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| <?php
| require_once "../Matrix.php";
| /*
| * @package JAMA
| * @author Michael Bommarito
| * @author Paul Meagher
| * @version 0.1
| *
| * Function to fit an order n polynomial function through
| * a series of x-y data points using least squares.
| *
| * @param $X array x values
| * @param $Y array y values
| * @param $n int order of polynomial to be used for fitting
| * @returns array $coeffs of polynomial coefficients
| * Pre-Conditions: the system is not underdetermined: sizeof($X) > $n+1
| */
| function polyfit($X, $Y, $n) {
| for ($i = 0; $i < sizeof($X); ++$i)
| for ($j = 0; $j <= $n; ++$j)
| $A[$i][$j] = pow($X[$i], $j);
| for ($i=0; $i < sizeof($Y); ++$i)
| $B[$i] = array($Y[$i]);
| $matrixA = new Matrix($A);
| $matrixB = new Matrix($B);
| $C = $matrixA->solve($matrixB);
| return $C->getMatrix(0, $n, 0, 1);
| }
|
| function printpoly( $C = null ) {
| for($i = $C->m - 1; $i >= 0; --$i) {
| $r = $C->get($i, 0);
| if ( abs($r) <= pow(10, -9) )
| $r = 0;
| if ($i == $C->m - 1)
| echo $r . "x<sup>$i</sup>";
| else if ($i < $C->m - 1)
| echo " + " . $r . "x<sup>$i</sup>";
| else if ($i == 0)
| echo " + " . $r;
| }
| }
|
| $X = array(0,1,2,3,4,5);
| $Y = array(4,3,12,67,228, 579);
| $points = new Matrix(array($X, $Y));
| $points->toHTML();
| printpoly(polyfit($X, $Y, 4));
|
| echo '<hr />';
|
| $X = array(0,1,2,3,4,5);
| $Y = array(1,2,5,10,17, 26);
| $points = new Matrix(array($X, $Y));
| $points->toHTML();
| printpoly(polyfit($X, $Y, 2));
|
| echo '<hr />';
|
| $X = array(0,1,2,3,4,5,6);
| $Y = array(-90,-104,-178,-252,-26, 1160, 4446);
| $points = new Matrix(array($X, $Y));
| $points->toHTML();
| printpoly(polyfit($X, $Y, 5));
|
| echo '<hr />';
|
| $X = array(0,1,2,3,4);
| $Y = array(mt_rand(0, 10), mt_rand(40, 80), mt_rand(240, 400), mt_rand(1800, 2215), mt_rand(8000, 9000));
| $points = new Matrix(array($X, $Y));
| $points->toHTML();
| printpoly(polyfit($X, $Y, 3));
| ?>
|
|
