/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math.special;
import org.apache.commons.math.util.ContinuedFraction;
import org.apache.commons.math.util.FastMath;
/**
* This is a utility class that provides computation methods related to the
* Beta family of functions.
*
* @version $Id: Beta.java 1131229 2011-06-03 20:49:25Z luc $
*/
public class Beta {
/** Maximum allowed numerical error. */
private static final double DEFAULT_EPSILON = 10e-15;
/**
* Default constructor. Prohibit instantiation.
*/
private Beta() {}
/**
* Returns the
* <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
* regularized beta function</a> I(x, a, b).
*
* @param x Value.
* @param a Parameter {@code a}.
* @param b Parameter {@code b}.
* @return the regularized beta function I(x, a, b).
* @throws org.apache.commons.math.exception.MaxCountExceededException
* if the algorithm fails to converge.
*/
public static double regularizedBeta(double x, double a, double b) {
return regularizedBeta(x, a, b, DEFAULT_EPSILON, Integer.MAX_VALUE);
}
/**
* Returns the
* <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
* regularized beta function</a> I(x, a, b).
*
* @param x Value.
* @param a Parameter {@code a}.
* @param b Parameter {@code 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 org.apache.commons.math.exception.MaxCountExceededException
* if the algorithm fails to converge.
*/
public static double regularizedBeta(double x,
double a, double b,
double epsilon) {
return regularizedBeta(x, a, b, epsilon, Integer.MAX_VALUE);
}
/**
* Returns the regularized beta function I(x, a, b).
*
* @param x the value.
* @param a Parameter {@code a}.
* @param b Parameter {@code b}.
* @param maxIterations Maximum number of "iterations" to complete.
* @return the regularized beta function I(x, a, b)
* @throws org.apache.commons.math.exception.MaxCountExceededException
* if the algorithm fails to converge.
*/
public static double regularizedBeta(double x,
double a, double b,
int maxIterations) {
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 the value.
* @param a Parameter {@code a}.
* @param b Parameter {@code 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 org.apache.commons.math.exception.MaxCountExceededException
* if the algorithm fails to converge.
*/
public static double regularizedBeta(double x,
final double a, final double b,
double epsilon, int maxIterations) {
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 + 2.0)) {
ret = 1.0 - regularizedBeta(1.0 - x, b, a, epsilon, maxIterations);
} else {
ContinuedFraction fraction = new ContinuedFraction() {
@Override
protected double getB(int n, double x) {
double ret;
double m;
if (n % 2 == 0) { // even
m = n / 2.0;
ret = (m * (b - m) * x) /
((a + (2 * m) - 1) * (a + (2 * m)));
} else {
m = (n - 1.0) / 2.0;
ret = -((a + m) * (a + b + m) * x) /
((a + (2 * m)) * (a + (2 * m) + 1.0));
}
return ret;
}
@Override
protected double getA(int n, double x) {
return 1.0;
}
};
ret = FastMath.exp((a * FastMath.log(x)) + (b * FastMath.log(1.0 - x)) -
FastMath.log(a) - logBeta(a, b, epsilon, maxIterations)) *
1.0 / fraction.evaluate(x, epsilon, maxIterations);
}
return ret;
}
/**
* Returns the natural logarithm of the beta function B(a, b).
*
* @param a Parameter {@code a}.
* @param b Parameter {@code 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 Parameter {@code a}.
* @param b Parameter {@code 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;
}
}