375 lines
14 KiB
Matlab
375 lines
14 KiB
Matlab
function [x, errorflag, fvec, fjac] = dynare_solve(f, x, options, varargin)
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% Solves a nonlinear system of equations, f(x) = 0 with n unknowns
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% and n equations.
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%
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% INPUTS
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% - f [char, fhandle] function to be solved
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% - x [double] n×1 vector, initial guess.
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% - options [struct] Dynare options, aka options_.
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% - varargin list of additional arguments to be passed to func.
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%
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% OUTPUTS
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% - x [double] n×1 vector, solution.
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% - errorflag [logical] scalar, true iff the model can not be solved.
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% - fvec [double] n×1 vector, function value at x (f(x), used for debugging when errorflag is true).
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% - fjac [double] n×n matrix, Jacobian value at x (J(x), used for debugging when errorflag is true).
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%
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% REMARKS
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% Copyright © 2001-2020 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 <http://www.gnu.org/licenses/>.
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jacobian_flag = options.jacobian_flag; % true iff Jacobian is returned by f routine (as a second output argument).
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% Set tolerance parameter depending the the caller function.
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stack = dbstack;
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if isoctave
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[~, name, ext]=fileparts(stack(2).file);
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caller_file_name=[name,ext];
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else
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caller_file_name=stack(2).file;
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end
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if strcmp(caller_file_name,'solve_stacked_problem.m')
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tolf = options.dynatol.f;
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tolx = options.dynatol.x;
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else
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tolf = options.solve_tolf;
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tolx = options.solve_tolx;
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end
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if strcmp(caller_file_name,'dyn_ramsey_static.m')
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maxit = options.ramsey.maxit;
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else
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maxit = options.steady.maxit;
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end
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errorflag = false;
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nn = size(x,1);
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% Get status of the initial guess (default values?)
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if any(x)
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% The current initial guess is not the default for all the variables.
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idx = find(x); % Indices of the variables with default initial guess values.
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in0 = length(idx);
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else
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% The current initial guess is the default for all the variables.
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idx = transpose(1:nn);
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in0 = nn;
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end
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% Get first element of varargin if solve_algo ∈ {12,14} and rename varargin.
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if ismember(options.solve_algo, [12, 14])
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isloggedlhs = varargin{1};
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isauxdiffloggedrhs = varargin{2};
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endo_names = varargin{3};
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lhs = varargin{4};
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arguments = varargin(5:end);
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else
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arguments = varargin;
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end
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% checking initial values
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if jacobian_flag
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[fvec, fjac] = feval(f, x, arguments{:});
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wrong_initial_guess_flag = false;
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if ~all(isfinite(fvec)) || any(isinf(fjac(:))) || any(isnan((fjac(:)))) ...
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|| any(~isreal(fvec)) || any(~isreal(fjac(:)))
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if max(abs(fvec)) < tolf %return if initial value solves problem
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info = 0;
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return;
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end
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disp('Randomize initial guess...')
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% Let's try random numbers for the variables initialized with the default value.
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wrong_initial_guess_flag = true;
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% First try with positive numbers.
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tentative_number = 0;
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while wrong_initial_guess_flag && tentative_number<=in0*10
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tentative_number = tentative_number+1;
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x(idx) = rand(in0, 1)*10;
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[fvec, fjac] = feval(f, x, arguments{:});
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wrong_initial_guess_flag = ~all(isfinite(fvec)) || any(isinf(fjac(:))) || any(isnan((fjac(:))));
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end
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% If all previous attempts failed, try with real numbers.
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tentative_number = 0;
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while wrong_initial_guess_flag && tentative_number<=in0*10
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tentative_number = tentative_number+1;
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x(idx) = randn(in0, 1)*10;
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[fvec, fjac] = feval(f, x, arguments{:});
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wrong_initial_guess_flag = ~all(isfinite(fvec)) || any(isinf(fjac(:))) || any(isnan((fjac(:))));
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end
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% Last tentative, ff all previous attempts failed, try with negative numbers.
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tentative_number = 0;
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while wrong_initial_guess_flag && tentative_number<=in0*10
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tentative_number = tentative_number+1;
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x(idx) = -rand(in0, 1)*10;
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[fvec, fjac] = feval(f, x, arguments{:});
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wrong_initial_guess_flag = ~all(isfinite(fvec)) || any(isinf(fjac(:))) || any(isnan((fjac(:))));
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end
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end
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else
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fvec = feval(f, x, arguments{:});
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fjac = zeros(nn, nn);
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wrong_initial_guess_flag = false;
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if ~all(isfinite(fvec))
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% Let's try random numbers for the variables initialized with the default value.
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wrong_initial_guess_flag = true;
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% First try with positive numbers.
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tentative_number = 0;
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while wrong_initial_guess_flag && tentative_number<=in0*10
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tentative_number = tentative_number+1;
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x(idx) = rand(in0, 1)*10;
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fvec = feval(f, x, arguments{:});
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wrong_initial_guess_flag = ~all(isfinite(fvec));
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end
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% If all previous attempts failed, try with real numbers.
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tentative_number = 0;
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while wrong_initial_guess_flag && tentative_number<=in0*10
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tentative_number = tentative_number+1;
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x(idx) = randn(in0, 1)*10;
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fvec = feval(f, x, arguments{:});
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wrong_initial_guess_flag = ~all(isfinite(fvec));
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end
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% Last tentative, ff all previous attempts failed, try with negative numbers.
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tentative_number = 0;
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while wrong_initial_guess_flag && tentative_number<=in0*10
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tentative_number = tentative_number+1;
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x(idx) = -rand(in0, 1)*10;
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fvec = feval(f, x, arguments{:});
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wrong_initial_guess_flag = ~all(isfinite(fvec));
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end
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end
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end
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% Exit with error if no initial guess has been found.
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if wrong_initial_guess_flag
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errorflag = true;
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x = NaN(size(fvec));
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return
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end
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% this test doesn't check complementarity conditions and is not used for
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% mixed complementarity problems
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if (~ismember(options.solve_algo,[10,11])) && (max(abs(fvec)) < tolf)
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return ;
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end
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if options.solve_algo == 0
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if ~isoctave
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if ~user_has_matlab_license('optimization_toolbox')
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error('You can''t use solve_algo=0 since you don''t have MATLAB''s Optimization Toolbox')
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end
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end
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options4fsolve=optimset('fsolve');
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options4fsolve.MaxFunEvals = 50000;
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options4fsolve.MaxIter = maxit;
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options4fsolve.TolFun = tolf;
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if options.debug==1
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options4fsolve.Display = 'final';
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else
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options4fsolve.Display = 'off';
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end
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if jacobian_flag
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options4fsolve.Jacobian = 'on';
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else
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options4fsolve.Jacobian = 'off';
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end
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if ~isoctave
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[x, ~, exitval] = fsolve(f, x, options4fsolve, arguments{:});
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else
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% Under Octave, use a wrapper, since fsolve() does not have a 4th arg
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if ischar(f)
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f2 = str2func(f);
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else
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f2 = f;
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end
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f = @(x) f2(x, arguments{:});
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% The Octave version of fsolve does not converge when it starts from the solution
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fvec = feval(f, x);
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if max(abs(fvec)) >= tolf
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[x, ~,exitval] = fsolve(f, x, options4fsolve);
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else
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exitval = 3;
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end
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end
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if exitval == 1
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errorflag = false;
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elseif exitval > 1
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if ischar(f)
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f2 = str2func(f);
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else
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f2 = f;
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end
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f = @(x) f2(x, arguments{:});
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fvec = feval(f, x);
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if max(abs(fvec)) >= tolf
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errorflag = true;
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else
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errorflag = false;
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end
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else
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errorflag = true;
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end
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elseif options.solve_algo==1
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[x, errorflag] = solve1(f, x, 1:nn, 1:nn, jacobian_flag, options.gstep, ...
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tolf, tolx, ...
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maxit, options.debug, arguments{:});
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elseif options.solve_algo==9
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[x, errorflag] = trust_region(f, x, 1:nn, 1:nn, jacobian_flag, options.gstep, ...
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tolf, tolx, ...
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maxit, options.debug, arguments{:});
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elseif ismember(options.solve_algo, [2, 12, 4])
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if ismember(options.solve_algo, [2, 12])
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solver = @solve1;
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else
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solver = @trust_region;
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end
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specializedunivariateblocks = options.solve_algo == 12;
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if ~jacobian_flag
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fjac = zeros(nn,nn) ;
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dh = max(abs(x), options.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(j) = xdh(j)+dh(j) ;
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fjac(:,j) = (feval(f, xdh, arguments{:})-fvec)./dh(j) ;
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end
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end
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[j1,j2,r,s] = dmperm(fjac);
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JAC = abs(fjac(j1,j2))>0;
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if options.debug
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disp(['DYNARE_SOLVE (solve_algo=2|4|12): number of blocks = ' num2str(length(r)-1)]);
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end
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l = 0;
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fre = false;
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for i=length(r)-1:-1:1
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blocklength = r(i+1)-r(i);
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if options.debug
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dprintf('DYNARE_SOLVE (solve_algo=2|4|12): solving block %u of size %u.', i, blocklength);
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end
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j = r(i):r(i+1)-1;
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if specializedunivariateblocks
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if options.debug
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dprintf('DYNARE_SOLVE (solve_algo=2|4|12): solving block %u by evaluating RHS.', i);
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end
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if isequal(blocklength, 1)
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if i<length(r)-1
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if fre || any(JAC(r(i), s(i)+(1:l)))
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% Reevaluation of the residuals is required because the current RHS depends on
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% variables that potentially have been updated previously.
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z = feval(f, x, arguments{:});
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l = 0;
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fre = false;
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end
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else
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% First iteration requires the evaluation of the residuals.
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z = feval(f, x, arguments{:});
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end
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l = l+1;
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if isequal(lhs{j1(j)}, endo_names{j2(j)}) || isequal(lhs{j1(j)}, sprintf('log(%s)', endo_names{j2(j)}))
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if isloggedlhs(j1(j))
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x(j2(j)) = exp(log(x(j2(j)))-z(j1(j)));
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else
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x(j2(j)) = x(j2(j))-z(j1(j));
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end
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else
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if options.debug
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dprintf('LHS variable is not determined by RHS expression (%u).', j1(j))
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dprintf('%s -> %s', lhs{j1(j)}, endo_names{j2(j)})
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end
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if ~isempty(regexp(lhs{j1(j)}, '\<AUX_DIFF_(\d*)\>', 'once'))
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if isauxdiffloggedrhs(j1(j))
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x(j2(j)) = exp(log(x(j2(j)))+z(j1(j)));
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else
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x(j2(j)) = x(j2(j))+z(j1(j));
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end
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else
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error('Algorithm solve_algo=%u cannot be used with this nonlinear problem.', options.solve_algo)
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end
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end
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continue
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end
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else
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if options.debug
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dprintf('DYNARE_SOLVE (solve_algo=2|4|12): solving block %u with trust_region routine.', i);
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end
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end
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[x, errorflag] = solver(f, x, j1(j), j2(j), jacobian_flag, ...
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options.gstep, ...
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tolf, options.solve_tolx, ...
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maxit, options.debug, arguments{:});
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fre = true;
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if errorflag
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return
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end
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end
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fvec = feval(f, x, arguments{:});
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if max(abs(fvec))>tolf
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disp('Call solver on the full nonlinear problem.')
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[x, errorflag] = solver(f, x, 1:nn, 1:nn, jacobian_flag, ...
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options.gstep, tolf, options.solve_tolx, ...
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maxit, options.debug, arguments{:});
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end
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elseif options.solve_algo==3
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if jacobian_flag
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[x, errorflag] = csolve(f, x, f, 1e-6, 500, arguments{:});
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else
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[x, errorflag] = csolve(f, x, [], 1e-6, 500, arguments{:});
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end
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[fvec, fjac] = feval(f, x, arguments{:});
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elseif options.solve_algo==10
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% LMMCP
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olmmcp = options.lmmcp;
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[x, ~, exitflag] = lmmcp(f, x, olmmcp.lb, olmmcp.ub, olmmcp, arguments{:});
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if exitflag==1
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errorflag = false;
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else
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errorflag = true;
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end
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elseif options.solve_algo == 11
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% PATH mixed complementary problem
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% PATH linear mixed complementary problem
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if ~exist('mcppath')
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error(['PATH can''t be provided with Dynare. You need to install it ' ...
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'yourself and add its location to Matlab/Octave path before ' ...
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'running Dynare'])
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end
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omcppath = options.mcppath;
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global mcp_data
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mcp_data.func = f;
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mcp_data.args = arguments;
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try
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[x, fval, jac, mu] = pathmcp(x,omcppath.lb,omcppath.ub,'mcp_func',omcppath.A,omcppath.b,omcppath.t,omcppath.mu0);
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catch
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errorflag = true;
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end
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elseif ismember(options.solve_algo, [13, 14])
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if ~jacobian_flag
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error('DYNARE_SOLVE: option solve_algo=13|14 needs computed Jacobian')
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end
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auxstruct = struct();
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if options.solve_algo == 14
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auxstruct.lhs = lhs;
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auxstruct.endo_names = endo_names;
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auxstruct.isloggedlhs = isloggedlhs;
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auxstruct.isauxdiffloggedrhs = isauxdiffloggedrhs;
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end
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[x, errorflag] = block_trust_region(f, x, tolf, options.solve_tolx, maxit, options.debug, auxstruct, arguments{:});
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[fvec, fjac] = feval(f, x, arguments{:});
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else
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error('DYNARE_SOLVE: option solve_algo must be one of [0,1,2,3,4,9,10,11,12,13,14]')
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end
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