org.apache.commons.math3.util

## Class 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:

• ### 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)
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:

Note: the implementation uses the terms ai and bi 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