[11692] | 1 | #region License Information
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| 2 | /* HeuristicLab
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[14185] | 3 | * Copyright (C) 2002-2016 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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[11692] | 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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[11699] | 24 | using HeuristicLab.Common;
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[11692] | 25 |
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| 26 | namespace HeuristicLab.Analysis.Statistics {
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| 27 | public static class KruskalWallisTest {
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| 28 | /// <summary>
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| 29 | /// Performs the Kruskal-Wallis test and returns the p-Value.
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| 30 | /// (source based on R's kruskal.test(), GNU GPL)
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| 31 | /// </summary>
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| 32 | public static double Test(double[][] data) {
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| 33 | double[] g;
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| 34 | double[] x = FlattenArray(data, out g);
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| 35 | int n = x.Length;
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| 36 | int parameter = data.Length - 1;
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| 37 |
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| 38 | int[] r = Rank(x);
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| 39 | double[][] ties = CountDuplicates(x);
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| 40 | double statistic = CalculateStatistic(r, g);
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| 41 | double tiesCorrection = CalculateTiesCorrection(ties);
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| 42 | statistic = ((12 * statistic / (n * (n + 1)) - 3 * (n + 1)) /
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| 43 | (1 - tiesCorrection / (Math.Pow(n, 3) - n)));
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| 44 |
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| 45 | return alglib.chisquarecdistribution(parameter, statistic);
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| 46 | }
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| 47 |
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| 48 | private static double CalculateStatistic(int[] r, double[] g) {
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| 49 | double result = 0.0;
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| 50 | double lastG = g[0];
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| 51 | double curSum = 0.0;
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| 52 | int cnt = 0;
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| 53 | for (int i = 0; i < r.Length; i++) {
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[11699] | 54 | if (lastG.IsAlmost(g[i])) {
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[11692] | 55 | curSum += r[i];
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| 56 | cnt++;
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| 57 | } else {
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| 58 | double sum = Math.Pow(curSum, 2);
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| 59 | sum /= cnt;
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| 60 | result += sum;
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| 61 |
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| 62 | lastG = g[i];
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| 63 | curSum = r[i];
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| 64 | cnt = 1;
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| 65 | }
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| 66 | }
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| 67 |
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| 68 | double lastSum = Math.Pow(curSum, 2);
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| 69 | lastSum /= cnt;
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| 70 | result += lastSum;
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| 71 |
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| 72 | return result;
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| 73 | }
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| 74 |
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| 75 | private static double CalculateTiesCorrection(double[][] ties) {
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| 76 | double sum = 0.0;
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| 77 | for (int i = 0; i < ties[1].Length; i++) {
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| 78 | double tic = Math.Pow(ties[1][i], 3) - ties[1][i];
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| 79 | sum += tic;
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| 80 | }
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| 81 | return sum;
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| 82 | }
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| 83 |
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| 84 | private static double[] FlattenArray(double[][] x, out double[] indizes) {
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| 85 | int compLenght = 0;
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| 86 | for (int i = 0; i < x.Length; i++) {
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| 87 | compLenght += x[i].Length;
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| 88 | }
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| 89 |
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| 90 | double[] result = new double[compLenght];
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| 91 | indizes = new double[compLenght];
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| 92 |
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| 93 | int resultPos = 0;
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| 94 | for (int i = 0; i < x.Length; i++) {
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| 95 | Array.Copy(x[i], 0, result, resultPos, x[i].Length);
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| 96 |
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| 97 | for (int j = resultPos; j < resultPos + x[i].Length; j++) {
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| 98 | indizes[j] = i;
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| 99 | }
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| 100 | resultPos += x[i].Length;
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| 101 | }
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| 102 |
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| 103 | return result;
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| 104 | }
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| 105 |
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| 106 | private static double[][] CountDuplicates(double[] x) {
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| 107 | List<double> number = new List<double>();
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| 108 | List<double> cnt = new List<double>();
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| 109 | double[] sortedX = new double[x.Length];
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| 110 |
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| 111 | Array.Copy(x, sortedX, x.Length);
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| 112 | Array.Sort(sortedX);
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| 113 |
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| 114 | double last = x[0];
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| 115 | number.Add(x[0]);
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| 116 | cnt.Add(1);
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| 117 |
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| 118 | for (int i = 1; i < x.Length; i++) {
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[11699] | 119 | if (!last.IsAlmost(x[i])) {
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[11692] | 120 | number.Add(x[i]);
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| 121 | last = x[i];
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| 122 | cnt.Add(1);
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| 123 | } else {
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| 124 | cnt[cnt.Count - 1] += 1;
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| 125 | }
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| 126 | }
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| 127 |
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| 128 | double[][] result = new double[2][];
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| 129 | result[0] = number.ToArray();
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| 130 | result[1] = cnt.ToArray();
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| 131 |
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| 132 | return result;
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| 133 | }
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| 134 |
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| 135 | private static int[] Rank(double[] x) {
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| 136 | double[] keys = new double[x.Length];
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| 137 | int[] items = new int[x.Length];
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| 138 | int[] ranks = new int[x.Length];
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| 139 |
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| 140 | Array.Copy(x, keys, x.Length);
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| 141 | for (int i = 0; i < x.Length; i++) items[i] = i;
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| 142 |
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| 143 | Array.Sort(keys, items);
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| 144 |
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| 145 | for (int i = 0; i < x.Length; i++) {
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| 146 | ranks[items[i]] = i + 1;
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| 147 | }
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| 148 | return ranks;
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| 149 | }
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| 150 | }
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| 151 | }
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