LM(M)          User Contributed Perl Documentation          LM(M)



NAME
       PDL::Fit::LM -- Levenber-Marquardt fitting routine for PDL

DESCRIPTION
       This module provides fitting functions for PDL. Currently,
       only Levenberg-Marquardt fitting is implemented. Other
       procedures should be added as required. For a fairly con-
       cise overview on fitting see Numerical Recipes, chapter 15
       "Modeling of data".

SYNOPSIS
        use PDL::Fit::LM;
        $ym = lmfit $x, $y, $sig, \&expfunc, $a, {Maxiter => 300};


FUNCTIONS
       lmfit

       Levenberg-Marquardt fitting of a user supplied model func-
       tion

        ($ym,$a,$covar,$iters) =
             lmfit $x, $y, $sig, \&expfunc, $a, {Maxiter => 300, Eps => 1e-3};

       Options:

        Maxiter:  maximum number of iterations before giving up
        Eps:      convergence citerium for fit; success when normalized change
                  in chisquare smaller than Eps

       The user supplied sub routine reference should accept 4
       arguments

       o   a vector of independent values $x

       o   a vector of fitting parameters

       o   a vector of dependent variables that will be assigned
           upon return

       o   a matrix of partial derivatives with respect to the
           fitting parameters that will be assigned upon return

       As an example take this definition of a single exponential
       with 3 parameters (width, amplitude, offset):

        sub expdec {
          my ($x,$par,$ym,$dyda) = @_;
          my ($a,$b,$c) = map {$par->slice("($_)")} (0..2);
          my $arg = $x/$a;
          my $ex = exp($arg);
          $ym .= $b*$ex+$c;
          my (@dy) = map {$dyda->slice(",($_)")} (0..2);
          $dy[0] .= -$b*$ex*$arg/$a;
          $dy[1] .= $ex;
          $dy[2] .= 1;
        }

       Note usage of the ".=" operator for assignment

       In scalar context returns a vector of the fitted dependent
       variable. In list context returns fitted y-values, vector
       of fitted parameters, an estimate of the covariance matrix
       (as an indicator of goodness of fit) and number of itera-
       tions performed.

       tlmfit

       threaded version of Levenberg-Marquardt fitting routine
       mfit

        tlmfit $x, $y, float(t)->dummy(y), $na, float(t), float(1e-4),
              $ym=null, $afit=null, \&expdec;

       Signature:

        tlmfit(x(x);y(y);sig(g);a(a);iter();eps();[o] ym(m);[o] ao(o);
                  OtherPar => subref)

       a threaded version of "lmfit" by using perl threading.
       Direct threading in "lmfit" seemed difficult since we have
       an if condition in the iteration. In principle that can be
       worked around by using "where" but .... Send a threaded
       "lmfit" version if you work it out!

       Since we are using perl threading here speed is not really
       great but it is just convenient to have a threaded version
       for many applications (no explicit for-loops required,
       etc). Suffers from some of the current limitations of perl
       level threading.

BUGS
       Not known yet.

AUTHOR
       This file copyright (C) 1999, Christian Soeller
       (c.soeller@auckland.ac.nz).  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                 2001-06-17                      LM(M)