/* ====================================================================
* The Apache Software License, Version 1.1
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package org.apache.commons.math.special;
import java.io.Serializable;
import org.apache.commons.math.MathException;
import org.apache.commons.math.util.ContinuedFraction;
/**
* This is a utility class that provides computation methods related to the
* Beta family of functions.
*
* @version $Revision: 1.14 $ $Date: 2003/11/19 03:28:25 $
*/
public class Beta implements Serializable {
/** Maximum allowed numerical error. */
private static final double DEFAULT_EPSILON = 10e-9;
/**
* Default constructor. Prohibit instantiation.
*/
private Beta() {
super();
}
/**
* Returns the regularized beta function I(x, a, b).
*
* @param x ???
* @param a ???
* @param b ???
* @return the regularized beta function I(x, a, b)
* @throws MathException if the algorithm fails to converge.
*/
public static double regularizedBeta(double x, double a, double b)
throws MathException
{
return regularizedBeta(x, a, b, DEFAULT_EPSILON, Integer.MAX_VALUE);
}
/**
* Returns the regularized beta function I(x, a, b).
*
* @param x ???
* @param a ???
* @param b ???
* @param epsilon When the absolute value of the nth item in the
* series is less than epsilon the approximation ceases
* to calculate further elements in the series.
* @return the regularized beta function I(x, a, b)
* @throws MathException if the algorithm fails to converge.
*/
public static double regularizedBeta(double x, double a, double b,
double epsilon) throws MathException
{
return regularizedBeta(x, a, b, epsilon, Integer.MAX_VALUE);
}
/**
* Returns the regularized beta function I(x, a, b).
*
* @param x ???
* @param a ???
* @param b ???
* @param maxIterations Maximum number of "iterations" to complete.
* @return the regularized beta function I(x, a, b)
* @throws MathException if the algorithm fails to converge.
*/
public static double regularizedBeta(double x, double a, double b,
int maxIterations) throws MathException
{
return regularizedBeta(x, a, b, DEFAULT_EPSILON, maxIterations);
}
/**
* Returns the regularized beta function I(x, a, b).
*
* The implementation of this method is based on:
* <ul>
* <li>
* <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
* Regularized Beta Function</a>.</li>
* <li>
* <a href="http://functions.wolfram.com/06.21.10.0001.01">
* Regularized Beta Function</a>.</li>
* </ul>
*
* @param x ???
* @param a ???
* @param b ???
* @param epsilon When the absolute value of the nth item in the
* series is less than epsilon the approximation ceases
* to calculate further elements in the series.
* @param maxIterations Maximum number of "iterations" to complete.
* @return the regularized beta function I(x, a, b)
* @throws MathException if the algorithm fails to converge.
*/
public static double regularizedBeta(double x, final double a,
final double b, double epsilon, int maxIterations) throws MathException
{
double ret;
if (Double.isNaN(x) || Double.isNaN(a) || Double.isNaN(b) || (x < 0) ||
(x > 1) || (a <= 0.0) || (b <= 0.0))
{
ret = Double.NaN;
} else if (x > (a + 1.0) / (a + b + 1.0)) {
ret = 1.0 - regularizedBeta(1.0 - x, b, a, epsilon, maxIterations);
} else {
ContinuedFraction fraction = new ContinuedFraction() {
protected double getB(int n, double x) {
double ret;
double m;
switch (n) {
case 1 :
ret = 1.0;
break;
default :
if (n % 2 == 0) { // even
m = (n - 2.0) / 2.0;
ret = -((a + m) * (a + b + m) * x) /
((a + (2 * m)) * (a + (2 * m) + 1.0));
} else {
m = (n - 1.0) / 2.0;
ret = (m * (b - m) * x) /
((a + (2 * m) - 1) * (a + (2 * m)));
}
break;
}
return ret;
}
protected double getA(int n, double x) {
double ret;
switch (n) {
case 0 :
ret = 0.0;
break;
default :
ret = 1.0;
break;
}
return ret;
}
};
ret = Math.exp((a * Math.log(x)) + (b * Math.log(1.0 - x)) -
Math.log(a) - logBeta(a, b, epsilon, maxIterations)) *
fraction.evaluate(x, epsilon, maxIterations);
}
return ret;
}
/**
* Returns the natural logarithm of the beta function B(a, b).
*
* @param a ???
* @param b ???
* @return log(B(a, b))
*/
public static double logBeta(double a, double b) {
return logBeta(a, b, DEFAULT_EPSILON, Integer.MAX_VALUE);
}
/**
* Returns the natural logarithm of the beta function B(a, b).
*
* The implementation of this method is based on:
* <ul>
* <li><a href="http://mathworld.wolfram.com/BetaFunction.html">
* Beta Function</a>, equation (1).</li>
* </ul>
*
* @param a ???
* @param b ???
* @param epsilon When the absolute value of the nth item in the
* series is less than epsilon the approximation ceases
* to calculate further elements in the series.
* @param maxIterations Maximum number of "iterations" to complete.
* @return log(B(a, b))
*/
public static double logBeta(double a, double b, double epsilon,
int maxIterations) {
double ret;
if (Double.isNaN(a) || Double.isNaN(b) || (a <= 0.0) || (b <= 0.0)) {
ret = Double.NaN;
} else {
ret = Gamma.logGamma(a) + Gamma.logGamma(b) -
Gamma.logGamma(a + b);
}
return ret;
}
}