jmathlib.toolbox.specfun._private
Class ContinuedFraction

java.lang.Object
  extended by jmathlib.toolbox.specfun._private.ContinuedFraction
All Implemented Interfaces:
java.io.Serializable

public abstract class ContinuedFraction
extends java.lang.Object
implements java.io.Serializable

Provides a generic means to evaluate continued fractions. Subclasses simply provided the a and b coefficients to evaluate the continued fraction.

References:

Version:
$Revision: 1.1 $ $Date: 2007/01/05 08:55:48 $
See Also:
Serialized Form

Field Summary
private static double DEFAULT_EPSILON
          Maximum allowed numerical error.
private static long serialVersionUID
          Serialization UID
 
Constructor Summary
protected ContinuedFraction()
          Default constructor.
 
Method Summary
 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
 

Field Detail

serialVersionUID

private static final long serialVersionUID
Serialization UID

See Also:
Constant Field Values

DEFAULT_EPSILON

private static final double DEFAULT_EPSILON
Maximum allowed numerical error.

See Also:
Constant Field Values
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 java.lang.Exception
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.
java.lang.Exception

evaluate

public double evaluate(double x,
                       double epsilon)
                throws java.lang.Exception
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.
java.lang.Exception

evaluate

public double evaluate(double x,
                       int maxIterations)
                throws java.lang.Exception
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.
java.lang.Exception

evaluate

public double evaluate(double x,
                       double epsilon,
                       int maxIterations)
                throws java.lang.Exception

Evaluates the continued fraction at the value x.

The implementation of this method is based on equations 14-17 of:

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.
java.lang.Exception

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