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

Version:

$Id: ContinuedFraction.java 1244107 2012-02-14 16:17:55Z erans $

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	ContinuedFraction() Default constructor.

Method Summary

Methods

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.

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 equations 14-17 of:

• Eric W. Weisstein. "Continued Fraction." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ContinuedFraction.html

The recurrence relationship defined in those equations can result in very large intermediate results which can result in numerical overflow. As a means to combat these overflow conditions, the intermediate results are scaled whenever they threaten to become numerically unstable.

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.