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function [g, badg] = numgrad3_(fcn,f0,x,penalty,epsilon,varargin)
% Computes the gradient of the objective function fcn using a three points
% formula if possible.
%
% Adapted from Sims' numgrad routine.
%
% See section 25.3.4 in Abramovitz and Stegun (1972, Tenth Printing, December) Handbook of Mathematical Functions.
% http://www.math.sfu.ca/~cbm/aands/
% Original file downloaded from:
% http://sims.princeton.edu/yftp/optimize/mfiles/numgrad.m
% Copyright (C) 1993-2007 Christopher Sims
% Copyright (C) 2008-2014 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/>.
rescale_step_length = 0;
delta = epsilon;
n = length(x);
g = zeros(n,1);
badg = 0;
if rescale_step_length
scale = [];
else
scale = ones(n,1);
end
for i=1:n
xiold = x(i);
h = step_length_correction(xiold,scale,i)*delta;
x(i) = xiold + h;
[f1,junk1,cost_flag1] = penalty_objective_function(x, fcn, penalty, varargin{:});
if ~cost_flag1
fprintf('Gradient w.r.t. parameter number %3d (x=%16.8f,+h=%16.8f,f0=%16.8f,f1=%16.8f,f2=%16.8f,g0=%16.8f): penalty on the right!\n',i,xiold,h,f0,f1,f2,(f1 - f2) / (2*h))
end
x(i) = xiold - h;
[f2,junk2,cost_flag2] = penalty_objective_function(x, fcn, penalty, varargin{:});
if ~cost_flag2
fprintf('Gradient w.r.t. parameter number %3d (x=%16.8f,+h=%16.8f,f0=%16.8f,f1=%16.8f,f2=%16.8f,g0=%16.8f): penalty on the left!\n',i,xiold,h,f0,f1,f2,(f1 - f2) / (2*h))
end
if f0<f1 && f0<f2
fprintf('Gradient w.r.t. parameter number %3d (x=%16.8f,h=%16.8f,f0=%16.8f,f1=%16.8f,f2=%16.8f,g0=%16.8f)\n',i,xiold,h,f0,f1,f2,(f1 - f2) / (2*h))
g0 = 0;
else
g0 = (f1 - f2) / (2*h);
end
if abs(g0)< 1e15
g(i) = g0;
else
disp('Bad gradient -----------------------------------')
fprintf('Gradient w.r.t. parameter number %3d (x=%16.8f,h=%16.8f,g0=%16.8f)\n',i,xiold,h,g0)
g(i) = 0;
badg = 1;
end
x(i) = xiold;
end
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