org.apache.commons.numbers.fraction

Class ContinuedFraction

java.lang.Object

org.apache.commons.numbers.fraction.ContinuedFraction

public abstract class ContinuedFraction
extends Object

Provides a generic means to evaluate continued fractions. Subclasses must provide the a and b coefficients to evaluate the continued fraction.

Constructor Summary

Constructors

Constructor and Description
ContinuedFraction()

Method Summary

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

public ContinuedFraction()

Method Detail

getA

protected abstract double getA(int n,
                               double x)

Defines the n-th "a" coefficient of the continued fraction.

Parameters:

n - Index of the coefficient to retrieve.

x - Evaluation point.

Returns:

the coefficient an.

getB

protected abstract double getB(int n,
                               double x)

Defines the n-th "b" coefficient of the continued fraction.

Parameters:

n - Index of the coefficient to retrieve.

x - Evaluation point.

Returns:

the coefficient bn.

evaluate

public double evaluate(double x)

Evaluates the continued fraction.

Parameters:

x - Point at which to evaluate the continued fraction.

Returns:

the value of the continued fraction evaluated at x.

Throws:

ArithmeticException - if the algorithm fails to converge.

ArithmeticException - if the maximal number of iterations is reached before the expected convergence is achieved.

See Also:

evaluate(double,double,int)

evaluate

public double evaluate(double x,
                       double epsilon)

Evaluates the continued fraction.

Parameters:

x - the evaluation point.

epsilon - Maximum error allowed.

Returns:

the value of the continued fraction evaluated at x.

Throws:

ArithmeticException - if the algorithm fails to converge.

ArithmeticException - if the maximal number of iterations is reached before the expected convergence is achieved.

See Also:

evaluate(double,double,int)

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 iterations.

Returns:

the value of the continued fraction evaluated at x.

Throws:

ArithmeticException - if the algorithm fails to converge.

ArithmeticException - if the maximal number of iterations is reached before the expected convergence is achieved.

See Also:

evaluate(double,double,int)

evaluate

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

Evaluates the continued fraction.

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

Parameters:

x - Point at which to evaluate the continued fraction.

epsilon - Maximum error allowed.

maxIterations - Maximum number of iterations.

Returns:

the value of the continued fraction evaluated at x.

Throws:

ArithmeticException - if the algorithm fails to converge.

ArithmeticException - if the maximal number of iterations is reached before the expected convergence is achieved.