net.sf.doodleproject.numerics4j.continuedfraction
Class ContinuedFraction

java.lang.Object
  net.sf.doodleproject.numerics4j.IterativeMethod
      net.sf.doodleproject.numerics4j.continuedfraction.ContinuedFraction

public abstract class ContinuedFraction
extends IterativeMethod

This class provides the means to evaluate continued fractions (1). To create a continued fraction, authors subclass this class and provided concrete a and b coefficient methods.

For example, this is the continued fraction for the exponential function defined by (2):

 ContinuedFraction exponential = new ContinuedFraction() {
     public double getA(int n, double x) {
         if (n == 0) {
             return 1.0;
         } else if (n % 2 == 0) { // even
             return 2.0;
         } else { // odd
             return n;
         }
     }
    
     public double getB(int n, double x) {
         if (n % 2 == 0) { // even
             return x;
         } else { // odd
             return -x;
         }
 }
 

References:

1. Eric W. Weisstein. "Continued Fraction." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ContinuedFraction.html
2. Exponential Function: Continued Fraction Representation. http://functions.wolfram.com/01.03.10.0001.01

Version:

$Revision: 1.2 $ $Date: 2007/10/25 04:44:21 $

Nested Class Summary

(package private) class

ContinuedFraction.IterativeState The internal state used during continued fraction evaluation.

Constructor Summary

protected	ContinuedFraction() Default constructor.
protected	ContinuedFraction(int iterations, double error) Create a continued fraction with the given number of maximum iterations and maximum relative error.

Method Summary

double	evaluate(double x) Evaluate this continued fraction at the given value.
protected abstract double	getA(int n, double x) Access the n-th a coefficient.
protected abstract double	getB(int n, double x) Access the n-th b coefficient.

Methods inherited from class net.sf.doodleproject.numerics4j.IterativeMethod

getMaximumIterations, getMaximumRelativeError, iterate, setMaximumIterations, setMaximumRelativeError

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.

ContinuedFraction

protected ContinuedFraction(int iterations,
                            double error)

Create a continued fraction with the given number of maximum iterations and maximum relative error.

Parameters:

iterations - maximum number of iterations.

error - maximum relative error.

Method Detail

evaluate

public double evaluate(double x)
                throws NumericException

Evaluate this continued fraction at the given value.

Parameters:

x - the point of evalutation.

Returns:

the value of this continued fraction evaluated at x.

Throws:

NumericException - if the continued fraction could not be evaluated.

getA

protected abstract double getA(int n,
                               double x)

Access the n-th a coefficient.

Parameters:

n - the coefficient index.

x - the continued fraction evaluation point.

Returns:

the n-th a coefficient.

getB

protected abstract double getB(int n,
                               double x)

Access the n-th b coefficient.

Parameters:

n - the coefficient index.

x - the continued fraction evaluation point.

Returns:

the n-th b coefficient.