org.jscience.mathematics.analysis.polynomials
Class JacobiDoublePolynomialFactory

java.lang.Object
  extended by org.jscience.mathematics.analysis.polynomials.OrthogonalDoublePolynomialFactory
      extended by 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)