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16 package org.apache.commons.math.special;
17
18 import java.io.Serializable;
19
20 import org.apache.commons.math.MathException;
21 import org.apache.commons.math.util.ContinuedFraction;
22
23 /**
24 * This is a utility class that provides computation methods related to the
25 * Beta family of functions.
26 *
27 * @version $Revision: 155427 $ $Date: 2005-02-26 06:11:52 -0700 (Sat, 26 Feb 2005) $
28 */
29 public class Beta implements Serializable {
30 /** Maximum allowed numerical error. */
31 private static final double DEFAULT_EPSILON = 10e-9;
32
33 /**
34 * Default constructor. Prohibit instantiation.
35 */
36 private Beta() {
37 super();
38 }
39
40 /**
41 * Returns the
42 * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
43 * regularized beta function</a> I(x, a, b).
44 *
45 * @param x the value.
46 * @param a the a parameter.
47 * @param b the b parameter.
48 * @return the regularized beta function I(x, a, b)
49 * @throws MathException if the algorithm fails to converge.
50 */
51 public static double regularizedBeta(double x, double a, double b)
52 throws MathException
53 {
54 return regularizedBeta(x, a, b, DEFAULT_EPSILON, Integer.MAX_VALUE);
55 }
56
57 /**
58 * Returns the
59 * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
60 * regularized beta function</a> I(x, a, b).
61 *
62 * @param x the value.
63 * @param a the a parameter.
64 * @param b the b parameter.
65 * @param epsilon When the absolute value of the nth item in the
66 * series is less than epsilon the approximation ceases
67 * to calculate further elements in the series.
68 * @return the regularized beta function I(x, a, b)
69 * @throws MathException if the algorithm fails to converge.
70 */
71 public static double regularizedBeta(double x, double a, double b,
72 double epsilon) throws MathException
73 {
74 return regularizedBeta(x, a, b, epsilon, Integer.MAX_VALUE);
75 }
76
77 /**
78 * Returns the regularized beta function I(x, a, b).
79 *
80 * @param x the value.
81 * @param a the a parameter.
82 * @param b the b parameter.
83 * @param maxIterations Maximum number of "iterations" to complete.
84 * @return the regularized beta function I(x, a, b)
85 * @throws MathException if the algorithm fails to converge.
86 */
87 public static double regularizedBeta(double x, double a, double b,
88 int maxIterations) throws MathException
89 {
90 return regularizedBeta(x, a, b, DEFAULT_EPSILON, maxIterations);
91 }
92
93 /**
94 * Returns the regularized beta function I(x, a, b).
95 *
96 * The implementation of this method is based on:
97 * <ul>
98 * <li>
99 * <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 protected double getB(int n, double x) {
130 double ret;
131 double m;
132 if (n % 2 == 0) {
133 m = n / 2.0;
134 ret = (m * (b - m) * x) /
135 ((a + (2 * m) - 1) * (a + (2 * m)));
136 } else {
137 m = (n - 1.0) / 2.0;
138 ret = -((a + m) * (a + b + m) * x) /
139 ((a + (2 * m)) * (a + (2 * m) + 1.0));
140 }
141 return ret;
142 }
143
144 protected double getA(int n, double x) {
145 return 1.0;
146 }
147 };
148 ret = Math.exp((a * Math.log(x)) + (b * Math.log(1.0 - x)) -
149 Math.log(a) - logBeta(a, b, epsilon, maxIterations)) *
150 1.0 / fraction.evaluate(x, epsilon, maxIterations);
151 }
152
153 return ret;
154 }
155
156 /**
157 * Returns the natural logarithm of the beta function B(a, b).
158 *
159 * @param a the a parameter.
160 * @param b the b parameter.
161 * @return log(B(a, b))
162 */
163 public static double logBeta(double a, double b) {
164 return logBeta(a, b, DEFAULT_EPSILON, Integer.MAX_VALUE);
165 }
166
167 /**
168 * Returns the natural logarithm of the beta function B(a, b).
169 *
170 * The implementation of this method is based on:
171 * <ul>
172 * <li><a href="http://mathworld.wolfram.com/BetaFunction.html">
173 * Beta Function</a>, equation (1).</li>
174 * </ul>
175 *
176 * @param a the a parameter.
177 * @param b the b parameter.
178 * @param epsilon When the absolute value of the nth item in the
179 * series is less than epsilon the approximation ceases
180 * to calculate further elements in the series.
181 * @param maxIterations Maximum number of "iterations" to complete.
182 * @return log(B(a, b))
183 */
184 public static double logBeta(double a, double b, double epsilon,
185 int maxIterations) {
186
187 double ret;
188
189 if (Double.isNaN(a) || Double.isNaN(b) || (a <= 0.0) || (b <= 0.0)) {
190 ret = Double.NaN;
191 } else {
192 ret = Gamma.logGamma(a) + Gamma.logGamma(b) -
193 Gamma.logGamma(a + b);
194 }
195
196 return ret;
197 }
198 }