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+<html>
+<head>
+<title>
+Netlab Reference Manual conjgrad
+</title>
+</head>
+<body>
+<H1> conjgrad
+</H1>
+<h2>
+Purpose
+</h2>
+Conjugate gradients optimization.
+
+<p><h2>
+Description
+</h2>
+<CODE>[x, options, flog, pointlog] = conjgrad(f, x, options, gradf)</CODE> uses a 
+conjugate gradients
+algorithm to find the minimum of the function <CODE>f(x)</CODE> whose
+gradient is given by <CODE>gradf(x)</CODE>.  Here <CODE>x</CODE> is a row vector
+and <CODE>f</CODE> returns a scalar value. 
+The point at which <CODE>f</CODE> has a local minimum
+is returned as <CODE>x</CODE>.  The function value at that point is returned
+in <CODE>options(8)</CODE>.  A log of the function values
+after each cycle is (optionally) returned in <CODE>flog</CODE>, and a log
+of the points visited is (optionally) returned in <CODE>pointlog</CODE>.
+
+<p><CODE>conjgrad(f, x, options, gradf, p1, p2, ...)</CODE> allows 
+additional arguments to be passed to <CODE>f()</CODE> and <CODE>gradf()</CODE>. 
+
+<p>The optional parameters have the following interpretations.
+
+<p><CODE>options(1)</CODE> is set to 1 to display error values; also logs error 
+values in the return argument <CODE>errlog</CODE>, and the points visited
+in the return argument <CODE>pointslog</CODE>.  If <CODE>options(1)</CODE> is set to 0,
+then only warning messages are displayed.  If <CODE>options(1)</CODE> is -1,
+then nothing is displayed.
+
+<p><CODE>options(2)</CODE> is a measure of the absolute precision required for the value
+of <CODE>x</CODE> at the solution.  If the absolute difference between
+the values of <CODE>x</CODE> between two successive steps is less than
+<CODE>options(2)</CODE>, then this condition is satisfied.
+
+<p><CODE>options(3)</CODE> is a measure of the precision required of the objective
+function at the solution.  If the absolute difference between the
+objective function values between two successive steps is less than
+<CODE>options(3)</CODE>, then this condition is satisfied.
+Both this and the previous condition must be
+satisfied for termination.
+
+<p><CODE>options(9)</CODE> is set to 1 to check the user defined gradient function.
+
+<p><CODE>options(10)</CODE> returns the total number of function evaluations (including
+those in any line searches).
+
+<p><CODE>options(11)</CODE> returns the total number of gradient evaluations.
+
+<p><CODE>options(14)</CODE> is the maximum number of iterations; default 100.
+
+<p><CODE>options(15)</CODE> is the precision in parameter space of the line search;
+default <CODE>1e-4</CODE>.
+
+<p><h2>
+Examples
+</h2>
+An example of 
+the use of the additional arguments is the minimization of an error
+function for a neural network:
+<PRE>
+
+w = quasinew('neterr', w, options, 'netgrad', net, x, t);
+</PRE>
+
+
+<p><h2>
+Algorithm
+</h2>
+
+The conjugate gradients algorithm constructs search
+directions <CODE>di</CODE> that are conjugate: i.e. <CODE>di*H*d(i-1) = 0</CODE>,
+where <CODE>H</CODE> is the Hessian matrix.  This means that minimising along
+<CODE>di</CODE> does not undo the effect of minimising along the previous
+direction. The Polak-Ribiere formula is used to calculate new search
+directions. The Hessian is not calculated, so there is only an
+<CODE>O(W)</CODE> storage requirement (where <CODE>W</CODE> is the number of
+parameters).  However, relatively accurate line searches must be used
+(default is <CODE>1e-04</CODE>).
+
+<p><h2>
+See Also
+</h2>
+<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>
+<b>Pages:</b>
+<a href="index.htm">Index</a>
+<hr>
+<p>Copyright (c) Ian T Nabney (1996-9)
+
+
+</body>
+</html>
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