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# Source for file LagrangeInterpolation.php Documentation is available at LagrangeInterpolation.php <?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 />"; } Documentation generated on Mon, 11 Jan 2010 08:11:49 +0100 by phpDocumentor 1.4.1