[10205] | 1 | #region License Information
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| 2 | /* HeuristicLab
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| 3 | * Copyright (C) 2002-2013 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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| 4 | *
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| 5 | * This file is part of HeuristicLab.
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| 6 | *
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| 7 | * HeuristicLab is free software: you can redistribute it and/or modify
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| 8 | * it under the terms of the GNU General Public License as published by
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| 9 | * the Free Software Foundation, either version 3 of the License, or
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| 10 | * (at your option) any later version.
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| 11 | *
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| 12 | * HeuristicLab is distributed in the hope that it will be useful,
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| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 15 | * GNU General Public License for more details.
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| 16 | *
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| 17 | * You should have received a copy of the GNU General Public License
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| 18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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| 19 | */
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| 20 | #endregion
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| 21 |
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| 22 | using System;
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| 23 | using System.Collections.Generic;
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| 24 | using System.Linq;
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| 25 | using System.Linq.Expressions;
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| 26 | using HeuristicLab.Common;
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| 27 | using HeuristicLab.Core;
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| 28 | using HeuristicLab.Data;
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| 29 | using HeuristicLab.Parameters;
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| 30 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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| 31 |
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| 32 | namespace HeuristicLab.Algorithms.DataAnalysis {
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| 33 | [StorableClass]
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| 34 | [Item(Name = "CovarianceSpectralMixture",
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| 35 | Description = "The spectral mixture kernel described in Wilson A. G. and Adams R.P., Gaussian Process Kernels for Pattern Discovery and Exptrapolation, ICML 2013.")]
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| 36 | public sealed class CovarianceSpectralMixture : ParameterizedNamedItem, ICovarianceFunction {
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| 37 | public const string QParameterName = "Number of components (Q)";
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| 38 | public const string WeightParameterName = "Weight";
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| 39 | public const string FrequencyParameterName = "Component frequency (mu)";
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| 40 | public const string LengthScaleParameterName = "Length scale (nu)";
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| 41 | public IValueParameter<IntValue> QParameter {
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| 42 | get { return (IValueParameter<IntValue>)Parameters[QParameterName]; }
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| 43 | }
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| 44 |
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| 45 | public IValueParameter<DoubleArray> WeightParameter {
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| 46 | get { return (IValueParameter<DoubleArray>)Parameters[WeightParameterName]; }
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| 47 | }
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| 48 | public IValueParameter<DoubleArray> FrequencyParameter {
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| 49 | get { return (IValueParameter<DoubleArray>)Parameters[FrequencyParameterName]; }
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| 50 | }
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| 51 |
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| 52 | public IValueParameter<DoubleArray> LengthScaleParameter {
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| 53 | get { return (IValueParameter<DoubleArray>)Parameters[LengthScaleParameterName]; }
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| 54 | }
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| 55 |
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| 56 | [StorableConstructor]
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| 57 | private CovarianceSpectralMixture(bool deserializing)
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| 58 | : base(deserializing) {
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| 59 | }
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| 60 |
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| 61 | private CovarianceSpectralMixture(CovarianceSpectralMixture original, Cloner cloner)
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| 62 | : base(original, cloner) {
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| 63 | }
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| 64 |
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| 65 | public CovarianceSpectralMixture()
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| 66 | : base() {
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| 67 | Name = ItemName;
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| 68 | Description = ItemDescription;
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| 69 | Parameters.Add(new ValueParameter<IntValue>(QParameterName, "The number of Gaussians (Q) to use for the spectral mixture.", new IntValue(10)));
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| 70 | Parameters.Add(new OptionalValueParameter<DoubleArray>(WeightParameterName, "The weight of the component w (peak height of the Gaussian in spectrum)."));
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| 71 | Parameters.Add(new OptionalValueParameter<DoubleArray>(FrequencyParameterName, "The inverse component period parameter mu_q (location of the Gaussian in spectrum)."));
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| 72 | Parameters.Add(new OptionalValueParameter<DoubleArray>(LengthScaleParameterName, "The length scale parameter (nu_q) (variance of the Gaussian in the spectrum)."));
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| 73 | }
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| 74 |
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| 75 | public override IDeepCloneable Clone(Cloner cloner) {
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| 76 | return new CovarianceSpectralMixture(this, cloner);
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| 77 | }
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| 78 |
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| 79 | public int GetNumberOfParameters(int numberOfVariables) {
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| 80 | var q = QParameter.Value.Value;
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| 81 | return
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| 82 | (WeightParameter.Value != null ? 0 : q) +
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| 83 | (FrequencyParameter.Value != null ? 0 : q * numberOfVariables) +
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| 84 | (LengthScaleParameter.Value != null ? 0 : q * numberOfVariables);
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| 85 | }
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| 86 |
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| 87 | public void SetParameter(double[] p) {
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| 88 | double[] weight, frequency, lengthScale;
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| 89 | GetParameterValues(p, out weight, out frequency, out lengthScale);
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| 90 | WeightParameter.Value = new DoubleArray(weight);
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| 91 | FrequencyParameter.Value = new DoubleArray(frequency);
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| 92 | LengthScaleParameter.Value = new DoubleArray(lengthScale);
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| 93 | }
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| 94 |
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| 95 |
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| 96 | private void GetParameterValues(double[] p, out double[] weight, out double[] frequency, out double[] lengthScale) {
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| 97 | // gather parameter values
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| 98 | int c = 0;
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| 99 | int q = QParameter.Value.Value;
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| 100 | // guess number of elements for frequency and length (=q * numberOfVariables)
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| 101 | int n = WeightParameter.Value == null ? ((p.Length - q) / 2) : (p.Length / 2);
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| 102 | if (WeightParameter.Value != null) {
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| 103 | weight = WeightParameter.Value.ToArray();
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| 104 | } else {
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| 105 | weight = p.Skip(c).Select(Math.Exp).Take(q).ToArray();
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| 106 | c += q;
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| 107 | }
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| 108 | if (FrequencyParameter.Value != null) {
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| 109 | frequency = FrequencyParameter.Value.ToArray();
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| 110 | } else {
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| 111 | frequency = p.Skip(c).Select(Math.Exp).Take(n).ToArray();
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| 112 | c += n;
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| 113 | }
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| 114 | if (LengthScaleParameter.Value != null) {
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| 115 | lengthScale = LengthScaleParameter.Value.ToArray();
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| 116 | } else {
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| 117 | lengthScale = p.Skip(c).Select(Math.Exp).Take(n).ToArray();
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| 118 | c += n;
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| 119 | }
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| 120 | if (p.Length != c) throw new ArgumentException("The length of the parameter vector does not match the number of free parameters for CovarianceSpectralMixture", "p");
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| 121 | }
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| 122 |
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| 123 | public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, IEnumerable<int> columnIndices) {
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| 124 | double[] weight, frequency, lengthScale;
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| 125 | GetParameterValues(p, out weight, out frequency, out lengthScale);
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| 126 | // create functions
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| 127 | var cov = new ParameterizedCovarianceFunction();
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| 128 | cov.Covariance = (x, i, j) => {
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| 129 | return GetCovariance(x, x, i, j, QParameter.Value.Value, weight, frequency,
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| 130 | lengthScale, columnIndices);
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| 131 | };
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| 132 | cov.CrossCovariance = (x, xt, i, j) => {
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| 133 | return GetCovariance(x, xt, i, j, QParameter.Value.Value, weight, frequency,
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| 134 | lengthScale, columnIndices);
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| 135 | };
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| 136 | cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, QParameter.Value.Value, weight, frequency,
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| 137 | lengthScale, columnIndices);
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| 138 | return cov;
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| 139 | }
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| 140 |
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| 141 | private static double GetCovariance(double[,] x, double[,] xt, int i, int j, int maxQ, double[] weight, double[] frequency, double[] lengthScale, IEnumerable<int> columnIndices) {
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| 142 | // tau = x - x' (only for selected variables)
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| 143 | double[] tau =
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| 144 | Util.GetRow(x, i, columnIndices).Zip(Util.GetRow(xt, j, columnIndices), (xi, xj) => xi - xj).ToArray();
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| 145 | int numberOfVariables = lengthScale.Length / maxQ;
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| 146 | double k = 0;
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| 147 | // for each component
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| 148 | for (int q = 0; q < maxQ; q++) {
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| 149 | double kc = weight[q]; // weighted kernel component
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| 150 |
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| 151 | int idx = 0; // helper index for tau
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| 152 | // for each selected variable
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| 153 | foreach (var c in columnIndices) {
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| 154 | kc *= f1(tau[idx], lengthScale[q * numberOfVariables + c]) * f2(tau[idx], frequency[q * numberOfVariables + c]);
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| 155 | idx++;
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| 156 | }
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| 157 | k += kc;
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| 158 | }
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| 159 | return k;
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| 160 | }
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| 161 |
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| 162 | public static double f1(double tau, double lengthScale) {
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| 163 | return Math.Exp(-2 * Math.PI * Math.PI * tau * tau * lengthScale);
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| 164 | }
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| 165 | public static double f2(double tau, double frequency) {
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| 166 | return Math.Cos(2 * Math.PI * tau * frequency);
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| 167 | }
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| 168 |
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| 169 | // order of returned gradients must match the order in GetParameterValues!
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| 170 | private static IEnumerable<double> GetGradient(double[,] x, int i, int j, int maxQ, double[] weight, double[] frequency, double[] lengthScale, IEnumerable<int> columnIndices) {
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| 171 | double[] tau = Util.GetRow(x, i, columnIndices).Zip(Util.GetRow(x, j, columnIndices), (xi, xj) => xi - xj).ToArray();
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| 172 | int numberOfVariables = lengthScale.Length / maxQ;
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| 173 |
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| 174 | // weight
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| 175 | // for each component
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| 176 | for (int q = 0; q < maxQ; q++) {
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[10473] | 177 | double k = weight[q];
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[10205] | 178 | int idx = 0; // helper index for tau
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| 179 | // for each selected variable
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| 180 | foreach (var c in columnIndices) {
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| 181 | k *= f1(tau[idx], lengthScale[q * numberOfVariables + c]) * f2(tau[idx], frequency[q * numberOfVariables + c]);
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| 182 | idx++;
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| 183 | }
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| 184 | yield return k;
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| 185 | }
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| 186 |
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| 187 | // frequency
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| 188 | // for each component
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| 189 | for (int q = 0; q < maxQ; q++) {
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| 190 | int idx = 0; // helper index for tau
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| 191 | // for each selected variable
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| 192 | foreach (var c in columnIndices) {
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| 193 | double k = f1(tau[idx], lengthScale[q * numberOfVariables + c]) *
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| 194 | -2 * Math.PI * tau[idx] * frequency[q * numberOfVariables + c] * Math.Sin(2 * Math.PI * tau[idx] * frequency[q * numberOfVariables + c]);
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| 195 | idx++;
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| 196 | yield return weight[q] * k;
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| 197 | }
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| 198 | }
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| 199 |
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| 200 | // length scale
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| 201 | // for each component
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| 202 | for (int q = 0; q < maxQ; q++) {
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| 203 | int idx = 0; // helper index for tau
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| 204 | // for each selected variable
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| 205 | foreach (var c in columnIndices) {
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[10473] | 206 | double k = -2 * Math.PI * Math.PI * tau[idx] * tau[idx] * lengthScale[q * numberOfVariables + c] *
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| 207 | f1(tau[idx], lengthScale[q * numberOfVariables + c]) * f2(tau[idx], frequency[q * numberOfVariables + c]);
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[10205] | 208 | idx++;
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| 209 | yield return weight[q] * k;
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| 210 | }
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| 211 | }
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| 212 |
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| 213 | }
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| 214 | }
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| 215 | }
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