Daniel@0: Daniel@0: Daniel@0: Daniel@0: Netlab Reference Manual linemin Daniel@0: Daniel@0: Daniel@0: Daniel@0:

linemin Daniel@0:

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Daniel@0: Purpose Daniel@0:

Daniel@0: One dimensional minimization. Daniel@0: Daniel@0:

Daniel@0: Description Daniel@0:

Daniel@0: [x, options] = linemin(f, pt, dir, fpt, options) uses Brent's Daniel@0: algorithm to find the minimum of the function f(x) along the Daniel@0: line dir through the point pt. The function value at the Daniel@0: starting point is fpt. The point at which f has a local minimum Daniel@0: is returned as x. The function value at that point is returned Daniel@0: in options(8). Daniel@0: Daniel@0:

linemin(f, pt, dir, fpt, options, p1, p2, ...) allows Daniel@0: additional arguments to be passed to f(). Daniel@0: Daniel@0:

The optional parameters have the following interpretations. Daniel@0: Daniel@0:

options(1) is set to 1 to display error values. Daniel@0: Daniel@0:

options(2) is a measure of the absolute precision required for the value Daniel@0: of x at the solution. Daniel@0: Daniel@0:

options(3) is a measure of the precision required of the objective Daniel@0: function at the solution. Both this and the previous condition must be Daniel@0: satisfied for termination. Daniel@0: Daniel@0:

options(14) is the maximum number of iterations; default 100. Daniel@0: Daniel@0:

Daniel@0: Examples Daniel@0:

Daniel@0: An example of the use of this function to find the minimum of a function Daniel@0: f in the direction sd can be found in conjgrad Daniel@0:

Daniel@0: 
Daniel@0: x = linemin(f, xold, sd, fold, lineoptions);
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Daniel@0: Daniel@0: Daniel@0:

Daniel@0: Algorithm Daniel@0:

Daniel@0: Daniel@0: Brent's algorithm uses a mixture of quadratic interpolation and golden Daniel@0: section search to find the minimum of a function of a single variable once Daniel@0: it has been bracketed (which is done with minbrack). This is adapted Daniel@0: to minimize a function along a line. Daniel@0: This implementation Daniel@0: is based on that in Numerical Recipes. Daniel@0: Daniel@0:

Daniel@0: See Also Daniel@0:

Daniel@0: conjgrad, minbrack, quasinew

Daniel@0: Pages: Daniel@0: Index Daniel@0:

Daniel@0: