NAME

           Math::Amoeba - Multidimensional Function Minimisation

SYNOPSIS

           use Math::Amoeba qw(ConstructVertices EvaluateVertices Amoeba MinimiseND);
           my ($vertice,$y)=MinimiseND(\@guess,\@scales,\&func,$tol,$itmax,$verbose);
           my @vertices=ConstructVertices(\@vector,\@offsets);
           my @y=EvaluateVertices(\@vertices,\&func);
           my ($vertice,$y)=Amoeba(\@vertices,\@y,\&func,$tol,$itmax,$verbose);

DESCRIPTION

       This is an implimenation of the Downhill Simpex Method in Multidimensions (Nelder and
       Mead) for finding the (local) minimum of a function. Doing this in Perl makes it easy for
       that function to actually be the output of another program such as a simulator.

       Arrays and the function are passed by reference to the routines.

       "MinimiseND"
           The simplest use is the MinimiseND function. This takes a reference to an array of
           guess values for the parameters at the function minimum, a reference to an array of
           scales for these parameters (sensible ranges around the guess in which to look), a
           reference to the function, a convergence tolerence for the minimum, the maximum number
           of iterations to be taken and the verbose flag (default ON).  It returns an array
           consisting of a reference to the function parameters at the minimum and the value
           there.

       "Amoeba"
           The Amoeba function is the actual implimentation of the Downhill Simpex Method in
           Multidimensions. It takes a reference to an array of references to arrays which are
           the initial n+1 vertices (where n is the number of function parameters), a reference
           to the function valuation at these vertices, a reference to the function, a
           convergence tolerence for the minimum, the maximum number of iterations to be taken
           and the verbose flag (default ON).  It returns an array consisting of a reference to
           the function parameters at the minimum and the value there.

       "ConstructVertices"
           The ConstructVertices is used by MinimiseND to construct the initial vertices for
           Amoeba as the initial guess plus the parameter scale parameters as vectors along the
           parameter axis.

       "EvaluateVertices"
           The EvaluateVertices takes these set of vertices, calling the function for each one
           and returning the vector of results.

EXAMPLE

           use Math::Amoeba qw(MinimiseND);
           sub afunc {
             my ($a,$b)=@_;
             print "$a\t$b\n";
             return ($a-7)**2+($b+3)**2;
           }
           my @guess=(1,1);
           my @scale=(1,1);
           ($p,$y)=MinimiseND(\@guess,\@scale,\&afunc,1e-7,100);
           print "(",join(',',@{$p}),")=$y\n";

       produces the output

       (6.99978191653352,-2.99981241563247)=1.00000008274829

LICENSE

       PERL

HISTORY

       See "REAME".

BUGS

       Let me know.

AUTHOR

       John A.R. Williams <J.A.R.Williams@aston.ac.uk>

       Tom Chau <tom@cpan.org>

SEE ALSO

       "Numerical Recipies: The Art of Scientific Computing" W.H. Press, B.P. Flannery, S.A.
       Teukolsky, W.T. Vetterling.  Cambridge University Press. ISBN 0 521 30811 9.

COPYRIGHT

       Copyright (c) 1995 John A.R. Williams. All rights reserved.  This program is free
       software; you can redistribute it and/or modify it under the same terms as Perl itself.

       Since 2005, this module was co-developed with Tom.