1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) 2002-2018 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 | using System.Linq;
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25 | using HeuristicLab.Common;
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26 | using HeuristicLab.Core;
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27 | using HeuristicLab.Data;
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28 | using HeuristicLab.Optimization;
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29 | using HeuristicLab.Parameters;
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30 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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31 | using HeuristicLab.Problems.DataAnalysis;
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32 | using HeuristicLab.Random;
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33 | using HeuristicLab.Selection;
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34 |
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35 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic.Regression {
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36 | /// <summary>
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37 | /// eps-Lexicase Selection
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38 | /// </summary>
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39 | [Item("EpsLexicaseSelection", "")]
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40 | [StorableClass]
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41 | public sealed class EpsLexicaseSelection : StochasticSingleObjectiveSelector, ISingleObjectiveSelector {
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42 |
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43 | [StorableConstructor]
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44 | private EpsLexicaseSelection(bool deserializing) : base(deserializing) { }
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45 | private EpsLexicaseSelection(EpsLexicaseSelection original, Cloner cloner) : base(original, cloner) { }
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46 | public override IDeepCloneable Clone(Cloner cloner) {
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47 | return new EpsLexicaseSelection(this, cloner);
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48 | }
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49 |
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50 | public EpsLexicaseSelection()
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51 | : base() {
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52 | Parameters.Add(new ScopeTreeLookupParameter<DoubleArray>("Errors", 1));
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53 |
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54 | var validPolicies = new ItemSet<StringValue>(new string[] { "ϵ_e", "ϵ_y", "ϵ_e,λ", "ϵ_y,λ" }.Select(s => new StringValue(s).AsReadOnly()));
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55 | Parameters.Add(new ConstrainedValueParameter<StringValue>("Policy", "The selection policy (see La Cava, Spector, Danai: eps-Lexicase Selection for Regression, GECCO 2016)", validPolicies));
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56 | Parameters.Add(new ValueParameter<DoubleValue>("ϵ", "The ϵ value for ϵ_e and ϵ_y policies", new DoubleValue(1.0)));
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57 | Parameters.Add(new LookupParameter<DoubleValue>("AvgConsideredTestCases", "The average number of considered test cases for selection."));
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58 | }
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59 |
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60 | [StorableHook(HookType.AfterDeserialization)]
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61 | private void AfterDeserialization() {
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62 | // remove
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63 | if (!Parameters.ContainsKey("AvgConsideredTestCases")) {
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64 | Parameters.Add(new LookupParameter<DoubleValue>("AvgConsideredTestCases", "The average number of considered test cases for selection."));
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65 | }
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66 | }
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67 |
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68 | protected override IScope[] Select(List<IScope> scopes) {
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69 | // NOT efficiently implemented, used only for exploration of diversity for a paper
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70 |
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71 | int parentCount = NumberOfSelectedSubScopesParameter.ActualValue.Value;
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72 | bool copy = CopySelectedParameter.Value.Value;
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73 | if (!copy) throw new ArgumentException("copy is false in eps-lexicase selection.");
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74 | IRandom random = RandomParameter.ActualValue;
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75 | bool maximization = MaximizationParameter.ActualValue.Value;
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76 | IScope[] selected = new IScope[parentCount];
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77 |
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78 | int nScopes = scopes.Count();
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79 | var errors = (ItemArray<DoubleArray>)((IScopeTreeLookupParameter)Parameters["Errors"]).ActualValue;
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80 | if (errors == null || !errors.Any())
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81 | throw new ArgumentException("Have not found errors of models. Have you used an analyzer that calculates the errors and stores them in the scope?");
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82 |
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83 | var e = errors.Select(e_m => e_m.ToArray()).ToArray();
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84 | errors = null; // don't use errors
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85 |
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86 |
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87 | // see La Cava, Spector, Danai: eps-Lexicase Selection for Regression, GECCO 2016
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88 | var ts = Enumerable.Range(0, e.First().Length).ToArray();
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89 |
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90 | double eps = ((DoubleValue)Parameters["ϵ"].ActualValue).Value;
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91 | var selectionPolicy = ((StringValue)Parameters["Policy"].ActualValue).Value;
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92 |
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93 | var selectedScopes = new IScope[parentCount];
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94 | var nCasesList = new List<double>(parentCount);
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95 | var lambda_e = ts.Select(t=> MAD(e.Select(e_m => e_m[t]).ToArray())).ToArray();
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96 |
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97 | for (int i = 0; i < parentCount; i++) {
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98 | int nCases;
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99 | var selectedIdx = SelectIdx(random, e, selectionPolicy, ts, eps, lambda_e, out nCases);
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100 | nCasesList.Add(nCases);
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101 | selectedScopes[i] = (IScope)(scopes[selectedIdx]).Clone();
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102 | }
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103 | Parameters["AvgConsideredTestCases"].ActualValue = new DoubleValue(nCasesList.Median());
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104 | return selectedScopes;
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105 | }
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106 |
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107 | public static int SelectIdx(IRandom random, double[][] errors, string selectionPolicy, int[] ts, double eps, double[] lambda_e, out int nCases) {
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108 | ts.ShuffleInPlace(random);
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109 |
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110 | var activeModelIdxs = new SortedSet<int>(Enumerable.Range(0, errors.Length));
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111 | nCases = 0;
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112 |
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113 | foreach (var t in ts) {
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114 | if (activeModelIdxs.Count <= 1) break;
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115 | nCases++;
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116 |
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117 | switch (selectionPolicy) {
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118 | case "ϵ_e": {
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119 | var bestError = errors.Select(err_m => err_m[t]).Min(); // as noted in corrected version of GECCO 2016 paper
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120 | activeModelIdxs.RemoveWhere(modelIdx => errors[modelIdx][t] > bestError * (1 + eps));
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121 | break;
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122 | }
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123 | case "ϵ_y": {
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124 | activeModelIdxs.RemoveWhere(modelIdx => errors[modelIdx][t] > eps);
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125 | break;
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126 | }
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127 | // Note in a corrected version of the GECCO Paper La Cava changed equations (2) and (5)
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128 | // Equations 2 and 5 have been corrected to
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129 | // indicate that the pass conditions for individuals in -lexicase
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130 | // selection are defined relative to the best error in the population
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131 | // on that training case, not in the selection pool.
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132 |
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133 | // a more recent and detailed description of the algorithm is given in https://arxiv.org/pdf/1709.05394.pdf
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134 | // which indicates that semi-dynamic eps-lexicase performs best (Algorithm 4.2)
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135 | // -> we also implement semi-dynamic eps-lexicase which calculates lambda over the whole population
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136 |
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137 | // I have not found a way to get reasonable convergence using MAD for lambda.
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138 | // If lambda_e[t] is zero this means that all models are effectively the same => select randomly.
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139 | // It seems that linear scaling (or the replacement of NaN outputs with the average of y)
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140 | // has the effect that MAD is zero (especially in the beginning), which means there is not selection pressure at the beginning.
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141 | // Semi-dynamic -Lexicase Selection
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142 | case "ϵ_e,λ": {
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143 | var bestError = activeModelIdxs.Select(modelIdx => errors[modelIdx][t]).Min(); // See https://arxiv.org/pdf/1709.05394.pdf Alg 4.2
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144 | activeModelIdxs.RemoveWhere(modelIdx => errors[modelIdx][t] > bestError + lambda_e[t]); // in the gecco paper the acceptance criterion is err < lambda_et this is later correct to err <= lambda_et
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145 | break;
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146 | }
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147 | case "ϵ_y,λ": {
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148 | activeModelIdxs.RemoveWhere(modelIdx => errors[modelIdx][t] > lambda_e[t]); // in the gecco paper the acceptance criterion is err < lambda_et this is later correct to err <= lambda_et
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149 | break;
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150 | }
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151 | default: throw new ArgumentException("unknown policy " + selectionPolicy);
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152 | }
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153 | }
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154 |
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155 | if (!activeModelIdxs.Any())
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156 | throw new ArgumentException("nothing left in the pool");
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157 | else
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158 | return activeModelIdxs.SampleRandom(random, 1).First();
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159 | }
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160 |
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161 | private static double MAD(double[] x) {
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162 | var median_x = x.Median();
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163 | return x.Select(xi => Math.Abs(xi - median_x)).Median();
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164 | }
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165 | private static double StdDev(double[] x) {
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166 | return x.StandardDeviation();
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167 | }
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168 | }
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169 | }
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