NAME

    Math::Amoeba - Multidimensional Function Minimisation

SYNOPSIS

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

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.

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 and the maximum number of iterations to be taken. It returns an array consisting of a reference to the function parameters at the minimum and the value there.

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 and the maximum number of iterations to be taken. It returns an array consisting of a reference to the function parameters at the minimum and the value there.

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.

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

HISTORY

$Log: Amoeba.pm,v $ Revision 1.2 1995/12/24 12:37:46 willijar General fixup. Added documentation.

BUGS

If the function value converges to exactly zero then the condition for convergence fails and maximum iterations will be exceeded or there will be a divide by zero error. There is no obvious way to test for convergence in this case however adding 1 onto the function value gives expected behaviour. i.e. replace '\&afunc' with 'sub { 1+afunc(@_); }' when calling the routines.

Let me know.

AUTHOR

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

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.