Set tolerance parameter depending the the caller function.
stack = dbstack;
if isoctave
    [~, name, ext]=fileparts(stack(2).file);
    caller_file_name=[name,ext];
else
    caller_file_name=stack(2).file;
end
if strcmp(caller_file_name,'solve_stacked_problem.m')
    tolf = options.dynatol.f;
    tolx = options.dynatol.x;
else
    tolf = options.solve_tolf;
    tolx = options.solve_tolx;
end

if strcmp(caller_file_name,'dyn_ramsey_static.m')
    maxit = options.ramsey.maxit;
else
    maxit = options.steady.maxit;
end

errorflag = false;
nn = size(x,1);

% Get status of the initial guess (default values?)
if any(x)
    % The current initial guess is not the default for all the variables.
    idx = find(x);      % Indices of the variables with default initial guess values.
    in0 = length(idx);
else
    % The current initial guess is the default for all the variables.
    idx = transpose(1:nn);
    in0 = nn;
end

% Get first element of varargin if solve_algo ∈ {12,14} and rename varargin.
if ismember(options.solve_algo, [12, 14])
    isloggedlhs = varargin{1};
    isauxdiffloggedrhs = varargin{2};
    endo_names = varargin{3};
    lhs = varargin{4};
    arguments = varargin(5:end);
else
    arguments = varargin;
end

% checking initial values
if jacobian_flag
    [fvec, fjac] = feval(f, x, arguments{:});
    wrong_initial_guess_flag = false;
    if ~all(isfinite(fvec)) || any(isinf(fjac(:))) || any(isnan((fjac(:)))) ...
            || any(~isreal(fvec)) || any(~isreal(fjac(:)))
        if max(abs(fvec)) < tolf %return if initial value solves problem
            info = 0;
            return;
        end
        disp('Randomize initial guess...')
        % Let's try random numbers for the variables initialized with the default value.
        wrong_initial_guess_flag = true;
        % First try with positive numbers.
        tentative_number = 0;
        while wrong_initial_guess_flag && tentative_number<=in0*10
            tentative_number = tentative_number+1;
            x(idx) = rand(in0, 1)*10;
            [fvec, fjac] = feval(f, x, arguments{:});
            wrong_initial_guess_flag = ~all(isfinite(fvec)) || any(isinf(fjac(:))) || any(isnan((fjac(:))));
        end
        % If all previous attempts failed, try with real numbers.
        tentative_number = 0;
        while wrong_initial_guess_flag && tentative_number<=in0*10
            tentative_number = tentative_number+1;
            x(idx) = randn(in0, 1)*10;
            [fvec, fjac] = feval(f, x, arguments{:});
            wrong_initial_guess_flag = ~all(isfinite(fvec)) || any(isinf(fjac(:))) || any(isnan((fjac(:))));
        end
        % Last tentative, ff all previous attempts failed, try with negative numbers.
        tentative_number = 0;
        while wrong_initial_guess_flag && tentative_number<=in0*10
            tentative_number = tentative_number+1;
            x(idx) = -rand(in0, 1)*10;
            [fvec, fjac] = feval(f, x, arguments{:});
            wrong_initial_guess_flag = ~all(isfinite(fvec)) || any(isinf(fjac(:))) || any(isnan((fjac(:))));
        end
    end
else
    fvec = feval(f, x, arguments{:});
    fjac = zeros(nn, nn);
    wrong_initial_guess_flag = false;
    if ~all(isfinite(fvec))
        % Let's try random numbers for the variables initialized with the default value.
        wrong_initial_guess_flag = true;
        % First try with positive numbers.
        tentative_number = 0;
        while wrong_initial_guess_flag && tentative_number<=in0*10
            tentative_number = tentative_number+1;
            x(idx) = rand(in0, 1)*10;
            fvec = feval(f, x, arguments{:});
            wrong_initial_guess_flag = ~all(isfinite(fvec));
        end
        % If all previous attempts failed, try with real numbers.
        tentative_number = 0;
        while wrong_initial_guess_flag && tentative_number<=in0*10
            tentative_number = tentative_number+1;
            x(idx) = randn(in0, 1)*10;
            fvec = feval(f, x, arguments{:});
            wrong_initial_guess_flag = ~all(isfinite(fvec));
        end
        % Last tentative, ff all previous attempts failed, try with negative numbers.
        tentative_number = 0;
        while wrong_initial_guess_flag && tentative_number<=in0*10
            tentative_number = tentative_number+1;
            x(idx) = -rand(in0, 1)*10;
            fvec = feval(f, x, arguments{:});
            wrong_initial_guess_flag = ~all(isfinite(fvec));
        end
    end
end

% Exit with error if no initial guess has been found.
if wrong_initial_guess_flag
    errorflag = true;
    x = NaN(size(fvec));
    return
end

% this test doesn't check complementarity conditions and is not used for
% mixed complementarity problems
if (~ismember(options.solve_algo,[10,11])) && (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
    options4fsolve=optimset('fsolve');
    options4fsolve.MaxFunEvals = 50000;
    options4fsolve.MaxIter = maxit;
    options4fsolve.TolFun = tolf;
    if options.debug==1
        options4fsolve.Display = 'final';
    else
        options4fsolve.Display = 'off';
    end
    if jacobian_flag
        options4fsolve.Jacobian = 'on';
    else
        options4fsolve.Jacobian = 'off';
    end
    if ~isoctave
        [x, ~, exitval] = fsolve(f, x, options4fsolve, arguments{:});
    else
        % Under Octave, use a wrapper, since fsolve() does not have a 4th arg
        if ischar(f)
            f2 = str2func(f);
        else
            f2 = f;
        end
        f = @(x) f2(x, arguments{:});
        % The Octave version of fsolve does not converge when it starts from the solution
        fvec = feval(f, x);
        if max(abs(fvec)) >= tolf
            [x, ~,exitval] = fsolve(f, x, options4fsolve);
        else
            exitval = 3;
        end
    end

    if exitval == 1
        errorflag = false;
    elseif exitval > 1
        if ischar(f)
            f2 = str2func(f);
        else
            f2 = f;
        end
        f = @(x) f2(x, arguments{:});
        fvec = feval(f, x);
        if max(abs(fvec)) >= tolf
            errorflag = true;
        else
            errorflag = false;
        end
    else
        errorflag = true;
    end
elseif options.solve_algo==1
    [x, errorflag] = solve1(f, x, 1:nn, 1:nn, jacobian_flag, options.gstep, ...
                       tolf, tolx, ...
                       maxit, options.debug, arguments{:});
elseif options.solve_algo==9
    [x, errorflag] = trust_region(f, x, 1:nn, 1:nn, jacobian_flag, options.gstep, ...
                             tolf, tolx, ...
                             maxit, options.debug, arguments{:});
elseif ismember(options.solve_algo, [2, 12, 4])
    if ismember(options.solve_algo, [2, 12])
        solver = @solve1;
    else
        solver = @trust_region;
    end
    specializedunivariateblocks = options.solve_algo == 12;
    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(f, xdh, arguments{:})-fvec)./dh(j) ;
        end
    end
    [j1,j2,r,s] = dmperm(fjac);
    JAC = abs(fjac(j1,j2))>0;
    if options.debug
        disp(['DYNARE_SOLVE (solve_algo=2|4|12): number of blocks = ' num2str(length(r)-1)]);
    end
    l = 0;
    fre = false;
    for i=length(r)-1:-1:1
        blocklength = r(i+1)-r(i);
        if options.debug
            dprintf('DYNARE_SOLVE (solve_algo=2|4|12): solving block %u of size %u.', i, blocklength);
        end
        j = r(i):r(i+1)-1;
        if specializedunivariateblocks
            if options.debug
                dprintf('DYNARE_SOLVE (solve_algo=2|4|12): solving block %u by evaluating RHS.', i);
            end
            if isequal(blocklength, 1)
                if i<length(r)-1
                    if fre || any(JAC(r(i), s(i)+(1:l)))
                        % Reevaluation of the residuals is required because the current RHS depends on
                        % variables that potentially have been updated previously.
                        z = feval(f, x, arguments{:});
                        l = 0;
                        fre = false;
                    end
                else
                    % First iteration requires the evaluation of the residuals.
                    z = feval(f, x, arguments{:});
                end
                l = l+1;
                if isequal(lhs{j1(j)}, endo_names{j2(j)}) || isequal(lhs{j1(j)}, sprintf('log(%s)', endo_names{j2(j)}))
                    if isloggedlhs(j1(j))
                        x(j2(j)) = exp(log(x(j2(j)))-z(j1(j)));
                    else
                        x(j2(j)) = x(j2(j))-z(j1(j));
                    end
                else
                    if options.debug
                        dprintf('LHS variable is not determined by RHS expression (%u).', j1(j))
                        dprintf('%s -> %s', lhs{j1(j)}, endo_names{j2(j)})
                    end
                    if ~isempty(regexp(lhs{j1(j)}, '\<AUX_DIFF_(\d*)\>', 'once'))
                        if isauxdiffloggedrhs(j1(j))
                            x(j2(j)) = exp(log(x(j2(j)))+z(j1(j)));
                        else
                            x(j2(j)) = x(j2(j))+z(j1(j));
                        end
                    else
                        error('Algorithm solve_algo=%u cannot be used with this nonlinear problem.', options.solve_algo)
                    end
                end
                continue
            end
        else
            if options.debug
                dprintf('DYNARE_SOLVE (solve_algo=2|4|12): solving block %u with trust_region routine.', i);
            end
        end
        [x, errorflag] = solver(f, x, j1(j), j2(j), jacobian_flag, ...
                                options.gstep, ...
                                tolf, options.solve_tolx, ...
                                maxit, options.debug, arguments{:});
        fre = true;
        if errorflag
            return
        end
    end
    fvec = feval(f, x, arguments{:});
    if max(abs(fvec))>tolf
        disp('Call solver on the full nonlinear problem.')
        [x, errorflag] = solver(f, x, 1:nn, 1:nn, jacobian_flag, ...
                                options.gstep, tolf, options.solve_tolx, ...
                                maxit, options.debug, arguments{:});
    end
elseif options.solve_algo==3
    if jacobian_flag
        [x, errorflag] = csolve(f, x, f, 1e-6, 500, arguments{:});
    else
        [x, errorflag] = csolve(f, x, [], 1e-6, 500, arguments{:});
    end
    [fvec, fjac] = feval(f, x, arguments{:});
elseif options.solve_algo==10
    % LMMCP
    olmmcp = options.lmmcp;
    [x, ~, exitflag] = lmmcp(f, x, olmmcp.lb, olmmcp.ub, olmmcp, arguments{:});
    if exitflag==1
        errorflag = false;
    else
        errorflag = true;
    end
elseif options.solve_algo == 11
    % PATH mixed complementary problem
    % PATH linear mixed complementary problem
    if ~exist('mcppath')
        error(['PATH can''t be provided with Dynare. You need to install it ' ...
               'yourself and add its location to Matlab/Octave path before ' ...
               'running Dynare'])
    end
    omcppath = options.mcppath;
    global mcp_data
    mcp_data.func = f;
    mcp_data.args = arguments;
    try
        [x, fval, jac, mu] = pathmcp(x,omcppath.lb,omcppath.ub,'mcp_func',omcppath.A,omcppath.b,omcppath.t,omcppath.mu0);
    catch
        errorflag = true;
    end
elseif ismember(options.solve_algo, [13, 14])
    if ~jacobian_flag
        error('DYNARE_SOLVE: option solve_algo=13|14 needs computed Jacobian')
    end
    auxstruct = struct();
    if options.solve_algo == 14
        auxstruct.lhs = lhs;
        auxstruct.endo_names = endo_names;
        auxstruct.isloggedlhs = isloggedlhs;
        auxstruct.isauxdiffloggedrhs = isauxdiffloggedrhs;
    end
    [x, errorflag] = block_trust_region(f, x, tolf, options.solve_tolx, maxit, options.debug, auxstruct, arguments{:});
    [fvec, fjac] = feval(f, x, arguments{:});
else
    error('DYNARE_SOLVE: option solve_algo must be one of [0,1,2,3,4,9,10,11,12,13,14]')
end