com.hedgehog.math.functions
Class LegendrePolynomialFunction

java.lang.Object
  com.hedgehog.HObject
      com.hedgehog.math.functions.Function
          com.hedgehog.math.functions.LegendrePolynomialFunction

All Implemented Interfaces:

java.lang.Comparable, java.util.Comparator

public class LegendrePolynomialFunction
extends Function

Title: LegendrePolynomialFunction - represents the Legendre polynomial function.<

Description: Legendre polynomial function.

Copyright: Copyright (c) Hedgehog Software 2007-2009.

Company: Hedgehog Software

Since:

1.0

Version:

1.1

Field Summary

protected int

n_order Order of polynomial.

Fields inherited from class com.hedgehog.math.functions.Function

method

Fields inherited from class com.hedgehog.HObject

mID, mName

Constructor Summary

LegendrePolynomialFunction()
Default constructor.

LegendrePolynomialFunction(int n)
Constructor.

LegendrePolynomialFunction(LegendrePolynomialFunction object)
Copy constructor.

Method Summary

double	derivative(int k, double x) Returns the kth derivative of Pn(x).
double	firstDerivative(double x) Returns the first derivative of Pn(x).
boolean	isValid() Returns logical-true if a valid object, else logical-false.
OneVariablePolynomial	legendrePolynomial() Returns the Legendre polynomials (default is linear).
java.util.Vector<HDouble>	rootsInIntervalAToB(double a, double b) Returns the roots of Pn(x)=0 in the interval [a:b] for n=2,4,6,8,10,12,14 and 16.
java.util.Vector<HDouble>	rootsInIntervalMinus1ToPlus1() Returns the Vector of roots of Pn(x)=0 in the interval [-1:+1] for n=1,...,10.
java.lang.String	toString() Returns a String representation of a LegendrePolynomialFunction object.
double	value(double x) Returns the value of a Legendre polynomial given x.

Methods inherited from class com.hedgehog.math.functions.Function

getMethod, setMethod

Methods inherited from class com.hedgehog.HObject

clone, compare, compareTo, copy, equals, getID, getName, hashCode, hasID, hasName, setID, setName

Methods inherited from class java.lang.Object

finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

n_order

protected int n_order

Order of polynomial.

Constructor Detail

LegendrePolynomialFunction

public LegendrePolynomialFunction()

Default constructor. Sets the order to 0.

LegendrePolynomialFunction

public LegendrePolynomialFunction(int n)
                           throws java.lang.IllegalArgumentException

Constructor. Sets the order to the specified value.

Parameters:

n - Order of polynomial.

Throws:

java.lang.IllegalArgumentException - Thrown if n<0.

LegendrePolynomialFunction

public LegendrePolynomialFunction(LegendrePolynomialFunction object)

Copy constructor.

Parameters:

object - Object to copy.

Method Detail

derivative

public double derivative(int k,
                         double x)

Returns the kth derivative of Pn(x).

Parameters:

k - Order of derivative.

x - Value to evaluate kth derivative.

Returns:

The derivative of Pn(x).

firstDerivative

public double firstDerivative(double x)

Returns the first derivative of Pn(x).

Parameters:

x - Value of x to evaluate first derivative

Returns:

The first derivative of Pn(x).

legendrePolynomial

public OneVariablePolynomial legendrePolynomial()
                                         throws java.lang.IllegalArgumentException

Returns the Legendre polynomials (default is linear).

Returns:

The Legendre polynomial.

Throws:

java.lang.IllegalArgumentException

rootsInIntervalMinus1ToPlus1

public java.util.Vector<HDouble> rootsInIntervalMinus1ToPlus1()

Returns the Vector of roots of Pn(x)=0 in the interval [-1:+1] for n=1,...,10.

Returns:

The Vector of roots of Pn(x)=0.

rootsInIntervalAToB

public java.util.Vector<HDouble> rootsInIntervalAToB(double a,
                                                     double b)

Returns the roots of Pn(x)=0 in the interval [a:b] for n=2,4,6,8,10,12,14 and 16.

Parameters:

a - Minimum interval value.

b - Maximum interval value.

Returns:

The Vector of roots.

value

public double value(double x)
             throws java.lang.IllegalArgumentException

Returns the value of a Legendre polynomial given x.

Parameters:

x - Value of x to evaluate polynomial.

Returns:

The evaluation of Pn(x).

Throws:

java.lang.IllegalArgumentException

isValid

public boolean isValid()

Returns logical-true if a valid object, else logical-false. Simply confirms that n_order > 0.

Specified by:

isValid in class Function

Returns:

Logical-true if a valid object, else logical-false.

toString

public java.lang.String toString()

Returns a String representation of a LegendrePolynomialFunction object.

Overrides:

toString in class Function

Returns:

A String representation of a LegendrePolynomialFunction object.