001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017 package org.apache.commons.math.special;
018
019 import org.apache.commons.math.MathException;
020 import org.apache.commons.math.util.ContinuedFraction;
021
022 /**
023 * This is a utility class that provides computation methods related to the
024 * Beta family of functions.
025 *
026 * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $
027 */
028 public class Beta {
029
030 /** Maximum allowed numerical error. */
031 private static final double DEFAULT_EPSILON = 10e-15;
032
033 /**
034 * Default constructor. Prohibit instantiation.
035 */
036 private Beta() {
037 super();
038 }
039
040 /**
041 * Returns the
042 * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
043 * regularized beta function</a> I(x, a, b).
044 *
045 * @param x the value.
046 * @param a the a parameter.
047 * @param b the b parameter.
048 * @return the regularized beta function I(x, a, b)
049 * @throws MathException if the algorithm fails to converge.
050 */
051 public static double regularizedBeta(double x, double a, double b)
052 throws MathException
053 {
054 return regularizedBeta(x, a, b, DEFAULT_EPSILON, Integer.MAX_VALUE);
055 }
056
057 /**
058 * Returns the
059 * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
060 * regularized beta function</a> I(x, a, b).
061 *
062 * @param x the value.
063 * @param a the a parameter.
064 * @param b the b parameter.
065 * @param epsilon When the absolute value of the nth item in the
066 * series is less than epsilon the approximation ceases
067 * to calculate further elements in the series.
068 * @return the regularized beta function I(x, a, b)
069 * @throws MathException if the algorithm fails to converge.
070 */
071 public static double regularizedBeta(double x, double a, double b,
072 double epsilon) throws MathException
073 {
074 return regularizedBeta(x, a, b, epsilon, Integer.MAX_VALUE);
075 }
076
077 /**
078 * Returns the regularized beta function I(x, a, b).
079 *
080 * @param x the value.
081 * @param a the a parameter.
082 * @param b the b parameter.
083 * @param maxIterations Maximum number of "iterations" to complete.
084 * @return the regularized beta function I(x, a, b)
085 * @throws MathException if the algorithm fails to converge.
086 */
087 public static double regularizedBeta(double x, double a, double b,
088 int maxIterations) throws MathException
089 {
090 return regularizedBeta(x, a, b, DEFAULT_EPSILON, maxIterations);
091 }
092
093 /**
094 * Returns the regularized beta function I(x, a, b).
095 *
096 * The implementation of this method is based on:
097 * <ul>
098 * <li>
099 * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
100 * Regularized Beta Function</a>.</li>
101 * <li>
102 * <a href="http://functions.wolfram.com/06.21.10.0001.01">
103 * Regularized Beta Function</a>.</li>
104 * </ul>
105 *
106 * @param x the value.
107 * @param a the a parameter.
108 * @param b the b parameter.
109 * @param epsilon When the absolute value of the nth item in the
110 * series is less than epsilon the approximation ceases
111 * to calculate further elements in the series.
112 * @param maxIterations Maximum number of "iterations" to complete.
113 * @return the regularized beta function I(x, a, b)
114 * @throws MathException if the algorithm fails to converge.
115 */
116 public static double regularizedBeta(double x, final double a,
117 final double b, double epsilon, int maxIterations) throws MathException
118 {
119 double ret;
120
121 if (Double.isNaN(x) || Double.isNaN(a) || Double.isNaN(b) || (x < 0) ||
122 (x > 1) || (a <= 0.0) || (b <= 0.0))
123 {
124 ret = Double.NaN;
125 } else if (x > (a + 1.0) / (a + b + 2.0)) {
126 ret = 1.0 - regularizedBeta(1.0 - x, b, a, epsilon, maxIterations);
127 } else {
128 ContinuedFraction fraction = new ContinuedFraction() {
129
130 @Override
131 protected double getB(int n, double x) {
132 double ret;
133 double m;
134 if (n % 2 == 0) { // even
135 m = n / 2.0;
136 ret = (m * (b - m) * x) /
137 ((a + (2 * m) - 1) * (a + (2 * m)));
138 } else {
139 m = (n - 1.0) / 2.0;
140 ret = -((a + m) * (a + b + m) * x) /
141 ((a + (2 * m)) * (a + (2 * m) + 1.0));
142 }
143 return ret;
144 }
145
146 @Override
147 protected double getA(int n, double x) {
148 return 1.0;
149 }
150 };
151 ret = Math.exp((a * Math.log(x)) + (b * Math.log(1.0 - x)) -
152 Math.log(a) - logBeta(a, b, epsilon, maxIterations)) *
153 1.0 / fraction.evaluate(x, epsilon, maxIterations);
154 }
155
156 return ret;
157 }
158
159 /**
160 * Returns the natural logarithm of the beta function B(a, b).
161 *
162 * @param a the a parameter.
163 * @param b the b parameter.
164 * @return log(B(a, b))
165 */
166 public static double logBeta(double a, double b) {
167 return logBeta(a, b, DEFAULT_EPSILON, Integer.MAX_VALUE);
168 }
169
170 /**
171 * Returns the natural logarithm of the beta function B(a, b).
172 *
173 * The implementation of this method is based on:
174 * <ul>
175 * <li><a href="http://mathworld.wolfram.com/BetaFunction.html">
176 * Beta Function</a>, equation (1).</li>
177 * </ul>
178 *
179 * @param a the a parameter.
180 * @param b the b parameter.
181 * @param epsilon When the absolute value of the nth item in the
182 * series is less than epsilon the approximation ceases
183 * to calculate further elements in the series.
184 * @param maxIterations Maximum number of "iterations" to complete.
185 * @return log(B(a, b))
186 */
187 public static double logBeta(double a, double b, double epsilon,
188 int maxIterations) {
189
190 double ret;
191
192 if (Double.isNaN(a) || Double.isNaN(b) || (a <= 0.0) || (b <= 0.0)) {
193 ret = Double.NaN;
194 } else {
195 ret = Gamma.logGamma(a) + Gamma.logGamma(b) -
196 Gamma.logGamma(a + b);
197 }
198
199 return ret;
200 }
201 }