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1 <html>
2 <head>
3 <title>
4 Netlab Reference Manual minbrack
5 </title>
6 </head>
7 <body>
8 <H1> minbrack
9 </H1>
10 <h2>
11 Purpose
12 </h2>
13 Bracket a minimum of a function of one variable.
14
15 <p><h2>
16 Description
17 </h2>
18 <CODE>brmin, brmid, brmax, numevals] = minbrack(f, a, b, fa)</CODE>
19 finds a bracket of three points around a local minimum of
20 <CODE>f</CODE>. The function <CODE>f</CODE> must have a one dimensional domain.
21 <CODE>a < b</CODE> is an initial guess at the minimum and maximum points
22 of a bracket, but <CODE>minbrack</CODE> will search outside this interval if
23 necessary. The bracket consists of three points (in increasing order)
24 such that <CODE>f(brmid) < f(brmin)</CODE> and <CODE>f(brmid) < f(brmax)</CODE>.
25 <CODE>fa</CODE> is the value of the function at <CODE>a</CODE>: it is included to
26 avoid unnecessary function evaluations in the optimization routines.
27 The return value <CODE>numevals</CODE> is the number of function evaluations
28 in <CODE>minbrack</CODE>.
29
30 <p><CODE>minbrack(f, a, b, fa, p1, p2, ...)</CODE> allows additional
31 arguments to be passed to <CODE>f</CODE>
32
33 <p><h2>
34 Examples
35 </h2>
36 An example of the use of this function to bracket the minimum of a function
37 <CODE>f</CODE> in the direction <CODE>sd</CODE> can be found in <CODE>linemin</CODE>
38 <PRE>
39
40 [min, mid, max, nevals]] = minbrack('linef', 0.0, 1.0, fa, f, pt, dir);
41 </PRE>
42
43 where the function <CODE>linef</CODE> is used to turn a general function <CODE>f</CODE>
44 into a one dimensional one.
45
46 <p><h2>
47 Algorithm
48 </h2>
49
50 Quadratic extrapolation with a limit to the maximum step size is
51 used to find the outside points of the bracket. This implementation
52 is based on that in Numerical Recipes.
53
54 <p><h2>
55 See Also
56 </h2>
57 <CODE><a href="linemin.htm">linemin</a></CODE>, <CODE><a href="linef.htm">linef</a></CODE><hr>
58 <b>Pages:</b>
59 <a href="index.htm">Index</a>
60 <hr>
61 <p>Copyright (c) Ian T Nabney (1996-9)
62
63
64 </body>
65 </html>