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 System.Runtime.InteropServices;
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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 |
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41 | namespace HeuristicLab.Problems.DynamicalSystemsModelling {
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42 |
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43 | public class Vector {
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44 | public readonly static Vector Zero = new Vector(new double[0]);
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45 |
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46 | public static Vector operator +(Vector a, Vector b) {
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47 | if (a == Zero) return b;
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48 | if (b == Zero) return a;
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49 | Debug.Assert(a.arr.Length == b.arr.Length);
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50 | var res = new double[a.arr.Length];
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51 | for (int i = 0; i < res.Length; i++)
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52 | res[i] = a.arr[i] + b.arr[i];
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53 | return new Vector(res);
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54 | }
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55 | public static Vector operator -(Vector a, Vector b) {
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56 | if (b == Zero) return a;
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57 | if (a == Zero) return -b;
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58 | Debug.Assert(a.arr.Length == b.arr.Length);
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59 | var res = new double[a.arr.Length];
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60 | for (int i = 0; i < res.Length; i++)
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61 | res[i] = a.arr[i] - b.arr[i];
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62 | return new Vector(res);
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63 | }
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64 | public static Vector operator -(Vector v) {
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65 | if (v == Zero) return Zero;
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66 | for (int i = 0; i < v.arr.Length; i++)
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67 | v.arr[i] = -v.arr[i];
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68 | return v;
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69 | }
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70 |
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71 | public static Vector operator *(double s, Vector v) {
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72 | if (v == Zero) return Zero;
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73 | if (s == 0.0) return Zero;
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74 | var res = new double[v.arr.Length];
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75 | for (int i = 0; i < res.Length; i++)
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76 | res[i] = s * v.arr[i];
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77 | return new Vector(res);
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78 | }
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79 |
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80 | public static Vector operator *(Vector v, double s) {
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81 | return s * v;
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82 | }
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83 | public static Vector operator *(Vector u, Vector v) {
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84 | if (v == Zero) return Zero;
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85 | if (u == Zero) return Zero;
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86 | var res = new double[v.arr.Length];
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87 | for (int i = 0; i < res.Length; i++)
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88 | res[i] = u.arr[i] * v.arr[i];
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89 | return new Vector(res);
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90 | }
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91 | public static Vector operator /(double s, Vector v) {
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92 | if (s == 0.0) return Zero;
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93 | if (v == Zero) throw new ArgumentException("Division by zero vector");
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94 | var res = new double[v.arr.Length];
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95 | for (int i = 0; i < res.Length; i++)
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96 | res[i] = 1.0 / v.arr[i];
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97 | return new Vector(res);
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98 | }
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99 | public static Vector operator /(Vector v, double s) {
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100 | return v * 1.0 / s;
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101 | }
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102 |
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103 | public static Vector Sin(Vector s) {
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104 | var res = new double[s.arr.Length];
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105 | for (int i = 0; i < res.Length; i++) res[i] = Math.Sin(s.arr[i]);
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106 | return new Vector(res);
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107 | }
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108 | public static Vector Cos(Vector s) {
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109 | var res = new double[s.arr.Length];
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110 | for (int i = 0; i < res.Length; i++) res[i] = Math.Cos(s.arr[i]);
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111 | return new Vector(res);
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112 | }
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113 |
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114 | private readonly double[] arr; // backing array;
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115 |
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116 | public Vector(double[] v) {
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117 | this.arr = v;
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118 | }
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119 |
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120 | public void CopyTo(double[] target) {
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121 | Debug.Assert(arr.Length <= target.Length);
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122 | Array.Copy(arr, target, arr.Length);
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123 | }
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124 | }
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125 |
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126 | [Item("Dynamical Systems Modelling Problem", "TODO")]
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127 | [Creatable(CreatableAttribute.Categories.GeneticProgrammingProblems, Priority = 900)]
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128 | [StorableClass]
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129 | public sealed class Problem : SingleObjectiveBasicProblem<MultiEncoding>, IRegressionProblem, IProblemInstanceConsumer<IRegressionProblemData>, IProblemInstanceExporter<IRegressionProblemData> {
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130 |
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131 | // CVODES types
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132 | public enum MultistepMethod : int { CV_ADAMS = 1, CV_BDF = 2 };
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133 | public enum NonlinearSolverIteration : int { CV_NEWTON = 1, CV_FUNCTIONAL = 2 };
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134 |
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135 |
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136 | /* itask */
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137 | public const int CV_NORMAL = 1;
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138 | public const int CV_ONE_STEP = 2;
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139 |
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140 | /* ism */
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141 | public const int CV_SIMULTANEOUS = 1;
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142 | public const int CV_STAGGERED = 2;
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143 | public const int CV_STAGGERED1 = 3;
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144 |
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145 | /* DQtype */
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146 | public const int CV_CENTERED = 1;
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147 | public const int CV_FORWARD = 2;
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148 |
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149 | /* interp */
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150 | public const int CV_HERMITE = 1;
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151 | public const int CV_POLYNOMIAL = 2;
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152 |
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153 | /*
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154 | * ----------------------------------------
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155 | * CVODES return flags
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156 | * ----------------------------------------
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157 | */
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158 |
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159 | public const int CV_SUCCESS = 0;
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160 | public const int CV_TSTOP_RETURN = 1;
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161 | public const int CV_ROOT_RETURN = 2;
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162 |
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163 | public const int CV_WARNING = 99;
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164 |
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165 | public const int CV_TOO_MUCH_WORK = -1;
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166 | public const int CV_TOO_MUCH_ACC = -2;
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167 | public const int CV_ERR_FAILURE = -3;
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168 | public const int CV_CONV_FAILURE = -4;
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169 |
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170 | public const int CV_LINIT_FAIL = -5;
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171 | public const int CV_LSETUP_FAIL = -6;
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172 | public const int CV_LSOLVE_FAIL = -7;
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173 | public const int CV_RHSFUNC_FAIL = -8;
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174 | public const int CV_FIRST_RHSFUNC_ERR = -9;
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175 | public const int CV_REPTD_RHSFUNC_ERR = -10;
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176 | public const int CV_UNREC_RHSFUNC_ERR = -11;
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177 | public const int CV_RTFUNC_FAIL = -12;
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178 | public const int CV_CONSTR_FAIL = -13;
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179 |
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180 | public const int CV_MEM_FAIL = -20;
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181 | public const int CV_MEM_NULL = -21;
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182 | public const int CV_ILL_INPUT = -22;
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183 | public const int CV_NO_MALLOC = -23;
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184 | public const int CV_BAD_K = -24;
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185 | public const int CV_BAD_T = -25;
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186 | public const int CV_BAD_DKY = -26;
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187 | public const int CV_TOO_CLOSE = -27;
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188 |
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189 | public const int CV_NO_QUAD = -30;
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190 | public const int CV_QRHSFUNC_FAIL = -31;
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191 | public const int CV_FIRST_QRHSFUNC_ERR = -32;
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192 | public const int CV_REPTD_QRHSFUNC_ERR = -33;
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193 | public const int CV_UNREC_QRHSFUNC_ERR = -34;
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194 |
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195 | public const int CV_NO_SENS = -40;
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196 | public const int CV_SRHSFUNC_FAIL = -41;
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197 | public const int CV_FIRST_SRHSFUNC_ERR = -42;
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198 | public const int CV_REPTD_SRHSFUNC_ERR = -43;
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199 | public const int CV_UNREC_SRHSFUNC_ERR = -44;
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200 |
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201 | public const int CV_BAD_IS = -45;
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202 |
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203 | public const int CV_NO_QUADSENS = -50;
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204 | public const int CV_QSRHSFUNC_FAIL = -51;
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205 | public const int CV_FIRST_QSRHSFUNC_ERR = -52;
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206 | public const int CV_REPTD_QSRHSFUNC_ERR = -53;
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207 | public const int CV_UNREC_QSRHSFUNC_ERR = -54;
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208 |
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209 | /*
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210 | * ----------------------------------------
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211 | * CVODEA return flags
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212 | * ----------------------------------------
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213 | */
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214 |
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215 | public const int CV_NO_ADJ = -101;
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216 | public const int CV_NO_FWD = -102;
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217 | public const int CV_NO_BCK = -103;
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218 | public const int CV_BAD_TB0 = -104;
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219 | public const int CV_REIFWD_FAIL = -105;
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220 | public const int CV_FWD_FAIL = -106;
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221 | public const int CV_GETY_BADT = -107;
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222 |
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223 | [UnmanagedFunctionPointer(CallingConvention.Cdecl)]
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224 | public delegate int CVRhsFunc(
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225 | double t, // realtype
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226 | IntPtr y, // N_Vector
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227 | IntPtr ydot, // N_Vector
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228 | IntPtr user_data
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229 | );
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230 |
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231 | [UnmanagedFunctionPointer(CallingConvention.Cdecl)]
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232 | public delegate int CVDlsJacFunc(
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233 | double t,
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234 | IntPtr y, // N_Vector
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235 | IntPtr fy, // N_Vector
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236 | IntPtr Jac, // SUNMatrix
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237 | IntPtr user_data,
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238 | IntPtr tmp1, // N_Vector
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239 | IntPtr tmp2, // N_Vector
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240 | IntPtr tmp3 // N_Vector
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241 | );
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242 |
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243 |
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244 | [DllImport("sundials_cvodes.dll", EntryPoint = "CVodeCreate", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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245 | // returns a void* to the cvodes memory block if successful otherwise NULL
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246 | public static extern IntPtr CVodeCreate(MultistepMethod lmm, NonlinearSolverIteration iter);
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247 |
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248 | [DllImport("sundials_cvodes.dll", EntryPoint = "CVodeInit", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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249 |
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250 | public static extern int CVodeInit(
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251 | IntPtr cvode_mem, // pointer returned by CVodeCreate
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252 | CVRhsFunc f,
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253 | double t0, // realtype, the inital value of t
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254 | IntPtr y0 // N_Vector the initial value of y
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255 | );
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256 |
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257 |
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258 | [DllImport("sundials_cvodes.dll", EntryPoint = "CVodeSStolerances", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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259 | public static extern int CVodeSStolerances(
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260 | IntPtr cvode_mem,
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261 | double reltol,
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262 | double abstol
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263 | );
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264 |
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265 | [DllImport("sundials_cvodes.dll", EntryPoint = "CVDlsSetLinearSolver", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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266 | public static extern int CVDlsSetLinearSolver(
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267 | IntPtr cvode_mem,
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268 | IntPtr linearSolver, // SUNLinearSolver
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269 | IntPtr j // SUNMatrix
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270 | );
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271 |
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272 | [DllImport("sundials_cvodes.dll", EntryPoint = "CVDlsSetJacFn", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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273 | public static extern int CVDlsSetJacFn(
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274 | IntPtr cvode_mem,
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275 | CVDlsJacFunc jacFunc
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276 | );
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277 |
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278 | [DllImport("sundials_cvodes.dll", EntryPoint = "CVode", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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279 | public static extern int CVode(
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280 | IntPtr cvode_mem,
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281 | double tout, // next time at which a solution is desired
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282 | IntPtr yout, // N_Vector
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283 | ref double tret, // the time reached by the solver (output)
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284 | int itask // flag indicating the job of the solver for the next step.
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285 | );
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286 |
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287 | [DllImport("sundials_cvodes.dll", EntryPoint = "CVodeFree", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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288 |
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289 | public static extern int CVodeFree(IntPtr cvode_mem);
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290 |
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291 | #region matrix
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292 | [DllImport("sundials_cvodes.dll", EntryPoint = "SUNDenseMatrix", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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293 | public static extern IntPtr SUNDenseMatrix(long m, long n);
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294 |
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295 | [DllImport("sundials_cvodes.dll", EntryPoint = "SUNMatDestroy", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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296 | public static extern void SUNMatDestroy(IntPtr A);
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297 | #endregion
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298 |
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299 | #region linear solver
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300 | [DllImport("sundials_cvodes.dll", EntryPoint = "SUNDenseLinearSolver", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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301 | public static extern IntPtr SUNDenseLinearSolver(
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302 | IntPtr y, // N_Vector
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303 | IntPtr A // SUNMatrix
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304 | );
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305 |
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306 | [DllImport("sundials_cvodes.dll", EntryPoint = "SUNLinSolInitialize", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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307 | public static extern int SUNLinSolInitialize(IntPtr linearSolver);
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308 |
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309 | [DllImport("sundials_cvodes.dll", EntryPoint = "SUNLinSolSetup", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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310 | public static extern int SUNLinSolSetup(
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311 | IntPtr linearSolver,
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312 | IntPtr A // SUNMatrix
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313 | );
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314 |
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315 | [DllImport("sundials_cvodes.dll", EntryPoint = "SUNLinSolSolve", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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316 | public static extern int SUNLinSolSolve(
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317 | IntPtr linearSolver,
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318 | IntPtr A, // SUNMatrix
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319 | IntPtr x, // N_Vector
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320 | IntPtr b, // N_Vector
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321 | double tol
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322 | );
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323 |
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324 | [DllImport("sundials_cvodes.dll", EntryPoint = "SUNLinSolFree", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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325 | public static extern int SUNLinSolFree(IntPtr linearSolver);
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326 |
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327 | #endregion
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328 |
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329 | #region N_Vector
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330 | [DllImport("sundials_cvodes.dll", EntryPoint = "N_VNew_Serial", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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331 | public static extern IntPtr N_VNew_Serial(long vec_length);
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332 |
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333 | [DllImport("sundials_cvodes.dll", EntryPoint = "N_VDestroy_Serial", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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334 | public static extern void N_VDestroy_Serial(IntPtr vec);
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335 |
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336 | [DllImport("sundials_cvodes.dll", EntryPoint = "N_VPrint_Serial", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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337 | public static extern void N_VPrint_Serial(IntPtr vec);
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338 |
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339 | [DllImport("sundials_cvodes.dll", EntryPoint = "N_VConst_Serial", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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340 | public static extern void N_VConst_Serial(double c, IntPtr vec);
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341 |
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342 |
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343 | [DllImport("sundials_cvodes.dll", EntryPoint = "N_VL1Norm_Serial", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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344 | public static extern double N_VL1Norm_Serial(IntPtr vec);
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345 |
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346 | [DllImport("sundials_cvodes.dll", EntryPoint = "N_VMake_Serial", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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347 | public static extern IntPtr N_VMake_Serial(long vec_length, double[] v_data);
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348 |
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349 | [DllImport("sundials_cvodes.dll", EntryPoint = "N_VScale", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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350 | /// Performs the operation z = c*x
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351 | public static extern void N_VScale(double s,
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352 | IntPtr x, // N_Vector
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353 | IntPtr z // N_Vector
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354 | );
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355 |
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356 | [DllImport("sundials_cvodes.dll", EntryPoint = "N_VMake_Serial", ExactSpelling = true, CallingConvention = CallingConvention.Cdecl)]
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357 | public unsafe static extern double* N_VGetArrayPointer_Serial(IntPtr vec);
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358 | #endregion
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359 |
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360 |
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361 |
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362 |
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363 |
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364 | #region parameter names
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365 | private const string ProblemDataParameterName = "Data";
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366 | private const string TargetVariablesParameterName = "Target variables";
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367 | private const string FunctionSetParameterName = "Function set";
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368 | private const string MaximumLengthParameterName = "Size limit";
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369 | private const string MaximumParameterOptimizationIterationsParameterName = "Max. parameter optimization iterations";
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370 | private const string NumberOfLatentVariablesParameterName = "Number of latent variables";
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371 | private const string NumericIntegrationStepsParameterName = "Steps for numeric integration";
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372 | private const string TrainingEpisodesParameterName = "Training episodes";
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373 | private const string OptimizeParametersForEpisodesParameterName = "Optimize parameters for episodes";
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374 | #endregion
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375 |
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376 | #region Parameter Properties
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377 | IParameter IDataAnalysisProblem.ProblemDataParameter { get { return ProblemDataParameter; } }
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378 |
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379 | public IValueParameter<IRegressionProblemData> ProblemDataParameter {
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380 | get { return (IValueParameter<IRegressionProblemData>)Parameters[ProblemDataParameterName]; }
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381 | }
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382 | public IValueParameter<ReadOnlyCheckedItemCollection<StringValue>> TargetVariablesParameter {
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383 | get { return (IValueParameter<ReadOnlyCheckedItemCollection<StringValue>>)Parameters[TargetVariablesParameterName]; }
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384 | }
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385 | public IValueParameter<ReadOnlyCheckedItemCollection<StringValue>> FunctionSetParameter {
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386 | get { return (IValueParameter<ReadOnlyCheckedItemCollection<StringValue>>)Parameters[FunctionSetParameterName]; }
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387 | }
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388 | public IFixedValueParameter<IntValue> MaximumLengthParameter {
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389 | get { return (IFixedValueParameter<IntValue>)Parameters[MaximumLengthParameterName]; }
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390 | }
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391 | public IFixedValueParameter<IntValue> MaximumParameterOptimizationIterationsParameter {
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392 | get { return (IFixedValueParameter<IntValue>)Parameters[MaximumParameterOptimizationIterationsParameterName]; }
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393 | }
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394 | public IFixedValueParameter<IntValue> NumberOfLatentVariablesParameter {
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395 | get { return (IFixedValueParameter<IntValue>)Parameters[NumberOfLatentVariablesParameterName]; }
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396 | }
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397 | public IFixedValueParameter<IntValue> NumericIntegrationStepsParameter {
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398 | get { return (IFixedValueParameter<IntValue>)Parameters[NumericIntegrationStepsParameterName]; }
|
---|
399 | }
|
---|
400 | public IValueParameter<ItemList<IntRange>> TrainingEpisodesParameter {
|
---|
401 | get { return (IValueParameter<ItemList<IntRange>>)Parameters[TrainingEpisodesParameterName]; }
|
---|
402 | }
|
---|
403 | public IFixedValueParameter<BoolValue> OptimizeParametersForEpisodesParameter {
|
---|
404 | get { return (IFixedValueParameter<BoolValue>)Parameters[OptimizeParametersForEpisodesParameterName]; }
|
---|
405 | }
|
---|
406 | #endregion
|
---|
407 |
|
---|
408 | #region Properties
|
---|
409 | public IRegressionProblemData ProblemData {
|
---|
410 | get { return ProblemDataParameter.Value; }
|
---|
411 | set { ProblemDataParameter.Value = value; }
|
---|
412 | }
|
---|
413 | IDataAnalysisProblemData IDataAnalysisProblem.ProblemData { get { return ProblemData; } }
|
---|
414 |
|
---|
415 | public ReadOnlyCheckedItemCollection<StringValue> TargetVariables {
|
---|
416 | get { return TargetVariablesParameter.Value; }
|
---|
417 | }
|
---|
418 |
|
---|
419 | public ReadOnlyCheckedItemCollection<StringValue> FunctionSet {
|
---|
420 | get { return FunctionSetParameter.Value; }
|
---|
421 | }
|
---|
422 |
|
---|
423 | public int MaximumLength {
|
---|
424 | get { return MaximumLengthParameter.Value.Value; }
|
---|
425 | }
|
---|
426 | public int MaximumParameterOptimizationIterations {
|
---|
427 | get { return MaximumParameterOptimizationIterationsParameter.Value.Value; }
|
---|
428 | }
|
---|
429 | public int NumberOfLatentVariables {
|
---|
430 | get { return NumberOfLatentVariablesParameter.Value.Value; }
|
---|
431 | }
|
---|
432 | public int NumericIntegrationSteps {
|
---|
433 | get { return NumericIntegrationStepsParameter.Value.Value; }
|
---|
434 | }
|
---|
435 | public IEnumerable<IntRange> TrainingEpisodes {
|
---|
436 | get { return TrainingEpisodesParameter.Value; }
|
---|
437 | }
|
---|
438 | public bool OptimizeParametersForEpisodes {
|
---|
439 | get { return OptimizeParametersForEpisodesParameter.Value.Value; }
|
---|
440 | }
|
---|
441 |
|
---|
442 | #endregion
|
---|
443 |
|
---|
444 | public event EventHandler ProblemDataChanged;
|
---|
445 |
|
---|
446 | public override bool Maximization {
|
---|
447 | get { return false; } // we minimize NMSE
|
---|
448 | }
|
---|
449 |
|
---|
450 | #region item cloning and persistence
|
---|
451 | // persistence
|
---|
452 | [StorableConstructor]
|
---|
453 | private Problem(bool deserializing) : base(deserializing) { }
|
---|
454 | [StorableHook(HookType.AfterDeserialization)]
|
---|
455 | private void AfterDeserialization() {
|
---|
456 | if (!Parameters.ContainsKey(OptimizeParametersForEpisodesParameterName)) {
|
---|
457 | Parameters.Add(new FixedValueParameter<BoolValue>(OptimizeParametersForEpisodesParameterName, "Flag to select if parameters should be optimized globally or for each episode individually.", new BoolValue(false)));
|
---|
458 | }
|
---|
459 | RegisterEventHandlers();
|
---|
460 | }
|
---|
461 |
|
---|
462 | // cloning
|
---|
463 | private Problem(Problem original, Cloner cloner)
|
---|
464 | : base(original, cloner) {
|
---|
465 | RegisterEventHandlers();
|
---|
466 | }
|
---|
467 | public override IDeepCloneable Clone(Cloner cloner) { return new Problem(this, cloner); }
|
---|
468 | #endregion
|
---|
469 |
|
---|
470 | public Problem()
|
---|
471 | : base() {
|
---|
472 | var targetVariables = new CheckedItemCollection<StringValue>().AsReadOnly(); // HACK: it would be better to provide a new class derived from IDataAnalysisProblem
|
---|
473 | var functions = CreateFunctionSet();
|
---|
474 | Parameters.Add(new ValueParameter<IRegressionProblemData>(ProblemDataParameterName, "The data captured from the dynamical system. Use CSV import functionality to import data.", new RegressionProblemData()));
|
---|
475 | Parameters.Add(new ValueParameter<ReadOnlyCheckedItemCollection<StringValue>>(TargetVariablesParameterName, "Target variables (overrides setting in ProblemData)", targetVariables));
|
---|
476 | Parameters.Add(new ValueParameter<ReadOnlyCheckedItemCollection<StringValue>>(FunctionSetParameterName, "The list of allowed functions", functions));
|
---|
477 | 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)));
|
---|
478 | 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)));
|
---|
479 | 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)));
|
---|
480 | 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)));
|
---|
481 | 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>()));
|
---|
482 | Parameters.Add(new FixedValueParameter<BoolValue>(OptimizeParametersForEpisodesParameterName, "Flag to select if parameters should be optimized globally or for each episode individually.", new BoolValue(false)));
|
---|
483 | RegisterEventHandlers();
|
---|
484 | InitAllParameters();
|
---|
485 |
|
---|
486 | // TODO: do not clear selection of target variables when the input variables are changed (keep selected target variables)
|
---|
487 | // TODO: UI hangs when selecting / deselecting input variables because the encoding is updated on each item
|
---|
488 | // TODO: use training range as default training episode
|
---|
489 |
|
---|
490 | }
|
---|
491 |
|
---|
492 | public override double Evaluate(Individual individual, IRandom random) {
|
---|
493 | var trees = individual.Values.Select(v => v.Value).OfType<ISymbolicExpressionTree>().ToArray(); // extract all trees from individual
|
---|
494 |
|
---|
495 | if (OptimizeParametersForEpisodes) {
|
---|
496 | int eIdx = 0;
|
---|
497 | double totalNMSE = 0.0;
|
---|
498 | int totalSize = 0;
|
---|
499 | foreach (var episode in TrainingEpisodes) {
|
---|
500 | double[] optTheta;
|
---|
501 | double nmse;
|
---|
502 | OptimizeForEpisodes(trees, random, new[] { episode }, out optTheta, out nmse);
|
---|
503 | individual["OptTheta_" + eIdx] = new DoubleArray(optTheta); // write back optimized parameters so that we can use them in the Analysis method
|
---|
504 | eIdx++;
|
---|
505 | totalNMSE += nmse * episode.Size;
|
---|
506 | totalSize += episode.Size;
|
---|
507 | }
|
---|
508 | return totalNMSE / totalSize;
|
---|
509 | } else {
|
---|
510 | double[] optTheta;
|
---|
511 | double nmse;
|
---|
512 | OptimizeForEpisodes(trees, random, TrainingEpisodes, out optTheta, out nmse);
|
---|
513 | individual["OptTheta"] = new DoubleArray(optTheta); // write back optimized parameters so that we can use them in the Analysis method
|
---|
514 | return nmse;
|
---|
515 | }
|
---|
516 | }
|
---|
517 |
|
---|
518 | private void OptimizeForEpisodes(ISymbolicExpressionTree[] trees, IRandom random, IEnumerable<IntRange> episodes, out double[] optTheta, out double nmse) {
|
---|
519 | var rows = episodes.SelectMany(e => Enumerable.Range(e.Start, e.End - e.Start)).ToArray();
|
---|
520 | var problemData = ProblemData;
|
---|
521 | var targetVars = TargetVariables.CheckedItems.Select(i => i.Value).ToArray();
|
---|
522 | 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
|
---|
523 | var targetValues = new double[rows.Length, targetVars.Length];
|
---|
524 |
|
---|
525 | // collect values of all target variables
|
---|
526 | var colIdx = 0;
|
---|
527 | foreach (var targetVar in targetVars) {
|
---|
528 | int rowIdx = 0;
|
---|
529 | foreach (var value in problemData.Dataset.GetDoubleValues(targetVar, rows)) {
|
---|
530 | targetValues[rowIdx, colIdx] = value;
|
---|
531 | rowIdx++;
|
---|
532 | }
|
---|
533 | colIdx++;
|
---|
534 | }
|
---|
535 |
|
---|
536 | var nodeIdx = new Dictionary<ISymbolicExpressionTreeNode, int>();
|
---|
537 |
|
---|
538 | foreach (var tree in trees) {
|
---|
539 | foreach (var node in tree.Root.IterateNodesPrefix().Where(n => IsConstantNode(n))) {
|
---|
540 | nodeIdx.Add(node, nodeIdx.Count);
|
---|
541 | }
|
---|
542 | }
|
---|
543 |
|
---|
544 | var theta = nodeIdx.Select(_ => random.NextDouble() * 2.0 - 1.0).ToArray(); // init params randomly from Unif(-1,1)
|
---|
545 |
|
---|
546 | optTheta = new double[0];
|
---|
547 | if (theta.Length > 0) {
|
---|
548 | alglib.minlbfgsstate state;
|
---|
549 | alglib.minlbfgsreport report;
|
---|
550 | alglib.minlbfgscreate(Math.Min(theta.Length, 5), theta, out state);
|
---|
551 | alglib.minlbfgssetcond(state, 0.0, 0.0, 0.0, MaximumParameterOptimizationIterations);
|
---|
552 | alglib.minlbfgsoptimize(state, EvaluateObjectiveAndGradient, null,
|
---|
553 | new object[] { trees, targetVars, problemData, nodeIdx, targetValues, episodes.ToArray(), NumericIntegrationSteps, latentVariables }); //TODO: create a type
|
---|
554 | alglib.minlbfgsresults(state, out optTheta, out report);
|
---|
555 |
|
---|
556 | /*
|
---|
557 | *
|
---|
558 | * L-BFGS algorithm results
|
---|
559 |
|
---|
560 | INPUT PARAMETERS:
|
---|
561 | State - algorithm state
|
---|
562 |
|
---|
563 | OUTPUT PARAMETERS:
|
---|
564 | X - array[0..N-1], solution
|
---|
565 | Rep - optimization report:
|
---|
566 | * Rep.TerminationType completetion code:
|
---|
567 | * -7 gradient verification failed.
|
---|
568 | See MinLBFGSSetGradientCheck() for more information.
|
---|
569 | * -2 rounding errors prevent further improvement.
|
---|
570 | X contains best point found.
|
---|
571 | * -1 incorrect parameters were specified
|
---|
572 | * 1 relative function improvement is no more than
|
---|
573 | EpsF.
|
---|
574 | * 2 relative step is no more than EpsX.
|
---|
575 | * 4 gradient norm is no more than EpsG
|
---|
576 | * 5 MaxIts steps was taken
|
---|
577 | * 7 stopping conditions are too stringent,
|
---|
578 | further improvement is impossible
|
---|
579 | * Rep.IterationsCount contains iterations count
|
---|
580 | * NFEV countains number of function calculations
|
---|
581 | */
|
---|
582 | if (report.terminationtype < 0) { nmse = 10E6; return; }
|
---|
583 | }
|
---|
584 |
|
---|
585 | // perform evaluation for optimal theta to get quality value
|
---|
586 | double[] grad = new double[optTheta.Length];
|
---|
587 | nmse = double.NaN;
|
---|
588 | EvaluateObjectiveAndGradient(optTheta, ref nmse, grad,
|
---|
589 | new object[] { trees, targetVars, problemData, nodeIdx, targetValues, episodes.ToArray(), NumericIntegrationSteps, latentVariables });
|
---|
590 | if (double.IsNaN(nmse) || double.IsInfinity(nmse)) { nmse = 10E6; return; } // return a large value (TODO: be consistent by using NMSE)
|
---|
591 | }
|
---|
592 |
|
---|
593 | private static void EvaluateObjectiveAndGradient(double[] x, ref double f, double[] grad, object obj) {
|
---|
594 | var trees = (ISymbolicExpressionTree[])((object[])obj)[0];
|
---|
595 | var targetVariables = (string[])((object[])obj)[1];
|
---|
596 | var problemData = (IRegressionProblemData)((object[])obj)[2];
|
---|
597 | var nodeIdx = (Dictionary<ISymbolicExpressionTreeNode, int>)((object[])obj)[3];
|
---|
598 | var targetValues = (double[,])((object[])obj)[4];
|
---|
599 | var episodes = (IntRange[])((object[])obj)[5];
|
---|
600 | var numericIntegrationSteps = (int)((object[])obj)[6];
|
---|
601 | var latentVariables = (string[])((object[])obj)[7];
|
---|
602 |
|
---|
603 | var predicted = Integrate(
|
---|
604 | trees, // we assume trees contain expressions for the change of each target variable over time y'(t)
|
---|
605 | problemData.Dataset,
|
---|
606 | problemData.AllowedInputVariables.ToArray(),
|
---|
607 | targetVariables,
|
---|
608 | latentVariables,
|
---|
609 | episodes,
|
---|
610 | nodeIdx,
|
---|
611 | x, numericIntegrationSteps).ToArray();
|
---|
612 |
|
---|
613 |
|
---|
614 | // for normalized MSE = 1/variance(t) * MSE(t, pred)
|
---|
615 | // TODO: Perf. (by standardization of target variables before evaluation of all trees)
|
---|
616 | var invVar = Enumerable.Range(0, targetVariables.Length)
|
---|
617 | .Select(c => Enumerable.Range(0, targetValues.GetLength(0)).Select(row => targetValues[row, c])) // column vectors
|
---|
618 | .Select(vec => vec.Variance())
|
---|
619 | .Select(v => 1.0 / v)
|
---|
620 | .ToArray();
|
---|
621 |
|
---|
622 | // objective function is NMSE
|
---|
623 | f = 0.0;
|
---|
624 | int n = predicted.Length;
|
---|
625 | double invN = 1.0 / n;
|
---|
626 | var g = Vector.Zero;
|
---|
627 | int r = 0;
|
---|
628 | foreach (var y_pred in predicted) {
|
---|
629 | for (int c = 0; c < y_pred.Length; c++) {
|
---|
630 |
|
---|
631 | var y_pred_f = y_pred[c].Item1;
|
---|
632 | var y = targetValues[r, c];
|
---|
633 |
|
---|
634 | var res = (y - y_pred_f);
|
---|
635 | var ressq = res * res;
|
---|
636 | f += ressq * invN * invVar[c];
|
---|
637 | g += -2.0 * res * y_pred[c].Item2 * invN * invVar[c];
|
---|
638 | }
|
---|
639 | r++;
|
---|
640 | }
|
---|
641 |
|
---|
642 | g.CopyTo(grad);
|
---|
643 | }
|
---|
644 |
|
---|
645 | public override void Analyze(Individual[] individuals, double[] qualities, ResultCollection results, IRandom random) {
|
---|
646 | base.Analyze(individuals, qualities, results, random);
|
---|
647 |
|
---|
648 | if (!results.ContainsKey("Prediction (training)")) {
|
---|
649 | results.Add(new Result("Prediction (training)", typeof(ReadOnlyItemList<DataTable>)));
|
---|
650 | }
|
---|
651 | if (!results.ContainsKey("Prediction (test)")) {
|
---|
652 | results.Add(new Result("Prediction (test)", typeof(ReadOnlyItemList<DataTable>)));
|
---|
653 | }
|
---|
654 | if (!results.ContainsKey("Models")) {
|
---|
655 | results.Add(new Result("Models", typeof(VariableCollection)));
|
---|
656 | }
|
---|
657 |
|
---|
658 | var bestIndividualAndQuality = this.GetBestIndividual(individuals, qualities);
|
---|
659 | var trees = bestIndividualAndQuality.Item1.Values.Select(v => v.Value).OfType<ISymbolicExpressionTree>().ToArray(); // extract all trees from individual
|
---|
660 |
|
---|
661 | // TODO extract common functionality from Evaluate and Analyze
|
---|
662 | var nodeIdx = new Dictionary<ISymbolicExpressionTreeNode, int>();
|
---|
663 | foreach (var tree in trees) {
|
---|
664 | foreach (var node in tree.Root.IterateNodesPrefix().Where(n => IsConstantNode(n))) {
|
---|
665 | nodeIdx.Add(node, nodeIdx.Count);
|
---|
666 | }
|
---|
667 | }
|
---|
668 | var problemData = ProblemData;
|
---|
669 | var targetVars = TargetVariables.CheckedItems.Select(i => i.Value).ToArray();
|
---|
670 | 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
|
---|
671 |
|
---|
672 | var trainingList = new ItemList<DataTable>();
|
---|
673 |
|
---|
674 | if (OptimizeParametersForEpisodes) {
|
---|
675 | var eIdx = 0;
|
---|
676 | var trainingPredictions = new List<Tuple<double, Vector>[][]>();
|
---|
677 | foreach (var episode in TrainingEpisodes) {
|
---|
678 | var episodes = new[] { episode };
|
---|
679 | var optTheta = ((DoubleArray)bestIndividualAndQuality.Item1["OptTheta_" + eIdx]).ToArray(); // see evaluate
|
---|
680 | var trainingPrediction = Integrate(
|
---|
681 | trees, // we assume trees contain expressions for the change of each target variable over time y'(t)
|
---|
682 | problemData.Dataset,
|
---|
683 | problemData.AllowedInputVariables.ToArray(),
|
---|
684 | targetVars,
|
---|
685 | latentVariables,
|
---|
686 | episodes,
|
---|
687 | nodeIdx,
|
---|
688 | optTheta,
|
---|
689 | NumericIntegrationSteps).ToArray();
|
---|
690 | trainingPredictions.Add(trainingPrediction);
|
---|
691 | eIdx++;
|
---|
692 | }
|
---|
693 |
|
---|
694 | // only for actual target values
|
---|
695 | var trainingRows = TrainingEpisodes.SelectMany(e => Enumerable.Range(e.Start, e.End - e.Start));
|
---|
696 | for (int colIdx = 0; colIdx < targetVars.Length; colIdx++) {
|
---|
697 | var targetVar = targetVars[colIdx];
|
---|
698 | var trainingDataTable = new DataTable(targetVar + " prediction (training)");
|
---|
699 | var actualValuesRow = new DataRow(targetVar, "The values of " + targetVar, problemData.Dataset.GetDoubleValues(targetVar, trainingRows));
|
---|
700 | var predictedValuesRow = new DataRow(targetVar + " pred.", "Predicted values for " + targetVar, trainingPredictions.SelectMany(arr => arr.Select(row => row[colIdx].Item1)).ToArray());
|
---|
701 | trainingDataTable.Rows.Add(actualValuesRow);
|
---|
702 | trainingDataTable.Rows.Add(predictedValuesRow);
|
---|
703 | trainingList.Add(trainingDataTable);
|
---|
704 | }
|
---|
705 | results["Prediction (training)"].Value = trainingList.AsReadOnly();
|
---|
706 |
|
---|
707 |
|
---|
708 | var models = new VariableCollection();
|
---|
709 |
|
---|
710 | foreach (var tup in targetVars.Zip(trees, Tuple.Create)) {
|
---|
711 | var targetVarName = tup.Item1;
|
---|
712 | var tree = tup.Item2;
|
---|
713 |
|
---|
714 | var origTreeVar = new HeuristicLab.Core.Variable(targetVarName + "(original)");
|
---|
715 | origTreeVar.Value = (ISymbolicExpressionTree)tree.Clone();
|
---|
716 | models.Add(origTreeVar);
|
---|
717 | }
|
---|
718 | results["Models"].Value = models;
|
---|
719 | } else {
|
---|
720 | var optTheta = ((DoubleArray)bestIndividualAndQuality.Item1["OptTheta"]).ToArray(); // see evaluate
|
---|
721 | var trainingPrediction = Integrate(
|
---|
722 | trees, // we assume trees contain expressions for the change of each target variable over time y'(t)
|
---|
723 | problemData.Dataset,
|
---|
724 | problemData.AllowedInputVariables.ToArray(),
|
---|
725 | targetVars,
|
---|
726 | latentVariables,
|
---|
727 | TrainingEpisodes,
|
---|
728 | nodeIdx,
|
---|
729 | optTheta,
|
---|
730 | NumericIntegrationSteps).ToArray();
|
---|
731 | // only for actual target values
|
---|
732 | var trainingRows = TrainingEpisodes.SelectMany(e => Enumerable.Range(e.Start, e.End - e.Start));
|
---|
733 | for (int colIdx = 0; colIdx < targetVars.Length; colIdx++) {
|
---|
734 | var targetVar = targetVars[colIdx];
|
---|
735 | var trainingDataTable = new DataTable(targetVar + " prediction (training)");
|
---|
736 | var actualValuesRow = new DataRow(targetVar, "The values of " + targetVar, problemData.Dataset.GetDoubleValues(targetVar, trainingRows));
|
---|
737 | var predictedValuesRow = new DataRow(targetVar + " pred.", "Predicted values for " + targetVar, trainingPrediction.Select(arr => arr[colIdx].Item1).ToArray());
|
---|
738 | trainingDataTable.Rows.Add(actualValuesRow);
|
---|
739 | trainingDataTable.Rows.Add(predictedValuesRow);
|
---|
740 | trainingList.Add(trainingDataTable);
|
---|
741 | }
|
---|
742 | // TODO: DRY for training and test
|
---|
743 | var testList = new ItemList<DataTable>();
|
---|
744 | var testRows = ProblemData.TestIndices.ToArray();
|
---|
745 | var testPrediction = Integrate(
|
---|
746 | trees, // we assume trees contain expressions for the change of each target variable over time y'(t)
|
---|
747 | problemData.Dataset,
|
---|
748 | problemData.AllowedInputVariables.ToArray(),
|
---|
749 | targetVars,
|
---|
750 | latentVariables,
|
---|
751 | new IntRange[] { ProblemData.TestPartition },
|
---|
752 | nodeIdx,
|
---|
753 | optTheta,
|
---|
754 | NumericIntegrationSteps).ToArray();
|
---|
755 |
|
---|
756 | for (int colIdx = 0; colIdx < targetVars.Length; colIdx++) {
|
---|
757 | var targetVar = targetVars[colIdx];
|
---|
758 | var testDataTable = new DataTable(targetVar + " prediction (test)");
|
---|
759 | var actualValuesRow = new DataRow(targetVar, "The values of " + targetVar, problemData.Dataset.GetDoubleValues(targetVar, testRows));
|
---|
760 | var predictedValuesRow = new DataRow(targetVar + " pred.", "Predicted values for " + targetVar, testPrediction.Select(arr => arr[colIdx].Item1).ToArray());
|
---|
761 | testDataTable.Rows.Add(actualValuesRow);
|
---|
762 | testDataTable.Rows.Add(predictedValuesRow);
|
---|
763 | testList.Add(testDataTable);
|
---|
764 | }
|
---|
765 |
|
---|
766 | results["Prediction (training)"].Value = trainingList.AsReadOnly();
|
---|
767 | results["Prediction (test)"].Value = testList.AsReadOnly();
|
---|
768 | #region simplification of models
|
---|
769 | // TODO the dependency of HeuristicLab.Problems.DataAnalysis.Symbolic is not ideal
|
---|
770 | var models = new VariableCollection(); // to store target var names and original version of tree
|
---|
771 |
|
---|
772 | foreach (var tup in targetVars.Zip(trees, Tuple.Create)) {
|
---|
773 | var targetVarName = tup.Item1;
|
---|
774 | var tree = tup.Item2;
|
---|
775 |
|
---|
776 | // when we reference HeuristicLab.Problems.DataAnalysis.Symbolic we can translate symbols
|
---|
777 | int nextParIdx = 0;
|
---|
778 | var shownTree = new SymbolicExpressionTree(TranslateTreeNode(tree.Root, optTheta, ref nextParIdx));
|
---|
779 |
|
---|
780 | // var shownTree = (SymbolicExpressionTree)tree.Clone();
|
---|
781 | // var constantsNodeOrig = tree.IterateNodesPrefix().Where(IsConstantNode);
|
---|
782 | // var constantsNodeShown = shownTree.IterateNodesPrefix().Where(IsConstantNode);
|
---|
783 | //
|
---|
784 | // foreach (var n in constantsNodeOrig.Zip(constantsNodeShown, (original, shown) => new { original, shown })) {
|
---|
785 | // double constantsVal = optTheta[nodeIdx[n.original]];
|
---|
786 | //
|
---|
787 | // ConstantTreeNode replacementNode = new ConstantTreeNode(new Constant()) { Value = constantsVal };
|
---|
788 | //
|
---|
789 | // var parentNode = n.shown.Parent;
|
---|
790 | // int replacementIndex = parentNode.IndexOfSubtree(n.shown);
|
---|
791 | // parentNode.RemoveSubtree(replacementIndex);
|
---|
792 | // parentNode.InsertSubtree(replacementIndex, replacementNode);
|
---|
793 | // }
|
---|
794 |
|
---|
795 | var origTreeVar = new HeuristicLab.Core.Variable(targetVarName + "(original)");
|
---|
796 | origTreeVar.Value = (ISymbolicExpressionTree)tree.Clone();
|
---|
797 | models.Add(origTreeVar);
|
---|
798 | var simplifiedTreeVar = new HeuristicLab.Core.Variable(targetVarName + "(simplified)");
|
---|
799 | simplifiedTreeVar.Value = TreeSimplifier.Simplify(shownTree);
|
---|
800 | models.Add(simplifiedTreeVar);
|
---|
801 |
|
---|
802 | }
|
---|
803 | results["Models"].Value = models;
|
---|
804 | #endregion
|
---|
805 | }
|
---|
806 | }
|
---|
807 |
|
---|
808 | private ISymbolicExpressionTreeNode TranslateTreeNode(ISymbolicExpressionTreeNode n, double[] parameterValues, ref int nextParIdx) {
|
---|
809 | ISymbolicExpressionTreeNode translatedNode = null;
|
---|
810 | if (n.Symbol is StartSymbol) {
|
---|
811 | translatedNode = new StartSymbol().CreateTreeNode();
|
---|
812 | } else if (n.Symbol is ProgramRootSymbol) {
|
---|
813 | translatedNode = new ProgramRootSymbol().CreateTreeNode();
|
---|
814 | } else if (n.Symbol.Name == "+") {
|
---|
815 | translatedNode = new Addition().CreateTreeNode();
|
---|
816 | } else if (n.Symbol.Name == "-") {
|
---|
817 | translatedNode = new Subtraction().CreateTreeNode();
|
---|
818 | } else if (n.Symbol.Name == "*") {
|
---|
819 | translatedNode = new Multiplication().CreateTreeNode();
|
---|
820 | } else if (n.Symbol.Name == "%") {
|
---|
821 | translatedNode = new Division().CreateTreeNode();
|
---|
822 | } else if (n.Symbol.Name == "sin") {
|
---|
823 | translatedNode = new Sine().CreateTreeNode();
|
---|
824 | } else if (n.Symbol.Name == "cos") {
|
---|
825 | translatedNode = new Cosine().CreateTreeNode();
|
---|
826 | } else if (IsConstantNode(n)) {
|
---|
827 | var constNode = (ConstantTreeNode)new Constant().CreateTreeNode();
|
---|
828 | constNode.Value = parameterValues[nextParIdx];
|
---|
829 | nextParIdx++;
|
---|
830 | translatedNode = constNode;
|
---|
831 | } else {
|
---|
832 | // assume a variable name
|
---|
833 | var varName = n.Symbol.Name;
|
---|
834 | var varNode = (VariableTreeNode)new Variable().CreateTreeNode();
|
---|
835 | varNode.Weight = 1.0;
|
---|
836 | varNode.VariableName = varName;
|
---|
837 | translatedNode = varNode;
|
---|
838 | }
|
---|
839 | foreach (var child in n.Subtrees) {
|
---|
840 | translatedNode.AddSubtree(TranslateTreeNode(child, parameterValues, ref nextParIdx));
|
---|
841 | }
|
---|
842 | return translatedNode;
|
---|
843 | }
|
---|
844 |
|
---|
845 | #region interpretation
|
---|
846 |
|
---|
847 | // the following uses auto-diff to calculate the gradient w.r.t. the parameters forward in time.
|
---|
848 | // 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.
|
---|
849 |
|
---|
850 | // a comparison of three potential calculation methods for the gradient is given in:
|
---|
851 | // 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
|
---|
852 | // "Our comparison establishes that the adjoint method is computationally more efficient for numerical estimation of parametric gradients
|
---|
853 | // for state-space models — both linear and non-linear, as in the case of a dynamical causal model (DCM)"
|
---|
854 |
|
---|
855 | // for a solver with the necessary features see: https://computation.llnl.gov/projects/sundials/cvodes
|
---|
856 | /*
|
---|
857 | * SUNDIALS: SUite of Nonlinear and DIfferential/ALgebraic Equation Solvers
|
---|
858 | * CVODES
|
---|
859 | * CVODES is a solver for stiff and nonstiff ODE systems (initial value problem) given in explicit
|
---|
860 | * form y’ = f(t,y,p) with sensitivity analysis capabilities (both forward and adjoint modes). CVODES
|
---|
861 | * is a superset of CVODE and hence all options available to CVODE (with the exception of the FCVODE
|
---|
862 | * interface module) are also available for CVODES. Both integration methods (Adams-Moulton and BDF)
|
---|
863 | * and the corresponding nonlinear iteration methods, as well as all linear solver and preconditioner
|
---|
864 | * modules, are available for the integration of the original ODEs, the sensitivity systems, or the
|
---|
865 | * adjoint system. Depending on the number of model parameters and the number of functional outputs,
|
---|
866 | * one of two sensitivity methods is more appropriate. The forward sensitivity analysis (FSA) method
|
---|
867 | * is mostly suitable when the gradients of many outputs (for example the entire solution vector) with
|
---|
868 | * respect to relatively few parameters are needed. In this approach, the model is differentiated with
|
---|
869 | * respect to each parameter in turn to yield an additional system of the same size as the original
|
---|
870 | * one, the result of which is the solution sensitivity. The gradient of any output function depending
|
---|
871 | * on the solution can then be directly obtained from these sensitivities by applying the chain rule
|
---|
872 | * of differentiation. The adjoint sensitivity analysis (ASA) method is more practical than the
|
---|
873 | * forward approach when the number of parameters is large and the gradients of only few output
|
---|
874 | * functionals are needed. In this approach, the solution sensitivities need not be computed
|
---|
875 | * explicitly. Instead, for each output functional of interest, an additional system, adjoint to the
|
---|
876 | * original one, is formed and solved. The solution of the adjoint system can then be used to evaluate
|
---|
877 | * the gradient of the output functional with respect to any set of model parameters. The FSA module
|
---|
878 | * in CVODES implements a simultaneous corrector method as well as two flavors of staggered corrector
|
---|
879 | * methods–for the case when sensitivity right hand sides are generated all at once or separated for
|
---|
880 | * each model parameter. The ASA module provides the infrastructure required for the backward
|
---|
881 | * integration in time of systems of differential equations dependent on the solution of the original
|
---|
882 | * ODEs. It employs a checkpointing scheme for efficient interpolation of forward solutions during the
|
---|
883 | * backward integration.
|
---|
884 | */
|
---|
885 | private static IEnumerable<Tuple<double, Vector>[]> Integrate(
|
---|
886 | ISymbolicExpressionTree[] trees, IDataset dataset, string[] inputVariables, string[] targetVariables, string[] latentVariables, IEnumerable<IntRange> episodes,
|
---|
887 | Dictionary<ISymbolicExpressionTreeNode, int> nodeIdx, double[] parameterValues, int numericIntegrationSteps = 100) {
|
---|
888 |
|
---|
889 | int NUM_STEPS = numericIntegrationSteps;
|
---|
890 | double h = 1.0 / NUM_STEPS;
|
---|
891 |
|
---|
892 | foreach (var episode in episodes) {
|
---|
893 | var rows = Enumerable.Range(episode.Start, episode.End - episode.Start);
|
---|
894 | // return first value as stored in the dataset
|
---|
895 | yield return targetVariables
|
---|
896 | .Select(targetVar => Tuple.Create(dataset.GetDoubleValue(targetVar, rows.First()), Vector.Zero))
|
---|
897 | .ToArray();
|
---|
898 |
|
---|
899 | // integrate forward starting with known values for the target in t0
|
---|
900 |
|
---|
901 | var variableValues = new Dictionary<string, Tuple<double, Vector>>();
|
---|
902 | var t0 = rows.First();
|
---|
903 | foreach (var varName in inputVariables) {
|
---|
904 | variableValues.Add(varName, Tuple.Create(dataset.GetDoubleValue(varName, t0), Vector.Zero));
|
---|
905 | }
|
---|
906 | foreach (var varName in targetVariables) {
|
---|
907 | variableValues.Add(varName, Tuple.Create(dataset.GetDoubleValue(varName, t0), Vector.Zero));
|
---|
908 | }
|
---|
909 | // add value entries for latent variables which are also integrated
|
---|
910 | foreach (var latentVar in latentVariables) {
|
---|
911 | variableValues.Add(latentVar, Tuple.Create(0.0, Vector.Zero)); // we don't have observations for latent variables -> assume zero as starting value
|
---|
912 | }
|
---|
913 | var calculatedVariables = targetVariables.Concat(latentVariables); // TODO: must conincide with the order of trees in the encoding
|
---|
914 |
|
---|
915 | foreach (var t in rows.Skip(1)) {
|
---|
916 | for (int step = 0; step < NUM_STEPS; step++) {
|
---|
917 | var deltaValues = new Dictionary<string, Tuple<double, Vector>>();
|
---|
918 | foreach (var tup in trees.Zip(calculatedVariables, Tuple.Create)) {
|
---|
919 | var tree = tup.Item1;
|
---|
920 | var targetVarName = tup.Item2;
|
---|
921 | // skip programRoot and startSymbol
|
---|
922 | var res = InterpretRec(tree.Root.GetSubtree(0).GetSubtree(0), variableValues, nodeIdx, parameterValues);
|
---|
923 | deltaValues.Add(targetVarName, res);
|
---|
924 | }
|
---|
925 |
|
---|
926 | // update variableValues for next step
|
---|
927 | foreach (var kvp in deltaValues) {
|
---|
928 | var oldVal = variableValues[kvp.Key];
|
---|
929 | variableValues[kvp.Key] = Tuple.Create(
|
---|
930 | oldVal.Item1 + h * kvp.Value.Item1,
|
---|
931 | oldVal.Item2 + h * kvp.Value.Item2
|
---|
932 | );
|
---|
933 | }
|
---|
934 | }
|
---|
935 |
|
---|
936 | // only return the target variables for calculation of errors
|
---|
937 | yield return targetVariables
|
---|
938 | .Select(targetVar => variableValues[targetVar])
|
---|
939 | .ToArray();
|
---|
940 |
|
---|
941 | // update for next time step
|
---|
942 | foreach (var varName in inputVariables) {
|
---|
943 | variableValues[varName] = Tuple.Create(dataset.GetDoubleValue(varName, t), Vector.Zero);
|
---|
944 | }
|
---|
945 | }
|
---|
946 | }
|
---|
947 | }
|
---|
948 |
|
---|
949 | private static Tuple<double, Vector> InterpretRec(
|
---|
950 | ISymbolicExpressionTreeNode node,
|
---|
951 | Dictionary<string, Tuple<double, Vector>> variableValues,
|
---|
952 | Dictionary<ISymbolicExpressionTreeNode, int> nodeIdx,
|
---|
953 | double[] parameterValues
|
---|
954 | ) {
|
---|
955 |
|
---|
956 | switch (node.Symbol.Name) {
|
---|
957 | case "+": {
|
---|
958 | var l = InterpretRec(node.GetSubtree(0), variableValues, nodeIdx, parameterValues); // TODO capture all parameters into a state type for interpretation
|
---|
959 | var r = InterpretRec(node.GetSubtree(1), variableValues, nodeIdx, parameterValues);
|
---|
960 |
|
---|
961 | return Tuple.Create(l.Item1 + r.Item1, l.Item2 + r.Item2);
|
---|
962 | }
|
---|
963 | case "*": {
|
---|
964 | var l = InterpretRec(node.GetSubtree(0), variableValues, nodeIdx, parameterValues);
|
---|
965 | var r = InterpretRec(node.GetSubtree(1), variableValues, nodeIdx, parameterValues);
|
---|
966 |
|
---|
967 | return Tuple.Create(l.Item1 * r.Item1, l.Item2 * r.Item1 + l.Item1 * r.Item2);
|
---|
968 | }
|
---|
969 |
|
---|
970 | case "-": {
|
---|
971 | var l = InterpretRec(node.GetSubtree(0), variableValues, nodeIdx, parameterValues);
|
---|
972 | var r = InterpretRec(node.GetSubtree(1), variableValues, nodeIdx, parameterValues);
|
---|
973 |
|
---|
974 | return Tuple.Create(l.Item1 - r.Item1, l.Item2 - r.Item2);
|
---|
975 | }
|
---|
976 | case "%": {
|
---|
977 | var l = InterpretRec(node.GetSubtree(0), variableValues, nodeIdx, parameterValues);
|
---|
978 | var r = InterpretRec(node.GetSubtree(1), variableValues, nodeIdx, parameterValues);
|
---|
979 |
|
---|
980 | // protected division
|
---|
981 | if (r.Item1.IsAlmost(0.0)) {
|
---|
982 | return Tuple.Create(0.0, Vector.Zero);
|
---|
983 | } else {
|
---|
984 | return Tuple.Create(
|
---|
985 | l.Item1 / r.Item1,
|
---|
986 | 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'
|
---|
987 | );
|
---|
988 | }
|
---|
989 | }
|
---|
990 | case "sin": {
|
---|
991 | var x = InterpretRec(node.GetSubtree(0), variableValues, nodeIdx, parameterValues);
|
---|
992 | return Tuple.Create(
|
---|
993 | Math.Sin(x.Item1),
|
---|
994 | Vector.Cos(x.Item2) * x.Item2
|
---|
995 | );
|
---|
996 | }
|
---|
997 | case "cos": {
|
---|
998 | var x = InterpretRec(node.GetSubtree(0), variableValues, nodeIdx, parameterValues);
|
---|
999 | return Tuple.Create(
|
---|
1000 | Math.Cos(x.Item1),
|
---|
1001 | -Vector.Sin(x.Item2) * x.Item2
|
---|
1002 | );
|
---|
1003 | }
|
---|
1004 | default: {
|
---|
1005 | // distinguish other cases
|
---|
1006 | if (IsConstantNode(node)) {
|
---|
1007 | var vArr = new double[parameterValues.Length]; // backing array for vector
|
---|
1008 | vArr[nodeIdx[node]] = 1.0;
|
---|
1009 | var g = new Vector(vArr);
|
---|
1010 | return Tuple.Create(parameterValues[nodeIdx[node]], g);
|
---|
1011 | } else {
|
---|
1012 | // assume a variable name
|
---|
1013 | var varName = node.Symbol.Name;
|
---|
1014 | return variableValues[varName];
|
---|
1015 | }
|
---|
1016 | }
|
---|
1017 | }
|
---|
1018 | }
|
---|
1019 | #endregion
|
---|
1020 |
|
---|
1021 | #region events
|
---|
1022 | /*
|
---|
1023 | * Dependencies between parameters:
|
---|
1024 | *
|
---|
1025 | * ProblemData
|
---|
1026 | * |
|
---|
1027 | * V
|
---|
1028 | * TargetVariables FunctionSet MaximumLength NumberOfLatentVariables
|
---|
1029 | * | | | |
|
---|
1030 | * V V | |
|
---|
1031 | * Grammar <---------------+-------------------
|
---|
1032 | * |
|
---|
1033 | * V
|
---|
1034 | * Encoding
|
---|
1035 | */
|
---|
1036 | private void RegisterEventHandlers() {
|
---|
1037 | ProblemDataParameter.ValueChanged += ProblemDataParameter_ValueChanged;
|
---|
1038 | if (ProblemDataParameter.Value != null) ProblemDataParameter.Value.Changed += ProblemData_Changed;
|
---|
1039 |
|
---|
1040 | TargetVariablesParameter.ValueChanged += TargetVariablesParameter_ValueChanged;
|
---|
1041 | if (TargetVariablesParameter.Value != null) TargetVariablesParameter.Value.CheckedItemsChanged += CheckedTargetVariablesChanged;
|
---|
1042 |
|
---|
1043 | FunctionSetParameter.ValueChanged += FunctionSetParameter_ValueChanged;
|
---|
1044 | if (FunctionSetParameter.Value != null) FunctionSetParameter.Value.CheckedItemsChanged += CheckedFunctionsChanged;
|
---|
1045 |
|
---|
1046 | MaximumLengthParameter.Value.ValueChanged += MaximumLengthChanged;
|
---|
1047 |
|
---|
1048 | NumberOfLatentVariablesParameter.Value.ValueChanged += NumLatentVariablesChanged;
|
---|
1049 | }
|
---|
1050 |
|
---|
1051 | private void NumLatentVariablesChanged(object sender, EventArgs e) {
|
---|
1052 | UpdateGrammarAndEncoding();
|
---|
1053 | }
|
---|
1054 |
|
---|
1055 | private void MaximumLengthChanged(object sender, EventArgs e) {
|
---|
1056 | UpdateGrammarAndEncoding();
|
---|
1057 | }
|
---|
1058 |
|
---|
1059 | private void FunctionSetParameter_ValueChanged(object sender, EventArgs e) {
|
---|
1060 | FunctionSetParameter.Value.CheckedItemsChanged += CheckedFunctionsChanged;
|
---|
1061 | }
|
---|
1062 |
|
---|
1063 | private void CheckedFunctionsChanged(object sender, CollectionItemsChangedEventArgs<StringValue> e) {
|
---|
1064 | UpdateGrammarAndEncoding();
|
---|
1065 | }
|
---|
1066 |
|
---|
1067 | private void TargetVariablesParameter_ValueChanged(object sender, EventArgs e) {
|
---|
1068 | TargetVariablesParameter.Value.CheckedItemsChanged += CheckedTargetVariablesChanged;
|
---|
1069 | }
|
---|
1070 |
|
---|
1071 | private void CheckedTargetVariablesChanged(object sender, CollectionItemsChangedEventArgs<StringValue> e) {
|
---|
1072 | UpdateGrammarAndEncoding();
|
---|
1073 | }
|
---|
1074 |
|
---|
1075 | private void ProblemDataParameter_ValueChanged(object sender, EventArgs e) {
|
---|
1076 | ProblemDataParameter.Value.Changed += ProblemData_Changed;
|
---|
1077 | OnProblemDataChanged();
|
---|
1078 | OnReset();
|
---|
1079 | }
|
---|
1080 |
|
---|
1081 | private void ProblemData_Changed(object sender, EventArgs e) {
|
---|
1082 | OnProblemDataChanged();
|
---|
1083 | OnReset();
|
---|
1084 | }
|
---|
1085 |
|
---|
1086 | private void OnProblemDataChanged() {
|
---|
1087 | UpdateTargetVariables(); // implicitly updates other dependent parameters
|
---|
1088 | var handler = ProblemDataChanged;
|
---|
1089 | if (handler != null) handler(this, EventArgs.Empty);
|
---|
1090 | }
|
---|
1091 |
|
---|
1092 | #endregion
|
---|
1093 |
|
---|
1094 | #region helper
|
---|
1095 |
|
---|
1096 | private void InitAllParameters() {
|
---|
1097 | UpdateTargetVariables(); // implicitly updates the grammar and the encoding
|
---|
1098 | }
|
---|
1099 |
|
---|
1100 | private ReadOnlyCheckedItemCollection<StringValue> CreateFunctionSet() {
|
---|
1101 | var l = new CheckedItemCollection<StringValue>();
|
---|
1102 | l.Add(new StringValue("+").AsReadOnly());
|
---|
1103 | l.Add(new StringValue("*").AsReadOnly());
|
---|
1104 | l.Add(new StringValue("%").AsReadOnly());
|
---|
1105 | l.Add(new StringValue("-").AsReadOnly());
|
---|
1106 | l.Add(new StringValue("sin").AsReadOnly());
|
---|
1107 | l.Add(new StringValue("cos").AsReadOnly());
|
---|
1108 | return l.AsReadOnly();
|
---|
1109 | }
|
---|
1110 |
|
---|
1111 | private static bool IsConstantNode(ISymbolicExpressionTreeNode n) {
|
---|
1112 | return n.Symbol.Name.StartsWith("θ");
|
---|
1113 | }
|
---|
1114 | private static bool IsLatentVariableNode(ISymbolicExpressionTreeNode n) {
|
---|
1115 | return n.Symbol.Name.StartsWith("λ");
|
---|
1116 | }
|
---|
1117 |
|
---|
1118 |
|
---|
1119 | private void UpdateTargetVariables() {
|
---|
1120 | var currentlySelectedVariables = TargetVariables.CheckedItems.Select(i => i.Value).ToArray();
|
---|
1121 |
|
---|
1122 | var newVariablesList = new CheckedItemCollection<StringValue>(ProblemData.Dataset.VariableNames.Select(str => new StringValue(str).AsReadOnly()).ToArray()).AsReadOnly();
|
---|
1123 | var matchingItems = newVariablesList.Where(item => currentlySelectedVariables.Contains(item.Value)).ToArray();
|
---|
1124 | foreach (var matchingItem in matchingItems) {
|
---|
1125 | newVariablesList.SetItemCheckedState(matchingItem, true);
|
---|
1126 | }
|
---|
1127 | TargetVariablesParameter.Value = newVariablesList;
|
---|
1128 | }
|
---|
1129 |
|
---|
1130 | private void UpdateGrammarAndEncoding() {
|
---|
1131 | var encoding = new MultiEncoding();
|
---|
1132 | var g = CreateGrammar();
|
---|
1133 | foreach (var targetVar in TargetVariables.CheckedItems) {
|
---|
1134 | encoding = encoding.Add(new SymbolicExpressionTreeEncoding(targetVar + "_tree", g, MaximumLength, MaximumLength)); // only limit by length
|
---|
1135 | }
|
---|
1136 | for (int i = 1; i <= NumberOfLatentVariables; i++) {
|
---|
1137 | encoding = encoding.Add(new SymbolicExpressionTreeEncoding("λ" + i + "_tree", g, MaximumLength, MaximumLength));
|
---|
1138 | }
|
---|
1139 | Encoding = encoding;
|
---|
1140 | }
|
---|
1141 |
|
---|
1142 | private ISymbolicExpressionGrammar CreateGrammar() {
|
---|
1143 | // whenever ProblemData is changed we create a new grammar with the necessary symbols
|
---|
1144 | var g = new SimpleSymbolicExpressionGrammar();
|
---|
1145 | g.AddSymbols(FunctionSet.CheckedItems.Select(i => i.Value).ToArray(), 2, 2);
|
---|
1146 |
|
---|
1147 | // TODO
|
---|
1148 | //g.AddSymbols(new[] {
|
---|
1149 | // "exp",
|
---|
1150 | // "log", // log( <expr> ) // TODO: init a theta to ensure the value is always positive
|
---|
1151 | // "exp_minus" // exp((-1) * <expr>
|
---|
1152 | //}, 1, 1);
|
---|
1153 |
|
---|
1154 | foreach (var variableName in ProblemData.AllowedInputVariables.Union(TargetVariables.CheckedItems.Select(i => i.Value)))
|
---|
1155 | g.AddTerminalSymbol(variableName);
|
---|
1156 |
|
---|
1157 | // generate symbols for numeric parameters for which the value is optimized using AutoDiff
|
---|
1158 | // we generate multiple symbols to balance the probability for selecting a numeric parameter in the generation of random trees
|
---|
1159 | var numericConstantsFactor = 2.0;
|
---|
1160 | for (int i = 0; i < numericConstantsFactor * (ProblemData.AllowedInputVariables.Count() + TargetVariables.CheckedItems.Count()); i++) {
|
---|
1161 | g.AddTerminalSymbol("θ" + i); // numeric parameter for which the value is optimized using AutoDiff
|
---|
1162 | }
|
---|
1163 |
|
---|
1164 | // generate symbols for latent variables
|
---|
1165 | for (int i = 1; i <= NumberOfLatentVariables; i++) {
|
---|
1166 | g.AddTerminalSymbol("λ" + i); // numeric parameter for which the value is optimized using AutoDiff
|
---|
1167 | }
|
---|
1168 |
|
---|
1169 | return g;
|
---|
1170 | }
|
---|
1171 |
|
---|
1172 | #endregion
|
---|
1173 |
|
---|
1174 | #region Import & Export
|
---|
1175 | public void Load(IRegressionProblemData data) {
|
---|
1176 | Name = data.Name;
|
---|
1177 | Description = data.Description;
|
---|
1178 | ProblemData = data;
|
---|
1179 | }
|
---|
1180 |
|
---|
1181 | public IRegressionProblemData Export() {
|
---|
1182 | return ProblemData;
|
---|
1183 | }
|
---|
1184 | #endregion
|
---|
1185 |
|
---|
1186 | }
|
---|
1187 | }
|
---|