<?php
|
|
require_once "../Matrix.php";
|
|
/**
|
* Given n points (x0,y0)...(xn-1,yn-1), the following methid computes
|
* the polynomial factors of the n-1't degree polynomial passing through
|
* the n points.
|
*
|
* Example: Passing in three points (2,3) (1,4) and (3,7) will produce
|
* the results [2.5, -8.5, 10] which means that the points are on the
|
* curve y = 2.5x² - 8.5x + 10.
|
*
|
* @see http://geosoft.no/software/lagrange/LagrangeInterpolation.java.html
|
* @author Jacob Dreyer
|
* @author Paul Meagher (port to PHP and minor changes)
|
*
|
* @param x[] float
|
* @param y[] float
|
*/
|
class LagrangeInterpolation {
|
|
public function findPolynomialFactors($x, $y) {
|
$n = count($x);
|
|
$data = array(); // double[n][n];
|
$rhs = array(); // double[n];
|
|
for ($i = 0; $i < $n; ++$i) {
|
$v = 1;
|
for ($j = 0; $j < $n; ++$j) {
|
$data[$i][$n-$j-1] = $v;
|
$v *= $x[$i];
|
}
|
$rhs[$i] = $y[$i];
|
}
|
|
// Solve m * s = b
|
$m = new Matrix($data);
|
$b = new Matrix($rhs, $n);
|
|
$s = $m->solve($b);
|
|
return $s->getRowPackedCopy();
|
} // function findPolynomialFactors()
|
|
} // class LagrangeInterpolation
|
|
|
$x = array(2.0, 1.0, 3.0);
|
$y = array(3.0, 4.0, 7.0);
|
|
$li = new LagrangeInterpolation;
|
$f = $li->findPolynomialFactors($x, $y);
|
|
|
for ($i = 0; $i < 3; ++$i) {
|
echo $f[$i]."<br />";
|
}
|
