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 * @since 1.0 25 */ 26 public class AhrensDieterExponentialSampler 27 extends SamplerBase 28 implements ContinuousSampler { 29 /** 30 * Table containing the constants 31 * \( q_i = sum_{j=1}^i (\ln 2)^j / j! = \ln 2 + (\ln 2)^2 / 2 + ... + (\ln 2)^i / i! \) 32 * until the largest representable fraction below 1 is exceeded. 33 * 34 * Note that 35 * \( 1 = 2 - 1 = \exp(\ln 2) - 1 = sum_{n=1}^\infinity (\ln 2)^n / n! \) 36 * thus \( q_i \rightarrow 1 as i \rightarrow +\infinity \), 37 * so the higher \( i \), the closer we get to 1 (the series is not alternating). 38 * 39 * By trying, n = 16 in Java is enough to reach 1. 40 */ 41 private static final double[] EXPONENTIAL_SA_QI = new double[16]; 42 /** The mean of this distribution. */ 43 private final double mean; 44 /** Underlying source of randomness. */ 45 private final UniformRandomProvider rng; 46 47 /** 48 * Initialize tables. 49 */ 50 static { 51 /** 52 * Filling EXPONENTIAL_SA_QI table. 53 * Note that we don't want qi = 0 in the table. 54 */ 55 final double ln2 = Math.log(2); 56 double qi = 0; 57 58 for (int i = 0; i < EXPONENTIAL_SA_QI.length; i++) { 59 qi += Math.pow(ln2, i + 1) / InternalUtils.factorial(i + 1); 60 EXPONENTIAL_SA_QI[i] = qi; 61 } 62 } 63 64 /** 65 * @param rng Generator of uniformly distributed random numbers. 66 * @param mean Mean of this distribution. 67 */ 68 public AhrensDieterExponentialSampler(UniformRandomProvider rng, 69 double mean) { 70 super(null); 71 this.rng = rng; 72 this.mean = mean; 73 } 74 75 /** {@inheritDoc} */ 76 @Override 77 public double sample() { 78 // Step 1: 79 double a = 0; 80 double u = rng.nextDouble(); 81 82 // Step 2 and 3: 83 while (u < 0.5) { 84 a += EXPONENTIAL_SA_QI[0]; 85 u *= 2; 86 } 87 88 // Step 4 (now u >= 0.5): 89 u += u - 1; 90 91 // Step 5: 92 if (u <= EXPONENTIAL_SA_QI[0]) { 93 return mean * (a + u); 94 } 95 96 // Step 6: 97 int i = 0; // Should be 1, be we iterate before it in while using 0. 98 double u2 = rng.nextDouble(); 99 double umin = u2; 100 101 // Step 7 and 8: 102 do { 103 ++i; 104 u2 = rng.nextDouble(); 105 106 if (u2 < umin) { 107 umin = u2; 108 } 109 110 // Step 8: 111 } while (u > EXPONENTIAL_SA_QI[i]); // Ensured to exit since EXPONENTIAL_SA_QI[MAX] = 1. 112 113 return mean * (a + umin * EXPONENTIAL_SA_QI[0]); 114 } 115 116 /** {@inheritDoc} */ 117 @Override 118 public String toString() { 119 return "Ahrens-Dieter Exponential deviate [" + rng.toString() + "]"; 120 } 121 }