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<?php
require_once "../Matrix.php";
/**
* Given n points (x0,y0)...(xn-1,yn-1), the following method 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
* @see http://source.freehep.org/jcvsweb/ilc/LCSIM/wdview/lcsim/src/org/lcsim/fit/polynomial/PolynomialFitter.java
* @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 />";
}
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