| /* |
| * 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.MathException; |
| 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 $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ |
| */ |
| public class Beta { |
| |
| /** Maximum allowed numerical error. */ |
| private static final double DEFAULT_EPSILON = 10e-15; |
| |
| /** |
| * Default constructor. Prohibit instantiation. |
| */ |
| private Beta() { |
| super(); |
| } |
| |
| /** |
| * Returns the |
| * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"> |
| * regularized beta function</a> I(x, a, b). |
| * |
| * @param x the value. |
| * @param a the a parameter. |
| * @param b the b parameter. |
| * @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 |
| * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"> |
| * regularized beta function</a> I(x, a, b). |
| * |
| * @param x the value. |
| * @param a the a parameter. |
| * @param b the b parameter. |
| * @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 the value. |
| * @param a the a parameter. |
| * @param b the b parameter. |
| * @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 the value. |
| * @param a the a parameter. |
| * @param b the b parameter. |
| * @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 + 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 the a parameter. |
| * @param b the b parameter. |
| * @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 the a parameter. |
| * @param b the b parameter. |
| * @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; |
| } |
| } |