1 | /** |
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2 | * Licensed to the Apache Software Foundation (ASF) under one or more |
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3 | * contributor license agreements. See the NOTICE file distributed with this |
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4 | * work for additional information regarding copyright ownership. The ASF |
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5 | * licenses this file to you under the Apache License, Version 2.0 (the |
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6 | * "License"); you may not use this file except in compliance with the License. |
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7 | * You may obtain a copy of the License at |
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8 | * |
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9 | * http://www.apache.org/licenses/LICENSE-2.0 |
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10 | * |
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11 | * Unless required by applicable law or agreed to in writing, software |
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12 | * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT |
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13 | * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the |
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14 | * License for the specific language governing permissions and limitations under |
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15 | * the License. |
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16 | */ |
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17 | package org.apache.hadoop.io.file.tfile; |
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18 | |
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19 | import java.util.ArrayList; |
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20 | import java.util.Arrays; |
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21 | import java.util.Collections; |
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22 | import java.util.Random; |
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23 | |
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24 | /** |
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25 | * A class that generates random numbers that follow some distribution. |
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26 | */ |
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27 | public class RandomDistribution { |
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28 | /** |
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29 | * Interface for discrete (integer) random distributions. |
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30 | */ |
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31 | public static interface DiscreteRNG { |
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32 | /** |
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33 | * Get the next random number |
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34 | * |
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35 | * @return the next random number. |
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36 | */ |
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37 | public int nextInt(); |
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38 | } |
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39 | |
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40 | /** |
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41 | * P(i)=1/(max-min) |
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42 | */ |
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43 | public static final class Flat implements DiscreteRNG { |
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44 | private final Random random; |
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45 | private final int min; |
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46 | private final int max; |
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47 | |
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48 | /** |
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49 | * Generate random integers from min (inclusive) to max (exclusive) |
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50 | * following even distribution. |
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51 | * |
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52 | * @param random |
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53 | * The basic random number generator. |
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54 | * @param min |
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55 | * Minimum integer |
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56 | * @param max |
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57 | * maximum integer (exclusive). |
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58 | * |
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59 | */ |
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60 | public Flat(Random random, int min, int max) { |
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61 | if (min >= max) { |
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62 | throw new IllegalArgumentException("Invalid range"); |
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63 | } |
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64 | this.random = random; |
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65 | this.min = min; |
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66 | this.max = max; |
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67 | } |
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68 | |
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69 | /** |
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70 | * @see DiscreteRNG#nextInt() |
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71 | */ |
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72 | @Override |
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73 | public int nextInt() { |
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74 | return random.nextInt(max - min) + min; |
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75 | } |
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76 | } |
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77 | |
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78 | /** |
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79 | * Zipf distribution. The ratio of the probabilities of integer i and j is |
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80 | * defined as follows: |
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81 | * |
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82 | * P(i)/P(j)=((j-min+1)/(i-min+1))^sigma. |
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83 | */ |
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84 | public static final class Zipf implements DiscreteRNG { |
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85 | private static final double DEFAULT_EPSILON = 0.001; |
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86 | private final Random random; |
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87 | private final ArrayList<Integer> k; |
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88 | private final ArrayList<Double> v; |
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89 | |
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90 | /** |
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91 | * Constructor |
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92 | * |
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93 | * @param r |
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94 | * The random number generator. |
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95 | * @param min |
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96 | * minimum integer (inclusvie) |
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97 | * @param max |
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98 | * maximum integer (exclusive) |
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99 | * @param sigma |
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100 | * parameter sigma. (sigma > 1.0) |
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101 | */ |
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102 | public Zipf(Random r, int min, int max, double sigma) { |
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103 | this(r, min, max, sigma, DEFAULT_EPSILON); |
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104 | } |
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105 | |
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106 | /** |
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107 | * Constructor. |
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108 | * |
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109 | * @param r |
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110 | * The random number generator. |
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111 | * @param min |
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112 | * minimum integer (inclusvie) |
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113 | * @param max |
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114 | * maximum integer (exclusive) |
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115 | * @param sigma |
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116 | * parameter sigma. (sigma > 1.0) |
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117 | * @param epsilon |
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118 | * Allowable error percentage (0 < epsilon < 1.0). |
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119 | */ |
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120 | public Zipf(Random r, int min, int max, double sigma, double epsilon) { |
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121 | if ((max <= min) || (sigma <= 1) || (epsilon <= 0) |
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122 | || (epsilon >= 0.5)) { |
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123 | throw new IllegalArgumentException("Invalid arguments"); |
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124 | } |
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125 | random = r; |
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126 | k = new ArrayList<Integer>(); |
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127 | v = new ArrayList<Double>(); |
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128 | |
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129 | double sum = 0; |
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130 | int last = -1; |
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131 | for (int i = min; i < max; ++i) { |
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132 | sum += Math.exp(-sigma * Math.log(i - min + 1)); |
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133 | if ((last == -1) || i * (1 - epsilon) > last) { |
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134 | k.add(i); |
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135 | v.add(sum); |
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136 | last = i; |
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137 | } |
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138 | } |
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139 | |
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140 | if (last != max - 1) { |
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141 | k.add(max - 1); |
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142 | v.add(sum); |
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143 | } |
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144 | |
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145 | v.set(v.size() - 1, 1.0); |
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146 | |
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147 | for (int i = v.size() - 2; i >= 0; --i) { |
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148 | v.set(i, v.get(i) / sum); |
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149 | } |
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150 | } |
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151 | |
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152 | /** |
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153 | * @see DiscreteRNG#nextInt() |
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154 | */ |
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155 | @Override |
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156 | public int nextInt() { |
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157 | double d = random.nextDouble(); |
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158 | int idx = Collections.binarySearch(v, d); |
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159 | |
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160 | if (idx > 0) { |
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161 | ++idx; |
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162 | } |
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163 | else { |
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164 | idx = -(idx + 1); |
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165 | } |
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166 | |
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167 | if (idx >= v.size()) { |
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168 | idx = v.size() - 1; |
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169 | } |
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170 | |
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171 | if (idx == 0) { |
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172 | return k.get(0); |
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173 | } |
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174 | |
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175 | int ceiling = k.get(idx); |
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176 | int lower = k.get(idx - 1); |
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177 | |
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178 | return ceiling - random.nextInt(ceiling - lower); |
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179 | } |
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180 | } |
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181 | |
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182 | /** |
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183 | * Binomial distribution. |
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184 | * |
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185 | * P(k)=select(n, k)*p^k*(1-p)^(n-k) (k = 0, 1, ..., n) |
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186 | * |
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187 | * P(k)=select(max-min-1, k-min)*p^(k-min)*(1-p)^(k-min)*(1-p)^(max-k-1) |
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188 | */ |
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189 | public static final class Binomial implements DiscreteRNG { |
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190 | private final Random random; |
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191 | private final int min; |
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192 | private final int n; |
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193 | private final double[] v; |
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194 | |
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195 | private static double select(int n, int k) { |
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196 | double ret = 1.0; |
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197 | for (int i = k + 1; i <= n; ++i) { |
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198 | ret *= (double) i / (i - k); |
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199 | } |
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200 | return ret; |
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201 | } |
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202 | |
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203 | private static double power(double p, int k) { |
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204 | return Math.exp(k * Math.log(p)); |
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205 | } |
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206 | |
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207 | /** |
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208 | * Generate random integers from min (inclusive) to max (exclusive) |
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209 | * following Binomial distribution. |
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210 | * |
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211 | * @param random |
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212 | * The basic random number generator. |
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213 | * @param min |
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214 | * Minimum integer |
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215 | * @param max |
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216 | * maximum integer (exclusive). |
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217 | * @param p |
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218 | * parameter. |
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219 | * |
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220 | */ |
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221 | public Binomial(Random random, int min, int max, double p) { |
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222 | if (min >= max) { |
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223 | throw new IllegalArgumentException("Invalid range"); |
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224 | } |
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225 | this.random = random; |
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226 | this.min = min; |
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227 | this.n = max - min - 1; |
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228 | if (n > 0) { |
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229 | v = new double[n + 1]; |
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230 | double sum = 0.0; |
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231 | for (int i = 0; i <= n; ++i) { |
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232 | sum += select(n, i) * power(p, i) * power(1 - p, n - i); |
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233 | v[i] = sum; |
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234 | } |
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235 | for (int i = 0; i <= n; ++i) { |
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236 | v[i] /= sum; |
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237 | } |
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238 | } |
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239 | else { |
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240 | v = null; |
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241 | } |
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242 | } |
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243 | |
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244 | /** |
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245 | * @see DiscreteRNG#nextInt() |
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246 | */ |
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247 | @Override |
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248 | public int nextInt() { |
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249 | if (v == null) { |
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250 | return min; |
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251 | } |
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252 | double d = random.nextDouble(); |
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253 | int idx = Arrays.binarySearch(v, d); |
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254 | if (idx > 0) { |
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255 | ++idx; |
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256 | } else { |
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257 | idx = -(idx + 1); |
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258 | } |
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259 | |
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260 | if (idx >= v.length) { |
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261 | idx = v.length - 1; |
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262 | } |
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263 | return idx + min; |
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264 | } |
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265 | } |
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266 | } |
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