LagrangeInterpolation Class Reference

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. More...

Collaboration diagram for LagrangeInterpolation:

Public Member Functions
	findPolynomialFactors ($x, $y)
	findPolynomialFactors ($x, $y)

Detailed Description

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.

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 Also

http://geosoft.no/software/lagrange/LagrangeInterpolation.java.html

Author

Jacob Dreyer

Paul Meagher (port to PHP and minor changes)

Parameters

x[]	float
y[]	float

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 Also

http://geosoft.no/software/lagrange/LagrangeInterpolation.java.html

http://source.freehep.org/jcvsweb/ilc/LCSIM/wdview/lcsim/src/org/lcsim/fit/polynomial/PolynomialFitter.java

Author

Jacob Dreyer

Paul Meagher (port to PHP and minor changes)

Parameters

x[]	float
y[]	float

Definition at line 21 of file LagrangeInterpolation.php.

Member Function Documentation

LagrangeInterpolation::findPolynomialFactors	(		$x,
			$y
	)

Definition at line 23 of file LagrangeInterpolation.php.

References $data, $n, $x, and $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()

LagrangeInterpolation::findPolynomialFactors	(		$x,
			$y
	)

Definition at line 24 of file LagrangeInterpolation2.php.

References $data, $n, $x, and $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()

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The documentation for this class was generated from the following files:

• Services/Excel/classes/PHPExcel/Shared/JAMA/examples/LagrangeInterpolation.php
• Services/Excel/classes/PHPExcel/Shared/JAMA/examples/LagrangeInterpolation2.php