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.Diagnostics;
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25 | using System.Globalization;
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26 | using System.Linq;
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27 | using HeuristicLab.Analysis;
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28 | using HeuristicLab.Collections;
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29 | using HeuristicLab.Common;
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30 | using HeuristicLab.Core;
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31 | using HeuristicLab.Data;
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32 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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33 | using HeuristicLab.Optimization;
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34 | using HeuristicLab.Parameters;
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35 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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36 | using HeuristicLab.Problems.DataAnalysis;
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37 | using HeuristicLab.Problems.DataAnalysis.Symbolic;
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38 | using HeuristicLab.Problems.Instances;
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39 | using Variable = HeuristicLab.Problems.DataAnalysis.Symbolic.Variable;
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40 | using HEAL.Attic;
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41 | using HeuristicLab.Problems.DataAnalysis.Symbolic.Regression;
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42 |
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43 | namespace HeuristicLab.Problems.DynamicalSystemsModelling {
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44 | [Item("Dynamical Systems Modelling Problem", "TODO")]
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45 | [Creatable(CreatableAttribute.Categories.GeneticProgrammingProblems, Priority = 900)]
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46 | [StorableType("065C6A61-773A-42C9-9DE5-61A5D1D823EB")]
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47 | public sealed class Problem : SingleObjectiveBasicProblem<MultiEncoding>, IRegressionProblem, IProblemInstanceConsumer<IRegressionProblemData>, IProblemInstanceExporter<IRegressionProblemData> {
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48 | #region parameter names
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49 | private const string ProblemDataParameterName = "Data";
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50 | private const string TargetVariablesParameterName = "Target variables";
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51 | private const string FunctionSetParameterName = "Function set";
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52 | private const string MaximumLengthParameterName = "Size limit";
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53 | private const string MaximumParameterOptimizationIterationsParameterName = "Max. parameter optimization iterations";
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54 | private const string NumberOfLatentVariablesParameterName = "Number of latent variables";
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55 | private const string NumericIntegrationStepsParameterName = "Steps for numeric integration";
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56 | private const string TrainingEpisodesParameterName = "Training episodes";
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57 | private const string OptimizeParametersForEpisodesParameterName = "Optimize parameters for episodes";
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58 | private const string OdeSolverParameterName = "ODE Solver";
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59 | #endregion
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60 |
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61 | #region Parameter Properties
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62 | IParameter IDataAnalysisProblem.ProblemDataParameter { get { return ProblemDataParameter; } }
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63 |
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64 | public IValueParameter<IRegressionProblemData> ProblemDataParameter {
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65 | get { return (IValueParameter<IRegressionProblemData>)Parameters[ProblemDataParameterName]; }
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66 | }
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67 | public IValueParameter<ReadOnlyCheckedItemList<StringValue>> TargetVariablesParameter {
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68 | get { return (IValueParameter<ReadOnlyCheckedItemList<StringValue>>)Parameters[TargetVariablesParameterName]; }
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69 | }
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70 | public IValueParameter<ReadOnlyCheckedItemList<StringValue>> FunctionSetParameter {
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71 | get { return (IValueParameter<ReadOnlyCheckedItemList<StringValue>>)Parameters[FunctionSetParameterName]; }
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72 | }
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73 | public IFixedValueParameter<IntValue> MaximumLengthParameter {
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74 | get { return (IFixedValueParameter<IntValue>)Parameters[MaximumLengthParameterName]; }
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75 | }
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76 |
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77 | public IFixedValueParameter<IntValue> MaximumParameterOptimizationIterationsParameter {
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78 | get { return (IFixedValueParameter<IntValue>)Parameters[MaximumParameterOptimizationIterationsParameterName]; }
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79 | }
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80 | public IFixedValueParameter<IntValue> NumberOfLatentVariablesParameter {
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81 | get { return (IFixedValueParameter<IntValue>)Parameters[NumberOfLatentVariablesParameterName]; }
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82 | }
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83 | public IFixedValueParameter<IntValue> NumericIntegrationStepsParameter {
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84 | get { return (IFixedValueParameter<IntValue>)Parameters[NumericIntegrationStepsParameterName]; }
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85 | }
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86 | public IValueParameter<ItemList<IntRange>> TrainingEpisodesParameter {
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87 | get { return (IValueParameter<ItemList<IntRange>>)Parameters[TrainingEpisodesParameterName]; }
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88 | }
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89 | public IFixedValueParameter<BoolValue> OptimizeParametersForEpisodesParameter {
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90 | get { return (IFixedValueParameter<BoolValue>)Parameters[OptimizeParametersForEpisodesParameterName]; }
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91 | }
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92 | public IConstrainedValueParameter<StringValue> OdeSolverParameter {
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93 | get { return (IConstrainedValueParameter<StringValue>)Parameters[OdeSolverParameterName]; }
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94 | }
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95 | #endregion
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96 |
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97 | #region Properties
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98 | public IRegressionProblemData ProblemData {
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99 | get { return ProblemDataParameter.Value; }
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100 | set { ProblemDataParameter.Value = value; }
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101 | }
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102 | IDataAnalysisProblemData IDataAnalysisProblem.ProblemData { get { return ProblemData; } }
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103 |
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104 | public ReadOnlyCheckedItemList<StringValue> TargetVariables {
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105 | get { return TargetVariablesParameter.Value; }
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106 | }
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107 |
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108 | public ReadOnlyCheckedItemList<StringValue> FunctionSet {
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109 | get { return FunctionSetParameter.Value; }
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110 | }
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111 |
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112 | public int MaximumLength {
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113 | get { return MaximumLengthParameter.Value.Value; }
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114 | }
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115 | public int MaximumParameterOptimizationIterations {
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116 | get { return MaximumParameterOptimizationIterationsParameter.Value.Value; }
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117 | }
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118 | public int NumberOfLatentVariables {
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119 | get { return NumberOfLatentVariablesParameter.Value.Value; }
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120 | }
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121 | public int NumericIntegrationSteps {
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122 | get { return NumericIntegrationStepsParameter.Value.Value; }
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123 | }
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124 | public IEnumerable<IntRange> TrainingEpisodes {
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125 | get { return TrainingEpisodesParameter.Value; }
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126 | }
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127 | public bool OptimizeParametersForEpisodes {
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128 | get { return OptimizeParametersForEpisodesParameter.Value.Value; }
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129 | }
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130 |
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131 | public string OdeSolver {
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132 | get { return OdeSolverParameter.Value.Value; }
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133 | set {
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134 | var matchingValue = OdeSolverParameter.ValidValues.FirstOrDefault(v => v.Value == value);
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135 | if (matchingValue == null) throw new ArgumentOutOfRangeException();
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136 | else OdeSolverParameter.Value = matchingValue;
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137 | }
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138 | }
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139 |
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140 | #endregion
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141 |
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142 | public event EventHandler ProblemDataChanged;
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143 |
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144 | public override bool Maximization {
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145 | get { return false; } // we minimize NMSE
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146 | }
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147 |
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148 | #region item cloning and persistence
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149 | // persistence
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150 | [StorableConstructor]
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151 | private Problem(StorableConstructorFlag _) : base(_) { }
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152 | [StorableHook(HookType.AfterDeserialization)]
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153 | private void AfterDeserialization() {
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154 | if (!Parameters.ContainsKey(OptimizeParametersForEpisodesParameterName)) {
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155 | Parameters.Add(new FixedValueParameter<BoolValue>(OptimizeParametersForEpisodesParameterName, "Flag to select if parameters should be optimized globally or for each episode individually.", new BoolValue(false)));
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156 | }
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157 | RegisterEventHandlers();
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158 | }
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159 |
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160 | // cloning
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161 | private Problem(Problem original, Cloner cloner)
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162 | : base(original, cloner) {
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163 | RegisterEventHandlers();
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164 | }
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165 | public override IDeepCloneable Clone(Cloner cloner) { return new Problem(this, cloner); }
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166 | #endregion
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167 |
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168 | public Problem()
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169 | : base() {
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170 | var targetVariables = new CheckedItemList<StringValue>().AsReadOnly(); // HACK: it would be better to provide a new class derived from IDataAnalysisProblem
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171 | var functions = CreateFunctionSet();
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172 | Parameters.Add(new ValueParameter<IRegressionProblemData>(ProblemDataParameterName, "The data captured from the dynamical system. Use CSV import functionality to import data.", new RegressionProblemData()));
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173 | Parameters.Add(new ValueParameter<ReadOnlyCheckedItemList<StringValue>>(TargetVariablesParameterName, "Target variables (overrides setting in ProblemData)", targetVariables));
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174 | Parameters.Add(new ValueParameter<ReadOnlyCheckedItemList<StringValue>>(FunctionSetParameterName, "The list of allowed functions", functions));
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175 | Parameters.Add(new FixedValueParameter<IntValue>(MaximumLengthParameterName, "The maximally allowed length of each expression. Set to a small value (5 - 25). Default = 10", new IntValue(10)));
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176 | Parameters.Add(new FixedValueParameter<IntValue>(MaximumParameterOptimizationIterationsParameterName, "The maximum number of iterations for optimization of parameters (using L-BFGS). More iterations makes the algorithm slower, fewer iterations might prevent convergence in the optimization scheme. Default = 100", new IntValue(100)));
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177 | Parameters.Add(new FixedValueParameter<IntValue>(NumberOfLatentVariablesParameterName, "Latent variables (unobserved variables) allow us to produce expressions which are integrated up and can be used in other expressions. They are handled similarly to target variables in forward simulation / integration. The difference to target variables is that there are no data to which the calculated values of latent variables are compared. Set to a small value (0 .. 5) as necessary (default = 0)", new IntValue(0)));
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178 | Parameters.Add(new FixedValueParameter<IntValue>(NumericIntegrationStepsParameterName, "Number of steps in the numeric integration that are taken from one row to the next (set to 1 to 100). More steps makes the algorithm slower, less steps worsens the accuracy of the numeric integration scheme.", new IntValue(10)));
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179 | Parameters.Add(new ValueParameter<ItemList<IntRange>>(TrainingEpisodesParameterName, "A list of ranges that should be used for training, each range represents an independent episode. This overrides the TrainingSet parameter in ProblemData.", new ItemList<IntRange>()));
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180 | Parameters.Add(new FixedValueParameter<BoolValue>(OptimizeParametersForEpisodesParameterName, "Flag to select if parameters should be optimized globally or for each episode individually.", new BoolValue(false)));
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181 |
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182 | var solversStr = new string[] { "HeuristicLab" /* , "CVODES" */};
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183 | var solvers = new ItemSet<StringValue>(
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184 | solversStr.Select(s => new StringValue(s).AsReadOnly())
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185 | );
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186 | Parameters.Add(new ConstrainedValueParameter<StringValue>(OdeSolverParameterName, "The solver to use for solving the initial value ODE problems", solvers, solvers.First()));
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187 |
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188 | RegisterEventHandlers();
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189 | InitAllParameters();
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190 |
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191 | // TODO: use training range as default training episode
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192 | // TODO: optimization of starting values for latent variables in CVODES solver
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193 | // TODO: allow to specify the name for the time variable in the dataset and allow variable step-sizes
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194 | }
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195 |
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196 | public override double Evaluate(Individual individual, IRandom random) {
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197 | var trees = individual.Values.Select(v => v.Value).OfType<ISymbolicExpressionTree>().ToArray(); // extract all trees from individual
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198 |
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199 | var problemData = ProblemData;
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200 | var targetVars = TargetVariables.CheckedItems.OrderBy(i => i.Index).Select(i => i.Value.Value).ToArray();
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201 | var latentVariables = Enumerable.Range(1, NumberOfLatentVariables).Select(i => "λ" + i).ToArray(); // TODO: must coincide with the variables which are actually defined in the grammar and also for which we actually have trees
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202 | if (OptimizeParametersForEpisodes) {
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203 | throw new NotImplementedException();
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204 | int eIdx = 0;
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205 | double totalNMSE = 0.0;
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206 | int totalSize = 0;
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207 | foreach (var episode in TrainingEpisodes) {
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208 | // double[] optTheta;
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209 | double nmse = OptimizeForEpisodes(trees, problemData, targetVars, latentVariables, random, new[] { episode }, MaximumParameterOptimizationIterations, NumericIntegrationSteps, OdeSolver);
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210 | // individual["OptTheta_" + eIdx] = new DoubleArray(optTheta); // write back optimized parameters so that we can use them in the Analysis method
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211 | eIdx++;
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212 | totalNMSE += nmse * episode.Size;
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213 | totalSize += episode.Size;
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214 | }
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215 | return totalNMSE / totalSize;
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216 | } else {
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217 | // double[] optTheta;
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218 | double nmse = OptimizeForEpisodes(trees, problemData, targetVars, latentVariables, random, TrainingEpisodes, MaximumParameterOptimizationIterations, NumericIntegrationSteps, OdeSolver);
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219 | // individual["OptTheta"] = new DoubleArray(optTheta); // write back optimized parameters so that we can use them in the Analysis method
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220 | return nmse;
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221 | }
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222 | }
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223 |
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224 | public static double OptimizeForEpisodes(
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225 | ISymbolicExpressionTree[] trees,
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226 | IRegressionProblemData problemData,
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227 | string[] targetVars,
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228 | string[] latentVariables,
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229 | IRandom random,
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230 | IEnumerable<IntRange> episodes,
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231 | int maxParameterOptIterations,
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232 | int numericIntegrationSteps,
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233 | string odeSolver) {
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234 |
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235 | // extract constants from trees (without trees for latent variables)
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236 | var targetVariableTrees = trees.Take(targetVars.Length).ToArray();
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237 | var latentVariableTrees = trees.Skip(targetVars.Length).ToArray();
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238 | var constantNodes = targetVariableTrees.Select(t => t.IterateNodesPrefix().OfType<ConstantTreeNode>().ToArray()).ToArray();
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239 | var initialTheta = constantNodes.Select(nodes => nodes.Select(n => n.Value).ToArray()).ToArray();
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240 |
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241 | // optimize parameters by fitting f(x,y) to calculated differences dy/dt(t)
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242 | double nmse = PreTuneParameters(trees, problemData, targetVars, latentVariables, random, episodes, maxParameterOptIterations,
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243 | initialTheta, out double[] pretunedParameters);
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244 |
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245 | // extend parameter vector to include parameters for latent variable trees
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246 | pretunedParameters = pretunedParameters
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247 | .Concat(latentVariableTrees
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248 | .SelectMany(t => t.IterateNodesPrefix().OfType<ConstantTreeNode>().Select(n => n.Value)))
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249 | .ToArray();
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250 |
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251 | // optimize parameters using integration of f(x,y) to calculate y(t)
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252 | nmse = OptimizeParameters(trees, problemData, targetVars, latentVariables, episodes, maxParameterOptIterations, pretunedParameters, numericIntegrationSteps, odeSolver,
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253 | out double[] optTheta);
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254 | // var optTheta = pretunedParameters;
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255 |
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256 | if (double.IsNaN(nmse) ||
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257 | double.IsInfinity(nmse) ||
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258 | nmse > 100 * trees.Length * episodes.Sum(ep => ep.Size))
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259 | return 100 * trees.Length * episodes.Sum(ep => ep.Size);
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260 |
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261 | // update tree nodes with optimized values
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262 | var paramIdx = 0;
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263 | for (var treeIdx = 0; treeIdx < constantNodes.Length; treeIdx++) {
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264 | for (int i = 0; i < constantNodes[treeIdx].Length; i++)
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265 | constantNodes[treeIdx][i].Value = optTheta[paramIdx++];
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266 | }
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267 | return nmse;
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268 | }
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269 |
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270 | private static double PreTuneParameters(
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271 | ISymbolicExpressionTree[] trees,
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272 | IRegressionProblemData problemData,
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273 | string[] targetVars,
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274 | string[] latentVariables,
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275 | IRandom random,
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276 | IEnumerable<IntRange> episodes,
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277 | int maxParameterOptIterations,
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278 | double[][] initialTheta,
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279 | out double[] optTheta) {
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280 | var thetas = new List<double>();
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281 | double nmse = 0.0;
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282 | var maxTreeNmse = 100 * episodes.Sum(ep => ep.Size);
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283 |
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284 | var targetTrees = trees.Take(targetVars.Length).ToArray();
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285 | var latentTrees = trees.Take(latentVariables.Length).ToArray();
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286 |
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287 | {
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288 | // first calculate values of latent variables by integration
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289 | var inputVariables = targetVars.Concat(latentTrees.SelectMany(t => t.IterateNodesPrefix().OfType<VariableTreeNode>().Select(n => n.VariableName))).Except(latentVariables).Distinct();
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290 | var myState = new OptimizationData(latentTrees, targetVars, inputVariables.ToArray(), problemData, null, episodes.ToArray(), 10, latentVariables, "HeuristicLab");
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291 |
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292 | var fi = new double[myState.rows.Length * targetVars.Length];
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293 | var jac = new double[myState.rows.Length * targetVars.Length, myState.nodeValueLookup.ParameterCount];
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294 | var latentValues = new double[myState.rows.Length, latentVariables.Length];
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295 | Integrate(myState, fi, jac, latentValues);
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296 |
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297 | // add integrated latent variables to dataset
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298 | var modifiedDataset = ((Dataset)problemData.Dataset).ToModifiable();
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299 | foreach (var variable in latentVariables) {
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300 | modifiedDataset.AddVariable(variable, Enumerable.Repeat(0.0, modifiedDataset.Rows).ToList()); // empty column
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301 | }
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302 | int predIdx = 0;
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303 | foreach (var ep in episodes) {
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304 | for (int r = ep.Start; r < ep.End; r++) {
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305 | for (int latVarIdx = 0; latVarIdx < latentVariables.Length; latVarIdx++) {
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306 | modifiedDataset.SetVariableValue(latentValues[predIdx, latVarIdx], latentVariables[latVarIdx], r);
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307 | }
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308 | predIdx++;
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309 | }
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310 | }
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311 |
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312 | problemData = new RegressionProblemData(modifiedDataset, problemData.AllowedInputVariables, problemData.TargetVariable);
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313 | }
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314 | // NOTE: the order of values in parameter matches prefix order of constant nodes in trees
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315 | for (int treeIdx = 0; treeIdx < targetTrees.Length; treeIdx++) {
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316 | var t = targetTrees[treeIdx];
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317 |
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318 | var targetValuesDiff = new List<double>();
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319 | foreach (var ep in episodes) {
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320 | var episodeRows = Enumerable.Range(ep.Start, ep.Size);
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321 | var targetValues = problemData.Dataset.GetDoubleValues(targetVars[treeIdx], episodeRows).ToArray();
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322 | targetValuesDiff.AddRange(targetValues.Skip(1).Zip(targetValues, (t1, t0) => t1 - t0));// TODO: smoothing or multi-pole);
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323 | }
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324 | var adjustedEpisodes = episodes.Select(ep => new IntRange(ep.Start, ep.End - 1)); // because we lose the last row in the differencing step
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325 |
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326 | // data for input variables is assumed to be known
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327 | // input variables in pretuning are all target variables and all variable names that occur in the tree
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328 | var inputVariables = targetVars.Concat(t.IterateNodesPrefix().OfType<VariableTreeNode>().Select(n => n.VariableName)).Distinct();
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329 |
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330 | var myState = new OptimizationData(new[] { t },
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331 | targetVars,
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332 | inputVariables.ToArray(),
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333 | problemData, new[] { targetValuesDiff.ToArray() }, adjustedEpisodes.ToArray(), -99, latentVariables, string.Empty); // TODO
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334 | var paramCount = myState.nodeValueLookup.ParameterCount;
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335 |
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336 | optTheta = new double[0];
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337 | if (initialTheta[treeIdx].Length > 0) {
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338 | try {
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339 | alglib.minlmstate state;
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340 | alglib.minlmreport report;
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341 | var p = new double[initialTheta[treeIdx].Length];
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342 | var lowerBounds = Enumerable.Repeat(-1000.0, p.Length).ToArray();
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343 | var upperBounds = Enumerable.Repeat(1000.0, p.Length).ToArray();
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344 | Array.Copy(initialTheta[treeIdx], p, p.Length);
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345 | alglib.minlmcreatevj(targetValuesDiff.Count, p, out state);
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346 | alglib.minlmsetcond(state, 0.0, 0.0, 0.0, maxParameterOptIterations);
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347 | alglib.minlmsetbc(state, lowerBounds, upperBounds);
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348 | #if DEBUG
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349 | //alglib.minlmsetgradientcheck(state, 1.0e-7);
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350 | #endif
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351 | alglib.minlmoptimize(state, EvaluateObjectiveVector, EvaluateObjectiveVectorAndJacobian, null, myState);
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352 |
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353 | alglib.minlmresults(state, out optTheta, out report);
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354 | if (report.terminationtype < 0) {
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355 | #if DEBUG
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356 | if (report.terminationtype == -7) throw new InvalidProgramException("gradient calculation fail!");
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357 | #endif
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358 | optTheta = initialTheta[treeIdx];
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359 | }
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360 | } catch (alglib.alglibexception) {
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361 | optTheta = initialTheta[treeIdx];
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362 | }
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363 | }
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364 | var tree_nmse = EvaluateMSE(optTheta, myState);
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365 | if (double.IsNaN(tree_nmse) || double.IsInfinity(tree_nmse) || tree_nmse > maxTreeNmse) {
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366 | nmse += maxTreeNmse;
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367 | thetas.AddRange(initialTheta[treeIdx]);
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368 | } else {
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369 | nmse += tree_nmse;
|
---|
370 | thetas.AddRange(optTheta);
|
---|
371 | }
|
---|
372 | } // foreach tree
|
---|
373 | optTheta = thetas.ToArray();
|
---|
374 |
|
---|
375 | return nmse;
|
---|
376 | }
|
---|
377 |
|
---|
378 |
|
---|
379 | // similar to above but this time we integrate and optimize all parameters for all targets concurrently
|
---|
380 | private static double OptimizeParameters(ISymbolicExpressionTree[] trees, IRegressionProblemData problemData, string[] targetVars, string[] latentVariables,
|
---|
381 | IEnumerable<IntRange> episodes, int maxParameterOptIterations, double[] initialTheta, int numericIntegrationSteps, string odeSolver, out double[] optTheta) {
|
---|
382 | var rowsForDataExtraction = episodes.SelectMany(e => Enumerable.Range(e.Start, e.Size)).ToArray();
|
---|
383 | var targetValues = new double[targetVars.Length][];
|
---|
384 | for (int treeIdx = 0; treeIdx < targetVars.Length; treeIdx++) {
|
---|
385 | var t = trees[treeIdx];
|
---|
386 |
|
---|
387 | targetValues[treeIdx] = problemData.Dataset.GetDoubleValues(targetVars[treeIdx], rowsForDataExtraction).ToArray();
|
---|
388 | }
|
---|
389 |
|
---|
390 | // data for input variables is assumed to be known
|
---|
391 | // input variables are all variable names that occur in the trees except for target variables (we assume that trees have been generated correctly)
|
---|
392 | var inputVariables = trees.SelectMany(t => t.IterateNodesPrefix().OfType<VariableTreeNode>().Select(n => n.VariableName))
|
---|
393 | .Except(targetVars)
|
---|
394 | .Except(latentVariables)
|
---|
395 | .Distinct();
|
---|
396 |
|
---|
397 | var myState = new OptimizationData(trees, targetVars, inputVariables.ToArray(), problemData, targetValues, episodes.ToArray(), numericIntegrationSteps, latentVariables, odeSolver);
|
---|
398 | optTheta = initialTheta;
|
---|
399 |
|
---|
400 | if (initialTheta.Length > 0) {
|
---|
401 | var lowerBounds = Enumerable.Repeat(-1000.0, initialTheta.Length).ToArray();
|
---|
402 | var upperBounds = Enumerable.Repeat(1000.0, initialTheta.Length).ToArray();
|
---|
403 | try {
|
---|
404 | alglib.minlmstate state;
|
---|
405 | alglib.minlmreport report;
|
---|
406 | alglib.minlmcreatevj(rowsForDataExtraction.Length * trees.Length, initialTheta, out state);
|
---|
407 | alglib.minlmsetbc(state, lowerBounds, upperBounds);
|
---|
408 | alglib.minlmsetcond(state, 0.0, 0.0, 0.0, maxParameterOptIterations);
|
---|
409 | #if DEBUG
|
---|
410 | //alglib.minlmsetgradientcheck(state, 1.0e-7);
|
---|
411 | #endif
|
---|
412 | alglib.minlmoptimize(state, IntegrateAndEvaluateObjectiveVector, IntegrateAndEvaluateObjectiveVectorAndJacobian, null, myState);
|
---|
413 |
|
---|
414 | alglib.minlmresults(state, out optTheta, out report);
|
---|
415 |
|
---|
416 | if (report.terminationtype < 0) {
|
---|
417 | #if DEBUG
|
---|
418 | if (report.terminationtype == -7) throw new InvalidProgramException("gradient calculation fail!");
|
---|
419 | #endif // there was a problem: reset theta and evaluate for inital values
|
---|
420 | optTheta = initialTheta;
|
---|
421 | }
|
---|
422 | } catch (alglib.alglibexception) {
|
---|
423 | optTheta = initialTheta;
|
---|
424 | }
|
---|
425 | }
|
---|
426 | var nmse = EvaluateIntegratedMSE(optTheta, myState);
|
---|
427 | var maxNmse = 100 * targetValues.Length * rowsForDataExtraction.Length;
|
---|
428 | if (double.IsNaN(nmse) || double.IsInfinity(nmse) || nmse > maxNmse) nmse = maxNmse;
|
---|
429 | return nmse;
|
---|
430 | }
|
---|
431 |
|
---|
432 |
|
---|
433 | // helper
|
---|
434 | public static double EvaluateMSE(double[] x, OptimizationData optimizationData) {
|
---|
435 | var fi = new double[optimizationData.rows.Count()];
|
---|
436 | EvaluateObjectiveVector(x, fi, optimizationData);
|
---|
437 | return fi.Sum(fii => fii * fii) / fi.Length;
|
---|
438 | }
|
---|
439 | public static void EvaluateObjectiveVector(double[] x, double[] fi, object optimizationData) { EvaluateObjectiveVector(x, fi, (OptimizationData)optimizationData); } // for alglib
|
---|
440 | public static void EvaluateObjectiveVector(double[] x, double[] fi, OptimizationData optimizationData) {
|
---|
441 | var rows = optimizationData.rows;
|
---|
442 | var problemData = optimizationData.problemData;
|
---|
443 | var nodeValueLookup = optimizationData.nodeValueLookup;
|
---|
444 | var ds = problemData.Dataset;
|
---|
445 | var variables = optimizationData.variables;
|
---|
446 |
|
---|
447 | nodeValueLookup.UpdateParamValues(x);
|
---|
448 |
|
---|
449 | int outputIdx = 0;
|
---|
450 | for (int trainIdx = 0; trainIdx < rows.Length; trainIdx++) {
|
---|
451 | // update variable values
|
---|
452 | foreach (var variable in variables) {
|
---|
453 | // in this problem we also allow fixed numeric parameters (represented as variables with the value as name)
|
---|
454 | if (double.TryParse(variable, NumberStyles.Float, CultureInfo.InvariantCulture, out double value)) {
|
---|
455 | nodeValueLookup.SetVariableValue(variable, value); // TODO: Perf we don't need to set this for each index
|
---|
456 | } else {
|
---|
457 | nodeValueLookup.SetVariableValue(variable, ds.GetDoubleValue(variable, rows[trainIdx])); // TODO: perf
|
---|
458 | }
|
---|
459 | }
|
---|
460 | // interpret all trees
|
---|
461 | for (int treeIdx = 0; treeIdx < optimizationData.trees.Length; treeIdx++) {
|
---|
462 | var tree = optimizationData.trees[treeIdx];
|
---|
463 | var pred = InterpretRec(tree.Root.GetSubtree(0).GetSubtree(0), nodeValueLookup);
|
---|
464 | var y = optimizationData.targetValues[treeIdx][trainIdx];
|
---|
465 | fi[outputIdx++] = (y - pred) * optimizationData.inverseStandardDeviation[treeIdx];
|
---|
466 | }
|
---|
467 | }
|
---|
468 | }
|
---|
469 |
|
---|
470 | public static void EvaluateObjectiveVectorAndJacobian(double[] x, double[] fi, double[,] jac, object optimizationData) { EvaluateObjectiveVectorAndJacobian(x, fi, jac, (OptimizationData)optimizationData); } // for alglib
|
---|
471 | public static void EvaluateObjectiveVectorAndJacobian(double[] x, double[] fi, double[,] jac, OptimizationData optimizationData) {
|
---|
472 | // extract variable values from dataset
|
---|
473 | var variableValues = new Dictionary<string, Tuple<double, Vector>>();
|
---|
474 | var problemData = optimizationData.problemData;
|
---|
475 | var ds = problemData.Dataset;
|
---|
476 | var rows = optimizationData.rows;
|
---|
477 | var variables = optimizationData.variables;
|
---|
478 |
|
---|
479 | var nodeValueLookup = optimizationData.nodeValueLookup;
|
---|
480 | nodeValueLookup.UpdateParamValues(x);
|
---|
481 |
|
---|
482 | int termIdx = 0;
|
---|
483 |
|
---|
484 | for (int trainIdx = 0; trainIdx < rows.Length; trainIdx++) {
|
---|
485 | // update variable values
|
---|
486 | foreach (var variable in variables) {
|
---|
487 | // in this problem we also allow fixed numeric parameters (represented as variables with the value as name)
|
---|
488 | if (double.TryParse(variable, NumberStyles.Float, CultureInfo.InvariantCulture, out double value)) {
|
---|
489 | nodeValueLookup.SetVariableValue(variable, value); // TODO: Perf we don't need to set this for each index
|
---|
490 | } else {
|
---|
491 | nodeValueLookup.SetVariableValue(variable, ds.GetDoubleValue(variable, rows[trainIdx])); // TODO: perf
|
---|
492 | }
|
---|
493 | }
|
---|
494 |
|
---|
495 | var calculatedVariables = optimizationData.targetVariables;
|
---|
496 |
|
---|
497 | var trees = optimizationData.trees;
|
---|
498 | for (int i = 0; i < trees.Length; i++) {
|
---|
499 | var tree = trees[i];
|
---|
500 | var targetVarName = calculatedVariables[i];
|
---|
501 |
|
---|
502 | double f; Vector g;
|
---|
503 | InterpretRec(tree.Root.GetSubtree(0).GetSubtree(0), nodeValueLookup, out f, out g);
|
---|
504 |
|
---|
505 | var y = optimizationData.targetValues[i][trainIdx];
|
---|
506 | fi[termIdx] = (y - f) * optimizationData.inverseStandardDeviation[i]; // scale of NMSE
|
---|
507 | if (jac != null && g != Vector.Zero) for (int j = 0; j < g.Length; j++) jac[termIdx, j] = -g[j] * optimizationData.inverseStandardDeviation[i];
|
---|
508 |
|
---|
509 | termIdx++;
|
---|
510 | }
|
---|
511 | }
|
---|
512 |
|
---|
513 | }
|
---|
514 |
|
---|
515 | // helper
|
---|
516 | public static double EvaluateIntegratedMSE(double[] x, OptimizationData optimizationData) {
|
---|
517 | var fi = new double[optimizationData.rows.Count() * optimizationData.targetVariables.Length];
|
---|
518 | IntegrateAndEvaluateObjectiveVector(x, fi, optimizationData);
|
---|
519 | return fi.Sum(fii => fii * fii) / fi.Length;
|
---|
520 | }
|
---|
521 | public static void IntegrateAndEvaluateObjectiveVector(double[] x, double[] fi, object optimizationData) { IntegrateAndEvaluateObjectiveVector(x, fi, (OptimizationData)optimizationData); } // for alglib
|
---|
522 | public static void IntegrateAndEvaluateObjectiveVector(double[] x, double[] fi, OptimizationData optimizationData) {
|
---|
523 | IntegrateAndEvaluateObjectiveVectorAndJacobian(x, fi, null, optimizationData);
|
---|
524 | }
|
---|
525 |
|
---|
526 | public static void IntegrateAndEvaluateObjectiveVectorAndJacobian(double[] x, double[] fi, double[,] jac, object optimizationData) { IntegrateAndEvaluateObjectiveVectorAndJacobian(x, fi, jac, (OptimizationData)optimizationData); } // for alglib
|
---|
527 | public static void IntegrateAndEvaluateObjectiveVectorAndJacobian(double[] x, double[] fi, double[,] jac, OptimizationData optimizationData) {
|
---|
528 | var rows = optimizationData.rows.ToArray();
|
---|
529 | var problemData = optimizationData.problemData;
|
---|
530 | var nodeValueLookup = optimizationData.nodeValueLookup;
|
---|
531 | var ds = problemData.Dataset;
|
---|
532 | int outputIdx = 0;
|
---|
533 |
|
---|
534 | nodeValueLookup.UpdateParamValues(x);
|
---|
535 |
|
---|
536 | Integrate(optimizationData, fi, jac, null);
|
---|
537 | var trees = optimizationData.trees;
|
---|
538 |
|
---|
539 | // update result with error
|
---|
540 | for (int trainIdx = 0; trainIdx < rows.Length; trainIdx++) {
|
---|
541 | for (int i = 0; i < optimizationData.targetVariables.Length; i++) {
|
---|
542 | var tree = trees[i];
|
---|
543 | var y = optimizationData.targetValues[i][trainIdx];
|
---|
544 | fi[outputIdx] = (y - fi[outputIdx]) * optimizationData.inverseStandardDeviation[i]; // scale for normalized squared error
|
---|
545 | if (jac != null) for (int j = 0; j < x.Length; j++) jac[outputIdx, j] = -jac[outputIdx, j] * optimizationData.inverseStandardDeviation[i];
|
---|
546 | outputIdx++;
|
---|
547 | }
|
---|
548 | }
|
---|
549 | }
|
---|
550 |
|
---|
551 | public override void Analyze(Individual[] individuals, double[] qualities, ResultCollection results, IRandom random) {
|
---|
552 | base.Analyze(individuals, qualities, results, random);
|
---|
553 |
|
---|
554 | if (!results.ContainsKey("Prediction (training)")) {
|
---|
555 | results.Add(new Result("Prediction (training)", typeof(ReadOnlyItemList<DataTable>)));
|
---|
556 | }
|
---|
557 | if (!results.ContainsKey("Prediction (test)")) {
|
---|
558 | results.Add(new Result("Prediction (test)", typeof(ReadOnlyItemList<DataTable>)));
|
---|
559 | }
|
---|
560 | if (!results.ContainsKey("Models")) {
|
---|
561 | results.Add(new Result("Models", typeof(VariableCollection)));
|
---|
562 | }
|
---|
563 | if (!results.ContainsKey("SNMSE")) {
|
---|
564 | results.Add(new Result("SNMSE", typeof(DoubleValue)));
|
---|
565 | }
|
---|
566 | if (!results.ContainsKey("Solution")) {
|
---|
567 | results.Add(new Result("Solution", typeof(Solution)));
|
---|
568 | }
|
---|
569 | if (!results.ContainsKey("Squared error and gradient")) {
|
---|
570 | results.Add(new Result("Squared error and gradient", typeof(DataTable)));
|
---|
571 | }
|
---|
572 |
|
---|
573 | var bestIndividualAndQuality = this.GetBestIndividual(individuals, qualities);
|
---|
574 | var trees = bestIndividualAndQuality.Item1.Values.Select(v => v.Value).OfType<ISymbolicExpressionTree>().ToArray(); // extract all trees from individual
|
---|
575 |
|
---|
576 | results["SNMSE"].Value = new DoubleValue(bestIndividualAndQuality.Item2);
|
---|
577 |
|
---|
578 | var problemData = ProblemData;
|
---|
579 | var targetVars = TargetVariables.CheckedItems.OrderBy(i => i.Index).Select(i => i.Value.Value).ToArray();
|
---|
580 | var latentVariables = Enumerable.Range(1, NumberOfLatentVariables).Select(i => "λ" + i).ToArray(); // TODO: must coincide with the variables which are actually defined in the grammar and also for which we actually have trees
|
---|
581 |
|
---|
582 | var trainingList = new ItemList<DataTable>();
|
---|
583 |
|
---|
584 | if (OptimizeParametersForEpisodes) {
|
---|
585 | throw new NotSupportedException();
|
---|
586 | var eIdx = 0;
|
---|
587 | var trainingPredictions = new List<Tuple<double, Vector>[][]>();
|
---|
588 | foreach (var episode in TrainingEpisodes) {
|
---|
589 | var episodes = new[] { episode };
|
---|
590 | var optimizationData = new OptimizationData(trees, targetVars, problemData.AllowedInputVariables.ToArray(), problemData, null, episodes, NumericIntegrationSteps, latentVariables, OdeSolver);
|
---|
591 | var trainingPrediction = Integrate(optimizationData).ToArray();
|
---|
592 | trainingPredictions.Add(trainingPrediction);
|
---|
593 | eIdx++;
|
---|
594 | }
|
---|
595 |
|
---|
596 | // only for target values
|
---|
597 | var trainingRows = TrainingEpisodes.SelectMany(e => Enumerable.Range(e.Start, e.End - e.Start));
|
---|
598 | for (int colIdx = 0; colIdx < targetVars.Length; colIdx++) {
|
---|
599 | var targetVar = targetVars[colIdx];
|
---|
600 | var trainingDataTable = new DataTable(targetVar + " prediction (training)");
|
---|
601 | var actualValuesRow = new DataRow(targetVar, "The values of " + targetVar, problemData.Dataset.GetDoubleValues(targetVar, trainingRows));
|
---|
602 | var predictedValuesRow = new DataRow(targetVar + " pred.", "Predicted values for " + targetVar, trainingPredictions.SelectMany(arr => arr.Select(row => row[colIdx].Item1)).ToArray());
|
---|
603 | trainingDataTable.Rows.Add(actualValuesRow);
|
---|
604 | trainingDataTable.Rows.Add(predictedValuesRow);
|
---|
605 | trainingList.Add(trainingDataTable);
|
---|
606 | }
|
---|
607 | results["Prediction (training)"].Value = trainingList.AsReadOnly();
|
---|
608 |
|
---|
609 |
|
---|
610 | var models = new VariableCollection();
|
---|
611 |
|
---|
612 | foreach (var tup in targetVars.Zip(trees, Tuple.Create)) {
|
---|
613 | var targetVarName = tup.Item1;
|
---|
614 | var tree = tup.Item2;
|
---|
615 |
|
---|
616 | var origTreeVar = new HeuristicLab.Core.Variable(targetVarName + "(original)");
|
---|
617 | origTreeVar.Value = (ISymbolicExpressionTree)tree.Clone();
|
---|
618 | models.Add(origTreeVar);
|
---|
619 | }
|
---|
620 | results["Models"].Value = models;
|
---|
621 | } else {
|
---|
622 | // data for input variables is assumed to be known
|
---|
623 | // input variables are all variable names that occur in the trees except for target variables (we assume that trees have been generated correctly)
|
---|
624 | var inputVariables = trees
|
---|
625 | .SelectMany(t => t.IterateNodesPrefix().OfType<VariableTreeNode>().Select(n => n.VariableName))
|
---|
626 | .Except(targetVars)
|
---|
627 | .Except(latentVariables)
|
---|
628 | .Distinct();
|
---|
629 |
|
---|
630 | var optimizationData = new OptimizationData(trees, targetVars, inputVariables.ToArray(), problemData, null, TrainingEpisodes.ToArray(), NumericIntegrationSteps, latentVariables, OdeSolver);
|
---|
631 | var numParams = optimizationData.nodeValueLookup.ParameterCount;
|
---|
632 |
|
---|
633 | var fi = new double[optimizationData.rows.Length * targetVars.Length];
|
---|
634 | var jac = new double[optimizationData.rows.Length * targetVars.Length, numParams];
|
---|
635 | var latentValues = new double[optimizationData.rows.Length, latentVariables.Length];
|
---|
636 | Integrate(optimizationData, fi, jac, latentValues);
|
---|
637 |
|
---|
638 |
|
---|
639 | // for target values and latent variables
|
---|
640 | var trainingRows = optimizationData.rows;
|
---|
641 | for (int colIdx = 0; colIdx < trees.Length; colIdx++) {
|
---|
642 | // is target variable
|
---|
643 | if (colIdx < targetVars.Length) {
|
---|
644 | var targetVar = targetVars[colIdx];
|
---|
645 | var trainingDataTable = new DataTable(targetVar + " prediction (training)");
|
---|
646 | var actualValuesRow = new DataRow(targetVar, "The values of " + targetVar, problemData.Dataset.GetDoubleValues(targetVar, trainingRows));
|
---|
647 | var idx = Enumerable.Range(0, trainingRows.Length).Select(i => i * targetVars.Length + colIdx);
|
---|
648 | var pred = idx.Select(i => fi[i]);
|
---|
649 | var predictedValuesRow = new DataRow(targetVar + " pred.", "Predicted values for " + targetVar, pred.ToArray());
|
---|
650 | trainingDataTable.Rows.Add(actualValuesRow);
|
---|
651 | trainingDataTable.Rows.Add(predictedValuesRow);
|
---|
652 |
|
---|
653 | for (int paramIdx = 0; paramIdx < numParams; paramIdx++) {
|
---|
654 | var paramSensitivityRow = new DataRow($"∂{targetVar}/∂θ{paramIdx}", $"Sensitivities of parameter {paramIdx}", idx.Select(i => jac[i, paramIdx]).ToArray());
|
---|
655 | paramSensitivityRow.VisualProperties.SecondYAxis = true;
|
---|
656 | trainingDataTable.Rows.Add(paramSensitivityRow);
|
---|
657 | }
|
---|
658 | trainingList.Add(trainingDataTable);
|
---|
659 | } else {
|
---|
660 | var latentVar = latentVariables[colIdx - targetVars.Length];
|
---|
661 | var trainingDataTable = new DataTable(latentVar + " prediction (training)");
|
---|
662 | var idx = Enumerable.Range(0, trainingRows.Length);
|
---|
663 | var pred = idx.Select(i => latentValues[i, colIdx - targetVars.Length]);
|
---|
664 | var predictedValuesRow = new DataRow(latentVar + " pred.", "Predicted values for " + latentVar, pred.ToArray());
|
---|
665 | var emptyRow = new DataRow(latentVar);
|
---|
666 | trainingDataTable.Rows.Add(emptyRow);
|
---|
667 | trainingDataTable.Rows.Add(predictedValuesRow);
|
---|
668 | trainingList.Add(trainingDataTable);
|
---|
669 | }
|
---|
670 | }
|
---|
671 |
|
---|
672 | var errorTable = new DataTable("Squared error and gradient");
|
---|
673 | var seRow = new DataRow("Squared error");
|
---|
674 | var gradientRows = Enumerable.Range(0, numParams).Select(i => new DataRow($"∂SE/∂θ{i}")).ToArray();
|
---|
675 | errorTable.Rows.Add(seRow);
|
---|
676 | foreach (var gRow in gradientRows) {
|
---|
677 | gRow.VisualProperties.SecondYAxis = true;
|
---|
678 | errorTable.Rows.Add(gRow);
|
---|
679 | }
|
---|
680 | var targetValues = targetVars.Select(v => problemData.Dataset.GetDoubleValues(v, trainingRows).ToArray()).ToArray();
|
---|
681 | int r = 0;
|
---|
682 |
|
---|
683 | // foreach (var y_pred in trainingPrediction) {
|
---|
684 | // // calculate objective function gradient
|
---|
685 | // double f_i = 0.0;
|
---|
686 | // Vector g_i = Vector.CreateNew(new double[numParams]);
|
---|
687 | // for (int colIdx = 0; colIdx < targetVars.Length; colIdx++) {
|
---|
688 | // var y_pred_f = y_pred[colIdx].Item1;
|
---|
689 | // var y = targetValues[colIdx][r];
|
---|
690 | //
|
---|
691 | // var res = (y - y_pred_f) * optimizationData.inverseStandardDeviation[colIdx];
|
---|
692 | // var ressq = res * res;
|
---|
693 | // f_i += ressq;
|
---|
694 | // g_i.Add(y_pred[colIdx].Item2.Scale(-2.0 * res));
|
---|
695 | // }
|
---|
696 | // seRow.Values.Add(f_i);
|
---|
697 | // for (int j = 0; j < g_i.Length; j++) gradientRows[j].Values.Add(g_i[j]);
|
---|
698 | // r++;
|
---|
699 | // }
|
---|
700 | // results["Squared error and gradient"].Value = errorTable;
|
---|
701 |
|
---|
702 | // TODO: DRY for training and test
|
---|
703 | var testList = new ItemList<DataTable>();
|
---|
704 | var testRows = ProblemData.TestIndices.ToArray();
|
---|
705 | var testOptimizationData = new OptimizationData(trees, targetVars, problemData.AllowedInputVariables.ToArray(), problemData, null, new IntRange[] { ProblemData.TestPartition }, NumericIntegrationSteps, latentVariables, OdeSolver);
|
---|
706 | var testPrediction = Integrate(testOptimizationData).ToArray();
|
---|
707 |
|
---|
708 | for (int colIdx = 0; colIdx < trees.Length; colIdx++) {
|
---|
709 | // is target variable
|
---|
710 | if (colIdx < targetVars.Length) {
|
---|
711 | var targetVar = targetVars[colIdx];
|
---|
712 | var testDataTable = new DataTable(targetVar + " prediction (test)");
|
---|
713 | var actualValuesRow = new DataRow(targetVar, "The values of " + targetVar, problemData.Dataset.GetDoubleValues(targetVar, testRows));
|
---|
714 | var predictedValuesRow = new DataRow(targetVar + " pred.", "Predicted values for " + targetVar, testPrediction.Select(arr => arr[colIdx].Item1).ToArray());
|
---|
715 | testDataTable.Rows.Add(actualValuesRow);
|
---|
716 | testDataTable.Rows.Add(predictedValuesRow);
|
---|
717 | testList.Add(testDataTable);
|
---|
718 |
|
---|
719 | } else {
|
---|
720 | // var latentVar = latentVariables[colIdx - targetVars.Length];
|
---|
721 | // var testDataTable = new DataTable(latentVar + " prediction (test)");
|
---|
722 | // var predictedValuesRow = new DataRow(latentVar + " pred.", "Predicted values for " + latentVar, testPrediction.Select(arr => arr[colIdx].Item1).ToArray());
|
---|
723 | // var emptyRow = new DataRow(latentVar);
|
---|
724 | // testDataTable.Rows.Add(emptyRow);
|
---|
725 | // testDataTable.Rows.Add(predictedValuesRow);
|
---|
726 | // testList.Add(testDataTable);
|
---|
727 | }
|
---|
728 | }
|
---|
729 |
|
---|
730 | results["Prediction (training)"].Value = trainingList.AsReadOnly();
|
---|
731 | results["Prediction (test)"].Value = testList.AsReadOnly();
|
---|
732 |
|
---|
733 |
|
---|
734 | #region simplification of models
|
---|
735 | // TODO the dependency of HeuristicLab.Problems.DataAnalysis.Symbolic is not ideal
|
---|
736 | var models = new VariableCollection(); // to store target var names and original version of tree
|
---|
737 |
|
---|
738 | var clonedTrees = new List<ISymbolicExpressionTree>();
|
---|
739 | for (int idx = 0; idx < trees.Length; idx++) {
|
---|
740 | clonedTrees.Add((ISymbolicExpressionTree)trees[idx].Clone());
|
---|
741 | }
|
---|
742 | var ds = problemData.Dataset;
|
---|
743 | var newProblemData = new RegressionProblemData((IDataset)ds.Clone(), problemData.AllowedInputVariables, problemData.TargetVariable);
|
---|
744 | results["Solution"].Value = new Solution(clonedTrees.ToArray(),
|
---|
745 | // optTheta,
|
---|
746 | newProblemData,
|
---|
747 | targetVars,
|
---|
748 | latentVariables,
|
---|
749 | TrainingEpisodes,
|
---|
750 | OdeSolver,
|
---|
751 | NumericIntegrationSteps);
|
---|
752 |
|
---|
753 |
|
---|
754 | for (int idx = 0; idx < trees.Length; idx++) {
|
---|
755 | var varName = string.Empty;
|
---|
756 | if (idx < targetVars.Length) {
|
---|
757 | varName = targetVars[idx];
|
---|
758 | } else {
|
---|
759 | varName = latentVariables[idx - targetVars.Length];
|
---|
760 | }
|
---|
761 | var tree = trees[idx];
|
---|
762 |
|
---|
763 | var origTreeVar = new HeuristicLab.Core.Variable(varName + "(original)");
|
---|
764 | origTreeVar.Value = (ISymbolicExpressionTree)tree.Clone();
|
---|
765 | models.Add(origTreeVar);
|
---|
766 | var simplifiedTreeVar = new HeuristicLab.Core.Variable(varName + "(simplified)");
|
---|
767 | simplifiedTreeVar.Value = TreeSimplifier.Simplify(tree);
|
---|
768 | models.Add(simplifiedTreeVar);
|
---|
769 | }
|
---|
770 |
|
---|
771 | results["Models"].Value = models;
|
---|
772 | #endregion
|
---|
773 |
|
---|
774 | #region produce classical solutions to allow visualization with PDP
|
---|
775 | for (int treeIdx = 0; treeIdx < trees.Length; treeIdx++) {
|
---|
776 | var t = (ISymbolicExpressionTree)trees[treeIdx].Clone();
|
---|
777 | var name = targetVars.Concat(latentVariables).ElementAt(treeIdx); // whatever
|
---|
778 | var model = new SymbolicRegressionModel(name + "_diff", t, new SymbolicDataAnalysisExpressionTreeLinearInterpreter());
|
---|
779 | var solutionDataset = ((Dataset)problemData.Dataset).ToModifiable();
|
---|
780 | if (treeIdx < targetVars.Length) {
|
---|
781 | var absValues = solutionDataset.GetDoubleValues(name).ToArray();
|
---|
782 | solutionDataset.AddVariable(name + "_diff", absValues.Skip(1).Zip(absValues, (v1, v0) => v1 - v0).Concat(new double[] { 0.0 }).ToList());
|
---|
783 | }
|
---|
784 | var solutionProblemData = new RegressionProblemData(solutionDataset, problemData.AllowedInputVariables, name + "_diff");
|
---|
785 | var solution = model.CreateRegressionSolution(solutionProblemData);
|
---|
786 | results.AddOrUpdateResult("Solution " + name, solution);
|
---|
787 | }
|
---|
788 | #endregion
|
---|
789 | }
|
---|
790 | }
|
---|
791 |
|
---|
792 | #region interpretation
|
---|
793 |
|
---|
794 | // the following uses auto-diff to calculate the gradient w.r.t. the parameters forward in time.
|
---|
795 | // this is basically the method described in Gronwall T. Note on the derivatives with respect to a parameter of the solutions of a system of differential equations. Ann. Math. 1919;20:292–296.
|
---|
796 |
|
---|
797 | // a comparison of three potential calculation methods for the gradient is given in:
|
---|
798 | // Sengupta, B., Friston, K. J., & Penny, W. D. (2014). Efficient gradient computation for dynamical models. Neuroimage, 98(100), 521–527. http://doi.org/10.1016/j.neuroimage.2014.04.040
|
---|
799 | // "Our comparison establishes that the adjoint method is computationally more efficient for numerical estimation of parametric gradients
|
---|
800 | // for state-space models — both linear and non-linear, as in the case of a dynamical causal model (DCM)"
|
---|
801 |
|
---|
802 | // for a solver with the necessary features see: https://computation.llnl.gov/projects/sundials/cvodes
|
---|
803 |
|
---|
804 | public static IEnumerable<Tuple<double, Vector>[]> Integrate(OptimizationData optimizationData) {
|
---|
805 | var nTargets = optimizationData.targetVariables.Length;
|
---|
806 | var n = optimizationData.rows.Length * optimizationData.targetVariables.Length;
|
---|
807 | var d = optimizationData.nodeValueLookup.ParameterCount;
|
---|
808 | double[] fi = new double[n];
|
---|
809 | double[,] jac = new double[n, d];
|
---|
810 | Integrate(optimizationData, fi, jac, null);
|
---|
811 | for (int i = 0; i < optimizationData.rows.Length; i++) {
|
---|
812 | var res = new Tuple<double, Vector>[nTargets];
|
---|
813 | for (int j = 0; j < nTargets; j++) {
|
---|
814 | res[j] = Tuple.Create(fi[i * nTargets + j], Vector.CreateFromMatrixRow(jac, i * nTargets + j));
|
---|
815 | }
|
---|
816 | yield return res;
|
---|
817 | }
|
---|
818 | }
|
---|
819 |
|
---|
820 | public static void Integrate(OptimizationData optimizationData, double[] fi, double[,] jac, double[,] latentValues) {
|
---|
821 | var trees = optimizationData.trees;
|
---|
822 | var dataset = optimizationData.problemData.Dataset;
|
---|
823 | var inputVariables = optimizationData.variables;
|
---|
824 | var targetVariables = optimizationData.targetVariables;
|
---|
825 | var latentVariables = optimizationData.latentVariables;
|
---|
826 | var episodes = optimizationData.episodes;
|
---|
827 | var odeSolver = optimizationData.odeSolver;
|
---|
828 | var numericIntegrationSteps = optimizationData.numericIntegrationSteps;
|
---|
829 | var calculatedVariables = targetVariables.Concat(latentVariables).ToArray(); // TODO: must conincide with the order of trees in the encoding
|
---|
830 |
|
---|
831 |
|
---|
832 |
|
---|
833 | var nodeValues = optimizationData.nodeValueLookup;
|
---|
834 |
|
---|
835 | // TODO: numericIntegrationSteps is only relevant for the HeuristicLab solver
|
---|
836 | var outputRowIdx = 0;
|
---|
837 | var episodeIdx = 0;
|
---|
838 | foreach (var episode in optimizationData.episodes) {
|
---|
839 | var rows = Enumerable.Range(episode.Start, episode.End - episode.Start).ToArray();
|
---|
840 |
|
---|
841 | var t0 = rows.First();
|
---|
842 |
|
---|
843 | // initialize values for inputs and targets from dataset
|
---|
844 | foreach (var varName in inputVariables) {
|
---|
845 | // in this problem we also allow fixed numeric parameters (represented as variables with the value as name)
|
---|
846 | if (double.TryParse(varName, NumberStyles.Float, CultureInfo.InvariantCulture, out double value)) {
|
---|
847 | nodeValues.SetVariableValue(varName, value, Vector.Zero);
|
---|
848 | } else {
|
---|
849 | var y0 = dataset.GetDoubleValue(varName, t0);
|
---|
850 | nodeValues.SetVariableValue(varName, y0, Vector.Zero);
|
---|
851 | }
|
---|
852 | }
|
---|
853 | foreach (var varName in targetVariables) {
|
---|
854 | var y0 = dataset.GetDoubleValue(varName, t0);
|
---|
855 | nodeValues.SetVariableValue(varName, y0, Vector.Zero);
|
---|
856 |
|
---|
857 | // output starting value
|
---|
858 | fi[outputRowIdx] = y0;
|
---|
859 | Vector.Zero.CopyTo(jac, outputRowIdx);
|
---|
860 |
|
---|
861 | outputRowIdx++;
|
---|
862 | }
|
---|
863 |
|
---|
864 | var latentValueRowIdx = 0;
|
---|
865 | var latentValueColIdx = 0;
|
---|
866 | foreach (var varName in latentVariables) {
|
---|
867 | var y0 = 0.0; // assume we start at zero
|
---|
868 | nodeValues.SetVariableValue(varName, y0, Vector.Zero);
|
---|
869 |
|
---|
870 | if (latentValues != null) {
|
---|
871 | latentValues[latentValueRowIdx, latentValueColIdx++] = y0;
|
---|
872 | }
|
---|
873 | }
|
---|
874 | latentValueColIdx = 0; latentValueRowIdx++;
|
---|
875 |
|
---|
876 | { // CODE BELOW DOESN'T WORK ANYMORE
|
---|
877 | // if (latentVariables.Length > 0) throw new NotImplementedException();
|
---|
878 | //
|
---|
879 | // // add value entries for latent variables which are also integrated
|
---|
880 | // // initial values are at the end of the parameter vector
|
---|
881 | // // separate initial values for each episode
|
---|
882 | // var initialValueIdx = parameterValues.Length - episodes.Count() * latentVariables.Length + episodeIdx * latentVariables.Length;
|
---|
883 | // foreach (var latentVar in latentVariables) {
|
---|
884 | // var arr = new double[parameterValues.Length]; // backing array
|
---|
885 | // arr[initialValueIdx] = 1.0;
|
---|
886 | // var g = new Vector(arr);
|
---|
887 | // nodeValues.SetVariableValue(latentVar, parameterValues[initialValueIdx], g); // we don't have observations for latent variables therefore we optimize the initial value for each episode
|
---|
888 | // initialValueIdx++;
|
---|
889 | // }
|
---|
890 | }
|
---|
891 |
|
---|
892 | var prevT = t0; // TODO: here we should use a variable for t if it is available. Right now we assume equidistant measurements.
|
---|
893 | foreach (var t in rows.Skip(1)) {
|
---|
894 | if (odeSolver == "HeuristicLab")
|
---|
895 | IntegrateHL(trees, calculatedVariables, nodeValues, numericIntegrationSteps); // integrator updates nodeValues
|
---|
896 | else if (odeSolver == "CVODES")
|
---|
897 | throw new NotImplementedException();
|
---|
898 | // IntegrateCVODES(trees, calculatedVariables, variableValues, parameterValues, t - prevT);
|
---|
899 | else throw new InvalidOperationException("Unknown ODE solver " + odeSolver);
|
---|
900 | prevT = t;
|
---|
901 |
|
---|
902 | // update output for target variables (TODO: if we want to visualize the latent variables then we need to provide a separate output)
|
---|
903 | for (int i = 0; i < targetVariables.Length; i++) {
|
---|
904 | var targetVar = targetVariables[i];
|
---|
905 | var yt = nodeValues.GetVariableValue(targetVar);
|
---|
906 |
|
---|
907 | // fill up remaining rows with last valid value if there are invalid values
|
---|
908 | if (double.IsNaN(yt.Item1) || double.IsInfinity(yt.Item1)) {
|
---|
909 | for (; outputRowIdx < fi.Length; outputRowIdx++) {
|
---|
910 | var prevIdx = outputRowIdx - targetVariables.Length;
|
---|
911 | fi[outputRowIdx] = fi[prevIdx]; // current <- prev
|
---|
912 | if (jac != null) for (int j = 0; j < jac.GetLength(1); j++) jac[outputRowIdx, j] = jac[prevIdx, j];
|
---|
913 | }
|
---|
914 | return;
|
---|
915 | };
|
---|
916 |
|
---|
917 | fi[outputRowIdx] = yt.Item1;
|
---|
918 | var g = yt.Item2;
|
---|
919 | g.CopyTo(jac, outputRowIdx);
|
---|
920 | outputRowIdx++;
|
---|
921 | }
|
---|
922 | if (latentValues != null) {
|
---|
923 | foreach (var latentVariable in latentVariables) {
|
---|
924 | var lt = nodeValues.GetVariableValue(latentVariable).Item1;
|
---|
925 | latentValues[latentValueRowIdx, latentValueColIdx++] = lt;
|
---|
926 | }
|
---|
927 | latentValueRowIdx++; latentValueColIdx = 0;
|
---|
928 | }
|
---|
929 |
|
---|
930 | // update for next time step (only the inputs)
|
---|
931 | foreach (var varName in inputVariables) {
|
---|
932 | // in this problem we also allow fixed numeric parameters (represented as variables with the value as name)
|
---|
933 | if (double.TryParse(varName, NumberStyles.Float, CultureInfo.InvariantCulture, out double value)) {
|
---|
934 | // value is unchanged
|
---|
935 | } else {
|
---|
936 | nodeValues.SetVariableValue(varName, dataset.GetDoubleValue(varName, t), Vector.Zero);
|
---|
937 | }
|
---|
938 | }
|
---|
939 | }
|
---|
940 | episodeIdx++;
|
---|
941 | }
|
---|
942 | }
|
---|
943 |
|
---|
944 | #region CVODES
|
---|
945 |
|
---|
946 | /*
|
---|
947 | /// <summary>
|
---|
948 | /// Here we use CVODES to solve the ODE. Forward sensitivities are used to calculate the gradient for parameter optimization
|
---|
949 | /// </summary>
|
---|
950 | /// <param name="trees">Each equation in the ODE represented as a tree</param>
|
---|
951 | /// <param name="calculatedVariables">The names of the calculated variables</param>
|
---|
952 | /// <param name="variableValues">The start values of the calculated variables as well as their sensitivites over parameters</param>
|
---|
953 | /// <param name="parameterValues">The current parameter values</param>
|
---|
954 | /// <param name="t">The time t up to which we need to integrate.</param>
|
---|
955 | private static void IntegrateCVODES(
|
---|
956 | ISymbolicExpressionTree[] trees, // f(y,p) in tree representation
|
---|
957 | string[] calculatedVariables, // names of elements of y
|
---|
958 | Dictionary<string, Tuple<double, Vector>> variableValues, // y (intput and output) input: y(t0), output: y(t0+t)
|
---|
959 | double[] parameterValues, // p
|
---|
960 | double t // duration t for which we want to integrate
|
---|
961 | ) {
|
---|
962 |
|
---|
963 | // the RHS of the ODE
|
---|
964 | // dy/dt = f(y_t,x_t,p)
|
---|
965 | CVODES.CVRhsFunc f = CreateOdeRhs(trees, calculatedVariables, parameterValues);
|
---|
966 | // the Jacobian ∂f/∂y
|
---|
967 | CVODES.CVDlsJacFunc jac = CreateJac(trees, calculatedVariables, parameterValues);
|
---|
968 |
|
---|
969 | // the RHS for the forward sensitivities (∂f/∂y)s_i(t) + ∂f/∂p_i
|
---|
970 | CVODES.CVSensRhsFn sensF = CreateSensitivityRhs(trees, calculatedVariables, parameterValues);
|
---|
971 |
|
---|
972 | // setup solver
|
---|
973 | int numberOfEquations = trees.Length;
|
---|
974 | IntPtr y = IntPtr.Zero;
|
---|
975 | IntPtr cvode_mem = IntPtr.Zero;
|
---|
976 | IntPtr A = IntPtr.Zero;
|
---|
977 | IntPtr yS0 = IntPtr.Zero;
|
---|
978 | IntPtr linearSolver = IntPtr.Zero;
|
---|
979 | var ns = parameterValues.Length; // number of parameters
|
---|
980 |
|
---|
981 | try {
|
---|
982 | y = CVODES.N_VNew_Serial(numberOfEquations);
|
---|
983 | // init y to current values of variables
|
---|
984 | // y must be initialized before calling CVodeInit
|
---|
985 | for (int i = 0; i < calculatedVariables.Length; i++) {
|
---|
986 | CVODES.NV_Set_Ith_S(y, i, variableValues[calculatedVariables[i]].Item1);
|
---|
987 | }
|
---|
988 |
|
---|
989 | cvode_mem = CVODES.CVodeCreate(CVODES.MultistepMethod.CV_ADAMS, CVODES.NonlinearSolverIteration.CV_FUNCTIONAL);
|
---|
990 |
|
---|
991 | var flag = CVODES.CVodeInit(cvode_mem, f, 0.0, y);
|
---|
992 | Assert(CVODES.CV_SUCCESS == flag);
|
---|
993 |
|
---|
994 | double relTol = 1.0e-2;
|
---|
995 | double absTol = 1.0;
|
---|
996 | flag = CVODES.CVodeSStolerances(cvode_mem, relTol, absTol); // TODO: probably need to adjust absTol per variable
|
---|
997 | Assert(CVODES.CV_SUCCESS == flag);
|
---|
998 |
|
---|
999 | A = CVODES.SUNDenseMatrix(numberOfEquations, numberOfEquations);
|
---|
1000 | Assert(A != IntPtr.Zero);
|
---|
1001 |
|
---|
1002 | linearSolver = CVODES.SUNDenseLinearSolver(y, A);
|
---|
1003 | Assert(linearSolver != IntPtr.Zero);
|
---|
1004 |
|
---|
1005 | flag = CVODES.CVDlsSetLinearSolver(cvode_mem, linearSolver, A);
|
---|
1006 | Assert(CVODES.CV_SUCCESS == flag);
|
---|
1007 |
|
---|
1008 | flag = CVODES.CVDlsSetJacFn(cvode_mem, jac);
|
---|
1009 | Assert(CVODES.CV_SUCCESS == flag);
|
---|
1010 |
|
---|
1011 | yS0 = CVODES.N_VCloneVectorArray_Serial(ns, y); // clone the output vector for each parameter
|
---|
1012 | unsafe {
|
---|
1013 | // set to initial sensitivities supplied by caller
|
---|
1014 | for (int pIdx = 0; pIdx < ns; pIdx++) {
|
---|
1015 | var yS0_i = *((IntPtr*)yS0.ToPointer() + pIdx);
|
---|
1016 | for (var varIdx = 0; varIdx < calculatedVariables.Length; varIdx++) {
|
---|
1017 | CVODES.NV_Set_Ith_S(yS0_i, varIdx, variableValues[calculatedVariables[varIdx]].Item2[pIdx]);
|
---|
1018 | }
|
---|
1019 | }
|
---|
1020 | }
|
---|
1021 |
|
---|
1022 | flag = CVODES.CVodeSensInit(cvode_mem, ns, CVODES.CV_SIMULTANEOUS, sensF, yS0);
|
---|
1023 | Assert(CVODES.CV_SUCCESS == flag);
|
---|
1024 |
|
---|
1025 | flag = CVODES.CVodeSensEEtolerances(cvode_mem);
|
---|
1026 | Assert(CVODES.CV_SUCCESS == flag);
|
---|
1027 |
|
---|
1028 | // make one forward integration step
|
---|
1029 | double tout = 0.0; // first output time
|
---|
1030 | flag = CVODES.CVode(cvode_mem, t, y, ref tout, CVODES.CV_NORMAL);
|
---|
1031 | if (flag == CVODES.CV_SUCCESS) {
|
---|
1032 | Assert(t == tout);
|
---|
1033 |
|
---|
1034 | // get sensitivities
|
---|
1035 | flag = CVODES.CVodeGetSens(cvode_mem, ref tout, yS0);
|
---|
1036 | Assert(CVODES.CV_SUCCESS == flag);
|
---|
1037 |
|
---|
1038 | // update variableValues based on integration results
|
---|
1039 | for (int varIdx = 0; varIdx < calculatedVariables.Length; varIdx++) {
|
---|
1040 | var yi = CVODES.NV_Get_Ith_S(y, varIdx);
|
---|
1041 | var gArr = new double[parameterValues.Length];
|
---|
1042 | for (var pIdx = 0; pIdx < parameterValues.Length; pIdx++) {
|
---|
1043 | unsafe {
|
---|
1044 | var yS0_pi = *((IntPtr*)yS0.ToPointer() + pIdx);
|
---|
1045 | gArr[pIdx] = CVODES.NV_Get_Ith_S(yS0_pi, varIdx);
|
---|
1046 | }
|
---|
1047 | }
|
---|
1048 | variableValues[calculatedVariables[varIdx]] = Tuple.Create(yi, new Vector(gArr));
|
---|
1049 | }
|
---|
1050 | } else {
|
---|
1051 | variableValues.Clear(); // indicate problems by not returning new values
|
---|
1052 | }
|
---|
1053 |
|
---|
1054 | // cleanup all allocated objects
|
---|
1055 | } finally {
|
---|
1056 | if (y != IntPtr.Zero) CVODES.N_VDestroy_Serial(y);
|
---|
1057 | if (cvode_mem != IntPtr.Zero) CVODES.CVodeFree(ref cvode_mem);
|
---|
1058 | if (linearSolver != IntPtr.Zero) CVODES.SUNLinSolFree(linearSolver);
|
---|
1059 | if (A != IntPtr.Zero) CVODES.SUNMatDestroy(A);
|
---|
1060 | if (yS0 != IntPtr.Zero) CVODES.N_VDestroyVectorArray_Serial(yS0, ns);
|
---|
1061 | }
|
---|
1062 | }
|
---|
1063 |
|
---|
1064 |
|
---|
1065 | private static CVODES.CVRhsFunc CreateOdeRhs(
|
---|
1066 | ISymbolicExpressionTree[] trees,
|
---|
1067 | string[] calculatedVariables,
|
---|
1068 | double[] parameterValues) {
|
---|
1069 | // we don't need to calculate a gradient here
|
---|
1070 | return (double t,
|
---|
1071 | IntPtr y, // N_Vector, current value of y (input)
|
---|
1072 | IntPtr ydot, // N_Vector (calculated value of y' (output)
|
---|
1073 | IntPtr user_data // optional user data, (unused here)
|
---|
1074 | ) => {
|
---|
1075 | // TODO: perf
|
---|
1076 | var nodeValues = new Dictionary<ISymbolicExpressionTreeNode, Tuple<double, Vector>>();
|
---|
1077 |
|
---|
1078 | int pIdx = 0;
|
---|
1079 | foreach (var tree in trees) {
|
---|
1080 | foreach (var n in tree.IterateNodesPrefix()) {
|
---|
1081 | if (IsConstantNode(n)) {
|
---|
1082 | nodeValues.Add(n, Tuple.Create(parameterValues[pIdx], Vector.Zero)); // here we do not need a gradient
|
---|
1083 | pIdx++;
|
---|
1084 | } else if (n.SubtreeCount == 0) {
|
---|
1085 | // for variables and latent variables get the value from variableValues
|
---|
1086 | var varName = n.Symbol.Name;
|
---|
1087 | var varIdx = Array.IndexOf(calculatedVariables, varName); // TODO: perf!
|
---|
1088 | if (varIdx < 0) throw new InvalidProgramException();
|
---|
1089 | var y_i = CVODES.NV_Get_Ith_S(y, (long)varIdx);
|
---|
1090 | nodeValues.Add(n, Tuple.Create(y_i, Vector.Zero)); // no gradient needed
|
---|
1091 | }
|
---|
1092 | }
|
---|
1093 | }
|
---|
1094 | for (int i = 0; i < trees.Length; i++) {
|
---|
1095 | var tree = trees[i];
|
---|
1096 | var res_i = InterpretRec(tree.Root.GetSubtree(0).GetSubtree(0), nodeValues);
|
---|
1097 | CVODES.NV_Set_Ith_S(ydot, i, res_i.Item1);
|
---|
1098 | }
|
---|
1099 | return 0;
|
---|
1100 | };
|
---|
1101 | }
|
---|
1102 |
|
---|
1103 | private static CVODES.CVDlsJacFunc CreateJac(
|
---|
1104 | ISymbolicExpressionTree[] trees,
|
---|
1105 | string[] calculatedVariables,
|
---|
1106 | double[] parameterValues) {
|
---|
1107 |
|
---|
1108 | return (
|
---|
1109 | double t, // current time (input)
|
---|
1110 | IntPtr y, // N_Vector, current value of y (input)
|
---|
1111 | IntPtr fy, // N_Vector, current value of f (input)
|
---|
1112 | IntPtr Jac, // SUNMatrix ∂f/∂y (output, rows i contains are ∂f_i/∂y vector)
|
---|
1113 | IntPtr user_data, // optional (unused here)
|
---|
1114 | IntPtr tmp1, // N_Vector, optional (unused here)
|
---|
1115 | IntPtr tmp2, // N_Vector, optional (unused here)
|
---|
1116 | IntPtr tmp3 // N_Vector, optional (unused here)
|
---|
1117 | ) => {
|
---|
1118 | // here we need to calculate partial derivatives for the calculated variables y
|
---|
1119 | var nodeValues = new Dictionary<ISymbolicExpressionTreeNode, Tuple<double, Vector>>();
|
---|
1120 | int pIdx = 0;
|
---|
1121 | foreach (var tree in trees) {
|
---|
1122 | foreach (var n in tree.IterateNodesPrefix()) {
|
---|
1123 | if (IsConstantNode(n)) {
|
---|
1124 | nodeValues.Add(n, Tuple.Create(parameterValues[pIdx], Vector.Zero)); // here we need a gradient over y which is zero for parameters
|
---|
1125 | pIdx++;
|
---|
1126 | } else if (n.SubtreeCount == 0) {
|
---|
1127 | // for variables and latent variables we use values supplied in y and init gradient vectors accordingly
|
---|
1128 | var varName = n.Symbol.Name;
|
---|
1129 | var varIdx = Array.IndexOf(calculatedVariables, varName); // TODO: perf!
|
---|
1130 | if (varIdx < 0) throw new InvalidProgramException();
|
---|
1131 |
|
---|
1132 | var y_i = CVODES.NV_Get_Ith_S(y, (long)varIdx);
|
---|
1133 | var gArr = new double[CVODES.NV_LENGTH_S(y)]; // backing array
|
---|
1134 | gArr[varIdx] = 1.0;
|
---|
1135 | var g = new Vector(gArr);
|
---|
1136 | nodeValues.Add(n, Tuple.Create(y_i, g));
|
---|
1137 | }
|
---|
1138 | }
|
---|
1139 | }
|
---|
1140 |
|
---|
1141 | for (int i = 0; i < trees.Length; i++) {
|
---|
1142 | var tree = trees[i];
|
---|
1143 | var res = InterpretRec(tree.Root.GetSubtree(0).GetSubtree(0), nodeValues);
|
---|
1144 | var g = res.Item2;
|
---|
1145 | for (int j = 0; j < calculatedVariables.Length; j++) {
|
---|
1146 | CVODES.SUNDenseMatrix_Set(Jac, i, j, g[j]);
|
---|
1147 | }
|
---|
1148 | }
|
---|
1149 | return 0; // on success
|
---|
1150 | };
|
---|
1151 | }
|
---|
1152 |
|
---|
1153 |
|
---|
1154 | // to calculate sensitivities RHS for all equations at once
|
---|
1155 | // must compute (∂f/∂y)s_i(t) + ∂f/∂p_i and store in ySdot.
|
---|
1156 | // Index i refers to parameters, dimensionality of matrix and vectors is number of equations
|
---|
1157 | private static CVODES.CVSensRhsFn CreateSensitivityRhs(ISymbolicExpressionTree[] trees, string[] calculatedVariables, double[] parameterValues) {
|
---|
1158 | return (
|
---|
1159 | int Ns, // number of parameters
|
---|
1160 | double t, // current time
|
---|
1161 | IntPtr y, // N_Vector y(t) (input)
|
---|
1162 | IntPtr ydot, // N_Vector dy/dt(t) (input)
|
---|
1163 | IntPtr yS, // N_Vector*, one vector for each parameter (input)
|
---|
1164 | IntPtr ySdot, // N_Vector*, one vector for each parameter (output)
|
---|
1165 | IntPtr user_data, // optional (unused here)
|
---|
1166 | IntPtr tmp1, // N_Vector, optional (unused here)
|
---|
1167 | IntPtr tmp2 // N_Vector, optional (unused here)
|
---|
1168 | ) => {
|
---|
1169 | // here we need to calculate partial derivatives for the calculated variables y as well as for the parameters
|
---|
1170 | var nodeValues = new Dictionary<ISymbolicExpressionTreeNode, Tuple<double, Vector>>();
|
---|
1171 | var d = calculatedVariables.Length + parameterValues.Length; // dimensionality of gradient
|
---|
1172 | // first collect variable values
|
---|
1173 | foreach (var tree in trees) {
|
---|
1174 | foreach (var n in tree.IterateNodesPrefix()) {
|
---|
1175 | if (IsVariableNode(n)) {
|
---|
1176 | // for variables and latent variables we use values supplied in y and init gradient vectors accordingly
|
---|
1177 | var varName = n.Symbol.Name;
|
---|
1178 | var varIdx = Array.IndexOf(calculatedVariables, varName); // TODO: perf!
|
---|
1179 | if (varIdx < 0) throw new InvalidProgramException();
|
---|
1180 |
|
---|
1181 | var y_i = CVODES.NV_Get_Ith_S(y, (long)varIdx);
|
---|
1182 | var gArr = new double[d]; // backing array
|
---|
1183 | gArr[varIdx] = 1.0;
|
---|
1184 | var g = new Vector(gArr);
|
---|
1185 | nodeValues.Add(n, Tuple.Create(y_i, g));
|
---|
1186 | }
|
---|
1187 | }
|
---|
1188 | }
|
---|
1189 | // then collect constants
|
---|
1190 | int pIdx = 0;
|
---|
1191 | foreach (var tree in trees) {
|
---|
1192 | foreach (var n in tree.IterateNodesPrefix()) {
|
---|
1193 | if (IsConstantNode(n)) {
|
---|
1194 | var gArr = new double[d];
|
---|
1195 | gArr[calculatedVariables.Length + pIdx] = 1.0;
|
---|
1196 | var g = new Vector(gArr);
|
---|
1197 | nodeValues.Add(n, Tuple.Create(parameterValues[pIdx], g));
|
---|
1198 | pIdx++;
|
---|
1199 | }
|
---|
1200 | }
|
---|
1201 | }
|
---|
1202 | // gradient vector is [∂f/∂y_1, ∂f/∂y_2, ... ∂f/∂yN, ∂f/∂p_1 ... ∂f/∂p_K]
|
---|
1203 |
|
---|
1204 |
|
---|
1205 | for (pIdx = 0; pIdx < Ns; pIdx++) {
|
---|
1206 | unsafe {
|
---|
1207 | var sDot_pi = *((IntPtr*)ySdot.ToPointer() + pIdx);
|
---|
1208 | CVODES.N_VConst_Serial(0.0, sDot_pi);
|
---|
1209 | }
|
---|
1210 | }
|
---|
1211 |
|
---|
1212 | for (int i = 0; i < trees.Length; i++) {
|
---|
1213 | var tree = trees[i];
|
---|
1214 | var res = InterpretRec(tree.Root.GetSubtree(0).GetSubtree(0), nodeValues);
|
---|
1215 | var g = res.Item2;
|
---|
1216 |
|
---|
1217 |
|
---|
1218 | // update ySdot = (∂f/∂y)s_i(t) + ∂f/∂p_i
|
---|
1219 |
|
---|
1220 | for (pIdx = 0; pIdx < Ns; pIdx++) {
|
---|
1221 | unsafe {
|
---|
1222 | var sDot_pi = *((IntPtr*)ySdot.ToPointer() + pIdx);
|
---|
1223 | var s_pi = *((IntPtr*)yS.ToPointer() + pIdx);
|
---|
1224 |
|
---|
1225 | var v = CVODES.NV_Get_Ith_S(sDot_pi, i);
|
---|
1226 | // (∂f/∂y)s_i(t)
|
---|
1227 | var p = 0.0;
|
---|
1228 | for (int yIdx = 0; yIdx < calculatedVariables.Length; yIdx++) {
|
---|
1229 | p += g[yIdx] * CVODES.NV_Get_Ith_S(s_pi, yIdx);
|
---|
1230 | }
|
---|
1231 | // + ∂f/∂p_i
|
---|
1232 | CVODES.NV_Set_Ith_S(sDot_pi, i, v + p + g[calculatedVariables.Length + pIdx]);
|
---|
1233 | }
|
---|
1234 | }
|
---|
1235 |
|
---|
1236 | }
|
---|
1237 | return 0; // on success
|
---|
1238 | };
|
---|
1239 | }
|
---|
1240 | */
|
---|
1241 | #endregion
|
---|
1242 |
|
---|
1243 | private static void IntegrateHL(
|
---|
1244 | ISymbolicExpressionTree[] trees,
|
---|
1245 | string[] calculatedVariables, // names of integrated variables
|
---|
1246 | NodeValueLookup nodeValues,
|
---|
1247 | int numericIntegrationSteps) {
|
---|
1248 |
|
---|
1249 |
|
---|
1250 | double[] deltaF = new double[calculatedVariables.Length];
|
---|
1251 | Vector[] deltaG = new Vector[calculatedVariables.Length];
|
---|
1252 |
|
---|
1253 | double h = 1.0 / numericIntegrationSteps;
|
---|
1254 | for (int step = 0; step < numericIntegrationSteps; step++) {
|
---|
1255 |
|
---|
1256 | // evaluate all trees
|
---|
1257 | for (int i = 0; i < trees.Length; i++) {
|
---|
1258 | var tree = trees[i];
|
---|
1259 |
|
---|
1260 | // Root.GetSubtree(0).GetSubtree(0) skips programRoot and startSymbol
|
---|
1261 | double f; Vector g;
|
---|
1262 | InterpretRec(tree.Root.GetSubtree(0).GetSubtree(0), nodeValues, out f, out g);
|
---|
1263 | deltaF[i] = f;
|
---|
1264 | deltaG[i] = g;
|
---|
1265 | }
|
---|
1266 |
|
---|
1267 | // update variableValues for next step, trapezoid integration
|
---|
1268 | for (int i = 0; i < trees.Length; i++) {
|
---|
1269 | var varName = calculatedVariables[i];
|
---|
1270 | var oldVal = nodeValues.GetVariableValue(varName);
|
---|
1271 | nodeValues.SetVariableValue(varName, oldVal.Item1 + h * deltaF[i], oldVal.Item2.Add(deltaG[i].Scale(h)));
|
---|
1272 | }
|
---|
1273 | }
|
---|
1274 | }
|
---|
1275 |
|
---|
1276 | // TODO: use an existing interpreter implementation instead
|
---|
1277 | private static double InterpretRec(ISymbolicExpressionTreeNode node, NodeValueLookup nodeValues) {
|
---|
1278 | if (node is ConstantTreeNode) {
|
---|
1279 | return ((ConstantTreeNode)node).Value;
|
---|
1280 | } else if (node is VariableTreeNode) {
|
---|
1281 | return nodeValues.NodeValue(node);
|
---|
1282 | } else if (node.Symbol is Addition) {
|
---|
1283 | var f = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1284 | for (int i = 1; i < node.SubtreeCount; i++) {
|
---|
1285 | f += InterpretRec(node.GetSubtree(i), nodeValues);
|
---|
1286 | }
|
---|
1287 | return f;
|
---|
1288 | } else if (node.Symbol is Multiplication) {
|
---|
1289 | var f = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1290 | for (int i = 1; i < node.SubtreeCount; i++) {
|
---|
1291 | f *= InterpretRec(node.GetSubtree(i), nodeValues);
|
---|
1292 | }
|
---|
1293 | return f;
|
---|
1294 | } else if (node.Symbol is Subtraction) {
|
---|
1295 | if (node.SubtreeCount == 1) {
|
---|
1296 | return -InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1297 | } else {
|
---|
1298 | var f = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1299 | for (int i = 1; i < node.SubtreeCount; i++) {
|
---|
1300 | f -= InterpretRec(node.GetSubtree(i), nodeValues);
|
---|
1301 | }
|
---|
1302 | return f;
|
---|
1303 | }
|
---|
1304 | } else if (node.Symbol is Division) {
|
---|
1305 | if (node.SubtreeCount == 1) {
|
---|
1306 | var f = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1307 | // protected division
|
---|
1308 | if (f.IsAlmost(0.0)) {
|
---|
1309 | return 0;
|
---|
1310 | } else {
|
---|
1311 | return 1.0 / f;
|
---|
1312 | }
|
---|
1313 | } else {
|
---|
1314 | var f = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1315 | for (int i = 1; i < node.SubtreeCount; i++) {
|
---|
1316 | var g = InterpretRec(node.GetSubtree(i), nodeValues);
|
---|
1317 | // protected division
|
---|
1318 | if (g.IsAlmost(0.0)) {
|
---|
1319 | return 0;
|
---|
1320 | } else {
|
---|
1321 | f /= g;
|
---|
1322 | }
|
---|
1323 | }
|
---|
1324 | return f;
|
---|
1325 | }
|
---|
1326 | } else if (node.Symbol is Sine) {
|
---|
1327 | Assert(node.SubtreeCount == 1);
|
---|
1328 |
|
---|
1329 | var f = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1330 | return Math.Sin(f);
|
---|
1331 | } else if (node.Symbol is Cosine) {
|
---|
1332 | Assert(node.SubtreeCount == 1);
|
---|
1333 |
|
---|
1334 | var f = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1335 | return Math.Cos(f);
|
---|
1336 | } else if (node.Symbol is Square) {
|
---|
1337 | Assert(node.SubtreeCount == 1);
|
---|
1338 |
|
---|
1339 | var f = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1340 | return f * f;
|
---|
1341 | } else if (node.Symbol is Exponential) {
|
---|
1342 | Assert(node.SubtreeCount == 1);
|
---|
1343 |
|
---|
1344 | var f = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1345 | return Math.Exp(f);
|
---|
1346 | } else if (node.Symbol is Logarithm) {
|
---|
1347 | Assert(node.SubtreeCount == 1);
|
---|
1348 |
|
---|
1349 | var f = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1350 | return Math.Log(f);
|
---|
1351 | } else if (node.Symbol is HyperbolicTangent) {
|
---|
1352 | Assert(node.SubtreeCount == 1);
|
---|
1353 |
|
---|
1354 | var f = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1355 | return Math.Tanh(f);
|
---|
1356 | } else if (node.Symbol is AnalyticQuotient) {
|
---|
1357 | Assert(node.SubtreeCount == 2);
|
---|
1358 |
|
---|
1359 | var f = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1360 | var g = InterpretRec(node.GetSubtree(1), nodeValues);
|
---|
1361 | return f / Math.Sqrt(1 + g * g);
|
---|
1362 | } else throw new NotSupportedException("unsupported symbol");
|
---|
1363 | }
|
---|
1364 |
|
---|
1365 | private static void Assert(bool cond) {
|
---|
1366 | #if DEBUG
|
---|
1367 | if (!cond) throw new InvalidOperationException("Assertion failed");
|
---|
1368 | #endif
|
---|
1369 | }
|
---|
1370 |
|
---|
1371 | private static void InterpretRec(
|
---|
1372 | ISymbolicExpressionTreeNode node,
|
---|
1373 | NodeValueLookup nodeValues, // contains value and gradient vector for a node (variables and constants only)
|
---|
1374 | out double z,
|
---|
1375 | out Vector dz
|
---|
1376 | ) {
|
---|
1377 | double f, g;
|
---|
1378 | Vector df, dg;
|
---|
1379 | if (node.Symbol is Constant || node.Symbol is Variable) {
|
---|
1380 | z = nodeValues.NodeValue(node);
|
---|
1381 | dz = Vector.CreateNew(nodeValues.NodeGradient(node)); // original gradient vectors are never changed by evaluation
|
---|
1382 | } else if (node.Symbol is Addition) {
|
---|
1383 | InterpretRec(node.GetSubtree(0), nodeValues, out f, out df);
|
---|
1384 | for (int i = 1; i < node.SubtreeCount; i++) {
|
---|
1385 | InterpretRec(node.GetSubtree(i), nodeValues, out g, out dg);
|
---|
1386 | f = f + g;
|
---|
1387 | df = df.Add(dg);
|
---|
1388 | }
|
---|
1389 | z = f;
|
---|
1390 | dz = df;
|
---|
1391 | } else if (node.Symbol is Multiplication) {
|
---|
1392 | InterpretRec(node.GetSubtree(0), nodeValues, out f, out df);
|
---|
1393 | for (int i = 1; i < node.SubtreeCount; i++) {
|
---|
1394 | InterpretRec(node.GetSubtree(i), nodeValues, out g, out dg);
|
---|
1395 | f = f * g;
|
---|
1396 | df = df.Scale(g).Add(dg.Scale(f)); // f'*g + f*g'
|
---|
1397 | }
|
---|
1398 | z = f;
|
---|
1399 | dz = df;
|
---|
1400 | } else if (node.Symbol is Subtraction) {
|
---|
1401 | if (node.SubtreeCount == 1) {
|
---|
1402 | InterpretRec(node.GetSubtree(0), nodeValues, out f, out df);
|
---|
1403 | z = -f;
|
---|
1404 | dz = df.Scale(-1.0);
|
---|
1405 | } else {
|
---|
1406 | InterpretRec(node.GetSubtree(0), nodeValues, out f, out df);
|
---|
1407 | for (int i = 1; i < node.SubtreeCount; i++) {
|
---|
1408 | InterpretRec(node.GetSubtree(i), nodeValues, out g, out dg);
|
---|
1409 | f = f - g;
|
---|
1410 | df = df.Subtract(dg);
|
---|
1411 | }
|
---|
1412 | z = f;
|
---|
1413 | dz = df;
|
---|
1414 | }
|
---|
1415 | } else if (node.Symbol is Division) {
|
---|
1416 | if (node.SubtreeCount == 1) {
|
---|
1417 | InterpretRec(node.GetSubtree(0), nodeValues, out f, out df);
|
---|
1418 | // protected division
|
---|
1419 | if (f.IsAlmost(0.0)) {
|
---|
1420 | z = 0;
|
---|
1421 | dz = Vector.Zero;
|
---|
1422 | } else {
|
---|
1423 | z = 1.0 / f;
|
---|
1424 | dz = df.Scale(-1 * z * z);
|
---|
1425 | }
|
---|
1426 | } else {
|
---|
1427 | InterpretRec(node.GetSubtree(0), nodeValues, out f, out df);
|
---|
1428 | for (int i = 1; i < node.SubtreeCount; i++) {
|
---|
1429 | InterpretRec(node.GetSubtree(i), nodeValues, out g, out dg);
|
---|
1430 | // protected division
|
---|
1431 | if (g.IsAlmost(0.0)) {
|
---|
1432 | z = 0;
|
---|
1433 | dz = Vector.Zero;
|
---|
1434 | return;
|
---|
1435 | } else {
|
---|
1436 | var inv_g = 1.0 / g;
|
---|
1437 | f = f * inv_g;
|
---|
1438 | df = dg.Scale(-f * inv_g * inv_g).Add(df.Scale(inv_g));
|
---|
1439 | }
|
---|
1440 | }
|
---|
1441 | z = f;
|
---|
1442 | dz = df;
|
---|
1443 | }
|
---|
1444 | } else if (node.Symbol is Sine) {
|
---|
1445 | Assert(node.SubtreeCount == 1);
|
---|
1446 | InterpretRec(node.GetSubtree(0), nodeValues, out f, out df);
|
---|
1447 | z = Math.Sin(f);
|
---|
1448 | dz = df.Scale(Math.Cos(f));
|
---|
1449 | } else if (node.Symbol is Cosine) {
|
---|
1450 | Assert(node.SubtreeCount == 1);
|
---|
1451 | InterpretRec(node.GetSubtree(0), nodeValues, out f, out df);
|
---|
1452 | z = Math.Cos(f);
|
---|
1453 | dz = df.Scale(-Math.Sin(f));
|
---|
1454 | } else if (node.Symbol is Square) {
|
---|
1455 | Assert(node.SubtreeCount == 1);
|
---|
1456 | InterpretRec(node.GetSubtree(0), nodeValues, out f, out df);
|
---|
1457 | z = f * f;
|
---|
1458 | dz = df.Scale(2.0 * f);
|
---|
1459 | } else if (node.Symbol is Exponential) {
|
---|
1460 | Assert(node.SubtreeCount == 1);
|
---|
1461 | InterpretRec(node.GetSubtree(0), nodeValues, out f, out df);
|
---|
1462 | z = Math.Exp(f);
|
---|
1463 | dz = df.Scale(Math.Exp(f));
|
---|
1464 | } else if (node.Symbol is Logarithm) {
|
---|
1465 | Assert(node.SubtreeCount == 1);
|
---|
1466 | InterpretRec(node.GetSubtree(0), nodeValues, out f, out df);
|
---|
1467 | z = Math.Log(f);
|
---|
1468 | dz = df.Scale(1.0 / f);
|
---|
1469 | } else if (node.Symbol is HyperbolicTangent) {
|
---|
1470 | Assert(node.SubtreeCount == 1);
|
---|
1471 | InterpretRec(node.GetSubtree(0), nodeValues, out f, out df);
|
---|
1472 | z = Math.Tanh(f);
|
---|
1473 | dz = df.Scale(1 - z * z); // tanh(f(x))' = f(x)'sech²(f(x)) = f(x)'(1 - tanh²(f(x)))
|
---|
1474 | } else if (node.Symbol is AnalyticQuotient) {
|
---|
1475 | Assert(node.SubtreeCount == 2);
|
---|
1476 | InterpretRec(node.GetSubtree(0), nodeValues, out f, out df);
|
---|
1477 | InterpretRec(node.GetSubtree(1), nodeValues, out g, out dg);
|
---|
1478 | z = f / Math.Sqrt(1 + g * g);
|
---|
1479 | var denom = 1.0 / Math.Pow(1 + g * g, 1.5);
|
---|
1480 | dz = df.Scale(1 + g * g).Subtract(dg.Scale(f * g)).Scale(denom);
|
---|
1481 | } else {
|
---|
1482 | throw new NotSupportedException("unsupported symbol");
|
---|
1483 | }
|
---|
1484 | }
|
---|
1485 |
|
---|
1486 | #endregion
|
---|
1487 |
|
---|
1488 | #region events
|
---|
1489 | /*
|
---|
1490 | * Dependencies between parameters:
|
---|
1491 | *
|
---|
1492 | * ProblemData
|
---|
1493 | * |
|
---|
1494 | * V
|
---|
1495 | * TargetVariables FunctionSet MaximumLength NumberOfLatentVariables
|
---|
1496 | * | | | |
|
---|
1497 | * V V | |
|
---|
1498 | * Grammar <---------------+-------------------
|
---|
1499 | * |
|
---|
1500 | * V
|
---|
1501 | * Encoding
|
---|
1502 | */
|
---|
1503 | private void RegisterEventHandlers() {
|
---|
1504 | ProblemDataParameter.ValueChanged += ProblemDataParameter_ValueChanged;
|
---|
1505 | if (ProblemDataParameter.Value != null) ProblemDataParameter.Value.Changed += ProblemData_Changed;
|
---|
1506 |
|
---|
1507 | TargetVariablesParameter.ValueChanged += TargetVariablesParameter_ValueChanged;
|
---|
1508 | if (TargetVariablesParameter.Value != null) TargetVariablesParameter.Value.CheckedItemsChanged += CheckedTargetVariablesChanged;
|
---|
1509 |
|
---|
1510 | FunctionSetParameter.ValueChanged += FunctionSetParameter_ValueChanged;
|
---|
1511 | if (FunctionSetParameter.Value != null) FunctionSetParameter.Value.CheckedItemsChanged += CheckedFunctionsChanged;
|
---|
1512 |
|
---|
1513 | MaximumLengthParameter.Value.ValueChanged += MaximumLengthChanged;
|
---|
1514 |
|
---|
1515 | NumberOfLatentVariablesParameter.Value.ValueChanged += NumLatentVariablesChanged;
|
---|
1516 | }
|
---|
1517 |
|
---|
1518 | private void NumLatentVariablesChanged(object sender, EventArgs e) {
|
---|
1519 | UpdateGrammarAndEncoding();
|
---|
1520 | }
|
---|
1521 |
|
---|
1522 | private void MaximumLengthChanged(object sender, EventArgs e) {
|
---|
1523 | UpdateGrammarAndEncoding();
|
---|
1524 | }
|
---|
1525 |
|
---|
1526 | private void FunctionSetParameter_ValueChanged(object sender, EventArgs e) {
|
---|
1527 | FunctionSetParameter.Value.CheckedItemsChanged += CheckedFunctionsChanged;
|
---|
1528 | }
|
---|
1529 |
|
---|
1530 | private void CheckedFunctionsChanged(object sender, CollectionItemsChangedEventArgs<IndexedItem<StringValue>> e) {
|
---|
1531 | UpdateGrammarAndEncoding();
|
---|
1532 | }
|
---|
1533 |
|
---|
1534 | private void TargetVariablesParameter_ValueChanged(object sender, EventArgs e) {
|
---|
1535 | TargetVariablesParameter.Value.CheckedItemsChanged += CheckedTargetVariablesChanged;
|
---|
1536 | }
|
---|
1537 |
|
---|
1538 | private void CheckedTargetVariablesChanged(object sender, CollectionItemsChangedEventArgs<IndexedItem<StringValue>> e) {
|
---|
1539 | UpdateGrammarAndEncoding();
|
---|
1540 | }
|
---|
1541 |
|
---|
1542 | private void ProblemDataParameter_ValueChanged(object sender, EventArgs e) {
|
---|
1543 | ProblemDataParameter.Value.Changed += ProblemData_Changed;
|
---|
1544 | OnProblemDataChanged();
|
---|
1545 | OnReset();
|
---|
1546 | }
|
---|
1547 |
|
---|
1548 | private void ProblemData_Changed(object sender, EventArgs e) {
|
---|
1549 | OnProblemDataChanged();
|
---|
1550 | OnReset();
|
---|
1551 | }
|
---|
1552 |
|
---|
1553 | private void OnProblemDataChanged() {
|
---|
1554 | UpdateTargetVariables(); // implicitly updates other dependent parameters
|
---|
1555 | var handler = ProblemDataChanged;
|
---|
1556 | if (handler != null) handler(this, EventArgs.Empty);
|
---|
1557 | }
|
---|
1558 |
|
---|
1559 | #endregion
|
---|
1560 |
|
---|
1561 | #region helper
|
---|
1562 |
|
---|
1563 | private static IEnumerable<T> EveryNth<T>(IEnumerable<T> xs, int step) {
|
---|
1564 | var e = xs.GetEnumerator();
|
---|
1565 | while (e.MoveNext()) {
|
---|
1566 | for (int i = 0; i < step; i++) {
|
---|
1567 | if (!e.MoveNext()) yield break;
|
---|
1568 | }
|
---|
1569 | yield return e.Current;
|
---|
1570 | }
|
---|
1571 | }
|
---|
1572 |
|
---|
1573 | private void InitAllParameters() {
|
---|
1574 | UpdateTargetVariables(); // implicitly updates the grammar and the encoding
|
---|
1575 | }
|
---|
1576 |
|
---|
1577 | private ReadOnlyCheckedItemList<StringValue> CreateFunctionSet() {
|
---|
1578 | var l = new CheckedItemList<StringValue>();
|
---|
1579 | l.Add(new StringValue("Addition").AsReadOnly());
|
---|
1580 | l.Add(new StringValue("Multiplication").AsReadOnly());
|
---|
1581 | l.Add(new StringValue("Division").AsReadOnly());
|
---|
1582 | l.Add(new StringValue("Subtraction").AsReadOnly());
|
---|
1583 | l.Add(new StringValue("Sine").AsReadOnly());
|
---|
1584 | l.Add(new StringValue("Cosine").AsReadOnly());
|
---|
1585 | l.Add(new StringValue("Square").AsReadOnly());
|
---|
1586 | l.Add(new StringValue("Logarithm").AsReadOnly());
|
---|
1587 | l.Add(new StringValue("Exponential").AsReadOnly());
|
---|
1588 | l.Add(new StringValue("HyperbolicTangent").AsReadOnly());
|
---|
1589 | l.Add(new StringValue("AnalyticQuotient").AsReadOnly());
|
---|
1590 | return l.AsReadOnly();
|
---|
1591 | }
|
---|
1592 |
|
---|
1593 | private static bool IsConstantNode(ISymbolicExpressionTreeNode n) {
|
---|
1594 | // return n.Symbol.Name[0] == 'θ';
|
---|
1595 | return n is ConstantTreeNode;
|
---|
1596 | }
|
---|
1597 | private static double GetConstantValue(ISymbolicExpressionTreeNode n) {
|
---|
1598 | return ((ConstantTreeNode)n).Value;
|
---|
1599 | }
|
---|
1600 | private static bool IsLatentVariableNode(ISymbolicExpressionTreeNode n) {
|
---|
1601 | return n.Symbol.Name[0] == 'λ';
|
---|
1602 | }
|
---|
1603 | private static bool IsVariableNode(ISymbolicExpressionTreeNode n) {
|
---|
1604 | return (n.SubtreeCount == 0) && !IsConstantNode(n) && !IsLatentVariableNode(n);
|
---|
1605 | }
|
---|
1606 | private static string GetVariableName(ISymbolicExpressionTreeNode n) {
|
---|
1607 | return ((VariableTreeNode)n).VariableName;
|
---|
1608 | }
|
---|
1609 |
|
---|
1610 | private void UpdateTargetVariables() {
|
---|
1611 | var currentlySelectedVariables = TargetVariables.CheckedItems
|
---|
1612 | .OrderBy(i => i.Index)
|
---|
1613 | .Select(i => i.Value.Value)
|
---|
1614 | .ToArray();
|
---|
1615 |
|
---|
1616 | var newVariablesList = new CheckedItemList<StringValue>(ProblemData.Dataset.VariableNames.Select(str => new StringValue(str).AsReadOnly()).ToArray()).AsReadOnly();
|
---|
1617 | var matchingItems = newVariablesList.Where(item => currentlySelectedVariables.Contains(item.Value)).ToArray();
|
---|
1618 | foreach (var item in newVariablesList) {
|
---|
1619 | if (currentlySelectedVariables.Contains(item.Value)) {
|
---|
1620 | newVariablesList.SetItemCheckedState(item, true);
|
---|
1621 | } else {
|
---|
1622 | newVariablesList.SetItemCheckedState(item, false);
|
---|
1623 | }
|
---|
1624 | }
|
---|
1625 | TargetVariablesParameter.Value = newVariablesList;
|
---|
1626 | }
|
---|
1627 |
|
---|
1628 | private void UpdateGrammarAndEncoding() {
|
---|
1629 | var encoding = new MultiEncoding();
|
---|
1630 | var g = CreateGrammar();
|
---|
1631 | foreach (var targetVar in TargetVariables.CheckedItems) {
|
---|
1632 | var e = new SymbolicExpressionTreeEncoding(targetVar + "_tree", g, MaximumLength, MaximumLength);
|
---|
1633 | var multiManipulator = e.Operators.Where(op => op is MultiSymbolicExpressionTreeManipulator).First();
|
---|
1634 | var filteredOperators = e.Operators.Where(op => !(op is IManipulator)).ToArray();
|
---|
1635 | // make sure our multi-manipulator is the only manipulator
|
---|
1636 | e.Operators = new IOperator[] { multiManipulator }.Concat(filteredOperators);
|
---|
1637 |
|
---|
1638 | // set the crossover probability to reduce likelihood that multiple trees are crossed at the same time
|
---|
1639 | var subtreeCrossovers = e.Operators.OfType<SubtreeCrossover>();
|
---|
1640 | foreach (var xover in subtreeCrossovers) {
|
---|
1641 | xover.CrossoverProbability.Value = 0.3;
|
---|
1642 | }
|
---|
1643 |
|
---|
1644 | encoding = encoding.Add(e); // only limit by length
|
---|
1645 | }
|
---|
1646 | for (int i = 1; i <= NumberOfLatentVariables; i++) {
|
---|
1647 | var e = new SymbolicExpressionTreeEncoding("λ" + i + "_tree", g, MaximumLength, MaximumLength);
|
---|
1648 | var multiManipulator = e.Operators.Where(op => op is MultiSymbolicExpressionTreeManipulator).First();
|
---|
1649 | var filteredOperators = e.Operators.Where(op => !(op is IManipulator)).ToArray();
|
---|
1650 | // make sure our multi-manipulator is the only manipulator
|
---|
1651 | e.Operators = new IOperator[] { multiManipulator }.Concat(filteredOperators);
|
---|
1652 |
|
---|
1653 | // set the crossover probability to reduce likelihood that multiple trees are crossed at the same time
|
---|
1654 | var subtreeCrossovers = e.Operators.OfType<SubtreeCrossover>();
|
---|
1655 | foreach (var xover in subtreeCrossovers) {
|
---|
1656 | xover.CrossoverProbability.Value = 0.3;
|
---|
1657 | }
|
---|
1658 |
|
---|
1659 | encoding = encoding.Add(e);
|
---|
1660 | }
|
---|
1661 | Encoding = encoding;
|
---|
1662 | }
|
---|
1663 |
|
---|
1664 | private ISymbolicExpressionGrammar CreateGrammar() {
|
---|
1665 | var grammar = new TypeCoherentExpressionGrammar();
|
---|
1666 | grammar.StartGrammarManipulation();
|
---|
1667 |
|
---|
1668 | var problemData = ProblemData;
|
---|
1669 | var ds = problemData.Dataset;
|
---|
1670 | grammar.MaximumFunctionArguments = 0;
|
---|
1671 | grammar.MaximumFunctionDefinitions = 0;
|
---|
1672 | var allowedVariables = problemData.AllowedInputVariables.Concat(TargetVariables.CheckedItems.Select(chk => chk.Value.Value));
|
---|
1673 | foreach (var varSymbol in grammar.Symbols.OfType<HeuristicLab.Problems.DataAnalysis.Symbolic.VariableBase>()) {
|
---|
1674 | if (!varSymbol.Fixed) {
|
---|
1675 | varSymbol.AllVariableNames = problemData.InputVariables.Select(x => x.Value).Where(x => ds.VariableHasType<double>(x));
|
---|
1676 | varSymbol.VariableNames = allowedVariables.Where(x => ds.VariableHasType<double>(x));
|
---|
1677 | }
|
---|
1678 | }
|
---|
1679 | foreach (var factorSymbol in grammar.Symbols.OfType<BinaryFactorVariable>()) {
|
---|
1680 | if (!factorSymbol.Fixed) {
|
---|
1681 | factorSymbol.AllVariableNames = problemData.InputVariables.Select(x => x.Value).Where(x => ds.VariableHasType<string>(x));
|
---|
1682 | factorSymbol.VariableNames = problemData.AllowedInputVariables.Where(x => ds.VariableHasType<string>(x));
|
---|
1683 | factorSymbol.VariableValues = factorSymbol.VariableNames
|
---|
1684 | .ToDictionary(varName => varName, varName => ds.GetStringValues(varName).Distinct().ToList());
|
---|
1685 | }
|
---|
1686 | }
|
---|
1687 | foreach (var factorSymbol in grammar.Symbols.OfType<FactorVariable>()) {
|
---|
1688 | if (!factorSymbol.Fixed) {
|
---|
1689 | factorSymbol.AllVariableNames = problemData.InputVariables.Select(x => x.Value).Where(x => ds.VariableHasType<string>(x));
|
---|
1690 | factorSymbol.VariableNames = problemData.AllowedInputVariables.Where(x => ds.VariableHasType<string>(x));
|
---|
1691 | factorSymbol.VariableValues = factorSymbol.VariableNames
|
---|
1692 | .ToDictionary(varName => varName,
|
---|
1693 | varName => ds.GetStringValues(varName).Distinct()
|
---|
1694 | .Select((n, i) => Tuple.Create(n, i))
|
---|
1695 | .ToDictionary(tup => tup.Item1, tup => tup.Item2));
|
---|
1696 | }
|
---|
1697 | }
|
---|
1698 |
|
---|
1699 | grammar.ConfigureAsDefaultRegressionGrammar();
|
---|
1700 | grammar.GetSymbol("Logarithm").Enabled = false; // not supported yet
|
---|
1701 | grammar.GetSymbol("Exponential").Enabled = false; // not supported yet
|
---|
1702 |
|
---|
1703 | // configure initialization of constants
|
---|
1704 | var constSy = (Constant)grammar.GetSymbol("Constant");
|
---|
1705 | // max and min are only relevant for initialization
|
---|
1706 | constSy.MaxValue = +1.0e-1; // small initial values for constant opt
|
---|
1707 | constSy.MinValue = -1.0e-1;
|
---|
1708 | constSy.MultiplicativeManipulatorSigma = 1.0; // allow large jumps for manipulation
|
---|
1709 | constSy.ManipulatorMu = 0.0;
|
---|
1710 | constSy.ManipulatorSigma = 1.0; // allow large jumps
|
---|
1711 |
|
---|
1712 | // configure initialization of variables
|
---|
1713 | var varSy = (Variable)grammar.GetSymbol("Variable");
|
---|
1714 | // fix variable weights to 1.0
|
---|
1715 | varSy.WeightMu = 1.0;
|
---|
1716 | varSy.WeightSigma = 0.0;
|
---|
1717 | varSy.WeightManipulatorMu = 0.0;
|
---|
1718 | varSy.WeightManipulatorSigma = 0.0;
|
---|
1719 | varSy.MultiplicativeWeightManipulatorSigma = 0.0;
|
---|
1720 |
|
---|
1721 | foreach (var f in FunctionSet) {
|
---|
1722 | grammar.GetSymbol(f.Value).Enabled = FunctionSet.ItemChecked(f);
|
---|
1723 | }
|
---|
1724 |
|
---|
1725 | grammar.FinishedGrammarManipulation();
|
---|
1726 | return grammar;
|
---|
1727 | // // whenever ProblemData is changed we create a new grammar with the necessary symbols
|
---|
1728 | // var g = new SimpleSymbolicExpressionGrammar();
|
---|
1729 | // var unaryFunc = new string[] { "sin", "cos", "sqr" };
|
---|
1730 | // var binaryFunc = new string[] { "+", "-", "*", "%" };
|
---|
1731 | // foreach (var func in unaryFunc) {
|
---|
1732 | // if (FunctionSet.CheckedItems.Any(ci => ci.Value.Value == func)) g.AddSymbol(func, 1, 1);
|
---|
1733 | // }
|
---|
1734 | // foreach (var func in binaryFunc) {
|
---|
1735 | // if (FunctionSet.CheckedItems.Any(ci => ci.Value.Value == func)) g.AddSymbol(func, 2, 2);
|
---|
1736 | // }
|
---|
1737 | //
|
---|
1738 | // foreach (var variableName in ProblemData.AllowedInputVariables.Union(TargetVariables.CheckedItems.Select(i => i.Value.Value)))
|
---|
1739 | // g.AddTerminalSymbol(variableName);
|
---|
1740 | //
|
---|
1741 | // // generate symbols for numeric parameters for which the value is optimized using AutoDiff
|
---|
1742 | // // we generate multiple symbols to balance the probability for selecting a numeric parameter in the generation of random trees
|
---|
1743 | // var numericConstantsFactor = 2.0;
|
---|
1744 | // for (int i = 0; i < numericConstantsFactor * (ProblemData.AllowedInputVariables.Count() + TargetVariables.CheckedItems.Count()); i++) {
|
---|
1745 | // g.AddTerminalSymbol("θ" + i); // numeric parameter for which the value is optimized using AutoDiff
|
---|
1746 | // }
|
---|
1747 | //
|
---|
1748 | // // generate symbols for latent variables
|
---|
1749 | // for (int i = 1; i <= NumberOfLatentVariables; i++) {
|
---|
1750 | // g.AddTerminalSymbol("λ" + i); // numeric parameter for which the value is optimized using AutoDiff
|
---|
1751 | // }
|
---|
1752 | //
|
---|
1753 | // return g;
|
---|
1754 | }
|
---|
1755 | #endregion
|
---|
1756 |
|
---|
1757 |
|
---|
1758 | #region Import & Export
|
---|
1759 | public void Load(IRegressionProblemData data) {
|
---|
1760 | Name = data.Name;
|
---|
1761 | Description = data.Description;
|
---|
1762 | ProblemData = data;
|
---|
1763 | }
|
---|
1764 |
|
---|
1765 | public IRegressionProblemData Export() {
|
---|
1766 | return ProblemData;
|
---|
1767 | }
|
---|
1768 | #endregion
|
---|
1769 |
|
---|
1770 |
|
---|
1771 | // TODO: for integration we only need a part of the data that we need for optimization
|
---|
1772 |
|
---|
1773 | public class OptimizationData {
|
---|
1774 | public readonly ISymbolicExpressionTree[] trees;
|
---|
1775 | public readonly string[] targetVariables;
|
---|
1776 | public readonly IRegressionProblemData problemData;
|
---|
1777 | public readonly double[][] targetValues;
|
---|
1778 | public readonly double[] inverseStandardDeviation;
|
---|
1779 | public readonly IntRange[] episodes;
|
---|
1780 | public readonly int numericIntegrationSteps;
|
---|
1781 | public readonly string[] latentVariables;
|
---|
1782 | public readonly string odeSolver;
|
---|
1783 | public readonly NodeValueLookup nodeValueLookup;
|
---|
1784 | public readonly int[] rows;
|
---|
1785 | internal readonly string[] variables;
|
---|
1786 |
|
---|
1787 | public OptimizationData(ISymbolicExpressionTree[] trees, string[] targetVars, string[] inputVariables,
|
---|
1788 | IRegressionProblemData problemData,
|
---|
1789 | double[][] targetValues,
|
---|
1790 | IntRange[] episodes,
|
---|
1791 | int numericIntegrationSteps, string[] latentVariables, string odeSolver) {
|
---|
1792 | this.trees = trees;
|
---|
1793 | this.targetVariables = targetVars;
|
---|
1794 | this.problemData = problemData;
|
---|
1795 | this.targetValues = targetValues;
|
---|
1796 | this.variables = inputVariables;
|
---|
1797 | if (targetValues != null) {
|
---|
1798 | this.inverseStandardDeviation = new double[targetValues.Length];
|
---|
1799 | for (int i = 0; i < targetValues.Length; i++) {
|
---|
1800 | // calculate variance for each episode separately and calc the average
|
---|
1801 | var epStartIdx = 0;
|
---|
1802 | var stdevs = new List<double>();
|
---|
1803 | foreach (var ep in episodes) {
|
---|
1804 | var epValues = targetValues[i].Skip(epStartIdx).Take(ep.Size);
|
---|
1805 | stdevs.Add(epValues.StandardDeviation());
|
---|
1806 | epStartIdx += ep.Size;
|
---|
1807 | }
|
---|
1808 | inverseStandardDeviation[i] = 1.0 / stdevs.Average();
|
---|
1809 | }
|
---|
1810 | } else
|
---|
1811 | this.inverseStandardDeviation = Enumerable.Repeat(1.0, trees.Length).ToArray();
|
---|
1812 | this.episodes = episodes;
|
---|
1813 | this.numericIntegrationSteps = numericIntegrationSteps;
|
---|
1814 | this.latentVariables = latentVariables;
|
---|
1815 | this.odeSolver = odeSolver;
|
---|
1816 | this.nodeValueLookup = new NodeValueLookup(trees);
|
---|
1817 | this.rows = episodes.SelectMany(ep => Enumerable.Range(ep.Start, ep.Size)).ToArray();
|
---|
1818 | }
|
---|
1819 | }
|
---|
1820 |
|
---|
1821 | public class NodeValueLookup {
|
---|
1822 | private readonly Dictionary<ISymbolicExpressionTreeNode, Tuple<double, Vector>> node2val = new Dictionary<ISymbolicExpressionTreeNode, Tuple<double, Vector>>();
|
---|
1823 | private readonly Dictionary<string, List<ISymbolicExpressionTreeNode>> name2nodes = new Dictionary<string, List<ISymbolicExpressionTreeNode>>();
|
---|
1824 | private readonly ConstantTreeNode[] constantNodes;
|
---|
1825 | private readonly Vector[] constantGradientVectors;
|
---|
1826 |
|
---|
1827 | // private readonly Dictionary<int, ISymbolicExpressionTreeNode> paramIdx2node = new Dictionary<int, ISymbolicExpressionTreeNode>();
|
---|
1828 |
|
---|
1829 | public double NodeValue(ISymbolicExpressionTreeNode node) => node2val[node].Item1;
|
---|
1830 | public Vector NodeGradient(ISymbolicExpressionTreeNode node) => node2val[node].Item2;
|
---|
1831 |
|
---|
1832 | public NodeValueLookup(ISymbolicExpressionTree[] trees) {
|
---|
1833 |
|
---|
1834 | this.constantNodes = trees.SelectMany(t => t.IterateNodesPrefix().OfType<ConstantTreeNode>()).ToArray();
|
---|
1835 | constantGradientVectors = new Vector[constantNodes.Length];
|
---|
1836 | for (int paramIdx = 0; paramIdx < constantNodes.Length; paramIdx++) {
|
---|
1837 | constantGradientVectors[paramIdx] = Vector.CreateIndicator(length: constantNodes.Length, idx: paramIdx);
|
---|
1838 |
|
---|
1839 | var node = constantNodes[paramIdx];
|
---|
1840 | node2val[node] = Tuple.Create(node.Value, constantGradientVectors[paramIdx]);
|
---|
1841 | }
|
---|
1842 |
|
---|
1843 | foreach (var tree in trees) {
|
---|
1844 | foreach (var node in tree.IterateNodesPrefix().Where(IsVariableNode)) {
|
---|
1845 | var varName = GetVariableName(node);
|
---|
1846 | if (!name2nodes.TryGetValue(varName, out List<ISymbolicExpressionTreeNode> nodes)) {
|
---|
1847 | nodes = new List<ISymbolicExpressionTreeNode>();
|
---|
1848 | name2nodes.Add(varName, nodes);
|
---|
1849 | }
|
---|
1850 | nodes.Add(node);
|
---|
1851 | SetVariableValue(varName, 0.0); // this value is updated in the prediction loop
|
---|
1852 | }
|
---|
1853 | }
|
---|
1854 | }
|
---|
1855 |
|
---|
1856 | public int ParameterCount => constantNodes.Length;
|
---|
1857 |
|
---|
1858 | public void SetVariableValue(string variableName, double val) {
|
---|
1859 | SetVariableValue(variableName, val, Vector.Zero);
|
---|
1860 | }
|
---|
1861 | public Tuple<double, Vector> GetVariableValue(string variableName) {
|
---|
1862 | return node2val[name2nodes[variableName].First()];
|
---|
1863 | }
|
---|
1864 | public void SetVariableValue(string variableName, double val, Vector dVal) {
|
---|
1865 | if (name2nodes.TryGetValue(variableName, out List<ISymbolicExpressionTreeNode> nodes)) {
|
---|
1866 | nodes.ForEach(n => node2val[n] = Tuple.Create(val, dVal));
|
---|
1867 | } else {
|
---|
1868 | var fakeNode = new VariableTreeNode(new Variable());
|
---|
1869 | fakeNode.Weight = 1.0;
|
---|
1870 | fakeNode.VariableName = variableName;
|
---|
1871 | var newNodeList = new List<ISymbolicExpressionTreeNode>();
|
---|
1872 | newNodeList.Add(fakeNode);
|
---|
1873 | name2nodes.Add(variableName, newNodeList);
|
---|
1874 | node2val[fakeNode] = Tuple.Create(val, dVal);
|
---|
1875 | }
|
---|
1876 | }
|
---|
1877 |
|
---|
1878 | internal void UpdateParamValues(double[] x) {
|
---|
1879 | for (int i = 0; i < x.Length; i++) {
|
---|
1880 | constantNodes[i].Value = x[i];
|
---|
1881 | node2val[constantNodes[i]] = Tuple.Create(x[i], constantGradientVectors[i]);
|
---|
1882 | }
|
---|
1883 | }
|
---|
1884 | }
|
---|
1885 | }
|
---|
1886 | }
|
---|