org.apache.commons.math.util

Class ContinuedFraction

java.lang.Object

org.apache.commons.math.util.ContinuedFraction

public abstract class ContinuedFraction
extends java.lang.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 MathException

Evaluates the continued fraction at the value x.

Parameters:

x - the evaluation point.

Returns:

the value of the continued fraction evaluated at x.

Throws:

MathException - if the algorithm fails to converge.

evaluate

public double evaluate(double x,
                       double epsilon)
                throws MathException

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:

MathException - if the algorithm fails to converge.

evaluate

public double evaluate(double x,
                       int maxIterations)
                throws MathException

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:

MathException - if the algorithm fails to converge.

evaluate

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

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:

MathException - if the algorithm fails to converge.