1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) 2002-2012 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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4 | *
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5 | * This file is part of HeuristicLab.
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6 | *
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7 | * HeuristicLab is free software: you can redistribute it and/or modify
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8 | * it under the terms of the GNU General Public License as published by
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9 | * the Free Software Foundation, either version 3 of the License, or
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10 | * (at your option) any later version.
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11 | *
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12 | * HeuristicLab is distributed in the hope that it will be useful,
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13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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15 | * GNU General Public License for more details.
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16 | *
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17 | * You should have received a copy of the GNU General Public License
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18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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19 | */
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20 | #endregion
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21 |
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22 | using System;
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23 | using System.Collections.Generic;
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24 |
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25 | namespace HeuristicLab.Analysis.AlgorithmBehavior.Analyzers {
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26 | // Kruskal Wallis test based on R's kruskal.test()
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27 | public class KruskalWallis {
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28 | public static double Test(double[][] data) {
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29 | double[] g;
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30 | double[] x = FlattenArray(data, out g);
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31 | int n = x.Length;
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32 | int parameter = data.Length - 1;
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33 |
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34 | int[] r = Rank(x);
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35 | double[][] ties = CountDuplicates(x);
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36 | double statistic = CalculateStatistic(r, g);
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37 | double tiesCorrection = CalculateTiesCorrection(ties);
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38 | statistic = ((12 * statistic / (n * (n + 1)) - 3 * (n + 1)) /
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39 | (1 - tiesCorrection / (Math.Pow(n, 3) - n)));
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40 |
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41 | return alglib.chisquarecdistribution(parameter, statistic);
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42 | }
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43 |
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44 | private static double CalculateStatistic(int[] r, double[] g) {
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45 | double result = 0.0;
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46 | double lastG = g[0];
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47 | double curSum = 0.0;
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48 | int cnt = 0;
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49 | for (int i = 0; i < r.Length; i++) {
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50 | if (lastG == g[i]) {
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51 | curSum += r[i];
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52 | cnt++;
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53 | } else {
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54 | double sum = Math.Pow(curSum, 2);
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55 | sum /= cnt;
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56 | result += sum;
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57 |
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58 | lastG = g[i];
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59 | curSum = r[i];
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60 | cnt = 1;
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61 | }
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62 | }
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63 |
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64 | double lastSum = Math.Pow(curSum, 2);
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65 | lastSum /= cnt;
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66 | result += lastSum;
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67 |
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68 | return result;
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69 | }
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70 |
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71 | private static double CalculateTiesCorrection(double[][] ties) {
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72 | double sum = 0.0;
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73 | for (int i = 0; i < ties[1].Length; i++) {
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74 | double tic = Math.Pow(ties[1][i], 3) - ties[1][i];
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75 | sum += tic;
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76 | }
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77 | return sum;
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78 | }
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79 |
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80 | public static double[] FlattenArray(double[][] x, out double[] indizes) {
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81 | int compLenght = 0;
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82 | for (int i = 0; i < x.Length; i++) {
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83 | compLenght += x[i].Length;
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84 | }
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85 |
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86 | double[] result = new double[compLenght];
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87 | indizes = new double[compLenght];
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88 |
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89 | int resultPos = 0;
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90 | for (int i = 0; i < x.Length; i++) {
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91 | Array.Copy(x[i], 0, result, resultPos, x[i].Length);
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92 |
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93 | for (int j = resultPos; j < resultPos + x[i].Length; j++) {
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94 | indizes[j] = i;
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95 | }
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96 | resultPos += x[i].Length;
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97 | }
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98 |
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99 | return result;
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100 | }
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101 |
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102 | public static double[][] CountDuplicates(double[] x) {
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103 | List<double> number = new List<double>();
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104 | List<double> cnt = new List<double>();
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105 | double[] sortedX = new double[x.Length];
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106 |
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107 | Array.Copy(x, sortedX, x.Length);
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108 | Array.Sort(sortedX);
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109 |
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110 | double last = x[0];
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111 | number.Add(x[0]);
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112 | cnt.Add(1);
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113 |
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114 | for (int i = 1; i < x.Length; i++) {
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115 | if (last != x[i]) {
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116 | number.Add(x[i]);
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117 | last = x[i];
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118 | cnt.Add(1);
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119 | } else {
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120 | cnt[cnt.Count - 1] += 1;
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121 | }
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122 | }
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123 |
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124 | double[][] result = new double[2][];
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125 | result[0] = number.ToArray();
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126 | result[1] = cnt.ToArray();
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127 |
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128 | return result;
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129 | }
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130 |
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131 | public static int[] Rank(double[] x) {
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132 | double[] keys = new double[x.Length];
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133 | int[] items = new int[x.Length];
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134 | int[] ranks = new int[x.Length];
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135 |
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136 | Array.Copy(x, keys, x.Length);
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137 | for (int i = 0; i < x.Length; i++) items[i] = i;
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138 |
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139 | Array.Sort(keys, items);
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140 |
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141 | for (int i = 0; i < x.Length; i++) {
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142 | ranks[items[i]] = i + 1;
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143 | }
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144 | return ranks;
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145 | }
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146 | }
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147 | }
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