#! /usr/bin/perl

use strict;
use warnings;

sub lagrange {
#x is an array of x values, f is an array of function values, LC are the reduced lagrange coefficients.
	my @x = shift;
	my @f = shift;
	my ($i, $j);
	my @LC;
	my $point = @x;
	my $den = 1;
		for ($i=0; $i < $point; $i++) {
			for ($j = 0; $j < $point; $j++) {
				unless ($j == $i) {
							$den *= ($x[$i] - $x[$j]);
				}
			$LC[$i] = $f[$i]/$den;
			$den = 1;	
			}
		
		}

	return \@LC;
}

sub lageval {
	my @x = shift;
	my @LC = shift;
	my $x0 = shift;
	my $point = @x;
	my @mult;
	my $sum = 0;
	my ($i, $j);

	for($i=0; $i<$point; $i++) {
		$mult[$i] = 1;
	}

	for ($i=0; $i<$point;$i++) {
		for ($j = 0; $j<$point; $j++) {
			unless ($j == $i) {
				$mult[$i] *= $x0 - $x[$j];
			}
		}
	$sum += $mult[$i] * $LC[$i];
	
	}

	return $sum;
}

1;