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1 function h = hesschek(net, x, t)
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2 %HESSCHEK Use central differences to confirm correct evaluation of Hessian matrix.
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3 %
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4 % Description
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5 %
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6 % HESSCHEK(NET, X, T) takes a network data structure NET, together with
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7 % input and target data matrices X and T, and compares the evaluation
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8 % of the Hessian matrix using the function NETHESS and using central
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9 % differences with the function NETERR.
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10 %
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11 % The optional return value H is the Hessian computed using NETHESS.
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12 %
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13 % See also
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14 % NETHESS, NETERR
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15 %
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16
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17 % Copyright (c) Ian T Nabney (1996-2001)
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18
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19 w0 = netpak(net);
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20 nwts = length(w0);
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21 h = nethess(w0, net, x, t);
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22
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23 w = w0;
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24 hcent = zeros(nwts, nwts);
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25 h1 = 0.0; h2 = 0.0; h3 = 0.0; h4 = 0.0;
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26 epsilon = 1.0e-4;
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27 fprintf(1, 'Checking Hessian ...\n\n');
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28 for k = 1:nwts;
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29 for l = 1:nwts;
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30 if(l == k)
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31 w(k) = w0(k) + 2.0*epsilon;
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32 h1 = neterr(w, net, x, t);
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33 w(k) = w0(k) - 2.0*epsilon;
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34 h2 = neterr(w, net, x, t);
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35 w(k) = w0(k);
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36 h3 = neterr(w, net, x, t);
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37 hcent(k, k) = (h1 + h2 - 2.0*h3)/(4.0*epsilon^2);
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38 else
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39 w(k) = w0(k) + epsilon;
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40 w(l) = w0(l) + epsilon;
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41 h1 = neterr(w, net, x, t);
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42 w(k) = w0(k) - epsilon;
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43 w(l) = w0(l) - epsilon;
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44 h2 = neterr(w, net, x, t);
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45 w(k) = w0(k) + epsilon;
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46 w(l) = w0(l) - epsilon;
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47 h3 = neterr(w, net, x, t);
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48 w(k) = w0(k) - epsilon;
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49 w(l) = w0(l) + epsilon;
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50 h4 = neterr(w, net, x, t);
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51 hcent(k, l) = (h1 + h2 - h3 - h4)/(4.0*epsilon^2);
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52 w(k) = w0(k);
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53 w(l) = w0(l);
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54 end
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55 end
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56 end
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57
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58 fprintf(1, ' analytical numerical delta\n\n');
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59 temp = [h(:), hcent(:), (h(:) - hcent(:))];
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60 fprintf(1, '%12.6f %12.6f %12.6f\n', temp'); |
