Package 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.

The continued fraction uses the following form for the numerator (a) and denominator (b) coefficients:

              a1
 b0 + ------------------
      b1 +      a2
           -------------
           b2 +    a3
                --------
                b3 + ...
 

Subclasses must provide the a and b coefficients to evaluate the continued fraction.

This class allows evaluation of the fraction for a specified evaluation point x; the point can be used to express the values of the coefficients. Evaluation of a continued fraction from a generator of the coefficients can be performed using GeneralizedContinuedFraction. This may be preferred if the coefficients can be computed with updates to the previous coefficients.

Constructor Summary

Constructors

Constructor	Description
ContinuedFraction()	Create an instance.

Method Summary

Modifier and Type	Method	Description
double	evaluate(double x, double epsilon)	Evaluates the continued fraction.
double	evaluate(double x, double epsilon, int maxIterations)	Evaluates the continued fraction.
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()

Create an instance.

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,
                       double epsilon)

Evaluates the continued fraction.

Parameters:

x - the evaluation point.

epsilon - Maximum relative 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,
                       double epsilon,
                       int maxIterations)

Evaluates the continued fraction.

The implementation of this method is based on the modified Lentz algorithm as described on page 508 in:

• I. J. Thompson, A. R. Barnett (1986). "Coulomb and Bessel Functions of Complex Arguments and Order." Journal of Computational Physics 64, 490-509. https://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf

Parameters:

x - Point at which to evaluate the continued fraction.

epsilon - Maximum relative 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.