org.jscience.mathematics.analysis.polynomials
Class JacobiDoublePolynomialFactory

java.lang.Object
  org.jscience.mathematics.analysis.polynomials.OrthogonalDoublePolynomialFactory
      org.jscience.mathematics.analysis.polynomials.JacobiDoublePolynomialFactory

All Implemented Interfaces:

OrthogonalPolynomialFactory

Direct Known Subclasses:

SecondKindChebyshevDoublePolynomialFactory

public class JacobiDoublePolynomialFactory
extends OrthogonalDoublePolynomialFactory

This class implements Jacobi polynomials.

Jacobi polynomials can be defined by the following recurrence relations:

  T0(X)   = 1
  T1(X)   = [2(a+1)+(a+b+2)(x-1)]/2
  2(n+1)(n+a+b+1)(2n+a+b)Tn+1(X) = [(2n+a+b+1)(a2-b2)+P(2n+a+b,3)X] Tn(X) - 2(n+a)(n+b)(2n+a+b+2)Tn-1(X)
 

P(x,y) stands for Pochhammer series, see org.jscience.mathematics.series.PochhammerSeries.

Constructor Summary

JacobiDoublePolynomialFactory(double a, double b)

Method Summary

double	getA()
double	getB()
Polynomial[]	getFirstTermsPolynomials() Initialize the recurrence coefficients for degree 0 and 1.
DoublePolynomial	getOrthogonalPolynomial(int degree) Simple constructor.
Field.Member[]	getRecurrenceCoefficients(int k) Initialize the recurrence coefficients.

Methods inherited from class org.jscience.mathematics.analysis.polynomials.OrthogonalDoublePolynomialFactory

getOrthogonalPolynomialCoefficients

Methods inherited from class java.lang.Object

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

Constructor Detail

JacobiDoublePolynomialFactory

public JacobiDoublePolynomialFactory(double a,
                                     double b)

Method Detail

getA

public double getA()

getB

public double getB()

getOrthogonalPolynomial

public DoublePolynomial getOrthogonalPolynomial(int degree)

Simple constructor. Build a degree d Chebyshev polynomial

Specified by:

getOrthogonalPolynomial in interface OrthogonalPolynomialFactory

Specified by:

getOrthogonalPolynomial in class OrthogonalDoublePolynomialFactory

Parameters:

degree - degree of the polynomial

Returns:

DOCUMENT ME!

getFirstTermsPolynomials

public Polynomial[] getFirstTermsPolynomials()

Initialize the recurrence coefficients for degree 0 and 1.

Specified by:

getFirstTermsPolynomials in interface OrthogonalPolynomialFactory

Specified by:

getFirstTermsPolynomials in class OrthogonalDoublePolynomialFactory

Returns:

an array which contains the coefficients for degree 0 and 1

getRecurrenceCoefficients

public Field.Member[] getRecurrenceCoefficients(int k)

Initialize the recurrence coefficients. The recurrence relation is 2(n+1)(n+a+b+1)(2n+a+b)Tn+1(X) = [(2n+a+b+1)(a2-b2)+P(2n+a+b,3)X] Tn(X) - 2(n+a)(n+b)(2n+a+b+2)Tn-1(X)

Specified by:

getRecurrenceCoefficients in interface OrthogonalPolynomialFactory

Specified by:

getRecurrenceCoefficients in class OrthogonalDoublePolynomialFactory

Parameters:

k - index of the current step

Returns:

a double array of 3 elements: b2k = double[0] coefficient to initialize (b2k = a2k / a1k) b3k = double[1] coefficient to initialize (b3k = a3k / a1k) b4k = double[2] coefficient to initialize (b4k = a4k / a1k)