NAME=20
SYNOPSIS=20
DESCRIPTION=20
FUNCTIONS=20
- simplex=20
CAVEATS=20
SEE=20 ALSO=20
AUTHOR=20

NAME

PDL::Opt::Simplex -- Simplex optimization routines

SYNOPSIS

 use =
PDL::Opt::Simplex;

 ($optimum,$ssize) =3D simplex($init,$initsize,$minsize,
                 $maxiter,
                 sub {evaluate_func_at($_[0])},
                 sub {display_simplex($_[0])}
                 );

DESCRIPTION

This package implements the commonly used simplex optimization = algorithm. The=20 basic idea of the algorithm is to move a "simplex" of N+1 points in the=20 N-dimensional search space according to certain rules. The main benefit = of the=20 algorithm is that you do not need to calculate the derivatives of your=20 function.

$init is a 1D vector holding the initial values of the N fitted = parameters,=20 $optimum is a vector holding the final solution.

$initsize is the size of $init (more...)

$minsize is some sort of convergence criterion (more...) - e.g. = $minsize =3D=20 1e-6

The sub is assumed to understand more than 1 dimensions and = threading. Its=20 signature is 'inp(nparams); [ret]out()'. An example would be

    =
    sub evaluate_func_at {
                my($xv) =3D @_;
                my $x1 =3D $xv->slice("(0)");
                my $x2 =3D $xv->slice("(1)");
                return $x1**4 + ($x2-5)**4 + $x1*$x2;
        }

Here $xv is a vector holding the current values of the parameters = being=20 fitted which are then sliced out explicitly as $x1 and $x2.

$ssize gives a very very approximate estimate of how close we might = be - it=20 might be miles wrong. It is the euclidean distance between the best and = the=20 worst vertices. If it is not very small, the algorithm has not = converged.

FUNCTIONS

simplex

Simplex optimization routine

 ($optimum,$ssize) =3D =
simplex($init,$initsize,$minsize,
                 $maxiter,
                 sub {evaluate_func_at($_[0])},
                 sub {display_simplex($_[0])}
                 );

See module PDL::Opt::Simplex for more information.

CAVEATS

Do not use the simplex method if your function has local minima. It = will not=20 work. Use genetic algorithms or simulated annealing or conjugate = gradient or=20 momentum gradient descent.

They will not really work either but they are not guaranteed not to = work ;)=20 (if you have infinite time, simulated annealing is guaranteed to work = but only=20 after it has visited every point in your space).

AUTHOR

Copyright(C) 1997 Tuomas J. Lukka. All rights reserved. There is no = warranty.=20 You are allowed to redistribute this software / documentation under = certain=20 conditions. For details, see the file COPYING in the PDL distribution. = If this=20 file is separated from the PDL distribution, the copyright notice should = be=20 included in the file.