PDL::Fit::Polynomial - routines for fitting with polynomials

       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.

perl v5.40.1                                       2025-04-12                                    Polynomial(3pm)

       May not work too well for data with large dynamic range.

       This module contains routines for doing simple polynomial fits to data

fitpoly1d
       Fit 1D polynomials to data using min chi^2 (least squares)

        Usage: ($yfit, [$coeffs]) = fitpoly1d [$xdata], $data, $order, [Options...]

         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 (in ascending order of degree, unlike "polyval"
       in PDL::Math).

       One can broadcast over extra dimensions to do multiple fits (except the order can not be broadcasted 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.

         $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

         Options:
            Weights    Weights to use in fit, e.g. 1/$sigma**2 (default=1)

       PDL::Fit::Polynomial - routines for fitting with polynomials

       "polyfit" in PDL::Slatec

         $x = sequence(20)-10;
         $coeff_orig = cdouble(30,-2,3,-2); # order used in this module
         $y = 30-2*$x+3*$x**2-2*$x**3; # or: $y = polyval($coeff_orig->slice("-1:0"), $x->r2C);
         $y += ($x->grandom - 0.5) * 100;
         ($yfit, $coeff) = fitpoly1d($x,$y,4);
         use PDL::Graphics::Simple;
         $w = pgswin();
         $xi = zeroes(100)->xlinvals(-10,9);
         $yi = polyval($coeff->r2C->slice("-1:0"), $xi->r2C);
         $w->plot(with=>'points',$x,$y,
           with=>'points',$x,$yfit, with=>'line',$xi,$yi);

         $yfit = fitpoly1d $data,2; # Least-squares line fit
         ($yfit, $coeffs) = fitpoly1d $x, $y, 4; # Fit a cubic