[16206] | 1 | #region License Information
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| 2 | /* HeuristicLab
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| 3 | * Copyright (C) 2002-2018 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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| 4 | *
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| 5 | * This file is part of HeuristicLab.
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| 6 | *
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| 7 | * HeuristicLab is free software: you can redistribute it and/or modify
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| 8 | * it under the terms of the GNU General Public License as published by
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| 9 | * the Free Software Foundation, either version 3 of the License, or
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| 10 | * (at your option) any later version.
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| 11 | *
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| 12 | * HeuristicLab is distributed in the hope that it will be useful,
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| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 15 | * GNU General Public License for more details.
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| 16 | *
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| 17 | * You should have received a copy of the GNU General Public License
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| 18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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| 19 | */
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| 20 | #endregion
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| 21 |
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| 22 | using System;
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| 23 | using System.Linq;
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| 24 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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| 25 |
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| 26 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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| 27 | public static class DerivativeCalculator {
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| 28 | public static ISymbolicExpressionTree Derive(ISymbolicExpressionTree tree, string variableName) {
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| 29 | var mainBranch = tree.Root.GetSubtree(0).GetSubtree(0);
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| 30 | var root = new ProgramRootSymbol().CreateTreeNode();
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| 31 | root.AddSubtree(new StartSymbol().CreateTreeNode());
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| 32 | var dTree = TreeSimplifier.GetSimplifiedTree(Derive(mainBranch, variableName));
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| 33 | // var dTree = Derive(mainBranch, variableName);
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| 34 | root.GetSubtree(0).AddSubtree(dTree);
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| 35 | return new SymbolicExpressionTree(root);
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| 36 | }
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| 37 |
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| 38 | private static Constant constantSy = new Constant();
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| 39 | private static Addition addSy = new Addition();
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| 40 | private static Subtraction subSy = new Subtraction();
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| 41 | private static Multiplication mulSy = new Multiplication();
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| 42 | private static Division divSy = new Division();
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| 43 |
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| 44 | public static ISymbolicExpressionTreeNode Derive(ISymbolicExpressionTreeNode branch, string variableName) {
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| 45 | if (branch.Symbol is Constant) {
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| 46 | return CreateConstant(0.0);
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| 47 | }
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| 48 | if (branch.Symbol is Variable) {
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| 49 | var varNode = branch as VariableTreeNode;
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| 50 | if (varNode.VariableName == variableName) {
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| 51 | return CreateConstant(varNode.Weight);
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| 52 | } else {
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| 53 | return CreateConstant(0.0);
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| 54 | }
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| 55 | }
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| 56 | if (branch.Symbol is Addition) {
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| 57 | var sum = addSy.CreateTreeNode();
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| 58 | foreach (var subTree in branch.Subtrees) {
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| 59 | sum.AddSubtree(Derive(subTree, variableName));
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| 60 | }
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| 61 | return sum;
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| 62 | }
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| 63 | if (branch.Symbol is Subtraction) {
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| 64 | var sum = subSy.CreateTreeNode();
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| 65 | foreach (var subTree in branch.Subtrees) {
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| 66 | sum.AddSubtree(Derive(subTree, variableName));
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| 67 | }
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| 68 | return sum;
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| 69 | }
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| 70 | if (branch.Symbol is Multiplication) {
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| 71 | // (f * g)' = f'*g + f*g'
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| 72 | // for multiple factors: (f * g * h)' = ((f*g) * h)' = (f*g)' * h + (f*g) * h'
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| 73 |
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| 74 | if (branch.SubtreeCount >= 2) {
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| 75 | var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 76 | var g = (ISymbolicExpressionTreeNode)branch.GetSubtree(1).Clone();
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| 77 | var fprime = Derive(f, variableName);
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| 78 | var gprime = Derive(g, variableName);
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| 79 | var fgPrime = Sum(Product(f, gprime), Product(fprime, g));
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| 80 | for (int i = 2; i < branch.SubtreeCount; i++) {
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| 81 | var fg = Product((ISymbolicExpressionTreeNode)f.Clone(), (ISymbolicExpressionTreeNode)g.Clone());
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| 82 | var h = (ISymbolicExpressionTreeNode)branch.GetSubtree(i).Clone();
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| 83 | var hPrime = Derive(h, variableName);
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| 84 | fgPrime = Sum(Product(fgPrime, h), Product(fg, hPrime));
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| 85 | }
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| 86 | return fgPrime;
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| 87 | } else throw new ArgumentException();
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| 88 | }
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| 89 | if (branch.Symbol is Division) {
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| 90 | // (f/g)' = (f'g - g'f) / g²
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| 91 | if (branch.SubtreeCount == 1) {
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| 92 | var g = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 93 | var gPrime = Product(CreateConstant(-1.0), Derive(g, variableName));
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| 94 | var sqrNode = new Square().CreateTreeNode();
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| 95 | sqrNode.AddSubtree(g);
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| 96 | return Div(gPrime, sqrNode);
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| 97 | } else if (branch.SubtreeCount == 2) {
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| 98 | var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 99 | var g = (ISymbolicExpressionTreeNode)branch.GetSubtree(1).Clone();
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| 100 | var fprime = Derive(f, variableName);
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| 101 | var gprime = Derive(g, variableName);
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| 102 | var sqrNode = new Square().CreateTreeNode();
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| 103 | sqrNode.AddSubtree((ISymbolicExpressionTreeNode)branch.GetSubtree(1).Clone());
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| 104 | return Div(Subtract(Product(fprime, g), Product(f, gprime)), sqrNode);
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| 105 | } else throw new NotSupportedException();
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| 106 | }
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| 107 | if (branch.Symbol is Logarithm) {
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| 108 | var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 109 | return Product(Div(CreateConstant(1.0), f), Derive(f, variableName));
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| 110 | }
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| 111 | if (branch.Symbol is Exponential) {
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| 112 | var f = (ISymbolicExpressionTreeNode)branch.Clone();
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| 113 | return Product(f, Derive(branch.GetSubtree(0), variableName));
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| 114 | }
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| 115 | if(branch.Symbol is Square) {
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| 116 | var f = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 117 | return Product(Product(CreateConstant(2.0), f), Derive(f, variableName));
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| 118 | }
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| 119 | if(branch.Symbol is SquareRoot) {
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| 120 | var f = (ISymbolicExpressionTreeNode)branch.Clone();
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| 121 | var u = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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[16213] | 122 | return Product(Div(CreateConstant(1.0), Product(CreateConstant(2.0), f)), Derive(u, variableName));
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[16206] | 123 | }
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| 124 | if (branch.Symbol is Sine) {
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| 125 | var u = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 126 | var cos = (new Cosine()).CreateTreeNode();
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| 127 | cos.AddSubtree(u);
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| 128 | return Product(cos, Derive(u, variableName));
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| 129 | }
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| 130 | if (branch.Symbol is Cosine) {
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| 131 | var u = (ISymbolicExpressionTreeNode)branch.GetSubtree(0).Clone();
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| 132 | var sin = (new Sine()).CreateTreeNode();
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| 133 | sin.AddSubtree(u);
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| 134 | return Product(CreateConstant(-1.0), Product(sin, Derive(u, variableName)));
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| 135 | }
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[16216] | 136 | throw new NotSupportedException(string.Format("Symbol {0} is not supported.", branch.Symbol));
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[16206] | 137 | }
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| 138 |
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| 139 |
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| 140 | private static ISymbolicExpressionTreeNode Product(ISymbolicExpressionTreeNode f, ISymbolicExpressionTreeNode g) {
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| 141 | var product = mulSy.CreateTreeNode();
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| 142 | product.AddSubtree(f);
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| 143 | product.AddSubtree(g);
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| 144 | return product;
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| 145 | }
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| 146 | private static ISymbolicExpressionTreeNode Div(ISymbolicExpressionTreeNode f, ISymbolicExpressionTreeNode g) {
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| 147 | var div = divSy.CreateTreeNode();
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| 148 | div.AddSubtree(f);
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| 149 | div.AddSubtree(g);
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| 150 | return div;
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| 151 | }
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| 152 |
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| 153 | private static ISymbolicExpressionTreeNode Sum(ISymbolicExpressionTreeNode f, ISymbolicExpressionTreeNode g) {
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| 154 | var sum = addSy.CreateTreeNode();
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| 155 | sum.AddSubtree(f);
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| 156 | sum.AddSubtree(g);
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| 157 | return sum;
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| 158 | }
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| 159 | private static ISymbolicExpressionTreeNode Subtract(ISymbolicExpressionTreeNode f, ISymbolicExpressionTreeNode g) {
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| 160 | var sum = subSy.CreateTreeNode();
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| 161 | sum.AddSubtree(f);
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| 162 | sum.AddSubtree(g);
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| 163 | return sum;
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| 164 | }
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| 165 |
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| 166 | private static ISymbolicExpressionTreeNode CreateConstant(double v) {
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| 167 | var constNode = (ConstantTreeNode)constantSy.CreateTreeNode();
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| 168 | constNode.Value = v;
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| 169 | return constNode;
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| 170 | }
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| 171 |
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| 172 | public static bool IsCompatible(ISymbolicExpressionTree tree) {
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| 173 | var containsUnknownSymbol = (
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| 174 | from n in tree.Root.GetSubtree(0).IterateNodesPrefix()
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| 175 | where
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| 176 | !(n.Symbol is Variable) &&
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| 177 | !(n.Symbol is Constant) &&
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| 178 | !(n.Symbol is Addition) &&
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| 179 | !(n.Symbol is Subtraction) &&
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| 180 | !(n.Symbol is Multiplication) &&
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| 181 | !(n.Symbol is Division) &&
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| 182 | !(n.Symbol is Logarithm) &&
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| 183 | !(n.Symbol is Exponential) &&
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| 184 | !(n.Symbol is Square) &&
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| 185 | !(n.Symbol is SquareRoot) &&
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| 186 | !(n.Symbol is Sine) &&
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| 187 | !(n.Symbol is Cosine) &&
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| 188 | !(n.Symbol is StartSymbol)
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| 189 | select n).Any();
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| 190 | return !containsUnknownSymbol;
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| 191 | }
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| 192 | }
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| 193 | }
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