[14378] | 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.Generic;
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| 24 | using System.Linq;
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| 25 | using AutoDiff;
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| 26 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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| 27 |
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| 28 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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[14390] | 29 | public class TreeToAutoDiffTermConverter {
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[14378] | 30 | public delegate double ParametricFunction(double[] vars, double[] @params);
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| 31 | public delegate Tuple<double[], double> ParametricFunctionGradient(double[] vars, double[] @params);
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| 32 |
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| 33 | #region derivations of functions
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| 34 | // create function factory for arctangent
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| 35 | private static readonly Func<Term, UnaryFunc> arctan = UnaryFunc.Factory(
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| 36 | eval: Math.Atan,
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| 37 | diff: x => 1 / (1 + x * x));
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| 38 | private static readonly Func<Term, UnaryFunc> sin = UnaryFunc.Factory(
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| 39 | eval: Math.Sin,
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| 40 | diff: Math.Cos);
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| 41 | private static readonly Func<Term, UnaryFunc> cos = UnaryFunc.Factory(
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| 42 | eval: Math.Cos,
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| 43 | diff: x => -Math.Sin(x));
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| 44 | private static readonly Func<Term, UnaryFunc> tan = UnaryFunc.Factory(
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| 45 | eval: Math.Tan,
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| 46 | diff: x => 1 + Math.Tan(x) * Math.Tan(x));
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| 47 | private static readonly Func<Term, UnaryFunc> erf = UnaryFunc.Factory(
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| 48 | eval: alglib.errorfunction,
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| 49 | diff: x => 2.0 * Math.Exp(-(x * x)) / Math.Sqrt(Math.PI));
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| 50 | private static readonly Func<Term, UnaryFunc> norm = UnaryFunc.Factory(
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| 51 | eval: alglib.normaldistribution,
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| 52 | diff: x => -(Math.Exp(-(x * x)) * Math.Sqrt(Math.Exp(x * x)) * x) / Math.Sqrt(2 * Math.PI));
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| 53 |
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| 54 | #endregion
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| 55 |
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| 56 | public static bool TryTransformToAutoDiff(ISymbolicExpressionTree tree, bool makeVariableWeightsVariable,
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| 57 | out string[] variableNames, out int[] lags, out double[] initialConstants,
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| 58 | out ParametricFunction func,
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| 59 | out ParametricFunctionGradient func_grad) {
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| 60 |
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| 61 | // use a transformator object which holds the state (variable list, parameter list, ...) for recursive transformation of the tree
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[14390] | 62 | var transformator = new TreeToAutoDiffTermConverter(makeVariableWeightsVariable);
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[14378] | 63 | AutoDiff.Term term;
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| 64 | var success = transformator.TryTransformToAutoDiff(tree.Root.GetSubtree(0), out term);
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| 65 | if (success) {
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| 66 | var compiledTerm = term.Compile(transformator.variables.ToArray(), transformator.parameters.ToArray());
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| 67 | variableNames = transformator.variableNames.ToArray();
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| 68 | lags = transformator.lags.ToArray();
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| 69 | initialConstants = transformator.initialConstants.ToArray();
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| 70 | func = (vars, @params) => compiledTerm.Evaluate(vars, @params);
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| 71 | func_grad = (vars, @params) => compiledTerm.Differentiate(vars, @params);
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| 72 | } else {
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| 73 | func = null;
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| 74 | func_grad = null;
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| 75 | variableNames = null;
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| 76 | lags = null;
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| 77 | initialConstants = null;
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| 78 | }
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| 79 | return success;
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| 80 | }
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| 81 |
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| 82 | // state for recursive transformation of trees
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| 83 | private readonly List<string> variableNames;
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| 84 | private readonly List<int> lags;
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| 85 | private readonly List<double> initialConstants;
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| 86 | private readonly List<AutoDiff.Variable> parameters;
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| 87 | private readonly List<AutoDiff.Variable> variables;
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| 88 | private readonly bool makeVariableWeightsVariable;
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| 89 |
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[14390] | 90 | private TreeToAutoDiffTermConverter(bool makeVariableWeightsVariable) {
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[14378] | 91 | this.makeVariableWeightsVariable = makeVariableWeightsVariable;
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| 92 | this.variableNames = new List<string>();
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| 93 | this.lags = new List<int>();
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| 94 | this.initialConstants = new List<double>();
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| 95 | this.parameters = new List<AutoDiff.Variable>();
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| 96 | this.variables = new List<AutoDiff.Variable>();
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| 97 | }
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| 98 |
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| 99 | private bool TryTransformToAutoDiff(ISymbolicExpressionTreeNode node, out AutoDiff.Term term) {
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| 100 | if (node.Symbol is Constant) {
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| 101 | initialConstants.Add(((ConstantTreeNode)node).Value);
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| 102 | var var = new AutoDiff.Variable();
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| 103 | variables.Add(var);
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| 104 | term = var;
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| 105 | return true;
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| 106 | }
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| 107 | if (node.Symbol is Variable) {
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| 108 | var varNode = node as VariableTreeNode;
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| 109 | var par = new AutoDiff.Variable();
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| 110 | parameters.Add(par);
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| 111 | variableNames.Add(varNode.VariableName);
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| 112 | lags.Add(0);
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| 113 |
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| 114 | if (makeVariableWeightsVariable) {
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| 115 | initialConstants.Add(varNode.Weight);
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| 116 | var w = new AutoDiff.Variable();
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| 117 | variables.Add(w);
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| 118 | term = AutoDiff.TermBuilder.Product(w, par);
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| 119 | } else {
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| 120 | term = varNode.Weight * par;
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| 121 | }
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| 122 | return true;
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| 123 | }
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| 124 | if (node.Symbol is LaggedVariable) {
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| 125 | var varNode = node as LaggedVariableTreeNode;
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| 126 | var par = new AutoDiff.Variable();
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| 127 | parameters.Add(par);
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| 128 | variableNames.Add(varNode.VariableName);
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| 129 | lags.Add(varNode.Lag);
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| 130 |
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| 131 | if (makeVariableWeightsVariable) {
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| 132 | initialConstants.Add(varNode.Weight);
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| 133 | var w = new AutoDiff.Variable();
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| 134 | variables.Add(w);
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| 135 | term = AutoDiff.TermBuilder.Product(w, par);
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| 136 | } else {
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| 137 | term = varNode.Weight * par;
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| 138 | }
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| 139 | return true;
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| 140 | }
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| 141 | if (node.Symbol is Addition) {
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| 142 | List<AutoDiff.Term> terms = new List<Term>();
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| 143 | foreach (var subTree in node.Subtrees) {
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| 144 | AutoDiff.Term t;
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| 145 | if (!TryTransformToAutoDiff(subTree, out t)) {
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| 146 | term = null;
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| 147 | return false;
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| 148 | }
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| 149 | terms.Add(t);
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| 150 | }
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| 151 | term = AutoDiff.TermBuilder.Sum(terms);
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| 152 | return true;
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| 153 | }
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| 154 | if (node.Symbol is Subtraction) {
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| 155 | List<AutoDiff.Term> terms = new List<Term>();
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| 156 | for (int i = 0; i < node.SubtreeCount; i++) {
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| 157 | AutoDiff.Term t;
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| 158 | if (!TryTransformToAutoDiff(node.GetSubtree(i), out t)) {
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| 159 | term = null;
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| 160 | return false;
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| 161 | }
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| 162 | if (i > 0) t = -t;
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| 163 | terms.Add(t);
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| 164 | }
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| 165 | if (terms.Count == 1) term = -terms[0];
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| 166 | else term = AutoDiff.TermBuilder.Sum(terms);
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| 167 | return true;
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| 168 | }
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| 169 | if (node.Symbol is Multiplication) {
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| 170 | List<AutoDiff.Term> terms = new List<Term>();
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| 171 | foreach (var subTree in node.Subtrees) {
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| 172 | AutoDiff.Term t;
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| 173 | if (!TryTransformToAutoDiff(subTree, out t)) {
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| 174 | term = null;
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| 175 | return false;
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| 176 | }
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| 177 | terms.Add(t);
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| 178 | }
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| 179 | if (terms.Count == 1) term = terms[0];
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| 180 | else term = terms.Aggregate((a, b) => new AutoDiff.Product(a, b));
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| 181 | return true;
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| 182 |
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| 183 | }
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| 184 | if (node.Symbol is Division) {
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| 185 | List<AutoDiff.Term> terms = new List<Term>();
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| 186 | foreach (var subTree in node.Subtrees) {
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| 187 | AutoDiff.Term t;
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| 188 | if (!TryTransformToAutoDiff(subTree, out t)) {
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| 189 | term = null;
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| 190 | return false;
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| 191 | }
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| 192 | terms.Add(t);
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| 193 | }
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| 194 | if (terms.Count == 1) term = 1.0 / terms[0];
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| 195 | else term = terms.Aggregate((a, b) => new AutoDiff.Product(a, 1.0 / b));
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| 196 | return true;
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| 197 | }
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| 198 | if (node.Symbol is Logarithm) {
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| 199 | AutoDiff.Term t;
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| 200 | if (!TryTransformToAutoDiff(node.GetSubtree(0), out t)) {
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| 201 | term = null;
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| 202 | return false;
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| 203 | } else {
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| 204 | term = AutoDiff.TermBuilder.Log(t);
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| 205 | return true;
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| 206 | }
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| 207 | }
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| 208 | if (node.Symbol is Exponential) {
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| 209 | AutoDiff.Term t;
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| 210 | if (!TryTransformToAutoDiff(node.GetSubtree(0), out t)) {
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| 211 | term = null;
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| 212 | return false;
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| 213 | } else {
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| 214 | term = AutoDiff.TermBuilder.Exp(t);
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| 215 | return true;
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| 216 | }
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| 217 | }
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| 218 | if (node.Symbol is Square) {
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| 219 | AutoDiff.Term t;
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| 220 | if (!TryTransformToAutoDiff(node.GetSubtree(0), out t)) {
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| 221 | term = null;
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| 222 | return false;
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| 223 | } else {
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| 224 | term = AutoDiff.TermBuilder.Power(t, 2.0);
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| 225 | return true;
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| 226 | }
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| 227 | }
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| 228 | if (node.Symbol is SquareRoot) {
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| 229 | AutoDiff.Term t;
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| 230 | if (!TryTransformToAutoDiff(node.GetSubtree(0), out t)) {
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| 231 | term = null;
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| 232 | return false;
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| 233 | } else {
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| 234 | term = AutoDiff.TermBuilder.Power(t, 0.5);
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| 235 | return true;
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| 236 | }
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| 237 | }
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| 238 | if (node.Symbol is Sine) {
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| 239 | AutoDiff.Term t;
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| 240 | if (!TryTransformToAutoDiff(node.GetSubtree(0), out t)) {
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| 241 | term = null;
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| 242 | return false;
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| 243 | } else {
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| 244 | term = sin(t);
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| 245 | return true;
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| 246 | }
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| 247 | }
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| 248 | if (node.Symbol is Cosine) {
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| 249 | AutoDiff.Term t;
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| 250 | if (!TryTransformToAutoDiff(node.GetSubtree(0), out t)) {
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| 251 | term = null;
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| 252 | return false;
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| 253 | } else {
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| 254 | term = cos(t);
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| 255 | return true;
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| 256 | }
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| 257 | }
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| 258 | if (node.Symbol is Tangent) {
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| 259 | AutoDiff.Term t;
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| 260 | if (!TryTransformToAutoDiff(node.GetSubtree(0), out t)) {
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| 261 | term = null;
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| 262 | return false;
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| 263 | } else {
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| 264 | term = tan(t);
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| 265 | return true;
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| 266 | }
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| 267 | }
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| 268 | if (node.Symbol is Erf) {
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| 269 | AutoDiff.Term t;
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| 270 | if (!TryTransformToAutoDiff(node.GetSubtree(0), out t)) {
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| 271 | term = null;
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| 272 | return false;
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| 273 | } else {
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| 274 | term = erf(t);
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| 275 | return true;
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| 276 | }
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| 277 | }
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| 278 | if (node.Symbol is Norm) {
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| 279 | AutoDiff.Term t;
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| 280 | if (!TryTransformToAutoDiff(node.GetSubtree(0), out t)) {
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| 281 | term = null;
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| 282 | return false;
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| 283 | } else {
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| 284 | term = norm(t);
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| 285 | return true;
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| 286 | }
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| 287 | }
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| 288 | if (node.Symbol is StartSymbol) {
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| 289 | var alpha = new AutoDiff.Variable(); // TODO
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| 290 | var beta = new AutoDiff.Variable();
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| 291 | variables.Add(beta);
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| 292 | variables.Add(alpha);
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| 293 | AutoDiff.Term branchTerm;
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| 294 | if (TryTransformToAutoDiff(node.GetSubtree(0), out branchTerm)) {
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| 295 | term = branchTerm * alpha + beta;
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| 296 | return true;
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| 297 | } else {
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| 298 | term = null;
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| 299 | return false;
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| 300 | }
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| 301 | }
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| 302 | term = null;
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| 303 | return false;
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| 304 | }
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| 305 |
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| 306 |
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| 307 | public static bool IsCompatible(ISymbolicExpressionTree tree) {
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| 308 | var containsUnknownSymbol = (
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| 309 | from n in tree.Root.GetSubtree(0).IterateNodesPrefix()
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| 310 | where
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| 311 | !(n.Symbol is Variable) &&
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| 312 | !(n.Symbol is LaggedVariable) &&
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| 313 | !(n.Symbol is Constant) &&
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| 314 | !(n.Symbol is Addition) &&
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| 315 | !(n.Symbol is Subtraction) &&
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| 316 | !(n.Symbol is Multiplication) &&
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| 317 | !(n.Symbol is Division) &&
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| 318 | !(n.Symbol is Logarithm) &&
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| 319 | !(n.Symbol is Exponential) &&
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| 320 | !(n.Symbol is SquareRoot) &&
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| 321 | !(n.Symbol is Square) &&
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| 322 | !(n.Symbol is Sine) &&
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| 323 | !(n.Symbol is Cosine) &&
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| 324 | !(n.Symbol is Tangent) &&
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| 325 | !(n.Symbol is Erf) &&
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| 326 | !(n.Symbol is Norm) &&
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| 327 | !(n.Symbol is StartSymbol)
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| 328 | select n).Any();
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| 329 | return !containsUnknownSymbol;
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| 330 | }
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| 331 | }
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| 332 | }
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