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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 minbrack
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5 </title>
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6 </head>
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7 <body>
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8 <H1> minbrack
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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 Bracket a minimum of a function of one variable.
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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>brmin, brmid, brmax, numevals] = minbrack(f, a, b, fa)</CODE>
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19 finds a bracket of three points around a local minimum of
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20 <CODE>f</CODE>. The function <CODE>f</CODE> must have a one dimensional domain.
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21 <CODE>a < b</CODE> is an initial guess at the minimum and maximum points
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22 of a bracket, but <CODE>minbrack</CODE> will search outside this interval if
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23 necessary. The bracket consists of three points (in increasing order)
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24 such that <CODE>f(brmid) < f(brmin)</CODE> and <CODE>f(brmid) < f(brmax)</CODE>.
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25 <CODE>fa</CODE> is the value of the function at <CODE>a</CODE>: it is included to
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26 avoid unnecessary function evaluations in the optimization routines.
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27 The return value <CODE>numevals</CODE> is the number of function evaluations
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28 in <CODE>minbrack</CODE>.
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29
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30 <p><CODE>minbrack(f, a, b, fa, p1, p2, ...)</CODE> allows additional
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31 arguments to be passed to <CODE>f</CODE>
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32
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33 <p><h2>
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34 Examples
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35 </h2>
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36 An example of the use of this function to bracket the minimum of a function
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37 <CODE>f</CODE> in the direction <CODE>sd</CODE> can be found in <CODE>linemin</CODE>
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38 <PRE>
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39
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40 [min, mid, max, nevals]] = minbrack('linef', 0.0, 1.0, fa, f, pt, dir);
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41 </PRE>
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42
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43 where the function <CODE>linef</CODE> is used to turn a general function <CODE>f</CODE>
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44 into a one dimensional one.
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45
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46 <p><h2>
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47 Algorithm
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48 </h2>
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49
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50 Quadratic extrapolation with a limit to the maximum step size is
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51 used to find the outside points of the bracket. This implementation
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52 is based on that in Numerical Recipes.
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53
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54 <p><h2>
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55 See Also
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56 </h2>
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57 <CODE><a href="linemin.htm">linemin</a></CODE>, <CODE><a href="linef.htm">linef</a></CODE><hr>
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58 <b>Pages:</b>
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59 <a href="index.htm">Index</a>
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60 <hr>
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61 <p>Copyright (c) Ian T Nabney (1996-9)
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62
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63
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64 </body>
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65 </html> |
