[14843] | 1 | #region License Information
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| 2 | /* HeuristicLab
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[15583] | 3 | * Copyright (C) 2002-2018 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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[14843] | 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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[14950] | 25 | using System.Runtime.Serialization;
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[14843] | 26 | using AutoDiff;
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| 27 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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| 28 |
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| 29 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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| 30 | public class TreeToAutoDiffTermConverter {
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| 31 | public delegate double ParametricFunction(double[] vars, double[] @params);
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[14950] | 32 |
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[14843] | 33 | public delegate Tuple<double[], double> ParametricFunctionGradient(double[] vars, double[] @params);
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| 34 |
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| 35 | #region helper class
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| 36 | public class DataForVariable {
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| 37 | public readonly string variableName;
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| 38 | public readonly string variableValue; // for factor vars
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| 39 | public readonly int lag;
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| 40 |
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| 41 | public DataForVariable(string varName, string varValue, int lag) {
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| 42 | this.variableName = varName;
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| 43 | this.variableValue = varValue;
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| 44 | this.lag = lag;
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| 45 | }
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| 46 |
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| 47 | public override bool Equals(object obj) {
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| 48 | var other = obj as DataForVariable;
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| 49 | if (other == null) return false;
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| 50 | return other.variableName.Equals(this.variableName) &&
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| 51 | other.variableValue.Equals(this.variableValue) &&
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| 52 | other.lag == this.lag;
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| 53 | }
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| 54 |
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| 55 | public override int GetHashCode() {
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| 56 | return variableName.GetHashCode() ^ variableValue.GetHashCode() ^ lag;
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| 57 | }
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| 58 | }
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| 59 | #endregion
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| 60 |
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| 61 | #region derivations of functions
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| 62 | // create function factory for arctangent
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| 63 | private static readonly Func<Term, UnaryFunc> arctan = UnaryFunc.Factory(
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| 64 | eval: Math.Atan,
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| 65 | diff: x => 1 / (1 + x * x));
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[14950] | 66 |
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[14843] | 67 | private static readonly Func<Term, UnaryFunc> sin = UnaryFunc.Factory(
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| 68 | eval: Math.Sin,
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| 69 | diff: Math.Cos);
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[14950] | 70 |
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[14843] | 71 | private static readonly Func<Term, UnaryFunc> cos = UnaryFunc.Factory(
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[14950] | 72 | eval: Math.Cos,
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| 73 | diff: x => -Math.Sin(x));
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| 74 |
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[14843] | 75 | private static readonly Func<Term, UnaryFunc> tan = UnaryFunc.Factory(
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| 76 | eval: Math.Tan,
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| 77 | diff: x => 1 + Math.Tan(x) * Math.Tan(x));
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[14950] | 78 |
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[14843] | 79 | private static readonly Func<Term, UnaryFunc> erf = UnaryFunc.Factory(
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| 80 | eval: alglib.errorfunction,
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| 81 | diff: x => 2.0 * Math.Exp(-(x * x)) / Math.Sqrt(Math.PI));
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[14950] | 82 |
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[14843] | 83 | private static readonly Func<Term, UnaryFunc> norm = UnaryFunc.Factory(
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| 84 | eval: alglib.normaldistribution,
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| 85 | diff: x => -(Math.Exp(-(x * x)) * Math.Sqrt(Math.Exp(x * x)) * x) / Math.Sqrt(2 * Math.PI));
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| 86 |
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[16356] | 87 | private static readonly Func<Term, UnaryFunc> abs = UnaryFunc.Factory(
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| 88 | eval: Math.Abs,
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| 89 | diff: x => Math.Sign(x)
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| 90 | );
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| 91 |
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[14843] | 92 | #endregion
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| 93 |
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[15447] | 94 | public static bool TryConvertToAutoDiff(ISymbolicExpressionTree tree, bool makeVariableWeightsVariable, bool addLinearScalingTerms,
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[14843] | 95 | out List<DataForVariable> parameters, out double[] initialConstants,
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| 96 | out ParametricFunction func,
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| 97 | out ParametricFunctionGradient func_grad) {
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| 98 |
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| 99 | // use a transformator object which holds the state (variable list, parameter list, ...) for recursive transformation of the tree
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[16457] | 100 | var transformator = new TreeToAutoDiffTermConverter(makeVariableWeightsVariable);
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[14843] | 101 | AutoDiff.Term term;
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[14950] | 102 | try {
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| 103 | term = transformator.ConvertToAutoDiff(tree.Root.GetSubtree(0));
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[16457] | 104 |
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| 105 | if (addLinearScalingTerms) {
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| 106 | // scaling variables α, β are given at the beginning of the parameter vector
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| 107 | var alpha = new AutoDiff.Variable();
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| 108 | var beta = new AutoDiff.Variable();
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| 109 | transformator.variables.Insert(0, alpha);
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| 110 | transformator.variables.Insert(0, beta);
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| 111 |
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| 112 | term = term * alpha + beta;
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| 113 | }
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| 114 |
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[14843] | 115 | var parameterEntries = transformator.parameters.ToArray(); // guarantee same order for keys and values
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[14950] | 116 | var compiledTerm = term.Compile(transformator.variables.ToArray(),
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| 117 | parameterEntries.Select(kvp => kvp.Value).ToArray());
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[16457] | 118 |
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[14843] | 119 | parameters = new List<DataForVariable>(parameterEntries.Select(kvp => kvp.Key));
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| 120 | initialConstants = transformator.initialConstants.ToArray();
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| 121 | func = (vars, @params) => compiledTerm.Evaluate(vars, @params);
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| 122 | func_grad = (vars, @params) => compiledTerm.Differentiate(vars, @params);
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[14950] | 123 | return true;
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| 124 | } catch (ConversionException) {
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[16457] | 125 | parameters = null;
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| 126 | initialConstants = null;
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[14843] | 127 | func = null;
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| 128 | func_grad = null;
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| 129 | }
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[14950] | 130 | return false;
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[14843] | 131 | }
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| 132 |
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[16461] | 133 | public static bool TryConvertToAutoDiff(ISymbolicExpressionTree tree, bool makeVariableWeightsVariable, bool addLinearScalingTerms, Dictionary<DataForVariable, AutoDiff.Variable> parameters,
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| 134 | out ParametricFunction func,
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| 135 | out ParametricFunctionGradient func_grad
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| 136 | ) {
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| 137 |
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| 138 | // use a transformator object which holds the state (variable list, parameter list, ...) for recursive transformation of the tree
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| 139 | var transformator = new TreeToAutoDiffTermConverter(makeVariableWeightsVariable, parameters);
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| 140 | AutoDiff.Term term;
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| 141 | try {
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| 142 | term = transformator.ConvertToAutoDiff(tree.Root.GetSubtree(0));
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| 143 |
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| 144 | if (addLinearScalingTerms) {
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| 145 | // scaling variables α, β are given at the beginning of the parameter vector
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| 146 | var alpha = new AutoDiff.Variable();
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| 147 | var beta = new AutoDiff.Variable();
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| 148 | transformator.variables.Insert(0, alpha);
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| 149 | transformator.variables.Insert(0, beta);
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| 150 |
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| 151 | term = term * alpha + beta;
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| 152 | }
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| 153 |
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| 154 | var compiledTerm = term.Compile(transformator.variables.ToArray(), parameters.Select(kvp => kvp.Value).ToArray());
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| 155 |
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| 156 |
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| 157 | func = (vars, @params) => compiledTerm.Evaluate(vars, @params);
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| 158 | func_grad = (vars, @params) => compiledTerm.Differentiate(vars, @params);
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| 159 | return true;
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| 160 | } catch (ConversionException) {
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| 161 | func = null;
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| 162 | func_grad = null;
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| 163 | }
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| 164 | return false;
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| 165 | }
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| 166 |
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[14843] | 167 | // state for recursive transformation of trees
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[16458] | 168 | private readonly List<double> initialConstants;
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| 169 | private readonly Dictionary<DataForVariable, AutoDiff.Variable> parameters;
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[14843] | 170 | private readonly List<AutoDiff.Variable> variables;
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| 171 | private readonly bool makeVariableWeightsVariable;
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| 172 |
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[16461] | 173 | private TreeToAutoDiffTermConverter(bool makeVariableWeightsVariable, Dictionary<DataForVariable, AutoDiff.Variable> parameters = null) {
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[14843] | 174 | this.makeVariableWeightsVariable = makeVariableWeightsVariable;
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| 175 | this.initialConstants = new List<double>();
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[16461] | 176 | if (parameters == null)
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| 177 | this.parameters = new Dictionary<DataForVariable, AutoDiff.Variable>();
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| 178 | else
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| 179 | this.parameters = parameters;
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[14843] | 180 | this.variables = new List<AutoDiff.Variable>();
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| 181 | }
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| 182 |
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[14950] | 183 | private AutoDiff.Term ConvertToAutoDiff(ISymbolicExpressionTreeNode node) {
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[14843] | 184 | if (node.Symbol is Constant) {
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| 185 | initialConstants.Add(((ConstantTreeNode)node).Value);
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| 186 | var var = new AutoDiff.Variable();
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| 187 | variables.Add(var);
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[14950] | 188 | return var;
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[14843] | 189 | }
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| 190 | if (node.Symbol is Variable || node.Symbol is BinaryFactorVariable) {
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| 191 | var varNode = node as VariableTreeNodeBase;
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| 192 | var factorVarNode = node as BinaryFactorVariableTreeNode;
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| 193 | // factor variable values are only 0 or 1 and set in x accordingly
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| 194 | var varValue = factorVarNode != null ? factorVarNode.VariableValue : string.Empty;
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| 195 | var par = FindOrCreateParameter(parameters, varNode.VariableName, varValue);
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| 196 |
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| 197 | if (makeVariableWeightsVariable) {
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| 198 | initialConstants.Add(varNode.Weight);
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| 199 | var w = new AutoDiff.Variable();
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| 200 | variables.Add(w);
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[14950] | 201 | return AutoDiff.TermBuilder.Product(w, par);
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[14843] | 202 | } else {
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[14950] | 203 | return varNode.Weight * par;
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[14843] | 204 | }
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| 205 | }
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| 206 | if (node.Symbol is FactorVariable) {
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| 207 | var factorVarNode = node as FactorVariableTreeNode;
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| 208 | var products = new List<Term>();
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| 209 | foreach (var variableValue in factorVarNode.Symbol.GetVariableValues(factorVarNode.VariableName)) {
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| 210 | var par = FindOrCreateParameter(parameters, factorVarNode.VariableName, variableValue);
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| 211 |
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| 212 | initialConstants.Add(factorVarNode.GetValue(variableValue));
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| 213 | var wVar = new AutoDiff.Variable();
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| 214 | variables.Add(wVar);
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| 215 |
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| 216 | products.Add(AutoDiff.TermBuilder.Product(wVar, par));
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| 217 | }
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[14950] | 218 | return AutoDiff.TermBuilder.Sum(products);
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[14843] | 219 | }
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| 220 | if (node.Symbol is LaggedVariable) {
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| 221 | var varNode = node as LaggedVariableTreeNode;
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| 222 | var par = FindOrCreateParameter(parameters, varNode.VariableName, string.Empty, varNode.Lag);
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| 223 |
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| 224 | if (makeVariableWeightsVariable) {
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| 225 | initialConstants.Add(varNode.Weight);
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| 226 | var w = new AutoDiff.Variable();
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| 227 | variables.Add(w);
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[14950] | 228 | return AutoDiff.TermBuilder.Product(w, par);
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[14843] | 229 | } else {
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[14950] | 230 | return varNode.Weight * par;
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[14843] | 231 | }
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| 232 | }
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| 233 | if (node.Symbol is Addition) {
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| 234 | List<AutoDiff.Term> terms = new List<Term>();
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| 235 | foreach (var subTree in node.Subtrees) {
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[14950] | 236 | terms.Add(ConvertToAutoDiff(subTree));
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[14843] | 237 | }
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[14950] | 238 | return AutoDiff.TermBuilder.Sum(terms);
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[14843] | 239 | }
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| 240 | if (node.Symbol is Subtraction) {
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| 241 | List<AutoDiff.Term> terms = new List<Term>();
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| 242 | for (int i = 0; i < node.SubtreeCount; i++) {
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[14950] | 243 | AutoDiff.Term t = ConvertToAutoDiff(node.GetSubtree(i));
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[14843] | 244 | if (i > 0) t = -t;
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| 245 | terms.Add(t);
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| 246 | }
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[14950] | 247 | if (terms.Count == 1) return -terms[0];
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| 248 | else return AutoDiff.TermBuilder.Sum(terms);
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[14843] | 249 | }
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| 250 | if (node.Symbol is Multiplication) {
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| 251 | List<AutoDiff.Term> terms = new List<Term>();
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| 252 | foreach (var subTree in node.Subtrees) {
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[14950] | 253 | terms.Add(ConvertToAutoDiff(subTree));
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[14843] | 254 | }
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[14950] | 255 | if (terms.Count == 1) return terms[0];
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| 256 | else return terms.Aggregate((a, b) => new AutoDiff.Product(a, b));
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[14843] | 257 | }
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| 258 | if (node.Symbol is Division) {
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| 259 | List<AutoDiff.Term> terms = new List<Term>();
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| 260 | foreach (var subTree in node.Subtrees) {
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[14950] | 261 | terms.Add(ConvertToAutoDiff(subTree));
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[14843] | 262 | }
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[14950] | 263 | if (terms.Count == 1) return 1.0 / terms[0];
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| 264 | else return terms.Aggregate((a, b) => new AutoDiff.Product(a, 1.0 / b));
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[14843] | 265 | }
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[16356] | 266 | if (node.Symbol is Absolute) {
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| 267 | var x1 = ConvertToAutoDiff(node.GetSubtree(0));
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| 268 | return abs(x1);
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| 269 | }
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[16360] | 270 | if (node.Symbol is AnalyticQuotient) {
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[16356] | 271 | var x1 = ConvertToAutoDiff(node.GetSubtree(0));
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| 272 | var x2 = ConvertToAutoDiff(node.GetSubtree(1));
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| 273 | return x1 / (TermBuilder.Power(1 + x2 * x2, 0.5));
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| 274 | }
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[14843] | 275 | if (node.Symbol is Logarithm) {
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[14950] | 276 | return AutoDiff.TermBuilder.Log(
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| 277 | ConvertToAutoDiff(node.GetSubtree(0)));
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[14843] | 278 | }
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| 279 | if (node.Symbol is Exponential) {
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[14950] | 280 | return AutoDiff.TermBuilder.Exp(
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| 281 | ConvertToAutoDiff(node.GetSubtree(0)));
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[14843] | 282 | }
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| 283 | if (node.Symbol is Square) {
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[14950] | 284 | return AutoDiff.TermBuilder.Power(
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| 285 | ConvertToAutoDiff(node.GetSubtree(0)), 2.0);
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[14843] | 286 | }
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| 287 | if (node.Symbol is SquareRoot) {
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[14950] | 288 | return AutoDiff.TermBuilder.Power(
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| 289 | ConvertToAutoDiff(node.GetSubtree(0)), 0.5);
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[14843] | 290 | }
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[16356] | 291 | if (node.Symbol is Cube) {
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| 292 | return AutoDiff.TermBuilder.Power(
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| 293 | ConvertToAutoDiff(node.GetSubtree(0)), 3.0);
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| 294 | }
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| 295 | if (node.Symbol is CubeRoot) {
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| 296 | return AutoDiff.TermBuilder.Power(
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[16457] | 297 | ConvertToAutoDiff(node.GetSubtree(0)), 1.0 / 3.0);
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[16356] | 298 | }
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[14843] | 299 | if (node.Symbol is Sine) {
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[14950] | 300 | return sin(
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| 301 | ConvertToAutoDiff(node.GetSubtree(0)));
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[14843] | 302 | }
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| 303 | if (node.Symbol is Cosine) {
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[14950] | 304 | return cos(
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| 305 | ConvertToAutoDiff(node.GetSubtree(0)));
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[14843] | 306 | }
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| 307 | if (node.Symbol is Tangent) {
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[14950] | 308 | return tan(
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| 309 | ConvertToAutoDiff(node.GetSubtree(0)));
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[14843] | 310 | }
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| 311 | if (node.Symbol is Erf) {
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[14950] | 312 | return erf(
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| 313 | ConvertToAutoDiff(node.GetSubtree(0)));
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[14843] | 314 | }
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| 315 | if (node.Symbol is Norm) {
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[14950] | 316 | return norm(
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| 317 | ConvertToAutoDiff(node.GetSubtree(0)));
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[14843] | 318 | }
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| 319 | if (node.Symbol is StartSymbol) {
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[16457] | 320 | return ConvertToAutoDiff(node.GetSubtree(0));
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[14843] | 321 | }
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[14950] | 322 | throw new ConversionException();
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[14843] | 323 | }
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| 324 |
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| 325 |
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| 326 | // for each factor variable value we need a parameter which represents a binary indicator for that variable & value combination
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| 327 | // each binary indicator is only necessary once. So we only create a parameter if this combination is not yet available
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| 328 | private static Term FindOrCreateParameter(Dictionary<DataForVariable, AutoDiff.Variable> parameters,
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| 329 | string varName, string varValue = "", int lag = 0) {
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| 330 | var data = new DataForVariable(varName, varValue, lag);
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| 331 |
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| 332 | AutoDiff.Variable par = null;
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| 333 | if (!parameters.TryGetValue(data, out par)) {
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| 334 | // not found -> create new parameter and entries in names and values lists
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| 335 | par = new AutoDiff.Variable();
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| 336 | parameters.Add(data, par);
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| 337 | }
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| 338 | return par;
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| 339 | }
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| 340 |
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| 341 | public static bool IsCompatible(ISymbolicExpressionTree tree) {
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| 342 | var containsUnknownSymbol = (
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| 343 | from n in tree.Root.GetSubtree(0).IterateNodesPrefix()
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| 344 | where
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[14950] | 345 | !(n.Symbol is Variable) &&
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| 346 | !(n.Symbol is BinaryFactorVariable) &&
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| 347 | !(n.Symbol is FactorVariable) &&
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| 348 | !(n.Symbol is LaggedVariable) &&
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| 349 | !(n.Symbol is Constant) &&
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| 350 | !(n.Symbol is Addition) &&
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| 351 | !(n.Symbol is Subtraction) &&
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| 352 | !(n.Symbol is Multiplication) &&
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| 353 | !(n.Symbol is Division) &&
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| 354 | !(n.Symbol is Logarithm) &&
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| 355 | !(n.Symbol is Exponential) &&
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| 356 | !(n.Symbol is SquareRoot) &&
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| 357 | !(n.Symbol is Square) &&
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| 358 | !(n.Symbol is Sine) &&
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| 359 | !(n.Symbol is Cosine) &&
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| 360 | !(n.Symbol is Tangent) &&
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| 361 | !(n.Symbol is Erf) &&
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| 362 | !(n.Symbol is Norm) &&
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[16356] | 363 | !(n.Symbol is StartSymbol) &&
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| 364 | !(n.Symbol is Absolute) &&
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[16360] | 365 | !(n.Symbol is AnalyticQuotient) &&
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[16356] | 366 | !(n.Symbol is Cube) &&
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| 367 | !(n.Symbol is CubeRoot)
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[14843] | 368 | select n).Any();
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| 369 | return !containsUnknownSymbol;
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| 370 | }
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[14950] | 371 | #region exception class
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| 372 | [Serializable]
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| 373 | public class ConversionException : Exception {
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| 374 |
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| 375 | public ConversionException() {
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| 376 | }
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| 377 |
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| 378 | public ConversionException(string message) : base(message) {
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| 379 | }
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| 380 |
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| 381 | public ConversionException(string message, Exception inner) : base(message, inner) {
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| 382 | }
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| 383 |
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| 384 | protected ConversionException(
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| 385 | SerializationInfo info,
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| 386 | StreamingContext context) : base(info, context) {
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| 387 | }
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| 388 | }
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| 389 | #endregion
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[14843] | 390 | }
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| 391 | }
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