Hi Gregory,
Here's a program that shows fitpoly1d in action. You may also be
interested in the subroutine pcoeff, which evaluates $coeffs for an
arbitrary iinput piddle of values.
Cheers,
Matt
#!/usr/bin/perl
#===============================================================================
# test_fitpoly1d
#===============================================================================
use strict;
use warnings;
use PDL;
use PDL::Fit::Polynomial;
use PDL::Graphics::PGPLOT;
dev("/xs",{Color=>1,AxisColour=>1, Linewidth=>1, WindowWidth=>8, Aspect=>1.0});
my $x = zeroes(20)->xlinvals(-1,5);
my $y = pow($x,2) + grandom($x)/5;
env (-1, 4, -1, 10);
# here's a parabola with some noise added to it
points $x, $y,{COLOR=>"YELLOW"};
# fit the data and return the coefficients and best y fit
my $order = 3;
my ($yfit, $coeffs) = fitpoly1d $x, $y, $order;
hold;
# green points are $yfit, which are the evaluation of $coeffs at $x
points $x, $yfit,{COLOR=>"GREEN"};
# if you want to evaluate the $coeffs at an arbitrary set of points, try
# this routine:
my $x_new = zeroes(100)->xlinvals(-1,5);
my $y_new = pcoeff($x_new, $coeffs);
line $x_new, $y_new, {COLOR=>"RED"};
sub pcoeff {
# pcoeff - take an N-D array of values, and a 1D set ofpolynomial
coefficients
# from fitpoly1d and return an N-D array with the calculated values
use strict;
my ($vals, $coeff) = @_;
# here is the x**0, x**1, x**2,.....
my $pow = $vals->dummy(0)**xvals($coeff);
# here is the C_0 , C_1, C_2, ....
my $a = $vals->dummy(0)*$coeff;
# result is C_0 x**0 + C_1 * x**1 + ....
my $result = ($pow*$coeff)->sumover;
return($result);
}
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