function h = hesschek(net, x, t)%HESSCHEK Use central differences to confirm correct evaluation of Hessian matrix.%%	Description%%	HESSCHEK(NET, X, T) takes a network data structure NET, together with%	input and target data matrices X and T, and compares the evaluation%	of the Hessian matrix using the function NETHESS and using central%	differences with the function NETERR.%%	The optional return value H is the Hessian computed using NETHESS.%%	See also%	NETHESS, NETERR%%	Copyright (c) Ian T Nabney (1996-2001)w0 = netpak(net);nwts = length(w0);h = nethess(w0, net, x, t);w = w0;hcent = zeros(nwts, nwts);h1 =  0.0; h2 =  0.0; h3 =  0.0; h4 = 0.0;epsilon = 1.0e-4;fprintf(1, 'Checking Hessian ...\n\n');for k = 1:nwts;  for l = 1:nwts;    if(l == k)      w(k) = w0(k) + 2.0*epsilon;      h1 = neterr(w, net, x, t);      w(k) = w0(k) - 2.0*epsilon;      h2 = neterr(w, net, x, t);      w(k) = w0(k);      h3 = neterr(w, net, x, t);      hcent(k, k) = (h1 + h2 - 2.0*h3)/(4.0*epsilon^2);    else      w(k) = w0(k) + epsilon;      w(l) = w0(l) + epsilon;      h1 = neterr(w, net, x, t);      w(k) = w0(k) - epsilon;      w(l) = w0(l) - epsilon;      h2 = neterr(w, net, x, t);      w(k) = w0(k) + epsilon;      w(l) = w0(l) - epsilon;      h3 = neterr(w, net, x, t);      w(k) = w0(k) - epsilon;      w(l) = w0(l) + epsilon;      h4 = neterr(w, net, x, t);      hcent(k, l) = (h1 + h2 - h3 - h4)/(4.0*epsilon^2);      w(k) = w0(k);      w(l) = w0(l);    end  endendfprintf(1, '   analytical    numerical       delta\n\n');temp = [h(:), hcent(:), (h(:) - hcent(:))];fprintf(1, '%12.6f  %12.6f  %12.6f\n', temp');