1 | #region License Information
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2 |
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3 | /* HeuristicLab
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4 | * Copyright (C) 2002-2016 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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5 | *
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6 | * This file is part of HeuristicLab.
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7 | *
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8 | * HeuristicLab is free software: you can redistribute it and/or modify
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9 | * it under the terms of the GNU General Public License as published by
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10 | * the Free Software Foundation, either version 3 of the License, or
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11 | * (at your option) any later version.
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12 | *
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13 | * HeuristicLab is distributed in the hope that it will be useful,
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14 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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15 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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16 | * GNU General Public License for more details.
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17 | *
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18 | * You should have received a copy of the GNU General Public License
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19 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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20 | */
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21 |
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22 | #endregion
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23 |
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24 | using System;
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25 | using System.Collections.Generic;
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26 | using System.Linq;
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27 | using HeuristicLab.Common;
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28 | using HeuristicLab.Core;
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29 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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30 |
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31 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic {
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32 | /// <summary>
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33 | /// Simplifier for symbolic expressions
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34 | /// </summary>
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35 | public class SymbolicDataAnalysisExpressionTreeSimplifier {
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36 | private Addition addSymbol = new Addition();
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37 | private Multiplication mulSymbol = new Multiplication();
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38 | private Division divSymbol = new Division();
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39 | private Constant constSymbol = new Constant();
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40 | private Variable varSymbol = new Variable();
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41 | private Logarithm logSymbol = new Logarithm();
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42 | private Exponential expSymbol = new Exponential();
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43 | private Root rootSymbol = new Root();
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44 | private Square sqrSymbol = new Square();
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45 | private SquareRoot sqrtSymbol = new SquareRoot();
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46 | private Power powSymbol = new Power();
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47 | private Sine sineSymbol = new Sine();
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48 | private Cosine cosineSymbol = new Cosine();
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49 | private Tangent tanSymbol = new Tangent();
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50 | private IfThenElse ifThenElseSymbol = new IfThenElse();
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51 | private And andSymbol = new And();
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52 | private Or orSymbol = new Or();
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53 | private Not notSymbol = new Not();
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54 | private GreaterThan gtSymbol = new GreaterThan();
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55 | private LessThan ltSymbol = new LessThan();
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56 | private Integral integralSymbol = new Integral();
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57 | private LaggedVariable laggedVariableSymbol = new LaggedVariable();
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58 | private TimeLag timeLagSymbol = new TimeLag();
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59 |
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60 | public ISymbolicExpressionTree Simplify(ISymbolicExpressionTree originalTree) {
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61 | var clone = (ISymbolicExpressionTreeNode)originalTree.Root.Clone();
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62 | // macro expand (initially no argument trees)
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63 | var macroExpandedTree = MacroExpand(clone, clone.GetSubtree(0), new List<ISymbolicExpressionTreeNode>());
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64 | ISymbolicExpressionTreeNode rootNode = (new ProgramRootSymbol()).CreateTreeNode();
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65 | rootNode.AddSubtree(GetSimplifiedTree(macroExpandedTree));
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66 | return new SymbolicExpressionTree(rootNode);
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67 | }
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68 |
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69 | // the argumentTrees list contains already expanded trees used as arguments for invocations
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70 | private ISymbolicExpressionTreeNode MacroExpand(ISymbolicExpressionTreeNode root, ISymbolicExpressionTreeNode node,
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71 | IList<ISymbolicExpressionTreeNode> argumentTrees) {
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72 | List<ISymbolicExpressionTreeNode> subtrees = new List<ISymbolicExpressionTreeNode>(node.Subtrees);
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73 | while (node.SubtreeCount > 0) node.RemoveSubtree(0);
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74 | if (node.Symbol is InvokeFunction) {
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75 | var invokeSym = node.Symbol as InvokeFunction;
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76 | var defunNode = FindFunctionDefinition(root, invokeSym.FunctionName);
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77 | var macroExpandedArguments = new List<ISymbolicExpressionTreeNode>();
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78 | foreach (var subtree in subtrees) {
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79 | macroExpandedArguments.Add(MacroExpand(root, subtree, argumentTrees));
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80 | }
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81 | return MacroExpand(root, defunNode, macroExpandedArguments);
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82 | } else if (node.Symbol is Argument) {
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83 | var argSym = node.Symbol as Argument;
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84 | // return the correct argument sub-tree (already macro-expanded)
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85 | return (SymbolicExpressionTreeNode)argumentTrees[argSym.ArgumentIndex].Clone();
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86 | } else {
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87 | // recursive application
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88 | foreach (var subtree in subtrees) {
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89 | node.AddSubtree(MacroExpand(root, subtree, argumentTrees));
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90 | }
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91 | return node;
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92 | }
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93 | }
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94 |
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95 | private ISymbolicExpressionTreeNode FindFunctionDefinition(ISymbolicExpressionTreeNode root, string functionName) {
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96 | foreach (var subtree in root.Subtrees.OfType<DefunTreeNode>()) {
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97 | if (subtree.FunctionName == functionName) return subtree.GetSubtree(0);
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98 | }
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99 |
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100 | throw new ArgumentException("Definition of function " + functionName + " not found.");
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101 | }
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102 |
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103 | #region symbol predicates
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104 |
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105 | // arithmetic
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106 | private bool IsDivision(ISymbolicExpressionTreeNode node) {
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107 | return node.Symbol is Division;
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108 | }
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109 |
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110 | private bool IsMultiplication(ISymbolicExpressionTreeNode node) {
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111 | return node.Symbol is Multiplication;
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112 | }
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113 |
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114 | private bool IsSubtraction(ISymbolicExpressionTreeNode node) {
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115 | return node.Symbol is Subtraction;
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116 | }
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117 |
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118 | private bool IsAddition(ISymbolicExpressionTreeNode node) {
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119 | return node.Symbol is Addition;
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120 | }
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121 |
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122 | private bool IsAverage(ISymbolicExpressionTreeNode node) {
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123 | return node.Symbol is Average;
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124 | }
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125 |
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126 | // exponential
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127 | private bool IsLog(ISymbolicExpressionTreeNode node) {
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128 | return node.Symbol is Logarithm;
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129 | }
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130 |
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131 | private bool IsExp(ISymbolicExpressionTreeNode node) {
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132 | return node.Symbol is Exponential;
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133 | }
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134 |
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135 | private bool IsRoot(ISymbolicExpressionTreeNode node) {
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136 | return node.Symbol is Root;
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137 | }
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138 |
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139 | private bool IsSquare(ISymbolicExpressionTreeNode node) {
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140 | return node.Symbol is Square;
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141 | }
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142 |
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143 | private bool IsSquareRoot(ISymbolicExpressionTreeNode node) {
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144 | return node.Symbol is SquareRoot;
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145 | }
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146 |
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147 | private bool IsPower(ISymbolicExpressionTreeNode node) {
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148 | return node.Symbol is Power;
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149 | }
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150 |
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151 | // trigonometric
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152 | private bool IsSine(ISymbolicExpressionTreeNode node) {
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153 | return node.Symbol is Sine;
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154 | }
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155 |
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156 | private bool IsCosine(ISymbolicExpressionTreeNode node) {
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157 | return node.Symbol is Cosine;
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158 | }
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159 |
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160 | private bool IsTangent(ISymbolicExpressionTreeNode node) {
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161 | return node.Symbol is Tangent;
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162 | }
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163 |
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164 | // boolean
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165 | private bool IsIfThenElse(ISymbolicExpressionTreeNode node) {
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166 | return node.Symbol is IfThenElse;
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167 | }
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168 |
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169 | private bool IsAnd(ISymbolicExpressionTreeNode node) {
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170 | return node.Symbol is And;
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171 | }
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172 |
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173 | private bool IsOr(ISymbolicExpressionTreeNode node) {
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174 | return node.Symbol is Or;
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175 | }
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176 |
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177 | private bool IsNot(ISymbolicExpressionTreeNode node) {
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178 | return node.Symbol is Not;
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179 | }
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180 |
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181 | // comparison
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182 | private bool IsGreaterThan(ISymbolicExpressionTreeNode node) {
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183 | return node.Symbol is GreaterThan;
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184 | }
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185 |
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186 | private bool IsLessThan(ISymbolicExpressionTreeNode node) {
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187 | return node.Symbol is LessThan;
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188 | }
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189 |
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190 | private bool IsBoolean(ISymbolicExpressionTreeNode node) {
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191 | return
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192 | node.Symbol is GreaterThan ||
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193 | node.Symbol is LessThan ||
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194 | node.Symbol is And ||
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195 | node.Symbol is Or;
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196 | }
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197 |
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198 | // terminals
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199 | private bool IsVariable(ISymbolicExpressionTreeNode node) {
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200 | return node.Symbol is Variable;
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201 | }
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202 |
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203 | private bool IsVariableBase(ISymbolicExpressionTreeNode node) {
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204 | return node is VariableTreeNodeBase;
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205 | }
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206 |
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207 | private bool IsFactor(ISymbolicExpressionTreeNode node) {
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208 | return node is FactorVariableTreeNode;
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209 | }
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210 |
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211 | private bool IsConstant(ISymbolicExpressionTreeNode node) {
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212 | return node.Symbol is Constant;
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213 | }
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214 |
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215 | // dynamic
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216 | private bool IsTimeLag(ISymbolicExpressionTreeNode node) {
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217 | return node.Symbol is TimeLag;
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218 | }
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219 |
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220 | private bool IsIntegral(ISymbolicExpressionTreeNode node) {
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221 | return node.Symbol is Integral;
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222 | }
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223 |
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224 | #endregion
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225 |
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226 | /// <summary>
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227 | /// Creates a new simplified tree
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228 | /// </summary>
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229 | /// <param name="original"></param>
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230 | /// <returns></returns>
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231 | public ISymbolicExpressionTreeNode GetSimplifiedTree(ISymbolicExpressionTreeNode original) {
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232 | if (IsConstant(original) || IsVariableBase(original)) {
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233 | return (ISymbolicExpressionTreeNode)original.Clone();
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234 | } else if (IsAddition(original)) {
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235 | return SimplifyAddition(original);
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236 | } else if (IsSubtraction(original)) {
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237 | return SimplifySubtraction(original);
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238 | } else if (IsMultiplication(original)) {
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239 | return SimplifyMultiplication(original);
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240 | } else if (IsDivision(original)) {
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241 | return SimplifyDivision(original);
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242 | } else if (IsAverage(original)) {
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243 | return SimplifyAverage(original);
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244 | } else if (IsLog(original)) {
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245 | return SimplifyLog(original);
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246 | } else if (IsExp(original)) {
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247 | return SimplifyExp(original);
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248 | } else if (IsSquare(original)) {
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249 | return SimplifySquare(original);
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250 | } else if (IsSquareRoot(original)) {
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251 | return SimplifySquareRoot(original);
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252 | } else if (IsPower(original)) {
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253 | return SimplifyPower(original);
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254 | } else if (IsRoot(original)) {
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255 | return SimplifyRoot(original);
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256 | } else if (IsSine(original)) {
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257 | return SimplifySine(original);
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258 | } else if (IsCosine(original)) {
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259 | return SimplifyCosine(original);
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260 | } else if (IsTangent(original)) {
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261 | return SimplifyTangent(original);
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262 | } else if (IsIfThenElse(original)) {
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263 | return SimplifyIfThenElse(original);
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264 | } else if (IsGreaterThan(original)) {
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265 | return SimplifyGreaterThan(original);
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266 | } else if (IsLessThan(original)) {
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267 | return SimplifyLessThan(original);
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268 | } else if (IsAnd(original)) {
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269 | return SimplifyAnd(original);
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270 | } else if (IsOr(original)) {
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271 | return SimplifyOr(original);
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272 | } else if (IsNot(original)) {
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273 | return SimplifyNot(original);
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274 | } else if (IsTimeLag(original)) {
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275 | return SimplifyTimeLag(original);
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276 | } else if (IsIntegral(original)) {
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277 | return SimplifyIntegral(original);
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278 | } else {
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279 | return SimplifyAny(original);
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280 | }
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281 | }
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282 |
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283 | #region specific simplification routines
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284 |
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285 | private ISymbolicExpressionTreeNode SimplifyAny(ISymbolicExpressionTreeNode original) {
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286 | // can't simplify this function but simplify all subtrees
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287 | List<ISymbolicExpressionTreeNode> subtrees = new List<ISymbolicExpressionTreeNode>(original.Subtrees);
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288 | while (original.Subtrees.Count() > 0) original.RemoveSubtree(0);
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289 | var clone = (SymbolicExpressionTreeNode)original.Clone();
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290 | List<ISymbolicExpressionTreeNode> simplifiedSubtrees = new List<ISymbolicExpressionTreeNode>();
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291 | foreach (var subtree in subtrees) {
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292 | simplifiedSubtrees.Add(GetSimplifiedTree(subtree));
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293 | original.AddSubtree(subtree);
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294 | }
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295 | foreach (var simplifiedSubtree in simplifiedSubtrees) {
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296 | clone.AddSubtree(simplifiedSubtree);
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297 | }
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298 | if (simplifiedSubtrees.TrueForAll(t => IsConstant(t))) {
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299 | SimplifyConstantExpression(clone);
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300 | }
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301 | return clone;
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302 | }
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303 |
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304 | private ISymbolicExpressionTreeNode SimplifyConstantExpression(ISymbolicExpressionTreeNode original) {
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305 | // not yet implemented
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306 | return original;
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307 | }
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308 |
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309 | private ISymbolicExpressionTreeNode SimplifyAverage(ISymbolicExpressionTreeNode original) {
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310 | if (original.Subtrees.Count() == 1) {
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311 | return GetSimplifiedTree(original.GetSubtree(0));
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312 | } else {
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313 | // simplify expressions x0..xn
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314 | // make sum(x0..xn) / n
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315 | var sum = original.Subtrees
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316 | .Select(GetSimplifiedTree)
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317 | .Aggregate(MakeSum);
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318 | return MakeFraction(sum, MakeConstant(original.Subtrees.Count()));
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319 | }
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320 | }
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321 |
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322 | private ISymbolicExpressionTreeNode SimplifyDivision(ISymbolicExpressionTreeNode original) {
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323 | if (original.Subtrees.Count() == 1) {
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324 | return Invert(GetSimplifiedTree(original.GetSubtree(0)));
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325 | } else {
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326 | // simplify expressions x0..xn
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327 | // make multiplication (x0 * 1/(x1 * x1 * .. * xn))
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328 | var first = original.GetSubtree(0);
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329 | var second = original.GetSubtree(1);
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330 | var remaining = original.Subtrees.Skip(2);
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331 | return
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332 | MakeProduct(GetSimplifiedTree(first),
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333 | Invert(remaining.Aggregate(GetSimplifiedTree(second), (a, b) => MakeProduct(a, GetSimplifiedTree(b)))));
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334 | }
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335 | }
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336 |
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337 | private ISymbolicExpressionTreeNode SimplifyMultiplication(ISymbolicExpressionTreeNode original) {
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338 | if (original.Subtrees.Count() == 1) {
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339 | return GetSimplifiedTree(original.GetSubtree(0));
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340 | } else {
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341 | return original.Subtrees
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342 | .Select(GetSimplifiedTree)
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343 | .Aggregate(MakeProduct);
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344 | }
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345 | }
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346 |
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347 | private ISymbolicExpressionTreeNode SimplifySubtraction(ISymbolicExpressionTreeNode original) {
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348 | if (original.Subtrees.Count() == 1) {
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349 | return Negate(GetSimplifiedTree(original.GetSubtree(0)));
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350 | } else {
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351 | // simplify expressions x0..xn
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352 | // make addition (x0,-x1..-xn)
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353 | var first = original.Subtrees.First();
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354 | var remaining = original.Subtrees.Skip(1);
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355 | return remaining.Aggregate(GetSimplifiedTree(first), (a, b) => MakeSum(a, Negate(GetSimplifiedTree(b))));
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356 | }
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357 | }
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358 |
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359 | private ISymbolicExpressionTreeNode SimplifyAddition(ISymbolicExpressionTreeNode original) {
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360 | if (original.Subtrees.Count() == 1) {
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361 | return GetSimplifiedTree(original.GetSubtree(0));
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362 | } else {
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363 | // simplify expression x0..xn
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364 | // make addition (x0..xn)
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365 | return original.Subtrees
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366 | .Select(GetSimplifiedTree)
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367 | .Aggregate(MakeSum);
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368 | }
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369 | }
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370 |
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371 | private ISymbolicExpressionTreeNode SimplifyNot(ISymbolicExpressionTreeNode original) {
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372 | return MakeNot(GetSimplifiedTree(original.GetSubtree(0)));
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373 | }
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374 |
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375 | private ISymbolicExpressionTreeNode SimplifyOr(ISymbolicExpressionTreeNode original) {
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376 | return original.Subtrees
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377 | .Select(GetSimplifiedTree)
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378 | .Aggregate(MakeOr);
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379 | }
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380 |
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381 | private ISymbolicExpressionTreeNode SimplifyAnd(ISymbolicExpressionTreeNode original) {
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382 | return original.Subtrees
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383 | .Select(GetSimplifiedTree)
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384 | .Aggregate(MakeAnd);
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385 | }
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386 |
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387 | private ISymbolicExpressionTreeNode SimplifyLessThan(ISymbolicExpressionTreeNode original) {
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388 | return MakeLessThan(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
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389 | }
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390 |
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391 | private ISymbolicExpressionTreeNode SimplifyGreaterThan(ISymbolicExpressionTreeNode original) {
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392 | return MakeGreaterThan(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
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393 | }
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394 |
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395 | private ISymbolicExpressionTreeNode SimplifyIfThenElse(ISymbolicExpressionTreeNode original) {
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396 | return MakeIfThenElse(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)),
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397 | GetSimplifiedTree(original.GetSubtree(2)));
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398 | }
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399 |
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400 | private ISymbolicExpressionTreeNode SimplifyTangent(ISymbolicExpressionTreeNode original) {
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401 | return MakeTangent(GetSimplifiedTree(original.GetSubtree(0)));
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402 | }
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403 |
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404 | private ISymbolicExpressionTreeNode SimplifyCosine(ISymbolicExpressionTreeNode original) {
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405 | return MakeCosine(GetSimplifiedTree(original.GetSubtree(0)));
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406 | }
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407 |
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408 | private ISymbolicExpressionTreeNode SimplifySine(ISymbolicExpressionTreeNode original) {
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409 | return MakeSine(GetSimplifiedTree(original.GetSubtree(0)));
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410 | }
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411 |
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412 | private ISymbolicExpressionTreeNode SimplifyExp(ISymbolicExpressionTreeNode original) {
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413 | return MakeExp(GetSimplifiedTree(original.GetSubtree(0)));
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414 | }
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415 |
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416 | private ISymbolicExpressionTreeNode SimplifySquare(ISymbolicExpressionTreeNode original) {
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417 | return MakeSquare(GetSimplifiedTree(original.GetSubtree(0)));
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418 | }
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419 |
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420 | private ISymbolicExpressionTreeNode SimplifySquareRoot(ISymbolicExpressionTreeNode original) {
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421 | return MakeSquareRoot(GetSimplifiedTree(original.GetSubtree(0)));
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422 | }
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423 |
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424 | private ISymbolicExpressionTreeNode SimplifyLog(ISymbolicExpressionTreeNode original) {
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425 | return MakeLog(GetSimplifiedTree(original.GetSubtree(0)));
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426 | }
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427 |
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428 | private ISymbolicExpressionTreeNode SimplifyRoot(ISymbolicExpressionTreeNode original) {
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429 | return MakeRoot(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
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430 | }
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431 |
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432 | private ISymbolicExpressionTreeNode SimplifyPower(ISymbolicExpressionTreeNode original) {
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433 | return MakePower(GetSimplifiedTree(original.GetSubtree(0)), GetSimplifiedTree(original.GetSubtree(1)));
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434 | }
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435 |
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436 | private ISymbolicExpressionTreeNode SimplifyTimeLag(ISymbolicExpressionTreeNode original) {
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437 | var laggedTreeNode = original as ILaggedTreeNode;
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438 | var simplifiedSubtree = GetSimplifiedTree(original.GetSubtree(0));
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439 | if (!ContainsVariableCondition(simplifiedSubtree)) {
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440 | return AddLagToDynamicNodes(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
441 | } else {
|
---|
442 | return MakeTimeLag(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
443 | }
|
---|
444 | }
|
---|
445 |
|
---|
446 | private ISymbolicExpressionTreeNode SimplifyIntegral(ISymbolicExpressionTreeNode original) {
|
---|
447 | var laggedTreeNode = original as ILaggedTreeNode;
|
---|
448 | var simplifiedSubtree = GetSimplifiedTree(original.GetSubtree(0));
|
---|
449 | if (IsConstant(simplifiedSubtree)) {
|
---|
450 | return GetSimplifiedTree(MakeProduct(simplifiedSubtree, MakeConstant(-laggedTreeNode.Lag)));
|
---|
451 | } else {
|
---|
452 | return MakeIntegral(simplifiedSubtree, laggedTreeNode.Lag);
|
---|
453 | }
|
---|
454 | }
|
---|
455 |
|
---|
456 | #endregion
|
---|
457 |
|
---|
458 | #region low level tree restructuring
|
---|
459 |
|
---|
460 | private ISymbolicExpressionTreeNode MakeTimeLag(ISymbolicExpressionTreeNode subtree, int lag) {
|
---|
461 | if (lag == 0) return subtree;
|
---|
462 | if (IsConstant(subtree)) return subtree;
|
---|
463 | var lagNode = (LaggedTreeNode)timeLagSymbol.CreateTreeNode();
|
---|
464 | lagNode.Lag = lag;
|
---|
465 | lagNode.AddSubtree(subtree);
|
---|
466 | return lagNode;
|
---|
467 | }
|
---|
468 |
|
---|
469 | private ISymbolicExpressionTreeNode MakeIntegral(ISymbolicExpressionTreeNode subtree, int lag) {
|
---|
470 | if (lag == 0) return subtree;
|
---|
471 | else if (lag == -1 || lag == 1) {
|
---|
472 | return MakeSum(subtree, AddLagToDynamicNodes((ISymbolicExpressionTreeNode)subtree.Clone(), lag));
|
---|
473 | } else {
|
---|
474 | var node = (LaggedTreeNode)integralSymbol.CreateTreeNode();
|
---|
475 | node.Lag = lag;
|
---|
476 | node.AddSubtree(subtree);
|
---|
477 | return node;
|
---|
478 | }
|
---|
479 | }
|
---|
480 |
|
---|
481 | private ISymbolicExpressionTreeNode MakeNot(ISymbolicExpressionTreeNode t) {
|
---|
482 | if (IsConstant(t)) {
|
---|
483 | var constNode = t as ConstantTreeNode;
|
---|
484 | if (constNode.Value > 0) return MakeConstant(-1.0);
|
---|
485 | else return MakeConstant(1.0);
|
---|
486 | } else if (IsNot(t)) {
|
---|
487 | return t.GetSubtree(0);
|
---|
488 | } else if (!IsBoolean(t)) {
|
---|
489 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
490 | gtNode.AddSubtree(t);
|
---|
491 | gtNode.AddSubtree(MakeConstant(0.0));
|
---|
492 | var notNode = notSymbol.CreateTreeNode();
|
---|
493 | notNode.AddSubtree(gtNode);
|
---|
494 | return notNode;
|
---|
495 | } else {
|
---|
496 | var notNode = notSymbol.CreateTreeNode();
|
---|
497 | notNode.AddSubtree(t);
|
---|
498 | return notNode;
|
---|
499 | }
|
---|
500 | }
|
---|
501 |
|
---|
502 | private ISymbolicExpressionTreeNode MakeOr(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
503 | if (IsConstant(a) && IsConstant(b)) {
|
---|
504 | var constA = a as ConstantTreeNode;
|
---|
505 | var constB = b as ConstantTreeNode;
|
---|
506 | if (constA.Value > 0.0 || constB.Value > 0.0) {
|
---|
507 | return MakeConstant(1.0);
|
---|
508 | } else {
|
---|
509 | return MakeConstant(-1.0);
|
---|
510 | }
|
---|
511 | } else if (IsConstant(a)) {
|
---|
512 | return MakeOr(b, a);
|
---|
513 | } else if (IsConstant(b)) {
|
---|
514 | var constT = b as ConstantTreeNode;
|
---|
515 | if (constT.Value > 0.0) {
|
---|
516 | // boolean expression is necessarily true
|
---|
517 | return MakeConstant(1.0);
|
---|
518 | } else {
|
---|
519 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
|
---|
520 | var orNode = orSymbol.CreateTreeNode();
|
---|
521 | orNode.AddSubtree(a);
|
---|
522 | return orNode;
|
---|
523 | }
|
---|
524 | } else {
|
---|
525 | var orNode = orSymbol.CreateTreeNode();
|
---|
526 | orNode.AddSubtree(a);
|
---|
527 | orNode.AddSubtree(b);
|
---|
528 | return orNode;
|
---|
529 | }
|
---|
530 | }
|
---|
531 |
|
---|
532 | private ISymbolicExpressionTreeNode MakeAnd(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
533 | if (IsConstant(a) && IsConstant(b)) {
|
---|
534 | var constA = a as ConstantTreeNode;
|
---|
535 | var constB = b as ConstantTreeNode;
|
---|
536 | if (constA.Value > 0.0 && constB.Value > 0.0) {
|
---|
537 | return MakeConstant(1.0);
|
---|
538 | } else {
|
---|
539 | return MakeConstant(-1.0);
|
---|
540 | }
|
---|
541 | } else if (IsConstant(a)) {
|
---|
542 | return MakeAnd(b, a);
|
---|
543 | } else if (IsConstant(b)) {
|
---|
544 | var constB = b as ConstantTreeNode;
|
---|
545 | if (constB.Value > 0.0) {
|
---|
546 | // the constant value has no effect on the result of the boolean condition so we can drop the constant term
|
---|
547 | var andNode = andSymbol.CreateTreeNode();
|
---|
548 | andNode.AddSubtree(a);
|
---|
549 | return andNode;
|
---|
550 | } else {
|
---|
551 | // boolean expression is necessarily false
|
---|
552 | return MakeConstant(-1.0);
|
---|
553 | }
|
---|
554 | } else {
|
---|
555 | var andNode = andSymbol.CreateTreeNode();
|
---|
556 | andNode.AddSubtree(a);
|
---|
557 | andNode.AddSubtree(b);
|
---|
558 | return andNode;
|
---|
559 | }
|
---|
560 | }
|
---|
561 |
|
---|
562 | private ISymbolicExpressionTreeNode MakeLessThan(ISymbolicExpressionTreeNode leftSide,
|
---|
563 | ISymbolicExpressionTreeNode rightSide) {
|
---|
564 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
565 | var lsConst = leftSide as ConstantTreeNode;
|
---|
566 | var rsConst = rightSide as ConstantTreeNode;
|
---|
567 | if (lsConst.Value < rsConst.Value) return MakeConstant(1.0);
|
---|
568 | else return MakeConstant(-1.0);
|
---|
569 | } else {
|
---|
570 | var ltNode = ltSymbol.CreateTreeNode();
|
---|
571 | ltNode.AddSubtree(leftSide);
|
---|
572 | ltNode.AddSubtree(rightSide);
|
---|
573 | return ltNode;
|
---|
574 | }
|
---|
575 | }
|
---|
576 |
|
---|
577 | private ISymbolicExpressionTreeNode MakeGreaterThan(ISymbolicExpressionTreeNode leftSide,
|
---|
578 | ISymbolicExpressionTreeNode rightSide) {
|
---|
579 | if (IsConstant(leftSide) && IsConstant(rightSide)) {
|
---|
580 | var lsConst = leftSide as ConstantTreeNode;
|
---|
581 | var rsConst = rightSide as ConstantTreeNode;
|
---|
582 | if (lsConst.Value > rsConst.Value) return MakeConstant(1.0);
|
---|
583 | else return MakeConstant(-1.0);
|
---|
584 | } else {
|
---|
585 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
586 | gtNode.AddSubtree(leftSide);
|
---|
587 | gtNode.AddSubtree(rightSide);
|
---|
588 | return gtNode;
|
---|
589 | }
|
---|
590 | }
|
---|
591 |
|
---|
592 | private ISymbolicExpressionTreeNode MakeIfThenElse(ISymbolicExpressionTreeNode condition,
|
---|
593 | ISymbolicExpressionTreeNode trueBranch, ISymbolicExpressionTreeNode falseBranch) {
|
---|
594 | if (IsConstant(condition)) {
|
---|
595 | var constT = condition as ConstantTreeNode;
|
---|
596 | if (constT.Value > 0.0) return trueBranch;
|
---|
597 | else return falseBranch;
|
---|
598 | } else {
|
---|
599 | var ifNode = ifThenElseSymbol.CreateTreeNode();
|
---|
600 | if (IsBoolean(condition)) {
|
---|
601 | ifNode.AddSubtree(condition);
|
---|
602 | } else {
|
---|
603 | var gtNode = gtSymbol.CreateTreeNode();
|
---|
604 | gtNode.AddSubtree(condition);
|
---|
605 | gtNode.AddSubtree(MakeConstant(0.0));
|
---|
606 | ifNode.AddSubtree(gtNode);
|
---|
607 | }
|
---|
608 | ifNode.AddSubtree(trueBranch);
|
---|
609 | ifNode.AddSubtree(falseBranch);
|
---|
610 | return ifNode;
|
---|
611 | }
|
---|
612 | }
|
---|
613 |
|
---|
614 | private ISymbolicExpressionTreeNode MakeSine(ISymbolicExpressionTreeNode node) {
|
---|
615 | if (IsConstant(node)) {
|
---|
616 | var constT = node as ConstantTreeNode;
|
---|
617 | return MakeConstant(Math.Sin(constT.Value));
|
---|
618 | } else {
|
---|
619 | var sineNode = sineSymbol.CreateTreeNode();
|
---|
620 | sineNode.AddSubtree(node);
|
---|
621 | return sineNode;
|
---|
622 | }
|
---|
623 | }
|
---|
624 |
|
---|
625 | private ISymbolicExpressionTreeNode MakeTangent(ISymbolicExpressionTreeNode node) {
|
---|
626 | if (IsConstant(node)) {
|
---|
627 | var constT = node as ConstantTreeNode;
|
---|
628 | return MakeConstant(Math.Tan(constT.Value));
|
---|
629 | } else {
|
---|
630 | var tanNode = tanSymbol.CreateTreeNode();
|
---|
631 | tanNode.AddSubtree(node);
|
---|
632 | return tanNode;
|
---|
633 | }
|
---|
634 | }
|
---|
635 |
|
---|
636 | private ISymbolicExpressionTreeNode MakeCosine(ISymbolicExpressionTreeNode node) {
|
---|
637 | if (IsConstant(node)) {
|
---|
638 | var constT = node as ConstantTreeNode;
|
---|
639 | return MakeConstant(Math.Cos(constT.Value));
|
---|
640 | } else {
|
---|
641 | var cosNode = cosineSymbol.CreateTreeNode();
|
---|
642 | cosNode.AddSubtree(node);
|
---|
643 | return cosNode;
|
---|
644 | }
|
---|
645 | }
|
---|
646 |
|
---|
647 | private ISymbolicExpressionTreeNode MakeExp(ISymbolicExpressionTreeNode node) {
|
---|
648 | if (IsConstant(node)) {
|
---|
649 | var constT = node as ConstantTreeNode;
|
---|
650 | return MakeConstant(Math.Exp(constT.Value));
|
---|
651 | } else if (IsFactor(node)) {
|
---|
652 | var factNode = node as FactorVariableTreeNode;
|
---|
653 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Exp(w)));
|
---|
654 | } else if (IsLog(node)) {
|
---|
655 | return node.GetSubtree(0);
|
---|
656 | } else if (IsAddition(node)) {
|
---|
657 | return node.Subtrees.Select(s => MakeExp(s)).Aggregate((s, t) => MakeProduct(s, t));
|
---|
658 | } else if (IsSubtraction(node)) {
|
---|
659 | return node.Subtrees.Select(s => MakeExp(s)).Aggregate((s, t) => MakeProduct(s, Negate(t)));
|
---|
660 | } else {
|
---|
661 | var expNode = expSymbol.CreateTreeNode();
|
---|
662 | expNode.AddSubtree(node);
|
---|
663 | return expNode;
|
---|
664 | }
|
---|
665 | }
|
---|
666 |
|
---|
667 | private ISymbolicExpressionTreeNode MakeSquare(ISymbolicExpressionTreeNode node) {
|
---|
668 | if (IsConstant(node)) {
|
---|
669 | var constT = node as ConstantTreeNode;
|
---|
670 | return MakeConstant(constT.Value * constT.Value);
|
---|
671 | } else if (IsFactor(node)) {
|
---|
672 | var factNode = node as FactorVariableTreeNode;
|
---|
673 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => w * w));
|
---|
674 | } else if (IsSquareRoot(node)) {
|
---|
675 | return node.GetSubtree(0);
|
---|
676 | } else {
|
---|
677 | var sqrNode = sqrSymbol.CreateTreeNode();
|
---|
678 | sqrNode.AddSubtree(node);
|
---|
679 | return sqrNode;
|
---|
680 | }
|
---|
681 | }
|
---|
682 |
|
---|
683 | private ISymbolicExpressionTreeNode MakeSquareRoot(ISymbolicExpressionTreeNode node) {
|
---|
684 | if (IsConstant(node)) {
|
---|
685 | var constT = node as ConstantTreeNode;
|
---|
686 | return MakeConstant(Math.Sqrt(constT.Value));
|
---|
687 | } else if (IsFactor(node)) {
|
---|
688 | var factNode = node as FactorVariableTreeNode;
|
---|
689 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Sqrt(w)));
|
---|
690 | } else if (IsSquare(node)) {
|
---|
691 | return node.GetSubtree(0);
|
---|
692 | } else {
|
---|
693 | var sqrtNode = sqrtSymbol.CreateTreeNode();
|
---|
694 | sqrtNode.AddSubtree(node);
|
---|
695 | return sqrtNode;
|
---|
696 | }
|
---|
697 | }
|
---|
698 |
|
---|
699 | private ISymbolicExpressionTreeNode MakeLog(ISymbolicExpressionTreeNode node) {
|
---|
700 | if (IsConstant(node)) {
|
---|
701 | var constT = node as ConstantTreeNode;
|
---|
702 | return MakeConstant(Math.Log(constT.Value));
|
---|
703 | } else if (IsFactor(node)) {
|
---|
704 | var factNode = node as FactorVariableTreeNode;
|
---|
705 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Log(w)));
|
---|
706 | } else if (IsExp(node)) {
|
---|
707 | return node.GetSubtree(0);
|
---|
708 | } else if (IsSquareRoot(node)) {
|
---|
709 | return MakeFraction(MakeLog(node.GetSubtree(0)), MakeConstant(2.0));
|
---|
710 | } else {
|
---|
711 | var logNode = logSymbol.CreateTreeNode();
|
---|
712 | logNode.AddSubtree(node);
|
---|
713 | return logNode;
|
---|
714 | }
|
---|
715 | }
|
---|
716 |
|
---|
717 | private ISymbolicExpressionTreeNode MakeRoot(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
718 | if (IsConstant(a) && IsConstant(b)) {
|
---|
719 | var constA = a as ConstantTreeNode;
|
---|
720 | var constB = b as ConstantTreeNode;
|
---|
721 | return MakeConstant(Math.Pow(constA.Value, 1.0 / Math.Round(constB.Value)));
|
---|
722 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
723 | var factNode = a as FactorVariableTreeNode;
|
---|
724 | var constNode = b as ConstantTreeNode;
|
---|
725 | return MakeFactor(factNode.Symbol, factNode.VariableName,
|
---|
726 | factNode.Weights.Select(w => Math.Pow(w, 1.0 / Math.Round(constNode.Value))));
|
---|
727 | } else if (IsConstant(a) && IsFactor(b)) {
|
---|
728 | var constNode = a as ConstantTreeNode;
|
---|
729 | var factNode = b as FactorVariableTreeNode;
|
---|
730 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(constNode.Value, 1.0 / Math.Round(w))));
|
---|
731 | } else if (IsFactor(a) && IsFactor(b) && AreSameVariable(a, b)) {
|
---|
732 | var node0 = a as FactorVariableTreeNode;
|
---|
733 | var node1 = b as FactorVariableTreeNode;
|
---|
734 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => Math.Pow(u, 1.0 / Math.Round(v))));
|
---|
735 | } else if (IsConstant(b)) {
|
---|
736 | var constB = b as ConstantTreeNode;
|
---|
737 | var constBValue = Math.Round(constB.Value);
|
---|
738 | if (constBValue.IsAlmost(1.0)) {
|
---|
739 | return a;
|
---|
740 | } else if (constBValue.IsAlmost(0.0)) {
|
---|
741 | return MakeConstant(1.0);
|
---|
742 | } else if (constBValue.IsAlmost(-1.0)) {
|
---|
743 | return MakeFraction(MakeConstant(1.0), a);
|
---|
744 | } else if (constBValue < 0) {
|
---|
745 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
746 | rootNode.AddSubtree(a);
|
---|
747 | rootNode.AddSubtree(MakeConstant(-1.0 * constBValue));
|
---|
748 | return MakeFraction(MakeConstant(1.0), rootNode);
|
---|
749 | } else {
|
---|
750 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
751 | rootNode.AddSubtree(a);
|
---|
752 | rootNode.AddSubtree(MakeConstant(constBValue));
|
---|
753 | return rootNode;
|
---|
754 | }
|
---|
755 | } else {
|
---|
756 | var rootNode = rootSymbol.CreateTreeNode();
|
---|
757 | rootNode.AddSubtree(a);
|
---|
758 | rootNode.AddSubtree(b);
|
---|
759 | return rootNode;
|
---|
760 | }
|
---|
761 | }
|
---|
762 |
|
---|
763 |
|
---|
764 | private ISymbolicExpressionTreeNode MakePower(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
765 | if (IsConstant(a) && IsConstant(b)) {
|
---|
766 | var constA = a as ConstantTreeNode;
|
---|
767 | var constB = b as ConstantTreeNode;
|
---|
768 | return MakeConstant(Math.Pow(constA.Value, Math.Round(constB.Value)));
|
---|
769 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
770 | var factNode = a as FactorVariableTreeNode;
|
---|
771 | var constNode = b as ConstantTreeNode;
|
---|
772 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(w, Math.Round(constNode.Value))));
|
---|
773 | } else if (IsConstant(a) && IsFactor(b)) {
|
---|
774 | var constNode = a as ConstantTreeNode;
|
---|
775 | var factNode = b as FactorVariableTreeNode;
|
---|
776 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => Math.Pow(constNode.Value, Math.Round(w))));
|
---|
777 | } else if (IsFactor(a) && IsFactor(b) && AreSameVariable(a, b)) {
|
---|
778 | var node0 = a as FactorVariableTreeNode;
|
---|
779 | var node1 = b as FactorVariableTreeNode;
|
---|
780 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => Math.Pow(u, Math.Round(v))));
|
---|
781 | } else if (IsConstant(b)) {
|
---|
782 | var constB = b as ConstantTreeNode;
|
---|
783 | double exponent = Math.Round(constB.Value);
|
---|
784 | if (exponent.IsAlmost(0.0)) {
|
---|
785 | return MakeConstant(1.0);
|
---|
786 | } else if (exponent.IsAlmost(1.0)) {
|
---|
787 | return a;
|
---|
788 | } else if (exponent.IsAlmost(-1.0)) {
|
---|
789 | return MakeFraction(MakeConstant(1.0), a);
|
---|
790 | } else if (exponent < 0) {
|
---|
791 | var powNode = powSymbol.CreateTreeNode();
|
---|
792 | powNode.AddSubtree(a);
|
---|
793 | powNode.AddSubtree(MakeConstant(-1.0 * exponent));
|
---|
794 | return MakeFraction(MakeConstant(1.0), powNode);
|
---|
795 | } else {
|
---|
796 | var powNode = powSymbol.CreateTreeNode();
|
---|
797 | powNode.AddSubtree(a);
|
---|
798 | powNode.AddSubtree(MakeConstant(exponent));
|
---|
799 | return powNode;
|
---|
800 | }
|
---|
801 | } else {
|
---|
802 | var powNode = powSymbol.CreateTreeNode();
|
---|
803 | powNode.AddSubtree(a);
|
---|
804 | powNode.AddSubtree(b);
|
---|
805 | return powNode;
|
---|
806 | }
|
---|
807 | }
|
---|
808 |
|
---|
809 |
|
---|
810 | // MakeFraction, MakeProduct and MakeSum take two already simplified trees and create a new simplified tree
|
---|
811 | private ISymbolicExpressionTreeNode MakeFraction(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
812 | if (IsConstant(a) && IsConstant(b)) {
|
---|
813 | // fold constants
|
---|
814 | return MakeConstant(((ConstantTreeNode)a).Value / ((ConstantTreeNode)b).Value);
|
---|
815 | } else if ((IsConstant(a) && !((ConstantTreeNode)a).Value.IsAlmost(1.0))) {
|
---|
816 | return MakeFraction(MakeConstant(1.0), MakeProduct(b, Invert(a)));
|
---|
817 | } else if (IsVariableBase(a) && IsConstant(b)) {
|
---|
818 | // merge constant values into variable weights
|
---|
819 | var constB = ((ConstantTreeNode)b).Value;
|
---|
820 | ((VariableTreeNodeBase)a).Weight /= constB;
|
---|
821 | return a;
|
---|
822 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
823 | var factNode = a as FactorVariableTreeNode;
|
---|
824 | var constNode = b as ConstantTreeNode;
|
---|
825 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select(w => w / constNode.Value));
|
---|
826 | } else if (IsFactor(a) && IsFactor(b) && AreSameVariable(a, b)) {
|
---|
827 | var node0 = a as FactorVariableTreeNode;
|
---|
828 | var node1 = b as FactorVariableTreeNode;
|
---|
829 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u / v));
|
---|
830 | } else if (IsFactor(a)) {
|
---|
831 | return MakeFraction(MakeConstant(1.0), MakeProduct(b, Invert(a)));
|
---|
832 | } else if (IsVariableBase(a) && IsVariableBase(b) && AreSameVariable(a, b)) {
|
---|
833 | // cancel variables
|
---|
834 | var aVar = a as VariableTreeNode;
|
---|
835 | var bVar = b as VariableTreeNode;
|
---|
836 | return MakeConstant(aVar.Weight / bVar.Weight);
|
---|
837 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
838 | return a.Subtrees
|
---|
839 | .Select(x => GetSimplifiedTree(x))
|
---|
840 | .Select(x => MakeFraction(x, b))
|
---|
841 | .Aggregate((c, d) => MakeSum(c, d));
|
---|
842 | } else if (IsMultiplication(a) && IsConstant(b)) {
|
---|
843 | return MakeProduct(a, Invert(b));
|
---|
844 | } else if (IsDivision(a) && IsConstant(b)) {
|
---|
845 | // (a1 / a2) / c => (a1 / (a2 * c))
|
---|
846 | return MakeFraction(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
847 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
848 | // (a1 / a2) / (b1 / b2) =>
|
---|
849 | return MakeFraction(MakeProduct(a.GetSubtree(0), b.GetSubtree(1)), MakeProduct(a.GetSubtree(1), b.GetSubtree(0)));
|
---|
850 | } else if (IsDivision(a)) {
|
---|
851 | // (a1 / a2) / b => (a1 / (a2 * b))
|
---|
852 | return MakeFraction(a.GetSubtree(0), MakeProduct(a.GetSubtree(1), b));
|
---|
853 | } else if (IsDivision(b)) {
|
---|
854 | // a / (b1 / b2) => (a * b2) / b1
|
---|
855 | return MakeFraction(MakeProduct(a, b.GetSubtree(1)), b.GetSubtree(0));
|
---|
856 | } else {
|
---|
857 | var div = divSymbol.CreateTreeNode();
|
---|
858 | div.AddSubtree(a);
|
---|
859 | div.AddSubtree(b);
|
---|
860 | return div;
|
---|
861 | }
|
---|
862 | }
|
---|
863 |
|
---|
864 | private ISymbolicExpressionTreeNode MakeSum(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
865 | if (IsConstant(a) && IsConstant(b)) {
|
---|
866 | // fold constants
|
---|
867 | ((ConstantTreeNode)a).Value += ((ConstantTreeNode)b).Value;
|
---|
868 | return a;
|
---|
869 | } else if (IsConstant(a)) {
|
---|
870 | // c + x => x + c
|
---|
871 | // b is not constant => make sure constant is on the right
|
---|
872 | return MakeSum(b, a);
|
---|
873 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(0.0)) {
|
---|
874 | // x + 0 => x
|
---|
875 | return a;
|
---|
876 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
877 | var factNode = a as FactorVariableTreeNode;
|
---|
878 | var constNode = b as ConstantTreeNode;
|
---|
879 | return MakeFactor(factNode.Symbol, factNode.VariableName, factNode.Weights.Select((w) => w + constNode.Value));
|
---|
880 | } else if (IsFactor(a) && IsFactor(b) && AreSameVariable(a, b)) {
|
---|
881 | var node0 = a as FactorVariableTreeNode;
|
---|
882 | var node1 = b as FactorVariableTreeNode;
|
---|
883 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u + v));
|
---|
884 | } else if (IsAddition(a) && IsAddition(b)) {
|
---|
885 | // merge additions
|
---|
886 | var add = addSymbol.CreateTreeNode();
|
---|
887 | // add all sub trees except for the last
|
---|
888 | for (int i = 0; i < a.Subtrees.Count() - 1; i++) add.AddSubtree(a.GetSubtree(i));
|
---|
889 | for (int i = 0; i < b.Subtrees.Count() - 1; i++) add.AddSubtree(b.GetSubtree(i));
|
---|
890 | if (IsConstant(a.Subtrees.Last()) && IsConstant(b.Subtrees.Last())) {
|
---|
891 | add.AddSubtree(MakeSum(a.Subtrees.Last(), b.Subtrees.Last()));
|
---|
892 | } else if (IsConstant(a.Subtrees.Last())) {
|
---|
893 | add.AddSubtree(b.Subtrees.Last());
|
---|
894 | add.AddSubtree(a.Subtrees.Last());
|
---|
895 | } else {
|
---|
896 | add.AddSubtree(a.Subtrees.Last());
|
---|
897 | add.AddSubtree(b.Subtrees.Last());
|
---|
898 | }
|
---|
899 | MergeVariablesInSum(add);
|
---|
900 | if (add.Subtrees.Count() == 1) {
|
---|
901 | return add.GetSubtree(0);
|
---|
902 | } else {
|
---|
903 | return add;
|
---|
904 | }
|
---|
905 | } else if (IsAddition(b)) {
|
---|
906 | return MakeSum(b, a);
|
---|
907 | } else if (IsAddition(a) && IsConstant(b)) {
|
---|
908 | // a is an addition and b is a constant => append b to a and make sure the constants are merged
|
---|
909 | var add = addSymbol.CreateTreeNode();
|
---|
910 | // add all sub trees except for the last
|
---|
911 | for (int i = 0; i < a.Subtrees.Count() - 1; i++) add.AddSubtree(a.GetSubtree(i));
|
---|
912 | if (IsConstant(a.Subtrees.Last()))
|
---|
913 | add.AddSubtree(MakeSum(a.Subtrees.Last(), b));
|
---|
914 | else {
|
---|
915 | add.AddSubtree(a.Subtrees.Last());
|
---|
916 | add.AddSubtree(b);
|
---|
917 | }
|
---|
918 | return add;
|
---|
919 | } else if (IsAddition(a)) {
|
---|
920 | // a is already an addition => append b
|
---|
921 | var add = addSymbol.CreateTreeNode();
|
---|
922 | add.AddSubtree(b);
|
---|
923 | foreach (var subtree in a.Subtrees) {
|
---|
924 | add.AddSubtree(subtree);
|
---|
925 | }
|
---|
926 | MergeVariablesInSum(add);
|
---|
927 | if (add.Subtrees.Count() == 1) {
|
---|
928 | return add.GetSubtree(0);
|
---|
929 | } else {
|
---|
930 | return add;
|
---|
931 | }
|
---|
932 | } else {
|
---|
933 | var add = addSymbol.CreateTreeNode();
|
---|
934 | add.AddSubtree(a);
|
---|
935 | add.AddSubtree(b);
|
---|
936 | MergeVariablesInSum(add);
|
---|
937 | if (add.Subtrees.Count() == 1) {
|
---|
938 | return add.GetSubtree(0);
|
---|
939 | } else {
|
---|
940 | return add;
|
---|
941 | }
|
---|
942 | }
|
---|
943 | }
|
---|
944 |
|
---|
945 | // makes sure variable symbols in sums are combined
|
---|
946 | // possible improvement: combine sums of products where the products only reference the same variable
|
---|
947 | private void MergeVariablesInSum(ISymbolicExpressionTreeNode sum) {
|
---|
948 | var subtrees = new List<ISymbolicExpressionTreeNode>(sum.Subtrees);
|
---|
949 | while (sum.Subtrees.Any()) sum.RemoveSubtree(0);
|
---|
950 | var groupedVarNodes = from node in subtrees.OfType<IVariableTreeNode>()
|
---|
951 | where node.SubtreeCount == 0
|
---|
952 | // only consider terminal nodes
|
---|
953 | let lag = (node is LaggedVariableTreeNode) ? ((LaggedVariableTreeNode)node).Lag : 0
|
---|
954 | let cat =
|
---|
955 | (node is BinaryFactorVariableTreeNode) ? ((BinaryFactorVariableTreeNode)node).VariableValue : string.Empty
|
---|
956 | group node by node.VariableName + cat + lag
|
---|
957 | into g
|
---|
958 | select g;
|
---|
959 | var constant = (from node in subtrees.OfType<ConstantTreeNode>()
|
---|
960 | select node.Value).DefaultIfEmpty(0.0).Sum();
|
---|
961 | var unchangedSubtrees = subtrees.Where(t => t.SubtreeCount > 0 || !(t is IVariableTreeNode) && !(t is ConstantTreeNode));
|
---|
962 |
|
---|
963 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
964 | var firstNode = variableNodeGroup.First();
|
---|
965 | if (firstNode is VariableTreeNodeBase) {
|
---|
966 | var representative = firstNode as VariableTreeNodeBase;
|
---|
967 | var weightSum = variableNodeGroup.Cast<VariableTreeNodeBase>().Select(t => t.Weight).Sum();
|
---|
968 | representative.Weight = weightSum;
|
---|
969 | sum.AddSubtree(representative);
|
---|
970 | } else if (firstNode is FactorVariableTreeNode) {
|
---|
971 | var representative = firstNode as FactorVariableTreeNode;
|
---|
972 | foreach (var node in variableNodeGroup.Skip(1).Cast<FactorVariableTreeNode>()) {
|
---|
973 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
974 | representative.Weights[j] += node.Weights[j];
|
---|
975 | }
|
---|
976 | }
|
---|
977 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
978 | representative.Weights[j] += constant;
|
---|
979 | }
|
---|
980 | sum.AddSubtree(representative);
|
---|
981 | }
|
---|
982 | }
|
---|
983 | foreach (var unchangedSubtree in unchangedSubtrees)
|
---|
984 | sum.AddSubtree(unchangedSubtree);
|
---|
985 | if (!constant.IsAlmost(0.0)) {
|
---|
986 | sum.AddSubtree(MakeConstant(constant));
|
---|
987 | }
|
---|
988 | }
|
---|
989 |
|
---|
990 |
|
---|
991 | private ISymbolicExpressionTreeNode MakeProduct(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
992 | if (IsConstant(a) && IsConstant(b)) {
|
---|
993 | // fold constants
|
---|
994 | ((ConstantTreeNode)a).Value *= ((ConstantTreeNode)b).Value;
|
---|
995 | return a;
|
---|
996 | } else if (IsConstant(a)) {
|
---|
997 | // a * $ => $ * a
|
---|
998 | return MakeProduct(b, a);
|
---|
999 | } else if (IsFactor(a) && IsFactor(b) && AreSameVariable(a, b)) {
|
---|
1000 | var node0 = a as FactorVariableTreeNode;
|
---|
1001 | var node1 = b as FactorVariableTreeNode;
|
---|
1002 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Zip(node1.Weights, (u, v) => u * v));
|
---|
1003 | } else if (IsFactor(a) && IsConstant(b)) {
|
---|
1004 | var node0 = a as FactorVariableTreeNode;
|
---|
1005 | var node1 = b as ConstantTreeNode;
|
---|
1006 | return MakeFactor(node0.Symbol, node0.VariableName, node0.Weights.Select(w => w * node1.Value));
|
---|
1007 | } else if (IsConstant(b) && ((ConstantTreeNode)b).Value.IsAlmost(1.0)) {
|
---|
1008 | // $ * 1.0 => $
|
---|
1009 | return a;
|
---|
1010 | } else if (IsConstant(b) && IsVariableBase(a)) {
|
---|
1011 | // multiply constants into variables weights
|
---|
1012 | ((VariableTreeNodeBase)a).Weight *= ((ConstantTreeNode)b).Value;
|
---|
1013 | return a;
|
---|
1014 | } else if (IsConstant(b) && IsAddition(a) ||
|
---|
1015 | IsFactor(b) && IsAddition(a)) {
|
---|
1016 | // multiply constants into additions
|
---|
1017 | return a.Subtrees.Select(x => MakeProduct(x, b)).Aggregate((c, d) => MakeSum(c, d));
|
---|
1018 | } else if (IsDivision(a) && IsDivision(b)) {
|
---|
1019 | // (a1 / a2) * (b1 / b2) => (a1 * b1) / (a2 * b2)
|
---|
1020 | return MakeFraction(MakeProduct(a.GetSubtree(0), b.GetSubtree(0)), MakeProduct(a.GetSubtree(1), b.GetSubtree(1)));
|
---|
1021 | } else if (IsDivision(a)) {
|
---|
1022 | // (a1 / a2) * b => (a1 * b) / a2
|
---|
1023 | return MakeFraction(MakeProduct(a.GetSubtree(0), b), a.GetSubtree(1));
|
---|
1024 | } else if (IsDivision(b)) {
|
---|
1025 | // a * (b1 / b2) => (b1 * a) / b2
|
---|
1026 | return MakeFraction(MakeProduct(b.GetSubtree(0), a), b.GetSubtree(1));
|
---|
1027 | } else if (IsMultiplication(a) && IsMultiplication(b)) {
|
---|
1028 | // merge multiplications (make sure constants are merged)
|
---|
1029 | var mul = mulSymbol.CreateTreeNode();
|
---|
1030 | for (int i = 0; i < a.Subtrees.Count(); i++) mul.AddSubtree(a.GetSubtree(i));
|
---|
1031 | for (int i = 0; i < b.Subtrees.Count(); i++) mul.AddSubtree(b.GetSubtree(i));
|
---|
1032 | MergeVariablesAndConstantsInProduct(mul);
|
---|
1033 | return mul;
|
---|
1034 | } else if (IsMultiplication(b)) {
|
---|
1035 | return MakeProduct(b, a);
|
---|
1036 | } else if (IsMultiplication(a)) {
|
---|
1037 | // a is already an multiplication => append b
|
---|
1038 | a.AddSubtree(b);
|
---|
1039 | MergeVariablesAndConstantsInProduct(a);
|
---|
1040 | return a;
|
---|
1041 | } else {
|
---|
1042 | var mul = mulSymbol.CreateTreeNode();
|
---|
1043 | mul.AddSubtree(a);
|
---|
1044 | mul.AddSubtree(b);
|
---|
1045 | MergeVariablesAndConstantsInProduct(mul);
|
---|
1046 | return mul;
|
---|
1047 | }
|
---|
1048 | }
|
---|
1049 |
|
---|
1050 | #endregion
|
---|
1051 |
|
---|
1052 | #region helper functions
|
---|
1053 |
|
---|
1054 | private bool ContainsVariableCondition(ISymbolicExpressionTreeNode node) {
|
---|
1055 | if (node.Symbol is VariableCondition) return true;
|
---|
1056 | foreach (var subtree in node.Subtrees)
|
---|
1057 | if (ContainsVariableCondition(subtree)) return true;
|
---|
1058 | return false;
|
---|
1059 | }
|
---|
1060 |
|
---|
1061 | private ISymbolicExpressionTreeNode AddLagToDynamicNodes(ISymbolicExpressionTreeNode node, int lag) {
|
---|
1062 | var laggedTreeNode = node as ILaggedTreeNode;
|
---|
1063 | var variableNode = node as VariableTreeNode;
|
---|
1064 | var variableConditionNode = node as VariableConditionTreeNode;
|
---|
1065 | if (laggedTreeNode != null)
|
---|
1066 | laggedTreeNode.Lag += lag;
|
---|
1067 | else if (variableNode != null) {
|
---|
1068 | var laggedVariableNode = (LaggedVariableTreeNode)laggedVariableSymbol.CreateTreeNode();
|
---|
1069 | laggedVariableNode.Lag = lag;
|
---|
1070 | laggedVariableNode.VariableName = variableNode.VariableName;
|
---|
1071 | return laggedVariableNode;
|
---|
1072 | } else if (variableConditionNode != null) {
|
---|
1073 | throw new NotSupportedException("Removal of time lags around variable condition symbols is not allowed.");
|
---|
1074 | }
|
---|
1075 | var subtrees = new List<ISymbolicExpressionTreeNode>(node.Subtrees);
|
---|
1076 | while (node.SubtreeCount > 0) node.RemoveSubtree(0);
|
---|
1077 | foreach (var subtree in subtrees) {
|
---|
1078 | node.AddSubtree(AddLagToDynamicNodes(subtree, lag));
|
---|
1079 | }
|
---|
1080 | return node;
|
---|
1081 | }
|
---|
1082 |
|
---|
1083 | private bool AreSameVariable(ISymbolicExpressionTreeNode a, ISymbolicExpressionTreeNode b) {
|
---|
1084 | var aLaggedVar = a as LaggedVariableTreeNode;
|
---|
1085 | var bLaggedVar = b as LaggedVariableTreeNode;
|
---|
1086 | if (aLaggedVar != null && bLaggedVar != null) {
|
---|
1087 | return aLaggedVar.VariableName == bLaggedVar.VariableName &&
|
---|
1088 | aLaggedVar.Lag == bLaggedVar.Lag;
|
---|
1089 | }
|
---|
1090 | var aVar = a as VariableTreeNode;
|
---|
1091 | var bVar = b as VariableTreeNode;
|
---|
1092 | if (aVar != null && bVar != null) {
|
---|
1093 | return aVar.VariableName == bVar.VariableName;
|
---|
1094 | }
|
---|
1095 | var aFactor = a as FactorVariableTreeNode;
|
---|
1096 | var bFactor = b as FactorVariableTreeNode;
|
---|
1097 | if (aFactor != null && bFactor != null) {
|
---|
1098 | return aFactor.VariableName == bFactor.VariableName;
|
---|
1099 | }
|
---|
1100 | var aBinFactor = a as BinaryFactorVariableTreeNode;
|
---|
1101 | var bBinFactor = b as BinaryFactorVariableTreeNode;
|
---|
1102 | if (aBinFactor != null && bBinFactor != null) {
|
---|
1103 | return aBinFactor.VariableName == bBinFactor.VariableName &&
|
---|
1104 | aBinFactor.VariableValue == bBinFactor.VariableValue;
|
---|
1105 | }
|
---|
1106 | return false;
|
---|
1107 | }
|
---|
1108 |
|
---|
1109 | // helper to combine the constant factors in products and to combine variables (powers of 2, 3...)
|
---|
1110 | private void MergeVariablesAndConstantsInProduct(ISymbolicExpressionTreeNode prod) {
|
---|
1111 | var subtrees = new List<ISymbolicExpressionTreeNode>(prod.Subtrees);
|
---|
1112 | while (prod.Subtrees.Any()) prod.RemoveSubtree(0);
|
---|
1113 | var groupedVarNodes = from node in subtrees.OfType<IVariableTreeNode>()
|
---|
1114 | where node.SubtreeCount == 0
|
---|
1115 | let lag = (node is LaggedVariableTreeNode) ? ((LaggedVariableTreeNode)node).Lag : 0
|
---|
1116 | let cat =
|
---|
1117 | (node is BinaryFactorVariableTreeNode) ? ((BinaryFactorVariableTreeNode)node).VariableValue : string.Empty
|
---|
1118 | group node by node.VariableName + cat + lag
|
---|
1119 | into g
|
---|
1120 | orderby g.Count()
|
---|
1121 | select g;
|
---|
1122 | var constantProduct = (from node in subtrees.OfType<VariableTreeNodeBase>()
|
---|
1123 | select node.Weight)
|
---|
1124 | .Concat(from node in subtrees.OfType<ConstantTreeNode>()
|
---|
1125 | select node.Value)
|
---|
1126 | .DefaultIfEmpty(1.0)
|
---|
1127 | .Aggregate((c1, c2) => c1 * c2);
|
---|
1128 |
|
---|
1129 | var unchangedSubtrees = from tree in subtrees
|
---|
1130 | where tree.SubtreeCount > 0 || !(tree is IVariableTreeNode) && !(tree is ConstantTreeNode)
|
---|
1131 | select tree;
|
---|
1132 |
|
---|
1133 | foreach (var variableNodeGroup in groupedVarNodes) {
|
---|
1134 | var firstNode = variableNodeGroup.First();
|
---|
1135 | if (firstNode is VariableTreeNodeBase) {
|
---|
1136 | var representative = (VariableTreeNodeBase)firstNode;
|
---|
1137 | representative.Weight = 1.0;
|
---|
1138 | if (variableNodeGroup.Count() > 1) {
|
---|
1139 | var poly = mulSymbol.CreateTreeNode();
|
---|
1140 | for (int p = 0; p < variableNodeGroup.Count(); p++) {
|
---|
1141 | poly.AddSubtree((ISymbolicExpressionTreeNode)representative.Clone());
|
---|
1142 | }
|
---|
1143 | prod.AddSubtree(poly);
|
---|
1144 | } else {
|
---|
1145 | prod.AddSubtree(representative);
|
---|
1146 | }
|
---|
1147 | } else if (firstNode is FactorVariableTreeNode) {
|
---|
1148 | var representative = (FactorVariableTreeNode)firstNode;
|
---|
1149 | foreach (var node in variableNodeGroup.Skip(1).Cast<FactorVariableTreeNode>()) {
|
---|
1150 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
1151 | representative.Weights[j] *= node.Weights[j];
|
---|
1152 | }
|
---|
1153 | }
|
---|
1154 | for (int j = 0; j < representative.Weights.Length; j++) {
|
---|
1155 | representative.Weights[j] *= constantProduct;
|
---|
1156 | }
|
---|
1157 | constantProduct = 1.0;
|
---|
1158 | // if the product already contains a factor it is not necessary to multiply a constant below
|
---|
1159 | prod.AddSubtree(representative);
|
---|
1160 | }
|
---|
1161 | }
|
---|
1162 |
|
---|
1163 | foreach (var unchangedSubtree in unchangedSubtrees)
|
---|
1164 | prod.AddSubtree(unchangedSubtree);
|
---|
1165 |
|
---|
1166 | if (!constantProduct.IsAlmost(1.0)) {
|
---|
1167 | prod.AddSubtree(MakeConstant(constantProduct));
|
---|
1168 | }
|
---|
1169 | }
|
---|
1170 |
|
---|
1171 |
|
---|
1172 | /// <summary>
|
---|
1173 | /// x => x * -1
|
---|
1174 | /// Doesn't create new trees and manipulates x
|
---|
1175 | /// </summary>
|
---|
1176 | /// <param name="x"></param>
|
---|
1177 | /// <returns>-x</returns>
|
---|
1178 | private ISymbolicExpressionTreeNode Negate(ISymbolicExpressionTreeNode x) {
|
---|
1179 | if (IsConstant(x)) {
|
---|
1180 | ((ConstantTreeNode)x).Value *= -1;
|
---|
1181 | } else if (IsVariableBase(x)) {
|
---|
1182 | var variableTree = (VariableTreeNodeBase)x;
|
---|
1183 | variableTree.Weight *= -1.0;
|
---|
1184 | } else if (IsFactor(x)) {
|
---|
1185 | var factorNode = (FactorVariableTreeNode)x;
|
---|
1186 | for (int i = 0; i < factorNode.Weights.Length; i++) factorNode.Weights[i] *= -1;
|
---|
1187 | } else if (IsAddition(x)) {
|
---|
1188 | // (x0 + x1 + .. + xn) * -1 => (-x0 + -x1 + .. + -xn)
|
---|
1189 | var subtrees = new List<ISymbolicExpressionTreeNode>(x.Subtrees);
|
---|
1190 | while (x.Subtrees.Any()) x.RemoveSubtree(0);
|
---|
1191 | foreach (var subtree in subtrees) {
|
---|
1192 | x.AddSubtree(Negate(subtree));
|
---|
1193 | }
|
---|
1194 | } else if (IsMultiplication(x) || IsDivision(x)) {
|
---|
1195 | // x0 * x1 * .. * xn * -1 => x0 * x1 * .. * -xn
|
---|
1196 | var lastSubTree = x.Subtrees.Last();
|
---|
1197 | x.RemoveSubtree(x.SubtreeCount - 1);
|
---|
1198 | x.AddSubtree(Negate(lastSubTree)); // last is maybe a constant, prefer to negate the constant
|
---|
1199 | } else {
|
---|
1200 | // any other function
|
---|
1201 | return MakeProduct(x, MakeConstant(-1));
|
---|
1202 | }
|
---|
1203 | return x;
|
---|
1204 | }
|
---|
1205 |
|
---|
1206 | /// <summary>
|
---|
1207 | /// x => 1/x
|
---|
1208 | /// Doesn't create new trees and manipulates x
|
---|
1209 | /// </summary>
|
---|
1210 | /// <param name="x"></param>
|
---|
1211 | /// <returns></returns>
|
---|
1212 | private ISymbolicExpressionTreeNode Invert(ISymbolicExpressionTreeNode x) {
|
---|
1213 | if (IsConstant(x)) {
|
---|
1214 | return MakeConstant(1.0 / ((ConstantTreeNode)x).Value);
|
---|
1215 | } else if (IsFactor(x)) {
|
---|
1216 | var factorNode = (FactorVariableTreeNode)x;
|
---|
1217 | for (int i = 0; i < factorNode.Weights.Length; i++) factorNode.Weights[i] = 1.0 / factorNode.Weights[i];
|
---|
1218 | return factorNode;
|
---|
1219 | } else if (IsDivision(x)) {
|
---|
1220 | return MakeFraction(x.GetSubtree(1), x.GetSubtree(0));
|
---|
1221 | } else {
|
---|
1222 | // any other function
|
---|
1223 | return MakeFraction(MakeConstant(1), x);
|
---|
1224 | }
|
---|
1225 | }
|
---|
1226 |
|
---|
1227 | private ISymbolicExpressionTreeNode MakeConstant(double value) {
|
---|
1228 | ConstantTreeNode constantTreeNode = (ConstantTreeNode)(constSymbol.CreateTreeNode());
|
---|
1229 | constantTreeNode.Value = value;
|
---|
1230 | return constantTreeNode;
|
---|
1231 | }
|
---|
1232 |
|
---|
1233 | private ISymbolicExpressionTreeNode MakeVariable(double weight, string name) {
|
---|
1234 | var tree = (VariableTreeNode)varSymbol.CreateTreeNode();
|
---|
1235 | tree.Weight = weight;
|
---|
1236 | tree.VariableName = name;
|
---|
1237 | return tree;
|
---|
1238 | }
|
---|
1239 | private ISymbolicExpressionTreeNode MakeFactor(FactorVariable sy, string variableName, IEnumerable<double> weights) {
|
---|
1240 | var tree = (FactorVariableTreeNode)sy.CreateTreeNode();
|
---|
1241 | tree.VariableName = variableName;
|
---|
1242 | tree.Weights = weights.ToArray();
|
---|
1243 | return tree;
|
---|
1244 | }
|
---|
1245 |
|
---|
1246 |
|
---|
1247 | #endregion
|
---|
1248 | }
|
---|
1249 | }
|
---|