1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) 2002-2016 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.Concurrent;
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24 | using System.Collections.Generic;
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25 | using System.Linq;
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26 | using System.Threading;
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27 | using System.Threading.Tasks;
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28 | using HeuristicLab.Common;
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29 | using HeuristicLab.Core;
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30 | using HeuristicLab.Data;
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31 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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32 | using HeuristicLab.Optimization;
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33 | using HeuristicLab.Parameters;
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34 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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35 | using HeuristicLab.Problems.DataAnalysis;
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36 | using HeuristicLab.Problems.DataAnalysis.Symbolic;
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37 | using HeuristicLab.Problems.DataAnalysis.Symbolic.Regression;
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38 | using HeuristicLab.Random;
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39 | using MathNet.Numerics.Interpolation;
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40 | using MathNet.Numerics.LinearAlgebra.Double;
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41 | using MathNet.Numerics.LinearAlgebra.Double.Solvers;
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42 |
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43 | namespace HeuristicLab.Algorithms.DataAnalysis.Experimental {
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44 | [Item("Splines", "")]
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45 | [Creatable(CreatableAttribute.Categories.DataAnalysisRegression, Priority = 102)]
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46 | [StorableClass]
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47 | public sealed class Splines : FixedDataAnalysisAlgorithm<IRegressionProblem> {
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48 | [StorableConstructor]
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49 | private Splines(bool deserializing) : base(deserializing) { }
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50 | [StorableHook(HookType.AfterDeserialization)]
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51 | private void AfterDeserialization() {
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52 | }
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53 |
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54 | private Splines(Splines original, Cloner cloner)
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55 | : base(original, cloner) {
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56 | }
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57 | public override IDeepCloneable Clone(Cloner cloner) {
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58 | return new Splines(this, cloner);
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59 | }
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60 |
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61 | public Splines()
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62 | : base() {
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63 | var validTypes = new ItemSet<StringValue>(
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64 | new[] {
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65 | "Monotone", "Akima", "Catmull-Rom", "Cubic", "Linear",
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66 | "Cubic - Natural (Math.NET)",
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67 | "Polynomial (Math.NET)",
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68 | "Rational (Math.NET)",
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69 | "LogLinear (Math.NET)",
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70 | "Common (Math.NET)",
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71 | "Smoothing Spline (Mine)",
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72 | "Smoothing Spline (Reinsch)",
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73 | "Smoothing Spline (Reinsch with automatic tolerance determination using CV)",
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74 | "B-Spline Smoothing"
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75 | }.Select(s => new StringValue(s)));
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76 |
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77 | Parameters.Add(new ConstrainedValueParameter<StringValue>("Type", "The type of spline (as supported by alglib)", validTypes, validTypes.First()));
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78 | Parameters.Add(new ValueParameter<DoubleValue>("Lambda", "Regularization parameter for smoothing splines (0..+inf)", new DoubleValue(100)));
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79 | Parameters.Add(new ValueParameter<DoubleValue>("StdDev (noise)", "Known error in y values. Used only be Reinsch Smoothing Splines", new DoubleValue(0.1)));
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80 | Problem = new RegressionProblem();
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81 | }
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82 |
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83 |
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84 | protected override void Run(CancellationToken cancellationToken) {
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85 | double[,] inputMatrix = Problem.ProblemData.Dataset.ToArray(Problem.ProblemData.AllowedInputVariables.Concat(new string[] { Problem.ProblemData.TargetVariable }), Problem.ProblemData.TrainingIndices);
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86 | if (inputMatrix.Cast<double>().Any(x => double.IsNaN(x) || double.IsInfinity(x)))
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87 | throw new NotSupportedException("Splines does not support NaN or infinity values in the input dataset.");
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88 |
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89 | var inputVars = Problem.ProblemData.AllowedInputVariables.ToArray();
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90 | if (inputVars.Length > 3) throw new ArgumentException();
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91 |
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92 | var y = Problem.ProblemData.TargetVariableTrainingValues.ToArray();
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93 | if (inputVars.Length == 1) {
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94 |
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95 | var x = Problem.ProblemData.Dataset.GetDoubleValues(inputVars.First(), Problem.ProblemData.TrainingIndices).ToArray();
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96 | alglib.spline1dinterpolant c;
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97 | var type = ((StringValue)Parameters["Type"].ActualValue).Value;
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98 | switch (type) {
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99 | case "Monotone":
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100 | alglib.spline1dbuildmonotone(x, y, out c);
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101 | AddAlglibSplineResult(c, inputVars);
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102 | break;
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103 | case "Akima":
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104 | alglib.spline1dbuildakima(x, y, out c); AddAlglibSplineResult(c, inputVars);
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105 | break;
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106 | ;
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107 | case "Catmull-Rom":
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108 | alglib.spline1dbuildcatmullrom(x, y, out c); AddAlglibSplineResult(c, inputVars);
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109 | break;
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110 |
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111 | case "Cubic":
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112 | alglib.spline1dbuildcubic(x, y, out c); AddAlglibSplineResult(c, inputVars);
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113 | break;
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114 |
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115 | case "Linear":
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116 | alglib.spline1dbuildlinear(x, y, out c); AddAlglibSplineResult(c, inputVars);
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117 | break;
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118 | case "Cubic - Natural (Math.NET)": {
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119 | var spline = MathNet.Numerics.Interpolation.CubicSpline.InterpolateNatural(x, y);
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120 | AddMathNetSplineResult(spline, inputVars);
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121 | break;
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122 | }
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123 | case "Common (Math.NET)": {
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124 | var spline = MathNet.Numerics.Interpolate.Common(x, y);
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125 | AddMathNetSplineResult(spline, inputVars);
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126 | break;
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127 | }
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128 | case "LogLinear (Math.NET)": {
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129 | var spline = MathNet.Numerics.Interpolate.LogLinear(x, y);
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130 | AddMathNetSplineResult(spline, inputVars);
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131 | break;
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132 | }
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133 | case "Polynomial (Math.NET)": {
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134 | var spline = MathNet.Numerics.Interpolate.Polynomial(x, y);
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135 | AddMathNetSplineResult(spline, inputVars);
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136 | break;
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137 | }
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138 | case "Rational (Math.NET)": {
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139 | var spline = MathNet.Numerics.Interpolate.RationalWithoutPoles(x, y);
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140 | AddMathNetSplineResult(spline, inputVars);
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141 | break;
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142 | }
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143 | case "Smoothing Spline (Mine)": {
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144 | CalculateSmoothingSpline(x, y, inputVars);
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145 | break;
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146 | }
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147 | case "Smoothing Spline (Reinsch)": {
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148 | CalculateSmoothingSplineReinsch(x, y, inputVars);
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149 | break;
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150 | }
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151 | case "Smoothing Spline (Reinsch with automatic tolerance determination using CV)": {
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152 | var model = CalculateSmoothingSplineReinschWithAutomaticTolerance(x, y, inputVars, Problem.ProblemData.TargetVariable);
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153 | Results.Add(new Result("Solution", new RegressionSolution(model, (IRegressionProblemData)Problem.ProblemData.Clone())));
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154 | break;
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155 | }
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156 | case "B-Spline Smoothing": {
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157 | BSplineSmoothing(x, y, inputVars);
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158 | break;
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159 | }
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160 | default: throw new NotSupportedException();
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161 | }
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162 |
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163 | }
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164 | }
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165 |
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166 | public void BSplineSmoothing(double[] x, double[] y, string[] inputVars) {
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167 | Array.Sort(x, y);
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168 |
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169 | CubicSpline2(x, y, inputVars);
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170 |
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171 | // // see Elements of Statistical Learning Appendix: Computations for Splines
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172 | // int M = 4; // order of spline (cubic)
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173 | // int K = x.Length;
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174 | // int n = x.Length;
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175 | //
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176 | // double[] t = new double[K + 2 * M];
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177 | // for (int i = 0; i < M; i++) t[i] = x[0];
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178 | // for (int i = K; i < K + 2 * M; i++) t[i] = x[K - 1];
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179 | //
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180 | // double[,] B = new double[n, n + 4]; // basis function matrix
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181 | // double[,] W = new double[n + 4, n + 4]; // penalty matrix (W[j,k] =
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182 | // for (int i = 0; i < M; i++) B[i] = new double[K + 2 * M];
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183 | // for (int j = 0; j < K; j++) {
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184 | // for (int i = 0; i < K + 2M - 1; i++) {
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185 | // if (t[i] <= x[j] && x[j] < t[i + 1])
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186 | // B[1][i] = 1.0;
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187 | // }
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188 | // }
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189 |
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190 |
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191 | }
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192 |
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193 | private struct SplineData {
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194 | public double a, b, c, d, x, y;
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195 | };
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196 |
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197 |
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198 | /*
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199 | * The procedure Quincunx, takes as arguments
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200 | the vectors u, v and w which are respectively the diagonal, the first supradiagonal
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201 | and the second supradiagonal of the banded matrix. The vector on
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202 | the LHS of the equation (80) is placed in q which contains the solution on the
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203 | completion of the procedure.
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204 | */
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205 | private void Quincunx(int n, MyArray<double> u, MyArray<double> v, MyArray<double> w, MyArray<double> q) {
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206 | // { factorisation}
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207 | u[-1] = 0;
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208 | u[0] = 0;
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209 | for (int j = 1; j <= n - 1; j++) {
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210 | u[j] = u[j] - u[j - 2] * Math.Pow(w[j - 2], 2) - u[j - 1] * Math.Pow(v[j - 1], 2);
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211 | v[j] = (v[j] - u[j - 1] * v[j - 1] * w[j - 1]) / u[j];
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212 | w[j] = w[j] / u[j];
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213 | }
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214 | // { forward substitution}
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215 | for (int j = 1; j <= n - 1; j++) {
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216 | q[j] = q[j] - v[j - 1] * q[j - 1] - w[j - 2] * q[j - 2];
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217 | }
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218 | for (int j = 1; j < n - 1; j++) {
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219 | q[j] = q[j] / u[j];
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220 | }
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221 | // { back substitution}
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222 | q[n + 1] = 0;
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223 | q[n] = 0;
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224 | for (int j = n - 1; j >= 1; j--) {
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225 | q[j] = q[j] - v[j] * q[j + 1] - w[j] * q[j + 2];
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226 | }
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227 | }
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228 |
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229 | public void CubicSpline2(double[] x, double[] y, string[] inputVars) {
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230 | // see Pollock: Smoothing Splines
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231 | int n = x.Length;
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232 | double lambda = 1.0;
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233 | double[] sigma = Enumerable.Repeat(1.0, n).ToArray();
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234 | SplineData[] S = new SplineData[x.Length + 1];
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235 | for (int i = 0; i < x.Length; i++) {
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236 | S[i].x = x[i];
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237 | S[i].y = y[i];
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238 | }
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239 | S[x.Length].x = S[x.Length - 1].x;
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240 | S[x.Length].y = S[x.Length - 1].y;
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241 |
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242 | // var
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243 | double[] h = new double[n],
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244 | r = new double[n],
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245 | f = new double[n],
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246 | p = new double[n];
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247 | var q = new MyArray<double>(-1, n + 3);
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248 | var u = new MyArray<double>(-1, n + 3);
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249 | var v = new MyArray<double>(-1, n + 3);
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250 | var w = new MyArray<double>(-1, n + 3);
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251 | double mu;
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252 |
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253 | mu = 2 * (1 - lambda) / (3 * lambda);
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254 | h[0] = S[1].x - S[0].x;
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255 | r[0] = 3 / h[0];
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256 | for (int i = 1; i < n - 1; i++) {
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257 | h[i] = S[i + 1].x - S[i].x;
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258 | r[i] = 3 / h[i];
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259 | f[i] = -(r[i - 1] + r[i]);
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260 | p[i] = 2 * (S[i + 1].x - S[i - 1].x);
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261 | q[i] = 3 * (S[i + 1].y - S[i].y) / h[i] - 3 * (S[i].y - S[i - 1].y) / h[i - 1];
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262 | }
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263 | for (int i = 1; i < n; i++) {
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264 | u[i] = Math.Pow(r[i - 1], 2) * sigma[i - 1] + Math.Pow(f[i], 2) * sigma[i] + Math.Pow(r[i], 2) * sigma[i + 1]; // TODO Sigma 1..n
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265 | u[i] = mu * u[i] + p[i];
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266 | v[i] = f[i] * r[i] * sigma[i] + r[i] * f[i + 1] * sigma[i + 1];
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267 | v[i] = mu * v[i] + h[i];
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268 | w[i] = mu * r[i] * r[i + 1] * sigma[i + 1];
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269 | }
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270 | Quincunx(n, u, v, w, q);
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271 | // { Spline P arameters}
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272 | S[0].d = S[0].y - mu * r[0] * q[1] * sigma[0];
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273 | S[1].d = S[1].y - mu * (f[1] * q[1] + r[1] * q[2]) * sigma[0];
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274 | S[0].a = q[1] / (3 * h[0]);
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275 | S[0].b = 0;
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276 | S[0].c = (S[1].d - S[0].d) / h[0] - q[1] * h[0] / 3;
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277 | r[0] = 0;
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278 | for (int j = 1; j < n; j++) {
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279 | S[j].a = (q[j + 1] - q[j]) / (3 * h[j]);
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280 | S[j].b = q[j];
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281 | S[j].c = (q[j] + q[j - 1]) * h[j - 1] + S[j - 1].c;
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282 | S[j].d = r[j - 1] * q[j - 1] + f[j] * q[j] + r[j] * q[j + 1];
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283 | S[j].d = y[j] - mu * S[j].d * sigma[j];
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284 | }
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285 |
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286 | // { SmoothingSpline}
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287 | }
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288 |
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289 | public void CalculateSmoothingSplineReinsch(double[] xOrig, double[] yOrig, string[] inputVars) {
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290 | double s = xOrig.Length + 1;
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291 | double stdTol = ((IValueParameter<DoubleValue>)Parameters["StdDev (noise)"]).Value.Value; // controls extent of smoothing
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292 |
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293 | var model = CalculateSmoothingSplineReinsch(xOrig, yOrig, inputVars, stdTol, s, Problem.ProblemData.TargetVariable);
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294 |
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295 | Results.Add(new Result("Solution", new RegressionSolution(model, (IRegressionProblemData)Problem.ProblemData.Clone())));
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296 |
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297 |
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298 | }
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299 |
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300 |
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301 |
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302 | public static IRegressionModel CalculateSmoothingSplineReinschWithAutomaticTolerance(double[] xOrig, double[] yOrig, string[] inputVars, string targetVar) {
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303 | int n = xOrig.Length;
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304 | var rows = Enumerable.Range(0, n);
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305 | var rand = new FastRandom(1234);
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306 | var trainRows = rows.Shuffle(rand).Take((int)(n * 0.66)).ToArray();
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307 | var testRows = rows.Except(trainRows).ToArray();
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308 |
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309 | var trainX = trainRows.Select(i => xOrig[i]).ToArray();
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310 | var trainY = trainRows.Select(i => yOrig[i]).ToArray();
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311 | var testX = testRows.Select(i => xOrig[i]).ToArray();
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312 | var testY = testRows.Select(i => yOrig[i]).ToArray();
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313 |
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314 | var shuffledDs = new Dataset(inputVars.Concat(new string[] { targetVar }), new[] { trainX.Concat(testX).ToArray(), trainY.Concat(testY).ToArray() });
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315 | var shuffeledProblemData = new RegressionProblemData(shuffledDs, inputVars, targetVar);
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316 | shuffeledProblemData.TrainingPartition.Start = 0;
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317 | shuffeledProblemData.TrainingPartition.End = trainX.Length;
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318 | shuffeledProblemData.TestPartition.Start = trainX.Length;
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319 | shuffeledProblemData.TestPartition.End = shuffledDs.Rows + 1;
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320 |
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321 | double curTol = trainY.StandardDeviation();
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322 | double prevTestRMSE = double.PositiveInfinity;
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323 | double testRMSE = double.PositiveInfinity;
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324 | IRegressionModel prevModel = null;
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325 | IRegressionModel model = null;
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326 | do {
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327 | prevModel = model;
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328 | prevTestRMSE = testRMSE;
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329 | model = CalculateSmoothingSplineReinsch(trainX, trainY, inputVars, curTol, s: trainX.Length + 1, targetVar: targetVar);
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330 |
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331 | var sol = model.CreateRegressionSolution(shuffeledProblemData);
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332 | var trainRMSE = sol.TrainingRootMeanSquaredError;
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333 | testRMSE = sol.TestRootMeanSquaredError;
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334 | curTol = Math.Max(curTol * 0.5, 1e-12 * trainY.StandardDeviation());
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335 | } while (testRMSE < prevTestRMSE);
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336 | return prevModel;
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337 | }
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338 |
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339 |
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340 | public static IRegressionModel CalculateSmoothingSplineReinsch(double[] xOrig, double[] yOrig, string[] inputVars, double stdTol, double s, string targetVar) {
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341 | var minX = xOrig.Min();
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342 | var maxX = xOrig.Max();
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343 | var range = maxX - minX;
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344 |
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345 | double[] w = Enumerable.Repeat(stdTol, xOrig.Length).ToArray();
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346 | SortAndBin((double[])xOrig.Clone(), (double[])yOrig.Clone(), w, out xOrig, out yOrig, out w, scaling: false);
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347 |
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348 | // See Smoothing by Spline Functions, Reinsch, 1967
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349 | // move x and y into an array indexed with 1..n to match indexing in Reinsch paper
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350 | int n = xOrig.Length;
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351 | var x = new MyArray<double>(1, xOrig);
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352 | var y = new MyArray<double>(1, yOrig);
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353 | var inv_dy = new MyArray<double>(1, w);
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354 |
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355 | int n1 = 1;
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356 | int n2 = n;
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357 |
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358 | // results
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359 | var a = new MyArray<double>(n1, n);
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360 | var b = new MyArray<double>(n1, n);
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361 | var c = new MyArray<double>(n1, n);
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362 | var d = new MyArray<double>(n1, n);
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363 |
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364 | // smooth
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365 | {
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366 | int i, m1, m2; double e, f, f2, g = 0.0, h, p;
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367 | MyArray<double>
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368 | r = new MyArray<double>(n1 - 1, n + 2),
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369 | r1 = new MyArray<double>(n1 - 1, n + 2),
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370 | r2 = new MyArray<double>(n1 - 1, n + 2),
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371 | t = new MyArray<double>(n1 - 1, n + 2),
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372 | t1 = new MyArray<double>(n1 - 1, n + 2),
|
---|
373 | u = new MyArray<double>(n1 - 1, n + 2),
|
---|
374 | v = new MyArray<double>(n1 - 1, n + 2);
|
---|
375 | m1 = n1 - 1;
|
---|
376 | m2 = n2 + 1;
|
---|
377 | r[m1] = r[n1] = r1[n2] = r2[n2] = r2[m2] =
|
---|
378 | u[m1] = u[n1] = u[n2] = u[m2] = p = 0.0;
|
---|
379 | m1 = n1 + 1;
|
---|
380 | m2 = n2 - 1;
|
---|
381 | h = x[m1] - x[n1]; f = (y[m1] - y[n1]) / h;
|
---|
382 | for (i = m1; i <= m2; i++) {
|
---|
383 | g = h; h = x[i + 1] - x[i];
|
---|
384 | e = f; f = (y[i + 1] - y[i]) / h;
|
---|
385 | a[i] = f - e; t[i] = 2 * (g + h) / 3; t1[i] = h / 3;
|
---|
386 | r2[i] = inv_dy[i - 1] / g; r[i] = inv_dy[i + 1] / h;
|
---|
387 | r1[i] = -inv_dy[i] / g - inv_dy[i] / h;
|
---|
388 | }
|
---|
389 | for (i = m1; i <= m2; i++) {
|
---|
390 | b[i] = r[i] * r[i] + r1[i] * r1[i] + r2[i] * r2[i];
|
---|
391 | c[i] = r[i] * r1[i + 1] + r1[i] * r2[i + 1];
|
---|
392 | d[i] = r[i] * r2[i + 2];
|
---|
393 | }
|
---|
394 | f2 = -s;
|
---|
395 | next:
|
---|
396 | for (i = m1; i <= m2; i++) {
|
---|
397 | r1[i - 1] = f * r[i - 1]; r2[i - 2] = g * r[i - 2];
|
---|
398 | r[i] = 1 / (p * b[i] + t[i] - f * r1[i - 1] - g * r2[i - 2]);
|
---|
399 | u[i] = a[i] - r1[i - 1] * u[i - 1] - r2[i - 2] * u[i - 2];
|
---|
400 | f = p * c[i] + t1[i] - h * r1[i - 1]; g = h; h = d[i] * p;
|
---|
401 | }
|
---|
402 | for (i = m2; i >= m1; i--) {
|
---|
403 | u[i] = r[i] * u[i] - r1[i] * u[i + 1] - r2[i] * u[i + 2];
|
---|
404 | }
|
---|
405 | e = h = 0;
|
---|
406 | for (i = n1; i <= m2; i++) {
|
---|
407 | g = h; h = (u[i + 1] - u[i]) / (x[i + 1] - x[i]);
|
---|
408 | v[i] = (h - g) * inv_dy[i] * inv_dy[i]; e = e + v[i] * (h - g);
|
---|
409 | }
|
---|
410 | g = v[n2] = -h * inv_dy[n2] * inv_dy[n2]; e = e - g * h;
|
---|
411 | g = f2; f2 = e * p * p;
|
---|
412 | if (f2 >= s || f2 <= g) goto fin;
|
---|
413 | f = 0; h = (v[m1] - v[n1]) / (x[m1] - x[n1]);
|
---|
414 | for (i = m1; i <= m2; i++) {
|
---|
415 | g = h; h = (v[i + 1] - v[i]) / (x[i + 1] - x[i]);
|
---|
416 | g = h - g - r1[i - 1] * r[i - 1] - r2[i - 2] * r[i - 2];
|
---|
417 | f = f + g * r[i] * g; r[i] = g;
|
---|
418 | }
|
---|
419 | h = e - p * f; if (h <= 0) goto fin;
|
---|
420 | p = p + (s - f2) / ((Math.Sqrt(s / e) + p) * h); goto next;
|
---|
421 |
|
---|
422 | fin:
|
---|
423 | for (i = n1; i <= n2; i++) {
|
---|
424 | a[i] = y[i] - p * v[i];
|
---|
425 | c[i] = u[i];
|
---|
426 | }
|
---|
427 | for (i = n1; i <= m2; i++) {
|
---|
428 | h = x[i + 1] - x[i];
|
---|
429 | d[i] = (c[i + 1] - c[i]) / (3 * h);
|
---|
430 | b[i] = (a[i + 1] - a[i]) / h - (h * d[i] + c[i]) * h;
|
---|
431 | }
|
---|
432 | }
|
---|
433 |
|
---|
434 | return new ReinschSmoothingSplineModel(a, b, c, d, x, targetVar, inputVars);
|
---|
435 | }
|
---|
436 |
|
---|
437 | private void CalculateSmoothingSpline(double[] x, double[] y, string[] inputVars) {
|
---|
438 | // see Smoothing and Non-Parametric Regression, Germán Rodríguez, 2001 2.3.1
|
---|
439 | double[] w = Enumerable.Repeat(1.0, x.Length).ToArray(); // weights necessary for sortAndBin but are ignored below (TODO)
|
---|
440 | SortAndBin(x, y, w, out x, out y, out w, scaling: false);
|
---|
441 | int n = x.Length;
|
---|
442 |
|
---|
443 | SparseMatrix delta = new SparseMatrix(n - 2, n);
|
---|
444 | // double[,] delta = new double[n - 2, n];
|
---|
445 | //double[,] W = new double[n - 2, n - 2];
|
---|
446 | SparseMatrix W = new SparseMatrix(n - 2, n - 2);
|
---|
447 | Matrix WInvD = new DenseMatrix(n - 2, n);
|
---|
448 |
|
---|
449 | // double[,] W_inv_D = new double[n - 2, n];
|
---|
450 | // double[,] K = new double[n, n];
|
---|
451 |
|
---|
452 | // go over successive knots to determine distances and fill Delta and W
|
---|
453 | for (int i = 0; i < n - 2; i++) {
|
---|
454 | double h = x[i + 1] - x[i];
|
---|
455 | double h_next = x[i + 2] - x[i + 1];
|
---|
456 | delta[i, i] = 1.0 / h;
|
---|
457 | delta[i, i + 1] = -1.0 / h - 1.0 / h_next;
|
---|
458 | delta[i, i + 2] = 1.0 / h_next;
|
---|
459 | W[i, i] = (h + h_next) / 3;
|
---|
460 | if (i > 0) {
|
---|
461 | W[i - 1, i] =
|
---|
462 | W[i, i - 1] = h / 6.0;
|
---|
463 | }
|
---|
464 | }
|
---|
465 |
|
---|
466 | // WInvD = W.Cholesky().Solve(delta);
|
---|
467 | var solvResult = W.TrySolveIterative(delta, WInvD, new MlkBiCgStab());
|
---|
468 |
|
---|
469 | // alglib.ablas.rmatrixgemm(n - 2, n, n - 2, 1.0, W, 0, 0, 0, delta, 0, 0, 0, 1.0, W_inv_D, 0, 0); // W^-1(M = n-2, K = n-2) D(K = n-2, N=n)
|
---|
470 | // alglib.ablas.rmatrixgemm(n, n, n - 2, 1.0, delta, 0, 0, 1, W_inv_D, 0, 0, 0, 1.0, K, 0, 0); // D(M=n-2, K=n)^T * W^-1D (K=n, N=n-2)
|
---|
471 |
|
---|
472 | var K = delta.TransposeThisAndMultiply(WInvD);
|
---|
473 |
|
---|
474 | double lambda = ((IValueParameter<DoubleValue>)Parameters["Lambda"]).Value.Value;
|
---|
475 |
|
---|
476 | for (int i = 0; i < n; i++) {
|
---|
477 | for (int j = 0; j < n; j++) {
|
---|
478 | K[i, j] *= lambda;
|
---|
479 | if (i == j) K[i, j] += 1;
|
---|
480 | }
|
---|
481 | }
|
---|
482 |
|
---|
483 | // solve for y
|
---|
484 | // double[] s;
|
---|
485 | // int solverInfo;
|
---|
486 | // alglib.densesolverreport solverRep;
|
---|
487 | // alglib.rmatrixsolve(K, n, y, out solverInfo, out solverRep, out s);
|
---|
488 |
|
---|
489 | var s = K.Solve(new DenseVector(y)).ToArray();
|
---|
490 |
|
---|
491 | Results.Add(new Result("Solution", new RegressionSolution(new SmoothingSplineModel(s, x, Problem.ProblemData.TargetVariable, inputVars),
|
---|
492 | (IRegressionProblemData)Problem.ProblemData.Clone())));
|
---|
493 | }
|
---|
494 |
|
---|
495 | private static void SortAndBin(double[] x, double[] y, double[] w, out double[] x2, out double[] y2, out double[] w2, bool scaling = false) {
|
---|
496 | var sortedIdx = Enumerable.Range(0, x.Length).ToArray();
|
---|
497 | // sort by x
|
---|
498 | Array.Sort(x, sortedIdx);
|
---|
499 |
|
---|
500 | var xl = new List<double>();
|
---|
501 | var yl = new List<double>();
|
---|
502 | var wl = new List<double>();
|
---|
503 |
|
---|
504 | int n = x.Length;
|
---|
505 | var range = x[n - 1] - x[0];
|
---|
506 | var binSize = range / n / 20;
|
---|
507 | {
|
---|
508 | // binning
|
---|
509 | int i = 0;
|
---|
510 | while (i < n) {
|
---|
511 | int k = 0;
|
---|
512 | int j = i;
|
---|
513 | double sumX = 0.0;
|
---|
514 | double sumY = 0.0;
|
---|
515 | double sumW = 0.0;
|
---|
516 | while (j < n && x[j] - x[i] <= binSize) {
|
---|
517 | k++;
|
---|
518 | sumX += x[j];
|
---|
519 | sumY += y[sortedIdx[j]];
|
---|
520 | sumW += w[sortedIdx[j]];
|
---|
521 | j++;
|
---|
522 | }
|
---|
523 | var avgX = sumX / k;
|
---|
524 | if (scaling) avgX = (avgX - x[0]) / range;
|
---|
525 | xl.Add(avgX);
|
---|
526 | yl.Add(sumY / k);
|
---|
527 | wl.Add(sumW);
|
---|
528 | i += k;
|
---|
529 | }
|
---|
530 | }
|
---|
531 |
|
---|
532 | x2 = xl.ToArray();
|
---|
533 | y2 = yl.ToArray();
|
---|
534 | w2 = wl.ToArray();
|
---|
535 | }
|
---|
536 |
|
---|
537 | private void AddAlglibSplineResult(alglib.spline1dinterpolant c, string[] inputVars) {
|
---|
538 | Results.Add(new Result("Solution", new RegressionSolution(new Spline1dModel(c, Problem.ProblemData.TargetVariable, inputVars),
|
---|
539 | (IRegressionProblemData)Problem.ProblemData.Clone())));
|
---|
540 |
|
---|
541 | }
|
---|
542 | private void AddMathNetSplineResult(IInterpolation c, string[] inputVars) {
|
---|
543 | Results.Add(new Result("Solution", new RegressionSolution(new MathNetSplineModel(c, Problem.ProblemData.TargetVariable, inputVars),
|
---|
544 | (IRegressionProblemData)Problem.ProblemData.Clone())));
|
---|
545 | }
|
---|
546 | }
|
---|
547 |
|
---|
548 |
|
---|
549 | // array with non-zero lower index
|
---|
550 | internal class MyArray<T> {
|
---|
551 | private T[] arr;
|
---|
552 | private int lowerBound;
|
---|
553 |
|
---|
554 | public int Length { get { return arr.Length; } }
|
---|
555 |
|
---|
556 | public T this[int key] {
|
---|
557 | get {
|
---|
558 | return arr[key - lowerBound];
|
---|
559 | }
|
---|
560 | set {
|
---|
561 | arr[key - lowerBound] = value;
|
---|
562 | }
|
---|
563 | }
|
---|
564 |
|
---|
565 | public MyArray(int lowerBound, int numElements) {
|
---|
566 | this.lowerBound = lowerBound;
|
---|
567 | arr = new T[numElements];
|
---|
568 | }
|
---|
569 | public MyArray(int lowerBound, T[] source) : this(lowerBound, source.Length) {
|
---|
570 | Array.Copy(source, arr, source.Length);
|
---|
571 | }
|
---|
572 |
|
---|
573 | public T[] ToArray() {
|
---|
574 | var res = new T[arr.Length];
|
---|
575 | Array.Copy(arr, res, res.Length);
|
---|
576 | return res;
|
---|
577 | }
|
---|
578 | }
|
---|
579 |
|
---|
580 |
|
---|
581 | // UNFINISHED
|
---|
582 | internal class ReinschSmoothingSplineModel : NamedItem, IRegressionModel {
|
---|
583 | private MyArray<double> a;
|
---|
584 | private MyArray<double> b;
|
---|
585 | private MyArray<double> c;
|
---|
586 | private MyArray<double> d;
|
---|
587 | private MyArray<double> x;
|
---|
588 | private double offset;
|
---|
589 | private double scale;
|
---|
590 |
|
---|
591 | public string TargetVariable { get; set; }
|
---|
592 |
|
---|
593 | public IEnumerable<string> VariablesUsedForPrediction { get; private set; }
|
---|
594 |
|
---|
595 | public event EventHandler TargetVariableChanged;
|
---|
596 |
|
---|
597 | public ReinschSmoothingSplineModel(ReinschSmoothingSplineModel orig, Cloner cloner) : base(orig, cloner) {
|
---|
598 | this.TargetVariable = orig.TargetVariable;
|
---|
599 | this.VariablesUsedForPrediction = orig.VariablesUsedForPrediction.ToArray();
|
---|
600 | this.a = orig.a;
|
---|
601 | this.b = orig.b;
|
---|
602 | this.c = orig.c;
|
---|
603 | this.d = orig.d;
|
---|
604 | this.x = orig.x;
|
---|
605 | this.scale = orig.scale;
|
---|
606 | this.offset = orig.offset;
|
---|
607 | }
|
---|
608 | public ReinschSmoothingSplineModel(
|
---|
609 | MyArray<double> a,
|
---|
610 | MyArray<double> b,
|
---|
611 | MyArray<double> c,
|
---|
612 | MyArray<double> d,
|
---|
613 | MyArray<double> x,
|
---|
614 | string targetVar, string[] inputs, double offset = 0, double scale = 1) : base("SplineModel", "SplineModel") {
|
---|
615 | this.a = a;
|
---|
616 | this.b = b;
|
---|
617 | this.c = c;
|
---|
618 | this.d = d;
|
---|
619 | this.x = x;
|
---|
620 | this.TargetVariable = targetVar;
|
---|
621 | this.VariablesUsedForPrediction = inputs;
|
---|
622 | this.scale = scale;
|
---|
623 | this.offset = offset;
|
---|
624 |
|
---|
625 | // extrapolate for xx > x[n2]
|
---|
626 | b[b.Length] = b[b.Length - 1];
|
---|
627 | d[b.Length] = d[d.Length - 1];
|
---|
628 | }
|
---|
629 |
|
---|
630 | public override IDeepCloneable Clone(Cloner cloner) {
|
---|
631 | return new ReinschSmoothingSplineModel(this, cloner);
|
---|
632 | }
|
---|
633 |
|
---|
634 | public IRegressionSolution CreateRegressionSolution(IRegressionProblemData problemData) {
|
---|
635 | return new RegressionSolution(this, (IRegressionProblemData)problemData.Clone());
|
---|
636 | }
|
---|
637 |
|
---|
638 | public IEnumerable<double> GetEstimatedValues(IDataset dataset, IEnumerable<int> rows) {
|
---|
639 | int n = x.Length;
|
---|
640 | foreach (var xx in dataset.GetDoubleValues(VariablesUsedForPrediction.First(), rows).Select(xi => (xi - offset) * scale)) {
|
---|
641 | if (xx <= x[1]) {
|
---|
642 | double h = xx - x[1];
|
---|
643 | yield return a[1] + h * (b[1] + h * (c[1] + h * d[1]));
|
---|
644 | } else if (xx >= x[n]) {
|
---|
645 | double h = xx - x[n];
|
---|
646 | yield return a[n] + h * (b[n] + h * (c[n] + h * d[n]));
|
---|
647 | } else {
|
---|
648 | // binary search
|
---|
649 | int lower = 1;
|
---|
650 | int upper = n;
|
---|
651 | while (true) {
|
---|
652 | if (upper < lower) throw new InvalidProgramException();
|
---|
653 | int i = lower + (upper - lower) / 2;
|
---|
654 | if (x[i] <= xx && xx < x[i + 1]) {
|
---|
655 | double h = xx - x[i];
|
---|
656 | yield return a[i] + h * (b[i] + h * (c[i] + h * d[i]));
|
---|
657 | break;
|
---|
658 | } else if (xx < x[i]) {
|
---|
659 | upper = i - 1;
|
---|
660 | } else {
|
---|
661 | lower = i + 1;
|
---|
662 | }
|
---|
663 | }
|
---|
664 | }
|
---|
665 | }
|
---|
666 | }
|
---|
667 | }
|
---|
668 |
|
---|
669 | // UNFINISHED
|
---|
670 | public class SmoothingSplineModel : NamedItem, IRegressionModel {
|
---|
671 | private double[] s;
|
---|
672 | private IInterpolation interpolation;
|
---|
673 |
|
---|
674 | public string TargetVariable { get; set; }
|
---|
675 |
|
---|
676 | public IEnumerable<string> VariablesUsedForPrediction { get; private set; }
|
---|
677 |
|
---|
678 | public event EventHandler TargetVariableChanged;
|
---|
679 |
|
---|
680 | public SmoothingSplineModel(SmoothingSplineModel orig, Cloner cloner) : base(orig, cloner) {
|
---|
681 | this.TargetVariable = orig.TargetVariable;
|
---|
682 | this.VariablesUsedForPrediction = orig.VariablesUsedForPrediction.ToArray();
|
---|
683 | this.s = orig.s; // TODO
|
---|
684 | this.interpolation = orig.interpolation;
|
---|
685 | }
|
---|
686 | public SmoothingSplineModel(double[] s, double[] x, string targetVar, string[] inputs) : base("SplineModel", "SplineModel") {
|
---|
687 | this.s = s;
|
---|
688 | this.TargetVariable = targetVar;
|
---|
689 | this.VariablesUsedForPrediction = inputs;
|
---|
690 | this.interpolation = MathNet.Numerics.Interpolate.CubicSpline(x, s);
|
---|
691 | }
|
---|
692 |
|
---|
693 | public override IDeepCloneable Clone(Cloner cloner) {
|
---|
694 | return new SmoothingSplineModel(this, cloner);
|
---|
695 | }
|
---|
696 |
|
---|
697 | public IRegressionSolution CreateRegressionSolution(IRegressionProblemData problemData) {
|
---|
698 | return new RegressionSolution(this, (IRegressionProblemData)problemData.Clone());
|
---|
699 | }
|
---|
700 |
|
---|
701 | public IEnumerable<double> GetEstimatedValues(IDataset dataset, IEnumerable<int> rows) {
|
---|
702 | foreach (var x in dataset.GetDoubleValues(VariablesUsedForPrediction.First(), rows)) {
|
---|
703 |
|
---|
704 | yield return interpolation.Interpolate(x);
|
---|
705 |
|
---|
706 | }
|
---|
707 | }
|
---|
708 | }
|
---|
709 |
|
---|
710 | // UNFINISHED
|
---|
711 | public class Spline1dModel : NamedItem, IRegressionModel {
|
---|
712 | private alglib.spline1dinterpolant interpolant;
|
---|
713 |
|
---|
714 | public string TargetVariable { get; set; }
|
---|
715 |
|
---|
716 | public IEnumerable<string> VariablesUsedForPrediction { get; private set; }
|
---|
717 |
|
---|
718 | public event EventHandler TargetVariableChanged;
|
---|
719 |
|
---|
720 | public Spline1dModel(Spline1dModel orig, Cloner cloner) : base(orig, cloner) {
|
---|
721 | this.TargetVariable = orig.TargetVariable;
|
---|
722 | this.VariablesUsedForPrediction = orig.VariablesUsedForPrediction.ToArray();
|
---|
723 | this.interpolant = (alglib.spline1dinterpolant)orig.interpolant.make_copy();
|
---|
724 | }
|
---|
725 | public Spline1dModel(alglib.spline1dinterpolant interpolant, string targetVar, string[] inputs) : base("SplineModel", "SplineModel") {
|
---|
726 | this.interpolant = interpolant;
|
---|
727 | this.TargetVariable = targetVar;
|
---|
728 | this.VariablesUsedForPrediction = inputs;
|
---|
729 | }
|
---|
730 |
|
---|
731 | public override IDeepCloneable Clone(Cloner cloner) {
|
---|
732 | return new Spline1dModel(this, cloner);
|
---|
733 | }
|
---|
734 |
|
---|
735 | public IRegressionSolution CreateRegressionSolution(IRegressionProblemData problemData) {
|
---|
736 | return new RegressionSolution(this, (IRegressionProblemData)problemData.Clone());
|
---|
737 | }
|
---|
738 |
|
---|
739 | public IEnumerable<double> GetEstimatedValues(IDataset dataset, IEnumerable<int> rows) {
|
---|
740 | foreach (var x in dataset.GetDoubleValues(VariablesUsedForPrediction.First(), rows)) {
|
---|
741 | yield return alglib.spline1dcalc(interpolant, x);
|
---|
742 | }
|
---|
743 | }
|
---|
744 | }
|
---|
745 |
|
---|
746 |
|
---|
747 | // UNFINISHED
|
---|
748 | public class MathNetSplineModel : NamedItem, IRegressionModel {
|
---|
749 | private IInterpolation interpolant;
|
---|
750 |
|
---|
751 | public string TargetVariable { get; set; }
|
---|
752 |
|
---|
753 | public IEnumerable<string> VariablesUsedForPrediction { get; private set; }
|
---|
754 |
|
---|
755 | public event EventHandler TargetVariableChanged;
|
---|
756 |
|
---|
757 | public MathNetSplineModel(MathNetSplineModel orig, Cloner cloner) : base(orig, cloner) {
|
---|
758 | this.TargetVariable = orig.TargetVariable;
|
---|
759 | this.VariablesUsedForPrediction = orig.VariablesUsedForPrediction.ToArray();
|
---|
760 | this.interpolant = orig.interpolant; // TODO COPY!
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761 | }
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762 | public MathNetSplineModel(IInterpolation interpolant, string targetVar, string[] inputs) : base("SplineModel", "SplineModel") {
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763 | this.interpolant = interpolant;
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764 | this.TargetVariable = targetVar;
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765 | this.VariablesUsedForPrediction = inputs;
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766 | }
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767 |
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768 | public override IDeepCloneable Clone(Cloner cloner) {
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769 | return new MathNetSplineModel(this, cloner);
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770 | }
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771 |
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772 | public IRegressionSolution CreateRegressionSolution(IRegressionProblemData problemData) {
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773 | return new RegressionSolution(this, (IRegressionProblemData)problemData.Clone());
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774 | }
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775 |
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776 | public IEnumerable<double> GetEstimatedValues(IDataset dataset, IEnumerable<int> rows) {
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777 | foreach (var x in dataset.GetDoubleValues(VariablesUsedForPrediction.First(), rows)) {
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778 | yield return interpolant.Interpolate(x);
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779 | }
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780 | }
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781 | }
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782 | }
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