97 lines
2.8 KiB
Matlab
97 lines
2.8 KiB
Matlab
function [x, objectivevalue, errorflag] = gauss_newton(fun, x0)
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% Minimization of the sum of squared residuals with the Gauss-Newton algorithm.
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%
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% The objective is to minimize:
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%
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% fun(x)'*fun(x)
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%
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% with respect to x.
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%
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% INPUTS:
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% - funres [handle] Function from Rᵖ to Rⁿ, which given parameters (x) return the residuals of a non linear equation.
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% - x0 [double] 1×p vector, initial guess.
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%
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% OUTPUTS:
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% - x [double] 1×p vector, vector of parameters minimizing the sum of squared residuals.
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% - objectivevalue [double] scalar, optimal value of the objective.
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% - errorflag [integer] scalar, nonzero if algorithm did not converge.
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% Copyright © 2018 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 <https://www.gnu.org/licenses/>.
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maxIter = 100; % Maximum number of iteration.
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h = sqrt(eps(1.0)); % Pertubation size for numerical computation of the Jacobian matrix
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xtol = 1e-6; % Stopping criterion.
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phi = .5*(sqrt(5)+1.0); % Golden number.
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errorflag = 0;
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noconvergence = true;
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counter = 0;
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while noconvergence
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% Compute residuals and descent direction
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[r0, J] = jacobian(fun, x0, h);
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d = pinv(J)*r0;
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% Update parameters
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x1 = x0+d;
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% Test if the step actually reduce the sum of squared residuals.
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r1 = fun(x1);
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s0 = r0'*r0;
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s1 = r1'*r1;
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if s1>s0
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% Gauss-Newton step increased the Sum of Squared Residuals...
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% We search for another point in the same direction using Golden section search.
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l1 = 0;
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l2 = 1;
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L1 = l2-(l2-l1)/phi;
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L2 = l1+(l2-l1)/phi;
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while abs(L1-L2)>1e-6
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if ssr(x0+L1*d)<ssr(x0+L2*d)
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l2 = L2;
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else
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l1 = L1;
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end
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L1 = l2-(l2-l1)/phi;
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L2 = l1+(l2-l1)/phi;
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end
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scale = .5*(l1+l2);
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x1 = x0+scale*d;
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else
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scale = 1.0;
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end
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noconvergence = max(abs(x1-x0))>xtol;
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counter = counter+1;
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x0 = x1;
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if counter>maxIter
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break
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end
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end
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x = x0;
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objectivevalue = s1;
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errorflag = isequal(counter, maxIter+1);
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function s = ssr(x)
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% Evaluate the sum of square residuals.
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r = fun(x);
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s = r'*r;
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end
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end |