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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.rng.sampling.distribution;
18  
19  import org.apache.commons.rng.UniformRandomProvider;
20  
21  /**
22   * Sampling from an <a href="http://mathworld.wolfram.com/ExponentialDistribution.html">exponential distribution</a>.
23   *
24   * <p>Sampling uses {@link UniformRandomProvider#nextDouble()}.</p>
25   *
26   * @since 1.0
27   */
28  public class AhrensDieterExponentialSampler
29      extends SamplerBase
30      implements SharedStateContinuousSampler {
31      /**
32       * Table containing the constants
33       * \( q_i = sum_{j=1}^i (\ln 2)^j / j! = \ln 2 + (\ln 2)^2 / 2 + ... + (\ln 2)^i / i! \)
34       * until the largest representable fraction below 1 is exceeded.
35       *
36       * Note that
37       * \( 1 = 2 - 1 = \exp(\ln 2) - 1 = sum_{n=1}^\infinity (\ln 2)^n / n! \)
38       * thus \( q_i \rightarrow 1 as i \rightarrow +\infinity \),
39       * so the higher \( i \), the closer we get to 1 (the series is not alternating).
40       *
41       * By trying, n = 16 in Java is enough to reach 1.
42       */
43      private static final double[] EXPONENTIAL_SA_QI = new double[16];
44      /** The mean of this distribution. */
45      private final double mean;
46      /** Underlying source of randomness. */
47      private final UniformRandomProvider rng;
48  
49      /**
50       * Initialize tables.
51       */
52      static {
53          /**
54           * Filling EXPONENTIAL_SA_QI table.
55           * Note that we don't want qi = 0 in the table.
56           */
57          final double ln2 = Math.log(2);
58          double qi = 0;
59  
60          for (int i = 0; i < EXPONENTIAL_SA_QI.length; i++) {
61              qi += Math.pow(ln2, i + 1.0) / InternalUtils.factorial(i + 1);
62              EXPONENTIAL_SA_QI[i] = qi;
63          }
64      }
65  
66      /**
67       * @param rng Generator of uniformly distributed random numbers.
68       * @param mean Mean of this distribution.
69       * @throws IllegalArgumentException if {@code mean <= 0}
70       */
71      public AhrensDieterExponentialSampler(UniformRandomProvider rng,
72                                            double mean) {
73          super(null);
74          if (mean <= 0) {
75              throw new IllegalArgumentException("mean is not strictly positive: " + mean);
76          }
77          this.rng = rng;
78          this.mean = mean;
79      }
80  
81      /**
82       * @param rng Generator of uniformly distributed random numbers.
83       * @param source Source to copy.
84       */
85      private AhrensDieterExponentialSampler(UniformRandomProvider rng,
86                                             AhrensDieterExponentialSampler source) {
87          super(null);
88          this.rng = rng;
89          this.mean = source.mean;
90      }
91  
92      /** {@inheritDoc} */
93      @Override
94      public double sample() {
95          // Step 1:
96          double a = 0;
97          double u = rng.nextDouble();
98  
99          // Step 2 and 3:
100         while (u < 0.5) {
101             a += EXPONENTIAL_SA_QI[0];
102             u *= 2;
103         }
104 
105         // Step 4 (now u >= 0.5):
106         u += u - 1;
107 
108         // Step 5:
109         if (u <= EXPONENTIAL_SA_QI[0]) {
110             return mean * (a + u);
111         }
112 
113         // Step 6:
114         int i = 0; // Should be 1, be we iterate before it in while using 0.
115         double u2 = rng.nextDouble();
116         double umin = u2;
117 
118         // Step 7 and 8:
119         do {
120             ++i;
121             u2 = rng.nextDouble();
122 
123             if (u2 < umin) {
124                 umin = u2;
125             }
126 
127             // Step 8:
128         } while (u > EXPONENTIAL_SA_QI[i]); // Ensured to exit since EXPONENTIAL_SA_QI[MAX] = 1.
129 
130         return mean * (a + umin * EXPONENTIAL_SA_QI[0]);
131     }
132 
133     /** {@inheritDoc} */
134     @Override
135     public String toString() {
136         return "Ahrens-Dieter Exponential deviate [" + rng.toString() + "]";
137     }
138 
139     /**
140      * {@inheritDoc}
141      *
142      * @since 1.3
143      */
144     @Override
145     public SharedStateContinuousSampler withUniformRandomProvider(UniformRandomProvider rng) {
146         return new AhrensDieterExponentialSampler(rng, this);
147     }
148 
149     /**
150      * Create a new exponential distribution sampler.
151      *
152      * @param rng Generator of uniformly distributed random numbers.
153      * @param mean Mean of the distribution.
154      * @return the sampler
155      * @throws IllegalArgumentException if {@code mean <= 0}
156      * @since 1.3
157      */
158     public static SharedStateContinuousSampler of(UniformRandomProvider rng,
159                                                   double mean) {
160         return new AhrensDieterExponentialSampler(rng, mean);
161     }
162 }