vec_math
Class Legendre

java.lang.Object
  vec_math.RecursivePolynom
      vec_math.Legendre

All Implemented Interfaces:

Derivative, Function

public class Legendre
extends RecursivePolynom
implements Derivative

The recursive formular for the Legendre polynomials. Start the recursion with i=0.

Nested Class Summary

static class	Legendre.Calc
static class	Legendre.Print

Nested classes/interfaces inherited from class vec_math.RecursivePolynom

RecursivePolynom.Constant, RecursivePolynom.Linear

Constructor Summary

Legendre(double[] c, double min, double max)
The coefficients of the Legendre polynomial must at least suffice for a linear relation.

Method Summary

double	derivative(double x) The first derivative of the Legendre polynomial with order n is defined as: (1-x&pow2;)P'_n(x)=(n+1)*x*P_n(x)-(n+1)*P_n+1(x)
static Derivative	ofOrder(int n) Returns the function that is the sole Legendre polynomial of the given order.
protected double	recursion(int o, double norm, double xm1, double xm2) The recursion for the Legendre polynomials is

Methods inherited from class vec_math.RecursivePolynom

evaluate, getCoefficient, getOrder, normalize, toString

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface vec_math.Function

evaluate

Constructor Detail

Legendre

public Legendre(double[] c,
                double min,
                double max)

The coefficients of the Legendre polynomial must at least suffice for a linear relation. The min and max define the range of allowed parameter space.

Method Detail

recursion

protected double recursion(int o,
                           double norm,
                           double xm1,
                           double xm2)

The recursion for the Legendre polynomials is

 x_i = 1/i*((2i-1)*norm*x_i-1-(i-1)*x_i-2), i >= 2
 

Specified by:

recursion in class RecursivePolynom

derivative

public double derivative(double x)

The first derivative of the Legendre polynomial with order n is defined as: (1-x&pow2;)P'_n(x)=(n+1)*x*P_n(x)-(n+1)*P_n+1(x)

Specified by:

derivative in interface Derivative

ofOrder

public static Derivative ofOrder(int n)

Returns the function that is the sole Legendre polynomial of the given order.