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1 <html>
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2 <head>
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3 <title>
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4 Netlab Reference Manual conjgrad
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5 </title>
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6 </head>
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7 <body>
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8 <H1> conjgrad
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9 </H1>
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10 <h2>
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11 Purpose
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12 </h2>
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13 Conjugate gradients optimization.
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14
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15 <p><h2>
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16 Description
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17 </h2>
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18 <CODE>[x, options, flog, pointlog] = conjgrad(f, x, options, gradf)</CODE> uses a
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19 conjugate gradients
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20 algorithm to find the minimum of the function <CODE>f(x)</CODE> whose
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21 gradient is given by <CODE>gradf(x)</CODE>. Here <CODE>x</CODE> is a row vector
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22 and <CODE>f</CODE> returns a scalar value.
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23 The point at which <CODE>f</CODE> has a local minimum
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24 is returned as <CODE>x</CODE>. The function value at that point is returned
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25 in <CODE>options(8)</CODE>. A log of the function values
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26 after each cycle is (optionally) returned in <CODE>flog</CODE>, and a log
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27 of the points visited is (optionally) returned in <CODE>pointlog</CODE>.
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28
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29 <p><CODE>conjgrad(f, x, options, gradf, p1, p2, ...)</CODE> allows
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30 additional arguments to be passed to <CODE>f()</CODE> and <CODE>gradf()</CODE>.
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31
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32 <p>The optional parameters have the following interpretations.
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33
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34 <p><CODE>options(1)</CODE> is set to 1 to display error values; also logs error
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35 values in the return argument <CODE>errlog</CODE>, and the points visited
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36 in the return argument <CODE>pointslog</CODE>. If <CODE>options(1)</CODE> is set to 0,
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37 then only warning messages are displayed. If <CODE>options(1)</CODE> is -1,
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38 then nothing is displayed.
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39
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40 <p><CODE>options(2)</CODE> is a measure of the absolute precision required for the value
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41 of <CODE>x</CODE> at the solution. If the absolute difference between
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42 the values of <CODE>x</CODE> between two successive steps is less than
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43 <CODE>options(2)</CODE>, then this condition is satisfied.
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44
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45 <p><CODE>options(3)</CODE> is a measure of the precision required of the objective
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46 function at the solution. If the absolute difference between the
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47 objective function values between two successive steps is less than
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48 <CODE>options(3)</CODE>, then this condition is satisfied.
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49 Both this and the previous condition must be
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50 satisfied for termination.
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51
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52 <p><CODE>options(9)</CODE> is set to 1 to check the user defined gradient function.
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53
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54 <p><CODE>options(10)</CODE> returns the total number of function evaluations (including
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55 those in any line searches).
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56
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57 <p><CODE>options(11)</CODE> returns the total number of gradient evaluations.
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58
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59 <p><CODE>options(14)</CODE> is the maximum number of iterations; default 100.
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60
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61 <p><CODE>options(15)</CODE> is the precision in parameter space of the line search;
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62 default <CODE>1e-4</CODE>.
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63
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64 <p><h2>
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65 Examples
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66 </h2>
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67 An example of
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68 the use of the additional arguments is the minimization of an error
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69 function for a neural network:
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70 <PRE>
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71
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72 w = quasinew('neterr', w, options, 'netgrad', net, x, t);
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73 </PRE>
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74
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75
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76 <p><h2>
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77 Algorithm
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78 </h2>
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79
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80 The conjugate gradients algorithm constructs search
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81 directions <CODE>di</CODE> that are conjugate: i.e. <CODE>di*H*d(i-1) = 0</CODE>,
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82 where <CODE>H</CODE> is the Hessian matrix. This means that minimising along
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83 <CODE>di</CODE> does not undo the effect of minimising along the previous
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84 direction. The Polak-Ribiere formula is used to calculate new search
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85 directions. The Hessian is not calculated, so there is only an
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86 <CODE>O(W)</CODE> storage requirement (where <CODE>W</CODE> is the number of
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87 parameters). However, relatively accurate line searches must be used
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88 (default is <CODE>1e-04</CODE>).
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89
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90 <p><h2>
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91 See Also
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92 </h2>
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93 <CODE><a href="graddesc.htm">graddesc</a></CODE>, <CODE><a href="linemin.htm">linemin</a></CODE>, <CODE><a href="minbrack.htm">minbrack</a></CODE>, <CODE><a href="quasinew.htm">quasinew</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE><hr>
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94 <b>Pages:</b>
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95 <a href="index.htm">Index</a>
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96 <hr>
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97 <p>Copyright (c) Ian T Nabney (1996-9)
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98
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99
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100 </body>
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101 </html> |
