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.\" ========================================================================
.\"
.IX Title "Math::Amoeba 3pm"
.TH Math::Amoeba 3pm "2023-01-03" "perl v5.36.0" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
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.SH "NAME"
.Vb 1
\&    Math::Amoeba \- Multidimensional Function Minimisation
.Ve
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 5
\&    use Math::Amoeba qw(ConstructVertices EvaluateVertices Amoeba MinimiseND);
\&    my ($vertice,$y)=MinimiseND(\e@guess,\e@scales,\e&func,$tol,$itmax,$verbose);
\&    my @vertices=ConstructVertices(\e@vector,\e@offsets);
\&    my @y=EvaluateVertices(\e@vertices,\e&func);
\&    my ($vertice,$y)=Amoeba(\e@vertices,\e@y,\e&func,$tol,$itmax,$verbose);
.Ve
.SH "DESCRIPTION"
.IX Header "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.
.PP
Arrays and the function are passed by reference to the routines.
.ie n .IP """MinimiseND""" 4
.el .IP "\f(CWMinimiseND\fR" 4
.IX Item "MinimiseND"
The simplest use is the \fBMinimiseND\fR 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 \s-1ON\s0). 
It returns an array consisting of a reference to the function parameters 
at the minimum and the value there.
.ie n .IP """Amoeba""" 4
.el .IP "\f(CWAmoeba\fR" 4
.IX Item "Amoeba"
The \fBAmoeba\fR 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 \s-1ON\s0). 
It returns an array consisting of a reference to the function parameters 
at the minimum and the value there.
.ie n .IP """ConstructVertices""" 4
.el .IP "\f(CWConstructVertices\fR" 4
.IX Item "ConstructVertices"
The \fBConstructVertices\fR is used by \fBMinimiseND\fR to construct the
initial vertices for \fBAmoeba\fR as the initial guess plus the parameter
scale parameters as vectors along the parameter axis.
.ie n .IP """EvaluateVertices""" 4
.el .IP "\f(CWEvaluateVertices\fR" 4
.IX Item "EvaluateVertices"
The \fBEvaluateVertices\fR takes these set of vertices, calling the
function for each one and returning the vector of results.
.SH "EXAMPLE"
.IX Header "EXAMPLE"
.Vb 10
\&    use Math::Amoeba qw(MinimiseND);
\&    sub afunc {
\&      my ($a,$b)=@_;
\&      print "$a\et$b\en";
\&      return ($a\-7)**2+($b+3)**2;
\&    }
\&    my @guess=(1,1);
\&    my @scale=(1,1);
\&    ($p,$y)=MinimiseND(\e@guess,\e@scale,\e&afunc,1e\-7,100);
\&    print "(",join(\*(Aq,\*(Aq,@{$p}),")=$y\en";
.Ve
.PP
produces the output
.PP
(6.99978191653352,\-2.99981241563247)=1.00000008274829
.SH "LICENSE"
.IX Header "LICENSE"
\&\s-1PERL\s0
.SH "HISTORY"
.IX Header "HISTORY"
See \*(L"\s-1REAME\*(R".\s0
.SH "BUGS"
.IX Header "BUGS"
Let me know.
.SH "AUTHOR"
.IX Header "AUTHOR"
John A.R. Williams <J.A.R.Williams@aston.ac.uk>
.PP
Tom Chau <tom@cpan.org>
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\*(L"Numerical Recipies: The Art of Scientific Computing\*(R"
W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling.
Cambridge University Press. \s-1ISBN 0 521 30811 9.\s0
.SH "COPYRIGHT"
.IX Header "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.
.PP
Since 2005, this module was co-developed with Tom.