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+<html>
+<head>
+<title>
+Netlab Reference Manual minbrack
+</title>
+</head>
+<body>
+<H1> minbrack
+</H1>
+<h2>
+Purpose
+</h2>
+Bracket a minimum of a function of one variable.
+
+<p><h2>
+Description
+</h2>
+<CODE>brmin, brmid, brmax, numevals] = minbrack(f, a, b, fa)</CODE>
+finds a bracket of three points around a local minimum of
+<CODE>f</CODE>.  The function <CODE>f</CODE> must have a one dimensional domain.
+<CODE>a < b</CODE> is an initial guess at the minimum and maximum points
+of a bracket, but <CODE>minbrack</CODE> will search outside this interval if
+necessary. The bracket consists of three points (in increasing order)
+such that <CODE>f(brmid) < f(brmin)</CODE> and <CODE>f(brmid) < f(brmax)</CODE>.
+<CODE>fa</CODE> is the value of the function at <CODE>a</CODE>: it is included to
+avoid unnecessary function evaluations in the optimization routines.
+The return value <CODE>numevals</CODE> is the number of function evaluations
+in <CODE>minbrack</CODE>.
+
+<p><CODE>minbrack(f, a, b, fa, p1, p2, ...)</CODE> allows additional
+arguments to be passed to <CODE>f</CODE>
+
+<p><h2>
+Examples
+</h2>
+An example of the use of this function to bracket the minimum of a function
+<CODE>f</CODE> in the direction <CODE>sd</CODE> can be found in <CODE>linemin</CODE>
+<PRE>
+
+[min, mid, max, nevals]] = minbrack('linef', 0.0, 1.0, fa, f, pt, dir);
+</PRE>
+
+where the function <CODE>linef</CODE> is used to turn a general function <CODE>f</CODE>
+into a one dimensional one.
+
+<p><h2>
+Algorithm
+</h2>
+
+Quadratic extrapolation with a limit to the maximum step size is
+used to find the outside points of the bracket.  This implementation
+is based on that in Numerical Recipes.
+
+<p><h2>
+See Also
+</h2>
+<CODE><a href="linemin.htm">linemin</a></CODE>, <CODE><a href="linef.htm">linef</a></CODE><hr>
+<b>Pages:</b>
+<a href="index.htm">Index</a>
+<hr>
+<p>Copyright (c) Ian T Nabney (1996-9)
+
+
+</body>
+</html>
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