=head1 NAME PDL::Fit::Polynomial - routines for fitting with polynomials =head1 DESCRIPTION This module contains routines for doing simple polynomial fits to data =head1 SYNOPSIS $yfit = fitpoly1d $data; =head1 FUNCTIONS =head2 fitpoly1d =for ref Fit 1D polynomials to data using min chi^2 (least squares) =for usage Usage: ($yfit, [$coeffs]) = fitpoly1d [$xdata], $data, $order, [Options...] =for sig Signature: (x(n); y(n); [o]yfit(n); [o]coeffs(order)) Uses a standard matrix inversion method to do a least squares/min chi^2 polynomial fit to data. Order=2 is a linear fit (two parameters). Returns the fitted data and optionally the coefficients. One can thread over extra dimensions to do multiple fits (except the order can not be threaded over - i.e. it must be one fixed scalar number like "4"). The data is normalised internally to avoid overflows (using the mean of the abs value) which are common in large polynomial series but the returned fit, coeffs are in unnormalised units. =for example $yfit = fitpoly1d $data,2; # Least-squares line fit ($yfit, $coeffs) = fitpoly1d $x, $y, 4; # Fit a cubic $fitimage = fitpoly1d $image,3 # Fit a quadratic to each row of an image $myfit = fitpoly1d $line, 2, {Weights => $w}; # Weighted fit =for options Options: Weights Weights to use in fit, e.g. 1/$sigma**2 (default=1) =cut package PDL::Fit::Polynomial; @EXPORT_OK = qw( fitpoly1d ); %EXPORT_TAGS = (Func=>[@EXPORT_OK]); use PDL::Core; use PDL::Basic; use PDL::Exporter; @ISA = qw( PDL::Exporter ); use PDL::Options ':Func'; # use PDL::Slatec; # For matinv() use PDL::MatrixOps; # for inv(), using this instead of call to Slatec routine sub PDL::fitpoly1d { my $opthash = ref($_[-1]) eq "HASH" ? pop(@_) : {} ; my %opt = parse( { Weights=>ones(1) }, $opthash ) ; barf "Usage: fitpoly1d incorrect args\n" if $#_<1 or $#_ > 2; my ($x, $y, $order) = @_; if ($#_ == 1) { ($y, $order) = @_; $x = $y->xvals; } my $wt = $opt{Weights}; # Internally normalise data # means for each 1D data set my $xmean = (abs($x)->average)->dummy(0); # dummy for correct threading my $ymean = (abs($y)->average)->dummy(0); (my $tmp = $ymean->where($ymean == 0)) .= 1 if any $ymean == 0; ($tmp = $xmean->where($xmean == 0)) .= 1 if any $xmean == 0; my $y2 = $y / $ymean; my $x2 = $x / $xmean; # Do the fit my $pow = sequence($order); my $M = $x2->dummy(0) ** $pow; my $C = $M->xchg(0,1) x ($M * $wt->dummy(0)) ; my $Y = $M->xchg(0,1) x ($y2->dummy(0) * $wt->dummy(0)); # Fitted coefficients vector ## $a1 = matinv($C) x $Y; ## print "matinv: \$C = $C, \$Y = $Y, \$a1 = $a1\n"; my $a1 = inv($C) x $Y; # use inv() instead of matinv() to avoid Slatec dependency ## print "inv: \$C = $C, \$Y = $Y, \$a1 = $a1\n"; # Fitted data $yfit = ($M x $a1)->clump(2); # Remove first dim=1 $yfit *= $ymean; # Un-normalise if (wantarray) { my $coeff = $a1->clump(2); $coeff *= $ymean / ($xmean ** $pow); # Un-normalise return ($yfit, $coeff); } else{ return $yfit; } } *fitpoly1d = \&PDL::fitpoly1d; =head1 BUGS May not work too well for data with large dynamic range. =head1 SEE ALSO L<PDL::Slatec/"polyfit"> =head1 AUTHOR This file copyright (C) 1999, Karl Glazebrook (kgb@aaoepp.aao.gov.au). 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. =cut 1;