fr.cnes.sirius.patrius.math.util

Class ContinuedFraction

java.lang.Object

fr.cnes.sirius.patrius.math.util.ContinuedFraction

public abstract class ContinuedFraction
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

Version:

$Id: ContinuedFraction.java 18108 2017-10-04 06:45:27Z bignon $

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	ContinuedFraction() Default constructor.

Method Summary

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

ContinuedFraction

protected ContinuedFraction()

Default constructor.

Method Detail

getA

protected abstract double getA(int n,
                               double 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.

Parameters:

n - the coefficient index to retrieve.

x - the evaluation point.

Returns:

the n-th a coefficient.

getB

protected abstract double getB(int n,
                               double 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.

Parameters:

n - the coefficient index to retrieve.

x - the evaluation point.

Returns:

the n-th b coefficient.

evaluate

public double evaluate(double x)

Evaluates the continued fraction at the value x.

Parameters:

x - the evaluation point.

Returns:

the value of the continued fraction evaluated at x.

Throws:

ConvergenceException - if the algorithm fails to converge.

evaluate

public double evaluate(double x,
                       double epsilon)

Evaluates the continued fraction at the value x.

Parameters:

x - the evaluation point.

epsilon - maximum error allowed.

Returns:

the value of the continued fraction evaluated at x.

Throws:

ConvergenceException - if the algorithm fails to converge.

evaluate

public double evaluate(double x,
                       int maxIterations)

Evaluates the continued fraction at the value x.

Parameters:

x - the evaluation point.

maxIterations - maximum number of convergents

Returns:

the value of the continued fraction evaluated at x.

Throws:

ConvergenceException - if the algorithm fails to converge.

MaxCountExceededException - if maximal number of iterations is reached

evaluate

public double evaluate(double x,
                       double epsilon,
                       int maxIterations)

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.

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:

ConvergenceException - if the algorithm fails to converge.

MaxCountExceededException - if maximal number of iterations is reached