org.apache.commons.math3.util

Class ContinuedFraction

java.lang.Object

org.apache.commons.math3.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

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.

Methods inherited from class java.lang.Object

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

Method Detail

evaluate

public double evaluate(double x)
                throws ConvergenceException

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)
                throws ConvergenceException

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)
                throws ConvergenceException,
                       MaxCountExceededException

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)
                throws ConvergenceException,
                       MaxCountExceededException

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