1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.apache.commons.numbers.gamma;
18
19 /**
20 * <a href="https://mathworld.wolfram.com/IncompleteGammaFunction.html">
21 * Incomplete Gamma functions</a>.
22 *
23 * <p>By definition, the lower and upper incomplete gamma functions satisfy:
24 *
25 * <p>\[ \Gamma(a) = \gamma(a, x) + \Gamma(a, x) \]
26 *
27 * <p>This code has been adapted from the <a href="https://www.boost.org/">Boost</a>
28 * {@code c++} implementation {@code <boost/math/special_functions/gamma.hpp>}.
29 *
30 * @see
31 * <a href="https://www.boost.org/doc/libs/1_77_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html">
32 * Boost C++ Incomplete Gamma functions</a>
33 * @since 1.1
34 */
35 public final class IncompleteGamma {
36 /** No instances. */
37 private IncompleteGamma() {}
38
39 /**
40 * <a href="http://mathworld.wolfram.com/IncompleteGammaFunction.html">
41 * Lower incomplete Gamma function</a> \( \gamma(a, x) \).
42 *
43 * <p>\[ \gamma(a,x) = \int_0^x t^{a-1}\,e^{-t}\,dt \]
44 * @since 1.1
45 */
46 public static final class Lower {
47 /** No instances. */
48 private Lower() {}
49
50 /**
51 * Computes the lower incomplete gamma function \( \gamma(a, x) \).
52 *
53 * @param a Argument.
54 * @param x Argument.
55 * @return \( \gamma(a, x) \).
56 * @throws ArithmeticException if the series evaluation fails to converge.
57 */
58 public static double value(double a,
59 double x) {
60 return BoostGamma.tgammaLower(a, x);
61 }
62
63 /**
64 * Computes the lower incomplete gamma function \( \gamma(a, x) \).
65 *
66 * @param a Argument.
67 * @param x Argument.
68 * @param epsilon Tolerance in series evaluation.
69 * @param maxIterations Maximum number of iterations in series evaluation.
70 * @return \( \gamma(a, x) \).
71 * @throws ArithmeticException if the series evaluation fails to converge.
72 */
73 public static double value(final double a,
74 double x,
75 double epsilon,
76 int maxIterations) {
77 return BoostGamma.tgammaLower(a, x, new Policy(epsilon, maxIterations));
78 }
79 }
80
81 /**
82 * <a href="http://mathworld.wolfram.com/IncompleteGammaFunction.html">
83 * Upper incomplete Gamma function</a> \( \Gamma(a, x) \).
84 *
85 * <p>\[ \Gamma(a,x) = \int_x^{\infty} t^{a-1}\,e^{-t}\,dt \]
86 * @since 1.1
87 */
88 public static final class Upper {
89 /** No instances. */
90 private Upper() {}
91
92 /**
93 * Computes the upper incomplete gamma function \( \Gamma(a, x) \).
94 *
95 * @param a Argument.
96 * @param x Argument.
97 * @return \( \Gamma(a, x) \).
98 * @throws ArithmeticException if the series evaluation fails to converge.
99 */
100 public static double value(double a,
101 double x) {
102 return BoostGamma.tgamma(a, x);
103 }
104
105 /**
106 * Computes the upper incomplete gamma function \( \Gamma(a, x) \).
107 *
108 * @param a Argument.
109 * @param x Argument.
110 * @param epsilon Tolerance in series evaluation.
111 * @param maxIterations Maximum number of iterations in series evaluation.
112 * @return \( \Gamma(a, x) \).
113 * @throws ArithmeticException if the series evaluation fails to converge.
114 */
115 public static double value(double a,
116 double x,
117 double epsilon,
118 int maxIterations) {
119 return BoostGamma.tgamma(a, x, new Policy(epsilon, maxIterations));
120 }
121 }
122 }