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.Linq;
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26 | using HeuristicLab.Common;
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27 | using HeuristicLab.Core;
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28 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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29 | using HeuristicLab.Parameters;
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30 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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31 | using HeuristicLab.Problems.DataAnalysis;
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32 | using HeuristicLab.Problems.Instances;
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33 |
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34 | namespace HeuristicLab.Problems.DynamicalSystemsModelling {
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35 | public class Vector {
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36 | public readonly static Vector Zero = new Vector(new double[0]);
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37 |
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38 | public static Vector operator +(Vector a, Vector b) {
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39 | if (a == Zero) return b;
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40 | if (b == Zero) return a;
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41 | Debug.Assert(a.arr.Length == b.arr.Length);
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42 | var res = new double[a.arr.Length];
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43 | for (int i = 0; i < res.Length; i++)
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44 | res[i] = a.arr[i] + b.arr[i];
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45 | return new Vector(res);
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46 | }
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47 | public static Vector operator -(Vector a, Vector b) {
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48 | if (b == Zero) return a;
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49 | if (a == Zero) return -b;
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50 | Debug.Assert(a.arr.Length == b.arr.Length);
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51 | var res = new double[a.arr.Length];
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52 | for (int i = 0; i < res.Length; i++)
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53 | res[i] = a.arr[i] - b.arr[i];
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54 | return new Vector(res);
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55 | }
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56 | public static Vector operator -(Vector v) {
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57 | if (v == Zero) return Zero;
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58 | for (int i = 0; i < v.arr.Length; i++)
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59 | v.arr[i] = -v.arr[i];
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60 | return v;
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61 | }
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62 |
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63 | public static Vector operator *(double s, Vector v) {
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64 | if (v == Zero) return Zero;
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65 | if (s == 0.0) return Zero;
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66 | var res = new double[v.arr.Length];
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67 | for (int i = 0; i < res.Length; i++)
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68 | res[i] = s * v.arr[i];
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69 | return new Vector(res);
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70 | }
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71 | public static Vector operator *(Vector v, double s) {
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72 | return s * v;
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73 | }
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74 | public static Vector operator /(double s, Vector v) {
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75 | if (s == 0.0) return Zero;
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76 | if (v == Zero) throw new ArgumentException("Division by zero vector");
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77 | var res = new double[v.arr.Length];
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78 | for (int i = 0; i < res.Length; i++)
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79 | res[i] = 1.0 / v.arr[i];
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80 | return new Vector(res);
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81 | }
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82 | public static Vector operator /(Vector v, double s) {
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83 | return v * 1.0 / s;
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84 | }
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85 |
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86 |
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87 | private readonly double[] arr; // backing array;
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88 |
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89 | public Vector(double[] v) {
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90 | this.arr = v;
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91 | }
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92 |
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93 | public void CopyTo(double[] target) {
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94 | Debug.Assert(arr.Length <= target.Length);
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95 | Array.Copy(arr, target, arr.Length);
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96 | }
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97 | }
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98 |
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99 | [Item("Dynamical Systems Modelling Problem", "TODO")]
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100 | [Creatable(CreatableAttribute.Categories.GeneticProgrammingProblems, Priority = 900)]
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101 | [StorableClass]
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102 | public sealed class Problem : SymbolicExpressionTreeProblem, IRegressionProblem, IProblemInstanceConsumer<IRegressionProblemData>, IProblemInstanceExporter<IRegressionProblemData> {
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103 |
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104 | #region parameter names
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105 | private const string ProblemDataParameterName = "ProblemData";
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106 | #endregion
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107 |
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108 | #region Parameter Properties
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109 | IParameter IDataAnalysisProblem.ProblemDataParameter { get { return ProblemDataParameter; } }
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110 |
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111 | public IValueParameter<IRegressionProblemData> ProblemDataParameter {
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112 | get { return (IValueParameter<IRegressionProblemData>)Parameters[ProblemDataParameterName]; }
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113 | }
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114 | #endregion
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115 |
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116 | #region Properties
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117 | public IRegressionProblemData ProblemData {
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118 | get { return ProblemDataParameter.Value; }
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119 | set { ProblemDataParameter.Value = value; }
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120 | }
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121 | IDataAnalysisProblemData IDataAnalysisProblem.ProblemData { get { return ProblemData; } }
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122 | #endregion
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123 |
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124 | public event EventHandler ProblemDataChanged;
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125 |
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126 | public override bool Maximization {
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127 | get { return false; } // we minimize NMSE
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128 | }
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129 |
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130 | #region item cloning and persistence
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131 | // persistence
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132 | [StorableConstructor]
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133 | private Problem(bool deserializing) : base(deserializing) { }
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134 | [StorableHook(HookType.AfterDeserialization)]
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135 | private void AfterDeserialization() {
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136 | RegisterEventHandlers();
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137 | }
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138 |
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139 | // cloning
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140 | private Problem(Problem original, Cloner cloner)
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141 | : base(original, cloner) {
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142 | RegisterEventHandlers();
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143 | }
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144 | public override IDeepCloneable Clone(Cloner cloner) { return new Problem(this, cloner); }
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145 | #endregion
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146 |
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147 | public Problem()
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148 | : base() {
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149 | Parameters.Add(new ValueParameter<IRegressionProblemData>(ProblemDataParameterName, "The data captured from the dynamical system", new RegressionProblemData()));
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150 |
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151 | // TODO: support multiple target variables
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152 |
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153 | var g = new SimpleSymbolicExpressionGrammar(); // empty grammar is replaced in UpdateGrammar()
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154 | base.Encoding = new SymbolicExpressionTreeEncoding(g, 10, 5); // small for testing
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155 |
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156 | UpdateGrammar();
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157 | RegisterEventHandlers();
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158 | }
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159 |
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160 |
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161 | public override double Evaluate(ISymbolicExpressionTree tree, IRandom random) {
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162 | var problemData = ProblemData;
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163 | var rows = ProblemData.TrainingIndices.ToArray();
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164 | var target = problemData.Dataset.GetDoubleValues(problemData.TargetVariable, rows);
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165 |
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166 | var nodeIdx = new Dictionary<ISymbolicExpressionTreeNode, int>();
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167 |
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168 | foreach(var node in tree.Root.IterateNodesPrefix().Where(n => IsConstantNode(n))) {
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169 | nodeIdx.Add(node, nodeIdx.Count);
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170 | }
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171 |
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172 | var theta = nodeIdx.Select(_ => random.NextDouble() * 2.0 - 1.0).ToArray(); // init params randomly from Unif(-1,1)
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173 |
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174 | double[] optTheta = new double[0];
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175 | if (theta.Length > 0) {
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176 | alglib.minlbfgsstate state;
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177 | alglib.minlbfgsreport report;
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178 | alglib.minlbfgscreate(Math.Min(theta.Length, 5), theta, out state);
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179 | alglib.minlbfgssetcond(state, 0.0, 0.0, 0.0, 100);
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180 | alglib.minlbfgsoptimize(state, EvaluateObjectiveAndGradient, null, new object[] { tree, problemData, nodeIdx });
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181 | alglib.minlbfgsresults(state, out optTheta, out report);
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182 |
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183 | /*
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184 | *
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185 | * L-BFGS algorithm results
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186 |
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187 | INPUT PARAMETERS:
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188 | State - algorithm state
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189 |
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190 | OUTPUT PARAMETERS:
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191 | X - array[0..N-1], solution
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192 | Rep - optimization report:
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193 | * Rep.TerminationType completetion code:
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194 | * -7 gradient verification failed.
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195 | See MinLBFGSSetGradientCheck() for more information.
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196 | * -2 rounding errors prevent further improvement.
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197 | X contains best point found.
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198 | * -1 incorrect parameters were specified
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199 | * 1 relative function improvement is no more than
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200 | EpsF.
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201 | * 2 relative step is no more than EpsX.
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202 | * 4 gradient norm is no more than EpsG
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203 | * 5 MaxIts steps was taken
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204 | * 7 stopping conditions are too stringent,
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205 | further improvement is impossible
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206 | * Rep.IterationsCount contains iterations count
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207 | * NFEV countains number of function calculations
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208 | */
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209 | if (report.terminationtype < 0) return double.MaxValue;
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210 | }
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211 |
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212 | // perform evaluation for optimal theta to get quality value
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213 | double[] grad = new double[optTheta.Length];
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214 | double optQuality = double.NaN;
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215 | EvaluateObjectiveAndGradient(optTheta, ref optQuality, grad, new object[] { tree, problemData, nodeIdx});
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216 | if (double.IsNaN(optQuality) || double.IsInfinity(optQuality)) return 10E6; // return a large value (TODO: be consistent by using NMSE)
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217 | // TODO: write back values
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218 | return optQuality;
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219 | }
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220 |
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221 | private static void EvaluateObjectiveAndGradient(double[] x, ref double f, double[] grad, object obj) {
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222 | var tree = (ISymbolicExpressionTree)((object[])obj)[0];
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223 | var problemData = (IRegressionProblemData)((object[])obj)[1];
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224 | var nodeIdx = (Dictionary<ISymbolicExpressionTreeNode, int>)((object[])obj)[2];
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225 |
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226 |
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227 | var predicted = Integrate(
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228 | new[] { tree }, // we assume tree contains an expression for the change of the target variable over time y'(t)
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229 | problemData.Dataset,
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230 | problemData.AllowedInputVariables.ToArray(),
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231 | new[] { problemData.TargetVariable },
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232 | problemData.TrainingIndices,
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233 | nodeIdx,
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234 | x).ToArray();
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235 |
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236 | // objective function is MSE
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237 | f = 0.0;
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238 | int n = predicted.Length;
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239 | double invN = 1.0 / n;
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240 | var g = Vector.Zero;
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241 | foreach(var pair in predicted.Zip(problemData.TargetVariableTrainingValues, Tuple.Create)) {
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242 | var y_pred = pair.Item1;
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243 | var y = pair.Item2;
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244 |
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245 | var res = (y - y_pred.Item1);
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246 | var ressq = res * res;
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247 | f += ressq * invN;
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248 | g += -2.0 * res * y_pred.Item2 * invN;
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249 | }
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250 |
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251 | g.CopyTo(grad);
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252 | }
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253 |
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254 |
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255 | private static IEnumerable<Tuple<double, Vector>> Integrate(
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256 | ISymbolicExpressionTree[] trees, IDataset dataset, string[] inputVariables, string[] targetVariables, IEnumerable<int> rows,
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257 | Dictionary<ISymbolicExpressionTreeNode, int> nodeIdx, double[] parameterValues) {
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258 |
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259 | int NUM_STEPS = 1;
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260 | double h = 1.0 / NUM_STEPS;
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261 |
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262 | // return first value as stored in the dataset
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263 | yield return Tuple.Create(dataset.GetDoubleValue(targetVariables.First(), rows.First()), Vector.Zero);
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264 |
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265 | // integrate forward starting with known values for the target in t0
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266 |
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267 | var variableValues = new Dictionary<string, Tuple<double, Vector>>();
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268 | var t0 = rows.First();
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269 | foreach (var varName in inputVariables) {
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270 | variableValues.Add(varName, Tuple.Create(dataset.GetDoubleValue(varName, t0), Vector.Zero));
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271 | }
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272 | foreach (var varName in targetVariables) {
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273 | variableValues.Add(varName, Tuple.Create(dataset.GetDoubleValue(varName, t0), Vector.Zero));
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274 | }
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275 |
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276 | foreach (var t in rows.Skip(1)) {
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277 | for (int step = 0; step < NUM_STEPS; step++) {
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278 | var deltaValues = new Dictionary<string, Tuple<double, Vector>>();
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279 | foreach (var tup in trees.Zip(targetVariables, Tuple.Create)) {
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280 | var tree = tup.Item1;
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281 | var targetVarName = tup.Item2;
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282 | // skip programRoot and startSymbol
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283 | var res = InterpretRec(tree.Root.GetSubtree(0).GetSubtree(0), variableValues, nodeIdx, parameterValues);
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284 | deltaValues.Add(targetVarName, res);
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285 | }
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286 |
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287 | // update variableValues for next step
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288 | foreach (var kvp in deltaValues) {
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289 | var oldVal = variableValues[kvp.Key];
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290 | variableValues[kvp.Key] = Tuple.Create(
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291 | oldVal.Item1 + h * kvp.Value.Item1,
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292 | oldVal.Item2 + h * kvp.Value.Item2
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293 | );
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294 | }
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295 | }
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296 |
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297 | // yield target values
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298 | foreach (var varName in targetVariables) {
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299 | yield return variableValues[varName];
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300 | }
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301 |
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302 | // update for next time step
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303 | foreach (var varName in inputVariables) {
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304 | variableValues[varName] = Tuple.Create(dataset.GetDoubleValue(varName, t), Vector.Zero);
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305 | }
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306 | }
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307 | }
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308 |
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309 | private static Tuple<double, Vector> InterpretRec(
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310 | ISymbolicExpressionTreeNode node,
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311 | Dictionary<string, Tuple<double, Vector>> variableValues,
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312 | Dictionary<ISymbolicExpressionTreeNode, int> nodeIdx,
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313 | double[] parameterValues
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314 | ) {
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315 |
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316 | switch (node.Symbol.Name) {
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317 | case "+": {
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318 | var l = InterpretRec(node.GetSubtree(0), variableValues, nodeIdx, parameterValues);
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319 | var r = InterpretRec(node.GetSubtree(1), variableValues, nodeIdx, parameterValues);
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320 |
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321 | return Tuple.Create(l.Item1 + r.Item1, l.Item2 + r.Item2);
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322 | }
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323 | case "*": {
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324 | var l = InterpretRec(node.GetSubtree(0), variableValues, nodeIdx,parameterValues);
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325 | var r = InterpretRec(node.GetSubtree(1), variableValues, nodeIdx, parameterValues);
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326 |
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327 | return Tuple.Create(l.Item1 * r.Item1, l.Item2 * r.Item1 + l.Item1 * r.Item2);
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328 | }
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329 |
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330 | case "-": {
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331 | var l = InterpretRec(node.GetSubtree(0), variableValues, nodeIdx,parameterValues);
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332 | var r = InterpretRec(node.GetSubtree(1), variableValues, nodeIdx, parameterValues);
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333 |
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334 | return Tuple.Create(l.Item1 - r.Item1, l.Item2 - r.Item2);
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335 | }
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336 | case "%": {
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337 | var l = InterpretRec(node.GetSubtree(0), variableValues, nodeIdx,parameterValues);
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338 | var r = InterpretRec(node.GetSubtree(1), variableValues, nodeIdx, parameterValues);
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339 |
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340 | // protected division
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341 | if (r.Item1.IsAlmost(0.0)) {
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342 | return Tuple.Create(0.0, Vector.Zero);
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343 | } else {
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344 | return Tuple.Create(
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345 | l.Item1 / r.Item1,
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346 | l.Item1 * -1.0 / (r.Item1 * r.Item1) * r.Item2 + 1.0 / r.Item1 * l.Item2 // (f/g)' = f * (1/g)' + 1/g * f' = f * -1/g² * g' + 1/g * f'
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347 | );
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348 | }
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349 | }
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350 | default: {
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351 | // distinguish other cases
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352 | if (IsConstantNode(node)) {
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353 | var vArr = new double[parameterValues.Length]; // backing array for vector
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354 | vArr[nodeIdx[node]] = 1.0;
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355 | var g = new Vector(vArr);
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356 | return Tuple.Create(parameterValues[nodeIdx[node]], g);
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357 | } else {
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358 | // assume a variable name
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359 | var varName = node.Symbol.Name;
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360 | return variableValues[varName];
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361 | }
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362 | }
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363 | }
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364 | }
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365 |
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366 |
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367 | #region events
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368 | private void RegisterEventHandlers() {
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369 | ProblemDataParameter.ValueChanged += new EventHandler(ProblemDataParameter_ValueChanged);
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370 | if (ProblemDataParameter.Value != null) ProblemDataParameter.Value.Changed += new EventHandler(ProblemData_Changed);
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371 | }
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372 |
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373 | private void ProblemDataParameter_ValueChanged(object sender, EventArgs e) {
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374 | ProblemDataParameter.Value.Changed += new EventHandler(ProblemData_Changed);
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375 | OnProblemDataChanged();
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376 | OnReset();
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377 | }
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378 |
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379 | private void ProblemData_Changed(object sender, EventArgs e) {
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380 | OnReset();
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381 | }
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382 |
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383 | private void OnProblemDataChanged() {
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384 | UpdateGrammar();
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385 |
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386 | var handler = ProblemDataChanged;
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387 | if (handler != null) handler(this, EventArgs.Empty);
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388 | }
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389 |
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390 | private void UpdateGrammar() {
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391 | // whenever ProblemData is changed we create a new grammar with the necessary symbols
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392 | var g = new SimpleSymbolicExpressionGrammar();
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393 | g.AddSymbols(new[] {
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394 | "+",
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395 | "*",
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396 | // "%", // % is protected division 1/0 := 0 // removed for testing
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397 | "-",
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398 | }, 2, 2);
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399 |
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400 | // TODO
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401 | //g.AddSymbols(new[] {
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402 | // "exp",
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403 | // "log", // log( <expr> ) // TODO: init a theta to ensure the value is always positive
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404 | // "exp_minus" // exp((-1) * <expr>
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405 | //}, 1, 1);
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406 |
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407 | foreach (var variableName in ProblemData.AllowedInputVariables)
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408 | g.AddTerminalSymbol(variableName);
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409 | foreach (var variableName in new string[] { ProblemData.TargetVariable }) // TODO: multiple target variables
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410 | g.AddTerminalSymbol(variableName);
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411 |
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412 | // generate symbols for numeric parameters for which the value is optimized using AutoDiff
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413 | // we generate multiple symbols to balance the probability for selecting a numeric parameter in the generation of random trees
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414 | var numericConstantsFactor = 2.0;
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415 | for (int i = 0; i < numericConstantsFactor * (ProblemData.AllowedInputVariables.Count() + 1); i++) {
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416 | g.AddTerminalSymbol("θ" + i); // numeric parameter for which the value is optimized using AutoDiff
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417 | }
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418 | Encoding.Grammar = g;
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419 | }
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420 | #endregion
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421 |
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422 | #region Import & Export
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423 | public void Load(IRegressionProblemData data) {
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424 | Name = data.Name;
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425 | Description = data.Description;
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426 | ProblemData = data;
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427 | }
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428 |
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429 | public IRegressionProblemData Export() {
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430 | return ProblemData;
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431 | }
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432 | #endregion
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433 |
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434 |
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435 | #region helper
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436 |
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437 | private static bool IsConstantNode(ISymbolicExpressionTreeNode n) {
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438 | return n.Symbol.Name.StartsWith("θ");
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439 | }
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440 |
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441 | #endregion
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442 |
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443 | }
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444 | }
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