Package org.hipparchus.util

Class FieldContinuedFraction

java.lang.Object

org.hipparchus.util.FieldContinuedFraction

public abstract class FieldContinuedFraction
extends Object

Provides a generic means to evaluate continued fractions. Subclasses simply provided the a and b coefficients to evaluate the continued fraction.

References:

• Continued Fraction

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	FieldContinuedFraction()	Default constructor.

Method Summary

Modifier and Type	Method	Description
<T extends CalculusFieldElement<T>> T	evaluate(T x)	Evaluates the continued fraction at the value x.
<T extends CalculusFieldElement<T>> T	evaluate(T x, double epsilon)	Evaluates the continued fraction at the value x.
<T extends CalculusFieldElement<T>> T	evaluate(T x, double epsilon, int maxIterations)	Evaluates the continued fraction at the value x.
<T extends CalculusFieldElement<T>> T	evaluate(T x, int maxIterations)	Evaluates the continued fraction at the value x.
abstract <T extends CalculusFieldElement<T>> T	getA(int n, T x)	Access the n-th a coefficient of the continued fraction.
abstract <T extends CalculusFieldElement<T>> T	getB(int n, T x)	Access the n-th b coefficient of the continued fraction.

Methods inherited from class java.lang.Object

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

Constructor Detail

FieldContinuedFraction

protected FieldContinuedFraction()

Default constructor.

Method Detail

getA

public abstract <T extends CalculusFieldElement<T>> T getA(int n,
                                                           T x)

Access the n-th a coefficient of the continued fraction. Since a can be a function of the evaluation point, x, that is passed in as well.

Type Parameters:

T - type of the field elements.

Parameters:

n - the coefficient index to retrieve.

x - the evaluation point.

Returns:

the n-th a coefficient.

getB

public abstract <T extends CalculusFieldElement<T>> T getB(int n,
                                                           T x)

Access the n-th b coefficient of the continued fraction. Since b can be a function of the evaluation point, x, that is passed in as well.

Type Parameters:

T - type of the field elements.

Parameters:

n - the coefficient index to retrieve.

x - the evaluation point.

Returns:

the n-th b coefficient.

evaluate

public <T extends CalculusFieldElement<T>> T evaluate(T x)
                                               throws MathIllegalStateException

Evaluates the continued fraction at the value x.

Type Parameters:

T - type of the field elements.

Parameters:

x - the evaluation point.

Returns:

the value of the continued fraction evaluated at x.

Throws:

MathIllegalStateException - if the algorithm fails to converge.

evaluate

public <T extends CalculusFieldElement<T>> T evaluate(T x,
                                                      double epsilon)
                                               throws MathIllegalStateException

Evaluates the continued fraction at the value x.

Type Parameters:

T - type of the field elements.

Parameters:

x - the evaluation point.

epsilon - maximum error allowed.

Returns:

the value of the continued fraction evaluated at x.

Throws:

MathIllegalStateException - if the algorithm fails to converge.

evaluate

public <T extends CalculusFieldElement<T>> T evaluate(T x,
                                                      int maxIterations)
                                               throws MathIllegalStateException

Evaluates the continued fraction at the value x.

Type Parameters:

T - type of the field elements.

Parameters:

x - the evaluation point.

maxIterations - maximum number of convergents

Returns:

the value of the continued fraction evaluated at x.

Throws:

MathIllegalStateException - if the algorithm fails to converge.

MathIllegalStateException - if maximal number of iterations is reached

evaluate

public <T extends CalculusFieldElement<T>> T evaluate(T x,
                                                      double epsilon,
                                                      int maxIterations)
                                               throws MathIllegalStateException

Evaluates the continued fraction at the value x.

The implementation of this method is based on the modified Lentz algorithm as described on page 18 ff. in:

• I. J. Thompson, A. R. Barnett. "Coulomb and Bessel Functions of Complex Arguments and Order." http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf

Note: the implementation uses the terms a_i and b_i as defined in Continued Fraction @ MathWorld.

Type Parameters:

T - type of the field elements.

Parameters:

x - the evaluation point.

epsilon - maximum error allowed.

maxIterations - maximum number of convergents

Returns:

the value of the continued fraction evaluated at x.

Throws:

MathIllegalStateException - if the algorithm fails to converge.

MathIllegalStateException - if maximal number of iterations is reached