num_hess.m

% num_hess.m
%
% [H, NFV] = num_hess(func, X, NFV, h)
%
% Function to compute the numerical Hessian of an arbitrary objective
% function.
%
% Inputs:
%   -> func: Function handle for which numerical Hessian is to be
%       obtained.
%   -> X: Sink of interest about which Hessian is to be obtained.
%   -> NFV: Accumulator to keep track of number of function
%       evaluations.
%   -> h: Tolerance for differentiation.
%
% Outputs:
%   -> H: Numerical Hessian of function func (square symmetric
%       matrix of size n=length(X)).
%   -> NFV: Accumulator incremented by the number of function
%       evaluations which have taken place.
%
% Created by: Brendan C. Wood
% Created on: February 14, 2011
%
% Copyright (c) 2011, Brendan C. Wood <b.wood@unb.ca>
%
 
function [H] = num_hess(func, X, h)
 
H = zeros(length(X));
 
% for each dimension of objective function
for i=1:length(X)
    % derivative at first point (left)
    x1 = X;
    x1(i) = X(i) - h;
    [df1] = num_grad(func, x1, h);
    
    % derivative at second point (right)
    x2 = X;
    x2(i) = X(i) + h;
    [df2] = num_grad(func, x2, h);
    
    % differentiate between the two derivatives
    d2f = (df2-df1) / (2*h);
    
    % assign as row i of Hessian
    H(i,:) = d2f';
end