Simplex(x)     User Contributed Perl Documentation     Simplex(x)



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

SYNOPSIS
        use PDL::Opt::Simplex;

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


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

       $init is a 1D vector holding the initial values of the N
       fitted parameters, $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 = 1e-6

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

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

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

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

FUNCTIONS
       simplex

       Simplex optimization routine

        ($optimum,$ssize) = 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 work. Use genetic algorithms or simu-
       lated annealing or conjugate gradient or momentum gradient
       descent.

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

SEE ALSO
       Ron Shaffer's chemometrics web page and references
       therein: "http://chem1.nrl.navy.mil/~shaf-
       fer/chemoweb.html".

       Numerical Recipes (bla bla bla XXX ref).

       The demonstration (Examples/Simplex/tsimp.pl and
       tsimp2.pl).

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



perl v5.6.1                 2000-05-30                 Simplex(x)