Simplex(3) User Contributed Perl Documentation Simplex(3)NAMEPDL::Opt::Simplex-- Simplex optimization routines
SYNOPSIS
use PDL::Opt::Simplex;
($optimum,$ssize,$optval) = simplex($init,$initsize,$minsize,
$maxiter,
sub {evaluate_func_at($_[0])},
sub {display_simplex($_[0])}
);
DESCRIPTION
This package implements the commonly used simplex optimization
algorithm. The 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 derivatives 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. $optval
is the evaluation of the final solution.
$initsize is the size of $init (more...)
$minsize is some sort of convergence criterion (more...) - e.g.
$minsize = 1e-6
The sub is assumed to understand more than 1 dimensions and threading.
Its signature is 'inp(nparams); [ret]out()'. An example would be
sub evaluate_func_at {
my($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 explicitly 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,$ssize,$optval) = 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 simulated annealing or
conjugate gradient or momentum gradient descent.
They will not really work either but they are not guaranteed not to
work ;) (if you have infinite time, simulated annealing is guaranteed
to work but only after it has visited every point in your space).
SEE ALSO
Ron Shaffer's chemometrics web page and references therein:
"http://chem1.nrl.navy.mil/~shaffer/chemoweb.html".
Numerical Recipes (bla bla bla XXX ref).
The demonstration (Examples/Simplex/tsimp.pl and tsimp2.pl).
AUTHORCopyright(C) 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 v5.14.1 2011-03-30 Simplex(3)