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